in Equation (2) generated by turbulent cascade can be given by where F ( q ) ∝ q -ζ p and ζ p is the index of the turbulent energy spectrum. q is within the range q ν < q < q η . q ν is linked to the viscous dissipation and q η is related to the magnetic resistive transfer. The Prandtl number Pr = 10 -5 T 4 /n constrains the value of q by q η /q ν = Pr 1 / 2 (Schekochihin & Cowley 2007), where aT/m e c 2 = Θ, Θ ∼ Γ sh and a is the Boltzmann constant. We adopt a length scale of viscous eddies (Kumar & Narayan 2009; Narayan & Kumar 2009; Lazar et al. 2009) for GRB prompt emission and obtain q ν = 2 πl -1 eddy = 2 π ( R/ Γ sh Γ t ) -1 = 6 . 3 × 10 -10 ( R/ 10 13 cm) -1 (Γ sh / 100)(Γ t / 10) cm -1 , where Γ t is the Lorentz factor of turbulent eddies. The magnetic resistive scale is q η = 3 . 9 × 10 4 ( n/ 3 × 10 10 cm -3 ) -1 / 2 (T / 5 . 6 × 10 11 K) 2 cm -1 . In the compressed two-dimensional case, magnetic fields can be < B > = [ ∫ q η q ν q -ζ p d q ] 1 / 2 = √ 2 πq (2 -ζ p ) / 2 ν / √ ζ p -2 under the condition q η /greatermuch q ν . Through the cascade process of a turbulent fluid, turbulent energy dissipation has a hierarchical fluctuation structure. A set of inertial-range scaling laws of fully developed turbulence can be derived. From the research of She & Leveque (1994) and She & Waymire (1995), the energy spectrum index ζ p of turbulent fields is related to the cascade process number p by the universal relation of ζ p = p/ 9+2[1 -(2 / 3) p/ 3 ]. The Kolmogorov turbulence is presented as ζ p = p/ 3. This turbulent feature was found recently to be valid in the relativistic regime (Zrake & MacFadyen 2012). At the fireball radius of R ∼ 10 13 cm, taking the turbulent spectrum index of ζ p = 3 . 25 from She & Leveque (1994), we obtain a the magnetic field value of 1 . 3 × 10 6 G. In the fireball scenario, a magnetic field of 10 14 G at 10 6 cm can easily reach 10 6 G at 10 14 cm, providing powerful prompt emission (Piran 2005). This estimation is dependent on the exact shock location and on the equipartition parameters. In our model, we take a magnetic field number of 10 6 G as a reference value. As we have shown in our model, the random magnetic field is generated by turbulence and the magnetic field number is dependent on the turbulent energy spectral index ζ p . Therefore, we solve Equation (2) and obtain the radiation property I ω ∝ ω -( ζ p -2) . This radiation spectrum can be reproduced by the numerical calculations of Teraki & Takahara (2011) in high-frequency regime. The gross radiative emission should be the contribution from all of the relativistic electrons with a certain electron energy distribution. However, we note that the jitter spectral index ζ p -2 of single electrons is fully determined by the fluid turbulence. Thus, the spectral index of the gross radiative emission is not related to the electron energy distribution. Finally, from Equation (2), we obtain We note that the term of the magnetic field is not related to the spectral index.\",\n \"pages\": [\n 5,\n 6,\n 7\n ]\n },\n {\n \"title\": \"2.2. Polarization\",\n \"content\": \"Magnetic field configurations is a dominant issue for the research of GRB radiation and polarization. In this paper, we apply the topology of random magnetic fields introduced by Laing (1980, 2002). A three-dimensional cube containing random and small-scale magnetic fields can be compressed into a two-dimensional slab by relativistic shocks. In the slab plane, the distribution of magnetic fields is still stochastic. The magnetic field vector at one point, denoted in rectangular coordinates, is B = B 0 (cos φ sin θ B , sin φ, cos φ cos θ B ), where θ B is the angle between the slab plane and the line of sight (see Figure 1) and φ is the azimuthal angle at any point randomly distributed in the slab plane. The position angle of the E -vector χ can be given as cos 2 χ = -(sin 2 θ B -tan 2 φ ) / (sin 2 θ B +tan 2 φ ). Thus, the magnetic field acting on the radiation is B = B 0 (cos 2 φ sin 2 θ B +sin 2 φ ) 1 / 2 . Because an electron obtains same acceleration on average from different directions in a random and small-scale magnetic field, the electron trajectory of jitter radiation can be approximated as a straight line (Medvedev 2000; Medvedev et al. 2011). Thus, jitter radiation is limited to the small radiation cone along the line of sight to the observer. Since the acceleration term of jitter radiation is proportional to B 2 , we can do a decomposition of jitter radiation in the electron radiation plane and obtain the polarization degree (see the detailed examination in the Appendix). If the slab is orientated so that the E -vector of the polarization radiation has a position angle of zero degrees, then the Stokes parameter U = 0. Following the magnetic field topology given by Laing (1980, 2002), we obtain Stokes parameters of single electron jitter radiation given by: I = C ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) dφ , Q = I cos2 χ = -C ∫ 2 π 0 (cos 2 φ sin 2 θ B -sin 2 φ )d φ , U = 0, and V = 0, where C = C ( γ, B 0 ). With a certain electron energy distribution N ( γ ), we obtain the following Stokes parameters of the gross jitter radiation: and Thus, the final polarization degree of the gross jitter emission is In our case, we emphasize that the magnetic field configuration is the only parameter that impacts the jitter polarization. Moreover, this polarization result is only valid in the jitter radiation case where the electron deflection angle is small (see Equation (11) in Section 4). Thus, in this two-dimensional case, we only select electrons moving roughly perpendicular to the slab plane. We present synchrotron polarization of a single electron applying the same magnetic field topology in the Appendix. We also repeat the Stokes parameters of the gross synchrotron radiation given by Laing (1980): I = C ( γ, B 0 ) ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) ( ν S +1) / 2 dφ , Q = -C ( γ, B 0 )( 3 ν S +3 3 ν S +5 ) ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) ( ν S -1) / 2 (cos 2 φ sin 2 θ B -sin 2 φ ) dφ , U = 0, and V = 0, where ν S is the synchrotron spectral index. We compare synchrotron polarization and jitter polarization in Figure 2. In this paper, we neglect the effect of light propagation in a thick and highly magnetized plasma screen (Macquart & Melrose 2000).\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"2.3. Jet-in-jet Scenario\",\n \"content\": \"The mini-jets emit photons in a bulk GRB jet. We simply take into account the geometric effect of the bulk jet. The solid angle element of the jet is 2 π sin θdθ . Since observers always see the forward jet and the backward jet is not observed, the detection probability is half of the result of above the estimation. As the full opening angle is θ , we suggest an upper limit of the integral to be θ/ 2. The probability should be normalized by the entire solid angle of 4 π . Thus, the observational probability of these mini-jets in a bulk GRB jet can be calculated as P = π ∫ θ/ 2 0 sin θ ' dθ ' / 4 π = 1 / 32Γ 2 and Γ ∼ θ . The gross Lorentz factor Γ was given by Giannios et al. (2010) as Γ = 2Γ j Γ t /α 2 , where Γ j ∼ Γ sh is the Lorentz factor of the bulk jet, Γ t is the Lorentz factor of relativistic turbulence in these mini-jets, and textbf α is the 'offaxis' parameter defined as θ j = α/ Γ j . From the investigation of the mini-jets emitting angle distribution (Giannios et al. 2010), the range of α is given as 0 < α < 2. We can furthermore estimate the number of mini-jets affected by the turbulent fluid as n ( γ ) = 4 πR 2 Γ j ct cool /l 3 s , where R is the fireball radius and t cool = 6 πm e c/σ T γB 2 is the cooling timescale of relativistic electrons. The length scale of those mini-jets is l s = γ Γ t ct cool . As the number of mini-jets n ( γ ) is a function of the electron Lorentz factor γ , the electron energy distribution N e ( γ ) is required to obtain a total number of mini-jets given by n = ∫ ∞ 1 n ( γ ) N e ( γ ) dγ/ ∫ ∞ 1 N e ( γ ) dγ . Due to diffusive shock acceleration, electrons can be accelerated and a power-law energy distribution is given. In our paper, turbulence is considered not only to generate magnetic fields but also to accelerate electrons and the electron energy distribution has a Maxwellian component (Stawarz & Petrosian 2008). If turbulent acceleration is considered in addition to shock acceleration, the electron energy distribution has a dual-natured shape with a Maxwellian component and a power-law component (Giannios & Spitkovsky 2009): where C is a constant. In the case that only a fraction of electrons have a non-thermal distribution, we take the characteristic temperature to be Θ = kT/m e c 2 ∼ 100. In our calculation, we adopt γ th = 10 3 ; p e = 2 . 2 is the power-law index. Combined with the observational probability P and the total number n of mini-jets affected by turbulence, the final observed polarization degree is Π obs = nP Π.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"3. Results\",\n \"content\": \"The intrinsic polarization results of GRB prompt emission without jet effects are shown in Figure 2. The jitter polarization degree is strongly dependent on θ B , which is the angle between the line of sight and the slab plane. If the line of sight is perpendicular to the slab plane, we successfully obtain jitter photons, but jitter radiation in the electron radiative plane is symmetric and the polarization degree is zero. Except in this extreme case, the degree of polarization can be measured with different values of θ B . With the same magnetic field configuration, we can compare jitter polarization and synchrotron polarization. Both jitter polarization and synchrotron polarization are related to θ B . On the other hand, as we discussed in Section 2.2, jitter polarization is not related to the radiation spectrum and it can reach a maximum value of 100 percent. Synchrotron polarization (see details in the Appendix) is related to the radiation spectral index and its maximum value is ( ν S +3) / ( ν S + 5). The cases of ν s = 2 . 0 , 1 . 0, and 0.6 are shown in Figure 2 as examples. We further provide examples of the observed jitter polarization degree in our jet-in-jet scenario shown in Figures 3 and 4. Different jet 'off-axis' parameters, 1.55, 1.3 and 1.0, are used to calculate the observed polarization degree shown in Figure 3. Here, we take Γ sh = 100, Γ t = 10, and R = 10 13 cm. We show that the polarization degree is significantly sensitive to the jet 'off-axis' parameter. A stronger jet 'off-axis' effect yields a stronger observed polarization degree. In Figure 4, we present examples of jitter polarization results affected by the shock Lorentz factor Γ sh . We fix the 'off-axis' parameter as 1.3, Γ t = 10, and R = 10 13 cm. Shock Lorentz factor values of 85, 100, and 120 are adopted. We see that a low polarization degree can be induced by a large shock Lorentz factor. This fact suggest that a large shock Lorentz factor provides powerful radiation along the jet axis while a powerful polarization can be measured in the strong off-axis case, which has a relatively small Lorentz factor and weak radiation. It is also useful to review the GRB polarization feature under the mechanism of synchrotron radiation in the jet structure. Gruzinov (1999) and Sari (1999) proposed the possibility of high-degree GRB polarization. Granot (2003) comprehensively discussed different GRB jet polarization cases. Here, for simplicity, we apply the model of Gruzinov (1999) to illustrate the configuration differences between the tangled magnetic field and the ordered magnetic field. The polarization degree derived from the magnetic field parallel/perpendicular to the jet direction was given as Π = Π 0 sin 2 α B ( B 2 ‖ -0 . 5 B 2 ⊥ ) / [ B 2 ‖ sin 2 α B + 0 . 5 B 2 ⊥ (1 + cos 2 α B )], where B ‖ is the magnetic field parallel to the shock propagation direction, B ⊥ is the magnetic field perpendicular to the shock propagation, and α B = π/ 2 -θ B is the angle between the line of sight from observer and the direction of the shock propagation (Gruzinov 1999). In our model, we have fully obtained the polarization feature of GRB prompt emission in the case of B ‖ /lessmuch B ⊥ (Laing 1980, 2002) and this condition is necessary for jitter radiation. If B ‖ /greatermuch B ⊥ , the polarization degree is Π ∼ Π 0 , which is the result obtained from an ordered magnetic field aligned with the jet direction. This result reproduces exactly the polarization degree of synchrotron radiation as Π 0 = (3 ν S +3) / (3 ν S +5); the electron energy distribution has a power-law distribution with a power-law index p e and ν S = ( p e -1) / 2. Considering a certain jet structure and line of sight effects, a high degree of GRB prompt polarization can be obtained (Granot 2003; Lazzati & Begelman 2009). In our paper, the two-dimensional magnetic slab and the jet-in-jet structure provide the possibility of asymmetric radiation in the electron radiative plane. Thus, the GRB prompt emission can be highly polarized as well.\",\n \"pages\": [\n 9,\n 10\n ]\n },\n {\n \"title\": \"4. Discussion and Conclusions\",\n \"content\": \"Relativistic electrons accelerated by diffusive shock acceleration with a power-law energy distribution can emit high-energy photons in an ordered magnetic field. Therefore, it is possible to explain the high-degree polarization detected in GRB prompt emission by synchrotron radiation. Alternatively, we present in this paper that turbulence can accelerate electrons and generate random and small-scale magnetic fields. The relativistic electrons emit X-ray/ γ -ray jitter photons in the jet-in-jet structure. Some important physical components, such as turbulence behind the shock front, random and small-scale magnetic fields, the electron energy distribution, and mini-jets, are self-consistently organized in the process of jitter radiation. We obtain a high-degree polarization of GRB prompt emission through jitter radiation considering a two-dimensional compressed magnetic field configuration. The intrinsic polarization degree is a function of the angle between the line of sight and the slab plane, and large polarization values can be achieved in the case of small angles. Moreover, the final observed polarization degree in the jet-in-jet scenario is affected by the 'off-axis' parameter and the shock Lorentz factor. In this paper, the electron trajectory of jitter radiation in random and small-scale magnetic fields is assumed to be a straight line. In other words, the condition of θ d /lessmuch 1 /γ should be satisfied by jitter radiation (Medvedev et al. 2011). Here, θ d = eBλ B /γm e c 2 is the deflection angle of electrons in a magnetic field, and λ B ∼ c/ω pe is the length scale of the magnetic field. We obtain This condition is strongly dependent on the magnetic field and the electron number density. We constrain the condition of jitter radiation in an example below. The electron number density is given by n = N/ ∆Ω R 2 ∆ R . N = 1 . 0 × 10 52 ∼ 6 × 10 54 is the total number of electrons in the radiative region (Kumar & Narayan 2009). We take the fireball radius to be R = 10 13 cm and fireball shell to be ∆ R = 10 10 cm. If the jet opening angle is about 5 degree, we obtain a solid angle ∆Ω = 3 . 3 × 10 -4 and the estimated value of number density is n = 3 . 0 × 10 20 cm -3 ∼ 1 . 8 × 10 22 cm -3 . Thus, θ d /lessmuch 1 /γ and the electron trajectory can be treated as a straight line. In order to satisfy this jitter condition in the two-dimensional case, we select electrons moving roughly perpendicular to the slab plane so that the electron deflection angle is small. The general case of electrons moving in a random walk in a stochastic magnetic field with a large deflection angle was discussed by Fleishman (2006) and numerical simulations may be required to solve this complicated issue. It is expected that the so-called depolarization due to the Faraday rotation of the polarization screen (Burn 1966) can be a powerful tool to further constrain the source structure and magnetic field topology. In general, stochastic Faraday rotation creates a polarization degree of Π ∝ exp( -λ 4 ), where λ is wavelength (Melrose & Macquart 1998). Tribble (1991) discussed a power-law structure function for a Faraday rotation measurement. The polarization degree was given as Π ∝ λ -4 /m , where m is related to the turbulent cascade. Even if we consider a polarization fluctuation proportional to λ , the final polarization degree still dramatically decreases as Π ∝ λ -2 . 2 if we adopt a typical value of m = ζ p -2 given in our model. Therefore, GRB prompt polarization measured in the soft band is about 20% of that measured in the hard band. This prediction can be examined by future observations if GRB prompt polarization measurements can be performed simultaneously in different energy bands. This simple analysis of the depolarization effect also indicates that GRB prompt polarization in optical bands is nearly impossible detect even if GRB is highly polarized in high-energy bands. On the other hand, the polarization of GRB optical afterglows was detected. The radiation case of external shocks of GRBs sweeping into the surrounding interstellar medium is beyond the scope of this paper. Here, we make some simple speculations. As optical afterglow is onset at early times after the GRB is triggered, and the jet is strongly anisotropic with a narrow beaming angle. Thus, the optical polarization degree can reach values of 10% (Uehara et al. 2012) and even higher polarization degrees were expected (Steele et al. 2009). In late times after a GRB is triggered, the beaming angle of the jet is wide and the jet anisotropy is not prominent. Thus, the polarization of the optical afterglow is weak 1 (Covino et al. 1999; Hjorth et al. 1999; Wijers et al. 1999). Moreover, high-energy photons from GRB prompt emission can pass through a dense medium without being strongly absorbed. Thus, the depolarization effect is weak and a high polarization degree can be detected, while UV/optical photons of GRB afterglows can be strongly absorbed by the surrounding dense material. Therefore, even though the initial polarization degree of GRB optical afterglows is very high, the external depolarization effect is strong as the diffraction in a Faraday prism is taken into account (Sazonov 1969; Macquart & Melrose 2000). Thus, due to the strong depolarization effect, the detected polarization degree of GRB optical afterglows is low. Further quantitative computations can be executed since the magnetic field configuration adopted in this paper is still valid for the depolarization cases mentioned above (Rossi et al. 2004). Rapid time variations of the polarization angle and polarization degree have been measured either in GRB prompt emission cases (Gotz et al. (2009) for GRB 041219A and Yonetoku et al. (2011) for GRB 100826A) or in GRB afterglow cases (Rol et al. (2000) for GRB 990712, Greiner et al. (2003) for GRB 030329, and Wiersema et al. (2012) for GRB 091018). The observed timescale of polarization variation in GRB prompt emission is about 50-100 s (Yonetoku et al. 2011), which corresponds to an intrinsic timescale of 0.5-1 s. Here, we list three possibilities to explain this rapid variation. First, GRB helical jets with helical magnetic fields and helical rotation generated by black holes (Mizuno et al. 2012) should be considered. With a helical jet, the slab may rotate and the magnetic field configuration may change quickly. Then, rapid polarization variation occurs. Second, Lazzati & Begelman (2009) proposed that faint pulses of GRB prompt emission are a main contributor to the polarization. If this is true, we can obtain the rapid time variation of the polarization since the pulses shown in GRB prompt lightcurves show rapid variation; Third, the turbulent feature in the slab should be revisited. We estimate the variability of GRB prompt polarization due to the variability of stochastic eddies as δt ∼ l eddy /c s . Given l eddy ∼ R/ Γ j Γ t and c s ∼ c/ √ 3, δt is about 1.7 s, which can be comparable to the observational timescale. Moreover, small-scale fluid turbulence and magnetic reconnection was suggested by Matthews & Scheuer (1990b). Recently, Zhang & Yan (2011) and McKinney & Uzdensky (2012) illustrated the possibility of magnetic reconnection for GRB energy dissipation. We suggest that small-scale magnetic reconnection in the compressed slab is likely to affect the rapid polarization variation. More observations (TSUBAME, NuSTAR, Astro-H) and quantitative explanations in detail are expected in the future. We thank the referee for his/her helpful suggestions and comments. We are grateful to Teraki, Y., Toma, K., Nagataki, S., Ito, H., Ono, M., and Lee, S.-H. for their useful discussions. The numerical computation in this work was carried out at the Yukawa Institute Computer Facility. This work is supported by Grants-in-Aid for Foreign JSPS Fellow (Number 24.02022). We acknowledge support from the Ministry of Education, Culture, Sports, Science and Technology (No. 23105709), the Japan Society for the Promotion of Science (No. 19104006 and No. 23340069), and the Global COE Program, The Next Generation of Physics, Spun from University and Emergence, from MEXT of Japan. J. Wang is supported by the National Basic Research Program of China (973 Program 2009CB824800), the National Natural Science Foundation of China 11133006, 11163006, 11173054, and the Policy Research Program of the Chinese Academy of Sciences (KJCX2-YW-T24).\",\n \"pages\": [\n 10,\n 11,\n 12,\n 13\n ]\n },\n {\n \"title\": \"A. Polarization of Single Electrons in A Random Magnetic Field\",\n \"content\": \"In this Appendix, we first introduce the polarization feature of single relativistic electrons in a magnetic field assuming jitter condition. We repeat the radiation property by Landau & Lifshitz (1971) as where the retarded time is t ' = t -R ( t ' ) /c ∼ = t -R 0 /c + n · r ( t ' ) /c ∼ = t -R 0 /c + n · v t ' /c ; n is the radiation direction. If we take dt = dt ' (1 -n · v /c ), we obtain If we adopt the notation ω ' = ω (1 -n · v /c ), we obtain The acceleration term is w ω ' = e v × B /γm e c . The electron trajectory is necessary to obtain the acceleration term and the calculation in Equation (A3). If the electron trajectory can be treated as a straight line in a magnetic field (see Equation (11) of jitter radiation condition), we have a compressed magnetic slab plane with an angle of θ B to the radiative X -Y plane, and the electron velocity is perpendicular to the slab plane since the electron deflection angle of the jitter radiation is smaller than 1 /γ . The jitter radiation direction follows the direction of the electron. Thus, we obtain the X -axis component as and the Y -axis component as The radiation intensity is I = c | E | 2 R 2 0 / 2 π . The Stokes parameters can be defined as and From Section 2.2, we know B x = B 0 cos φ sin θ B and B y = B 0 sin φ . Finally, we obtain the jitter polarization Π = Q/I , which is only related to the configuration of the magnetic field; Equation (9) is verified. In this Appendix, we also review the synchrotron polarization of a single electron. We keep the same random magnetic field topology used in the jitter polarization case to calculate the synchrotron polarization and we can repeat the calculation of Laing (1980). The radiation intensity of the synchrotron mechanism is where ν c = (3 / 2) γ 2 ν L , ν L = eB/ (2 πm e c ) is the Larmor frequency ,and K is a modified Bessel function. The synchrotron polarization of a single electron is related to the magnetic field, electron Lorentz factor γ and radiation frequency ν (Rybicki & Lightman 1979). In order to compare synchrotron polarization with jitter polarization, we apply the same magnetic field topology described in Section 2.2 to synchrotron polarization; our results are shown in Figure 5. In the calculation, we fix the magnetic field value at 1 . 3 × 10 6 G. For a given θ B , the degree of synchrotron polarization increases, if the radiation is toward a higher frequency ν and/or the electron Lorentz factor γ tends toward smaller values. This property is typical of synchrotron polarization of single electrons. In Figure 5, we plot the jitter polarization as well, which is independent of the radiation frequency ν and the electron Lorentz factor γ . Even though synchrotron polarization degrees can be coincidentally the same as the jitter polarization degree by adjusting the parameters of ν and γ , we emphasize that jitter polarization and synchrotron polarization are physically different because jitter radiation and synchrotron radiation are two different radiation mechanisms. If the synchrotron power-law spectrum with a power-law index ν S is given and an electron energy distribution is assumed to be a power-law with an index of 2 ν S + 1, we obtain the Stokes parameters of the gross electrons: and where C is constant. Thus, the final polarization degree of the gross synchrotron emission is These are the results given by Laing (1980) and we also plot them in Figure 2.\",\n \"pages\": [\n 13,\n 14,\n 15\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Bersier, D., et al. 2003, ApJ, 583, L63 Bhatt, N., & Bhattacharyya, S. 2012, MNRAS, 420, 1706 Burn, B. J. 1966, MNRAS, 133, 67 Cawthorne, T. V., & Cobb, W. K. 1990, ApJ, 350, 536 Lazzati, D., & Begelman, M. C. 2009, ApJ, 700, L141 Lemoine, M. 2013, MNRAS, 428, 845 Lyutikov, M. 2006, MNRAS, 369, L5 Macquart, J.-P., & Melrose, D. B. 2000, ApJ, 545, 798 Mao, J., & Wang, J. 2011, ApJ, 731, 26 Mao, J., & Wang, J. 2012, ApJ, 748, 135 Martins, J. L., Martins, S. F., Fonseca, R. A., & Silva, L. O. 2009, Proc. of SPIE, 7359, 73590V-1-8 Matthews, A. P., & Scheuer, P. A. G. 1990a, MNRAS, 242, 616 Matthews, A. P., & Scheuer, P. A. G. 1990b, MNRAS, 242, 623 McGlynn, S. et al., 2007, A&A, 466, 895 MvKinney, J. C., & Uzdensky, D. 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Rouˇcka 2 , W.\nD. Geppert 3 , T. J. Millar 4 , and R. Wester 1\n1 Institut fur Ionenphysik und Angewandte Physik, Universitat Innsbruck, A -6020 Innsbruck, Austria\n2 Charles University in Prague, Faculty of Mathematics and Physics, Department of Surface and Plasma Science, 18000 Prague, Czech Republic\n3 Department of Physics, AlbaNova, Stockholm University, SE -10691 Stockholm, Sweden\n4 Astrophysics Research Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, UK\nE-mail:\nroland.wester@uibk.ac.at\nAbstract. Absolute photodetachment cross sections of two anions of astrophysical importance CN -and C 3 N -were measured to be (1.18 ± (0.03) stat (0.17) sys ) × 10 -17 cm 2 and (1.43 ± (0.14) stat (0.37) sys ) × 10 -17 cm 2 respectively at the ultraviolet wavelength of 266 nm (4.66 eV). These relatively large values of the cross sections imply that photodetachment can play a major role in the destruction mechanisms of these anions particularly in photon-dominated regions. We have therefore carried out model calculations using the newly measured cross sections to investigate the abundance of these molecular anions in the cirumstellar envelope of the carbon-rich star IRC+10216. The model predicts the relative importance of the various mechanisms of formation and destruction of these species in different regions of the envelope. UV photodetachment was found to be the major destruction mechanism for both CN -and C 3 N -anions in those regions of the envelope, where they occur in peak abundance. It was also found that photodetachment plays a crucial role in the degradation of these anions throughout the circumstellar envelope.\n1. Introduction\n1.1. Molecular anions in space: Observation and astrophysical relevance\nThe discovery of molecules in the interstellar medium about seven decades ago was particularly intriguing since the chemistry governing the formation of molecules in such hostile regions of space was not familiar. Gradually the number of molecules and their cations found in extraterrestrial space increased and it became clear that we in fact live in a 'molecular Universe' (Larsson et al. 2012). However, after the first molecule was identified in the interstellar medium, it took six decades before a molecular anion could be discovered in such environment. This delay was primarily due to the low abundance of anions in space compared to their neutral counterparts and due to the lack of laboratory measurements of high resolution rotational spectra of the anions that could allow their search in space. The first molecular anion ever observed outside our solar system is C 6 H -(McCarthy et al. 2006), which was detected in the envelope of the carbon-rich star IRC+10216. The identification of this molecular anion was followed by the discovery of several other carbon chain anions, C n H -( n = 4, 8) and C n N -( n = 1, 3, 5) in various regions of space such as dark clouds, circumstellar envelopes, and also in Titan's atmosphere (Cernicharo et al. 2007, Cernicharo et al. 2008, Sakai et al. 2007, Sakai et al. 2008, Sakai et al. 2010, Ag'undez et al. 2008, Ag'undez et al. 2010, Remijan et al. 2007, Brunken et al. 2007, Kasai et al. 2007, Kawaguchi et al. 2007, Thaddeus et al. 2008, Gupta et al. 2009). Of these anions, C 5 N -was only tentatively identified. The role of anions in the synthesis of molecules in the interstellar medium has been investigated by Dalgarno & McCray (1973) many years ago, whereas the formation of molecular hydrogen in stars from H -had been pointed out by McDowell (1961) much earlier. The recent discovery of anions in extraterrestrial environments has initiated a fresh interest towards the understanding of anion chemistry in exotic environments. The importance of gas-phase molecular ions in space has been described in detail in a recent review by Larsson et al. (2012).\n1.2. Significance of the present work\nExtraterrestrial molecular anions are believed to be produced predominantly via electron capture processes such as dissociative or radiative attachment (Larsson et al. 2012). The destruction processes are largely due to photodetachment, associative detachment and mutual neutralization reactions. In photon-dominated regions, the abundance of molecular anions can be mainly determined by their UV photodetachment. Even in the dark clouds where UV photons cannot penetrate UV photodetachment may still contribute to photodestruction of anions because the secondary electrons produced by cosmic rays can excite the molecules to high Rydberg states, which emit UV radiation upon decay. The study of photodetachment processes is also of particular importance in fundamental physics since the extra electron in an anion is bound to the system by means of strong correlated motion of the electrons in the system and the electron-\nelectron correlation plays the most crucial role in such processes. In addition, no theoretical or experimental values of photodetachment cross sections for CN -or C 3 N -have been reported in the literature despite the fact that there have been a number of studies on these molecular anions (Andersen et al. 2001, Bradforth et al. 1993, Gottlieb et al. 2007, Yen et al. 2010). Since these anions have high electron affinities (CN -: 3.862 ± 0.004 eV (Bradforth et al. 1993), C 3 N -: 4.305 ± 0.001 eV (Yen et al. 2010)) their photodetachment requires photons in the ultraviolet range. In the present work, we measured the photodetachment cross sections of CN -and C 3 N -anions at an energy (4.66 eV) near the photodetachment thresholds. Furthermore, we used the measured values as an input to model calculations to investigate the impact of the new cross sections on the predicted abundance of anions in the circumstellar envelope of IRC+10216.\n2. Experimental Method and Theoretical Modelling\n2.1. Experimental Setup\nThe basic elements of the experimental setup are an ion source, an octupole ion trap, an MCP detector and a laser system. The ion source consists of a piezoelectric pulsed gas valve with a pair of electrodes (referred to as 'plasma electrodes') attached at the exit of the valve. A suitable gas mixture is sent through the gas valve at a certain repetition rate. The ions are generated in a pulsed DC discharge of the gas jet between the plasma electrodes when a high potential difference is applied between them. These ions are then extracted towards the ion trap by a Wiley-McLaren time-of-flight spectrometer oriented perpendicular to the gas jet from the piezo valve. Deflection plates and lenses are used for guiding and focusing the ions into the ion trap. The unique octupole ion trap is made of 100 µ m gold plated molybdenum wires unlike in conventional designs where rods of specific diameter are used as RF electrodes. A short description of this ion trap has been provided by Deiglmayr et al. (2012), where it was used in conjunction with a magneto-optical trap to study reactive collisions of trapped OH -anions with trapped rubidium atoms. A second piezoelectric pulsed gas valve allows for helium buffer gas cooling of the trapped ions. There are two additional electrodes (termed as 'shield plates') above and below the trap that enable us to shape the ion density distribution inside the ion trap. The use of thin wires to construct the trap allows one to probe the trapped ions, for instance with a laser, from the sides. The laser beam can be focused at various positions inside the trap by means of a two-dimensional translation stage with a lens attached to it. This configuration is used to map the ion density distribution inside the trap.\nIn the present experiments, CN -and C 3 N -anions were generated by passing argon gas (at a pressure of about 2-3 bar) over acetonitrile vapor and sending the resulting mixture into the source piezo valve which was operated at 14 Hz. The discharge between the plasma electrodes ionized the gas mixture resulting in the production of several\nanions including CN -and C 3 N -. The plasma was stabilized by the electrons emitted from a hot filament placed opposite to the pulsed gas valve. The ions were injected into the Wiley-McLaren region, where they were extracted towards the trap with an average kinetic energy of about 240 eV. The desired ionic species can be stored in the ion trap by appropriate timing of the switchable voltages applied on the entrance and exit electrodes of the ion trap in accordance with the time of flight of the various molecular ions. The trap was operated at a radiofrequency of 9 MHz with an amplitude of 180 V on top of a DC voltage of about 240 V. The DC voltage of the trap served to reduce the kinetic energy of the ions coming from the source region to about a few eV. The entrance and exit endcap electrodes of the ion trap were between 10 V and 30 V, the exact value of which did not significantly affect the ion distribution except that the signal strength was slightly modified.\nThe photodetachment measurements were performed with a pulsed laser beam (266 nm, 10 Hz) obtained by frequency quadrupling of the output from a 1064 nm IR laser system with output pulse energy of about 30 mJ and with pulse width of 7 ns. The pulse energy of the laser beam was reduced to a few tens of microjoule and was then sent through a beam splitter. The transmitted beam was used to measure the fluctuations in the laser energy throughout the experiment and these data were used to correct the measured photodetachment cross section. The reflected beam was focused into the trap using the lens attached on the translation stage. The pulse energy of the beam fired into the trap was as low as 25 µ J so as to ensure that there was only single photon absorption and that the wires constituting the trap were not damaged when the laser beam struck them.\n2.2. Measurement procedure\nThe measurement procedure was very similar to the one described previously (Trippel et al. 2006, Hlavenka et al. 2009, Best et al. 2011) except that in the present experiments the laser beam was sent into the ion trap perpendicular to its symmetry axis. Briefly, the ions can be stored in the trap for a few hundred seconds (1 /e lifetime, determined from the exponential decay of the ions stored in the trap). In the first part of the experiment, the background decay rate was determined by measuring the amount of ions left in the trap after different storage times. In the second part, the rates of decay were measured with the UV laser pointing at different positions inside the trap. The photodetachment decay rates when plotted as a function of the positions form a tomography image which reflects the ion density distribution inside the trap. The integral of the rate map is proportional to the photodetachment cross section as detailed elsewhere (Trippel et al. 2006, Best et al. 2011).\nThe photodetachment cross section, σ pd , is given by the expression (Trippel et al. 2006, Best et al. 2011):\nσ pd = 1 Φ L ∫ [ k pd ( x, y ) -k bg ] dx dy, (1)\nwhere k pd ( x, y ) is the position dependent decay rate due to photodetachment, k bg is the background decay rate (decay rate measured without laser) and Φ L is the photon flux.\n2.3. Model Calculations for IRC+10216\nThe photodetachment cross sections measured for CN -and C 3 N -anions in the present experiments, together with those obtained previously (Best et al. 2011) for the carbon chain anions C 2 H -, C 4 H -and C 6 H -, were used as input for model calculations of the circumstellar envelope of IRC+10216. The photodetachment cross sections of CN -and C 3 N -were fitted to the expression used in previous model calculations (Millar et al. 2007):\nσ = σ ∞ √ 1 -E A //epsilon1, (2)\nin which σ is the cross section, σ ∞ the cross section at infinite photon energy, E A the photodetachment threshold energy and /epsilon1 the photon energy. Since our cross section measurements have been carried out only at a wavelength of 266 nm (at which a sufficiently intense UV beam was available from our laser systems) only two points exist for the fit of the photon energy/cross section curve for each of the nitrile anions, the cross section at threshold energy (where σ = 0) and the one measured at 266 nm. Of course, there exists the possibility of strong resonances, especially at photon energies only slightly above the threshold, which cannot be ruled out in the absence of complementary experimental data on photodetachment cross sections of these anions. For a more accurate treatment of the model, one would require experimental cross sections at higher photon energies necessitating radiation from sources such as synchrotrons or free electron lasers (FELs). Regarding the threshold energy ( E A ) of CN -, the value obtained by Bradforth et al. (1993) who employed a pulsed fixed-frequency negative ion photoelectron spectrometer (3.862 ± 0.004 eV) was used for the fit. In the case of C 3 N -the result from Yen et al. (2010) measured using slow electron velocity-map imaging (4.305 ± 0.001 eV) and field-free time-of-flight was applied. For the photodetachment cross sections of the hydrocarbon anions the fitted values from Best et al. (2011) were used.\nThe chemical models are based on the assumption of a uniform mass-loss rate for the circumstellar envelope of IRC+10216 described by Millar et al. (2000) together with a second model, described by Cordiner & Millar (2009), in which density-enhanced shells are included. With density-enhanced shells of gas and dust, a more realistic modelling of the circumstellar envelope is achieved by introducing a set of density enhancements with the physical parameters of the envelope based on the dust-shell observation by Mauron & Huggins (2000). For modelling, the conditions expected for the well-studied circumstellar envelope of IRC+10216 were applied. Consequently, a spherically symmetric outflow velocity from the central star of 1.45 × 10 6 cm s -1 and a mass loss of 1.5 × 10 -5 solar masses per year were assumed for the envelope (Men'shchikov et al. 2001). The adopted temperature profile is based on a fit to the gas kinetic temperature profile of Crosas & Menten (1997), with a minimum temperature\n
\n\n
Table 1. Abundances of parent species used in the model.
\n
\nof 10 K fixed in the outer region of the envelope and is the same as used by Cordiner & Millar (2009). The initial chemical abundances of parent molecules relative to that of H 2 used in the model are listed in Table 1. These species are formed in the inner envelope close to the star at high density and temperature and blown outwards in a spherically symmetric outflow (Millar et al. 2000). The calculations begin at an inner radius of 10 15 cm where photons from the external, interstellar radiation field begin to destroy parent species creating reactive radicals and ions and initiating the synthesis of anions and other species. The number density n ( r ) declines with the radius as 1 /r 2 . In the second set of calculations, in addition to the 1 /r 2 dependence of the number density, a series of step-like density enhancements of the form βn ( r ) is introduced. The parameter β is set to 5 for all shells in the model. According to dust shell parameters deduced from scattered light observations by Mauron & Huggins (2000), we assume that each shell has a thickness of 2 arcsec and the spacing between the shells is 12 arcsec. This distance corresponds to roughly 530 years between the peaks of enhanced mass loss (See Cordiner & Millar (2009) for details.).\n3. Results and Discussion\n3.1. Experimental results\n\n\n
Figure 1 presents the tomography images for the CN -anions at two different configurations of the shield plate voltages. One can clearly see a difference in the ion distributions inside the trap. In fact, the ion trap exhibits two local minima in the vertical direction due to the presence of the holes in the shield plates placed above and below the trap. By adjusting the voltages on these plates, one can redistribute the ions in the trap into these local minima. On the left-hand side of Figure 1, the ions are more or less equally distributed in the two minima, whereas on the right-hand side, the lower minimum is mostly populated. The cross sections measured from these strongly different distributions agree to within 4%. A similar procedure was employed for C 3 N -. For C 3 N -, the error is larger, about 10%, because its signal strength was almost an order of magnitude less than that of CN -, and hence the fluctuations in the ion signal limited the accuracy with which the rates could be determined. The values of the measured cross sections for both CN -and C 3 N -from different measurements are summarized in Table 2. The determination of the systematic uncertainties (as percentage error) in the measurements involves several factors which are listed in Table 3.
\n\n\n\n
Figure 1. Tomography images for the CN -ions for two different ion density distributions in the trap. The numbers on the color bars are in the units of s -1 . The cross sections determined from these distributions agree to within 4%. Similar results were obtained for C 3 N -also (not shown).
\n\n
\n\n
Table 2. Cross sections ( × 10 -17 cm 2 ) from a few sets of measurements on CN -and C 3 N -at 266 nm together with the average values and the values from the fit to Equation (2). For accuracy, see Table 3.
\n
\n
\n\n
Photodetachment as destruction mechanism for CN -and C 3 N -anions ... 8Table 3. Possible contribution of errors (%) in calculating the cross sections of CN -and C 3 N -. The various contributions are assumed to be independent. Integration limits and background subtraction are in fact not completely independent. However, the dependence is not systematic. Further, this correction does not make any significant difference in the estimation of errors.
\n
\nThe photodetachment cross sections of CN -and C 3 N -are a factor of at least two larger than the cross sections measured for other carbon chain anions C n H -(Best et al. 2011). Hence the abundance of these cyano anions in photon-dominated regions is likely to be significantly influenced by their photodetachment. Furthermore, the cross sections are determined at an energy which is not far away from the photodetachment threshold for both CN -and C 3 N -. Therefore, the large cross section values may indicate the presence of strong resonances.\n3.2. Results from model calculations\nThe photodetachment rate constants that function as input data for the model calculations were obtained using a standard interstellar radiation field (Draine 1978). The obtained values were 2.55 × 10 -9 , 1.99 × 10 -9 , 1.16 × 10 -9 , 6.72 × 10 -9 and 1.03 × 10 -8 s -1 for C 2 H -, C 4 H -, C 6 H -, CN -and C 3 N -, respectively. In this calculation we have used the entire reaction set and the rate coefficients of the UMIST database for astrochemistry 2012 (McElroy et al. 2013), which includes the additional anion production mechanisms mentioned by Cordiner et al. (2008), to calculate molecular abundances as a function of the radial distance from the centre of the star (See Cordiner & Millar (2009) for details.). In a second set of calculations, shells of matter with densities that are enhanced relative to the surrounding circumstellar medium were included in the model. Figures 2a (no shells) and 2b (with shells) show the fractional abundances of the important anions, as well as the electron fraction, as a function of radius in the circumstellar envelope. When integrated over radius, these abundances yield the total column densities which were compared with those using the cross section function, σ = 1 × 10 -17 √ 1 -E A //epsilon1 cm 2 , employed in previous studies (Millar et al. 2007). The column densities using these two approaches are listed in Table 4.\nIt can be seen that the input of the experimental cross sections somewhat reduces the column densities and thus slightly deteriorates the agreement between the modelled and observed cross sections. Also, the C 3 N -/C 3 N ratio predicted by the model\n/s32\n\n\n
Figure 2. Fractional abundances of the important anions, as well as the electron fraction, as a function of radius in the circumstellar envelope of IRC+10216 without (a) and with (b) shells.
\n\n
\n\n
Table 4. Calculated and observed column densities (in cm -2 ) of anions in IRC+10216.
\n
\n(1 . 4 × 10 -3 ) now lies below the observed value (5 × 10 -3 ), whereas previous models tended to overestimate it (Herbst 2009, and references therein). The inclusion of highdensity shells does increase the anion column densities by around 10-20%. However, they remain smaller, but within the same order of magnitude, than those observed.\nThe predicted densities not only depend strongly on the rates of photodetachment but also on the efficiency of the formation reactions, such as radiative attachment, radical-ion and dissociative attachment reactions. Regarding the generation of the two cyano anions the model predicts that reactions of N radicals with C -n ions, e.g.,\nC -6 +N → C 3 N -+C 3 (3)\nC -6 +N → CN -+C 5 (4)\ndominate as formation pathways in the outer and middle parts of the envelope (r ≥ 10 16 cm) for both CN -and C 3 N -. These processes might be partly responsible for the extraordinarily high anion to neutral abundance ratio for C 3 N -(Cordiner & Millar 2009, Ag'undez et al. 2010, Thaddeus et al. 2008, Cernicharo et al. 2007). In the innermost regions (r ≤ 10 16 cm), formation of CN -proceeds via reaction of H -with HCN:\nH -+HCN → CN -+H 2 . (5)\nThe importance of the latter process is due to the formation of H -through cosmic ray induced ion pair formation in the inner shells of the envelope (Cordiner &\n/s32\nMillar 2009, Prasad & Huntress Jr 1980). At these small radii, radiative attachment of C 3 N and dissociative attachment of HNC 3 are predominant formation routes of C 3 N -:\nC 3 N+e -→ C 3 N -+h ν (6)\nHNC 3 +e -→ C 3 N -+H . (7)\nWhereas the reactions of N atoms with C n chain anions have been characterized in a selected ion flow tube experiment (Eichelberger et al. 2007), there are, as yet, no laboratory studies on the formation of the cyanide anion from H -and HCN.\nThere are also uncertainties in the destruction processes. At a distance from the central star of around 6 × 10 16 cm, where the abundance of the CN -and the C 3 N -anions peaks, photodetachment clearly is the most important degradation mechanism of the two anions and accounts for 45 % of the breakdown of C 3 N -and 35 % for CN -. In the case of CN -, other decay processes are mutual neutralization with C + (30 %) and Si + (7 %) as well as associative detachment with H (15 %). Minor loss processes of C 3 N -are mutual neutralization with C + (25 %) and Si + (6 %) and associative detachment with H (11 %). In the outer regions of the cloud (r > 10 17 cm) mutual neutralization with C + actually becomes predominant for both C 3 N -(accounting for 72 % of the loss at a distance of 2 . 5 × 10 17 cm from the star) and CN -(79 % at the same radius). This behavior is most likely due to the increase of C + abundance towards the edge of the cloud (the peak density of this species there is around 5.4 × 10 -2 cm -3 with an abundance ratio C + /H 2 of 2 . 1 × 10 -4 at a radius of 2 . 2 × 10 17 cm), which is caused by photoionization of C through the interstellar radiation field. In the inner regions of the circumstellar envelope (r < 10 16 cm) mutual neutralization with Mg + is predicted to be the main degradation process. This can be explained by the fact that the Mg + number density is fairly constant throughout the envelope (ranging between 2 × 10 -4 cm -3 and 2 × 10 -3 cm -3 ), whereas the C + abundance is as low as 1 . 5 × 10 -6 cm -3 at a radius of 2 × 10 16 cm. Consequently, the abundance ratio of C + to H 2 increases from 1 . 0 × 10 -12 at a radius of 2 . 2 × 10 15 cm to 7 . 8 × 10 -4 at a radius of 7 . 1 × 10 17 cm, whereas the one of Mg + to H 2 spans only 5 orders of magnitude, rising from 2 . 1 × 10 -10 at a radius of 2 . 2 × 10 15 cm to 1 . 0 × 10 -5 at a radius of 7 . 1 × 10 17 cm. But even at the outermost and the innermost distances photodetachment significantly contributes to the destruction of CN -and C 3 N -.\nThe peak abundances of the two cyano anions investigated in this study lie at the radii 6 . 3 × 10 16 cm and 5 . 6 × 10 16 cm for CN -and C 3 N -, respectively, and the maxima of the fractional abundances at 7 . 9 × 10 16 cm for CN -and 7 . 1 × 10 16 cm for C 3 N -. This implies that the CN -peak radius predicted by the model is somewhat larger than the one concluded from observations (2 × 10 16 cm), but slightly lower than the one predicted by model calculations of Ag'undez et al. (2010) (8 × 10 16 cm). From the present data it can be concluded that photodetachment is a very crucial process in the degradation of anions throughout the envelope. However, one has to consider the uncertainties regarding the rate constants of the formation and destruction mechanisms\nof the two anions. The relative importance of photodetachment depends on the rate constants of the competing processes, namely the mutual neutralization processes of the cyano anions with C + and other metallic ions. Harada & Herbst (2008) estimated the rate constant of the reaction of C 3 N -with C + based on earlier flowing afterglow Langmuir probe measurements (Smith et al. 1978) of other ions to follow the expression:\nk = 7 . 5 × 10 -8 (T / 300) -0 . 5 cm 3 s -1 . (8)\nTo the best of our knowledge, no experimental data on the reaction rate constants of these processes have so far been obtained. The new DESIREE double storage ring at Stockholm University will amend this shortcoming (Schmidt et al. 2008).\nIn agreement with other model calculations, the abundances of the anions peak at larger radii than the corresponding neutrals (Guelin et al. 2011). The inclusion of shells with enhanced density similar to the model of Cordiner & Millar (2009) increases the column densities of the anions by about 20% and improves the agreement with observed column densities, predominantly through reducing the rates of photodetachment through the increased dust extinction that they provide.\n4. Conclusions\nThe absolute photodetachment cross sections of two molecular anions of astrophysical importance, CN -and C 3 N -, were measured at the ultraviolet wavelength of 266 nm. The measured cross sections are relatively high and might indicate the possibility of strong resonances near the photodetachment threshold. High cross sections imply that the abundance of these molecular anions can be crucially dependent on their destruction by photodetachment especially in photon-dominated regions. The presented model calculations, carried out to investigate molecular anions in the circumstellar envelope of IRC+10216, predict the relative importance of the various mechanisms of production and destruction of cyano anions in different regions of the envelope. It was found that in regions where these molecular anions have their peak abundance, photodetachment serves as the most important destruction mechanism. The calculations also predict that photodetachment significantly contributes to the destruction of these anions throughout the circumstellar envelope. Thus photodetachment plays a fundamental role in the degradation of anions in circumstellar envelopes. However, its exact significance can only be determined if more data on other competing pathways are available. Future experimental investigations on these processes are therefore vital for our understanding of the anion chemistry of circumstellar envelopes.\nThis work has been supported by the European Research Council under ERC grant agreement No. 279898 and by the ESF COST Action CM0805 'The Chemical Cosmos: Understanding Chemistry in Astronomical Environments'. We thank Eric Endres for his support during the experiments. Research in molecular astrophysics at QUB is supported by a grant from the STFC. ˇ S. R. ackowledges support by Czech Grant Agency under contract No. P209/12/0233.\n5. 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McDowell M R C 1961 The Observatory 81 , 240-243.\nMcElroy D, Walsh C, Markwick A J, Cordiner M A, Smith K & Millar T J 2013 Astronomy & Astrophysics 550 , A36.\nMen'shchikov A B, Balega Y, Blocker T, Osterbart R & Weigelt G 2001 Astronomy & Astrophysics 368 (2), 497-526.\nMillar T J, Herbst E & Bettens R P A 2000 Monthly Notices of the Royal Astronomical Society\n316 (1), 195-203.\nMillar T J, Walsh C, Cordiner M A, N'ı Chuim'ın R & Herbst E 2007 The Astrophysical Journal Letters 662 (2), L87-L90.\nPrasad S S & Huntress Jr W T 1980 The Astrophysical Journal Supplement Series 43 , 1-35.\nRemijan A J, Hollis J M, Lovas F J, Cordiner M A, Millar T J, Markwick-Kemper A J & Jewell P R 2007 The Astrophysical Journal 664 (1), L47-L50.\nSakai N, Sakai T, Osamura Y & Yamamoto S 2007 The Astrophysical Journal 667 (1), L65-L68.\nSakai N, Sakai T & Yamamoto S 2008 The Astrophysical Journal 673 (1), L71-L74.\nSakai N, Shiino T, Hirota T, Sakai T & Yamamoto S 2010 The Astrophysical Journal Letters 718 (2), L49-L52.\nSchmidt H T, Johansson H A B, Thomas R D, Geppert W D, Haag N, Reinhed P, Ros'en S, Larsson M, Danared H, Rensfelt K G et al. 2008 International Journal of Astrobiology 7 (3-4), 205-208. Smith D, Church M J & Miller T M 1978 The Journal of Chemical Physics 68 , 1224.\nThaddeus P, Gottlieb C A, Gupta H, Brunken S, McCarthy M C, Ag'undez M, Gu'elin M & Cernicharo J 2008 The Astrophysical Journal 677 (2), 1132.\n\nTrippel S, Mikosch J, Berhane R, Otto R, Weidemuller M & Wester R 2006 Physical Review Letters 97 (19), 193003.\n\nYen T A, Garand E, Shreve A T & Neumark D M 2010 The Journal of Physical Chemistry A 114 (9), 3215-3220.\n"},"sections":{"kind":"list like","value":[{"title":"PHOTODETACHMENT AS DESTRUCTION MECHANISM FOR CN -and C 3 N -ANIONS IN CIRCUMSTELLAR ENVELOPES","content":"S. S. Kumar 1 , D. Hauser 1 , R. Jindra 1 , T. Best 1 , ˇ S. Rouˇcka 2 , W.","pages":[1]},{"title":"D. Geppert 3 , T. J. Millar 4 , and R. Wester 1","content":"1 Institut fur Ionenphysik und Angewandte Physik, Universitat Innsbruck, A -6020 Innsbruck, Austria 2 Charles University in Prague, Faculty of Mathematics and Physics, Department of Surface and Plasma Science, 18000 Prague, Czech Republic 3 Department of Physics, AlbaNova, Stockholm University, SE -10691 Stockholm, Sweden 4 Astrophysics Research Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, UK E-mail: roland.wester@uibk.ac.at Abstract. Absolute photodetachment cross sections of two anions of astrophysical importance CN -and C 3 N -were measured to be (1.18 ± (0.03) stat (0.17) sys ) × 10 -17 cm 2 and (1.43 ± (0.14) stat (0.37) sys ) × 10 -17 cm 2 respectively at the ultraviolet wavelength of 266 nm (4.66 eV). These relatively large values of the cross sections imply that photodetachment can play a major role in the destruction mechanisms of these anions particularly in photon-dominated regions. We have therefore carried out model calculations using the newly measured cross sections to investigate the abundance of these molecular anions in the cirumstellar envelope of the carbon-rich star IRC+10216. The model predicts the relative importance of the various mechanisms of formation and destruction of these species in different regions of the envelope. UV photodetachment was found to be the major destruction mechanism for both CN -and C 3 N -anions in those regions of the envelope, where they occur in peak abundance. It was also found that photodetachment plays a crucial role in the degradation of these anions throughout the circumstellar envelope.","pages":[1]},{"title":"1.1. Molecular anions in space: Observation and astrophysical relevance","content":"The discovery of molecules in the interstellar medium about seven decades ago was particularly intriguing since the chemistry governing the formation of molecules in such hostile regions of space was not familiar. Gradually the number of molecules and their cations found in extraterrestrial space increased and it became clear that we in fact live in a 'molecular Universe' (Larsson et al. 2012). However, after the first molecule was identified in the interstellar medium, it took six decades before a molecular anion could be discovered in such environment. This delay was primarily due to the low abundance of anions in space compared to their neutral counterparts and due to the lack of laboratory measurements of high resolution rotational spectra of the anions that could allow their search in space. The first molecular anion ever observed outside our solar system is C 6 H -(McCarthy et al. 2006), which was detected in the envelope of the carbon-rich star IRC+10216. The identification of this molecular anion was followed by the discovery of several other carbon chain anions, C n H -( n = 4, 8) and C n N -( n = 1, 3, 5) in various regions of space such as dark clouds, circumstellar envelopes, and also in Titan's atmosphere (Cernicharo et al. 2007, Cernicharo et al. 2008, Sakai et al. 2007, Sakai et al. 2008, Sakai et al. 2010, Ag'undez et al. 2008, Ag'undez et al. 2010, Remijan et al. 2007, Brunken et al. 2007, Kasai et al. 2007, Kawaguchi et al. 2007, Thaddeus et al. 2008, Gupta et al. 2009). Of these anions, C 5 N -was only tentatively identified. The role of anions in the synthesis of molecules in the interstellar medium has been investigated by Dalgarno & McCray (1973) many years ago, whereas the formation of molecular hydrogen in stars from H -had been pointed out by McDowell (1961) much earlier. The recent discovery of anions in extraterrestrial environments has initiated a fresh interest towards the understanding of anion chemistry in exotic environments. The importance of gas-phase molecular ions in space has been described in detail in a recent review by Larsson et al. (2012).","pages":[2]},{"title":"1.2. Significance of the present work","content":"Extraterrestrial molecular anions are believed to be produced predominantly via electron capture processes such as dissociative or radiative attachment (Larsson et al. 2012). The destruction processes are largely due to photodetachment, associative detachment and mutual neutralization reactions. In photon-dominated regions, the abundance of molecular anions can be mainly determined by their UV photodetachment. Even in the dark clouds where UV photons cannot penetrate UV photodetachment may still contribute to photodestruction of anions because the secondary electrons produced by cosmic rays can excite the molecules to high Rydberg states, which emit UV radiation upon decay. The study of photodetachment processes is also of particular importance in fundamental physics since the extra electron in an anion is bound to the system by means of strong correlated motion of the electrons in the system and the electron- electron correlation plays the most crucial role in such processes. In addition, no theoretical or experimental values of photodetachment cross sections for CN -or C 3 N -have been reported in the literature despite the fact that there have been a number of studies on these molecular anions (Andersen et al. 2001, Bradforth et al. 1993, Gottlieb et al. 2007, Yen et al. 2010). Since these anions have high electron affinities (CN -: 3.862 ± 0.004 eV (Bradforth et al. 1993), C 3 N -: 4.305 ± 0.001 eV (Yen et al. 2010)) their photodetachment requires photons in the ultraviolet range. In the present work, we measured the photodetachment cross sections of CN -and C 3 N -anions at an energy (4.66 eV) near the photodetachment thresholds. Furthermore, we used the measured values as an input to model calculations to investigate the impact of the new cross sections on the predicted abundance of anions in the circumstellar envelope of IRC+10216.","pages":[2,3]},{"title":"2.1. Experimental Setup","content":"The basic elements of the experimental setup are an ion source, an octupole ion trap, an MCP detector and a laser system. The ion source consists of a piezoelectric pulsed gas valve with a pair of electrodes (referred to as 'plasma electrodes') attached at the exit of the valve. A suitable gas mixture is sent through the gas valve at a certain repetition rate. The ions are generated in a pulsed DC discharge of the gas jet between the plasma electrodes when a high potential difference is applied between them. These ions are then extracted towards the ion trap by a Wiley-McLaren time-of-flight spectrometer oriented perpendicular to the gas jet from the piezo valve. Deflection plates and lenses are used for guiding and focusing the ions into the ion trap. The unique octupole ion trap is made of 100 µ m gold plated molybdenum wires unlike in conventional designs where rods of specific diameter are used as RF electrodes. A short description of this ion trap has been provided by Deiglmayr et al. (2012), where it was used in conjunction with a magneto-optical trap to study reactive collisions of trapped OH -anions with trapped rubidium atoms. A second piezoelectric pulsed gas valve allows for helium buffer gas cooling of the trapped ions. There are two additional electrodes (termed as 'shield plates') above and below the trap that enable us to shape the ion density distribution inside the ion trap. The use of thin wires to construct the trap allows one to probe the trapped ions, for instance with a laser, from the sides. The laser beam can be focused at various positions inside the trap by means of a two-dimensional translation stage with a lens attached to it. This configuration is used to map the ion density distribution inside the trap. In the present experiments, CN -and C 3 N -anions were generated by passing argon gas (at a pressure of about 2-3 bar) over acetonitrile vapor and sending the resulting mixture into the source piezo valve which was operated at 14 Hz. The discharge between the plasma electrodes ionized the gas mixture resulting in the production of several anions including CN -and C 3 N -. The plasma was stabilized by the electrons emitted from a hot filament placed opposite to the pulsed gas valve. The ions were injected into the Wiley-McLaren region, where they were extracted towards the trap with an average kinetic energy of about 240 eV. The desired ionic species can be stored in the ion trap by appropriate timing of the switchable voltages applied on the entrance and exit electrodes of the ion trap in accordance with the time of flight of the various molecular ions. The trap was operated at a radiofrequency of 9 MHz with an amplitude of 180 V on top of a DC voltage of about 240 V. The DC voltage of the trap served to reduce the kinetic energy of the ions coming from the source region to about a few eV. The entrance and exit endcap electrodes of the ion trap were between 10 V and 30 V, the exact value of which did not significantly affect the ion distribution except that the signal strength was slightly modified. The photodetachment measurements were performed with a pulsed laser beam (266 nm, 10 Hz) obtained by frequency quadrupling of the output from a 1064 nm IR laser system with output pulse energy of about 30 mJ and with pulse width of 7 ns. The pulse energy of the laser beam was reduced to a few tens of microjoule and was then sent through a beam splitter. The transmitted beam was used to measure the fluctuations in the laser energy throughout the experiment and these data were used to correct the measured photodetachment cross section. The reflected beam was focused into the trap using the lens attached on the translation stage. The pulse energy of the beam fired into the trap was as low as 25 µ J so as to ensure that there was only single photon absorption and that the wires constituting the trap were not damaged when the laser beam struck them.","pages":[3,4]},{"title":"2.2. Measurement procedure","content":"The measurement procedure was very similar to the one described previously (Trippel et al. 2006, Hlavenka et al. 2009, Best et al. 2011) except that in the present experiments the laser beam was sent into the ion trap perpendicular to its symmetry axis. Briefly, the ions can be stored in the trap for a few hundred seconds (1 /e lifetime, determined from the exponential decay of the ions stored in the trap). In the first part of the experiment, the background decay rate was determined by measuring the amount of ions left in the trap after different storage times. In the second part, the rates of decay were measured with the UV laser pointing at different positions inside the trap. The photodetachment decay rates when plotted as a function of the positions form a tomography image which reflects the ion density distribution inside the trap. The integral of the rate map is proportional to the photodetachment cross section as detailed elsewhere (Trippel et al. 2006, Best et al. 2011). The photodetachment cross section, σ pd , is given by the expression (Trippel et al. 2006, Best et al. 2011): where k pd ( x, y ) is the position dependent decay rate due to photodetachment, k bg is the background decay rate (decay rate measured without laser) and Φ L is the photon flux.","pages":[4,5]},{"title":"2.3. Model Calculations for IRC+10216","content":"The photodetachment cross sections measured for CN -and C 3 N -anions in the present experiments, together with those obtained previously (Best et al. 2011) for the carbon chain anions C 2 H -, C 4 H -and C 6 H -, were used as input for model calculations of the circumstellar envelope of IRC+10216. The photodetachment cross sections of CN -and C 3 N -were fitted to the expression used in previous model calculations (Millar et al. 2007): in which σ is the cross section, σ ∞ the cross section at infinite photon energy, E A the photodetachment threshold energy and /epsilon1 the photon energy. Since our cross section measurements have been carried out only at a wavelength of 266 nm (at which a sufficiently intense UV beam was available from our laser systems) only two points exist for the fit of the photon energy/cross section curve for each of the nitrile anions, the cross section at threshold energy (where σ = 0) and the one measured at 266 nm. Of course, there exists the possibility of strong resonances, especially at photon energies only slightly above the threshold, which cannot be ruled out in the absence of complementary experimental data on photodetachment cross sections of these anions. For a more accurate treatment of the model, one would require experimental cross sections at higher photon energies necessitating radiation from sources such as synchrotrons or free electron lasers (FELs). Regarding the threshold energy ( E A ) of CN -, the value obtained by Bradforth et al. (1993) who employed a pulsed fixed-frequency negative ion photoelectron spectrometer (3.862 ± 0.004 eV) was used for the fit. In the case of C 3 N -the result from Yen et al. (2010) measured using slow electron velocity-map imaging (4.305 ± 0.001 eV) and field-free time-of-flight was applied. For the photodetachment cross sections of the hydrocarbon anions the fitted values from Best et al. (2011) were used. The chemical models are based on the assumption of a uniform mass-loss rate for the circumstellar envelope of IRC+10216 described by Millar et al. (2000) together with a second model, described by Cordiner & Millar (2009), in which density-enhanced shells are included. With density-enhanced shells of gas and dust, a more realistic modelling of the circumstellar envelope is achieved by introducing a set of density enhancements with the physical parameters of the envelope based on the dust-shell observation by Mauron & Huggins (2000). For modelling, the conditions expected for the well-studied circumstellar envelope of IRC+10216 were applied. Consequently, a spherically symmetric outflow velocity from the central star of 1.45 × 10 6 cm s -1 and a mass loss of 1.5 × 10 -5 solar masses per year were assumed for the envelope (Men'shchikov et al. 2001). The adopted temperature profile is based on a fit to the gas kinetic temperature profile of Crosas & Menten (1997), with a minimum temperature of 10 K fixed in the outer region of the envelope and is the same as used by Cordiner & Millar (2009). The initial chemical abundances of parent molecules relative to that of H 2 used in the model are listed in Table 1. These species are formed in the inner envelope close to the star at high density and temperature and blown outwards in a spherically symmetric outflow (Millar et al. 2000). The calculations begin at an inner radius of 10 15 cm where photons from the external, interstellar radiation field begin to destroy parent species creating reactive radicals and ions and initiating the synthesis of anions and other species. The number density n ( r ) declines with the radius as 1 /r 2 . In the second set of calculations, in addition to the 1 /r 2 dependence of the number density, a series of step-like density enhancements of the form βn ( r ) is introduced. The parameter β is set to 5 for all shells in the model. According to dust shell parameters deduced from scattered light observations by Mauron & Huggins (2000), we assume that each shell has a thickness of 2 arcsec and the spacing between the shells is 12 arcsec. This distance corresponds to roughly 530 years between the peaks of enhanced mass loss (See Cordiner & Millar (2009) for details.).","pages":[5,6]},{"title":"3.1. Experimental results","content":"The photodetachment cross sections of CN -and C 3 N -are a factor of at least two larger than the cross sections measured for other carbon chain anions C n H -(Best et al. 2011). Hence the abundance of these cyano anions in photon-dominated regions is likely to be significantly influenced by their photodetachment. Furthermore, the cross sections are determined at an energy which is not far away from the photodetachment threshold for both CN -and C 3 N -. Therefore, the large cross section values may indicate the presence of strong resonances.","pages":[8]},{"title":"3.2. Results from model calculations","content":"The photodetachment rate constants that function as input data for the model calculations were obtained using a standard interstellar radiation field (Draine 1978). The obtained values were 2.55 × 10 -9 , 1.99 × 10 -9 , 1.16 × 10 -9 , 6.72 × 10 -9 and 1.03 × 10 -8 s -1 for C 2 H -, C 4 H -, C 6 H -, CN -and C 3 N -, respectively. In this calculation we have used the entire reaction set and the rate coefficients of the UMIST database for astrochemistry 2012 (McElroy et al. 2013), which includes the additional anion production mechanisms mentioned by Cordiner et al. (2008), to calculate molecular abundances as a function of the radial distance from the centre of the star (See Cordiner & Millar (2009) for details.). In a second set of calculations, shells of matter with densities that are enhanced relative to the surrounding circumstellar medium were included in the model. Figures 2a (no shells) and 2b (with shells) show the fractional abundances of the important anions, as well as the electron fraction, as a function of radius in the circumstellar envelope. When integrated over radius, these abundances yield the total column densities which were compared with those using the cross section function, σ = 1 × 10 -17 √ 1 -E A //epsilon1 cm 2 , employed in previous studies (Millar et al. 2007). The column densities using these two approaches are listed in Table 4. It can be seen that the input of the experimental cross sections somewhat reduces the column densities and thus slightly deteriorates the agreement between the modelled and observed cross sections. Also, the C 3 N -/C 3 N ratio predicted by the model /s32 (1 . 4 × 10 -3 ) now lies below the observed value (5 × 10 -3 ), whereas previous models tended to overestimate it (Herbst 2009, and references therein). The inclusion of highdensity shells does increase the anion column densities by around 10-20%. However, they remain smaller, but within the same order of magnitude, than those observed. The predicted densities not only depend strongly on the rates of photodetachment but also on the efficiency of the formation reactions, such as radiative attachment, radical-ion and dissociative attachment reactions. Regarding the generation of the two cyano anions the model predicts that reactions of N radicals with C -n ions, e.g., dominate as formation pathways in the outer and middle parts of the envelope (r ≥ 10 16 cm) for both CN -and C 3 N -. These processes might be partly responsible for the extraordinarily high anion to neutral abundance ratio for C 3 N -(Cordiner & Millar 2009, Ag'undez et al. 2010, Thaddeus et al. 2008, Cernicharo et al. 2007). In the innermost regions (r ≤ 10 16 cm), formation of CN -proceeds via reaction of H -with HCN: The importance of the latter process is due to the formation of H -through cosmic ray induced ion pair formation in the inner shells of the envelope (Cordiner & /s32 Millar 2009, Prasad & Huntress Jr 1980). At these small radii, radiative attachment of C 3 N and dissociative attachment of HNC 3 are predominant formation routes of C 3 N -: Whereas the reactions of N atoms with C n chain anions have been characterized in a selected ion flow tube experiment (Eichelberger et al. 2007), there are, as yet, no laboratory studies on the formation of the cyanide anion from H -and HCN. There are also uncertainties in the destruction processes. At a distance from the central star of around 6 × 10 16 cm, where the abundance of the CN -and the C 3 N -anions peaks, photodetachment clearly is the most important degradation mechanism of the two anions and accounts for 45 % of the breakdown of C 3 N -and 35 % for CN -. In the case of CN -, other decay processes are mutual neutralization with C + (30 %) and Si + (7 %) as well as associative detachment with H (15 %). Minor loss processes of C 3 N -are mutual neutralization with C + (25 %) and Si + (6 %) and associative detachment with H (11 %). In the outer regions of the cloud (r > 10 17 cm) mutual neutralization with C + actually becomes predominant for both C 3 N -(accounting for 72 % of the loss at a distance of 2 . 5 × 10 17 cm from the star) and CN -(79 % at the same radius). This behavior is most likely due to the increase of C + abundance towards the edge of the cloud (the peak density of this species there is around 5.4 × 10 -2 cm -3 with an abundance ratio C + /H 2 of 2 . 1 × 10 -4 at a radius of 2 . 2 × 10 17 cm), which is caused by photoionization of C through the interstellar radiation field. In the inner regions of the circumstellar envelope (r < 10 16 cm) mutual neutralization with Mg + is predicted to be the main degradation process. This can be explained by the fact that the Mg + number density is fairly constant throughout the envelope (ranging between 2 × 10 -4 cm -3 and 2 × 10 -3 cm -3 ), whereas the C + abundance is as low as 1 . 5 × 10 -6 cm -3 at a radius of 2 × 10 16 cm. Consequently, the abundance ratio of C + to H 2 increases from 1 . 0 × 10 -12 at a radius of 2 . 2 × 10 15 cm to 7 . 8 × 10 -4 at a radius of 7 . 1 × 10 17 cm, whereas the one of Mg + to H 2 spans only 5 orders of magnitude, rising from 2 . 1 × 10 -10 at a radius of 2 . 2 × 10 15 cm to 1 . 0 × 10 -5 at a radius of 7 . 1 × 10 17 cm. But even at the outermost and the innermost distances photodetachment significantly contributes to the destruction of CN -and C 3 N -. The peak abundances of the two cyano anions investigated in this study lie at the radii 6 . 3 × 10 16 cm and 5 . 6 × 10 16 cm for CN -and C 3 N -, respectively, and the maxima of the fractional abundances at 7 . 9 × 10 16 cm for CN -and 7 . 1 × 10 16 cm for C 3 N -. This implies that the CN -peak radius predicted by the model is somewhat larger than the one concluded from observations (2 × 10 16 cm), but slightly lower than the one predicted by model calculations of Ag'undez et al. (2010) (8 × 10 16 cm). From the present data it can be concluded that photodetachment is a very crucial process in the degradation of anions throughout the envelope. However, one has to consider the uncertainties regarding the rate constants of the formation and destruction mechanisms of the two anions. The relative importance of photodetachment depends on the rate constants of the competing processes, namely the mutual neutralization processes of the cyano anions with C + and other metallic ions. Harada & Herbst (2008) estimated the rate constant of the reaction of C 3 N -with C + based on earlier flowing afterglow Langmuir probe measurements (Smith et al. 1978) of other ions to follow the expression: To the best of our knowledge, no experimental data on the reaction rate constants of these processes have so far been obtained. The new DESIREE double storage ring at Stockholm University will amend this shortcoming (Schmidt et al. 2008). In agreement with other model calculations, the abundances of the anions peak at larger radii than the corresponding neutrals (Guelin et al. 2011). The inclusion of shells with enhanced density similar to the model of Cordiner & Millar (2009) increases the column densities of the anions by about 20% and improves the agreement with observed column densities, predominantly through reducing the rates of photodetachment through the increased dust extinction that they provide.","pages":[8,9,10,11]},{"title":"4. Conclusions","content":"The absolute photodetachment cross sections of two molecular anions of astrophysical importance, CN -and C 3 N -, were measured at the ultraviolet wavelength of 266 nm. The measured cross sections are relatively high and might indicate the possibility of strong resonances near the photodetachment threshold. High cross sections imply that the abundance of these molecular anions can be crucially dependent on their destruction by photodetachment especially in photon-dominated regions. The presented model calculations, carried out to investigate molecular anions in the circumstellar envelope of IRC+10216, predict the relative importance of the various mechanisms of production and destruction of cyano anions in different regions of the envelope. It was found that in regions where these molecular anions have their peak abundance, photodetachment serves as the most important destruction mechanism. The calculations also predict that photodetachment significantly contributes to the destruction of these anions throughout the circumstellar envelope. Thus photodetachment plays a fundamental role in the degradation of anions in circumstellar envelopes. However, its exact significance can only be determined if more data on other competing pathways are available. Future experimental investigations on these processes are therefore vital for our understanding of the anion chemistry of circumstellar envelopes. This work has been supported by the European Research Council under ERC grant agreement No. 279898 and by the ESF COST Action CM0805 'The Chemical Cosmos: Understanding Chemistry in Astronomical Environments'. We thank Eric Endres for his support during the experiments. Research in molecular astrophysics at QUB is supported by a grant from the STFC. ˇ S. R. ackowledges support by Czech Grant Agency under contract No. P209/12/0233.","pages":[11]},{"title":"5. References","content":"Ag'undez M, Cernicharo J, Gu'elin M, Gerin M, McCarthy M C & Thaddeus P 2008 Astronomy & Astrophysics 478 (1), L19-L22. Ag'undez M, Cernicharo J, Gu'elin M, Kahane C, Roueff E, K/suppresslos J, Aoiz F J, Lique F, Marcelino N, Goicoechea J R, Gonz'alez Garc'ıa M, Gottlieb C A, McCarthy M C & Thaddeus P 2010 Astronomy & Astrophysics 517 , L2. Andersen L H, Bak J, Boye S, Clausen M, Hovgaard M, Jensen M J, Lapierre A & Seiersen K 2001 The Journal of Chemical Physics 115 , 3566. Best T, Otto R, Trippel S, Hlavenka P, von Zastrow A, Eisenbach S, J'ezouin S, Wester R, Vigren E, Hamberg M & Geppert W D 2011 The Astrophysical Journal 742 (2), 63. Bradforth S E, Kim E H, Arnold D W & Neumark D M 1993 The Journal of Chemical Physics 98 (2), 800. Brunken S, Gupta H, Gottlieb C A, McCarthy M C & Thaddeus P 2007 The Astrophysical Journal 664 (1), L43-L46. Cernicharo J, Gu'elin M, Ag'undez M, Kawaguchi K, McCarthy M & Thaddeus P 2007 Astronomy & Astrophysics 467 (2), L37-L40. Cernicharo J, Gu'elin M, Ag'undez M, McCarthy M C & Thaddeus P 2008 The Astrophysical Journal 688 , L83-L86. Cordiner M A & Millar T J 2009 The Astrophysical Journal 697 (1), 68. Cordiner M A, Millar T J, Walsh C, Herbst E, Lis D C, Bell T A & Roueff E 2008 Proceedings of the International Astronomical Union 251 , 157. Crosas M & Menten K M 1997 The Astrophysical Journal 483 (2), 913. Dalgarno A & McCray R A 1973 The Astrophysical Journal 181 , 95-100. Deiglmayr J, Goritz A, Best T, Weidemuller M & Wester R 2012 Physical Review A 86 (4), 043438. Draine B T 1978 The Astrophysical Journal Supplement Series 36 , 595. Eichelberger B, Snow T P, Barckholtz C & Bierbaum V M 2007 The Astrophysical Journal 667 (2), 1283. Gottlieb C A, Brunken S, McCarthy M C & Thaddeus P 2007 The Journal of Chemical Physics 126 (19), 191101. Guelin M, Agundez M, Cernicharo J, Gottlieb C, McCarthy M & Thaddeus P 2011 in 'IAU Symposium' Vol. 280 p. 21. Gupta H, Gottlieb C A, McCarthy M C & Thaddeus P 2009 The Astrophysical Journal 691 (2), 14941500. Harada N & Herbst E 2008 The Astrophysical Journal 685 (1), 272. Herbst E 2009 in 'Submillimeter Astrophysics and Technology: a Symposium Honoring Thomas G. Phillips' Vol. 417 p. 153. Hlavenka P, Otto R, Trippel S, Mikosch J, Weidemuller M & Wester R 2009 The Journal of Chemical Physics 130 (6), 061105. Kasai Y, Kagi E & Kawaguchi K 2007 The Astrophysical Journal 661 , L61-L64. Kawaguchi K, Fujimori R, Aimi S, Takano S, Okabayashi E Y, Gupta H, Brunken S, Gottlieb C A, McCarthy M C & Thaddeus P 2007 Publications of the Astronomical Society of Japan 59 , L47L50. Larsson M, Geppert W D & Nyman G 2012 Reports on Progress in Physics 75 (6), 066901. Mauron N & Huggins P J 2000 Astronomy & Astrophysics 359 , 707-715. McCarthy M C, Gottlieb C A, Gupta H & Thaddeus P 2006 The Astrophysical Journal 652 (2), L141. McDowell M R C 1961 The Observatory 81 , 240-243. McElroy D, Walsh C, Markwick A J, Cordiner M A, Smith K & Millar T J 2013 Astronomy & Astrophysics 550 , A36. Men'shchikov A B, Balega Y, Blocker T, Osterbart R & Weigelt G 2001 Astronomy & Astrophysics 368 (2), 497-526. Millar T J, Herbst E & Bettens R P A 2000 Monthly Notices of the Royal Astronomical Society 316 (1), 195-203. Millar T J, Walsh C, Cordiner M A, N'ı Chuim'ın R & Herbst E 2007 The Astrophysical Journal Letters 662 (2), L87-L90. Prasad S S & Huntress Jr W T 1980 The Astrophysical Journal Supplement Series 43 , 1-35. Remijan A J, Hollis J M, Lovas F J, Cordiner M A, Millar T J, Markwick-Kemper A J & Jewell P R 2007 The Astrophysical Journal 664 (1), L47-L50. Sakai N, Sakai T, Osamura Y & Yamamoto S 2007 The Astrophysical Journal 667 (1), L65-L68. Sakai N, Sakai T & Yamamoto S 2008 The Astrophysical Journal 673 (1), L71-L74. Sakai N, Shiino T, Hirota T, Sakai T & Yamamoto S 2010 The Astrophysical Journal Letters 718 (2), L49-L52. Schmidt H T, Johansson H A B, Thomas R D, Geppert W D, Haag N, Reinhed P, Ros'en S, Larsson M, Danared H, Rensfelt K G et al. 2008 International Journal of Astrobiology 7 (3-4), 205-208. Smith D, Church M J & Miller T M 1978 The Journal of Chemical Physics 68 , 1224. Thaddeus P, Gottlieb C A, Gupta H, Brunken S, McCarthy M C, Ag'undez M, Gu'elin M & Cernicharo J 2008 The Astrophysical Journal 677 (2), 1132. Yen T A, Garand E, Shreve A T & Neumark D M 2010 The Journal of Physical Chemistry A 114 (9), 3215-3220.","pages":[12,13]}],"string":"[\n {\n \"title\": \"PHOTODETACHMENT AS DESTRUCTION MECHANISM FOR CN -and C 3 N -ANIONS IN CIRCUMSTELLAR ENVELOPES\",\n \"content\": \"S. S. Kumar 1 , D. Hauser 1 , R. Jindra 1 , T. Best 1 , ˇ S. Rouˇcka 2 , W.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"D. Geppert 3 , T. J. Millar 4 , and R. Wester 1\",\n \"content\": \"1 Institut fur Ionenphysik und Angewandte Physik, Universitat Innsbruck, A -6020 Innsbruck, Austria 2 Charles University in Prague, Faculty of Mathematics and Physics, Department of Surface and Plasma Science, 18000 Prague, Czech Republic 3 Department of Physics, AlbaNova, Stockholm University, SE -10691 Stockholm, Sweden 4 Astrophysics Research Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, UK E-mail: roland.wester@uibk.ac.at Abstract. Absolute photodetachment cross sections of two anions of astrophysical importance CN -and C 3 N -were measured to be (1.18 ± (0.03) stat (0.17) sys ) × 10 -17 cm 2 and (1.43 ± (0.14) stat (0.37) sys ) × 10 -17 cm 2 respectively at the ultraviolet wavelength of 266 nm (4.66 eV). These relatively large values of the cross sections imply that photodetachment can play a major role in the destruction mechanisms of these anions particularly in photon-dominated regions. We have therefore carried out model calculations using the newly measured cross sections to investigate the abundance of these molecular anions in the cirumstellar envelope of the carbon-rich star IRC+10216. The model predicts the relative importance of the various mechanisms of formation and destruction of these species in different regions of the envelope. UV photodetachment was found to be the major destruction mechanism for both CN -and C 3 N -anions in those regions of the envelope, where they occur in peak abundance. It was also found that photodetachment plays a crucial role in the degradation of these anions throughout the circumstellar envelope.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1.1. Molecular anions in space: Observation and astrophysical relevance\",\n \"content\": \"The discovery of molecules in the interstellar medium about seven decades ago was particularly intriguing since the chemistry governing the formation of molecules in such hostile regions of space was not familiar. Gradually the number of molecules and their cations found in extraterrestrial space increased and it became clear that we in fact live in a 'molecular Universe' (Larsson et al. 2012). However, after the first molecule was identified in the interstellar medium, it took six decades before a molecular anion could be discovered in such environment. This delay was primarily due to the low abundance of anions in space compared to their neutral counterparts and due to the lack of laboratory measurements of high resolution rotational spectra of the anions that could allow their search in space. The first molecular anion ever observed outside our solar system is C 6 H -(McCarthy et al. 2006), which was detected in the envelope of the carbon-rich star IRC+10216. The identification of this molecular anion was followed by the discovery of several other carbon chain anions, C n H -( n = 4, 8) and C n N -( n = 1, 3, 5) in various regions of space such as dark clouds, circumstellar envelopes, and also in Titan's atmosphere (Cernicharo et al. 2007, Cernicharo et al. 2008, Sakai et al. 2007, Sakai et al. 2008, Sakai et al. 2010, Ag'undez et al. 2008, Ag'undez et al. 2010, Remijan et al. 2007, Brunken et al. 2007, Kasai et al. 2007, Kawaguchi et al. 2007, Thaddeus et al. 2008, Gupta et al. 2009). Of these anions, C 5 N -was only tentatively identified. The role of anions in the synthesis of molecules in the interstellar medium has been investigated by Dalgarno & McCray (1973) many years ago, whereas the formation of molecular hydrogen in stars from H -had been pointed out by McDowell (1961) much earlier. The recent discovery of anions in extraterrestrial environments has initiated a fresh interest towards the understanding of anion chemistry in exotic environments. The importance of gas-phase molecular ions in space has been described in detail in a recent review by Larsson et al. (2012).\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"1.2. Significance of the present work\",\n \"content\": \"Extraterrestrial molecular anions are believed to be produced predominantly via electron capture processes such as dissociative or radiative attachment (Larsson et al. 2012). The destruction processes are largely due to photodetachment, associative detachment and mutual neutralization reactions. In photon-dominated regions, the abundance of molecular anions can be mainly determined by their UV photodetachment. Even in the dark clouds where UV photons cannot penetrate UV photodetachment may still contribute to photodestruction of anions because the secondary electrons produced by cosmic rays can excite the molecules to high Rydberg states, which emit UV radiation upon decay. The study of photodetachment processes is also of particular importance in fundamental physics since the extra electron in an anion is bound to the system by means of strong correlated motion of the electrons in the system and the electron- electron correlation plays the most crucial role in such processes. In addition, no theoretical or experimental values of photodetachment cross sections for CN -or C 3 N -have been reported in the literature despite the fact that there have been a number of studies on these molecular anions (Andersen et al. 2001, Bradforth et al. 1993, Gottlieb et al. 2007, Yen et al. 2010). Since these anions have high electron affinities (CN -: 3.862 ± 0.004 eV (Bradforth et al. 1993), C 3 N -: 4.305 ± 0.001 eV (Yen et al. 2010)) their photodetachment requires photons in the ultraviolet range. In the present work, we measured the photodetachment cross sections of CN -and C 3 N -anions at an energy (4.66 eV) near the photodetachment thresholds. Furthermore, we used the measured values as an input to model calculations to investigate the impact of the new cross sections on the predicted abundance of anions in the circumstellar envelope of IRC+10216.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"2.1. Experimental Setup\",\n \"content\": \"The basic elements of the experimental setup are an ion source, an octupole ion trap, an MCP detector and a laser system. The ion source consists of a piezoelectric pulsed gas valve with a pair of electrodes (referred to as 'plasma electrodes') attached at the exit of the valve. A suitable gas mixture is sent through the gas valve at a certain repetition rate. The ions are generated in a pulsed DC discharge of the gas jet between the plasma electrodes when a high potential difference is applied between them. These ions are then extracted towards the ion trap by a Wiley-McLaren time-of-flight spectrometer oriented perpendicular to the gas jet from the piezo valve. Deflection plates and lenses are used for guiding and focusing the ions into the ion trap. The unique octupole ion trap is made of 100 µ m gold plated molybdenum wires unlike in conventional designs where rods of specific diameter are used as RF electrodes. A short description of this ion trap has been provided by Deiglmayr et al. (2012), where it was used in conjunction with a magneto-optical trap to study reactive collisions of trapped OH -anions with trapped rubidium atoms. A second piezoelectric pulsed gas valve allows for helium buffer gas cooling of the trapped ions. There are two additional electrodes (termed as 'shield plates') above and below the trap that enable us to shape the ion density distribution inside the ion trap. The use of thin wires to construct the trap allows one to probe the trapped ions, for instance with a laser, from the sides. The laser beam can be focused at various positions inside the trap by means of a two-dimensional translation stage with a lens attached to it. This configuration is used to map the ion density distribution inside the trap. In the present experiments, CN -and C 3 N -anions were generated by passing argon gas (at a pressure of about 2-3 bar) over acetonitrile vapor and sending the resulting mixture into the source piezo valve which was operated at 14 Hz. The discharge between the plasma electrodes ionized the gas mixture resulting in the production of several anions including CN -and C 3 N -. The plasma was stabilized by the electrons emitted from a hot filament placed opposite to the pulsed gas valve. The ions were injected into the Wiley-McLaren region, where they were extracted towards the trap with an average kinetic energy of about 240 eV. The desired ionic species can be stored in the ion trap by appropriate timing of the switchable voltages applied on the entrance and exit electrodes of the ion trap in accordance with the time of flight of the various molecular ions. The trap was operated at a radiofrequency of 9 MHz with an amplitude of 180 V on top of a DC voltage of about 240 V. The DC voltage of the trap served to reduce the kinetic energy of the ions coming from the source region to about a few eV. The entrance and exit endcap electrodes of the ion trap were between 10 V and 30 V, the exact value of which did not significantly affect the ion distribution except that the signal strength was slightly modified. The photodetachment measurements were performed with a pulsed laser beam (266 nm, 10 Hz) obtained by frequency quadrupling of the output from a 1064 nm IR laser system with output pulse energy of about 30 mJ and with pulse width of 7 ns. The pulse energy of the laser beam was reduced to a few tens of microjoule and was then sent through a beam splitter. The transmitted beam was used to measure the fluctuations in the laser energy throughout the experiment and these data were used to correct the measured photodetachment cross section. The reflected beam was focused into the trap using the lens attached on the translation stage. The pulse energy of the beam fired into the trap was as low as 25 µ J so as to ensure that there was only single photon absorption and that the wires constituting the trap were not damaged when the laser beam struck them.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"2.2. Measurement procedure\",\n \"content\": \"The measurement procedure was very similar to the one described previously (Trippel et al. 2006, Hlavenka et al. 2009, Best et al. 2011) except that in the present experiments the laser beam was sent into the ion trap perpendicular to its symmetry axis. Briefly, the ions can be stored in the trap for a few hundred seconds (1 /e lifetime, determined from the exponential decay of the ions stored in the trap). In the first part of the experiment, the background decay rate was determined by measuring the amount of ions left in the trap after different storage times. In the second part, the rates of decay were measured with the UV laser pointing at different positions inside the trap. The photodetachment decay rates when plotted as a function of the positions form a tomography image which reflects the ion density distribution inside the trap. The integral of the rate map is proportional to the photodetachment cross section as detailed elsewhere (Trippel et al. 2006, Best et al. 2011). The photodetachment cross section, σ pd , is given by the expression (Trippel et al. 2006, Best et al. 2011): where k pd ( x, y ) is the position dependent decay rate due to photodetachment, k bg is the background decay rate (decay rate measured without laser) and Φ L is the photon flux.\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"2.3. Model Calculations for IRC+10216\",\n \"content\": \"The photodetachment cross sections measured for CN -and C 3 N -anions in the present experiments, together with those obtained previously (Best et al. 2011) for the carbon chain anions C 2 H -, C 4 H -and C 6 H -, were used as input for model calculations of the circumstellar envelope of IRC+10216. The photodetachment cross sections of CN -and C 3 N -were fitted to the expression used in previous model calculations (Millar et al. 2007): in which σ is the cross section, σ ∞ the cross section at infinite photon energy, E A the photodetachment threshold energy and /epsilon1 the photon energy. Since our cross section measurements have been carried out only at a wavelength of 266 nm (at which a sufficiently intense UV beam was available from our laser systems) only two points exist for the fit of the photon energy/cross section curve for each of the nitrile anions, the cross section at threshold energy (where σ = 0) and the one measured at 266 nm. Of course, there exists the possibility of strong resonances, especially at photon energies only slightly above the threshold, which cannot be ruled out in the absence of complementary experimental data on photodetachment cross sections of these anions. For a more accurate treatment of the model, one would require experimental cross sections at higher photon energies necessitating radiation from sources such as synchrotrons or free electron lasers (FELs). Regarding the threshold energy ( E A ) of CN -, the value obtained by Bradforth et al. (1993) who employed a pulsed fixed-frequency negative ion photoelectron spectrometer (3.862 ± 0.004 eV) was used for the fit. In the case of C 3 N -the result from Yen et al. (2010) measured using slow electron velocity-map imaging (4.305 ± 0.001 eV) and field-free time-of-flight was applied. For the photodetachment cross sections of the hydrocarbon anions the fitted values from Best et al. (2011) were used. The chemical models are based on the assumption of a uniform mass-loss rate for the circumstellar envelope of IRC+10216 described by Millar et al. (2000) together with a second model, described by Cordiner & Millar (2009), in which density-enhanced shells are included. With density-enhanced shells of gas and dust, a more realistic modelling of the circumstellar envelope is achieved by introducing a set of density enhancements with the physical parameters of the envelope based on the dust-shell observation by Mauron & Huggins (2000). For modelling, the conditions expected for the well-studied circumstellar envelope of IRC+10216 were applied. Consequently, a spherically symmetric outflow velocity from the central star of 1.45 × 10 6 cm s -1 and a mass loss of 1.5 × 10 -5 solar masses per year were assumed for the envelope (Men'shchikov et al. 2001). The adopted temperature profile is based on a fit to the gas kinetic temperature profile of Crosas & Menten (1997), with a minimum temperature of 10 K fixed in the outer region of the envelope and is the same as used by Cordiner & Millar (2009). The initial chemical abundances of parent molecules relative to that of H 2 used in the model are listed in Table 1. These species are formed in the inner envelope close to the star at high density and temperature and blown outwards in a spherically symmetric outflow (Millar et al. 2000). The calculations begin at an inner radius of 10 15 cm where photons from the external, interstellar radiation field begin to destroy parent species creating reactive radicals and ions and initiating the synthesis of anions and other species. The number density n ( r ) declines with the radius as 1 /r 2 . In the second set of calculations, in addition to the 1 /r 2 dependence of the number density, a series of step-like density enhancements of the form βn ( r ) is introduced. The parameter β is set to 5 for all shells in the model. According to dust shell parameters deduced from scattered light observations by Mauron & Huggins (2000), we assume that each shell has a thickness of 2 arcsec and the spacing between the shells is 12 arcsec. This distance corresponds to roughly 530 years between the peaks of enhanced mass loss (See Cordiner & Millar (2009) for details.).\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"3.1. Experimental results\",\n \"content\": \"The photodetachment cross sections of CN -and C 3 N -are a factor of at least two larger than the cross sections measured for other carbon chain anions C n H -(Best et al. 2011). Hence the abundance of these cyano anions in photon-dominated regions is likely to be significantly influenced by their photodetachment. Furthermore, the cross sections are determined at an energy which is not far away from the photodetachment threshold for both CN -and C 3 N -. Therefore, the large cross section values may indicate the presence of strong resonances.\",\n \"pages\": [\n 8\n ]\n },\n {\n \"title\": \"3.2. Results from model calculations\",\n \"content\": \"The photodetachment rate constants that function as input data for the model calculations were obtained using a standard interstellar radiation field (Draine 1978). The obtained values were 2.55 × 10 -9 , 1.99 × 10 -9 , 1.16 × 10 -9 , 6.72 × 10 -9 and 1.03 × 10 -8 s -1 for C 2 H -, C 4 H -, C 6 H -, CN -and C 3 N -, respectively. In this calculation we have used the entire reaction set and the rate coefficients of the UMIST database for astrochemistry 2012 (McElroy et al. 2013), which includes the additional anion production mechanisms mentioned by Cordiner et al. (2008), to calculate molecular abundances as a function of the radial distance from the centre of the star (See Cordiner & Millar (2009) for details.). In a second set of calculations, shells of matter with densities that are enhanced relative to the surrounding circumstellar medium were included in the model. Figures 2a (no shells) and 2b (with shells) show the fractional abundances of the important anions, as well as the electron fraction, as a function of radius in the circumstellar envelope. When integrated over radius, these abundances yield the total column densities which were compared with those using the cross section function, σ = 1 × 10 -17 √ 1 -E A //epsilon1 cm 2 , employed in previous studies (Millar et al. 2007). The column densities using these two approaches are listed in Table 4. It can be seen that the input of the experimental cross sections somewhat reduces the column densities and thus slightly deteriorates the agreement between the modelled and observed cross sections. Also, the C 3 N -/C 3 N ratio predicted by the model /s32 (1 . 4 × 10 -3 ) now lies below the observed value (5 × 10 -3 ), whereas previous models tended to overestimate it (Herbst 2009, and references therein). The inclusion of highdensity shells does increase the anion column densities by around 10-20%. However, they remain smaller, but within the same order of magnitude, than those observed. The predicted densities not only depend strongly on the rates of photodetachment but also on the efficiency of the formation reactions, such as radiative attachment, radical-ion and dissociative attachment reactions. Regarding the generation of the two cyano anions the model predicts that reactions of N radicals with C -n ions, e.g., dominate as formation pathways in the outer and middle parts of the envelope (r ≥ 10 16 cm) for both CN -and C 3 N -. These processes might be partly responsible for the extraordinarily high anion to neutral abundance ratio for C 3 N -(Cordiner & Millar 2009, Ag'undez et al. 2010, Thaddeus et al. 2008, Cernicharo et al. 2007). In the innermost regions (r ≤ 10 16 cm), formation of CN -proceeds via reaction of H -with HCN: The importance of the latter process is due to the formation of H -through cosmic ray induced ion pair formation in the inner shells of the envelope (Cordiner & /s32 Millar 2009, Prasad & Huntress Jr 1980). At these small radii, radiative attachment of C 3 N and dissociative attachment of HNC 3 are predominant formation routes of C 3 N -: Whereas the reactions of N atoms with C n chain anions have been characterized in a selected ion flow tube experiment (Eichelberger et al. 2007), there are, as yet, no laboratory studies on the formation of the cyanide anion from H -and HCN. There are also uncertainties in the destruction processes. At a distance from the central star of around 6 × 10 16 cm, where the abundance of the CN -and the C 3 N -anions peaks, photodetachment clearly is the most important degradation mechanism of the two anions and accounts for 45 % of the breakdown of C 3 N -and 35 % for CN -. In the case of CN -, other decay processes are mutual neutralization with C + (30 %) and Si + (7 %) as well as associative detachment with H (15 %). Minor loss processes of C 3 N -are mutual neutralization with C + (25 %) and Si + (6 %) and associative detachment with H (11 %). In the outer regions of the cloud (r > 10 17 cm) mutual neutralization with C + actually becomes predominant for both C 3 N -(accounting for 72 % of the loss at a distance of 2 . 5 × 10 17 cm from the star) and CN -(79 % at the same radius). This behavior is most likely due to the increase of C + abundance towards the edge of the cloud (the peak density of this species there is around 5.4 × 10 -2 cm -3 with an abundance ratio C + /H 2 of 2 . 1 × 10 -4 at a radius of 2 . 2 × 10 17 cm), which is caused by photoionization of C through the interstellar radiation field. In the inner regions of the circumstellar envelope (r < 10 16 cm) mutual neutralization with Mg + is predicted to be the main degradation process. This can be explained by the fact that the Mg + number density is fairly constant throughout the envelope (ranging between 2 × 10 -4 cm -3 and 2 × 10 -3 cm -3 ), whereas the C + abundance is as low as 1 . 5 × 10 -6 cm -3 at a radius of 2 × 10 16 cm. Consequently, the abundance ratio of C + to H 2 increases from 1 . 0 × 10 -12 at a radius of 2 . 2 × 10 15 cm to 7 . 8 × 10 -4 at a radius of 7 . 1 × 10 17 cm, whereas the one of Mg + to H 2 spans only 5 orders of magnitude, rising from 2 . 1 × 10 -10 at a radius of 2 . 2 × 10 15 cm to 1 . 0 × 10 -5 at a radius of 7 . 1 × 10 17 cm. But even at the outermost and the innermost distances photodetachment significantly contributes to the destruction of CN -and C 3 N -. The peak abundances of the two cyano anions investigated in this study lie at the radii 6 . 3 × 10 16 cm and 5 . 6 × 10 16 cm for CN -and C 3 N -, respectively, and the maxima of the fractional abundances at 7 . 9 × 10 16 cm for CN -and 7 . 1 × 10 16 cm for C 3 N -. This implies that the CN -peak radius predicted by the model is somewhat larger than the one concluded from observations (2 × 10 16 cm), but slightly lower than the one predicted by model calculations of Ag'undez et al. (2010) (8 × 10 16 cm). From the present data it can be concluded that photodetachment is a very crucial process in the degradation of anions throughout the envelope. However, one has to consider the uncertainties regarding the rate constants of the formation and destruction mechanisms of the two anions. The relative importance of photodetachment depends on the rate constants of the competing processes, namely the mutual neutralization processes of the cyano anions with C + and other metallic ions. Harada & Herbst (2008) estimated the rate constant of the reaction of C 3 N -with C + based on earlier flowing afterglow Langmuir probe measurements (Smith et al. 1978) of other ions to follow the expression: To the best of our knowledge, no experimental data on the reaction rate constants of these processes have so far been obtained. The new DESIREE double storage ring at Stockholm University will amend this shortcoming (Schmidt et al. 2008). In agreement with other model calculations, the abundances of the anions peak at larger radii than the corresponding neutrals (Guelin et al. 2011). The inclusion of shells with enhanced density similar to the model of Cordiner & Millar (2009) increases the column densities of the anions by about 20% and improves the agreement with observed column densities, predominantly through reducing the rates of photodetachment through the increased dust extinction that they provide.\",\n \"pages\": [\n 8,\n 9,\n 10,\n 11\n ]\n },\n {\n \"title\": \"4. Conclusions\",\n \"content\": \"The absolute photodetachment cross sections of two molecular anions of astrophysical importance, CN -and C 3 N -, were measured at the ultraviolet wavelength of 266 nm. The measured cross sections are relatively high and might indicate the possibility of strong resonances near the photodetachment threshold. High cross sections imply that the abundance of these molecular anions can be crucially dependent on their destruction by photodetachment especially in photon-dominated regions. The presented model calculations, carried out to investigate molecular anions in the circumstellar envelope of IRC+10216, predict the relative importance of the various mechanisms of production and destruction of cyano anions in different regions of the envelope. It was found that in regions where these molecular anions have their peak abundance, photodetachment serves as the most important destruction mechanism. The calculations also predict that photodetachment significantly contributes to the destruction of these anions throughout the circumstellar envelope. Thus photodetachment plays a fundamental role in the degradation of anions in circumstellar envelopes. However, its exact significance can only be determined if more data on other competing pathways are available. Future experimental investigations on these processes are therefore vital for our understanding of the anion chemistry of circumstellar envelopes. This work has been supported by the European Research Council under ERC grant agreement No. 279898 and by the ESF COST Action CM0805 'The Chemical Cosmos: Understanding Chemistry in Astronomical Environments'. We thank Eric Endres for his support during the experiments. Research in molecular astrophysics at QUB is supported by a grant from the STFC. ˇ S. R. ackowledges support by Czech Grant Agency under contract No. P209/12/0233.\",\n \"pages\": [\n 11\n ]\n },\n {\n \"title\": \"5. References\",\n \"content\": \"Ag'undez M, Cernicharo J, Gu'elin M, Gerin M, McCarthy M C & Thaddeus P 2008 Astronomy & Astrophysics 478 (1), L19-L22. Ag'undez M, Cernicharo J, Gu'elin M, Kahane C, Roueff E, K/suppresslos J, Aoiz F J, Lique F, Marcelino N, Goicoechea J R, Gonz'alez Garc'ıa M, Gottlieb C A, McCarthy M C & Thaddeus P 2010 Astronomy & Astrophysics 517 , L2. Andersen L H, Bak J, Boye S, Clausen M, Hovgaard M, Jensen M J, Lapierre A & Seiersen K 2001 The Journal of Chemical Physics 115 , 3566. Best T, Otto R, Trippel S, Hlavenka P, von Zastrow A, Eisenbach S, J'ezouin S, Wester R, Vigren E, Hamberg M & Geppert W D 2011 The Astrophysical Journal 742 (2), 63. Bradforth S E, Kim E H, Arnold D W & Neumark D M 1993 The Journal of Chemical Physics 98 (2), 800. Brunken S, Gupta H, Gottlieb C A, McCarthy M C & Thaddeus P 2007 The Astrophysical Journal 664 (1), L43-L46. Cernicharo J, Gu'elin M, Ag'undez M, Kawaguchi K, McCarthy M & Thaddeus P 2007 Astronomy & Astrophysics 467 (2), L37-L40. Cernicharo J, Gu'elin M, Ag'undez M, McCarthy M C & Thaddeus P 2008 The Astrophysical Journal 688 , L83-L86. Cordiner M A & Millar T J 2009 The Astrophysical Journal 697 (1), 68. Cordiner M A, Millar T J, Walsh C, Herbst E, Lis D C, Bell T A & Roueff E 2008 Proceedings of the International Astronomical Union 251 , 157. Crosas M & Menten K M 1997 The Astrophysical Journal 483 (2), 913. Dalgarno A & McCray R A 1973 The Astrophysical Journal 181 , 95-100. Deiglmayr J, Goritz A, Best T, Weidemuller M & Wester R 2012 Physical Review A 86 (4), 043438. Draine B T 1978 The Astrophysical Journal Supplement Series 36 , 595. Eichelberger B, Snow T P, Barckholtz C & Bierbaum V M 2007 The Astrophysical Journal 667 (2), 1283. Gottlieb C A, Brunken S, McCarthy M C & Thaddeus P 2007 The Journal of Chemical Physics 126 (19), 191101. Guelin M, Agundez M, Cernicharo J, Gottlieb C, McCarthy M & Thaddeus P 2011 in 'IAU Symposium' Vol. 280 p. 21. Gupta H, Gottlieb C A, McCarthy M C & Thaddeus P 2009 The Astrophysical Journal 691 (2), 14941500. Harada N & Herbst E 2008 The Astrophysical Journal 685 (1), 272. Herbst E 2009 in 'Submillimeter Astrophysics and Technology: a Symposium Honoring Thomas G. Phillips' Vol. 417 p. 153. Hlavenka P, Otto R, Trippel S, Mikosch J, Weidemuller M & Wester R 2009 The Journal of Chemical Physics 130 (6), 061105. Kasai Y, Kagi E & Kawaguchi K 2007 The Astrophysical Journal 661 , L61-L64. Kawaguchi K, Fujimori R, Aimi S, Takano S, Okabayashi E Y, Gupta H, Brunken S, Gottlieb C A, McCarthy M C & Thaddeus P 2007 Publications of the Astronomical Society of Japan 59 , L47L50. Larsson M, Geppert W D & Nyman G 2012 Reports on Progress in Physics 75 (6), 066901. Mauron N & Huggins P J 2000 Astronomy & Astrophysics 359 , 707-715. McCarthy M C, Gottlieb C A, Gupta H & Thaddeus P 2006 The Astrophysical Journal 652 (2), L141. McDowell M R C 1961 The Observatory 81 , 240-243. McElroy D, Walsh C, Markwick A J, Cordiner M A, Smith K & Millar T J 2013 Astronomy & Astrophysics 550 , A36. Men'shchikov A B, Balega Y, Blocker T, Osterbart R & Weigelt G 2001 Astronomy & Astrophysics 368 (2), 497-526. Millar T J, Herbst E & Bettens R P A 2000 Monthly Notices of the Royal Astronomical Society 316 (1), 195-203. Millar T J, Walsh C, Cordiner M A, N'ı Chuim'ın R & Herbst E 2007 The Astrophysical Journal Letters 662 (2), L87-L90. Prasad S S & Huntress Jr W T 1980 The Astrophysical Journal Supplement Series 43 , 1-35. Remijan A J, Hollis J M, Lovas F J, Cordiner M A, Millar T J, Markwick-Kemper A J & Jewell P R 2007 The Astrophysical Journal 664 (1), L47-L50. Sakai N, Sakai T, Osamura Y & Yamamoto S 2007 The Astrophysical Journal 667 (1), L65-L68. Sakai N, Sakai T & Yamamoto S 2008 The Astrophysical Journal 673 (1), L71-L74. Sakai N, Shiino T, Hirota T, Sakai T & Yamamoto S 2010 The Astrophysical Journal Letters 718 (2), L49-L52. Schmidt H T, Johansson H A B, Thomas R D, Geppert W D, Haag N, Reinhed P, Ros'en S, Larsson M, Danared H, Rensfelt K G et al. 2008 International Journal of Astrobiology 7 (3-4), 205-208. Smith D, Church M J & Miller T M 1978 The Journal of Chemical Physics 68 , 1224. Thaddeus P, Gottlieb C A, Gupta H, Brunken S, McCarthy M C, Ag'undez M, Gu'elin M & Cernicharo J 2008 The Astrophysical Journal 677 (2), 1132. Yen T A, Garand E, Shreve A T & Neumark D M 2010 The Journal of Physical Chemistry A 114 (9), 3215-3220.\",\n \"pages\": [\n 12,\n 13\n ]\n }\n]"}}},{"rowIdx":69,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...776...53B"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1307.8038.pdf"},"content":{"kind":"string","value":"\nMAGNETICALLY CONTROLLED CIRCULATION ON HOT EXTRASOLAR PLANETS\nKonstantin Batygin 1 , Sabine Stanley 2 & David J. Stevenson 3\n1 Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 2 Department of Physics, University of Toronto, 60 St. George St., Toronto, ON and 3\nDivision of Geological and Planetary Sciences, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125\nDraft version September 19, 2018\nABSTRACT\nThrough the process of thermal ionization, intense stellar irradiation renders Hot Jupiter atmospheres electrically conductive. Simultaneously, lateral variability in the irradiation drives the global circulation with peak wind speeds of order ∼ km/s. In turn, the interactions between the atmospheric flows and the background magnetic field give rise to Lorentz forces that can act to perturb the flow away from its purely hydrodynamical counterpart. Using analytical theory and numerical simulations, here we show that significant deviations away from axisymmetric circulation are unstable in presence of a non-negligible axisymmetric magnetic field. Specifically, our results suggest that dayside-to-nightside flows, often obtained within the context of three-dimensional circulation models, only exist on objects with anomalously low magnetic fields, while the majority of highly irradiated exoplanetary atmospheres are entirely dominated by zonal jets.\n1. INTRODUCTION\nThe last decade's discovery and rapid accumulation of the transiting extrasolar planetary aggregate has uncovered a multitude of previously unexplored regimes of various physical phenomena. Perhaps the first unexpected discovery was the existence of Hot Jupiters (i.e. gaseous giant planets that reside within ∼ 0 . 1AU of their host star), which arose from the earliest exoplanetary detections (Mayor & Queloz 1995; Marcy & Butler 1996). Accordingly, among the most intriguing novel theoretical subjects, is the study of atmospheric dynamics on highly irradiated planets.\nToday, it is well known that the orbital region occupied by Hot Jupiters can also be occupied by lower mass (including terrestrial) planets (Batalha et al. 2012). However, because of their higher likelihood of transit and comparative predisposition for characterization, Hot Jupiters remain at the forefront of the study of extrasolar atmospheric circulation (Showman et al. 2011).\n1.1. Hydrodynamic Global Circulation Models\nDynamic meteorology is a phenomenologically rich subject because of the lack of separation of physical scales. In other words, differences in microphysical nature of a given system can have profound effects on its macroscopic state. As a result, it comes as no surprise that circulation patterns on Hot Jupiters generally do not resemble those on Solar System gas giants (Showman et al. 2008; Menou & Rauscher 2009).\nFrom a hydrodynamical point of view, the circulational modes of typical Hot Jupiter atmospheres differ in two principal ways, compared to Solar System gas giants. The first and most obvious difference is the energetics. Unlike the outer Solar System, Hot Jupiters reside in an environment where the incoming stellar irradiation completely dominates over the intrinsic planetary heat-flux. As a result, circulation patterns on Hot Jupiters are driven primarily by the congenital\nkbatygin@cfa.harvard.edu\ndayside-to-nightside temperature differences (Showman & Polvani 2011). Furthermore, concurrent with the cooling of the planetary interior, the top-down heating of the atmosphere ensures the onset of stable stratification in the observable ( P > 100 bars) atmospheric region (Guillot & Showman 2002; Burrows et al. 2007).\nThe second difference lies in the extent to which the atmospheres are rotationally dominated. While Solar System gas giants rotate rapidly (i.e. T Jup glyph[similarequal] T Sat glyph[similarequal] 10 hours), Hot Jupiters are thought to rotate pseudosynchronously with their orbital periods (i.e. T HJ ∼ 3 -5 days) as a result of tidal de-spinning (see Hut (1981)). This implies that although still dynamically significant, rotation alone does not exhibit commanding control over the atmospheric flow.\nSince the discovery of the first transiting extrasolar gas giant HD209458b (Charbonneau et al. 2000; Henry et al. 2000), numerous authors have explored the atmospheric dynamics of Hot Jupiters with a variety of numerical techniques. Because of the inherent differences in the frameworks of the simulations, today, there exists a hierarchical collection of results that correspond to variable degrees of sophistication. On the simpler end of the spectrum are 2D shallow-water simulations (Cho et al. 2008, 2003; Langton & Laughlin 2008, 2007) while the more intricate global circulation models (GCM's) include solvers of the 3D 'primitive' equations (Cooper & Showman 2005; Showman et al. 2008; Menou & Rauscher 2009; Heng et al. 2011) as well as the 3D fully compressible Navier-Stokes equations (Dobbs-Dixon & Lin 2008; Dobbs-Dixon & Agol 2012). Simultaneously, various groups have gone to different lengths in their treatment of radiative transfer, with exploited models ranging from simple prescriptions such as Newtonian cooling (Showman et al. 2008) to double-gray (Rauscher & Menou 2012) and non-gray (Showman et al. 2009) schemes. An important step towards delineating the correspondence among results obtained with different solvers has been recently performed by Heng et al. (2011).\nAlthough there are quantitative differences in the re-\nsults generated by different GCM's, there is general agreement on the qualitative features of the circulation. Specifically, there are three aspects of interest. First, super-rotating zonal jets exist in all simulations. Their number (and naturally, the widths) ranges between 1 and 4, depending on the model (see Showman et al. (2009)), but the relative sparsity of the jets compared to Jupiter and Saturn is understood to be a result of diminished rotation rate (Showman & Guillot 2002). Moreover, in a recent study, Showman & Polvani (2011) showed that the formation of jets is ordained by the interaction of the atmospheric flow with standing Rossby waves that in turn result from the strong difference in the radiative forcing between the planetary dayside and the nightside.\nSecond, the characteristic wind speeds produced by different models are consistent within a factor of a few, and are generally in the ∼ km/s range. This is likely a direct result of the overall similarity in the force-balance setup within the models. Specifically, Showman et al. (2011) argue that near the equator, the horizontal pressuregradient acceleration caused by the asymmetric irradiation is balanced by the advective acceleration. Meanwhile, Coriolis force takes the place of advective acceleration as the primary balancing term in the mid-latitudes. Both force-balances yield ∼ km/s as the characteristic wind speeds, in agreement with the numerical models.\nFinally, in GCMs that resolve the vertical structure of the atmosphere (e.g. Showman et al. (2008); Menou & Rauscher (2009); Heng et al. (2011)) eastward jets consistently dominate the lower atmosphere while the upper atmosphere is characterized by more or less symmetric dayside-to-nightside circulation. In other words, winds originate at the sub-solar point and flow to the anti-solar point over the terminator in the upper atmosphere. The transition between the circulation patterns takes place at P ∼ 0 . 1 -0 . 01 bars and is a consequence of the substantial reduction of the radiative time constant with diminishing pressure (Iro et al. 2005). In particular, because the radiative adjustment timescale is much shorter than the advective timescale in the upper atmosphere, the flow is unable to perturb the temperature structure away from radiative equilibrium significantly. Figure (1) depicts a schematic representation of the characteristic features of atmospheric circulation on Hot Jupiters.\n1.2. Magnetically Dragged Global Circulation Models\nThere exists another important, distinctive feature of Hot Jupiter atmospheres, namely their non-negligible electrical conductivity (see Figure 2). Electrical conductivity in Hot Jupiter atmospheres does not originate from the ionization of H or He, but rather from the stripping of the valence electrons belonging to alkali metals such as K and Na (Batygin & Stevenson 2010; Perna et al. 2010). While these elements are thought to be present in trace abundances (e.g. [K]/[H] ∼ 10 -6 . 5 , [Na]/[H] ∼ 10 -5 . 5 ) (Lodders 1999), temperatures of ∼ 2000K at upper atmospheric pressures, lead to total and partial ionization of K and Na respectively. In fact, at mbar levels, the conductivity can reach values as high as σ ∼ 1 S/m (Batygin et al. 2011; Rauscher & Menou 2012; Heng 2012). Furthermore, it is generally expected that much like solar system gas giants, Hot Jupiters posses interior dynamos, that produce surface fields comparable to, or in slight ex-\n\n\n
Fig. 1.A schematic diagram of the problem considered in this work. A spin-pole aligned dipole magnetic field is thought to arise from a dynamo operating in the deep interior of the planet. As a result of thermal ionization of Alkali metals present in the radiative atmosphere, the interactions between high-velocity flows and the background field lead to non-trivial corrections to the hydrodynamic solution of the global atmospheric circulation. It is likely that the topologically more complex dayside-to-nightside flows in the upper atmosphere ( P ∼ mbar) are more affected by magnetohydrodynamic effects than the zonal flows that reside in the deep atmosphere.
\n\nupiter's field 1 (e.g. B ∼ 3 -30 Gauss) (Stevenson 2003; Christensen et al. 2009). Consequently, there is a distinct possibility that atmospheric circulation on Hot Jupiters may be in part magnetically controlled. That is to say, highly irradiated atmospheres may be sufficiently conductive for the Lorentz force to play an appreciable, if not dominant role in the force-balance.\nRealizing the potential importance of the coupling between the mean flow and the planetary magnetic field, Perna et al. (2010) modeled the Lorentz force as a Rayleigh drag (a velocity-dependent force that opposes the flow) and incorporated it into the GCM previously utilized by Menou & Rauscher (2010). This effort was later amended by Rauscher & Menou (2013), who also modeled the Lorentz force as a Rayleigh drag but selfconsistently accounted for spatial variability in the electrical conductivity (by extension the drag timescale) in the weather layer. The results obtained with dragged GCMs exhibit significant differences in the obtained flow velocities relative to the standard GCMs. Namely, Perna et al. (2010) found a factor of ∼ 3 decrease in the peak wind speeds as the background dipole magnetic field was increased from B dip = 3 G to B dip = 30 G, while Rauscher & Menou (2012) found a similar decline in the jet speeds as the field was increased from B dip = 0 G to B dip = 10 G. The magnetic limitation of the peak wind speeds is of considerable importance as it may prevent the global circulation from approaching a super-sonic state (note that the characteristic sound speed is order c s ∼ √ k B T/µ ∼ 3 km/s, where k B is Boltzmann's con-\n\n1 Although, it is possible that bodies with diminished internal heat fluxes (see e.g. Burrows et al. (2007)) may have comparatively lower fields. Unfortunately at present, strengths and morphologies of exoplanetary magnetic fields remain observationally elusive (Hallinan et al. 2013).\n\n\n\n
Fig. 2.Electrical conductivity at various pressure levels in a typical Hot Jupiter atmosphere. The conductivity arises as a result of thermal ionization of Alkali metals and the curves are computed as done in (Batygin & Stevenson 2010). While the ionization of K dominates at lower temperatures, it saturates at T ∼ 1500K, giving way to Na as the primary additional source of free electrons. Note that the conductivity is only weakly dependent on density.
\n\nstant, T is the temperature, and µ is the mean molecular weight), thereby inhibiting the formation of shocks.\n1.3. The Necessity for Magnetohydrodynamic Circulation Models\nAlthough dragged 3D GCMs clearly highlight the quantitative importance of the magnetic effects in Hot Jupiter atmospheres, they fail to accentuate significant qualitative differences in the obtained flows. Specifically, much like conventional GCMs, magnetically dragged GCMs still show deep-seated zonal jets, overlaid by complex flow patterns that intersect the poles of the planets. This lack of qualitative differences may arise from two distinct possibilities. The first is that beyond diminishing the peak wind speeds, the background magnetic field has little effect on the global circulation. In actuality, this may very well be true for pressure levels where the circulation is dominated by zonal jets, because of the geometrical simplicity of the flow-field interactions. Indeed, the coupling between the zonal flow and the polealigned background dipole field is azimuthally symmetric: differentially rotating jets convert the poloidal field into toroidal field (Liu et al. 2008; Batygin & Stevenson 2010). As will be discussed in detail below, beyond the reduction of velocities, this conversion poses few dynamical ramifications for the jets. Furthermore, owing to higher pressure and somewhat diminished temperatures compared with the upper atmosphere (and the associated decrease in conductivity), the zonal jets may reside in the kinematic regime, where the effects of the Lorentz force are modest (Batygin et al. 2011; Menou 2012).\nThe second possibility is that although in reality the interactions with the background field impel the circulation to strongly deviate from its purely hydrodynamical counterpart, the procedure of modeling the Lorentz force as a Rayleigh drag does not capture the essential features of the dynamics. This is likely true in the upper atmosphere, where azimuthal symmetry is broken and the flow takes on a more topologically complex form. After all, in such a setting there is no requirement for the Lorentz force to simply oppose the flow everywhere, as is done by Rayleigh drag. Thus, there is a distinct possibil-\nity that previous modeling efforts have consistently misrepresented the circulation patterns of the upper atmospheres of Hot Jupiters. Accordingly, the investigation of this possibility is the primary purpose of this work.\nA statistically sound comparison between theoretical models and observations requires the incremental decrease in the goodness of fit to outweigh the cost of introducing new degrees of freedom into the model (see Rodgers (2000) for an in-depth review). Within the context of extrasolar planets, the limitations in observational capabilities and the quality of the data render the construction of highly sophisticated models unjustified (Line et al. 2012). Although a rigorous comparison with observational data is not the focus of this paper, our modeling efforts will lie in the same rudimentary spirit. In other words, here we shall focus on understanding the qualitative, rather than quantitative nature of the circulation. Numerous simplifying assumptions will be made and the representation of the flow (including flow velocities, dayside-to-nightside temperature differences, etc) should only be viewed as approximate. However unlike all previous works on the subject, the model we shall utilize will remain self-consistently magneto-hydrodynamic (MHD). In taking this approach, we hope to successfully capture the essential features of magnetic effects in highly irradiated planetary atmospheres.\nThe paper is organized as follows. In section 2, we describe the equations inherent to our numerical GCM and reproduce the main features of Hot Jupiter atmospheric flows in the purely hydrodynamic regime. In section 3, we discuss the qualitative features of the atmospheric flows, treating the Lorentz force as a hydrodynamic drag. Specifically, we develop an analytical theory for magetically-dragged circulation patterns in the upper atmosphere and test the resulting scaling law against numerical simulations with enhanced viscosity and explore the effects of varying the radiative timescale. In section 4, we introduce a pole-aligned background magnetic field and demonstrate the transition of the upper atmosphere's dayside-to-nightside circulation into a globally zonal state with the onset of the background field. We conclude and discuss our results in section 5.\n2. NUMERICAL GLOBAL CIRCULATION MODEL\nThe Hot Jupiter GCM we have adopted here is a variant of the numerical geodynamo model constructed by Kuang & Bloxham (1999). Since its conception, the model's versatility has been exploited extensively to explain the geodynamo (Kuang & Bloxham 1999; Dumberry & Bloxham 2002), the ancient Martian dyanamo (Stanley et al. 2008), Mercury's thin-shell dyanamo (Stanley et al. 2005; Zuber et al. 2007), Saturn's dynamo (Stanley 2010), as well as dynamos of Uranus & Neptune (Stanley & Bloxham 2004, 2006).\nThe details of the implementation of the model and the utilized numerical methods are throughly described by Kuang & Bloxham (1999). Here, rather than exhaustively restating the particularities of the framework, we limit ourselves to presenting the set of equations under consideration and the underlying assumptions, while referring the interested reader to Kuang & Bloxham (1999) for further information.\n2.1. The Governing Equations\nMomentum. -The circulation model solves the NavierStokes equation for an electrically conductive, Boussinesq fluid\nD v Dt = -2 Ω × v -∇P ¯ ρ + δρ ¯ ρ g + J × B ¯ ρ + ν ∇ 2 v (1)\nin a rotating spherical shell of finite thickness. Here, D/Dt = ∂/∂t + v · ∇ is the material derivative, v is the velocity vector, Ω = (2 π/ T ) ˆz is the rotation vector, P is the modified pressure, ρ is the density, J is the current density and ν is the kinematic viscosity. The bar denotes an average, whereas δ denotes the perturbation away from the background state. The density and temperature are related to the pressure through the ideal gas equation of state 2 :\nP = ρ µ k B T, (2)\nwhere P is the total pressure. The dynamic domain where the equation is solved is confined above a rigidly rotating spherical shell. We denote the inner and outer radii of the atmosphere as r 1 < r 2 respectively.\nContinuity. -The model is formally 3D and the vertical component of the motion enters into the continuity equation:\n∇· v = 0 . (3)\nHowever, the nearly-constant density, incompressible fluid approximation prevents us from self-consistently modeling a radially extensive atmosphere. Indeed, the atmospheric density does not change, except by thermal expansion/contraction 3 :\nδρ ¯ ρ = -δT ¯ T . (4)\nConsequently, we limit the thickness of the atmosphere to a single scale-height in our simulations: r 2 -r 1 = H = k B ¯ T/µg , where g is the acceleration due to gravity. Additionally, we set r 1 = R , the radius of the planet.\nGenerally, because of the above-stated reasons, our model should be viewed as more closely related to the 2D shallow-water GCMs (Cho et al. 2003; Langton & Laughlin 2008) rather than the family of 3D models (Showman et al. 2009; Perna et al. 2010; Rauscher & Menou 2012). However, proper treatment of the of the induction equation (see below) in absence of pre-described symmetry requires the model to remain 3 dimensional.\nEnergy. -The energy equation, that governs the temperature, inherent to the model reads:\nDT Dt = κ ∇ 2 T, (5)\nwhere κ is the coefficient of thermal diffusivity (kept constant throughout the computational domain). Strictly speaking, this equation governs diffusive heat flux and (in direct interpretation) is unsuitable for modeling a medium where energy transport is accomplished mainly\nby radiation. This is because the above equation rests on the approximations of short photon mean free path and the neglect of the temperature-dependence of the opacity (in the context of the Boussinesq treatment employed here, the latter makes sense but the former breaks down at pressure levels corresponding to optical depth of order unity, allowing for only a crude approximation to reality). However, shall it be possible to relate κ to radiative properties of the gas, the above energy equation can still be used to effectively mimic the appropriate heat transport.\nIn a radiatively-dominated atmosphere, the correct energy equation reads (Peixoto & Oort 1992)\nDT Dt = 1 ¯ ρc p ∇· F , (6)\nwhere c p is the specific heat capacity at constant pressure and F is the radiative heat flux. The expression for the radiative heat flux reads (Clayton 1968):\nF = 4 σ sb ¯ T 3 3¯ ρψ ∇ T, (7)\nwhere σ sb is the Stefan-Boltzmann constant and ψ is the opacity. At this point, the relationship between κ and the atmospheric temperature, density, opacity, and heat capacity is obvious. However, before proceeding further, let us recall that to an order of magnitude, the Newtonian cooling timescale τ N is given by the ratio of the atmosphere's excess heat content to its excess radiative flux:\nτ N glyph[similarequal] ¯ ρc p H 4 σ sb ¯ T 3 . (8)\nConsequently, we may express:\nκ = 4 σ sb ¯ T 3 3¯ ρ 2 c P ψ glyph[similarequal] H 2 τ N , (9)\nwhere we have implicitly assumed an infrared optical depth of order unity at the pressure-level of interest. The relationship between κ and τ N is convenient, as it can be related to previous works. In particular, Showman et al. (2008) have calculated τ N using a state of the art radiative transfer model and tabulated the results on a pressure-temperature grid. Here, we utilize their computations as a guide in estimating the thermal diffusivity.\nNote that we could have arrived at the relationship (9) more intuitively by dimensional analysis. Specifically, noting that the radial extent of the atmosphere is much smaller than the lateral extent, the relevant length scale is the vertical scale-height, H . Meanwhile, because the heat transport is primarily radiative, τ N is clearly the relevant timescale. Bearing in mind the units of diffusivities (i.e. m 2 /s), equation (9) naturally emerges as an estimate.\nMagnetic Field. -The evolution of the magnetic field is governed by the induction equation (Moffatt 1978)\n∂ B ∂t = η ∇ 2 B + ∇× ( v × B ) , (10)\nwhere η = 1 /µ 0 σ is the magnetic diffusivity (kept constant throughout the computational domain) and µ 0 is the permeability of free space. Meanwhile, the absence of\nmagnetic monopoles implies a divergence-free magnetic field:\n∇· B = 0 . (11)\nOnce the structure of B is known, the current density (within the MHD approximation) is given by\nJ = 1 µ 0 ∇× B . (12)\nAt this point, the full set of governing differential equations is presented. Paired with a matching set of boundary and initial conditions, the system can be integrated forward in time self-consistently.\nThe equations are solved using a mixed spectral-finite difference algorithm and following Kuang & Bloxham (1999), the spherical harmonic decomposition is taken up to degree glyph[lscript] max = 33 in the latitude m max = 21 in the azimuthal angle. The computational domain is broken up into 64 radial shells. The model is integrated forward in time until equilibration in the thermal, kinetic and magnetic energies is attained.\n2.2. Boundary and Initial Conditions\nThe physical parameters employed in the numerical experiments we report are loosely based on the planet HD209458b (Charbonneau et al. 2000). Aside from being the first extrasolar planet found to transit its host star, it has become a canonical example used in the studies of Hot Jupiter atmospheres (Burrows et al. 2007; Snellen et al. 2010). To this day, (along with HD189733b (Knutson et al. 2009)) it remains the best characterized extrasolar planet. The object has a mass M = 0 . 69 M Jup , a radius R = 1 . 35 R Jup and a rotational (assumed synchronous with orbit) period of T HD209458b = 3 . 5 days.\nMomentum. -Because we are integrating a quasi-2D atmospheric shell, intended to be representative of a single pressure level, we apply impenetrable, stress-free boundary conditions to the velocity field. Thus, flows are free to develop without friction along the boundaries, although at initialization the planet is cast into solid-body rotation meaning v = 0 at t = 0.\nEnergy. -The temperature is initialized at ¯ T = 2000K with δT/ ¯ T = δρ/ ¯ ρ = 0. The atmosphere is kept stablystratified by the imposition of a stable background temperature gradient (set to the adiabatic lapse rate h = g/c p ) similar to the implementation in other Boussinesq dynamo models with stable layers (e.g. Stanley & Mohammadi (2008); Stanley (2010); Christensen & Wicht (2008)). Additionally, an azimuthally variable heat-flux is applied at the outer boundary, r 2 , to account for the variable stellar irradiation (in practice it doesn't matter whether the variable heat flux is applied at the outer or the inner boundaries, since it is the horizontal temperature gradient that controls the flow). The functional form of the heat-flux is chosen to be that of the F ∝ Y 1 1 spherical harmonic, while the amplitude is taken to be a free parameter (see the discussion in the next section).\nMagnetic Field. -Nominally, an electrical conductivity of σ = 1S/m, characteristic of P glyph[similarequal] 1mbar, T glyph[similarequal] 2000K is prescribed to the computational domain. Simultaneously, negligible electrical conductivity is assigned outside the computational domain. That is, σ glyph[similarequal] 0 at r < r 1\nand r > r 2 , meaning all of the current generated by the atmospheric flow is confined to the weather layer. This is in agreement with the approach of Perna et al. (2010); Rauscher & Menou (2013), but in some contrast with the analytical work of Batygin & Stevenson (2010); Batygin et al. (2011), where the current is allowed to penetrate the convective interior of the planet.\nBecause this work is primarily aimed at studying the upper atmosphere, the pressure-level of interest may reside above the atmospheric temperature inversion, characteristic of some Hot Jupiter atmospheres (Burrows et al. 2007; Spiegel et al. 2009). The presence of such an inversion may provide an electrically insulating layer 4 , justifying σ glyph[similarequal] 0 at r < r 1 . The capability of electrical currents to penetrate the upper atmosphere and close in the magnetosphere is determined by the upper atmosphere's temperature structure and the abundance of Alkali metals at P glyph[lessorsimilar] 1 mbar altitudes. Although a clear possibility, the physics of atmosphere-magnetosphere coupling is no-doubt complex and is beyond the scope of the present study. Consequently, we neglect it for the sake of simplicity.\nIn all of our simulations, we initialize J = 0 in the weather layer. However, the weather layer is still permeated by the background magnetic field, B dip , presumed to be generated by dynamo action in the convective interior of the planet. This zero current field reads:\nB dip = ∇× ( k m sin( θ ) r 2 ˆ φ ) , (13)\nwhere k m is a constant that sets the surface field strength i.e. | B dip | = k m / R 3 at the equator. Within the context of the model, the background field is implemented by modifying the governing equations to account for a timeindependent axially-dipolar external field. This occurs specifically in two terms. In the momentum equation (1), the Lorenz force ( J × B ) / ¯ ρ is replaced by J × ( B + B dip ) / ¯ ρ . In the magnetic induction equation (10), the induction term ∇× ( v × B ) is replaced by ∇× ( v × ( B + B dip )). This method is similar to that used by Sarson et al. (1997) and Cebron et al. (2012) to implement external fields.\n2.3. Dimensionless Numbers\nUpon non-dimensionalization of the governing equations (Kuang & Bloxham 1999), we obtain 6 dimensionless numbers that completely describe the system. They are the Ekman number E , the magnetic Rossby number R o , the magnetic Prandtl number q , the magnetic Rayleigh number R th and the aspect ratio χ as well as an additional value, Γ, that parameterizes the incoming stellar flux. In terms of physical parameters, these quantities read:\nE ≡ ν 2Ω R 2 , R o ≡ η 2Ω R 2 , Γ ≡ F κ ¯ ρc p h , q ≡ κ η , R th ≡ gh R 2 2 ¯ T Ω η , χ ≡ H R . (14)\nThe aspect ratio of the atmosphere we consider is\n4 This idea is not new. The models of Batygin & Stevenson (2010) as well as Batygin et al. (2011) used the presence of such a layer to confine the current generated by zonal flows to the lower atmosphere and the interior of the planet.\nχ = 7 × 10 -3 . For numerical stability, the model requires the Ekman number to exceed a critical value (which we adopt in the simulations) of order E crit ∼ 10 -5 . If we consider the molecular viscosity of Hydrogen ν = ¯ na √ 3 k B ¯ T/m H 2 / 2, where ¯ n is the number density and a is the molecular cross-section, we obtain a hopelessly small E ∼ 10 -20 glyph[lessmuch] E crit at mbar pressure. We note that the actual Ekman number is orders of magnitude higher, since on the global planetary scale, small-scale turbulence is a far more relevant source of viscosity than transfer of momentum at the molecular level (Peixoto & Oort 1992). Still, the true value of E is probably much smaller than E crit . x = 619K = 104 m/s\n003\nFor a given electrical conductivity (equivalently diffusivity), R o and R th simply encompass the physical units of the model. Specifically, for σ = 1S/m, R o = 1 . 79 × 10 -6 and R th = 1 . 38 × 10 9 . Meanwhile, all of the information regarding the considered pressure level is provided by q . Taking σ = 1S/m as before, we obtain q glyph[similarequal] 6 , 60 and 600, corresponding to τ N = 10 5 , 10 4 , and 10 3 sec, appropriate for P = 1 , 0 . 1 and 0 . 001 bars respectively. Finally, as already mentioned above, we take Γ to be an adjustable parameter, tuned to obtain the desired temperature gradients. It is important to note that our model differs somewhat from typical dynamo models in a sense that Γ, rather than R th , parameterizes the extent to which the system is driven. 680K m/s\nLet us conclude the description of the numerical model with a brief discussion of its shortcomings as a guide for future work. First and foremost, the limitation of the atmosphere to a single scale-height may be prejudicial, as previous work has shown that including an extended vertical extent of the atmosphere is important to capture circulation features (Heng et al. 2011). Second, while we have kept thermal and magnetic diffusivities uniform throughout the computational domain, it should be understood that in reality these values vary with temperature and pressure. Third, an implicit assumption of an infrared optical depth of order unity is rather crude at ∼ mbar pressure levels and should be lifted in more rigorous treatments of radiative transfer. Finally, as already mentioned above, the artificially enhanced viscosity inherent to our model almost certainly smoothes out smaller-scale flow to an unphysical extent. x = 258K = 442 m/s\n2.4. Hydrodynamical Simulations\nPrior to performing unabridged MHD simulations, it is useful to first compare our model to previously published results. Accordingly, we begin by setting the strength of the background field to B dip = 0. Because the computational domain is initialized with a null current density, no magnetic fields are generated yielding purely hydrodynamic simulations.\nHorizontal slices of the atmosphere (through the center of the computational domain) in the cylindrical projection are shown in Figure (3). The figures are centered on the substellar point and the background color shows the temperature distribution. The arrows denote the circulation vector field. Peak wind speeds as well as the maximal temperature deviations from ¯ T = 2000K are labeled.\nThe typically observed transition from zonal flows to dayside-nightside flows is observed as the pressure is de-\n\n\n\n\n\n\n\n\n
Fig. 3.Hydrodynamical simulations of the global circulation obtained using the numerical global circulation model of Kuang & Bloxham (1999). The arrows depict the currents of the flow and the color map is representative of the temperature structure. The background and initial atmospheric magnetic fields are set to zero, while the variable heat flux used to mimic insolation is tuned such that the maximal deviation of temperature from the background state is δT max = 620K. The three panels of the Figure correspond to different pressure levels: P = 1 mbar (A), P = 0 . 1 bar (B) and P = 1 bar (C). Note that here, we have plotted the latitude, rather than colatitude used throughout the paper on the y-axis.
\n\ncreased sequentially from P = 1 bars (Panel C of Figure 3) to P = 0 . 001 bars (Panel A of Figure 3). However, important differences exist in our results, contrasted against say, the results of Showman et al. (2008). The first important distinction is that in the zonally-dominated parameter regime, rather than developing a single broad\njet, our model shows the development of three counterrotating jets.\nThis is a simple consequence of angular momentum conservation in the computational domain, and is not uncharacteristic of 2D models (Showman et al. 2011). Because of free-slip boundary conditions employed in our model, the atmosphere is not allowed to exchange angular momentum with the interior. As such, because the atmosphere is initialized in solid-body rotation, the development of any prograde jets must be accompanied by the development of retrograde jets. Because the retrograde jets reside at a high latitude θ ret , whereas the prograde jets are essentially equatorial, angular momentum conservation requires them to be faster by a factor of | v ret / v pro | ∼ 1 / cos θ ret , as observed in the simulations. The angular momentum conserving 3D simulations of Heng et al. (2011) exhibit similar behavior, although in their model the counter-rotating jets develop below the prograde ones, and are considerably slower because of the associated density enhancement.\nThe second distinction of interest is the direction of the equatorial jet. While 3D GCMs consistently produce eastward equatorial jets, the equatorial jets in our hydrodynamical simulations are westward. This is not too surprising, as shallow-water and equivalent barotropic models are known to produce both eastward and westward equatorial jets, depending on the details of the simulation setup (Showman et al. 2011; Heng et al. 2011). Consequently, this difference can probably be attributed to the limited vertical extent of our model.\nThe third important difference is the fact that flow velocities are not consistent along the pressure levels. In particular for the same values of δT , zonal flows have ∼ few km/s peak wind speeds, while the dayside-tonightside flows are more than an order of magnitdue slower. This is largely a consequence of difference in the geometry of the circulation and the fact that viscosity enters as a significant member in the force balance for dayside-to-nightside flows. This can be seen by approximating ν ∇ 2 ∼ ν/ L 2 (Holton 1992), where L is a characteristic length scale associated with the curvature of the circulation. For zonal jets, L z ∼ R while for dayside-to-nightside circulation, the return flow is in part radial implying L dn ∼ H . As will be shown in the following section, faster velocities can be attained by either increasing the aspect ratio of the atmosphere or by artificially enhancing the radiative heat flux, as a result of a linear proportionality between peak wind speeds and δT . An additional point of importance is that in typical 3D simulations, dayside-to-nightside circulation is nearly uniform over the terminator with the return flow residing at greater depth, while our results depict a partial return flow over the poles. This is again a consequence of the quasi-2D geometry of our model.\nAlthough these quantitative distinctions are certainly worthy of attention, the typical features of the flow are approximately captured by our simplified model. Consequently, while being mindful of the model's limitation we do not view the quantitative dissimilarities as critical, as they are not central to the argument of the paper. After all, recall that we are primarily concerned with the possibility of a qualitative alteration of the dayside-tonightside flow by magnetic effects.\n3. DRAGGED CIRCULATION IN THE UPPER ATMOSPHERE\nIn the previous section, we performed baseline hydrodynamical simulations of atmospheric circulation at different pressure levels. In the following sections, we will focus primarily on the mbar pressure level, where the flow takes on a dayside-to-nightside character. As discussed above, in our simulations viscosity plays an important role in determining the flow velocities. Conceptually, the situation may be synonymous to simulations of invicid GCMs that parameterize the effect of magnetic coupling as Rayleigh drag (Perna et al. 2010; Rauscher & Menou 2012). In interest of understanding the dependence of the flow velocities on the magnitude of the dayside-tonightside temperature gradient as well as the imposed frictional forces, in this section we shall develop a simple analytical model for dragged upper-atmospheric circulation and confirm it numerically.\n3.1. Analytical Theory\nLet us begin with estimation of characteristic timescales. In order to accomplish this, we first simplify the Lorentz and viscous forces to resemble the functional form of Rayleigh drag. Utilizing Ohm's law, we have 5 :\nJ × B ¯ ρ ∼ σ ( v × B dip ) × B dip ¯ ρ ∼ -( σk 2 m R 6 ¯ ρ ) v = -v τ L ν ∇ 2 v ∼-( 3 ν R 2 ) v = -v τ ν (15)\nThis allows us to rewrite equation (1) in a simpler form:\nD v Dt = -2 Ω × v -∇P ¯ ρ + δρ ¯ ρ g -v τ f , (16)\nwhere τ f = (1 /τ L + 1 /τ ν ) -1 . Taking | B dip | = 1 G, the characteristic timescales are: τ L ∼ 10 3 sec and τ ν ∼ 10 5 sec. Other relevant timescales in the problem is the rotational (Coriolis) timescale τ Ω ∼ 2 π/ Ω ∼ 10 5 sec, radiative timescale τ N ∼ 10 3 sec and the advective timescale τ adv ∼ R /v ∼ 10 5 sec.\nThere exists a clear separation of timescales in the system. As a result, upon including the parameterized Lorentz force into the equations of motion, the inertial and Coriolis terms can be dropped (the viscous term can be dropped as well, although this simplification is unnecessary). The removal of the inertial terms implies a steady-state solution. The removal of the Coriolis term creates a symmetry characterized by an axis that intersects the sub-solar and anti-solar points. Taking advantage of this symmetry, we orient the polar axis of the coordinate system such that it intersects the sub-solar point. Upon doing so, we can specify a null azimuthal velocity and drop all azimuthal derivatives in the equations of motion. In a local cartesian reference frame, this leaves us with horizontal (ˆ y ) and vertical (ˆ z ) momentum equations, where the latter simplifies to the equation of\n5 Although this approximation is often made, it is not necessarily sensible for systems where the magnetic Reynold's number, Re m ≡ v L /η glyph[greatermuch] 1. Adopting v ∼ km/s and L ∼ H , we obtain Re m ∼ 10 3 , placing the magnetic drag approximation on shaky footing. Further, the electric field in Ohm's law can only be neglected when the radial current is negligible.\nhydrostatic balance:\n1 ¯ ρ ∂ P ∂y = -v y τ f 1 ¯ ρ ∂ P ∂z = g δT ¯ T (17)\nFollowing Schneider & Lindzen (1977) and Held & Hou (1980), we shall adopt a Newtonian energy equation with implicit stable stratification (recall that we have set the potential temperature gradient to h = g/c p ):\nξv z ( g c p ) = -δT -δT rad τ N . (18)\nHere, ξ glyph[greaterorequalslant] 1 is a constant that parameterizes lateral heat advection and δT rad is a purely radiative perturbation to the background state, ¯ T . In other words, as the damping of the circulation is strengthened and v → 0, δT → δT rad .\nRetaining the incompressibility condition (3), we introduce a stream-function Ψ, defined through v = ∇× Ψ (Landau & Lifshitz 1959). Taking a partial derivative of the y -momentum equation with respect to z and of the z -momentum equation with respect to y , we obtain\n-1 τ f ∂ 2 Ψ ∂z 2 = g ¯ T ∂ ( δT ) ∂y . (19)\nTaking a derivative of equation (19) with respect to y and switching the order of partial differentiation yields:\n-1 τ f ∂ ∂z ( ∂ 2 Ψ ∂y∂z ) = g ¯ T ∂ 2 ( δT ) ∂y 2 . (20)\nMeanwhile, differentiating the Newtonian cooling equation (18) with respect to z gives:\n( ∂ 2 Ψ ∂y∂z ) = c p gξ ∂ ∂z ( δT -δT rad τ N ) , (21)\nallowing us to eliminate ∂ 2 Ψ /∂y∂z :\n∂ 2 ( δT rad ) ∂z 2 -∂ 2 ( δT ) ∂z 2 = ξ τ f τ N g 2 c p ¯ T ∂ 2 ( δT ) ∂y 2 . (22)\nsimply the square of the Brunt-\nNote that g 2 /c p ¯ T is Vaisala frequency for an isothermal atmosphere.\nEquation (22) admits the trial solutions\nδ T rad = ( δT 0 rad ) cos ( y R ) sin ( πz H ) δ T = ( δT 0 ) cos ( y R ) sin ( πz H ) , (23)\nwhere ( δT 0 rad ) and ( δT 0 ) are constants that represent the maximal deviations in the respective quantities from the background state. Note that ( δT 0 rad ) is a parameter inherent to the model rather than a variable. Upon substitution of the above solutions (23) into equation (22), we obtain a relationship between ( δT 0 ) and ( δT 0 rad ):\n( δT 0 ) = ( δT 0 rad ) [ 1 + ξζ τ f τ N g 2 π 2 c p ¯ T ( H R ) 2 ] -1 . (24)\nIn the above equation, ζ is an empirical factor that has been introduced to account for the approximations inherent to equations (15).\nWith an analytical solution for the temperature perturbation in hand, we substitute equations (23) into equation (19) and integrate twice to obtain:\nΨ = [ gζτ f H 2 ( δT 0 ) π 2 ¯ T R ] sin ( y R ) sin ( πz H ) ˆ x . (25)\nThis solution implies the same functional form for laterally-averaged heat transport in the vertical and horizontal advection terms in the energy equation (6), lending some support for the approximation inherent to equation (18). Once the stream function is obtained, the maximal horizontal and vertical velocities are given by:\nv max y = Ψ 0 π H v max z = Ψ 0 1 R , (26)\nwhere Ψ 0 is the term in square brackets in (25). Note that the above theory automatically implies a quasi-2D flow since v max z /v max y ∼ ( H / R ) glyph[lessmuch] 1 .\n3.2. Numerical Experiments\nWith a simple analytical theory at hand, we performed a series of numerical simulations, varying the radiative and drag timescales in the ranges 10 2 < τ N < 10 3 sec and 10 3 < τ f < 10 5 sec. Although we observed a considerable variability in the wind speeds and dayside-to-nightside temperature differences in our simulations, the nature of the flow was largely the same as that seen in panel A of Figure (3) across the runs. The peak wind speeds obtained in the simulations as functions of τ N and τ f are presented as black dots in Figure (4).\nIn addition to the simulation results, Figure (4) shows v max y given by equation (26) for the same parameters. As can be seen from the figures, the scaling law inherent to equation (25) matches the numerical experiments quite well. Extrapolating towards larger values of τ f , it can be inferred that our simulations would have produced peak wind speeds of order ∼ km/s if not for the numerical requirements of enhanced viscosity. However, it can also be expected that the character of the flow would also change qualitatively with diminishing viscosity, as the force balance shifts away from that implied by equations (15) 6 .\nIt should be kept in mind that the adjustable parameters ξ and ζ were fit to the data. Moreover, the value of ( δT 0 rad ) = 3360K 7 was chosen by running a simulation where viscous forces completely dominated the force balance ensuring v = 0. In other words, the quantitative agreement seen in Figure (4) is a consequence of the fact that the adjustable parameters of the analytical solution have been fit to the numerical data, but the fact that the functional form of the analytical model conforms with numerical experiments suggest that the stream-function (25) captures the main features of dragged upper-atmospheric circulation on Hot Jupiters.\n4. MAGNETICALLY CONTROLLED CIRCULATION\nIn the last section, we examined the extent to which dayside-nightside flow can be damped by imposing a\n\n\n
Fig. 4.Dependence of peak wind speeds on the radiative and drag timescales obtained within the context of dragged hydrodynamical solutions. The black points represent the results of numerical experiments, where enhanced viscosity is used to mimic the effects of the magnetic field, while the curves represent the analytical solution derived from equations (23) and (25). The values ξ = 8630 and ζ = 0 . 16 have been adopted for the analytical solution. Note that the fact that ξ glyph[greatermuch] 1 is simply a consequence of the fact that lateral advection of heat completely dominates over vertical advection of heat as the transport mechanism of importance. That is to say that in the numerical solutions, v z ( ∂T/∂z ) glyph[lessmuch] v y ( ∂T/∂y ) Nominal values of τ f and τ N are adopted in panels A and B respectively.
\n\ndrag. However, both the analytical theory and numerical experiments showed that the qualitative character of the circulation remained largely unchanged. As already mentioned in the introduction, the rough consistency of the flow patterns across a range of characteristic drag timescales is in broad agreement with the results of 'primitive' 3D GCMs (Perna et al. 2010; Rauscher & Menou 2012). In this section, we challenge this assertion with MHD calculations.\n4.1. Theoretical Arguments\nWith the exception of a rather limited number of problems, self-consistent magneto-hydrodynamic solutions can only be attained with the aid of numerical simulations. However, for the system at hand, the qualitative effect of magnetic induction can be understood from simple theoretical considerations. As we already argued, the two characteristic states of Hot Jupiter atmospheric circulation are a zonally-dominated state and a meridionally-dominated state (Showman et al. 2011). Whether or not a given configuration will be significantly affected by the introduction of the magnetic field can be established by analyzing its stability. More specifically, we can work within a purely kinematic (rather than dynamic) framework to understand if the Lorentz force acts to perturb the flow away from its hydrodynamic counterpart or simply damps the circulation.\nZonal Flows. -Although not directly applicable, recent studies of Ohmic dissipation that arises from zonal flows performed by Liu et al. (2008) (within the context of solar system gas giants) and by Batygin & Stevenson (2010) as well as Menou (2012) (within the context of Hot Jupiters) have already produced some results on a related problem. Here we work in the same spirit as these studies and prescribe the following functional form to the zonal flow to approximately represent three jets, such as those shown in panel C of Figure (3):\n˜ v = ˜ v 0 sin(3 θ ) ˆ φ, (27)\nwhere ˜ v 0 is a negative constant, whose magnitude corresponds to the peak wind speed. This prescription triv-\nally satisfies the continuity equation (3), although we note that a more realistic zonal flow should also exhibit differential rotation.\nThe interaction between this flow and the background magnetic field (13) will induce a field B ind in the atmosphere. Because B dip is entirely poloidal, and ˜ v is strictly toroidal, B ind will also be strictly toroidal (Moffatt 1978). As can be readily deduced from equation (10), this means that B ind cannot interact with ˜ v to further induce new field unless ˜ v deviates from a purely zonal flow. As a result, in steady state, the induction equation reads:\n-η ∇ 2 B ind = ∇× (˜ v × B dip ) = -6 k m ˜ v 0 r 4 cos( θ ) sin( θ ) ˆ φ. (28)\nIt is noteworthy that had we chosen to represent a single broad jet (such as that seen in most 3D simulations (Showman et al. 2008; Menou & Rauscher 2010; Rauscher & Menou 2013)) by setting ˜ v ∝ sin( θ ) (in this case ˜ v 0 is positive), equation (28) would have looked the same, with the exception of the coefficient on the RHS, which would have been 2 instead of 6. As a result, it should be kept in mind that the following kinematic solution applies to the case of a single jet as well.\nφ (deg) The angular part of equation (28) is satisfied by the expression\nB ind = A ( r ) cos( θ ) sin( θ ) ˆ φ, (29)\nwhere A ( r ) is a yet undefined function. This form ensures that the meridional component of the induced current vanishes at the poles. Meanwhile, the radial impenetrability of the boundaries requires A ( R ) = A ( R + H ) = 0 as dictated by equation (12). With these boundary conditions, equation (28) can be solved to yield\nA ( r ) = 3 k m ˜ v 0 ( Rr )( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +4 R 4 -R 3 r -R 2 r 2 -R r 3 -r 4 ) / (2 ηr 3 × ( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +5 R 4 )) . (30)\nThe induced field and the associated electrical current are shown in panel A of Figure (5).\nr\n\n\n\nr\n\n\n
Fig. 5.Toroidal magnetic fields induced in the atmospheric shell. Panel A represents the kinematic analytical solution obtained through equations (29) and (30), while panel B depicts a result obtained from a dynamic numerical simulation, also shown in panel C of Figure (6). Green colors correspond to eastward (positive) fields, and the converse is true for blue colors. The contour lines depict the associated electrical currents. The maximal induced field strengths are max(B ind ) = 0 . 64 G and max(B ind ) = 0 . 52 G corresponding to the analytical solution (panel A) and the numerical solution (panel B) respectively. Because the Lorentz force associated with this induced field acts in the same sense as the flow itself, it can only act to accelerate/decelerate the jets but not alter their directions.
\n\nThe Lorentz force that arises from the interactions between B ind and B dip takes the form\nF L = ( ∇× B ind ) × B dip ρµ 0 = ( σk 2 m r 6 ρ ) ˜ v 0 ˆ φ × (3 sin( θ )( -11 R ( H + R )( H +2 R )( H 2 +2 HR +2 R 2 ) + 9 r ( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +5 R 4 ) -r 5 ) + sin(3 θ )( -7 R ( H + R )( H +2 R ) × ( H 2 +2 HR +2 R 2 ) + 5 r ( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +5 R 4 ) + 3 r 5 )) / (8 r × ( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +5 R 4 )) . (31)\nBecause the Lorentz force acts in the same sense as the flow itself (that is, F L × ˜ v = 0), it can only act to accelerate/decelerate the jets but not alter their directions. Indeed, the functional form of F L is that of a Rayleigh drag (equation 15), however the characteristic timescale is non-uniform in latitude and radius i.e.\nτ L = f ( r, θ ). The non-uniformity we derive here should not be confused with the variability in F L that can arise from the spatial dependence of the electrical conductivity (see Rauscher & Menou (2013)).\nIt is noteworthy that the radial dependence of F L can give rise to differential rotation. However, this is not particularly important, since in some similarity with the above discussion, differential rotation will only induce toroidal fields through the ω -effect (Moffatt 1978) and will therefore only change the solution obtained here on a detailed level (i.e. the added dependence of ˜ B on r will subtly modify the function A ( r )). In other words, a differentially rotating zonal flow still results in a purely toroidal induced field.\nFor a sensible comparison with previous works (e.g. (Perna et al. 2010; Menou 2012; Rauscher & Menou 2012)) and the simple theory presented in the previous section, it is instructive to evaluate the maximal magnitude of F L , which corresponds to the upper and lower boundaries of the domain in question 8 i.e. r = R , r = R + H . To leading order in χ , the expression reads:\nmax( F L ) glyph[similarequal] -6 ( σ k 2 m R 6 ρ ) ˜ v 0 χ cos( θ ) 2 sin( θ ) ˆ φ. (32)\nFrom this expression it is clear that F L acts primarily in the mid-latiudes rather than the equator. As a result, the damping of the jets is latitudinally differential, meaning that even if the flow is initially composed of multiple bands (as we consider here), it will approach a single equatorial jet as the conductivity and/or the magnetic field is increased. Furthermore, recall that the functional form of equation (32) is also valid in the case of a single jet. Qualitatively, this seems to imply that the Lorentz force acts to collimate the jet towards the equator. Such an effect is sensible given that the radial component of the field is stronger as one approaches the pole for a simple dipole. However, it should also be kept in mind that a true planetary magnetic field might be more complicated, leading to further lack of triviality in the circulation.\nDayside-to-Nightside Flows. -Let us now consider the more topologically complex interaction between meridional flows and a spin-pole aligned dipole magnetic field. As in section (3.1) we shall work in a coordinate frame where the polar axis intersects the sub-solar point and is directed at the host star. Unlike the case of zonal circulation, this configuration has no exploitable symmetry. Consequently, a simple solution to the steady-state induction equation (28) is difficult, if not impossible, to obtain. We shall therefore make substantial simplifications.\nIn our prescription for the velocity field, we neglect radial flow altogether (thereby violating continuity) and adopt an expression similar to equation (27):\n˜ v = ˜ v 0 sin( θ ) ˆ θ. (33)\nBecause of our choice of coordinate system, equation (13) cannot be used directly. However, keeping in mind\n8 Although the Lorentz force is equal and opposite at r = R and r = R + H , its radial distribution is such that its vertically integrated value acts to oppose the flow on average.\nthat the background dipole field originates in a much deeper region of the planet than the atmosphere, we can write down the magnetic field in a current-free representation (Jackson 1998):\nB dip = -∇ Υ = -∇ ( k m sin( θ ) cos( φ ) r 2 ) . (34)\nAs in Batygin & Stevenson (2010), we assume that the induction term is dominated by the interaction with the background field, rather than the induced field: (˜ v × B ) glyph[similarequal] (˜ v × B dip ). Upon making this simplification and uncurling equation (10), the steady state induction equation reduces to Ohm's law:\nJ = σ (˜ v ×∇ Υ -∇ Φ) , (35)\nwhere ∇ Φ is the electric field.\nBecause the current is necessarily divergence-free, the scalar potential Φ can be obtained from the following equation:\n∇ 2 Φ = ∇· (˜ v ×∇ Υ) = k m ˜ v 0 r 3 sin( θ ) sin( φ ) . (36)\nIt can be easily checked that the angular part of this relationship is satisfied by:\nΦ = A ( r ) sin( θ ) sin( φ ) . (37)\nAs before, confining the current to the atmosphere implies the boundary conditions: k m ˜ v 0 = R 3 A ( R ) = ( R + H ) 3 A ( R + H ). In turn, the radial part of the solution reads:\nA ( r ) = k m ˜ v 0 (( -H ( H 2 +3 HR +3 R 2 )(log( r ) + 2) +log( R )( H 3 +3 H 2 R +3 HR 2 + R 3 +2 r 3 ) -( R 3 +2 r 3 ) log( H + R ))) / (3 H r 2 × ( H 2 +3 HR +3 R 2 )) . (38)\nThe induced current density can now be obtained through Ohm's law.\nThe Lorentz force can be approximated as originating from the interactions between the induced current and the background magnetic field. The resulting expression is quite cumbersome. However, all of the important features of F L can be seen by evaluating it at the center of the dynamic domain. To leading order in χ , the expression takes the form:\nF L | ( r = R + H / 2) glyph[similarequal] ( σk 2 m R 6 ρ ) ˜ v 0 × [ ˆ r cos( θ )(1 -2 sin 2 ( θ ) cos(2 φ ) + cos(2 θ )) / 2 + ˆ θ (sin(3 θ ) -sin( θ )) cos 2 ( φ ) -2 ˆ φ sin( θ ) cos( θ ) sin( φ ) cos( φ ) ] . (39)\nAsimilar evaluation of F L at r = R and r = R + H shows that the ˆ r and ˆ φ components of the force do not change significantly with radius, although the ˆ θ component does.\nIndeed, the Lorentz force that arises from the interactions between the dayside-to-nightside circulation and the background magnetic field does not only oppose the flow. Instead, it acts to introduce both radial and zonal components to the circulation. Importantly, the typical\nmagnitude of the zonal component of F L is commensurate with the meridional component (although of course their spatial dependence is different). As argued in section (3.1), the characteristic timescale associated with the Lorentz force is comparable to the radiative timescale at mbar pressures and is generally shorter than that, corresponding to other relevant forces. This means that the force-balance implied by equations (17) is in essence not relevant to circulation on hot planetary atmospheres.\nIn summary, we conclude that dayside-to-nightside flow is unstable to perturbations arising from the Lorentz force. Consequently, we expect that the upper atmospheric circulation will change qualitatively once a substantial magnetic field is introduced into the system. We now turn our attention to numerical MHD simulations with the aim of testing this presumption and quantifying the dynamical state of magnetized upper atmospheres of Hot Jupters.\n4.2. Magnetohydrodynamic Simulations\nThe hydrodynamic simulation parameters are chosen as described in section (2), corresponding to the P = 1mbar pressure level (i.e. τ L = 10 3 sec.). We start out with the equilibrated hydrodynamic flow shown in panel A of Figure (3) and introduce a weak pole-aligned dipole magnetic field into the system. Upon equilibration, we take the approach of sequentially increasing the magnitude of B dip . At each step, we allow the flow to reach a steady state before increasing the field strength further. We have checked that the flows obtained by successive enhancement of B dip are identical to those obtained by initializing the atmosphere in solid-body rotation with a given value of B dip . Consequently, in agreement with Liu & Showman (2012), we conclude that the obtained flows are insensitive to initial conditions.\nThe panels of Figure (6) show the upper atmospheric circulation for a series of magnetic field strengths. From this series of results, a clear pattern emerges: as the magnitude of B dip is increased, the flow takes on an exclusively zonal character. Specifically, it is clear that the circulation patterns characteristic of | B dip | = 0 . 33 G (panel B) are already markedly different from the | B dip | = 0 . 025 G case (panel A), which clearly resembles the unmagnetized circulation. The flow is in essence entirely azimuthal once the field is increased to | B dip | = 0 . 5 G (panel C). This is in contrast to the non-uniformly dragged simulations of Rauscher & Menou (2013), who find the flow to become less zonally-dominated with enhanced field strength.\nIt is noteworthy that the flow speeds up once it takes on a zonal nature. This is almost certainly due to the fact that viscosity acting on vertical motion more strongly affects the divergent flow, and is therefore not a physically significant result. Increasing the field strength further diminished the flow velocities but did not alter the qualitative nature of the solution, although somewhat higher values of the Ekman number were required to ensure numerical stability.\nAt the expense of a great inflation in the required computational time, we have extended the simulations presented in Figure (6) to higher resolution. Namely, we prolonged the spherical harmonic decomposition up to degree glyph[lscript] max = 34 and m max = 29 while eliminating hyperviscosity from our runs entirely. Aside from a mild\n\n\n\n\n\n\n\n\n
Fig. 6.Magnetohydrodynamical simulations of the global circulation performed using the numerical model of Kuang & Bloxham (1999). The arrows depict the currents of the flow and the color map is representative of the temperature structure. All panels correspond to the same pressure level, namely P = 1 mbar. However, the background magnetic field is gradually increased from panel A to panel C. Clearly, the qualitative character of the flow changes substantially once the field is increased above B glyph[similarequal] 0 . 3 G (Panel B). The fact that the flow transitions to a globally zonal state at a value of background field strength that is considerably smaller than the inferred field surface strengths of Hot Jupiters suggests that dayside-to-nightside flows exist only on planets occupying the cooler end of close-in orbital distribution. For reference, the amplitudes of the axisymmetric component of the induced field corresponding to panels A, B, and C are max(B ind ) = 0 . 075 , 0 . 35, and 0 . 52 G respectively. Note that here, we have plotted the latitude, rather than colatitude used throughout the paper on the y-axis.
\n\n(i.e. few percent) increase in the velocities, the results observed in these simulations were largely unchanged from the nominal simulations. This implies that the presented solutions do not depend sensitively on small-scale flows. In other words, the transition of the atmosphere to a state dominated by zonal jets is a result of interactions between global circulation and the large-scale magnetic field.\nProvided the zonal nature of the flow observed in the magnetized simulation, we can expect that the induced field will be almost entirely toroidal and will approximately be described by equations (29) and (30). As shown in Figure (5), this indeed appears to be the case. The numerically obtained azimuthal component of the field (panel B) is qualitatively similar to its analytically computed counterpart (panel A), although the field lines are concentrated towards the vicinity of the equator in the numerical solution (this is simply a consequence of the fact that the circulation is not exactly given by the expression (27)). The magnitude of the induced field is also in good agreement with the analytical theory. For ˜ v 0 = 440 m/s, and k m / R 3 = 0 . 5 G, equation (29) yields max(B ind ) = 0 . 64 G, where as the numerically computed value is max(B ind ) = 0 . 52 G.\nUnlike the case considered in the previous section (where the Lorentz force is treated as a drag), within the framework of MHD simulations, the relationship between the peak wind speed and the temperature perturbation is not necessarily simple. Consequently, in order to preliminarily explore the sensitivity of our results on irradiation, we performed an additional suite of simulations where the applied heat flux was enhanced by a factor of three, compared to the simulations shown in Figure (6). In these overdriven simulations, we found the peak wind speeds to be a factor of ∼ 2 -2 . 5 higher. However, the characteristic flow patterns closely resembled those, shown in Figure (6) and specifically, the circulation with | B dip | = 0 . 5 G remained dominated by azimuthal jets. Consequently, we conclude that the transition of the circulation to a zonal regime with increasing magnetic field strength is robust within the context of our model.\nIt is interesting to note that the zonal nature of the circulation is ensured at a comparatively low magnetic field strength. If we adopt a scaling based on an Elsasser number of order unity (Stevenson 2003), typical hot Jupiter magnetic fields should exceed that of Jupiter by a factor of a few e.g. | B dip | ∼ 10 G. Moreover, the arguably more physically sensible scaling based on the intrinsic energy flux (Christensen et al. 2009) suggests that typical hot Jupiter fields may be still higher by another factor of ∼ 5. Cumulatively, this places the critical magnetic field needed for the onset of zonal flows a factor of ∼ 10 -100 below the typical field strengths. As a result, it would be surprising if a more sophisticated treatment of the hydrodynamics and radiative transfer proved the critical field strength to be higher than the typical one. Nevertheless, such simulations should no doubt be performed.\n5. DISCUSSION\nIn this paper, we have characterized the nature of atmospheric circulation on Hot Jupiters, in a regime where magnetic effects play an appreciable role. We began by performing baseline Boussinesq hydrodynamical simulations and augmenting them to crudely account for the\nLorentz force by expressing it in the form of a Rayleigh drag. Using a simple analytical theory, we showed that within the framework of such a treatment, the interactions between the circulation and the background magnetic field lead to a well-formulated reduction in wind velocities. However, in agreement with published literature (Perna et al. 2010; Rauscher & Menou 2012) and dragged simulations of our own, we noted that regardless of the background field strength, the functional form of the upper-atmospheric stream function remains characteristic of a flow pattern where wind originates at the substellar point and blows towards the anti-stellar points quasi-symmetrically over the terminator (see also Showman et al. (2008)).\nAlthough simplifying, the assumption that the Lorentz force (even approximately) opposes the flow everywhere, as done by a Rayleigh drag, appears inappropriate for dayside-to-nightside circulation. Consequently, relying on theoretical considerations based on a kinematic treatment of magnetic induction (Moffatt 1978), we showed that if the Lorentz force is not reduced to a form of a drag, dayside-to-nighside flows become unstable in presence of a spin pole aligned magnetic field. On the contrary, the interactions between zonal jets and the background magnetic field do not give rise to meridional or radial flows, thanks to an inherent symmetry. Instead, the jets are stably damped by the background field (Liu et al. 2008; Menou 2012). However, the damping rate generally need not be latitudinally uniform.\nAs demonstrated by magnetohydrodynamical simulations, this has profound implications for upperatmospheric circulation. Specifically, the MHD calculations indicate that once the background magnetic field is stronger than a critical value, the upper atmospheric circulation transitions from a state dominated by daysideto-nightside flows to an azimuthally symmetric pattern dominated by zonal jets. Qualitatively, this transition can be understood as a point where redistribution of heat from the dayside to the nightside by flow patterns that intersect the magnetic poles ceases to be energetically favorable against purely zonal circulation. For the standard case considered here (that is, τ N = 10 3 sec), the critical field strength is approximately B crit glyph[similarequal] 0 . 5 G, considerably less than the typically inferred field strengths of Hot Jupiters (Christensen et al. 2009). However, it should be understood that the critical field strength must unavoidably depend on various system parameters including the radiative timescale and the electrical conductivity. The variability due to the latter may be particularly important since thermal ionization is extremely sensitive to the atmospheric temperature (see Figure 2). The form of this dependence and the extent to which atmospheres within the current observational aggregate are magnetically dominated merits further investigation.\nThe fact that dayside-to-nightside flows tend to simplify to a zonal state in magnetized atmospheres has a number of important implications. As already discussed to some extent in section (3), axisymmetric flows give rise to exclusively toroidal fields (Moffatt 1978). This means that additional atmospheric dynamo generation, that would act to augment a deep seated field, cannot be supported by large-scale circulation. Moreover, because the induced field lacks a strong poloidal component, its observational characterization is at present hopeless.\nConsequently, observational inference of magnetohydrodynamic processes in exoplanetary atmospheres is likely to be limited to indirect methods.\nThis discussion overlooks the possibility of field generation by small-scale turbulence (i.e. the α -effect) in the atmosphere. Indeed such a process may be at play if the turbulent magnetic Reynolds number Re t m ≡ ν/η glyph[greaterorsimilar] 1 -10. For highly turbulent atmospheres, this criterion may indeed be satisfied. Our simulations aimed at determining the viability as well as characterization of field generation by small-scale turbulence in Hot Jupiter atmospheres are currently ongoing and will be reported in a follow-up study.\nIn this work, we briefly hinted at the fact that the damping of zonal jets by dipole magnetic fields is not only non-uniform latitudinally but also radially. The radial dependence of the Lorentz force found here is specific to the boundary conditions imposed on the induced current. However, if we do not choose to confine the current to a single scale-height but allow it to penetrate the convective interior of the planet (as for example envisioned within the context of the Batygin & Stevenson (2010) Ohmic dissipation model), the induced toroidal field is free to occupy a much deeper portion of the planet. In such a case, the resulting Lorentz force may act to produce deep-seated azimuthal flows and give rise to largescale differential rotation within the planet (Goldreich private communication). However, the extent to which such differential rotation can persist is subject to a number of constraints, including the magnitude of interior Ohmic dissipation (Liu et al. 2008).\nIn addition to the various simplifications inherent to our model that are already described throughout the paper, it is further noteworthy that we have restricted the morphology of the background magnetic field to a pole-aligned dipole for simplicity. Within the solar system, a dipolar, axisymmetric magnetic field created by an internal dynamo is possessed only by Saturn (Acuna & Ness 1980; Dougherty et al. 2005). On the contrary, Jupiter and the Earth have dipole-dominated fields that are significantly tilted with respect to their spin-axes, while Neptune and Uranus possess rather unusual nondipolar, non-axisymmetric fields (Stevenson 2003). As a result it is quite likely that even on a qualitative level, the discussion presented in this work is not comprehensive. That is, unlike axisymmetric jets found in this work, one could envision the generation of substantial stationary eddies, yielding longitudinally and latitudinally asymmetric jets in exoplanetary atmospheres, by complex background magnetic fields.\nFurthermore, orbital variations may also be of importance. Specifically, while the assumption of a circular orbit is secure for the majority of hot Jupiters, null eccentricities are certainly not universal to the observational sample (an extreme example is HD80606b (Naef et al. 2001) which has e = 0 . 93). The time-variability of stellar irradiation associated with significant eccentricity produces rather complex circulation patterns even in hydrodynamic regime (Langton & Laughlin 2008; Kataria et al. 2013). However, recalling that electrical conductivity in hot planetary atmospheres arises primarily as a result of thermal ionization, the circulation patterns are likely to be even more complex than those typically envisioned, since magnetic effects in the atmosphere will\nalso be time-dependent.\nWe would like to finish with a few words about observational implications of our results. At present, the resolution and signal to noise of the spectroscopic data aimed at characterizing the temperature structure and chemical composition of exoplanetary atmospheres (Charbonneau et al. 2005; Knutson et al. 2008; Swain et al. 2010) is such that even fits obtained with one-dimensional atmospheric models are susceptible to numerous degeneracies (Madhusudhan & Seager 2009). Consequently, it is unlikely that the qualitative change in the flow structure observed in this work will strongly affect the already-limited interpretation of the information contained within this data, in the near future (Line et al. 2012).\nOn the other hand, theoretical interpretation of observed dayside-to-nightside temperature differences and the associated shifts in the location of the subsolar hot spot (Knutson 2007) rely heavily on a sensible understanding of atmospheric dynamics, which as we have seen requires a more or less self-consistent account of magnetic effects. To this end, the results obtained in this study are of great importance. Indeed, one can expect that the advective transport of heat changes character and weakens with increased electrical conductivity (by extension, the atmospheric temperature) and magnetic field due to the mechanism described above (see also Liu et al. (2008); Perna et al. (2010); Batygin et al. (2011); Menou (2012); Rauscher & Menou (2012)). Thus, a thorough comparison between a substantial sample of model\nresults and data may eventually shed light on the typical atmospheric conductivity structure and field strengths of Hot Jupiters. Such activity would no-doubt further benefit from direct measurements of high-altitude atmospheric wind velocities obtained via ground-based spectroscopy (Snellen et al. 2010). That said, in order for an endeavor of this sort to be meaningful, substantial improvements in theoretical modeling aimed at meliorating the shortcomings outlined above are required, along with a wealth of additional observational data.\nIn conclusion, the above discussion clearly indicates that the degree of complexity of the physical regime in which hot exoplanetary atmospheres reside is indeed very extensive. There is no doubt that much additional work remains. In this work, we have taken an ample step towards a self-consistent characterization of magnetically controlled circulation on Hot Jupiters. As such, this study should serve as a stepping stone for future developments.\nAcknowledgments . We thank Adam Showman, Tami Rogers, Kristen Menou, Peter Goldreich and Greg Laughlin for useful conversations, as well as the anonymous referee for a thorough and insightful report. K.B. acknowledges the generous support from the ITC Prize Postdoctoral Fellowship at the Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics. S.S. acknowledges funding by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Alfred P. Sloan Foundation.\nREFERENCES\n\nAcuna, M. H., & Ness, N. F. 1980, Science, 207, 444 Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2012, arXiv:1202.5852 Batygin, K., & Stevenson, D. J. 2010, ApJ, 714, L238 Batygin, K., Stevenson, D. J., & Bodenheimer, P. 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Using analytical theory and numerical simulations, here we show that significant deviations away from axisymmetric circulation are unstable in presence of a non-negligible axisymmetric magnetic field. Specifically, our results suggest that dayside-to-nightside flows, often obtained within the context of three-dimensional circulation models, only exist on objects with anomalously low magnetic fields, while the majority of highly irradiated exoplanetary atmospheres are entirely dominated by zonal jets.","pages":[1]},{"title":"MAGNETICALLY CONTROLLED CIRCULATION ON HOT EXTRASOLAR PLANETS","content":"Konstantin Batygin 1 , Sabine Stanley 2 & David J. Stevenson 3 1 Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 2 Department of Physics, University of Toronto, 60 St. George St., Toronto, ON and 3 Division of Geological and Planetary Sciences, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125 Draft version September 19, 2018","pages":[1]},{"title":"1. INTRODUCTION","content":"The last decade's discovery and rapid accumulation of the transiting extrasolar planetary aggregate has uncovered a multitude of previously unexplored regimes of various physical phenomena. Perhaps the first unexpected discovery was the existence of Hot Jupiters (i.e. gaseous giant planets that reside within ∼ 0 . 1AU of their host star), which arose from the earliest exoplanetary detections (Mayor & Queloz 1995; Marcy & Butler 1996). Accordingly, among the most intriguing novel theoretical subjects, is the study of atmospheric dynamics on highly irradiated planets. Today, it is well known that the orbital region occupied by Hot Jupiters can also be occupied by lower mass (including terrestrial) planets (Batalha et al. 2012). However, because of their higher likelihood of transit and comparative predisposition for characterization, Hot Jupiters remain at the forefront of the study of extrasolar atmospheric circulation (Showman et al. 2011).","pages":[1]},{"title":"1.1. Hydrodynamic Global Circulation Models","content":"Dynamic meteorology is a phenomenologically rich subject because of the lack of separation of physical scales. In other words, differences in microphysical nature of a given system can have profound effects on its macroscopic state. As a result, it comes as no surprise that circulation patterns on Hot Jupiters generally do not resemble those on Solar System gas giants (Showman et al. 2008; Menou & Rauscher 2009). From a hydrodynamical point of view, the circulational modes of typical Hot Jupiter atmospheres differ in two principal ways, compared to Solar System gas giants. The first and most obvious difference is the energetics. Unlike the outer Solar System, Hot Jupiters reside in an environment where the incoming stellar irradiation completely dominates over the intrinsic planetary heat-flux. As a result, circulation patterns on Hot Jupiters are driven primarily by the congenital kbatygin@cfa.harvard.edu dayside-to-nightside temperature differences (Showman & Polvani 2011). Furthermore, concurrent with the cooling of the planetary interior, the top-down heating of the atmosphere ensures the onset of stable stratification in the observable ( P > 100 bars) atmospheric region (Guillot & Showman 2002; Burrows et al. 2007). The second difference lies in the extent to which the atmospheres are rotationally dominated. While Solar System gas giants rotate rapidly (i.e. T Jup glyph[similarequal] T Sat glyph[similarequal] 10 hours), Hot Jupiters are thought to rotate pseudosynchronously with their orbital periods (i.e. T HJ ∼ 3 -5 days) as a result of tidal de-spinning (see Hut (1981)). This implies that although still dynamically significant, rotation alone does not exhibit commanding control over the atmospheric flow. Since the discovery of the first transiting extrasolar gas giant HD209458b (Charbonneau et al. 2000; Henry et al. 2000), numerous authors have explored the atmospheric dynamics of Hot Jupiters with a variety of numerical techniques. Because of the inherent differences in the frameworks of the simulations, today, there exists a hierarchical collection of results that correspond to variable degrees of sophistication. On the simpler end of the spectrum are 2D shallow-water simulations (Cho et al. 2008, 2003; Langton & Laughlin 2008, 2007) while the more intricate global circulation models (GCM's) include solvers of the 3D 'primitive' equations (Cooper & Showman 2005; Showman et al. 2008; Menou & Rauscher 2009; Heng et al. 2011) as well as the 3D fully compressible Navier-Stokes equations (Dobbs-Dixon & Lin 2008; Dobbs-Dixon & Agol 2012). Simultaneously, various groups have gone to different lengths in their treatment of radiative transfer, with exploited models ranging from simple prescriptions such as Newtonian cooling (Showman et al. 2008) to double-gray (Rauscher & Menou 2012) and non-gray (Showman et al. 2009) schemes. An important step towards delineating the correspondence among results obtained with different solvers has been recently performed by Heng et al. (2011). Although there are quantitative differences in the re- sults generated by different GCM's, there is general agreement on the qualitative features of the circulation. Specifically, there are three aspects of interest. First, super-rotating zonal jets exist in all simulations. Their number (and naturally, the widths) ranges between 1 and 4, depending on the model (see Showman et al. (2009)), but the relative sparsity of the jets compared to Jupiter and Saturn is understood to be a result of diminished rotation rate (Showman & Guillot 2002). Moreover, in a recent study, Showman & Polvani (2011) showed that the formation of jets is ordained by the interaction of the atmospheric flow with standing Rossby waves that in turn result from the strong difference in the radiative forcing between the planetary dayside and the nightside. Second, the characteristic wind speeds produced by different models are consistent within a factor of a few, and are generally in the ∼ km/s range. This is likely a direct result of the overall similarity in the force-balance setup within the models. Specifically, Showman et al. (2011) argue that near the equator, the horizontal pressuregradient acceleration caused by the asymmetric irradiation is balanced by the advective acceleration. Meanwhile, Coriolis force takes the place of advective acceleration as the primary balancing term in the mid-latitudes. Both force-balances yield ∼ km/s as the characteristic wind speeds, in agreement with the numerical models. Finally, in GCMs that resolve the vertical structure of the atmosphere (e.g. Showman et al. (2008); Menou & Rauscher (2009); Heng et al. (2011)) eastward jets consistently dominate the lower atmosphere while the upper atmosphere is characterized by more or less symmetric dayside-to-nightside circulation. In other words, winds originate at the sub-solar point and flow to the anti-solar point over the terminator in the upper atmosphere. The transition between the circulation patterns takes place at P ∼ 0 . 1 -0 . 01 bars and is a consequence of the substantial reduction of the radiative time constant with diminishing pressure (Iro et al. 2005). In particular, because the radiative adjustment timescale is much shorter than the advective timescale in the upper atmosphere, the flow is unable to perturb the temperature structure away from radiative equilibrium significantly. Figure (1) depicts a schematic representation of the characteristic features of atmospheric circulation on Hot Jupiters.","pages":[1,2]},{"title":"1.2. Magnetically Dragged Global Circulation Models","content":"There exists another important, distinctive feature of Hot Jupiter atmospheres, namely their non-negligible electrical conductivity (see Figure 2). Electrical conductivity in Hot Jupiter atmospheres does not originate from the ionization of H or He, but rather from the stripping of the valence electrons belonging to alkali metals such as K and Na (Batygin & Stevenson 2010; Perna et al. 2010). While these elements are thought to be present in trace abundances (e.g. [K]/[H] ∼ 10 -6 . 5 , [Na]/[H] ∼ 10 -5 . 5 ) (Lodders 1999), temperatures of ∼ 2000K at upper atmospheric pressures, lead to total and partial ionization of K and Na respectively. In fact, at mbar levels, the conductivity can reach values as high as σ ∼ 1 S/m (Batygin et al. 2011; Rauscher & Menou 2012; Heng 2012). Furthermore, it is generally expected that much like solar system gas giants, Hot Jupiters posses interior dynamos, that produce surface fields comparable to, or in slight ex- upiter's field 1 (e.g. B ∼ 3 -30 Gauss) (Stevenson 2003; Christensen et al. 2009). Consequently, there is a distinct possibility that atmospheric circulation on Hot Jupiters may be in part magnetically controlled. That is to say, highly irradiated atmospheres may be sufficiently conductive for the Lorentz force to play an appreciable, if not dominant role in the force-balance. Realizing the potential importance of the coupling between the mean flow and the planetary magnetic field, Perna et al. (2010) modeled the Lorentz force as a Rayleigh drag (a velocity-dependent force that opposes the flow) and incorporated it into the GCM previously utilized by Menou & Rauscher (2010). This effort was later amended by Rauscher & Menou (2013), who also modeled the Lorentz force as a Rayleigh drag but selfconsistently accounted for spatial variability in the electrical conductivity (by extension the drag timescale) in the weather layer. The results obtained with dragged GCMs exhibit significant differences in the obtained flow velocities relative to the standard GCMs. Namely, Perna et al. (2010) found a factor of ∼ 3 decrease in the peak wind speeds as the background dipole magnetic field was increased from B dip = 3 G to B dip = 30 G, while Rauscher & Menou (2012) found a similar decline in the jet speeds as the field was increased from B dip = 0 G to B dip = 10 G. The magnetic limitation of the peak wind speeds is of considerable importance as it may prevent the global circulation from approaching a super-sonic state (note that the characteristic sound speed is order c s ∼ √ k B T/µ ∼ 3 km/s, where k B is Boltzmann's con- stant, T is the temperature, and µ is the mean molecular weight), thereby inhibiting the formation of shocks.","pages":[2,3]},{"title":"1.3. The Necessity for Magnetohydrodynamic Circulation Models","content":"Although dragged 3D GCMs clearly highlight the quantitative importance of the magnetic effects in Hot Jupiter atmospheres, they fail to accentuate significant qualitative differences in the obtained flows. Specifically, much like conventional GCMs, magnetically dragged GCMs still show deep-seated zonal jets, overlaid by complex flow patterns that intersect the poles of the planets. This lack of qualitative differences may arise from two distinct possibilities. The first is that beyond diminishing the peak wind speeds, the background magnetic field has little effect on the global circulation. In actuality, this may very well be true for pressure levels where the circulation is dominated by zonal jets, because of the geometrical simplicity of the flow-field interactions. Indeed, the coupling between the zonal flow and the polealigned background dipole field is azimuthally symmetric: differentially rotating jets convert the poloidal field into toroidal field (Liu et al. 2008; Batygin & Stevenson 2010). As will be discussed in detail below, beyond the reduction of velocities, this conversion poses few dynamical ramifications for the jets. Furthermore, owing to higher pressure and somewhat diminished temperatures compared with the upper atmosphere (and the associated decrease in conductivity), the zonal jets may reside in the kinematic regime, where the effects of the Lorentz force are modest (Batygin et al. 2011; Menou 2012). The second possibility is that although in reality the interactions with the background field impel the circulation to strongly deviate from its purely hydrodynamical counterpart, the procedure of modeling the Lorentz force as a Rayleigh drag does not capture the essential features of the dynamics. This is likely true in the upper atmosphere, where azimuthal symmetry is broken and the flow takes on a more topologically complex form. After all, in such a setting there is no requirement for the Lorentz force to simply oppose the flow everywhere, as is done by Rayleigh drag. Thus, there is a distinct possibil- ity that previous modeling efforts have consistently misrepresented the circulation patterns of the upper atmospheres of Hot Jupiters. Accordingly, the investigation of this possibility is the primary purpose of this work. A statistically sound comparison between theoretical models and observations requires the incremental decrease in the goodness of fit to outweigh the cost of introducing new degrees of freedom into the model (see Rodgers (2000) for an in-depth review). Within the context of extrasolar planets, the limitations in observational capabilities and the quality of the data render the construction of highly sophisticated models unjustified (Line et al. 2012). Although a rigorous comparison with observational data is not the focus of this paper, our modeling efforts will lie in the same rudimentary spirit. In other words, here we shall focus on understanding the qualitative, rather than quantitative nature of the circulation. Numerous simplifying assumptions will be made and the representation of the flow (including flow velocities, dayside-to-nightside temperature differences, etc) should only be viewed as approximate. However unlike all previous works on the subject, the model we shall utilize will remain self-consistently magneto-hydrodynamic (MHD). In taking this approach, we hope to successfully capture the essential features of magnetic effects in highly irradiated planetary atmospheres. The paper is organized as follows. In section 2, we describe the equations inherent to our numerical GCM and reproduce the main features of Hot Jupiter atmospheric flows in the purely hydrodynamic regime. In section 3, we discuss the qualitative features of the atmospheric flows, treating the Lorentz force as a hydrodynamic drag. Specifically, we develop an analytical theory for magetically-dragged circulation patterns in the upper atmosphere and test the resulting scaling law against numerical simulations with enhanced viscosity and explore the effects of varying the radiative timescale. In section 4, we introduce a pole-aligned background magnetic field and demonstrate the transition of the upper atmosphere's dayside-to-nightside circulation into a globally zonal state with the onset of the background field. We conclude and discuss our results in section 5.","pages":[3]},{"title":"2. NUMERICAL GLOBAL CIRCULATION MODEL","content":"The Hot Jupiter GCM we have adopted here is a variant of the numerical geodynamo model constructed by Kuang & Bloxham (1999). Since its conception, the model's versatility has been exploited extensively to explain the geodynamo (Kuang & Bloxham 1999; Dumberry & Bloxham 2002), the ancient Martian dyanamo (Stanley et al. 2008), Mercury's thin-shell dyanamo (Stanley et al. 2005; Zuber et al. 2007), Saturn's dynamo (Stanley 2010), as well as dynamos of Uranus & Neptune (Stanley & Bloxham 2004, 2006). The details of the implementation of the model and the utilized numerical methods are throughly described by Kuang & Bloxham (1999). Here, rather than exhaustively restating the particularities of the framework, we limit ourselves to presenting the set of equations under consideration and the underlying assumptions, while referring the interested reader to Kuang & Bloxham (1999) for further information.","pages":[3]},{"title":"2.1. The Governing Equations","content":"Momentum. -The circulation model solves the NavierStokes equation for an electrically conductive, Boussinesq fluid in a rotating spherical shell of finite thickness. Here, D/Dt = ∂/∂t + v · ∇ is the material derivative, v is the velocity vector, Ω = (2 π/ T ) ˆz is the rotation vector, P is the modified pressure, ρ is the density, J is the current density and ν is the kinematic viscosity. The bar denotes an average, whereas δ denotes the perturbation away from the background state. The density and temperature are related to the pressure through the ideal gas equation of state 2 : where P is the total pressure. The dynamic domain where the equation is solved is confined above a rigidly rotating spherical shell. We denote the inner and outer radii of the atmosphere as r 1 < r 2 respectively. Continuity. -The model is formally 3D and the vertical component of the motion enters into the continuity equation: However, the nearly-constant density, incompressible fluid approximation prevents us from self-consistently modeling a radially extensive atmosphere. Indeed, the atmospheric density does not change, except by thermal expansion/contraction 3 : Consequently, we limit the thickness of the atmosphere to a single scale-height in our simulations: r 2 -r 1 = H = k B ¯ T/µg , where g is the acceleration due to gravity. Additionally, we set r 1 = R , the radius of the planet. Generally, because of the above-stated reasons, our model should be viewed as more closely related to the 2D shallow-water GCMs (Cho et al. 2003; Langton & Laughlin 2008) rather than the family of 3D models (Showman et al. 2009; Perna et al. 2010; Rauscher & Menou 2012). However, proper treatment of the of the induction equation (see below) in absence of pre-described symmetry requires the model to remain 3 dimensional. Energy. -The energy equation, that governs the temperature, inherent to the model reads: where κ is the coefficient of thermal diffusivity (kept constant throughout the computational domain). Strictly speaking, this equation governs diffusive heat flux and (in direct interpretation) is unsuitable for modeling a medium where energy transport is accomplished mainly by radiation. This is because the above equation rests on the approximations of short photon mean free path and the neglect of the temperature-dependence of the opacity (in the context of the Boussinesq treatment employed here, the latter makes sense but the former breaks down at pressure levels corresponding to optical depth of order unity, allowing for only a crude approximation to reality). However, shall it be possible to relate κ to radiative properties of the gas, the above energy equation can still be used to effectively mimic the appropriate heat transport. In a radiatively-dominated atmosphere, the correct energy equation reads (Peixoto & Oort 1992) where c p is the specific heat capacity at constant pressure and F is the radiative heat flux. The expression for the radiative heat flux reads (Clayton 1968): where σ sb is the Stefan-Boltzmann constant and ψ is the opacity. At this point, the relationship between κ and the atmospheric temperature, density, opacity, and heat capacity is obvious. However, before proceeding further, let us recall that to an order of magnitude, the Newtonian cooling timescale τ N is given by the ratio of the atmosphere's excess heat content to its excess radiative flux: Consequently, we may express: where we have implicitly assumed an infrared optical depth of order unity at the pressure-level of interest. The relationship between κ and τ N is convenient, as it can be related to previous works. In particular, Showman et al. (2008) have calculated τ N using a state of the art radiative transfer model and tabulated the results on a pressure-temperature grid. Here, we utilize their computations as a guide in estimating the thermal diffusivity. Note that we could have arrived at the relationship (9) more intuitively by dimensional analysis. Specifically, noting that the radial extent of the atmosphere is much smaller than the lateral extent, the relevant length scale is the vertical scale-height, H . Meanwhile, because the heat transport is primarily radiative, τ N is clearly the relevant timescale. Bearing in mind the units of diffusivities (i.e. m 2 /s), equation (9) naturally emerges as an estimate. Magnetic Field. -The evolution of the magnetic field is governed by the induction equation (Moffatt 1978) where η = 1 /µ 0 σ is the magnetic diffusivity (kept constant throughout the computational domain) and µ 0 is the permeability of free space. Meanwhile, the absence of magnetic monopoles implies a divergence-free magnetic field: Once the structure of B is known, the current density (within the MHD approximation) is given by At this point, the full set of governing differential equations is presented. Paired with a matching set of boundary and initial conditions, the system can be integrated forward in time self-consistently. The equations are solved using a mixed spectral-finite difference algorithm and following Kuang & Bloxham (1999), the spherical harmonic decomposition is taken up to degree glyph[lscript] max = 33 in the latitude m max = 21 in the azimuthal angle. The computational domain is broken up into 64 radial shells. The model is integrated forward in time until equilibration in the thermal, kinetic and magnetic energies is attained.","pages":[4,5]},{"title":"2.2. Boundary and Initial Conditions","content":"The physical parameters employed in the numerical experiments we report are loosely based on the planet HD209458b (Charbonneau et al. 2000). Aside from being the first extrasolar planet found to transit its host star, it has become a canonical example used in the studies of Hot Jupiter atmospheres (Burrows et al. 2007; Snellen et al. 2010). To this day, (along with HD189733b (Knutson et al. 2009)) it remains the best characterized extrasolar planet. The object has a mass M = 0 . 69 M Jup , a radius R = 1 . 35 R Jup and a rotational (assumed synchronous with orbit) period of T HD209458b = 3 . 5 days. Momentum. -Because we are integrating a quasi-2D atmospheric shell, intended to be representative of a single pressure level, we apply impenetrable, stress-free boundary conditions to the velocity field. Thus, flows are free to develop without friction along the boundaries, although at initialization the planet is cast into solid-body rotation meaning v = 0 at t = 0. Energy. -The temperature is initialized at ¯ T = 2000K with δT/ ¯ T = δρ/ ¯ ρ = 0. The atmosphere is kept stablystratified by the imposition of a stable background temperature gradient (set to the adiabatic lapse rate h = g/c p ) similar to the implementation in other Boussinesq dynamo models with stable layers (e.g. Stanley & Mohammadi (2008); Stanley (2010); Christensen & Wicht (2008)). Additionally, an azimuthally variable heat-flux is applied at the outer boundary, r 2 , to account for the variable stellar irradiation (in practice it doesn't matter whether the variable heat flux is applied at the outer or the inner boundaries, since it is the horizontal temperature gradient that controls the flow). The functional form of the heat-flux is chosen to be that of the F ∝ Y 1 1 spherical harmonic, while the amplitude is taken to be a free parameter (see the discussion in the next section). Magnetic Field. -Nominally, an electrical conductivity of σ = 1S/m, characteristic of P glyph[similarequal] 1mbar, T glyph[similarequal] 2000K is prescribed to the computational domain. Simultaneously, negligible electrical conductivity is assigned outside the computational domain. That is, σ glyph[similarequal] 0 at r < r 1 and r > r 2 , meaning all of the current generated by the atmospheric flow is confined to the weather layer. This is in agreement with the approach of Perna et al. (2010); Rauscher & Menou (2013), but in some contrast with the analytical work of Batygin & Stevenson (2010); Batygin et al. (2011), where the current is allowed to penetrate the convective interior of the planet. Because this work is primarily aimed at studying the upper atmosphere, the pressure-level of interest may reside above the atmospheric temperature inversion, characteristic of some Hot Jupiter atmospheres (Burrows et al. 2007; Spiegel et al. 2009). The presence of such an inversion may provide an electrically insulating layer 4 , justifying σ glyph[similarequal] 0 at r < r 1 . The capability of electrical currents to penetrate the upper atmosphere and close in the magnetosphere is determined by the upper atmosphere's temperature structure and the abundance of Alkali metals at P glyph[lessorsimilar] 1 mbar altitudes. Although a clear possibility, the physics of atmosphere-magnetosphere coupling is no-doubt complex and is beyond the scope of the present study. Consequently, we neglect it for the sake of simplicity. In all of our simulations, we initialize J = 0 in the weather layer. However, the weather layer is still permeated by the background magnetic field, B dip , presumed to be generated by dynamo action in the convective interior of the planet. This zero current field reads: where k m is a constant that sets the surface field strength i.e. | B dip | = k m / R 3 at the equator. Within the context of the model, the background field is implemented by modifying the governing equations to account for a timeindependent axially-dipolar external field. This occurs specifically in two terms. In the momentum equation (1), the Lorenz force ( J × B ) / ¯ ρ is replaced by J × ( B + B dip ) / ¯ ρ . In the magnetic induction equation (10), the induction term ∇× ( v × B ) is replaced by ∇× ( v × ( B + B dip )). This method is similar to that used by Sarson et al. (1997) and Cebron et al. (2012) to implement external fields.","pages":[5]},{"title":"2.3. Dimensionless Numbers","content":"Upon non-dimensionalization of the governing equations (Kuang & Bloxham 1999), we obtain 6 dimensionless numbers that completely describe the system. They are the Ekman number E , the magnetic Rossby number R o , the magnetic Prandtl number q , the magnetic Rayleigh number R th and the aspect ratio χ as well as an additional value, Γ, that parameterizes the incoming stellar flux. In terms of physical parameters, these quantities read: The aspect ratio of the atmosphere we consider is 4 This idea is not new. The models of Batygin & Stevenson (2010) as well as Batygin et al. (2011) used the presence of such a layer to confine the current generated by zonal flows to the lower atmosphere and the interior of the planet. χ = 7 × 10 -3 . For numerical stability, the model requires the Ekman number to exceed a critical value (which we adopt in the simulations) of order E crit ∼ 10 -5 . If we consider the molecular viscosity of Hydrogen ν = ¯ na √ 3 k B ¯ T/m H 2 / 2, where ¯ n is the number density and a is the molecular cross-section, we obtain a hopelessly small E ∼ 10 -20 glyph[lessmuch] E crit at mbar pressure. We note that the actual Ekman number is orders of magnitude higher, since on the global planetary scale, small-scale turbulence is a far more relevant source of viscosity than transfer of momentum at the molecular level (Peixoto & Oort 1992). Still, the true value of E is probably much smaller than E crit . x = 619K = 104 m/s 003 For a given electrical conductivity (equivalently diffusivity), R o and R th simply encompass the physical units of the model. Specifically, for σ = 1S/m, R o = 1 . 79 × 10 -6 and R th = 1 . 38 × 10 9 . Meanwhile, all of the information regarding the considered pressure level is provided by q . Taking σ = 1S/m as before, we obtain q glyph[similarequal] 6 , 60 and 600, corresponding to τ N = 10 5 , 10 4 , and 10 3 sec, appropriate for P = 1 , 0 . 1 and 0 . 001 bars respectively. Finally, as already mentioned above, we take Γ to be an adjustable parameter, tuned to obtain the desired temperature gradients. It is important to note that our model differs somewhat from typical dynamo models in a sense that Γ, rather than R th , parameterizes the extent to which the system is driven. 680K m/s Let us conclude the description of the numerical model with a brief discussion of its shortcomings as a guide for future work. First and foremost, the limitation of the atmosphere to a single scale-height may be prejudicial, as previous work has shown that including an extended vertical extent of the atmosphere is important to capture circulation features (Heng et al. 2011). Second, while we have kept thermal and magnetic diffusivities uniform throughout the computational domain, it should be understood that in reality these values vary with temperature and pressure. Third, an implicit assumption of an infrared optical depth of order unity is rather crude at ∼ mbar pressure levels and should be lifted in more rigorous treatments of radiative transfer. Finally, as already mentioned above, the artificially enhanced viscosity inherent to our model almost certainly smoothes out smaller-scale flow to an unphysical extent. x = 258K = 442 m/s","pages":[5,6]},{"title":"2.4. Hydrodynamical Simulations","content":"Prior to performing unabridged MHD simulations, it is useful to first compare our model to previously published results. Accordingly, we begin by setting the strength of the background field to B dip = 0. Because the computational domain is initialized with a null current density, no magnetic fields are generated yielding purely hydrodynamic simulations. Horizontal slices of the atmosphere (through the center of the computational domain) in the cylindrical projection are shown in Figure (3). The figures are centered on the substellar point and the background color shows the temperature distribution. The arrows denote the circulation vector field. Peak wind speeds as well as the maximal temperature deviations from ¯ T = 2000K are labeled. The typically observed transition from zonal flows to dayside-nightside flows is observed as the pressure is de- creased sequentially from P = 1 bars (Panel C of Figure 3) to P = 0 . 001 bars (Panel A of Figure 3). However, important differences exist in our results, contrasted against say, the results of Showman et al. (2008). The first important distinction is that in the zonally-dominated parameter regime, rather than developing a single broad jet, our model shows the development of three counterrotating jets. This is a simple consequence of angular momentum conservation in the computational domain, and is not uncharacteristic of 2D models (Showman et al. 2011). Because of free-slip boundary conditions employed in our model, the atmosphere is not allowed to exchange angular momentum with the interior. As such, because the atmosphere is initialized in solid-body rotation, the development of any prograde jets must be accompanied by the development of retrograde jets. Because the retrograde jets reside at a high latitude θ ret , whereas the prograde jets are essentially equatorial, angular momentum conservation requires them to be faster by a factor of | v ret / v pro | ∼ 1 / cos θ ret , as observed in the simulations. The angular momentum conserving 3D simulations of Heng et al. (2011) exhibit similar behavior, although in their model the counter-rotating jets develop below the prograde ones, and are considerably slower because of the associated density enhancement. The second distinction of interest is the direction of the equatorial jet. While 3D GCMs consistently produce eastward equatorial jets, the equatorial jets in our hydrodynamical simulations are westward. This is not too surprising, as shallow-water and equivalent barotropic models are known to produce both eastward and westward equatorial jets, depending on the details of the simulation setup (Showman et al. 2011; Heng et al. 2011). Consequently, this difference can probably be attributed to the limited vertical extent of our model. The third important difference is the fact that flow velocities are not consistent along the pressure levels. In particular for the same values of δT , zonal flows have ∼ few km/s peak wind speeds, while the dayside-tonightside flows are more than an order of magnitdue slower. This is largely a consequence of difference in the geometry of the circulation and the fact that viscosity enters as a significant member in the force balance for dayside-to-nightside flows. This can be seen by approximating ν ∇ 2 ∼ ν/ L 2 (Holton 1992), where L is a characteristic length scale associated with the curvature of the circulation. For zonal jets, L z ∼ R while for dayside-to-nightside circulation, the return flow is in part radial implying L dn ∼ H . As will be shown in the following section, faster velocities can be attained by either increasing the aspect ratio of the atmosphere or by artificially enhancing the radiative heat flux, as a result of a linear proportionality between peak wind speeds and δT . An additional point of importance is that in typical 3D simulations, dayside-to-nightside circulation is nearly uniform over the terminator with the return flow residing at greater depth, while our results depict a partial return flow over the poles. This is again a consequence of the quasi-2D geometry of our model. Although these quantitative distinctions are certainly worthy of attention, the typical features of the flow are approximately captured by our simplified model. Consequently, while being mindful of the model's limitation we do not view the quantitative dissimilarities as critical, as they are not central to the argument of the paper. After all, recall that we are primarily concerned with the possibility of a qualitative alteration of the dayside-tonightside flow by magnetic effects.","pages":[6,7]},{"title":"3. DRAGGED CIRCULATION IN THE UPPER ATMOSPHERE","content":"In the previous section, we performed baseline hydrodynamical simulations of atmospheric circulation at different pressure levels. In the following sections, we will focus primarily on the mbar pressure level, where the flow takes on a dayside-to-nightside character. As discussed above, in our simulations viscosity plays an important role in determining the flow velocities. Conceptually, the situation may be synonymous to simulations of invicid GCMs that parameterize the effect of magnetic coupling as Rayleigh drag (Perna et al. 2010; Rauscher & Menou 2012). In interest of understanding the dependence of the flow velocities on the magnitude of the dayside-tonightside temperature gradient as well as the imposed frictional forces, in this section we shall develop a simple analytical model for dragged upper-atmospheric circulation and confirm it numerically.","pages":[7]},{"title":"3.1. Analytical Theory","content":"Let us begin with estimation of characteristic timescales. In order to accomplish this, we first simplify the Lorentz and viscous forces to resemble the functional form of Rayleigh drag. Utilizing Ohm's law, we have 5 : This allows us to rewrite equation (1) in a simpler form: where τ f = (1 /τ L + 1 /τ ν ) -1 . Taking | B dip | = 1 G, the characteristic timescales are: τ L ∼ 10 3 sec and τ ν ∼ 10 5 sec. Other relevant timescales in the problem is the rotational (Coriolis) timescale τ Ω ∼ 2 π/ Ω ∼ 10 5 sec, radiative timescale τ N ∼ 10 3 sec and the advective timescale τ adv ∼ R /v ∼ 10 5 sec. There exists a clear separation of timescales in the system. As a result, upon including the parameterized Lorentz force into the equations of motion, the inertial and Coriolis terms can be dropped (the viscous term can be dropped as well, although this simplification is unnecessary). The removal of the inertial terms implies a steady-state solution. The removal of the Coriolis term creates a symmetry characterized by an axis that intersects the sub-solar and anti-solar points. Taking advantage of this symmetry, we orient the polar axis of the coordinate system such that it intersects the sub-solar point. Upon doing so, we can specify a null azimuthal velocity and drop all azimuthal derivatives in the equations of motion. In a local cartesian reference frame, this leaves us with horizontal (ˆ y ) and vertical (ˆ z ) momentum equations, where the latter simplifies to the equation of 5 Although this approximation is often made, it is not necessarily sensible for systems where the magnetic Reynold's number, Re m ≡ v L /η glyph[greatermuch] 1. Adopting v ∼ km/s and L ∼ H , we obtain Re m ∼ 10 3 , placing the magnetic drag approximation on shaky footing. Further, the electric field in Ohm's law can only be neglected when the radial current is negligible. hydrostatic balance: Following Schneider & Lindzen (1977) and Held & Hou (1980), we shall adopt a Newtonian energy equation with implicit stable stratification (recall that we have set the potential temperature gradient to h = g/c p ): Here, ξ glyph[greaterorequalslant] 1 is a constant that parameterizes lateral heat advection and δT rad is a purely radiative perturbation to the background state, ¯ T . In other words, as the damping of the circulation is strengthened and v → 0, δT → δT rad . Retaining the incompressibility condition (3), we introduce a stream-function Ψ, defined through v = ∇× Ψ (Landau & Lifshitz 1959). Taking a partial derivative of the y -momentum equation with respect to z and of the z -momentum equation with respect to y , we obtain Taking a derivative of equation (19) with respect to y and switching the order of partial differentiation yields: Meanwhile, differentiating the Newtonian cooling equation (18) with respect to z gives: allowing us to eliminate ∂ 2 Ψ /∂y∂z : simply the square of the Brunt- Note that g 2 /c p ¯ T is Vaisala frequency for an isothermal atmosphere. Equation (22) admits the trial solutions where ( δT 0 rad ) and ( δT 0 ) are constants that represent the maximal deviations in the respective quantities from the background state. Note that ( δT 0 rad ) is a parameter inherent to the model rather than a variable. Upon substitution of the above solutions (23) into equation (22), we obtain a relationship between ( δT 0 ) and ( δT 0 rad ): In the above equation, ζ is an empirical factor that has been introduced to account for the approximations inherent to equations (15). With an analytical solution for the temperature perturbation in hand, we substitute equations (23) into equation (19) and integrate twice to obtain: This solution implies the same functional form for laterally-averaged heat transport in the vertical and horizontal advection terms in the energy equation (6), lending some support for the approximation inherent to equation (18). Once the stream function is obtained, the maximal horizontal and vertical velocities are given by: where Ψ 0 is the term in square brackets in (25). Note that the above theory automatically implies a quasi-2D flow since v max z /v max y ∼ ( H / R ) glyph[lessmuch] 1 .","pages":[7,8]},{"title":"3.2. Numerical Experiments","content":"With a simple analytical theory at hand, we performed a series of numerical simulations, varying the radiative and drag timescales in the ranges 10 2 < τ N < 10 3 sec and 10 3 < τ f < 10 5 sec. Although we observed a considerable variability in the wind speeds and dayside-to-nightside temperature differences in our simulations, the nature of the flow was largely the same as that seen in panel A of Figure (3) across the runs. The peak wind speeds obtained in the simulations as functions of τ N and τ f are presented as black dots in Figure (4). In addition to the simulation results, Figure (4) shows v max y given by equation (26) for the same parameters. As can be seen from the figures, the scaling law inherent to equation (25) matches the numerical experiments quite well. Extrapolating towards larger values of τ f , it can be inferred that our simulations would have produced peak wind speeds of order ∼ km/s if not for the numerical requirements of enhanced viscosity. However, it can also be expected that the character of the flow would also change qualitatively with diminishing viscosity, as the force balance shifts away from that implied by equations (15) 6 . It should be kept in mind that the adjustable parameters ξ and ζ were fit to the data. Moreover, the value of ( δT 0 rad ) = 3360K 7 was chosen by running a simulation where viscous forces completely dominated the force balance ensuring v = 0. In other words, the quantitative agreement seen in Figure (4) is a consequence of the fact that the adjustable parameters of the analytical solution have been fit to the numerical data, but the fact that the functional form of the analytical model conforms with numerical experiments suggest that the stream-function (25) captures the main features of dragged upper-atmospheric circulation on Hot Jupiters.","pages":[8]},{"title":"4. MAGNETICALLY CONTROLLED CIRCULATION","content":"In the last section, we examined the extent to which dayside-nightside flow can be damped by imposing a drag. However, both the analytical theory and numerical experiments showed that the qualitative character of the circulation remained largely unchanged. As already mentioned in the introduction, the rough consistency of the flow patterns across a range of characteristic drag timescales is in broad agreement with the results of 'primitive' 3D GCMs (Perna et al. 2010; Rauscher & Menou 2012). In this section, we challenge this assertion with MHD calculations.","pages":[8,9]},{"title":"4.1. Theoretical Arguments","content":"With the exception of a rather limited number of problems, self-consistent magneto-hydrodynamic solutions can only be attained with the aid of numerical simulations. However, for the system at hand, the qualitative effect of magnetic induction can be understood from simple theoretical considerations. As we already argued, the two characteristic states of Hot Jupiter atmospheric circulation are a zonally-dominated state and a meridionally-dominated state (Showman et al. 2011). Whether or not a given configuration will be significantly affected by the introduction of the magnetic field can be established by analyzing its stability. More specifically, we can work within a purely kinematic (rather than dynamic) framework to understand if the Lorentz force acts to perturb the flow away from its hydrodynamic counterpart or simply damps the circulation. Zonal Flows. -Although not directly applicable, recent studies of Ohmic dissipation that arises from zonal flows performed by Liu et al. (2008) (within the context of solar system gas giants) and by Batygin & Stevenson (2010) as well as Menou (2012) (within the context of Hot Jupiters) have already produced some results on a related problem. Here we work in the same spirit as these studies and prescribe the following functional form to the zonal flow to approximately represent three jets, such as those shown in panel C of Figure (3): where ˜ v 0 is a negative constant, whose magnitude corresponds to the peak wind speed. This prescription triv- ally satisfies the continuity equation (3), although we note that a more realistic zonal flow should also exhibit differential rotation. The interaction between this flow and the background magnetic field (13) will induce a field B ind in the atmosphere. Because B dip is entirely poloidal, and ˜ v is strictly toroidal, B ind will also be strictly toroidal (Moffatt 1978). As can be readily deduced from equation (10), this means that B ind cannot interact with ˜ v to further induce new field unless ˜ v deviates from a purely zonal flow. As a result, in steady state, the induction equation reads: It is noteworthy that had we chosen to represent a single broad jet (such as that seen in most 3D simulations (Showman et al. 2008; Menou & Rauscher 2010; Rauscher & Menou 2013)) by setting ˜ v ∝ sin( θ ) (in this case ˜ v 0 is positive), equation (28) would have looked the same, with the exception of the coefficient on the RHS, which would have been 2 instead of 6. As a result, it should be kept in mind that the following kinematic solution applies to the case of a single jet as well. φ (deg) The angular part of equation (28) is satisfied by the expression where A ( r ) is a yet undefined function. This form ensures that the meridional component of the induced current vanishes at the poles. Meanwhile, the radial impenetrability of the boundaries requires A ( R ) = A ( R + H ) = 0 as dictated by equation (12). With these boundary conditions, equation (28) can be solved to yield The induced field and the associated electrical current are shown in panel A of Figure (5). r r The Lorentz force that arises from the interactions between B ind and B dip takes the form Because the Lorentz force acts in the same sense as the flow itself (that is, F L × ˜ v = 0), it can only act to accelerate/decelerate the jets but not alter their directions. Indeed, the functional form of F L is that of a Rayleigh drag (equation 15), however the characteristic timescale is non-uniform in latitude and radius i.e. τ L = f ( r, θ ). The non-uniformity we derive here should not be confused with the variability in F L that can arise from the spatial dependence of the electrical conductivity (see Rauscher & Menou (2013)). It is noteworthy that the radial dependence of F L can give rise to differential rotation. However, this is not particularly important, since in some similarity with the above discussion, differential rotation will only induce toroidal fields through the ω -effect (Moffatt 1978) and will therefore only change the solution obtained here on a detailed level (i.e. the added dependence of ˜ B on r will subtly modify the function A ( r )). In other words, a differentially rotating zonal flow still results in a purely toroidal induced field. For a sensible comparison with previous works (e.g. (Perna et al. 2010; Menou 2012; Rauscher & Menou 2012)) and the simple theory presented in the previous section, it is instructive to evaluate the maximal magnitude of F L , which corresponds to the upper and lower boundaries of the domain in question 8 i.e. r = R , r = R + H . To leading order in χ , the expression reads: From this expression it is clear that F L acts primarily in the mid-latiudes rather than the equator. As a result, the damping of the jets is latitudinally differential, meaning that even if the flow is initially composed of multiple bands (as we consider here), it will approach a single equatorial jet as the conductivity and/or the magnetic field is increased. Furthermore, recall that the functional form of equation (32) is also valid in the case of a single jet. Qualitatively, this seems to imply that the Lorentz force acts to collimate the jet towards the equator. Such an effect is sensible given that the radial component of the field is stronger as one approaches the pole for a simple dipole. However, it should also be kept in mind that a true planetary magnetic field might be more complicated, leading to further lack of triviality in the circulation. Dayside-to-Nightside Flows. -Let us now consider the more topologically complex interaction between meridional flows and a spin-pole aligned dipole magnetic field. As in section (3.1) we shall work in a coordinate frame where the polar axis intersects the sub-solar point and is directed at the host star. Unlike the case of zonal circulation, this configuration has no exploitable symmetry. Consequently, a simple solution to the steady-state induction equation (28) is difficult, if not impossible, to obtain. We shall therefore make substantial simplifications. In our prescription for the velocity field, we neglect radial flow altogether (thereby violating continuity) and adopt an expression similar to equation (27): Because of our choice of coordinate system, equation (13) cannot be used directly. However, keeping in mind 8 Although the Lorentz force is equal and opposite at r = R and r = R + H , its radial distribution is such that its vertically integrated value acts to oppose the flow on average. that the background dipole field originates in a much deeper region of the planet than the atmosphere, we can write down the magnetic field in a current-free representation (Jackson 1998): As in Batygin & Stevenson (2010), we assume that the induction term is dominated by the interaction with the background field, rather than the induced field: (˜ v × B ) glyph[similarequal] (˜ v × B dip ). Upon making this simplification and uncurling equation (10), the steady state induction equation reduces to Ohm's law: where ∇ Φ is the electric field. Because the current is necessarily divergence-free, the scalar potential Φ can be obtained from the following equation: It can be easily checked that the angular part of this relationship is satisfied by: As before, confining the current to the atmosphere implies the boundary conditions: k m ˜ v 0 = R 3 A ( R ) = ( R + H ) 3 A ( R + H ). In turn, the radial part of the solution reads: The induced current density can now be obtained through Ohm's law. The Lorentz force can be approximated as originating from the interactions between the induced current and the background magnetic field. The resulting expression is quite cumbersome. However, all of the important features of F L can be seen by evaluating it at the center of the dynamic domain. To leading order in χ , the expression takes the form: Asimilar evaluation of F L at r = R and r = R + H shows that the ˆ r and ˆ φ components of the force do not change significantly with radius, although the ˆ θ component does. Indeed, the Lorentz force that arises from the interactions between the dayside-to-nightside circulation and the background magnetic field does not only oppose the flow. Instead, it acts to introduce both radial and zonal components to the circulation. Importantly, the typical magnitude of the zonal component of F L is commensurate with the meridional component (although of course their spatial dependence is different). As argued in section (3.1), the characteristic timescale associated with the Lorentz force is comparable to the radiative timescale at mbar pressures and is generally shorter than that, corresponding to other relevant forces. This means that the force-balance implied by equations (17) is in essence not relevant to circulation on hot planetary atmospheres. In summary, we conclude that dayside-to-nightside flow is unstable to perturbations arising from the Lorentz force. Consequently, we expect that the upper atmospheric circulation will change qualitatively once a substantial magnetic field is introduced into the system. We now turn our attention to numerical MHD simulations with the aim of testing this presumption and quantifying the dynamical state of magnetized upper atmospheres of Hot Jupters.","pages":[9,10,11]},{"title":"4.2. Magnetohydrodynamic Simulations","content":"The hydrodynamic simulation parameters are chosen as described in section (2), corresponding to the P = 1mbar pressure level (i.e. τ L = 10 3 sec.). We start out with the equilibrated hydrodynamic flow shown in panel A of Figure (3) and introduce a weak pole-aligned dipole magnetic field into the system. Upon equilibration, we take the approach of sequentially increasing the magnitude of B dip . At each step, we allow the flow to reach a steady state before increasing the field strength further. We have checked that the flows obtained by successive enhancement of B dip are identical to those obtained by initializing the atmosphere in solid-body rotation with a given value of B dip . Consequently, in agreement with Liu & Showman (2012), we conclude that the obtained flows are insensitive to initial conditions. The panels of Figure (6) show the upper atmospheric circulation for a series of magnetic field strengths. From this series of results, a clear pattern emerges: as the magnitude of B dip is increased, the flow takes on an exclusively zonal character. Specifically, it is clear that the circulation patterns characteristic of | B dip | = 0 . 33 G (panel B) are already markedly different from the | B dip | = 0 . 025 G case (panel A), which clearly resembles the unmagnetized circulation. The flow is in essence entirely azimuthal once the field is increased to | B dip | = 0 . 5 G (panel C). This is in contrast to the non-uniformly dragged simulations of Rauscher & Menou (2013), who find the flow to become less zonally-dominated with enhanced field strength. It is noteworthy that the flow speeds up once it takes on a zonal nature. This is almost certainly due to the fact that viscosity acting on vertical motion more strongly affects the divergent flow, and is therefore not a physically significant result. Increasing the field strength further diminished the flow velocities but did not alter the qualitative nature of the solution, although somewhat higher values of the Ekman number were required to ensure numerical stability. At the expense of a great inflation in the required computational time, we have extended the simulations presented in Figure (6) to higher resolution. Namely, we prolonged the spherical harmonic decomposition up to degree glyph[lscript] max = 34 and m max = 29 while eliminating hyperviscosity from our runs entirely. Aside from a mild (i.e. few percent) increase in the velocities, the results observed in these simulations were largely unchanged from the nominal simulations. This implies that the presented solutions do not depend sensitively on small-scale flows. In other words, the transition of the atmosphere to a state dominated by zonal jets is a result of interactions between global circulation and the large-scale magnetic field. Provided the zonal nature of the flow observed in the magnetized simulation, we can expect that the induced field will be almost entirely toroidal and will approximately be described by equations (29) and (30). As shown in Figure (5), this indeed appears to be the case. The numerically obtained azimuthal component of the field (panel B) is qualitatively similar to its analytically computed counterpart (panel A), although the field lines are concentrated towards the vicinity of the equator in the numerical solution (this is simply a consequence of the fact that the circulation is not exactly given by the expression (27)). The magnitude of the induced field is also in good agreement with the analytical theory. For ˜ v 0 = 440 m/s, and k m / R 3 = 0 . 5 G, equation (29) yields max(B ind ) = 0 . 64 G, where as the numerically computed value is max(B ind ) = 0 . 52 G. Unlike the case considered in the previous section (where the Lorentz force is treated as a drag), within the framework of MHD simulations, the relationship between the peak wind speed and the temperature perturbation is not necessarily simple. Consequently, in order to preliminarily explore the sensitivity of our results on irradiation, we performed an additional suite of simulations where the applied heat flux was enhanced by a factor of three, compared to the simulations shown in Figure (6). In these overdriven simulations, we found the peak wind speeds to be a factor of ∼ 2 -2 . 5 higher. However, the characteristic flow patterns closely resembled those, shown in Figure (6) and specifically, the circulation with | B dip | = 0 . 5 G remained dominated by azimuthal jets. Consequently, we conclude that the transition of the circulation to a zonal regime with increasing magnetic field strength is robust within the context of our model. It is interesting to note that the zonal nature of the circulation is ensured at a comparatively low magnetic field strength. If we adopt a scaling based on an Elsasser number of order unity (Stevenson 2003), typical hot Jupiter magnetic fields should exceed that of Jupiter by a factor of a few e.g. | B dip | ∼ 10 G. Moreover, the arguably more physically sensible scaling based on the intrinsic energy flux (Christensen et al. 2009) suggests that typical hot Jupiter fields may be still higher by another factor of ∼ 5. Cumulatively, this places the critical magnetic field needed for the onset of zonal flows a factor of ∼ 10 -100 below the typical field strengths. As a result, it would be surprising if a more sophisticated treatment of the hydrodynamics and radiative transfer proved the critical field strength to be higher than the typical one. Nevertheless, such simulations should no doubt be performed.","pages":[11,12]},{"title":"5. DISCUSSION","content":"In this paper, we have characterized the nature of atmospheric circulation on Hot Jupiters, in a regime where magnetic effects play an appreciable role. We began by performing baseline Boussinesq hydrodynamical simulations and augmenting them to crudely account for the Lorentz force by expressing it in the form of a Rayleigh drag. Using a simple analytical theory, we showed that within the framework of such a treatment, the interactions between the circulation and the background magnetic field lead to a well-formulated reduction in wind velocities. However, in agreement with published literature (Perna et al. 2010; Rauscher & Menou 2012) and dragged simulations of our own, we noted that regardless of the background field strength, the functional form of the upper-atmospheric stream function remains characteristic of a flow pattern where wind originates at the substellar point and blows towards the anti-stellar points quasi-symmetrically over the terminator (see also Showman et al. (2008)). Although simplifying, the assumption that the Lorentz force (even approximately) opposes the flow everywhere, as done by a Rayleigh drag, appears inappropriate for dayside-to-nightside circulation. Consequently, relying on theoretical considerations based on a kinematic treatment of magnetic induction (Moffatt 1978), we showed that if the Lorentz force is not reduced to a form of a drag, dayside-to-nighside flows become unstable in presence of a spin pole aligned magnetic field. On the contrary, the interactions between zonal jets and the background magnetic field do not give rise to meridional or radial flows, thanks to an inherent symmetry. Instead, the jets are stably damped by the background field (Liu et al. 2008; Menou 2012). However, the damping rate generally need not be latitudinally uniform. As demonstrated by magnetohydrodynamical simulations, this has profound implications for upperatmospheric circulation. Specifically, the MHD calculations indicate that once the background magnetic field is stronger than a critical value, the upper atmospheric circulation transitions from a state dominated by daysideto-nightside flows to an azimuthally symmetric pattern dominated by zonal jets. Qualitatively, this transition can be understood as a point where redistribution of heat from the dayside to the nightside by flow patterns that intersect the magnetic poles ceases to be energetically favorable against purely zonal circulation. For the standard case considered here (that is, τ N = 10 3 sec), the critical field strength is approximately B crit glyph[similarequal] 0 . 5 G, considerably less than the typically inferred field strengths of Hot Jupiters (Christensen et al. 2009). However, it should be understood that the critical field strength must unavoidably depend on various system parameters including the radiative timescale and the electrical conductivity. The variability due to the latter may be particularly important since thermal ionization is extremely sensitive to the atmospheric temperature (see Figure 2). The form of this dependence and the extent to which atmospheres within the current observational aggregate are magnetically dominated merits further investigation. The fact that dayside-to-nightside flows tend to simplify to a zonal state in magnetized atmospheres has a number of important implications. As already discussed to some extent in section (3), axisymmetric flows give rise to exclusively toroidal fields (Moffatt 1978). This means that additional atmospheric dynamo generation, that would act to augment a deep seated field, cannot be supported by large-scale circulation. Moreover, because the induced field lacks a strong poloidal component, its observational characterization is at present hopeless. Consequently, observational inference of magnetohydrodynamic processes in exoplanetary atmospheres is likely to be limited to indirect methods. This discussion overlooks the possibility of field generation by small-scale turbulence (i.e. the α -effect) in the atmosphere. Indeed such a process may be at play if the turbulent magnetic Reynolds number Re t m ≡ ν/η glyph[greaterorsimilar] 1 -10. For highly turbulent atmospheres, this criterion may indeed be satisfied. Our simulations aimed at determining the viability as well as characterization of field generation by small-scale turbulence in Hot Jupiter atmospheres are currently ongoing and will be reported in a follow-up study. In this work, we briefly hinted at the fact that the damping of zonal jets by dipole magnetic fields is not only non-uniform latitudinally but also radially. The radial dependence of the Lorentz force found here is specific to the boundary conditions imposed on the induced current. However, if we do not choose to confine the current to a single scale-height but allow it to penetrate the convective interior of the planet (as for example envisioned within the context of the Batygin & Stevenson (2010) Ohmic dissipation model), the induced toroidal field is free to occupy a much deeper portion of the planet. In such a case, the resulting Lorentz force may act to produce deep-seated azimuthal flows and give rise to largescale differential rotation within the planet (Goldreich private communication). However, the extent to which such differential rotation can persist is subject to a number of constraints, including the magnitude of interior Ohmic dissipation (Liu et al. 2008). In addition to the various simplifications inherent to our model that are already described throughout the paper, it is further noteworthy that we have restricted the morphology of the background magnetic field to a pole-aligned dipole for simplicity. Within the solar system, a dipolar, axisymmetric magnetic field created by an internal dynamo is possessed only by Saturn (Acuna & Ness 1980; Dougherty et al. 2005). On the contrary, Jupiter and the Earth have dipole-dominated fields that are significantly tilted with respect to their spin-axes, while Neptune and Uranus possess rather unusual nondipolar, non-axisymmetric fields (Stevenson 2003). As a result it is quite likely that even on a qualitative level, the discussion presented in this work is not comprehensive. That is, unlike axisymmetric jets found in this work, one could envision the generation of substantial stationary eddies, yielding longitudinally and latitudinally asymmetric jets in exoplanetary atmospheres, by complex background magnetic fields. Furthermore, orbital variations may also be of importance. Specifically, while the assumption of a circular orbit is secure for the majority of hot Jupiters, null eccentricities are certainly not universal to the observational sample (an extreme example is HD80606b (Naef et al. 2001) which has e = 0 . 93). The time-variability of stellar irradiation associated with significant eccentricity produces rather complex circulation patterns even in hydrodynamic regime (Langton & Laughlin 2008; Kataria et al. 2013). However, recalling that electrical conductivity in hot planetary atmospheres arises primarily as a result of thermal ionization, the circulation patterns are likely to be even more complex than those typically envisioned, since magnetic effects in the atmosphere will also be time-dependent. We would like to finish with a few words about observational implications of our results. At present, the resolution and signal to noise of the spectroscopic data aimed at characterizing the temperature structure and chemical composition of exoplanetary atmospheres (Charbonneau et al. 2005; Knutson et al. 2008; Swain et al. 2010) is such that even fits obtained with one-dimensional atmospheric models are susceptible to numerous degeneracies (Madhusudhan & Seager 2009). Consequently, it is unlikely that the qualitative change in the flow structure observed in this work will strongly affect the already-limited interpretation of the information contained within this data, in the near future (Line et al. 2012). On the other hand, theoretical interpretation of observed dayside-to-nightside temperature differences and the associated shifts in the location of the subsolar hot spot (Knutson 2007) rely heavily on a sensible understanding of atmospheric dynamics, which as we have seen requires a more or less self-consistent account of magnetic effects. To this end, the results obtained in this study are of great importance. Indeed, one can expect that the advective transport of heat changes character and weakens with increased electrical conductivity (by extension, the atmospheric temperature) and magnetic field due to the mechanism described above (see also Liu et al. (2008); Perna et al. (2010); Batygin et al. (2011); Menou (2012); Rauscher & Menou (2012)). Thus, a thorough comparison between a substantial sample of model results and data may eventually shed light on the typical atmospheric conductivity structure and field strengths of Hot Jupiters. Such activity would no-doubt further benefit from direct measurements of high-altitude atmospheric wind velocities obtained via ground-based spectroscopy (Snellen et al. 2010). That said, in order for an endeavor of this sort to be meaningful, substantial improvements in theoretical modeling aimed at meliorating the shortcomings outlined above are required, along with a wealth of additional observational data. In conclusion, the above discussion clearly indicates that the degree of complexity of the physical regime in which hot exoplanetary atmospheres reside is indeed very extensive. There is no doubt that much additional work remains. In this work, we have taken an ample step towards a self-consistent characterization of magnetically controlled circulation on Hot Jupiters. As such, this study should serve as a stepping stone for future developments. Acknowledgments . We thank Adam Showman, Tami Rogers, Kristen Menou, Peter Goldreich and Greg Laughlin for useful conversations, as well as the anonymous referee for a thorough and insightful report. K.B. acknowledges the generous support from the ITC Prize Postdoctoral Fellowship at the Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics. S.S. acknowledges funding by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Alfred P. Sloan Foundation.","pages":[12,13,14]},{"title":"REFERENCES","content":"Heng, K. 2012, ApJ, 748, L17","pages":[14]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"Through the process of thermal ionization, intense stellar irradiation renders Hot Jupiter atmospheres electrically conductive. Simultaneously, lateral variability in the irradiation drives the global circulation with peak wind speeds of order ∼ km/s. In turn, the interactions between the atmospheric flows and the background magnetic field give rise to Lorentz forces that can act to perturb the flow away from its purely hydrodynamical counterpart. Using analytical theory and numerical simulations, here we show that significant deviations away from axisymmetric circulation are unstable in presence of a non-negligible axisymmetric magnetic field. Specifically, our results suggest that dayside-to-nightside flows, often obtained within the context of three-dimensional circulation models, only exist on objects with anomalously low magnetic fields, while the majority of highly irradiated exoplanetary atmospheres are entirely dominated by zonal jets.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"MAGNETICALLY CONTROLLED CIRCULATION ON HOT EXTRASOLAR PLANETS\",\n \"content\": \"Konstantin Batygin 1 , Sabine Stanley 2 & David J. Stevenson 3 1 Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 2 Department of Physics, University of Toronto, 60 St. George St., Toronto, ON and 3 Division of Geological and Planetary Sciences, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125 Draft version September 19, 2018\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"The last decade's discovery and rapid accumulation of the transiting extrasolar planetary aggregate has uncovered a multitude of previously unexplored regimes of various physical phenomena. Perhaps the first unexpected discovery was the existence of Hot Jupiters (i.e. gaseous giant planets that reside within ∼ 0 . 1AU of their host star), which arose from the earliest exoplanetary detections (Mayor & Queloz 1995; Marcy & Butler 1996). Accordingly, among the most intriguing novel theoretical subjects, is the study of atmospheric dynamics on highly irradiated planets. Today, it is well known that the orbital region occupied by Hot Jupiters can also be occupied by lower mass (including terrestrial) planets (Batalha et al. 2012). However, because of their higher likelihood of transit and comparative predisposition for characterization, Hot Jupiters remain at the forefront of the study of extrasolar atmospheric circulation (Showman et al. 2011).\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1.1. Hydrodynamic Global Circulation Models\",\n \"content\": \"Dynamic meteorology is a phenomenologically rich subject because of the lack of separation of physical scales. In other words, differences in microphysical nature of a given system can have profound effects on its macroscopic state. As a result, it comes as no surprise that circulation patterns on Hot Jupiters generally do not resemble those on Solar System gas giants (Showman et al. 2008; Menou & Rauscher 2009). From a hydrodynamical point of view, the circulational modes of typical Hot Jupiter atmospheres differ in two principal ways, compared to Solar System gas giants. The first and most obvious difference is the energetics. Unlike the outer Solar System, Hot Jupiters reside in an environment where the incoming stellar irradiation completely dominates over the intrinsic planetary heat-flux. As a result, circulation patterns on Hot Jupiters are driven primarily by the congenital kbatygin@cfa.harvard.edu dayside-to-nightside temperature differences (Showman & Polvani 2011). Furthermore, concurrent with the cooling of the planetary interior, the top-down heating of the atmosphere ensures the onset of stable stratification in the observable ( P > 100 bars) atmospheric region (Guillot & Showman 2002; Burrows et al. 2007). The second difference lies in the extent to which the atmospheres are rotationally dominated. While Solar System gas giants rotate rapidly (i.e. T Jup glyph[similarequal] T Sat glyph[similarequal] 10 hours), Hot Jupiters are thought to rotate pseudosynchronously with their orbital periods (i.e. T HJ ∼ 3 -5 days) as a result of tidal de-spinning (see Hut (1981)). This implies that although still dynamically significant, rotation alone does not exhibit commanding control over the atmospheric flow. Since the discovery of the first transiting extrasolar gas giant HD209458b (Charbonneau et al. 2000; Henry et al. 2000), numerous authors have explored the atmospheric dynamics of Hot Jupiters with a variety of numerical techniques. Because of the inherent differences in the frameworks of the simulations, today, there exists a hierarchical collection of results that correspond to variable degrees of sophistication. On the simpler end of the spectrum are 2D shallow-water simulations (Cho et al. 2008, 2003; Langton & Laughlin 2008, 2007) while the more intricate global circulation models (GCM's) include solvers of the 3D 'primitive' equations (Cooper & Showman 2005; Showman et al. 2008; Menou & Rauscher 2009; Heng et al. 2011) as well as the 3D fully compressible Navier-Stokes equations (Dobbs-Dixon & Lin 2008; Dobbs-Dixon & Agol 2012). Simultaneously, various groups have gone to different lengths in their treatment of radiative transfer, with exploited models ranging from simple prescriptions such as Newtonian cooling (Showman et al. 2008) to double-gray (Rauscher & Menou 2012) and non-gray (Showman et al. 2009) schemes. An important step towards delineating the correspondence among results obtained with different solvers has been recently performed by Heng et al. (2011). Although there are quantitative differences in the re- sults generated by different GCM's, there is general agreement on the qualitative features of the circulation. Specifically, there are three aspects of interest. First, super-rotating zonal jets exist in all simulations. Their number (and naturally, the widths) ranges between 1 and 4, depending on the model (see Showman et al. (2009)), but the relative sparsity of the jets compared to Jupiter and Saturn is understood to be a result of diminished rotation rate (Showman & Guillot 2002). Moreover, in a recent study, Showman & Polvani (2011) showed that the formation of jets is ordained by the interaction of the atmospheric flow with standing Rossby waves that in turn result from the strong difference in the radiative forcing between the planetary dayside and the nightside. Second, the characteristic wind speeds produced by different models are consistent within a factor of a few, and are generally in the ∼ km/s range. This is likely a direct result of the overall similarity in the force-balance setup within the models. Specifically, Showman et al. (2011) argue that near the equator, the horizontal pressuregradient acceleration caused by the asymmetric irradiation is balanced by the advective acceleration. Meanwhile, Coriolis force takes the place of advective acceleration as the primary balancing term in the mid-latitudes. Both force-balances yield ∼ km/s as the characteristic wind speeds, in agreement with the numerical models. Finally, in GCMs that resolve the vertical structure of the atmosphere (e.g. Showman et al. (2008); Menou & Rauscher (2009); Heng et al. (2011)) eastward jets consistently dominate the lower atmosphere while the upper atmosphere is characterized by more or less symmetric dayside-to-nightside circulation. In other words, winds originate at the sub-solar point and flow to the anti-solar point over the terminator in the upper atmosphere. The transition between the circulation patterns takes place at P ∼ 0 . 1 -0 . 01 bars and is a consequence of the substantial reduction of the radiative time constant with diminishing pressure (Iro et al. 2005). In particular, because the radiative adjustment timescale is much shorter than the advective timescale in the upper atmosphere, the flow is unable to perturb the temperature structure away from radiative equilibrium significantly. Figure (1) depicts a schematic representation of the characteristic features of atmospheric circulation on Hot Jupiters.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"1.2. Magnetically Dragged Global Circulation Models\",\n \"content\": \"There exists another important, distinctive feature of Hot Jupiter atmospheres, namely their non-negligible electrical conductivity (see Figure 2). Electrical conductivity in Hot Jupiter atmospheres does not originate from the ionization of H or He, but rather from the stripping of the valence electrons belonging to alkali metals such as K and Na (Batygin & Stevenson 2010; Perna et al. 2010). While these elements are thought to be present in trace abundances (e.g. [K]/[H] ∼ 10 -6 . 5 , [Na]/[H] ∼ 10 -5 . 5 ) (Lodders 1999), temperatures of ∼ 2000K at upper atmospheric pressures, lead to total and partial ionization of K and Na respectively. In fact, at mbar levels, the conductivity can reach values as high as σ ∼ 1 S/m (Batygin et al. 2011; Rauscher & Menou 2012; Heng 2012). Furthermore, it is generally expected that much like solar system gas giants, Hot Jupiters posses interior dynamos, that produce surface fields comparable to, or in slight ex- upiter's field 1 (e.g. B ∼ 3 -30 Gauss) (Stevenson 2003; Christensen et al. 2009). Consequently, there is a distinct possibility that atmospheric circulation on Hot Jupiters may be in part magnetically controlled. That is to say, highly irradiated atmospheres may be sufficiently conductive for the Lorentz force to play an appreciable, if not dominant role in the force-balance. Realizing the potential importance of the coupling between the mean flow and the planetary magnetic field, Perna et al. (2010) modeled the Lorentz force as a Rayleigh drag (a velocity-dependent force that opposes the flow) and incorporated it into the GCM previously utilized by Menou & Rauscher (2010). This effort was later amended by Rauscher & Menou (2013), who also modeled the Lorentz force as a Rayleigh drag but selfconsistently accounted for spatial variability in the electrical conductivity (by extension the drag timescale) in the weather layer. The results obtained with dragged GCMs exhibit significant differences in the obtained flow velocities relative to the standard GCMs. Namely, Perna et al. (2010) found a factor of ∼ 3 decrease in the peak wind speeds as the background dipole magnetic field was increased from B dip = 3 G to B dip = 30 G, while Rauscher & Menou (2012) found a similar decline in the jet speeds as the field was increased from B dip = 0 G to B dip = 10 G. The magnetic limitation of the peak wind speeds is of considerable importance as it may prevent the global circulation from approaching a super-sonic state (note that the characteristic sound speed is order c s ∼ √ k B T/µ ∼ 3 km/s, where k B is Boltzmann's con- stant, T is the temperature, and µ is the mean molecular weight), thereby inhibiting the formation of shocks.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"1.3. The Necessity for Magnetohydrodynamic Circulation Models\",\n \"content\": \"Although dragged 3D GCMs clearly highlight the quantitative importance of the magnetic effects in Hot Jupiter atmospheres, they fail to accentuate significant qualitative differences in the obtained flows. Specifically, much like conventional GCMs, magnetically dragged GCMs still show deep-seated zonal jets, overlaid by complex flow patterns that intersect the poles of the planets. This lack of qualitative differences may arise from two distinct possibilities. The first is that beyond diminishing the peak wind speeds, the background magnetic field has little effect on the global circulation. In actuality, this may very well be true for pressure levels where the circulation is dominated by zonal jets, because of the geometrical simplicity of the flow-field interactions. Indeed, the coupling between the zonal flow and the polealigned background dipole field is azimuthally symmetric: differentially rotating jets convert the poloidal field into toroidal field (Liu et al. 2008; Batygin & Stevenson 2010). As will be discussed in detail below, beyond the reduction of velocities, this conversion poses few dynamical ramifications for the jets. Furthermore, owing to higher pressure and somewhat diminished temperatures compared with the upper atmosphere (and the associated decrease in conductivity), the zonal jets may reside in the kinematic regime, where the effects of the Lorentz force are modest (Batygin et al. 2011; Menou 2012). The second possibility is that although in reality the interactions with the background field impel the circulation to strongly deviate from its purely hydrodynamical counterpart, the procedure of modeling the Lorentz force as a Rayleigh drag does not capture the essential features of the dynamics. This is likely true in the upper atmosphere, where azimuthal symmetry is broken and the flow takes on a more topologically complex form. After all, in such a setting there is no requirement for the Lorentz force to simply oppose the flow everywhere, as is done by Rayleigh drag. Thus, there is a distinct possibil- ity that previous modeling efforts have consistently misrepresented the circulation patterns of the upper atmospheres of Hot Jupiters. Accordingly, the investigation of this possibility is the primary purpose of this work. A statistically sound comparison between theoretical models and observations requires the incremental decrease in the goodness of fit to outweigh the cost of introducing new degrees of freedom into the model (see Rodgers (2000) for an in-depth review). Within the context of extrasolar planets, the limitations in observational capabilities and the quality of the data render the construction of highly sophisticated models unjustified (Line et al. 2012). Although a rigorous comparison with observational data is not the focus of this paper, our modeling efforts will lie in the same rudimentary spirit. In other words, here we shall focus on understanding the qualitative, rather than quantitative nature of the circulation. Numerous simplifying assumptions will be made and the representation of the flow (including flow velocities, dayside-to-nightside temperature differences, etc) should only be viewed as approximate. However unlike all previous works on the subject, the model we shall utilize will remain self-consistently magneto-hydrodynamic (MHD). In taking this approach, we hope to successfully capture the essential features of magnetic effects in highly irradiated planetary atmospheres. The paper is organized as follows. In section 2, we describe the equations inherent to our numerical GCM and reproduce the main features of Hot Jupiter atmospheric flows in the purely hydrodynamic regime. In section 3, we discuss the qualitative features of the atmospheric flows, treating the Lorentz force as a hydrodynamic drag. Specifically, we develop an analytical theory for magetically-dragged circulation patterns in the upper atmosphere and test the resulting scaling law against numerical simulations with enhanced viscosity and explore the effects of varying the radiative timescale. In section 4, we introduce a pole-aligned background magnetic field and demonstrate the transition of the upper atmosphere's dayside-to-nightside circulation into a globally zonal state with the onset of the background field. We conclude and discuss our results in section 5.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"2. NUMERICAL GLOBAL CIRCULATION MODEL\",\n \"content\": \"The Hot Jupiter GCM we have adopted here is a variant of the numerical geodynamo model constructed by Kuang & Bloxham (1999). Since its conception, the model's versatility has been exploited extensively to explain the geodynamo (Kuang & Bloxham 1999; Dumberry & Bloxham 2002), the ancient Martian dyanamo (Stanley et al. 2008), Mercury's thin-shell dyanamo (Stanley et al. 2005; Zuber et al. 2007), Saturn's dynamo (Stanley 2010), as well as dynamos of Uranus & Neptune (Stanley & Bloxham 2004, 2006). The details of the implementation of the model and the utilized numerical methods are throughly described by Kuang & Bloxham (1999). Here, rather than exhaustively restating the particularities of the framework, we limit ourselves to presenting the set of equations under consideration and the underlying assumptions, while referring the interested reader to Kuang & Bloxham (1999) for further information.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"2.1. The Governing Equations\",\n \"content\": \"Momentum. -The circulation model solves the NavierStokes equation for an electrically conductive, Boussinesq fluid in a rotating spherical shell of finite thickness. Here, D/Dt = ∂/∂t + v · ∇ is the material derivative, v is the velocity vector, Ω = (2 π/ T ) ˆz is the rotation vector, P is the modified pressure, ρ is the density, J is the current density and ν is the kinematic viscosity. The bar denotes an average, whereas δ denotes the perturbation away from the background state. The density and temperature are related to the pressure through the ideal gas equation of state 2 : where P is the total pressure. The dynamic domain where the equation is solved is confined above a rigidly rotating spherical shell. We denote the inner and outer radii of the atmosphere as r 1 < r 2 respectively. Continuity. -The model is formally 3D and the vertical component of the motion enters into the continuity equation: However, the nearly-constant density, incompressible fluid approximation prevents us from self-consistently modeling a radially extensive atmosphere. Indeed, the atmospheric density does not change, except by thermal expansion/contraction 3 : Consequently, we limit the thickness of the atmosphere to a single scale-height in our simulations: r 2 -r 1 = H = k B ¯ T/µg , where g is the acceleration due to gravity. Additionally, we set r 1 = R , the radius of the planet. Generally, because of the above-stated reasons, our model should be viewed as more closely related to the 2D shallow-water GCMs (Cho et al. 2003; Langton & Laughlin 2008) rather than the family of 3D models (Showman et al. 2009; Perna et al. 2010; Rauscher & Menou 2012). However, proper treatment of the of the induction equation (see below) in absence of pre-described symmetry requires the model to remain 3 dimensional. Energy. -The energy equation, that governs the temperature, inherent to the model reads: where κ is the coefficient of thermal diffusivity (kept constant throughout the computational domain). Strictly speaking, this equation governs diffusive heat flux and (in direct interpretation) is unsuitable for modeling a medium where energy transport is accomplished mainly by radiation. This is because the above equation rests on the approximations of short photon mean free path and the neglect of the temperature-dependence of the opacity (in the context of the Boussinesq treatment employed here, the latter makes sense but the former breaks down at pressure levels corresponding to optical depth of order unity, allowing for only a crude approximation to reality). However, shall it be possible to relate κ to radiative properties of the gas, the above energy equation can still be used to effectively mimic the appropriate heat transport. In a radiatively-dominated atmosphere, the correct energy equation reads (Peixoto & Oort 1992) where c p is the specific heat capacity at constant pressure and F is the radiative heat flux. The expression for the radiative heat flux reads (Clayton 1968): where σ sb is the Stefan-Boltzmann constant and ψ is the opacity. At this point, the relationship between κ and the atmospheric temperature, density, opacity, and heat capacity is obvious. However, before proceeding further, let us recall that to an order of magnitude, the Newtonian cooling timescale τ N is given by the ratio of the atmosphere's excess heat content to its excess radiative flux: Consequently, we may express: where we have implicitly assumed an infrared optical depth of order unity at the pressure-level of interest. The relationship between κ and τ N is convenient, as it can be related to previous works. In particular, Showman et al. (2008) have calculated τ N using a state of the art radiative transfer model and tabulated the results on a pressure-temperature grid. Here, we utilize their computations as a guide in estimating the thermal diffusivity. Note that we could have arrived at the relationship (9) more intuitively by dimensional analysis. Specifically, noting that the radial extent of the atmosphere is much smaller than the lateral extent, the relevant length scale is the vertical scale-height, H . Meanwhile, because the heat transport is primarily radiative, τ N is clearly the relevant timescale. Bearing in mind the units of diffusivities (i.e. m 2 /s), equation (9) naturally emerges as an estimate. Magnetic Field. -The evolution of the magnetic field is governed by the induction equation (Moffatt 1978) where η = 1 /µ 0 σ is the magnetic diffusivity (kept constant throughout the computational domain) and µ 0 is the permeability of free space. Meanwhile, the absence of magnetic monopoles implies a divergence-free magnetic field: Once the structure of B is known, the current density (within the MHD approximation) is given by At this point, the full set of governing differential equations is presented. Paired with a matching set of boundary and initial conditions, the system can be integrated forward in time self-consistently. The equations are solved using a mixed spectral-finite difference algorithm and following Kuang & Bloxham (1999), the spherical harmonic decomposition is taken up to degree glyph[lscript] max = 33 in the latitude m max = 21 in the azimuthal angle. The computational domain is broken up into 64 radial shells. The model is integrated forward in time until equilibration in the thermal, kinetic and magnetic energies is attained.\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"2.2. Boundary and Initial Conditions\",\n \"content\": \"The physical parameters employed in the numerical experiments we report are loosely based on the planet HD209458b (Charbonneau et al. 2000). Aside from being the first extrasolar planet found to transit its host star, it has become a canonical example used in the studies of Hot Jupiter atmospheres (Burrows et al. 2007; Snellen et al. 2010). To this day, (along with HD189733b (Knutson et al. 2009)) it remains the best characterized extrasolar planet. The object has a mass M = 0 . 69 M Jup , a radius R = 1 . 35 R Jup and a rotational (assumed synchronous with orbit) period of T HD209458b = 3 . 5 days. Momentum. -Because we are integrating a quasi-2D atmospheric shell, intended to be representative of a single pressure level, we apply impenetrable, stress-free boundary conditions to the velocity field. Thus, flows are free to develop without friction along the boundaries, although at initialization the planet is cast into solid-body rotation meaning v = 0 at t = 0. Energy. -The temperature is initialized at ¯ T = 2000K with δT/ ¯ T = δρ/ ¯ ρ = 0. The atmosphere is kept stablystratified by the imposition of a stable background temperature gradient (set to the adiabatic lapse rate h = g/c p ) similar to the implementation in other Boussinesq dynamo models with stable layers (e.g. Stanley & Mohammadi (2008); Stanley (2010); Christensen & Wicht (2008)). Additionally, an azimuthally variable heat-flux is applied at the outer boundary, r 2 , to account for the variable stellar irradiation (in practice it doesn't matter whether the variable heat flux is applied at the outer or the inner boundaries, since it is the horizontal temperature gradient that controls the flow). The functional form of the heat-flux is chosen to be that of the F ∝ Y 1 1 spherical harmonic, while the amplitude is taken to be a free parameter (see the discussion in the next section). Magnetic Field. -Nominally, an electrical conductivity of σ = 1S/m, characteristic of P glyph[similarequal] 1mbar, T glyph[similarequal] 2000K is prescribed to the computational domain. Simultaneously, negligible electrical conductivity is assigned outside the computational domain. That is, σ glyph[similarequal] 0 at r < r 1 and r > r 2 , meaning all of the current generated by the atmospheric flow is confined to the weather layer. This is in agreement with the approach of Perna et al. (2010); Rauscher & Menou (2013), but in some contrast with the analytical work of Batygin & Stevenson (2010); Batygin et al. (2011), where the current is allowed to penetrate the convective interior of the planet. Because this work is primarily aimed at studying the upper atmosphere, the pressure-level of interest may reside above the atmospheric temperature inversion, characteristic of some Hot Jupiter atmospheres (Burrows et al. 2007; Spiegel et al. 2009). The presence of such an inversion may provide an electrically insulating layer 4 , justifying σ glyph[similarequal] 0 at r < r 1 . The capability of electrical currents to penetrate the upper atmosphere and close in the magnetosphere is determined by the upper atmosphere's temperature structure and the abundance of Alkali metals at P glyph[lessorsimilar] 1 mbar altitudes. Although a clear possibility, the physics of atmosphere-magnetosphere coupling is no-doubt complex and is beyond the scope of the present study. Consequently, we neglect it for the sake of simplicity. In all of our simulations, we initialize J = 0 in the weather layer. However, the weather layer is still permeated by the background magnetic field, B dip , presumed to be generated by dynamo action in the convective interior of the planet. This zero current field reads: where k m is a constant that sets the surface field strength i.e. | B dip | = k m / R 3 at the equator. Within the context of the model, the background field is implemented by modifying the governing equations to account for a timeindependent axially-dipolar external field. This occurs specifically in two terms. In the momentum equation (1), the Lorenz force ( J × B ) / ¯ ρ is replaced by J × ( B + B dip ) / ¯ ρ . In the magnetic induction equation (10), the induction term ∇× ( v × B ) is replaced by ∇× ( v × ( B + B dip )). This method is similar to that used by Sarson et al. (1997) and Cebron et al. (2012) to implement external fields.\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"2.3. Dimensionless Numbers\",\n \"content\": \"Upon non-dimensionalization of the governing equations (Kuang & Bloxham 1999), we obtain 6 dimensionless numbers that completely describe the system. They are the Ekman number E , the magnetic Rossby number R o , the magnetic Prandtl number q , the magnetic Rayleigh number R th and the aspect ratio χ as well as an additional value, Γ, that parameterizes the incoming stellar flux. In terms of physical parameters, these quantities read: The aspect ratio of the atmosphere we consider is 4 This idea is not new. The models of Batygin & Stevenson (2010) as well as Batygin et al. (2011) used the presence of such a layer to confine the current generated by zonal flows to the lower atmosphere and the interior of the planet. χ = 7 × 10 -3 . For numerical stability, the model requires the Ekman number to exceed a critical value (which we adopt in the simulations) of order E crit ∼ 10 -5 . If we consider the molecular viscosity of Hydrogen ν = ¯ na √ 3 k B ¯ T/m H 2 / 2, where ¯ n is the number density and a is the molecular cross-section, we obtain a hopelessly small E ∼ 10 -20 glyph[lessmuch] E crit at mbar pressure. We note that the actual Ekman number is orders of magnitude higher, since on the global planetary scale, small-scale turbulence is a far more relevant source of viscosity than transfer of momentum at the molecular level (Peixoto & Oort 1992). Still, the true value of E is probably much smaller than E crit . x = 619K = 104 m/s 003 For a given electrical conductivity (equivalently diffusivity), R o and R th simply encompass the physical units of the model. Specifically, for σ = 1S/m, R o = 1 . 79 × 10 -6 and R th = 1 . 38 × 10 9 . Meanwhile, all of the information regarding the considered pressure level is provided by q . Taking σ = 1S/m as before, we obtain q glyph[similarequal] 6 , 60 and 600, corresponding to τ N = 10 5 , 10 4 , and 10 3 sec, appropriate for P = 1 , 0 . 1 and 0 . 001 bars respectively. Finally, as already mentioned above, we take Γ to be an adjustable parameter, tuned to obtain the desired temperature gradients. It is important to note that our model differs somewhat from typical dynamo models in a sense that Γ, rather than R th , parameterizes the extent to which the system is driven. 680K m/s Let us conclude the description of the numerical model with a brief discussion of its shortcomings as a guide for future work. First and foremost, the limitation of the atmosphere to a single scale-height may be prejudicial, as previous work has shown that including an extended vertical extent of the atmosphere is important to capture circulation features (Heng et al. 2011). Second, while we have kept thermal and magnetic diffusivities uniform throughout the computational domain, it should be understood that in reality these values vary with temperature and pressure. Third, an implicit assumption of an infrared optical depth of order unity is rather crude at ∼ mbar pressure levels and should be lifted in more rigorous treatments of radiative transfer. Finally, as already mentioned above, the artificially enhanced viscosity inherent to our model almost certainly smoothes out smaller-scale flow to an unphysical extent. x = 258K = 442 m/s\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"2.4. Hydrodynamical Simulations\",\n \"content\": \"Prior to performing unabridged MHD simulations, it is useful to first compare our model to previously published results. Accordingly, we begin by setting the strength of the background field to B dip = 0. Because the computational domain is initialized with a null current density, no magnetic fields are generated yielding purely hydrodynamic simulations. Horizontal slices of the atmosphere (through the center of the computational domain) in the cylindrical projection are shown in Figure (3). The figures are centered on the substellar point and the background color shows the temperature distribution. The arrows denote the circulation vector field. Peak wind speeds as well as the maximal temperature deviations from ¯ T = 2000K are labeled. The typically observed transition from zonal flows to dayside-nightside flows is observed as the pressure is de- creased sequentially from P = 1 bars (Panel C of Figure 3) to P = 0 . 001 bars (Panel A of Figure 3). However, important differences exist in our results, contrasted against say, the results of Showman et al. (2008). The first important distinction is that in the zonally-dominated parameter regime, rather than developing a single broad jet, our model shows the development of three counterrotating jets. This is a simple consequence of angular momentum conservation in the computational domain, and is not uncharacteristic of 2D models (Showman et al. 2011). Because of free-slip boundary conditions employed in our model, the atmosphere is not allowed to exchange angular momentum with the interior. As such, because the atmosphere is initialized in solid-body rotation, the development of any prograde jets must be accompanied by the development of retrograde jets. Because the retrograde jets reside at a high latitude θ ret , whereas the prograde jets are essentially equatorial, angular momentum conservation requires them to be faster by a factor of | v ret / v pro | ∼ 1 / cos θ ret , as observed in the simulations. The angular momentum conserving 3D simulations of Heng et al. (2011) exhibit similar behavior, although in their model the counter-rotating jets develop below the prograde ones, and are considerably slower because of the associated density enhancement. The second distinction of interest is the direction of the equatorial jet. While 3D GCMs consistently produce eastward equatorial jets, the equatorial jets in our hydrodynamical simulations are westward. This is not too surprising, as shallow-water and equivalent barotropic models are known to produce both eastward and westward equatorial jets, depending on the details of the simulation setup (Showman et al. 2011; Heng et al. 2011). Consequently, this difference can probably be attributed to the limited vertical extent of our model. The third important difference is the fact that flow velocities are not consistent along the pressure levels. In particular for the same values of δT , zonal flows have ∼ few km/s peak wind speeds, while the dayside-tonightside flows are more than an order of magnitdue slower. This is largely a consequence of difference in the geometry of the circulation and the fact that viscosity enters as a significant member in the force balance for dayside-to-nightside flows. This can be seen by approximating ν ∇ 2 ∼ ν/ L 2 (Holton 1992), where L is a characteristic length scale associated with the curvature of the circulation. For zonal jets, L z ∼ R while for dayside-to-nightside circulation, the return flow is in part radial implying L dn ∼ H . As will be shown in the following section, faster velocities can be attained by either increasing the aspect ratio of the atmosphere or by artificially enhancing the radiative heat flux, as a result of a linear proportionality between peak wind speeds and δT . An additional point of importance is that in typical 3D simulations, dayside-to-nightside circulation is nearly uniform over the terminator with the return flow residing at greater depth, while our results depict a partial return flow over the poles. This is again a consequence of the quasi-2D geometry of our model. Although these quantitative distinctions are certainly worthy of attention, the typical features of the flow are approximately captured by our simplified model. Consequently, while being mindful of the model's limitation we do not view the quantitative dissimilarities as critical, as they are not central to the argument of the paper. After all, recall that we are primarily concerned with the possibility of a qualitative alteration of the dayside-tonightside flow by magnetic effects.\",\n \"pages\": [\n 6,\n 7\n ]\n },\n {\n \"title\": \"3. DRAGGED CIRCULATION IN THE UPPER ATMOSPHERE\",\n \"content\": \"In the previous section, we performed baseline hydrodynamical simulations of atmospheric circulation at different pressure levels. In the following sections, we will focus primarily on the mbar pressure level, where the flow takes on a dayside-to-nightside character. As discussed above, in our simulations viscosity plays an important role in determining the flow velocities. Conceptually, the situation may be synonymous to simulations of invicid GCMs that parameterize the effect of magnetic coupling as Rayleigh drag (Perna et al. 2010; Rauscher & Menou 2012). In interest of understanding the dependence of the flow velocities on the magnitude of the dayside-tonightside temperature gradient as well as the imposed frictional forces, in this section we shall develop a simple analytical model for dragged upper-atmospheric circulation and confirm it numerically.\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"3.1. Analytical Theory\",\n \"content\": \"Let us begin with estimation of characteristic timescales. In order to accomplish this, we first simplify the Lorentz and viscous forces to resemble the functional form of Rayleigh drag. Utilizing Ohm's law, we have 5 : This allows us to rewrite equation (1) in a simpler form: where τ f = (1 /τ L + 1 /τ ν ) -1 . Taking | B dip | = 1 G, the characteristic timescales are: τ L ∼ 10 3 sec and τ ν ∼ 10 5 sec. Other relevant timescales in the problem is the rotational (Coriolis) timescale τ Ω ∼ 2 π/ Ω ∼ 10 5 sec, radiative timescale τ N ∼ 10 3 sec and the advective timescale τ adv ∼ R /v ∼ 10 5 sec. There exists a clear separation of timescales in the system. As a result, upon including the parameterized Lorentz force into the equations of motion, the inertial and Coriolis terms can be dropped (the viscous term can be dropped as well, although this simplification is unnecessary). The removal of the inertial terms implies a steady-state solution. The removal of the Coriolis term creates a symmetry characterized by an axis that intersects the sub-solar and anti-solar points. Taking advantage of this symmetry, we orient the polar axis of the coordinate system such that it intersects the sub-solar point. Upon doing so, we can specify a null azimuthal velocity and drop all azimuthal derivatives in the equations of motion. In a local cartesian reference frame, this leaves us with horizontal (ˆ y ) and vertical (ˆ z ) momentum equations, where the latter simplifies to the equation of 5 Although this approximation is often made, it is not necessarily sensible for systems where the magnetic Reynold's number, Re m ≡ v L /η glyph[greatermuch] 1. Adopting v ∼ km/s and L ∼ H , we obtain Re m ∼ 10 3 , placing the magnetic drag approximation on shaky footing. Further, the electric field in Ohm's law can only be neglected when the radial current is negligible. hydrostatic balance: Following Schneider & Lindzen (1977) and Held & Hou (1980), we shall adopt a Newtonian energy equation with implicit stable stratification (recall that we have set the potential temperature gradient to h = g/c p ): Here, ξ glyph[greaterorequalslant] 1 is a constant that parameterizes lateral heat advection and δT rad is a purely radiative perturbation to the background state, ¯ T . In other words, as the damping of the circulation is strengthened and v → 0, δT → δT rad . Retaining the incompressibility condition (3), we introduce a stream-function Ψ, defined through v = ∇× Ψ (Landau & Lifshitz 1959). Taking a partial derivative of the y -momentum equation with respect to z and of the z -momentum equation with respect to y , we obtain Taking a derivative of equation (19) with respect to y and switching the order of partial differentiation yields: Meanwhile, differentiating the Newtonian cooling equation (18) with respect to z gives: allowing us to eliminate ∂ 2 Ψ /∂y∂z : simply the square of the Brunt- Note that g 2 /c p ¯ T is Vaisala frequency for an isothermal atmosphere. Equation (22) admits the trial solutions where ( δT 0 rad ) and ( δT 0 ) are constants that represent the maximal deviations in the respective quantities from the background state. Note that ( δT 0 rad ) is a parameter inherent to the model rather than a variable. Upon substitution of the above solutions (23) into equation (22), we obtain a relationship between ( δT 0 ) and ( δT 0 rad ): In the above equation, ζ is an empirical factor that has been introduced to account for the approximations inherent to equations (15). With an analytical solution for the temperature perturbation in hand, we substitute equations (23) into equation (19) and integrate twice to obtain: This solution implies the same functional form for laterally-averaged heat transport in the vertical and horizontal advection terms in the energy equation (6), lending some support for the approximation inherent to equation (18). Once the stream function is obtained, the maximal horizontal and vertical velocities are given by: where Ψ 0 is the term in square brackets in (25). Note that the above theory automatically implies a quasi-2D flow since v max z /v max y ∼ ( H / R ) glyph[lessmuch] 1 .\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"3.2. Numerical Experiments\",\n \"content\": \"With a simple analytical theory at hand, we performed a series of numerical simulations, varying the radiative and drag timescales in the ranges 10 2 < τ N < 10 3 sec and 10 3 < τ f < 10 5 sec. Although we observed a considerable variability in the wind speeds and dayside-to-nightside temperature differences in our simulations, the nature of the flow was largely the same as that seen in panel A of Figure (3) across the runs. The peak wind speeds obtained in the simulations as functions of τ N and τ f are presented as black dots in Figure (4). In addition to the simulation results, Figure (4) shows v max y given by equation (26) for the same parameters. As can be seen from the figures, the scaling law inherent to equation (25) matches the numerical experiments quite well. Extrapolating towards larger values of τ f , it can be inferred that our simulations would have produced peak wind speeds of order ∼ km/s if not for the numerical requirements of enhanced viscosity. However, it can also be expected that the character of the flow would also change qualitatively with diminishing viscosity, as the force balance shifts away from that implied by equations (15) 6 . It should be kept in mind that the adjustable parameters ξ and ζ were fit to the data. Moreover, the value of ( δT 0 rad ) = 3360K 7 was chosen by running a simulation where viscous forces completely dominated the force balance ensuring v = 0. In other words, the quantitative agreement seen in Figure (4) is a consequence of the fact that the adjustable parameters of the analytical solution have been fit to the numerical data, but the fact that the functional form of the analytical model conforms with numerical experiments suggest that the stream-function (25) captures the main features of dragged upper-atmospheric circulation on Hot Jupiters.\",\n \"pages\": [\n 8\n ]\n },\n {\n \"title\": \"4. MAGNETICALLY CONTROLLED CIRCULATION\",\n \"content\": \"In the last section, we examined the extent to which dayside-nightside flow can be damped by imposing a drag. However, both the analytical theory and numerical experiments showed that the qualitative character of the circulation remained largely unchanged. As already mentioned in the introduction, the rough consistency of the flow patterns across a range of characteristic drag timescales is in broad agreement with the results of 'primitive' 3D GCMs (Perna et al. 2010; Rauscher & Menou 2012). In this section, we challenge this assertion with MHD calculations.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"4.1. Theoretical Arguments\",\n \"content\": \"With the exception of a rather limited number of problems, self-consistent magneto-hydrodynamic solutions can only be attained with the aid of numerical simulations. However, for the system at hand, the qualitative effect of magnetic induction can be understood from simple theoretical considerations. As we already argued, the two characteristic states of Hot Jupiter atmospheric circulation are a zonally-dominated state and a meridionally-dominated state (Showman et al. 2011). Whether or not a given configuration will be significantly affected by the introduction of the magnetic field can be established by analyzing its stability. More specifically, we can work within a purely kinematic (rather than dynamic) framework to understand if the Lorentz force acts to perturb the flow away from its hydrodynamic counterpart or simply damps the circulation. Zonal Flows. -Although not directly applicable, recent studies of Ohmic dissipation that arises from zonal flows performed by Liu et al. (2008) (within the context of solar system gas giants) and by Batygin & Stevenson (2010) as well as Menou (2012) (within the context of Hot Jupiters) have already produced some results on a related problem. Here we work in the same spirit as these studies and prescribe the following functional form to the zonal flow to approximately represent three jets, such as those shown in panel C of Figure (3): where ˜ v 0 is a negative constant, whose magnitude corresponds to the peak wind speed. This prescription triv- ally satisfies the continuity equation (3), although we note that a more realistic zonal flow should also exhibit differential rotation. The interaction between this flow and the background magnetic field (13) will induce a field B ind in the atmosphere. Because B dip is entirely poloidal, and ˜ v is strictly toroidal, B ind will also be strictly toroidal (Moffatt 1978). As can be readily deduced from equation (10), this means that B ind cannot interact with ˜ v to further induce new field unless ˜ v deviates from a purely zonal flow. As a result, in steady state, the induction equation reads: It is noteworthy that had we chosen to represent a single broad jet (such as that seen in most 3D simulations (Showman et al. 2008; Menou & Rauscher 2010; Rauscher & Menou 2013)) by setting ˜ v ∝ sin( θ ) (in this case ˜ v 0 is positive), equation (28) would have looked the same, with the exception of the coefficient on the RHS, which would have been 2 instead of 6. As a result, it should be kept in mind that the following kinematic solution applies to the case of a single jet as well. φ (deg) The angular part of equation (28) is satisfied by the expression where A ( r ) is a yet undefined function. This form ensures that the meridional component of the induced current vanishes at the poles. Meanwhile, the radial impenetrability of the boundaries requires A ( R ) = A ( R + H ) = 0 as dictated by equation (12). With these boundary conditions, equation (28) can be solved to yield The induced field and the associated electrical current are shown in panel A of Figure (5). r r The Lorentz force that arises from the interactions between B ind and B dip takes the form Because the Lorentz force acts in the same sense as the flow itself (that is, F L × ˜ v = 0), it can only act to accelerate/decelerate the jets but not alter their directions. Indeed, the functional form of F L is that of a Rayleigh drag (equation 15), however the characteristic timescale is non-uniform in latitude and radius i.e. τ L = f ( r, θ ). The non-uniformity we derive here should not be confused with the variability in F L that can arise from the spatial dependence of the electrical conductivity (see Rauscher & Menou (2013)). It is noteworthy that the radial dependence of F L can give rise to differential rotation. However, this is not particularly important, since in some similarity with the above discussion, differential rotation will only induce toroidal fields through the ω -effect (Moffatt 1978) and will therefore only change the solution obtained here on a detailed level (i.e. the added dependence of ˜ B on r will subtly modify the function A ( r )). In other words, a differentially rotating zonal flow still results in a purely toroidal induced field. For a sensible comparison with previous works (e.g. (Perna et al. 2010; Menou 2012; Rauscher & Menou 2012)) and the simple theory presented in the previous section, it is instructive to evaluate the maximal magnitude of F L , which corresponds to the upper and lower boundaries of the domain in question 8 i.e. r = R , r = R + H . To leading order in χ , the expression reads: From this expression it is clear that F L acts primarily in the mid-latiudes rather than the equator. As a result, the damping of the jets is latitudinally differential, meaning that even if the flow is initially composed of multiple bands (as we consider here), it will approach a single equatorial jet as the conductivity and/or the magnetic field is increased. Furthermore, recall that the functional form of equation (32) is also valid in the case of a single jet. Qualitatively, this seems to imply that the Lorentz force acts to collimate the jet towards the equator. Such an effect is sensible given that the radial component of the field is stronger as one approaches the pole for a simple dipole. However, it should also be kept in mind that a true planetary magnetic field might be more complicated, leading to further lack of triviality in the circulation. Dayside-to-Nightside Flows. -Let us now consider the more topologically complex interaction between meridional flows and a spin-pole aligned dipole magnetic field. As in section (3.1) we shall work in a coordinate frame where the polar axis intersects the sub-solar point and is directed at the host star. Unlike the case of zonal circulation, this configuration has no exploitable symmetry. Consequently, a simple solution to the steady-state induction equation (28) is difficult, if not impossible, to obtain. We shall therefore make substantial simplifications. In our prescription for the velocity field, we neglect radial flow altogether (thereby violating continuity) and adopt an expression similar to equation (27): Because of our choice of coordinate system, equation (13) cannot be used directly. However, keeping in mind 8 Although the Lorentz force is equal and opposite at r = R and r = R + H , its radial distribution is such that its vertically integrated value acts to oppose the flow on average. that the background dipole field originates in a much deeper region of the planet than the atmosphere, we can write down the magnetic field in a current-free representation (Jackson 1998): As in Batygin & Stevenson (2010), we assume that the induction term is dominated by the interaction with the background field, rather than the induced field: (˜ v × B ) glyph[similarequal] (˜ v × B dip ). Upon making this simplification and uncurling equation (10), the steady state induction equation reduces to Ohm's law: where ∇ Φ is the electric field. Because the current is necessarily divergence-free, the scalar potential Φ can be obtained from the following equation: It can be easily checked that the angular part of this relationship is satisfied by: As before, confining the current to the atmosphere implies the boundary conditions: k m ˜ v 0 = R 3 A ( R ) = ( R + H ) 3 A ( R + H ). In turn, the radial part of the solution reads: The induced current density can now be obtained through Ohm's law. The Lorentz force can be approximated as originating from the interactions between the induced current and the background magnetic field. The resulting expression is quite cumbersome. However, all of the important features of F L can be seen by evaluating it at the center of the dynamic domain. To leading order in χ , the expression takes the form: Asimilar evaluation of F L at r = R and r = R + H shows that the ˆ r and ˆ φ components of the force do not change significantly with radius, although the ˆ θ component does. Indeed, the Lorentz force that arises from the interactions between the dayside-to-nightside circulation and the background magnetic field does not only oppose the flow. Instead, it acts to introduce both radial and zonal components to the circulation. Importantly, the typical magnitude of the zonal component of F L is commensurate with the meridional component (although of course their spatial dependence is different). As argued in section (3.1), the characteristic timescale associated with the Lorentz force is comparable to the radiative timescale at mbar pressures and is generally shorter than that, corresponding to other relevant forces. This means that the force-balance implied by equations (17) is in essence not relevant to circulation on hot planetary atmospheres. In summary, we conclude that dayside-to-nightside flow is unstable to perturbations arising from the Lorentz force. Consequently, we expect that the upper atmospheric circulation will change qualitatively once a substantial magnetic field is introduced into the system. We now turn our attention to numerical MHD simulations with the aim of testing this presumption and quantifying the dynamical state of magnetized upper atmospheres of Hot Jupters.\",\n \"pages\": [\n 9,\n 10,\n 11\n ]\n },\n {\n \"title\": \"4.2. Magnetohydrodynamic Simulations\",\n \"content\": \"The hydrodynamic simulation parameters are chosen as described in section (2), corresponding to the P = 1mbar pressure level (i.e. τ L = 10 3 sec.). We start out with the equilibrated hydrodynamic flow shown in panel A of Figure (3) and introduce a weak pole-aligned dipole magnetic field into the system. Upon equilibration, we take the approach of sequentially increasing the magnitude of B dip . At each step, we allow the flow to reach a steady state before increasing the field strength further. We have checked that the flows obtained by successive enhancement of B dip are identical to those obtained by initializing the atmosphere in solid-body rotation with a given value of B dip . Consequently, in agreement with Liu & Showman (2012), we conclude that the obtained flows are insensitive to initial conditions. The panels of Figure (6) show the upper atmospheric circulation for a series of magnetic field strengths. From this series of results, a clear pattern emerges: as the magnitude of B dip is increased, the flow takes on an exclusively zonal character. Specifically, it is clear that the circulation patterns characteristic of | B dip | = 0 . 33 G (panel B) are already markedly different from the | B dip | = 0 . 025 G case (panel A), which clearly resembles the unmagnetized circulation. The flow is in essence entirely azimuthal once the field is increased to | B dip | = 0 . 5 G (panel C). This is in contrast to the non-uniformly dragged simulations of Rauscher & Menou (2013), who find the flow to become less zonally-dominated with enhanced field strength. It is noteworthy that the flow speeds up once it takes on a zonal nature. This is almost certainly due to the fact that viscosity acting on vertical motion more strongly affects the divergent flow, and is therefore not a physically significant result. Increasing the field strength further diminished the flow velocities but did not alter the qualitative nature of the solution, although somewhat higher values of the Ekman number were required to ensure numerical stability. At the expense of a great inflation in the required computational time, we have extended the simulations presented in Figure (6) to higher resolution. Namely, we prolonged the spherical harmonic decomposition up to degree glyph[lscript] max = 34 and m max = 29 while eliminating hyperviscosity from our runs entirely. Aside from a mild (i.e. few percent) increase in the velocities, the results observed in these simulations were largely unchanged from the nominal simulations. This implies that the presented solutions do not depend sensitively on small-scale flows. In other words, the transition of the atmosphere to a state dominated by zonal jets is a result of interactions between global circulation and the large-scale magnetic field. Provided the zonal nature of the flow observed in the magnetized simulation, we can expect that the induced field will be almost entirely toroidal and will approximately be described by equations (29) and (30). As shown in Figure (5), this indeed appears to be the case. The numerically obtained azimuthal component of the field (panel B) is qualitatively similar to its analytically computed counterpart (panel A), although the field lines are concentrated towards the vicinity of the equator in the numerical solution (this is simply a consequence of the fact that the circulation is not exactly given by the expression (27)). The magnitude of the induced field is also in good agreement with the analytical theory. For ˜ v 0 = 440 m/s, and k m / R 3 = 0 . 5 G, equation (29) yields max(B ind ) = 0 . 64 G, where as the numerically computed value is max(B ind ) = 0 . 52 G. Unlike the case considered in the previous section (where the Lorentz force is treated as a drag), within the framework of MHD simulations, the relationship between the peak wind speed and the temperature perturbation is not necessarily simple. Consequently, in order to preliminarily explore the sensitivity of our results on irradiation, we performed an additional suite of simulations where the applied heat flux was enhanced by a factor of three, compared to the simulations shown in Figure (6). In these overdriven simulations, we found the peak wind speeds to be a factor of ∼ 2 -2 . 5 higher. However, the characteristic flow patterns closely resembled those, shown in Figure (6) and specifically, the circulation with | B dip | = 0 . 5 G remained dominated by azimuthal jets. Consequently, we conclude that the transition of the circulation to a zonal regime with increasing magnetic field strength is robust within the context of our model. It is interesting to note that the zonal nature of the circulation is ensured at a comparatively low magnetic field strength. If we adopt a scaling based on an Elsasser number of order unity (Stevenson 2003), typical hot Jupiter magnetic fields should exceed that of Jupiter by a factor of a few e.g. | B dip | ∼ 10 G. Moreover, the arguably more physically sensible scaling based on the intrinsic energy flux (Christensen et al. 2009) suggests that typical hot Jupiter fields may be still higher by another factor of ∼ 5. Cumulatively, this places the critical magnetic field needed for the onset of zonal flows a factor of ∼ 10 -100 below the typical field strengths. As a result, it would be surprising if a more sophisticated treatment of the hydrodynamics and radiative transfer proved the critical field strength to be higher than the typical one. Nevertheless, such simulations should no doubt be performed.\",\n \"pages\": [\n 11,\n 12\n ]\n },\n {\n \"title\": \"5. DISCUSSION\",\n \"content\": \"In this paper, we have characterized the nature of atmospheric circulation on Hot Jupiters, in a regime where magnetic effects play an appreciable role. We began by performing baseline Boussinesq hydrodynamical simulations and augmenting them to crudely account for the Lorentz force by expressing it in the form of a Rayleigh drag. Using a simple analytical theory, we showed that within the framework of such a treatment, the interactions between the circulation and the background magnetic field lead to a well-formulated reduction in wind velocities. However, in agreement with published literature (Perna et al. 2010; Rauscher & Menou 2012) and dragged simulations of our own, we noted that regardless of the background field strength, the functional form of the upper-atmospheric stream function remains characteristic of a flow pattern where wind originates at the substellar point and blows towards the anti-stellar points quasi-symmetrically over the terminator (see also Showman et al. (2008)). Although simplifying, the assumption that the Lorentz force (even approximately) opposes the flow everywhere, as done by a Rayleigh drag, appears inappropriate for dayside-to-nightside circulation. Consequently, relying on theoretical considerations based on a kinematic treatment of magnetic induction (Moffatt 1978), we showed that if the Lorentz force is not reduced to a form of a drag, dayside-to-nighside flows become unstable in presence of a spin pole aligned magnetic field. On the contrary, the interactions between zonal jets and the background magnetic field do not give rise to meridional or radial flows, thanks to an inherent symmetry. Instead, the jets are stably damped by the background field (Liu et al. 2008; Menou 2012). However, the damping rate generally need not be latitudinally uniform. As demonstrated by magnetohydrodynamical simulations, this has profound implications for upperatmospheric circulation. Specifically, the MHD calculations indicate that once the background magnetic field is stronger than a critical value, the upper atmospheric circulation transitions from a state dominated by daysideto-nightside flows to an azimuthally symmetric pattern dominated by zonal jets. Qualitatively, this transition can be understood as a point where redistribution of heat from the dayside to the nightside by flow patterns that intersect the magnetic poles ceases to be energetically favorable against purely zonal circulation. For the standard case considered here (that is, τ N = 10 3 sec), the critical field strength is approximately B crit glyph[similarequal] 0 . 5 G, considerably less than the typically inferred field strengths of Hot Jupiters (Christensen et al. 2009). However, it should be understood that the critical field strength must unavoidably depend on various system parameters including the radiative timescale and the electrical conductivity. The variability due to the latter may be particularly important since thermal ionization is extremely sensitive to the atmospheric temperature (see Figure 2). The form of this dependence and the extent to which atmospheres within the current observational aggregate are magnetically dominated merits further investigation. The fact that dayside-to-nightside flows tend to simplify to a zonal state in magnetized atmospheres has a number of important implications. As already discussed to some extent in section (3), axisymmetric flows give rise to exclusively toroidal fields (Moffatt 1978). This means that additional atmospheric dynamo generation, that would act to augment a deep seated field, cannot be supported by large-scale circulation. Moreover, because the induced field lacks a strong poloidal component, its observational characterization is at present hopeless. Consequently, observational inference of magnetohydrodynamic processes in exoplanetary atmospheres is likely to be limited to indirect methods. This discussion overlooks the possibility of field generation by small-scale turbulence (i.e. the α -effect) in the atmosphere. Indeed such a process may be at play if the turbulent magnetic Reynolds number Re t m ≡ ν/η glyph[greaterorsimilar] 1 -10. For highly turbulent atmospheres, this criterion may indeed be satisfied. Our simulations aimed at determining the viability as well as characterization of field generation by small-scale turbulence in Hot Jupiter atmospheres are currently ongoing and will be reported in a follow-up study. In this work, we briefly hinted at the fact that the damping of zonal jets by dipole magnetic fields is not only non-uniform latitudinally but also radially. The radial dependence of the Lorentz force found here is specific to the boundary conditions imposed on the induced current. However, if we do not choose to confine the current to a single scale-height but allow it to penetrate the convective interior of the planet (as for example envisioned within the context of the Batygin & Stevenson (2010) Ohmic dissipation model), the induced toroidal field is free to occupy a much deeper portion of the planet. In such a case, the resulting Lorentz force may act to produce deep-seated azimuthal flows and give rise to largescale differential rotation within the planet (Goldreich private communication). However, the extent to which such differential rotation can persist is subject to a number of constraints, including the magnitude of interior Ohmic dissipation (Liu et al. 2008). In addition to the various simplifications inherent to our model that are already described throughout the paper, it is further noteworthy that we have restricted the morphology of the background magnetic field to a pole-aligned dipole for simplicity. Within the solar system, a dipolar, axisymmetric magnetic field created by an internal dynamo is possessed only by Saturn (Acuna & Ness 1980; Dougherty et al. 2005). On the contrary, Jupiter and the Earth have dipole-dominated fields that are significantly tilted with respect to their spin-axes, while Neptune and Uranus possess rather unusual nondipolar, non-axisymmetric fields (Stevenson 2003). As a result it is quite likely that even on a qualitative level, the discussion presented in this work is not comprehensive. That is, unlike axisymmetric jets found in this work, one could envision the generation of substantial stationary eddies, yielding longitudinally and latitudinally asymmetric jets in exoplanetary atmospheres, by complex background magnetic fields. Furthermore, orbital variations may also be of importance. Specifically, while the assumption of a circular orbit is secure for the majority of hot Jupiters, null eccentricities are certainly not universal to the observational sample (an extreme example is HD80606b (Naef et al. 2001) which has e = 0 . 93). The time-variability of stellar irradiation associated with significant eccentricity produces rather complex circulation patterns even in hydrodynamic regime (Langton & Laughlin 2008; Kataria et al. 2013). However, recalling that electrical conductivity in hot planetary atmospheres arises primarily as a result of thermal ionization, the circulation patterns are likely to be even more complex than those typically envisioned, since magnetic effects in the atmosphere will also be time-dependent. We would like to finish with a few words about observational implications of our results. At present, the resolution and signal to noise of the spectroscopic data aimed at characterizing the temperature structure and chemical composition of exoplanetary atmospheres (Charbonneau et al. 2005; Knutson et al. 2008; Swain et al. 2010) is such that even fits obtained with one-dimensional atmospheric models are susceptible to numerous degeneracies (Madhusudhan & Seager 2009). Consequently, it is unlikely that the qualitative change in the flow structure observed in this work will strongly affect the already-limited interpretation of the information contained within this data, in the near future (Line et al. 2012). On the other hand, theoretical interpretation of observed dayside-to-nightside temperature differences and the associated shifts in the location of the subsolar hot spot (Knutson 2007) rely heavily on a sensible understanding of atmospheric dynamics, which as we have seen requires a more or less self-consistent account of magnetic effects. To this end, the results obtained in this study are of great importance. Indeed, one can expect that the advective transport of heat changes character and weakens with increased electrical conductivity (by extension, the atmospheric temperature) and magnetic field due to the mechanism described above (see also Liu et al. (2008); Perna et al. (2010); Batygin et al. (2011); Menou (2012); Rauscher & Menou (2012)). Thus, a thorough comparison between a substantial sample of model results and data may eventually shed light on the typical atmospheric conductivity structure and field strengths of Hot Jupiters. Such activity would no-doubt further benefit from direct measurements of high-altitude atmospheric wind velocities obtained via ground-based spectroscopy (Snellen et al. 2010). That said, in order for an endeavor of this sort to be meaningful, substantial improvements in theoretical modeling aimed at meliorating the shortcomings outlined above are required, along with a wealth of additional observational data. In conclusion, the above discussion clearly indicates that the degree of complexity of the physical regime in which hot exoplanetary atmospheres reside is indeed very extensive. There is no doubt that much additional work remains. In this work, we have taken an ample step towards a self-consistent characterization of magnetically controlled circulation on Hot Jupiters. As such, this study should serve as a stepping stone for future developments. Acknowledgments . We thank Adam Showman, Tami Rogers, Kristen Menou, Peter Goldreich and Greg Laughlin for useful conversations, as well as the anonymous referee for a thorough and insightful report. K.B. acknowledges the generous support from the ITC Prize Postdoctoral Fellowship at the Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics. S.S. acknowledges funding by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Alfred P. Sloan Foundation.\",\n \"pages\": [\n 12,\n 13,\n 14\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Heng, K. 2012, ApJ, 748, L17\",\n \"pages\": [\n 14\n ]\n }\n]"}}},{"rowIdx":70,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...776..135M"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1308.3160.pdf"},"content":{"kind":"string","value":"\nSubmitted: ApJ, March 03, 2013; Revised: August 09, 2013\nA Preliminary Calibration of the RR Lyrae Period-Luminosity Relation at Mid-Infrared Wavelengths: WISE Data\nBarry F. Madore\nObservatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101\nDouglas Hoffman\nInfrared Processing and Analysis Center 770 South Wilson, Pasadena, CA 91125\nWendy L. Freedman, Juna A. Kollmeier, Andy Monson\nS. Eric Persson, Jeff A. Rich Jr., Victoria Scowcroft, Mark Seibert\nObservatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101\nbarry@obs.carnegiescience.edu, dhoffman@ipac.caltech.edu wendy@obs.carnegiescience.edu, jak@obs.carnegiescience.edu amonson@obs.carnegiescience.edu, persson@obs.carnegiescience.edu jrich@obs.carnegiescience.edu, vs@obs.carnegiescience.edu, mseibert@obs.carnegiescience.edu\nABSTRACT\nUsing time-resolved, mid-infrared data from WISE and geometric parallaxes from HST for four Galactic RR Lyrae variables, we derive the following Population II Period-Luminosity (PL) relations for the WISE[W1], [W2] and [W3] bands at 3.4, 4.6 & 12 µ m, respectively:\nM [ W 1] = -2 . 44 ( ± 0 . 95) × log ( P ) -1 . 26 ( ± 0 . 25) σ = 0 . 10 M [ W 2] = -2 . 55 ( ± 0 . 89) × log ( P ) -1 . 29 ( ± 0 . 23) σ = 0 . 10 10\nM [ W 3] = -2 . 58 ( ± 0 . 97) × log ( P ) -1 . 32 ( ± 0 . 25) σ = 0 .\nThe slopes and the scatter around the fits are consistent with a smooth extrapolation of those same quantities from previously-published K-band observations at 2.2 µ m, where the asymptotic (long-wavelength) behavior is consistent with a Period-Radius relation having a slope of 0.5. No obvious correlation with metallicity (spanning 0.4 dex in [Fe/H]) is found in the residuals of the four calibrating RR Lyrae stars about the mean PL regression line.\nSubject headings: Stars: Variables: RR Lyrae stars- Stars: Variables: W Virginis stars\n1. Introduction\nThe advantages of moving the Population I calibration of the Classical Cepheid PeriodLuminosity relation (the Leavitt Law) from the optical to the infrared were outlined some three decades ago by McGonegal et al. (1983), and they have been borne out repeatedly over the years, as reviewed and elaborated upon by Freedman & Madore (2010). But only now is it possible to extend these same advantages to the parallel path offered by the Population II variable stars (the short-period RR Lyrae variables and their longer-period siblings the W Virginis stars). Two impressive accomplishments have made this possible: (1) the completion of the WISE mission (Wright et al. 2010) and the release of its sky survey of point sources measured in the mid-infrared in four bands ranging from 3.4 to 22 µ m, and then (2) the innovative application of the HST Fine-Guidance Sensor ( FGS ) cameras to the\ndetermination of trigonometric parallaxes to four field RR Lyrae variables by Benedict et al. (2011).\nThe many, now well-known, advantages of calibrating and using period-luminosity relations in the mid-IR include the following: (1) the effects of line-of-sight extinction are reduced with respect to optical observations by at least an order of magnitude for even the shortest wavelength ([W1] at 3.4 µ m) observations, (2) concerns about the systematic impact of the possible non-universality of the reddening law are similarly reduced by going away from the optical and into the mid-IR, (3) the total amplitude of the light variation of the target star during its pulsation cycle is greatly reduced because of the largely diminished contribution of temperature variation to the change in surface brightness, in comparison to the much smaller (but essentially irreducible) wavelength-independent radius/areal variations, (4) the corresponding collapse in the width (i.e., intrinsic scatter) of the period-luminosity relations, again because of the reduced sensitivity of infrared luminosities to temperature variations (across the instability strip), combined with the intrinsic narrowness of the residual periodradius relations. And finally, (5) at mid-infrared wavelengths, for the temperatures and surface gravities encountered in Population I & II Cepheids and RR Lyrae stars, there are so few metallic line or molecular transitions in those parts of the spectrum that atmospheric metallicity effects are expected to have minimal impact on the calibration. 1 This is especially true for the RR Lyrae stars which are significantly hotter than their longer-period (cooler) Cepheid counterparts.\nAs described in Freedman et al. (2012), the Carnegie Hubble Program (CHP) is designed to minimize and/or eliminate the remaining known systematics in the measurement of the Hubble constant using mid-infrared data from NASA's Spitzer Space Telescope . Here we broaden the base in two distinct ways: (a) the incorporation of WISE mid-infrared data and (b) the preliminary calibration of the Population II RR Lyrae variables as mid-infrared distance indicators. This new initiative is known as the Carnegie RR Lyrae Program (CRRP).\n2. The Calibrators: WISE Observations\nWISE conducted an all-sky survey at four mid-infrared wavelengths, 3.4, 4.6, 12 and 22 µ m (W1, W2, W3 and W4, hereafter). As such all of the RR Lyrae variables having trigonometric parallaxes (Benedict et al. 2011) were also observed by the satellite. By design, the slowly precessing orbit of WISE, allowed the satellite to scan across every object on the sky at least 12 times (with progressively more coverage at higher ecliptic latitudes). These successive observations were obtained within a relatively narrow window of time (over about 18 hours for those fields nearest the ecliptic equator) with each observation being separated by about 90 minutes (the orbital period of the satellite). Fortuitously RR Lyrae stars have periods that are generally less than 16 hours, meaning that even the sparsest of these multiple mid-infrared observations covered at least one full pulsational cycle of these particular variable stars.\nThe light curves based on the time-resolved WISE observations of our calibrating stars are shown in Figures 1 & 2 for the four RR Lyrae variables, SU Dra , RR Lyr , XZ Cyg , & UV Oct . These stars were observed by WISE 51, 23, 24 and 23 times, respectively. Data were retrieved from the WISE All-Sky Single Exposure (L1b) Source Table, which is available at the Infrared Science Archive (http://irsa.ipac.caltech.edu/Missions/wise.html). The source positions were queried with a 2.5 arcsec cone search radius, ignoring observations flagged as contaminated by artifacts. The observations are very uniformly distributed around the cycle and the resulting light curves are exceedingly well defined. All three of the shortest-wavelength light curves show convergence in their properties, exemplified by their mutual phases, shapes and amplitudes 2 . As expected these light curves closely track the anticipated light variations due to surface-area variations of the star, where at these wavelengths the sensitivity of the surface brightness to a temperature variation is much diminished as compared to its sensitivity at optical wavelengths. This then fully accounts for the mutual phasing (tracking the radius variations, and not the off-set temperature variations), the shape (the cycloid-like radius variation, in contrast to the highly asymmetric color/temperature variation) and the low amplitude (around 0.3 mag, peak-to-peak, in line with the small, radius-induced cyclical change in surface area of these stars).\nThe non-parametric fitting methodology, GLOESS was used to derive intensity-averaged magnitudes and amplitudes, as given in Table 1 (see Persson et al. 2004 for a description\nand an early application of this fitting technique).\n3. RR Lyrae Period-Luminosity Relations\nTable 1 contains the parameters needed to compute absolute mean magnitudes. The parallaxes, E(B-V) reddenings, and Lutz-Kelker-Hanson (LKH; Lutz and Kelker 1973; Hanson 1979) corrections as taken from Benedict et al 2011, are listed for convenience. We have converted the A V extinctions listed by Benedict et al. (2011) to those in the W1 and W2 bands using the Yuan et al. (2011) compilation of A WISE /E(B-V) results with A V /E(B-V) = 3.1. Indebetouw et al. (2005) give values of A Spitzer / A K 3 , which we converted to A WISE / A V via the Cardelli et al.(1989) law. The values of A WISE /A V given by Yuan et al. (2011) and our pseudo-values from Indebetouw et al. (2005) agree well. Neither the Yuan et al. (2011) nor Indebetouw et al. (2005) results extend to the W3 band, and here we have referred to Fitzpatrick (1999) for an approximate value. The extinctions for the four stars are so small as to make no difference to the absolute magnitude values and we take A W 3 /A V to be 0.01. The adopted mid-IR extinctions A WISE /A V we adopt are 0.065, 0.052, and 0.01 for W1, W2, and W3, respectively. The adopted mid-IR extinctions A WISE /E(B-V) are also given in Table 1. The above parameters and our observed mean magnitudes lead to the W1, W2, and W3 absolute magnitudes in Table 1 4 . and the Period-Luminosity relations for RR Lyrae variables follow:\nM [ W 1] = -2 . 44 ( ± 0 . 95) × log ( P ) -1 . 26 ( ± 0 . 25) σ = 0 . 10 M [ W 2] = -2 . 55 ( ± 0 . 89) × log ( P ) -1 . 29 ( ± 0 . 23) σ = 0 . 10 10\nM [ W 3] = -2 . 58 ( ± 0 . 97) × log ( P ) -1 . 32 ( ± 0 . 25) σ = 0 .\nThe absolute magnitude values and the respective fits to the first two WISE bands and as well as K-band data (from Benedict et al. 2011 and Dall'Ora et al. 2004, respectively) are shown in Figure 3. Despite the very small (less than a factor of two) range in period covered by RR Lyrae stars, the PL relations are well defined, largely because of their intrinsically small scatter. The intrinsic scatter is especially well illustrated by the K-band PL relation,\nwhere we also show the RR Lyrae data of Dall'Ora et al. for 21 fundamental-mode RR Lyrae stars in the well-populated LMC globular cluster, Reticulum (shifted by 18.47 mag). A comparison of these two datasets is very illuminating. The slope of the adopted PL relation at K and the total width of it, as defined by the two samples, are for all intents and purposes, identical. The very good agreement in these two independently-determined slopes and the small dispersion in each of the datasets suggest that the means of the Milky Way variables are already well constrained even though the Galactic calibrating sample itself is currently very small.\nOn the other hand, we note that the small (observed) scatter of the Milky Way RR Lyrae variables around each of the adopted PL relations is apparently at variance with the individually quoted error bars for each of the calibrating variables. That is, the formal scatter of ± 0 . 10 mag in the WISE PL relations is to be compared with the quoted parallax errors on the individual distance moduli of ± 0 . 22, ± 0 . 16, ± 0 . 25 and ± 0 . 07 mag for XZ Cyg, UV Oct, SU Dra and RR Lyr, respectively. The average scatter for the variables ( ± 0 . 18 mag) is then about two time larger that their observed scatter around the PL fit. This suggests that the published errors may be somewhat overestimated. There are independent data that support this assertion. The 10 Galactic Cepheids for which Benedict et al. (2010) obtained parallaxes, using the same instrument, telescope and reduction methodology have individually quoted internal errors in their true distance moduli ranging from ± 0 . 11 to ± 0 . 30 mag. Their average uncertainty is ± 0 . 19 mag, and yet, once again, as with the RR Lyrae variables the PL fit to these data yields a formal dispersion of only ± 0 . 10 mag. In both cases the observed dispersions, for the Galactic samples, are in total agreement with independently determined dispersions for the much more robustly determined dispersions for the LMC samples. We suggest therefore that the random errors reported for the HST parallaxes for both the Cepheids and for the RR Lyrae variables may have been over-estimated. This is not simply of academic interest. If the observed scatter is used to calculate the systematic uncertainty in the calibration of the RR Lyrae PL relation that uncertainty would be 0 . 10 / √ 4 = ± 0 . 05 mag, a 2-3% error in the Population II distance scale. However, if the quoted errors on the individual distance moduli are used, then the uncertainty rises to 0 . 18 / √ 4 = ± 0 . 09 mag, a 5% error. Similar conclusions would also apply to the base uncertainty in the Cepheid distance scale using the Benedict sample; is the uncertainty in the Galactic Cepheid zero point 1.6% in distance, or is it 3.0%? It is therefore important to note that in their first paper discussing the use of FGS on HST , Benedict et al. (2002) state that the 'standard deviations of the HST and Hipparcos data points may have been overstated by a factor of ∼ 1.5.' and since the Hipparcos errors had been subjected to many confirming tests '... that it is likely that the HST errors are overstated.' Parallaxes from Gaia are anxiously awaited; they will improve the number of calibrators by orders of magnitude and convincingly set the zero point.\nIn Figure 3 we show, using thick vertical lines, the full magnitude of the LKH corrections as published by Benedict et al (2011) and applied to the true distance moduli used here. It is noteworthy that, if these corrections had not been applied, the dispersion in the data points around the fit would have exceeded the independently determined dispersion from the Reticulum data, and the slope of the Milky Way solution would have been more shallow than the LMC slope. We take the final agreement of both the slopes and the dispersions to suggest that the individually determined and independently-applied LKH corrections are appropriate.\nFinally, it needs to be noted that Klein et al. (2011) have published slopes that are much shallower than the ones derived here (e.g., -1.7 compared to our -2.6). This is because in their Bayesian analysis they chose to leave the overtone pulsators in the global solution, without correcting them to their equivalent fundamental periods. We have recomputed the slopes from their data after applying the appropriate period shift to the overtones, and those PL slopes are plotted in Figure 4. Their slopes and ours now agree well within the errors, but they are still systematically somewhat shallower than our solutions.\n4. The Run of PL Slope with Wavelength\nFor Cepheids it is well known that the slope of the PL relation is a monotonically increasing function of wavelength. In Figure 4 we show that the same overall trend is now made explicit for the first time for the RR Lyrae variables as well, and for the same physical reasons. As one moves from shorter to longer wavelengths one is moving from PL relations where the slope is dominated by the trend of decreasing temperature (i.e., decreasing surface brightness) with period, to relations that are dominated by the opposing run of increasing mean radius with period. The plotted slopes of the optical and nearinfrared PL relations are representative of a variety of published studies (e.g, Catelan, Pritzl & Smith 2004, Benedict et al. 2011, Dall'Ora et al. 2004) while the mid-IR slopes are from this study. As the relative contribution from the temperature-sensitive surface brightness drops off with wavelength, the observed slope is expected to asymptotically approach the wavelength-independent (geometric) slope of the Period-Area relation. That behavior is indeed seen in Figure 4. Moreover the level at which the plateau is occurring would suggest that the period-radius relation of Burki & Meylan (1986) (giving a slope of -2.60, based on Baade-Wesselink studies) is marginally preferred over the period-radius (slope = -3.25) and\nperiod-radius-metallicity (slope = -2.90) solutions given by Marconi et al. (2005) 5\nFrom a practical point of view it is not immediately clear what advantage the increased slope of the long-wavelength PL relations would have to offer applications to the distance scale, until it is realized that increased slope in the PL relation is causally and physically connected to decreased width (i.e., decreased intrinsic scatter and therefore increased precision) in the PL relation as proven in the general case by Madore & Freedman (2012). This effect can be seen for the RR Lyrae variables in Figure 2 of Catelan, Pritzl & Smith (2004), and it is apparent here in Figure 3 where the scatter has already reached a minimum in the K-band where simultaneously the plateau in slope (seen in Figure 4) is very nearly complete.\n5. A First Test of the Metallicity Dependence in the Mid-IR\nIn Figure 5 we plot the measured magnitude residuals from the [W1] 3.4 µ m PL relation versus the published metallicities of the four RR Lyrae stars in our sample, as given in Table 1 of Benedict et al. (2011). The RR Lyrae stars only sample a 0.4 dex range in [Fe/H] so the test is not a strong one, but there is clearly no significant dependence of the already small magnitude residuals on metallicity.\n6. Conclusions\nAs can be dramatically seen in the study of Catelan, Pritzl & Smith (2008, especially their Figure 2) operating anywhere in the near to mid-infrared, from H = 1.6 µ m (accessible to HST ) to 3.6 µ m (accessible to Spitzer now, and with JWST in the near future) will each accrue the benefits of low scatter and ever decreasing sensitivity (with wavelength) to line-of-sight extinction. Collecting power, availability and spatial resolution will determine which of these instruments will be used at any given time. But suffice it to say that the Population II RR Lyrae variables are proving themselves to be a powerful means of establishing an independent, highly precise and accurate distance scale that is completely decoupled in its systematics from the Population I Cepheid path to the extragalactic distance scale and\nthe Hubble constant.\nThis work is based in part on observations made with the Wide-field Infrared Survey Explorer (WISE), which was is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. This research also made use of the NASA/IPAC Extragalactic Database (NED) and the NASA/ IPAC Infrared Science Archive (IRSA), both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We thank Fritz Benedict for numerous frank and useful communications. The referee was especially helpful in bringing this paper to a more correct and fruitful completion.\nReferences\n
\n\n
\nXZCyg, P = 0.466584 days\n\n\n
Fig. 1.- WISE Mid-Infrared light curves for XZ Cyg (upper panel) and UV Oct (lower panel) phase-folded over two and a half cycles using the periods given in the titles. GLOESS fits are shown as solid black lines.
\n\nRRLyr, P = 0.566826 days\n\n\n
Fig. 2.- WISE Mid-Infrared light curves for RR Lyr (upper panel) and SU Dra (lower panel) phase-folded over two and a half cycles using the periods given in the titles. GLOESS fits are shown as solid black lines.
\n\n\n\n
Fig. 3.RR Lyrae PL relations in the K-band (top) and the two WISE bands [W1] (middle and [W2] bottom. The K-band relation also contains data from Dall'Ora et al. (2004) for the LMC globular cluster, Reticulum, shifted by 18.47 mag. (This distance modulus shift is remarkably close to the independentlydetermined true modulus of 18.48 mag recently reported by Monson et al. 2012 for the LMC Cepheid mid-infrared distance modulus.) The Reticulum data are shown only for the RRab (fundamental) pulsators, and are presented here to illustrate that they are consistent in slope and scatter in comparison with the Galactic calibration. A detailed discussion of Reticulum will be given in a forthcoming paper (Monson et al. 2013). The solid lines flanking each of the fitted PL relations are each separated by two sigma from their respective ridge lines. Despite the small numbers of stars represented here the full width of the PL relation in each of the bands is well defined. The solid vertical lines to the right of each of the [W1] data points
\n\n\n\n
Fig. 4.The expected monotonic increase of the slope of the RR Lyrae Period-Luminosity relation as a function of increasing wavelength. The asymptotic behavior of the slope, approaching a value of about -2.6 indicates that the PL relation is converging on the Period-Radius relation, as theory would predict, given that the sensitivity of the surface brightness to temperature rapidly drops as one progressively moves into the infrared. The open diamonds are the slopes published by Klein et al. (2011); the filled (red) diamonds indicate the 'fundamentalized' slopes (where we have corrected the periods of the overtone pulsators to their corresponding fundamental periods by adding 0.127 to the log of their observed periods, as in Dall'Ora et al. 2004), based on the data published by Klein et al. (2011) and re-fit for this paper. The optical and near-infrared PL relation slopes are from Catelan, Pritzl & Smith (2004), Benedict et al. (2011) and Sollima, Cacciari & Valenti al. (2006), while the mid-IR slopes are from this study. The equivalent slopes derived from Period-Radius relations are from Burki & Meylan (1986; BM86) and Marconi et al. (2005; M05).
\n\n\n\n
Fig. 5.- Mid-Infrared [W1] (3.4 µ m) deviations from the mean Period-Luminosity relation as a function of metallicity. The currently available sample is small, and the metallicity range is limited. No obvious correlation is seen.
\n\n
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Table 1. Mid-Infrared (WISE) Magnitudes for Galactic RR Lyrae Variables
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Table 2. WISE Observations of RR Lyrae
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Table 3. WISE Observations of SU Draconis
\n
\n
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Table 4. WISE Observations of UV Oct
\n
\n
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Table 5. WISE Observations of XZ Cyg
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Table 5-Continued
\n
\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"Using time-resolved, mid-infrared data from WISE and geometric parallaxes from HST for four Galactic RR Lyrae variables, we derive the following Population II Period-Luminosity (PL) relations for the WISE[W1], [W2] and [W3] bands at 3.4, 4.6 & 12 µ m, respectively: The slopes and the scatter around the fits are consistent with a smooth extrapolation of those same quantities from previously-published K-band observations at 2.2 µ m, where the asymptotic (long-wavelength) behavior is consistent with a Period-Radius relation having a slope of 0.5. No obvious correlation with metallicity (spanning 0.4 dex in [Fe/H]) is found in the residuals of the four calibrating RR Lyrae stars about the mean PL regression line. Subject headings: Stars: Variables: RR Lyrae stars- Stars: Variables: W Virginis stars","pages":[2]},{"title":"Barry F. Madore","content":"Observatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101","pages":[1]},{"title":"Douglas Hoffman","content":"Infrared Processing and Analysis Center 770 South Wilson, Pasadena, CA 91125","pages":[1]},{"title":"S. Eric Persson, Jeff A. Rich Jr., Victoria Scowcroft, Mark Seibert","content":"Observatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101 barry@obs.carnegiescience.edu, dhoffman@ipac.caltech.edu wendy@obs.carnegiescience.edu, jak@obs.carnegiescience.edu amonson@obs.carnegiescience.edu, persson@obs.carnegiescience.edu jrich@obs.carnegiescience.edu, vs@obs.carnegiescience.edu, mseibert@obs.carnegiescience.edu","pages":[1]},{"title":"1. Introduction","content":"The advantages of moving the Population I calibration of the Classical Cepheid PeriodLuminosity relation (the Leavitt Law) from the optical to the infrared were outlined some three decades ago by McGonegal et al. (1983), and they have been borne out repeatedly over the years, as reviewed and elaborated upon by Freedman & Madore (2010). But only now is it possible to extend these same advantages to the parallel path offered by the Population II variable stars (the short-period RR Lyrae variables and their longer-period siblings the W Virginis stars). Two impressive accomplishments have made this possible: (1) the completion of the WISE mission (Wright et al. 2010) and the release of its sky survey of point sources measured in the mid-infrared in four bands ranging from 3.4 to 22 µ m, and then (2) the innovative application of the HST Fine-Guidance Sensor ( FGS ) cameras to the determination of trigonometric parallaxes to four field RR Lyrae variables by Benedict et al. (2011). The many, now well-known, advantages of calibrating and using period-luminosity relations in the mid-IR include the following: (1) the effects of line-of-sight extinction are reduced with respect to optical observations by at least an order of magnitude for even the shortest wavelength ([W1] at 3.4 µ m) observations, (2) concerns about the systematic impact of the possible non-universality of the reddening law are similarly reduced by going away from the optical and into the mid-IR, (3) the total amplitude of the light variation of the target star during its pulsation cycle is greatly reduced because of the largely diminished contribution of temperature variation to the change in surface brightness, in comparison to the much smaller (but essentially irreducible) wavelength-independent radius/areal variations, (4) the corresponding collapse in the width (i.e., intrinsic scatter) of the period-luminosity relations, again because of the reduced sensitivity of infrared luminosities to temperature variations (across the instability strip), combined with the intrinsic narrowness of the residual periodradius relations. And finally, (5) at mid-infrared wavelengths, for the temperatures and surface gravities encountered in Population I & II Cepheids and RR Lyrae stars, there are so few metallic line or molecular transitions in those parts of the spectrum that atmospheric metallicity effects are expected to have minimal impact on the calibration. 1 This is especially true for the RR Lyrae stars which are significantly hotter than their longer-period (cooler) Cepheid counterparts. As described in Freedman et al. (2012), the Carnegie Hubble Program (CHP) is designed to minimize and/or eliminate the remaining known systematics in the measurement of the Hubble constant using mid-infrared data from NASA's Spitzer Space Telescope . Here we broaden the base in two distinct ways: (a) the incorporation of WISE mid-infrared data and (b) the preliminary calibration of the Population II RR Lyrae variables as mid-infrared distance indicators. This new initiative is known as the Carnegie RR Lyrae Program (CRRP).","pages":[2,3]},{"title":"2. The Calibrators: WISE Observations","content":"WISE conducted an all-sky survey at four mid-infrared wavelengths, 3.4, 4.6, 12 and 22 µ m (W1, W2, W3 and W4, hereafter). As such all of the RR Lyrae variables having trigonometric parallaxes (Benedict et al. 2011) were also observed by the satellite. By design, the slowly precessing orbit of WISE, allowed the satellite to scan across every object on the sky at least 12 times (with progressively more coverage at higher ecliptic latitudes). These successive observations were obtained within a relatively narrow window of time (over about 18 hours for those fields nearest the ecliptic equator) with each observation being separated by about 90 minutes (the orbital period of the satellite). Fortuitously RR Lyrae stars have periods that are generally less than 16 hours, meaning that even the sparsest of these multiple mid-infrared observations covered at least one full pulsational cycle of these particular variable stars. The light curves based on the time-resolved WISE observations of our calibrating stars are shown in Figures 1 & 2 for the four RR Lyrae variables, SU Dra , RR Lyr , XZ Cyg , & UV Oct . These stars were observed by WISE 51, 23, 24 and 23 times, respectively. Data were retrieved from the WISE All-Sky Single Exposure (L1b) Source Table, which is available at the Infrared Science Archive (http://irsa.ipac.caltech.edu/Missions/wise.html). The source positions were queried with a 2.5 arcsec cone search radius, ignoring observations flagged as contaminated by artifacts. The observations are very uniformly distributed around the cycle and the resulting light curves are exceedingly well defined. All three of the shortest-wavelength light curves show convergence in their properties, exemplified by their mutual phases, shapes and amplitudes 2 . As expected these light curves closely track the anticipated light variations due to surface-area variations of the star, where at these wavelengths the sensitivity of the surface brightness to a temperature variation is much diminished as compared to its sensitivity at optical wavelengths. This then fully accounts for the mutual phasing (tracking the radius variations, and not the off-set temperature variations), the shape (the cycloid-like radius variation, in contrast to the highly asymmetric color/temperature variation) and the low amplitude (around 0.3 mag, peak-to-peak, in line with the small, radius-induced cyclical change in surface area of these stars). The non-parametric fitting methodology, GLOESS was used to derive intensity-averaged magnitudes and amplitudes, as given in Table 1 (see Persson et al. 2004 for a description and an early application of this fitting technique).","pages":[4,5]},{"title":"3. RR Lyrae Period-Luminosity Relations","content":"Table 1 contains the parameters needed to compute absolute mean magnitudes. The parallaxes, E(B-V) reddenings, and Lutz-Kelker-Hanson (LKH; Lutz and Kelker 1973; Hanson 1979) corrections as taken from Benedict et al 2011, are listed for convenience. We have converted the A V extinctions listed by Benedict et al. (2011) to those in the W1 and W2 bands using the Yuan et al. (2011) compilation of A WISE /E(B-V) results with A V /E(B-V) = 3.1. Indebetouw et al. (2005) give values of A Spitzer / A K 3 , which we converted to A WISE / A V via the Cardelli et al.(1989) law. The values of A WISE /A V given by Yuan et al. (2011) and our pseudo-values from Indebetouw et al. (2005) agree well. Neither the Yuan et al. (2011) nor Indebetouw et al. (2005) results extend to the W3 band, and here we have referred to Fitzpatrick (1999) for an approximate value. The extinctions for the four stars are so small as to make no difference to the absolute magnitude values and we take A W 3 /A V to be 0.01. The adopted mid-IR extinctions A WISE /A V we adopt are 0.065, 0.052, and 0.01 for W1, W2, and W3, respectively. The adopted mid-IR extinctions A WISE /E(B-V) are also given in Table 1. The above parameters and our observed mean magnitudes lead to the W1, W2, and W3 absolute magnitudes in Table 1 4 . and the Period-Luminosity relations for RR Lyrae variables follow: The absolute magnitude values and the respective fits to the first two WISE bands and as well as K-band data (from Benedict et al. 2011 and Dall'Ora et al. 2004, respectively) are shown in Figure 3. Despite the very small (less than a factor of two) range in period covered by RR Lyrae stars, the PL relations are well defined, largely because of their intrinsically small scatter. The intrinsic scatter is especially well illustrated by the K-band PL relation, where we also show the RR Lyrae data of Dall'Ora et al. for 21 fundamental-mode RR Lyrae stars in the well-populated LMC globular cluster, Reticulum (shifted by 18.47 mag). A comparison of these two datasets is very illuminating. The slope of the adopted PL relation at K and the total width of it, as defined by the two samples, are for all intents and purposes, identical. The very good agreement in these two independently-determined slopes and the small dispersion in each of the datasets suggest that the means of the Milky Way variables are already well constrained even though the Galactic calibrating sample itself is currently very small. On the other hand, we note that the small (observed) scatter of the Milky Way RR Lyrae variables around each of the adopted PL relations is apparently at variance with the individually quoted error bars for each of the calibrating variables. That is, the formal scatter of ± 0 . 10 mag in the WISE PL relations is to be compared with the quoted parallax errors on the individual distance moduli of ± 0 . 22, ± 0 . 16, ± 0 . 25 and ± 0 . 07 mag for XZ Cyg, UV Oct, SU Dra and RR Lyr, respectively. The average scatter for the variables ( ± 0 . 18 mag) is then about two time larger that their observed scatter around the PL fit. This suggests that the published errors may be somewhat overestimated. There are independent data that support this assertion. The 10 Galactic Cepheids for which Benedict et al. (2010) obtained parallaxes, using the same instrument, telescope and reduction methodology have individually quoted internal errors in their true distance moduli ranging from ± 0 . 11 to ± 0 . 30 mag. Their average uncertainty is ± 0 . 19 mag, and yet, once again, as with the RR Lyrae variables the PL fit to these data yields a formal dispersion of only ± 0 . 10 mag. In both cases the observed dispersions, for the Galactic samples, are in total agreement with independently determined dispersions for the much more robustly determined dispersions for the LMC samples. We suggest therefore that the random errors reported for the HST parallaxes for both the Cepheids and for the RR Lyrae variables may have been over-estimated. This is not simply of academic interest. If the observed scatter is used to calculate the systematic uncertainty in the calibration of the RR Lyrae PL relation that uncertainty would be 0 . 10 / √ 4 = ± 0 . 05 mag, a 2-3% error in the Population II distance scale. However, if the quoted errors on the individual distance moduli are used, then the uncertainty rises to 0 . 18 / √ 4 = ± 0 . 09 mag, a 5% error. Similar conclusions would also apply to the base uncertainty in the Cepheid distance scale using the Benedict sample; is the uncertainty in the Galactic Cepheid zero point 1.6% in distance, or is it 3.0%? It is therefore important to note that in their first paper discussing the use of FGS on HST , Benedict et al. (2002) state that the 'standard deviations of the HST and Hipparcos data points may have been overstated by a factor of ∼ 1.5.' and since the Hipparcos errors had been subjected to many confirming tests '... that it is likely that the HST errors are overstated.' Parallaxes from Gaia are anxiously awaited; they will improve the number of calibrators by orders of magnitude and convincingly set the zero point. In Figure 3 we show, using thick vertical lines, the full magnitude of the LKH corrections as published by Benedict et al (2011) and applied to the true distance moduli used here. It is noteworthy that, if these corrections had not been applied, the dispersion in the data points around the fit would have exceeded the independently determined dispersion from the Reticulum data, and the slope of the Milky Way solution would have been more shallow than the LMC slope. We take the final agreement of both the slopes and the dispersions to suggest that the individually determined and independently-applied LKH corrections are appropriate. Finally, it needs to be noted that Klein et al. (2011) have published slopes that are much shallower than the ones derived here (e.g., -1.7 compared to our -2.6). This is because in their Bayesian analysis they chose to leave the overtone pulsators in the global solution, without correcting them to their equivalent fundamental periods. We have recomputed the slopes from their data after applying the appropriate period shift to the overtones, and those PL slopes are plotted in Figure 4. Their slopes and ours now agree well within the errors, but they are still systematically somewhat shallower than our solutions.","pages":[5,6,7]},{"title":"4. The Run of PL Slope with Wavelength","content":"For Cepheids it is well known that the slope of the PL relation is a monotonically increasing function of wavelength. In Figure 4 we show that the same overall trend is now made explicit for the first time for the RR Lyrae variables as well, and for the same physical reasons. As one moves from shorter to longer wavelengths one is moving from PL relations where the slope is dominated by the trend of decreasing temperature (i.e., decreasing surface brightness) with period, to relations that are dominated by the opposing run of increasing mean radius with period. The plotted slopes of the optical and nearinfrared PL relations are representative of a variety of published studies (e.g, Catelan, Pritzl & Smith 2004, Benedict et al. 2011, Dall'Ora et al. 2004) while the mid-IR slopes are from this study. As the relative contribution from the temperature-sensitive surface brightness drops off with wavelength, the observed slope is expected to asymptotically approach the wavelength-independent (geometric) slope of the Period-Area relation. That behavior is indeed seen in Figure 4. Moreover the level at which the plateau is occurring would suggest that the period-radius relation of Burki & Meylan (1986) (giving a slope of -2.60, based on Baade-Wesselink studies) is marginally preferred over the period-radius (slope = -3.25) and period-radius-metallicity (slope = -2.90) solutions given by Marconi et al. (2005) 5 From a practical point of view it is not immediately clear what advantage the increased slope of the long-wavelength PL relations would have to offer applications to the distance scale, until it is realized that increased slope in the PL relation is causally and physically connected to decreased width (i.e., decreased intrinsic scatter and therefore increased precision) in the PL relation as proven in the general case by Madore & Freedman (2012). This effect can be seen for the RR Lyrae variables in Figure 2 of Catelan, Pritzl & Smith (2004), and it is apparent here in Figure 3 where the scatter has already reached a minimum in the K-band where simultaneously the plateau in slope (seen in Figure 4) is very nearly complete.","pages":[7,8]},{"title":"5. A First Test of the Metallicity Dependence in the Mid-IR","content":"In Figure 5 we plot the measured magnitude residuals from the [W1] 3.4 µ m PL relation versus the published metallicities of the four RR Lyrae stars in our sample, as given in Table 1 of Benedict et al. (2011). The RR Lyrae stars only sample a 0.4 dex range in [Fe/H] so the test is not a strong one, but there is clearly no significant dependence of the already small magnitude residuals on metallicity.","pages":[8]},{"title":"6. Conclusions","content":"As can be dramatically seen in the study of Catelan, Pritzl & Smith (2008, especially their Figure 2) operating anywhere in the near to mid-infrared, from H = 1.6 µ m (accessible to HST ) to 3.6 µ m (accessible to Spitzer now, and with JWST in the near future) will each accrue the benefits of low scatter and ever decreasing sensitivity (with wavelength) to line-of-sight extinction. Collecting power, availability and spatial resolution will determine which of these instruments will be used at any given time. But suffice it to say that the Population II RR Lyrae variables are proving themselves to be a powerful means of establishing an independent, highly precise and accurate distance scale that is completely decoupled in its systematics from the Population I Cepheid path to the extragalactic distance scale and the Hubble constant. This work is based in part on observations made with the Wide-field Infrared Survey Explorer (WISE), which was is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. This research also made use of the NASA/IPAC Extragalactic Database (NED) and the NASA/ IPAC Infrared Science Archive (IRSA), both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We thank Fritz Benedict for numerous frank and useful communications. The referee was especially helpful in bringing this paper to a more correct and fruitful completion.","pages":[8,9]},{"title":"References","content":"XZCyg, P = 0.466584 days RRLyr, P = 0.566826 days","pages":[11,12]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"Using time-resolved, mid-infrared data from WISE and geometric parallaxes from HST for four Galactic RR Lyrae variables, we derive the following Population II Period-Luminosity (PL) relations for the WISE[W1], [W2] and [W3] bands at 3.4, 4.6 & 12 µ m, respectively: The slopes and the scatter around the fits are consistent with a smooth extrapolation of those same quantities from previously-published K-band observations at 2.2 µ m, where the asymptotic (long-wavelength) behavior is consistent with a Period-Radius relation having a slope of 0.5. No obvious correlation with metallicity (spanning 0.4 dex in [Fe/H]) is found in the residuals of the four calibrating RR Lyrae stars about the mean PL regression line. Subject headings: Stars: Variables: RR Lyrae stars- Stars: Variables: W Virginis stars\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"Barry F. Madore\",\n \"content\": \"Observatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Douglas Hoffman\",\n \"content\": \"Infrared Processing and Analysis Center 770 South Wilson, Pasadena, CA 91125\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"S. Eric Persson, Jeff A. Rich Jr., Victoria Scowcroft, Mark Seibert\",\n \"content\": \"Observatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101 barry@obs.carnegiescience.edu, dhoffman@ipac.caltech.edu wendy@obs.carnegiescience.edu, jak@obs.carnegiescience.edu amonson@obs.carnegiescience.edu, persson@obs.carnegiescience.edu jrich@obs.carnegiescience.edu, vs@obs.carnegiescience.edu, mseibert@obs.carnegiescience.edu\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"The advantages of moving the Population I calibration of the Classical Cepheid PeriodLuminosity relation (the Leavitt Law) from the optical to the infrared were outlined some three decades ago by McGonegal et al. (1983), and they have been borne out repeatedly over the years, as reviewed and elaborated upon by Freedman & Madore (2010). But only now is it possible to extend these same advantages to the parallel path offered by the Population II variable stars (the short-period RR Lyrae variables and their longer-period siblings the W Virginis stars). Two impressive accomplishments have made this possible: (1) the completion of the WISE mission (Wright et al. 2010) and the release of its sky survey of point sources measured in the mid-infrared in four bands ranging from 3.4 to 22 µ m, and then (2) the innovative application of the HST Fine-Guidance Sensor ( FGS ) cameras to the determination of trigonometric parallaxes to four field RR Lyrae variables by Benedict et al. (2011). The many, now well-known, advantages of calibrating and using period-luminosity relations in the mid-IR include the following: (1) the effects of line-of-sight extinction are reduced with respect to optical observations by at least an order of magnitude for even the shortest wavelength ([W1] at 3.4 µ m) observations, (2) concerns about the systematic impact of the possible non-universality of the reddening law are similarly reduced by going away from the optical and into the mid-IR, (3) the total amplitude of the light variation of the target star during its pulsation cycle is greatly reduced because of the largely diminished contribution of temperature variation to the change in surface brightness, in comparison to the much smaller (but essentially irreducible) wavelength-independent radius/areal variations, (4) the corresponding collapse in the width (i.e., intrinsic scatter) of the period-luminosity relations, again because of the reduced sensitivity of infrared luminosities to temperature variations (across the instability strip), combined with the intrinsic narrowness of the residual periodradius relations. And finally, (5) at mid-infrared wavelengths, for the temperatures and surface gravities encountered in Population I & II Cepheids and RR Lyrae stars, there are so few metallic line or molecular transitions in those parts of the spectrum that atmospheric metallicity effects are expected to have minimal impact on the calibration. 1 This is especially true for the RR Lyrae stars which are significantly hotter than their longer-period (cooler) Cepheid counterparts. As described in Freedman et al. (2012), the Carnegie Hubble Program (CHP) is designed to minimize and/or eliminate the remaining known systematics in the measurement of the Hubble constant using mid-infrared data from NASA's Spitzer Space Telescope . Here we broaden the base in two distinct ways: (a) the incorporation of WISE mid-infrared data and (b) the preliminary calibration of the Population II RR Lyrae variables as mid-infrared distance indicators. This new initiative is known as the Carnegie RR Lyrae Program (CRRP).\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"2. The Calibrators: WISE Observations\",\n \"content\": \"WISE conducted an all-sky survey at four mid-infrared wavelengths, 3.4, 4.6, 12 and 22 µ m (W1, W2, W3 and W4, hereafter). As such all of the RR Lyrae variables having trigonometric parallaxes (Benedict et al. 2011) were also observed by the satellite. By design, the slowly precessing orbit of WISE, allowed the satellite to scan across every object on the sky at least 12 times (with progressively more coverage at higher ecliptic latitudes). These successive observations were obtained within a relatively narrow window of time (over about 18 hours for those fields nearest the ecliptic equator) with each observation being separated by about 90 minutes (the orbital period of the satellite). Fortuitously RR Lyrae stars have periods that are generally less than 16 hours, meaning that even the sparsest of these multiple mid-infrared observations covered at least one full pulsational cycle of these particular variable stars. The light curves based on the time-resolved WISE observations of our calibrating stars are shown in Figures 1 & 2 for the four RR Lyrae variables, SU Dra , RR Lyr , XZ Cyg , & UV Oct . These stars were observed by WISE 51, 23, 24 and 23 times, respectively. Data were retrieved from the WISE All-Sky Single Exposure (L1b) Source Table, which is available at the Infrared Science Archive (http://irsa.ipac.caltech.edu/Missions/wise.html). The source positions were queried with a 2.5 arcsec cone search radius, ignoring observations flagged as contaminated by artifacts. The observations are very uniformly distributed around the cycle and the resulting light curves are exceedingly well defined. All three of the shortest-wavelength light curves show convergence in their properties, exemplified by their mutual phases, shapes and amplitudes 2 . As expected these light curves closely track the anticipated light variations due to surface-area variations of the star, where at these wavelengths the sensitivity of the surface brightness to a temperature variation is much diminished as compared to its sensitivity at optical wavelengths. This then fully accounts for the mutual phasing (tracking the radius variations, and not the off-set temperature variations), the shape (the cycloid-like radius variation, in contrast to the highly asymmetric color/temperature variation) and the low amplitude (around 0.3 mag, peak-to-peak, in line with the small, radius-induced cyclical change in surface area of these stars). The non-parametric fitting methodology, GLOESS was used to derive intensity-averaged magnitudes and amplitudes, as given in Table 1 (see Persson et al. 2004 for a description and an early application of this fitting technique).\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"3. RR Lyrae Period-Luminosity Relations\",\n \"content\": \"Table 1 contains the parameters needed to compute absolute mean magnitudes. The parallaxes, E(B-V) reddenings, and Lutz-Kelker-Hanson (LKH; Lutz and Kelker 1973; Hanson 1979) corrections as taken from Benedict et al 2011, are listed for convenience. We have converted the A V extinctions listed by Benedict et al. (2011) to those in the W1 and W2 bands using the Yuan et al. (2011) compilation of A WISE /E(B-V) results with A V /E(B-V) = 3.1. Indebetouw et al. (2005) give values of A Spitzer / A K 3 , which we converted to A WISE / A V via the Cardelli et al.(1989) law. The values of A WISE /A V given by Yuan et al. (2011) and our pseudo-values from Indebetouw et al. (2005) agree well. Neither the Yuan et al. (2011) nor Indebetouw et al. (2005) results extend to the W3 band, and here we have referred to Fitzpatrick (1999) for an approximate value. The extinctions for the four stars are so small as to make no difference to the absolute magnitude values and we take A W 3 /A V to be 0.01. The adopted mid-IR extinctions A WISE /A V we adopt are 0.065, 0.052, and 0.01 for W1, W2, and W3, respectively. The adopted mid-IR extinctions A WISE /E(B-V) are also given in Table 1. The above parameters and our observed mean magnitudes lead to the W1, W2, and W3 absolute magnitudes in Table 1 4 . and the Period-Luminosity relations for RR Lyrae variables follow: The absolute magnitude values and the respective fits to the first two WISE bands and as well as K-band data (from Benedict et al. 2011 and Dall'Ora et al. 2004, respectively) are shown in Figure 3. Despite the very small (less than a factor of two) range in period covered by RR Lyrae stars, the PL relations are well defined, largely because of their intrinsically small scatter. The intrinsic scatter is especially well illustrated by the K-band PL relation, where we also show the RR Lyrae data of Dall'Ora et al. for 21 fundamental-mode RR Lyrae stars in the well-populated LMC globular cluster, Reticulum (shifted by 18.47 mag). A comparison of these two datasets is very illuminating. The slope of the adopted PL relation at K and the total width of it, as defined by the two samples, are for all intents and purposes, identical. The very good agreement in these two independently-determined slopes and the small dispersion in each of the datasets suggest that the means of the Milky Way variables are already well constrained even though the Galactic calibrating sample itself is currently very small. On the other hand, we note that the small (observed) scatter of the Milky Way RR Lyrae variables around each of the adopted PL relations is apparently at variance with the individually quoted error bars for each of the calibrating variables. That is, the formal scatter of ± 0 . 10 mag in the WISE PL relations is to be compared with the quoted parallax errors on the individual distance moduli of ± 0 . 22, ± 0 . 16, ± 0 . 25 and ± 0 . 07 mag for XZ Cyg, UV Oct, SU Dra and RR Lyr, respectively. The average scatter for the variables ( ± 0 . 18 mag) is then about two time larger that their observed scatter around the PL fit. This suggests that the published errors may be somewhat overestimated. There are independent data that support this assertion. The 10 Galactic Cepheids for which Benedict et al. (2010) obtained parallaxes, using the same instrument, telescope and reduction methodology have individually quoted internal errors in their true distance moduli ranging from ± 0 . 11 to ± 0 . 30 mag. Their average uncertainty is ± 0 . 19 mag, and yet, once again, as with the RR Lyrae variables the PL fit to these data yields a formal dispersion of only ± 0 . 10 mag. In both cases the observed dispersions, for the Galactic samples, are in total agreement with independently determined dispersions for the much more robustly determined dispersions for the LMC samples. We suggest therefore that the random errors reported for the HST parallaxes for both the Cepheids and for the RR Lyrae variables may have been over-estimated. This is not simply of academic interest. If the observed scatter is used to calculate the systematic uncertainty in the calibration of the RR Lyrae PL relation that uncertainty would be 0 . 10 / √ 4 = ± 0 . 05 mag, a 2-3% error in the Population II distance scale. However, if the quoted errors on the individual distance moduli are used, then the uncertainty rises to 0 . 18 / √ 4 = ± 0 . 09 mag, a 5% error. Similar conclusions would also apply to the base uncertainty in the Cepheid distance scale using the Benedict sample; is the uncertainty in the Galactic Cepheid zero point 1.6% in distance, or is it 3.0%? It is therefore important to note that in their first paper discussing the use of FGS on HST , Benedict et al. (2002) state that the 'standard deviations of the HST and Hipparcos data points may have been overstated by a factor of ∼ 1.5.' and since the Hipparcos errors had been subjected to many confirming tests '... that it is likely that the HST errors are overstated.' Parallaxes from Gaia are anxiously awaited; they will improve the number of calibrators by orders of magnitude and convincingly set the zero point. In Figure 3 we show, using thick vertical lines, the full magnitude of the LKH corrections as published by Benedict et al (2011) and applied to the true distance moduli used here. It is noteworthy that, if these corrections had not been applied, the dispersion in the data points around the fit would have exceeded the independently determined dispersion from the Reticulum data, and the slope of the Milky Way solution would have been more shallow than the LMC slope. We take the final agreement of both the slopes and the dispersions to suggest that the individually determined and independently-applied LKH corrections are appropriate. Finally, it needs to be noted that Klein et al. (2011) have published slopes that are much shallower than the ones derived here (e.g., -1.7 compared to our -2.6). This is because in their Bayesian analysis they chose to leave the overtone pulsators in the global solution, without correcting them to their equivalent fundamental periods. We have recomputed the slopes from their data after applying the appropriate period shift to the overtones, and those PL slopes are plotted in Figure 4. Their slopes and ours now agree well within the errors, but they are still systematically somewhat shallower than our solutions.\",\n \"pages\": [\n 5,\n 6,\n 7\n ]\n },\n {\n \"title\": \"4. The Run of PL Slope with Wavelength\",\n \"content\": \"For Cepheids it is well known that the slope of the PL relation is a monotonically increasing function of wavelength. In Figure 4 we show that the same overall trend is now made explicit for the first time for the RR Lyrae variables as well, and for the same physical reasons. As one moves from shorter to longer wavelengths one is moving from PL relations where the slope is dominated by the trend of decreasing temperature (i.e., decreasing surface brightness) with period, to relations that are dominated by the opposing run of increasing mean radius with period. The plotted slopes of the optical and nearinfrared PL relations are representative of a variety of published studies (e.g, Catelan, Pritzl & Smith 2004, Benedict et al. 2011, Dall'Ora et al. 2004) while the mid-IR slopes are from this study. As the relative contribution from the temperature-sensitive surface brightness drops off with wavelength, the observed slope is expected to asymptotically approach the wavelength-independent (geometric) slope of the Period-Area relation. That behavior is indeed seen in Figure 4. Moreover the level at which the plateau is occurring would suggest that the period-radius relation of Burki & Meylan (1986) (giving a slope of -2.60, based on Baade-Wesselink studies) is marginally preferred over the period-radius (slope = -3.25) and period-radius-metallicity (slope = -2.90) solutions given by Marconi et al. (2005) 5 From a practical point of view it is not immediately clear what advantage the increased slope of the long-wavelength PL relations would have to offer applications to the distance scale, until it is realized that increased slope in the PL relation is causally and physically connected to decreased width (i.e., decreased intrinsic scatter and therefore increased precision) in the PL relation as proven in the general case by Madore & Freedman (2012). This effect can be seen for the RR Lyrae variables in Figure 2 of Catelan, Pritzl & Smith (2004), and it is apparent here in Figure 3 where the scatter has already reached a minimum in the K-band where simultaneously the plateau in slope (seen in Figure 4) is very nearly complete.\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"5. A First Test of the Metallicity Dependence in the Mid-IR\",\n \"content\": \"In Figure 5 we plot the measured magnitude residuals from the [W1] 3.4 µ m PL relation versus the published metallicities of the four RR Lyrae stars in our sample, as given in Table 1 of Benedict et al. (2011). The RR Lyrae stars only sample a 0.4 dex range in [Fe/H] so the test is not a strong one, but there is clearly no significant dependence of the already small magnitude residuals on metallicity.\",\n \"pages\": [\n 8\n ]\n },\n {\n \"title\": \"6. Conclusions\",\n \"content\": \"As can be dramatically seen in the study of Catelan, Pritzl & Smith (2008, especially their Figure 2) operating anywhere in the near to mid-infrared, from H = 1.6 µ m (accessible to HST ) to 3.6 µ m (accessible to Spitzer now, and with JWST in the near future) will each accrue the benefits of low scatter and ever decreasing sensitivity (with wavelength) to line-of-sight extinction. Collecting power, availability and spatial resolution will determine which of these instruments will be used at any given time. But suffice it to say that the Population II RR Lyrae variables are proving themselves to be a powerful means of establishing an independent, highly precise and accurate distance scale that is completely decoupled in its systematics from the Population I Cepheid path to the extragalactic distance scale and the Hubble constant. This work is based in part on observations made with the Wide-field Infrared Survey Explorer (WISE), which was is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. This research also made use of the NASA/IPAC Extragalactic Database (NED) and the NASA/ IPAC Infrared Science Archive (IRSA), both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We thank Fritz Benedict for numerous frank and useful communications. The referee was especially helpful in bringing this paper to a more correct and fruitful completion.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"XZCyg, P = 0.466584 days RRLyr, P = 0.566826 days\",\n \"pages\": [\n 11,\n 12\n ]\n }\n]"}}},{"rowIdx":71,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...777...32X"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1308.3376.pdf"},"content":{"kind":"string","value":"\nUSING COORDINATED OBSERVATIONS IN POLARISED WHITE LIGHT AND FARADAY ROTATION TO PROBE THE SPATIAL POSITION AND MAGNETIC FIELD OF AN INTERPLANETARY SHEATH\nMing Xiong 1, 2 , Jackie A. Davies 3 , Xueshang Feng 1 , Mathew J. Owens 4 , Richard A. Harrison 3 , Chris J. Davis 4 , and Ying D. Liu 1\nDraft version September 8, 2018\nABSTRACT\nCoronal mass ejections (CMEs) can be continuously tracked through a large portion of the inner heliosphere by direct imaging in visible and radio wavebands. White-light (WL) signatures of solar wind transients, such as CMEs, result from Thomson scattering of sunlight by free electrons, and therefore depend on both the viewing geometry and the electron density. The Faraday rotation (FR) of radio waves from extragalactic pulsars and quasars, which arises due to the presence of such solar wind features, depends on the line-of-sight magnetic field component B ‖ , and the electron density. To understand coordinated WL and FR observations of CMEs, we perform forward magnetohydrodynamic modelling of an Earth-directed shock and synthesise the signatures that would be remotely sensed at a number of widely distributed vantage points in the inner heliosphere. Removal of the background solar wind contribution reveals the shock-associated enhancements in WL and FR. While the efficiency of Thomson scattering depends on scattering angle, WL radiance I decreases with heliocentric distance r roughly according to the expression I ∝ r -3 . The sheath region downstream of the Earth-directed shock is well viewed from the L4 and L5 Lagrangian points, demonstrating the benefits of these points in terms of space weather forecasting. The spatial position of the main scattering site r sheath and the mass of plasma at that position M sheath can be inferred from the polarisation of the shock-associated enhancement in WL radiance. From the FR measurements, the local B ‖ sheath at r sheath can then be estimated. Simultaneous observations in polarised WL and FR can not only be used to detect CMEs, but also to diagnose their plasma and magnetic field properties.\nSubject headings: methods: numerical - shock waves - solar-terrestrial relations - solar wind Sun: coronal mass ejections (CMEs) - Sun: heliosphere\n1. INTRODUCTION\n1.1. The Inner Heliosphere\nThe inner heliosphere is permeated with the magnetised solar wind from the Sun. At solar minimum, the solar wind is inherently bimodal (McComas et al. 2000), with slow flow tending to emanate from near the ecliptic and fast flow tending to emanate at higher latitudes. Several large-scale structures, which pervade interplanetary space, are associated with the 'ambient' solar wind: (1) a spiralling interplanetary magnetic field (the Parker spiral) that forms as a result of solar rotation (Parker 1958), (2) corotating interacting regions (CIRs) that are formed at the interface between a preceding slow solar wind stream and a following fast solar wind stream (Gosling & Pizzo 1999), and (3) the heliospheric current sheet typically embedded in the heliospheric plasma sheet (Winterhalter et al. 1994; Crooker et al. 2004).\nThe background solar wind flow is frequently disturbed by coronal mass ejections (CMEs), large-scale expulsions of plasma and magnetic field from the solar atmosphere. CMEs typically expand during their propagation, because the total solar wind pressure de-\nmxiong@spacweather.ac.cn\n\n1 State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing, China\n2 Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing Aerospace Control Center, Beijing, China\n3 Rutherford-Appleton Laboratory (RAL) Space, Harwell Oxford, UK\n\n4 Reading University, Reading, UK\ncreases with heliocentric distance (D'emoulin & Dasso 2009; Gulisano et al. 2010). The expansion speed of a CME depends on its spatial size, translation speed, and heliocentric distance, as well as the pre-existing solar wind conditions (Nakwacki et al. 2011; Gulisano et al. 2012). A number of popular models describe the motion of a CME as governed by two forces: a propelling Lorentz force (Chen 1989, 1996; Chen et al. 2006) and an aerodynamic drag force (Cargill et al. 1996; Vrˇsnak & Gopalswamy 2002; Cargill 2004). According to these models, the drag force gradually becomes dominant in interplanetary space, and the CME speed finally adjusts to the ambient solar wind speed. The equalisation of the CME and solar wind speed occurs at very different heliospheric distances, from below 30 solar radii to beyond 1 AU, depending on the characteristics of the CME and the solar wind (Temmer et al. 2011). A CME can undergo significant, nonlinear, and irreversible evolution during its propagation, as it interacts with the ambient solar wind and other CMEs (e.g., Burlaga et al. 2002; D'emoulin 2010). Coronagraph observations show that CME morphology is distorted rapidly and significantly in a structured solar wind (e.g., Savani et al. 2010, 2012; Feng et al. 2012a). Such a distortion occurs over a relatively short heliocentric distance. Interaction between multiple CMEs has been revealed by in-situ observations (e.g., Burlaga et al. 1987; Wang et al. 2003a; Steed et al. 2011; Mostl et al. 2012), radio burst observations (e.g., Gopalswamy et al. 2001; Oliveros et al. 2012), white-light (WL) imaging (e.g., Harrison et al.\n2012; Liu et al. 2012; Lugaz et al. 2012; Temmer et al. 2012; Shen et al. 2012a; Bemporad et al. 2012), and numerical magnetohydrodynamic (MHD) simulation (e.g., Lugaz et al. 2005; Xiong et al. 2007, 2009; Shen et al. 2012b).\nCMEs cause phenomena at Earth, such as geomagnetic storms and solar energetic particles, that can result in major space weather effects (Gopalswamy 2006; Webb & Howard 2012). Traditionally, a CME has been defined in terms of a three-part structure, involving a bright sheath, a dark cavity, and a bright filament. It is now accepted that the cavity component is an escaping magnetic flux rope that drives the CME (e.g., Rouillard et al. 2009b; DeForest et al. 2011). A highspeed flux rope can drive a fast shock ahead of itself that is much wider in angular extent than the flux rope itself. The region between the shock front and the flux rope is defined as a sheath. Within the sheath, (1) magnetic field lines are draped and compressed, and (2) a plasma flow is deviated, compressed, and turbulent (e.g., Gosling & McComas 1987; Owens et al. 2005; Liu et al. 2008). Precursor southward magnetic fields ahead of CMEs are generally compressed, making them particularly geoeffective (Tsurutani et al. 1992; Gonzalez et al. 1999). The magnetic fields in the sheath and in the flux rope can be equally important in driving major geomagnetic storms (Tsurutani et al. 1988, 1992; Szajko et al. 2013). In so-called two-dip storms, it is often the case that the first dip in the Dst index is produced by the upstream sheath and the second is produced by the driving flux rope (Echer et al. 2004; Zhang et al. 2008; Mostl et al. 2012).\n1.2. Heliospheric White Light Observations\nHeliospheric imagers (HIs) detect WL that has been Thomson-scattered from free electrons. For resolved objects, such as CMEs, the power detected by an individual pixel depends linearly on the solid angle subtended by that pixel ( δω ) and the area subtended by the corresponding aperture ( δA ), and is proportional to the radiance (measured in W m -2 SR -1 ). The light from unresolved objects, such as stars, which are much narrower in angular extent, tends to fall within individual pixels. For a resolved heliospheric electron density feature, such as a CME, a single pixel provides a measure of its radiance (surface brightness), while summing contributions from all pixels over the entire extent of the feature provides a measure of its intensity (total brightness). The intensity is an integral of the radiance over the apparent feature size. Therefore, the feature's intensity determines its detectability of an object, be it resolved or unresolved (Howard & DeForest 2012).\nThe background zodiacal and stellar signals detected by heliospheric imagers are much more intense than the signal due to Thomson-scattering from plasma features such as CMEs (Leinert & Pitz 1989). Fortunately, using an image-differencing technique, the much more stable background radiance can be removed, such that the more transient Thomson-scattering signal can be extracted. From such processed Thomsonscattering images, the sunlight-irradiated CMEs can be easily identified and tracked. According to theory, the heliospheric Thomson-scattering radiance is governed by the Thomson-scattering geometry fac-\ntors and electron number density (Vourlidas & Howard 2006; Howard & Tappin 2009; Howard & DeForest 2012; Xiong et al. 2013). The CME detectability in WL is actually more limited by perspective and field-of-view (FOV) effects than by location relative to the Thomsonscattering sphere (Howard & DeForest 2012).\nHeliospheric imaging from two vantage points, both off the Sun-Earth line, was made possible by the Heliospheric Imagers (HIs) onboard the Solar-TErrestrial RElations Observatory ( STEREO ) (Eyles et al. 2009). With the STEREO /SECCHI package, a CME can be imaged from its nascent stage in the inner corona all the way out to 1 AU and beyond (e.g., Harrison et al. 2008; Davies et al. 2009; Davis et al. 2009; Liu et al. 2010b; DeForest et al. 2011; Liu et al. 2013). In particular, images from STEREO /HI-2 have revealed detailed spatial structures within interplanetary CMEs, including leading-edge pileup, interior cavities, filamentary structure, and rear cusps (DeForest et al. 2011). Comparison with in-situ observations has revealed that the leadingedge pileup of solar wind material, which is evident as a bright arc in WL imaging, corresponds to the sheath region. However, the interpretation of the leading edge of the radiance pattern, especially at larger elongations, is fraught with ambiguity (e.g., Howard & Tappin 2009; Xiong et al. 2013). Elongation ε is defined as the angle between the Sun-observer line and a line-of-sight (LOS). Because a CME occupies a significant three-dimensional (3D) volume, different parts of the CME will contribute to the radiance pattern imaged by observers situated at different heliocentric longitudes (Xiong et al. 2013). Even for an observer at a fixed longitude, a different part of the CME will contribute to the imaged radiance at any given time (Xiong et al. 2013). Various techniques have been developed that enable the spatial locations and propagation directions of CMEs to be inferred, based on the fitting of their moving radiance patterns (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Thernisien et al. 2009; Liu et al. 2010b; Lugaz et al. 2010; Mostl et al. 2011; Davies et al. 2012). However, the determination of interplanetary CME kinematics, propagation direction in particular, are somewhat ambiguous (Howard & Tappin 2009; Davis et al. 2010; Davies et al. 2012; Howard & DeForest 2012; Xiong et al. 2013; Lugaz & Kintner 2013).\n1.3. Faraday Rotation Measurement\nFaraday rotation (FR) is the rotation of the plane of polarisation of an incident electromagnetic wave as it passes through a magnetised ionic medium. The FR observations of linearly polarised radio sources can be used to estimate magnetic field in the corona and interplanetary space (e.g., Levy et al. 1969; Bird et al. 1980; Sakurai & Spangler 1994; Liu et al. 2007; Jensen 2007; Jensen & Russell 2008; You et al. 2012; Jensen et al. 2013). The FR measurement of a radio signal corresponds to the path integral of the product of electron density n and the projection of the magnetic field along the LOS, B ‖ . The first FR experiment was conducted in 1968 by Levy et al. (1969), when solar plasma occulted the radio down-link from the Pioneer 6 spacecraft. As well as man-made radio sources, FR experiments can also exploit natural radio sources such as pulsars and quasars. The first FR experiments of this type were conducted by\nBird et al. (1980) during the solar occultation of a pulsar. In terms of their locations on a sky map, many pulsars and quasars lie in the vicinity of the Sun. Therefore, simultaneous FR measurements along multiple beams can be used to map the inner heliosphere with a reasonable spatial resolution.\nAdditional observations, for example in WL, would generally be necessary to confirm whether an FR transient was indeed caused by a CME. For instance, the first FR event, reported by Levy et al. (1969), could not be attributed unambiguously to the presence of any particular solar wind structure. The FR signatures, observed by Levy et al. (1969), exhibited a W-shaped profile over a time period of 2 -3 hours, with rotation angles of up to 40 · relative to the quiescent baseline. Woo (1997) interpreted the FR signature as the result of a coronal streamer stalk of angular size 1 · -2 · , whereas Patzold & Bird (1998) argued that it was caused by the passage of a series of CMEs. However, by comparing observations from the Solwind coronagraph and measurements of Helios down-link radio signals, Bird et al. (1985) were able to identify the signatures of five CMEs simultaneously in WL and FR. Moreover, the electron density derived from WL imaging can be used to enable magnetic field magnitude to be inferred from FR measurements.\nThe heliospheric magnetic field can be remotely probed in FR, using low-frequency radio interferometers such as the Murchison Widefield Array (MWA) (Lonsdale, C. J., et. al. 2009), the LOw Frequency ARray (LOFAR) (de Vos et al. 2009), and the Very Large Array (VLA) (Thompson et al. 1980). Disturbance of the background solar wind by CMEs will cause the observed FR signatures to become variable (e.g., Levy et al. 1969; Bird et al. 1985; Jensen & Russell 2008). A change in either the electron density ( δn ) or the LOS magnetic field component ( δB ‖ ), or indeed both, will contribute to the rotation in the plane of polarisation of the radio signal by δ Ω RM . Interplanetary magnetic clouds (MCs) in particular, which have a magnetic flux rope configuration (Burlaga et al. 1981; Klein & Burlaga 1982; Lepping et al. 1990), can be identified from WL images (Rouillard et al. 2009b; DeForest et al. 2011) and are expected to be easily identifiable in FR measurements. Moreover, δn and | δ B | are often enhanced simultaneously within the sheath ahead of a fast MC. The FR due to a MC-driven sheath can be comparable to that due to the MC itself (Jensen et al. 2010). It is expected that the orientation and helicity of a MC will be able to be determined unambiguously from multi-beam FR measurements (Liu et al. 2007; Jensen 2007; Jensen et al. 2010). In contrast, the in-situ detection of magnetic flux ropes can be significantly hindered by the location of the observing spacecraft (e.g., Hu & Sonnerup 2002; Mostl et al. 2012; D'emoulin et al. 2013). FR imaging can be used to provide the magnetic orientation of a fast MC, and indeed its preceding sheath, prior to its arrival at Earth, which is crucial for predicting potential space weather effects at Earth.\n1.4. Forward Magnetohydrodynamic Modelling\nForward modelling of WL and FR signatures is proving extremely useful for inferring the in-situ properties of interplanetary CMEs from remote-sensing data. Sophis-\nticated numerical MHD models of the inner heliosphere (e.g., Groth et al. 2000; Lugaz et al. 2005; Hayashi 2005; Xiong et al. 2006a; Li et al. 2006; Wu et al. 2006; Li & Li 2008; Odstrˇcil & Pizzo 2009; Shen et al. 2012b) can serve as a digital laboratory, to enable the synthesis of a variety of observable remote-sensing signatures. In this paper, we perform a numerical MHD simulation of an interplanetary shock in the ecliptic, from which we synthesise the signatures of that feature that would be remotely sensed at visible and radio wavelengths. Details of the MHD model, and the formulae required to synthesise the remote-sensing observations, are given in Section 2. The resultant synthesised remote-sensing signatures of the sheath, which would be observed from vantage points at 0.5 and 1 AU, are described and compared in Section 3. In Section 4, we discuss the radiance patterns that are observed in the synthesised WL and FR sky maps. In Section 5, we explore the role that the vantage point of the observer plays in the 'observability' of such WL and FR features. CME detection in the presence of background noise, and the heliospheric imaging of more complex interplanetary phenomena, are discussed in Section 6. The potentially important role that forward modelling can play in our understanding of coordinated WL and FR observations is summarised in Section 7.\n2. METHOD\nForward MHD modelling can self-consistently establish the links between interplanetary dynamics and the resultant observable signatures. A complete flow chart of forward modelling is illustrated in Figure 8 from Xiong et al. (2011). The travelling fast shock studied by Xiong et al. (2013) is revisited here. Our methodology consists of three general steps: (1) forward modelling of the shock using the numerical Inner-Heliosphere MHD (IH-MHD) model (Xiong et al. 2006a, 2013), (2) calculation of its Thomson-scattered WL signature, in Section 2.1, and (3) calculation of its FR signature, in Section 2.2. Characterisation of the IH-MHD model, the background solar wind conditions, and the initial shock injection is summarised respectively in Tables 1, 2, and 3 of Xiong et al. (2013). The simulated electron density n and magnetic field B are used to generate synthetic WL and FR images, which enable us to explore the WL and FR signatures of an interplanetary sheath.\nA plasma parcel emitted from the Sun would be observed, at the same elongation and the same Thomsonscattering angle, firstly by an observer situated at a radial distance of 0.5 AU from the Sun centre, and subsequently by an observer at 1 AU (Figure 1a). Such a configuration was discussed qualitatively by Jackson et al. (2010) and is analysed quantitatively in Section 3 of this paper. Observations from STEREO /HI suggest that a travelling sheath can be approximated as an expanding bubble (e.g., Howard & Tappin 2009; Lugaz et al. 2010; Davies et al. 2012; Mostl & Davies 2013). In-situ observations indicate that CMEs undergo self-similar expansion, as the speed profiles within CMEs themselves tend to be a linear function of time (e.g., Farrugia et al. 1993; Gulisano et al. 2012). In the schematic Figures 1b-d, the sheath region following an Earth-directed interplanetary shock is represented as a self-similarly expanding bubble. The sheath can look quite different when viewed\nfrom different heliocentric distances (Figures 1b and 1c) and/or different heliospheric longitudes (Figures 1b and 1d).\n2.1. Thomson-Scattering WL Formulae\nA small parcel of free electrons, that is illuminated by a known intensity of incident sunlight (measured in W m -2 ), will scatter a certain amount of power per unit solid angle (measured in W rad -1 ). The effect of the Thomson-scattering geometry can be characterised by the so-called scattering angle χ , as depicted in Figure 1 of Xiong et al. (2013). Scattering can be backward ( χ < 90 · ), perpendicular ( χ = 90 · ), and forward ( χ > 90 · ). All photons that are scattered into an optical cone defined by the point spread function of an individual pixel will be attributed to that pixel (Figure 1b, Xiong et al. 2013). The classic principles of WL Thomson-scattering, as applied to coronagraph observations (Billings 1966), have been adapted to heliospheric imaging (Vourlidas & Howard 2006; Howard & Tappin 2009; Jackson et al. 2010; Howard & DeForest 2012; Xiong et al. 2013). The transverse electric field oscillation δ E of the Thomson-scattered radiance, which is inherently a continuum, can be considered in terms of its two orthogonal components, a tangential component δ E T and a radial component δ E R . The amplitudes of these two orthogonal oscillations ( I T = | δ E T | 2 and I R = | δ E R | 2 ) can be measured separately, using a polariser. The total radiance I and degree of polarisation p are defined as follows:\nI = I T + I R (1)\np = I T -I R I (2)\nAlthough the incident sunlight is unpolarised ( p = 0), the scattered WL radiance remains unpolarised only when the scattering angle | χ -90 · | = 90 · . The scattered light is elliptically polarised (0 < p < 1) for 0 · < | χ -90 · | < 90 · and linearly polarised ( p = 1) for χ = 90 · . Each pixel of a detector records the LOS integral of local WL radiance.\n( I I T I R ) = ∫ ∞ 0 ( i i T i R ) dz = ∫ ∞ 0 nz 2 ( G G T G R ) dz (3)\nHere z refers to a distance between the detector and the scattering site, as shown in Figure 1b of Xiong et al. (2013). The mathematical expressions for G , G R , and G T are given by Equations 1 and 2 of Xiong et al. (2013). The observed WL radiance is determined jointly by the heliospheric distribution of electrons n and Thomsonscattering geometry factors ( z 2 G , z 2 G R , z 2 G T ).\nAs noted above, the efficiency of Thomson scattering depends significantly on the Thomson scattering angle χ . The perpendicular scattering, χ = 90 · , received by an observer comes from the Thomson Sphere. The 'Thomson sphere', sometimes called the 'Thomson surface', is the sphere in which the Sun and observer lie at opposite ends of a diameter (e.g., Vourlidas & Howard 2006; Howard & DeForest 2012). The ecliptic cross sections of the Thomson scattering spheres for three observers are shown as dotted circles in Figures 1b-d. The LOS from an observer crosses its Thomson sphere at a so-called p point (Figure 2, Tappin et al. 2004), where both the\nintensity of incident sunlight and local electron density are greatest, but the efficiency of Thomson scattering is least. Competition between these three effects results in the spread of local radiance ( i , i T , i R in Equation 3) to large distances from the Thomson surface, an effect that is greater at larger elongations ε from the Sun. Howard & DeForest (2012) described this broad spreading effect, using the term 'Thomson plateau'. Namely, along a single LOS, the radiance per unit electron density is virtually constant over a broad range of scattering angles χ centred at the p point. The Thomson plateau, in terms of its relevance to heliospheric image, was discussed in detail by Howard & Tappin (2009), Howard & DeForest (2012), and Xiong et al. (2013).\nA major milestone in stereoscopic WL imaging of interplanetary CMEs was achieved by the STEREO /HI instruments (e.g., Eyles et al. 2009; Davies et al. 2009; Davis et al. 2009; Harrison et al. 2009). This heliospheric imaging capability was built on the heritage of the Solar Mass Ejection Imager ( SMEI ) instrument on the Coriolis spacecraft (Eyles et al. 2003). The STEREO mission is comprised of two spacecraft, with one leading ( STEREO A) and the other trailing ( STEREO B) the Earth in its orbit. Both spacecraft separate from the Earth by 22 . 5 · per year. The HI instrument on each STEREO spacecraft consists of two cameras, HI-1 and HI-2, whose optical axes lie in the ecliptic. Elongation coverage in the ecliptic is 4 · - 24 · for HI-1 and 18 . 7 · - 88 . 7 · for HI-2. The field of view (FOV) is 20 · × 20 · for HI-1 and 70 · × 70 · for HI-2. The cadence of HI1 is usually 40 minutes and that of HI-2 is 2 hours (Eyles et al. 2009). The current generation of heliospheric imagers do not have WL polarisers. Polarisation measurements have, up until now, only been made by coronagraphs (e.g., Poland & Munro 1976; Crifo et al. 1983; Moran & Davila 2004; Pizzo & Biesecker 2004; de Koning et al. 2009; Moran et al. 2010). For instance, Moran & Davila (2004) used polarisation measurements of WL radiance by the SOHO /LASCO coronagraph to reconstruct CME orientations near the Sun.\nSky maps, often presented in the Hammer-Aitoff projection, can be used to highlight and track WL transients (e.g., Tappin et al. 2004; Zhang et al. 2013). Timeelongation maps (J-maps) are usually constructed by stacking differenced radiance between observed sky maps along a fixed position angle (sometimes background subtracted images are used instead of difference images). Using such J-maps, transients such as CMEs are manifest as inclined streaks (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Xiong et al. 2011; Harrison et al. 2012; Davies et al. 2012; Xiong et al. 2013). As a propagating transient is viewed along larger elongations, its WL signatures become fainter.\n2.2. Faraday Rotation Formula\nDue to a FR effect, the plane of polarisation of linearly polarised radio emission is continuously rotated as the radio wave passes through the heliosphere. For radio waves, the ubiquitous magnetised solar wind flow serves as a magneto-optical birefringence medium. The formulae for FR are expressed below:\nΩ = Ω RM · λ 2 (4)\nΩ RM = ∫ ω RM dz (5)\nδ ω RM ∝ δ ( nB ‖ ) (7)\nω RM = e 3 8 π 2 /epsilon1 0 m 2 e c 3 nB ‖ = [ 2 . 63 × 10 -13 rad T ] nB ‖ (6)\nδ Ω RM ∝ ∫ δ ω RM dz (8)\nWhere q , /epsilon1 , m e , and c represent the constants that are the electron charge, the permittivity of free space, the mass of an electron, and the speed of light, respectively. A FR measurement of Ω RM = 1 rad m -2 corresponds to Ω = 0 . 97 · at 2.3 GHz (wavelength λ = 0 . 13 m), Ω = 57 . 3 · at 300 MHz ( λ = 1 m), and Ω = 1432 · at 60 MHz ( λ = 5 m). The calibration of ground-based FR observations is difficult, as the radio wave passes through the magnetised plasma of the ionosphere, magnetosphere (including the plasmasphere), and solar wind. Oberoi & Lonsdale (2012) surveyed and compared the FR signatures associated with each of these different regions.\nA large portion of the inner heliosphere can be monitored, using FR imaging. Prime heliospheric targets measured in FR include interplanetary CMEs and CIRs (Oberoi & Lonsdale 2012). Because the low-frequency radio interferometers such as the MWA , LOFAR , and VLA feature a wide FOV, high sensitivity, and multibeam forming capabilities, it is expected to be capable of mapping the magnetic field in the inner heliosphere with a remarkable sensitivity. The high sensitivity of FR measurements enables fluctuations in the heliospheric/interstellar magnetic field and plasma density, resulting from MHD turbulence, to be revealed (e.g., Jokipii & Lerche 1969; Goldshmidt & Rephaeli 1993; Hollweg et al. 2010). For instance, gradients in FR measurement have been observed across active Galactic Nuclei (AGN) jets, using the Very Long Baseline Array , which demonstrate that ordered helical magnetic fields are associated with these jets (e.g., Zavala & Taylor 2002; G'omez et al. 2008; Reichstein & Gabuzda 2012). The sheath region associated with a fast CME can be similarly probed. FR measurements of the sheath would provide a value for Ω RM in Equations 4-8. Any measured value of the FR, Ω RM , would correspond to a statistical average, as the plasma and magnetic fields within such sheath regions are in a highly turbulent state.\n3. WHITE-LIGHT AND FARADAY ROTATION SIGNALS RECEIVED AT 0.5 AND 1 AU\nThe remote imaging in WL and FR of an Earthdirected sheath from two vantage points, one at 0.5 AU and the other at 1 AU, is considered in Section 3.1. Section 3.2 demonstrates how spatial position and electron number density can be inferred from polarisation observations of WL radiance. Section 3.3 presents a means by which magnetic field can be diagnosed from FR measurements.\n3.1. Comparing Remotely-Sensed WL and FR Observations from Different Vantage Points\nFigure 2 shows the modelling results of an Earthdirected sheath propagating from the Sun to 1 AU. The travelling sheath is supposed to be imaged simultaneously by two observers at 0.5 and 1 AU. The WL and FR signatures of the sheath are synthesised, using the methods in Section 2. Representative LOSs, which cut through the sheath (LOS1-6), are denoted using arrows in Figure 2. The variations of various physical parameters along LOS1-3 are shown in Figure 3. LOS1, LOS2, LOS3, and LOS5 are approximately tangential to the left flank of the shock; LOS4 and LOS6 are tangential to the nose of the shock. LOS1 and LOS4 are directed towards the observer situated at 0.5 AU; all other LOSs are directed towards the observer at 1 AU. The viewing configuration for LOS1 (Figure 2a) is equivalent to that for LOS3 (Figure 2c), as the elongation of the shock front is the same for LOS1 and LOS3. Thus, the Thomson scattering geometry is identical for these two LOSs, leading to similar LOS profiles in Figure 3. Of course, the observed radiance along LOS1 is much stronger than that along LOS3 (Table 1). Similarly, the observations along LOS4 and LOS6 (Figures 2d and 2f) have identical Thomson scattering geometries. At any given time, the sheath is viewed at greater elongations from a vantage point closer to the Sun. For instance, at an elapsed time of 5.5 hours, the foremost elongation ε of the sheath is 20 · for an observer at 1 AU (LOS1) compared with 7 · for an observer at 0.5 AU (LOS2). While the sheath is undetectable in WL along LOS2 (Figure 3g), it can be observed in FR (Figure 3l). The portion of an LOS that contributes most to the WL radiance broadens and flattens with increasing elongation, and shifts gradually towards the observer. At elongations beyond 90 · , only back-scattered photons are received; electrons in the vicinity of the observer mainly contribute to remote-sensing signatures for elongations beyond 90 · . Such observations for elongations of ε ≥ 90 · are less useful for the purposes of space weather prediction. In Figures 2d and 2f, the shock front has already reached the observer, and can be detected in-situ.\n3.2. Inferences of Sheath Position from Polarised White Light\nThe WL radiance of CMEs is determined by both the electron number density distribution and the Thomsonscattering geometry (Equation 3). The total radiance at a scattering site ( i ), and its constituent radial ( i R ) and tangential ( i T ) components, are associated with Thomson-scattering factors z 2 G , z 2 G R , and z 2 G T , respectively. Near the Thomson-scattering surface, z 2 G T is much larger than z 2 G R . If a dense parcel of plasma, viewed at large elongations, approaches the Thomson surface, its WL signatures will comprise (1) an increase in I , (2) an increase in I T , (3) a decrease in I R , and (4) an increase in the degree of polarisation p . The variation of p is largest, while that of I is negligible. A plasma parcel's distance from the Thomson sphere has a less significant effect on I at larger elongations. However, the determination of the plasma parcel's location will be more uncertain, if only unpolarised WL observations are available, as with current operational heliospheric imaging systems. Polarisation observations can provide an important clue to the primary scattering site. LOS1 in Figure 2 is used to demonstrate these inferences.\nThe Thomson-scattering geometry is independent of the distribution of heliospheric electrons. The degree of polarisation ( p ) and the Thomson-scattering factors ( z 2 G , z 2 G R , z 2 G T ), as presented in Figure 3b and 3d, only depend on the modified scattering angle χ ∗ = 90 · -χ . The profiles of p , z 2 G , z 2 G R , and z 2 G T are symmetrical around χ ∗ = 0 · . The dependence of χ ∗ , z 2 G , and LOS distance z on p can be seen in Figure 4. p = 1 corresponds to perpendicular scattering (i.e. χ ∗ = 0 · ). p = 1 corresponds to two solutions for χ ∗ : one resulting from forward scattering ( χ ∗ < 0 · ), and the other associated with backward scattering ( χ ∗ > 0 · ). In response to the passage of the shock, the initial radiance components at t = 0, I T0 and I R0 , are enhanced to values denoted by I T and I R , respectively. The increase in the radiance components define a so-called modified degree of polarisation that we denote using p ∗ . p ∗ is given by\n/negationslash\np ∗ = I T -I T0 -I R + I R0 I -I 0 (9)\np is 0.62 along LOS1 at t = 0 hours. This effectively defines the degree of polarisation associated with the background solar wind. During the sheath passage, at t = 5 . 5 hours, p is 0.58 along this LOS. The modified degree of polarisation p ∗ , derived using Equation 9, is therefore 0.29 at t = 5 . 5 hours. The radiance enhancement is due to the presence of the sheath in the LOS. The sheath, which trails the shock front, occupies a relatively small volume of interplanetary space. The sheath occupies the portion of LOS1 bounded by -55 · < χ ∗ < -35 · (Figures 3a and 3c). Within this region, p smoothly varies from 0.15 to 0.5 (Figure 3d). The average value of p ∗ within the sheath is 0.29. In an inverse approach, p ∗ can be used to estimate the scattering angle χ ∗ within the sheath. This is demonstrated in Figure 4a. p ∗ = 0 . 29 corresponds to χ ∗ = ± 46 · and z 2 G = 6 . 5 × 10 -29 , where z 2 G is the average value of z 2 G in the sheath. The solution of χ ∗ = 46 · can be immediately excluded, as an Earth-directed CME can generally be identified (indeed much earlier) as being front-sided based on Extreme Ultraviolet (EUV) images of the full solar disk (e.g., Thompson et al. 1998; Plunkett et al. 1998). The other solution, χ ∗ = -46 · , is physical and yields a value of 60 R S for the distance, z , of the main scattering site (corresponding to the sheath) from the detector. How best to judge which solutions for χ ∗ are physical is explained in detail in Section 4. Once the Thomsonscattering factor z 2 G of the sheath has been inferred, its column-integrated electron number density can be estimated based on the following equation:\nδN sheath = ∫ δndz /similarequal ∫ δnz 2 Gdz z 2 G (10)\nIt is clear that WL polarisation measurement can prove extremely valuable in the study of interplanetary CMEs and shocks.\n3.3. Magnetic Field Inferred from Faraday Rotation\nAs discussed in Section 3.2, the column-integrated electron number density along any LOS can be inferred from its WL observations. Thus, if a radio beam lies within the FOV of a WL imager such that they remotely probe\nthe same plasma volume, the WL density measurements can be used to retrieve magnetic field strength from the received FR signal. We demonstrate this, for LOS1, in Figure 5. After subtracting the background solar wind contribution, the enhancements in FR measurement and WL radiance, due to the presence of the sheath of the simulated Earth-directed shock, are given by δ Ω RM and δI , respectively. The ratio of δ Ω RM and δI can be expressed as\nδ Ω RM δ I = ∫ δ ω RM dz ∫ δ i dz = ∫ δ ( nB ‖ ) dz ∫ z 2 Gδn dz ≈ ∫ δ ( nB ‖ ) dz z 2 G ∫ δn dz ≈ 1 z 2 G δ ( nB ‖ ) δ n (11)\nAs discussed in Section 3.2, z 2 G corresponds to the average value of z 2 G in the sheath. The derivable parameter δ ( nB ‖ ) δ n , which we call B ∗ ‖ , can be expressed in the form\nB ∗ ‖ ≡ δ ( nB ‖ ) δ n = δB ‖ + B ‖ 0 + n 0 δB ‖ δn = B ‖ + n 0 δB ‖ δn > B ‖ (12)\nwhere B ‖ 0 and n 0 denote the initial background values of B ‖ and n , respectively. The inferred value of B ∗ ‖ serves as an upper limit for B ‖ .\n4. RADIANCE PATTERNS IN J-MAPS OF WHITE LIGHT AND FARADAY ROTATION\nShock propagation through the inner heliosphere can be identified through the inclined trace with which it is associated in a time-elongation map (J-map). J-maps of WL radiance ( I/I ∗ , I ) and degree of polarisation ( p , p ∗ ), and FR measurement | δ Ω RM | , as viewed from observers at 0.5 and 1 AU, are presented in Figure 6 and compared in Figure 7. The normalisation factor I ∗ in Figure 6 corresponds to an electron number density distribution that varies according to n ∝ r -2 . A radiance threshold of I/I ∗ ≥ 3 . 68 × 10 -15 is used to demarcate the sheath region in time-elongation ( t -ε ) parameter space. The modified polarisation p ∗ is only calculated, using Equation 9, inside the sheath (Figures 6g-h). The absolute values of I and | δ Ω RM | within the sheath region are much larger for the observer at 0.5 AU, whereas the sheath values of I/I ∗ , p , and p ∗ are comparable when viewed from either vantage point. Over the elongation range 15 · ≤ ε ≤ 180 · , the radiance ratio Max. ( I 0 . 5AU ) Max. ( I 1AU ) is limited to values between 8 and 11 (Figure 7c). This demonstrates that interplanetary CMEs and shocks are viewed better from a location closer to the Sun.\nThe position, mass, and magnetic field of the sheath can be inferred from those directly-measurable parameters presented in Figure 6, using the analytical methods presented in Sections 2.1 and 3.3. As shown in Figure 4, and explained in Section 3.2, the Thomson-scattering factors are symmetrical around χ ∗ = 0 · . As a result, a single value of degree of polarisation p ∗ corresponds to two symmetrical solutions for the scattering angle χ ∗ . The results shown in Figure 8 are derived from those in Figure 6 (for an observer at 0.5 AU) under the assumption of forward scattering, while those in Figure 9 assume backward scattering. For the forward-scattering situation, presented in Figure 8b, the inferred longitude\nof the sheath ϕ sheath is 22 · at an elapsed time of 5 hours and 9 · at 11 hours. For the backward-scattering case, shown in Figure 9b, the sheath is at ϕ sheath = 140 · and 60 · at these times. So, an observer at 0.5 AU infers a longitude change ∆ ϕ sheath of 13 · (Figure 8b) and 80 · (Figure 9b) for the forward and backward-scattering cases, respectively. The dramatic change in sheath longitude for the backward-scattering case might indicate that the shock is significantly deflected during its interplanetary propagation. However, such an abnormal degree of lateral deflection of ∆ ϕ sheath = 80 · would be highly unphysical, and may imply a 'ghost trajectory' (Figure 6, DeForest et al. 2013). The east-west symmetry of the radiance pattern suggests that the shock is actually front-sided and Earth-directed, rendering the assumption of backward-scattering invalid (Figure 9). If we assume that the radiance pattern shown in Figure 6 is attributable to forward scattering, the inferred position of the sheath is shown as the solid white curve in Figure 2. This agrees very well with the actual position of the sheath. At any given time, only a certain portion of the sheath will be visible from a fixed observing location (Xiong et al. 2013). For example, at an elapsed time of 5.5 hours, it is the flank of the sheath (Figure 2a) that corresponds to the leading edge of the radiance pattern in 6a, while 6 hours later it is the nose (Figure 2d). So, in fact, the longitudinal change of ∆ ϕ sheath = 13 · inferred from Figure 8b is actually an artefact of the viewing geometry and does not represent an actual deflection of the shock front. Along with the inferred position of the sheath, the column-integrated electron number density, δN sheath , and the parallel magnetic field component, B ‖ , are also presented in Figure 8. The derived value of | B ‖ | provides an upper limit for the actual magnetic field, as explained in Section 3.3. By making coordinated observations in WL and FR, CMEs can not only be continuously tracked, but quantitatively diagnosed as they propagate through interplanetary space.\n5. INTERPLANETARY IMAGING FROM DIFFERENT OBSERVATION SITES\nAn interplanetary CME looks different when viewed from different vantage points, but can be readily imaged from a wide range of longitudes. The observed WL radiance pattern depends not only on the longitude ϕ o of the observer, as discussed by Xiong et al. (2013), but also on its heliocentric distance r o . In Section 3.1, we compare observations made from radial distances of 0.5 and 1 AU. In Section 5.1, we consider two particular observation sites that are often considered favourable in terms of WL imaging, the L4 and L5 Lagrangian points. In Section 5.2, we quantify more fully the dependence of WL imaging on r o .\n5.1. Observing an Earth-Directed shock from the L4 and L5 Lagrangian Points\nThe L4 and L5 Lagrangian points of the Sun-Earth system are often considered advantageous for observing Earth-directed CMEs. There are five Lagrangian points, all in the ecliptic, i.e., L1-L5. A spacecraft at L1, L2, or L3 is metastable in terms of its orbital configuration, and hence must frequently use propulsion to remain in the same orbit. In contrast, a spacecraft at L4 or L5 is resistant to gravitational perturbations, and\nis believed to be more stable. The L4 and L5 points lie 60 · ahead of and behind the Earth in its orbit, respectively. STEREO A reached the L4 point in September 2009 and STEREO B reached L5 in October 2009. The twin STEREO spacecraft were pathfinders for future L4/L5 missions (Akioka et al. 2005; Biesecker et al. 2008; Gopalswamy et al. 2011). A spacecraft at either L4 or L5 can perform routine side-on imaging of Earthdirected CMEs, and hence is of great merit for space weather monitoring.\nFigure 10a illustrates the imaging, be it in WL or FR, of an Earth-directed sheath from the L5 point. LOS7 intersects the nose of the shock at an elapsed time of 14.5 hours, when the shock nose lies on the Thomsonscattering sphere. The variation, along LOS7, of a number of salient physical parameters is shown in Figures 10 e-j. The interplanetary magnetic field lines are compressed and rotated within the sheath. This rotation results in the closer alignment of the field lines with LOS7, such that the magnetic field component along the LOS, | B ‖ | , is greatly enhanced (Figure 10i). The enhancements of both | B ‖ | and electron number density n within the sheath are responsible for the resultant increases in WL radiance I and FR measurement | Ω RM | . The degree of WL polarisation p , as viewed along LOS7 that is at an elongation of 34 · , is 0.67 for the background solar wind and increases to 0.75 during the shock passage at 14.5 hours. This corresponds to a value of the modified WL polarisation p ∗ of 0.98, based on Equation 9. As was done for LOS1 in Section 3, we evaluate the WL radiance along LOS7 (Figure 10a), from which we infer the shock position (Figure 10d). Again, a single value of p ∗ corresponds to two symmetrical solutions for scattering angle χ ∗ , i.e., p ∗ = 0 . 29 and χ ∗ = ± 46 · for LOS1, and p ∗ = 0 . 98 and χ ∗ = ± 5 · for LOS7. For LOS1, only one solution for χ ∗ = -46 · was deemed physical; for LOS7, both solutions for χ ∗ are potentially physical. The scattering sites corresponding to χ ∗ = ± 5 · are very close to one another, and both agree well with the actual position of the sheath (Figure 10a). The section of LOS7 bounded by -5 · ≤ χ ∗ ≤ 5 · lies within the sheath. Both forward scattering ( -5 · ≤ χ ∗ < 0 · ) and backward scattering (0 · < χ ∗ ≤ 5 · ) will contribute to the radiance I observed along this LOS. The propagating sheath can be tracked continuously and easily in WL from the L5 vantage point, such that it leaves an obvious signature in the J-map of synthesised radiance (Figures 10b and 10c). This confirms previous assertions that the L4 and L5 points are very favourable in terms of space weather monitoring.\n5.2. Dependence of White-Light Radiance on Heliocentric Distance\nThe background intensity at a fixed elongation in a WL sky map is greater for an observer closer to the Sun. For a heliospheric imager at any distance from the Sun, Jackson et al. (2010) proposed the following Thomsonscattering principles: (1) The WL radiance I at a given solar elongation falls off with the heliocentric distance r according to r -3 ; (2) Such a dependence of I ∝ r -3 is valid for almost any viewing elongation, and for any radial distance from 0.1 AU out to 1 AU and beyond. The WL radiance I depends on the heliospheric distribution of electron number density n . In interplanetary space,\nthe background solar wind speed is nearly constant, and the background electron number density n 0 varies approximately with r -2 . However, the equilibrium defined by n 0 ∝ r -2 is disturbed by the presence of interplanetary transients, such as CMEs and CIRs. A travelling shock can sweep up, and hence compress significantly, the background solar wind plasma. Figures 2 and 10a show a density enhancement of n -n 0 n 0 ≈ 2 . 2 within the sheath. The associated compression ratio n n 0 ≈ 3 . 2 indicates that the shock is very strong. However, when viewed along elongations less than 60 · , the strongest signatures of shock passage (characterised by Max.( I )) vary very closely with r -3 (Figures 11b and 11c). The relationship of Max.( I ) ∝ r -3 is slightly violated at large elongations ε > 60 · . Figure 7c reveals that the ratio between Max.( I 0 . 5AU ) and Max.( I 1AU ) is close to 8 for ε ≤ 60 · , increasing thereafter to 10.8 at ε = 180 · . The premise that the WL radiance decreases with the third power of Sun-observer distance generally holds true for both the background solar wind and propagating CMEs.\n6. DISCUSSION\nThe detectability in WL of a particular electron density feature is determined by its signal above the noise background. In STEREO /HI-1 images, the dominant WL signal is zodiacal light due to scattering of sunlight from the F-corona, which is centred around the ecliptic. In the STEREO /HI-2 FOV, the noise floor is primarily determined by photon noise and the background star-field (DeForest et al. 2011). Away from the ecliptic, the background WL noise has a sharp radial gradient in coronal images, and is nearly constant in heliospheric images. The signal-to-noise ratio for heliospheric electron density features is discussed by Howard et al. (2013). We will address the detection of CMEs in the presence of background noise in future forward-modelling work.\nIf both a transient CME and background (Heliospheric Current Sheet (HCS) - Heliospheric Plasma Sheet (HPS)) plasma structures are present along the same LOS, both will contribute to the total LOS-integrated radiance. In this case, the interpretation of the data would clearly be more problematic. Moreover, if the LOS were to penetrate a HCS, the magnetic field vector would, at that point, rotate through 180 · . Due to the mutual cancellation of B ‖ across the HCS, there may be no net FR signature according to Equations 4-6. Hence, even such a significant interplanetary structure may be associated with only a weak FR measurement. Conversely, the relatively dense plasma within a HPS can significantly contribute to WL radiance. Thus the potential effects of the presence of HCS-HPS structures need to be borne in mind in the remote imaging of CMEs. In the current work, however, we find that such effects are negligible. In our numerical simulation, there are two HCS-HPS structures, which are initially rooted at longitudes of ϕ = ± 90 · at the inner boundary of our numerical simulation. The simulated shock emerges at a longitude of ϕ = 0 · . The large longitudinal difference between the HCS-HPS and the shock means that the remote-sensing signatures are principally contributed by the sheath. Thus, in our forward-modelling work, the signal enhancements of synthesised imaging in WL and FR are unambiguously the result of the propagating sheath.\nIn general, the more complex the interplanetary dynamics, the more complex the resultant remote-sensing observations will be. For instance, a CME can interact with other CMEs and/or background solar wind structures such as CIRs, HCSs, and HPSs; mutual interaction between CMEs is, however, generally more perturbing than interactions between CMEs and such background structures. Interactions can result in the background solar wind structures becoming warped or distorted (e.g., Odstrˇcil et al. 1996; Hu & Jia 2001), and CMEs being accelerated/decelerated (e.g., Lugaz et al. 2005; Xiong et al. 2007; Shen et al. 2012b), deflected (e.g., Xiong et al. 2006b, 2009; Lugaz et al. 2012), distorted (e.g., Xiong et al. 2006b, 2009), or entrained (e.g., Rouillard et al. 2009a). In particular, during such interactions, the behavior of a sheath can become much more complex: the shock aphelion can be deflected, spatial asymmetries can develop along the shock front, and the shock front can potentially merge completely with other shock fronts. At an interaction site, both the plasma density and magnetic field would be compressed; this would lead to enhanced signatures in both WL and FR observations. For example, the interaction between two CMEs was manifest as a very bright arc in WL images (e.g., Harrison et al. 2012; Liu et al. 2012; Temmer et al. 2012). Different types of interaction would likely result in different WL radiance signatures; in fact, through a single interaction, the corresponding radiance pattern would evolve. The interpretation of such complex WL radiance patterns would be prone to large uncertainties, but can be rigorously constrained if interplanetary imaging was performed from multiple vantage points and complemented by numerical modelling. For stereoscopic WLimaging, ray-paths from one observer intersect those from the other observer. Thus the 3D distribution of electrons in the inner heliosphere can be reconstructed using a time-dependent tomography algorithm (Jackson et al. 2006; Bisi et al. 2008; Webb et al. 2013). With the aid of numerical modelling, coordinated imaging in WL and FR would enable the properties and evolution of complex interplanetary dynamics to be diagnosed.\n7. CONCLUDING REMARKS\nIn this paper, we have investigated the WL and FR signatures of an interplanetary shock based on an approach of forward MHD modelling. The WL Thomsonscattering geometry is increasingly more significant at larger elongations. The degree of WL polarisation can be used to estimate the 3D location of the main scattering region, while FR measurement can be used to infer, to some extent, the magnetic configurations of CMEs. This work presented here demonstrates, as a proof-of-concept, that the availability of coordinated observations in polarised WL and FR measurement would enable the local LOS magnetic component to be estimated. Although the current generation of heliospheric WL imagers, such as the STEREO /HI instruments, do not have polarisers, there are advances underway in terms of FR imaging using Low-frequency radio arrays. Coordinated imaging in WL and FR would enable the inner heliosphere to be mapped in fine detail; the location, mass, and magnetic field of CMEs can be diagnosed on the basis of such combined observations. Forward modelling is crucial in establishing the causal link between interplanetary dynam-\nics and observable signatures, and can provide valuable guidance for future coordinated WL and FR imaging.\nAlthough not the methodology of the current work, numerical MHD models of the inner heliosphere can also be directly driven by photospheric observations (e.g., Hayashi 2005; Wu et al. 2006; Feng et al. 2012b). A comparison of synthesised and observed WL and FR sky maps, the former based on the use of such datadriven models, would prove highly beneficial in validating the forward modelling and interpreting the observations. Such an integration of observation data analysis and numerical forward modelling will be explored as the continuation of the preliminary modelling work presented in this paper.\nThis work is jointly supported by the National Basic Research Program (973 program) under grant 2012CB825601, the Chinese Academy of Sciences (KZZD-EW-01-4), the National Natural Science Foun-\ndation of China (41231068, 41031066, 41204129), the Strategic Priority Research Program on Space Science from the Chinese Academy of Sciences (XDA04060801), the Specialized Research Fund for State Key Laboratories of China, the Chinese Public Science and Technology Research Funds Projects of Ocean (201005017), open research foundation of Science and Technology on Aerospace Flight Dynamics Laboratory of China (AFDL2012002), research fund for recipient of excellent award of the Chinese Academy of Sciences President's scholarship (startup fund). 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Fig. 1.Examples of the Thomson-scattering geometry for observers at different radial distances r o and longitudes ϕ o . In panel (a), a radially-propagating solar wind parcel is viewed sequentially, but at the same scattering angle, by observers situated at radial distances of 0.5 AU (point A ) and 1 AU (point B ). Panels (b-d) illustrate the observation of an interplanetary sheath, denoted as a shaded region, by observers with different combinations of r o and ϕ o . Longitude is defined to be positive (negative) for an observer situated to the west (east) of Earth.
\n\n\n\n
Fig. 2.Relative enhancement of electron number density, in the ecliptic, ( n -n 0 ) /n 0 within an Earth-directed interplanetary sheath. Red and black solid lines indicate sunward and anti-sunward interplanetary magnetic field lines, respectively. The sheath is imaged by two observers on the Sun-Earth line ( ϕ = 0 · ), at heliocentric distances of r o = 0 . 5 (left column) and 1 AU (central and right columns). For each observer, the ecliptic cross-section of its corresponding WL Thomson-scattering sphere is depicted as a dotted circle. Six lines-of-sight, LOS1-LOS6, are superimposed as straight arrows. All LOSs look westward. At any given time t , the two observers, both located on the Sun-Earth line, detect the sheath at different elongations ε (compare panel a with panel b, and panel d with panel e). Conversely, when viewing along the same ε , the two observers detect the sheath at different t (compare panel a with panel c, and panel d with panel f). Solid white curves overlaid on each panel indicate the position of the sheath inferred from polarised WL imaging.
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Fig. 3.WL radiance i , WL Thomson-scattering geometry factors ( z 2 G , z 2 G R , z 2 G T ), electron number density n , degree of WL polarisation p , parallel magnetic field | B ‖ | , and FR measurement | ω RM | , plotted as a function of modified scattering angle χ ∗ = 90 -χ along LOS1 (column A), LOS2 (column B), and LOS3 (column C). Each parameter is normalised to its maximum value along each LOS, as given in Table 1. Note that i = nZ 2 G and ω RM ∝ nB ‖ . For the parameters i , n , | B ‖ | , and | ω RM | , initial and disturbed profiles are depicted as dashed and solid lines, respectively. The black and red sections of the | B ‖ | and | ω RM | profiles (two bottom rows) correspond to negative and positive values of B ‖ , respectively.
\n\n\n\n
Fig. 4.Dependence of the scattering angle χ ∗ , the Thomson-scattering geometry factor z 2 G , and the LOS depth z on the degree of polarisation p for LOS1 in Figure 2a. In response to shock passage, the initial radiance components, I T0 and I R0 , are enhanced to values of I T and I R , respectively. The enhancement in these radiance components determines the modified degree of polarisation p ∗ , according to the expression p ∗ = I T -I T0 -I R + I R0 I -I 0 . The vertical dashed line, demarking p ∗ , crosses the χ ∗ and z profiles twice.
\n\n\n\n
Fig. 5.The deviation of various parameters, from their initial values, plotted as a function of z along LOS1. Note that δ ( nB ‖ ) δ n = δB ‖ + B ‖ 0 + n 0 δB ‖ δn = B ‖ + n 0 δB ‖ δn . The parallel magnetic field component B ∗ ‖ (plotted as a horizontal dashed line in panel d) is calculated using the expression δ Ω RM δ I = ∫ δ ω RM dz ∫ δ i dz = ∫ δ ( nB ‖ ) dz ∫ z 2 Gδn dz ≈ 1 z 2 G δ ( nB ‖ ) δ n = 1 z 2 G B ∗ ‖ .
\n\n\n\n
Fig. 6.Time-elongation maps of WL radiance (panels a and b: I/I ∗ , panels c and d: I ), degree of WL polarisation (panels e and f: p , panels g and h: p ∗ ), and FR measurement (panels i and j: | δ Ω RM | ), as viewed by observers at longitude ϕ o = 0 · and at radii r o = 0.5 AU (left column) and 1 AU (right column). I ∗ is the normalisation factor for I , and corresponds to the radial variation of electron number density n ∝ r -2 . The dotted lines in panels a-f correspond to I/I ∗ = 3 . 68 × 10 -15 . p and p ∗ are determined from the radiance and the enhancement in the radiance, respectively, as given by p = I T -I R I and p ∗ = I T -I T0 -I R + I R0 I -I 0 . Panels g and h only show p ∗ within the sheath region.
\n\n\n\n
Fig. 7.A comparison of the WL radiance I (panels a, b, and c), the degree of WL polarisation p (panel d), and the FR measurement δ Ω RM (panel e) over the elongation range from 15 · to 180 · , as viewed by observers at 0.5 AU (solid line) and 1 AU (dashed line). The attribution 'Max' refers to the strongest signal during the sheath passage.
\n\n\n\n
Fig. 8.Panels a-e present the location of the scattering site ( z sheath , ϕ sheath , r sheath ), the column-integrated electron number density δN sheath , and the parallel magnetic field B ‖ , plotted as a function of time and elongation, derived by assuming forward-scattering ( χ ∗ < 0 · ).
\n\n\n\n
Fig. 9.Panels a-b present the location of the scattering site ( z sheath , ϕ sheath ), plotted as a function of time and elongation, derived by assuming backward-scattering ( χ ∗ > 0 · ).
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Fig. 10.Simulated results corresponding to the observation of an Earth-directed shock from the L5 vantage point, i.e., along LOS7 ( r o = 1 AU, ϕ o = -60 · ): (panel a) relative enhancement of electron number density ( n -n 0 ) /n 0 in the ecliptic; (panels b and c) synthesised WL time-elongation maps of I/I ∗ and I ; (panel d) modified scattering angle χ ∗ as a function of the degree of polarisation p ; (panels e-j) a number of synthesised WL and FR parameters, plotted as a function of χ ∗ along LOS7.
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Fig. 11.Simulated WL radiance, as a function of r o , viewed along an elongation of 30 · by an observer on the Sun-Earth line ( ϕ o = 0 · , 50 R S ≤ r ≤ 215 R S ). Again, 'Max' refers to the strongest signal associated with the sheath passage. The dashed red lines in the two upper panels show, for comparison, an r -3 variation. Both I ∗ and Max.( I ) are well described by such a variation.
\n\n20\nXiong et al.\n)\nt\nn\ne\nm\ne\nr\nu\ns\na\ne\nm\nR\nF\nc\ni\nt\ne\nn\ng\na\nm\nl\ne\nl\nl\na\nr\na\nP\nn\no\nr\nt\nc\ne\nl\nE\n3\n-\nm\nd\na\nr\n2\n1\n-\n0\n1\n×\n(\n)\nT\nn\n(\n)\n3\n-\nm\nc\n(\n)\n.\n0\n1\ne\nr\nu\ng\ni\nF\nn\no\nd\ni\na\nl\nr\ne\nv\no\ns\ni\n7\nS\nO\nL\nd\nn\na\n2\ne\nr\nu\ng\ni\nF\nn\no\nd\ni\na\nl\nr\ne\nv\no\ne\nr\na\n6\n-\n, L O S 3 L O S s 1 t t e r i n g o r s G T\nh\nc\na\nE\n.\nj\n-\ne\n0\n1\nd\nn\na\n3\ns\ne\nr\nu\ng\ni\nF\nn\ni\nn\no\ni\nt\na\ns\ni\nl\na\nm\nr\no\nn\nr\no\nf\nd\ne\ns\nu\n,\n7\nS\nO\nL\nd\nn\na\n,\n2\n;\nt\nc\n|\n‖\nB\n|\nn\ny\nt\ni\ns\nn\ne\nd\n2\nz\n
\n\n
\nn\na\n,\n|\n‖\nB\n|\n,\nn\n,\nT\nG\n2\nz\n,\nR\nG\n2\nz\n,\nG\n2\nz\n,\ni\ns\nr\ne\nt\ne\nm\na\nr\na\np\ne\nh\nt\nf\no\ns\ne\nu\nl\na\nv\nm\nu\nm\ni\nx\na\nM\nl\ne\nn\na\nd\nn\na\n,\no\nϕ\ne\nd\nu\nt\ni\ng\nn\no\nl\na\n,\no\nr\ns\nu\ni\nd\na\nr\na\n,\nt\ne\nm\ni\nt\na\nd\ne\nt\na\nn\ng\ni\ns\ne\nd\ns\ni\nS\nO\nL\na\nc\nL\nW\nn\no\ni\nt\na\ng\nn\no\nl\nE\ne\nd\nu\nt\ni\ng\nn\no\nL\ni\ni\nd\na\nR\ne\nm\ni\nT\nS\nO\nL\n(\n)\n·\n(\n)\nε\no\nϕ\no\nr\nt\n·\n(\n)\nU\nA\n(\n)\nr\nu\no\nh\n(\nd\nl\ne\nfi\nr\ne\nb\nm\nu\nn\n|\nM\nR\nω\n|\n4\n.\n4\n1\n7\n0\n2\n2\n9\n3\n0\n2\n0\n5\n.\n0\n5\n.\n5\n1\nS\nO\nL\n2\n.\n8\n1\n3\n2\n2\n3\n9\n8\n1\n7\n0\n1\n5\n.\n5\n2\nS\nO\nL\n1\n5\n.\n1\n9\n.\n8\n6\n7\n8\n0\n2\n0\n1\n4\n1\n3\nS\nO\nL\n2\n4\n.\n0\n5\n.\n8\n2\n3\n.\n0\n6\n4\n3\n0\n6\n-\n1\n5\n.\n4\n1\n7\nS\nO\nL\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"Coronal mass ejections (CMEs) can be continuously tracked through a large portion of the inner heliosphere by direct imaging in visible and radio wavebands. White-light (WL) signatures of solar wind transients, such as CMEs, result from Thomson scattering of sunlight by free electrons, and therefore depend on both the viewing geometry and the electron density. The Faraday rotation (FR) of radio waves from extragalactic pulsars and quasars, which arises due to the presence of such solar wind features, depends on the line-of-sight magnetic field component B ‖ , and the electron density. To understand coordinated WL and FR observations of CMEs, we perform forward magnetohydrodynamic modelling of an Earth-directed shock and synthesise the signatures that would be remotely sensed at a number of widely distributed vantage points in the inner heliosphere. Removal of the background solar wind contribution reveals the shock-associated enhancements in WL and FR. While the efficiency of Thomson scattering depends on scattering angle, WL radiance I decreases with heliocentric distance r roughly according to the expression I ∝ r -3 . The sheath region downstream of the Earth-directed shock is well viewed from the L4 and L5 Lagrangian points, demonstrating the benefits of these points in terms of space weather forecasting. The spatial position of the main scattering site r sheath and the mass of plasma at that position M sheath can be inferred from the polarisation of the shock-associated enhancement in WL radiance. From the FR measurements, the local B ‖ sheath at r sheath can then be estimated. Simultaneous observations in polarised WL and FR can not only be used to detect CMEs, but also to diagnose their plasma and magnetic field properties. Subject headings: methods: numerical - shock waves - solar-terrestrial relations - solar wind Sun: coronal mass ejections (CMEs) - Sun: heliosphere","pages":[1]},{"title":"USING COORDINATED OBSERVATIONS IN POLARISED WHITE LIGHT AND FARADAY ROTATION TO PROBE THE SPATIAL POSITION AND MAGNETIC FIELD OF AN INTERPLANETARY SHEATH","content":"Ming Xiong 1, 2 , Jackie A. Davies 3 , Xueshang Feng 1 , Mathew J. Owens 4 , Richard A. Harrison 3 , Chris J. Davis 4 , and Ying D. Liu 1 Draft version September 8, 2018","pages":[1]},{"title":"1.1. The Inner Heliosphere","content":"The inner heliosphere is permeated with the magnetised solar wind from the Sun. At solar minimum, the solar wind is inherently bimodal (McComas et al. 2000), with slow flow tending to emanate from near the ecliptic and fast flow tending to emanate at higher latitudes. Several large-scale structures, which pervade interplanetary space, are associated with the 'ambient' solar wind: (1) a spiralling interplanetary magnetic field (the Parker spiral) that forms as a result of solar rotation (Parker 1958), (2) corotating interacting regions (CIRs) that are formed at the interface between a preceding slow solar wind stream and a following fast solar wind stream (Gosling & Pizzo 1999), and (3) the heliospheric current sheet typically embedded in the heliospheric plasma sheet (Winterhalter et al. 1994; Crooker et al. 2004). The background solar wind flow is frequently disturbed by coronal mass ejections (CMEs), large-scale expulsions of plasma and magnetic field from the solar atmosphere. CMEs typically expand during their propagation, because the total solar wind pressure de- mxiong@spacweather.ac.cn 4 Reading University, Reading, UK creases with heliocentric distance (D'emoulin & Dasso 2009; Gulisano et al. 2010). The expansion speed of a CME depends on its spatial size, translation speed, and heliocentric distance, as well as the pre-existing solar wind conditions (Nakwacki et al. 2011; Gulisano et al. 2012). A number of popular models describe the motion of a CME as governed by two forces: a propelling Lorentz force (Chen 1989, 1996; Chen et al. 2006) and an aerodynamic drag force (Cargill et al. 1996; Vrˇsnak & Gopalswamy 2002; Cargill 2004). According to these models, the drag force gradually becomes dominant in interplanetary space, and the CME speed finally adjusts to the ambient solar wind speed. The equalisation of the CME and solar wind speed occurs at very different heliospheric distances, from below 30 solar radii to beyond 1 AU, depending on the characteristics of the CME and the solar wind (Temmer et al. 2011). A CME can undergo significant, nonlinear, and irreversible evolution during its propagation, as it interacts with the ambient solar wind and other CMEs (e.g., Burlaga et al. 2002; D'emoulin 2010). Coronagraph observations show that CME morphology is distorted rapidly and significantly in a structured solar wind (e.g., Savani et al. 2010, 2012; Feng et al. 2012a). Such a distortion occurs over a relatively short heliocentric distance. Interaction between multiple CMEs has been revealed by in-situ observations (e.g., Burlaga et al. 1987; Wang et al. 2003a; Steed et al. 2011; Mostl et al. 2012), radio burst observations (e.g., Gopalswamy et al. 2001; Oliveros et al. 2012), white-light (WL) imaging (e.g., Harrison et al. 2012; Liu et al. 2012; Lugaz et al. 2012; Temmer et al. 2012; Shen et al. 2012a; Bemporad et al. 2012), and numerical magnetohydrodynamic (MHD) simulation (e.g., Lugaz et al. 2005; Xiong et al. 2007, 2009; Shen et al. 2012b). CMEs cause phenomena at Earth, such as geomagnetic storms and solar energetic particles, that can result in major space weather effects (Gopalswamy 2006; Webb & Howard 2012). Traditionally, a CME has been defined in terms of a three-part structure, involving a bright sheath, a dark cavity, and a bright filament. It is now accepted that the cavity component is an escaping magnetic flux rope that drives the CME (e.g., Rouillard et al. 2009b; DeForest et al. 2011). A highspeed flux rope can drive a fast shock ahead of itself that is much wider in angular extent than the flux rope itself. The region between the shock front and the flux rope is defined as a sheath. Within the sheath, (1) magnetic field lines are draped and compressed, and (2) a plasma flow is deviated, compressed, and turbulent (e.g., Gosling & McComas 1987; Owens et al. 2005; Liu et al. 2008). Precursor southward magnetic fields ahead of CMEs are generally compressed, making them particularly geoeffective (Tsurutani et al. 1992; Gonzalez et al. 1999). The magnetic fields in the sheath and in the flux rope can be equally important in driving major geomagnetic storms (Tsurutani et al. 1988, 1992; Szajko et al. 2013). In so-called two-dip storms, it is often the case that the first dip in the Dst index is produced by the upstream sheath and the second is produced by the driving flux rope (Echer et al. 2004; Zhang et al. 2008; Mostl et al. 2012).","pages":[1,2]},{"title":"1.2. Heliospheric White Light Observations","content":"Heliospheric imagers (HIs) detect WL that has been Thomson-scattered from free electrons. For resolved objects, such as CMEs, the power detected by an individual pixel depends linearly on the solid angle subtended by that pixel ( δω ) and the area subtended by the corresponding aperture ( δA ), and is proportional to the radiance (measured in W m -2 SR -1 ). The light from unresolved objects, such as stars, which are much narrower in angular extent, tends to fall within individual pixels. For a resolved heliospheric electron density feature, such as a CME, a single pixel provides a measure of its radiance (surface brightness), while summing contributions from all pixels over the entire extent of the feature provides a measure of its intensity (total brightness). The intensity is an integral of the radiance over the apparent feature size. Therefore, the feature's intensity determines its detectability of an object, be it resolved or unresolved (Howard & DeForest 2012). The background zodiacal and stellar signals detected by heliospheric imagers are much more intense than the signal due to Thomson-scattering from plasma features such as CMEs (Leinert & Pitz 1989). Fortunately, using an image-differencing technique, the much more stable background radiance can be removed, such that the more transient Thomson-scattering signal can be extracted. From such processed Thomsonscattering images, the sunlight-irradiated CMEs can be easily identified and tracked. According to theory, the heliospheric Thomson-scattering radiance is governed by the Thomson-scattering geometry fac- tors and electron number density (Vourlidas & Howard 2006; Howard & Tappin 2009; Howard & DeForest 2012; Xiong et al. 2013). The CME detectability in WL is actually more limited by perspective and field-of-view (FOV) effects than by location relative to the Thomsonscattering sphere (Howard & DeForest 2012). Heliospheric imaging from two vantage points, both off the Sun-Earth line, was made possible by the Heliospheric Imagers (HIs) onboard the Solar-TErrestrial RElations Observatory ( STEREO ) (Eyles et al. 2009). With the STEREO /SECCHI package, a CME can be imaged from its nascent stage in the inner corona all the way out to 1 AU and beyond (e.g., Harrison et al. 2008; Davies et al. 2009; Davis et al. 2009; Liu et al. 2010b; DeForest et al. 2011; Liu et al. 2013). In particular, images from STEREO /HI-2 have revealed detailed spatial structures within interplanetary CMEs, including leading-edge pileup, interior cavities, filamentary structure, and rear cusps (DeForest et al. 2011). Comparison with in-situ observations has revealed that the leadingedge pileup of solar wind material, which is evident as a bright arc in WL imaging, corresponds to the sheath region. However, the interpretation of the leading edge of the radiance pattern, especially at larger elongations, is fraught with ambiguity (e.g., Howard & Tappin 2009; Xiong et al. 2013). Elongation ε is defined as the angle between the Sun-observer line and a line-of-sight (LOS). Because a CME occupies a significant three-dimensional (3D) volume, different parts of the CME will contribute to the radiance pattern imaged by observers situated at different heliocentric longitudes (Xiong et al. 2013). Even for an observer at a fixed longitude, a different part of the CME will contribute to the imaged radiance at any given time (Xiong et al. 2013). Various techniques have been developed that enable the spatial locations and propagation directions of CMEs to be inferred, based on the fitting of their moving radiance patterns (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Thernisien et al. 2009; Liu et al. 2010b; Lugaz et al. 2010; Mostl et al. 2011; Davies et al. 2012). However, the determination of interplanetary CME kinematics, propagation direction in particular, are somewhat ambiguous (Howard & Tappin 2009; Davis et al. 2010; Davies et al. 2012; Howard & DeForest 2012; Xiong et al. 2013; Lugaz & Kintner 2013).","pages":[2]},{"title":"1.3. Faraday Rotation Measurement","content":"Faraday rotation (FR) is the rotation of the plane of polarisation of an incident electromagnetic wave as it passes through a magnetised ionic medium. The FR observations of linearly polarised radio sources can be used to estimate magnetic field in the corona and interplanetary space (e.g., Levy et al. 1969; Bird et al. 1980; Sakurai & Spangler 1994; Liu et al. 2007; Jensen 2007; Jensen & Russell 2008; You et al. 2012; Jensen et al. 2013). The FR measurement of a radio signal corresponds to the path integral of the product of electron density n and the projection of the magnetic field along the LOS, B ‖ . The first FR experiment was conducted in 1968 by Levy et al. (1969), when solar plasma occulted the radio down-link from the Pioneer 6 spacecraft. As well as man-made radio sources, FR experiments can also exploit natural radio sources such as pulsars and quasars. The first FR experiments of this type were conducted by Bird et al. (1980) during the solar occultation of a pulsar. In terms of their locations on a sky map, many pulsars and quasars lie in the vicinity of the Sun. Therefore, simultaneous FR measurements along multiple beams can be used to map the inner heliosphere with a reasonable spatial resolution. Additional observations, for example in WL, would generally be necessary to confirm whether an FR transient was indeed caused by a CME. For instance, the first FR event, reported by Levy et al. (1969), could not be attributed unambiguously to the presence of any particular solar wind structure. The FR signatures, observed by Levy et al. (1969), exhibited a W-shaped profile over a time period of 2 -3 hours, with rotation angles of up to 40 · relative to the quiescent baseline. Woo (1997) interpreted the FR signature as the result of a coronal streamer stalk of angular size 1 · -2 · , whereas Patzold & Bird (1998) argued that it was caused by the passage of a series of CMEs. However, by comparing observations from the Solwind coronagraph and measurements of Helios down-link radio signals, Bird et al. (1985) were able to identify the signatures of five CMEs simultaneously in WL and FR. Moreover, the electron density derived from WL imaging can be used to enable magnetic field magnitude to be inferred from FR measurements. The heliospheric magnetic field can be remotely probed in FR, using low-frequency radio interferometers such as the Murchison Widefield Array (MWA) (Lonsdale, C. J., et. al. 2009), the LOw Frequency ARray (LOFAR) (de Vos et al. 2009), and the Very Large Array (VLA) (Thompson et al. 1980). Disturbance of the background solar wind by CMEs will cause the observed FR signatures to become variable (e.g., Levy et al. 1969; Bird et al. 1985; Jensen & Russell 2008). A change in either the electron density ( δn ) or the LOS magnetic field component ( δB ‖ ), or indeed both, will contribute to the rotation in the plane of polarisation of the radio signal by δ Ω RM . Interplanetary magnetic clouds (MCs) in particular, which have a magnetic flux rope configuration (Burlaga et al. 1981; Klein & Burlaga 1982; Lepping et al. 1990), can be identified from WL images (Rouillard et al. 2009b; DeForest et al. 2011) and are expected to be easily identifiable in FR measurements. Moreover, δn and | δ B | are often enhanced simultaneously within the sheath ahead of a fast MC. The FR due to a MC-driven sheath can be comparable to that due to the MC itself (Jensen et al. 2010). It is expected that the orientation and helicity of a MC will be able to be determined unambiguously from multi-beam FR measurements (Liu et al. 2007; Jensen 2007; Jensen et al. 2010). In contrast, the in-situ detection of magnetic flux ropes can be significantly hindered by the location of the observing spacecraft (e.g., Hu & Sonnerup 2002; Mostl et al. 2012; D'emoulin et al. 2013). FR imaging can be used to provide the magnetic orientation of a fast MC, and indeed its preceding sheath, prior to its arrival at Earth, which is crucial for predicting potential space weather effects at Earth.","pages":[2,3]},{"title":"1.4. Forward Magnetohydrodynamic Modelling","content":"Forward modelling of WL and FR signatures is proving extremely useful for inferring the in-situ properties of interplanetary CMEs from remote-sensing data. Sophis- ticated numerical MHD models of the inner heliosphere (e.g., Groth et al. 2000; Lugaz et al. 2005; Hayashi 2005; Xiong et al. 2006a; Li et al. 2006; Wu et al. 2006; Li & Li 2008; Odstrˇcil & Pizzo 2009; Shen et al. 2012b) can serve as a digital laboratory, to enable the synthesis of a variety of observable remote-sensing signatures. In this paper, we perform a numerical MHD simulation of an interplanetary shock in the ecliptic, from which we synthesise the signatures of that feature that would be remotely sensed at visible and radio wavelengths. Details of the MHD model, and the formulae required to synthesise the remote-sensing observations, are given in Section 2. The resultant synthesised remote-sensing signatures of the sheath, which would be observed from vantage points at 0.5 and 1 AU, are described and compared in Section 3. In Section 4, we discuss the radiance patterns that are observed in the synthesised WL and FR sky maps. In Section 5, we explore the role that the vantage point of the observer plays in the 'observability' of such WL and FR features. CME detection in the presence of background noise, and the heliospheric imaging of more complex interplanetary phenomena, are discussed in Section 6. The potentially important role that forward modelling can play in our understanding of coordinated WL and FR observations is summarised in Section 7.","pages":[3]},{"title":"2. METHOD","content":"Forward MHD modelling can self-consistently establish the links between interplanetary dynamics and the resultant observable signatures. A complete flow chart of forward modelling is illustrated in Figure 8 from Xiong et al. (2011). The travelling fast shock studied by Xiong et al. (2013) is revisited here. Our methodology consists of three general steps: (1) forward modelling of the shock using the numerical Inner-Heliosphere MHD (IH-MHD) model (Xiong et al. 2006a, 2013), (2) calculation of its Thomson-scattered WL signature, in Section 2.1, and (3) calculation of its FR signature, in Section 2.2. Characterisation of the IH-MHD model, the background solar wind conditions, and the initial shock injection is summarised respectively in Tables 1, 2, and 3 of Xiong et al. (2013). The simulated electron density n and magnetic field B are used to generate synthetic WL and FR images, which enable us to explore the WL and FR signatures of an interplanetary sheath. A plasma parcel emitted from the Sun would be observed, at the same elongation and the same Thomsonscattering angle, firstly by an observer situated at a radial distance of 0.5 AU from the Sun centre, and subsequently by an observer at 1 AU (Figure 1a). Such a configuration was discussed qualitatively by Jackson et al. (2010) and is analysed quantitatively in Section 3 of this paper. Observations from STEREO /HI suggest that a travelling sheath can be approximated as an expanding bubble (e.g., Howard & Tappin 2009; Lugaz et al. 2010; Davies et al. 2012; Mostl & Davies 2013). In-situ observations indicate that CMEs undergo self-similar expansion, as the speed profiles within CMEs themselves tend to be a linear function of time (e.g., Farrugia et al. 1993; Gulisano et al. 2012). In the schematic Figures 1b-d, the sheath region following an Earth-directed interplanetary shock is represented as a self-similarly expanding bubble. The sheath can look quite different when viewed from different heliocentric distances (Figures 1b and 1c) and/or different heliospheric longitudes (Figures 1b and 1d).","pages":[3,4]},{"title":"2.1. Thomson-Scattering WL Formulae","content":"A small parcel of free electrons, that is illuminated by a known intensity of incident sunlight (measured in W m -2 ), will scatter a certain amount of power per unit solid angle (measured in W rad -1 ). The effect of the Thomson-scattering geometry can be characterised by the so-called scattering angle χ , as depicted in Figure 1 of Xiong et al. (2013). Scattering can be backward ( χ < 90 · ), perpendicular ( χ = 90 · ), and forward ( χ > 90 · ). All photons that are scattered into an optical cone defined by the point spread function of an individual pixel will be attributed to that pixel (Figure 1b, Xiong et al. 2013). The classic principles of WL Thomson-scattering, as applied to coronagraph observations (Billings 1966), have been adapted to heliospheric imaging (Vourlidas & Howard 2006; Howard & Tappin 2009; Jackson et al. 2010; Howard & DeForest 2012; Xiong et al. 2013). The transverse electric field oscillation δ E of the Thomson-scattered radiance, which is inherently a continuum, can be considered in terms of its two orthogonal components, a tangential component δ E T and a radial component δ E R . The amplitudes of these two orthogonal oscillations ( I T = | δ E T | 2 and I R = | δ E R | 2 ) can be measured separately, using a polariser. The total radiance I and degree of polarisation p are defined as follows: Although the incident sunlight is unpolarised ( p = 0), the scattered WL radiance remains unpolarised only when the scattering angle | χ -90 · | = 90 · . The scattered light is elliptically polarised (0 < p < 1) for 0 · < | χ -90 · | < 90 · and linearly polarised ( p = 1) for χ = 90 · . Each pixel of a detector records the LOS integral of local WL radiance. Here z refers to a distance between the detector and the scattering site, as shown in Figure 1b of Xiong et al. (2013). The mathematical expressions for G , G R , and G T are given by Equations 1 and 2 of Xiong et al. (2013). The observed WL radiance is determined jointly by the heliospheric distribution of electrons n and Thomsonscattering geometry factors ( z 2 G , z 2 G R , z 2 G T ). As noted above, the efficiency of Thomson scattering depends significantly on the Thomson scattering angle χ . The perpendicular scattering, χ = 90 · , received by an observer comes from the Thomson Sphere. The 'Thomson sphere', sometimes called the 'Thomson surface', is the sphere in which the Sun and observer lie at opposite ends of a diameter (e.g., Vourlidas & Howard 2006; Howard & DeForest 2012). The ecliptic cross sections of the Thomson scattering spheres for three observers are shown as dotted circles in Figures 1b-d. The LOS from an observer crosses its Thomson sphere at a so-called p point (Figure 2, Tappin et al. 2004), where both the intensity of incident sunlight and local electron density are greatest, but the efficiency of Thomson scattering is least. Competition between these three effects results in the spread of local radiance ( i , i T , i R in Equation 3) to large distances from the Thomson surface, an effect that is greater at larger elongations ε from the Sun. Howard & DeForest (2012) described this broad spreading effect, using the term 'Thomson plateau'. Namely, along a single LOS, the radiance per unit electron density is virtually constant over a broad range of scattering angles χ centred at the p point. The Thomson plateau, in terms of its relevance to heliospheric image, was discussed in detail by Howard & Tappin (2009), Howard & DeForest (2012), and Xiong et al. (2013). A major milestone in stereoscopic WL imaging of interplanetary CMEs was achieved by the STEREO /HI instruments (e.g., Eyles et al. 2009; Davies et al. 2009; Davis et al. 2009; Harrison et al. 2009). This heliospheric imaging capability was built on the heritage of the Solar Mass Ejection Imager ( SMEI ) instrument on the Coriolis spacecraft (Eyles et al. 2003). The STEREO mission is comprised of two spacecraft, with one leading ( STEREO A) and the other trailing ( STEREO B) the Earth in its orbit. Both spacecraft separate from the Earth by 22 . 5 · per year. The HI instrument on each STEREO spacecraft consists of two cameras, HI-1 and HI-2, whose optical axes lie in the ecliptic. Elongation coverage in the ecliptic is 4 · - 24 · for HI-1 and 18 . 7 · - 88 . 7 · for HI-2. The field of view (FOV) is 20 · × 20 · for HI-1 and 70 · × 70 · for HI-2. The cadence of HI1 is usually 40 minutes and that of HI-2 is 2 hours (Eyles et al. 2009). The current generation of heliospheric imagers do not have WL polarisers. Polarisation measurements have, up until now, only been made by coronagraphs (e.g., Poland & Munro 1976; Crifo et al. 1983; Moran & Davila 2004; Pizzo & Biesecker 2004; de Koning et al. 2009; Moran et al. 2010). For instance, Moran & Davila (2004) used polarisation measurements of WL radiance by the SOHO /LASCO coronagraph to reconstruct CME orientations near the Sun. Sky maps, often presented in the Hammer-Aitoff projection, can be used to highlight and track WL transients (e.g., Tappin et al. 2004; Zhang et al. 2013). Timeelongation maps (J-maps) are usually constructed by stacking differenced radiance between observed sky maps along a fixed position angle (sometimes background subtracted images are used instead of difference images). Using such J-maps, transients such as CMEs are manifest as inclined streaks (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Xiong et al. 2011; Harrison et al. 2012; Davies et al. 2012; Xiong et al. 2013). As a propagating transient is viewed along larger elongations, its WL signatures become fainter.","pages":[4]},{"title":"2.2. Faraday Rotation Formula","content":"Due to a FR effect, the plane of polarisation of linearly polarised radio emission is continuously rotated as the radio wave passes through the heliosphere. For radio waves, the ubiquitous magnetised solar wind flow serves as a magneto-optical birefringence medium. The formulae for FR are expressed below: Where q , /epsilon1 , m e , and c represent the constants that are the electron charge, the permittivity of free space, the mass of an electron, and the speed of light, respectively. A FR measurement of Ω RM = 1 rad m -2 corresponds to Ω = 0 . 97 · at 2.3 GHz (wavelength λ = 0 . 13 m), Ω = 57 . 3 · at 300 MHz ( λ = 1 m), and Ω = 1432 · at 60 MHz ( λ = 5 m). The calibration of ground-based FR observations is difficult, as the radio wave passes through the magnetised plasma of the ionosphere, magnetosphere (including the plasmasphere), and solar wind. Oberoi & Lonsdale (2012) surveyed and compared the FR signatures associated with each of these different regions. A large portion of the inner heliosphere can be monitored, using FR imaging. Prime heliospheric targets measured in FR include interplanetary CMEs and CIRs (Oberoi & Lonsdale 2012). Because the low-frequency radio interferometers such as the MWA , LOFAR , and VLA feature a wide FOV, high sensitivity, and multibeam forming capabilities, it is expected to be capable of mapping the magnetic field in the inner heliosphere with a remarkable sensitivity. The high sensitivity of FR measurements enables fluctuations in the heliospheric/interstellar magnetic field and plasma density, resulting from MHD turbulence, to be revealed (e.g., Jokipii & Lerche 1969; Goldshmidt & Rephaeli 1993; Hollweg et al. 2010). For instance, gradients in FR measurement have been observed across active Galactic Nuclei (AGN) jets, using the Very Long Baseline Array , which demonstrate that ordered helical magnetic fields are associated with these jets (e.g., Zavala & Taylor 2002; G'omez et al. 2008; Reichstein & Gabuzda 2012). The sheath region associated with a fast CME can be similarly probed. FR measurements of the sheath would provide a value for Ω RM in Equations 4-8. Any measured value of the FR, Ω RM , would correspond to a statistical average, as the plasma and magnetic fields within such sheath regions are in a highly turbulent state.","pages":[4,5]},{"title":"3. WHITE-LIGHT AND FARADAY ROTATION SIGNALS RECEIVED AT 0.5 AND 1 AU","content":"The remote imaging in WL and FR of an Earthdirected sheath from two vantage points, one at 0.5 AU and the other at 1 AU, is considered in Section 3.1. Section 3.2 demonstrates how spatial position and electron number density can be inferred from polarisation observations of WL radiance. Section 3.3 presents a means by which magnetic field can be diagnosed from FR measurements. 3.1. Comparing Remotely-Sensed WL and FR Observations from Different Vantage Points Figure 2 shows the modelling results of an Earthdirected sheath propagating from the Sun to 1 AU. The travelling sheath is supposed to be imaged simultaneously by two observers at 0.5 and 1 AU. The WL and FR signatures of the sheath are synthesised, using the methods in Section 2. Representative LOSs, which cut through the sheath (LOS1-6), are denoted using arrows in Figure 2. The variations of various physical parameters along LOS1-3 are shown in Figure 3. LOS1, LOS2, LOS3, and LOS5 are approximately tangential to the left flank of the shock; LOS4 and LOS6 are tangential to the nose of the shock. LOS1 and LOS4 are directed towards the observer situated at 0.5 AU; all other LOSs are directed towards the observer at 1 AU. The viewing configuration for LOS1 (Figure 2a) is equivalent to that for LOS3 (Figure 2c), as the elongation of the shock front is the same for LOS1 and LOS3. Thus, the Thomson scattering geometry is identical for these two LOSs, leading to similar LOS profiles in Figure 3. Of course, the observed radiance along LOS1 is much stronger than that along LOS3 (Table 1). Similarly, the observations along LOS4 and LOS6 (Figures 2d and 2f) have identical Thomson scattering geometries. At any given time, the sheath is viewed at greater elongations from a vantage point closer to the Sun. For instance, at an elapsed time of 5.5 hours, the foremost elongation ε of the sheath is 20 · for an observer at 1 AU (LOS1) compared with 7 · for an observer at 0.5 AU (LOS2). While the sheath is undetectable in WL along LOS2 (Figure 3g), it can be observed in FR (Figure 3l). The portion of an LOS that contributes most to the WL radiance broadens and flattens with increasing elongation, and shifts gradually towards the observer. At elongations beyond 90 · , only back-scattered photons are received; electrons in the vicinity of the observer mainly contribute to remote-sensing signatures for elongations beyond 90 · . Such observations for elongations of ε ≥ 90 · are less useful for the purposes of space weather prediction. In Figures 2d and 2f, the shock front has already reached the observer, and can be detected in-situ.","pages":[5]},{"title":"3.2. Inferences of Sheath Position from Polarised White Light","content":"The WL radiance of CMEs is determined by both the electron number density distribution and the Thomsonscattering geometry (Equation 3). The total radiance at a scattering site ( i ), and its constituent radial ( i R ) and tangential ( i T ) components, are associated with Thomson-scattering factors z 2 G , z 2 G R , and z 2 G T , respectively. Near the Thomson-scattering surface, z 2 G T is much larger than z 2 G R . If a dense parcel of plasma, viewed at large elongations, approaches the Thomson surface, its WL signatures will comprise (1) an increase in I , (2) an increase in I T , (3) a decrease in I R , and (4) an increase in the degree of polarisation p . The variation of p is largest, while that of I is negligible. A plasma parcel's distance from the Thomson sphere has a less significant effect on I at larger elongations. However, the determination of the plasma parcel's location will be more uncertain, if only unpolarised WL observations are available, as with current operational heliospheric imaging systems. Polarisation observations can provide an important clue to the primary scattering site. LOS1 in Figure 2 is used to demonstrate these inferences. The Thomson-scattering geometry is independent of the distribution of heliospheric electrons. The degree of polarisation ( p ) and the Thomson-scattering factors ( z 2 G , z 2 G R , z 2 G T ), as presented in Figure 3b and 3d, only depend on the modified scattering angle χ ∗ = 90 · -χ . The profiles of p , z 2 G , z 2 G R , and z 2 G T are symmetrical around χ ∗ = 0 · . The dependence of χ ∗ , z 2 G , and LOS distance z on p can be seen in Figure 4. p = 1 corresponds to perpendicular scattering (i.e. χ ∗ = 0 · ). p = 1 corresponds to two solutions for χ ∗ : one resulting from forward scattering ( χ ∗ < 0 · ), and the other associated with backward scattering ( χ ∗ > 0 · ). In response to the passage of the shock, the initial radiance components at t = 0, I T0 and I R0 , are enhanced to values denoted by I T and I R , respectively. The increase in the radiance components define a so-called modified degree of polarisation that we denote using p ∗ . p ∗ is given by /negationslash p is 0.62 along LOS1 at t = 0 hours. This effectively defines the degree of polarisation associated with the background solar wind. During the sheath passage, at t = 5 . 5 hours, p is 0.58 along this LOS. The modified degree of polarisation p ∗ , derived using Equation 9, is therefore 0.29 at t = 5 . 5 hours. The radiance enhancement is due to the presence of the sheath in the LOS. The sheath, which trails the shock front, occupies a relatively small volume of interplanetary space. The sheath occupies the portion of LOS1 bounded by -55 · < χ ∗ < -35 · (Figures 3a and 3c). Within this region, p smoothly varies from 0.15 to 0.5 (Figure 3d). The average value of p ∗ within the sheath is 0.29. In an inverse approach, p ∗ can be used to estimate the scattering angle χ ∗ within the sheath. This is demonstrated in Figure 4a. p ∗ = 0 . 29 corresponds to χ ∗ = ± 46 · and z 2 G = 6 . 5 × 10 -29 , where z 2 G is the average value of z 2 G in the sheath. The solution of χ ∗ = 46 · can be immediately excluded, as an Earth-directed CME can generally be identified (indeed much earlier) as being front-sided based on Extreme Ultraviolet (EUV) images of the full solar disk (e.g., Thompson et al. 1998; Plunkett et al. 1998). The other solution, χ ∗ = -46 · , is physical and yields a value of 60 R S for the distance, z , of the main scattering site (corresponding to the sheath) from the detector. How best to judge which solutions for χ ∗ are physical is explained in detail in Section 4. Once the Thomsonscattering factor z 2 G of the sheath has been inferred, its column-integrated electron number density can be estimated based on the following equation: It is clear that WL polarisation measurement can prove extremely valuable in the study of interplanetary CMEs and shocks.","pages":[5,6]},{"title":"3.3. Magnetic Field Inferred from Faraday Rotation","content":"As discussed in Section 3.2, the column-integrated electron number density along any LOS can be inferred from its WL observations. Thus, if a radio beam lies within the FOV of a WL imager such that they remotely probe the same plasma volume, the WL density measurements can be used to retrieve magnetic field strength from the received FR signal. We demonstrate this, for LOS1, in Figure 5. After subtracting the background solar wind contribution, the enhancements in FR measurement and WL radiance, due to the presence of the sheath of the simulated Earth-directed shock, are given by δ Ω RM and δI , respectively. The ratio of δ Ω RM and δI can be expressed as As discussed in Section 3.2, z 2 G corresponds to the average value of z 2 G in the sheath. The derivable parameter δ ( nB ‖ ) δ n , which we call B ∗ ‖ , can be expressed in the form where B ‖ 0 and n 0 denote the initial background values of B ‖ and n , respectively. The inferred value of B ∗ ‖ serves as an upper limit for B ‖ .","pages":[6]},{"title":"4. RADIANCE PATTERNS IN J-MAPS OF WHITE LIGHT AND FARADAY ROTATION","content":"Shock propagation through the inner heliosphere can be identified through the inclined trace with which it is associated in a time-elongation map (J-map). J-maps of WL radiance ( I/I ∗ , I ) and degree of polarisation ( p , p ∗ ), and FR measurement | δ Ω RM | , as viewed from observers at 0.5 and 1 AU, are presented in Figure 6 and compared in Figure 7. The normalisation factor I ∗ in Figure 6 corresponds to an electron number density distribution that varies according to n ∝ r -2 . A radiance threshold of I/I ∗ ≥ 3 . 68 × 10 -15 is used to demarcate the sheath region in time-elongation ( t -ε ) parameter space. The modified polarisation p ∗ is only calculated, using Equation 9, inside the sheath (Figures 6g-h). The absolute values of I and | δ Ω RM | within the sheath region are much larger for the observer at 0.5 AU, whereas the sheath values of I/I ∗ , p , and p ∗ are comparable when viewed from either vantage point. Over the elongation range 15 · ≤ ε ≤ 180 · , the radiance ratio Max. ( I 0 . 5AU ) Max. ( I 1AU ) is limited to values between 8 and 11 (Figure 7c). This demonstrates that interplanetary CMEs and shocks are viewed better from a location closer to the Sun. The position, mass, and magnetic field of the sheath can be inferred from those directly-measurable parameters presented in Figure 6, using the analytical methods presented in Sections 2.1 and 3.3. As shown in Figure 4, and explained in Section 3.2, the Thomson-scattering factors are symmetrical around χ ∗ = 0 · . As a result, a single value of degree of polarisation p ∗ corresponds to two symmetrical solutions for the scattering angle χ ∗ . The results shown in Figure 8 are derived from those in Figure 6 (for an observer at 0.5 AU) under the assumption of forward scattering, while those in Figure 9 assume backward scattering. For the forward-scattering situation, presented in Figure 8b, the inferred longitude of the sheath ϕ sheath is 22 · at an elapsed time of 5 hours and 9 · at 11 hours. For the backward-scattering case, shown in Figure 9b, the sheath is at ϕ sheath = 140 · and 60 · at these times. So, an observer at 0.5 AU infers a longitude change ∆ ϕ sheath of 13 · (Figure 8b) and 80 · (Figure 9b) for the forward and backward-scattering cases, respectively. The dramatic change in sheath longitude for the backward-scattering case might indicate that the shock is significantly deflected during its interplanetary propagation. However, such an abnormal degree of lateral deflection of ∆ ϕ sheath = 80 · would be highly unphysical, and may imply a 'ghost trajectory' (Figure 6, DeForest et al. 2013). The east-west symmetry of the radiance pattern suggests that the shock is actually front-sided and Earth-directed, rendering the assumption of backward-scattering invalid (Figure 9). If we assume that the radiance pattern shown in Figure 6 is attributable to forward scattering, the inferred position of the sheath is shown as the solid white curve in Figure 2. This agrees very well with the actual position of the sheath. At any given time, only a certain portion of the sheath will be visible from a fixed observing location (Xiong et al. 2013). For example, at an elapsed time of 5.5 hours, it is the flank of the sheath (Figure 2a) that corresponds to the leading edge of the radiance pattern in 6a, while 6 hours later it is the nose (Figure 2d). So, in fact, the longitudinal change of ∆ ϕ sheath = 13 · inferred from Figure 8b is actually an artefact of the viewing geometry and does not represent an actual deflection of the shock front. Along with the inferred position of the sheath, the column-integrated electron number density, δN sheath , and the parallel magnetic field component, B ‖ , are also presented in Figure 8. The derived value of | B ‖ | provides an upper limit for the actual magnetic field, as explained in Section 3.3. By making coordinated observations in WL and FR, CMEs can not only be continuously tracked, but quantitatively diagnosed as they propagate through interplanetary space.","pages":[6,7]},{"title":"5. INTERPLANETARY IMAGING FROM DIFFERENT OBSERVATION SITES","content":"An interplanetary CME looks different when viewed from different vantage points, but can be readily imaged from a wide range of longitudes. The observed WL radiance pattern depends not only on the longitude ϕ o of the observer, as discussed by Xiong et al. (2013), but also on its heliocentric distance r o . In Section 3.1, we compare observations made from radial distances of 0.5 and 1 AU. In Section 5.1, we consider two particular observation sites that are often considered favourable in terms of WL imaging, the L4 and L5 Lagrangian points. In Section 5.2, we quantify more fully the dependence of WL imaging on r o .","pages":[7]},{"title":"5.1. Observing an Earth-Directed shock from the L4 and L5 Lagrangian Points","content":"The L4 and L5 Lagrangian points of the Sun-Earth system are often considered advantageous for observing Earth-directed CMEs. There are five Lagrangian points, all in the ecliptic, i.e., L1-L5. A spacecraft at L1, L2, or L3 is metastable in terms of its orbital configuration, and hence must frequently use propulsion to remain in the same orbit. In contrast, a spacecraft at L4 or L5 is resistant to gravitational perturbations, and is believed to be more stable. The L4 and L5 points lie 60 · ahead of and behind the Earth in its orbit, respectively. STEREO A reached the L4 point in September 2009 and STEREO B reached L5 in October 2009. The twin STEREO spacecraft were pathfinders for future L4/L5 missions (Akioka et al. 2005; Biesecker et al. 2008; Gopalswamy et al. 2011). A spacecraft at either L4 or L5 can perform routine side-on imaging of Earthdirected CMEs, and hence is of great merit for space weather monitoring. Figure 10a illustrates the imaging, be it in WL or FR, of an Earth-directed sheath from the L5 point. LOS7 intersects the nose of the shock at an elapsed time of 14.5 hours, when the shock nose lies on the Thomsonscattering sphere. The variation, along LOS7, of a number of salient physical parameters is shown in Figures 10 e-j. The interplanetary magnetic field lines are compressed and rotated within the sheath. This rotation results in the closer alignment of the field lines with LOS7, such that the magnetic field component along the LOS, | B ‖ | , is greatly enhanced (Figure 10i). The enhancements of both | B ‖ | and electron number density n within the sheath are responsible for the resultant increases in WL radiance I and FR measurement | Ω RM | . The degree of WL polarisation p , as viewed along LOS7 that is at an elongation of 34 · , is 0.67 for the background solar wind and increases to 0.75 during the shock passage at 14.5 hours. This corresponds to a value of the modified WL polarisation p ∗ of 0.98, based on Equation 9. As was done for LOS1 in Section 3, we evaluate the WL radiance along LOS7 (Figure 10a), from which we infer the shock position (Figure 10d). Again, a single value of p ∗ corresponds to two symmetrical solutions for scattering angle χ ∗ , i.e., p ∗ = 0 . 29 and χ ∗ = ± 46 · for LOS1, and p ∗ = 0 . 98 and χ ∗ = ± 5 · for LOS7. For LOS1, only one solution for χ ∗ = -46 · was deemed physical; for LOS7, both solutions for χ ∗ are potentially physical. The scattering sites corresponding to χ ∗ = ± 5 · are very close to one another, and both agree well with the actual position of the sheath (Figure 10a). The section of LOS7 bounded by -5 · ≤ χ ∗ ≤ 5 · lies within the sheath. Both forward scattering ( -5 · ≤ χ ∗ < 0 · ) and backward scattering (0 · < χ ∗ ≤ 5 · ) will contribute to the radiance I observed along this LOS. The propagating sheath can be tracked continuously and easily in WL from the L5 vantage point, such that it leaves an obvious signature in the J-map of synthesised radiance (Figures 10b and 10c). This confirms previous assertions that the L4 and L5 points are very favourable in terms of space weather monitoring.","pages":[7]},{"title":"5.2. Dependence of White-Light Radiance on Heliocentric Distance","content":"The background intensity at a fixed elongation in a WL sky map is greater for an observer closer to the Sun. For a heliospheric imager at any distance from the Sun, Jackson et al. (2010) proposed the following Thomsonscattering principles: (1) The WL radiance I at a given solar elongation falls off with the heliocentric distance r according to r -3 ; (2) Such a dependence of I ∝ r -3 is valid for almost any viewing elongation, and for any radial distance from 0.1 AU out to 1 AU and beyond. The WL radiance I depends on the heliospheric distribution of electron number density n . In interplanetary space, the background solar wind speed is nearly constant, and the background electron number density n 0 varies approximately with r -2 . However, the equilibrium defined by n 0 ∝ r -2 is disturbed by the presence of interplanetary transients, such as CMEs and CIRs. A travelling shock can sweep up, and hence compress significantly, the background solar wind plasma. Figures 2 and 10a show a density enhancement of n -n 0 n 0 ≈ 2 . 2 within the sheath. The associated compression ratio n n 0 ≈ 3 . 2 indicates that the shock is very strong. However, when viewed along elongations less than 60 · , the strongest signatures of shock passage (characterised by Max.( I )) vary very closely with r -3 (Figures 11b and 11c). The relationship of Max.( I ) ∝ r -3 is slightly violated at large elongations ε > 60 · . Figure 7c reveals that the ratio between Max.( I 0 . 5AU ) and Max.( I 1AU ) is close to 8 for ε ≤ 60 · , increasing thereafter to 10.8 at ε = 180 · . The premise that the WL radiance decreases with the third power of Sun-observer distance generally holds true for both the background solar wind and propagating CMEs.","pages":[7,8]},{"title":"6. DISCUSSION","content":"The detectability in WL of a particular electron density feature is determined by its signal above the noise background. In STEREO /HI-1 images, the dominant WL signal is zodiacal light due to scattering of sunlight from the F-corona, which is centred around the ecliptic. In the STEREO /HI-2 FOV, the noise floor is primarily determined by photon noise and the background star-field (DeForest et al. 2011). Away from the ecliptic, the background WL noise has a sharp radial gradient in coronal images, and is nearly constant in heliospheric images. The signal-to-noise ratio for heliospheric electron density features is discussed by Howard et al. (2013). We will address the detection of CMEs in the presence of background noise in future forward-modelling work. If both a transient CME and background (Heliospheric Current Sheet (HCS) - Heliospheric Plasma Sheet (HPS)) plasma structures are present along the same LOS, both will contribute to the total LOS-integrated radiance. In this case, the interpretation of the data would clearly be more problematic. Moreover, if the LOS were to penetrate a HCS, the magnetic field vector would, at that point, rotate through 180 · . Due to the mutual cancellation of B ‖ across the HCS, there may be no net FR signature according to Equations 4-6. Hence, even such a significant interplanetary structure may be associated with only a weak FR measurement. Conversely, the relatively dense plasma within a HPS can significantly contribute to WL radiance. Thus the potential effects of the presence of HCS-HPS structures need to be borne in mind in the remote imaging of CMEs. In the current work, however, we find that such effects are negligible. In our numerical simulation, there are two HCS-HPS structures, which are initially rooted at longitudes of ϕ = ± 90 · at the inner boundary of our numerical simulation. The simulated shock emerges at a longitude of ϕ = 0 · . The large longitudinal difference between the HCS-HPS and the shock means that the remote-sensing signatures are principally contributed by the sheath. Thus, in our forward-modelling work, the signal enhancements of synthesised imaging in WL and FR are unambiguously the result of the propagating sheath. In general, the more complex the interplanetary dynamics, the more complex the resultant remote-sensing observations will be. For instance, a CME can interact with other CMEs and/or background solar wind structures such as CIRs, HCSs, and HPSs; mutual interaction between CMEs is, however, generally more perturbing than interactions between CMEs and such background structures. Interactions can result in the background solar wind structures becoming warped or distorted (e.g., Odstrˇcil et al. 1996; Hu & Jia 2001), and CMEs being accelerated/decelerated (e.g., Lugaz et al. 2005; Xiong et al. 2007; Shen et al. 2012b), deflected (e.g., Xiong et al. 2006b, 2009; Lugaz et al. 2012), distorted (e.g., Xiong et al. 2006b, 2009), or entrained (e.g., Rouillard et al. 2009a). In particular, during such interactions, the behavior of a sheath can become much more complex: the shock aphelion can be deflected, spatial asymmetries can develop along the shock front, and the shock front can potentially merge completely with other shock fronts. At an interaction site, both the plasma density and magnetic field would be compressed; this would lead to enhanced signatures in both WL and FR observations. For example, the interaction between two CMEs was manifest as a very bright arc in WL images (e.g., Harrison et al. 2012; Liu et al. 2012; Temmer et al. 2012). Different types of interaction would likely result in different WL radiance signatures; in fact, through a single interaction, the corresponding radiance pattern would evolve. The interpretation of such complex WL radiance patterns would be prone to large uncertainties, but can be rigorously constrained if interplanetary imaging was performed from multiple vantage points and complemented by numerical modelling. For stereoscopic WLimaging, ray-paths from one observer intersect those from the other observer. Thus the 3D distribution of electrons in the inner heliosphere can be reconstructed using a time-dependent tomography algorithm (Jackson et al. 2006; Bisi et al. 2008; Webb et al. 2013). With the aid of numerical modelling, coordinated imaging in WL and FR would enable the properties and evolution of complex interplanetary dynamics to be diagnosed.","pages":[8]},{"title":"7. CONCLUDING REMARKS","content":"In this paper, we have investigated the WL and FR signatures of an interplanetary shock based on an approach of forward MHD modelling. The WL Thomsonscattering geometry is increasingly more significant at larger elongations. The degree of WL polarisation can be used to estimate the 3D location of the main scattering region, while FR measurement can be used to infer, to some extent, the magnetic configurations of CMEs. This work presented here demonstrates, as a proof-of-concept, that the availability of coordinated observations in polarised WL and FR measurement would enable the local LOS magnetic component to be estimated. Although the current generation of heliospheric WL imagers, such as the STEREO /HI instruments, do not have polarisers, there are advances underway in terms of FR imaging using Low-frequency radio arrays. Coordinated imaging in WL and FR would enable the inner heliosphere to be mapped in fine detail; the location, mass, and magnetic field of CMEs can be diagnosed on the basis of such combined observations. Forward modelling is crucial in establishing the causal link between interplanetary dynam- ics and observable signatures, and can provide valuable guidance for future coordinated WL and FR imaging. Although not the methodology of the current work, numerical MHD models of the inner heliosphere can also be directly driven by photospheric observations (e.g., Hayashi 2005; Wu et al. 2006; Feng et al. 2012b). A comparison of synthesised and observed WL and FR sky maps, the former based on the use of such datadriven models, would prove highly beneficial in validating the forward modelling and interpreting the observations. Such an integration of observation data analysis and numerical forward modelling will be explored as the continuation of the preliminary modelling work presented in this paper. This work is jointly supported by the National Basic Research Program (973 program) under grant 2012CB825601, the Chinese Academy of Sciences (KZZD-EW-01-4), the National Natural Science Foun- dation of China (41231068, 41031066, 41204129), the Strategic Priority Research Program on Space Science from the Chinese Academy of Sciences (XDA04060801), the Specialized Research Fund for State Key Laboratories of China, the Chinese Public Science and Technology Research Funds Projects of Ocean (201005017), open research foundation of Science and Technology on Aerospace Flight Dynamics Laboratory of China (AFDL2012002), research fund for recipient of excellent award of the Chinese Academy of Sciences President's scholarship (startup fund). Ming Xiong is also partially supported by an institutional project of 'Key Fostering Direction in Pulsar Science and Application' from the Center of Space Science and Applied Research, China. Ming Xiong sincerely thanks Drs. Bo Li, Ding Chen, Craig DeForest, James Tappin, and Tim Howard for their beneficial discussions and thoughtful suggestions. We sincerely thank the anonymous referee for his/her constructive suggestions.","pages":[8,9]},{"title":"REFERENCES","content":"Feng, L., Inhester, B., Wei, Y., et al. 2012a, ApJ, 751, 18 Roca-Sogorb, M. 2008, ApJ, 681, L69 Space Sci. Rev., 88, 529 20 Xiong et al. ) t n e m e r u s a e m R F c i t e n g a m l e l l a r a P n o r t c e l E 3 - m d a r 2 1 - 0 1 × ( ) T n ( ) 3 - m c ( ) . 0 1 e r u g i F n o d i a l r e v o s i 7 S O L d n a 2 e r u g i F n o d i a l r e v o e r a 6 - , L O S 3 L O S s 1 t t e r i n g o r s G T h c a E . j - e 0 1 d n a 3 s e r u g i F n i n o i t a s i l a m r o n r o f d e s u , 7 S O L d n a , 2 ; t c | ‖ B | n y t i s n e d 2 z n a , | ‖ B | , n , T G 2 z , R G 2 z , G 2 z , i s r e t e m a r a p e h t f o s e u l a v m u m i x a M l e n a d n a , o ϕ e d u t i g n o l a , o r s u i d a r a , t e m i t a d e t a n g i s e d s i S O L a c L W n o i t a g n o l E e d u t i g n o L i i d a R e m i T S O L ( ) · ( ) ε o ϕ o r t · ( ) U A ( ) r u o h ( d l e fi r e b m u n | M R ω | 4 . 4 1 7 0 2 2 9 3 0 2 0 5 . 0 5 . 5 1 S O L 2 . 8 1 3 2 2 3 9 8 1 7 0 1 5 . 5 2 S O L 1 5 . 1 9 . 8 6 7 8 0 2 0 1 4 1 3 S O L 2 4 . 0 5 . 8 2 3 . 0 6 4 3 0 6 - 1 5 . 4 1 7 S O L","pages":[9,20]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"Coronal mass ejections (CMEs) can be continuously tracked through a large portion of the inner heliosphere by direct imaging in visible and radio wavebands. White-light (WL) signatures of solar wind transients, such as CMEs, result from Thomson scattering of sunlight by free electrons, and therefore depend on both the viewing geometry and the electron density. The Faraday rotation (FR) of radio waves from extragalactic pulsars and quasars, which arises due to the presence of such solar wind features, depends on the line-of-sight magnetic field component B ‖ , and the electron density. To understand coordinated WL and FR observations of CMEs, we perform forward magnetohydrodynamic modelling of an Earth-directed shock and synthesise the signatures that would be remotely sensed at a number of widely distributed vantage points in the inner heliosphere. Removal of the background solar wind contribution reveals the shock-associated enhancements in WL and FR. While the efficiency of Thomson scattering depends on scattering angle, WL radiance I decreases with heliocentric distance r roughly according to the expression I ∝ r -3 . The sheath region downstream of the Earth-directed shock is well viewed from the L4 and L5 Lagrangian points, demonstrating the benefits of these points in terms of space weather forecasting. The spatial position of the main scattering site r sheath and the mass of plasma at that position M sheath can be inferred from the polarisation of the shock-associated enhancement in WL radiance. From the FR measurements, the local B ‖ sheath at r sheath can then be estimated. Simultaneous observations in polarised WL and FR can not only be used to detect CMEs, but also to diagnose their plasma and magnetic field properties. Subject headings: methods: numerical - shock waves - solar-terrestrial relations - solar wind Sun: coronal mass ejections (CMEs) - Sun: heliosphere\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"USING COORDINATED OBSERVATIONS IN POLARISED WHITE LIGHT AND FARADAY ROTATION TO PROBE THE SPATIAL POSITION AND MAGNETIC FIELD OF AN INTERPLANETARY SHEATH\",\n \"content\": \"Ming Xiong 1, 2 , Jackie A. Davies 3 , Xueshang Feng 1 , Mathew J. Owens 4 , Richard A. Harrison 3 , Chris J. Davis 4 , and Ying D. Liu 1 Draft version September 8, 2018\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1.1. The Inner Heliosphere\",\n \"content\": \"The inner heliosphere is permeated with the magnetised solar wind from the Sun. At solar minimum, the solar wind is inherently bimodal (McComas et al. 2000), with slow flow tending to emanate from near the ecliptic and fast flow tending to emanate at higher latitudes. Several large-scale structures, which pervade interplanetary space, are associated with the 'ambient' solar wind: (1) a spiralling interplanetary magnetic field (the Parker spiral) that forms as a result of solar rotation (Parker 1958), (2) corotating interacting regions (CIRs) that are formed at the interface between a preceding slow solar wind stream and a following fast solar wind stream (Gosling & Pizzo 1999), and (3) the heliospheric current sheet typically embedded in the heliospheric plasma sheet (Winterhalter et al. 1994; Crooker et al. 2004). The background solar wind flow is frequently disturbed by coronal mass ejections (CMEs), large-scale expulsions of plasma and magnetic field from the solar atmosphere. CMEs typically expand during their propagation, because the total solar wind pressure de- mxiong@spacweather.ac.cn 4 Reading University, Reading, UK creases with heliocentric distance (D'emoulin & Dasso 2009; Gulisano et al. 2010). The expansion speed of a CME depends on its spatial size, translation speed, and heliocentric distance, as well as the pre-existing solar wind conditions (Nakwacki et al. 2011; Gulisano et al. 2012). A number of popular models describe the motion of a CME as governed by two forces: a propelling Lorentz force (Chen 1989, 1996; Chen et al. 2006) and an aerodynamic drag force (Cargill et al. 1996; Vrˇsnak & Gopalswamy 2002; Cargill 2004). According to these models, the drag force gradually becomes dominant in interplanetary space, and the CME speed finally adjusts to the ambient solar wind speed. The equalisation of the CME and solar wind speed occurs at very different heliospheric distances, from below 30 solar radii to beyond 1 AU, depending on the characteristics of the CME and the solar wind (Temmer et al. 2011). A CME can undergo significant, nonlinear, and irreversible evolution during its propagation, as it interacts with the ambient solar wind and other CMEs (e.g., Burlaga et al. 2002; D'emoulin 2010). Coronagraph observations show that CME morphology is distorted rapidly and significantly in a structured solar wind (e.g., Savani et al. 2010, 2012; Feng et al. 2012a). Such a distortion occurs over a relatively short heliocentric distance. Interaction between multiple CMEs has been revealed by in-situ observations (e.g., Burlaga et al. 1987; Wang et al. 2003a; Steed et al. 2011; Mostl et al. 2012), radio burst observations (e.g., Gopalswamy et al. 2001; Oliveros et al. 2012), white-light (WL) imaging (e.g., Harrison et al. 2012; Liu et al. 2012; Lugaz et al. 2012; Temmer et al. 2012; Shen et al. 2012a; Bemporad et al. 2012), and numerical magnetohydrodynamic (MHD) simulation (e.g., Lugaz et al. 2005; Xiong et al. 2007, 2009; Shen et al. 2012b). CMEs cause phenomena at Earth, such as geomagnetic storms and solar energetic particles, that can result in major space weather effects (Gopalswamy 2006; Webb & Howard 2012). Traditionally, a CME has been defined in terms of a three-part structure, involving a bright sheath, a dark cavity, and a bright filament. It is now accepted that the cavity component is an escaping magnetic flux rope that drives the CME (e.g., Rouillard et al. 2009b; DeForest et al. 2011). A highspeed flux rope can drive a fast shock ahead of itself that is much wider in angular extent than the flux rope itself. The region between the shock front and the flux rope is defined as a sheath. Within the sheath, (1) magnetic field lines are draped and compressed, and (2) a plasma flow is deviated, compressed, and turbulent (e.g., Gosling & McComas 1987; Owens et al. 2005; Liu et al. 2008). Precursor southward magnetic fields ahead of CMEs are generally compressed, making them particularly geoeffective (Tsurutani et al. 1992; Gonzalez et al. 1999). The magnetic fields in the sheath and in the flux rope can be equally important in driving major geomagnetic storms (Tsurutani et al. 1988, 1992; Szajko et al. 2013). In so-called two-dip storms, it is often the case that the first dip in the Dst index is produced by the upstream sheath and the second is produced by the driving flux rope (Echer et al. 2004; Zhang et al. 2008; Mostl et al. 2012).\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"1.2. Heliospheric White Light Observations\",\n \"content\": \"Heliospheric imagers (HIs) detect WL that has been Thomson-scattered from free electrons. For resolved objects, such as CMEs, the power detected by an individual pixel depends linearly on the solid angle subtended by that pixel ( δω ) and the area subtended by the corresponding aperture ( δA ), and is proportional to the radiance (measured in W m -2 SR -1 ). The light from unresolved objects, such as stars, which are much narrower in angular extent, tends to fall within individual pixels. For a resolved heliospheric electron density feature, such as a CME, a single pixel provides a measure of its radiance (surface brightness), while summing contributions from all pixels over the entire extent of the feature provides a measure of its intensity (total brightness). The intensity is an integral of the radiance over the apparent feature size. Therefore, the feature's intensity determines its detectability of an object, be it resolved or unresolved (Howard & DeForest 2012). The background zodiacal and stellar signals detected by heliospheric imagers are much more intense than the signal due to Thomson-scattering from plasma features such as CMEs (Leinert & Pitz 1989). Fortunately, using an image-differencing technique, the much more stable background radiance can be removed, such that the more transient Thomson-scattering signal can be extracted. From such processed Thomsonscattering images, the sunlight-irradiated CMEs can be easily identified and tracked. According to theory, the heliospheric Thomson-scattering radiance is governed by the Thomson-scattering geometry fac- tors and electron number density (Vourlidas & Howard 2006; Howard & Tappin 2009; Howard & DeForest 2012; Xiong et al. 2013). The CME detectability in WL is actually more limited by perspective and field-of-view (FOV) effects than by location relative to the Thomsonscattering sphere (Howard & DeForest 2012). Heliospheric imaging from two vantage points, both off the Sun-Earth line, was made possible by the Heliospheric Imagers (HIs) onboard the Solar-TErrestrial RElations Observatory ( STEREO ) (Eyles et al. 2009). With the STEREO /SECCHI package, a CME can be imaged from its nascent stage in the inner corona all the way out to 1 AU and beyond (e.g., Harrison et al. 2008; Davies et al. 2009; Davis et al. 2009; Liu et al. 2010b; DeForest et al. 2011; Liu et al. 2013). In particular, images from STEREO /HI-2 have revealed detailed spatial structures within interplanetary CMEs, including leading-edge pileup, interior cavities, filamentary structure, and rear cusps (DeForest et al. 2011). Comparison with in-situ observations has revealed that the leadingedge pileup of solar wind material, which is evident as a bright arc in WL imaging, corresponds to the sheath region. However, the interpretation of the leading edge of the radiance pattern, especially at larger elongations, is fraught with ambiguity (e.g., Howard & Tappin 2009; Xiong et al. 2013). Elongation ε is defined as the angle between the Sun-observer line and a line-of-sight (LOS). Because a CME occupies a significant three-dimensional (3D) volume, different parts of the CME will contribute to the radiance pattern imaged by observers situated at different heliocentric longitudes (Xiong et al. 2013). Even for an observer at a fixed longitude, a different part of the CME will contribute to the imaged radiance at any given time (Xiong et al. 2013). Various techniques have been developed that enable the spatial locations and propagation directions of CMEs to be inferred, based on the fitting of their moving radiance patterns (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Thernisien et al. 2009; Liu et al. 2010b; Lugaz et al. 2010; Mostl et al. 2011; Davies et al. 2012). However, the determination of interplanetary CME kinematics, propagation direction in particular, are somewhat ambiguous (Howard & Tappin 2009; Davis et al. 2010; Davies et al. 2012; Howard & DeForest 2012; Xiong et al. 2013; Lugaz & Kintner 2013).\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"1.3. Faraday Rotation Measurement\",\n \"content\": \"Faraday rotation (FR) is the rotation of the plane of polarisation of an incident electromagnetic wave as it passes through a magnetised ionic medium. The FR observations of linearly polarised radio sources can be used to estimate magnetic field in the corona and interplanetary space (e.g., Levy et al. 1969; Bird et al. 1980; Sakurai & Spangler 1994; Liu et al. 2007; Jensen 2007; Jensen & Russell 2008; You et al. 2012; Jensen et al. 2013). The FR measurement of a radio signal corresponds to the path integral of the product of electron density n and the projection of the magnetic field along the LOS, B ‖ . The first FR experiment was conducted in 1968 by Levy et al. (1969), when solar plasma occulted the radio down-link from the Pioneer 6 spacecraft. As well as man-made radio sources, FR experiments can also exploit natural radio sources such as pulsars and quasars. The first FR experiments of this type were conducted by Bird et al. (1980) during the solar occultation of a pulsar. In terms of their locations on a sky map, many pulsars and quasars lie in the vicinity of the Sun. Therefore, simultaneous FR measurements along multiple beams can be used to map the inner heliosphere with a reasonable spatial resolution. Additional observations, for example in WL, would generally be necessary to confirm whether an FR transient was indeed caused by a CME. For instance, the first FR event, reported by Levy et al. (1969), could not be attributed unambiguously to the presence of any particular solar wind structure. The FR signatures, observed by Levy et al. (1969), exhibited a W-shaped profile over a time period of 2 -3 hours, with rotation angles of up to 40 · relative to the quiescent baseline. Woo (1997) interpreted the FR signature as the result of a coronal streamer stalk of angular size 1 · -2 · , whereas Patzold & Bird (1998) argued that it was caused by the passage of a series of CMEs. However, by comparing observations from the Solwind coronagraph and measurements of Helios down-link radio signals, Bird et al. (1985) were able to identify the signatures of five CMEs simultaneously in WL and FR. Moreover, the electron density derived from WL imaging can be used to enable magnetic field magnitude to be inferred from FR measurements. The heliospheric magnetic field can be remotely probed in FR, using low-frequency radio interferometers such as the Murchison Widefield Array (MWA) (Lonsdale, C. J., et. al. 2009), the LOw Frequency ARray (LOFAR) (de Vos et al. 2009), and the Very Large Array (VLA) (Thompson et al. 1980). Disturbance of the background solar wind by CMEs will cause the observed FR signatures to become variable (e.g., Levy et al. 1969; Bird et al. 1985; Jensen & Russell 2008). A change in either the electron density ( δn ) or the LOS magnetic field component ( δB ‖ ), or indeed both, will contribute to the rotation in the plane of polarisation of the radio signal by δ Ω RM . Interplanetary magnetic clouds (MCs) in particular, which have a magnetic flux rope configuration (Burlaga et al. 1981; Klein & Burlaga 1982; Lepping et al. 1990), can be identified from WL images (Rouillard et al. 2009b; DeForest et al. 2011) and are expected to be easily identifiable in FR measurements. Moreover, δn and | δ B | are often enhanced simultaneously within the sheath ahead of a fast MC. The FR due to a MC-driven sheath can be comparable to that due to the MC itself (Jensen et al. 2010). It is expected that the orientation and helicity of a MC will be able to be determined unambiguously from multi-beam FR measurements (Liu et al. 2007; Jensen 2007; Jensen et al. 2010). In contrast, the in-situ detection of magnetic flux ropes can be significantly hindered by the location of the observing spacecraft (e.g., Hu & Sonnerup 2002; Mostl et al. 2012; D'emoulin et al. 2013). FR imaging can be used to provide the magnetic orientation of a fast MC, and indeed its preceding sheath, prior to its arrival at Earth, which is crucial for predicting potential space weather effects at Earth.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"1.4. Forward Magnetohydrodynamic Modelling\",\n \"content\": \"Forward modelling of WL and FR signatures is proving extremely useful for inferring the in-situ properties of interplanetary CMEs from remote-sensing data. Sophis- ticated numerical MHD models of the inner heliosphere (e.g., Groth et al. 2000; Lugaz et al. 2005; Hayashi 2005; Xiong et al. 2006a; Li et al. 2006; Wu et al. 2006; Li & Li 2008; Odstrˇcil & Pizzo 2009; Shen et al. 2012b) can serve as a digital laboratory, to enable the synthesis of a variety of observable remote-sensing signatures. In this paper, we perform a numerical MHD simulation of an interplanetary shock in the ecliptic, from which we synthesise the signatures of that feature that would be remotely sensed at visible and radio wavelengths. Details of the MHD model, and the formulae required to synthesise the remote-sensing observations, are given in Section 2. The resultant synthesised remote-sensing signatures of the sheath, which would be observed from vantage points at 0.5 and 1 AU, are described and compared in Section 3. In Section 4, we discuss the radiance patterns that are observed in the synthesised WL and FR sky maps. In Section 5, we explore the role that the vantage point of the observer plays in the 'observability' of such WL and FR features. CME detection in the presence of background noise, and the heliospheric imaging of more complex interplanetary phenomena, are discussed in Section 6. The potentially important role that forward modelling can play in our understanding of coordinated WL and FR observations is summarised in Section 7.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"2. METHOD\",\n \"content\": \"Forward MHD modelling can self-consistently establish the links between interplanetary dynamics and the resultant observable signatures. A complete flow chart of forward modelling is illustrated in Figure 8 from Xiong et al. (2011). The travelling fast shock studied by Xiong et al. (2013) is revisited here. Our methodology consists of three general steps: (1) forward modelling of the shock using the numerical Inner-Heliosphere MHD (IH-MHD) model (Xiong et al. 2006a, 2013), (2) calculation of its Thomson-scattered WL signature, in Section 2.1, and (3) calculation of its FR signature, in Section 2.2. Characterisation of the IH-MHD model, the background solar wind conditions, and the initial shock injection is summarised respectively in Tables 1, 2, and 3 of Xiong et al. (2013). The simulated electron density n and magnetic field B are used to generate synthetic WL and FR images, which enable us to explore the WL and FR signatures of an interplanetary sheath. A plasma parcel emitted from the Sun would be observed, at the same elongation and the same Thomsonscattering angle, firstly by an observer situated at a radial distance of 0.5 AU from the Sun centre, and subsequently by an observer at 1 AU (Figure 1a). Such a configuration was discussed qualitatively by Jackson et al. (2010) and is analysed quantitatively in Section 3 of this paper. Observations from STEREO /HI suggest that a travelling sheath can be approximated as an expanding bubble (e.g., Howard & Tappin 2009; Lugaz et al. 2010; Davies et al. 2012; Mostl & Davies 2013). In-situ observations indicate that CMEs undergo self-similar expansion, as the speed profiles within CMEs themselves tend to be a linear function of time (e.g., Farrugia et al. 1993; Gulisano et al. 2012). In the schematic Figures 1b-d, the sheath region following an Earth-directed interplanetary shock is represented as a self-similarly expanding bubble. The sheath can look quite different when viewed from different heliocentric distances (Figures 1b and 1c) and/or different heliospheric longitudes (Figures 1b and 1d).\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"2.1. Thomson-Scattering WL Formulae\",\n \"content\": \"A small parcel of free electrons, that is illuminated by a known intensity of incident sunlight (measured in W m -2 ), will scatter a certain amount of power per unit solid angle (measured in W rad -1 ). The effect of the Thomson-scattering geometry can be characterised by the so-called scattering angle χ , as depicted in Figure 1 of Xiong et al. (2013). Scattering can be backward ( χ < 90 · ), perpendicular ( χ = 90 · ), and forward ( χ > 90 · ). All photons that are scattered into an optical cone defined by the point spread function of an individual pixel will be attributed to that pixel (Figure 1b, Xiong et al. 2013). The classic principles of WL Thomson-scattering, as applied to coronagraph observations (Billings 1966), have been adapted to heliospheric imaging (Vourlidas & Howard 2006; Howard & Tappin 2009; Jackson et al. 2010; Howard & DeForest 2012; Xiong et al. 2013). The transverse electric field oscillation δ E of the Thomson-scattered radiance, which is inherently a continuum, can be considered in terms of its two orthogonal components, a tangential component δ E T and a radial component δ E R . The amplitudes of these two orthogonal oscillations ( I T = | δ E T | 2 and I R = | δ E R | 2 ) can be measured separately, using a polariser. The total radiance I and degree of polarisation p are defined as follows: Although the incident sunlight is unpolarised ( p = 0), the scattered WL radiance remains unpolarised only when the scattering angle | χ -90 · | = 90 · . The scattered light is elliptically polarised (0 < p < 1) for 0 · < | χ -90 · | < 90 · and linearly polarised ( p = 1) for χ = 90 · . Each pixel of a detector records the LOS integral of local WL radiance. Here z refers to a distance between the detector and the scattering site, as shown in Figure 1b of Xiong et al. (2013). The mathematical expressions for G , G R , and G T are given by Equations 1 and 2 of Xiong et al. (2013). The observed WL radiance is determined jointly by the heliospheric distribution of electrons n and Thomsonscattering geometry factors ( z 2 G , z 2 G R , z 2 G T ). As noted above, the efficiency of Thomson scattering depends significantly on the Thomson scattering angle χ . The perpendicular scattering, χ = 90 · , received by an observer comes from the Thomson Sphere. The 'Thomson sphere', sometimes called the 'Thomson surface', is the sphere in which the Sun and observer lie at opposite ends of a diameter (e.g., Vourlidas & Howard 2006; Howard & DeForest 2012). The ecliptic cross sections of the Thomson scattering spheres for three observers are shown as dotted circles in Figures 1b-d. The LOS from an observer crosses its Thomson sphere at a so-called p point (Figure 2, Tappin et al. 2004), where both the intensity of incident sunlight and local electron density are greatest, but the efficiency of Thomson scattering is least. Competition between these three effects results in the spread of local radiance ( i , i T , i R in Equation 3) to large distances from the Thomson surface, an effect that is greater at larger elongations ε from the Sun. Howard & DeForest (2012) described this broad spreading effect, using the term 'Thomson plateau'. Namely, along a single LOS, the radiance per unit electron density is virtually constant over a broad range of scattering angles χ centred at the p point. The Thomson plateau, in terms of its relevance to heliospheric image, was discussed in detail by Howard & Tappin (2009), Howard & DeForest (2012), and Xiong et al. (2013). A major milestone in stereoscopic WL imaging of interplanetary CMEs was achieved by the STEREO /HI instruments (e.g., Eyles et al. 2009; Davies et al. 2009; Davis et al. 2009; Harrison et al. 2009). This heliospheric imaging capability was built on the heritage of the Solar Mass Ejection Imager ( SMEI ) instrument on the Coriolis spacecraft (Eyles et al. 2003). The STEREO mission is comprised of two spacecraft, with one leading ( STEREO A) and the other trailing ( STEREO B) the Earth in its orbit. Both spacecraft separate from the Earth by 22 . 5 · per year. The HI instrument on each STEREO spacecraft consists of two cameras, HI-1 and HI-2, whose optical axes lie in the ecliptic. Elongation coverage in the ecliptic is 4 · - 24 · for HI-1 and 18 . 7 · - 88 . 7 · for HI-2. The field of view (FOV) is 20 · × 20 · for HI-1 and 70 · × 70 · for HI-2. The cadence of HI1 is usually 40 minutes and that of HI-2 is 2 hours (Eyles et al. 2009). The current generation of heliospheric imagers do not have WL polarisers. Polarisation measurements have, up until now, only been made by coronagraphs (e.g., Poland & Munro 1976; Crifo et al. 1983; Moran & Davila 2004; Pizzo & Biesecker 2004; de Koning et al. 2009; Moran et al. 2010). For instance, Moran & Davila (2004) used polarisation measurements of WL radiance by the SOHO /LASCO coronagraph to reconstruct CME orientations near the Sun. Sky maps, often presented in the Hammer-Aitoff projection, can be used to highlight and track WL transients (e.g., Tappin et al. 2004; Zhang et al. 2013). Timeelongation maps (J-maps) are usually constructed by stacking differenced radiance between observed sky maps along a fixed position angle (sometimes background subtracted images are used instead of difference images). Using such J-maps, transients such as CMEs are manifest as inclined streaks (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Xiong et al. 2011; Harrison et al. 2012; Davies et al. 2012; Xiong et al. 2013). As a propagating transient is viewed along larger elongations, its WL signatures become fainter.\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"2.2. Faraday Rotation Formula\",\n \"content\": \"Due to a FR effect, the plane of polarisation of linearly polarised radio emission is continuously rotated as the radio wave passes through the heliosphere. For radio waves, the ubiquitous magnetised solar wind flow serves as a magneto-optical birefringence medium. The formulae for FR are expressed below: Where q , /epsilon1 , m e , and c represent the constants that are the electron charge, the permittivity of free space, the mass of an electron, and the speed of light, respectively. A FR measurement of Ω RM = 1 rad m -2 corresponds to Ω = 0 . 97 · at 2.3 GHz (wavelength λ = 0 . 13 m), Ω = 57 . 3 · at 300 MHz ( λ = 1 m), and Ω = 1432 · at 60 MHz ( λ = 5 m). The calibration of ground-based FR observations is difficult, as the radio wave passes through the magnetised plasma of the ionosphere, magnetosphere (including the plasmasphere), and solar wind. Oberoi & Lonsdale (2012) surveyed and compared the FR signatures associated with each of these different regions. A large portion of the inner heliosphere can be monitored, using FR imaging. Prime heliospheric targets measured in FR include interplanetary CMEs and CIRs (Oberoi & Lonsdale 2012). Because the low-frequency radio interferometers such as the MWA , LOFAR , and VLA feature a wide FOV, high sensitivity, and multibeam forming capabilities, it is expected to be capable of mapping the magnetic field in the inner heliosphere with a remarkable sensitivity. The high sensitivity of FR measurements enables fluctuations in the heliospheric/interstellar magnetic field and plasma density, resulting from MHD turbulence, to be revealed (e.g., Jokipii & Lerche 1969; Goldshmidt & Rephaeli 1993; Hollweg et al. 2010). For instance, gradients in FR measurement have been observed across active Galactic Nuclei (AGN) jets, using the Very Long Baseline Array , which demonstrate that ordered helical magnetic fields are associated with these jets (e.g., Zavala & Taylor 2002; G'omez et al. 2008; Reichstein & Gabuzda 2012). The sheath region associated with a fast CME can be similarly probed. FR measurements of the sheath would provide a value for Ω RM in Equations 4-8. Any measured value of the FR, Ω RM , would correspond to a statistical average, as the plasma and magnetic fields within such sheath regions are in a highly turbulent state.\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"3. WHITE-LIGHT AND FARADAY ROTATION SIGNALS RECEIVED AT 0.5 AND 1 AU\",\n \"content\": \"The remote imaging in WL and FR of an Earthdirected sheath from two vantage points, one at 0.5 AU and the other at 1 AU, is considered in Section 3.1. Section 3.2 demonstrates how spatial position and electron number density can be inferred from polarisation observations of WL radiance. Section 3.3 presents a means by which magnetic field can be diagnosed from FR measurements. 3.1. Comparing Remotely-Sensed WL and FR Observations from Different Vantage Points Figure 2 shows the modelling results of an Earthdirected sheath propagating from the Sun to 1 AU. The travelling sheath is supposed to be imaged simultaneously by two observers at 0.5 and 1 AU. The WL and FR signatures of the sheath are synthesised, using the methods in Section 2. Representative LOSs, which cut through the sheath (LOS1-6), are denoted using arrows in Figure 2. The variations of various physical parameters along LOS1-3 are shown in Figure 3. LOS1, LOS2, LOS3, and LOS5 are approximately tangential to the left flank of the shock; LOS4 and LOS6 are tangential to the nose of the shock. LOS1 and LOS4 are directed towards the observer situated at 0.5 AU; all other LOSs are directed towards the observer at 1 AU. The viewing configuration for LOS1 (Figure 2a) is equivalent to that for LOS3 (Figure 2c), as the elongation of the shock front is the same for LOS1 and LOS3. Thus, the Thomson scattering geometry is identical for these two LOSs, leading to similar LOS profiles in Figure 3. Of course, the observed radiance along LOS1 is much stronger than that along LOS3 (Table 1). Similarly, the observations along LOS4 and LOS6 (Figures 2d and 2f) have identical Thomson scattering geometries. At any given time, the sheath is viewed at greater elongations from a vantage point closer to the Sun. For instance, at an elapsed time of 5.5 hours, the foremost elongation ε of the sheath is 20 · for an observer at 1 AU (LOS1) compared with 7 · for an observer at 0.5 AU (LOS2). While the sheath is undetectable in WL along LOS2 (Figure 3g), it can be observed in FR (Figure 3l). The portion of an LOS that contributes most to the WL radiance broadens and flattens with increasing elongation, and shifts gradually towards the observer. At elongations beyond 90 · , only back-scattered photons are received; electrons in the vicinity of the observer mainly contribute to remote-sensing signatures for elongations beyond 90 · . Such observations for elongations of ε ≥ 90 · are less useful for the purposes of space weather prediction. In Figures 2d and 2f, the shock front has already reached the observer, and can be detected in-situ.\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"3.2. Inferences of Sheath Position from Polarised White Light\",\n \"content\": \"The WL radiance of CMEs is determined by both the electron number density distribution and the Thomsonscattering geometry (Equation 3). The total radiance at a scattering site ( i ), and its constituent radial ( i R ) and tangential ( i T ) components, are associated with Thomson-scattering factors z 2 G , z 2 G R , and z 2 G T , respectively. Near the Thomson-scattering surface, z 2 G T is much larger than z 2 G R . If a dense parcel of plasma, viewed at large elongations, approaches the Thomson surface, its WL signatures will comprise (1) an increase in I , (2) an increase in I T , (3) a decrease in I R , and (4) an increase in the degree of polarisation p . The variation of p is largest, while that of I is negligible. A plasma parcel's distance from the Thomson sphere has a less significant effect on I at larger elongations. However, the determination of the plasma parcel's location will be more uncertain, if only unpolarised WL observations are available, as with current operational heliospheric imaging systems. Polarisation observations can provide an important clue to the primary scattering site. LOS1 in Figure 2 is used to demonstrate these inferences. The Thomson-scattering geometry is independent of the distribution of heliospheric electrons. The degree of polarisation ( p ) and the Thomson-scattering factors ( z 2 G , z 2 G R , z 2 G T ), as presented in Figure 3b and 3d, only depend on the modified scattering angle χ ∗ = 90 · -χ . The profiles of p , z 2 G , z 2 G R , and z 2 G T are symmetrical around χ ∗ = 0 · . The dependence of χ ∗ , z 2 G , and LOS distance z on p can be seen in Figure 4. p = 1 corresponds to perpendicular scattering (i.e. χ ∗ = 0 · ). p = 1 corresponds to two solutions for χ ∗ : one resulting from forward scattering ( χ ∗ < 0 · ), and the other associated with backward scattering ( χ ∗ > 0 · ). In response to the passage of the shock, the initial radiance components at t = 0, I T0 and I R0 , are enhanced to values denoted by I T and I R , respectively. The increase in the radiance components define a so-called modified degree of polarisation that we denote using p ∗ . p ∗ is given by /negationslash p is 0.62 along LOS1 at t = 0 hours. This effectively defines the degree of polarisation associated with the background solar wind. During the sheath passage, at t = 5 . 5 hours, p is 0.58 along this LOS. The modified degree of polarisation p ∗ , derived using Equation 9, is therefore 0.29 at t = 5 . 5 hours. The radiance enhancement is due to the presence of the sheath in the LOS. The sheath, which trails the shock front, occupies a relatively small volume of interplanetary space. The sheath occupies the portion of LOS1 bounded by -55 · < χ ∗ < -35 · (Figures 3a and 3c). Within this region, p smoothly varies from 0.15 to 0.5 (Figure 3d). The average value of p ∗ within the sheath is 0.29. In an inverse approach, p ∗ can be used to estimate the scattering angle χ ∗ within the sheath. This is demonstrated in Figure 4a. p ∗ = 0 . 29 corresponds to χ ∗ = ± 46 · and z 2 G = 6 . 5 × 10 -29 , where z 2 G is the average value of z 2 G in the sheath. The solution of χ ∗ = 46 · can be immediately excluded, as an Earth-directed CME can generally be identified (indeed much earlier) as being front-sided based on Extreme Ultraviolet (EUV) images of the full solar disk (e.g., Thompson et al. 1998; Plunkett et al. 1998). The other solution, χ ∗ = -46 · , is physical and yields a value of 60 R S for the distance, z , of the main scattering site (corresponding to the sheath) from the detector. How best to judge which solutions for χ ∗ are physical is explained in detail in Section 4. Once the Thomsonscattering factor z 2 G of the sheath has been inferred, its column-integrated electron number density can be estimated based on the following equation: It is clear that WL polarisation measurement can prove extremely valuable in the study of interplanetary CMEs and shocks.\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"3.3. Magnetic Field Inferred from Faraday Rotation\",\n \"content\": \"As discussed in Section 3.2, the column-integrated electron number density along any LOS can be inferred from its WL observations. Thus, if a radio beam lies within the FOV of a WL imager such that they remotely probe the same plasma volume, the WL density measurements can be used to retrieve magnetic field strength from the received FR signal. We demonstrate this, for LOS1, in Figure 5. After subtracting the background solar wind contribution, the enhancements in FR measurement and WL radiance, due to the presence of the sheath of the simulated Earth-directed shock, are given by δ Ω RM and δI , respectively. The ratio of δ Ω RM and δI can be expressed as As discussed in Section 3.2, z 2 G corresponds to the average value of z 2 G in the sheath. The derivable parameter δ ( nB ‖ ) δ n , which we call B ∗ ‖ , can be expressed in the form where B ‖ 0 and n 0 denote the initial background values of B ‖ and n , respectively. The inferred value of B ∗ ‖ serves as an upper limit for B ‖ .\",\n \"pages\": [\n 6\n ]\n },\n {\n \"title\": \"4. RADIANCE PATTERNS IN J-MAPS OF WHITE LIGHT AND FARADAY ROTATION\",\n \"content\": \"Shock propagation through the inner heliosphere can be identified through the inclined trace with which it is associated in a time-elongation map (J-map). J-maps of WL radiance ( I/I ∗ , I ) and degree of polarisation ( p , p ∗ ), and FR measurement | δ Ω RM | , as viewed from observers at 0.5 and 1 AU, are presented in Figure 6 and compared in Figure 7. The normalisation factor I ∗ in Figure 6 corresponds to an electron number density distribution that varies according to n ∝ r -2 . A radiance threshold of I/I ∗ ≥ 3 . 68 × 10 -15 is used to demarcate the sheath region in time-elongation ( t -ε ) parameter space. The modified polarisation p ∗ is only calculated, using Equation 9, inside the sheath (Figures 6g-h). The absolute values of I and | δ Ω RM | within the sheath region are much larger for the observer at 0.5 AU, whereas the sheath values of I/I ∗ , p , and p ∗ are comparable when viewed from either vantage point. Over the elongation range 15 · ≤ ε ≤ 180 · , the radiance ratio Max. ( I 0 . 5AU ) Max. ( I 1AU ) is limited to values between 8 and 11 (Figure 7c). This demonstrates that interplanetary CMEs and shocks are viewed better from a location closer to the Sun. The position, mass, and magnetic field of the sheath can be inferred from those directly-measurable parameters presented in Figure 6, using the analytical methods presented in Sections 2.1 and 3.3. As shown in Figure 4, and explained in Section 3.2, the Thomson-scattering factors are symmetrical around χ ∗ = 0 · . As a result, a single value of degree of polarisation p ∗ corresponds to two symmetrical solutions for the scattering angle χ ∗ . The results shown in Figure 8 are derived from those in Figure 6 (for an observer at 0.5 AU) under the assumption of forward scattering, while those in Figure 9 assume backward scattering. For the forward-scattering situation, presented in Figure 8b, the inferred longitude of the sheath ϕ sheath is 22 · at an elapsed time of 5 hours and 9 · at 11 hours. For the backward-scattering case, shown in Figure 9b, the sheath is at ϕ sheath = 140 · and 60 · at these times. So, an observer at 0.5 AU infers a longitude change ∆ ϕ sheath of 13 · (Figure 8b) and 80 · (Figure 9b) for the forward and backward-scattering cases, respectively. The dramatic change in sheath longitude for the backward-scattering case might indicate that the shock is significantly deflected during its interplanetary propagation. However, such an abnormal degree of lateral deflection of ∆ ϕ sheath = 80 · would be highly unphysical, and may imply a 'ghost trajectory' (Figure 6, DeForest et al. 2013). The east-west symmetry of the radiance pattern suggests that the shock is actually front-sided and Earth-directed, rendering the assumption of backward-scattering invalid (Figure 9). If we assume that the radiance pattern shown in Figure 6 is attributable to forward scattering, the inferred position of the sheath is shown as the solid white curve in Figure 2. This agrees very well with the actual position of the sheath. At any given time, only a certain portion of the sheath will be visible from a fixed observing location (Xiong et al. 2013). For example, at an elapsed time of 5.5 hours, it is the flank of the sheath (Figure 2a) that corresponds to the leading edge of the radiance pattern in 6a, while 6 hours later it is the nose (Figure 2d). So, in fact, the longitudinal change of ∆ ϕ sheath = 13 · inferred from Figure 8b is actually an artefact of the viewing geometry and does not represent an actual deflection of the shock front. Along with the inferred position of the sheath, the column-integrated electron number density, δN sheath , and the parallel magnetic field component, B ‖ , are also presented in Figure 8. The derived value of | B ‖ | provides an upper limit for the actual magnetic field, as explained in Section 3.3. By making coordinated observations in WL and FR, CMEs can not only be continuously tracked, but quantitatively diagnosed as they propagate through interplanetary space.\",\n \"pages\": [\n 6,\n 7\n ]\n },\n {\n \"title\": \"5. INTERPLANETARY IMAGING FROM DIFFERENT OBSERVATION SITES\",\n \"content\": \"An interplanetary CME looks different when viewed from different vantage points, but can be readily imaged from a wide range of longitudes. The observed WL radiance pattern depends not only on the longitude ϕ o of the observer, as discussed by Xiong et al. (2013), but also on its heliocentric distance r o . In Section 3.1, we compare observations made from radial distances of 0.5 and 1 AU. In Section 5.1, we consider two particular observation sites that are often considered favourable in terms of WL imaging, the L4 and L5 Lagrangian points. In Section 5.2, we quantify more fully the dependence of WL imaging on r o .\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"5.1. Observing an Earth-Directed shock from the L4 and L5 Lagrangian Points\",\n \"content\": \"The L4 and L5 Lagrangian points of the Sun-Earth system are often considered advantageous for observing Earth-directed CMEs. There are five Lagrangian points, all in the ecliptic, i.e., L1-L5. A spacecraft at L1, L2, or L3 is metastable in terms of its orbital configuration, and hence must frequently use propulsion to remain in the same orbit. In contrast, a spacecraft at L4 or L5 is resistant to gravitational perturbations, and is believed to be more stable. The L4 and L5 points lie 60 · ahead of and behind the Earth in its orbit, respectively. STEREO A reached the L4 point in September 2009 and STEREO B reached L5 in October 2009. The twin STEREO spacecraft were pathfinders for future L4/L5 missions (Akioka et al. 2005; Biesecker et al. 2008; Gopalswamy et al. 2011). A spacecraft at either L4 or L5 can perform routine side-on imaging of Earthdirected CMEs, and hence is of great merit for space weather monitoring. Figure 10a illustrates the imaging, be it in WL or FR, of an Earth-directed sheath from the L5 point. LOS7 intersects the nose of the shock at an elapsed time of 14.5 hours, when the shock nose lies on the Thomsonscattering sphere. The variation, along LOS7, of a number of salient physical parameters is shown in Figures 10 e-j. The interplanetary magnetic field lines are compressed and rotated within the sheath. This rotation results in the closer alignment of the field lines with LOS7, such that the magnetic field component along the LOS, | B ‖ | , is greatly enhanced (Figure 10i). The enhancements of both | B ‖ | and electron number density n within the sheath are responsible for the resultant increases in WL radiance I and FR measurement | Ω RM | . The degree of WL polarisation p , as viewed along LOS7 that is at an elongation of 34 · , is 0.67 for the background solar wind and increases to 0.75 during the shock passage at 14.5 hours. This corresponds to a value of the modified WL polarisation p ∗ of 0.98, based on Equation 9. As was done for LOS1 in Section 3, we evaluate the WL radiance along LOS7 (Figure 10a), from which we infer the shock position (Figure 10d). Again, a single value of p ∗ corresponds to two symmetrical solutions for scattering angle χ ∗ , i.e., p ∗ = 0 . 29 and χ ∗ = ± 46 · for LOS1, and p ∗ = 0 . 98 and χ ∗ = ± 5 · for LOS7. For LOS1, only one solution for χ ∗ = -46 · was deemed physical; for LOS7, both solutions for χ ∗ are potentially physical. The scattering sites corresponding to χ ∗ = ± 5 · are very close to one another, and both agree well with the actual position of the sheath (Figure 10a). The section of LOS7 bounded by -5 · ≤ χ ∗ ≤ 5 · lies within the sheath. Both forward scattering ( -5 · ≤ χ ∗ < 0 · ) and backward scattering (0 · < χ ∗ ≤ 5 · ) will contribute to the radiance I observed along this LOS. The propagating sheath can be tracked continuously and easily in WL from the L5 vantage point, such that it leaves an obvious signature in the J-map of synthesised radiance (Figures 10b and 10c). This confirms previous assertions that the L4 and L5 points are very favourable in terms of space weather monitoring.\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"5.2. Dependence of White-Light Radiance on Heliocentric Distance\",\n \"content\": \"The background intensity at a fixed elongation in a WL sky map is greater for an observer closer to the Sun. For a heliospheric imager at any distance from the Sun, Jackson et al. (2010) proposed the following Thomsonscattering principles: (1) The WL radiance I at a given solar elongation falls off with the heliocentric distance r according to r -3 ; (2) Such a dependence of I ∝ r -3 is valid for almost any viewing elongation, and for any radial distance from 0.1 AU out to 1 AU and beyond. The WL radiance I depends on the heliospheric distribution of electron number density n . In interplanetary space, the background solar wind speed is nearly constant, and the background electron number density n 0 varies approximately with r -2 . However, the equilibrium defined by n 0 ∝ r -2 is disturbed by the presence of interplanetary transients, such as CMEs and CIRs. A travelling shock can sweep up, and hence compress significantly, the background solar wind plasma. Figures 2 and 10a show a density enhancement of n -n 0 n 0 ≈ 2 . 2 within the sheath. The associated compression ratio n n 0 ≈ 3 . 2 indicates that the shock is very strong. However, when viewed along elongations less than 60 · , the strongest signatures of shock passage (characterised by Max.( I )) vary very closely with r -3 (Figures 11b and 11c). The relationship of Max.( I ) ∝ r -3 is slightly violated at large elongations ε > 60 · . Figure 7c reveals that the ratio between Max.( I 0 . 5AU ) and Max.( I 1AU ) is close to 8 for ε ≤ 60 · , increasing thereafter to 10.8 at ε = 180 · . The premise that the WL radiance decreases with the third power of Sun-observer distance generally holds true for both the background solar wind and propagating CMEs.\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"6. DISCUSSION\",\n \"content\": \"The detectability in WL of a particular electron density feature is determined by its signal above the noise background. In STEREO /HI-1 images, the dominant WL signal is zodiacal light due to scattering of sunlight from the F-corona, which is centred around the ecliptic. In the STEREO /HI-2 FOV, the noise floor is primarily determined by photon noise and the background star-field (DeForest et al. 2011). Away from the ecliptic, the background WL noise has a sharp radial gradient in coronal images, and is nearly constant in heliospheric images. The signal-to-noise ratio for heliospheric electron density features is discussed by Howard et al. (2013). We will address the detection of CMEs in the presence of background noise in future forward-modelling work. If both a transient CME and background (Heliospheric Current Sheet (HCS) - Heliospheric Plasma Sheet (HPS)) plasma structures are present along the same LOS, both will contribute to the total LOS-integrated radiance. In this case, the interpretation of the data would clearly be more problematic. Moreover, if the LOS were to penetrate a HCS, the magnetic field vector would, at that point, rotate through 180 · . Due to the mutual cancellation of B ‖ across the HCS, there may be no net FR signature according to Equations 4-6. Hence, even such a significant interplanetary structure may be associated with only a weak FR measurement. Conversely, the relatively dense plasma within a HPS can significantly contribute to WL radiance. Thus the potential effects of the presence of HCS-HPS structures need to be borne in mind in the remote imaging of CMEs. In the current work, however, we find that such effects are negligible. In our numerical simulation, there are two HCS-HPS structures, which are initially rooted at longitudes of ϕ = ± 90 · at the inner boundary of our numerical simulation. The simulated shock emerges at a longitude of ϕ = 0 · . The large longitudinal difference between the HCS-HPS and the shock means that the remote-sensing signatures are principally contributed by the sheath. Thus, in our forward-modelling work, the signal enhancements of synthesised imaging in WL and FR are unambiguously the result of the propagating sheath. In general, the more complex the interplanetary dynamics, the more complex the resultant remote-sensing observations will be. For instance, a CME can interact with other CMEs and/or background solar wind structures such as CIRs, HCSs, and HPSs; mutual interaction between CMEs is, however, generally more perturbing than interactions between CMEs and such background structures. Interactions can result in the background solar wind structures becoming warped or distorted (e.g., Odstrˇcil et al. 1996; Hu & Jia 2001), and CMEs being accelerated/decelerated (e.g., Lugaz et al. 2005; Xiong et al. 2007; Shen et al. 2012b), deflected (e.g., Xiong et al. 2006b, 2009; Lugaz et al. 2012), distorted (e.g., Xiong et al. 2006b, 2009), or entrained (e.g., Rouillard et al. 2009a). In particular, during such interactions, the behavior of a sheath can become much more complex: the shock aphelion can be deflected, spatial asymmetries can develop along the shock front, and the shock front can potentially merge completely with other shock fronts. At an interaction site, both the plasma density and magnetic field would be compressed; this would lead to enhanced signatures in both WL and FR observations. For example, the interaction between two CMEs was manifest as a very bright arc in WL images (e.g., Harrison et al. 2012; Liu et al. 2012; Temmer et al. 2012). Different types of interaction would likely result in different WL radiance signatures; in fact, through a single interaction, the corresponding radiance pattern would evolve. The interpretation of such complex WL radiance patterns would be prone to large uncertainties, but can be rigorously constrained if interplanetary imaging was performed from multiple vantage points and complemented by numerical modelling. For stereoscopic WLimaging, ray-paths from one observer intersect those from the other observer. Thus the 3D distribution of electrons in the inner heliosphere can be reconstructed using a time-dependent tomography algorithm (Jackson et al. 2006; Bisi et al. 2008; Webb et al. 2013). With the aid of numerical modelling, coordinated imaging in WL and FR would enable the properties and evolution of complex interplanetary dynamics to be diagnosed.\",\n \"pages\": [\n 8\n ]\n },\n {\n \"title\": \"7. CONCLUDING REMARKS\",\n \"content\": \"In this paper, we have investigated the WL and FR signatures of an interplanetary shock based on an approach of forward MHD modelling. The WL Thomsonscattering geometry is increasingly more significant at larger elongations. The degree of WL polarisation can be used to estimate the 3D location of the main scattering region, while FR measurement can be used to infer, to some extent, the magnetic configurations of CMEs. This work presented here demonstrates, as a proof-of-concept, that the availability of coordinated observations in polarised WL and FR measurement would enable the local LOS magnetic component to be estimated. Although the current generation of heliospheric WL imagers, such as the STEREO /HI instruments, do not have polarisers, there are advances underway in terms of FR imaging using Low-frequency radio arrays. Coordinated imaging in WL and FR would enable the inner heliosphere to be mapped in fine detail; the location, mass, and magnetic field of CMEs can be diagnosed on the basis of such combined observations. Forward modelling is crucial in establishing the causal link between interplanetary dynam- ics and observable signatures, and can provide valuable guidance for future coordinated WL and FR imaging. Although not the methodology of the current work, numerical MHD models of the inner heliosphere can also be directly driven by photospheric observations (e.g., Hayashi 2005; Wu et al. 2006; Feng et al. 2012b). A comparison of synthesised and observed WL and FR sky maps, the former based on the use of such datadriven models, would prove highly beneficial in validating the forward modelling and interpreting the observations. Such an integration of observation data analysis and numerical forward modelling will be explored as the continuation of the preliminary modelling work presented in this paper. This work is jointly supported by the National Basic Research Program (973 program) under grant 2012CB825601, the Chinese Academy of Sciences (KZZD-EW-01-4), the National Natural Science Foun- dation of China (41231068, 41031066, 41204129), the Strategic Priority Research Program on Space Science from the Chinese Academy of Sciences (XDA04060801), the Specialized Research Fund for State Key Laboratories of China, the Chinese Public Science and Technology Research Funds Projects of Ocean (201005017), open research foundation of Science and Technology on Aerospace Flight Dynamics Laboratory of China (AFDL2012002), research fund for recipient of excellent award of the Chinese Academy of Sciences President's scholarship (startup fund). Ming Xiong is also partially supported by an institutional project of 'Key Fostering Direction in Pulsar Science and Application' from the Center of Space Science and Applied Research, China. Ming Xiong sincerely thanks Drs. Bo Li, Ding Chen, Craig DeForest, James Tappin, and Tim Howard for their beneficial discussions and thoughtful suggestions. We sincerely thank the anonymous referee for his/her constructive suggestions.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Feng, L., Inhester, B., Wei, Y., et al. 2012a, ApJ, 751, 18 Roca-Sogorb, M. 2008, ApJ, 681, L69 Space Sci. Rev., 88, 529 20 Xiong et al. ) t n e m e r u s a e m R F c i t e n g a m l e l l a r a P n o r t c e l E 3 - m d a r 2 1 - 0 1 × ( ) T n ( ) 3 - m c ( ) . 0 1 e r u g i F n o d i a l r e v o s i 7 S O L d n a 2 e r u g i F n o d i a l r e v o e r a 6 - , L O S 3 L O S s 1 t t e r i n g o r s G T h c a E . j - e 0 1 d n a 3 s e r u g i F n i n o i t a s i l a m r o n r o f d e s u , 7 S O L d n a , 2 ; t c | ‖ B | n y t i s n e d 2 z n a , | ‖ B | , n , T G 2 z , R G 2 z , G 2 z , i s r e t e m a r a p e h t f o s e u l a v m u m i x a M l e n a d n a , o ϕ e d u t i g n o l a , o r s u i d a r a , t e m i t a d e t a n g i s e d s i S O L a c L W n o i t a g n o l E e d u t i g n o L i i d a R e m i T S O L ( ) · ( ) ε o ϕ o r t · ( ) U A ( ) r u o h ( d l e fi r e b m u n | M R ω | 4 . 4 1 7 0 2 2 9 3 0 2 0 5 . 0 5 . 5 1 S O L 2 . 8 1 3 2 2 3 9 8 1 7 0 1 5 . 5 2 S O L 1 5 . 1 9 . 8 6 7 8 0 2 0 1 4 1 3 S O L 2 4 . 0 5 . 8 2 3 . 0 6 4 3 0 6 - 1 5 . 4 1 7 S O L\",\n \"pages\": [\n 9,\n 20\n ]\n }\n]"}}},{"rowIdx":72,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...777...82K"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1308.5468.pdf"},"content":{"kind":"string","value":"\nK s BAND LUMINOSITY EVOLUTION OF THE ASYMPTOTIC GIANT BRANCH POPULATION BASED ON STAR CLUSTERS IN THE LARGE MAGELLANIC CLOUD\nYoukyung Ko, Myung Gyoon Lee, and Sungsoon Lim\nAstronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea\nykko@astro.snu.ac.kr, mglee@astro.snu.ac.kr, slim@astro.snu.ac.kr\nABSTRACT\nWe present a study of K s band luminosity evolution of the asymptotic giant branch (AGB) population in simple stellar systems using star clusters in the Large Magellanic Cloud (LMC). We determine physical parameters of LMC star clusters including center coordinates, radii, and foreground reddenings. Ages of 83 star clusters are derived from isochrone fitting with the Padova models, and those of 19 star clusters are taken from the literature. The AGB stars in 102 star clusters with log(age) = 7.3 - 9.5 are selected using near-infrared color magnitude diagrams based on 2MASS photometry. Then we obtain the K s band luminosity fraction of AGB stars in these star clusters as a function of ages. The K s band luminosity fraction of AGB stars increases, on average, as age increases from log(age) ∼ 8.0, reaching a maximum at log(age) ∼ 8.5, and it decreases thereafter. There is a large scatter in the AGB luminosity fraction for given ages, which is mainly due to stochastic effects. We discuss this result in comparison with five simple stellar population models. The maximum K s band AGB luminosity fraction for bright clusters is reproduced by the models that expect the value of 0.7 - 0.8 at log(age) = 8.5 - 8.7. We discuss the implication of our results with regard to the study of size and mass evolution of galaxies.\nSubject headings: galaxies: star clusters: general - infrared: stars - stars: AGB and post-AGB - Magellanic Clouds - galaxies: evolution\n1. Introduction\nThe asymptotic giant branch (AGB), a representative intermediate-age population, is the most luminous evolutionary stage for low- and intermediate-mass (1 - 8 M /circledot ) stars.\nAGB stars emit a huge amount of near- to mid-infrared light because of their low effective temperature (T eff ∼ 1000 - 4000 K) and circumstellar dust. Hence it is expected that they contribute significantly to the infrared light of galaxies. However, their infrared luminosity contribution in galaxies, even in a simple stellar population (SSP), is still a debating issue with regard to constructing evolutionary population synthesis (EPS) models (Maraston 2011, Bruzual et al. 2013, Noel et al. 2013, and references therein).\nThe EPS models are an useful tool to determine physical parameters of stellar complexes such as star clusters and galaxies by spectral energy distribution (SED) fitting. These models reproduce SEDs of stellar systems by synthesizing the SEDs of stellar populations in various evolutionary stages, assuming age, metallicity, foreground and internal reddening values, star formation history, and so on. Therefore, the spectral energy contribution of individual stellar populations influences the estimation of physical parameters of stellar systems, and especially that of the AGB population plays a key for understanding of the SEDs for stellar systems expected by EPS models.\nThere are various EPS models that include the AGB evolutionary process (e.g., Charlot & Bruzual 1991, Bruzual & Charlot 1993, Fioc & Rocca-Volmerange 1997, Maraston 1998, Leitherer et al. 1999, Vazdekis 1999, Schulz et al. 2002, Bruzual & Charlot 2003, Jimenez et al. 2004, Maraston 2005, Conroy et al. 2009, Kotulla et al. 2009, Conroy & Gunn 2010, Vazdekis et al. 2010, Maraston & Stromback 2011). Bruzual & Charlot (2003, hereafter BC03), for example, presented an EPS model based on Padova evolutionary tracks including just two evolutionary stages for thermally pulsing AGB (TP-AGB) (Girardi et al. 2000), while their recent model includes 15 evolutionary stages of the TP-AGB oxygen-rich and carbon-rich phases (Bruzual A. 2010). The Padova evolutionary tracks adopted in the BC03 model include a given core overshooting efficiency. On the other hand, Maraston (1998, 2005) used evolutionary tracks assuming zero efficiency of the core overshooting from Cassisi et al.(1997, 2000) to determine luminosity contribution of main-sequence populations. It makes the lifetime of main-sequence stars in the Maraston (2005) model shorter compared with Padova isochrones. In addition, she used the fuel consumption theorem (Renzini & Buzzoni 1986) for post-main-sequence stars, not adopting the isochrone synthesis method. In the model of Maraston (1998), the TP-AGB evolutionary process is modified in the fuel consumption theorem, applying the advanced envelope burning process of AGB stars. Renzini & Buzzoni (1986) estimated the contribution of TP-AGB population in the young SSPs with ages < 10 8 yr, and compared it with the star clusters in the the Magellanic Clouds (MCs). They found that it is too high to be consistent with the observational results based on these star clusters. Considering this difference, Maraston (2005) suggested a revised model, assuming shorter lifetime and lower fuel consumption of TP-AGB stars than Renzini & Buzzoni (1986).\nBC03 and Maraston (2005) adopted different stellar population synthetic methods, and the SEDs reproduced by these models show recognizable differences. A number of studies argue whether or not these EPS models reproduce well observational quantities of stellar systems related with the AGB population as follows. Some studies found that spectra and SEDs of post-starburst galaxies or distant galaxies (z ∼ 1 - 2) have no near-infrared boosted features, which is similar to the expectation of the BC03 model (Muzzin et al. 2009, Kriek et al. 2010, Zibetti et al. 2013). In addition, Conroy & Gunn (2010) suggested that the BC03 model and their own EPS model, a flexible stellar population synthesis model, reproduce the color of star clusters and post-starburst galaxies better than the Maraston (2005) model. In contrast, others confirmed that the Maraston (2005) model performs well in reproducing near-infrared colors, ( Y -K ) and ( H -K ), and SEDs of low to high redshift galaxies (Maraston et al. 2006, Eminian et al. 2008, MacArthur et al. 2010). Moreover, van der Wel et al. (2006) and Henriques et al. (2011) showed that the rest-frame K band mass-to-light ratio evolution and K s band luminosity evolution of galaxies are explained better by the Maraston (2005) model than by the BC03 model.\nIn addition to these galaxy studies, there are several studies investigating star clusters, especially star clusters in the MCs, considering the relevance between the model performance and ages of stellar systems. Because of their proximity, they are very useful to examine not only the individual stellar population directly but also the integrated properties of star clusters. Therefore, they are an ideal object to calibrate SSP models. Pessev et al. (2008) investigated optical to near-infrared colors, ( B -J ), ( V -J ), and ( J -K ), of 54 star clusters in the MCs, and concluded that the BC03 and the Maraston (2005) present the best performance for intermediate-age (0.2 - 2 Gyr) and old ( > 2 Gyr) star clusters, respectively. Lyubenova et al. (2010, 2012) analyzed integrated near-infrared high-resolution spectra of six globular clusters in the Large Magellanic Cloud (LMC) with ages ∼ 1 - 13 Gyr. They showed that the Maraston (2005) model expects J and H band spectra of all their sample star clusters adequately, while it does not for K band spectra of the star clusters with ages < 2 Gyr. Recently Noel et al. (2013) presented the calibration data for stellar population models using 43 star clusters in the MCs. They compared the observed colors of the star clusters, ( V -K ) 0 , ( J -K ) 0 , and ( V -I ) 0 , as a function of ages with the theoretical expectation of various models including BC03 and Maraston (2005). In conclusion, for the ages older than 1 Gyr, the models of Maraston (2005) and BC03 are along the upper end lower end of the observed color, respectively. In the case of the younger ages, BC03 model reproduces well the observed color of star clusters, while Maraston (2005) model expects them too red.\nWhile above studies investigated the integrated properties of star clusters, Mucciarelli et al. (2006) analyzed the resolved AGB population in the LMC star clusters in detail. They investigated 19 LMC star clusters in terms of K s band luminosity contribution of AGB stars\nas a function of cluster ages. The star clusters used in Mucciarelli et al. (2006) have ages of 100 Myr - 3 Gyr (log(age) ∼ 8.0 - 9.5). They concluded that their empirical results are consistent with the expectation of Maraston (2005) for this age range. Later, Mucciarelli et al. (2009) suggested a similar conclusion from the additional study of four old star clusters in the Small Magellanic Cloud (SMC).\nIn this study, we investigate the evolution of AGB luminosity contribution with a large number of LMC star clusters with log(age) ∼ 7.3 - 9.5, overcoming the shortcomings in the previous studies. Because Mucciarelli et al. (2006, 2009) included few star clusters with log(age) ∼ 8.3 - 8.7 (see Figure 5 in Mucciarelli et al. 2009), we enlarged the number of star cluster samples with this age range. In this age range, the AGB luminosity contribution is expected to change rapidly according to the Maraston (2005) model. In addition, most of previous star cluster studies adopted star cluster ages from various literature. We determine ages of LMC star clusters by isochrone fitting homogeneously, using the resolved stars.\nThis paper is organized as follows. In § 2, we introduce the photometric data and images used in this study. § 3 describes the method to estimate physical parameters of sample star clusters such as center coordinates, radii, ages, and foreground reddenings including the cluster sample section. In § 4, we select AGB stars in each star cluster and derive the K s band luminosity contribution of AGB stars to total luminosity of star clusters as a function of ages. In § 5, we compare our results with previous studies, and also compare the primary results with the theoretical expectation from EPS models, including the discussion of stochastic effects. Final section summarizes the main results and presents the conclusion of this study.\n2. Data\nBica et al. (2008) presented an extended source catalog of the MCs including star clusters, emission nebulae, associations, and HI shells. They compiled data from various literature including the findings based on photographic survey plates. It contains center coordinates (R.A. and Declination), major and minor axes, and position angles of 3,700 star clusters of the MCs including the LMC, SMC, and the Magellanic Bridge regions. We redetermined the centers and radii of LMC star clusters based on the center coordinates presented in Bica et al. (2008).\nWe used optical ( UBVI ) and near-infrared ( JHK s ) point source catalogs of the LMC. Zaritsky et al. (2004) presented U, B, V , and I band photometry of 24,107,004 point sources in the central 64 deg 2 of the LMC from the Magellanic Clouds Photometric Survey (MCPS; Zaritsky et al. 1997). The MCPS obtained drift-scan images using 1-m Las Campanas Swope\nTelescope and Great Circle Camera (Zaritsky et al. 1996). Their photometry is incomplete below 21.5, 23.5, 23, and 22 mag in U, B, V , and I bands in sparse regions, respectively. This catalog is used to determine center coordinates, radii, ages, and foreground reddenings of the star clusters.\nIn order to distinguish AGB stars from other populations, we used a near-infrared point source catalog from the two micron all sky survey (2MASS; Skrutskie et al. 2006). In the central 100 deg 2 region of the LMC (10 · × 10 · ), there are 1,430,676 point sources detected in the 2MASS. The limiting magnitudes of photometry are 15.8, 15.1, and 14.3 mag in J, H , and K s bands, respectively, which correspond to 10 σ point source detection level. The AGB stars in the LMC are brighter than K s ∼ 12 . 3 mag, much brighter than the limiting magnitudes. We also used 2MASS Atlas Images to estimate the integrated luminosity of the star clusters, retrieving the K s band images of our sample clusters using 2MASS interactive image service 1 .\n3. Physical Parameters of LMC Star Clusters and Sample Selection\n3.1. Center Coordinates and Sizes of Star Clusters\nWe determined centers for 1,645 star clusters and radii for 1,708 star clusters, respectively, using the MCPS catalog (Zaritsky et al. 2004) as a part of our study of LMC star clusters. We constructed 2-dimensional number density maps of bright stars with V < 20.5 mag around the center coordinates of the star clusters presented by Bica et al. (2008). The number density maps are smoothed with a boxcar filter whose width is 20 '' . Center coordinates, coordinate errors, and position angles of each star cluster were estimated by 2-dimensional Gaussian fitting of this smoothed number density map. The field of view for the fitting region is 3 times larger than the radius of each cluster given in Bica et al. (2008). Figure 1 shows an example of centering process for one cluster NGC 1861. We attempted 2-dimensional Gaussian fitting to 3,064 LMC star clusters in Bica et al. (2008), but stellar number density maps could obtain acceptable fits for only 1,645 star clusters. The fitting results are not reliable in the case of poor, faint, or binary clusters, in which case that the center coordinates presented by Bica et al. (2008) are adopted.\nThe radius of each cluster was determined from radial number density profiles (see Figure 2). The radial number density profile is obtained by counting point sources with V < 20.5 mag. We estimated a median value of the background number density (n bg ) of\nstars located between 200 '' and 300 '' from the center of each cluster. The standard deviation from n bg ( σ bg ) is calculated, and the area of which number density greater than n bg +3 σ bg is considered as a cluster area. Finally, we determined radii of 1,708 LMC star clusters, and radii of the other clusters that do not show a prominent concentration are adopted from Bica et al. (2008). Most of these clusters are poor, faint, or binary ones. Bica et al. (2008) presented major and minor axes of star clusters, from which we define the radius of each star cluster as the mean value of semi-major and semi-minor axes.\nIn addition to Bica et al. (2008), Werchan & Zaritsky (2011) also presented a catalog of star clusters they found in the MCPS images. They investigated stellar overdensities in LMC fields using stars brighter than 20.5 mag in V band. By both King and Elson-FallFreeman model fitting of the surface brightness profiles of each cluster, they determined center coordinates, central surface brightness, tidal radii, and 90% enclosed luminosity radii of 1,066 LMC star clusters. We compare the center coordinates and radii determined in this study with those given by Bica et al. (2008) and Werchan & Zaritsky (2011) in Figure 3.\nFigure 3(a) - (f) show the differences of center coordinates of star clusters among three studies. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 626, 1,645, and 677, respectively. The center coordinates of star clusters from all three different studies are mostly consistent within 10 '' . Figure 3(g) - (i) show the differences of radii of star clusters. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 615, 1,708, and 681, respectively. Werchan & Zaritsky (2011) presented four kinds of radii for each cluster, core radii and 90% enclosed luminosity radii obtained by fitting using two different models, respectively, and we adopted the 90% enclosed luminosity radius from King model fitting results as a radius to compare with the results from other studies. The values for the cluster radii derived in this study are in better agreement with Bica et al. (2008) than with Werchan & Zaritsky (2011).\n3.2. Cluster Sample Selection and Age Estimation\nFor this study, we selected 102 star clusters that have red and bright stars in nearinfrared ( K s -( J -K s )) CMDs based on 2MASS catalog (Skrutskie et al. 2006). These stars are considered as AGB star candidates. The AGB selection method is described in § 4.1. For 96 and 83 of these star clusters, we estimated foreground reddenings and ages, respectively, with reasonable optical photometry as follows.\nWe chose member stars of each star cluster using the center coordinates and the radii estimated before (see § 3.1). The value of foreground reddening, E ( B -V ), was estimated by shifting the zero age main-sequence (ZAMS) in the (( U -B ) -( B -V )) color-color diagram (CCD). We used the bright main-sequence stars ( V /lessorsimilar 18) located in the outer region up to 200 - 300 '' of each star cluster to obtain the CCDs, and compared the sequence of stars in the CCDs with the ZAMS in the Padova models (Marigo et al. 2008) as in Figure 4(b). The errors of E ( B -V ) values are about 0.02 mag typically.\nFigure 5(a) and (b) show ( V -( B -V )) CMDs of both a cluster and a field region for NGC 1861, as an example. The cluster CMD is expected to contain field stars as well as cluster stars. In order to minimize the field contamination, we performed statistical subtraction of field CMDs for cluster CMDs. We counted the number of stars in cluster CMDs with that of stars in field CMDs for the same area as the cluster area for each color and magnitude bin (∆( B -V ) ∼ 0 . 5 and ∆ V ∼ 1), and subtracted statistically field stars from cluster stars for each bin. Figure 5(c) displays a field-subtracted CMD of NGC 1861. It shows a clear stellar sequence with a smaller number of stars than the original CMD. We determined ages of 83 star clusters by isochrone fitting in the field-subtracted ( V -( B -V )) CMDs, assuming the distance modulus (m -M) 0 = 18.50 mag and Z = 0 . 008 . Cluster ages were derived using isochrones of Marigo et al. (2008). We used only the stars with small errors of colors with err ( B -V ) < 0 . 1 mag for isochrone fitting. The ages of the other 19 star clusters could not be derived, because they were not covered by the MCPS observation fields or are older than 1 Gyr. In this case, we adopted the ages of these clusters from the literature (Elson & Fall 1985, Girardi et al. 1995, Pietrzynski & Udalski 2000, Goudfrooij et al. 2011, Popescu et al. 2012). Table 1 lists physical parameters of 102 star clusters that will be used for AGB star selection.\nWe compared the ages derived in this study with those given in other references, Elson & Fall (1985), Pietrzynski & Udalski (2000), Hunter et al. (2003), Glatt et al. (2010), and Popescu et al. (2012), as shown in Figure 6. The isochrone fitting method used for the resolved stars in star clusters is considered to be more reliable than other age-dating methods based on the integrated color or spectra of the star clusters. Pietrzynski & Udalski (2000), Glatt et al. (2010), and this study used the isochrone fitting method, while Elson & Fall (1985), Hunter et al. (2003), and Popescu et al. (2012) analyzed the integrated color of the star clusters. Elson & Fall (1985) and Hunter et al. (2003) analyzed ( U -B ) and ( B -V ) colors of the star clusters, and Popescu et al. (2012) performed a Monte Carlo simulation with their own star cluster simulation software (MASSive CLuster Evolution and ANalysis, MASSCLEAN; Popescu & Hanson 2010) to reproduce the cluster colors, ( U -B ) 0 and ( B -V ) 0 . The ages based on the isochrone fitting method show good agreement with each other. They also show correlations with the ages based on integrated colors, but with signif-\nicant scatters and non-unity slopes. It is noted that the ages derived from integrated colors by Popescu et al. (2012) show a better correlation with the isochrone-fitting ages, compared with other results in Elson & Fall (1985) and Hunter et al. (2003).\nFigure 7 shows the CMDs of five star clusters that have the largest difference of ages between this study and others: SL482 (Glatt et al. 2010), NGC 1782 (Elson & Fall 1985), SL294 (Popescu et al. 2012), SL503 (Hunter et al. 2003), and H88-182 (Pietrzynski & Udalski 2000). We plotted the Padova isochrones for Z = 0 . 008 and the ages corresponding to the values derived in this study and other references. In the case of SL482, NGC 1782, and H88182, it is difficult to determine their ages reliably because the number of the brightest stars around the main-sequence turnoff is small. However, in the case of other two star clusters, SL294 and SL503, their CMDs are not matched by the isochrones for the ages derived by Popescu et al. (2012) and Hunter et al. (2003) respectively, while they are by the isochrones for the ages derived in this study.\n4. Results\n4.1. Selection of AGB Stars\nWhile it is difficult to distinguish AGB stars from RGB stars in optical CMDs, it is relatively easier in near-infrared CMDs. Therefore, we plotted the near-infrared ( K s, 0 -( J -K s ) 0 ) CMDs of resolved stars in 102 star clusters using the 2MASS point source catalog (Skrutskie et al. 2006), and selected AGB stars using two criteria: (1) stars brighter than the tip of the RGB (TRGB); K s, 0 < 12 . 3, and (2) stars redder than the RGB; ( J -K s ) 0 > -0 . 075 × K s, 0 +1 . 85. We adopted the TRGB magnitude, K s = 12.3 ± 0.1 estimated from 2MASS point sources in the LMC region (Nikolaev & Weinberg 2000). The second criterion was suggested from the analysis of the 2MASS photometry for LMC stars by Cioni et al. (2006). There is no constraint for the brightest and reddest stars. We use the extinction law in Cardelli et al. (1989) to derive extinction values for each band, adopting R V = 3 . 1.\nFigure 8(b) and (d) show the combined ( K s, 0 -( J -K s ) 0 ) CMDs of all stars in 41 young star clusters with log(age) < 8 . 5 and 61 old star clusters with log(age) ≥ 8 . 5, respectively. We selected the AGB stars brighter and redder than AGB boundary lines as described above (dashed lines). We also plotted other AGB boundaries used in the references in Figure 8(b) and (d): dot-dashed lines used by Mucciarelli et al. (2006) and gray shaded regions used by Nikolaev & Weinberg (2000). The AGB boundary used in this study is working in the similar way to that in Nikolaev & Weinberg (2000). However, the AGB boundary used by Mucciarelli et al. (2006) includes a significant number of bluer stars, compared with that in\nthis study. This difference will be discussed in § 5.1.\n4.2. Measurement of K s Band Luminosity Fraction of the AGB Population in Star Clusters\nWe estimated the K s band luminosity of star clusters by aperture photometry using 2MASS K s band images. Photometry was performed with IRAF 2 APPHOT package. For background estimation we used annular apertures with the inner radius to be the sum of the star cluster radius and its error and the aperture width of 10 '' . The background level was estimated using the mode value of the annulus region. For cluster photometry we used circular apertures with radius that is the same as the cluster radius. Figure 9 displays a K s band image of an example star cluster, NGC 1861, showing the position of apertures for the cluster and background area. We calculated the K s band luminosity of AGB stars in each cluster by summing their luminosity converted from 2MASS magnitudes, and obtained the K s band luminosity fraction of AGB stars in the star clusters.\nTable 2 summarizes the properties of AGB populations as well as other basic parameters of 102 LMC star clusters. It lists the number of AGB stars, and the K s band luminosity and luminosity fraction of AGB stars in each cluster, as well as K s band integrated magnitude and luminosity of the star clusters. The magnitudes are based on 2MASS magnitude system. We adopted the K s band absolute magnitude M K s /circledot = 3 . 27 mag for the Sun, using M V /circledot = 3 . 83 mag (Allen 1976) and ( V -K s ) = 1 . 56 mag (Casagrande et al. 2012), to convert the magnitude into the luminosity.\nThe error of the AGB luminosity fraction is contributed by various errors in addition to the photometric ones estimated for the integrated magnitude of star clusters and presented for the 2MASS magnitude of AGB stars. First, there exist the errors of center coordinates and radii of star clusters, influencing the estimation of their integrated luminosity. We performed aperture photometry for all sample clusters, setting different center positions and radii according to their errors. We selected the upper and lower errors of the integrated luminosity of star clusters, also considering photometric errors. Secondly, there are the errors for the luminosity of AGB stars, which consist of (a) 2MASS photometric error for individual AGB stars and (b) the uncertainty from the Poisson error for the number of AGB stars in each star cluster associated with AGB star counts. Of these two, the latter is much larger\nthan the former. The AGB luminosity error from Poisson error is calculated by multiplying the square root of the number of AGB stars by the mean luminosity for an AGB star in each cluster. We tabulated upper and lower errors of the K s band luminosity fraction obtained by error propagation, considering overall error budget mentioned above (see Table 2). Note that the smaller the numbers of AGB stars in star clusters are, the larger the errors of the luminosity fraction are.\nAdditionally, we checked the field contamination in AGB star count. We investigated the outer region of each star cluster with the radius five times larger than the cluster radius. The number of the AGB stars in this field region is normalized to the cluster area. We calculated the amount of field contamination by multiplying the mean luminosity of AGB stars in star clusters by the number of the normalized field AGB stars, and subtracted it from the luminosity of AGB stars in star clusters. However, the effect of the field contamination to estimating the luminosity fraction of AGB stars is much smaller than that of the Poisson error of the AGB star count. These field-subtracted values are also listed in Table 2.\nFigure 10(a) shows the K s band luminosity fraction of AGB stars in our sample clusters as a function of ages. Figure 10(b) displays the mean values of the K s band luminosity fraction of AGB stars in the star clusters. These values are also listed in Table 3 including the field-subtracted values. The mean values represent the ratios of the total K s band luminosity of AGB stars in the star clusters to the total K s band luminosity of the star clusters for each age bin. The error of mean values is calculated from the individual errors of the star clusters by error propagation. We also derived a sequence to represent approximately the sequence of bright clusters, as plotted in the figure. The bright clusters have the luminosity of L K s > 8 . 5 × 10 4 L /circledot . Following features are noted in Figure 10. First, the mean values and the bright cluster sequence increase, as log(age) increases from 8.0 to 8.5, reaching 0.6 and 0.8 at log(age) ∼ 8 . 5, respectively. They decrease thereafter. Second, there is a large scatter in the mean values for given ages. We discuss these features in § 5.2.2 in detail.\n5. Discussion\n5.1. Comparison with Previous Studies\nIn Figure 10(b), we also plotted the results for 19 LMC star clusters given by Mucciarelli et al. (2006) for comparison. There are 12 star clusters common between this study and Mucciarelli et al. (2006). We determined foreground reddenings of six star clusters (NGC 1806, NGC 1866, NGC 1987, NGC 2108, NGC 2134, and NGC 2136) by using the method mentioned above (see § 3.2). For the other three star clusters(NGC 1831, NGC 2173, and NGC 2249), the field\nstars were not covered by the MCPS. In this case, we adopted foreground reddening values from the optical reddening map of the MCs given by Haschke et al. (2011). Haschke et al. (2011) presented the optical reddening map of the MCs obtained by comparing the theoretical color of the red clump with its observed one based on the OGLE III data. The reddening values of the others (NGC 2162, NGC 2190, and NGC 2231) could not be determined neither in this study nor in Haschke et al. (2011). We assumed the typical extinction value, E ( B -V ) = 0 . 1, for these three clusters. For ages, we determined ages of three of these clusters (NGC 1866, NGC 2134, and NGC 2136). The ages of the others are adopted from Elson & Fall (1985) and Girardi et al. (1995), because we could not use the MCPS catalog for these clusters.\nWe also noticed that the AGB selection criteria of Mucciarelli et al. (2006) are different from those of this study (see Figure 8). Mucciarelli et al. (2006) included as AGB candidates the blue stars that are excluded in this study, but the color and magnitude of these stars indicate that they are bright RGB and supergiant populations according to the analysis of Nikolaev & Weinberg (2000). The color distribution of the stars brighter than K s = 12.3 for young star clusters with log(age) < 8.5 shows a blue excess at ( J -K s ) 0 < 1 . 0 (see Figure 8(a)), while little blue excess is seen for the case of old star clusters with log(age) > 8.5 (see Figure 8(c)). However, those blue stars used in the analysis of Mucciarelli et al. (2006) do not significantly influence the luminosity fraction of AGB stars in the star clusters, because they are somewhat faint (see Figure 11). In addition, there are three red stars not included in the AGB boundary of Mucciarelli et al. (2006) but contained in that of this study, which can be dusty AGB stars. We found that these stars affect little our results.\nThe number of AGB stars shows a large discrepancy between our results and Mucciarelli et al. (2006) for the young star clusters as shown in Figure 11(a), but the difference in the luminosity fraction of AGB stars in the star clusters is much smaller as shown in Figure 11(b).\nIn Figure 10(b), the results for 19 star clusters from Mucciarelli et al. (2006) are included, and those derived in this study are also plotted for four star clusters that show a large discrepancy ( > 0.2) in the AGB luminosity fraction (see Figure 11(b)). Other eight clusters show the consistent results with Mucciarelli et al. (2006). Most of these clusters studied by Mucciarelli et al. (2006) are brighter than L K s = 10 5 L /circledot , except for two star clusters, NGC 2249 and NGC 2231. Indeed they are following the bright cluster sequence derived in this study, with some scatter.\n5.2. Comparison with SSP Models\n5.2.1. Mock Cluster Experiments with SSP models\nWe compare our results with the expectation of five theoretical models: (1) an EPS model of Maraston (2005) (called Maraston model), (2) a model based on the isochrone set of Girardi et al. (2002) (called Padova02 model), (3) a model based on the improved isochrone set of Marigo et al. (2008) corrected by Girardi et al. (2010) (called Padova10 model), (4) a model based on the isochrone set of Pietrinferni et al. (2004, 2006) assuming a given overshooting efficiency (called BaSTI os model), and (5) the same as (4), but for null overshooting efficiency (called BaSTI std model). The Maraston model calculates the luminosity contribution of AGB stars directly using the fuel consumption approach. Girardi et al. (2002) and Marigo et al. (2008) corrected by Girardi et al. (2010) presented theoretical stellar evolutionary tracks and isochrones used in various EPS models. The detailed information of these models is described as follows.\nThe Maraston model calculated the amount of the fuel consumption of each population in the post-main-sequence phases (Renzini & Buzzoni 1986) directly, and converted it to observables assuming the effective temperature and surface gravity for evolutionary stages. We obtained the Maraston model prediction for the luminosity contribution of AGB stars in SSPs as a function of ages (Mucciarelli et al. 2006).\nThe theoretical isochrones of Girardi et al. (2002) are based on isochrones of Girardi et al. (2000) for low- and intermediate-mass stars (M ≤ 7 M /circledot ) and Bertelli et al. (1994) for highmass stars (M > 7 M /circledot ). Note that stellar evolutionary tracks of Girardi et al. (2000) are adopted in the BC03 model. In this model, they included the simplified TP-AGB phase and no circumstellar dust that form in AGB stars.\nMarigo et al. (2008) presented optical to far-infrared isochrones with improved TP-AGB models. Girardi et al. (2010) searched for the TP-AGB population of 12 galaxies in the ACS Nearby Galaxy Survey Treasury, and found that the model of Marigo et al. (2008) creates more TP-AGB populations than observed ones. They corrected the mass-loss rate of TPAGB stars in this model by reducing their lifetime (Bowen & Willson 1991, Willson 2000). This model reproduces the number of TP-AGB stars well, but still has uncertainties in their 1.6 µ m band flux contribution (Melbourne et al. 2012). Additionally, we adopted the isochrone set that includes the circumstellar dust from AGB stars (Groenewegen 2006) and assumed that the dust composition is 100% silicate and 100% amorphous carbonate dust for O-rich and C-rich AGB stars, respectively.\nThese two kinds of Padova isochrones consider the core convective overshooting. In\norder to investigate this effect, we used the BaSTI isochrone dataset (Pietrinferni et al. 2004, 2006) without overshooting efficiency. We selected a scaled solar isochrone set that contains the extended AGB population. We calculated the predicted K s band luminosity fraction of AGB stars in SSPs by analyzing the mock star clusters produced from the isochrones of Girardi et al. (2002), Marigo et al. (2008), and Pietrinferni et al. (2004). We used the isochrone sets with metallicity Z = 0.008, corresponding to [Z/H] ∼ -0.35 for mock cluster experiments. This value is close to the mean value for the LMC, for our cluster samples. The method is described as follows.\nWe created model stars in mock star clusters assuming the Salpeter initial mass function, and assigned J and K s magnitudes to each star using four different isochrone sets. In addition, we considered magnitude errors for each star in order to make the model prediction more realistic. In the 2MASS catalog, mean magnitude errors and error variances of stars in each magnitude bin vary as a function of magnitudes. We assumed that photometric errors of model stars are distributed normally with the mean value and the variance according to magnitude bins. In ( K s, 0 -( J -K s ) 0 ) CMDs of model stars in mock star clusters with empirical magnitude errors, AGB stars are selected with the same criteria as done for observational data (see § 4.1). The K s band luminosities of mock star clusters and AGB stars are calculated by summing the K s band luminosity of member stars and AGB stars, respectively. Note that for the BaSTI models, they do not provide the magnitudes of 2MASS filter system, so that we adopted those of the Bessell filter system. Finally, we obtained the K s band luminosity fraction of AGB stars in mock star clusters with three different mass (10 4 , 10 5 , and 10 6 M /circledot ), assuming 15 different ages (8.0 ≤ log(age) ≤ 9.5) for each mass scale.\n5.2.2. Stochastic Effect in Estimating Light from AGB Stars\nStochastic effects are inevitable in AGB star counts because of the short lifetime of AGB stars. In Figure 10(a), there is a large scatter in the K s band luminosity fraction of AGB stars in the star clusters derived in this study. The AGB stars evolve fast, and become blue and faint when they enter the post-AGB phase. Therefore, we cannot detect all stars that have entered the AGB phase. As a result it makes the luminosity fraction of AGB stars in star clusters lower than expected. Especially, this effect becomes significant for faint star clusters, because of a smaller number of stars. Bright star clusters (L K s tot /greaterorsimilar 8 . 5 × 10 4 L /circledot ) show relatively smaller scatters and seem to be located along a sequence.\nThis trend also appears in the mock star clusters (see Figure 12). We made mock star clusters with 15 different ages and three different masses using four different isochrone sets as above. For each age and mass bin, we made 10 mock star clusters in order to analyze\nthem statistically. Figure 12 shows the K s band luminosity fraction of AGB stars in the mock star clusters as a function of ages. In this figure, the most massive mock star clusters with M = 10 6 M /circledot show the smallest scatter among mock clusters with other mass scale, and make a well-defined sequence (shaded region). However, mock star clusters with M = 10 5 M /circledot (circles) are distributed with large scatter from the massive mock cluster sequence. Therefore we presented two representatives for the observational data: mean values and the bright cluster sequence.\n5.2.3. Comparison with Model Expectation\nFigure 13 shows a comparison of our results and those expected from five models. In the case of Padova and BaSTI models, we adopted the mean locus line of the massive mock star clusters presented in Figure 12. Note that the Padova02 and BaSTI os models show almost same results of AGB luminosity evolution in SSPs. It reflects that the Padova models include the same ingredients as the BaSTI os model in terms of the core overshooting. Except for these two models, there are several differences in model expectations. First, peak values of the luminosity contribution of AGB stars expected in models are different. The Maraston and Padova10 models suggest 0.7 - 0.8 for the value of the highest AGB fraction, while other three models (Padova02, BaSTI std, and BaSTI os) do just up to ∼ 0.6. Second, all models expect peak values at the similar age range with log(age) ∼ 8.6 - 8.8, except for the BaSTI std model. The peak position of the BaSTI model expectation lies at slightly younger age compared with the expectation of other models. It is because the null overshooting efficiency leads to the shorter lifetime of main-sequence stars. Third, both young and old parts are different between the Maraston model and other models. Padova02, Padova10, and BaSTI os models show that the AGB luminosity fraction in SSPs is lowest at log(age) ∼ 8.0 and increases continuously up to the highest value as SSPs are getting older, while the Maraston model suggests that it comes up to already ∼ 0.4 at log(age) = 8.0 - 8.3 and increases drastically afterwards. The BaSTI std model, however, expects higher AGB luminosity contribution than any other models at log(age) ∼ 8.0 as mentioned above. In the case of SSPs older than 1 Gyr, the AGB luminosity contribution decreases in all models, but the Maraston model shows the steepest decrease.\nThe bright cluster sequence represents well-populated systems that are less influenced by the stochastic fluctuation than faint star clusters, so that it is more appropriate to compare with the expectation of SSP models. In Figure 13, we notice two points with regard to the comparison between the bright cluster sequence and the model expectation: (1) the maximum value of the bright cluster sequence and (2) the age range corresponding to the\nmaximum AGB luminosity contribution. First, the peak value of the AGB luminosity contribution for bright clusters is up to 0.7 - 0.8. Only two models, Maraston and Padova10 models, reproduce this maximum value. Second, the peak position for the bright cluster sequence appears at log(age) = 8.5 - 8.7, which is slightly younger than for model predictions (log(age) = 8.6 - 8.8). However, this discrepancy is not significant because the errors of ages are around 0.1.\n5.3. Implication for the study of size and mass evolution of galaxies\nThe calibration of the EPS models influences galaxy studies because the determination of physical parameters of galaxies depends on the amount of the AGB near-infrared luminosity contribution in EPS models. The difference between the AGB luminosity fractions expected by Padova02 and Maraston models is largest at log(age) ∼ 8.7 - 8.9 (age ∼ 0.5 - 0.8 Gyr), as shown Figure 13. This indicates that the differences of galaxy mass estimates based on the EPS models can be significant at this age range. This can be important for galaxies with young stellar ages, such as high-redshift ( z ≥ 2 - 3) or post-starburst galaxies. In these kinds of galaxies, the young stellar component with ages ∼ 1 Gyr is dominant. For example, Raichoor et al. (2011) presented SED fitting results of 79 early-type galaxies at z ∼ 1.3, finding the differences in stellar ages and masses of galaxies estimated with the BC03 and Maraston models, respectively. They showed that the masses of galaxies derived with the Maraston model tend to be lower than those estimated with the BC03 model, and this discrepancy is prominent (by a factor of two) at galaxy ages ∼ 1.0 - 1.3 Gyr with uncertainty of ∼ 1.0 - 1.5 Gyr (see Figure 5 in Raichoor et al. 2011).\nMuzzin et al. (2009) reported how the galaxy evolution process depends on EPS models. They investigated the size and mass growth of high-redshift galaxies ( z ∼ 2.3). From the galaxy mass differences based on the EPS models, they found that the galaxy size growth from z ∼ 2.3 to z = 0 is faster in the case of the BC03 model than the case of the Maraston model, assuming that the mass growth rate is same in these two cases. Thus, the sizemass relation of galaxies can be influenced by the AGB luminosity contribution in each EPS model. Our results of the bright cluster sequence are closer to the Maraston model so that they support the size-mass relation of galaxies derived with this model.\n6. Summary and Conclusion\nWe investigated the K s band luminosity evolution of the AGB population in SSPs using 102 LMC star clusters. First, we determined ages and foreground reddening of star clusters from the UBV photometry in the MCPS (Zaritsky et al. 2004) using Padova isochrones (Marigo et al. 2008). Then AGB stars in each cluster were selected using 2MASS ( K s -( J -K s )) CMDs. We derived the K s band luminosity fraction of AGB stars in 102 star clusters as a function of ages. The K s band luminosity fraction of AGB stars in star clusters increases as age increases from log(age) ∼ 8.0. It reaches a maximum up to ∼ 0.6 for mean values and ∼ 0.8 for bright cluster sequences at log(age) ∼ 8.5, and decreases afterwards. The AGB luminosity fraction for given ages shows a large scatter caused by stochastic effects. We compared our results with five SSP models: Padova02, Padova10, Maraston, BaSTI std, and BaSTI os models. It is found that the only two models (Padova10 and Maraston models) match approximately the observational K s band AGB luminosity contribution of bright star clusters derived in this study, while other models predict the AGB luminosity contribution much lower.\nThis work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 2012R1A4A1028713).\nREFERENCES\nAllen, C. W. 1976, Astrophysical Quantities, London: Athlone (3rd edition), 1976 Bertelli, G., Bressan, A., Chiosi, C., Fagotto, F., & Nasi, E. 1994, A&AS, 106, 275 Bica, E., Bonatto, C., Dutra, C. M., & Santos, J. F. 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Table 1. Physical parameters of 102 star clusters in the LMC
\n
\nNote. - Table 1 is published in its entirety in the electronic edition. The five sample star clusters are shown here regarding its form and content.\nr\n)\nt\ne\nn\n(\ns\nK\nt\no\nG\nA\nB / L t .4 1 8 2 0 ± .6 6 0 .5 6 7 .3 3 6 m a n\ns\nK\nL\n4\n0\n1\n(\nB\n.\nt\nn\ne\nt\nn\no\nc\nd\nr\no\nf\n
\n\n
\ne\nt\ns\nlu\nc\n±\n4\n.4\n1\n±\n0\n.4\n3\n±\n9\n.9\n2\n±\n0\n.3\n3\n±\n7\n.7\n7\nr\ne\nt\ns\nlu\nc\nr\n0 2 s t a r ) L K s A G m p le s t a\n9\n.5\n1\n±\n9\n.5\n1\n0\n.1\n0\n1\n5\n5\n.\n0\n+\n6\n3\n.\n0\n-\n4\n.4\n3\n7\n2\n.0\n0\n±\n9\n2\n.4\n0\n1\n8\nL\nS\n7\n.6\n2\n±\n8\n.7\n3\n0\n.2\n0\n2\n2\n5\n.\n0\n+\n7\n7\n.\n0\n-\n9\n.4\n5\n1\n9\n0\n.0\n0\n±\n5\n9\n.7\n8\n3\n9\n6\n1\nC\nG\nN\n9\n.4\n3\n±\n9\n.4\n3\n4\n.1\n0\n1\n5\n1\n.\n0\n+\n8\n0\n.\n0\n-\n3\n.5\n4\n5\n1\n.0\n0\n±\n9\n2\n.1\n0\n1\n7\n3\nS\nH\n9\n.8\n2\n±\n9\n.0\n4\n9\n.3\n0\n2\n9\n9\n.\n1\n+\n3\n7\n.\n1\n-\n2\n.8\n5\n9\n1\n.0\n0\n±\n8\n5\n.8\n9\n0\n7\nL\nS\n.8\n7\n±\n.6\n5\n1\n1\n.0\n2\n4\n5\n0\n.\n2\n+\n7\n3\n.\n3\n-\n4\n.1\n3\n2\n1\n1\n.0\n0\n±\n9\n5\n.3\n8\n7\n1\n1\nL\nS\na\ns\ne\nv\nfi\ne\nh\nT\n.\nn\nio\nit\nd\ne\nic\nn\no\nr\nt\nc\nle\ne\ne\nh\nt\nin\ny\nt\ne\nir\nt\nn\ne\ns\nit\nin\nd\ne\nh\nlis\nb\nu\np\nis\n2\nle\nb\na\nT\n-\n.\ne\nt\no\nN\n1\nin\ns\nn\nio\nt\nla\nu\np\no\np\nB\nG\nA\nf\no\ns\nie\nt\nr\ne\np\no\nr\np\ne\nh\nT\n.\n2\nle\nb\na\nT\n/circledot\nL\n4\n0\n1\n(\nB\nG\nA\ns\nK\nL\nd\nl\ne\nfi\nB\nG\nA\nN\nB\nG\nA\nN\n)\n/circledot\nL\n4\n0\n1\n(\ns\nK\nt\no\nt\nL\ns\nK\nr\ne\nt\ns\nlu\nC\n4\n4\n4\n.\n0\n+\n1\n4\n4\n.\n0\n-\n0\n4\n1\n7\n.\n0\n+\n3\n1\n7\n.\n0\n-\n0\n7\n8\n4\n.\n0\n+\n7\n7\n4\n.\n0\n-\n0\n0\n4\n2\n.\n0\n+\n3\n4\n2\n.\n0\n-\n0\n4\n6\n.1\n0\n.2\n0\n.\ns\ne\nlu\na\nv\nd\ne\nt\nc\na\nr\nt\nb\nu\ns\n-\nld\ne\nfi\ne\nh\nt\ne\nt\na\nic\nd\nin\n)\nt\ne\nn\n(\ns\nK\nt\no\nt\nL\n/\nB\nG\nA\ns\nK\nL\nd\nn\na\n)\nt\ne\nn\n(\nB\nG\nA\ns\nK\nL\n- 21 -\nG\ns\no\nI\ng )\nn\ni\nt\no\n6\n0\n5\n8\n3\n0\n2\n
\n\n
\nA\nf\no\nP\na\nv\n1\n3\n1\n5\n1\n8\n9\nio n P a d o 0 2 0 . 2 0 . 4 0 . 5 0 . 5 0 . 5 0 . 3 0 . 2 a l u e s\nt\nc\na\nr\nf\ny\nit\ns\no\nin\nm\nlu\nd\nn\na\nb\ns\nK\nf\no\nn\no\nis\nr\na\np\nm\no\nC\n.\n3\nle\nb\na\nT\n.\nv\nd\ne\nt\nc\na\nr\nt\nb\nu\ns\n-\nd\nl\ne\nfi\ne\nh\nt\ne\nt\na\nc\ni\nd\nn\ni\n)\nt\ne\nn\n(\ne\nc\nn\ne\nu\nq\ne\ns\nr\ne\nt\ns\nu\nl\nc\nt\nh\ng\ni\nr\nb\nd\nn\na\n)\nt\ne\nn\n(\nn\na\ne\nM\n-\n.\ne\nt\no\nN\n)\ny\nd\nu\nt\ns\ns\ni\nh\nT\n(\nn\no\ni\nt\na\nv\nr\ne\ns\nb\nO\nr\ne\nt\ns\nu\nl\nc\nt\nh\ng\ni\nr\nB\nr\ne\nt\ns\nu\nl\nc\nt\nh\ng\ni\nr\nB\n)\nt\ne\nn\n(\ne\nc\nn\ne\nu\nq\ne\ns\ne\nc\nn\ne\nu\nq\ne\ns\n)\nt\ne\nn\n(\nn\na\ne\nM\nn\na\ne\nM\n)\n]\nr\ny\n[\ne\ng\na\n(\ng\no\nl\n0\n2\n.\n0\n0\n3\n.\n0\n7\n0\n.\n0\n±\n4\n2\n.\n0\n6\n0\n.\n0\n+\n7\n0\n.\n0\n-\n5\n2\n.\n0\n0\n0\n.\n8\n0\n5\n.\n0\n2\n6\n.\n0\n0\n1\n.\n0\n±\n8\n3\n.\n0\n1\n1\n.\n0\n±\n3\n5\n.\n0\n5\n2\n.\n8\n7\n6\n.\n0\n1\n8\n.\n0\n1\n1\n.\n0\n±\n7\n4\n.\n0\n1\n1\n.\n0\n±\n4\n5\n.\n0\n0\n5\n.\n8\n0\n7\n.\n0\n8\n7\n.\n0\n3\n1\n.\n0\n±\n2\n5\n.\n0\n4\n1\n.\n0\n+\n3\n1\n.\n0\n-\n7\n5\n.\n0\n5\n7\n.\n8\n5\n5\n.\n0\n0\n6\n.\n0\n9\n0\n.\n0\n±\n8\n3\n.\n0\n1\n1\n.\n0\n±\n2\n5\n.\n0\n0\n0\n.\n9\n0\n3\n.\n0\n3\n3\n.\n0\n8\n0\n.\n0\n±\n7\n2\n.\n0\n9\n0\n.\n0\n±\n1\n3\n.\n0\n5\n2\n.\n9\n5\n1\n.\n0\n0\n2\n.\n0\n5\n1\n.\n0\n±\n1\n2\n.\n0\n9\n1\n.\n0\n±\n2\n3\n.\n0\n0\n5\n.\n9\n- 22 -\n\n\n
Fig. 1.- An example for determination of the center of a star cluster, NGC 1861. (a) 2-dimensional number density map smoothed with a boxcar filter for the bright stars with V < 20 . 5 mag around NGC 1861 derived from the MCPS catalog of Zaritsky et al. (2004), (b) Fitted number density map with 2-dimensional Gaussian fitting. The plus and cross mark, respectively, represent the cluster center presented by Bica et al. (2008) and that derived in this study. (c) Residual number density map derived from subtraction of (b) from (a). (d) A gray scale map of a digitized sky survey R band image. The plus and cross mark represent the same as in (b).
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Fig. 2.- Radial number density profile for the bright stars with V < 20 . 5 mag around NGC 1861 in the MCPS catalog of Zaritsky et al. (2004). Error bars indicate the Poisson errors estimated in each bin. The solid line and dot-dashed line represent the cluster radius presented by Bica et al. (2008) and that determined in this study, respectively. The background level (dotted line) is the median value of the number density of the stars located in the annulus, 200 '' < R < 300 '' . We adopted 3 σ upper level (dashed line) to determine the radius of each cluster (see texts). The stamp image is a gray scale map of a digitized sky survey R band image of NGC 1861, showing the cluster size determined in this study by a large circle.
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Fig. 3.- Comparison of center coordinates and radii of star clusters between this study and other references, Werchan & Zaritsky (2011) (a,d, and g panels) and Bica et al. (2008) (b, e, and h panels). The bottom three panels show the differences between Bica et al. (2008) and Werchan & Zaritsky (2011). In the case of Werchan & Zaritsky (2011), the 90% enclosed luminosity radii are adopted to compare with other studies. These histograms are normalized by peak values. The numbers of star clusters found in both studies are presented in each panel. The solid and dashed lines represent zero points and peak positions of differences, respectively.
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Fig. 4.- (a) ( V -( B -V )) CMD of stars at 44 '' - 200 '' from the center of NGC 1861. The box represents a region where most of stars are field main-sequence stars (open circles). (b) (( U -B ) -( B -V )) CCD of field main-sequence stars selected in (a). The solid line is a ZAMS (Marigo et al. 2008) shifted according to E ( B -V ) = 0 . 10 mag. The arrow indicates a direction of reddening vector.
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Fig. 5.- (a) ( V -( B -V )) CMD of stars in NGC 1861 region. (b) ( V -( B -V )) CMD of stars in the field region around NGC 1861 with the same area as the cluster region. (c) ( V -( B -V )) CMD of stars in NGC 1861 after statistical subtraction of field stars. The filled and open circles represent the stars with the photometric errors of err ( B -V ) ≤ 0.1 mag and > 0.1 mag, respectively. The solid line is a Padova isochrone for log(age [yr]) = 8.55 and Z = 0 . 008 (Marigo et al. 2008). It is shifted according to E ( B -V ) = 0 . 10 mag and ( m -M ) 0 = 18 . 50 mag, and the two dashed lines represent isochrones for log(age[yr]) = 8.5 and 8.6, which tell errors of ages. The arrow indicates a direction of reddening vector. The values of physical parameters of NGC 1861 (metallicity, distance modulus, reddening, and age) are shown in the right lower corner.
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Fig. 6.- Comparison of the ages determined by various references (Elson & Fall 1985; EF85, Pietrzynski & Udalski 2000; PU00, Hunter et al. 2003; Hun+03, Glatt et al. 2010; Gla+10, Popescu et al. 2012; Pop+12). The dotted lines are one-to-one relations. The dashed lines represent linear fitting results, and their slopes, zero points, and the root mean square errors are shown in the left upper corner of each panel.
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Fig. 7.- ( V -( B -V )) CMDs and isochrone fitting results of the star clusters that show the largest difference of ages from other references: (a) SL482 (Glatt et al. 2010), (b) NGC 1782 (Elson & Fall 1985), (c) SL294 (Popescu et al. 2012), (d) SL503 (Hunter et al. 2003), and (e) H88-182 (Pietrzynski & Udalski 2000). The filled and open circles represent the same as in Figure 5(c). The solid lines and dashed lines represent Padova isochrones ( Z = 0 . 008) for the ages determined in this study and other studies, respectively. These are shifted according to the determined foreground reddening and ( m -M ) 0 = 18 . 50 mag. The arrow indicates a direction of reddening vector.
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Fig. 8.- AGB selection criteria. (a) The color distribution of the bright stars brighter with K s < 12 . 3 in 41 young star clusters with log(age) < 8.5. (b) A combined and dereddened ( K s, 0 -( J -K s ) 0 ) CMD for star clusters with log(age) < 8.5. The dashed lines and the dot-dashed lines indicate criteria to distinguish AGB stars from other populations in this study and Mucciarelli et al. (2006), respectively. The shaded area represents the area where Nikolaev & Weinberg (2000) suggested that AGB stars are concentrated. (c) and (d) the same as (a) and (b) for 61 star clusters with log(age) ≥ 8.5.
\n\n\n\n
Fig. 9.- A gray scale map of a 2MASS K s band image of NGC 1861. The solid line circle indicates an aperture with radius 44 '' for cluster photometry. The two dashed line circles represent the annuli with radii 48 '' and 58 '' , used for background estimation.
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Fig. 10.- (a) The K s band luminosity fraction of AGB stars in 102 LMC star clusters as a function of ages. The circles and other symbols represent the star clusters of which ages were determined in this study and other studies, respectively (triangles: Elson & Fall 1985 and Girardi et al. 1995, stars: Goudfrooij et al. 2011, upside-down triangles: Pietrzynski & Udalski 2000, and squares: Popescu et al. 2012). The symbol size reflects the integrated luminosity of each cluster. (b) Mean values in each age bin (squares) and bright cluster sequence (shaded region) of the K s band luminosity fraction of AGB stars in star clusters. The lower boundary of the shaded region show the result after fieldsubtraction, and for mean values, the field-subtracted results are within error bars. The error bars for mean values indicate the errors estimated by error propagation. The open circles represent the result from Mucciarelli et al. (2006) including NGC 2249 and NGC2231 with L K s < 10 5 L /circledot (cross marks). The filled circles indicate the result derived in this study for the star clusters that show a large discrepancy in the AGB luminosity contribution.
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Fig. 11.- (a) The difference of the number of AGB stars in 12 star clusters between Mucciarelli et al. (2006) and this study (filled circles). The open diamonds represent the field-subtracted results. The error bars indicate Poisson errors for the number of AGB stars. (b) Same as (a) but for the K s band luminosity fraction of AGB stars in star clusters. The error bars indicate the errors estimated by error propagation.
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Fig. 12.- The K s band luminosity fraction of AGB stars in mock star clusters using four different isochrone sets: (a) Padova02, (b) Padova10, (c) BaSTI std, and (d) BaSTI os models. The shaded region indicates the sequence of the massive mock clusters with M = 10 6 M /circledot . The circles represent the mock star clusters with M = 10 5 M /circledot . Note that the scatter in the AGB luminosity fraction in SSPs is smaller in the Padova10 model than other models. The Padova10 model creates more AGB stars than other models, so that the stochastic fluctuation can be less.
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Fig. 13.- Comparison of five SSP model predictions with our results. Squares and shaded region are the same as in Figure 10(b). The solid line represents the Maraston model expectation for both the E-AGB and TP-AGB computed at [Z/H] = - 0.33, and the dashed line and the dot-dashed line indicate respectively Padova02 and Padova10 model expectations from massive mock star clusters with M = 10 6 M /circledot . The BaSTI std (triple-dot dashed line) and BaSTI os (long dashed line) model predictions for massive clusters are also plotted.
\n\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"We present a study of K s band luminosity evolution of the asymptotic giant branch (AGB) population in simple stellar systems using star clusters in the Large Magellanic Cloud (LMC). We determine physical parameters of LMC star clusters including center coordinates, radii, and foreground reddenings. Ages of 83 star clusters are derived from isochrone fitting with the Padova models, and those of 19 star clusters are taken from the literature. The AGB stars in 102 star clusters with log(age) = 7.3 - 9.5 are selected using near-infrared color magnitude diagrams based on 2MASS photometry. Then we obtain the K s band luminosity fraction of AGB stars in these star clusters as a function of ages. The K s band luminosity fraction of AGB stars increases, on average, as age increases from log(age) ∼ 8.0, reaching a maximum at log(age) ∼ 8.5, and it decreases thereafter. There is a large scatter in the AGB luminosity fraction for given ages, which is mainly due to stochastic effects. We discuss this result in comparison with five simple stellar population models. The maximum K s band AGB luminosity fraction for bright clusters is reproduced by the models that expect the value of 0.7 - 0.8 at log(age) = 8.5 - 8.7. We discuss the implication of our results with regard to the study of size and mass evolution of galaxies. Subject headings: galaxies: star clusters: general - infrared: stars - stars: AGB and post-AGB - Magellanic Clouds - galaxies: evolution","pages":[1]},{"title":"K s BAND LUMINOSITY EVOLUTION OF THE ASYMPTOTIC GIANT BRANCH POPULATION BASED ON STAR CLUSTERS IN THE LARGE MAGELLANIC CLOUD","content":"Youkyung Ko, Myung Gyoon Lee, and Sungsoon Lim Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea ykko@astro.snu.ac.kr, mglee@astro.snu.ac.kr, slim@astro.snu.ac.kr","pages":[1]},{"title":"1. Introduction","content":"The asymptotic giant branch (AGB), a representative intermediate-age population, is the most luminous evolutionary stage for low- and intermediate-mass (1 - 8 M /circledot ) stars. AGB stars emit a huge amount of near- to mid-infrared light because of their low effective temperature (T eff ∼ 1000 - 4000 K) and circumstellar dust. Hence it is expected that they contribute significantly to the infrared light of galaxies. However, their infrared luminosity contribution in galaxies, even in a simple stellar population (SSP), is still a debating issue with regard to constructing evolutionary population synthesis (EPS) models (Maraston 2011, Bruzual et al. 2013, Noel et al. 2013, and references therein). The EPS models are an useful tool to determine physical parameters of stellar complexes such as star clusters and galaxies by spectral energy distribution (SED) fitting. These models reproduce SEDs of stellar systems by synthesizing the SEDs of stellar populations in various evolutionary stages, assuming age, metallicity, foreground and internal reddening values, star formation history, and so on. Therefore, the spectral energy contribution of individual stellar populations influences the estimation of physical parameters of stellar systems, and especially that of the AGB population plays a key for understanding of the SEDs for stellar systems expected by EPS models. There are various EPS models that include the AGB evolutionary process (e.g., Charlot & Bruzual 1991, Bruzual & Charlot 1993, Fioc & Rocca-Volmerange 1997, Maraston 1998, Leitherer et al. 1999, Vazdekis 1999, Schulz et al. 2002, Bruzual & Charlot 2003, Jimenez et al. 2004, Maraston 2005, Conroy et al. 2009, Kotulla et al. 2009, Conroy & Gunn 2010, Vazdekis et al. 2010, Maraston & Stromback 2011). Bruzual & Charlot (2003, hereafter BC03), for example, presented an EPS model based on Padova evolutionary tracks including just two evolutionary stages for thermally pulsing AGB (TP-AGB) (Girardi et al. 2000), while their recent model includes 15 evolutionary stages of the TP-AGB oxygen-rich and carbon-rich phases (Bruzual A. 2010). The Padova evolutionary tracks adopted in the BC03 model include a given core overshooting efficiency. On the other hand, Maraston (1998, 2005) used evolutionary tracks assuming zero efficiency of the core overshooting from Cassisi et al.(1997, 2000) to determine luminosity contribution of main-sequence populations. It makes the lifetime of main-sequence stars in the Maraston (2005) model shorter compared with Padova isochrones. In addition, she used the fuel consumption theorem (Renzini & Buzzoni 1986) for post-main-sequence stars, not adopting the isochrone synthesis method. In the model of Maraston (1998), the TP-AGB evolutionary process is modified in the fuel consumption theorem, applying the advanced envelope burning process of AGB stars. Renzini & Buzzoni (1986) estimated the contribution of TP-AGB population in the young SSPs with ages < 10 8 yr, and compared it with the star clusters in the the Magellanic Clouds (MCs). They found that it is too high to be consistent with the observational results based on these star clusters. Considering this difference, Maraston (2005) suggested a revised model, assuming shorter lifetime and lower fuel consumption of TP-AGB stars than Renzini & Buzzoni (1986). BC03 and Maraston (2005) adopted different stellar population synthetic methods, and the SEDs reproduced by these models show recognizable differences. A number of studies argue whether or not these EPS models reproduce well observational quantities of stellar systems related with the AGB population as follows. Some studies found that spectra and SEDs of post-starburst galaxies or distant galaxies (z ∼ 1 - 2) have no near-infrared boosted features, which is similar to the expectation of the BC03 model (Muzzin et al. 2009, Kriek et al. 2010, Zibetti et al. 2013). In addition, Conroy & Gunn (2010) suggested that the BC03 model and their own EPS model, a flexible stellar population synthesis model, reproduce the color of star clusters and post-starburst galaxies better than the Maraston (2005) model. In contrast, others confirmed that the Maraston (2005) model performs well in reproducing near-infrared colors, ( Y -K ) and ( H -K ), and SEDs of low to high redshift galaxies (Maraston et al. 2006, Eminian et al. 2008, MacArthur et al. 2010). Moreover, van der Wel et al. (2006) and Henriques et al. (2011) showed that the rest-frame K band mass-to-light ratio evolution and K s band luminosity evolution of galaxies are explained better by the Maraston (2005) model than by the BC03 model. In addition to these galaxy studies, there are several studies investigating star clusters, especially star clusters in the MCs, considering the relevance between the model performance and ages of stellar systems. Because of their proximity, they are very useful to examine not only the individual stellar population directly but also the integrated properties of star clusters. Therefore, they are an ideal object to calibrate SSP models. Pessev et al. (2008) investigated optical to near-infrared colors, ( B -J ), ( V -J ), and ( J -K ), of 54 star clusters in the MCs, and concluded that the BC03 and the Maraston (2005) present the best performance for intermediate-age (0.2 - 2 Gyr) and old ( > 2 Gyr) star clusters, respectively. Lyubenova et al. (2010, 2012) analyzed integrated near-infrared high-resolution spectra of six globular clusters in the Large Magellanic Cloud (LMC) with ages ∼ 1 - 13 Gyr. They showed that the Maraston (2005) model expects J and H band spectra of all their sample star clusters adequately, while it does not for K band spectra of the star clusters with ages < 2 Gyr. Recently Noel et al. (2013) presented the calibration data for stellar population models using 43 star clusters in the MCs. They compared the observed colors of the star clusters, ( V -K ) 0 , ( J -K ) 0 , and ( V -I ) 0 , as a function of ages with the theoretical expectation of various models including BC03 and Maraston (2005). In conclusion, for the ages older than 1 Gyr, the models of Maraston (2005) and BC03 are along the upper end lower end of the observed color, respectively. In the case of the younger ages, BC03 model reproduces well the observed color of star clusters, while Maraston (2005) model expects them too red. While above studies investigated the integrated properties of star clusters, Mucciarelli et al. (2006) analyzed the resolved AGB population in the LMC star clusters in detail. They investigated 19 LMC star clusters in terms of K s band luminosity contribution of AGB stars as a function of cluster ages. The star clusters used in Mucciarelli et al. (2006) have ages of 100 Myr - 3 Gyr (log(age) ∼ 8.0 - 9.5). They concluded that their empirical results are consistent with the expectation of Maraston (2005) for this age range. Later, Mucciarelli et al. (2009) suggested a similar conclusion from the additional study of four old star clusters in the Small Magellanic Cloud (SMC). In this study, we investigate the evolution of AGB luminosity contribution with a large number of LMC star clusters with log(age) ∼ 7.3 - 9.5, overcoming the shortcomings in the previous studies. Because Mucciarelli et al. (2006, 2009) included few star clusters with log(age) ∼ 8.3 - 8.7 (see Figure 5 in Mucciarelli et al. 2009), we enlarged the number of star cluster samples with this age range. In this age range, the AGB luminosity contribution is expected to change rapidly according to the Maraston (2005) model. In addition, most of previous star cluster studies adopted star cluster ages from various literature. We determine ages of LMC star clusters by isochrone fitting homogeneously, using the resolved stars. This paper is organized as follows. In § 2, we introduce the photometric data and images used in this study. § 3 describes the method to estimate physical parameters of sample star clusters such as center coordinates, radii, ages, and foreground reddenings including the cluster sample section. In § 4, we select AGB stars in each star cluster and derive the K s band luminosity contribution of AGB stars to total luminosity of star clusters as a function of ages. In § 5, we compare our results with previous studies, and also compare the primary results with the theoretical expectation from EPS models, including the discussion of stochastic effects. Final section summarizes the main results and presents the conclusion of this study.","pages":[1,2,3,4]},{"title":"2. Data","content":"Bica et al. (2008) presented an extended source catalog of the MCs including star clusters, emission nebulae, associations, and HI shells. They compiled data from various literature including the findings based on photographic survey plates. It contains center coordinates (R.A. and Declination), major and minor axes, and position angles of 3,700 star clusters of the MCs including the LMC, SMC, and the Magellanic Bridge regions. We redetermined the centers and radii of LMC star clusters based on the center coordinates presented in Bica et al. (2008). We used optical ( UBVI ) and near-infrared ( JHK s ) point source catalogs of the LMC. Zaritsky et al. (2004) presented U, B, V , and I band photometry of 24,107,004 point sources in the central 64 deg 2 of the LMC from the Magellanic Clouds Photometric Survey (MCPS; Zaritsky et al. 1997). The MCPS obtained drift-scan images using 1-m Las Campanas Swope Telescope and Great Circle Camera (Zaritsky et al. 1996). Their photometry is incomplete below 21.5, 23.5, 23, and 22 mag in U, B, V , and I bands in sparse regions, respectively. This catalog is used to determine center coordinates, radii, ages, and foreground reddenings of the star clusters. In order to distinguish AGB stars from other populations, we used a near-infrared point source catalog from the two micron all sky survey (2MASS; Skrutskie et al. 2006). In the central 100 deg 2 region of the LMC (10 · × 10 · ), there are 1,430,676 point sources detected in the 2MASS. The limiting magnitudes of photometry are 15.8, 15.1, and 14.3 mag in J, H , and K s bands, respectively, which correspond to 10 σ point source detection level. The AGB stars in the LMC are brighter than K s ∼ 12 . 3 mag, much brighter than the limiting magnitudes. We also used 2MASS Atlas Images to estimate the integrated luminosity of the star clusters, retrieving the K s band images of our sample clusters using 2MASS interactive image service 1 .","pages":[4,5]},{"title":"3.1. Center Coordinates and Sizes of Star Clusters","content":"We determined centers for 1,645 star clusters and radii for 1,708 star clusters, respectively, using the MCPS catalog (Zaritsky et al. 2004) as a part of our study of LMC star clusters. We constructed 2-dimensional number density maps of bright stars with V < 20.5 mag around the center coordinates of the star clusters presented by Bica et al. (2008). The number density maps are smoothed with a boxcar filter whose width is 20 '' . Center coordinates, coordinate errors, and position angles of each star cluster were estimated by 2-dimensional Gaussian fitting of this smoothed number density map. The field of view for the fitting region is 3 times larger than the radius of each cluster given in Bica et al. (2008). Figure 1 shows an example of centering process for one cluster NGC 1861. We attempted 2-dimensional Gaussian fitting to 3,064 LMC star clusters in Bica et al. (2008), but stellar number density maps could obtain acceptable fits for only 1,645 star clusters. The fitting results are not reliable in the case of poor, faint, or binary clusters, in which case that the center coordinates presented by Bica et al. (2008) are adopted. The radius of each cluster was determined from radial number density profiles (see Figure 2). The radial number density profile is obtained by counting point sources with V < 20.5 mag. We estimated a median value of the background number density (n bg ) of stars located between 200 '' and 300 '' from the center of each cluster. The standard deviation from n bg ( σ bg ) is calculated, and the area of which number density greater than n bg +3 σ bg is considered as a cluster area. Finally, we determined radii of 1,708 LMC star clusters, and radii of the other clusters that do not show a prominent concentration are adopted from Bica et al. (2008). Most of these clusters are poor, faint, or binary ones. Bica et al. (2008) presented major and minor axes of star clusters, from which we define the radius of each star cluster as the mean value of semi-major and semi-minor axes. In addition to Bica et al. (2008), Werchan & Zaritsky (2011) also presented a catalog of star clusters they found in the MCPS images. They investigated stellar overdensities in LMC fields using stars brighter than 20.5 mag in V band. By both King and Elson-FallFreeman model fitting of the surface brightness profiles of each cluster, they determined center coordinates, central surface brightness, tidal radii, and 90% enclosed luminosity radii of 1,066 LMC star clusters. We compare the center coordinates and radii determined in this study with those given by Bica et al. (2008) and Werchan & Zaritsky (2011) in Figure 3. Figure 3(a) - (f) show the differences of center coordinates of star clusters among three studies. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 626, 1,645, and 677, respectively. The center coordinates of star clusters from all three different studies are mostly consistent within 10 '' . Figure 3(g) - (i) show the differences of radii of star clusters. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 615, 1,708, and 681, respectively. Werchan & Zaritsky (2011) presented four kinds of radii for each cluster, core radii and 90% enclosed luminosity radii obtained by fitting using two different models, respectively, and we adopted the 90% enclosed luminosity radius from King model fitting results as a radius to compare with the results from other studies. The values for the cluster radii derived in this study are in better agreement with Bica et al. (2008) than with Werchan & Zaritsky (2011).","pages":[5,6]},{"title":"3.2. Cluster Sample Selection and Age Estimation","content":"For this study, we selected 102 star clusters that have red and bright stars in nearinfrared ( K s -( J -K s )) CMDs based on 2MASS catalog (Skrutskie et al. 2006). These stars are considered as AGB star candidates. The AGB selection method is described in § 4.1. For 96 and 83 of these star clusters, we estimated foreground reddenings and ages, respectively, with reasonable optical photometry as follows. We chose member stars of each star cluster using the center coordinates and the radii estimated before (see § 3.1). The value of foreground reddening, E ( B -V ), was estimated by shifting the zero age main-sequence (ZAMS) in the (( U -B ) -( B -V )) color-color diagram (CCD). We used the bright main-sequence stars ( V /lessorsimilar 18) located in the outer region up to 200 - 300 '' of each star cluster to obtain the CCDs, and compared the sequence of stars in the CCDs with the ZAMS in the Padova models (Marigo et al. 2008) as in Figure 4(b). The errors of E ( B -V ) values are about 0.02 mag typically. Figure 5(a) and (b) show ( V -( B -V )) CMDs of both a cluster and a field region for NGC 1861, as an example. The cluster CMD is expected to contain field stars as well as cluster stars. In order to minimize the field contamination, we performed statistical subtraction of field CMDs for cluster CMDs. We counted the number of stars in cluster CMDs with that of stars in field CMDs for the same area as the cluster area for each color and magnitude bin (∆( B -V ) ∼ 0 . 5 and ∆ V ∼ 1), and subtracted statistically field stars from cluster stars for each bin. Figure 5(c) displays a field-subtracted CMD of NGC 1861. It shows a clear stellar sequence with a smaller number of stars than the original CMD. We determined ages of 83 star clusters by isochrone fitting in the field-subtracted ( V -( B -V )) CMDs, assuming the distance modulus (m -M) 0 = 18.50 mag and Z = 0 . 008 . Cluster ages were derived using isochrones of Marigo et al. (2008). We used only the stars with small errors of colors with err ( B -V ) < 0 . 1 mag for isochrone fitting. The ages of the other 19 star clusters could not be derived, because they were not covered by the MCPS observation fields or are older than 1 Gyr. In this case, we adopted the ages of these clusters from the literature (Elson & Fall 1985, Girardi et al. 1995, Pietrzynski & Udalski 2000, Goudfrooij et al. 2011, Popescu et al. 2012). Table 1 lists physical parameters of 102 star clusters that will be used for AGB star selection. We compared the ages derived in this study with those given in other references, Elson & Fall (1985), Pietrzynski & Udalski (2000), Hunter et al. (2003), Glatt et al. (2010), and Popescu et al. (2012), as shown in Figure 6. The isochrone fitting method used for the resolved stars in star clusters is considered to be more reliable than other age-dating methods based on the integrated color or spectra of the star clusters. Pietrzynski & Udalski (2000), Glatt et al. (2010), and this study used the isochrone fitting method, while Elson & Fall (1985), Hunter et al. (2003), and Popescu et al. (2012) analyzed the integrated color of the star clusters. Elson & Fall (1985) and Hunter et al. (2003) analyzed ( U -B ) and ( B -V ) colors of the star clusters, and Popescu et al. (2012) performed a Monte Carlo simulation with their own star cluster simulation software (MASSive CLuster Evolution and ANalysis, MASSCLEAN; Popescu & Hanson 2010) to reproduce the cluster colors, ( U -B ) 0 and ( B -V ) 0 . The ages based on the isochrone fitting method show good agreement with each other. They also show correlations with the ages based on integrated colors, but with signif- icant scatters and non-unity slopes. It is noted that the ages derived from integrated colors by Popescu et al. (2012) show a better correlation with the isochrone-fitting ages, compared with other results in Elson & Fall (1985) and Hunter et al. (2003). Figure 7 shows the CMDs of five star clusters that have the largest difference of ages between this study and others: SL482 (Glatt et al. 2010), NGC 1782 (Elson & Fall 1985), SL294 (Popescu et al. 2012), SL503 (Hunter et al. 2003), and H88-182 (Pietrzynski & Udalski 2000). We plotted the Padova isochrones for Z = 0 . 008 and the ages corresponding to the values derived in this study and other references. In the case of SL482, NGC 1782, and H88182, it is difficult to determine their ages reliably because the number of the brightest stars around the main-sequence turnoff is small. However, in the case of other two star clusters, SL294 and SL503, their CMDs are not matched by the isochrones for the ages derived by Popescu et al. (2012) and Hunter et al. (2003) respectively, while they are by the isochrones for the ages derived in this study.","pages":[6,7,8]},{"title":"4.1. Selection of AGB Stars","content":"While it is difficult to distinguish AGB stars from RGB stars in optical CMDs, it is relatively easier in near-infrared CMDs. Therefore, we plotted the near-infrared ( K s, 0 -( J -K s ) 0 ) CMDs of resolved stars in 102 star clusters using the 2MASS point source catalog (Skrutskie et al. 2006), and selected AGB stars using two criteria: (1) stars brighter than the tip of the RGB (TRGB); K s, 0 < 12 . 3, and (2) stars redder than the RGB; ( J -K s ) 0 > -0 . 075 × K s, 0 +1 . 85. We adopted the TRGB magnitude, K s = 12.3 ± 0.1 estimated from 2MASS point sources in the LMC region (Nikolaev & Weinberg 2000). The second criterion was suggested from the analysis of the 2MASS photometry for LMC stars by Cioni et al. (2006). There is no constraint for the brightest and reddest stars. We use the extinction law in Cardelli et al. (1989) to derive extinction values for each band, adopting R V = 3 . 1. Figure 8(b) and (d) show the combined ( K s, 0 -( J -K s ) 0 ) CMDs of all stars in 41 young star clusters with log(age) < 8 . 5 and 61 old star clusters with log(age) ≥ 8 . 5, respectively. We selected the AGB stars brighter and redder than AGB boundary lines as described above (dashed lines). We also plotted other AGB boundaries used in the references in Figure 8(b) and (d): dot-dashed lines used by Mucciarelli et al. (2006) and gray shaded regions used by Nikolaev & Weinberg (2000). The AGB boundary used in this study is working in the similar way to that in Nikolaev & Weinberg (2000). However, the AGB boundary used by Mucciarelli et al. (2006) includes a significant number of bluer stars, compared with that in this study. This difference will be discussed in § 5.1.","pages":[8,9]},{"title":"4.2. Measurement of K s Band Luminosity Fraction of the AGB Population in Star Clusters","content":"We estimated the K s band luminosity of star clusters by aperture photometry using 2MASS K s band images. Photometry was performed with IRAF 2 APPHOT package. For background estimation we used annular apertures with the inner radius to be the sum of the star cluster radius and its error and the aperture width of 10 '' . The background level was estimated using the mode value of the annulus region. For cluster photometry we used circular apertures with radius that is the same as the cluster radius. Figure 9 displays a K s band image of an example star cluster, NGC 1861, showing the position of apertures for the cluster and background area. We calculated the K s band luminosity of AGB stars in each cluster by summing their luminosity converted from 2MASS magnitudes, and obtained the K s band luminosity fraction of AGB stars in the star clusters. Table 2 summarizes the properties of AGB populations as well as other basic parameters of 102 LMC star clusters. It lists the number of AGB stars, and the K s band luminosity and luminosity fraction of AGB stars in each cluster, as well as K s band integrated magnitude and luminosity of the star clusters. The magnitudes are based on 2MASS magnitude system. We adopted the K s band absolute magnitude M K s /circledot = 3 . 27 mag for the Sun, using M V /circledot = 3 . 83 mag (Allen 1976) and ( V -K s ) = 1 . 56 mag (Casagrande et al. 2012), to convert the magnitude into the luminosity. The error of the AGB luminosity fraction is contributed by various errors in addition to the photometric ones estimated for the integrated magnitude of star clusters and presented for the 2MASS magnitude of AGB stars. First, there exist the errors of center coordinates and radii of star clusters, influencing the estimation of their integrated luminosity. We performed aperture photometry for all sample clusters, setting different center positions and radii according to their errors. We selected the upper and lower errors of the integrated luminosity of star clusters, also considering photometric errors. Secondly, there are the errors for the luminosity of AGB stars, which consist of (a) 2MASS photometric error for individual AGB stars and (b) the uncertainty from the Poisson error for the number of AGB stars in each star cluster associated with AGB star counts. Of these two, the latter is much larger than the former. The AGB luminosity error from Poisson error is calculated by multiplying the square root of the number of AGB stars by the mean luminosity for an AGB star in each cluster. We tabulated upper and lower errors of the K s band luminosity fraction obtained by error propagation, considering overall error budget mentioned above (see Table 2). Note that the smaller the numbers of AGB stars in star clusters are, the larger the errors of the luminosity fraction are. Additionally, we checked the field contamination in AGB star count. We investigated the outer region of each star cluster with the radius five times larger than the cluster radius. The number of the AGB stars in this field region is normalized to the cluster area. We calculated the amount of field contamination by multiplying the mean luminosity of AGB stars in star clusters by the number of the normalized field AGB stars, and subtracted it from the luminosity of AGB stars in star clusters. However, the effect of the field contamination to estimating the luminosity fraction of AGB stars is much smaller than that of the Poisson error of the AGB star count. These field-subtracted values are also listed in Table 2. Figure 10(a) shows the K s band luminosity fraction of AGB stars in our sample clusters as a function of ages. Figure 10(b) displays the mean values of the K s band luminosity fraction of AGB stars in the star clusters. These values are also listed in Table 3 including the field-subtracted values. The mean values represent the ratios of the total K s band luminosity of AGB stars in the star clusters to the total K s band luminosity of the star clusters for each age bin. The error of mean values is calculated from the individual errors of the star clusters by error propagation. We also derived a sequence to represent approximately the sequence of bright clusters, as plotted in the figure. The bright clusters have the luminosity of L K s > 8 . 5 × 10 4 L /circledot . Following features are noted in Figure 10. First, the mean values and the bright cluster sequence increase, as log(age) increases from 8.0 to 8.5, reaching 0.6 and 0.8 at log(age) ∼ 8 . 5, respectively. They decrease thereafter. Second, there is a large scatter in the mean values for given ages. We discuss these features in § 5.2.2 in detail.","pages":[9,10]},{"title":"5.1. Comparison with Previous Studies","content":"In Figure 10(b), we also plotted the results for 19 LMC star clusters given by Mucciarelli et al. (2006) for comparison. There are 12 star clusters common between this study and Mucciarelli et al. (2006). We determined foreground reddenings of six star clusters (NGC 1806, NGC 1866, NGC 1987, NGC 2108, NGC 2134, and NGC 2136) by using the method mentioned above (see § 3.2). For the other three star clusters(NGC 1831, NGC 2173, and NGC 2249), the field stars were not covered by the MCPS. In this case, we adopted foreground reddening values from the optical reddening map of the MCs given by Haschke et al. (2011). Haschke et al. (2011) presented the optical reddening map of the MCs obtained by comparing the theoretical color of the red clump with its observed one based on the OGLE III data. The reddening values of the others (NGC 2162, NGC 2190, and NGC 2231) could not be determined neither in this study nor in Haschke et al. (2011). We assumed the typical extinction value, E ( B -V ) = 0 . 1, for these three clusters. For ages, we determined ages of three of these clusters (NGC 1866, NGC 2134, and NGC 2136). The ages of the others are adopted from Elson & Fall (1985) and Girardi et al. (1995), because we could not use the MCPS catalog for these clusters. We also noticed that the AGB selection criteria of Mucciarelli et al. (2006) are different from those of this study (see Figure 8). Mucciarelli et al. (2006) included as AGB candidates the blue stars that are excluded in this study, but the color and magnitude of these stars indicate that they are bright RGB and supergiant populations according to the analysis of Nikolaev & Weinberg (2000). The color distribution of the stars brighter than K s = 12.3 for young star clusters with log(age) < 8.5 shows a blue excess at ( J -K s ) 0 < 1 . 0 (see Figure 8(a)), while little blue excess is seen for the case of old star clusters with log(age) > 8.5 (see Figure 8(c)). However, those blue stars used in the analysis of Mucciarelli et al. (2006) do not significantly influence the luminosity fraction of AGB stars in the star clusters, because they are somewhat faint (see Figure 11). In addition, there are three red stars not included in the AGB boundary of Mucciarelli et al. (2006) but contained in that of this study, which can be dusty AGB stars. We found that these stars affect little our results. The number of AGB stars shows a large discrepancy between our results and Mucciarelli et al. (2006) for the young star clusters as shown in Figure 11(a), but the difference in the luminosity fraction of AGB stars in the star clusters is much smaller as shown in Figure 11(b). In Figure 10(b), the results for 19 star clusters from Mucciarelli et al. (2006) are included, and those derived in this study are also plotted for four star clusters that show a large discrepancy ( > 0.2) in the AGB luminosity fraction (see Figure 11(b)). Other eight clusters show the consistent results with Mucciarelli et al. (2006). Most of these clusters studied by Mucciarelli et al. (2006) are brighter than L K s = 10 5 L /circledot , except for two star clusters, NGC 2249 and NGC 2231. Indeed they are following the bright cluster sequence derived in this study, with some scatter.","pages":[10,11]},{"title":"5.2.1. Mock Cluster Experiments with SSP models","content":"We compare our results with the expectation of five theoretical models: (1) an EPS model of Maraston (2005) (called Maraston model), (2) a model based on the isochrone set of Girardi et al. (2002) (called Padova02 model), (3) a model based on the improved isochrone set of Marigo et al. (2008) corrected by Girardi et al. (2010) (called Padova10 model), (4) a model based on the isochrone set of Pietrinferni et al. (2004, 2006) assuming a given overshooting efficiency (called BaSTI os model), and (5) the same as (4), but for null overshooting efficiency (called BaSTI std model). The Maraston model calculates the luminosity contribution of AGB stars directly using the fuel consumption approach. Girardi et al. (2002) and Marigo et al. (2008) corrected by Girardi et al. (2010) presented theoretical stellar evolutionary tracks and isochrones used in various EPS models. The detailed information of these models is described as follows. The Maraston model calculated the amount of the fuel consumption of each population in the post-main-sequence phases (Renzini & Buzzoni 1986) directly, and converted it to observables assuming the effective temperature and surface gravity for evolutionary stages. We obtained the Maraston model prediction for the luminosity contribution of AGB stars in SSPs as a function of ages (Mucciarelli et al. 2006). The theoretical isochrones of Girardi et al. (2002) are based on isochrones of Girardi et al. (2000) for low- and intermediate-mass stars (M ≤ 7 M /circledot ) and Bertelli et al. (1994) for highmass stars (M > 7 M /circledot ). Note that stellar evolutionary tracks of Girardi et al. (2000) are adopted in the BC03 model. In this model, they included the simplified TP-AGB phase and no circumstellar dust that form in AGB stars. Marigo et al. (2008) presented optical to far-infrared isochrones with improved TP-AGB models. Girardi et al. (2010) searched for the TP-AGB population of 12 galaxies in the ACS Nearby Galaxy Survey Treasury, and found that the model of Marigo et al. (2008) creates more TP-AGB populations than observed ones. They corrected the mass-loss rate of TPAGB stars in this model by reducing their lifetime (Bowen & Willson 1991, Willson 2000). This model reproduces the number of TP-AGB stars well, but still has uncertainties in their 1.6 µ m band flux contribution (Melbourne et al. 2012). Additionally, we adopted the isochrone set that includes the circumstellar dust from AGB stars (Groenewegen 2006) and assumed that the dust composition is 100% silicate and 100% amorphous carbonate dust for O-rich and C-rich AGB stars, respectively. These two kinds of Padova isochrones consider the core convective overshooting. In order to investigate this effect, we used the BaSTI isochrone dataset (Pietrinferni et al. 2004, 2006) without overshooting efficiency. We selected a scaled solar isochrone set that contains the extended AGB population. We calculated the predicted K s band luminosity fraction of AGB stars in SSPs by analyzing the mock star clusters produced from the isochrones of Girardi et al. (2002), Marigo et al. (2008), and Pietrinferni et al. (2004). We used the isochrone sets with metallicity Z = 0.008, corresponding to [Z/H] ∼ -0.35 for mock cluster experiments. This value is close to the mean value for the LMC, for our cluster samples. The method is described as follows. We created model stars in mock star clusters assuming the Salpeter initial mass function, and assigned J and K s magnitudes to each star using four different isochrone sets. In addition, we considered magnitude errors for each star in order to make the model prediction more realistic. In the 2MASS catalog, mean magnitude errors and error variances of stars in each magnitude bin vary as a function of magnitudes. We assumed that photometric errors of model stars are distributed normally with the mean value and the variance according to magnitude bins. In ( K s, 0 -( J -K s ) 0 ) CMDs of model stars in mock star clusters with empirical magnitude errors, AGB stars are selected with the same criteria as done for observational data (see § 4.1). The K s band luminosities of mock star clusters and AGB stars are calculated by summing the K s band luminosity of member stars and AGB stars, respectively. Note that for the BaSTI models, they do not provide the magnitudes of 2MASS filter system, so that we adopted those of the Bessell filter system. Finally, we obtained the K s band luminosity fraction of AGB stars in mock star clusters with three different mass (10 4 , 10 5 , and 10 6 M /circledot ), assuming 15 different ages (8.0 ≤ log(age) ≤ 9.5) for each mass scale.","pages":[12,13]},{"title":"5.2.2. Stochastic Effect in Estimating Light from AGB Stars","content":"Stochastic effects are inevitable in AGB star counts because of the short lifetime of AGB stars. In Figure 10(a), there is a large scatter in the K s band luminosity fraction of AGB stars in the star clusters derived in this study. The AGB stars evolve fast, and become blue and faint when they enter the post-AGB phase. Therefore, we cannot detect all stars that have entered the AGB phase. As a result it makes the luminosity fraction of AGB stars in star clusters lower than expected. Especially, this effect becomes significant for faint star clusters, because of a smaller number of stars. Bright star clusters (L K s tot /greaterorsimilar 8 . 5 × 10 4 L /circledot ) show relatively smaller scatters and seem to be located along a sequence. This trend also appears in the mock star clusters (see Figure 12). We made mock star clusters with 15 different ages and three different masses using four different isochrone sets as above. For each age and mass bin, we made 10 mock star clusters in order to analyze them statistically. Figure 12 shows the K s band luminosity fraction of AGB stars in the mock star clusters as a function of ages. In this figure, the most massive mock star clusters with M = 10 6 M /circledot show the smallest scatter among mock clusters with other mass scale, and make a well-defined sequence (shaded region). However, mock star clusters with M = 10 5 M /circledot (circles) are distributed with large scatter from the massive mock cluster sequence. Therefore we presented two representatives for the observational data: mean values and the bright cluster sequence.","pages":[13,14]},{"title":"5.2.3. Comparison with Model Expectation","content":"Figure 13 shows a comparison of our results and those expected from five models. In the case of Padova and BaSTI models, we adopted the mean locus line of the massive mock star clusters presented in Figure 12. Note that the Padova02 and BaSTI os models show almost same results of AGB luminosity evolution in SSPs. It reflects that the Padova models include the same ingredients as the BaSTI os model in terms of the core overshooting. Except for these two models, there are several differences in model expectations. First, peak values of the luminosity contribution of AGB stars expected in models are different. The Maraston and Padova10 models suggest 0.7 - 0.8 for the value of the highest AGB fraction, while other three models (Padova02, BaSTI std, and BaSTI os) do just up to ∼ 0.6. Second, all models expect peak values at the similar age range with log(age) ∼ 8.6 - 8.8, except for the BaSTI std model. The peak position of the BaSTI model expectation lies at slightly younger age compared with the expectation of other models. It is because the null overshooting efficiency leads to the shorter lifetime of main-sequence stars. Third, both young and old parts are different between the Maraston model and other models. Padova02, Padova10, and BaSTI os models show that the AGB luminosity fraction in SSPs is lowest at log(age) ∼ 8.0 and increases continuously up to the highest value as SSPs are getting older, while the Maraston model suggests that it comes up to already ∼ 0.4 at log(age) = 8.0 - 8.3 and increases drastically afterwards. The BaSTI std model, however, expects higher AGB luminosity contribution than any other models at log(age) ∼ 8.0 as mentioned above. In the case of SSPs older than 1 Gyr, the AGB luminosity contribution decreases in all models, but the Maraston model shows the steepest decrease. The bright cluster sequence represents well-populated systems that are less influenced by the stochastic fluctuation than faint star clusters, so that it is more appropriate to compare with the expectation of SSP models. In Figure 13, we notice two points with regard to the comparison between the bright cluster sequence and the model expectation: (1) the maximum value of the bright cluster sequence and (2) the age range corresponding to the maximum AGB luminosity contribution. First, the peak value of the AGB luminosity contribution for bright clusters is up to 0.7 - 0.8. Only two models, Maraston and Padova10 models, reproduce this maximum value. Second, the peak position for the bright cluster sequence appears at log(age) = 8.5 - 8.7, which is slightly younger than for model predictions (log(age) = 8.6 - 8.8). However, this discrepancy is not significant because the errors of ages are around 0.1.","pages":[14,15]},{"title":"5.3. Implication for the study of size and mass evolution of galaxies","content":"The calibration of the EPS models influences galaxy studies because the determination of physical parameters of galaxies depends on the amount of the AGB near-infrared luminosity contribution in EPS models. The difference between the AGB luminosity fractions expected by Padova02 and Maraston models is largest at log(age) ∼ 8.7 - 8.9 (age ∼ 0.5 - 0.8 Gyr), as shown Figure 13. This indicates that the differences of galaxy mass estimates based on the EPS models can be significant at this age range. This can be important for galaxies with young stellar ages, such as high-redshift ( z ≥ 2 - 3) or post-starburst galaxies. In these kinds of galaxies, the young stellar component with ages ∼ 1 Gyr is dominant. For example, Raichoor et al. (2011) presented SED fitting results of 79 early-type galaxies at z ∼ 1.3, finding the differences in stellar ages and masses of galaxies estimated with the BC03 and Maraston models, respectively. They showed that the masses of galaxies derived with the Maraston model tend to be lower than those estimated with the BC03 model, and this discrepancy is prominent (by a factor of two) at galaxy ages ∼ 1.0 - 1.3 Gyr with uncertainty of ∼ 1.0 - 1.5 Gyr (see Figure 5 in Raichoor et al. 2011). Muzzin et al. (2009) reported how the galaxy evolution process depends on EPS models. They investigated the size and mass growth of high-redshift galaxies ( z ∼ 2.3). From the galaxy mass differences based on the EPS models, they found that the galaxy size growth from z ∼ 2.3 to z = 0 is faster in the case of the BC03 model than the case of the Maraston model, assuming that the mass growth rate is same in these two cases. Thus, the sizemass relation of galaxies can be influenced by the AGB luminosity contribution in each EPS model. Our results of the bright cluster sequence are closer to the Maraston model so that they support the size-mass relation of galaxies derived with this model.","pages":[15]},{"title":"6. Summary and Conclusion","content":"We investigated the K s band luminosity evolution of the AGB population in SSPs using 102 LMC star clusters. First, we determined ages and foreground reddening of star clusters from the UBV photometry in the MCPS (Zaritsky et al. 2004) using Padova isochrones (Marigo et al. 2008). Then AGB stars in each cluster were selected using 2MASS ( K s -( J -K s )) CMDs. We derived the K s band luminosity fraction of AGB stars in 102 star clusters as a function of ages. The K s band luminosity fraction of AGB stars in star clusters increases as age increases from log(age) ∼ 8.0. It reaches a maximum up to ∼ 0.6 for mean values and ∼ 0.8 for bright cluster sequences at log(age) ∼ 8.5, and decreases afterwards. The AGB luminosity fraction for given ages shows a large scatter caused by stochastic effects. We compared our results with five SSP models: Padova02, Padova10, Maraston, BaSTI std, and BaSTI os models. It is found that the only two models (Padova10 and Maraston models) match approximately the observational K s band AGB luminosity contribution of bright star clusters derived in this study, while other models predict the AGB luminosity contribution much lower. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 2012R1A4A1028713).","pages":[16]},{"title":"REFERENCES","content":"Allen, C. W. 1976, Astrophysical Quantities, London: Athlone (3rd edition), 1976 Bertelli, G., Bressan, A., Chiosi, C., Fagotto, F., & Nasi, E. 1994, A&AS, 106, 275 Bica, E., Bonatto, C., Dutra, C. 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The five sample star clusters are shown here regarding its form and content. r ) t e n ( s K t o G A s K L 4 0 1 ( B . t n e t n o c d r o f e t s lu c ± 4 .4 1 ± 0 .4 3 ± 9 .9 2 ± 0 .3 3 ± 7 .7 7 r e t s lu c r 0 2 s t a r ) L K s A G m p le s t a 9 .5 1 ± 9 .5 1 0 .1 0 1 5 5 . 0 + 6 3 . 0 - 4 .4 3 7 2 .0 0 ± 9 2 .4 0 1 8 L S 7 .6 2 ± 8 .7 3 0 .2 0 2 2 5 . 0 + 7 7 . 0 - 9 .4 5 1 9 0 .0 0 ± 5 9 .7 8 3 9 6 1 C G N 9 .4 3 ± 9 .4 3 4 .1 0 1 5 1 . 0 + 8 0 . 0 - 3 .5 4 5 1 .0 0 ± 9 2 .1 0 1 7 3 S H 9 .8 2 ± 9 .0 4 9 .3 0 2 9 9 . 1 + 3 7 . 1 - 2 .8 5 9 1 .0 0 ± 8 5 .8 9 0 7 L S .8 7 ± .6 5 1 1 .0 2 4 5 0 . 2 + 7 3 . 3 - 4 .1 3 2 1 1 .0 0 ± 9 5 .3 8 7 1 1 L S a s e v fi e h T . n io it d e ic n o r t c le e e h t in y t e ir t n e s it in d e h lis b u p is 2 le b a T - . e t o N 1 in s n io t la u p o p B G A f o s ie t r e p o r p e h T . 2 le b a T /circledot L 4 0 1 ( B G A s K L d l e fi B G A N B G A N ) /circledot L 4 0 1 ( s K t o t L s K r e t s lu C 4 4 4 . 0 + 1 4 4 . 0 - 0 4 1 7 . 0 + 3 1 7 . 0 - 0 7 8 4 . 0 + 7 7 4 . 0 - 0 0 4 2 . 0 + 3 4 2 . 0 - 0 4 6 .1 0 .2 0 . s e lu a v d e t c a r t b u s - ld e fi e h t e t a ic d in ) t e n ( s K t o t L / B G A s K L d n a ) t e n ( B G A s K L - 21 - G s o I n i t o 6 0 5 8 3 0 2 A f o P a v 1 3 1 5 1 8 9 io n P a d o 0 2 0 . 2 0 . 4 0 . 5 0 . 5 0 . 5 0 . 3 0 . 2 a l u e s t c a r f y it s o in m lu d n a b s K f o n o is r a p m o C . 3 le b a T . v d e t c a r t b u s - d l e fi e h t e t a c i d n i ) t e n ( e c n e u q e s r e t s u l c t h g i r b d n a ) t e n ( n a e M - . e t o N ) y d u t s s i h T ( n o i t a v r e s b O r e t s u l c t h g i r B r e t s u l c t h g i r B ) t e n ( e c n e u q e s e c n e u q e s ) t e n ( n a e M n a e M ) ] r y [ e g a ( g o l 0 2 . 0 0 3 . 0 7 0 . 0 ± 4 2 . 0 6 0 . 0 + 7 0 . 0 - 5 2 . 0 0 0 . 8 0 5 . 0 2 6 . 0 0 1 . 0 ± 8 3 . 0 1 1 . 0 ± 3 5 . 0 5 2 . 8 7 6 . 0 1 8 . 0 1 1 . 0 ± 7 4 . 0 1 1 . 0 ± 4 5 . 0 0 5 . 8 0 7 . 0 8 7 . 0 3 1 . 0 ± 2 5 . 0 4 1 . 0 + 3 1 . 0 - 7 5 . 0 5 7 . 8 5 5 . 0 0 6 . 0 9 0 . 0 ± 8 3 . 0 1 1 . 0 ± 2 5 . 0 0 0 . 9 0 3 . 0 3 3 . 0 8 0 . 0 ± 7 2 . 0 9 0 . 0 ± 1 3 . 0 5 2 . 9 5 1 . 0 0 2 . 0 5 1 . 0 ± 1 2 . 0 9 1 . 0 ± 2 3 . 0 0 5 . 9 - 22 -","pages":[16,18,20,21,22]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"We present a study of K s band luminosity evolution of the asymptotic giant branch (AGB) population in simple stellar systems using star clusters in the Large Magellanic Cloud (LMC). We determine physical parameters of LMC star clusters including center coordinates, radii, and foreground reddenings. Ages of 83 star clusters are derived from isochrone fitting with the Padova models, and those of 19 star clusters are taken from the literature. The AGB stars in 102 star clusters with log(age) = 7.3 - 9.5 are selected using near-infrared color magnitude diagrams based on 2MASS photometry. Then we obtain the K s band luminosity fraction of AGB stars in these star clusters as a function of ages. The K s band luminosity fraction of AGB stars increases, on average, as age increases from log(age) ∼ 8.0, reaching a maximum at log(age) ∼ 8.5, and it decreases thereafter. There is a large scatter in the AGB luminosity fraction for given ages, which is mainly due to stochastic effects. We discuss this result in comparison with five simple stellar population models. The maximum K s band AGB luminosity fraction for bright clusters is reproduced by the models that expect the value of 0.7 - 0.8 at log(age) = 8.5 - 8.7. We discuss the implication of our results with regard to the study of size and mass evolution of galaxies. Subject headings: galaxies: star clusters: general - infrared: stars - stars: AGB and post-AGB - Magellanic Clouds - galaxies: evolution\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"K s BAND LUMINOSITY EVOLUTION OF THE ASYMPTOTIC GIANT BRANCH POPULATION BASED ON STAR CLUSTERS IN THE LARGE MAGELLANIC CLOUD\",\n \"content\": \"Youkyung Ko, Myung Gyoon Lee, and Sungsoon Lim Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea ykko@astro.snu.ac.kr, mglee@astro.snu.ac.kr, slim@astro.snu.ac.kr\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"The asymptotic giant branch (AGB), a representative intermediate-age population, is the most luminous evolutionary stage for low- and intermediate-mass (1 - 8 M /circledot ) stars. AGB stars emit a huge amount of near- to mid-infrared light because of their low effective temperature (T eff ∼ 1000 - 4000 K) and circumstellar dust. Hence it is expected that they contribute significantly to the infrared light of galaxies. However, their infrared luminosity contribution in galaxies, even in a simple stellar population (SSP), is still a debating issue with regard to constructing evolutionary population synthesis (EPS) models (Maraston 2011, Bruzual et al. 2013, Noel et al. 2013, and references therein). The EPS models are an useful tool to determine physical parameters of stellar complexes such as star clusters and galaxies by spectral energy distribution (SED) fitting. These models reproduce SEDs of stellar systems by synthesizing the SEDs of stellar populations in various evolutionary stages, assuming age, metallicity, foreground and internal reddening values, star formation history, and so on. Therefore, the spectral energy contribution of individual stellar populations influences the estimation of physical parameters of stellar systems, and especially that of the AGB population plays a key for understanding of the SEDs for stellar systems expected by EPS models. There are various EPS models that include the AGB evolutionary process (e.g., Charlot & Bruzual 1991, Bruzual & Charlot 1993, Fioc & Rocca-Volmerange 1997, Maraston 1998, Leitherer et al. 1999, Vazdekis 1999, Schulz et al. 2002, Bruzual & Charlot 2003, Jimenez et al. 2004, Maraston 2005, Conroy et al. 2009, Kotulla et al. 2009, Conroy & Gunn 2010, Vazdekis et al. 2010, Maraston & Stromback 2011). Bruzual & Charlot (2003, hereafter BC03), for example, presented an EPS model based on Padova evolutionary tracks including just two evolutionary stages for thermally pulsing AGB (TP-AGB) (Girardi et al. 2000), while their recent model includes 15 evolutionary stages of the TP-AGB oxygen-rich and carbon-rich phases (Bruzual A. 2010). The Padova evolutionary tracks adopted in the BC03 model include a given core overshooting efficiency. On the other hand, Maraston (1998, 2005) used evolutionary tracks assuming zero efficiency of the core overshooting from Cassisi et al.(1997, 2000) to determine luminosity contribution of main-sequence populations. It makes the lifetime of main-sequence stars in the Maraston (2005) model shorter compared with Padova isochrones. In addition, she used the fuel consumption theorem (Renzini & Buzzoni 1986) for post-main-sequence stars, not adopting the isochrone synthesis method. In the model of Maraston (1998), the TP-AGB evolutionary process is modified in the fuel consumption theorem, applying the advanced envelope burning process of AGB stars. Renzini & Buzzoni (1986) estimated the contribution of TP-AGB population in the young SSPs with ages < 10 8 yr, and compared it with the star clusters in the the Magellanic Clouds (MCs). They found that it is too high to be consistent with the observational results based on these star clusters. Considering this difference, Maraston (2005) suggested a revised model, assuming shorter lifetime and lower fuel consumption of TP-AGB stars than Renzini & Buzzoni (1986). BC03 and Maraston (2005) adopted different stellar population synthetic methods, and the SEDs reproduced by these models show recognizable differences. A number of studies argue whether or not these EPS models reproduce well observational quantities of stellar systems related with the AGB population as follows. Some studies found that spectra and SEDs of post-starburst galaxies or distant galaxies (z ∼ 1 - 2) have no near-infrared boosted features, which is similar to the expectation of the BC03 model (Muzzin et al. 2009, Kriek et al. 2010, Zibetti et al. 2013). In addition, Conroy & Gunn (2010) suggested that the BC03 model and their own EPS model, a flexible stellar population synthesis model, reproduce the color of star clusters and post-starburst galaxies better than the Maraston (2005) model. In contrast, others confirmed that the Maraston (2005) model performs well in reproducing near-infrared colors, ( Y -K ) and ( H -K ), and SEDs of low to high redshift galaxies (Maraston et al. 2006, Eminian et al. 2008, MacArthur et al. 2010). Moreover, van der Wel et al. (2006) and Henriques et al. (2011) showed that the rest-frame K band mass-to-light ratio evolution and K s band luminosity evolution of galaxies are explained better by the Maraston (2005) model than by the BC03 model. In addition to these galaxy studies, there are several studies investigating star clusters, especially star clusters in the MCs, considering the relevance between the model performance and ages of stellar systems. Because of their proximity, they are very useful to examine not only the individual stellar population directly but also the integrated properties of star clusters. Therefore, they are an ideal object to calibrate SSP models. Pessev et al. (2008) investigated optical to near-infrared colors, ( B -J ), ( V -J ), and ( J -K ), of 54 star clusters in the MCs, and concluded that the BC03 and the Maraston (2005) present the best performance for intermediate-age (0.2 - 2 Gyr) and old ( > 2 Gyr) star clusters, respectively. Lyubenova et al. (2010, 2012) analyzed integrated near-infrared high-resolution spectra of six globular clusters in the Large Magellanic Cloud (LMC) with ages ∼ 1 - 13 Gyr. They showed that the Maraston (2005) model expects J and H band spectra of all their sample star clusters adequately, while it does not for K band spectra of the star clusters with ages < 2 Gyr. Recently Noel et al. (2013) presented the calibration data for stellar population models using 43 star clusters in the MCs. They compared the observed colors of the star clusters, ( V -K ) 0 , ( J -K ) 0 , and ( V -I ) 0 , as a function of ages with the theoretical expectation of various models including BC03 and Maraston (2005). In conclusion, for the ages older than 1 Gyr, the models of Maraston (2005) and BC03 are along the upper end lower end of the observed color, respectively. In the case of the younger ages, BC03 model reproduces well the observed color of star clusters, while Maraston (2005) model expects them too red. While above studies investigated the integrated properties of star clusters, Mucciarelli et al. (2006) analyzed the resolved AGB population in the LMC star clusters in detail. They investigated 19 LMC star clusters in terms of K s band luminosity contribution of AGB stars as a function of cluster ages. The star clusters used in Mucciarelli et al. (2006) have ages of 100 Myr - 3 Gyr (log(age) ∼ 8.0 - 9.5). They concluded that their empirical results are consistent with the expectation of Maraston (2005) for this age range. Later, Mucciarelli et al. (2009) suggested a similar conclusion from the additional study of four old star clusters in the Small Magellanic Cloud (SMC). In this study, we investigate the evolution of AGB luminosity contribution with a large number of LMC star clusters with log(age) ∼ 7.3 - 9.5, overcoming the shortcomings in the previous studies. Because Mucciarelli et al. (2006, 2009) included few star clusters with log(age) ∼ 8.3 - 8.7 (see Figure 5 in Mucciarelli et al. 2009), we enlarged the number of star cluster samples with this age range. In this age range, the AGB luminosity contribution is expected to change rapidly according to the Maraston (2005) model. In addition, most of previous star cluster studies adopted star cluster ages from various literature. We determine ages of LMC star clusters by isochrone fitting homogeneously, using the resolved stars. This paper is organized as follows. In § 2, we introduce the photometric data and images used in this study. § 3 describes the method to estimate physical parameters of sample star clusters such as center coordinates, radii, ages, and foreground reddenings including the cluster sample section. In § 4, we select AGB stars in each star cluster and derive the K s band luminosity contribution of AGB stars to total luminosity of star clusters as a function of ages. In § 5, we compare our results with previous studies, and also compare the primary results with the theoretical expectation from EPS models, including the discussion of stochastic effects. Final section summarizes the main results and presents the conclusion of this study.\",\n \"pages\": [\n 1,\n 2,\n 3,\n 4\n ]\n },\n {\n \"title\": \"2. Data\",\n \"content\": \"Bica et al. (2008) presented an extended source catalog of the MCs including star clusters, emission nebulae, associations, and HI shells. They compiled data from various literature including the findings based on photographic survey plates. It contains center coordinates (R.A. and Declination), major and minor axes, and position angles of 3,700 star clusters of the MCs including the LMC, SMC, and the Magellanic Bridge regions. We redetermined the centers and radii of LMC star clusters based on the center coordinates presented in Bica et al. (2008). We used optical ( UBVI ) and near-infrared ( JHK s ) point source catalogs of the LMC. Zaritsky et al. (2004) presented U, B, V , and I band photometry of 24,107,004 point sources in the central 64 deg 2 of the LMC from the Magellanic Clouds Photometric Survey (MCPS; Zaritsky et al. 1997). The MCPS obtained drift-scan images using 1-m Las Campanas Swope Telescope and Great Circle Camera (Zaritsky et al. 1996). Their photometry is incomplete below 21.5, 23.5, 23, and 22 mag in U, B, V , and I bands in sparse regions, respectively. This catalog is used to determine center coordinates, radii, ages, and foreground reddenings of the star clusters. In order to distinguish AGB stars from other populations, we used a near-infrared point source catalog from the two micron all sky survey (2MASS; Skrutskie et al. 2006). In the central 100 deg 2 region of the LMC (10 · × 10 · ), there are 1,430,676 point sources detected in the 2MASS. The limiting magnitudes of photometry are 15.8, 15.1, and 14.3 mag in J, H , and K s bands, respectively, which correspond to 10 σ point source detection level. The AGB stars in the LMC are brighter than K s ∼ 12 . 3 mag, much brighter than the limiting magnitudes. We also used 2MASS Atlas Images to estimate the integrated luminosity of the star clusters, retrieving the K s band images of our sample clusters using 2MASS interactive image service 1 .\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"3.1. Center Coordinates and Sizes of Star Clusters\",\n \"content\": \"We determined centers for 1,645 star clusters and radii for 1,708 star clusters, respectively, using the MCPS catalog (Zaritsky et al. 2004) as a part of our study of LMC star clusters. We constructed 2-dimensional number density maps of bright stars with V < 20.5 mag around the center coordinates of the star clusters presented by Bica et al. (2008). The number density maps are smoothed with a boxcar filter whose width is 20 '' . Center coordinates, coordinate errors, and position angles of each star cluster were estimated by 2-dimensional Gaussian fitting of this smoothed number density map. The field of view for the fitting region is 3 times larger than the radius of each cluster given in Bica et al. (2008). Figure 1 shows an example of centering process for one cluster NGC 1861. We attempted 2-dimensional Gaussian fitting to 3,064 LMC star clusters in Bica et al. (2008), but stellar number density maps could obtain acceptable fits for only 1,645 star clusters. The fitting results are not reliable in the case of poor, faint, or binary clusters, in which case that the center coordinates presented by Bica et al. (2008) are adopted. The radius of each cluster was determined from radial number density profiles (see Figure 2). The radial number density profile is obtained by counting point sources with V < 20.5 mag. We estimated a median value of the background number density (n bg ) of stars located between 200 '' and 300 '' from the center of each cluster. The standard deviation from n bg ( σ bg ) is calculated, and the area of which number density greater than n bg +3 σ bg is considered as a cluster area. Finally, we determined radii of 1,708 LMC star clusters, and radii of the other clusters that do not show a prominent concentration are adopted from Bica et al. (2008). Most of these clusters are poor, faint, or binary ones. Bica et al. (2008) presented major and minor axes of star clusters, from which we define the radius of each star cluster as the mean value of semi-major and semi-minor axes. In addition to Bica et al. (2008), Werchan & Zaritsky (2011) also presented a catalog of star clusters they found in the MCPS images. They investigated stellar overdensities in LMC fields using stars brighter than 20.5 mag in V band. By both King and Elson-FallFreeman model fitting of the surface brightness profiles of each cluster, they determined center coordinates, central surface brightness, tidal radii, and 90% enclosed luminosity radii of 1,066 LMC star clusters. We compare the center coordinates and radii determined in this study with those given by Bica et al. (2008) and Werchan & Zaritsky (2011) in Figure 3. Figure 3(a) - (f) show the differences of center coordinates of star clusters among three studies. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 626, 1,645, and 677, respectively. The center coordinates of star clusters from all three different studies are mostly consistent within 10 '' . Figure 3(g) - (i) show the differences of radii of star clusters. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 615, 1,708, and 681, respectively. Werchan & Zaritsky (2011) presented four kinds of radii for each cluster, core radii and 90% enclosed luminosity radii obtained by fitting using two different models, respectively, and we adopted the 90% enclosed luminosity radius from King model fitting results as a radius to compare with the results from other studies. The values for the cluster radii derived in this study are in better agreement with Bica et al. (2008) than with Werchan & Zaritsky (2011).\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"3.2. Cluster Sample Selection and Age Estimation\",\n \"content\": \"For this study, we selected 102 star clusters that have red and bright stars in nearinfrared ( K s -( J -K s )) CMDs based on 2MASS catalog (Skrutskie et al. 2006). These stars are considered as AGB star candidates. The AGB selection method is described in § 4.1. For 96 and 83 of these star clusters, we estimated foreground reddenings and ages, respectively, with reasonable optical photometry as follows. We chose member stars of each star cluster using the center coordinates and the radii estimated before (see § 3.1). The value of foreground reddening, E ( B -V ), was estimated by shifting the zero age main-sequence (ZAMS) in the (( U -B ) -( B -V )) color-color diagram (CCD). We used the bright main-sequence stars ( V /lessorsimilar 18) located in the outer region up to 200 - 300 '' of each star cluster to obtain the CCDs, and compared the sequence of stars in the CCDs with the ZAMS in the Padova models (Marigo et al. 2008) as in Figure 4(b). The errors of E ( B -V ) values are about 0.02 mag typically. Figure 5(a) and (b) show ( V -( B -V )) CMDs of both a cluster and a field region for NGC 1861, as an example. The cluster CMD is expected to contain field stars as well as cluster stars. In order to minimize the field contamination, we performed statistical subtraction of field CMDs for cluster CMDs. We counted the number of stars in cluster CMDs with that of stars in field CMDs for the same area as the cluster area for each color and magnitude bin (∆( B -V ) ∼ 0 . 5 and ∆ V ∼ 1), and subtracted statistically field stars from cluster stars for each bin. Figure 5(c) displays a field-subtracted CMD of NGC 1861. It shows a clear stellar sequence with a smaller number of stars than the original CMD. We determined ages of 83 star clusters by isochrone fitting in the field-subtracted ( V -( B -V )) CMDs, assuming the distance modulus (m -M) 0 = 18.50 mag and Z = 0 . 008 . Cluster ages were derived using isochrones of Marigo et al. (2008). We used only the stars with small errors of colors with err ( B -V ) < 0 . 1 mag for isochrone fitting. The ages of the other 19 star clusters could not be derived, because they were not covered by the MCPS observation fields or are older than 1 Gyr. In this case, we adopted the ages of these clusters from the literature (Elson & Fall 1985, Girardi et al. 1995, Pietrzynski & Udalski 2000, Goudfrooij et al. 2011, Popescu et al. 2012). Table 1 lists physical parameters of 102 star clusters that will be used for AGB star selection. We compared the ages derived in this study with those given in other references, Elson & Fall (1985), Pietrzynski & Udalski (2000), Hunter et al. (2003), Glatt et al. (2010), and Popescu et al. (2012), as shown in Figure 6. The isochrone fitting method used for the resolved stars in star clusters is considered to be more reliable than other age-dating methods based on the integrated color or spectra of the star clusters. Pietrzynski & Udalski (2000), Glatt et al. (2010), and this study used the isochrone fitting method, while Elson & Fall (1985), Hunter et al. (2003), and Popescu et al. (2012) analyzed the integrated color of the star clusters. Elson & Fall (1985) and Hunter et al. (2003) analyzed ( U -B ) and ( B -V ) colors of the star clusters, and Popescu et al. (2012) performed a Monte Carlo simulation with their own star cluster simulation software (MASSive CLuster Evolution and ANalysis, MASSCLEAN; Popescu & Hanson 2010) to reproduce the cluster colors, ( U -B ) 0 and ( B -V ) 0 . The ages based on the isochrone fitting method show good agreement with each other. They also show correlations with the ages based on integrated colors, but with signif- icant scatters and non-unity slopes. It is noted that the ages derived from integrated colors by Popescu et al. (2012) show a better correlation with the isochrone-fitting ages, compared with other results in Elson & Fall (1985) and Hunter et al. (2003). Figure 7 shows the CMDs of five star clusters that have the largest difference of ages between this study and others: SL482 (Glatt et al. 2010), NGC 1782 (Elson & Fall 1985), SL294 (Popescu et al. 2012), SL503 (Hunter et al. 2003), and H88-182 (Pietrzynski & Udalski 2000). We plotted the Padova isochrones for Z = 0 . 008 and the ages corresponding to the values derived in this study and other references. In the case of SL482, NGC 1782, and H88182, it is difficult to determine their ages reliably because the number of the brightest stars around the main-sequence turnoff is small. However, in the case of other two star clusters, SL294 and SL503, their CMDs are not matched by the isochrones for the ages derived by Popescu et al. (2012) and Hunter et al. (2003) respectively, while they are by the isochrones for the ages derived in this study.\",\n \"pages\": [\n 6,\n 7,\n 8\n ]\n },\n {\n \"title\": \"4.1. Selection of AGB Stars\",\n \"content\": \"While it is difficult to distinguish AGB stars from RGB stars in optical CMDs, it is relatively easier in near-infrared CMDs. Therefore, we plotted the near-infrared ( K s, 0 -( J -K s ) 0 ) CMDs of resolved stars in 102 star clusters using the 2MASS point source catalog (Skrutskie et al. 2006), and selected AGB stars using two criteria: (1) stars brighter than the tip of the RGB (TRGB); K s, 0 < 12 . 3, and (2) stars redder than the RGB; ( J -K s ) 0 > -0 . 075 × K s, 0 +1 . 85. We adopted the TRGB magnitude, K s = 12.3 ± 0.1 estimated from 2MASS point sources in the LMC region (Nikolaev & Weinberg 2000). The second criterion was suggested from the analysis of the 2MASS photometry for LMC stars by Cioni et al. (2006). There is no constraint for the brightest and reddest stars. We use the extinction law in Cardelli et al. (1989) to derive extinction values for each band, adopting R V = 3 . 1. Figure 8(b) and (d) show the combined ( K s, 0 -( J -K s ) 0 ) CMDs of all stars in 41 young star clusters with log(age) < 8 . 5 and 61 old star clusters with log(age) ≥ 8 . 5, respectively. We selected the AGB stars brighter and redder than AGB boundary lines as described above (dashed lines). We also plotted other AGB boundaries used in the references in Figure 8(b) and (d): dot-dashed lines used by Mucciarelli et al. (2006) and gray shaded regions used by Nikolaev & Weinberg (2000). The AGB boundary used in this study is working in the similar way to that in Nikolaev & Weinberg (2000). However, the AGB boundary used by Mucciarelli et al. (2006) includes a significant number of bluer stars, compared with that in this study. This difference will be discussed in § 5.1.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"4.2. Measurement of K s Band Luminosity Fraction of the AGB Population in Star Clusters\",\n \"content\": \"We estimated the K s band luminosity of star clusters by aperture photometry using 2MASS K s band images. Photometry was performed with IRAF 2 APPHOT package. For background estimation we used annular apertures with the inner radius to be the sum of the star cluster radius and its error and the aperture width of 10 '' . The background level was estimated using the mode value of the annulus region. For cluster photometry we used circular apertures with radius that is the same as the cluster radius. Figure 9 displays a K s band image of an example star cluster, NGC 1861, showing the position of apertures for the cluster and background area. We calculated the K s band luminosity of AGB stars in each cluster by summing their luminosity converted from 2MASS magnitudes, and obtained the K s band luminosity fraction of AGB stars in the star clusters. Table 2 summarizes the properties of AGB populations as well as other basic parameters of 102 LMC star clusters. It lists the number of AGB stars, and the K s band luminosity and luminosity fraction of AGB stars in each cluster, as well as K s band integrated magnitude and luminosity of the star clusters. The magnitudes are based on 2MASS magnitude system. We adopted the K s band absolute magnitude M K s /circledot = 3 . 27 mag for the Sun, using M V /circledot = 3 . 83 mag (Allen 1976) and ( V -K s ) = 1 . 56 mag (Casagrande et al. 2012), to convert the magnitude into the luminosity. The error of the AGB luminosity fraction is contributed by various errors in addition to the photometric ones estimated for the integrated magnitude of star clusters and presented for the 2MASS magnitude of AGB stars. First, there exist the errors of center coordinates and radii of star clusters, influencing the estimation of their integrated luminosity. We performed aperture photometry for all sample clusters, setting different center positions and radii according to their errors. We selected the upper and lower errors of the integrated luminosity of star clusters, also considering photometric errors. Secondly, there are the errors for the luminosity of AGB stars, which consist of (a) 2MASS photometric error for individual AGB stars and (b) the uncertainty from the Poisson error for the number of AGB stars in each star cluster associated with AGB star counts. Of these two, the latter is much larger than the former. The AGB luminosity error from Poisson error is calculated by multiplying the square root of the number of AGB stars by the mean luminosity for an AGB star in each cluster. We tabulated upper and lower errors of the K s band luminosity fraction obtained by error propagation, considering overall error budget mentioned above (see Table 2). Note that the smaller the numbers of AGB stars in star clusters are, the larger the errors of the luminosity fraction are. Additionally, we checked the field contamination in AGB star count. We investigated the outer region of each star cluster with the radius five times larger than the cluster radius. The number of the AGB stars in this field region is normalized to the cluster area. We calculated the amount of field contamination by multiplying the mean luminosity of AGB stars in star clusters by the number of the normalized field AGB stars, and subtracted it from the luminosity of AGB stars in star clusters. However, the effect of the field contamination to estimating the luminosity fraction of AGB stars is much smaller than that of the Poisson error of the AGB star count. These field-subtracted values are also listed in Table 2. Figure 10(a) shows the K s band luminosity fraction of AGB stars in our sample clusters as a function of ages. Figure 10(b) displays the mean values of the K s band luminosity fraction of AGB stars in the star clusters. These values are also listed in Table 3 including the field-subtracted values. The mean values represent the ratios of the total K s band luminosity of AGB stars in the star clusters to the total K s band luminosity of the star clusters for each age bin. The error of mean values is calculated from the individual errors of the star clusters by error propagation. We also derived a sequence to represent approximately the sequence of bright clusters, as plotted in the figure. The bright clusters have the luminosity of L K s > 8 . 5 × 10 4 L /circledot . Following features are noted in Figure 10. First, the mean values and the bright cluster sequence increase, as log(age) increases from 8.0 to 8.5, reaching 0.6 and 0.8 at log(age) ∼ 8 . 5, respectively. They decrease thereafter. Second, there is a large scatter in the mean values for given ages. We discuss these features in § 5.2.2 in detail.\",\n \"pages\": [\n 9,\n 10\n ]\n },\n {\n \"title\": \"5.1. Comparison with Previous Studies\",\n \"content\": \"In Figure 10(b), we also plotted the results for 19 LMC star clusters given by Mucciarelli et al. (2006) for comparison. There are 12 star clusters common between this study and Mucciarelli et al. (2006). We determined foreground reddenings of six star clusters (NGC 1806, NGC 1866, NGC 1987, NGC 2108, NGC 2134, and NGC 2136) by using the method mentioned above (see § 3.2). For the other three star clusters(NGC 1831, NGC 2173, and NGC 2249), the field stars were not covered by the MCPS. In this case, we adopted foreground reddening values from the optical reddening map of the MCs given by Haschke et al. (2011). Haschke et al. (2011) presented the optical reddening map of the MCs obtained by comparing the theoretical color of the red clump with its observed one based on the OGLE III data. The reddening values of the others (NGC 2162, NGC 2190, and NGC 2231) could not be determined neither in this study nor in Haschke et al. (2011). We assumed the typical extinction value, E ( B -V ) = 0 . 1, for these three clusters. For ages, we determined ages of three of these clusters (NGC 1866, NGC 2134, and NGC 2136). The ages of the others are adopted from Elson & Fall (1985) and Girardi et al. (1995), because we could not use the MCPS catalog for these clusters. We also noticed that the AGB selection criteria of Mucciarelli et al. (2006) are different from those of this study (see Figure 8). Mucciarelli et al. (2006) included as AGB candidates the blue stars that are excluded in this study, but the color and magnitude of these stars indicate that they are bright RGB and supergiant populations according to the analysis of Nikolaev & Weinberg (2000). The color distribution of the stars brighter than K s = 12.3 for young star clusters with log(age) < 8.5 shows a blue excess at ( J -K s ) 0 < 1 . 0 (see Figure 8(a)), while little blue excess is seen for the case of old star clusters with log(age) > 8.5 (see Figure 8(c)). However, those blue stars used in the analysis of Mucciarelli et al. (2006) do not significantly influence the luminosity fraction of AGB stars in the star clusters, because they are somewhat faint (see Figure 11). In addition, there are three red stars not included in the AGB boundary of Mucciarelli et al. (2006) but contained in that of this study, which can be dusty AGB stars. We found that these stars affect little our results. The number of AGB stars shows a large discrepancy between our results and Mucciarelli et al. (2006) for the young star clusters as shown in Figure 11(a), but the difference in the luminosity fraction of AGB stars in the star clusters is much smaller as shown in Figure 11(b). In Figure 10(b), the results for 19 star clusters from Mucciarelli et al. (2006) are included, and those derived in this study are also plotted for four star clusters that show a large discrepancy ( > 0.2) in the AGB luminosity fraction (see Figure 11(b)). Other eight clusters show the consistent results with Mucciarelli et al. (2006). Most of these clusters studied by Mucciarelli et al. (2006) are brighter than L K s = 10 5 L /circledot , except for two star clusters, NGC 2249 and NGC 2231. Indeed they are following the bright cluster sequence derived in this study, with some scatter.\",\n \"pages\": [\n 10,\n 11\n ]\n },\n {\n \"title\": \"5.2.1. Mock Cluster Experiments with SSP models\",\n \"content\": \"We compare our results with the expectation of five theoretical models: (1) an EPS model of Maraston (2005) (called Maraston model), (2) a model based on the isochrone set of Girardi et al. (2002) (called Padova02 model), (3) a model based on the improved isochrone set of Marigo et al. (2008) corrected by Girardi et al. (2010) (called Padova10 model), (4) a model based on the isochrone set of Pietrinferni et al. (2004, 2006) assuming a given overshooting efficiency (called BaSTI os model), and (5) the same as (4), but for null overshooting efficiency (called BaSTI std model). The Maraston model calculates the luminosity contribution of AGB stars directly using the fuel consumption approach. Girardi et al. (2002) and Marigo et al. (2008) corrected by Girardi et al. (2010) presented theoretical stellar evolutionary tracks and isochrones used in various EPS models. The detailed information of these models is described as follows. The Maraston model calculated the amount of the fuel consumption of each population in the post-main-sequence phases (Renzini & Buzzoni 1986) directly, and converted it to observables assuming the effective temperature and surface gravity for evolutionary stages. We obtained the Maraston model prediction for the luminosity contribution of AGB stars in SSPs as a function of ages (Mucciarelli et al. 2006). The theoretical isochrones of Girardi et al. (2002) are based on isochrones of Girardi et al. (2000) for low- and intermediate-mass stars (M ≤ 7 M /circledot ) and Bertelli et al. (1994) for highmass stars (M > 7 M /circledot ). Note that stellar evolutionary tracks of Girardi et al. (2000) are adopted in the BC03 model. In this model, they included the simplified TP-AGB phase and no circumstellar dust that form in AGB stars. Marigo et al. (2008) presented optical to far-infrared isochrones with improved TP-AGB models. Girardi et al. (2010) searched for the TP-AGB population of 12 galaxies in the ACS Nearby Galaxy Survey Treasury, and found that the model of Marigo et al. (2008) creates more TP-AGB populations than observed ones. They corrected the mass-loss rate of TPAGB stars in this model by reducing their lifetime (Bowen & Willson 1991, Willson 2000). This model reproduces the number of TP-AGB stars well, but still has uncertainties in their 1.6 µ m band flux contribution (Melbourne et al. 2012). Additionally, we adopted the isochrone set that includes the circumstellar dust from AGB stars (Groenewegen 2006) and assumed that the dust composition is 100% silicate and 100% amorphous carbonate dust for O-rich and C-rich AGB stars, respectively. These two kinds of Padova isochrones consider the core convective overshooting. In order to investigate this effect, we used the BaSTI isochrone dataset (Pietrinferni et al. 2004, 2006) without overshooting efficiency. We selected a scaled solar isochrone set that contains the extended AGB population. We calculated the predicted K s band luminosity fraction of AGB stars in SSPs by analyzing the mock star clusters produced from the isochrones of Girardi et al. (2002), Marigo et al. (2008), and Pietrinferni et al. (2004). We used the isochrone sets with metallicity Z = 0.008, corresponding to [Z/H] ∼ -0.35 for mock cluster experiments. This value is close to the mean value for the LMC, for our cluster samples. The method is described as follows. We created model stars in mock star clusters assuming the Salpeter initial mass function, and assigned J and K s magnitudes to each star using four different isochrone sets. In addition, we considered magnitude errors for each star in order to make the model prediction more realistic. In the 2MASS catalog, mean magnitude errors and error variances of stars in each magnitude bin vary as a function of magnitudes. We assumed that photometric errors of model stars are distributed normally with the mean value and the variance according to magnitude bins. In ( K s, 0 -( J -K s ) 0 ) CMDs of model stars in mock star clusters with empirical magnitude errors, AGB stars are selected with the same criteria as done for observational data (see § 4.1). The K s band luminosities of mock star clusters and AGB stars are calculated by summing the K s band luminosity of member stars and AGB stars, respectively. Note that for the BaSTI models, they do not provide the magnitudes of 2MASS filter system, so that we adopted those of the Bessell filter system. Finally, we obtained the K s band luminosity fraction of AGB stars in mock star clusters with three different mass (10 4 , 10 5 , and 10 6 M /circledot ), assuming 15 different ages (8.0 ≤ log(age) ≤ 9.5) for each mass scale.\",\n \"pages\": [\n 12,\n 13\n ]\n },\n {\n \"title\": \"5.2.2. Stochastic Effect in Estimating Light from AGB Stars\",\n \"content\": \"Stochastic effects are inevitable in AGB star counts because of the short lifetime of AGB stars. In Figure 10(a), there is a large scatter in the K s band luminosity fraction of AGB stars in the star clusters derived in this study. The AGB stars evolve fast, and become blue and faint when they enter the post-AGB phase. Therefore, we cannot detect all stars that have entered the AGB phase. As a result it makes the luminosity fraction of AGB stars in star clusters lower than expected. Especially, this effect becomes significant for faint star clusters, because of a smaller number of stars. Bright star clusters (L K s tot /greaterorsimilar 8 . 5 × 10 4 L /circledot ) show relatively smaller scatters and seem to be located along a sequence. This trend also appears in the mock star clusters (see Figure 12). We made mock star clusters with 15 different ages and three different masses using four different isochrone sets as above. For each age and mass bin, we made 10 mock star clusters in order to analyze them statistically. Figure 12 shows the K s band luminosity fraction of AGB stars in the mock star clusters as a function of ages. In this figure, the most massive mock star clusters with M = 10 6 M /circledot show the smallest scatter among mock clusters with other mass scale, and make a well-defined sequence (shaded region). However, mock star clusters with M = 10 5 M /circledot (circles) are distributed with large scatter from the massive mock cluster sequence. Therefore we presented two representatives for the observational data: mean values and the bright cluster sequence.\",\n \"pages\": [\n 13,\n 14\n ]\n },\n {\n \"title\": \"5.2.3. Comparison with Model Expectation\",\n \"content\": \"Figure 13 shows a comparison of our results and those expected from five models. In the case of Padova and BaSTI models, we adopted the mean locus line of the massive mock star clusters presented in Figure 12. Note that the Padova02 and BaSTI os models show almost same results of AGB luminosity evolution in SSPs. It reflects that the Padova models include the same ingredients as the BaSTI os model in terms of the core overshooting. Except for these two models, there are several differences in model expectations. First, peak values of the luminosity contribution of AGB stars expected in models are different. The Maraston and Padova10 models suggest 0.7 - 0.8 for the value of the highest AGB fraction, while other three models (Padova02, BaSTI std, and BaSTI os) do just up to ∼ 0.6. Second, all models expect peak values at the similar age range with log(age) ∼ 8.6 - 8.8, except for the BaSTI std model. The peak position of the BaSTI model expectation lies at slightly younger age compared with the expectation of other models. It is because the null overshooting efficiency leads to the shorter lifetime of main-sequence stars. Third, both young and old parts are different between the Maraston model and other models. Padova02, Padova10, and BaSTI os models show that the AGB luminosity fraction in SSPs is lowest at log(age) ∼ 8.0 and increases continuously up to the highest value as SSPs are getting older, while the Maraston model suggests that it comes up to already ∼ 0.4 at log(age) = 8.0 - 8.3 and increases drastically afterwards. The BaSTI std model, however, expects higher AGB luminosity contribution than any other models at log(age) ∼ 8.0 as mentioned above. In the case of SSPs older than 1 Gyr, the AGB luminosity contribution decreases in all models, but the Maraston model shows the steepest decrease. The bright cluster sequence represents well-populated systems that are less influenced by the stochastic fluctuation than faint star clusters, so that it is more appropriate to compare with the expectation of SSP models. In Figure 13, we notice two points with regard to the comparison between the bright cluster sequence and the model expectation: (1) the maximum value of the bright cluster sequence and (2) the age range corresponding to the maximum AGB luminosity contribution. First, the peak value of the AGB luminosity contribution for bright clusters is up to 0.7 - 0.8. Only two models, Maraston and Padova10 models, reproduce this maximum value. Second, the peak position for the bright cluster sequence appears at log(age) = 8.5 - 8.7, which is slightly younger than for model predictions (log(age) = 8.6 - 8.8). However, this discrepancy is not significant because the errors of ages are around 0.1.\",\n \"pages\": [\n 14,\n 15\n ]\n },\n {\n \"title\": \"5.3. Implication for the study of size and mass evolution of galaxies\",\n \"content\": \"The calibration of the EPS models influences galaxy studies because the determination of physical parameters of galaxies depends on the amount of the AGB near-infrared luminosity contribution in EPS models. The difference between the AGB luminosity fractions expected by Padova02 and Maraston models is largest at log(age) ∼ 8.7 - 8.9 (age ∼ 0.5 - 0.8 Gyr), as shown Figure 13. This indicates that the differences of galaxy mass estimates based on the EPS models can be significant at this age range. This can be important for galaxies with young stellar ages, such as high-redshift ( z ≥ 2 - 3) or post-starburst galaxies. In these kinds of galaxies, the young stellar component with ages ∼ 1 Gyr is dominant. For example, Raichoor et al. (2011) presented SED fitting results of 79 early-type galaxies at z ∼ 1.3, finding the differences in stellar ages and masses of galaxies estimated with the BC03 and Maraston models, respectively. They showed that the masses of galaxies derived with the Maraston model tend to be lower than those estimated with the BC03 model, and this discrepancy is prominent (by a factor of two) at galaxy ages ∼ 1.0 - 1.3 Gyr with uncertainty of ∼ 1.0 - 1.5 Gyr (see Figure 5 in Raichoor et al. 2011). Muzzin et al. (2009) reported how the galaxy evolution process depends on EPS models. They investigated the size and mass growth of high-redshift galaxies ( z ∼ 2.3). From the galaxy mass differences based on the EPS models, they found that the galaxy size growth from z ∼ 2.3 to z = 0 is faster in the case of the BC03 model than the case of the Maraston model, assuming that the mass growth rate is same in these two cases. Thus, the sizemass relation of galaxies can be influenced by the AGB luminosity contribution in each EPS model. Our results of the bright cluster sequence are closer to the Maraston model so that they support the size-mass relation of galaxies derived with this model.\",\n \"pages\": [\n 15\n ]\n },\n {\n \"title\": \"6. Summary and Conclusion\",\n \"content\": \"We investigated the K s band luminosity evolution of the AGB population in SSPs using 102 LMC star clusters. First, we determined ages and foreground reddening of star clusters from the UBV photometry in the MCPS (Zaritsky et al. 2004) using Padova isochrones (Marigo et al. 2008). Then AGB stars in each cluster were selected using 2MASS ( K s -( J -K s )) CMDs. We derived the K s band luminosity fraction of AGB stars in 102 star clusters as a function of ages. The K s band luminosity fraction of AGB stars in star clusters increases as age increases from log(age) ∼ 8.0. It reaches a maximum up to ∼ 0.6 for mean values and ∼ 0.8 for bright cluster sequences at log(age) ∼ 8.5, and decreases afterwards. The AGB luminosity fraction for given ages shows a large scatter caused by stochastic effects. We compared our results with five SSP models: Padova02, Padova10, Maraston, BaSTI std, and BaSTI os models. It is found that the only two models (Padova10 and Maraston models) match approximately the observational K s band AGB luminosity contribution of bright star clusters derived in this study, while other models predict the AGB luminosity contribution much lower. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 2012R1A4A1028713).\",\n \"pages\": [\n 16\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Allen, C. 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The five sample star clusters are shown here regarding its form and content. r ) t e n ( s K t o G A s K L 4 0 1 ( B . t n e t n o c d r o f e t s lu c ± 4 .4 1 ± 0 .4 3 ± 9 .9 2 ± 0 .3 3 ± 7 .7 7 r e t s lu c r 0 2 s t a r ) L K s A G m p le s t a 9 .5 1 ± 9 .5 1 0 .1 0 1 5 5 . 0 + 6 3 . 0 - 4 .4 3 7 2 .0 0 ± 9 2 .4 0 1 8 L S 7 .6 2 ± 8 .7 3 0 .2 0 2 2 5 . 0 + 7 7 . 0 - 9 .4 5 1 9 0 .0 0 ± 5 9 .7 8 3 9 6 1 C G N 9 .4 3 ± 9 .4 3 4 .1 0 1 5 1 . 0 + 8 0 . 0 - 3 .5 4 5 1 .0 0 ± 9 2 .1 0 1 7 3 S H 9 .8 2 ± 9 .0 4 9 .3 0 2 9 9 . 1 + 3 7 . 1 - 2 .8 5 9 1 .0 0 ± 8 5 .8 9 0 7 L S .8 7 ± .6 5 1 1 .0 2 4 5 0 . 2 + 7 3 . 3 - 4 .1 3 2 1 1 .0 0 ± 9 5 .3 8 7 1 1 L S a s e v fi e h T . n io it d e ic n o r t c le e e h t in y t e ir t n e s it in d e h lis b u p is 2 le b a T - . e t o N 1 in s n io t la u p o p B G A f o s ie t r e p o r p e h T . 2 le b a T /circledot L 4 0 1 ( B G A s K L d l e fi B G A N B G A N ) /circledot L 4 0 1 ( s K t o t L s K r e t s lu C 4 4 4 . 0 + 1 4 4 . 0 - 0 4 1 7 . 0 + 3 1 7 . 0 - 0 7 8 4 . 0 + 7 7 4 . 0 - 0 0 4 2 . 0 + 3 4 2 . 0 - 0 4 6 .1 0 .2 0 . s e lu a v d e t c a r t b u s - ld e fi e h t e t a ic d in ) t e n ( s K t o t L / B G A s K L d n a ) t e n ( B G A s K L - 21 - G s o I n i t o 6 0 5 8 3 0 2 A f o P a v 1 3 1 5 1 8 9 io n P a d o 0 2 0 . 2 0 . 4 0 . 5 0 . 5 0 . 5 0 . 3 0 . 2 a l u e s t c a r f y it s o in m lu d n a b s K f o n o is r a p m o C . 3 le b a T . v d e t c a r t b u s - d l e fi e h t e t a c i d n i ) t e n ( e c n e u q e s r e t s u l c t h g i r b d n a ) t e n ( n a e M - . e t o N ) y d u t s s i h T ( n o i t a v r e s b O r e t s u l c t h g i r B r e t s u l c t h g i r B ) t e n ( e c n e u q e s e c n e u q e s ) t e n ( n a e M n a e M ) ] r y [ e g a ( g o l 0 2 . 0 0 3 . 0 7 0 . 0 ± 4 2 . 0 6 0 . 0 + 7 0 . 0 - 5 2 . 0 0 0 . 8 0 5 . 0 2 6 . 0 0 1 . 0 ± 8 3 . 0 1 1 . 0 ± 3 5 . 0 5 2 . 8 7 6 . 0 1 8 . 0 1 1 . 0 ± 7 4 . 0 1 1 . 0 ± 4 5 . 0 0 5 . 8 0 7 . 0 8 7 . 0 3 1 . 0 ± 2 5 . 0 4 1 . 0 + 3 1 . 0 - 7 5 . 0 5 7 . 8 5 5 . 0 0 6 . 0 9 0 . 0 ± 8 3 . 0 1 1 . 0 ± 2 5 . 0 0 0 . 9 0 3 . 0 3 3 . 0 8 0 . 0 ± 7 2 . 0 9 0 . 0 ± 1 3 . 0 5 2 . 9 5 1 . 0 0 2 . 0 5 1 . 0 ± 1 2 . 0 9 1 . 0 ± 2 3 . 0 0 5 . 9 - 22 -\",\n \"pages\": [\n 16,\n 18,\n 20,\n 21,\n 22\n ]\n }\n]"}}},{"rowIdx":73,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...777..109Z"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1309.4956.pdf"},"content":{"kind":"string","value":"\nSYNCHROTRON LIGHTCURVES OF BLAZARS IN A TIME-DEPENDENT SYNCHROTRON-SELF COMPTON COOLING SCENARIO\nMichael Zacharias & Reinhard Schlickeiser\nInstitut fur Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universitat Bochum, 44780 Bochum, Germany (Received; Revised; Accepted) Draft version September 7, 2021\nABSTRACT\nBlazars emit non-thermal radiation in all frequency bands from radio to γ -rays. Additionally, they often exhibit rapid flaring events at all frequencies with doubling time scale of the TeV and X-ray flux on the order of minutes, and such rapid flaring events are hard to explain theoretically. We explore the effect of the synchrotron-self Compton cooling, which is inherently time-dependent, leading to a rapid cooling of the electrons. Having discussed intensively the resulting effects of this cooling scenario on the spectral energy distribution of blazars in previous papers, the effects of the time-dependent approach on the synchrotron lightcurve are investigated here. Taking into account the retardation due to the finite size of the source and the source geometry, we show that the time-dependent synchrotronself Compton (SSC) cooling still has profound effects on the lightcurve compared to the usual linear (synchrotron and external Compton) cooling terms. This is most obvious if the SSC cooling takes longer than the light crossing time scale. Then in most frequency bands the variability time scale is up to an order of magnitude shorter than under linear cooling conditions. This is yet another strong indication that the time-dependent approach should be taken into account for modeling blazar flares from compact emission regions.\nSubject headings: radiation mechanisms: non-thermal - BL Lacertae objects: general - gamma-rays: theory\n1. INTRODUCTION\nBlazars, a subclass of active galactic nuclei in the accepted unification scheme of Urry & Padovani (1995), are characterized by a broad non-thermal spectrum exhibiting two characteristic humps and stretching from radio to γ -ray frequencies. In leptonic models the lowenergy component is attributed to synchrotron radiation of highly relativistic electrons, while the high-energy component is inverse Compton emission of the same electron population (for recent reviews see Bottcher 2007, 2012). Several target photon fields are relevant for the inverse Compton process.\nJones et al. (1974) proposed the synchrotron radiation emitted by the relativistic electrons as the target photon field, which is then up-scattered by the same electrons, the so-called synchrotron-self Compton (SSC) process.\nThe vicinity of an active galactic nucleus harbors also additional strong external (to the jet) photon fields, which can potentially contribute in the form of so-called external Compton radiation to the high-energy component of blazars. Such external fields could come from the accretion disk (Dermer & Schlickeiser 1993), the broad line region (Sikora et al. 1994) or the dusty torus (Blazejowski et al. 2000, Arbeiter et al. 2002). These external fields are usually preferred over the SSC, if the highenergy component dominates the synchrotron component in the spectral energy distribution (SED) of blazars.\nIt is well established that blazars are far from being steady sources. They exhibit strong flares in all frequency bands, which can in some cases outshine even the brightest galactic sources. The brightest γ -ray flare ever detected is from 3C 454.3, reported by Vercellone et al.\n(2011), reaching a γ -ray flux of F γ = (6 . 8 ± 1 . 0) × 10 -5 photons cm -2 s -1 , which is six times higher than the Vela pulsar. Additionally, blazars also exhibit very rapid flares with doubling time scales on the order of minutes as in the case of PKS 2155-304 (Aharonian et al. 2007) or PKS 1222+216 (Tavecchio et al. 2011) in the TeV regime, or Mrk 421 in the X-rays (Cui 2004).\nSuch rapid flares are theoretically challenging, since typical cooling time scales of the radiating electrons are considerably longer. Several models have thus been invoked to explain these rapid flares, such as the jet-in-a-jet model (Giannios et al. 2009), the similar minijets-in-a-jet model (Biteau & Giebels 2012, Giannios 2013), magnetocentrifugal acceleration of beams of particles (Ghisellini et al. 2009a), a star traversing the jet (Barkov et al. 2012), and others. Quite common in all these models is the assumption of an emission blob being smaller than the jet cross-section and moving much faster than the surrounding relativistic jet material. This gives rise to a very short light-crossing time scale, which is usually equaled to the variability time scale.\nIn many theoretical investigations, as the ones cited above, and in most modeling attempts (e.g. Ghisellini et al. 2009b) the electron distribution is assumed to be stationary. This eases the computational effort, of course, and might be suitable for steady sources or those varying over a long time scale. However, it is certainly not justified for rapid flares as in PKS 2155-304 or PKS 1222+216. The time-dependence of the relativistic electron distribution function has important effects on the resulting SED, as is demonstrated in a recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (hereafter SBM); Zacharias & Schlickeiser 2010, 2012a (hereafter ZSa), 2012b (hereafter ZSb)).\n\n\n
Figure 1. Sketch of the situation: The light of the slice at position l (with volume d V ( l ) = A ( l ) d l ) is received by the observer at time t = t em + l/c .
\n\nRelativistic electrons in a relativistically moving emission blob along the jet of the active galactic nucleus lose energy by emitting synchrotron radiation. These synchrotron photons are a prime target for the same electrons to inverse Compton scatter them to higher energies. This is the SSC process, as mentioned above, which is an additional energy loss process for the electrons. This in turn implies that the subsequently emitted synchrotron photons are less energetic, and so will be the SSC photons. Thus, this results in a decreased efficiency of the SSC process and in a decreased efficiency of the SSC energy loss process with respect to time. Consequently, even if the SSC process dominates initially the electron losses, eventually the time-independent loss processes such as synchrotron and external Compton losses dominate the loss rate. Schlickeiser (2009), as well as Zacharias & Schlickeiser (2010) were able to show that the time-dependent treatment of the SSC losses leads to a much faster electron cooling compared to the steadystate approach.\nTherefore, it is interesting to discuss the effects of this rapid cooling on blazar lightcurves, where the variability can be displayed in an obvious way.\nIt is the purpose of this paper to highlight the different effects of the linear and the time-dependent (nonlinear) SSC cooling on the synchrotron lightcurves. To keep the problem simple and analytically tractable, we utilize only the retardation effect due to the finite size of the emission region, and the geometry of the source. This will be discussed in section 2, where we will derive the necessary formula to calculate the lightcurve from the synchrotron intensity. The latter was already calculated by SBM, and we will summarize their results in section 3 for the sake of completeness. We will then use the derived formula from section 2 to calculate the resulting lightcurves in sections 4 and 5. We will discuss the results in section 6 and conclude in section 7.\nThe more involved calculations of the inverse Compton lightcurves will be discussed in a future publication.\n2. GEOMETRY OF THE SITUATION\nWe assume a spherical, uniform radiation zone in the jet as depicted in figure 1.\nFor negligible retardation the received monochromatic intensity at intrinsic time t em is I ( t em , /epsilon1 ), where /epsilon1 is the intrinsic energy of the photon. Since, however, the source\nhas a finite size, photons emitted at the back of the source will arrive at the observer at a later time ∆ t = 2 R/c than the photons emitted at the front, with R being the radius of the spherical source and c = 3 · 10 10 cm / s the speed of light.\nWe include this retardation effect, but assume that the source is (i) spatially homogeneous, and (ii) optically thin. For optically thin sources all photons can leave the emission region without further spatial diffusion (Eichmann et al. 2010). Then the received intensity is just a function of the distance l of the production site from the front. Using a similar approach as Chiaberge & Ghisellini (1999), we cut the source into slices of length d l , as shown in figure 1. The received intensity of each slice is\nd I ( t -l/c, l, /epsilon1 ) = I ( t -l/c, /epsilon1 ) d V ( l ) V H [ t -l/c ] . (1)\nHere, t is the time of the observer, which equals t em for l = 0 (the front of the source). The Heaviside function H [ x ] displays the fact that light from a specific slice can only be detected after it has crossed the distance l to the front of the source.\nThe fraction d V ( l ) /V is a geometrical weight function, which is defined in such a way that the integral over d V ( l ) /V equals unity. Since in a spherical source each slice has a different volume than the other slices, its contribution depends on its position in the source. The volume of the slice is given by d V ( l ) = A ( l ) d l , where A ( l ) = π (2 Rl -l 2 ) is the cross section of the slice at position l . The geometrical weight function then becomes\nd V ( l ) V = π (2 Rl -l 2 ) 4 3 πR 3 d l = 3 R [ l 2 R -( l 2 R ) 2 ] d l . (2)\nThe complete received monochromatic lightcurve L ( t, /epsilon1 ) then equals the sum over the contribution from all slices:\nL ( t, /epsilon1 ) = ∫ d I ( t -l/c, l, /epsilon1 ) = 2 R ∫ 0 I ( t -l/c, /epsilon1 ) H [ t -l/c ] 3 R [ l 2 R -( l 2 R ) 2 ] d l = 6 1 ∫ 0 I ( t -λ 0 λ, /epsilon1 )( λ -λ 2 ) H [ t -λ 0 λ ] d λ , (3)\nafter an obvious substitution. Here we introduced the light-crossing time scale λ 0 = 2 R/c .\nWe note that equation (1) is general as long as the assumptions (i) and (ii) are satisfied. Thus, it is not limited to spherical geometries, and for example cylindrical sources could also be chosen. In fact, a cylindrical geometry would lead to a simpler form of the geometrical weight function. However, the assumption of isotropy for the electron distribution and the radiation fields (see below) would not be valid any more. 1\n\n1 For example, Chiaberge & Ghisellini (1999) chose a cubed geometry.\n\n3. SYNCHROTRON INTENSITY\nIn this section we summarize results previously obtained (SBM, ZSa, ZSb) in order to introduce the relevant functions and parameters.\nThe isotropic, optically thin synchrotron intensity from relativistic electrons with the volume-averaged differential density n ( γ, t ) is given by\nI syn ( /epsilon1, t ) = R 4 π ∞ ∫ 0 n ( γ, t ) P syn ( /epsilon1, γ ) d γ , (4)\nwith\nrelative strength of external to synchrotron cooling, and has profound consequences for the SED, as we showed in Zacharias & Schlickeiser (2012b). We note that it is less important for the discussion of synchrotron lightcurves and only introduced for the sake of completeness.\nMore importantly, as one can see from equation (9), is the fact that the SSC cooling term by its dependence on n ( γ, t ) is time-dependent, which means that its strength decreases over time. Consequently, even if the SSC cooling dominates the total cooling term initially, after some time the SSC cooling will become weaker than the linear cooling, and thus the synchrotron or external Compton cooling will dominate for later times. Obviously, if the linear cooling terms are stronger than the SSC cooling at the beginning, they will be stronger for all times.\nThis can be further quantified by the injection parameter\nα = √ A 0 q 0 D 0 (1 + l ec ) γ 0 . (11)\nIt is defined in such a way that\nα 2 = | ˙ γ ( t em = 0) | ssc | ˙ γ | syn + | ˙ γ | ec . (12)\nAs a consequence (ZSa and ZSb) the Compton dominance in the SED depends on α 2 , at least in the Thomson limit. This demonstrates the importance of this parameter, which can also be expressed as\nα = 46 γ 4 N 1 / 2 50 R 15 (1 + l ec ) 1 / 2 , (13)\nwhere we scale the total number of electrons N = 10 50 N 50 , and the initial electron Lorentz factor γ 0 = 10 4 γ 4 . Obviously, α increases for increasing γ 0 and N , and decreases for increasing R and l ec . If α /greatermuch 1 the cooling will initially be dominated by the SSC cooling, while for α /lessmuch 1 the cooling is dominated by the linear terms for all times.\nWe note that both inverse Compton cooling terms operate in the Thomson limit. In the Klein-Nishina limit the efficiencies of both cooling terms are much reduced, and become unimportant compared to the synchrotron cooling. This resembles the case α /lessmuch 1 and l ec /lessmuch 1 and is, therefore, covered by our approach.\nThe differential equation (7) with the loss term (9) and the source term (8) has been solved by SBM. For α /lessmuch 1 (i.e. negligible SSC-losses) they obtained\nn ( γ, t em ) = q 0 δ ( γ -γ 0 1 + D 0 (1 + l ec ) γ 0 t em ) , (14)\nwhich is, indeed, a linear cooling solution. For α /greatermuch 1 (i.e. initially dominating SSC-losses) SBM found\nn ( γ, t em < t c ) = q 0 H [ t c -t em ] × δ ( γ -γ 0 (1 + 3 α 2 D 0 (1 + l ec ) γ 0 t em ) 1 / 3 ) , (15)\nyielding a nonlinear dependence of γ on time. For later times the electron density approaches\nn ( γ, t em > t c ) = q 0 H [ t em -t c ]\nP syn ( /epsilon1, γ ) = P 0 /epsilon1 γ 2 CS ( 2 /epsilon1 3 /epsilon1 0 γ 2 ) (5)\nbeing the synchrotron power of a single electron in a large-scale random magnetic field of constant strength B = b Gauss (Crusius & Schlickeiser 1988). Here P 0 = 2 · 10 24 erg -1 s -1 , and /epsilon1 0 = 1 . 9 · 10 -20 b erg. The function CS ( x ) is well approximated by\nCS ( x ) ≈ a 0 x -2 / 3 e -x , (6)\nwith a 0 = 1 . 151275.\nThe differential relativistic electron density can be calculated from the kinetic equation (Kardashev 1962)\n∂n ( γ, t em ) ∂t -∂ ∂γ [ | ˙ γ | n ( γ, t em )] = S ( γ, t em ) , (7)\nwhere | ˙ γ | is the electron energy loss term, and S ( γ, t em ) is the source term.\nFor demonstration purposes and ease of calculation we use a relatively simple source term\nS ( γ, t em ) = q 0 δ ( γ -γ 0 ) δ ( t em ) , (8)\nthat is a single injection of monochromatic electrons with the injection Lorentz factor γ 0 and the electron density q 0 .\nIn the scenario depicted here we consider electron losses via the synchrotron, external Compton and synchrotron-self Compton channels. Since the latter depends on the produced synchrotron radiation, and thus directly on the electron distribution, the kinetic equation becomes non-linear (Schlickeiser 2009). The total electron loss term is given by\n| ˙ γ | = | ˙ γ | syn + | ˙ γ | ec + | ˙ γ ( t em ) | ssc = D 0 (1 + l ec ) γ 2 + A 0 γ 2 ∞ ∫ 0 γ 2 n ( γ, t em ) d γ . (9)\nThe parameters are D 0 = 1 . 3 · 10 -9 b 2 s -1 , and A 0 = 1 . 2 · 10 -18 R 15 b 2 cm 3 s -1 , where we scaled the radius of the source as R = 10 15 R 15 cm.\nWe define\nl ec = | ˙ γ | ec | ˙ γ | syn = 4Γ 2 b 3 u ' ec u B . (10)\nwhere Γ b is the Lorentz factor of the plasma blob, u ' ec is the isotropic energy density of the external radiation field in the frame of the host galaxy, and u B is the energy density of the magnetic field. This parameter describes the\n× δ ( γ -γ 0 1+2 α 3 3 α 2 + D 0 (1 + l ec ) γ 0 t em ) , (16)\nwhich is a modified linear cooling solution. The transition time is defined as\nt c = α 3 -1 3 α 2 D 0 (1 + l ec ) γ 0 . (17)\nThe intensity (4) for both cases of α has also been calculated by SBM. For α /lessmuch 1 they obtained with equation (14)\nI syn ( t em , /epsilon1 ) = I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t em t syn ) 2 / 3 × e -/epsilon1 E 0 ( 1+ tem tsyn ) 2 . (18)\nFor α /greatermuch 1 with equations (15) and (16)\nI syn ( t em < t c , /epsilon1 ) = I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + 3 α 2 t syn t em ) 2 / 9 × e -/epsilon1 E 0 ( 1+ 3 α 2 tsyn t em ) 2 / 3 , (19)\nand\nI syn ( t em > t c , /epsilon1 ) = I 0 ( /epsilon1 E 0 ) 1 / 3 ( α g + t em t syn ) 2 / 3 × e -/epsilon1 E 0 ( α g + tem tsyn ) 2 . (20)\nHere we used the definitions I 0 = 3 a 0 RP 0 q 0 /epsilon1 0 / (8 π ), t syn = 1 / ( D 0 (1 + l ec ) γ 0 ), E 0 = 3 /epsilon1 0 γ 2 0 / 2, and α g = (1 + 2 α 3 ) / (3 α 2 ).\nThese intensities are equal to a monochromatic lightcurve, where the retardation and, thus, the source's finite size have not been taken into account. Below, we will refer to them as the 'unretarded' lightcurves.\nNow, we have collected all necessary ingredients to calculate the retarded synchrotron lightcurves, which we present in the following sections.\n4. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING LINEAR COOLING\nUsing equation (18) in equation (3) we obtain the retarded lightcurve for the case α /lessmuch 1:\nL ( t, /epsilon1 ) = 6 I 0 ( /epsilon1 E 0 ) 1 / 3 1 ∫ 0 ( 1 + t -λ 0 λ t syn ) 2 / 3 × e -/epsilon1 E 0 ( 1+ t -λ 0 λ tsyn ) 2 λ -λ 2 H [ t -λ 0 λ ] d λ . (21)\nThe integral (21) can be solved in terms of several incomplete Gamma-functions. However, this would not give many insights. Instead, we will use meaningful approximations for the integral in three time domains. These domains can later be glued together to give a continuous analytic result.\n( )\nFirst of all, we define two characteristic time scales of the unretarded lightcurve. They can later be connected to the light-crossing time scale, yielding some information about the resulting retarded lightcurve. The first\none is the local maximum of the unretarded lightcurve, which is:\nt 1 ( /epsilon1 ) = t syn ( √ E 0 3 /epsilon1 -1 ) . (22)\nThis expression is negative for /epsilon1 > E 0 / 3, indicating that for such energies there is no local maximum. If t 1 ( /epsilon1 ) > λ 0 the variability will mostly take place for times later than the light-crossing time scale. Solving the resulting inequality for /epsilon1 , results in\n/epsilon1 < /epsilon1 1 = E 0 3 ( 1 + λ 0 t syn ) 2 < E 0 3 . (23)\nThis equation implies that for energies /epsilon1 < /epsilon1 1 the variability due to the flare will be longer than the lightcrossing time scale. Hence, we expect the global maximum of the lightcurve to occur later than λ 0 , and thus be unaffected by the retardation.\nThe second characteristic time scale is related to the argument of the exponential in the unretarded lightcurve A = /epsilon1 E 0 (1 + t em /t syn ) 2 . As soon as t em ≥ t syn the unretarded lightcurve exponentially decays, which should also be visible in the retarded lightcurve. Since, however, A ≈ /epsilon1 E 0 for t em /lessmuch t syn , we set\nA = /epsilon1 E 0 ( 1 + t em t syn ) 2 = /epsilon1 E 0 + A ∗ ( /epsilon1, t em ) , (24)\nwith\nA ∗ ( /epsilon1, t em ) = /epsilon1 E 0 [ ( 1 + t em t syn ) 2 -1 ] . (25)\nOnce A ∗ ( /epsilon1, t em ) is larger than unity the unretarded lightcurve will exponentially decay. Thus, we obtain the second characteristic time scale t 2 ( /epsilon1 ) by A ( /epsilon1, t 2 ( /epsilon1 )) = 1, yielding\nt 2 ( /epsilon1 ) = t syn ( √ 1 + E 0 /epsilon1 -1 ) . (26)\nUnlike t 1 ( /epsilon1 ), the second characteristic time scale exhibits no restrictions by /epsilon1 . Obviously, t 1 ( /epsilon1 ) < t 2 ( /epsilon1 ). For t 2 ( /epsilon1 ) > λ 0 the exponential will become important only after the light-crossing time scale. Solving the inequality for /epsilon1 we obtain\nWe can now begin with the actual calculation of the retarded lightcurve. The simplest case is obviously for t > λ 0 , since in this case the retarded lightcurve should be the same as the unretarded lightcurve. This is due to the fact that the retardation is not important for time scales much longer than λ 0 . Inspecting the difference t -λ 0 λ , we see that λ 0 λ can be at most equal to λ 0 . Thus, for t /greatermuch λ 0 we can approximate t -λ 0 λ ≈ t . Hence,\n/epsilon1 < /epsilon1 2 = E 0 ( 1 + λ 0 t syn ) 2 -1 . (27)\nL ( t > λ 0 , /epsilon1 ) ≈ 6 I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t t syn ) 2 / 3\n× e -/epsilon1 E 0 ( 1+ t tsyn ) 2 1 ∫ 0 ( λ -λ 2 ) d λ = I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 , (28)\nwhich, indeed, equals the unretarded lightcurve.\nThe other rather simple case is for t < λ 0 with the further requirement that t < t 1 , 2 ( /epsilon1 ) (the subscript refers to both t 1 and t 2 ). The latter implies that the unretarded lightcurves were neither variable nor have they decayed already. Then in eq. (21) the terms ( t -λ 0 λ ) /t syn can be neglected compared to unity, yielding\nL ( t < λ 0 , /epsilon1 ) ≈ 6 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 t/λ 0 ∫ 0 ( λ -λ 2 ) d λ = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 [ 1 -2 3 t λ 0 ] . (29)\nFor times below the light-crossing time scale and below the variability time scale of the unretarded lightcurve the retarded lightcurve increases rapidly L ∝ t 2 .\nFor intermediate times the calculation is quite involved, and the details can be found in appendix A. We obtain\nL ( t 1 , 2 < t < λ 0 , /epsilon1 ) = 6 I 0 ( /epsilon1 E 0 ) 1 / 3 × t/λ 0 ∫ 0 ( 1 + t -λ 0 λ t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t -λ 0 λ tsyn ) 2 ( λ -λ 2 ) d λ 2 / 3\n≈ 3 I 0 ( /epsilon1 E 0 ) -e -/epsilon1 E 0 t 2 syn λ 2 0 ( t t syn )[ 1 -t λ 0 ] . (30)\nWe note that the exact form of the intermediate regime is not so important, since it will be glued to the approximation (29) at t ≈ t 2 . The most important result is the linear increase of the the lightcurve (30), which leads to a break at t 2 in the retarded lightcurve. However, if t 1 , 2 ( /epsilon1 ) > λ 0 the intermediate part does not play a role, and the lightcurve breaks immediately at t = λ 0 from the initial t 2 -dependence to the time dependence given by equation (28).\nDepending on the synchrotron photon energy /epsilon1 , we can now construct the lightcurves from the three approximations (28) - (30). We obtain two cases, divided in additional sub-cases.\nBeginning with /epsilon1 < E 0 / 3, we get:\nL ( t, /epsilon1 < /epsilon1 1 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 , (31)\nL ( t, /epsilon1 1 < /epsilon1 < /epsilon1 2 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 ( 1 + t t 2 ) 5 / 3\n× ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 , (32)\nL ( t, /epsilon1 2 < /epsilon1 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 ( 1 + t 2 t 2 ) 5 / 3 × ( 1 + t t syn ) 2 / 3 [ 1 -t λ 0 ] . (33)\nFor /epsilon1 > E 0 / 3 the solutions become:\nL ( t, E 0 / 3 < /epsilon1 < /epsilon1 2 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 , (34)\nL ( t, /epsilon1 2 < /epsilon1 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 1 + t 2 t 2 [ 1 -t λ 0 ] . (35)\nThe lightcurves (33) and (35) cut off at t = λ 0 . Obviously, light from the back reaches the observer only at later times, causing the radiation to be visible on longer time scales than implied by the unretarded lightcurve.\nThe analytical results (31) - (35) are plotted along with a numerical integration of equation (21) in Figure 2 for two cases of γ 0 . For comparison, we also show the unretarded lightcurve.\nThe first obvious result is that the retarded synchrotron lightcurve increases rapidly as long as t < λ 0 . Afterwards the retarded lightcurve behaves as the unretarded one, which is reasonable, as we discussed above.\nThe other points mentioned earlier are also quite obvious. Even though the unretarded lightcurve for very high energies cuts off long before the light-crossing time scale, the retarded lightcurves are extended until λ 0 . The break in the lightcurve in the intermediate time regime is also evident. However, as discussed above, the low energetic cases, where the variability time scales are much longer than the light-crossing time scale, do not exhibit this break.\nAs one can see, the analytical result matches the numerical integration rather well, which is reassuring and validates a posteriori our approximations. However, there is one caveat: The distinction of cases by t 2 and /epsilon1 2 is rather sharp (esp. equations (33) and (35)). This is obvious in the left plot of Figure 2 in the analytical curve for /epsilon1 = 10 E 0 , which cuts off at t = λ 0 . On the other hand, the numerical curve in this case decays exponentially. The distinction of the cases divided by /epsilon1 2 is, therefore, not as strict as implied by the analytical result. It is a more gradual transition, which is, however, difficult to implement in one equation.\nThe problem is probably due to the rather artificial definition of t 2 , which is also indicated by the fact that the break for the high-energy lightcurves is better placed at 2 t 2 instead of t 2 .\n\n\n\n\n\n
Figure 2. Unretarded (full), as well as numerical (dashed) and analytical (dotted) retarded lightcurve for α /greatermuch 1 and two cases of γ 0 over a logarithmic time-axis. The values of /epsilon1 in the legend are given in units of E 0 . The curves are normalized with I 0 and we set b = 1.
\n\n5. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING INITIAL SSC COOLING\nFor the case α /greatermuch 1 we use equations (19) and (20) in equation (3) to obtain the retarded lightcurve\nL 1 ( t, /epsilon1 ) = 6 I 0 /epsilon1 E 0 1 / 3 1 1 + 3 α 2 t syn ( t -λ 0 λ ) 2 / 9\n( ) ∫ 0 ( ) × e -/epsilon1 E 0 ( 1+ 3 α 2 tsyn ( t -λ 0 λ ) ) 2 / 3 ( λ -λ 2 ) × H [ t -λ 0 λ ] H [ t c -( t -λ 0 λ )] d λ , (36)\nL 2 ( t, /epsilon1 ) = 6 I 0 ( /epsilon1 E 0 ) 1 / 3 1 ∫ 0 ( α g + t -λ 0 λ t syn ) 2 / 3\n× e -/epsilon1 E 0 ( α g + t -λ 0 λ tsyn ) 2 ( λ -λ 2 ) × H [ t -λ 0 λ ] H [( t -λ 0 λ ) -t c ] d λ . (37)\nFor t c < t < t c + λ 0 both L 1 and L 2 contribute to the emitted lightcurve, which differs from the strict division of the unretarded lightcurves (19) and (20). This is, again, an effect of the retardation: Even if light received from the front of the source is from electrons already cooling in the linear regime ( t em > t c ), the light received from the back of the source is still from electrons cooling in the nonlinear regime ( t em < t c ). If t c < λ 0 this period can be quite extended.\nAlthough there are several sub-cases to consider in the analytical calculation, we can use the same approximation for the integrals (36) and (37), as we used to obtain equations (28) - (30). It is therefore unnecessary to repeat them in detail. Instead, we will summarize the results in the most compact form possible, where the sub-cases are combined in such a way that the resulting lightcurve is continuous.\nThe characteristic time scales t 3 ( /epsilon1 ) and t 4 ( /epsilon1 ) are obtained by the same arguments as t 1 ( /epsilon1 ) and t 2 ( /epsilon1 ), giving\nt 3 ( /epsilon1 ) = t syn 3 α 2 [ ( E 0 3 /epsilon1 ) 3 / 2 -1 ] , (38)\nt 4 ( /epsilon1 ) = t syn 3 α 2 [ ( 1 + E 0 /epsilon1 ) 3 / 2 -1 ] . (39)\nFor t 3 , 4 ( /epsilon1 ) > λ 0 we find\n/epsilon1 < /epsilon1 3 = E 0 3 ( 1 + 3 α 2 λ 0 t syn ) 2 / 3 , (40)\nwhile for t 3 , 4 ( /epsilon1 ) > t c we obtain\n/epsilon1 < /epsilon1 4 = E 0 ( 1 + 3 α 2 λ 0 t syn ) 2 / 3 -1 , (41)\n/epsilon1 < /epsilon1 c 3 = E 0 3 α 2 , (42)\n/epsilon1 < /epsilon1 c 4 = E 0 α 2 -1 , (43)\nrespectively.\nWith these definitions, we sum up the results of the analytical calculation.\nWe begin with the case t c < λ 0 :\n2\nL ( t, /epsilon1 < /epsilon1 3 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( α g + t tsyn ) 2 , (44)\nL ( t, /epsilon1 3 < /epsilon1 < /epsilon1 c 3 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( α g + t tsyn ) 2 , (45)\nL ( t, /epsilon1 c 3 < /epsilon1 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2\n× ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( α g + t tsyn ) 2 , (46)\nL ( t, E 0 / 3 < /epsilon1 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 1 + t 2 t 4 [ 1 -t λ 0 ] . (47)\nFor t c > λ 0 the analytical calculation yields for /epsilon1 < E 0 / 3\nL ( t < t c , /epsilon1 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 9 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 / 3 (48)\nL ( t > t c , /epsilon1 < E 0 / 3) = I 0 ( /epsilon1 E 0 ) 1 / 3 × ( α g + t t syn ) 2 / 3 e -/epsilon1 E 0 ( α g + t tsyn ) 2 , (49)\nwhich is the only case where L must be divided. For /epsilon1 > E 0 / 3 we obtain\nL ( t, E 0 / 3 < /epsilon1 < /epsilon1 4 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 9 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 / 3 , (50)\nL ( t, E 0 / 3 < /epsilon1 4 < /epsilon1 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 1 + t 2 t 4 [ 1 -t λ 0 ] . (51)\nIn Figure 3 we compare the analytical results with the numerical results, and achieve quite good agreement. The unretarded lightcurve is shown again for comparison.\nSince the basic properties of the plot are the same as in Figure 2, we do not need to repeat them here. The problem with t 4 and /epsilon1 4 , mentioned in the discussion for Figure 2, is evident here, again.\n6. DISCUSSION\nIn Figures 2 and 3 we show lightcurves in a logarithmic plot, which has the advantage of having several cases in one plot. This makes it much easier to compare variability aspects which occur on very different time scales. Our discussion will focus on these logarithmic plots. On the other hand, lightcurves are commonly displayed in a linear plot, which highlights the behavior of lightcurves around their respective maxima. We present such linear plots in Figure 4. The results are completely compatible.\nComparing Figures 2 and 3 one can see that there are some points, where the results are similar, and some other points, which are remarkably different.\nFirst of all, we note that the 'variability time scale' of any given lightcurve is determined by its global maximum. Thus, the minimal variability time scale, which is\npossible at all, is given by the light-crossing time scale, since the source is evenly contributing to the radiative output. If the source only partially radiates, the variability time scale can be much lower (Eichmann et al. 2010). The rising phase until λ 0 is dominated by the source geometry, giving a t 2 -dependence up to the break times t 2 ( /epsilon1 ) for α /lessmuch 1 and t 4 ( /epsilon1 ) for α /greatermuch 1, respectively. If t 2 , 4 ( /epsilon1 ) < λ 0 , the lightcurve exhibits a break to a t 1 -dependence. Otherwise the spectrum breaks directly to the unretarded lightcurve at λ 0 . 2\nSecondly, for larger initial electron energies γ 0 the variability time scale is much reduced compared to lower initial electron energies. Hence, in the low-energetic frequency bands the variability time scale shifts closer to λ 0 for larger γ 0 . Thus, one can get information about the initial electron energy by observing the peak times of different frequency bands.\nThe plots for the high-energetic cases ( γ 0 = 10 5 ) look quite similar in both cases of α , since t c is smaller than λ 0 , and the lightcurves are the same for t > t c . However, they can be distinguished by the high-energetic frequency bands. Both are less luminous for α /greatermuch 1 compared to α /lessmuch 1, because the synchrotron SED exhibits a broken power-law for α /greatermuch 1, leading to a decreased flux for high energies compared to the α /lessmuch 1 case (cf. SBM). Additionally, the break in the lightcurve from the quadratic time-dependence to the linear timedependence takes place a factor 3 α 2 earlier in the α /greatermuch 1 case than for α /lessmuch 1, since the unretarded lightcurve cuts off much earlier for α /greatermuch 1 than for α /lessmuch 1. Thus, the sum over all unretarded lightcurves of each slice (that is the retarded lightcurve) for α /greatermuch 1 must be less luminous and increase less strongly than for α /lessmuch 1.\nThe low-energetic cases ( γ 0 = 10 3 ) differ strongly for α larger and smaller than unity, since t c is larger than λ 0 . The features, which are plainly visible in the unretarded lightcurve, are thus also visible in the retarded lightcurve. The lightcurve for /epsilon1 = 10 E 0 cuts off in both cases at around λ 0 . However, for α /greatermuch 1 the break is clearly visible in the lightcurve, which is due to the faster cooling of the electrons in this case of α . Similarly, the lightcurve for /epsilon1 = E 0 cuts off for α /greatermuch 1 at λ 0 because of the faster cooling, and for α /lessmuch 1 the lightcurve shows a rather broad exponential decay. 3 The lightcurves for /epsilon1 = 10 -2 E 0 can be distinguished quite well, since the lightcurve for α /lessmuch 1 shows a rapid increase to the narrow maximum, while the light curve for α /greatermuch 1 exhibits a broad and flat maximum, which covers almost two orders of magnitude in time. As stated above, because of the broken power-law in the SED for α /greatermuch 1 the maximum of the SED is attained at /epsilon1 = E 0 /α 2 , which is in our example the lightcurve for /epsilon1 = 10 -2 E 0 . This explains the broad maximum, and also why the higher energies are again less luminous compared to the α /lessmuch 1 case. In the lightcurves for /epsilon1 = 10 -4 E 0 there is only a very slight difference, since the rising part after λ 0 sets in earlier for α /greatermuch 1 than for α /lessmuch 1. However, the increase is quite\n2 The powers of t depend sensitively on the chosen geometry. E.g. for a cylindrical source the power is reduced by unity giving a t 1 - and a flat t 0 -dependence.\n\n\n\n\n\n
Figure 3. Unretarded (full), as well as numerical (dashed) and analytical (dotted) retarded lightcurve for α /lessmuch 1 and two cases of γ 0 over a logarithmic time-axis. The values of /epsilon1 in the legend are given in units of E 0 . The curves are normalized with I 0 and we set b = 1.
\n\nsmall until t c and detailed observations are needed to distinguish the models.\nObviously, for smaller emission regions the lightcrossing time scale λ 0 is reduced and the effects of the time-dependent cooling will be even more pronounced with very short variability time scales. Additionally, a smaller emission region leads to a larger α according to equation (13). Thus, the time-dependent SSC cooling is quite important for models which assume a small emission region to explain the rapid variability in blazars, like those cited in the introduction.\nWe numerically checked if our results are also valid for different injection scenarios, such as a power-law, and obtained qualitatively similar results as one can see in Figure 5 of appendix B. Thus, we are confident that the discussion presented here is robust.\n6.1. Caveats of the approach\nOf course, our approach is simplified, leaving aside several, possibly important aspects.\nAs stated in section 2, we assume that the source is spatially homogeneous. Additionally, we neglect the 'internal' retardation of the inverse Compton processes. The time, a photon travels before it is inverse Compton scattered, should on average be much less than λ 0 . Thus, the effect on the light curve is small, apart from a short delay of the SSC light curve (which we do not calculate in this paper). However, cooling might be affected, since the SSC cooling should be similarly delayed as the SSC light curve. On the other hand, as shown in Schlickeiser (2009) and Zacharias & Schlickeiser (2010), the SSC cooling is orders of magnitude quicker than the synchrotron and external Compton cooling, which should more than compensate the small retardation delay.\nWe do not expect a delay effect for the external Compton scattering, since they are present all the time and are more or less homogeneously distributed (ZSb, Sokolov & Marscher 2005).\nWe also do not discuss the acceleration of the electrons. This might have a significant impact on the light curve, since the variability is governed by the longest time scale (in our case just λ 0 and t syn , with an influence by t c for α /greatermuch 1). If the acceleration takes particularly long the\neffects due to retardation or cooling would be washed out. If the acceleration takes only a small amount of time, it will certainly influence the rising phase of the light curve, but its effect on the main part of the variability will not be significant. This argument might not hold for very small emission regions.\nOn the other hand, the acceleration time scale is only important, if the acceleration and radiation zone are spatially and temporally coincident. This is still under debate, and only recently these conditions are incorporated in numerical studies (e.g. Weidinger et al. 2010; Weidinger & Spanier 2010). Thus, we follow the assumption or simplification that acceleration and radiation are (especially) temporally separated. Then, the acceleration time scale does not influence the resulting light curve.\nChiaberge & Ghisellini (1999), and also e.g. Kataoka et al. (2000) or Li & Kusunose (2000), used similar assumptions in their numerical analysis. In fact, most theoretical investigations use numerical schemes with the advantage of employing more and more realistic scenarios, such as time-dependency (Bottcher & Chiang, 2002), inclusion of shock acceleration (Sokolov et al., 2004), hydrodynamic simulations (Mimica et al., 2004; Cabrera et al., 2013), and multizone models that incorporate the full retardation of all processes (Graff et al., 2008, Joshi & Bottcher 2011). In our analytical discussion we are for obvious reason not able to include all these details. That is why we focus on the details of the time-dependency, showing analytically that time-dependent effects, especially from SSC, are very important for rapid flares.\n7. CONCLUSIONS\nIn this paper we introduced our approach to calculate theoretical synchrotron lightcurves for flaring blazars, where the radiating relativistic electrons are cooled by the combined synchrotron, external Compton and timedependent SSC mechanisms. This complements the recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (SBM); Zacharias & Schlickeiser 2010, 2012a (ZSa), 2012b (ZSb)) on the effects of the combined cooling on the SED. Lightcurves show the intensity of a specific frequency band over time. Thus, they are a perfect tool to analyze the flaring behavior of blazars in different energies, such as correlations between different frequency\n\n\n
Figure 4. Analytical (dotted) and numerical (dashed) retarded lightcurves over a liner time-axis. The parameters are given at the top and values of /epsilon1 in the legend are given in units of E 0 . The curves are normalized by the respective maximum. The vertical line marks the light-crossing time scale λ 0 , and the horizontal range is 15 λ 0 .
\n\nbands.\nWe were able to show that the synchrotron lightcurves exhibit a different form, if the time-dependent nature of the SSC cooling is taken into account, compared to the usual time-independent approaches. For that we first derived a formula to calculate the lightcurve from the intensity distribution, where we introduced the retardation due to the finite size of the radiation source. Using the intensities derived by SBM for the time-independent and the time-dependent cooling scenarios, we calculated the resulting lightcurves.\nOur calculations highlight the differences between the usual linear and the time-dependent cooling scenarios, giving us confidence that the important effects in the lightcurves are really due to the different cooling terms, and are not hidden by other effects.\nThe main results can be summarized as follows.\n(1) Until the light crossing time scale λ 0 is reached, the initial synchrotron lightcurves depend strongly on the geometry of the source. In our example of a spherical source the lightcurve increases ∝ t 2 , which, depending on the synchrotron photon energy /epsilon1 , is followed by a linear t -dependence. We note, however, that this rising phase might be hard to observe depending on the sampling rate\nin specific frequency bands.\n(2) If the transition time t c from time-dependent SSC to linear cooling is larger than the light crossing time scale (i.e., t c > λ 0 ), the effects of the rapid SSC cooling are clearly visible for t > λ 0 . The lightcurves exhibit their respective maximum up to an order of magnitude earlier, if the electrons cool initially by the timedependent SSC process. In this cooling regime variability can be 10 times faster than in the linear cooling regime. The different spectral powers below and above the transition time t c probably need very precise measurements to be distinguishable in the data of blazars.\n(3) The lightcurves are rather similar, if t c < λ 0 , since the effects of the time-dependent SSC cooling are smeared out by the retardation.\nThe results (2) and (3) obviously depend sensitively on the source parameters. In very compact emission regions with a short light crossing time scale and a large injection parameter α , the effects of the time-dependent SSC cooling are most significant. This in combination with the strong effects on the SED (e.g. ZSb) should help to clearly discriminate between different models, and to restrict the parameter space. In this context theoretical prediction of the SSC and EC lightcurve are also manda-\nory, and we intend to publish the results in a future work, where also a much deeper discussion of correlations is possible.\nTo conclude, we argue for a wide utilization of the timedependent SSC cooling scenario, at least for the modeling of rapid flares in blazars, where compact emission regions are necessary.\nWe thank the anonymous referee for constructive comments, which helped significantly to improve the manuscript.\nWe acknowledge support from the German Ministry for Education and Research (BMBF) through Verbundforschung Astroteilchenphysik grant 05A11PC1 and the Deutsche Forschungsgemeinschaft through grant Schl 201/23-1.\nREFERENCES\nAharonian F.A., et al., 2007, ApJ 664, L71 Arbeiter C., Pohl M., Schlickeiser R., 2002, A&A 386, 415 Barkov M.V., Aharonian F.A., Bogovalov S.V., Kelner S.R., Khangulyan D, 2012, ApJ 749, 119 Biteau J., Giebels B., 2012, A&A 548, A123 Blazejowski M., et al., 2000, ApJ 545, 107 B¨ottcher M., 2007, Astroph. & Space Sci. 309, 95 B¨ottcher M., 2012, preprint: arXiv:1205.0539 B¨ottcher M., Chiang J., 2002, ApJ 581, 127 Cabrera J.I., Coronade Y., Benitez E., Mendoza S., Hiriart D., Sorcia M., 2013, MNRASL, 434, L6 Chiaberge M., Ghisellini G., 1999, MNRAS 306, 551\nCrusius A., Schlickeiser R., 1988, A&A 196, 327\nCui W., 2004, ApJ 605, 662\nDermer C. D., Schlickeiser R., 1993, ApJ 416, 458\nEichmann B., Schlickeiser R., Rhode W., 2010, A&A 511, A26\nGiannios D., 2013, MNRAS 431, 355\n\nGiannios D., Uzdensky D.A., Begelman M.C., 2009, MNRAS 395, L29\n\nGhisellini G., Tavecchio F., Bodo G., Celotti A., 2009a, MNRAS 393, L16\nGhisellini G., Tavecchio F., Ghirlanda G., 2009b, MNRAS 399, 2041\n\nGraff P.B., Georganopoulos M., Perlman E.S., Kazanas D., 2008, ApJ 689, 68\nJones T. W., O'Dell S. L., Stein W. A., 1974, ApJ 188, 353\nJoshi M., Bottcher M., 2011, ApJ 727, 21\n\nKataoka J., et al., 2000, ApJ 528, 243\nKardashev, N. S., 1962, Sov. Astron. J. 6, 317\n\nLi H., Kusunose M., 2000, ApJ 536, 729\nMimica P., Aloy M.A., Muller E., Brinkmann W., 2004, A&A 418, 947\n\nSchlickeiser R., 2009, MNRAS 398, 1483\n\nSchlickeiser R., Bottcher M., Menzler U., 2010, A&A 519, A9 (SBM)\nSikora M., Begelman M. C., Rees M. J., 1994, ApJ 421, 153\nSokolov A., Marscher A.P., McHardy I.M., 2004, ApJ 613, 725\n\nSokolov A., Marscher A.P., 2005, ApJ 629, 52\nTavecchio F., Becerra-Gonzalez J. Ghisellini G., Stamerra A.,\nBonnoli G., Foschini L., Maraschi L., 2011, A&A 534, A86\nUrry C. M., Padovani P., 1995, PASP 107, 803\nVercellone S., et al., 2011, ApJL 736, L38\nWeidinger M., Ruger M., Spanier F., 2010, ASTRA 6, 1\nWeidinger M., Spanier F., 2010, A&A 515, A18\nZacharias M., Schlickeiser R., 2010, A&A 524, A31\nZacharias M., Schlickeiser R., 2012a, MNRAS 420, 84 (ZSa)\nZacharias M., Schlickeiser R., 2012b, ApJ 761, 110 (ZSb)\nAPPENDIX\nCALCULATION OF THE INTERMEDIATE PART\nThe intermediate time regime t 1 , 2 < t < λ 0 requires another approach. The approximations of the other regimes cannot be used here.\nL ( t 1 , 2 < t < λ 0 , /epsilon1 ) = 6 I 0 ( /epsilon1 E 0 ) 1 / 3 t/λ 0 ∫ 0 ( 1 + t -λ 0 λ t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t -λ 0 λ tsyn ) 2 ( λ -λ 2 ) d λ ≈ 6 I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 t/λ 0 ∫ 0 ( 1 -2 3 λ 0 λ t syn + t ) e 2 /epsilon1 E 0 ( 1+ t tsyn ) λ 0 λ tsyn ( λ -λ 2 ) d λ =6 I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 × t/λ 0 ∫ 0 ( λ -( 1 + 2 λ 0 3( t syn + t ) ) λ 2 + 2 λ 0 3( t syn + t ) λ 3 ) e 2 /epsilon1λ 0 E 0 tsyn ( 1+ t tsyn ) λ d λ (A1)\nIntegrating by parts and approximating to first order yields\nL ( t 1 , 2 < t < λ 0 , /epsilon1 ) ≈ 3 I 0 ( /epsilon1 E 0 ) -2 / 3 e -/epsilon1 E 0 t 2 syn λ 2 0 ( t t syn )[ 1 -t λ 0 ] , (A2)\nwhere we also approximated for t < t syn . This is the result (30), which fits very well the numerical solution for intermediate times.\n\n\n
Figure 5. Unretarded (full) and numerical (dashed) retarded lightcurves for a power-law injection with spectral index s = 2. The parameters are given at the top. The legend is for frequencies ν . The vertical dotted line marks the light-crossing time scale λ 0 .
\n\nPOWER-LAW PLOTS\nIn order to check if our analytical results can be regarded as qualitatively general, we performed a numerical integration of equation (3) with a power-law injection of the form\nS ( γ, t em ) = q 0 γ -s H [ γ -γ 1 ] H [ γ 2 -γ ] δ ( t em ) . (B1)\nThe differential equation (7) with this type of injection has been solved by Zacharias & Schlickeiser (2010), and we use their result in equation (4) in order to calculate the intensity distribution.\nFor the illustrative case s = 2 the results are plotted in Fig. 5 for two cases of α and two cases of the upper limit γ 2 , respectively. Without going into details, one can see that the results discussed in section 6 are qualitatively recovered, which gives us confidence that our approach is robust.\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"Blazars emit non-thermal radiation in all frequency bands from radio to γ -rays. Additionally, they often exhibit rapid flaring events at all frequencies with doubling time scale of the TeV and X-ray flux on the order of minutes, and such rapid flaring events are hard to explain theoretically. We explore the effect of the synchrotron-self Compton cooling, which is inherently time-dependent, leading to a rapid cooling of the electrons. Having discussed intensively the resulting effects of this cooling scenario on the spectral energy distribution of blazars in previous papers, the effects of the time-dependent approach on the synchrotron lightcurve are investigated here. Taking into account the retardation due to the finite size of the source and the source geometry, we show that the time-dependent synchrotronself Compton (SSC) cooling still has profound effects on the lightcurve compared to the usual linear (synchrotron and external Compton) cooling terms. This is most obvious if the SSC cooling takes longer than the light crossing time scale. Then in most frequency bands the variability time scale is up to an order of magnitude shorter than under linear cooling conditions. This is yet another strong indication that the time-dependent approach should be taken into account for modeling blazar flares from compact emission regions. Subject headings: radiation mechanisms: non-thermal - BL Lacertae objects: general - gamma-rays: theory","pages":[1]},{"title":"SYNCHROTRON LIGHTCURVES OF BLAZARS IN A TIME-DEPENDENT SYNCHROTRON-SELF COMPTON COOLING SCENARIO","content":"Michael Zacharias & Reinhard Schlickeiser Institut fur Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universitat Bochum, 44780 Bochum, Germany (Received; Revised; Accepted) Draft version September 7, 2021","pages":[1]},{"title":"1. INTRODUCTION","content":"Blazars, a subclass of active galactic nuclei in the accepted unification scheme of Urry & Padovani (1995), are characterized by a broad non-thermal spectrum exhibiting two characteristic humps and stretching from radio to γ -ray frequencies. In leptonic models the lowenergy component is attributed to synchrotron radiation of highly relativistic electrons, while the high-energy component is inverse Compton emission of the same electron population (for recent reviews see Bottcher 2007, 2012). Several target photon fields are relevant for the inverse Compton process. Jones et al. (1974) proposed the synchrotron radiation emitted by the relativistic electrons as the target photon field, which is then up-scattered by the same electrons, the so-called synchrotron-self Compton (SSC) process. The vicinity of an active galactic nucleus harbors also additional strong external (to the jet) photon fields, which can potentially contribute in the form of so-called external Compton radiation to the high-energy component of blazars. Such external fields could come from the accretion disk (Dermer & Schlickeiser 1993), the broad line region (Sikora et al. 1994) or the dusty torus (Blazejowski et al. 2000, Arbeiter et al. 2002). These external fields are usually preferred over the SSC, if the highenergy component dominates the synchrotron component in the spectral energy distribution (SED) of blazars. It is well established that blazars are far from being steady sources. They exhibit strong flares in all frequency bands, which can in some cases outshine even the brightest galactic sources. The brightest γ -ray flare ever detected is from 3C 454.3, reported by Vercellone et al. (2011), reaching a γ -ray flux of F γ = (6 . 8 ± 1 . 0) × 10 -5 photons cm -2 s -1 , which is six times higher than the Vela pulsar. Additionally, blazars also exhibit very rapid flares with doubling time scales on the order of minutes as in the case of PKS 2155-304 (Aharonian et al. 2007) or PKS 1222+216 (Tavecchio et al. 2011) in the TeV regime, or Mrk 421 in the X-rays (Cui 2004). Such rapid flares are theoretically challenging, since typical cooling time scales of the radiating electrons are considerably longer. Several models have thus been invoked to explain these rapid flares, such as the jet-in-a-jet model (Giannios et al. 2009), the similar minijets-in-a-jet model (Biteau & Giebels 2012, Giannios 2013), magnetocentrifugal acceleration of beams of particles (Ghisellini et al. 2009a), a star traversing the jet (Barkov et al. 2012), and others. Quite common in all these models is the assumption of an emission blob being smaller than the jet cross-section and moving much faster than the surrounding relativistic jet material. This gives rise to a very short light-crossing time scale, which is usually equaled to the variability time scale. In many theoretical investigations, as the ones cited above, and in most modeling attempts (e.g. Ghisellini et al. 2009b) the electron distribution is assumed to be stationary. This eases the computational effort, of course, and might be suitable for steady sources or those varying over a long time scale. However, it is certainly not justified for rapid flares as in PKS 2155-304 or PKS 1222+216. The time-dependence of the relativistic electron distribution function has important effects on the resulting SED, as is demonstrated in a recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (hereafter SBM); Zacharias & Schlickeiser 2010, 2012a (hereafter ZSa), 2012b (hereafter ZSb)). Relativistic electrons in a relativistically moving emission blob along the jet of the active galactic nucleus lose energy by emitting synchrotron radiation. These synchrotron photons are a prime target for the same electrons to inverse Compton scatter them to higher energies. This is the SSC process, as mentioned above, which is an additional energy loss process for the electrons. This in turn implies that the subsequently emitted synchrotron photons are less energetic, and so will be the SSC photons. Thus, this results in a decreased efficiency of the SSC process and in a decreased efficiency of the SSC energy loss process with respect to time. Consequently, even if the SSC process dominates initially the electron losses, eventually the time-independent loss processes such as synchrotron and external Compton losses dominate the loss rate. Schlickeiser (2009), as well as Zacharias & Schlickeiser (2010) were able to show that the time-dependent treatment of the SSC losses leads to a much faster electron cooling compared to the steadystate approach. Therefore, it is interesting to discuss the effects of this rapid cooling on blazar lightcurves, where the variability can be displayed in an obvious way. It is the purpose of this paper to highlight the different effects of the linear and the time-dependent (nonlinear) SSC cooling on the synchrotron lightcurves. To keep the problem simple and analytically tractable, we utilize only the retardation effect due to the finite size of the emission region, and the geometry of the source. This will be discussed in section 2, where we will derive the necessary formula to calculate the lightcurve from the synchrotron intensity. The latter was already calculated by SBM, and we will summarize their results in section 3 for the sake of completeness. We will then use the derived formula from section 2 to calculate the resulting lightcurves in sections 4 and 5. We will discuss the results in section 6 and conclude in section 7. The more involved calculations of the inverse Compton lightcurves will be discussed in a future publication.","pages":[1,2]},{"title":"2. GEOMETRY OF THE SITUATION","content":"We assume a spherical, uniform radiation zone in the jet as depicted in figure 1. For negligible retardation the received monochromatic intensity at intrinsic time t em is I ( t em , /epsilon1 ), where /epsilon1 is the intrinsic energy of the photon. Since, however, the source has a finite size, photons emitted at the back of the source will arrive at the observer at a later time ∆ t = 2 R/c than the photons emitted at the front, with R being the radius of the spherical source and c = 3 · 10 10 cm / s the speed of light. We include this retardation effect, but assume that the source is (i) spatially homogeneous, and (ii) optically thin. For optically thin sources all photons can leave the emission region without further spatial diffusion (Eichmann et al. 2010). Then the received intensity is just a function of the distance l of the production site from the front. Using a similar approach as Chiaberge & Ghisellini (1999), we cut the source into slices of length d l , as shown in figure 1. The received intensity of each slice is Here, t is the time of the observer, which equals t em for l = 0 (the front of the source). The Heaviside function H [ x ] displays the fact that light from a specific slice can only be detected after it has crossed the distance l to the front of the source. The fraction d V ( l ) /V is a geometrical weight function, which is defined in such a way that the integral over d V ( l ) /V equals unity. Since in a spherical source each slice has a different volume than the other slices, its contribution depends on its position in the source. The volume of the slice is given by d V ( l ) = A ( l ) d l , where A ( l ) = π (2 Rl -l 2 ) is the cross section of the slice at position l . The geometrical weight function then becomes The complete received monochromatic lightcurve L ( t, /epsilon1 ) then equals the sum over the contribution from all slices: after an obvious substitution. Here we introduced the light-crossing time scale λ 0 = 2 R/c . We note that equation (1) is general as long as the assumptions (i) and (ii) are satisfied. Thus, it is not limited to spherical geometries, and for example cylindrical sources could also be chosen. In fact, a cylindrical geometry would lead to a simpler form of the geometrical weight function. However, the assumption of isotropy for the electron distribution and the radiation fields (see below) would not be valid any more. 1","pages":[2]},{"title":"3. SYNCHROTRON INTENSITY","content":"In this section we summarize results previously obtained (SBM, ZSa, ZSb) in order to introduce the relevant functions and parameters. The isotropic, optically thin synchrotron intensity from relativistic electrons with the volume-averaged differential density n ( γ, t ) is given by with relative strength of external to synchrotron cooling, and has profound consequences for the SED, as we showed in Zacharias & Schlickeiser (2012b). We note that it is less important for the discussion of synchrotron lightcurves and only introduced for the sake of completeness. More importantly, as one can see from equation (9), is the fact that the SSC cooling term by its dependence on n ( γ, t ) is time-dependent, which means that its strength decreases over time. Consequently, even if the SSC cooling dominates the total cooling term initially, after some time the SSC cooling will become weaker than the linear cooling, and thus the synchrotron or external Compton cooling will dominate for later times. Obviously, if the linear cooling terms are stronger than the SSC cooling at the beginning, they will be stronger for all times. This can be further quantified by the injection parameter It is defined in such a way that As a consequence (ZSa and ZSb) the Compton dominance in the SED depends on α 2 , at least in the Thomson limit. This demonstrates the importance of this parameter, which can also be expressed as where we scale the total number of electrons N = 10 50 N 50 , and the initial electron Lorentz factor γ 0 = 10 4 γ 4 . Obviously, α increases for increasing γ 0 and N , and decreases for increasing R and l ec . If α /greatermuch 1 the cooling will initially be dominated by the SSC cooling, while for α /lessmuch 1 the cooling is dominated by the linear terms for all times. We note that both inverse Compton cooling terms operate in the Thomson limit. In the Klein-Nishina limit the efficiencies of both cooling terms are much reduced, and become unimportant compared to the synchrotron cooling. This resembles the case α /lessmuch 1 and l ec /lessmuch 1 and is, therefore, covered by our approach. The differential equation (7) with the loss term (9) and the source term (8) has been solved by SBM. For α /lessmuch 1 (i.e. negligible SSC-losses) they obtained which is, indeed, a linear cooling solution. For α /greatermuch 1 (i.e. initially dominating SSC-losses) SBM found yielding a nonlinear dependence of γ on time. For later times the electron density approaches being the synchrotron power of a single electron in a large-scale random magnetic field of constant strength B = b Gauss (Crusius & Schlickeiser 1988). Here P 0 = 2 · 10 24 erg -1 s -1 , and /epsilon1 0 = 1 . 9 · 10 -20 b erg. The function CS ( x ) is well approximated by with a 0 = 1 . 151275. The differential relativistic electron density can be calculated from the kinetic equation (Kardashev 1962) where | ˙ γ | is the electron energy loss term, and S ( γ, t em ) is the source term. For demonstration purposes and ease of calculation we use a relatively simple source term that is a single injection of monochromatic electrons with the injection Lorentz factor γ 0 and the electron density q 0 . In the scenario depicted here we consider electron losses via the synchrotron, external Compton and synchrotron-self Compton channels. Since the latter depends on the produced synchrotron radiation, and thus directly on the electron distribution, the kinetic equation becomes non-linear (Schlickeiser 2009). The total electron loss term is given by The parameters are D 0 = 1 . 3 · 10 -9 b 2 s -1 , and A 0 = 1 . 2 · 10 -18 R 15 b 2 cm 3 s -1 , where we scaled the radius of the source as R = 10 15 R 15 cm. We define where Γ b is the Lorentz factor of the plasma blob, u ' ec is the isotropic energy density of the external radiation field in the frame of the host galaxy, and u B is the energy density of the magnetic field. This parameter describes the which is a modified linear cooling solution. The transition time is defined as The intensity (4) for both cases of α has also been calculated by SBM. For α /lessmuch 1 they obtained with equation (14) For α /greatermuch 1 with equations (15) and (16) and Here we used the definitions I 0 = 3 a 0 RP 0 q 0 /epsilon1 0 / (8 π ), t syn = 1 / ( D 0 (1 + l ec ) γ 0 ), E 0 = 3 /epsilon1 0 γ 2 0 / 2, and α g = (1 + 2 α 3 ) / (3 α 2 ). These intensities are equal to a monochromatic lightcurve, where the retardation and, thus, the source's finite size have not been taken into account. Below, we will refer to them as the 'unretarded' lightcurves. Now, we have collected all necessary ingredients to calculate the retarded synchrotron lightcurves, which we present in the following sections.","pages":[3,4]},{"title":"4. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING LINEAR COOLING","content":"Using equation (18) in equation (3) we obtain the retarded lightcurve for the case α /lessmuch 1: The integral (21) can be solved in terms of several incomplete Gamma-functions. However, this would not give many insights. Instead, we will use meaningful approximations for the integral in three time domains. These domains can later be glued together to give a continuous analytic result. First of all, we define two characteristic time scales of the unretarded lightcurve. They can later be connected to the light-crossing time scale, yielding some information about the resulting retarded lightcurve. The first one is the local maximum of the unretarded lightcurve, which is: This expression is negative for /epsilon1 > E 0 / 3, indicating that for such energies there is no local maximum. If t 1 ( /epsilon1 ) > λ 0 the variability will mostly take place for times later than the light-crossing time scale. Solving the resulting inequality for /epsilon1 , results in This equation implies that for energies /epsilon1 < /epsilon1 1 the variability due to the flare will be longer than the lightcrossing time scale. Hence, we expect the global maximum of the lightcurve to occur later than λ 0 , and thus be unaffected by the retardation. The second characteristic time scale is related to the argument of the exponential in the unretarded lightcurve A = /epsilon1 E 0 (1 + t em /t syn ) 2 . As soon as t em ≥ t syn the unretarded lightcurve exponentially decays, which should also be visible in the retarded lightcurve. Since, however, A ≈ /epsilon1 E 0 for t em /lessmuch t syn , we set with Once A ∗ ( /epsilon1, t em ) is larger than unity the unretarded lightcurve will exponentially decay. Thus, we obtain the second characteristic time scale t 2 ( /epsilon1 ) by A ( /epsilon1, t 2 ( /epsilon1 )) = 1, yielding Unlike t 1 ( /epsilon1 ), the second characteristic time scale exhibits no restrictions by /epsilon1 . Obviously, t 1 ( /epsilon1 ) < t 2 ( /epsilon1 ). For t 2 ( /epsilon1 ) > λ 0 the exponential will become important only after the light-crossing time scale. Solving the inequality for /epsilon1 we obtain We can now begin with the actual calculation of the retarded lightcurve. The simplest case is obviously for t > λ 0 , since in this case the retarded lightcurve should be the same as the unretarded lightcurve. This is due to the fact that the retardation is not important for time scales much longer than λ 0 . Inspecting the difference t -λ 0 λ , we see that λ 0 λ can be at most equal to λ 0 . Thus, for t /greatermuch λ 0 we can approximate t -λ 0 λ ≈ t . Hence, which, indeed, equals the unretarded lightcurve. The other rather simple case is for t < λ 0 with the further requirement that t < t 1 , 2 ( /epsilon1 ) (the subscript refers to both t 1 and t 2 ). The latter implies that the unretarded lightcurves were neither variable nor have they decayed already. Then in eq. (21) the terms ( t -λ 0 λ ) /t syn can be neglected compared to unity, yielding For times below the light-crossing time scale and below the variability time scale of the unretarded lightcurve the retarded lightcurve increases rapidly L ∝ t 2 . For intermediate times the calculation is quite involved, and the details can be found in appendix A. We obtain We note that the exact form of the intermediate regime is not so important, since it will be glued to the approximation (29) at t ≈ t 2 . The most important result is the linear increase of the the lightcurve (30), which leads to a break at t 2 in the retarded lightcurve. However, if t 1 , 2 ( /epsilon1 ) > λ 0 the intermediate part does not play a role, and the lightcurve breaks immediately at t = λ 0 from the initial t 2 -dependence to the time dependence given by equation (28). Depending on the synchrotron photon energy /epsilon1 , we can now construct the lightcurves from the three approximations (28) - (30). We obtain two cases, divided in additional sub-cases. Beginning with /epsilon1 < E 0 / 3, we get: For /epsilon1 > E 0 / 3 the solutions become: The lightcurves (33) and (35) cut off at t = λ 0 . Obviously, light from the back reaches the observer only at later times, causing the radiation to be visible on longer time scales than implied by the unretarded lightcurve. The analytical results (31) - (35) are plotted along with a numerical integration of equation (21) in Figure 2 for two cases of γ 0 . For comparison, we also show the unretarded lightcurve. The first obvious result is that the retarded synchrotron lightcurve increases rapidly as long as t < λ 0 . Afterwards the retarded lightcurve behaves as the unretarded one, which is reasonable, as we discussed above. The other points mentioned earlier are also quite obvious. Even though the unretarded lightcurve for very high energies cuts off long before the light-crossing time scale, the retarded lightcurves are extended until λ 0 . The break in the lightcurve in the intermediate time regime is also evident. However, as discussed above, the low energetic cases, where the variability time scales are much longer than the light-crossing time scale, do not exhibit this break. As one can see, the analytical result matches the numerical integration rather well, which is reassuring and validates a posteriori our approximations. However, there is one caveat: The distinction of cases by t 2 and /epsilon1 2 is rather sharp (esp. equations (33) and (35)). This is obvious in the left plot of Figure 2 in the analytical curve for /epsilon1 = 10 E 0 , which cuts off at t = λ 0 . On the other hand, the numerical curve in this case decays exponentially. The distinction of the cases divided by /epsilon1 2 is, therefore, not as strict as implied by the analytical result. It is a more gradual transition, which is, however, difficult to implement in one equation. The problem is probably due to the rather artificial definition of t 2 , which is also indicated by the fact that the break for the high-energy lightcurves is better placed at 2 t 2 instead of t 2 .","pages":[4,5]},{"title":"5. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING INITIAL SSC COOLING","content":"For the case α /greatermuch 1 we use equations (19) and (20) in equation (3) to obtain the retarded lightcurve For t c < t < t c + λ 0 both L 1 and L 2 contribute to the emitted lightcurve, which differs from the strict division of the unretarded lightcurves (19) and (20). This is, again, an effect of the retardation: Even if light received from the front of the source is from electrons already cooling in the linear regime ( t em > t c ), the light received from the back of the source is still from electrons cooling in the nonlinear regime ( t em < t c ). If t c < λ 0 this period can be quite extended. Although there are several sub-cases to consider in the analytical calculation, we can use the same approximation for the integrals (36) and (37), as we used to obtain equations (28) - (30). It is therefore unnecessary to repeat them in detail. Instead, we will summarize the results in the most compact form possible, where the sub-cases are combined in such a way that the resulting lightcurve is continuous. The characteristic time scales t 3 ( /epsilon1 ) and t 4 ( /epsilon1 ) are obtained by the same arguments as t 1 ( /epsilon1 ) and t 2 ( /epsilon1 ), giving For t 3 , 4 ( /epsilon1 ) > λ 0 we find while for t 3 , 4 ( /epsilon1 ) > t c we obtain respectively. With these definitions, we sum up the results of the analytical calculation. We begin with the case t c < λ 0 : For t c > λ 0 the analytical calculation yields for /epsilon1 < E 0 / 3 which is the only case where L must be divided. For /epsilon1 > E 0 / 3 we obtain In Figure 3 we compare the analytical results with the numerical results, and achieve quite good agreement. The unretarded lightcurve is shown again for comparison. Since the basic properties of the plot are the same as in Figure 2, we do not need to repeat them here. The problem with t 4 and /epsilon1 4 , mentioned in the discussion for Figure 2, is evident here, again.","pages":[6,7]},{"title":"6. DISCUSSION","content":"In Figures 2 and 3 we show lightcurves in a logarithmic plot, which has the advantage of having several cases in one plot. This makes it much easier to compare variability aspects which occur on very different time scales. Our discussion will focus on these logarithmic plots. On the other hand, lightcurves are commonly displayed in a linear plot, which highlights the behavior of lightcurves around their respective maxima. We present such linear plots in Figure 4. The results are completely compatible. Comparing Figures 2 and 3 one can see that there are some points, where the results are similar, and some other points, which are remarkably different. First of all, we note that the 'variability time scale' of any given lightcurve is determined by its global maximum. Thus, the minimal variability time scale, which is possible at all, is given by the light-crossing time scale, since the source is evenly contributing to the radiative output. If the source only partially radiates, the variability time scale can be much lower (Eichmann et al. 2010). The rising phase until λ 0 is dominated by the source geometry, giving a t 2 -dependence up to the break times t 2 ( /epsilon1 ) for α /lessmuch 1 and t 4 ( /epsilon1 ) for α /greatermuch 1, respectively. If t 2 , 4 ( /epsilon1 ) < λ 0 , the lightcurve exhibits a break to a t 1 -dependence. Otherwise the spectrum breaks directly to the unretarded lightcurve at λ 0 . 2 Secondly, for larger initial electron energies γ 0 the variability time scale is much reduced compared to lower initial electron energies. Hence, in the low-energetic frequency bands the variability time scale shifts closer to λ 0 for larger γ 0 . Thus, one can get information about the initial electron energy by observing the peak times of different frequency bands. The plots for the high-energetic cases ( γ 0 = 10 5 ) look quite similar in both cases of α , since t c is smaller than λ 0 , and the lightcurves are the same for t > t c . However, they can be distinguished by the high-energetic frequency bands. Both are less luminous for α /greatermuch 1 compared to α /lessmuch 1, because the synchrotron SED exhibits a broken power-law for α /greatermuch 1, leading to a decreased flux for high energies compared to the α /lessmuch 1 case (cf. SBM). Additionally, the break in the lightcurve from the quadratic time-dependence to the linear timedependence takes place a factor 3 α 2 earlier in the α /greatermuch 1 case than for α /lessmuch 1, since the unretarded lightcurve cuts off much earlier for α /greatermuch 1 than for α /lessmuch 1. Thus, the sum over all unretarded lightcurves of each slice (that is the retarded lightcurve) for α /greatermuch 1 must be less luminous and increase less strongly than for α /lessmuch 1. The low-energetic cases ( γ 0 = 10 3 ) differ strongly for α larger and smaller than unity, since t c is larger than λ 0 . The features, which are plainly visible in the unretarded lightcurve, are thus also visible in the retarded lightcurve. The lightcurve for /epsilon1 = 10 E 0 cuts off in both cases at around λ 0 . However, for α /greatermuch 1 the break is clearly visible in the lightcurve, which is due to the faster cooling of the electrons in this case of α . Similarly, the lightcurve for /epsilon1 = E 0 cuts off for α /greatermuch 1 at λ 0 because of the faster cooling, and for α /lessmuch 1 the lightcurve shows a rather broad exponential decay. 3 The lightcurves for /epsilon1 = 10 -2 E 0 can be distinguished quite well, since the lightcurve for α /lessmuch 1 shows a rapid increase to the narrow maximum, while the light curve for α /greatermuch 1 exhibits a broad and flat maximum, which covers almost two orders of magnitude in time. As stated above, because of the broken power-law in the SED for α /greatermuch 1 the maximum of the SED is attained at /epsilon1 = E 0 /α 2 , which is in our example the lightcurve for /epsilon1 = 10 -2 E 0 . This explains the broad maximum, and also why the higher energies are again less luminous compared to the α /lessmuch 1 case. In the lightcurves for /epsilon1 = 10 -4 E 0 there is only a very slight difference, since the rising part after λ 0 sets in earlier for α /greatermuch 1 than for α /lessmuch 1. However, the increase is quite 2 The powers of t depend sensitively on the chosen geometry. E.g. for a cylindrical source the power is reduced by unity giving a t 1 - and a flat t 0 -dependence. small until t c and detailed observations are needed to distinguish the models. Obviously, for smaller emission regions the lightcrossing time scale λ 0 is reduced and the effects of the time-dependent cooling will be even more pronounced with very short variability time scales. Additionally, a smaller emission region leads to a larger α according to equation (13). Thus, the time-dependent SSC cooling is quite important for models which assume a small emission region to explain the rapid variability in blazars, like those cited in the introduction. We numerically checked if our results are also valid for different injection scenarios, such as a power-law, and obtained qualitatively similar results as one can see in Figure 5 of appendix B. Thus, we are confident that the discussion presented here is robust.","pages":[7,8]},{"title":"6.1. Caveats of the approach","content":"Of course, our approach is simplified, leaving aside several, possibly important aspects. As stated in section 2, we assume that the source is spatially homogeneous. Additionally, we neglect the 'internal' retardation of the inverse Compton processes. The time, a photon travels before it is inverse Compton scattered, should on average be much less than λ 0 . Thus, the effect on the light curve is small, apart from a short delay of the SSC light curve (which we do not calculate in this paper). However, cooling might be affected, since the SSC cooling should be similarly delayed as the SSC light curve. On the other hand, as shown in Schlickeiser (2009) and Zacharias & Schlickeiser (2010), the SSC cooling is orders of magnitude quicker than the synchrotron and external Compton cooling, which should more than compensate the small retardation delay. We do not expect a delay effect for the external Compton scattering, since they are present all the time and are more or less homogeneously distributed (ZSb, Sokolov & Marscher 2005). We also do not discuss the acceleration of the electrons. This might have a significant impact on the light curve, since the variability is governed by the longest time scale (in our case just λ 0 and t syn , with an influence by t c for α /greatermuch 1). If the acceleration takes particularly long the effects due to retardation or cooling would be washed out. If the acceleration takes only a small amount of time, it will certainly influence the rising phase of the light curve, but its effect on the main part of the variability will not be significant. This argument might not hold for very small emission regions. On the other hand, the acceleration time scale is only important, if the acceleration and radiation zone are spatially and temporally coincident. This is still under debate, and only recently these conditions are incorporated in numerical studies (e.g. Weidinger et al. 2010; Weidinger & Spanier 2010). Thus, we follow the assumption or simplification that acceleration and radiation are (especially) temporally separated. Then, the acceleration time scale does not influence the resulting light curve. Chiaberge & Ghisellini (1999), and also e.g. Kataoka et al. (2000) or Li & Kusunose (2000), used similar assumptions in their numerical analysis. In fact, most theoretical investigations use numerical schemes with the advantage of employing more and more realistic scenarios, such as time-dependency (Bottcher & Chiang, 2002), inclusion of shock acceleration (Sokolov et al., 2004), hydrodynamic simulations (Mimica et al., 2004; Cabrera et al., 2013), and multizone models that incorporate the full retardation of all processes (Graff et al., 2008, Joshi & Bottcher 2011). In our analytical discussion we are for obvious reason not able to include all these details. That is why we focus on the details of the time-dependency, showing analytically that time-dependent effects, especially from SSC, are very important for rapid flares.","pages":[8]},{"title":"7. CONCLUSIONS","content":"In this paper we introduced our approach to calculate theoretical synchrotron lightcurves for flaring blazars, where the radiating relativistic electrons are cooled by the combined synchrotron, external Compton and timedependent SSC mechanisms. This complements the recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (SBM); Zacharias & Schlickeiser 2010, 2012a (ZSa), 2012b (ZSb)) on the effects of the combined cooling on the SED. Lightcurves show the intensity of a specific frequency band over time. Thus, they are a perfect tool to analyze the flaring behavior of blazars in different energies, such as correlations between different frequency bands. We were able to show that the synchrotron lightcurves exhibit a different form, if the time-dependent nature of the SSC cooling is taken into account, compared to the usual time-independent approaches. For that we first derived a formula to calculate the lightcurve from the intensity distribution, where we introduced the retardation due to the finite size of the radiation source. Using the intensities derived by SBM for the time-independent and the time-dependent cooling scenarios, we calculated the resulting lightcurves. Our calculations highlight the differences between the usual linear and the time-dependent cooling scenarios, giving us confidence that the important effects in the lightcurves are really due to the different cooling terms, and are not hidden by other effects. The main results can be summarized as follows. (1) Until the light crossing time scale λ 0 is reached, the initial synchrotron lightcurves depend strongly on the geometry of the source. In our example of a spherical source the lightcurve increases ∝ t 2 , which, depending on the synchrotron photon energy /epsilon1 , is followed by a linear t -dependence. We note, however, that this rising phase might be hard to observe depending on the sampling rate in specific frequency bands. (2) If the transition time t c from time-dependent SSC to linear cooling is larger than the light crossing time scale (i.e., t c > λ 0 ), the effects of the rapid SSC cooling are clearly visible for t > λ 0 . The lightcurves exhibit their respective maximum up to an order of magnitude earlier, if the electrons cool initially by the timedependent SSC process. In this cooling regime variability can be 10 times faster than in the linear cooling regime. The different spectral powers below and above the transition time t c probably need very precise measurements to be distinguishable in the data of blazars. (3) The lightcurves are rather similar, if t c < λ 0 , since the effects of the time-dependent SSC cooling are smeared out by the retardation. The results (2) and (3) obviously depend sensitively on the source parameters. In very compact emission regions with a short light crossing time scale and a large injection parameter α , the effects of the time-dependent SSC cooling are most significant. This in combination with the strong effects on the SED (e.g. ZSb) should help to clearly discriminate between different models, and to restrict the parameter space. In this context theoretical prediction of the SSC and EC lightcurve are also manda- ory, and we intend to publish the results in a future work, where also a much deeper discussion of correlations is possible. To conclude, we argue for a wide utilization of the timedependent SSC cooling scenario, at least for the modeling of rapid flares in blazars, where compact emission regions are necessary. We thank the anonymous referee for constructive comments, which helped significantly to improve the manuscript. We acknowledge support from the German Ministry for Education and Research (BMBF) through Verbundforschung Astroteilchenphysik grant 05A11PC1 and the Deutsche Forschungsgemeinschaft through grant Schl 201/23-1.","pages":[8,9,10]},{"title":"REFERENCES","content":"Aharonian F.A., et al., 2007, ApJ 664, L71 Arbeiter C., Pohl M., Schlickeiser R., 2002, A&A 386, 415 Barkov M.V., Aharonian F.A., Bogovalov S.V., Kelner S.R., Khangulyan D, 2012, ApJ 749, 119 Biteau J., Giebels B., 2012, A&A 548, A123 Blazejowski M., et al., 2000, ApJ 545, 107 B¨ottcher M., 2007, Astroph. & Space Sci. 309, 95 B¨ottcher M., 2012, preprint: arXiv:1205.0539 B¨ottcher M., Chiang J., 2002, ApJ 581, 127 Cabrera J.I., Coronade Y., Benitez E., Mendoza S., Hiriart D., Sorcia M., 2013, MNRASL, 434, L6 Chiaberge M., Ghisellini G., 1999, MNRAS 306, 551 Crusius A., Schlickeiser R., 1988, A&A 196, 327 Cui W., 2004, ApJ 605, 662 Dermer C. D., Schlickeiser R., 1993, ApJ 416, 458 Eichmann B., Schlickeiser R., Rhode W., 2010, A&A 511, A26 Giannios D., 2013, MNRAS 431, 355 Ghisellini G., Tavecchio F., Bodo G., Celotti A., 2009a, MNRAS 393, L16 Ghisellini G., Tavecchio F., Ghirlanda G., 2009b, MNRAS 399, 2041 Kataoka J., et al., 2000, ApJ 528, 243 Kardashev, N. S., 1962, Sov. Astron. J. 6, 317 Schlickeiser R., 2009, MNRAS 398, 1483 Sokolov A., Marscher A.P., 2005, ApJ 629, 52 Tavecchio F., Becerra-Gonzalez J. Ghisellini G., Stamerra A., Bonnoli G., Foschini L., Maraschi L., 2011, A&A 534, A86 Urry C. M., Padovani P., 1995, PASP 107, 803 Vercellone S., et al., 2011, ApJL 736, L38 Weidinger M., Ruger M., Spanier F., 2010, ASTRA 6, 1 Weidinger M., Spanier F., 2010, A&A 515, A18 Zacharias M., Schlickeiser R., 2010, A&A 524, A31 Zacharias M., Schlickeiser R., 2012a, MNRAS 420, 84 (ZSa) Zacharias M., Schlickeiser R., 2012b, ApJ 761, 110 (ZSb)","pages":[10]},{"title":"CALCULATION OF THE INTERMEDIATE PART","content":"The intermediate time regime t 1 , 2 < t < λ 0 requires another approach. The approximations of the other regimes cannot be used here. Integrating by parts and approximating to first order yields where we also approximated for t < t syn . This is the result (30), which fits very well the numerical solution for intermediate times. In order to check if our analytical results can be regarded as qualitatively general, we performed a numerical integration of equation (3) with a power-law injection of the form The differential equation (7) with this type of injection has been solved by Zacharias & Schlickeiser (2010), and we use their result in equation (4) in order to calculate the intensity distribution. For the illustrative case s = 2 the results are plotted in Fig. 5 for two cases of α and two cases of the upper limit γ 2 , respectively. Without going into details, one can see that the results discussed in section 6 are qualitatively recovered, which gives us confidence that our approach is robust.","pages":[10,11]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"Blazars emit non-thermal radiation in all frequency bands from radio to γ -rays. Additionally, they often exhibit rapid flaring events at all frequencies with doubling time scale of the TeV and X-ray flux on the order of minutes, and such rapid flaring events are hard to explain theoretically. We explore the effect of the synchrotron-self Compton cooling, which is inherently time-dependent, leading to a rapid cooling of the electrons. Having discussed intensively the resulting effects of this cooling scenario on the spectral energy distribution of blazars in previous papers, the effects of the time-dependent approach on the synchrotron lightcurve are investigated here. Taking into account the retardation due to the finite size of the source and the source geometry, we show that the time-dependent synchrotronself Compton (SSC) cooling still has profound effects on the lightcurve compared to the usual linear (synchrotron and external Compton) cooling terms. This is most obvious if the SSC cooling takes longer than the light crossing time scale. Then in most frequency bands the variability time scale is up to an order of magnitude shorter than under linear cooling conditions. This is yet another strong indication that the time-dependent approach should be taken into account for modeling blazar flares from compact emission regions. Subject headings: radiation mechanisms: non-thermal - BL Lacertae objects: general - gamma-rays: theory\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"SYNCHROTRON LIGHTCURVES OF BLAZARS IN A TIME-DEPENDENT SYNCHROTRON-SELF COMPTON COOLING SCENARIO\",\n \"content\": \"Michael Zacharias & Reinhard Schlickeiser Institut fur Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universitat Bochum, 44780 Bochum, Germany (Received; Revised; Accepted) Draft version September 7, 2021\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"Blazars, a subclass of active galactic nuclei in the accepted unification scheme of Urry & Padovani (1995), are characterized by a broad non-thermal spectrum exhibiting two characteristic humps and stretching from radio to γ -ray frequencies. In leptonic models the lowenergy component is attributed to synchrotron radiation of highly relativistic electrons, while the high-energy component is inverse Compton emission of the same electron population (for recent reviews see Bottcher 2007, 2012). Several target photon fields are relevant for the inverse Compton process. Jones et al. (1974) proposed the synchrotron radiation emitted by the relativistic electrons as the target photon field, which is then up-scattered by the same electrons, the so-called synchrotron-self Compton (SSC) process. The vicinity of an active galactic nucleus harbors also additional strong external (to the jet) photon fields, which can potentially contribute in the form of so-called external Compton radiation to the high-energy component of blazars. Such external fields could come from the accretion disk (Dermer & Schlickeiser 1993), the broad line region (Sikora et al. 1994) or the dusty torus (Blazejowski et al. 2000, Arbeiter et al. 2002). These external fields are usually preferred over the SSC, if the highenergy component dominates the synchrotron component in the spectral energy distribution (SED) of blazars. It is well established that blazars are far from being steady sources. They exhibit strong flares in all frequency bands, which can in some cases outshine even the brightest galactic sources. The brightest γ -ray flare ever detected is from 3C 454.3, reported by Vercellone et al. (2011), reaching a γ -ray flux of F γ = (6 . 8 ± 1 . 0) × 10 -5 photons cm -2 s -1 , which is six times higher than the Vela pulsar. Additionally, blazars also exhibit very rapid flares with doubling time scales on the order of minutes as in the case of PKS 2155-304 (Aharonian et al. 2007) or PKS 1222+216 (Tavecchio et al. 2011) in the TeV regime, or Mrk 421 in the X-rays (Cui 2004). Such rapid flares are theoretically challenging, since typical cooling time scales of the radiating electrons are considerably longer. Several models have thus been invoked to explain these rapid flares, such as the jet-in-a-jet model (Giannios et al. 2009), the similar minijets-in-a-jet model (Biteau & Giebels 2012, Giannios 2013), magnetocentrifugal acceleration of beams of particles (Ghisellini et al. 2009a), a star traversing the jet (Barkov et al. 2012), and others. Quite common in all these models is the assumption of an emission blob being smaller than the jet cross-section and moving much faster than the surrounding relativistic jet material. This gives rise to a very short light-crossing time scale, which is usually equaled to the variability time scale. In many theoretical investigations, as the ones cited above, and in most modeling attempts (e.g. Ghisellini et al. 2009b) the electron distribution is assumed to be stationary. This eases the computational effort, of course, and might be suitable for steady sources or those varying over a long time scale. However, it is certainly not justified for rapid flares as in PKS 2155-304 or PKS 1222+216. The time-dependence of the relativistic electron distribution function has important effects on the resulting SED, as is demonstrated in a recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (hereafter SBM); Zacharias & Schlickeiser 2010, 2012a (hereafter ZSa), 2012b (hereafter ZSb)). Relativistic electrons in a relativistically moving emission blob along the jet of the active galactic nucleus lose energy by emitting synchrotron radiation. These synchrotron photons are a prime target for the same electrons to inverse Compton scatter them to higher energies. This is the SSC process, as mentioned above, which is an additional energy loss process for the electrons. This in turn implies that the subsequently emitted synchrotron photons are less energetic, and so will be the SSC photons. Thus, this results in a decreased efficiency of the SSC process and in a decreased efficiency of the SSC energy loss process with respect to time. Consequently, even if the SSC process dominates initially the electron losses, eventually the time-independent loss processes such as synchrotron and external Compton losses dominate the loss rate. Schlickeiser (2009), as well as Zacharias & Schlickeiser (2010) were able to show that the time-dependent treatment of the SSC losses leads to a much faster electron cooling compared to the steadystate approach. Therefore, it is interesting to discuss the effects of this rapid cooling on blazar lightcurves, where the variability can be displayed in an obvious way. It is the purpose of this paper to highlight the different effects of the linear and the time-dependent (nonlinear) SSC cooling on the synchrotron lightcurves. To keep the problem simple and analytically tractable, we utilize only the retardation effect due to the finite size of the emission region, and the geometry of the source. This will be discussed in section 2, where we will derive the necessary formula to calculate the lightcurve from the synchrotron intensity. The latter was already calculated by SBM, and we will summarize their results in section 3 for the sake of completeness. We will then use the derived formula from section 2 to calculate the resulting lightcurves in sections 4 and 5. We will discuss the results in section 6 and conclude in section 7. The more involved calculations of the inverse Compton lightcurves will be discussed in a future publication.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2. GEOMETRY OF THE SITUATION\",\n \"content\": \"We assume a spherical, uniform radiation zone in the jet as depicted in figure 1. For negligible retardation the received monochromatic intensity at intrinsic time t em is I ( t em , /epsilon1 ), where /epsilon1 is the intrinsic energy of the photon. Since, however, the source has a finite size, photons emitted at the back of the source will arrive at the observer at a later time ∆ t = 2 R/c than the photons emitted at the front, with R being the radius of the spherical source and c = 3 · 10 10 cm / s the speed of light. We include this retardation effect, but assume that the source is (i) spatially homogeneous, and (ii) optically thin. For optically thin sources all photons can leave the emission region without further spatial diffusion (Eichmann et al. 2010). Then the received intensity is just a function of the distance l of the production site from the front. Using a similar approach as Chiaberge & Ghisellini (1999), we cut the source into slices of length d l , as shown in figure 1. The received intensity of each slice is Here, t is the time of the observer, which equals t em for l = 0 (the front of the source). The Heaviside function H [ x ] displays the fact that light from a specific slice can only be detected after it has crossed the distance l to the front of the source. The fraction d V ( l ) /V is a geometrical weight function, which is defined in such a way that the integral over d V ( l ) /V equals unity. Since in a spherical source each slice has a different volume than the other slices, its contribution depends on its position in the source. The volume of the slice is given by d V ( l ) = A ( l ) d l , where A ( l ) = π (2 Rl -l 2 ) is the cross section of the slice at position l . The geometrical weight function then becomes The complete received monochromatic lightcurve L ( t, /epsilon1 ) then equals the sum over the contribution from all slices: after an obvious substitution. Here we introduced the light-crossing time scale λ 0 = 2 R/c . We note that equation (1) is general as long as the assumptions (i) and (ii) are satisfied. Thus, it is not limited to spherical geometries, and for example cylindrical sources could also be chosen. In fact, a cylindrical geometry would lead to a simpler form of the geometrical weight function. However, the assumption of isotropy for the electron distribution and the radiation fields (see below) would not be valid any more. 1\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"3. SYNCHROTRON INTENSITY\",\n \"content\": \"In this section we summarize results previously obtained (SBM, ZSa, ZSb) in order to introduce the relevant functions and parameters. The isotropic, optically thin synchrotron intensity from relativistic electrons with the volume-averaged differential density n ( γ, t ) is given by with relative strength of external to synchrotron cooling, and has profound consequences for the SED, as we showed in Zacharias & Schlickeiser (2012b). We note that it is less important for the discussion of synchrotron lightcurves and only introduced for the sake of completeness. More importantly, as one can see from equation (9), is the fact that the SSC cooling term by its dependence on n ( γ, t ) is time-dependent, which means that its strength decreases over time. Consequently, even if the SSC cooling dominates the total cooling term initially, after some time the SSC cooling will become weaker than the linear cooling, and thus the synchrotron or external Compton cooling will dominate for later times. Obviously, if the linear cooling terms are stronger than the SSC cooling at the beginning, they will be stronger for all times. This can be further quantified by the injection parameter It is defined in such a way that As a consequence (ZSa and ZSb) the Compton dominance in the SED depends on α 2 , at least in the Thomson limit. This demonstrates the importance of this parameter, which can also be expressed as where we scale the total number of electrons N = 10 50 N 50 , and the initial electron Lorentz factor γ 0 = 10 4 γ 4 . Obviously, α increases for increasing γ 0 and N , and decreases for increasing R and l ec . If α /greatermuch 1 the cooling will initially be dominated by the SSC cooling, while for α /lessmuch 1 the cooling is dominated by the linear terms for all times. We note that both inverse Compton cooling terms operate in the Thomson limit. In the Klein-Nishina limit the efficiencies of both cooling terms are much reduced, and become unimportant compared to the synchrotron cooling. This resembles the case α /lessmuch 1 and l ec /lessmuch 1 and is, therefore, covered by our approach. The differential equation (7) with the loss term (9) and the source term (8) has been solved by SBM. For α /lessmuch 1 (i.e. negligible SSC-losses) they obtained which is, indeed, a linear cooling solution. For α /greatermuch 1 (i.e. initially dominating SSC-losses) SBM found yielding a nonlinear dependence of γ on time. For later times the electron density approaches being the synchrotron power of a single electron in a large-scale random magnetic field of constant strength B = b Gauss (Crusius & Schlickeiser 1988). Here P 0 = 2 · 10 24 erg -1 s -1 , and /epsilon1 0 = 1 . 9 · 10 -20 b erg. The function CS ( x ) is well approximated by with a 0 = 1 . 151275. The differential relativistic electron density can be calculated from the kinetic equation (Kardashev 1962) where | ˙ γ | is the electron energy loss term, and S ( γ, t em ) is the source term. For demonstration purposes and ease of calculation we use a relatively simple source term that is a single injection of monochromatic electrons with the injection Lorentz factor γ 0 and the electron density q 0 . In the scenario depicted here we consider electron losses via the synchrotron, external Compton and synchrotron-self Compton channels. Since the latter depends on the produced synchrotron radiation, and thus directly on the electron distribution, the kinetic equation becomes non-linear (Schlickeiser 2009). The total electron loss term is given by The parameters are D 0 = 1 . 3 · 10 -9 b 2 s -1 , and A 0 = 1 . 2 · 10 -18 R 15 b 2 cm 3 s -1 , where we scaled the radius of the source as R = 10 15 R 15 cm. We define where Γ b is the Lorentz factor of the plasma blob, u ' ec is the isotropic energy density of the external radiation field in the frame of the host galaxy, and u B is the energy density of the magnetic field. This parameter describes the which is a modified linear cooling solution. The transition time is defined as The intensity (4) for both cases of α has also been calculated by SBM. For α /lessmuch 1 they obtained with equation (14) For α /greatermuch 1 with equations (15) and (16) and Here we used the definitions I 0 = 3 a 0 RP 0 q 0 /epsilon1 0 / (8 π ), t syn = 1 / ( D 0 (1 + l ec ) γ 0 ), E 0 = 3 /epsilon1 0 γ 2 0 / 2, and α g = (1 + 2 α 3 ) / (3 α 2 ). These intensities are equal to a monochromatic lightcurve, where the retardation and, thus, the source's finite size have not been taken into account. Below, we will refer to them as the 'unretarded' lightcurves. Now, we have collected all necessary ingredients to calculate the retarded synchrotron lightcurves, which we present in the following sections.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"4. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING LINEAR COOLING\",\n \"content\": \"Using equation (18) in equation (3) we obtain the retarded lightcurve for the case α /lessmuch 1: The integral (21) can be solved in terms of several incomplete Gamma-functions. However, this would not give many insights. Instead, we will use meaningful approximations for the integral in three time domains. These domains can later be glued together to give a continuous analytic result. First of all, we define two characteristic time scales of the unretarded lightcurve. They can later be connected to the light-crossing time scale, yielding some information about the resulting retarded lightcurve. The first one is the local maximum of the unretarded lightcurve, which is: This expression is negative for /epsilon1 > E 0 / 3, indicating that for such energies there is no local maximum. If t 1 ( /epsilon1 ) > λ 0 the variability will mostly take place for times later than the light-crossing time scale. Solving the resulting inequality for /epsilon1 , results in This equation implies that for energies /epsilon1 < /epsilon1 1 the variability due to the flare will be longer than the lightcrossing time scale. Hence, we expect the global maximum of the lightcurve to occur later than λ 0 , and thus be unaffected by the retardation. The second characteristic time scale is related to the argument of the exponential in the unretarded lightcurve A = /epsilon1 E 0 (1 + t em /t syn ) 2 . As soon as t em ≥ t syn the unretarded lightcurve exponentially decays, which should also be visible in the retarded lightcurve. Since, however, A ≈ /epsilon1 E 0 for t em /lessmuch t syn , we set with Once A ∗ ( /epsilon1, t em ) is larger than unity the unretarded lightcurve will exponentially decay. Thus, we obtain the second characteristic time scale t 2 ( /epsilon1 ) by A ( /epsilon1, t 2 ( /epsilon1 )) = 1, yielding Unlike t 1 ( /epsilon1 ), the second characteristic time scale exhibits no restrictions by /epsilon1 . Obviously, t 1 ( /epsilon1 ) < t 2 ( /epsilon1 ). For t 2 ( /epsilon1 ) > λ 0 the exponential will become important only after the light-crossing time scale. Solving the inequality for /epsilon1 we obtain We can now begin with the actual calculation of the retarded lightcurve. The simplest case is obviously for t > λ 0 , since in this case the retarded lightcurve should be the same as the unretarded lightcurve. This is due to the fact that the retardation is not important for time scales much longer than λ 0 . Inspecting the difference t -λ 0 λ , we see that λ 0 λ can be at most equal to λ 0 . Thus, for t /greatermuch λ 0 we can approximate t -λ 0 λ ≈ t . Hence, which, indeed, equals the unretarded lightcurve. The other rather simple case is for t < λ 0 with the further requirement that t < t 1 , 2 ( /epsilon1 ) (the subscript refers to both t 1 and t 2 ). The latter implies that the unretarded lightcurves were neither variable nor have they decayed already. Then in eq. (21) the terms ( t -λ 0 λ ) /t syn can be neglected compared to unity, yielding For times below the light-crossing time scale and below the variability time scale of the unretarded lightcurve the retarded lightcurve increases rapidly L ∝ t 2 . For intermediate times the calculation is quite involved, and the details can be found in appendix A. We obtain We note that the exact form of the intermediate regime is not so important, since it will be glued to the approximation (29) at t ≈ t 2 . The most important result is the linear increase of the the lightcurve (30), which leads to a break at t 2 in the retarded lightcurve. However, if t 1 , 2 ( /epsilon1 ) > λ 0 the intermediate part does not play a role, and the lightcurve breaks immediately at t = λ 0 from the initial t 2 -dependence to the time dependence given by equation (28). Depending on the synchrotron photon energy /epsilon1 , we can now construct the lightcurves from the three approximations (28) - (30). We obtain two cases, divided in additional sub-cases. Beginning with /epsilon1 < E 0 / 3, we get: For /epsilon1 > E 0 / 3 the solutions become: The lightcurves (33) and (35) cut off at t = λ 0 . Obviously, light from the back reaches the observer only at later times, causing the radiation to be visible on longer time scales than implied by the unretarded lightcurve. The analytical results (31) - (35) are plotted along with a numerical integration of equation (21) in Figure 2 for two cases of γ 0 . For comparison, we also show the unretarded lightcurve. The first obvious result is that the retarded synchrotron lightcurve increases rapidly as long as t < λ 0 . Afterwards the retarded lightcurve behaves as the unretarded one, which is reasonable, as we discussed above. The other points mentioned earlier are also quite obvious. Even though the unretarded lightcurve for very high energies cuts off long before the light-crossing time scale, the retarded lightcurves are extended until λ 0 . The break in the lightcurve in the intermediate time regime is also evident. However, as discussed above, the low energetic cases, where the variability time scales are much longer than the light-crossing time scale, do not exhibit this break. As one can see, the analytical result matches the numerical integration rather well, which is reassuring and validates a posteriori our approximations. However, there is one caveat: The distinction of cases by t 2 and /epsilon1 2 is rather sharp (esp. equations (33) and (35)). This is obvious in the left plot of Figure 2 in the analytical curve for /epsilon1 = 10 E 0 , which cuts off at t = λ 0 . On the other hand, the numerical curve in this case decays exponentially. The distinction of the cases divided by /epsilon1 2 is, therefore, not as strict as implied by the analytical result. It is a more gradual transition, which is, however, difficult to implement in one equation. The problem is probably due to the rather artificial definition of t 2 , which is also indicated by the fact that the break for the high-energy lightcurves is better placed at 2 t 2 instead of t 2 .\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"5. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING INITIAL SSC COOLING\",\n \"content\": \"For the case α /greatermuch 1 we use equations (19) and (20) in equation (3) to obtain the retarded lightcurve For t c < t < t c + λ 0 both L 1 and L 2 contribute to the emitted lightcurve, which differs from the strict division of the unretarded lightcurves (19) and (20). This is, again, an effect of the retardation: Even if light received from the front of the source is from electrons already cooling in the linear regime ( t em > t c ), the light received from the back of the source is still from electrons cooling in the nonlinear regime ( t em < t c ). If t c < λ 0 this period can be quite extended. Although there are several sub-cases to consider in the analytical calculation, we can use the same approximation for the integrals (36) and (37), as we used to obtain equations (28) - (30). It is therefore unnecessary to repeat them in detail. Instead, we will summarize the results in the most compact form possible, where the sub-cases are combined in such a way that the resulting lightcurve is continuous. The characteristic time scales t 3 ( /epsilon1 ) and t 4 ( /epsilon1 ) are obtained by the same arguments as t 1 ( /epsilon1 ) and t 2 ( /epsilon1 ), giving For t 3 , 4 ( /epsilon1 ) > λ 0 we find while for t 3 , 4 ( /epsilon1 ) > t c we obtain respectively. With these definitions, we sum up the results of the analytical calculation. We begin with the case t c < λ 0 : For t c > λ 0 the analytical calculation yields for /epsilon1 < E 0 / 3 which is the only case where L must be divided. For /epsilon1 > E 0 / 3 we obtain In Figure 3 we compare the analytical results with the numerical results, and achieve quite good agreement. The unretarded lightcurve is shown again for comparison. Since the basic properties of the plot are the same as in Figure 2, we do not need to repeat them here. The problem with t 4 and /epsilon1 4 , mentioned in the discussion for Figure 2, is evident here, again.\",\n \"pages\": [\n 6,\n 7\n ]\n },\n {\n \"title\": \"6. DISCUSSION\",\n \"content\": \"In Figures 2 and 3 we show lightcurves in a logarithmic plot, which has the advantage of having several cases in one plot. This makes it much easier to compare variability aspects which occur on very different time scales. Our discussion will focus on these logarithmic plots. On the other hand, lightcurves are commonly displayed in a linear plot, which highlights the behavior of lightcurves around their respective maxima. We present such linear plots in Figure 4. The results are completely compatible. Comparing Figures 2 and 3 one can see that there are some points, where the results are similar, and some other points, which are remarkably different. First of all, we note that the 'variability time scale' of any given lightcurve is determined by its global maximum. Thus, the minimal variability time scale, which is possible at all, is given by the light-crossing time scale, since the source is evenly contributing to the radiative output. If the source only partially radiates, the variability time scale can be much lower (Eichmann et al. 2010). The rising phase until λ 0 is dominated by the source geometry, giving a t 2 -dependence up to the break times t 2 ( /epsilon1 ) for α /lessmuch 1 and t 4 ( /epsilon1 ) for α /greatermuch 1, respectively. If t 2 , 4 ( /epsilon1 ) < λ 0 , the lightcurve exhibits a break to a t 1 -dependence. Otherwise the spectrum breaks directly to the unretarded lightcurve at λ 0 . 2 Secondly, for larger initial electron energies γ 0 the variability time scale is much reduced compared to lower initial electron energies. Hence, in the low-energetic frequency bands the variability time scale shifts closer to λ 0 for larger γ 0 . Thus, one can get information about the initial electron energy by observing the peak times of different frequency bands. The plots for the high-energetic cases ( γ 0 = 10 5 ) look quite similar in both cases of α , since t c is smaller than λ 0 , and the lightcurves are the same for t > t c . However, they can be distinguished by the high-energetic frequency bands. Both are less luminous for α /greatermuch 1 compared to α /lessmuch 1, because the synchrotron SED exhibits a broken power-law for α /greatermuch 1, leading to a decreased flux for high energies compared to the α /lessmuch 1 case (cf. SBM). Additionally, the break in the lightcurve from the quadratic time-dependence to the linear timedependence takes place a factor 3 α 2 earlier in the α /greatermuch 1 case than for α /lessmuch 1, since the unretarded lightcurve cuts off much earlier for α /greatermuch 1 than for α /lessmuch 1. Thus, the sum over all unretarded lightcurves of each slice (that is the retarded lightcurve) for α /greatermuch 1 must be less luminous and increase less strongly than for α /lessmuch 1. The low-energetic cases ( γ 0 = 10 3 ) differ strongly for α larger and smaller than unity, since t c is larger than λ 0 . The features, which are plainly visible in the unretarded lightcurve, are thus also visible in the retarded lightcurve. The lightcurve for /epsilon1 = 10 E 0 cuts off in both cases at around λ 0 . However, for α /greatermuch 1 the break is clearly visible in the lightcurve, which is due to the faster cooling of the electrons in this case of α . Similarly, the lightcurve for /epsilon1 = E 0 cuts off for α /greatermuch 1 at λ 0 because of the faster cooling, and for α /lessmuch 1 the lightcurve shows a rather broad exponential decay. 3 The lightcurves for /epsilon1 = 10 -2 E 0 can be distinguished quite well, since the lightcurve for α /lessmuch 1 shows a rapid increase to the narrow maximum, while the light curve for α /greatermuch 1 exhibits a broad and flat maximum, which covers almost two orders of magnitude in time. As stated above, because of the broken power-law in the SED for α /greatermuch 1 the maximum of the SED is attained at /epsilon1 = E 0 /α 2 , which is in our example the lightcurve for /epsilon1 = 10 -2 E 0 . This explains the broad maximum, and also why the higher energies are again less luminous compared to the α /lessmuch 1 case. In the lightcurves for /epsilon1 = 10 -4 E 0 there is only a very slight difference, since the rising part after λ 0 sets in earlier for α /greatermuch 1 than for α /lessmuch 1. However, the increase is quite 2 The powers of t depend sensitively on the chosen geometry. E.g. for a cylindrical source the power is reduced by unity giving a t 1 - and a flat t 0 -dependence. small until t c and detailed observations are needed to distinguish the models. Obviously, for smaller emission regions the lightcrossing time scale λ 0 is reduced and the effects of the time-dependent cooling will be even more pronounced with very short variability time scales. Additionally, a smaller emission region leads to a larger α according to equation (13). Thus, the time-dependent SSC cooling is quite important for models which assume a small emission region to explain the rapid variability in blazars, like those cited in the introduction. We numerically checked if our results are also valid for different injection scenarios, such as a power-law, and obtained qualitatively similar results as one can see in Figure 5 of appendix B. Thus, we are confident that the discussion presented here is robust.\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"6.1. Caveats of the approach\",\n \"content\": \"Of course, our approach is simplified, leaving aside several, possibly important aspects. As stated in section 2, we assume that the source is spatially homogeneous. Additionally, we neglect the 'internal' retardation of the inverse Compton processes. The time, a photon travels before it is inverse Compton scattered, should on average be much less than λ 0 . Thus, the effect on the light curve is small, apart from a short delay of the SSC light curve (which we do not calculate in this paper). However, cooling might be affected, since the SSC cooling should be similarly delayed as the SSC light curve. On the other hand, as shown in Schlickeiser (2009) and Zacharias & Schlickeiser (2010), the SSC cooling is orders of magnitude quicker than the synchrotron and external Compton cooling, which should more than compensate the small retardation delay. We do not expect a delay effect for the external Compton scattering, since they are present all the time and are more or less homogeneously distributed (ZSb, Sokolov & Marscher 2005). We also do not discuss the acceleration of the electrons. This might have a significant impact on the light curve, since the variability is governed by the longest time scale (in our case just λ 0 and t syn , with an influence by t c for α /greatermuch 1). If the acceleration takes particularly long the effects due to retardation or cooling would be washed out. If the acceleration takes only a small amount of time, it will certainly influence the rising phase of the light curve, but its effect on the main part of the variability will not be significant. This argument might not hold for very small emission regions. On the other hand, the acceleration time scale is only important, if the acceleration and radiation zone are spatially and temporally coincident. This is still under debate, and only recently these conditions are incorporated in numerical studies (e.g. Weidinger et al. 2010; Weidinger & Spanier 2010). Thus, we follow the assumption or simplification that acceleration and radiation are (especially) temporally separated. Then, the acceleration time scale does not influence the resulting light curve. Chiaberge & Ghisellini (1999), and also e.g. Kataoka et al. (2000) or Li & Kusunose (2000), used similar assumptions in their numerical analysis. In fact, most theoretical investigations use numerical schemes with the advantage of employing more and more realistic scenarios, such as time-dependency (Bottcher & Chiang, 2002), inclusion of shock acceleration (Sokolov et al., 2004), hydrodynamic simulations (Mimica et al., 2004; Cabrera et al., 2013), and multizone models that incorporate the full retardation of all processes (Graff et al., 2008, Joshi & Bottcher 2011). In our analytical discussion we are for obvious reason not able to include all these details. That is why we focus on the details of the time-dependency, showing analytically that time-dependent effects, especially from SSC, are very important for rapid flares.\",\n \"pages\": [\n 8\n ]\n },\n {\n \"title\": \"7. CONCLUSIONS\",\n \"content\": \"In this paper we introduced our approach to calculate theoretical synchrotron lightcurves for flaring blazars, where the radiating relativistic electrons are cooled by the combined synchrotron, external Compton and timedependent SSC mechanisms. This complements the recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (SBM); Zacharias & Schlickeiser 2010, 2012a (ZSa), 2012b (ZSb)) on the effects of the combined cooling on the SED. Lightcurves show the intensity of a specific frequency band over time. Thus, they are a perfect tool to analyze the flaring behavior of blazars in different energies, such as correlations between different frequency bands. We were able to show that the synchrotron lightcurves exhibit a different form, if the time-dependent nature of the SSC cooling is taken into account, compared to the usual time-independent approaches. For that we first derived a formula to calculate the lightcurve from the intensity distribution, where we introduced the retardation due to the finite size of the radiation source. Using the intensities derived by SBM for the time-independent and the time-dependent cooling scenarios, we calculated the resulting lightcurves. Our calculations highlight the differences between the usual linear and the time-dependent cooling scenarios, giving us confidence that the important effects in the lightcurves are really due to the different cooling terms, and are not hidden by other effects. The main results can be summarized as follows. (1) Until the light crossing time scale λ 0 is reached, the initial synchrotron lightcurves depend strongly on the geometry of the source. In our example of a spherical source the lightcurve increases ∝ t 2 , which, depending on the synchrotron photon energy /epsilon1 , is followed by a linear t -dependence. We note, however, that this rising phase might be hard to observe depending on the sampling rate in specific frequency bands. (2) If the transition time t c from time-dependent SSC to linear cooling is larger than the light crossing time scale (i.e., t c > λ 0 ), the effects of the rapid SSC cooling are clearly visible for t > λ 0 . The lightcurves exhibit their respective maximum up to an order of magnitude earlier, if the electrons cool initially by the timedependent SSC process. In this cooling regime variability can be 10 times faster than in the linear cooling regime. The different spectral powers below and above the transition time t c probably need very precise measurements to be distinguishable in the data of blazars. (3) The lightcurves are rather similar, if t c < λ 0 , since the effects of the time-dependent SSC cooling are smeared out by the retardation. The results (2) and (3) obviously depend sensitively on the source parameters. In very compact emission regions with a short light crossing time scale and a large injection parameter α , the effects of the time-dependent SSC cooling are most significant. This in combination with the strong effects on the SED (e.g. ZSb) should help to clearly discriminate between different models, and to restrict the parameter space. In this context theoretical prediction of the SSC and EC lightcurve are also manda- ory, and we intend to publish the results in a future work, where also a much deeper discussion of correlations is possible. To conclude, we argue for a wide utilization of the timedependent SSC cooling scenario, at least for the modeling of rapid flares in blazars, where compact emission regions are necessary. We thank the anonymous referee for constructive comments, which helped significantly to improve the manuscript. We acknowledge support from the German Ministry for Education and Research (BMBF) through Verbundforschung Astroteilchenphysik grant 05A11PC1 and the Deutsche Forschungsgemeinschaft through grant Schl 201/23-1.\",\n \"pages\": [\n 8,\n 9,\n 10\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Aharonian F.A., et al., 2007, ApJ 664, L71 Arbeiter C., Pohl M., Schlickeiser R., 2002, A&A 386, 415 Barkov M.V., Aharonian F.A., Bogovalov S.V., Kelner S.R., Khangulyan D, 2012, ApJ 749, 119 Biteau J., Giebels B., 2012, A&A 548, A123 Blazejowski M., et al., 2000, ApJ 545, 107 B¨ottcher M., 2007, Astroph. & Space Sci. 309, 95 B¨ottcher M., 2012, preprint: arXiv:1205.0539 B¨ottcher M., Chiang J., 2002, ApJ 581, 127 Cabrera J.I., Coronade Y., Benitez E., Mendoza S., Hiriart D., Sorcia M., 2013, MNRASL, 434, L6 Chiaberge M., Ghisellini G., 1999, MNRAS 306, 551 Crusius A., Schlickeiser R., 1988, A&A 196, 327 Cui W., 2004, ApJ 605, 662 Dermer C. D., Schlickeiser R., 1993, ApJ 416, 458 Eichmann B., Schlickeiser R., Rhode W., 2010, A&A 511, A26 Giannios D., 2013, MNRAS 431, 355 Ghisellini G., Tavecchio F., Bodo G., Celotti A., 2009a, MNRAS 393, L16 Ghisellini G., Tavecchio F., Ghirlanda G., 2009b, MNRAS 399, 2041 Kataoka J., et al., 2000, ApJ 528, 243 Kardashev, N. S., 1962, Sov. Astron. J. 6, 317 Schlickeiser R., 2009, MNRAS 398, 1483 Sokolov A., Marscher A.P., 2005, ApJ 629, 52 Tavecchio F., Becerra-Gonzalez J. Ghisellini G., Stamerra A., Bonnoli G., Foschini L., Maraschi L., 2011, A&A 534, A86 Urry C. M., Padovani P., 1995, PASP 107, 803 Vercellone S., et al., 2011, ApJL 736, L38 Weidinger M., Ruger M., Spanier F., 2010, ASTRA 6, 1 Weidinger M., Spanier F., 2010, A&A 515, A18 Zacharias M., Schlickeiser R., 2010, A&A 524, A31 Zacharias M., Schlickeiser R., 2012a, MNRAS 420, 84 (ZSa) Zacharias M., Schlickeiser R., 2012b, ApJ 761, 110 (ZSb)\",\n \"pages\": [\n 10\n ]\n },\n {\n \"title\": \"CALCULATION OF THE INTERMEDIATE PART\",\n \"content\": \"The intermediate time regime t 1 , 2 < t < λ 0 requires another approach. The approximations of the other regimes cannot be used here. Integrating by parts and approximating to first order yields where we also approximated for t < t syn . This is the result (30), which fits very well the numerical solution for intermediate times. In order to check if our analytical results can be regarded as qualitatively general, we performed a numerical integration of equation (3) with a power-law injection of the form The differential equation (7) with this type of injection has been solved by Zacharias & Schlickeiser (2010), and we use their result in equation (4) in order to calculate the intensity distribution. For the illustrative case s = 2 the results are plotted in Fig. 5 for two cases of α and two cases of the upper limit γ 2 , respectively. Without going into details, one can see that the results discussed in section 6 are qualitatively recovered, which gives us confidence that our approach is robust.\",\n \"pages\": [\n 10,\n 11\n ]\n }\n]"}}},{"rowIdx":74,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...778...45C"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1309.4119.pdf"},"content":{"kind":"string","value":"\nSUPERORBITAL PERIODIC MODULATION IN WIND-ACCRETION HIGH-MASS X-RAY BINARIES FROM Swift BAT OBSERVATIONS\n1,2 3,4\nRobin H. D. Corbet and Hans A. Krimm Draft version October 17, 2018\nABSTRACT\nWe report the discovery using data from the Swift Burst Alert Telescope (BAT) of superorbital modulation in the wind-accretion supergiant high-mass X-ray binaries 4U 1909+07 (= X 1908+075), IGR J16418-4532, and IGR J16479-4514. Together with already known superorbital periodicities in 2S0114+650 and IGR J16493-4348, the systems exhibit a monotonic relationship between superorbital and orbital periods. These systems include both supergiant fast X-ray transients (SFXTs) and classical supergiant systems, and have a range of inclination angles. This suggests an underlying physical mechanism which is connected to the orbital period. In addition to these sources with clear detections of superorbital periods, IGR J16393-4643 (= AX J16390.4-4642) is identified as a system that may have superorbital modulation due to the coincidence of low-amplitude peaks in power spectra derived from BAT, RXTE PCA, and INTEGRAL light curves. 1E 1145.1-6141 may also be worthy of further attention due to the amount of low-frequency modulation of its light curve. However, we find that the presence of superorbital modulation is not a universal feature of wind-accretion supergiant X-ray binaries.\nSubject headings: stars: individual (2S 0114+650, 1E 1145.1-6141, IGR J16393-4643, IGR J164184532, IGR J16479-4514, IGR J16493-4348, 4U 1909+07) - stars: neutron - Xrays: stars\n1. INTRODUCTION\nSuperorbital modulation is seen in a variety of X-ray binaries. A review of superorbital modulation in several types of systems is presented by Kotze & Charles (2012). In some cases such as Her X-1, SMC X-1 and LMC X-4, where accretion occurs by Roche-lobe overflow via an accretion disk onto a neutron star, the mechanism driving superorbital modulation can be understood as either precession of the accretion disk (e.g. Petterson 1975) or of the neutron star (e.g. Postnov et al. 2013). Irradiation of the accretion disk by the central X-ray source provides a possible mechanism for driving disk precession (e.g. Ogilvie & Dubus 2001, and references therein). Be star systems also exhibit long timescale, possibly periodic, variability at optical wavelengths. This long timescale variability has been claimed to be correlated with orbital period (Rajoelimanana et al. 2011).\nA more puzzling variety of superorbital variability was found in a supergiant high-mass X-ray binary (sgHMXB). The sgHMXBs can be broadly classified into 'classical' systems, which may suffer from high levels of absorption, and supergiant fast X-ray transients (SFXTs; e.g. Blay et al. 2012; Sidoli 2013). In the sgHMXB 2S0114+650 there are three periodicities: a ∼ 9700 s neutron star rotation period, an 11.6 day orbital period, and a 30.7 day superorbital modulation (Corbet et al.\n1 University of Maryland, Baltimore County, MD, USA; corbet@umbc.edu\n2 CRESST/Mail Code 662, X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n3 Universities Space Research Association, 10211 Wincopin Circle, Suite 500, Columbia, MD 21044, USA\n4 CRESST/Mail Code 661, Astroparticle Physics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n1999; Wen et al. 2006; Farrell et al. 2008). A question has been whether 2S 0114+650 is exceptional, perhaps because of its unusually long pulse period, or whether other wind-accretion HMXBs also show similar superorbital periodicities. If similar behavior is found in other systems, then this may provide a way to determine, or at least constrain, the underlying mechanism. A suggestion that the phenomenon might be more general than just the case of 2S 0114+650 came when a superorbital period was found in the sgHMXB IGR J16493-4348 (Corbet et al. 2010b).\nThe Swift BAT provides an excellent way to monitor sgHMXBs. These systems are often highly absorbed, which presents difficulties for an instrument such as the Rossi X-ray Timing Explorer ( RXTE ) All Sky Monitor (ASM) which is sensitive in the 2 - 12 keV band (Levine et al. 1996). The Swift BAT's sensitivity to higher energy X-rays ( > 15 keV) provides a way to peer through this absorption. We present here a review of our searches of BAT light curves of sources thought to be HMXBs, in order to find additional sources that may also display superorbital modulation. In a few cases we also employ data collected from Galactic plane scans (Markwardt 2006) made with the RXTE Proportional Counter Array (PCA). The large effective area of the PCA enables observations to be made in the lower energy range of 2 - 10 keV. Although the PCA data cover only a limited fraction of the sky they have greater sensitivity than the RXTE ASM. MAXI light curves (Sugizaki et al. 2011) are not available for the majority of systems considered here.\nWe present here the results of a search for superorbital modulation in additional wind-accretion supergiant HMXBs. We find three new systems with clear superorbital modulation, initial reports of which were made in\nCorbet & Krimm (2013a,b). We also find hints of modulation in two other systems. Although the number of systems is small, three new systems plus two previously known, we note a monotonic relationship between orbital and superorbital periods. We consider possible mechanisms that might cause superorbital modulation in some, but not all, sgHMXBs.\n2. DATA AND ANALYSIS\nThe Burst Alert Telescope (BAT) on board the Swift satellite (Gehrels et al. 2004) is described in detail by Barthelmy et al. (2005). It uses a 2.7 m 2 coded-aperture mask and a 0.52 m 2 CdZnTe detector array. The BAT has a wide field of view, 1.4 sr half-coded, 2.85 sr 0% coded. The pointing direction of Swift is driven by the narrow-field XRT and UVOT instruments on board the satellite. The BAT typically observes 50%-80% of the sky each day. We used data from the Swift /BAT transient monitor (Krimm et al. 2006, 2013) covering the energy range 15 - 50 keV, and selected data with time resolution of Swift pointing durations. The transient monitor data are available shortly after observations have been performed. The light curves considered here cover the time range of MJD 53,416 to 56,452 (2005-02-15 to 2013-06-09). The light curves of some sources, not including the ones discussed in detail here, were more recently added to the analysis and hence have shorter durations. BAT light curves are also available from the catalogs such as described by Tueller et al. (2010). However, the most recent BAT catalog is from 70 months of data (Baumgartner et al. 2012) and the transient monitor light curves are hence of longer duration. The transient monitor light curves generally cover more than 3000 days, approximately 50% longer than the 70-month catalog light curves.\nWe used only data for which the data quality flag ('DATA FLAG') was set to 0, indicating good quality. In addition, we found that even data flagged as 'good' were sometimes suspect. In particular we identified a small number of data points with very low fluxes and implausibly small uncertainties. We therefore removed these points from the light curves. A total of 1244 light curves were available, this includes 106 blank fields that are used for test purposes.\nTo search for periodic modulation in the light curves, we calculated discrete Fourier transforms (DFTs) of all available light curves. We calculated the DFTs for a frequency range which corresponds to periods of between 0.07 days to the length of the light curves - i.e. generally ∼ 3000 days. The contribution of each data point to the power spectrum was weighted by its uncertainty using the 'semi-weighting' technique (Corbet et al. 2007a,b). This takes into account both the error bars on each data point and the excess variability of the light curve. Scargle (1989) notes that the weighting of data points in a power spectrum can be compared to combining individual data points. In this way, the use of semi-weighting is analogous to combining data points using the semi-weighted mean (Cochran 1937, 1954). We oversampled the DFTs by a factor of five compared to their nominal resolution. Calculations of the significance of peaks seen are expressed in terms of false alarm probability (FAP; Scargle 1982) which takes into account the DFT oversampling. Uncertainties in periods are generally derived using the\nexpression of Horne & Baliunas (1986). In the figures showing power spectra we mark in 'white noise' 99.9% and 99.99% significance levels. However, many sources exhibit noise continua which are not 'white'. In our calculations of FAP, we therefore determined local noise levels by fitting the continuum power levels in a narrow frequency range around each peak of interest.\n3. SOURCES WITH PREVIOUSLY REPORTED PERIODIC SUPERORBITAL MODULATION\n3.1. 2S0114+650\n2S0114+650 is an unusual HMXB system that has an exceptionally long pulse period of ∼ 9700 s (e.g. Corbet et al. 1999). There has been controversy over the spectral classification of the mass donor, but Reig et al. (1996) derive a spectral type of B1 Ia. From optical radial velocity measurements, Grundstrom et al. (2007) determine an orbital period of 11.5983 ± 0.0006 days and a moderate eccentricity of 0.18 ± 0.05. The orbital period is also seen in the RXTE ASM light curve (Corbet et al. 1999; Wen et al. 2006). A 30.7 ± 0.1 day superorbital period was found by Farrell et al. (2006) from RXTE ASM observations, and the period was later refined to 30.75 ± 0.03 days by Wen et al. (2006). Farrell et al. (2008) performed extensive RXTE PCA observations covering approximately 2 cycles of the superorbital period. Although Farrell et al. (2008) found variations in the X-ray absorption on the orbital period, they found no such changes over the superorbital period. However, a significant increase in the photon index of the power-law model used to fit the X-ray spectrum was reported at the minimum flux phase of the superorbital period. Farrell et al. (2008) concluded that the superorbital modulation was due to mass-accretion rate variations, although the mechanism causing this could not be determined.\nThe power spectrum of the BAT light curve of 2S0114+650 is shown in Figure 1, both the orbital and superorbital periods are strongly detected, with the superorbital period being stronger than the orbital modulation. We determine orbital and superorbital periods of 11.591 ± 0.003 and 30.76 ± 0.03 days respectively. The BAT light curve of 2S0114+650 folded on the orbital and superorbital periods is shown in Figure 2. For consistency with the work of Farrell et al. (2008) the light curve folded on the superorbital period uses a definition of phase zero as the time of minimum flux. However, for the other sources considered in this paper we use the time of maximum flux as phase zero. Both the orbital and superorbital modulations are quasi-sinusoidal and no evidence for an eclipse is seen in the light curve folded on the orbital period.\n3.2. IGR J16493-4348\nIGR J16493-4348 was discovered by Grebenev et al. (2005) and subsequent X-ray observations suggested that the source is an X-ray binary (Hill et al. 2008). Nespoli et al. (2010) classified the infrared counterpart as a B0.5 I supergiant. A 6.8 day orbital period was independently found by Corbet et al. (2010b) and Cusumano et al. (2010) using BAT 54 month survey data with the two groups finding periods of 6.7906 ± 0.0020 and 6.782 ± 0.005 days respectively. The BAT modulation was interpreted by Cusumano et al. (2010) as show-\n\n\n
Figure 1. Power spectrum of the BAT light curve of 2S 0114+650. Note that the superorbital peak at 30.7 days is stronger than the orbital modulation at 11.6 days. The horizontal dashed lines indicate 'white noise' 99.9% and 99.99% significance levels.
\n\n\n\n
Figure 2. Swift BAT light curve of 2S 0114+650 folded on its orbital period (top) and folded on its superorbital period (bottom). The period values are given in Table 1. Phase zero for the orbital period is the time of periastron passage from Grundstrom et al. (2007) and is MJD 51,824.8. Phase zero for the superorbital period is the time of minimum flux from Farrell et al. (2008) and is MJD 53,488. We note that this definition of phase zero differs from the other sources considered in this paper where phase zero for the superorbital modulation is defined as the time of maximum flux.
\n\ng the presence of an eclipse. Corbet et al. (2010b) confirmed the orbital period using PCA Galactic plane scan data which gave an orbital period of 6.7851 ± 0.0016 days. In addition, Corbet et al. (2010b) noted the presence of a 20.07 ± 0.02 day superorbital period in the BAT data which was confirmed by modulation at 20.09 ± 0.02 days in the PCA observations. Pointed RXTE PCA observations revealed a ∼ 1093 s pulse period (Corbet et al. 2010c), and pulse timing with the PCA yielded a mass function of 14.0 ± 2.3 M /circledot (Pearlman et al. 2013) which confirms the interpretation of IGR J16493-4348 as a supergiant HMXB.\nThe power spectrum of the BAT light curve of IGR\n\n\n
Figure 3. Power spectrum of the BAT light curve of IGR J164934348.
\n\n\n\n
Figure 4. Swift BAT light curve of IGR J16493-4348 folded on its orbital period (top) and folded on its superorbital period (bottom). Phase zero for the orbital light curve corresponds to the center of the eclipse and is MJD 54,175.92 (Cusumano et al. 2010). Phase zero for the superorbital light curve corresponds to the time of maximum flux and is MJD 54,265.1 (Corbet et al. 2010b).
\n\nJ16493-4348 is shown in Figure 3. This clearly shows the presence of the already known orbital and superorbital periods. However, the statistical significances of the periods are somewhat less than previously found from the BAT 54-month catalog data and the FAPs were ∼ 10 -6 and 0.04 respectively. We refine the period measurements to be 6.782 ± 0.001 and 20.07 ± 0.01 days for the orbital and superorbital periods respectively. The BAT light curve of IGR J16493-4348 folded on the orbital and superorbital periods is shown in Figure 4. The orbital modulation shows the presence of an eclipse, while the superorbital modulation is quasi-sinusoidal.\n4. SOURCES WITH NEW DETECTIONS OF PERIODIC SUPERORBITAL MODULATION\n4.1. IGR J16418-4532\nChaty et al. (2008) determined that the optical coun-\n\n\n
Figure 5. Power spectrum of the BAT light curve of IGR J164184532.
\n\nterpart of IGR J16418-4532 is probably an OB supergiant. Rahoui et al. (2008) fitted the spectral energy distribution of the likely 2MASS counterpart and found that this was consistent with an O/B massive star classification with a best fit spectral type of O8.5, although the luminosity type could not be determined. IGR J16418-4532 exhibits large flux variability, classifying it as an SFXT (Romano et al. 2011, 2012; Sidoli et al. 2012). Pulsations from the source were discovered by Walter et al. (2006) and refined to a period of 1212 ± 6 s by Sidoli et al. (2012). A 3.74 day orbital period has been found for IGR J16418-4532 from RXTE ASM and Swift BAT observations (e.g. Corbet et al. 2006; Levine et al. 2011). INTEGRAL and XMMNewton observations of IGR J16418-4532 are discussed by Drave et al. (2013a).\nThe power spectrum of the BAT light curve of IGR J16418-4532 (Figure 5) shows modulation at the 3.74 day orbital period and the second and third harmonics of this. In addition the power spectrum shows a peak near 14.7 days with an FAP of < 10 -6 . The light curve folded on this period (Figure 6) shows an approximately sinusoidal modulation. From a sine wave fit to the light curve we obtain:\nT max = MJD 55 , 994 . 6 ± 0 . 4 + n × 14 . 730 ± 0 . 006\nwhere T max is the time of maximum flux.\nThe full amplitude of the modulation, defined as (maximum - minimum)/ mean flux, from the sine fit is approximately 70%. From the fundamental of the orbital peak in the power spectrum we determine an orbital period of 3.73834 ± 0.00022 days, while the second harmonic yields 3.73886 ± 0.00014 days. This is consistent with the period of 3.73886 +0.00028, -0.00140 days given by Levine et al. (2011). The BAT light curve of IGR J16418-4532 folded on the orbital period is also shown in Figure 6 and this shows the presence of an eclipse.\n4.2. IGR J16479-4514\nIGR J16479-4514 is an SFXT with a rather short orbital period of near 3.3 days with periods of 3.3194 ± 0.0010 and 3.3193 ± 0.0005 days determined by Jain et al. (2009) and Romano et al. (2009), respectively, using Swift BAT data in both cases. The folded light\n\n\n
Figure 6. Swift BAT light curve of IGR J16418-4532 folded on its orbital period (top), and folded on its superorbital period (bottom). The period values are given in Table 1. Phase zero for the orbital period corresponds to the time of minimum flux and is MJD 52,735.84 (Levine et al. 2011). For the superorbital period phase zero corresponds to the time of maximum flux and is MJD 55,994.6 (Section 4.1).
\n\ncurve shows the presence of X-ray eclipses. The mass donor has a spectral type of O8.5I (Chaty et al. 2008; Rahoui et al. 2008) or O9.5 Iab (Nespoli et al. 2008). No X-ray pulsations have yet been reported.\nThe power spectrum of the BAT light curve (Figure 7) shows modulation at the 3.32 day orbital period and harmonics of this. From the fundamental we determine an orbital period of 3.3199 ± 0.0005 days. In addition to this, peaks are seen near 11.9 days and its second harmonic. The FAP of the harmonic is 0.0006 while that of the fundamental is 0.05. The second harmonic is stronger than the fundamental and from this we derive a superorbital period of 11.880 ± 0.002 days. The period determined from the fundamental is consistent with this at 11.871 ± 0.005 days. The BAT light curve of IGR J16479-4514 folded on the orbital and superorbital periods is shown in Figure 8. An eclipse is clearly seen in the light curve folded on the orbital period. The light curve folded on the superorbital period shows a relatively sharp rise from minimum to maximum followed by a plateau. The time of minimum flux is approximately MJD 55,993 ± 1.0 with maximum flux occurring approximately 0.25 in phase after this. The full amplitude of the modulation is approximately 130%.\n4.3. 4U 1909+07 (X 1908+075)\nWen et al. (2000) found a 4.400 ± 0.001 day orbital period for the X-ray binary 4U 1909+07 using RXTE ASM observations. X-ray pulsations with a period of 605 s were found with the RXTE PCA by Levine et al. (2004) and from a pulse arrival time analysis they found the orbit to be circular with an orbital period of 4.4007 ± 0.0009 days and derived a mass function of 6.1 M /circledot . Although Levine et al. (2004) proposed that the primary might be a Wolf-Rayet star, Morel & Grosdidier (2005) identified a likely near-IR candidate which they proposed to be a late O-type supergiant. Levine et al. (2004)\n\n\n
Figure 7. Power spectrum of the BAT light curve of IGR J164794514.
\n\n\n\n
Figure 8. Swift BAT light curve of IGR J16479-4514 folded on its orbital period (top) and folded on its superorbital period (bottom). The period values are given in Table 1. Phase zero for the orbital period is the center of the eclipse and is MJD 54,547.05 (Bozzo et al. 2009). Phase zero for the superorbital period corresponds to maximum flux and is MJD 55,996 (Section 4.2).
\n\nfound large orbital phase dependence of the X-ray absorption. The orbital period was further refined with additional ASM observations to 4.4005 ± 0.0004 days by Wen et al. (2006).\nThe power spectrum of the BAT light curve of 4U 1909+07 (Figure 9) shows strong modulation at the orbital period and we derive a period of 4.4003 ± 0.0004 days. In addition, significant modulation at a superorbital period near 15.2 days (FAP ∼ 10 -5 ) and the second harmonic of this are seen. Combining the detections at the fundamental and second harmonic, we determine a period of 15.180 ± 0.003 days.\nAs expected from the presence of harmonics in the power spectrum, the light curve folded on the superorbital period (Figure 10) shows a multi-peaked profile. The minimum is somewhat more clearly defined than the maximum. From an inspection of the folded light curve,\n\n\n
Figure 9. Power spectrum of the BAT light curve of 4U 1909+07.
\n\n\n\n
Figure 10. Swift BAT light curve of 4U 1909+07 folded on its orbital period (top) and folded on its superorbital period (bottom). The period values are given in Table 1. Phase zero for the orbital period is the time of superior conjunction from Levine et al. (2004) and is MJD 52,631.383. Phase zero for the superorbital period is the time of maximum flux and is MJD 56,004 (Section 4.3).
\n\nthe minimum occurs at approximately MJD 55,999 ± 1.5. The time of maximum flux occurs about 0.35 in phase after the minimum. The amplitude of the modulation, defined as (maximum - minimum)/ mean flux is approximately 50%. The BAT light curve folded on the orbital period is shown in Figure 10. This shows a quasisinusoidal modulation with no evidence for the presence of an eclipse.\n5. PROPERTIES OF SELECTED OTHER SGHMXBS\nFor comparison with the sgHMXB systems discussed above where superorbital modulation is seen, we present here examples of systems where there is no strong superorbital modulation, and two examples of systems which appear to be weak candidates for also possessing superorbital modulation.\n\n\n
Figure 11. Power spectra of the BAT light curves of IGR J180272016 (top), IGR J18483-0311 (middle), and IGR J19140+0951 (bottom) The horizontal dashed lines indicate 'white noise' 99.9% and 99.99% significance levels..
\n\n5.1. Examples of Systems with Strong Orbital Modulation but Lacking Superorbital Modulation\nThe Swift BAT set of light curves includes a number of other sgHMXBs. However, the majority of these do not show evidence for superorbital modulation. As examples we discuss here three systems. We choose 'IGR' systems which are typically rather hard sources and so suitable for study with the BAT. The examples selected here all have very significant orbital modulations of their light curves which have previously been reported.\n5.1.1. IGR J18027-2016 (= SAX J1802.7-2017)\nIGR J18027-2016 (= SAX J1802.7-2017) has a pulse period of 139.6s (Augello et al. 2003) and pulse arrival time analysis suggested a ∼ 4.6 day orbital period. From a timing analysis Hill et al. (2005) refined this to 4.5696 ± 0.0009 days. The spectral type of the mass donor has been proposed to be B1 Ib (Torrej'on et al. 2010) and B0-B1 I (Mason et al. 2011), thus making it an sgHMXB. The power spectrum of the BAT light curve of IGR J18027-2016 (Figure 11, bottom panel) is very flat with the exception of the orbital period and its second and third harmonics, together with a small peak corresponding to a period of one year.\n5.1.2. IGR J18483-0311\nIGR J18483-0311 is an SFXT with an early B supergiant optical counterpart (Rahoui & Chaty 2008). Orbital modulation is seen at a period near 18.55 days in RXTE ASM (Levine et al. 2011), BAT (Jain et al. 2009) and INTEGRAL observations (Sguera et al. 2007). This source also has a 21 s pulse period (Sguera et al. 2007). The power spectrum of the BAT light curve of IGR J18483-0311 (Figure 11, middle panel) shows strong modulation at the orbital period and the second harmonic of this. The power spectrum exhibits somewhat larger 'noise' at intermediate frequencies. A small nonstatistically significant ∼ 95 day bump is the third highest peak.\nIGR J19140+0951 (= IGR J19140+098) was discovered with INTEGRAL (Hannikainen et al. 2004) and a 13.558 ± 0.004 day period was found from RXTE ASM and Swift BAT observations (Corbet et al. 2004). From infrared observations the optical counterpart was determined to be a B0.5 supergiant (Hannikainen et al. 2007), later refined to B0.5 Ia by Torrej'on et al. (2010). No pulsations have yet been reported from this source despite INTEGRAL and RXTE PCA observations (Prat et al. 2008). The power spectrum of the BAT light curve of IGR J19140+0951 (Figure 11, top panel) shows an extremely flat power spectrum with the exception of strong peaks at the orbital period and the second harmonic of this.\n5.2. Sources of Potential Superorbital Interest\nAlthough the presence of superorbital periods in sgHMXBs does not appear to be ubiquitous, we can examine the power spectra of other wind-accretion HMXBs for the possible presence of superorbital periods under the assumption that the apparent correlation between orbital period and superorbital periods discussed in Section 6.3 is indeed correct. This then yields a restricted frequency range to be searched for superorbital modulation.\n5.2.1. 1E 1145.1-6141\nThe spectral type of the primary of 1E 1145.1-6141 was found to be B2 Iae by Hutchings et al. (1981) and Densham & Charles (1982). The pulse period is ∼ 297 s and pulse timing enabled Ray & Chakrabarty (2002) to determine a 14.365 ± 0.002 day orbital period with a modest eccentricity of 0.20 ± 0.03. Ray & Chakrabarty (2002) report that no eclipse was seen. No detection of orbital modulation of the X-ray flux from RXTE ASM observations is reported in the papers of Wen et al. (2006) and Levine et al. (2011). However, Corbet et al. (2007b) reported detection of the orbital period of 1E 1145.1-6141 in Swift BAT data with the presence of flares at both periastron and apastron. The presence of flares at apastron is also reported from INTEGRAL observations by Ferrigno et al. (2008).\nFor 1E 1145.1-6141, the strongest peak in the power spectrum of the BAT light curve (Figure 12) is at the second harmonic of the 14.4 day orbital period and the second highest peak is at the orbital period itself. The blind-search FAPs of the fundamental and second harmonic peaks would be 0.1 and ∼ 10 -5 respectively. The much lower significance of the fundamental is due to the increase in continuum power at lower frequencies. From the second harmonic we derive an orbital period of 14.365 ± 0.003 days, which is the same as that derived by Ray & Chakrabarty (2002) from pulse timing. The peak at the fundamental yields a period of 14.373 ± 0.007 days, which is also consistent, although with a somewhat larger uncertainty.\nThe BAT light curve folded on the orbital period (Figure 13) shows a double-peaked profile with maxima at periastron and apastron based on the ephemeris of Ray & Chakrabarty (2002). The third and the fourth highest peaks in the power spectrum are at periods of 67.8 ± 0.2 (equivalent to 135.6 ± 0.4, if regarded as a second harmonic) and 131.4 ± 0.8 days. The very low FAP of 0.2 of the ∼ 68 day peak means that this is not a\n\n\n
Figure 12. Power spectrum of the BAT light curve of 1E 1145.16141.
\n\n\n\n
Figure 13. Swift BAT light curve of 1E 1145.1-6141 folded on its orbital period (top) and folded on a 67.8 day period (bottom). For the orbital period phase zero corresponds to the time of periastron passage (MJD 51,008.1) determined by Ray & Chakrabarty (2002). For the 68 day modulation, phase zero corresponds to the time of maximum flux from a sine wave fit to the BAT light curve and is MJD 55,142.4 (Section 5.2.1).
\n\nstrong candidate for a superorbital period. However, the large amount of variability in the light curve compared to the orbital modulation makes this a potentially interesting system to continue to monitor. From a sine wave fit to the BAT light curve, we derive an epoch of maximum flux for the 68 day modulation of MJD 55,142.4 ± 0.6. The BAT light curve folded on the 68 day period is shown in Figure 13.\n5.2.2. IGR J16393-4643 (= AX J16390.4-4642)\nThe 910 s X-ray pulsar IGR J16393-4643 was reported by Thompson et al. (2006) to have a 3.7 day orbital period from a pulse timing analysis, although other solutions with orbital periods of 50.2 and 8.1 days could not be excluded. Thompson et al. (2006) proposed, on the basis of their orbital parameters, that IGR J16393-\n\n\n
Figure 14. Power spectrum of the BAT light curve of IGR J16393-4643.
\n\n4643 is a supergiant wind-accretion powered HMXB. Nespoli et al. (2010) instead suggested that this is a symbiotic X-ray binary with a 50 day period. However, Swift BAT and PCA Galactic plane scan observations clearly showed the system to have a 4.2 day orbital period (Corbet et al. 2010a) which is consistent with an interpretation of the system as an sgHMXB. The periods obtained from the BAT and PCA were 4.2368 ± 0.0007 and 4.2371 ± 0.0007 days respectively.\nBodaghee et al. (2012) obtained a precise position for IGR J16393-4643 using a Chandra observation, which excluded a previously proposed counterpart that had led to the symbiotic classification by Nespoli et al. (2010), and instead suggested that the correct counterpart to IGR J16393-4643 might be a distant reddened star.\nThe 4.2 day orbital period of IGR J16393-4643 is similar to the 4.4 day orbital period of 4U 1909+07 which has a superorbital period of 15.2 days. If there is indeed a relationship between superorbital and orbital periods, as discussed in Section 6.3, a superorbital period of ∼ 15 days would thus be predicted.\nThe strongest peak in the power spectrum of the updated Swift BAT light curve (Figure 14) is at the orbital period with a value of 4.2380 ± 0.0005 days. The second highest peak in the power spectrum (Figures 14 and 15) is at a period near 15 days at 14.99 ± 0.01 days, and there is another peak at half this period. The possible second harmonic is at a period of 7.485 ± 0.002 days, equivalent to a fundamental period of 14.971 ± 0.005 days if regarded as a harmonic. However, the 'blind search' FAPs of both peaks, even restricting ourselves to a search of periods longer than the orbital period, are very high at ∼ 17% and ∼ 7% for the 15 and 15/2 day peaks respectively. From a sine wave fit to the BAT light curve, with the period held fixed at 14.99 days, we obtain an epoch of maximum flux of MJD 55,092.6 ± 0.4. The BAT light curve of IGR J16393-4643 folded on the orbital period and the possible 14.99 day period are shown in Figure 16. The folded profile on the 14.99 day period suggests any modulation may not be perfectly sinusoidal, with the maximum slightly preceding the value predicted by the sine wave fit. The light curve folded on the orbital period suggests the presence of an eclipse.\nWe therefore also investigated the PCA Galactic plane\n\n\n
Figure 15. Power spectra of Swift BAT (top), RXTE PCA Galactic Plane scan (middle) and INTEGRAL (bottom) light curves of IGR J16393-4643 for periods longer than the orbital period. The vertical dashed red lines and the arrow mark the possible superorbital period.
\n\n\n\n
Figure 16. Swift BAT light curve of IGR J16393-4643 folded on its orbital period (top) and folded on its possible superorbital period (bottom). Period values are given in Table 1. Phase zero for the orbital period is time of maximum flux from Corbet et al. (2010a) (MJD 54,352.50) and for the possible superorbital period it is MJD 55,092.6, the epoch of maximum flux from a sine wave fit to the BAT light curve (Section 5.2.2)
\n\nscans of this source obtained between MJD 53163 and 55863 (2004-06-07 and 2011-10-29). This is 566 days longer than the light curve used in Corbet et al. (2010a). The PCA data yield an orbital period of 4.2376 ± 0.0005 days, consistent with our updated BAT result. In the power spectrum of the PCA scan observations (Figure 15), the largest peak for periods longer than the orbital period is at 14.99 ± 0.01 days, consistent with the possible BAT period.\nWe next examined the INTEGRAL light curve of IGR J16393-4643 that we obtained from the Heavens service of the ISDC. This covers a time range of MJD 52,650 to 55,856 (2003-01-11 to 2011-10-22) although with only very sparse sampling. This limited sampling yields large\n\n\n
Figure 17. Swift BAT (top), INTEGRAL IBIS (middle) and RXTE PCA scan (bottom) light curves of IGR J16393-4643 folded on its possible superorbital period. Phase zero is MJD 55,092.6, the epoch of maximum flux from a sine wave fit to the BAT light curve (Section 5.2.2)
\n\namounts of artifacts in the power spectrum of the light curve. For example, the 4.2 day orbital period is not the strongest peak. However, examining the peak nearest the orbital period yields a value of 4.2382 ± 0.0006, consistent with the periods derived from the BAT and PCA observations. The INTEGRAL power spectrum for periods longer than the orbital period (Figure 15) also shows a small peak near 15 days. This has a value of 14.98 ± 0.01 days, which is consistent with the periods obtained from the BAT and PCA observations.\nThe BAT, PCA, and INTEGRAL data folded on the possible superorbital period derived from the BAT data are shown in Figure 17. The three light curves appear to have roughly coincident maxima. While the coincidence of the periods obtained from three separate instruments is intriguing, additional data are required to confirm whether there truly is a superorbital period in this system. Such data may come from continued monitoring with the BAT, or from future missions such as the proposed Wide Field Monitor (WFM; Bozzo & LOFT Consortium 2013) on board the Large Observatory for X-ray Timing (LOFT; Feroci et al. 2012).\n6. DISCUSSION\n6.1. Excluding Period Artifacts\nSince the presence of superorbital periods in sgHMXBs is somewhat surprising, we consider whether they could be some type of artifact. We note that they are not present in other types of systems, and there is no obvious way to create superorbital modulation in only a subset of supergiant wind accretors. Superorbital modulation in 2S 0114+650 and IGR J16493-4348 was previously seen in other detectors ( RXTE ASM and RXTE PCA Galactic plane scan data respectively). In several cases there are pulse arrival time orbits that show that the orbital period really is the orbital period. In addition, Drave et al. (2013b) report that INTEGRAL /IBIS data\nconfirm the superorbital periods found for 4U 1909+07, IGR J16418-4532, and IGR J16479-4514.\nThe superorbital periods are rather prominent relative to the orbital periods in the BAT energy range. This appears to differ from results of lower-energy observations such as RXTE ASM observations of 4U 1909+07, where the orbital period is strongly detected, but the superorbital period is not seen. Similarly, for 2S 0114+650, although the superorbital period was initially detected from RXTE ASM data (Farrell et al. 2006), the superorbital modulation has lower amplitude than the orbital modulation in the ASM energy band. In contrast, the superorbital modulation of 2S 0114+650 is stronger than the orbital modulation in the BAT observations. One reason for this is likely to be the lower fractional modulation of the X-ray flux on the orbital period in the BAT energy range for non-eclipsing systems. For these types of systems a large component of the orbital modulation seen with lower-energy instruments is due to the changing absorption as the neutron star orbits its companion, which the BAT is relatively insensitive to.\n6.2. Coherence\nSuperorbital modulation from Roche-lobe overflow systems is not necessarily coherent. For example, there is considerable variation in the superorbital periods of SMC X-1 (Coe et al. 2013; Wojdowski et al. 1998) and Her X-1 (Leahy & Igna 2010), although not in LMC X4 (Hung et al. 2010). The sampling of the BAT light curves is very variable. This potentially makes it more difficult to calculate the true resolution of the power spectra. Therefore, in order to investigate the coherency of the superorbital modulation, we compared the widths of the superorbital peaks to those of the orbital peaks. This uses the assumption that the orbital modulation should be essentially periodic. We fitted Gaussian functions to the superorbital and orbital peaks in the power spectra in the five systems for which superorbital modulation is definitely observed and determined the following ratios of superorbital to orbital peak widths: 2S 0114+650, 1.05; IGR J16493-4348, 1.16; IGR J16418-4532, 0.92; IGR J16479-4514, 0.98; 4U 1909+07, 0.92. We therefore conclude that the superorbital modulations have very high coherence. For the two low-significance candidates we obtain ratios of superorbital to orbital peak widths of: IGR J16393-4643, 0.66; 1E 1145.1-6141, 0.89.\n6.3. Relationship Between Superorbital and Orbital Periods\nSystem parameters are summarized in Table 1, and in Figure 18 we plot superorbital period against orbital period. For the five systems with definite superorbital modulation, the linear correlation coefficient between P super and P orb is 0.996 and the associated probability of obtaining this level of correlation from a random data set is 0.03%. Because this possible correlation comes from such a small number of systems, a determination whether this possible dependence of superorbital period on orbital period is correct requires the candidate superorbital period in IGR J16393-4643 to be investigated with additional data, and further superorbital periods must be found in other systems. For the five systems the best linear fit for superorbital periods vs. orbital period has parameters\n\n\n
Figure 18. Superorbital period plotted against orbital period for the wind-accretion HMXBs discussed in the text. Statistical uncertainties on period measurements are smaller than symbol sizes. The filled symbols show definite superorbital period detections. The gray open symbol marks the modulation seen in IGR J163934643 which is not yet considered to be a definite detection of a superorbital period.
\n\nof:\nP super = 2 . 2 ± 0 . 1 × P orb +5 . 6 ± 0 . 8 days\nFor comparison, in Figure 19 we plot superorbital period against orbital period for a wide variety of systems. These include these Roche-lobe overflow powered systems: LMC X-4 (neutron star HMXB, P orb = 1.4 days, P super = 30.3 days), Her X-1 (neutron star intermediatemass system, P orb =1.7 days, P super = 35 days), SMC X-1 (neutron star HMXB, P orb = 3.89 days, P super = 56 days), and SS 433 (black hole candidate microquasar, P orb = 13.1 days, P super = 162.5 days). These parameters are taken from Kotze & Charles (2012). Be star systems are also shown with their parameters taken from Rajoelimanana et al. (2011). For the Be star systems the superorbital modulation periods may be quasi-periodic rather than strictly periodic. It the mechanisms driving superorbital modulation differ between different types of object, then the different types of system could be located in different regions of this diagram. We note that the sgHMXB superorbital periods are rather short relative to their orbital periods, compared to other types of systems. This is suggestive that, as expected, a different driving mechanism may be at work in the sgHMXBs superorbital modulation compared to the other types of system.\n6.4. Possible Mechanisms Driving Superorbital Modulation\nWe note that Farrell et al. (2008)'s extensive RXTE PCA observations of 2S 0114+650 showed that there were changes in absorption over the orbital period of this system, but not on the superorbital period. Farrell et al. (2008) therefore concluded that the superorbital modulation was related to variability in the mass accretion rate caused by an unknown mechanism. This is consistent with the stronger detection of superorbital periods with the BAT compared to orbital periods for noneclipsing systems than is the case with the RXTE ASM (Section 6.1). The ASM is more sensitive to changes in\n\n\n
Figure 19. Superorbital period plotted against orbital period for the a variety of HMXBs including both neutron star and black hole systems. 'R' indicates Roche-lobe overflow systems, 'W' are the five wind-accretion systems discussed in this paper, and 'B' shows Be star system parameters taken from Rajoelimanana et al. (2011). The sources included as Roche-lobe overflow systems are the high-mass neutron star systems LMC X-4 and SMC X-1, the intermediate-mass neutron star system Her X-1, and the black hole candidate SS 433.
\n\nabsorption over the orbital period. However, the BAT has overall better sensitivity for changes in the flux of highly-absorbed systems.\nIf mass-transfer rate variations are the cause of periodic superorbital modulation, then this suggests that the wind from the primary star could itself be modulated in some way by a mechanism related to the length of the orbital period. However, any satisfactory model must be able to account for the lack of superorbital variability in many systems. Thus, the modulation must be related to some parameter independent of inclination angle and whether the system is an SFXT or classical supergiant system. For example, an offset between the orbital plane and the rotation axis of the primary star, or a small orbital eccentricity, might satisfy such a requirement. The light curves folded on the superorbital periods exhibit a variety of morphologies, and so any model for the modulation must be able to account for this. We note the work of Koenigsberger et al. (2003) and Moreno et al. (2005) indicates that oscillations can be induced in nonsynchronously rotating stars in binary systems on periods longer than the orbital period. As discussed by Koenigsberger et al. (2006), such oscillations result in changes in the mass-loss rate of the primary star which would cause correlated changes in the X-ray luminosity. This model may also be consistent with the lack of superorbital modulation in all systems if only a fraction of primary stars are rotating non-synchronously. However, as noted by Farrell et al. (2008), the Koenigsberger et al. (2006) model applies to circular orbits and 2S 0114+650 has a modest eccentricity of 0.2. In addition, the high coherency of the superorbital modulations seems difficult to account for with oscillations of the primary star unless there is some way to keep strict phase stability.\nIn principle, the presence of a third object in the systems might drive superorbital modulation. The modulation from a third body would also naturally account for the coherency of the superorbital modulation. How-\never, the apparent correlation between superorbital and orbital periods would, if confirmed, place stringent constraints on how such multi-star systems might be formed. In addition, typically such triple body models for X-ray sources involve hierarchical systems with a distant third object (e.g. Mazeh & Shaham 1979).\n7. CONCLUSION\nObservations with the Swift BAT have shown the presence of superorbital periods in three additional sgHMXBs for a total of five definite such systems. The superorbital modulations have a variety of morphologies, ranging from approximately sinusoidal to multi-peaked profiles. However, superorbital modulation is not a ubiquitous property of sgHMXBs. With this limited set of data, a possible dependence of superorbital period on orbital period is suggested. The mechanism(s) driving such superorbital modulation remain unclear. However, possible models based on oscillations in the primary star driven by non-synchronous rotation, and three-body systems deserve further investigation. Continued monitoring of sgHMXBs in hard X-rays both with additional Swift BAT data and also potential new missions with high-energy X-ray sensitivity such as the LOFT WFM may reveal additional sources with superorbital periodicities.\nWe thank an anonymous referee for useful comments. This paper used Swift /BAT transient monitor results provided by the Swift /BAT team. The Swift/BAT transient monitor and H. A. 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\n\n
Table 1 Wind-Accretion sgHMXBs with Periodic Superorbital Modulation
\n
\nNote . - The superorbital period for the system below the line is a candidate and not a definite detection. The references for system parameters are given in the individual sections on each source. The orbital and superorbital periods and their errors are derived from the BAT light curves. For some systems additional determinations of periods may be available from other work, as given in the individual source sections.\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"We report the discovery using data from the Swift Burst Alert Telescope (BAT) of superorbital modulation in the wind-accretion supergiant high-mass X-ray binaries 4U 1909+07 (= X 1908+075), IGR J16418-4532, and IGR J16479-4514. Together with already known superorbital periodicities in 2S0114+650 and IGR J16493-4348, the systems exhibit a monotonic relationship between superorbital and orbital periods. These systems include both supergiant fast X-ray transients (SFXTs) and classical supergiant systems, and have a range of inclination angles. This suggests an underlying physical mechanism which is connected to the orbital period. In addition to these sources with clear detections of superorbital periods, IGR J16393-4643 (= AX J16390.4-4642) is identified as a system that may have superorbital modulation due to the coincidence of low-amplitude peaks in power spectra derived from BAT, RXTE PCA, and INTEGRAL light curves. 1E 1145.1-6141 may also be worthy of further attention due to the amount of low-frequency modulation of its light curve. However, we find that the presence of superorbital modulation is not a universal feature of wind-accretion supergiant X-ray binaries. Subject headings: stars: individual (2S 0114+650, 1E 1145.1-6141, IGR J16393-4643, IGR J164184532, IGR J16479-4514, IGR J16493-4348, 4U 1909+07) - stars: neutron - Xrays: stars","pages":[1]},{"title":"SUPERORBITAL PERIODIC MODULATION IN WIND-ACCRETION HIGH-MASS X-RAY BINARIES FROM Swift BAT OBSERVATIONS","content":"1,2 3,4 Robin H. D. Corbet and Hans A. Krimm Draft version October 17, 2018","pages":[1]},{"title":"1. INTRODUCTION","content":"Superorbital modulation is seen in a variety of X-ray binaries. A review of superorbital modulation in several types of systems is presented by Kotze & Charles (2012). In some cases such as Her X-1, SMC X-1 and LMC X-4, where accretion occurs by Roche-lobe overflow via an accretion disk onto a neutron star, the mechanism driving superorbital modulation can be understood as either precession of the accretion disk (e.g. Petterson 1975) or of the neutron star (e.g. Postnov et al. 2013). Irradiation of the accretion disk by the central X-ray source provides a possible mechanism for driving disk precession (e.g. Ogilvie & Dubus 2001, and references therein). Be star systems also exhibit long timescale, possibly periodic, variability at optical wavelengths. This long timescale variability has been claimed to be correlated with orbital period (Rajoelimanana et al. 2011). A more puzzling variety of superorbital variability was found in a supergiant high-mass X-ray binary (sgHMXB). The sgHMXBs can be broadly classified into 'classical' systems, which may suffer from high levels of absorption, and supergiant fast X-ray transients (SFXTs; e.g. Blay et al. 2012; Sidoli 2013). In the sgHMXB 2S0114+650 there are three periodicities: a ∼ 9700 s neutron star rotation period, an 11.6 day orbital period, and a 30.7 day superorbital modulation (Corbet et al. 1 University of Maryland, Baltimore County, MD, USA; corbet@umbc.edu 2 CRESST/Mail Code 662, X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 3 Universities Space Research Association, 10211 Wincopin Circle, Suite 500, Columbia, MD 21044, USA 4 CRESST/Mail Code 661, Astroparticle Physics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 1999; Wen et al. 2006; Farrell et al. 2008). A question has been whether 2S 0114+650 is exceptional, perhaps because of its unusually long pulse period, or whether other wind-accretion HMXBs also show similar superorbital periodicities. If similar behavior is found in other systems, then this may provide a way to determine, or at least constrain, the underlying mechanism. A suggestion that the phenomenon might be more general than just the case of 2S 0114+650 came when a superorbital period was found in the sgHMXB IGR J16493-4348 (Corbet et al. 2010b). The Swift BAT provides an excellent way to monitor sgHMXBs. These systems are often highly absorbed, which presents difficulties for an instrument such as the Rossi X-ray Timing Explorer ( RXTE ) All Sky Monitor (ASM) which is sensitive in the 2 - 12 keV band (Levine et al. 1996). The Swift BAT's sensitivity to higher energy X-rays ( > 15 keV) provides a way to peer through this absorption. We present here a review of our searches of BAT light curves of sources thought to be HMXBs, in order to find additional sources that may also display superorbital modulation. In a few cases we also employ data collected from Galactic plane scans (Markwardt 2006) made with the RXTE Proportional Counter Array (PCA). The large effective area of the PCA enables observations to be made in the lower energy range of 2 - 10 keV. Although the PCA data cover only a limited fraction of the sky they have greater sensitivity than the RXTE ASM. MAXI light curves (Sugizaki et al. 2011) are not available for the majority of systems considered here. We present here the results of a search for superorbital modulation in additional wind-accretion supergiant HMXBs. We find three new systems with clear superorbital modulation, initial reports of which were made in Corbet & Krimm (2013a,b). We also find hints of modulation in two other systems. Although the number of systems is small, three new systems plus two previously known, we note a monotonic relationship between orbital and superorbital periods. We consider possible mechanisms that might cause superorbital modulation in some, but not all, sgHMXBs.","pages":[1,2]},{"title":"2. DATA AND ANALYSIS","content":"The Burst Alert Telescope (BAT) on board the Swift satellite (Gehrels et al. 2004) is described in detail by Barthelmy et al. (2005). It uses a 2.7 m 2 coded-aperture mask and a 0.52 m 2 CdZnTe detector array. The BAT has a wide field of view, 1.4 sr half-coded, 2.85 sr 0% coded. The pointing direction of Swift is driven by the narrow-field XRT and UVOT instruments on board the satellite. The BAT typically observes 50%-80% of the sky each day. We used data from the Swift /BAT transient monitor (Krimm et al. 2006, 2013) covering the energy range 15 - 50 keV, and selected data with time resolution of Swift pointing durations. The transient monitor data are available shortly after observations have been performed. The light curves considered here cover the time range of MJD 53,416 to 56,452 (2005-02-15 to 2013-06-09). The light curves of some sources, not including the ones discussed in detail here, were more recently added to the analysis and hence have shorter durations. BAT light curves are also available from the catalogs such as described by Tueller et al. (2010). However, the most recent BAT catalog is from 70 months of data (Baumgartner et al. 2012) and the transient monitor light curves are hence of longer duration. The transient monitor light curves generally cover more than 3000 days, approximately 50% longer than the 70-month catalog light curves. We used only data for which the data quality flag ('DATA FLAG') was set to 0, indicating good quality. In addition, we found that even data flagged as 'good' were sometimes suspect. In particular we identified a small number of data points with very low fluxes and implausibly small uncertainties. We therefore removed these points from the light curves. A total of 1244 light curves were available, this includes 106 blank fields that are used for test purposes. To search for periodic modulation in the light curves, we calculated discrete Fourier transforms (DFTs) of all available light curves. We calculated the DFTs for a frequency range which corresponds to periods of between 0.07 days to the length of the light curves - i.e. generally ∼ 3000 days. The contribution of each data point to the power spectrum was weighted by its uncertainty using the 'semi-weighting' technique (Corbet et al. 2007a,b). This takes into account both the error bars on each data point and the excess variability of the light curve. Scargle (1989) notes that the weighting of data points in a power spectrum can be compared to combining individual data points. In this way, the use of semi-weighting is analogous to combining data points using the semi-weighted mean (Cochran 1937, 1954). We oversampled the DFTs by a factor of five compared to their nominal resolution. Calculations of the significance of peaks seen are expressed in terms of false alarm probability (FAP; Scargle 1982) which takes into account the DFT oversampling. Uncertainties in periods are generally derived using the expression of Horne & Baliunas (1986). In the figures showing power spectra we mark in 'white noise' 99.9% and 99.99% significance levels. However, many sources exhibit noise continua which are not 'white'. In our calculations of FAP, we therefore determined local noise levels by fitting the continuum power levels in a narrow frequency range around each peak of interest.","pages":[2]},{"title":"3.1. 2S0114+650","content":"2S0114+650 is an unusual HMXB system that has an exceptionally long pulse period of ∼ 9700 s (e.g. Corbet et al. 1999). There has been controversy over the spectral classification of the mass donor, but Reig et al. (1996) derive a spectral type of B1 Ia. From optical radial velocity measurements, Grundstrom et al. (2007) determine an orbital period of 11.5983 ± 0.0006 days and a moderate eccentricity of 0.18 ± 0.05. The orbital period is also seen in the RXTE ASM light curve (Corbet et al. 1999; Wen et al. 2006). A 30.7 ± 0.1 day superorbital period was found by Farrell et al. (2006) from RXTE ASM observations, and the period was later refined to 30.75 ± 0.03 days by Wen et al. (2006). Farrell et al. (2008) performed extensive RXTE PCA observations covering approximately 2 cycles of the superorbital period. Although Farrell et al. (2008) found variations in the X-ray absorption on the orbital period, they found no such changes over the superorbital period. However, a significant increase in the photon index of the power-law model used to fit the X-ray spectrum was reported at the minimum flux phase of the superorbital period. Farrell et al. (2008) concluded that the superorbital modulation was due to mass-accretion rate variations, although the mechanism causing this could not be determined. The power spectrum of the BAT light curve of 2S0114+650 is shown in Figure 1, both the orbital and superorbital periods are strongly detected, with the superorbital period being stronger than the orbital modulation. We determine orbital and superorbital periods of 11.591 ± 0.003 and 30.76 ± 0.03 days respectively. The BAT light curve of 2S0114+650 folded on the orbital and superorbital periods is shown in Figure 2. For consistency with the work of Farrell et al. (2008) the light curve folded on the superorbital period uses a definition of phase zero as the time of minimum flux. However, for the other sources considered in this paper we use the time of maximum flux as phase zero. Both the orbital and superorbital modulations are quasi-sinusoidal and no evidence for an eclipse is seen in the light curve folded on the orbital period.","pages":[2]},{"title":"3.2. IGR J16493-4348","content":"IGR J16493-4348 was discovered by Grebenev et al. (2005) and subsequent X-ray observations suggested that the source is an X-ray binary (Hill et al. 2008). Nespoli et al. (2010) classified the infrared counterpart as a B0.5 I supergiant. A 6.8 day orbital period was independently found by Corbet et al. (2010b) and Cusumano et al. (2010) using BAT 54 month survey data with the two groups finding periods of 6.7906 ± 0.0020 and 6.782 ± 0.005 days respectively. The BAT modulation was interpreted by Cusumano et al. (2010) as show- g the presence of an eclipse. Corbet et al. (2010b) confirmed the orbital period using PCA Galactic plane scan data which gave an orbital period of 6.7851 ± 0.0016 days. In addition, Corbet et al. (2010b) noted the presence of a 20.07 ± 0.02 day superorbital period in the BAT data which was confirmed by modulation at 20.09 ± 0.02 days in the PCA observations. Pointed RXTE PCA observations revealed a ∼ 1093 s pulse period (Corbet et al. 2010c), and pulse timing with the PCA yielded a mass function of 14.0 ± 2.3 M /circledot (Pearlman et al. 2013) which confirms the interpretation of IGR J16493-4348 as a supergiant HMXB. The power spectrum of the BAT light curve of IGR J16493-4348 is shown in Figure 3. This clearly shows the presence of the already known orbital and superorbital periods. However, the statistical significances of the periods are somewhat less than previously found from the BAT 54-month catalog data and the FAPs were ∼ 10 -6 and 0.04 respectively. We refine the period measurements to be 6.782 ± 0.001 and 20.07 ± 0.01 days for the orbital and superorbital periods respectively. The BAT light curve of IGR J16493-4348 folded on the orbital and superorbital periods is shown in Figure 4. The orbital modulation shows the presence of an eclipse, while the superorbital modulation is quasi-sinusoidal.","pages":[2,3]},{"title":"4. SOURCES WITH NEW DETECTIONS OF PERIODIC SUPERORBITAL MODULATION","content":"4.1. IGR J16418-4532 Chaty et al. (2008) determined that the optical coun- terpart of IGR J16418-4532 is probably an OB supergiant. Rahoui et al. (2008) fitted the spectral energy distribution of the likely 2MASS counterpart and found that this was consistent with an O/B massive star classification with a best fit spectral type of O8.5, although the luminosity type could not be determined. IGR J16418-4532 exhibits large flux variability, classifying it as an SFXT (Romano et al. 2011, 2012; Sidoli et al. 2012). Pulsations from the source were discovered by Walter et al. (2006) and refined to a period of 1212 ± 6 s by Sidoli et al. (2012). A 3.74 day orbital period has been found for IGR J16418-4532 from RXTE ASM and Swift BAT observations (e.g. Corbet et al. 2006; Levine et al. 2011). INTEGRAL and XMMNewton observations of IGR J16418-4532 are discussed by Drave et al. (2013a). The power spectrum of the BAT light curve of IGR J16418-4532 (Figure 5) shows modulation at the 3.74 day orbital period and the second and third harmonics of this. In addition the power spectrum shows a peak near 14.7 days with an FAP of < 10 -6 . The light curve folded on this period (Figure 6) shows an approximately sinusoidal modulation. From a sine wave fit to the light curve we obtain:","pages":[3,4]},{"title":"T max = MJD 55 , 994 . 6 ± 0 . 4 + n × 14 . 730 ± 0 . 006","content":"where T max is the time of maximum flux. The full amplitude of the modulation, defined as (maximum - minimum)/ mean flux, from the sine fit is approximately 70%. From the fundamental of the orbital peak in the power spectrum we determine an orbital period of 3.73834 ± 0.00022 days, while the second harmonic yields 3.73886 ± 0.00014 days. This is consistent with the period of 3.73886 +0.00028, -0.00140 days given by Levine et al. (2011). The BAT light curve of IGR J16418-4532 folded on the orbital period is also shown in Figure 6 and this shows the presence of an eclipse.","pages":[4]},{"title":"4.2. IGR J16479-4514","content":"IGR J16479-4514 is an SFXT with a rather short orbital period of near 3.3 days with periods of 3.3194 ± 0.0010 and 3.3193 ± 0.0005 days determined by Jain et al. (2009) and Romano et al. (2009), respectively, using Swift BAT data in both cases. The folded light curve shows the presence of X-ray eclipses. The mass donor has a spectral type of O8.5I (Chaty et al. 2008; Rahoui et al. 2008) or O9.5 Iab (Nespoli et al. 2008). No X-ray pulsations have yet been reported. The power spectrum of the BAT light curve (Figure 7) shows modulation at the 3.32 day orbital period and harmonics of this. From the fundamental we determine an orbital period of 3.3199 ± 0.0005 days. In addition to this, peaks are seen near 11.9 days and its second harmonic. The FAP of the harmonic is 0.0006 while that of the fundamental is 0.05. The second harmonic is stronger than the fundamental and from this we derive a superorbital period of 11.880 ± 0.002 days. The period determined from the fundamental is consistent with this at 11.871 ± 0.005 days. The BAT light curve of IGR J16479-4514 folded on the orbital and superorbital periods is shown in Figure 8. An eclipse is clearly seen in the light curve folded on the orbital period. The light curve folded on the superorbital period shows a relatively sharp rise from minimum to maximum followed by a plateau. The time of minimum flux is approximately MJD 55,993 ± 1.0 with maximum flux occurring approximately 0.25 in phase after this. The full amplitude of the modulation is approximately 130%.","pages":[4]},{"title":"4.3. 4U 1909+07 (X 1908+075)","content":"Wen et al. (2000) found a 4.400 ± 0.001 day orbital period for the X-ray binary 4U 1909+07 using RXTE ASM observations. X-ray pulsations with a period of 605 s were found with the RXTE PCA by Levine et al. (2004) and from a pulse arrival time analysis they found the orbit to be circular with an orbital period of 4.4007 ± 0.0009 days and derived a mass function of 6.1 M /circledot . Although Levine et al. (2004) proposed that the primary might be a Wolf-Rayet star, Morel & Grosdidier (2005) identified a likely near-IR candidate which they proposed to be a late O-type supergiant. Levine et al. (2004) found large orbital phase dependence of the X-ray absorption. The orbital period was further refined with additional ASM observations to 4.4005 ± 0.0004 days by Wen et al. (2006). The power spectrum of the BAT light curve of 4U 1909+07 (Figure 9) shows strong modulation at the orbital period and we derive a period of 4.4003 ± 0.0004 days. In addition, significant modulation at a superorbital period near 15.2 days (FAP ∼ 10 -5 ) and the second harmonic of this are seen. Combining the detections at the fundamental and second harmonic, we determine a period of 15.180 ± 0.003 days. As expected from the presence of harmonics in the power spectrum, the light curve folded on the superorbital period (Figure 10) shows a multi-peaked profile. The minimum is somewhat more clearly defined than the maximum. From an inspection of the folded light curve, the minimum occurs at approximately MJD 55,999 ± 1.5. The time of maximum flux occurs about 0.35 in phase after the minimum. The amplitude of the modulation, defined as (maximum - minimum)/ mean flux is approximately 50%. The BAT light curve folded on the orbital period is shown in Figure 10. This shows a quasisinusoidal modulation with no evidence for the presence of an eclipse.","pages":[4,5]},{"title":"5. PROPERTIES OF SELECTED OTHER SGHMXBS","content":"For comparison with the sgHMXB systems discussed above where superorbital modulation is seen, we present here examples of systems where there is no strong superorbital modulation, and two examples of systems which appear to be weak candidates for also possessing superorbital modulation.","pages":[5]},{"title":"5.1. Examples of Systems with Strong Orbital Modulation but Lacking Superorbital Modulation","content":"The Swift BAT set of light curves includes a number of other sgHMXBs. However, the majority of these do not show evidence for superorbital modulation. As examples we discuss here three systems. We choose 'IGR' systems which are typically rather hard sources and so suitable for study with the BAT. The examples selected here all have very significant orbital modulations of their light curves which have previously been reported.","pages":[6]},{"title":"5.1.1. IGR J18027-2016 (= SAX J1802.7-2017)","content":"IGR J18027-2016 (= SAX J1802.7-2017) has a pulse period of 139.6s (Augello et al. 2003) and pulse arrival time analysis suggested a ∼ 4.6 day orbital period. From a timing analysis Hill et al. (2005) refined this to 4.5696 ± 0.0009 days. The spectral type of the mass donor has been proposed to be B1 Ib (Torrej'on et al. 2010) and B0-B1 I (Mason et al. 2011), thus making it an sgHMXB. The power spectrum of the BAT light curve of IGR J18027-2016 (Figure 11, bottom panel) is very flat with the exception of the orbital period and its second and third harmonics, together with a small peak corresponding to a period of one year.","pages":[6]},{"title":"5.1.2. IGR J18483-0311","content":"IGR J18483-0311 is an SFXT with an early B supergiant optical counterpart (Rahoui & Chaty 2008). Orbital modulation is seen at a period near 18.55 days in RXTE ASM (Levine et al. 2011), BAT (Jain et al. 2009) and INTEGRAL observations (Sguera et al. 2007). This source also has a 21 s pulse period (Sguera et al. 2007). The power spectrum of the BAT light curve of IGR J18483-0311 (Figure 11, middle panel) shows strong modulation at the orbital period and the second harmonic of this. The power spectrum exhibits somewhat larger 'noise' at intermediate frequencies. A small nonstatistically significant ∼ 95 day bump is the third highest peak. IGR J19140+0951 (= IGR J19140+098) was discovered with INTEGRAL (Hannikainen et al. 2004) and a 13.558 ± 0.004 day period was found from RXTE ASM and Swift BAT observations (Corbet et al. 2004). From infrared observations the optical counterpart was determined to be a B0.5 supergiant (Hannikainen et al. 2007), later refined to B0.5 Ia by Torrej'on et al. (2010). No pulsations have yet been reported from this source despite INTEGRAL and RXTE PCA observations (Prat et al. 2008). The power spectrum of the BAT light curve of IGR J19140+0951 (Figure 11, top panel) shows an extremely flat power spectrum with the exception of strong peaks at the orbital period and the second harmonic of this.","pages":[6]},{"title":"5.2. Sources of Potential Superorbital Interest","content":"Although the presence of superorbital periods in sgHMXBs does not appear to be ubiquitous, we can examine the power spectra of other wind-accretion HMXBs for the possible presence of superorbital periods under the assumption that the apparent correlation between orbital period and superorbital periods discussed in Section 6.3 is indeed correct. This then yields a restricted frequency range to be searched for superorbital modulation.","pages":[6]},{"title":"5.2.1. 1E 1145.1-6141","content":"The spectral type of the primary of 1E 1145.1-6141 was found to be B2 Iae by Hutchings et al. (1981) and Densham & Charles (1982). The pulse period is ∼ 297 s and pulse timing enabled Ray & Chakrabarty (2002) to determine a 14.365 ± 0.002 day orbital period with a modest eccentricity of 0.20 ± 0.03. Ray & Chakrabarty (2002) report that no eclipse was seen. No detection of orbital modulation of the X-ray flux from RXTE ASM observations is reported in the papers of Wen et al. (2006) and Levine et al. (2011). However, Corbet et al. (2007b) reported detection of the orbital period of 1E 1145.1-6141 in Swift BAT data with the presence of flares at both periastron and apastron. The presence of flares at apastron is also reported from INTEGRAL observations by Ferrigno et al. (2008). For 1E 1145.1-6141, the strongest peak in the power spectrum of the BAT light curve (Figure 12) is at the second harmonic of the 14.4 day orbital period and the second highest peak is at the orbital period itself. The blind-search FAPs of the fundamental and second harmonic peaks would be 0.1 and ∼ 10 -5 respectively. The much lower significance of the fundamental is due to the increase in continuum power at lower frequencies. From the second harmonic we derive an orbital period of 14.365 ± 0.003 days, which is the same as that derived by Ray & Chakrabarty (2002) from pulse timing. The peak at the fundamental yields a period of 14.373 ± 0.007 days, which is also consistent, although with a somewhat larger uncertainty. The BAT light curve folded on the orbital period (Figure 13) shows a double-peaked profile with maxima at periastron and apastron based on the ephemeris of Ray & Chakrabarty (2002). The third and the fourth highest peaks in the power spectrum are at periods of 67.8 ± 0.2 (equivalent to 135.6 ± 0.4, if regarded as a second harmonic) and 131.4 ± 0.8 days. The very low FAP of 0.2 of the ∼ 68 day peak means that this is not a strong candidate for a superorbital period. However, the large amount of variability in the light curve compared to the orbital modulation makes this a potentially interesting system to continue to monitor. From a sine wave fit to the BAT light curve, we derive an epoch of maximum flux for the 68 day modulation of MJD 55,142.4 ± 0.6. The BAT light curve folded on the 68 day period is shown in Figure 13.","pages":[6,7]},{"title":"5.2.2. IGR J16393-4643 (= AX J16390.4-4642)","content":"The 910 s X-ray pulsar IGR J16393-4643 was reported by Thompson et al. (2006) to have a 3.7 day orbital period from a pulse timing analysis, although other solutions with orbital periods of 50.2 and 8.1 days could not be excluded. Thompson et al. (2006) proposed, on the basis of their orbital parameters, that IGR J16393- 4643 is a supergiant wind-accretion powered HMXB. Nespoli et al. (2010) instead suggested that this is a symbiotic X-ray binary with a 50 day period. However, Swift BAT and PCA Galactic plane scan observations clearly showed the system to have a 4.2 day orbital period (Corbet et al. 2010a) which is consistent with an interpretation of the system as an sgHMXB. The periods obtained from the BAT and PCA were 4.2368 ± 0.0007 and 4.2371 ± 0.0007 days respectively. Bodaghee et al. (2012) obtained a precise position for IGR J16393-4643 using a Chandra observation, which excluded a previously proposed counterpart that had led to the symbiotic classification by Nespoli et al. (2010), and instead suggested that the correct counterpart to IGR J16393-4643 might be a distant reddened star. The 4.2 day orbital period of IGR J16393-4643 is similar to the 4.4 day orbital period of 4U 1909+07 which has a superorbital period of 15.2 days. If there is indeed a relationship between superorbital and orbital periods, as discussed in Section 6.3, a superorbital period of ∼ 15 days would thus be predicted. The strongest peak in the power spectrum of the updated Swift BAT light curve (Figure 14) is at the orbital period with a value of 4.2380 ± 0.0005 days. The second highest peak in the power spectrum (Figures 14 and 15) is at a period near 15 days at 14.99 ± 0.01 days, and there is another peak at half this period. The possible second harmonic is at a period of 7.485 ± 0.002 days, equivalent to a fundamental period of 14.971 ± 0.005 days if regarded as a harmonic. However, the 'blind search' FAPs of both peaks, even restricting ourselves to a search of periods longer than the orbital period, are very high at ∼ 17% and ∼ 7% for the 15 and 15/2 day peaks respectively. From a sine wave fit to the BAT light curve, with the period held fixed at 14.99 days, we obtain an epoch of maximum flux of MJD 55,092.6 ± 0.4. The BAT light curve of IGR J16393-4643 folded on the orbital period and the possible 14.99 day period are shown in Figure 16. The folded profile on the 14.99 day period suggests any modulation may not be perfectly sinusoidal, with the maximum slightly preceding the value predicted by the sine wave fit. The light curve folded on the orbital period suggests the presence of an eclipse. We therefore also investigated the PCA Galactic plane scans of this source obtained between MJD 53163 and 55863 (2004-06-07 and 2011-10-29). This is 566 days longer than the light curve used in Corbet et al. (2010a). The PCA data yield an orbital period of 4.2376 ± 0.0005 days, consistent with our updated BAT result. In the power spectrum of the PCA scan observations (Figure 15), the largest peak for periods longer than the orbital period is at 14.99 ± 0.01 days, consistent with the possible BAT period. We next examined the INTEGRAL light curve of IGR J16393-4643 that we obtained from the Heavens service of the ISDC. This covers a time range of MJD 52,650 to 55,856 (2003-01-11 to 2011-10-22) although with only very sparse sampling. This limited sampling yields large amounts of artifacts in the power spectrum of the light curve. For example, the 4.2 day orbital period is not the strongest peak. However, examining the peak nearest the orbital period yields a value of 4.2382 ± 0.0006, consistent with the periods derived from the BAT and PCA observations. The INTEGRAL power spectrum for periods longer than the orbital period (Figure 15) also shows a small peak near 15 days. This has a value of 14.98 ± 0.01 days, which is consistent with the periods obtained from the BAT and PCA observations. The BAT, PCA, and INTEGRAL data folded on the possible superorbital period derived from the BAT data are shown in Figure 17. The three light curves appear to have roughly coincident maxima. While the coincidence of the periods obtained from three separate instruments is intriguing, additional data are required to confirm whether there truly is a superorbital period in this system. Such data may come from continued monitoring with the BAT, or from future missions such as the proposed Wide Field Monitor (WFM; Bozzo & LOFT Consortium 2013) on board the Large Observatory for X-ray Timing (LOFT; Feroci et al. 2012).","pages":[7,8]},{"title":"6.1. Excluding Period Artifacts","content":"Since the presence of superorbital periods in sgHMXBs is somewhat surprising, we consider whether they could be some type of artifact. We note that they are not present in other types of systems, and there is no obvious way to create superorbital modulation in only a subset of supergiant wind accretors. Superorbital modulation in 2S 0114+650 and IGR J16493-4348 was previously seen in other detectors ( RXTE ASM and RXTE PCA Galactic plane scan data respectively). In several cases there are pulse arrival time orbits that show that the orbital period really is the orbital period. In addition, Drave et al. (2013b) report that INTEGRAL /IBIS data confirm the superorbital periods found for 4U 1909+07, IGR J16418-4532, and IGR J16479-4514. The superorbital periods are rather prominent relative to the orbital periods in the BAT energy range. This appears to differ from results of lower-energy observations such as RXTE ASM observations of 4U 1909+07, where the orbital period is strongly detected, but the superorbital period is not seen. Similarly, for 2S 0114+650, although the superorbital period was initially detected from RXTE ASM data (Farrell et al. 2006), the superorbital modulation has lower amplitude than the orbital modulation in the ASM energy band. In contrast, the superorbital modulation of 2S 0114+650 is stronger than the orbital modulation in the BAT observations. One reason for this is likely to be the lower fractional modulation of the X-ray flux on the orbital period in the BAT energy range for non-eclipsing systems. For these types of systems a large component of the orbital modulation seen with lower-energy instruments is due to the changing absorption as the neutron star orbits its companion, which the BAT is relatively insensitive to.","pages":[8,9]},{"title":"6.2. Coherence","content":"Superorbital modulation from Roche-lobe overflow systems is not necessarily coherent. For example, there is considerable variation in the superorbital periods of SMC X-1 (Coe et al. 2013; Wojdowski et al. 1998) and Her X-1 (Leahy & Igna 2010), although not in LMC X4 (Hung et al. 2010). The sampling of the BAT light curves is very variable. This potentially makes it more difficult to calculate the true resolution of the power spectra. Therefore, in order to investigate the coherency of the superorbital modulation, we compared the widths of the superorbital peaks to those of the orbital peaks. This uses the assumption that the orbital modulation should be essentially periodic. We fitted Gaussian functions to the superorbital and orbital peaks in the power spectra in the five systems for which superorbital modulation is definitely observed and determined the following ratios of superorbital to orbital peak widths: 2S 0114+650, 1.05; IGR J16493-4348, 1.16; IGR J16418-4532, 0.92; IGR J16479-4514, 0.98; 4U 1909+07, 0.92. We therefore conclude that the superorbital modulations have very high coherence. For the two low-significance candidates we obtain ratios of superorbital to orbital peak widths of: IGR J16393-4643, 0.66; 1E 1145.1-6141, 0.89.","pages":[9]},{"title":"6.3. Relationship Between Superorbital and Orbital Periods","content":"System parameters are summarized in Table 1, and in Figure 18 we plot superorbital period against orbital period. For the five systems with definite superorbital modulation, the linear correlation coefficient between P super and P orb is 0.996 and the associated probability of obtaining this level of correlation from a random data set is 0.03%. Because this possible correlation comes from such a small number of systems, a determination whether this possible dependence of superorbital period on orbital period is correct requires the candidate superorbital period in IGR J16393-4643 to be investigated with additional data, and further superorbital periods must be found in other systems. For the five systems the best linear fit for superorbital periods vs. orbital period has parameters of: For comparison, in Figure 19 we plot superorbital period against orbital period for a wide variety of systems. These include these Roche-lobe overflow powered systems: LMC X-4 (neutron star HMXB, P orb = 1.4 days, P super = 30.3 days), Her X-1 (neutron star intermediatemass system, P orb =1.7 days, P super = 35 days), SMC X-1 (neutron star HMXB, P orb = 3.89 days, P super = 56 days), and SS 433 (black hole candidate microquasar, P orb = 13.1 days, P super = 162.5 days). These parameters are taken from Kotze & Charles (2012). Be star systems are also shown with their parameters taken from Rajoelimanana et al. (2011). For the Be star systems the superorbital modulation periods may be quasi-periodic rather than strictly periodic. It the mechanisms driving superorbital modulation differ between different types of object, then the different types of system could be located in different regions of this diagram. We note that the sgHMXB superorbital periods are rather short relative to their orbital periods, compared to other types of systems. This is suggestive that, as expected, a different driving mechanism may be at work in the sgHMXBs superorbital modulation compared to the other types of system.","pages":[9]},{"title":"6.4. Possible Mechanisms Driving Superorbital Modulation","content":"We note that Farrell et al. (2008)'s extensive RXTE PCA observations of 2S 0114+650 showed that there were changes in absorption over the orbital period of this system, but not on the superorbital period. Farrell et al. (2008) therefore concluded that the superorbital modulation was related to variability in the mass accretion rate caused by an unknown mechanism. This is consistent with the stronger detection of superorbital periods with the BAT compared to orbital periods for noneclipsing systems than is the case with the RXTE ASM (Section 6.1). The ASM is more sensitive to changes in absorption over the orbital period. However, the BAT has overall better sensitivity for changes in the flux of highly-absorbed systems. If mass-transfer rate variations are the cause of periodic superorbital modulation, then this suggests that the wind from the primary star could itself be modulated in some way by a mechanism related to the length of the orbital period. However, any satisfactory model must be able to account for the lack of superorbital variability in many systems. Thus, the modulation must be related to some parameter independent of inclination angle and whether the system is an SFXT or classical supergiant system. For example, an offset between the orbital plane and the rotation axis of the primary star, or a small orbital eccentricity, might satisfy such a requirement. The light curves folded on the superorbital periods exhibit a variety of morphologies, and so any model for the modulation must be able to account for this. We note the work of Koenigsberger et al. (2003) and Moreno et al. (2005) indicates that oscillations can be induced in nonsynchronously rotating stars in binary systems on periods longer than the orbital period. As discussed by Koenigsberger et al. (2006), such oscillations result in changes in the mass-loss rate of the primary star which would cause correlated changes in the X-ray luminosity. This model may also be consistent with the lack of superorbital modulation in all systems if only a fraction of primary stars are rotating non-synchronously. However, as noted by Farrell et al. (2008), the Koenigsberger et al. (2006) model applies to circular orbits and 2S 0114+650 has a modest eccentricity of 0.2. In addition, the high coherency of the superorbital modulations seems difficult to account for with oscillations of the primary star unless there is some way to keep strict phase stability. In principle, the presence of a third object in the systems might drive superorbital modulation. The modulation from a third body would also naturally account for the coherency of the superorbital modulation. How- ever, the apparent correlation between superorbital and orbital periods would, if confirmed, place stringent constraints on how such multi-star systems might be formed. In addition, typically such triple body models for X-ray sources involve hierarchical systems with a distant third object (e.g. Mazeh & Shaham 1979).","pages":[9,10]},{"title":"7. CONCLUSION","content":"Observations with the Swift BAT have shown the presence of superorbital periods in three additional sgHMXBs for a total of five definite such systems. The superorbital modulations have a variety of morphologies, ranging from approximately sinusoidal to multi-peaked profiles. However, superorbital modulation is not a ubiquitous property of sgHMXBs. With this limited set of data, a possible dependence of superorbital period on orbital period is suggested. The mechanism(s) driving such superorbital modulation remain unclear. However, possible models based on oscillations in the primary star driven by non-synchronous rotation, and three-body systems deserve further investigation. Continued monitoring of sgHMXBs in hard X-rays both with additional Swift BAT data and also potential new missions with high-energy X-ray sensitivity such as the LOFT WFM may reveal additional sources with superorbital periodicities. We thank an anonymous referee for useful comments. This paper used Swift /BAT transient monitor results provided by the Swift /BAT team. The Swift/BAT transient monitor and H. A. K. are supported by NASA under Swift Guest Observer grants NNX09AU85G, NNX12AD32G, NNX12AE57G and NNX13AC75G. MNRAS, 413, 1600 Note . - The superorbital period for the system below the line is a candidate and not a definite detection. The references for system parameters are given in the individual sections on each source. The orbital and superorbital periods and their errors are derived from the BAT light curves. For some systems additional determinations of periods may be available from other work, as given in the individual source sections.","pages":[10,11,12]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"We report the discovery using data from the Swift Burst Alert Telescope (BAT) of superorbital modulation in the wind-accretion supergiant high-mass X-ray binaries 4U 1909+07 (= X 1908+075), IGR J16418-4532, and IGR J16479-4514. Together with already known superorbital periodicities in 2S0114+650 and IGR J16493-4348, the systems exhibit a monotonic relationship between superorbital and orbital periods. These systems include both supergiant fast X-ray transients (SFXTs) and classical supergiant systems, and have a range of inclination angles. This suggests an underlying physical mechanism which is connected to the orbital period. In addition to these sources with clear detections of superorbital periods, IGR J16393-4643 (= AX J16390.4-4642) is identified as a system that may have superorbital modulation due to the coincidence of low-amplitude peaks in power spectra derived from BAT, RXTE PCA, and INTEGRAL light curves. 1E 1145.1-6141 may also be worthy of further attention due to the amount of low-frequency modulation of its light curve. However, we find that the presence of superorbital modulation is not a universal feature of wind-accretion supergiant X-ray binaries. Subject headings: stars: individual (2S 0114+650, 1E 1145.1-6141, IGR J16393-4643, IGR J164184532, IGR J16479-4514, IGR J16493-4348, 4U 1909+07) - stars: neutron - Xrays: stars\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"SUPERORBITAL PERIODIC MODULATION IN WIND-ACCRETION HIGH-MASS X-RAY BINARIES FROM Swift BAT OBSERVATIONS\",\n \"content\": \"1,2 3,4 Robin H. D. Corbet and Hans A. Krimm Draft version October 17, 2018\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"Superorbital modulation is seen in a variety of X-ray binaries. A review of superorbital modulation in several types of systems is presented by Kotze & Charles (2012). In some cases such as Her X-1, SMC X-1 and LMC X-4, where accretion occurs by Roche-lobe overflow via an accretion disk onto a neutron star, the mechanism driving superorbital modulation can be understood as either precession of the accretion disk (e.g. Petterson 1975) or of the neutron star (e.g. Postnov et al. 2013). Irradiation of the accretion disk by the central X-ray source provides a possible mechanism for driving disk precession (e.g. Ogilvie & Dubus 2001, and references therein). Be star systems also exhibit long timescale, possibly periodic, variability at optical wavelengths. This long timescale variability has been claimed to be correlated with orbital period (Rajoelimanana et al. 2011). A more puzzling variety of superorbital variability was found in a supergiant high-mass X-ray binary (sgHMXB). The sgHMXBs can be broadly classified into 'classical' systems, which may suffer from high levels of absorption, and supergiant fast X-ray transients (SFXTs; e.g. Blay et al. 2012; Sidoli 2013). In the sgHMXB 2S0114+650 there are three periodicities: a ∼ 9700 s neutron star rotation period, an 11.6 day orbital period, and a 30.7 day superorbital modulation (Corbet et al. 1 University of Maryland, Baltimore County, MD, USA; corbet@umbc.edu 2 CRESST/Mail Code 662, X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 3 Universities Space Research Association, 10211 Wincopin Circle, Suite 500, Columbia, MD 21044, USA 4 CRESST/Mail Code 661, Astroparticle Physics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 1999; Wen et al. 2006; Farrell et al. 2008). A question has been whether 2S 0114+650 is exceptional, perhaps because of its unusually long pulse period, or whether other wind-accretion HMXBs also show similar superorbital periodicities. If similar behavior is found in other systems, then this may provide a way to determine, or at least constrain, the underlying mechanism. A suggestion that the phenomenon might be more general than just the case of 2S 0114+650 came when a superorbital period was found in the sgHMXB IGR J16493-4348 (Corbet et al. 2010b). The Swift BAT provides an excellent way to monitor sgHMXBs. These systems are often highly absorbed, which presents difficulties for an instrument such as the Rossi X-ray Timing Explorer ( RXTE ) All Sky Monitor (ASM) which is sensitive in the 2 - 12 keV band (Levine et al. 1996). The Swift BAT's sensitivity to higher energy X-rays ( > 15 keV) provides a way to peer through this absorption. We present here a review of our searches of BAT light curves of sources thought to be HMXBs, in order to find additional sources that may also display superorbital modulation. In a few cases we also employ data collected from Galactic plane scans (Markwardt 2006) made with the RXTE Proportional Counter Array (PCA). The large effective area of the PCA enables observations to be made in the lower energy range of 2 - 10 keV. Although the PCA data cover only a limited fraction of the sky they have greater sensitivity than the RXTE ASM. MAXI light curves (Sugizaki et al. 2011) are not available for the majority of systems considered here. We present here the results of a search for superorbital modulation in additional wind-accretion supergiant HMXBs. We find three new systems with clear superorbital modulation, initial reports of which were made in Corbet & Krimm (2013a,b). We also find hints of modulation in two other systems. Although the number of systems is small, three new systems plus two previously known, we note a monotonic relationship between orbital and superorbital periods. We consider possible mechanisms that might cause superorbital modulation in some, but not all, sgHMXBs.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2. DATA AND ANALYSIS\",\n \"content\": \"The Burst Alert Telescope (BAT) on board the Swift satellite (Gehrels et al. 2004) is described in detail by Barthelmy et al. (2005). It uses a 2.7 m 2 coded-aperture mask and a 0.52 m 2 CdZnTe detector array. The BAT has a wide field of view, 1.4 sr half-coded, 2.85 sr 0% coded. The pointing direction of Swift is driven by the narrow-field XRT and UVOT instruments on board the satellite. The BAT typically observes 50%-80% of the sky each day. We used data from the Swift /BAT transient monitor (Krimm et al. 2006, 2013) covering the energy range 15 - 50 keV, and selected data with time resolution of Swift pointing durations. The transient monitor data are available shortly after observations have been performed. The light curves considered here cover the time range of MJD 53,416 to 56,452 (2005-02-15 to 2013-06-09). The light curves of some sources, not including the ones discussed in detail here, were more recently added to the analysis and hence have shorter durations. BAT light curves are also available from the catalogs such as described by Tueller et al. (2010). However, the most recent BAT catalog is from 70 months of data (Baumgartner et al. 2012) and the transient monitor light curves are hence of longer duration. The transient monitor light curves generally cover more than 3000 days, approximately 50% longer than the 70-month catalog light curves. We used only data for which the data quality flag ('DATA FLAG') was set to 0, indicating good quality. In addition, we found that even data flagged as 'good' were sometimes suspect. In particular we identified a small number of data points with very low fluxes and implausibly small uncertainties. We therefore removed these points from the light curves. A total of 1244 light curves were available, this includes 106 blank fields that are used for test purposes. To search for periodic modulation in the light curves, we calculated discrete Fourier transforms (DFTs) of all available light curves. We calculated the DFTs for a frequency range which corresponds to periods of between 0.07 days to the length of the light curves - i.e. generally ∼ 3000 days. The contribution of each data point to the power spectrum was weighted by its uncertainty using the 'semi-weighting' technique (Corbet et al. 2007a,b). This takes into account both the error bars on each data point and the excess variability of the light curve. Scargle (1989) notes that the weighting of data points in a power spectrum can be compared to combining individual data points. In this way, the use of semi-weighting is analogous to combining data points using the semi-weighted mean (Cochran 1937, 1954). We oversampled the DFTs by a factor of five compared to their nominal resolution. Calculations of the significance of peaks seen are expressed in terms of false alarm probability (FAP; Scargle 1982) which takes into account the DFT oversampling. Uncertainties in periods are generally derived using the expression of Horne & Baliunas (1986). In the figures showing power spectra we mark in 'white noise' 99.9% and 99.99% significance levels. However, many sources exhibit noise continua which are not 'white'. In our calculations of FAP, we therefore determined local noise levels by fitting the continuum power levels in a narrow frequency range around each peak of interest.\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"3.1. 2S0114+650\",\n \"content\": \"2S0114+650 is an unusual HMXB system that has an exceptionally long pulse period of ∼ 9700 s (e.g. Corbet et al. 1999). There has been controversy over the spectral classification of the mass donor, but Reig et al. (1996) derive a spectral type of B1 Ia. From optical radial velocity measurements, Grundstrom et al. (2007) determine an orbital period of 11.5983 ± 0.0006 days and a moderate eccentricity of 0.18 ± 0.05. The orbital period is also seen in the RXTE ASM light curve (Corbet et al. 1999; Wen et al. 2006). A 30.7 ± 0.1 day superorbital period was found by Farrell et al. (2006) from RXTE ASM observations, and the period was later refined to 30.75 ± 0.03 days by Wen et al. (2006). Farrell et al. (2008) performed extensive RXTE PCA observations covering approximately 2 cycles of the superorbital period. Although Farrell et al. (2008) found variations in the X-ray absorption on the orbital period, they found no such changes over the superorbital period. However, a significant increase in the photon index of the power-law model used to fit the X-ray spectrum was reported at the minimum flux phase of the superorbital period. Farrell et al. (2008) concluded that the superorbital modulation was due to mass-accretion rate variations, although the mechanism causing this could not be determined. The power spectrum of the BAT light curve of 2S0114+650 is shown in Figure 1, both the orbital and superorbital periods are strongly detected, with the superorbital period being stronger than the orbital modulation. We determine orbital and superorbital periods of 11.591 ± 0.003 and 30.76 ± 0.03 days respectively. The BAT light curve of 2S0114+650 folded on the orbital and superorbital periods is shown in Figure 2. For consistency with the work of Farrell et al. (2008) the light curve folded on the superorbital period uses a definition of phase zero as the time of minimum flux. However, for the other sources considered in this paper we use the time of maximum flux as phase zero. Both the orbital and superorbital modulations are quasi-sinusoidal and no evidence for an eclipse is seen in the light curve folded on the orbital period.\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"3.2. IGR J16493-4348\",\n \"content\": \"IGR J16493-4348 was discovered by Grebenev et al. (2005) and subsequent X-ray observations suggested that the source is an X-ray binary (Hill et al. 2008). Nespoli et al. (2010) classified the infrared counterpart as a B0.5 I supergiant. A 6.8 day orbital period was independently found by Corbet et al. (2010b) and Cusumano et al. (2010) using BAT 54 month survey data with the two groups finding periods of 6.7906 ± 0.0020 and 6.782 ± 0.005 days respectively. The BAT modulation was interpreted by Cusumano et al. (2010) as show- g the presence of an eclipse. Corbet et al. (2010b) confirmed the orbital period using PCA Galactic plane scan data which gave an orbital period of 6.7851 ± 0.0016 days. In addition, Corbet et al. (2010b) noted the presence of a 20.07 ± 0.02 day superorbital period in the BAT data which was confirmed by modulation at 20.09 ± 0.02 days in the PCA observations. Pointed RXTE PCA observations revealed a ∼ 1093 s pulse period (Corbet et al. 2010c), and pulse timing with the PCA yielded a mass function of 14.0 ± 2.3 M /circledot (Pearlman et al. 2013) which confirms the interpretation of IGR J16493-4348 as a supergiant HMXB. The power spectrum of the BAT light curve of IGR J16493-4348 is shown in Figure 3. This clearly shows the presence of the already known orbital and superorbital periods. However, the statistical significances of the periods are somewhat less than previously found from the BAT 54-month catalog data and the FAPs were ∼ 10 -6 and 0.04 respectively. We refine the period measurements to be 6.782 ± 0.001 and 20.07 ± 0.01 days for the orbital and superorbital periods respectively. The BAT light curve of IGR J16493-4348 folded on the orbital and superorbital periods is shown in Figure 4. The orbital modulation shows the presence of an eclipse, while the superorbital modulation is quasi-sinusoidal.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"4. SOURCES WITH NEW DETECTIONS OF PERIODIC SUPERORBITAL MODULATION\",\n \"content\": \"4.1. IGR J16418-4532 Chaty et al. (2008) determined that the optical coun- terpart of IGR J16418-4532 is probably an OB supergiant. Rahoui et al. (2008) fitted the spectral energy distribution of the likely 2MASS counterpart and found that this was consistent with an O/B massive star classification with a best fit spectral type of O8.5, although the luminosity type could not be determined. IGR J16418-4532 exhibits large flux variability, classifying it as an SFXT (Romano et al. 2011, 2012; Sidoli et al. 2012). Pulsations from the source were discovered by Walter et al. (2006) and refined to a period of 1212 ± 6 s by Sidoli et al. (2012). A 3.74 day orbital period has been found for IGR J16418-4532 from RXTE ASM and Swift BAT observations (e.g. Corbet et al. 2006; Levine et al. 2011). INTEGRAL and XMMNewton observations of IGR J16418-4532 are discussed by Drave et al. (2013a). The power spectrum of the BAT light curve of IGR J16418-4532 (Figure 5) shows modulation at the 3.74 day orbital period and the second and third harmonics of this. In addition the power spectrum shows a peak near 14.7 days with an FAP of < 10 -6 . The light curve folded on this period (Figure 6) shows an approximately sinusoidal modulation. From a sine wave fit to the light curve we obtain:\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"T max = MJD 55 , 994 . 6 ± 0 . 4 + n × 14 . 730 ± 0 . 006\",\n \"content\": \"where T max is the time of maximum flux. The full amplitude of the modulation, defined as (maximum - minimum)/ mean flux, from the sine fit is approximately 70%. From the fundamental of the orbital peak in the power spectrum we determine an orbital period of 3.73834 ± 0.00022 days, while the second harmonic yields 3.73886 ± 0.00014 days. This is consistent with the period of 3.73886 +0.00028, -0.00140 days given by Levine et al. (2011). The BAT light curve of IGR J16418-4532 folded on the orbital period is also shown in Figure 6 and this shows the presence of an eclipse.\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"4.2. IGR J16479-4514\",\n \"content\": \"IGR J16479-4514 is an SFXT with a rather short orbital period of near 3.3 days with periods of 3.3194 ± 0.0010 and 3.3193 ± 0.0005 days determined by Jain et al. (2009) and Romano et al. (2009), respectively, using Swift BAT data in both cases. The folded light curve shows the presence of X-ray eclipses. The mass donor has a spectral type of O8.5I (Chaty et al. 2008; Rahoui et al. 2008) or O9.5 Iab (Nespoli et al. 2008). No X-ray pulsations have yet been reported. The power spectrum of the BAT light curve (Figure 7) shows modulation at the 3.32 day orbital period and harmonics of this. From the fundamental we determine an orbital period of 3.3199 ± 0.0005 days. In addition to this, peaks are seen near 11.9 days and its second harmonic. The FAP of the harmonic is 0.0006 while that of the fundamental is 0.05. The second harmonic is stronger than the fundamental and from this we derive a superorbital period of 11.880 ± 0.002 days. The period determined from the fundamental is consistent with this at 11.871 ± 0.005 days. The BAT light curve of IGR J16479-4514 folded on the orbital and superorbital periods is shown in Figure 8. An eclipse is clearly seen in the light curve folded on the orbital period. The light curve folded on the superorbital period shows a relatively sharp rise from minimum to maximum followed by a plateau. The time of minimum flux is approximately MJD 55,993 ± 1.0 with maximum flux occurring approximately 0.25 in phase after this. The full amplitude of the modulation is approximately 130%.\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"4.3. 4U 1909+07 (X 1908+075)\",\n \"content\": \"Wen et al. (2000) found a 4.400 ± 0.001 day orbital period for the X-ray binary 4U 1909+07 using RXTE ASM observations. X-ray pulsations with a period of 605 s were found with the RXTE PCA by Levine et al. (2004) and from a pulse arrival time analysis they found the orbit to be circular with an orbital period of 4.4007 ± 0.0009 days and derived a mass function of 6.1 M /circledot . Although Levine et al. (2004) proposed that the primary might be a Wolf-Rayet star, Morel & Grosdidier (2005) identified a likely near-IR candidate which they proposed to be a late O-type supergiant. Levine et al. (2004) found large orbital phase dependence of the X-ray absorption. The orbital period was further refined with additional ASM observations to 4.4005 ± 0.0004 days by Wen et al. (2006). The power spectrum of the BAT light curve of 4U 1909+07 (Figure 9) shows strong modulation at the orbital period and we derive a period of 4.4003 ± 0.0004 days. In addition, significant modulation at a superorbital period near 15.2 days (FAP ∼ 10 -5 ) and the second harmonic of this are seen. Combining the detections at the fundamental and second harmonic, we determine a period of 15.180 ± 0.003 days. As expected from the presence of harmonics in the power spectrum, the light curve folded on the superorbital period (Figure 10) shows a multi-peaked profile. The minimum is somewhat more clearly defined than the maximum. From an inspection of the folded light curve, the minimum occurs at approximately MJD 55,999 ± 1.5. The time of maximum flux occurs about 0.35 in phase after the minimum. The amplitude of the modulation, defined as (maximum - minimum)/ mean flux is approximately 50%. The BAT light curve folded on the orbital period is shown in Figure 10. This shows a quasisinusoidal modulation with no evidence for the presence of an eclipse.\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"5. PROPERTIES OF SELECTED OTHER SGHMXBS\",\n \"content\": \"For comparison with the sgHMXB systems discussed above where superorbital modulation is seen, we present here examples of systems where there is no strong superorbital modulation, and two examples of systems which appear to be weak candidates for also possessing superorbital modulation.\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"5.1. Examples of Systems with Strong Orbital Modulation but Lacking Superorbital Modulation\",\n \"content\": \"The Swift BAT set of light curves includes a number of other sgHMXBs. However, the majority of these do not show evidence for superorbital modulation. As examples we discuss here three systems. We choose 'IGR' systems which are typically rather hard sources and so suitable for study with the BAT. The examples selected here all have very significant orbital modulations of their light curves which have previously been reported.\",\n \"pages\": [\n 6\n ]\n },\n {\n \"title\": \"5.1.1. IGR J18027-2016 (= SAX J1802.7-2017)\",\n \"content\": \"IGR J18027-2016 (= SAX J1802.7-2017) has a pulse period of 139.6s (Augello et al. 2003) and pulse arrival time analysis suggested a ∼ 4.6 day orbital period. From a timing analysis Hill et al. (2005) refined this to 4.5696 ± 0.0009 days. The spectral type of the mass donor has been proposed to be B1 Ib (Torrej'on et al. 2010) and B0-B1 I (Mason et al. 2011), thus making it an sgHMXB. The power spectrum of the BAT light curve of IGR J18027-2016 (Figure 11, bottom panel) is very flat with the exception of the orbital period and its second and third harmonics, together with a small peak corresponding to a period of one year.\",\n \"pages\": [\n 6\n ]\n },\n {\n \"title\": \"5.1.2. IGR J18483-0311\",\n \"content\": \"IGR J18483-0311 is an SFXT with an early B supergiant optical counterpart (Rahoui & Chaty 2008). Orbital modulation is seen at a period near 18.55 days in RXTE ASM (Levine et al. 2011), BAT (Jain et al. 2009) and INTEGRAL observations (Sguera et al. 2007). This source also has a 21 s pulse period (Sguera et al. 2007). The power spectrum of the BAT light curve of IGR J18483-0311 (Figure 11, middle panel) shows strong modulation at the orbital period and the second harmonic of this. The power spectrum exhibits somewhat larger 'noise' at intermediate frequencies. A small nonstatistically significant ∼ 95 day bump is the third highest peak. IGR J19140+0951 (= IGR J19140+098) was discovered with INTEGRAL (Hannikainen et al. 2004) and a 13.558 ± 0.004 day period was found from RXTE ASM and Swift BAT observations (Corbet et al. 2004). From infrared observations the optical counterpart was determined to be a B0.5 supergiant (Hannikainen et al. 2007), later refined to B0.5 Ia by Torrej'on et al. (2010). No pulsations have yet been reported from this source despite INTEGRAL and RXTE PCA observations (Prat et al. 2008). The power spectrum of the BAT light curve of IGR J19140+0951 (Figure 11, top panel) shows an extremely flat power spectrum with the exception of strong peaks at the orbital period and the second harmonic of this.\",\n \"pages\": [\n 6\n ]\n },\n {\n \"title\": \"5.2. Sources of Potential Superorbital Interest\",\n \"content\": \"Although the presence of superorbital periods in sgHMXBs does not appear to be ubiquitous, we can examine the power spectra of other wind-accretion HMXBs for the possible presence of superorbital periods under the assumption that the apparent correlation between orbital period and superorbital periods discussed in Section 6.3 is indeed correct. This then yields a restricted frequency range to be searched for superorbital modulation.\",\n \"pages\": [\n 6\n ]\n },\n {\n \"title\": \"5.2.1. 1E 1145.1-6141\",\n \"content\": \"The spectral type of the primary of 1E 1145.1-6141 was found to be B2 Iae by Hutchings et al. (1981) and Densham & Charles (1982). The pulse period is ∼ 297 s and pulse timing enabled Ray & Chakrabarty (2002) to determine a 14.365 ± 0.002 day orbital period with a modest eccentricity of 0.20 ± 0.03. Ray & Chakrabarty (2002) report that no eclipse was seen. No detection of orbital modulation of the X-ray flux from RXTE ASM observations is reported in the papers of Wen et al. (2006) and Levine et al. (2011). However, Corbet et al. (2007b) reported detection of the orbital period of 1E 1145.1-6141 in Swift BAT data with the presence of flares at both periastron and apastron. The presence of flares at apastron is also reported from INTEGRAL observations by Ferrigno et al. (2008). For 1E 1145.1-6141, the strongest peak in the power spectrum of the BAT light curve (Figure 12) is at the second harmonic of the 14.4 day orbital period and the second highest peak is at the orbital period itself. The blind-search FAPs of the fundamental and second harmonic peaks would be 0.1 and ∼ 10 -5 respectively. The much lower significance of the fundamental is due to the increase in continuum power at lower frequencies. From the second harmonic we derive an orbital period of 14.365 ± 0.003 days, which is the same as that derived by Ray & Chakrabarty (2002) from pulse timing. The peak at the fundamental yields a period of 14.373 ± 0.007 days, which is also consistent, although with a somewhat larger uncertainty. The BAT light curve folded on the orbital period (Figure 13) shows a double-peaked profile with maxima at periastron and apastron based on the ephemeris of Ray & Chakrabarty (2002). The third and the fourth highest peaks in the power spectrum are at periods of 67.8 ± 0.2 (equivalent to 135.6 ± 0.4, if regarded as a second harmonic) and 131.4 ± 0.8 days. The very low FAP of 0.2 of the ∼ 68 day peak means that this is not a strong candidate for a superorbital period. However, the large amount of variability in the light curve compared to the orbital modulation makes this a potentially interesting system to continue to monitor. From a sine wave fit to the BAT light curve, we derive an epoch of maximum flux for the 68 day modulation of MJD 55,142.4 ± 0.6. The BAT light curve folded on the 68 day period is shown in Figure 13.\",\n \"pages\": [\n 6,\n 7\n ]\n },\n {\n \"title\": \"5.2.2. IGR J16393-4643 (= AX J16390.4-4642)\",\n \"content\": \"The 910 s X-ray pulsar IGR J16393-4643 was reported by Thompson et al. (2006) to have a 3.7 day orbital period from a pulse timing analysis, although other solutions with orbital periods of 50.2 and 8.1 days could not be excluded. Thompson et al. (2006) proposed, on the basis of their orbital parameters, that IGR J16393- 4643 is a supergiant wind-accretion powered HMXB. Nespoli et al. (2010) instead suggested that this is a symbiotic X-ray binary with a 50 day period. However, Swift BAT and PCA Galactic plane scan observations clearly showed the system to have a 4.2 day orbital period (Corbet et al. 2010a) which is consistent with an interpretation of the system as an sgHMXB. The periods obtained from the BAT and PCA were 4.2368 ± 0.0007 and 4.2371 ± 0.0007 days respectively. Bodaghee et al. (2012) obtained a precise position for IGR J16393-4643 using a Chandra observation, which excluded a previously proposed counterpart that had led to the symbiotic classification by Nespoli et al. (2010), and instead suggested that the correct counterpart to IGR J16393-4643 might be a distant reddened star. The 4.2 day orbital period of IGR J16393-4643 is similar to the 4.4 day orbital period of 4U 1909+07 which has a superorbital period of 15.2 days. If there is indeed a relationship between superorbital and orbital periods, as discussed in Section 6.3, a superorbital period of ∼ 15 days would thus be predicted. The strongest peak in the power spectrum of the updated Swift BAT light curve (Figure 14) is at the orbital period with a value of 4.2380 ± 0.0005 days. The second highest peak in the power spectrum (Figures 14 and 15) is at a period near 15 days at 14.99 ± 0.01 days, and there is another peak at half this period. The possible second harmonic is at a period of 7.485 ± 0.002 days, equivalent to a fundamental period of 14.971 ± 0.005 days if regarded as a harmonic. However, the 'blind search' FAPs of both peaks, even restricting ourselves to a search of periods longer than the orbital period, are very high at ∼ 17% and ∼ 7% for the 15 and 15/2 day peaks respectively. From a sine wave fit to the BAT light curve, with the period held fixed at 14.99 days, we obtain an epoch of maximum flux of MJD 55,092.6 ± 0.4. The BAT light curve of IGR J16393-4643 folded on the orbital period and the possible 14.99 day period are shown in Figure 16. The folded profile on the 14.99 day period suggests any modulation may not be perfectly sinusoidal, with the maximum slightly preceding the value predicted by the sine wave fit. The light curve folded on the orbital period suggests the presence of an eclipse. We therefore also investigated the PCA Galactic plane scans of this source obtained between MJD 53163 and 55863 (2004-06-07 and 2011-10-29). This is 566 days longer than the light curve used in Corbet et al. (2010a). The PCA data yield an orbital period of 4.2376 ± 0.0005 days, consistent with our updated BAT result. In the power spectrum of the PCA scan observations (Figure 15), the largest peak for periods longer than the orbital period is at 14.99 ± 0.01 days, consistent with the possible BAT period. We next examined the INTEGRAL light curve of IGR J16393-4643 that we obtained from the Heavens service of the ISDC. This covers a time range of MJD 52,650 to 55,856 (2003-01-11 to 2011-10-22) although with only very sparse sampling. This limited sampling yields large amounts of artifacts in the power spectrum of the light curve. For example, the 4.2 day orbital period is not the strongest peak. However, examining the peak nearest the orbital period yields a value of 4.2382 ± 0.0006, consistent with the periods derived from the BAT and PCA observations. The INTEGRAL power spectrum for periods longer than the orbital period (Figure 15) also shows a small peak near 15 days. This has a value of 14.98 ± 0.01 days, which is consistent with the periods obtained from the BAT and PCA observations. The BAT, PCA, and INTEGRAL data folded on the possible superorbital period derived from the BAT data are shown in Figure 17. The three light curves appear to have roughly coincident maxima. While the coincidence of the periods obtained from three separate instruments is intriguing, additional data are required to confirm whether there truly is a superorbital period in this system. Such data may come from continued monitoring with the BAT, or from future missions such as the proposed Wide Field Monitor (WFM; Bozzo & LOFT Consortium 2013) on board the Large Observatory for X-ray Timing (LOFT; Feroci et al. 2012).\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"6.1. Excluding Period Artifacts\",\n \"content\": \"Since the presence of superorbital periods in sgHMXBs is somewhat surprising, we consider whether they could be some type of artifact. We note that they are not present in other types of systems, and there is no obvious way to create superorbital modulation in only a subset of supergiant wind accretors. Superorbital modulation in 2S 0114+650 and IGR J16493-4348 was previously seen in other detectors ( RXTE ASM and RXTE PCA Galactic plane scan data respectively). In several cases there are pulse arrival time orbits that show that the orbital period really is the orbital period. In addition, Drave et al. (2013b) report that INTEGRAL /IBIS data confirm the superorbital periods found for 4U 1909+07, IGR J16418-4532, and IGR J16479-4514. The superorbital periods are rather prominent relative to the orbital periods in the BAT energy range. This appears to differ from results of lower-energy observations such as RXTE ASM observations of 4U 1909+07, where the orbital period is strongly detected, but the superorbital period is not seen. Similarly, for 2S 0114+650, although the superorbital period was initially detected from RXTE ASM data (Farrell et al. 2006), the superorbital modulation has lower amplitude than the orbital modulation in the ASM energy band. In contrast, the superorbital modulation of 2S 0114+650 is stronger than the orbital modulation in the BAT observations. One reason for this is likely to be the lower fractional modulation of the X-ray flux on the orbital period in the BAT energy range for non-eclipsing systems. For these types of systems a large component of the orbital modulation seen with lower-energy instruments is due to the changing absorption as the neutron star orbits its companion, which the BAT is relatively insensitive to.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"6.2. Coherence\",\n \"content\": \"Superorbital modulation from Roche-lobe overflow systems is not necessarily coherent. For example, there is considerable variation in the superorbital periods of SMC X-1 (Coe et al. 2013; Wojdowski et al. 1998) and Her X-1 (Leahy & Igna 2010), although not in LMC X4 (Hung et al. 2010). The sampling of the BAT light curves is very variable. This potentially makes it more difficult to calculate the true resolution of the power spectra. Therefore, in order to investigate the coherency of the superorbital modulation, we compared the widths of the superorbital peaks to those of the orbital peaks. This uses the assumption that the orbital modulation should be essentially periodic. We fitted Gaussian functions to the superorbital and orbital peaks in the power spectra in the five systems for which superorbital modulation is definitely observed and determined the following ratios of superorbital to orbital peak widths: 2S 0114+650, 1.05; IGR J16493-4348, 1.16; IGR J16418-4532, 0.92; IGR J16479-4514, 0.98; 4U 1909+07, 0.92. We therefore conclude that the superorbital modulations have very high coherence. For the two low-significance candidates we obtain ratios of superorbital to orbital peak widths of: IGR J16393-4643, 0.66; 1E 1145.1-6141, 0.89.\",\n \"pages\": [\n 9\n ]\n },\n {\n \"title\": \"6.3. Relationship Between Superorbital and Orbital Periods\",\n \"content\": \"System parameters are summarized in Table 1, and in Figure 18 we plot superorbital period against orbital period. For the five systems with definite superorbital modulation, the linear correlation coefficient between P super and P orb is 0.996 and the associated probability of obtaining this level of correlation from a random data set is 0.03%. Because this possible correlation comes from such a small number of systems, a determination whether this possible dependence of superorbital period on orbital period is correct requires the candidate superorbital period in IGR J16393-4643 to be investigated with additional data, and further superorbital periods must be found in other systems. For the five systems the best linear fit for superorbital periods vs. orbital period has parameters of: For comparison, in Figure 19 we plot superorbital period against orbital period for a wide variety of systems. These include these Roche-lobe overflow powered systems: LMC X-4 (neutron star HMXB, P orb = 1.4 days, P super = 30.3 days), Her X-1 (neutron star intermediatemass system, P orb =1.7 days, P super = 35 days), SMC X-1 (neutron star HMXB, P orb = 3.89 days, P super = 56 days), and SS 433 (black hole candidate microquasar, P orb = 13.1 days, P super = 162.5 days). These parameters are taken from Kotze & Charles (2012). Be star systems are also shown with their parameters taken from Rajoelimanana et al. (2011). For the Be star systems the superorbital modulation periods may be quasi-periodic rather than strictly periodic. It the mechanisms driving superorbital modulation differ between different types of object, then the different types of system could be located in different regions of this diagram. We note that the sgHMXB superorbital periods are rather short relative to their orbital periods, compared to other types of systems. This is suggestive that, as expected, a different driving mechanism may be at work in the sgHMXBs superorbital modulation compared to the other types of system.\",\n \"pages\": [\n 9\n ]\n },\n {\n \"title\": \"6.4. Possible Mechanisms Driving Superorbital Modulation\",\n \"content\": \"We note that Farrell et al. (2008)'s extensive RXTE PCA observations of 2S 0114+650 showed that there were changes in absorption over the orbital period of this system, but not on the superorbital period. Farrell et al. (2008) therefore concluded that the superorbital modulation was related to variability in the mass accretion rate caused by an unknown mechanism. This is consistent with the stronger detection of superorbital periods with the BAT compared to orbital periods for noneclipsing systems than is the case with the RXTE ASM (Section 6.1). The ASM is more sensitive to changes in absorption over the orbital period. However, the BAT has overall better sensitivity for changes in the flux of highly-absorbed systems. If mass-transfer rate variations are the cause of periodic superorbital modulation, then this suggests that the wind from the primary star could itself be modulated in some way by a mechanism related to the length of the orbital period. However, any satisfactory model must be able to account for the lack of superorbital variability in many systems. Thus, the modulation must be related to some parameter independent of inclination angle and whether the system is an SFXT or classical supergiant system. For example, an offset between the orbital plane and the rotation axis of the primary star, or a small orbital eccentricity, might satisfy such a requirement. The light curves folded on the superorbital periods exhibit a variety of morphologies, and so any model for the modulation must be able to account for this. We note the work of Koenigsberger et al. (2003) and Moreno et al. (2005) indicates that oscillations can be induced in nonsynchronously rotating stars in binary systems on periods longer than the orbital period. As discussed by Koenigsberger et al. (2006), such oscillations result in changes in the mass-loss rate of the primary star which would cause correlated changes in the X-ray luminosity. This model may also be consistent with the lack of superorbital modulation in all systems if only a fraction of primary stars are rotating non-synchronously. However, as noted by Farrell et al. (2008), the Koenigsberger et al. (2006) model applies to circular orbits and 2S 0114+650 has a modest eccentricity of 0.2. In addition, the high coherency of the superorbital modulations seems difficult to account for with oscillations of the primary star unless there is some way to keep strict phase stability. In principle, the presence of a third object in the systems might drive superorbital modulation. The modulation from a third body would also naturally account for the coherency of the superorbital modulation. How- ever, the apparent correlation between superorbital and orbital periods would, if confirmed, place stringent constraints on how such multi-star systems might be formed. In addition, typically such triple body models for X-ray sources involve hierarchical systems with a distant third object (e.g. Mazeh & Shaham 1979).\",\n \"pages\": [\n 9,\n 10\n ]\n },\n {\n \"title\": \"7. CONCLUSION\",\n \"content\": \"Observations with the Swift BAT have shown the presence of superorbital periods in three additional sgHMXBs for a total of five definite such systems. The superorbital modulations have a variety of morphologies, ranging from approximately sinusoidal to multi-peaked profiles. However, superorbital modulation is not a ubiquitous property of sgHMXBs. With this limited set of data, a possible dependence of superorbital period on orbital period is suggested. The mechanism(s) driving such superorbital modulation remain unclear. However, possible models based on oscillations in the primary star driven by non-synchronous rotation, and three-body systems deserve further investigation. Continued monitoring of sgHMXBs in hard X-rays both with additional Swift BAT data and also potential new missions with high-energy X-ray sensitivity such as the LOFT WFM may reveal additional sources with superorbital periodicities. We thank an anonymous referee for useful comments. This paper used Swift /BAT transient monitor results provided by the Swift /BAT team. The Swift/BAT transient monitor and H. A. K. are supported by NASA under Swift Guest Observer grants NNX09AU85G, NNX12AD32G, NNX12AE57G and NNX13AC75G. MNRAS, 413, 1600 Note . - The superorbital period for the system below the line is a candidate and not a definite detection. The references for system parameters are given in the individual sections on each source. The orbital and superorbital periods and their errors are derived from the BAT light curves. For some systems additional determinations of periods may be available from other work, as given in the individual source sections.\",\n \"pages\": [\n 10,\n 11,\n 12\n ]\n }\n]"}}},{"rowIdx":75,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...778...51K"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1310.0456.pdf"},"content":{"kind":"string","value":"\nINVESTIGATING THE PRESENCE OF 500 µ M SUBMILLIMETER EXCESS EMISSION IN LOCAL STAR FORMING GALAXIES\nAllison Kirkpatrick 1 , Daniela Calzetti 1 , Maud Galametz 2 , Rob Kennicutt, Jr. 2 , Daniel Dale 3 , Gonzalo Aniano 4 , Karin Sandstrom 5 , Lee Armus 6 , Alison Crocker 7 , Joannah Hinz 8 , Leslie Hunt 9 , Jin Koda 10 , Fabian Walter 5\nDraft version September 24, 2018\nABSTRACT\nSubmillimeter excess emission has been reported at 500 µ m in a handful of local galaxies, and previous studies suggest that it could be correlated with metal abundance. We investigate the presence of an excess submillimeter emission at 500 µ m for a sample of 20 galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH) that span a range of morphologies and metallicities (12 + log(O/H) = 7 . 8 -8 . 7). We probe the far-infrared (IR) emission using images from the Spitzer Space Telescope and Herschel Space Observatory in the wavelength range 24 -500 µ m. We model the far-IR peak of the dust emission with a two-temperature modified blackbody and measure excess of the 500 µ m photometry relative to that predicted by our model. We compare the submillimeter excess, where present, with global galaxy metallicity and, where available, resolved metallicity measurements. We do not find any correlation between the 500 µ m excess and metallicity. A few individual sources do show excess (10-20%) at 500 µ m; conversely, for other sources, the model overpredicts the measured 500 µ m flux density by as much as 20%, creating a 500 µ m 'deficit'. None of our sources has an excess larger than the calculated 1 σ uncertainty, leading us to conclude that there is no substantial excess at submillimeter wavelengths at or shorter than 500 µ m in our sample. Our results differ from previous studies detecting 500 µ m excess in KINGFISH galaxies largely due to new, improved photometry used in this study.\n1. INTRODUCTION\nDust in the interstellar medium (ISM) is formed by grain growth in both the diffuse ISM and the ejecta of dying stars, such as red giant winds, planetary nebula, and supernovae (Draine 2009). Once formed, dust absorbs UV and optical light and reemits this radiation in the infrared. UV radiation is dominated by photons from young O and B stars, so the dust mass and infrared (IR) radiation can provide important constraints on the current star formation rates and the star formation history of a galaxy.\nSpace-based telescopes such as the Spitzer Space Telescope, the InfraRed Astronomical Satellite, and the Infrared Space Observatory have provided insights on the dust emission from mid-IR wavelengths out to ∼ 200 µ m. However, the majority, by mass, of the dust is cold\n\n1 Department of Astronomy, University of Massachusetts, Amherst, MA 01002, USA, kirkpatr@astro.umass.edu\n2 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK\n3 Department of Physics & Astronomy, University of Wyoming, Laramie, WY 82071, USA\n4 Institut d'Astrophysique Spatiale, Universit'e of Paris-Sud, 91405 Orsay, France\n5 Max-Planck Institut f ' 'ur Astronomie, K ' 'onigstuhl 17, D69117, Heidelberg, Germany\n6 Spitzer Science Center, California Institute of Technology, MC 314-6, Pasadena, CA 91125, USA\n7 Ritter Astrophysical Observatory, University of Toledo, Toledo, OH 43606, USA\n8 MMT Observatory, University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA\n9 INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy\n10 Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA\n\n( T /lessorsimilar 25 K, Dunne & Eales 2001) and emits at far-IR and submillimeter wavelengths, where the emission spectrum is dominated by large grains in thermal equilibrium. Ground-based observations of these wavelengths are limited to a few atmospheric windows, and until recently, space-based observatories lacked coverage of the far-IR beyond ∼ 200 µ m. Now, with the advent of the Herschel Space Observatory, the peak and long wavelength tail of the dust spectral energy distribution (SED) is being observed at unprecedented angular resolution.\nWith submillimeter observations, the dust mass and the dust to gas ratios can be more accurately estimated. Dust formation models show that the dust to gas ratios should be tied to the chemical enrichment of galaxies, as measured by the metallicity (Dwek 1998; Edmunds 2001). Galametz et al. (2011) combine submillimeter data at 450 and 850 µ m with shorter wavelength IR observations ( /lessorsimilar 160 µ m) for a large sample of local star forming galaxies. They model the spectral energy distributions of each galaxy with and without the submillimeter data and find that for high metallicity galaxies, not including the submillimeter data can cause the dust mass to be overestimated by factors of 2-10, whereas for low metallicity galaxies (12+log(O/H) /lessorsimilar 8 . 0), the SEDs without the submillimeter data can underpredict the true dust mass by as much as a factor of three. Gordon et al. (2010) use Herschel photometry to model the dust emission from the Large Magellanic Cloud (LMC) and find that dust mass derived using just 100 µ m and 160 µ m photometry underestimate the dust mass derived when using 350 µ m and 500 µ m photometry as well by as much as 36%.\nIn measuring dust masses by modeling the far-IR and submillimeter SED, a variety of studies have sug-\ngested the existence of excess emission at submillimeter wavelengths above what is predicted by fits to shorter wavelength data. Furthermore, this excess could preferentially affect lower metallicity and dwarf galaxies. Dale et al. (2012, hereafter D12) report significant excess emission at 500 µ m, above that predicted by fitting the observed SEDs with the Draine & Li (2007) models, for a sample of eight dwarf and irregular galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH, Kennicutt et al. 2011). Excess emission has also been reported in the Small Magellanic Cloud (SMC) and LMC, both of which have lower than solar metallicities (12+log(O/H) = 8 . 0 , 8 . 4, respectively Bot et al. 2010; Gordon et al. 2010).\nOn the other hand, excess emission is also seen at solar metallicities or larger. Paradis et al. (2012) model emission in the Galaxy and find excess emission (16 -20%) at 500 µ m in peripheral H ii regions. Recently, Galametz et al. (2013, in prep.) have detected excess at 870 µ m on a resolved and global scale for a sample of 11 KINGFISH galaxies. Galametz et al. (2011) finds a submillmeter excess at 870 µ m for 8 galaxies spanning a metallicity range of 12 + log(O/H) = 7 . 8 -9 . 0.\nThe presence of excess emission does not appear to be universal, however, as Draine et al. (2007) found only a marginal difference in deriving the dust masses for a set of SINGS galaxies with and without including submillimeter data from SCUBA 12 + log(O/H) ≈ 7 . 5 -8 . 7 . More recently, Aniano et al. (2012) apply the Draine & Li (2007) models to the IR SEDs (3 . 6 -500 µ m) of the local star forming galaxies NGC 0628 and NGC 6946 and do not detect any significant excess ( > 10%) at 500 µ m.\nThe excess emission seen at submillimeter wavelengths can be attributed to a cold dust component which is shielded from starlight (T < 10K; e.g., Galametz et al. 2009; O'Halloran et al. 2010). However, in the Milky Way, excess emission is seen at high latitudes, making it unlikely to be due to shielded cold dust (Reach et al. 1995). Studies of other galaxies have argued that a cold dust origin for the excess emission leads to unphysically high dust to gas ratios (Lisenfeld et al. 2002; Zhu et al. 2009; Galametz et al. 2010).\nA competing explanation is that the spectral emissivity index, β , of the dust grains changes to lower values at longer wavelengths, leading to a flattening of the submillimeter spectrum, thus mimicking a cold dust component (Dupac et al. 2003; Augierre et al. 2003; Planck Collaboration 2011). Such a change in emissivity has been suggested in the Milky Way (Paradis et al. 2009). (Galametz et al. 2012) showed that modeling the far-IR /submillimeter emission with a modified blackbody with β = 1 . 5 can increase the dust masses up to 50% compared to when β = 2, possibly explaining the discrepancies between dust masses calculated with far-IR data alone and those calculated with farIR and submillimeter data. The emission from very small grains exhibits a frequency dependence with a spectral emissivity index of β = 1, and if a galaxy has a relative abundance of very small grains greater than the Milky Way, this can cause a flattening of the emissivity index at longer wavelengths (Lisenfeld et al. 2002; Zhu et al. 2009). Alternatively, the properties of amorphous solids could explain the change in emissivity\n(Meny et al. 2007). Modeling the emission of amorphous solids accounts for the submillimeter excess in the LMC and SMC (Bot et al. 2010), although recent work suggests that much of the excess emission in the LMC is accounted for by fluctuations in the cosmic microwave background (Planck Collaboration 2011). Finally, an increase in the amount of magnetic material has also been proposed as a plausible explanation for the SMC submillimeter excess (Draine & Hensley 2012).\nAchange in dust properties can also be linked to metallicity. Draine et al. (2007) showed that 12 + log(O/H) = 8 . 1 is a threshold metallicity for galaxies in the range 12 + log(O/H) ≈ 7 . 5 -8 . 7, above which the percentage of dust mass contained in PAH molecules drastically increases. If submillimeter excess emission is due to a change in the emissivity properties of the dust population, then there might be a correlation with abundances in this metallicity range.\nIn the present study, we seek to investigate the submillimeter excess at 500 µ m for a sample of KINGFISH galaxies. We define such excess as being emission above that predicted by a two-temperature modified blackbody model where the emissivity is not constrained, following the method outlined in Galametz et al. (2012). We have selected a sample that spans a range of metallicities, including many dwarf galaxies, in order to probe whether such excess correlates with metallicity, as has been found in some earlier studies (Galametz et al. 2009, 2011). The paper is laid out as follows: in Section 2, we describe our sample selection and modeling of the dust emission; in Section 3, we report on the excess emission and how our findings relate to the results of D12; and in Section 4, we present our conclusions.\n2. DATA ANALYSIS\n2.1. The KINGFISH Sample\nThe KINGFISH sample (Kennicutt et al. 2011) was selected to include a wide range of luminosities, morphologies, and metallicities in local galaxies. The sample overlaps with 57 of the galaxies observed as part of the Spitzer Infrared Nearby Galaxies Survey (SINGS, Kennicutt et al. 2003b), as well as incorporating NGC 2146, NGC 3077, M 101 (NGC 5457), and IC 342 for a total of 61 galaxies. The luminosity range spans four orders of magnitude, but all galaxies have L < 10 11 L /circledot . While some of the galaxies display a nucleus with LINER or Seyfert properties, no galaxy's global SED is dominated by an AGN.\nWe select a sample (7) of disk galaxies possessing a large angular size ( ∼ 30arcmin 2 ) and a known metallicity gradient with which we perform a resolved study of the excess emission and search for any correspondence with metallicity. We refer to this sample as the 'extended' galaxies. Since excess emission seems to be found in dwarf/irregular galaxies, we include the dwarf/irregular galaxies (9) in KINGFISH for which we have a signal-tonoise ratio (SNR) > 3 σ in all of the SPIRE bandpasses. The dwarf/irregulars are more compact objects than our normal disk galaxies, and in general, do not have a known metallicity gradients, so we measure the excess emission globally for these objects. The resolved nature of the normal disk galaxies might bias our comparison with the dwarf/irregular galaxies, so we complement our sample\n(4) with normal disk galaxies that have small angular size which allows for global measurements of excess emission. These more compact, normal galaxies were selected to span a range of metallicity and have high SNRs at the SPIRE bandwidths. Our complete sample consists of 20 galaxies and is listed in Table 1. We also list in Table 1 dwarf/irregular galaxies that were rejected due to low SNRs.\n2.2. Data Reduction\nData observations and reduction are discussed in detail in Engelbracht et al. (2010), Sandstrom et al. (2010) and Kennicutt et al. (2011). In the present study, we use images from the PACS and SPIRE instruments on the Herschel Space Observatory spanning a wavelength range of 70 -500 µ m and MIPS 24 µ m images from the Spitzer Space Telescope (Kennicutt et al. 2003b). We use PACS 70 and 160 µ m images instead of MIPS due to the better resolution provided by PACS. All galaxy maps are at least 1.5 times the diameter of the optical disk, allowing us to probe the cold dust emission beyond the optical disk.\nThe raw PACS and SPIRE images were processed from level 0 to 1 with Herschel Interactive Processing Environment (HIPE) v. 8. The PACS and SPIRE maps were then created using the IDL package Scanamorphos v. 17 (Roussel 2012). Scanamorphos is preferred to HIPE for its ability to better preserve low level flux density, reduce striping in area of high background, and correct brightness drifts caused by low level noise. The maps are converted from units of Jy beam -1 to MJy sr -1 by accounting for beam sizes of 469.1, 827.2, and 1779.6 arcsec 2 for the 250, 350, and 500 µ m maps, respectively. The design and performance of the SPIRE instrument is discussed in detail in Griffin et al. (2010). In the SPIRE images used in this study, the full width at half maximum (FWHM) of the beam profile has been modeled with a wavelength dependence, so that FWHM ∝ λ γ , where γ = 0 . 85. As part of the calibration process, a 'color-correction' has been applied to each beam so that the measured specific intensity I ν will be equal to the actual specific intensity I 0 when ν = ν 0 . The correction factors applied to these images assume a power-law spectrum with α = -1 . 9.\nWe compare our results to those of D12, so it is crucial to explicitly state that we are using different versions of the PACS and SPIRE images. In D12, the raw PACS and SPIRE images were processed from level 0 to 1 with HIPE v.5. The SPIRE data were then mosaicked using the mapper in HIPE. The images were converted to MJy sr -1 using beam sizes of 423, 751, and 1587 arcsec 2 at 250, 350, and 500 µ m, respectively, and the FWHM was not modeled with a wavelength dependence; furthermore, the color-correction was not included in the beam size, but was applied a posteriori.The PACS data were mapped using Scanamorphos v. 12.5.\nThe main difference between the version of KINGFISH images that we use and the previous version used by D12 is that the SPIRE 250 and 350 µ m images contain slightly less flux density ( ∼ 2%) while the 500 µ m image is less luminous by ∼ 10%. The point response function area is also slightly larger ( ∼ 3%) than for the v. 2 images. The more recent HIPE v. 11 pipeline has revised the SPIRE beam sizes in the direction of yielding lower fluxes for extended sources by ∼ 6%, 6%, and 8% at 250,\n350, and 500 µ m, respectively. This is in the direction of reinforcing the results that are presented in this paper.\n2.3. Background subtraction and Convolution of Images\nThe background subtraction is described in detail in Aniano et al. (2012), and we will briefly summarize here. 'Non-background' regions are determined in all cameras (IRAC, MIPS, PACS, and SPIRE) by those pixels which have a SNR > 2. Masks of the non-background regions are made, and then the masked images from all cameras are combined in order to unambiguously determine which regions are truly background regions. The signals in the background regions are then averaged, smoothed, and subtracted according to an algorithm outlined in Aniano et al. (2012).\nSince we compare our results with those of D12, it is worthwhile to note that a different procedure for background subtraction is followed in that study. The authors use a set of sky apertures to measure the local sky around each galaxy while avoiding any contamination from galaxy emission. The mean sky level per pixel is computed from these sky apertures, scaled to the number of pixels in the galaxy photometry aperture, and the result is subtracted from the overall galaxy photometry aperture counts.\nIn order to consistently measure photometry for each galaxy, we used images that had been convolved to the resolution of the SPIRE 500 µ m bandpass. The convolution was done with publicly available kernels from Aniano et al. (2011) which transform the point source functions (PSFs) of individual images to the PSF of the SPIRE instrument at 500 µ m (FWHM of 38'). The convolution kernels and methodology are described in detail in Aniano et al. (2011, 2012). After the convolution to a common PSF, the images for each galaxy are resampled to a standard grid, where each pixel is ∼ 14'.\n2.4. Photometry and SED fitting\nFor the extended galaxies, we measure photometry in apertures with diameters of 42', chosen to be slightly larger than the beam size of the SPIRE 500 µ m bandpass, from the center of the galaxy to the outskirts. We reject regions of galaxies without at least 3 σ flux density measurements at every bandpass from 24 -500 µ m. For the galaxies which are compact at the 500 µ m resolution, including the dwarf/irregulars, we measure the photometry globally in apertures with diameters ranging from 42' to 1' 52', which is the angular area covered by the galaxies with a signal to noise ratio > 3 σ . The diameter and the physical scales of each photometric aperture are listed in Table 1.\nThe dwarf/irregular galaxies DDO 053, DDO 154, and DDO 165 have a 3 σ flux density measurement in only one of the far-IR bandpasses; Ho I, Ho II, and M 81 DwB have measurements in three of the six bandpasses. We do not model the far-IR emission for these galaxies, but we do plot the photometry and 3 σ upper limits in Figure 1.\nThe physically-based DL07 models have been used to derive dust properties at global and local scales (e.g., Draine et al. 2007; Aniano et al. 2012). The DL07 models use the assumption of a diffuse ISM component to describe the shape of the interstellar radiation field, and\n
\n\n
TABLE 1 Basic properties of our sample
\n
\nWe do not calculate an excess for Ho I, Ho II, DDO 053, DDO 154, DDO 165, and M81 DwB since we are not able to measure flux densities at the 3 σ level covering the full wavelength range 24 -500 µ m. The metallicity range for which we can derive excess measurements is then 12 + log(O/H) = 7 . 8 -8 . 7.\n\na Morphology as listed in the NASA Extragalactic Database (NED).\nb We indicate how we have classified the galaxies in this study. E = extended, C = compact, and D = dwarf/irregular/Magellanic.\nc Distances are taken from Kennicutt et al. (2011) and references therein.\nd Characteristic metallicity for most galaxies is taken from Moustakas et al. (2010) where the metallicity is calculated using the method of Pilyugin & Thuan (2005). For the extended galaxies, we list the metallicity gradients in the brackets, where ρ is the radius in arcminutes. The metal abundance of NGC 1377 is calculated using the luminosity-metallicity relationship (Kennicutt et al. 2011), the abundance for NGC 3077 is empirically calculated in Storchi-Bergmann et al. (1994), and the metallcity for M 101 is derived from observations in Kennicutt et al. (2003a) and Bresolin et al. (2004).\ne The ratio of the major axis to minor axis, which we use to correct for inclination effects when calculating the metallicity.\nf The physical region size of the photometry aperture.\ng The diameter (in arcminutes and arcseconds) of the circular apertures used for photometry.\nh The number of circular apertures used to calculate the photometry.\n\nuse distribution function to represent the distribution of starlight intensities, which are then scaled to the SED being modeled. In addition, the submm slope of the DL07 models tends to resemble that of a modified blackbody with an emissivity of β = 2, which could prevent us from testing for flattening of the submm slope or variations in the emissivity index. We choose to model the farIR SEDs with a simple modified blackbody equation to test various assumptions on the emissivity index and will compare our results to the D12 study to investigate how the choice of model affects the observed excess emission.\nWe model the far-IR SEDs of each region within each galaxy using a two temperature modified blackbody of the form\nF ν = a w × B ν ( T w ) × ν β w + a c × B ν ( T c ) × ν β c (1)\nwhere B ν is the Planck function. The temperatures of the warm and cold dust components are T w and T c , the scalings for each component are a w and a c , and β w and β c are the emissivity indexes. Only the scalings, T c , and β c are allowed to be free parameters, due to the limited number of data points being fit. The warm dust com-\nnt is necessary to account for some of the emission at 70 µ m and 100 µ m so as not to bias the cold dust temperature or emissivity. When only one temperature is used, the peak of the modified blackbody is biased towards shorter wavelengths, leading to warmer temperatures, which is then compensated at longer wavelengths by a β c shallower than otherwise measured. We include the 24 µ m data point in the fit to better constrain the warm dust modified blackbody, but the fitted warm dust parameters should not be interpreted in a physical manner, since this portion of the SED also likely contains contribution from stochastically heated dust. We list the fraction of 100 µ m flux density due to the warm dust component in Table 2.\nThe effective dust emissivity we derive comprises the intrinsic spectral emissivity properties of dust and the variation of the dust temperature within a resolution element that could lead to a shallower β c than that obtained in isothermal cases (e.g., Shetty et al. 2009). We nevertheless allow both the cold temperature and cold emissivity, β c , to vary simultaneously, though the two parameters are degenerate. We refer to Galametz et al.\n\n\n
Fig. 1.Our photometry for the dwarfs/irregular galaxies in the KINGFISH sample is plotted as the black circles. The photometry listed in D12 is over plotted as the red squares. The two sets of photometry were extracted from slightly different calibrations of the PACS and SPIRE images, and our photometry was taken after the images had been convolved to the 500 µ m resolution. When we fit the D12 photometry with our model, we are able to reproduce the excesses reported in that work.
\n\n(2012) and Kirkpatrick et al. (2013b, in prep.), and references therein, for a further discussion of degeneracies on the individual temperatures and emissivities.\nWe fit the photometry from 24 -350 µ m. The 500 µ m data are not included to allow comparison with our model predictions at the same wavelength. We use a Monte Carlo technique to determine the parameters and errors. We randomly sample each data point within its errors 1000 times and determine the parameters of the two temperature modified blackbody via χ 2 minimization. The final parameters and associated errors are the medians and standard deviations of our Monte Carlo simulation. An example of the SED fitting is shown in Figure 2.\nWhen fitting, we allow the cold dust temperature, T c , to vary between 0 and 50 K and β c to vary between 0 and 5. We experimented with allowing T w to vary, but the derived temperature was approximately constant in the range 55 -60K, and simultaneously varying T w did not\nchange the derived cold dust temperature or emissivity values. Since the warm dust component peaks in an area of the SED that is sparsely sampled, we opt to hold both T w and β w fixed. We hold the emissivity of the warm dust component fixed to a value of two and T w fixed to 60K. Fixing β w = 2 is a good approximation of the opacity of graphite/silicate dust models (Li & Draine 2001). Galametz et al. (2012) find that changing β w to 1.5 decreases the cold dust temperatures by less than 1.6%, and Tabatabaei et al. (2011) test the two temperature modified blackbody approach on M33, holding β w fixed to 1.0, 1.5, and 2.0, and conclude that β w = 2 most accurately reproduces the observed flux densities. We test a fixed β c in Section 3.3. As β w is always fixed to a value of two in all of our subsequent analysis, in the remainder of this paper, we refer to β c simply as β .\n\n\n
Fig. 2.The SED of NGC 337 is fitted with a two-temperature modified blackbody. The warm temperature component is shown in green, the cold temperature component in orange, and the composite in blue. The excess emission is calculated relative to the composite fit at 500 µ m. The 24 µ m photometric data is from Spitzer MIPS, while the other far-IR/submillimeter photometric data are from Herschel PACS and SPIRE.
\n\n3.1. PACS-SPIRE colors\nThe color S 100 /S 160 , where S 100 is the flux density in the 100 µ m bandpass, is commonly used as a proxy for temperature, since it usually spans the peak of the blackbody emission, while S 350 /S 500 depends sensitively on the slope of the Rayleigh-Jeans tail, and so is a good proxy for β (with the same caveats given earlier about the mixing of dust with different temperatures along the line of sight). We plot these two colors in the left panel of Figure 3 for each of the regions in our extended galaxies. We calculate the positions of theoretical modified blackbodies and overplot as a grid. When calculating the theoretical tracks, we use a two temperature modified blackbody (Equation 1); we set T w = 60 K, β w = 2, and we scale the warm dust component to peak at a flux density 10% of the cold dust component peak flux density, which is the average scaling we see in our fitted SEDs at the SPIRE wavelengths. We set β = 1 , 1 . 5 , and 2, and we set T c to discrete temperature values between 15 and 27 K. Lines of constant β and T c are marked on the figure.\nThe colors of our galaxies tend to cluster around the β = 2 , T c = 20K lines. At higher temperatures, galaxy colors start to sparsely occupy the same part of color space as the β = 1 model. No galaxies exhibit colors indicating a low temperature ( T c < 21 K) and a shallow emissivity, which could hint at physical link between the two parameters (see Yang & Phillips 2007; Ysard et al. 2012; Kirkpatrick et al. 2013b, in prep., for a discussion of the physical nature of the T c -β relationship). Although our galaxy colors tend to lie near the β = 2 model line, we observe a large scatter. This illustrates a significant difference of physical conditions from one object to another but also within our objects. Letting both parameters vary in our multiple blackbody approach can be a way to probe these variations, in spite of the degeneracies.\nIn the right panel of Figure 3, we plot the same colors, but this time we use the predicted 500 µ m flux density, which has been calculated by fitting Equation 1 to the 24 -350 µ m flux densities. Substituting the predicted 500 µ m flux density has two interesting effects. First, it increases the amount of scatter visible in the colors. For example, in both NGC 5055 and NGC 4321, which dis-\ny the largest increase in scatter, the mean S 350 /S 500 observed ratio and predicted ratio is approximately the same ( ∼ 2 . 7). For NGC 5055, the standard deviation increases from 0.16 to 0.24, and for NGC 4321 it increases from 0.11 to 0.23. This increase is indicative of the uncertainties inherent in fitting modified blackbody models without enough data to adequately constrain the slope of the Rayleigh-Jeans tail. The second effect we see is that now the galaxy colors, particularly for M 101, occupy a region of the color space to the right of the β = 2 model line. The predicted S 350 /S 500 ratio is larger than the observed S 350 /S 500 ratio. Again, this illustrates the importance of using data above 350 µ m to constrain the submillimeter SED. Without including the 500 µ m data point in the modeling of the far-IR/submillimeter SED, the predicted slope will be steeper than the true value; in other words, the model underpredicts the measured 500 µ m flux density.\n3.2. 500 µ m excess when β varies\nWe calculate the excess emission at 500 µ m as\nexcess = S ν (500 µ m) -F ν (500 µ m) S ν (500 µ m) (2)\nwhere F ν (500 µ m) is the predicted flux density of the two-temperature modified blackbody and S ν is the measured flux density. We plot the excess emission as a function of metallicity in Figure 4. We correct the radius of each photometric region for the inclination of the galaxy, and then convert the radius to metallicity using the gradients listed in Moustakas et al. (2010) which were calculated according to the Pilyugin & Thuan (2005) relationship (see Table 1). For M 101, which is not included in Moustakas et al. (2010), we use a metallicity gradient calculated directly from electron temperature measurements in H ii regions (Kennicutt et al. 2003a; Bresolin et al. 2004), which creates a slight offset between M 101 and the rest of our sample in metallicity.\nFigure 4 shows that there is no systematic dependence of the excess emission on metallicity for the sample as a whole, nor is there any trend within the individual galaxies that have a metallicity gradient. None of the galaxies display an excess larger than 25%, and for many galaxies, the modeling actually overpredicts the 500 µ m emission by this amount, creating a 500 µ m deficit. Furthermore, the spread in excess is largely accounted for by the uncertainty attached to each data point (the typical uncertainty for each region in the extended galaxies is shown in the bottom right of Figure 4). For some of the dwarf/irregulars, the uncertainties are rather large (particularly NGC 1377, NGC 2915, NGC 3773, NGC 5408, and IC 2574). The uncertainties are correlated with the SNR ratios of the SPIRE data since noisier photometry exacerbates the degeneracy between temperature and β (Juvela & Ysard 2012). The dwarf/irregulars with the lowest SNRs have the largest uncertainty on the derived β .\nWe find that no extended galaxy has an excess emission greater than 10%, in agreement with the results of Gordon et al. (2010) for a resolved study of the LMC using a modified blackbody model, and with Aniano et al. (2013, in prep.), in which the authors create dust maps for the full sample of KINGFISH galaxies using the DL07\n\n\n
Fig. 3.LeftWe plot the far-IR colors of each region in our extended galaxies. We calculate the theoretical colors of a two-temperature modified blackbody for different temperatures and different values any regions with low temperatures and low emissivity values, hinting at a physical link between the two parameters. The typical errors are shown in the lower righthand corner. RightWe replace the observed 500 µ m flux densities by those predicted from our two-temperature modified blackbody fitting. Using the predicted the 500 µ m flux density increases the scatter in color space for some galaxies, and increases the S 350 /S 500 ratios, illustrating the importance of including submillimeter data when modeling the far-IR dust emission.
\n\nmodels. We show the distribution of excess emission in the right panel of Figure 4 for all regions in the extended galaxies, as well as the galaxies that were fit globally. We find that the resolved elements of the extended galaxies do not preferentially show an excess or a deficit. The mean excess of our sample is ∼ 0 . 02. This confirms that the majority of regions display a low excess or deficit ( < 10%). Given the large uncertainties (the dispersion is ∼ 0 . 1), this excess is thus marginal. In practice, we do not find excess 500 µ m emission greater than the scatter in the data.\n3.3. 500 µ m excess dependence on β\nThe derived emissivity contains information about the slope of the Rayleigh-Jeans tail, and it is possible that β is correlated with the measured excess emission (Galametz et al. 2012) We test this hypothesis for our sample in Figure 5. For simplicity, we average together all of the derived excesses and β values for each galaxy as we do not see any trends for individual galaxies. There is no apparent correlation between the excess emission and the value of β when β is allowed to be a free parameter. However, since β and T c exhibit a degeneracy which is possibly enhanced by the particular fitting method used (e.g., Juvela et al. 2013), a common technique for blackbody fitting is to hold β fixed (e.g., Yang & Phillips 2007; Xilouris et al. 2012). It is possible that holding β fixed will cause us to measure an excess emission, since the slope of the Rayleigh-Jeans tail changes from region to region within each galaxy (see Figure 3). We test this hypothesis by refitting all of our photometry holding β fixed to the values of 1, 1.5, and 2.\nThe 500 µ m excesses for each value of β are plotted in Figure 6. An emissivity of one generally produces very bad fits to the SEDs with high χ 2 values for several galaxies, reflected in the error bars. The slope of\nthe Rayleigh-Jeans tail is too shallow and overestimates the 500 µ m emission, as can be seen in the top panel of Figure 6. Setting β = 2 provides the best fits to the SEDs when fixing the emissivity as can be seen by the small uncertainties in the bottom panel of Figure 6. The excess emission is now ∼ 30% for galaxies which had only a 10% excess when β was allowed to vary (Figure 4). The result is consistent with R'emy-Ruyer et al. (2013), who also calculate the excess 500 µ m emission keeping β fixed at a value of 2. Holding β fixed does increase the amount of excess emission measured. It also increases the so-called emission 'deficit', meaning we now overpredict the 500 µ m emission by ∼ 20 -30%; the excess emission for each galaxy is listed in Table 2. We stress that the amount of excess emission is affected by the particular fitting method used. In our study, where we achieve good reduced χ 2 fits when holding β fixed to a value of two, and when letting β be a free parameter, we find excess values differing by as much as 20% depending on the fitting method.\nThere is a linear correlation between the excess emission and the metallicity. This is most strongly exhibited by M 101, which has a Pearsons correlation coefficient of ρ = -0 . 86 for all three values of β . NGC 4321 also has a strong trend between excess emission and metallicity. With the exception of NGC 5055, the other extended galaxies have fewer points, so it is difficult to see a trend. The dwarf galaxies also display a high correlation with ρ in the range 0 . 54 -0 . 61 depending on the value of β . On the other hand, NGC 4321 shows no correlation between metallicity and excess for any value of β . When all of the galaxies are considered together, there is a strong anti-correlation ( ρ = -0 . 70) for β = 1 and only a low anti-correlation ( ρ = -0 . 30) for β = 2.\nIC 2574, NGC 2915, and NGC 5408 have a marked ex-\n\n\n
Fig. 4.Excess emission as a function of metallicity. We plot the excess for each individual region within an extended galaxy (colored crosses). The typical uncertainty is shown in the lower right corner. The dwarf/irregulars and compact galaxies are plotted as the black symbols. The galaxies with large uncertainties have low SPIRE SNRs. There is no trend in excess emission with decreasing metallicity for the extended galaxies or dwarf/irregular galaxies. On the right, we plot the distribution of the 500 µ m excess for all regions in the extended galaxies, as well as the galaxies that were fit globally; we have scaled the distribution to have a peak value of 1. The mean excess is ∼ 2%. We indicate the mean with the dotted line. The spike in excess above 2% is largely due to NGC 5457 (M 101).
\n\n\n\n
Fig. 5.The excess emission as a function of the derived emissivity. No obvious trend is evident, so allowing β to vary does not produce any dependence between the derived β and measured excess. The large uncertainties on the emissivities are caused by an increased degeneracy between temperature and β with low SNRs.
\n\ncess when β = 2. However, for IC 2574 and NGC 2915, there is no substantial excess when β = 1 , 1 . 5 or when β is allowed to vary. From this, we conclude that there is a flattening of the SED in these two galaxies that a steeper value of β is unable to account for. Because β is an effective emissivity, and contains information about the intrinsic properties of the dust grains as well as the heating of the dust within a resolution element, we cannot conclusively determine whether this flattening is due to changing properties of the dust grains in low metallicity galaxies.\nFor most galaxies, including the individual regions in the extended galaxies, the use of β = 2 as opposed to β = 1 produces much lower reduced χ 2 values during the Monte Carlo fitting. We plot the distribution of reduced\nχ 2 values over 1000 Monte Carlo fits for NGC 1377 in the top panel of Figure 7. The mean reduced χ 2 is 2.3 when β = 2 but is 10.6 when β = 1. We also show the distribution of reduced χ 2 values for NGC 2915, for which the choice of β makes little difference in the goodness of the fits. When β = 2, the mean reduced χ 2 = 1 . 1, and when β = 1, the mean reduced χ 2 = 1 . 3. This effect is also seen for NGC 3773, NGC 5408, and IC 2574, all of which exhibit no decrease in the uncertainty on the excess depending on the value of β . These are the four galaxies with the lowest SNRs at 250 µ m and 350 µ m, illustrating the difficulty of using modified blackbody fitting with low signal-to-noise photometry.\n3.4. Exploring the Submillimeter Dust Emission\nWhen β is a free parameter, we do not see any systematic excess trend with metallicity, nor do we measure strong excess emission. However, when β = 2, we see a weak dependence on metallicity, and we do detect some excess for individual galaxies (Table 2). One explanation for excess submillimeter emission is temperature mixing within a resolution element (e.g., Shetty et al. 2009). The emissivity we measure is comprised both of the intrinsic emissivity of the dust and the range of temperatures of the dust components in the resolution element. This range of temperatures can produce a shallower effective β than would be measured in the ideal case of only one temperature component. We can test this explanation by comparing the excess emission with both the distance of our galaxies and the physical region size subtended by the photometry aperture (see Table 1). Both a larger region size and a larger distance will correspond to more dust emission within the resolution element, and hence more temperature mixing. We find no trend between physical size and excess emission, demonstrating that the particular photometry aperture used does not\n\n\n
Fig. 6.We explore the effect of holding the emissivity constant on the measured excess emission. We set β = 1 (top panel), β = 1 . 5 (middle panel), and β = 2 (bottom panel). The typical uncertainty for the regions in the extended galaxies is shown in the upper right corner of each panel. When β = 2, we have the smallest uncertainties and best χ 2 fits, whereas β = 1 results in very poor χ 2 values.
\n\naffect the resulting excess.\nIn Figure 8, we plot the excess emission calculated when the emissivity was allowed to vary (see Figure 4) and when β = 2 (see Figure 6) as a function of distance. There is a weak trend between the excess emission and the distance when β = 2. When the emissivity is held fixed, galaxies that are within 10 Mpc have on average a higher excess emission, whereas the 500 µ m emission has in general been overpredicted for the galaxies further than 10 Mpc. This does not appear to be an effect of galaxy type, since the nearby galaxies showing excess are both extended and dwarfs. The trend seen when β = 2 is the opposite of what is expected. Galaxies that are further should have more temperature mixing within the resolution element producing a shallower farIR slope, which would cause an excess when compared to the emission predicted with β = 2. With the exceptions of NGC 0925 and NGC 4559, this trend is driven by the dwarf galaxies. Since we see no correlation between excess emission and physical region size, or excess emission and distance when β is a free parameter, we conclude that the excess emission is not due to temperature variations within the resolution element.\nNGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574 have the highest excesses when β = 2. Mul-\n\n\n\n\n\n
Fig. 7.The distribution of reduced χ 2 values from each Monte Carlo repitiion when holding the emissivity fixed to a value of one (red) and two (black). For NGC 1377 (top), the choice of β makes a large difference in the goodness of the fits, but for NGC 2915 (bottom), it does not, though it does change the amount of excess emission calculated.
\n\niple studies advocate using a third temperature component (T ∼ 10K) instead of a lower emissivity to account for the submillimeter excess (Galametz et al. 2011; Galliano et al. 2003, 2005; Marleau et al. 2006). We attempted to fit these four galaxies with a three temperature modified blackbody. We have only six photometric data points in each galaxy to fit three modified blackbodies to, so we hold several parameters constant to avoid degeneracies. We set T w = 60K and β w = 2, as described in Section2.4. We hold the emissivities of the cold components fixed to a commonly applied value of 1.8, though we note that using β = 2 caused our derived temperatures to change by only ± 1 K. We hold the scaling of the warm dust component fixed to what we derived when fitting only two modified blackbodies. Finally, we restrict the temperature range of one of the cold components to be T ∈ [20 , 50] K and the other to be T ∈ [0 , 20] K. We find that if we do not restrict the temperature ranges, then both cold components will have the same derived temperature. We are able to achieve good fits (reduced χ 2 < 1) for NGC 5408 and NGC 5398 but not for NGC 2915 or IC 2574. For NGC 5408, our three dust temperatures are 60 K, 29 ± 3K, and 13 ± 7K; for NGC 5398, they are 60 K, 22 ± 1K, and 13 ± 5K. Also, it is important to note that not only are the uncertainties rather large on the coldest dust temperature, but the distribution of the derived temperatures for the\n\n\n
Fig. 8.The excess emission as a function of distance for the cases of a free emissivity (top see Fig. 4) and β = 2 (bottom, see Fig. 6). When the emissivity is held fixed, there is a trend with distance with the closer galaxies having more excess, and the farthest galaxies having on average a negative excess.
\n\nMonte Carlo simulations is not gaussian. There is only marginal excess ( < 10%) when using three temperatures for these two galaxies, but given the large uncertainties, non-gaussian distribution, and the necessity of imposing many restrictions on the fitting routine, we do not consider this method an improvement over using only two temperatures but allowing β to vary.\n3.5. Comparison with Dale et al. (2012)\nD12 calculate the excess emission at 500 µ m for all galaxies in the KINGFISH sample. They use a different approach and fit the physically motivated DL07 models and find that a dozen galaxies, including eight dwarf/irregular/Magellanic have an excess > 0 . 6 at 500 µ m. We do not fit three of the dwarf/irregulars (Ho I, Ho II, and M81dwB) because we do not have 3 σ detections at all far-IR wavelengths. For the remaining dwarf/irregulars with substantial reported excess (NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574) we find at most excesses of 30% when β is fixed at two. Another key difference in the two fitting approaches is that we are only concerned with fitting photometry spanning the range 24 -500 µ m, while D12 fit all IR photometry from 3.6 µ m and long ward. Specifically, D12 had to balance emission from the stellar continuum, PAH features, and thermal dust emission, meaning that they were unable to tailor their fits to the far-IR/submillimeter portion of the SED.\nThe discrepancy between the results of the present study and those of D12 can also be attributed to a difference in the photometry (Section 2.2). The KINGFISH 500 µ m images used in D12 were recently recalibrated downward by of order 10%. In addition, the\nPACS images were processed with different versions of the Scanamorphos package (Roussel 2012). In this work, all images were convolved to the 500 µ m resolution before measuring the photometry, whereas in D12, photometry was calculated using the original images. As noted in Section 2.3, our background subtraction methods are different. It is also important to bear in mind that our photometry aperture sizes are not identical to D12. We use circular apertures whose diameters are listed in Table 1 while D12 uses elliptical apertures of varying sizes. Figure 1 shows our photometry and the photometry for D12 overplotted. The main discrepancies are between the PACS data and the 500 µ m. D12 calculate the excess slightly differently than this work; namely, they divide the excess by the model flux density, whereas we use the measured flux density (Eq. 2).\nWe fit the D12 photometry for NGC 2915, NGC 4236, NGC5398, NGC 5408, and IC 2574 with our two temperature modified blackbody model. We hold the emissivity fixed to a value of two, and we calculate the fractional excess according to the prescription in D12. For four of the galaxies, we find fractional excesses between 55% and 75% (IC 2574 has an excess of 44%), leading us to conclude that discrepancy between our work and D12 is primarily due to the difference in the flux density calibration and convolution of the images, and the photometric apertures, and not a result of using different modeling techniques.\n4. CONCLUSIONS\nWe measure the emission at 500 µ m for a sample of star forming KINGFISH galaxies spanning a range of metallicities. We model the far-IR SED with a two temperature modified blackbody, and calculate the excess emission as the measured 500 µ memission relative to the predicted emission. For extended galaxies, we measure the excess in circular apertures with a diameter of 42' from the center to the edge of the galaxy. We supplement the sample of extended galaxies with a sample of compact and of dwarf/irregular galaxies, for which we model the far-IR emission on a global scale.\nWhile we do see excesses of ∼ 10% for a handful of galaxies when we allow β to vary, we do not see any overall trend as a function of metallicity for the range 12 + log(O/H) = 7 . 8 -8 . 7. Furthermore, this excess is completely accounted for by the uncertainties in the fitting procedure. In addition, several of our galaxies exhibit a 500 µ m deficit of ∼ 10%. We conclude that if any strong excess is present at 500 µ m in lower metallicity galaxies, it must occur in galaxies with 12 + log(O/H) < 7 . 8. Our findings are qualitatively consistent with the work of Galametz et al. (2011). They find a submillimeter excess at 870 µ m in galaxies with 8 < 12 + log(O/H) < 9; however, when this excess is present, it is not universally seen at 500 µ m. The authors successfully account for the excess with a very cold (T ∼ 10K) dust component. Galametz et al. (2013, in prep.) reports a submillimeter excess in some of the galaxies in this sample, but it is detected at 870 µ m. It is possible that such an excess is present universally in our sample, but that longer wavelength observations are required to detect it.\nAs for the flattening of the Rayleigh Jeans tail in the submillimeter regime, we find that β = 2 most accurately reproduces the slope of SED around 500 µ m.\n
\n\n
TABLE 2 Derived Properties from SED fitting
\n
\nFor the 7 extended galaxies, all of the values listed in this table are averages and standard deviations of all of the photometric regions we modeled. a The percentage of the 100 µ m flux density due to the warm temperature modified blackbody (see Eq. 1).\nIn fact, using β = 1, as has been suggested to be appropriate at longer submillimeter wavelengths, consistently overestimates the emission at 500 µ m. Therefore, any change in the emissivity does not occur until λ > 500 µ m. An emissivity index of two results in the lowest uncertainties in the SED fits and shows only a weak trend metallicity, which varies from galaxy to galaxy. Fitting with a standard value of β = 2, which results in reduced χ 2 < 1, produces an excess of ∼ 30% in six galaxies, but over predicts emission by ∼ 20% in five galaxies. We conclude that though a small 500 µ m excess may be present in individual galaxies, this is compensated by equal amounts of 500 µ m'deficiency' in comparable numbers of galaxies, and only preferentially\naffects the lower metallicity galaxies when modeling with a fixed β .\nHerschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. IRAF, the Image Reduction and Analysis Facility, has been developed by the National Optical Astronomy Observatories and the Space Telescope Science Institute. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.\nREFERENCES\n\nAniano, G., Draine, B. T., Gordon, K. D., et al. 2011, PASP, 123, 1218\nAniano, G., Draine, B. 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[arXiv:1309.1371]\n\nRoussel, H. 2012, arXiv:1205.2576\n\nSandstrom, K., Krause, O., Linz, H., et al. 2010, A&A, 518, L59 Storchi-Bergmann, T., Calzetti, D., and Kinney, A. L. 1994, ApJ, 429, 572\n\nShetty, R., Kauffmann, J., Schnee, S., et al. 2009, ApJ, 696, 2234 Tabatabaei F. S., Braine J., Kramer C., et al. 2011, arXiv:1111.6740\nXilouris, E. M., Tabatabaei, F. S., Boquien, M., et al. 2012, A&A, 543, 74\nYang, M. & Phillips, T. 2007, ApJ, 662, 284\nYsard, N., Juvela, M., Demyk, K., et al. 2012, A&A, 542, A21 Zhu, M., Papadopoulos, P. P., Xilouris, E. M., et al. 2009, ApJ,\n706, 941\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"Submillimeter excess emission has been reported at 500 µ m in a handful of local galaxies, and previous studies suggest that it could be correlated with metal abundance. We investigate the presence of an excess submillimeter emission at 500 µ m for a sample of 20 galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH) that span a range of morphologies and metallicities (12 + log(O/H) = 7 . 8 -8 . 7). We probe the far-infrared (IR) emission using images from the Spitzer Space Telescope and Herschel Space Observatory in the wavelength range 24 -500 µ m. We model the far-IR peak of the dust emission with a two-temperature modified blackbody and measure excess of the 500 µ m photometry relative to that predicted by our model. We compare the submillimeter excess, where present, with global galaxy metallicity and, where available, resolved metallicity measurements. We do not find any correlation between the 500 µ m excess and metallicity. A few individual sources do show excess (10-20%) at 500 µ m; conversely, for other sources, the model overpredicts the measured 500 µ m flux density by as much as 20%, creating a 500 µ m 'deficit'. None of our sources has an excess larger than the calculated 1 σ uncertainty, leading us to conclude that there is no substantial excess at submillimeter wavelengths at or shorter than 500 µ m in our sample. Our results differ from previous studies detecting 500 µ m excess in KINGFISH galaxies largely due to new, improved photometry used in this study.","pages":[1]},{"title":"INVESTIGATING THE PRESENCE OF 500 µ M SUBMILLIMETER EXCESS EMISSION IN LOCAL STAR FORMING GALAXIES","content":"Allison Kirkpatrick 1 , Daniela Calzetti 1 , Maud Galametz 2 , Rob Kennicutt, Jr. 2 , Daniel Dale 3 , Gonzalo Aniano 4 , Karin Sandstrom 5 , Lee Armus 6 , Alison Crocker 7 , Joannah Hinz 8 , Leslie Hunt 9 , Jin Koda 10 , Fabian Walter 5 Draft version September 24, 2018","pages":[1]},{"title":"1. INTRODUCTION","content":"Dust in the interstellar medium (ISM) is formed by grain growth in both the diffuse ISM and the ejecta of dying stars, such as red giant winds, planetary nebula, and supernovae (Draine 2009). Once formed, dust absorbs UV and optical light and reemits this radiation in the infrared. UV radiation is dominated by photons from young O and B stars, so the dust mass and infrared (IR) radiation can provide important constraints on the current star formation rates and the star formation history of a galaxy. Space-based telescopes such as the Spitzer Space Telescope, the InfraRed Astronomical Satellite, and the Infrared Space Observatory have provided insights on the dust emission from mid-IR wavelengths out to ∼ 200 µ m. However, the majority, by mass, of the dust is cold ( T /lessorsimilar 25 K, Dunne & Eales 2001) and emits at far-IR and submillimeter wavelengths, where the emission spectrum is dominated by large grains in thermal equilibrium. Ground-based observations of these wavelengths are limited to a few atmospheric windows, and until recently, space-based observatories lacked coverage of the far-IR beyond ∼ 200 µ m. Now, with the advent of the Herschel Space Observatory, the peak and long wavelength tail of the dust spectral energy distribution (SED) is being observed at unprecedented angular resolution. With submillimeter observations, the dust mass and the dust to gas ratios can be more accurately estimated. Dust formation models show that the dust to gas ratios should be tied to the chemical enrichment of galaxies, as measured by the metallicity (Dwek 1998; Edmunds 2001). Galametz et al. (2011) combine submillimeter data at 450 and 850 µ m with shorter wavelength IR observations ( /lessorsimilar 160 µ m) for a large sample of local star forming galaxies. They model the spectral energy distributions of each galaxy with and without the submillimeter data and find that for high metallicity galaxies, not including the submillimeter data can cause the dust mass to be overestimated by factors of 2-10, whereas for low metallicity galaxies (12+log(O/H) /lessorsimilar 8 . 0), the SEDs without the submillimeter data can underpredict the true dust mass by as much as a factor of three. Gordon et al. (2010) use Herschel photometry to model the dust emission from the Large Magellanic Cloud (LMC) and find that dust mass derived using just 100 µ m and 160 µ m photometry underestimate the dust mass derived when using 350 µ m and 500 µ m photometry as well by as much as 36%. In measuring dust masses by modeling the far-IR and submillimeter SED, a variety of studies have sug- gested the existence of excess emission at submillimeter wavelengths above what is predicted by fits to shorter wavelength data. Furthermore, this excess could preferentially affect lower metallicity and dwarf galaxies. Dale et al. (2012, hereafter D12) report significant excess emission at 500 µ m, above that predicted by fitting the observed SEDs with the Draine & Li (2007) models, for a sample of eight dwarf and irregular galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH, Kennicutt et al. 2011). Excess emission has also been reported in the Small Magellanic Cloud (SMC) and LMC, both of which have lower than solar metallicities (12+log(O/H) = 8 . 0 , 8 . 4, respectively Bot et al. 2010; Gordon et al. 2010). On the other hand, excess emission is also seen at solar metallicities or larger. Paradis et al. (2012) model emission in the Galaxy and find excess emission (16 -20%) at 500 µ m in peripheral H ii regions. Recently, Galametz et al. (2013, in prep.) have detected excess at 870 µ m on a resolved and global scale for a sample of 11 KINGFISH galaxies. Galametz et al. (2011) finds a submillmeter excess at 870 µ m for 8 galaxies spanning a metallicity range of 12 + log(O/H) = 7 . 8 -9 . 0. The presence of excess emission does not appear to be universal, however, as Draine et al. (2007) found only a marginal difference in deriving the dust masses for a set of SINGS galaxies with and without including submillimeter data from SCUBA 12 + log(O/H) ≈ 7 . 5 -8 . 7 . More recently, Aniano et al. (2012) apply the Draine & Li (2007) models to the IR SEDs (3 . 6 -500 µ m) of the local star forming galaxies NGC 0628 and NGC 6946 and do not detect any significant excess ( > 10%) at 500 µ m. The excess emission seen at submillimeter wavelengths can be attributed to a cold dust component which is shielded from starlight (T < 10K; e.g., Galametz et al. 2009; O'Halloran et al. 2010). However, in the Milky Way, excess emission is seen at high latitudes, making it unlikely to be due to shielded cold dust (Reach et al. 1995). Studies of other galaxies have argued that a cold dust origin for the excess emission leads to unphysically high dust to gas ratios (Lisenfeld et al. 2002; Zhu et al. 2009; Galametz et al. 2010). A competing explanation is that the spectral emissivity index, β , of the dust grains changes to lower values at longer wavelengths, leading to a flattening of the submillimeter spectrum, thus mimicking a cold dust component (Dupac et al. 2003; Augierre et al. 2003; Planck Collaboration 2011). Such a change in emissivity has been suggested in the Milky Way (Paradis et al. 2009). (Galametz et al. 2012) showed that modeling the far-IR /submillimeter emission with a modified blackbody with β = 1 . 5 can increase the dust masses up to 50% compared to when β = 2, possibly explaining the discrepancies between dust masses calculated with far-IR data alone and those calculated with farIR and submillimeter data. The emission from very small grains exhibits a frequency dependence with a spectral emissivity index of β = 1, and if a galaxy has a relative abundance of very small grains greater than the Milky Way, this can cause a flattening of the emissivity index at longer wavelengths (Lisenfeld et al. 2002; Zhu et al. 2009). Alternatively, the properties of amorphous solids could explain the change in emissivity (Meny et al. 2007). Modeling the emission of amorphous solids accounts for the submillimeter excess in the LMC and SMC (Bot et al. 2010), although recent work suggests that much of the excess emission in the LMC is accounted for by fluctuations in the cosmic microwave background (Planck Collaboration 2011). Finally, an increase in the amount of magnetic material has also been proposed as a plausible explanation for the SMC submillimeter excess (Draine & Hensley 2012). Achange in dust properties can also be linked to metallicity. Draine et al. (2007) showed that 12 + log(O/H) = 8 . 1 is a threshold metallicity for galaxies in the range 12 + log(O/H) ≈ 7 . 5 -8 . 7, above which the percentage of dust mass contained in PAH molecules drastically increases. If submillimeter excess emission is due to a change in the emissivity properties of the dust population, then there might be a correlation with abundances in this metallicity range. In the present study, we seek to investigate the submillimeter excess at 500 µ m for a sample of KINGFISH galaxies. We define such excess as being emission above that predicted by a two-temperature modified blackbody model where the emissivity is not constrained, following the method outlined in Galametz et al. (2012). We have selected a sample that spans a range of metallicities, including many dwarf galaxies, in order to probe whether such excess correlates with metallicity, as has been found in some earlier studies (Galametz et al. 2009, 2011). The paper is laid out as follows: in Section 2, we describe our sample selection and modeling of the dust emission; in Section 3, we report on the excess emission and how our findings relate to the results of D12; and in Section 4, we present our conclusions.","pages":[1,2]},{"title":"2.1. The KINGFISH Sample","content":"The KINGFISH sample (Kennicutt et al. 2011) was selected to include a wide range of luminosities, morphologies, and metallicities in local galaxies. The sample overlaps with 57 of the galaxies observed as part of the Spitzer Infrared Nearby Galaxies Survey (SINGS, Kennicutt et al. 2003b), as well as incorporating NGC 2146, NGC 3077, M 101 (NGC 5457), and IC 342 for a total of 61 galaxies. The luminosity range spans four orders of magnitude, but all galaxies have L < 10 11 L /circledot . While some of the galaxies display a nucleus with LINER or Seyfert properties, no galaxy's global SED is dominated by an AGN. We select a sample (7) of disk galaxies possessing a large angular size ( ∼ 30arcmin 2 ) and a known metallicity gradient with which we perform a resolved study of the excess emission and search for any correspondence with metallicity. We refer to this sample as the 'extended' galaxies. Since excess emission seems to be found in dwarf/irregular galaxies, we include the dwarf/irregular galaxies (9) in KINGFISH for which we have a signal-tonoise ratio (SNR) > 3 σ in all of the SPIRE bandpasses. The dwarf/irregulars are more compact objects than our normal disk galaxies, and in general, do not have a known metallicity gradients, so we measure the excess emission globally for these objects. The resolved nature of the normal disk galaxies might bias our comparison with the dwarf/irregular galaxies, so we complement our sample (4) with normal disk galaxies that have small angular size which allows for global measurements of excess emission. These more compact, normal galaxies were selected to span a range of metallicity and have high SNRs at the SPIRE bandwidths. Our complete sample consists of 20 galaxies and is listed in Table 1. We also list in Table 1 dwarf/irregular galaxies that were rejected due to low SNRs.","pages":[2,3]},{"title":"2.2. Data Reduction","content":"Data observations and reduction are discussed in detail in Engelbracht et al. (2010), Sandstrom et al. (2010) and Kennicutt et al. (2011). In the present study, we use images from the PACS and SPIRE instruments on the Herschel Space Observatory spanning a wavelength range of 70 -500 µ m and MIPS 24 µ m images from the Spitzer Space Telescope (Kennicutt et al. 2003b). We use PACS 70 and 160 µ m images instead of MIPS due to the better resolution provided by PACS. All galaxy maps are at least 1.5 times the diameter of the optical disk, allowing us to probe the cold dust emission beyond the optical disk. The raw PACS and SPIRE images were processed from level 0 to 1 with Herschel Interactive Processing Environment (HIPE) v. 8. The PACS and SPIRE maps were then created using the IDL package Scanamorphos v. 17 (Roussel 2012). Scanamorphos is preferred to HIPE for its ability to better preserve low level flux density, reduce striping in area of high background, and correct brightness drifts caused by low level noise. The maps are converted from units of Jy beam -1 to MJy sr -1 by accounting for beam sizes of 469.1, 827.2, and 1779.6 arcsec 2 for the 250, 350, and 500 µ m maps, respectively. The design and performance of the SPIRE instrument is discussed in detail in Griffin et al. (2010). In the SPIRE images used in this study, the full width at half maximum (FWHM) of the beam profile has been modeled with a wavelength dependence, so that FWHM ∝ λ γ , where γ = 0 . 85. As part of the calibration process, a 'color-correction' has been applied to each beam so that the measured specific intensity I ν will be equal to the actual specific intensity I 0 when ν = ν 0 . The correction factors applied to these images assume a power-law spectrum with α = -1 . 9. We compare our results to those of D12, so it is crucial to explicitly state that we are using different versions of the PACS and SPIRE images. In D12, the raw PACS and SPIRE images were processed from level 0 to 1 with HIPE v.5. The SPIRE data were then mosaicked using the mapper in HIPE. The images were converted to MJy sr -1 using beam sizes of 423, 751, and 1587 arcsec 2 at 250, 350, and 500 µ m, respectively, and the FWHM was not modeled with a wavelength dependence; furthermore, the color-correction was not included in the beam size, but was applied a posteriori.The PACS data were mapped using Scanamorphos v. 12.5. The main difference between the version of KINGFISH images that we use and the previous version used by D12 is that the SPIRE 250 and 350 µ m images contain slightly less flux density ( ∼ 2%) while the 500 µ m image is less luminous by ∼ 10%. The point response function area is also slightly larger ( ∼ 3%) than for the v. 2 images. The more recent HIPE v. 11 pipeline has revised the SPIRE beam sizes in the direction of yielding lower fluxes for extended sources by ∼ 6%, 6%, and 8% at 250, 350, and 500 µ m, respectively. This is in the direction of reinforcing the results that are presented in this paper.","pages":[3]},{"title":"2.3. Background subtraction and Convolution of Images","content":"The background subtraction is described in detail in Aniano et al. (2012), and we will briefly summarize here. 'Non-background' regions are determined in all cameras (IRAC, MIPS, PACS, and SPIRE) by those pixels which have a SNR > 2. Masks of the non-background regions are made, and then the masked images from all cameras are combined in order to unambiguously determine which regions are truly background regions. The signals in the background regions are then averaged, smoothed, and subtracted according to an algorithm outlined in Aniano et al. (2012). Since we compare our results with those of D12, it is worthwhile to note that a different procedure for background subtraction is followed in that study. The authors use a set of sky apertures to measure the local sky around each galaxy while avoiding any contamination from galaxy emission. The mean sky level per pixel is computed from these sky apertures, scaled to the number of pixels in the galaxy photometry aperture, and the result is subtracted from the overall galaxy photometry aperture counts. In order to consistently measure photometry for each galaxy, we used images that had been convolved to the resolution of the SPIRE 500 µ m bandpass. The convolution was done with publicly available kernels from Aniano et al. (2011) which transform the point source functions (PSFs) of individual images to the PSF of the SPIRE instrument at 500 µ m (FWHM of 38'). The convolution kernels and methodology are described in detail in Aniano et al. (2011, 2012). After the convolution to a common PSF, the images for each galaxy are resampled to a standard grid, where each pixel is ∼ 14'.","pages":[3]},{"title":"2.4. Photometry and SED fitting","content":"For the extended galaxies, we measure photometry in apertures with diameters of 42', chosen to be slightly larger than the beam size of the SPIRE 500 µ m bandpass, from the center of the galaxy to the outskirts. We reject regions of galaxies without at least 3 σ flux density measurements at every bandpass from 24 -500 µ m. For the galaxies which are compact at the 500 µ m resolution, including the dwarf/irregulars, we measure the photometry globally in apertures with diameters ranging from 42' to 1' 52', which is the angular area covered by the galaxies with a signal to noise ratio > 3 σ . The diameter and the physical scales of each photometric aperture are listed in Table 1. The dwarf/irregular galaxies DDO 053, DDO 154, and DDO 165 have a 3 σ flux density measurement in only one of the far-IR bandpasses; Ho I, Ho II, and M 81 DwB have measurements in three of the six bandpasses. We do not model the far-IR emission for these galaxies, but we do plot the photometry and 3 σ upper limits in Figure 1. The physically-based DL07 models have been used to derive dust properties at global and local scales (e.g., Draine et al. 2007; Aniano et al. 2012). The DL07 models use the assumption of a diffuse ISM component to describe the shape of the interstellar radiation field, and We do not calculate an excess for Ho I, Ho II, DDO 053, DDO 154, DDO 165, and M81 DwB since we are not able to measure flux densities at the 3 σ level covering the full wavelength range 24 -500 µ m. The metallicity range for which we can derive excess measurements is then 12 + log(O/H) = 7 . 8 -8 . 7. use distribution function to represent the distribution of starlight intensities, which are then scaled to the SED being modeled. In addition, the submm slope of the DL07 models tends to resemble that of a modified blackbody with an emissivity of β = 2, which could prevent us from testing for flattening of the submm slope or variations in the emissivity index. We choose to model the farIR SEDs with a simple modified blackbody equation to test various assumptions on the emissivity index and will compare our results to the D12 study to investigate how the choice of model affects the observed excess emission. We model the far-IR SEDs of each region within each galaxy using a two temperature modified blackbody of the form where B ν is the Planck function. The temperatures of the warm and cold dust components are T w and T c , the scalings for each component are a w and a c , and β w and β c are the emissivity indexes. Only the scalings, T c , and β c are allowed to be free parameters, due to the limited number of data points being fit. The warm dust com- nt is necessary to account for some of the emission at 70 µ m and 100 µ m so as not to bias the cold dust temperature or emissivity. When only one temperature is used, the peak of the modified blackbody is biased towards shorter wavelengths, leading to warmer temperatures, which is then compensated at longer wavelengths by a β c shallower than otherwise measured. We include the 24 µ m data point in the fit to better constrain the warm dust modified blackbody, but the fitted warm dust parameters should not be interpreted in a physical manner, since this portion of the SED also likely contains contribution from stochastically heated dust. We list the fraction of 100 µ m flux density due to the warm dust component in Table 2. The effective dust emissivity we derive comprises the intrinsic spectral emissivity properties of dust and the variation of the dust temperature within a resolution element that could lead to a shallower β c than that obtained in isothermal cases (e.g., Shetty et al. 2009). We nevertheless allow both the cold temperature and cold emissivity, β c , to vary simultaneously, though the two parameters are degenerate. We refer to Galametz et al. (2012) and Kirkpatrick et al. (2013b, in prep.), and references therein, for a further discussion of degeneracies on the individual temperatures and emissivities. We fit the photometry from 24 -350 µ m. The 500 µ m data are not included to allow comparison with our model predictions at the same wavelength. We use a Monte Carlo technique to determine the parameters and errors. We randomly sample each data point within its errors 1000 times and determine the parameters of the two temperature modified blackbody via χ 2 minimization. The final parameters and associated errors are the medians and standard deviations of our Monte Carlo simulation. An example of the SED fitting is shown in Figure 2. When fitting, we allow the cold dust temperature, T c , to vary between 0 and 50 K and β c to vary between 0 and 5. We experimented with allowing T w to vary, but the derived temperature was approximately constant in the range 55 -60K, and simultaneously varying T w did not change the derived cold dust temperature or emissivity values. Since the warm dust component peaks in an area of the SED that is sparsely sampled, we opt to hold both T w and β w fixed. We hold the emissivity of the warm dust component fixed to a value of two and T w fixed to 60K. Fixing β w = 2 is a good approximation of the opacity of graphite/silicate dust models (Li & Draine 2001). Galametz et al. (2012) find that changing β w to 1.5 decreases the cold dust temperatures by less than 1.6%, and Tabatabaei et al. (2011) test the two temperature modified blackbody approach on M33, holding β w fixed to 1.0, 1.5, and 2.0, and conclude that β w = 2 most accurately reproduces the observed flux densities. We test a fixed β c in Section 3.3. As β w is always fixed to a value of two in all of our subsequent analysis, in the remainder of this paper, we refer to β c simply as β .","pages":[3,4,5]},{"title":"3.1. PACS-SPIRE colors","content":"The color S 100 /S 160 , where S 100 is the flux density in the 100 µ m bandpass, is commonly used as a proxy for temperature, since it usually spans the peak of the blackbody emission, while S 350 /S 500 depends sensitively on the slope of the Rayleigh-Jeans tail, and so is a good proxy for β (with the same caveats given earlier about the mixing of dust with different temperatures along the line of sight). We plot these two colors in the left panel of Figure 3 for each of the regions in our extended galaxies. We calculate the positions of theoretical modified blackbodies and overplot as a grid. When calculating the theoretical tracks, we use a two temperature modified blackbody (Equation 1); we set T w = 60 K, β w = 2, and we scale the warm dust component to peak at a flux density 10% of the cold dust component peak flux density, which is the average scaling we see in our fitted SEDs at the SPIRE wavelengths. We set β = 1 , 1 . 5 , and 2, and we set T c to discrete temperature values between 15 and 27 K. Lines of constant β and T c are marked on the figure. The colors of our galaxies tend to cluster around the β = 2 , T c = 20K lines. At higher temperatures, galaxy colors start to sparsely occupy the same part of color space as the β = 1 model. No galaxies exhibit colors indicating a low temperature ( T c < 21 K) and a shallow emissivity, which could hint at physical link between the two parameters (see Yang & Phillips 2007; Ysard et al. 2012; Kirkpatrick et al. 2013b, in prep., for a discussion of the physical nature of the T c -β relationship). Although our galaxy colors tend to lie near the β = 2 model line, we observe a large scatter. This illustrates a significant difference of physical conditions from one object to another but also within our objects. Letting both parameters vary in our multiple blackbody approach can be a way to probe these variations, in spite of the degeneracies. In the right panel of Figure 3, we plot the same colors, but this time we use the predicted 500 µ m flux density, which has been calculated by fitting Equation 1 to the 24 -350 µ m flux densities. Substituting the predicted 500 µ m flux density has two interesting effects. First, it increases the amount of scatter visible in the colors. For example, in both NGC 5055 and NGC 4321, which dis- y the largest increase in scatter, the mean S 350 /S 500 observed ratio and predicted ratio is approximately the same ( ∼ 2 . 7). For NGC 5055, the standard deviation increases from 0.16 to 0.24, and for NGC 4321 it increases from 0.11 to 0.23. This increase is indicative of the uncertainties inherent in fitting modified blackbody models without enough data to adequately constrain the slope of the Rayleigh-Jeans tail. The second effect we see is that now the galaxy colors, particularly for M 101, occupy a region of the color space to the right of the β = 2 model line. The predicted S 350 /S 500 ratio is larger than the observed S 350 /S 500 ratio. Again, this illustrates the importance of using data above 350 µ m to constrain the submillimeter SED. Without including the 500 µ m data point in the modeling of the far-IR/submillimeter SED, the predicted slope will be steeper than the true value; in other words, the model underpredicts the measured 500 µ m flux density. We calculate the excess emission at 500 µ m as where F ν (500 µ m) is the predicted flux density of the two-temperature modified blackbody and S ν is the measured flux density. We plot the excess emission as a function of metallicity in Figure 4. We correct the radius of each photometric region for the inclination of the galaxy, and then convert the radius to metallicity using the gradients listed in Moustakas et al. (2010) which were calculated according to the Pilyugin & Thuan (2005) relationship (see Table 1). For M 101, which is not included in Moustakas et al. (2010), we use a metallicity gradient calculated directly from electron temperature measurements in H ii regions (Kennicutt et al. 2003a; Bresolin et al. 2004), which creates a slight offset between M 101 and the rest of our sample in metallicity. Figure 4 shows that there is no systematic dependence of the excess emission on metallicity for the sample as a whole, nor is there any trend within the individual galaxies that have a metallicity gradient. None of the galaxies display an excess larger than 25%, and for many galaxies, the modeling actually overpredicts the 500 µ m emission by this amount, creating a 500 µ m deficit. Furthermore, the spread in excess is largely accounted for by the uncertainty attached to each data point (the typical uncertainty for each region in the extended galaxies is shown in the bottom right of Figure 4). For some of the dwarf/irregulars, the uncertainties are rather large (particularly NGC 1377, NGC 2915, NGC 3773, NGC 5408, and IC 2574). The uncertainties are correlated with the SNR ratios of the SPIRE data since noisier photometry exacerbates the degeneracy between temperature and β (Juvela & Ysard 2012). The dwarf/irregulars with the lowest SNRs have the largest uncertainty on the derived β . We find that no extended galaxy has an excess emission greater than 10%, in agreement with the results of Gordon et al. (2010) for a resolved study of the LMC using a modified blackbody model, and with Aniano et al. (2013, in prep.), in which the authors create dust maps for the full sample of KINGFISH galaxies using the DL07 models. We show the distribution of excess emission in the right panel of Figure 4 for all regions in the extended galaxies, as well as the galaxies that were fit globally. We find that the resolved elements of the extended galaxies do not preferentially show an excess or a deficit. The mean excess of our sample is ∼ 0 . 02. This confirms that the majority of regions display a low excess or deficit ( < 10%). Given the large uncertainties (the dispersion is ∼ 0 . 1), this excess is thus marginal. In practice, we do not find excess 500 µ m emission greater than the scatter in the data.","pages":[6,7]},{"title":"3.3. 500 µ m excess dependence on β","content":"The derived emissivity contains information about the slope of the Rayleigh-Jeans tail, and it is possible that β is correlated with the measured excess emission (Galametz et al. 2012) We test this hypothesis for our sample in Figure 5. For simplicity, we average together all of the derived excesses and β values for each galaxy as we do not see any trends for individual galaxies. There is no apparent correlation between the excess emission and the value of β when β is allowed to be a free parameter. However, since β and T c exhibit a degeneracy which is possibly enhanced by the particular fitting method used (e.g., Juvela et al. 2013), a common technique for blackbody fitting is to hold β fixed (e.g., Yang & Phillips 2007; Xilouris et al. 2012). It is possible that holding β fixed will cause us to measure an excess emission, since the slope of the Rayleigh-Jeans tail changes from region to region within each galaxy (see Figure 3). We test this hypothesis by refitting all of our photometry holding β fixed to the values of 1, 1.5, and 2. The 500 µ m excesses for each value of β are plotted in Figure 6. An emissivity of one generally produces very bad fits to the SEDs with high χ 2 values for several galaxies, reflected in the error bars. The slope of the Rayleigh-Jeans tail is too shallow and overestimates the 500 µ m emission, as can be seen in the top panel of Figure 6. Setting β = 2 provides the best fits to the SEDs when fixing the emissivity as can be seen by the small uncertainties in the bottom panel of Figure 6. The excess emission is now ∼ 30% for galaxies which had only a 10% excess when β was allowed to vary (Figure 4). The result is consistent with R'emy-Ruyer et al. (2013), who also calculate the excess 500 µ m emission keeping β fixed at a value of 2. Holding β fixed does increase the amount of excess emission measured. It also increases the so-called emission 'deficit', meaning we now overpredict the 500 µ m emission by ∼ 20 -30%; the excess emission for each galaxy is listed in Table 2. We stress that the amount of excess emission is affected by the particular fitting method used. In our study, where we achieve good reduced χ 2 fits when holding β fixed to a value of two, and when letting β be a free parameter, we find excess values differing by as much as 20% depending on the fitting method. There is a linear correlation between the excess emission and the metallicity. This is most strongly exhibited by M 101, which has a Pearsons correlation coefficient of ρ = -0 . 86 for all three values of β . NGC 4321 also has a strong trend between excess emission and metallicity. With the exception of NGC 5055, the other extended galaxies have fewer points, so it is difficult to see a trend. The dwarf galaxies also display a high correlation with ρ in the range 0 . 54 -0 . 61 depending on the value of β . On the other hand, NGC 4321 shows no correlation between metallicity and excess for any value of β . When all of the galaxies are considered together, there is a strong anti-correlation ( ρ = -0 . 70) for β = 1 and only a low anti-correlation ( ρ = -0 . 30) for β = 2. IC 2574, NGC 2915, and NGC 5408 have a marked ex- cess when β = 2. However, for IC 2574 and NGC 2915, there is no substantial excess when β = 1 , 1 . 5 or when β is allowed to vary. From this, we conclude that there is a flattening of the SED in these two galaxies that a steeper value of β is unable to account for. Because β is an effective emissivity, and contains information about the intrinsic properties of the dust grains as well as the heating of the dust within a resolution element, we cannot conclusively determine whether this flattening is due to changing properties of the dust grains in low metallicity galaxies. For most galaxies, including the individual regions in the extended galaxies, the use of β = 2 as opposed to β = 1 produces much lower reduced χ 2 values during the Monte Carlo fitting. We plot the distribution of reduced χ 2 values over 1000 Monte Carlo fits for NGC 1377 in the top panel of Figure 7. The mean reduced χ 2 is 2.3 when β = 2 but is 10.6 when β = 1. We also show the distribution of reduced χ 2 values for NGC 2915, for which the choice of β makes little difference in the goodness of the fits. When β = 2, the mean reduced χ 2 = 1 . 1, and when β = 1, the mean reduced χ 2 = 1 . 3. This effect is also seen for NGC 3773, NGC 5408, and IC 2574, all of which exhibit no decrease in the uncertainty on the excess depending on the value of β . These are the four galaxies with the lowest SNRs at 250 µ m and 350 µ m, illustrating the difficulty of using modified blackbody fitting with low signal-to-noise photometry.","pages":[7,8]},{"title":"3.4. Exploring the Submillimeter Dust Emission","content":"When β is a free parameter, we do not see any systematic excess trend with metallicity, nor do we measure strong excess emission. However, when β = 2, we see a weak dependence on metallicity, and we do detect some excess for individual galaxies (Table 2). One explanation for excess submillimeter emission is temperature mixing within a resolution element (e.g., Shetty et al. 2009). The emissivity we measure is comprised both of the intrinsic emissivity of the dust and the range of temperatures of the dust components in the resolution element. This range of temperatures can produce a shallower effective β than would be measured in the ideal case of only one temperature component. We can test this explanation by comparing the excess emission with both the distance of our galaxies and the physical region size subtended by the photometry aperture (see Table 1). Both a larger region size and a larger distance will correspond to more dust emission within the resolution element, and hence more temperature mixing. We find no trend between physical size and excess emission, demonstrating that the particular photometry aperture used does not affect the resulting excess. In Figure 8, we plot the excess emission calculated when the emissivity was allowed to vary (see Figure 4) and when β = 2 (see Figure 6) as a function of distance. There is a weak trend between the excess emission and the distance when β = 2. When the emissivity is held fixed, galaxies that are within 10 Mpc have on average a higher excess emission, whereas the 500 µ m emission has in general been overpredicted for the galaxies further than 10 Mpc. This does not appear to be an effect of galaxy type, since the nearby galaxies showing excess are both extended and dwarfs. The trend seen when β = 2 is the opposite of what is expected. Galaxies that are further should have more temperature mixing within the resolution element producing a shallower farIR slope, which would cause an excess when compared to the emission predicted with β = 2. With the exceptions of NGC 0925 and NGC 4559, this trend is driven by the dwarf galaxies. Since we see no correlation between excess emission and physical region size, or excess emission and distance when β is a free parameter, we conclude that the excess emission is not due to temperature variations within the resolution element. NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574 have the highest excesses when β = 2. Mul- iple studies advocate using a third temperature component (T ∼ 10K) instead of a lower emissivity to account for the submillimeter excess (Galametz et al. 2011; Galliano et al. 2003, 2005; Marleau et al. 2006). We attempted to fit these four galaxies with a three temperature modified blackbody. We have only six photometric data points in each galaxy to fit three modified blackbodies to, so we hold several parameters constant to avoid degeneracies. We set T w = 60K and β w = 2, as described in Section2.4. We hold the emissivities of the cold components fixed to a commonly applied value of 1.8, though we note that using β = 2 caused our derived temperatures to change by only ± 1 K. We hold the scaling of the warm dust component fixed to what we derived when fitting only two modified blackbodies. Finally, we restrict the temperature range of one of the cold components to be T ∈ [20 , 50] K and the other to be T ∈ [0 , 20] K. We find that if we do not restrict the temperature ranges, then both cold components will have the same derived temperature. We are able to achieve good fits (reduced χ 2 < 1) for NGC 5408 and NGC 5398 but not for NGC 2915 or IC 2574. For NGC 5408, our three dust temperatures are 60 K, 29 ± 3K, and 13 ± 7K; for NGC 5398, they are 60 K, 22 ± 1K, and 13 ± 5K. Also, it is important to note that not only are the uncertainties rather large on the coldest dust temperature, but the distribution of the derived temperatures for the Monte Carlo simulations is not gaussian. There is only marginal excess ( < 10%) when using three temperatures for these two galaxies, but given the large uncertainties, non-gaussian distribution, and the necessity of imposing many restrictions on the fitting routine, we do not consider this method an improvement over using only two temperatures but allowing β to vary.","pages":[8,9,10]},{"title":"3.5. Comparison with Dale et al. (2012)","content":"D12 calculate the excess emission at 500 µ m for all galaxies in the KINGFISH sample. They use a different approach and fit the physically motivated DL07 models and find that a dozen galaxies, including eight dwarf/irregular/Magellanic have an excess > 0 . 6 at 500 µ m. We do not fit three of the dwarf/irregulars (Ho I, Ho II, and M81dwB) because we do not have 3 σ detections at all far-IR wavelengths. For the remaining dwarf/irregulars with substantial reported excess (NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574) we find at most excesses of 30% when β is fixed at two. Another key difference in the two fitting approaches is that we are only concerned with fitting photometry spanning the range 24 -500 µ m, while D12 fit all IR photometry from 3.6 µ m and long ward. Specifically, D12 had to balance emission from the stellar continuum, PAH features, and thermal dust emission, meaning that they were unable to tailor their fits to the far-IR/submillimeter portion of the SED. The discrepancy between the results of the present study and those of D12 can also be attributed to a difference in the photometry (Section 2.2). The KINGFISH 500 µ m images used in D12 were recently recalibrated downward by of order 10%. In addition, the PACS images were processed with different versions of the Scanamorphos package (Roussel 2012). In this work, all images were convolved to the 500 µ m resolution before measuring the photometry, whereas in D12, photometry was calculated using the original images. As noted in Section 2.3, our background subtraction methods are different. It is also important to bear in mind that our photometry aperture sizes are not identical to D12. We use circular apertures whose diameters are listed in Table 1 while D12 uses elliptical apertures of varying sizes. Figure 1 shows our photometry and the photometry for D12 overplotted. The main discrepancies are between the PACS data and the 500 µ m. D12 calculate the excess slightly differently than this work; namely, they divide the excess by the model flux density, whereas we use the measured flux density (Eq. 2). We fit the D12 photometry for NGC 2915, NGC 4236, NGC5398, NGC 5408, and IC 2574 with our two temperature modified blackbody model. We hold the emissivity fixed to a value of two, and we calculate the fractional excess according to the prescription in D12. For four of the galaxies, we find fractional excesses between 55% and 75% (IC 2574 has an excess of 44%), leading us to conclude that discrepancy between our work and D12 is primarily due to the difference in the flux density calibration and convolution of the images, and the photometric apertures, and not a result of using different modeling techniques.","pages":[10]},{"title":"4. CONCLUSIONS","content":"We measure the emission at 500 µ m for a sample of star forming KINGFISH galaxies spanning a range of metallicities. We model the far-IR SED with a two temperature modified blackbody, and calculate the excess emission as the measured 500 µ memission relative to the predicted emission. For extended galaxies, we measure the excess in circular apertures with a diameter of 42' from the center to the edge of the galaxy. We supplement the sample of extended galaxies with a sample of compact and of dwarf/irregular galaxies, for which we model the far-IR emission on a global scale. While we do see excesses of ∼ 10% for a handful of galaxies when we allow β to vary, we do not see any overall trend as a function of metallicity for the range 12 + log(O/H) = 7 . 8 -8 . 7. Furthermore, this excess is completely accounted for by the uncertainties in the fitting procedure. In addition, several of our galaxies exhibit a 500 µ m deficit of ∼ 10%. We conclude that if any strong excess is present at 500 µ m in lower metallicity galaxies, it must occur in galaxies with 12 + log(O/H) < 7 . 8. Our findings are qualitatively consistent with the work of Galametz et al. (2011). They find a submillimeter excess at 870 µ m in galaxies with 8 < 12 + log(O/H) < 9; however, when this excess is present, it is not universally seen at 500 µ m. The authors successfully account for the excess with a very cold (T ∼ 10K) dust component. Galametz et al. (2013, in prep.) reports a submillimeter excess in some of the galaxies in this sample, but it is detected at 870 µ m. It is possible that such an excess is present universally in our sample, but that longer wavelength observations are required to detect it. As for the flattening of the Rayleigh Jeans tail in the submillimeter regime, we find that β = 2 most accurately reproduces the slope of SED around 500 µ m. For the 7 extended galaxies, all of the values listed in this table are averages and standard deviations of all of the photometric regions we modeled. a The percentage of the 100 µ m flux density due to the warm temperature modified blackbody (see Eq. 1). In fact, using β = 1, as has been suggested to be appropriate at longer submillimeter wavelengths, consistently overestimates the emission at 500 µ m. Therefore, any change in the emissivity does not occur until λ > 500 µ m. An emissivity index of two results in the lowest uncertainties in the SED fits and shows only a weak trend metallicity, which varies from galaxy to galaxy. Fitting with a standard value of β = 2, which results in reduced χ 2 < 1, produces an excess of ∼ 30% in six galaxies, but over predicts emission by ∼ 20% in five galaxies. We conclude that though a small 500 µ m excess may be present in individual galaxies, this is compensated by equal amounts of 500 µ m'deficiency' in comparable numbers of galaxies, and only preferentially affects the lower metallicity galaxies when modeling with a fixed β . Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. IRAF, the Image Reduction and Analysis Facility, has been developed by the National Optical Astronomy Observatories and the Space Telescope Science Institute. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.","pages":[10,11]},{"title":"REFERENCES","content":"Meny, C., Gromov, V., Boudet, N., et al. 2007, A&A, 468, 171 Moustakas, J., Kennicutt, R. C., Tremonti, C. A., et al. 2010, ApJS, 190, 233 O'Halloran, B., Galametz, M., Madden, S. C., et al. 2010, A&A, 518, L58 Paradis, D., Bernard, J.-Ph., and Meny, C. 2009, A&A, 506, 745 Paradis, D., Paladini, R., Noriega-Crespo, A., et al. 2012, A&A, 537, A113 Pilyugin, L. S., & Thuan, T. X. 2005, ApJ, 631, 231 Planck Collaboration. 2011, A&A, 536, 17 Reach, W. T., Dwek, E., Fixsen, D. J., et al. 1995, ApJ, 451, 188 R'emy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2013, A&A, accepted. [arXiv:1309.1371] Sandstrom, K., Krause, O., Linz, H., et al. 2010, A&A, 518, L59 Storchi-Bergmann, T., Calzetti, D., and Kinney, A. L. 1994, ApJ, 429, 572","pages":[12]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"Submillimeter excess emission has been reported at 500 µ m in a handful of local galaxies, and previous studies suggest that it could be correlated with metal abundance. We investigate the presence of an excess submillimeter emission at 500 µ m for a sample of 20 galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH) that span a range of morphologies and metallicities (12 + log(O/H) = 7 . 8 -8 . 7). We probe the far-infrared (IR) emission using images from the Spitzer Space Telescope and Herschel Space Observatory in the wavelength range 24 -500 µ m. We model the far-IR peak of the dust emission with a two-temperature modified blackbody and measure excess of the 500 µ m photometry relative to that predicted by our model. We compare the submillimeter excess, where present, with global galaxy metallicity and, where available, resolved metallicity measurements. We do not find any correlation between the 500 µ m excess and metallicity. A few individual sources do show excess (10-20%) at 500 µ m; conversely, for other sources, the model overpredicts the measured 500 µ m flux density by as much as 20%, creating a 500 µ m 'deficit'. None of our sources has an excess larger than the calculated 1 σ uncertainty, leading us to conclude that there is no substantial excess at submillimeter wavelengths at or shorter than 500 µ m in our sample. Our results differ from previous studies detecting 500 µ m excess in KINGFISH galaxies largely due to new, improved photometry used in this study.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"INVESTIGATING THE PRESENCE OF 500 µ M SUBMILLIMETER EXCESS EMISSION IN LOCAL STAR FORMING GALAXIES\",\n \"content\": \"Allison Kirkpatrick 1 , Daniela Calzetti 1 , Maud Galametz 2 , Rob Kennicutt, Jr. 2 , Daniel Dale 3 , Gonzalo Aniano 4 , Karin Sandstrom 5 , Lee Armus 6 , Alison Crocker 7 , Joannah Hinz 8 , Leslie Hunt 9 , Jin Koda 10 , Fabian Walter 5 Draft version September 24, 2018\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"Dust in the interstellar medium (ISM) is formed by grain growth in both the diffuse ISM and the ejecta of dying stars, such as red giant winds, planetary nebula, and supernovae (Draine 2009). Once formed, dust absorbs UV and optical light and reemits this radiation in the infrared. UV radiation is dominated by photons from young O and B stars, so the dust mass and infrared (IR) radiation can provide important constraints on the current star formation rates and the star formation history of a galaxy. Space-based telescopes such as the Spitzer Space Telescope, the InfraRed Astronomical Satellite, and the Infrared Space Observatory have provided insights on the dust emission from mid-IR wavelengths out to ∼ 200 µ m. However, the majority, by mass, of the dust is cold ( T /lessorsimilar 25 K, Dunne & Eales 2001) and emits at far-IR and submillimeter wavelengths, where the emission spectrum is dominated by large grains in thermal equilibrium. Ground-based observations of these wavelengths are limited to a few atmospheric windows, and until recently, space-based observatories lacked coverage of the far-IR beyond ∼ 200 µ m. Now, with the advent of the Herschel Space Observatory, the peak and long wavelength tail of the dust spectral energy distribution (SED) is being observed at unprecedented angular resolution. With submillimeter observations, the dust mass and the dust to gas ratios can be more accurately estimated. Dust formation models show that the dust to gas ratios should be tied to the chemical enrichment of galaxies, as measured by the metallicity (Dwek 1998; Edmunds 2001). Galametz et al. (2011) combine submillimeter data at 450 and 850 µ m with shorter wavelength IR observations ( /lessorsimilar 160 µ m) for a large sample of local star forming galaxies. They model the spectral energy distributions of each galaxy with and without the submillimeter data and find that for high metallicity galaxies, not including the submillimeter data can cause the dust mass to be overestimated by factors of 2-10, whereas for low metallicity galaxies (12+log(O/H) /lessorsimilar 8 . 0), the SEDs without the submillimeter data can underpredict the true dust mass by as much as a factor of three. Gordon et al. (2010) use Herschel photometry to model the dust emission from the Large Magellanic Cloud (LMC) and find that dust mass derived using just 100 µ m and 160 µ m photometry underestimate the dust mass derived when using 350 µ m and 500 µ m photometry as well by as much as 36%. In measuring dust masses by modeling the far-IR and submillimeter SED, a variety of studies have sug- gested the existence of excess emission at submillimeter wavelengths above what is predicted by fits to shorter wavelength data. Furthermore, this excess could preferentially affect lower metallicity and dwarf galaxies. Dale et al. (2012, hereafter D12) report significant excess emission at 500 µ m, above that predicted by fitting the observed SEDs with the Draine & Li (2007) models, for a sample of eight dwarf and irregular galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH, Kennicutt et al. 2011). Excess emission has also been reported in the Small Magellanic Cloud (SMC) and LMC, both of which have lower than solar metallicities (12+log(O/H) = 8 . 0 , 8 . 4, respectively Bot et al. 2010; Gordon et al. 2010). On the other hand, excess emission is also seen at solar metallicities or larger. Paradis et al. (2012) model emission in the Galaxy and find excess emission (16 -20%) at 500 µ m in peripheral H ii regions. Recently, Galametz et al. (2013, in prep.) have detected excess at 870 µ m on a resolved and global scale for a sample of 11 KINGFISH galaxies. Galametz et al. (2011) finds a submillmeter excess at 870 µ m for 8 galaxies spanning a metallicity range of 12 + log(O/H) = 7 . 8 -9 . 0. The presence of excess emission does not appear to be universal, however, as Draine et al. (2007) found only a marginal difference in deriving the dust masses for a set of SINGS galaxies with and without including submillimeter data from SCUBA 12 + log(O/H) ≈ 7 . 5 -8 . 7 . More recently, Aniano et al. (2012) apply the Draine & Li (2007) models to the IR SEDs (3 . 6 -500 µ m) of the local star forming galaxies NGC 0628 and NGC 6946 and do not detect any significant excess ( > 10%) at 500 µ m. The excess emission seen at submillimeter wavelengths can be attributed to a cold dust component which is shielded from starlight (T < 10K; e.g., Galametz et al. 2009; O'Halloran et al. 2010). However, in the Milky Way, excess emission is seen at high latitudes, making it unlikely to be due to shielded cold dust (Reach et al. 1995). Studies of other galaxies have argued that a cold dust origin for the excess emission leads to unphysically high dust to gas ratios (Lisenfeld et al. 2002; Zhu et al. 2009; Galametz et al. 2010). A competing explanation is that the spectral emissivity index, β , of the dust grains changes to lower values at longer wavelengths, leading to a flattening of the submillimeter spectrum, thus mimicking a cold dust component (Dupac et al. 2003; Augierre et al. 2003; Planck Collaboration 2011). Such a change in emissivity has been suggested in the Milky Way (Paradis et al. 2009). (Galametz et al. 2012) showed that modeling the far-IR /submillimeter emission with a modified blackbody with β = 1 . 5 can increase the dust masses up to 50% compared to when β = 2, possibly explaining the discrepancies between dust masses calculated with far-IR data alone and those calculated with farIR and submillimeter data. The emission from very small grains exhibits a frequency dependence with a spectral emissivity index of β = 1, and if a galaxy has a relative abundance of very small grains greater than the Milky Way, this can cause a flattening of the emissivity index at longer wavelengths (Lisenfeld et al. 2002; Zhu et al. 2009). Alternatively, the properties of amorphous solids could explain the change in emissivity (Meny et al. 2007). Modeling the emission of amorphous solids accounts for the submillimeter excess in the LMC and SMC (Bot et al. 2010), although recent work suggests that much of the excess emission in the LMC is accounted for by fluctuations in the cosmic microwave background (Planck Collaboration 2011). Finally, an increase in the amount of magnetic material has also been proposed as a plausible explanation for the SMC submillimeter excess (Draine & Hensley 2012). Achange in dust properties can also be linked to metallicity. Draine et al. (2007) showed that 12 + log(O/H) = 8 . 1 is a threshold metallicity for galaxies in the range 12 + log(O/H) ≈ 7 . 5 -8 . 7, above which the percentage of dust mass contained in PAH molecules drastically increases. If submillimeter excess emission is due to a change in the emissivity properties of the dust population, then there might be a correlation with abundances in this metallicity range. In the present study, we seek to investigate the submillimeter excess at 500 µ m for a sample of KINGFISH galaxies. We define such excess as being emission above that predicted by a two-temperature modified blackbody model where the emissivity is not constrained, following the method outlined in Galametz et al. (2012). We have selected a sample that spans a range of metallicities, including many dwarf galaxies, in order to probe whether such excess correlates with metallicity, as has been found in some earlier studies (Galametz et al. 2009, 2011). The paper is laid out as follows: in Section 2, we describe our sample selection and modeling of the dust emission; in Section 3, we report on the excess emission and how our findings relate to the results of D12; and in Section 4, we present our conclusions.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2.1. The KINGFISH Sample\",\n \"content\": \"The KINGFISH sample (Kennicutt et al. 2011) was selected to include a wide range of luminosities, morphologies, and metallicities in local galaxies. The sample overlaps with 57 of the galaxies observed as part of the Spitzer Infrared Nearby Galaxies Survey (SINGS, Kennicutt et al. 2003b), as well as incorporating NGC 2146, NGC 3077, M 101 (NGC 5457), and IC 342 for a total of 61 galaxies. The luminosity range spans four orders of magnitude, but all galaxies have L < 10 11 L /circledot . While some of the galaxies display a nucleus with LINER or Seyfert properties, no galaxy's global SED is dominated by an AGN. We select a sample (7) of disk galaxies possessing a large angular size ( ∼ 30arcmin 2 ) and a known metallicity gradient with which we perform a resolved study of the excess emission and search for any correspondence with metallicity. We refer to this sample as the 'extended' galaxies. Since excess emission seems to be found in dwarf/irregular galaxies, we include the dwarf/irregular galaxies (9) in KINGFISH for which we have a signal-tonoise ratio (SNR) > 3 σ in all of the SPIRE bandpasses. The dwarf/irregulars are more compact objects than our normal disk galaxies, and in general, do not have a known metallicity gradients, so we measure the excess emission globally for these objects. The resolved nature of the normal disk galaxies might bias our comparison with the dwarf/irregular galaxies, so we complement our sample (4) with normal disk galaxies that have small angular size which allows for global measurements of excess emission. These more compact, normal galaxies were selected to span a range of metallicity and have high SNRs at the SPIRE bandwidths. Our complete sample consists of 20 galaxies and is listed in Table 1. We also list in Table 1 dwarf/irregular galaxies that were rejected due to low SNRs.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"2.2. Data Reduction\",\n \"content\": \"Data observations and reduction are discussed in detail in Engelbracht et al. (2010), Sandstrom et al. (2010) and Kennicutt et al. (2011). In the present study, we use images from the PACS and SPIRE instruments on the Herschel Space Observatory spanning a wavelength range of 70 -500 µ m and MIPS 24 µ m images from the Spitzer Space Telescope (Kennicutt et al. 2003b). We use PACS 70 and 160 µ m images instead of MIPS due to the better resolution provided by PACS. All galaxy maps are at least 1.5 times the diameter of the optical disk, allowing us to probe the cold dust emission beyond the optical disk. The raw PACS and SPIRE images were processed from level 0 to 1 with Herschel Interactive Processing Environment (HIPE) v. 8. The PACS and SPIRE maps were then created using the IDL package Scanamorphos v. 17 (Roussel 2012). Scanamorphos is preferred to HIPE for its ability to better preserve low level flux density, reduce striping in area of high background, and correct brightness drifts caused by low level noise. The maps are converted from units of Jy beam -1 to MJy sr -1 by accounting for beam sizes of 469.1, 827.2, and 1779.6 arcsec 2 for the 250, 350, and 500 µ m maps, respectively. The design and performance of the SPIRE instrument is discussed in detail in Griffin et al. (2010). In the SPIRE images used in this study, the full width at half maximum (FWHM) of the beam profile has been modeled with a wavelength dependence, so that FWHM ∝ λ γ , where γ = 0 . 85. As part of the calibration process, a 'color-correction' has been applied to each beam so that the measured specific intensity I ν will be equal to the actual specific intensity I 0 when ν = ν 0 . The correction factors applied to these images assume a power-law spectrum with α = -1 . 9. We compare our results to those of D12, so it is crucial to explicitly state that we are using different versions of the PACS and SPIRE images. In D12, the raw PACS and SPIRE images were processed from level 0 to 1 with HIPE v.5. The SPIRE data were then mosaicked using the mapper in HIPE. The images were converted to MJy sr -1 using beam sizes of 423, 751, and 1587 arcsec 2 at 250, 350, and 500 µ m, respectively, and the FWHM was not modeled with a wavelength dependence; furthermore, the color-correction was not included in the beam size, but was applied a posteriori.The PACS data were mapped using Scanamorphos v. 12.5. The main difference between the version of KINGFISH images that we use and the previous version used by D12 is that the SPIRE 250 and 350 µ m images contain slightly less flux density ( ∼ 2%) while the 500 µ m image is less luminous by ∼ 10%. The point response function area is also slightly larger ( ∼ 3%) than for the v. 2 images. The more recent HIPE v. 11 pipeline has revised the SPIRE beam sizes in the direction of yielding lower fluxes for extended sources by ∼ 6%, 6%, and 8% at 250, 350, and 500 µ m, respectively. This is in the direction of reinforcing the results that are presented in this paper.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"2.3. Background subtraction and Convolution of Images\",\n \"content\": \"The background subtraction is described in detail in Aniano et al. (2012), and we will briefly summarize here. 'Non-background' regions are determined in all cameras (IRAC, MIPS, PACS, and SPIRE) by those pixels which have a SNR > 2. Masks of the non-background regions are made, and then the masked images from all cameras are combined in order to unambiguously determine which regions are truly background regions. The signals in the background regions are then averaged, smoothed, and subtracted according to an algorithm outlined in Aniano et al. (2012). Since we compare our results with those of D12, it is worthwhile to note that a different procedure for background subtraction is followed in that study. The authors use a set of sky apertures to measure the local sky around each galaxy while avoiding any contamination from galaxy emission. The mean sky level per pixel is computed from these sky apertures, scaled to the number of pixels in the galaxy photometry aperture, and the result is subtracted from the overall galaxy photometry aperture counts. In order to consistently measure photometry for each galaxy, we used images that had been convolved to the resolution of the SPIRE 500 µ m bandpass. The convolution was done with publicly available kernels from Aniano et al. (2011) which transform the point source functions (PSFs) of individual images to the PSF of the SPIRE instrument at 500 µ m (FWHM of 38'). The convolution kernels and methodology are described in detail in Aniano et al. (2011, 2012). After the convolution to a common PSF, the images for each galaxy are resampled to a standard grid, where each pixel is ∼ 14'.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"2.4. Photometry and SED fitting\",\n \"content\": \"For the extended galaxies, we measure photometry in apertures with diameters of 42', chosen to be slightly larger than the beam size of the SPIRE 500 µ m bandpass, from the center of the galaxy to the outskirts. We reject regions of galaxies without at least 3 σ flux density measurements at every bandpass from 24 -500 µ m. For the galaxies which are compact at the 500 µ m resolution, including the dwarf/irregulars, we measure the photometry globally in apertures with diameters ranging from 42' to 1' 52', which is the angular area covered by the galaxies with a signal to noise ratio > 3 σ . The diameter and the physical scales of each photometric aperture are listed in Table 1. The dwarf/irregular galaxies DDO 053, DDO 154, and DDO 165 have a 3 σ flux density measurement in only one of the far-IR bandpasses; Ho I, Ho II, and M 81 DwB have measurements in three of the six bandpasses. We do not model the far-IR emission for these galaxies, but we do plot the photometry and 3 σ upper limits in Figure 1. The physically-based DL07 models have been used to derive dust properties at global and local scales (e.g., Draine et al. 2007; Aniano et al. 2012). The DL07 models use the assumption of a diffuse ISM component to describe the shape of the interstellar radiation field, and We do not calculate an excess for Ho I, Ho II, DDO 053, DDO 154, DDO 165, and M81 DwB since we are not able to measure flux densities at the 3 σ level covering the full wavelength range 24 -500 µ m. The metallicity range for which we can derive excess measurements is then 12 + log(O/H) = 7 . 8 -8 . 7. use distribution function to represent the distribution of starlight intensities, which are then scaled to the SED being modeled. In addition, the submm slope of the DL07 models tends to resemble that of a modified blackbody with an emissivity of β = 2, which could prevent us from testing for flattening of the submm slope or variations in the emissivity index. We choose to model the farIR SEDs with a simple modified blackbody equation to test various assumptions on the emissivity index and will compare our results to the D12 study to investigate how the choice of model affects the observed excess emission. We model the far-IR SEDs of each region within each galaxy using a two temperature modified blackbody of the form where B ν is the Planck function. The temperatures of the warm and cold dust components are T w and T c , the scalings for each component are a w and a c , and β w and β c are the emissivity indexes. Only the scalings, T c , and β c are allowed to be free parameters, due to the limited number of data points being fit. The warm dust com- nt is necessary to account for some of the emission at 70 µ m and 100 µ m so as not to bias the cold dust temperature or emissivity. When only one temperature is used, the peak of the modified blackbody is biased towards shorter wavelengths, leading to warmer temperatures, which is then compensated at longer wavelengths by a β c shallower than otherwise measured. We include the 24 µ m data point in the fit to better constrain the warm dust modified blackbody, but the fitted warm dust parameters should not be interpreted in a physical manner, since this portion of the SED also likely contains contribution from stochastically heated dust. We list the fraction of 100 µ m flux density due to the warm dust component in Table 2. The effective dust emissivity we derive comprises the intrinsic spectral emissivity properties of dust and the variation of the dust temperature within a resolution element that could lead to a shallower β c than that obtained in isothermal cases (e.g., Shetty et al. 2009). We nevertheless allow both the cold temperature and cold emissivity, β c , to vary simultaneously, though the two parameters are degenerate. We refer to Galametz et al. (2012) and Kirkpatrick et al. (2013b, in prep.), and references therein, for a further discussion of degeneracies on the individual temperatures and emissivities. We fit the photometry from 24 -350 µ m. The 500 µ m data are not included to allow comparison with our model predictions at the same wavelength. We use a Monte Carlo technique to determine the parameters and errors. We randomly sample each data point within its errors 1000 times and determine the parameters of the two temperature modified blackbody via χ 2 minimization. The final parameters and associated errors are the medians and standard deviations of our Monte Carlo simulation. An example of the SED fitting is shown in Figure 2. When fitting, we allow the cold dust temperature, T c , to vary between 0 and 50 K and β c to vary between 0 and 5. We experimented with allowing T w to vary, but the derived temperature was approximately constant in the range 55 -60K, and simultaneously varying T w did not change the derived cold dust temperature or emissivity values. Since the warm dust component peaks in an area of the SED that is sparsely sampled, we opt to hold both T w and β w fixed. We hold the emissivity of the warm dust component fixed to a value of two and T w fixed to 60K. Fixing β w = 2 is a good approximation of the opacity of graphite/silicate dust models (Li & Draine 2001). Galametz et al. (2012) find that changing β w to 1.5 decreases the cold dust temperatures by less than 1.6%, and Tabatabaei et al. (2011) test the two temperature modified blackbody approach on M33, holding β w fixed to 1.0, 1.5, and 2.0, and conclude that β w = 2 most accurately reproduces the observed flux densities. We test a fixed β c in Section 3.3. As β w is always fixed to a value of two in all of our subsequent analysis, in the remainder of this paper, we refer to β c simply as β .\",\n \"pages\": [\n 3,\n 4,\n 5\n ]\n },\n {\n \"title\": \"3.1. PACS-SPIRE colors\",\n \"content\": \"The color S 100 /S 160 , where S 100 is the flux density in the 100 µ m bandpass, is commonly used as a proxy for temperature, since it usually spans the peak of the blackbody emission, while S 350 /S 500 depends sensitively on the slope of the Rayleigh-Jeans tail, and so is a good proxy for β (with the same caveats given earlier about the mixing of dust with different temperatures along the line of sight). We plot these two colors in the left panel of Figure 3 for each of the regions in our extended galaxies. We calculate the positions of theoretical modified blackbodies and overplot as a grid. When calculating the theoretical tracks, we use a two temperature modified blackbody (Equation 1); we set T w = 60 K, β w = 2, and we scale the warm dust component to peak at a flux density 10% of the cold dust component peak flux density, which is the average scaling we see in our fitted SEDs at the SPIRE wavelengths. We set β = 1 , 1 . 5 , and 2, and we set T c to discrete temperature values between 15 and 27 K. Lines of constant β and T c are marked on the figure. The colors of our galaxies tend to cluster around the β = 2 , T c = 20K lines. At higher temperatures, galaxy colors start to sparsely occupy the same part of color space as the β = 1 model. No galaxies exhibit colors indicating a low temperature ( T c < 21 K) and a shallow emissivity, which could hint at physical link between the two parameters (see Yang & Phillips 2007; Ysard et al. 2012; Kirkpatrick et al. 2013b, in prep., for a discussion of the physical nature of the T c -β relationship). Although our galaxy colors tend to lie near the β = 2 model line, we observe a large scatter. This illustrates a significant difference of physical conditions from one object to another but also within our objects. Letting both parameters vary in our multiple blackbody approach can be a way to probe these variations, in spite of the degeneracies. In the right panel of Figure 3, we plot the same colors, but this time we use the predicted 500 µ m flux density, which has been calculated by fitting Equation 1 to the 24 -350 µ m flux densities. Substituting the predicted 500 µ m flux density has two interesting effects. First, it increases the amount of scatter visible in the colors. For example, in both NGC 5055 and NGC 4321, which dis- y the largest increase in scatter, the mean S 350 /S 500 observed ratio and predicted ratio is approximately the same ( ∼ 2 . 7). For NGC 5055, the standard deviation increases from 0.16 to 0.24, and for NGC 4321 it increases from 0.11 to 0.23. This increase is indicative of the uncertainties inherent in fitting modified blackbody models without enough data to adequately constrain the slope of the Rayleigh-Jeans tail. The second effect we see is that now the galaxy colors, particularly for M 101, occupy a region of the color space to the right of the β = 2 model line. The predicted S 350 /S 500 ratio is larger than the observed S 350 /S 500 ratio. Again, this illustrates the importance of using data above 350 µ m to constrain the submillimeter SED. Without including the 500 µ m data point in the modeling of the far-IR/submillimeter SED, the predicted slope will be steeper than the true value; in other words, the model underpredicts the measured 500 µ m flux density. We calculate the excess emission at 500 µ m as where F ν (500 µ m) is the predicted flux density of the two-temperature modified blackbody and S ν is the measured flux density. We plot the excess emission as a function of metallicity in Figure 4. We correct the radius of each photometric region for the inclination of the galaxy, and then convert the radius to metallicity using the gradients listed in Moustakas et al. (2010) which were calculated according to the Pilyugin & Thuan (2005) relationship (see Table 1). For M 101, which is not included in Moustakas et al. (2010), we use a metallicity gradient calculated directly from electron temperature measurements in H ii regions (Kennicutt et al. 2003a; Bresolin et al. 2004), which creates a slight offset between M 101 and the rest of our sample in metallicity. Figure 4 shows that there is no systematic dependence of the excess emission on metallicity for the sample as a whole, nor is there any trend within the individual galaxies that have a metallicity gradient. None of the galaxies display an excess larger than 25%, and for many galaxies, the modeling actually overpredicts the 500 µ m emission by this amount, creating a 500 µ m deficit. Furthermore, the spread in excess is largely accounted for by the uncertainty attached to each data point (the typical uncertainty for each region in the extended galaxies is shown in the bottom right of Figure 4). For some of the dwarf/irregulars, the uncertainties are rather large (particularly NGC 1377, NGC 2915, NGC 3773, NGC 5408, and IC 2574). The uncertainties are correlated with the SNR ratios of the SPIRE data since noisier photometry exacerbates the degeneracy between temperature and β (Juvela & Ysard 2012). The dwarf/irregulars with the lowest SNRs have the largest uncertainty on the derived β . We find that no extended galaxy has an excess emission greater than 10%, in agreement with the results of Gordon et al. (2010) for a resolved study of the LMC using a modified blackbody model, and with Aniano et al. (2013, in prep.), in which the authors create dust maps for the full sample of KINGFISH galaxies using the DL07 models. We show the distribution of excess emission in the right panel of Figure 4 for all regions in the extended galaxies, as well as the galaxies that were fit globally. We find that the resolved elements of the extended galaxies do not preferentially show an excess or a deficit. The mean excess of our sample is ∼ 0 . 02. This confirms that the majority of regions display a low excess or deficit ( < 10%). Given the large uncertainties (the dispersion is ∼ 0 . 1), this excess is thus marginal. In practice, we do not find excess 500 µ m emission greater than the scatter in the data.\",\n \"pages\": [\n 6,\n 7\n ]\n },\n {\n \"title\": \"3.3. 500 µ m excess dependence on β\",\n \"content\": \"The derived emissivity contains information about the slope of the Rayleigh-Jeans tail, and it is possible that β is correlated with the measured excess emission (Galametz et al. 2012) We test this hypothesis for our sample in Figure 5. For simplicity, we average together all of the derived excesses and β values for each galaxy as we do not see any trends for individual galaxies. There is no apparent correlation between the excess emission and the value of β when β is allowed to be a free parameter. However, since β and T c exhibit a degeneracy which is possibly enhanced by the particular fitting method used (e.g., Juvela et al. 2013), a common technique for blackbody fitting is to hold β fixed (e.g., Yang & Phillips 2007; Xilouris et al. 2012). It is possible that holding β fixed will cause us to measure an excess emission, since the slope of the Rayleigh-Jeans tail changes from region to region within each galaxy (see Figure 3). We test this hypothesis by refitting all of our photometry holding β fixed to the values of 1, 1.5, and 2. The 500 µ m excesses for each value of β are plotted in Figure 6. An emissivity of one generally produces very bad fits to the SEDs with high χ 2 values for several galaxies, reflected in the error bars. The slope of the Rayleigh-Jeans tail is too shallow and overestimates the 500 µ m emission, as can be seen in the top panel of Figure 6. Setting β = 2 provides the best fits to the SEDs when fixing the emissivity as can be seen by the small uncertainties in the bottom panel of Figure 6. The excess emission is now ∼ 30% for galaxies which had only a 10% excess when β was allowed to vary (Figure 4). The result is consistent with R'emy-Ruyer et al. (2013), who also calculate the excess 500 µ m emission keeping β fixed at a value of 2. Holding β fixed does increase the amount of excess emission measured. It also increases the so-called emission 'deficit', meaning we now overpredict the 500 µ m emission by ∼ 20 -30%; the excess emission for each galaxy is listed in Table 2. We stress that the amount of excess emission is affected by the particular fitting method used. In our study, where we achieve good reduced χ 2 fits when holding β fixed to a value of two, and when letting β be a free parameter, we find excess values differing by as much as 20% depending on the fitting method. There is a linear correlation between the excess emission and the metallicity. This is most strongly exhibited by M 101, which has a Pearsons correlation coefficient of ρ = -0 . 86 for all three values of β . NGC 4321 also has a strong trend between excess emission and metallicity. With the exception of NGC 5055, the other extended galaxies have fewer points, so it is difficult to see a trend. The dwarf galaxies also display a high correlation with ρ in the range 0 . 54 -0 . 61 depending on the value of β . On the other hand, NGC 4321 shows no correlation between metallicity and excess for any value of β . When all of the galaxies are considered together, there is a strong anti-correlation ( ρ = -0 . 70) for β = 1 and only a low anti-correlation ( ρ = -0 . 30) for β = 2. IC 2574, NGC 2915, and NGC 5408 have a marked ex- cess when β = 2. However, for IC 2574 and NGC 2915, there is no substantial excess when β = 1 , 1 . 5 or when β is allowed to vary. From this, we conclude that there is a flattening of the SED in these two galaxies that a steeper value of β is unable to account for. Because β is an effective emissivity, and contains information about the intrinsic properties of the dust grains as well as the heating of the dust within a resolution element, we cannot conclusively determine whether this flattening is due to changing properties of the dust grains in low metallicity galaxies. For most galaxies, including the individual regions in the extended galaxies, the use of β = 2 as opposed to β = 1 produces much lower reduced χ 2 values during the Monte Carlo fitting. We plot the distribution of reduced χ 2 values over 1000 Monte Carlo fits for NGC 1377 in the top panel of Figure 7. The mean reduced χ 2 is 2.3 when β = 2 but is 10.6 when β = 1. We also show the distribution of reduced χ 2 values for NGC 2915, for which the choice of β makes little difference in the goodness of the fits. When β = 2, the mean reduced χ 2 = 1 . 1, and when β = 1, the mean reduced χ 2 = 1 . 3. This effect is also seen for NGC 3773, NGC 5408, and IC 2574, all of which exhibit no decrease in the uncertainty on the excess depending on the value of β . These are the four galaxies with the lowest SNRs at 250 µ m and 350 µ m, illustrating the difficulty of using modified blackbody fitting with low signal-to-noise photometry.\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"3.4. Exploring the Submillimeter Dust Emission\",\n \"content\": \"When β is a free parameter, we do not see any systematic excess trend with metallicity, nor do we measure strong excess emission. However, when β = 2, we see a weak dependence on metallicity, and we do detect some excess for individual galaxies (Table 2). One explanation for excess submillimeter emission is temperature mixing within a resolution element (e.g., Shetty et al. 2009). The emissivity we measure is comprised both of the intrinsic emissivity of the dust and the range of temperatures of the dust components in the resolution element. This range of temperatures can produce a shallower effective β than would be measured in the ideal case of only one temperature component. We can test this explanation by comparing the excess emission with both the distance of our galaxies and the physical region size subtended by the photometry aperture (see Table 1). Both a larger region size and a larger distance will correspond to more dust emission within the resolution element, and hence more temperature mixing. We find no trend between physical size and excess emission, demonstrating that the particular photometry aperture used does not affect the resulting excess. In Figure 8, we plot the excess emission calculated when the emissivity was allowed to vary (see Figure 4) and when β = 2 (see Figure 6) as a function of distance. There is a weak trend between the excess emission and the distance when β = 2. When the emissivity is held fixed, galaxies that are within 10 Mpc have on average a higher excess emission, whereas the 500 µ m emission has in general been overpredicted for the galaxies further than 10 Mpc. This does not appear to be an effect of galaxy type, since the nearby galaxies showing excess are both extended and dwarfs. The trend seen when β = 2 is the opposite of what is expected. Galaxies that are further should have more temperature mixing within the resolution element producing a shallower farIR slope, which would cause an excess when compared to the emission predicted with β = 2. With the exceptions of NGC 0925 and NGC 4559, this trend is driven by the dwarf galaxies. Since we see no correlation between excess emission and physical region size, or excess emission and distance when β is a free parameter, we conclude that the excess emission is not due to temperature variations within the resolution element. NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574 have the highest excesses when β = 2. Mul- iple studies advocate using a third temperature component (T ∼ 10K) instead of a lower emissivity to account for the submillimeter excess (Galametz et al. 2011; Galliano et al. 2003, 2005; Marleau et al. 2006). We attempted to fit these four galaxies with a three temperature modified blackbody. We have only six photometric data points in each galaxy to fit three modified blackbodies to, so we hold several parameters constant to avoid degeneracies. We set T w = 60K and β w = 2, as described in Section2.4. We hold the emissivities of the cold components fixed to a commonly applied value of 1.8, though we note that using β = 2 caused our derived temperatures to change by only ± 1 K. We hold the scaling of the warm dust component fixed to what we derived when fitting only two modified blackbodies. Finally, we restrict the temperature range of one of the cold components to be T ∈ [20 , 50] K and the other to be T ∈ [0 , 20] K. We find that if we do not restrict the temperature ranges, then both cold components will have the same derived temperature. We are able to achieve good fits (reduced χ 2 < 1) for NGC 5408 and NGC 5398 but not for NGC 2915 or IC 2574. For NGC 5408, our three dust temperatures are 60 K, 29 ± 3K, and 13 ± 7K; for NGC 5398, they are 60 K, 22 ± 1K, and 13 ± 5K. Also, it is important to note that not only are the uncertainties rather large on the coldest dust temperature, but the distribution of the derived temperatures for the Monte Carlo simulations is not gaussian. There is only marginal excess ( < 10%) when using three temperatures for these two galaxies, but given the large uncertainties, non-gaussian distribution, and the necessity of imposing many restrictions on the fitting routine, we do not consider this method an improvement over using only two temperatures but allowing β to vary.\",\n \"pages\": [\n 8,\n 9,\n 10\n ]\n },\n {\n \"title\": \"3.5. Comparison with Dale et al. (2012)\",\n \"content\": \"D12 calculate the excess emission at 500 µ m for all galaxies in the KINGFISH sample. They use a different approach and fit the physically motivated DL07 models and find that a dozen galaxies, including eight dwarf/irregular/Magellanic have an excess > 0 . 6 at 500 µ m. We do not fit three of the dwarf/irregulars (Ho I, Ho II, and M81dwB) because we do not have 3 σ detections at all far-IR wavelengths. For the remaining dwarf/irregulars with substantial reported excess (NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574) we find at most excesses of 30% when β is fixed at two. Another key difference in the two fitting approaches is that we are only concerned with fitting photometry spanning the range 24 -500 µ m, while D12 fit all IR photometry from 3.6 µ m and long ward. Specifically, D12 had to balance emission from the stellar continuum, PAH features, and thermal dust emission, meaning that they were unable to tailor their fits to the far-IR/submillimeter portion of the SED. The discrepancy between the results of the present study and those of D12 can also be attributed to a difference in the photometry (Section 2.2). The KINGFISH 500 µ m images used in D12 were recently recalibrated downward by of order 10%. In addition, the PACS images were processed with different versions of the Scanamorphos package (Roussel 2012). In this work, all images were convolved to the 500 µ m resolution before measuring the photometry, whereas in D12, photometry was calculated using the original images. As noted in Section 2.3, our background subtraction methods are different. It is also important to bear in mind that our photometry aperture sizes are not identical to D12. We use circular apertures whose diameters are listed in Table 1 while D12 uses elliptical apertures of varying sizes. Figure 1 shows our photometry and the photometry for D12 overplotted. The main discrepancies are between the PACS data and the 500 µ m. D12 calculate the excess slightly differently than this work; namely, they divide the excess by the model flux density, whereas we use the measured flux density (Eq. 2). We fit the D12 photometry for NGC 2915, NGC 4236, NGC5398, NGC 5408, and IC 2574 with our two temperature modified blackbody model. We hold the emissivity fixed to a value of two, and we calculate the fractional excess according to the prescription in D12. For four of the galaxies, we find fractional excesses between 55% and 75% (IC 2574 has an excess of 44%), leading us to conclude that discrepancy between our work and D12 is primarily due to the difference in the flux density calibration and convolution of the images, and the photometric apertures, and not a result of using different modeling techniques.\",\n \"pages\": [\n 10\n ]\n },\n {\n \"title\": \"4. CONCLUSIONS\",\n \"content\": \"We measure the emission at 500 µ m for a sample of star forming KINGFISH galaxies spanning a range of metallicities. We model the far-IR SED with a two temperature modified blackbody, and calculate the excess emission as the measured 500 µ memission relative to the predicted emission. For extended galaxies, we measure the excess in circular apertures with a diameter of 42' from the center to the edge of the galaxy. We supplement the sample of extended galaxies with a sample of compact and of dwarf/irregular galaxies, for which we model the far-IR emission on a global scale. While we do see excesses of ∼ 10% for a handful of galaxies when we allow β to vary, we do not see any overall trend as a function of metallicity for the range 12 + log(O/H) = 7 . 8 -8 . 7. Furthermore, this excess is completely accounted for by the uncertainties in the fitting procedure. In addition, several of our galaxies exhibit a 500 µ m deficit of ∼ 10%. We conclude that if any strong excess is present at 500 µ m in lower metallicity galaxies, it must occur in galaxies with 12 + log(O/H) < 7 . 8. Our findings are qualitatively consistent with the work of Galametz et al. (2011). They find a submillimeter excess at 870 µ m in galaxies with 8 < 12 + log(O/H) < 9; however, when this excess is present, it is not universally seen at 500 µ m. The authors successfully account for the excess with a very cold (T ∼ 10K) dust component. Galametz et al. (2013, in prep.) reports a submillimeter excess in some of the galaxies in this sample, but it is detected at 870 µ m. It is possible that such an excess is present universally in our sample, but that longer wavelength observations are required to detect it. As for the flattening of the Rayleigh Jeans tail in the submillimeter regime, we find that β = 2 most accurately reproduces the slope of SED around 500 µ m. For the 7 extended galaxies, all of the values listed in this table are averages and standard deviations of all of the photometric regions we modeled. a The percentage of the 100 µ m flux density due to the warm temperature modified blackbody (see Eq. 1). In fact, using β = 1, as has been suggested to be appropriate at longer submillimeter wavelengths, consistently overestimates the emission at 500 µ m. Therefore, any change in the emissivity does not occur until λ > 500 µ m. An emissivity index of two results in the lowest uncertainties in the SED fits and shows only a weak trend metallicity, which varies from galaxy to galaxy. Fitting with a standard value of β = 2, which results in reduced χ 2 < 1, produces an excess of ∼ 30% in six galaxies, but over predicts emission by ∼ 20% in five galaxies. We conclude that though a small 500 µ m excess may be present in individual galaxies, this is compensated by equal amounts of 500 µ m'deficiency' in comparable numbers of galaxies, and only preferentially affects the lower metallicity galaxies when modeling with a fixed β . Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. IRAF, the Image Reduction and Analysis Facility, has been developed by the National Optical Astronomy Observatories and the Space Telescope Science Institute. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.\",\n \"pages\": [\n 10,\n 11\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Meny, C., Gromov, V., Boudet, N., et al. 2007, A&A, 468, 171 Moustakas, J., Kennicutt, R. C., Tremonti, C. A., et al. 2010, ApJS, 190, 233 O'Halloran, B., Galametz, M., Madden, S. C., et al. 2010, A&A, 518, L58 Paradis, D., Bernard, J.-Ph., and Meny, C. 2009, A&A, 506, 745 Paradis, D., Paladini, R., Noriega-Crespo, A., et al. 2012, A&A, 537, A113 Pilyugin, L. S., & Thuan, T. X. 2005, ApJ, 631, 231 Planck Collaboration. 2011, A&A, 536, 17 Reach, W. T., Dwek, E., Fixsen, D. J., et al. 1995, ApJ, 451, 188 R'emy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2013, A&A, accepted. [arXiv:1309.1371] Sandstrom, K., Krause, O., Linz, H., et al. 2010, A&A, 518, L59 Storchi-Bergmann, T., Calzetti, D., and Kinney, A. L. 1994, ApJ, 429, 572\",\n \"pages\": [\n 12\n ]\n }\n]"}}},{"rowIdx":76,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...778..116N"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1309.4967.pdf"},"content":{"kind":"string","value":"\nRE-APPEARANCE OF MCNEIL'S NEBULA (V1647 ORIONIS) AND ITS OUTBURST ENVIRONMENT\nJ. P. Ninan, D. K. Ojha\nDepartment of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India\nB. C. Bhatt\nIndian Institute of Astrophysics, Koramangala, Bangalore 560 034, India\nS. K. Ghosh\nNational Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune 411 007, India\nV. Mohan\nInter-University Centre for Astronomy and Astrophysics, Pune 411 007, India\nK. K. Mallick\nDepartment of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India\nM. Tamura\nNational Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan\nand\nTh. Henning\nMax-Planck-Institute for Astronomy, Konigstuhl 17, 69117 Heidelberg, Germany Draft version September 5, 2021\nABSTRACT\nWe present a detailed study of McNeil's nebula (V1647 Ori) in its ongoing outburst phase starting from September 2008 to March 2013. Our 124 nights of photometric observations were carried out in optical V , R , I and near-infrared (NIR) J , H , K bands, and 59 nights of medium resolution spectroscopic observations were done in 5200 - 9000 ˚ A wavelength range. All observations were carried out with 2-m Himalayan Chandra Telescope (HCT) and 2-m IUCAA Girawali Telescope. Our observations show that over last four and a half years, V1647 Ori and the region C near Herbig-Haro object, HH 22A, have been undergoing a slow dimming at a rate of ∼ 0 . 04 mag yr -1 and ∼ 0 . 05 mag yr -1 respectively in R -band, which is 6 times slower than the rate during similar stage of V1647 Ori in 2003 outburst. We detected change in flux distribution over the reflection nebula implying changes in circumstellar matter distribution between 2003 and 2008 outbursts. Apart from steady wind of velocity ∼ 350 km s -1 we detected two episodic magnetic reconnection driven winds. Forbidden [O I] 6300 ˚ A and [Fe II] 7155 ˚ A lines were also detected implying shock regions probably from jets. We tried to explain the outburst timescales of V1647 Ori using the standard models of FUors kind of outburst and found that pure thermal instability models like Bell & Lin (1994) cannot explain the variations in timescales. In the framework of various instability models we conclude that one possible reason for sudden ending of 2003 outburst in 2005 November was due to a low density region or gap in the inner region ( ∼ 1 AU) of the disc.\nSubject headings: stars: formation, stars: pre-main-sequence, stars: outflows, stars: variables: general, stars: individual: (V1647 Ori), ISM: individual: (McNeil's nebula)\n1. INTRODUCTION\nWhen low-mass stars like our Sun are born, they slowly accrete gas from the collapsing cloud through an accretion disc. Collimated outflows are also typically seen in most of these objects. The discontinuous knots seen in outflows from these objects, and the mismatch of accretion rate between envelope to disc and disc to star (known as 'Luminosity Problem') in young stellar ob-\njects (YSOs), all hint to an episodic nature of accretion instead of an ideal steady inflow (Kenyon et al. 1990; Evans et al. 2009; Ioannidis & Froebrich 2012). The other important feature seen in these objects is the outburst. Rare outbursts that we see among these YSOs are found to be correlated with an order of magnitude increase in mass infall rate and they could be the episodic accretion events required to explain the outflow discontinuities and 'Luminosity Problem'. These outbursts are empirically classified as FUors (decades long outbursts\nwith 4-5 magnitude change in optical) and EXors (few months-years long outbursts with 2-3 magnitude change in optical) (Herbig 1977; Hartmann 1998; Hartmann & Kenyon 1996). Due to the short timescales of outbursts in comparison to millions of years timescale of star formation, these events are extremely rare and only less than a dozen confirmed FUor outbursts have been detected so far. From their frequency of outburst it is estimated that every low-mass YSO should go through these outbursts at least 50 times in its protostellar phase (Scholz et al. 2013). Regarding the discontinuous knots seen in outflows, it should be noted that the timescales between discontinuities were estimated to be of the order of 10 3 years by Ioannidis & Froebrich (2012) and the timescales between FUor outbursts in a single star were estimated to be of the order of 10 4 years by Scholz et al. (2013). So the discontinuities could be due to some other shorter timescale variations in accretion rate rather than classical FUors. But as Scholz et al. (2013) pointed out, we do not have a good estimate of FUors' timescales in the early Class I stage. Hence we cannot rule out the possibility that discontinuities in outflows are created during FUors events.\nOne such object which was extensively studied recently in literature is V1647 Ori (V1647 Orionis), 400 pc away in the L1630 dark cloud of Orion. It underwent a sudden outburst of ∼ 5 mag in optical in 2003 (McNeil 2004; Brice˜no et al. 2004) and illuminated a reflection nebula, now named as McNeil's nebula after its discoverer Jay McNeil. Reipurth & Aspin (2004) reported 3 mag increase in near-infrared (NIR) and Andrews et al. (2004) reported 25 times increase in 12 µm flux and no flux change in submillimeter of V1647 Ori during the outburst. Kastner et al. (2004) reported a 50 times increase in X-ray flux of V1647 Ori during the outburst, and noted that the derived temperature of the plasma is too high for accretion alone to explain and hinted that magnetic reconnection events might be heating up the plasma. Based on the upper limit on radio continuum emission from McNeil's nebula at 1272 MHz from Giant Metrewave Radio Telescope (GMRT), India, Vig et al. (2006) constrained the extent of HII region corresponding to a temperature glyph[greaterorsimilar] 2500 K to be glyph[lessorsimilar] 26 AU. Spectroscopic studies showed strong H α and Ca II IR triplet lines in emission (Brice˜no et al. 2004; Ojha et al. 2006). In NIR region, strong CO bandheads (2.29 µm ) and Br γ line (2.16 µm ; implying strong accretion) were detected in emission (Reipurth & Aspin 2004; Vacca et al. 2004). The strong P-Cygni profile in H α emission indicated wind-velocity ranging from 600 - 300 km s -1 (Ojha et al. 2006; Vacca et al. 2004). ' Abrah'am et al. (2006) carried out AU scale observations using Very Large Telescope Interferometer/ Mid-Infrared interferometric Instrument (VLTI/MIDI). By fitting both spectral energy distribution (SED) and visibility values they deduced a moderately flaring disc with temperature profile T ∼ r -0 . 53 (T(1AU)=680K) and mass ∼ 0 . 05 M glyph[circledot] , with inner radius of 7 R glyph[circledot] (0.03 AU) and outer radius of 100 AU. This temperature profile is shallower than the T ∼ r -0 . 75 canonical model (Pringle 1981). They also reported that the mid-infrared emitting region at 10 µm has a size of ∼ 7 AU. Rettig et al. (2005) used the CO lines in infrared (IR) to measure the temperature of the\ninner accretion disc region which was estimated to be T ≈ 2500 K.\nOjha et al. (2006) and K'osp'al et al. (2005) reported a sudden dimming and termination of the 2003 outburst in November 2005. Thus, 2003 outburst lasted for a total of ∼ 2 years and V1647 Ori returned to its pre-outburst phase in early 2006. Acosta-Pulido et al. (2007) estimated the inclination angle of disc to be 61 · and also estimated the accretion rate to be 5 × 10 -6 M glyph[circledot] yr -1 during outburst and 5 × 10 -7 M glyph[circledot] yr -1 in 2006 quiescent state. Aspin et al. (2006) reported that ∼ 37 years prior to 2003 outburst, i.e. in 1966, V1647 Ori had undergone a similar magnitude of outburst, lasting for a duration somewhere between 5 to 20 months.\nContrary to expected decades long quiescense, V1647 Ori underwent a second outburst in 2008 just after spending two years in quiescent state (Aspin et al. 2009). It brightened up to the same magnitude and had almost identical spectral features in optical and NIR as the first outburst. One striking difference was that the strong CO bandhead emission at 2.29 µm was absent in second outburst (Aspin 2011). The X-ray flux with plasma temperature of 2-6 keV during both outbursts was postulated to be due to magnetic reconnection events in the disc-star magnetic field interaction (Teets et al. 2011, and references therein). Hamaguchi et al. (2012) normalised and combined both outbursts' data in X-ray and detected one day periodicity in light curve, which they modeled with two accretion hot spots on the top and bottom hemispheres of the star rotating with one day period and inclination of 68 · . Figure 1 shows the overall cross-section picture of the surroundings of V1647 Ori we know so far.\nV1647 Ori provides a unique opportunity to understand the physical processes undergone in FUors or EXors kind of outbursts. The short time scale behaviors of this object make it possible for us to make a detailed study of the object. In literature there exists mainly three kinds of model for explaining the outburst phenomena (see Section 4). The differences between these models are all in the inner region of disc ( < 1 AU), and optical and NIR are the right wavelength regime to probe this region of the disc. Detailed understanding of V1647 Ori will thus provide us a laboratory to check our understanding of various instabilities like thermal, gravitational and magnetorotational in proto-planetary disc around young low-mass stars.\nWe have carried out continuous observations for more than four and a half years (2008 - 2013) of V1647 Ori in optical and NIR wavelengths for detailed study of its dynamics during outburst and post-outburst stages of the second outburst. This data combined with previous outbursts' provide us more insight on the nature of outburst and also constrain the existing physical models. In this paper, we present the results of our long-term optical and NIR photometric and spectroscopic observations of the outburst source and associated McNeil's nebula. In Section 2 we describe the observational details and the data reduction procedures. In Section 3 we present our new findings and results from observations. In Section 4 we analyse the ability of each existing physical models to explain V1647 Ori's outburst history. Finally, in Section 5 we summarise our main results.\n2.1. Optical Photometry\nOur long-term optical observations span from 2008 September 14 to 2013 March 11 and were carried out with 2-m Himalayan Chandra Telescope (HCT) at Indian Astronomical Observatory, Hanle (Ladakh), India and with 2-m Inter-University Centre for Astronomy and Astrophysics (IUCAA) Girawali Telescope at IUCAA Girawali Observatory (IGO), Girawali (Pune), India. At HCT, for photometry central 2K × 2K section of Himalaya Faint Object Spectrograph & Camera (HFOSC) CCD, which has a pixel scale of 0.296 arcsec was used, giving us a field of view (FoV) of ∼ 10 × 10 arcmin 2 . At IGO, 2K × 2K IUCAA Faint Object Spectrograph & Camera (IFOSC) CCD was used which also has a similar pixel scale of 0.3 arcsec, giving us a FoV of ∼ 10 × 10 arcmin 2 . Further details of the instruments and telescopes are available at http://www.iiap.res.in/iao/hfosc.html and http://www.iucaa.ernet.in/ itp/igoweb/igo tele and inst.htm. Out of our total observation of 110 nights, 84 nights were observed from HCT and 26 nights from IGO.\nThe V1647 Ori's field ( α, δ ) 2000 = (05 h 46 m 13 s . 135 , -00 · 06 ' 04 '' . 82) was observed in standard V RI Bessel filters. Nearby Landolt's standard star fields (Landolt 1992) were also observed for magnitude calibration and for solving color transformation equation coefficients of each night. For nights which do not have standard star observations, we identified six stars in the object's frame whose magnitudes remain constant throughout. Four of them were used as secondary standards (see Figure 2) and other two were used to check consistency and error. Apart from object frames, bias and sky flats were also taken in each night for the basic data reduction. For fringe removal in IGO I -band images, blank sky frames were also taken. The log of photometric observations is given in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material.\nBlank sky images in I -band were used to create fringe templates by MKFRINGECOR task in IRAF 1 , which were later used to subtract the fringes that appeared in I -band images taken from IGO. Data reduction was done with the semi-automatic pipeline written in PyRAF 2 and IRAF CL scripts. Standard photometric data reduction steps like bias-subtraction and median flat-fielding were done for all the nights. Point-spread function (PSF) photometry (using PSF & ALLSTAR tasks in DAOPHOT package of IRAF) on V1647 Ori was not able to fully remove the nebular contamination. We found a strong correlation between fluctuation in magnitude of V1647 Ori and fluctuation in atmospheric seeing condition. This is because the contamination of flux from nebula into V1647 Ori's aperture was a function of atmospheric seeing. So we generated a set of images by convolving each frame with 2-D Gaussian kernel of different standard deviation (using IMFILTER.GAUSS task in IRAF) for sim-\n\n1 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.\n\nulating different atmospheric seeing conditions. We then recalculated the magnitudes by DAOPHOT, PSF and ALLSTAR algorithms of IRAF for various atmospheric seeing conditions. The differential magnitudes obtained from each frame's set was interpolated to obtain magnitude at an atmospheric seeing of 1.18 arcsec, which was taken to be the seeing to be interpolated to, for all nights and it was chosen to minimise interpolation error. This method reduced our error bars in magnitude by a factor of 2. Apart from the Gaussian convolution step, the PSF photometry steps were all same as Ojha et al. (2006).\nMagnitudes of the whole nebula and other objects in the nebula like region C (near HH 22A) and region B defined by Brice˜no et al. (2004) in their figure 2 (also see Figure 2) were measured by simple aperture photometry with an aperture radius of 80 arcsec for nebula and 12 arcsec for the regions C and B. For obtaining the flux, the aperture of the objects like regions C and B were centered at the objects itself.\n2.2. Optical Spectroscopy\nOur long-term spectroscopic observations also span the same duration as that of photometric observations (2008 September to 2013 March) using both 2-m HCT and 2-m IGO. The full 2K × 4K section of HFOSC CCD spectrograph was used in HCT observations and 2K × 2K IFOSC CCD spectrograph was used for IGO observations. Spectroscopic observations were carried out on 35 nights from HCT and 24 nights from IGO, thus totalling to 59 nights of V1647 Ori's spectroscopic observations. The log of spectroscopic observations is listed in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. In order to detect the prominent Hα λ 6563 ˚ A and Ca II IR triplet lines ( λ 8498, λ 8542, λ 8662 ˚ A ), we observed in the effective wavelength range of 5200 -9000 ˚ A using grism 8 (center wavelength 7200 ˚ A ) and grism 7 (center wavelength 5300 ˚ A ). The spectral resolution obtained for grism 8 and 7 with 150 micron slit at IGO and 167 micron slit at HCT was ∼ 7 ˚ A . Nebulosity contamination in spectrum of V1647 Ori was minimised by keeping the slit in east-west orientation. Standard IRAF tasks like APALL and APSUM were used for spectral reduction. Wavelength calibration was carried out using the FeNe, FeAr and HeCu lamps. For final measurement of equivalent width the extracted 1-D spectra were normalised with respect to continuum. For spectroscopic data reduction of HCT and IGO data, semi-automated pipeline written in PyRAF was used.\n2.3. Near-Infrared Photometry\nAlong with optical monitoring we also carried out photometric monitoring in JHK bands using the HCT NIR camera (NIRCAM) and TIFR NIR Imaging CameraII (TIRCAM2). NIRCAM has a 512 × 512 Mercury Cadmium Telluride (HgCdTe) array, with a pixel size of 18 µm , which gives a FoV of 3 . 6 × 3 . 6 arcmin 2 with HCT. Filters used for observation were J ( λ center = 1.28 µm , ∆ λ = 0.28 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.33 µm ) and K ( λ center = 2.22 µm , ∆ λ = 0.38 µm ). Further details of the instrument are available at http://www.iiap.res.in/iao/nir.html. TIRCAM2 has a 512 × 512 Indium Antimonide (InSb) array with a pixel\nsize of 27 µm . We observed McNeil's nebula during the engineering run of TIRCAM2 at 2-m IGO and 1.2-m Physical Research Laboratory (PRL) Mount Abu telescope. Filters used for observation were J ( λ center = 1.20 µm , ∆ λ = 0.36 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.30 µm ) and K ( λ center = 2.19 µm , ∆ λ = 0.40 µm ). Further details of the instrument are available in Naik et al. (2012). We have a total of 14 nights of NIR photometric observations, with the first set of data taken during the quiescent phase in 2007, i.e. before the 2008 outburst. Observations of V1647 Ori were carried out by taking several sets of exposures; each set contains exposure with the telescope pointing at five different dithered positions. The master sky frame for sky-subtraction was generated by median combining all the dithered object frames. Data reduction and final photometry were done using standard IRAF aperture photometric tasks. To be consistent with magnitude estimates by Ojha et al. (2006), for flux calibration we used an aperture ∼ 7 arcsec, and for background sky estimation we used an annulus with an inner radius of ∼ 50 '' and width ∼ 5 '' . For instrumental to apparent magnitude calibration, we observed standard stars around AS13, AS9 and HD225023 fields (Hunt et al 1998) on the same night with similar airmass as V1647 Ori observations. On 2011 December 6, standard stars were not observed, hence we used the magnitude measured on other nights of the nearby star (2MASS J05461162-0006279) for photometric calibration.\n3. RESULTS AND DISCUSSION\n3.1. Photometric Results\nFigure 2 shows the three-color composite image ( V : blue, R : green, I : red) of the McNeil's nebula field (FoV ∼ 10 × 10 arcmin 2 ) obtained from IGO on 2010 February 13. Secondary standard stars used for flux calibration are marked as A, B, C and D. The outburst source V1647 Ori, illuminating the nebula, is marked at the center. The region C, possibly unrelated to Herbig-Haro object, HH 22A, which is illuminated by V1647 Ori is also marked. V1647 Ori had already reached its peak outburst phase before our first optical observation in September 2008. Its light curve steadily continued in peak outburst flux ('high plateau') phase even until our last observation taken in March 2013. However, our longterm continuous monitoring from 2008 September 14 to 2013 March 11 shows a slow but steady linear declining trend in the brightness of the source and nebula (Ninan et al. 2012). The linear slopes and the error in estimates of slopes were obtained by simple linear regression by ordinary least square fitting. V , R and I magnitudes of V1647 Ori and of region C, which is illuminated by the V1647 Ori from its face-on angle of the disc, are listed in Table 2. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. Light curves of V1647 Ori in I and R -bands clearly show a steady dimming (see Figure 3). During the last four and a half years of its second outburst, the brightness in I and R bands have decreased by ∼ 0 . 2 mag. The rate of decline in magnitude of V1647 Ori is 0.036 ± 0 . 007 mag yr -1 in I -band and 0.038 ± 0 . 007 mag yr -1 in R -band. We do not see any statistically significant decline in V -band magnitude of V1647 Ori. This could be due to higher fraction of contamination of\nnebula over V1647 Ori's aperture and slightly higher error in magnitudes due to faintness of source in V -band. These flux changes are along our direct line of sight at an angle of ∼ 30 · to the plane of disc (Acosta-Pulido et al. 2007). However, the flux measured along the cavity in perpendicular direction to the disc, which is reflected from region C, shows a dimming trend of 0.059 ± 0 . 005 mag yr -1 in I -band, 0.051 ± 0 . 005 mag yr -1 in R -band and 0.060 ± 0 . 005 mag yr -1 in V -band (see Figure 4). Hence, the region C, seems to be dimming faster than V1647 Ori. This could be either due to material inflow into cavity between region C and V1647 Ori as the outburst is progressing or due to a change in extinction along the cavity induced by slow dimming of V1647 Ori's brightness. During the first outburst in 2003, the linear dimming rate during the plateau stage was 0.24 mag yr -1 in R -band (Fedele et al. 2007), which was ∼ 6 . 3 times faster in magnitude scale than the present dimming rate in second outburst. Just like in other T-Tauri stars, we also see a lot of short time scale random variations in the source magnitude (peak-to-peak ∆ V glyph[similarequal] 0 . 35 mag, ∆ R glyph[similarequal] 0 . 30 mag and ∆ I glyph[similarequal] 0 . 20 mag), which could be due to density fluctuations in the infalling gas on to the star.\nOur lightcurve of V1647 Ori does not show any 56 day periodicity which was reported by Acosta-Pulido et al. (2007) during the first 2003 outburst. Based on the correlated reddening of flux during the minima of light curve, they proposed that periodicity was due to occultation of a dense clump in accretion disc at a distance of 0.25 AU from the star. The peak-to-peak amplitude in I -band was ∼ 0.3 mag in 2003. We have not detected this variability in 2008 outburst which implies the dense clump might have got dissipated between 2003 and 2008 outburst events. Our Lomb-Scargle periodogram analysis of magnitudes did not show any other statistically significant periodicity.\nThe optical magnitudes during the second outburst are almost similar to that of the first outburst in 2003. In fact the first known outburst of V1647 Ori in 1966 ( ∼ 38 years prior to 2003), reported by Aspin et al. (2006), also had similar magnitude to the present one, however, all these three outbursts have different timescales. Implications of this fact on outburst model will be discussed in Section 4.\nOur NIR J , H and K magnitudes are listed in Table 3. Similar to optical light curve, there is a faint dimming trend in NIR also. Venkata Raman et al. (2013), with more NIR data points, estimated the fading rate in J -band to be 0.08 ± 0 . 02 mag yr -1 . The J -H/H -K color-color (CC) diagram (Figure 5) shows the movement of V1647 Ori from 2007 data point taken in quiescent phase to outburst state. It is similar to what was seen in 2003 outburst. From the quiescent phase position in CC diagram, V1647 Ori has moved towards the classical T-Tauri (CTT) locus along the redenning vector and presently occupies the same position as in 2003 outburst. The position of V1647 Ori in CC diagram is consistent with similar CC diagram published by Venkata Raman et al. (2013). This implies that the decrease in line of sight extinction during the outburst is same as that seen during the 2003 outburst. Since our line of sight is through the envelope, it must be likely due to a reversible mechanism like dust sublimation in the inner region of en-\nelope during each outburst (Acosta-Pulido et al. 2007; Mosoni et al. 2013; Aspin et al. 2009). Since the star is deeply embedded, we have reflections and dust emission effects also affecting the position of V1647 Ori in the CC diagram. So the extinction estimated from CC diagram is not very reliable. Otherwise, we can see that the second outburst has cleared out circumstellar matter of δA V ∼ 6 ± 2 mag. This is also consistent with the estimate of extinction change during first outburst by Mosoni et al. (2013), δA V ∼ 4 . 5 mag (see also Aspin et al. (2008)).\n3.2. Morphological Results\nBetween 2003 and 2008 outbursts, the McNeil's nebula does not have any significant morphological changes, however the intensity distribution of the nebula has changed between the outbursts. Figure 6 shows the difference in R -band flux along the nebula between 2011 and 2004. Images of similar atmospheric conditions were taken and scaled to match the brightness of V1647 Ori before subtracting 2004 image from that of 2011. Brighter shade implies that region is brighter in 2011 than 2004. We can see that the region C is brighter in second outburst than it was in 2004. This could be due to dust clearing up between the last two outbursts along the cavity seen in NIR in region C direction (Ojha et al. 2005). Our photometric results show region C is dimming faster than V1647 Ori and one of the explanations for that could be material inflow into cavity during the outburst. However, region C is relatively brighter in 2008 outburst than in 2004 for the same brightness of V1647 Ori. This implies that the matter inflow to cavity was not occurring during the quiescent phase between 2006 and 2008. This is also based on the implicit assumption that the extinction along the line of sight direction to V1647 Ori is same between 2003 and 2008 outbursts. The other significant change is in illumination of the south-western knot (region B) of the nebula; its illumination seems to have shifted slightly towards west. These illumination changes in nebula imply a structural change in the circumstellar matter above the disc and cavity. A similar pattern and conclusion were also reported between 1966, 2003 and 2008 outbursts by Aspin et al. (2006, 2009). Similar analysis of image pairs taken between 2008 and 2012 did not show any significant morphological changes. Our image pairs had a seeing of 1.6 '' . Hence, to check whether any change in illumination of nebula is undergoing during the present outburst, we need images with seeing less than 1.6 '' .\n3.3. Spectroscopic Results\nV1647 Ori optical spectra show strong H α (6563 ˚ A ) emission and Ca II IR triplet at 8498, 8542 and 8662 ˚ A in emission. Other weak lines seen are Na D (5890+5896 ˚ A ) and OI (7773 ˚ A ) in absorption, and [O I] (6300 ˚ A ), O I (8446 ˚ A ), [Fe II] (7155 ˚ A ) and Fe I (8388, 8514 ˚ A ) in emission (see Figure 7). The equivalent widths of H α , Ca II IR triplet lines and OI (7773 ˚ A ) are listed in Table 4.\n3.3.1. H α line\nStrong Hα line in V1647 Ori shows a clear P-Cygni profile as well as substantial variations. Figure 8 shows\nthe variations of Hα profiles during our four and a half years of observations. P-Cygni profiles were more prominent in early part of the outburst in 2008. To see the absorption component clearly, a Gaussian is fitted to the right wing of the profile in red color and the difference of the fit to actual spectra is plotted in green color. Figure 9 shows the outflow velocity and associated error bar of expanding wind from the blue-shifted absorption minima in Hα profile. These blue-shifted absorption components were present in 2003 outburst also and disappeared during the fading stage of the outburst (Ojha et al. 2006; Fedele et al. 2007). Figure 10 shows the variation in equivalent width ( W λ in ˚ A ) of Hα emission. The calculation of W λ was very sensitive to the weak continuum flux around λ 6563 ˚ A , and the error estimate for each data point is ∼ ± 3 ˚ A . The W λ of 2008 outburst is in similar range of that during first outburst in 2003. Since Hα emission comes from the innermost accretion powered hot zone, we can expect its strength to be proportional to the accretion rate. The optical photometric magnitude in second outburst is similar to that of first outburst, which implies the continuum flux is almost of the same value. Hence from the fact that W λ is of similar value as of first outburst, we can deduce that the accretion rate is also of the same order in both the outbursts during its 'high plateau'stage.\n3.3.2. Ca II IR triplet lines\nThe plots of equivalent widths of Ca II IR triplet lines (8498, 8542 and 8662 ˚ A ) are shown in Figure 11. We have much lesser error bars ( ± 0 . 5 ˚ A ) for the W λ due to the higher continuum flux in these wavelengths. The Ca II IR triplet emission lines are seen to be in the ratio 1 . 07 ± 0 . 09 : 1 . 15 ± 0 . 1 : 1. This nearly equal ratio is due to optically thick gas with the collision decay rates larger than the effective radiative decay rates of upper states of Ca II lines. Such environment is typically seen in many T-Tauri stars. Optical thickness along with the non-detection of forbidden [Ca II] lines above noise, implies number density of electrons to be ≈ 10 11 cm -3 (Hamann & Persson 1992). For comparison with Figure 8 of Hamann & Persson (1992), Figure 12 shows the scatter plot between the ratios of equivalent widths, W λ 8498 / W λ 8542 and W λ 8662 / W λ 8542 , of our data as well as previously published data from literature. The error bar in our new data (black squares) is ± 0 . 1. From the position of 2007 data point (red diamond) taken during quiescent phase (Aspin et al. 2008) in this scatter plot, Aspin et al. (2008, 2009) had concluded that the optical density of the region emitting Ca II IR triplet lines changed significantly between outburst and quiescent phases. But since there is only one data point from quiescent phase and it is lying within the scatter of points from ongoing outburst, it might be difficult to conclude that the change in ratios observed was actually due to V1647 Ori moving from quiescent phase to outburst phase. We could see strong correlation between the equivalent widths ( W λ ) of Ca II IR triplet lines (see Figure 13). The Pearson correlation coefficient (PCC) between both W λ 8662 and W λ 8498 , and W λ 8542 and W λ 8498 is 0.88 with a 2-tailed p value glyph[lessmuch] 0 . 0001. This implies that the fluctuations in W λ are not random statistical error. It could be due to fluctuations of continuum flux around λ 8500 ˚ A . Peak-to-\nW λ is ∼ 5 ˚ A , which means if the flux from these lines is assumed to be constant then the continuum flux has fluctuated by a factor of ∼ 1 . 6, which in terms of the log scale of magnitude is ∼ 0 . 5. This indeed matches with peak-to-peak fluctuation in I -band magnitude during the entire period. We do not see any strong correlation between W λ of Hα line and Ca II IR triplets. However, it should be noted that the error bars in W λ of Hα are much higher than that of Ca II IR lines due to low continuum flux around λ 6563 ˚ A .\nIn 2008 October 29 spectrum, we could clearly detect P-Cygni profile in Ca II IR triplet lines (Figure 14). The strengths of absorption trough of the three lines were in the same pattern as that of T-Tauri star WL 22 (Hamann & Persson 1992), i.e. the pattern with strongest absorption in λ 8542 ˚ A , then λ 8662 ˚ A and very weak in λ 8498 ˚ A . The ratio of W λ of the blue-shifted absorption between λ 8542 ˚ A and λ 8662 ˚ A is 0.76 : 0.45 =1.69 : 1. This ratio is consistent within error bars to the 1.8 : 1 ratio of intensity from atomic transition strength of these lines. Hence, unlike the region producing emission lines, this absorption regions are optically thin. So by using optically thin assumption, we can estimate the column density of Ca II by the formula (Spitzer 1978):\nN CaII = 1 . 1 × 10 20 × ˚ A λ 2 1 f W λ ˚ cm -2 ,\nlu A where the oscillator strength f lu for the lines 8542 and 8662 ˚ A are 0.39355 and 0.21478 respectively, taken from Merle et al. (2011). Substituting the W λ , wavelength and oscillator strength for both the lines, we get the column density ( N CaII ) as 2 . 9 × 10 12 cm -2 and 3 × 10 12 cm -2 respectively. This is the column density of Ca II atoms in this small duration of outflow wind. Assuming reasonable estimates of temperature T= 2600K (disc temperature estimated by Rettig et al. (2005)) and pressure P=1 Pascal (typical pressure in solar winds), we get the fraction of ionisation using Saha's formula to be ≈ 0 . 004. Hence, dividing by this fraction we obtain the column density of Ca atoms in gas blob to be ≈ 7 . 5 × 10 14 cm -2 . Assuming solar metalicity, we obtained column density of hydrogen (H) in outflowing gas blob as ≈ 3 . 4 × 10 20 cm -2 . From the doppler shift of the absorption minima, we also obtained the wind velocity to be 313 ± 10 km s -1 (in λ 8542 ˚ A line) and 303 ± 10 km s -1 (in λ 8662 ˚ A line). We also detected a faint P-Cygni profile in λ 8542 ˚ A line on 2008 December 30, with a blue-shifted velocity of 329 ± 10 km s -1 . Apart from these two episodic events, none of our other spectra show any detectable P-Cygni profile. The episodic nature of these two winds implies they are magnetic reconnection driven winds rather than pressure driven steady winds.\nEven though our medium resolution spectra cannot be used to study line widths, since the Ca II IR triplets are near by, we could do relative comparison of the widths of the Ca II IR triplet lines, where width is taken to be the full width half maximum (FWHM) of Gaussian fit of the continuum normalised profile. Since this quantity is the FWHM of Gaussian profile that we get after the convolution of instrument response on the actual line, it is not the FWHM of the line. However, since the lines are very close and the instrumental convolution is common, the wider line will give a wider FWHM after convolution. Figure 15 shows a scatter plot of the ratio\nof the widths of λ 8498 ˚ A and λ 8542 ˚ A versus equivalent width of the line λ 8542 ˚ A . Most of the points lie below 1.0 in the ratio axis. Using the 'test statistic' for mean with 34 data points, we could reject null hypothesis H o : The mean of the ratio is 1, with 6 sigma confidence. This shows that the λ 8498 ˚ A line is slightly narrower than λ 8542 ˚ A line. Similar trend is seen in most of the T-Tauri stars (Hamann & Persson 1992). Apart from showing this skewness, since our spectra are of only medium resolution, we cannot quantify the narrowness of the line. This narrowness of optically thinner line λ 8498 ˚ A could be explained by either substantial opacity broadening in λ 8542 ˚ A (since 1:9 is the ratio of atomic line strength) or by lower dispersion velocity in the inner part of the region of Ca II IR emission (Hamann & Persson 1992).\nOur period search in the equivalent width ( W λ ) of Ca II IR triplet lines found six faint periodicities in all three lines in the range of 1 - 100 days with ∼ 2 sigma confidence level in amplitude. The possible periodicities and confidence were estimated by Lomb-Scargle periodogram along with Monte Carlo simulation. The possible periods are 3.39, 8.09, 27.94, 30.8, 40.77 and 45.81 day. Since the amplitudes are only of 2 sigma confidence level, they can be confirmed only with more observations. Figure Set 16 shows the folded data of the entire four and a half year observations and the statistical significance of the amplitudes. The amplitude of the least square fitted cosine function is ∼ 1. If this periodicity is due to change in the continuum flux, the corresponding amplitude of magnitude change we expect in logarithmatic I -band magnitude is ∼ 0 . 1. This is not much above our error in magnitude estimate, so the fact that we do not see similar periodicity in I -band magnitude does not rule out the cause of change in W λ as change in continuum flux. We also do not see any corresponding significant periodicity in W λ of H α .\nAspin et al. (2008) took the spectrum of V1647 Ori during the quiescent phase in February 2007. The W λ of both Ca II IR triplet lines and H α were ∼ 3 . 3 times the present value. Aspin & Reipurth (2009) had used ratio of W λ of H α between 2003 outburst and quiescent phase to estimate change in accretion rate. Similarly, since the continuum flux changed by a factor of ∼ 40 between the quiescent and 2008 outburst phase, we can estimate that the change in the line flux of both set of lines is by a factor of ∼ 10. This agrees with the change in accretion rate. Thus the origin of Ca II IR triplet lines are directly connected to the accretion rate just like H α . This is in agreement with finding of tight correlation between Ca II IR line flux and accretion rate in T-Tauri stars by Muzerolle et al. (1998), which suggests the origin of these lines to be in the magnetospheric infall zone. The similar value of W λ of Ca II IR lines with that of 2003 also strengthens the claim that the accretion rate on to the star from inner disc was same during both the outbursts.\n3.3.3. Oxygen lines\nThe most prominent oxygen line is OI 7773 ˚ A in absorption, however, weak OI 8446 ˚ A line is also detected in emission. We should be careful in interpreting the W λ of OI λ 7773 ˚ A absorption line because the profile shape of the line seems to be a combination of red-shifted emis-\ncomponent and more stronger blue-shifted absorption component (see Figure 7). A weak anti-correlation is seen between H α and OI λ 7773 ˚ A (see Figure 17). Correlation had PCC = 0.54, with a 2 tailed p value of 0.001. This anti-correlation in W λ of OI 7773 ˚ A and H α could be due to positive correlation between emission component of OI λ 7773 ˚ A filling in the absorption dip and H α . Since OI λ 7773 ˚ A cannot be formed in photosphere of cool stars, the absorption component is due to warm gas in the envelope or hot photosphere above disc, while the emission component might be due to the hot gas region from which H α is also being emitted. Ojha et al. (2006) reported a decreasing trend in the W λ of OI λ 7773 ˚ A from the beginning till end of the 2003 outburst which was interpreted to be possible decrease in turbulence in outer envelope during the outburst period. We do not see such a trend in 2008 outburst, but the values of W λ in 2008 outburst remain same as that during the second half of the 2003 outburst. A slight decrease of W λ in the later part of 2003 outburst observed on 2005 September 8, as reported by Ojha et al. (2006), in contrast to the increase of W λ of other lines, could be due to increase in the W λ of OI λ 7773 ˚ A emission component.\n3.3.4. Forbidden lines\nWe detected [O I] (6300 ˚ A ) and [Fe II] (7155 ˚ A ) forbidden line emissions in V1647 Ori's spectra. The presence of [O I] λ 6300 ˚ A and [Fe II] λ 7155 ˚ A implies shock regions probably originating from jets. This combined with non-detection of [S II] (6731 ˚ A ) line above our noise level implies the shock region has temperature T ≈ 9000 -11000 K and electron number density ≈ 10 5 -10 6 cm -3 (Hamann 1994). We see significant variations in the strengths of the forbidden lines [O I] and [Fe II], however, the lines are too faint in our individual spectra to quantify statistically. During the fading stage of 2003 outburst in 2006 January, when the bright continuum flux decreased, Fedele et al. (2007) were also able to detect various strong forbidden line emissions, namely [O I] λλ 6300 ˚ A, 6363 ˚ A , [S II] λλ 6717 ˚ A, 6731 ˚ A and [Fe II] λ 7172 ˚ A .\n4. IMPLICATION ON MODELS OF OUTBURST\nThe models which are known for FUor / EXor outbursts can be broadly classified into three. First kind of model is purely a thermal instability model, initially proposed for dwarf nova systems and was later adapted for FUors kind of outbursts (Bell & Lin 1994). The second kind of model involves a binary companion or planet, which perturbs the disc causing repeated sudden high accretion events (Bonnell & Bastien 1992; Lodato & Clarke 2004 ). The third kind involves mainly gravitational instability triggering magnetorotational instability (MRI) (Zhu et al. 2009, and references therein). Bell & Lin (1994) model (hereafter BL94) is a pure thermal instability model. In BL94, the thermal instability is triggered when the surface density at a region in disc rises above a critical density. The viscous timescales determine duration of outbursts and quiescent phase. The inner region at a radius r during outburst will deplete below the critical surface density in viscous time scale τ visc = r 2 /ν . Based on α prescription of viscosity, ν = αc s H , where\nc s is the isothermal sound speed, H ≈ c s / Ω is the disc thickness, Ω is orbital angular velocity at radius r and α ( < 1) is a dimensionless parameter (see Figure 18). Substituting, we get a relation :\nτ visc = r 2 Ω αc 2 s = 1 α Ω ( r H ) 2 .\nLet v R ≈ r/τ visc ≈ ν/r be the effective inward radial velocity component of gas in inner accretion disc. Then the mass infall rate at radius R is ˙ M = -2 πR Σ v R , where Σ is the surface density of disc at that radius. Substituting v R , ν and H in above equation of ˙ M , we get ˙ M ≈ 2 π Σ αc 2 s / Ω. The time scale of transition between outburst and quiescent phases is much smaller than the viscous timescale. Hence, Σ will remain constant, Ω will also remain constant at a given R , which leaves only the parameter αc 2 s to explain the change by a factor of ∼ 10 in inner disc accretion rate to V1647 Ori between the outburst and quiescent phases. Since the square of isothermal sound speed c 2 s = R g T/µ (where R g is the gas constant, T is temperature and µ is mean molecular weight), the temperature change by a factor 10 between the phases at the trigger of thermal instability (Zhu et al. (2009), Appendix B, their Figure 14) alone will cause a net change in accretion rate by factor of 10. Hence, at least in the inner region of disc, α can change only by a multiplicative factor of order 1 to remain consistent with the observed change in accretion rate.\nIn BL94, assuming the mass infall rate to the inner disc region ˙ M in = constant , the α determines the timescales and the ratio α outburst /α quiescent is proportional to the ratio of time in quiescent phase to time in outburst phase (BL94; Table 2). Figure 19 shows the schematic of the lightcurve of V1647 Ori in optical band we know so far. The photometric magnitudes and overall SED during the quiescent phase in 2007 match with pre 2003 outburst data (Aspin et al. 2008). Even though accretion rate had fallen by a factor of 10 during quiescent phase, it was still in the order of 10 -6 M glyph[circledot] yr -1 . Based on this, Aspin et al. (2009) had suggested that the 2003 outburst might not have actually terminated in 2006. Since we do not have a good estimate of pre-outburst accretion rate, we shall consider this sudden drop in accretion rate by a factor of 10 as a drop from outburst state to quiescent phase in outburst models.\nLet α o 1 , α o 2 and α o 3 represent the three outburst phase α values and α q 1 and α q 2 represent the two quiescent phase α values. If we assume ˙ M in = constant in BL94, from the ratio of periods, we get the following relations: α o 1 = k (22 -89) α q 1 ; α o 2 = k 21 α q 1 ; α o 3 < k 9 α q 1 ; α o 3 < k 0 . 6 α q 2 ; where k is just the proportionality constant corresponding to the constant ˙ M in .\nWe also get α o 2 = (0 . 23 -0 . 95) α o 1 ; α o 3 < 0 . 4 α o 2 ; α q 2 = 15 α q 1 .\nThis is a very huge variation in α parameter. However, our accretion estimates, during the 2003 as well as 2008 outbursts show the accretion rate of matter on to the star from inner disc was quite stable at ∼ 10 times the rate in quiescent phase. Thus the α parameter cannot be fluctuating as much as we estimated; especially α o 3 < k 0 . 6 α q 2 is impossible from the fact that viscosity has to be more in outburst phase than quiescent phase. Then the assumption ˙ M in = constant in BL94 might be wrong. An increase in ˙ M in can decrease the draining rate of inner\ndisc and can account for a longer duration of outburst period. It can also explain the slower rate of dimming in the magnitude of the V1647 Ori during its plateau stage in present outburst compared to 2003 outburst.\nBy letting ˙ M in to be a variable and substituting R limit to be the radius upto which instability extends, to constrain parameters, we compared the viscous timescale τ visc = R 2 limit /ν ≈ R 2 limit Ω /αc 2 s between 2003 and 2008 outbursts. The instability triggering temperature at the boundary has to be same for both outbursts, so the sound speed c s will be the same. Parameter α can also be taken to be same during both the outbursts based on our previous conclusion. Now the only free variable parameter which determines the timescale is R limit . Substituting Keplarian Ω ∝ R -3 2 , we finally obtain the relation for viscous timescale in terms of R to be τ ∝ R 1 2 .\nR limit = 20 R glyph[circledot] ( ˙ M in 3 × 10 -6 M glyph[circledot] yr -1 ) 1 3 ( M ∗ M glyph[circledot] ) 1 3 ( T eff 2000 ) -4 3 ∝ ˙ M 1 3 in\nlimit visc limit BL94 gives the radius upto which instability extends to be :\n˙ 1\nSubstituting this proportionality, we get τ visc ∝ M 6 in . Thus the ratios of mass infall rate from outer to inner disc during each outburst is related to the duration of outburst by the relation ˙ M in 2008 ˙ M in 2003 > ( 52 21 ) 6 ≈ 230. Thus the infall of gas from outer to inner disc during 2008 outburst is at least 230 times (2 orders) more than that during 2003 outburst.\nModel presented by Zhu et al. (2010) includes an MRI instability contribution to viscosity parameter if the temperature of the disc goes above MRI triggering temperature ( T M ) and also includes an effective viscosity contribution from gravitational instability beyond the radius given by Toomre's instability parameter Q. The relation between R limit and ˙ M in this model is R limit ∝ ˙ M 2 9\nThus, τ visc ∝ ˙ M 1 9 in , and hence ˙ M in 2008 ˙ M in > ( 52 21 ) 9 ≈ 3500.\n2003 Therefore, the infall of gas from outer to inner disc during 2008 outburst is at least 3500 times (3 orders) more than that during 2003 outburst. This estimate is one order more than BL94. It should be kept in mind that the viscosity timescale gives only order of magnitude estimate of the duration of outburst. For a comparison of actual simulated duration of outburst and viscous timescale see Table 1 in Zhu et al. (2010). If the present outburst continues for a larger period, ˙ M in 2008 ˙ M in 2003 ratio will further\nincrease. Since we have an upper limit in ˙ M in for FUors, the increased ratio could only be explained as a dip in mass inflow in 2003. For example, a gap in disc could have resulted in sudden ending of 2003 outburst. This gap or low density region has to be near the typical R limit predicted by each model, i.e. ∼ 1 AU .\nTo estimate the change in photometric magnitudes between 2003 and 2008 outburst phase due to predicted change in radius R limit , we modelled a disc with temperature profile given by outburst accretion rate inside R limit and quiescent accretion rate outside R limit . The magnitude variations in optical I and NIR J bands were found to be less than 1 mag for variation of R limit by a factor of 6. Mosoni et al. (2013) reported an increase in visibility of resolved interferometric study of V1647 Ori using VLTI/MIDI observations in 8-13 µ m range during\nthe early stage of fading in 2003 outburst (between 2005 March and 2005 September). Apart from the possible scenarios discussed by Mosoni et al. (2013), it could also be explained by the relative increase in contribution in total flux from the extended outburst disc when the central star's accretion slowed down. A similar VLTI/MIDI visibility study of the ongoing 2008 outburst will give more input to constrain R limit and outburst models.\nThus, we conclude that a pure thermal instability alone cannot explain the varying timescales of outbursts occurring in V1647 Ori. As proposed for other short rise timescale FUors, V1647 Ori can also be explained only by an outside-in triggering of the instability from outer radius (Bell & Lin 1994). The change in inflow of material from outer to inner disc could be due to many possibilities like MRI, gravitational instability (GI) or planet perturbation. The smooth surface density assumptions of disc also might not be a good model in light of detection of clump in the disc at 0.27 AU and disappearance of it in second outburst.\nOur observations detected a variety of episodic events like sudden short duration winds with hydrogen column density ≈ 3 . 4 × 10 20 cm -2 , fluctuations in H α flux, short timescale variation in continuum flux etc. The short timescale variation in continuum flux could be explained by the convections in the inner disc as suggested by Zhu et al. (2009) for their model of FU Orionis disc. The variations in Hα flux could have origin in some magnetic phenomena in the accretion funnel. The episodic wind events, [Fe II] λ 7155 and [OI] λ 6300 could be originating from jets or disc/stellar winds region. If we compare between 2008 and 2003 outbursts, the accretion rate on to the star from inner disc, extinction in NIR colorcolor diagram, outburst magnitude and spectral signatures in optical are the same. The main difference between 2008 compared to 2003 is the larger duration of outburst phase, 6 times slower dimming rate in optical during its 'plateau' stage and the change in circumstellar gas distribution revealed by morphological change in nebula's illumination.\n5. CONCLUSIONS\nWe have carried out four and a half years of continuous monitoring of V1647 Ori in its second outburst phase starting from 2008. Following are our main conclusions:\n\n1. V1647 Ori is still in outburst 'plateau' stage, at similar magnitude to 2003 outburst in optical and NIR bands. It is undergoing a slow dimming at a rate of 0.04 mag yr -1 , which is 6 times slower than the rate during 2003 outburst. The magnitude shows significant short timescale ( ∼ 1 day) variations.\n2. Morphological studies on illumination of nebula show a consistent change in the circumstellar gas distribution between 2008, 2003 and 1966 outbursts.\n3. P-Cygni profiles in H α emission lines show outflowing wind velocities of ∼ 350 km s -1 . Apart from the continuous wind we also detected twice short duration episodic winds driven by magnetic reconnection events, with H column density ≈ 3 . 4 × 10 20 cm -2 from P-Cygni profiles in Ca II IR triplet lines\n\nin 2008 October and December. From Ca II IR triplet and H α line strengths, the accretion rate was found to be same as that during the 2003 outburst and is ∼ 10 times more than quiescent phase.\n\n4. We could not detect the 56 day periodicity seen in 2003 outburst.\n5. Detection of the forbidden [OI] λ 6300 and [Fe II] λ 7155 lines implies shock regions of T ≈ 9000 -11000 K and n e ≈ 10 5 -10 6 cm -3 , probably originating from jets.\n6. Timescales of outburst history of V1647 Ori cannot be explained by a simple thermal instability model by Bell & Lin (1994) alone. To explain the large change in accretion rate from outer to inner disc between last two outbursts we require more comprehensive models which includes contribution from MRI, GI and planetary perturbations. From\n\nthe framework of instability models we conclude that the sudden ending of 2003 outburst could be due to a gap or low density region in inner ( ∼ 1 AU) disc.\nWe thank the anonymous referee for giving us invaluable comments and suggestions that improved the content of the paper. The authors thank the staff of HCT, operated by Indian Institute of Astrophysics, Bangalore and IGO at Girawali, operated by Inter-University Centre for Astronomy and Astrophysics, Pune for their assistance and support during observations. It is a pleasure to thank J. S. Joshi and all the members of the Infrared Astronomy Group of TIFR for their support during the TIRCAM2 campaign. 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Fig. 2.Color-composite image of McNeil's nebula (V1647 Ori) region taken from IGO ( V : blue, R : green, I : red) on 2010 February 13. FoV is ∼ 10 × 10 arcmin 2 . North is up and east is to the left-hand side. Stars marked as A, B, C and D are the secondary standard stars used for magnitude calibration. The location of V1647 Ori is marked at the center by two perpendicular lines. Region C, overlapping Herbig-Haro object HH 22A, is marked together. A knot in south-western section (region B) of nebula is also marked. At 400 pc distance, the scale 1 ' corresponds to 24000 AU.
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Fig. 3.Magnitude variation of V1647 Ori in the I, R and V -band from September 2008 to March 2013. Typical photometric error bar is given at the left bottom corner. The filled circles are from HCT and filled squares are from IGO measurements. The rate of dimming in I, R and V -bands are 0 . 036 ± 0 . 007 mag yr -1 , 0 . 038 ± 0 . 007 mag yr -1 and 0 . 021 ± 0 . 009 mag yr -1 respectively.
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Fig. 4.Magnitude variation of region C, illuminated by V1647 Ori, in the I, R and V -band from September 2008 to March 2013. Typical photometric error bar is given at the left bottom corner. The filled circles are from HCT and filled squares are from IGO measurements. The rate of dimming in I, R and V -bands are 0 . 059 ± 0 . 005 mag yr -1 , 0 . 051 ± 0 . 005 mag yr -1 and 0 . 060 ± 0 . 005 mag yr -1 respectively.
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Fig. 6.HCT R -band image of 2011 minus 2004, after normalising with respect to the brightness of V1647 Ori. The images were chosen from the nights with same atmospheric seeing and aligned using other field stars in the FoV. The bright portions show the regions which were relatively brighter in 2011 and dark portions show the regions which were relatively brighter in 2004. For example, region C shown in upper box is brighter in 2011. Also note the change in illumination of south-western knot region B marked by lower box in the nebula. North is up and east is to the left-hand side.
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Fig. 7.The spectral lines present in the spectrum of V1647 Ori are labelled above. To improve the S/N ratio, the normalised spectrum was obtained by weighted averaging of 33 HCT spectra taken over the outburst period 2008 September to 2013 March, each with an average exposure time of 40 minutes. The spectra are not corrected for atmospheric absorption lines. The absorption lines which are not labelled are atmospheric lines. H α and OI λ 7773 line profiles are shown more clearly in insets.
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Fig. 8.The variations of Hα profiles during our four and a half year observations. P-Cygni profiles were more prominent in the early part of the outburst in 2008. A Gaussian is fitted to the right wing of the profile in red color and the difference of that Gaussian fit to actual spectra is plotted in green color to see the absorption component clearly. Figure 8 with 70 other plots of remaining nights are available in the online version of the Journal.
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Fig. 9.The velocity of expanding wind from the blue-shifted absorption minima in Hα P-Cygni profile. The filled circles are from HCT, and grey filled squares are from IGO measurements. The error bar on the bottom right corner shows the typical ± 39 km/sec error estimated for data points.
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Fig. 10.The variation in equivalent width of Hα emission. The filled circles are from HCT, and filled grey squares are from IGO measurements. Each data point has an error bar of ∼ ± 3 ˚ A . This error bar is shown at the right bottom corner.
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Fig. 11.The variation in equivalent widths of Ca II IR triplet lines (8498, 8542 and 8662 ˚ A ) during the outburst period 2008 September to 2013 March. All data points are from HCT measurement and each point has an error bar of ∼ ± 0 . 5 ˚ A . This error bar is shown at the right bottom corner.
\n\nDue to limited spectral range in IGO grism, Ca II triplet lines were not observed from IGO.\n\n\n
Fig. 12.Ratio of Ca II IR triplet lines' equivalent widths, W λ 8498 / W λ 8542 versus W λ 8662 / W λ 8542 , of our data as well as previously published data from literature. 2003 outburst points are shown as circles (Walter et al. 2004; Ojha et al. 2006), 2008 outburst points are shown as squares (Kun 2008; Aspin et al. 2009; Aspin 2011, and this work) and 2007 quiescent phase point is shown as diamond (Aspin et al. 2008). The typical error bar on our new data (black squares) is ∼ ± 0 . 1.
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Fig. 13.Strong correlation between the equivalent widths of Ca II IR triplet lines. Typical error bar is given at the right bottom corner. The Pearson correlation coefficient (PCC) between both W λ 8662 and W λ 8498 , and W λ 8542 and W λ 8498 is 0.88 with a 2-tailed p value glyph[lessmuch] 0 . 0001.
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Fig. 14.The spectrum of V1647 Ori taken on 2008 October 29 showing clear P-Cygni profile in Ca II IR triplet lines. Similar, but fainter profile was once more detected in 2008 December 30. None of the other nights' spectra showed this profile. For comparison, available nearby nights' spectra are also plotted.
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Fig. 15.Scatter plot of the ratio of the widths of 8498 and 8542 ˚ A versus equivalent width of the line 8542 ˚ A . Most of the points lie below 1.0 in Y-axis. Box and whisker plot of the distribution is also ploted on the right side. This shows that the 8498 ˚ A line is slightly narrower than 8542 ˚ A line.
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Fig. 16.Folded phase plot of the W λ of Ca II IR triplet lines λ 8498, λ 8542 and λ 8662 (in ˚ A ), and I -band magnitude. The folding is done over the entire four and a half years of data. The red, black, green, pink and blue circles correspond to data of 2008, 2009, 2010, 2011, and 2012 winter observations respectively. The amplitudes (in ˚ A ) of the three lines in each folded plot are as follows. For a period of 3.39 days:- 1.26 ± 0.69, 1.22 ± 0.75, 1.03 ± 0.67; For a period of 8.09 days:- 1.13 ± 0.70, 1.33 ± 0.71, 1.17 ± 0.65; For a period of 27.94 days:- 1.13 ± 0.72, 1.11 ± 0.79, 1.14 ± 0.67; For a period of 30.8 days:- 1.26 ± 0.61, 1.25 ± 0.63, 0.98 ± 0.58; For a period of 40.77 days:1.26 ± 0.65, 1.42 ± 0.58, 1.18 ± 0.59; For a period of 45.81 days:- 0.95 ± 0.76, 1.29 ± 0.74, 1.10 ± 0.68. Figures 16.2 - 16.6 are available in the online version of the Journal.
\n\n\n\n
Fig. 17.Correlation between equivalent width of H α and OI λ 7773 ˚ A . Typical error bar is given at the right bottom corner. PCC is 0.54 with a 2-tailed p value of 0.001. The weak anti-correlation could be due to a positive correlation between the H α and red-shifted emission component which is filling the absorption component in OI λ 7773 ˚ A profile. Bootstrap analysis gave 95% confidence range of PCC to be [0.29, 0.72].
\n\n\n\n
Fig. 18.Cross-section of an α disc is shown above. R is the radial distance from the star and H is the thickness of the disc, which flares up as the radius R increases. R limit is the radius upto which the outburst extends. We are looking into the system at ∼ 60 · along the dashed line drawn in the figure. In α disc model, the viscosity is due to large turbulent eddies. The speed of eddies is upperbounded by the velocity of sound ( c s ) because any supersonic flow will get dissipated by shock. The size of eddies is also upper bounded by the thickness ( H ) of disc. Thus taking α to be a free parameter < 1 we get the viscosity in the disc as ν = αc s H . The orbital velocity is taken to be Keplarian in our problem.
\n\n\n\n
Fig. 19.Optical light curve history of V1647 Ori. The duration of each outburst and quiescent period is marked in units of months. The X-axis of the image is not drawn to scale.
\n\nTABLE 1\n
\n\n
Observation log of the photometric and spectroscopic observations
\n
\nNote . - Table 1 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.\n\n† Measured average FWHM. This is a measure of the seeing.\n†† Observed from IGO, all other nights are from HCT.\n\n
\n\n
TABLE 2 Optical V RI photometry of V1647 Ori and region C
\n
\nNote . - Table 2 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.\n†† Observed from IGO, all other nights are from HCT.\n
\n\n
TABLE 3 NIR JHK photometry of V1647 Ori
\n
\nNote . - Estimated error in magnitude is ≤ ± 0.1 ( K ) and ≤ ± 0.05 ( H and J ).\n
\n\n
TABLE 4 Equivalent widths (in ˚ A ) of optical lines in V1647 Ori
\n
\nNote . -Table 4 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"We present a detailed study of McNeil's nebula (V1647 Ori) in its ongoing outburst phase starting from September 2008 to March 2013. Our 124 nights of photometric observations were carried out in optical V , R , I and near-infrared (NIR) J , H , K bands, and 59 nights of medium resolution spectroscopic observations were done in 5200 - 9000 ˚ A wavelength range. All observations were carried out with 2-m Himalayan Chandra Telescope (HCT) and 2-m IUCAA Girawali Telescope. Our observations show that over last four and a half years, V1647 Ori and the region C near Herbig-Haro object, HH 22A, have been undergoing a slow dimming at a rate of ∼ 0 . 04 mag yr -1 and ∼ 0 . 05 mag yr -1 respectively in R -band, which is 6 times slower than the rate during similar stage of V1647 Ori in 2003 outburst. We detected change in flux distribution over the reflection nebula implying changes in circumstellar matter distribution between 2003 and 2008 outbursts. Apart from steady wind of velocity ∼ 350 km s -1 we detected two episodic magnetic reconnection driven winds. Forbidden [O I] 6300 ˚ A and [Fe II] 7155 ˚ A lines were also detected implying shock regions probably from jets. We tried to explain the outburst timescales of V1647 Ori using the standard models of FUors kind of outburst and found that pure thermal instability models like Bell & Lin (1994) cannot explain the variations in timescales. In the framework of various instability models we conclude that one possible reason for sudden ending of 2003 outburst in 2005 November was due to a low density region or gap in the inner region ( ∼ 1 AU) of the disc. Subject headings: stars: formation, stars: pre-main-sequence, stars: outflows, stars: variables: general, stars: individual: (V1647 Ori), ISM: individual: (McNeil's nebula)","pages":[1]},{"title":"J. P. Ninan, D. K. Ojha","content":"Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India","pages":[1]},{"title":"B. C. Bhatt","content":"Indian Institute of Astrophysics, Koramangala, Bangalore 560 034, India","pages":[1]},{"title":"S. K. Ghosh","content":"National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune 411 007, India","pages":[1]},{"title":"V. Mohan","content":"Inter-University Centre for Astronomy and Astrophysics, Pune 411 007, India","pages":[1]},{"title":"K. K. Mallick","content":"Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India","pages":[1]},{"title":"M. Tamura","content":"National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan and","pages":[1]},{"title":"Th. Henning","content":"Max-Planck-Institute for Astronomy, Konigstuhl 17, 69117 Heidelberg, Germany Draft version September 5, 2021","pages":[1]},{"title":"1. INTRODUCTION","content":"When low-mass stars like our Sun are born, they slowly accrete gas from the collapsing cloud through an accretion disc. Collimated outflows are also typically seen in most of these objects. The discontinuous knots seen in outflows from these objects, and the mismatch of accretion rate between envelope to disc and disc to star (known as 'Luminosity Problem') in young stellar ob- jects (YSOs), all hint to an episodic nature of accretion instead of an ideal steady inflow (Kenyon et al. 1990; Evans et al. 2009; Ioannidis & Froebrich 2012). The other important feature seen in these objects is the outburst. Rare outbursts that we see among these YSOs are found to be correlated with an order of magnitude increase in mass infall rate and they could be the episodic accretion events required to explain the outflow discontinuities and 'Luminosity Problem'. These outbursts are empirically classified as FUors (decades long outbursts with 4-5 magnitude change in optical) and EXors (few months-years long outbursts with 2-3 magnitude change in optical) (Herbig 1977; Hartmann 1998; Hartmann & Kenyon 1996). Due to the short timescales of outbursts in comparison to millions of years timescale of star formation, these events are extremely rare and only less than a dozen confirmed FUor outbursts have been detected so far. From their frequency of outburst it is estimated that every low-mass YSO should go through these outbursts at least 50 times in its protostellar phase (Scholz et al. 2013). Regarding the discontinuous knots seen in outflows, it should be noted that the timescales between discontinuities were estimated to be of the order of 10 3 years by Ioannidis & Froebrich (2012) and the timescales between FUor outbursts in a single star were estimated to be of the order of 10 4 years by Scholz et al. (2013). So the discontinuities could be due to some other shorter timescale variations in accretion rate rather than classical FUors. But as Scholz et al. (2013) pointed out, we do not have a good estimate of FUors' timescales in the early Class I stage. Hence we cannot rule out the possibility that discontinuities in outflows are created during FUors events. One such object which was extensively studied recently in literature is V1647 Ori (V1647 Orionis), 400 pc away in the L1630 dark cloud of Orion. It underwent a sudden outburst of ∼ 5 mag in optical in 2003 (McNeil 2004; Brice˜no et al. 2004) and illuminated a reflection nebula, now named as McNeil's nebula after its discoverer Jay McNeil. Reipurth & Aspin (2004) reported 3 mag increase in near-infrared (NIR) and Andrews et al. (2004) reported 25 times increase in 12 µm flux and no flux change in submillimeter of V1647 Ori during the outburst. Kastner et al. (2004) reported a 50 times increase in X-ray flux of V1647 Ori during the outburst, and noted that the derived temperature of the plasma is too high for accretion alone to explain and hinted that magnetic reconnection events might be heating up the plasma. Based on the upper limit on radio continuum emission from McNeil's nebula at 1272 MHz from Giant Metrewave Radio Telescope (GMRT), India, Vig et al. (2006) constrained the extent of HII region corresponding to a temperature glyph[greaterorsimilar] 2500 K to be glyph[lessorsimilar] 26 AU. Spectroscopic studies showed strong H α and Ca II IR triplet lines in emission (Brice˜no et al. 2004; Ojha et al. 2006). In NIR region, strong CO bandheads (2.29 µm ) and Br γ line (2.16 µm ; implying strong accretion) were detected in emission (Reipurth & Aspin 2004; Vacca et al. 2004). The strong P-Cygni profile in H α emission indicated wind-velocity ranging from 600 - 300 km s -1 (Ojha et al. 2006; Vacca et al. 2004). ' Abrah'am et al. (2006) carried out AU scale observations using Very Large Telescope Interferometer/ Mid-Infrared interferometric Instrument (VLTI/MIDI). By fitting both spectral energy distribution (SED) and visibility values they deduced a moderately flaring disc with temperature profile T ∼ r -0 . 53 (T(1AU)=680K) and mass ∼ 0 . 05 M glyph[circledot] , with inner radius of 7 R glyph[circledot] (0.03 AU) and outer radius of 100 AU. This temperature profile is shallower than the T ∼ r -0 . 75 canonical model (Pringle 1981). They also reported that the mid-infrared emitting region at 10 µm has a size of ∼ 7 AU. Rettig et al. (2005) used the CO lines in infrared (IR) to measure the temperature of the inner accretion disc region which was estimated to be T ≈ 2500 K. Ojha et al. (2006) and K'osp'al et al. (2005) reported a sudden dimming and termination of the 2003 outburst in November 2005. Thus, 2003 outburst lasted for a total of ∼ 2 years and V1647 Ori returned to its pre-outburst phase in early 2006. Acosta-Pulido et al. (2007) estimated the inclination angle of disc to be 61 · and also estimated the accretion rate to be 5 × 10 -6 M glyph[circledot] yr -1 during outburst and 5 × 10 -7 M glyph[circledot] yr -1 in 2006 quiescent state. Aspin et al. (2006) reported that ∼ 37 years prior to 2003 outburst, i.e. in 1966, V1647 Ori had undergone a similar magnitude of outburst, lasting for a duration somewhere between 5 to 20 months. Contrary to expected decades long quiescense, V1647 Ori underwent a second outburst in 2008 just after spending two years in quiescent state (Aspin et al. 2009). It brightened up to the same magnitude and had almost identical spectral features in optical and NIR as the first outburst. One striking difference was that the strong CO bandhead emission at 2.29 µm was absent in second outburst (Aspin 2011). The X-ray flux with plasma temperature of 2-6 keV during both outbursts was postulated to be due to magnetic reconnection events in the disc-star magnetic field interaction (Teets et al. 2011, and references therein). Hamaguchi et al. (2012) normalised and combined both outbursts' data in X-ray and detected one day periodicity in light curve, which they modeled with two accretion hot spots on the top and bottom hemispheres of the star rotating with one day period and inclination of 68 · . Figure 1 shows the overall cross-section picture of the surroundings of V1647 Ori we know so far. V1647 Ori provides a unique opportunity to understand the physical processes undergone in FUors or EXors kind of outbursts. The short time scale behaviors of this object make it possible for us to make a detailed study of the object. In literature there exists mainly three kinds of model for explaining the outburst phenomena (see Section 4). The differences between these models are all in the inner region of disc ( < 1 AU), and optical and NIR are the right wavelength regime to probe this region of the disc. Detailed understanding of V1647 Ori will thus provide us a laboratory to check our understanding of various instabilities like thermal, gravitational and magnetorotational in proto-planetary disc around young low-mass stars. We have carried out continuous observations for more than four and a half years (2008 - 2013) of V1647 Ori in optical and NIR wavelengths for detailed study of its dynamics during outburst and post-outburst stages of the second outburst. This data combined with previous outbursts' provide us more insight on the nature of outburst and also constrain the existing physical models. In this paper, we present the results of our long-term optical and NIR photometric and spectroscopic observations of the outburst source and associated McNeil's nebula. In Section 2 we describe the observational details and the data reduction procedures. In Section 3 we present our new findings and results from observations. In Section 4 we analyse the ability of each existing physical models to explain V1647 Ori's outburst history. Finally, in Section 5 we summarise our main results.","pages":[1,2]},{"title":"2.1. Optical Photometry","content":"Our long-term optical observations span from 2008 September 14 to 2013 March 11 and were carried out with 2-m Himalayan Chandra Telescope (HCT) at Indian Astronomical Observatory, Hanle (Ladakh), India and with 2-m Inter-University Centre for Astronomy and Astrophysics (IUCAA) Girawali Telescope at IUCAA Girawali Observatory (IGO), Girawali (Pune), India. At HCT, for photometry central 2K × 2K section of Himalaya Faint Object Spectrograph & Camera (HFOSC) CCD, which has a pixel scale of 0.296 arcsec was used, giving us a field of view (FoV) of ∼ 10 × 10 arcmin 2 . At IGO, 2K × 2K IUCAA Faint Object Spectrograph & Camera (IFOSC) CCD was used which also has a similar pixel scale of 0.3 arcsec, giving us a FoV of ∼ 10 × 10 arcmin 2 . Further details of the instruments and telescopes are available at http://www.iiap.res.in/iao/hfosc.html and http://www.iucaa.ernet.in/ itp/igoweb/igo tele and inst.htm. Out of our total observation of 110 nights, 84 nights were observed from HCT and 26 nights from IGO. The V1647 Ori's field ( α, δ ) 2000 = (05 h 46 m 13 s . 135 , -00 · 06 ' 04 '' . 82) was observed in standard V RI Bessel filters. Nearby Landolt's standard star fields (Landolt 1992) were also observed for magnitude calibration and for solving color transformation equation coefficients of each night. For nights which do not have standard star observations, we identified six stars in the object's frame whose magnitudes remain constant throughout. Four of them were used as secondary standards (see Figure 2) and other two were used to check consistency and error. Apart from object frames, bias and sky flats were also taken in each night for the basic data reduction. For fringe removal in IGO I -band images, blank sky frames were also taken. The log of photometric observations is given in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. Blank sky images in I -band were used to create fringe templates by MKFRINGECOR task in IRAF 1 , which were later used to subtract the fringes that appeared in I -band images taken from IGO. Data reduction was done with the semi-automatic pipeline written in PyRAF 2 and IRAF CL scripts. Standard photometric data reduction steps like bias-subtraction and median flat-fielding were done for all the nights. Point-spread function (PSF) photometry (using PSF & ALLSTAR tasks in DAOPHOT package of IRAF) on V1647 Ori was not able to fully remove the nebular contamination. We found a strong correlation between fluctuation in magnitude of V1647 Ori and fluctuation in atmospheric seeing condition. This is because the contamination of flux from nebula into V1647 Ori's aperture was a function of atmospheric seeing. So we generated a set of images by convolving each frame with 2-D Gaussian kernel of different standard deviation (using IMFILTER.GAUSS task in IRAF) for sim- ulating different atmospheric seeing conditions. We then recalculated the magnitudes by DAOPHOT, PSF and ALLSTAR algorithms of IRAF for various atmospheric seeing conditions. The differential magnitudes obtained from each frame's set was interpolated to obtain magnitude at an atmospheric seeing of 1.18 arcsec, which was taken to be the seeing to be interpolated to, for all nights and it was chosen to minimise interpolation error. This method reduced our error bars in magnitude by a factor of 2. Apart from the Gaussian convolution step, the PSF photometry steps were all same as Ojha et al. (2006). Magnitudes of the whole nebula and other objects in the nebula like region C (near HH 22A) and region B defined by Brice˜no et al. (2004) in their figure 2 (also see Figure 2) were measured by simple aperture photometry with an aperture radius of 80 arcsec for nebula and 12 arcsec for the regions C and B. For obtaining the flux, the aperture of the objects like regions C and B were centered at the objects itself.","pages":[3]},{"title":"2.2. Optical Spectroscopy","content":"Our long-term spectroscopic observations also span the same duration as that of photometric observations (2008 September to 2013 March) using both 2-m HCT and 2-m IGO. The full 2K × 4K section of HFOSC CCD spectrograph was used in HCT observations and 2K × 2K IFOSC CCD spectrograph was used for IGO observations. Spectroscopic observations were carried out on 35 nights from HCT and 24 nights from IGO, thus totalling to 59 nights of V1647 Ori's spectroscopic observations. The log of spectroscopic observations is listed in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. In order to detect the prominent Hα λ 6563 ˚ A and Ca II IR triplet lines ( λ 8498, λ 8542, λ 8662 ˚ A ), we observed in the effective wavelength range of 5200 -9000 ˚ A using grism 8 (center wavelength 7200 ˚ A ) and grism 7 (center wavelength 5300 ˚ A ). The spectral resolution obtained for grism 8 and 7 with 150 micron slit at IGO and 167 micron slit at HCT was ∼ 7 ˚ A . Nebulosity contamination in spectrum of V1647 Ori was minimised by keeping the slit in east-west orientation. Standard IRAF tasks like APALL and APSUM were used for spectral reduction. Wavelength calibration was carried out using the FeNe, FeAr and HeCu lamps. For final measurement of equivalent width the extracted 1-D spectra were normalised with respect to continuum. For spectroscopic data reduction of HCT and IGO data, semi-automated pipeline written in PyRAF was used.","pages":[3]},{"title":"2.3. Near-Infrared Photometry","content":"Along with optical monitoring we also carried out photometric monitoring in JHK bands using the HCT NIR camera (NIRCAM) and TIFR NIR Imaging CameraII (TIRCAM2). NIRCAM has a 512 × 512 Mercury Cadmium Telluride (HgCdTe) array, with a pixel size of 18 µm , which gives a FoV of 3 . 6 × 3 . 6 arcmin 2 with HCT. Filters used for observation were J ( λ center = 1.28 µm , ∆ λ = 0.28 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.33 µm ) and K ( λ center = 2.22 µm , ∆ λ = 0.38 µm ). Further details of the instrument are available at http://www.iiap.res.in/iao/nir.html. TIRCAM2 has a 512 × 512 Indium Antimonide (InSb) array with a pixel size of 27 µm . We observed McNeil's nebula during the engineering run of TIRCAM2 at 2-m IGO and 1.2-m Physical Research Laboratory (PRL) Mount Abu telescope. Filters used for observation were J ( λ center = 1.20 µm , ∆ λ = 0.36 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.30 µm ) and K ( λ center = 2.19 µm , ∆ λ = 0.40 µm ). Further details of the instrument are available in Naik et al. (2012). We have a total of 14 nights of NIR photometric observations, with the first set of data taken during the quiescent phase in 2007, i.e. before the 2008 outburst. Observations of V1647 Ori were carried out by taking several sets of exposures; each set contains exposure with the telescope pointing at five different dithered positions. The master sky frame for sky-subtraction was generated by median combining all the dithered object frames. Data reduction and final photometry were done using standard IRAF aperture photometric tasks. To be consistent with magnitude estimates by Ojha et al. (2006), for flux calibration we used an aperture ∼ 7 arcsec, and for background sky estimation we used an annulus with an inner radius of ∼ 50 '' and width ∼ 5 '' . For instrumental to apparent magnitude calibration, we observed standard stars around AS13, AS9 and HD225023 fields (Hunt et al 1998) on the same night with similar airmass as V1647 Ori observations. On 2011 December 6, standard stars were not observed, hence we used the magnitude measured on other nights of the nearby star (2MASS J05461162-0006279) for photometric calibration.","pages":[3,4]},{"title":"3.1. Photometric Results","content":"Figure 2 shows the three-color composite image ( V : blue, R : green, I : red) of the McNeil's nebula field (FoV ∼ 10 × 10 arcmin 2 ) obtained from IGO on 2010 February 13. Secondary standard stars used for flux calibration are marked as A, B, C and D. The outburst source V1647 Ori, illuminating the nebula, is marked at the center. The region C, possibly unrelated to Herbig-Haro object, HH 22A, which is illuminated by V1647 Ori is also marked. V1647 Ori had already reached its peak outburst phase before our first optical observation in September 2008. Its light curve steadily continued in peak outburst flux ('high plateau') phase even until our last observation taken in March 2013. However, our longterm continuous monitoring from 2008 September 14 to 2013 March 11 shows a slow but steady linear declining trend in the brightness of the source and nebula (Ninan et al. 2012). The linear slopes and the error in estimates of slopes were obtained by simple linear regression by ordinary least square fitting. V , R and I magnitudes of V1647 Ori and of region C, which is illuminated by the V1647 Ori from its face-on angle of the disc, are listed in Table 2. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. Light curves of V1647 Ori in I and R -bands clearly show a steady dimming (see Figure 3). During the last four and a half years of its second outburst, the brightness in I and R bands have decreased by ∼ 0 . 2 mag. The rate of decline in magnitude of V1647 Ori is 0.036 ± 0 . 007 mag yr -1 in I -band and 0.038 ± 0 . 007 mag yr -1 in R -band. We do not see any statistically significant decline in V -band magnitude of V1647 Ori. This could be due to higher fraction of contamination of nebula over V1647 Ori's aperture and slightly higher error in magnitudes due to faintness of source in V -band. These flux changes are along our direct line of sight at an angle of ∼ 30 · to the plane of disc (Acosta-Pulido et al. 2007). However, the flux measured along the cavity in perpendicular direction to the disc, which is reflected from region C, shows a dimming trend of 0.059 ± 0 . 005 mag yr -1 in I -band, 0.051 ± 0 . 005 mag yr -1 in R -band and 0.060 ± 0 . 005 mag yr -1 in V -band (see Figure 4). Hence, the region C, seems to be dimming faster than V1647 Ori. This could be either due to material inflow into cavity between region C and V1647 Ori as the outburst is progressing or due to a change in extinction along the cavity induced by slow dimming of V1647 Ori's brightness. During the first outburst in 2003, the linear dimming rate during the plateau stage was 0.24 mag yr -1 in R -band (Fedele et al. 2007), which was ∼ 6 . 3 times faster in magnitude scale than the present dimming rate in second outburst. Just like in other T-Tauri stars, we also see a lot of short time scale random variations in the source magnitude (peak-to-peak ∆ V glyph[similarequal] 0 . 35 mag, ∆ R glyph[similarequal] 0 . 30 mag and ∆ I glyph[similarequal] 0 . 20 mag), which could be due to density fluctuations in the infalling gas on to the star. Our lightcurve of V1647 Ori does not show any 56 day periodicity which was reported by Acosta-Pulido et al. (2007) during the first 2003 outburst. Based on the correlated reddening of flux during the minima of light curve, they proposed that periodicity was due to occultation of a dense clump in accretion disc at a distance of 0.25 AU from the star. The peak-to-peak amplitude in I -band was ∼ 0.3 mag in 2003. We have not detected this variability in 2008 outburst which implies the dense clump might have got dissipated between 2003 and 2008 outburst events. Our Lomb-Scargle periodogram analysis of magnitudes did not show any other statistically significant periodicity. The optical magnitudes during the second outburst are almost similar to that of the first outburst in 2003. In fact the first known outburst of V1647 Ori in 1966 ( ∼ 38 years prior to 2003), reported by Aspin et al. (2006), also had similar magnitude to the present one, however, all these three outbursts have different timescales. Implications of this fact on outburst model will be discussed in Section 4. Our NIR J , H and K magnitudes are listed in Table 3. Similar to optical light curve, there is a faint dimming trend in NIR also. Venkata Raman et al. (2013), with more NIR data points, estimated the fading rate in J -band to be 0.08 ± 0 . 02 mag yr -1 . The J -H/H -K color-color (CC) diagram (Figure 5) shows the movement of V1647 Ori from 2007 data point taken in quiescent phase to outburst state. It is similar to what was seen in 2003 outburst. From the quiescent phase position in CC diagram, V1647 Ori has moved towards the classical T-Tauri (CTT) locus along the redenning vector and presently occupies the same position as in 2003 outburst. The position of V1647 Ori in CC diagram is consistent with similar CC diagram published by Venkata Raman et al. (2013). This implies that the decrease in line of sight extinction during the outburst is same as that seen during the 2003 outburst. Since our line of sight is through the envelope, it must be likely due to a reversible mechanism like dust sublimation in the inner region of en- elope during each outburst (Acosta-Pulido et al. 2007; Mosoni et al. 2013; Aspin et al. 2009). Since the star is deeply embedded, we have reflections and dust emission effects also affecting the position of V1647 Ori in the CC diagram. So the extinction estimated from CC diagram is not very reliable. Otherwise, we can see that the second outburst has cleared out circumstellar matter of δA V ∼ 6 ± 2 mag. This is also consistent with the estimate of extinction change during first outburst by Mosoni et al. (2013), δA V ∼ 4 . 5 mag (see also Aspin et al. (2008)).","pages":[4,5]},{"title":"3.2. Morphological Results","content":"Between 2003 and 2008 outbursts, the McNeil's nebula does not have any significant morphological changes, however the intensity distribution of the nebula has changed between the outbursts. Figure 6 shows the difference in R -band flux along the nebula between 2011 and 2004. Images of similar atmospheric conditions were taken and scaled to match the brightness of V1647 Ori before subtracting 2004 image from that of 2011. Brighter shade implies that region is brighter in 2011 than 2004. We can see that the region C is brighter in second outburst than it was in 2004. This could be due to dust clearing up between the last two outbursts along the cavity seen in NIR in region C direction (Ojha et al. 2005). Our photometric results show region C is dimming faster than V1647 Ori and one of the explanations for that could be material inflow into cavity during the outburst. However, region C is relatively brighter in 2008 outburst than in 2004 for the same brightness of V1647 Ori. This implies that the matter inflow to cavity was not occurring during the quiescent phase between 2006 and 2008. This is also based on the implicit assumption that the extinction along the line of sight direction to V1647 Ori is same between 2003 and 2008 outbursts. The other significant change is in illumination of the south-western knot (region B) of the nebula; its illumination seems to have shifted slightly towards west. These illumination changes in nebula imply a structural change in the circumstellar matter above the disc and cavity. A similar pattern and conclusion were also reported between 1966, 2003 and 2008 outbursts by Aspin et al. (2006, 2009). Similar analysis of image pairs taken between 2008 and 2012 did not show any significant morphological changes. Our image pairs had a seeing of 1.6 '' . Hence, to check whether any change in illumination of nebula is undergoing during the present outburst, we need images with seeing less than 1.6 '' .","pages":[5]},{"title":"3.3. Spectroscopic Results","content":"V1647 Ori optical spectra show strong H α (6563 ˚ A ) emission and Ca II IR triplet at 8498, 8542 and 8662 ˚ A in emission. Other weak lines seen are Na D (5890+5896 ˚ A ) and OI (7773 ˚ A ) in absorption, and [O I] (6300 ˚ A ), O I (8446 ˚ A ), [Fe II] (7155 ˚ A ) and Fe I (8388, 8514 ˚ A ) in emission (see Figure 7). The equivalent widths of H α , Ca II IR triplet lines and OI (7773 ˚ A ) are listed in Table 4.","pages":[5]},{"title":"3.3.1. H α line","content":"Strong Hα line in V1647 Ori shows a clear P-Cygni profile as well as substantial variations. Figure 8 shows the variations of Hα profiles during our four and a half years of observations. P-Cygni profiles were more prominent in early part of the outburst in 2008. To see the absorption component clearly, a Gaussian is fitted to the right wing of the profile in red color and the difference of the fit to actual spectra is plotted in green color. Figure 9 shows the outflow velocity and associated error bar of expanding wind from the blue-shifted absorption minima in Hα profile. These blue-shifted absorption components were present in 2003 outburst also and disappeared during the fading stage of the outburst (Ojha et al. 2006; Fedele et al. 2007). Figure 10 shows the variation in equivalent width ( W λ in ˚ A ) of Hα emission. The calculation of W λ was very sensitive to the weak continuum flux around λ 6563 ˚ A , and the error estimate for each data point is ∼ ± 3 ˚ A . The W λ of 2008 outburst is in similar range of that during first outburst in 2003. Since Hα emission comes from the innermost accretion powered hot zone, we can expect its strength to be proportional to the accretion rate. The optical photometric magnitude in second outburst is similar to that of first outburst, which implies the continuum flux is almost of the same value. Hence from the fact that W λ is of similar value as of first outburst, we can deduce that the accretion rate is also of the same order in both the outbursts during its 'high plateau'stage.","pages":[5]},{"title":"3.3.2. Ca II IR triplet lines","content":"The plots of equivalent widths of Ca II IR triplet lines (8498, 8542 and 8662 ˚ A ) are shown in Figure 11. We have much lesser error bars ( ± 0 . 5 ˚ A ) for the W λ due to the higher continuum flux in these wavelengths. The Ca II IR triplet emission lines are seen to be in the ratio 1 . 07 ± 0 . 09 : 1 . 15 ± 0 . 1 : 1. This nearly equal ratio is due to optically thick gas with the collision decay rates larger than the effective radiative decay rates of upper states of Ca II lines. Such environment is typically seen in many T-Tauri stars. Optical thickness along with the non-detection of forbidden [Ca II] lines above noise, implies number density of electrons to be ≈ 10 11 cm -3 (Hamann & Persson 1992). For comparison with Figure 8 of Hamann & Persson (1992), Figure 12 shows the scatter plot between the ratios of equivalent widths, W λ 8498 / W λ 8542 and W λ 8662 / W λ 8542 , of our data as well as previously published data from literature. The error bar in our new data (black squares) is ± 0 . 1. From the position of 2007 data point (red diamond) taken during quiescent phase (Aspin et al. 2008) in this scatter plot, Aspin et al. (2008, 2009) had concluded that the optical density of the region emitting Ca II IR triplet lines changed significantly between outburst and quiescent phases. But since there is only one data point from quiescent phase and it is lying within the scatter of points from ongoing outburst, it might be difficult to conclude that the change in ratios observed was actually due to V1647 Ori moving from quiescent phase to outburst phase. We could see strong correlation between the equivalent widths ( W λ ) of Ca II IR triplet lines (see Figure 13). The Pearson correlation coefficient (PCC) between both W λ 8662 and W λ 8498 , and W λ 8542 and W λ 8498 is 0.88 with a 2-tailed p value glyph[lessmuch] 0 . 0001. This implies that the fluctuations in W λ are not random statistical error. It could be due to fluctuations of continuum flux around λ 8500 ˚ A . Peak-to- W λ is ∼ 5 ˚ A , which means if the flux from these lines is assumed to be constant then the continuum flux has fluctuated by a factor of ∼ 1 . 6, which in terms of the log scale of magnitude is ∼ 0 . 5. This indeed matches with peak-to-peak fluctuation in I -band magnitude during the entire period. We do not see any strong correlation between W λ of Hα line and Ca II IR triplets. However, it should be noted that the error bars in W λ of Hα are much higher than that of Ca II IR lines due to low continuum flux around λ 6563 ˚ A . In 2008 October 29 spectrum, we could clearly detect P-Cygni profile in Ca II IR triplet lines (Figure 14). The strengths of absorption trough of the three lines were in the same pattern as that of T-Tauri star WL 22 (Hamann & Persson 1992), i.e. the pattern with strongest absorption in λ 8542 ˚ A , then λ 8662 ˚ A and very weak in λ 8498 ˚ A . The ratio of W λ of the blue-shifted absorption between λ 8542 ˚ A and λ 8662 ˚ A is 0.76 : 0.45 =1.69 : 1. This ratio is consistent within error bars to the 1.8 : 1 ratio of intensity from atomic transition strength of these lines. Hence, unlike the region producing emission lines, this absorption regions are optically thin. So by using optically thin assumption, we can estimate the column density of Ca II by the formula (Spitzer 1978): lu A where the oscillator strength f lu for the lines 8542 and 8662 ˚ A are 0.39355 and 0.21478 respectively, taken from Merle et al. (2011). Substituting the W λ , wavelength and oscillator strength for both the lines, we get the column density ( N CaII ) as 2 . 9 × 10 12 cm -2 and 3 × 10 12 cm -2 respectively. This is the column density of Ca II atoms in this small duration of outflow wind. Assuming reasonable estimates of temperature T= 2600K (disc temperature estimated by Rettig et al. (2005)) and pressure P=1 Pascal (typical pressure in solar winds), we get the fraction of ionisation using Saha's formula to be ≈ 0 . 004. Hence, dividing by this fraction we obtain the column density of Ca atoms in gas blob to be ≈ 7 . 5 × 10 14 cm -2 . Assuming solar metalicity, we obtained column density of hydrogen (H) in outflowing gas blob as ≈ 3 . 4 × 10 20 cm -2 . From the doppler shift of the absorption minima, we also obtained the wind velocity to be 313 ± 10 km s -1 (in λ 8542 ˚ A line) and 303 ± 10 km s -1 (in λ 8662 ˚ A line). We also detected a faint P-Cygni profile in λ 8542 ˚ A line on 2008 December 30, with a blue-shifted velocity of 329 ± 10 km s -1 . Apart from these two episodic events, none of our other spectra show any detectable P-Cygni profile. The episodic nature of these two winds implies they are magnetic reconnection driven winds rather than pressure driven steady winds. Even though our medium resolution spectra cannot be used to study line widths, since the Ca II IR triplets are near by, we could do relative comparison of the widths of the Ca II IR triplet lines, where width is taken to be the full width half maximum (FWHM) of Gaussian fit of the continuum normalised profile. Since this quantity is the FWHM of Gaussian profile that we get after the convolution of instrument response on the actual line, it is not the FWHM of the line. However, since the lines are very close and the instrumental convolution is common, the wider line will give a wider FWHM after convolution. Figure 15 shows a scatter plot of the ratio of the widths of λ 8498 ˚ A and λ 8542 ˚ A versus equivalent width of the line λ 8542 ˚ A . Most of the points lie below 1.0 in the ratio axis. Using the 'test statistic' for mean with 34 data points, we could reject null hypothesis H o : The mean of the ratio is 1, with 6 sigma confidence. This shows that the λ 8498 ˚ A line is slightly narrower than λ 8542 ˚ A line. Similar trend is seen in most of the T-Tauri stars (Hamann & Persson 1992). Apart from showing this skewness, since our spectra are of only medium resolution, we cannot quantify the narrowness of the line. This narrowness of optically thinner line λ 8498 ˚ A could be explained by either substantial opacity broadening in λ 8542 ˚ A (since 1:9 is the ratio of atomic line strength) or by lower dispersion velocity in the inner part of the region of Ca II IR emission (Hamann & Persson 1992). Our period search in the equivalent width ( W λ ) of Ca II IR triplet lines found six faint periodicities in all three lines in the range of 1 - 100 days with ∼ 2 sigma confidence level in amplitude. The possible periodicities and confidence were estimated by Lomb-Scargle periodogram along with Monte Carlo simulation. The possible periods are 3.39, 8.09, 27.94, 30.8, 40.77 and 45.81 day. Since the amplitudes are only of 2 sigma confidence level, they can be confirmed only with more observations. Figure Set 16 shows the folded data of the entire four and a half year observations and the statistical significance of the amplitudes. The amplitude of the least square fitted cosine function is ∼ 1. If this periodicity is due to change in the continuum flux, the corresponding amplitude of magnitude change we expect in logarithmatic I -band magnitude is ∼ 0 . 1. This is not much above our error in magnitude estimate, so the fact that we do not see similar periodicity in I -band magnitude does not rule out the cause of change in W λ as change in continuum flux. We also do not see any corresponding significant periodicity in W λ of H α . Aspin et al. (2008) took the spectrum of V1647 Ori during the quiescent phase in February 2007. The W λ of both Ca II IR triplet lines and H α were ∼ 3 . 3 times the present value. Aspin & Reipurth (2009) had used ratio of W λ of H α between 2003 outburst and quiescent phase to estimate change in accretion rate. Similarly, since the continuum flux changed by a factor of ∼ 40 between the quiescent and 2008 outburst phase, we can estimate that the change in the line flux of both set of lines is by a factor of ∼ 10. This agrees with the change in accretion rate. Thus the origin of Ca II IR triplet lines are directly connected to the accretion rate just like H α . This is in agreement with finding of tight correlation between Ca II IR line flux and accretion rate in T-Tauri stars by Muzerolle et al. (1998), which suggests the origin of these lines to be in the magnetospheric infall zone. The similar value of W λ of Ca II IR lines with that of 2003 also strengthens the claim that the accretion rate on to the star from inner disc was same during both the outbursts.","pages":[5,6]},{"title":"3.3.3. Oxygen lines","content":"The most prominent oxygen line is OI 7773 ˚ A in absorption, however, weak OI 8446 ˚ A line is also detected in emission. We should be careful in interpreting the W λ of OI λ 7773 ˚ A absorption line because the profile shape of the line seems to be a combination of red-shifted emis- component and more stronger blue-shifted absorption component (see Figure 7). A weak anti-correlation is seen between H α and OI λ 7773 ˚ A (see Figure 17). Correlation had PCC = 0.54, with a 2 tailed p value of 0.001. This anti-correlation in W λ of OI 7773 ˚ A and H α could be due to positive correlation between emission component of OI λ 7773 ˚ A filling in the absorption dip and H α . Since OI λ 7773 ˚ A cannot be formed in photosphere of cool stars, the absorption component is due to warm gas in the envelope or hot photosphere above disc, while the emission component might be due to the hot gas region from which H α is also being emitted. Ojha et al. (2006) reported a decreasing trend in the W λ of OI λ 7773 ˚ A from the beginning till end of the 2003 outburst which was interpreted to be possible decrease in turbulence in outer envelope during the outburst period. We do not see such a trend in 2008 outburst, but the values of W λ in 2008 outburst remain same as that during the second half of the 2003 outburst. A slight decrease of W λ in the later part of 2003 outburst observed on 2005 September 8, as reported by Ojha et al. (2006), in contrast to the increase of W λ of other lines, could be due to increase in the W λ of OI λ 7773 ˚ A emission component.","pages":[6,7]},{"title":"3.3.4. Forbidden lines","content":"We detected [O I] (6300 ˚ A ) and [Fe II] (7155 ˚ A ) forbidden line emissions in V1647 Ori's spectra. The presence of [O I] λ 6300 ˚ A and [Fe II] λ 7155 ˚ A implies shock regions probably originating from jets. This combined with non-detection of [S II] (6731 ˚ A ) line above our noise level implies the shock region has temperature T ≈ 9000 -11000 K and electron number density ≈ 10 5 -10 6 cm -3 (Hamann 1994). We see significant variations in the strengths of the forbidden lines [O I] and [Fe II], however, the lines are too faint in our individual spectra to quantify statistically. During the fading stage of 2003 outburst in 2006 January, when the bright continuum flux decreased, Fedele et al. (2007) were also able to detect various strong forbidden line emissions, namely [O I] λλ 6300 ˚ A, 6363 ˚ A , [S II] λλ 6717 ˚ A, 6731 ˚ A and [Fe II] λ 7172 ˚ A .","pages":[7]},{"title":"4. IMPLICATION ON MODELS OF OUTBURST","content":"The models which are known for FUor / EXor outbursts can be broadly classified into three. First kind of model is purely a thermal instability model, initially proposed for dwarf nova systems and was later adapted for FUors kind of outbursts (Bell & Lin 1994). The second kind of model involves a binary companion or planet, which perturbs the disc causing repeated sudden high accretion events (Bonnell & Bastien 1992; Lodato & Clarke 2004 ). The third kind involves mainly gravitational instability triggering magnetorotational instability (MRI) (Zhu et al. 2009, and references therein). Bell & Lin (1994) model (hereafter BL94) is a pure thermal instability model. In BL94, the thermal instability is triggered when the surface density at a region in disc rises above a critical density. The viscous timescales determine duration of outbursts and quiescent phase. The inner region at a radius r during outburst will deplete below the critical surface density in viscous time scale τ visc = r 2 /ν . Based on α prescription of viscosity, ν = αc s H , where c s is the isothermal sound speed, H ≈ c s / Ω is the disc thickness, Ω is orbital angular velocity at radius r and α ( < 1) is a dimensionless parameter (see Figure 18). Substituting, we get a relation :","pages":[7]},{"title":"τ visc = r 2 Ω αc 2 s = 1 α Ω ( r H ) 2 .","content":"Let v R ≈ r/τ visc ≈ ν/r be the effective inward radial velocity component of gas in inner accretion disc. Then the mass infall rate at radius R is ˙ M = -2 πR Σ v R , where Σ is the surface density of disc at that radius. Substituting v R , ν and H in above equation of ˙ M , we get ˙ M ≈ 2 π Σ αc 2 s / Ω. The time scale of transition between outburst and quiescent phases is much smaller than the viscous timescale. Hence, Σ will remain constant, Ω will also remain constant at a given R , which leaves only the parameter αc 2 s to explain the change by a factor of ∼ 10 in inner disc accretion rate to V1647 Ori between the outburst and quiescent phases. Since the square of isothermal sound speed c 2 s = R g T/µ (where R g is the gas constant, T is temperature and µ is mean molecular weight), the temperature change by a factor 10 between the phases at the trigger of thermal instability (Zhu et al. (2009), Appendix B, their Figure 14) alone will cause a net change in accretion rate by factor of 10. Hence, at least in the inner region of disc, α can change only by a multiplicative factor of order 1 to remain consistent with the observed change in accretion rate. In BL94, assuming the mass infall rate to the inner disc region ˙ M in = constant , the α determines the timescales and the ratio α outburst /α quiescent is proportional to the ratio of time in quiescent phase to time in outburst phase (BL94; Table 2). Figure 19 shows the schematic of the lightcurve of V1647 Ori in optical band we know so far. The photometric magnitudes and overall SED during the quiescent phase in 2007 match with pre 2003 outburst data (Aspin et al. 2008). Even though accretion rate had fallen by a factor of 10 during quiescent phase, it was still in the order of 10 -6 M glyph[circledot] yr -1 . Based on this, Aspin et al. (2009) had suggested that the 2003 outburst might not have actually terminated in 2006. Since we do not have a good estimate of pre-outburst accretion rate, we shall consider this sudden drop in accretion rate by a factor of 10 as a drop from outburst state to quiescent phase in outburst models. Let α o 1 , α o 2 and α o 3 represent the three outburst phase α values and α q 1 and α q 2 represent the two quiescent phase α values. If we assume ˙ M in = constant in BL94, from the ratio of periods, we get the following relations: α o 1 = k (22 -89) α q 1 ; α o 2 = k 21 α q 1 ; α o 3 < k 9 α q 1 ; α o 3 < k 0 . 6 α q 2 ; where k is just the proportionality constant corresponding to the constant ˙ M in . We also get α o 2 = (0 . 23 -0 . 95) α o 1 ; α o 3 < 0 . 4 α o 2 ; α q 2 = 15 α q 1 . This is a very huge variation in α parameter. However, our accretion estimates, during the 2003 as well as 2008 outbursts show the accretion rate of matter on to the star from inner disc was quite stable at ∼ 10 times the rate in quiescent phase. Thus the α parameter cannot be fluctuating as much as we estimated; especially α o 3 < k 0 . 6 α q 2 is impossible from the fact that viscosity has to be more in outburst phase than quiescent phase. Then the assumption ˙ M in = constant in BL94 might be wrong. An increase in ˙ M in can decrease the draining rate of inner disc and can account for a longer duration of outburst period. It can also explain the slower rate of dimming in the magnitude of the V1647 Ori during its plateau stage in present outburst compared to 2003 outburst. By letting ˙ M in to be a variable and substituting R limit to be the radius upto which instability extends, to constrain parameters, we compared the viscous timescale τ visc = R 2 limit /ν ≈ R 2 limit Ω /αc 2 s between 2003 and 2008 outbursts. The instability triggering temperature at the boundary has to be same for both outbursts, so the sound speed c s will be the same. Parameter α can also be taken to be same during both the outbursts based on our previous conclusion. Now the only free variable parameter which determines the timescale is R limit . Substituting Keplarian Ω ∝ R -3 2 , we finally obtain the relation for viscous timescale in terms of R to be τ ∝ R 1 2 . limit visc limit BL94 gives the radius upto which instability extends to be : ˙ 1 Substituting this proportionality, we get τ visc ∝ M 6 in . Thus the ratios of mass infall rate from outer to inner disc during each outburst is related to the duration of outburst by the relation ˙ M in 2008 ˙ M in 2003 > ( 52 21 ) 6 ≈ 230. Thus the infall of gas from outer to inner disc during 2008 outburst is at least 230 times (2 orders) more than that during 2003 outburst. Model presented by Zhu et al. (2010) includes an MRI instability contribution to viscosity parameter if the temperature of the disc goes above MRI triggering temperature ( T M ) and also includes an effective viscosity contribution from gravitational instability beyond the radius given by Toomre's instability parameter Q. The relation between R limit and ˙ M in this model is R limit ∝ ˙ M 2 9 2003 Therefore, the infall of gas from outer to inner disc during 2008 outburst is at least 3500 times (3 orders) more than that during 2003 outburst. This estimate is one order more than BL94. It should be kept in mind that the viscosity timescale gives only order of magnitude estimate of the duration of outburst. For a comparison of actual simulated duration of outburst and viscous timescale see Table 1 in Zhu et al. (2010). If the present outburst continues for a larger period, ˙ M in 2008 ˙ M in 2003 ratio will further increase. Since we have an upper limit in ˙ M in for FUors, the increased ratio could only be explained as a dip in mass inflow in 2003. For example, a gap in disc could have resulted in sudden ending of 2003 outburst. This gap or low density region has to be near the typical R limit predicted by each model, i.e. ∼ 1 AU . To estimate the change in photometric magnitudes between 2003 and 2008 outburst phase due to predicted change in radius R limit , we modelled a disc with temperature profile given by outburst accretion rate inside R limit and quiescent accretion rate outside R limit . The magnitude variations in optical I and NIR J bands were found to be less than 1 mag for variation of R limit by a factor of 6. Mosoni et al. (2013) reported an increase in visibility of resolved interferometric study of V1647 Ori using VLTI/MIDI observations in 8-13 µ m range during the early stage of fading in 2003 outburst (between 2005 March and 2005 September). Apart from the possible scenarios discussed by Mosoni et al. (2013), it could also be explained by the relative increase in contribution in total flux from the extended outburst disc when the central star's accretion slowed down. A similar VLTI/MIDI visibility study of the ongoing 2008 outburst will give more input to constrain R limit and outburst models. Thus, we conclude that a pure thermal instability alone cannot explain the varying timescales of outbursts occurring in V1647 Ori. As proposed for other short rise timescale FUors, V1647 Ori can also be explained only by an outside-in triggering of the instability from outer radius (Bell & Lin 1994). The change in inflow of material from outer to inner disc could be due to many possibilities like MRI, gravitational instability (GI) or planet perturbation. The smooth surface density assumptions of disc also might not be a good model in light of detection of clump in the disc at 0.27 AU and disappearance of it in second outburst. Our observations detected a variety of episodic events like sudden short duration winds with hydrogen column density ≈ 3 . 4 × 10 20 cm -2 , fluctuations in H α flux, short timescale variation in continuum flux etc. The short timescale variation in continuum flux could be explained by the convections in the inner disc as suggested by Zhu et al. (2009) for their model of FU Orionis disc. The variations in Hα flux could have origin in some magnetic phenomena in the accretion funnel. The episodic wind events, [Fe II] λ 7155 and [OI] λ 6300 could be originating from jets or disc/stellar winds region. If we compare between 2008 and 2003 outbursts, the accretion rate on to the star from inner disc, extinction in NIR colorcolor diagram, outburst magnitude and spectral signatures in optical are the same. The main difference between 2008 compared to 2003 is the larger duration of outburst phase, 6 times slower dimming rate in optical during its 'plateau' stage and the change in circumstellar gas distribution revealed by morphological change in nebula's illumination.","pages":[7,8]},{"title":"5. CONCLUSIONS","content":"We have carried out four and a half years of continuous monitoring of V1647 Ori in its second outburst phase starting from 2008. Following are our main conclusions: in 2008 October and December. From Ca II IR triplet and H α line strengths, the accretion rate was found to be same as that during the 2003 outburst and is ∼ 10 times more than quiescent phase. the framework of instability models we conclude that the sudden ending of 2003 outburst could be due to a gap or low density region in inner ( ∼ 1 AU) disc. We thank the anonymous referee for giving us invaluable comments and suggestions that improved the content of the paper. The authors thank the staff of HCT, operated by Indian Institute of Astrophysics, Bangalore and IGO at Girawali, operated by Inter-University Centre for Astronomy and Astrophysics, Pune for their assistance and support during observations. It is a pleasure to thank J. S. Joshi and all the members of the Infrared Astronomy Group of TIFR for their support during the TIRCAM2 campaign. All the plots were generated using the 2D graphics environment Matplotlib (Hunter 2007).","pages":[8,9]},{"title":"REFERENCES","content":"' Abrah'am, P., Mosoni, L., Henning, T., et al. 2006, A&A, 449, 13 Acosta-Pulido, J. A., Kun, M., ' Abrah'am, P., et al. 2007, AJ, 133, 2020 Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90 Lodato, G. & Clarke, C.J. 2004, MNRAS, 353, 841 McNeil, J.W. 2004, IAU Circ. 8284 . Due to limited spectral range in IGO grism, Ca II triplet lines were not observed from IGO. Note . - Table 1 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content. Note . - Table 2 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content. †† Observed from IGO, all other nights are from HCT. Note . - Estimated error in magnitude is ≤ ± 0.1 ( K ) and ≤ ± 0.05 ( H and J ). Note . -Table 4 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.","pages":[9,19,20,29,30]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"We present a detailed study of McNeil's nebula (V1647 Ori) in its ongoing outburst phase starting from September 2008 to March 2013. Our 124 nights of photometric observations were carried out in optical V , R , I and near-infrared (NIR) J , H , K bands, and 59 nights of medium resolution spectroscopic observations were done in 5200 - 9000 ˚ A wavelength range. All observations were carried out with 2-m Himalayan Chandra Telescope (HCT) and 2-m IUCAA Girawali Telescope. Our observations show that over last four and a half years, V1647 Ori and the region C near Herbig-Haro object, HH 22A, have been undergoing a slow dimming at a rate of ∼ 0 . 04 mag yr -1 and ∼ 0 . 05 mag yr -1 respectively in R -band, which is 6 times slower than the rate during similar stage of V1647 Ori in 2003 outburst. We detected change in flux distribution over the reflection nebula implying changes in circumstellar matter distribution between 2003 and 2008 outbursts. Apart from steady wind of velocity ∼ 350 km s -1 we detected two episodic magnetic reconnection driven winds. Forbidden [O I] 6300 ˚ A and [Fe II] 7155 ˚ A lines were also detected implying shock regions probably from jets. We tried to explain the outburst timescales of V1647 Ori using the standard models of FUors kind of outburst and found that pure thermal instability models like Bell & Lin (1994) cannot explain the variations in timescales. In the framework of various instability models we conclude that one possible reason for sudden ending of 2003 outburst in 2005 November was due to a low density region or gap in the inner region ( ∼ 1 AU) of the disc. Subject headings: stars: formation, stars: pre-main-sequence, stars: outflows, stars: variables: general, stars: individual: (V1647 Ori), ISM: individual: (McNeil's nebula)\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"J. P. Ninan, D. K. Ojha\",\n \"content\": \"Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"B. C. Bhatt\",\n \"content\": \"Indian Institute of Astrophysics, Koramangala, Bangalore 560 034, India\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"S. K. Ghosh\",\n \"content\": \"National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune 411 007, India\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"V. Mohan\",\n \"content\": \"Inter-University Centre for Astronomy and Astrophysics, Pune 411 007, India\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"K. K. Mallick\",\n \"content\": \"Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"M. Tamura\",\n \"content\": \"National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan and\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Th. Henning\",\n \"content\": \"Max-Planck-Institute for Astronomy, Konigstuhl 17, 69117 Heidelberg, Germany Draft version September 5, 2021\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"When low-mass stars like our Sun are born, they slowly accrete gas from the collapsing cloud through an accretion disc. Collimated outflows are also typically seen in most of these objects. The discontinuous knots seen in outflows from these objects, and the mismatch of accretion rate between envelope to disc and disc to star (known as 'Luminosity Problem') in young stellar ob- jects (YSOs), all hint to an episodic nature of accretion instead of an ideal steady inflow (Kenyon et al. 1990; Evans et al. 2009; Ioannidis & Froebrich 2012). The other important feature seen in these objects is the outburst. Rare outbursts that we see among these YSOs are found to be correlated with an order of magnitude increase in mass infall rate and they could be the episodic accretion events required to explain the outflow discontinuities and 'Luminosity Problem'. These outbursts are empirically classified as FUors (decades long outbursts with 4-5 magnitude change in optical) and EXors (few months-years long outbursts with 2-3 magnitude change in optical) (Herbig 1977; Hartmann 1998; Hartmann & Kenyon 1996). Due to the short timescales of outbursts in comparison to millions of years timescale of star formation, these events are extremely rare and only less than a dozen confirmed FUor outbursts have been detected so far. From their frequency of outburst it is estimated that every low-mass YSO should go through these outbursts at least 50 times in its protostellar phase (Scholz et al. 2013). Regarding the discontinuous knots seen in outflows, it should be noted that the timescales between discontinuities were estimated to be of the order of 10 3 years by Ioannidis & Froebrich (2012) and the timescales between FUor outbursts in a single star were estimated to be of the order of 10 4 years by Scholz et al. (2013). So the discontinuities could be due to some other shorter timescale variations in accretion rate rather than classical FUors. But as Scholz et al. (2013) pointed out, we do not have a good estimate of FUors' timescales in the early Class I stage. Hence we cannot rule out the possibility that discontinuities in outflows are created during FUors events. One such object which was extensively studied recently in literature is V1647 Ori (V1647 Orionis), 400 pc away in the L1630 dark cloud of Orion. It underwent a sudden outburst of ∼ 5 mag in optical in 2003 (McNeil 2004; Brice˜no et al. 2004) and illuminated a reflection nebula, now named as McNeil's nebula after its discoverer Jay McNeil. Reipurth & Aspin (2004) reported 3 mag increase in near-infrared (NIR) and Andrews et al. (2004) reported 25 times increase in 12 µm flux and no flux change in submillimeter of V1647 Ori during the outburst. Kastner et al. (2004) reported a 50 times increase in X-ray flux of V1647 Ori during the outburst, and noted that the derived temperature of the plasma is too high for accretion alone to explain and hinted that magnetic reconnection events might be heating up the plasma. Based on the upper limit on radio continuum emission from McNeil's nebula at 1272 MHz from Giant Metrewave Radio Telescope (GMRT), India, Vig et al. (2006) constrained the extent of HII region corresponding to a temperature glyph[greaterorsimilar] 2500 K to be glyph[lessorsimilar] 26 AU. Spectroscopic studies showed strong H α and Ca II IR triplet lines in emission (Brice˜no et al. 2004; Ojha et al. 2006). In NIR region, strong CO bandheads (2.29 µm ) and Br γ line (2.16 µm ; implying strong accretion) were detected in emission (Reipurth & Aspin 2004; Vacca et al. 2004). The strong P-Cygni profile in H α emission indicated wind-velocity ranging from 600 - 300 km s -1 (Ojha et al. 2006; Vacca et al. 2004). ' Abrah'am et al. (2006) carried out AU scale observations using Very Large Telescope Interferometer/ Mid-Infrared interferometric Instrument (VLTI/MIDI). By fitting both spectral energy distribution (SED) and visibility values they deduced a moderately flaring disc with temperature profile T ∼ r -0 . 53 (T(1AU)=680K) and mass ∼ 0 . 05 M glyph[circledot] , with inner radius of 7 R glyph[circledot] (0.03 AU) and outer radius of 100 AU. This temperature profile is shallower than the T ∼ r -0 . 75 canonical model (Pringle 1981). They also reported that the mid-infrared emitting region at 10 µm has a size of ∼ 7 AU. Rettig et al. (2005) used the CO lines in infrared (IR) to measure the temperature of the inner accretion disc region which was estimated to be T ≈ 2500 K. Ojha et al. (2006) and K'osp'al et al. (2005) reported a sudden dimming and termination of the 2003 outburst in November 2005. Thus, 2003 outburst lasted for a total of ∼ 2 years and V1647 Ori returned to its pre-outburst phase in early 2006. Acosta-Pulido et al. (2007) estimated the inclination angle of disc to be 61 · and also estimated the accretion rate to be 5 × 10 -6 M glyph[circledot] yr -1 during outburst and 5 × 10 -7 M glyph[circledot] yr -1 in 2006 quiescent state. Aspin et al. (2006) reported that ∼ 37 years prior to 2003 outburst, i.e. in 1966, V1647 Ori had undergone a similar magnitude of outburst, lasting for a duration somewhere between 5 to 20 months. Contrary to expected decades long quiescense, V1647 Ori underwent a second outburst in 2008 just after spending two years in quiescent state (Aspin et al. 2009). It brightened up to the same magnitude and had almost identical spectral features in optical and NIR as the first outburst. One striking difference was that the strong CO bandhead emission at 2.29 µm was absent in second outburst (Aspin 2011). The X-ray flux with plasma temperature of 2-6 keV during both outbursts was postulated to be due to magnetic reconnection events in the disc-star magnetic field interaction (Teets et al. 2011, and references therein). Hamaguchi et al. (2012) normalised and combined both outbursts' data in X-ray and detected one day periodicity in light curve, which they modeled with two accretion hot spots on the top and bottom hemispheres of the star rotating with one day period and inclination of 68 · . Figure 1 shows the overall cross-section picture of the surroundings of V1647 Ori we know so far. V1647 Ori provides a unique opportunity to understand the physical processes undergone in FUors or EXors kind of outbursts. The short time scale behaviors of this object make it possible for us to make a detailed study of the object. In literature there exists mainly three kinds of model for explaining the outburst phenomena (see Section 4). The differences between these models are all in the inner region of disc ( < 1 AU), and optical and NIR are the right wavelength regime to probe this region of the disc. Detailed understanding of V1647 Ori will thus provide us a laboratory to check our understanding of various instabilities like thermal, gravitational and magnetorotational in proto-planetary disc around young low-mass stars. We have carried out continuous observations for more than four and a half years (2008 - 2013) of V1647 Ori in optical and NIR wavelengths for detailed study of its dynamics during outburst and post-outburst stages of the second outburst. This data combined with previous outbursts' provide us more insight on the nature of outburst and also constrain the existing physical models. In this paper, we present the results of our long-term optical and NIR photometric and spectroscopic observations of the outburst source and associated McNeil's nebula. In Section 2 we describe the observational details and the data reduction procedures. In Section 3 we present our new findings and results from observations. In Section 4 we analyse the ability of each existing physical models to explain V1647 Ori's outburst history. Finally, in Section 5 we summarise our main results.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2.1. Optical Photometry\",\n \"content\": \"Our long-term optical observations span from 2008 September 14 to 2013 March 11 and were carried out with 2-m Himalayan Chandra Telescope (HCT) at Indian Astronomical Observatory, Hanle (Ladakh), India and with 2-m Inter-University Centre for Astronomy and Astrophysics (IUCAA) Girawali Telescope at IUCAA Girawali Observatory (IGO), Girawali (Pune), India. At HCT, for photometry central 2K × 2K section of Himalaya Faint Object Spectrograph & Camera (HFOSC) CCD, which has a pixel scale of 0.296 arcsec was used, giving us a field of view (FoV) of ∼ 10 × 10 arcmin 2 . At IGO, 2K × 2K IUCAA Faint Object Spectrograph & Camera (IFOSC) CCD was used which also has a similar pixel scale of 0.3 arcsec, giving us a FoV of ∼ 10 × 10 arcmin 2 . Further details of the instruments and telescopes are available at http://www.iiap.res.in/iao/hfosc.html and http://www.iucaa.ernet.in/ itp/igoweb/igo tele and inst.htm. Out of our total observation of 110 nights, 84 nights were observed from HCT and 26 nights from IGO. The V1647 Ori's field ( α, δ ) 2000 = (05 h 46 m 13 s . 135 , -00 · 06 ' 04 '' . 82) was observed in standard V RI Bessel filters. Nearby Landolt's standard star fields (Landolt 1992) were also observed for magnitude calibration and for solving color transformation equation coefficients of each night. For nights which do not have standard star observations, we identified six stars in the object's frame whose magnitudes remain constant throughout. Four of them were used as secondary standards (see Figure 2) and other two were used to check consistency and error. Apart from object frames, bias and sky flats were also taken in each night for the basic data reduction. For fringe removal in IGO I -band images, blank sky frames were also taken. The log of photometric observations is given in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. Blank sky images in I -band were used to create fringe templates by MKFRINGECOR task in IRAF 1 , which were later used to subtract the fringes that appeared in I -band images taken from IGO. Data reduction was done with the semi-automatic pipeline written in PyRAF 2 and IRAF CL scripts. Standard photometric data reduction steps like bias-subtraction and median flat-fielding were done for all the nights. Point-spread function (PSF) photometry (using PSF & ALLSTAR tasks in DAOPHOT package of IRAF) on V1647 Ori was not able to fully remove the nebular contamination. We found a strong correlation between fluctuation in magnitude of V1647 Ori and fluctuation in atmospheric seeing condition. This is because the contamination of flux from nebula into V1647 Ori's aperture was a function of atmospheric seeing. So we generated a set of images by convolving each frame with 2-D Gaussian kernel of different standard deviation (using IMFILTER.GAUSS task in IRAF) for sim- ulating different atmospheric seeing conditions. We then recalculated the magnitudes by DAOPHOT, PSF and ALLSTAR algorithms of IRAF for various atmospheric seeing conditions. The differential magnitudes obtained from each frame's set was interpolated to obtain magnitude at an atmospheric seeing of 1.18 arcsec, which was taken to be the seeing to be interpolated to, for all nights and it was chosen to minimise interpolation error. This method reduced our error bars in magnitude by a factor of 2. Apart from the Gaussian convolution step, the PSF photometry steps were all same as Ojha et al. (2006). Magnitudes of the whole nebula and other objects in the nebula like region C (near HH 22A) and region B defined by Brice˜no et al. (2004) in their figure 2 (also see Figure 2) were measured by simple aperture photometry with an aperture radius of 80 arcsec for nebula and 12 arcsec for the regions C and B. For obtaining the flux, the aperture of the objects like regions C and B were centered at the objects itself.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"2.2. Optical Spectroscopy\",\n \"content\": \"Our long-term spectroscopic observations also span the same duration as that of photometric observations (2008 September to 2013 March) using both 2-m HCT and 2-m IGO. The full 2K × 4K section of HFOSC CCD spectrograph was used in HCT observations and 2K × 2K IFOSC CCD spectrograph was used for IGO observations. Spectroscopic observations were carried out on 35 nights from HCT and 24 nights from IGO, thus totalling to 59 nights of V1647 Ori's spectroscopic observations. The log of spectroscopic observations is listed in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. In order to detect the prominent Hα λ 6563 ˚ A and Ca II IR triplet lines ( λ 8498, λ 8542, λ 8662 ˚ A ), we observed in the effective wavelength range of 5200 -9000 ˚ A using grism 8 (center wavelength 7200 ˚ A ) and grism 7 (center wavelength 5300 ˚ A ). The spectral resolution obtained for grism 8 and 7 with 150 micron slit at IGO and 167 micron slit at HCT was ∼ 7 ˚ A . Nebulosity contamination in spectrum of V1647 Ori was minimised by keeping the slit in east-west orientation. Standard IRAF tasks like APALL and APSUM were used for spectral reduction. Wavelength calibration was carried out using the FeNe, FeAr and HeCu lamps. For final measurement of equivalent width the extracted 1-D spectra were normalised with respect to continuum. For spectroscopic data reduction of HCT and IGO data, semi-automated pipeline written in PyRAF was used.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"2.3. Near-Infrared Photometry\",\n \"content\": \"Along with optical monitoring we also carried out photometric monitoring in JHK bands using the HCT NIR camera (NIRCAM) and TIFR NIR Imaging CameraII (TIRCAM2). NIRCAM has a 512 × 512 Mercury Cadmium Telluride (HgCdTe) array, with a pixel size of 18 µm , which gives a FoV of 3 . 6 × 3 . 6 arcmin 2 with HCT. Filters used for observation were J ( λ center = 1.28 µm , ∆ λ = 0.28 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.33 µm ) and K ( λ center = 2.22 µm , ∆ λ = 0.38 µm ). Further details of the instrument are available at http://www.iiap.res.in/iao/nir.html. TIRCAM2 has a 512 × 512 Indium Antimonide (InSb) array with a pixel size of 27 µm . We observed McNeil's nebula during the engineering run of TIRCAM2 at 2-m IGO and 1.2-m Physical Research Laboratory (PRL) Mount Abu telescope. Filters used for observation were J ( λ center = 1.20 µm , ∆ λ = 0.36 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.30 µm ) and K ( λ center = 2.19 µm , ∆ λ = 0.40 µm ). Further details of the instrument are available in Naik et al. (2012). We have a total of 14 nights of NIR photometric observations, with the first set of data taken during the quiescent phase in 2007, i.e. before the 2008 outburst. Observations of V1647 Ori were carried out by taking several sets of exposures; each set contains exposure with the telescope pointing at five different dithered positions. The master sky frame for sky-subtraction was generated by median combining all the dithered object frames. Data reduction and final photometry were done using standard IRAF aperture photometric tasks. To be consistent with magnitude estimates by Ojha et al. (2006), for flux calibration we used an aperture ∼ 7 arcsec, and for background sky estimation we used an annulus with an inner radius of ∼ 50 '' and width ∼ 5 '' . For instrumental to apparent magnitude calibration, we observed standard stars around AS13, AS9 and HD225023 fields (Hunt et al 1998) on the same night with similar airmass as V1647 Ori observations. On 2011 December 6, standard stars were not observed, hence we used the magnitude measured on other nights of the nearby star (2MASS J05461162-0006279) for photometric calibration.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"3.1. Photometric Results\",\n \"content\": \"Figure 2 shows the three-color composite image ( V : blue, R : green, I : red) of the McNeil's nebula field (FoV ∼ 10 × 10 arcmin 2 ) obtained from IGO on 2010 February 13. Secondary standard stars used for flux calibration are marked as A, B, C and D. The outburst source V1647 Ori, illuminating the nebula, is marked at the center. The region C, possibly unrelated to Herbig-Haro object, HH 22A, which is illuminated by V1647 Ori is also marked. V1647 Ori had already reached its peak outburst phase before our first optical observation in September 2008. Its light curve steadily continued in peak outburst flux ('high plateau') phase even until our last observation taken in March 2013. However, our longterm continuous monitoring from 2008 September 14 to 2013 March 11 shows a slow but steady linear declining trend in the brightness of the source and nebula (Ninan et al. 2012). The linear slopes and the error in estimates of slopes were obtained by simple linear regression by ordinary least square fitting. V , R and I magnitudes of V1647 Ori and of region C, which is illuminated by the V1647 Ori from its face-on angle of the disc, are listed in Table 2. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. Light curves of V1647 Ori in I and R -bands clearly show a steady dimming (see Figure 3). During the last four and a half years of its second outburst, the brightness in I and R bands have decreased by ∼ 0 . 2 mag. The rate of decline in magnitude of V1647 Ori is 0.036 ± 0 . 007 mag yr -1 in I -band and 0.038 ± 0 . 007 mag yr -1 in R -band. We do not see any statistically significant decline in V -band magnitude of V1647 Ori. This could be due to higher fraction of contamination of nebula over V1647 Ori's aperture and slightly higher error in magnitudes due to faintness of source in V -band. These flux changes are along our direct line of sight at an angle of ∼ 30 · to the plane of disc (Acosta-Pulido et al. 2007). However, the flux measured along the cavity in perpendicular direction to the disc, which is reflected from region C, shows a dimming trend of 0.059 ± 0 . 005 mag yr -1 in I -band, 0.051 ± 0 . 005 mag yr -1 in R -band and 0.060 ± 0 . 005 mag yr -1 in V -band (see Figure 4). Hence, the region C, seems to be dimming faster than V1647 Ori. This could be either due to material inflow into cavity between region C and V1647 Ori as the outburst is progressing or due to a change in extinction along the cavity induced by slow dimming of V1647 Ori's brightness. During the first outburst in 2003, the linear dimming rate during the plateau stage was 0.24 mag yr -1 in R -band (Fedele et al. 2007), which was ∼ 6 . 3 times faster in magnitude scale than the present dimming rate in second outburst. Just like in other T-Tauri stars, we also see a lot of short time scale random variations in the source magnitude (peak-to-peak ∆ V glyph[similarequal] 0 . 35 mag, ∆ R glyph[similarequal] 0 . 30 mag and ∆ I glyph[similarequal] 0 . 20 mag), which could be due to density fluctuations in the infalling gas on to the star. Our lightcurve of V1647 Ori does not show any 56 day periodicity which was reported by Acosta-Pulido et al. (2007) during the first 2003 outburst. Based on the correlated reddening of flux during the minima of light curve, they proposed that periodicity was due to occultation of a dense clump in accretion disc at a distance of 0.25 AU from the star. The peak-to-peak amplitude in I -band was ∼ 0.3 mag in 2003. We have not detected this variability in 2008 outburst which implies the dense clump might have got dissipated between 2003 and 2008 outburst events. Our Lomb-Scargle periodogram analysis of magnitudes did not show any other statistically significant periodicity. The optical magnitudes during the second outburst are almost similar to that of the first outburst in 2003. In fact the first known outburst of V1647 Ori in 1966 ( ∼ 38 years prior to 2003), reported by Aspin et al. (2006), also had similar magnitude to the present one, however, all these three outbursts have different timescales. Implications of this fact on outburst model will be discussed in Section 4. Our NIR J , H and K magnitudes are listed in Table 3. Similar to optical light curve, there is a faint dimming trend in NIR also. Venkata Raman et al. (2013), with more NIR data points, estimated the fading rate in J -band to be 0.08 ± 0 . 02 mag yr -1 . The J -H/H -K color-color (CC) diagram (Figure 5) shows the movement of V1647 Ori from 2007 data point taken in quiescent phase to outburst state. It is similar to what was seen in 2003 outburst. From the quiescent phase position in CC diagram, V1647 Ori has moved towards the classical T-Tauri (CTT) locus along the redenning vector and presently occupies the same position as in 2003 outburst. The position of V1647 Ori in CC diagram is consistent with similar CC diagram published by Venkata Raman et al. (2013). This implies that the decrease in line of sight extinction during the outburst is same as that seen during the 2003 outburst. Since our line of sight is through the envelope, it must be likely due to a reversible mechanism like dust sublimation in the inner region of en- elope during each outburst (Acosta-Pulido et al. 2007; Mosoni et al. 2013; Aspin et al. 2009). Since the star is deeply embedded, we have reflections and dust emission effects also affecting the position of V1647 Ori in the CC diagram. So the extinction estimated from CC diagram is not very reliable. Otherwise, we can see that the second outburst has cleared out circumstellar matter of δA V ∼ 6 ± 2 mag. This is also consistent with the estimate of extinction change during first outburst by Mosoni et al. (2013), δA V ∼ 4 . 5 mag (see also Aspin et al. (2008)).\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"3.2. Morphological Results\",\n \"content\": \"Between 2003 and 2008 outbursts, the McNeil's nebula does not have any significant morphological changes, however the intensity distribution of the nebula has changed between the outbursts. Figure 6 shows the difference in R -band flux along the nebula between 2011 and 2004. Images of similar atmospheric conditions were taken and scaled to match the brightness of V1647 Ori before subtracting 2004 image from that of 2011. Brighter shade implies that region is brighter in 2011 than 2004. We can see that the region C is brighter in second outburst than it was in 2004. This could be due to dust clearing up between the last two outbursts along the cavity seen in NIR in region C direction (Ojha et al. 2005). Our photometric results show region C is dimming faster than V1647 Ori and one of the explanations for that could be material inflow into cavity during the outburst. However, region C is relatively brighter in 2008 outburst than in 2004 for the same brightness of V1647 Ori. This implies that the matter inflow to cavity was not occurring during the quiescent phase between 2006 and 2008. This is also based on the implicit assumption that the extinction along the line of sight direction to V1647 Ori is same between 2003 and 2008 outbursts. The other significant change is in illumination of the south-western knot (region B) of the nebula; its illumination seems to have shifted slightly towards west. These illumination changes in nebula imply a structural change in the circumstellar matter above the disc and cavity. A similar pattern and conclusion were also reported between 1966, 2003 and 2008 outbursts by Aspin et al. (2006, 2009). Similar analysis of image pairs taken between 2008 and 2012 did not show any significant morphological changes. Our image pairs had a seeing of 1.6 '' . Hence, to check whether any change in illumination of nebula is undergoing during the present outburst, we need images with seeing less than 1.6 '' .\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"3.3. Spectroscopic Results\",\n \"content\": \"V1647 Ori optical spectra show strong H α (6563 ˚ A ) emission and Ca II IR triplet at 8498, 8542 and 8662 ˚ A in emission. Other weak lines seen are Na D (5890+5896 ˚ A ) and OI (7773 ˚ A ) in absorption, and [O I] (6300 ˚ A ), O I (8446 ˚ A ), [Fe II] (7155 ˚ A ) and Fe I (8388, 8514 ˚ A ) in emission (see Figure 7). The equivalent widths of H α , Ca II IR triplet lines and OI (7773 ˚ A ) are listed in Table 4.\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"3.3.1. H α line\",\n \"content\": \"Strong Hα line in V1647 Ori shows a clear P-Cygni profile as well as substantial variations. Figure 8 shows the variations of Hα profiles during our four and a half years of observations. P-Cygni profiles were more prominent in early part of the outburst in 2008. To see the absorption component clearly, a Gaussian is fitted to the right wing of the profile in red color and the difference of the fit to actual spectra is plotted in green color. Figure 9 shows the outflow velocity and associated error bar of expanding wind from the blue-shifted absorption minima in Hα profile. These blue-shifted absorption components were present in 2003 outburst also and disappeared during the fading stage of the outburst (Ojha et al. 2006; Fedele et al. 2007). Figure 10 shows the variation in equivalent width ( W λ in ˚ A ) of Hα emission. The calculation of W λ was very sensitive to the weak continuum flux around λ 6563 ˚ A , and the error estimate for each data point is ∼ ± 3 ˚ A . The W λ of 2008 outburst is in similar range of that during first outburst in 2003. Since Hα emission comes from the innermost accretion powered hot zone, we can expect its strength to be proportional to the accretion rate. The optical photometric magnitude in second outburst is similar to that of first outburst, which implies the continuum flux is almost of the same value. Hence from the fact that W λ is of similar value as of first outburst, we can deduce that the accretion rate is also of the same order in both the outbursts during its 'high plateau'stage.\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"3.3.2. Ca II IR triplet lines\",\n \"content\": \"The plots of equivalent widths of Ca II IR triplet lines (8498, 8542 and 8662 ˚ A ) are shown in Figure 11. We have much lesser error bars ( ± 0 . 5 ˚ A ) for the W λ due to the higher continuum flux in these wavelengths. The Ca II IR triplet emission lines are seen to be in the ratio 1 . 07 ± 0 . 09 : 1 . 15 ± 0 . 1 : 1. This nearly equal ratio is due to optically thick gas with the collision decay rates larger than the effective radiative decay rates of upper states of Ca II lines. Such environment is typically seen in many T-Tauri stars. Optical thickness along with the non-detection of forbidden [Ca II] lines above noise, implies number density of electrons to be ≈ 10 11 cm -3 (Hamann & Persson 1992). For comparison with Figure 8 of Hamann & Persson (1992), Figure 12 shows the scatter plot between the ratios of equivalent widths, W λ 8498 / W λ 8542 and W λ 8662 / W λ 8542 , of our data as well as previously published data from literature. The error bar in our new data (black squares) is ± 0 . 1. From the position of 2007 data point (red diamond) taken during quiescent phase (Aspin et al. 2008) in this scatter plot, Aspin et al. (2008, 2009) had concluded that the optical density of the region emitting Ca II IR triplet lines changed significantly between outburst and quiescent phases. But since there is only one data point from quiescent phase and it is lying within the scatter of points from ongoing outburst, it might be difficult to conclude that the change in ratios observed was actually due to V1647 Ori moving from quiescent phase to outburst phase. We could see strong correlation between the equivalent widths ( W λ ) of Ca II IR triplet lines (see Figure 13). The Pearson correlation coefficient (PCC) between both W λ 8662 and W λ 8498 , and W λ 8542 and W λ 8498 is 0.88 with a 2-tailed p value glyph[lessmuch] 0 . 0001. This implies that the fluctuations in W λ are not random statistical error. It could be due to fluctuations of continuum flux around λ 8500 ˚ A . Peak-to- W λ is ∼ 5 ˚ A , which means if the flux from these lines is assumed to be constant then the continuum flux has fluctuated by a factor of ∼ 1 . 6, which in terms of the log scale of magnitude is ∼ 0 . 5. This indeed matches with peak-to-peak fluctuation in I -band magnitude during the entire period. We do not see any strong correlation between W λ of Hα line and Ca II IR triplets. However, it should be noted that the error bars in W λ of Hα are much higher than that of Ca II IR lines due to low continuum flux around λ 6563 ˚ A . In 2008 October 29 spectrum, we could clearly detect P-Cygni profile in Ca II IR triplet lines (Figure 14). The strengths of absorption trough of the three lines were in the same pattern as that of T-Tauri star WL 22 (Hamann & Persson 1992), i.e. the pattern with strongest absorption in λ 8542 ˚ A , then λ 8662 ˚ A and very weak in λ 8498 ˚ A . The ratio of W λ of the blue-shifted absorption between λ 8542 ˚ A and λ 8662 ˚ A is 0.76 : 0.45 =1.69 : 1. This ratio is consistent within error bars to the 1.8 : 1 ratio of intensity from atomic transition strength of these lines. Hence, unlike the region producing emission lines, this absorption regions are optically thin. So by using optically thin assumption, we can estimate the column density of Ca II by the formula (Spitzer 1978): lu A where the oscillator strength f lu for the lines 8542 and 8662 ˚ A are 0.39355 and 0.21478 respectively, taken from Merle et al. (2011). Substituting the W λ , wavelength and oscillator strength for both the lines, we get the column density ( N CaII ) as 2 . 9 × 10 12 cm -2 and 3 × 10 12 cm -2 respectively. This is the column density of Ca II atoms in this small duration of outflow wind. Assuming reasonable estimates of temperature T= 2600K (disc temperature estimated by Rettig et al. (2005)) and pressure P=1 Pascal (typical pressure in solar winds), we get the fraction of ionisation using Saha's formula to be ≈ 0 . 004. Hence, dividing by this fraction we obtain the column density of Ca atoms in gas blob to be ≈ 7 . 5 × 10 14 cm -2 . Assuming solar metalicity, we obtained column density of hydrogen (H) in outflowing gas blob as ≈ 3 . 4 × 10 20 cm -2 . From the doppler shift of the absorption minima, we also obtained the wind velocity to be 313 ± 10 km s -1 (in λ 8542 ˚ A line) and 303 ± 10 km s -1 (in λ 8662 ˚ A line). We also detected a faint P-Cygni profile in λ 8542 ˚ A line on 2008 December 30, with a blue-shifted velocity of 329 ± 10 km s -1 . Apart from these two episodic events, none of our other spectra show any detectable P-Cygni profile. The episodic nature of these two winds implies they are magnetic reconnection driven winds rather than pressure driven steady winds. Even though our medium resolution spectra cannot be used to study line widths, since the Ca II IR triplets are near by, we could do relative comparison of the widths of the Ca II IR triplet lines, where width is taken to be the full width half maximum (FWHM) of Gaussian fit of the continuum normalised profile. Since this quantity is the FWHM of Gaussian profile that we get after the convolution of instrument response on the actual line, it is not the FWHM of the line. However, since the lines are very close and the instrumental convolution is common, the wider line will give a wider FWHM after convolution. Figure 15 shows a scatter plot of the ratio of the widths of λ 8498 ˚ A and λ 8542 ˚ A versus equivalent width of the line λ 8542 ˚ A . Most of the points lie below 1.0 in the ratio axis. Using the 'test statistic' for mean with 34 data points, we could reject null hypothesis H o : The mean of the ratio is 1, with 6 sigma confidence. This shows that the λ 8498 ˚ A line is slightly narrower than λ 8542 ˚ A line. Similar trend is seen in most of the T-Tauri stars (Hamann & Persson 1992). Apart from showing this skewness, since our spectra are of only medium resolution, we cannot quantify the narrowness of the line. This narrowness of optically thinner line λ 8498 ˚ A could be explained by either substantial opacity broadening in λ 8542 ˚ A (since 1:9 is the ratio of atomic line strength) or by lower dispersion velocity in the inner part of the region of Ca II IR emission (Hamann & Persson 1992). Our period search in the equivalent width ( W λ ) of Ca II IR triplet lines found six faint periodicities in all three lines in the range of 1 - 100 days with ∼ 2 sigma confidence level in amplitude. The possible periodicities and confidence were estimated by Lomb-Scargle periodogram along with Monte Carlo simulation. The possible periods are 3.39, 8.09, 27.94, 30.8, 40.77 and 45.81 day. Since the amplitudes are only of 2 sigma confidence level, they can be confirmed only with more observations. Figure Set 16 shows the folded data of the entire four and a half year observations and the statistical significance of the amplitudes. The amplitude of the least square fitted cosine function is ∼ 1. If this periodicity is due to change in the continuum flux, the corresponding amplitude of magnitude change we expect in logarithmatic I -band magnitude is ∼ 0 . 1. This is not much above our error in magnitude estimate, so the fact that we do not see similar periodicity in I -band magnitude does not rule out the cause of change in W λ as change in continuum flux. We also do not see any corresponding significant periodicity in W λ of H α . Aspin et al. (2008) took the spectrum of V1647 Ori during the quiescent phase in February 2007. The W λ of both Ca II IR triplet lines and H α were ∼ 3 . 3 times the present value. Aspin & Reipurth (2009) had used ratio of W λ of H α between 2003 outburst and quiescent phase to estimate change in accretion rate. Similarly, since the continuum flux changed by a factor of ∼ 40 between the quiescent and 2008 outburst phase, we can estimate that the change in the line flux of both set of lines is by a factor of ∼ 10. This agrees with the change in accretion rate. Thus the origin of Ca II IR triplet lines are directly connected to the accretion rate just like H α . This is in agreement with finding of tight correlation between Ca II IR line flux and accretion rate in T-Tauri stars by Muzerolle et al. (1998), which suggests the origin of these lines to be in the magnetospheric infall zone. The similar value of W λ of Ca II IR lines with that of 2003 also strengthens the claim that the accretion rate on to the star from inner disc was same during both the outbursts.\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"3.3.3. Oxygen lines\",\n \"content\": \"The most prominent oxygen line is OI 7773 ˚ A in absorption, however, weak OI 8446 ˚ A line is also detected in emission. We should be careful in interpreting the W λ of OI λ 7773 ˚ A absorption line because the profile shape of the line seems to be a combination of red-shifted emis- component and more stronger blue-shifted absorption component (see Figure 7). A weak anti-correlation is seen between H α and OI λ 7773 ˚ A (see Figure 17). Correlation had PCC = 0.54, with a 2 tailed p value of 0.001. This anti-correlation in W λ of OI 7773 ˚ A and H α could be due to positive correlation between emission component of OI λ 7773 ˚ A filling in the absorption dip and H α . Since OI λ 7773 ˚ A cannot be formed in photosphere of cool stars, the absorption component is due to warm gas in the envelope or hot photosphere above disc, while the emission component might be due to the hot gas region from which H α is also being emitted. Ojha et al. (2006) reported a decreasing trend in the W λ of OI λ 7773 ˚ A from the beginning till end of the 2003 outburst which was interpreted to be possible decrease in turbulence in outer envelope during the outburst period. We do not see such a trend in 2008 outburst, but the values of W λ in 2008 outburst remain same as that during the second half of the 2003 outburst. A slight decrease of W λ in the later part of 2003 outburst observed on 2005 September 8, as reported by Ojha et al. (2006), in contrast to the increase of W λ of other lines, could be due to increase in the W λ of OI λ 7773 ˚ A emission component.\",\n \"pages\": [\n 6,\n 7\n ]\n },\n {\n \"title\": \"3.3.4. Forbidden lines\",\n \"content\": \"We detected [O I] (6300 ˚ A ) and [Fe II] (7155 ˚ A ) forbidden line emissions in V1647 Ori's spectra. The presence of [O I] λ 6300 ˚ A and [Fe II] λ 7155 ˚ A implies shock regions probably originating from jets. This combined with non-detection of [S II] (6731 ˚ A ) line above our noise level implies the shock region has temperature T ≈ 9000 -11000 K and electron number density ≈ 10 5 -10 6 cm -3 (Hamann 1994). We see significant variations in the strengths of the forbidden lines [O I] and [Fe II], however, the lines are too faint in our individual spectra to quantify statistically. During the fading stage of 2003 outburst in 2006 January, when the bright continuum flux decreased, Fedele et al. (2007) were also able to detect various strong forbidden line emissions, namely [O I] λλ 6300 ˚ A, 6363 ˚ A , [S II] λλ 6717 ˚ A, 6731 ˚ A and [Fe II] λ 7172 ˚ A .\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"4. IMPLICATION ON MODELS OF OUTBURST\",\n \"content\": \"The models which are known for FUor / EXor outbursts can be broadly classified into three. First kind of model is purely a thermal instability model, initially proposed for dwarf nova systems and was later adapted for FUors kind of outbursts (Bell & Lin 1994). The second kind of model involves a binary companion or planet, which perturbs the disc causing repeated sudden high accretion events (Bonnell & Bastien 1992; Lodato & Clarke 2004 ). The third kind involves mainly gravitational instability triggering magnetorotational instability (MRI) (Zhu et al. 2009, and references therein). Bell & Lin (1994) model (hereafter BL94) is a pure thermal instability model. In BL94, the thermal instability is triggered when the surface density at a region in disc rises above a critical density. The viscous timescales determine duration of outbursts and quiescent phase. The inner region at a radius r during outburst will deplete below the critical surface density in viscous time scale τ visc = r 2 /ν . Based on α prescription of viscosity, ν = αc s H , where c s is the isothermal sound speed, H ≈ c s / Ω is the disc thickness, Ω is orbital angular velocity at radius r and α ( < 1) is a dimensionless parameter (see Figure 18). Substituting, we get a relation :\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"τ visc = r 2 Ω αc 2 s = 1 α Ω ( r H ) 2 .\",\n \"content\": \"Let v R ≈ r/τ visc ≈ ν/r be the effective inward radial velocity component of gas in inner accretion disc. Then the mass infall rate at radius R is ˙ M = -2 πR Σ v R , where Σ is the surface density of disc at that radius. Substituting v R , ν and H in above equation of ˙ M , we get ˙ M ≈ 2 π Σ αc 2 s / Ω. The time scale of transition between outburst and quiescent phases is much smaller than the viscous timescale. Hence, Σ will remain constant, Ω will also remain constant at a given R , which leaves only the parameter αc 2 s to explain the change by a factor of ∼ 10 in inner disc accretion rate to V1647 Ori between the outburst and quiescent phases. Since the square of isothermal sound speed c 2 s = R g T/µ (where R g is the gas constant, T is temperature and µ is mean molecular weight), the temperature change by a factor 10 between the phases at the trigger of thermal instability (Zhu et al. (2009), Appendix B, their Figure 14) alone will cause a net change in accretion rate by factor of 10. Hence, at least in the inner region of disc, α can change only by a multiplicative factor of order 1 to remain consistent with the observed change in accretion rate. In BL94, assuming the mass infall rate to the inner disc region ˙ M in = constant , the α determines the timescales and the ratio α outburst /α quiescent is proportional to the ratio of time in quiescent phase to time in outburst phase (BL94; Table 2). Figure 19 shows the schematic of the lightcurve of V1647 Ori in optical band we know so far. The photometric magnitudes and overall SED during the quiescent phase in 2007 match with pre 2003 outburst data (Aspin et al. 2008). Even though accretion rate had fallen by a factor of 10 during quiescent phase, it was still in the order of 10 -6 M glyph[circledot] yr -1 . Based on this, Aspin et al. (2009) had suggested that the 2003 outburst might not have actually terminated in 2006. Since we do not have a good estimate of pre-outburst accretion rate, we shall consider this sudden drop in accretion rate by a factor of 10 as a drop from outburst state to quiescent phase in outburst models. Let α o 1 , α o 2 and α o 3 represent the three outburst phase α values and α q 1 and α q 2 represent the two quiescent phase α values. If we assume ˙ M in = constant in BL94, from the ratio of periods, we get the following relations: α o 1 = k (22 -89) α q 1 ; α o 2 = k 21 α q 1 ; α o 3 < k 9 α q 1 ; α o 3 < k 0 . 6 α q 2 ; where k is just the proportionality constant corresponding to the constant ˙ M in . We also get α o 2 = (0 . 23 -0 . 95) α o 1 ; α o 3 < 0 . 4 α o 2 ; α q 2 = 15 α q 1 . This is a very huge variation in α parameter. However, our accretion estimates, during the 2003 as well as 2008 outbursts show the accretion rate of matter on to the star from inner disc was quite stable at ∼ 10 times the rate in quiescent phase. Thus the α parameter cannot be fluctuating as much as we estimated; especially α o 3 < k 0 . 6 α q 2 is impossible from the fact that viscosity has to be more in outburst phase than quiescent phase. Then the assumption ˙ M in = constant in BL94 might be wrong. An increase in ˙ M in can decrease the draining rate of inner disc and can account for a longer duration of outburst period. It can also explain the slower rate of dimming in the magnitude of the V1647 Ori during its plateau stage in present outburst compared to 2003 outburst. By letting ˙ M in to be a variable and substituting R limit to be the radius upto which instability extends, to constrain parameters, we compared the viscous timescale τ visc = R 2 limit /ν ≈ R 2 limit Ω /αc 2 s between 2003 and 2008 outbursts. The instability triggering temperature at the boundary has to be same for both outbursts, so the sound speed c s will be the same. Parameter α can also be taken to be same during both the outbursts based on our previous conclusion. Now the only free variable parameter which determines the timescale is R limit . Substituting Keplarian Ω ∝ R -3 2 , we finally obtain the relation for viscous timescale in terms of R to be τ ∝ R 1 2 . limit visc limit BL94 gives the radius upto which instability extends to be : ˙ 1 Substituting this proportionality, we get τ visc ∝ M 6 in . Thus the ratios of mass infall rate from outer to inner disc during each outburst is related to the duration of outburst by the relation ˙ M in 2008 ˙ M in 2003 > ( 52 21 ) 6 ≈ 230. Thus the infall of gas from outer to inner disc during 2008 outburst is at least 230 times (2 orders) more than that during 2003 outburst. Model presented by Zhu et al. (2010) includes an MRI instability contribution to viscosity parameter if the temperature of the disc goes above MRI triggering temperature ( T M ) and also includes an effective viscosity contribution from gravitational instability beyond the radius given by Toomre's instability parameter Q. The relation between R limit and ˙ M in this model is R limit ∝ ˙ M 2 9 2003 Therefore, the infall of gas from outer to inner disc during 2008 outburst is at least 3500 times (3 orders) more than that during 2003 outburst. This estimate is one order more than BL94. It should be kept in mind that the viscosity timescale gives only order of magnitude estimate of the duration of outburst. For a comparison of actual simulated duration of outburst and viscous timescale see Table 1 in Zhu et al. (2010). If the present outburst continues for a larger period, ˙ M in 2008 ˙ M in 2003 ratio will further increase. Since we have an upper limit in ˙ M in for FUors, the increased ratio could only be explained as a dip in mass inflow in 2003. For example, a gap in disc could have resulted in sudden ending of 2003 outburst. This gap or low density region has to be near the typical R limit predicted by each model, i.e. ∼ 1 AU . To estimate the change in photometric magnitudes between 2003 and 2008 outburst phase due to predicted change in radius R limit , we modelled a disc with temperature profile given by outburst accretion rate inside R limit and quiescent accretion rate outside R limit . The magnitude variations in optical I and NIR J bands were found to be less than 1 mag for variation of R limit by a factor of 6. Mosoni et al. (2013) reported an increase in visibility of resolved interferometric study of V1647 Ori using VLTI/MIDI observations in 8-13 µ m range during the early stage of fading in 2003 outburst (between 2005 March and 2005 September). Apart from the possible scenarios discussed by Mosoni et al. (2013), it could also be explained by the relative increase in contribution in total flux from the extended outburst disc when the central star's accretion slowed down. A similar VLTI/MIDI visibility study of the ongoing 2008 outburst will give more input to constrain R limit and outburst models. Thus, we conclude that a pure thermal instability alone cannot explain the varying timescales of outbursts occurring in V1647 Ori. As proposed for other short rise timescale FUors, V1647 Ori can also be explained only by an outside-in triggering of the instability from outer radius (Bell & Lin 1994). The change in inflow of material from outer to inner disc could be due to many possibilities like MRI, gravitational instability (GI) or planet perturbation. The smooth surface density assumptions of disc also might not be a good model in light of detection of clump in the disc at 0.27 AU and disappearance of it in second outburst. Our observations detected a variety of episodic events like sudden short duration winds with hydrogen column density ≈ 3 . 4 × 10 20 cm -2 , fluctuations in H α flux, short timescale variation in continuum flux etc. The short timescale variation in continuum flux could be explained by the convections in the inner disc as suggested by Zhu et al. (2009) for their model of FU Orionis disc. The variations in Hα flux could have origin in some magnetic phenomena in the accretion funnel. The episodic wind events, [Fe II] λ 7155 and [OI] λ 6300 could be originating from jets or disc/stellar winds region. If we compare between 2008 and 2003 outbursts, the accretion rate on to the star from inner disc, extinction in NIR colorcolor diagram, outburst magnitude and spectral signatures in optical are the same. The main difference between 2008 compared to 2003 is the larger duration of outburst phase, 6 times slower dimming rate in optical during its 'plateau' stage and the change in circumstellar gas distribution revealed by morphological change in nebula's illumination.\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"5. CONCLUSIONS\",\n \"content\": \"We have carried out four and a half years of continuous monitoring of V1647 Ori in its second outburst phase starting from 2008. Following are our main conclusions: in 2008 October and December. From Ca II IR triplet and H α line strengths, the accretion rate was found to be same as that during the 2003 outburst and is ∼ 10 times more than quiescent phase. the framework of instability models we conclude that the sudden ending of 2003 outburst could be due to a gap or low density region in inner ( ∼ 1 AU) disc. We thank the anonymous referee for giving us invaluable comments and suggestions that improved the content of the paper. The authors thank the staff of HCT, operated by Indian Institute of Astrophysics, Bangalore and IGO at Girawali, operated by Inter-University Centre for Astronomy and Astrophysics, Pune for their assistance and support during observations. It is a pleasure to thank J. S. Joshi and all the members of the Infrared Astronomy Group of TIFR for their support during the TIRCAM2 campaign. All the plots were generated using the 2D graphics environment Matplotlib (Hunter 2007).\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"' Abrah'am, P., Mosoni, L., Henning, T., et al. 2006, A&A, 449, 13 Acosta-Pulido, J. A., Kun, M., ' Abrah'am, P., et al. 2007, AJ, 133, 2020 Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90 Lodato, G. & Clarke, C.J. 2004, MNRAS, 353, 841 McNeil, J.W. 2004, IAU Circ. 8284 . Due to limited spectral range in IGO grism, Ca II triplet lines were not observed from IGO. Note . - Table 1 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content. Note . - Table 2 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content. †† Observed from IGO, all other nights are from HCT. Note . - Estimated error in magnitude is ≤ ± 0.1 ( K ) and ≤ ± 0.05 ( H and J ). Note . -Table 4 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.\",\n \"pages\": [\n 9,\n 19,\n 20,\n 29,\n 30\n ]\n }\n]"}}},{"rowIdx":77,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...779..145N"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1310.4824.pdf"},"content":{"kind":"string","value":"\nA TIDALLY-STRIPPED STELLAR COMPONENT OF THE MAGELLANIC BRIDGE\nDavid L. Nidever 1,2 , Antonela Monachesi 1 , Eric F. Bell 1 , Steven R. Majewski 2 , Ricardo R. Mu˜noz 3 , Rachael L. Beaton 2\nDraft version September 14, 2021\nABSTRACT\nDeep photometry of the Small Magellanic Cloud (SMC) stellar periphery ( R =4 · , 4.2 kpc) is used to study its line-of-sight depth with red clump (RC) stars. The RC luminosity function is affected little by young ( glyph[lessorsimilar] 1 Gyr) blue-loop stars in these regions because their main-sequence counterparts are not observed in the color magnitude diagrams. The SMC's eastern side is found to have a large line-of-sight depth ( ∼ 23 kpc) while the western side has a much shallower depth ( ∼ 10 kpc), consistent with previous photographic plate photometry results. We use a model SMC RC luminosity function to deconvolve the observed RC magnitudes and construct the density function in distance for our fields. Three of the eastern fields show a distance bimodality with one component at the 'systemic' ∼ 67 kpc SMC distance and a second component at ∼ 55 kpc. Our data are not reproduced well by the various extant Magellanic Cloud and Stream simulations. However, the models predict that the known H I Magellanic Bridge (stretching from the SMC eastward towards the LMC) has a decreasing distance with angle from the SMC and should be seen in both the gaseous and stellar components. From comparison with these models we conclude that the most likely explanation for our newly identified ∼ 55 kpc stellar structure in the eastern SMC is a stellar counterpart of the H I Magellanic Bridge that was tidally stripped from the SMC ∼ 200 Myr ago during a close encounter with the LMC. This discovery has important implications for microlensing surveys of the SMC.\nSubject headings: Galaxies: interactions - Local Group - Magellanic Clouds - Galaxies: dwarf Galaxies: individual (SMC) - Galaxies: photometry\n1. INTRODUCTION\nThe Large and Small Magellanic Clouds (LMC and SMC respectively) are the two largest satellite galaxies of the Milky Way (MW) and, due to their proximity, offer the best possibility for detailed study of dwarf galaxies, especially interacting dwarf irregulars. One of the most striking features of the Magellanic system is the vast extent of its H I component - including the 200 · -long Magellanic Stream (MS) and Leading Arm (Nidever et al. 2010) as well as the Magellanic Bridge (Muller et al. 2003). These gaseous structures are the result of past interactions of the Magellanic Clouds (MCs) with each other and the MW galaxy (Murai & Fujimoto 1980; Gardiner & Noguchi 1996; Connors et al. 2006; R˚uˇziˇcka et al. 2010; Diaz & Bekki 2012; Besla et al. 2010, 2012, 2013). The Magellanic Bridge is widely believed to have been tidally stripped from the SMC by a recent close encounter with the LMC ∼ 200 Myr ago (e.g., Muller & Bekki 2007).\nWhile the evidence of MC interactions is quite evident in H I it is less obvious in the stellar structures of the Clouds. The SMC, which is approximately ten times less massive than the LMC, is more likely to be affected by any past interactions (and is the source of much of the MS H I material in many models), and, therefore, may be the most obvious place to search for stellar signs of tidal disturbances.\n\n1 Dept. of Astronomy, University of Michigan, Ann Arbor, MI, 48104, USA (dnidever@umich.edu)\n2 Dept. of Astronomy, University of Virginia, Charlottesville, VA, 22904-4325, USA\n3 Departamento de Astronom'ıa, Universidad de Chile, Casilla 36-D, Santiago, Chile (rmunoz@das.uchile.cl)\n\nTwo decades ago, a series of papers analyzing photographic plate photometry (Hatzidimitriou et al. 1989) reaching to just below the SMC horizontal branch (HB) performed the first detailed study of the SMC stellar periphery. Using red clump (RC) stars as standard candles in two fields, Hatzidimitriou & Hawkins (1989) found the line-of-sight depth to be much larger in the northeast than in the southwest. Follow-up spectroscopy showed a correlation between distance and radial velocity (RV) in the northeast RC stars (Hatzidimitriou et al. 1993) similar to that seen by Mathewson et al. (1986) in Cepheid variables closer to the center. Gardiner & Hatzidimitriou (1992) used the photographic plate photometry of all their SMC fields to trace HB stars to R ∼ 5 · in all directions, uncovering a fairly symmetric structure but with a quick decline in density towards the west. In contrast, the young main-sequence stars have a much more irregular shape extending towards the LMC into the Magellanic Bridge region (see black contours in Fig. 1). Gardiner & Hawkins (1991) found that the change of line-of-sight depth with radius in the western SMC, increasing with radius, was more consistent with a spheroidal than disklike structure. The notion of the stellar SMC having a spheroidal structure is argued by Zaritsky et al. (2000) and supported by a recent spectroscopic study of ∼ 2000 red giant branch (RGB) stars in the central 4 kpc × 2 kpc of the SMC that found no sign of rotation (Harris & Zaritsky 2006). In contrast, rotation is observed in the H I component of the SMC (Stanimirovi'c et al. 2004). Many of the structural and kinematical features of the SMC are reproduced by the LMC-SMC-MW interaction simulations of Bekki & Chiba (2009) by using a spheroidal stellar distribution and extended gaseous disk.\nMore recent work on the SMC periphery has shown it to extend much further than previously thought. Noel & Gallart (2007) detected intermediate-age and old stars in deep photometric data at ∼ 6 · south of the SMC center, while De Propris et al. (2010) found spectroscopicallyconfirmed RGB stars out to R ∼ 6 · in the eastern SMC. Nidever et al. (2011) used photometrically-selected RGB stars to trace the structure of the SMC periphery to R ∼ 11 · (in multiple directions) and showed that the SMC has a fairly azimuthally-symmetric structure. Nidever et al. also found that the center of the outer SMC population ( R> 4 · ) is offset by ∼ 0.6 · (to the east) from the center of the inner population ( R glyph[lessorsimilar] 3 · ) and postulated that this is due to a perspective effect because, on average, the stars to the eastern side are closer than the stars on the western side. In addition, Bagheri et al. (2013) used 2MASS and WISE catalogs to find evidence for some candidate older stars in the region between the Magellanic Clouds, while Noel et al. (2013) used deep photometry to find intermediate-age stars in a field at ∼ 7 · from the SMC in the Magellanic Bridge.\nVariable stars and stars clusters have been widely used to study the 3D structure of the inner SMC. Several studies in the 1980s found a large line-of-sight depth in the central SMC using young Cepheids (Mathewson et al. 1986, 1988), with Caldwell & Coulson (1986) finding hints of two arms in the southwest. Haschke et al. (2012) used multi-epoch OGLE-III (Udalski et al. 2008) photometry to study the 3D distribution of cepheids ( ∼ 30300 Myr old) and RR Lyrae ( glyph[greaterorsimilar] 10 Gyr old) stars in the inner SMC ( R< 2 · ). While both populations are found to have an extended scale height, the older stars have a fairly homogeneous distribution whereas the young stars are in an inclined orientation that is closer in the northeast than in the southwest. Finally, Crowl et al. (2001) used populous SMC clusters to study the line-of-sight depth in the inner SMC ( R glyph[lessorsimilar] 3 kpc) and found a ± 1 σ depth between ∼ 6 and ∼ 12 kpc.\nEven with all of these studies, the detailed 3D structure of the SMC stellar periphery is still not well understood in large part due to the lack of high-quality, wide-area CCD photometry in this region of the southern sky. This is unfortunate because this knowledge would enable us not only to produce a better 3D map of the SMC but also provide us with observational data of collisionless particles that would much better constrain the recent ( ∼ 200 Myr) close encounter of the MCs with each other. It is thought that during that encounter the SMC might have passed right through the LMC disk (Besla et al. 2012) and produced the H I Magellanic Bridge.\nIn this paper we use deep Washington M and T 2 photometry from the MAgellanic Periphery Survey (MAPS) to study the line-of-sight depth of core helium-burning RC stars in the SMC periphery. We find a much larger line-of-sight depth ( ∼ 23 kpc) in four eastern fields than in our four western fields ( ∼ 10 kpc), and a distance bimodality in three eastern fields with a newly identified component at ∼ 55 kpc ( ∼ 12 kpc closer than the component at the 'systemic', ∼ 67 kpc SMC distance) that is most likely an intermediate-age/old stellar counterpart of the recently tidally-stripped H I Magellanic Bridge. In Section 2 we briefly describe the observations and main features of the color magnitude diagrams (CMDs). We argue in Section 3 that the extended RC seen in many of\n\n\n
Fig. 1.Map of the SMC showing our CTIO-4m+MOSAIC fields as filled squares (red-shallow, purple-deep). A circle at R SMC =4 · highlights the eight fields used in our analysis. The colored image of the SMC shows the RGB starcounts using the combined Magellanic Clouds Photometric Survey (Zaritsky et al. 2002) and OGLE-III (Udalski et al. 2008) photometry (for R glyph[lessorsimilar] 2 · ) and RC starcounts from the photographic plate photometry of Hatzidimitriou et al. (1989) at larger radii. The LMC is shown in RGB starcounts selected from 2MASS (Skrutskie et al. 2006). The black contours indicate the HI in the Magellanic Clouds and Bridge from Bruns et al. (2005) at levels of log( N HI )=20.7, 21.1, 21.5 and 21.9.
\n\nour CMDs are due to large line-of-sight depths and not population effects. Density distributions as a function of distance are derived in Section 4 and compared to simulations in Section 5. Finally, a discussion of the results and their implications are presented in Section 6 and a brief summary in Section 7.\n2. DATA\nWe use CTIO-4m+MOSAIC Washington M and T 2 (equivalent to I C ) photometry from the MAgellanic Periphery Survey (MAPS) for our analysis. The observations and data reduction are described in Nidever et al. (2011). Figure 1 shows the MAPS fields (filled squares) in the area of the SMC. While we have 'deep' photometry (to M ∼ 24) in fields extending to R ≈ 12 · the red clump (RC) is most prominent in our R =4 · fields, which are the focus of the present study.\nFigure 2 shows the full M 0 vs. ( M -T 2 ) 0 Hess diagrams (dereddened with the Schlegel et al. 1998 extinction maps) of four, evenly spaced in azimuth, deep fields 4 at R =4 · . The SMC RGB, RC, and main-sequence stars are clearly visible. Hess diagrams of the RC region for all eight R =4 · fields are shown in Figure 3. The RC morphology clearly varies substantially from field to field. The eastern fields (PA=26-161 · ) show a much larger RC extent in magnitude than the western fields (PA=206-341 · ). It was previously noted by Hatzidimitriou & Hawkins (1989) that the horizontal branch stars in the northeast of the SMC periphery have a larger lineof-sight depth (and extend to brighter magnitudes) than in the southwest.\n4 The field names are constructured from the field's radius and position angle (east of north), i.e. 40S026 is R=4.0 · and PA=26 · .\n\n\n
Fig. 2.Hess diagrams for the four deepest fields at R =4 · showing the RGB, RC and main-sequence populations. The extended RC can be seen in the two eastern fields (40S026 and 40S116) while the two western fields display a much more compact RC. The 40S116 field is in the HI Magellanic Bridge where there is ongoing star formation and young stars extending to bright magnitudes at ( M -T 2 ) 0 ∼-0.2 can be seen.
\n\n3. THE NATURE OF THE EXTENDED RED CLUMP LUMINOSITY FUNCTION\nAn elongated distribution of the red clump (to the bright end) can be caused by reasons other than a large line-of-sight depth. The evolution of intermediate-mass He-core burning stars moves them along loops in the HR diagram at nearly constant luminosity ('blue loop' stars). Their age at a given magnitude depends on metallicity but blue loop stars are generally quite young (a few hundred Myr to 1 Gyr; Sweigart 1987; Xu & Li 2004, and references therein) and theoretical models predict that their CMD location depends strongly on metallicity (e.g., Girardi et al. 2000). Many stars pile up on the red end of the blue loops (BL) and define a nearly vertical feature that stretches to brighter magnitudes than the RC (often spanning ∼ 2-3 mag) and trending to the blue (as seen in Fig. 3 of Gallart 1998). This feature of stellar evolution can be easily confused with an extended red clump and was the primary point of contention regarding the nature of the 'vertical red clump' of the LMC identified by Zaritsky & Lin (1997); these authors interpreted the feature as an intervening stellar population but this was subsequently called into question by Beaulieu & Sackett (1998). Given this precedent, we have taken steps to rule out BL stars as the cause for the extended feature observed in the CMDs of the eastern SMC fields.\nWe have computed a synthetic CMD that reproduces the overall features of the stellar populations of the SMC in the CMD (see Fig. 2) to compare its RC and BL distributions with the elongated feature observed at the RC\nlevel. We have assumed a constant star formation rate (SFR) from 0.7 to 12 Gyr and metallicities of [Fe/H]= -1 dex ([Fe/H]= -1 . 5 dex) for stars younger (older) than 6 Gyr 5 . The model CMD was computed using the IAC-STAR code (Aparicio & Gallart 2004) adopting the BaSTI stellar library (Pietrinferni et al. 2004), a Reimers mass loss efficiency parameter value of η =0.2, and a Kroupa (2002) initial mass function (IMF) from 0.1 to 100 M glyph[circledot] . The magnitudes of the model CMD are expressed in the Johnson-Cousins photometric system; in particular we have chosen the bolometric correction library from Girardi et al. (2002). The magnitudes were transformed into the Washington M and T 2 photometric system using the transformation equations from Majewski et al. (2000). We assumed a distance modulus of 18.9 for the SMC and did not correct the model CMD due to observational effects (incompleteness and photometric errors). Given that we expect a near 100% completeness and a ∼ 2% photometric accuracy ( ∼ 0.3% internal precision) at the RC level, this correction should have little impact on the model CMD for our purposes.\nFigures 4 and 5 show the observed (a) and model (b) CMDs for the 40S026 (eastern SMC) and 40S206 (western SMC) fields, respectively. The model in Figure 4b has ages ranging from 1.4 Gyr to 12 Gyr whereas the model in Figure 5b has ages ranging from 2.0 Gyr to 12\n\n\n
Fig. 3.Hess diagrams of the RC region for the eight fields at R=4 · (arranged from left to right with increasing position angle). The Hess diagrams are scaled to the same density of SMC stars to highlight the differences in RC morphology. The four eastern fields (40S026-40S161) show an extended RC that is not seen in the western fields (40S206-40S341).
\n\nGyr. These age ranges were chosen so that the position and characteristics of the main features (main sequence, subgiant branch, tip of the RGB) are well reproduced by the models. In Figure 4, however, there is a clear difference in the RC morphology between the model and the data. We find that the RC is much less elongated in magnitude in the model than in the CMD of the observed eastern field. This discrepancy cannot be accounted for by stellar evolutionary features such as BL stars; the model predicts that there should be almost no BL stars, given that its youngest population has an age of 1.4 Gyr. A CMD model with stars as young as 0.7 Gyr predicts more BL stars, but also shows evidence of a brighter and more populous young main-sequence, which is not seen in the data. Moreover, even if the young main-sequence from the model CMD were to agree with the data, the density of the model BL stars would still be significantly lower than that of the RC stars. Figure 6a is an attempt to reproduce the morphology of the RC region of the CMD (seen in panel b) using a spread in age and star formation rate only (which requires most of the young and old stars to be removed). The resulting simulated Hess diagram is not a good representation of the observed data, particularly on the main sequence. On the other hand, the simulated Hess diagram with a distance spread (convolved with the distance function for this field found in § 4) in Figure 6c is a good representation. Thus, a BL population cannot explain the elongated RC that we observe in the eastern field. On the other hand, Figure 5 shows that the western field and model RC morphologies agree fairly well. Figures 4c and 5c show the RC luminosity function both for the data and the model. The RC stars were isolated as explained in the next section.\nNote the much wider RC distribution in the eastern field when compared with the model.\n4. DISTANCES\nTo study the distance distributions, we isolate the RC stars in the CMD. Because the RC and RGB are very close in the CMD and sometimes overlap we decided to model the RGB distributions to produce a 'clean' RC sample. A Hess density map of stars was created for each field in ( M -I ) 0 and M 0 in bins of 0.02 and 0.05 mag respectively. These were then smoothed with a Gaussian kernel having FWHM=2 bins. Each row, at a given magnitude, was modeled with a double-Gaussian for the RC and RGB over the magnitude range 18.5 \nNext, we use the model SMC CMD to construct an ab-\n2\n\n\n\n\n\n\n\n\n
Fig. 4.(a) Hess diagram of the 40S026 field in the eastern portion of the SMC. (b) Simulated CMD for the 40S026 field with ages of 1.4 to 12 Gyr. The red lines are [Fe/H]= -1.488 age=8.0 Gyr BaSTI isochrones (Pietrinferni et al. 2004) at 60 kpc. (c) Red clump luminosity function for the data (red) and simulation (black). The observed luminosity function is much broader than the model suggesting a large line-of-sight depth.
\n\n\n\n\n\n\n\n\n\n
Fig. 5.Same as Figure 4 but for the 40S206 field with model ages of 2.0 to 12 Gyr. While not as wide as the RC luminosity function of 40S026, the observed luminosity function of 40S206 is wider than the model and indicates some depth is needed to explain the observations.
\n\nsolute RC luminosity function (isolating RC stars with 1.025 \nfunction is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner.\n\n\n
Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data.
\n\nThe models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields.\n5. COMPARISON TO MODELS\nTo help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors\nsuggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream).\nFigure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to\n\n\n
Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process.
Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41.
\n\nthe east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section).\n6. DISCUSSION\nWe detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'.\nIn Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80\nkpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge.\nEven though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC.\nThe large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of\n\n\n
Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc.
\n\n\n\n
Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc.
\n\nthe SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected.\nA new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago.\n\n\n
Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component.
\n\nWhile it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the\ncentral SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012).\nIn the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC.\nWe plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure.\nFinally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV).\n7. SUMMARY\nWe use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are:\n\n1. The four eastern fields show very large line-of-sight depths ( ∼ 23 kpc) over ∼ 135 · of position angle.\n2. Three eastern fields show a strong distance bimodality with one component at ∼ 67 kpc (near the\n\nmean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances.\n\n3. The newly-found stellar component in the east at ∼ 55 kpc is qualitatively consistent with the Diaz & Bekki (2012) model distribution of particles in the tidally-stripped Magellanic Bridge, previously only detected in H I . We conclude that this new component is likely an intermediate-age/old ( ∼ 112 Gyr) stellar component of the Magellanic Bridge and call it the SMC 'eastern stellar structure'.\n\nA tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge.\nWe find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered.\nWe dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013.\nFacilities: CTIO (MOSAIC II).\nREFERENCES\nAbbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. 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J., & Tautvaisiene, G. 1998, MNRAS, 299, 535 Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ, 612, 168 R˚uˇziˇcka, A., Theis, C., & Palouˇs, J. 2010, ApJ, 725, 369 Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525 Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stanimirovi'c, S., Staveley-Smith, L., & Jones, P. A. 2004, ApJ, 604, 176 Sweigart, A. V. 1987, ApJS, 65, 95 Udalski, A., et al. 2008, Acta Astronomica, 58, 329 Xu, H. Y., & Li, Y. 2004, A&A, 418, 225 Zaritsky, D., & Lin, D. N. C. 1997, AJ, 114, 2545 Zaritsky, D., Harris, J., Grebel, E. K., & Thompson, I. B. 2000, ApJ, 534, L53\nZaritsky, D., Harris, J., Thompson, I. B., Grebel, E. K., & Massey, P. 2002, AJ, 123, 855\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"Deep photometry of the Small Magellanic Cloud (SMC) stellar periphery ( R =4 · , 4.2 kpc) is used to study its line-of-sight depth with red clump (RC) stars. The RC luminosity function is affected little by young ( glyph[lessorsimilar] 1 Gyr) blue-loop stars in these regions because their main-sequence counterparts are not observed in the color magnitude diagrams. The SMC's eastern side is found to have a large line-of-sight depth ( ∼ 23 kpc) while the western side has a much shallower depth ( ∼ 10 kpc), consistent with previous photographic plate photometry results. We use a model SMC RC luminosity function to deconvolve the observed RC magnitudes and construct the density function in distance for our fields. Three of the eastern fields show a distance bimodality with one component at the 'systemic' ∼ 67 kpc SMC distance and a second component at ∼ 55 kpc. Our data are not reproduced well by the various extant Magellanic Cloud and Stream simulations. However, the models predict that the known H I Magellanic Bridge (stretching from the SMC eastward towards the LMC) has a decreasing distance with angle from the SMC and should be seen in both the gaseous and stellar components. From comparison with these models we conclude that the most likely explanation for our newly identified ∼ 55 kpc stellar structure in the eastern SMC is a stellar counterpart of the H I Magellanic Bridge that was tidally stripped from the SMC ∼ 200 Myr ago during a close encounter with the LMC. This discovery has important implications for microlensing surveys of the SMC. Subject headings: Galaxies: interactions - Local Group - Magellanic Clouds - Galaxies: dwarf Galaxies: individual (SMC) - Galaxies: photometry","pages":[1]},{"title":"A TIDALLY-STRIPPED STELLAR COMPONENT OF THE MAGELLANIC BRIDGE","content":"David L. Nidever 1,2 , Antonela Monachesi 1 , Eric F. Bell 1 , Steven R. Majewski 2 , Ricardo R. Mu˜noz 3 , Rachael L. Beaton 2 Draft version September 14, 2021","pages":[1]},{"title":"1. INTRODUCTION","content":"The Large and Small Magellanic Clouds (LMC and SMC respectively) are the two largest satellite galaxies of the Milky Way (MW) and, due to their proximity, offer the best possibility for detailed study of dwarf galaxies, especially interacting dwarf irregulars. One of the most striking features of the Magellanic system is the vast extent of its H I component - including the 200 · -long Magellanic Stream (MS) and Leading Arm (Nidever et al. 2010) as well as the Magellanic Bridge (Muller et al. 2003). These gaseous structures are the result of past interactions of the Magellanic Clouds (MCs) with each other and the MW galaxy (Murai & Fujimoto 1980; Gardiner & Noguchi 1996; Connors et al. 2006; R˚uˇziˇcka et al. 2010; Diaz & Bekki 2012; Besla et al. 2010, 2012, 2013). The Magellanic Bridge is widely believed to have been tidally stripped from the SMC by a recent close encounter with the LMC ∼ 200 Myr ago (e.g., Muller & Bekki 2007). While the evidence of MC interactions is quite evident in H I it is less obvious in the stellar structures of the Clouds. The SMC, which is approximately ten times less massive than the LMC, is more likely to be affected by any past interactions (and is the source of much of the MS H I material in many models), and, therefore, may be the most obvious place to search for stellar signs of tidal disturbances. Two decades ago, a series of papers analyzing photographic plate photometry (Hatzidimitriou et al. 1989) reaching to just below the SMC horizontal branch (HB) performed the first detailed study of the SMC stellar periphery. Using red clump (RC) stars as standard candles in two fields, Hatzidimitriou & Hawkins (1989) found the line-of-sight depth to be much larger in the northeast than in the southwest. Follow-up spectroscopy showed a correlation between distance and radial velocity (RV) in the northeast RC stars (Hatzidimitriou et al. 1993) similar to that seen by Mathewson et al. (1986) in Cepheid variables closer to the center. Gardiner & Hatzidimitriou (1992) used the photographic plate photometry of all their SMC fields to trace HB stars to R ∼ 5 · in all directions, uncovering a fairly symmetric structure but with a quick decline in density towards the west. In contrast, the young main-sequence stars have a much more irregular shape extending towards the LMC into the Magellanic Bridge region (see black contours in Fig. 1). Gardiner & Hawkins (1991) found that the change of line-of-sight depth with radius in the western SMC, increasing with radius, was more consistent with a spheroidal than disklike structure. The notion of the stellar SMC having a spheroidal structure is argued by Zaritsky et al. (2000) and supported by a recent spectroscopic study of ∼ 2000 red giant branch (RGB) stars in the central 4 kpc × 2 kpc of the SMC that found no sign of rotation (Harris & Zaritsky 2006). In contrast, rotation is observed in the H I component of the SMC (Stanimirovi'c et al. 2004). Many of the structural and kinematical features of the SMC are reproduced by the LMC-SMC-MW interaction simulations of Bekki & Chiba (2009) by using a spheroidal stellar distribution and extended gaseous disk. More recent work on the SMC periphery has shown it to extend much further than previously thought. Noel & Gallart (2007) detected intermediate-age and old stars in deep photometric data at ∼ 6 · south of the SMC center, while De Propris et al. (2010) found spectroscopicallyconfirmed RGB stars out to R ∼ 6 · in the eastern SMC. Nidever et al. (2011) used photometrically-selected RGB stars to trace the structure of the SMC periphery to R ∼ 11 · (in multiple directions) and showed that the SMC has a fairly azimuthally-symmetric structure. Nidever et al. also found that the center of the outer SMC population ( R> 4 · ) is offset by ∼ 0.6 · (to the east) from the center of the inner population ( R glyph[lessorsimilar] 3 · ) and postulated that this is due to a perspective effect because, on average, the stars to the eastern side are closer than the stars on the western side. In addition, Bagheri et al. (2013) used 2MASS and WISE catalogs to find evidence for some candidate older stars in the region between the Magellanic Clouds, while Noel et al. (2013) used deep photometry to find intermediate-age stars in a field at ∼ 7 · from the SMC in the Magellanic Bridge. Variable stars and stars clusters have been widely used to study the 3D structure of the inner SMC. Several studies in the 1980s found a large line-of-sight depth in the central SMC using young Cepheids (Mathewson et al. 1986, 1988), with Caldwell & Coulson (1986) finding hints of two arms in the southwest. Haschke et al. (2012) used multi-epoch OGLE-III (Udalski et al. 2008) photometry to study the 3D distribution of cepheids ( ∼ 30300 Myr old) and RR Lyrae ( glyph[greaterorsimilar] 10 Gyr old) stars in the inner SMC ( R< 2 · ). While both populations are found to have an extended scale height, the older stars have a fairly homogeneous distribution whereas the young stars are in an inclined orientation that is closer in the northeast than in the southwest. Finally, Crowl et al. (2001) used populous SMC clusters to study the line-of-sight depth in the inner SMC ( R glyph[lessorsimilar] 3 kpc) and found a ± 1 σ depth between ∼ 6 and ∼ 12 kpc. Even with all of these studies, the detailed 3D structure of the SMC stellar periphery is still not well understood in large part due to the lack of high-quality, wide-area CCD photometry in this region of the southern sky. This is unfortunate because this knowledge would enable us not only to produce a better 3D map of the SMC but also provide us with observational data of collisionless particles that would much better constrain the recent ( ∼ 200 Myr) close encounter of the MCs with each other. It is thought that during that encounter the SMC might have passed right through the LMC disk (Besla et al. 2012) and produced the H I Magellanic Bridge. In this paper we use deep Washington M and T 2 photometry from the MAgellanic Periphery Survey (MAPS) to study the line-of-sight depth of core helium-burning RC stars in the SMC periphery. We find a much larger line-of-sight depth ( ∼ 23 kpc) in four eastern fields than in our four western fields ( ∼ 10 kpc), and a distance bimodality in three eastern fields with a newly identified component at ∼ 55 kpc ( ∼ 12 kpc closer than the component at the 'systemic', ∼ 67 kpc SMC distance) that is most likely an intermediate-age/old stellar counterpart of the recently tidally-stripped H I Magellanic Bridge. In Section 2 we briefly describe the observations and main features of the color magnitude diagrams (CMDs). We argue in Section 3 that the extended RC seen in many of our CMDs are due to large line-of-sight depths and not population effects. Density distributions as a function of distance are derived in Section 4 and compared to simulations in Section 5. Finally, a discussion of the results and their implications are presented in Section 6 and a brief summary in Section 7.","pages":[1,2]},{"title":"2. DATA","content":"We use CTIO-4m+MOSAIC Washington M and T 2 (equivalent to I C ) photometry from the MAgellanic Periphery Survey (MAPS) for our analysis. The observations and data reduction are described in Nidever et al. (2011). Figure 1 shows the MAPS fields (filled squares) in the area of the SMC. While we have 'deep' photometry (to M ∼ 24) in fields extending to R ≈ 12 · the red clump (RC) is most prominent in our R =4 · fields, which are the focus of the present study. Figure 2 shows the full M 0 vs. ( M -T 2 ) 0 Hess diagrams (dereddened with the Schlegel et al. 1998 extinction maps) of four, evenly spaced in azimuth, deep fields 4 at R =4 · . The SMC RGB, RC, and main-sequence stars are clearly visible. Hess diagrams of the RC region for all eight R =4 · fields are shown in Figure 3. The RC morphology clearly varies substantially from field to field. The eastern fields (PA=26-161 · ) show a much larger RC extent in magnitude than the western fields (PA=206-341 · ). It was previously noted by Hatzidimitriou & Hawkins (1989) that the horizontal branch stars in the northeast of the SMC periphery have a larger lineof-sight depth (and extend to brighter magnitudes) than in the southwest. 4 The field names are constructured from the field's radius and position angle (east of north), i.e. 40S026 is R=4.0 · and PA=26 · .","pages":[2]},{"title":"3. THE NATURE OF THE EXTENDED RED CLUMP LUMINOSITY FUNCTION","content":"An elongated distribution of the red clump (to the bright end) can be caused by reasons other than a large line-of-sight depth. The evolution of intermediate-mass He-core burning stars moves them along loops in the HR diagram at nearly constant luminosity ('blue loop' stars). Their age at a given magnitude depends on metallicity but blue loop stars are generally quite young (a few hundred Myr to 1 Gyr; Sweigart 1987; Xu & Li 2004, and references therein) and theoretical models predict that their CMD location depends strongly on metallicity (e.g., Girardi et al. 2000). Many stars pile up on the red end of the blue loops (BL) and define a nearly vertical feature that stretches to brighter magnitudes than the RC (often spanning ∼ 2-3 mag) and trending to the blue (as seen in Fig. 3 of Gallart 1998). This feature of stellar evolution can be easily confused with an extended red clump and was the primary point of contention regarding the nature of the 'vertical red clump' of the LMC identified by Zaritsky & Lin (1997); these authors interpreted the feature as an intervening stellar population but this was subsequently called into question by Beaulieu & Sackett (1998). Given this precedent, we have taken steps to rule out BL stars as the cause for the extended feature observed in the CMDs of the eastern SMC fields. We have computed a synthetic CMD that reproduces the overall features of the stellar populations of the SMC in the CMD (see Fig. 2) to compare its RC and BL distributions with the elongated feature observed at the RC level. We have assumed a constant star formation rate (SFR) from 0.7 to 12 Gyr and metallicities of [Fe/H]= -1 dex ([Fe/H]= -1 . 5 dex) for stars younger (older) than 6 Gyr 5 . The model CMD was computed using the IAC-STAR code (Aparicio & Gallart 2004) adopting the BaSTI stellar library (Pietrinferni et al. 2004), a Reimers mass loss efficiency parameter value of η =0.2, and a Kroupa (2002) initial mass function (IMF) from 0.1 to 100 M glyph[circledot] . The magnitudes of the model CMD are expressed in the Johnson-Cousins photometric system; in particular we have chosen the bolometric correction library from Girardi et al. (2002). The magnitudes were transformed into the Washington M and T 2 photometric system using the transformation equations from Majewski et al. (2000). We assumed a distance modulus of 18.9 for the SMC and did not correct the model CMD due to observational effects (incompleteness and photometric errors). Given that we expect a near 100% completeness and a ∼ 2% photometric accuracy ( ∼ 0.3% internal precision) at the RC level, this correction should have little impact on the model CMD for our purposes. Figures 4 and 5 show the observed (a) and model (b) CMDs for the 40S026 (eastern SMC) and 40S206 (western SMC) fields, respectively. The model in Figure 4b has ages ranging from 1.4 Gyr to 12 Gyr whereas the model in Figure 5b has ages ranging from 2.0 Gyr to 12 Gyr. These age ranges were chosen so that the position and characteristics of the main features (main sequence, subgiant branch, tip of the RGB) are well reproduced by the models. In Figure 4, however, there is a clear difference in the RC morphology between the model and the data. We find that the RC is much less elongated in magnitude in the model than in the CMD of the observed eastern field. This discrepancy cannot be accounted for by stellar evolutionary features such as BL stars; the model predicts that there should be almost no BL stars, given that its youngest population has an age of 1.4 Gyr. A CMD model with stars as young as 0.7 Gyr predicts more BL stars, but also shows evidence of a brighter and more populous young main-sequence, which is not seen in the data. Moreover, even if the young main-sequence from the model CMD were to agree with the data, the density of the model BL stars would still be significantly lower than that of the RC stars. Figure 6a is an attempt to reproduce the morphology of the RC region of the CMD (seen in panel b) using a spread in age and star formation rate only (which requires most of the young and old stars to be removed). The resulting simulated Hess diagram is not a good representation of the observed data, particularly on the main sequence. On the other hand, the simulated Hess diagram with a distance spread (convolved with the distance function for this field found in § 4) in Figure 6c is a good representation. Thus, a BL population cannot explain the elongated RC that we observe in the eastern field. On the other hand, Figure 5 shows that the western field and model RC morphologies agree fairly well. Figures 4c and 5c show the RC luminosity function both for the data and the model. The RC stars were isolated as explained in the next section. Note the much wider RC distribution in the eastern field when compared with the model.","pages":[3,4]},{"title":"4. DISTANCES","content":"To study the distance distributions, we isolate the RC stars in the CMD. Because the RC and RGB are very close in the CMD and sometimes overlap we decided to model the RGB distributions to produce a 'clean' RC sample. A Hess density map of stars was created for each field in ( M -I ) 0 and M 0 in bins of 0.02 and 0.05 mag respectively. These were then smoothed with a Gaussian kernel having FWHM=2 bins. Each row, at a given magnitude, was modeled with a double-Gaussian for the RC and RGB over the magnitude range 18.5 Next, we use the model SMC CMD to construct an ab- 2 Fig. 4.(a) Hess diagram of the 40S026 field in the eastern portion of the SMC. (b) Simulated CMD for the 40S026 field with ages of 1.4 to 12 Gyr. The red lines are [Fe/H]= -1.488 age=8.0 Gyr BaSTI isochrones (Pietrinferni et al. 2004) at 60 kpc. (c) Red clump luminosity function for the data (red) and simulation (black). The observed luminosity function is much broader than the model suggesting a large line-of-sight depth. Fig. 4.(a) Hess diagram of the 40S026 field in the eastern portion of the SMC. (b) Simulated CMD for the 40S026 field with ages of 1.4 to 12 Gyr. The red lines are [Fe/H]= -1.488 age=8.0 Gyr BaSTI isochrones (Pietrinferni et al. 2004) at 60 kpc. (c) Red clump luminosity function for the data (red) and simulation (black). The observed luminosity function is much broader than the model suggesting a large line-of-sight depth. Fig. 5.Same as Figure 4 but for the 40S206 field with model ages of 2.0 to 12 Gyr. While not as wide as the RC luminosity function of 40S026, the observed luminosity function of 40S206 is wider than the model and indicates some depth is needed to explain the observations. Fig. 5.Same as Figure 4 but for the 40S206 field with model ages of 2.0 to 12 Gyr. While not as wide as the RC luminosity function of 40S026, the observed luminosity function of 40S206 is wider than the model and indicates some depth is needed to explain the observations. solute RC luminosity function (isolating RC stars with 1.025 function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields. 5. COMPARISON TO MODELS To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section). 6. DISCUSSION We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV). 7. SUMMARY We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: 1. The four eastern fields show very large line-of-sight depths ( ∼ 23 kpc) over ∼ 135 · of position angle. 2. Three eastern fields show a strong distance bimodality with one component at ∼ 67 kpc (near the mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. 3. The newly-found stellar component in the east at ∼ 55 kpc is qualitatively consistent with the Diaz & Bekki (2012) model distribution of particles in the tidally-stripped Magellanic Bridge, previously only detected in H I . We conclude that this new component is likely an intermediate-age/old ( ∼ 112 Gyr) stellar component of the Magellanic Bridge and call it the SMC 'eastern stellar structure'. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II). REFERENCES Abbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. D. 1998, AJ, 116, 209 Bekki, K., & Chiba, M. 2009, PASA, 26, 48 Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. 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F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stanimirovi'c, S., Staveley-Smith, L., & Jones, P. A. 2004, ApJ, 604, 176 Sweigart, A. V. 1987, ApJS, 65, 95 Udalski, A., et al. 2008, Acta Astronomica, 58, 329 Xu, H. Y., & Li, Y. 2004, A&A, 418, 225 Zaritsky, D., & Lin, D. N. C. 1997, AJ, 114, 2545 Zaritsky, D., Harris, J., Grebel, E. K., & Thompson, I. B. 2000, ApJ, 534, L53 Zaritsky, D., Harris, J., Thompson, I. B., Grebel, E. K., & Massey, P. 2002, AJ, 123, 855 Next, we use the model SMC CMD to construct an ab- 2 solute RC luminosity function (isolating RC stars with 1.025 function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields. 5. COMPARISON TO MODELS To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section). 6. DISCUSSION We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV). 7. SUMMARY We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: 1. The four eastern fields show very large line-of-sight depths ( ∼ 23 kpc) over ∼ 135 · of position angle. 2. Three eastern fields show a strong distance bimodality with one component at ∼ 67 kpc (near the mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. 3. The newly-found stellar component in the east at ∼ 55 kpc is qualitatively consistent with the Diaz & Bekki (2012) model distribution of particles in the tidally-stripped Magellanic Bridge, previously only detected in H I . We conclude that this new component is likely an intermediate-age/old ( ∼ 112 Gyr) stellar component of the Magellanic Bridge and call it the SMC 'eastern stellar structure'. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II). REFERENCES Abbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. D. 1998, AJ, 116, 209 Bekki, K., & Chiba, M. 2009, PASA, 26, 48 Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. 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F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stanimirovi'c, S., Staveley-Smith, L., & Jones, P. A. 2004, ApJ, 604, 176 Sweigart, A. V. 1987, ApJS, 65, 95 Udalski, A., et al. 2008, Acta Astronomica, 58, 329 Xu, H. Y., & Li, Y. 2004, A&A, 418, 225 Zaritsky, D., & Lin, D. N. C. 1997, AJ, 114, 2545 Zaritsky, D., Harris, J., Grebel, E. K., & Thompson, I. B. 2000, ApJ, 534, L53 Zaritsky, D., Harris, J., Thompson, I. B., Grebel, E. K., & Massey, P. 2002, AJ, 123, 855 function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields.","pages":[4,5,6]},{"title":"5. COMPARISON TO MODELS","content":"To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section).","pages":[6,7,8]},{"title":"6. DISCUSSION","content":"We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV).","pages":[8,10,11]},{"title":"7. SUMMARY","content":"We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II).","pages":[11]},{"title":"REFERENCES","content":"Abbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. D. 1998, AJ, 116, 209 Bekki, K., & Chiba, M. 2009, PASA, 26, 48 Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. P., & Alcock, C. 2007, ApJ, 668, 949 Besla, G., Kallivayalil, N., Hernquist, L., et al. 2010, ApJ, 721, L97 Besla, G., Kallivayalil, N., Hernquist, L., et al. 2012, MNRAS, 421, 2109 (B12) Besla, G., Hernquist, L., & Loeb, A. 2013, MNRAS, 428, 2342 Bruns, C., et al. 2005, A&A, 432, 45B (B05) Calchi Novati, S., Mirzoyan, S., Jetzer, P., & Scarpetta, G. 2013, MNRAS, 2104 Caldwell, J. A. R., & Coulson, I. M. 1986, MNRAS, 218, 223 Connors, T. W., Kawata, D., & Gibson, B. K. 2006, MNRAS, 371, 108 De Propris, R., Rich, R. M., Mallery, R. C., & Howard, C. D. 2010, ApJ, 714, L249 Diaz, J. D., & Bekki, K. 2012, ApJ, 750, 36 (DB12) Gallart, C. 1998, ApJ, 495, L43 Gardiner, L. T., & Hawkins, M. R. S. 1991, MNRAS, 251, 174 Gardiner, L. T., & Hatzidimitriou, D. 1992, MNRAS, 257, 195 Gardiner, L. T., & Noguchi, M. 1996, MNRAS, 278, 191 Girardi, L., Groenewegen, M. A. T., Weiss, A., & Salaris, M. 1998, MNRAS, 301, 149 Girardi, L., Bressan, A., Bertelli, G., & Chiosi, C. 2000, A&AS, 141, 371 Girardi, L., Bertelli, G., Bressan, A., Chiosi, C., Groenewegen, M. A. T., Marigo, P., Salasnich, B., & Weiss, A. 2002, A&A, 391, 195 Harris, J., & Zaritsky, D. 2006, AJ, 131, 2514 Haschke, R., Grebel, E. K., & Duffau, S. 2012, AJ, 144, 107 Hatzidimitriou, D., Hawkins, M. R. S., & Gyldenkerne, K. 1989, MNRAS, 241, 645 Hatzidimitriou, D., & Hawkins, M. R. S. 1989, MNRAS, 241, 667 Hatzidimitriou, D., Cannon, R. D., & Hawkins, M. R. S. 1993, MNRAS, 261, 873 Keller, S. C., Skymapper Team, & Aegis Team 2012, Galactic Archaeology: Near-Field Cosmology and the Formation of the Milky Way, 458, 409 Kozlowski, S., Udalski, A., Wyrzykowski, L., et al. 2013, Acta Astron., 63, 1 Kroupa, P. 2002, Science, 295, 82 Kunkel, W. E., Demers, S., & Irwin, M. J. 2000, AJ, 119, 2789 Majewski, S. R., Ostheimer, J. C., Kunkel, W. E., & Patterson, R. J. 2000, AJ, 120, 2550 Mathewson, D. S., Ford, V. L., & Visvanathan, N. 1986, ApJ, 301, 664 Mathewson, D. S., Ford, V. L., & Visvanathan, N. 1988, ApJ, 333, 617","pages":[11,12]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"Deep photometry of the Small Magellanic Cloud (SMC) stellar periphery ( R =4 · , 4.2 kpc) is used to study its line-of-sight depth with red clump (RC) stars. The RC luminosity function is affected little by young ( glyph[lessorsimilar] 1 Gyr) blue-loop stars in these regions because their main-sequence counterparts are not observed in the color magnitude diagrams. The SMC's eastern side is found to have a large line-of-sight depth ( ∼ 23 kpc) while the western side has a much shallower depth ( ∼ 10 kpc), consistent with previous photographic plate photometry results. We use a model SMC RC luminosity function to deconvolve the observed RC magnitudes and construct the density function in distance for our fields. Three of the eastern fields show a distance bimodality with one component at the 'systemic' ∼ 67 kpc SMC distance and a second component at ∼ 55 kpc. Our data are not reproduced well by the various extant Magellanic Cloud and Stream simulations. However, the models predict that the known H I Magellanic Bridge (stretching from the SMC eastward towards the LMC) has a decreasing distance with angle from the SMC and should be seen in both the gaseous and stellar components. From comparison with these models we conclude that the most likely explanation for our newly identified ∼ 55 kpc stellar structure in the eastern SMC is a stellar counterpart of the H I Magellanic Bridge that was tidally stripped from the SMC ∼ 200 Myr ago during a close encounter with the LMC. This discovery has important implications for microlensing surveys of the SMC. Subject headings: Galaxies: interactions - Local Group - Magellanic Clouds - Galaxies: dwarf Galaxies: individual (SMC) - Galaxies: photometry\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"A TIDALLY-STRIPPED STELLAR COMPONENT OF THE MAGELLANIC BRIDGE\",\n \"content\": \"David L. Nidever 1,2 , Antonela Monachesi 1 , Eric F. Bell 1 , Steven R. Majewski 2 , Ricardo R. Mu˜noz 3 , Rachael L. Beaton 2 Draft version September 14, 2021\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"The Large and Small Magellanic Clouds (LMC and SMC respectively) are the two largest satellite galaxies of the Milky Way (MW) and, due to their proximity, offer the best possibility for detailed study of dwarf galaxies, especially interacting dwarf irregulars. One of the most striking features of the Magellanic system is the vast extent of its H I component - including the 200 · -long Magellanic Stream (MS) and Leading Arm (Nidever et al. 2010) as well as the Magellanic Bridge (Muller et al. 2003). These gaseous structures are the result of past interactions of the Magellanic Clouds (MCs) with each other and the MW galaxy (Murai & Fujimoto 1980; Gardiner & Noguchi 1996; Connors et al. 2006; R˚uˇziˇcka et al. 2010; Diaz & Bekki 2012; Besla et al. 2010, 2012, 2013). The Magellanic Bridge is widely believed to have been tidally stripped from the SMC by a recent close encounter with the LMC ∼ 200 Myr ago (e.g., Muller & Bekki 2007). While the evidence of MC interactions is quite evident in H I it is less obvious in the stellar structures of the Clouds. The SMC, which is approximately ten times less massive than the LMC, is more likely to be affected by any past interactions (and is the source of much of the MS H I material in many models), and, therefore, may be the most obvious place to search for stellar signs of tidal disturbances. Two decades ago, a series of papers analyzing photographic plate photometry (Hatzidimitriou et al. 1989) reaching to just below the SMC horizontal branch (HB) performed the first detailed study of the SMC stellar periphery. Using red clump (RC) stars as standard candles in two fields, Hatzidimitriou & Hawkins (1989) found the line-of-sight depth to be much larger in the northeast than in the southwest. Follow-up spectroscopy showed a correlation between distance and radial velocity (RV) in the northeast RC stars (Hatzidimitriou et al. 1993) similar to that seen by Mathewson et al. (1986) in Cepheid variables closer to the center. Gardiner & Hatzidimitriou (1992) used the photographic plate photometry of all their SMC fields to trace HB stars to R ∼ 5 · in all directions, uncovering a fairly symmetric structure but with a quick decline in density towards the west. In contrast, the young main-sequence stars have a much more irregular shape extending towards the LMC into the Magellanic Bridge region (see black contours in Fig. 1). Gardiner & Hawkins (1991) found that the change of line-of-sight depth with radius in the western SMC, increasing with radius, was more consistent with a spheroidal than disklike structure. The notion of the stellar SMC having a spheroidal structure is argued by Zaritsky et al. (2000) and supported by a recent spectroscopic study of ∼ 2000 red giant branch (RGB) stars in the central 4 kpc × 2 kpc of the SMC that found no sign of rotation (Harris & Zaritsky 2006). In contrast, rotation is observed in the H I component of the SMC (Stanimirovi'c et al. 2004). Many of the structural and kinematical features of the SMC are reproduced by the LMC-SMC-MW interaction simulations of Bekki & Chiba (2009) by using a spheroidal stellar distribution and extended gaseous disk. More recent work on the SMC periphery has shown it to extend much further than previously thought. Noel & Gallart (2007) detected intermediate-age and old stars in deep photometric data at ∼ 6 · south of the SMC center, while De Propris et al. (2010) found spectroscopicallyconfirmed RGB stars out to R ∼ 6 · in the eastern SMC. Nidever et al. (2011) used photometrically-selected RGB stars to trace the structure of the SMC periphery to R ∼ 11 · (in multiple directions) and showed that the SMC has a fairly azimuthally-symmetric structure. Nidever et al. also found that the center of the outer SMC population ( R> 4 · ) is offset by ∼ 0.6 · (to the east) from the center of the inner population ( R glyph[lessorsimilar] 3 · ) and postulated that this is due to a perspective effect because, on average, the stars to the eastern side are closer than the stars on the western side. In addition, Bagheri et al. (2013) used 2MASS and WISE catalogs to find evidence for some candidate older stars in the region between the Magellanic Clouds, while Noel et al. (2013) used deep photometry to find intermediate-age stars in a field at ∼ 7 · from the SMC in the Magellanic Bridge. Variable stars and stars clusters have been widely used to study the 3D structure of the inner SMC. Several studies in the 1980s found a large line-of-sight depth in the central SMC using young Cepheids (Mathewson et al. 1986, 1988), with Caldwell & Coulson (1986) finding hints of two arms in the southwest. Haschke et al. (2012) used multi-epoch OGLE-III (Udalski et al. 2008) photometry to study the 3D distribution of cepheids ( ∼ 30300 Myr old) and RR Lyrae ( glyph[greaterorsimilar] 10 Gyr old) stars in the inner SMC ( R< 2 · ). While both populations are found to have an extended scale height, the older stars have a fairly homogeneous distribution whereas the young stars are in an inclined orientation that is closer in the northeast than in the southwest. Finally, Crowl et al. (2001) used populous SMC clusters to study the line-of-sight depth in the inner SMC ( R glyph[lessorsimilar] 3 kpc) and found a ± 1 σ depth between ∼ 6 and ∼ 12 kpc. Even with all of these studies, the detailed 3D structure of the SMC stellar periphery is still not well understood in large part due to the lack of high-quality, wide-area CCD photometry in this region of the southern sky. This is unfortunate because this knowledge would enable us not only to produce a better 3D map of the SMC but also provide us with observational data of collisionless particles that would much better constrain the recent ( ∼ 200 Myr) close encounter of the MCs with each other. It is thought that during that encounter the SMC might have passed right through the LMC disk (Besla et al. 2012) and produced the H I Magellanic Bridge. In this paper we use deep Washington M and T 2 photometry from the MAgellanic Periphery Survey (MAPS) to study the line-of-sight depth of core helium-burning RC stars in the SMC periphery. We find a much larger line-of-sight depth ( ∼ 23 kpc) in four eastern fields than in our four western fields ( ∼ 10 kpc), and a distance bimodality in three eastern fields with a newly identified component at ∼ 55 kpc ( ∼ 12 kpc closer than the component at the 'systemic', ∼ 67 kpc SMC distance) that is most likely an intermediate-age/old stellar counterpart of the recently tidally-stripped H I Magellanic Bridge. In Section 2 we briefly describe the observations and main features of the color magnitude diagrams (CMDs). We argue in Section 3 that the extended RC seen in many of our CMDs are due to large line-of-sight depths and not population effects. Density distributions as a function of distance are derived in Section 4 and compared to simulations in Section 5. Finally, a discussion of the results and their implications are presented in Section 6 and a brief summary in Section 7.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2. DATA\",\n \"content\": \"We use CTIO-4m+MOSAIC Washington M and T 2 (equivalent to I C ) photometry from the MAgellanic Periphery Survey (MAPS) for our analysis. The observations and data reduction are described in Nidever et al. (2011). Figure 1 shows the MAPS fields (filled squares) in the area of the SMC. While we have 'deep' photometry (to M ∼ 24) in fields extending to R ≈ 12 · the red clump (RC) is most prominent in our R =4 · fields, which are the focus of the present study. Figure 2 shows the full M 0 vs. ( M -T 2 ) 0 Hess diagrams (dereddened with the Schlegel et al. 1998 extinction maps) of four, evenly spaced in azimuth, deep fields 4 at R =4 · . The SMC RGB, RC, and main-sequence stars are clearly visible. Hess diagrams of the RC region for all eight R =4 · fields are shown in Figure 3. The RC morphology clearly varies substantially from field to field. The eastern fields (PA=26-161 · ) show a much larger RC extent in magnitude than the western fields (PA=206-341 · ). It was previously noted by Hatzidimitriou & Hawkins (1989) that the horizontal branch stars in the northeast of the SMC periphery have a larger lineof-sight depth (and extend to brighter magnitudes) than in the southwest. 4 The field names are constructured from the field's radius and position angle (east of north), i.e. 40S026 is R=4.0 · and PA=26 · .\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"3. THE NATURE OF THE EXTENDED RED CLUMP LUMINOSITY FUNCTION\",\n \"content\": \"An elongated distribution of the red clump (to the bright end) can be caused by reasons other than a large line-of-sight depth. The evolution of intermediate-mass He-core burning stars moves them along loops in the HR diagram at nearly constant luminosity ('blue loop' stars). Their age at a given magnitude depends on metallicity but blue loop stars are generally quite young (a few hundred Myr to 1 Gyr; Sweigart 1987; Xu & Li 2004, and references therein) and theoretical models predict that their CMD location depends strongly on metallicity (e.g., Girardi et al. 2000). Many stars pile up on the red end of the blue loops (BL) and define a nearly vertical feature that stretches to brighter magnitudes than the RC (often spanning ∼ 2-3 mag) and trending to the blue (as seen in Fig. 3 of Gallart 1998). This feature of stellar evolution can be easily confused with an extended red clump and was the primary point of contention regarding the nature of the 'vertical red clump' of the LMC identified by Zaritsky & Lin (1997); these authors interpreted the feature as an intervening stellar population but this was subsequently called into question by Beaulieu & Sackett (1998). Given this precedent, we have taken steps to rule out BL stars as the cause for the extended feature observed in the CMDs of the eastern SMC fields. We have computed a synthetic CMD that reproduces the overall features of the stellar populations of the SMC in the CMD (see Fig. 2) to compare its RC and BL distributions with the elongated feature observed at the RC level. We have assumed a constant star formation rate (SFR) from 0.7 to 12 Gyr and metallicities of [Fe/H]= -1 dex ([Fe/H]= -1 . 5 dex) for stars younger (older) than 6 Gyr 5 . The model CMD was computed using the IAC-STAR code (Aparicio & Gallart 2004) adopting the BaSTI stellar library (Pietrinferni et al. 2004), a Reimers mass loss efficiency parameter value of η =0.2, and a Kroupa (2002) initial mass function (IMF) from 0.1 to 100 M glyph[circledot] . The magnitudes of the model CMD are expressed in the Johnson-Cousins photometric system; in particular we have chosen the bolometric correction library from Girardi et al. (2002). The magnitudes were transformed into the Washington M and T 2 photometric system using the transformation equations from Majewski et al. (2000). We assumed a distance modulus of 18.9 for the SMC and did not correct the model CMD due to observational effects (incompleteness and photometric errors). Given that we expect a near 100% completeness and a ∼ 2% photometric accuracy ( ∼ 0.3% internal precision) at the RC level, this correction should have little impact on the model CMD for our purposes. Figures 4 and 5 show the observed (a) and model (b) CMDs for the 40S026 (eastern SMC) and 40S206 (western SMC) fields, respectively. The model in Figure 4b has ages ranging from 1.4 Gyr to 12 Gyr whereas the model in Figure 5b has ages ranging from 2.0 Gyr to 12 Gyr. These age ranges were chosen so that the position and characteristics of the main features (main sequence, subgiant branch, tip of the RGB) are well reproduced by the models. In Figure 4, however, there is a clear difference in the RC morphology between the model and the data. We find that the RC is much less elongated in magnitude in the model than in the CMD of the observed eastern field. This discrepancy cannot be accounted for by stellar evolutionary features such as BL stars; the model predicts that there should be almost no BL stars, given that its youngest population has an age of 1.4 Gyr. A CMD model with stars as young as 0.7 Gyr predicts more BL stars, but also shows evidence of a brighter and more populous young main-sequence, which is not seen in the data. Moreover, even if the young main-sequence from the model CMD were to agree with the data, the density of the model BL stars would still be significantly lower than that of the RC stars. Figure 6a is an attempt to reproduce the morphology of the RC region of the CMD (seen in panel b) using a spread in age and star formation rate only (which requires most of the young and old stars to be removed). The resulting simulated Hess diagram is not a good representation of the observed data, particularly on the main sequence. On the other hand, the simulated Hess diagram with a distance spread (convolved with the distance function for this field found in § 4) in Figure 6c is a good representation. Thus, a BL population cannot explain the elongated RC that we observe in the eastern field. On the other hand, Figure 5 shows that the western field and model RC morphologies agree fairly well. Figures 4c and 5c show the RC luminosity function both for the data and the model. The RC stars were isolated as explained in the next section. Note the much wider RC distribution in the eastern field when compared with the model.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"4. DISTANCES\",\n \"content\": \"To study the distance distributions, we isolate the RC stars in the CMD. Because the RC and RGB are very close in the CMD and sometimes overlap we decided to model the RGB distributions to produce a 'clean' RC sample. A Hess density map of stars was created for each field in ( M -I ) 0 and M 0 in bins of 0.02 and 0.05 mag respectively. These were then smoothed with a Gaussian kernel having FWHM=2 bins. Each row, at a given magnitude, was modeled with a double-Gaussian for the RC and RGB over the magnitude range 18.5 Next, we use the model SMC CMD to construct an ab- 2 Fig. 4.(a) Hess diagram of the 40S026 field in the eastern portion of the SMC. (b) Simulated CMD for the 40S026 field with ages of 1.4 to 12 Gyr. The red lines are [Fe/H]= -1.488 age=8.0 Gyr BaSTI isochrones (Pietrinferni et al. 2004) at 60 kpc. (c) Red clump luminosity function for the data (red) and simulation (black). The observed luminosity function is much broader than the model suggesting a large line-of-sight depth. Fig. 4.(a) Hess diagram of the 40S026 field in the eastern portion of the SMC. (b) Simulated CMD for the 40S026 field with ages of 1.4 to 12 Gyr. The red lines are [Fe/H]= -1.488 age=8.0 Gyr BaSTI isochrones (Pietrinferni et al. 2004) at 60 kpc. (c) Red clump luminosity function for the data (red) and simulation (black). The observed luminosity function is much broader than the model suggesting a large line-of-sight depth. Fig. 5.Same as Figure 4 but for the 40S206 field with model ages of 2.0 to 12 Gyr. While not as wide as the RC luminosity function of 40S026, the observed luminosity function of 40S206 is wider than the model and indicates some depth is needed to explain the observations. Fig. 5.Same as Figure 4 but for the 40S206 field with model ages of 2.0 to 12 Gyr. While not as wide as the RC luminosity function of 40S026, the observed luminosity function of 40S206 is wider than the model and indicates some depth is needed to explain the observations. solute RC luminosity function (isolating RC stars with 1.025 function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields. 5. COMPARISON TO MODELS To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section). 6. DISCUSSION We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV). 7. SUMMARY We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: 1. The four eastern fields show very large line-of-sight depths ( ∼ 23 kpc) over ∼ 135 · of position angle. 2. Three eastern fields show a strong distance bimodality with one component at ∼ 67 kpc (near the mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. 3. The newly-found stellar component in the east at ∼ 55 kpc is qualitatively consistent with the Diaz & Bekki (2012) model distribution of particles in the tidally-stripped Magellanic Bridge, previously only detected in H I . We conclude that this new component is likely an intermediate-age/old ( ∼ 112 Gyr) stellar component of the Magellanic Bridge and call it the SMC 'eastern stellar structure'. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II). REFERENCES Abbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. D. 1998, AJ, 116, 209 Bekki, K., & Chiba, M. 2009, PASA, 26, 48 Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. 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F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stanimirovi'c, S., Staveley-Smith, L., & Jones, P. A. 2004, ApJ, 604, 176 Sweigart, A. V. 1987, ApJS, 65, 95 Udalski, A., et al. 2008, Acta Astronomica, 58, 329 Xu, H. Y., & Li, Y. 2004, A&A, 418, 225 Zaritsky, D., & Lin, D. N. C. 1997, AJ, 114, 2545 Zaritsky, D., Harris, J., Grebel, E. K., & Thompson, I. B. 2000, ApJ, 534, L53 Zaritsky, D., Harris, J., Thompson, I. B., Grebel, E. K., & Massey, P. 2002, AJ, 123, 855 Next, we use the model SMC CMD to construct an ab- 2 solute RC luminosity function (isolating RC stars with 1.025 function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields. 5. COMPARISON TO MODELS To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section). 6. DISCUSSION We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV). 7. SUMMARY We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: 1. The four eastern fields show very large line-of-sight depths ( ∼ 23 kpc) over ∼ 135 · of position angle. 2. Three eastern fields show a strong distance bimodality with one component at ∼ 67 kpc (near the mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. 3. The newly-found stellar component in the east at ∼ 55 kpc is qualitatively consistent with the Diaz & Bekki (2012) model distribution of particles in the tidally-stripped Magellanic Bridge, previously only detected in H I . We conclude that this new component is likely an intermediate-age/old ( ∼ 112 Gyr) stellar component of the Magellanic Bridge and call it the SMC 'eastern stellar structure'. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II). REFERENCES Abbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. D. 1998, AJ, 116, 209 Bekki, K., & Chiba, M. 2009, PASA, 26, 48 Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. 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This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields.\",\n \"pages\": [\n 4,\n 5,\n 6\n ]\n },\n {\n \"title\": \"5. COMPARISON TO MODELS\",\n \"content\": \"To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section).\",\n \"pages\": [\n 6,\n 7,\n 8\n ]\n },\n {\n \"title\": \"6. DISCUSSION\",\n \"content\": \"We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV).\",\n \"pages\": [\n 8,\n 10,\n 11\n ]\n },\n {\n \"title\": \"7. SUMMARY\",\n \"content\": \"We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II).\",\n \"pages\": [\n 11\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Abbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. D. 1998, AJ, 116, 209 Bekki, K., & Chiba, M. 2009, PASA, 26, 48 Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. P., & Alcock, C. 2007, ApJ, 668, 949 Besla, G., Kallivayalil, N., Hernquist, L., et al. 2010, ApJ, 721, L97 Besla, G., Kallivayalil, N., Hernquist, L., et al. 2012, MNRAS, 421, 2109 (B12) Besla, G., Hernquist, L., & Loeb, A. 2013, MNRAS, 428, 2342 Bruns, C., et al. 2005, A&A, 432, 45B (B05) Calchi Novati, S., Mirzoyan, S., Jetzer, P., & Scarpetta, G. 2013, MNRAS, 2104 Caldwell, J. A. R., & Coulson, I. M. 1986, MNRAS, 218, 223 Connors, T. W., Kawata, D., & Gibson, B. K. 2006, MNRAS, 371, 108 De Propris, R., Rich, R. M., Mallery, R. C., & Howard, C. D. 2010, ApJ, 714, L249 Diaz, J. D., & Bekki, K. 2012, ApJ, 750, 36 (DB12) Gallart, C. 1998, ApJ, 495, L43 Gardiner, L. T., & Hawkins, M. R. S. 1991, MNRAS, 251, 174 Gardiner, L. T., & Hatzidimitriou, D. 1992, MNRAS, 257, 195 Gardiner, L. T., & Noguchi, M. 1996, MNRAS, 278, 191 Girardi, L., Groenewegen, M. A. T., Weiss, A., & Salaris, M. 1998, MNRAS, 301, 149 Girardi, L., Bressan, A., Bertelli, G., & Chiosi, C. 2000, A&AS, 141, 371 Girardi, L., Bertelli, G., Bressan, A., Chiosi, C., Groenewegen, M. A. T., Marigo, P., Salasnich, B., & Weiss, A. 2002, A&A, 391, 195 Harris, J., & Zaritsky, D. 2006, AJ, 131, 2514 Haschke, R., Grebel, E. K., & Duffau, S. 2012, AJ, 144, 107 Hatzidimitriou, D., Hawkins, M. R. S., & Gyldenkerne, K. 1989, MNRAS, 241, 645 Hatzidimitriou, D., & Hawkins, M. R. S. 1989, MNRAS, 241, 667 Hatzidimitriou, D., Cannon, R. D., & Hawkins, M. R. S. 1993, MNRAS, 261, 873 Keller, S. C., Skymapper Team, & Aegis Team 2012, Galactic Archaeology: Near-Field Cosmology and the Formation of the Milky Way, 458, 409 Kozlowski, S., Udalski, A., Wyrzykowski, L., et al. 2013, Acta Astron., 63, 1 Kroupa, P. 2002, Science, 295, 82 Kunkel, W. E., Demers, S., & Irwin, M. J. 2000, AJ, 119, 2789 Majewski, S. R., Ostheimer, J. C., Kunkel, W. E., & Patterson, R. J. 2000, AJ, 120, 2550 Mathewson, D. S., Ford, V. L., & Visvanathan, N. 1986, ApJ, 301, 664 Mathewson, D. S., Ford, V. L., & Visvanathan, N. 1988, ApJ, 333, 617\",\n \"pages\": [\n 11,\n 12\n ]\n }\n]"}}},{"rowIdx":78,"cells":{"bibcode":{"kind":"string","value":"2013ApJ...779L...5O"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1311.1706.pdf"},"content":{"kind":"string","value":"\nThe Terzan 5 puzzle: discovery of a third, metal-poor component\nL. Origlia 2 , D. Massari 3 , R. M. Rich 4 , A. Mucciarelli 3 , F. R. Ferraro 3 , E. Dalessandro 3 Lanzoni 3\n\n, B.\n2 INAF-Osservatorio Astronomico di Bologna, Via Ranzani 1, I-40127 Bologna, Italy, livia.origlia@oabo.inaf.it\n3 Dipartimento di Fisica e Astronomia, Universit'a degli Studi di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy\n4 Physics and Astronomy Bldg, 430 Portola Plaza Box 951547 Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, CA 90095-1547\n\nABSTRACT\nWe report on the discovery of 3 metal-poor giant stars in Terzan 5, a complex stellar system in the the Galactic bulge, known to have two populations at [Fe/H]=-0.25 and +0.3. For these 3 stars we present new echelle spectra obtained with NIRSPEC at Keck II, which confirm their radial velocity membership and provide average [Fe/H]=-0.79 dex iron abundance and [alpha/Fe]=+0.36 dex enhancement. This new population extends the metallicity range of Terzan 5 0.5 dex more metal poor, and it has properties consistent with having formed from a gas polluted by core collapse supernovae.\nSubject headings: Galaxy: bulge - Galaxy: abundances - stars: abundances - stars: late-type techniques: spectroscopic - infrared: stars\n1. Introduction\nTerzan 5 is a complex stellar system in the Galactic Bulge. It suffers from huge extinction, its average color excess being E( B -V ) = 2 . 38 (Barbuy et al. 1998; Valenti et al. 2007), and it is also affected by significant differential reddening (∆E( B -V ) /similarequal 0 . 7 mag, Massari et al. 2013). For years it has been classified as a globular cluster, although soon after its discovery its true nature was already disputed (see, e.g., King 1972).\nRecent high resolution imaging in the near infrared (IR) obtained with the Multi-conjugate Adaptive Optics Demonstrator (MAD) at ESOVLT, revealed the presence of two distinct red clumps that cannot be explained by differen-\ntial reddening or distance effects (Ferraro et al. 2009). Prompt near infrared spectroscopy with NIRSPEC at Keck II demonstrated that the two stellar populations are characterized by very different iron abundances ([Fe/H]= -0 . 2 and +0.3). Subsequent spectroscopic studies of 33 red giant stars (Origlia et al. 2011) fully confirmed the large metallicity difference between the two populations. The sub-Solar component has [Fe/H]= -0 . 25 ± 0 . 07 r.m.s. and it is α -enhanced, similar to the old bulge population that likely formed at early epochs and from a gas enriched by a huge amount of type II supernovae (SNe). The super-Solar component, which is possibly a few Gyr younger, has [Fe/H]= +0 . 27 ± 0 . 04 and approximately Solar [ α /Fe] abundance ratio, indicating that it should have originated from a gas polluted by both SNe II and Ia on a longer timescale. Both components show a small internal metallicity spread and the most metal-rich population is also more centrally concentrated (Ferraro et al. 2009; Lanzoni et al. 2010). These observational\n1\nfacts could be accounted for by a proto-Terzan 5 more massive in the past than today (its current mass being 2 ∼ 10 6 M /circledot , Lanzoni et al. 2010), which possibly experienced at least two relatively short episodes of star formation with a time delay of a few Gyr.\nThere is an interesting chemical similarity between Terzan 5 and the bulge stellar population, which shows a metallicity distribution with two major peaks at sub-Solar and superSolar [Fe/H] and a third, minor component with significantly lower ([Fe/H] ≈ -1 . 0) metallicity (see e.g. Zoccali et al. 2008; Hill et al. 2011; Johnson et al. 2011; Rich, Origlia & Valenti 2012; Uttenthaler et al. 2012; Ness et al. 2013a,b, and references therein). These bulge stellar populations show [ α /Fe] enhancement up to about Solar [Fe/H], and then a progressive decline towards Solar values at super-Solar [Fe/H]. Such a trend is at variance either with the one observed in the thick disk, where the knee occurs at significantly lower values of [Fe/H], and with the rather flat distribution of the thin disc with about Solar [ α /Fe]. Chemical abundances of bulge dwarf stars from microlensing experiments (see e.g. Cohen et al. 2010; Bensby et al. 2013, and references therein) also suggest the presence of two populations, a sub-Solar and old one with [ α /Fe] enhancement, and a possibly younger, more metal-rich one with decreasing [ α /Fe] enhancement with increasing [Fe/H].\nThis Letter presents the discovery of 3 red giant stars belonging to Terzan 5, with metallicity far below the sub-Solar component observed so far.\n2. Observations and chemical abundance analysis\nIn the context of an ongoing spectroscopic survey with VLT-FLAMES and Keck-DEIMOS of the Terzan 5 stellar populations, aimed at constructing a massive database of radial velocities and metallicities (Massari et al.; Ferraro et al.; 2014 in preparation), we found some indications of the presence of a minor ( ∼ 3%) component significantly more metal-poor than the sub-Solar population of Terzan 5. We acquired high resolution spectra of 3 radial velocity candidate metal-poor giants members of Terzan 5. Observations using NIRSPEC (McLean 1998) at Keck II were under-\nken on 17 June 2013. We used the NIRSPEC-5 setting to enable observations in the H -band and a 0 . 43 '' slit width that provides an overall spectral resolution R=25,000.\nData reduction has been performed by using the REDSPEC IDL-based package developed at the UCLA IR Laboratory. Each spectrum has been sky subtracted by using nod pairs, corrected for flat-field and calibrated in wavelength using arc lamps. An O-star spectrum observed during the same night has been used to remove to check and remove telluric features. The signal to noise ratio iper rersolution element of the final spectra is always > 30. Figure 1 shows portions of the observed spectra and the comparison with a Terzan 5 giant with similar stellar parameters and higher iron content from the sub-Solar population studied by Origlia et al. (2011).\nWe compare the observed spectra with synthetic ones and we obtain accurate chemical abundances of C and O using molecular lines and of Fe, Ca, Si, Mg, Ti and Al using neutral atomic lines, as also described in Origlia et al. (2011) and references therein.\nWe made use of both spectral synthesis analysis and equivalent width measurements of isolated lines. Synthetic spectra covering a wide range of stellar parameters and elemental abundances have been computed by using the same code as in Origlia et al. (2011) and described in detail in Origlia, Rich & Castro (2002) and Origlia & Rich (2004). The code uses the LTE approximation, the molecular blanketed model atmospheres of Johnson, Bernat & Krupp (1980) at temperatures ≤ 4000 K, and the Grevesse & Sauval (1998) abundances for the Solar reference.\nStellar temperatures have been first estimated from colors, by using the reddening estimates by Massari et al. (2013) and the color-temperature scale by Montegriffo et al. (1998), calibrated on globular cluster giants. Gravity has been estimated from theoretical isochrones (Pietrinferni et al. 2004, 2006), according to the position of the stars on the red giant branch (RGB). An average microturbulence velocity of 2 km/s has been adopted (see e.g. Origlia et al. 1997, for a detailed discussion). The simultaneous spectral fitting of the CO and OH molecular lines that are especially sensitive to temperature, gravity and microturbulence variations (see also Origlia, Rich & Castro 2002),\nallow us to fine-tune our best-fit adopted stellar parameters.\n3. Results\nOur provisional estimate for the systemic velocity of Terzan 5, as inferred from our VLTFLAMES and Keck-DEIMOS survey, is -82 km/s with a velocity dispersion of ≈ 15 km/s.\nFrom the NIRSPEC spectra we first measured the radial velocity of the 3 stars under study and confirm values within ≈ 1 σ from the systemic velocity of Terzan 5 (see Table 1). These stars are located in the central region of Terzan 5, at distances between 13 and 71 arcsec from the center (see Table 1). Our VLT-FLAMES and KeckDEIMOS survey shows that in this central region the contamination by field stars with similar radial velocities and metallicity is negligible (well below 1%). Preliminary analysis of proper motions also indicates that these stars are likely members of Terzan 5.\nWe then measured the chemical abundances of iron, alpha-elements, carbon and aluminum. Our best-fit estimates of the stellar temperature and gravity, radial velocity and chemical abundances with 1 σ random errors are listed in Table 1. In the evaluation of the overall error budget we also estimate that systematics due to ∆T eff ± 200 K, ∆log g ± 0.5 dex, ∆ ξ ± 0.5 km/s variations in the adopted stellar parameters can affect the inferred abundances by ≈ ± 0 . 15 dex. However, the derived abundance ratios are less dependent on the systematic error, since most of the spectral features used to measure abundance ratios have similar trends with varying the stellar parameters, and at least some degeneracy between abundance and the latter is canceled out.\nWe find the average iron abundance [Fe/H]=0.79 ± 0.04 r.m.s. to be significantly lower (by a factor of ∼ 3) than the value of the sub-Solar population ([Fe/H]= -0 . 25), pointing towards the presence of a distinct population in Terzan 5, rather than to the low metallicity tail of the subSolar component.\nAs shown in Figure 2, our newly discovered metal-poor population has an average α -enhancement ([ α /Fe]= +0 . 36 ± 0 . 04 r.m.s.) similar to that of the sub-Solar one, indicating that both populations likely formed early and on short\ntimescales from a gas polluted by type II SNe.\nAs the stars belonging to the sub-Solar component, also these other giants with low iron content show an enhanced [Al/Fe] abundance ratio (average [Al/Fe]= +0 . 41 ± 0 . 18 r.m.s.) and no evidence of Al-Mg and Al-O anti-correlations, and/or large [O/Fe] and [Al/Fe] scatters, although no firm conclusion can be drawn with 3 stars only.\nWe also measured some [C/Fe] depletion (at least in stars #243 and #262), as commonly found in giant stars and explained with mixing processes in the stellar interiors during the evolution along the RGB.\n4. Discussion and Conclusions\nNew spectroscopic observations of 3 stars, members of Terzan 5, have provided a further evidence of the complex nature of this stellar system and of its likely connection with the bulge formation and evolution history.\nWe find that Terzan 5 hosts a third, metalpoorer population with average [Fe/H]= -0 . 79 ± 0 . 04 r.m.s. and [ α /Fe] enhancement. From our VLT-FLAMES/Keck-DEIMOS survey, we estimate that this component represents a minor fraction (a few percent) of the stellar populations in Terzan 5.\nNotably, a similar fraction ( ≈ 5%) of metalpoor stars ([Fe/H] ≈ -1) has been also detected in the bulge (see e.g. Ness et al. 2013a,b, and references therein). This metal-poor population shows a kinematics typical of a slowly rotating spheroidal or a metal weak thick disk component.\nOur discovery significantly enlarges the metallicity range covered by Terzan 5, which amounts to ∆[Fe/H] ≈ 1 dex. Such a value is completely unexpected and unobserved in genuine globular clusters. Indeed, within the Galaxy only another globular-like system, namely ω Centauri, harbors stellar populations with a large ( > 1 dex) spread in iron (Norris & Da Costa 1995; Sollima et al. 2005; Johnson & Pilachowski 2010; Pancino et al. 2011). This evidence strongly sets Terzan 5 and ω Centauri apart from the class of genuine globular clusters, and suggests a more complex formation and evolutionary history for these two multi-iron systems.\nIt is also interesting to note that detailed spectroscopic screening recently performed in\nω Centauri revealed an additional sub-component significantly more metal-poor (by ∆[Fe/H] ∼ 0 . 3 -0 . 4 dex) than the dominant population (Pancino et al. 2011). The authors suggest that this is best accounted for in a self-enrichment scenario, where these stars could be the remnants of the fist stellar generation in ω Centauri.\nThe three populations of Terzan 5 may also be explained with some self-enrichment. The narrow peaks in their metallicity distribution can be the result of a quite bursty star formation activity in the proto-Terzan 5, which should have been much more massive in the past to retain the SN ejecta and progressively enrich in metals its gas. However, Terzan 5 might also be the result of an early merging of fragments with sub-Solar metallicity at the epoch of the bulge/bar formation, and with younger and more metal-rich sub-structures following subsequent interactions with the central disk.\nHowever, apart from the similarity in terms of large iron range and possible self-enrichment, ω Centauri and Terzan 5 likely had quite different origins and evolution. It is now commonly accepted that ω Centauri can be the remnant of a dwarf galaxy accreted from outside the Milky Way (e.g. Bekki & Freeman 2003). At variance, the much higher metallicity of Terzan 5 and its chemical similarity to the bulge populations suggests some symbiotic evolution between these two stellar systems.\nThis research was supported by the Istituto Nazionale di Astrofisica (INAF, under contract PRIN-INAF 2010). The research is also part of the project COSMIC-LAB (http://www.cosmic-lab.eu) funded by the European Research Council (under contract ERC-2010-AdG-267675). The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The authors wish to thank the anonymous Referee for his/her useful comments.\nREFERENCES\nBarbuy, B., Bica, E., & Ortolani, S. 1998, A&A, 333, 117\nBensby, T. et al. 2013, A&A, 549, 147\nBekki, K., & Freeman, K. C. 2003, MNRAS, 346, L11\nCohen, J.G., Gould, A., Thompson, I.B., Feltzing, S., Bensby, T., Johnson, J.A., Huang, W., Melendez, J., Lucatello, S., & Asplund, M. 2010, ApJ, 711, L48\nFerraro, F.R., et al., 2009, Nature, 462, 483\nGrevesse, N., & Sauval, A. J. 1998, Space Science Reviews , 85, 161\nHill, V., Lecureur, A., Gomez, A., Zoccali, M., Schultheis, M., Babusiaux, C., Royer, F., Barbuy, B., Arenou, F., Minniti, D., & Ortolani, S. 2011, A&A, 535, 80\nJohnson, H. R., Bernat, A. P., & Krupp, B. M. 1980, ApJS, 42, 501\nJohnson, C. I., & Pilachowski, C. A. 2010, ApJ, 722, 1373\nJohnson, C.I., Rich, R.M., Fulbright, J.P, Valenti, E., & McWilliam, A. 2011, ApJ, 732, 108\nKing, I.R. 1972, A&A, 19, 166\nLanzoni, B., et al., 2010, ApJ, 717, 653\nMcLean, I. et al. 1998, SPIE, 3354, 566\nMassari, D., Mucciarelli, A., Dalessandro, E., Ferraro, F.R., Origlia, L., Lanzoni, B., Beccari, G., Rich, R.M., Valenti, E., & Ransom, S.M. 2012, ApJ, 755, L32\nMontegriffo, P., Ferraro, F.R., Fusi Pecci, F., & Origlia, L., 1998, MNRAS, 297, 872\nNess, M., Freeman, K., Athanassoula, E., WylieDe-Boer, E., Bland-Hawthorn, J., Asplund, M., Lewis, G.F., Yong, D., Lane, R.R., & Kiss, L.L. 2013a, MNRAS, 430, 836\nNess, M., Freeman, K., Athanassoula, E., WylieDe-Boer, E., Bland-Hawthorn, J., Asplund, M., Lewis, G.F., Yong, D., Lane, R.R., Kiss, L.L., & Ibata, R. 2013b, MNRAS, 432, 2092\nNorris, J. E., & Da Costa, G. S. 1995, ApJ, 447, 680\nOriglia, L., Moorwood, A. F. M., & Oliva, E. 1993, A&A, 280, 536\nOriglia, L., Ferraro, F. R., Fusi Pecci, F., & Oliva, E. 1997, A&A, 321, 859\nOriglia, L., Rich, R. M., & Castro, S. 2002, AJ, 123, 1559\nOriglia, L., & Rich, R. M. 2004, AJ, 127, 3422\nOriglia, L., Rich, R.M., Ferraro, F.R., Lanzoni, B., Bellazzini, M., Dalessandro, E., Mucciarelli, A., Valenti, E., Beccari, G. 2011, ApJ, 726, L20\nPancino, E., Mucciarelli, A., Sbordone, L., et al. 2011, A&A, 527, A18\nPietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ, 612, 168\nPietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2006, ApJ, 642, 797\nRich, R.M., Origlia, L., & Valenti, E. 2012, ApJ, 746, 59\nSollima, A., Pancino, E., Ferraro, F. R., et al. 2005, ApJ, 634, 332\nUttenthaler, S., Schultheis, M., Nataf, D.M., Robin, A.C., Lebzelter, T., & Chen, B. 2012, A&A, 546, 57\nValenti, E., Ferraro, F. R., & Origlia, L., 2007, AJ, 133, 1287\nZoccali, M., Hill, V., Lecureur, A., Barbuy, B., Renzini, A., Minniti, D., G'omez, A., & Ortolani, S. 2008, A&A, 486, 177\n\n\n
Fig. 1.- Portion of the NIRSPEC H -band spectra of two red giants of Terzan 5 with similar temperature (T eff ≈ 3800 K), but different chemical abundance patterns (solid line for the metal-poor star #243, dotted line for a sub-Solar star at [Fe/H] ≈ -0.22 from Origlia et al. 2011). The metal poor giant #243 has significantly shallower features. A few atomic lines and molecular bands of interest are marked.
\n\n\n\n
Fig. 2.- Individual [ α /Fe] and [Al/Fe] abundance ratios as a function of [Fe/H] for the 3 observed metalpoor giants (solid dots), and the 20 sub-Solar (open squares) and 13 super-Solar (open triangles) giants from Origlia et al. (2011), for comparison. Typical errorbars are plotted in the top-right corner of each panel.
\n\n
\n\n
Table 1 Stellar parameters and abundances for the 3 observed giants in Terzan 5.
\n
\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"We report on the discovery of 3 metal-poor giant stars in Terzan 5, a complex stellar system in the the Galactic bulge, known to have two populations at [Fe/H]=-0.25 and +0.3. For these 3 stars we present new echelle spectra obtained with NIRSPEC at Keck II, which confirm their radial velocity membership and provide average [Fe/H]=-0.79 dex iron abundance and [alpha/Fe]=+0.36 dex enhancement. This new population extends the metallicity range of Terzan 5 0.5 dex more metal poor, and it has properties consistent with having formed from a gas polluted by core collapse supernovae. Subject headings: Galaxy: bulge - Galaxy: abundances - stars: abundances - stars: late-type techniques: spectroscopic - infrared: stars","pages":[1]},{"title":"1. Introduction","content":"Terzan 5 is a complex stellar system in the Galactic Bulge. It suffers from huge extinction, its average color excess being E( B -V ) = 2 . 38 (Barbuy et al. 1998; Valenti et al. 2007), and it is also affected by significant differential reddening (∆E( B -V ) /similarequal 0 . 7 mag, Massari et al. 2013). For years it has been classified as a globular cluster, although soon after its discovery its true nature was already disputed (see, e.g., King 1972). Recent high resolution imaging in the near infrared (IR) obtained with the Multi-conjugate Adaptive Optics Demonstrator (MAD) at ESOVLT, revealed the presence of two distinct red clumps that cannot be explained by differen- tial reddening or distance effects (Ferraro et al. 2009). Prompt near infrared spectroscopy with NIRSPEC at Keck II demonstrated that the two stellar populations are characterized by very different iron abundances ([Fe/H]= -0 . 2 and +0.3). Subsequent spectroscopic studies of 33 red giant stars (Origlia et al. 2011) fully confirmed the large metallicity difference between the two populations. The sub-Solar component has [Fe/H]= -0 . 25 ± 0 . 07 r.m.s. and it is α -enhanced, similar to the old bulge population that likely formed at early epochs and from a gas enriched by a huge amount of type II supernovae (SNe). The super-Solar component, which is possibly a few Gyr younger, has [Fe/H]= +0 . 27 ± 0 . 04 and approximately Solar [ α /Fe] abundance ratio, indicating that it should have originated from a gas polluted by both SNe II and Ia on a longer timescale. Both components show a small internal metallicity spread and the most metal-rich population is also more centrally concentrated (Ferraro et al. 2009; Lanzoni et al. 2010). These observational 1 facts could be accounted for by a proto-Terzan 5 more massive in the past than today (its current mass being 2 ∼ 10 6 M /circledot , Lanzoni et al. 2010), which possibly experienced at least two relatively short episodes of star formation with a time delay of a few Gyr. There is an interesting chemical similarity between Terzan 5 and the bulge stellar population, which shows a metallicity distribution with two major peaks at sub-Solar and superSolar [Fe/H] and a third, minor component with significantly lower ([Fe/H] ≈ -1 . 0) metallicity (see e.g. Zoccali et al. 2008; Hill et al. 2011; Johnson et al. 2011; Rich, Origlia & Valenti 2012; Uttenthaler et al. 2012; Ness et al. 2013a,b, and references therein). These bulge stellar populations show [ α /Fe] enhancement up to about Solar [Fe/H], and then a progressive decline towards Solar values at super-Solar [Fe/H]. Such a trend is at variance either with the one observed in the thick disk, where the knee occurs at significantly lower values of [Fe/H], and with the rather flat distribution of the thin disc with about Solar [ α /Fe]. Chemical abundances of bulge dwarf stars from microlensing experiments (see e.g. Cohen et al. 2010; Bensby et al. 2013, and references therein) also suggest the presence of two populations, a sub-Solar and old one with [ α /Fe] enhancement, and a possibly younger, more metal-rich one with decreasing [ α /Fe] enhancement with increasing [Fe/H]. This Letter presents the discovery of 3 red giant stars belonging to Terzan 5, with metallicity far below the sub-Solar component observed so far.","pages":[1,2]},{"title":"2. Observations and chemical abundance analysis","content":"In the context of an ongoing spectroscopic survey with VLT-FLAMES and Keck-DEIMOS of the Terzan 5 stellar populations, aimed at constructing a massive database of radial velocities and metallicities (Massari et al.; Ferraro et al.; 2014 in preparation), we found some indications of the presence of a minor ( ∼ 3%) component significantly more metal-poor than the sub-Solar population of Terzan 5. We acquired high resolution spectra of 3 radial velocity candidate metal-poor giants members of Terzan 5. Observations using NIRSPEC (McLean 1998) at Keck II were under- ken on 17 June 2013. We used the NIRSPEC-5 setting to enable observations in the H -band and a 0 . 43 '' slit width that provides an overall spectral resolution R=25,000. Data reduction has been performed by using the REDSPEC IDL-based package developed at the UCLA IR Laboratory. Each spectrum has been sky subtracted by using nod pairs, corrected for flat-field and calibrated in wavelength using arc lamps. An O-star spectrum observed during the same night has been used to remove to check and remove telluric features. The signal to noise ratio iper rersolution element of the final spectra is always > 30. Figure 1 shows portions of the observed spectra and the comparison with a Terzan 5 giant with similar stellar parameters and higher iron content from the sub-Solar population studied by Origlia et al. (2011). We compare the observed spectra with synthetic ones and we obtain accurate chemical abundances of C and O using molecular lines and of Fe, Ca, Si, Mg, Ti and Al using neutral atomic lines, as also described in Origlia et al. (2011) and references therein. We made use of both spectral synthesis analysis and equivalent width measurements of isolated lines. Synthetic spectra covering a wide range of stellar parameters and elemental abundances have been computed by using the same code as in Origlia et al. (2011) and described in detail in Origlia, Rich & Castro (2002) and Origlia & Rich (2004). The code uses the LTE approximation, the molecular blanketed model atmospheres of Johnson, Bernat & Krupp (1980) at temperatures ≤ 4000 K, and the Grevesse & Sauval (1998) abundances for the Solar reference. Stellar temperatures have been first estimated from colors, by using the reddening estimates by Massari et al. (2013) and the color-temperature scale by Montegriffo et al. (1998), calibrated on globular cluster giants. Gravity has been estimated from theoretical isochrones (Pietrinferni et al. 2004, 2006), according to the position of the stars on the red giant branch (RGB). An average microturbulence velocity of 2 km/s has been adopted (see e.g. Origlia et al. 1997, for a detailed discussion). The simultaneous spectral fitting of the CO and OH molecular lines that are especially sensitive to temperature, gravity and microturbulence variations (see also Origlia, Rich & Castro 2002), allow us to fine-tune our best-fit adopted stellar parameters.","pages":[2,3]},{"title":"3. Results","content":"Our provisional estimate for the systemic velocity of Terzan 5, as inferred from our VLTFLAMES and Keck-DEIMOS survey, is -82 km/s with a velocity dispersion of ≈ 15 km/s. From the NIRSPEC spectra we first measured the radial velocity of the 3 stars under study and confirm values within ≈ 1 σ from the systemic velocity of Terzan 5 (see Table 1). These stars are located in the central region of Terzan 5, at distances between 13 and 71 arcsec from the center (see Table 1). Our VLT-FLAMES and KeckDEIMOS survey shows that in this central region the contamination by field stars with similar radial velocities and metallicity is negligible (well below 1%). Preliminary analysis of proper motions also indicates that these stars are likely members of Terzan 5. We then measured the chemical abundances of iron, alpha-elements, carbon and aluminum. Our best-fit estimates of the stellar temperature and gravity, radial velocity and chemical abundances with 1 σ random errors are listed in Table 1. In the evaluation of the overall error budget we also estimate that systematics due to ∆T eff ± 200 K, ∆log g ± 0.5 dex, ∆ ξ ± 0.5 km/s variations in the adopted stellar parameters can affect the inferred abundances by ≈ ± 0 . 15 dex. However, the derived abundance ratios are less dependent on the systematic error, since most of the spectral features used to measure abundance ratios have similar trends with varying the stellar parameters, and at least some degeneracy between abundance and the latter is canceled out. We find the average iron abundance [Fe/H]=0.79 ± 0.04 r.m.s. to be significantly lower (by a factor of ∼ 3) than the value of the sub-Solar population ([Fe/H]= -0 . 25), pointing towards the presence of a distinct population in Terzan 5, rather than to the low metallicity tail of the subSolar component. As shown in Figure 2, our newly discovered metal-poor population has an average α -enhancement ([ α /Fe]= +0 . 36 ± 0 . 04 r.m.s.) similar to that of the sub-Solar one, indicating that both populations likely formed early and on short timescales from a gas polluted by type II SNe. As the stars belonging to the sub-Solar component, also these other giants with low iron content show an enhanced [Al/Fe] abundance ratio (average [Al/Fe]= +0 . 41 ± 0 . 18 r.m.s.) and no evidence of Al-Mg and Al-O anti-correlations, and/or large [O/Fe] and [Al/Fe] scatters, although no firm conclusion can be drawn with 3 stars only. We also measured some [C/Fe] depletion (at least in stars #243 and #262), as commonly found in giant stars and explained with mixing processes in the stellar interiors during the evolution along the RGB.","pages":[3]},{"title":"4. Discussion and Conclusions","content":"New spectroscopic observations of 3 stars, members of Terzan 5, have provided a further evidence of the complex nature of this stellar system and of its likely connection with the bulge formation and evolution history. We find that Terzan 5 hosts a third, metalpoorer population with average [Fe/H]= -0 . 79 ± 0 . 04 r.m.s. and [ α /Fe] enhancement. From our VLT-FLAMES/Keck-DEIMOS survey, we estimate that this component represents a minor fraction (a few percent) of the stellar populations in Terzan 5. Notably, a similar fraction ( ≈ 5%) of metalpoor stars ([Fe/H] ≈ -1) has been also detected in the bulge (see e.g. Ness et al. 2013a,b, and references therein). This metal-poor population shows a kinematics typical of a slowly rotating spheroidal or a metal weak thick disk component. Our discovery significantly enlarges the metallicity range covered by Terzan 5, which amounts to ∆[Fe/H] ≈ 1 dex. Such a value is completely unexpected and unobserved in genuine globular clusters. Indeed, within the Galaxy only another globular-like system, namely ω Centauri, harbors stellar populations with a large ( > 1 dex) spread in iron (Norris & Da Costa 1995; Sollima et al. 2005; Johnson & Pilachowski 2010; Pancino et al. 2011). This evidence strongly sets Terzan 5 and ω Centauri apart from the class of genuine globular clusters, and suggests a more complex formation and evolutionary history for these two multi-iron systems. It is also interesting to note that detailed spectroscopic screening recently performed in ω Centauri revealed an additional sub-component significantly more metal-poor (by ∆[Fe/H] ∼ 0 . 3 -0 . 4 dex) than the dominant population (Pancino et al. 2011). The authors suggest that this is best accounted for in a self-enrichment scenario, where these stars could be the remnants of the fist stellar generation in ω Centauri. The three populations of Terzan 5 may also be explained with some self-enrichment. The narrow peaks in their metallicity distribution can be the result of a quite bursty star formation activity in the proto-Terzan 5, which should have been much more massive in the past to retain the SN ejecta and progressively enrich in metals its gas. However, Terzan 5 might also be the result of an early merging of fragments with sub-Solar metallicity at the epoch of the bulge/bar formation, and with younger and more metal-rich sub-structures following subsequent interactions with the central disk. However, apart from the similarity in terms of large iron range and possible self-enrichment, ω Centauri and Terzan 5 likely had quite different origins and evolution. It is now commonly accepted that ω Centauri can be the remnant of a dwarf galaxy accreted from outside the Milky Way (e.g. Bekki & Freeman 2003). At variance, the much higher metallicity of Terzan 5 and its chemical similarity to the bulge populations suggests some symbiotic evolution between these two stellar systems. This research was supported by the Istituto Nazionale di Astrofisica (INAF, under contract PRIN-INAF 2010). The research is also part of the project COSMIC-LAB (http://www.cosmic-lab.eu) funded by the European Research Council (under contract ERC-2010-AdG-267675). The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The authors wish to thank the anonymous Referee for his/her useful comments.","pages":[3,4]},{"title":"REFERENCES","content":"Barbuy, B., Bica, E., & Ortolani, S. 1998, A&A, 333, 117 Bensby, T. et al. 2013, A&A, 549, 147 Bekki, K., & Freeman, K. C. 2003, MNRAS, 346, L11 Cohen, J.G., Gould, A., Thompson, I.B., Feltzing, S., Bensby, T., Johnson, J.A., Huang, W., Melendez, J., Lucatello, S., & Asplund, M. 2010, ApJ, 711, L48 Ferraro, F.R., et al., 2009, Nature, 462, 483 Grevesse, N., & Sauval, A. J. 1998, Space Science Reviews , 85, 161 Hill, V., Lecureur, A., Gomez, A., Zoccali, M., Schultheis, M., Babusiaux, C., Royer, F., Barbuy, B., Arenou, F., Minniti, D., & Ortolani, S. 2011, A&A, 535, 80 Johnson, H. R., Bernat, A. P., & Krupp, B. M. 1980, ApJS, 42, 501 Johnson, C. I., & Pilachowski, C. A. 2010, ApJ, 722, 1373 Johnson, C.I., Rich, R.M., Fulbright, J.P, Valenti, E., & McWilliam, A. 2011, ApJ, 732, 108 King, I.R. 1972, A&A, 19, 166 Lanzoni, B., et al., 2010, ApJ, 717, 653 McLean, I. et al. 1998, SPIE, 3354, 566 Massari, D., Mucciarelli, A., Dalessandro, E., Ferraro, F.R., Origlia, L., Lanzoni, B., Beccari, G., Rich, R.M., Valenti, E., & Ransom, S.M. 2012, ApJ, 755, L32 Montegriffo, P., Ferraro, F.R., Fusi Pecci, F., & Origlia, L., 1998, MNRAS, 297, 872 Ness, M., Freeman, K., Athanassoula, E., WylieDe-Boer, E., Bland-Hawthorn, J., Asplund, M., Lewis, G.F., Yong, D., Lane, R.R., & Kiss, L.L. 2013a, MNRAS, 430, 836 Ness, M., Freeman, K., Athanassoula, E., WylieDe-Boer, E., Bland-Hawthorn, J., Asplund, M., Lewis, G.F., Yong, D., Lane, R.R., Kiss, L.L., & Ibata, R. 2013b, MNRAS, 432, 2092 Norris, J. E., & Da Costa, G. S. 1995, ApJ, 447, 680 Origlia, L., Moorwood, A. F. M., & Oliva, E. 1993, A&A, 280, 536 Origlia, L., Ferraro, F. R., Fusi Pecci, F., & Oliva, E. 1997, A&A, 321, 859 Origlia, L., Rich, R. M., & Castro, S. 2002, AJ, 123, 1559 Origlia, L., & Rich, R. M. 2004, AJ, 127, 3422 Origlia, L., Rich, R.M., Ferraro, F.R., Lanzoni, B., Bellazzini, M., Dalessandro, E., Mucciarelli, A., Valenti, E., Beccari, G. 2011, ApJ, 726, L20 Pancino, E., Mucciarelli, A., Sbordone, L., et al. 2011, A&A, 527, A18 Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ, 612, 168 Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2006, ApJ, 642, 797 Rich, R.M., Origlia, L., & Valenti, E. 2012, ApJ, 746, 59 Sollima, A., Pancino, E., Ferraro, F. R., et al. 2005, ApJ, 634, 332 Uttenthaler, S., Schultheis, M., Nataf, D.M., Robin, A.C., Lebzelter, T., & Chen, B. 2012, A&A, 546, 57 Valenti, E., Ferraro, F. R., & Origlia, L., 2007, AJ, 133, 1287 Zoccali, M., Hill, V., Lecureur, A., Barbuy, B., Renzini, A., Minniti, D., G'omez, A., & Ortolani, S. 2008, A&A, 486, 177","pages":[4,5]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"We report on the discovery of 3 metal-poor giant stars in Terzan 5, a complex stellar system in the the Galactic bulge, known to have two populations at [Fe/H]=-0.25 and +0.3. For these 3 stars we present new echelle spectra obtained with NIRSPEC at Keck II, which confirm their radial velocity membership and provide average [Fe/H]=-0.79 dex iron abundance and [alpha/Fe]=+0.36 dex enhancement. This new population extends the metallicity range of Terzan 5 0.5 dex more metal poor, and it has properties consistent with having formed from a gas polluted by core collapse supernovae. Subject headings: Galaxy: bulge - Galaxy: abundances - stars: abundances - stars: late-type techniques: spectroscopic - infrared: stars\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"Terzan 5 is a complex stellar system in the Galactic Bulge. It suffers from huge extinction, its average color excess being E( B -V ) = 2 . 38 (Barbuy et al. 1998; Valenti et al. 2007), and it is also affected by significant differential reddening (∆E( B -V ) /similarequal 0 . 7 mag, Massari et al. 2013). For years it has been classified as a globular cluster, although soon after its discovery its true nature was already disputed (see, e.g., King 1972). Recent high resolution imaging in the near infrared (IR) obtained with the Multi-conjugate Adaptive Optics Demonstrator (MAD) at ESOVLT, revealed the presence of two distinct red clumps that cannot be explained by differen- tial reddening or distance effects (Ferraro et al. 2009). Prompt near infrared spectroscopy with NIRSPEC at Keck II demonstrated that the two stellar populations are characterized by very different iron abundances ([Fe/H]= -0 . 2 and +0.3). Subsequent spectroscopic studies of 33 red giant stars (Origlia et al. 2011) fully confirmed the large metallicity difference between the two populations. The sub-Solar component has [Fe/H]= -0 . 25 ± 0 . 07 r.m.s. and it is α -enhanced, similar to the old bulge population that likely formed at early epochs and from a gas enriched by a huge amount of type II supernovae (SNe). The super-Solar component, which is possibly a few Gyr younger, has [Fe/H]= +0 . 27 ± 0 . 04 and approximately Solar [ α /Fe] abundance ratio, indicating that it should have originated from a gas polluted by both SNe II and Ia on a longer timescale. Both components show a small internal metallicity spread and the most metal-rich population is also more centrally concentrated (Ferraro et al. 2009; Lanzoni et al. 2010). These observational 1 facts could be accounted for by a proto-Terzan 5 more massive in the past than today (its current mass being 2 ∼ 10 6 M /circledot , Lanzoni et al. 2010), which possibly experienced at least two relatively short episodes of star formation with a time delay of a few Gyr. There is an interesting chemical similarity between Terzan 5 and the bulge stellar population, which shows a metallicity distribution with two major peaks at sub-Solar and superSolar [Fe/H] and a third, minor component with significantly lower ([Fe/H] ≈ -1 . 0) metallicity (see e.g. Zoccali et al. 2008; Hill et al. 2011; Johnson et al. 2011; Rich, Origlia & Valenti 2012; Uttenthaler et al. 2012; Ness et al. 2013a,b, and references therein). These bulge stellar populations show [ α /Fe] enhancement up to about Solar [Fe/H], and then a progressive decline towards Solar values at super-Solar [Fe/H]. Such a trend is at variance either with the one observed in the thick disk, where the knee occurs at significantly lower values of [Fe/H], and with the rather flat distribution of the thin disc with about Solar [ α /Fe]. Chemical abundances of bulge dwarf stars from microlensing experiments (see e.g. Cohen et al. 2010; Bensby et al. 2013, and references therein) also suggest the presence of two populations, a sub-Solar and old one with [ α /Fe] enhancement, and a possibly younger, more metal-rich one with decreasing [ α /Fe] enhancement with increasing [Fe/H]. This Letter presents the discovery of 3 red giant stars belonging to Terzan 5, with metallicity far below the sub-Solar component observed so far.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2. Observations and chemical abundance analysis\",\n \"content\": \"In the context of an ongoing spectroscopic survey with VLT-FLAMES and Keck-DEIMOS of the Terzan 5 stellar populations, aimed at constructing a massive database of radial velocities and metallicities (Massari et al.; Ferraro et al.; 2014 in preparation), we found some indications of the presence of a minor ( ∼ 3%) component significantly more metal-poor than the sub-Solar population of Terzan 5. We acquired high resolution spectra of 3 radial velocity candidate metal-poor giants members of Terzan 5. Observations using NIRSPEC (McLean 1998) at Keck II were under- ken on 17 June 2013. We used the NIRSPEC-5 setting to enable observations in the H -band and a 0 . 43 '' slit width that provides an overall spectral resolution R=25,000. Data reduction has been performed by using the REDSPEC IDL-based package developed at the UCLA IR Laboratory. Each spectrum has been sky subtracted by using nod pairs, corrected for flat-field and calibrated in wavelength using arc lamps. An O-star spectrum observed during the same night has been used to remove to check and remove telluric features. The signal to noise ratio iper rersolution element of the final spectra is always > 30. Figure 1 shows portions of the observed spectra and the comparison with a Terzan 5 giant with similar stellar parameters and higher iron content from the sub-Solar population studied by Origlia et al. (2011). We compare the observed spectra with synthetic ones and we obtain accurate chemical abundances of C and O using molecular lines and of Fe, Ca, Si, Mg, Ti and Al using neutral atomic lines, as also described in Origlia et al. (2011) and references therein. We made use of both spectral synthesis analysis and equivalent width measurements of isolated lines. Synthetic spectra covering a wide range of stellar parameters and elemental abundances have been computed by using the same code as in Origlia et al. (2011) and described in detail in Origlia, Rich & Castro (2002) and Origlia & Rich (2004). The code uses the LTE approximation, the molecular blanketed model atmospheres of Johnson, Bernat & Krupp (1980) at temperatures ≤ 4000 K, and the Grevesse & Sauval (1998) abundances for the Solar reference. Stellar temperatures have been first estimated from colors, by using the reddening estimates by Massari et al. (2013) and the color-temperature scale by Montegriffo et al. (1998), calibrated on globular cluster giants. Gravity has been estimated from theoretical isochrones (Pietrinferni et al. 2004, 2006), according to the position of the stars on the red giant branch (RGB). An average microturbulence velocity of 2 km/s has been adopted (see e.g. Origlia et al. 1997, for a detailed discussion). The simultaneous spectral fitting of the CO and OH molecular lines that are especially sensitive to temperature, gravity and microturbulence variations (see also Origlia, Rich & Castro 2002), allow us to fine-tune our best-fit adopted stellar parameters.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"3. Results\",\n \"content\": \"Our provisional estimate for the systemic velocity of Terzan 5, as inferred from our VLTFLAMES and Keck-DEIMOS survey, is -82 km/s with a velocity dispersion of ≈ 15 km/s. From the NIRSPEC spectra we first measured the radial velocity of the 3 stars under study and confirm values within ≈ 1 σ from the systemic velocity of Terzan 5 (see Table 1). These stars are located in the central region of Terzan 5, at distances between 13 and 71 arcsec from the center (see Table 1). Our VLT-FLAMES and KeckDEIMOS survey shows that in this central region the contamination by field stars with similar radial velocities and metallicity is negligible (well below 1%). Preliminary analysis of proper motions also indicates that these stars are likely members of Terzan 5. We then measured the chemical abundances of iron, alpha-elements, carbon and aluminum. Our best-fit estimates of the stellar temperature and gravity, radial velocity and chemical abundances with 1 σ random errors are listed in Table 1. In the evaluation of the overall error budget we also estimate that systematics due to ∆T eff ± 200 K, ∆log g ± 0.5 dex, ∆ ξ ± 0.5 km/s variations in the adopted stellar parameters can affect the inferred abundances by ≈ ± 0 . 15 dex. However, the derived abundance ratios are less dependent on the systematic error, since most of the spectral features used to measure abundance ratios have similar trends with varying the stellar parameters, and at least some degeneracy between abundance and the latter is canceled out. We find the average iron abundance [Fe/H]=0.79 ± 0.04 r.m.s. to be significantly lower (by a factor of ∼ 3) than the value of the sub-Solar population ([Fe/H]= -0 . 25), pointing towards the presence of a distinct population in Terzan 5, rather than to the low metallicity tail of the subSolar component. As shown in Figure 2, our newly discovered metal-poor population has an average α -enhancement ([ α /Fe]= +0 . 36 ± 0 . 04 r.m.s.) similar to that of the sub-Solar one, indicating that both populations likely formed early and on short timescales from a gas polluted by type II SNe. As the stars belonging to the sub-Solar component, also these other giants with low iron content show an enhanced [Al/Fe] abundance ratio (average [Al/Fe]= +0 . 41 ± 0 . 18 r.m.s.) and no evidence of Al-Mg and Al-O anti-correlations, and/or large [O/Fe] and [Al/Fe] scatters, although no firm conclusion can be drawn with 3 stars only. We also measured some [C/Fe] depletion (at least in stars #243 and #262), as commonly found in giant stars and explained with mixing processes in the stellar interiors during the evolution along the RGB.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"4. Discussion and Conclusions\",\n \"content\": \"New spectroscopic observations of 3 stars, members of Terzan 5, have provided a further evidence of the complex nature of this stellar system and of its likely connection with the bulge formation and evolution history. We find that Terzan 5 hosts a third, metalpoorer population with average [Fe/H]= -0 . 79 ± 0 . 04 r.m.s. and [ α /Fe] enhancement. From our VLT-FLAMES/Keck-DEIMOS survey, we estimate that this component represents a minor fraction (a few percent) of the stellar populations in Terzan 5. Notably, a similar fraction ( ≈ 5%) of metalpoor stars ([Fe/H] ≈ -1) has been also detected in the bulge (see e.g. Ness et al. 2013a,b, and references therein). This metal-poor population shows a kinematics typical of a slowly rotating spheroidal or a metal weak thick disk component. Our discovery significantly enlarges the metallicity range covered by Terzan 5, which amounts to ∆[Fe/H] ≈ 1 dex. Such a value is completely unexpected and unobserved in genuine globular clusters. Indeed, within the Galaxy only another globular-like system, namely ω Centauri, harbors stellar populations with a large ( > 1 dex) spread in iron (Norris & Da Costa 1995; Sollima et al. 2005; Johnson & Pilachowski 2010; Pancino et al. 2011). This evidence strongly sets Terzan 5 and ω Centauri apart from the class of genuine globular clusters, and suggests a more complex formation and evolutionary history for these two multi-iron systems. It is also interesting to note that detailed spectroscopic screening recently performed in ω Centauri revealed an additional sub-component significantly more metal-poor (by ∆[Fe/H] ∼ 0 . 3 -0 . 4 dex) than the dominant population (Pancino et al. 2011). The authors suggest that this is best accounted for in a self-enrichment scenario, where these stars could be the remnants of the fist stellar generation in ω Centauri. The three populations of Terzan 5 may also be explained with some self-enrichment. The narrow peaks in their metallicity distribution can be the result of a quite bursty star formation activity in the proto-Terzan 5, which should have been much more massive in the past to retain the SN ejecta and progressively enrich in metals its gas. However, Terzan 5 might also be the result of an early merging of fragments with sub-Solar metallicity at the epoch of the bulge/bar formation, and with younger and more metal-rich sub-structures following subsequent interactions with the central disk. However, apart from the similarity in terms of large iron range and possible self-enrichment, ω Centauri and Terzan 5 likely had quite different origins and evolution. It is now commonly accepted that ω Centauri can be the remnant of a dwarf galaxy accreted from outside the Milky Way (e.g. Bekki & Freeman 2003). At variance, the much higher metallicity of Terzan 5 and its chemical similarity to the bulge populations suggests some symbiotic evolution between these two stellar systems. This research was supported by the Istituto Nazionale di Astrofisica (INAF, under contract PRIN-INAF 2010). The research is also part of the project COSMIC-LAB (http://www.cosmic-lab.eu) funded by the European Research Council (under contract ERC-2010-AdG-267675). The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The authors wish to thank the anonymous Referee for his/her useful comments.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Barbuy, B., Bica, E., & Ortolani, S. 1998, A&A, 333, 117 Bensby, T. et al. 2013, A&A, 549, 147 Bekki, K., & Freeman, K. C. 2003, MNRAS, 346, L11 Cohen, J.G., Gould, A., Thompson, I.B., Feltzing, S., Bensby, T., Johnson, J.A., Huang, W., Melendez, J., Lucatello, S., & Asplund, M. 2010, ApJ, 711, L48 Ferraro, F.R., et al., 2009, Nature, 462, 483 Grevesse, N., & Sauval, A. J. 1998, Space Science Reviews , 85, 161 Hill, V., Lecureur, A., Gomez, A., Zoccali, M., Schultheis, M., Babusiaux, C., Royer, F., Barbuy, B., Arenou, F., Minniti, D., & Ortolani, S. 2011, A&A, 535, 80 Johnson, H. R., Bernat, A. P., & Krupp, B. M. 1980, ApJS, 42, 501 Johnson, C. I., & Pilachowski, C. A. 2010, ApJ, 722, 1373 Johnson, C.I., Rich, R.M., Fulbright, J.P, Valenti, E., & McWilliam, A. 2011, ApJ, 732, 108 King, I.R. 1972, A&A, 19, 166 Lanzoni, B., et al., 2010, ApJ, 717, 653 McLean, I. et al. 1998, SPIE, 3354, 566 Massari, D., Mucciarelli, A., Dalessandro, E., Ferraro, F.R., Origlia, L., Lanzoni, B., Beccari, G., Rich, R.M., Valenti, E., & Ransom, S.M. 2012, ApJ, 755, L32 Montegriffo, P., Ferraro, F.R., Fusi Pecci, F., & Origlia, L., 1998, MNRAS, 297, 872 Ness, M., Freeman, K., Athanassoula, E., WylieDe-Boer, E., Bland-Hawthorn, J., Asplund, M., Lewis, G.F., Yong, D., Lane, R.R., & Kiss, L.L. 2013a, MNRAS, 430, 836 Ness, M., Freeman, K., Athanassoula, E., WylieDe-Boer, E., Bland-Hawthorn, J., Asplund, M., Lewis, G.F., Yong, D., Lane, R.R., Kiss, L.L., & Ibata, R. 2013b, MNRAS, 432, 2092 Norris, J. E., & Da Costa, G. S. 1995, ApJ, 447, 680 Origlia, L., Moorwood, A. F. M., & Oliva, E. 1993, A&A, 280, 536 Origlia, L., Ferraro, F. R., Fusi Pecci, F., & Oliva, E. 1997, A&A, 321, 859 Origlia, L., Rich, R. M., & Castro, S. 2002, AJ, 123, 1559 Origlia, L., & Rich, R. M. 2004, AJ, 127, 3422 Origlia, L., Rich, R.M., Ferraro, F.R., Lanzoni, B., Bellazzini, M., Dalessandro, E., Mucciarelli, A., Valenti, E., Beccari, G. 2011, ApJ, 726, L20 Pancino, E., Mucciarelli, A., Sbordone, L., et al. 2011, A&A, 527, A18 Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ, 612, 168 Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2006, ApJ, 642, 797 Rich, R.M., Origlia, L., & Valenti, E. 2012, ApJ, 746, 59 Sollima, A., Pancino, E., Ferraro, F. R., et al. 2005, ApJ, 634, 332 Uttenthaler, S., Schultheis, M., Nataf, D.M., Robin, A.C., Lebzelter, T., & Chen, B. 2012, A&A, 546, 57 Valenti, E., Ferraro, F. R., & Origlia, L., 2007, AJ, 133, 1287 Zoccali, M., Hill, V., Lecureur, A., Barbuy, B., Renzini, A., Minniti, D., G'omez, A., & Ortolani, S. 2008, A&A, 486, 177\",\n \"pages\": [\n 4,\n 5\n ]\n }\n]"}}},{"rowIdx":79,"cells":{"bibcode":{"kind":"string","value":"2013ApJS..205...19F"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1302.2087.pdf"},"content":{"kind":"string","value":"\nMHD modeling of solar system processes on geodesic grids\nV. Florinski 1 , 2 , X. Guo 2 , D. S. Balsara 3 , and C. Meyer 3\nReceived\n;\naccepted\nABSTRACT\nThis report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.\nSubject headings: magnetohydrodynamics (MHD) - methods: numerical - planets and satellites: magnetic fields - solar wind\n1. Introduction\nMany astrophysical plasma processes occur is regions of space surrounding a central compact object such as a star or a planet. Examples include stellar winds, planetary magnetospheres, supernova blast waves, and mass accretion onto compact objects. In all these environments the central body (a star or a planet) is typically much smaller than the characteristic scales of the plasma flows. In solving this class of problem on a computer, radial grids are commonly used because resolution can be readily increased near the origin. The simplest and the most commonly used is the standard spherical polar ( r , θ , ϕ ) grid (e.g., Washimi & Tanaka 1996; Pogorelov & Matsuda 1998; Ratkiewicz et al. 1998). This grid has a singularity on the z axis, where the control volume ∆ V = r 2 ∆ r sin θ ∆ θ ∆ ϕ , ∆ r , ∆ θ and ∆ ϕ being the grid cell dimensions in the radial, latitudinal, and azimuthal directions, respectively, vanishes as sin θ → 0. For explicit methods, this requires a small global time step to satisfy the Courant stability condition for a system of hyperbolic conservation laws for the entire grid (implicit or semi-implicit methods (e.g., T'oth et al. 1998) don't suffer from this limitation).\nSpherical grids are also used in simulating the transport of energetic charged particle, such as galactic cosmic rays, in turbulent astrophysical flows (Florinski & Pogorelov 2009). Transport models based on stochastic trajectory (Monte-Carlo) methods also suffer from the singularity on the polar axis. For example, in modeling cosmic-ray transport in the heliosphere it is common to align the z axis with the solar rotation axis. Because energetic particle transport (diffusion and drift) is very rapid at high latitudes due to a weaker magnetic field, a model must take vanishingly small time steps when a particle ventures close to the polar axis, which results in an inferior overall model efficiency.\nTime step requirements can be relaxed substantially by employing a grid that has a (nearly) uniform solid angle coverage. Examples include triangle, hexagon, or diamond\nbased geodesic grids (Du et al. 2003; Yeh 2007; Upadhyaya et al. 2010), obtained by a recursive division of a base platonic solid, and cubed sphere grids (Ronchi et al. 1996; Putman & Lin 2007). This paper introduces a framework for finite volume methods of solution of hyperbolic conservation laws in three dimensions, such as gas-dynamic or MHD systems, using spherical geodesic grids composed of hexagonal prism elements. Results are illustrated on a three-dimensional simulation of solar rotation and formation of corotating interaction regions (CIRs), an interaction between the solar wind and the surrounding local interstellar medium or LISM, and a simulation of Earth's magnetosphere. The new framework can be employed to model a broad range of large-scale 3D astrophysical plasma flows around a compact object where high computational efficiency is a priority.\n2. Grid structure\nOur three-dimensional grid consist of a 2D geodesic unstructured grid on a sphere combined with a concentric nonuniform radial stepping with smaller cells near the origin. The 2D surface grid is a Voronoi tesselation of a sphere produced from a dual triangular (Delaunay) tesselation. The latter is generated by a recursive subdivision of an icosahedron. We use the geodesic grid generator software developed by the ICON project ( http://icon.enes.org ) for use in atmospheric circulation modeling. An optimization algorithm (Heikes & Randall 1995), included in their code, produces a mesh with a difference in spherical surface areas between the largest and the smallest cells of less than 10%.\nThe number of vertices (V), edges (E) and faces (F) on a grid produced by l th division is given by\nN V = 20 · 2 2 l , N E = 30 · 2 2 l , N F = 10 · 2 2 l +2 . (1)\nIn this notation a level 0 grid is dual to the original icosahedron projected onto a unit\n\n\n
Fig. 1.- From left to right: level 3, 4, and 5 geodesic Voronoi grids produced by a recursive division of the base icosahedron.
\n\nsphere. The base shape of a control volume in a finite volume method is a spherical hexagonal prism with the exception of 12 pentagonal prisms located at the vertices of the original icosahedron. Level 3, 4, and 5 hexagonal geodesic grids are shown in Figure 1.\nA more detailed view of the Voronoi grid structure is given in Figure 2. A hexagonal face F m (shaded) is shown surrounded by six adjacent faces F m 1 .. F m 6 . The face centers of the dual triangle-based Delaunay grid (blue lines) are located at the Voronoi vertices (V); likewise, the former's vertices are at the Voronoi grid's face centers (F). The edges of the Voronoi and Delaunay grids on a sphere are mutually orthogonal and intersect at their midpoints. To achieve acceptable resolution in typical astrophysical flow modeling problems level 5 or higher geodesic grids should be used. Most of our simulations use level 6 mesh containing 40,962 Voronoi polygons. We emphasize that these 40,962 hexagons are distributed evenly over the surface of each spherical layer of cells. This gives us a resolution of about 3 × 10 -4 steradians in solid angle which corresponds to an angular resolution of one degree. By condensing the mesh in the radial direction, one can achieve a further degree of refinement as required by the problem.\nWe introduce a set of unit vectors normal to the edges of the Voronoi grid ˆ n mn , where the index m refers to the m th face and n = [1 , 6] is the number of the edge counted in a counter-clockwise direction. The unit vectors are tangential to the surface of the sphere. The corresponding edge lengths, measured along great circles, are designated L mn . The outward radial unit vector at the cell center is ˆ r m . We also designate the area of the face on the unit sphere as A m . In this notation the control volume is equal to\n∆ V im = A m r 2 i ∆ r i , (2)\nwhere i is the index on the radial axis. The areas A m are calculated by dividing each hexagonal face into six (five for pentagons) spherical triangles and adding up their areas using standard expressions from spherical trigonometry. Having defined our cell dimensions\n\n\n
Fig. 2.- A close up view of the geodesic grid illustrating the relationships between a face F m and its neighboring faces F m 1 .. F m 6 . Unit vectors normal to the edges of the Voronoi face ˆ n m 1 .. ˆ n m 6 are shown. A fragment of the Delaunay grid is drawn with blue lines.
\n\nis this way we can proceed to integrate a system of conservation laws inside a control volume.\nIt is worth pointing out that a similar geodesic-mesh-based model was developed by Nakamizo et al. (2009) Their mesh was generated from a dodecahedron by first dividing each face into five triangles followed by a recursive subdivision of each triangle into four smaller triangles. The resulting unstructured grid topology is similar (but not identical) to our dual Delaunay grid. Interestingly, in the model of Nakamizo et al. (2009) computations are also performed on a hexagonal grid, generated by connecting the centroids of the Delaunay triangles.\n3. MHD conservation laws\nFor the heliospheric and magnetospheric problems ( § 6) we solve a modified set of MHD equations, written in terms of conservative variables U and fluxes F as\n∂ U ∂t + ∇· F = Q , (3)\nwhere\nin CGS units. Here ρ is density, u is velocity, B is magnetic field, I is a unit dyadic, p = p g + B 2 / (8 π ) is the total pressure, p g being the gas kinetic pressure, and the energy density e is given by\nU = ρ ρ u e B , F = ρ u ρ uu + p I -BB / (4 π ) ( e + p ) u -B ( u · B ) / (4 π ) uB -Bu (4)\ne = ρu 2 2 + p g γ -1 + B 2 8 π . (5)\nWe employ two alternative models to control the divergence of magnetic field. The first\nis the numerical scheme proposed by Powell et al. (1999), where numerical magnetic field divergence is advected out of the simulation domain with the flow velocity. This scheme modifies the system of conservation laws with a hyperbolic source term\nQ = -∇· B 0 B / (4 π ) u · B / (4 π ) u . (6)\nThe second scheme employs a generalized Lagrange multiplier (GLM) ψ for a mixed hyperbolic-parabolic correction (Dedner et al. 2002). The system (4) is extended with an additional transport equation for ψ\n∂ψ ∂t + ∇· ( c 2 h B ) = -c 2 h c 2 p ψ, (7)\nwhere c h is a constant, isotropic advection speed, taken to be somewhat faster than the fastest wave speed in the problem, and c p is related to the rate of decay of ψ . Dedner et al. (2002) proposed two methods to fix the value of c p : (a) by fixing the time rate of decay of the GLM variable r d = exp( -∆ tc 2 h /c 2 p ), where ∆ t is the time step, and (b) by fixing the characteristic length over which the decay occurs, given by l d = c 2 p /c h . Both methods are available in our code. In the GLM scheme the conservation law for magnetic field (Faraday's law) is modified to read\n∂ B ∂t + ∇· ( uB -Bu + ψ I ) = 0 . (8)\nThe system (3) is integrated over a control volume ∆ V im shown in Figure 3 to obtain the finite volume method\n∆ V im ∆ U im ∆ t = -A m ( r 2 i +1 / 2 F i +1 / 2 ,m -r 2 i -1 / 2 F i -1 / 2 ,m ) · ˆ r m -r i ∆ r i 6 ∑ n =1 L mn F i ( mn ) · ˆ n mn +∆ V im Q im . (9)\n\n\n
Fig. 3.- A prismatic control volume showing the unit vectors normal to the interfaces.
\n\nHere F i ( mn ) is the flux at the center of the edge shared by the m th cell and its n th neighbor (where n = [1 , 6]). Note that the source term Q does not involve the right hand side of Eq. (7). The parabolic correction is applied by multiplying the value of ψ obtained from the finite volume scheme (9) by the decay factor,\nψ → ψ × r d , method (a) , e -∆ tc h /l d , method (b) . (10)\nIn our simulations we typically use 0 . 9 < r d < 1 and l d equal to several times the smallest linear grid size.\nThe divergence of the magnetic field is obtained from Gauss's theorem in the same way as ∇· F is calculated in Eq. (9). More generally, the divergence and curl operators acting on an arbitrary vector v may be written as\n∇· v = ˆ r m · ( r 2 i +1 / 2 v i +1 / 2 ,m -r 2 i -1 / 2 v i -1 / 2 ,m ) r 2 i ∆ r i + 6 ∑ n =1 L mn ˆ n mn · v i ( mn ) r i A m , (11)\n∇× v = ˆ r m × ( r 2 i +1 / 2 v i +1 / 2 ,m -r 2 i -1 / 2 v i -1 / 2 ,m ) r 2 i ∆ r i + 6 ∑ n =1 L mn ˆ n mn × v i ( mn ) r i A m . (12)\nAn evaluation of a curl is necessary when modeling energetic charged particle transport, where the particle's drift velocity is proportional to ∇× ( B /B 2 ). The values of primitive variables at face centers v i ± 1 / 2 and v i ( mn ) may be approximated as arithmetic averages of the values in the two cells separated by the face. A more accurate approach, adopted here, is to use interface resolved states obtained from a solution to the corresponding Riemann problem (see § 5).\nThe finite volume system of conservation laws is integrated with a second order unsplit TVD-like method (see below). Right and left interface values are calculated in the usual way using some appropriate linear reconstruction to achieve second-order spatial accuracy. Fluxes are calculated from a solution to a one-dimensional (projected) Riemann problem\nat each cell interface. Finally, time is advanced using either a first order (Euler) or, more commonly, a second order (Runge-Kutta) scheme, depending on the nature of the problem.\n4. Reconstruction\nTo achieve second order spatial accuracy we employ limited piecewise linear reconstruction on primitive variables V = ( ρ, u , p g , B , ψ ) T . In the radial direction the simplest and the most robust limiter available is the MinMod, with slopes S im given by\nS MM im = minmod( S -im , S + im ) , (13)\nwhere the left and the right slopes on an asymmetric stencil are, respectively\nS -im = 2 V im -V i -1 ,m ∆ r i -1 +∆ r i , S + im = 2 V i +1 ,m -V im ∆ r i +∆ r i +1 . (14)\nAlso available is the more compressive monotonized central (MC) limiter (van Leer 1977) with\nS MC im = minmod [ 2 S -im , 2 S + im , (∆ r i +∆ r i +1 ) S -im +(∆ r i -1 +∆ r i ) S + im ∆ r i -1 +2∆ r i +∆ r i +1 ] . (15)\nThe third option is the weighted essentially non-oscillatory (WENO) limiter\nS WENO im = ¯ w -im S -im + ¯ w + im S + im , (16)\nwhere the WENO weights ¯ w are given by\n¯ w -im = ( S -im 2 + /epsilon1 ) -p ( S -im 2 + /epsilon1 ) -p +( S + im 2 + /epsilon1 ) -p , ¯ w + im = ( S + im 2 + /epsilon1 ) -p ( S -im 2 + /epsilon1 ) -p +( S + im 2 + /epsilon1 ) -p , (17)\nwhere p is an integer constant here taken to be 2, and /epsilon1 is a small number, which we took to be 10 -12 in our simulations. The ( S + im ) 2 p and ( S -im ) 2 p terms are traditionally referred to as smoothness measures in WENO methodology.\nFor two-dimensional reconstruction on the surface of a sphere the code can use either a minimum angle plane (MAPR) method (Christov & Popov 2008) or a 2D version of the\nweighted essentially non-oscillatory (WENO) scheme (Friedrich 1998). Common to both schemes, a local two-dimensional coordinate system ( ξ , η ) is introduced on the sphere, with its origin at the face center F m . The coordinates of the six adjacent cell centers ( ξ mn , η mn ) are then calculated in this frame. These coordinates are measured along two arbitrary great circles intersecting at right angles at the position of the central face F m . The procedure is illustrated in Figure 4. The angle A and the great circle distance between the face centers c are effectively polar coordinates on the surface of a sphere. The local coordinates of F mn are calculated as\nξ mn = c cos A, η mn = c sin A. (18)\nNext, the six two-dimensional slopes S ξ , S η are calculated from the triangles with vertices located at the cell centers F m , F mn , F m,n +1 (shown in blue in Figure 2) as\nS ξ imn = η mn ( V im,n +1 -V im ) -η m,n +1 ( V imn -V im ) η mn ξ m,n +1 -ξ mn η m,n +1 , (19)\nS η imn = -ξ mn ( V im,n +1 -V im ) -ξ m,n +1 ( V imn -V im ) η mn ξ m,n +1 -ξ mn η m,n +1 . (20)\nIn the MAPR method we evaluated the average slopes as\n¯ S imn = √ S ξ imn 2 + S η imn 2 . (21)\nThe reconstructed slopes S MAPR ξ,η im are those given by Eqs. (19) and (20) for which the average slope (20) is the smallest. Thus the method is a two-dimensional equivalent of the MinMod limiter. In the WENO method the reconstructed slopes are weighted arithmetic averages of all six slopes, namely\nS WENO ξ,η im = 6 ∑ n =1 ¯ w imn S ξ,η imn . (22)\nThe weights ¯ w imn of each slope are calculated as\n¯ w imn = w imn ∑ n w imn , (23)\n\n\n
Fig. 4.- Calculation of adjacent cell center (F mn ) coordinates in a local coordinate frame associated with a face F m . Every line shown is a segment of a great circle.
\n\nwhere\nw imn = ( S ξ imn 2 + S η imn 2 + /epsilon1 ) -p , (24)\nwhere we again use p = 2 and /epsilon1 = 10 -12 . Because edge centers lie midway between the corresponding two face centers F m and F mn on the Voronoi grid, the reconstructed values at edge midpoints V i ( mn ) can be computed as\nV i ( mn ) = V im + 1 2 S ξ im ξ mn + 1 2 S η im η mn . (25)\nThese values are used to calculate the intercell fluxes according to Eqs. (4), (7), and (8).\nThe code also implements a slope flattening algorithm that reduces the value of the slopes calculated by the reconstruction module in the vicinity of strong compressions (shocks). This prevents the occurrence of oscillations downstream of the shock. To construct a flattener, we calculate the minimum value of the fast magnetosonic wave speed a min f,im in each computational cell and its neighbors in the same spherical layer and in the layers above and below (a total of 21 cells). The shock detector function in each cell d im is then calculated as (Balsara et al. 2009)\nd im = min [ 1 , ∣ ∣ ∣ ∣ ( ∇· u ) im ∆ l im a min f,im δ +1 ∣ ∣ ∣ ∣ ] H [ -( ∇· u ) im ∆ l im a min f,im δ -1 ] , (26)\n∣ ∣ where ∆ l im is a characteristic dimension of the cell ∆ V im , δ is a constant of order 1 and H is the Heaviside step function. Subsequently, the slope in the cell im is calculated as a weighted sum of a slope obtained with the standard limiter, such as WENO, and that from a more diffusive limiter, such as MinMod or MAPR. For example, in the radial direction we could use\nS im = (1 -d im ) S WENO im + d im S MM im . (27)\n5. Riemann solvers\nThe fluxes F are calculated from an (approximate) solution to the one-dimensional Riemann problem at each interface between the prismatic cells. A suitable solver must be able to handle supersonic and transonic flows without losing positivity. Our tests revealed that modern HLL-type solvers (Batten et al. 1997; Gurski 2004) were generally superior to other solver types for the solar wind-LISM interaction problem, where they were least likely to produce a negative pressure upstream of a very strong (Mach number > 10) shock. Genuinely multi-dimensional Riemann solvers are now appearing in the literature (Balsara 2010, 2012), and they offer substantial advantages on logically rectangular meshes. However, the analogous work for unstructured meshes is the topic of vigorous research and was not incorporated in the present work.\nAn HLLC solver consists of four states: the left and the right unperturbed states plus two intermediate states separated by a tangential discontinuity. Designating the left and the right bounding wave speeds of the Riemann fan by S l and S r , respectively, the intercell flux may be written as\nF = F l , S l > 0 , F l + S l ( U ∗ l -U l ) , S l ≤ 0 ≤ S ∗ , F r + S r ( U ∗ r -U r ) , S ∗ ≤ 0 ≤ S r , F r , S r < 0 , (28)\n where F l = F ( U l ), F r = F ( U r ), and S ∗ is the speed of the intermediate wave (a tangential discontinuity). Because in a HLLC solver the normal velocity component and the total pressure only change across the outermost waves, the speed of the tangential discontinuity is readily calculated by applying the Rankine-Hugoniot conditions across these waves. This yields the speed\nS ∗ = ρ r u n,r ( S r -u n,r ) -p r + B 2 n,r / (4 π ) -ρ l u n,l ( S l -u n,l ) + p l -B 2 n,l / (4 π ) ρ r ( S r -u n,r ) -ρ l ( S l -u n,l ) , (29)\nwhere u n ( l,r ) and B n ( l,r ) are the normal-projected velocities and magnetic fields in the left and right states, respectively. Suppose two prismatic cells ( i, m 1 ) and ( i, m 2 ) share an interface with an index n 1 = [1 , 6] in the neighbor list of the first cell and n 2 = [1 , 6] in the neighbor list of the second cell (the definitions of 'first' and ''second' are arbitrary here; they could be defined, for example, by using the condition that m 1 < m 2 ). Then a normal velocity projection is defined as\nu n,l = u i ( m 1 n 1 ) · ˆ n m 1 n 1 , u n,r = u i ( m 2 n 2 ) · ˆ n m 1 n 1 , (30)\nwhere u i ( m 1 n 1 ) and u i ( m 2 n 2 ) are the reconstructed velocities given by (25), and ˆ n n 1 n 1 is the unit vector normal to the interface n 1 of the cell ( i, m 1 ), pointing outward. The values for B n ( l,r ) are computed in the same way.\nSeveral HLLC MHD solvers may be found in the literature, distinguished by their choice of the tangential velocity and magnetic field components in the intermediate states U ∗ l,r (unlike in gas dynamics, these states are not unique in MHD). Currently we employ a solver proposed by Li (2005). Its main feature is that no jump in magnetic field is permitted across the tangential discontinuity.\nA second option available in our model is the HLLD Riemann solver (Miyoshi & Kusano 2005). This type of solver incorporates two additional states U ∗∗ l,r separated from the corresponding 'single star' states by rotational (Alfv'enic) discontinuities, propagating to the left and to the right of the middle wave with speeds S ∗ l and S ∗ r respectively, given by\nS ∗ l = S ∗ -| B ∗ n | (4 πρ ∗ l ) 1 / 2 , S ∗ r = S ∗ + | B ∗ n | (4 πρ ∗ r ) 1 / 2 , (31)\nwhere B ∗ n is given by Eq. (34) below, and\nρ ∗ l = ρ l S l -u n,l S l -S ∗ , ρ ∗ r = ρ r S r -u n,r S r -S ∗ . (32)\nThe intercell flux is computed as\nF = F l , S l > 0 , F l + S l ( U ∗ l -U l ) , S l ≤ 0 ≤ S ∗ l , F l + S l ( U ∗ l -U l ) + S ∗ l ( U ∗∗ l -U ∗ l ) , S ∗ l ≤ 0 ≤ S ∗ , F r + S r ( U ∗ r -U r ) + S ∗ r ( U ∗∗ r -U ∗ r ) , S ∗ ≤ 0 ≤ S ∗ r , F r + S r ( U ∗ r -U r ) , S ∗ r ≤ 0 ≤ S r , F r , S r < 0 , (33)\n The HLLD solver is somewhat less robust than the HLLC counterpart because it has a singularity when one of the extremal waves is a switch-on shock. When this condition is encountered, the program falls back to the HLLC algorithm which is singularity-free.\nBecause of nonlinearity of the solvers, under rare circumstances one of the intermediate waves could fall outside of the bounding (fast) waves. To prevent this from happening, we take the speed of the bounding waves to be the maximum of the left, right, and intermediate HLL states. Because the HLL state depends on the wave speeds themselves, we perform an iteration procedure until the external waves could be moved out no further. In the event that either HLLC or HLLD solver fails to produce a positive pressure in any of the intermediate states, we fall back to the very robust but dissipative HLLE Riemann solver (Einfeldt et al. 1991) with a single intermediate state U ∗ .\nThe methods described above are used without modification with the source term divergence cleaning algorithm (Eq. 6). However, the GLM method introduces two additional waves moving with the speeds ± c h that carry changes in B n and ψ only. Because c h is the fastest wave speed, these waves bound the 'base' Riemann fan, comprised of 2, 3, or 5 waves in the HLLE, HLLC, and HLLD solvers, respectively. The intermediate states are readily obtained from the Rankine-Hugoniot conditions at the bounding waves as\nB ∗ n = B n,l + B n,r 2 -ψ r -ψ l 2 c h ,\n\n\n
Fig. 5.- Magnetic field magnitude at time t = 0 . 07 from the blast wave problem.
\n\nψ ∗ = ψ l + ψ r 2 -c h ( B n,r -B n,l ) 2 . (34)\nThese intermediate states serve as both the right and the left states for the actual Riemann solver. The advantage of this approach is that any possible jump in the normal component of B is taken up by these additional external waves.\nVery few genuinely three-dimensional test problems are available for spherical grids. For code verification we used a 3D blast wave problem similar to those presented by Gardiner & Stone (2008) and Balsara et al. (2009). The simulation region is constrained between r min = 0 . 01 and r max = 0 . 5. The radial cell width ∆ r increased outward monotonically from 0.00052 to 0.047. The inner boundary was treated as a perfectly conducting sphere with reflecting boundary conditions imposed. The initial conditions are ρ = 1, u = 0, and p = 10 ( r < 0 . 1), p = 0 . 1 ( r > 0 . 1). The initial magnetic field is given by the standard potential solution for a perfectly conducting sphere in a uniform external field, namely\nB r = B 0 ( 1 -r 3 min r 3 ) cos θ, (35)\nB θ = -B 0 ( 1 + r 3 min 2 r 3 ) sin θ. (36)\nThis solution was rotated such that the external field pointed in the direction (1 / √ 3 , 1 / √ 3 , 1 / √ 3). We used B 0 = 10 and γ = 1 . 4. The system was evolved until t = 0 . 07.\nFor this problem we chose a level 6 grid with 256 cells in the radial direction. The GLM version of the numerical scheme was used with the HLLC Riemann solver and WENO reconstruction. Figure 5 shows the magnitude of magnetic field at the end of the simulation on a linear scale. The flow structure of the solution is qualitatively similar to Gardiner & Stone (2008) and Balsara et al. (2009), consisting of an outermost fast shock wave and two dense shells of material elongated along the magnetic field. This problem did not trigger the slope flattening or positivity correction routines meaning it is not a very\ngood stress test of the code. Several more difficult problems simulating actual astrophysical plasma flows are discussed next.\n6. Numerical solutions of test problems\nTo illustrate the capabilities of the new model we present results from three different simulations of solar system plasma environments. The first is a dynamic MHD simulation of compressive structures in the solar wind known as corotating interaction regions (CIRs). This is a simple test problem with a strong degree of spherical symmetry. The second is a simulation of the structure of the global heliosphere, including regions on each side of the interface between the solar wind and LISM known as the heliopause. This problem involves mode complex transonic flows and a population of neutral atoms in addition to the plasma. Finally, our third test problem is a stationary structure of the Earth's magnetosphere. Unlike the two previous cases, this one is an example of a highly magnetized plasma environment.\n6.1. Test problem 1: Corotating interaction regions in the solar wind\nCorotating interaction regions (CIRs) are compressive structures produced through an interaction between high and low speed streams in the solar wind. CIRs are fully formed by the time they reach Earth's orbit (Siscoe 1972; Gosling et al. 1972). When the streams emanating from the Sun are approximately steady in the co-rotating frame, these compression regions form spirals in the solar equatorial plane that co-rotate with the Sun. The leading edge of a CIR is a forward compressional wave propagating into the slower solar wind ahead, whereas the tailing edge is a reverse wave propagating back into the trailing high speed stream. At large heliospheric distances the waves steepen into forward\nand reverse shocks. The entire plasma structure is convected with the solar wind and plays an important role in the dynamics of the heliosphere.\nCIRs have been extensively studied using global MHD simulation (Pizzo 1994; Riley et al. 2001; Usmanov & Goldstein 2006). To generate CIRs in a global MHD simulation we adopt the tilted-dipole flow geometry of Pizzo (1982) at the inner boundary, which is illustrated in Figure 6. In this figure 0 xyz is the fixed (heliographic) frame, where z is the solar rotation axis, and 0 x ' y ' z ' is a frame aligned with the Sun's magnetic axis z ' . The parameter γ is the dipole tilt angle, and β is the latitude of the fast-slow transition boundaries (blue circles) in the coordinate system 0 x ' y ' z ' . In the simulation discussed below we used β = ± 30 · .\nFollowing Pogorelov et al. (2007), one readily derives a quadratic equation for the latitude of the transition line θ as a function of the azimuthal angle ϕ ,\na sin 2 θ + b sin θ + c = 0 , (37)\nwhere\na = cos 2 γ +sin 2 γ tan 2 ϕ (cot γ cos γ +sin γ ) 2 b = 2sin β cos γ (1 + tan 2 ϕ ) (38) c = sin 2 β (1 + tan 2 ϕ cos 2 γ ) -cos 2 β sin 2 γ tan 2 ϕ.\nNote that when β = 0, θ ( ϕ ) reduces to the expression for the latitude of the magnetic equator given by Eq. (A6) of Pogorelov et al. (2007).\nWe simulated a region of the solar wind between r min = 0 . 5 AU and r max = 30 AU using 512 concentric grid layers of variable thickness (increasing outward). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s in the fast solar wind and n = 7 cm -3 , u = 400 km/s in the slow solar wind. The radial component of the magnetic field at 1 AU was B r = 28 µ G. These conditions were extended\n\n\n
Fig. 6.- A diagram of the assumed titled-dipole plasma flow geometry for the CIR simulation.
\n\nto the inner boundary using the conventional Parker solution for the solar wind and its magnetic field (Parker 1958). The dipole tilt angle was taken to be γ = 20 · . The boundary (shear layer) between the fast and the slow solar wind flows was located at a latitude of 30 · in the coordinate system aligned with the dipole axis. This simulation was performed on a level 6 geodesic grid. We chose the HLLC solver to evolve the time-dependent MHD equations, combined with the GLM divergence cleaning method; WENO reconstructions was used in all directions.\nFigure 7 (left) shows the logarithm of the magnetic field magnitude in the xz and xy planes using a cutout plot. Plasma velocity vectors are shown as arrows of variable length. The CIRs can be visually identified as higher density and magnetic field intensity regions (red). The maximum latitudinal extent of CIRs is given by the sum of the angle between the rotation and the dipole axes and the extent of the slow solar wind in the frame aligned with the dipole axis, i.e., γ + β = 50 · . In the equatorial plane, the spiral CIR structure is seen to be bounded by shock-like discontinuities.\nSeveral characteristic CIR features can be recognized in the plasma radial profiles shown in Figure 7 (right). We chose the profile along the direction 25 · northern latitude relative to the solar equatorial ( xy ) plane. The forward-reverse shock pairs are commonly observed at mid-latitudes, below the heliographic latitude of 26 · (Gosling & Pizzo 1999). They are shown with vertical dashed lines in the Figure. Shock pairs associated with CIRs are believed to be responsible for the observed 26-day recurrent decreases in galactic cosmic-ray intensity (Kota & Jokipii 1991; McKibben et al. 1999). Other features, such as the south-north flows are also identified through the north-south flow deflection angle /epsilon1 = sin -1 ( -u θ / | u | ) shown in the bottom panel. The transitions from northward (positive) to southward (negative) velocity are separated by roughly one Carrington rotation period (26 days) in our simulation. We conclude that the model is capable of reproducing the\n(km/s)\nv\n\n\n\n\n\n
Fig. 7.- Left: Magnetic field magnitude (log scale) in the meridional plane ( xz ) and the solar equatorial plane ( xy ) for the CIR simulation. Arrows are the plasma velocity vectors. Right: radial profiles along the direction ( θ , ϕ ) = (25 · , 135 · ) of (from top to bottom): plasma density (log scale), radial velocity, log thermal pressure, log magnetic field intensity, log temperature, and the north-south flow deflection angle /epsilon1 . Arrows mark the forward (pointing right) and reverse (pointing left) propagation of wave fronts.
\n\nessential CIR features and is consistent with the earlier simulations of this phenomenon.\n6.2. Test problem 2: The global heliosphere\nThe energy density in a supersonic stellar wind, such as the solar wind, decreases in inverse proportion to the square of the distance from the star. Eventually the outflow is unable to maintain pressure balance with the galactic environment near the star, comprised mostly of partially ionized hydrogen gas. The stellar wind undergoes a transition to a subsonic flow at a structure called a termination shock. A tangential discontinuity called an astropause (heliopause for the solar wind) separates the shocked stellar flow from the interstellar gas. A bow shock may develop in front of the astropause if the relative motion between the star and LISM is supersonic. In the case of heliosphere, the region between the termination shock and the boundary is called the heliosheath. The theory of stellar wind interfaces (as applied primarily to the heliosphere) has been developed in Parker (1961), Axford (1972), and Baranov et al. (1976). Recent three-dimensional MHD simulations of the interface could be found in Pogorelov et al. (2007) and Opher et al. (2007).\nTo simulate the structure of the heliospheric interface we used a relatively coarse level 5 geodesic grid with 240 radial points. As in the CIR problem, the concentric layer spacing was nonuniform with the smallest cells at the inner radial boundary located at 10 AU; the outer boundary was placed at 900 AU. A heliographic coordinate system is used here, where the z axis is aligned with the solar rotation axis (Beck & Giles 2005), and the x axis is in the plane formed by the z axis and the interstellar helium flow direction (Lallement et al. 2005). The y axis completes the right-handed orthogonal system. The geometry of the problem is illustrated in Figure 8.\nThe heliospheric configuration computed here is representative of a solar minimum\n\n\n
Fig. 8.- The heliographic coordinate system used in the simulation of the global heliosphere. The directions of the flow of interstellar hydrogen ( V H ) and helium ( V He ) span the so-called hydrogen deflection plane (HDP) with a normal n . Here the interstellar magnetic field B lies in the HDP, with an angle of 45 · relative to V He .
\n\n(Florinski 2011). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s at heliographic latitudes above 30 · (fast solar wind) and n = 7 cm -3 , u = 400 km/s at low latitudes (slow solar wind). The magnetic field is a Parker spiral with a radial component B r = 28 µ G at 1 AU. The azimuthal magnetic field component is a function of the solar wind speed. The heliospheric current sheet is not included in this simulation, so that the solar magnetic field is always directed outward from the Sun. The observed current sheet is between 10 4 km (1 AU, Winterhalter et al. 1994) and a few times 10 5 km (heliosheath, Burlaga & Ness 2011) in width, which is much too narrow to be resolved with a global model.\nThe interstellar flow has a total density of 0.2 cm -3 , and is ionization rate of 0.25. Its velocity vector is V He = ( -26 . 3 , 0 , -0 . 23) km/s in the chosen heliographic coordinate system. The interstellar magnetic field lies in the so-called hydrogen deflection plane (the plane spanned by the velocity vectors of neutral interstellar hydrogen and helium) and is inclined by 45 · with respect to the LISM flow vector. Its components are ( -1 . 3 , 1 . 38 , -2 . 32) µ G in our coordinate system. The temperature of both ionized and neutral components in the LISM is taken to be 6530 K. The neutral and the plasma fluids are coupled via the charge exchange process (Axford 1972). We simulate both fluids using the same code by explicitly fixing B = 0 for the neutral hydrogen. The charge exchange terms used are those of Pauls et al. (1995). For simplicity we only include interstellar hydrogen in this simulation and ignore atoms produced by charge exchange in the heliosheath or the solar wind. To separate the interstellar region from the heliosphere we use a passively advected indicator variable q which satisfies the equation\n∂ ( ρq ) ∂t + ∇· ( ρq u ) = 0 . (39)\nThe indicator variable is set to 1 in the solar wind and -1 in the interstellar flow. The condition q = 0 then gives the location of the heliopause.\n\n\n
Fig. 9.- Left: Constant plasma pressure surfaces (log scale) cut by the meridional ( xz ) plane for the heliosphere simulation. Selected magnetic field lines in the LISM are shown. Right: Radial profiles in the upwind (nose) direction of (from top to bottom): log plasma number density, radial speed, log thermal pressure, magnetic field magnitude, and log temperature. The positions of the termination shock and the heliopause are marked with vertical dashed lines.
\n\n\n\n\nHeliocentric Distance (AU)\nWe chose the HLLC solver for this work because of its more robust handling of a strong flow shear between the fast and the slow solar wind. We used the GLM ∇· B control method and WENO reconstruction in all directions. Simulations were run until a steady state was achieved which took about 300 years of simulated time. Figure 9, left, shows a cutout view of the heliospheric interface. Surfaces of constant plasma pressure are plotted together with magnetic field lines in the LISM, illustrating their draping around the heliopause (the transition between the red and the green colors). The innermost pressure surface approximately traces the outline of the termination shock.\nWe show radial profiles of several physical quantities in the upwind, or 'nose' direction in the right panel of Figure 9. Before the termination shock, located at 67 AU in this simulation, the solar wind velocity is gradually decreasing because of a loss of momentum to charge exchange with interstellar hydrogen. In the heliosheath, the plasma density is nearly a constant while the magnetic pressure increases toward the heliopause where the flow becomes essentially stagnant. The effective heliosheath temperature ( ∼ 3 × 10 6 K) is that of the solar-wind and pickup-ion mixture, which is significantly higher than that of the core solar wind ( ∼ 2 × 10 5 K, Richardson et al. 2008). From the top panel one can see that the density on the interstellar side of the heliopause is some 25 times higher than in the heliosheath. There is a very weak bow shock in this model barely visible in the pressure and temperature profiles.\nThe results presented here were obtained using a single population of neutral hydrogen (the interstellar atoms). The computer code is actually capable of integrating conservation laws for multiple neutral hydrogen populations. It would be straightforward to include the heliosheath energetic neutral atoms and the neutral solar wind atoms in a simulation, at an added computational time expense (e.g., Williams et al. 1997).\n6.3. Test problem 3: Magnetosphere of Earth\nThe Earth's magnetosphere is a product of an interaction between the supersonic solar wind and the geomagnetic field. Two major discontinuities, the bow shock and the magnetopause, are located between the undisturbed solar wind region and the geomagnetic field. The magnetosheath, filled with shocked solar wind plasma, lies between the bow shock and the magnetopause, which is the external boundary of the magnetosphere. The magnetopause thus separates the hot, tenuous magnetospheric plasma from the cold and dense solar wind plasma in the magnetosheath. Global MHD simulations, coupled with ionospheric models, have been widely used to study large-scale processes in the magnetosphere (e.g., Fedder & Lyon 1995; Tanaka 1995; Raeder 1999; Hu et al. 2007).\nThe geomagnetic field can be treated as a dipole field in the inner magnetosphere, its strength varying as r -3 , where r is the distance from the center of the Earth. The thermal pressure varies more modestly leading to a very low plasma β (the ratio of the plasma thermal pressure to the magnetic field pressure) in the inner magnetosphere. Such low values of β ( ∼ 10 -5 -10 -4 ) tend to produce numerical errors with conservative numerical schemes (Raeder 1999). To overcome this difficulty, the dipole field is treated apart from the total magnetic field according to the decomposition method introduced by Tanaka (1995). The momentum and energy fluxes in the Riemann solvers are revised accordingly. The WENO reconstruction method is used in all directions and the GLM algorithm is used to control ∇· B . An interested reader will find more details on the GLM-MHD equations with a dipole field decomposition in the Appendix.\nThe Geocentric Solar Magnetospheric (GSM) coordinate system is used in this simulation. It is centered at Earth, and the x , y , and z axes point to the Sun, the dawn-dusk direction, and along the north dipole axis, respectively. We choose the inner boundary to be a sphere with a radius r = 3 R E (Earth radii), and apply the Dirichlet boundary\nconditions. In particular, the number density is 370 cm -3 , which is 1/27 of a typical value in the ionosphere. The thermal pressure is 4 . 65 × 10 -10 dyn/cm 2 , which is 9 times smaller than its ionospheric value. The magnetic field is taken to be a dipole field at the inner boundary. For the sake of simplicity, the magnetosphere-ionosphere electrostatic coupling (e.g., Janhunen 1998) is not included, therefore the feedback of the ionosphere on the magnetosphere is ignored. We simply set the velocity to zero, which means there is no convection at the inner boundary. The free outer boundary is located at r = 100 R E .\nWe simulate a common configuration with a southward interplanetary magnetic field (IMF) of 50 µ G. The solar wind velocity is 600 km/s along the Sun-Earth line (the negative x direction), its number density is 5 cm -3 and temperature 9 . 1 × 10 4 K. The magnetic field is initially calculated as a superposition of a dipole field, centered at the origin, and a mirror dipole, located at (30 R E , 0 , 0), The field on the sunward side is subsequently replaced with the solar wind field with B z = -50 µ G to make the initial configuration divergence free. In the simulation we used a level 6 geodesic grid and 256 grid points along the radial direction.\nA steady state configuration is obtained some 30 minutes (simulated time) into the simulation. The left panel of Figure 10 shows the color contours of the thermal pressure in the meridional ( xz ) plane and in the equatorial ( xy ) plane. The geomagnetic field and the IMF lines of force are also plotted. In the equatorial plane the geomagnetic field points northward, being opposite to the polarity of the southward IMF. We can see that the magnetosphere is open to the interplanetary medium and the geomagnetic field lines connect with the IMF (Dungey 1961). In that case the solar wind plasma momentum and energy can be transported into the magnetosphere through the site of magnetic reconnection. We did not observe surface waves or vortices induced by the Kelvin-Helmholtz instability (e.g., Guo et al. 2010) along the low-latitude magnetopause (the surface of the magnetopause is smooth in the equatorial plane).\n\n\n
Fig. 10.- Left: plasma pressure (color) and magnetic field lines for the magnetosphere simulation. Plane cuts for z = 0 and y = 0 are shown. The magnitude of the magnetic field is shown by the color of the field lines in the figure. Right: radial profiles along the Sun-Earth line of (from top to bottom): log plasma number density, velocity, log thermal pressure, log magnetic field intensity, and log temperature. The bow shock and the magnetopause are marked by vertical dashed lines.
\n\nThe profiles of the physical quantities along the Sun-Earth line are shown in the right panel of Figure 10. The magnetopause is located at the neutral point for southward IMF case. The x velocity component approaches zero at the subsolar point, where the Sun-Earth line intersects the magnetopause. The shocked plasma becomes dense and hot in the magnetosheath, compared with the undisturbed solar wind. For southward IMF, the neutral point is found from the magnetic field strength profile (fourth panel from the top), where magnetic reconnection could occur in the presence of dissipation.\nOur result has all the relevant features of a typical MHD magnetospheric simulation. In this illustrative solution, we only calculate a steady state representative magnetosphere. Of course, the model can be also used with more realistic time-dependent IMF conditions derived from observations.\n7. Summary\nIn this report we have presented a novel approach to numerical modeling of space\nplasma flows using geodesic spherical meshes with a nearly uniform solid angle coverage. This approach avoids the singularity on the symmetry axis inherent in polar spherical grids, leading to improved efficiency by allowing larger time steps. Our integration technique for gas-dynamic or MHD conservation laws is based on dimensionally unsplit time advance and uses two-dimensional reconstruction on the surface of a sphere. The new code has a number of useful features, such as a choice of multiple nonlinear Riemann solvers, weighted reconstruction limiters, and slope flattening to reduce possible oscillations near strong shocks.\nWe have tested the new model on several common problems in space physics: a formation of corotating interaction regions in the solar wind, global modeling of the\nheliospheric interface, and finally, the magnetosphere of a planet. Our results are consistent with those found in the literature and every feature of the resulting structures is well reproduced. At this time the model lacks an adaptive mesh refinement feature, which would permit a superior numerical resolution of shocks and discontinuities. Whereas a hexagonal (Voronoi) grid cannot be easily refined, its dual Delaunay grid can. The process starts with the original icosahedron that divides a sphere into 20 identical spherical triangles. Each triangle then may be recursively subdivided into four smaller triangles by connecting the midpoints of the original cell edges with great circle arcs. The Delaunay mesh is therefore naturally amenable to refinement based on an oct-tree formulation. Because each locally refined zone is further split in the radial direction, this is tantamount to each 3D patch giving rise to 8 identically-sized refined patches if it is to undergo one more level of refinement.\nThe model could be potentially adapted to solve problems where the compact object is not at the center of the region of interest. For example, following Tanaka (2000), one could introduce a non-concentric grid, where different spherical layer boundaries are offset from the origin. The offset distance increases for each subsequent layer, so that the mesh becomes denser in one direction and more rarefied in the opposite direction. Such an arrangement could be more efficient for modeling, e.g., a magnetosphere with a long tail.\nThe new code by itself could be a valuable tool to investigate plasma flows around a source whose dimensions are small compared with the scale of the flow. Nevertheless, its chief intended purpose is to provide plasma background for subsequent simulations of the transport of energetic charged particles in the solar system and other astrophysical environments. Additional modules, recently added to the code, calculate the diffusion coefficients and drift velocity vectors based on magnetic field and other plasma properties.\nThe use of geodesic grids will permit a more efficient calculation of phase space trajectories\nin the stochastic integration method popular in cosmic-ray transport work (Ball et al. 2005; Florinski & Pogorelov 2009). The difference with polar grid-based models is expected to be quite pronounced in the polar regions of the heliosphere, where the diffusion and drift coefficients are typically very large.\nV.F. and X.G. were supported, in part, by NASA grants NNX10AE46G and NNX12AH44G, NSF grant AGS-0955700, and by a cooperative agreement with NASA Marshall Space Flight Center NNM11AA01A.\nA. Dipole field decomposition\nIn the magnetosphere, the external field B 1 = B -B d , where B is the total magnetic field, and B d is the internal dipole field. Since B d is both curl-free (no current) and divergence free, we can write\n∇· ( B d B d -1 2 B 2 d I ) = 0 , (A1)\n( ∇× B d ) · ( u × B ) = 0 . (A2)\nUsing (A1) the momemtum flux from Eq. (4) can be expressed as\nρ uu + p I -1 4 π ( BB + 1 2 B 2 d I -B d B d ) . (A3)\nNext, from (A2) we obtain\nB d · ∇ × ( u × B ) -∇· ( u × B ) × B d = 0 , (A4)\nwhich, upon substitution into the magnetic induction equation\n∂ B ∂t -∇× ( u × B ) = 0 (A5)\nyields\nB d · ∂ B 1 ∂t -∇· [ B ( u · B d ) -u ( B · B d )] = 0 . (A6)\nWe now define\np ∗ 1 = p g + B 2 1 8 π , e 1 = ρu 2 2 + p g γ -1 + B 2 1 8 π . (A7)\nUsing these definitions the energy equation may be written as\n∂e 1 ∂t + B d 4 π · ∂ B 1 ∂t + ∇· { ( e 1 + p ∗ 1 ) u + 1 4 π [ u ( B 1 · B d ) + u ( B · B d ) -B ( u · B 1 ) -B ( u · B d )] } = 0 . (A8)\nCombining equations (A6) and (A8) yields\n∂e 1 ∂t + ∇· { ( e 1 + p ∗ 1 ) u -1 4 π [ B 1 ( u · B 1 ) -u ( B d · B 1 ) + B d ( u · B 1 )] } = 0 . (A9)\nUsing (A3) and (A9) the system of GLM-MHD equations with dipole field decomposition may be written as\n∂ρ ∂t + ∇· ( ρ u ) = 0 , (A10)\n∂ ( ρ u ) ∂t + ∇· [ ρ uu + p ∗ I -1 4 π ( BB + 1 2 B 2 d I -B d B d )] = 0 , (A11)\n∂ B 1 ∂t + ∇· ( uB -Bu + ψ I ) = 0 , (A12)\n∂e 1 ∂t + ∇· { ( e 1 + p ∗ 1 ) u -1 4 π [( u · B 1 ) B 1 -( B d × u ) × B 1 ] } = 0 , (A13)\n∂ψ ∂t + c 2 h ∇· B 1 = -c 2 h c 2 p ψ, (A14)\nNote that the system (A10)-A(14) uses B 1 and e 1 instead of B and e as conserved quantities\nConsider the simplest three-state HLL solver (Harten et al. 1983). Its Riemann flux is given by\nF = F l , S l > 0 , F lr , S l ≤ 0 ≤ S r , F r , S r < 0 , (A15)\nwhere F l = F ( U l ) and F r = F ( U r ) are the left and right unperturbed fluxes, respectively. 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Phys., 225, 1632\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere. Subject headings: magnetohydrodynamics (MHD) - methods: numerical - planets and satellites: magnetic fields - solar wind","pages":[2]},{"title":"MHD modeling of solar system processes on geodesic grids","content":"V. Florinski 1 , 2 , X. Guo 2 , D. S. Balsara 3 , and C. Meyer 3 Received ; accepted","pages":[1]},{"title":"1. Introduction","content":"Many astrophysical plasma processes occur is regions of space surrounding a central compact object such as a star or a planet. Examples include stellar winds, planetary magnetospheres, supernova blast waves, and mass accretion onto compact objects. In all these environments the central body (a star or a planet) is typically much smaller than the characteristic scales of the plasma flows. In solving this class of problem on a computer, radial grids are commonly used because resolution can be readily increased near the origin. The simplest and the most commonly used is the standard spherical polar ( r , θ , ϕ ) grid (e.g., Washimi & Tanaka 1996; Pogorelov & Matsuda 1998; Ratkiewicz et al. 1998). This grid has a singularity on the z axis, where the control volume ∆ V = r 2 ∆ r sin θ ∆ θ ∆ ϕ , ∆ r , ∆ θ and ∆ ϕ being the grid cell dimensions in the radial, latitudinal, and azimuthal directions, respectively, vanishes as sin θ → 0. For explicit methods, this requires a small global time step to satisfy the Courant stability condition for a system of hyperbolic conservation laws for the entire grid (implicit or semi-implicit methods (e.g., T'oth et al. 1998) don't suffer from this limitation). Spherical grids are also used in simulating the transport of energetic charged particle, such as galactic cosmic rays, in turbulent astrophysical flows (Florinski & Pogorelov 2009). Transport models based on stochastic trajectory (Monte-Carlo) methods also suffer from the singularity on the polar axis. For example, in modeling cosmic-ray transport in the heliosphere it is common to align the z axis with the solar rotation axis. Because energetic particle transport (diffusion and drift) is very rapid at high latitudes due to a weaker magnetic field, a model must take vanishingly small time steps when a particle ventures close to the polar axis, which results in an inferior overall model efficiency. Time step requirements can be relaxed substantially by employing a grid that has a (nearly) uniform solid angle coverage. Examples include triangle, hexagon, or diamond based geodesic grids (Du et al. 2003; Yeh 2007; Upadhyaya et al. 2010), obtained by a recursive division of a base platonic solid, and cubed sphere grids (Ronchi et al. 1996; Putman & Lin 2007). This paper introduces a framework for finite volume methods of solution of hyperbolic conservation laws in three dimensions, such as gas-dynamic or MHD systems, using spherical geodesic grids composed of hexagonal prism elements. Results are illustrated on a three-dimensional simulation of solar rotation and formation of corotating interaction regions (CIRs), an interaction between the solar wind and the surrounding local interstellar medium or LISM, and a simulation of Earth's magnetosphere. The new framework can be employed to model a broad range of large-scale 3D astrophysical plasma flows around a compact object where high computational efficiency is a priority.","pages":[3,4]},{"title":"2. Grid structure","content":"Our three-dimensional grid consist of a 2D geodesic unstructured grid on a sphere combined with a concentric nonuniform radial stepping with smaller cells near the origin. The 2D surface grid is a Voronoi tesselation of a sphere produced from a dual triangular (Delaunay) tesselation. The latter is generated by a recursive subdivision of an icosahedron. We use the geodesic grid generator software developed by the ICON project ( http://icon.enes.org ) for use in atmospheric circulation modeling. An optimization algorithm (Heikes & Randall 1995), included in their code, produces a mesh with a difference in spherical surface areas between the largest and the smallest cells of less than 10%. The number of vertices (V), edges (E) and faces (F) on a grid produced by l th division is given by In this notation a level 0 grid is dual to the original icosahedron projected onto a unit sphere. The base shape of a control volume in a finite volume method is a spherical hexagonal prism with the exception of 12 pentagonal prisms located at the vertices of the original icosahedron. Level 3, 4, and 5 hexagonal geodesic grids are shown in Figure 1. A more detailed view of the Voronoi grid structure is given in Figure 2. A hexagonal face F m (shaded) is shown surrounded by six adjacent faces F m 1 .. F m 6 . The face centers of the dual triangle-based Delaunay grid (blue lines) are located at the Voronoi vertices (V); likewise, the former's vertices are at the Voronoi grid's face centers (F). The edges of the Voronoi and Delaunay grids on a sphere are mutually orthogonal and intersect at their midpoints. To achieve acceptable resolution in typical astrophysical flow modeling problems level 5 or higher geodesic grids should be used. Most of our simulations use level 6 mesh containing 40,962 Voronoi polygons. We emphasize that these 40,962 hexagons are distributed evenly over the surface of each spherical layer of cells. This gives us a resolution of about 3 × 10 -4 steradians in solid angle which corresponds to an angular resolution of one degree. By condensing the mesh in the radial direction, one can achieve a further degree of refinement as required by the problem. We introduce a set of unit vectors normal to the edges of the Voronoi grid ˆ n mn , where the index m refers to the m th face and n = [1 , 6] is the number of the edge counted in a counter-clockwise direction. The unit vectors are tangential to the surface of the sphere. The corresponding edge lengths, measured along great circles, are designated L mn . The outward radial unit vector at the cell center is ˆ r m . We also designate the area of the face on the unit sphere as A m . In this notation the control volume is equal to where i is the index on the radial axis. The areas A m are calculated by dividing each hexagonal face into six (five for pentagons) spherical triangles and adding up their areas using standard expressions from spherical trigonometry. Having defined our cell dimensions is this way we can proceed to integrate a system of conservation laws inside a control volume. It is worth pointing out that a similar geodesic-mesh-based model was developed by Nakamizo et al. (2009) Their mesh was generated from a dodecahedron by first dividing each face into five triangles followed by a recursive subdivision of each triangle into four smaller triangles. The resulting unstructured grid topology is similar (but not identical) to our dual Delaunay grid. Interestingly, in the model of Nakamizo et al. (2009) computations are also performed on a hexagonal grid, generated by connecting the centroids of the Delaunay triangles.","pages":[4,6,8]},{"title":"3. MHD conservation laws","content":"For the heliospheric and magnetospheric problems ( § 6) we solve a modified set of MHD equations, written in terms of conservative variables U and fluxes F as where in CGS units. Here ρ is density, u is velocity, B is magnetic field, I is a unit dyadic, p = p g + B 2 / (8 π ) is the total pressure, p g being the gas kinetic pressure, and the energy density e is given by We employ two alternative models to control the divergence of magnetic field. The first is the numerical scheme proposed by Powell et al. (1999), where numerical magnetic field divergence is advected out of the simulation domain with the flow velocity. This scheme modifies the system of conservation laws with a hyperbolic source term The second scheme employs a generalized Lagrange multiplier (GLM) ψ for a mixed hyperbolic-parabolic correction (Dedner et al. 2002). The system (4) is extended with an additional transport equation for ψ where c h is a constant, isotropic advection speed, taken to be somewhat faster than the fastest wave speed in the problem, and c p is related to the rate of decay of ψ . Dedner et al. (2002) proposed two methods to fix the value of c p : (a) by fixing the time rate of decay of the GLM variable r d = exp( -∆ tc 2 h /c 2 p ), where ∆ t is the time step, and (b) by fixing the characteristic length over which the decay occurs, given by l d = c 2 p /c h . Both methods are available in our code. In the GLM scheme the conservation law for magnetic field (Faraday's law) is modified to read The system (3) is integrated over a control volume ∆ V im shown in Figure 3 to obtain the finite volume method Here F i ( mn ) is the flux at the center of the edge shared by the m th cell and its n th neighbor (where n = [1 , 6]). Note that the source term Q does not involve the right hand side of Eq. (7). The parabolic correction is applied by multiplying the value of ψ obtained from the finite volume scheme (9) by the decay factor, In our simulations we typically use 0 . 9 < r d < 1 and l d equal to several times the smallest linear grid size. The divergence of the magnetic field is obtained from Gauss's theorem in the same way as ∇· F is calculated in Eq. (9). More generally, the divergence and curl operators acting on an arbitrary vector v may be written as An evaluation of a curl is necessary when modeling energetic charged particle transport, where the particle's drift velocity is proportional to ∇× ( B /B 2 ). The values of primitive variables at face centers v i ± 1 / 2 and v i ( mn ) may be approximated as arithmetic averages of the values in the two cells separated by the face. A more accurate approach, adopted here, is to use interface resolved states obtained from a solution to the corresponding Riemann problem (see § 5). The finite volume system of conservation laws is integrated with a second order unsplit TVD-like method (see below). Right and left interface values are calculated in the usual way using some appropriate linear reconstruction to achieve second-order spatial accuracy. Fluxes are calculated from a solution to a one-dimensional (projected) Riemann problem at each cell interface. Finally, time is advanced using either a first order (Euler) or, more commonly, a second order (Runge-Kutta) scheme, depending on the nature of the problem.","pages":[8,9,11,12]},{"title":"4. Reconstruction","content":"To achieve second order spatial accuracy we employ limited piecewise linear reconstruction on primitive variables V = ( ρ, u , p g , B , ψ ) T . In the radial direction the simplest and the most robust limiter available is the MinMod, with slopes S im given by where the left and the right slopes on an asymmetric stencil are, respectively Also available is the more compressive monotonized central (MC) limiter (van Leer 1977) with The third option is the weighted essentially non-oscillatory (WENO) limiter where the WENO weights ¯ w are given by where p is an integer constant here taken to be 2, and /epsilon1 is a small number, which we took to be 10 -12 in our simulations. The ( S + im ) 2 p and ( S -im ) 2 p terms are traditionally referred to as smoothness measures in WENO methodology. For two-dimensional reconstruction on the surface of a sphere the code can use either a minimum angle plane (MAPR) method (Christov & Popov 2008) or a 2D version of the weighted essentially non-oscillatory (WENO) scheme (Friedrich 1998). Common to both schemes, a local two-dimensional coordinate system ( ξ , η ) is introduced on the sphere, with its origin at the face center F m . The coordinates of the six adjacent cell centers ( ξ mn , η mn ) are then calculated in this frame. These coordinates are measured along two arbitrary great circles intersecting at right angles at the position of the central face F m . The procedure is illustrated in Figure 4. The angle A and the great circle distance between the face centers c are effectively polar coordinates on the surface of a sphere. The local coordinates of F mn are calculated as Next, the six two-dimensional slopes S ξ , S η are calculated from the triangles with vertices located at the cell centers F m , F mn , F m,n +1 (shown in blue in Figure 2) as In the MAPR method we evaluated the average slopes as The reconstructed slopes S MAPR ξ,η im are those given by Eqs. (19) and (20) for which the average slope (20) is the smallest. Thus the method is a two-dimensional equivalent of the MinMod limiter. In the WENO method the reconstructed slopes are weighted arithmetic averages of all six slopes, namely The weights ¯ w imn of each slope are calculated as where where we again use p = 2 and /epsilon1 = 10 -12 . Because edge centers lie midway between the corresponding two face centers F m and F mn on the Voronoi grid, the reconstructed values at edge midpoints V i ( mn ) can be computed as These values are used to calculate the intercell fluxes according to Eqs. (4), (7), and (8). The code also implements a slope flattening algorithm that reduces the value of the slopes calculated by the reconstruction module in the vicinity of strong compressions (shocks). This prevents the occurrence of oscillations downstream of the shock. To construct a flattener, we calculate the minimum value of the fast magnetosonic wave speed a min f,im in each computational cell and its neighbors in the same spherical layer and in the layers above and below (a total of 21 cells). The shock detector function in each cell d im is then calculated as (Balsara et al. 2009) ∣ ∣ where ∆ l im is a characteristic dimension of the cell ∆ V im , δ is a constant of order 1 and H is the Heaviside step function. Subsequently, the slope in the cell im is calculated as a weighted sum of a slope obtained with the standard limiter, such as WENO, and that from a more diffusive limiter, such as MinMod or MAPR. For example, in the radial direction we could use","pages":[12,13,15]},{"title":"5. Riemann solvers","content":"The fluxes F are calculated from an (approximate) solution to the one-dimensional Riemann problem at each interface between the prismatic cells. A suitable solver must be able to handle supersonic and transonic flows without losing positivity. Our tests revealed that modern HLL-type solvers (Batten et al. 1997; Gurski 2004) were generally superior to other solver types for the solar wind-LISM interaction problem, where they were least likely to produce a negative pressure upstream of a very strong (Mach number > 10) shock. Genuinely multi-dimensional Riemann solvers are now appearing in the literature (Balsara 2010, 2012), and they offer substantial advantages on logically rectangular meshes. However, the analogous work for unstructured meshes is the topic of vigorous research and was not incorporated in the present work. An HLLC solver consists of four states: the left and the right unperturbed states plus two intermediate states separated by a tangential discontinuity. Designating the left and the right bounding wave speeds of the Riemann fan by S l and S r , respectively, the intercell flux may be written as where F l = F ( U l ), F r = F ( U r ), and S ∗ is the speed of the intermediate wave (a tangential discontinuity). Because in a HLLC solver the normal velocity component and the total pressure only change across the outermost waves, the speed of the tangential discontinuity is readily calculated by applying the Rankine-Hugoniot conditions across these waves. This yields the speed where u n ( l,r ) and B n ( l,r ) are the normal-projected velocities and magnetic fields in the left and right states, respectively. Suppose two prismatic cells ( i, m 1 ) and ( i, m 2 ) share an interface with an index n 1 = [1 , 6] in the neighbor list of the first cell and n 2 = [1 , 6] in the neighbor list of the second cell (the definitions of 'first' and ''second' are arbitrary here; they could be defined, for example, by using the condition that m 1 < m 2 ). Then a normal velocity projection is defined as where u i ( m 1 n 1 ) and u i ( m 2 n 2 ) are the reconstructed velocities given by (25), and ˆ n n 1 n 1 is the unit vector normal to the interface n 1 of the cell ( i, m 1 ), pointing outward. The values for B n ( l,r ) are computed in the same way. Several HLLC MHD solvers may be found in the literature, distinguished by their choice of the tangential velocity and magnetic field components in the intermediate states U ∗ l,r (unlike in gas dynamics, these states are not unique in MHD). Currently we employ a solver proposed by Li (2005). Its main feature is that no jump in magnetic field is permitted across the tangential discontinuity. A second option available in our model is the HLLD Riemann solver (Miyoshi & Kusano 2005). This type of solver incorporates two additional states U ∗∗ l,r separated from the corresponding 'single star' states by rotational (Alfv'enic) discontinuities, propagating to the left and to the right of the middle wave with speeds S ∗ l and S ∗ r respectively, given by where B ∗ n is given by Eq. (34) below, and The intercell flux is computed as The HLLD solver is somewhat less robust than the HLLC counterpart because it has a singularity when one of the extremal waves is a switch-on shock. When this condition is encountered, the program falls back to the HLLC algorithm which is singularity-free. Because of nonlinearity of the solvers, under rare circumstances one of the intermediate waves could fall outside of the bounding (fast) waves. To prevent this from happening, we take the speed of the bounding waves to be the maximum of the left, right, and intermediate HLL states. Because the HLL state depends on the wave speeds themselves, we perform an iteration procedure until the external waves could be moved out no further. In the event that either HLLC or HLLD solver fails to produce a positive pressure in any of the intermediate states, we fall back to the very robust but dissipative HLLE Riemann solver (Einfeldt et al. 1991) with a single intermediate state U ∗ . The methods described above are used without modification with the source term divergence cleaning algorithm (Eq. 6). However, the GLM method introduces two additional waves moving with the speeds ± c h that carry changes in B n and ψ only. Because c h is the fastest wave speed, these waves bound the 'base' Riemann fan, comprised of 2, 3, or 5 waves in the HLLE, HLLC, and HLLD solvers, respectively. The intermediate states are readily obtained from the Rankine-Hugoniot conditions at the bounding waves as These intermediate states serve as both the right and the left states for the actual Riemann solver. The advantage of this approach is that any possible jump in the normal component of B is taken up by these additional external waves. Very few genuinely three-dimensional test problems are available for spherical grids. For code verification we used a 3D blast wave problem similar to those presented by Gardiner & Stone (2008) and Balsara et al. (2009). The simulation region is constrained between r min = 0 . 01 and r max = 0 . 5. The radial cell width ∆ r increased outward monotonically from 0.00052 to 0.047. The inner boundary was treated as a perfectly conducting sphere with reflecting boundary conditions imposed. The initial conditions are ρ = 1, u = 0, and p = 10 ( r < 0 . 1), p = 0 . 1 ( r > 0 . 1). The initial magnetic field is given by the standard potential solution for a perfectly conducting sphere in a uniform external field, namely This solution was rotated such that the external field pointed in the direction (1 / √ 3 , 1 / √ 3 , 1 / √ 3). We used B 0 = 10 and γ = 1 . 4. The system was evolved until t = 0 . 07. For this problem we chose a level 6 grid with 256 cells in the radial direction. The GLM version of the numerical scheme was used with the HLLC Riemann solver and WENO reconstruction. Figure 5 shows the magnitude of magnetic field at the end of the simulation on a linear scale. The flow structure of the solution is qualitatively similar to Gardiner & Stone (2008) and Balsara et al. (2009), consisting of an outermost fast shock wave and two dense shells of material elongated along the magnetic field. This problem did not trigger the slope flattening or positivity correction routines meaning it is not a very good stress test of the code. Several more difficult problems simulating actual astrophysical plasma flows are discussed next.","pages":[16,17,18,20,21]},{"title":"6. Numerical solutions of test problems","content":"To illustrate the capabilities of the new model we present results from three different simulations of solar system plasma environments. The first is a dynamic MHD simulation of compressive structures in the solar wind known as corotating interaction regions (CIRs). This is a simple test problem with a strong degree of spherical symmetry. The second is a simulation of the structure of the global heliosphere, including regions on each side of the interface between the solar wind and LISM known as the heliopause. This problem involves mode complex transonic flows and a population of neutral atoms in addition to the plasma. Finally, our third test problem is a stationary structure of the Earth's magnetosphere. Unlike the two previous cases, this one is an example of a highly magnetized plasma environment.","pages":[21]},{"title":"6.1. Test problem 1: Corotating interaction regions in the solar wind","content":"Corotating interaction regions (CIRs) are compressive structures produced through an interaction between high and low speed streams in the solar wind. CIRs are fully formed by the time they reach Earth's orbit (Siscoe 1972; Gosling et al. 1972). When the streams emanating from the Sun are approximately steady in the co-rotating frame, these compression regions form spirals in the solar equatorial plane that co-rotate with the Sun. The leading edge of a CIR is a forward compressional wave propagating into the slower solar wind ahead, whereas the tailing edge is a reverse wave propagating back into the trailing high speed stream. At large heliospheric distances the waves steepen into forward and reverse shocks. The entire plasma structure is convected with the solar wind and plays an important role in the dynamics of the heliosphere. CIRs have been extensively studied using global MHD simulation (Pizzo 1994; Riley et al. 2001; Usmanov & Goldstein 2006). To generate CIRs in a global MHD simulation we adopt the tilted-dipole flow geometry of Pizzo (1982) at the inner boundary, which is illustrated in Figure 6. In this figure 0 xyz is the fixed (heliographic) frame, where z is the solar rotation axis, and 0 x ' y ' z ' is a frame aligned with the Sun's magnetic axis z ' . The parameter γ is the dipole tilt angle, and β is the latitude of the fast-slow transition boundaries (blue circles) in the coordinate system 0 x ' y ' z ' . In the simulation discussed below we used β = ± 30 · . Following Pogorelov et al. (2007), one readily derives a quadratic equation for the latitude of the transition line θ as a function of the azimuthal angle ϕ , where Note that when β = 0, θ ( ϕ ) reduces to the expression for the latitude of the magnetic equator given by Eq. (A6) of Pogorelov et al. (2007). We simulated a region of the solar wind between r min = 0 . 5 AU and r max = 30 AU using 512 concentric grid layers of variable thickness (increasing outward). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s in the fast solar wind and n = 7 cm -3 , u = 400 km/s in the slow solar wind. The radial component of the magnetic field at 1 AU was B r = 28 µ G. These conditions were extended to the inner boundary using the conventional Parker solution for the solar wind and its magnetic field (Parker 1958). The dipole tilt angle was taken to be γ = 20 · . The boundary (shear layer) between the fast and the slow solar wind flows was located at a latitude of 30 · in the coordinate system aligned with the dipole axis. This simulation was performed on a level 6 geodesic grid. We chose the HLLC solver to evolve the time-dependent MHD equations, combined with the GLM divergence cleaning method; WENO reconstructions was used in all directions. Figure 7 (left) shows the logarithm of the magnetic field magnitude in the xz and xy planes using a cutout plot. Plasma velocity vectors are shown as arrows of variable length. The CIRs can be visually identified as higher density and magnetic field intensity regions (red). The maximum latitudinal extent of CIRs is given by the sum of the angle between the rotation and the dipole axes and the extent of the slow solar wind in the frame aligned with the dipole axis, i.e., γ + β = 50 · . In the equatorial plane, the spiral CIR structure is seen to be bounded by shock-like discontinuities. Several characteristic CIR features can be recognized in the plasma radial profiles shown in Figure 7 (right). We chose the profile along the direction 25 · northern latitude relative to the solar equatorial ( xy ) plane. The forward-reverse shock pairs are commonly observed at mid-latitudes, below the heliographic latitude of 26 · (Gosling & Pizzo 1999). They are shown with vertical dashed lines in the Figure. Shock pairs associated with CIRs are believed to be responsible for the observed 26-day recurrent decreases in galactic cosmic-ray intensity (Kota & Jokipii 1991; McKibben et al. 1999). Other features, such as the south-north flows are also identified through the north-south flow deflection angle /epsilon1 = sin -1 ( -u θ / | u | ) shown in the bottom panel. The transitions from northward (positive) to southward (negative) velocity are separated by roughly one Carrington rotation period (26 days) in our simulation. We conclude that the model is capable of reproducing the (km/s) v essential CIR features and is consistent with the earlier simulations of this phenomenon.","pages":[21,22,24,25,26]},{"title":"6.2. Test problem 2: The global heliosphere","content":"The energy density in a supersonic stellar wind, such as the solar wind, decreases in inverse proportion to the square of the distance from the star. Eventually the outflow is unable to maintain pressure balance with the galactic environment near the star, comprised mostly of partially ionized hydrogen gas. The stellar wind undergoes a transition to a subsonic flow at a structure called a termination shock. A tangential discontinuity called an astropause (heliopause for the solar wind) separates the shocked stellar flow from the interstellar gas. A bow shock may develop in front of the astropause if the relative motion between the star and LISM is supersonic. In the case of heliosphere, the region between the termination shock and the boundary is called the heliosheath. The theory of stellar wind interfaces (as applied primarily to the heliosphere) has been developed in Parker (1961), Axford (1972), and Baranov et al. (1976). Recent three-dimensional MHD simulations of the interface could be found in Pogorelov et al. (2007) and Opher et al. (2007). To simulate the structure of the heliospheric interface we used a relatively coarse level 5 geodesic grid with 240 radial points. As in the CIR problem, the concentric layer spacing was nonuniform with the smallest cells at the inner radial boundary located at 10 AU; the outer boundary was placed at 900 AU. A heliographic coordinate system is used here, where the z axis is aligned with the solar rotation axis (Beck & Giles 2005), and the x axis is in the plane formed by the z axis and the interstellar helium flow direction (Lallement et al. 2005). The y axis completes the right-handed orthogonal system. The geometry of the problem is illustrated in Figure 8. The heliospheric configuration computed here is representative of a solar minimum (Florinski 2011). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s at heliographic latitudes above 30 · (fast solar wind) and n = 7 cm -3 , u = 400 km/s at low latitudes (slow solar wind). The magnetic field is a Parker spiral with a radial component B r = 28 µ G at 1 AU. The azimuthal magnetic field component is a function of the solar wind speed. The heliospheric current sheet is not included in this simulation, so that the solar magnetic field is always directed outward from the Sun. The observed current sheet is between 10 4 km (1 AU, Winterhalter et al. 1994) and a few times 10 5 km (heliosheath, Burlaga & Ness 2011) in width, which is much too narrow to be resolved with a global model. The interstellar flow has a total density of 0.2 cm -3 , and is ionization rate of 0.25. Its velocity vector is V He = ( -26 . 3 , 0 , -0 . 23) km/s in the chosen heliographic coordinate system. The interstellar magnetic field lies in the so-called hydrogen deflection plane (the plane spanned by the velocity vectors of neutral interstellar hydrogen and helium) and is inclined by 45 · with respect to the LISM flow vector. Its components are ( -1 . 3 , 1 . 38 , -2 . 32) µ G in our coordinate system. The temperature of both ionized and neutral components in the LISM is taken to be 6530 K. The neutral and the plasma fluids are coupled via the charge exchange process (Axford 1972). We simulate both fluids using the same code by explicitly fixing B = 0 for the neutral hydrogen. The charge exchange terms used are those of Pauls et al. (1995). For simplicity we only include interstellar hydrogen in this simulation and ignore atoms produced by charge exchange in the heliosheath or the solar wind. To separate the interstellar region from the heliosphere we use a passively advected indicator variable q which satisfies the equation The indicator variable is set to 1 in the solar wind and -1 in the interstellar flow. The condition q = 0 then gives the location of the heliopause. Heliocentric Distance (AU) We chose the HLLC solver for this work because of its more robust handling of a strong flow shear between the fast and the slow solar wind. We used the GLM ∇· B control method and WENO reconstruction in all directions. Simulations were run until a steady state was achieved which took about 300 years of simulated time. Figure 9, left, shows a cutout view of the heliospheric interface. Surfaces of constant plasma pressure are plotted together with magnetic field lines in the LISM, illustrating their draping around the heliopause (the transition between the red and the green colors). The innermost pressure surface approximately traces the outline of the termination shock. We show radial profiles of several physical quantities in the upwind, or 'nose' direction in the right panel of Figure 9. Before the termination shock, located at 67 AU in this simulation, the solar wind velocity is gradually decreasing because of a loss of momentum to charge exchange with interstellar hydrogen. In the heliosheath, the plasma density is nearly a constant while the magnetic pressure increases toward the heliopause where the flow becomes essentially stagnant. The effective heliosheath temperature ( ∼ 3 × 10 6 K) is that of the solar-wind and pickup-ion mixture, which is significantly higher than that of the core solar wind ( ∼ 2 × 10 5 K, Richardson et al. 2008). From the top panel one can see that the density on the interstellar side of the heliopause is some 25 times higher than in the heliosheath. There is a very weak bow shock in this model barely visible in the pressure and temperature profiles. The results presented here were obtained using a single population of neutral hydrogen (the interstellar atoms). The computer code is actually capable of integrating conservation laws for multiple neutral hydrogen populations. It would be straightforward to include the heliosheath energetic neutral atoms and the neutral solar wind atoms in a simulation, at an added computational time expense (e.g., Williams et al. 1997).","pages":[26,28,29,30]},{"title":"6.3. Test problem 3: Magnetosphere of Earth","content":"The Earth's magnetosphere is a product of an interaction between the supersonic solar wind and the geomagnetic field. Two major discontinuities, the bow shock and the magnetopause, are located between the undisturbed solar wind region and the geomagnetic field. The magnetosheath, filled with shocked solar wind plasma, lies between the bow shock and the magnetopause, which is the external boundary of the magnetosphere. The magnetopause thus separates the hot, tenuous magnetospheric plasma from the cold and dense solar wind plasma in the magnetosheath. Global MHD simulations, coupled with ionospheric models, have been widely used to study large-scale processes in the magnetosphere (e.g., Fedder & Lyon 1995; Tanaka 1995; Raeder 1999; Hu et al. 2007). The geomagnetic field can be treated as a dipole field in the inner magnetosphere, its strength varying as r -3 , where r is the distance from the center of the Earth. The thermal pressure varies more modestly leading to a very low plasma β (the ratio of the plasma thermal pressure to the magnetic field pressure) in the inner magnetosphere. Such low values of β ( ∼ 10 -5 -10 -4 ) tend to produce numerical errors with conservative numerical schemes (Raeder 1999). To overcome this difficulty, the dipole field is treated apart from the total magnetic field according to the decomposition method introduced by Tanaka (1995). The momentum and energy fluxes in the Riemann solvers are revised accordingly. The WENO reconstruction method is used in all directions and the GLM algorithm is used to control ∇· B . An interested reader will find more details on the GLM-MHD equations with a dipole field decomposition in the Appendix. The Geocentric Solar Magnetospheric (GSM) coordinate system is used in this simulation. It is centered at Earth, and the x , y , and z axes point to the Sun, the dawn-dusk direction, and along the north dipole axis, respectively. We choose the inner boundary to be a sphere with a radius r = 3 R E (Earth radii), and apply the Dirichlet boundary conditions. In particular, the number density is 370 cm -3 , which is 1/27 of a typical value in the ionosphere. The thermal pressure is 4 . 65 × 10 -10 dyn/cm 2 , which is 9 times smaller than its ionospheric value. The magnetic field is taken to be a dipole field at the inner boundary. For the sake of simplicity, the magnetosphere-ionosphere electrostatic coupling (e.g., Janhunen 1998) is not included, therefore the feedback of the ionosphere on the magnetosphere is ignored. We simply set the velocity to zero, which means there is no convection at the inner boundary. The free outer boundary is located at r = 100 R E . We simulate a common configuration with a southward interplanetary magnetic field (IMF) of 50 µ G. The solar wind velocity is 600 km/s along the Sun-Earth line (the negative x direction), its number density is 5 cm -3 and temperature 9 . 1 × 10 4 K. The magnetic field is initially calculated as a superposition of a dipole field, centered at the origin, and a mirror dipole, located at (30 R E , 0 , 0), The field on the sunward side is subsequently replaced with the solar wind field with B z = -50 µ G to make the initial configuration divergence free. In the simulation we used a level 6 geodesic grid and 256 grid points along the radial direction. A steady state configuration is obtained some 30 minutes (simulated time) into the simulation. The left panel of Figure 10 shows the color contours of the thermal pressure in the meridional ( xz ) plane and in the equatorial ( xy ) plane. The geomagnetic field and the IMF lines of force are also plotted. In the equatorial plane the geomagnetic field points northward, being opposite to the polarity of the southward IMF. We can see that the magnetosphere is open to the interplanetary medium and the geomagnetic field lines connect with the IMF (Dungey 1961). In that case the solar wind plasma momentum and energy can be transported into the magnetosphere through the site of magnetic reconnection. We did not observe surface waves or vortices induced by the Kelvin-Helmholtz instability (e.g., Guo et al. 2010) along the low-latitude magnetopause (the surface of the magnetopause is smooth in the equatorial plane). The profiles of the physical quantities along the Sun-Earth line are shown in the right panel of Figure 10. The magnetopause is located at the neutral point for southward IMF case. The x velocity component approaches zero at the subsolar point, where the Sun-Earth line intersects the magnetopause. The shocked plasma becomes dense and hot in the magnetosheath, compared with the undisturbed solar wind. For southward IMF, the neutral point is found from the magnetic field strength profile (fourth panel from the top), where magnetic reconnection could occur in the presence of dissipation. Our result has all the relevant features of a typical MHD magnetospheric simulation. In this illustrative solution, we only calculate a steady state representative magnetosphere. Of course, the model can be also used with more realistic time-dependent IMF conditions derived from observations.","pages":[31,32,34]},{"title":"7. Summary","content":"In this report we have presented a novel approach to numerical modeling of space plasma flows using geodesic spherical meshes with a nearly uniform solid angle coverage. This approach avoids the singularity on the symmetry axis inherent in polar spherical grids, leading to improved efficiency by allowing larger time steps. Our integration technique for gas-dynamic or MHD conservation laws is based on dimensionally unsplit time advance and uses two-dimensional reconstruction on the surface of a sphere. The new code has a number of useful features, such as a choice of multiple nonlinear Riemann solvers, weighted reconstruction limiters, and slope flattening to reduce possible oscillations near strong shocks. We have tested the new model on several common problems in space physics: a formation of corotating interaction regions in the solar wind, global modeling of the heliospheric interface, and finally, the magnetosphere of a planet. Our results are consistent with those found in the literature and every feature of the resulting structures is well reproduced. At this time the model lacks an adaptive mesh refinement feature, which would permit a superior numerical resolution of shocks and discontinuities. Whereas a hexagonal (Voronoi) grid cannot be easily refined, its dual Delaunay grid can. The process starts with the original icosahedron that divides a sphere into 20 identical spherical triangles. Each triangle then may be recursively subdivided into four smaller triangles by connecting the midpoints of the original cell edges with great circle arcs. The Delaunay mesh is therefore naturally amenable to refinement based on an oct-tree formulation. Because each locally refined zone is further split in the radial direction, this is tantamount to each 3D patch giving rise to 8 identically-sized refined patches if it is to undergo one more level of refinement. The model could be potentially adapted to solve problems where the compact object is not at the center of the region of interest. For example, following Tanaka (2000), one could introduce a non-concentric grid, where different spherical layer boundaries are offset from the origin. The offset distance increases for each subsequent layer, so that the mesh becomes denser in one direction and more rarefied in the opposite direction. Such an arrangement could be more efficient for modeling, e.g., a magnetosphere with a long tail. The new code by itself could be a valuable tool to investigate plasma flows around a source whose dimensions are small compared with the scale of the flow. Nevertheless, its chief intended purpose is to provide plasma background for subsequent simulations of the transport of energetic charged particles in the solar system and other astrophysical environments. Additional modules, recently added to the code, calculate the diffusion coefficients and drift velocity vectors based on magnetic field and other plasma properties. The use of geodesic grids will permit a more efficient calculation of phase space trajectories in the stochastic integration method popular in cosmic-ray transport work (Ball et al. 2005; Florinski & Pogorelov 2009). The difference with polar grid-based models is expected to be quite pronounced in the polar regions of the heliosphere, where the diffusion and drift coefficients are typically very large. V.F. and X.G. were supported, in part, by NASA grants NNX10AE46G and NNX12AH44G, NSF grant AGS-0955700, and by a cooperative agreement with NASA Marshall Space Flight Center NNM11AA01A.","pages":[34,35,36]},{"title":"A. Dipole field decomposition","content":"In the magnetosphere, the external field B 1 = B -B d , where B is the total magnetic field, and B d is the internal dipole field. Since B d is both curl-free (no current) and divergence free, we can write Using (A1) the momemtum flux from Eq. (4) can be expressed as Next, from (A2) we obtain which, upon substitution into the magnetic induction equation yields We now define Using these definitions the energy equation may be written as Combining equations (A6) and (A8) yields Using (A3) and (A9) the system of GLM-MHD equations with dipole field decomposition may be written as Note that the system (A10)-A(14) uses B 1 and e 1 instead of B and e as conserved quantities Consider the simplest three-state HLL solver (Harten et al. 1983). Its Riemann flux is given by where F l = F ( U l ) and F r = F ( U r ) are the left and right unperturbed fluxes, respectively. The intermediate flux F lr is given by Since only the definition of a conserved flux is required to solve (A15), the system (A10)-(A14) can be readily used in place of (4). The decomposition of magnetic field does not affect the GLM scheme. For example, in the x direction we have two GLM equations, One can see that the external field component B 1 x can be integrated directly because the internal field ( B d related terms) does not appear in these equations.","pages":[36,37,38]},{"title":"REFERENCES","content":"Axford, W. I. 1972, in NASA Special Pub. 308, Solar Wind, ed. C. P. Sonnett, et al. (Washington, DC: NASA) 609 Balsara, D. S., 2010, J. Comput. Phys., 229, 1970 Balsara, D. S., 2012, J. Comput. Phys., doi:10.1016/j.jcp.2011.12.025 Balsara, D. S., Rumpf, T., Dumbser, M., & Munz, C.-D. 2009, J. Comput. Phys., 228, 2480 Ball, B., Zhang, M., Rassoul, H., & Linde, T. 2005, ApJ, 634, 1116 Baranov, V. B., Krasnobaev, K. V., & Ruderman, M. S. 1976, Ap&SS, 41, 481 Batten, P., Clarke, N., Lambert, C., & Causon, D. M. 1997, SIAM J. Sci. Comput., 18, 1553 Beck, J. G., & Giles, P. 2005, ApJ, L153 Burlaga, L. F., & Ness, N. F. 2011, J. Geophys. Res., 116, A051012 Christov, I., & Popov, B. 2008, J. Comput. 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The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere. Subject headings: magnetohydrodynamics (MHD) - methods: numerical - planets and satellites: magnetic fields - solar wind\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"MHD modeling of solar system processes on geodesic grids\",\n \"content\": \"V. Florinski 1 , 2 , X. Guo 2 , D. S. Balsara 3 , and C. Meyer 3 Received ; accepted\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"Many astrophysical plasma processes occur is regions of space surrounding a central compact object such as a star or a planet. Examples include stellar winds, planetary magnetospheres, supernova blast waves, and mass accretion onto compact objects. In all these environments the central body (a star or a planet) is typically much smaller than the characteristic scales of the plasma flows. In solving this class of problem on a computer, radial grids are commonly used because resolution can be readily increased near the origin. The simplest and the most commonly used is the standard spherical polar ( r , θ , ϕ ) grid (e.g., Washimi & Tanaka 1996; Pogorelov & Matsuda 1998; Ratkiewicz et al. 1998). This grid has a singularity on the z axis, where the control volume ∆ V = r 2 ∆ r sin θ ∆ θ ∆ ϕ , ∆ r , ∆ θ and ∆ ϕ being the grid cell dimensions in the radial, latitudinal, and azimuthal directions, respectively, vanishes as sin θ → 0. For explicit methods, this requires a small global time step to satisfy the Courant stability condition for a system of hyperbolic conservation laws for the entire grid (implicit or semi-implicit methods (e.g., T'oth et al. 1998) don't suffer from this limitation). Spherical grids are also used in simulating the transport of energetic charged particle, such as galactic cosmic rays, in turbulent astrophysical flows (Florinski & Pogorelov 2009). Transport models based on stochastic trajectory (Monte-Carlo) methods also suffer from the singularity on the polar axis. For example, in modeling cosmic-ray transport in the heliosphere it is common to align the z axis with the solar rotation axis. Because energetic particle transport (diffusion and drift) is very rapid at high latitudes due to a weaker magnetic field, a model must take vanishingly small time steps when a particle ventures close to the polar axis, which results in an inferior overall model efficiency. Time step requirements can be relaxed substantially by employing a grid that has a (nearly) uniform solid angle coverage. Examples include triangle, hexagon, or diamond based geodesic grids (Du et al. 2003; Yeh 2007; Upadhyaya et al. 2010), obtained by a recursive division of a base platonic solid, and cubed sphere grids (Ronchi et al. 1996; Putman & Lin 2007). This paper introduces a framework for finite volume methods of solution of hyperbolic conservation laws in three dimensions, such as gas-dynamic or MHD systems, using spherical geodesic grids composed of hexagonal prism elements. Results are illustrated on a three-dimensional simulation of solar rotation and formation of corotating interaction regions (CIRs), an interaction between the solar wind and the surrounding local interstellar medium or LISM, and a simulation of Earth's magnetosphere. The new framework can be employed to model a broad range of large-scale 3D astrophysical plasma flows around a compact object where high computational efficiency is a priority.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"2. Grid structure\",\n \"content\": \"Our three-dimensional grid consist of a 2D geodesic unstructured grid on a sphere combined with a concentric nonuniform radial stepping with smaller cells near the origin. The 2D surface grid is a Voronoi tesselation of a sphere produced from a dual triangular (Delaunay) tesselation. The latter is generated by a recursive subdivision of an icosahedron. We use the geodesic grid generator software developed by the ICON project ( http://icon.enes.org ) for use in atmospheric circulation modeling. An optimization algorithm (Heikes & Randall 1995), included in their code, produces a mesh with a difference in spherical surface areas between the largest and the smallest cells of less than 10%. The number of vertices (V), edges (E) and faces (F) on a grid produced by l th division is given by In this notation a level 0 grid is dual to the original icosahedron projected onto a unit sphere. The base shape of a control volume in a finite volume method is a spherical hexagonal prism with the exception of 12 pentagonal prisms located at the vertices of the original icosahedron. Level 3, 4, and 5 hexagonal geodesic grids are shown in Figure 1. A more detailed view of the Voronoi grid structure is given in Figure 2. A hexagonal face F m (shaded) is shown surrounded by six adjacent faces F m 1 .. F m 6 . The face centers of the dual triangle-based Delaunay grid (blue lines) are located at the Voronoi vertices (V); likewise, the former's vertices are at the Voronoi grid's face centers (F). The edges of the Voronoi and Delaunay grids on a sphere are mutually orthogonal and intersect at their midpoints. To achieve acceptable resolution in typical astrophysical flow modeling problems level 5 or higher geodesic grids should be used. Most of our simulations use level 6 mesh containing 40,962 Voronoi polygons. We emphasize that these 40,962 hexagons are distributed evenly over the surface of each spherical layer of cells. This gives us a resolution of about 3 × 10 -4 steradians in solid angle which corresponds to an angular resolution of one degree. By condensing the mesh in the radial direction, one can achieve a further degree of refinement as required by the problem. We introduce a set of unit vectors normal to the edges of the Voronoi grid ˆ n mn , where the index m refers to the m th face and n = [1 , 6] is the number of the edge counted in a counter-clockwise direction. The unit vectors are tangential to the surface of the sphere. The corresponding edge lengths, measured along great circles, are designated L mn . The outward radial unit vector at the cell center is ˆ r m . We also designate the area of the face on the unit sphere as A m . In this notation the control volume is equal to where i is the index on the radial axis. The areas A m are calculated by dividing each hexagonal face into six (five for pentagons) spherical triangles and adding up their areas using standard expressions from spherical trigonometry. Having defined our cell dimensions is this way we can proceed to integrate a system of conservation laws inside a control volume. It is worth pointing out that a similar geodesic-mesh-based model was developed by Nakamizo et al. (2009) Their mesh was generated from a dodecahedron by first dividing each face into five triangles followed by a recursive subdivision of each triangle into four smaller triangles. The resulting unstructured grid topology is similar (but not identical) to our dual Delaunay grid. Interestingly, in the model of Nakamizo et al. (2009) computations are also performed on a hexagonal grid, generated by connecting the centroids of the Delaunay triangles.\",\n \"pages\": [\n 4,\n 6,\n 8\n ]\n },\n {\n \"title\": \"3. MHD conservation laws\",\n \"content\": \"For the heliospheric and magnetospheric problems ( § 6) we solve a modified set of MHD equations, written in terms of conservative variables U and fluxes F as where in CGS units. Here ρ is density, u is velocity, B is magnetic field, I is a unit dyadic, p = p g + B 2 / (8 π ) is the total pressure, p g being the gas kinetic pressure, and the energy density e is given by We employ two alternative models to control the divergence of magnetic field. The first is the numerical scheme proposed by Powell et al. (1999), where numerical magnetic field divergence is advected out of the simulation domain with the flow velocity. This scheme modifies the system of conservation laws with a hyperbolic source term The second scheme employs a generalized Lagrange multiplier (GLM) ψ for a mixed hyperbolic-parabolic correction (Dedner et al. 2002). The system (4) is extended with an additional transport equation for ψ where c h is a constant, isotropic advection speed, taken to be somewhat faster than the fastest wave speed in the problem, and c p is related to the rate of decay of ψ . Dedner et al. (2002) proposed two methods to fix the value of c p : (a) by fixing the time rate of decay of the GLM variable r d = exp( -∆ tc 2 h /c 2 p ), where ∆ t is the time step, and (b) by fixing the characteristic length over which the decay occurs, given by l d = c 2 p /c h . Both methods are available in our code. In the GLM scheme the conservation law for magnetic field (Faraday's law) is modified to read The system (3) is integrated over a control volume ∆ V im shown in Figure 3 to obtain the finite volume method Here F i ( mn ) is the flux at the center of the edge shared by the m th cell and its n th neighbor (where n = [1 , 6]). Note that the source term Q does not involve the right hand side of Eq. (7). The parabolic correction is applied by multiplying the value of ψ obtained from the finite volume scheme (9) by the decay factor, In our simulations we typically use 0 . 9 < r d < 1 and l d equal to several times the smallest linear grid size. The divergence of the magnetic field is obtained from Gauss's theorem in the same way as ∇· F is calculated in Eq. (9). More generally, the divergence and curl operators acting on an arbitrary vector v may be written as An evaluation of a curl is necessary when modeling energetic charged particle transport, where the particle's drift velocity is proportional to ∇× ( B /B 2 ). The values of primitive variables at face centers v i ± 1 / 2 and v i ( mn ) may be approximated as arithmetic averages of the values in the two cells separated by the face. A more accurate approach, adopted here, is to use interface resolved states obtained from a solution to the corresponding Riemann problem (see § 5). The finite volume system of conservation laws is integrated with a second order unsplit TVD-like method (see below). Right and left interface values are calculated in the usual way using some appropriate linear reconstruction to achieve second-order spatial accuracy. Fluxes are calculated from a solution to a one-dimensional (projected) Riemann problem at each cell interface. Finally, time is advanced using either a first order (Euler) or, more commonly, a second order (Runge-Kutta) scheme, depending on the nature of the problem.\",\n \"pages\": [\n 8,\n 9,\n 11,\n 12\n ]\n },\n {\n \"title\": \"4. Reconstruction\",\n \"content\": \"To achieve second order spatial accuracy we employ limited piecewise linear reconstruction on primitive variables V = ( ρ, u , p g , B , ψ ) T . In the radial direction the simplest and the most robust limiter available is the MinMod, with slopes S im given by where the left and the right slopes on an asymmetric stencil are, respectively Also available is the more compressive monotonized central (MC) limiter (van Leer 1977) with The third option is the weighted essentially non-oscillatory (WENO) limiter where the WENO weights ¯ w are given by where p is an integer constant here taken to be 2, and /epsilon1 is a small number, which we took to be 10 -12 in our simulations. The ( S + im ) 2 p and ( S -im ) 2 p terms are traditionally referred to as smoothness measures in WENO methodology. For two-dimensional reconstruction on the surface of a sphere the code can use either a minimum angle plane (MAPR) method (Christov & Popov 2008) or a 2D version of the weighted essentially non-oscillatory (WENO) scheme (Friedrich 1998). Common to both schemes, a local two-dimensional coordinate system ( ξ , η ) is introduced on the sphere, with its origin at the face center F m . The coordinates of the six adjacent cell centers ( ξ mn , η mn ) are then calculated in this frame. These coordinates are measured along two arbitrary great circles intersecting at right angles at the position of the central face F m . The procedure is illustrated in Figure 4. The angle A and the great circle distance between the face centers c are effectively polar coordinates on the surface of a sphere. The local coordinates of F mn are calculated as Next, the six two-dimensional slopes S ξ , S η are calculated from the triangles with vertices located at the cell centers F m , F mn , F m,n +1 (shown in blue in Figure 2) as In the MAPR method we evaluated the average slopes as The reconstructed slopes S MAPR ξ,η im are those given by Eqs. (19) and (20) for which the average slope (20) is the smallest. Thus the method is a two-dimensional equivalent of the MinMod limiter. In the WENO method the reconstructed slopes are weighted arithmetic averages of all six slopes, namely The weights ¯ w imn of each slope are calculated as where where we again use p = 2 and /epsilon1 = 10 -12 . Because edge centers lie midway between the corresponding two face centers F m and F mn on the Voronoi grid, the reconstructed values at edge midpoints V i ( mn ) can be computed as These values are used to calculate the intercell fluxes according to Eqs. (4), (7), and (8). The code also implements a slope flattening algorithm that reduces the value of the slopes calculated by the reconstruction module in the vicinity of strong compressions (shocks). This prevents the occurrence of oscillations downstream of the shock. To construct a flattener, we calculate the minimum value of the fast magnetosonic wave speed a min f,im in each computational cell and its neighbors in the same spherical layer and in the layers above and below (a total of 21 cells). The shock detector function in each cell d im is then calculated as (Balsara et al. 2009) ∣ ∣ where ∆ l im is a characteristic dimension of the cell ∆ V im , δ is a constant of order 1 and H is the Heaviside step function. Subsequently, the slope in the cell im is calculated as a weighted sum of a slope obtained with the standard limiter, such as WENO, and that from a more diffusive limiter, such as MinMod or MAPR. For example, in the radial direction we could use\",\n \"pages\": [\n 12,\n 13,\n 15\n ]\n },\n {\n \"title\": \"5. Riemann solvers\",\n \"content\": \"The fluxes F are calculated from an (approximate) solution to the one-dimensional Riemann problem at each interface between the prismatic cells. A suitable solver must be able to handle supersonic and transonic flows without losing positivity. Our tests revealed that modern HLL-type solvers (Batten et al. 1997; Gurski 2004) were generally superior to other solver types for the solar wind-LISM interaction problem, where they were least likely to produce a negative pressure upstream of a very strong (Mach number > 10) shock. Genuinely multi-dimensional Riemann solvers are now appearing in the literature (Balsara 2010, 2012), and they offer substantial advantages on logically rectangular meshes. However, the analogous work for unstructured meshes is the topic of vigorous research and was not incorporated in the present work. An HLLC solver consists of four states: the left and the right unperturbed states plus two intermediate states separated by a tangential discontinuity. Designating the left and the right bounding wave speeds of the Riemann fan by S l and S r , respectively, the intercell flux may be written as where F l = F ( U l ), F r = F ( U r ), and S ∗ is the speed of the intermediate wave (a tangential discontinuity). Because in a HLLC solver the normal velocity component and the total pressure only change across the outermost waves, the speed of the tangential discontinuity is readily calculated by applying the Rankine-Hugoniot conditions across these waves. This yields the speed where u n ( l,r ) and B n ( l,r ) are the normal-projected velocities and magnetic fields in the left and right states, respectively. Suppose two prismatic cells ( i, m 1 ) and ( i, m 2 ) share an interface with an index n 1 = [1 , 6] in the neighbor list of the first cell and n 2 = [1 , 6] in the neighbor list of the second cell (the definitions of 'first' and ''second' are arbitrary here; they could be defined, for example, by using the condition that m 1 < m 2 ). Then a normal velocity projection is defined as where u i ( m 1 n 1 ) and u i ( m 2 n 2 ) are the reconstructed velocities given by (25), and ˆ n n 1 n 1 is the unit vector normal to the interface n 1 of the cell ( i, m 1 ), pointing outward. The values for B n ( l,r ) are computed in the same way. Several HLLC MHD solvers may be found in the literature, distinguished by their choice of the tangential velocity and magnetic field components in the intermediate states U ∗ l,r (unlike in gas dynamics, these states are not unique in MHD). Currently we employ a solver proposed by Li (2005). Its main feature is that no jump in magnetic field is permitted across the tangential discontinuity. A second option available in our model is the HLLD Riemann solver (Miyoshi & Kusano 2005). This type of solver incorporates two additional states U ∗∗ l,r separated from the corresponding 'single star' states by rotational (Alfv'enic) discontinuities, propagating to the left and to the right of the middle wave with speeds S ∗ l and S ∗ r respectively, given by where B ∗ n is given by Eq. (34) below, and The intercell flux is computed as The HLLD solver is somewhat less robust than the HLLC counterpart because it has a singularity when one of the extremal waves is a switch-on shock. When this condition is encountered, the program falls back to the HLLC algorithm which is singularity-free. Because of nonlinearity of the solvers, under rare circumstances one of the intermediate waves could fall outside of the bounding (fast) waves. To prevent this from happening, we take the speed of the bounding waves to be the maximum of the left, right, and intermediate HLL states. Because the HLL state depends on the wave speeds themselves, we perform an iteration procedure until the external waves could be moved out no further. In the event that either HLLC or HLLD solver fails to produce a positive pressure in any of the intermediate states, we fall back to the very robust but dissipative HLLE Riemann solver (Einfeldt et al. 1991) with a single intermediate state U ∗ . The methods described above are used without modification with the source term divergence cleaning algorithm (Eq. 6). However, the GLM method introduces two additional waves moving with the speeds ± c h that carry changes in B n and ψ only. Because c h is the fastest wave speed, these waves bound the 'base' Riemann fan, comprised of 2, 3, or 5 waves in the HLLE, HLLC, and HLLD solvers, respectively. The intermediate states are readily obtained from the Rankine-Hugoniot conditions at the bounding waves as These intermediate states serve as both the right and the left states for the actual Riemann solver. The advantage of this approach is that any possible jump in the normal component of B is taken up by these additional external waves. Very few genuinely three-dimensional test problems are available for spherical grids. For code verification we used a 3D blast wave problem similar to those presented by Gardiner & Stone (2008) and Balsara et al. (2009). The simulation region is constrained between r min = 0 . 01 and r max = 0 . 5. The radial cell width ∆ r increased outward monotonically from 0.00052 to 0.047. The inner boundary was treated as a perfectly conducting sphere with reflecting boundary conditions imposed. The initial conditions are ρ = 1, u = 0, and p = 10 ( r < 0 . 1), p = 0 . 1 ( r > 0 . 1). The initial magnetic field is given by the standard potential solution for a perfectly conducting sphere in a uniform external field, namely This solution was rotated such that the external field pointed in the direction (1 / √ 3 , 1 / √ 3 , 1 / √ 3). We used B 0 = 10 and γ = 1 . 4. The system was evolved until t = 0 . 07. For this problem we chose a level 6 grid with 256 cells in the radial direction. The GLM version of the numerical scheme was used with the HLLC Riemann solver and WENO reconstruction. Figure 5 shows the magnitude of magnetic field at the end of the simulation on a linear scale. The flow structure of the solution is qualitatively similar to Gardiner & Stone (2008) and Balsara et al. (2009), consisting of an outermost fast shock wave and two dense shells of material elongated along the magnetic field. This problem did not trigger the slope flattening or positivity correction routines meaning it is not a very good stress test of the code. Several more difficult problems simulating actual astrophysical plasma flows are discussed next.\",\n \"pages\": [\n 16,\n 17,\n 18,\n 20,\n 21\n ]\n },\n {\n \"title\": \"6. Numerical solutions of test problems\",\n \"content\": \"To illustrate the capabilities of the new model we present results from three different simulations of solar system plasma environments. The first is a dynamic MHD simulation of compressive structures in the solar wind known as corotating interaction regions (CIRs). This is a simple test problem with a strong degree of spherical symmetry. The second is a simulation of the structure of the global heliosphere, including regions on each side of the interface between the solar wind and LISM known as the heliopause. This problem involves mode complex transonic flows and a population of neutral atoms in addition to the plasma. Finally, our third test problem is a stationary structure of the Earth's magnetosphere. Unlike the two previous cases, this one is an example of a highly magnetized plasma environment.\",\n \"pages\": [\n 21\n ]\n },\n {\n \"title\": \"6.1. Test problem 1: Corotating interaction regions in the solar wind\",\n \"content\": \"Corotating interaction regions (CIRs) are compressive structures produced through an interaction between high and low speed streams in the solar wind. CIRs are fully formed by the time they reach Earth's orbit (Siscoe 1972; Gosling et al. 1972). When the streams emanating from the Sun are approximately steady in the co-rotating frame, these compression regions form spirals in the solar equatorial plane that co-rotate with the Sun. The leading edge of a CIR is a forward compressional wave propagating into the slower solar wind ahead, whereas the tailing edge is a reverse wave propagating back into the trailing high speed stream. At large heliospheric distances the waves steepen into forward and reverse shocks. The entire plasma structure is convected with the solar wind and plays an important role in the dynamics of the heliosphere. CIRs have been extensively studied using global MHD simulation (Pizzo 1994; Riley et al. 2001; Usmanov & Goldstein 2006). To generate CIRs in a global MHD simulation we adopt the tilted-dipole flow geometry of Pizzo (1982) at the inner boundary, which is illustrated in Figure 6. In this figure 0 xyz is the fixed (heliographic) frame, where z is the solar rotation axis, and 0 x ' y ' z ' is a frame aligned with the Sun's magnetic axis z ' . The parameter γ is the dipole tilt angle, and β is the latitude of the fast-slow transition boundaries (blue circles) in the coordinate system 0 x ' y ' z ' . In the simulation discussed below we used β = ± 30 · . Following Pogorelov et al. (2007), one readily derives a quadratic equation for the latitude of the transition line θ as a function of the azimuthal angle ϕ , where Note that when β = 0, θ ( ϕ ) reduces to the expression for the latitude of the magnetic equator given by Eq. (A6) of Pogorelov et al. (2007). We simulated a region of the solar wind between r min = 0 . 5 AU and r max = 30 AU using 512 concentric grid layers of variable thickness (increasing outward). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s in the fast solar wind and n = 7 cm -3 , u = 400 km/s in the slow solar wind. The radial component of the magnetic field at 1 AU was B r = 28 µ G. These conditions were extended to the inner boundary using the conventional Parker solution for the solar wind and its magnetic field (Parker 1958). The dipole tilt angle was taken to be γ = 20 · . The boundary (shear layer) between the fast and the slow solar wind flows was located at a latitude of 30 · in the coordinate system aligned with the dipole axis. This simulation was performed on a level 6 geodesic grid. We chose the HLLC solver to evolve the time-dependent MHD equations, combined with the GLM divergence cleaning method; WENO reconstructions was used in all directions. Figure 7 (left) shows the logarithm of the magnetic field magnitude in the xz and xy planes using a cutout plot. Plasma velocity vectors are shown as arrows of variable length. The CIRs can be visually identified as higher density and magnetic field intensity regions (red). The maximum latitudinal extent of CIRs is given by the sum of the angle between the rotation and the dipole axes and the extent of the slow solar wind in the frame aligned with the dipole axis, i.e., γ + β = 50 · . In the equatorial plane, the spiral CIR structure is seen to be bounded by shock-like discontinuities. Several characteristic CIR features can be recognized in the plasma radial profiles shown in Figure 7 (right). We chose the profile along the direction 25 · northern latitude relative to the solar equatorial ( xy ) plane. The forward-reverse shock pairs are commonly observed at mid-latitudes, below the heliographic latitude of 26 · (Gosling & Pizzo 1999). They are shown with vertical dashed lines in the Figure. Shock pairs associated with CIRs are believed to be responsible for the observed 26-day recurrent decreases in galactic cosmic-ray intensity (Kota & Jokipii 1991; McKibben et al. 1999). Other features, such as the south-north flows are also identified through the north-south flow deflection angle /epsilon1 = sin -1 ( -u θ / | u | ) shown in the bottom panel. The transitions from northward (positive) to southward (negative) velocity are separated by roughly one Carrington rotation period (26 days) in our simulation. We conclude that the model is capable of reproducing the (km/s) v essential CIR features and is consistent with the earlier simulations of this phenomenon.\",\n \"pages\": [\n 21,\n 22,\n 24,\n 25,\n 26\n ]\n },\n {\n \"title\": \"6.2. Test problem 2: The global heliosphere\",\n \"content\": \"The energy density in a supersonic stellar wind, such as the solar wind, decreases in inverse proportion to the square of the distance from the star. Eventually the outflow is unable to maintain pressure balance with the galactic environment near the star, comprised mostly of partially ionized hydrogen gas. The stellar wind undergoes a transition to a subsonic flow at a structure called a termination shock. A tangential discontinuity called an astropause (heliopause for the solar wind) separates the shocked stellar flow from the interstellar gas. A bow shock may develop in front of the astropause if the relative motion between the star and LISM is supersonic. In the case of heliosphere, the region between the termination shock and the boundary is called the heliosheath. The theory of stellar wind interfaces (as applied primarily to the heliosphere) has been developed in Parker (1961), Axford (1972), and Baranov et al. (1976). Recent three-dimensional MHD simulations of the interface could be found in Pogorelov et al. (2007) and Opher et al. (2007). To simulate the structure of the heliospheric interface we used a relatively coarse level 5 geodesic grid with 240 radial points. As in the CIR problem, the concentric layer spacing was nonuniform with the smallest cells at the inner radial boundary located at 10 AU; the outer boundary was placed at 900 AU. A heliographic coordinate system is used here, where the z axis is aligned with the solar rotation axis (Beck & Giles 2005), and the x axis is in the plane formed by the z axis and the interstellar helium flow direction (Lallement et al. 2005). The y axis completes the right-handed orthogonal system. The geometry of the problem is illustrated in Figure 8. The heliospheric configuration computed here is representative of a solar minimum (Florinski 2011). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s at heliographic latitudes above 30 · (fast solar wind) and n = 7 cm -3 , u = 400 km/s at low latitudes (slow solar wind). The magnetic field is a Parker spiral with a radial component B r = 28 µ G at 1 AU. The azimuthal magnetic field component is a function of the solar wind speed. The heliospheric current sheet is not included in this simulation, so that the solar magnetic field is always directed outward from the Sun. The observed current sheet is between 10 4 km (1 AU, Winterhalter et al. 1994) and a few times 10 5 km (heliosheath, Burlaga & Ness 2011) in width, which is much too narrow to be resolved with a global model. The interstellar flow has a total density of 0.2 cm -3 , and is ionization rate of 0.25. Its velocity vector is V He = ( -26 . 3 , 0 , -0 . 23) km/s in the chosen heliographic coordinate system. The interstellar magnetic field lies in the so-called hydrogen deflection plane (the plane spanned by the velocity vectors of neutral interstellar hydrogen and helium) and is inclined by 45 · with respect to the LISM flow vector. Its components are ( -1 . 3 , 1 . 38 , -2 . 32) µ G in our coordinate system. The temperature of both ionized and neutral components in the LISM is taken to be 6530 K. The neutral and the plasma fluids are coupled via the charge exchange process (Axford 1972). We simulate both fluids using the same code by explicitly fixing B = 0 for the neutral hydrogen. The charge exchange terms used are those of Pauls et al. (1995). For simplicity we only include interstellar hydrogen in this simulation and ignore atoms produced by charge exchange in the heliosheath or the solar wind. To separate the interstellar region from the heliosphere we use a passively advected indicator variable q which satisfies the equation The indicator variable is set to 1 in the solar wind and -1 in the interstellar flow. The condition q = 0 then gives the location of the heliopause. Heliocentric Distance (AU) We chose the HLLC solver for this work because of its more robust handling of a strong flow shear between the fast and the slow solar wind. We used the GLM ∇· B control method and WENO reconstruction in all directions. Simulations were run until a steady state was achieved which took about 300 years of simulated time. Figure 9, left, shows a cutout view of the heliospheric interface. Surfaces of constant plasma pressure are plotted together with magnetic field lines in the LISM, illustrating their draping around the heliopause (the transition between the red and the green colors). The innermost pressure surface approximately traces the outline of the termination shock. We show radial profiles of several physical quantities in the upwind, or 'nose' direction in the right panel of Figure 9. Before the termination shock, located at 67 AU in this simulation, the solar wind velocity is gradually decreasing because of a loss of momentum to charge exchange with interstellar hydrogen. In the heliosheath, the plasma density is nearly a constant while the magnetic pressure increases toward the heliopause where the flow becomes essentially stagnant. The effective heliosheath temperature ( ∼ 3 × 10 6 K) is that of the solar-wind and pickup-ion mixture, which is significantly higher than that of the core solar wind ( ∼ 2 × 10 5 K, Richardson et al. 2008). From the top panel one can see that the density on the interstellar side of the heliopause is some 25 times higher than in the heliosheath. There is a very weak bow shock in this model barely visible in the pressure and temperature profiles. The results presented here were obtained using a single population of neutral hydrogen (the interstellar atoms). The computer code is actually capable of integrating conservation laws for multiple neutral hydrogen populations. It would be straightforward to include the heliosheath energetic neutral atoms and the neutral solar wind atoms in a simulation, at an added computational time expense (e.g., Williams et al. 1997).\",\n \"pages\": [\n 26,\n 28,\n 29,\n 30\n ]\n },\n {\n \"title\": \"6.3. Test problem 3: Magnetosphere of Earth\",\n \"content\": \"The Earth's magnetosphere is a product of an interaction between the supersonic solar wind and the geomagnetic field. Two major discontinuities, the bow shock and the magnetopause, are located between the undisturbed solar wind region and the geomagnetic field. The magnetosheath, filled with shocked solar wind plasma, lies between the bow shock and the magnetopause, which is the external boundary of the magnetosphere. The magnetopause thus separates the hot, tenuous magnetospheric plasma from the cold and dense solar wind plasma in the magnetosheath. Global MHD simulations, coupled with ionospheric models, have been widely used to study large-scale processes in the magnetosphere (e.g., Fedder & Lyon 1995; Tanaka 1995; Raeder 1999; Hu et al. 2007). The geomagnetic field can be treated as a dipole field in the inner magnetosphere, its strength varying as r -3 , where r is the distance from the center of the Earth. The thermal pressure varies more modestly leading to a very low plasma β (the ratio of the plasma thermal pressure to the magnetic field pressure) in the inner magnetosphere. Such low values of β ( ∼ 10 -5 -10 -4 ) tend to produce numerical errors with conservative numerical schemes (Raeder 1999). To overcome this difficulty, the dipole field is treated apart from the total magnetic field according to the decomposition method introduced by Tanaka (1995). The momentum and energy fluxes in the Riemann solvers are revised accordingly. The WENO reconstruction method is used in all directions and the GLM algorithm is used to control ∇· B . An interested reader will find more details on the GLM-MHD equations with a dipole field decomposition in the Appendix. The Geocentric Solar Magnetospheric (GSM) coordinate system is used in this simulation. It is centered at Earth, and the x , y , and z axes point to the Sun, the dawn-dusk direction, and along the north dipole axis, respectively. We choose the inner boundary to be a sphere with a radius r = 3 R E (Earth radii), and apply the Dirichlet boundary conditions. In particular, the number density is 370 cm -3 , which is 1/27 of a typical value in the ionosphere. The thermal pressure is 4 . 65 × 10 -10 dyn/cm 2 , which is 9 times smaller than its ionospheric value. The magnetic field is taken to be a dipole field at the inner boundary. For the sake of simplicity, the magnetosphere-ionosphere electrostatic coupling (e.g., Janhunen 1998) is not included, therefore the feedback of the ionosphere on the magnetosphere is ignored. We simply set the velocity to zero, which means there is no convection at the inner boundary. The free outer boundary is located at r = 100 R E . We simulate a common configuration with a southward interplanetary magnetic field (IMF) of 50 µ G. The solar wind velocity is 600 km/s along the Sun-Earth line (the negative x direction), its number density is 5 cm -3 and temperature 9 . 1 × 10 4 K. The magnetic field is initially calculated as a superposition of a dipole field, centered at the origin, and a mirror dipole, located at (30 R E , 0 , 0), The field on the sunward side is subsequently replaced with the solar wind field with B z = -50 µ G to make the initial configuration divergence free. In the simulation we used a level 6 geodesic grid and 256 grid points along the radial direction. A steady state configuration is obtained some 30 minutes (simulated time) into the simulation. The left panel of Figure 10 shows the color contours of the thermal pressure in the meridional ( xz ) plane and in the equatorial ( xy ) plane. The geomagnetic field and the IMF lines of force are also plotted. In the equatorial plane the geomagnetic field points northward, being opposite to the polarity of the southward IMF. We can see that the magnetosphere is open to the interplanetary medium and the geomagnetic field lines connect with the IMF (Dungey 1961). In that case the solar wind plasma momentum and energy can be transported into the magnetosphere through the site of magnetic reconnection. We did not observe surface waves or vortices induced by the Kelvin-Helmholtz instability (e.g., Guo et al. 2010) along the low-latitude magnetopause (the surface of the magnetopause is smooth in the equatorial plane). The profiles of the physical quantities along the Sun-Earth line are shown in the right panel of Figure 10. The magnetopause is located at the neutral point for southward IMF case. The x velocity component approaches zero at the subsolar point, where the Sun-Earth line intersects the magnetopause. The shocked plasma becomes dense and hot in the magnetosheath, compared with the undisturbed solar wind. For southward IMF, the neutral point is found from the magnetic field strength profile (fourth panel from the top), where magnetic reconnection could occur in the presence of dissipation. Our result has all the relevant features of a typical MHD magnetospheric simulation. In this illustrative solution, we only calculate a steady state representative magnetosphere. Of course, the model can be also used with more realistic time-dependent IMF conditions derived from observations.\",\n \"pages\": [\n 31,\n 32,\n 34\n ]\n },\n {\n \"title\": \"7. Summary\",\n \"content\": \"In this report we have presented a novel approach to numerical modeling of space plasma flows using geodesic spherical meshes with a nearly uniform solid angle coverage. This approach avoids the singularity on the symmetry axis inherent in polar spherical grids, leading to improved efficiency by allowing larger time steps. Our integration technique for gas-dynamic or MHD conservation laws is based on dimensionally unsplit time advance and uses two-dimensional reconstruction on the surface of a sphere. The new code has a number of useful features, such as a choice of multiple nonlinear Riemann solvers, weighted reconstruction limiters, and slope flattening to reduce possible oscillations near strong shocks. We have tested the new model on several common problems in space physics: a formation of corotating interaction regions in the solar wind, global modeling of the heliospheric interface, and finally, the magnetosphere of a planet. Our results are consistent with those found in the literature and every feature of the resulting structures is well reproduced. At this time the model lacks an adaptive mesh refinement feature, which would permit a superior numerical resolution of shocks and discontinuities. Whereas a hexagonal (Voronoi) grid cannot be easily refined, its dual Delaunay grid can. The process starts with the original icosahedron that divides a sphere into 20 identical spherical triangles. Each triangle then may be recursively subdivided into four smaller triangles by connecting the midpoints of the original cell edges with great circle arcs. The Delaunay mesh is therefore naturally amenable to refinement based on an oct-tree formulation. Because each locally refined zone is further split in the radial direction, this is tantamount to each 3D patch giving rise to 8 identically-sized refined patches if it is to undergo one more level of refinement. The model could be potentially adapted to solve problems where the compact object is not at the center of the region of interest. For example, following Tanaka (2000), one could introduce a non-concentric grid, where different spherical layer boundaries are offset from the origin. The offset distance increases for each subsequent layer, so that the mesh becomes denser in one direction and more rarefied in the opposite direction. Such an arrangement could be more efficient for modeling, e.g., a magnetosphere with a long tail. The new code by itself could be a valuable tool to investigate plasma flows around a source whose dimensions are small compared with the scale of the flow. Nevertheless, its chief intended purpose is to provide plasma background for subsequent simulations of the transport of energetic charged particles in the solar system and other astrophysical environments. Additional modules, recently added to the code, calculate the diffusion coefficients and drift velocity vectors based on magnetic field and other plasma properties. The use of geodesic grids will permit a more efficient calculation of phase space trajectories in the stochastic integration method popular in cosmic-ray transport work (Ball et al. 2005; Florinski & Pogorelov 2009). The difference with polar grid-based models is expected to be quite pronounced in the polar regions of the heliosphere, where the diffusion and drift coefficients are typically very large. V.F. and X.G. were supported, in part, by NASA grants NNX10AE46G and NNX12AH44G, NSF grant AGS-0955700, and by a cooperative agreement with NASA Marshall Space Flight Center NNM11AA01A.\",\n \"pages\": [\n 34,\n 35,\n 36\n ]\n },\n {\n \"title\": \"A. Dipole field decomposition\",\n \"content\": \"In the magnetosphere, the external field B 1 = B -B d , where B is the total magnetic field, and B d is the internal dipole field. Since B d is both curl-free (no current) and divergence free, we can write Using (A1) the momemtum flux from Eq. (4) can be expressed as Next, from (A2) we obtain which, upon substitution into the magnetic induction equation yields We now define Using these definitions the energy equation may be written as Combining equations (A6) and (A8) yields Using (A3) and (A9) the system of GLM-MHD equations with dipole field decomposition may be written as Note that the system (A10)-A(14) uses B 1 and e 1 instead of B and e as conserved quantities Consider the simplest three-state HLL solver (Harten et al. 1983). Its Riemann flux is given by where F l = F ( U l ) and F r = F ( U r ) are the left and right unperturbed fluxes, respectively. The intermediate flux F lr is given by Since only the definition of a conserved flux is required to solve (A15), the system (A10)-(A14) can be readily used in place of (4). The decomposition of magnetic field does not affect the GLM scheme. 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A. 1998, A&A, 332, 1159 Upadhyaya, H. C., Sharma, O. P., Mittal, R., & Fatima, H. 2010, Asia-Pac. J. Chem. Eng., doi: 10.1029/apj.479 Usmanov, A. V., & Goldstein, M. L. 2006, J. Geophys. Res., 111, A07101 van Leer, B. 1977, J. Comput. Phys., 23, 276 Washimi, H., & Tanaka, T. 1996, Space Sci. Rev., 78, 85 Williams, L. L., Hall, D. T., Pauls, H. L., & Zank, G. P. 1997, ApJ, 476, 366 Winterhalter, D., Smith, E. J., Burton, M. E., Murphy, N., & McComas, D. J. 1994, J. Geophys. Res., 99, 6667 Yeh, K-S. 2007, J. Comput. Phys., 225, 1632\",\n \"pages\": [\n 39,\n 40,\n 41,\n 42\n ]\n }\n]"}}},{"rowIdx":80,"cells":{"bibcode":{"kind":"string","value":"2013ApJS..206....6D"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1304.4064.pdf"},"content":{"kind":"string","value":"\nH TO ZN IONIZATION EQUILIBRIUM FOR THE NON-MAXWELLIAN ELECTRON κ -DISTRIBUTIONS: UPDATED CALCULATIONS\nE. Dzifˇc'akov'a 1\nAstronomical Institute of the Academy of Sciences of the Czech Republic, Friˇcova 298, 251 65 Ondˇrejov, Czech Republic\nJ. Dud'ık 1\nNewton International Fellow, DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom Draft version March 7, 2022\nABSTRACT\nNew data for calculation of the ionization and recombination rates have have been published in the past few years. Most of these are included in CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian κ -distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The κ -distributions significantly influence both the ionization and recombination rates and widen the ion abundance peaks. In comparison with Maxwellian distribution, the ion abundance peaks can also be shifted to lower or higher temperatures. The updated ionization equilibrium calculations result in large changes for several ions, notably Fe VIII-XIV. The results are supplied in electronic form compatible with the CHIANTI database.\nKeywords: Atomic data - Atomic processes - Radiation mechanisms: non-thermal - Sun: corona Sun: UV radiation - Sun: X-rays, gamma rays\n1. INTRODUCTION\nOne of the most widely used assumptions in the interpretation of astrophysical spectra is that the emitting system is in thermal equilibrium. This means that the distribution of particle energies is at least locally Maxwellian, and can be characterized by the BoltzmannGibbs statistics which has one parameter, the temperature.\nThe generalization of the Bolzmann-Gibbs statistics proposed by Tsallis (1988, 2009), results in κ -distributions (e.g., Leubner 2002, 2004a,b; Collier 2004; Livadiotis & McComas 2009), characterized by a parameter κ and exhibiting a near-Maxwellian core and a high-energy power-law tail (Sect. 2). First proposed by Vasyliunas (1968), the κ distributions are now used to fit the observations of a wide variety of astrophysical environments, e.g. in-situ measurements of particle distributions in planetary magnetic environments (e.g., Pierrard & Lemaire 1996; Mauk et al. 2004; Schippers et al. 2008; Xiao et al. 2008; Dialynas et al. 2009) and solar wind (e.g., Collier et al. 1996; Maksimovic et al. 1997a,b; Pierrard et al. 1999; Nieves-Chinchilla & Vi˜nas 2008; Le Chat et al. 2009, 2011; Pierrard 2012), as well as photon spectra of solar flare plasmas (e.g., Kaˇsparov'a & Karlick'y 2009; Oka et al. 2013), emission line spectra of planetary nebulae and galactic sources (Nicholls et al. 2012; see also Binette et al. 2012) and even solar transition region (Dzifˇc'akov'a et al. 2011). A review on the κ -distributions and their applications in astrophysical plasma can be found, e.g., in Pierrard & Lazar (2010).\nelena@asu.cas.cz\n1 DAPEM, Faculty of Mathematics Physics and Computer Science, Comenius University, Mlynsk'a Dolina F2, 842 48 Bratislava, Slovakia\nIn the solar corona, presence of the κ -distributions, or distributions exhibiting high-energy tails, can be expected due to particle acceleration processes arising as a result of 'nanoflare' heating. The nanoflares are an unknown energy release process of impulsive nature, occuring possibly in storms heating the solar corona (e.g., Tripathi et al. 2010; Viall & Klimchuk 2011; Bradshaw et al. 2012; Winebarger 2012). While the direct evidence for enhanced suprathermal populations in the solar corona is still lacking (Feldman et al. 2007; Hannah et al. 2010), Pinfield et al. (1999) reported that the intensities of the Si III transition region lines observed by the SOHO/SUMER instrument do not correspond to a single Maxwellian distribution. Using their data, Dzifˇc'akov'a & Kulinov'a (2011) showed that the observed intensities can be explained by κ -distributions once the photoexcitation is taken into account. These authors diagnosed κ =7 in the active region observed on the solar limb. Higher values of κ were diagnosed for the quiet Sun and coronal hole, indiciating that the departures from the Maxwellian distribution can be connected to the local magnetic activity. The diagnostic method also works for inhomogeneous plasmas characterized by differential emission measure. That the κ -distributions can be present in the solar corona is also suggested by their presence in the solar wind (e.g., Pierrard et al. 1999; Vocks & Mann 2003).\nDirect diagnostics of κ -distributions in the solar corona using extreme-ultraviolet lines observed by the Hinode/EIS spectrometer (Culhane et al. 2007) were attempted by Dzifˇc'akov'a & Kulinov'a (2010) and Mackovjak et al. (2013). These authors proposed methods for simultaneous diagnostics of the plasma temperature, electron density, and κ . However, majority of the line ratios sensitive to κ -distributions suffer from poor\nphoton statistics, errors in atomic data and/or plasma inhomogeneities. In spite of this, one of the main results of these works is that the sensitivity to κ -distributions, or to departures from the Maxwellian distribution in general, is enhanced if the line ratios involve lines originating in neighbooring ionization stages. This is due the sensitivity of the line emissivity to the abundance of the emitting ion that depends directly on the ionization equilibrium in turn highly dependent on the type of the distribution (e.g., Dzifˇc'akov'a 2002; Wannawichian et al. 2003; Dzifˇc'akov'a 2006).\nIn the past decade, new calculations of the ionization, recombination rates and ionization equilibirium for the Maxwellian electron distribution were published. These are summarized in the continually updated CHIANTI database, currently available in version 7.1 (e.g., Dere et al. 1997, 2009; Landi et al. 2012, 2013). These new calculations of the ionization and recombination rates result in significant differences with respect to the earlier calculations, e.g. of Mazzotta et al. (1998).\nThe availability of accurate atomic data are of crucial importance in correct determination of the properties of the radiating astrophysical environment, and the solar corona in particular. In this paper, we present upto-date calculations of the ionization and recombination rates (Sect. 3), and ionization equilibria (Sect. 4) for κ -distributions for elements from H to Zn. Such calculations are necessary for diagnostics of the κ -distributions in both the solar transition region and the corona, as well as subsequent calculations of the radiative losses (Dud'ık et al. 2011) or responses of various extremeultraviolet or X-ray filters (Dud'ık et al. 2009) used both to model and observe these portions of the solar atmosphere, with potential applications to other astrophysical environments.\n2. THE NON-MAXWELLIAN κ -DISTRIBUTIONS\nThe κ -distributions of electron kinetic energies E represent a family of non-Maxwellian distributions characterized by two parameters, κ and T\nf κ ( E ) d E = A κ 2 π 1 / 2 ( k B T ) 3 / 2 E 1 / 2 d E (1 + E ( κ -1 . 5) kT ) κ +1 , (1)\nwhere the A κ = Γ( κ +1) / [ Γ( κ -0 . 5)( κ -1 . 5) 3 / 2 ] is the normalization constant, k B =1.38 × 10 -23 J kg -1 is the Boltzmann constant, and κ ∈ (3 / 2 , + ∞ ), T ∈ (0 , + ∞ ). We note that the definition of κ -distributions in Eq. (1 top ) corresponds to the κ -distributions of the second kind (e.g., Livadiotis & McComas 2009).\nThe shape of the distribution is controlled by the parameter κ . Maxwellian distribution is recovered for κ → + ∞ , while the departures from the Maxwellian increase with κ → 3/2. The departures from the Maxwellian distribution with decreasing κ include increase of the number of particles in the high-energy tail as well as increase in the relative number of lowenergy electrons (Fig. 1 top ). However, the mean energy 〈E〉 =3/2 k B T of the distribution does not depend on κ . This allows for calculation of all quantities depending on the mean energy of the distribution, e.g. pressure (Dzifˇc'akov'a 2006). The parameter T has in the frame of nonextensive statistics (Tsallis 1988, 2009) an analogous meaning as thermodynamic temperature in the\nBoltzmann-Gibbs statistics. The reader is referred e.g. to the work of Livadiotis & McComas (2009, 2010) for details.\nWhile the shape of the κ -distribution differs from the Maxwellian with the same T at all energies E , the core of the κ -distribution can be approximated by a Maxwellian distribution with lower T C = T ( κ -3 / 2) /κ (Oka et al. 2013). An example for κ =5 and T =1MK is shown in Fig. 1 bottom , where the approximating Maxwellian distribution has T C = 0 . 7 T and has been scaled by the factor C\nC = 2 . 718 Γ( κ +1) Γ( κ -1 / 2) κ -3 / 2 ( 1 + 1 κ ) -( κ +1) (2)\n(Oka et al. 2013), which is ≈ 0.84 for κ =5. The difference between the f κ ( T ) and f Maxw ( T C ) are then mainly in the pronounced high-energy tail. This shows that the κ distributions offer straightforward approximation of situations where a non-Maxwellian high-energy tail is present.\n3. IONIZATION AND RECOMBINATION RATES\nTo calculate the ionization and recombination rates for κ -distributions, we use the atomic data available through the CHIANTI database for astrophysical spectroscopy of optically thin plasmas (Dere et al. 1997; Landi et al. 2013). The analytical functional form of the κ -distributions allows for relatively simple direct integration of the ionization cross-sections (Sect 3.2). However, the recombination cross-sections are not contained in CHIANTI. These then have to be reverse-engineered from the Maxwellian recombination rates using assumptions detailed in Sect. 3.3.\nWe note that the CHIANTI database allows for the treatment of non-Maxwellian distributions only if these can be represented by a series of individual Maxwellian distributions (with different T s). The technique for calculation of ionization and recombination rates presented here can in principle be extended for any type of particle distribution, not only κ -distributions.\n3.1. Atomic Data\nThe CHIANTI atomic database since version 6 (Dere et al. 2009) contains continually updated ionization equilibrium for the Maxwellian distribution. This ionization equilibrium utilizes the cross-sections for direct ionization and autoionization, and the corresponding rate coefficients from the work of Dere (2007). Dielectronic and radiative recombination coefficients for the H to Al and Ar isoelectronic sequences are taken from the works of N. Badnell and colleagues, listed at http://amdpp.phys.strath.ac.uk/tamoc/DATA/ (Badnell et al. 2003; Colgan et al. 2003, 2004; Mitnik & Badnell 2004; Badnell 2006; Altun et al. 2005, 2006, 2007; Zatsarinny et al. 2005a,b, 2006; Bautista & Badnell 2007; Nikoli'c et al. 2010; Abdel-Naby et al. 2012). For the Si to Mn isoelectronic sequences, the recombination rates are based on the works of Shull & van Steenberg (1982), Nahar (1996, 1997), Nahar & Bautista (2001), Mazzotta et al. (1998) and Mazzitelli & Mattioli (2002). The reader is referred to Dere et al. (2009) for details. In the calculations presented in this paper, all atomic data for\nionization and recombination correspond to the ones used to produce the chianti.ioneq file in the CHIANTI v7.1. We note that ionization equilibria were published also by other authors (e.g. Bryans et al. 2009), but these use mostly the same atomic data as the CHIANTI database.\n3.2. Ionization Rates\nThe ionization rates have been calculated by a numerical integration of the ionization cross section, σ i , available in CHIANTI database\nR i = < σ i v > = ∫ ∞ 0 σ i ( 2 E m ) 1 / 2 f κ ( E ) d E , (3)\nfor κ =2,3,5,7,10, 25, and 33. Each numerical integral is calculated as a sum of individual integrals splitted according to the ionization and auto-ionizaton energies.\nTypical changes in behaviour of the direct ionization and autoionization rates with κ -distributions are shown in Fig. 2 for the ions C IV , Fe XII , and Fe XVII formed at transition region, quiet coronal, and flare conditions, respectively. For lower κ , the temperature dependence of the ionization rates is much flatter, with lower maxima. Typically, for temperatures lower than those at which the ion abundance peaks (denoted by arrow in Fig. 2, see also Sect. 4), the κ -distributions result in increase of the ionization rates by up to several orders of magnitude with respect to the Maxwellian distribution. These deviations from Maxwellian ionization rates increase with decreasing κ .\n3.3. Recombination Rates\nSince the individual recombination cross-sections are not available in CHIANTI, the calculation of the recombination rates for κ -distributions was performed using the method of Dzifˇc'akov'a (1992), used also by Wannawichian et al. (2003). This method allows for calculation of the recombination rates using approximations to the rates for the Maxwellian distribution.\nThe cross-section σ RR for the radiative recombination is assumed to have a power-law dependence on energy (Osterbrock 1974)\nσ RR ( E ) = C RR / E η +0 . 5 , (4)\nwhere C RR is a constant and η +0 . 5 is a power-law index. Subsequently, the radiative recombination rate for the κ -distribution is of the form:\nR κ RR = 4 C RR (2 πm ) 1 / 2 Γ( κ + η -0 . 5)( κ -1 . 5) η Γ( κ -0 . 5) Γ(1 . 5 -η ) ( k B T ) η , (5)\nwhile the radiative recombition rate for the Maxwellian distribution is\nR Maxw RR = 4 C RR (2 πm ) 1 / 2 Γ(1 . 5 -η ) ( k B T ) η . (6)\nTherefore, it holds that\nR κ RR = R Maxw RR Γ( κ + η -0 . 5)( κ -1 . 5) η Γ( κ -0 . 5) . (7)\nThe level of error introduced by this approximation is typically several per cent, i.e., lower than the error of the atomic data themselves.\nFor the dielectronic recombination, following approximation has been taken (Dzifˇc'akov'a 1992)\nR κ DR = A κ T 1 / 3 ∑ i a i (1 + t i / ( κ -1 . 5) T ) ( κ +1) , (8)\nwhere parameters a i and t i are the same as in similar expressions for the Maxwellian distribution\nR Maxw DR = 1 T 1 / 3 ∑ i a i exp( -t i /T ) , (9)\nwhere the coefficients a i and t i are provided within the CHIANTI database. The precision of this approximation is given by the magnitude of the second-order terms in the expansion of the coefficients a i and t i into series (Eqs. 37-44 in Dzifˇc'akov'a 1992).\nThe typical behavior of the total recombination rates ( R RR + R DR ) for κ -distributions and for Maxwellian distribution is shown in Fig. 2. It can be seen that the radiative recombination rate increases with decrease of κ . This is a result of increasing number of low energy electrons for the κ -distributions (Fig. 1), which dominate the recombination processes. The local change of slope of total recombination rate is caused by the contribution of dielectronic recombination. For some ions, e.g. Fe XVII , the contribution of dielectronic recombination is dominant in temperature interval where these ions have a non-negligible abundance.\n4. THE IONIZATION EQUILIBRIUM\nCalculations of the collisional ionization equilibrium assume that there are no temporal variations in plasma temperature T . In the coronal conditions, the resulting relative ion populations are given by the equilibrium between the direct collisional ionization with autoionization and the radiative and dielectronic recombination. Three-body processes can be neglected at low electron densities typical in the solar corona (Phillips et al. 2008). The radiative field is also usually assumed to be too weak, i.e., photoionization can be neglected as well. However, we note that photoionization may be important for some transition-region ions with low ionization thresholds, but the effect will vary depending on the distance from the radiation field (e.g., the solar photosphere).\nThe ionization equilibrium for κ -distributions with κ =2,3,5,7,10, 25, and 33 was calculated for ions of astrophysical interests, ranging from H ( Z =1) to Zn ( Z =30). Previous calculations of Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002), and Wannawichian et al. (2003) involved only 12 most abundant elements. The current calculations are performed for the same set of temperatures as the calculations in the CHIANTI database in the chianti.ioneq file. I.e., the temperature spans the interval of log( T /K) ∈〈 4 , 9 〉 with the step of ∆log( T /K)=0.05. The calculations are available in the same format as the chianti.ioneq file and are easily readable using the routines read ioneq.pro and plot ioneq.pro available in CHIANTI running under SolarSoftware in IDL. More information on the CHIANTI .ioneq file format is provided in Appendix A.\nExamples of the current ionization equilibrium calculations for iron are in Fig. 3 and for carbon in\nFig. 4. The typical behavior is that the lower κ , the flatter the ionization peaks. In addition, ionization peaks can be shifted to lower or higher T , depending on κ , T and the individual ion. This means that a given relative ion abundance can be formed at a wider range of T for a κ -distribution, with different peak formation temperature. Such behavior was already reported by Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002) and Wannawichian et al. (2003). Typically, the shifts of Fe and C ion abundance peaks are to lower T with respect to the Maxwellian ionization equilibrium if log( T /K) /lessorapproxeql 5.5. At coronal temperatures, the Fe IX - Fe XVI ions are shifted to higher T . An interesting example is the ion Fe XVII , whose ionization peak is shifted to lower T for κ lessapprox 3, but to higher T for κ =2(Fig. 3 bottom ).\nThere are a number of differences with respect to the earlier calculations of Dzifˇc'akov'a (2002), which used the atomic data corresponding to those of Mazzotta et al. (1998). These differences are illustrated in Fig. 5. In general, the lower the value of κ , the greater the differences with respect to the previous calculations. The most conspicuous examples are the Fe IX , which is shifted to slightly higher T instead to lower T as in the previous calculations of Dzifˇc'akov'a (2002). The Fe XII and Fe XIII ions are shifted to higher T (up to 0.1-0.15 dex). We note that the changes in the ionization equilibria due to the updated atomic data will reflect e.g. on changes in the total radiative losses (Dud'ık et al. 2011) and will also modify the proposed diagnostic methods for κ -distributions (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013).\nRatios of relative abundances of individual ions can be used to diagnose the value of κ and simultaneously T . Such diagnostics can be applied e.g. in the solar wind (Owocki & Scudder 1983). An example of diagnostic diagrams is given in Fig. 6. We note that such diagrams cannot be directly applied on the observed line intensities unless the additional effect of κ -distributions on the excitation and deexcitation rates is considered. However, these diagrams provide quantification of the expected changes to ratios of line intensities due to ionization equilibrium. Ratios of lines involving different ionization stages provide better options for determining κ , as noted already by (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013).\n5. SUMMARY\nCollisional ionization equilibrium calculations for κ -distributions and optically thin plasmas were performed for all ions of elements H to Zn. To do that, the latest available atomic data for ionization and recombination were used. The calculations are available in the form of ionization equilibrium files compatible with the CHIANTI database, v7.1.\nFor κ -distributions, the ionization peaks are in general flatter and can be shifted to lower or higher T . This means that for κ -distributions, individual ions are typically formed in a wider range of temperatures, with different peak formation temperatures. Typically, ions formed at transition region temperatures are shifted to lower T , while the majority of coronal iron ions are shifted to higher T . Comparison to previous calculations is provided. Due to updated atomic data calculations, several ions in the present calculations are shifted to different temperatures with respect to previous calculations of Dzifˇc'akov'a (2002). The effect of κ on the ratios of ion abundances is documented.\nThe present calculations provide an accurate, necessary and useful tool for detection of astrophysical plasmas out of thermal equilibrium, where the distribution of particles is characterized by an enhanced power-law tail. The supplied files compatible with the CHIANTI database and software should greatly facilitate synthetization of both line and continuum spectra for optically thin astrophysical plasmas.\nThe authors are grateful to Dr. G. Del Zanna and Dr. H. E. Mason for helpful discussions. This work was supported by Grant Agency of the Czech Republic, Grant No. P209/12/1652, the project RVO:67985815, Scientific Grant Agency, VEGA, Slovakia, Grant No. 1/0240/11, and the bilateral project APVV CZ-SK0153-11 (7AMB12SK154) involving the Slovak Research and Development Agency and the Ministry of Education of the Czech Republic. JD acknowledges support from the Comenius University Grant No. UK/11/2012. CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK), the Universities of Florence (Italy) and Cambridge (UK), and George Mason University (USA). CHIANTI is great spectroscopic database and software, and the authors are very grateful for its existence and availability.\nAPPENDIX\nCHIANTI .IONEQ FILE FORMAT\nThe .ioneq files, used by the CHIANTI database and software to store data on the ionization equilibrium, are in essence formatted ASCII files. An example of their format is given in Table 1. The file begins with two numbers, N , giving the number of temperature points T i , 1 ≤ i ≤ N , and Z max , denoting the maximum proton number Z for which the ionization equilibrium is provided. The next line gives the tabulated temperatures log( T i / K). All other following lines begin with the Z and a positive integer + k denoting the roman numeral for the corresponding ion; e.g., 26 and 9 stands for Fe IX . The line then contains relative ion abundances A + k -1 Z ( T i ) in floating-point precision for the tabulated temperatures.\nPortion of the actual content of the kappa 05.ioneq file is given in Table 2. There, the relative abundances of the ions Fe IX -Fe XI are listed for κ =5 and for log( T/ K)=5.80 - 6.15.\n
\n\n
Table 1 ASCII format of the CHIANTI .ioneq file. Explanation of the symbols is given in the text.
\n
\nTable 2\n
\n\n
Example of the kappa 05.ioneq file produced for κ = 5. The table shows relative abundances of the ions Fe IX - Fe XI .
\n
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Figure 1. Top : The κ -distributions with κ =2, 3, 5, 10, 25 and the Maxwellian distribution plotted for log( T /K)=6.0. Bottom : The κ =5 distribution and the approximation of its core with Maxwellian distribution with lower T C . Colors and linestyles correspond to different values of κ . (A color version of this figure is available in the online journal.)
\n\n\n\n
Figure 2. Total ionization and recombination rates for C IV ( top row ), Fe XII ( middle row ) and Fe XVII ( bottom row ). Different linestyles correspond to different κ . Black and red arrows denote maximum of the relative ion abundance for the Maxwellian and κ =2 distributions, respectively. (A color version of this figure is available in the online journal.)
\n\n\n\n
Figure 3. Changes in the ionization equilibrium with κ for iron. Top : κ =10; Second row : κ =5; Third row : κ =5; Bottom row : κ =2. Individual ionization stages are indicated. (A color version of this figure is available in the online journal.)
\n\n\n\n
Figure 4. Ionization equilibrium for Carbon. Different linestyles correspond to different κ . (A color version of this figure is available in the online journal.)
\n\n\n\n
Figure 5. Comparison of the current, updated calculations with the previous ones. Top : Comparison between the ionization equilibrium according to Dere et al. (2009) and Mazzotta et al. (1998). Middle and Bottom : Comparison of the current calculations with the ones of Dzifˇc'akov'a (2002) for κ =5 and2, respectively. Individual ionization stages are indicated. (A color version of this figure is available in the online journal.)
\n\n\n\n\n\n\n
Figure 6. Diagnostics of κ from ratios of ion abundances. The values of κ for each line are indicated. Thin lines represent isotherms for the given value of log( T /K). (A color version of this figure is available in the online journal.)
\n\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"New data for calculation of the ionization and recombination rates have have been published in the past few years. Most of these are included in CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian κ -distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The κ -distributions significantly influence both the ionization and recombination rates and widen the ion abundance peaks. In comparison with Maxwellian distribution, the ion abundance peaks can also be shifted to lower or higher temperatures. The updated ionization equilibrium calculations result in large changes for several ions, notably Fe VIII-XIV. The results are supplied in electronic form compatible with the CHIANTI database. Keywords: Atomic data - Atomic processes - Radiation mechanisms: non-thermal - Sun: corona Sun: UV radiation - Sun: X-rays, gamma rays","pages":[1]},{"title":"H TO ZN IONIZATION EQUILIBRIUM FOR THE NON-MAXWELLIAN ELECTRON κ -DISTRIBUTIONS: UPDATED CALCULATIONS","content":"E. Dzifˇc'akov'a 1 Astronomical Institute of the Academy of Sciences of the Czech Republic, Friˇcova 298, 251 65 Ondˇrejov, Czech Republic","pages":[1]},{"title":"J. Dud'ık 1","content":"Newton International Fellow, DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom Draft version March 7, 2022","pages":[1]},{"title":"1. INTRODUCTION","content":"One of the most widely used assumptions in the interpretation of astrophysical spectra is that the emitting system is in thermal equilibrium. This means that the distribution of particle energies is at least locally Maxwellian, and can be characterized by the BoltzmannGibbs statistics which has one parameter, the temperature. The generalization of the Bolzmann-Gibbs statistics proposed by Tsallis (1988, 2009), results in κ -distributions (e.g., Leubner 2002, 2004a,b; Collier 2004; Livadiotis & McComas 2009), characterized by a parameter κ and exhibiting a near-Maxwellian core and a high-energy power-law tail (Sect. 2). First proposed by Vasyliunas (1968), the κ distributions are now used to fit the observations of a wide variety of astrophysical environments, e.g. in-situ measurements of particle distributions in planetary magnetic environments (e.g., Pierrard & Lemaire 1996; Mauk et al. 2004; Schippers et al. 2008; Xiao et al. 2008; Dialynas et al. 2009) and solar wind (e.g., Collier et al. 1996; Maksimovic et al. 1997a,b; Pierrard et al. 1999; Nieves-Chinchilla & Vi˜nas 2008; Le Chat et al. 2009, 2011; Pierrard 2012), as well as photon spectra of solar flare plasmas (e.g., Kaˇsparov'a & Karlick'y 2009; Oka et al. 2013), emission line spectra of planetary nebulae and galactic sources (Nicholls et al. 2012; see also Binette et al. 2012) and even solar transition region (Dzifˇc'akov'a et al. 2011). A review on the κ -distributions and their applications in astrophysical plasma can be found, e.g., in Pierrard & Lazar (2010). elena@asu.cas.cz 1 DAPEM, Faculty of Mathematics Physics and Computer Science, Comenius University, Mlynsk'a Dolina F2, 842 48 Bratislava, Slovakia In the solar corona, presence of the κ -distributions, or distributions exhibiting high-energy tails, can be expected due to particle acceleration processes arising as a result of 'nanoflare' heating. The nanoflares are an unknown energy release process of impulsive nature, occuring possibly in storms heating the solar corona (e.g., Tripathi et al. 2010; Viall & Klimchuk 2011; Bradshaw et al. 2012; Winebarger 2012). While the direct evidence for enhanced suprathermal populations in the solar corona is still lacking (Feldman et al. 2007; Hannah et al. 2010), Pinfield et al. (1999) reported that the intensities of the Si III transition region lines observed by the SOHO/SUMER instrument do not correspond to a single Maxwellian distribution. Using their data, Dzifˇc'akov'a & Kulinov'a (2011) showed that the observed intensities can be explained by κ -distributions once the photoexcitation is taken into account. These authors diagnosed κ =7 in the active region observed on the solar limb. Higher values of κ were diagnosed for the quiet Sun and coronal hole, indiciating that the departures from the Maxwellian distribution can be connected to the local magnetic activity. The diagnostic method also works for inhomogeneous plasmas characterized by differential emission measure. That the κ -distributions can be present in the solar corona is also suggested by their presence in the solar wind (e.g., Pierrard et al. 1999; Vocks & Mann 2003). Direct diagnostics of κ -distributions in the solar corona using extreme-ultraviolet lines observed by the Hinode/EIS spectrometer (Culhane et al. 2007) were attempted by Dzifˇc'akov'a & Kulinov'a (2010) and Mackovjak et al. (2013). These authors proposed methods for simultaneous diagnostics of the plasma temperature, electron density, and κ . However, majority of the line ratios sensitive to κ -distributions suffer from poor photon statistics, errors in atomic data and/or plasma inhomogeneities. In spite of this, one of the main results of these works is that the sensitivity to κ -distributions, or to departures from the Maxwellian distribution in general, is enhanced if the line ratios involve lines originating in neighbooring ionization stages. This is due the sensitivity of the line emissivity to the abundance of the emitting ion that depends directly on the ionization equilibrium in turn highly dependent on the type of the distribution (e.g., Dzifˇc'akov'a 2002; Wannawichian et al. 2003; Dzifˇc'akov'a 2006). In the past decade, new calculations of the ionization, recombination rates and ionization equilibirium for the Maxwellian electron distribution were published. These are summarized in the continually updated CHIANTI database, currently available in version 7.1 (e.g., Dere et al. 1997, 2009; Landi et al. 2012, 2013). These new calculations of the ionization and recombination rates result in significant differences with respect to the earlier calculations, e.g. of Mazzotta et al. (1998). The availability of accurate atomic data are of crucial importance in correct determination of the properties of the radiating astrophysical environment, and the solar corona in particular. In this paper, we present upto-date calculations of the ionization and recombination rates (Sect. 3), and ionization equilibria (Sect. 4) for κ -distributions for elements from H to Zn. Such calculations are necessary for diagnostics of the κ -distributions in both the solar transition region and the corona, as well as subsequent calculations of the radiative losses (Dud'ık et al. 2011) or responses of various extremeultraviolet or X-ray filters (Dud'ık et al. 2009) used both to model and observe these portions of the solar atmosphere, with potential applications to other astrophysical environments.","pages":[1,2]},{"title":"2. THE NON-MAXWELLIAN κ -DISTRIBUTIONS","content":"The κ -distributions of electron kinetic energies E represent a family of non-Maxwellian distributions characterized by two parameters, κ and T where the A κ = Γ( κ +1) / [ Γ( κ -0 . 5)( κ -1 . 5) 3 / 2 ] is the normalization constant, k B =1.38 × 10 -23 J kg -1 is the Boltzmann constant, and κ ∈ (3 / 2 , + ∞ ), T ∈ (0 , + ∞ ). We note that the definition of κ -distributions in Eq. (1 top ) corresponds to the κ -distributions of the second kind (e.g., Livadiotis & McComas 2009). The shape of the distribution is controlled by the parameter κ . Maxwellian distribution is recovered for κ → + ∞ , while the departures from the Maxwellian increase with κ → 3/2. The departures from the Maxwellian distribution with decreasing κ include increase of the number of particles in the high-energy tail as well as increase in the relative number of lowenergy electrons (Fig. 1 top ). However, the mean energy 〈E〉 =3/2 k B T of the distribution does not depend on κ . This allows for calculation of all quantities depending on the mean energy of the distribution, e.g. pressure (Dzifˇc'akov'a 2006). The parameter T has in the frame of nonextensive statistics (Tsallis 1988, 2009) an analogous meaning as thermodynamic temperature in the Boltzmann-Gibbs statistics. The reader is referred e.g. to the work of Livadiotis & McComas (2009, 2010) for details. While the shape of the κ -distribution differs from the Maxwellian with the same T at all energies E , the core of the κ -distribution can be approximated by a Maxwellian distribution with lower T C = T ( κ -3 / 2) /κ (Oka et al. 2013). An example for κ =5 and T =1MK is shown in Fig. 1 bottom , where the approximating Maxwellian distribution has T C = 0 . 7 T and has been scaled by the factor C (Oka et al. 2013), which is ≈ 0.84 for κ =5. The difference between the f κ ( T ) and f Maxw ( T C ) are then mainly in the pronounced high-energy tail. This shows that the κ distributions offer straightforward approximation of situations where a non-Maxwellian high-energy tail is present.","pages":[2]},{"title":"3. IONIZATION AND RECOMBINATION RATES","content":"To calculate the ionization and recombination rates for κ -distributions, we use the atomic data available through the CHIANTI database for astrophysical spectroscopy of optically thin plasmas (Dere et al. 1997; Landi et al. 2013). The analytical functional form of the κ -distributions allows for relatively simple direct integration of the ionization cross-sections (Sect 3.2). However, the recombination cross-sections are not contained in CHIANTI. These then have to be reverse-engineered from the Maxwellian recombination rates using assumptions detailed in Sect. 3.3. We note that the CHIANTI database allows for the treatment of non-Maxwellian distributions only if these can be represented by a series of individual Maxwellian distributions (with different T s). The technique for calculation of ionization and recombination rates presented here can in principle be extended for any type of particle distribution, not only κ -distributions.","pages":[2]},{"title":"3.1. Atomic Data","content":"The CHIANTI atomic database since version 6 (Dere et al. 2009) contains continually updated ionization equilibrium for the Maxwellian distribution. This ionization equilibrium utilizes the cross-sections for direct ionization and autoionization, and the corresponding rate coefficients from the work of Dere (2007). Dielectronic and radiative recombination coefficients for the H to Al and Ar isoelectronic sequences are taken from the works of N. Badnell and colleagues, listed at http://amdpp.phys.strath.ac.uk/tamoc/DATA/ (Badnell et al. 2003; Colgan et al. 2003, 2004; Mitnik & Badnell 2004; Badnell 2006; Altun et al. 2005, 2006, 2007; Zatsarinny et al. 2005a,b, 2006; Bautista & Badnell 2007; Nikoli'c et al. 2010; Abdel-Naby et al. 2012). For the Si to Mn isoelectronic sequences, the recombination rates are based on the works of Shull & van Steenberg (1982), Nahar (1996, 1997), Nahar & Bautista (2001), Mazzotta et al. (1998) and Mazzitelli & Mattioli (2002). The reader is referred to Dere et al. (2009) for details. In the calculations presented in this paper, all atomic data for ionization and recombination correspond to the ones used to produce the chianti.ioneq file in the CHIANTI v7.1. We note that ionization equilibria were published also by other authors (e.g. Bryans et al. 2009), but these use mostly the same atomic data as the CHIANTI database.","pages":[2,3]},{"title":"3.2. Ionization Rates","content":"The ionization rates have been calculated by a numerical integration of the ionization cross section, σ i , available in CHIANTI database for κ =2,3,5,7,10, 25, and 33. Each numerical integral is calculated as a sum of individual integrals splitted according to the ionization and auto-ionizaton energies. Typical changes in behaviour of the direct ionization and autoionization rates with κ -distributions are shown in Fig. 2 for the ions C IV , Fe XII , and Fe XVII formed at transition region, quiet coronal, and flare conditions, respectively. For lower κ , the temperature dependence of the ionization rates is much flatter, with lower maxima. Typically, for temperatures lower than those at which the ion abundance peaks (denoted by arrow in Fig. 2, see also Sect. 4), the κ -distributions result in increase of the ionization rates by up to several orders of magnitude with respect to the Maxwellian distribution. These deviations from Maxwellian ionization rates increase with decreasing κ .","pages":[3]},{"title":"3.3. Recombination Rates","content":"Since the individual recombination cross-sections are not available in CHIANTI, the calculation of the recombination rates for κ -distributions was performed using the method of Dzifˇc'akov'a (1992), used also by Wannawichian et al. (2003). This method allows for calculation of the recombination rates using approximations to the rates for the Maxwellian distribution. The cross-section σ RR for the radiative recombination is assumed to have a power-law dependence on energy (Osterbrock 1974) where C RR is a constant and η +0 . 5 is a power-law index. Subsequently, the radiative recombination rate for the κ -distribution is of the form: while the radiative recombition rate for the Maxwellian distribution is Therefore, it holds that The level of error introduced by this approximation is typically several per cent, i.e., lower than the error of the atomic data themselves. For the dielectronic recombination, following approximation has been taken (Dzifˇc'akov'a 1992) where parameters a i and t i are the same as in similar expressions for the Maxwellian distribution where the coefficients a i and t i are provided within the CHIANTI database. The precision of this approximation is given by the magnitude of the second-order terms in the expansion of the coefficients a i and t i into series (Eqs. 37-44 in Dzifˇc'akov'a 1992). The typical behavior of the total recombination rates ( R RR + R DR ) for κ -distributions and for Maxwellian distribution is shown in Fig. 2. It can be seen that the radiative recombination rate increases with decrease of κ . This is a result of increasing number of low energy electrons for the κ -distributions (Fig. 1), which dominate the recombination processes. The local change of slope of total recombination rate is caused by the contribution of dielectronic recombination. For some ions, e.g. Fe XVII , the contribution of dielectronic recombination is dominant in temperature interval where these ions have a non-negligible abundance.","pages":[3]},{"title":"4. THE IONIZATION EQUILIBRIUM","content":"Calculations of the collisional ionization equilibrium assume that there are no temporal variations in plasma temperature T . In the coronal conditions, the resulting relative ion populations are given by the equilibrium between the direct collisional ionization with autoionization and the radiative and dielectronic recombination. Three-body processes can be neglected at low electron densities typical in the solar corona (Phillips et al. 2008). The radiative field is also usually assumed to be too weak, i.e., photoionization can be neglected as well. However, we note that photoionization may be important for some transition-region ions with low ionization thresholds, but the effect will vary depending on the distance from the radiation field (e.g., the solar photosphere). The ionization equilibrium for κ -distributions with κ =2,3,5,7,10, 25, and 33 was calculated for ions of astrophysical interests, ranging from H ( Z =1) to Zn ( Z =30). Previous calculations of Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002), and Wannawichian et al. (2003) involved only 12 most abundant elements. The current calculations are performed for the same set of temperatures as the calculations in the CHIANTI database in the chianti.ioneq file. I.e., the temperature spans the interval of log( T /K) ∈〈 4 , 9 〉 with the step of ∆log( T /K)=0.05. The calculations are available in the same format as the chianti.ioneq file and are easily readable using the routines read ioneq.pro and plot ioneq.pro available in CHIANTI running under SolarSoftware in IDL. More information on the CHIANTI .ioneq file format is provided in Appendix A. Examples of the current ionization equilibrium calculations for iron are in Fig. 3 and for carbon in Fig. 4. The typical behavior is that the lower κ , the flatter the ionization peaks. In addition, ionization peaks can be shifted to lower or higher T , depending on κ , T and the individual ion. This means that a given relative ion abundance can be formed at a wider range of T for a κ -distribution, with different peak formation temperature. Such behavior was already reported by Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002) and Wannawichian et al. (2003). Typically, the shifts of Fe and C ion abundance peaks are to lower T with respect to the Maxwellian ionization equilibrium if log( T /K) /lessorapproxeql 5.5. At coronal temperatures, the Fe IX - Fe XVI ions are shifted to higher T . An interesting example is the ion Fe XVII , whose ionization peak is shifted to lower T for κ lessapprox 3, but to higher T for κ =2(Fig. 3 bottom ). There are a number of differences with respect to the earlier calculations of Dzifˇc'akov'a (2002), which used the atomic data corresponding to those of Mazzotta et al. (1998). These differences are illustrated in Fig. 5. In general, the lower the value of κ , the greater the differences with respect to the previous calculations. The most conspicuous examples are the Fe IX , which is shifted to slightly higher T instead to lower T as in the previous calculations of Dzifˇc'akov'a (2002). The Fe XII and Fe XIII ions are shifted to higher T (up to 0.1-0.15 dex). We note that the changes in the ionization equilibria due to the updated atomic data will reflect e.g. on changes in the total radiative losses (Dud'ık et al. 2011) and will also modify the proposed diagnostic methods for κ -distributions (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013). Ratios of relative abundances of individual ions can be used to diagnose the value of κ and simultaneously T . Such diagnostics can be applied e.g. in the solar wind (Owocki & Scudder 1983). An example of diagnostic diagrams is given in Fig. 6. We note that such diagrams cannot be directly applied on the observed line intensities unless the additional effect of κ -distributions on the excitation and deexcitation rates is considered. However, these diagrams provide quantification of the expected changes to ratios of line intensities due to ionization equilibrium. Ratios of lines involving different ionization stages provide better options for determining κ , as noted already by (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013).","pages":[3,4]},{"title":"5. SUMMARY","content":"Collisional ionization equilibrium calculations for κ -distributions and optically thin plasmas were performed for all ions of elements H to Zn. To do that, the latest available atomic data for ionization and recombination were used. The calculations are available in the form of ionization equilibrium files compatible with the CHIANTI database, v7.1. For κ -distributions, the ionization peaks are in general flatter and can be shifted to lower or higher T . This means that for κ -distributions, individual ions are typically formed in a wider range of temperatures, with different peak formation temperatures. Typically, ions formed at transition region temperatures are shifted to lower T , while the majority of coronal iron ions are shifted to higher T . Comparison to previous calculations is provided. Due to updated atomic data calculations, several ions in the present calculations are shifted to different temperatures with respect to previous calculations of Dzifˇc'akov'a (2002). The effect of κ on the ratios of ion abundances is documented. The present calculations provide an accurate, necessary and useful tool for detection of astrophysical plasmas out of thermal equilibrium, where the distribution of particles is characterized by an enhanced power-law tail. The supplied files compatible with the CHIANTI database and software should greatly facilitate synthetization of both line and continuum spectra for optically thin astrophysical plasmas. The authors are grateful to Dr. G. Del Zanna and Dr. H. E. Mason for helpful discussions. This work was supported by Grant Agency of the Czech Republic, Grant No. P209/12/1652, the project RVO:67985815, Scientific Grant Agency, VEGA, Slovakia, Grant No. 1/0240/11, and the bilateral project APVV CZ-SK0153-11 (7AMB12SK154) involving the Slovak Research and Development Agency and the Ministry of Education of the Czech Republic. JD acknowledges support from the Comenius University Grant No. UK/11/2012. CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK), the Universities of Florence (Italy) and Cambridge (UK), and George Mason University (USA). CHIANTI is great spectroscopic database and software, and the authors are very grateful for its existence and availability.","pages":[4]},{"title":"CHIANTI .IONEQ FILE FORMAT","content":"The .ioneq files, used by the CHIANTI database and software to store data on the ionization equilibrium, are in essence formatted ASCII files. An example of their format is given in Table 1. The file begins with two numbers, N , giving the number of temperature points T i , 1 ≤ i ≤ N , and Z max , denoting the maximum proton number Z for which the ionization equilibrium is provided. The next line gives the tabulated temperatures log( T i / K). All other following lines begin with the Z and a positive integer + k denoting the roman numeral for the corresponding ion; e.g., 26 and 9 stands for Fe IX . The line then contains relative ion abundances A + k -1 Z ( T i ) in floating-point precision for the tabulated temperatures. Portion of the actual content of the kappa 05.ioneq file is given in Table 2. There, the relative abundances of the ions Fe IX -Fe XI are listed for κ =5 and for log( T/ K)=5.80 - 6.15.","pages":[4]},{"title":"REFERENCES","content":"Collier, M. R., Hamilton, D. C., Gloeckler, G., Bochsler, P., & Sheldon, R. B. 1996, Geophys. Res. Lett., 23, 1191 J. Geophys. Res., 114, A01212 -. 2006, Sol. Phys., 234, 243 Geophys. Res. Lett., 24, 1151 Tripathi, D., Mason, H. E., & Klimchuk, J. A. 2010, ApJ, 723, 713 Tsallis, C. 1988, Journal of Statistical Physics, 52, 479 Viall, N. M., & Klimchuk, J. A. 2011, ApJ, 738, 24 Xiao, F., Shen, C., Wang, Y., Zheng, H., & Wang, S. 2008, Journal of Geophysical Research (Space Physics), 113, 5203","pages":[6]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"New data for calculation of the ionization and recombination rates have have been published in the past few years. Most of these are included in CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian κ -distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The κ -distributions significantly influence both the ionization and recombination rates and widen the ion abundance peaks. In comparison with Maxwellian distribution, the ion abundance peaks can also be shifted to lower or higher temperatures. The updated ionization equilibrium calculations result in large changes for several ions, notably Fe VIII-XIV. The results are supplied in electronic form compatible with the CHIANTI database. Keywords: Atomic data - Atomic processes - Radiation mechanisms: non-thermal - Sun: corona Sun: UV radiation - Sun: X-rays, gamma rays\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"H TO ZN IONIZATION EQUILIBRIUM FOR THE NON-MAXWELLIAN ELECTRON κ -DISTRIBUTIONS: UPDATED CALCULATIONS\",\n \"content\": \"E. Dzifˇc'akov'a 1 Astronomical Institute of the Academy of Sciences of the Czech Republic, Friˇcova 298, 251 65 Ondˇrejov, Czech Republic\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"J. Dud'ık 1\",\n \"content\": \"Newton International Fellow, DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom Draft version March 7, 2022\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"One of the most widely used assumptions in the interpretation of astrophysical spectra is that the emitting system is in thermal equilibrium. This means that the distribution of particle energies is at least locally Maxwellian, and can be characterized by the BoltzmannGibbs statistics which has one parameter, the temperature. The generalization of the Bolzmann-Gibbs statistics proposed by Tsallis (1988, 2009), results in κ -distributions (e.g., Leubner 2002, 2004a,b; Collier 2004; Livadiotis & McComas 2009), characterized by a parameter κ and exhibiting a near-Maxwellian core and a high-energy power-law tail (Sect. 2). First proposed by Vasyliunas (1968), the κ distributions are now used to fit the observations of a wide variety of astrophysical environments, e.g. in-situ measurements of particle distributions in planetary magnetic environments (e.g., Pierrard & Lemaire 1996; Mauk et al. 2004; Schippers et al. 2008; Xiao et al. 2008; Dialynas et al. 2009) and solar wind (e.g., Collier et al. 1996; Maksimovic et al. 1997a,b; Pierrard et al. 1999; Nieves-Chinchilla & Vi˜nas 2008; Le Chat et al. 2009, 2011; Pierrard 2012), as well as photon spectra of solar flare plasmas (e.g., Kaˇsparov'a & Karlick'y 2009; Oka et al. 2013), emission line spectra of planetary nebulae and galactic sources (Nicholls et al. 2012; see also Binette et al. 2012) and even solar transition region (Dzifˇc'akov'a et al. 2011). A review on the κ -distributions and their applications in astrophysical plasma can be found, e.g., in Pierrard & Lazar (2010). elena@asu.cas.cz 1 DAPEM, Faculty of Mathematics Physics and Computer Science, Comenius University, Mlynsk'a Dolina F2, 842 48 Bratislava, Slovakia In the solar corona, presence of the κ -distributions, or distributions exhibiting high-energy tails, can be expected due to particle acceleration processes arising as a result of 'nanoflare' heating. The nanoflares are an unknown energy release process of impulsive nature, occuring possibly in storms heating the solar corona (e.g., Tripathi et al. 2010; Viall & Klimchuk 2011; Bradshaw et al. 2012; Winebarger 2012). While the direct evidence for enhanced suprathermal populations in the solar corona is still lacking (Feldman et al. 2007; Hannah et al. 2010), Pinfield et al. (1999) reported that the intensities of the Si III transition region lines observed by the SOHO/SUMER instrument do not correspond to a single Maxwellian distribution. Using their data, Dzifˇc'akov'a & Kulinov'a (2011) showed that the observed intensities can be explained by κ -distributions once the photoexcitation is taken into account. These authors diagnosed κ =7 in the active region observed on the solar limb. Higher values of κ were diagnosed for the quiet Sun and coronal hole, indiciating that the departures from the Maxwellian distribution can be connected to the local magnetic activity. The diagnostic method also works for inhomogeneous plasmas characterized by differential emission measure. That the κ -distributions can be present in the solar corona is also suggested by their presence in the solar wind (e.g., Pierrard et al. 1999; Vocks & Mann 2003). Direct diagnostics of κ -distributions in the solar corona using extreme-ultraviolet lines observed by the Hinode/EIS spectrometer (Culhane et al. 2007) were attempted by Dzifˇc'akov'a & Kulinov'a (2010) and Mackovjak et al. (2013). These authors proposed methods for simultaneous diagnostics of the plasma temperature, electron density, and κ . However, majority of the line ratios sensitive to κ -distributions suffer from poor photon statistics, errors in atomic data and/or plasma inhomogeneities. In spite of this, one of the main results of these works is that the sensitivity to κ -distributions, or to departures from the Maxwellian distribution in general, is enhanced if the line ratios involve lines originating in neighbooring ionization stages. This is due the sensitivity of the line emissivity to the abundance of the emitting ion that depends directly on the ionization equilibrium in turn highly dependent on the type of the distribution (e.g., Dzifˇc'akov'a 2002; Wannawichian et al. 2003; Dzifˇc'akov'a 2006). In the past decade, new calculations of the ionization, recombination rates and ionization equilibirium for the Maxwellian electron distribution were published. These are summarized in the continually updated CHIANTI database, currently available in version 7.1 (e.g., Dere et al. 1997, 2009; Landi et al. 2012, 2013). These new calculations of the ionization and recombination rates result in significant differences with respect to the earlier calculations, e.g. of Mazzotta et al. (1998). The availability of accurate atomic data are of crucial importance in correct determination of the properties of the radiating astrophysical environment, and the solar corona in particular. In this paper, we present upto-date calculations of the ionization and recombination rates (Sect. 3), and ionization equilibria (Sect. 4) for κ -distributions for elements from H to Zn. Such calculations are necessary for diagnostics of the κ -distributions in both the solar transition region and the corona, as well as subsequent calculations of the radiative losses (Dud'ık et al. 2011) or responses of various extremeultraviolet or X-ray filters (Dud'ık et al. 2009) used both to model and observe these portions of the solar atmosphere, with potential applications to other astrophysical environments.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2. THE NON-MAXWELLIAN κ -DISTRIBUTIONS\",\n \"content\": \"The κ -distributions of electron kinetic energies E represent a family of non-Maxwellian distributions characterized by two parameters, κ and T where the A κ = Γ( κ +1) / [ Γ( κ -0 . 5)( κ -1 . 5) 3 / 2 ] is the normalization constant, k B =1.38 × 10 -23 J kg -1 is the Boltzmann constant, and κ ∈ (3 / 2 , + ∞ ), T ∈ (0 , + ∞ ). We note that the definition of κ -distributions in Eq. (1 top ) corresponds to the κ -distributions of the second kind (e.g., Livadiotis & McComas 2009). The shape of the distribution is controlled by the parameter κ . Maxwellian distribution is recovered for κ → + ∞ , while the departures from the Maxwellian increase with κ → 3/2. The departures from the Maxwellian distribution with decreasing κ include increase of the number of particles in the high-energy tail as well as increase in the relative number of lowenergy electrons (Fig. 1 top ). However, the mean energy 〈E〉 =3/2 k B T of the distribution does not depend on κ . This allows for calculation of all quantities depending on the mean energy of the distribution, e.g. pressure (Dzifˇc'akov'a 2006). The parameter T has in the frame of nonextensive statistics (Tsallis 1988, 2009) an analogous meaning as thermodynamic temperature in the Boltzmann-Gibbs statistics. The reader is referred e.g. to the work of Livadiotis & McComas (2009, 2010) for details. While the shape of the κ -distribution differs from the Maxwellian with the same T at all energies E , the core of the κ -distribution can be approximated by a Maxwellian distribution with lower T C = T ( κ -3 / 2) /κ (Oka et al. 2013). An example for κ =5 and T =1MK is shown in Fig. 1 bottom , where the approximating Maxwellian distribution has T C = 0 . 7 T and has been scaled by the factor C (Oka et al. 2013), which is ≈ 0.84 for κ =5. The difference between the f κ ( T ) and f Maxw ( T C ) are then mainly in the pronounced high-energy tail. This shows that the κ distributions offer straightforward approximation of situations where a non-Maxwellian high-energy tail is present.\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"3. IONIZATION AND RECOMBINATION RATES\",\n \"content\": \"To calculate the ionization and recombination rates for κ -distributions, we use the atomic data available through the CHIANTI database for astrophysical spectroscopy of optically thin plasmas (Dere et al. 1997; Landi et al. 2013). The analytical functional form of the κ -distributions allows for relatively simple direct integration of the ionization cross-sections (Sect 3.2). However, the recombination cross-sections are not contained in CHIANTI. These then have to be reverse-engineered from the Maxwellian recombination rates using assumptions detailed in Sect. 3.3. We note that the CHIANTI database allows for the treatment of non-Maxwellian distributions only if these can be represented by a series of individual Maxwellian distributions (with different T s). The technique for calculation of ionization and recombination rates presented here can in principle be extended for any type of particle distribution, not only κ -distributions.\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"3.1. Atomic Data\",\n \"content\": \"The CHIANTI atomic database since version 6 (Dere et al. 2009) contains continually updated ionization equilibrium for the Maxwellian distribution. This ionization equilibrium utilizes the cross-sections for direct ionization and autoionization, and the corresponding rate coefficients from the work of Dere (2007). Dielectronic and radiative recombination coefficients for the H to Al and Ar isoelectronic sequences are taken from the works of N. Badnell and colleagues, listed at http://amdpp.phys.strath.ac.uk/tamoc/DATA/ (Badnell et al. 2003; Colgan et al. 2003, 2004; Mitnik & Badnell 2004; Badnell 2006; Altun et al. 2005, 2006, 2007; Zatsarinny et al. 2005a,b, 2006; Bautista & Badnell 2007; Nikoli'c et al. 2010; Abdel-Naby et al. 2012). For the Si to Mn isoelectronic sequences, the recombination rates are based on the works of Shull & van Steenberg (1982), Nahar (1996, 1997), Nahar & Bautista (2001), Mazzotta et al. (1998) and Mazzitelli & Mattioli (2002). The reader is referred to Dere et al. (2009) for details. In the calculations presented in this paper, all atomic data for ionization and recombination correspond to the ones used to produce the chianti.ioneq file in the CHIANTI v7.1. We note that ionization equilibria were published also by other authors (e.g. Bryans et al. 2009), but these use mostly the same atomic data as the CHIANTI database.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"3.2. Ionization Rates\",\n \"content\": \"The ionization rates have been calculated by a numerical integration of the ionization cross section, σ i , available in CHIANTI database for κ =2,3,5,7,10, 25, and 33. Each numerical integral is calculated as a sum of individual integrals splitted according to the ionization and auto-ionizaton energies. Typical changes in behaviour of the direct ionization and autoionization rates with κ -distributions are shown in Fig. 2 for the ions C IV , Fe XII , and Fe XVII formed at transition region, quiet coronal, and flare conditions, respectively. For lower κ , the temperature dependence of the ionization rates is much flatter, with lower maxima. Typically, for temperatures lower than those at which the ion abundance peaks (denoted by arrow in Fig. 2, see also Sect. 4), the κ -distributions result in increase of the ionization rates by up to several orders of magnitude with respect to the Maxwellian distribution. These deviations from Maxwellian ionization rates increase with decreasing κ .\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"3.3. Recombination Rates\",\n \"content\": \"Since the individual recombination cross-sections are not available in CHIANTI, the calculation of the recombination rates for κ -distributions was performed using the method of Dzifˇc'akov'a (1992), used also by Wannawichian et al. (2003). This method allows for calculation of the recombination rates using approximations to the rates for the Maxwellian distribution. The cross-section σ RR for the radiative recombination is assumed to have a power-law dependence on energy (Osterbrock 1974) where C RR is a constant and η +0 . 5 is a power-law index. Subsequently, the radiative recombination rate for the κ -distribution is of the form: while the radiative recombition rate for the Maxwellian distribution is Therefore, it holds that The level of error introduced by this approximation is typically several per cent, i.e., lower than the error of the atomic data themselves. For the dielectronic recombination, following approximation has been taken (Dzifˇc'akov'a 1992) where parameters a i and t i are the same as in similar expressions for the Maxwellian distribution where the coefficients a i and t i are provided within the CHIANTI database. The precision of this approximation is given by the magnitude of the second-order terms in the expansion of the coefficients a i and t i into series (Eqs. 37-44 in Dzifˇc'akov'a 1992). The typical behavior of the total recombination rates ( R RR + R DR ) for κ -distributions and for Maxwellian distribution is shown in Fig. 2. It can be seen that the radiative recombination rate increases with decrease of κ . This is a result of increasing number of low energy electrons for the κ -distributions (Fig. 1), which dominate the recombination processes. The local change of slope of total recombination rate is caused by the contribution of dielectronic recombination. For some ions, e.g. Fe XVII , the contribution of dielectronic recombination is dominant in temperature interval where these ions have a non-negligible abundance.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"4. THE IONIZATION EQUILIBRIUM\",\n \"content\": \"Calculations of the collisional ionization equilibrium assume that there are no temporal variations in plasma temperature T . In the coronal conditions, the resulting relative ion populations are given by the equilibrium between the direct collisional ionization with autoionization and the radiative and dielectronic recombination. Three-body processes can be neglected at low electron densities typical in the solar corona (Phillips et al. 2008). The radiative field is also usually assumed to be too weak, i.e., photoionization can be neglected as well. However, we note that photoionization may be important for some transition-region ions with low ionization thresholds, but the effect will vary depending on the distance from the radiation field (e.g., the solar photosphere). The ionization equilibrium for κ -distributions with κ =2,3,5,7,10, 25, and 33 was calculated for ions of astrophysical interests, ranging from H ( Z =1) to Zn ( Z =30). Previous calculations of Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002), and Wannawichian et al. (2003) involved only 12 most abundant elements. The current calculations are performed for the same set of temperatures as the calculations in the CHIANTI database in the chianti.ioneq file. I.e., the temperature spans the interval of log( T /K) ∈〈 4 , 9 〉 with the step of ∆log( T /K)=0.05. The calculations are available in the same format as the chianti.ioneq file and are easily readable using the routines read ioneq.pro and plot ioneq.pro available in CHIANTI running under SolarSoftware in IDL. More information on the CHIANTI .ioneq file format is provided in Appendix A. Examples of the current ionization equilibrium calculations for iron are in Fig. 3 and for carbon in Fig. 4. The typical behavior is that the lower κ , the flatter the ionization peaks. In addition, ionization peaks can be shifted to lower or higher T , depending on κ , T and the individual ion. This means that a given relative ion abundance can be formed at a wider range of T for a κ -distribution, with different peak formation temperature. Such behavior was already reported by Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002) and Wannawichian et al. (2003). Typically, the shifts of Fe and C ion abundance peaks are to lower T with respect to the Maxwellian ionization equilibrium if log( T /K) /lessorapproxeql 5.5. At coronal temperatures, the Fe IX - Fe XVI ions are shifted to higher T . An interesting example is the ion Fe XVII , whose ionization peak is shifted to lower T for κ lessapprox 3, but to higher T for κ =2(Fig. 3 bottom ). There are a number of differences with respect to the earlier calculations of Dzifˇc'akov'a (2002), which used the atomic data corresponding to those of Mazzotta et al. (1998). These differences are illustrated in Fig. 5. In general, the lower the value of κ , the greater the differences with respect to the previous calculations. The most conspicuous examples are the Fe IX , which is shifted to slightly higher T instead to lower T as in the previous calculations of Dzifˇc'akov'a (2002). The Fe XII and Fe XIII ions are shifted to higher T (up to 0.1-0.15 dex). We note that the changes in the ionization equilibria due to the updated atomic data will reflect e.g. on changes in the total radiative losses (Dud'ık et al. 2011) and will also modify the proposed diagnostic methods for κ -distributions (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013). Ratios of relative abundances of individual ions can be used to diagnose the value of κ and simultaneously T . Such diagnostics can be applied e.g. in the solar wind (Owocki & Scudder 1983). An example of diagnostic diagrams is given in Fig. 6. We note that such diagrams cannot be directly applied on the observed line intensities unless the additional effect of κ -distributions on the excitation and deexcitation rates is considered. However, these diagrams provide quantification of the expected changes to ratios of line intensities due to ionization equilibrium. Ratios of lines involving different ionization stages provide better options for determining κ , as noted already by (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013).\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"5. SUMMARY\",\n \"content\": \"Collisional ionization equilibrium calculations for κ -distributions and optically thin plasmas were performed for all ions of elements H to Zn. To do that, the latest available atomic data for ionization and recombination were used. The calculations are available in the form of ionization equilibrium files compatible with the CHIANTI database, v7.1. For κ -distributions, the ionization peaks are in general flatter and can be shifted to lower or higher T . This means that for κ -distributions, individual ions are typically formed in a wider range of temperatures, with different peak formation temperatures. Typically, ions formed at transition region temperatures are shifted to lower T , while the majority of coronal iron ions are shifted to higher T . Comparison to previous calculations is provided. Due to updated atomic data calculations, several ions in the present calculations are shifted to different temperatures with respect to previous calculations of Dzifˇc'akov'a (2002). The effect of κ on the ratios of ion abundances is documented. The present calculations provide an accurate, necessary and useful tool for detection of astrophysical plasmas out of thermal equilibrium, where the distribution of particles is characterized by an enhanced power-law tail. The supplied files compatible with the CHIANTI database and software should greatly facilitate synthetization of both line and continuum spectra for optically thin astrophysical plasmas. The authors are grateful to Dr. G. Del Zanna and Dr. H. E. Mason for helpful discussions. This work was supported by Grant Agency of the Czech Republic, Grant No. P209/12/1652, the project RVO:67985815, Scientific Grant Agency, VEGA, Slovakia, Grant No. 1/0240/11, and the bilateral project APVV CZ-SK0153-11 (7AMB12SK154) involving the Slovak Research and Development Agency and the Ministry of Education of the Czech Republic. JD acknowledges support from the Comenius University Grant No. UK/11/2012. CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK), the Universities of Florence (Italy) and Cambridge (UK), and George Mason University (USA). CHIANTI is great spectroscopic database and software, and the authors are very grateful for its existence and availability.\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"CHIANTI .IONEQ FILE FORMAT\",\n \"content\": \"The .ioneq files, used by the CHIANTI database and software to store data on the ionization equilibrium, are in essence formatted ASCII files. An example of their format is given in Table 1. The file begins with two numbers, N , giving the number of temperature points T i , 1 ≤ i ≤ N , and Z max , denoting the maximum proton number Z for which the ionization equilibrium is provided. The next line gives the tabulated temperatures log( T i / K). All other following lines begin with the Z and a positive integer + k denoting the roman numeral for the corresponding ion; e.g., 26 and 9 stands for Fe IX . The line then contains relative ion abundances A + k -1 Z ( T i ) in floating-point precision for the tabulated temperatures. Portion of the actual content of the kappa 05.ioneq file is given in Table 2. There, the relative abundances of the ions Fe IX -Fe XI are listed for κ =5 and for log( T/ K)=5.80 - 6.15.\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Collier, M. R., Hamilton, D. C., Gloeckler, G., Bochsler, P., & Sheldon, R. B. 1996, Geophys. Res. Lett., 23, 1191 J. Geophys. Res., 114, A01212 -. 2006, Sol. Phys., 234, 243 Geophys. Res. Lett., 24, 1151 Tripathi, D., Mason, H. E., & Klimchuk, J. A. 2010, ApJ, 723, 713 Tsallis, C. 1988, Journal of Statistical Physics, 52, 479 Viall, N. M., & Klimchuk, J. A. 2011, ApJ, 738, 24 Xiao, F., Shen, C., Wang, Y., Zheng, H., & Wang, S. 2008, Journal of Geophysical Research (Space Physics), 113, 5203\",\n \"pages\": [\n 6\n ]\n }\n]"}}},{"rowIdx":81,"cells":{"bibcode":{"kind":"string","value":"2013ApJS..207...12R"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1307.2321.pdf"},"content":{"kind":"string","value":"\nMETHYL CYANIDE OBSERVATIONS TOWARD MASSIVE PROTOSTARS\nV. Rosero 1 , P. Hofner 1 , † , S. Kurtz 2 , J. Bieging 3 & E. D. Araya 4\n1 Physics Department, New Mexico Tech, 801 Leroy Pl., Socorro, NM 87801, USA\n2 Centro de Radioastronom'ıa y Astrof'ısica, Universidad Nacional Aut'onoma de M'exico, Morelia 58090, M'exico 3 Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA and 4 Physics Department, Western Illinois University, 1 University Circle, Macomb, IL 61455, USA To appear in The Astrophysical Journal Supplement Series.\nABSTRACT\nWe report the results of a survey in the CH 3 CN J=12 → 11 transition toward a sample of massive proto-stellar candidates. The observations were carried out with the 10 m Submillimeter telescope on Mount Graham, AZ. We detected this molecular line in 9 out of 21 observed sources. In six cases this is the first detection of this transition. We also obtained full beam sampled cross-scans for five sources which show that the lower K -components can be extended on the arcminute angular scale. The higher K -components however are always found to be compact with respect to our 36 '' beam. A Boltzmann population diagram analysis of the central spectra indicates CH 3 CN column densities of about 10 14 cm -2 , and rotational temperatures above 50 K, which confirms these sources as hot molecular cores. Independent fits to line velocity and width for the individual K -components resulted in the detection of an increasing blue shift with increasing line excitation for four sources. Comparison with mid-infrared images from the SPITZER GLIMPSE /IRAC archive for six sources show that the CH 3 CN emission is generally coincident with a bright mid-IR source. Our data clearly show that the CH 3 CN J=12 → 11 transition is a good probe of the hot molecular gas near massive protostars, and provide the basis for future interferometric studies.\nSubject headings: ISM: molecules - stars: formation\n1. INTRODUCTION\nDespite the central role of massive stars in almost all areas of astronomy, the physical processes involved in the formation of stars with masses > 8 M /circledot are at present poorly understood (e.g., Zinnecker & Yorke (2007)). Theoretical and observational studies favor the idea that massive stars, similar to their lower mass counterparts, form from a collapsing cloud core. However, whether the subsequent formation of a protostar and further mass accretion occurs from an isolated massive molecular core (e.g., McKee & Tan (2003), Keto (2007)), or under the influence of a cluster environment (e.g., Bonnell et al. (2004)) remains a persistent question.\nOne of the earliest observational manifestations of massive proto-stars are so-called hot molecular cores (hereafter HMCs). Named after the prototype object in the Orion KL region, they have been surveyed throughout the Galaxy in an effort to identify candidates for massive proto-stars (e.g., Sridharan et al. (2002)). Common search criteria were high FIR luminosity, high molecular column densities and temperature, and the absence of strong radio continuum emission - the latter to ensure an earlier evolutionary phase than ultra-compact (UC) or hyper-compact (HC) HII regions.\nA particularly useful tracer of HMCs is the methyl cyanide (CH 3 CN) molecule. Due to the centrifugal deformation of this symmetric top molecule, its rotational spectrum consists of a series of closely spaced K -components tracing rapidly increasing excitation energies. The K -ladders are connected only through collisions so that excitation temperatures can in principle be measured from the ratios of K -components, thus avoiding the usual calibration uncertainties that occur when\ncomparing rotational transitions observed in different frequency bands. An extensive discussion of the microwave spectroscopy of methyl cyanide is given in Boucher et al. (1980). Because of these spectroscopic properties, the CH 3 CNmolecule is frequently used to determine temperatures in the dense molecular cores where massive stars form, using both statistical equilibrium calculations (e.g., Loren & Mundy (1984)), or the simpler rotation diagram technique (e.g., Goldsmith & Langer (1999)).\nAnother factor that favors the use of CH 3 CN as a tracer of HMCs is its enhanced abundance in warm (T= 100 -300 K), dense ( n H 2 = 10 6 -10 8 cm -3 ) environments (e.g., Blake et al. (1987)). This is generally thought to be caused by grain surface chemistry, either by primary reactions on the grain surface with subsequent release into the gas phase when the grain mantle evaporates, or, alternatively, by secondary reactions in the gas phase (e.g., Charnley et al. (1992), Bisschop et al. (2008)). Recently, Codella et al. (2009) reported detection of CH 3 CN in the outflow lobes of the low-mass protostar L1157-B1, and attributed the enhanced CH 3 CN abundance to shock chemistry. From these studies it is well-established that CH 3 CN traces an energetic environment similar to that expected in the immediate vicinity of massive proto-stars.\nTo investigate the HMC phase of massive star formation, several single dish CH 3 CN surveys have been made (e.g., Olmi et al. (1993), Araya et al. (2005), Pankonin et al. (2001)), and a small number of sources have also been studied with mm-interferometers (e.g., Cesaroni et al. (1994), Hofner et al. (1996), Furuya et al. (2008)). Several of the interferometric studies resulted in images of CH 3 CN structures that are elongated perpendicular to the direction of molecular outflows, with velocity gradients along the elongated structures; this is usually explained as rotational motion of a circum-\n
\n\n
Table 1 Observed Sources
\n
\nNote . -Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds.\nReferences. (1) Sridharan et al. (2002); (2) Codella et al. (1997); (3) Beuther & Steinacker (2007); (4) Brunthaler et al. (2009); (5) Araya et al. (2008); (6) Pestalozzi et al. (2005); (7) Sewilo et al. (2004); (8) Araya et al. (2006); (9) Purcell et al. (2006); (10) Churchwell et al. (1990); (11) Watt & Mundy (1999); (12) Shepherd et al. (2000); (13) Truch et al. (2008); (14) Molinari et al. (2002); (15) Su et al. (2004); (16) Werner et al. (1979); (17) Sandell & Sievers (2004); (18) Thronson & Harper (1979)\nstellar disk or torus (e.g., Beltr'an et al. (2011)). The CH 3 CN molecule is thus a good choice to trace accretion disks around massive proto-stars, whose existence (if confirmed), and properties will be important input for current models of massive star formation.\nFrom the above discussion it is clear that observations of CH 3 CN with high sensitivity and angular resolution are well-suited to study accretion disks around massive stars. Such observations have recently become more accessible using instruments such as the Submillimeter Array (SMA) and ALMA. To facilitate such observations in the CH 3 CN J=12 → 11 line, the present study adds to the existing database of single dish studies of methyl cyanide.\nIn Section 2 we describe the observations and data reduction, and we present the observational results in Section 3. We conclude in Section 4 with a discussion of these observational results.\n2. OBSERVATIONS AND DATA REDUCTION\nWe observed 21 sources in 2008 from May 26 to 31 in the 1.3 mm CH 3 CN J=12 → 11 transition with the\n10 m Heinrich Hertz Submillimeter Telescope (SMT) 2 on Mt. Graham, AZ. The telescope beam width at 1 . 3 mm is approximately 36 '' , and the pointing accuracy during our observing run was better than 7 '' . The pointing positions and LSR velocities for the observed sources are given in Table 1. Most of our target sources are prominent HMC candidates with large IRAS luminosities. They all show the typical observational indicators of massive star formation in the HMC stage, namely massive molecular cores, H 2 O and CH 3 OH maser emission, warm molecular gas, weak (or absent) radio continuum emission, and the presence of jets and molecular flows. An exception is IRDC 18223-3, which is a massive infrared dark cloud with an embedded protostar, which may be in an earlier evolutionary state (Beuther & Steinacker 2007).\nThe observations were conducted in double sideband mode using the 1.3 mm J-T ALMA sideband separating receiver 3 , which simultaneously recorded two linear orthogonal polarizations. The CH 3 CN J=12 → 11 K = 5 transition ( ν 0 = 220 . 641089 GHz, Boucher et al. 1980) was tuned to the center of the lower sideband. We used\nall six available backends; four low spectral resolution and two high spectral resolution. The low spectral resolution backends were the acoustic-optic spectrometers (AOSs) AOS-A and AOS-B with bandwidths and spectral resolutions of 975 MHz (1325 km s -1 ) and 953 kHz (1 . 3 kms -1 ), and two filterbanks which have bandwidths and spectral resolutions of 1.024 GHz (1392 km s -1 ) and 1 MHz (1 . 4 kms -1 ), respectively. Most of the data used for the analysis in this paper were taken with the AOSC and the Chirp Transform Spectrometers (CTS-A), which have bandwidths and channel widths of 250 . 5 MHz (340 km s -1 ) and 122kHz (0 . 17 kms -1 ) and 215MHz (292 km s -1 ) and 29 kHz (0 . 04 kms -1 ), respectively.\nThe AOS-C bandwidth does not cover all K -components of the CH 3 CN J=12 → 11 transition, hence we centered this backend on the K = 5 component. This setup allowed us to observe the K = 0 -7 components simultaneously. The AOS-A and AOS-B and the filterbanks offer bandwidths between 950 and 1000 MHz so in principle the higher K -components could be detected. In practice, however, the lower line strengths of the higher components prevented us from detecting them in all but the strongest source, G34.26+0.15. Furthermore, the 13 CO J=2 → 1 transition blends with the K = 9 component of the CH 3 CN J=12 → 11 transition, thus limiting the usefulness of this K -component.\nThe 12 CO J=2 → 1 transition located in the upper sideband (USB) contaminated the lower sideband data approximately 50 MHz away from the CH 3 CN J=12 → 11 K = 0 line. With the exception of G28.87+0.07, this contamination had little effect on the quality of our data. The USB rejection was approximately 17 dB over the course of our observations. Given the relatively weak appearance of the 12 CO J=2 → 1 line (normally a very strong line) in our spectra, we do not believe that there is significant contamination from other spectral lines located in the USB.\nOur observations were conducted using double beam switching with a switch rate of 2 Hz and a beamthrow of 2 ' with a total on/off cycle of approximately 6 minutes per scan. System temperatures ranged from 350 K to just under 200K with an average temperature of 212K. Focus corrections were obtained from observations of Jupiter. Whenever possible we also derived pointing corrections from cross scans of Jupiter. When Jupiter was not available or was located at a large angular distance from the target source, pointing corrections were made by observing asymptotic giant branch stars in the CO J = 2 → 1 transition falling in the USB. In the case of IRAS 20126+4104 we could line point using the 13 CO J=1 → 0 emission from the source.\nAt the beginning of each night of observations, we observed the strong source G34.26+0.15 for at least one scan to check for day-to-day consistency of our observations and to obtain a template source to identify contaminating spectral lines. Subsequently, all sources were observed for 12-18 minutes to determine the intensity of the K -components of the CH 3 CN J=12 → 11 transition. Promising sources were then re-observed for at least 2 hr. Additionally, we obtained full beam spaced cross scans for five sources, typically with 1 . 5 hr spent at each offset position.\nThe data were reduced in CLASS, which is part of the GILDAS 4 software package. All spectra were first inspected to check for bad channels or any obvious artifacts; bad scans were discarded. Subsequently, we subtracted baselines using low order polynomials, and initially averaged the spectra for each spectrometer and each day separately. After further inspection, all data taken on different days were averaged to form a final data set for each source. After Hanning smoothing and resampling to the same spectral resolution, we averaged the AOS-C and CTS-A spectrometer data. We will refer to the latter data set as 'high resolution' spectra. The data were calibrated using the chopper-wheel method and the antenna temperature was converted to mainbeam brightness temperature by dividing the antenna temperature by the main-beam efficiency of the telescope ( η b = 0 . 74) 5 .\nUsing the daily spectra of the strong source G34.26+0.15, we checked our data for amplitude stability, which maximum deviation from the average was found to be smaller than 16 %. Measured line widths had maximum deviations of 13 %, and the repeatability of measured frequencies, as well as the linearity of the spectrometers, was better than 1 %.\nWe have three common sources with Pankonin et al. (2001), who observed the same CH 3 CN transition with the SMT, albeit with a different receiver. These three sources are G34.26+0.15, IRAS 23139+5939 and IRAS 23385+6053, the latter two being non-detections by us as well. The results of our line fitting of G34.26+0.15 agree very well with the spectrum of the same source shown in Pankonin et al. (2001).\n3. RESULTS\n3.1. Line Contamination\nAs mentioned above, we obtained spectra of the strong source G34.26+0.15 to study possible line contamination of the CH 3 CN J=12 → 11 transition. In Figure 1 we show the full 1 GHz bandpass for this source. In addition to the K -components of the CH 3 CN J=12 → 11 transition many other molecular lines were detected. We used the JPL Molecular Spectroscopy Catalog (Pickett et al. 1998) in conjunction with the Cologne Database for molecular spectroscopy (CDMS, Muller et al. (2001)) to identify the detected lines.\nIn some cases there was a high level of ambiguity in the identities of the spectral lines. In these cases, molecules that were unambiguously detected elsewhere in the bandpass were preferentially chosen. Lines that we were unable to identify are labeled as 'U' for unknown lines and are numbered according to their order of appearance. Over 60 lines were identified across the full bandpass and we have detections in the CH 3 CN J=12 → 11 transition up to K = 10. The same transitions in the isotopologue CH 13 3 CN were also detected, possibly out to K = 9. In the case of this isotopologue the K = 0 , 1 and 3 components and the K = 7 and higher components are blended with other lines. Absorption features are observed around the 13 CO J= 2 → 1 line; these features are possible artifacts arising from 13 CO emission in the\n\n\n
Figure 1. The above spectrum shows the full bandwidth of the combined AOS-A and B spectrometers for the source G34.26+0.15. The spectral resolution is about 1 MHz. Line identifications are indicated by vertical lines.
\n\noff-beam, and the line identifications in this area of the spectrum are tentative at best.\nFrom inspection of Figure 1, we conclude that the CH 3 CN J=12 → 11 K = 0 - 4 , 7, 8, and 10 suffer no significant contamination but the K = 5, 6 components suffer some blending with lines from other molecular species. The K = 9 component is rendered useless by overlap with the 13 CO(2 -1) line. In the analysis that follows we use the K = 5, 6 components only when we are confident that we can reasonably separate them from the other lines; the K = 9 component we do not use at\nall.\n3.2. CH 3 CN Line Detection and Analysis\nWe detected emission in the CH 3 CN J=12 → 11 transition towards 9 of the 21 sources of the sample (see Table 1). In Figure 2 we show our high resolution spectra at the center position. K -components were detected up to K = 7 for several sources. The upper excitation energy of the K = 7 component is about 420 K (Boucher et al. 1980), thus indicating the presence of hot molecular gas.\nWe have performed simultaneous Gaussian fits for all\n\n\n
Figure 2. Spectra at the central position for the sources with CH 3 CN J=12 → 11 detections. The dashed lines indicate K -components for the main isotopologue. In the spectrum for the source G34.26+0.15 we also indicate the detected K -components of CH 3 13 CN with solid lines. USB emission is affecting the K = 0, 1, 2 lines in G28.87+0.07.
\n\nK -components of the CH 3 CN J=12 → 11 transition. The FWHM of all lines was kept constant at the value measured for the unblended K = 3 component, and the relative position of all lines was fixed at the theoretical values. For the main isotopologue the K = 5 line was fit with 3 Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN.\nThe magnitude of the hyperfine splitting (hfs) of the CH 3 CN molecule reported in Boucher et al. (1980) for the CH 3 CN J=12 → 11 transition is ≤ 0 . 3 MHz. Due to the large FWHM ( ∼ 8 MHz), and the relatively low signal-to-noise detections of the higher K -components,\nwe omitted the hfs in the line fitting. In Table 2 we list the line parameters from the Gaussian fits.\nIn Figure 3 we show the full beam spaced cross scans that we obtained toward five sources. Inspection of the figure shows that the methyl cyanide emission peaks strongly at the central position. Occasionally the lower K -components ( K = 0 -2) were detected away from the center position (IRAS20126+4104, NGC 7538S), indicating that for these sources the warm gas giving rise to the emission is extended on arc-minute scales, but the higher K -components ( K > 3) are always found to be compact with respect to our beam.\nWe used the population diagram technique to derive the rotation temperature and column density for our\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Figure 3. Full beam spaced cross scans towards 5 sources obtained with the SMT 10 m telescope (beam size 36 '' ). The dashed lines below the spectra indicate the position of the K -components of the CH 3 CN J=12 → 11 transition. The telescope beam at FWHM is shown at the bottom left corner.
\nNote . - A Gaussian source with FWHM of ''\ntargets. This analysis assumes optically thin lines and level populations described by a Boltzmann distribution (e.g., Goldsmith & Langer (1999)) and furthermore that all lines trace the same volume of gas. The data are characterized by a linear fit where the negative reciprocal of the slope is T rot and the y -intercept is used to infer the column density (N CH 3 CN ) (see Araya et al. (2005) for a detailed description). When calculating the CH 3 CN column density we adopted a gaussian source size of FWHM of 10 '' .\nFigure 4 shows Boltzmann plots for all detected sources. N JK , g JK and E JK are the column density, statistical weight and upper state energy for the (J,K) state, respectively. The linear fit was made using only the CH 3 CN main isotopologue data. The results of our population diagram analysis are presented in Table 3.\nWith the low signal-to-noise (S/N) ratio of our spectra, detection of the CH 3 13 CN isotopologue would indicate optically thick lines. However, only for G34.26+0.15 we detected the first three K -components of CH 3 13 CN above a 3 σ level. The optical depth of the main line K = 2 (which is less blended) estimated from the ratio of the line intensities is ∼ 8, assuming 12 C/ 13 C= 50. The ratio was calculated based on the abundance variation with galacto-centric distance (Wilson & Rood 1994).\nFor the other targets, no reliable detection of isotopologue lines was made, therefore a detailed analysis correcting for optical depth effects was not feasible. If the assumption of optically thin conditions is incorrect, the derived temperature values are overestimated, and the column density underestimated. However, optical depths effects will not affect our principal result that relatively hot molecular gas is present in our targets.\n3.3. Kinematics\nThe above analysis of the physical parameters assumed uniform conditions in the emitting gas. This is clearly a simplification, as in most cases one would expect gradients in the density and temperature. Allowing for nonuniformity in these parameters is not possible with the present low angular resolution data, however we consider here whether kinematic features can be detected in the\nCH 3 CN lines.\nOur data in principle allow us to check for gradients in line velocity and/or line width. For most of our sources the assumption of central heating, and hence increasing temperature toward the center of the core is reasonable. Thus, any change of line kinematic parameters for the different K -components which have rapidly increasing excitation energies, would imply radial gradients toward the core center.\nTo search for radial gradients we have thus obtained independent fits for each line, where each K -component was fit with a Gaussian function independent of the other components. Therefore, the FWHM, line position, and intensity of the lines are free parameters in the fit. For the main isotopologue the K = 5 line was fit with three Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN and a vibrational line of CH 3 CH 2 OH. The results of these alternative fits are shown in Table 4.\nFigures 5 and 6 show plots of velocity and linewidth as a function of the upper level energy. From Figure 5 there appears to be a trend in velocity for G16.59 -0.05, G34.26+0.15, IRAS 18566+0408, and IRAS 20126+4104. In all cases the putative velocity gradient is towards lower velocity with increasing upper state energy. The situation for the line-widths (Figure 6) is less clear. Weak evidence for increasing line width towards higher energies is present in IRAS 18264 -1152, and G23.01 -0.41, whereas the opposite trend is seen in IRAS 20126+4104. We comment further on these findings in the next section.\n4. DISCUSSION\nWe have used the 10 m SMT to search for CH 3 CN emission toward 21 regions of massive star formation. All of the regions (except for G34.26+0.15) are clearly in an evolutionary phase prior to that of UC or HC HII regions. We detected nine sources in the CH 3 CN J=12 → 11 transition. For six of these sources this is the first detection in this transition. The low detection rate is likely due to the limited sensitivity of a single dish telescope with the relatively small aperture of 10 m.\nOur cross scans for 5 sources show that the K ≤ 3 are occasionally detected outside the central beam, but the higher K -components are always compact with respect to our angular resolution. This is consistent with a warm (T ≤ 50 K), extended envelope which surrounds a much smaller and hotter (T ≥ 50 K) region near the massive star. This finding is consistent with observations of other molecular transitions of lower excitation and critical density (e.g., NH 3 (1,1)) which probe the more extended envelope.\nOur data thus indicate the presence of gradients in temperature and density. Hence, to obtain precise physical parameters interferometric observations are necessary. The single dish beam will receive emission from regions of different physical characteristics, and performing the simple technique of rotation diagram technique corresponds to obtaining average physical properties of the emitting gas. Taking also into account a number of additional uncertainties intrinsic to single dish data analyzed with the rotation diagram method (e.g., Pankonin et al.\n\n\n
Figure 4. The above figure shows Boltzmann plots for the detected sources. No reliable fit could be obtained for G28.87+0.07. A FWHM of 10 '' gaussian source size have been adopted. The error bars are 1 σ .
\n\n(2001)) it is difficult to compare our results with the of Olmi et al. (1993) and Araya et al. (2005). Nonetheless we note that our results for the column densities ( ≈ 10 14 cm -2 ) are quite similar to what was obtained in these studies. However, our derived temperatures appear to be higher compared to the values of Olmi et al. (1993) and Araya et al. (2005). This might be related to the different evolutionary state of the target samples. Olmi et al. (1993) observed many known UCHII regions and the Araya et al. (2005) sample was selected from IRAS colors typical of UCHII regions, whereas our sample should represent a pre-UCHII region evolutionary phase. Higher S/N ratio data, which can put more stringent constraints on the optical depth in the lines will be required to verify\nthis speculation.\nWe conclude that all detected regions contain molecular gas with T > 50 K and methyl cyanide column densities of approximately 10 14 cm -2 . Assuming a strongly enhanced CH 3 CN abundance of 10 -8 the hydrogen column density in these regions on a scale of 10 '' , is then approximately 10 22 cm -2 . These numbers are consistent with the HMC nature of the detected sources.\nIf the core is heated from the center, then lower K -component emission arises predominantly from outer, and hence cooler regions and higher K -components will dominate in the inner, hotter regions. Consequently, velocity gradients in the K -ladder components can trace radial dynamics and possible kinematic scenarios may be either collapse, out-\n\n\n
Figure 5. Plots of central line velocity vs. upper energy level for all K -components which could be fitted independently. Trends of increasing blueshift with increasing energy are evident for four sources. The error bars are 1 σ .
\n\nflows, expansion or rotation (e.g, Cesaroni et al. (1997), Beltr'an et al. (2004)). We have searched our high resolution spectra for evidence of systematic variation in velocity or line-width as a function of excitation energies.\nA small number of kinematic analyses in CH 3 CN has been done but often no conclusive results have been found due to spectral resolution or S/N limitations. For instance, Olmi et al. (1993) did not find any reliable trend in their results. On the other hand, Cesaroni et al. (1999) observed IRAS 20126+4104 using the IRAM Plateau de Bure interferometer. These authors reported an increase in the velocity and line-width toward the center of the core. They suggested that this behavior may be due to rotation of a Keplerian disk sur-\nrounding an embedded massive protostar. Our results for this same region show a decrease in the velocity and the line-width toward the center, contrary to the results obtained by Cesaroni et al. (1999). A possible explanation for this discrepancy is the much larger beam of the SMT which will include more extended gas than the observations of Cesaroni et al. (1999).\nWe detected an increasing blue-shift, i.e., toward lower velocities with higher K -component for four sources. This trend could be explained by expansion or outflow motion as seen in an optically thick line. Another explanation for this behavior could be self absorption of an infalling molecular core which causes a blue asymmetry in an optically thick line. However with the given S/N ratio of our spectra we cannot clearly distinguish these\n\n\n
Figure 6. Plots of line width vs. upper energy level for all K -components which could be fitted independently. The error bars are 1 σ .
\n\nscenarios. A further complication that we can not address is the multiple core scenario. In this case, the cores have some dispersion of radial velocities that may be unresolved in the beam. Therefore, to correctly interpret the detected velocity trends, further observations with higher S/N and angular resolution are needed.\nMost of the HMCs observed in this paper are associated with bright IRAS sources, indicating that a massive object has already heated the surrounding matter. In Figure 7 we show mid-infrared images of six sources for which SPITZER GLIMPSE /IRAC data are available. For five out of these six sources there is evidence for extended 4 . 5 µ m excess emission (e.g., Cyganowski et al. (2008)). The presence of an extended 4 . 5 µ m excess is generally thought to be caused by emission of high ex-\ntation lines from the H 2 molecule, and is hence an indicator of shocked gas. Also, five out of the six sources shown in Figure 7 have strong mid-IR sources, which clearly shows that at least these HMCs have already formed massive stars which cause substantial heating of the molecular cores. One source, G25.83 -0.18, shows only a dark cloud at the suspected position of the massive protostar. This source also harbors one of the few 6 cm H 2 CO masers known (Araya et al. 2008). We note that this source shows quite strong CH 3 CNemission, and since this molecule is thought be effectively formed only with the presence of an energy source, it is likely that a massive protostar is present in this dark cloud also. It is tempting then to speculate that due to the different mid-IR properties G25.83 -0.18 is in an earlier evolution-ar\n\n\n\n\n\n\n\n\n\n\n\n
Figure 7. SPITZER GLIMPSE /IRAC three-color (3.6 µm -blue, 4.5 µm -green and 8.0 µm -red) images toward six of our target sources. The CH 3 CN J=12 → 11 spectra toward these sources are overlaid on the images. The center of each spectrum is placed at the corresponding pointing position, and the size of each spectrum corresponds to the beam size.
\n\ny state compared to the other sources which have very bright mid-IR emission. However, using the extinction curve of Mathis (1990) we find that hydrogen column densities of ≥ 2 × 10 23 cm -2 could render a possible midIR source undetectable. Since hydrogen column densities of this order, and larger, are common in massive star forming cores, it is conceivable that the different mid-IR appearance of G25.83 -0.18 is caused by extinction.\n5. SUMMARY\nWe have observed a sample of 21 massive proto-stellar candidates in the CH 3 CN J=12 → 11 transition using\nthe 10 m SMT. We detected methyl cyanide in nine of the sources of the sample.\nRotation temperatures and column densities were estimated using the population diagram technique. Detected sources have temperatures > 50 K and column densities of ∼ 10 14 cm -2 , hence they are consistent with HMC nature. Higher spectral resolution is needed in order to understand the structure of the kinematics in molecular cores.\nThis project was partially supported by the New Mex-\n\n\n\n\n\n\nico Space Grant Consortium. PH acknowledges partial support from NSF grant AST-0908901. SK acknowledges partial support from UNAM DGAPA grant IN101310. We thank E. Jordan for help with the observations and initial data reduction. We thank the anonymous referee for suggestions which improved this manuscript.\nREFERENCES\nAraya, E., Hofner, P., Goss, W. M., et al. 2006, ApJ, 643, L33 Araya, E., Hofner, P., Kurtz, S., Bronfman, L., & DeDeo, S. 2005, ApJS, 157, 279\n\nAraya, E. D., Hofner, P., Goss, W. M., et al. 2008, ApJS, 178, 330 Beltr'an, M. T., Cesaroni, R., Neri, R., & Codella, C. 2011, A&A, 525, A151\nBeltr'an, M. T., Cesaroni, R., Neri, R., et al. 2004, ApJ, 601, L187 Beuther, H., & Steinacker, J. 2007, ApJ, 656, L85\nBisschop, S. E., Jørgensen, J. K., Bourke, T. L., Bottinelli, S., & van Dishoeck, E. F. 2008, A&A, 488, 959\nBlake, G. A., Sutton, E. C., Masson, C. R., & Phillips, T. G. 1987, ApJ, 315, 621\n\nBonnell, I. A., Vine, S. G., & Bate, M. R. 2004, MNRAS, 349, 735 Boucher, D., Burie, J., Bauer, A., Dubrulle, A., & Demaison, J. 1980, Journal of Physical and Chemical Reference Data, 9, 659 Brunthaler, A., Reid, M. J., Menten, K. M., et al. 2009, ApJ, 693, 424\n\nCesaroni, R., Felli, M., Jenness, T., et al. 1999, A&A, 345, 949 Cesaroni, R., Felli, M., Testi, L., Walmsley, C. M., & Olmi, L. 1997, A&A, 325, 725\nCesaroni, R., Olmi, L., Walmsley, C. M., Churchwell, E., & Hofner, P. 1994, ApJ, 435, L137\nCharnley, S. B., Tielens, A. G. G. M., & Millar, T. J. 1992, ApJ, 399, L71\nChurchwell, E., Walmsley, C. M., & Cesaroni, R. 1990, A&AS, 83, 119\nCodella, C., Testi, L., & Cesaroni, R. 1997, A&A, 325, 282 Codella, C., Benedettini, M., Beltr'an, M. T., et al. 2009, A&A, 507, L25\nCyganowski, C. J., Whitney, B. A., Holden, E., et al. 2008, AJ,\n136, 2391 Furuya, R. S., Cesaroni, R., Takahashi, S., et al. 2008, ApJ, 673, 363 Goldsmith, P. F., & Langer, W. D. 1999, ApJ, 517, 209 Hofner, P., Kurtz, S., Churchwell, E., Walmsley, C. M., & Cesaroni, R. 1996, ApJ, 460, 359 Keto, E. 2007, ApJ, 666, 976 Loren, R. B., & Mundy, L. G. 1984, ApJ, 286, 232 Mathis, J. S. 1990, ARA&A, 28, 37 McKee, C. F., & Tan, J. C. 2003, ApJ, 585, 850 Molinari, S., Testi, L., Rodr'ıguez, L. F., & Zhang, Q. 2002, ApJ, 570, 758 Muller, H. S. P., Thorwirth, S., Roth, D. A., & Winnewisser, G. 2001, A&A, 370, L49 Olmi, L., Cesaroni, R., & Walmsley, C. M. 1993, A&A, 276, 489 Pankonin, V., Churchwell, E., Watson, C., & Bieging, J. H. 2001, ApJ, 558, 194 Pestalozzi, M. R., Minier, V., & Booth, R. S. 2005, A&A, 432, 737 Pickett, H. M., Poynter, R. L., Cohen, E. A., et al. 1998, J. Quant. Spec. Radiat. Transf., 60, 883 Purcell, C. R., Balasubramanyam, R., Burton, M. G., et al. 2006, MNRAS, 367, 553 Sandell, G., & Sievers, A. 2004, ApJ, 600, 269 Sewilo, M., Watson, C., Araya, E., et al. 2004, ApJS, 154, 553 Shepherd, D. S., Yu, K. C., Bally, J., & Testi, L. 2000, ApJ, 535, 833 Sridharan, T. K., Beuther, H., Schilke, P., Menten, K. M., & Wyrowski, F. 2002, ApJ, 566, 931 Su, Y.-N., Zhang, Q., & Lim, J. 2004, ApJ, 604, 258 Thronson, Jr., H. A., & Harper, D. A. 1979, ApJ, 230, 133 Truch, M. D. P., Ade, P. A. R., Bock, J. J., et al. 2008, ApJ, 681, 415 Watt, S., & Mundy, L. G. 1999, ApJS, 125, 143 Werner, M. W., Becklin, E. E., Gatley, I., et al. 1979, MNRAS, 188, 463 Wilson, T. L., & Rood, R. 1994, ARA&A, 32, 191 Zinnecker, H., & Yorke, H. W. 2007, ARA&A, 45, 481\n\n
\n\nd Molecule t -CH 3 CH 2 OH not included in fit.\n\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"We report the results of a survey in the CH 3 CN J=12 → 11 transition toward a sample of massive proto-stellar candidates. The observations were carried out with the 10 m Submillimeter telescope on Mount Graham, AZ. We detected this molecular line in 9 out of 21 observed sources. In six cases this is the first detection of this transition. We also obtained full beam sampled cross-scans for five sources which show that the lower K -components can be extended on the arcminute angular scale. The higher K -components however are always found to be compact with respect to our 36 '' beam. A Boltzmann population diagram analysis of the central spectra indicates CH 3 CN column densities of about 10 14 cm -2 , and rotational temperatures above 50 K, which confirms these sources as hot molecular cores. Independent fits to line velocity and width for the individual K -components resulted in the detection of an increasing blue shift with increasing line excitation for four sources. Comparison with mid-infrared images from the SPITZER GLIMPSE /IRAC archive for six sources show that the CH 3 CN emission is generally coincident with a bright mid-IR source. Our data clearly show that the CH 3 CN J=12 → 11 transition is a good probe of the hot molecular gas near massive protostars, and provide the basis for future interferometric studies. Subject headings: ISM: molecules - stars: formation","pages":[1]},{"title":"METHYL CYANIDE OBSERVATIONS TOWARD MASSIVE PROTOSTARS","content":"V. Rosero 1 , P. Hofner 1 , † , S. Kurtz 2 , J. Bieging 3 & E. D. Araya 4 1 Physics Department, New Mexico Tech, 801 Leroy Pl., Socorro, NM 87801, USA 2 Centro de Radioastronom'ıa y Astrof'ısica, Universidad Nacional Aut'onoma de M'exico, Morelia 58090, M'exico 3 Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA and 4 Physics Department, Western Illinois University, 1 University Circle, Macomb, IL 61455, USA To appear in The Astrophysical Journal Supplement Series.","pages":[1]},{"title":"1. INTRODUCTION","content":"Despite the central role of massive stars in almost all areas of astronomy, the physical processes involved in the formation of stars with masses > 8 M /circledot are at present poorly understood (e.g., Zinnecker & Yorke (2007)). Theoretical and observational studies favor the idea that massive stars, similar to their lower mass counterparts, form from a collapsing cloud core. However, whether the subsequent formation of a protostar and further mass accretion occurs from an isolated massive molecular core (e.g., McKee & Tan (2003), Keto (2007)), or under the influence of a cluster environment (e.g., Bonnell et al. (2004)) remains a persistent question. One of the earliest observational manifestations of massive proto-stars are so-called hot molecular cores (hereafter HMCs). Named after the prototype object in the Orion KL region, they have been surveyed throughout the Galaxy in an effort to identify candidates for massive proto-stars (e.g., Sridharan et al. (2002)). Common search criteria were high FIR luminosity, high molecular column densities and temperature, and the absence of strong radio continuum emission - the latter to ensure an earlier evolutionary phase than ultra-compact (UC) or hyper-compact (HC) HII regions. A particularly useful tracer of HMCs is the methyl cyanide (CH 3 CN) molecule. Due to the centrifugal deformation of this symmetric top molecule, its rotational spectrum consists of a series of closely spaced K -components tracing rapidly increasing excitation energies. The K -ladders are connected only through collisions so that excitation temperatures can in principle be measured from the ratios of K -components, thus avoiding the usual calibration uncertainties that occur when comparing rotational transitions observed in different frequency bands. An extensive discussion of the microwave spectroscopy of methyl cyanide is given in Boucher et al. (1980). Because of these spectroscopic properties, the CH 3 CNmolecule is frequently used to determine temperatures in the dense molecular cores where massive stars form, using both statistical equilibrium calculations (e.g., Loren & Mundy (1984)), or the simpler rotation diagram technique (e.g., Goldsmith & Langer (1999)). Another factor that favors the use of CH 3 CN as a tracer of HMCs is its enhanced abundance in warm (T= 100 -300 K), dense ( n H 2 = 10 6 -10 8 cm -3 ) environments (e.g., Blake et al. (1987)). This is generally thought to be caused by grain surface chemistry, either by primary reactions on the grain surface with subsequent release into the gas phase when the grain mantle evaporates, or, alternatively, by secondary reactions in the gas phase (e.g., Charnley et al. (1992), Bisschop et al. (2008)). Recently, Codella et al. (2009) reported detection of CH 3 CN in the outflow lobes of the low-mass protostar L1157-B1, and attributed the enhanced CH 3 CN abundance to shock chemistry. From these studies it is well-established that CH 3 CN traces an energetic environment similar to that expected in the immediate vicinity of massive proto-stars. To investigate the HMC phase of massive star formation, several single dish CH 3 CN surveys have been made (e.g., Olmi et al. (1993), Araya et al. (2005), Pankonin et al. (2001)), and a small number of sources have also been studied with mm-interferometers (e.g., Cesaroni et al. (1994), Hofner et al. (1996), Furuya et al. (2008)). Several of the interferometric studies resulted in images of CH 3 CN structures that are elongated perpendicular to the direction of molecular outflows, with velocity gradients along the elongated structures; this is usually explained as rotational motion of a circum- Note . -Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. References. (1) Sridharan et al. (2002); (2) Codella et al. (1997); (3) Beuther & Steinacker (2007); (4) Brunthaler et al. (2009); (5) Araya et al. (2008); (6) Pestalozzi et al. (2005); (7) Sewilo et al. (2004); (8) Araya et al. (2006); (9) Purcell et al. (2006); (10) Churchwell et al. (1990); (11) Watt & Mundy (1999); (12) Shepherd et al. (2000); (13) Truch et al. (2008); (14) Molinari et al. (2002); (15) Su et al. (2004); (16) Werner et al. (1979); (17) Sandell & Sievers (2004); (18) Thronson & Harper (1979) stellar disk or torus (e.g., Beltr'an et al. (2011)). The CH 3 CN molecule is thus a good choice to trace accretion disks around massive proto-stars, whose existence (if confirmed), and properties will be important input for current models of massive star formation. From the above discussion it is clear that observations of CH 3 CN with high sensitivity and angular resolution are well-suited to study accretion disks around massive stars. Such observations have recently become more accessible using instruments such as the Submillimeter Array (SMA) and ALMA. To facilitate such observations in the CH 3 CN J=12 → 11 line, the present study adds to the existing database of single dish studies of methyl cyanide. In Section 2 we describe the observations and data reduction, and we present the observational results in Section 3. We conclude in Section 4 with a discussion of these observational results.","pages":[1,2]},{"title":"2. OBSERVATIONS AND DATA REDUCTION","content":"We observed 21 sources in 2008 from May 26 to 31 in the 1.3 mm CH 3 CN J=12 → 11 transition with the 10 m Heinrich Hertz Submillimeter Telescope (SMT) 2 on Mt. Graham, AZ. The telescope beam width at 1 . 3 mm is approximately 36 '' , and the pointing accuracy during our observing run was better than 7 '' . The pointing positions and LSR velocities for the observed sources are given in Table 1. Most of our target sources are prominent HMC candidates with large IRAS luminosities. They all show the typical observational indicators of massive star formation in the HMC stage, namely massive molecular cores, H 2 O and CH 3 OH maser emission, warm molecular gas, weak (or absent) radio continuum emission, and the presence of jets and molecular flows. An exception is IRDC 18223-3, which is a massive infrared dark cloud with an embedded protostar, which may be in an earlier evolutionary state (Beuther & Steinacker 2007). The observations were conducted in double sideband mode using the 1.3 mm J-T ALMA sideband separating receiver 3 , which simultaneously recorded two linear orthogonal polarizations. The CH 3 CN J=12 → 11 K = 5 transition ( ν 0 = 220 . 641089 GHz, Boucher et al. 1980) was tuned to the center of the lower sideband. We used all six available backends; four low spectral resolution and two high spectral resolution. The low spectral resolution backends were the acoustic-optic spectrometers (AOSs) AOS-A and AOS-B with bandwidths and spectral resolutions of 975 MHz (1325 km s -1 ) and 953 kHz (1 . 3 kms -1 ), and two filterbanks which have bandwidths and spectral resolutions of 1.024 GHz (1392 km s -1 ) and 1 MHz (1 . 4 kms -1 ), respectively. Most of the data used for the analysis in this paper were taken with the AOSC and the Chirp Transform Spectrometers (CTS-A), which have bandwidths and channel widths of 250 . 5 MHz (340 km s -1 ) and 122kHz (0 . 17 kms -1 ) and 215MHz (292 km s -1 ) and 29 kHz (0 . 04 kms -1 ), respectively. The AOS-C bandwidth does not cover all K -components of the CH 3 CN J=12 → 11 transition, hence we centered this backend on the K = 5 component. This setup allowed us to observe the K = 0 -7 components simultaneously. The AOS-A and AOS-B and the filterbanks offer bandwidths between 950 and 1000 MHz so in principle the higher K -components could be detected. In practice, however, the lower line strengths of the higher components prevented us from detecting them in all but the strongest source, G34.26+0.15. Furthermore, the 13 CO J=2 → 1 transition blends with the K = 9 component of the CH 3 CN J=12 → 11 transition, thus limiting the usefulness of this K -component. The 12 CO J=2 → 1 transition located in the upper sideband (USB) contaminated the lower sideband data approximately 50 MHz away from the CH 3 CN J=12 → 11 K = 0 line. With the exception of G28.87+0.07, this contamination had little effect on the quality of our data. The USB rejection was approximately 17 dB over the course of our observations. Given the relatively weak appearance of the 12 CO J=2 → 1 line (normally a very strong line) in our spectra, we do not believe that there is significant contamination from other spectral lines located in the USB. Our observations were conducted using double beam switching with a switch rate of 2 Hz and a beamthrow of 2 ' with a total on/off cycle of approximately 6 minutes per scan. System temperatures ranged from 350 K to just under 200K with an average temperature of 212K. Focus corrections were obtained from observations of Jupiter. Whenever possible we also derived pointing corrections from cross scans of Jupiter. When Jupiter was not available or was located at a large angular distance from the target source, pointing corrections were made by observing asymptotic giant branch stars in the CO J = 2 → 1 transition falling in the USB. In the case of IRAS 20126+4104 we could line point using the 13 CO J=1 → 0 emission from the source. At the beginning of each night of observations, we observed the strong source G34.26+0.15 for at least one scan to check for day-to-day consistency of our observations and to obtain a template source to identify contaminating spectral lines. Subsequently, all sources were observed for 12-18 minutes to determine the intensity of the K -components of the CH 3 CN J=12 → 11 transition. Promising sources were then re-observed for at least 2 hr. Additionally, we obtained full beam spaced cross scans for five sources, typically with 1 . 5 hr spent at each offset position. The data were reduced in CLASS, which is part of the GILDAS 4 software package. All spectra were first inspected to check for bad channels or any obvious artifacts; bad scans were discarded. Subsequently, we subtracted baselines using low order polynomials, and initially averaged the spectra for each spectrometer and each day separately. After further inspection, all data taken on different days were averaged to form a final data set for each source. After Hanning smoothing and resampling to the same spectral resolution, we averaged the AOS-C and CTS-A spectrometer data. We will refer to the latter data set as 'high resolution' spectra. The data were calibrated using the chopper-wheel method and the antenna temperature was converted to mainbeam brightness temperature by dividing the antenna temperature by the main-beam efficiency of the telescope ( η b = 0 . 74) 5 . Using the daily spectra of the strong source G34.26+0.15, we checked our data for amplitude stability, which maximum deviation from the average was found to be smaller than 16 %. Measured line widths had maximum deviations of 13 %, and the repeatability of measured frequencies, as well as the linearity of the spectrometers, was better than 1 %. We have three common sources with Pankonin et al. (2001), who observed the same CH 3 CN transition with the SMT, albeit with a different receiver. These three sources are G34.26+0.15, IRAS 23139+5939 and IRAS 23385+6053, the latter two being non-detections by us as well. The results of our line fitting of G34.26+0.15 agree very well with the spectrum of the same source shown in Pankonin et al. (2001).","pages":[2,3]},{"title":"3.1. Line Contamination","content":"As mentioned above, we obtained spectra of the strong source G34.26+0.15 to study possible line contamination of the CH 3 CN J=12 → 11 transition. In Figure 1 we show the full 1 GHz bandpass for this source. In addition to the K -components of the CH 3 CN J=12 → 11 transition many other molecular lines were detected. We used the JPL Molecular Spectroscopy Catalog (Pickett et al. 1998) in conjunction with the Cologne Database for molecular spectroscopy (CDMS, Muller et al. (2001)) to identify the detected lines. In some cases there was a high level of ambiguity in the identities of the spectral lines. In these cases, molecules that were unambiguously detected elsewhere in the bandpass were preferentially chosen. Lines that we were unable to identify are labeled as 'U' for unknown lines and are numbered according to their order of appearance. Over 60 lines were identified across the full bandpass and we have detections in the CH 3 CN J=12 → 11 transition up to K = 10. The same transitions in the isotopologue CH 13 3 CN were also detected, possibly out to K = 9. In the case of this isotopologue the K = 0 , 1 and 3 components and the K = 7 and higher components are blended with other lines. Absorption features are observed around the 13 CO J= 2 → 1 line; these features are possible artifacts arising from 13 CO emission in the off-beam, and the line identifications in this area of the spectrum are tentative at best. From inspection of Figure 1, we conclude that the CH 3 CN J=12 → 11 K = 0 - 4 , 7, 8, and 10 suffer no significant contamination but the K = 5, 6 components suffer some blending with lines from other molecular species. The K = 9 component is rendered useless by overlap with the 13 CO(2 -1) line. In the analysis that follows we use the K = 5, 6 components only when we are confident that we can reasonably separate them from the other lines; the K = 9 component we do not use at all.","pages":[3,4]},{"title":"3.2. CH 3 CN Line Detection and Analysis","content":"We detected emission in the CH 3 CN J=12 → 11 transition towards 9 of the 21 sources of the sample (see Table 1). In Figure 2 we show our high resolution spectra at the center position. K -components were detected up to K = 7 for several sources. The upper excitation energy of the K = 7 component is about 420 K (Boucher et al. 1980), thus indicating the presence of hot molecular gas. We have performed simultaneous Gaussian fits for all K -components of the CH 3 CN J=12 → 11 transition. The FWHM of all lines was kept constant at the value measured for the unblended K = 3 component, and the relative position of all lines was fixed at the theoretical values. For the main isotopologue the K = 5 line was fit with 3 Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN. The magnitude of the hyperfine splitting (hfs) of the CH 3 CN molecule reported in Boucher et al. (1980) for the CH 3 CN J=12 → 11 transition is ≤ 0 . 3 MHz. Due to the large FWHM ( ∼ 8 MHz), and the relatively low signal-to-noise detections of the higher K -components, we omitted the hfs in the line fitting. In Table 2 we list the line parameters from the Gaussian fits. In Figure 3 we show the full beam spaced cross scans that we obtained toward five sources. Inspection of the figure shows that the methyl cyanide emission peaks strongly at the central position. Occasionally the lower K -components ( K = 0 -2) were detected away from the center position (IRAS20126+4104, NGC 7538S), indicating that for these sources the warm gas giving rise to the emission is extended on arc-minute scales, but the higher K -components ( K > 3) are always found to be compact with respect to our beam. We used the population diagram technique to derive the rotation temperature and column density for our Note . - A Gaussian source with FWHM of '' targets. This analysis assumes optically thin lines and level populations described by a Boltzmann distribution (e.g., Goldsmith & Langer (1999)) and furthermore that all lines trace the same volume of gas. The data are characterized by a linear fit where the negative reciprocal of the slope is T rot and the y -intercept is used to infer the column density (N CH 3 CN ) (see Araya et al. (2005) for a detailed description). When calculating the CH 3 CN column density we adopted a gaussian source size of FWHM of 10 '' . Figure 4 shows Boltzmann plots for all detected sources. N JK , g JK and E JK are the column density, statistical weight and upper state energy for the (J,K) state, respectively. The linear fit was made using only the CH 3 CN main isotopologue data. The results of our population diagram analysis are presented in Table 3. With the low signal-to-noise (S/N) ratio of our spectra, detection of the CH 3 13 CN isotopologue would indicate optically thick lines. However, only for G34.26+0.15 we detected the first three K -components of CH 3 13 CN above a 3 σ level. The optical depth of the main line K = 2 (which is less blended) estimated from the ratio of the line intensities is ∼ 8, assuming 12 C/ 13 C= 50. The ratio was calculated based on the abundance variation with galacto-centric distance (Wilson & Rood 1994). For the other targets, no reliable detection of isotopologue lines was made, therefore a detailed analysis correcting for optical depth effects was not feasible. If the assumption of optically thin conditions is incorrect, the derived temperature values are overestimated, and the column density underestimated. However, optical depths effects will not affect our principal result that relatively hot molecular gas is present in our targets.","pages":[4,5,7]},{"title":"3.3. Kinematics","content":"The above analysis of the physical parameters assumed uniform conditions in the emitting gas. This is clearly a simplification, as in most cases one would expect gradients in the density and temperature. Allowing for nonuniformity in these parameters is not possible with the present low angular resolution data, however we consider here whether kinematic features can be detected in the CH 3 CN lines. Our data in principle allow us to check for gradients in line velocity and/or line width. For most of our sources the assumption of central heating, and hence increasing temperature toward the center of the core is reasonable. Thus, any change of line kinematic parameters for the different K -components which have rapidly increasing excitation energies, would imply radial gradients toward the core center. To search for radial gradients we have thus obtained independent fits for each line, where each K -component was fit with a Gaussian function independent of the other components. Therefore, the FWHM, line position, and intensity of the lines are free parameters in the fit. For the main isotopologue the K = 5 line was fit with three Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN and a vibrational line of CH 3 CH 2 OH. The results of these alternative fits are shown in Table 4. Figures 5 and 6 show plots of velocity and linewidth as a function of the upper level energy. From Figure 5 there appears to be a trend in velocity for G16.59 -0.05, G34.26+0.15, IRAS 18566+0408, and IRAS 20126+4104. In all cases the putative velocity gradient is towards lower velocity with increasing upper state energy. The situation for the line-widths (Figure 6) is less clear. Weak evidence for increasing line width towards higher energies is present in IRAS 18264 -1152, and G23.01 -0.41, whereas the opposite trend is seen in IRAS 20126+4104. We comment further on these findings in the next section.","pages":[7]},{"title":"4. DISCUSSION","content":"We have used the 10 m SMT to search for CH 3 CN emission toward 21 regions of massive star formation. All of the regions (except for G34.26+0.15) are clearly in an evolutionary phase prior to that of UC or HC HII regions. We detected nine sources in the CH 3 CN J=12 → 11 transition. For six of these sources this is the first detection in this transition. The low detection rate is likely due to the limited sensitivity of a single dish telescope with the relatively small aperture of 10 m. Our cross scans for 5 sources show that the K ≤ 3 are occasionally detected outside the central beam, but the higher K -components are always compact with respect to our angular resolution. This is consistent with a warm (T ≤ 50 K), extended envelope which surrounds a much smaller and hotter (T ≥ 50 K) region near the massive star. This finding is consistent with observations of other molecular transitions of lower excitation and critical density (e.g., NH 3 (1,1)) which probe the more extended envelope. Our data thus indicate the presence of gradients in temperature and density. Hence, to obtain precise physical parameters interferometric observations are necessary. The single dish beam will receive emission from regions of different physical characteristics, and performing the simple technique of rotation diagram technique corresponds to obtaining average physical properties of the emitting gas. Taking also into account a number of additional uncertainties intrinsic to single dish data analyzed with the rotation diagram method (e.g., Pankonin et al. (2001)) it is difficult to compare our results with the of Olmi et al. (1993) and Araya et al. (2005). Nonetheless we note that our results for the column densities ( ≈ 10 14 cm -2 ) are quite similar to what was obtained in these studies. However, our derived temperatures appear to be higher compared to the values of Olmi et al. (1993) and Araya et al. (2005). This might be related to the different evolutionary state of the target samples. Olmi et al. (1993) observed many known UCHII regions and the Araya et al. (2005) sample was selected from IRAS colors typical of UCHII regions, whereas our sample should represent a pre-UCHII region evolutionary phase. Higher S/N ratio data, which can put more stringent constraints on the optical depth in the lines will be required to verify this speculation. We conclude that all detected regions contain molecular gas with T > 50 K and methyl cyanide column densities of approximately 10 14 cm -2 . Assuming a strongly enhanced CH 3 CN abundance of 10 -8 the hydrogen column density in these regions on a scale of 10 '' , is then approximately 10 22 cm -2 . These numbers are consistent with the HMC nature of the detected sources. If the core is heated from the center, then lower K -component emission arises predominantly from outer, and hence cooler regions and higher K -components will dominate in the inner, hotter regions. Consequently, velocity gradients in the K -ladder components can trace radial dynamics and possible kinematic scenarios may be either collapse, out- flows, expansion or rotation (e.g, Cesaroni et al. (1997), Beltr'an et al. (2004)). We have searched our high resolution spectra for evidence of systematic variation in velocity or line-width as a function of excitation energies. A small number of kinematic analyses in CH 3 CN has been done but often no conclusive results have been found due to spectral resolution or S/N limitations. For instance, Olmi et al. (1993) did not find any reliable trend in their results. On the other hand, Cesaroni et al. (1999) observed IRAS 20126+4104 using the IRAM Plateau de Bure interferometer. These authors reported an increase in the velocity and line-width toward the center of the core. They suggested that this behavior may be due to rotation of a Keplerian disk sur- rounding an embedded massive protostar. Our results for this same region show a decrease in the velocity and the line-width toward the center, contrary to the results obtained by Cesaroni et al. (1999). A possible explanation for this discrepancy is the much larger beam of the SMT which will include more extended gas than the observations of Cesaroni et al. (1999). We detected an increasing blue-shift, i.e., toward lower velocities with higher K -component for four sources. This trend could be explained by expansion or outflow motion as seen in an optically thick line. Another explanation for this behavior could be self absorption of an infalling molecular core which causes a blue asymmetry in an optically thick line. However with the given S/N ratio of our spectra we cannot clearly distinguish these scenarios. A further complication that we can not address is the multiple core scenario. In this case, the cores have some dispersion of radial velocities that may be unresolved in the beam. Therefore, to correctly interpret the detected velocity trends, further observations with higher S/N and angular resolution are needed. Most of the HMCs observed in this paper are associated with bright IRAS sources, indicating that a massive object has already heated the surrounding matter. In Figure 7 we show mid-infrared images of six sources for which SPITZER GLIMPSE /IRAC data are available. For five out of these six sources there is evidence for extended 4 . 5 µ m excess emission (e.g., Cyganowski et al. (2008)). The presence of an extended 4 . 5 µ m excess is generally thought to be caused by emission of high ex- tation lines from the H 2 molecule, and is hence an indicator of shocked gas. Also, five out of the six sources shown in Figure 7 have strong mid-IR sources, which clearly shows that at least these HMCs have already formed massive stars which cause substantial heating of the molecular cores. One source, G25.83 -0.18, shows only a dark cloud at the suspected position of the massive protostar. This source also harbors one of the few 6 cm H 2 CO masers known (Araya et al. 2008). We note that this source shows quite strong CH 3 CNemission, and since this molecule is thought be effectively formed only with the presence of an energy source, it is likely that a massive protostar is present in this dark cloud also. It is tempting then to speculate that due to the different mid-IR properties G25.83 -0.18 is in an earlier evolution-ar y state compared to the other sources which have very bright mid-IR emission. However, using the extinction curve of Mathis (1990) we find that hydrogen column densities of ≥ 2 × 10 23 cm -2 could render a possible midIR source undetectable. Since hydrogen column densities of this order, and larger, are common in massive star forming cores, it is conceivable that the different mid-IR appearance of G25.83 -0.18 is caused by extinction.","pages":[7,8,9,10,11]},{"title":"5. SUMMARY","content":"We have observed a sample of 21 massive proto-stellar candidates in the CH 3 CN J=12 → 11 transition using the 10 m SMT. We detected methyl cyanide in nine of the sources of the sample. Rotation temperatures and column densities were estimated using the population diagram technique. Detected sources have temperatures > 50 K and column densities of ∼ 10 14 cm -2 , hence they are consistent with HMC nature. Higher spectral resolution is needed in order to understand the structure of the kinematics in molecular cores. This project was partially supported by the New Mex- ico Space Grant Consortium. PH acknowledges partial support from NSF grant AST-0908901. SK acknowledges partial support from UNAM DGAPA grant IN101310. We thank E. Jordan for help with the observations and initial data reduction. We thank the anonymous referee for suggestions which improved this manuscript.","pages":[11,12]},{"title":"REFERENCES","content":"Araya, E., Hofner, P., Goss, W. M., et al. 2006, ApJ, 643, L33 Araya, E., Hofner, P., Kurtz, S., Bronfman, L., & DeDeo, S. 2005, ApJS, 157, 279 Bonnell, I. A., Vine, S. G., & Bate, M. R. 2004, MNRAS, 349, 735 Boucher, D., Burie, J., Bauer, A., Dubrulle, A., & Demaison, J. 1980, Journal of Physical and Chemical Reference Data, 9, 659 Brunthaler, A., Reid, M. J., Menten, K. M., et al. 2009, ApJ, 693, 424","pages":[12]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"We report the results of a survey in the CH 3 CN J=12 → 11 transition toward a sample of massive proto-stellar candidates. The observations were carried out with the 10 m Submillimeter telescope on Mount Graham, AZ. We detected this molecular line in 9 out of 21 observed sources. In six cases this is the first detection of this transition. We also obtained full beam sampled cross-scans for five sources which show that the lower K -components can be extended on the arcminute angular scale. The higher K -components however are always found to be compact with respect to our 36 '' beam. A Boltzmann population diagram analysis of the central spectra indicates CH 3 CN column densities of about 10 14 cm -2 , and rotational temperatures above 50 K, which confirms these sources as hot molecular cores. Independent fits to line velocity and width for the individual K -components resulted in the detection of an increasing blue shift with increasing line excitation for four sources. Comparison with mid-infrared images from the SPITZER GLIMPSE /IRAC archive for six sources show that the CH 3 CN emission is generally coincident with a bright mid-IR source. Our data clearly show that the CH 3 CN J=12 → 11 transition is a good probe of the hot molecular gas near massive protostars, and provide the basis for future interferometric studies. Subject headings: ISM: molecules - stars: formation\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"METHYL CYANIDE OBSERVATIONS TOWARD MASSIVE PROTOSTARS\",\n \"content\": \"V. Rosero 1 , P. Hofner 1 , † , S. Kurtz 2 , J. Bieging 3 & E. D. Araya 4 1 Physics Department, New Mexico Tech, 801 Leroy Pl., Socorro, NM 87801, USA 2 Centro de Radioastronom'ıa y Astrof'ısica, Universidad Nacional Aut'onoma de M'exico, Morelia 58090, M'exico 3 Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA and 4 Physics Department, Western Illinois University, 1 University Circle, Macomb, IL 61455, USA To appear in The Astrophysical Journal Supplement Series.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"Despite the central role of massive stars in almost all areas of astronomy, the physical processes involved in the formation of stars with masses > 8 M /circledot are at present poorly understood (e.g., Zinnecker & Yorke (2007)). Theoretical and observational studies favor the idea that massive stars, similar to their lower mass counterparts, form from a collapsing cloud core. However, whether the subsequent formation of a protostar and further mass accretion occurs from an isolated massive molecular core (e.g., McKee & Tan (2003), Keto (2007)), or under the influence of a cluster environment (e.g., Bonnell et al. (2004)) remains a persistent question. One of the earliest observational manifestations of massive proto-stars are so-called hot molecular cores (hereafter HMCs). Named after the prototype object in the Orion KL region, they have been surveyed throughout the Galaxy in an effort to identify candidates for massive proto-stars (e.g., Sridharan et al. (2002)). Common search criteria were high FIR luminosity, high molecular column densities and temperature, and the absence of strong radio continuum emission - the latter to ensure an earlier evolutionary phase than ultra-compact (UC) or hyper-compact (HC) HII regions. A particularly useful tracer of HMCs is the methyl cyanide (CH 3 CN) molecule. Due to the centrifugal deformation of this symmetric top molecule, its rotational spectrum consists of a series of closely spaced K -components tracing rapidly increasing excitation energies. The K -ladders are connected only through collisions so that excitation temperatures can in principle be measured from the ratios of K -components, thus avoiding the usual calibration uncertainties that occur when comparing rotational transitions observed in different frequency bands. An extensive discussion of the microwave spectroscopy of methyl cyanide is given in Boucher et al. (1980). Because of these spectroscopic properties, the CH 3 CNmolecule is frequently used to determine temperatures in the dense molecular cores where massive stars form, using both statistical equilibrium calculations (e.g., Loren & Mundy (1984)), or the simpler rotation diagram technique (e.g., Goldsmith & Langer (1999)). Another factor that favors the use of CH 3 CN as a tracer of HMCs is its enhanced abundance in warm (T= 100 -300 K), dense ( n H 2 = 10 6 -10 8 cm -3 ) environments (e.g., Blake et al. (1987)). This is generally thought to be caused by grain surface chemistry, either by primary reactions on the grain surface with subsequent release into the gas phase when the grain mantle evaporates, or, alternatively, by secondary reactions in the gas phase (e.g., Charnley et al. (1992), Bisschop et al. (2008)). Recently, Codella et al. (2009) reported detection of CH 3 CN in the outflow lobes of the low-mass protostar L1157-B1, and attributed the enhanced CH 3 CN abundance to shock chemistry. From these studies it is well-established that CH 3 CN traces an energetic environment similar to that expected in the immediate vicinity of massive proto-stars. To investigate the HMC phase of massive star formation, several single dish CH 3 CN surveys have been made (e.g., Olmi et al. (1993), Araya et al. (2005), Pankonin et al. (2001)), and a small number of sources have also been studied with mm-interferometers (e.g., Cesaroni et al. (1994), Hofner et al. (1996), Furuya et al. (2008)). Several of the interferometric studies resulted in images of CH 3 CN structures that are elongated perpendicular to the direction of molecular outflows, with velocity gradients along the elongated structures; this is usually explained as rotational motion of a circum- Note . -Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. References. (1) Sridharan et al. (2002); (2) Codella et al. (1997); (3) Beuther & Steinacker (2007); (4) Brunthaler et al. (2009); (5) Araya et al. (2008); (6) Pestalozzi et al. (2005); (7) Sewilo et al. (2004); (8) Araya et al. (2006); (9) Purcell et al. (2006); (10) Churchwell et al. (1990); (11) Watt & Mundy (1999); (12) Shepherd et al. (2000); (13) Truch et al. (2008); (14) Molinari et al. (2002); (15) Su et al. (2004); (16) Werner et al. (1979); (17) Sandell & Sievers (2004); (18) Thronson & Harper (1979) stellar disk or torus (e.g., Beltr'an et al. (2011)). The CH 3 CN molecule is thus a good choice to trace accretion disks around massive proto-stars, whose existence (if confirmed), and properties will be important input for current models of massive star formation. From the above discussion it is clear that observations of CH 3 CN with high sensitivity and angular resolution are well-suited to study accretion disks around massive stars. Such observations have recently become more accessible using instruments such as the Submillimeter Array (SMA) and ALMA. To facilitate such observations in the CH 3 CN J=12 → 11 line, the present study adds to the existing database of single dish studies of methyl cyanide. In Section 2 we describe the observations and data reduction, and we present the observational results in Section 3. We conclude in Section 4 with a discussion of these observational results.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2. OBSERVATIONS AND DATA REDUCTION\",\n \"content\": \"We observed 21 sources in 2008 from May 26 to 31 in the 1.3 mm CH 3 CN J=12 → 11 transition with the 10 m Heinrich Hertz Submillimeter Telescope (SMT) 2 on Mt. Graham, AZ. The telescope beam width at 1 . 3 mm is approximately 36 '' , and the pointing accuracy during our observing run was better than 7 '' . The pointing positions and LSR velocities for the observed sources are given in Table 1. Most of our target sources are prominent HMC candidates with large IRAS luminosities. They all show the typical observational indicators of massive star formation in the HMC stage, namely massive molecular cores, H 2 O and CH 3 OH maser emission, warm molecular gas, weak (or absent) radio continuum emission, and the presence of jets and molecular flows. An exception is IRDC 18223-3, which is a massive infrared dark cloud with an embedded protostar, which may be in an earlier evolutionary state (Beuther & Steinacker 2007). The observations were conducted in double sideband mode using the 1.3 mm J-T ALMA sideband separating receiver 3 , which simultaneously recorded two linear orthogonal polarizations. The CH 3 CN J=12 → 11 K = 5 transition ( ν 0 = 220 . 641089 GHz, Boucher et al. 1980) was tuned to the center of the lower sideband. We used all six available backends; four low spectral resolution and two high spectral resolution. The low spectral resolution backends were the acoustic-optic spectrometers (AOSs) AOS-A and AOS-B with bandwidths and spectral resolutions of 975 MHz (1325 km s -1 ) and 953 kHz (1 . 3 kms -1 ), and two filterbanks which have bandwidths and spectral resolutions of 1.024 GHz (1392 km s -1 ) and 1 MHz (1 . 4 kms -1 ), respectively. Most of the data used for the analysis in this paper were taken with the AOSC and the Chirp Transform Spectrometers (CTS-A), which have bandwidths and channel widths of 250 . 5 MHz (340 km s -1 ) and 122kHz (0 . 17 kms -1 ) and 215MHz (292 km s -1 ) and 29 kHz (0 . 04 kms -1 ), respectively. The AOS-C bandwidth does not cover all K -components of the CH 3 CN J=12 → 11 transition, hence we centered this backend on the K = 5 component. This setup allowed us to observe the K = 0 -7 components simultaneously. The AOS-A and AOS-B and the filterbanks offer bandwidths between 950 and 1000 MHz so in principle the higher K -components could be detected. In practice, however, the lower line strengths of the higher components prevented us from detecting them in all but the strongest source, G34.26+0.15. Furthermore, the 13 CO J=2 → 1 transition blends with the K = 9 component of the CH 3 CN J=12 → 11 transition, thus limiting the usefulness of this K -component. The 12 CO J=2 → 1 transition located in the upper sideband (USB) contaminated the lower sideband data approximately 50 MHz away from the CH 3 CN J=12 → 11 K = 0 line. With the exception of G28.87+0.07, this contamination had little effect on the quality of our data. The USB rejection was approximately 17 dB over the course of our observations. Given the relatively weak appearance of the 12 CO J=2 → 1 line (normally a very strong line) in our spectra, we do not believe that there is significant contamination from other spectral lines located in the USB. Our observations were conducted using double beam switching with a switch rate of 2 Hz and a beamthrow of 2 ' with a total on/off cycle of approximately 6 minutes per scan. System temperatures ranged from 350 K to just under 200K with an average temperature of 212K. Focus corrections were obtained from observations of Jupiter. Whenever possible we also derived pointing corrections from cross scans of Jupiter. When Jupiter was not available or was located at a large angular distance from the target source, pointing corrections were made by observing asymptotic giant branch stars in the CO J = 2 → 1 transition falling in the USB. In the case of IRAS 20126+4104 we could line point using the 13 CO J=1 → 0 emission from the source. At the beginning of each night of observations, we observed the strong source G34.26+0.15 for at least one scan to check for day-to-day consistency of our observations and to obtain a template source to identify contaminating spectral lines. Subsequently, all sources were observed for 12-18 minutes to determine the intensity of the K -components of the CH 3 CN J=12 → 11 transition. Promising sources were then re-observed for at least 2 hr. Additionally, we obtained full beam spaced cross scans for five sources, typically with 1 . 5 hr spent at each offset position. The data were reduced in CLASS, which is part of the GILDAS 4 software package. All spectra were first inspected to check for bad channels or any obvious artifacts; bad scans were discarded. Subsequently, we subtracted baselines using low order polynomials, and initially averaged the spectra for each spectrometer and each day separately. After further inspection, all data taken on different days were averaged to form a final data set for each source. After Hanning smoothing and resampling to the same spectral resolution, we averaged the AOS-C and CTS-A spectrometer data. We will refer to the latter data set as 'high resolution' spectra. The data were calibrated using the chopper-wheel method and the antenna temperature was converted to mainbeam brightness temperature by dividing the antenna temperature by the main-beam efficiency of the telescope ( η b = 0 . 74) 5 . Using the daily spectra of the strong source G34.26+0.15, we checked our data for amplitude stability, which maximum deviation from the average was found to be smaller than 16 %. Measured line widths had maximum deviations of 13 %, and the repeatability of measured frequencies, as well as the linearity of the spectrometers, was better than 1 %. We have three common sources with Pankonin et al. (2001), who observed the same CH 3 CN transition with the SMT, albeit with a different receiver. These three sources are G34.26+0.15, IRAS 23139+5939 and IRAS 23385+6053, the latter two being non-detections by us as well. The results of our line fitting of G34.26+0.15 agree very well with the spectrum of the same source shown in Pankonin et al. (2001).\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"3.1. Line Contamination\",\n \"content\": \"As mentioned above, we obtained spectra of the strong source G34.26+0.15 to study possible line contamination of the CH 3 CN J=12 → 11 transition. In Figure 1 we show the full 1 GHz bandpass for this source. In addition to the K -components of the CH 3 CN J=12 → 11 transition many other molecular lines were detected. We used the JPL Molecular Spectroscopy Catalog (Pickett et al. 1998) in conjunction with the Cologne Database for molecular spectroscopy (CDMS, Muller et al. (2001)) to identify the detected lines. In some cases there was a high level of ambiguity in the identities of the spectral lines. In these cases, molecules that were unambiguously detected elsewhere in the bandpass were preferentially chosen. Lines that we were unable to identify are labeled as 'U' for unknown lines and are numbered according to their order of appearance. Over 60 lines were identified across the full bandpass and we have detections in the CH 3 CN J=12 → 11 transition up to K = 10. The same transitions in the isotopologue CH 13 3 CN were also detected, possibly out to K = 9. In the case of this isotopologue the K = 0 , 1 and 3 components and the K = 7 and higher components are blended with other lines. Absorption features are observed around the 13 CO J= 2 → 1 line; these features are possible artifacts arising from 13 CO emission in the off-beam, and the line identifications in this area of the spectrum are tentative at best. From inspection of Figure 1, we conclude that the CH 3 CN J=12 → 11 K = 0 - 4 , 7, 8, and 10 suffer no significant contamination but the K = 5, 6 components suffer some blending with lines from other molecular species. The K = 9 component is rendered useless by overlap with the 13 CO(2 -1) line. In the analysis that follows we use the K = 5, 6 components only when we are confident that we can reasonably separate them from the other lines; the K = 9 component we do not use at all.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"3.2. CH 3 CN Line Detection and Analysis\",\n \"content\": \"We detected emission in the CH 3 CN J=12 → 11 transition towards 9 of the 21 sources of the sample (see Table 1). In Figure 2 we show our high resolution spectra at the center position. K -components were detected up to K = 7 for several sources. The upper excitation energy of the K = 7 component is about 420 K (Boucher et al. 1980), thus indicating the presence of hot molecular gas. We have performed simultaneous Gaussian fits for all K -components of the CH 3 CN J=12 → 11 transition. The FWHM of all lines was kept constant at the value measured for the unblended K = 3 component, and the relative position of all lines was fixed at the theoretical values. For the main isotopologue the K = 5 line was fit with 3 Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN. The magnitude of the hyperfine splitting (hfs) of the CH 3 CN molecule reported in Boucher et al. (1980) for the CH 3 CN J=12 → 11 transition is ≤ 0 . 3 MHz. Due to the large FWHM ( ∼ 8 MHz), and the relatively low signal-to-noise detections of the higher K -components, we omitted the hfs in the line fitting. In Table 2 we list the line parameters from the Gaussian fits. In Figure 3 we show the full beam spaced cross scans that we obtained toward five sources. Inspection of the figure shows that the methyl cyanide emission peaks strongly at the central position. Occasionally the lower K -components ( K = 0 -2) were detected away from the center position (IRAS20126+4104, NGC 7538S), indicating that for these sources the warm gas giving rise to the emission is extended on arc-minute scales, but the higher K -components ( K > 3) are always found to be compact with respect to our beam. We used the population diagram technique to derive the rotation temperature and column density for our Note . - A Gaussian source with FWHM of '' targets. This analysis assumes optically thin lines and level populations described by a Boltzmann distribution (e.g., Goldsmith & Langer (1999)) and furthermore that all lines trace the same volume of gas. The data are characterized by a linear fit where the negative reciprocal of the slope is T rot and the y -intercept is used to infer the column density (N CH 3 CN ) (see Araya et al. (2005) for a detailed description). When calculating the CH 3 CN column density we adopted a gaussian source size of FWHM of 10 '' . Figure 4 shows Boltzmann plots for all detected sources. N JK , g JK and E JK are the column density, statistical weight and upper state energy for the (J,K) state, respectively. The linear fit was made using only the CH 3 CN main isotopologue data. The results of our population diagram analysis are presented in Table 3. With the low signal-to-noise (S/N) ratio of our spectra, detection of the CH 3 13 CN isotopologue would indicate optically thick lines. However, only for G34.26+0.15 we detected the first three K -components of CH 3 13 CN above a 3 σ level. The optical depth of the main line K = 2 (which is less blended) estimated from the ratio of the line intensities is ∼ 8, assuming 12 C/ 13 C= 50. The ratio was calculated based on the abundance variation with galacto-centric distance (Wilson & Rood 1994). For the other targets, no reliable detection of isotopologue lines was made, therefore a detailed analysis correcting for optical depth effects was not feasible. If the assumption of optically thin conditions is incorrect, the derived temperature values are overestimated, and the column density underestimated. However, optical depths effects will not affect our principal result that relatively hot molecular gas is present in our targets.\",\n \"pages\": [\n 4,\n 5,\n 7\n ]\n },\n {\n \"title\": \"3.3. Kinematics\",\n \"content\": \"The above analysis of the physical parameters assumed uniform conditions in the emitting gas. This is clearly a simplification, as in most cases one would expect gradients in the density and temperature. Allowing for nonuniformity in these parameters is not possible with the present low angular resolution data, however we consider here whether kinematic features can be detected in the CH 3 CN lines. Our data in principle allow us to check for gradients in line velocity and/or line width. For most of our sources the assumption of central heating, and hence increasing temperature toward the center of the core is reasonable. Thus, any change of line kinematic parameters for the different K -components which have rapidly increasing excitation energies, would imply radial gradients toward the core center. To search for radial gradients we have thus obtained independent fits for each line, where each K -component was fit with a Gaussian function independent of the other components. Therefore, the FWHM, line position, and intensity of the lines are free parameters in the fit. For the main isotopologue the K = 5 line was fit with three Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN and a vibrational line of CH 3 CH 2 OH. The results of these alternative fits are shown in Table 4. Figures 5 and 6 show plots of velocity and linewidth as a function of the upper level energy. From Figure 5 there appears to be a trend in velocity for G16.59 -0.05, G34.26+0.15, IRAS 18566+0408, and IRAS 20126+4104. In all cases the putative velocity gradient is towards lower velocity with increasing upper state energy. The situation for the line-widths (Figure 6) is less clear. Weak evidence for increasing line width towards higher energies is present in IRAS 18264 -1152, and G23.01 -0.41, whereas the opposite trend is seen in IRAS 20126+4104. We comment further on these findings in the next section.\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"4. DISCUSSION\",\n \"content\": \"We have used the 10 m SMT to search for CH 3 CN emission toward 21 regions of massive star formation. All of the regions (except for G34.26+0.15) are clearly in an evolutionary phase prior to that of UC or HC HII regions. We detected nine sources in the CH 3 CN J=12 → 11 transition. For six of these sources this is the first detection in this transition. The low detection rate is likely due to the limited sensitivity of a single dish telescope with the relatively small aperture of 10 m. Our cross scans for 5 sources show that the K ≤ 3 are occasionally detected outside the central beam, but the higher K -components are always compact with respect to our angular resolution. This is consistent with a warm (T ≤ 50 K), extended envelope which surrounds a much smaller and hotter (T ≥ 50 K) region near the massive star. This finding is consistent with observations of other molecular transitions of lower excitation and critical density (e.g., NH 3 (1,1)) which probe the more extended envelope. Our data thus indicate the presence of gradients in temperature and density. Hence, to obtain precise physical parameters interferometric observations are necessary. The single dish beam will receive emission from regions of different physical characteristics, and performing the simple technique of rotation diagram technique corresponds to obtaining average physical properties of the emitting gas. Taking also into account a number of additional uncertainties intrinsic to single dish data analyzed with the rotation diagram method (e.g., Pankonin et al. (2001)) it is difficult to compare our results with the of Olmi et al. (1993) and Araya et al. (2005). Nonetheless we note that our results for the column densities ( ≈ 10 14 cm -2 ) are quite similar to what was obtained in these studies. However, our derived temperatures appear to be higher compared to the values of Olmi et al. (1993) and Araya et al. (2005). This might be related to the different evolutionary state of the target samples. Olmi et al. (1993) observed many known UCHII regions and the Araya et al. (2005) sample was selected from IRAS colors typical of UCHII regions, whereas our sample should represent a pre-UCHII region evolutionary phase. Higher S/N ratio data, which can put more stringent constraints on the optical depth in the lines will be required to verify this speculation. We conclude that all detected regions contain molecular gas with T > 50 K and methyl cyanide column densities of approximately 10 14 cm -2 . Assuming a strongly enhanced CH 3 CN abundance of 10 -8 the hydrogen column density in these regions on a scale of 10 '' , is then approximately 10 22 cm -2 . These numbers are consistent with the HMC nature of the detected sources. If the core is heated from the center, then lower K -component emission arises predominantly from outer, and hence cooler regions and higher K -components will dominate in the inner, hotter regions. Consequently, velocity gradients in the K -ladder components can trace radial dynamics and possible kinematic scenarios may be either collapse, out- flows, expansion or rotation (e.g, Cesaroni et al. (1997), Beltr'an et al. (2004)). We have searched our high resolution spectra for evidence of systematic variation in velocity or line-width as a function of excitation energies. A small number of kinematic analyses in CH 3 CN has been done but often no conclusive results have been found due to spectral resolution or S/N limitations. For instance, Olmi et al. (1993) did not find any reliable trend in their results. On the other hand, Cesaroni et al. (1999) observed IRAS 20126+4104 using the IRAM Plateau de Bure interferometer. These authors reported an increase in the velocity and line-width toward the center of the core. They suggested that this behavior may be due to rotation of a Keplerian disk sur- rounding an embedded massive protostar. Our results for this same region show a decrease in the velocity and the line-width toward the center, contrary to the results obtained by Cesaroni et al. (1999). A possible explanation for this discrepancy is the much larger beam of the SMT which will include more extended gas than the observations of Cesaroni et al. (1999). We detected an increasing blue-shift, i.e., toward lower velocities with higher K -component for four sources. This trend could be explained by expansion or outflow motion as seen in an optically thick line. Another explanation for this behavior could be self absorption of an infalling molecular core which causes a blue asymmetry in an optically thick line. However with the given S/N ratio of our spectra we cannot clearly distinguish these scenarios. A further complication that we can not address is the multiple core scenario. In this case, the cores have some dispersion of radial velocities that may be unresolved in the beam. Therefore, to correctly interpret the detected velocity trends, further observations with higher S/N and angular resolution are needed. Most of the HMCs observed in this paper are associated with bright IRAS sources, indicating that a massive object has already heated the surrounding matter. In Figure 7 we show mid-infrared images of six sources for which SPITZER GLIMPSE /IRAC data are available. For five out of these six sources there is evidence for extended 4 . 5 µ m excess emission (e.g., Cyganowski et al. (2008)). The presence of an extended 4 . 5 µ m excess is generally thought to be caused by emission of high ex- tation lines from the H 2 molecule, and is hence an indicator of shocked gas. Also, five out of the six sources shown in Figure 7 have strong mid-IR sources, which clearly shows that at least these HMCs have already formed massive stars which cause substantial heating of the molecular cores. One source, G25.83 -0.18, shows only a dark cloud at the suspected position of the massive protostar. This source also harbors one of the few 6 cm H 2 CO masers known (Araya et al. 2008). We note that this source shows quite strong CH 3 CNemission, and since this molecule is thought be effectively formed only with the presence of an energy source, it is likely that a massive protostar is present in this dark cloud also. It is tempting then to speculate that due to the different mid-IR properties G25.83 -0.18 is in an earlier evolution-ar y state compared to the other sources which have very bright mid-IR emission. However, using the extinction curve of Mathis (1990) we find that hydrogen column densities of ≥ 2 × 10 23 cm -2 could render a possible midIR source undetectable. Since hydrogen column densities of this order, and larger, are common in massive star forming cores, it is conceivable that the different mid-IR appearance of G25.83 -0.18 is caused by extinction.\",\n \"pages\": [\n 7,\n 8,\n 9,\n 10,\n 11\n ]\n },\n {\n \"title\": \"5. SUMMARY\",\n \"content\": \"We have observed a sample of 21 massive proto-stellar candidates in the CH 3 CN J=12 → 11 transition using the 10 m SMT. We detected methyl cyanide in nine of the sources of the sample. Rotation temperatures and column densities were estimated using the population diagram technique. Detected sources have temperatures > 50 K and column densities of ∼ 10 14 cm -2 , hence they are consistent with HMC nature. Higher spectral resolution is needed in order to understand the structure of the kinematics in molecular cores. This project was partially supported by the New Mex- ico Space Grant Consortium. PH acknowledges partial support from NSF grant AST-0908901. SK acknowledges partial support from UNAM DGAPA grant IN101310. We thank E. Jordan for help with the observations and initial data reduction. We thank the anonymous referee for suggestions which improved this manuscript.\",\n \"pages\": [\n 11,\n 12\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Araya, E., Hofner, P., Goss, W. M., et al. 2006, ApJ, 643, L33 Araya, E., Hofner, P., Kurtz, S., Bronfman, L., & DeDeo, S. 2005, ApJS, 157, 279 Bonnell, I. A., Vine, S. G., & Bate, M. R. 2004, MNRAS, 349, 735 Boucher, D., Burie, J., Bauer, A., Dubrulle, A., & Demaison, J. 1980, Journal of Physical and Chemical Reference Data, 9, 659 Brunthaler, A., Reid, M. J., Menten, K. M., et al. 2009, ApJ, 693, 424\",\n \"pages\": [\n 12\n ]\n }\n]"}}},{"rowIdx":82,"cells":{"bibcode":{"kind":"string","value":"2013ApJS..209...29K"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1309.4490.pdf"},"content":{"kind":"string","value":"\nAccepted 12 September, 2013\nA Massive Young Star-Forming Complex Study in Infrared and X-ray: Mid-Infrared Observations and Catalogs\nMichael A. Kuhn 1 , Matthew S. Povich 1 , 2 , Kevin L. Luhman 1 , 3 , Konstantin V. Getman 1 , Heather S. Busk 1 , Eric D. Feigelson 1 , 3\nABSTRACT\nSpitzer IRAC observations and stellar photometric catalogs are presented for the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX). MYStIX is a multiwavelength census of young stellar members of twenty nearby ( d < 4 kpc), Galactic, star-forming regions that contain at least one O star. All regions have data available from the Spitzer Space Telescope, consisting of GLIMPSE or other published catalogs for eleven regions and results of our own photometric analysis of archival data for the remaining nine regions. This paper seeks to construct deep and reliable catalogs of sources from the Spitzer images. Mid-infrared study of these regions faces challenges of crowding and high nebulosity. Our new catalogs typically contain fainter sources than existing Spitzer studies, which improves the match rate to Chandra X-ray sources that are likely to be young stars, but increases the possibility of spurious point-source detections, especially peaks in the nebulosity. IRAC color-color diagrams help distinguish spurious detections of nebular PAH emission from the infrared excess associated with dusty disks around young stars. The distributions of sources on the mid-infrared color-magnitude and color-color diagrams reflect differences between MYStIX regions, including astrophysical effects such as stellar ages and disk evolution.\nSubject headings: methods: data analysis - stars: pre-main-sequence - infrared: stars - planetary systems: protoplanetary disks\n1. Introduction\nA significant fraction of star formation activity in the Galaxy occurs in massive starforming complexes, dominated by OB stars and containing thousands of young stars. Studies of the cluster mass function indicate that stars are more likely to be born in rich clusters than in small groups (e.g. Lada & Lada 2003; Fall et al. 2009; Chandar et al. 2011). Because of the importance of such clusters, the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX) constructs a census of stars in twenty of the nearest ( d < 4 kpc), Galactic massive star-forming regions (Feigelson et al. 2013) with the Chandra X-ray Observatory , the Spitzer Space Telescope , and ground based near-infrared (NIR) observatories. Studies in the IR and X-ray provide complementary pictures of populations of new stars in star-forming regions. The infrared (IR) images identify stars with circumstellar disks or infalling envelopes through infrared excess (IRE), but cannot distinguish disk-free cluster members from field stars. Meanwhile, X-ray images can detect both disk-bearing and disk-free stars, although the sensitivity to the former is lower (Getman et al. 2009; Stelzer et al. 2011). Thus, the combination of both X-ray and IR observations provide more complete and less biased samples of complex members than either waveband alone.\nIn this paper, we describe the observations and source catalogs used by the MYStIX project from the Infrared Array Camera (IRAC; Fazio et al. 2004) onboard the Spitzer Space Telescope (Werner et al. 2004). This instrument has four bands centered at 3.6, 4.5, 5.8, and 8.0 µ m, which are useful for identifying IRE stars (e.g. Allen et al. 2004; Hartmann et al. 2005; Robitaille et al. 2006; Gutermuth et al. 2009). We use source catalogs produced by the pipeline of the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE; Benjamin et al. 2003) for nine regions, and we measure new aperture photometry from archival IRAC data for nine regions. We adopt pre-existing IRE star catalogs for two additional regions, the Orion Nebula (Megeath et al. 2012) and the Carina Nebula (Povich et al. 2011). In addition to the data from Spitzer , the MYStIX project includes NIR data obtained by United Kingdom Infra-Red Telescope (King et al. 2013) and the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and X-ray data obtained by the Chandra X-ray Observatory (Kuhn et al. 2013a). The procedures for constructing the combined sample of X-ray selected member, IRE selected members, and spectrally selected OB members is described by Naylor et al. (2013), Povich et al. (2013), and Broos et al. (2013). We describe the available GLIMPSE data (Section 2) and our procedures for analyzing other archival images from IRAC (Section 3). We then discuss the distributions of probable members and field stars on color-magnitude and color-color diagrams (Section 4) and summarize our results (Section 5).\n2. GLIMPSE Data\nThe GLIMPSE survey is a Legacy Science Program of NASAÕs Spitzer Space Telescope to study star formation in the disk of the Milky Way Galaxy (Benjamin et al. 2003; Churchwell et al. 2009). It contains six MYStIX regions Ð the Lagoon Nebula, the Trifid Nebula, NGC 6334, the Eagle Nebula, M 17, and NGC 6357 Ð within the 2 · -wide strip along the Galactic equator (GLIMPSE I and II data releases). Furthermore, Spitzer images and photometry for RCW 38 and NGC 3576 come from the Vela-Carina survey (Majewski et al. 2007), using a similar observing strategy with mosaicking and photometric analysis performed with GLIMPSE pipeline.\nFor the GLIMPSE observations, every position was visited at least twice with 1.2 s integrations. The data-reduction pipeline produces image mosaics (v3.0) and point-source lists (v2.0) for all four IRAC bands, which are publicly available 1 . Photometry is obtained through point response function (PRF) fitting. A 5 σ detection limit is used, corresponding to fluxes 0.2, 0.2, 0.4, and 0.4 mJy in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively (Benjamin et al. 2003). However, the detection sensitivity is lower in nebulous regions, and bright sources or regions with high backgrounds may be saturated. The GLIMPSE Catalog contains the sources with reliability ≥ 99.5%, and the GLIMPSE Archive contains all sources ≥ 5 σ above the background level.\nThe GLIMPSE pipeline was run on a deep, high-dynamic range observation of the W 3 star-forming region (AOR 5050624). This GLIMPSE Catalog (Archive) contains > 10,000 ( > 16,000 sources) shown in Table 2. These data were also reduced using the aperture photometry method ( / 3) to compare results from the two methodologies.\n3. New IRAC Analysis\nThe MYStIX project uses a combination of IRAC data from multiple provenances, as available. In addition to the GLIMPSE data described above, new analysis is performed on archival IRAC data for remaining MYStIX targets Ð the new catalogs have photometry extracted using aperture photometry (hereafter the aperture photometry catalogs) in contrast to GLIMPSE which makes use of PRF-fitting photometry. To guarantee that the MYStIX project has uniform data quality, our analysis includes a method comparison to study the effect of any biases produced by the variation in photometric method.\nThe aperture photometry catalogs contain fainter sources than the GLIMPSE catalogs Ð which is primarily an effect of the longer observations from which the aperture photometry catalogs are derived, rather than an effect of differences in extraction method. This will improve the match rate to Chandra sources that are likely to be young stars, but a greater source density in the MIR catalogs will also increase the chance of incorrect matches (e.g. Naylor et al. 2013). Many such sources can be removed from further studies due to incongruous NIR/MIR photometry (Povich et al. 2013). In addition more extragalactic MIR sources are detected in the deeper catalogs, many of which have extragalactic X-ray counterparts. This is desirable because MIR properties (e.g. [4 . 5] > 13 mag) may help classify an X-ray source as being extragalactic (Harvey et al. 2007; Broos et al. 2013). Extragalactic IR sources without X-ray matches can be filtered out using cuts on the IR color-color diagram (Povich et al. 2013).\n3.1. Observations\nWe obtained publicly available raw IRAC images from the Spitzer Heritage Archive 2 for nine MYStIX regions without GLIMPSE coverage. The target list and details of the Astronomical Observation Requests (AORs) are provided in Table 1. The IRAC field of view is 5 . 1 2 × 5 . 1 2, and various mapping and/or dither strategies were used for the IRAC observation programs included in this analysis. The camera spatial resolutions are FWHM = 1 . 11 6 to 1 . 11 9 from 3.6 to 8.0 µ m. Each field was observed in high dynamic range (HDR) mode where both 0.4 s and 10.4 s exposures are collected to provide unsaturated photometry for both brighter and fainter sources. Observations from different epochs are combined in our analysis.\nWe also analyzed archival data for M 17 and W 3 for comparison to the GLIMPSE data. For M 17 we analyzed images that are deeper than the Spitzer images from the GLIMPSE survey Ð useful for comparing relative sensitivities for the different catalogs. However, for W 3 we analyzed the same deep, archival Spitzer data using both the GLIMPSE and aperture photometry methods Ð useful for investigating biases of different data reduction methodologies.\n3.2. Mosaics\nThe basic calibrated data (BCD) products were created by the Spitzer pipeline. Image reduction and mosaicking was performed via WCSmosaic IDL package (Gutermuth et al. 2008). This procedure uses algorithms developed by the IRAC instrument team to mitigate image artifacts, such as jailbar, pulldown, muxbleed, and banding (Hora et al. 2004; Pipher et al. 2004). Long and short frames were merged to create an HDR mosaic for each target, and corrections are applied including cosmic ray identification, distortion corrections in each frame, derotation and subpixel offsetting, and background matching. Sub-pixel sampling was performed using the dithered images. The pixel size of the reduced mosaics is 0 . 11 86 × 0 . 11 86, which is 1 / √ 2 the native pixel width.\nMosaicked images of two sample targets Ð W 40 and NGC 2264 Ð are shown in Figure 1 in 3.6 and 8.0 µ m bands. These examples demonstrate some of the variety of MYStIX regions in the MIR. For example, the stars in W 40 are centrally concentrated in the region where infrared nebulosity is highest, while the stars in NGC 2264 are divided into a number of subclusters and lie in regions with both high and low nebulosity (Feigelson et al. 2013, Kuhn et al. in preparation). Both regions have large amounts of absorption from dust Ð the dust absorption for W 40 is highest in a dust lane crossing the middle of the hour-glass structure (partially visible in the mosaics as infrared dark clouds), while the most highly absorbed stars in NGC 2264 are in subclusters that are embedded in their natal molecular cloud. The surface density of field stars also varies from region to region depending on the Galactic coordinates Ð W 40, ( l, b ) = (28 . 8 , +03 . 5), has a particularly high surface density, while the Flame Nebula, ( l, b ) = (206 . 5 , -16 . 4), has a much lower density. Several MYStIX regions, like NGC 2362, have almost no nebulosity around the star clusters because most of the molecular material has been removed.\n3.3. Point-Source Photometry\nThe data reduction makes use of photometric procedures from Luhman et al. (2008a, 2008b, 2010), software from the Image Reduction and Analysis Facility (IRAF), codes from the IDL Astronomy Users Library (Landsman 1993), and visualization software from Broos et al. (2010). The methods are modified for the MYStIX regions, which are more distant, and have higher stellar crowding and nebulosity than the Taurus and Chamaeleon star forming regions treated by Luhman and colleagues. These modified methods have also been used by Getman et al. (2012) in their study of the IC 1396A star-forming region.\nSource detection was performed on mosaicked images using the IRAF task STARFIND.\nSome spurious detections appear in these initial lists, including statistically insignificant sources, IRAC image artifacts, the point-spread-function (PSF) wings of bright sources, and extended sources. The extended sources include peaks in the nebulosity, which are particularly prevalent in regions with bright, complex nebulosity, particularly in the 5.8 and 8.0 µ m bands. Several strategies are used later to filter out unreliable sources. However, sources with bad or saturated pixels and duplicate detections are removed immediately.\nAperture photometry was performed on mosaicked images using the IRAF task PHOT. The targets lie near the Galactic plane and are crowded by field stars, so photometry is calculated for several small aperture sizes: 2-pixel (1.7 11 ), 3-pixel (2.6 11 ), 4-pixel (3.5 11 ), and 14-pixel (12.1 11 ) radii with an adjoining background annuli 1 pixel (0.86 11 ) in width. The aperture/background sizes were chosen in accordance with the strategy of Lada et al. (2006), Luhman et al. (2008), Getman et al. (2009), and Getman et al. (2012); the latter finding no evident improvement in photometry using a ÒstandardÓ 4-pixel-wide background instead of a 1-pixel-wide background used here. The zero-point IRAC magnitudes for the 14-pixel aperture are from Reach et al. (2005): ZP = 19.670, 18.921, 16.855, and 17.394 in the 3.6, 4.5, 5.8, and 8.0 µ m bands, where M = -2 . 5 log(DN / sec) + ZP. Aperture corrections for the other apertures are 0.640 -0.016, 0.725 -0.012, 0.968 -0.030, and 0.955 -0.040 for the 2 pixel aperture; 0.384 -0.011, 0.298 -0.010, 0.474 -0.033, 0.699 -0.031, for the 3 pixel aperture; 0.175 -0.011, 0.169 -0.010, 0.144 -0.021, and 0.222 -0.025 for the 4 pixel aperture in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Aperture sizes of 2, 3, or 4 pixels were assigned to each source depending on the crowding so that the error in flux is minimized. Calculation of aperture corrections, choice of apertures, and identification of crowded sources are discussed in Appendix A.\nA cross-correlated IRAC catalog was generated from the four bands, using a threshold of 2 11 for matching (see Appendix B). To ensure the quality of the aperture photometry catalog in Table 3, only > 5 σ detections are reported and every object must be detected in both 3.6 and 4.5 µ m bands to be included. Sources with high levels of contamination from a neighboring source ( > 100% of the source flux) are excluded. An archive of the less reliable sources detected at > 3 σ is also preserved (see Appendix C).\n3.4. IRAC Source Lists\nTable 3 presents the aperture photometry catalog for the nine MYStIX fields analyzed here. Columns in Table 3 include positions, IRAC band magnitudes and their uncertainties, and aperture size flags. The uncertainty incorporates the statistical uncertainty calculated by aperture photometry, added in quadrature to a ∼ 0.02 mag uncertainty in the calibration\nof IRAC (Reach et al. 2005), and a ∼ 0.01 mag uncertainty in the aperture correction. YSO variability of ∼ 0.05 mag to ∼ 0.2 mag may contribute to photometric scatter from one observation to another (Morales-Calder«on et al. 2009). The aperture flag indicates which photometric aperture size is used and whether errors due to crowding exceed 10% of the flux in the 3.6 µ m band.\nTable 4 summarizes the aperture photometry and GLIMPSE catalogs for each region Ð the total number of sources is given in Column 8. Variation in number of sources is strongly related to the size of the field of view (Column 3), its Galactic coordinates (Column 2), and the depth of the observation. Of the aperture photometry sources, only 25% are detected in the 5.8 µ m band and 18% are detected in the 8.0 µ m band (14% are detected in both bands). The distribution of aperture sizes is: 13% use 4 pixels, 11% use 3 pixels, and 76% use 2 pixels (43% of catalog sources have flags indicating crowding).\n3.4.1. Completeness Limits\nPhotometric reliability and completeness are spatially variable in regions with bright, structured background. Histograms of source flux provide a rough estimate of spatial completeness due to the sharp turnover beyond the completeness limit. The histograms of IRAC magnitudes for each field are shown in Figure 2 with bin widths of 0.2 mag. The completeness limits, estimated to be the center for the bin preceding the bin with the most sources, are listed in Table 4. However, these values do not hold where there is high nebulosity. For a typical field Ð a cluster age of 2 Myr, a distance of 2 kpc, and a completeness limit of [3 . 6] c = 16 . 0 Ð disk-free members would be detectible down to ∼ 0.1 M 8 in regions with low nebulosity for the pre-main-sequence models of Siess et al. (1997). Completeness limits for IRE sources may occur at lower magnitudes due to selection effects when multiple bands and their errors are combined.\n3.4.2. Photometric Quality in Comparison to GLIMPSE\nIt is helpful to compare the aperture photometry to the GLIMPSE photometry to examine how the various MIR challenges in MYStIX regions, such as nebulosity and crowding, affect the catalogs. For comparative purposes, aperture photometry catalogs were produced for W 3 using the same deep HDR data used by GLIMPSE, and for M 17 using a deeper observation than GLIMPSE (see Table 1).\nThe aperture photometry catalog for W 3 is sensitive to ∼ 1 magnitude deeper than\nGLIMPSE. More than 90% of GLIMPSE W 3 sources are detected at > 5 σ by our aperture photometry method, and many of the undetected sources are the dimmer components of close double sources.\nFigure 3 shows difference in measurements of magnitude for the two W 3 catalogs. As expected, scatter increases with magnitude: the root mean square (RMS) 3.6 µ m band residuals are 0.06 mag for bright sources ([3 . 6] < 12 mag) and 0.17 mag for dim sources ([3 . 6] > 12 mag). There is also a slight systematic shift in the 3.6 µ m band of +0 . 01 mag for bright sources and +0 . 05 mag for dim sources. Overall, the RMS residuals are 0.17 mag, 0.18 mag, 0.21 mag, and 0.22 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Furthermore, the scatter increases for smaller aperture sizes: in the 3.6 µ m band for sources with [3 . 6] < 12 mag the RMS residuals are 0.05 mag for 4 pixels, 0.06 mag for 3 pixels, 0.10 mag for 2 pixels (without high crowding or 0.14 for 2 pixels with high crowding). This is consistent with the aperture comparisons in the IC 1396A field performed by Getman et al. (2012).\nSimilar trends are seen in for M 17 (Figure 4), for which we compare aperture photometry of HDR observation of M 17 to the shallower GLIMPSE survey data. For bright sources ([3 . 6] < 12 mag) the RMS residuals are 0.14 mag, 0.13 mag, 0.22 mag, and 0.29 mag, and for dim sources ([3 . 6] > 12 mag), these are 0.22 mag, 0.23 mag, 0.33 mag, and 0.50 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. For bright sources ([3 . 6] < 12 mag) in the two M 17 catalogs, 95% of the photometry is within 0.2 mag in the 3.6 µ m band, which drops to 85% for the 8.0 µ m band. For dim sources, the consistency is ∼ 73% for the 3.6 µ m band, dropping to ∼ 68% for the 8.0 µ m band. A comparison of Figures 3 and 4 shows significantly more scatter for M 17 than for W 3; this is due to the shallowness of the M 17 GLIMPSE observation, which demonstrates, not only the benefits of the deeper HDR observations, but that the effect of net exposure duration is more important than any bias due to different photometry extraction methods in MYStIX.\nFigure 5 shows a band-by-band comparison of signal-to-noise from the two W 3 catalogs. Sources that are in one catalog but not in the other are also indicated. As expected, the aperture photometry catalog includes somewhat more sources with low signal-to-noise (5 < S/N < 10) than in the GLIMPSE Catalog. For sources in both catalogs, the signal-to-noise values lie near y = x (for the 3.6 and 4.5 µ m bands, signal-to-noise from aperture photometry is on average 1.5 times smaller) but can vary by a factor of ∼ 2.\nIn Figure 5, the overlap between the catalogs decreases with increasing wavelength bands, with most sources in common in the 3.6 µ m band and fewest in the 8.0 µ m band. This may be an effect of marginally detectable sources in the nebulous and crowded W 3 region; detection sensitivity decreases with longer wavelength bands due to lower efficiency\nof the detectors, less photospheric flux, and higher nebulosity. Both GLIMPSE catalogs and the aperture photometry catalogs may capture only a fraction of the sources near the sensitivity limit, but the sources that are detected are not necessarily the same sources.\nSources that are likely to be spurious detections of nebulosity (see / 3.5) are also indicated. Many of these are have low signal-to-noise (particularly sources not detected by GLIMPSE); however, a few have high signal-to-noise values.\n3.5. Contamination by Nebulosity\nThe 3.6, 5.8, and 8.0 µ m bands are tuned to emission bands of polycyclic aromatic hydrocarbons (PAH; Reach et al. 2006) excited by the ultraviolet light of OB stars in the MYStIX fields. This results in extremely bright nebulosity in these bands when observing massive star-forming complexes. This nebulosity is often similar in surface brightness to young stars at the resolution of Spitzer , making it difficult to distinguish between point sources and contaminants due to confusion. Ideally, peaks in the nebulosity should be filtered out by STARFIND using the source profile, but this often fails, and this judgement is often difficult to make by eye as well. The level of nebulosity ranges from almost none in NGC 2362 to levels at which IRAC point-source photometry is impossible. In Figure 1, the 8 µ m nebular emission can be seen to be higher in W 40 than in NGC 2264. For the regions with most nebulosity, including W 40, RCW 36, and W 3, source detection sensitivity can be severely limited.\nNebular contamination may result in two types of spurious entries in the aperture photometry catalog: patches of nebulosity with emission in all four bands that mimic stars, and false matches between stellar sources in the 3.6 and 4.5 µ m bands and nebular patches in the 5.8 and 8.0 µ m bands. These effects are also present in GLIMPSE (Povich et al. 2013), but are more prevalent here due to both the improved identification of extended sources using GLIMPSEÕs PSF fitting and the higher sensitivity of our aperture extraction method. Selecting sources with high signal-to-noise (reported in Table 3) can produce lists of more reliable sources, since nebulous sources are likely to have background extraction with greater pixel-to-pixel variation. However, nebulous sources can occasionally have small measurement errors because these sources can be very bright.\nNebulosity at 5.8 or 8.0 µ m can make a source appear red, but the colors are distinct from the colors of young stellar objects. The [4.5]-[5.8] vs. [5.8]-[8.0] diagram can be used to separate these sources from stellar sources (Povich et al. 2013). In Figure 6 this diagram is shown for NGC 2264 and W 40, with sources color-coded by signal-to-noise < 10 (green)\nand > 10 (black). This plot includes only sources with photometric data in all four bands, which is the minority of MYStIX MIR sources, and is strongly biased toward IRE sources or sources with nebulosity in the 5.8 and 8.0 µ m bands. Stars without IRE are centered near (0,0) on the diagram, while stars with IRE are shifted slightly to the upper right. However, there is another population with [4 . 5] -[8 . 0] ≥ 1 . 6 and [5 . 8] -[8 . 0] ≥ 0 . 5 that are likely due to nebulosity (Povich et al. 2013). Nearly all of these sources have S/N < 10 σ in at least one band. However, a number of low signal-to-noise sources also have colors consistent with stellar photospheres or young stellar objects.\nFigure 7 shows the 8.0 µ m sources from the aperture photometry catalog and from the literature plotted on the 8.0 µ m image for NGC 2264 (Sung et al. 2009), NGC 2362 (Currie et al. 2009), Rosette (Balog et al. 2007), and NGC 1893 (Caramazza et al. 2008). In this comparison there are examples of detections in the aperture photometry catalog that are not in theirs and vice versa. It is difficult to determine through visual inspection of the 8 µ m images which of these are real. The X-ray sources from Kuhn et al. (2013a) are also plotted Ð most of which are young stars Ð and these show that many of the new 8 µ m sources found from aperture photometry coincide with X-ray sources. This phenomenon is particularly strong for NGC 1893, which has a long X-ray exposure but is distant, so many of the young stars are near the detection threshold in the MIR. Thus, we gain many new MIR counterparts for cluster members by using these more sensitive catalogs.\n4. Classes of MIR Sources\nThe MYStIX MIR catalogs include young stellar members of the star-forming complex (with and without IRE), non-member point sources (field stars, extragalactic sources, shock emission), and spurious sources. MYStIX IRE Sources (MIRES; Povich et al. 2013) are identified using the MIR and NIR photometry, and a list of MYStIX Probable Complex Members (MPCM; Broos et al. 2013) is generated using X-ray selected members, IRE selected members, and spectroscopic OB stars. The distributions of these classes of sources on the MIR color-magnitude and color-color diagrams can give insight into how the MYStIX census is affected by the MIR catalog properties Ð properties such as the completeness limits, uncertainties on photometry, and spurious sources. Furthermore, these diagrams reveal global differences from region to region in terms of member populations, disk evolution, and star-formation environments.\n4.1. MIR Color-Magnitude Diagram\nFigure 8 shows the [3 . 6] vs. [3 . 6] -[4 . 5] diagrams for the nine regions analyzed here. The distributions of disk-free MPCMs (green circles) and MIRES sources (red circles) are plotted along with unclassified MIR sources (grey points). The A K = 2 reddening vector points to the lower right. Selection effects such as the size of the sample, the completeness limit, and larger photometric uncertainties for faint points can be seen for each region. The locus of disk-free members overlaps with the locus of field stars, and the 3.6 µ m band magnitude relates to stellar mass. In older or more distant regions, the dereddened, disk-free isochrones are shifted downwards on the plot (e.g. Roccatagliata et al. 2011, their Figure 7). The MYStIX MIR catalogs are typically deeper than the MYStIX X-ray catalogs, so X-ray selected MPCMs have a lower 3.6 µ m band magnitude completeness limit.\nThere is a population of stars that shows [3 . 6] -[4 . 5] excess on this diagram, many of which are identified as IRE sources in the MIRES catalog (red circles). However, the distribution of these sources varies from region to region. In some cases there are many sources with [3 . 6] -[4 . 5] > 1 . 5 (including NGC 2264, Rosette, and DR 21) while for other cases nearly all IRE sources have [3 . 6] -[4 . 5] < 1 . 0 (including NGC 2362, W 4, and NGC 1893). Other fields (like Flame, W 40, and RCW 36) are intermediate. NGC 2264, Rosette, and DR 21 all have young embedded clusters, while the clusters in NGC 2362, W 4, and NGC 1893 are mostly lightly absorbed. The sources with [3 . 6] -[4 . 5] > 1 . 5 are mostly clustered within the embedded clusters identified by (Kuhn et al. in preparation). The different distributions of [3 . 6] -[4 . 5] colors for different regions is primarily due to effects of IRE emission rather than reddening from dust. It would require ∼ 100 mag of absorption in the V band to cause a reddening of 1 mag in [3 . 6] -[4 . 5], and most of the cluster members in our sample do not have this much reddening (Povich et al. 2013; Broos et al. 2013). Therefore, the larger [3 . 6] -[4 . 5] excesses in some regions is likely to be an age effect of disk evolution.\n4.2. MIR Color-Color Diagram\nFigure 9 shows the [3.6]-[4.5] vs. [4.5]-[8.0] color-color diagram for sources in the Rosette Nebula. Here, the reddening vector is nearly vertical, and IRE from disks or envelopes appears as an excess in both colors. Sources contaminated by PAH nebulosity will have large [4.5]-[8.0] values but [3.6]-[4.5] colors near or below 0, so they can be distinguished from young stars. There are a variety of possible cuts on the color-color diagram that are designed to identify young stars, and the IRE selection polygon from Simon et al. (2007) is shown as an example that uses this color-color plot. But, the IRE sources found by Povich et al. (2013) in the MYStIX IR catalogs are a somewhat different set of sources than are\nfound using the other schemes 3 . Figure 10 shows color-color diagrams for each region with points color-coded by results of the classification done by Povich et al. (2013) and Broos et al. (2013), which includes cluster members with and without IRE in addition to various types of contaminants and spurious sources.\nReddened stellar photosphere fitting may quickly remove a large fraction of IR catalog sources from a list of possible IRE stars and relies on well understood field-star photospheric models. The procedures for fitting these stars using photometry in seven NIR and MIR bands are described in Povich et al. (2013). Some of the sources rejected for being insignificantly different from the reddened photospheric model (shown in black in Figure 10) would have been selected as IRE stars by the color cuts from Simon et al. (2007).\nThe color-color polygon used by Simon et al. (2007), and other color-based decision trees, have both false positives and false negatives with respect to the more elaborate analysis of the infrared spectral energy distributions by Povich et al. (2013) for the MYStIX analysis. Many of the stars lying in the polygon do not satisfy the more conservative criteria for disk-bearing young stars adopted by Povich et al. These sources may often be nebular (rather than stellar) sources in the 8.0 µ m band, as they are more common in the W 40 and DR 21 where the PAH contamination is high. The MPCM source lists also show a small population of disk-free stars (green circles in Figure 10) with MIR colors likely to arise from PAH nebulosity. These may be faulty matches between true X-ray sources and spurious MIR PAH sources.\n5. Summary\nThis work describes the Spitzer IRAC observations and source catalogs that will be used by the MYStIX project. These data include nine regions where archival data is available, and we perform aperture photometry on the HDR observations. The MYStIX MIR catalogs will be combined with X-ray (Kuhn et al. 2013, Townsley et al. in preparation) and NIR (King et al. 2013) for a multiwavelength study of star formation in massive young starforming complexes (Feigelson et al. 2013; Naylor et al. 2013; Povich et al. 2013; Broos et al. 2013). The aperture photometry catalogs are typically deeper and have higher photometric precision than typical GLIMPSE fields or other available catalogs of the same regions.\nIn addition, the MYStIX project makes use of the GLIMPSE photometry for ten regions (including a deep catalog for W 3 presented here). Furthermore, the MYStIX study of the Orion Nebula and Carina Nebula uses stellar membership censuses from the literature, and we do not reanalyze Spitzer data for these regions.\nThere are a total of ∼ 750,000 infrared sources in the aperture photometry catalogs. Photometry is extracted using variable aperture size depending on source crowding. We use a > 5 σ detection threshold, require sources to be detected in both the shorter wavelength IRAC bands, and clean the catalog of various instrumental and data-processing effects. In the study of MYStIX X-ray sources, lower reliability ( > 3 σ ) detections will also be included (the aperture-photometry archive) because the presence of an X-ray counterpart provides corroborating evidence for a sourceÕs legitimacy.\nWe investigate a variety of possible photometric problems empirically by comparing detection rates, fluxes, and flux uncertainties for the aperture photometry catalogs to other available catalogs. A particular problem we encounter is spurious sources due to nebulosity, which affect all bands, but particularly strongly affect the 5.8 and 8.0 µ m bands. These sources are difficult to eliminate completely through signal-to-noise cuts, although they usually affect detections with 5 < S/N < 10. However, color-color diagrams can be used to separate colors associated with PAH nebulosity from IRE candidate young stars. In addition, spatial completeness limits vary across the field due to strong variation in nebulosity and crowding.\nFinally, we present MIR color-magnitude and color-color diagrams showing the locus of MYStIX Probable Cluster Members (Broos et al. 2013) in comparison to the field stars. The nine MYStIX regions studied here show considerable differences in the distribution of IRE stars in these plots.\nThe MYStIX project is supported at Penn State by NASA grant NNX09AC74G, NSF grant AST-0908038, and the Chandra ACIS Team contract SV4-74018 (G. Garmire & L. Townsley, Principal Investigators), issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. We thank Marilyn R. Meade and Brian L. Babler for providing us with the reduced images and photometry for W 3. We thank the anonymous referee for closely reading the manuscript and providing useful comments and suggestions. This work is based on observations made with the Spitzer Space Telescope, obtained from the NASA/ IPAC Infrared Science Archive, both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. This research has also made use of SAOImage DS9 software de-\nveloped by Smithsonian Astrophysical Observatory and NASAÕs Astrophysics Data System Bibliographic Services.\nA. Photometric Aperture Sizes\nLarger aperture sizes are favored for stars that are not in crowded regions because they have less Òaperture noise,Ó which is an effect of resampling the pixelated image into the aperture (Shahbaz et al. 1994). This effect can lead to several percent error in flux measurement using our two-pixel apertures, which is independent of source flux. Thus, we use simulations of artificial sources to determine the largest aperture size that will not cause inaccurate flux measurements due to crowding.\nUsing the IRAC PSF 4 , pairs of point sources were simulated with various separation angles (1 to 20 pixels), orientations, and flux differences (10 -3 to 10 3 ), and their photometry was extracted using PHOT to investigate the effect of nearby neighbors on flux measurements. This was performed using the same 2-pixel, 3-pixel, and 4-pixel apertures with 1-pixel-wide background annuluses that were used for the photometric analysis. For each separation angle and difference in difference in flux, the largest aperture (2-pixels, 3-pixels, or 4-pixels) is chosen that keeps contamination from a nearby source < 5% of the true flux; these choices are listed in Table 5 along with the associated error in flux. For sources in the Spitzer catalogs using the 2-pixel aperture, sources with flux errors larger than 10% are flagged and sources with flux errors larger than 100% of the true flux are excluded from the catalog. Getman et al. (2012, / 2.2) has shown that the use of small aperture extraction produces negligible bias in derived magnitudes, but leads to reduced photometric precision. These larger photometric uncertainties are incorporated in the aperture photometry catalogs given in the present paper.\nAperture corrections for the 2-pixel, 3-pixel, and 4-pixel apertures are calculated for each field with respect to magnitudes derived for the 14 pixel aperture, which is assumed to contain all the light. Corrections are found by comparing magnitudes for the 14-pixel aperture to the 4-pixel aperture, the 4-pixel aperture to the 3-pixel aperture, and the 4-pixel aperture to the 2-pixel aperture. Typically, bright sources that are not saturated and do not show signs of anomalous magnitudes in either aperture are used, and the correction is the median difference in calculated magnitudes. For IRAC channels 3 and 4, there is an artifact in the PSF of bright sources, so dimmer sources are used for the calibration.\nB. Matching Sources from Different IRAC Bands\nThe matching algorithm is based on the Delaunay triangulation, which is a computationally efficient strategy for identifying neighboring points in a set of points (see review by de Berg et al. 2008). To match sources from two bands, the sets of source positions from the two bands are combined, the Delaunay triangulation is constructed for the union of both sets, and matches are obtained as a subset of edges in the triangulation that join points from both bands and are shorter than a threshold length. In ambiguous cases, preference is given to the smallest separation.\nHere, we use a matching radius of 2 11 , and match sources in the 4.5, 5.8, and 8.0 µ m bands to the 3.6 µ m band sources. An astrometric correction is applied to the entire field in the 4.5, 5.8, and 8.0 µ m bands based on the median offsets relative to 3 . 6 µ m band positions, and matching is performed again with the improved positions. Right ascensions and declinations are reported for the 3.6 µ m source.\nThe PSF has a similar size for all bands, so it is uncommon for matches to be ambiguous within the IRAC aperture photometry catalogs. Ambiguous matches do commonly occur when comparing IRAC catalogs with UKIRT (King et al. 2013) or C handra (Kuhn et al. 2013, Townsley et al. in preparation) catalogs later in the MYStIX analysis. For this reason, a probabilistic approach to cross-waveband source matching is developed by Naylor et al. (2013). However, occasional intra-IRAC matching errors do arise from matches between real 3.6 and 4.5 µ m point sources to peaks in the nebulosity at 5.8 or 8.0 µ m within the 2 11 radius. These are filtered out using a conservative analysis of the near- and mid-infrared spectral energy distributions later in the MYStIX analysis (Povich et al. 2013).\nC. Archive of Lower-Reliability IRAC Sources\nFor the matching of IR sources to X-ray sources, the MYStIX project makes use of some MIR counterparts that have less-reliable photometry, including measurements with 5 > S/N > 3 and measurements that may be contaminated by bright, neighboring sources. The extra information provided by X-ray selection allows us to take this bifurcated approach to MIR reliability criteria. When we are considering the tens-of-thousands to hundredsof-thousands of MIR sources without X-ray counterparts, rare photometric errors could produce numerous false IRE-star candidates, so the reliability criteria must be strict. In contrast, there are orders-of-magnitude fewer MIR sources with X-ray counterparts Ð which already have a good chance of being young stars by virtue of X-ray emission Ð so rare photometric errors will be less important. The same approach is taken with the GLIMPSE\ndata with respect to the highly reliable GLIMPSE Catalog and the less reliable GLIMPSE Archive. MIR photometry for MYStIX sources that used data from the GLIMPSE Archive or aperture-photometry archive is provided by Broos et al. (2013, their Table 2).\nREFERENCES\nAllen, L. E., Calvet, N., DÕAlessio, P., et al. 2004, ApJS, 154, 363 Balog, Z., Muzerolle, J., Rieke, G. H., et al. 2007, ApJ, 660, 1532 Benjamin, R. A., et al. 2003, PASP, 115, 953 Broos, P. B., Getman, K. V., Povich, M. S., et al. 2013, ApJS, in press Broos, P. S., Townsley, L. K., Feigelson, E. D., et al. 2010, ApJ, 714, 1582 Caramazza, M., Micela, G., Prisinzano, L., et al. 2008, A&A, 488, 211 Chandar, R., Whitmore, B. C., Calzetti, D., et al. 2011, ApJ, 727, 88 Churchwell, E., Babler, B. L., Meade, M. R., et al. 2009, PASP, 121, 213 Currie, T., Lada, C. J., Plavchan, P., et al. 2009, ApJ, 698, 1 de Berg, M., Cheong, O., van Kreveld, M. 2008, Computational Geometry: Algorithms and Applications, (3rd ed.; New York, NY: Springer) Fall, S. M., Chandar, R., & Whitmore, B. C. 2009, ApJ, 704, 453 Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10 Feigelson, E. D., Townsley, L. K., & Broos, P. S. 2013, ApJS, in press Getman, K. V., Feigelson, E. D., Luhman, K. L., et al. 2009, ApJ, 699, 1454 Getman, K. V., Feigelson, E. D., Sicilia-Aguilar, A., et al. 2012, MNRAS, 426, 2917 Gutermuth, R. A., Megeath, S. T., Myers, P. C., et al. 2009, ApJS, 184, 18 Gutermuth, R. A., Myers, P. C., Megeath, S. T., et al. 2008, ApJ, 674, 336 Hartmann, L., Megeath, S. T., Allen, L., et al. 2005, ApJ, 629, 881 Harvey, P., Mer«õn, B., Huard, T. L., et al. 2007, ApJ, 663, 1149\nHora, J. L., Fazio, G. G., Allen, L. E., et al. 2004, Proc. SPIE, 5487, 77 Indebetouw, R., Mathis, J. S., Babler, B. L., et al. 2005, ApJ, 619, 931 King, R. R., Naylor, T., Broos, P. S., Getman, K. V., & Feigelson, E. D. 2013, ApJS, in press Kuhn, M. A., Getman, K. V., Broos, P. B., Townsley, L. K, & Feigelson, E. D. 2013, ApJS, in press Kuhn, M. A., Getman, K. V., Feigelson, E. D., et al. 2010, ApJ, 725, 2485 Lada, C. J. & Lada, E. A. 2003, ARA&A, 41, 57 Lada, C. J., Muench, A. A., Luhman, K. L., et al. 2006, AJ, 131, 1574 Landsman, W. B. 1993, Astronomical Data Analysis Software and Systems II, 52, 246 Luhman, K. L., Allen, L. E., Allen, P. R., et al. 2008, ApJ, 675, 1375 Luhman, K. L., Allen, P. R., Espaillat, C., Hartmann, L., & Calvert, N. 2010, ApJS, 186, 111 Luhman, K. L. & Muench, A. A. 2008, ApJ, 684, 654 Majewski, S., Babler, B., Churchwell, E., et al. 2007, Spitzer Proposal, 40791 Megeath, S. T., Gutermuth, R., Muzerolle, J., et al. 2012, AJ, 144, 192 Morales-Calder«on, M., Stauffer, J. R., Rebull, L., et al. 2009, ApJ, 702, 1507 Naylor, T., Broos, P. S., & Feigelson, E. D. 2013, ApJS, submitted Pipher, J. L., McMurtry, C. W., Forrest, W. J., et al. 2004, Proc. SPIE, 5487, 234 Povich, M. S., Kuhn, M. A., Getman, K. V., et al. 2013, ApJS, in press Povich, M. S., Smith, N., Majewski, S. R., et al. 2011, ApJS, 194, 14 Reach, W. T., Megeath, S. T., Cohen, M., et al. 2005, PASP, 117, 978 Reach, W. T., Rho, J., Tappe, A., et al. 2006, AJ, 131, 1479 Robitaille, T. P., Whitney, B. A., Indebetouw, R., & Wood, K. 2007, ApJS, 169, 328\nRobitaille, T. P., Whitney, B. A., Indebetouw, R., Wood, K., & Denzmore, P. 2006, ApJS, 167, 256 Roccatagliata, V., Bouwman, J., Henning, T., et al. 2011, ApJ, 733, 113 Shahbaz, T., Naylor, T., & Charles, P. A. 1994, MNRAS, 268, 756 Siess, L., Forestini, M., & Dougados, C. 1997, A&A, 324, 556 Simon, J. D., Bolatto, A. D., Whitney, B. A., et al. 2007, ApJ, 669, 327 Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stelzer, B., Preibisch, T., Alexander, F., et al. 2012, A&A, 537, A135 Sung, H., Stauffer, J. R., & Bessell, M. S. 2009, AJ, 138, 1116 Werner, M. W., Roellig, T. L., Low, F. J., et al. 2004, ApJS, 154, 1\n
\n\n
Table 1. IRAC Observing Log
\n
\n
\n\n
Table 1ÑContinued
\n
\nNote. Ñ Column 1: Target name. Column 2: Astronomical Object Request number. Column 3: Spitzer program identification number. Column 4: AOR central right ascension and declination for epoch (J2000.0). Column 5: The total area of the AOR field of view. Column 6: Total integration time per pixel for long frames. Column 7: Date of the start of the observation.\n
\n\n
Table 2. GLIMPSE W 3 IRAC Photometry
\n
\nNote. Ñ Column 1: GLIMPSE source designation. Column 2: A - source is in the GLIMPSE Archive, C - source is in the GLIMPSE Catalog. Columns 3-4: Right ascension and declination for epoch (J2000.0). Columns 5-8: GLIMPSE IRAC magnitudes.\n
\n\n
Table 3. IRAC Aperture Photometry
\n
\nNote. Ñ Column 1: Target name. Column 2: Source Designation. Columns 3-4: Right ascension and declination for epoch (J2000.0). Columns 5-8: IRAC magnitudes from aperture photometry. Column 9: Aperture size in pixels used for photometric extraction. Table 3 is published in its entirety in an electronic form. A portion is shown here for guidance regarding its form and content.\n
\n\n
Table 4. IRAC Catalog Properties
\n
\nNote. Ñ Column 1: Target name. Column 2: Galactic coordinates. Column 3: Angular area of IRAC mosaic field of view. Columns 4-7: Completeness limits for catalog sources (bands [3.6], [4.5], [5.8], and [8.0], respectively). Column 8: The number of point sources in the catalog.\n
\n\n
Table 5. Aperture Size
\n
\nNote. Ñ For each pair of magnitude difference (first column) and angular separation (first row), the chosen aperture size (in pixels) and the simulated error in flux measurement for that aperture size (rounded to the nearest percentage) are given.\nÐ\n24\nÐ\n\n\n
Fig. 1.Ñ IRAC mosaics. (a) 3.6 µ m band image of W 40. (b) 8.0 µ m band image of W 40. (c) 3.6 µ m band image of NGC 2264. (d) 8.0 µ m band image of NGC 2264. Both regions have structurally complex nebulosity; however, nebulosity is higher in W 40 than in NGC 2264.
\n\n\n\n
Fig. 2.Ñ Histograms of 3.6 (a), 4.5 (b), 5.8 (c), and 8.0 µ m (d) band point-source magnitudes for nine MYStIX regions using a bin width of 0.2 mag. The completeness limit is assumed to be one bin brighter than the peak of the histogram.
\n\n\n\n
Fig. 3.Ñ A comparison of aperture photometry to GLIMPSE photometry for W 3. Plot of magnitude residuals (aperture minus GLIMPSE) vs. magnitude using aperture and GLIMPSE catalogs produced from the HDR Spitzer observation of the W 3 region. Plots ( top to bottom ) are the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Colors indicate the aperture used: black for the 4 pixel aperture, red for the 3 pixel aperture, blue for the 2 pixel aperture with low crowding, and green for the 2 pixel aperture with high crowding.
\n\n\n\n
Fig. 4.Ñ A comparison of aperture photometry to GLIMPSE photometry for M 17, similar to Figure 3. Plots ( top to bottom ) are the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Here, the M 17 GLIMPSE data comes from significantly shorter observations than the aperturephotometry data, leading to more scatter than is seen in the comparison for W 3.
\n\n\n\n
Fig. 5.Ñ Signal-to-noise of the aperture photometry catalog vs. signal-to-noise in the GLIMPSE catalog for all W 3 sources present in both catalogs for each band; non-detections are set to S/N=4 on the graph. The green points are the sources flagged as possible spurious detections of nebulosity. The red line indicates equal error from both catalogs.
\n\n\n\n
Fig. 6.Ñ [4.5]-[5.8] vs. [5.8]-[8.0] color-color diagrams -Left: NGC 2264, Right: W 40. Sources with S/N > 10 in all four IRAC bands are black circles and sources with S/N < 10 in at least one band are green circles. The dashed lines show the color cuts for PAH knots from Povich et al. (2013).
\n\n\n\n
Fig. 8.Ñ [3.6] vs. [3.6]-[4.6] color-magnitude diagrams for MIR sources in the each region. MPCMs with no IRE are shown by green circles, MPCMs with IRE are shown by red circles, and remaining sources (field stars, unclassified members, and non-stellar sources) are shown by grey circles. The arrow indicates reddening of A K = 2 mag using the Indebetouw et al. (2005) extinction law.
\n\n\n\n
Fig. 9.Ñ [3 . 6] -[4 . 5] vs. [4 . 5] -[8 . 0] color-color diagrams for MIR sources in the Rosette Nebula. The color cuts used by Simon et al. (2007) are shown with the gray lines. These cuts identify a slightly different set of IRE sources compared to Povich et al. (2013). The black arrow is the A K = 2 mag reddening vector.
\n\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"Spitzer IRAC observations and stellar photometric catalogs are presented for the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX). MYStIX is a multiwavelength census of young stellar members of twenty nearby ( d < 4 kpc), Galactic, star-forming regions that contain at least one O star. All regions have data available from the Spitzer Space Telescope, consisting of GLIMPSE or other published catalogs for eleven regions and results of our own photometric analysis of archival data for the remaining nine regions. This paper seeks to construct deep and reliable catalogs of sources from the Spitzer images. Mid-infrared study of these regions faces challenges of crowding and high nebulosity. Our new catalogs typically contain fainter sources than existing Spitzer studies, which improves the match rate to Chandra X-ray sources that are likely to be young stars, but increases the possibility of spurious point-source detections, especially peaks in the nebulosity. IRAC color-color diagrams help distinguish spurious detections of nebular PAH emission from the infrared excess associated with dusty disks around young stars. The distributions of sources on the mid-infrared color-magnitude and color-color diagrams reflect differences between MYStIX regions, including astrophysical effects such as stellar ages and disk evolution. Subject headings: methods: data analysis - stars: pre-main-sequence - infrared: stars - planetary systems: protoplanetary disks","pages":[1]},{"title":"A Massive Young Star-Forming Complex Study in Infrared and X-ray: Mid-Infrared Observations and Catalogs","content":"Michael A. Kuhn 1 , Matthew S. Povich 1 , 2 , Kevin L. Luhman 1 , 3 , Konstantin V. Getman 1 , Heather S. Busk 1 , Eric D. Feigelson 1 , 3","pages":[1]},{"title":"1. Introduction","content":"A significant fraction of star formation activity in the Galaxy occurs in massive starforming complexes, dominated by OB stars and containing thousands of young stars. Studies of the cluster mass function indicate that stars are more likely to be born in rich clusters than in small groups (e.g. Lada & Lada 2003; Fall et al. 2009; Chandar et al. 2011). Because of the importance of such clusters, the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX) constructs a census of stars in twenty of the nearest ( d < 4 kpc), Galactic massive star-forming regions (Feigelson et al. 2013) with the Chandra X-ray Observatory , the Spitzer Space Telescope , and ground based near-infrared (NIR) observatories. Studies in the IR and X-ray provide complementary pictures of populations of new stars in star-forming regions. The infrared (IR) images identify stars with circumstellar disks or infalling envelopes through infrared excess (IRE), but cannot distinguish disk-free cluster members from field stars. Meanwhile, X-ray images can detect both disk-bearing and disk-free stars, although the sensitivity to the former is lower (Getman et al. 2009; Stelzer et al. 2011). Thus, the combination of both X-ray and IR observations provide more complete and less biased samples of complex members than either waveband alone. In this paper, we describe the observations and source catalogs used by the MYStIX project from the Infrared Array Camera (IRAC; Fazio et al. 2004) onboard the Spitzer Space Telescope (Werner et al. 2004). This instrument has four bands centered at 3.6, 4.5, 5.8, and 8.0 µ m, which are useful for identifying IRE stars (e.g. Allen et al. 2004; Hartmann et al. 2005; Robitaille et al. 2006; Gutermuth et al. 2009). We use source catalogs produced by the pipeline of the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE; Benjamin et al. 2003) for nine regions, and we measure new aperture photometry from archival IRAC data for nine regions. We adopt pre-existing IRE star catalogs for two additional regions, the Orion Nebula (Megeath et al. 2012) and the Carina Nebula (Povich et al. 2011). In addition to the data from Spitzer , the MYStIX project includes NIR data obtained by United Kingdom Infra-Red Telescope (King et al. 2013) and the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and X-ray data obtained by the Chandra X-ray Observatory (Kuhn et al. 2013a). The procedures for constructing the combined sample of X-ray selected member, IRE selected members, and spectrally selected OB members is described by Naylor et al. (2013), Povich et al. (2013), and Broos et al. (2013). We describe the available GLIMPSE data (Section 2) and our procedures for analyzing other archival images from IRAC (Section 3). We then discuss the distributions of probable members and field stars on color-magnitude and color-color diagrams (Section 4) and summarize our results (Section 5).","pages":[2]},{"title":"2. GLIMPSE Data","content":"The GLIMPSE survey is a Legacy Science Program of NASAÕs Spitzer Space Telescope to study star formation in the disk of the Milky Way Galaxy (Benjamin et al. 2003; Churchwell et al. 2009). It contains six MYStIX regions Ð the Lagoon Nebula, the Trifid Nebula, NGC 6334, the Eagle Nebula, M 17, and NGC 6357 Ð within the 2 · -wide strip along the Galactic equator (GLIMPSE I and II data releases). Furthermore, Spitzer images and photometry for RCW 38 and NGC 3576 come from the Vela-Carina survey (Majewski et al. 2007), using a similar observing strategy with mosaicking and photometric analysis performed with GLIMPSE pipeline. For the GLIMPSE observations, every position was visited at least twice with 1.2 s integrations. The data-reduction pipeline produces image mosaics (v3.0) and point-source lists (v2.0) for all four IRAC bands, which are publicly available 1 . Photometry is obtained through point response function (PRF) fitting. A 5 σ detection limit is used, corresponding to fluxes 0.2, 0.2, 0.4, and 0.4 mJy in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively (Benjamin et al. 2003). However, the detection sensitivity is lower in nebulous regions, and bright sources or regions with high backgrounds may be saturated. The GLIMPSE Catalog contains the sources with reliability ≥ 99.5%, and the GLIMPSE Archive contains all sources ≥ 5 σ above the background level. The GLIMPSE pipeline was run on a deep, high-dynamic range observation of the W 3 star-forming region (AOR 5050624). This GLIMPSE Catalog (Archive) contains > 10,000 ( > 16,000 sources) shown in Table 2. These data were also reduced using the aperture photometry method ( / 3) to compare results from the two methodologies.","pages":[3]},{"title":"3. New IRAC Analysis","content":"The MYStIX project uses a combination of IRAC data from multiple provenances, as available. In addition to the GLIMPSE data described above, new analysis is performed on archival IRAC data for remaining MYStIX targets Ð the new catalogs have photometry extracted using aperture photometry (hereafter the aperture photometry catalogs) in contrast to GLIMPSE which makes use of PRF-fitting photometry. To guarantee that the MYStIX project has uniform data quality, our analysis includes a method comparison to study the effect of any biases produced by the variation in photometric method. The aperture photometry catalogs contain fainter sources than the GLIMPSE catalogs Ð which is primarily an effect of the longer observations from which the aperture photometry catalogs are derived, rather than an effect of differences in extraction method. This will improve the match rate to Chandra sources that are likely to be young stars, but a greater source density in the MIR catalogs will also increase the chance of incorrect matches (e.g. Naylor et al. 2013). Many such sources can be removed from further studies due to incongruous NIR/MIR photometry (Povich et al. 2013). In addition more extragalactic MIR sources are detected in the deeper catalogs, many of which have extragalactic X-ray counterparts. This is desirable because MIR properties (e.g. [4 . 5] > 13 mag) may help classify an X-ray source as being extragalactic (Harvey et al. 2007; Broos et al. 2013). Extragalactic IR sources without X-ray matches can be filtered out using cuts on the IR color-color diagram (Povich et al. 2013).","pages":[3,4]},{"title":"3.1. Observations","content":"We obtained publicly available raw IRAC images from the Spitzer Heritage Archive 2 for nine MYStIX regions without GLIMPSE coverage. The target list and details of the Astronomical Observation Requests (AORs) are provided in Table 1. The IRAC field of view is 5 . 1 2 × 5 . 1 2, and various mapping and/or dither strategies were used for the IRAC observation programs included in this analysis. The camera spatial resolutions are FWHM = 1 . 11 6 to 1 . 11 9 from 3.6 to 8.0 µ m. Each field was observed in high dynamic range (HDR) mode where both 0.4 s and 10.4 s exposures are collected to provide unsaturated photometry for both brighter and fainter sources. Observations from different epochs are combined in our analysis. We also analyzed archival data for M 17 and W 3 for comparison to the GLIMPSE data. For M 17 we analyzed images that are deeper than the Spitzer images from the GLIMPSE survey Ð useful for comparing relative sensitivities for the different catalogs. However, for W 3 we analyzed the same deep, archival Spitzer data using both the GLIMPSE and aperture photometry methods Ð useful for investigating biases of different data reduction methodologies.","pages":[4]},{"title":"3.2. Mosaics","content":"The basic calibrated data (BCD) products were created by the Spitzer pipeline. Image reduction and mosaicking was performed via WCSmosaic IDL package (Gutermuth et al. 2008). This procedure uses algorithms developed by the IRAC instrument team to mitigate image artifacts, such as jailbar, pulldown, muxbleed, and banding (Hora et al. 2004; Pipher et al. 2004). Long and short frames were merged to create an HDR mosaic for each target, and corrections are applied including cosmic ray identification, distortion corrections in each frame, derotation and subpixel offsetting, and background matching. Sub-pixel sampling was performed using the dithered images. The pixel size of the reduced mosaics is 0 . 11 86 × 0 . 11 86, which is 1 / √ 2 the native pixel width. Mosaicked images of two sample targets Ð W 40 and NGC 2264 Ð are shown in Figure 1 in 3.6 and 8.0 µ m bands. These examples demonstrate some of the variety of MYStIX regions in the MIR. For example, the stars in W 40 are centrally concentrated in the region where infrared nebulosity is highest, while the stars in NGC 2264 are divided into a number of subclusters and lie in regions with both high and low nebulosity (Feigelson et al. 2013, Kuhn et al. in preparation). Both regions have large amounts of absorption from dust Ð the dust absorption for W 40 is highest in a dust lane crossing the middle of the hour-glass structure (partially visible in the mosaics as infrared dark clouds), while the most highly absorbed stars in NGC 2264 are in subclusters that are embedded in their natal molecular cloud. The surface density of field stars also varies from region to region depending on the Galactic coordinates Ð W 40, ( l, b ) = (28 . 8 , +03 . 5), has a particularly high surface density, while the Flame Nebula, ( l, b ) = (206 . 5 , -16 . 4), has a much lower density. Several MYStIX regions, like NGC 2362, have almost no nebulosity around the star clusters because most of the molecular material has been removed.","pages":[5]},{"title":"3.3. Point-Source Photometry","content":"The data reduction makes use of photometric procedures from Luhman et al. (2008a, 2008b, 2010), software from the Image Reduction and Analysis Facility (IRAF), codes from the IDL Astronomy Users Library (Landsman 1993), and visualization software from Broos et al. (2010). The methods are modified for the MYStIX regions, which are more distant, and have higher stellar crowding and nebulosity than the Taurus and Chamaeleon star forming regions treated by Luhman and colleagues. These modified methods have also been used by Getman et al. (2012) in their study of the IC 1396A star-forming region. Source detection was performed on mosaicked images using the IRAF task STARFIND. Some spurious detections appear in these initial lists, including statistically insignificant sources, IRAC image artifacts, the point-spread-function (PSF) wings of bright sources, and extended sources. The extended sources include peaks in the nebulosity, which are particularly prevalent in regions with bright, complex nebulosity, particularly in the 5.8 and 8.0 µ m bands. Several strategies are used later to filter out unreliable sources. However, sources with bad or saturated pixels and duplicate detections are removed immediately. Aperture photometry was performed on mosaicked images using the IRAF task PHOT. The targets lie near the Galactic plane and are crowded by field stars, so photometry is calculated for several small aperture sizes: 2-pixel (1.7 11 ), 3-pixel (2.6 11 ), 4-pixel (3.5 11 ), and 14-pixel (12.1 11 ) radii with an adjoining background annuli 1 pixel (0.86 11 ) in width. The aperture/background sizes were chosen in accordance with the strategy of Lada et al. (2006), Luhman et al. (2008), Getman et al. (2009), and Getman et al. (2012); the latter finding no evident improvement in photometry using a ÒstandardÓ 4-pixel-wide background instead of a 1-pixel-wide background used here. The zero-point IRAC magnitudes for the 14-pixel aperture are from Reach et al. (2005): ZP = 19.670, 18.921, 16.855, and 17.394 in the 3.6, 4.5, 5.8, and 8.0 µ m bands, where M = -2 . 5 log(DN / sec) + ZP. Aperture corrections for the other apertures are 0.640 -0.016, 0.725 -0.012, 0.968 -0.030, and 0.955 -0.040 for the 2 pixel aperture; 0.384 -0.011, 0.298 -0.010, 0.474 -0.033, 0.699 -0.031, for the 3 pixel aperture; 0.175 -0.011, 0.169 -0.010, 0.144 -0.021, and 0.222 -0.025 for the 4 pixel aperture in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Aperture sizes of 2, 3, or 4 pixels were assigned to each source depending on the crowding so that the error in flux is minimized. Calculation of aperture corrections, choice of apertures, and identification of crowded sources are discussed in Appendix A. A cross-correlated IRAC catalog was generated from the four bands, using a threshold of 2 11 for matching (see Appendix B). To ensure the quality of the aperture photometry catalog in Table 3, only > 5 σ detections are reported and every object must be detected in both 3.6 and 4.5 µ m bands to be included. Sources with high levels of contamination from a neighboring source ( > 100% of the source flux) are excluded. An archive of the less reliable sources detected at > 3 σ is also preserved (see Appendix C).","pages":[5,6]},{"title":"3.4. IRAC Source Lists","content":"Table 3 presents the aperture photometry catalog for the nine MYStIX fields analyzed here. Columns in Table 3 include positions, IRAC band magnitudes and their uncertainties, and aperture size flags. The uncertainty incorporates the statistical uncertainty calculated by aperture photometry, added in quadrature to a ∼ 0.02 mag uncertainty in the calibration of IRAC (Reach et al. 2005), and a ∼ 0.01 mag uncertainty in the aperture correction. YSO variability of ∼ 0.05 mag to ∼ 0.2 mag may contribute to photometric scatter from one observation to another (Morales-Calder«on et al. 2009). The aperture flag indicates which photometric aperture size is used and whether errors due to crowding exceed 10% of the flux in the 3.6 µ m band. Table 4 summarizes the aperture photometry and GLIMPSE catalogs for each region Ð the total number of sources is given in Column 8. Variation in number of sources is strongly related to the size of the field of view (Column 3), its Galactic coordinates (Column 2), and the depth of the observation. Of the aperture photometry sources, only 25% are detected in the 5.8 µ m band and 18% are detected in the 8.0 µ m band (14% are detected in both bands). The distribution of aperture sizes is: 13% use 4 pixels, 11% use 3 pixels, and 76% use 2 pixels (43% of catalog sources have flags indicating crowding).","pages":[6,7]},{"title":"3.4.1. Completeness Limits","content":"Photometric reliability and completeness are spatially variable in regions with bright, structured background. Histograms of source flux provide a rough estimate of spatial completeness due to the sharp turnover beyond the completeness limit. The histograms of IRAC magnitudes for each field are shown in Figure 2 with bin widths of 0.2 mag. The completeness limits, estimated to be the center for the bin preceding the bin with the most sources, are listed in Table 4. However, these values do not hold where there is high nebulosity. For a typical field Ð a cluster age of 2 Myr, a distance of 2 kpc, and a completeness limit of [3 . 6] c = 16 . 0 Ð disk-free members would be detectible down to ∼ 0.1 M 8 in regions with low nebulosity for the pre-main-sequence models of Siess et al. (1997). Completeness limits for IRE sources may occur at lower magnitudes due to selection effects when multiple bands and their errors are combined.","pages":[7]},{"title":"3.4.2. Photometric Quality in Comparison to GLIMPSE","content":"It is helpful to compare the aperture photometry to the GLIMPSE photometry to examine how the various MIR challenges in MYStIX regions, such as nebulosity and crowding, affect the catalogs. For comparative purposes, aperture photometry catalogs were produced for W 3 using the same deep HDR data used by GLIMPSE, and for M 17 using a deeper observation than GLIMPSE (see Table 1). The aperture photometry catalog for W 3 is sensitive to ∼ 1 magnitude deeper than GLIMPSE. More than 90% of GLIMPSE W 3 sources are detected at > 5 σ by our aperture photometry method, and many of the undetected sources are the dimmer components of close double sources. Figure 3 shows difference in measurements of magnitude for the two W 3 catalogs. As expected, scatter increases with magnitude: the root mean square (RMS) 3.6 µ m band residuals are 0.06 mag for bright sources ([3 . 6] < 12 mag) and 0.17 mag for dim sources ([3 . 6] > 12 mag). There is also a slight systematic shift in the 3.6 µ m band of +0 . 01 mag for bright sources and +0 . 05 mag for dim sources. Overall, the RMS residuals are 0.17 mag, 0.18 mag, 0.21 mag, and 0.22 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Furthermore, the scatter increases for smaller aperture sizes: in the 3.6 µ m band for sources with [3 . 6] < 12 mag the RMS residuals are 0.05 mag for 4 pixels, 0.06 mag for 3 pixels, 0.10 mag for 2 pixels (without high crowding or 0.14 for 2 pixels with high crowding). This is consistent with the aperture comparisons in the IC 1396A field performed by Getman et al. (2012). Similar trends are seen in for M 17 (Figure 4), for which we compare aperture photometry of HDR observation of M 17 to the shallower GLIMPSE survey data. For bright sources ([3 . 6] < 12 mag) the RMS residuals are 0.14 mag, 0.13 mag, 0.22 mag, and 0.29 mag, and for dim sources ([3 . 6] > 12 mag), these are 0.22 mag, 0.23 mag, 0.33 mag, and 0.50 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. For bright sources ([3 . 6] < 12 mag) in the two M 17 catalogs, 95% of the photometry is within 0.2 mag in the 3.6 µ m band, which drops to 85% for the 8.0 µ m band. For dim sources, the consistency is ∼ 73% for the 3.6 µ m band, dropping to ∼ 68% for the 8.0 µ m band. A comparison of Figures 3 and 4 shows significantly more scatter for M 17 than for W 3; this is due to the shallowness of the M 17 GLIMPSE observation, which demonstrates, not only the benefits of the deeper HDR observations, but that the effect of net exposure duration is more important than any bias due to different photometry extraction methods in MYStIX. Figure 5 shows a band-by-band comparison of signal-to-noise from the two W 3 catalogs. Sources that are in one catalog but not in the other are also indicated. As expected, the aperture photometry catalog includes somewhat more sources with low signal-to-noise (5 < S/N < 10) than in the GLIMPSE Catalog. For sources in both catalogs, the signal-to-noise values lie near y = x (for the 3.6 and 4.5 µ m bands, signal-to-noise from aperture photometry is on average 1.5 times smaller) but can vary by a factor of ∼ 2. In Figure 5, the overlap between the catalogs decreases with increasing wavelength bands, with most sources in common in the 3.6 µ m band and fewest in the 8.0 µ m band. This may be an effect of marginally detectable sources in the nebulous and crowded W 3 region; detection sensitivity decreases with longer wavelength bands due to lower efficiency of the detectors, less photospheric flux, and higher nebulosity. Both GLIMPSE catalogs and the aperture photometry catalogs may capture only a fraction of the sources near the sensitivity limit, but the sources that are detected are not necessarily the same sources. Sources that are likely to be spurious detections of nebulosity (see / 3.5) are also indicated. Many of these are have low signal-to-noise (particularly sources not detected by GLIMPSE); however, a few have high signal-to-noise values.","pages":[7,8,9]},{"title":"3.5. Contamination by Nebulosity","content":"The 3.6, 5.8, and 8.0 µ m bands are tuned to emission bands of polycyclic aromatic hydrocarbons (PAH; Reach et al. 2006) excited by the ultraviolet light of OB stars in the MYStIX fields. This results in extremely bright nebulosity in these bands when observing massive star-forming complexes. This nebulosity is often similar in surface brightness to young stars at the resolution of Spitzer , making it difficult to distinguish between point sources and contaminants due to confusion. Ideally, peaks in the nebulosity should be filtered out by STARFIND using the source profile, but this often fails, and this judgement is often difficult to make by eye as well. The level of nebulosity ranges from almost none in NGC 2362 to levels at which IRAC point-source photometry is impossible. In Figure 1, the 8 µ m nebular emission can be seen to be higher in W 40 than in NGC 2264. For the regions with most nebulosity, including W 40, RCW 36, and W 3, source detection sensitivity can be severely limited. Nebular contamination may result in two types of spurious entries in the aperture photometry catalog: patches of nebulosity with emission in all four bands that mimic stars, and false matches between stellar sources in the 3.6 and 4.5 µ m bands and nebular patches in the 5.8 and 8.0 µ m bands. These effects are also present in GLIMPSE (Povich et al. 2013), but are more prevalent here due to both the improved identification of extended sources using GLIMPSEÕs PSF fitting and the higher sensitivity of our aperture extraction method. Selecting sources with high signal-to-noise (reported in Table 3) can produce lists of more reliable sources, since nebulous sources are likely to have background extraction with greater pixel-to-pixel variation. However, nebulous sources can occasionally have small measurement errors because these sources can be very bright. Nebulosity at 5.8 or 8.0 µ m can make a source appear red, but the colors are distinct from the colors of young stellar objects. The [4.5]-[5.8] vs. [5.8]-[8.0] diagram can be used to separate these sources from stellar sources (Povich et al. 2013). In Figure 6 this diagram is shown for NGC 2264 and W 40, with sources color-coded by signal-to-noise < 10 (green) and > 10 (black). This plot includes only sources with photometric data in all four bands, which is the minority of MYStIX MIR sources, and is strongly biased toward IRE sources or sources with nebulosity in the 5.8 and 8.0 µ m bands. Stars without IRE are centered near (0,0) on the diagram, while stars with IRE are shifted slightly to the upper right. However, there is another population with [4 . 5] -[8 . 0] ≥ 1 . 6 and [5 . 8] -[8 . 0] ≥ 0 . 5 that are likely due to nebulosity (Povich et al. 2013). Nearly all of these sources have S/N < 10 σ in at least one band. However, a number of low signal-to-noise sources also have colors consistent with stellar photospheres or young stellar objects. Figure 7 shows the 8.0 µ m sources from the aperture photometry catalog and from the literature plotted on the 8.0 µ m image for NGC 2264 (Sung et al. 2009), NGC 2362 (Currie et al. 2009), Rosette (Balog et al. 2007), and NGC 1893 (Caramazza et al. 2008). In this comparison there are examples of detections in the aperture photometry catalog that are not in theirs and vice versa. It is difficult to determine through visual inspection of the 8 µ m images which of these are real. The X-ray sources from Kuhn et al. (2013a) are also plotted Ð most of which are young stars Ð and these show that many of the new 8 µ m sources found from aperture photometry coincide with X-ray sources. This phenomenon is particularly strong for NGC 1893, which has a long X-ray exposure but is distant, so many of the young stars are near the detection threshold in the MIR. Thus, we gain many new MIR counterparts for cluster members by using these more sensitive catalogs.","pages":[9,10]},{"title":"4. Classes of MIR Sources","content":"The MYStIX MIR catalogs include young stellar members of the star-forming complex (with and without IRE), non-member point sources (field stars, extragalactic sources, shock emission), and spurious sources. MYStIX IRE Sources (MIRES; Povich et al. 2013) are identified using the MIR and NIR photometry, and a list of MYStIX Probable Complex Members (MPCM; Broos et al. 2013) is generated using X-ray selected members, IRE selected members, and spectroscopic OB stars. The distributions of these classes of sources on the MIR color-magnitude and color-color diagrams can give insight into how the MYStIX census is affected by the MIR catalog properties Ð properties such as the completeness limits, uncertainties on photometry, and spurious sources. Furthermore, these diagrams reveal global differences from region to region in terms of member populations, disk evolution, and star-formation environments.","pages":[10]},{"title":"4.1. MIR Color-Magnitude Diagram","content":"Figure 8 shows the [3 . 6] vs. [3 . 6] -[4 . 5] diagrams for the nine regions analyzed here. The distributions of disk-free MPCMs (green circles) and MIRES sources (red circles) are plotted along with unclassified MIR sources (grey points). The A K = 2 reddening vector points to the lower right. Selection effects such as the size of the sample, the completeness limit, and larger photometric uncertainties for faint points can be seen for each region. The locus of disk-free members overlaps with the locus of field stars, and the 3.6 µ m band magnitude relates to stellar mass. In older or more distant regions, the dereddened, disk-free isochrones are shifted downwards on the plot (e.g. Roccatagliata et al. 2011, their Figure 7). The MYStIX MIR catalogs are typically deeper than the MYStIX X-ray catalogs, so X-ray selected MPCMs have a lower 3.6 µ m band magnitude completeness limit. There is a population of stars that shows [3 . 6] -[4 . 5] excess on this diagram, many of which are identified as IRE sources in the MIRES catalog (red circles). However, the distribution of these sources varies from region to region. In some cases there are many sources with [3 . 6] -[4 . 5] > 1 . 5 (including NGC 2264, Rosette, and DR 21) while for other cases nearly all IRE sources have [3 . 6] -[4 . 5] < 1 . 0 (including NGC 2362, W 4, and NGC 1893). Other fields (like Flame, W 40, and RCW 36) are intermediate. NGC 2264, Rosette, and DR 21 all have young embedded clusters, while the clusters in NGC 2362, W 4, and NGC 1893 are mostly lightly absorbed. The sources with [3 . 6] -[4 . 5] > 1 . 5 are mostly clustered within the embedded clusters identified by (Kuhn et al. in preparation). The different distributions of [3 . 6] -[4 . 5] colors for different regions is primarily due to effects of IRE emission rather than reddening from dust. It would require ∼ 100 mag of absorption in the V band to cause a reddening of 1 mag in [3 . 6] -[4 . 5], and most of the cluster members in our sample do not have this much reddening (Povich et al. 2013; Broos et al. 2013). Therefore, the larger [3 . 6] -[4 . 5] excesses in some regions is likely to be an age effect of disk evolution.","pages":[11]},{"title":"4.2. MIR Color-Color Diagram","content":"Figure 9 shows the [3.6]-[4.5] vs. [4.5]-[8.0] color-color diagram for sources in the Rosette Nebula. Here, the reddening vector is nearly vertical, and IRE from disks or envelopes appears as an excess in both colors. Sources contaminated by PAH nebulosity will have large [4.5]-[8.0] values but [3.6]-[4.5] colors near or below 0, so they can be distinguished from young stars. There are a variety of possible cuts on the color-color diagram that are designed to identify young stars, and the IRE selection polygon from Simon et al. (2007) is shown as an example that uses this color-color plot. But, the IRE sources found by Povich et al. (2013) in the MYStIX IR catalogs are a somewhat different set of sources than are found using the other schemes 3 . Figure 10 shows color-color diagrams for each region with points color-coded by results of the classification done by Povich et al. (2013) and Broos et al. (2013), which includes cluster members with and without IRE in addition to various types of contaminants and spurious sources. Reddened stellar photosphere fitting may quickly remove a large fraction of IR catalog sources from a list of possible IRE stars and relies on well understood field-star photospheric models. The procedures for fitting these stars using photometry in seven NIR and MIR bands are described in Povich et al. (2013). Some of the sources rejected for being insignificantly different from the reddened photospheric model (shown in black in Figure 10) would have been selected as IRE stars by the color cuts from Simon et al. (2007). The color-color polygon used by Simon et al. (2007), and other color-based decision trees, have both false positives and false negatives with respect to the more elaborate analysis of the infrared spectral energy distributions by Povich et al. (2013) for the MYStIX analysis. Many of the stars lying in the polygon do not satisfy the more conservative criteria for disk-bearing young stars adopted by Povich et al. These sources may often be nebular (rather than stellar) sources in the 8.0 µ m band, as they are more common in the W 40 and DR 21 where the PAH contamination is high. The MPCM source lists also show a small population of disk-free stars (green circles in Figure 10) with MIR colors likely to arise from PAH nebulosity. These may be faulty matches between true X-ray sources and spurious MIR PAH sources.","pages":[11,12]},{"title":"5. Summary","content":"This work describes the Spitzer IRAC observations and source catalogs that will be used by the MYStIX project. These data include nine regions where archival data is available, and we perform aperture photometry on the HDR observations. The MYStIX MIR catalogs will be combined with X-ray (Kuhn et al. 2013, Townsley et al. in preparation) and NIR (King et al. 2013) for a multiwavelength study of star formation in massive young starforming complexes (Feigelson et al. 2013; Naylor et al. 2013; Povich et al. 2013; Broos et al. 2013). The aperture photometry catalogs are typically deeper and have higher photometric precision than typical GLIMPSE fields or other available catalogs of the same regions. In addition, the MYStIX project makes use of the GLIMPSE photometry for ten regions (including a deep catalog for W 3 presented here). Furthermore, the MYStIX study of the Orion Nebula and Carina Nebula uses stellar membership censuses from the literature, and we do not reanalyze Spitzer data for these regions. There are a total of ∼ 750,000 infrared sources in the aperture photometry catalogs. Photometry is extracted using variable aperture size depending on source crowding. We use a > 5 σ detection threshold, require sources to be detected in both the shorter wavelength IRAC bands, and clean the catalog of various instrumental and data-processing effects. In the study of MYStIX X-ray sources, lower reliability ( > 3 σ ) detections will also be included (the aperture-photometry archive) because the presence of an X-ray counterpart provides corroborating evidence for a sourceÕs legitimacy. We investigate a variety of possible photometric problems empirically by comparing detection rates, fluxes, and flux uncertainties for the aperture photometry catalogs to other available catalogs. A particular problem we encounter is spurious sources due to nebulosity, which affect all bands, but particularly strongly affect the 5.8 and 8.0 µ m bands. These sources are difficult to eliminate completely through signal-to-noise cuts, although they usually affect detections with 5 < S/N < 10. However, color-color diagrams can be used to separate colors associated with PAH nebulosity from IRE candidate young stars. In addition, spatial completeness limits vary across the field due to strong variation in nebulosity and crowding. Finally, we present MIR color-magnitude and color-color diagrams showing the locus of MYStIX Probable Cluster Members (Broos et al. 2013) in comparison to the field stars. The nine MYStIX regions studied here show considerable differences in the distribution of IRE stars in these plots. The MYStIX project is supported at Penn State by NASA grant NNX09AC74G, NSF grant AST-0908038, and the Chandra ACIS Team contract SV4-74018 (G. Garmire & L. Townsley, Principal Investigators), issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. We thank Marilyn R. Meade and Brian L. Babler for providing us with the reduced images and photometry for W 3. We thank the anonymous referee for closely reading the manuscript and providing useful comments and suggestions. This work is based on observations made with the Spitzer Space Telescope, obtained from the NASA/ IPAC Infrared Science Archive, both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. This research has also made use of SAOImage DS9 software de- veloped by Smithsonian Astrophysical Observatory and NASAÕs Astrophysics Data System Bibliographic Services.","pages":[12,13,14]},{"title":"A. Photometric Aperture Sizes","content":"Larger aperture sizes are favored for stars that are not in crowded regions because they have less Òaperture noise,Ó which is an effect of resampling the pixelated image into the aperture (Shahbaz et al. 1994). This effect can lead to several percent error in flux measurement using our two-pixel apertures, which is independent of source flux. Thus, we use simulations of artificial sources to determine the largest aperture size that will not cause inaccurate flux measurements due to crowding. Using the IRAC PSF 4 , pairs of point sources were simulated with various separation angles (1 to 20 pixels), orientations, and flux differences (10 -3 to 10 3 ), and their photometry was extracted using PHOT to investigate the effect of nearby neighbors on flux measurements. This was performed using the same 2-pixel, 3-pixel, and 4-pixel apertures with 1-pixel-wide background annuluses that were used for the photometric analysis. For each separation angle and difference in difference in flux, the largest aperture (2-pixels, 3-pixels, or 4-pixels) is chosen that keeps contamination from a nearby source < 5% of the true flux; these choices are listed in Table 5 along with the associated error in flux. For sources in the Spitzer catalogs using the 2-pixel aperture, sources with flux errors larger than 10% are flagged and sources with flux errors larger than 100% of the true flux are excluded from the catalog. Getman et al. (2012, / 2.2) has shown that the use of small aperture extraction produces negligible bias in derived magnitudes, but leads to reduced photometric precision. These larger photometric uncertainties are incorporated in the aperture photometry catalogs given in the present paper. Aperture corrections for the 2-pixel, 3-pixel, and 4-pixel apertures are calculated for each field with respect to magnitudes derived for the 14 pixel aperture, which is assumed to contain all the light. Corrections are found by comparing magnitudes for the 14-pixel aperture to the 4-pixel aperture, the 4-pixel aperture to the 3-pixel aperture, and the 4-pixel aperture to the 2-pixel aperture. Typically, bright sources that are not saturated and do not show signs of anomalous magnitudes in either aperture are used, and the correction is the median difference in calculated magnitudes. For IRAC channels 3 and 4, there is an artifact in the PSF of bright sources, so dimmer sources are used for the calibration.","pages":[14]},{"title":"B. Matching Sources from Different IRAC Bands","content":"The matching algorithm is based on the Delaunay triangulation, which is a computationally efficient strategy for identifying neighboring points in a set of points (see review by de Berg et al. 2008). To match sources from two bands, the sets of source positions from the two bands are combined, the Delaunay triangulation is constructed for the union of both sets, and matches are obtained as a subset of edges in the triangulation that join points from both bands and are shorter than a threshold length. In ambiguous cases, preference is given to the smallest separation. Here, we use a matching radius of 2 11 , and match sources in the 4.5, 5.8, and 8.0 µ m bands to the 3.6 µ m band sources. An astrometric correction is applied to the entire field in the 4.5, 5.8, and 8.0 µ m bands based on the median offsets relative to 3 . 6 µ m band positions, and matching is performed again with the improved positions. Right ascensions and declinations are reported for the 3.6 µ m source. The PSF has a similar size for all bands, so it is uncommon for matches to be ambiguous within the IRAC aperture photometry catalogs. Ambiguous matches do commonly occur when comparing IRAC catalogs with UKIRT (King et al. 2013) or C handra (Kuhn et al. 2013, Townsley et al. in preparation) catalogs later in the MYStIX analysis. For this reason, a probabilistic approach to cross-waveband source matching is developed by Naylor et al. (2013). However, occasional intra-IRAC matching errors do arise from matches between real 3.6 and 4.5 µ m point sources to peaks in the nebulosity at 5.8 or 8.0 µ m within the 2 11 radius. These are filtered out using a conservative analysis of the near- and mid-infrared spectral energy distributions later in the MYStIX analysis (Povich et al. 2013).","pages":[15]},{"title":"C. Archive of Lower-Reliability IRAC Sources","content":"For the matching of IR sources to X-ray sources, the MYStIX project makes use of some MIR counterparts that have less-reliable photometry, including measurements with 5 > S/N > 3 and measurements that may be contaminated by bright, neighboring sources. The extra information provided by X-ray selection allows us to take this bifurcated approach to MIR reliability criteria. When we are considering the tens-of-thousands to hundredsof-thousands of MIR sources without X-ray counterparts, rare photometric errors could produce numerous false IRE-star candidates, so the reliability criteria must be strict. In contrast, there are orders-of-magnitude fewer MIR sources with X-ray counterparts Ð which already have a good chance of being young stars by virtue of X-ray emission Ð so rare photometric errors will be less important. The same approach is taken with the GLIMPSE data with respect to the highly reliable GLIMPSE Catalog and the less reliable GLIMPSE Archive. MIR photometry for MYStIX sources that used data from the GLIMPSE Archive or aperture-photometry archive is provided by Broos et al. (2013, their Table 2).","pages":[15,16]},{"title":"REFERENCES","content":"Allen, L. E., Calvet, N., DÕAlessio, P., et al. 2004, ApJS, 154, 363 Balog, Z., Muzerolle, J., Rieke, G. H., et al. 2007, ApJ, 660, 1532 Benjamin, R. A., et al. 2003, PASP, 115, 953 Broos, P. B., Getman, K. V., Povich, M. S., et al. 2013, ApJS, in press Broos, P. S., Townsley, L. K., Feigelson, E. D., et al. 2010, ApJ, 714, 1582 Caramazza, M., Micela, G., Prisinzano, L., et al. 2008, A&A, 488, 211 Chandar, R., Whitmore, B. C., Calzetti, D., et al. 2011, ApJ, 727, 88 Churchwell, E., Babler, B. L., Meade, M. R., et al. 2009, PASP, 121, 213 Currie, T., Lada, C. J., Plavchan, P., et al. 2009, ApJ, 698, 1 de Berg, M., Cheong, O., van Kreveld, M. 2008, Computational Geometry: Algorithms and Applications, (3rd ed.; New York, NY: Springer) Fall, S. M., Chandar, R., & Whitmore, B. C. 2009, ApJ, 704, 453 Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10 Feigelson, E. D., Townsley, L. K., & Broos, P. S. 2013, ApJS, in press Getman, K. V., Feigelson, E. D., Luhman, K. 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A., Indebetouw, R., & Wood, K. 2007, ApJS, 169, 328 Note. Ñ Column 1: Target name. Column 2: Astronomical Object Request number. Column 3: Spitzer program identification number. Column 4: AOR central right ascension and declination for epoch (J2000.0). Column 5: The total area of the AOR field of view. Column 6: Total integration time per pixel for long frames. Column 7: Date of the start of the observation. Note. Ñ Column 1: GLIMPSE source designation. Column 2: A - source is in the GLIMPSE Archive, C - source is in the GLIMPSE Catalog. Columns 3-4: Right ascension and declination for epoch (J2000.0). Columns 5-8: GLIMPSE IRAC magnitudes. Note. Ñ Column 1: Target name. Column 2: Source Designation. Columns 3-4: Right ascension and declination for epoch (J2000.0). Columns 5-8: IRAC magnitudes from aperture photometry. Column 9: Aperture size in pixels used for photometric extraction. Table 3 is published in its entirety in an electronic form. A portion is shown here for guidance regarding its form and content. Note. Ñ Column 1: Target name. Column 2: Galactic coordinates. Column 3: Angular area of IRAC mosaic field of view. Columns 4-7: Completeness limits for catalog sources (bands [3.6], [4.5], [5.8], and [8.0], respectively). Column 8: The number of point sources in the catalog. Note. Ñ For each pair of magnitude difference (first column) and angular separation (first row), the chosen aperture size (in pixels) and the simulated error in flux measurement for that aperture size (rounded to the nearest percentage) are given. Ð 24 Ð","pages":[16,17,20,21,22,23,24]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"Spitzer IRAC observations and stellar photometric catalogs are presented for the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX). MYStIX is a multiwavelength census of young stellar members of twenty nearby ( d < 4 kpc), Galactic, star-forming regions that contain at least one O star. All regions have data available from the Spitzer Space Telescope, consisting of GLIMPSE or other published catalogs for eleven regions and results of our own photometric analysis of archival data for the remaining nine regions. This paper seeks to construct deep and reliable catalogs of sources from the Spitzer images. Mid-infrared study of these regions faces challenges of crowding and high nebulosity. Our new catalogs typically contain fainter sources than existing Spitzer studies, which improves the match rate to Chandra X-ray sources that are likely to be young stars, but increases the possibility of spurious point-source detections, especially peaks in the nebulosity. IRAC color-color diagrams help distinguish spurious detections of nebular PAH emission from the infrared excess associated with dusty disks around young stars. The distributions of sources on the mid-infrared color-magnitude and color-color diagrams reflect differences between MYStIX regions, including astrophysical effects such as stellar ages and disk evolution. Subject headings: methods: data analysis - stars: pre-main-sequence - infrared: stars - planetary systems: protoplanetary disks\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"A Massive Young Star-Forming Complex Study in Infrared and X-ray: Mid-Infrared Observations and Catalogs\",\n \"content\": \"Michael A. Kuhn 1 , Matthew S. Povich 1 , 2 , Kevin L. Luhman 1 , 3 , Konstantin V. Getman 1 , Heather S. Busk 1 , Eric D. Feigelson 1 , 3\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"A significant fraction of star formation activity in the Galaxy occurs in massive starforming complexes, dominated by OB stars and containing thousands of young stars. Studies of the cluster mass function indicate that stars are more likely to be born in rich clusters than in small groups (e.g. Lada & Lada 2003; Fall et al. 2009; Chandar et al. 2011). Because of the importance of such clusters, the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX) constructs a census of stars in twenty of the nearest ( d < 4 kpc), Galactic massive star-forming regions (Feigelson et al. 2013) with the Chandra X-ray Observatory , the Spitzer Space Telescope , and ground based near-infrared (NIR) observatories. Studies in the IR and X-ray provide complementary pictures of populations of new stars in star-forming regions. The infrared (IR) images identify stars with circumstellar disks or infalling envelopes through infrared excess (IRE), but cannot distinguish disk-free cluster members from field stars. Meanwhile, X-ray images can detect both disk-bearing and disk-free stars, although the sensitivity to the former is lower (Getman et al. 2009; Stelzer et al. 2011). Thus, the combination of both X-ray and IR observations provide more complete and less biased samples of complex members than either waveband alone. In this paper, we describe the observations and source catalogs used by the MYStIX project from the Infrared Array Camera (IRAC; Fazio et al. 2004) onboard the Spitzer Space Telescope (Werner et al. 2004). This instrument has four bands centered at 3.6, 4.5, 5.8, and 8.0 µ m, which are useful for identifying IRE stars (e.g. Allen et al. 2004; Hartmann et al. 2005; Robitaille et al. 2006; Gutermuth et al. 2009). We use source catalogs produced by the pipeline of the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE; Benjamin et al. 2003) for nine regions, and we measure new aperture photometry from archival IRAC data for nine regions. We adopt pre-existing IRE star catalogs for two additional regions, the Orion Nebula (Megeath et al. 2012) and the Carina Nebula (Povich et al. 2011). In addition to the data from Spitzer , the MYStIX project includes NIR data obtained by United Kingdom Infra-Red Telescope (King et al. 2013) and the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and X-ray data obtained by the Chandra X-ray Observatory (Kuhn et al. 2013a). The procedures for constructing the combined sample of X-ray selected member, IRE selected members, and spectrally selected OB members is described by Naylor et al. (2013), Povich et al. (2013), and Broos et al. (2013). We describe the available GLIMPSE data (Section 2) and our procedures for analyzing other archival images from IRAC (Section 3). We then discuss the distributions of probable members and field stars on color-magnitude and color-color diagrams (Section 4) and summarize our results (Section 5).\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"2. GLIMPSE Data\",\n \"content\": \"The GLIMPSE survey is a Legacy Science Program of NASAÕs Spitzer Space Telescope to study star formation in the disk of the Milky Way Galaxy (Benjamin et al. 2003; Churchwell et al. 2009). It contains six MYStIX regions Ð the Lagoon Nebula, the Trifid Nebula, NGC 6334, the Eagle Nebula, M 17, and NGC 6357 Ð within the 2 · -wide strip along the Galactic equator (GLIMPSE I and II data releases). Furthermore, Spitzer images and photometry for RCW 38 and NGC 3576 come from the Vela-Carina survey (Majewski et al. 2007), using a similar observing strategy with mosaicking and photometric analysis performed with GLIMPSE pipeline. For the GLIMPSE observations, every position was visited at least twice with 1.2 s integrations. The data-reduction pipeline produces image mosaics (v3.0) and point-source lists (v2.0) for all four IRAC bands, which are publicly available 1 . Photometry is obtained through point response function (PRF) fitting. A 5 σ detection limit is used, corresponding to fluxes 0.2, 0.2, 0.4, and 0.4 mJy in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively (Benjamin et al. 2003). However, the detection sensitivity is lower in nebulous regions, and bright sources or regions with high backgrounds may be saturated. The GLIMPSE Catalog contains the sources with reliability ≥ 99.5%, and the GLIMPSE Archive contains all sources ≥ 5 σ above the background level. The GLIMPSE pipeline was run on a deep, high-dynamic range observation of the W 3 star-forming region (AOR 5050624). This GLIMPSE Catalog (Archive) contains > 10,000 ( > 16,000 sources) shown in Table 2. These data were also reduced using the aperture photometry method ( / 3) to compare results from the two methodologies.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"3. New IRAC Analysis\",\n \"content\": \"The MYStIX project uses a combination of IRAC data from multiple provenances, as available. In addition to the GLIMPSE data described above, new analysis is performed on archival IRAC data for remaining MYStIX targets Ð the new catalogs have photometry extracted using aperture photometry (hereafter the aperture photometry catalogs) in contrast to GLIMPSE which makes use of PRF-fitting photometry. To guarantee that the MYStIX project has uniform data quality, our analysis includes a method comparison to study the effect of any biases produced by the variation in photometric method. The aperture photometry catalogs contain fainter sources than the GLIMPSE catalogs Ð which is primarily an effect of the longer observations from which the aperture photometry catalogs are derived, rather than an effect of differences in extraction method. This will improve the match rate to Chandra sources that are likely to be young stars, but a greater source density in the MIR catalogs will also increase the chance of incorrect matches (e.g. Naylor et al. 2013). Many such sources can be removed from further studies due to incongruous NIR/MIR photometry (Povich et al. 2013). In addition more extragalactic MIR sources are detected in the deeper catalogs, many of which have extragalactic X-ray counterparts. This is desirable because MIR properties (e.g. [4 . 5] > 13 mag) may help classify an X-ray source as being extragalactic (Harvey et al. 2007; Broos et al. 2013). Extragalactic IR sources without X-ray matches can be filtered out using cuts on the IR color-color diagram (Povich et al. 2013).\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"3.1. Observations\",\n \"content\": \"We obtained publicly available raw IRAC images from the Spitzer Heritage Archive 2 for nine MYStIX regions without GLIMPSE coverage. The target list and details of the Astronomical Observation Requests (AORs) are provided in Table 1. The IRAC field of view is 5 . 1 2 × 5 . 1 2, and various mapping and/or dither strategies were used for the IRAC observation programs included in this analysis. The camera spatial resolutions are FWHM = 1 . 11 6 to 1 . 11 9 from 3.6 to 8.0 µ m. Each field was observed in high dynamic range (HDR) mode where both 0.4 s and 10.4 s exposures are collected to provide unsaturated photometry for both brighter and fainter sources. Observations from different epochs are combined in our analysis. We also analyzed archival data for M 17 and W 3 for comparison to the GLIMPSE data. For M 17 we analyzed images that are deeper than the Spitzer images from the GLIMPSE survey Ð useful for comparing relative sensitivities for the different catalogs. However, for W 3 we analyzed the same deep, archival Spitzer data using both the GLIMPSE and aperture photometry methods Ð useful for investigating biases of different data reduction methodologies.\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"3.2. Mosaics\",\n \"content\": \"The basic calibrated data (BCD) products were created by the Spitzer pipeline. Image reduction and mosaicking was performed via WCSmosaic IDL package (Gutermuth et al. 2008). This procedure uses algorithms developed by the IRAC instrument team to mitigate image artifacts, such as jailbar, pulldown, muxbleed, and banding (Hora et al. 2004; Pipher et al. 2004). Long and short frames were merged to create an HDR mosaic for each target, and corrections are applied including cosmic ray identification, distortion corrections in each frame, derotation and subpixel offsetting, and background matching. Sub-pixel sampling was performed using the dithered images. The pixel size of the reduced mosaics is 0 . 11 86 × 0 . 11 86, which is 1 / √ 2 the native pixel width. Mosaicked images of two sample targets Ð W 40 and NGC 2264 Ð are shown in Figure 1 in 3.6 and 8.0 µ m bands. These examples demonstrate some of the variety of MYStIX regions in the MIR. For example, the stars in W 40 are centrally concentrated in the region where infrared nebulosity is highest, while the stars in NGC 2264 are divided into a number of subclusters and lie in regions with both high and low nebulosity (Feigelson et al. 2013, Kuhn et al. in preparation). Both regions have large amounts of absorption from dust Ð the dust absorption for W 40 is highest in a dust lane crossing the middle of the hour-glass structure (partially visible in the mosaics as infrared dark clouds), while the most highly absorbed stars in NGC 2264 are in subclusters that are embedded in their natal molecular cloud. The surface density of field stars also varies from region to region depending on the Galactic coordinates Ð W 40, ( l, b ) = (28 . 8 , +03 . 5), has a particularly high surface density, while the Flame Nebula, ( l, b ) = (206 . 5 , -16 . 4), has a much lower density. Several MYStIX regions, like NGC 2362, have almost no nebulosity around the star clusters because most of the molecular material has been removed.\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"3.3. Point-Source Photometry\",\n \"content\": \"The data reduction makes use of photometric procedures from Luhman et al. (2008a, 2008b, 2010), software from the Image Reduction and Analysis Facility (IRAF), codes from the IDL Astronomy Users Library (Landsman 1993), and visualization software from Broos et al. (2010). The methods are modified for the MYStIX regions, which are more distant, and have higher stellar crowding and nebulosity than the Taurus and Chamaeleon star forming regions treated by Luhman and colleagues. These modified methods have also been used by Getman et al. (2012) in their study of the IC 1396A star-forming region. Source detection was performed on mosaicked images using the IRAF task STARFIND. Some spurious detections appear in these initial lists, including statistically insignificant sources, IRAC image artifacts, the point-spread-function (PSF) wings of bright sources, and extended sources. The extended sources include peaks in the nebulosity, which are particularly prevalent in regions with bright, complex nebulosity, particularly in the 5.8 and 8.0 µ m bands. Several strategies are used later to filter out unreliable sources. However, sources with bad or saturated pixels and duplicate detections are removed immediately. Aperture photometry was performed on mosaicked images using the IRAF task PHOT. The targets lie near the Galactic plane and are crowded by field stars, so photometry is calculated for several small aperture sizes: 2-pixel (1.7 11 ), 3-pixel (2.6 11 ), 4-pixel (3.5 11 ), and 14-pixel (12.1 11 ) radii with an adjoining background annuli 1 pixel (0.86 11 ) in width. The aperture/background sizes were chosen in accordance with the strategy of Lada et al. (2006), Luhman et al. (2008), Getman et al. (2009), and Getman et al. (2012); the latter finding no evident improvement in photometry using a ÒstandardÓ 4-pixel-wide background instead of a 1-pixel-wide background used here. The zero-point IRAC magnitudes for the 14-pixel aperture are from Reach et al. (2005): ZP = 19.670, 18.921, 16.855, and 17.394 in the 3.6, 4.5, 5.8, and 8.0 µ m bands, where M = -2 . 5 log(DN / sec) + ZP. Aperture corrections for the other apertures are 0.640 -0.016, 0.725 -0.012, 0.968 -0.030, and 0.955 -0.040 for the 2 pixel aperture; 0.384 -0.011, 0.298 -0.010, 0.474 -0.033, 0.699 -0.031, for the 3 pixel aperture; 0.175 -0.011, 0.169 -0.010, 0.144 -0.021, and 0.222 -0.025 for the 4 pixel aperture in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Aperture sizes of 2, 3, or 4 pixels were assigned to each source depending on the crowding so that the error in flux is minimized. Calculation of aperture corrections, choice of apertures, and identification of crowded sources are discussed in Appendix A. A cross-correlated IRAC catalog was generated from the four bands, using a threshold of 2 11 for matching (see Appendix B). To ensure the quality of the aperture photometry catalog in Table 3, only > 5 σ detections are reported and every object must be detected in both 3.6 and 4.5 µ m bands to be included. Sources with high levels of contamination from a neighboring source ( > 100% of the source flux) are excluded. An archive of the less reliable sources detected at > 3 σ is also preserved (see Appendix C).\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"3.4. IRAC Source Lists\",\n \"content\": \"Table 3 presents the aperture photometry catalog for the nine MYStIX fields analyzed here. Columns in Table 3 include positions, IRAC band magnitudes and their uncertainties, and aperture size flags. The uncertainty incorporates the statistical uncertainty calculated by aperture photometry, added in quadrature to a ∼ 0.02 mag uncertainty in the calibration of IRAC (Reach et al. 2005), and a ∼ 0.01 mag uncertainty in the aperture correction. YSO variability of ∼ 0.05 mag to ∼ 0.2 mag may contribute to photometric scatter from one observation to another (Morales-Calder«on et al. 2009). The aperture flag indicates which photometric aperture size is used and whether errors due to crowding exceed 10% of the flux in the 3.6 µ m band. Table 4 summarizes the aperture photometry and GLIMPSE catalogs for each region Ð the total number of sources is given in Column 8. Variation in number of sources is strongly related to the size of the field of view (Column 3), its Galactic coordinates (Column 2), and the depth of the observation. Of the aperture photometry sources, only 25% are detected in the 5.8 µ m band and 18% are detected in the 8.0 µ m band (14% are detected in both bands). The distribution of aperture sizes is: 13% use 4 pixels, 11% use 3 pixels, and 76% use 2 pixels (43% of catalog sources have flags indicating crowding).\",\n \"pages\": [\n 6,\n 7\n ]\n },\n {\n \"title\": \"3.4.1. Completeness Limits\",\n \"content\": \"Photometric reliability and completeness are spatially variable in regions with bright, structured background. Histograms of source flux provide a rough estimate of spatial completeness due to the sharp turnover beyond the completeness limit. The histograms of IRAC magnitudes for each field are shown in Figure 2 with bin widths of 0.2 mag. The completeness limits, estimated to be the center for the bin preceding the bin with the most sources, are listed in Table 4. However, these values do not hold where there is high nebulosity. For a typical field Ð a cluster age of 2 Myr, a distance of 2 kpc, and a completeness limit of [3 . 6] c = 16 . 0 Ð disk-free members would be detectible down to ∼ 0.1 M 8 in regions with low nebulosity for the pre-main-sequence models of Siess et al. (1997). Completeness limits for IRE sources may occur at lower magnitudes due to selection effects when multiple bands and their errors are combined.\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"3.4.2. Photometric Quality in Comparison to GLIMPSE\",\n \"content\": \"It is helpful to compare the aperture photometry to the GLIMPSE photometry to examine how the various MIR challenges in MYStIX regions, such as nebulosity and crowding, affect the catalogs. For comparative purposes, aperture photometry catalogs were produced for W 3 using the same deep HDR data used by GLIMPSE, and for M 17 using a deeper observation than GLIMPSE (see Table 1). The aperture photometry catalog for W 3 is sensitive to ∼ 1 magnitude deeper than GLIMPSE. More than 90% of GLIMPSE W 3 sources are detected at > 5 σ by our aperture photometry method, and many of the undetected sources are the dimmer components of close double sources. Figure 3 shows difference in measurements of magnitude for the two W 3 catalogs. As expected, scatter increases with magnitude: the root mean square (RMS) 3.6 µ m band residuals are 0.06 mag for bright sources ([3 . 6] < 12 mag) and 0.17 mag for dim sources ([3 . 6] > 12 mag). There is also a slight systematic shift in the 3.6 µ m band of +0 . 01 mag for bright sources and +0 . 05 mag for dim sources. Overall, the RMS residuals are 0.17 mag, 0.18 mag, 0.21 mag, and 0.22 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Furthermore, the scatter increases for smaller aperture sizes: in the 3.6 µ m band for sources with [3 . 6] < 12 mag the RMS residuals are 0.05 mag for 4 pixels, 0.06 mag for 3 pixels, 0.10 mag for 2 pixels (without high crowding or 0.14 for 2 pixels with high crowding). This is consistent with the aperture comparisons in the IC 1396A field performed by Getman et al. (2012). Similar trends are seen in for M 17 (Figure 4), for which we compare aperture photometry of HDR observation of M 17 to the shallower GLIMPSE survey data. For bright sources ([3 . 6] < 12 mag) the RMS residuals are 0.14 mag, 0.13 mag, 0.22 mag, and 0.29 mag, and for dim sources ([3 . 6] > 12 mag), these are 0.22 mag, 0.23 mag, 0.33 mag, and 0.50 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. For bright sources ([3 . 6] < 12 mag) in the two M 17 catalogs, 95% of the photometry is within 0.2 mag in the 3.6 µ m band, which drops to 85% for the 8.0 µ m band. For dim sources, the consistency is ∼ 73% for the 3.6 µ m band, dropping to ∼ 68% for the 8.0 µ m band. A comparison of Figures 3 and 4 shows significantly more scatter for M 17 than for W 3; this is due to the shallowness of the M 17 GLIMPSE observation, which demonstrates, not only the benefits of the deeper HDR observations, but that the effect of net exposure duration is more important than any bias due to different photometry extraction methods in MYStIX. Figure 5 shows a band-by-band comparison of signal-to-noise from the two W 3 catalogs. Sources that are in one catalog but not in the other are also indicated. As expected, the aperture photometry catalog includes somewhat more sources with low signal-to-noise (5 < S/N < 10) than in the GLIMPSE Catalog. For sources in both catalogs, the signal-to-noise values lie near y = x (for the 3.6 and 4.5 µ m bands, signal-to-noise from aperture photometry is on average 1.5 times smaller) but can vary by a factor of ∼ 2. In Figure 5, the overlap between the catalogs decreases with increasing wavelength bands, with most sources in common in the 3.6 µ m band and fewest in the 8.0 µ m band. This may be an effect of marginally detectable sources in the nebulous and crowded W 3 region; detection sensitivity decreases with longer wavelength bands due to lower efficiency of the detectors, less photospheric flux, and higher nebulosity. Both GLIMPSE catalogs and the aperture photometry catalogs may capture only a fraction of the sources near the sensitivity limit, but the sources that are detected are not necessarily the same sources. Sources that are likely to be spurious detections of nebulosity (see / 3.5) are also indicated. Many of these are have low signal-to-noise (particularly sources not detected by GLIMPSE); however, a few have high signal-to-noise values.\",\n \"pages\": [\n 7,\n 8,\n 9\n ]\n },\n {\n \"title\": \"3.5. Contamination by Nebulosity\",\n \"content\": \"The 3.6, 5.8, and 8.0 µ m bands are tuned to emission bands of polycyclic aromatic hydrocarbons (PAH; Reach et al. 2006) excited by the ultraviolet light of OB stars in the MYStIX fields. This results in extremely bright nebulosity in these bands when observing massive star-forming complexes. This nebulosity is often similar in surface brightness to young stars at the resolution of Spitzer , making it difficult to distinguish between point sources and contaminants due to confusion. Ideally, peaks in the nebulosity should be filtered out by STARFIND using the source profile, but this often fails, and this judgement is often difficult to make by eye as well. The level of nebulosity ranges from almost none in NGC 2362 to levels at which IRAC point-source photometry is impossible. In Figure 1, the 8 µ m nebular emission can be seen to be higher in W 40 than in NGC 2264. For the regions with most nebulosity, including W 40, RCW 36, and W 3, source detection sensitivity can be severely limited. Nebular contamination may result in two types of spurious entries in the aperture photometry catalog: patches of nebulosity with emission in all four bands that mimic stars, and false matches between stellar sources in the 3.6 and 4.5 µ m bands and nebular patches in the 5.8 and 8.0 µ m bands. These effects are also present in GLIMPSE (Povich et al. 2013), but are more prevalent here due to both the improved identification of extended sources using GLIMPSEÕs PSF fitting and the higher sensitivity of our aperture extraction method. Selecting sources with high signal-to-noise (reported in Table 3) can produce lists of more reliable sources, since nebulous sources are likely to have background extraction with greater pixel-to-pixel variation. However, nebulous sources can occasionally have small measurement errors because these sources can be very bright. Nebulosity at 5.8 or 8.0 µ m can make a source appear red, but the colors are distinct from the colors of young stellar objects. The [4.5]-[5.8] vs. [5.8]-[8.0] diagram can be used to separate these sources from stellar sources (Povich et al. 2013). In Figure 6 this diagram is shown for NGC 2264 and W 40, with sources color-coded by signal-to-noise < 10 (green) and > 10 (black). This plot includes only sources with photometric data in all four bands, which is the minority of MYStIX MIR sources, and is strongly biased toward IRE sources or sources with nebulosity in the 5.8 and 8.0 µ m bands. Stars without IRE are centered near (0,0) on the diagram, while stars with IRE are shifted slightly to the upper right. However, there is another population with [4 . 5] -[8 . 0] ≥ 1 . 6 and [5 . 8] -[8 . 0] ≥ 0 . 5 that are likely due to nebulosity (Povich et al. 2013). Nearly all of these sources have S/N < 10 σ in at least one band. However, a number of low signal-to-noise sources also have colors consistent with stellar photospheres or young stellar objects. Figure 7 shows the 8.0 µ m sources from the aperture photometry catalog and from the literature plotted on the 8.0 µ m image for NGC 2264 (Sung et al. 2009), NGC 2362 (Currie et al. 2009), Rosette (Balog et al. 2007), and NGC 1893 (Caramazza et al. 2008). In this comparison there are examples of detections in the aperture photometry catalog that are not in theirs and vice versa. It is difficult to determine through visual inspection of the 8 µ m images which of these are real. The X-ray sources from Kuhn et al. (2013a) are also plotted Ð most of which are young stars Ð and these show that many of the new 8 µ m sources found from aperture photometry coincide with X-ray sources. This phenomenon is particularly strong for NGC 1893, which has a long X-ray exposure but is distant, so many of the young stars are near the detection threshold in the MIR. Thus, we gain many new MIR counterparts for cluster members by using these more sensitive catalogs.\",\n \"pages\": [\n 9,\n 10\n ]\n },\n {\n \"title\": \"4. Classes of MIR Sources\",\n \"content\": \"The MYStIX MIR catalogs include young stellar members of the star-forming complex (with and without IRE), non-member point sources (field stars, extragalactic sources, shock emission), and spurious sources. MYStIX IRE Sources (MIRES; Povich et al. 2013) are identified using the MIR and NIR photometry, and a list of MYStIX Probable Complex Members (MPCM; Broos et al. 2013) is generated using X-ray selected members, IRE selected members, and spectroscopic OB stars. The distributions of these classes of sources on the MIR color-magnitude and color-color diagrams can give insight into how the MYStIX census is affected by the MIR catalog properties Ð properties such as the completeness limits, uncertainties on photometry, and spurious sources. Furthermore, these diagrams reveal global differences from region to region in terms of member populations, disk evolution, and star-formation environments.\",\n \"pages\": [\n 10\n ]\n },\n {\n \"title\": \"4.1. MIR Color-Magnitude Diagram\",\n \"content\": \"Figure 8 shows the [3 . 6] vs. [3 . 6] -[4 . 5] diagrams for the nine regions analyzed here. The distributions of disk-free MPCMs (green circles) and MIRES sources (red circles) are plotted along with unclassified MIR sources (grey points). The A K = 2 reddening vector points to the lower right. Selection effects such as the size of the sample, the completeness limit, and larger photometric uncertainties for faint points can be seen for each region. The locus of disk-free members overlaps with the locus of field stars, and the 3.6 µ m band magnitude relates to stellar mass. In older or more distant regions, the dereddened, disk-free isochrones are shifted downwards on the plot (e.g. Roccatagliata et al. 2011, their Figure 7). The MYStIX MIR catalogs are typically deeper than the MYStIX X-ray catalogs, so X-ray selected MPCMs have a lower 3.6 µ m band magnitude completeness limit. There is a population of stars that shows [3 . 6] -[4 . 5] excess on this diagram, many of which are identified as IRE sources in the MIRES catalog (red circles). However, the distribution of these sources varies from region to region. In some cases there are many sources with [3 . 6] -[4 . 5] > 1 . 5 (including NGC 2264, Rosette, and DR 21) while for other cases nearly all IRE sources have [3 . 6] -[4 . 5] < 1 . 0 (including NGC 2362, W 4, and NGC 1893). Other fields (like Flame, W 40, and RCW 36) are intermediate. NGC 2264, Rosette, and DR 21 all have young embedded clusters, while the clusters in NGC 2362, W 4, and NGC 1893 are mostly lightly absorbed. The sources with [3 . 6] -[4 . 5] > 1 . 5 are mostly clustered within the embedded clusters identified by (Kuhn et al. in preparation). The different distributions of [3 . 6] -[4 . 5] colors for different regions is primarily due to effects of IRE emission rather than reddening from dust. It would require ∼ 100 mag of absorption in the V band to cause a reddening of 1 mag in [3 . 6] -[4 . 5], and most of the cluster members in our sample do not have this much reddening (Povich et al. 2013; Broos et al. 2013). Therefore, the larger [3 . 6] -[4 . 5] excesses in some regions is likely to be an age effect of disk evolution.\",\n \"pages\": [\n 11\n ]\n },\n {\n \"title\": \"4.2. MIR Color-Color Diagram\",\n \"content\": \"Figure 9 shows the [3.6]-[4.5] vs. [4.5]-[8.0] color-color diagram for sources in the Rosette Nebula. Here, the reddening vector is nearly vertical, and IRE from disks or envelopes appears as an excess in both colors. Sources contaminated by PAH nebulosity will have large [4.5]-[8.0] values but [3.6]-[4.5] colors near or below 0, so they can be distinguished from young stars. There are a variety of possible cuts on the color-color diagram that are designed to identify young stars, and the IRE selection polygon from Simon et al. (2007) is shown as an example that uses this color-color plot. But, the IRE sources found by Povich et al. (2013) in the MYStIX IR catalogs are a somewhat different set of sources than are found using the other schemes 3 . Figure 10 shows color-color diagrams for each region with points color-coded by results of the classification done by Povich et al. (2013) and Broos et al. (2013), which includes cluster members with and without IRE in addition to various types of contaminants and spurious sources. Reddened stellar photosphere fitting may quickly remove a large fraction of IR catalog sources from a list of possible IRE stars and relies on well understood field-star photospheric models. The procedures for fitting these stars using photometry in seven NIR and MIR bands are described in Povich et al. (2013). Some of the sources rejected for being insignificantly different from the reddened photospheric model (shown in black in Figure 10) would have been selected as IRE stars by the color cuts from Simon et al. (2007). The color-color polygon used by Simon et al. (2007), and other color-based decision trees, have both false positives and false negatives with respect to the more elaborate analysis of the infrared spectral energy distributions by Povich et al. (2013) for the MYStIX analysis. Many of the stars lying in the polygon do not satisfy the more conservative criteria for disk-bearing young stars adopted by Povich et al. These sources may often be nebular (rather than stellar) sources in the 8.0 µ m band, as they are more common in the W 40 and DR 21 where the PAH contamination is high. The MPCM source lists also show a small population of disk-free stars (green circles in Figure 10) with MIR colors likely to arise from PAH nebulosity. These may be faulty matches between true X-ray sources and spurious MIR PAH sources.\",\n \"pages\": [\n 11,\n 12\n ]\n },\n {\n \"title\": \"5. Summary\",\n \"content\": \"This work describes the Spitzer IRAC observations and source catalogs that will be used by the MYStIX project. These data include nine regions where archival data is available, and we perform aperture photometry on the HDR observations. The MYStIX MIR catalogs will be combined with X-ray (Kuhn et al. 2013, Townsley et al. in preparation) and NIR (King et al. 2013) for a multiwavelength study of star formation in massive young starforming complexes (Feigelson et al. 2013; Naylor et al. 2013; Povich et al. 2013; Broos et al. 2013). The aperture photometry catalogs are typically deeper and have higher photometric precision than typical GLIMPSE fields or other available catalogs of the same regions. In addition, the MYStIX project makes use of the GLIMPSE photometry for ten regions (including a deep catalog for W 3 presented here). Furthermore, the MYStIX study of the Orion Nebula and Carina Nebula uses stellar membership censuses from the literature, and we do not reanalyze Spitzer data for these regions. There are a total of ∼ 750,000 infrared sources in the aperture photometry catalogs. Photometry is extracted using variable aperture size depending on source crowding. We use a > 5 σ detection threshold, require sources to be detected in both the shorter wavelength IRAC bands, and clean the catalog of various instrumental and data-processing effects. In the study of MYStIX X-ray sources, lower reliability ( > 3 σ ) detections will also be included (the aperture-photometry archive) because the presence of an X-ray counterpart provides corroborating evidence for a sourceÕs legitimacy. We investigate a variety of possible photometric problems empirically by comparing detection rates, fluxes, and flux uncertainties for the aperture photometry catalogs to other available catalogs. A particular problem we encounter is spurious sources due to nebulosity, which affect all bands, but particularly strongly affect the 5.8 and 8.0 µ m bands. These sources are difficult to eliminate completely through signal-to-noise cuts, although they usually affect detections with 5 < S/N < 10. However, color-color diagrams can be used to separate colors associated with PAH nebulosity from IRE candidate young stars. In addition, spatial completeness limits vary across the field due to strong variation in nebulosity and crowding. Finally, we present MIR color-magnitude and color-color diagrams showing the locus of MYStIX Probable Cluster Members (Broos et al. 2013) in comparison to the field stars. The nine MYStIX regions studied here show considerable differences in the distribution of IRE stars in these plots. The MYStIX project is supported at Penn State by NASA grant NNX09AC74G, NSF grant AST-0908038, and the Chandra ACIS Team contract SV4-74018 (G. Garmire & L. Townsley, Principal Investigators), issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. We thank Marilyn R. Meade and Brian L. Babler for providing us with the reduced images and photometry for W 3. We thank the anonymous referee for closely reading the manuscript and providing useful comments and suggestions. This work is based on observations made with the Spitzer Space Telescope, obtained from the NASA/ IPAC Infrared Science Archive, both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. This research has also made use of SAOImage DS9 software de- veloped by Smithsonian Astrophysical Observatory and NASAÕs Astrophysics Data System Bibliographic Services.\",\n \"pages\": [\n 12,\n 13,\n 14\n ]\n },\n {\n \"title\": \"A. Photometric Aperture Sizes\",\n \"content\": \"Larger aperture sizes are favored for stars that are not in crowded regions because they have less Òaperture noise,Ó which is an effect of resampling the pixelated image into the aperture (Shahbaz et al. 1994). This effect can lead to several percent error in flux measurement using our two-pixel apertures, which is independent of source flux. Thus, we use simulations of artificial sources to determine the largest aperture size that will not cause inaccurate flux measurements due to crowding. Using the IRAC PSF 4 , pairs of point sources were simulated with various separation angles (1 to 20 pixels), orientations, and flux differences (10 -3 to 10 3 ), and their photometry was extracted using PHOT to investigate the effect of nearby neighbors on flux measurements. This was performed using the same 2-pixel, 3-pixel, and 4-pixel apertures with 1-pixel-wide background annuluses that were used for the photometric analysis. For each separation angle and difference in difference in flux, the largest aperture (2-pixels, 3-pixels, or 4-pixels) is chosen that keeps contamination from a nearby source < 5% of the true flux; these choices are listed in Table 5 along with the associated error in flux. For sources in the Spitzer catalogs using the 2-pixel aperture, sources with flux errors larger than 10% are flagged and sources with flux errors larger than 100% of the true flux are excluded from the catalog. Getman et al. (2012, / 2.2) has shown that the use of small aperture extraction produces negligible bias in derived magnitudes, but leads to reduced photometric precision. These larger photometric uncertainties are incorporated in the aperture photometry catalogs given in the present paper. Aperture corrections for the 2-pixel, 3-pixel, and 4-pixel apertures are calculated for each field with respect to magnitudes derived for the 14 pixel aperture, which is assumed to contain all the light. Corrections are found by comparing magnitudes for the 14-pixel aperture to the 4-pixel aperture, the 4-pixel aperture to the 3-pixel aperture, and the 4-pixel aperture to the 2-pixel aperture. Typically, bright sources that are not saturated and do not show signs of anomalous magnitudes in either aperture are used, and the correction is the median difference in calculated magnitudes. For IRAC channels 3 and 4, there is an artifact in the PSF of bright sources, so dimmer sources are used for the calibration.\",\n \"pages\": [\n 14\n ]\n },\n {\n \"title\": \"B. Matching Sources from Different IRAC Bands\",\n \"content\": \"The matching algorithm is based on the Delaunay triangulation, which is a computationally efficient strategy for identifying neighboring points in a set of points (see review by de Berg et al. 2008). To match sources from two bands, the sets of source positions from the two bands are combined, the Delaunay triangulation is constructed for the union of both sets, and matches are obtained as a subset of edges in the triangulation that join points from both bands and are shorter than a threshold length. In ambiguous cases, preference is given to the smallest separation. Here, we use a matching radius of 2 11 , and match sources in the 4.5, 5.8, and 8.0 µ m bands to the 3.6 µ m band sources. An astrometric correction is applied to the entire field in the 4.5, 5.8, and 8.0 µ m bands based on the median offsets relative to 3 . 6 µ m band positions, and matching is performed again with the improved positions. Right ascensions and declinations are reported for the 3.6 µ m source. The PSF has a similar size for all bands, so it is uncommon for matches to be ambiguous within the IRAC aperture photometry catalogs. Ambiguous matches do commonly occur when comparing IRAC catalogs with UKIRT (King et al. 2013) or C handra (Kuhn et al. 2013, Townsley et al. in preparation) catalogs later in the MYStIX analysis. For this reason, a probabilistic approach to cross-waveband source matching is developed by Naylor et al. (2013). However, occasional intra-IRAC matching errors do arise from matches between real 3.6 and 4.5 µ m point sources to peaks in the nebulosity at 5.8 or 8.0 µ m within the 2 11 radius. These are filtered out using a conservative analysis of the near- and mid-infrared spectral energy distributions later in the MYStIX analysis (Povich et al. 2013).\",\n \"pages\": [\n 15\n ]\n },\n {\n \"title\": \"C. Archive of Lower-Reliability IRAC Sources\",\n \"content\": \"For the matching of IR sources to X-ray sources, the MYStIX project makes use of some MIR counterparts that have less-reliable photometry, including measurements with 5 > S/N > 3 and measurements that may be contaminated by bright, neighboring sources. The extra information provided by X-ray selection allows us to take this bifurcated approach to MIR reliability criteria. When we are considering the tens-of-thousands to hundredsof-thousands of MIR sources without X-ray counterparts, rare photometric errors could produce numerous false IRE-star candidates, so the reliability criteria must be strict. In contrast, there are orders-of-magnitude fewer MIR sources with X-ray counterparts Ð which already have a good chance of being young stars by virtue of X-ray emission Ð so rare photometric errors will be less important. The same approach is taken with the GLIMPSE data with respect to the highly reliable GLIMPSE Catalog and the less reliable GLIMPSE Archive. MIR photometry for MYStIX sources that used data from the GLIMPSE Archive or aperture-photometry archive is provided by Broos et al. (2013, their Table 2).\",\n \"pages\": [\n 15,\n 16\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Allen, L. E., Calvet, N., DÕAlessio, P., et al. 2004, ApJS, 154, 363 Balog, Z., Muzerolle, J., Rieke, G. H., et al. 2007, ApJ, 660, 1532 Benjamin, R. A., et al. 2003, PASP, 115, 953 Broos, P. B., Getman, K. V., Povich, M. S., et al. 2013, ApJS, in press Broos, P. S., Townsley, L. K., Feigelson, E. 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T., Allen, L., et al. 2005, ApJ, 629, 881 Harvey, P., Mer«õn, B., Huard, T. L., et al. 2007, ApJ, 663, 1149 Hora, J. L., Fazio, G. G., Allen, L. E., et al. 2004, Proc. SPIE, 5487, 77 Indebetouw, R., Mathis, J. S., Babler, B. L., et al. 2005, ApJ, 619, 931 King, R. R., Naylor, T., Broos, P. S., Getman, K. V., & Feigelson, E. D. 2013, ApJS, in press Kuhn, M. A., Getman, K. V., Broos, P. B., Townsley, L. K, & Feigelson, E. D. 2013, ApJS, in press Kuhn, M. A., Getman, K. V., Feigelson, E. D., et al. 2010, ApJ, 725, 2485 Lada, C. J. & Lada, E. A. 2003, ARA&A, 41, 57 Lada, C. J., Muench, A. A., Luhman, K. L., et al. 2006, AJ, 131, 1574 Landsman, W. B. 1993, Astronomical Data Analysis Software and Systems II, 52, 246 Luhman, K. L., Allen, L. E., Allen, P. R., et al. 2008, ApJ, 675, 1375 Luhman, K. L., Allen, P. R., Espaillat, C., Hartmann, L., & Calvert, N. 2010, ApJS, 186, 111 Luhman, K. L. & Muench, A. A. 2008, ApJ, 684, 654 Majewski, S., Babler, B., Churchwell, E., et al. 2007, Spitzer Proposal, 40791 Megeath, S. T., Gutermuth, R., Muzerolle, J., et al. 2012, AJ, 144, 192 Morales-Calder«on, M., Stauffer, J. R., Rebull, L., et al. 2009, ApJ, 702, 1507 Naylor, T., Broos, P. S., & Feigelson, E. D. 2013, ApJS, submitted Pipher, J. L., McMurtry, C. W., Forrest, W. J., et al. 2004, Proc. SPIE, 5487, 234 Povich, M. S., Kuhn, M. A., Getman, K. V., et al. 2013, ApJS, in press Povich, M. S., Smith, N., Majewski, S. R., et al. 2011, ApJS, 194, 14 Reach, W. T., Megeath, S. T., Cohen, M., et al. 2005, PASP, 117, 978 Reach, W. T., Rho, J., Tappe, A., et al. 2006, AJ, 131, 1479 Robitaille, T. P., Whitney, B. A., Indebetouw, R., & Wood, K. 2007, ApJS, 169, 328 Note. Ñ Column 1: Target name. Column 2: Astronomical Object Request number. Column 3: Spitzer program identification number. Column 4: AOR central right ascension and declination for epoch (J2000.0). Column 5: The total area of the AOR field of view. Column 6: Total integration time per pixel for long frames. Column 7: Date of the start of the observation. Note. Ñ Column 1: GLIMPSE source designation. Column 2: A - source is in the GLIMPSE Archive, C - source is in the GLIMPSE Catalog. Columns 3-4: Right ascension and declination for epoch (J2000.0). Columns 5-8: GLIMPSE IRAC magnitudes. Note. Ñ Column 1: Target name. Column 2: Source Designation. Columns 3-4: Right ascension and declination for epoch (J2000.0). Columns 5-8: IRAC magnitudes from aperture photometry. Column 9: Aperture size in pixels used for photometric extraction. Table 3 is published in its entirety in an electronic form. A portion is shown here for guidance regarding its form and content. Note. Ñ Column 1: Target name. Column 2: Galactic coordinates. Column 3: Angular area of IRAC mosaic field of view. Columns 4-7: Completeness limits for catalog sources (bands [3.6], [4.5], [5.8], and [8.0], respectively). Column 8: The number of point sources in the catalog. Note. Ñ For each pair of magnitude difference (first column) and angular separation (first row), the chosen aperture size (in pixels) and the simulated error in flux measurement for that aperture size (rounded to the nearest percentage) are given. Ð 24 Ð\",\n \"pages\": [\n 16,\n 17,\n 20,\n 21,\n 22,\n 23,\n 24\n ]\n }\n]"}}},{"rowIdx":83,"cells":{"bibcode":{"kind":"string","value":"2013AsBio..13.1030K"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1212.4710.pdf"},"content":{"kind":"string","value":"\nXUV exposed, non-hydrostatic hydrogen-rich upper atmospheres of terrestrial planets II: Hydrogen coronae and ion escape\nKristina G. Kislyakova 1,2 , Helmut Lammer 1 , Mats Holmström 3 , Mykhaylo Panchenko 1 , Petra Odert 1,2 , Nikolai V. Erkaev 4 , Martin Leitzinger 2 , Maxim L. Khodachenko 1 , Yuri N. Kulikov 5 , Manuel Güdel 6 , Arnold Hanslmeier 2\n1\nAustrian Academy of Sciences, Space Research Institute,\nSchmiedlstr. 6, A-8042 Graz, Austria (kristina.kislyakova@oeaw.ac.at, maxim.khodachenko@oeaw.ac.at, helmut.lammer@oeaw.ac.at, petra.odert@oeaw.ac.at, mykhaylo.panchenko@oeaw.ac.at) 2 Institute for Physics, University of Graz, Universitätsplatz 5, A-8010 Graz, Austria (martin.leitzinger@uni-graz.at, arnold.hanslmeier@uni-graz.at) 3 Swedish Institute of Space Physics, P.O. Box 812, SE-98128 Kiruna, Sweden (matsh@irf.se) 4 Institute of Computational Modelling, Siberian Division of Russian Academy of Sciences, Akademgorodok 28/44 660036 Krasnoyarsk, Russian Federation (erkaev@icm.krasn.ru) 5 Polar Geophysical Institute (PGI), Russian Academy of Sciences, Khalturina Str. 15, Murmansk, 183010, Russian Federation (kulikov@pgi.ru) 6 Institute for Astrophysics, University of Vienna, Türkenschanzstr. 17, 1180, Austria\n(manuel.guedel@univie.ac.at)\nCorresponding Authors: Kristina G. Kislyakova E-mail: kislyakova.kristina@oeaw.ac.at Austrian Academy of Sciences Space Research Institute Schmiedlstr. 6, A-8042 Graz Austria\nSubmitted to ASTROBIOLOGY\nABSTRACT\nWe study the interactions between the stellar wind plasma flow of a typical M star, such as GJ 436, and hydrogen-rich upper atmospheres of an Earth-like planet and a 'superEarth' with the radius of 2 R Earth and a mass of 10 M Earth, located within the habitable zone at ~0.24 AU. We investigate the formation of extended atomic hydrogen coronae under the influences of the stellar XUV flux (soft X-rays and EUV), stellar wind density and velocity, shape of a planetary obstacle (e.g., magnetosphere, ionopause), and the loss of planetary pick-up ions on the evolution of hydrogen-dominated upper atmospheres. Stellar XUV fluxes which are 1, 10, 50 and 100 times higher compared to that of the present-day Sun are considered and the formation of high-energy neutral hydrogen clouds around the planets due to the charge-exchange reaction under various stellar conditions have been modeled. Charge-exchange between stellar wind protons with planetary hydrogen atoms, and photoionization, leads to the production of initially cold ions of planetary origin. We found that the ion production rates for the studied planets can vary over a wide range, from ~ 25 10 0 . 1 s -1 to ~ 30 10 3 . 5 s -1 , depending on the stellar wind conditions and the assumed XUV exposure of the upper atmosphere. Our findings indicate that most likely the majority of these planetary ions are picked up by the stellar wind and lost from the planet. Finally, we estimate the long-time non-thermal ion pick-up escape for the studied planets and compare them with the thermal escape. According to our estimates, non-thermal escape of picked up ionized hydrogen atoms over a planet's lifetime varies between ~0.4 Earth ocean equivalent amounts of hydrogen (EOH) to < 3 EOH and usually is several times smaller in comparison to the thermal atmospheric escape rates.\nKeywords: stellar activity, low mass stars, early atmospheres, Earth-like exoplanets, ENAs, ion escape, habitability\n1. INTRODUCTION\nRecent discoveries of so-called low density 'super-Earths' by various ground- and spacebased exoplanet-transit surveys indicate large populations of volatile-rich big rocky planets. Findings from ESOs High Accuracy Radial velocity Planetary Search project\n(HARPS), and from NASAs Kepler space observatory, revealed that planets which are slightly larger and more massive compared to the Earth may be very common in the Universe. From the available statistics and the discovery of Kepler-22b, a 'super-Earth' with the size of about 2.38 ± 0.13REarth within the habitable zone (HZ) of a Sun-type star, one can expect that planets orbiting within the HZ should be frequent in the Universe and should also orbit cooler, lower mass M dwarfs. Approximately 100 of them are found in the immediate neighborhood of the Sun (Scalo et al. 2007; Bonfils et al. 2011). These earlier estimations are now supported by a recent study by Dressing and Charbonneau (2013), which used optical and near-infrared photometry from the Kepler Input Catalog to estimate the occurrence rate of Earth-like planets orbiting dwarf stars. The estimation of Dressing and Charbonneau (2013), from the 248 early M dwarfs within 10 parsecs of the Sun, shows that there should be at least 9 Earth-size planets in their habitable zones.\nMoreover, from the radius-mass relation and the resulting density of discovered 'super-Earths', one finds that these bodies probably have rocky cores but are surrounded by significant H/He and/or H2O envelopes. These findings are in agreement with recent theoretical studies, which suggest that small planets are not necessarily rocky Earth-like bodies (e.g., Wuchterl 1993; Kuchner 2003; Léger et al . 2004; Ikoma and Hory 2012; Elkins-Tanton 2011; Lammer, 2012; Lammer et al. 2011a). For explaining the mean density of Kepler 11d, Kepler 11e, and Kepler 11f these 'super-Earths'' require dense H/He envelopes, similar to Uranus and Neptune, while Kepler-11b and 11c may have also additional H2O to their H/He gas envelopes (Lissauer et al . 2011), and GJ 1214b (Charbonneau et al. , 2009) or 55Cnc e (Endl et al. , 2012) may contain a huge amount of H2O.\nIf Earth-like and 'super-Earth'- type exoplanets can accumulate hydrogen from the nebula gas of an equivalent amount of 100 to 1000, and even up to 10 4 times, that of an Earth ocean depends on the nebula dissipation time, the formation time of the protoplanet, its luminosity, and nebula characteristics such as grain depletion factors, etc. (e.g., Mizuno et al ., 1978; Hayashi et al ., 1979; Ikoma and Genda, 2006; Rafikov, 2006). Although Solar System planets such as Venus, Earth and Mars lost their nebula-based hydrogen envelopes during the first 100 Myr after their origin, or never accumulated such huge amounts due to step-wise accretion after the nebula gas disappeared, terrestrial\nplanets in other systems evolve under different conditions and may capture such a dense protoatmosphere which they may not lose during the extreme active period of their host stars.\nTo understand how frequent 'rocky' terrestrial planets really are, more observations are certainly needed. From the available statistics one can conclude that Earth-analogue class I habitats (Lammer et al. , 2009a; Lammer, 2013) have to be\n\n-located at the right distance inside the HZ of their host stars,\n-must lose their nebula-captured H/He or degassed H2O and volatile-rich protoatmospheres during the right time period, i.e. not remain as mini-Neptune type bodies,\n-should maintain plate tectonics, liquid water and landmass above the water level over the planet's lifetime,\n\nand\n\n-nitrogen should be the main atmospheric species after the stellar activity decreased to moderate values.\n\nThe question if more massive 'super-Earths' can maintain plate tectonics over time spans of several Gyr is controversial (e.g., Valencia et al. , 2007; van Heck and Tackley, 2011; Korenaga, 2010). However, in this work we will not discuss the pro and contra about geophysical processes, but focus on the stellar wind erosion of captured H/He envelopes, orand? the hydrogen content of outgassed hydrogen-rich steam atmospheres, because the proto-atmosphere escape determines if a planet will evolve to an Earth-like habitat or may remain as a mini-Neptune.\nAs it is shown by Erkaev et al. (2013) (part I of this study), depending on the availability of possible IR-cooling molecules and the planets average density, hydrogenrich 'super-Earths' orbiting inside the HZ will experience hydrodynamic blow-off only for XUV fluxes several 10 times higher compared to today's Sun. Most of their lifetime the upper atmospheres of these planets will experience strong Jeans escape which is still weaker compared to blow-off, so that they may not lose efficiently their dense hydrogen envelopes. Jeans escape is the classical thermal escape mechanism based on the fact that the atmospheric particles have velocities according to the Maxwell distribution. Individual particles in the high tail of the distribution may reach escape velocity at the\nexobase altitude, where the mean free path is comparable to the scale height, so that they can escape from the planet's atmosphere. When the thermosphere temperature rises due to heating by the stellar XUV radiation, the number of these energetic particles increases and the atmosphere finally reaches the state when the majority of the particles have velocities equal to or exceeding the escape velocity. In this case the atmosphere is not hydrostatic anymore, and starts to expand similar to the Parker-type solar corona. This mechanism is called blow-off and leads to a stronger escape in comparison to the Jeans mechanism.\nThe blow-off stage is more easily reached at less massive hydrogen-rich planets with mass equal to that of the Earth. These planets experience hydrodynamic blow-off for much longer, and change from the blow-off regime to the Jeans-type escape for XUV fluxes which are < 10 times of today's Sun. Because of XUV heating and expansion of their upper atmospheres, both of our test planets should produce extended exospheres or hydrogen coronae distributed above possible magnetic obstacles defined by intrinsic or induced magnetic fields. In such cases the hydrogen-rich upper atmosphere will not be protected by possible magnetospheres like on present-day Earth, but could be eroded by the stellar wind plasma flow and lost from the planet in the form of ions (Erkaev et al ., 2005; Lammer et al. , 2007).\nBesides thermal escape from the hydrogen-dominated upper atmosphere of the two considered test-planets (Erkaev et al ., 2013), briefly discussed above, one can expect that non-thermal atmospheric escape processes will also contribute to the losses. Nonthermal escape processes can be separated in ion escape and photochemical, as well as kinetic, processes which accelerate atoms beyond escape energy. Ions can escape from an upper atmosphere if the exosphere is not protected by a strong magnetic field and stretches above the magnetopause. In such a case exospheric neutral atoms can interact with the host stars solar/stellar plasma (i.e., winds, CMEs) environment. The hydrogen atoms which flow upward from the lower thermosphere will be ionized by the stellar radiation, electron impact or charge exchange and then accelerated by electric fields within the solar/stellar wind plasma flow around the planetary obstacle (i.e. ionopause, magnetopause), so that they are finally picked up and lost form the planet's gravity field (e.g., Lammer et al ., 2007; Ma and Nagy, 2007; Lammer, 2013).\nFrom space missions to non- or weakly magnetized planets such as Venus and/or Mars it is known that planetary ions can also be detached from an ionopause by plasma instabilities in the form of ionospheric clouds (Terada et al ., 2002; Penz et al. , 2004; Möstl et al ., 2011), or by momentum transport triggered outflow through the planetary tail. On Earth ions outflow also over Polar Regions along open magnetic field lines (Lundin et al ., 2007; Yau and André, 1997; Wei et al ., 2012).\nFrom the analysis of the available ion escape data from Venus and Mars by the ASPERA instruments on board of Venus Express and Mars Express, as well as from theoretical models, one can conclude that ion pick-up is a very dominant permanently acting non-thermal ion escape process, and most likely more efficient compared to the sporadic losses triggered by plasma instabilities or outflow through the planets tail. However, there may be extreme solar events which can enhance the ion outflow sporadically by cool ion outflow or plasma instabilities.\nNon-thermal escape processes of neutral atoms are caused by sputtering of atmospheric neutral atoms, photochemical processes such as dissociative recombination, and charge exchange. Direct escape by sputtering is only a relevant process for low mass bodies which have a mass ≤ Mars. utHowever, even in the case of Mars one can expect that sputter loss rates are an order of magnitude lower compared for instance to ion pickup (e.g., Leblanc and Johnson, 2002; Chassefière and Leblanc, 2004; Lammer et al ., 2013). Direct escape of heavy neutral atoms, such as O and C, caused by photochemical processes is expected to be higher compared to ion escape from Mars (e.g., Krestyanikova and Shematovich, 2005; Chaufray et al., 2007; 2006; Fox and Hać, 2009; Lammer et al., 2013) but negligible or lower at more massive planets such as Venus (Gröller et al., 2010; 2012) or the Earth.\nLighter atoms such as atomic hydrogen can also escape directly from more massive planets with escape rates lower or comparable to ion escape. Theoretical models which studied the photochemical escape rates of H atoms (Shematovich, 2010) and ion pick-up ion escape rates (Erkaev et al ., 2005) from the hot Jupiter HD 208459b indicate comparable loss rates of the order of ≤ 10 9 g s -1 , which are an order of magnitude lower compared to the modeled thermal escape (e.g., Yelle, 2004; 2006; Tian et al ., 2005a;\nPenz et al ., 2008b; García Muñoz, 2007; Murray-Clay et al. , 2009; Linsky et al ., 2010; Koskinen et al ., 2012).\nFrom the brief overview on various non-thermal atmospheric escape processes, one can conclude that stellar wind induced ion erosion from XUV-heated and extended hydrogen-rich thermospheres (Erkaev et al ., 2013), where H atoms will most likely not be protected by a possible magnetosphere, so-called ion pick-up will be one of the most efficient non-thermal atmospheric escape process. Because of many unknowns related to minor atmospheric species in exoplanet atmospheres, as well as magnetic field properties, a study of more complex but most likely less effective processes, such as cool ion or polar outflow and photochemical non-thermal escape processes which are not even well understood at Solar System planets including the Earth, would yield highly speculative results. Therefore, in this study we focus on the modeling of the stellar wind plasma interaction, related ion production rates via charge-exchange and photoionization, and escape estimates of planetary pick-up ions from XUV exposed upper atmospheres which originate from hydrogen-rich thermospheres of an Earth-like ( R pl=1 R Earth, M pl=1 M Earth) planet in comparison with a 'super-Earth' ( R pl=2 R Earth, M pl=10 M Earth). For reasons of comparative escape studies between thermal and non-thermal ion pick-up, we study the same test planets as investigated by Erkaev et al. (2013) within an orbit of a typical HZ of an M star with the size and mass of ~0.45 R Sun. For the host star of our test planets we use the well observed dwarf star GJ 436 (Ehrenreich et al. , 2011; von Braun et al. , 2012, France et al. , 2012) as a proxy.\nSo far the formation of such extended hydrogen coronae was only addressed in a brief way in Lammer et al. (2011a; 2011b), but never modeled in detail. In this study we apply a coupled Direct Simulation Monte Carlo (DSMC) upper atmosphere - stellar wind plasma interaction model (Holmström et al. , 2008; Ekenbäck et al. , 2010) to the results of Erkaev et al. (2012).\nIn Sect. 2 we describe the DSMC model, which is used for the calculation of the exosphere and related hydrogen coronae, as well as the coupled solar/stellar wind plasma upper atmosphere interaction model. We validate our model by applying it to the Earth's geocorona and comparing the simulation results with the present-day exosphere hydrogen density and energetic neutral atom (ENA) observations by NASAs Interstellar Boundary\nExplorer (IBEX) satellite near the magnetopause boundary at ~10 R Earth. After validating our model for the geocorona of present-day Earth, in Sect. 3 we describe the radiation and plasma parameters of our chosen M-type host star proxy, Gliese 436. In Sect. 4 we present the modeling results for the extended hydrogen coronae. In Sect. 4.1 the results of the stellar wind plasma interaction and the production of ENAs are shown as well as related planetary hydrogen ion pick-up escape rates as a function of the XUV flux values from 1 to 100 times that of today's Sun. The atmospheric ion escape rates are compared with the thermal hydrogen neutral loss rates modeled by Erkaev et al. (2012) in Section 4.2. In Section 4.3 we estimate the possible mass loss of hydrogen ions during the planetary lifetime and discuss the implications of our findings for the evolution of Earthlike and more massive 'super-Earths'. Section 5 summarizes the findings of our study.\n2 STELLAR WIND-UPPER ATMOSPHERE INTERACTION\nAs shown by previous studies of Watson et al. (1981), Kasting and Pollack (1983), Tian et al. (2005b; 2008a; 2008b), Volkov et al. (2011), and Erkaev et al. (2013), hydrogen-rich terrestrial planets experience XUV-heated and hydrodynamically expanding non-hydrostatic upper atmosphere conditions. Depending on the particular environment (e.g., XUV flux, orbital distance, availability of IR-cooling molecules, the planet's average density, etc.) the results of these studies indicate that such planets can expand their exobase level, which separates the collision dominated atmosphere from the collisionless region to distances from a few R pl up to more than 20 R pl. As a result of such an expansion of the upper atmosphere an intrinsic planetary magnetic field will most likely not protect the exosphere against the stellar wind plasma flow (Lichtenegger et al ., 2010; Lammer, 2012; Lammer et al ., 2011a).\nDue to the interaction between the stellar wind plasma flow and the XUV-heated non-hydrostatic upper neutral atmosphere of the planet, energetic neutral atoms (ENAs) are produced. ENAs originate due to charge-exchange when an electron is transferred from a planetary neutral atom to a stellar wind proton which then becomes an ENA. This interaction process between the stellar wind plasma and the upper atmosphere plays a significant role in the ion erosion of upper planetary atmospheres (e.g., Lundin et al. , 2007; Lammer, 2013). The production of ENAs after the interaction of stellar wind\nprotons via charge exchange with various upper atmosphere species is described by the reactions in eq. (1-3).\nENA pl pl SW H H H H (1)\nENA pl pl SW H O O H (2)\nENA pl pl SW H N N H (3)\nAfter its production an ENA continues to travel with the initial velocity and energy of the stellar wind proton. The atmospheric atom in turn becomes an initially cold ion which can afterwards be lost from the atmosphere due to the ion pick-up process (Lammer, 2013). In the current study we focus our attention only on the reaction shown in eq. (1) which will dominate the stellar wind interaction with planetary hydrogen coronae around hydrogen-rich terrestrial planets.\n2.1 Model description\nIn the current study the plasma interaction between the stellar wind and the upper atmosphere of the Earth-like planet and 'super-Earth' is modeled applying a Direct Simulation Monte Carlo (DSMC) upper atmosphere-exosphere particle model which is coupled with a stellar wind particle interaction code. The 3D model is described in detail in Holmström et al. (2008) and Ekenbäck et al. (2010) and includes stellar wind protons and planetary hydrogen atoms. The latter are launched into the simulation domain from the upper atmosphere. The applied collision cross sections for hydrogen atoms, σ H-H, and for protons and hydrogen atoms, σ H+-H, are 10 -17 cm 2 and 2 × 10 -15 cm 2 (Ekenbäck et al ., 2010) respectively. Charge exchange between stellar wind protons and exospheric hydrogen atoms takes place outside a conic shaped obstacle that represents the magnetoionopause of the studied planet. Stellar wind protons that have charge-exchanged according to the reaction shown in eq. (1) become ENAs.\nBesides of the charge-exchange reaction, the model includes gravitation of the planet and tidal effects as well as scattering by atmospheric atoms of UV photons (radiation pressure) and photoionization by stellar photons. Inclusion of the tidalgenerating potential into the equations leads to the extension of the atmosphere toward and backward from the host star, and in extreme cases to Roche lobe overflow. Nevertheless, these effects are important for 'hot Jupiters' which are located at very\nclose distance to their host stars, and do not play a significant role for the test planets we consider in the present study. All collisions are modeled using a DSMC algorithm (Holmström et al., 2008; Ekenbäck et al., 2010). The main code uses the FLASH software developed at the University of Chicago which provides adaptive grids and is fully parallelized (Fryxell et al. , 2000). The coordinate system is centered at the center of the planet with mass pl M , the 1 x -axis is pointing towards the center of mass of the system, the 3 x -axis is parallel to the direction of the angular velocity of rotation , and the 2 x -axis points in the opposite direction to the planet's velocity. St M is the mass of the planets host star.\nTidal potential, Coriolis and centrifugal forces, as well as the gravitation of the star and planet acting on a hydrogen neutral atom, are included in the code in the following way (Chandrasekhar, 1963)\n l il St pl St St i i v x M M R M R GM x x x x x x dt dv 3 1 2 2 2 3 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 1 (4)\nHere i v are the components of the velocity vector of a particle, G is Newton's gravitational constant, R the distance between the centers of mass, the Levi-Civita symbol, and 3 R GM St . The first term in the right-hand side of the eq. (4) represents the centrifugal force, the second is the tidal-generating potential, the third the gravitation of the planet's host star and the planet while the last term stands for the Coriolis force. The self-gravitational potential of a particle is neglected.\nCharge exchange reactions between a neutral planetary hydrogen atom and a stellar wind proton may take place outside the obstacle representing a magneto- or ionopause\n 2 2 3 2 2 1 1 t s R x x R x (5)\nHere s R stands for the magnetosphere or planetary obstacle stand-off distance and t R the width of the obstacle. Since the obstacle shape and location depend strongly on the planetary magnetic field strength, one may model the interaction of the stellar wind with\nmagnetized as well as with non- or weakly magnetized planets by the appropriate choice of s R and t R .\n2.2 Exosphere modeling of Earth's observed atomic hydrogen geocorona\nENAs have been observed around all Solar System planets where a spacecraft was equipped with a corresponding instrument (e.g., Futaana et al ., 2006; Galli et al. , 2008; Lammer et al ., 2011a; 2011b). As shown in Fig. 1, the Interstellar Boundary Explorer (IBEX) satellite recently observed an ENA formation zone around Earth's subsolar magnetopause stand-off distance, which is located at 10 R Earth from the planet's center (Fuselier et al. , 2010).\nBefore we apply our model to hydrogen-rich exoplanets, we validate it by reproducing the geocorona and recent ENA observations (Fuselier et al. 2010) around the Earth's magnetopause by the NASAs IBEX satellite of present-day Earth. Fig. 2 shows our modeling results for Earth's geocorona interacting with the present-day solar wind by taking all parameters of Earth's exosphere as given in Table 1 as an input.\nThe average neutral hydrogen atom density at the magnetopause level obtained from our model is estimated to be ~8 cm -3 at the distance of ~10 R Earth. This density value coincides very well with the exospheric number densities inferred from the IBEX observations of ENAs near the magnetopause. In the case of the IBEX observation at March 28 2009, the computed and observed proton fluxes show an exosphere hydrogen density at a geocentric distance of ~10 R Earth of ~4 - 11 cm -3 (Fuselier et al ., 2010). The estimates of the modeled ENA flux are in good agreement with the observed flux as well, predicting the flux of approximately 600 (cm² s sr keV) -1 . This value falls inside the observed ENA interval of ~530 - 2300 (cm² s sr keV) -1 (Fuselier et al ., 2010).\nThe IBEX observation and our model validation can also be seen as a confirmation that under extreme radiation and plasma environments of the young Sun or more active stars a huge ENA formation zone, as suggested by Chassefière (1996) and Lammer et al. (2011; 2012), should be produced in the stellar wind interaction region of a hydrogen-rich extended upper atmosphere of an Earth-size planet when the exosphere density near the magnetopause is more than 10 6 times larger than that observed at present-day Earth. In the following sections we describe the input parameters and our\napplied exosphere and ENA models to the XUV exposed hydrogen-rich Earth-size test planets.\n3. GLIESE 436: A HOST STAR PROXY FOR HYDROGEN-RICH TERRESTRIAL TEST PLANETS\n3.1 The radiation environment of Gliese 436\nRecently Ehrenreich et al. (2011) observed with the Hubble Space Telescope Imaging Spectrograph (HST/STIS) the Lyman-α emission (1215.67 Å) of neutral hydrogen atoms from the low mass M star, GJ 436. Because this emission is a main contributor to the ultraviolet flux it can also be used as a main tracer in studies of thermospheric heating, thermal escape, and possible absorption by extended hydrogen coronae and/or ENAs (e.g. Vidal-Madjar et al. , 2003; Holmström et al ., 2008; Ekenbäck et al ., 2010; Ben-Jaffel and Hosseini, 2010; Lecavelier des Etangs et al ., 2010; Lammer et al. , 2011b; Ehrenreich et al ., 2012, Lammer, 2013) during transit observations with ultraviolet transmission spectroscopy. We use GJ 436 as a typical M-type host star for our test-planet parameter studies. GJ 436 is a M2.5 dwarf star which is 10.2 pc away from the Sun. The dwarf star hosts a transiting 'hot Neptune' at an orbital distance of about 0.03 AU (Butler et al. , 2004; Gillon et al. , 2007). We adopt values for stellar mass and radius of 0.45 MSun and 0.45 RSun, respectively, which are consistent with several independent parameter determinations of GJ 436 (Torres, 2007; Maness et al. , 2007; von Braun et al. , 2012). The location of the habitable zone (HZ) is calculated following Selsis et al. (2007). As their relations are only valid for effective temperatures down to 3700 K, this value is used instead of the true temperature of GJ 436, which is slightly lower (3400-3600 K; Torres 2007; von Braun et al. 2012). Further, we adopt a bolometric luminosity of 0.026 LSun (Torres, 2007). This leads to a HZ extent of 0.12-0.36 AU assuming the limit of 50% clouds, as typical for the Earth. Hence, the center of the HZ is located at 0.24 AU, which we adopt as the orbit of our hypothetical exo-Earth. The orbital period of an Earth-analog planet within the HZ of GJ 436 corresponds to approximately 63.7 days, the orbital velocity to about 41 km s -1 , and the angular velocity to 1.14·10 -6 rad s -1 . The age of GJ 436 is about 6±5 Gyr and is not well constrained (Torres, 2007). However, the rotation period of 48 days (Demory et al. , 2007) yields an estimated age of 2.5-3 Gyr (Barnes,\n2007; Engle and Guinan, 2011). This estimation is in agreement with the lack of chromospheric activity indicated by the presence of Hα in absorption spectra.\nGJ 436 has been detected by the ROSAT All-Sky Survey, which revealed an Xray luminosity of log LX = 27.13 erg s -1 . Recent observations by the XMM-Newton spacecraft yielded a smaller value of only ~25.96 erg s -1 (Sanz-Forcada et al. , 2011). We adopt the latter result because of the longer exposure time and better S/N of the XMMNewton observations compared to ROSAT data. Using coronal models, Sanz-Forcada et al . (2011) extrapolated the stellar emission in the total XUV range (5 - 920Å) and found log L XUV=26.92 erg s -1 . Adopting this value and scaling it to the HZ center at 0.24 AU, we estimate an XUV flux of about 5.14 erg cm -2 s -1 , comparable to the present solar XUV flux at 1 AU of 4.64 erg cm -2 s -1 (Ribas et al. , 2005).\nIn the past, the stellar XUV flux, which was emitted from GJ 436 was certainly higher. The high-energy emission of young M dwarfs is saturated at log( L X/ L bol)~ -3 (e.g. Scalo et al ., 2007), hence the maximum possible log( L X) for GJ 436 is ~29 erg s -1 . Assuming that the XUV emission of young stars occurs predominantly in X-rays because of their hotter coronae, the maximum XUV flux at the Earth-equivalent orbit around GJ 436 was roughly 700 erg cm -2 s -1 , or ~150 F XUV,now.\nLyman-alpha emission of GJ 436 was detected by Ehrenreich et al. (2011) using HST/STIS observations. They reconstructed the intrinsic stellar emission by correcting for interstellar medium (ISM) absorption, leading to an apparent flux observed at Earth of ~2.7±0.7 × 10 -13 erg cm -2 s -1 . Scaled to the HZ center, this yields ~20.51 erg cm -2 s -1 , a factor of ~3.3 larger than the present solar value at 1 AU of 6.19 erg cm -2 s -1 (Ribas et al ., 2005). Recently, France et al. (2013) reconstructed the intrinsic Lyman-alpha flux of GJ 436 by using a different approach. They obtained a value of 3.5 × 10 -13 erg cm -2 s -1 with an uncertainty of about 15 - 30 %, which is slightly higher than the value given by Ehrenreich et al. (2011), but is consistent with the errors. The relevant stellar parameters and the measured radiation properties used in the model simulations for various assumed XUV flux values of a Gliese 436-type M dwarf are shown in Table 2.\nThe photoionization rates corresponding to the four XUV flux enhancement factors were scaled from the average present solar value at Earth (1.1 × 10 -7 s -1 ; Hodges, 1994, Bzowski, 2008) to the corresponding enhancement factors. The photoionization\nrate is usually calculated as the product of ionization cross-section and spectral flux integrated over all wavelengths below the ionization threshold. Since full M star XUV spectra for different activity levels are currently not available, we assume that the present spectral energy distribution is equal to the solar one and scale it up by the constant factors given in Table 2.\nThe UV absorption rates correspond to the product of the photon flux at the center of the Lyman-alpha line and the total absorption cross-section (5.47 × 10 -15 cm 2 Å; e.g. Quémerais, 2006). Adopting the reconstructed intrinsic line profile of Ehrenreich et al. (2011), the present value of the photon flux at the HZ center of GJ 436 is estimated to be ~6.9 × 10 -3 s -1 .. To scale the Lyman-alpha flux and, hence, the absorption rate to higher XUV flux emission levels, we use the scaling between X-rays and Lyman-α from Ehrenreich et al. (2011). This assumes that L X/ L bol ≈ L XUV/ L bol and that the central Lyman-α flux scales approximately as the integrated line emission. The resulting absorption rates are also shown in Table 2.\n3.2 Expected stellar wind plasma properties\nDepending on the mass, size and resulting luminosity of the host star, the corresponding scaled HZ location in the case of GJ 436 is at 0.24 AU. This is a much closer orbital distance compared to that of the Earth (1 AU). As pointed out by Khodachenko et al. (2007), at orbital locations < 0.5 AU the flow of dense plasma related to stellar winds and coronal mass ejections (CMEs), energetic particle fluxes and XUV radiation cannot be neglected. Depending on the stand-off distance of the planetary obstacle which forms when the stellar plasma flow is deflected around the planet, previous test particle model results of Lammer et al. (2007) indicate that CO2-rich Earth-like exoplanets having no or only weak magnetic moments may lose from tens to hundreds of bars of atmospheric pressure, or even their whole atmospheres, due to the CME induced O + ion pick-up at orbital distances ≤ 0.2 AU.\nDue to the uncertainties on the mass loss and related plasma outflow from M dwarfs, we assume in our study, as in Khodachenko et al. (2007) and Lammer et al . (2007), the plasma environment close to the stars obtained from solar observations. There exist a limited number of measurements of the mass loss rates for M stars (Wood et al., 2005, Ehrenreich et al. , 2011), which in principle may be used for estimation of specific\nstellar wind density and velocity. For these stars the mass loss rates are comparable or less than the mass loss rate of the Sun. At the same time, for the Sun we have a much better knowledge of the distribution and evolution of active solar regions and of the mass outflow in the form of solar wind and CMEs, which we use in the present study. Note that stellar wind density and/or velocity lower than the solar (assumed) values would reduce the portion of the produced and picked up ions. Such a reduction would not change our main conclusion that the ion pick-up loss makes up only several percent of the thermal loss, and the further results can be considered as an upper limit for ion pickup near an M dwarf like Gliese 436.\nFor the accurate study of stellar-planetary interactions one needs a reliable model which can simulate the propagation and evolution of the stellar wind plasma. For modeling the propagation and evolution of the stellar wind we use the Versatile Advection Code (VAC) (Toth, 1996). This model is able to simulate spatial and temporal evolution of the solar/stellar wind, as well as CMEs, from orbital distances ≥0.14 AU. It/The model includes a self-consistent Parker-type co-rotating magnetic field, and is based on the solution of the set of the ideal (non-resistive) non-relativistic magnetohydrodynamic equations (Toth, 1996). We use a spherical uniform computation domain, which occupies a radial distance region between 0.14 < R < 1 AU. The stellar wind in the model flows through the inner boundary of the computation domain at a semi-major axis location d = 0.14 AU and propagates out through the outer radial boundary at d = 1 AU. A self-consistent expanding stellar wind plasma flow under the conditions of a frozen-in, co-rotating, Parker-type, spiral magnetic field is numerically simulated (Odstrčil et al ., 1999; Rucker et al. , 2008).\nThe typical parameters of the expected flow of the stellar wind plasma at d = 0.14 AU are imposed along the inner radial boundary (Odstrčil et al ., 1999) with an initial proton concentration n 0 = 500 cm -3 , stellar wind proton temperature, T 0 = 500 kK, and a radial stellar wind velocity v r0 = 300 km s -1 . For investigating the propagation of CMEs, in a second step the simulation of a CME cloud with an initial proton density n 0 = 1000 cm -3 , proton temperature, T 0 = 1700 kK, and a radial stellar wind velocity v r0 = 600 km s -1 is imposed at the inner boundary of the computation domain as a time-dependent\ninjection of hot and dense plasma into the ambient stellar wind (Odstrčil et al ., 1999; Odstrčil et al. , 2004).\nFig. 3 shows radial profiles of the maximum values of plasma parameters ( n , v r, T ) during a solar analogue CME event (dashed lines, Case II) for a typical M-star with mass M s ~ 0.45 M Sun and a rotation period 2.5 days, and those for the stellar wind itself (solid lines Case I). Therefore, in the stellar wind plasma interaction modeling with the upper atmosphere, described below, two types of stellar plasma parameters representing the lower (Case I) and upper limit (Case II) conditions at the HZ location of our test planets at 0.24 AU were used as inputs:\n\n Case I: 250 SW n cm -3 , 330 SW v km/s, 6 10 SW T K,\n Case II: 700 SW n cm -3 , 550 SW v km/s, 6 10 2 SW T K.\n\nHere n sw corresponds to stellar wind concentration, v sw denotes its bulk velocity and T sw stands for the stellar wind temperature. These values cover the predicted range for the expected stellar wind plasma parameters of GJ 436 at the HZ of the system. The upper limit (Case II) can also be considered as a proxy for modeling of frequent CME events in the system when the next CME event hits the planet immediately after the previous one. We can estimate the recovery time of the planetary atmosphere after the CME event on a very simple way. Since the test planets considered in the article are not magnetized, we assume that the recovery speed coincides with the sound speed (or the speed of slow\nmagnetoacoustic wave), so that 2 / 1 / H exo B t s t CME m T k R c R where t R is the obstacle\nwidth, 3 / 5 is the ratio of the specific heats, B k is the Boltzmann constant, H m is the mass of a hydrogen atom and exo T is the exobase temperature. Taking the parameters from Tables 3 and 4 and depending on the characteristic size of the obstacle and the temperature, this time varies between approximately 7 and 14 hours for the Earth-type planet and 64 and 80 hours for the 'super-Earth'.\nThe next section is dedicated to the discussion of the obtained results and presents also the ion production rates for the hydrogen-rich Earth-like planet and the 'super-Earth'.\n4. HYDROGEN EXOSPHERES, ENA PRODUCTION AND ION ESCAPE\nIn the following section we study the modification of the extended hydrogen exosphere due to the interaction of it with the stellar XUV and plasma flux. Because our hydrogenrich test-planets orbit within a typical M-star HZ at ~0.24 AU they will be affected by tides. As it was discussed in Khodachenko et al. (2007) tides arise because of the finite extension of the planetary body in the inhomogeneous gravitational field of its host star so that the continuous action of the tides will reduce the planetary rotation rate or may result in a synchronous rotation (Grießmeier et al. , 2005).\nThe intrinsic magnetic field of a terrestrial planet is an essential factor for planetary protection from the ion pick-up atmosphere loss process. As shown in Khodachenko et al. (2007) and Lammer et al . (2007), because of the close orbital location within M-star HZs, the magnetosphere field of a terrestrial planet is more compressed due to the denser stellar wind impact compared with that of the solar wind at present-day Earth at 1 AU. In view of this fact the radial distance of the extended exobase of an XUV heated hydrogen rich upper atmosphere will most likely coincide with the planetary magnetopause or ionopause distance (e.g., Lammer et al ., 2009a; Lammer et al ., 2012, Lammer, 2013).\n4.1 Input parameters and modeling results\nAs it was briefly discussed in Sect. 3.2, the magnetic moments of terrestrial planets, and especially that of 'super-Earths' within close orbital distances, are expected to be weak (e.g., Gaidos et al ., 2010; Tachinami et al ., 2011; Morad et al ., 2011; Stamenkovic' et al., 2011Stamenkovi'c et al., 2012). This would lead to magnetoshperes or ionospheres which are compressed towards the planet's expanded non-hydrostatic upper atmosphere by the strong dynamic ram pressure of the dense stellar wind plasma. On the other hand if the exobase level expands beyond several planetary radii one can also expect that an Earth-type magnetosphere will not protect the exosphere (Fig. 5: Lammer et al ., 2007; Fig. 6 right panel: Lammer et al ., 2011a). Taking this considerations into account, the planetary obstacle most likely is located very close above the exobase level (Lammer et al. 2009b). Because the shape of the planetary obstacle affects the ENA production and resulting loss of planetary hydrogen ions, we study also the influence of the obstacle width on the ion production rate and the upper atmosphere erosion.\nIn the first case the magnetic obstacle width t R in the eq. (5) was assumed to be 1.5 times greater than the magnetopause distance. This relation and its resulting obstacle shape is close to the observed magnetosphere of the present-day Earth and may occur if the planet has an intrinsic magnetic dynamo. In the second case we choose t s R R so that it resembles more a Venus-type planetary obstacle which may correspond to a planet with no magnetic field, or only a very weak dynamo. By decreasing of the planetary obstacle width the ion production will significantly increase, so that a terrestrial planet with a Venus-type obstacle, where t s R R , may lose larger amounts of atmospheric gas in ionized form (see Sect. 4.2). In the present study we do not specify the magnetic moment of a planet, but only chose a magnetospheric obstacle.\nFor illustrating the differences between the stellar wind plasma interaction with a hydrogen-rich terrestrial planet which is exposed to both a weak XUV flux and an extremely strong one, we irradiate the two test-planets with the XUV flux of the present Sun (1 XUV) and with a 100 times higher XUV flux (100 XUV). Moreover, we investigate for these two XUV flux cases several stellar wind and obstacle scenarios. The main input parameters at the inner boundary of our simulation domain are shown for 4 selected cases in Tables 3 and 4. As it was mentioned earlier, we apply the results obtained by Erkaev et al. (2012) to the upper atmosphere input paramters of our model. Erkaev et al. (2012) studied the thermosphere structure of a hydrogen-dominated Earth and a 'super-Earth' ( R pl=2 R Earth; M pl=10 M pl) with a hydrodynamic upper atmosphere model which solves the equations of mass, momentum and energy conservation for low and high heating efficiencies, η of 15 % and 40 %, respectively. η defines the percentage of the incoming XUV energy which is transferred into heating of the neutral gas. Table 4 shows the same input paramters for our model for a hotter atmosphere corresponding to the upper atmosphere values of Erkaev et al . (2013) with η = 40%.\nAs one can see from Tables 3 and 4, the exobase distance which is chosen as our inner model boundary and the temperature are increasing for higher XUV fluxes. This behavior can be expected by taking into account a more intensive radiation flux from the parent star. Enhanced heating flux makes the scale height of the atmosphere increase, which in its turn moves the exobase to higher location. One can also see that an increase of the heating efficiency leads to an increase of the planet's obstacle stand-off (which for\nthe studied non-magnetized planets practically coincides with the exobase) distances as well. Because of the expansion of the upper atmosphere under more extreme heating conditions (40%) the exobase densities are smaller in comparison to the 15% cases.\nFigs. 4 and 5 show the modeled hydrogen exospheres and the related stellar plasma interaction under various conditions around the test planets. All the figures show cross-sections of a 3D cloud in the 2 1 , x x plane similar to those in Fig. 2. Fig. 4 illustrates the appearance of the extended hydrogen coronae around the Earth-type planet while Fig. 5 corresponds to the 'super-Earth'. In all the cases the wider Earth-type planetary obstacle is assumed, except for Fig. 4d where a smaller Venus-like obstacle is adopted.\nThe white area around the planets (which are shown as black dots) represents the inner atmosphere (non-hydrostatic thermosphere), which is not considered in the present study. Fig.4a and Fig.4b illustrate the influence of the XUV flux on the cloud formation. All simulation parameters for these two pictures are the same except for the XUV flux, which is chosen to be equal to and 50 times higher than the XUV flux of the present Sun. As one can see, the higher XUV flux leads to a more efficient expansion of the upper atmosphere so that charge exchange can be more intensive in the surrounding hydrogen corona. The effect of the planetary obstacle can be seen in a comparison of Fig. 4c, for an Earth-type planetary obstacle shape, with Fig.4d, for a Venus-type obstacle. In these two cases the upper atmosphere is exposed to the XUV flux which is 50 times higher compared to that of today's Sun.\nFigs. 5a and 5b illustrate the importance of the heating efficiency. We show two model runs for the 'super-Earth' for a comparison. Only the upper atmosphere parameters corresponding to the heating efficiencies were changed. A higher heating efficiency results in additional expansion of the upper atmosphere and in increasing production of ENAs in the vicinity of the planet (blue and red dots). Figs. 5c and 5d show the effect of the stellar wind velocity and density on the hydrogen coronae formation.\nBoth figures, 5c and 5d, correspond to the most extreme XUV case, which is 100 times higher than that of today's Sun.\nAs expected, the extreme stellar conditions result in a denser and faster stellar plasma flow, higher XUV fluxes and more intense heating of the upper atmosphere, as well as a decrease of the planetary obstacle width, which all lead to more intensive interaction\nprocesses. The ENA part of the hydrogen corona (blue and red dots) becomes more visible, meaning an increase of the atmospheric erosion processes. One can see that a huge amount of exospheric hydrogen atoms is ionized or underwent charge exchange reactions in both cases, but stronger stellar wind significantly increases the number of ENAs in the vicinity of the planet as suggested by Chassefière, (1996).\nChassefìère (1996) studied the hydrodynamic outflow and escape of hydrogen atoms from a hydrogen-dominated expanded thermosphere from early Venus. From this study it was estimated that the huge ENA cloud, which is generated via charge exchange due to the interaction between an extended exosphere and the surrounding solar wind plasma of the young Sun, may contribute to about 75 % of the energy inside the thermosphere which is used for escape of the outward flowing H atoms (see Fig. 3 in Chassefière, 1996). The stellar EUV flux is deposited mainly in the lower thermosphere (Erkaev et al ., 2013), while the ENA flux directed toward the planet should be deposited at an atmospheric layer below the exobase. It can contribute to thermospheric heating and may as a consequence modify the upper atmosphere structure which could result in an enhancement of the thermal escape rate.\nOur results related to the efficient production of ENAs around the planetary obstacle support the hypothesis of Chassefière (1996) that ENAs may contribute to upper atmosphere heating. A study which investigates the possible heating contribution of ENAs additionally to the stellar XUV flux is beyond the scope of this particular work, but is in progress for a follow up study during the near future. We note also that ENA clouds near the terrestrial exoplanets within orbits around M dwarfs might be observable in the stellar Lyman-alpha line by the Hubble Space Telescope and in higher resolution beyond the geocorona in the near future by the World Space Observatory-UV (Shustov et al. , 2009; Lammer et al ., 2011b).\nIn the next section we estimate how many of the produced planetary ions in the hydrogen coronae are picked up by the stellar wind plasma, and hence are lost from the planet.\n4.2 Stellar wind induced atmospheric erosion of planetary hydrogen ions\nAs discussed above, interaction processes between the stellar wind and the upper atmosphere together with the photoionization by stellar photons lead in the case of\nhydrogen-rich atmospheres to the production of atmospheric H + ions, see eq. (1). After ionization, the ions can be picked up by the stellar wind plasma and swept away from the planet. Because we are interested in the efficiency of the atmospheric ion escape, we estimate the average ion production rates under various conditions. We assume as discussed below that in the considered cases the production of planetary ions and the escape rate are most likely of the same order.\nIons produced near and above the planet's obstacle can be lost because of the ion pick-up process. Since these particles are not neutral anymore, they can follow the magnetic field lines in the stellar wind plasma and can be swept away from the planet's gravity field. We consider the H + ions produced above the planetary obstacle, where the collisions between atmospheric particles can be neglected. It is assumed that the ions may be lost if the gyro radius\n(6) , qB v m r i i g \nis small enough in comparison to the planetary radius (e.g. if the magnetic field in the vicinity of a planet is strong enough to change the trajectory of the ions significantly). Here i m is the mass of the ion, i v is the velocity of the 'cold' planetary ion assumed to be ~7 km s -1 , q is the ion charge and B is the magnetic field near the planetary obstacle. In the case of a pure hydrogen upper atmosphere the ion mass and charge coincide with the mass and charge of a proton. The velocity of ~7 km s -1 is chosen as being slightly faster than the mean thermal velocity of a hydrogen atom for a temperature of about 2000 K. The magnetic field at the distance ~0.24 AU from an M dwarf can be roughly estimated if one assumes a dipole character of the stellar field with the initial global value in the range of ~2 - 3 kG or ~0.2 - 0.3 T (Phan-Bao et al. , 2009, Reiners, 2012). By assuming an average magnetic field on the star of 2 kG, the magnetic field at 0.24 AU is ≈ 3 10 4 . 1 G, which yields for an ion velocity of 7 km s -1 an ion gyro radius of ~525 m which is several orders of magnitude smaller compared to the radii of the studied planets. In such a case it is justified to assume that most of the produced H + ions will be swept away from the planets by the stellar wind. If we assume that the ions are accelerated by the stellar wind electric field to the velocity of the stellar wind (Case I: 330 km/s, Case II: 550 km/s), the ion gyro radius increases proportionally to ~25 - 40 km in two extreme\ncases. Here we assume the filling factor f=1 (see Phan-Bao et al. , 2009), i.e. the maximal possible field strength.\nSince the magnetic field of ~2 - 3 kG is typical for young and active M dwarfs, it could be convenient to determine the gyro radii for a weaker field of ~50 G for an older star with the age of several Gyr (Phan-Bao et al. , 2009). The magnetic field at 0.24 AU is approximately 5 10 57 . 3 G. A decrease of the magnetic field causes a proportional increase of the gyro radius (21 km for an ion velocity of 7 km s -1 , 10 3 km and 3 10 6 . 1 km for 330 km/s and 550 km/s respectively). But even the highest value of ~1600 km is several times less if compared to the planetary radius, and more than an order of magnitude lower compared to the exobase radius where most ENAs are produced. These estimates support our assumption that the majority of the exospheric ions are lost from the planet and that the ion production rate is balanced by the escape rate at least during a significant part of the stellar life time.\nEstimates of the ion production rates and corresponding escape rates described in the previous sections are summarized in the Tables 5 and 6 for planetary obstacles which have an Earth-like magnetosphere shape. Table 5 presents the results obtained for a hydrogen-rich Earth-like planet for two stellar wind conditions and a heating efficiency η =15% and of a higher heating efficiency η = 40%, while Table 6 summarize the similar scenarios for the 'super-Earth'. Atmospheric loss rates L ion are given in units of particles per second. As one can see from Tables 5 and 6, in the most cases the ion production and loss rate increases with the increasing XUV flux. Loss rates for faster stellar wind also exceed the corresponding values for the wind with lower velocity which is not surprising. Since the ion production rates depend not only on the assumed heating efficiency and the XUV flux, but also on the exobase density, the values for the lower-density case corresponding to a heating efficiency of 40% (Erkaev et al. , 2013) are slightly lower in comparison to the 15% case shown in Table 6.\nThis is also the reason why the values for the cases where the stellar XUV flux is about 100 times higher than that of the present Sun are not dramatically higher (or even slightly smaller) that the ion production rates for the lower XUV fluxes, although the intensity of the interaction increases. Under the intensity of the interaction in this case we mean the ratio of produced ions to the mean exospheric density. This value increases\nmonotonically for higher XUV fluxes in all cases considered in the present study. The reason for that is related to the corresponding exobase density that is lower because of expansion in the case of a hydrogen-rich upper atmosphere which is exposed to high XUV fluxes such as in the 100 XUV case (Erkaev et al. , 2013).\nTo investigate the influence of the planetary obstacle shape on the H + escape rate L ion, we performed an analogous set of simulations by assuming a Venusian type planetary obstacle ( t s R R ). Tables 7 and 8 present the calculated ion production rates and estimated ion escape rates for the two test planets under the same conditions as described in Tables 5 and 6 except for the shape of the planetary obstacle. As one may see from the comparison of Tables 5 - 6 and Tables 7 - 8, reducing the width of the obstacle by 1.5 times leads to an increase in the ion production rate (i.e. the escape in general) of ≈30%. Other factors which lead to an increase of the ion production rate are related to the increase of the stellar wind density and velocity, heating efficiency η , and enhancement of the stellar XUV flux of the parent star. All these dependencies should be considered and expected.\nFor comparison, thermal loss rates change in the range from 29 10 0 . 4 (1 XUV, η=15%) to 31 10 3 . 4 (100 XUV, η=40%) for a hydrogen-rich Earth-type planet and from 29 10 6 . 1 (1 XUV, η=15%) to 31 10 3 . 5 (100 XUV, η=40%) for a hydrogen-rich 'superEarth'. In all cases these rates exceed the presented in the current study. For more information, see Erkaev et al., (2013).\nIf we compare the modeled H + ion pick-up loss rates with that of Mars (e.g., Lammer et al ., 2003) or Venus (Lammer et al. , 2006), which are in the order of ~10 25 s -1 , one can see that the pick-up loss rates for the hydrogen-dominated Earth-like planet are comparable for the 1 XUV case with a heating efficiency of 15 % and an Earth-like magnetopause shape, but would be a factor 10 3 higher in the case of 40 % heating efficiency and/or a more narrower Venus-type planetary obstacle. For the larger 'superEarth' and XUV cases with higher values than that of the present-day Sun the loss rates are up to 10 4 - 10 5 times higher.\n4.3 Total ion escape\nThe loss rates shown in Tables 5 - 8 can be used for rough estimation of the total ion loss from the hydrogen envelopes around the studied planets. This question is important because, as shown by Erkaev et al. (2013), volatile rich 'super-Earths' which contain IRcooling molecules can result in lower heating efficiencies of about 15 % so that for most of their lifetime they will not be in the hydrodynamic blow-off regime. In such cases nonthermal atmospheric escape processes, like the studied H + ion pick-up process, will contribute to the loss of their hydrogen-rich protoatmospheres.\nBefore we investigate this mass loss one needs to know how long a typical M dwarf like Gliese 436 may keep a high level of the XUV and X-ray flux. According to Penz et al. (2008a) the temporal scaling law for the soft X-ray (0.6-12.4 nm or 0.1-2 keV) flux of a typical M dwarf with the mass of ≈ Sun M 4 . 0 can be described by the following relation\n77 . 0 0 17 . 0 ) 6 . 0 ( t L Gyr t L X , 34 . 1 0 13 . 0 ) 6 . 0 ( t L Gyr t L X , (6)\nwhere 28 0 10 6 . 5 L erg s -1 and t is given in Gyr. The soft X-ray flux can then be scaled for the appropriate orbital distance by using the relation 2 4 / d L F X X .\nFig. 6 shows, approximately, the decrease of the soft X-ray flux of a Gliese 436 analogous M dwarf during the first 1.3 Gyr of its life time. Since at present time the scaling law for the XUV radiation of M dwarfs is not yet well constrained, we use this soft X-ray scaling law instead of the XUV scaling law in our estimation for the total H + escape. Assuming this temporal scaling law for the star and taking the ion production rates from Tables 5 - 8, we can estimate the mass loss from the hydrogen-rich Earth-like planet and the 'super-Earth' in the HZ of a Gliese 436 type M star after 4.5 Gyr (see Tables 9 and 10). For comparison the thermal escape rates are shown by using the values from Table 2 in Erkaev et al. (2013).\nThe total ion loss is given in Earth ocean equivalent amounts of hydrogen (1EOH = 23 10 5 . 1 g) . It should also be mentioned that we do not consider escape during the first ~100 Myr, the time of extreme stellar activity of an M dwarf, so that our estimates cover the time span ~0.1 - 4.5 Gyr. As discussed in Erkaev et al. (2013) during this early extreme period the temperature in the lower thermosphere may be >> 250 K, due to\nmagma oceans and frequent impacts. Hot lower atmosphere will enhance the atmospheric thermal escape during this early period. A follow up study which will investigate the earliest extreme evolutionary periods is in progress.\nIn the present work we do not take into account the gradual decrease of the amount of gas in the planetary atmosphere due to escape processes, as we assume that the hydrogen reservoir contains much more gas in comparison to the amount lost . As discussed in Sect. 1, such scenarios can be considered as real because most of the recently discovered 'super-Earths' may have huge hydrogen envelopes which contain a few % of their whole mass (e.g., Lammer, 2013).\nIf we compare the estimated atmospheric escape rates obtained for the thermal and ion pick-up processes for both test-planets in the HZ, it is clear that the thermal escape rate substantially exceeds the pick-up rate under the studied conditions. This is also the case when we consider the most extreme XUV and stellar plasma conditions, including a narrow planetary obstacle. A fraction of the evaporating neutral exosphere will be ionized so that ion pick-up will contribute to the total atmospheric escape rate, but as long as the upper atmosphere is in blow-off thermal escape will be the most important.\nIn our study the escape rate of ionized hydrogen atoms can vary for an Earth-type planet from ~0.6 EOH under moderate conditions (15% heating efficiency, moderate stellar wind, Earth-type planetary obstacle) up to ~2.5 EOH for extreme environments (40% heating efficiency, denser and faster wind and a narrow Venusian obstacle type).\nThe stronger gravity of the more massive 'super-Earth' keeps the atmosphere closer to the planet's surface, which slows down the charge exchange and photoionization processes. In this case the escape changes from ~0.4 EOH to ~2.14 EOH depending on the environment but remains smaller compared to escape from an Earthtype planet (ranging from ~0.6 EOH to 2.5 EOH, see above). In all studied cases the nonthermal H + pick-up rate is several times smaller in comparison with the thermal one, but makes up a significant fraction of the whole loss processes.\nThe results of our study, together with those of Erkaev et al. (2013), indicate that terrestrial exoplanets ranging in mass and size from Earth- to 'super-Earths' may experience difficulties in losing dense hydrogen envelopes if they have H-dominated protoatmosphere remnants with >9 EOH (Earth: η = 15%) and >19 EOH (Earth: η = 40%).\nFor 'super-Earth' these amounts are >3.5 EOH (η = 15%) and >10 (η = 40%). Dense hydrogen envelopes may be removed more easily if a particular exoplanet is located closer to its parent star such as Corot-7b or Kepler-10b (e.g., Leitzinger et al ., 2011) which orbit their parent stars at ~ 0.017 AU, but not inside the HZ. We note also that due to the HZ location at greater distances from the parent stars, the stellar wind erosion of hydrogen-envelopes will be less efficient for planets inside the HZs of K, G and F-type stars.\n5. CONCLUSIONS\nIn this study we investigated the non-thermal ion pick-up escape process from hydrogenrich, non-hydrostatic upper atmospheres of an Earth-like planet, and a hydrogen-rich 'super-Earth' which is twice as large as Earth and ten times more massive. Both planets are supposed to be located inside the HZ of a typical M dwarf star with stellar properties similar as GJ 436. We showed that in the case of an M dwarf the produced planetary H + ions have a high probability to be picked up from the extended hydrogen coronae by the stellar wind plasma flow so that the ion production rate and the ion escape rate are perhaps of the same order. We exposed the two test-planets to various XUV fluxes from 1 to 100 times that of the present Sun and found that in all studied cases the ionization of exospheric neutral hydrogen atoms by charge-exchange and photoionization contributes to the total atmospheric escape of the upper atmosphere, but do not prevail over the thermal escape. The total non-thermal atmospheric escape by ion pick-up from possible dense hydrogen envelopes during the life time of the studied planets is < 3 EOH. Our results indicate that if a rocky exoplanet did not lose the majority of its nebula captured hydrogen gas envelope, or degassed a huge amount of hydrogen-rich volatiles by thermal blow-off during the first hundred Myr after the planet's origin, it is questionable if the stellar wind can erode a remaining dense hydrogen envelope non-thermally. The thermal escape is higher during the planet's history, but is probably unable to remove such dense hydrogen envelopes as well. The situation may change dramatically for exoplanets which are located closer to their parent stars. Depending on the nebula life time, the formation process, planetary mass, stellar activity and plasma properties in the vicinity of the planet, the initial amount of hydrogen, thermal and non-thermal atmospheric escape processes\nwill determine if a planet becomes a world with an Earth-type atmosphere (and no hydrogen envelope) or remains a sub-Neptune type body.\nACKNOWLEDGEMENTS\nM. Güdel, K. G. Kislyakova, M. L. Khodachenko, and H. Lammer acknowledge the support by the FWF NFN project S116 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subprojects, S116 604-N16 'Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond', S116 606-N16 'Magnetospheric Electrodynamics of Exoplanets', S116607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. K. G. Kislyakova, Yu. N. Kulikov, H. Lammer, and P. Odert thank also the Helmholtz Alliance project 'Planetary Evolution and Life'. P. Odert and M. Leitzinger acknowledges support from the FWF project P22950-N16. The authors also acknowledge support from the EU FP7 project IMPEx (No.262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science WG5. The authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar- and exoplanetary environments'. Finally, N. V. Erkaev acknowledges support by the RFBR grant No 12-05-00152-a. This research was conducted using resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North (HPC2N), Umeå University, Sweden. The software used in this work was in part developed by the DOE-supported ASC / Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. 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\n\n
Table 1. Model inner boundary 'ib' atmospheric and solar wind input parameters for present-day Earth's geocorona (Prölss, 2004).Table 2 . Default stellar parameters as well as values of constants used in the simulations.
\n
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\n\n
Table 3 . Planetary input parameters taken from Erkaev et al . (2013) for different stellar wind properties and XUV fluxes which correspond to that of the present Sun and an XUV enhancement factor of about 100 times for a low heating efficiency η = 15%.
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\n\n
TABLES
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Table 4 . Planetary input parameters taken from Erkaev et al. (2013) for different stellar wind properties and XUV fluxes which correspond to that of the present Sun and an XUV enhancement factor of about 100 times for a higher heating efficiency η = 40%.Table 5 . Ion escape rates Lion in s -1 for a hydrogen-rich Earth-like planet and for a heating efficiency of 15 %, exposed to the XUV flux values which are 1, 10, 50 and 100 times higher than that of the present Sun. The shape of the planetary obstacle is assumed to be similar to an Earth-type magnetosphere.
\n
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\n\n
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Table 6 . Ion escape rates Lion in s -1 for a hydrogen-rich 'super-Earth' for a heating efficiency of 15 % and 40%, exposed to the XUV flux values which are 1, 10, 50 and 100 times higher than that of the present Sun. The shape of the planetary obstacle is assumed to be similar to an Earth-type magnetosphere.Table 7 . Ion escape rates Lion in s -1 for a hydrogen-rich Earth-like planet for a heating efficiency of 15% and 40%, exposed to the XUV flux values which are 1, 10, 50 and 100 times higher compared to that of the present Sun. The shape of the planetary obstacle is assumed to be Venus-like.
\n
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\n\n
\n
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Table 8 . Ion escape rates Lion in s -1 for a hydrogen-rich 'super-Earth' for a heating efficiency of 15 % and 40%, exposed to the XUV flux values which are 1, 10, 50 and 100 times higher compared to that of the present Sun. The shape of the planetary obstacle is assumed to be Venus-like.Table 9 . Thermal ( th L ) and non-thermal ( ion L , H + ion pick-up) loss over the time span of 4.5 Gyr for a H-rich Earth-like planet and a H-rich 'super-Earth', orbiting an M dwarf in the habitable zone at 0.24 AU by considering an Earth-type magnetosphere shape for the planetary obstacle form and the low and high heating efficiency of 15% and 40 %.
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\n\n
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Table 10 . Non-thermal ( ion L , H + ion pick-up) loss over the time span of 4.5 Gyr for an H-rich Earth-like planet and an H-rich 'super-Earth', orbiting an M dwarf in the habitable zone at 0.24 AU by considering a Venusian-type planetary obstacle shape and the low and high heating efficiency of 15% and 40 %.
\n
\nFIGURE CAPTIONS\nFIG. 1 : Observed hydrogen ENAs by the IBEX spacecraft around Earth. The H ENAs count rate was integrated from 0.7-6 keV on 28 March 2009 from 04:54-15:54 UT. The peak is centered on the subsolar magnetopause and a significant ENA flux extends to ±10 R Earth (Fuselier et al ., 2010).\nFIG. 2 . Modeling results of Earth's solar wind plasma interaction with the present-day geocorona. Green dots correspond to the solar wind protons, yellow dots represent the neutral hydrogen atoms moving with velocities below 10 km s -1 (particles which belong to the atmosphere) while the red and the blue dots represent ENAs with velocities above 10 km s -1 , moving towards and away from the Sun respectively. The dashed line denotes the magnetosphere obstacle.\nFIG. 3 . Radial profiles for density, velocity and temperature as a function of orbital location in AU and of expected plasma properties of an ordinary stellar wind (solid lines) and during an CME event (dashed lines) on an M-type star with a mass M s ~0.45 M Sun and a rotation period 2.5 days. For the simulation of stellar wind the initial proton density at 0.1 AU n 0 = 400 cm -3 , temperature T 0 = 500 kK, and radial stellar wind velocity v r0 = 300 km s -1 were taken. Simulation of a solar-analogue CME event uses the initial proton density n 0 = 800 cm -3 , proton temperature T 0 = 1500 kK, and a radial stellar wind velocity v r0 = 600 km s -1 .\nFIG. 4 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around an Earth-like hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig.4a corresponds to the XUV flux which is equal to that of the present Sun, the moderate stellar wind (Case I) and a lower heating efficiency of 15%. Fig.4b corresponds to the similar input parameters as in Fig.4a, but the XUV flux is 50 times higher. Fig.4c corresponds to the 10 times higher XUV flux than the present one and a heating efficiency of 15%, as well as the moderate stellar wind\n(Case I). Fig.4d: corresponds to the similar input parameters as in Fig.4c, but for the Venus-type narrower planetary obstacle.\nFIG. 5 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around a 'super-Earth' hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig5a: the XUV flux is 50 times higher than that of the present Sun, heating efficiency of 15%, the planet is exposed to a moderate stellar wind (Case I). Fig5b: similar conditions except for heating efficiency of 40%. Fig.5c: the XUV flux is 100 times higher compared to that of the present Sun, 40% heating efficiency, moderate stellar wind (Case I). Fig.5d: similar input parameters as in Fig.5c, but exposed to a faster and denser stellar plasma flow (case II).\nFIG. 6 . Illustration of the soft X-ray flux time-dependence for an M dwarf star with 0.4 solar masses (dashed line) and the same curve for a Sun-like star (solid line) in the corresponding HZs normalized by the present Sun flux. The M star within this mass range remains about 200 Myr longer in its activity saturation phase compared to a solar like G star.\n\n\n
\n\n\n\n\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"We study the interactions between the stellar wind plasma flow of a typical M star, such as GJ 436, and hydrogen-rich upper atmospheres of an Earth-like planet and a 'superEarth' with the radius of 2 R Earth and a mass of 10 M Earth, located within the habitable zone at ~0.24 AU. We investigate the formation of extended atomic hydrogen coronae under the influences of the stellar XUV flux (soft X-rays and EUV), stellar wind density and velocity, shape of a planetary obstacle (e.g., magnetosphere, ionopause), and the loss of planetary pick-up ions on the evolution of hydrogen-dominated upper atmospheres. Stellar XUV fluxes which are 1, 10, 50 and 100 times higher compared to that of the present-day Sun are considered and the formation of high-energy neutral hydrogen clouds around the planets due to the charge-exchange reaction under various stellar conditions have been modeled. Charge-exchange between stellar wind protons with planetary hydrogen atoms, and photoionization, leads to the production of initially cold ions of planetary origin. We found that the ion production rates for the studied planets can vary over a wide range, from ~ 25 10 0 . 1 s -1 to ~ 30 10 3 . 5 s -1 , depending on the stellar wind conditions and the assumed XUV exposure of the upper atmosphere. Our findings indicate that most likely the majority of these planetary ions are picked up by the stellar wind and lost from the planet. Finally, we estimate the long-time non-thermal ion pick-up escape for the studied planets and compare them with the thermal escape. According to our estimates, non-thermal escape of picked up ionized hydrogen atoms over a planet's lifetime varies between ~0.4 Earth ocean equivalent amounts of hydrogen (EOH) to < 3 EOH and usually is several times smaller in comparison to the thermal atmospheric escape rates. Keywords: stellar activity, low mass stars, early atmospheres, Earth-like exoplanets, ENAs, ion escape, habitability","pages":[2]},{"title":"XUV exposed, non-hydrostatic hydrogen-rich upper atmospheres of terrestrial planets II: Hydrogen coronae and ion escape","content":"Kristina G. Kislyakova 1,2 , Helmut Lammer 1 , Mats Holmström 3 , Mykhaylo Panchenko 1 , Petra Odert 1,2 , Nikolai V. Erkaev 4 , Martin Leitzinger 2 , Maxim L. Khodachenko 1 , Yuri N. Kulikov 5 , Manuel Güdel 6 , Arnold Hanslmeier 2 1 Austrian Academy of Sciences, Space Research Institute, Schmiedlstr. 6, A-8042 Graz, Austria (kristina.kislyakova@oeaw.ac.at, maxim.khodachenko@oeaw.ac.at, helmut.lammer@oeaw.ac.at, petra.odert@oeaw.ac.at, mykhaylo.panchenko@oeaw.ac.at) 2 Institute for Physics, University of Graz, Universitätsplatz 5, A-8010 Graz, Austria (martin.leitzinger@uni-graz.at, arnold.hanslmeier@uni-graz.at) 3 Swedish Institute of Space Physics, P.O. Box 812, SE-98128 Kiruna, Sweden (matsh@irf.se) 4 Institute of Computational Modelling, Siberian Division of Russian Academy of Sciences, Akademgorodok 28/44 660036 Krasnoyarsk, Russian Federation (erkaev@icm.krasn.ru) 5 Polar Geophysical Institute (PGI), Russian Academy of Sciences, Khalturina Str. 15, Murmansk, 183010, Russian Federation (kulikov@pgi.ru) 6 Institute for Astrophysics, University of Vienna, Türkenschanzstr. 17, 1180, Austria (manuel.guedel@univie.ac.at) Corresponding Authors: Kristina G. Kislyakova E-mail: kislyakova.kristina@oeaw.ac.at Austrian Academy of Sciences Space Research Institute Schmiedlstr. 6, A-8042 Graz Austria Submitted to ASTROBIOLOGY","pages":[1]},{"title":"1. INTRODUCTION","content":"Recent discoveries of so-called low density 'super-Earths' by various ground- and spacebased exoplanet-transit surveys indicate large populations of volatile-rich big rocky planets. Findings from ESOs High Accuracy Radial velocity Planetary Search project (HARPS), and from NASAs Kepler space observatory, revealed that planets which are slightly larger and more massive compared to the Earth may be very common in the Universe. From the available statistics and the discovery of Kepler-22b, a 'super-Earth' with the size of about 2.38 ± 0.13REarth within the habitable zone (HZ) of a Sun-type star, one can expect that planets orbiting within the HZ should be frequent in the Universe and should also orbit cooler, lower mass M dwarfs. Approximately 100 of them are found in the immediate neighborhood of the Sun (Scalo et al. 2007; Bonfils et al. 2011). These earlier estimations are now supported by a recent study by Dressing and Charbonneau (2013), which used optical and near-infrared photometry from the Kepler Input Catalog to estimate the occurrence rate of Earth-like planets orbiting dwarf stars. The estimation of Dressing and Charbonneau (2013), from the 248 early M dwarfs within 10 parsecs of the Sun, shows that there should be at least 9 Earth-size planets in their habitable zones. Moreover, from the radius-mass relation and the resulting density of discovered 'super-Earths', one finds that these bodies probably have rocky cores but are surrounded by significant H/He and/or H2O envelopes. These findings are in agreement with recent theoretical studies, which suggest that small planets are not necessarily rocky Earth-like bodies (e.g., Wuchterl 1993; Kuchner 2003; Léger et al . 2004; Ikoma and Hory 2012; Elkins-Tanton 2011; Lammer, 2012; Lammer et al. 2011a). For explaining the mean density of Kepler 11d, Kepler 11e, and Kepler 11f these 'super-Earths'' require dense H/He envelopes, similar to Uranus and Neptune, while Kepler-11b and 11c may have also additional H2O to their H/He gas envelopes (Lissauer et al . 2011), and GJ 1214b (Charbonneau et al. , 2009) or 55Cnc e (Endl et al. , 2012) may contain a huge amount of H2O. If Earth-like and 'super-Earth'- type exoplanets can accumulate hydrogen from the nebula gas of an equivalent amount of 100 to 1000, and even up to 10 4 times, that of an Earth ocean depends on the nebula dissipation time, the formation time of the protoplanet, its luminosity, and nebula characteristics such as grain depletion factors, etc. (e.g., Mizuno et al ., 1978; Hayashi et al ., 1979; Ikoma and Genda, 2006; Rafikov, 2006). Although Solar System planets such as Venus, Earth and Mars lost their nebula-based hydrogen envelopes during the first 100 Myr after their origin, or never accumulated such huge amounts due to step-wise accretion after the nebula gas disappeared, terrestrial planets in other systems evolve under different conditions and may capture such a dense protoatmosphere which they may not lose during the extreme active period of their host stars. To understand how frequent 'rocky' terrestrial planets really are, more observations are certainly needed. From the available statistics one can conclude that Earth-analogue class I habitats (Lammer et al. , 2009a; Lammer, 2013) have to be","pages":[2,3,4]},{"title":"and","content":"The question if more massive 'super-Earths' can maintain plate tectonics over time spans of several Gyr is controversial (e.g., Valencia et al. , 2007; van Heck and Tackley, 2011; Korenaga, 2010). However, in this work we will not discuss the pro and contra about geophysical processes, but focus on the stellar wind erosion of captured H/He envelopes, orand? the hydrogen content of outgassed hydrogen-rich steam atmospheres, because the proto-atmosphere escape determines if a planet will evolve to an Earth-like habitat or may remain as a mini-Neptune. As it is shown by Erkaev et al. (2013) (part I of this study), depending on the availability of possible IR-cooling molecules and the planets average density, hydrogenrich 'super-Earths' orbiting inside the HZ will experience hydrodynamic blow-off only for XUV fluxes several 10 times higher compared to today's Sun. Most of their lifetime the upper atmospheres of these planets will experience strong Jeans escape which is still weaker compared to blow-off, so that they may not lose efficiently their dense hydrogen envelopes. Jeans escape is the classical thermal escape mechanism based on the fact that the atmospheric particles have velocities according to the Maxwell distribution. Individual particles in the high tail of the distribution may reach escape velocity at the exobase altitude, where the mean free path is comparable to the scale height, so that they can escape from the planet's atmosphere. When the thermosphere temperature rises due to heating by the stellar XUV radiation, the number of these energetic particles increases and the atmosphere finally reaches the state when the majority of the particles have velocities equal to or exceeding the escape velocity. In this case the atmosphere is not hydrostatic anymore, and starts to expand similar to the Parker-type solar corona. This mechanism is called blow-off and leads to a stronger escape in comparison to the Jeans mechanism. The blow-off stage is more easily reached at less massive hydrogen-rich planets with mass equal to that of the Earth. These planets experience hydrodynamic blow-off for much longer, and change from the blow-off regime to the Jeans-type escape for XUV fluxes which are < 10 times of today's Sun. Because of XUV heating and expansion of their upper atmospheres, both of our test planets should produce extended exospheres or hydrogen coronae distributed above possible magnetic obstacles defined by intrinsic or induced magnetic fields. In such cases the hydrogen-rich upper atmosphere will not be protected by possible magnetospheres like on present-day Earth, but could be eroded by the stellar wind plasma flow and lost from the planet in the form of ions (Erkaev et al ., 2005; Lammer et al. , 2007). Besides thermal escape from the hydrogen-dominated upper atmosphere of the two considered test-planets (Erkaev et al ., 2013), briefly discussed above, one can expect that non-thermal atmospheric escape processes will also contribute to the losses. Nonthermal escape processes can be separated in ion escape and photochemical, as well as kinetic, processes which accelerate atoms beyond escape energy. Ions can escape from an upper atmosphere if the exosphere is not protected by a strong magnetic field and stretches above the magnetopause. In such a case exospheric neutral atoms can interact with the host stars solar/stellar plasma (i.e., winds, CMEs) environment. The hydrogen atoms which flow upward from the lower thermosphere will be ionized by the stellar radiation, electron impact or charge exchange and then accelerated by electric fields within the solar/stellar wind plasma flow around the planetary obstacle (i.e. ionopause, magnetopause), so that they are finally picked up and lost form the planet's gravity field (e.g., Lammer et al ., 2007; Ma and Nagy, 2007; Lammer, 2013). From space missions to non- or weakly magnetized planets such as Venus and/or Mars it is known that planetary ions can also be detached from an ionopause by plasma instabilities in the form of ionospheric clouds (Terada et al ., 2002; Penz et al. , 2004; Möstl et al ., 2011), or by momentum transport triggered outflow through the planetary tail. On Earth ions outflow also over Polar Regions along open magnetic field lines (Lundin et al ., 2007; Yau and André, 1997; Wei et al ., 2012). From the analysis of the available ion escape data from Venus and Mars by the ASPERA instruments on board of Venus Express and Mars Express, as well as from theoretical models, one can conclude that ion pick-up is a very dominant permanently acting non-thermal ion escape process, and most likely more efficient compared to the sporadic losses triggered by plasma instabilities or outflow through the planets tail. However, there may be extreme solar events which can enhance the ion outflow sporadically by cool ion outflow or plasma instabilities. Non-thermal escape processes of neutral atoms are caused by sputtering of atmospheric neutral atoms, photochemical processes such as dissociative recombination, and charge exchange. Direct escape by sputtering is only a relevant process for low mass bodies which have a mass ≤ Mars. utHowever, even in the case of Mars one can expect that sputter loss rates are an order of magnitude lower compared for instance to ion pickup (e.g., Leblanc and Johnson, 2002; Chassefière and Leblanc, 2004; Lammer et al ., 2013). Direct escape of heavy neutral atoms, such as O and C, caused by photochemical processes is expected to be higher compared to ion escape from Mars (e.g., Krestyanikova and Shematovich, 2005; Chaufray et al., 2007; 2006; Fox and Hać, 2009; Lammer et al., 2013) but negligible or lower at more massive planets such as Venus (Gröller et al., 2010; 2012) or the Earth. Lighter atoms such as atomic hydrogen can also escape directly from more massive planets with escape rates lower or comparable to ion escape. Theoretical models which studied the photochemical escape rates of H atoms (Shematovich, 2010) and ion pick-up ion escape rates (Erkaev et al ., 2005) from the hot Jupiter HD 208459b indicate comparable loss rates of the order of ≤ 10 9 g s -1 , which are an order of magnitude lower compared to the modeled thermal escape (e.g., Yelle, 2004; 2006; Tian et al ., 2005a; Penz et al ., 2008b; García Muñoz, 2007; Murray-Clay et al. , 2009; Linsky et al ., 2010; Koskinen et al ., 2012). From the brief overview on various non-thermal atmospheric escape processes, one can conclude that stellar wind induced ion erosion from XUV-heated and extended hydrogen-rich thermospheres (Erkaev et al ., 2013), where H atoms will most likely not be protected by a possible magnetosphere, so-called ion pick-up will be one of the most efficient non-thermal atmospheric escape process. Because of many unknowns related to minor atmospheric species in exoplanet atmospheres, as well as magnetic field properties, a study of more complex but most likely less effective processes, such as cool ion or polar outflow and photochemical non-thermal escape processes which are not even well understood at Solar System planets including the Earth, would yield highly speculative results. Therefore, in this study we focus on the modeling of the stellar wind plasma interaction, related ion production rates via charge-exchange and photoionization, and escape estimates of planetary pick-up ions from XUV exposed upper atmospheres which originate from hydrogen-rich thermospheres of an Earth-like ( R pl=1 R Earth, M pl=1 M Earth) planet in comparison with a 'super-Earth' ( R pl=2 R Earth, M pl=10 M Earth). For reasons of comparative escape studies between thermal and non-thermal ion pick-up, we study the same test planets as investigated by Erkaev et al. (2013) within an orbit of a typical HZ of an M star with the size and mass of ~0.45 R Sun. For the host star of our test planets we use the well observed dwarf star GJ 436 (Ehrenreich et al. , 2011; von Braun et al. , 2012, France et al. , 2012) as a proxy. So far the formation of such extended hydrogen coronae was only addressed in a brief way in Lammer et al. (2011a; 2011b), but never modeled in detail. In this study we apply a coupled Direct Simulation Monte Carlo (DSMC) upper atmosphere - stellar wind plasma interaction model (Holmström et al. , 2008; Ekenbäck et al. , 2010) to the results of Erkaev et al. (2012). In Sect. 2 we describe the DSMC model, which is used for the calculation of the exosphere and related hydrogen coronae, as well as the coupled solar/stellar wind plasma upper atmosphere interaction model. We validate our model by applying it to the Earth's geocorona and comparing the simulation results with the present-day exosphere hydrogen density and energetic neutral atom (ENA) observations by NASAs Interstellar Boundary Explorer (IBEX) satellite near the magnetopause boundary at ~10 R Earth. After validating our model for the geocorona of present-day Earth, in Sect. 3 we describe the radiation and plasma parameters of our chosen M-type host star proxy, Gliese 436. In Sect. 4 we present the modeling results for the extended hydrogen coronae. In Sect. 4.1 the results of the stellar wind plasma interaction and the production of ENAs are shown as well as related planetary hydrogen ion pick-up escape rates as a function of the XUV flux values from 1 to 100 times that of today's Sun. The atmospheric ion escape rates are compared with the thermal hydrogen neutral loss rates modeled by Erkaev et al. (2012) in Section 4.2. In Section 4.3 we estimate the possible mass loss of hydrogen ions during the planetary lifetime and discuss the implications of our findings for the evolution of Earthlike and more massive 'super-Earths'. Section 5 summarizes the findings of our study.","pages":[4,5,6,7,8]},{"title":"2 STELLAR WIND-UPPER ATMOSPHERE INTERACTION","content":"As shown by previous studies of Watson et al. (1981), Kasting and Pollack (1983), Tian et al. (2005b; 2008a; 2008b), Volkov et al. (2011), and Erkaev et al. (2013), hydrogen-rich terrestrial planets experience XUV-heated and hydrodynamically expanding non-hydrostatic upper atmosphere conditions. Depending on the particular environment (e.g., XUV flux, orbital distance, availability of IR-cooling molecules, the planet's average density, etc.) the results of these studies indicate that such planets can expand their exobase level, which separates the collision dominated atmosphere from the collisionless region to distances from a few R pl up to more than 20 R pl. As a result of such an expansion of the upper atmosphere an intrinsic planetary magnetic field will most likely not protect the exosphere against the stellar wind plasma flow (Lichtenegger et al ., 2010; Lammer, 2012; Lammer et al ., 2011a). Due to the interaction between the stellar wind plasma flow and the XUV-heated non-hydrostatic upper neutral atmosphere of the planet, energetic neutral atoms (ENAs) are produced. ENAs originate due to charge-exchange when an electron is transferred from a planetary neutral atom to a stellar wind proton which then becomes an ENA. This interaction process between the stellar wind plasma and the upper atmosphere plays a significant role in the ion erosion of upper planetary atmospheres (e.g., Lundin et al. , 2007; Lammer, 2013). The production of ENAs after the interaction of stellar wind protons via charge exchange with various upper atmosphere species is described by the reactions in eq. (1-3). After its production an ENA continues to travel with the initial velocity and energy of the stellar wind proton. The atmospheric atom in turn becomes an initially cold ion which can afterwards be lost from the atmosphere due to the ion pick-up process (Lammer, 2013). In the current study we focus our attention only on the reaction shown in eq. (1) which will dominate the stellar wind interaction with planetary hydrogen coronae around hydrogen-rich terrestrial planets.","pages":[8,9]},{"title":"2.1 Model description","content":"In the current study the plasma interaction between the stellar wind and the upper atmosphere of the Earth-like planet and 'super-Earth' is modeled applying a Direct Simulation Monte Carlo (DSMC) upper atmosphere-exosphere particle model which is coupled with a stellar wind particle interaction code. The 3D model is described in detail in Holmström et al. (2008) and Ekenbäck et al. (2010) and includes stellar wind protons and planetary hydrogen atoms. The latter are launched into the simulation domain from the upper atmosphere. The applied collision cross sections for hydrogen atoms, σ H-H, and for protons and hydrogen atoms, σ H+-H, are 10 -17 cm 2 and 2 × 10 -15 cm 2 (Ekenbäck et al ., 2010) respectively. Charge exchange between stellar wind protons and exospheric hydrogen atoms takes place outside a conic shaped obstacle that represents the magnetoionopause of the studied planet. Stellar wind protons that have charge-exchanged according to the reaction shown in eq. (1) become ENAs. Besides of the charge-exchange reaction, the model includes gravitation of the planet and tidal effects as well as scattering by atmospheric atoms of UV photons (radiation pressure) and photoionization by stellar photons. Inclusion of the tidalgenerating potential into the equations leads to the extension of the atmosphere toward and backward from the host star, and in extreme cases to Roche lobe overflow. Nevertheless, these effects are important for 'hot Jupiters' which are located at very close distance to their host stars, and do not play a significant role for the test planets we consider in the present study. All collisions are modeled using a DSMC algorithm (Holmström et al., 2008; Ekenbäck et al., 2010). The main code uses the FLASH software developed at the University of Chicago which provides adaptive grids and is fully parallelized (Fryxell et al. , 2000). The coordinate system is centered at the center of the planet with mass pl M , the 1 x -axis is pointing towards the center of mass of the system, the 3 x -axis is parallel to the direction of the angular velocity of rotation , and the 2 x -axis points in the opposite direction to the planet's velocity. St M is the mass of the planets host star. Tidal potential, Coriolis and centrifugal forces, as well as the gravitation of the star and planet acting on a hydrogen neutral atom, are included in the code in the following way (Chandrasekhar, 1963) Here i v are the components of the velocity vector of a particle, G is Newton's gravitational constant, R the distance between the centers of mass, the Levi-Civita symbol, and 3 R GM St . The first term in the right-hand side of the eq. (4) represents the centrifugal force, the second is the tidal-generating potential, the third the gravitation of the planet's host star and the planet while the last term stands for the Coriolis force. The self-gravitational potential of a particle is neglected. Charge exchange reactions between a neutral planetary hydrogen atom and a stellar wind proton may take place outside the obstacle representing a magneto- or ionopause Here s R stands for the magnetosphere or planetary obstacle stand-off distance and t R the width of the obstacle. Since the obstacle shape and location depend strongly on the planetary magnetic field strength, one may model the interaction of the stellar wind with magnetized as well as with non- or weakly magnetized planets by the appropriate choice of s R and t R .","pages":[9,10,11]},{"title":"2.2 Exosphere modeling of Earth's observed atomic hydrogen geocorona","content":"ENAs have been observed around all Solar System planets where a spacecraft was equipped with a corresponding instrument (e.g., Futaana et al ., 2006; Galli et al. , 2008; Lammer et al ., 2011a; 2011b). As shown in Fig. 1, the Interstellar Boundary Explorer (IBEX) satellite recently observed an ENA formation zone around Earth's subsolar magnetopause stand-off distance, which is located at 10 R Earth from the planet's center (Fuselier et al. , 2010). Before we apply our model to hydrogen-rich exoplanets, we validate it by reproducing the geocorona and recent ENA observations (Fuselier et al. 2010) around the Earth's magnetopause by the NASAs IBEX satellite of present-day Earth. Fig. 2 shows our modeling results for Earth's geocorona interacting with the present-day solar wind by taking all parameters of Earth's exosphere as given in Table 1 as an input. The average neutral hydrogen atom density at the magnetopause level obtained from our model is estimated to be ~8 cm -3 at the distance of ~10 R Earth. This density value coincides very well with the exospheric number densities inferred from the IBEX observations of ENAs near the magnetopause. In the case of the IBEX observation at March 28 2009, the computed and observed proton fluxes show an exosphere hydrogen density at a geocentric distance of ~10 R Earth of ~4 - 11 cm -3 (Fuselier et al ., 2010). The estimates of the modeled ENA flux are in good agreement with the observed flux as well, predicting the flux of approximately 600 (cm² s sr keV) -1 . This value falls inside the observed ENA interval of ~530 - 2300 (cm² s sr keV) -1 (Fuselier et al ., 2010). The IBEX observation and our model validation can also be seen as a confirmation that under extreme radiation and plasma environments of the young Sun or more active stars a huge ENA formation zone, as suggested by Chassefière (1996) and Lammer et al. (2011; 2012), should be produced in the stellar wind interaction region of a hydrogen-rich extended upper atmosphere of an Earth-size planet when the exosphere density near the magnetopause is more than 10 6 times larger than that observed at present-day Earth. In the following sections we describe the input parameters and our applied exosphere and ENA models to the XUV exposed hydrogen-rich Earth-size test planets.","pages":[11,12]},{"title":"3. GLIESE 436: A HOST STAR PROXY FOR HYDROGEN-RICH TERRESTRIAL TEST PLANETS","content":"3.1 The radiation environment of Gliese 436 Recently Ehrenreich et al. (2011) observed with the Hubble Space Telescope Imaging Spectrograph (HST/STIS) the Lyman-α emission (1215.67 Å) of neutral hydrogen atoms from the low mass M star, GJ 436. Because this emission is a main contributor to the ultraviolet flux it can also be used as a main tracer in studies of thermospheric heating, thermal escape, and possible absorption by extended hydrogen coronae and/or ENAs (e.g. Vidal-Madjar et al. , 2003; Holmström et al ., 2008; Ekenbäck et al ., 2010; Ben-Jaffel and Hosseini, 2010; Lecavelier des Etangs et al ., 2010; Lammer et al. , 2011b; Ehrenreich et al ., 2012, Lammer, 2013) during transit observations with ultraviolet transmission spectroscopy. We use GJ 436 as a typical M-type host star for our test-planet parameter studies. GJ 436 is a M2.5 dwarf star which is 10.2 pc away from the Sun. The dwarf star hosts a transiting 'hot Neptune' at an orbital distance of about 0.03 AU (Butler et al. , 2004; Gillon et al. , 2007). We adopt values for stellar mass and radius of 0.45 MSun and 0.45 RSun, respectively, which are consistent with several independent parameter determinations of GJ 436 (Torres, 2007; Maness et al. , 2007; von Braun et al. , 2012). The location of the habitable zone (HZ) is calculated following Selsis et al. (2007). As their relations are only valid for effective temperatures down to 3700 K, this value is used instead of the true temperature of GJ 436, which is slightly lower (3400-3600 K; Torres 2007; von Braun et al. 2012). Further, we adopt a bolometric luminosity of 0.026 LSun (Torres, 2007). This leads to a HZ extent of 0.12-0.36 AU assuming the limit of 50% clouds, as typical for the Earth. Hence, the center of the HZ is located at 0.24 AU, which we adopt as the orbit of our hypothetical exo-Earth. The orbital period of an Earth-analog planet within the HZ of GJ 436 corresponds to approximately 63.7 days, the orbital velocity to about 41 km s -1 , and the angular velocity to 1.14·10 -6 rad s -1 . The age of GJ 436 is about 6±5 Gyr and is not well constrained (Torres, 2007). However, the rotation period of 48 days (Demory et al. , 2007) yields an estimated age of 2.5-3 Gyr (Barnes, 2007; Engle and Guinan, 2011). This estimation is in agreement with the lack of chromospheric activity indicated by the presence of Hα in absorption spectra. GJ 436 has been detected by the ROSAT All-Sky Survey, which revealed an Xray luminosity of log LX = 27.13 erg s -1 . Recent observations by the XMM-Newton spacecraft yielded a smaller value of only ~25.96 erg s -1 (Sanz-Forcada et al. , 2011). We adopt the latter result because of the longer exposure time and better S/N of the XMMNewton observations compared to ROSAT data. Using coronal models, Sanz-Forcada et al . (2011) extrapolated the stellar emission in the total XUV range (5 - 920Å) and found log L XUV=26.92 erg s -1 . Adopting this value and scaling it to the HZ center at 0.24 AU, we estimate an XUV flux of about 5.14 erg cm -2 s -1 , comparable to the present solar XUV flux at 1 AU of 4.64 erg cm -2 s -1 (Ribas et al. , 2005). In the past, the stellar XUV flux, which was emitted from GJ 436 was certainly higher. The high-energy emission of young M dwarfs is saturated at log( L X/ L bol)~ -3 (e.g. Scalo et al ., 2007), hence the maximum possible log( L X) for GJ 436 is ~29 erg s -1 . Assuming that the XUV emission of young stars occurs predominantly in X-rays because of their hotter coronae, the maximum XUV flux at the Earth-equivalent orbit around GJ 436 was roughly 700 erg cm -2 s -1 , or ~150 F XUV,now. Lyman-alpha emission of GJ 436 was detected by Ehrenreich et al. (2011) using HST/STIS observations. They reconstructed the intrinsic stellar emission by correcting for interstellar medium (ISM) absorption, leading to an apparent flux observed at Earth of ~2.7±0.7 × 10 -13 erg cm -2 s -1 . Scaled to the HZ center, this yields ~20.51 erg cm -2 s -1 , a factor of ~3.3 larger than the present solar value at 1 AU of 6.19 erg cm -2 s -1 (Ribas et al ., 2005). Recently, France et al. (2013) reconstructed the intrinsic Lyman-alpha flux of GJ 436 by using a different approach. They obtained a value of 3.5 × 10 -13 erg cm -2 s -1 with an uncertainty of about 15 - 30 %, which is slightly higher than the value given by Ehrenreich et al. (2011), but is consistent with the errors. The relevant stellar parameters and the measured radiation properties used in the model simulations for various assumed XUV flux values of a Gliese 436-type M dwarf are shown in Table 2. The photoionization rates corresponding to the four XUV flux enhancement factors were scaled from the average present solar value at Earth (1.1 × 10 -7 s -1 ; Hodges, 1994, Bzowski, 2008) to the corresponding enhancement factors. The photoionization rate is usually calculated as the product of ionization cross-section and spectral flux integrated over all wavelengths below the ionization threshold. Since full M star XUV spectra for different activity levels are currently not available, we assume that the present spectral energy distribution is equal to the solar one and scale it up by the constant factors given in Table 2. The UV absorption rates correspond to the product of the photon flux at the center of the Lyman-alpha line and the total absorption cross-section (5.47 × 10 -15 cm 2 Å; e.g. Quémerais, 2006). Adopting the reconstructed intrinsic line profile of Ehrenreich et al. (2011), the present value of the photon flux at the HZ center of GJ 436 is estimated to be ~6.9 × 10 -3 s -1 .. To scale the Lyman-alpha flux and, hence, the absorption rate to higher XUV flux emission levels, we use the scaling between X-rays and Lyman-α from Ehrenreich et al. (2011). This assumes that L X/ L bol ≈ L XUV/ L bol and that the central Lyman-α flux scales approximately as the integrated line emission. The resulting absorption rates are also shown in Table 2.","pages":[12,13,14]},{"title":"3.2 Expected stellar wind plasma properties","content":"Depending on the mass, size and resulting luminosity of the host star, the corresponding scaled HZ location in the case of GJ 436 is at 0.24 AU. This is a much closer orbital distance compared to that of the Earth (1 AU). As pointed out by Khodachenko et al. (2007), at orbital locations < 0.5 AU the flow of dense plasma related to stellar winds and coronal mass ejections (CMEs), energetic particle fluxes and XUV radiation cannot be neglected. Depending on the stand-off distance of the planetary obstacle which forms when the stellar plasma flow is deflected around the planet, previous test particle model results of Lammer et al. (2007) indicate that CO2-rich Earth-like exoplanets having no or only weak magnetic moments may lose from tens to hundreds of bars of atmospheric pressure, or even their whole atmospheres, due to the CME induced O + ion pick-up at orbital distances ≤ 0.2 AU. Due to the uncertainties on the mass loss and related plasma outflow from M dwarfs, we assume in our study, as in Khodachenko et al. (2007) and Lammer et al . (2007), the plasma environment close to the stars obtained from solar observations. There exist a limited number of measurements of the mass loss rates for M stars (Wood et al., 2005, Ehrenreich et al. , 2011), which in principle may be used for estimation of specific stellar wind density and velocity. For these stars the mass loss rates are comparable or less than the mass loss rate of the Sun. At the same time, for the Sun we have a much better knowledge of the distribution and evolution of active solar regions and of the mass outflow in the form of solar wind and CMEs, which we use in the present study. Note that stellar wind density and/or velocity lower than the solar (assumed) values would reduce the portion of the produced and picked up ions. Such a reduction would not change our main conclusion that the ion pick-up loss makes up only several percent of the thermal loss, and the further results can be considered as an upper limit for ion pickup near an M dwarf like Gliese 436. For the accurate study of stellar-planetary interactions one needs a reliable model which can simulate the propagation and evolution of the stellar wind plasma. For modeling the propagation and evolution of the stellar wind we use the Versatile Advection Code (VAC) (Toth, 1996). This model is able to simulate spatial and temporal evolution of the solar/stellar wind, as well as CMEs, from orbital distances ≥0.14 AU. It/The model includes a self-consistent Parker-type co-rotating magnetic field, and is based on the solution of the set of the ideal (non-resistive) non-relativistic magnetohydrodynamic equations (Toth, 1996). We use a spherical uniform computation domain, which occupies a radial distance region between 0.14 < R < 1 AU. The stellar wind in the model flows through the inner boundary of the computation domain at a semi-major axis location d = 0.14 AU and propagates out through the outer radial boundary at d = 1 AU. A self-consistent expanding stellar wind plasma flow under the conditions of a frozen-in, co-rotating, Parker-type, spiral magnetic field is numerically simulated (Odstrčil et al ., 1999; Rucker et al. , 2008). The typical parameters of the expected flow of the stellar wind plasma at d = 0.14 AU are imposed along the inner radial boundary (Odstrčil et al ., 1999) with an initial proton concentration n 0 = 500 cm -3 , stellar wind proton temperature, T 0 = 500 kK, and a radial stellar wind velocity v r0 = 300 km s -1 . For investigating the propagation of CMEs, in a second step the simulation of a CME cloud with an initial proton density n 0 = 1000 cm -3 , proton temperature, T 0 = 1700 kK, and a radial stellar wind velocity v r0 = 600 km s -1 is imposed at the inner boundary of the computation domain as a time-dependent injection of hot and dense plasma into the ambient stellar wind (Odstrčil et al ., 1999; Odstrčil et al. , 2004). Fig. 3 shows radial profiles of the maximum values of plasma parameters ( n , v r, T ) during a solar analogue CME event (dashed lines, Case II) for a typical M-star with mass M s ~ 0.45 M Sun and a rotation period 2.5 days, and those for the stellar wind itself (solid lines Case I). Therefore, in the stellar wind plasma interaction modeling with the upper atmosphere, described below, two types of stellar plasma parameters representing the lower (Case I) and upper limit (Case II) conditions at the HZ location of our test planets at 0.24 AU were used as inputs: Here n sw corresponds to stellar wind concentration, v sw denotes its bulk velocity and T sw stands for the stellar wind temperature. These values cover the predicted range for the expected stellar wind plasma parameters of GJ 436 at the HZ of the system. The upper limit (Case II) can also be considered as a proxy for modeling of frequent CME events in the system when the next CME event hits the planet immediately after the previous one. We can estimate the recovery time of the planetary atmosphere after the CME event on a very simple way. Since the test planets considered in the article are not magnetized, we assume that the recovery speed coincides with the sound speed (or the speed of slow magnetoacoustic wave), so that 2 / 1 / H exo B t s t CME m T k R c R where t R is the obstacle width, 3 / 5 is the ratio of the specific heats, B k is the Boltzmann constant, H m is the mass of a hydrogen atom and exo T is the exobase temperature. Taking the parameters from Tables 3 and 4 and depending on the characteristic size of the obstacle and the temperature, this time varies between approximately 7 and 14 hours for the Earth-type planet and 64 and 80 hours for the 'super-Earth'. The next section is dedicated to the discussion of the obtained results and presents also the ion production rates for the hydrogen-rich Earth-like planet and the 'super-Earth'.","pages":[14,15,16]},{"title":"4. HYDROGEN EXOSPHERES, ENA PRODUCTION AND ION ESCAPE","content":"In the following section we study the modification of the extended hydrogen exosphere due to the interaction of it with the stellar XUV and plasma flux. Because our hydrogenrich test-planets orbit within a typical M-star HZ at ~0.24 AU they will be affected by tides. As it was discussed in Khodachenko et al. (2007) tides arise because of the finite extension of the planetary body in the inhomogeneous gravitational field of its host star so that the continuous action of the tides will reduce the planetary rotation rate or may result in a synchronous rotation (Grießmeier et al. , 2005). The intrinsic magnetic field of a terrestrial planet is an essential factor for planetary protection from the ion pick-up atmosphere loss process. As shown in Khodachenko et al. (2007) and Lammer et al . (2007), because of the close orbital location within M-star HZs, the magnetosphere field of a terrestrial planet is more compressed due to the denser stellar wind impact compared with that of the solar wind at present-day Earth at 1 AU. In view of this fact the radial distance of the extended exobase of an XUV heated hydrogen rich upper atmosphere will most likely coincide with the planetary magnetopause or ionopause distance (e.g., Lammer et al ., 2009a; Lammer et al ., 2012, Lammer, 2013).","pages":[17]},{"title":"4.1 Input parameters and modeling results","content":"As it was briefly discussed in Sect. 3.2, the magnetic moments of terrestrial planets, and especially that of 'super-Earths' within close orbital distances, are expected to be weak (e.g., Gaidos et al ., 2010; Tachinami et al ., 2011; Morad et al ., 2011; Stamenkovic' et al., 2011Stamenkovi'c et al., 2012). This would lead to magnetoshperes or ionospheres which are compressed towards the planet's expanded non-hydrostatic upper atmosphere by the strong dynamic ram pressure of the dense stellar wind plasma. On the other hand if the exobase level expands beyond several planetary radii one can also expect that an Earth-type magnetosphere will not protect the exosphere (Fig. 5: Lammer et al ., 2007; Fig. 6 right panel: Lammer et al ., 2011a). Taking this considerations into account, the planetary obstacle most likely is located very close above the exobase level (Lammer et al. 2009b). Because the shape of the planetary obstacle affects the ENA production and resulting loss of planetary hydrogen ions, we study also the influence of the obstacle width on the ion production rate and the upper atmosphere erosion. In the first case the magnetic obstacle width t R in the eq. (5) was assumed to be 1.5 times greater than the magnetopause distance. This relation and its resulting obstacle shape is close to the observed magnetosphere of the present-day Earth and may occur if the planet has an intrinsic magnetic dynamo. In the second case we choose t s R R so that it resembles more a Venus-type planetary obstacle which may correspond to a planet with no magnetic field, or only a very weak dynamo. By decreasing of the planetary obstacle width the ion production will significantly increase, so that a terrestrial planet with a Venus-type obstacle, where t s R R , may lose larger amounts of atmospheric gas in ionized form (see Sect. 4.2). In the present study we do not specify the magnetic moment of a planet, but only chose a magnetospheric obstacle. For illustrating the differences between the stellar wind plasma interaction with a hydrogen-rich terrestrial planet which is exposed to both a weak XUV flux and an extremely strong one, we irradiate the two test-planets with the XUV flux of the present Sun (1 XUV) and with a 100 times higher XUV flux (100 XUV). Moreover, we investigate for these two XUV flux cases several stellar wind and obstacle scenarios. The main input parameters at the inner boundary of our simulation domain are shown for 4 selected cases in Tables 3 and 4. As it was mentioned earlier, we apply the results obtained by Erkaev et al. (2012) to the upper atmosphere input paramters of our model. Erkaev et al. (2012) studied the thermosphere structure of a hydrogen-dominated Earth and a 'super-Earth' ( R pl=2 R Earth; M pl=10 M pl) with a hydrodynamic upper atmosphere model which solves the equations of mass, momentum and energy conservation for low and high heating efficiencies, η of 15 % and 40 %, respectively. η defines the percentage of the incoming XUV energy which is transferred into heating of the neutral gas. Table 4 shows the same input paramters for our model for a hotter atmosphere corresponding to the upper atmosphere values of Erkaev et al . (2013) with η = 40%. As one can see from Tables 3 and 4, the exobase distance which is chosen as our inner model boundary and the temperature are increasing for higher XUV fluxes. This behavior can be expected by taking into account a more intensive radiation flux from the parent star. Enhanced heating flux makes the scale height of the atmosphere increase, which in its turn moves the exobase to higher location. One can also see that an increase of the heating efficiency leads to an increase of the planet's obstacle stand-off (which for the studied non-magnetized planets practically coincides with the exobase) distances as well. Because of the expansion of the upper atmosphere under more extreme heating conditions (40%) the exobase densities are smaller in comparison to the 15% cases. Figs. 4 and 5 show the modeled hydrogen exospheres and the related stellar plasma interaction under various conditions around the test planets. All the figures show cross-sections of a 3D cloud in the 2 1 , x x plane similar to those in Fig. 2. Fig. 4 illustrates the appearance of the extended hydrogen coronae around the Earth-type planet while Fig. 5 corresponds to the 'super-Earth'. In all the cases the wider Earth-type planetary obstacle is assumed, except for Fig. 4d where a smaller Venus-like obstacle is adopted. The white area around the planets (which are shown as black dots) represents the inner atmosphere (non-hydrostatic thermosphere), which is not considered in the present study. Fig.4a and Fig.4b illustrate the influence of the XUV flux on the cloud formation. All simulation parameters for these two pictures are the same except for the XUV flux, which is chosen to be equal to and 50 times higher than the XUV flux of the present Sun. As one can see, the higher XUV flux leads to a more efficient expansion of the upper atmosphere so that charge exchange can be more intensive in the surrounding hydrogen corona. The effect of the planetary obstacle can be seen in a comparison of Fig. 4c, for an Earth-type planetary obstacle shape, with Fig.4d, for a Venus-type obstacle. In these two cases the upper atmosphere is exposed to the XUV flux which is 50 times higher compared to that of today's Sun. Figs. 5a and 5b illustrate the importance of the heating efficiency. We show two model runs for the 'super-Earth' for a comparison. Only the upper atmosphere parameters corresponding to the heating efficiencies were changed. A higher heating efficiency results in additional expansion of the upper atmosphere and in increasing production of ENAs in the vicinity of the planet (blue and red dots). Figs. 5c and 5d show the effect of the stellar wind velocity and density on the hydrogen coronae formation. Both figures, 5c and 5d, correspond to the most extreme XUV case, which is 100 times higher than that of today's Sun. As expected, the extreme stellar conditions result in a denser and faster stellar plasma flow, higher XUV fluxes and more intense heating of the upper atmosphere, as well as a decrease of the planetary obstacle width, which all lead to more intensive interaction processes. The ENA part of the hydrogen corona (blue and red dots) becomes more visible, meaning an increase of the atmospheric erosion processes. One can see that a huge amount of exospheric hydrogen atoms is ionized or underwent charge exchange reactions in both cases, but stronger stellar wind significantly increases the number of ENAs in the vicinity of the planet as suggested by Chassefière, (1996). Chassefìère (1996) studied the hydrodynamic outflow and escape of hydrogen atoms from a hydrogen-dominated expanded thermosphere from early Venus. From this study it was estimated that the huge ENA cloud, which is generated via charge exchange due to the interaction between an extended exosphere and the surrounding solar wind plasma of the young Sun, may contribute to about 75 % of the energy inside the thermosphere which is used for escape of the outward flowing H atoms (see Fig. 3 in Chassefière, 1996). The stellar EUV flux is deposited mainly in the lower thermosphere (Erkaev et al ., 2013), while the ENA flux directed toward the planet should be deposited at an atmospheric layer below the exobase. It can contribute to thermospheric heating and may as a consequence modify the upper atmosphere structure which could result in an enhancement of the thermal escape rate. Our results related to the efficient production of ENAs around the planetary obstacle support the hypothesis of Chassefière (1996) that ENAs may contribute to upper atmosphere heating. A study which investigates the possible heating contribution of ENAs additionally to the stellar XUV flux is beyond the scope of this particular work, but is in progress for a follow up study during the near future. We note also that ENA clouds near the terrestrial exoplanets within orbits around M dwarfs might be observable in the stellar Lyman-alpha line by the Hubble Space Telescope and in higher resolution beyond the geocorona in the near future by the World Space Observatory-UV (Shustov et al. , 2009; Lammer et al ., 2011b). In the next section we estimate how many of the produced planetary ions in the hydrogen coronae are picked up by the stellar wind plasma, and hence are lost from the planet.","pages":[17,18,19,20]},{"title":"4.2 Stellar wind induced atmospheric erosion of planetary hydrogen ions","content":"As discussed above, interaction processes between the stellar wind and the upper atmosphere together with the photoionization by stellar photons lead in the case of hydrogen-rich atmospheres to the production of atmospheric H + ions, see eq. (1). After ionization, the ions can be picked up by the stellar wind plasma and swept away from the planet. Because we are interested in the efficiency of the atmospheric ion escape, we estimate the average ion production rates under various conditions. We assume as discussed below that in the considered cases the production of planetary ions and the escape rate are most likely of the same order. Ions produced near and above the planet's obstacle can be lost because of the ion pick-up process. Since these particles are not neutral anymore, they can follow the magnetic field lines in the stellar wind plasma and can be swept away from the planet's gravity field. We consider the H + ions produced above the planetary obstacle, where the collisions between atmospheric particles can be neglected. It is assumed that the ions may be lost if the gyro radius is small enough in comparison to the planetary radius (e.g. if the magnetic field in the vicinity of a planet is strong enough to change the trajectory of the ions significantly). Here i m is the mass of the ion, i v is the velocity of the 'cold' planetary ion assumed to be ~7 km s -1 , q is the ion charge and B is the magnetic field near the planetary obstacle. In the case of a pure hydrogen upper atmosphere the ion mass and charge coincide with the mass and charge of a proton. The velocity of ~7 km s -1 is chosen as being slightly faster than the mean thermal velocity of a hydrogen atom for a temperature of about 2000 K. The magnetic field at the distance ~0.24 AU from an M dwarf can be roughly estimated if one assumes a dipole character of the stellar field with the initial global value in the range of ~2 - 3 kG or ~0.2 - 0.3 T (Phan-Bao et al. , 2009, Reiners, 2012). By assuming an average magnetic field on the star of 2 kG, the magnetic field at 0.24 AU is ≈ 3 10 4 . 1 G, which yields for an ion velocity of 7 km s -1 an ion gyro radius of ~525 m which is several orders of magnitude smaller compared to the radii of the studied planets. In such a case it is justified to assume that most of the produced H + ions will be swept away from the planets by the stellar wind. If we assume that the ions are accelerated by the stellar wind electric field to the velocity of the stellar wind (Case I: 330 km/s, Case II: 550 km/s), the ion gyro radius increases proportionally to ~25 - 40 km in two extreme cases. Here we assume the filling factor f=1 (see Phan-Bao et al. , 2009), i.e. the maximal possible field strength. Since the magnetic field of ~2 - 3 kG is typical for young and active M dwarfs, it could be convenient to determine the gyro radii for a weaker field of ~50 G for an older star with the age of several Gyr (Phan-Bao et al. , 2009). The magnetic field at 0.24 AU is approximately 5 10 57 . 3 G. A decrease of the magnetic field causes a proportional increase of the gyro radius (21 km for an ion velocity of 7 km s -1 , 10 3 km and 3 10 6 . 1 km for 330 km/s and 550 km/s respectively). But even the highest value of ~1600 km is several times less if compared to the planetary radius, and more than an order of magnitude lower compared to the exobase radius where most ENAs are produced. These estimates support our assumption that the majority of the exospheric ions are lost from the planet and that the ion production rate is balanced by the escape rate at least during a significant part of the stellar life time. Estimates of the ion production rates and corresponding escape rates described in the previous sections are summarized in the Tables 5 and 6 for planetary obstacles which have an Earth-like magnetosphere shape. Table 5 presents the results obtained for a hydrogen-rich Earth-like planet for two stellar wind conditions and a heating efficiency η =15% and of a higher heating efficiency η = 40%, while Table 6 summarize the similar scenarios for the 'super-Earth'. Atmospheric loss rates L ion are given in units of particles per second. As one can see from Tables 5 and 6, in the most cases the ion production and loss rate increases with the increasing XUV flux. Loss rates for faster stellar wind also exceed the corresponding values for the wind with lower velocity which is not surprising. Since the ion production rates depend not only on the assumed heating efficiency and the XUV flux, but also on the exobase density, the values for the lower-density case corresponding to a heating efficiency of 40% (Erkaev et al. , 2013) are slightly lower in comparison to the 15% case shown in Table 6. This is also the reason why the values for the cases where the stellar XUV flux is about 100 times higher than that of the present Sun are not dramatically higher (or even slightly smaller) that the ion production rates for the lower XUV fluxes, although the intensity of the interaction increases. Under the intensity of the interaction in this case we mean the ratio of produced ions to the mean exospheric density. This value increases monotonically for higher XUV fluxes in all cases considered in the present study. The reason for that is related to the corresponding exobase density that is lower because of expansion in the case of a hydrogen-rich upper atmosphere which is exposed to high XUV fluxes such as in the 100 XUV case (Erkaev et al. , 2013). To investigate the influence of the planetary obstacle shape on the H + escape rate L ion, we performed an analogous set of simulations by assuming a Venusian type planetary obstacle ( t s R R ). Tables 7 and 8 present the calculated ion production rates and estimated ion escape rates for the two test planets under the same conditions as described in Tables 5 and 6 except for the shape of the planetary obstacle. As one may see from the comparison of Tables 5 - 6 and Tables 7 - 8, reducing the width of the obstacle by 1.5 times leads to an increase in the ion production rate (i.e. the escape in general) of ≈30%. Other factors which lead to an increase of the ion production rate are related to the increase of the stellar wind density and velocity, heating efficiency η , and enhancement of the stellar XUV flux of the parent star. All these dependencies should be considered and expected. For comparison, thermal loss rates change in the range from 29 10 0 . 4 (1 XUV, η=15%) to 31 10 3 . 4 (100 XUV, η=40%) for a hydrogen-rich Earth-type planet and from 29 10 6 . 1 (1 XUV, η=15%) to 31 10 3 . 5 (100 XUV, η=40%) for a hydrogen-rich 'superEarth'. In all cases these rates exceed the presented in the current study. For more information, see Erkaev et al., (2013). If we compare the modeled H + ion pick-up loss rates with that of Mars (e.g., Lammer et al ., 2003) or Venus (Lammer et al. , 2006), which are in the order of ~10 25 s -1 , one can see that the pick-up loss rates for the hydrogen-dominated Earth-like planet are comparable for the 1 XUV case with a heating efficiency of 15 % and an Earth-like magnetopause shape, but would be a factor 10 3 higher in the case of 40 % heating efficiency and/or a more narrower Venus-type planetary obstacle. For the larger 'superEarth' and XUV cases with higher values than that of the present-day Sun the loss rates are up to 10 4 - 10 5 times higher. 4.3 Total ion escape The loss rates shown in Tables 5 - 8 can be used for rough estimation of the total ion loss from the hydrogen envelopes around the studied planets. This question is important because, as shown by Erkaev et al. (2013), volatile rich 'super-Earths' which contain IRcooling molecules can result in lower heating efficiencies of about 15 % so that for most of their lifetime they will not be in the hydrodynamic blow-off regime. In such cases nonthermal atmospheric escape processes, like the studied H + ion pick-up process, will contribute to the loss of their hydrogen-rich protoatmospheres. Before we investigate this mass loss one needs to know how long a typical M dwarf like Gliese 436 may keep a high level of the XUV and X-ray flux. According to Penz et al. (2008a) the temporal scaling law for the soft X-ray (0.6-12.4 nm or 0.1-2 keV) flux of a typical M dwarf with the mass of ≈ Sun M 4 . 0 can be described by the following relation where 28 0 10 6 . 5 L erg s -1 and t is given in Gyr. The soft X-ray flux can then be scaled for the appropriate orbital distance by using the relation 2 4 / d L F X X . Fig. 6 shows, approximately, the decrease of the soft X-ray flux of a Gliese 436 analogous M dwarf during the first 1.3 Gyr of its life time. Since at present time the scaling law for the XUV radiation of M dwarfs is not yet well constrained, we use this soft X-ray scaling law instead of the XUV scaling law in our estimation for the total H + escape. Assuming this temporal scaling law for the star and taking the ion production rates from Tables 5 - 8, we can estimate the mass loss from the hydrogen-rich Earth-like planet and the 'super-Earth' in the HZ of a Gliese 436 type M star after 4.5 Gyr (see Tables 9 and 10). For comparison the thermal escape rates are shown by using the values from Table 2 in Erkaev et al. (2013). The total ion loss is given in Earth ocean equivalent amounts of hydrogen (1EOH = 23 10 5 . 1 g) . It should also be mentioned that we do not consider escape during the first ~100 Myr, the time of extreme stellar activity of an M dwarf, so that our estimates cover the time span ~0.1 - 4.5 Gyr. As discussed in Erkaev et al. (2013) during this early extreme period the temperature in the lower thermosphere may be >> 250 K, due to magma oceans and frequent impacts. Hot lower atmosphere will enhance the atmospheric thermal escape during this early period. A follow up study which will investigate the earliest extreme evolutionary periods is in progress. In the present work we do not take into account the gradual decrease of the amount of gas in the planetary atmosphere due to escape processes, as we assume that the hydrogen reservoir contains much more gas in comparison to the amount lost . As discussed in Sect. 1, such scenarios can be considered as real because most of the recently discovered 'super-Earths' may have huge hydrogen envelopes which contain a few % of their whole mass (e.g., Lammer, 2013). If we compare the estimated atmospheric escape rates obtained for the thermal and ion pick-up processes for both test-planets in the HZ, it is clear that the thermal escape rate substantially exceeds the pick-up rate under the studied conditions. This is also the case when we consider the most extreme XUV and stellar plasma conditions, including a narrow planetary obstacle. A fraction of the evaporating neutral exosphere will be ionized so that ion pick-up will contribute to the total atmospheric escape rate, but as long as the upper atmosphere is in blow-off thermal escape will be the most important. In our study the escape rate of ionized hydrogen atoms can vary for an Earth-type planet from ~0.6 EOH under moderate conditions (15% heating efficiency, moderate stellar wind, Earth-type planetary obstacle) up to ~2.5 EOH for extreme environments (40% heating efficiency, denser and faster wind and a narrow Venusian obstacle type). The stronger gravity of the more massive 'super-Earth' keeps the atmosphere closer to the planet's surface, which slows down the charge exchange and photoionization processes. In this case the escape changes from ~0.4 EOH to ~2.14 EOH depending on the environment but remains smaller compared to escape from an Earthtype planet (ranging from ~0.6 EOH to 2.5 EOH, see above). In all studied cases the nonthermal H + pick-up rate is several times smaller in comparison with the thermal one, but makes up a significant fraction of the whole loss processes. The results of our study, together with those of Erkaev et al. (2013), indicate that terrestrial exoplanets ranging in mass and size from Earth- to 'super-Earths' may experience difficulties in losing dense hydrogen envelopes if they have H-dominated protoatmosphere remnants with >9 EOH (Earth: η = 15%) and >19 EOH (Earth: η = 40%). For 'super-Earth' these amounts are >3.5 EOH (η = 15%) and >10 (η = 40%). Dense hydrogen envelopes may be removed more easily if a particular exoplanet is located closer to its parent star such as Corot-7b or Kepler-10b (e.g., Leitzinger et al ., 2011) which orbit their parent stars at ~ 0.017 AU, but not inside the HZ. We note also that due to the HZ location at greater distances from the parent stars, the stellar wind erosion of hydrogen-envelopes will be less efficient for planets inside the HZs of K, G and F-type stars.","pages":[20,21,22,23,24,25,26]},{"title":"5. CONCLUSIONS","content":"In this study we investigated the non-thermal ion pick-up escape process from hydrogenrich, non-hydrostatic upper atmospheres of an Earth-like planet, and a hydrogen-rich 'super-Earth' which is twice as large as Earth and ten times more massive. Both planets are supposed to be located inside the HZ of a typical M dwarf star with stellar properties similar as GJ 436. We showed that in the case of an M dwarf the produced planetary H + ions have a high probability to be picked up from the extended hydrogen coronae by the stellar wind plasma flow so that the ion production rate and the ion escape rate are perhaps of the same order. We exposed the two test-planets to various XUV fluxes from 1 to 100 times that of the present Sun and found that in all studied cases the ionization of exospheric neutral hydrogen atoms by charge-exchange and photoionization contributes to the total atmospheric escape of the upper atmosphere, but do not prevail over the thermal escape. The total non-thermal atmospheric escape by ion pick-up from possible dense hydrogen envelopes during the life time of the studied planets is < 3 EOH. Our results indicate that if a rocky exoplanet did not lose the majority of its nebula captured hydrogen gas envelope, or degassed a huge amount of hydrogen-rich volatiles by thermal blow-off during the first hundred Myr after the planet's origin, it is questionable if the stellar wind can erode a remaining dense hydrogen envelope non-thermally. The thermal escape is higher during the planet's history, but is probably unable to remove such dense hydrogen envelopes as well. The situation may change dramatically for exoplanets which are located closer to their parent stars. Depending on the nebula life time, the formation process, planetary mass, stellar activity and plasma properties in the vicinity of the planet, the initial amount of hydrogen, thermal and non-thermal atmospheric escape processes will determine if a planet becomes a world with an Earth-type atmosphere (and no hydrogen envelope) or remains a sub-Neptune type body.","pages":[26,27]},{"title":"ACKNOWLEDGEMENTS","content":"M. Güdel, K. G. Kislyakova, M. L. Khodachenko, and H. Lammer acknowledge the support by the FWF NFN project S116 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subprojects, S116 604-N16 'Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond', S116 606-N16 'Magnetospheric Electrodynamics of Exoplanets', S116607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. K. G. Kislyakova, Yu. N. Kulikov, H. Lammer, and P. Odert thank also the Helmholtz Alliance project 'Planetary Evolution and Life'. P. Odert and M. Leitzinger acknowledges support from the FWF project P22950-N16. The authors also acknowledge support from the EU FP7 project IMPEx (No.262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science WG5. The authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar- and exoplanetary environments'. Finally, N. V. Erkaev acknowledges support by the RFBR grant No 12-05-00152-a. This research was conducted using resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North (HPC2N), Umeå University, Sweden. The software used in this work was in part developed by the DOE-supported ASC / Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. 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The H ENAs count rate was integrated from 0.7-6 keV on 28 March 2009 from 04:54-15:54 UT. The peak is centered on the subsolar magnetopause and a significant ENA flux extends to ±10 R Earth (Fuselier et al ., 2010). FIG. 2 . Modeling results of Earth's solar wind plasma interaction with the present-day geocorona. Green dots correspond to the solar wind protons, yellow dots represent the neutral hydrogen atoms moving with velocities below 10 km s -1 (particles which belong to the atmosphere) while the red and the blue dots represent ENAs with velocities above 10 km s -1 , moving towards and away from the Sun respectively. The dashed line denotes the magnetosphere obstacle. FIG. 3 . Radial profiles for density, velocity and temperature as a function of orbital location in AU and of expected plasma properties of an ordinary stellar wind (solid lines) and during an CME event (dashed lines) on an M-type star with a mass M s ~0.45 M Sun and a rotation period 2.5 days. For the simulation of stellar wind the initial proton density at 0.1 AU n 0 = 400 cm -3 , temperature T 0 = 500 kK, and radial stellar wind velocity v r0 = 300 km s -1 were taken. Simulation of a solar-analogue CME event uses the initial proton density n 0 = 800 cm -3 , proton temperature T 0 = 1500 kK, and a radial stellar wind velocity v r0 = 600 km s -1 . FIG. 4 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around an Earth-like hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig.4a corresponds to the XUV flux which is equal to that of the present Sun, the moderate stellar wind (Case I) and a lower heating efficiency of 15%. Fig.4b corresponds to the similar input parameters as in Fig.4a, but the XUV flux is 50 times higher. Fig.4c corresponds to the 10 times higher XUV flux than the present one and a heating efficiency of 15%, as well as the moderate stellar wind (Case I). Fig.4d: corresponds to the similar input parameters as in Fig.4c, but for the Venus-type narrower planetary obstacle. FIG. 5 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around a 'super-Earth' hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig5a: the XUV flux is 50 times higher than that of the present Sun, heating efficiency of 15%, the planet is exposed to a moderate stellar wind (Case I). Fig5b: similar conditions except for heating efficiency of 40%. Fig.5c: the XUV flux is 100 times higher compared to that of the present Sun, 40% heating efficiency, moderate stellar wind (Case I). Fig.5d: similar input parameters as in Fig.5c, but exposed to a faster and denser stellar plasma flow (case II). FIG. 6 . Illustration of the soft X-ray flux time-dependence for an M dwarf star with 0.4 solar masses (dashed line) and the same curve for a Sun-like star (solid line) in the corresponding HZs normalized by the present Sun flux. The M star within this mass range remains about 200 Myr longer in its activity saturation phase compared to a solar like G star.","pages":[47,48]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"We study the interactions between the stellar wind plasma flow of a typical M star, such as GJ 436, and hydrogen-rich upper atmospheres of an Earth-like planet and a 'superEarth' with the radius of 2 R Earth and a mass of 10 M Earth, located within the habitable zone at ~0.24 AU. We investigate the formation of extended atomic hydrogen coronae under the influences of the stellar XUV flux (soft X-rays and EUV), stellar wind density and velocity, shape of a planetary obstacle (e.g., magnetosphere, ionopause), and the loss of planetary pick-up ions on the evolution of hydrogen-dominated upper atmospheres. Stellar XUV fluxes which are 1, 10, 50 and 100 times higher compared to that of the present-day Sun are considered and the formation of high-energy neutral hydrogen clouds around the planets due to the charge-exchange reaction under various stellar conditions have been modeled. Charge-exchange between stellar wind protons with planetary hydrogen atoms, and photoionization, leads to the production of initially cold ions of planetary origin. We found that the ion production rates for the studied planets can vary over a wide range, from ~ 25 10 0 . 1 s -1 to ~ 30 10 3 . 5 s -1 , depending on the stellar wind conditions and the assumed XUV exposure of the upper atmosphere. Our findings indicate that most likely the majority of these planetary ions are picked up by the stellar wind and lost from the planet. Finally, we estimate the long-time non-thermal ion pick-up escape for the studied planets and compare them with the thermal escape. According to our estimates, non-thermal escape of picked up ionized hydrogen atoms over a planet's lifetime varies between ~0.4 Earth ocean equivalent amounts of hydrogen (EOH) to < 3 EOH and usually is several times smaller in comparison to the thermal atmospheric escape rates. Keywords: stellar activity, low mass stars, early atmospheres, Earth-like exoplanets, ENAs, ion escape, habitability\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"XUV exposed, non-hydrostatic hydrogen-rich upper atmospheres of terrestrial planets II: Hydrogen coronae and ion escape\",\n \"content\": \"Kristina G. Kislyakova 1,2 , Helmut Lammer 1 , Mats Holmström 3 , Mykhaylo Panchenko 1 , Petra Odert 1,2 , Nikolai V. Erkaev 4 , Martin Leitzinger 2 , Maxim L. Khodachenko 1 , Yuri N. Kulikov 5 , Manuel Güdel 6 , Arnold Hanslmeier 2 1 Austrian Academy of Sciences, Space Research Institute, Schmiedlstr. 6, A-8042 Graz, Austria (kristina.kislyakova@oeaw.ac.at, maxim.khodachenko@oeaw.ac.at, helmut.lammer@oeaw.ac.at, petra.odert@oeaw.ac.at, mykhaylo.panchenko@oeaw.ac.at) 2 Institute for Physics, University of Graz, Universitätsplatz 5, A-8010 Graz, Austria (martin.leitzinger@uni-graz.at, arnold.hanslmeier@uni-graz.at) 3 Swedish Institute of Space Physics, P.O. Box 812, SE-98128 Kiruna, Sweden (matsh@irf.se) 4 Institute of Computational Modelling, Siberian Division of Russian Academy of Sciences, Akademgorodok 28/44 660036 Krasnoyarsk, Russian Federation (erkaev@icm.krasn.ru) 5 Polar Geophysical Institute (PGI), Russian Academy of Sciences, Khalturina Str. 15, Murmansk, 183010, Russian Federation (kulikov@pgi.ru) 6 Institute for Astrophysics, University of Vienna, Türkenschanzstr. 17, 1180, Austria (manuel.guedel@univie.ac.at) Corresponding Authors: Kristina G. Kislyakova E-mail: kislyakova.kristina@oeaw.ac.at Austrian Academy of Sciences Space Research Institute Schmiedlstr. 6, A-8042 Graz Austria Submitted to ASTROBIOLOGY\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. INTRODUCTION\",\n \"content\": \"Recent discoveries of so-called low density 'super-Earths' by various ground- and spacebased exoplanet-transit surveys indicate large populations of volatile-rich big rocky planets. Findings from ESOs High Accuracy Radial velocity Planetary Search project (HARPS), and from NASAs Kepler space observatory, revealed that planets which are slightly larger and more massive compared to the Earth may be very common in the Universe. From the available statistics and the discovery of Kepler-22b, a 'super-Earth' with the size of about 2.38 ± 0.13REarth within the habitable zone (HZ) of a Sun-type star, one can expect that planets orbiting within the HZ should be frequent in the Universe and should also orbit cooler, lower mass M dwarfs. Approximately 100 of them are found in the immediate neighborhood of the Sun (Scalo et al. 2007; Bonfils et al. 2011). These earlier estimations are now supported by a recent study by Dressing and Charbonneau (2013), which used optical and near-infrared photometry from the Kepler Input Catalog to estimate the occurrence rate of Earth-like planets orbiting dwarf stars. The estimation of Dressing and Charbonneau (2013), from the 248 early M dwarfs within 10 parsecs of the Sun, shows that there should be at least 9 Earth-size planets in their habitable zones. Moreover, from the radius-mass relation and the resulting density of discovered 'super-Earths', one finds that these bodies probably have rocky cores but are surrounded by significant H/He and/or H2O envelopes. These findings are in agreement with recent theoretical studies, which suggest that small planets are not necessarily rocky Earth-like bodies (e.g., Wuchterl 1993; Kuchner 2003; Léger et al . 2004; Ikoma and Hory 2012; Elkins-Tanton 2011; Lammer, 2012; Lammer et al. 2011a). For explaining the mean density of Kepler 11d, Kepler 11e, and Kepler 11f these 'super-Earths'' require dense H/He envelopes, similar to Uranus and Neptune, while Kepler-11b and 11c may have also additional H2O to their H/He gas envelopes (Lissauer et al . 2011), and GJ 1214b (Charbonneau et al. , 2009) or 55Cnc e (Endl et al. , 2012) may contain a huge amount of H2O. If Earth-like and 'super-Earth'- type exoplanets can accumulate hydrogen from the nebula gas of an equivalent amount of 100 to 1000, and even up to 10 4 times, that of an Earth ocean depends on the nebula dissipation time, the formation time of the protoplanet, its luminosity, and nebula characteristics such as grain depletion factors, etc. (e.g., Mizuno et al ., 1978; Hayashi et al ., 1979; Ikoma and Genda, 2006; Rafikov, 2006). Although Solar System planets such as Venus, Earth and Mars lost their nebula-based hydrogen envelopes during the first 100 Myr after their origin, or never accumulated such huge amounts due to step-wise accretion after the nebula gas disappeared, terrestrial planets in other systems evolve under different conditions and may capture such a dense protoatmosphere which they may not lose during the extreme active period of their host stars. To understand how frequent 'rocky' terrestrial planets really are, more observations are certainly needed. From the available statistics one can conclude that Earth-analogue class I habitats (Lammer et al. , 2009a; Lammer, 2013) have to be\",\n \"pages\": [\n 2,\n 3,\n 4\n ]\n },\n {\n \"title\": \"and\",\n \"content\": \"The question if more massive 'super-Earths' can maintain plate tectonics over time spans of several Gyr is controversial (e.g., Valencia et al. , 2007; van Heck and Tackley, 2011; Korenaga, 2010). However, in this work we will not discuss the pro and contra about geophysical processes, but focus on the stellar wind erosion of captured H/He envelopes, orand? the hydrogen content of outgassed hydrogen-rich steam atmospheres, because the proto-atmosphere escape determines if a planet will evolve to an Earth-like habitat or may remain as a mini-Neptune. As it is shown by Erkaev et al. (2013) (part I of this study), depending on the availability of possible IR-cooling molecules and the planets average density, hydrogenrich 'super-Earths' orbiting inside the HZ will experience hydrodynamic blow-off only for XUV fluxes several 10 times higher compared to today's Sun. Most of their lifetime the upper atmospheres of these planets will experience strong Jeans escape which is still weaker compared to blow-off, so that they may not lose efficiently their dense hydrogen envelopes. Jeans escape is the classical thermal escape mechanism based on the fact that the atmospheric particles have velocities according to the Maxwell distribution. Individual particles in the high tail of the distribution may reach escape velocity at the exobase altitude, where the mean free path is comparable to the scale height, so that they can escape from the planet's atmosphere. When the thermosphere temperature rises due to heating by the stellar XUV radiation, the number of these energetic particles increases and the atmosphere finally reaches the state when the majority of the particles have velocities equal to or exceeding the escape velocity. In this case the atmosphere is not hydrostatic anymore, and starts to expand similar to the Parker-type solar corona. This mechanism is called blow-off and leads to a stronger escape in comparison to the Jeans mechanism. The blow-off stage is more easily reached at less massive hydrogen-rich planets with mass equal to that of the Earth. These planets experience hydrodynamic blow-off for much longer, and change from the blow-off regime to the Jeans-type escape for XUV fluxes which are < 10 times of today's Sun. Because of XUV heating and expansion of their upper atmospheres, both of our test planets should produce extended exospheres or hydrogen coronae distributed above possible magnetic obstacles defined by intrinsic or induced magnetic fields. In such cases the hydrogen-rich upper atmosphere will not be protected by possible magnetospheres like on present-day Earth, but could be eroded by the stellar wind plasma flow and lost from the planet in the form of ions (Erkaev et al ., 2005; Lammer et al. , 2007). Besides thermal escape from the hydrogen-dominated upper atmosphere of the two considered test-planets (Erkaev et al ., 2013), briefly discussed above, one can expect that non-thermal atmospheric escape processes will also contribute to the losses. Nonthermal escape processes can be separated in ion escape and photochemical, as well as kinetic, processes which accelerate atoms beyond escape energy. Ions can escape from an upper atmosphere if the exosphere is not protected by a strong magnetic field and stretches above the magnetopause. In such a case exospheric neutral atoms can interact with the host stars solar/stellar plasma (i.e., winds, CMEs) environment. The hydrogen atoms which flow upward from the lower thermosphere will be ionized by the stellar radiation, electron impact or charge exchange and then accelerated by electric fields within the solar/stellar wind plasma flow around the planetary obstacle (i.e. ionopause, magnetopause), so that they are finally picked up and lost form the planet's gravity field (e.g., Lammer et al ., 2007; Ma and Nagy, 2007; Lammer, 2013). From space missions to non- or weakly magnetized planets such as Venus and/or Mars it is known that planetary ions can also be detached from an ionopause by plasma instabilities in the form of ionospheric clouds (Terada et al ., 2002; Penz et al. , 2004; Möstl et al ., 2011), or by momentum transport triggered outflow through the planetary tail. On Earth ions outflow also over Polar Regions along open magnetic field lines (Lundin et al ., 2007; Yau and André, 1997; Wei et al ., 2012). From the analysis of the available ion escape data from Venus and Mars by the ASPERA instruments on board of Venus Express and Mars Express, as well as from theoretical models, one can conclude that ion pick-up is a very dominant permanently acting non-thermal ion escape process, and most likely more efficient compared to the sporadic losses triggered by plasma instabilities or outflow through the planets tail. However, there may be extreme solar events which can enhance the ion outflow sporadically by cool ion outflow or plasma instabilities. Non-thermal escape processes of neutral atoms are caused by sputtering of atmospheric neutral atoms, photochemical processes such as dissociative recombination, and charge exchange. Direct escape by sputtering is only a relevant process for low mass bodies which have a mass ≤ Mars. utHowever, even in the case of Mars one can expect that sputter loss rates are an order of magnitude lower compared for instance to ion pickup (e.g., Leblanc and Johnson, 2002; Chassefière and Leblanc, 2004; Lammer et al ., 2013). Direct escape of heavy neutral atoms, such as O and C, caused by photochemical processes is expected to be higher compared to ion escape from Mars (e.g., Krestyanikova and Shematovich, 2005; Chaufray et al., 2007; 2006; Fox and Hać, 2009; Lammer et al., 2013) but negligible or lower at more massive planets such as Venus (Gröller et al., 2010; 2012) or the Earth. Lighter atoms such as atomic hydrogen can also escape directly from more massive planets with escape rates lower or comparable to ion escape. Theoretical models which studied the photochemical escape rates of H atoms (Shematovich, 2010) and ion pick-up ion escape rates (Erkaev et al ., 2005) from the hot Jupiter HD 208459b indicate comparable loss rates of the order of ≤ 10 9 g s -1 , which are an order of magnitude lower compared to the modeled thermal escape (e.g., Yelle, 2004; 2006; Tian et al ., 2005a; Penz et al ., 2008b; García Muñoz, 2007; Murray-Clay et al. , 2009; Linsky et al ., 2010; Koskinen et al ., 2012). From the brief overview on various non-thermal atmospheric escape processes, one can conclude that stellar wind induced ion erosion from XUV-heated and extended hydrogen-rich thermospheres (Erkaev et al ., 2013), where H atoms will most likely not be protected by a possible magnetosphere, so-called ion pick-up will be one of the most efficient non-thermal atmospheric escape process. Because of many unknowns related to minor atmospheric species in exoplanet atmospheres, as well as magnetic field properties, a study of more complex but most likely less effective processes, such as cool ion or polar outflow and photochemical non-thermal escape processes which are not even well understood at Solar System planets including the Earth, would yield highly speculative results. Therefore, in this study we focus on the modeling of the stellar wind plasma interaction, related ion production rates via charge-exchange and photoionization, and escape estimates of planetary pick-up ions from XUV exposed upper atmospheres which originate from hydrogen-rich thermospheres of an Earth-like ( R pl=1 R Earth, M pl=1 M Earth) planet in comparison with a 'super-Earth' ( R pl=2 R Earth, M pl=10 M Earth). For reasons of comparative escape studies between thermal and non-thermal ion pick-up, we study the same test planets as investigated by Erkaev et al. (2013) within an orbit of a typical HZ of an M star with the size and mass of ~0.45 R Sun. For the host star of our test planets we use the well observed dwarf star GJ 436 (Ehrenreich et al. , 2011; von Braun et al. , 2012, France et al. , 2012) as a proxy. So far the formation of such extended hydrogen coronae was only addressed in a brief way in Lammer et al. (2011a; 2011b), but never modeled in detail. In this study we apply a coupled Direct Simulation Monte Carlo (DSMC) upper atmosphere - stellar wind plasma interaction model (Holmström et al. , 2008; Ekenbäck et al. , 2010) to the results of Erkaev et al. (2012). In Sect. 2 we describe the DSMC model, which is used for the calculation of the exosphere and related hydrogen coronae, as well as the coupled solar/stellar wind plasma upper atmosphere interaction model. We validate our model by applying it to the Earth's geocorona and comparing the simulation results with the present-day exosphere hydrogen density and energetic neutral atom (ENA) observations by NASAs Interstellar Boundary Explorer (IBEX) satellite near the magnetopause boundary at ~10 R Earth. After validating our model for the geocorona of present-day Earth, in Sect. 3 we describe the radiation and plasma parameters of our chosen M-type host star proxy, Gliese 436. In Sect. 4 we present the modeling results for the extended hydrogen coronae. In Sect. 4.1 the results of the stellar wind plasma interaction and the production of ENAs are shown as well as related planetary hydrogen ion pick-up escape rates as a function of the XUV flux values from 1 to 100 times that of today's Sun. The atmospheric ion escape rates are compared with the thermal hydrogen neutral loss rates modeled by Erkaev et al. (2012) in Section 4.2. In Section 4.3 we estimate the possible mass loss of hydrogen ions during the planetary lifetime and discuss the implications of our findings for the evolution of Earthlike and more massive 'super-Earths'. Section 5 summarizes the findings of our study.\",\n \"pages\": [\n 4,\n 5,\n 6,\n 7,\n 8\n ]\n },\n {\n \"title\": \"2 STELLAR WIND-UPPER ATMOSPHERE INTERACTION\",\n \"content\": \"As shown by previous studies of Watson et al. (1981), Kasting and Pollack (1983), Tian et al. (2005b; 2008a; 2008b), Volkov et al. (2011), and Erkaev et al. (2013), hydrogen-rich terrestrial planets experience XUV-heated and hydrodynamically expanding non-hydrostatic upper atmosphere conditions. Depending on the particular environment (e.g., XUV flux, orbital distance, availability of IR-cooling molecules, the planet's average density, etc.) the results of these studies indicate that such planets can expand their exobase level, which separates the collision dominated atmosphere from the collisionless region to distances from a few R pl up to more than 20 R pl. As a result of such an expansion of the upper atmosphere an intrinsic planetary magnetic field will most likely not protect the exosphere against the stellar wind plasma flow (Lichtenegger et al ., 2010; Lammer, 2012; Lammer et al ., 2011a). Due to the interaction between the stellar wind plasma flow and the XUV-heated non-hydrostatic upper neutral atmosphere of the planet, energetic neutral atoms (ENAs) are produced. ENAs originate due to charge-exchange when an electron is transferred from a planetary neutral atom to a stellar wind proton which then becomes an ENA. This interaction process between the stellar wind plasma and the upper atmosphere plays a significant role in the ion erosion of upper planetary atmospheres (e.g., Lundin et al. , 2007; Lammer, 2013). The production of ENAs after the interaction of stellar wind protons via charge exchange with various upper atmosphere species is described by the reactions in eq. (1-3). After its production an ENA continues to travel with the initial velocity and energy of the stellar wind proton. The atmospheric atom in turn becomes an initially cold ion which can afterwards be lost from the atmosphere due to the ion pick-up process (Lammer, 2013). In the current study we focus our attention only on the reaction shown in eq. (1) which will dominate the stellar wind interaction with planetary hydrogen coronae around hydrogen-rich terrestrial planets.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"2.1 Model description\",\n \"content\": \"In the current study the plasma interaction between the stellar wind and the upper atmosphere of the Earth-like planet and 'super-Earth' is modeled applying a Direct Simulation Monte Carlo (DSMC) upper atmosphere-exosphere particle model which is coupled with a stellar wind particle interaction code. The 3D model is described in detail in Holmström et al. (2008) and Ekenbäck et al. (2010) and includes stellar wind protons and planetary hydrogen atoms. The latter are launched into the simulation domain from the upper atmosphere. The applied collision cross sections for hydrogen atoms, σ H-H, and for protons and hydrogen atoms, σ H+-H, are 10 -17 cm 2 and 2 × 10 -15 cm 2 (Ekenbäck et al ., 2010) respectively. Charge exchange between stellar wind protons and exospheric hydrogen atoms takes place outside a conic shaped obstacle that represents the magnetoionopause of the studied planet. Stellar wind protons that have charge-exchanged according to the reaction shown in eq. (1) become ENAs. Besides of the charge-exchange reaction, the model includes gravitation of the planet and tidal effects as well as scattering by atmospheric atoms of UV photons (radiation pressure) and photoionization by stellar photons. Inclusion of the tidalgenerating potential into the equations leads to the extension of the atmosphere toward and backward from the host star, and in extreme cases to Roche lobe overflow. Nevertheless, these effects are important for 'hot Jupiters' which are located at very close distance to their host stars, and do not play a significant role for the test planets we consider in the present study. All collisions are modeled using a DSMC algorithm (Holmström et al., 2008; Ekenbäck et al., 2010). The main code uses the FLASH software developed at the University of Chicago which provides adaptive grids and is fully parallelized (Fryxell et al. , 2000). The coordinate system is centered at the center of the planet with mass pl M , the 1 x -axis is pointing towards the center of mass of the system, the 3 x -axis is parallel to the direction of the angular velocity of rotation , and the 2 x -axis points in the opposite direction to the planet's velocity. St M is the mass of the planets host star. Tidal potential, Coriolis and centrifugal forces, as well as the gravitation of the star and planet acting on a hydrogen neutral atom, are included in the code in the following way (Chandrasekhar, 1963) Here i v are the components of the velocity vector of a particle, G is Newton's gravitational constant, R the distance between the centers of mass, the Levi-Civita symbol, and 3 R GM St . The first term in the right-hand side of the eq. (4) represents the centrifugal force, the second is the tidal-generating potential, the third the gravitation of the planet's host star and the planet while the last term stands for the Coriolis force. The self-gravitational potential of a particle is neglected. Charge exchange reactions between a neutral planetary hydrogen atom and a stellar wind proton may take place outside the obstacle representing a magneto- or ionopause Here s R stands for the magnetosphere or planetary obstacle stand-off distance and t R the width of the obstacle. Since the obstacle shape and location depend strongly on the planetary magnetic field strength, one may model the interaction of the stellar wind with magnetized as well as with non- or weakly magnetized planets by the appropriate choice of s R and t R .\",\n \"pages\": [\n 9,\n 10,\n 11\n ]\n },\n {\n \"title\": \"2.2 Exosphere modeling of Earth's observed atomic hydrogen geocorona\",\n \"content\": \"ENAs have been observed around all Solar System planets where a spacecraft was equipped with a corresponding instrument (e.g., Futaana et al ., 2006; Galli et al. , 2008; Lammer et al ., 2011a; 2011b). As shown in Fig. 1, the Interstellar Boundary Explorer (IBEX) satellite recently observed an ENA formation zone around Earth's subsolar magnetopause stand-off distance, which is located at 10 R Earth from the planet's center (Fuselier et al. , 2010). Before we apply our model to hydrogen-rich exoplanets, we validate it by reproducing the geocorona and recent ENA observations (Fuselier et al. 2010) around the Earth's magnetopause by the NASAs IBEX satellite of present-day Earth. Fig. 2 shows our modeling results for Earth's geocorona interacting with the present-day solar wind by taking all parameters of Earth's exosphere as given in Table 1 as an input. The average neutral hydrogen atom density at the magnetopause level obtained from our model is estimated to be ~8 cm -3 at the distance of ~10 R Earth. This density value coincides very well with the exospheric number densities inferred from the IBEX observations of ENAs near the magnetopause. In the case of the IBEX observation at March 28 2009, the computed and observed proton fluxes show an exosphere hydrogen density at a geocentric distance of ~10 R Earth of ~4 - 11 cm -3 (Fuselier et al ., 2010). The estimates of the modeled ENA flux are in good agreement with the observed flux as well, predicting the flux of approximately 600 (cm² s sr keV) -1 . This value falls inside the observed ENA interval of ~530 - 2300 (cm² s sr keV) -1 (Fuselier et al ., 2010). The IBEX observation and our model validation can also be seen as a confirmation that under extreme radiation and plasma environments of the young Sun or more active stars a huge ENA formation zone, as suggested by Chassefière (1996) and Lammer et al. (2011; 2012), should be produced in the stellar wind interaction region of a hydrogen-rich extended upper atmosphere of an Earth-size planet when the exosphere density near the magnetopause is more than 10 6 times larger than that observed at present-day Earth. In the following sections we describe the input parameters and our applied exosphere and ENA models to the XUV exposed hydrogen-rich Earth-size test planets.\",\n \"pages\": [\n 11,\n 12\n ]\n },\n {\n \"title\": \"3. GLIESE 436: A HOST STAR PROXY FOR HYDROGEN-RICH TERRESTRIAL TEST PLANETS\",\n \"content\": \"3.1 The radiation environment of Gliese 436 Recently Ehrenreich et al. (2011) observed with the Hubble Space Telescope Imaging Spectrograph (HST/STIS) the Lyman-α emission (1215.67 Å) of neutral hydrogen atoms from the low mass M star, GJ 436. Because this emission is a main contributor to the ultraviolet flux it can also be used as a main tracer in studies of thermospheric heating, thermal escape, and possible absorption by extended hydrogen coronae and/or ENAs (e.g. Vidal-Madjar et al. , 2003; Holmström et al ., 2008; Ekenbäck et al ., 2010; Ben-Jaffel and Hosseini, 2010; Lecavelier des Etangs et al ., 2010; Lammer et al. , 2011b; Ehrenreich et al ., 2012, Lammer, 2013) during transit observations with ultraviolet transmission spectroscopy. We use GJ 436 as a typical M-type host star for our test-planet parameter studies. GJ 436 is a M2.5 dwarf star which is 10.2 pc away from the Sun. The dwarf star hosts a transiting 'hot Neptune' at an orbital distance of about 0.03 AU (Butler et al. , 2004; Gillon et al. , 2007). We adopt values for stellar mass and radius of 0.45 MSun and 0.45 RSun, respectively, which are consistent with several independent parameter determinations of GJ 436 (Torres, 2007; Maness et al. , 2007; von Braun et al. , 2012). The location of the habitable zone (HZ) is calculated following Selsis et al. (2007). As their relations are only valid for effective temperatures down to 3700 K, this value is used instead of the true temperature of GJ 436, which is slightly lower (3400-3600 K; Torres 2007; von Braun et al. 2012). Further, we adopt a bolometric luminosity of 0.026 LSun (Torres, 2007). This leads to a HZ extent of 0.12-0.36 AU assuming the limit of 50% clouds, as typical for the Earth. Hence, the center of the HZ is located at 0.24 AU, which we adopt as the orbit of our hypothetical exo-Earth. The orbital period of an Earth-analog planet within the HZ of GJ 436 corresponds to approximately 63.7 days, the orbital velocity to about 41 km s -1 , and the angular velocity to 1.14·10 -6 rad s -1 . The age of GJ 436 is about 6±5 Gyr and is not well constrained (Torres, 2007). However, the rotation period of 48 days (Demory et al. , 2007) yields an estimated age of 2.5-3 Gyr (Barnes, 2007; Engle and Guinan, 2011). This estimation is in agreement with the lack of chromospheric activity indicated by the presence of Hα in absorption spectra. GJ 436 has been detected by the ROSAT All-Sky Survey, which revealed an Xray luminosity of log LX = 27.13 erg s -1 . Recent observations by the XMM-Newton spacecraft yielded a smaller value of only ~25.96 erg s -1 (Sanz-Forcada et al. , 2011). We adopt the latter result because of the longer exposure time and better S/N of the XMMNewton observations compared to ROSAT data. Using coronal models, Sanz-Forcada et al . (2011) extrapolated the stellar emission in the total XUV range (5 - 920Å) and found log L XUV=26.92 erg s -1 . Adopting this value and scaling it to the HZ center at 0.24 AU, we estimate an XUV flux of about 5.14 erg cm -2 s -1 , comparable to the present solar XUV flux at 1 AU of 4.64 erg cm -2 s -1 (Ribas et al. , 2005). In the past, the stellar XUV flux, which was emitted from GJ 436 was certainly higher. The high-energy emission of young M dwarfs is saturated at log( L X/ L bol)~ -3 (e.g. Scalo et al ., 2007), hence the maximum possible log( L X) for GJ 436 is ~29 erg s -1 . Assuming that the XUV emission of young stars occurs predominantly in X-rays because of their hotter coronae, the maximum XUV flux at the Earth-equivalent orbit around GJ 436 was roughly 700 erg cm -2 s -1 , or ~150 F XUV,now. Lyman-alpha emission of GJ 436 was detected by Ehrenreich et al. (2011) using HST/STIS observations. They reconstructed the intrinsic stellar emission by correcting for interstellar medium (ISM) absorption, leading to an apparent flux observed at Earth of ~2.7±0.7 × 10 -13 erg cm -2 s -1 . Scaled to the HZ center, this yields ~20.51 erg cm -2 s -1 , a factor of ~3.3 larger than the present solar value at 1 AU of 6.19 erg cm -2 s -1 (Ribas et al ., 2005). Recently, France et al. (2013) reconstructed the intrinsic Lyman-alpha flux of GJ 436 by using a different approach. They obtained a value of 3.5 × 10 -13 erg cm -2 s -1 with an uncertainty of about 15 - 30 %, which is slightly higher than the value given by Ehrenreich et al. (2011), but is consistent with the errors. The relevant stellar parameters and the measured radiation properties used in the model simulations for various assumed XUV flux values of a Gliese 436-type M dwarf are shown in Table 2. The photoionization rates corresponding to the four XUV flux enhancement factors were scaled from the average present solar value at Earth (1.1 × 10 -7 s -1 ; Hodges, 1994, Bzowski, 2008) to the corresponding enhancement factors. The photoionization rate is usually calculated as the product of ionization cross-section and spectral flux integrated over all wavelengths below the ionization threshold. Since full M star XUV spectra for different activity levels are currently not available, we assume that the present spectral energy distribution is equal to the solar one and scale it up by the constant factors given in Table 2. The UV absorption rates correspond to the product of the photon flux at the center of the Lyman-alpha line and the total absorption cross-section (5.47 × 10 -15 cm 2 Å; e.g. Quémerais, 2006). Adopting the reconstructed intrinsic line profile of Ehrenreich et al. (2011), the present value of the photon flux at the HZ center of GJ 436 is estimated to be ~6.9 × 10 -3 s -1 .. To scale the Lyman-alpha flux and, hence, the absorption rate to higher XUV flux emission levels, we use the scaling between X-rays and Lyman-α from Ehrenreich et al. (2011). This assumes that L X/ L bol ≈ L XUV/ L bol and that the central Lyman-α flux scales approximately as the integrated line emission. The resulting absorption rates are also shown in Table 2.\",\n \"pages\": [\n 12,\n 13,\n 14\n ]\n },\n {\n \"title\": \"3.2 Expected stellar wind plasma properties\",\n \"content\": \"Depending on the mass, size and resulting luminosity of the host star, the corresponding scaled HZ location in the case of GJ 436 is at 0.24 AU. This is a much closer orbital distance compared to that of the Earth (1 AU). As pointed out by Khodachenko et al. (2007), at orbital locations < 0.5 AU the flow of dense plasma related to stellar winds and coronal mass ejections (CMEs), energetic particle fluxes and XUV radiation cannot be neglected. Depending on the stand-off distance of the planetary obstacle which forms when the stellar plasma flow is deflected around the planet, previous test particle model results of Lammer et al. (2007) indicate that CO2-rich Earth-like exoplanets having no or only weak magnetic moments may lose from tens to hundreds of bars of atmospheric pressure, or even their whole atmospheres, due to the CME induced O + ion pick-up at orbital distances ≤ 0.2 AU. Due to the uncertainties on the mass loss and related plasma outflow from M dwarfs, we assume in our study, as in Khodachenko et al. (2007) and Lammer et al . (2007), the plasma environment close to the stars obtained from solar observations. There exist a limited number of measurements of the mass loss rates for M stars (Wood et al., 2005, Ehrenreich et al. , 2011), which in principle may be used for estimation of specific stellar wind density and velocity. For these stars the mass loss rates are comparable or less than the mass loss rate of the Sun. At the same time, for the Sun we have a much better knowledge of the distribution and evolution of active solar regions and of the mass outflow in the form of solar wind and CMEs, which we use in the present study. Note that stellar wind density and/or velocity lower than the solar (assumed) values would reduce the portion of the produced and picked up ions. Such a reduction would not change our main conclusion that the ion pick-up loss makes up only several percent of the thermal loss, and the further results can be considered as an upper limit for ion pickup near an M dwarf like Gliese 436. For the accurate study of stellar-planetary interactions one needs a reliable model which can simulate the propagation and evolution of the stellar wind plasma. For modeling the propagation and evolution of the stellar wind we use the Versatile Advection Code (VAC) (Toth, 1996). This model is able to simulate spatial and temporal evolution of the solar/stellar wind, as well as CMEs, from orbital distances ≥0.14 AU. It/The model includes a self-consistent Parker-type co-rotating magnetic field, and is based on the solution of the set of the ideal (non-resistive) non-relativistic magnetohydrodynamic equations (Toth, 1996). We use a spherical uniform computation domain, which occupies a radial distance region between 0.14 < R < 1 AU. The stellar wind in the model flows through the inner boundary of the computation domain at a semi-major axis location d = 0.14 AU and propagates out through the outer radial boundary at d = 1 AU. A self-consistent expanding stellar wind plasma flow under the conditions of a frozen-in, co-rotating, Parker-type, spiral magnetic field is numerically simulated (Odstrčil et al ., 1999; Rucker et al. , 2008). The typical parameters of the expected flow of the stellar wind plasma at d = 0.14 AU are imposed along the inner radial boundary (Odstrčil et al ., 1999) with an initial proton concentration n 0 = 500 cm -3 , stellar wind proton temperature, T 0 = 500 kK, and a radial stellar wind velocity v r0 = 300 km s -1 . For investigating the propagation of CMEs, in a second step the simulation of a CME cloud with an initial proton density n 0 = 1000 cm -3 , proton temperature, T 0 = 1700 kK, and a radial stellar wind velocity v r0 = 600 km s -1 is imposed at the inner boundary of the computation domain as a time-dependent injection of hot and dense plasma into the ambient stellar wind (Odstrčil et al ., 1999; Odstrčil et al. , 2004). Fig. 3 shows radial profiles of the maximum values of plasma parameters ( n , v r, T ) during a solar analogue CME event (dashed lines, Case II) for a typical M-star with mass M s ~ 0.45 M Sun and a rotation period 2.5 days, and those for the stellar wind itself (solid lines Case I). Therefore, in the stellar wind plasma interaction modeling with the upper atmosphere, described below, two types of stellar plasma parameters representing the lower (Case I) and upper limit (Case II) conditions at the HZ location of our test planets at 0.24 AU were used as inputs: Here n sw corresponds to stellar wind concentration, v sw denotes its bulk velocity and T sw stands for the stellar wind temperature. These values cover the predicted range for the expected stellar wind plasma parameters of GJ 436 at the HZ of the system. The upper limit (Case II) can also be considered as a proxy for modeling of frequent CME events in the system when the next CME event hits the planet immediately after the previous one. We can estimate the recovery time of the planetary atmosphere after the CME event on a very simple way. Since the test planets considered in the article are not magnetized, we assume that the recovery speed coincides with the sound speed (or the speed of slow magnetoacoustic wave), so that 2 / 1 / H exo B t s t CME m T k R c R where t R is the obstacle width, 3 / 5 is the ratio of the specific heats, B k is the Boltzmann constant, H m is the mass of a hydrogen atom and exo T is the exobase temperature. Taking the parameters from Tables 3 and 4 and depending on the characteristic size of the obstacle and the temperature, this time varies between approximately 7 and 14 hours for the Earth-type planet and 64 and 80 hours for the 'super-Earth'. The next section is dedicated to the discussion of the obtained results and presents also the ion production rates for the hydrogen-rich Earth-like planet and the 'super-Earth'.\",\n \"pages\": [\n 14,\n 15,\n 16\n ]\n },\n {\n \"title\": \"4. HYDROGEN EXOSPHERES, ENA PRODUCTION AND ION ESCAPE\",\n \"content\": \"In the following section we study the modification of the extended hydrogen exosphere due to the interaction of it with the stellar XUV and plasma flux. Because our hydrogenrich test-planets orbit within a typical M-star HZ at ~0.24 AU they will be affected by tides. As it was discussed in Khodachenko et al. (2007) tides arise because of the finite extension of the planetary body in the inhomogeneous gravitational field of its host star so that the continuous action of the tides will reduce the planetary rotation rate or may result in a synchronous rotation (Grießmeier et al. , 2005). The intrinsic magnetic field of a terrestrial planet is an essential factor for planetary protection from the ion pick-up atmosphere loss process. As shown in Khodachenko et al. (2007) and Lammer et al . (2007), because of the close orbital location within M-star HZs, the magnetosphere field of a terrestrial planet is more compressed due to the denser stellar wind impact compared with that of the solar wind at present-day Earth at 1 AU. In view of this fact the radial distance of the extended exobase of an XUV heated hydrogen rich upper atmosphere will most likely coincide with the planetary magnetopause or ionopause distance (e.g., Lammer et al ., 2009a; Lammer et al ., 2012, Lammer, 2013).\",\n \"pages\": [\n 17\n ]\n },\n {\n \"title\": \"4.1 Input parameters and modeling results\",\n \"content\": \"As it was briefly discussed in Sect. 3.2, the magnetic moments of terrestrial planets, and especially that of 'super-Earths' within close orbital distances, are expected to be weak (e.g., Gaidos et al ., 2010; Tachinami et al ., 2011; Morad et al ., 2011; Stamenkovic' et al., 2011Stamenkovi'c et al., 2012). This would lead to magnetoshperes or ionospheres which are compressed towards the planet's expanded non-hydrostatic upper atmosphere by the strong dynamic ram pressure of the dense stellar wind plasma. On the other hand if the exobase level expands beyond several planetary radii one can also expect that an Earth-type magnetosphere will not protect the exosphere (Fig. 5: Lammer et al ., 2007; Fig. 6 right panel: Lammer et al ., 2011a). Taking this considerations into account, the planetary obstacle most likely is located very close above the exobase level (Lammer et al. 2009b). Because the shape of the planetary obstacle affects the ENA production and resulting loss of planetary hydrogen ions, we study also the influence of the obstacle width on the ion production rate and the upper atmosphere erosion. In the first case the magnetic obstacle width t R in the eq. (5) was assumed to be 1.5 times greater than the magnetopause distance. This relation and its resulting obstacle shape is close to the observed magnetosphere of the present-day Earth and may occur if the planet has an intrinsic magnetic dynamo. In the second case we choose t s R R so that it resembles more a Venus-type planetary obstacle which may correspond to a planet with no magnetic field, or only a very weak dynamo. By decreasing of the planetary obstacle width the ion production will significantly increase, so that a terrestrial planet with a Venus-type obstacle, where t s R R , may lose larger amounts of atmospheric gas in ionized form (see Sect. 4.2). In the present study we do not specify the magnetic moment of a planet, but only chose a magnetospheric obstacle. For illustrating the differences between the stellar wind plasma interaction with a hydrogen-rich terrestrial planet which is exposed to both a weak XUV flux and an extremely strong one, we irradiate the two test-planets with the XUV flux of the present Sun (1 XUV) and with a 100 times higher XUV flux (100 XUV). Moreover, we investigate for these two XUV flux cases several stellar wind and obstacle scenarios. The main input parameters at the inner boundary of our simulation domain are shown for 4 selected cases in Tables 3 and 4. As it was mentioned earlier, we apply the results obtained by Erkaev et al. (2012) to the upper atmosphere input paramters of our model. Erkaev et al. (2012) studied the thermosphere structure of a hydrogen-dominated Earth and a 'super-Earth' ( R pl=2 R Earth; M pl=10 M pl) with a hydrodynamic upper atmosphere model which solves the equations of mass, momentum and energy conservation for low and high heating efficiencies, η of 15 % and 40 %, respectively. η defines the percentage of the incoming XUV energy which is transferred into heating of the neutral gas. Table 4 shows the same input paramters for our model for a hotter atmosphere corresponding to the upper atmosphere values of Erkaev et al . (2013) with η = 40%. As one can see from Tables 3 and 4, the exobase distance which is chosen as our inner model boundary and the temperature are increasing for higher XUV fluxes. This behavior can be expected by taking into account a more intensive radiation flux from the parent star. Enhanced heating flux makes the scale height of the atmosphere increase, which in its turn moves the exobase to higher location. One can also see that an increase of the heating efficiency leads to an increase of the planet's obstacle stand-off (which for the studied non-magnetized planets practically coincides with the exobase) distances as well. Because of the expansion of the upper atmosphere under more extreme heating conditions (40%) the exobase densities are smaller in comparison to the 15% cases. Figs. 4 and 5 show the modeled hydrogen exospheres and the related stellar plasma interaction under various conditions around the test planets. All the figures show cross-sections of a 3D cloud in the 2 1 , x x plane similar to those in Fig. 2. Fig. 4 illustrates the appearance of the extended hydrogen coronae around the Earth-type planet while Fig. 5 corresponds to the 'super-Earth'. In all the cases the wider Earth-type planetary obstacle is assumed, except for Fig. 4d where a smaller Venus-like obstacle is adopted. The white area around the planets (which are shown as black dots) represents the inner atmosphere (non-hydrostatic thermosphere), which is not considered in the present study. Fig.4a and Fig.4b illustrate the influence of the XUV flux on the cloud formation. All simulation parameters for these two pictures are the same except for the XUV flux, which is chosen to be equal to and 50 times higher than the XUV flux of the present Sun. As one can see, the higher XUV flux leads to a more efficient expansion of the upper atmosphere so that charge exchange can be more intensive in the surrounding hydrogen corona. The effect of the planetary obstacle can be seen in a comparison of Fig. 4c, for an Earth-type planetary obstacle shape, with Fig.4d, for a Venus-type obstacle. In these two cases the upper atmosphere is exposed to the XUV flux which is 50 times higher compared to that of today's Sun. Figs. 5a and 5b illustrate the importance of the heating efficiency. We show two model runs for the 'super-Earth' for a comparison. Only the upper atmosphere parameters corresponding to the heating efficiencies were changed. A higher heating efficiency results in additional expansion of the upper atmosphere and in increasing production of ENAs in the vicinity of the planet (blue and red dots). Figs. 5c and 5d show the effect of the stellar wind velocity and density on the hydrogen coronae formation. Both figures, 5c and 5d, correspond to the most extreme XUV case, which is 100 times higher than that of today's Sun. As expected, the extreme stellar conditions result in a denser and faster stellar plasma flow, higher XUV fluxes and more intense heating of the upper atmosphere, as well as a decrease of the planetary obstacle width, which all lead to more intensive interaction processes. The ENA part of the hydrogen corona (blue and red dots) becomes more visible, meaning an increase of the atmospheric erosion processes. One can see that a huge amount of exospheric hydrogen atoms is ionized or underwent charge exchange reactions in both cases, but stronger stellar wind significantly increases the number of ENAs in the vicinity of the planet as suggested by Chassefière, (1996). Chassefìère (1996) studied the hydrodynamic outflow and escape of hydrogen atoms from a hydrogen-dominated expanded thermosphere from early Venus. From this study it was estimated that the huge ENA cloud, which is generated via charge exchange due to the interaction between an extended exosphere and the surrounding solar wind plasma of the young Sun, may contribute to about 75 % of the energy inside the thermosphere which is used for escape of the outward flowing H atoms (see Fig. 3 in Chassefière, 1996). The stellar EUV flux is deposited mainly in the lower thermosphere (Erkaev et al ., 2013), while the ENA flux directed toward the planet should be deposited at an atmospheric layer below the exobase. It can contribute to thermospheric heating and may as a consequence modify the upper atmosphere structure which could result in an enhancement of the thermal escape rate. Our results related to the efficient production of ENAs around the planetary obstacle support the hypothesis of Chassefière (1996) that ENAs may contribute to upper atmosphere heating. A study which investigates the possible heating contribution of ENAs additionally to the stellar XUV flux is beyond the scope of this particular work, but is in progress for a follow up study during the near future. We note also that ENA clouds near the terrestrial exoplanets within orbits around M dwarfs might be observable in the stellar Lyman-alpha line by the Hubble Space Telescope and in higher resolution beyond the geocorona in the near future by the World Space Observatory-UV (Shustov et al. , 2009; Lammer et al ., 2011b). In the next section we estimate how many of the produced planetary ions in the hydrogen coronae are picked up by the stellar wind plasma, and hence are lost from the planet.\",\n \"pages\": [\n 17,\n 18,\n 19,\n 20\n ]\n },\n {\n \"title\": \"4.2 Stellar wind induced atmospheric erosion of planetary hydrogen ions\",\n \"content\": \"As discussed above, interaction processes between the stellar wind and the upper atmosphere together with the photoionization by stellar photons lead in the case of hydrogen-rich atmospheres to the production of atmospheric H + ions, see eq. (1). After ionization, the ions can be picked up by the stellar wind plasma and swept away from the planet. Because we are interested in the efficiency of the atmospheric ion escape, we estimate the average ion production rates under various conditions. We assume as discussed below that in the considered cases the production of planetary ions and the escape rate are most likely of the same order. Ions produced near and above the planet's obstacle can be lost because of the ion pick-up process. Since these particles are not neutral anymore, they can follow the magnetic field lines in the stellar wind plasma and can be swept away from the planet's gravity field. We consider the H + ions produced above the planetary obstacle, where the collisions between atmospheric particles can be neglected. It is assumed that the ions may be lost if the gyro radius is small enough in comparison to the planetary radius (e.g. if the magnetic field in the vicinity of a planet is strong enough to change the trajectory of the ions significantly). Here i m is the mass of the ion, i v is the velocity of the 'cold' planetary ion assumed to be ~7 km s -1 , q is the ion charge and B is the magnetic field near the planetary obstacle. In the case of a pure hydrogen upper atmosphere the ion mass and charge coincide with the mass and charge of a proton. The velocity of ~7 km s -1 is chosen as being slightly faster than the mean thermal velocity of a hydrogen atom for a temperature of about 2000 K. The magnetic field at the distance ~0.24 AU from an M dwarf can be roughly estimated if one assumes a dipole character of the stellar field with the initial global value in the range of ~2 - 3 kG or ~0.2 - 0.3 T (Phan-Bao et al. , 2009, Reiners, 2012). By assuming an average magnetic field on the star of 2 kG, the magnetic field at 0.24 AU is ≈ 3 10 4 . 1 G, which yields for an ion velocity of 7 km s -1 an ion gyro radius of ~525 m which is several orders of magnitude smaller compared to the radii of the studied planets. In such a case it is justified to assume that most of the produced H + ions will be swept away from the planets by the stellar wind. If we assume that the ions are accelerated by the stellar wind electric field to the velocity of the stellar wind (Case I: 330 km/s, Case II: 550 km/s), the ion gyro radius increases proportionally to ~25 - 40 km in two extreme cases. Here we assume the filling factor f=1 (see Phan-Bao et al. , 2009), i.e. the maximal possible field strength. Since the magnetic field of ~2 - 3 kG is typical for young and active M dwarfs, it could be convenient to determine the gyro radii for a weaker field of ~50 G for an older star with the age of several Gyr (Phan-Bao et al. , 2009). The magnetic field at 0.24 AU is approximately 5 10 57 . 3 G. A decrease of the magnetic field causes a proportional increase of the gyro radius (21 km for an ion velocity of 7 km s -1 , 10 3 km and 3 10 6 . 1 km for 330 km/s and 550 km/s respectively). But even the highest value of ~1600 km is several times less if compared to the planetary radius, and more than an order of magnitude lower compared to the exobase radius where most ENAs are produced. These estimates support our assumption that the majority of the exospheric ions are lost from the planet and that the ion production rate is balanced by the escape rate at least during a significant part of the stellar life time. Estimates of the ion production rates and corresponding escape rates described in the previous sections are summarized in the Tables 5 and 6 for planetary obstacles which have an Earth-like magnetosphere shape. Table 5 presents the results obtained for a hydrogen-rich Earth-like planet for two stellar wind conditions and a heating efficiency η =15% and of a higher heating efficiency η = 40%, while Table 6 summarize the similar scenarios for the 'super-Earth'. Atmospheric loss rates L ion are given in units of particles per second. As one can see from Tables 5 and 6, in the most cases the ion production and loss rate increases with the increasing XUV flux. Loss rates for faster stellar wind also exceed the corresponding values for the wind with lower velocity which is not surprising. Since the ion production rates depend not only on the assumed heating efficiency and the XUV flux, but also on the exobase density, the values for the lower-density case corresponding to a heating efficiency of 40% (Erkaev et al. , 2013) are slightly lower in comparison to the 15% case shown in Table 6. This is also the reason why the values for the cases where the stellar XUV flux is about 100 times higher than that of the present Sun are not dramatically higher (or even slightly smaller) that the ion production rates for the lower XUV fluxes, although the intensity of the interaction increases. Under the intensity of the interaction in this case we mean the ratio of produced ions to the mean exospheric density. This value increases monotonically for higher XUV fluxes in all cases considered in the present study. The reason for that is related to the corresponding exobase density that is lower because of expansion in the case of a hydrogen-rich upper atmosphere which is exposed to high XUV fluxes such as in the 100 XUV case (Erkaev et al. , 2013). To investigate the influence of the planetary obstacle shape on the H + escape rate L ion, we performed an analogous set of simulations by assuming a Venusian type planetary obstacle ( t s R R ). Tables 7 and 8 present the calculated ion production rates and estimated ion escape rates for the two test planets under the same conditions as described in Tables 5 and 6 except for the shape of the planetary obstacle. As one may see from the comparison of Tables 5 - 6 and Tables 7 - 8, reducing the width of the obstacle by 1.5 times leads to an increase in the ion production rate (i.e. the escape in general) of ≈30%. Other factors which lead to an increase of the ion production rate are related to the increase of the stellar wind density and velocity, heating efficiency η , and enhancement of the stellar XUV flux of the parent star. All these dependencies should be considered and expected. For comparison, thermal loss rates change in the range from 29 10 0 . 4 (1 XUV, η=15%) to 31 10 3 . 4 (100 XUV, η=40%) for a hydrogen-rich Earth-type planet and from 29 10 6 . 1 (1 XUV, η=15%) to 31 10 3 . 5 (100 XUV, η=40%) for a hydrogen-rich 'superEarth'. In all cases these rates exceed the presented in the current study. For more information, see Erkaev et al., (2013). If we compare the modeled H + ion pick-up loss rates with that of Mars (e.g., Lammer et al ., 2003) or Venus (Lammer et al. , 2006), which are in the order of ~10 25 s -1 , one can see that the pick-up loss rates for the hydrogen-dominated Earth-like planet are comparable for the 1 XUV case with a heating efficiency of 15 % and an Earth-like magnetopause shape, but would be a factor 10 3 higher in the case of 40 % heating efficiency and/or a more narrower Venus-type planetary obstacle. For the larger 'superEarth' and XUV cases with higher values than that of the present-day Sun the loss rates are up to 10 4 - 10 5 times higher. 4.3 Total ion escape The loss rates shown in Tables 5 - 8 can be used for rough estimation of the total ion loss from the hydrogen envelopes around the studied planets. This question is important because, as shown by Erkaev et al. (2013), volatile rich 'super-Earths' which contain IRcooling molecules can result in lower heating efficiencies of about 15 % so that for most of their lifetime they will not be in the hydrodynamic blow-off regime. In such cases nonthermal atmospheric escape processes, like the studied H + ion pick-up process, will contribute to the loss of their hydrogen-rich protoatmospheres. Before we investigate this mass loss one needs to know how long a typical M dwarf like Gliese 436 may keep a high level of the XUV and X-ray flux. According to Penz et al. (2008a) the temporal scaling law for the soft X-ray (0.6-12.4 nm or 0.1-2 keV) flux of a typical M dwarf with the mass of ≈ Sun M 4 . 0 can be described by the following relation where 28 0 10 6 . 5 L erg s -1 and t is given in Gyr. The soft X-ray flux can then be scaled for the appropriate orbital distance by using the relation 2 4 / d L F X X . Fig. 6 shows, approximately, the decrease of the soft X-ray flux of a Gliese 436 analogous M dwarf during the first 1.3 Gyr of its life time. Since at present time the scaling law for the XUV radiation of M dwarfs is not yet well constrained, we use this soft X-ray scaling law instead of the XUV scaling law in our estimation for the total H + escape. Assuming this temporal scaling law for the star and taking the ion production rates from Tables 5 - 8, we can estimate the mass loss from the hydrogen-rich Earth-like planet and the 'super-Earth' in the HZ of a Gliese 436 type M star after 4.5 Gyr (see Tables 9 and 10). For comparison the thermal escape rates are shown by using the values from Table 2 in Erkaev et al. (2013). The total ion loss is given in Earth ocean equivalent amounts of hydrogen (1EOH = 23 10 5 . 1 g) . It should also be mentioned that we do not consider escape during the first ~100 Myr, the time of extreme stellar activity of an M dwarf, so that our estimates cover the time span ~0.1 - 4.5 Gyr. As discussed in Erkaev et al. (2013) during this early extreme period the temperature in the lower thermosphere may be >> 250 K, due to magma oceans and frequent impacts. Hot lower atmosphere will enhance the atmospheric thermal escape during this early period. A follow up study which will investigate the earliest extreme evolutionary periods is in progress. In the present work we do not take into account the gradual decrease of the amount of gas in the planetary atmosphere due to escape processes, as we assume that the hydrogen reservoir contains much more gas in comparison to the amount lost . As discussed in Sect. 1, such scenarios can be considered as real because most of the recently discovered 'super-Earths' may have huge hydrogen envelopes which contain a few % of their whole mass (e.g., Lammer, 2013). If we compare the estimated atmospheric escape rates obtained for the thermal and ion pick-up processes for both test-planets in the HZ, it is clear that the thermal escape rate substantially exceeds the pick-up rate under the studied conditions. This is also the case when we consider the most extreme XUV and stellar plasma conditions, including a narrow planetary obstacle. A fraction of the evaporating neutral exosphere will be ionized so that ion pick-up will contribute to the total atmospheric escape rate, but as long as the upper atmosphere is in blow-off thermal escape will be the most important. In our study the escape rate of ionized hydrogen atoms can vary for an Earth-type planet from ~0.6 EOH under moderate conditions (15% heating efficiency, moderate stellar wind, Earth-type planetary obstacle) up to ~2.5 EOH for extreme environments (40% heating efficiency, denser and faster wind and a narrow Venusian obstacle type). The stronger gravity of the more massive 'super-Earth' keeps the atmosphere closer to the planet's surface, which slows down the charge exchange and photoionization processes. In this case the escape changes from ~0.4 EOH to ~2.14 EOH depending on the environment but remains smaller compared to escape from an Earthtype planet (ranging from ~0.6 EOH to 2.5 EOH, see above). In all studied cases the nonthermal H + pick-up rate is several times smaller in comparison with the thermal one, but makes up a significant fraction of the whole loss processes. The results of our study, together with those of Erkaev et al. (2013), indicate that terrestrial exoplanets ranging in mass and size from Earth- to 'super-Earths' may experience difficulties in losing dense hydrogen envelopes if they have H-dominated protoatmosphere remnants with >9 EOH (Earth: η = 15%) and >19 EOH (Earth: η = 40%). For 'super-Earth' these amounts are >3.5 EOH (η = 15%) and >10 (η = 40%). Dense hydrogen envelopes may be removed more easily if a particular exoplanet is located closer to its parent star such as Corot-7b or Kepler-10b (e.g., Leitzinger et al ., 2011) which orbit their parent stars at ~ 0.017 AU, but not inside the HZ. We note also that due to the HZ location at greater distances from the parent stars, the stellar wind erosion of hydrogen-envelopes will be less efficient for planets inside the HZs of K, G and F-type stars.\",\n \"pages\": [\n 20,\n 21,\n 22,\n 23,\n 24,\n 25,\n 26\n ]\n },\n {\n \"title\": \"5. CONCLUSIONS\",\n \"content\": \"In this study we investigated the non-thermal ion pick-up escape process from hydrogenrich, non-hydrostatic upper atmospheres of an Earth-like planet, and a hydrogen-rich 'super-Earth' which is twice as large as Earth and ten times more massive. Both planets are supposed to be located inside the HZ of a typical M dwarf star with stellar properties similar as GJ 436. We showed that in the case of an M dwarf the produced planetary H + ions have a high probability to be picked up from the extended hydrogen coronae by the stellar wind plasma flow so that the ion production rate and the ion escape rate are perhaps of the same order. We exposed the two test-planets to various XUV fluxes from 1 to 100 times that of the present Sun and found that in all studied cases the ionization of exospheric neutral hydrogen atoms by charge-exchange and photoionization contributes to the total atmospheric escape of the upper atmosphere, but do not prevail over the thermal escape. The total non-thermal atmospheric escape by ion pick-up from possible dense hydrogen envelopes during the life time of the studied planets is < 3 EOH. Our results indicate that if a rocky exoplanet did not lose the majority of its nebula captured hydrogen gas envelope, or degassed a huge amount of hydrogen-rich volatiles by thermal blow-off during the first hundred Myr after the planet's origin, it is questionable if the stellar wind can erode a remaining dense hydrogen envelope non-thermally. The thermal escape is higher during the planet's history, but is probably unable to remove such dense hydrogen envelopes as well. The situation may change dramatically for exoplanets which are located closer to their parent stars. Depending on the nebula life time, the formation process, planetary mass, stellar activity and plasma properties in the vicinity of the planet, the initial amount of hydrogen, thermal and non-thermal atmospheric escape processes will determine if a planet becomes a world with an Earth-type atmosphere (and no hydrogen envelope) or remains a sub-Neptune type body.\",\n \"pages\": [\n 26,\n 27\n ]\n },\n {\n \"title\": \"ACKNOWLEDGEMENTS\",\n \"content\": \"M. Güdel, K. G. Kislyakova, M. L. Khodachenko, and H. Lammer acknowledge the support by the FWF NFN project S116 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subprojects, S116 604-N16 'Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond', S116 606-N16 'Magnetospheric Electrodynamics of Exoplanets', S116607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. K. G. Kislyakova, Yu. N. Kulikov, H. Lammer, and P. Odert thank also the Helmholtz Alliance project 'Planetary Evolution and Life'. P. Odert and M. Leitzinger acknowledges support from the FWF project P22950-N16. The authors also acknowledge support from the EU FP7 project IMPEx (No.262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science WG5. The authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar- and exoplanetary environments'. Finally, N. V. Erkaev acknowledges support by the RFBR grant No 12-05-00152-a. This research was conducted using resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North (HPC2N), Umeå University, Sweden. The software used in this work was in part developed by the DOE-supported ASC / Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. Finally, the authors thank the referees for very useful suggestions and recommendations which helped to improve the work.\",\n \"pages\": [\n 27\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Barnes, S. A. (2007) Ages for Illustrative Field Stars Using Gyrochronology: Viability, Limitations, and Errors, ApJ , 669, 1167-1189. Ben-Jaffel, L., Sona Hosseini, S. (2010) On the existence of energetic atoms in the upper atmosphere of exoplanet HD 209458b, ApJ , 709, 1284-1296. 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Icarus , 183, 508.\",\n \"pages\": [\n 27,\n 28,\n 29,\n 30,\n 31,\n 32,\n 33,\n 34,\n 35,\n 36,\n 37,\n 38,\n 39,\n 40,\n 41\n ]\n },\n {\n \"title\": \"FIGURE CAPTIONS\",\n \"content\": \"FIG. 1 : Observed hydrogen ENAs by the IBEX spacecraft around Earth. The H ENAs count rate was integrated from 0.7-6 keV on 28 March 2009 from 04:54-15:54 UT. The peak is centered on the subsolar magnetopause and a significant ENA flux extends to ±10 R Earth (Fuselier et al ., 2010). FIG. 2 . Modeling results of Earth's solar wind plasma interaction with the present-day geocorona. Green dots correspond to the solar wind protons, yellow dots represent the neutral hydrogen atoms moving with velocities below 10 km s -1 (particles which belong to the atmosphere) while the red and the blue dots represent ENAs with velocities above 10 km s -1 , moving towards and away from the Sun respectively. The dashed line denotes the magnetosphere obstacle. FIG. 3 . Radial profiles for density, velocity and temperature as a function of orbital location in AU and of expected plasma properties of an ordinary stellar wind (solid lines) and during an CME event (dashed lines) on an M-type star with a mass M s ~0.45 M Sun and a rotation period 2.5 days. For the simulation of stellar wind the initial proton density at 0.1 AU n 0 = 400 cm -3 , temperature T 0 = 500 kK, and radial stellar wind velocity v r0 = 300 km s -1 were taken. Simulation of a solar-analogue CME event uses the initial proton density n 0 = 800 cm -3 , proton temperature T 0 = 1500 kK, and a radial stellar wind velocity v r0 = 600 km s -1 . FIG. 4 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around an Earth-like hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig.4a corresponds to the XUV flux which is equal to that of the present Sun, the moderate stellar wind (Case I) and a lower heating efficiency of 15%. Fig.4b corresponds to the similar input parameters as in Fig.4a, but the XUV flux is 50 times higher. Fig.4c corresponds to the 10 times higher XUV flux than the present one and a heating efficiency of 15%, as well as the moderate stellar wind (Case I). Fig.4d: corresponds to the similar input parameters as in Fig.4c, but for the Venus-type narrower planetary obstacle. FIG. 5 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around a 'super-Earth' hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig5a: the XUV flux is 50 times higher than that of the present Sun, heating efficiency of 15%, the planet is exposed to a moderate stellar wind (Case I). Fig5b: similar conditions except for heating efficiency of 40%. Fig.5c: the XUV flux is 100 times higher compared to that of the present Sun, 40% heating efficiency, moderate stellar wind (Case I). Fig.5d: similar input parameters as in Fig.5c, but exposed to a faster and denser stellar plasma flow (case II). FIG. 6 . Illustration of the soft X-ray flux time-dependence for an M dwarf star with 0.4 solar masses (dashed line) and the same curve for a Sun-like star (solid line) in the corresponding HZs normalized by the present Sun flux. The M star within this mass range remains about 200 Myr longer in its activity saturation phase compared to a solar like G star.\",\n \"pages\": [\n 47,\n 48\n ]\n }\n]"}}},{"rowIdx":84,"cells":{"bibcode":{"kind":"string","value":"2013AstBu..68...14S"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1203.2763.pdf"},"content":{"kind":"string","value":"\nMagnetic fields of active galactic nuclei and quasars with polarized broad H α lines\nN.A. Silant'ev 1 , Yu.N. Gnedin 1 , 2 ∗ , S.D. Buliga 1 , M.Yu. Piotrovich 1 and T.M. Natsvlishvili 1 1 Central Astronomical Observatory at Pulkovo of Russian Academy of Sciences, Pulkovskoye chaussee 65, Saint-Petersburg, 196140, Russia 2 St.-Petersburg State Polytechnical University, Polytechnicheskaya 29, Saint-Petersburg, 195251, Russia\nFebruary 19, 2018\nAbstract\n1 Introduction\nWe present estimates of magnetic field in a number of AGNs from the Spectropolarimetric atlas of Smith, Young & Robinson (2002) from the observed degrees of linear polarization and the positional angles of spectral lines (H α ) (broad line regions of AGNs) and nearby continuum. The observed degree of polarization is lower than the Milne value in a nonmagnetized atmosphere. We hypothesize that the polarized radiation escapes from optically thick magnetized accretion discs and is weakened by the Faraday rotation effect. The Faraday rotation depolarization effect is able to explain both the value of the polarization and the position angle. We estimate the required magnetic field in the broad line region by using simple asymptotic analytical formulas for Milne's problem in magnetized atmosphere, which take into account the last scattering of radiation before escaping from the accretion disc. The polarization of a broad spectral line escaping from disc is described by the same mechanism. The characteristic features of polarization of a broad line is the minimum of the degree of polarization in the center of the line and continuous rotation of the position angle from one wing to another. These effects can be explained by existence of clouds in the left (keplerian velocity is directed to an observer) and the right (keplerian velocity is directed from an observer) parts of the orbit in a rotating keplerian magnetized accretion disc. The base of explanation is existence of azimuthal magnetic field in the orbit. The existence of normal component of magnetic field (usually weak) makes the picture of polarization asymmetric. The existence of clouds in left and right parts of the orbit with different emissions also give the contribution in asymmetry effect. Assuming a power-law dependence of the magnetic field inside the disc, we obtain the estimate of the magnetic field strength at first stable orbit near the central supermassive black hole (SMBH) for a number of AGNs from the mentioned Spectropolarimetric atlas.\nKeywords : accretion discs, magnetic fields, polarization, active galactic nuclei.\nSmith et al. (2002) presented optical spectropolarimetric atlas of 36 nuclei of Seyfert 1 Galaxies. The data were obtained with the William Herschel and the Anglo-Australian Telescopes from 1996 to 1999. It is well-known that spectropolarimetry is an important tool in studies of active galactic nuclei (AGN). The spectropolarimetric data provide the detailed view into the inner regions of active galactic nuclei, including an accretion disc and accretion flows around a supermassive black hole (SMBH), thus allowing one to probe the structure and kinematics of the polarizing material around the accreting SMBH.\nSmith et al. (2002) objects exhibit a variety of characteristics with the average degree of polarization ranging from 0 . 2 to 5 percent. They show many variations both in the degree p line ( λ ) and position angle χ line ( λ ) of polarization across the broad H α emission line. The characteristic feature of p line ( λ ) is the minimum in the line centre, which is usually less than the polarization degree p c ( λ ) in nearby continuum. The second feature is the monotonic increase of positional angle from one line wing to the other. Note also that there exists little difference in the mean polarization degrees and position angles of nearby continuum and H α line for nine of Seyfert galaxies (Mrk 6, Akn 120, Mrk 896, Mrk 926, NGC 4051, NGC 6814, NGC 7603, UGC 3478, ESO 012-G21). For 22 measurements out of 45, the mean positional angles χ line and χ c are practically the same. It should be emphasized that the position angles of polarized continuum and H α line coincide more frequently than their polarization degrees. The mean value of the polarization degree in continuum over all sources is 0.68%, and the same value for H α lines is 0.66%. A position angle is most sensitive to the geometry of emitting region. For that reason, it is most probable that both emitting regions are located near one another, i.e. they located in an accretion disc and their scale sizes are similar: R BLR ≈ R λ , where R λ corresponds to the scale size of an accretion disc for the continuum radiation with given wavelength λ .\nIt is generally accepted that AGNs are powered by the release of gravitational energy from gas accreted onto supermassive black holes (SMBH). The well-known anti-correlation\nbetween the radius of the broad-line region (BLR) and the velocity width of broad emission lines for AGNs supports the idea that the BLR gas is virialized and that its velocity is dominated by the gravity of the SMBH (Peterson & Wandel 2000; Onken & Peterson 2002).\nMost of the recent results lead to the conclusion that BLR presents a flattened rotating system. Many authors (Vestergaard et al. 2000; Nikolajuk et al. 2006; Sulentic et al. 2006; La Mura et al. 2009; Bon et al. 2009; Punsly & Zhang 2010) pointed out that considerable flattening and a predominantly planar orientation are likely to be the intrinsic property of the BLR structure. This conclusion allows us to consider BLR as an outer part of geometrically thin accretion disc that is optically thick with respect to the electron Thomson and the Rayleigh scattering processes.\nSeyfert galaxies were traditionally divided into two classes according to the presence or absence of broad optical lines. Antonucci & Miller (1985) explained this phenomenon by obscuration by a dusty torus with different orientation with respect to an observer. The orientation-based unification model has become quite popular, but it has also been confronted by more specialized observations (see, for example, Zhang & Wang 2006; Wang & Zhang 2007); in particular, there is evidence for the existence of a special subclass of Seyfert 2 lacking hidden broad-line regions (Zhang & Wang 2006). Thus, the paradigm of unification scheme for all Seyfert galaxies remains a matter of debate (Miller & Goodrich 1990; Tran 2001, 2003).\nThe basic feature of Smith et al. (2002, 2004, 2005) models is that the polarization plane for most of Seyfert galaxies is parallel to the direction of the radio jet. Simultaneously, these models postulate that the radio jet direction is perpendicular to the accretion plane. The latter assumption is questionable. In reality, the radio jets frequently have significant bends near the radio core. The angle of the bend depends on the ratio of radial and toroidal magnetic fields in the accretion disc. Besides, the direction of the jet appears to change with time (see, for example, Britzen et al. 2009; Rastorgueva et al. 2011). Therefore, the coincidence of the direction of the radio jet and the polarization plane does not mean that the electrical vector of the polarized radiation E is perpendicular to the accretion disc. Of course, one can introduce the angle between the radio jet and the electric field E as an additional characteristic of AGNs. But, strictly speaking, this angle is not necessarily related to the real inclination of E with respect to the accretion disc. As a last resort, this angle may be considered in a probabilistic sense.\nThe existence of many cases when the position angle of radiation has intermediate value between parallel or perpendicular to the direction of the radio jet also demonstrates that real direction of E does not correlate with the jet direction. As a result, we conclude that the models describing the polarization behavior in AGNs should not assume that the radio jets are perpendicular to accretion discs; instead, the explicit dependence on the inclination angle i of the accretion disc needs to be taken into account.\nIt is commonly accepted (see, for example, Blaes, 2003) that the accretion discs are magnetized. The existence of radio jets is usually associated with strong magnetic fields in\ncenters of AGNs and quasars. Numerous theoretical models demonstrate the power-law dependence of the magnetic field distribution in an accretion disc. Usually accretion discs are considered as geometrically thin slabs with Thomson optically depth τ /greatermuch 1. The scattering-induced linear polarization can be as high as ∼ 12% for edge-on viewing (Chandrasekhar 1960). However, in the real situation of a magnetized accretion disc, the degree of polarization p will be reduced due to Faraday rotation of the radiation polarization plane while a free photon travels between the consequent scatterings. Recall that the angle of Faraday rotation Ψ at the Thomson optical length τ is equal to\nΨ = 1 2 δτ cos Θ , δ = 0 . 8 λ 2 B, (1)\nwhere the wavelength of radiation λ is measured in microns and the magnetic field B is measured in Gauss. The angle Θ is the angle between the direction of light propagation n and the direction of B .\nThe decrease of the polarization degree due to Faraday rotation occurs as a result of summation of chaotic angles of rotations in the multiple scattering process. This process has been considered in many papers (for example, Silant'ev 1994; Agol & Blaes 1996; Gnedin & Silant'ev 1997). Clearly, the value Ψ ∼ 1 at the mean free path τ ∼ 1 can decrease considerably the standard Chandrasekhar's polarization degree. Besides, the dependence of Ψ on the wavelength and magnetic field gives rise to characteristic dependencies of the polarization degree p and the position angle χ of radiation on λ , which allows us to estimate the strength and direction of the magnetic field in the scattering region.\nBelow we develop a new model for the formation of polarization in AGNs, which does not use the assumption of the position angle of observed radiation being correlated with the direction of the radio jet. We hypothesize that the observed polarization is due to intrinsic polarization of radiation outgoing from the magnetized optically thick accretion disc (the Milne problem in magnetized atmosphere). In our model, the characteristic features of polarization mentioned above are explained by the topology of the magnetic field in the accretion disc, when the Faraday rotation of the polarization plane is taken into account. Primarily, we suppose that the whole radiating surface of the magnetized accretion disc is observed, i.e. that the inclination angle i is such that the obscuring torus (if it really exists) does not intersect the line of sight. We also consider the case when we observe only a part of total surface of accretion disc, i.e. we take into account the obscuring torus. It appears that our model and the usual pure geometrical model of Smith et al. (2002, 2004, 2005), which takes into account single scattering of BLR-photons in nearby clouds, are two competing explanations for the polarization properties of the accretion discs.\nAll actually observed polarization degrees p c are much smaller than the value in the Milne problem in nonmagnetized atmosphere at the same inclination angle. Recall that the Milne problem deals with the radiative transfer in an optically thick atmosphere, where the sources of thermal radiation are located far from the surface, at depth with τ /greatermuch 1. In optically thick accretion discs the main source\nof thermal radiation is found at the midplane of the disc, and the outgoing radiation is described by the solution of the Milne problem. The mean value of p c in the atmosphere with pure electron scattering is equal to 3.1%, and the maximum value is 11.7%. The outgoing radiation in case of an absorbing atmosphere has a much greater polarization, because the intensity peaks near the surface. In this case, most of polarization arises analogously to the process of a single scattering of a radiation beam near the surface. For the Milne problem in spectral lines, the value p line is less than in continuum (see, for example, Ivanov et al. 1997).\nFor the accretion disc models, the main challenge is to determine the scale length of the disc - i.e. the radius where the disc temperature matches the rest frame wavelength of the monitoring band. A semi-empirical method for measuring the disc scale length has been developed (Kochanek et al. 2006; Morgan et al. 2006, 2008; Poindexter, Morgan & Kochanek 2008). These authors used microlensing variability, observed for gravitationally lensed quasars, to find the accretion disc scale length for a given observed (or rest-frame) wavelength. Clearly, such a scaling has to be consistent with the most popular accretion disc model of Shakura & Sunyaev (1973). As a result, Poindexter et al. (2008) presented the following relation for the scale length of a standard geometrically thin accretion disc:\nR λ = 10 9 . 987 ( λ rest µm ) 4 / 3 ( M BH M /circledot ) 2 / 3 ( L bol εL Edd ) 1 / 3 cm. (2)\nThe wavelength dependence, R λ ∼ λ 4 / 3 rest , corresponds to the typical (for Shakura-Sunyaev disc model) effective temperature: T e = T in ( R/R in ) -3 / 4 , where R in is the inner radius of an accretion disc and T in is the temperature corresponding to that radius. Here L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ) erg s -1 is the Eddington luminosity, M BH is the black hole mass, ε is the rest-mass radiation conversion efficiency, and L bol is the bolometric luminosity.\nNumerous papers provided measurements of BLR sizes for AGNs (see, for example, Peterson et al. 1994, 2004; Wu et al. 2004; Bentz et al. 2009; Shen & Loeb 2010; Greene et al. 2010). Kaspi et al. (2007) have compiled the observational data for Seyfert galaxies and nearby quasars with black hole masses estimated with the reverberation mapping technique.\nMost recently Shen & Loeb (2010) have suggested an empirical analytic formula for R BLR that is very useful for various estimates and applications:\nR BLR = 2 . 1 · 10 17 M 1 / 2 8 ( L bol L Edd ) 1 / 2 . (3)\nHere M 8 = M BH / 10 8 M /circledot . We will use this formula in our further calculations.\nBelow we estimate the magnetic field strength in BLR of AGN and QSO from the data from the spectropolarimetric atlas presented by Smith et al. (2002). The λ - dependence of the observed polarization degree and position angle in H α line is very complicated. It appears to be produced by large-scale chaotic motions in the accretion disc.\n2 Basic equations\nTo estimate the degree of polarization p and the position angle χ of radiation escaping from the magnetized atmosphere we use the standard radiative transfer equations for Stokes parameters I, Q and U (see, for example, Silant'ev 1994; Dolginov, Gnedin & Silant'ev 1995; Silant'ev 2002, 2005). This system of equations has a fairly complicated form. Numerical solutions have so far been obtained only for the case when magnetic field B is parallel to the normal N to an atmosphere (see Silant'ev 1994; Agol and Blaes 1996; Shternin et al. 2003).\nFor our purpose, however, it is sufficient to use a simple asymptotic theory, which can be presented in an analytical form for an arbitrary direction of the magnetic field in the atmosphere (Silant'ev 2002, 2005; Silant'ev et al. 2009). In this approximation, the intensity of the radiation I ( z, µ ) obeys a usual transfer equation with the Rayleigh phase function, and the system of equations for parameters Q and U can be presented in the following form:\nµ d dz ( -Q + iU ) =\n= -α [1 + C + i (1 -q ) δ cos Θ]( -Q + iU ) + B Q ( z, µ ) , (4)\nwhere B Q ( z, µ ) describes the source function for parameter Q due to the contribution of intensity scattering in nonmagnetized atmosphere (in this case B U ≡ 0), µ = nN is the cosine of the angle between the direction of light propagation n and the normal N to the atmosphere, α is the total extinction factor due to Thomson scattering and pure absorption on dust particles, the value q = σ a / ( σ a + σ s ) (Silant'ev et al., 2009) is the degree of absorption, C describes the additional extinction of polarized radiation due to the fluctuating component B ' of the magnetic field in the atmosphere (see below). Eq.(4) is valid in the limit of large Faraday rotation parameter δ ≥ 1.\nA solution of Eq.(4) results in the following expression for parameters Q ( n , B ) and U ( n , B ) for the radiation escaping from the magnetized atmosphere:\n-Q ( n , B ) + iU ( n , B ) =\n= -∫ ∞ 0 dτ µ B Q ( τ, µ ) exp ( -[1 + C + i (1 -q ) δ cos Θ] τ µ ) (5)\n/negationslash\nAt δ ≥ 1, the first non-zero term of integrating by parts of Eq.(5) gives rise to the asymptotic expression which has an analytical form and can be used for an arbitrary direction of the magnetic field. For example, for the case B Q (0 , µ ) = 0 we have:\nQ ( n , B ) /similarequal B Q (0 , µ )(1 + C ) (1 + C ) 2 +(1 -q ) 2 δ 2 cos 2 Θ , U ( n , B ) /similarequal B Q (0 , µ )(1 -q ) δ cos Θ (1 + C ) 2 +(1 -q ) 2 δ 2 cos 2 Θ . (6)\nFor the Milne problem in absorbing atmosphere, a more sophisticated theory (see Silant'ev 1994, 2002) gives rise to the following expressions:\nQ ( n , B ) /similarequal I (0 , µ ) p (1) ( µ )(1 -sµ ) (1 + C -sµ ) 2 +(1 -q ) 2 δ 2 cos 2 Θ , U ( n , B ) Q ( n , B ) /similarequal (1 -q ) δ cos Θ 1 + C -sµ . (7)\nHere p (1) ( µ ) is the polarization degree of outgoing radiation, which takes into account only the last scattering before escaping the atmosphere. The value p (1) ( µ ) gives the main contribution to p ( µ ) - exact polarization degree of outgoing radiation for a non-magnetized atmosphere. For this reason, below we use the value p ( µ ) instead of p (1) ( µ ), which for q = 0 is presented in Chandrasekhar (1960), and for the absorbing atmosphere in Silant'ev (1980). The value s is the root of the characteristic equation, tabulated by Silant'ev (1980). If the degree of the true absorption is small ( q /lessmuch 1), the parameter s = √ 3 q .\nFirst, let us consider the case when the whole surface of a radiating accretion disc is observed. In this case, the Stokes polarization parameters of continuum radiation Q c ( ϕ ) and U c ( ϕ ) must be averaged over all azimuthal angles ϕ , characterizing the position of a radiating surface element on a circular orbit in the accretion disc ( -π ≤ ϕ ≤ π ). The normal N and the direction to an observer n are the same for all parts of the accretion disc surface. Therefore, the reference frame of the accretion disc is common to all parameters Q c ( ϕ ) and U c ( ϕ ) of radiation escaping from the disc. In this case, the averaging procedure consists of integrating these parameters over the azimuthal angle ϕ . Note, that cos Θ depends on ϕ and the integral over ϕ can be taken analytically only over the interval ( -π, π ). As a result, the observed values for the degree of polarization and the position angle can be derived analytically. Silant'ev et al. (2009) presented the detailed description of the behavior of these quantities for continuum radiation. The degree of linear polarization of continuum p c and the position angle χ c for an accretion disc can be expressed in the analytical form:\np c ( B , µ ) = p c ( µ )(1 -sµ ) [ g 4 c +2 g 2 c ( a 2 + b 2 ) + ( a 2 -b 2 ) 2 ] 1 / 4 , (8)\ntan2 χ c = U c Q c =\n= 2 ag c ( p c ( µ )(1 -sµ ) /p c ( B , µ )) 2 +( g 2 c + b 2 -a 2 ) . (9)\nHere µ = cos i , where i is the inclination angle (angle between the light propagation direction n and the normal N to the accretion disc). The degree of polarization p c ( µ ) corresponds to a non-magnetized accretion disc. The value of p c ( µ ) for the continuum radiation presents the classical solution of Milne problem (Chandrasekhar 1960) with p (0) = 11 . 7%. The value of the position angle χ c = 0 corresponds to oscillations of the wave electric vector perpendicular to the plane ( nN ).\nFor spectral lines in isotropic medium the value p line ( µ ) depends on the specific quantum numbers of the transitions (see,\nfor example, Chandrasekhar 1960) and on the shape of the line. For a dipole type transition and the Doppler line shape, p line ( µ ) in the atmosphere with pure electron scattering has the same functional form as Chandrasekhar value p c ( µ ), with maximum value of 9.44% instead of 11.71% (see Ivanov et al. 1997). In isotropic medium we have to average an atom over all orientations. For such medium the transfer equation coincides with the usual system for Rayleigh scattering with an additional term, which describes unpolarized radiation. Such average naturally occurs due to usual thermal motions. Considering various quantum numbers for H α line, we see that this additional term is larger than the Rayleigh scattering term (see Chandrasekhar 1960), and the maximum degree of polarization becomes ∼ 3% instead of 9.44%. Therefore, the observed polarization can be explained if the atmosphere also has pure absorption of H α line (the existence of dust). In absorbing atmosphere the polarization degree p line can be larger than that in the non-absorbing atmosphere.\nBroad H α lines presented in atlas Smith et al. (2002) have very high widths, laying in the interval 50 - 200 angstroms. In such situations the total line (sum of 5 sub levels) can be described by one absorption coefficient with the Doppler shape (see, for example, Varshalovich, Ivanchik & Babkovskaya 2006; Lekht et al. 2008). Our technique takes into account the Faraday rotation during propagation of polarized radiation after the last scattering before escaping from the atmosphere. The region of broad-line emission is too far from the center of an accretion disc and has low magnetic fields. For this reason, one does not need to take into account the known Zeeman effect.\nThe parameter\ng c = 1 + C -sµ, (10)\nwhere the negative term ( -sµ ) arises in the Milne problem in absorbing atmosphere (see Chandrasekhar 1960). For small degree of true absorption q = σ absorb / ( σ scattering + σ absorb ) /lessmuch 1 the factor s /similarequal √ 3 q . The regions of the line emission are different from those of continuum radiation. Usually one assumes that the parameter g c /similarequal 1 in most of areas of the accretion disc. To explain polarization of the line emission, we have to consider that this emission escapes from optically thick clouds with its own dimensionless parameters g line .\nThe dimensionless parameters a and b describe the Faraday depolarization of radiation:\na = 0 . 8 λ 2 µB z , b = 0 . 8 λ 2 √ 1 -µ 2 B ⊥ , (11)\nwhere B z ≡ B ‖ is the component of the magnetic field directed perpendicular to the accretion disc surface, and B ⊥ = √ B 2 ρ + B 2 ϕ is the magnetic field in the accretion disc plane. The component B ⊥ is perpendicular to B ‖ . Due to axial symmetry, the inclination angle ϕ ∗ ( B ϕ /B ρ = tan ϕ ∗ ) is constant along a circular orbit. The value 0 . 8 λ 2 B is numerically equal to the Faraday rotation angle at the Thomson optical depth of τ = 2, if the polarized radiation propagates along the magnetic field direction. Here and in what follows, we take magnetic field in Gauss and wavelengths in microns.\nThe dimensionless parameter C describes the real situation in a turbulent magnetized plasma and characterizes a\nnew effect - additional extinction of the polarized radiation (parameters Q and U ) due to incoherence of the Faraday rotation in small-scale turbulent eddies (see Silant'ev 2005):\nC = 0 . 64 τλ 4 〈 ( B ' ) 2 〉 f B 3 , (12)\nwhere τ is the Thomson optical depth of a turbulent eddy ( τ /lessmuch 1), 〈 ( B ' ) 2 〉 is the mean value of fluctuations of the magnetic field, and f B ≈ 1 is a parameter describing the integrated correlation of the B ' values at two-closely spaced points in the accretion disc.\nIt should be noted that the diffusion of radiation in the inner regions of the accretion disc also produces depolarization due to multiple scatterings. Presence of magnetic field and, therefore, the Faraday rotation effect, only increases the depolarization process. As a result, the polarized radiation emitted by a plane-parallel atmosphere at a specific inclination angle is considerably lower as compared to the classical Chandrasekhar-Sobolev value (see, for example, Gnedin & Silant'ev 1997). But the main feature of Faraday depolarization is the explicit wavelength dependence for both the polarization degree and the position angle.\nIt is interesting to note that at a = b the polarization degree p c ( B , µ ) takes a maximum value (the term ( a 2 -b 2 ) 2 is zero in expression (8)). This effect takes place due to the opposite Faraday rotations from magnetic fields B ‖ and B ⊥ in some places along an orbit.\nAll formulas presented above show that polarimetric observations allow us to derive the magnetic field strength and its topology in the BLR region, where the polarized radiation escapes the accretion disc. Using various models connecting magnetic field B H at the black hole horizon with the magnetic field B ms at the first stable orbit R ms nearest to the centre of the system, and then using the power law dependence of the magnetic field from R ms up to R BLR , we can estimate the magnetic field strength and the parameters that control it, such as the spin of the black hole a ∗ , the conversion efficiency of kinetic into radiative energy ε , and the magnetization parameter k = P magn /P gas ( P magn and P gas are magnetic pressure and gas pressure, in accreting plasma, respectively).\nFrequently one uses simple formulas for p c and χ c , corresponding to particular cases of pure normal B ‖ and of pure perpendicular B ⊥ :\np c ( B ‖ , µ ) = p c ( µ )(1 -sµ ) √ g 2 c + a 2 , tan 2 χ c = a g c , (13)\nIn the latter case χ c ≡ 0 due to the axial symmetry of the problem.\np c ( B ⊥ , µ ) = p c ( µ )(1 -sµ ) √ g 2 c + b 2 , χ c ≡ 0 . (14)\nNow let us consider the case when the radiating gas along a particular orbit in the accretion disc is partly obscured by some dust cloud (an obscuring torus). Clearly, for pure normal magnetic field B ‖ N , the unobscured part of the orbit has the same polarization degree p c ( B ‖ ) and the position angle χ c ( B ‖ ) as in the case of completely unobscured orbit (see Eq. (13)). If the magnetic field is toroidal B ϕ , i.e. is tangent\n\n\n
Figure 1: Dependence of p c ( B ϕ ) /p c ( µ )(1 -sµ ) on ϕ 0 .
\n\nto the orbit, we can derive the following analytical expressions:\np c ( B ϕ ) = p c ( µ )(1 -sµ ) √ g 2 c + b 2 ϕ f Q ( ϕ 0 ) , χ c ≡ 0 ,\nf Q ( ϕ 0 ) = 1 ϕ 0 arctan √ g 2 c + b 2 ϕ g c tan ϕ 0 . (15)\nHere the parameter b ϕ = 0 . 8 λ 2 B ϕ √ 1 -µ 2 , the angle ϕ 0 describes the unobscured part of the orbit (we see the orbit within azimuthal angles -ϕ 0 ≤ ϕ ≤ ϕ 0 ). At ϕ 0 = π (complete orbit), Eq.(15) coincides with Eq.(14). Eq.(15) for f Q ( ϕ 0 ) is valid for ϕ 0 ≤ π/ 2. For π/ 2 ≤ ϕ 0 ≤ π one can use the relation f Q ( ϕ 0 ) = [ πf Q ( π/ 2) -( π -ϕ 0 ) f Q ( π -ϕ 0 )] /ϕ 0 . A more detailed derivation of these formulas is given below, in subsection 2.2 (for a spectral line case).\nDependence of p c ( B ϕ ) /p c ( µ )(1 -sµ ) on ϕ 0 is presented in Fig.1 for values g c = 1, b ϕ = 1 , 2 , 3 , 4 , 5, and s = 0. It is interesting that for ϕ 0 = π/ 2 (half of the full orbit is observed) the polarization degree coincides with the result (14) for the fully unobscured orbit ( f Q ( π/ 2) = f Q ( π ) = 1).\n2.1 The case of a spectral emission line\nIn the catalog of Smith et al. (2002) the polarimetric data both in the continuum and in the H α emission line are presented. In our model of a rotating accretion disc (with the Keplerian velocity u k ) one part (the right side) of the disc ( ϕ = 0 ÷ π ) corresponds to motion from an observer and the second part (the left side) moves towards the observer ( ϕ = π ÷ 2 π ). According to the Doppler formula, wavelengths of radiation from the first part are greater than the central value λ 0 , and from the second part are smaller than λ 0 . The value λ 0 = (1 + z ) λ rest , where z is redshift parameter of the system and λ rest = 0 . 6563 µ m is the rest frame wavelength of the H α line.\nHere we restrict ourselves to a specific case of a spectral line with the Doppler shape. The line is described by following normalized shape function:\nφ ( λ ) = 1 √ π ∆ λ T exp [ -( λ -λ 0 ∆ λ T ) 2 ] . (16)\nAs in the previous case of continuum radiation, we assume that the X-axis is perpendicular to plane ( nN ). The Keplerian velocity u k corresponds to the radius R BLR : u k = √ GM BH /R BLR , where G is gravitation constant. The usual Doppler line width ∆ λ T = ( u turb /c ) λ 0 is mainly due to chaotic turbulent velocities. The displacement of the line centre for radiation emitted from the part of the disc with the azimuthal angle ϕ is ( u k /c ) λ 0 √ 1 -µ 2 sin ϕ . Thus, the normalized shape function of radiation emitted from ϕ -part of the orbit has the form:\nφ ( λ, ϕ ) = = 1 √ π ∆ λ T exp -( λ -λ 0 -u k c λ 0 √ 1 -µ 2 sin ϕ ∆ λ T ) 2 . (17)\nObserved radiation flux F λ from a surface element dS of the ring with the radius R BLR is proportional to dϕ . The flux from the total radiating circular orbit can be obtained by integration over all azimuthal angles ϕ . If we suppose that all sources are distributed uniformly along the orbit, this flux is described by the following expression:\nF ( λ ) = dSµI ( µ ) 1 2 π ∫ π -π dϕφ ( λ, ϕ ) . (18)\nObserved fluxes of linearly polarized radiation differ from the continuum radiation case by an additional factor φ ( λ, ϕ ):\nF Q ( λ ) =\n= dSµI ( µ ) p line ( µ )(1 -sµ ) 1 2 π ∫ π -π dϕ φ ( λ, ϕ ) g line g 2 line + δ 2 cos 2 Θ , (19)\nF U ( λ ) =\n= dSµI ( µ ) p line ( µ )(1 -sµ ) 1 2 π ∫ π -π dϕ φ ( λ, ϕ ) δ cos Θ g 2 line + δ 2 cos 2 Θ . (20)\nHere Θ is the angle between the magnetic field B and the light propagation direction n , I ( µ ) is total intensity of the spectral line escaping from the surface dS . The azimuthal angle ϕ = 0 corresponds to a surface element dS perpendicular to the plane ( nN ). Faraday depolarization term δ cos Θ has the form:\nδ cos Θ = 0 . 8 λ 2 Bn = a + b cos( ϕ + ϕ ∗ ) = = a + b ρ cos ϕ -b ϕ sin ϕ,\nwhere the parameters b ρ and b ϕ are:\nb ρ = 0 . 8 λ 2 √ 1 -µ 2 B ρ ≡ b cos ϕ ∗ , b ϕ = 0 . 8 λ 2 √ 1 -µ 2 B ϕ ≡ b sin ϕ ∗ .\n(21)\n(22)\nHere angle ϕ ∗ is the angle between B ⊥ and the radius-vector ρ , lying in the disc plane. The sign minus before b ϕ sin ϕ\ncorresponds to the right-hand screw rotation of the accretion disc with the frozen magnetic field B ϕ directed along the rotation velocity. If the rotation of the disc is opposite, we have to change b ϕ to b ϕ .\nIf we take the factor φ ( λ, ϕ ) = 1 and g line → g c , all the formulas will describe the case of the continuum radiation. In this case the integrals over ϕ can be evaluated analytically (for the combination -F Q + iF U the ϕ -integral can be evaluated by the complex residue method, and we obtain Eqs.(8) and (9)). Note, that these formulas are approximate, they take into account only the last scattering before the escape from the atmosphere. This is a rather satisfactory approximation (see Silant'ev 2002). It describes the main contribution to the polarization. The main merit of these analytical formulas is that they describe the polarization for any direction of the magnetic field. For our purpose this approach is sufficient.\nWe note that ϕ -integration in Eqs.(18) - (20) gives rise to rather low polarization effects. For this reason they hardly can be used for describing the polarization data presented in the atlas (Smith et al. 2002). Below we present two models that are more acceptable for explaining the data.\n2.2 The model of H α line polarization with parameters p and χ , averaged over the right and left parts of an orbit\nIt is clear from Eqs.(18), (19) and (20) that the right parts of circular orbits mostly contribute to gaussian shape lines at wavelengths λ > λ 0 , and the left parts mostly contribute to λ < λ 0 . Qualitatively, we can consider that these contributions are equivalent to sum of two gaussian shaped polarized lines. We assume that the effective polarizations and position angles of these lines correspond to mean values from the right side ( p right , χ right ) and the left side ( p left , χ left ) of the orbit. These values follow from Eqs.(19) and (20) if we take there the factor φ ( λ, ϕ ) = 1.\nUnlike the situation described by Eqs.(19) and (20), in this model we assume that a part of the accretion disc is invisible due to obscuring torus. The right part corresponds to integration over ϕ = 0 ÷ ϕ 0 , and the left part corresponds to integration in the interval ϕ = 0 ÷ -ϕ 0 . Here the angle ϕ 0 characterizes the boundary azimuthal angle for the visible part of the BLR orbit. The mean values 〈 Q 〉 and 〈 U 〉 for visible right part are described by the integrals:\n= I line p line ( µ )(1 -sµ ) 1 ϕ 0 0 dϕ g line g 2 + δ 2 cos 2 Θ ,\n〈 Q right ( n , B ) 〉 = ∫ ϕ 0 line 〈 U right ( n , B ) 〉 =\n= I line p line ( µ )(1 -sµ ) 1 ϕ 0 ∫ ϕ 0 0 dϕ δ cos Θ g 2 line + δ 2 cos 2 Θ , (23)\nwhere δ cos Θ is given in Eqs. (21) and (22). The corresponding mean values for the left part of the BLR orbit are given by integrals in the interval (0 , -ϕ 0 ).\n/negationslash\nThese integrals cannot be evaluated analytically in a general case. We present below the cases ( a = 0 , b ρ = 0 , b ϕ = 0) and ( a = 0 , b ρ = 0 , b ϕ = 0). The first case corresponds to the magnetic field B ‖ parallel to normal N . Clearly, in this case the polarization degree and the position angle are the same in the right and left parts of the orbit, and can be obtained from Eqs.(8) and (9) (see Eq.(13)).\n/negationslash\nThe second case corresponds to a toroidal magnetic field B ⊥ , laying in the plane of the accretion disc and tangential to the radiating circular orbit. In this case the Faraday rotations are opposite in the right and the left parts of the orbit. This gives the same value for the polarization degree p right = p left and the opposite values for the position angles χ right = -χ left . We present below the results for the right part of the orbit:\n〈 Q right 〉 = I right p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ f Q ( ϕ 0 ) ,\nf Q ( ϕ 0 ) = 1 ϕ 0 arctan √ g 2 line + b 2 ϕ g line tan ϕ 0 , (24)\nf\n〈 U right 〉 = I right p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ f U ( ϕ 0 ) .\nU\n(\nϕ\n0\n) =\n-1 2 ϕ 0 ln ∣ ∣ ∣ ∣ ∣ √ g 2 line + b 2 ϕ + b ϕ √ g 2 line + b 2 ϕ -b ϕ · √ g 2 line + b 2 ϕ -b ϕ cos ϕ 0 √ g 2 line + b 2 ϕ + b ϕ cos ϕ 0 ∣ ∣ ∣ ∣ ∣ . (25)\nIt is interesting to note that f Q ( ϕ 0 ) monotonically grows from f Q ( π/ 2) = 1 to f Q = √ g 2 line + b 2 ϕ /g line ≥ 1 as ϕ 0 → 0.\n∣ ∣ The expression for f Q is valid only for ϕ 0 ≤ π/ 2, and the formula for f U is valid for total interval 0 ≤ ϕ 0 ≤ π . The integrands in Eqs. (23) are symmetric relative to the angle ϕ 0 = π/ 2. This gives equalities f Q ( π/ 2) = f Q ( π ) = 1 and f U ( π/ 2) = f U ( π ). Due to the aforementioned symmetry, we can calculate values f Q and f U for π/ 2 ≤ ϕ 0 ≤ π from the values for interval 0 ≤ ϕ 0 ≤ π/ 2: f Q,U ( ϕ 0 ) = [ f Q,U ( π ) π -f Q,U ( π -ϕ 0 )( π -ϕ 0 )] /ϕ 0 .\nThe mean polarization degree p right ( B ϕ ) and the position angle χ right ( B ϕ ) can be derived from the following expressions:\nχ right = U f . (26)\np right ( B ϕ ) = p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ √ f 2 Q + f 2 U , tan2 f Q\nIn Fig.2 we present the values p right ( B ϕ ) /p ( µ )(1 -sµ ) and | χ right | at b ϕ = 1 , 2 , 3 , 4 , 5 and g line = 1 , s = 0. Comparison of p right ( B ϕ ) with p c ( B ϕ ) in Fig.1 shows that p right > p c . This is evident, because p c corresponds to the sum of radiation from the right and the left parts of the observed areas (in this sum U = 0), and p right corresponds to the half of this area, where parameter U = 0. It means that in the wings of\n/negationslash\n\n\n
Figure 2: The values p right ( B ϕ ) /p ( µ )(1 -sµ ) and | χ right | (dotted lines) at b ϕ = 1 , 2 , 3 , 4 , 5 and g line = 1 , s = 0.
\n\nthe emitting lines the polarization is greater than in nearby continuum.\nLet us consider the behavior of the polarization degree p line ( B ϕ , λ ) and the position angle χ line ( B ϕ , λ ) inside the broad spectral line in more detail, using our simple model of two equal gaussian lines with the equal right and left displacements from the central wavelength λ 0 . We label the intensities of these lines as I right and I left . According to Eqs.(24) and (25), we present the total observed Stokes parameters I, Q and U in the form:\nI ( µ ) = I right ( λ ) + I left ( λ ) , (27)\nQ ( B ϕ , λ ) = ( I right ( λ ) + I left ( λ )) p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ f Q , (28)\nU ( B ϕ , λ ) = ( I right ( λ ) -I left ( λ )) p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ f U . (29)\nRecall that due to the displacement of the centers of the right and left lines with the gaussian shape the intensities I right ( λ ) and I left ( λ ) are different at a particular considered wavelength inside the full line. Only at the central wavelength λ 0 these intensities are equal due to the axial symmetry of our model.\nUsing Eqs.(27), (28) and (29), we obtain the following expressions for the total observed polarization degree p ( B ϕ , λ ) and the position angle χ ( B ϕ , λ ):\np ( B ϕ , λ ) = p line ( µ )(1 -sµ ) f Q g 2 line + b 2 ϕ ( µ )\n√ 1 + ( I right -I left ) 2 ( I right + I left ) 2 f U f Q 2 , (30)\n√ × × ( )\ntan 2 χ ( B ϕ , λ ) = I right -I left I right + I left · f U f Q . (31)\n\n\n
Figure 3: The schematic illustration of the model of two emitting clouds.
\n\nTaking in Eqs.(30) and (31) I left = 0, we revert to Eq.(26) for the right part of the orbit.\nThe total rotation of the position angle inside the line width is equal to the difference of ∆ χ ≡ χ right -χ left , where χ right corresponds to the right-hand wing of line with I right /greatermuch I left . The χ left corresponds to the left-hand wing with I left /greatermuch I right . As a result, we have:\n| ∆ χ | = arctan ∣ ∣ ∣ f U f Q ∣ ∣ ∣ . (32)\nNow let us discuss shortly the polarization degree p inside the broad line. First of all, we notice that in the centre of the line λ = λ 0 the polarization is less than in the wings (c.f. Eq.(30) with I right = I left ). The polarization grows with the departure from λ 0 . This behavior of p line ( λ ) is observed in many objects from the catalog of Smith et al.(2002). According to Eq.(30), the ratio of p wing ( B ϕ , λ ) to p center ( B ϕ , λ ) becomes\n∣ ∣ Note that the difference ∆ χ does not depend on the choice of the observer's reference frame. A non-zero value of ∆ χ is observed in many objects presented in the catalog of Smith et al. (2002) and is due to two reasons - the presence of the magnetic field B ϕ and the Keplerian rotation of the magnetized accretion disc. Fig.2 shows that ∆ χ depends on the parameter b ϕ and the angle ϕ 0 . Thus, for b ϕ = 5 and ϕ 0 /similarequal (140 · -160 · ) the value | ∆ χ | /similarequal 60 · .\np wing ( B ϕ , λ ) p centre ( B ϕ , λ ) = √ 1 + (tan | ∆ χ | ) 2 . (33)\nFor ∆ χ = 60 · this ratio is equal to 2.\nClearly, it is not possible to explain all details of p and χ in the our model of the sum of two spectral lines. But, above considerations tell us that the main characteristic features can be explained.\n2.3 The model of H α line as two emitting compact clouds located in the right and left part of the orbit\nThe spectra of H α lines in the atlas of Smith et al.(2002) for many objects have sufficiently complicated structure - the existence of separate peaks and asymmetric shapes. There are only a few objects with symmetric shapes. They have comparatively small widths as compared to other, more complicated spectra.\nA line with a complicated shape frequently can be approximated as a sum of two or more lines with gaussian shapes. For this reason we present the model of two compact optically thick clouds located in the opposite parts of an orbit in the accretion disc (Fig.3). The advantage of this model compared with the previous one is that we can take into account all the depolarizing Faraday parameters a, b ϕ and b ρ in a simple analytical form.\nLet us take the first cloud in the right part of the orbit, characterized by the azimuthal angle ϕ , and the second cloud in the left part, characterized by ϕ . If it is necessary, locations of the emitting clouds can be chosen at arbitrary angles along the orbit. Our choice is the simplest for consideration. As usually, we write the Stokes parameters in the coordinate system with X-axis being perpendicular to the plane ( nN ), where the formulas have the simplest form. Further we will\nuse the observed polarization degree p and the total difference of the position angles between right and left parts of the spectral line ∆ χ , which do not depend on the choice of the reference frame. We also include in our formulas the contribution of the continuum radiation ( I c , Q c , U c ) in the region of spectral line. Then, the observed Stokes parameters are:\nI = I c + I right + I left , ξ = I right I left , (34)\n+ I left p line ( µ )(1 -sµ ) g line , (35)\nQ = Q c + I right p line ( µ )(1 -sµ ) g line A + + A -\nU = U c + I right p line ( µ )(1 -sµ )( a + b ϕ ) A + +\n+ I left p line ( µ )(1 -sµ )( a -b ϕ ) A -, (36)\nA + = g 2 line +( a + b ϕ ) 2 ,\nA -= g 2 line +( a -b ϕ ) 2 (37)\nThe explicit formulas for Q c and U c are as follows:\nQ c = r +( g 2 c + b 2 -a 2 ) I c p c ( µ )(1 sµ ) ,\nU c = r -( g 2 c + b 2 -a 2 ) √ I c p c ( µ )(1 sµ ) . (38)\n√ √ 2 r -√ 2 r -\nHere r 2 = ( g 2 c + b 2 -a 2 ) 2 +4 a 2 g 2 c = g 4 c +2 g 2 c ( a 2 + b 2 )+( a 2 -b 2 ) 2 . Introducing the notation η c = p c ( µ )(1 -sµ ) /p c ( B , µ ), and using expressions (8) and (9), we can present formulas for Q c and U c in a simpler form:\nQ c = √ 1 + √ 1 -2 ag c η 2 c 2 I c p c ( B , µ ) √ 2 → I c p c ( B , µ ) ,\nU c = √ √ √ √ 1 -√ 1 -( 2 ag c η 2 c ) 2 I c p c ( B , µ ) √ 2 → 0 .\n√ √ √ ( ) (39)\nThe last expressions are valid in the limit (2 ag c ) /η 2 c → 0.\nIn most sources from the catalog of Smith et al. (2002), the intensity I c is much smaller than I right + I left . For these cases one can neglect the contribution of the continuum radiation and the formulas for p line and χ line acquire fairly simple form:\ntan2 χ line = U line Q line = a g line + b ϕ g line · 1 -ξA + /A -1 + ξA + /A -, (40)\np line = p line ( µ )(1 -sµ ) g line (1 + ξA + /A -) (1 + ξ ) A + ×\n× √ 1 + (tan 2 χ line ) 2 . (41)\nIn the right wing, where ξ /similarequal 0, we have\ntan 2 χ right = a + b ϕ g line . (42)\nFor the left wing one finds the same expression with ( -b ϕ ) instead of b ϕ . Using formula (42), we can obtain expression for the difference of the position angles between the right and left wings of the line:\n∆ χ = χ right -χ left =\n= 1 2 ( arctan a + b ϕ g line -arctan a -b ϕ g line ) . (43)\nFor the polarization degree in the right wing we derive the formula:\np right = p line ( µ )(1 -sµ ) √ g 2 line +( a + b ϕ ) 2 . (44)\nFor the left wing the polarization degree is higher because the Faraday depolarization parameter | a -b ϕ | is lower than in the right wing. If a = 0, the polarization degree p right = p left and χ right = -χ left . Presence of the magnetic field B ‖ (parameter a = 0) diminishes the polarization degree both in the right and left wings of the line, and also diminishes the difference | ∆ χ | = | χ right -χ left | . Besides, the functions p line ( λ ) and χ line ( λ ) become asymmetric relative to the center of the line λ 0 (if the intensities of lines I right ( λ ) and I left ( λ ) are the same gaussian functions).\nAnalogously, for the left wing one replaces b ϕ with ( -b ϕ ).\n/negationslash\nIt is interesting to compare the polarization degrees in the wings and in the center of line. The general formula for ratio p wing /p center is very complex and we consider only the case a = 0, where this ratio reaches a maximum value. Taking ξ = 1 for the center of the line and ξ = 0 for the line wing, we obtain the following expression from the general formula (41):\np wing p center = √ g 2 line + b 2 ϕ . (45)\nFor b ϕ = 5 and g line = 1 this ratio is equal to 5.1, i.e. is considerably greater than the value from formula (33). It is quite natural, because formula (33) describes the mean value of the effect. Clearly, the averaging procedure diminishes the effect. Physically this effect arises as a consequence of the Faraday rotation of the polarization plane. In the center of the line the rotations from the right and the left lines have opposite directions and the parameter Q center reaches a lower value than that in the line wing.\nThe most important conclusion from the theoretical consideration of the structure of broad lines in AGN is the treatment of the symmetry of the polarization degree p line ( λ ) as the result of the azimuthal magnetic field B ϕ . If the symmetry of p ( λ ) is considerably broken, one can consider that B ϕ ∼ B ‖ , or the intensities of the right and the left emitting clouds are different.\n3 The magnetic field strength in a broad line region of AGN\nThe standard Unified Sheme for AGN includes a central source of continuum (accreting SMBH); a region close to the outer radius of the accretion disc emitting broad emission lines (broad line region - BLR); a dusty rotating 'torus' on parsec scales; and gas emitting narrow emission lines on a scale of tens to hundreds of parsecs, ionized through the open cone defined by the torus edge (Antonucci & Miller 1985; Krolik & Begelman 1988; Urry & Padovani 1995).\nThe main unknown is the mechanism for the generation of the magnetic field during the process of accretion onto SMBH. Li (2002), Wang et al. (2002, 2003), Zhang et al. (2005) have studied the magnetic coupling process (MC) as an affective mechanism for transforming the kinetic energy of accreting gas into the magnetic energy. It is assumed that the disc is stable, perfectly conducting and Keplerian. The magnetic field on the black hole horizon is poloidal and varying as a power law with the distance from the central region.\nSince the magnetic field on the horizon B H is brought and held by its surrounding magnetized matter of the accretion disc, there must exist the relation between the magnetic field strength near the BH horizon and the accretion rate ˙ M .\nAs a result, the magnetic field strength on the event horizon R H = R G (1+ √ 1 -a 2 ∗ ) is determined by the relation between the magnetic energy and the accretion kinetic energy densities (see Li 2002; Wang et al. 2002):\nB H = √ 2 k ˙ Mc R H = (2 kL bol /εc ) 1 / 2 R G [ 1 + √ 1 -a 2 ∗ ] . (46)\nHere R G = GM BH /c 2 , the bolometric luminosity L bol = ε ˙ Mc 2 , ˙ M is the accretion rate, c is the light velocity and ε is the radiative efficiency calculated by numerical simulations of Novikov & Thorne 1973, Krolik 2007, Shapiro 2007. The coefficient k presents the inverse plasma parameter k = P magn /P gas = 1 /β , where P gas and P magn are the gas and the magnetic pressures, respectively. For the equipartition case β = 1 and k = 1.\nEq.(46) is easily transformed into:\nB H = 6 . 3 · 10 8 ( M /circledot M BH ) 1 / 2 ( kl E ε ) 1 / 2 1 1 + √ 1 -a 2 ∗ , (47)\nThe basic problem is the relation between the magnetic fields strengths at the first stable circular orbit R ms and the event horizon R H . The value of the radius R ms depends on the radius R G and the spin a ∗ , and can be presented in a form:\nwhere l E = L bol /L Edd and the Eddington luminosity L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ).\nR ms = q ( a ∗ ) R G , (48)\nwhere parameter q > 1. For example, for a Schwarzschild black hole q = 6 and for the Kerr BH with the spin a ∗ = 0 . 998 q = 1 . 22 (Murphy et al. 2009).\nReynolds, Garofalo & Begelman (2006) argued that the plunging inflow can greatly enhance the trapping of large scale magnetic field on the black hole. Blandford (1990) has shown that the interaction of the large-scale magnetic field with the event horizon of rotating black hole can enhance the trapping of large-scale poloidal magnetic field on the horizon of the black hole, compared with the inner accretion flow and compared to the magnetic field strength derived from the relation between magnetic energy and accretion kinetic energy (Eq.(47)).\nRecently Garofalo (2009) has showed that the dynamics of the plunge region of a thin black hole accretion disc and magnetic flux trapping can enhance the strength of the magnetic field threading the horizon by a significant factor. The results of his calculations were presented in fig.7 of Garofalo paper. It means that we obtain the following relation between the magnetic field strength at the first stable orbit B ms and the magnetic field strength at the event horizon of a black hole B H :\nB H = η ( a ∗ ) B ms . (49)\nThe coefficient η can be obtained from fig.7 of the paper by Garofalo (2009). From this figure it follows that for a ∗ = 0 . 5 the value is η = 5 and for a ∗ = 0 . 0 and a ∗ = 0 . 998 we have η = 7 . 5.\nNumerical simulations have been used to study magnetic field generation in astrophysical objects. For example, the existence of large-scale dynamos in magneto-convection under the influence of shear and rotation has been studied by Kapyla, Korpi & Brandenburg (2008). These authors have shown that the saturation field strength reaches, practically, the equipartition level B ≈ 0 . 7 B eq , i.e. k ≈ 0 . 5. Taking into account the shear flows can increase the magnetic field level. It means that the magnetization parameter can be equal to k ≈ 1.\nWe suggest that the magnetic field far inside in the accretion disc, and, especially, in the Broad Line Region (BLR) takes the toroidal form. Namely, the differential rotation in the accretion disc leads to an increase of the azimuthal field by winding up the poloidal field lines into the toroidal field lines (Bonanno & Urpin 2007).\nIn astrophysical objects differential rotation is often associated with magnetic fields of various strength and geometry. If the poloidal field has a component parallel to the gradient of the angular velocity, then differential rotation can stretch toroidal field lines from the poloidal ones. In the presence of the magnetic field, differential rotation can be a reason for various MHD instabilities, especially if the field geometry is complex.\nMayer & Pringle (2006) assumed that a dynamo process generates a local poloidal field B z in the accretion disc, and the magnitude of the poloidal component is small: B z /lessmuch B ⊥ .\nUsually one assumes that regular dependence of the magnetic field on the radius R in the accretion disc exists from the first stable orbit R ms , and that dependence has a power law form:\nB ⊥ ( R ) = B ms ( R ms R ) n . (50)\nWe assume two values for the parameter n . The value n = 1 derives the toroidal topology of the magnetic field (see Bonanno & Urpin 2007). The value n = 5 / 4 corresponds to the accretion process with hot accretion flows (Medvedev 2000).\nFor pure toroidal topology of the magnetic field in the accretion disc we have the depolarization parameter a = 0, and in this case Eqs.(8) and (9) for non-turbulent case ( C = 0) are transformed into Eq.(14). Recall that, according to definitions (11), magnetic field B ( R BLR ) can be determined, if the parameter b is known from the observed polarization:\nB ( R BLR ) = b 0 . 8 λ 2 √ 1 -µ 2 . (51)\nThis field can be related to B ms . In the case of a power-law dependence (50) with n = 1, this relation becomes\nB ( R BLR ) = B ms R ms R BLR = 2 . 22 · 10 -4 ( M 9 l E ) 1 / 2 q ( a ∗ ) B ms . (52)\nWe used here Eq.(3) for determining R BLR . Note that M 9 = M BH / 10 9 M /circledot . In this situation the depolarization parameter b for H α wavelength ( λ = 0 . 6563 µ m) is:\nb = 7 . 7 √ 1 -µ 2 q ( a ∗ ) ( M 9 l E ) 1 / 2 ( B ms 10 5 G ) . (53)\nFor hot accretion flows n = 5 / 4 and the depolarization parameter b becomes\nb = 0 . 93 √ 1 -µ 2 ( M 9 l E ) 5 / 8 q 5 / 4 ( a ∗ ) ( B ms 10 5 G ) , (54)\nwhere q ( a ∗ ) = R ms /R G and R G = GM BH /c 2 . The explicit form of q ( a ∗ ) is given, for example, in Zhang et al. (2005).\nBelow we shall also consider the case of the equipartition between the gas and the magnetic pressures, i.e. k ≈ 1. Namely, the magnetic coupling process corresponds to this case (Li 2002; Wang et al. 2003; Zhang et al. 2005; Ma, Wang & Zuo 2006).\nUsing Eqs.(47) and (49), we transform relations (53) and (54) into the following forms:\nand for n = 5 / 4:\nb = 1 . 53 √ 1 -µ 2 √ k ε q ( a ∗ ) η ( a ∗ )(1 + √ 1 -a 2 ∗ ) , (55)\nq ( a ∗ ) η ( a ∗ )(1 + 1 a 2 ) . (56)\nEqs.(55) and (56) allow us to estimate the radiation efficiency and therefore the rotation rate a ∗ of an accreting black holes. Below we use the spectropolarimetric atlas of AGNs by Smith et al. (2002) for specific estimates.\n4 Magnetic field strength of Akn 120\nAccording to Smith et al. (2002) the mean polarization degree in the continuum of Akn 120 is equal to p c /similarequal 0 . 35%, and is equal to /similarequal 0 . 4% in the H α line emission. We use here the data obtained by Smith et al. (2002) in 1998 October. The mean observed position angle have the same value for the continuum and line emission χ /similarequal 76 · . The inclination angle i = 48 · , µ /similarequal 0 . 67. Its value has been derived by Braatz & Gugliucci (2008) from water maser observations. The central black hole mass in Akn 120 is equal to M BH /similarequal 10 7 . 74 M /circledot (see Peterson et al. 2004).\nFor the inclination angle i = 48 · the polarization in the continuum from the accretion disc without magnetic field is expected at the level p c ( µ ) = 1 . 26% (Chandrasekhar 1960). This value is higher than the observed polarization degree and it means that the Faraday depolarization effect is really acting. The H α line spectrum shows the two-peak structure and can be represented as sum of two intensities with gaussian shapes. The difference of the positional angles ∆ χ is estimated to be between 70 · and 80 · . The intensity of the continuum radiation reaches ≈ 18% of the maximum line intensity near the centre. The behaviour of polarization in the continuum is very complex. It seems this behaviour occurs due to the existence of large-scale turbulent curls along the observed orbit. For that reason, it is more convenient to use the continuum - subtracted spectrum of Akn 120, presented in fig.24 of the mentioned Atlas by Smith et al. (2002).\nWe used formulas (31)-(37) to find the estimates for the parameters a, b ϕ , p line ( µ ) and g line . Attempts to estimate these parameters under the assumption p c ( µ ) /similarequal p line ( µ ) were unsuccessful. We propose that in the line radiating clouds there is true absorption of radiation (the existence of dust particles). As it is known (see, for example, Silant'ev 1980), the existence of absorption gives rise to a considerable increase of polarization escaping from the optically thick atmosphere. This effect is the consequence of absorption creating a peak like form of escaping emission.\ng c /similarequal 1 , a g line /similarequal 0 , b ϕ g line /similarequal 3 . 55 , p line ( µ ) g line /similarequal 4 . 07% . (57)\nIntroducing first three parameters in Eq.(8), we obtain g line /similarequal 0 . 975. The estimate g line = 0 . 975 = 1 + C -sµ gives the relation between C and s . It means that the clouds are absorbing and the small scales are turbulent. The existence of large scale turbulence in clouds directly follows from very high line width. For the rest of radiation from the accretion disc outside the compact clouds we assume that absorption is absent and small scale turbulence is negligible ( C ≈ 0). From Eq.(57) it follows that p line /similarequal 3 . 97% and b ϕ /similarequal 3 . 46. The estimated value p line /similarequal 3 . 97% corresponds to the case when one takes into account the pure absorption of radiation by dust particles existing into emitting clouds. From Eq.(11) one can obtain an estimate of magnetic fields B ‖ /similarequal 0 G and B ϕ /similarequal 14 G.\nIn Fig.4 we present the observed intensity, polarization degree and variation of the azimuthal angle χ , and our model results. It is seen that the model curves practi-\nb = 0 . 19 √ 1 -µ 2 ( M 9 l E ) 1 / 8 q 1 / 4 ( a ∗ ) √ k ε × × √ -∗\n/s32\n\n\n
Figure 4: The comparison of observed (solid curves) and model data (dot curves) for Akn 120
\n\ncally coincide with the observed values. The observed intensity is approximated as sum of two gaussian intensities from symmetrically located clouds. The Doppler widths of these intensities are taken equal to ∆ λ T =70 ˚ A, the value ( u k /u turb ) sin ϕ √ 1 -µ 2 = 0 . 3, the ratio of maximum intensities of gaussians is I left /I right = 20 / 18. The centers of gaussian curves coincide with the observed places in Fig.24 of Smith et al. (2002).\nThe main problem is that the exact value of index n is unknown and its value depends strongly on the model of the accretion disc. Pariev, Blackman & Boldyrev (2003) suggest the following interval of values of this index 1 ≤ n ≤ 2. The value n = 1 corresponds to toroidal magnetic field (see Bonanno & Urpin 2007).\nTo estimate the magnetic field strength at the last inner circular orbit B ms we need to know the rotation rate of the central supermassive black hole (parameter a ∗ ). For a Schwarzschild black hole with a ∗ = 0 and q = 6 and for the toroidal magnetic field ( n = 1) we obtain from Eq.(49) B ms = 14 . 5 · 10 3 G . Now we can estimate the magnetic field strength B H at the horizon of the central black hole using the results of calculations by Garofalo (2009). He has calculated the ratio of the horizon-threading magnetic field and the magnetic field in the accretion disc as a function of the black hole spin. According to this calculations, for a ∗ = 0 the ratio B H /B ms = 7 . 5 and B H = 10 . 7 · 10 4 G .\nOur results demonstrate that for a given value of the polarization degree the magnetic field strength at the inner radius r ms (and therefore on the horizon radius) is stronger for a Kerr black hole compared to Schwarzschild one. This result means also that for black holes with the same magnetic field strengths the degree of polarization for Kerr black holes is\nlarger than for Schwarzschild black holes (see Silant'ev et al. 2011).\n5 Magnetic field strength of Mrk 6\nAccording to Ho, Darling & Greene (2008), the mass of the central black hole in Mrk 6 is log( M BH /M /circledot ) = 7 . 97 ± 0 . 5, the ratio of the bolometric luminosity to the Eddington value is log( L bol /L E dd ) = -1 . 72. The inclination angle is i = 62 · . 7 , µ = 0 . 46 (Ho et al. 2008). It means that the standard (Sobolev-Chandrasekhar) magnitude of the polarization degree is p c ( µ ) = 2 . 52%. The observed mean polarization has been found at the level of p c = 0 . 90 ± 0 . 03, p ( H α ) = 0 . 85 ± 0 . 04 (Smith et al. 2002). The most remarkable fact is the jump of the mean position angle for two observational seasons of Feb 97 and Oct 98: ∆ χ ≈ 25 · . It is interesting that the value of the mean polarization remained the same. This jump occurred over 1-2 years, which is too short a time for such a large object as the accretion disc near the supermassive black hole. Thus, this problem remains unsolved.\nLet us return now to the analysis of the data in the H α line. First of all, we see that the polarization degrees in the right and the left sides of the spectrum are practically equal - the left side has p line /similarequal 1 . 5%, and in the right side p line /similarequal 1 . 4%. From the theoretical considerations in section 2, it is clear that such a symmetrical form of the polarization degree can occur if the magnetic field B ‖ is much less than the azimuthal magnetic field B ϕ . A small decrease of polarization in the right-hand part is due to the reason that small value of the B ‖ component, directed to an observer, coincides with direction of B ϕ . In this situation the polarization of radiation slightly decreases compared to the left-hand part of the orbit, where the aforementioned magnetic fields are directed opposite to each other. Considering polarization near the line center, we assume p line ( centre ) /similarequal 0 . 5%. We also assume that in the center of the line the intensity from the left part of the orbit is approximately equal to that from the right part. The value of the intensity of the continuum radiation in Mrk 6 is relatively small, and we neglect it in our computation. Using formulas (34)-(36), one obtain:\ng c /similarequal 1 , a g line /similarequal 0 . 1 , b ϕ g line /similarequal 2 . 615 , p line ( µ ) g line /similarequal 3 . 9% . (58)\nSubstitution of these parameters in Eq.(8) gives g line /similarequal 1 . 0006, i.e. practically 1. As in the case of Akn 120, the polarization p line /similarequal 3 . 9% implies that in H α -clouds there exists the absorption of radiation. Under the assumption of dipole radiation we have q c /similarequal 0 . 01 and the parameter s /similarequal 0 . 17. Because g line = 1 . 0006 /similarequal 1 = 1+ C -0 . 17 · 0 . 46 we find that the small scale turbulent parameter C /similarequal 0 . 08. For the difference ∆ χ of the position angles between the left and the right wings of the spectral line the expression (43) gives ∆ χ = 42 · . This value is consistent with the observational results. Eqs.(11) and (58) give estimate: B ‖ /similarequal 0 . 6G and B ϕ /similarequal 8 . 5G. Note that expression (58) supposes that I c p c /lessmuch I right,left p line ( µ ).\nNow let us estimate the magnetic field strength in the accretion disc of Mrk 6 using the results of the polarimetric obser-\nFor the spin value of a ∗ = 0 . 5, ε = 0 . 081, q = 4 . 25 (Novikov & Thorne 1973) we obtain B ms = 6 . 8 · 10 3 G and B H = 3 . 4 · 10 4 G . At last, for a ∗ = 0 . 998, q = 1 . 22, ε = 0 . 32 we have B ms = 2 . 8 · 10 4 G and B H = 14 · 10 4 G .\n/s32\n/s32\n/s32\nvations from Smith et al. (2002). Eqs. (53)-(56) allow us to derive the magnetic field strength B ms at the inner radius of the accretion disc: B ms = (1 . 72 × 10 4 /q ) G . For a Swarzschild black hole, when q = 6, the magnetic field B ms = 2 . 9 · 10 3 G . For a Kerr black hole with a ∗ = 0 . 998 the parameter q = 1 . 22 and the magnetic field strength B ms = 1 . 4 · 10 4 G . According to Garofalo (2009, fig.7) the magnetic field strength at the horizon of the supermassive black hole is B H = 1 . 4 · 10 4 G for a ∗ = 0 and B H = 10 5 G for a ∗ = 0 . 998.\n6 Magnetic fields of Mrk 985 and IZw1\nThe intensity spectrum of Mrk 985 has a two-peak shape and the spectrum of the polarization degree p line ( λ ) is quite symmetric (the p line ( left ) /similarequal 1 . 27% and p line ( right ) /similarequal 1 . 16%). In the centre of line p line ( centre ) /similarequal 0 . 5%. The mean polarization of the continuum radiation is 1.12%. Using formulas (33)-(37), we find that\ng c /similarequal 1 , a g line /similarequal 0 . 114 ,\nb ϕ g line /similarequal 2 . 035 , p line ( µ ) g line /similarequal 2 . 75% . (59)\nWe see that a nearly symmetric form of p line ( λ ) implies that a /lessmuch b ϕ , i.e. B ‖ /lessmuch B ϕ .\nFrom Fig.15 in the atlas of Smith et al. (2002) we see that the difference of position angles between the right wing and the centre of line is equal ∆ χ /similarequal 31 -33 · . From general theory one finds that tan2∆ χ = a/g line + b ϕ /g line . Our estimates (59) give this value for the angle difference. The estimates of magnetic fields at distances R ms and R H can be obtained analogously as in the previous sections.\nIn the atlas of Smith et al. (2002) there is no information on the inclination angle i . It is interesting to estimate this angle assuming that g line /similarequal 1. Substituting parameters g c = 1 , a = 0 . 114 and b ϕ = 2 . 035 into formula (8) gives the value p c ( µ ) = 2 . 54%. This implies an estimate i /similarequal 64 · , µ /similarequal 0 . 44. Using the value p c ( µ ) = 2 . 54% we can calculate the value g line , corresponding to this polarization. This calculation demonstrates that the parameter g line acquires the value g line /similarequal 1 . 0013. The value p line ( µ ) = 2 . 75 at µ = 0 . 44 takes place at q a /similarequal 0 . 01 ( s = 0 . 17). The value g line /similarequal 1 . 0013 = 1 + C -0 . 17 · 0 . 44 occurs at C /similarequal 0 . 08. Using Eq.(11) and the value µ /similarequal 0 . 44, we find the estimates: B ‖ /similarequal 0 . 75 G and B ϕ /similarequal 6 . 6 G.\nNow let consider the AGN IZw1. This object has p c /similarequal 0 . 67%, p line ( left ) /similarequal 0 . 7%, p line ( centre ) /similarequal 0 . 2% and p line ( right ) /similarequal 0 . 9%. The form of the polarization spectrum is slightly more asymmetric than in Mrk 985. Using general formulas (33)-(35) we find the following estimates:\na\ng c /similarequal 1 , g line /similarequal 0 . 52 ,\nb ϕ g line /similarequal 3 . 905 , p line ( µ ) g line /similarequal 3 . 18% . (60)\n
\n\n
Table 1: The obtained estimates of the magnetic field strengths.
\n
\nAs in the case of Mrk 985, we found, that g line /similarequal 1 and p c ( µ ) /similarequal 2 . 68%. This corresponds to µ /similarequal 0 . 44. The value p line /similarequal 3 . 9% occurs at the absorption degree q a /similarequal 0 . 01 , s /similarequal 0 . 17. As a result, the small scale turbulence parameter C /similarequal 0 . 08.\nAs in the previous cases, using Eq.(11) and the value µ = 0 . 44 we can estimate the magnetic field strength for IZw 1: B ‖ = 3 . 42G and B ⊥ = 12 . 7G. It should be noted that in these cases we estimated the inclination angle i from the analysis of the polarization data.\nThe obtained estimates of the magnetic field strengths in BLR of these AGNs are presented in Table 1. The last value in the table is close to the one estimated by Afanasiev et al.(2011) where the polarimetric observations were made only for the continuum emission and did not include the emission from the broad line region.\n7 Conclusions\nFor many objects of Smith et al. (2002) spectropolarimetric atlas the polarization spectra of a broad H α -line p line ( λ ) have a characteristic minimum at the center of the line and different maxima at the left and right wings. Usually the wing polarizations are higher than those in the nearby continuum. For many objects the position angle changes continuously from the left wing to the right one. We develop a new theoretical explanation for these features, different from the original explanation of Smith et al. (2002, 2004, 2005), taking into account that accretion discs can be magnetized.\nSmith et al. explain the characteristic features of the H α -line assuming that the observed polarization is due to single scattering of non-polarized radiation from the BLR on two types of scattering clouds - a polar cloud around the radio jet, and clouds in the equatorial region. It appears (see Smith et al. 2005) that their mechanism has two characteristic features: a relatively low amplitude ( | ∆ χ | ≤ 20 -40 · ) of the position angle rotation from one line wing to the other one, and the need for a very high electron temperature ( T ∼ 10 6 K) in a nearby scattering cloud. In their atlas there are cases with both low ∆ χ < 20 · and high ∆ χ ∼ 80 · position angle rotations. The need for the high electron temperature arises from the observed polarization minimum in the line core. Besides, they neglect the intrinsic linear polarization of the radiation in BLR.\nIn our mechanism both effects can be explain by a single cause - the Faraday rotation of the polarization plane. The wide line width results from turbulence, which is related to the Keplerian rotation in the orbit. Clearly both explanations take place in reality.\nThe basis of our explanation is the assumption that both the continuum radiation and the spectral line emission originate in an optically thick magnetized accretion disc around the center of an AGN. The observed characteristic shape of the line polarization appears as a result of the Faraday rotation of the polarization plane in the accretion disc having a normal magnetic field B ‖ and an azimuthal field B ϕ .\nWe propose that the regions of the line emission can be represented as a comparatively dense absorbing turbulent clouds rotating with the Keplerian velocity around the center of the AGN. These clouds are flattened, optically thick and magnetized. They emit the polarized radiation in accordance with the Milne problem law. The observed emission line is a sum of radiation from clouds rotating in the right and the left sides of the orbit. Due to Doppler displacements, emission from the one side is, as a whole, reddened ( λ ≥ λ 0 ), and emission from the other side has the opposite λ -displacement. The Faraday rotations by azimuthal magnetic field B ϕ in the left and the right sides of the orbit are opposite and, as a result, in the center of line the sum of emissions is less polarized than in the wings. The continuous rotation of the position angle χ from one wing of line to the opposite wing arises for the same reason. The projection of the normal magnetic field B ‖ along the line of sight gives an additional Faraday rotation. It is the same in both sides of the radiating orbit. This additional rotation in one side of orbit increases the total Faraday rotation, and in opposite side decreases the total rotation. For this reason B ‖ magnetic field gives rise to an asymmetric (relative to the central wavelength λ 0 ) profiles for both the polarization degree p line ( λ ) and the position angle χ line ( λ ). The presented theory allows us to estimate the components B ϕ and B ‖ in the broad line emission regions, and also in nearby regions of the continuum radiation.\nIf the polarizations in the left and the right wings are slightly different, then the value B ‖ /lessmuch B ϕ . This helps us to estimate the B ϕ -component from more simple formulas for continuum polarization. Objects in which this is the case are ESO 141-635, IZw1, Mrk 6, Mrk 290, Mrk 985 and NGC 5548. The objects with a strong asymmetry of p line ( λ ) are characterized by magnetic fields B ϕ ∼ B ‖ . Such objects are Akn 120, Akn 564,KUV 18217+6419, Mrk 304, Mrk 335, Mrk 841, MS1849.2-7832 and NGC 4593. Other objects have fairly complex polarization spectra, they appear to be distorted by large-scale turbulent motions.\nUsing the estimated values of the magnetic field in broad line regions (usually B ‖ /lessmuch B ϕ and B ϕ ∼ 10 G) , one can estimate the magnetic field B ms at the last stable orbit near the black hole, and then the field B H at the radius of the event horizon. These estimates are dependent on the different assumptions about the slope of the power-law distribution of the magnetic field inside the accretion disc. We have used the most common assumptions to obtain the values of the magnetic field ∼ 10 4 -10 5 G. These values of the magnetic field are in a good agreement with other estimates. Thus, we determined the magnetic field strengths in various places in the accretion discs of AGNs from the real observational polarization data.\nAcknowledgments\nThis research was supported by the program of Prezidium of RAS No.21, the program of the Department of Physical Sciences of RAS No.16, by the Federal Target Program 'Scientific and scientific-pedagogical personnel of innovative Russia' 2009-2013 and the Grant from President of the Russian Federation 'The Basic Scientific Schools' NSh-1625.2012.2.\nReferences\nAfanasiev V.L., Borisov N.V., Gnedin Yu.N., Natsvlishvili T.M., Piotrovich M.Yu., Buliga S.D., 2011, Astron.Letters, 37, 302\nAgol E., Blaes O., 1996, MNRAS, 282, 965\nAntonucci R.R.J., Miller J.S., 1985, ApJ, 297, 621\nBentz M.C., Peterson B.M., Netzer H., Pogge R. W., Vestergaard M., 2009, ApJ, 697, 160\nBlaes O.M., in: Accretion discs, jets and high energy phenomena in astrophysics, Les Houches Session LXXVIII, eds. V.Beskin et al., Springer, N.Y. 2003, p.147\nBlandford R.D., 1990, in Courvoiseir T.J.-L., Mayor M., eds, Active galactic nuclear. Springer, Berlin, p. 161\nBon E., Popovic L.C., Gavrilova N., La Mura G., Medavilla E., 2009, MNRAS, 400, 924\nBonanno A., Urpin V., 2007, A&A, 473, 701\nBraatz J.A., Gugliucci N.E., 2008, ApJ, 678, 96\nBritzen S., Kam V.A., Witzel A. et al., 2009, A&A, 508, 1205\nChandrasekhar S., 1960, Radiative Transfer, Dover Publ., New York.\nDolginov A.Z., Gnedin Yu.N., Silant'ev N.A., 1995, Propagation and polarization of radiation in cosmic media, Gordon&Breach, New York, p.72\nGarofalo D., 2009, ApJ, 699, 400\nGnedin Y.N., Silant'ev N.A., 1997, Ap&SSR, 10, 1\nGreene J.E., Peng C.Y., Ludwig R.R., 2010, ApJ, 709, 937\nHo L.S., Darling J., Greene J.E., 2008, ApJ, 177, 103\nIvanov V. V., Grachev S. I., Loskutov V. M., 1997, A&A, 321, 968\nKaspi S., Brandt W.N., Maoz D., Netzer H., Schneider D.P., Shemmer O., 2007, ApJ, 659, 997\nKochanek C.S., Dai X., Morgan C., Morgan N., Poindexter S., Chartas G., 2006, preprint (astro-ph/0609112)\nKrolik J.H., Begelman M.C., 1988, ApJ, 329, 702\nKrolik J.H., 2007, preprint (astro-ph/0709.1489)\n
\n\n
\n"},"sections":{"kind":"list like","value":[{"title":"Magnetic fields of active galactic nuclei and quasars with polarized broad H α lines","content":"N.A. Silant'ev 1 , Yu.N. Gnedin 1 , 2 ∗ , S.D. Buliga 1 , M.Yu. Piotrovich 1 and T.M. Natsvlishvili 1 1 Central Astronomical Observatory at Pulkovo of Russian Academy of Sciences, Pulkovskoye chaussee 65, Saint-Petersburg, 196140, Russia 2 St.-Petersburg State Polytechnical University, Polytechnicheskaya 29, Saint-Petersburg, 195251, Russia February 19, 2018","pages":[1]},{"title":"1 Introduction","content":"We present estimates of magnetic field in a number of AGNs from the Spectropolarimetric atlas of Smith, Young & Robinson (2002) from the observed degrees of linear polarization and the positional angles of spectral lines (H α ) (broad line regions of AGNs) and nearby continuum. The observed degree of polarization is lower than the Milne value in a nonmagnetized atmosphere. We hypothesize that the polarized radiation escapes from optically thick magnetized accretion discs and is weakened by the Faraday rotation effect. The Faraday rotation depolarization effect is able to explain both the value of the polarization and the position angle. We estimate the required magnetic field in the broad line region by using simple asymptotic analytical formulas for Milne's problem in magnetized atmosphere, which take into account the last scattering of radiation before escaping from the accretion disc. The polarization of a broad spectral line escaping from disc is described by the same mechanism. The characteristic features of polarization of a broad line is the minimum of the degree of polarization in the center of the line and continuous rotation of the position angle from one wing to another. These effects can be explained by existence of clouds in the left (keplerian velocity is directed to an observer) and the right (keplerian velocity is directed from an observer) parts of the orbit in a rotating keplerian magnetized accretion disc. The base of explanation is existence of azimuthal magnetic field in the orbit. The existence of normal component of magnetic field (usually weak) makes the picture of polarization asymmetric. The existence of clouds in left and right parts of the orbit with different emissions also give the contribution in asymmetry effect. Assuming a power-law dependence of the magnetic field inside the disc, we obtain the estimate of the magnetic field strength at first stable orbit near the central supermassive black hole (SMBH) for a number of AGNs from the mentioned Spectropolarimetric atlas. Keywords : accretion discs, magnetic fields, polarization, active galactic nuclei. Smith et al. (2002) presented optical spectropolarimetric atlas of 36 nuclei of Seyfert 1 Galaxies. The data were obtained with the William Herschel and the Anglo-Australian Telescopes from 1996 to 1999. It is well-known that spectropolarimetry is an important tool in studies of active galactic nuclei (AGN). The spectropolarimetric data provide the detailed view into the inner regions of active galactic nuclei, including an accretion disc and accretion flows around a supermassive black hole (SMBH), thus allowing one to probe the structure and kinematics of the polarizing material around the accreting SMBH. Smith et al. (2002) objects exhibit a variety of characteristics with the average degree of polarization ranging from 0 . 2 to 5 percent. They show many variations both in the degree p line ( λ ) and position angle χ line ( λ ) of polarization across the broad H α emission line. The characteristic feature of p line ( λ ) is the minimum in the line centre, which is usually less than the polarization degree p c ( λ ) in nearby continuum. The second feature is the monotonic increase of positional angle from one line wing to the other. Note also that there exists little difference in the mean polarization degrees and position angles of nearby continuum and H α line for nine of Seyfert galaxies (Mrk 6, Akn 120, Mrk 896, Mrk 926, NGC 4051, NGC 6814, NGC 7603, UGC 3478, ESO 012-G21). For 22 measurements out of 45, the mean positional angles χ line and χ c are practically the same. It should be emphasized that the position angles of polarized continuum and H α line coincide more frequently than their polarization degrees. The mean value of the polarization degree in continuum over all sources is 0.68%, and the same value for H α lines is 0.66%. A position angle is most sensitive to the geometry of emitting region. For that reason, it is most probable that both emitting regions are located near one another, i.e. they located in an accretion disc and their scale sizes are similar: R BLR ≈ R λ , where R λ corresponds to the scale size of an accretion disc for the continuum radiation with given wavelength λ . It is generally accepted that AGNs are powered by the release of gravitational energy from gas accreted onto supermassive black holes (SMBH). The well-known anti-correlation between the radius of the broad-line region (BLR) and the velocity width of broad emission lines for AGNs supports the idea that the BLR gas is virialized and that its velocity is dominated by the gravity of the SMBH (Peterson & Wandel 2000; Onken & Peterson 2002). Most of the recent results lead to the conclusion that BLR presents a flattened rotating system. Many authors (Vestergaard et al. 2000; Nikolajuk et al. 2006; Sulentic et al. 2006; La Mura et al. 2009; Bon et al. 2009; Punsly & Zhang 2010) pointed out that considerable flattening and a predominantly planar orientation are likely to be the intrinsic property of the BLR structure. This conclusion allows us to consider BLR as an outer part of geometrically thin accretion disc that is optically thick with respect to the electron Thomson and the Rayleigh scattering processes. Seyfert galaxies were traditionally divided into two classes according to the presence or absence of broad optical lines. Antonucci & Miller (1985) explained this phenomenon by obscuration by a dusty torus with different orientation with respect to an observer. The orientation-based unification model has become quite popular, but it has also been confronted by more specialized observations (see, for example, Zhang & Wang 2006; Wang & Zhang 2007); in particular, there is evidence for the existence of a special subclass of Seyfert 2 lacking hidden broad-line regions (Zhang & Wang 2006). Thus, the paradigm of unification scheme for all Seyfert galaxies remains a matter of debate (Miller & Goodrich 1990; Tran 2001, 2003). The basic feature of Smith et al. (2002, 2004, 2005) models is that the polarization plane for most of Seyfert galaxies is parallel to the direction of the radio jet. Simultaneously, these models postulate that the radio jet direction is perpendicular to the accretion plane. The latter assumption is questionable. In reality, the radio jets frequently have significant bends near the radio core. The angle of the bend depends on the ratio of radial and toroidal magnetic fields in the accretion disc. Besides, the direction of the jet appears to change with time (see, for example, Britzen et al. 2009; Rastorgueva et al. 2011). Therefore, the coincidence of the direction of the radio jet and the polarization plane does not mean that the electrical vector of the polarized radiation E is perpendicular to the accretion disc. Of course, one can introduce the angle between the radio jet and the electric field E as an additional characteristic of AGNs. But, strictly speaking, this angle is not necessarily related to the real inclination of E with respect to the accretion disc. As a last resort, this angle may be considered in a probabilistic sense. The existence of many cases when the position angle of radiation has intermediate value between parallel or perpendicular to the direction of the radio jet also demonstrates that real direction of E does not correlate with the jet direction. As a result, we conclude that the models describing the polarization behavior in AGNs should not assume that the radio jets are perpendicular to accretion discs; instead, the explicit dependence on the inclination angle i of the accretion disc needs to be taken into account. It is commonly accepted (see, for example, Blaes, 2003) that the accretion discs are magnetized. The existence of radio jets is usually associated with strong magnetic fields in centers of AGNs and quasars. Numerous theoretical models demonstrate the power-law dependence of the magnetic field distribution in an accretion disc. Usually accretion discs are considered as geometrically thin slabs with Thomson optically depth τ /greatermuch 1. The scattering-induced linear polarization can be as high as ∼ 12% for edge-on viewing (Chandrasekhar 1960). However, in the real situation of a magnetized accretion disc, the degree of polarization p will be reduced due to Faraday rotation of the radiation polarization plane while a free photon travels between the consequent scatterings. Recall that the angle of Faraday rotation Ψ at the Thomson optical length τ is equal to where the wavelength of radiation λ is measured in microns and the magnetic field B is measured in Gauss. The angle Θ is the angle between the direction of light propagation n and the direction of B . The decrease of the polarization degree due to Faraday rotation occurs as a result of summation of chaotic angles of rotations in the multiple scattering process. This process has been considered in many papers (for example, Silant'ev 1994; Agol & Blaes 1996; Gnedin & Silant'ev 1997). Clearly, the value Ψ ∼ 1 at the mean free path τ ∼ 1 can decrease considerably the standard Chandrasekhar's polarization degree. Besides, the dependence of Ψ on the wavelength and magnetic field gives rise to characteristic dependencies of the polarization degree p and the position angle χ of radiation on λ , which allows us to estimate the strength and direction of the magnetic field in the scattering region. Below we develop a new model for the formation of polarization in AGNs, which does not use the assumption of the position angle of observed radiation being correlated with the direction of the radio jet. We hypothesize that the observed polarization is due to intrinsic polarization of radiation outgoing from the magnetized optically thick accretion disc (the Milne problem in magnetized atmosphere). In our model, the characteristic features of polarization mentioned above are explained by the topology of the magnetic field in the accretion disc, when the Faraday rotation of the polarization plane is taken into account. Primarily, we suppose that the whole radiating surface of the magnetized accretion disc is observed, i.e. that the inclination angle i is such that the obscuring torus (if it really exists) does not intersect the line of sight. We also consider the case when we observe only a part of total surface of accretion disc, i.e. we take into account the obscuring torus. It appears that our model and the usual pure geometrical model of Smith et al. (2002, 2004, 2005), which takes into account single scattering of BLR-photons in nearby clouds, are two competing explanations for the polarization properties of the accretion discs. All actually observed polarization degrees p c are much smaller than the value in the Milne problem in nonmagnetized atmosphere at the same inclination angle. Recall that the Milne problem deals with the radiative transfer in an optically thick atmosphere, where the sources of thermal radiation are located far from the surface, at depth with τ /greatermuch 1. In optically thick accretion discs the main source of thermal radiation is found at the midplane of the disc, and the outgoing radiation is described by the solution of the Milne problem. The mean value of p c in the atmosphere with pure electron scattering is equal to 3.1%, and the maximum value is 11.7%. The outgoing radiation in case of an absorbing atmosphere has a much greater polarization, because the intensity peaks near the surface. In this case, most of polarization arises analogously to the process of a single scattering of a radiation beam near the surface. For the Milne problem in spectral lines, the value p line is less than in continuum (see, for example, Ivanov et al. 1997). For the accretion disc models, the main challenge is to determine the scale length of the disc - i.e. the radius where the disc temperature matches the rest frame wavelength of the monitoring band. A semi-empirical method for measuring the disc scale length has been developed (Kochanek et al. 2006; Morgan et al. 2006, 2008; Poindexter, Morgan & Kochanek 2008). These authors used microlensing variability, observed for gravitationally lensed quasars, to find the accretion disc scale length for a given observed (or rest-frame) wavelength. Clearly, such a scaling has to be consistent with the most popular accretion disc model of Shakura & Sunyaev (1973). As a result, Poindexter et al. (2008) presented the following relation for the scale length of a standard geometrically thin accretion disc: The wavelength dependence, R λ ∼ λ 4 / 3 rest , corresponds to the typical (for Shakura-Sunyaev disc model) effective temperature: T e = T in ( R/R in ) -3 / 4 , where R in is the inner radius of an accretion disc and T in is the temperature corresponding to that radius. Here L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ) erg s -1 is the Eddington luminosity, M BH is the black hole mass, ε is the rest-mass radiation conversion efficiency, and L bol is the bolometric luminosity. Numerous papers provided measurements of BLR sizes for AGNs (see, for example, Peterson et al. 1994, 2004; Wu et al. 2004; Bentz et al. 2009; Shen & Loeb 2010; Greene et al. 2010). Kaspi et al. (2007) have compiled the observational data for Seyfert galaxies and nearby quasars with black hole masses estimated with the reverberation mapping technique. Most recently Shen & Loeb (2010) have suggested an empirical analytic formula for R BLR that is very useful for various estimates and applications: Here M 8 = M BH / 10 8 M /circledot . We will use this formula in our further calculations. Below we estimate the magnetic field strength in BLR of AGN and QSO from the data from the spectropolarimetric atlas presented by Smith et al. (2002). The λ - dependence of the observed polarization degree and position angle in H α line is very complicated. It appears to be produced by large-scale chaotic motions in the accretion disc.","pages":[1,2,3]},{"title":"2 Basic equations","content":"To estimate the degree of polarization p and the position angle χ of radiation escaping from the magnetized atmosphere we use the standard radiative transfer equations for Stokes parameters I, Q and U (see, for example, Silant'ev 1994; Dolginov, Gnedin & Silant'ev 1995; Silant'ev 2002, 2005). This system of equations has a fairly complicated form. Numerical solutions have so far been obtained only for the case when magnetic field B is parallel to the normal N to an atmosphere (see Silant'ev 1994; Agol and Blaes 1996; Shternin et al. 2003). For our purpose, however, it is sufficient to use a simple asymptotic theory, which can be presented in an analytical form for an arbitrary direction of the magnetic field in the atmosphere (Silant'ev 2002, 2005; Silant'ev et al. 2009). In this approximation, the intensity of the radiation I ( z, µ ) obeys a usual transfer equation with the Rayleigh phase function, and the system of equations for parameters Q and U can be presented in the following form: where B Q ( z, µ ) describes the source function for parameter Q due to the contribution of intensity scattering in nonmagnetized atmosphere (in this case B U ≡ 0), µ = nN is the cosine of the angle between the direction of light propagation n and the normal N to the atmosphere, α is the total extinction factor due to Thomson scattering and pure absorption on dust particles, the value q = σ a / ( σ a + σ s ) (Silant'ev et al., 2009) is the degree of absorption, C describes the additional extinction of polarized radiation due to the fluctuating component B ' of the magnetic field in the atmosphere (see below). Eq.(4) is valid in the limit of large Faraday rotation parameter δ ≥ 1. A solution of Eq.(4) results in the following expression for parameters Q ( n , B ) and U ( n , B ) for the radiation escaping from the magnetized atmosphere: /negationslash At δ ≥ 1, the first non-zero term of integrating by parts of Eq.(5) gives rise to the asymptotic expression which has an analytical form and can be used for an arbitrary direction of the magnetic field. For example, for the case B Q (0 , µ ) = 0 we have: For the Milne problem in absorbing atmosphere, a more sophisticated theory (see Silant'ev 1994, 2002) gives rise to the following expressions: Here p (1) ( µ ) is the polarization degree of outgoing radiation, which takes into account only the last scattering before escaping the atmosphere. The value p (1) ( µ ) gives the main contribution to p ( µ ) - exact polarization degree of outgoing radiation for a non-magnetized atmosphere. For this reason, below we use the value p ( µ ) instead of p (1) ( µ ), which for q = 0 is presented in Chandrasekhar (1960), and for the absorbing atmosphere in Silant'ev (1980). The value s is the root of the characteristic equation, tabulated by Silant'ev (1980). If the degree of the true absorption is small ( q /lessmuch 1), the parameter s = √ 3 q . First, let us consider the case when the whole surface of a radiating accretion disc is observed. In this case, the Stokes polarization parameters of continuum radiation Q c ( ϕ ) and U c ( ϕ ) must be averaged over all azimuthal angles ϕ , characterizing the position of a radiating surface element on a circular orbit in the accretion disc ( -π ≤ ϕ ≤ π ). The normal N and the direction to an observer n are the same for all parts of the accretion disc surface. Therefore, the reference frame of the accretion disc is common to all parameters Q c ( ϕ ) and U c ( ϕ ) of radiation escaping from the disc. In this case, the averaging procedure consists of integrating these parameters over the azimuthal angle ϕ . Note, that cos Θ depends on ϕ and the integral over ϕ can be taken analytically only over the interval ( -π, π ). As a result, the observed values for the degree of polarization and the position angle can be derived analytically. Silant'ev et al. (2009) presented the detailed description of the behavior of these quantities for continuum radiation. The degree of linear polarization of continuum p c and the position angle χ c for an accretion disc can be expressed in the analytical form: Here µ = cos i , where i is the inclination angle (angle between the light propagation direction n and the normal N to the accretion disc). The degree of polarization p c ( µ ) corresponds to a non-magnetized accretion disc. The value of p c ( µ ) for the continuum radiation presents the classical solution of Milne problem (Chandrasekhar 1960) with p (0) = 11 . 7%. The value of the position angle χ c = 0 corresponds to oscillations of the wave electric vector perpendicular to the plane ( nN ). For spectral lines in isotropic medium the value p line ( µ ) depends on the specific quantum numbers of the transitions (see, for example, Chandrasekhar 1960) and on the shape of the line. For a dipole type transition and the Doppler line shape, p line ( µ ) in the atmosphere with pure electron scattering has the same functional form as Chandrasekhar value p c ( µ ), with maximum value of 9.44% instead of 11.71% (see Ivanov et al. 1997). In isotropic medium we have to average an atom over all orientations. For such medium the transfer equation coincides with the usual system for Rayleigh scattering with an additional term, which describes unpolarized radiation. Such average naturally occurs due to usual thermal motions. Considering various quantum numbers for H α line, we see that this additional term is larger than the Rayleigh scattering term (see Chandrasekhar 1960), and the maximum degree of polarization becomes ∼ 3% instead of 9.44%. Therefore, the observed polarization can be explained if the atmosphere also has pure absorption of H α line (the existence of dust). In absorbing atmosphere the polarization degree p line can be larger than that in the non-absorbing atmosphere. Broad H α lines presented in atlas Smith et al. (2002) have very high widths, laying in the interval 50 - 200 angstroms. In such situations the total line (sum of 5 sub levels) can be described by one absorption coefficient with the Doppler shape (see, for example, Varshalovich, Ivanchik & Babkovskaya 2006; Lekht et al. 2008). Our technique takes into account the Faraday rotation during propagation of polarized radiation after the last scattering before escaping from the atmosphere. The region of broad-line emission is too far from the center of an accretion disc and has low magnetic fields. For this reason, one does not need to take into account the known Zeeman effect. The parameter where the negative term ( -sµ ) arises in the Milne problem in absorbing atmosphere (see Chandrasekhar 1960). For small degree of true absorption q = σ absorb / ( σ scattering + σ absorb ) /lessmuch 1 the factor s /similarequal √ 3 q . The regions of the line emission are different from those of continuum radiation. Usually one assumes that the parameter g c /similarequal 1 in most of areas of the accretion disc. To explain polarization of the line emission, we have to consider that this emission escapes from optically thick clouds with its own dimensionless parameters g line . The dimensionless parameters a and b describe the Faraday depolarization of radiation: where B z ≡ B ‖ is the component of the magnetic field directed perpendicular to the accretion disc surface, and B ⊥ = √ B 2 ρ + B 2 ϕ is the magnetic field in the accretion disc plane. The component B ⊥ is perpendicular to B ‖ . Due to axial symmetry, the inclination angle ϕ ∗ ( B ϕ /B ρ = tan ϕ ∗ ) is constant along a circular orbit. The value 0 . 8 λ 2 B is numerically equal to the Faraday rotation angle at the Thomson optical depth of τ = 2, if the polarized radiation propagates along the magnetic field direction. Here and in what follows, we take magnetic field in Gauss and wavelengths in microns. The dimensionless parameter C describes the real situation in a turbulent magnetized plasma and characterizes a new effect - additional extinction of the polarized radiation (parameters Q and U ) due to incoherence of the Faraday rotation in small-scale turbulent eddies (see Silant'ev 2005): where τ is the Thomson optical depth of a turbulent eddy ( τ /lessmuch 1), 〈 ( B ' ) 2 〉 is the mean value of fluctuations of the magnetic field, and f B ≈ 1 is a parameter describing the integrated correlation of the B ' values at two-closely spaced points in the accretion disc. It should be noted that the diffusion of radiation in the inner regions of the accretion disc also produces depolarization due to multiple scatterings. Presence of magnetic field and, therefore, the Faraday rotation effect, only increases the depolarization process. As a result, the polarized radiation emitted by a plane-parallel atmosphere at a specific inclination angle is considerably lower as compared to the classical Chandrasekhar-Sobolev value (see, for example, Gnedin & Silant'ev 1997). But the main feature of Faraday depolarization is the explicit wavelength dependence for both the polarization degree and the position angle. It is interesting to note that at a = b the polarization degree p c ( B , µ ) takes a maximum value (the term ( a 2 -b 2 ) 2 is zero in expression (8)). This effect takes place due to the opposite Faraday rotations from magnetic fields B ‖ and B ⊥ in some places along an orbit. All formulas presented above show that polarimetric observations allow us to derive the magnetic field strength and its topology in the BLR region, where the polarized radiation escapes the accretion disc. Using various models connecting magnetic field B H at the black hole horizon with the magnetic field B ms at the first stable orbit R ms nearest to the centre of the system, and then using the power law dependence of the magnetic field from R ms up to R BLR , we can estimate the magnetic field strength and the parameters that control it, such as the spin of the black hole a ∗ , the conversion efficiency of kinetic into radiative energy ε , and the magnetization parameter k = P magn /P gas ( P magn and P gas are magnetic pressure and gas pressure, in accreting plasma, respectively). Frequently one uses simple formulas for p c and χ c , corresponding to particular cases of pure normal B ‖ and of pure perpendicular B ⊥ : In the latter case χ c ≡ 0 due to the axial symmetry of the problem. Now let us consider the case when the radiating gas along a particular orbit in the accretion disc is partly obscured by some dust cloud (an obscuring torus). Clearly, for pure normal magnetic field B ‖ N , the unobscured part of the orbit has the same polarization degree p c ( B ‖ ) and the position angle χ c ( B ‖ ) as in the case of completely unobscured orbit (see Eq. (13)). If the magnetic field is toroidal B ϕ , i.e. is tangent to the orbit, we can derive the following analytical expressions: Here the parameter b ϕ = 0 . 8 λ 2 B ϕ √ 1 -µ 2 , the angle ϕ 0 describes the unobscured part of the orbit (we see the orbit within azimuthal angles -ϕ 0 ≤ ϕ ≤ ϕ 0 ). At ϕ 0 = π (complete orbit), Eq.(15) coincides with Eq.(14). Eq.(15) for f Q ( ϕ 0 ) is valid for ϕ 0 ≤ π/ 2. For π/ 2 ≤ ϕ 0 ≤ π one can use the relation f Q ( ϕ 0 ) = [ πf Q ( π/ 2) -( π -ϕ 0 ) f Q ( π -ϕ 0 )] /ϕ 0 . A more detailed derivation of these formulas is given below, in subsection 2.2 (for a spectral line case). Dependence of p c ( B ϕ ) /p c ( µ )(1 -sµ ) on ϕ 0 is presented in Fig.1 for values g c = 1, b ϕ = 1 , 2 , 3 , 4 , 5, and s = 0. It is interesting that for ϕ 0 = π/ 2 (half of the full orbit is observed) the polarization degree coincides with the result (14) for the fully unobscured orbit ( f Q ( π/ 2) = f Q ( π ) = 1).","pages":[3,4,5]},{"title":"2.1 The case of a spectral emission line","content":"In the catalog of Smith et al. (2002) the polarimetric data both in the continuum and in the H α emission line are presented. In our model of a rotating accretion disc (with the Keplerian velocity u k ) one part (the right side) of the disc ( ϕ = 0 ÷ π ) corresponds to motion from an observer and the second part (the left side) moves towards the observer ( ϕ = π ÷ 2 π ). According to the Doppler formula, wavelengths of radiation from the first part are greater than the central value λ 0 , and from the second part are smaller than λ 0 . The value λ 0 = (1 + z ) λ rest , where z is redshift parameter of the system and λ rest = 0 . 6563 µ m is the rest frame wavelength of the H α line. Here we restrict ourselves to a specific case of a spectral line with the Doppler shape. The line is described by following normalized shape function: As in the previous case of continuum radiation, we assume that the X-axis is perpendicular to plane ( nN ). The Keplerian velocity u k corresponds to the radius R BLR : u k = √ GM BH /R BLR , where G is gravitation constant. The usual Doppler line width ∆ λ T = ( u turb /c ) λ 0 is mainly due to chaotic turbulent velocities. The displacement of the line centre for radiation emitted from the part of the disc with the azimuthal angle ϕ is ( u k /c ) λ 0 √ 1 -µ 2 sin ϕ . Thus, the normalized shape function of radiation emitted from ϕ -part of the orbit has the form: Observed radiation flux F λ from a surface element dS of the ring with the radius R BLR is proportional to dϕ . The flux from the total radiating circular orbit can be obtained by integration over all azimuthal angles ϕ . If we suppose that all sources are distributed uniformly along the orbit, this flux is described by the following expression: Observed fluxes of linearly polarized radiation differ from the continuum radiation case by an additional factor φ ( λ, ϕ ): Here Θ is the angle between the magnetic field B and the light propagation direction n , I ( µ ) is total intensity of the spectral line escaping from the surface dS . The azimuthal angle ϕ = 0 corresponds to a surface element dS perpendicular to the plane ( nN ). Faraday depolarization term δ cos Θ has the form: where the parameters b ρ and b ϕ are: Here angle ϕ ∗ is the angle between B ⊥ and the radius-vector ρ , lying in the disc plane. The sign minus before b ϕ sin ϕ corresponds to the right-hand screw rotation of the accretion disc with the frozen magnetic field B ϕ directed along the rotation velocity. If the rotation of the disc is opposite, we have to change b ϕ to b ϕ . If we take the factor φ ( λ, ϕ ) = 1 and g line → g c , all the formulas will describe the case of the continuum radiation. In this case the integrals over ϕ can be evaluated analytically (for the combination -F Q + iF U the ϕ -integral can be evaluated by the complex residue method, and we obtain Eqs.(8) and (9)). Note, that these formulas are approximate, they take into account only the last scattering before the escape from the atmosphere. This is a rather satisfactory approximation (see Silant'ev 2002). It describes the main contribution to the polarization. The main merit of these analytical formulas is that they describe the polarization for any direction of the magnetic field. For our purpose this approach is sufficient. We note that ϕ -integration in Eqs.(18) - (20) gives rise to rather low polarization effects. For this reason they hardly can be used for describing the polarization data presented in the atlas (Smith et al. 2002). Below we present two models that are more acceptable for explaining the data.","pages":[5,6]},{"title":"2.2 The model of H α line polarization with parameters p and χ , averaged over the right and left parts of an orbit","content":"It is clear from Eqs.(18), (19) and (20) that the right parts of circular orbits mostly contribute to gaussian shape lines at wavelengths λ > λ 0 , and the left parts mostly contribute to λ < λ 0 . Qualitatively, we can consider that these contributions are equivalent to sum of two gaussian shaped polarized lines. We assume that the effective polarizations and position angles of these lines correspond to mean values from the right side ( p right , χ right ) and the left side ( p left , χ left ) of the orbit. These values follow from Eqs.(19) and (20) if we take there the factor φ ( λ, ϕ ) = 1. Unlike the situation described by Eqs.(19) and (20), in this model we assume that a part of the accretion disc is invisible due to obscuring torus. The right part corresponds to integration over ϕ = 0 ÷ ϕ 0 , and the left part corresponds to integration in the interval ϕ = 0 ÷ -ϕ 0 . Here the angle ϕ 0 characterizes the boundary azimuthal angle for the visible part of the BLR orbit. The mean values 〈 Q 〉 and 〈 U 〉 for visible right part are described by the integrals: where δ cos Θ is given in Eqs. (21) and (22). The corresponding mean values for the left part of the BLR orbit are given by integrals in the interval (0 , -ϕ 0 ). /negationslash These integrals cannot be evaluated analytically in a general case. We present below the cases ( a = 0 , b ρ = 0 , b ϕ = 0) and ( a = 0 , b ρ = 0 , b ϕ = 0). The first case corresponds to the magnetic field B ‖ parallel to normal N . Clearly, in this case the polarization degree and the position angle are the same in the right and left parts of the orbit, and can be obtained from Eqs.(8) and (9) (see Eq.(13)). /negationslash The second case corresponds to a toroidal magnetic field B ⊥ , laying in the plane of the accretion disc and tangential to the radiating circular orbit. In this case the Faraday rotations are opposite in the right and the left parts of the orbit. This gives the same value for the polarization degree p right = p left and the opposite values for the position angles χ right = -χ left . We present below the results for the right part of the orbit: f U ( ϕ 0 ) = It is interesting to note that f Q ( ϕ 0 ) monotonically grows from f Q ( π/ 2) = 1 to f Q = √ g 2 line + b 2 ϕ /g line ≥ 1 as ϕ 0 → 0. ∣ ∣ The expression for f Q is valid only for ϕ 0 ≤ π/ 2, and the formula for f U is valid for total interval 0 ≤ ϕ 0 ≤ π . The integrands in Eqs. (23) are symmetric relative to the angle ϕ 0 = π/ 2. This gives equalities f Q ( π/ 2) = f Q ( π ) = 1 and f U ( π/ 2) = f U ( π ). Due to the aforementioned symmetry, we can calculate values f Q and f U for π/ 2 ≤ ϕ 0 ≤ π from the values for interval 0 ≤ ϕ 0 ≤ π/ 2: f Q,U ( ϕ 0 ) = [ f Q,U ( π ) π -f Q,U ( π -ϕ 0 )( π -ϕ 0 )] /ϕ 0 . The mean polarization degree p right ( B ϕ ) and the position angle χ right ( B ϕ ) can be derived from the following expressions: In Fig.2 we present the values p right ( B ϕ ) /p ( µ )(1 -sµ ) and | χ right | at b ϕ = 1 , 2 , 3 , 4 , 5 and g line = 1 , s = 0. Comparison of p right ( B ϕ ) with p c ( B ϕ ) in Fig.1 shows that p right > p c . This is evident, because p c corresponds to the sum of radiation from the right and the left parts of the observed areas (in this sum U = 0), and p right corresponds to the half of this area, where parameter U = 0. It means that in the wings of /negationslash the emitting lines the polarization is greater than in nearby continuum. Let us consider the behavior of the polarization degree p line ( B ϕ , λ ) and the position angle χ line ( B ϕ , λ ) inside the broad spectral line in more detail, using our simple model of two equal gaussian lines with the equal right and left displacements from the central wavelength λ 0 . We label the intensities of these lines as I right and I left . According to Eqs.(24) and (25), we present the total observed Stokes parameters I, Q and U in the form: Recall that due to the displacement of the centers of the right and left lines with the gaussian shape the intensities I right ( λ ) and I left ( λ ) are different at a particular considered wavelength inside the full line. Only at the central wavelength λ 0 these intensities are equal due to the axial symmetry of our model. Using Eqs.(27), (28) and (29), we obtain the following expressions for the total observed polarization degree p ( B ϕ , λ ) and the position angle χ ( B ϕ , λ ): Taking in Eqs.(30) and (31) I left = 0, we revert to Eq.(26) for the right part of the orbit. The total rotation of the position angle inside the line width is equal to the difference of ∆ χ ≡ χ right -χ left , where χ right corresponds to the right-hand wing of line with I right /greatermuch I left . The χ left corresponds to the left-hand wing with I left /greatermuch I right . As a result, we have: Now let us discuss shortly the polarization degree p inside the broad line. First of all, we notice that in the centre of the line λ = λ 0 the polarization is less than in the wings (c.f. Eq.(30) with I right = I left ). The polarization grows with the departure from λ 0 . This behavior of p line ( λ ) is observed in many objects from the catalog of Smith et al.(2002). According to Eq.(30), the ratio of p wing ( B ϕ , λ ) to p center ( B ϕ , λ ) becomes ∣ ∣ Note that the difference ∆ χ does not depend on the choice of the observer's reference frame. A non-zero value of ∆ χ is observed in many objects presented in the catalog of Smith et al. (2002) and is due to two reasons - the presence of the magnetic field B ϕ and the Keplerian rotation of the magnetized accretion disc. Fig.2 shows that ∆ χ depends on the parameter b ϕ and the angle ϕ 0 . Thus, for b ϕ = 5 and ϕ 0 /similarequal (140 · -160 · ) the value | ∆ χ | /similarequal 60 · . For ∆ χ = 60 · this ratio is equal to 2. Clearly, it is not possible to explain all details of p and χ in the our model of the sum of two spectral lines. But, above considerations tell us that the main characteristic features can be explained.","pages":[6,7,8]},{"title":"2.3 The model of H α line as two emitting compact clouds located in the right and left part of the orbit","content":"The spectra of H α lines in the atlas of Smith et al.(2002) for many objects have sufficiently complicated structure - the existence of separate peaks and asymmetric shapes. There are only a few objects with symmetric shapes. They have comparatively small widths as compared to other, more complicated spectra. A line with a complicated shape frequently can be approximated as a sum of two or more lines with gaussian shapes. For this reason we present the model of two compact optically thick clouds located in the opposite parts of an orbit in the accretion disc (Fig.3). The advantage of this model compared with the previous one is that we can take into account all the depolarizing Faraday parameters a, b ϕ and b ρ in a simple analytical form. Let us take the first cloud in the right part of the orbit, characterized by the azimuthal angle ϕ , and the second cloud in the left part, characterized by ϕ . If it is necessary, locations of the emitting clouds can be chosen at arbitrary angles along the orbit. Our choice is the simplest for consideration. As usually, we write the Stokes parameters in the coordinate system with X-axis being perpendicular to the plane ( nN ), where the formulas have the simplest form. Further we will use the observed polarization degree p and the total difference of the position angles between right and left parts of the spectral line ∆ χ , which do not depend on the choice of the reference frame. We also include in our formulas the contribution of the continuum radiation ( I c , Q c , U c ) in the region of spectral line. Then, the observed Stokes parameters are: The explicit formulas for Q c and U c are as follows: Here r 2 = ( g 2 c + b 2 -a 2 ) 2 +4 a 2 g 2 c = g 4 c +2 g 2 c ( a 2 + b 2 )+( a 2 -b 2 ) 2 . Introducing the notation η c = p c ( µ )(1 -sµ ) /p c ( B , µ ), and using expressions (8) and (9), we can present formulas for Q c and U c in a simpler form: The last expressions are valid in the limit (2 ag c ) /η 2 c → 0. In most sources from the catalog of Smith et al. (2002), the intensity I c is much smaller than I right + I left . For these cases one can neglect the contribution of the continuum radiation and the formulas for p line and χ line acquire fairly simple form: In the right wing, where ξ /similarequal 0, we have For the left wing one finds the same expression with ( -b ϕ ) instead of b ϕ . Using formula (42), we can obtain expression for the difference of the position angles between the right and left wings of the line: For the polarization degree in the right wing we derive the formula: For the left wing the polarization degree is higher because the Faraday depolarization parameter | a -b ϕ | is lower than in the right wing. If a = 0, the polarization degree p right = p left and χ right = -χ left . Presence of the magnetic field B ‖ (parameter a = 0) diminishes the polarization degree both in the right and left wings of the line, and also diminishes the difference | ∆ χ | = | χ right -χ left | . Besides, the functions p line ( λ ) and χ line ( λ ) become asymmetric relative to the center of the line λ 0 (if the intensities of lines I right ( λ ) and I left ( λ ) are the same gaussian functions). Analogously, for the left wing one replaces b ϕ with ( -b ϕ ). /negationslash It is interesting to compare the polarization degrees in the wings and in the center of line. The general formula for ratio p wing /p center is very complex and we consider only the case a = 0, where this ratio reaches a maximum value. Taking ξ = 1 for the center of the line and ξ = 0 for the line wing, we obtain the following expression from the general formula (41): For b ϕ = 5 and g line = 1 this ratio is equal to 5.1, i.e. is considerably greater than the value from formula (33). It is quite natural, because formula (33) describes the mean value of the effect. Clearly, the averaging procedure diminishes the effect. Physically this effect arises as a consequence of the Faraday rotation of the polarization plane. In the center of the line the rotations from the right and the left lines have opposite directions and the parameter Q center reaches a lower value than that in the line wing. The most important conclusion from the theoretical consideration of the structure of broad lines in AGN is the treatment of the symmetry of the polarization degree p line ( λ ) as the result of the azimuthal magnetic field B ϕ . If the symmetry of p ( λ ) is considerably broken, one can consider that B ϕ ∼ B ‖ , or the intensities of the right and the left emitting clouds are different.","pages":[8,9]},{"title":"3 The magnetic field strength in a broad line region of AGN","content":"The standard Unified Sheme for AGN includes a central source of continuum (accreting SMBH); a region close to the outer radius of the accretion disc emitting broad emission lines (broad line region - BLR); a dusty rotating 'torus' on parsec scales; and gas emitting narrow emission lines on a scale of tens to hundreds of parsecs, ionized through the open cone defined by the torus edge (Antonucci & Miller 1985; Krolik & Begelman 1988; Urry & Padovani 1995). The main unknown is the mechanism for the generation of the magnetic field during the process of accretion onto SMBH. Li (2002), Wang et al. (2002, 2003), Zhang et al. (2005) have studied the magnetic coupling process (MC) as an affective mechanism for transforming the kinetic energy of accreting gas into the magnetic energy. It is assumed that the disc is stable, perfectly conducting and Keplerian. The magnetic field on the black hole horizon is poloidal and varying as a power law with the distance from the central region. Since the magnetic field on the horizon B H is brought and held by its surrounding magnetized matter of the accretion disc, there must exist the relation between the magnetic field strength near the BH horizon and the accretion rate ˙ M . As a result, the magnetic field strength on the event horizon R H = R G (1+ √ 1 -a 2 ∗ ) is determined by the relation between the magnetic energy and the accretion kinetic energy densities (see Li 2002; Wang et al. 2002): Here R G = GM BH /c 2 , the bolometric luminosity L bol = ε ˙ Mc 2 , ˙ M is the accretion rate, c is the light velocity and ε is the radiative efficiency calculated by numerical simulations of Novikov & Thorne 1973, Krolik 2007, Shapiro 2007. The coefficient k presents the inverse plasma parameter k = P magn /P gas = 1 /β , where P gas and P magn are the gas and the magnetic pressures, respectively. For the equipartition case β = 1 and k = 1. Eq.(46) is easily transformed into: The basic problem is the relation between the magnetic fields strengths at the first stable circular orbit R ms and the event horizon R H . The value of the radius R ms depends on the radius R G and the spin a ∗ , and can be presented in a form: where l E = L bol /L Edd and the Eddington luminosity L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ). where parameter q > 1. For example, for a Schwarzschild black hole q = 6 and for the Kerr BH with the spin a ∗ = 0 . 998 q = 1 . 22 (Murphy et al. 2009). Reynolds, Garofalo & Begelman (2006) argued that the plunging inflow can greatly enhance the trapping of large scale magnetic field on the black hole. Blandford (1990) has shown that the interaction of the large-scale magnetic field with the event horizon of rotating black hole can enhance the trapping of large-scale poloidal magnetic field on the horizon of the black hole, compared with the inner accretion flow and compared to the magnetic field strength derived from the relation between magnetic energy and accretion kinetic energy (Eq.(47)). Recently Garofalo (2009) has showed that the dynamics of the plunge region of a thin black hole accretion disc and magnetic flux trapping can enhance the strength of the magnetic field threading the horizon by a significant factor. The results of his calculations were presented in fig.7 of Garofalo paper. It means that we obtain the following relation between the magnetic field strength at the first stable orbit B ms and the magnetic field strength at the event horizon of a black hole B H : The coefficient η can be obtained from fig.7 of the paper by Garofalo (2009). From this figure it follows that for a ∗ = 0 . 5 the value is η = 5 and for a ∗ = 0 . 0 and a ∗ = 0 . 998 we have η = 7 . 5. Numerical simulations have been used to study magnetic field generation in astrophysical objects. For example, the existence of large-scale dynamos in magneto-convection under the influence of shear and rotation has been studied by Kapyla, Korpi & Brandenburg (2008). These authors have shown that the saturation field strength reaches, practically, the equipartition level B ≈ 0 . 7 B eq , i.e. k ≈ 0 . 5. Taking into account the shear flows can increase the magnetic field level. It means that the magnetization parameter can be equal to k ≈ 1. We suggest that the magnetic field far inside in the accretion disc, and, especially, in the Broad Line Region (BLR) takes the toroidal form. Namely, the differential rotation in the accretion disc leads to an increase of the azimuthal field by winding up the poloidal field lines into the toroidal field lines (Bonanno & Urpin 2007). In astrophysical objects differential rotation is often associated with magnetic fields of various strength and geometry. If the poloidal field has a component parallel to the gradient of the angular velocity, then differential rotation can stretch toroidal field lines from the poloidal ones. In the presence of the magnetic field, differential rotation can be a reason for various MHD instabilities, especially if the field geometry is complex. Mayer & Pringle (2006) assumed that a dynamo process generates a local poloidal field B z in the accretion disc, and the magnitude of the poloidal component is small: B z /lessmuch B ⊥ . Usually one assumes that regular dependence of the magnetic field on the radius R in the accretion disc exists from the first stable orbit R ms , and that dependence has a power law form: We assume two values for the parameter n . The value n = 1 derives the toroidal topology of the magnetic field (see Bonanno & Urpin 2007). The value n = 5 / 4 corresponds to the accretion process with hot accretion flows (Medvedev 2000). For pure toroidal topology of the magnetic field in the accretion disc we have the depolarization parameter a = 0, and in this case Eqs.(8) and (9) for non-turbulent case ( C = 0) are transformed into Eq.(14). Recall that, according to definitions (11), magnetic field B ( R BLR ) can be determined, if the parameter b is known from the observed polarization: This field can be related to B ms . In the case of a power-law dependence (50) with n = 1, this relation becomes We used here Eq.(3) for determining R BLR . Note that M 9 = M BH / 10 9 M /circledot . In this situation the depolarization parameter b for H α wavelength ( λ = 0 . 6563 µ m) is: For hot accretion flows n = 5 / 4 and the depolarization parameter b becomes where q ( a ∗ ) = R ms /R G and R G = GM BH /c 2 . The explicit form of q ( a ∗ ) is given, for example, in Zhang et al. (2005). Below we shall also consider the case of the equipartition between the gas and the magnetic pressures, i.e. k ≈ 1. Namely, the magnetic coupling process corresponds to this case (Li 2002; Wang et al. 2003; Zhang et al. 2005; Ma, Wang & Zuo 2006). Using Eqs.(47) and (49), we transform relations (53) and (54) into the following forms: and for n = 5 / 4: Eqs.(55) and (56) allow us to estimate the radiation efficiency and therefore the rotation rate a ∗ of an accreting black holes. Below we use the spectropolarimetric atlas of AGNs by Smith et al. (2002) for specific estimates.","pages":[10,11]},{"title":"4 Magnetic field strength of Akn 120","content":"According to Smith et al. (2002) the mean polarization degree in the continuum of Akn 120 is equal to p c /similarequal 0 . 35%, and is equal to /similarequal 0 . 4% in the H α line emission. We use here the data obtained by Smith et al. (2002) in 1998 October. The mean observed position angle have the same value for the continuum and line emission χ /similarequal 76 · . The inclination angle i = 48 · , µ /similarequal 0 . 67. Its value has been derived by Braatz & Gugliucci (2008) from water maser observations. The central black hole mass in Akn 120 is equal to M BH /similarequal 10 7 . 74 M /circledot (see Peterson et al. 2004). For the inclination angle i = 48 · the polarization in the continuum from the accretion disc without magnetic field is expected at the level p c ( µ ) = 1 . 26% (Chandrasekhar 1960). This value is higher than the observed polarization degree and it means that the Faraday depolarization effect is really acting. The H α line spectrum shows the two-peak structure and can be represented as sum of two intensities with gaussian shapes. The difference of the positional angles ∆ χ is estimated to be between 70 · and 80 · . The intensity of the continuum radiation reaches ≈ 18% of the maximum line intensity near the centre. The behaviour of polarization in the continuum is very complex. It seems this behaviour occurs due to the existence of large-scale turbulent curls along the observed orbit. For that reason, it is more convenient to use the continuum - subtracted spectrum of Akn 120, presented in fig.24 of the mentioned Atlas by Smith et al. (2002). We used formulas (31)-(37) to find the estimates for the parameters a, b ϕ , p line ( µ ) and g line . Attempts to estimate these parameters under the assumption p c ( µ ) /similarequal p line ( µ ) were unsuccessful. We propose that in the line radiating clouds there is true absorption of radiation (the existence of dust particles). As it is known (see, for example, Silant'ev 1980), the existence of absorption gives rise to a considerable increase of polarization escaping from the optically thick atmosphere. This effect is the consequence of absorption creating a peak like form of escaping emission. Introducing first three parameters in Eq.(8), we obtain g line /similarequal 0 . 975. The estimate g line = 0 . 975 = 1 + C -sµ gives the relation between C and s . It means that the clouds are absorbing and the small scales are turbulent. The existence of large scale turbulence in clouds directly follows from very high line width. For the rest of radiation from the accretion disc outside the compact clouds we assume that absorption is absent and small scale turbulence is negligible ( C ≈ 0). From Eq.(57) it follows that p line /similarequal 3 . 97% and b ϕ /similarequal 3 . 46. The estimated value p line /similarequal 3 . 97% corresponds to the case when one takes into account the pure absorption of radiation by dust particles existing into emitting clouds. From Eq.(11) one can obtain an estimate of magnetic fields B ‖ /similarequal 0 G and B ϕ /similarequal 14 G. In Fig.4 we present the observed intensity, polarization degree and variation of the azimuthal angle χ , and our model results. It is seen that the model curves practi- /s32 cally coincide with the observed values. The observed intensity is approximated as sum of two gaussian intensities from symmetrically located clouds. The Doppler widths of these intensities are taken equal to ∆ λ T =70 ˚ A, the value ( u k /u turb ) sin ϕ √ 1 -µ 2 = 0 . 3, the ratio of maximum intensities of gaussians is I left /I right = 20 / 18. The centers of gaussian curves coincide with the observed places in Fig.24 of Smith et al. (2002). The main problem is that the exact value of index n is unknown and its value depends strongly on the model of the accretion disc. Pariev, Blackman & Boldyrev (2003) suggest the following interval of values of this index 1 ≤ n ≤ 2. The value n = 1 corresponds to toroidal magnetic field (see Bonanno & Urpin 2007). To estimate the magnetic field strength at the last inner circular orbit B ms we need to know the rotation rate of the central supermassive black hole (parameter a ∗ ). For a Schwarzschild black hole with a ∗ = 0 and q = 6 and for the toroidal magnetic field ( n = 1) we obtain from Eq.(49) B ms = 14 . 5 · 10 3 G . Now we can estimate the magnetic field strength B H at the horizon of the central black hole using the results of calculations by Garofalo (2009). He has calculated the ratio of the horizon-threading magnetic field and the magnetic field in the accretion disc as a function of the black hole spin. According to this calculations, for a ∗ = 0 the ratio B H /B ms = 7 . 5 and B H = 10 . 7 · 10 4 G . Our results demonstrate that for a given value of the polarization degree the magnetic field strength at the inner radius r ms (and therefore on the horizon radius) is stronger for a Kerr black hole compared to Schwarzschild one. This result means also that for black holes with the same magnetic field strengths the degree of polarization for Kerr black holes is larger than for Schwarzschild black holes (see Silant'ev et al. 2011).","pages":[11,12]},{"title":"5 Magnetic field strength of Mrk 6","content":"According to Ho, Darling & Greene (2008), the mass of the central black hole in Mrk 6 is log( M BH /M /circledot ) = 7 . 97 ± 0 . 5, the ratio of the bolometric luminosity to the Eddington value is log( L bol /L E dd ) = -1 . 72. The inclination angle is i = 62 · . 7 , µ = 0 . 46 (Ho et al. 2008). It means that the standard (Sobolev-Chandrasekhar) magnitude of the polarization degree is p c ( µ ) = 2 . 52%. The observed mean polarization has been found at the level of p c = 0 . 90 ± 0 . 03, p ( H α ) = 0 . 85 ± 0 . 04 (Smith et al. 2002). The most remarkable fact is the jump of the mean position angle for two observational seasons of Feb 97 and Oct 98: ∆ χ ≈ 25 · . It is interesting that the value of the mean polarization remained the same. This jump occurred over 1-2 years, which is too short a time for such a large object as the accretion disc near the supermassive black hole. Thus, this problem remains unsolved. Let us return now to the analysis of the data in the H α line. First of all, we see that the polarization degrees in the right and the left sides of the spectrum are practically equal - the left side has p line /similarequal 1 . 5%, and in the right side p line /similarequal 1 . 4%. From the theoretical considerations in section 2, it is clear that such a symmetrical form of the polarization degree can occur if the magnetic field B ‖ is much less than the azimuthal magnetic field B ϕ . A small decrease of polarization in the right-hand part is due to the reason that small value of the B ‖ component, directed to an observer, coincides with direction of B ϕ . In this situation the polarization of radiation slightly decreases compared to the left-hand part of the orbit, where the aforementioned magnetic fields are directed opposite to each other. Considering polarization near the line center, we assume p line ( centre ) /similarequal 0 . 5%. We also assume that in the center of the line the intensity from the left part of the orbit is approximately equal to that from the right part. The value of the intensity of the continuum radiation in Mrk 6 is relatively small, and we neglect it in our computation. Using formulas (34)-(36), one obtain: Substitution of these parameters in Eq.(8) gives g line /similarequal 1 . 0006, i.e. practically 1. As in the case of Akn 120, the polarization p line /similarequal 3 . 9% implies that in H α -clouds there exists the absorption of radiation. Under the assumption of dipole radiation we have q c /similarequal 0 . 01 and the parameter s /similarequal 0 . 17. Because g line = 1 . 0006 /similarequal 1 = 1+ C -0 . 17 · 0 . 46 we find that the small scale turbulent parameter C /similarequal 0 . 08. For the difference ∆ χ of the position angles between the left and the right wings of the spectral line the expression (43) gives ∆ χ = 42 · . This value is consistent with the observational results. Eqs.(11) and (58) give estimate: B ‖ /similarequal 0 . 6G and B ϕ /similarequal 8 . 5G. Note that expression (58) supposes that I c p c /lessmuch I right,left p line ( µ ). Now let us estimate the magnetic field strength in the accretion disc of Mrk 6 using the results of the polarimetric obser- For the spin value of a ∗ = 0 . 5, ε = 0 . 081, q = 4 . 25 (Novikov & Thorne 1973) we obtain B ms = 6 . 8 · 10 3 G and B H = 3 . 4 · 10 4 G . At last, for a ∗ = 0 . 998, q = 1 . 22, ε = 0 . 32 we have B ms = 2 . 8 · 10 4 G and B H = 14 · 10 4 G . /s32 /s32 /s32 vations from Smith et al. (2002). Eqs. (53)-(56) allow us to derive the magnetic field strength B ms at the inner radius of the accretion disc: B ms = (1 . 72 × 10 4 /q ) G . For a Swarzschild black hole, when q = 6, the magnetic field B ms = 2 . 9 · 10 3 G . For a Kerr black hole with a ∗ = 0 . 998 the parameter q = 1 . 22 and the magnetic field strength B ms = 1 . 4 · 10 4 G . According to Garofalo (2009, fig.7) the magnetic field strength at the horizon of the supermassive black hole is B H = 1 . 4 · 10 4 G for a ∗ = 0 and B H = 10 5 G for a ∗ = 0 . 998.","pages":[12,13]},{"title":"6 Magnetic fields of Mrk 985 and IZw1","content":"The intensity spectrum of Mrk 985 has a two-peak shape and the spectrum of the polarization degree p line ( λ ) is quite symmetric (the p line ( left ) /similarequal 1 . 27% and p line ( right ) /similarequal 1 . 16%). In the centre of line p line ( centre ) /similarequal 0 . 5%. The mean polarization of the continuum radiation is 1.12%. Using formulas (33)-(37), we find that We see that a nearly symmetric form of p line ( λ ) implies that a /lessmuch b ϕ , i.e. B ‖ /lessmuch B ϕ . From Fig.15 in the atlas of Smith et al. (2002) we see that the difference of position angles between the right wing and the centre of line is equal ∆ χ /similarequal 31 -33 · . From general theory one finds that tan2∆ χ = a/g line + b ϕ /g line . Our estimates (59) give this value for the angle difference. The estimates of magnetic fields at distances R ms and R H can be obtained analogously as in the previous sections. In the atlas of Smith et al. (2002) there is no information on the inclination angle i . It is interesting to estimate this angle assuming that g line /similarequal 1. Substituting parameters g c = 1 , a = 0 . 114 and b ϕ = 2 . 035 into formula (8) gives the value p c ( µ ) = 2 . 54%. This implies an estimate i /similarequal 64 · , µ /similarequal 0 . 44. Using the value p c ( µ ) = 2 . 54% we can calculate the value g line , corresponding to this polarization. This calculation demonstrates that the parameter g line acquires the value g line /similarequal 1 . 0013. The value p line ( µ ) = 2 . 75 at µ = 0 . 44 takes place at q a /similarequal 0 . 01 ( s = 0 . 17). The value g line /similarequal 1 . 0013 = 1 + C -0 . 17 · 0 . 44 occurs at C /similarequal 0 . 08. Using Eq.(11) and the value µ /similarequal 0 . 44, we find the estimates: B ‖ /similarequal 0 . 75 G and B ϕ /similarequal 6 . 6 G. Now let consider the AGN IZw1. This object has p c /similarequal 0 . 67%, p line ( left ) /similarequal 0 . 7%, p line ( centre ) /similarequal 0 . 2% and p line ( right ) /similarequal 0 . 9%. The form of the polarization spectrum is slightly more asymmetric than in Mrk 985. Using general formulas (33)-(35) we find the following estimates: As in the case of Mrk 985, we found, that g line /similarequal 1 and p c ( µ ) /similarequal 2 . 68%. This corresponds to µ /similarequal 0 . 44. The value p line /similarequal 3 . 9% occurs at the absorption degree q a /similarequal 0 . 01 , s /similarequal 0 . 17. As a result, the small scale turbulence parameter C /similarequal 0 . 08. As in the previous cases, using Eq.(11) and the value µ = 0 . 44 we can estimate the magnetic field strength for IZw 1: B ‖ = 3 . 42G and B ⊥ = 12 . 7G. It should be noted that in these cases we estimated the inclination angle i from the analysis of the polarization data. The obtained estimates of the magnetic field strengths in BLR of these AGNs are presented in Table 1. The last value in the table is close to the one estimated by Afanasiev et al.(2011) where the polarimetric observations were made only for the continuum emission and did not include the emission from the broad line region.","pages":[13]},{"title":"7 Conclusions","content":"For many objects of Smith et al. (2002) spectropolarimetric atlas the polarization spectra of a broad H α -line p line ( λ ) have a characteristic minimum at the center of the line and different maxima at the left and right wings. Usually the wing polarizations are higher than those in the nearby continuum. For many objects the position angle changes continuously from the left wing to the right one. We develop a new theoretical explanation for these features, different from the original explanation of Smith et al. (2002, 2004, 2005), taking into account that accretion discs can be magnetized. Smith et al. explain the characteristic features of the H α -line assuming that the observed polarization is due to single scattering of non-polarized radiation from the BLR on two types of scattering clouds - a polar cloud around the radio jet, and clouds in the equatorial region. It appears (see Smith et al. 2005) that their mechanism has two characteristic features: a relatively low amplitude ( | ∆ χ | ≤ 20 -40 · ) of the position angle rotation from one line wing to the other one, and the need for a very high electron temperature ( T ∼ 10 6 K) in a nearby scattering cloud. In their atlas there are cases with both low ∆ χ < 20 · and high ∆ χ ∼ 80 · position angle rotations. The need for the high electron temperature arises from the observed polarization minimum in the line core. Besides, they neglect the intrinsic linear polarization of the radiation in BLR. In our mechanism both effects can be explain by a single cause - the Faraday rotation of the polarization plane. The wide line width results from turbulence, which is related to the Keplerian rotation in the orbit. Clearly both explanations take place in reality. The basis of our explanation is the assumption that both the continuum radiation and the spectral line emission originate in an optically thick magnetized accretion disc around the center of an AGN. The observed characteristic shape of the line polarization appears as a result of the Faraday rotation of the polarization plane in the accretion disc having a normal magnetic field B ‖ and an azimuthal field B ϕ . We propose that the regions of the line emission can be represented as a comparatively dense absorbing turbulent clouds rotating with the Keplerian velocity around the center of the AGN. These clouds are flattened, optically thick and magnetized. They emit the polarized radiation in accordance with the Milne problem law. The observed emission line is a sum of radiation from clouds rotating in the right and the left sides of the orbit. Due to Doppler displacements, emission from the one side is, as a whole, reddened ( λ ≥ λ 0 ), and emission from the other side has the opposite λ -displacement. The Faraday rotations by azimuthal magnetic field B ϕ in the left and the right sides of the orbit are opposite and, as a result, in the center of line the sum of emissions is less polarized than in the wings. The continuous rotation of the position angle χ from one wing of line to the opposite wing arises for the same reason. The projection of the normal magnetic field B ‖ along the line of sight gives an additional Faraday rotation. It is the same in both sides of the radiating orbit. This additional rotation in one side of orbit increases the total Faraday rotation, and in opposite side decreases the total rotation. For this reason B ‖ magnetic field gives rise to an asymmetric (relative to the central wavelength λ 0 ) profiles for both the polarization degree p line ( λ ) and the position angle χ line ( λ ). The presented theory allows us to estimate the components B ϕ and B ‖ in the broad line emission regions, and also in nearby regions of the continuum radiation. If the polarizations in the left and the right wings are slightly different, then the value B ‖ /lessmuch B ϕ . This helps us to estimate the B ϕ -component from more simple formulas for continuum polarization. Objects in which this is the case are ESO 141-635, IZw1, Mrk 6, Mrk 290, Mrk 985 and NGC 5548. The objects with a strong asymmetry of p line ( λ ) are characterized by magnetic fields B ϕ ∼ B ‖ . Such objects are Akn 120, Akn 564,KUV 18217+6419, Mrk 304, Mrk 335, Mrk 841, MS1849.2-7832 and NGC 4593. Other objects have fairly complex polarization spectra, they appear to be distorted by large-scale turbulent motions. Using the estimated values of the magnetic field in broad line regions (usually B ‖ /lessmuch B ϕ and B ϕ ∼ 10 G) , one can estimate the magnetic field B ms at the last stable orbit near the black hole, and then the field B H at the radius of the event horizon. These estimates are dependent on the different assumptions about the slope of the power-law distribution of the magnetic field inside the accretion disc. We have used the most common assumptions to obtain the values of the magnetic field ∼ 10 4 -10 5 G. These values of the magnetic field are in a good agreement with other estimates. Thus, we determined the magnetic field strengths in various places in the accretion discs of AGNs from the real observational polarization data.","pages":[13,14]},{"title":"Acknowledgments","content":"This research was supported by the program of Prezidium of RAS No.21, the program of the Department of Physical Sciences of RAS No.16, by the Federal Target Program 'Scientific and scientific-pedagogical personnel of innovative Russia' 2009-2013 and the Grant from President of the Russian Federation 'The Basic Scientific Schools' NSh-1625.2012.2.","pages":[14]},{"title":"References","content":"Afanasiev V.L., Borisov N.V., Gnedin Yu.N., Natsvlishvili T.M., Piotrovich M.Yu., Buliga S.D., 2011, Astron.Letters, 37, 302 Agol E., Blaes O., 1996, MNRAS, 282, 965 Antonucci R.R.J., Miller J.S., 1985, ApJ, 297, 621 Bentz M.C., Peterson B.M., Netzer H., Pogge R. W., Vestergaard M., 2009, ApJ, 697, 160 Blaes O.M., in: Accretion discs, jets and high energy phenomena in astrophysics, Les Houches Session LXXVIII, eds. V.Beskin et al., Springer, N.Y. 2003, p.147 Blandford R.D., 1990, in Courvoiseir T.J.-L., Mayor M., eds, Active galactic nuclear. Springer, Berlin, p. 161 Bon E., Popovic L.C., Gavrilova N., La Mura G., Medavilla E., 2009, MNRAS, 400, 924 Bonanno A., Urpin V., 2007, A&A, 473, 701 Braatz J.A., Gugliucci N.E., 2008, ApJ, 678, 96 Britzen S., Kam V.A., Witzel A. et al., 2009, A&A, 508, 1205 Chandrasekhar S., 1960, Radiative Transfer, Dover Publ., New York. Dolginov A.Z., Gnedin Yu.N., Silant'ev N.A., 1995, Propagation and polarization of radiation in cosmic media, Gordon&Breach, New York, p.72 Garofalo D., 2009, ApJ, 699, 400 Gnedin Y.N., Silant'ev N.A., 1997, Ap&SSR, 10, 1 Greene J.E., Peng C.Y., Ludwig R.R., 2010, ApJ, 709, 937 Ho L.S., Darling J., Greene J.E., 2008, ApJ, 177, 103 Ivanov V. V., Grachev S. I., Loskutov V. M., 1997, A&A, 321, 968 Kaspi S., Brandt W.N., Maoz D., Netzer H., Schneider D.P., Shemmer O., 2007, ApJ, 659, 997 Kochanek C.S., Dai X., Morgan C., Morgan N., Poindexter S., Chartas G., 2006, preprint (astro-ph/0609112) Krolik J.H., Begelman M.C., 1988, ApJ, 329, 702 Krolik J.H., 2007, preprint (astro-ph/0709.1489)","pages":[14]}],"string":"[\n {\n \"title\": \"Magnetic fields of active galactic nuclei and quasars with polarized broad H α lines\",\n \"content\": \"N.A. Silant'ev 1 , Yu.N. Gnedin 1 , 2 ∗ , S.D. Buliga 1 , M.Yu. Piotrovich 1 and T.M. Natsvlishvili 1 1 Central Astronomical Observatory at Pulkovo of Russian Academy of Sciences, Pulkovskoye chaussee 65, Saint-Petersburg, 196140, Russia 2 St.-Petersburg State Polytechnical University, Polytechnicheskaya 29, Saint-Petersburg, 195251, Russia February 19, 2018\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1 Introduction\",\n \"content\": \"We present estimates of magnetic field in a number of AGNs from the Spectropolarimetric atlas of Smith, Young & Robinson (2002) from the observed degrees of linear polarization and the positional angles of spectral lines (H α ) (broad line regions of AGNs) and nearby continuum. The observed degree of polarization is lower than the Milne value in a nonmagnetized atmosphere. We hypothesize that the polarized radiation escapes from optically thick magnetized accretion discs and is weakened by the Faraday rotation effect. The Faraday rotation depolarization effect is able to explain both the value of the polarization and the position angle. We estimate the required magnetic field in the broad line region by using simple asymptotic analytical formulas for Milne's problem in magnetized atmosphere, which take into account the last scattering of radiation before escaping from the accretion disc. The polarization of a broad spectral line escaping from disc is described by the same mechanism. The characteristic features of polarization of a broad line is the minimum of the degree of polarization in the center of the line and continuous rotation of the position angle from one wing to another. These effects can be explained by existence of clouds in the left (keplerian velocity is directed to an observer) and the right (keplerian velocity is directed from an observer) parts of the orbit in a rotating keplerian magnetized accretion disc. The base of explanation is existence of azimuthal magnetic field in the orbit. The existence of normal component of magnetic field (usually weak) makes the picture of polarization asymmetric. The existence of clouds in left and right parts of the orbit with different emissions also give the contribution in asymmetry effect. Assuming a power-law dependence of the magnetic field inside the disc, we obtain the estimate of the magnetic field strength at first stable orbit near the central supermassive black hole (SMBH) for a number of AGNs from the mentioned Spectropolarimetric atlas. Keywords : accretion discs, magnetic fields, polarization, active galactic nuclei. Smith et al. (2002) presented optical spectropolarimetric atlas of 36 nuclei of Seyfert 1 Galaxies. The data were obtained with the William Herschel and the Anglo-Australian Telescopes from 1996 to 1999. It is well-known that spectropolarimetry is an important tool in studies of active galactic nuclei (AGN). The spectropolarimetric data provide the detailed view into the inner regions of active galactic nuclei, including an accretion disc and accretion flows around a supermassive black hole (SMBH), thus allowing one to probe the structure and kinematics of the polarizing material around the accreting SMBH. Smith et al. (2002) objects exhibit a variety of characteristics with the average degree of polarization ranging from 0 . 2 to 5 percent. They show many variations both in the degree p line ( λ ) and position angle χ line ( λ ) of polarization across the broad H α emission line. The characteristic feature of p line ( λ ) is the minimum in the line centre, which is usually less than the polarization degree p c ( λ ) in nearby continuum. The second feature is the monotonic increase of positional angle from one line wing to the other. Note also that there exists little difference in the mean polarization degrees and position angles of nearby continuum and H α line for nine of Seyfert galaxies (Mrk 6, Akn 120, Mrk 896, Mrk 926, NGC 4051, NGC 6814, NGC 7603, UGC 3478, ESO 012-G21). For 22 measurements out of 45, the mean positional angles χ line and χ c are practically the same. It should be emphasized that the position angles of polarized continuum and H α line coincide more frequently than their polarization degrees. The mean value of the polarization degree in continuum over all sources is 0.68%, and the same value for H α lines is 0.66%. A position angle is most sensitive to the geometry of emitting region. For that reason, it is most probable that both emitting regions are located near one another, i.e. they located in an accretion disc and their scale sizes are similar: R BLR ≈ R λ , where R λ corresponds to the scale size of an accretion disc for the continuum radiation with given wavelength λ . It is generally accepted that AGNs are powered by the release of gravitational energy from gas accreted onto supermassive black holes (SMBH). The well-known anti-correlation between the radius of the broad-line region (BLR) and the velocity width of broad emission lines for AGNs supports the idea that the BLR gas is virialized and that its velocity is dominated by the gravity of the SMBH (Peterson & Wandel 2000; Onken & Peterson 2002). Most of the recent results lead to the conclusion that BLR presents a flattened rotating system. Many authors (Vestergaard et al. 2000; Nikolajuk et al. 2006; Sulentic et al. 2006; La Mura et al. 2009; Bon et al. 2009; Punsly & Zhang 2010) pointed out that considerable flattening and a predominantly planar orientation are likely to be the intrinsic property of the BLR structure. This conclusion allows us to consider BLR as an outer part of geometrically thin accretion disc that is optically thick with respect to the electron Thomson and the Rayleigh scattering processes. Seyfert galaxies were traditionally divided into two classes according to the presence or absence of broad optical lines. Antonucci & Miller (1985) explained this phenomenon by obscuration by a dusty torus with different orientation with respect to an observer. The orientation-based unification model has become quite popular, but it has also been confronted by more specialized observations (see, for example, Zhang & Wang 2006; Wang & Zhang 2007); in particular, there is evidence for the existence of a special subclass of Seyfert 2 lacking hidden broad-line regions (Zhang & Wang 2006). Thus, the paradigm of unification scheme for all Seyfert galaxies remains a matter of debate (Miller & Goodrich 1990; Tran 2001, 2003). The basic feature of Smith et al. (2002, 2004, 2005) models is that the polarization plane for most of Seyfert galaxies is parallel to the direction of the radio jet. Simultaneously, these models postulate that the radio jet direction is perpendicular to the accretion plane. The latter assumption is questionable. In reality, the radio jets frequently have significant bends near the radio core. The angle of the bend depends on the ratio of radial and toroidal magnetic fields in the accretion disc. Besides, the direction of the jet appears to change with time (see, for example, Britzen et al. 2009; Rastorgueva et al. 2011). Therefore, the coincidence of the direction of the radio jet and the polarization plane does not mean that the electrical vector of the polarized radiation E is perpendicular to the accretion disc. Of course, one can introduce the angle between the radio jet and the electric field E as an additional characteristic of AGNs. But, strictly speaking, this angle is not necessarily related to the real inclination of E with respect to the accretion disc. As a last resort, this angle may be considered in a probabilistic sense. The existence of many cases when the position angle of radiation has intermediate value between parallel or perpendicular to the direction of the radio jet also demonstrates that real direction of E does not correlate with the jet direction. As a result, we conclude that the models describing the polarization behavior in AGNs should not assume that the radio jets are perpendicular to accretion discs; instead, the explicit dependence on the inclination angle i of the accretion disc needs to be taken into account. It is commonly accepted (see, for example, Blaes, 2003) that the accretion discs are magnetized. The existence of radio jets is usually associated with strong magnetic fields in centers of AGNs and quasars. Numerous theoretical models demonstrate the power-law dependence of the magnetic field distribution in an accretion disc. Usually accretion discs are considered as geometrically thin slabs with Thomson optically depth τ /greatermuch 1. The scattering-induced linear polarization can be as high as ∼ 12% for edge-on viewing (Chandrasekhar 1960). However, in the real situation of a magnetized accretion disc, the degree of polarization p will be reduced due to Faraday rotation of the radiation polarization plane while a free photon travels between the consequent scatterings. Recall that the angle of Faraday rotation Ψ at the Thomson optical length τ is equal to where the wavelength of radiation λ is measured in microns and the magnetic field B is measured in Gauss. The angle Θ is the angle between the direction of light propagation n and the direction of B . The decrease of the polarization degree due to Faraday rotation occurs as a result of summation of chaotic angles of rotations in the multiple scattering process. This process has been considered in many papers (for example, Silant'ev 1994; Agol & Blaes 1996; Gnedin & Silant'ev 1997). Clearly, the value Ψ ∼ 1 at the mean free path τ ∼ 1 can decrease considerably the standard Chandrasekhar's polarization degree. Besides, the dependence of Ψ on the wavelength and magnetic field gives rise to characteristic dependencies of the polarization degree p and the position angle χ of radiation on λ , which allows us to estimate the strength and direction of the magnetic field in the scattering region. Below we develop a new model for the formation of polarization in AGNs, which does not use the assumption of the position angle of observed radiation being correlated with the direction of the radio jet. We hypothesize that the observed polarization is due to intrinsic polarization of radiation outgoing from the magnetized optically thick accretion disc (the Milne problem in magnetized atmosphere). In our model, the characteristic features of polarization mentioned above are explained by the topology of the magnetic field in the accretion disc, when the Faraday rotation of the polarization plane is taken into account. Primarily, we suppose that the whole radiating surface of the magnetized accretion disc is observed, i.e. that the inclination angle i is such that the obscuring torus (if it really exists) does not intersect the line of sight. We also consider the case when we observe only a part of total surface of accretion disc, i.e. we take into account the obscuring torus. It appears that our model and the usual pure geometrical model of Smith et al. (2002, 2004, 2005), which takes into account single scattering of BLR-photons in nearby clouds, are two competing explanations for the polarization properties of the accretion discs. All actually observed polarization degrees p c are much smaller than the value in the Milne problem in nonmagnetized atmosphere at the same inclination angle. Recall that the Milne problem deals with the radiative transfer in an optically thick atmosphere, where the sources of thermal radiation are located far from the surface, at depth with τ /greatermuch 1. In optically thick accretion discs the main source of thermal radiation is found at the midplane of the disc, and the outgoing radiation is described by the solution of the Milne problem. The mean value of p c in the atmosphere with pure electron scattering is equal to 3.1%, and the maximum value is 11.7%. The outgoing radiation in case of an absorbing atmosphere has a much greater polarization, because the intensity peaks near the surface. In this case, most of polarization arises analogously to the process of a single scattering of a radiation beam near the surface. For the Milne problem in spectral lines, the value p line is less than in continuum (see, for example, Ivanov et al. 1997). For the accretion disc models, the main challenge is to determine the scale length of the disc - i.e. the radius where the disc temperature matches the rest frame wavelength of the monitoring band. A semi-empirical method for measuring the disc scale length has been developed (Kochanek et al. 2006; Morgan et al. 2006, 2008; Poindexter, Morgan & Kochanek 2008). These authors used microlensing variability, observed for gravitationally lensed quasars, to find the accretion disc scale length for a given observed (or rest-frame) wavelength. Clearly, such a scaling has to be consistent with the most popular accretion disc model of Shakura & Sunyaev (1973). As a result, Poindexter et al. (2008) presented the following relation for the scale length of a standard geometrically thin accretion disc: The wavelength dependence, R λ ∼ λ 4 / 3 rest , corresponds to the typical (for Shakura-Sunyaev disc model) effective temperature: T e = T in ( R/R in ) -3 / 4 , where R in is the inner radius of an accretion disc and T in is the temperature corresponding to that radius. Here L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ) erg s -1 is the Eddington luminosity, M BH is the black hole mass, ε is the rest-mass radiation conversion efficiency, and L bol is the bolometric luminosity. Numerous papers provided measurements of BLR sizes for AGNs (see, for example, Peterson et al. 1994, 2004; Wu et al. 2004; Bentz et al. 2009; Shen & Loeb 2010; Greene et al. 2010). Kaspi et al. (2007) have compiled the observational data for Seyfert galaxies and nearby quasars with black hole masses estimated with the reverberation mapping technique. Most recently Shen & Loeb (2010) have suggested an empirical analytic formula for R BLR that is very useful for various estimates and applications: Here M 8 = M BH / 10 8 M /circledot . We will use this formula in our further calculations. Below we estimate the magnetic field strength in BLR of AGN and QSO from the data from the spectropolarimetric atlas presented by Smith et al. (2002). The λ - dependence of the observed polarization degree and position angle in H α line is very complicated. It appears to be produced by large-scale chaotic motions in the accretion disc.\",\n \"pages\": [\n 1,\n 2,\n 3\n ]\n },\n {\n \"title\": \"2 Basic equations\",\n \"content\": \"To estimate the degree of polarization p and the position angle χ of radiation escaping from the magnetized atmosphere we use the standard radiative transfer equations for Stokes parameters I, Q and U (see, for example, Silant'ev 1994; Dolginov, Gnedin & Silant'ev 1995; Silant'ev 2002, 2005). This system of equations has a fairly complicated form. Numerical solutions have so far been obtained only for the case when magnetic field B is parallel to the normal N to an atmosphere (see Silant'ev 1994; Agol and Blaes 1996; Shternin et al. 2003). For our purpose, however, it is sufficient to use a simple asymptotic theory, which can be presented in an analytical form for an arbitrary direction of the magnetic field in the atmosphere (Silant'ev 2002, 2005; Silant'ev et al. 2009). In this approximation, the intensity of the radiation I ( z, µ ) obeys a usual transfer equation with the Rayleigh phase function, and the system of equations for parameters Q and U can be presented in the following form: where B Q ( z, µ ) describes the source function for parameter Q due to the contribution of intensity scattering in nonmagnetized atmosphere (in this case B U ≡ 0), µ = nN is the cosine of the angle between the direction of light propagation n and the normal N to the atmosphere, α is the total extinction factor due to Thomson scattering and pure absorption on dust particles, the value q = σ a / ( σ a + σ s ) (Silant'ev et al., 2009) is the degree of absorption, C describes the additional extinction of polarized radiation due to the fluctuating component B ' of the magnetic field in the atmosphere (see below). Eq.(4) is valid in the limit of large Faraday rotation parameter δ ≥ 1. A solution of Eq.(4) results in the following expression for parameters Q ( n , B ) and U ( n , B ) for the radiation escaping from the magnetized atmosphere: /negationslash At δ ≥ 1, the first non-zero term of integrating by parts of Eq.(5) gives rise to the asymptotic expression which has an analytical form and can be used for an arbitrary direction of the magnetic field. For example, for the case B Q (0 , µ ) = 0 we have: For the Milne problem in absorbing atmosphere, a more sophisticated theory (see Silant'ev 1994, 2002) gives rise to the following expressions: Here p (1) ( µ ) is the polarization degree of outgoing radiation, which takes into account only the last scattering before escaping the atmosphere. The value p (1) ( µ ) gives the main contribution to p ( µ ) - exact polarization degree of outgoing radiation for a non-magnetized atmosphere. For this reason, below we use the value p ( µ ) instead of p (1) ( µ ), which for q = 0 is presented in Chandrasekhar (1960), and for the absorbing atmosphere in Silant'ev (1980). The value s is the root of the characteristic equation, tabulated by Silant'ev (1980). If the degree of the true absorption is small ( q /lessmuch 1), the parameter s = √ 3 q . First, let us consider the case when the whole surface of a radiating accretion disc is observed. In this case, the Stokes polarization parameters of continuum radiation Q c ( ϕ ) and U c ( ϕ ) must be averaged over all azimuthal angles ϕ , characterizing the position of a radiating surface element on a circular orbit in the accretion disc ( -π ≤ ϕ ≤ π ). The normal N and the direction to an observer n are the same for all parts of the accretion disc surface. Therefore, the reference frame of the accretion disc is common to all parameters Q c ( ϕ ) and U c ( ϕ ) of radiation escaping from the disc. In this case, the averaging procedure consists of integrating these parameters over the azimuthal angle ϕ . Note, that cos Θ depends on ϕ and the integral over ϕ can be taken analytically only over the interval ( -π, π ). As a result, the observed values for the degree of polarization and the position angle can be derived analytically. Silant'ev et al. (2009) presented the detailed description of the behavior of these quantities for continuum radiation. The degree of linear polarization of continuum p c and the position angle χ c for an accretion disc can be expressed in the analytical form: Here µ = cos i , where i is the inclination angle (angle between the light propagation direction n and the normal N to the accretion disc). The degree of polarization p c ( µ ) corresponds to a non-magnetized accretion disc. The value of p c ( µ ) for the continuum radiation presents the classical solution of Milne problem (Chandrasekhar 1960) with p (0) = 11 . 7%. The value of the position angle χ c = 0 corresponds to oscillations of the wave electric vector perpendicular to the plane ( nN ). For spectral lines in isotropic medium the value p line ( µ ) depends on the specific quantum numbers of the transitions (see, for example, Chandrasekhar 1960) and on the shape of the line. For a dipole type transition and the Doppler line shape, p line ( µ ) in the atmosphere with pure electron scattering has the same functional form as Chandrasekhar value p c ( µ ), with maximum value of 9.44% instead of 11.71% (see Ivanov et al. 1997). In isotropic medium we have to average an atom over all orientations. For such medium the transfer equation coincides with the usual system for Rayleigh scattering with an additional term, which describes unpolarized radiation. Such average naturally occurs due to usual thermal motions. Considering various quantum numbers for H α line, we see that this additional term is larger than the Rayleigh scattering term (see Chandrasekhar 1960), and the maximum degree of polarization becomes ∼ 3% instead of 9.44%. Therefore, the observed polarization can be explained if the atmosphere also has pure absorption of H α line (the existence of dust). In absorbing atmosphere the polarization degree p line can be larger than that in the non-absorbing atmosphere. Broad H α lines presented in atlas Smith et al. (2002) have very high widths, laying in the interval 50 - 200 angstroms. In such situations the total line (sum of 5 sub levels) can be described by one absorption coefficient with the Doppler shape (see, for example, Varshalovich, Ivanchik & Babkovskaya 2006; Lekht et al. 2008). Our technique takes into account the Faraday rotation during propagation of polarized radiation after the last scattering before escaping from the atmosphere. The region of broad-line emission is too far from the center of an accretion disc and has low magnetic fields. For this reason, one does not need to take into account the known Zeeman effect. The parameter where the negative term ( -sµ ) arises in the Milne problem in absorbing atmosphere (see Chandrasekhar 1960). For small degree of true absorption q = σ absorb / ( σ scattering + σ absorb ) /lessmuch 1 the factor s /similarequal √ 3 q . The regions of the line emission are different from those of continuum radiation. Usually one assumes that the parameter g c /similarequal 1 in most of areas of the accretion disc. To explain polarization of the line emission, we have to consider that this emission escapes from optically thick clouds with its own dimensionless parameters g line . The dimensionless parameters a and b describe the Faraday depolarization of radiation: where B z ≡ B ‖ is the component of the magnetic field directed perpendicular to the accretion disc surface, and B ⊥ = √ B 2 ρ + B 2 ϕ is the magnetic field in the accretion disc plane. The component B ⊥ is perpendicular to B ‖ . Due to axial symmetry, the inclination angle ϕ ∗ ( B ϕ /B ρ = tan ϕ ∗ ) is constant along a circular orbit. The value 0 . 8 λ 2 B is numerically equal to the Faraday rotation angle at the Thomson optical depth of τ = 2, if the polarized radiation propagates along the magnetic field direction. Here and in what follows, we take magnetic field in Gauss and wavelengths in microns. The dimensionless parameter C describes the real situation in a turbulent magnetized plasma and characterizes a new effect - additional extinction of the polarized radiation (parameters Q and U ) due to incoherence of the Faraday rotation in small-scale turbulent eddies (see Silant'ev 2005): where τ is the Thomson optical depth of a turbulent eddy ( τ /lessmuch 1), 〈 ( B ' ) 2 〉 is the mean value of fluctuations of the magnetic field, and f B ≈ 1 is a parameter describing the integrated correlation of the B ' values at two-closely spaced points in the accretion disc. It should be noted that the diffusion of radiation in the inner regions of the accretion disc also produces depolarization due to multiple scatterings. Presence of magnetic field and, therefore, the Faraday rotation effect, only increases the depolarization process. As a result, the polarized radiation emitted by a plane-parallel atmosphere at a specific inclination angle is considerably lower as compared to the classical Chandrasekhar-Sobolev value (see, for example, Gnedin & Silant'ev 1997). But the main feature of Faraday depolarization is the explicit wavelength dependence for both the polarization degree and the position angle. It is interesting to note that at a = b the polarization degree p c ( B , µ ) takes a maximum value (the term ( a 2 -b 2 ) 2 is zero in expression (8)). This effect takes place due to the opposite Faraday rotations from magnetic fields B ‖ and B ⊥ in some places along an orbit. All formulas presented above show that polarimetric observations allow us to derive the magnetic field strength and its topology in the BLR region, where the polarized radiation escapes the accretion disc. Using various models connecting magnetic field B H at the black hole horizon with the magnetic field B ms at the first stable orbit R ms nearest to the centre of the system, and then using the power law dependence of the magnetic field from R ms up to R BLR , we can estimate the magnetic field strength and the parameters that control it, such as the spin of the black hole a ∗ , the conversion efficiency of kinetic into radiative energy ε , and the magnetization parameter k = P magn /P gas ( P magn and P gas are magnetic pressure and gas pressure, in accreting plasma, respectively). Frequently one uses simple formulas for p c and χ c , corresponding to particular cases of pure normal B ‖ and of pure perpendicular B ⊥ : In the latter case χ c ≡ 0 due to the axial symmetry of the problem. Now let us consider the case when the radiating gas along a particular orbit in the accretion disc is partly obscured by some dust cloud (an obscuring torus). Clearly, for pure normal magnetic field B ‖ N , the unobscured part of the orbit has the same polarization degree p c ( B ‖ ) and the position angle χ c ( B ‖ ) as in the case of completely unobscured orbit (see Eq. (13)). If the magnetic field is toroidal B ϕ , i.e. is tangent to the orbit, we can derive the following analytical expressions: Here the parameter b ϕ = 0 . 8 λ 2 B ϕ √ 1 -µ 2 , the angle ϕ 0 describes the unobscured part of the orbit (we see the orbit within azimuthal angles -ϕ 0 ≤ ϕ ≤ ϕ 0 ). At ϕ 0 = π (complete orbit), Eq.(15) coincides with Eq.(14). Eq.(15) for f Q ( ϕ 0 ) is valid for ϕ 0 ≤ π/ 2. For π/ 2 ≤ ϕ 0 ≤ π one can use the relation f Q ( ϕ 0 ) = [ πf Q ( π/ 2) -( π -ϕ 0 ) f Q ( π -ϕ 0 )] /ϕ 0 . A more detailed derivation of these formulas is given below, in subsection 2.2 (for a spectral line case). Dependence of p c ( B ϕ ) /p c ( µ )(1 -sµ ) on ϕ 0 is presented in Fig.1 for values g c = 1, b ϕ = 1 , 2 , 3 , 4 , 5, and s = 0. It is interesting that for ϕ 0 = π/ 2 (half of the full orbit is observed) the polarization degree coincides with the result (14) for the fully unobscured orbit ( f Q ( π/ 2) = f Q ( π ) = 1).\",\n \"pages\": [\n 3,\n 4,\n 5\n ]\n },\n {\n \"title\": \"2.1 The case of a spectral emission line\",\n \"content\": \"In the catalog of Smith et al. (2002) the polarimetric data both in the continuum and in the H α emission line are presented. In our model of a rotating accretion disc (with the Keplerian velocity u k ) one part (the right side) of the disc ( ϕ = 0 ÷ π ) corresponds to motion from an observer and the second part (the left side) moves towards the observer ( ϕ = π ÷ 2 π ). According to the Doppler formula, wavelengths of radiation from the first part are greater than the central value λ 0 , and from the second part are smaller than λ 0 . The value λ 0 = (1 + z ) λ rest , where z is redshift parameter of the system and λ rest = 0 . 6563 µ m is the rest frame wavelength of the H α line. Here we restrict ourselves to a specific case of a spectral line with the Doppler shape. The line is described by following normalized shape function: As in the previous case of continuum radiation, we assume that the X-axis is perpendicular to plane ( nN ). The Keplerian velocity u k corresponds to the radius R BLR : u k = √ GM BH /R BLR , where G is gravitation constant. The usual Doppler line width ∆ λ T = ( u turb /c ) λ 0 is mainly due to chaotic turbulent velocities. The displacement of the line centre for radiation emitted from the part of the disc with the azimuthal angle ϕ is ( u k /c ) λ 0 √ 1 -µ 2 sin ϕ . Thus, the normalized shape function of radiation emitted from ϕ -part of the orbit has the form: Observed radiation flux F λ from a surface element dS of the ring with the radius R BLR is proportional to dϕ . The flux from the total radiating circular orbit can be obtained by integration over all azimuthal angles ϕ . If we suppose that all sources are distributed uniformly along the orbit, this flux is described by the following expression: Observed fluxes of linearly polarized radiation differ from the continuum radiation case by an additional factor φ ( λ, ϕ ): Here Θ is the angle between the magnetic field B and the light propagation direction n , I ( µ ) is total intensity of the spectral line escaping from the surface dS . The azimuthal angle ϕ = 0 corresponds to a surface element dS perpendicular to the plane ( nN ). Faraday depolarization term δ cos Θ has the form: where the parameters b ρ and b ϕ are: Here angle ϕ ∗ is the angle between B ⊥ and the radius-vector ρ , lying in the disc plane. The sign minus before b ϕ sin ϕ corresponds to the right-hand screw rotation of the accretion disc with the frozen magnetic field B ϕ directed along the rotation velocity. If the rotation of the disc is opposite, we have to change b ϕ to b ϕ . If we take the factor φ ( λ, ϕ ) = 1 and g line → g c , all the formulas will describe the case of the continuum radiation. In this case the integrals over ϕ can be evaluated analytically (for the combination -F Q + iF U the ϕ -integral can be evaluated by the complex residue method, and we obtain Eqs.(8) and (9)). Note, that these formulas are approximate, they take into account only the last scattering before the escape from the atmosphere. This is a rather satisfactory approximation (see Silant'ev 2002). It describes the main contribution to the polarization. The main merit of these analytical formulas is that they describe the polarization for any direction of the magnetic field. For our purpose this approach is sufficient. We note that ϕ -integration in Eqs.(18) - (20) gives rise to rather low polarization effects. For this reason they hardly can be used for describing the polarization data presented in the atlas (Smith et al. 2002). Below we present two models that are more acceptable for explaining the data.\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"2.2 The model of H α line polarization with parameters p and χ , averaged over the right and left parts of an orbit\",\n \"content\": \"It is clear from Eqs.(18), (19) and (20) that the right parts of circular orbits mostly contribute to gaussian shape lines at wavelengths λ > λ 0 , and the left parts mostly contribute to λ < λ 0 . Qualitatively, we can consider that these contributions are equivalent to sum of two gaussian shaped polarized lines. We assume that the effective polarizations and position angles of these lines correspond to mean values from the right side ( p right , χ right ) and the left side ( p left , χ left ) of the orbit. These values follow from Eqs.(19) and (20) if we take there the factor φ ( λ, ϕ ) = 1. Unlike the situation described by Eqs.(19) and (20), in this model we assume that a part of the accretion disc is invisible due to obscuring torus. The right part corresponds to integration over ϕ = 0 ÷ ϕ 0 , and the left part corresponds to integration in the interval ϕ = 0 ÷ -ϕ 0 . Here the angle ϕ 0 characterizes the boundary azimuthal angle for the visible part of the BLR orbit. The mean values 〈 Q 〉 and 〈 U 〉 for visible right part are described by the integrals: where δ cos Θ is given in Eqs. (21) and (22). The corresponding mean values for the left part of the BLR orbit are given by integrals in the interval (0 , -ϕ 0 ). /negationslash These integrals cannot be evaluated analytically in a general case. We present below the cases ( a = 0 , b ρ = 0 , b ϕ = 0) and ( a = 0 , b ρ = 0 , b ϕ = 0). The first case corresponds to the magnetic field B ‖ parallel to normal N . Clearly, in this case the polarization degree and the position angle are the same in the right and left parts of the orbit, and can be obtained from Eqs.(8) and (9) (see Eq.(13)). /negationslash The second case corresponds to a toroidal magnetic field B ⊥ , laying in the plane of the accretion disc and tangential to the radiating circular orbit. In this case the Faraday rotations are opposite in the right and the left parts of the orbit. This gives the same value for the polarization degree p right = p left and the opposite values for the position angles χ right = -χ left . We present below the results for the right part of the orbit: f U ( ϕ 0 ) = It is interesting to note that f Q ( ϕ 0 ) monotonically grows from f Q ( π/ 2) = 1 to f Q = √ g 2 line + b 2 ϕ /g line ≥ 1 as ϕ 0 → 0. ∣ ∣ The expression for f Q is valid only for ϕ 0 ≤ π/ 2, and the formula for f U is valid for total interval 0 ≤ ϕ 0 ≤ π . The integrands in Eqs. (23) are symmetric relative to the angle ϕ 0 = π/ 2. This gives equalities f Q ( π/ 2) = f Q ( π ) = 1 and f U ( π/ 2) = f U ( π ). Due to the aforementioned symmetry, we can calculate values f Q and f U for π/ 2 ≤ ϕ 0 ≤ π from the values for interval 0 ≤ ϕ 0 ≤ π/ 2: f Q,U ( ϕ 0 ) = [ f Q,U ( π ) π -f Q,U ( π -ϕ 0 )( π -ϕ 0 )] /ϕ 0 . The mean polarization degree p right ( B ϕ ) and the position angle χ right ( B ϕ ) can be derived from the following expressions: In Fig.2 we present the values p right ( B ϕ ) /p ( µ )(1 -sµ ) and | χ right | at b ϕ = 1 , 2 , 3 , 4 , 5 and g line = 1 , s = 0. Comparison of p right ( B ϕ ) with p c ( B ϕ ) in Fig.1 shows that p right > p c . This is evident, because p c corresponds to the sum of radiation from the right and the left parts of the observed areas (in this sum U = 0), and p right corresponds to the half of this area, where parameter U = 0. It means that in the wings of /negationslash the emitting lines the polarization is greater than in nearby continuum. Let us consider the behavior of the polarization degree p line ( B ϕ , λ ) and the position angle χ line ( B ϕ , λ ) inside the broad spectral line in more detail, using our simple model of two equal gaussian lines with the equal right and left displacements from the central wavelength λ 0 . We label the intensities of these lines as I right and I left . According to Eqs.(24) and (25), we present the total observed Stokes parameters I, Q and U in the form: Recall that due to the displacement of the centers of the right and left lines with the gaussian shape the intensities I right ( λ ) and I left ( λ ) are different at a particular considered wavelength inside the full line. Only at the central wavelength λ 0 these intensities are equal due to the axial symmetry of our model. Using Eqs.(27), (28) and (29), we obtain the following expressions for the total observed polarization degree p ( B ϕ , λ ) and the position angle χ ( B ϕ , λ ): Taking in Eqs.(30) and (31) I left = 0, we revert to Eq.(26) for the right part of the orbit. The total rotation of the position angle inside the line width is equal to the difference of ∆ χ ≡ χ right -χ left , where χ right corresponds to the right-hand wing of line with I right /greatermuch I left . The χ left corresponds to the left-hand wing with I left /greatermuch I right . As a result, we have: Now let us discuss shortly the polarization degree p inside the broad line. First of all, we notice that in the centre of the line λ = λ 0 the polarization is less than in the wings (c.f. Eq.(30) with I right = I left ). The polarization grows with the departure from λ 0 . This behavior of p line ( λ ) is observed in many objects from the catalog of Smith et al.(2002). According to Eq.(30), the ratio of p wing ( B ϕ , λ ) to p center ( B ϕ , λ ) becomes ∣ ∣ Note that the difference ∆ χ does not depend on the choice of the observer's reference frame. A non-zero value of ∆ χ is observed in many objects presented in the catalog of Smith et al. (2002) and is due to two reasons - the presence of the magnetic field B ϕ and the Keplerian rotation of the magnetized accretion disc. Fig.2 shows that ∆ χ depends on the parameter b ϕ and the angle ϕ 0 . Thus, for b ϕ = 5 and ϕ 0 /similarequal (140 · -160 · ) the value | ∆ χ | /similarequal 60 · . For ∆ χ = 60 · this ratio is equal to 2. Clearly, it is not possible to explain all details of p and χ in the our model of the sum of two spectral lines. But, above considerations tell us that the main characteristic features can be explained.\",\n \"pages\": [\n 6,\n 7,\n 8\n ]\n },\n {\n \"title\": \"2.3 The model of H α line as two emitting compact clouds located in the right and left part of the orbit\",\n \"content\": \"The spectra of H α lines in the atlas of Smith et al.(2002) for many objects have sufficiently complicated structure - the existence of separate peaks and asymmetric shapes. There are only a few objects with symmetric shapes. They have comparatively small widths as compared to other, more complicated spectra. A line with a complicated shape frequently can be approximated as a sum of two or more lines with gaussian shapes. For this reason we present the model of two compact optically thick clouds located in the opposite parts of an orbit in the accretion disc (Fig.3). The advantage of this model compared with the previous one is that we can take into account all the depolarizing Faraday parameters a, b ϕ and b ρ in a simple analytical form. Let us take the first cloud in the right part of the orbit, characterized by the azimuthal angle ϕ , and the second cloud in the left part, characterized by ϕ . If it is necessary, locations of the emitting clouds can be chosen at arbitrary angles along the orbit. Our choice is the simplest for consideration. As usually, we write the Stokes parameters in the coordinate system with X-axis being perpendicular to the plane ( nN ), where the formulas have the simplest form. Further we will use the observed polarization degree p and the total difference of the position angles between right and left parts of the spectral line ∆ χ , which do not depend on the choice of the reference frame. We also include in our formulas the contribution of the continuum radiation ( I c , Q c , U c ) in the region of spectral line. Then, the observed Stokes parameters are: The explicit formulas for Q c and U c are as follows: Here r 2 = ( g 2 c + b 2 -a 2 ) 2 +4 a 2 g 2 c = g 4 c +2 g 2 c ( a 2 + b 2 )+( a 2 -b 2 ) 2 . Introducing the notation η c = p c ( µ )(1 -sµ ) /p c ( B , µ ), and using expressions (8) and (9), we can present formulas for Q c and U c in a simpler form: The last expressions are valid in the limit (2 ag c ) /η 2 c → 0. In most sources from the catalog of Smith et al. (2002), the intensity I c is much smaller than I right + I left . For these cases one can neglect the contribution of the continuum radiation and the formulas for p line and χ line acquire fairly simple form: In the right wing, where ξ /similarequal 0, we have For the left wing one finds the same expression with ( -b ϕ ) instead of b ϕ . Using formula (42), we can obtain expression for the difference of the position angles between the right and left wings of the line: For the polarization degree in the right wing we derive the formula: For the left wing the polarization degree is higher because the Faraday depolarization parameter | a -b ϕ | is lower than in the right wing. If a = 0, the polarization degree p right = p left and χ right = -χ left . Presence of the magnetic field B ‖ (parameter a = 0) diminishes the polarization degree both in the right and left wings of the line, and also diminishes the difference | ∆ χ | = | χ right -χ left | . Besides, the functions p line ( λ ) and χ line ( λ ) become asymmetric relative to the center of the line λ 0 (if the intensities of lines I right ( λ ) and I left ( λ ) are the same gaussian functions). Analogously, for the left wing one replaces b ϕ with ( -b ϕ ). /negationslash It is interesting to compare the polarization degrees in the wings and in the center of line. The general formula for ratio p wing /p center is very complex and we consider only the case a = 0, where this ratio reaches a maximum value. Taking ξ = 1 for the center of the line and ξ = 0 for the line wing, we obtain the following expression from the general formula (41): For b ϕ = 5 and g line = 1 this ratio is equal to 5.1, i.e. is considerably greater than the value from formula (33). It is quite natural, because formula (33) describes the mean value of the effect. Clearly, the averaging procedure diminishes the effect. Physically this effect arises as a consequence of the Faraday rotation of the polarization plane. In the center of the line the rotations from the right and the left lines have opposite directions and the parameter Q center reaches a lower value than that in the line wing. The most important conclusion from the theoretical consideration of the structure of broad lines in AGN is the treatment of the symmetry of the polarization degree p line ( λ ) as the result of the azimuthal magnetic field B ϕ . If the symmetry of p ( λ ) is considerably broken, one can consider that B ϕ ∼ B ‖ , or the intensities of the right and the left emitting clouds are different.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"3 The magnetic field strength in a broad line region of AGN\",\n \"content\": \"The standard Unified Sheme for AGN includes a central source of continuum (accreting SMBH); a region close to the outer radius of the accretion disc emitting broad emission lines (broad line region - BLR); a dusty rotating 'torus' on parsec scales; and gas emitting narrow emission lines on a scale of tens to hundreds of parsecs, ionized through the open cone defined by the torus edge (Antonucci & Miller 1985; Krolik & Begelman 1988; Urry & Padovani 1995). The main unknown is the mechanism for the generation of the magnetic field during the process of accretion onto SMBH. Li (2002), Wang et al. (2002, 2003), Zhang et al. (2005) have studied the magnetic coupling process (MC) as an affective mechanism for transforming the kinetic energy of accreting gas into the magnetic energy. It is assumed that the disc is stable, perfectly conducting and Keplerian. The magnetic field on the black hole horizon is poloidal and varying as a power law with the distance from the central region. Since the magnetic field on the horizon B H is brought and held by its surrounding magnetized matter of the accretion disc, there must exist the relation between the magnetic field strength near the BH horizon and the accretion rate ˙ M . As a result, the magnetic field strength on the event horizon R H = R G (1+ √ 1 -a 2 ∗ ) is determined by the relation between the magnetic energy and the accretion kinetic energy densities (see Li 2002; Wang et al. 2002): Here R G = GM BH /c 2 , the bolometric luminosity L bol = ε ˙ Mc 2 , ˙ M is the accretion rate, c is the light velocity and ε is the radiative efficiency calculated by numerical simulations of Novikov & Thorne 1973, Krolik 2007, Shapiro 2007. The coefficient k presents the inverse plasma parameter k = P magn /P gas = 1 /β , where P gas and P magn are the gas and the magnetic pressures, respectively. For the equipartition case β = 1 and k = 1. Eq.(46) is easily transformed into: The basic problem is the relation between the magnetic fields strengths at the first stable circular orbit R ms and the event horizon R H . The value of the radius R ms depends on the radius R G and the spin a ∗ , and can be presented in a form: where l E = L bol /L Edd and the Eddington luminosity L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ). where parameter q > 1. For example, for a Schwarzschild black hole q = 6 and for the Kerr BH with the spin a ∗ = 0 . 998 q = 1 . 22 (Murphy et al. 2009). Reynolds, Garofalo & Begelman (2006) argued that the plunging inflow can greatly enhance the trapping of large scale magnetic field on the black hole. Blandford (1990) has shown that the interaction of the large-scale magnetic field with the event horizon of rotating black hole can enhance the trapping of large-scale poloidal magnetic field on the horizon of the black hole, compared with the inner accretion flow and compared to the magnetic field strength derived from the relation between magnetic energy and accretion kinetic energy (Eq.(47)). Recently Garofalo (2009) has showed that the dynamics of the plunge region of a thin black hole accretion disc and magnetic flux trapping can enhance the strength of the magnetic field threading the horizon by a significant factor. The results of his calculations were presented in fig.7 of Garofalo paper. It means that we obtain the following relation between the magnetic field strength at the first stable orbit B ms and the magnetic field strength at the event horizon of a black hole B H : The coefficient η can be obtained from fig.7 of the paper by Garofalo (2009). From this figure it follows that for a ∗ = 0 . 5 the value is η = 5 and for a ∗ = 0 . 0 and a ∗ = 0 . 998 we have η = 7 . 5. Numerical simulations have been used to study magnetic field generation in astrophysical objects. For example, the existence of large-scale dynamos in magneto-convection under the influence of shear and rotation has been studied by Kapyla, Korpi & Brandenburg (2008). These authors have shown that the saturation field strength reaches, practically, the equipartition level B ≈ 0 . 7 B eq , i.e. k ≈ 0 . 5. Taking into account the shear flows can increase the magnetic field level. It means that the magnetization parameter can be equal to k ≈ 1. We suggest that the magnetic field far inside in the accretion disc, and, especially, in the Broad Line Region (BLR) takes the toroidal form. Namely, the differential rotation in the accretion disc leads to an increase of the azimuthal field by winding up the poloidal field lines into the toroidal field lines (Bonanno & Urpin 2007). In astrophysical objects differential rotation is often associated with magnetic fields of various strength and geometry. If the poloidal field has a component parallel to the gradient of the angular velocity, then differential rotation can stretch toroidal field lines from the poloidal ones. In the presence of the magnetic field, differential rotation can be a reason for various MHD instabilities, especially if the field geometry is complex. Mayer & Pringle (2006) assumed that a dynamo process generates a local poloidal field B z in the accretion disc, and the magnitude of the poloidal component is small: B z /lessmuch B ⊥ . Usually one assumes that regular dependence of the magnetic field on the radius R in the accretion disc exists from the first stable orbit R ms , and that dependence has a power law form: We assume two values for the parameter n . The value n = 1 derives the toroidal topology of the magnetic field (see Bonanno & Urpin 2007). The value n = 5 / 4 corresponds to the accretion process with hot accretion flows (Medvedev 2000). For pure toroidal topology of the magnetic field in the accretion disc we have the depolarization parameter a = 0, and in this case Eqs.(8) and (9) for non-turbulent case ( C = 0) are transformed into Eq.(14). Recall that, according to definitions (11), magnetic field B ( R BLR ) can be determined, if the parameter b is known from the observed polarization: This field can be related to B ms . In the case of a power-law dependence (50) with n = 1, this relation becomes We used here Eq.(3) for determining R BLR . Note that M 9 = M BH / 10 9 M /circledot . In this situation the depolarization parameter b for H α wavelength ( λ = 0 . 6563 µ m) is: For hot accretion flows n = 5 / 4 and the depolarization parameter b becomes where q ( a ∗ ) = R ms /R G and R G = GM BH /c 2 . The explicit form of q ( a ∗ ) is given, for example, in Zhang et al. (2005). Below we shall also consider the case of the equipartition between the gas and the magnetic pressures, i.e. k ≈ 1. Namely, the magnetic coupling process corresponds to this case (Li 2002; Wang et al. 2003; Zhang et al. 2005; Ma, Wang & Zuo 2006). Using Eqs.(47) and (49), we transform relations (53) and (54) into the following forms: and for n = 5 / 4: Eqs.(55) and (56) allow us to estimate the radiation efficiency and therefore the rotation rate a ∗ of an accreting black holes. Below we use the spectropolarimetric atlas of AGNs by Smith et al. (2002) for specific estimates.\",\n \"pages\": [\n 10,\n 11\n ]\n },\n {\n \"title\": \"4 Magnetic field strength of Akn 120\",\n \"content\": \"According to Smith et al. (2002) the mean polarization degree in the continuum of Akn 120 is equal to p c /similarequal 0 . 35%, and is equal to /similarequal 0 . 4% in the H α line emission. We use here the data obtained by Smith et al. (2002) in 1998 October. The mean observed position angle have the same value for the continuum and line emission χ /similarequal 76 · . The inclination angle i = 48 · , µ /similarequal 0 . 67. Its value has been derived by Braatz & Gugliucci (2008) from water maser observations. The central black hole mass in Akn 120 is equal to M BH /similarequal 10 7 . 74 M /circledot (see Peterson et al. 2004). For the inclination angle i = 48 · the polarization in the continuum from the accretion disc without magnetic field is expected at the level p c ( µ ) = 1 . 26% (Chandrasekhar 1960). This value is higher than the observed polarization degree and it means that the Faraday depolarization effect is really acting. The H α line spectrum shows the two-peak structure and can be represented as sum of two intensities with gaussian shapes. The difference of the positional angles ∆ χ is estimated to be between 70 · and 80 · . The intensity of the continuum radiation reaches ≈ 18% of the maximum line intensity near the centre. The behaviour of polarization in the continuum is very complex. It seems this behaviour occurs due to the existence of large-scale turbulent curls along the observed orbit. For that reason, it is more convenient to use the continuum - subtracted spectrum of Akn 120, presented in fig.24 of the mentioned Atlas by Smith et al. (2002). We used formulas (31)-(37) to find the estimates for the parameters a, b ϕ , p line ( µ ) and g line . Attempts to estimate these parameters under the assumption p c ( µ ) /similarequal p line ( µ ) were unsuccessful. We propose that in the line radiating clouds there is true absorption of radiation (the existence of dust particles). As it is known (see, for example, Silant'ev 1980), the existence of absorption gives rise to a considerable increase of polarization escaping from the optically thick atmosphere. This effect is the consequence of absorption creating a peak like form of escaping emission. Introducing first three parameters in Eq.(8), we obtain g line /similarequal 0 . 975. The estimate g line = 0 . 975 = 1 + C -sµ gives the relation between C and s . It means that the clouds are absorbing and the small scales are turbulent. The existence of large scale turbulence in clouds directly follows from very high line width. For the rest of radiation from the accretion disc outside the compact clouds we assume that absorption is absent and small scale turbulence is negligible ( C ≈ 0). From Eq.(57) it follows that p line /similarequal 3 . 97% and b ϕ /similarequal 3 . 46. The estimated value p line /similarequal 3 . 97% corresponds to the case when one takes into account the pure absorption of radiation by dust particles existing into emitting clouds. From Eq.(11) one can obtain an estimate of magnetic fields B ‖ /similarequal 0 G and B ϕ /similarequal 14 G. In Fig.4 we present the observed intensity, polarization degree and variation of the azimuthal angle χ , and our model results. It is seen that the model curves practi- /s32 cally coincide with the observed values. The observed intensity is approximated as sum of two gaussian intensities from symmetrically located clouds. The Doppler widths of these intensities are taken equal to ∆ λ T =70 ˚ A, the value ( u k /u turb ) sin ϕ √ 1 -µ 2 = 0 . 3, the ratio of maximum intensities of gaussians is I left /I right = 20 / 18. The centers of gaussian curves coincide with the observed places in Fig.24 of Smith et al. (2002). The main problem is that the exact value of index n is unknown and its value depends strongly on the model of the accretion disc. Pariev, Blackman & Boldyrev (2003) suggest the following interval of values of this index 1 ≤ n ≤ 2. The value n = 1 corresponds to toroidal magnetic field (see Bonanno & Urpin 2007). To estimate the magnetic field strength at the last inner circular orbit B ms we need to know the rotation rate of the central supermassive black hole (parameter a ∗ ). For a Schwarzschild black hole with a ∗ = 0 and q = 6 and for the toroidal magnetic field ( n = 1) we obtain from Eq.(49) B ms = 14 . 5 · 10 3 G . Now we can estimate the magnetic field strength B H at the horizon of the central black hole using the results of calculations by Garofalo (2009). He has calculated the ratio of the horizon-threading magnetic field and the magnetic field in the accretion disc as a function of the black hole spin. According to this calculations, for a ∗ = 0 the ratio B H /B ms = 7 . 5 and B H = 10 . 7 · 10 4 G . Our results demonstrate that for a given value of the polarization degree the magnetic field strength at the inner radius r ms (and therefore on the horizon radius) is stronger for a Kerr black hole compared to Schwarzschild one. This result means also that for black holes with the same magnetic field strengths the degree of polarization for Kerr black holes is larger than for Schwarzschild black holes (see Silant'ev et al. 2011).\",\n \"pages\": [\n 11,\n 12\n ]\n },\n {\n \"title\": \"5 Magnetic field strength of Mrk 6\",\n \"content\": \"According to Ho, Darling & Greene (2008), the mass of the central black hole in Mrk 6 is log( M BH /M /circledot ) = 7 . 97 ± 0 . 5, the ratio of the bolometric luminosity to the Eddington value is log( L bol /L E dd ) = -1 . 72. The inclination angle is i = 62 · . 7 , µ = 0 . 46 (Ho et al. 2008). It means that the standard (Sobolev-Chandrasekhar) magnitude of the polarization degree is p c ( µ ) = 2 . 52%. The observed mean polarization has been found at the level of p c = 0 . 90 ± 0 . 03, p ( H α ) = 0 . 85 ± 0 . 04 (Smith et al. 2002). The most remarkable fact is the jump of the mean position angle for two observational seasons of Feb 97 and Oct 98: ∆ χ ≈ 25 · . It is interesting that the value of the mean polarization remained the same. This jump occurred over 1-2 years, which is too short a time for such a large object as the accretion disc near the supermassive black hole. Thus, this problem remains unsolved. Let us return now to the analysis of the data in the H α line. First of all, we see that the polarization degrees in the right and the left sides of the spectrum are practically equal - the left side has p line /similarequal 1 . 5%, and in the right side p line /similarequal 1 . 4%. From the theoretical considerations in section 2, it is clear that such a symmetrical form of the polarization degree can occur if the magnetic field B ‖ is much less than the azimuthal magnetic field B ϕ . A small decrease of polarization in the right-hand part is due to the reason that small value of the B ‖ component, directed to an observer, coincides with direction of B ϕ . In this situation the polarization of radiation slightly decreases compared to the left-hand part of the orbit, where the aforementioned magnetic fields are directed opposite to each other. Considering polarization near the line center, we assume p line ( centre ) /similarequal 0 . 5%. We also assume that in the center of the line the intensity from the left part of the orbit is approximately equal to that from the right part. The value of the intensity of the continuum radiation in Mrk 6 is relatively small, and we neglect it in our computation. Using formulas (34)-(36), one obtain: Substitution of these parameters in Eq.(8) gives g line /similarequal 1 . 0006, i.e. practically 1. As in the case of Akn 120, the polarization p line /similarequal 3 . 9% implies that in H α -clouds there exists the absorption of radiation. Under the assumption of dipole radiation we have q c /similarequal 0 . 01 and the parameter s /similarequal 0 . 17. Because g line = 1 . 0006 /similarequal 1 = 1+ C -0 . 17 · 0 . 46 we find that the small scale turbulent parameter C /similarequal 0 . 08. For the difference ∆ χ of the position angles between the left and the right wings of the spectral line the expression (43) gives ∆ χ = 42 · . This value is consistent with the observational results. Eqs.(11) and (58) give estimate: B ‖ /similarequal 0 . 6G and B ϕ /similarequal 8 . 5G. Note that expression (58) supposes that I c p c /lessmuch I right,left p line ( µ ). Now let us estimate the magnetic field strength in the accretion disc of Mrk 6 using the results of the polarimetric obser- For the spin value of a ∗ = 0 . 5, ε = 0 . 081, q = 4 . 25 (Novikov & Thorne 1973) we obtain B ms = 6 . 8 · 10 3 G and B H = 3 . 4 · 10 4 G . At last, for a ∗ = 0 . 998, q = 1 . 22, ε = 0 . 32 we have B ms = 2 . 8 · 10 4 G and B H = 14 · 10 4 G . /s32 /s32 /s32 vations from Smith et al. (2002). Eqs. (53)-(56) allow us to derive the magnetic field strength B ms at the inner radius of the accretion disc: B ms = (1 . 72 × 10 4 /q ) G . For a Swarzschild black hole, when q = 6, the magnetic field B ms = 2 . 9 · 10 3 G . For a Kerr black hole with a ∗ = 0 . 998 the parameter q = 1 . 22 and the magnetic field strength B ms = 1 . 4 · 10 4 G . According to Garofalo (2009, fig.7) the magnetic field strength at the horizon of the supermassive black hole is B H = 1 . 4 · 10 4 G for a ∗ = 0 and B H = 10 5 G for a ∗ = 0 . 998.\",\n \"pages\": [\n 12,\n 13\n ]\n },\n {\n \"title\": \"6 Magnetic fields of Mrk 985 and IZw1\",\n \"content\": \"The intensity spectrum of Mrk 985 has a two-peak shape and the spectrum of the polarization degree p line ( λ ) is quite symmetric (the p line ( left ) /similarequal 1 . 27% and p line ( right ) /similarequal 1 . 16%). In the centre of line p line ( centre ) /similarequal 0 . 5%. The mean polarization of the continuum radiation is 1.12%. Using formulas (33)-(37), we find that We see that a nearly symmetric form of p line ( λ ) implies that a /lessmuch b ϕ , i.e. B ‖ /lessmuch B ϕ . From Fig.15 in the atlas of Smith et al. (2002) we see that the difference of position angles between the right wing and the centre of line is equal ∆ χ /similarequal 31 -33 · . From general theory one finds that tan2∆ χ = a/g line + b ϕ /g line . Our estimates (59) give this value for the angle difference. The estimates of magnetic fields at distances R ms and R H can be obtained analogously as in the previous sections. In the atlas of Smith et al. (2002) there is no information on the inclination angle i . It is interesting to estimate this angle assuming that g line /similarequal 1. Substituting parameters g c = 1 , a = 0 . 114 and b ϕ = 2 . 035 into formula (8) gives the value p c ( µ ) = 2 . 54%. This implies an estimate i /similarequal 64 · , µ /similarequal 0 . 44. Using the value p c ( µ ) = 2 . 54% we can calculate the value g line , corresponding to this polarization. This calculation demonstrates that the parameter g line acquires the value g line /similarequal 1 . 0013. The value p line ( µ ) = 2 . 75 at µ = 0 . 44 takes place at q a /similarequal 0 . 01 ( s = 0 . 17). The value g line /similarequal 1 . 0013 = 1 + C -0 . 17 · 0 . 44 occurs at C /similarequal 0 . 08. Using Eq.(11) and the value µ /similarequal 0 . 44, we find the estimates: B ‖ /similarequal 0 . 75 G and B ϕ /similarequal 6 . 6 G. Now let consider the AGN IZw1. This object has p c /similarequal 0 . 67%, p line ( left ) /similarequal 0 . 7%, p line ( centre ) /similarequal 0 . 2% and p line ( right ) /similarequal 0 . 9%. The form of the polarization spectrum is slightly more asymmetric than in Mrk 985. Using general formulas (33)-(35) we find the following estimates: As in the case of Mrk 985, we found, that g line /similarequal 1 and p c ( µ ) /similarequal 2 . 68%. This corresponds to µ /similarequal 0 . 44. The value p line /similarequal 3 . 9% occurs at the absorption degree q a /similarequal 0 . 01 , s /similarequal 0 . 17. As a result, the small scale turbulence parameter C /similarequal 0 . 08. As in the previous cases, using Eq.(11) and the value µ = 0 . 44 we can estimate the magnetic field strength for IZw 1: B ‖ = 3 . 42G and B ⊥ = 12 . 7G. It should be noted that in these cases we estimated the inclination angle i from the analysis of the polarization data. The obtained estimates of the magnetic field strengths in BLR of these AGNs are presented in Table 1. The last value in the table is close to the one estimated by Afanasiev et al.(2011) where the polarimetric observations were made only for the continuum emission and did not include the emission from the broad line region.\",\n \"pages\": [\n 13\n ]\n },\n {\n \"title\": \"7 Conclusions\",\n \"content\": \"For many objects of Smith et al. (2002) spectropolarimetric atlas the polarization spectra of a broad H α -line p line ( λ ) have a characteristic minimum at the center of the line and different maxima at the left and right wings. Usually the wing polarizations are higher than those in the nearby continuum. For many objects the position angle changes continuously from the left wing to the right one. We develop a new theoretical explanation for these features, different from the original explanation of Smith et al. (2002, 2004, 2005), taking into account that accretion discs can be magnetized. Smith et al. explain the characteristic features of the H α -line assuming that the observed polarization is due to single scattering of non-polarized radiation from the BLR on two types of scattering clouds - a polar cloud around the radio jet, and clouds in the equatorial region. It appears (see Smith et al. 2005) that their mechanism has two characteristic features: a relatively low amplitude ( | ∆ χ | ≤ 20 -40 · ) of the position angle rotation from one line wing to the other one, and the need for a very high electron temperature ( T ∼ 10 6 K) in a nearby scattering cloud. In their atlas there are cases with both low ∆ χ < 20 · and high ∆ χ ∼ 80 · position angle rotations. The need for the high electron temperature arises from the observed polarization minimum in the line core. Besides, they neglect the intrinsic linear polarization of the radiation in BLR. In our mechanism both effects can be explain by a single cause - the Faraday rotation of the polarization plane. The wide line width results from turbulence, which is related to the Keplerian rotation in the orbit. Clearly both explanations take place in reality. The basis of our explanation is the assumption that both the continuum radiation and the spectral line emission originate in an optically thick magnetized accretion disc around the center of an AGN. The observed characteristic shape of the line polarization appears as a result of the Faraday rotation of the polarization plane in the accretion disc having a normal magnetic field B ‖ and an azimuthal field B ϕ . We propose that the regions of the line emission can be represented as a comparatively dense absorbing turbulent clouds rotating with the Keplerian velocity around the center of the AGN. These clouds are flattened, optically thick and magnetized. They emit the polarized radiation in accordance with the Milne problem law. The observed emission line is a sum of radiation from clouds rotating in the right and the left sides of the orbit. Due to Doppler displacements, emission from the one side is, as a whole, reddened ( λ ≥ λ 0 ), and emission from the other side has the opposite λ -displacement. The Faraday rotations by azimuthal magnetic field B ϕ in the left and the right sides of the orbit are opposite and, as a result, in the center of line the sum of emissions is less polarized than in the wings. The continuous rotation of the position angle χ from one wing of line to the opposite wing arises for the same reason. The projection of the normal magnetic field B ‖ along the line of sight gives an additional Faraday rotation. It is the same in both sides of the radiating orbit. This additional rotation in one side of orbit increases the total Faraday rotation, and in opposite side decreases the total rotation. For this reason B ‖ magnetic field gives rise to an asymmetric (relative to the central wavelength λ 0 ) profiles for both the polarization degree p line ( λ ) and the position angle χ line ( λ ). The presented theory allows us to estimate the components B ϕ and B ‖ in the broad line emission regions, and also in nearby regions of the continuum radiation. If the polarizations in the left and the right wings are slightly different, then the value B ‖ /lessmuch B ϕ . This helps us to estimate the B ϕ -component from more simple formulas for continuum polarization. Objects in which this is the case are ESO 141-635, IZw1, Mrk 6, Mrk 290, Mrk 985 and NGC 5548. The objects with a strong asymmetry of p line ( λ ) are characterized by magnetic fields B ϕ ∼ B ‖ . Such objects are Akn 120, Akn 564,KUV 18217+6419, Mrk 304, Mrk 335, Mrk 841, MS1849.2-7832 and NGC 4593. Other objects have fairly complex polarization spectra, they appear to be distorted by large-scale turbulent motions. Using the estimated values of the magnetic field in broad line regions (usually B ‖ /lessmuch B ϕ and B ϕ ∼ 10 G) , one can estimate the magnetic field B ms at the last stable orbit near the black hole, and then the field B H at the radius of the event horizon. These estimates are dependent on the different assumptions about the slope of the power-law distribution of the magnetic field inside the accretion disc. We have used the most common assumptions to obtain the values of the magnetic field ∼ 10 4 -10 5 G. These values of the magnetic field are in a good agreement with other estimates. Thus, we determined the magnetic field strengths in various places in the accretion discs of AGNs from the real observational polarization data.\",\n \"pages\": [\n 13,\n 14\n ]\n },\n {\n \"title\": \"Acknowledgments\",\n \"content\": \"This research was supported by the program of Prezidium of RAS No.21, the program of the Department of Physical Sciences of RAS No.16, by the Federal Target Program 'Scientific and scientific-pedagogical personnel of innovative Russia' 2009-2013 and the Grant from President of the Russian Federation 'The Basic Scientific Schools' NSh-1625.2012.2.\",\n \"pages\": [\n 14\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Afanasiev V.L., Borisov N.V., Gnedin Yu.N., Natsvlishvili T.M., Piotrovich M.Yu., Buliga S.D., 2011, Astron.Letters, 37, 302 Agol E., Blaes O., 1996, MNRAS, 282, 965 Antonucci R.R.J., Miller J.S., 1985, ApJ, 297, 621 Bentz M.C., Peterson B.M., Netzer H., Pogge R. W., Vestergaard M., 2009, ApJ, 697, 160 Blaes O.M., in: Accretion discs, jets and high energy phenomena in astrophysics, Les Houches Session LXXVIII, eds. V.Beskin et al., Springer, N.Y. 2003, p.147 Blandford R.D., 1990, in Courvoiseir T.J.-L., Mayor M., eds, Active galactic nuclear. Springer, Berlin, p. 161 Bon E., Popovic L.C., Gavrilova N., La Mura G., Medavilla E., 2009, MNRAS, 400, 924 Bonanno A., Urpin V., 2007, A&A, 473, 701 Braatz J.A., Gugliucci N.E., 2008, ApJ, 678, 96 Britzen S., Kam V.A., Witzel A. et al., 2009, A&A, 508, 1205 Chandrasekhar S., 1960, Radiative Transfer, Dover Publ., New York. Dolginov A.Z., Gnedin Yu.N., Silant'ev N.A., 1995, Propagation and polarization of radiation in cosmic media, Gordon&Breach, New York, p.72 Garofalo D., 2009, ApJ, 699, 400 Gnedin Y.N., Silant'ev N.A., 1997, Ap&SSR, 10, 1 Greene J.E., Peng C.Y., Ludwig R.R., 2010, ApJ, 709, 937 Ho L.S., Darling J., Greene J.E., 2008, ApJ, 177, 103 Ivanov V. V., Grachev S. I., Loskutov V. M., 1997, A&A, 321, 968 Kaspi S., Brandt W.N., Maoz D., Netzer H., Schneider D.P., Shemmer O., 2007, ApJ, 659, 997 Kochanek C.S., Dai X., Morgan C., Morgan N., Poindexter S., Chartas G., 2006, preprint (astro-ph/0609112) Krolik J.H., Begelman M.C., 1988, ApJ, 329, 702 Krolik J.H., 2007, preprint (astro-ph/0709.1489)\",\n \"pages\": [\n 14\n ]\n }\n]"}}},{"rowIdx":85,"cells":{"bibcode":{"kind":"string","value":"2013AuArc..77...30F"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1305.0881.pdf"},"content":{"kind":"string","value":"\nAstronomical Orientations of Bora Ceremonial Grounds in Southeast Australia\nRobert S. Fuller 1,2 , Duane W. Hamacher 1,3 and Ray P. Norris 1,2,4\n1 Warawara - Department of Indigenous Studies, Macquarie University, NSW, 2109, Australia Email: robert.fuller1@students.mq.edu.au\n2 Research Centre for Astronomy, Astrophysics & Astrophotonics, Macquarie University, NSW, 2109, Australia\n3 Nura Gili Centre for Indigenous Programs, University of New South Wales, NSW, 2052, Australia Email: d.hamacher@unsw.edu.au\n4 CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW, 1710, Australia Email: raypnorris@gmail.com\nAbstract\nEthnographic evidence indicates that bora (initiation) ceremonial sites in southeast Australia, which typically comprise a pair of circles connected by a pathway, are symbolically reflected in the Milky Way as the ÔSky BoraÕ. This evidence also indicates that the position of the Sky Bora signifies the time of the year when initiation ceremonies are held. We use archaeological data to test the hypothesis that southeast Australian bora grounds have a preferred orientation to the position of the Milky Way in the night sky in August, when the plane of the galaxy from Crux to Sagittarius is roughly vertical in the evening sky to the south-southwest. We accomplish this by measuring the orientations of 68 bora grounds using a combination of data from the archaeological literature and site cards in the New South Wales Aboriginal Heritage Information Management System database. We find that bora grounds have a preferred orientation to the south and southwest, consistent with the Sky Bora hypothesis. Monte Carlo statistics show that these preferences were not the result of chance alignments, but were deliberate.\nNotice to Aboriginal and Torres Strait Islander Readers\nThis paper discusses bora ceremonies and contains the names of people who have passed away. The exact locations of these sites are concealed in order to protect them. The coordinates provided are within 10 km of the site and are used only to demonstrate the general distribution of the known bora grounds in southeast Australia.\nKeywords: Aboriginal Australian, Cultural Astronomy, Ceremonial Sites\nIntroduction\nIn traditional Aboriginal cultures across Australia, young males are taught the laws, customs and traditions of the community and undergo a transition ceremony from boyhood to manhood. This ceremony often includes a Ôrite of passageÕ event in which the initiated males undergo some form of body modification (Jacob 1991), typically involving tooth evulsion in southeast Australia (e.g. Berndt 1974:27Ð30). This ceremony goes by many names, but in\nQueensland (Qld) and New South Wales (NSW) it has come to be generally known as ÔboraÕ, the name used by the Kamilaroi of north-central NSW (Ridley 1873:269). Bora grounds generally consist of two circles of differing diameter connected by a pathway. The larger circle is regarded as a public space, while the smaller circle some distance away is restricted to initiates and elders. Bora ceremonies were one of the first Aboriginal cultural activities described by early Australian colonists in the Sydney region (Collins 1798:468-480; Hunter 1793:499-500). Because information about bora ceremonies is culturally sensitive, here we limit discussion of the ceremony itself.\nThere is a variety of evidence from the anthropological literature (e.g. Berndt 1974; Love 1988; Winterbotham 1957) that bora ceremonies are related to the Milky Way and that ceremonial grounds are oriented to the position of the Milky Way in the night sky at particular times of the year.\nIn this paper, we begin by exploring connections between bora ceremonies and the Milky Way using ethnographic and ethnohistoric literature. We then use the archaeological record to determine if bora grounds are oriented to the position of the Milky Way at particular times of the year. Finally, we use Monte Carlo statistics to see if these orientations were deliberate or the result of chance.\nBora Ceremonial Grounds\nThe layout of bora grounds is similar across southeast Australia, with only minor differences from region to region (Bowdler 2001:3; Mathews 1894:99). Several reports (e.g. Black 1944; Collins 1798:391; Fraser 1883; Howitt 1904; Mathews 1897a) describe the grounds as consisting of two rings of different sizes, connected by a pathway. In some places, Bora sites may comprise three or more rings (Steele 1984; Bowdler 2001). The border of each ring is made of raised earth or stone, and the area within is cleared of debris and the earth is stamped until firm. The larger ring, which is considered public, has a typical diameter of 20Ð30 m. The smaller ring (generally 10Ð15 m diameter) is considered the sacred area, where body modification takes place, and is restricted to initiates and elders. The two rings are connected by a pathway that ranges from a few tens to a few hundred metres in length. In 2004, an Aboriginal man from Marulan, NSW advised that parts of many such sites were destroyed immediately after the ceremony to conceal their location (Hardie 2004). For this reason, some bora sites reported in the archaeological literature feature only a single circle, with the smaller, sacred circle having been destroyed.\nBora grounds are distributed throughout southeast Australia, covering most of NSW and southern Qld and may extend into South Australia (Howitt 1904:501Ð508) and northern Qld (Roth 1909). Ceremonial rings, which may be bora grounds, have been found near Sunbury, Victoria (Vic.), although there are no ethnographic records attesting to their ceremonial use (Frankel 1982). Howitt (1904:512) cited a western boundary for bora running from the mouth of the Murray River to the Gulf of Carpentaria. Mathews (1897b:114) noted the bora can be found across three-quarters of NSW and some distance into western Qld, with a boundary extending from Twofold Bay near Eden, NSW in the south, to Moulamein, NSW in the west, and Barringun, Qld in the north. We recognise that the geographical area covered by this paper includes several distinct language groups, each of whom may have separate culture and traditions, and it may be misleading to aggregate the data from such a wide area. However, (a) the existence of similarly constructed bora rings implies some commonality in culture, and (b) aggregating orientations from a large geographic area will dilute any preferred orientations\narising from a single Aboriginal group, rather than forming a correlation of spurious significance.\nAccording to Love (1988), the bora ceremonies were predominantly held in August each year, although other authors report a variety of dates including MarchÐMay (Winterbotham 1957), AprilÐJune (Mathews 1894:99), MayÐJuly (Mathews 1894), August (Needham 1981:70), SeptemberÐNovember (Winterbotham 1957), and OctoberÐDecember (Mathews 1894). This suggests that, in some cases, a number of variables influence the date of the bora ceremony, including the availability of food and water or having a sufficient number of boys to initiate (e.g. Mathews 1910). While these factors vary across the region, here we test the hypothesis advanced by Love (1988) who presents evidence associating the bora ceremony with the night sky and the orientation of the Milky Way, and suggests that most initiation ceremonies occur around August.\nAnthropological Support of an Astronomical Connection\nIt is well established that the night sky plays a significant role in several Aboriginal cultures (e.g. Cairns and Harney 2004; Johnson 1998; Norris and Hamacher 2009; Hamacher 2012). In Aboriginal astronomical traditions, dark spaces within the Milky Way are as significant as bright objects. Two animals symbolically link bora ceremonies to these dark spaces. One was a spiritual serpent, commonly referred to as the ÔRainbow SerpentÕ across Australia, traced out by the curving dust lanes in the Milky Way. Needham (1981:69) explained that in Aboriginal communities of the Hunter Valley, motifs of the spiritual serpent were represented in bora ceremonies, with information about the serpent being recounted during the ceremony itself. The other animal was an emu, which is also traced by dust lanes in the Milky Way (Norris and Norris 2009). Love (1988:129Ð138) argued that the emu was an important part of the bora ceremony in southeast Australia, as did Berndt (1974:27Ð30), since male emus brood and hatch the emu chicks and rear the young (Love 1987). This is symbolic of the initiation of adolescent boys by their male elders.\nNeedham (1981) provided an illustration of the night sky and associated stars in local Aboriginal astronomical traditions. The illustration, which cites the ÔAll FatherÕ as the star Altair, provides the positions of celestial objects in August, Ôthe month when Aboriginal initiation ceremonies were heldÕ (Needham 1981:70). During the early part of the night in August, the Milky Way stretches across the sky from the northeast to the southwest. Many early colonial reports referred to an Aboriginal religion based on a deity variously described as Baiame, Bunjil or Mungan-ngaua (Henderson 1832:147; Howitt 1904:490Ð491; Ridley 1873:268). These names roughly translate to ÔfatherÕ or Ôfather of all of usÕ (Howitt 1904:491). According to Fraser (1883:208) and Howitt (1884:458), Baiame gave his son, Daramulan, to the people and it is through Daramulan that Baiame sees all. Baiame is worshipped at the bora ceremony (Ridley 1873:269) and Daramulan is believed to come back to the earth by a pathway from the sky (Fraser 1883:212). Eliade (1996:41) reported that Baiame Ôdwells in the sky, beside a great stream of waterÕ (i.e. the Milky Way) and various reports (e.g. Berndt 1974; Hartland 1898; Howitt 1884) have claimed that the wife of Baiame (or in some cases Daramulan) is an emu. Reports of Baiame, Daramulan and Bunjil come from various cultures across southeast Australia, resulting in variations in these reports. However, they share some features, such as a close connection between bora ceremonies and the Milky Way.\nTesting the Hypothesis\nTo focus the discussion, we concentrate specifically on the hypothesis advanced by Love (1987, 1988), who argued that ancestral spirits in the heavens held bora ceremonies in the Milky Way, which we refer to as the ÔSky BoraÕ. Love based his work, in part, on Winterbotham (1957), who obtained information from a Jinibara man from southeast Qld named Gaiarbau. According to Winterbotham (1957:38), bora circles,\nÉ were always oriented towards points of the compass, the larger one to the north, and the smaller to the south ... They conformed in this rule to the position of two dark (black) spaces (circles)Ñthe Coal Sacks in the heavens.\nAccording to Love (1988 : 130Ð131), the Jinibara account identifies the Sky Bora with the Emu in the Sky (Gaiarbau et al. 1982:77; Winterbotham 1957:46). The ÔCoal SacksÕ, or Mimburi , to which Winterbotham referred, are a dark absorption nebula bordering the western constellations Crux (Southern Cross), Centaurus and Musca, representing the head of the emu, with the star BZ Crucis representing the eye. The dust lanes that run through the stars Alpha and Beta Centauri represent the neck, while the Galactic bulge, near the intersection of Sagittarius, Scorpius and Ophiuchus, represents the body. This area is the centre of our Milky Way galaxy. The dust lanes along the Milky Way through Sagittarius trace out the legs (Figure 1). The motif of the celestial emu is found across Australia (e.g. Cairns and Harney 2004; Norris and Hamacher 2009:13; Stanbridge 1861:302; Wellard 1983:51).\n\n\n
Figure 1: The ÔEmu in the SkyÕ visible over an emu engraving at Elvina Track in Kuringai Chase National Park north of Sydney, which may represent her celestial counterpart (image reproduced courtesy of Barnaby Norris).
\n\nAccording to Winterbotham, other Aboriginal groups also knew of the dark nebulae, including the Badjala people of Fraser Island and the adjacent mainland, who call them Wurubilum , and the Wakka Wakka people near Murgon, Qld. This concept extends beyond southeast Australia. For example, Smith (1913) explained that during an initiation ceremony in Western Australia (WA) the initiate is left tied to the ground until the Milky Way is visible. He is then asked if Ôhe can see the two dark spotsÕ and when he is able to see them, he is released. While this account is not from the area of this study, it may be similar to the example that Gaiarbau described.\nGaiarbau said that bora ceremonies were not held until the celestial bora rings returned to their Ôproper points of the compassÕ (Winterbotham 1957:38). In clear winter skies in southeast Australia, the Milky Way is visible about an hour after sunset. The orientation of the plane of the Milky Way, as seen from southeast Australia an hour after sunset, changes from near vertical in the south-southeast in March to horizontal across the southern sky from east-southeast to west in June and back to vertical (but inverted) in the southwest in September. The Galactic bulge and the Coalsack (celestial emu) are not visible in the sky together an hour after sunset until May. At this time, the emu is not vertical in the sky (perpendicular to the horizon), but stretches from south to east.\nThe only time that the Sky Bora is vertically aligned to the horizon and can be seen in the sky together an hour after sunset is in August (or later in the night as the year progresses). The Galactic plane, which goes straight through the celestial emu, is vertical in August an hour or two after sunset (earlier in the evening later in the month, Figure 2). At this time, the azimuth is approximately 213¼ (south-southwest).\n\n\n
Figure 2: The sky bora in the Milky Way oriented vertically in the south-southwest sky in mid-August an hour after sunset, as seen from Brisbane. The large circle represents the larger bora circle and the body of the emu (near zenith). The smaller circle represents the Coalsack and the head of the emu. Graphics are from the Stellarium astronomical software package.
\n\nIf LoveÕs hypothesis is correct, we expect the orientation of each bora site from the larger circle to the smaller circle to be oriented to roughly 213¼, corresponding to the time ceremonies are held (August). This expectation agrees with Needham (1981:70), who claimed that bora ceremonies in the Hunter Valley (NSW) were held in August when the Milky Way was vertical in the south-southwest.\nOther researchers report that bora ceremonies in Qld and NSW are held at various times of the year, as noted in the previous section (Winterbotham 1957; Mathews 1894:99). Bora ceremonies may be held at times of the year that have little or nothing to do with the position of the Milky Way in the sky, even if the ceremonies are symbolically linked to the Milky Way. For example, Mathews (1894:128) claimed that the direction of one bora ring to the other Ôis entirely dependent on the conformation of the country within which the ceremony is being heldÕ. If bora grounds are not oriented to any particular object or direction, we expect to find a roughly uniform distribution in their orientations. However, if at least some bora grounds are oriented to the position of the Sky Bora, then we expect to find a preference for south-southwest orientations when we look at the overall distribution of bora ground orientations.\nMethodology\nTo determine the orientations of bora ceremonial sites, we obtained data for 63 such sites from the following published literature: Mathews (1894, 1896a, 1896b, 1897a, 1907, 1917), Hopkins (1901), Towle (1942), Bartholomai and Breeden (1961), Anon. (1973), McBryde (1974), Steele (1984), Satterthwait and Heather (1987), and Bowdler (2001). We also obtained 1107 archaeological site cards from the NSW Aboriginal Heritage Information Management System (AHIMS) related to stone arrangements and ceremonial grounds.\nWe then filtered the data through a rigorous selection process, discarding data for any bora ground that failed to meet any of the following criteria:\n\n1. The site is clearly described as a bora ceremonial ground;\n2. The site is in NSW or southeast Qld (see Figure 3);\n3. Measurements were made by an appropriately trained or qualified person (e.g. a surveyor or archaeologist);\n4. The data are either first-hand, or second-hand from a trusted source;\n5. There is unambiguous information on the direction from the large to the small circle; and,\n6. a. Both rings and the pathway between them are identifiable, or\nb. Both rings and at least one opening are identifiable , or\nc. Only one ring is identifiable, but it has a clearly identifiable opening and there is unambiguous information as to whether it is the larger or the smaller ring.\n\nThe orientation of each site was measured from the centre of the largest circle to the centre of the smaller circle. If the second circle was missing, the orientation was taken from the centre of the circle to the middle of the opening. Measurements were either taken directly from the records given by the surveyor or measured from the survey with a protractor and ruler. We divided the azimuths into 16 bins (N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, NNW), each with a width of 22.5¼ with N centred at 0¡, NNE at 22.5¡, and so on (see Table 1).\nAustralian Archaeology, No. 77 | Preprint\n
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Table 1: Azimuths of the inter-ordinal (left), ordinal (right top) and cardinal (right bottom) orientations (in degrees) used to bin the data in Figure 4, given in degrees. Each bin in the left-hand column has a width of 22.5 ¡ (±11.25¡) centred on the Central Azimuth.
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\nResults and Analysis\nOf the 1170 sites obtained from the literature and AHIMS site card search, only 68 fit the specified selection criteria (Table 2, Figure 3). The 68 sites can be divided into two groups:\n\n1) Those 46 sites for which the orientation has been recorded individually for each site; and,\n2) Those 22 sites in Satterthwait and Heather (1987: Table 9), which provide the distribution of orientations without providing individual site orientations.\n\nThe 46 data points whose orientations are recorded individually, are provided in Table 2 and are grouped into 22.5¼ bins, shown as a histogram in Figure 4a. The histogram reveals a clear preference for the S, SW and W orientations. Table 2 contains 34 orientations in ordinal (N, S, E, W, NW, NE, SE, SW) directions, but only 12 orientations in inter-ordinal (NNE, ENE, etc.) directions. The low number of inter-ordinal orientations suggests either that the sites tend to be oriented on ordinal points, or that some authors rounded to the nearest ordinal point. To avoid a statistical bias in our results, we re-binned the data into the eight ordinal directions, dividing the counts of each inter-ordinal bin equally between the two neighbouring ordinal bins, resulting in eight 45¼ bins (Table 1, Figure 4b).\nA preferred orientation to the south is evident (28% of the 46 data points), with lesser but significant preferences to the SW (17%) and W (15%) bins. The combined S, SW and W bins account for 61% of the total data points, while the remaining are evenly spread across the remaining bins. The highest peak of 12.5 orientations occurs in the S bin.\nWe compare this result with the 22 data points from Satterthwait and Heather (1987) (hereafter referred to as ÔSHÕ) by re-binning our data to four quadrants centred on the cardinal points (N, S, E, W), as shown in Figure 4c. This reveals a strong preference for the southern\nquadrant and a lesser but significant preference to the western quadrant, which, when combined, account for 74% of the 46 data points. The SH data (Figure 4d) is similar, with a significant preference for the southern quadrant (68% of the 22 data points), but with an even distribution among the remaining quadrants. We then combined our 46 data points with the 22 SH data points, resulting in Figure 4e. A clear preference for the southern quadrant is evident, with 35 of the 68 orientations (51%) falling in the S bin. This result is consistent with the Love hypothesis.\n\n\n
Figure 3: Locations of all bora grounds in Table 2, excluding the data from Satterthwait and Heather (1987). The coordinates given are adjusted to as to protect exact location of each site. The coordinates given are within 10 km of the site, which is why some appear over the sea.
\n\nTo determine if this is a chance clumping of a random distribution of orientations, we conducted a Monte Carlo simulation, in which 68 orientations were distributed randomly in each of the bins shown in Figure 4e. We repeated this process 100 million times. In only 303 of the 100 million runs did the number in any one bin equal or exceed 35, from which we can conclude that the likelihood of the peak in Figure 4b occurring by chance is about 3x10 -6 or 0.0003%. We therefore conclude that this distribution is clearly not the result of chance, and that the constructors of the bora rings intentionally aligned most of them to the south quadrant.\n
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Table 2: The bora grounds after filtering the original data through the selection criteria, grouped alphabetically by reference author, followed by the SH data. The coordinates given are approximate and do not reveal the exact location of the site. Data includes the site number, name and location. Also included is the site layout type: Type 1 consists of two circles and a pathway; Type 2 consists of two circles and one opening; Type 3 consists of one circle and an opening. All orientations are given in terms of cardinal, ordinal or inter-ordinal points measured from the large ring to the small ring, with the specific azimuth given where applicable. SH do not give coordinates or azimuthsÑonly orientations in four quadrants (N, S, E and W).
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Figure 4: Orientations of bora sites using data from Table 1. Data in (a) is given in 22.5¼ bins, (b) is given in 45¼ bins, and (c) through (e) are given in 90¼ bins.
\n\nDiscussion and Conclusion\nWe have shown that the bora grounds studied have a preferred orientation to southerly directions and that these orientations are not the result of chance, but were deliberate. The reason for this is not known, but it is consistent with the Love hypothesis that southeast Australian bora ceremonial grounds have a preferred orientation to the celestial emu in the Milky Way in the south-southwest skies. The celestial emu is in this position in the evening sky during the month of August, the time during which Winterbotham (1957) and Needham (1981) claimed that bora ceremonies were held. Hamacher et al. (2012) showed that linear stone arrangements in NSW also have a preferred orientation to the cardinal points, especially north-south orientations. Since many stone arrangements are ceremonial sites, this lends support to the claim that orientation is an important factor utilised by Aboriginal people when laying out ceremonial sites.\nAlthough our analysis supports the Love hypothesis, it is not definitive evidence that bora grounds are oriented to the Sky Bora. Some researchers, including Winterbotham (1957) and Mathews (1894), state that many Bora ceremonies across NSW and Qld were held at various\ntimes throughout the year, which do not correspond to any particular orientation of the Milky Way. However, there is strong ethnographic evidence that the Milky Way is associated with the bora ceremony and we consider it likely that some ceremonies were timed, and bora sites oriented, such that the vertical Milky Way was visible above the path connecting the two circles during bora ceremonies. Additional research is necessary to understand these links; we are currently engaged in further research projects to explore this.\nAcknowledgements\nWe acknowledge the Aboriginal Elders and custodians, past and present, on whose land the bora sites are located. For archaeological data and literature sources, we thank staff from the State Library of NSW, the Australian Institute for Aboriginal and Torres Strait Islander Studies and the NSW Office of Environment and Heritage. This research made use of the TROVE and JSTOR databases, Google Maps, and the Stellarium astronomical software package. Hamacher conducted his component of this research while a PhD student at Macquarie University, but finished the analysis and writing as a staff member at the University of New South Wales.\nReferences\nAnon. 1973 The layout of bora grounds. Bulletin of the Richmond River Historical Society 65:12Ð13.\nBartholomai, A. and S. Breeden 1961 Stone ceremonial grounds of the Aborigines in the Darling Downs area, Queensland. Memoirs of the Queensland Museum 13(6):231Ð237.\nBerndt, R.M. 1974 Aboriginal Religion . Leiden: Brill Archive.\nBlack, L. 1944 The Bora Ground: Being a Continuation of a Series on the Customs of the Aborigines of the Darling River Valley and of Central New South Wales, Part IV . Sydney: F.H. Booth.\nBowdler, S. 2001 The management of Indigenous ceremonial (ÔboraÕ) sites as components of cultural landscapes. In M. Cotter, W.E. Boyd and J. Gardiner (eds), Heritage Landscapes: Understanding Place and Communities , pp.1Ð19. Lismore: Southern Cross University Press.\nCairns, H.C. and B. Yidumduma Harney 2004 Dark Sparklers . Sydney: Hugh Cairns.\nCollins, D. 1798 An Account of the English Colony in New South Wales, Vol. I . London: T. Cadell Jr and W. Davies.\nEliade, M. 1996 Patterns in Comparative Religion . Lincoln: University of Nebraska Press.\nFrankel, D. 1982 Earth rings at Sunbury, Victoria. Archaeology in Oceania 17:83Ð89.\nFraser, J.F. 1883 The Aborigines of New South Wales. Transactions and Proceedings of the Royal Society of New South Wales 16:193Ð233.\nLangevad, G. 1982 Some Original Views Around Kilcoy. Book 1: The Aboriginal Perspective . Queensland Ethnographic Transcripts 1. Brisbane: Archaeology Branch, Queensland Department of Aboriginal and Islanders Advancement.\nHamacher, D.W. 2012 On the Astronomical Knowledge and Traditions of Aboriginal Australians . PhD thesis by publication, Department of Indigenous Studies, Macquarie University. [ www.academia.edu/1905624/On_the_Astronomical_Knowledge_and_Traditions_of_Aboriginal_Australians ]\nHamacher, D.W., R.S. Fuller and R.P. Norris 2012 Orientations of linear stone arrangements in New South Wales. Australian Archaeology 75:46Ð54.\nAustralian Archaeology, No. 77 | Preprint\nHardie, B. 2004 MRN9 . Aboriginal Heritage Information Management System, Card No. 51-6-0250. Sydney: Office of Environment and Heritage, NSW State Government.\nHartland, E.S. 1898 The ÔHigh GodsÕ of Australia. Folklore 9(4):290Ð329.\nHenderson, J. 1832 Observations on the Colonies of New South Wales and Van DiemenÕs Land . Calcutta: Baptist Mission Press.\nHopkins, A. 1901 Bora ceremony. Science of Man 4(4):62Ð63.\nHowitt, A.W. 1884 The native tribes of south-eastern Australia. Journal of the Anthropological Institute of Great Britain and Ireland 13:432Ð459.\nHowitt, A.W. 1904. The Native Tribes of South-East Australia . London: McMillan.\nHunter, J. 1793 An Historical Journal of the Transactions at Port Jackson and Norfolk Island . London: John Stockdale.\nJacob, T. 1991 In the Beginning: A Perspective on Traditional Aboriginal Societies . Perth: Western Australia Ministry of Education.\nJohnson, D. 1998 Night Skies of Aboriginal Australia: A Noctuary . Oceania Monograph No. 47. Sydney: Sydney University Press.\nLove, W.R.F. 1987 There is an emu on the bora ground. Anthropological Society of Queensland Newsletter 177:1Ð5.\nLove, W.R.F. 1988 Aboriginal Ceremonies of South East Australia. Unpublished MA thesis, Department of Anthropology and Sociology, University of Queensland, Brisbane.\nMcBryde, I. 1974 Aboriginal Prehistory in New England: An Archaeological Survey of Northeastern New South Wales . Sydney: Sydney University Press.\nMathews, R.H. 1894 Aboriginal bora held at Gundabloui in 1894. Journal of the Royal Society of New South Wales 28:98Ð129.\nMathews, R.H. 1896a The bora, or initiation ceremonies of the Kamilaroi tribe. Journal of the Anthropological Institute 24:411Ð418.\nMathews, R.H. 1896b The burbung of the Wiradthuri tribes, Part 1. Journal of the Royal Anthropological Institute 25:295Ð318.\nMathews, R.H. 1897a The burbung of the Darkinung tribes. Proceedings of the Royal Society of Victoria 10(1):1Ð3.\nMathews, R.H. 1897b The burbung, or initiation ceremonies of the Murrumbidgee tribes. Journal and Proceedings of the Royal Society of New South Wales 31:111Ð153.\nMathews, R.H. 1907 Notes on the Aborigines of New South Wales . Sydney: Government Printer.\nMathews, R.H. 1910 Initiation ceremonies of some Queensland tribes. Proceedings and Transactions of the Royal Geographical Society of Australia, Queensland 25:103-118\nMathews, R.H. 1917 Description of two bora grounds of the Kamilaroi tribe. Journal and Proceedings of the Royal Society of New South Wales 51:427Ð30.\nNeedham, W. 1981 Burragurra-A Study of the Aboriginal Sites in the Cessnock-Wollombi Region of the Hunter Valley . Adamstown: Dobson and McEwan.\nNorris, R.P. and D.W. Hamacher 2009 The astronomy of Aboriginal Australia. In D. Valls-Gabaud and A.\nAustralian Archaeology, No. 77 | Preprint\nBoksenberg (eds), The Role of Astronomy in Society and Culture , pp.39Ð47. Cambridge: Cambridge University Press.\nNorris, R. and P. Norris 2009 Emu Dreaming: An Introduction to Australian Aboriginal Astronomy . Sydney: Emu Dreaming Press.\nRidley, W. 1873 Australian languages and traditions. The Journal of the Anthropological Institute Great Britain and Ireland 2:257Ð275.\nRoth, W.E. 1909 On Certain Initiation ceremonies. North Queensland Ethnography 12:166-85\nSatterthwait, L. and A. Heather 1987 Determinants of earth circle site location in the Moreton region, southeast Queensland. Queensland Archaeological Research 4:1Ð33.\nSmith, W. 1913 Sketcher, Aboriginal folk-lore. The Queenslander , 11 October, p. 8.\nStanbridge, W. 1861 Some Particulars of the General Characteristics, Astronomy, and Mythology of the Tribes in the Central Part of Victoria, Southern Australia. Transactions of the Ethnological Society of London 1:286304.\nSteele, J.G. 1984 Aboriginal Pathways in Southeast Queensland and the Richmond River . Brisbane: University of Queensland Press.\nTowle, C.C. 1942 Bora ground near Ruby Creek, NSW. Victorian Naturalist 59(5):80Ð81.\nWinterbotham, L. 1957 GaiarbauÕs Story of the Jinibara Tribe of Southeast Queensland. Unpublished manuscript held on file at the Australian Institute for Aboriginal and Torres Strait Islander Studies, Canberra (MS #45/7460).\nWellard, G.E.P. 1983 Bushlore - or this and that from here and there . Perth: Artlook Books.\n"},"sections":{"kind":"list like","value":[{"title":"Astronomical Orientations of Bora Ceremonial Grounds in Southeast Australia","content":"Robert S. Fuller 1,2 , Duane W. Hamacher 1,3 and Ray P. Norris 1,2,4 1 Warawara - Department of Indigenous Studies, Macquarie University, NSW, 2109, Australia Email: robert.fuller1@students.mq.edu.au 2 Research Centre for Astronomy, Astrophysics & Astrophotonics, Macquarie University, NSW, 2109, Australia 3 Nura Gili Centre for Indigenous Programs, University of New South Wales, NSW, 2052, Australia Email: d.hamacher@unsw.edu.au 4 CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW, 1710, Australia Email: raypnorris@gmail.com","pages":[1]},{"title":"Abstract","content":"Ethnographic evidence indicates that bora (initiation) ceremonial sites in southeast Australia, which typically comprise a pair of circles connected by a pathway, are symbolically reflected in the Milky Way as the ÔSky BoraÕ. This evidence also indicates that the position of the Sky Bora signifies the time of the year when initiation ceremonies are held. We use archaeological data to test the hypothesis that southeast Australian bora grounds have a preferred orientation to the position of the Milky Way in the night sky in August, when the plane of the galaxy from Crux to Sagittarius is roughly vertical in the evening sky to the south-southwest. We accomplish this by measuring the orientations of 68 bora grounds using a combination of data from the archaeological literature and site cards in the New South Wales Aboriginal Heritage Information Management System database. We find that bora grounds have a preferred orientation to the south and southwest, consistent with the Sky Bora hypothesis. Monte Carlo statistics show that these preferences were not the result of chance alignments, but were deliberate.","pages":[1]},{"title":"Notice to Aboriginal and Torres Strait Islander Readers","content":"This paper discusses bora ceremonies and contains the names of people who have passed away. The exact locations of these sites are concealed in order to protect them. The coordinates provided are within 10 km of the site and are used only to demonstrate the general distribution of the known bora grounds in southeast Australia. Keywords: Aboriginal Australian, Cultural Astronomy, Ceremonial Sites","pages":[1]},{"title":"Introduction","content":"In traditional Aboriginal cultures across Australia, young males are taught the laws, customs and traditions of the community and undergo a transition ceremony from boyhood to manhood. This ceremony often includes a Ôrite of passageÕ event in which the initiated males undergo some form of body modification (Jacob 1991), typically involving tooth evulsion in southeast Australia (e.g. Berndt 1974:27Ð30). This ceremony goes by many names, but in Queensland (Qld) and New South Wales (NSW) it has come to be generally known as ÔboraÕ, the name used by the Kamilaroi of north-central NSW (Ridley 1873:269). Bora grounds generally consist of two circles of differing diameter connected by a pathway. The larger circle is regarded as a public space, while the smaller circle some distance away is restricted to initiates and elders. Bora ceremonies were one of the first Aboriginal cultural activities described by early Australian colonists in the Sydney region (Collins 1798:468-480; Hunter 1793:499-500). Because information about bora ceremonies is culturally sensitive, here we limit discussion of the ceremony itself. There is a variety of evidence from the anthropological literature (e.g. Berndt 1974; Love 1988; Winterbotham 1957) that bora ceremonies are related to the Milky Way and that ceremonial grounds are oriented to the position of the Milky Way in the night sky at particular times of the year. In this paper, we begin by exploring connections between bora ceremonies and the Milky Way using ethnographic and ethnohistoric literature. We then use the archaeological record to determine if bora grounds are oriented to the position of the Milky Way at particular times of the year. Finally, we use Monte Carlo statistics to see if these orientations were deliberate or the result of chance.","pages":[1,2]},{"title":"Bora Ceremonial Grounds","content":"The layout of bora grounds is similar across southeast Australia, with only minor differences from region to region (Bowdler 2001:3; Mathews 1894:99). Several reports (e.g. Black 1944; Collins 1798:391; Fraser 1883; Howitt 1904; Mathews 1897a) describe the grounds as consisting of two rings of different sizes, connected by a pathway. In some places, Bora sites may comprise three or more rings (Steele 1984; Bowdler 2001). The border of each ring is made of raised earth or stone, and the area within is cleared of debris and the earth is stamped until firm. The larger ring, which is considered public, has a typical diameter of 20Ð30 m. The smaller ring (generally 10Ð15 m diameter) is considered the sacred area, where body modification takes place, and is restricted to initiates and elders. The two rings are connected by a pathway that ranges from a few tens to a few hundred metres in length. In 2004, an Aboriginal man from Marulan, NSW advised that parts of many such sites were destroyed immediately after the ceremony to conceal their location (Hardie 2004). For this reason, some bora sites reported in the archaeological literature feature only a single circle, with the smaller, sacred circle having been destroyed. Bora grounds are distributed throughout southeast Australia, covering most of NSW and southern Qld and may extend into South Australia (Howitt 1904:501Ð508) and northern Qld (Roth 1909). Ceremonial rings, which may be bora grounds, have been found near Sunbury, Victoria (Vic.), although there are no ethnographic records attesting to their ceremonial use (Frankel 1982). Howitt (1904:512) cited a western boundary for bora running from the mouth of the Murray River to the Gulf of Carpentaria. Mathews (1897b:114) noted the bora can be found across three-quarters of NSW and some distance into western Qld, with a boundary extending from Twofold Bay near Eden, NSW in the south, to Moulamein, NSW in the west, and Barringun, Qld in the north. We recognise that the geographical area covered by this paper includes several distinct language groups, each of whom may have separate culture and traditions, and it may be misleading to aggregate the data from such a wide area. However, (a) the existence of similarly constructed bora rings implies some commonality in culture, and (b) aggregating orientations from a large geographic area will dilute any preferred orientations arising from a single Aboriginal group, rather than forming a correlation of spurious significance. According to Love (1988), the bora ceremonies were predominantly held in August each year, although other authors report a variety of dates including MarchÐMay (Winterbotham 1957), AprilÐJune (Mathews 1894:99), MayÐJuly (Mathews 1894), August (Needham 1981:70), SeptemberÐNovember (Winterbotham 1957), and OctoberÐDecember (Mathews 1894). This suggests that, in some cases, a number of variables influence the date of the bora ceremony, including the availability of food and water or having a sufficient number of boys to initiate (e.g. Mathews 1910). While these factors vary across the region, here we test the hypothesis advanced by Love (1988) who presents evidence associating the bora ceremony with the night sky and the orientation of the Milky Way, and suggests that most initiation ceremonies occur around August.","pages":[2,3]},{"title":"Anthropological Support of an Astronomical Connection","content":"It is well established that the night sky plays a significant role in several Aboriginal cultures (e.g. Cairns and Harney 2004; Johnson 1998; Norris and Hamacher 2009; Hamacher 2012). In Aboriginal astronomical traditions, dark spaces within the Milky Way are as significant as bright objects. Two animals symbolically link bora ceremonies to these dark spaces. One was a spiritual serpent, commonly referred to as the ÔRainbow SerpentÕ across Australia, traced out by the curving dust lanes in the Milky Way. Needham (1981:69) explained that in Aboriginal communities of the Hunter Valley, motifs of the spiritual serpent were represented in bora ceremonies, with information about the serpent being recounted during the ceremony itself. The other animal was an emu, which is also traced by dust lanes in the Milky Way (Norris and Norris 2009). Love (1988:129Ð138) argued that the emu was an important part of the bora ceremony in southeast Australia, as did Berndt (1974:27Ð30), since male emus brood and hatch the emu chicks and rear the young (Love 1987). This is symbolic of the initiation of adolescent boys by their male elders. Needham (1981) provided an illustration of the night sky and associated stars in local Aboriginal astronomical traditions. The illustration, which cites the ÔAll FatherÕ as the star Altair, provides the positions of celestial objects in August, Ôthe month when Aboriginal initiation ceremonies were heldÕ (Needham 1981:70). During the early part of the night in August, the Milky Way stretches across the sky from the northeast to the southwest. Many early colonial reports referred to an Aboriginal religion based on a deity variously described as Baiame, Bunjil or Mungan-ngaua (Henderson 1832:147; Howitt 1904:490Ð491; Ridley 1873:268). These names roughly translate to ÔfatherÕ or Ôfather of all of usÕ (Howitt 1904:491). According to Fraser (1883:208) and Howitt (1884:458), Baiame gave his son, Daramulan, to the people and it is through Daramulan that Baiame sees all. Baiame is worshipped at the bora ceremony (Ridley 1873:269) and Daramulan is believed to come back to the earth by a pathway from the sky (Fraser 1883:212). Eliade (1996:41) reported that Baiame Ôdwells in the sky, beside a great stream of waterÕ (i.e. the Milky Way) and various reports (e.g. Berndt 1974; Hartland 1898; Howitt 1884) have claimed that the wife of Baiame (or in some cases Daramulan) is an emu. Reports of Baiame, Daramulan and Bunjil come from various cultures across southeast Australia, resulting in variations in these reports. However, they share some features, such as a close connection between bora ceremonies and the Milky Way.","pages":[3]},{"title":"Testing the Hypothesis","content":"To focus the discussion, we concentrate specifically on the hypothesis advanced by Love (1987, 1988), who argued that ancestral spirits in the heavens held bora ceremonies in the Milky Way, which we refer to as the ÔSky BoraÕ. Love based his work, in part, on Winterbotham (1957), who obtained information from a Jinibara man from southeast Qld named Gaiarbau. According to Winterbotham (1957:38), bora circles, É were always oriented towards points of the compass, the larger one to the north, and the smaller to the south ... They conformed in this rule to the position of two dark (black) spaces (circles)Ñthe Coal Sacks in the heavens. According to Love (1988 : 130Ð131), the Jinibara account identifies the Sky Bora with the Emu in the Sky (Gaiarbau et al. 1982:77; Winterbotham 1957:46). The ÔCoal SacksÕ, or Mimburi , to which Winterbotham referred, are a dark absorption nebula bordering the western constellations Crux (Southern Cross), Centaurus and Musca, representing the head of the emu, with the star BZ Crucis representing the eye. The dust lanes that run through the stars Alpha and Beta Centauri represent the neck, while the Galactic bulge, near the intersection of Sagittarius, Scorpius and Ophiuchus, represents the body. This area is the centre of our Milky Way galaxy. The dust lanes along the Milky Way through Sagittarius trace out the legs (Figure 1). The motif of the celestial emu is found across Australia (e.g. Cairns and Harney 2004; Norris and Hamacher 2009:13; Stanbridge 1861:302; Wellard 1983:51). According to Winterbotham, other Aboriginal groups also knew of the dark nebulae, including the Badjala people of Fraser Island and the adjacent mainland, who call them Wurubilum , and the Wakka Wakka people near Murgon, Qld. This concept extends beyond southeast Australia. For example, Smith (1913) explained that during an initiation ceremony in Western Australia (WA) the initiate is left tied to the ground until the Milky Way is visible. He is then asked if Ôhe can see the two dark spotsÕ and when he is able to see them, he is released. While this account is not from the area of this study, it may be similar to the example that Gaiarbau described. Gaiarbau said that bora ceremonies were not held until the celestial bora rings returned to their Ôproper points of the compassÕ (Winterbotham 1957:38). In clear winter skies in southeast Australia, the Milky Way is visible about an hour after sunset. The orientation of the plane of the Milky Way, as seen from southeast Australia an hour after sunset, changes from near vertical in the south-southeast in March to horizontal across the southern sky from east-southeast to west in June and back to vertical (but inverted) in the southwest in September. The Galactic bulge and the Coalsack (celestial emu) are not visible in the sky together an hour after sunset until May. At this time, the emu is not vertical in the sky (perpendicular to the horizon), but stretches from south to east. The only time that the Sky Bora is vertically aligned to the horizon and can be seen in the sky together an hour after sunset is in August (or later in the night as the year progresses). The Galactic plane, which goes straight through the celestial emu, is vertical in August an hour or two after sunset (earlier in the evening later in the month, Figure 2). At this time, the azimuth is approximately 213¼ (south-southwest). If LoveÕs hypothesis is correct, we expect the orientation of each bora site from the larger circle to the smaller circle to be oriented to roughly 213¼, corresponding to the time ceremonies are held (August). This expectation agrees with Needham (1981:70), who claimed that bora ceremonies in the Hunter Valley (NSW) were held in August when the Milky Way was vertical in the south-southwest. Other researchers report that bora ceremonies in Qld and NSW are held at various times of the year, as noted in the previous section (Winterbotham 1957; Mathews 1894:99). Bora ceremonies may be held at times of the year that have little or nothing to do with the position of the Milky Way in the sky, even if the ceremonies are symbolically linked to the Milky Way. For example, Mathews (1894:128) claimed that the direction of one bora ring to the other Ôis entirely dependent on the conformation of the country within which the ceremony is being heldÕ. If bora grounds are not oriented to any particular object or direction, we expect to find a roughly uniform distribution in their orientations. However, if at least some bora grounds are oriented to the position of the Sky Bora, then we expect to find a preference for south-southwest orientations when we look at the overall distribution of bora ground orientations.","pages":[4,5,6]},{"title":"Methodology","content":"To determine the orientations of bora ceremonial sites, we obtained data for 63 such sites from the following published literature: Mathews (1894, 1896a, 1896b, 1897a, 1907, 1917), Hopkins (1901), Towle (1942), Bartholomai and Breeden (1961), Anon. (1973), McBryde (1974), Steele (1984), Satterthwait and Heather (1987), and Bowdler (2001). We also obtained 1107 archaeological site cards from the NSW Aboriginal Heritage Information Management System (AHIMS) related to stone arrangements and ceremonial grounds. We then filtered the data through a rigorous selection process, discarding data for any bora ground that failed to meet any of the following criteria: The orientation of each site was measured from the centre of the largest circle to the centre of the smaller circle. If the second circle was missing, the orientation was taken from the centre of the circle to the middle of the opening. Measurements were either taken directly from the records given by the surveyor or measured from the survey with a protractor and ruler. We divided the azimuths into 16 bins (N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, NNW), each with a width of 22.5¼ with N centred at 0¡, NNE at 22.5¡, and so on (see Table 1).","pages":[6]},{"title":"Results and Analysis","content":"Of the 1170 sites obtained from the literature and AHIMS site card search, only 68 fit the specified selection criteria (Table 2, Figure 3). The 68 sites can be divided into two groups: The 46 data points whose orientations are recorded individually, are provided in Table 2 and are grouped into 22.5¼ bins, shown as a histogram in Figure 4a. The histogram reveals a clear preference for the S, SW and W orientations. Table 2 contains 34 orientations in ordinal (N, S, E, W, NW, NE, SE, SW) directions, but only 12 orientations in inter-ordinal (NNE, ENE, etc.) directions. The low number of inter-ordinal orientations suggests either that the sites tend to be oriented on ordinal points, or that some authors rounded to the nearest ordinal point. To avoid a statistical bias in our results, we re-binned the data into the eight ordinal directions, dividing the counts of each inter-ordinal bin equally between the two neighbouring ordinal bins, resulting in eight 45¼ bins (Table 1, Figure 4b). A preferred orientation to the south is evident (28% of the 46 data points), with lesser but significant preferences to the SW (17%) and W (15%) bins. The combined S, SW and W bins account for 61% of the total data points, while the remaining are evenly spread across the remaining bins. The highest peak of 12.5 orientations occurs in the S bin. We compare this result with the 22 data points from Satterthwait and Heather (1987) (hereafter referred to as ÔSHÕ) by re-binning our data to four quadrants centred on the cardinal points (N, S, E, W), as shown in Figure 4c. This reveals a strong preference for the southern quadrant and a lesser but significant preference to the western quadrant, which, when combined, account for 74% of the 46 data points. The SH data (Figure 4d) is similar, with a significant preference for the southern quadrant (68% of the 22 data points), but with an even distribution among the remaining quadrants. We then combined our 46 data points with the 22 SH data points, resulting in Figure 4e. A clear preference for the southern quadrant is evident, with 35 of the 68 orientations (51%) falling in the S bin. This result is consistent with the Love hypothesis. To determine if this is a chance clumping of a random distribution of orientations, we conducted a Monte Carlo simulation, in which 68 orientations were distributed randomly in each of the bins shown in Figure 4e. We repeated this process 100 million times. In only 303 of the 100 million runs did the number in any one bin equal or exceed 35, from which we can conclude that the likelihood of the peak in Figure 4b occurring by chance is about 3x10 -6 or 0.0003%. We therefore conclude that this distribution is clearly not the result of chance, and that the constructors of the bora rings intentionally aligned most of them to the south quadrant.","pages":[7,8]},{"title":"Discussion and Conclusion","content":"We have shown that the bora grounds studied have a preferred orientation to southerly directions and that these orientations are not the result of chance, but were deliberate. The reason for this is not known, but it is consistent with the Love hypothesis that southeast Australian bora ceremonial grounds have a preferred orientation to the celestial emu in the Milky Way in the south-southwest skies. The celestial emu is in this position in the evening sky during the month of August, the time during which Winterbotham (1957) and Needham (1981) claimed that bora ceremonies were held. Hamacher et al. (2012) showed that linear stone arrangements in NSW also have a preferred orientation to the cardinal points, especially north-south orientations. Since many stone arrangements are ceremonial sites, this lends support to the claim that orientation is an important factor utilised by Aboriginal people when laying out ceremonial sites. Although our analysis supports the Love hypothesis, it is not definitive evidence that bora grounds are oriented to the Sky Bora. Some researchers, including Winterbotham (1957) and Mathews (1894), state that many Bora ceremonies across NSW and Qld were held at various times throughout the year, which do not correspond to any particular orientation of the Milky Way. However, there is strong ethnographic evidence that the Milky Way is associated with the bora ceremony and we consider it likely that some ceremonies were timed, and bora sites oriented, such that the vertical Milky Way was visible above the path connecting the two circles during bora ceremonies. Additional research is necessary to understand these links; we are currently engaged in further research projects to explore this.","pages":[10,11]},{"title":"Acknowledgements","content":"We acknowledge the Aboriginal Elders and custodians, past and present, on whose land the bora sites are located. For archaeological data and literature sources, we thank staff from the State Library of NSW, the Australian Institute for Aboriginal and Torres Strait Islander Studies and the NSW Office of Environment and Heritage. This research made use of the TROVE and JSTOR databases, Google Maps, and the Stellarium astronomical software package. Hamacher conducted his component of this research while a PhD student at Macquarie University, but finished the analysis and writing as a staff member at the University of New South Wales.","pages":[11]},{"title":"References","content":"Anon. 1973 The layout of bora grounds. Bulletin of the Richmond River Historical Society 65:12Ð13. Bartholomai, A. and S. Breeden 1961 Stone ceremonial grounds of the Aborigines in the Darling Downs area, Queensland. Memoirs of the Queensland Museum 13(6):231Ð237. Berndt, R.M. 1974 Aboriginal Religion . Leiden: Brill Archive. Black, L. 1944 The Bora Ground: Being a Continuation of a Series on the Customs of the Aborigines of the Darling River Valley and of Central New South Wales, Part IV . Sydney: F.H. Booth. Bowdler, S. 2001 The management of Indigenous ceremonial (ÔboraÕ) sites as components of cultural landscapes. In M. Cotter, W.E. Boyd and J. Gardiner (eds), Heritage Landscapes: Understanding Place and Communities , pp.1Ð19. Lismore: Southern Cross University Press. Cairns, H.C. and B. Yidumduma Harney 2004 Dark Sparklers . Sydney: Hugh Cairns. Collins, D. 1798 An Account of the English Colony in New South Wales, Vol. I . London: T. Cadell Jr and W. Davies. Eliade, M. 1996 Patterns in Comparative Religion . Lincoln: University of Nebraska Press. Frankel, D. 1982 Earth rings at Sunbury, Victoria. Archaeology in Oceania 17:83Ð89. Fraser, J.F. 1883 The Aborigines of New South Wales. Transactions and Proceedings of the Royal Society of New South Wales 16:193Ð233. Langevad, G. 1982 Some Original Views Around Kilcoy. Book 1: The Aboriginal Perspective . Queensland Ethnographic Transcripts 1. Brisbane: Archaeology Branch, Queensland Department of Aboriginal and Islanders Advancement. Hamacher, D.W. 2012 On the Astronomical Knowledge and Traditions of Aboriginal Australians . PhD thesis by publication, Department of Indigenous Studies, Macquarie University. [ www.academia.edu/1905624/On_the_Astronomical_Knowledge_and_Traditions_of_Aboriginal_Australians ] Hamacher, D.W., R.S. Fuller and R.P. Norris 2012 Orientations of linear stone arrangements in New South Wales. Australian Archaeology 75:46Ð54.","pages":[11]},{"title":"Australian Archaeology, No. 77 | Preprint","content":"Boksenberg (eds), The Role of Astronomy in Society and Culture , pp.39Ð47. Cambridge: Cambridge University Press. Norris, R. and P. Norris 2009 Emu Dreaming: An Introduction to Australian Aboriginal Astronomy . Sydney: Emu Dreaming Press. Ridley, W. 1873 Australian languages and traditions. The Journal of the Anthropological Institute Great Britain and Ireland 2:257Ð275. Roth, W.E. 1909 On Certain Initiation ceremonies. North Queensland Ethnography 12:166-85 Satterthwait, L. and A. Heather 1987 Determinants of earth circle site location in the Moreton region, southeast Queensland. Queensland Archaeological Research 4:1Ð33. Smith, W. 1913 Sketcher, Aboriginal folk-lore. The Queenslander , 11 October, p. 8. Stanbridge, W. 1861 Some Particulars of the General Characteristics, Astronomy, and Mythology of the Tribes in the Central Part of Victoria, Southern Australia. Transactions of the Ethnological Society of London 1:286304. Steele, J.G. 1984 Aboriginal Pathways in Southeast Queensland and the Richmond River . Brisbane: University of Queensland Press. Towle, C.C. 1942 Bora ground near Ruby Creek, NSW. Victorian Naturalist 59(5):80Ð81. Winterbotham, L. 1957 GaiarbauÕs Story of the Jinibara Tribe of Southeast Queensland. Unpublished manuscript held on file at the Australian Institute for Aboriginal and Torres Strait Islander Studies, Canberra (MS #45/7460). Wellard, G.E.P. 1983 Bushlore - or this and that from here and there . Perth: Artlook Books.","pages":[13]}],"string":"[\n {\n \"title\": \"Astronomical Orientations of Bora Ceremonial Grounds in Southeast Australia\",\n \"content\": \"Robert S. Fuller 1,2 , Duane W. Hamacher 1,3 and Ray P. Norris 1,2,4 1 Warawara - Department of Indigenous Studies, Macquarie University, NSW, 2109, Australia Email: robert.fuller1@students.mq.edu.au 2 Research Centre for Astronomy, Astrophysics & Astrophotonics, Macquarie University, NSW, 2109, Australia 3 Nura Gili Centre for Indigenous Programs, University of New South Wales, NSW, 2052, Australia Email: d.hamacher@unsw.edu.au 4 CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW, 1710, Australia Email: raypnorris@gmail.com\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Abstract\",\n \"content\": \"Ethnographic evidence indicates that bora (initiation) ceremonial sites in southeast Australia, which typically comprise a pair of circles connected by a pathway, are symbolically reflected in the Milky Way as the ÔSky BoraÕ. This evidence also indicates that the position of the Sky Bora signifies the time of the year when initiation ceremonies are held. We use archaeological data to test the hypothesis that southeast Australian bora grounds have a preferred orientation to the position of the Milky Way in the night sky in August, when the plane of the galaxy from Crux to Sagittarius is roughly vertical in the evening sky to the south-southwest. We accomplish this by measuring the orientations of 68 bora grounds using a combination of data from the archaeological literature and site cards in the New South Wales Aboriginal Heritage Information Management System database. We find that bora grounds have a preferred orientation to the south and southwest, consistent with the Sky Bora hypothesis. Monte Carlo statistics show that these preferences were not the result of chance alignments, but were deliberate.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Notice to Aboriginal and Torres Strait Islander Readers\",\n \"content\": \"This paper discusses bora ceremonies and contains the names of people who have passed away. The exact locations of these sites are concealed in order to protect them. The coordinates provided are within 10 km of the site and are used only to demonstrate the general distribution of the known bora grounds in southeast Australia. Keywords: Aboriginal Australian, Cultural Astronomy, Ceremonial Sites\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Introduction\",\n \"content\": \"In traditional Aboriginal cultures across Australia, young males are taught the laws, customs and traditions of the community and undergo a transition ceremony from boyhood to manhood. This ceremony often includes a Ôrite of passageÕ event in which the initiated males undergo some form of body modification (Jacob 1991), typically involving tooth evulsion in southeast Australia (e.g. Berndt 1974:27Ð30). This ceremony goes by many names, but in Queensland (Qld) and New South Wales (NSW) it has come to be generally known as ÔboraÕ, the name used by the Kamilaroi of north-central NSW (Ridley 1873:269). Bora grounds generally consist of two circles of differing diameter connected by a pathway. The larger circle is regarded as a public space, while the smaller circle some distance away is restricted to initiates and elders. Bora ceremonies were one of the first Aboriginal cultural activities described by early Australian colonists in the Sydney region (Collins 1798:468-480; Hunter 1793:499-500). Because information about bora ceremonies is culturally sensitive, here we limit discussion of the ceremony itself. There is a variety of evidence from the anthropological literature (e.g. Berndt 1974; Love 1988; Winterbotham 1957) that bora ceremonies are related to the Milky Way and that ceremonial grounds are oriented to the position of the Milky Way in the night sky at particular times of the year. In this paper, we begin by exploring connections between bora ceremonies and the Milky Way using ethnographic and ethnohistoric literature. We then use the archaeological record to determine if bora grounds are oriented to the position of the Milky Way at particular times of the year. Finally, we use Monte Carlo statistics to see if these orientations were deliberate or the result of chance.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"Bora Ceremonial Grounds\",\n \"content\": \"The layout of bora grounds is similar across southeast Australia, with only minor differences from region to region (Bowdler 2001:3; Mathews 1894:99). Several reports (e.g. Black 1944; Collins 1798:391; Fraser 1883; Howitt 1904; Mathews 1897a) describe the grounds as consisting of two rings of different sizes, connected by a pathway. In some places, Bora sites may comprise three or more rings (Steele 1984; Bowdler 2001). The border of each ring is made of raised earth or stone, and the area within is cleared of debris and the earth is stamped until firm. The larger ring, which is considered public, has a typical diameter of 20Ð30 m. The smaller ring (generally 10Ð15 m diameter) is considered the sacred area, where body modification takes place, and is restricted to initiates and elders. The two rings are connected by a pathway that ranges from a few tens to a few hundred metres in length. In 2004, an Aboriginal man from Marulan, NSW advised that parts of many such sites were destroyed immediately after the ceremony to conceal their location (Hardie 2004). For this reason, some bora sites reported in the archaeological literature feature only a single circle, with the smaller, sacred circle having been destroyed. Bora grounds are distributed throughout southeast Australia, covering most of NSW and southern Qld and may extend into South Australia (Howitt 1904:501Ð508) and northern Qld (Roth 1909). Ceremonial rings, which may be bora grounds, have been found near Sunbury, Victoria (Vic.), although there are no ethnographic records attesting to their ceremonial use (Frankel 1982). Howitt (1904:512) cited a western boundary for bora running from the mouth of the Murray River to the Gulf of Carpentaria. Mathews (1897b:114) noted the bora can be found across three-quarters of NSW and some distance into western Qld, with a boundary extending from Twofold Bay near Eden, NSW in the south, to Moulamein, NSW in the west, and Barringun, Qld in the north. We recognise that the geographical area covered by this paper includes several distinct language groups, each of whom may have separate culture and traditions, and it may be misleading to aggregate the data from such a wide area. However, (a) the existence of similarly constructed bora rings implies some commonality in culture, and (b) aggregating orientations from a large geographic area will dilute any preferred orientations arising from a single Aboriginal group, rather than forming a correlation of spurious significance. According to Love (1988), the bora ceremonies were predominantly held in August each year, although other authors report a variety of dates including MarchÐMay (Winterbotham 1957), AprilÐJune (Mathews 1894:99), MayÐJuly (Mathews 1894), August (Needham 1981:70), SeptemberÐNovember (Winterbotham 1957), and OctoberÐDecember (Mathews 1894). This suggests that, in some cases, a number of variables influence the date of the bora ceremony, including the availability of food and water or having a sufficient number of boys to initiate (e.g. Mathews 1910). While these factors vary across the region, here we test the hypothesis advanced by Love (1988) who presents evidence associating the bora ceremony with the night sky and the orientation of the Milky Way, and suggests that most initiation ceremonies occur around August.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"Anthropological Support of an Astronomical Connection\",\n \"content\": \"It is well established that the night sky plays a significant role in several Aboriginal cultures (e.g. Cairns and Harney 2004; Johnson 1998; Norris and Hamacher 2009; Hamacher 2012). In Aboriginal astronomical traditions, dark spaces within the Milky Way are as significant as bright objects. Two animals symbolically link bora ceremonies to these dark spaces. One was a spiritual serpent, commonly referred to as the ÔRainbow SerpentÕ across Australia, traced out by the curving dust lanes in the Milky Way. Needham (1981:69) explained that in Aboriginal communities of the Hunter Valley, motifs of the spiritual serpent were represented in bora ceremonies, with information about the serpent being recounted during the ceremony itself. The other animal was an emu, which is also traced by dust lanes in the Milky Way (Norris and Norris 2009). Love (1988:129Ð138) argued that the emu was an important part of the bora ceremony in southeast Australia, as did Berndt (1974:27Ð30), since male emus brood and hatch the emu chicks and rear the young (Love 1987). This is symbolic of the initiation of adolescent boys by their male elders. Needham (1981) provided an illustration of the night sky and associated stars in local Aboriginal astronomical traditions. The illustration, which cites the ÔAll FatherÕ as the star Altair, provides the positions of celestial objects in August, Ôthe month when Aboriginal initiation ceremonies were heldÕ (Needham 1981:70). During the early part of the night in August, the Milky Way stretches across the sky from the northeast to the southwest. Many early colonial reports referred to an Aboriginal religion based on a deity variously described as Baiame, Bunjil or Mungan-ngaua (Henderson 1832:147; Howitt 1904:490Ð491; Ridley 1873:268). These names roughly translate to ÔfatherÕ or Ôfather of all of usÕ (Howitt 1904:491). According to Fraser (1883:208) and Howitt (1884:458), Baiame gave his son, Daramulan, to the people and it is through Daramulan that Baiame sees all. Baiame is worshipped at the bora ceremony (Ridley 1873:269) and Daramulan is believed to come back to the earth by a pathway from the sky (Fraser 1883:212). Eliade (1996:41) reported that Baiame Ôdwells in the sky, beside a great stream of waterÕ (i.e. the Milky Way) and various reports (e.g. Berndt 1974; Hartland 1898; Howitt 1884) have claimed that the wife of Baiame (or in some cases Daramulan) is an emu. Reports of Baiame, Daramulan and Bunjil come from various cultures across southeast Australia, resulting in variations in these reports. However, they share some features, such as a close connection between bora ceremonies and the Milky Way.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"Testing the Hypothesis\",\n \"content\": \"To focus the discussion, we concentrate specifically on the hypothesis advanced by Love (1987, 1988), who argued that ancestral spirits in the heavens held bora ceremonies in the Milky Way, which we refer to as the ÔSky BoraÕ. Love based his work, in part, on Winterbotham (1957), who obtained information from a Jinibara man from southeast Qld named Gaiarbau. According to Winterbotham (1957:38), bora circles, É were always oriented towards points of the compass, the larger one to the north, and the smaller to the south ... They conformed in this rule to the position of two dark (black) spaces (circles)Ñthe Coal Sacks in the heavens. According to Love (1988 : 130Ð131), the Jinibara account identifies the Sky Bora with the Emu in the Sky (Gaiarbau et al. 1982:77; Winterbotham 1957:46). The ÔCoal SacksÕ, or Mimburi , to which Winterbotham referred, are a dark absorption nebula bordering the western constellations Crux (Southern Cross), Centaurus and Musca, representing the head of the emu, with the star BZ Crucis representing the eye. The dust lanes that run through the stars Alpha and Beta Centauri represent the neck, while the Galactic bulge, near the intersection of Sagittarius, Scorpius and Ophiuchus, represents the body. This area is the centre of our Milky Way galaxy. The dust lanes along the Milky Way through Sagittarius trace out the legs (Figure 1). The motif of the celestial emu is found across Australia (e.g. Cairns and Harney 2004; Norris and Hamacher 2009:13; Stanbridge 1861:302; Wellard 1983:51). According to Winterbotham, other Aboriginal groups also knew of the dark nebulae, including the Badjala people of Fraser Island and the adjacent mainland, who call them Wurubilum , and the Wakka Wakka people near Murgon, Qld. This concept extends beyond southeast Australia. For example, Smith (1913) explained that during an initiation ceremony in Western Australia (WA) the initiate is left tied to the ground until the Milky Way is visible. He is then asked if Ôhe can see the two dark spotsÕ and when he is able to see them, he is released. While this account is not from the area of this study, it may be similar to the example that Gaiarbau described. Gaiarbau said that bora ceremonies were not held until the celestial bora rings returned to their Ôproper points of the compassÕ (Winterbotham 1957:38). In clear winter skies in southeast Australia, the Milky Way is visible about an hour after sunset. The orientation of the plane of the Milky Way, as seen from southeast Australia an hour after sunset, changes from near vertical in the south-southeast in March to horizontal across the southern sky from east-southeast to west in June and back to vertical (but inverted) in the southwest in September. The Galactic bulge and the Coalsack (celestial emu) are not visible in the sky together an hour after sunset until May. At this time, the emu is not vertical in the sky (perpendicular to the horizon), but stretches from south to east. The only time that the Sky Bora is vertically aligned to the horizon and can be seen in the sky together an hour after sunset is in August (or later in the night as the year progresses). The Galactic plane, which goes straight through the celestial emu, is vertical in August an hour or two after sunset (earlier in the evening later in the month, Figure 2). At this time, the azimuth is approximately 213¼ (south-southwest). If LoveÕs hypothesis is correct, we expect the orientation of each bora site from the larger circle to the smaller circle to be oriented to roughly 213¼, corresponding to the time ceremonies are held (August). This expectation agrees with Needham (1981:70), who claimed that bora ceremonies in the Hunter Valley (NSW) were held in August when the Milky Way was vertical in the south-southwest. Other researchers report that bora ceremonies in Qld and NSW are held at various times of the year, as noted in the previous section (Winterbotham 1957; Mathews 1894:99). Bora ceremonies may be held at times of the year that have little or nothing to do with the position of the Milky Way in the sky, even if the ceremonies are symbolically linked to the Milky Way. For example, Mathews (1894:128) claimed that the direction of one bora ring to the other Ôis entirely dependent on the conformation of the country within which the ceremony is being heldÕ. If bora grounds are not oriented to any particular object or direction, we expect to find a roughly uniform distribution in their orientations. However, if at least some bora grounds are oriented to the position of the Sky Bora, then we expect to find a preference for south-southwest orientations when we look at the overall distribution of bora ground orientations.\",\n \"pages\": [\n 4,\n 5,\n 6\n ]\n },\n {\n \"title\": \"Methodology\",\n \"content\": \"To determine the orientations of bora ceremonial sites, we obtained data for 63 such sites from the following published literature: Mathews (1894, 1896a, 1896b, 1897a, 1907, 1917), Hopkins (1901), Towle (1942), Bartholomai and Breeden (1961), Anon. (1973), McBryde (1974), Steele (1984), Satterthwait and Heather (1987), and Bowdler (2001). We also obtained 1107 archaeological site cards from the NSW Aboriginal Heritage Information Management System (AHIMS) related to stone arrangements and ceremonial grounds. We then filtered the data through a rigorous selection process, discarding data for any bora ground that failed to meet any of the following criteria: The orientation of each site was measured from the centre of the largest circle to the centre of the smaller circle. If the second circle was missing, the orientation was taken from the centre of the circle to the middle of the opening. Measurements were either taken directly from the records given by the surveyor or measured from the survey with a protractor and ruler. We divided the azimuths into 16 bins (N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, NNW), each with a width of 22.5¼ with N centred at 0¡, NNE at 22.5¡, and so on (see Table 1).\",\n \"pages\": [\n 6\n ]\n },\n {\n \"title\": \"Results and Analysis\",\n \"content\": \"Of the 1170 sites obtained from the literature and AHIMS site card search, only 68 fit the specified selection criteria (Table 2, Figure 3). The 68 sites can be divided into two groups: The 46 data points whose orientations are recorded individually, are provided in Table 2 and are grouped into 22.5¼ bins, shown as a histogram in Figure 4a. The histogram reveals a clear preference for the S, SW and W orientations. Table 2 contains 34 orientations in ordinal (N, S, E, W, NW, NE, SE, SW) directions, but only 12 orientations in inter-ordinal (NNE, ENE, etc.) directions. The low number of inter-ordinal orientations suggests either that the sites tend to be oriented on ordinal points, or that some authors rounded to the nearest ordinal point. To avoid a statistical bias in our results, we re-binned the data into the eight ordinal directions, dividing the counts of each inter-ordinal bin equally between the two neighbouring ordinal bins, resulting in eight 45¼ bins (Table 1, Figure 4b). A preferred orientation to the south is evident (28% of the 46 data points), with lesser but significant preferences to the SW (17%) and W (15%) bins. The combined S, SW and W bins account for 61% of the total data points, while the remaining are evenly spread across the remaining bins. The highest peak of 12.5 orientations occurs in the S bin. We compare this result with the 22 data points from Satterthwait and Heather (1987) (hereafter referred to as ÔSHÕ) by re-binning our data to four quadrants centred on the cardinal points (N, S, E, W), as shown in Figure 4c. This reveals a strong preference for the southern quadrant and a lesser but significant preference to the western quadrant, which, when combined, account for 74% of the 46 data points. The SH data (Figure 4d) is similar, with a significant preference for the southern quadrant (68% of the 22 data points), but with an even distribution among the remaining quadrants. We then combined our 46 data points with the 22 SH data points, resulting in Figure 4e. A clear preference for the southern quadrant is evident, with 35 of the 68 orientations (51%) falling in the S bin. This result is consistent with the Love hypothesis. To determine if this is a chance clumping of a random distribution of orientations, we conducted a Monte Carlo simulation, in which 68 orientations were distributed randomly in each of the bins shown in Figure 4e. We repeated this process 100 million times. In only 303 of the 100 million runs did the number in any one bin equal or exceed 35, from which we can conclude that the likelihood of the peak in Figure 4b occurring by chance is about 3x10 -6 or 0.0003%. We therefore conclude that this distribution is clearly not the result of chance, and that the constructors of the bora rings intentionally aligned most of them to the south quadrant.\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"Discussion and Conclusion\",\n \"content\": \"We have shown that the bora grounds studied have a preferred orientation to southerly directions and that these orientations are not the result of chance, but were deliberate. The reason for this is not known, but it is consistent with the Love hypothesis that southeast Australian bora ceremonial grounds have a preferred orientation to the celestial emu in the Milky Way in the south-southwest skies. The celestial emu is in this position in the evening sky during the month of August, the time during which Winterbotham (1957) and Needham (1981) claimed that bora ceremonies were held. Hamacher et al. (2012) showed that linear stone arrangements in NSW also have a preferred orientation to the cardinal points, especially north-south orientations. Since many stone arrangements are ceremonial sites, this lends support to the claim that orientation is an important factor utilised by Aboriginal people when laying out ceremonial sites. Although our analysis supports the Love hypothesis, it is not definitive evidence that bora grounds are oriented to the Sky Bora. Some researchers, including Winterbotham (1957) and Mathews (1894), state that many Bora ceremonies across NSW and Qld were held at various times throughout the year, which do not correspond to any particular orientation of the Milky Way. However, there is strong ethnographic evidence that the Milky Way is associated with the bora ceremony and we consider it likely that some ceremonies were timed, and bora sites oriented, such that the vertical Milky Way was visible above the path connecting the two circles during bora ceremonies. Additional research is necessary to understand these links; we are currently engaged in further research projects to explore this.\",\n \"pages\": [\n 10,\n 11\n ]\n },\n {\n \"title\": \"Acknowledgements\",\n \"content\": \"We acknowledge the Aboriginal Elders and custodians, past and present, on whose land the bora sites are located. For archaeological data and literature sources, we thank staff from the State Library of NSW, the Australian Institute for Aboriginal and Torres Strait Islander Studies and the NSW Office of Environment and Heritage. This research made use of the TROVE and JSTOR databases, Google Maps, and the Stellarium astronomical software package. Hamacher conducted his component of this research while a PhD student at Macquarie University, but finished the analysis and writing as a staff member at the University of New South Wales.\",\n \"pages\": [\n 11\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Anon. 1973 The layout of bora grounds. Bulletin of the Richmond River Historical Society 65:12Ð13. Bartholomai, A. and S. Breeden 1961 Stone ceremonial grounds of the Aborigines in the Darling Downs area, Queensland. Memoirs of the Queensland Museum 13(6):231Ð237. Berndt, R.M. 1974 Aboriginal Religion . Leiden: Brill Archive. Black, L. 1944 The Bora Ground: Being a Continuation of a Series on the Customs of the Aborigines of the Darling River Valley and of Central New South Wales, Part IV . Sydney: F.H. Booth. Bowdler, S. 2001 The management of Indigenous ceremonial (ÔboraÕ) sites as components of cultural landscapes. In M. Cotter, W.E. Boyd and J. Gardiner (eds), Heritage Landscapes: Understanding Place and Communities , pp.1Ð19. Lismore: Southern Cross University Press. Cairns, H.C. and B. Yidumduma Harney 2004 Dark Sparklers . Sydney: Hugh Cairns. Collins, D. 1798 An Account of the English Colony in New South Wales, Vol. I . London: T. Cadell Jr and W. Davies. Eliade, M. 1996 Patterns in Comparative Religion . Lincoln: University of Nebraska Press. Frankel, D. 1982 Earth rings at Sunbury, Victoria. Archaeology in Oceania 17:83Ð89. Fraser, J.F. 1883 The Aborigines of New South Wales. Transactions and Proceedings of the Royal Society of New South Wales 16:193Ð233. Langevad, G. 1982 Some Original Views Around Kilcoy. Book 1: The Aboriginal Perspective . Queensland Ethnographic Transcripts 1. Brisbane: Archaeology Branch, Queensland Department of Aboriginal and Islanders Advancement. Hamacher, D.W. 2012 On the Astronomical Knowledge and Traditions of Aboriginal Australians . PhD thesis by publication, Department of Indigenous Studies, Macquarie University. [ www.academia.edu/1905624/On_the_Astronomical_Knowledge_and_Traditions_of_Aboriginal_Australians ] Hamacher, D.W., R.S. Fuller and R.P. Norris 2012 Orientations of linear stone arrangements in New South Wales. Australian Archaeology 75:46Ð54.\",\n \"pages\": [\n 11\n ]\n },\n {\n \"title\": \"Australian Archaeology, No. 77 | Preprint\",\n \"content\": \"Boksenberg (eds), The Role of Astronomy in Society and Culture , pp.39Ð47. Cambridge: Cambridge University Press. Norris, R. and P. Norris 2009 Emu Dreaming: An Introduction to Australian Aboriginal Astronomy . Sydney: Emu Dreaming Press. Ridley, W. 1873 Australian languages and traditions. The Journal of the Anthropological Institute Great Britain and Ireland 2:257Ð275. Roth, W.E. 1909 On Certain Initiation ceremonies. North Queensland Ethnography 12:166-85 Satterthwait, L. and A. Heather 1987 Determinants of earth circle site location in the Moreton region, southeast Queensland. Queensland Archaeological Research 4:1Ð33. Smith, W. 1913 Sketcher, Aboriginal folk-lore. The Queenslander , 11 October, p. 8. Stanbridge, W. 1861 Some Particulars of the General Characteristics, Astronomy, and Mythology of the Tribes in the Central Part of Victoria, Southern Australia. Transactions of the Ethnological Society of London 1:286304. Steele, J.G. 1984 Aboriginal Pathways in Southeast Queensland and the Richmond River . Brisbane: University of Queensland Press. Towle, C.C. 1942 Bora ground near Ruby Creek, NSW. Victorian Naturalist 59(5):80Ð81. Winterbotham, L. 1957 GaiarbauÕs Story of the Jinibara Tribe of Southeast Queensland. Unpublished manuscript held on file at the Australian Institute for Aboriginal and Torres Strait Islander Studies, Canberra (MS #45/7460). Wellard, G.E.P. 1983 Bushlore - or this and that from here and there . Perth: Artlook Books.\",\n \"pages\": [\n 13\n ]\n }\n]"}}},{"rowIdx":86,"cells":{"bibcode":{"kind":"string","value":"2013BrJPh..43..375K"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1305.2363.pdf"},"content":{"kind":"string","value":"\nUltra-High Energy Cosmic Rays: Results and Prospects\nKarl-Heinz Kampert\nUniversity of Wuppertal, Department of Physics, Gaußstrasse 20, D-42119 Wuppertal 1\nAbstract. Observations of cosmic rays have been improved at all energies, both in terms of higher statistics and reduced systematics. As a result, the all particle cosmic ray energy spectrum starts to exhibit more structures than could be seen previously. Most importantly, a second knee in the cosmic ray spectrum - dominated by heavy primaries - is reported just below 10 17 eV. The light component, on the other hand, exhibits an ankle like feature above 10 17 eV and starts to dominate the flux at the ankle. The key question at the highest energies is about the origin of the flux suppression observed at energies above 5 · 10 19 eV. Is this the long awaited GZK-effect or the exhaustion of sources? The key to answering this question is again given by the still largely unknown mass composition at the highest energies. Data from different observatories don't quite agree and common efforts have been started to settle that question. The high level of isotropy observed even at the highest energies starts to challenge a proton dominated composition if extragalactic (EG) magnetic fields are on the order of a few nG or more. We shall discuss the experimental and theoretical progress in the field and the prospects for the next decade.\nKeywords:\nUHECR, EAS\nPACS:\n13.85.Tp, 96.50.sd, 96.50.sb,\nINTRODUCTION\nThe Texas-Symposium 2012 completes a series of conferences at which the discovery of cosmic rays (CR) a hundred years ago by Franz Viktor Hess has been commemorated. Less known is a breakthrough made 50 years ago by John Linsley: in 1962 he reported the first observation of a primary CR particle with an energy exceeding 10 20 eV [1]. This event remains one of the most energetic CRs ever recorded and Linsley was extremely lucky to observe such an event after just three years of data taking of the 2 km 2 large Volcano Ranch air shower array. The cosmic microwave background (CMB) radiation, discovered three years later, immediately led to the prediction of a flux suppression either due to photo-pion production by protons propagating through the CMB at energies above 5 · 10 19 eV or due to photodisintegration of nuclei at about the same threshold energy. This process is known as GZK-effect, predicted independently by Greisen and by Zatsepin and Kuz'min [2, 3]. This has been the only firm prediction about a structure in the CR energy spectrum [4] and it has taken nearly 50 years to observe such a feature in data [5, 6]. However, can we be sure about having observed the GZK-effect? The spectral feature may equally be caused by the exhaustion of nearby sources or by a mixture of both as will be discussed below.\nAt lower energies, Kulikov and Khristiansen [7] in 1958 reported a structure in the shower size spectrum which became known as the 'knee' in the CR spectrum. Observations made by KASCADE [8] and other air shower experiments showed that the mean mass increases above the knee, indicating that the knee marks the maximum acceleration energy of the most abundant Galactic sources. This led to speculations that heavy primaries would experience the same limitation of particle acceleration and a second, so-called 'Iron-knee', would be observed around E Fe knee ∼ 26 × E p knee . Such an observation has now been reported and it may mark the end of the Galactic CR spectrum.\nLarge- and small-scale anisotropies in the arrival directions have been reported at TeV energies and now reach to beyond a PeV. This has come as a surprise and its interpretation starts to result in a better understanding and modeling of CR propagation within our Galaxy and about the transition from Galactic to EG CRs. At the highest energies, only upper limits on large scale anisotropies have been reported so far but, due to limited statistics, the amplitudes cannot be probed down to the levels observed below the knee region. Instead, a weak correlation of the highest energy particles to the position of nearby AGN has been reported by Auger [9]. This gave support to the picture that some fraction of the highest energy CRs results from sources within about 200 Mpc distance.\nMuch progress has also been made in particle acceleration emphasizing the importance of non-linear effects in diffuse shock acceleration (DSA) with magnetic field amplification due to CR current driven instabilities. These effects may not only substantially increase the maximum energy reachable in CR accelerators but may also reduce the time scales required for the acceleration process. While Galactic CRs are believed to originate from supernova remnants (SNR), those at the highest energies are thought to originate in the lobes of Radio Galaxies (RG) if they are large and luminous enough and, again, a substantial energy is contained in the turbulent component of the magnetic field.\nThus, it is fair so say that enormous progress has been made in CR physics particularly in recent years, both in observations and in accompanying theory. However, despite such advancements, the key questions about the CR origin and acceleration remain open even 100 years after their discovery. This paper aims to address some key topics in the field.\nTHE COSMIC RAY ENERGY SPECTRUM\nRecent progress in the knee-to-ankle energy range has been driven mostly by KASCADE-Grande with Tunka and IceTop ramping up and providing more data with high statistics and good resolution. Using complex 2-dimensional unfolding techniques to the electron vs muon numbers measured on shower-by-shower basis by the KASCADE air shower experiment, the mean mass was shown to become heavier above the knee energy with the energy spectra of primary mass groups supporting a scaling with rigidity according to E Z knee glyph[similarequal] Z × 3 · 10 15 eV [8], such as was suggested long time ago by Peters [10]. This observation, supported by other experiments, has renewed the question about the existence of a Fe-like knee at about 10 17 eV. Such a structure has been reported very recently and is shown in Fig. 1. The significance of the second knee at E glyph[similarequal] 80 PeV in the all-particle energy spectrum of KASCADE-Grande is just above\n17\n\n\n
FIGURE 1. All-particle, electron-poor, and electron rich energy spectra from KASCADE-Grande. The all-particle (black triangles; 105,000 events) and heavy enriched spectrum (blue circles; 52,000 events) is taken from [11] and the all-particle (grey squares) and light primary spectrum (red triangles; 6,300 events) results from a larger data set and employs stronger cuts to the light-component to select essentially p+He primaries [13]. The bands indicate systematic uncertainties resulting mostly from hadronic interaction models. The heavy enriched data sample exhibits a knee at 10 16 . 9 eV with a statistical significance of 3 . 5 s while the ankle-like feature in the light component is found at 10 17 . 1 eV with a significance of 5 . 8 s .
\n\n2 s but increases to 3 . 5 s for the electron poor (heavy) sample [11]. Similarly, IceTop data [12] show an indication of a flattening above 22 PeV, i.e. in the energy range between the two knees. Another very interesting recent result by KASCADE-Grande is reported in [13]. Using a larger data set and applying stronger cuts to electron-rich showers than were applied in [11], to accept essentially only p+He primaries, there is an ankle-like feature at 10 17 . 1 eV with a significance of 5 . 8 s .\nObviously, the CR energy spectrum, once measured with high precision, exhibits much more structure and information than just the knee energy and the indices of an apparent power-law like spectrum below and above. The observation of the 'Fe-knee' and 'p-ankle' (with 'Fe' and 'p' meant as synonym for 'heavy' and 'light' primaries, respectively) is a remarkable achievement. The Fe-knee at 8 · 10 16 eV supports the picture of a rigidity scaling - also named the 'Peters cycle' [10] - in the knee energy range and the p-ankle E glyph[similarequal] 1 . 2 · 10 17 eV has in fact been expected because of the steep fall-off of the p-component at the knee [8] and the p-like composition at the ankle (see next section). Thus, the p-ankle would either mark the transition from Galactic to EG sources or the onset of a new high energy (Galactic) source population (see e.g. [14, 15]).\nAt the highest energies, from the ankle to beyond 10 20 eV, the Pierre Auger Observatory [16, 17] is the flagship in the field with an accumulated exposure of about 30 000 km 2 sr yr. The Telescope Array [18], due to a later start and its more than 4 times smaller area, has collected about 10 times less events. A detailed comparison of the energy spectra of various observatories is presented in Fig. 2. As discussed in great detail in [19], it is found that the energy spectra determined by the larger experiments are con-\n\n\n
FIGURE 2. Compilation of cosmic ray energy spectra, with the flux multiplied by E 3 , published by Auger (combined Hybrid/SD), TA SD, Yakutsk SD, HiRes I, and HiRes II after energy-rescaling as shown in the figure has been applied. The reference spectrum is the average of those from Auger and TA. From [19] where also references to the respective data sets can be found.
\n\nsistent in normalization and shape after energy scaling factors, as shown in Fig. 2, are applied. Those scaling factors are within systematic uncertainties in the energy scale quoted by the experiments. This is quite remarkable and demonstrates how well the data are understood. Nevertheless, cross-checks of photometric calibrations and atmospheric corrections have been started and as a next step, common models (e.g. fluorescence yield) should be used where possible. The data in Fig. 2 clearly exhibit the ankle at ∼ 4 · 10 18 eV and a flux suppression above ∼ 4 · 10 19 eV. The flux suppression at the highest energies is in accordance with the long-awaited GZK-effect [5, 6]. However, as discussed below, the data of the Auger observatory suggest that the maximum energy of nearby sources or the source population is seen, instead.\nCOSMIC RAY COMPOSITION AND INTERACTION MODELS\nObviously the energy spectra by itself, despite their high level of precision reached, do not allow one to conclude about the origin of the spectral structures and thereby about the origin of CRs in different energy regions. Additional key information is obtained from the mass composition of CRs. Unfortunately, the measurement of primary masses is the most difficult task in air shower physics as such measurements rely on comparisons of data to EAS simulations with the latter serving as reference [20]. EAS simulations, however, are subject to uncertainties mostly because hadronic interaction models need to be employed at energy ranges much beyond those accessible to man-made particle accel-\n\n\n
FIGURE 3. Left: Average logarithmic mass of cosmic rays as a function of energy derived from X max measurements with optical detectors for the EPOS 1.99 interaction model. Lines are estimates of the experimental systematics, i.e. upper and lower boundaries of the data presented [20]. Right: Propagated CR spectrum assuming a mixed composition similar to the Galactic one with a maximum energy at the sources of E max ( Z ) = Z × 4 · 10 18 eV and a spectral index b = 1 . 6 [24].
\n\nerators. Therefore, the advent of LHC data, particularly those measured in the extreme forward region of the collisions, is of great importance to CR and EAS physics and have been awaited with great interest [21]. Remarkably, interaction models employed in EAS simulations provide a somewhat better description of global observables (multiplicities, p ⊥ -distributions, forward and transverse energy flow, etc.) than typical tunes of HEP models, such as PYTHIA or PHOJET [22]. This demonstrates once more that the CR community has taken great care in extrapolating models to the highest energies. Moreover, as demonstrated e.g. in [23], CR data provide important information about particle physics at centre-of-mass energies ten or more times higher than is accessible at LHC. The pp -inelastic cross section extracted from data of the Auger Observatory supports only a modest rise of the inelastic cross section with energy [23].\nA careful analysis of composition data from various experiments has been presented in [20] with exemplary results depicted in Fig. 3 (left). These data complement those of the energy spectrum in a remarkable way. As can be seen, the breaks in the energy spectrum coincide with the turning points of changes in the composition: the mean mass becomes increasingly heavier above the knee, reaches a maximum at the 2 nd knee, another minimum at the ankle before it starts to rise again towards the highest energies. Different interaction models provide the same answer concerning changes in the composition but differ by their absolute values of 〈 ln A 〉 . It should also be noted that the suggested increase in the mean mass at the highest energies is not without dispute. It has been looked at in great detail in [25]. At ultra-high energies, the Auger data suggest a larger 〈 ln A 〉 than all other experiments. TA and Yakutsk are consistent within systematic uncertainties with Auger data while HiRes is compatible with Auger only at energies below 10 18 . 5 eV when using QGSJet-II. When using the SIBYLL model, Auger and HiRes become compatible within a larger energy range [25].\nThe importance of measuring the composition up to the highest energy cannot be\noverstated as it will be the key to answering the question about the origin of the GZKlike flux suppression. The same mechanism of limiting source energy that appears to cause the increasingly heavy above the knee may work also for EG-CRs above the ankle. Thereby, the break at ∼ 4 · 10 19 eV may mark the maximum energy of nearby EG CR-accelerators, rather than the GZK-effect. This is shown in Fig. 3 (right), where propagated CR spectra are shown for a maximum energy at the source of E max ( Z ) = Z × 4 · 10 18 eV and assuming a hard spectral source index of b = 1 . 6 [24]. Clearly, such a - in view of the hard spectral index - more exotic scenario provides a good description of the energy spectrum. Moreover, other than the GZK-like interpretation, it also describes the 〈 X max 〉 and the fluctuation RMS( X max ) of the Pierre Auger Observatory [26].\nA mixture of light and intermediate/heavy primaries at the highest energies may also explain the low level of directional correlations to nearby AGN. Enhancements, presently foreseen by the Auger Collaboration will address this issue.\nTwo models about the putative transition from Galactic- to EG-CRs have received much attention: In the classical 'ankle model' the transition is assumed to occur at the ankle. In this model, Galactic CRs above the 2 nd knee are dominated by heavy primaries before protons of EG origin start to take over and to dominate at the ankle. In the dipmodel [27], on the other hand, the transition occurs already at the 2 nd knee and is characterized by a sharp change of the composition from Galactic iron to EG protons while the ankle is due to e + e -production of protons in the CMB. A third, 'mixed composition', model has been suggested more recently [28] in which EG-CRs taking over are not considered being protons but an EG mixed CR composition. Clearly, the dip-model requires a proton dominated composition essentially at all energies starting somewhat above the 2 nd knee. The answer may be difficult to determine based on 〈 X max 〉 or 〈 ln A 〉 alone. A much better quantity would again be the RMS of these quantities, such as studied at higher energies in [26]. A rather abrupt change of composition as required by the dip-model near the 2 nd knee vs a smooth change of composition as expected near the ankle in the ankle model, should become distinguishable by the RMS ( X max ) -values already in the very near future. This has been a prime motivation for the HEAT and TALE extensions of Auger and TA, respectively.\nANISOTROPIES AT DIFFERENT ENERGIES AND ANGULAR SCALES\nThe main obstacle in identifying Galactic CR-sources is the diffusion of CRs in the Galactic magnetic field (GMF), erasing directional information on the position of their sources. The GMF has a turbulent component that varies on scales between l min ∼ 1 AU and l max few to 200 pc. Since CRs scatter on inhomogeneities with variation scales comparable to their Larmor radius, the propagation of Galactic CRs in the GMF resembles a random walk and is well described by the diffusion approximation. Large scale anisotropies observed by the Tibet Air-Shower experiment [31] in the northern hemisphere for CRs at energies of a few to several hundred TeV and at angular scales of 60 · and above, thus came as a surprise. The data have been confirmed and complemented by Milagro [32] and more recently also by high statistics measurements of IceTop in the southern hemisphere [33, 34] (cf. Fig. 4). Moreover, the structure changes with energy\n\n\n\n\n\n
FIGURE 4. Left: Upper limits on the equatorial dipole component as a function of energy, from several experiments [29]. Also shown are the predictions up to 1 EeV from two different Galactic magnetic field models with different symmetries (A and S), the predictions for a purely Galactic origin of UHECRs up to a few tens of 10 19 eV (Gal), and the expectations from the Compton-Getting effect for an EG component isotropic in the CMB rest frame (C-G Xgal) with references given in [29]. Right: Reconstructed declination and right-ascension of the dipole with corresponding uncertainties, as a function of the energy, in orthographic projection [30].
\n\nand appears to persist to beyond PeV energies. This anisotropy reveals a new feature of the Galactic cosmic-ray distribution, which must be incorporated into theories of the origin and propagation of cosmic rays. As was emphasized e.g. in [35, 28], changes of the anisotropy patterns with energy can, in principle, be accounted for by specific distributions (in space and time) and individual source energy spectra of nearby recent SNRs.\nAnother long-standing problem is the high level of isotropy even at energies beyond 10 18 eV. For non-relativistic diffusive acceleration g g = 2 and the index of the observed spectrum, g g + m = 2 . 7, one derives m = 0 . 7. At very high energy this results in a too large anisotropy, d ( E ) GLYPH<181> D ( E ) GLYPH<181> E m and in a too small traversed grammage, X cr ( E ) GLYPH<181> 1 / D ( E ) , with the diffusion coefficient D ( E ) , and would contradict experimental data (cf. Fig. 4). However, d ( E ) GLYPH<181> D ( E ) refers again to an average of the anisotropy amplitude computed over many source realizations, i.e. over a continuum of sources and thus does not apply to concrete realizations of nearby SNRs and turbulent magnetic fields within the cosmic ray scattering length. Moreover, as pointed out in [35], diffusion breaks down for propagation of CRs within our Galaxy at E > ∼ 10 17 eV. Recently, the Pierre Auger Observatory reported the first large scale anisotropy searches as a function of both right ascension and declination. Again, within the systematic uncertainties, no significant deviation from isotropy is revealed and the upper limits on dipole and quadrupole amplitudes challenge an origin from stationary galactic sources densely distributed in the galactic disk and emitting predominantly light particles in all directions. In Fig. 4 (right), the corresponding directions are shown in orthographic projection with the associated uncertainties, as a function of the energy. Both angles are expected to be randomly distributed in the case of independent samples whose parent distribution is isotropic. It is\nthus interesting to note that all reconstructed declinations are in the equatorial southern hemisphere, and to note also the intriguing smooth alignment of the phases in right ascension as a function of the energy.\nDirectional correlations of the most energetic CRs with nearby AGN observed by the Pierre Auger Observatory provided the first signature about anisotropies of the most energetic CRs and thereby about their EG origin [9, 36, 37]. Initially very strong, the fraction of Auger events above 55 EeV correlating within 3 . 1 · with a nearby ( z ≤ 0 . 018) AGN from the VCV-catalogue has stabilized at a level of ( 33 ± 5 ) % [38]. With an accidental rate for an isotropic distribution of 21 %, this corresponds to a chance probability of less than 1 %. Recently, TA reported a correlation fraction of 44 % at an isotropic fraction of 24 % yielding a chance probability of about 2 % [39]. Thus, the data are in perfect agreement with each other yielding a combined chance probability of observing such a correlation at the 10 -3 level. However, more statistics is needed to consolidate the picture and to allow subdividing data sets in bins of related CR observables. The sky region around Cen A remains populated by a larger number of high energy events compared to the rest of the sky, with the largest departure from isotropy at 24 · around the center of Cen A with 19 events observed and 7.6 expected for isotropy, corresponding to a chance probability for this to occur at a level of 4 % [38].\nThe Pierre Auger Collaboration has also performed a search for ultra-high neutrons from sources located within the Galaxy [40]. Their mean path length is 9 . 2 × E kpc before decaying, where E is the energy of the neutron in EeV. A stacking analysis was performed in the direction of bright Galactic gamma-ray sources: the ones detected by Fermi-Lat instrument in the 100 MeV - 100 GeV range and the ones detected by H.E.S.S. in the range of 100 GeV - 100 TeV. Neither analysis provided evidence for significant excess and upper limits on the flux were derived for all directions within the Auger coverage. For directions along the Galactic plane for instance, the upper limits are below 0.024 km -2 yr -1 , 0.014 km -2 yr -1 and 0.026 km -2 yr -1 for energy bins of [1-2] EeV, [2-3] EeV and E ≥ 1 EeV, respectively. For energies above 1 EeV, the 95 % C.L. upper limit on the flux is 0.065 km -2 yr -1 , which corresponds to the energy flux of 0.13 EeV km -2 yr -1 = 0.4 eV cm -2 s -1 in the EeV range. Here a differential energy spectrum E -2 was assumed [40]. Those upper limits call into question the existence of persistent sources of EeV protons in the Galaxy. They also place useful constraints on the UHE emissions from the known Galactic sources of TeV gamma-rays.\nADVANCES IN THEORY\nThe observed knees may be interpreted as the end of the Galactic CR spectrum with their position defining the maximum acceleration energy. Although this picture may look very natural, the way to its adoption was not straight forward (see e.g. [28] for a recent review). Diffuse shock acceleration in SNR was discovered in the late 1970s but it took two decades more to realize that CR-streaming amplifies the magnetic fields upstream of the shock to create highly turbulent fields with strengths up to d B ∼ B ∼ 10 -4 G (see e.g. [41, 42]). The importance of non-linear magnetic fields amplification at SNR shocks, now also well accounted for by 3d MHD simulations, surely became one of the most discussed theory topics recently and there is general consensus that this is vital to\nreach the knee even on relatively short timescales on the order of tens to hundreds of years, i.e. much faster than it takes to reach the Sedov phase.\nThis drives the discussion to another important theoretical CR-problem. It is challenging to allow CRs to escape from SNR into the interstellar medium in large numbers without significant energy losses. This issue was first addressed by Ptuskin and co-workers [43] where it was shown that only particles accelerated up to the maximum energy E max can escape the acceleration region. In their original model, E max reaches its highest value only at the beginning of the Sedov phase. The E -2 CR energy spectrum in this model is then given by integrating the narrow peak of E max ( t ) over time.\nThe diffusion of Galactic CRs close to their sources has been addressed recently by Kachelrieß and coworkers (see also [35]). Propagating individual CRs in purely isotropic turbulent magnetic fields with maximal scale of spatial variations l max , they find anisotropic CR diffusion at distances r < l max from their sources. As a result, the CR densities around the sources become strongly irregular and show filamentary structures that could be probed by TeV g -rays.\nAt the highest energies, Radio Galaxies (RG) remain being the most promising candidates for UHECR acceleration. An interesting argument linking UHECR sources to their luminosity at radio frequencies has been put forward in this context by Hardcastle [44] and he concludes that RGs can accelerate protons to the highest observed energies in the lobes if a substantial amount of energy is in the turbulent component of the magnetic field, i.e. B > ∼ B equipart , and the Hillas criterion is met. In Cen A, existing observations do in fact constrain B > ∼ B equipart for the kpc-scale jet. Moreover, if UHECRs are predominantly protons, then very few sources should contribute to the observed flux. These sources should be easy to identify in the radio and their UHECR spectrum should cut off steeply at the observed highest energies. In contrast, if the mass composition is heavy at the highest energies then many radio galaxies could contribute to the UHECR flux but due to the much stronger deflection only the nearby Radio Galaxy Cen A may be identifiable [44]. Of course, such a conclusion depends very much on the strength of the EG magnetic fields and the maximum energy reached in the sources.\nNEWPROJECTS AND OUTLOOK\nMotivated by the large body of important experimental findings and new insights, the field continues to evolve very dynamically with new projects being planned or existing ones to be upgraded. In the study of low energy CRs, AMS is the by far most complex instrument in orbit, launched on May 16, 2011. It will measure light CR isotopes from about 500 MeV to 10 GeV and is hoped to improve our understanding of CR propagation in Galaxy. First data about the positron/electron ratio have been released recently [45] and confirm findings of PAMELA. The CALET (CALorimeteric Electron Telescope) project is a Japanese led international mission being developed as part of the utilization plan for the International Space Station (ISS) and aims at studying details of particle propagation in the Galaxy by a combination of energy spectrum measurements of electrons, protons and higher-charged nuclei. In Siberia, the German-Russian project HiScore is planned to be constructed at the Tunka site. This project will use open Cherenkov counters for CR measurements around the knee and will be complemented\nby radio antennas to explore this new detection technology. HAWK is being constructed in Mexico. Although its prime goal is the study of the g -ray sky above 100 GeV, it will also contribute to measuring CR anisotropies at TeV-energies. LHAASO , mostly driven by the Chinese community and much larger and more complex than HAWK, serves the same scientific goals.\nAt the highest energies, Auger and TA plan upgrades in performance and size, respectively: Auger aims at improving the mass composition measurement and particle physics capabilities at the highest energies to answer the question about the origin of the flux suppression and TA aims at increasing their surface detector with a 2 km grid up to 2800 km 2 . Both collaborations have started to join efforts for a Next Generation Ground-based CR Observatory NGGO , much larger than existing experiments and aiming at good energy and mass resolution and exploring particle physics aspects at the highest energies. Four proposed and planned space missions constitute the roadmap of the space oriented community: TUS, JEM-EUSO, KLPVE, and Super-EUSO aim at contributing step-by-step to establish this challenging field of research. They will reach very large exposures aimed at seeing CR sources, which will be at the expense of energy resolution, composition measurements and particle physics capabilities. Given the resources of funding available in the next decade or two, it is unlikely that all of the above mentioned projects can be realized. Thus, priority should be given to complementarity rather than on duplication.\nACKNOWLEDGMENTS\nIts a pleasure to thank the organizers of the Texas Symposium 2012 for inviting me to participate in this vibrant conference. I am also grateful for many stimulating discussions with colleagues from KASCADE-Grande, Auger and TA. Financial support by the German Ministry of Research and Education (Grants 05A11PX1 and 05A11PXA) and by the Helmholtz Alliance for Astroparticle Physics (HAP) is gratefully acknowledged.\nREFERENCES\n\n1. J. Linsley, Phys. Rev. Lett. 10 , 146 (1963).\n2. K. Greisen, Phys. Rev. Lett. 16 , 748 (1966).\n3. G. Zatsepin, and V. Kuzmin, JEPT Letters 4 , 78-80 (1966).\n4. K.-H. Kampert, and A. A. Watson, The European Physical Journal H 37 , 359-412 (2012).\n5. R U Abbasi et al., [HiRes Collaboration], Phys. Rev. Lett. 100 , 101101 (2008).\n6. J Abraham et al., [Pierre-Auger-Collaboration], Phys. Rev. Lett. 101 , 061101 (2008).\n7. G. Kulikov, and G. Khristiansen, JETP 35 , 635 (1959).\n8. T Antoni et al., [KASCADE-Collaboration], Astrop. Phys. 24 , 1-25 (2005).\n9. J Abraham et al, [Pierre Auger Collaboration], Science 318 , 938 (2007).\n10. B. Peters, Il Nuov. Cim. 22 , 800 (1961).\n11. WDApel et al., [KASCADE-Grande-Collaboration], Phys. Rev. Lett. 107 , 171104 (2011).\n12. R U Abbasi et al, [IceCube Collaboration], Astrop. Phys. 44 , 40 (2013).\n13. WDApel et al., [KASCADE-Grande-Collaboration], Phys. Rev. D 87 , 081101(R) (2013).\n14. J. R. Jokipii, and G. Morfill, Astroph. J. 312 , 170 (1987).\n15. P. L. Biermann, and V. De Souza, Astroph. J. 746 , 72 (2012).\n16. J Abraham et al, [Pierre Auger Collaboration], Nucl. Instr. Meth. A523 , 50 (2004).\n17. J Abraham et al., [Pierre Auger Collaboration], Nucl. Instr. Meth. A620 , 227-251 (2010).\n18. T Abu-Zayyad et al. [TA Collaboration], Nucl. Instr. Meth. A689 , 87 (2012).\n19. B. Dawson, et al., Working Group report at UHECR2012, to appear in EPJ (Web of Conf.) (2013).\n20. K.-H. Kampert, and M. Unger, Astrop. Phys. 35 , 660 (2012).\n21. K.-H. Kampert, Summary talk at ISVHECRI 2012, to appear in EPJ (Web of Conf.) (2013).\n22. D. d'Enterria, R. Engel, T. Pierog, S. Ostapchenko, and K. Werner, Astrop. Phys. 35 , 98-113 (2011).\n23. P Abreu et al., [Pierre Auger Collaboration], Phys. Rev. Lett. 109 , 062002 (2012).\n24. D. Allard, Astrop. Phys. 39-40 , 33-43 (2012).\n25. EBarcikowski, et al., Working Group report at UHECR2012, to appear in EPJ (Web of Conf.) (2013).\n26. J Abraham et al., [Pierre Auger Collaboration], Phys. Rev. Lett. 104 , 091101 (2010).\n27. V. Berezinsky, and S. Grigorieva, Astronomy & Astrophysics 199 , 1 (1988).\n28. R. Aloisio, V. S. Berezinsky, and A. Gazizov, Astrop. Phys. 39-40 , 129 (2012).\n29. P Abreu et al. [Pierre Auger Collaboration], Astrop. Phys. 34 , 627-639 (2011).\n30. P Abreu et al, [Pierre Auger Collaboration], ApJ (2013).\n31. MAmenomori et al., [Tibet AS g Collaboration], Science 314 , 439 (2006).\n32. AA Abdo et al., [MILAGRO-Collaboration], Phys. Rev. Lett. 101 , 221101 (2008).\n33. R U Abbasi et al. [IceCube Collaboration], Astroph. J. 718 , L194-L198 (2010).\n34. R U Abbasi et al., [IceCube Collaboration], Astroph. J. 746 , 33 (2012).\n35. G. Giacinti, M. Kachelrieß, D. V. Semikoz, and G. Sigl, JCAP 2012 , 031-031 (2012).\n36. J Abraham et al, [Pierre Auger Collaboration], Astrop. Phys. 29 , 188-204 (2008).\n37. P Abreu et al., [Pierre Auger Collaboration], Astrop. Phys. 34 , 314-326 (2010).\n38. K.-H. Kampert et al, [Pierre Auger Collaboration], arXiv:1207.4823 (2012).\n39. T Abu-Zayyad et al., TA Collaboration], Astroph. J. 757 , 26 (2012).\n40. P. Abreu et al., [The Pierre Auger Collaboration], Astroph. J. 760 , 148 (2012).\n41. S. Lucek, and A. Bell, MNRAS 314 , 65 (2000).\n42. A. Bell, and S. Lucek, MNRAS 321 , 433 (2001).\n43. V. S. Ptuskin, and V. N. Zirakashvili, Advances in Space Research 37 , 1898-1901 (2006).\n44. M. J. Hardcastle, MNRAS 405 , 2810 (2010).\n45. MAguilar et al., [AMS Collaboration], Phys. Rev. Lett. 110 , 141102 (2013).\n"},"sections":{"kind":"list like","value":[{"title":"Karl-Heinz Kampert","content":"University of Wuppertal, Department of Physics, Gaußstrasse 20, D-42119 Wuppertal 1 Abstract. Observations of cosmic rays have been improved at all energies, both in terms of higher statistics and reduced systematics. As a result, the all particle cosmic ray energy spectrum starts to exhibit more structures than could be seen previously. Most importantly, a second knee in the cosmic ray spectrum - dominated by heavy primaries - is reported just below 10 17 eV. The light component, on the other hand, exhibits an ankle like feature above 10 17 eV and starts to dominate the flux at the ankle. The key question at the highest energies is about the origin of the flux suppression observed at energies above 5 · 10 19 eV. Is this the long awaited GZK-effect or the exhaustion of sources? The key to answering this question is again given by the still largely unknown mass composition at the highest energies. Data from different observatories don't quite agree and common efforts have been started to settle that question. The high level of isotropy observed even at the highest energies starts to challenge a proton dominated composition if extragalactic (EG) magnetic fields are on the order of a few nG or more. We shall discuss the experimental and theoretical progress in the field and the prospects for the next decade. Keywords: UHECR, EAS PACS: 13.85.Tp, 96.50.sd, 96.50.sb,","pages":[1]},{"title":"INTRODUCTION","content":"The Texas-Symposium 2012 completes a series of conferences at which the discovery of cosmic rays (CR) a hundred years ago by Franz Viktor Hess has been commemorated. Less known is a breakthrough made 50 years ago by John Linsley: in 1962 he reported the first observation of a primary CR particle with an energy exceeding 10 20 eV [1]. This event remains one of the most energetic CRs ever recorded and Linsley was extremely lucky to observe such an event after just three years of data taking of the 2 km 2 large Volcano Ranch air shower array. The cosmic microwave background (CMB) radiation, discovered three years later, immediately led to the prediction of a flux suppression either due to photo-pion production by protons propagating through the CMB at energies above 5 · 10 19 eV or due to photodisintegration of nuclei at about the same threshold energy. This process is known as GZK-effect, predicted independently by Greisen and by Zatsepin and Kuz'min [2, 3]. This has been the only firm prediction about a structure in the CR energy spectrum [4] and it has taken nearly 50 years to observe such a feature in data [5, 6]. However, can we be sure about having observed the GZK-effect? The spectral feature may equally be caused by the exhaustion of nearby sources or by a mixture of both as will be discussed below. At lower energies, Kulikov and Khristiansen [7] in 1958 reported a structure in the shower size spectrum which became known as the 'knee' in the CR spectrum. Observations made by KASCADE [8] and other air shower experiments showed that the mean mass increases above the knee, indicating that the knee marks the maximum acceleration energy of the most abundant Galactic sources. This led to speculations that heavy primaries would experience the same limitation of particle acceleration and a second, so-called 'Iron-knee', would be observed around E Fe knee ∼ 26 × E p knee . Such an observation has now been reported and it may mark the end of the Galactic CR spectrum. Large- and small-scale anisotropies in the arrival directions have been reported at TeV energies and now reach to beyond a PeV. This has come as a surprise and its interpretation starts to result in a better understanding and modeling of CR propagation within our Galaxy and about the transition from Galactic to EG CRs. At the highest energies, only upper limits on large scale anisotropies have been reported so far but, due to limited statistics, the amplitudes cannot be probed down to the levels observed below the knee region. Instead, a weak correlation of the highest energy particles to the position of nearby AGN has been reported by Auger [9]. This gave support to the picture that some fraction of the highest energy CRs results from sources within about 200 Mpc distance. Much progress has also been made in particle acceleration emphasizing the importance of non-linear effects in diffuse shock acceleration (DSA) with magnetic field amplification due to CR current driven instabilities. These effects may not only substantially increase the maximum energy reachable in CR accelerators but may also reduce the time scales required for the acceleration process. While Galactic CRs are believed to originate from supernova remnants (SNR), those at the highest energies are thought to originate in the lobes of Radio Galaxies (RG) if they are large and luminous enough and, again, a substantial energy is contained in the turbulent component of the magnetic field. Thus, it is fair so say that enormous progress has been made in CR physics particularly in recent years, both in observations and in accompanying theory. However, despite such advancements, the key questions about the CR origin and acceleration remain open even 100 years after their discovery. This paper aims to address some key topics in the field.","pages":[1,2]},{"title":"THE COSMIC RAY ENERGY SPECTRUM","content":"Recent progress in the knee-to-ankle energy range has been driven mostly by KASCADE-Grande with Tunka and IceTop ramping up and providing more data with high statistics and good resolution. Using complex 2-dimensional unfolding techniques to the electron vs muon numbers measured on shower-by-shower basis by the KASCADE air shower experiment, the mean mass was shown to become heavier above the knee energy with the energy spectra of primary mass groups supporting a scaling with rigidity according to E Z knee glyph[similarequal] Z × 3 · 10 15 eV [8], such as was suggested long time ago by Peters [10]. This observation, supported by other experiments, has renewed the question about the existence of a Fe-like knee at about 10 17 eV. Such a structure has been reported very recently and is shown in Fig. 1. The significance of the second knee at E glyph[similarequal] 80 PeV in the all-particle energy spectrum of KASCADE-Grande is just above 17 2 s but increases to 3 . 5 s for the electron poor (heavy) sample [11]. Similarly, IceTop data [12] show an indication of a flattening above 22 PeV, i.e. in the energy range between the two knees. Another very interesting recent result by KASCADE-Grande is reported in [13]. Using a larger data set and applying stronger cuts to electron-rich showers than were applied in [11], to accept essentially only p+He primaries, there is an ankle-like feature at 10 17 . 1 eV with a significance of 5 . 8 s . Obviously, the CR energy spectrum, once measured with high precision, exhibits much more structure and information than just the knee energy and the indices of an apparent power-law like spectrum below and above. The observation of the 'Fe-knee' and 'p-ankle' (with 'Fe' and 'p' meant as synonym for 'heavy' and 'light' primaries, respectively) is a remarkable achievement. The Fe-knee at 8 · 10 16 eV supports the picture of a rigidity scaling - also named the 'Peters cycle' [10] - in the knee energy range and the p-ankle E glyph[similarequal] 1 . 2 · 10 17 eV has in fact been expected because of the steep fall-off of the p-component at the knee [8] and the p-like composition at the ankle (see next section). Thus, the p-ankle would either mark the transition from Galactic to EG sources or the onset of a new high energy (Galactic) source population (see e.g. [14, 15]). At the highest energies, from the ankle to beyond 10 20 eV, the Pierre Auger Observatory [16, 17] is the flagship in the field with an accumulated exposure of about 30 000 km 2 sr yr. The Telescope Array [18], due to a later start and its more than 4 times smaller area, has collected about 10 times less events. A detailed comparison of the energy spectra of various observatories is presented in Fig. 2. As discussed in great detail in [19], it is found that the energy spectra determined by the larger experiments are con- sistent in normalization and shape after energy scaling factors, as shown in Fig. 2, are applied. Those scaling factors are within systematic uncertainties in the energy scale quoted by the experiments. This is quite remarkable and demonstrates how well the data are understood. Nevertheless, cross-checks of photometric calibrations and atmospheric corrections have been started and as a next step, common models (e.g. fluorescence yield) should be used where possible. The data in Fig. 2 clearly exhibit the ankle at ∼ 4 · 10 18 eV and a flux suppression above ∼ 4 · 10 19 eV. The flux suppression at the highest energies is in accordance with the long-awaited GZK-effect [5, 6]. However, as discussed below, the data of the Auger observatory suggest that the maximum energy of nearby sources or the source population is seen, instead.","pages":[2,3,4]},{"title":"COSMIC RAY COMPOSITION AND INTERACTION MODELS","content":"Obviously the energy spectra by itself, despite their high level of precision reached, do not allow one to conclude about the origin of the spectral structures and thereby about the origin of CRs in different energy regions. Additional key information is obtained from the mass composition of CRs. Unfortunately, the measurement of primary masses is the most difficult task in air shower physics as such measurements rely on comparisons of data to EAS simulations with the latter serving as reference [20]. EAS simulations, however, are subject to uncertainties mostly because hadronic interaction models need to be employed at energy ranges much beyond those accessible to man-made particle accel- erators. Therefore, the advent of LHC data, particularly those measured in the extreme forward region of the collisions, is of great importance to CR and EAS physics and have been awaited with great interest [21]. Remarkably, interaction models employed in EAS simulations provide a somewhat better description of global observables (multiplicities, p ⊥ -distributions, forward and transverse energy flow, etc.) than typical tunes of HEP models, such as PYTHIA or PHOJET [22]. This demonstrates once more that the CR community has taken great care in extrapolating models to the highest energies. Moreover, as demonstrated e.g. in [23], CR data provide important information about particle physics at centre-of-mass energies ten or more times higher than is accessible at LHC. The pp -inelastic cross section extracted from data of the Auger Observatory supports only a modest rise of the inelastic cross section with energy [23]. A careful analysis of composition data from various experiments has been presented in [20] with exemplary results depicted in Fig. 3 (left). These data complement those of the energy spectrum in a remarkable way. As can be seen, the breaks in the energy spectrum coincide with the turning points of changes in the composition: the mean mass becomes increasingly heavier above the knee, reaches a maximum at the 2 nd knee, another minimum at the ankle before it starts to rise again towards the highest energies. Different interaction models provide the same answer concerning changes in the composition but differ by their absolute values of 〈 ln A 〉 . It should also be noted that the suggested increase in the mean mass at the highest energies is not without dispute. It has been looked at in great detail in [25]. At ultra-high energies, the Auger data suggest a larger 〈 ln A 〉 than all other experiments. TA and Yakutsk are consistent within systematic uncertainties with Auger data while HiRes is compatible with Auger only at energies below 10 18 . 5 eV when using QGSJet-II. When using the SIBYLL model, Auger and HiRes become compatible within a larger energy range [25]. The importance of measuring the composition up to the highest energy cannot be overstated as it will be the key to answering the question about the origin of the GZKlike flux suppression. The same mechanism of limiting source energy that appears to cause the increasingly heavy above the knee may work also for EG-CRs above the ankle. Thereby, the break at ∼ 4 · 10 19 eV may mark the maximum energy of nearby EG CR-accelerators, rather than the GZK-effect. This is shown in Fig. 3 (right), where propagated CR spectra are shown for a maximum energy at the source of E max ( Z ) = Z × 4 · 10 18 eV and assuming a hard spectral source index of b = 1 . 6 [24]. Clearly, such a - in view of the hard spectral index - more exotic scenario provides a good description of the energy spectrum. Moreover, other than the GZK-like interpretation, it also describes the 〈 X max 〉 and the fluctuation RMS( X max ) of the Pierre Auger Observatory [26]. A mixture of light and intermediate/heavy primaries at the highest energies may also explain the low level of directional correlations to nearby AGN. Enhancements, presently foreseen by the Auger Collaboration will address this issue. Two models about the putative transition from Galactic- to EG-CRs have received much attention: In the classical 'ankle model' the transition is assumed to occur at the ankle. In this model, Galactic CRs above the 2 nd knee are dominated by heavy primaries before protons of EG origin start to take over and to dominate at the ankle. In the dipmodel [27], on the other hand, the transition occurs already at the 2 nd knee and is characterized by a sharp change of the composition from Galactic iron to EG protons while the ankle is due to e + e -production of protons in the CMB. A third, 'mixed composition', model has been suggested more recently [28] in which EG-CRs taking over are not considered being protons but an EG mixed CR composition. Clearly, the dip-model requires a proton dominated composition essentially at all energies starting somewhat above the 2 nd knee. The answer may be difficult to determine based on 〈 X max 〉 or 〈 ln A 〉 alone. A much better quantity would again be the RMS of these quantities, such as studied at higher energies in [26]. A rather abrupt change of composition as required by the dip-model near the 2 nd knee vs a smooth change of composition as expected near the ankle in the ankle model, should become distinguishable by the RMS ( X max ) -values already in the very near future. This has been a prime motivation for the HEAT and TALE extensions of Auger and TA, respectively.","pages":[4,5,6]},{"title":"ANISOTROPIES AT DIFFERENT ENERGIES AND ANGULAR SCALES","content":"The main obstacle in identifying Galactic CR-sources is the diffusion of CRs in the Galactic magnetic field (GMF), erasing directional information on the position of their sources. The GMF has a turbulent component that varies on scales between l min ∼ 1 AU and l max few to 200 pc. Since CRs scatter on inhomogeneities with variation scales comparable to their Larmor radius, the propagation of Galactic CRs in the GMF resembles a random walk and is well described by the diffusion approximation. Large scale anisotropies observed by the Tibet Air-Shower experiment [31] in the northern hemisphere for CRs at energies of a few to several hundred TeV and at angular scales of 60 · and above, thus came as a surprise. The data have been confirmed and complemented by Milagro [32] and more recently also by high statistics measurements of IceTop in the southern hemisphere [33, 34] (cf. Fig. 4). Moreover, the structure changes with energy and appears to persist to beyond PeV energies. This anisotropy reveals a new feature of the Galactic cosmic-ray distribution, which must be incorporated into theories of the origin and propagation of cosmic rays. As was emphasized e.g. in [35, 28], changes of the anisotropy patterns with energy can, in principle, be accounted for by specific distributions (in space and time) and individual source energy spectra of nearby recent SNRs. Another long-standing problem is the high level of isotropy even at energies beyond 10 18 eV. For non-relativistic diffusive acceleration g g = 2 and the index of the observed spectrum, g g + m = 2 . 7, one derives m = 0 . 7. At very high energy this results in a too large anisotropy, d ( E ) GLYPH<181> D ( E ) GLYPH<181> E m and in a too small traversed grammage, X cr ( E ) GLYPH<181> 1 / D ( E ) , with the diffusion coefficient D ( E ) , and would contradict experimental data (cf. Fig. 4). However, d ( E ) GLYPH<181> D ( E ) refers again to an average of the anisotropy amplitude computed over many source realizations, i.e. over a continuum of sources and thus does not apply to concrete realizations of nearby SNRs and turbulent magnetic fields within the cosmic ray scattering length. Moreover, as pointed out in [35], diffusion breaks down for propagation of CRs within our Galaxy at E > ∼ 10 17 eV. Recently, the Pierre Auger Observatory reported the first large scale anisotropy searches as a function of both right ascension and declination. Again, within the systematic uncertainties, no significant deviation from isotropy is revealed and the upper limits on dipole and quadrupole amplitudes challenge an origin from stationary galactic sources densely distributed in the galactic disk and emitting predominantly light particles in all directions. In Fig. 4 (right), the corresponding directions are shown in orthographic projection with the associated uncertainties, as a function of the energy. Both angles are expected to be randomly distributed in the case of independent samples whose parent distribution is isotropic. It is thus interesting to note that all reconstructed declinations are in the equatorial southern hemisphere, and to note also the intriguing smooth alignment of the phases in right ascension as a function of the energy. Directional correlations of the most energetic CRs with nearby AGN observed by the Pierre Auger Observatory provided the first signature about anisotropies of the most energetic CRs and thereby about their EG origin [9, 36, 37]. Initially very strong, the fraction of Auger events above 55 EeV correlating within 3 . 1 · with a nearby ( z ≤ 0 . 018) AGN from the VCV-catalogue has stabilized at a level of ( 33 ± 5 ) % [38]. With an accidental rate for an isotropic distribution of 21 %, this corresponds to a chance probability of less than 1 %. Recently, TA reported a correlation fraction of 44 % at an isotropic fraction of 24 % yielding a chance probability of about 2 % [39]. Thus, the data are in perfect agreement with each other yielding a combined chance probability of observing such a correlation at the 10 -3 level. However, more statistics is needed to consolidate the picture and to allow subdividing data sets in bins of related CR observables. The sky region around Cen A remains populated by a larger number of high energy events compared to the rest of the sky, with the largest departure from isotropy at 24 · around the center of Cen A with 19 events observed and 7.6 expected for isotropy, corresponding to a chance probability for this to occur at a level of 4 % [38]. The Pierre Auger Collaboration has also performed a search for ultra-high neutrons from sources located within the Galaxy [40]. Their mean path length is 9 . 2 × E kpc before decaying, where E is the energy of the neutron in EeV. A stacking analysis was performed in the direction of bright Galactic gamma-ray sources: the ones detected by Fermi-Lat instrument in the 100 MeV - 100 GeV range and the ones detected by H.E.S.S. in the range of 100 GeV - 100 TeV. Neither analysis provided evidence for significant excess and upper limits on the flux were derived for all directions within the Auger coverage. For directions along the Galactic plane for instance, the upper limits are below 0.024 km -2 yr -1 , 0.014 km -2 yr -1 and 0.026 km -2 yr -1 for energy bins of [1-2] EeV, [2-3] EeV and E ≥ 1 EeV, respectively. For energies above 1 EeV, the 95 % C.L. upper limit on the flux is 0.065 km -2 yr -1 , which corresponds to the energy flux of 0.13 EeV km -2 yr -1 = 0.4 eV cm -2 s -1 in the EeV range. Here a differential energy spectrum E -2 was assumed [40]. Those upper limits call into question the existence of persistent sources of EeV protons in the Galaxy. They also place useful constraints on the UHE emissions from the known Galactic sources of TeV gamma-rays.","pages":[6,7,8]},{"title":"ADVANCES IN THEORY","content":"The observed knees may be interpreted as the end of the Galactic CR spectrum with their position defining the maximum acceleration energy. Although this picture may look very natural, the way to its adoption was not straight forward (see e.g. [28] for a recent review). Diffuse shock acceleration in SNR was discovered in the late 1970s but it took two decades more to realize that CR-streaming amplifies the magnetic fields upstream of the shock to create highly turbulent fields with strengths up to d B ∼ B ∼ 10 -4 G (see e.g. [41, 42]). The importance of non-linear magnetic fields amplification at SNR shocks, now also well accounted for by 3d MHD simulations, surely became one of the most discussed theory topics recently and there is general consensus that this is vital to reach the knee even on relatively short timescales on the order of tens to hundreds of years, i.e. much faster than it takes to reach the Sedov phase. This drives the discussion to another important theoretical CR-problem. It is challenging to allow CRs to escape from SNR into the interstellar medium in large numbers without significant energy losses. This issue was first addressed by Ptuskin and co-workers [43] where it was shown that only particles accelerated up to the maximum energy E max can escape the acceleration region. In their original model, E max reaches its highest value only at the beginning of the Sedov phase. The E -2 CR energy spectrum in this model is then given by integrating the narrow peak of E max ( t ) over time. The diffusion of Galactic CRs close to their sources has been addressed recently by Kachelrieß and coworkers (see also [35]). Propagating individual CRs in purely isotropic turbulent magnetic fields with maximal scale of spatial variations l max , they find anisotropic CR diffusion at distances r < l max from their sources. As a result, the CR densities around the sources become strongly irregular and show filamentary structures that could be probed by TeV g -rays. At the highest energies, Radio Galaxies (RG) remain being the most promising candidates for UHECR acceleration. An interesting argument linking UHECR sources to their luminosity at radio frequencies has been put forward in this context by Hardcastle [44] and he concludes that RGs can accelerate protons to the highest observed energies in the lobes if a substantial amount of energy is in the turbulent component of the magnetic field, i.e. B > ∼ B equipart , and the Hillas criterion is met. In Cen A, existing observations do in fact constrain B > ∼ B equipart for the kpc-scale jet. Moreover, if UHECRs are predominantly protons, then very few sources should contribute to the observed flux. These sources should be easy to identify in the radio and their UHECR spectrum should cut off steeply at the observed highest energies. In contrast, if the mass composition is heavy at the highest energies then many radio galaxies could contribute to the UHECR flux but due to the much stronger deflection only the nearby Radio Galaxy Cen A may be identifiable [44]. Of course, such a conclusion depends very much on the strength of the EG magnetic fields and the maximum energy reached in the sources.","pages":[8,9]},{"title":"NEWPROJECTS AND OUTLOOK","content":"Motivated by the large body of important experimental findings and new insights, the field continues to evolve very dynamically with new projects being planned or existing ones to be upgraded. In the study of low energy CRs, AMS is the by far most complex instrument in orbit, launched on May 16, 2011. It will measure light CR isotopes from about 500 MeV to 10 GeV and is hoped to improve our understanding of CR propagation in Galaxy. First data about the positron/electron ratio have been released recently [45] and confirm findings of PAMELA. The CALET (CALorimeteric Electron Telescope) project is a Japanese led international mission being developed as part of the utilization plan for the International Space Station (ISS) and aims at studying details of particle propagation in the Galaxy by a combination of energy spectrum measurements of electrons, protons and higher-charged nuclei. In Siberia, the German-Russian project HiScore is planned to be constructed at the Tunka site. This project will use open Cherenkov counters for CR measurements around the knee and will be complemented by radio antennas to explore this new detection technology. HAWK is being constructed in Mexico. Although its prime goal is the study of the g -ray sky above 100 GeV, it will also contribute to measuring CR anisotropies at TeV-energies. LHAASO , mostly driven by the Chinese community and much larger and more complex than HAWK, serves the same scientific goals. At the highest energies, Auger and TA plan upgrades in performance and size, respectively: Auger aims at improving the mass composition measurement and particle physics capabilities at the highest energies to answer the question about the origin of the flux suppression and TA aims at increasing their surface detector with a 2 km grid up to 2800 km 2 . Both collaborations have started to join efforts for a Next Generation Ground-based CR Observatory NGGO , much larger than existing experiments and aiming at good energy and mass resolution and exploring particle physics aspects at the highest energies. Four proposed and planned space missions constitute the roadmap of the space oriented community: TUS, JEM-EUSO, KLPVE, and Super-EUSO aim at contributing step-by-step to establish this challenging field of research. They will reach very large exposures aimed at seeing CR sources, which will be at the expense of energy resolution, composition measurements and particle physics capabilities. Given the resources of funding available in the next decade or two, it is unlikely that all of the above mentioned projects can be realized. Thus, priority should be given to complementarity rather than on duplication.","pages":[9,10]},{"title":"ACKNOWLEDGMENTS","content":"Its a pleasure to thank the organizers of the Texas Symposium 2012 for inviting me to participate in this vibrant conference. I am also grateful for many stimulating discussions with colleagues from KASCADE-Grande, Auger and TA. Financial support by the German Ministry of Research and Education (Grants 05A11PX1 and 05A11PXA) and by the Helmholtz Alliance for Astroparticle Physics (HAP) is gratefully acknowledged.","pages":[10]}],"string":"[\n {\n \"title\": \"Karl-Heinz Kampert\",\n \"content\": \"University of Wuppertal, Department of Physics, Gaußstrasse 20, D-42119 Wuppertal 1 Abstract. Observations of cosmic rays have been improved at all energies, both in terms of higher statistics and reduced systematics. As a result, the all particle cosmic ray energy spectrum starts to exhibit more structures than could be seen previously. Most importantly, a second knee in the cosmic ray spectrum - dominated by heavy primaries - is reported just below 10 17 eV. The light component, on the other hand, exhibits an ankle like feature above 10 17 eV and starts to dominate the flux at the ankle. The key question at the highest energies is about the origin of the flux suppression observed at energies above 5 · 10 19 eV. Is this the long awaited GZK-effect or the exhaustion of sources? The key to answering this question is again given by the still largely unknown mass composition at the highest energies. Data from different observatories don't quite agree and common efforts have been started to settle that question. The high level of isotropy observed even at the highest energies starts to challenge a proton dominated composition if extragalactic (EG) magnetic fields are on the order of a few nG or more. We shall discuss the experimental and theoretical progress in the field and the prospects for the next decade. Keywords: UHECR, EAS PACS: 13.85.Tp, 96.50.sd, 96.50.sb,\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"INTRODUCTION\",\n \"content\": \"The Texas-Symposium 2012 completes a series of conferences at which the discovery of cosmic rays (CR) a hundred years ago by Franz Viktor Hess has been commemorated. Less known is a breakthrough made 50 years ago by John Linsley: in 1962 he reported the first observation of a primary CR particle with an energy exceeding 10 20 eV [1]. This event remains one of the most energetic CRs ever recorded and Linsley was extremely lucky to observe such an event after just three years of data taking of the 2 km 2 large Volcano Ranch air shower array. The cosmic microwave background (CMB) radiation, discovered three years later, immediately led to the prediction of a flux suppression either due to photo-pion production by protons propagating through the CMB at energies above 5 · 10 19 eV or due to photodisintegration of nuclei at about the same threshold energy. This process is known as GZK-effect, predicted independently by Greisen and by Zatsepin and Kuz'min [2, 3]. This has been the only firm prediction about a structure in the CR energy spectrum [4] and it has taken nearly 50 years to observe such a feature in data [5, 6]. However, can we be sure about having observed the GZK-effect? The spectral feature may equally be caused by the exhaustion of nearby sources or by a mixture of both as will be discussed below. At lower energies, Kulikov and Khristiansen [7] in 1958 reported a structure in the shower size spectrum which became known as the 'knee' in the CR spectrum. Observations made by KASCADE [8] and other air shower experiments showed that the mean mass increases above the knee, indicating that the knee marks the maximum acceleration energy of the most abundant Galactic sources. This led to speculations that heavy primaries would experience the same limitation of particle acceleration and a second, so-called 'Iron-knee', would be observed around E Fe knee ∼ 26 × E p knee . Such an observation has now been reported and it may mark the end of the Galactic CR spectrum. Large- and small-scale anisotropies in the arrival directions have been reported at TeV energies and now reach to beyond a PeV. This has come as a surprise and its interpretation starts to result in a better understanding and modeling of CR propagation within our Galaxy and about the transition from Galactic to EG CRs. At the highest energies, only upper limits on large scale anisotropies have been reported so far but, due to limited statistics, the amplitudes cannot be probed down to the levels observed below the knee region. Instead, a weak correlation of the highest energy particles to the position of nearby AGN has been reported by Auger [9]. This gave support to the picture that some fraction of the highest energy CRs results from sources within about 200 Mpc distance. Much progress has also been made in particle acceleration emphasizing the importance of non-linear effects in diffuse shock acceleration (DSA) with magnetic field amplification due to CR current driven instabilities. These effects may not only substantially increase the maximum energy reachable in CR accelerators but may also reduce the time scales required for the acceleration process. While Galactic CRs are believed to originate from supernova remnants (SNR), those at the highest energies are thought to originate in the lobes of Radio Galaxies (RG) if they are large and luminous enough and, again, a substantial energy is contained in the turbulent component of the magnetic field. Thus, it is fair so say that enormous progress has been made in CR physics particularly in recent years, both in observations and in accompanying theory. However, despite such advancements, the key questions about the CR origin and acceleration remain open even 100 years after their discovery. This paper aims to address some key topics in the field.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"THE COSMIC RAY ENERGY SPECTRUM\",\n \"content\": \"Recent progress in the knee-to-ankle energy range has been driven mostly by KASCADE-Grande with Tunka and IceTop ramping up and providing more data with high statistics and good resolution. Using complex 2-dimensional unfolding techniques to the electron vs muon numbers measured on shower-by-shower basis by the KASCADE air shower experiment, the mean mass was shown to become heavier above the knee energy with the energy spectra of primary mass groups supporting a scaling with rigidity according to E Z knee glyph[similarequal] Z × 3 · 10 15 eV [8], such as was suggested long time ago by Peters [10]. This observation, supported by other experiments, has renewed the question about the existence of a Fe-like knee at about 10 17 eV. Such a structure has been reported very recently and is shown in Fig. 1. The significance of the second knee at E glyph[similarequal] 80 PeV in the all-particle energy spectrum of KASCADE-Grande is just above 17 2 s but increases to 3 . 5 s for the electron poor (heavy) sample [11]. Similarly, IceTop data [12] show an indication of a flattening above 22 PeV, i.e. in the energy range between the two knees. Another very interesting recent result by KASCADE-Grande is reported in [13]. Using a larger data set and applying stronger cuts to electron-rich showers than were applied in [11], to accept essentially only p+He primaries, there is an ankle-like feature at 10 17 . 1 eV with a significance of 5 . 8 s . Obviously, the CR energy spectrum, once measured with high precision, exhibits much more structure and information than just the knee energy and the indices of an apparent power-law like spectrum below and above. The observation of the 'Fe-knee' and 'p-ankle' (with 'Fe' and 'p' meant as synonym for 'heavy' and 'light' primaries, respectively) is a remarkable achievement. The Fe-knee at 8 · 10 16 eV supports the picture of a rigidity scaling - also named the 'Peters cycle' [10] - in the knee energy range and the p-ankle E glyph[similarequal] 1 . 2 · 10 17 eV has in fact been expected because of the steep fall-off of the p-component at the knee [8] and the p-like composition at the ankle (see next section). Thus, the p-ankle would either mark the transition from Galactic to EG sources or the onset of a new high energy (Galactic) source population (see e.g. [14, 15]). At the highest energies, from the ankle to beyond 10 20 eV, the Pierre Auger Observatory [16, 17] is the flagship in the field with an accumulated exposure of about 30 000 km 2 sr yr. The Telescope Array [18], due to a later start and its more than 4 times smaller area, has collected about 10 times less events. A detailed comparison of the energy spectra of various observatories is presented in Fig. 2. As discussed in great detail in [19], it is found that the energy spectra determined by the larger experiments are con- sistent in normalization and shape after energy scaling factors, as shown in Fig. 2, are applied. Those scaling factors are within systematic uncertainties in the energy scale quoted by the experiments. This is quite remarkable and demonstrates how well the data are understood. Nevertheless, cross-checks of photometric calibrations and atmospheric corrections have been started and as a next step, common models (e.g. fluorescence yield) should be used where possible. The data in Fig. 2 clearly exhibit the ankle at ∼ 4 · 10 18 eV and a flux suppression above ∼ 4 · 10 19 eV. The flux suppression at the highest energies is in accordance with the long-awaited GZK-effect [5, 6]. However, as discussed below, the data of the Auger observatory suggest that the maximum energy of nearby sources or the source population is seen, instead.\",\n \"pages\": [\n 2,\n 3,\n 4\n ]\n },\n {\n \"title\": \"COSMIC RAY COMPOSITION AND INTERACTION MODELS\",\n \"content\": \"Obviously the energy spectra by itself, despite their high level of precision reached, do not allow one to conclude about the origin of the spectral structures and thereby about the origin of CRs in different energy regions. Additional key information is obtained from the mass composition of CRs. Unfortunately, the measurement of primary masses is the most difficult task in air shower physics as such measurements rely on comparisons of data to EAS simulations with the latter serving as reference [20]. EAS simulations, however, are subject to uncertainties mostly because hadronic interaction models need to be employed at energy ranges much beyond those accessible to man-made particle accel- erators. Therefore, the advent of LHC data, particularly those measured in the extreme forward region of the collisions, is of great importance to CR and EAS physics and have been awaited with great interest [21]. Remarkably, interaction models employed in EAS simulations provide a somewhat better description of global observables (multiplicities, p ⊥ -distributions, forward and transverse energy flow, etc.) than typical tunes of HEP models, such as PYTHIA or PHOJET [22]. This demonstrates once more that the CR community has taken great care in extrapolating models to the highest energies. Moreover, as demonstrated e.g. in [23], CR data provide important information about particle physics at centre-of-mass energies ten or more times higher than is accessible at LHC. The pp -inelastic cross section extracted from data of the Auger Observatory supports only a modest rise of the inelastic cross section with energy [23]. A careful analysis of composition data from various experiments has been presented in [20] with exemplary results depicted in Fig. 3 (left). These data complement those of the energy spectrum in a remarkable way. As can be seen, the breaks in the energy spectrum coincide with the turning points of changes in the composition: the mean mass becomes increasingly heavier above the knee, reaches a maximum at the 2 nd knee, another minimum at the ankle before it starts to rise again towards the highest energies. Different interaction models provide the same answer concerning changes in the composition but differ by their absolute values of 〈 ln A 〉 . It should also be noted that the suggested increase in the mean mass at the highest energies is not without dispute. It has been looked at in great detail in [25]. At ultra-high energies, the Auger data suggest a larger 〈 ln A 〉 than all other experiments. TA and Yakutsk are consistent within systematic uncertainties with Auger data while HiRes is compatible with Auger only at energies below 10 18 . 5 eV when using QGSJet-II. When using the SIBYLL model, Auger and HiRes become compatible within a larger energy range [25]. The importance of measuring the composition up to the highest energy cannot be overstated as it will be the key to answering the question about the origin of the GZKlike flux suppression. The same mechanism of limiting source energy that appears to cause the increasingly heavy above the knee may work also for EG-CRs above the ankle. Thereby, the break at ∼ 4 · 10 19 eV may mark the maximum energy of nearby EG CR-accelerators, rather than the GZK-effect. This is shown in Fig. 3 (right), where propagated CR spectra are shown for a maximum energy at the source of E max ( Z ) = Z × 4 · 10 18 eV and assuming a hard spectral source index of b = 1 . 6 [24]. Clearly, such a - in view of the hard spectral index - more exotic scenario provides a good description of the energy spectrum. Moreover, other than the GZK-like interpretation, it also describes the 〈 X max 〉 and the fluctuation RMS( X max ) of the Pierre Auger Observatory [26]. A mixture of light and intermediate/heavy primaries at the highest energies may also explain the low level of directional correlations to nearby AGN. Enhancements, presently foreseen by the Auger Collaboration will address this issue. Two models about the putative transition from Galactic- to EG-CRs have received much attention: In the classical 'ankle model' the transition is assumed to occur at the ankle. In this model, Galactic CRs above the 2 nd knee are dominated by heavy primaries before protons of EG origin start to take over and to dominate at the ankle. In the dipmodel [27], on the other hand, the transition occurs already at the 2 nd knee and is characterized by a sharp change of the composition from Galactic iron to EG protons while the ankle is due to e + e -production of protons in the CMB. A third, 'mixed composition', model has been suggested more recently [28] in which EG-CRs taking over are not considered being protons but an EG mixed CR composition. Clearly, the dip-model requires a proton dominated composition essentially at all energies starting somewhat above the 2 nd knee. The answer may be difficult to determine based on 〈 X max 〉 or 〈 ln A 〉 alone. A much better quantity would again be the RMS of these quantities, such as studied at higher energies in [26]. A rather abrupt change of composition as required by the dip-model near the 2 nd knee vs a smooth change of composition as expected near the ankle in the ankle model, should become distinguishable by the RMS ( X max ) -values already in the very near future. This has been a prime motivation for the HEAT and TALE extensions of Auger and TA, respectively.\",\n \"pages\": [\n 4,\n 5,\n 6\n ]\n },\n {\n \"title\": \"ANISOTROPIES AT DIFFERENT ENERGIES AND ANGULAR SCALES\",\n \"content\": \"The main obstacle in identifying Galactic CR-sources is the diffusion of CRs in the Galactic magnetic field (GMF), erasing directional information on the position of their sources. The GMF has a turbulent component that varies on scales between l min ∼ 1 AU and l max few to 200 pc. Since CRs scatter on inhomogeneities with variation scales comparable to their Larmor radius, the propagation of Galactic CRs in the GMF resembles a random walk and is well described by the diffusion approximation. Large scale anisotropies observed by the Tibet Air-Shower experiment [31] in the northern hemisphere for CRs at energies of a few to several hundred TeV and at angular scales of 60 · and above, thus came as a surprise. The data have been confirmed and complemented by Milagro [32] and more recently also by high statistics measurements of IceTop in the southern hemisphere [33, 34] (cf. Fig. 4). Moreover, the structure changes with energy and appears to persist to beyond PeV energies. This anisotropy reveals a new feature of the Galactic cosmic-ray distribution, which must be incorporated into theories of the origin and propagation of cosmic rays. As was emphasized e.g. in [35, 28], changes of the anisotropy patterns with energy can, in principle, be accounted for by specific distributions (in space and time) and individual source energy spectra of nearby recent SNRs. Another long-standing problem is the high level of isotropy even at energies beyond 10 18 eV. For non-relativistic diffusive acceleration g g = 2 and the index of the observed spectrum, g g + m = 2 . 7, one derives m = 0 . 7. At very high energy this results in a too large anisotropy, d ( E ) GLYPH<181> D ( E ) GLYPH<181> E m and in a too small traversed grammage, X cr ( E ) GLYPH<181> 1 / D ( E ) , with the diffusion coefficient D ( E ) , and would contradict experimental data (cf. Fig. 4). However, d ( E ) GLYPH<181> D ( E ) refers again to an average of the anisotropy amplitude computed over many source realizations, i.e. over a continuum of sources and thus does not apply to concrete realizations of nearby SNRs and turbulent magnetic fields within the cosmic ray scattering length. Moreover, as pointed out in [35], diffusion breaks down for propagation of CRs within our Galaxy at E > ∼ 10 17 eV. Recently, the Pierre Auger Observatory reported the first large scale anisotropy searches as a function of both right ascension and declination. Again, within the systematic uncertainties, no significant deviation from isotropy is revealed and the upper limits on dipole and quadrupole amplitudes challenge an origin from stationary galactic sources densely distributed in the galactic disk and emitting predominantly light particles in all directions. In Fig. 4 (right), the corresponding directions are shown in orthographic projection with the associated uncertainties, as a function of the energy. Both angles are expected to be randomly distributed in the case of independent samples whose parent distribution is isotropic. It is thus interesting to note that all reconstructed declinations are in the equatorial southern hemisphere, and to note also the intriguing smooth alignment of the phases in right ascension as a function of the energy. Directional correlations of the most energetic CRs with nearby AGN observed by the Pierre Auger Observatory provided the first signature about anisotropies of the most energetic CRs and thereby about their EG origin [9, 36, 37]. Initially very strong, the fraction of Auger events above 55 EeV correlating within 3 . 1 · with a nearby ( z ≤ 0 . 018) AGN from the VCV-catalogue has stabilized at a level of ( 33 ± 5 ) % [38]. With an accidental rate for an isotropic distribution of 21 %, this corresponds to a chance probability of less than 1 %. Recently, TA reported a correlation fraction of 44 % at an isotropic fraction of 24 % yielding a chance probability of about 2 % [39]. Thus, the data are in perfect agreement with each other yielding a combined chance probability of observing such a correlation at the 10 -3 level. However, more statistics is needed to consolidate the picture and to allow subdividing data sets in bins of related CR observables. The sky region around Cen A remains populated by a larger number of high energy events compared to the rest of the sky, with the largest departure from isotropy at 24 · around the center of Cen A with 19 events observed and 7.6 expected for isotropy, corresponding to a chance probability for this to occur at a level of 4 % [38]. The Pierre Auger Collaboration has also performed a search for ultra-high neutrons from sources located within the Galaxy [40]. Their mean path length is 9 . 2 × E kpc before decaying, where E is the energy of the neutron in EeV. A stacking analysis was performed in the direction of bright Galactic gamma-ray sources: the ones detected by Fermi-Lat instrument in the 100 MeV - 100 GeV range and the ones detected by H.E.S.S. in the range of 100 GeV - 100 TeV. Neither analysis provided evidence for significant excess and upper limits on the flux were derived for all directions within the Auger coverage. For directions along the Galactic plane for instance, the upper limits are below 0.024 km -2 yr -1 , 0.014 km -2 yr -1 and 0.026 km -2 yr -1 for energy bins of [1-2] EeV, [2-3] EeV and E ≥ 1 EeV, respectively. For energies above 1 EeV, the 95 % C.L. upper limit on the flux is 0.065 km -2 yr -1 , which corresponds to the energy flux of 0.13 EeV km -2 yr -1 = 0.4 eV cm -2 s -1 in the EeV range. Here a differential energy spectrum E -2 was assumed [40]. Those upper limits call into question the existence of persistent sources of EeV protons in the Galaxy. They also place useful constraints on the UHE emissions from the known Galactic sources of TeV gamma-rays.\",\n \"pages\": [\n 6,\n 7,\n 8\n ]\n },\n {\n \"title\": \"ADVANCES IN THEORY\",\n \"content\": \"The observed knees may be interpreted as the end of the Galactic CR spectrum with their position defining the maximum acceleration energy. Although this picture may look very natural, the way to its adoption was not straight forward (see e.g. [28] for a recent review). Diffuse shock acceleration in SNR was discovered in the late 1970s but it took two decades more to realize that CR-streaming amplifies the magnetic fields upstream of the shock to create highly turbulent fields with strengths up to d B ∼ B ∼ 10 -4 G (see e.g. [41, 42]). The importance of non-linear magnetic fields amplification at SNR shocks, now also well accounted for by 3d MHD simulations, surely became one of the most discussed theory topics recently and there is general consensus that this is vital to reach the knee even on relatively short timescales on the order of tens to hundreds of years, i.e. much faster than it takes to reach the Sedov phase. This drives the discussion to another important theoretical CR-problem. It is challenging to allow CRs to escape from SNR into the interstellar medium in large numbers without significant energy losses. This issue was first addressed by Ptuskin and co-workers [43] where it was shown that only particles accelerated up to the maximum energy E max can escape the acceleration region. In their original model, E max reaches its highest value only at the beginning of the Sedov phase. The E -2 CR energy spectrum in this model is then given by integrating the narrow peak of E max ( t ) over time. The diffusion of Galactic CRs close to their sources has been addressed recently by Kachelrieß and coworkers (see also [35]). Propagating individual CRs in purely isotropic turbulent magnetic fields with maximal scale of spatial variations l max , they find anisotropic CR diffusion at distances r < l max from their sources. As a result, the CR densities around the sources become strongly irregular and show filamentary structures that could be probed by TeV g -rays. At the highest energies, Radio Galaxies (RG) remain being the most promising candidates for UHECR acceleration. An interesting argument linking UHECR sources to their luminosity at radio frequencies has been put forward in this context by Hardcastle [44] and he concludes that RGs can accelerate protons to the highest observed energies in the lobes if a substantial amount of energy is in the turbulent component of the magnetic field, i.e. B > ∼ B equipart , and the Hillas criterion is met. In Cen A, existing observations do in fact constrain B > ∼ B equipart for the kpc-scale jet. Moreover, if UHECRs are predominantly protons, then very few sources should contribute to the observed flux. These sources should be easy to identify in the radio and their UHECR spectrum should cut off steeply at the observed highest energies. In contrast, if the mass composition is heavy at the highest energies then many radio galaxies could contribute to the UHECR flux but due to the much stronger deflection only the nearby Radio Galaxy Cen A may be identifiable [44]. Of course, such a conclusion depends very much on the strength of the EG magnetic fields and the maximum energy reached in the sources.\",\n \"pages\": [\n 8,\n 9\n ]\n },\n {\n \"title\": \"NEWPROJECTS AND OUTLOOK\",\n \"content\": \"Motivated by the large body of important experimental findings and new insights, the field continues to evolve very dynamically with new projects being planned or existing ones to be upgraded. In the study of low energy CRs, AMS is the by far most complex instrument in orbit, launched on May 16, 2011. It will measure light CR isotopes from about 500 MeV to 10 GeV and is hoped to improve our understanding of CR propagation in Galaxy. First data about the positron/electron ratio have been released recently [45] and confirm findings of PAMELA. The CALET (CALorimeteric Electron Telescope) project is a Japanese led international mission being developed as part of the utilization plan for the International Space Station (ISS) and aims at studying details of particle propagation in the Galaxy by a combination of energy spectrum measurements of electrons, protons and higher-charged nuclei. In Siberia, the German-Russian project HiScore is planned to be constructed at the Tunka site. This project will use open Cherenkov counters for CR measurements around the knee and will be complemented by radio antennas to explore this new detection technology. HAWK is being constructed in Mexico. Although its prime goal is the study of the g -ray sky above 100 GeV, it will also contribute to measuring CR anisotropies at TeV-energies. LHAASO , mostly driven by the Chinese community and much larger and more complex than HAWK, serves the same scientific goals. At the highest energies, Auger and TA plan upgrades in performance and size, respectively: Auger aims at improving the mass composition measurement and particle physics capabilities at the highest energies to answer the question about the origin of the flux suppression and TA aims at increasing their surface detector with a 2 km grid up to 2800 km 2 . Both collaborations have started to join efforts for a Next Generation Ground-based CR Observatory NGGO , much larger than existing experiments and aiming at good energy and mass resolution and exploring particle physics aspects at the highest energies. Four proposed and planned space missions constitute the roadmap of the space oriented community: TUS, JEM-EUSO, KLPVE, and Super-EUSO aim at contributing step-by-step to establish this challenging field of research. They will reach very large exposures aimed at seeing CR sources, which will be at the expense of energy resolution, composition measurements and particle physics capabilities. Given the resources of funding available in the next decade or two, it is unlikely that all of the above mentioned projects can be realized. Thus, priority should be given to complementarity rather than on duplication.\",\n \"pages\": [\n 9,\n 10\n ]\n },\n {\n \"title\": \"ACKNOWLEDGMENTS\",\n \"content\": \"Its a pleasure to thank the organizers of the Texas Symposium 2012 for inviting me to participate in this vibrant conference. I am also grateful for many stimulating discussions with colleagues from KASCADE-Grande, Auger and TA. Financial support by the German Ministry of Research and Education (Grants 05A11PX1 and 05A11PXA) and by the Helmholtz Alliance for Astroparticle Physics (HAP) is gratefully acknowledged.\",\n \"pages\": [\n 10\n ]\n }\n]"}}},{"rowIdx":87,"cells":{"bibcode":{"kind":"string","value":"2013CEAB...37..261D"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1305.2223.pdf"},"content":{"kind":"string","value":"\nBG GEM - A POORLY-STUDIED BINARY WITH A POSSIBLE BLACK HOLE COMPONENT\nN. A. Drake 1 , 2 , A. S. Miroshnichenko 3 , S. Danford 3 , and C. B. Pereira 1 Observatório Nacional/MCTI, Rio de Janeiro, Brazil 2 Sobolev Astronomical Institute, Saint-Petersburg State University, Saint-Petersburg, Russia 3 University of North Carolina at Greensboro, Department of Physics and Astronomy, Greensboro, NC, USA\n1\nAbstract. BG Gem is an eclipsing binary with a 91.6-day orbital period. The more massive primary component does not seem to show absorption lines in the spectrum, while the less massive secondary is thought to be a K-type star, possibly a supergiant. These results were obtained with optical low-resolution spectroscopy and photometry. The primary was suggested to be a black hole, although with a low confidence. We present a high-resolution optical spectrum of the system along with new BVR -photometry. Analysis of the spectrum shows that the K-type star rotates rapidly at v sin i = 18 kms -1 compared to most evolved stars of this temperature range. We also discuss constraints on the secondary's luminosity using spectroscopic criteria and on the entire system parameters using both the spectrum and photometry.\nKey words: Emission-line stars - circumstellar matter - binary systems - stars: fundamental parameters\n1. Introduction\nBG Gem is a 13-mag stellar object that shows brightness variations with a period of 91.645 days and an amplitude of ∼ 0.5 mag at visible wavelengths (Benson et al. 2000). The primary eclipse is only observed at λ ≤ 4400Å, while the light curves are shallower at longer wavelengths. From low-resolution ( ∼ 6 Å) observations of the system, Kenyon, Groot, & Benson (2002) deduced that the optical spectrum is dominated by absorption lines from a K0 i secondary component. They suggested that line emission which occurs in the Balmer and some He i lines may originate from a Btype or a black hole primary component. From the radial velocity curve, they determined a components mass ratio of 0.22 ± 0.07.\nElebert et al. (2007) took a high-resolution optical spectrum, retrieved\nan archival UV spectrum obtained with HST, and found an upper limit for the X-ray flux from INTEGRAL. They detected a weak UV continuum (more indicative of a black hole than of a normal star), but a low X-ray luminosity ( ≤ 10 35 erg s -1 ) and a low rotational velocity of the disk material (500 kms -1 in the Balmer lines and ≤ 1000 kms -1 in the UV emission lines). Therefore, these findings are inconclusive. However, if BG Gem does have a black hole component, it becomes the longest-period system of this kind in the Milky Way.\nOpen questions in studies of this system include the poorly known fundamental parameters of the cool secondary companion, the unknown nature of the primary component, and the evolutionary status of the entire system.\n2. Observations\nIn order to refine the secondary component parameters as well as those of the entire system and check the light curve, we took new spectroscopic and photometric observations of the BG Gem system.\n\n\n
Figure 1 : Balmer line profiles in our spectrum of BG Gem. The intensity is normalized to the nearby continuum and plotted against the heliocentric radial velocity.
\n\nThe photometric data were obtained in the V RHα filters during 11 nights\nin 2005-2006 at the 0.81-m telescope of the Three College Observatory near\nGreensboro, North Carolina, USA. The main goal of these observations was to look for changes of the light curves compared to the published data. Our data show the same brightness level at covered phases, but they are insufficient to detect any possible change of the orbital period. A high-resolution échelle spectrum ( λλ 4800-10500 Å, R = 60000) was obtained at the 2.7-m Harlan J. Smith telescope of the McDonald Observatory in December 2006. The spectrum was taken at an orbital phase of 0.62 (from the primary minimum). It has a signal-to-noise ratio of ∼ 30 in continuum near λ 4800 Å that rises towards longer wavelengths reaching ∼ 100\nnear λ 1 µ m. Parts of the spectrum are shown in Figures 1 and 2.\n\n\n
Figure 2 : Comparison of our spectrum of BG Gem (upper line) and that of a K1 iii star HD 19745 obtained with the same resolution. The spectral lines of HD 19745 were broadened to a rotational velocity of 18 km s -1 to match the line widths of BG Gem. The spectrum of BG Gem resembles the spectrum of HD 19745 except for the Li i line at λ 6707 . 8 Å which is absent in the spectrum of BG Gem.
\n\n3. Atmospheric parameters\nSignificant rotational broadening of the lines in the spectrum of BG Gem, an insufficient S/N ratio, and veiling of the spectrum caused by the primary's\n\n\n\n\n\n
Figure 3 : Comparison of the observed BG Gem spectrum (dotted line) with synthetic spectra calculated for T eff = 4500 K and log g = 0.8, 1.6, and 2.4 (from bottom to top).
\n\naccretion disk emission make it difficult to measure equivalent widths of individual Fe i and Fe ii lines and perform the usual analysis based on excitation and ionization equilibrium.\nTo derive the atmospheric parameters of BG Gem, we compared its spectrum with those of various K-type giant and supergiant stars with well-known parameters. We broadened lines in these spectra to the rotation velocity of BG Gem.\nProjected rotation velocity of BG Gem was determined by means of fitting the observed spectrum with synthetic spectra, calculated with different values of rotation velocity. Taking into account the FWHM of the instrumental profile of the spectrograph and adopting a macroturbulent velocity of 2 km s -1 , we determined a rotation velocity of v sin i = 18 . 0 ± 1 . 0 kms -1 for BG Gem.\nUsing these parameters, we calculated a grid of synthetic spectra in a wide range of effective temperatures and surface gravities ( T eff / log g ) in the spectral region 6080 -6180 Å containing lines of neutral elements with different excitation potentials and two lines of Fe ii (at λ 6084 . 1 Å and λ 6149 . 2 Å) which are sensitive to surface gravity.\nSynthetic spectra were calculated using the local thermodynamic equilibrium (LTE) model atmospheres of Kurucz (1993) and the current version (August 2010) of the spectral analysis code moog (Sneden 1973). The solar\nabundances taken from Anders & Grevesse (1989) were adopted except the carbon and nitrogen abundances, which are known to be modified in giant stars (see, e.g., Lambert & Ries 1981). The VALD atomic data base (Kupka et al. 1999) was used to create the line list. A microturbulent velocity of 2.0 km s -1 was adopted in our synthetic spectra calculations. An additional flux of 30% in continuum ( F disk /F cont ) was added to the synthetic spectra.\nAs an example, in Fig. 3 we show a comparison of the observed and synthetic spectra calculated with T eff = 4500 K and different values of log g (from 0.8 to 2.4) in two spectral regions containing Fe ii lines at λ 6084 . 1 Å and λ 6149 . 2 Å used to estimate the surface gravity.\nAmong high-rotating K giants with infrared excesses, nearly half have a high Li abundance (Drake et al. 2002). Such an abundance was found by González Hernández et al. (2004) for the secondary component in the black hole binary A0620-00 and by Sabbi et al. (2003) in the companion star to the millisecond pulsar J1740-5340 in NGC 6397 suggesting some Li production in these systems. We calculated synthetic spectra in the region of the Li i 6708 Å resonance line and found a low Li abundance in BG Gem, log ε (Li) ≤ 0 . 2 (in the notation log ε (X) = log( N X /N H ) + 12 . 0) .\n4. Results\nAnalysis of the absorption line spectrum shows that the secondary component is a K2 ii / iii star with a projected rotational velocity of 18 ± 1 kms -1 , an effective temperature of 4500 ± 300 K, and a surface gravity log g = 1.5 ± 0.5. The derived surface gravity implies a mass of the secondary component of 1 M /circledot , if it is filling its Roche lobe. Diffuse interstellar bands are weak implying a noticeable contribution of the primary's disk to the near-IR excess. Assuming an interstellar extinction of A V = 1.5 mag and M V = -0 . 8 mag for the K2-giant, the system is located at a distance of at least 3.5 kpc (no disk contribution at its eclipse by the secondary). No features that could be a result of an explosion in the system due to formation of the black hole are seen in the WISE data between λ 3.4 and λ 11.5 µ m.\n5. Conclusions\nWe refined the fundamental parameters of the visible star in the BG Gem binary system and showed that it is a rapidly rotating K2 ii / iii star rather\nthan a K0 i star suggested by Benson et al. (2000) and Kenyon et al. (2002).\nIt is still unclear whether a black hole is present in the system. The fact that we detect no light from a hot star implies that the primary's disk completely veils it. Spectroscopic observations at both eclipses are needed to put further constraints on the system properties.\nAcknowledgements\nA.M. acknowledges support from the American Astronomical Society International Travel Grant program and from the Department of Physics and Astronomy of the University of North Carolina at Greensboro. N.A.D. acknowledges support of a PCI/MCTI (Brazil) grant under the Project 311.868/2011-8. This paper is party based on observations obtained at the McDonald Observatory of the University of Texas at Austin. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, as well of the Wide-Field Infrared Survey Explorer ( WISE ) database.\nReferences\nAnders, E., and Grevesse, N.: 1989, Geochim. et Cosmochim. Acta , 53 , 197.\nBenson, P., Dullighan, A., Bonanos, A., McLeod, K.K., and Kenyon, S.J.: 2000, Astron. J. 119 , 890.\nDrake, N.A., de la Reza, R., da Silva, L., and Lambert, D. L.: 2002, Astron. J. 123 , 2703.\nElebert, P., Callanan, P.J., Russel, L., and Shaw, S.E.: 2007, Proc. IAU Symp. 238 , 361.\nGonzález Hernández, Rebolo, R., Israelian, G., and Casares, J.: 2004, Astrophys. J., 609 , 998.\nKenyon, S.J., Groot, P.J., and Benson, P.: 2002, Astron. J. 124 , 1054.\nKupka, F., Piskunov, N., Ryabchikova, T.A., Stempels, H. C., and Weiss, W.W.: 1999, Astron. Astrophys., Suppl. Ser. 138 , 119.\nKurucz, R.L.: 1993, CD-ROM No. 13, Smithsonian Astrophysical Observatory . Lambert, D.L., and Ries, L.M.: 1981, Astrophys. J. 248 , 228.\nSabbi, E., Gratton, R.G., Bragaglia, A., Ferraro, F.R., Possenti, A., Camilo, F., and D'Amico, N. : 2003, Astron. Astrophys. 412 , 829.\nSneden, C.: 1973, Ph.D. Thesis, Univ. of Texas.\n"},"sections":{"kind":"list like","value":[{"title":"BG GEM - A POORLY-STUDIED BINARY WITH A POSSIBLE BLACK HOLE COMPONENT","content":"N. A. Drake 1 , 2 , A. S. Miroshnichenko 3 , S. Danford 3 , and C. B. Pereira 1 Observatório Nacional/MCTI, Rio de Janeiro, Brazil 2 Sobolev Astronomical Institute, Saint-Petersburg State University, Saint-Petersburg, Russia 3 University of North Carolina at Greensboro, Department of Physics and Astronomy, Greensboro, NC, USA 1 Abstract. BG Gem is an eclipsing binary with a 91.6-day orbital period. The more massive primary component does not seem to show absorption lines in the spectrum, while the less massive secondary is thought to be a K-type star, possibly a supergiant. These results were obtained with optical low-resolution spectroscopy and photometry. The primary was suggested to be a black hole, although with a low confidence. We present a high-resolution optical spectrum of the system along with new BVR -photometry. Analysis of the spectrum shows that the K-type star rotates rapidly at v sin i = 18 kms -1 compared to most evolved stars of this temperature range. We also discuss constraints on the secondary's luminosity using spectroscopic criteria and on the entire system parameters using both the spectrum and photometry. Key words: Emission-line stars - circumstellar matter - binary systems - stars: fundamental parameters","pages":[1]},{"title":"1. Introduction","content":"BG Gem is a 13-mag stellar object that shows brightness variations with a period of 91.645 days and an amplitude of ∼ 0.5 mag at visible wavelengths (Benson et al. 2000). The primary eclipse is only observed at λ ≤ 4400Å, while the light curves are shallower at longer wavelengths. From low-resolution ( ∼ 6 Å) observations of the system, Kenyon, Groot, & Benson (2002) deduced that the optical spectrum is dominated by absorption lines from a K0 i secondary component. They suggested that line emission which occurs in the Balmer and some He i lines may originate from a Btype or a black hole primary component. From the radial velocity curve, they determined a components mass ratio of 0.22 ± 0.07. Elebert et al. (2007) took a high-resolution optical spectrum, retrieved an archival UV spectrum obtained with HST, and found an upper limit for the X-ray flux from INTEGRAL. They detected a weak UV continuum (more indicative of a black hole than of a normal star), but a low X-ray luminosity ( ≤ 10 35 erg s -1 ) and a low rotational velocity of the disk material (500 kms -1 in the Balmer lines and ≤ 1000 kms -1 in the UV emission lines). Therefore, these findings are inconclusive. However, if BG Gem does have a black hole component, it becomes the longest-period system of this kind in the Milky Way. Open questions in studies of this system include the poorly known fundamental parameters of the cool secondary companion, the unknown nature of the primary component, and the evolutionary status of the entire system.","pages":[1,2]},{"title":"2. Observations","content":"In order to refine the secondary component parameters as well as those of the entire system and check the light curve, we took new spectroscopic and photometric observations of the BG Gem system. The photometric data were obtained in the V RHα filters during 11 nights in 2005-2006 at the 0.81-m telescope of the Three College Observatory near Greensboro, North Carolina, USA. The main goal of these observations was to look for changes of the light curves compared to the published data. Our data show the same brightness level at covered phases, but they are insufficient to detect any possible change of the orbital period. A high-resolution échelle spectrum ( λλ 4800-10500 Å, R = 60000) was obtained at the 2.7-m Harlan J. Smith telescope of the McDonald Observatory in December 2006. The spectrum was taken at an orbital phase of 0.62 (from the primary minimum). It has a signal-to-noise ratio of ∼ 30 in continuum near λ 4800 Å that rises towards longer wavelengths reaching ∼ 100 near λ 1 µ m. Parts of the spectrum are shown in Figures 1 and 2.","pages":[2,3]},{"title":"3. Atmospheric parameters","content":"Significant rotational broadening of the lines in the spectrum of BG Gem, an insufficient S/N ratio, and veiling of the spectrum caused by the primary's accretion disk emission make it difficult to measure equivalent widths of individual Fe i and Fe ii lines and perform the usual analysis based on excitation and ionization equilibrium. To derive the atmospheric parameters of BG Gem, we compared its spectrum with those of various K-type giant and supergiant stars with well-known parameters. We broadened lines in these spectra to the rotation velocity of BG Gem. Projected rotation velocity of BG Gem was determined by means of fitting the observed spectrum with synthetic spectra, calculated with different values of rotation velocity. Taking into account the FWHM of the instrumental profile of the spectrograph and adopting a macroturbulent velocity of 2 km s -1 , we determined a rotation velocity of v sin i = 18 . 0 ± 1 . 0 kms -1 for BG Gem. Using these parameters, we calculated a grid of synthetic spectra in a wide range of effective temperatures and surface gravities ( T eff / log g ) in the spectral region 6080 -6180 Å containing lines of neutral elements with different excitation potentials and two lines of Fe ii (at λ 6084 . 1 Å and λ 6149 . 2 Å) which are sensitive to surface gravity. Synthetic spectra were calculated using the local thermodynamic equilibrium (LTE) model atmospheres of Kurucz (1993) and the current version (August 2010) of the spectral analysis code moog (Sneden 1973). The solar abundances taken from Anders & Grevesse (1989) were adopted except the carbon and nitrogen abundances, which are known to be modified in giant stars (see, e.g., Lambert & Ries 1981). The VALD atomic data base (Kupka et al. 1999) was used to create the line list. A microturbulent velocity of 2.0 km s -1 was adopted in our synthetic spectra calculations. An additional flux of 30% in continuum ( F disk /F cont ) was added to the synthetic spectra. As an example, in Fig. 3 we show a comparison of the observed and synthetic spectra calculated with T eff = 4500 K and different values of log g (from 0.8 to 2.4) in two spectral regions containing Fe ii lines at λ 6084 . 1 Å and λ 6149 . 2 Å used to estimate the surface gravity. Among high-rotating K giants with infrared excesses, nearly half have a high Li abundance (Drake et al. 2002). Such an abundance was found by González Hernández et al. (2004) for the secondary component in the black hole binary A0620-00 and by Sabbi et al. (2003) in the companion star to the millisecond pulsar J1740-5340 in NGC 6397 suggesting some Li production in these systems. We calculated synthetic spectra in the region of the Li i 6708 Å resonance line and found a low Li abundance in BG Gem, log ε (Li) ≤ 0 . 2 (in the notation log ε (X) = log( N X /N H ) + 12 . 0) .","pages":[3,4,5]},{"title":"4. Results","content":"Analysis of the absorption line spectrum shows that the secondary component is a K2 ii / iii star with a projected rotational velocity of 18 ± 1 kms -1 , an effective temperature of 4500 ± 300 K, and a surface gravity log g = 1.5 ± 0.5. The derived surface gravity implies a mass of the secondary component of 1 M /circledot , if it is filling its Roche lobe. Diffuse interstellar bands are weak implying a noticeable contribution of the primary's disk to the near-IR excess. Assuming an interstellar extinction of A V = 1.5 mag and M V = -0 . 8 mag for the K2-giant, the system is located at a distance of at least 3.5 kpc (no disk contribution at its eclipse by the secondary). No features that could be a result of an explosion in the system due to formation of the black hole are seen in the WISE data between λ 3.4 and λ 11.5 µ m.","pages":[5]},{"title":"5. Conclusions","content":"We refined the fundamental parameters of the visible star in the BG Gem binary system and showed that it is a rapidly rotating K2 ii / iii star rather than a K0 i star suggested by Benson et al. (2000) and Kenyon et al. (2002). It is still unclear whether a black hole is present in the system. The fact that we detect no light from a hot star implies that the primary's disk completely veils it. Spectroscopic observations at both eclipses are needed to put further constraints on the system properties.","pages":[5,6]},{"title":"Acknowledgements","content":"A.M. acknowledges support from the American Astronomical Society International Travel Grant program and from the Department of Physics and Astronomy of the University of North Carolina at Greensboro. N.A.D. acknowledges support of a PCI/MCTI (Brazil) grant under the Project 311.868/2011-8. This paper is party based on observations obtained at the McDonald Observatory of the University of Texas at Austin. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, as well of the Wide-Field Infrared Survey Explorer ( WISE ) database.","pages":[6]},{"title":"References","content":"Anders, E., and Grevesse, N.: 1989, Geochim. et Cosmochim. Acta , 53 , 197. Benson, P., Dullighan, A., Bonanos, A., McLeod, K.K., and Kenyon, S.J.: 2000, Astron. J. 119 , 890. Drake, N.A., de la Reza, R., da Silva, L., and Lambert, D. L.: 2002, Astron. J. 123 , 2703. Elebert, P., Callanan, P.J., Russel, L., and Shaw, S.E.: 2007, Proc. IAU Symp. 238 , 361. González Hernández, Rebolo, R., Israelian, G., and Casares, J.: 2004, Astrophys. J., 609 , 998. Kenyon, S.J., Groot, P.J., and Benson, P.: 2002, Astron. J. 124 , 1054. Kupka, F., Piskunov, N., Ryabchikova, T.A., Stempels, H. C., and Weiss, W.W.: 1999, Astron. Astrophys., Suppl. Ser. 138 , 119. Kurucz, R.L.: 1993, CD-ROM No. 13, Smithsonian Astrophysical Observatory . Lambert, D.L., and Ries, L.M.: 1981, Astrophys. J. 248 , 228. Sabbi, E., Gratton, R.G., Bragaglia, A., Ferraro, F.R., Possenti, A., Camilo, F., and D'Amico, N. : 2003, Astron. Astrophys. 412 , 829. Sneden, C.: 1973, Ph.D. Thesis, Univ. of Texas.","pages":[6]}],"string":"[\n {\n \"title\": \"BG GEM - A POORLY-STUDIED BINARY WITH A POSSIBLE BLACK HOLE COMPONENT\",\n \"content\": \"N. A. Drake 1 , 2 , A. S. Miroshnichenko 3 , S. Danford 3 , and C. B. Pereira 1 Observatório Nacional/MCTI, Rio de Janeiro, Brazil 2 Sobolev Astronomical Institute, Saint-Petersburg State University, Saint-Petersburg, Russia 3 University of North Carolina at Greensboro, Department of Physics and Astronomy, Greensboro, NC, USA 1 Abstract. BG Gem is an eclipsing binary with a 91.6-day orbital period. The more massive primary component does not seem to show absorption lines in the spectrum, while the less massive secondary is thought to be a K-type star, possibly a supergiant. These results were obtained with optical low-resolution spectroscopy and photometry. The primary was suggested to be a black hole, although with a low confidence. We present a high-resolution optical spectrum of the system along with new BVR -photometry. Analysis of the spectrum shows that the K-type star rotates rapidly at v sin i = 18 kms -1 compared to most evolved stars of this temperature range. We also discuss constraints on the secondary's luminosity using spectroscopic criteria and on the entire system parameters using both the spectrum and photometry. Key words: Emission-line stars - circumstellar matter - binary systems - stars: fundamental parameters\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"BG Gem is a 13-mag stellar object that shows brightness variations with a period of 91.645 days and an amplitude of ∼ 0.5 mag at visible wavelengths (Benson et al. 2000). The primary eclipse is only observed at λ ≤ 4400Å, while the light curves are shallower at longer wavelengths. From low-resolution ( ∼ 6 Å) observations of the system, Kenyon, Groot, & Benson (2002) deduced that the optical spectrum is dominated by absorption lines from a K0 i secondary component. They suggested that line emission which occurs in the Balmer and some He i lines may originate from a Btype or a black hole primary component. From the radial velocity curve, they determined a components mass ratio of 0.22 ± 0.07. Elebert et al. (2007) took a high-resolution optical spectrum, retrieved an archival UV spectrum obtained with HST, and found an upper limit for the X-ray flux from INTEGRAL. They detected a weak UV continuum (more indicative of a black hole than of a normal star), but a low X-ray luminosity ( ≤ 10 35 erg s -1 ) and a low rotational velocity of the disk material (500 kms -1 in the Balmer lines and ≤ 1000 kms -1 in the UV emission lines). Therefore, these findings are inconclusive. However, if BG Gem does have a black hole component, it becomes the longest-period system of this kind in the Milky Way. Open questions in studies of this system include the poorly known fundamental parameters of the cool secondary companion, the unknown nature of the primary component, and the evolutionary status of the entire system.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2. Observations\",\n \"content\": \"In order to refine the secondary component parameters as well as those of the entire system and check the light curve, we took new spectroscopic and photometric observations of the BG Gem system. The photometric data were obtained in the V RHα filters during 11 nights in 2005-2006 at the 0.81-m telescope of the Three College Observatory near Greensboro, North Carolina, USA. The main goal of these observations was to look for changes of the light curves compared to the published data. Our data show the same brightness level at covered phases, but they are insufficient to detect any possible change of the orbital period. A high-resolution échelle spectrum ( λλ 4800-10500 Å, R = 60000) was obtained at the 2.7-m Harlan J. Smith telescope of the McDonald Observatory in December 2006. The spectrum was taken at an orbital phase of 0.62 (from the primary minimum). It has a signal-to-noise ratio of ∼ 30 in continuum near λ 4800 Å that rises towards longer wavelengths reaching ∼ 100 near λ 1 µ m. Parts of the spectrum are shown in Figures 1 and 2.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"3. Atmospheric parameters\",\n \"content\": \"Significant rotational broadening of the lines in the spectrum of BG Gem, an insufficient S/N ratio, and veiling of the spectrum caused by the primary's accretion disk emission make it difficult to measure equivalent widths of individual Fe i and Fe ii lines and perform the usual analysis based on excitation and ionization equilibrium. To derive the atmospheric parameters of BG Gem, we compared its spectrum with those of various K-type giant and supergiant stars with well-known parameters. We broadened lines in these spectra to the rotation velocity of BG Gem. Projected rotation velocity of BG Gem was determined by means of fitting the observed spectrum with synthetic spectra, calculated with different values of rotation velocity. Taking into account the FWHM of the instrumental profile of the spectrograph and adopting a macroturbulent velocity of 2 km s -1 , we determined a rotation velocity of v sin i = 18 . 0 ± 1 . 0 kms -1 for BG Gem. Using these parameters, we calculated a grid of synthetic spectra in a wide range of effective temperatures and surface gravities ( T eff / log g ) in the spectral region 6080 -6180 Å containing lines of neutral elements with different excitation potentials and two lines of Fe ii (at λ 6084 . 1 Å and λ 6149 . 2 Å) which are sensitive to surface gravity. Synthetic spectra were calculated using the local thermodynamic equilibrium (LTE) model atmospheres of Kurucz (1993) and the current version (August 2010) of the spectral analysis code moog (Sneden 1973). The solar abundances taken from Anders & Grevesse (1989) were adopted except the carbon and nitrogen abundances, which are known to be modified in giant stars (see, e.g., Lambert & Ries 1981). The VALD atomic data base (Kupka et al. 1999) was used to create the line list. A microturbulent velocity of 2.0 km s -1 was adopted in our synthetic spectra calculations. An additional flux of 30% in continuum ( F disk /F cont ) was added to the synthetic spectra. As an example, in Fig. 3 we show a comparison of the observed and synthetic spectra calculated with T eff = 4500 K and different values of log g (from 0.8 to 2.4) in two spectral regions containing Fe ii lines at λ 6084 . 1 Å and λ 6149 . 2 Å used to estimate the surface gravity. Among high-rotating K giants with infrared excesses, nearly half have a high Li abundance (Drake et al. 2002). Such an abundance was found by González Hernández et al. (2004) for the secondary component in the black hole binary A0620-00 and by Sabbi et al. (2003) in the companion star to the millisecond pulsar J1740-5340 in NGC 6397 suggesting some Li production in these systems. We calculated synthetic spectra in the region of the Li i 6708 Å resonance line and found a low Li abundance in BG Gem, log ε (Li) ≤ 0 . 2 (in the notation log ε (X) = log( N X /N H ) + 12 . 0) .\",\n \"pages\": [\n 3,\n 4,\n 5\n ]\n },\n {\n \"title\": \"4. Results\",\n \"content\": \"Analysis of the absorption line spectrum shows that the secondary component is a K2 ii / iii star with a projected rotational velocity of 18 ± 1 kms -1 , an effective temperature of 4500 ± 300 K, and a surface gravity log g = 1.5 ± 0.5. The derived surface gravity implies a mass of the secondary component of 1 M /circledot , if it is filling its Roche lobe. Diffuse interstellar bands are weak implying a noticeable contribution of the primary's disk to the near-IR excess. Assuming an interstellar extinction of A V = 1.5 mag and M V = -0 . 8 mag for the K2-giant, the system is located at a distance of at least 3.5 kpc (no disk contribution at its eclipse by the secondary). No features that could be a result of an explosion in the system due to formation of the black hole are seen in the WISE data between λ 3.4 and λ 11.5 µ m.\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"5. Conclusions\",\n \"content\": \"We refined the fundamental parameters of the visible star in the BG Gem binary system and showed that it is a rapidly rotating K2 ii / iii star rather than a K0 i star suggested by Benson et al. (2000) and Kenyon et al. (2002). It is still unclear whether a black hole is present in the system. The fact that we detect no light from a hot star implies that the primary's disk completely veils it. Spectroscopic observations at both eclipses are needed to put further constraints on the system properties.\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"Acknowledgements\",\n \"content\": \"A.M. acknowledges support from the American Astronomical Society International Travel Grant program and from the Department of Physics and Astronomy of the University of North Carolina at Greensboro. N.A.D. acknowledges support of a PCI/MCTI (Brazil) grant under the Project 311.868/2011-8. This paper is party based on observations obtained at the McDonald Observatory of the University of Texas at Austin. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, as well of the Wide-Field Infrared Survey Explorer ( WISE ) database.\",\n \"pages\": [\n 6\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Anders, E., and Grevesse, N.: 1989, Geochim. et Cosmochim. Acta , 53 , 197. Benson, P., Dullighan, A., Bonanos, A., McLeod, K.K., and Kenyon, S.J.: 2000, Astron. J. 119 , 890. Drake, N.A., de la Reza, R., da Silva, L., and Lambert, D. L.: 2002, Astron. J. 123 , 2703. Elebert, P., Callanan, P.J., Russel, L., and Shaw, S.E.: 2007, Proc. IAU Symp. 238 , 361. González Hernández, Rebolo, R., Israelian, G., and Casares, J.: 2004, Astrophys. J., 609 , 998. Kenyon, S.J., Groot, P.J., and Benson, P.: 2002, Astron. J. 124 , 1054. Kupka, F., Piskunov, N., Ryabchikova, T.A., Stempels, H. C., and Weiss, W.W.: 1999, Astron. Astrophys., Suppl. Ser. 138 , 119. Kurucz, R.L.: 1993, CD-ROM No. 13, Smithsonian Astrophysical Observatory . Lambert, D.L., and Ries, L.M.: 1981, Astrophys. J. 248 , 228. Sabbi, E., Gratton, R.G., Bragaglia, A., Ferraro, F.R., Possenti, A., Camilo, F., and D'Amico, N. : 2003, Astron. Astrophys. 412 , 829. Sneden, C.: 1973, Ph.D. Thesis, Univ. of Texas.\",\n \"pages\": [\n 6\n ]\n }\n]"}}},{"rowIdx":88,"cells":{"bibcode":{"kind":"string","value":"2013CEAB...37..541M"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1402.6442.pdf"},"content":{"kind":"string","value":"\nRADIO SIGNATURES OF SOLAR ENERGETIC PARTICLES DURING THE 23 RD SOLAR CYCLE\nR. MITEVA 1 , K.-L. KLEIN 1 , S. W. SAMWEL 2 , A. NINDOS 3 , A. KOULOUMVAKOS 3 , 4 and H. REID 1 , 5\n\n1 LESIA-Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon, CNRS, UPMC, Univ. Paris-Diderot, France 2 National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo, Egypt 3 Section of Astrogeophysics, Physics Department, University of Ioannina, Ioannina GR-45110, Greece 4 Department of Astrophysics, Astronomy and Mechanics, Faculty of Physics, University of Athens, Athens, Greece SUPA School of Physics and Astronomy, University of Glasgow,\n5 Glasgow G12 8QQ, UK\n\nAbstract. We present the association rates between solar energetic particles (SEPs) and the radio emission signatures in the corona and IP space during the entire solar cycle 23. We selected SEPs associated with X and M-class flares from the visible solar hemisphere. All SEP events are also accompanied by coronal mass ejections. Here, we focus on the correlation between the SEP events and the appearance of radio type II, III and IV bursts on dynamic spectra. For this we used the available radio data from ground-based stations and the Wind/WAVES spacecraft. The associations are presented separately for SEP events accompanying activity in the eastern and western solar hemisphere. We find the highest association rate of SEP events to be with type III bursts, followed by types II and IV. Whereas for types III and IV no longitudinal dependence is noticed, these is a tendency for a higher SEP-association rate with type II bursts in the eastern hemisphere. A comparison with reports from previous studies is briefly discussed.\nKey words: Solar energetic particles - radio bursts - solar cycle 23\n1. Introduction\nSolar energetic particle (SEP) events are transient flux enhancements of electrons, protons and ions due to acceleration processes in the solar corona and interplanetary (IP) space. The high energy particles can pose a serious risk for the near Earth and ground-based technological devices, may dis-\nMITEVA ET AL.\nturb communications and be a health hazard (Mewaldt, 2006). This is why energetic particles are of major space weather interest. The accelerator of these particles, however, is still a subject of debate. Presently, the reconnection processes during flares (Cane et al. , 2002) and the shock-acceleration at coronal mass ejections (CMEs), Reames (1999), are recognized as efficient particle accelerators. An important issue is whether both acceleration processes act simultaneously with comparable efficiency or one of them dominates the particle energization process. In the current two-class SEP picture, the flares are thought to dominate the impulsive events and the shock waves dominate the large gradual events. Observations, however, are not able to relate unambiguously the SEP parameters measured in situ to the parent solar activity (e.g., flares vs. shocks). The large uncertainties usually present when doing different correlation analyses may arise due to the poorly known particle transport in the turbulent IP magnetic field, the magnetic connection between the acceleration site and the Earth, and that SEPs are often just measured at a single point in space.\nRadio observations can provide additional information and constraints for identifying the particle accelerator in the corona and IP space. When nonthermal electrons propagate through the solar corona they may emit radio waves, if certain conditions apply (Nindos et al. , 2008). The different types of radio bursts in the dynamic radio spectrum (see e.g., a review by Pick and Vilmer (2008)), are usually interpreted as signatures from electrons accelerated in the vicinity of a shock wave (type IIs), as electron beams (type IIIs) or as electrons confined in closed loop structure during the early evolution of a CME (type IVs). Type III bursts usually extend to low frequencies (reaching as far as the Earth orbit, ∼ 20 kHz) which is the main indicator that accelerated electrons (and by inference also protons) can efficiently escape from the solar corona (Cane et al. , 2002). Interplanetary counterparts of type II are also observed, but to lesser extent, whereas type IVs can be seen only to few MHz, but not to lower frequencies. Here we focus on the comparison of the particle (mainly proton) intensities measured in situ with the electromagnetic emission of electrons in the corona and IP space over the entire solar cycle 23.\nNumerous previous studies reported different association rates of SEPs and emission of radio bursts of type II (Cliver et al. , 2004; Gopalswamy et al. , 2008), III (Cane et al. , 2002) and IV (Kahler, 1982). The aim here is to identify the different types of radio emission from the dynamic spectra, to\ncomplement our results with reports from the different radio observatories and to compare them with previous works on the topic.\n2. Particle data\nIn the present work we selected all proton events with energy above 25 MeV as identified by Cane et al. (2010) that are associated with both strong flares (X and M-class) at eastern and western heliolongitudes and CMEs. Here we will differentiate the SEP events into eastern/western only and not by other SEP classifications schemes (Reames, 1999; Cliver, 2009), since any classification may leave out many 'mixed' cases in abundances, charge states, associated phenomena, etc. However, in order to facilitate comparison with previous work, we note if the SEP event was described as 'gradual' or 'impulsive' in Reames and Ng (2004) and Cliver and Ling (2009) by the superscripts 'g' and 'i', respectively.\nIn order to improve the statistics for the radio analysis (see next Section) we included SEP events that have high background level due to a previous event 1 , that are observed during SOHO data gap, those for which no value for the peak intensity was given due to instrument saturation (with superscript 's') and those with parent activity at the limb (with superscript 'l' we denote events at the solar limb and with 'c', events close to the disc center, between ± 10 degrees in heliolongitude). That lead finally to 175 particle events during solar cycle 23, of which 49 had sources in the eastern hemisphere, 124 in the western and two had uncertain source locations.\n3. Radio spectrograph data\nThe radio emission observed on ground and in space is usually presented in a frequency vs. time plot, where the strength of the radio emission is color-coded. This is known as a dynamic radio spectrum. Several features were recognized on such spectrum plots, e.g., fast drifting emission stripes extending from high to low frequencies (type IIIs); slowly drifting lanes of emission (type IIs) and a broad band stationary or/and drifting emission of type IV. Each of these radio emission types is a result of a unstable electron population (produced by a different process) generating Langmuir\n
\n\n
Table I : List of radio data sources
\n
\nwaves that convert into electromagnetic radiation via wave-wave processes. Namely, type IIs are usually assumed to be the shock signatures in the corona/IP space (Nelson and Melrose, 1985), type IIIs are electron beams propagating through the corona (Suzuki and Dulk, 1985), and the type IVs are the signatures from trapped electrons in coronal loops (Stewart, 1985; Pick, 1986). Here, we will use this standard interpretation for the radio burst emission in order to identify the probable particle accelerator. As a preparatory work for the analysis we collected all available radio spectral data (summarized in Table I) and the associated GOES soft X-ray (SXR) emission for each SEP event. The results of the associated radio bursts to each particle event are summarized in Tables II and III. There, we start with the SEP event date followed by the onset (in UT) of the SXR emission associated with each event as provided by GOES satellite (1 -8 Å channel).\nThe so-identified radio emissions of type II, III and IV are organized in several frequency (wavelength) ranges in Tables II and III. Namely, the decimeter (dm) range is subdivided into high (0.8 -3 GHz) and lower (0.3 -0.8 GHz) frequency parts. Similarly, we divided the metric (m) range into 100 -300 and 30 -100 MHz subbands. The IP space (dekameter/hectometer, DH, and kilometer wavelengths) is represented by one column. The radio bursts were ordered by their type and not by their temporal appearance on the radio spectral plot.\nSince we primarily used quicklook radio spectral data where image quality may be low, we also collected all available radio observatory reports for each event. In case radio emission of a given type was reported but could not be identified by us (due to low resolution of the actual image or because no radio spectrum plot was found), we give the result in squared brackets\nin Tables II and III. Any uncertain radio burst identification is indicated by a question mark following the roman number of the corresponding radio burst type. Weak emission signatures are denoted with superscript 'w', delayed emission with 'd' and low (high)-frequency emission onset with 'LFo' ('HFo'). Unclassified emission is given with 'UNCLF', fine structures with 'FS' and fundamental-harmonic emission with 'FH'. Continuum ('CONT') and decimeter ('DCIM') emission in the 0.3 -3 GHz range is considered as type IV-like emission in the analysis. The complete particle event list together with the associated radio bursts is given in Tables II and III (for western and eastern events, respectively).\n4. Results\nThe results are given as normalized number of the SEP events vs. radio frequency for each wavelength range (dm, m and DH), see the histograms on Figure 1, for eastern (on the left) and western (right) SEP events. The numerical value of the association rates, graphically presented on the histograms, is given by the height of each color bar. The SEP events associated with specific burst types as identified on the radio spectral plots are given with black color. With dark gray is shown the association in cases where the burst type was only given in the observatory reports (no spectra found at present) or where its identification is questionable. Whenever we give a value for an association rate, we will always sum up these two sections. Finally, with light gray color we denote the number of SEP events for which no radio information could be found (neither plots nor observatory reports). The majority of the missing radio plots is in the dm-range due to poor data coverage. Note that the highest discrepancy between the results given by us and by observatory reports is for the type II burst identification in the DHrange. This is mostly due to the weak and intermittent appearance of the IP type II bursts which makes an identification on quick-look plots difficult. In addition, the subjectivity of the observer plays a prominent role here, whereas the DH-type III identification, for example, is straightforward.\nOn the histograms, the number of events in each column is normalized to the total number of events in each group (eastern and western, correspondingly) and is also given explicitly in Table IV. While representing the association rate in the dm and m-range, we chose the greater association rate among their two subbands. For the total number of SEP events, given\nMITEVA ET AL.\n\n\n
Figure 1 : Histograms of the association rates of eastern (lest) and western (right) SEP events and the corresponding radio burst types for dm (3 -0.8 and 0.8 -0.3 GHz), m (300 -100 and 100 -30 MHz) and DH (30 -0.02 MHz) range. For the color-code see text.
\n\nwith 'All' in Table IV, we sum up the eastern, western and the uncertain SEP events. Since the dm-type II burst and the DH-type IV bursts are intrinsically rare phenomena, they will be excluded from the further analysis.\nThe highest association rate of SEPs is with the m and DH-type III bursts, usually /greaterorsimilar 90 % (see Table IV for details). A much lower association rate between SEPs and type IIIs is found in the dm-range (from about 30 to 50%). No dependence on the eastern vs. western heliolongitudes is seen for type III and type IV bursts, with the association rate of the type IV bursts being in the range from 50% up to 75%. In contrast, the SEP-association rate with the 30 -100 MHz metric (94%) and the DH type II bursts (88%)\nis slightly higher for eastern SEP events than for western ones (71 %).\n5. Discussion\nWe present the association rates of the SEP events (protons) and their accompanying radio emission (from electrons) in the corona (dm and m wavelength) and IP space (DH-range). Since there are no signatures of protons interacting with the solar atmosphere (with the exception of gamma-ray emission), we use electron signatures as a diagnostic for particle acceleration from the corona up to 1 AU.\nCane et al. (2002) were the first to identify long-lasting groups of DH type III bursts as a typical radio counterpart of large SEP events. They found the groups to be of significantly longer duration than type III bursts associated with impulsive flares, see also MacDowall et al. (1987). In the analysis performed here, we did not take into account the burst duration of DH-type III, nor explicitly separate the SEP events into gradual or impulsive. Still we find that SEP events have the highest association rate with type III radio bursts. This implies that the electrons accelerated in the corona (within one solar radius) have a ready access to the IP space, irrespective of whether the SEP event is impulsive or gradual.\nShock signatures (type II bursts) were also considered in correlation studies with SEP events. We found a lower association rate (up to 75%) of the DH-type II bursts with SEP events, compared to the m- and DH-type III association rates. The number increases when only SEP events with strong intensities are considered, in agreement with Gopalswamy et al. (2002) and Cliver et al. (2004).\nThe association of SEP events with types III and IV is comparable in the eastern and western groups (see Figure 1). But for the type II bursts there is a slight trend for a higher association rate in the eastern hemisphere. This result could be understood it terms of different sources contributing to SEP events. Shocks could be the dominant accelerator when the parent activity is poorly connected to Earth (as in the eastern solar hemisphere). In the western hemisphere (where more than twice as many events were detected) both flare and shock acceleration could contribute. When no shock signatures accompany the eastern SEP events, their propagation through the IP space and detection at Earth could be facilitated by a large-scale magnetic structure, e.g., interplanetary coronal mass ejections (ICMEs). Richardson et al.\nMITEVA ET AL.\n(1991) estimated that for about 15% of the eastern events this is likely the case. Recently Miteva et al. (2013) showed similar occurrence rate of ICMEs for the western SEP events (20%).\nThe association with the type IIIs seems to be increasing with the decreasing of the radio frequency (from dm to DH-range). At first, the type III identification in the dm-range might be masked due to overlying decimeter continuum often present in the dynamic radio spectra (observational bias). Hence, the obtained association rates of dm-IIIs are to be considered as lower limits only. In addition, high frequencies and dense plasma impede the production and growth of Langmuir waves. Also, the electron beam must travel an 'instability distance' from the acceleration site before Langmuir waves are generated (Reid et al. , 2011). This can cause a lack of high frequency type III emission in even the most energetic of electron beams. Moreover, collisions of both waves and electrons can suppress Langmuir wave growth at high frequencies, e.g., Kane et al. (1982); Reid and Kontar (2012).\nWithout the intention to give a complete overview on the results from previous work, we selected few statistical studies that are (partially) covering solar cycle 23. The different association rates are given in Table IV and are mostly consistent, although in many earlier studies only large SEP events were considered.\nAcknowledgements\nR.M. acknowledges a post-doctoral fellowship from Paris Observatory. A.N. was partly supported by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program \"Education and Lifelong Learning\" of the National Strategic Reference Framework (NSRF) Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. H.R. asknowledges the suport of the Scottish Universities Physics Alliance. We acknowledge the open data policy for the radio data used in this study and partial funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 262773 (SEPServer) and HESPE network (FP7-SPACE-2010-263086).\nReferences\nCane, H. V., Erickson, W. C., and Prestage, N. P.: 2002, Journal of Geophysical Research (Space Physics) 107 , 1315.\nCane, H. V., Richardson, I. G., and von Rosenvinge, T. T.: 2010, J. Geophys. Res. 115 , A08101.\nCliver, E. W.: 2009, Central European Astrophysical Bulletin 33 , 253-270.\nCliver, E. W., Kahler, S. W., and Reames, D. V.: 2004, Astrophys. J. 605 , 902910.\nCliver, E. W. and Ling, A. G.: 2007, Astrophys. J. 658 , 1349-1356.\nCliver, E. W. and Ling, A. G.: 2009, Astrophys. J. 690 , 598-609.\nGopalswamy, N.: 2003, Geophys. Res. Lett. 30 (12), 120000-1.\nGopalswamy, N., Yashiro, S., Akiyama, S., Mäkelä, P., Xie, H., Kaiser, M. L., Howard, R. A., and Bougeret, J. L.: 2008, Annales Geophysicae 26 , 30333047.\nGopalswamy, N., Yashiro, S., Michałek, G., Kaiser, M. L., Howard, R. A., Reames, D. V., Leske, R., and von Rosenvinge, T.: 2002, Astrophys. J., 572\nLett. , L103-L107.\nKahler, S. W.: 1982, Astrophys. J. 261 , 710-719.\nKane, S. R., Benz, A. O., and Treumann, R. A.: 1982, Astrophys. J. 263 , 423-432. Klein, K.-L., Trottet, G., Samwel, S., and Malandraki, O.: 2011, Solar Phys. 269\n, 309-333.\nMacDowall, R. J., Kundu, M. R., and Stone, R. G.: 1987, Solar Phys. 111 , 397418.\nMacDowall, R. J., Lara, A., Manoharan, P. K., Nitta, N. V., Rosas, A. M., and Bougeret, J. L.: 2003, Geophys. Res. Lett. 30 (12), 120000-1.\nMewaldt, R. A.: 2006, Space Sci. Rev. 124 , 303-316.\nMiteva, R., Klein, K.-L., Malandraki, O., and Dorrian, G.: 2013, Solar Phys. 282 , 579-613.\nNelson, G. J. and Melrose, D. B.: 1985, Type II bursts , pp. 333-359.\nNindos, A., Aurass, H., Klein, K.-L., and Trottet, G.: 2008, Solar Phys. 253 , 341.\nPick, M.: 1986, Solar Phys. 104 , 19-32.\nPick, M. and Vilmer, N.: 2008, Astron. Astrophys. Rev. 16 , 1-153.\nReames, D. V.: 1999, Space Sci. Rev. 90 , 413-491.\nReames, D. V. and Ng, C. K.: 2004, Astrophys. J. 610 , 510-522.\nReid, H. A. S. and Kontar, E. P.: 2012, Solar Phys. p. 109.\nReid, H. A. S., Vilmer, N., and Kontar, E. P.: 2011, Astron. Astrophys. 529 , A66. Richardson, I. G., Cane, H. V., and von Rosenvinge, T. T.: 1991, J. Geophys. Res. 96\n, 7853-7860.\nStewart, R. T.: 1985, Moving Type IV bursts , pp. 361-383.\nSuzuki, S. and Dulk, G. A.: 1985, Bursts of Type III and Type V , pp. 289-332.\nMITEVA ET AL.\n
\n\n
Table II : Solar energetic particle events with origin at western heliolongitudes: visual identification and [observatory reports] of type II, III and IV radio bursts.
\n
\n
\n\n
Table II : cont'd
\n
\nMITEVA ET AL.\n
\n\n
Table III : Solar energetic particle events with origin at eastern or uncertain (with superscript 'u') heliolongitudes: visual identification and [observatory reports] of type II, III and IV radio bursts.
\nE\nS\nRADIO SIGNATURES OF SEP EVENTS\n)\nw\n4\n0\n5\nd\na\nR\nv\ne\n(\ng\nn\no\nr\nt\ns\n:\n)\nw\n(\ns\ns\n1\n-\n3\nf\no\ns\nn\no\nt\no\nr\np\nV\ne\nM\nT D H -8 8 7 1 9 0 s r 7 5 8 0 w ) 6 3 ( 9 6 s / 1 0 0 8 y N / 5 2 y Y 2 5 y N / 9 0 y Y Y / 5 2 n Y / 3 0 y N w e a k ) S E P ∼ 1 0 4 c m -2 s 1 0 c m -2 s -1\nI\n-\nm\ny\nr\no\ng\ne\nt\na\nc\n4\n9\nn\nr\ne\nt\ns\na\nE\nCent. Eur. Astrophys. Bull.\n37\n(2018) 1, ??-??\n13\n/\ns\n8\n8\n(\n2\n8\ny\n1\n6\nl\nl\nA\ne\nM\n≥\nf\no\ns\nn\no\nt\no\nr\np\nV\ne\nM\n1\n7\nn\nr\ne\nt\ns\ne\nW\n8\n7\nl\nl\nA\nm\nm\n,\nf\n0\n9\nn\nr\ne\nt\ns\na\nE\nn\nr\ne\nt\ns\ne\nW\n"},"sections":{"kind":"list like","value":[{"title":"RADIO SIGNATURES OF SOLAR ENERGETIC PARTICLES DURING THE 23 RD SOLAR CYCLE","content":"R. MITEVA 1 , K.-L. KLEIN 1 , S. W. SAMWEL 2 , A. NINDOS 3 , A. KOULOUMVAKOS 3 , 4 and H. REID 1 , 5 Abstract. We present the association rates between solar energetic particles (SEPs) and the radio emission signatures in the corona and IP space during the entire solar cycle 23. We selected SEPs associated with X and M-class flares from the visible solar hemisphere. All SEP events are also accompanied by coronal mass ejections. Here, we focus on the correlation between the SEP events and the appearance of radio type II, III and IV bursts on dynamic spectra. For this we used the available radio data from ground-based stations and the Wind/WAVES spacecraft. The associations are presented separately for SEP events accompanying activity in the eastern and western solar hemisphere. We find the highest association rate of SEP events to be with type III bursts, followed by types II and IV. Whereas for types III and IV no longitudinal dependence is noticed, these is a tendency for a higher SEP-association rate with type II bursts in the eastern hemisphere. A comparison with reports from previous studies is briefly discussed. Key words: Solar energetic particles - radio bursts - solar cycle 23","pages":[1]},{"title":"1. Introduction","content":"Solar energetic particle (SEP) events are transient flux enhancements of electrons, protons and ions due to acceleration processes in the solar corona and interplanetary (IP) space. The high energy particles can pose a serious risk for the near Earth and ground-based technological devices, may dis-","pages":[1]},{"title":"MITEVA ET AL.","content":"b a r P E S I I I s 6 0 1 > 0 1 > E S RADIO SIGNATURES OF SEP EVENTS ) w 4 0 5 d a R v e ( g n o r t s : ) w ( s s 1 - 3 f o s n o t o r p V e M T D H -8 8 7 1 9 0 s r 7 5 8 0 w ) 6 3 ( 9 6 s / 1 0 0 8 y N / 5 2 y Y 2 5 y N / 9 0 y Y Y / 5 2 n Y / 3 0 y N w e a k ) S E P ∼ 1 0 4 c m -2 s 1 0 c m -2 s -1 I - m y r o g e t a c 4 9 n r e t s a E Cent. Eur. Astrophys. Bull. 37 (2018) 1, ??-?? 13 / s 8 8 ( 2 8 y 1 6 l l A e M ≥ f o s n o t o r p V e M 1 7 n r e t s e W 8 7 l l A m m , f 0 9 n r e t s a E n r e t s e W","pages":[13]},{"title":"2. Particle data","content":"In the present work we selected all proton events with energy above 25 MeV as identified by Cane et al. (2010) that are associated with both strong flares (X and M-class) at eastern and western heliolongitudes and CMEs. Here we will differentiate the SEP events into eastern/western only and not by other SEP classifications schemes (Reames, 1999; Cliver, 2009), since any classification may leave out many 'mixed' cases in abundances, charge states, associated phenomena, etc. However, in order to facilitate comparison with previous work, we note if the SEP event was described as 'gradual' or 'impulsive' in Reames and Ng (2004) and Cliver and Ling (2009) by the superscripts 'g' and 'i', respectively. In order to improve the statistics for the radio analysis (see next Section) we included SEP events that have high background level due to a previous event 1 , that are observed during SOHO data gap, those for which no value for the peak intensity was given due to instrument saturation (with superscript 's') and those with parent activity at the limb (with superscript 'l' we denote events at the solar limb and with 'c', events close to the disc center, between ± 10 degrees in heliolongitude). That lead finally to 175 particle events during solar cycle 23, of which 49 had sources in the eastern hemisphere, 124 in the western and two had uncertain source locations.","pages":[3]},{"title":"3. Radio spectrograph data","content":"The radio emission observed on ground and in space is usually presented in a frequency vs. time plot, where the strength of the radio emission is color-coded. This is known as a dynamic radio spectrum. Several features were recognized on such spectrum plots, e.g., fast drifting emission stripes extending from high to low frequencies (type IIIs); slowly drifting lanes of emission (type IIs) and a broad band stationary or/and drifting emission of type IV. Each of these radio emission types is a result of a unstable electron population (produced by a different process) generating Langmuir waves that convert into electromagnetic radiation via wave-wave processes. Namely, type IIs are usually assumed to be the shock signatures in the corona/IP space (Nelson and Melrose, 1985), type IIIs are electron beams propagating through the corona (Suzuki and Dulk, 1985), and the type IVs are the signatures from trapped electrons in coronal loops (Stewart, 1985; Pick, 1986). Here, we will use this standard interpretation for the radio burst emission in order to identify the probable particle accelerator. As a preparatory work for the analysis we collected all available radio spectral data (summarized in Table I) and the associated GOES soft X-ray (SXR) emission for each SEP event. The results of the associated radio bursts to each particle event are summarized in Tables II and III. There, we start with the SEP event date followed by the onset (in UT) of the SXR emission associated with each event as provided by GOES satellite (1 -8 Å channel). The so-identified radio emissions of type II, III and IV are organized in several frequency (wavelength) ranges in Tables II and III. Namely, the decimeter (dm) range is subdivided into high (0.8 -3 GHz) and lower (0.3 -0.8 GHz) frequency parts. Similarly, we divided the metric (m) range into 100 -300 and 30 -100 MHz subbands. The IP space (dekameter/hectometer, DH, and kilometer wavelengths) is represented by one column. The radio bursts were ordered by their type and not by their temporal appearance on the radio spectral plot. Since we primarily used quicklook radio spectral data where image quality may be low, we also collected all available radio observatory reports for each event. In case radio emission of a given type was reported but could not be identified by us (due to low resolution of the actual image or because no radio spectrum plot was found), we give the result in squared brackets in Tables II and III. Any uncertain radio burst identification is indicated by a question mark following the roman number of the corresponding radio burst type. Weak emission signatures are denoted with superscript 'w', delayed emission with 'd' and low (high)-frequency emission onset with 'LFo' ('HFo'). Unclassified emission is given with 'UNCLF', fine structures with 'FS' and fundamental-harmonic emission with 'FH'. Continuum ('CONT') and decimeter ('DCIM') emission in the 0.3 -3 GHz range is considered as type IV-like emission in the analysis. The complete particle event list together with the associated radio bursts is given in Tables II and III (for western and eastern events, respectively).","pages":[3,4,5]},{"title":"4. Results","content":"The results are given as normalized number of the SEP events vs. radio frequency for each wavelength range (dm, m and DH), see the histograms on Figure 1, for eastern (on the left) and western (right) SEP events. The numerical value of the association rates, graphically presented on the histograms, is given by the height of each color bar. The SEP events associated with specific burst types as identified on the radio spectral plots are given with black color. With dark gray is shown the association in cases where the burst type was only given in the observatory reports (no spectra found at present) or where its identification is questionable. Whenever we give a value for an association rate, we will always sum up these two sections. Finally, with light gray color we denote the number of SEP events for which no radio information could be found (neither plots nor observatory reports). The majority of the missing radio plots is in the dm-range due to poor data coverage. Note that the highest discrepancy between the results given by us and by observatory reports is for the type II burst identification in the DHrange. This is mostly due to the weak and intermittent appearance of the IP type II bursts which makes an identification on quick-look plots difficult. In addition, the subjectivity of the observer plays a prominent role here, whereas the DH-type III identification, for example, is straightforward. On the histograms, the number of events in each column is normalized to the total number of events in each group (eastern and western, correspondingly) and is also given explicitly in Table IV. While representing the association rate in the dm and m-range, we chose the greater association rate among their two subbands. For the total number of SEP events, given","pages":[5]},{"title":"5. Discussion","content":"We present the association rates of the SEP events (protons) and their accompanying radio emission (from electrons) in the corona (dm and m wavelength) and IP space (DH-range). Since there are no signatures of protons interacting with the solar atmosphere (with the exception of gamma-ray emission), we use electron signatures as a diagnostic for particle acceleration from the corona up to 1 AU. Cane et al. (2002) were the first to identify long-lasting groups of DH type III bursts as a typical radio counterpart of large SEP events. They found the groups to be of significantly longer duration than type III bursts associated with impulsive flares, see also MacDowall et al. (1987). In the analysis performed here, we did not take into account the burst duration of DH-type III, nor explicitly separate the SEP events into gradual or impulsive. Still we find that SEP events have the highest association rate with type III radio bursts. This implies that the electrons accelerated in the corona (within one solar radius) have a ready access to the IP space, irrespective of whether the SEP event is impulsive or gradual. Shock signatures (type II bursts) were also considered in correlation studies with SEP events. We found a lower association rate (up to 75%) of the DH-type II bursts with SEP events, compared to the m- and DH-type III association rates. The number increases when only SEP events with strong intensities are considered, in agreement with Gopalswamy et al. (2002) and Cliver et al. (2004). The association of SEP events with types III and IV is comparable in the eastern and western groups (see Figure 1). But for the type II bursts there is a slight trend for a higher association rate in the eastern hemisphere. This result could be understood it terms of different sources contributing to SEP events. Shocks could be the dominant accelerator when the parent activity is poorly connected to Earth (as in the eastern solar hemisphere). In the western hemisphere (where more than twice as many events were detected) both flare and shock acceleration could contribute. When no shock signatures accompany the eastern SEP events, their propagation through the IP space and detection at Earth could be facilitated by a large-scale magnetic structure, e.g., interplanetary coronal mass ejections (ICMEs). Richardson et al.","pages":[7]},{"title":"Acknowledgements","content":"R.M. acknowledges a post-doctoral fellowship from Paris Observatory. A.N. was partly supported by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program \"Education and Lifelong Learning\" of the National Strategic Reference Framework (NSRF) Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. H.R. asknowledges the suport of the Scottish Universities Physics Alliance. We acknowledge the open data policy for the radio data used in this study and partial funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 262773 (SEPServer) and HESPE network (FP7-SPACE-2010-263086).","pages":[8]},{"title":"References","content":"Cane, H. V., Erickson, W. C., and Prestage, N. P.: 2002, Journal of Geophysical Research (Space Physics) 107 , 1315. Cane, H. V., Richardson, I. G., and von Rosenvinge, T. T.: 2010, J. Geophys. Res. 115 , A08101. Cliver, E. W.: 2009, Central European Astrophysical Bulletin 33 , 253-270. Cliver, E. W., Kahler, S. W., and Reames, D. V.: 2004, Astrophys. J. 605 , 902910. Cliver, E. W. and Ling, A. G.: 2007, Astrophys. J. 658 , 1349-1356. Cliver, E. W. and Ling, A. G.: 2009, Astrophys. J. 690 , 598-609. Gopalswamy, N.: 2003, Geophys. Res. Lett. 30 (12), 120000-1. Gopalswamy, N., Yashiro, S., Akiyama, S., Mäkelä, P., Xie, H., Kaiser, M. L., Howard, R. A., and Bougeret, J. L.: 2008, Annales Geophysicae 26 , 30333047. Gopalswamy, N., Yashiro, S., Michałek, G., Kaiser, M. L., Howard, R. A., Reames, D. V., Leske, R., and von Rosenvinge, T.: 2002, Astrophys. J., 572 Lett. , L103-L107. Kahler, S. W.: 1982, Astrophys. J. 261 , 710-719. Kane, S. R., Benz, A. O., and Treumann, R. A.: 1982, Astrophys. J. 263 , 423-432. Klein, K.-L., Trottet, G., Samwel, S., and Malandraki, O.: 2011, Solar Phys. 269 , 309-333. MacDowall, R. J., Kundu, M. R., and Stone, R. G.: 1987, Solar Phys. 111 , 397418. MacDowall, R. J., Lara, A., Manoharan, P. K., Nitta, N. V., Rosas, A. M., and Bougeret, J. L.: 2003, Geophys. Res. Lett. 30 (12), 120000-1. Mewaldt, R. A.: 2006, Space Sci. Rev. 124 , 303-316. Miteva, R., Klein, K.-L., Malandraki, O., and Dorrian, G.: 2013, Solar Phys. 282 , 579-613. Nelson, G. J. and Melrose, D. B.: 1985, Type II bursts , pp. 333-359. Nindos, A., Aurass, H., Klein, K.-L., and Trottet, G.: 2008, Solar Phys. 253 , 341. Pick, M.: 1986, Solar Phys. 104 , 19-32. Pick, M. and Vilmer, N.: 2008, Astron. Astrophys. Rev. 16 , 1-153. Reames, D. V.: 1999, Space Sci. Rev. 90 , 413-491. Reames, D. V. and Ng, C. K.: 2004, Astrophys. J. 610 , 510-522. Reid, H. A. S. and Kontar, E. P.: 2012, Solar Phys. p. 109. Reid, H. A. S., Vilmer, N., and Kontar, E. P.: 2011, Astron. Astrophys. 529 , A66. Richardson, I. G., Cane, H. V., and von Rosenvinge, T. T.: 1991, J. Geophys. Res. 96 , 7853-7860. Stewart, R. T.: 1985, Moving Type IV bursts , pp. 361-383. Suzuki, S. and Dulk, G. A.: 1985, Bursts of Type III and Type V , pp. 289-332.","pages":[9]}],"string":"[\n {\n \"title\": \"RADIO SIGNATURES OF SOLAR ENERGETIC PARTICLES DURING THE 23 RD SOLAR CYCLE\",\n \"content\": \"R. MITEVA 1 , K.-L. KLEIN 1 , S. W. SAMWEL 2 , A. NINDOS 3 , A. KOULOUMVAKOS 3 , 4 and H. REID 1 , 5 Abstract. We present the association rates between solar energetic particles (SEPs) and the radio emission signatures in the corona and IP space during the entire solar cycle 23. We selected SEPs associated with X and M-class flares from the visible solar hemisphere. All SEP events are also accompanied by coronal mass ejections. Here, we focus on the correlation between the SEP events and the appearance of radio type II, III and IV bursts on dynamic spectra. For this we used the available radio data from ground-based stations and the Wind/WAVES spacecraft. The associations are presented separately for SEP events accompanying activity in the eastern and western solar hemisphere. We find the highest association rate of SEP events to be with type III bursts, followed by types II and IV. Whereas for types III and IV no longitudinal dependence is noticed, these is a tendency for a higher SEP-association rate with type II bursts in the eastern hemisphere. A comparison with reports from previous studies is briefly discussed. Key words: Solar energetic particles - radio bursts - solar cycle 23\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"Solar energetic particle (SEP) events are transient flux enhancements of electrons, protons and ions due to acceleration processes in the solar corona and interplanetary (IP) space. The high energy particles can pose a serious risk for the near Earth and ground-based technological devices, may dis-\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"MITEVA ET AL.\",\n \"content\": \"b a r P E S I I I s 6 0 1 > 0 1 > E S RADIO SIGNATURES OF SEP EVENTS ) w 4 0 5 d a R v e ( g n o r t s : ) w ( s s 1 - 3 f o s n o t o r p V e M T D H -8 8 7 1 9 0 s r 7 5 8 0 w ) 6 3 ( 9 6 s / 1 0 0 8 y N / 5 2 y Y 2 5 y N / 9 0 y Y Y / 5 2 n Y / 3 0 y N w e a k ) S E P ∼ 1 0 4 c m -2 s 1 0 c m -2 s -1 I - m y r o g e t a c 4 9 n r e t s a E Cent. Eur. Astrophys. Bull. 37 (2018) 1, ??-?? 13 / s 8 8 ( 2 8 y 1 6 l l A e M ≥ f o s n o t o r p V e M 1 7 n r e t s e W 8 7 l l A m m , f 0 9 n r e t s a E n r e t s e W\",\n \"pages\": [\n 13\n ]\n },\n {\n \"title\": \"2. Particle data\",\n \"content\": \"In the present work we selected all proton events with energy above 25 MeV as identified by Cane et al. (2010) that are associated with both strong flares (X and M-class) at eastern and western heliolongitudes and CMEs. Here we will differentiate the SEP events into eastern/western only and not by other SEP classifications schemes (Reames, 1999; Cliver, 2009), since any classification may leave out many 'mixed' cases in abundances, charge states, associated phenomena, etc. However, in order to facilitate comparison with previous work, we note if the SEP event was described as 'gradual' or 'impulsive' in Reames and Ng (2004) and Cliver and Ling (2009) by the superscripts 'g' and 'i', respectively. In order to improve the statistics for the radio analysis (see next Section) we included SEP events that have high background level due to a previous event 1 , that are observed during SOHO data gap, those for which no value for the peak intensity was given due to instrument saturation (with superscript 's') and those with parent activity at the limb (with superscript 'l' we denote events at the solar limb and with 'c', events close to the disc center, between ± 10 degrees in heliolongitude). That lead finally to 175 particle events during solar cycle 23, of which 49 had sources in the eastern hemisphere, 124 in the western and two had uncertain source locations.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"3. Radio spectrograph data\",\n \"content\": \"The radio emission observed on ground and in space is usually presented in a frequency vs. time plot, where the strength of the radio emission is color-coded. This is known as a dynamic radio spectrum. Several features were recognized on such spectrum plots, e.g., fast drifting emission stripes extending from high to low frequencies (type IIIs); slowly drifting lanes of emission (type IIs) and a broad band stationary or/and drifting emission of type IV. Each of these radio emission types is a result of a unstable electron population (produced by a different process) generating Langmuir waves that convert into electromagnetic radiation via wave-wave processes. Namely, type IIs are usually assumed to be the shock signatures in the corona/IP space (Nelson and Melrose, 1985), type IIIs are electron beams propagating through the corona (Suzuki and Dulk, 1985), and the type IVs are the signatures from trapped electrons in coronal loops (Stewart, 1985; Pick, 1986). Here, we will use this standard interpretation for the radio burst emission in order to identify the probable particle accelerator. As a preparatory work for the analysis we collected all available radio spectral data (summarized in Table I) and the associated GOES soft X-ray (SXR) emission for each SEP event. The results of the associated radio bursts to each particle event are summarized in Tables II and III. There, we start with the SEP event date followed by the onset (in UT) of the SXR emission associated with each event as provided by GOES satellite (1 -8 Å channel). The so-identified radio emissions of type II, III and IV are organized in several frequency (wavelength) ranges in Tables II and III. Namely, the decimeter (dm) range is subdivided into high (0.8 -3 GHz) and lower (0.3 -0.8 GHz) frequency parts. Similarly, we divided the metric (m) range into 100 -300 and 30 -100 MHz subbands. The IP space (dekameter/hectometer, DH, and kilometer wavelengths) is represented by one column. The radio bursts were ordered by their type and not by their temporal appearance on the radio spectral plot. Since we primarily used quicklook radio spectral data where image quality may be low, we also collected all available radio observatory reports for each event. In case radio emission of a given type was reported but could not be identified by us (due to low resolution of the actual image or because no radio spectrum plot was found), we give the result in squared brackets in Tables II and III. Any uncertain radio burst identification is indicated by a question mark following the roman number of the corresponding radio burst type. Weak emission signatures are denoted with superscript 'w', delayed emission with 'd' and low (high)-frequency emission onset with 'LFo' ('HFo'). Unclassified emission is given with 'UNCLF', fine structures with 'FS' and fundamental-harmonic emission with 'FH'. Continuum ('CONT') and decimeter ('DCIM') emission in the 0.3 -3 GHz range is considered as type IV-like emission in the analysis. The complete particle event list together with the associated radio bursts is given in Tables II and III (for western and eastern events, respectively).\",\n \"pages\": [\n 3,\n 4,\n 5\n ]\n },\n {\n \"title\": \"4. Results\",\n \"content\": \"The results are given as normalized number of the SEP events vs. radio frequency for each wavelength range (dm, m and DH), see the histograms on Figure 1, for eastern (on the left) and western (right) SEP events. The numerical value of the association rates, graphically presented on the histograms, is given by the height of each color bar. The SEP events associated with specific burst types as identified on the radio spectral plots are given with black color. With dark gray is shown the association in cases where the burst type was only given in the observatory reports (no spectra found at present) or where its identification is questionable. Whenever we give a value for an association rate, we will always sum up these two sections. Finally, with light gray color we denote the number of SEP events for which no radio information could be found (neither plots nor observatory reports). The majority of the missing radio plots is in the dm-range due to poor data coverage. Note that the highest discrepancy between the results given by us and by observatory reports is for the type II burst identification in the DHrange. This is mostly due to the weak and intermittent appearance of the IP type II bursts which makes an identification on quick-look plots difficult. In addition, the subjectivity of the observer plays a prominent role here, whereas the DH-type III identification, for example, is straightforward. On the histograms, the number of events in each column is normalized to the total number of events in each group (eastern and western, correspondingly) and is also given explicitly in Table IV. While representing the association rate in the dm and m-range, we chose the greater association rate among their two subbands. For the total number of SEP events, given\",\n \"pages\": [\n 5\n ]\n },\n {\n \"title\": \"5. Discussion\",\n \"content\": \"We present the association rates of the SEP events (protons) and their accompanying radio emission (from electrons) in the corona (dm and m wavelength) and IP space (DH-range). Since there are no signatures of protons interacting with the solar atmosphere (with the exception of gamma-ray emission), we use electron signatures as a diagnostic for particle acceleration from the corona up to 1 AU. Cane et al. (2002) were the first to identify long-lasting groups of DH type III bursts as a typical radio counterpart of large SEP events. They found the groups to be of significantly longer duration than type III bursts associated with impulsive flares, see also MacDowall et al. (1987). In the analysis performed here, we did not take into account the burst duration of DH-type III, nor explicitly separate the SEP events into gradual or impulsive. Still we find that SEP events have the highest association rate with type III radio bursts. This implies that the electrons accelerated in the corona (within one solar radius) have a ready access to the IP space, irrespective of whether the SEP event is impulsive or gradual. Shock signatures (type II bursts) were also considered in correlation studies with SEP events. We found a lower association rate (up to 75%) of the DH-type II bursts with SEP events, compared to the m- and DH-type III association rates. The number increases when only SEP events with strong intensities are considered, in agreement with Gopalswamy et al. (2002) and Cliver et al. (2004). The association of SEP events with types III and IV is comparable in the eastern and western groups (see Figure 1). But for the type II bursts there is a slight trend for a higher association rate in the eastern hemisphere. This result could be understood it terms of different sources contributing to SEP events. Shocks could be the dominant accelerator when the parent activity is poorly connected to Earth (as in the eastern solar hemisphere). In the western hemisphere (where more than twice as many events were detected) both flare and shock acceleration could contribute. When no shock signatures accompany the eastern SEP events, their propagation through the IP space and detection at Earth could be facilitated by a large-scale magnetic structure, e.g., interplanetary coronal mass ejections (ICMEs). Richardson et al.\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"Acknowledgements\",\n \"content\": \"R.M. acknowledges a post-doctoral fellowship from Paris Observatory. A.N. was partly supported by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program \\\"Education and Lifelong Learning\\\" of the National Strategic Reference Framework (NSRF) Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. H.R. asknowledges the suport of the Scottish Universities Physics Alliance. We acknowledge the open data policy for the radio data used in this study and partial funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 262773 (SEPServer) and HESPE network (FP7-SPACE-2010-263086).\",\n \"pages\": [\n 8\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Cane, H. V., Erickson, W. C., and Prestage, N. P.: 2002, Journal of Geophysical Research (Space Physics) 107 , 1315. Cane, H. V., Richardson, I. G., and von Rosenvinge, T. T.: 2010, J. Geophys. Res. 115 , A08101. Cliver, E. W.: 2009, Central European Astrophysical Bulletin 33 , 253-270. Cliver, E. W., Kahler, S. W., and Reames, D. V.: 2004, Astrophys. J. 605 , 902910. Cliver, E. W. and Ling, A. G.: 2007, Astrophys. J. 658 , 1349-1356. Cliver, E. W. and Ling, A. G.: 2009, Astrophys. J. 690 , 598-609. Gopalswamy, N.: 2003, Geophys. Res. Lett. 30 (12), 120000-1. Gopalswamy, N., Yashiro, S., Akiyama, S., Mäkelä, P., Xie, H., Kaiser, M. L., Howard, R. A., and Bougeret, J. L.: 2008, Annales Geophysicae 26 , 30333047. Gopalswamy, N., Yashiro, S., Michałek, G., Kaiser, M. L., Howard, R. A., Reames, D. V., Leske, R., and von Rosenvinge, T.: 2002, Astrophys. J., 572 Lett. , L103-L107. Kahler, S. W.: 1982, Astrophys. J. 261 , 710-719. Kane, S. R., Benz, A. O., and Treumann, R. A.: 1982, Astrophys. J. 263 , 423-432. Klein, K.-L., Trottet, G., Samwel, S., and Malandraki, O.: 2011, Solar Phys. 269 , 309-333. MacDowall, R. J., Kundu, M. R., and Stone, R. G.: 1987, Solar Phys. 111 , 397418. MacDowall, R. J., Lara, A., Manoharan, P. K., Nitta, N. V., Rosas, A. M., and Bougeret, J. L.: 2003, Geophys. Res. Lett. 30 (12), 120000-1. Mewaldt, R. A.: 2006, Space Sci. Rev. 124 , 303-316. Miteva, R., Klein, K.-L., Malandraki, O., and Dorrian, G.: 2013, Solar Phys. 282 , 579-613. Nelson, G. J. and Melrose, D. B.: 1985, Type II bursts , pp. 333-359. Nindos, A., Aurass, H., Klein, K.-L., and Trottet, G.: 2008, Solar Phys. 253 , 341. Pick, M.: 1986, Solar Phys. 104 , 19-32. Pick, M. and Vilmer, N.: 2008, Astron. Astrophys. Rev. 16 , 1-153. Reames, D. V.: 1999, Space Sci. Rev. 90 , 413-491. Reames, D. V. and Ng, C. K.: 2004, Astrophys. J. 610 , 510-522. Reid, H. A. S. and Kontar, E. P.: 2012, Solar Phys. p. 109. Reid, H. A. S., Vilmer, N., and Kontar, E. P.: 2011, Astron. Astrophys. 529 , A66. Richardson, I. G., Cane, H. V., and von Rosenvinge, T. T.: 1991, J. Geophys. Res. 96 , 7853-7860. Stewart, R. T.: 1985, Moving Type IV bursts , pp. 361-383. Suzuki, S. and Dulk, G. A.: 1985, Bursts of Type III and Type V , pp. 289-332.\",\n \"pages\": [\n 9\n ]\n }\n]"}}},{"rowIdx":89,"cells":{"bibcode":{"kind":"string","value":"2013E&PSL.379..104T"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1308.0511.pdf"},"content":{"kind":"string","value":"\n1\n2\n\n3\n\nConservation of Total Escape from Hydrodynamic\nPlanetary Atmospheres\nFeng Tian 1,2\n\n1. National Astronomical Observatories, Chinese Academy of Sciences 4\n2. Center for Earth System Sciences, Tsinghua University 5\n\n6\n\nAbstract: Atmosphere escape is one key process controlling the 7\nevolution of planets. However, estimating the escape rate in any detail 8\nis difficult because there are many physical processes contributing to 9\nthe total escape rate. Here we show that as a result of energy 10\nconservation the total escape rate from hydrodynamic planetary 11\natmospheres where the outflow remains subsonic is nearly constant 12\nunder the same stellar XUV photon flux when increasing the escape 13\nefficiency from the exobase level, consistent with the energy limited 14\nescape approximation. Thus the estimate of atmospheric escape in a 15\nplanet's evolution history can be greatly simplified. 16\n\n17\n1. Introduction 18\n\nRecently it is proposed that a high hydrogen content (at least a few 19 percent) in early Earth's atmosphere could be important to keep early 20\nEarth warm, contributing to the solution of the faint young Sun problem 21\n(Wordsworth and Pierrehumbert 2013). A hydrogen rich early Earth 22\n\n\natmosphere has been proposed based on hydrodynamic calculations of 23\nhydrogen escape and such an atmosphere could have been important for 24\nprebiotic photochemistry (Tian et al. 2005a). The numerical scheme in 25\nTian et al. (2005a) contains large numerical diffusion especially near the 26\nlower boundary where the density gradient is the largest (Tian et al. 27\n\n28\n2005b). However, the calculated upper atmosphere structures are\n\nconsistent with transit observations of hot Jupiter HD209458b 29\n(Vidar-Madjar et al. 2003) and the calculated escape rates are consistent 30\nwith follow-up independent works (Yelle 2006, Garcia-Munoz 2007, 31\nPenz et al. 2008, Koskinen et al. 2012). On the other hand, it is suggested 32\nthat nonthermal escape processes could have increased total hydrogen 33\nescape (Catling 2006) so that the hydrogen content in early Earth 34\n\n35\natmosphere would have been in the order of 0.1% instead of a few\n\npercent or greater. But no calculation has been carried out to estimate the 36\nnonthermal hydrogen escape rate from early Earth's atmosphere. 37\n\n38\n39\nLammer et al. (2007) showed that planets in the habitable zones of M\n\ndwarfs should experience frequent exposure to stellar corona mass 40\nejection events and as a result Earth-like planets in such environments 41\ncould have lost hundreds of bars of CO2 in the timescale of 1 Gyrs 42\nthrough stellar wind interactions. But the energy consumed in such 43\nmassive atmospheric loss is not considered. Tian (2009) showed that 44\n\n\nCO2-dominant atmospheres of super Earths with masses greater than 6 45 Earth masses should survive the long active phase of M dwarfs. But 46\nnonthermal escape processes were not included. 47\n\n48\nObserved close-in exoplanets with masses in the range between Earth 49 and Uranus/Neptune, such as Corot-7B (Leger et al. 2009), GJ1214b 50 (Charbonneau 2009), 55 Cnc e (Winn et al. 2011), and several Kepler-11 51 planets (Lissauer et al. 2011), have inferred densities much different from 52 each other. Considering the small orbital distances between these planets 53 and their parent stars, these planetary atmospheres must be highly 54 expanded and atmospheric escape must be an important physical process 55 controlling the evolution histories and the nature of these objects. A better 56 understanding of the relationship between different atmospheric escape 57 processes and how upper atmosphere structure influences atmospheric 58 escape is urgently needed. 59\n60\nOne classical theory on atmospheric escape is the diffusion-limited 61 escape (Hunten 1973), which provides an upper limit for the total escape 62 rate of minor species. In the case of hydrogen, its escape rate should be 63 proportional to the total mixing ratio of hydrogen-bearing species at the 64 homopause level. The diffusion-limited escape theory is the result of the 65 kinetics at the homopause level and does not consider the energy aspect 66\n67\nof atmospheric escape.\n68\nWhen a planetary atmosphere is exposed to intense stellar XUV 69 photon flux, which occurs on terrestrial planets during their early 70 evolution histories, close-in exoplanets, and small dwarf planets such as 71 present Pluto, the upper atmosphere is heated and temperature rises and 72 the atmosphere expands. For this scenario to occur, thermal conduction 73 through the lower boundary must be less than the net heating. When the 74 atmosphere expands to large distance, the gravity of the planet at the 75 exobase, the top of the atmosphere, becomes weak enough and major 76 atmospheric species escape more efficiently through either thermal or 77 nonthermal processes. When the escape of major atmospheric species is 78 efficient, the upper atmosphere flows outward and the adiabatic cooling 79 associated with the expansion of the rapidly escaping atmosphere 80 becomes a dominant part of the energy budget of planetary atmospheres 81 -- the hydrodynamic regime or a hydrodynamic planetary atmosphere 82 (Tian et al. 2008a, b). Because the diffusion-limited theory does not 83 consider energy required to support rapid escape, it cannot provide us a 84 good estimate on escape rate of major atmospheric species 85\n86\n87\n88\nNote that there is a difference between the above-mentioned hydrodynamic planetary atmosphere and the traditional hydrodynamic\n\n100 101\nescape, or blowoff, in that the hydrodynamic regime is reached when the 89 outflow is important in the energy budget of the upper atmosphere, while 90 the blowoff occurs when the heating of the upper atmosphere is so strong 91 that the kinetic energy of the upper atmosphere overcomes the gravity of 92 the planet. Thus a planetary atmosphere in the hydrodynamic regime does 93 not necessarily blow off. In such an atmosphere the gravitational potential 94 energy is more than the heat content or kinetic energy of the atmosphere 95 and the atmospheric escape is Jeans-like (evaporation) no matter whether 96 the actual escape process is thermal or nonthermal. Thus a planetary 97 atmosphere could be experiencing Jeans-like escape and in the 98 hydrodynamic regime simultaneously (Tian et al. 2008a). On the other 99 hand, blowoff can be considered an extreme case of planetary atmospheres in the hydrodynamic regime and energy consumption in the\noutflow is the ultimate factor controlling the mass loss rate. 102\n\n103\n104\n105\n106\n107\nLinking the hydrogen content of early Earth's atmosphere with the nature of close-in super Earths, the key question this paper intends to address is: can the energy requirement in a hydrodynamic planetary atmosphere limit atmospheric escape?\n108\n\n2. Hydrodynamic Planetary Upper Atmospheres and the 109 Conservation of Total Escape Rate 110\n\nHere a 1-D upper planetary atmosphere model, validated against the 111 upper atmosphere of the present Earth, is used to study the problem. The 112 model details can be found in Tian et al. (2008a, b). A key feature of the 113 model is that it can automatically adjust its upper boundary so that the 114 exobase, defined as where the scale height is comparable to the mean free 115 path, can be found and the adjusted Jeans escape rates of all species can 116 be calculated. When increasing the level of solar XUV radiation, both the 117 upper atmosphere temperature and the exobase altitude increase. At 5 118 times present solar mean XUV level (XUVx5), the exobase altitude can 119 reach more than 10 4 km and the upper atmosphere temperature can be 120 near 9000 K (Tian et al. 2008b). 121\n122\nTo include other escape processes at the exobase level in addition to 123 Jeans escape, the Jeans escape effusion velocity at the exobase is 124 multiplied by 3, 10, and 20 times respectively. The calculated upper 125 atmosphere temperature profiles are shown in Fig. 1. The peak 126 temperature in the upper atmosphere cools with increasing escape 127 efficiency from 9000 K in the Jeans escape only case to 8000, 7500, and 128 7000 K in the 3x, 10x, and 20x more efficient atmosphere escape cases. 129 Correspondingly the exobase altitude decreases with increased escape 130 efficiency because of decreased scaleheight. Note that although the 131 scaleheight is inversely proportional to the temperature, the exobase 132\n133\naltitude is not.\n134\nThe shrinking of the upper atmosphere with increasing escape 135 efficiency at the exobase level has an interesting consequence on the total 136 atmospheric escape rate, shown as a solid curve in Fig. 2. In comparison 137 the dashed line in Fig. 2 shows a linear increase of total escape with 138 enhanced escape efficiency if the upper atmosphere structure is not 139 influenced by atmospheric escape. When considering the energy required 140 to support a strong outflow, which is a consequence of rapid escape of 141 major atmosphere species, the total escape rate of such species remains 142 almost a constant (a conservation of total escape rate) when increasing 143 escape efficiency from the exobase level. The conservation of total escape 144 rate from a hydrodynamic planetary atmosphere is a demonstration of the 145 law of the conservation of energy -- changing the escape efficiency at the 146 exobase level does not change the total amount of energy heating the 147 upper atmosphere. 148\n149\n3. Discussion 150\nThe heating and cooling terms in the hydrodynamic planetary 151 atmosphere are shown in Fig. 3. The solid curves correspond to the black 152 curve in Fig. 1 (Jeans escape only). The dashed curves correspond to the 153 red curve in Fig. 1 (escape efficiency 10 times that of Jeans escape). 154\nThe blue curves represent the adiabatic cooling. The red curves represent 155 the net radiative heating, which includes absorption of stellar XUV 156 photons, the ionization, excitation, and dissociation of atmospheric 157 species, and transport of energetic electrons and the deposition of their 158 energy, heating from chemical reactions, and radiative cooling (for details 159 see Tian et al. 2008a, b). The magenta curves represent the thermal 160 conduction. 161\n162\nFig. 3 shows that the adiabatic cooling associated with outflow is a 163 dominant cooling term in the upper thermosphere and its importance 164 increases with altitude, reflecting the increasing velocity of the outflow. 165 Although thermal conduction cooling is dominant near where the net 166 radiative heating peaks, because the net radiative heating is inadequate to 167 match the adiabatic cooling, thermal conduction becomes an important 168 heating term in the upper thermosphere, contributing to support the 169 outflow. When increasing the escape efficiency at the exobase level, the 170 outflow is enhanced in upper thermosphere, which causes the dashed blue 171 curve to increase more rapidly with altitude than the solid blue curve does. 172 The peak of the net radiative heating moves lower in altitude because the 173 atmosphere shrinks, which allows more stellar XUV photons to penetrate 174 to deeper altitudes. Fig. 3 and Fig. 1 show how a planetary upper 175 atmosphere in the hydrodynamic regime adjusts its structure and energy 176\n\ndistribution when different escape processes occur at the exobase level. 177 As a result of the law of the conservation of energy, the total escape rates 178 from the two atmospheres with quite different structures are almost 179 identical. 180\n\n181\nWe further tested the 1-D upper atmosphere model with greater XUV 182 levels and in all cases the enhancements of atmospheric escape efficiency 183 lead to shrink of the upper atmosphere and the conservation of total 184 escape rate. For an upper atmosphere under weak XUV heating, the 185 escape is insignificant and the increased escape efficiency does not lead 186 to a strong outflow or cooling of the upper atmosphere. Thus the total 187 escape increases linearly with enhanced escape efficiency. Analysis 188 shows that the difference between the two cases is whether the cooling 189 caused by the gas outflow is important in the energy budget of the upper 190 atmosphere, which is the division between a hydrostatic and a 191 hydrodynamic planetary upper atmosphere. 192\n193\nJohnson et al. (2013) pointed out that if the deposition of energy in 194 the upmost layer of the thermosphere (where the ratio between the mean 195 free path and the scaleheight is >~0.1) is inefficient, nonthermal escape 196 processes can be ignored. This is equivalent of saying that the energy 197 deposited in the collision-dominant part of the atmosphere contributes to 198\n\nthe heating of the atmosphere and not to nonthermal escape processes. 199\n\nOur model atmospheres include this heating process. From the 200 perspective of the exobase, the escape is Jeans-like in that the bulk 201 outflow velocity in our model remains subsonic, consistent with the 202 findings in Johnson et al. (2013). From the perspective of the energy 203 budget of the upper atmosphere, the escape is hydrodynamic because the 204 outflow cooling dominates the energy budget when the atmosphere is 205 under strong XUV radiation (Tian et al. 2008a). Thus escape can be 206 Jeans-like and hydrodynamic simultaneously, depending on from which 207 point of view the issue is observed. 208\n209\nGarcia-Munoz (2007) showed that the model calculated escape rates 210 from HD209458b are insensitive to the upper boundary conditions but the 211 upper atmospheric structures are. Koskinen et al. (2012) compared the 212 effects of different boundary conditions on the escape from hot Jupiters 213 and found that models with similar escape rates could produce different 214 upper atmospheric structures depending on the boundary conditions 215 applied. These results are in good agreement with ours and thus the 216 conservation of total escape rate theory proposed in this paper is also 217 supported by models with transonic hydrogen outflow from hot Jupiters. 218 In agreement with Koskinen et al. (2012), we emphasize that details of 219 the escape processes functioning at the exobase level are important for 220\nunderstanding the upper atmosphere structures and thus are important to 221 compare with observations. 222\n223\nA recent hybrid fluid/kinetic model for the upper atmosphere of Pluto 224 (Erwin et al. 2013) shows that Pluto's exobase altitude and temperature 225 decreases as a result of increasing escape efficiency at the exobase level 226 and as a result the total escape rate from Pluto's N2-dominant atmosphere 227 remains near constant. This shows that the theory of the conservation of 228 total escape rate applies to hydrodynamic planetary atmosphere with 229 different composition. Erwin et al. (2013) pointed out that in order to 230 predict the upper atmosphere structure, a hybrid fluid/kinetic model is 231 needed because the enhancement of escape efficiency at the exobase level 232 does influence the upper atmosphere structure. We emphasize that if the 233 theory of the conservation of total escape is correct, a fluid model for the 234 planetary upper atmosphere would be adequate to understand the 235 atmospheric escape history of a planet. 236\n237\nThe conservation of total escape rate from planetary atmospheres in 238 the hydrodynamic regime is demonstrated in 1-D models for the Earth's 239 current atmosphere composition under intense XUV heating, for the 240 current N2-dominant atmosphere of Pluto (Erwin et al. 2013), and for 241 transonic outflow from hot Jupiters (Garcia-Munoz 2007, Koskinen et al. 242\n2012). Numerical simulations for atmospheres with different composition 243 around planets with different masses in 3-D models will be needed in 244 future studies to prove or disprove it. However we speculate that the 245 theory should apply to planetary atmospheres with different composition 246 because the law of the conservation of energy is universal and the escape 247 of hydrogen from such atmospheres under intense stellar/solar XUV 248 heating is always energy-limited. 249\n250\nIf the theory is confirmed, one implication is that early Earth's 251 atmospheric hydrogen content should be close to those in Tian et al. 252 (2005) suggested, provided that those calculations are correct, and thus 253 hydrogen could have helped early Earth to stay warm (Wordsworth and 254 Pierrehumbert 2013). And the calculations of atmosphere escape during 255 the evolution histories of different planets could be significantly 256 simplified. The theory also implies that super Earths in close-in orbits can 257 have a better chance to keep their atmospheres and oceans, which might 258 help to explain the existence of low density rocky exoplanets such as 55 259 Cnc e and GJ1214b, and planets in the habitable zones of M dwarfs 260 should be able to keep their CO2-dominant atmospheres, supporting the 261 conclusion of Tian (2009), which could have consequences in the 262 evaluation of planetary habitability. 263\n264\n4. Conclusions 265\nAs a result of the law of the conservation of energy, the total escape 266 rate from planetary atmospheres in the hydrodynamic regime is nearly 267 constant under the same stellar XUV photon flux when increasing the 268 escape efficiency from the exobase level. Thus an energy-limited escape 269 approximation can be applied to such atmospheres, provided that the 270 upper atmosphere structures are calculated accurately. The estimate of 271 atmospheric escape in a planet's evolution history can be greatly 272 simplified. 273\n274\nAcknowledgement : The author thanks R.E. Johnson and the other 275 anonymous reviewer for their helpful comments and suggestions. 276\n277\nReferences: 278\nCatling, D.C. www.sciencemag.org/cgi/content/full/311/5757/38a. 279 Science 311, 38 (2006) 280\nCharbonneau, David et al. A super-Earth transiting a nearby low-mass 281 star. Nature 462, 891-894 (2009). 282\nErwin, J., Tucker, O.J., Johnson, R.E. Hybrid fluid/kinetic modeling of 283 Pluto's atmosphere\", Icarus in press (2013) [arXiv:1211.3994 (2012)] 284\n285\nGarcía-Muñoz, A. Physical and chemical aeronomy of HD 209458b.\nPlanet. Space Sci. , 55 , 1426-1455 (2007) 286\nHunten, D.M. The escape of light gases from planetary atmospheres. J.\n,\n
\n\n
\ndiscoveries, Part II: Long time thermal atmospheric evaporation 309 modeling. Planet. Space Sci ., 56 , 1260-1272 (2008) 310\n\nTian, F., Toon, O.B., Pavlov, A.A., DeSterck H. A Hydrogen-Rich Early 311 Earth Atmosphere, Science 308, 1014-1017 (2005a) 312\nTian, F., Toon, O.B., Pavlov, A.A., de Sterck, H. Transonic 313 hydrodynamic escape of hydrogen from extrasolar planetary 314 atmospheres. Astrophys. J. 621, 1049-1060 (2005b) 315\n\n316\n317\n318\n\nTian, F., Kasting, J.F., Liu, H., Roble, R.G. Hydrodynamic planetary thermosphere model:. 1. The response of the Earth's thermosphere to extreme solar EUV conditions and the significance of adiabatic cooling,\nJ. Geophys. Res., 113, E05008 doi:10.1029/2007JE002946 (2008a) 319\nTian, F., Solomon, S.C., Qian, L., Lei, J., Roble R.G. Hydrodynamic 320 planetary thermosphere model: 2. coupling of an electron 321 transport/energy deposition model, J. Geophys. Res., 113, E07005, 322 doi:10.1029/2007JE003043 (2008b) 323\n\nTian, F. Thermal escape from super-Earth atmospheres in the habitable 324 zones of M stars. ApJ 703, 905-909 (2009) 325\n\nWinn, J.N. et al. A super-Earth transiting a naked-eye star. The 326 Astrophysical Journal Letters, 737, L18 (2011) 327\nWordsworth R.D., Pierrehumbert R. Hydrogen-nitrogen Greenhouse 328 warming in Earth's early atmosphere. Science 339, 64 (2013) 329\n\nYelle, R.V. Corrigendum to ''Aeronomy of extra-solar giant planets at 330\nsmall orbital distances''. Icarus 183, 508 (2006) 331\n332\n\n\n
Fig. 1 Upper atmosphere structures of the Earth under 5 times present 333 XUV radiation level with different escape effusion velocities at the 334 exobase level, which are where the curves end. 335
\n\n336\n337\n\n\n
Fig. 2 Total escape rate of major atmosphere species as a function of 338 escape efficiency from the exobase level. The atmospheres used in these 339 simulations have composition the same as that of present Earth but are 340 under 5 times present Earth's XUV radiation level. If the upper 341 atmosphere structure is not influenced by escape of major atmospheric 342 species and the subsequent outflow, the total escape rate would have 343 increased linearly with enhanced escape efficiency at the exobase level as 344 shown by the dashed line. However, when considering the energy 345 consumption of outflow in the upper atmosphere, the upper atmosphere 346 cools and shrinks (shown in Fig. 1) and the total escape rate remains 347 conserved with enhanced escape efficiency at the exobase level. 348
\n\n349\n351\n\n\n
Fig. 3 Heating and cooling terms in a hydrodynamic planetary 352 atmosphere. The solid curves correspond to the black curve in Fig. 1. The 353 dashed curves correspond to the red curve in Fig. 1. The blue curves are 354 the adiabatic cooling. The red curves are the net radiative heating. The 355 magenta curves are the thermal conduction. 356
\n\n"},"sections":{"kind":"list like","value":[{"title":"ABSTRACT","content":"1","pages":[1]},{"title":"Feng Tian 1,2","content":"6 17","pages":[1]},{"title":"1. Introduction 18","content":"28 2005b). However, the calculated upper atmosphere structures are 35 atmosphere would have been in the order of 0.1% instead of a few 38 39 Lammer et al. (2007) showed that planets in the habitable zones of M 48 Observed close-in exoplanets with masses in the range between Earth 49 and Uranus/Neptune, such as Corot-7B (Leger et al. 2009), GJ1214b 50 (Charbonneau 2009), 55 Cnc e (Winn et al. 2011), and several Kepler-11 51 planets (Lissauer et al. 2011), have inferred densities much different from 52 each other. Considering the small orbital distances between these planets 53 and their parent stars, these planetary atmospheres must be highly 54 expanded and atmospheric escape must be an important physical process 55 controlling the evolution histories and the nature of these objects. A better 56 understanding of the relationship between different atmospheric escape 57 processes and how upper atmosphere structure influences atmospheric 58 escape is urgently needed. 59 60 One classical theory on atmospheric escape is the diffusion-limited 61 escape (Hunten 1973), which provides an upper limit for the total escape 62 rate of minor species. In the case of hydrogen, its escape rate should be 63 proportional to the total mixing ratio of hydrogen-bearing species at the 64 homopause level. The diffusion-limited escape theory is the result of the 65 kinetics at the homopause level and does not consider the energy aspect 66 67 of atmospheric escape. 68 When a planetary atmosphere is exposed to intense stellar XUV 69 photon flux, which occurs on terrestrial planets during their early 70 evolution histories, close-in exoplanets, and small dwarf planets such as 71 present Pluto, the upper atmosphere is heated and temperature rises and 72 the atmosphere expands. For this scenario to occur, thermal conduction 73 through the lower boundary must be less than the net heating. When the 74 atmosphere expands to large distance, the gravity of the planet at the 75 exobase, the top of the atmosphere, becomes weak enough and major 76 atmospheric species escape more efficiently through either thermal or 77 nonthermal processes. When the escape of major atmospheric species is 78 efficient, the upper atmosphere flows outward and the adiabatic cooling 79 associated with the expansion of the rapidly escaping atmosphere 80 becomes a dominant part of the energy budget of planetary atmospheres 81 -- the hydrodynamic regime or a hydrodynamic planetary atmosphere 82 (Tian et al. 2008a, b). Because the diffusion-limited theory does not 83 consider energy required to support rapid escape, it cannot provide us a 84 good estimate on escape rate of major atmospheric species 85 86 87 88 Note that there is a difference between the above-mentioned hydrodynamic planetary atmosphere and the traditional hydrodynamic 103 104 105 106 107 Linking the hydrogen content of early Earth's atmosphere with the nature of close-in super Earths, the key question this paper intends to address is: can the energy requirement in a hydrodynamic planetary atmosphere limit atmospheric escape? 108 Here a 1-D upper planetary atmosphere model, validated against the 111 upper atmosphere of the present Earth, is used to study the problem. The 112 model details can be found in Tian et al. (2008a, b). A key feature of the 113 model is that it can automatically adjust its upper boundary so that the 114 exobase, defined as where the scale height is comparable to the mean free 115 path, can be found and the adjusted Jeans escape rates of all species can 116 be calculated. When increasing the level of solar XUV radiation, both the 117 upper atmosphere temperature and the exobase altitude increase. At 5 118 times present solar mean XUV level (XUVx5), the exobase altitude can 119 reach more than 10 4 km and the upper atmosphere temperature can be 120 near 9000 K (Tian et al. 2008b). 121 122 To include other escape processes at the exobase level in addition to 123 Jeans escape, the Jeans escape effusion velocity at the exobase is 124 multiplied by 3, 10, and 20 times respectively. The calculated upper 125 atmosphere temperature profiles are shown in Fig. 1. The peak 126 temperature in the upper atmosphere cools with increasing escape 127 efficiency from 9000 K in the Jeans escape only case to 8000, 7500, and 128 7000 K in the 3x, 10x, and 20x more efficient atmosphere escape cases. 129 Correspondingly the exobase altitude decreases with increased escape 130 efficiency because of decreased scaleheight. Note that although the 131 scaleheight is inversely proportional to the temperature, the exobase 132 133 altitude is not. 134 The shrinking of the upper atmosphere with increasing escape 135 efficiency at the exobase level has an interesting consequence on the total 136 atmospheric escape rate, shown as a solid curve in Fig. 2. In comparison 137 the dashed line in Fig. 2 shows a linear increase of total escape with 138 enhanced escape efficiency if the upper atmosphere structure is not 139 influenced by atmospheric escape. When considering the energy required 140 to support a strong outflow, which is a consequence of rapid escape of 141 major atmosphere species, the total escape rate of such species remains 142 almost a constant (a conservation of total escape rate) when increasing 143 escape efficiency from the exobase level. The conservation of total escape 144 rate from a hydrodynamic planetary atmosphere is a demonstration of the 145 law of the conservation of energy -- changing the escape efficiency at the 146 exobase level does not change the total amount of energy heating the 147 upper atmosphere. 148 149","pages":[2,3,4,5,6,7]},{"title":"3. Discussion 150","content":"The heating and cooling terms in the hydrodynamic planetary 151 atmosphere are shown in Fig. 3. The solid curves correspond to the black 152 curve in Fig. 1 (Jeans escape only). The dashed curves correspond to the 153 red curve in Fig. 1 (escape efficiency 10 times that of Jeans escape). 154 The blue curves represent the adiabatic cooling. The red curves represent 155 the net radiative heating, which includes absorption of stellar XUV 156 photons, the ionization, excitation, and dissociation of atmospheric 157 species, and transport of energetic electrons and the deposition of their 158 energy, heating from chemical reactions, and radiative cooling (for details 159 see Tian et al. 2008a, b). The magenta curves represent the thermal 160 conduction. 161 162 Fig. 3 shows that the adiabatic cooling associated with outflow is a 163 dominant cooling term in the upper thermosphere and its importance 164 increases with altitude, reflecting the increasing velocity of the outflow. 165 Although thermal conduction cooling is dominant near where the net 166 radiative heating peaks, because the net radiative heating is inadequate to 167 match the adiabatic cooling, thermal conduction becomes an important 168 heating term in the upper thermosphere, contributing to support the 169 outflow. When increasing the escape efficiency at the exobase level, the 170 outflow is enhanced in upper thermosphere, which causes the dashed blue 171 curve to increase more rapidly with altitude than the solid blue curve does. 172 The peak of the net radiative heating moves lower in altitude because the 173 atmosphere shrinks, which allows more stellar XUV photons to penetrate 174 to deeper altitudes. Fig. 3 and Fig. 1 show how a planetary upper 175 atmosphere in the hydrodynamic regime adjusts its structure and energy 176 181 We further tested the 1-D upper atmosphere model with greater XUV 182 levels and in all cases the enhancements of atmospheric escape efficiency 183 lead to shrink of the upper atmosphere and the conservation of total 184 escape rate. For an upper atmosphere under weak XUV heating, the 185 escape is insignificant and the increased escape efficiency does not lead 186 to a strong outflow or cooling of the upper atmosphere. Thus the total 187 escape increases linearly with enhanced escape efficiency. Analysis 188 shows that the difference between the two cases is whether the cooling 189 caused by the gas outflow is important in the energy budget of the upper 190 atmosphere, which is the division between a hydrostatic and a 191 hydrodynamic planetary upper atmosphere. 192 193 Johnson et al. (2013) pointed out that if the deposition of energy in 194 the upmost layer of the thermosphere (where the ratio between the mean 195 free path and the scaleheight is >~0.1) is inefficient, nonthermal escape 196 processes can be ignored. This is equivalent of saying that the energy 197 deposited in the collision-dominant part of the atmosphere contributes to 198 Our model atmospheres include this heating process. From the 200 perspective of the exobase, the escape is Jeans-like in that the bulk 201 outflow velocity in our model remains subsonic, consistent with the 202 findings in Johnson et al. (2013). From the perspective of the energy 203 budget of the upper atmosphere, the escape is hydrodynamic because the 204 outflow cooling dominates the energy budget when the atmosphere is 205 under strong XUV radiation (Tian et al. 2008a). Thus escape can be 206 Jeans-like and hydrodynamic simultaneously, depending on from which 207 point of view the issue is observed. 208 209 Garcia-Munoz (2007) showed that the model calculated escape rates 210 from HD209458b are insensitive to the upper boundary conditions but the 211 upper atmospheric structures are. Koskinen et al. (2012) compared the 212 effects of different boundary conditions on the escape from hot Jupiters 213 and found that models with similar escape rates could produce different 214 upper atmospheric structures depending on the boundary conditions 215 applied. These results are in good agreement with ours and thus the 216 conservation of total escape rate theory proposed in this paper is also 217 supported by models with transonic hydrogen outflow from hot Jupiters. 218 In agreement with Koskinen et al. (2012), we emphasize that details of 219 the escape processes functioning at the exobase level are important for 220 understanding the upper atmosphere structures and thus are important to 221 compare with observations. 222 223 A recent hybrid fluid/kinetic model for the upper atmosphere of Pluto 224 (Erwin et al. 2013) shows that Pluto's exobase altitude and temperature 225 decreases as a result of increasing escape efficiency at the exobase level 226 and as a result the total escape rate from Pluto's N2-dominant atmosphere 227 remains near constant. This shows that the theory of the conservation of 228 total escape rate applies to hydrodynamic planetary atmosphere with 229 different composition. Erwin et al. (2013) pointed out that in order to 230 predict the upper atmosphere structure, a hybrid fluid/kinetic model is 231 needed because the enhancement of escape efficiency at the exobase level 232 does influence the upper atmosphere structure. We emphasize that if the 233 theory of the conservation of total escape is correct, a fluid model for the 234 planetary upper atmosphere would be adequate to understand the 235 atmospheric escape history of a planet. 236 237 The conservation of total escape rate from planetary atmospheres in 238 the hydrodynamic regime is demonstrated in 1-D models for the Earth's 239 current atmosphere composition under intense XUV heating, for the 240 current N2-dominant atmosphere of Pluto (Erwin et al. 2013), and for 241 transonic outflow from hot Jupiters (Garcia-Munoz 2007, Koskinen et al. 242 2012). Numerical simulations for atmospheres with different composition 243 around planets with different masses in 3-D models will be needed in 244 future studies to prove or disprove it. However we speculate that the 245 theory should apply to planetary atmospheres with different composition 246 because the law of the conservation of energy is universal and the escape 247 of hydrogen from such atmospheres under intense stellar/solar XUV 248 heating is always energy-limited. 249 250 If the theory is confirmed, one implication is that early Earth's 251 atmospheric hydrogen content should be close to those in Tian et al. 252 (2005) suggested, provided that those calculations are correct, and thus 253 hydrogen could have helped early Earth to stay warm (Wordsworth and 254 Pierrehumbert 2013). And the calculations of atmosphere escape during 255 the evolution histories of different planets could be significantly 256 simplified. The theory also implies that super Earths in close-in orbits can 257 have a better chance to keep their atmospheres and oceans, which might 258 help to explain the existence of low density rocky exoplanets such as 55 259 Cnc e and GJ1214b, and planets in the habitable zones of M dwarfs 260 should be able to keep their CO2-dominant atmospheres, supporting the 261 conclusion of Tian (2009), which could have consequences in the 262 evaluation of planetary habitability. 263 264","pages":[7,8,9,10,11,12]},{"title":"4. Conclusions 265","content":"As a result of the law of the conservation of energy, the total escape 266 rate from planetary atmospheres in the hydrodynamic regime is nearly 267 constant under the same stellar XUV photon flux when increasing the 268 escape efficiency from the exobase level. Thus an energy-limited escape 269 approximation can be applied to such atmospheres, provided that the 270 upper atmosphere structures are calculated accurately. The estimate of 271 atmospheric escape in a planet's evolution history can be greatly 272 simplified. 273 274 Acknowledgement : The author thanks R.E. Johnson and the other 275 anonymous reviewer for their helpful comments and suggestions. 276 277","pages":[13]},{"title":"References: 278","content":"Catling, D.C. www.sciencemag.org/cgi/content/full/311/5757/38a. 279 Science 311, 38 (2006) 280 Charbonneau, David et al. A super-Earth transiting a nearby low-mass 281 star. Nature 462, 891-894 (2009). 282 Erwin, J., Tucker, O.J., Johnson, R.E. Hybrid fluid/kinetic modeling of 283 Pluto's atmosphere\", Icarus in press (2013) [arXiv:1211.3994 (2012)] 284 285 García-Muñoz, A. Physical and chemical aeronomy of HD 209458b. Planet. Space Sci. , 55 , 1426-1455 (2007) 286 Hunten, D.M. The escape of light gases from planetary atmospheres. J. , discoveries, Part II: Long time thermal atmospheric evaporation 309 modeling. Planet. Space Sci ., 56 , 1260-1272 (2008) 310 316 317 318 Tian, F. Thermal escape from super-Earth atmospheres in the habitable 324 zones of M stars. ApJ 703, 905-909 (2009) 325 Yelle, R.V. Corrigendum to ''Aeronomy of extra-solar giant planets at 330","pages":[13,14,15]},{"title":"small orbital distances''. Icarus 183, 508 (2006) 331","content":"332 336 337 349 351","pages":[16,17,18]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"1\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Feng Tian 1,2\",\n \"content\": \"6 17\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction 18\",\n \"content\": \"28 2005b). However, the calculated upper atmosphere structures are 35 atmosphere would have been in the order of 0.1% instead of a few 38 39 Lammer et al. (2007) showed that planets in the habitable zones of M 48 Observed close-in exoplanets with masses in the range between Earth 49 and Uranus/Neptune, such as Corot-7B (Leger et al. 2009), GJ1214b 50 (Charbonneau 2009), 55 Cnc e (Winn et al. 2011), and several Kepler-11 51 planets (Lissauer et al. 2011), have inferred densities much different from 52 each other. Considering the small orbital distances between these planets 53 and their parent stars, these planetary atmospheres must be highly 54 expanded and atmospheric escape must be an important physical process 55 controlling the evolution histories and the nature of these objects. A better 56 understanding of the relationship between different atmospheric escape 57 processes and how upper atmosphere structure influences atmospheric 58 escape is urgently needed. 59 60 One classical theory on atmospheric escape is the diffusion-limited 61 escape (Hunten 1973), which provides an upper limit for the total escape 62 rate of minor species. In the case of hydrogen, its escape rate should be 63 proportional to the total mixing ratio of hydrogen-bearing species at the 64 homopause level. The diffusion-limited escape theory is the result of the 65 kinetics at the homopause level and does not consider the energy aspect 66 67 of atmospheric escape. 68 When a planetary atmosphere is exposed to intense stellar XUV 69 photon flux, which occurs on terrestrial planets during their early 70 evolution histories, close-in exoplanets, and small dwarf planets such as 71 present Pluto, the upper atmosphere is heated and temperature rises and 72 the atmosphere expands. For this scenario to occur, thermal conduction 73 through the lower boundary must be less than the net heating. When the 74 atmosphere expands to large distance, the gravity of the planet at the 75 exobase, the top of the atmosphere, becomes weak enough and major 76 atmospheric species escape more efficiently through either thermal or 77 nonthermal processes. When the escape of major atmospheric species is 78 efficient, the upper atmosphere flows outward and the adiabatic cooling 79 associated with the expansion of the rapidly escaping atmosphere 80 becomes a dominant part of the energy budget of planetary atmospheres 81 -- the hydrodynamic regime or a hydrodynamic planetary atmosphere 82 (Tian et al. 2008a, b). Because the diffusion-limited theory does not 83 consider energy required to support rapid escape, it cannot provide us a 84 good estimate on escape rate of major atmospheric species 85 86 87 88 Note that there is a difference between the above-mentioned hydrodynamic planetary atmosphere and the traditional hydrodynamic 103 104 105 106 107 Linking the hydrogen content of early Earth's atmosphere with the nature of close-in super Earths, the key question this paper intends to address is: can the energy requirement in a hydrodynamic planetary atmosphere limit atmospheric escape? 108 Here a 1-D upper planetary atmosphere model, validated against the 111 upper atmosphere of the present Earth, is used to study the problem. The 112 model details can be found in Tian et al. (2008a, b). A key feature of the 113 model is that it can automatically adjust its upper boundary so that the 114 exobase, defined as where the scale height is comparable to the mean free 115 path, can be found and the adjusted Jeans escape rates of all species can 116 be calculated. When increasing the level of solar XUV radiation, both the 117 upper atmosphere temperature and the exobase altitude increase. At 5 118 times present solar mean XUV level (XUVx5), the exobase altitude can 119 reach more than 10 4 km and the upper atmosphere temperature can be 120 near 9000 K (Tian et al. 2008b). 121 122 To include other escape processes at the exobase level in addition to 123 Jeans escape, the Jeans escape effusion velocity at the exobase is 124 multiplied by 3, 10, and 20 times respectively. The calculated upper 125 atmosphere temperature profiles are shown in Fig. 1. The peak 126 temperature in the upper atmosphere cools with increasing escape 127 efficiency from 9000 K in the Jeans escape only case to 8000, 7500, and 128 7000 K in the 3x, 10x, and 20x more efficient atmosphere escape cases. 129 Correspondingly the exobase altitude decreases with increased escape 130 efficiency because of decreased scaleheight. Note that although the 131 scaleheight is inversely proportional to the temperature, the exobase 132 133 altitude is not. 134 The shrinking of the upper atmosphere with increasing escape 135 efficiency at the exobase level has an interesting consequence on the total 136 atmospheric escape rate, shown as a solid curve in Fig. 2. In comparison 137 the dashed line in Fig. 2 shows a linear increase of total escape with 138 enhanced escape efficiency if the upper atmosphere structure is not 139 influenced by atmospheric escape. When considering the energy required 140 to support a strong outflow, which is a consequence of rapid escape of 141 major atmosphere species, the total escape rate of such species remains 142 almost a constant (a conservation of total escape rate) when increasing 143 escape efficiency from the exobase level. The conservation of total escape 144 rate from a hydrodynamic planetary atmosphere is a demonstration of the 145 law of the conservation of energy -- changing the escape efficiency at the 146 exobase level does not change the total amount of energy heating the 147 upper atmosphere. 148 149\",\n \"pages\": [\n 2,\n 3,\n 4,\n 5,\n 6,\n 7\n ]\n },\n {\n \"title\": \"3. Discussion 150\",\n \"content\": \"The heating and cooling terms in the hydrodynamic planetary 151 atmosphere are shown in Fig. 3. The solid curves correspond to the black 152 curve in Fig. 1 (Jeans escape only). The dashed curves correspond to the 153 red curve in Fig. 1 (escape efficiency 10 times that of Jeans escape). 154 The blue curves represent the adiabatic cooling. The red curves represent 155 the net radiative heating, which includes absorption of stellar XUV 156 photons, the ionization, excitation, and dissociation of atmospheric 157 species, and transport of energetic electrons and the deposition of their 158 energy, heating from chemical reactions, and radiative cooling (for details 159 see Tian et al. 2008a, b). The magenta curves represent the thermal 160 conduction. 161 162 Fig. 3 shows that the adiabatic cooling associated with outflow is a 163 dominant cooling term in the upper thermosphere and its importance 164 increases with altitude, reflecting the increasing velocity of the outflow. 165 Although thermal conduction cooling is dominant near where the net 166 radiative heating peaks, because the net radiative heating is inadequate to 167 match the adiabatic cooling, thermal conduction becomes an important 168 heating term in the upper thermosphere, contributing to support the 169 outflow. When increasing the escape efficiency at the exobase level, the 170 outflow is enhanced in upper thermosphere, which causes the dashed blue 171 curve to increase more rapidly with altitude than the solid blue curve does. 172 The peak of the net radiative heating moves lower in altitude because the 173 atmosphere shrinks, which allows more stellar XUV photons to penetrate 174 to deeper altitudes. Fig. 3 and Fig. 1 show how a planetary upper 175 atmosphere in the hydrodynamic regime adjusts its structure and energy 176 181 We further tested the 1-D upper atmosphere model with greater XUV 182 levels and in all cases the enhancements of atmospheric escape efficiency 183 lead to shrink of the upper atmosphere and the conservation of total 184 escape rate. For an upper atmosphere under weak XUV heating, the 185 escape is insignificant and the increased escape efficiency does not lead 186 to a strong outflow or cooling of the upper atmosphere. Thus the total 187 escape increases linearly with enhanced escape efficiency. Analysis 188 shows that the difference between the two cases is whether the cooling 189 caused by the gas outflow is important in the energy budget of the upper 190 atmosphere, which is the division between a hydrostatic and a 191 hydrodynamic planetary upper atmosphere. 192 193 Johnson et al. (2013) pointed out that if the deposition of energy in 194 the upmost layer of the thermosphere (where the ratio between the mean 195 free path and the scaleheight is >~0.1) is inefficient, nonthermal escape 196 processes can be ignored. This is equivalent of saying that the energy 197 deposited in the collision-dominant part of the atmosphere contributes to 198 Our model atmospheres include this heating process. From the 200 perspective of the exobase, the escape is Jeans-like in that the bulk 201 outflow velocity in our model remains subsonic, consistent with the 202 findings in Johnson et al. (2013). From the perspective of the energy 203 budget of the upper atmosphere, the escape is hydrodynamic because the 204 outflow cooling dominates the energy budget when the atmosphere is 205 under strong XUV radiation (Tian et al. 2008a). Thus escape can be 206 Jeans-like and hydrodynamic simultaneously, depending on from which 207 point of view the issue is observed. 208 209 Garcia-Munoz (2007) showed that the model calculated escape rates 210 from HD209458b are insensitive to the upper boundary conditions but the 211 upper atmospheric structures are. Koskinen et al. (2012) compared the 212 effects of different boundary conditions on the escape from hot Jupiters 213 and found that models with similar escape rates could produce different 214 upper atmospheric structures depending on the boundary conditions 215 applied. These results are in good agreement with ours and thus the 216 conservation of total escape rate theory proposed in this paper is also 217 supported by models with transonic hydrogen outflow from hot Jupiters. 218 In agreement with Koskinen et al. (2012), we emphasize that details of 219 the escape processes functioning at the exobase level are important for 220 understanding the upper atmosphere structures and thus are important to 221 compare with observations. 222 223 A recent hybrid fluid/kinetic model for the upper atmosphere of Pluto 224 (Erwin et al. 2013) shows that Pluto's exobase altitude and temperature 225 decreases as a result of increasing escape efficiency at the exobase level 226 and as a result the total escape rate from Pluto's N2-dominant atmosphere 227 remains near constant. This shows that the theory of the conservation of 228 total escape rate applies to hydrodynamic planetary atmosphere with 229 different composition. Erwin et al. (2013) pointed out that in order to 230 predict the upper atmosphere structure, a hybrid fluid/kinetic model is 231 needed because the enhancement of escape efficiency at the exobase level 232 does influence the upper atmosphere structure. We emphasize that if the 233 theory of the conservation of total escape is correct, a fluid model for the 234 planetary upper atmosphere would be adequate to understand the 235 atmospheric escape history of a planet. 236 237 The conservation of total escape rate from planetary atmospheres in 238 the hydrodynamic regime is demonstrated in 1-D models for the Earth's 239 current atmosphere composition under intense XUV heating, for the 240 current N2-dominant atmosphere of Pluto (Erwin et al. 2013), and for 241 transonic outflow from hot Jupiters (Garcia-Munoz 2007, Koskinen et al. 242 2012). Numerical simulations for atmospheres with different composition 243 around planets with different masses in 3-D models will be needed in 244 future studies to prove or disprove it. However we speculate that the 245 theory should apply to planetary atmospheres with different composition 246 because the law of the conservation of energy is universal and the escape 247 of hydrogen from such atmospheres under intense stellar/solar XUV 248 heating is always energy-limited. 249 250 If the theory is confirmed, one implication is that early Earth's 251 atmospheric hydrogen content should be close to those in Tian et al. 252 (2005) suggested, provided that those calculations are correct, and thus 253 hydrogen could have helped early Earth to stay warm (Wordsworth and 254 Pierrehumbert 2013). And the calculations of atmosphere escape during 255 the evolution histories of different planets could be significantly 256 simplified. The theory also implies that super Earths in close-in orbits can 257 have a better chance to keep their atmospheres and oceans, which might 258 help to explain the existence of low density rocky exoplanets such as 55 259 Cnc e and GJ1214b, and planets in the habitable zones of M dwarfs 260 should be able to keep their CO2-dominant atmospheres, supporting the 261 conclusion of Tian (2009), which could have consequences in the 262 evaluation of planetary habitability. 263 264\",\n \"pages\": [\n 7,\n 8,\n 9,\n 10,\n 11,\n 12\n ]\n },\n {\n \"title\": \"4. Conclusions 265\",\n \"content\": \"As a result of the law of the conservation of energy, the total escape 266 rate from planetary atmospheres in the hydrodynamic regime is nearly 267 constant under the same stellar XUV photon flux when increasing the 268 escape efficiency from the exobase level. Thus an energy-limited escape 269 approximation can be applied to such atmospheres, provided that the 270 upper atmosphere structures are calculated accurately. The estimate of 271 atmospheric escape in a planet's evolution history can be greatly 272 simplified. 273 274 Acknowledgement : The author thanks R.E. Johnson and the other 275 anonymous reviewer for their helpful comments and suggestions. 276 277\",\n \"pages\": [\n 13\n ]\n },\n {\n \"title\": \"References: 278\",\n \"content\": \"Catling, D.C. www.sciencemag.org/cgi/content/full/311/5757/38a. 279 Science 311, 38 (2006) 280 Charbonneau, David et al. A super-Earth transiting a nearby low-mass 281 star. Nature 462, 891-894 (2009). 282 Erwin, J., Tucker, O.J., Johnson, R.E. Hybrid fluid/kinetic modeling of 283 Pluto's atmosphere\\\", Icarus in press (2013) [arXiv:1211.3994 (2012)] 284 285 García-Muñoz, A. Physical and chemical aeronomy of HD 209458b. Planet. Space Sci. , 55 , 1426-1455 (2007) 286 Hunten, D.M. The escape of light gases from planetary atmospheres. J. , discoveries, Part II: Long time thermal atmospheric evaporation 309 modeling. Planet. Space Sci ., 56 , 1260-1272 (2008) 310 316 317 318 Tian, F. Thermal escape from super-Earth atmospheres in the habitable 324 zones of M stars. ApJ 703, 905-909 (2009) 325 Yelle, R.V. Corrigendum to ''Aeronomy of extra-solar giant planets at 330\",\n \"pages\": [\n 13,\n 14,\n 15\n ]\n },\n {\n \"title\": \"small orbital distances''. Icarus 183, 508 (2006) 331\",\n \"content\": \"332 336 337 349 351\",\n \"pages\": [\n 16,\n 17,\n 18\n ]\n }\n]"}}},{"rowIdx":90,"cells":{"bibcode":{"kind":"string","value":"2013GReGr..45..691L"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1301.5796.pdf"},"content":{"kind":"string","value":"\nWeak field approximation in a model of de Sitter gravity: Schwarzschild solutions and galactic rotation curves\nJia-An Lu a ∗ and Chao-Guang Huang b †\n\na School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China\nb Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049, China\n\nAbstract\nWeak field approximate solutions in the Λ → 0 limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotation curves without invoking dark matter.\nKeywords: de Sitter gravity, Schwarzschild solutions, torsion, dark matter\n1 Introduction\nIn the 1970s a model of de Sitter (dS) gravity had been proposed [1-4]. In this model the Einstein-Hilbert action with a cosmological term could be deduced from a gauge-like action besides two quadratic terms of the curvature and torsion. The astronomical observation [5, 6] on the asymptotically dS behavior of our universe has increased interest in the model as it may offer a way to deal with the dark energy problem [7]. If the EinsteinHilbert term is required to be the main part of the gauge-like action, the cosmological constant should be large. The large cosmological constant may be canceled out by the vacuum energy density, leaving a small cosmological constant [4]. But it is difficult to explain why the large cosmological constant and the vacuum energy density are so close, but not exactly equal, to each other. On the other hand, if the cosmological constant is required to be small [1-3, 8], the quadratic curvature term would become the main part of the action. Note that in one of the field equations, the quadratic curvature term only contributes to the symmetric trace-free part. It is worth checking carefully whether the\nmodel under this case could explain the experimental observations. Actually it has been shown [9, 10] that the model with a small cosmological constant may explain the accelerating expansion of the universe and supply a natural transit from decelerating expansion to accelerating expansion without the help of introducing matter fields in addition to dust. It has also been shown [11, 12] that all torsion-free vacuum solutions of this model are the vacuum solutions of Einstein's field equation with the same cosmological constant, and vise versa. Therefore, one may expect that the model with a small cosmological constant may pass all solar-system-scale experimental tests for general relativity (GR).\nHowever, it has been pointed out [9] that the energy-momentum-stress tensor of a spinless fluid in the torsion-free case of this model should be with a constant trace. Questions would then appear such as, could the torsion-free Schwarzschild-dS (S-dS) solution be smoothly connected to internal solutions with nonzero torsion, or are there any S-dS solutions with nonzero torsion? In fact, the different dS spacetimes with nonzero torsion in this model have been obtained in [13, 14], but they are sill not the S-dS solutions. On the other hand, S-dS solutions with long-range spherically symmetric torsion have been given [15] in some special cases (not necessarily under the double duality ansatz [16]) of quadratic models of Poincar'e gauge theory of gravity, but our model does not fall into those special cases.\nWe would like to firstly check the existence of the S-dS solutions with nonzero torsion in the weak field approximation. The Newtonian limit of general quadratic models in Poincar'e gauge theory of gravity has been calculated [17, 18] in the 1980's. In those calculations, quadratic terms in the field equations have been thrown away as usual. However, in the weak field approximation of our model, the quadratic curvature terms could not be easily thrown away, for the reason that they are the main parts of one of the field equations. In fact, we may let the cosmological constant be Λ → 0, then only those quadratic curvature terms would appear in the limit of the field equation which contains the energy-momentum-stress tensor of the matter field. On the other hand, as those quadratic curvature terms are symmetric and trace-free, they would not appear in the trace part and the antisymmetric part of the field equations. The Newtonian limit of the trace equations has been recently analyzed [19], but a more complete analysis of all components of the field equations is needed.\nAs was well known, Newton's theory of gravity meets great difficulties in the explanation of the flat rotation curves [20] of spiral galaxies. The most widely adopted way to resolve this problem is the dark matter hypothesis. But up to now, all of the possible candidates of dark matter (such as neutralino, axion, etc.) are either undetected or unsatisfactory. In the meanwhile, there also exist some models [21-24] which could deduce the galactic rotation curves without involving dark matter. We would like to explore the possibility of a new explanation for the galactic rotation curves from the dS gravity model.\nThe paper is arranged as follows. We first briefly review the model of the dS gravity in section 2. In the third section, after dividing a field equation into its trace part, symmetric trace-free part and antisymmetric part, we attain the Λ → 0 limit of the model and calculate its weak field approximation in the static and spherically symmetric case. The weak field approximate solutions contain the weak Schwarzschild fields with nonzero torsion, which could be smoothly linked to regular internal solutions obeying the Newtonian gravitational law. The coupling constant is determined by the existence of such solutions. Moreover, solutions that could deduce the galactic rotation curves without invoking dark matter are also attained. Finally we end with some remarks in the\nlast section.\n2 A model of dS gravity\nA model of dS gravity has been constructed with a gauge-like action [1-4]\nS G = ∫ L G = ∫ κ [ -tr( F ab F ab )] = ∫ κ [ R abcd R abcd -4 l 2 ( R -6 l 2 ) + 2 l 2 S abc S abc ] (1)\nin the units of /planckover2pi1 = c = 1, where κ is a dimensionless coupling constant to be determined, and\nF ab = ( d A + 1 2 [ A , A ]) ab (2)\nor explicitly\nF A Bab = ( d A A B ) ab + A A Ca ∧A C Bb = ( R ab α β -l -2 e α a ∧ e βb l -1 S α ab -l -1 S βab 0 ) (3)\nis a dS algebra-valued 2-form and\nA A Ba = ( Γ α βa l -1 e α a -l -1 e βa 0 ) (4)\nis a dS algebra-valued 1-form. Here A, B... = 0 , 1 , 2 , 3 , 4 stand for matrix indices (internal indices) and the trace in Eq. (1) is taken for those indices. In addition, { e α a } is some local orthonormal frame field on the spacetime manifold and Γ α βa is the connection 1-form in this frame field, where a, b... stand for abstract indices [25, 26] and α, β... = 0 , 1 , 2 , 3 are concrete indices related to the frame field mentioned above. The curvature 2-form R ab α β and torsion 2-form S α ab are related to the connection 1-form Γ α βa as follows:\nR ab α β = ( d Γ α β ) ab +Γ α γa ∧ Γ γ βb , (5)\nS α ab = ( de α ) ab +Γ α βa ∧ e β b . (6)\nMoreover,\nR abc d = R abα β e α c e β d , S c ab = S α ab e α c , R ab = R acb c , R = g ab R ab .\nIn fact, if spacetime is an umbilical submanifold of some (1+4)-dimensional ambient manifold and with positive normal curvature, then A a and F ab could be viewed [8] as the connection 1-form and curvature 2-form (in the dS-Lorentz frame) of the ambient manifold restricted to spacetime. Here, an umbilical submanifold means a submanifold with constant normal curvature, such as the dS spacetime which could be seen as an umbilical submanifold of a 5d Minkowski spacetime with positive normal curvature. A a could also be seen [27] as the Cartan connection of a Cartan geometry modeled on the dS spacetime and based on the spacetime manifold, with F ab the corresponding curvature\n2-form. The Cartan geometry is a generalization of homogenous spaces with fibre bundle language, and one may refer to [27] for more details. In addition, it should be noted that 3 /l 2 is identified [8] with a small cosmological constant Λ here, which is very different from the viewpoint of [4] where l is identified with the Planck length. The signature is chosen such that the metric coefficients are η αβ = diag( -1 , 1 , 1 , 1).\nThe total action is S = S M + S G , where S M is the action of the matter fields and the field equations can be given via the variational principle with respect to e α a , Γ α βa :\n8 l 2 ( G ab +Λ g ab ) + | R | 2 g ab -4 R acde R b cde + 2 l 2 | S | 2 g ab -8 l 2 S cda S cd b + 8 l 2 ∇ c S ab c + 4 l 2 S acd T b cd + 1 κ Σ ab = 0 , (7)\n-4 l 2 T a bc -4 ∇ d R da bc +2 T a de R de bc -8 l 2 S [ bc ] a + 1 κ τ bc a = 0 , (8)\nG ab = R ab -1 2 Rg ab , T c ab = S c ab +2 δ c [ a S d b ] d , | R | 2 = R abcd R abcd , | S | 2 = S abc S abc , Σ α a = δS M /δe α a , Σ b a = Σ α a e α b , τ α βa = δS M /δ Γ α βa , τ b ca = τ α βa e α b e β c ,\nwhere\nand the variational derivatives are defined as follows: if\nδS M = ∫ ( X α a δe α a + Y αβ a δ Γ αβ a ) ,\nthen\nδS M /δe α a = X α a , δS M /δ Γ αβ a = Y [ αβ ] a .\n3 Weak field approximation in the case with Λ → 0\nAs Λ is very small, it is interesting to see the case with Λ → 0 ( l → ∞ ). If Λ → 0 is directly set in the first field equation, then only the quadratic curvature terms are left, which are symmetric and trace-free. Thus, we would like to perform the following procedure. Divide the first field equation into its symmetric trace-free part, trace part, and antisymmetric part, then let l tend to infinity ( l →∞ ) in the above three parts and in the second field equation. The limiting equations are:\n| R | 2 g ab -4 R acde R b cde = 0 , (9)\n-R -∇ c S bc b + 1 2 S bcd T bcd +( l 2 / 8 κ )Σ = 0 , (10)\nR [ ab ] + ∇ c S [ ab ] c + 1 2 S [ a cd T b ] cd +( l 2 / 8 κ )Σ [ ab ] = 0 , (11)\n-2 ∇ d R da bc + T a de R de bc = 0 . (12)\nWhen l → ∞ , l 2 /κ should tend to a finite value, otherwise Eqs. (10) and (11) would give Σ = 0 and Σ [ ab ] = 0, which are unreasonable. In the torsion-free case, the scalar\ncurvature would be a constant from Eq. (12), and, therefore, Σ = const from Eq. (10). This property has been pointed out by [9]. Now we are going to consider the week field approximation of the above equations. It would be assumed that\ng ab = η ab + γ ab , γ ab = O ( s ) , S c ab = O ( s ) , (13)\nΣ ab = O ( s ) , τ ab c = O ( s ) , (14)\nwhere s is a dimensionless parameter, called the weak field parameter. We will restrict ourselves to the static and O (3)-symmetric case, with the static spherical coordinate system { t, r, θ, ϕ } . η ab could be defined by its components η µν = diag( -1 , 1 , 1 , 1) in the approximate inertial coordinate system { x µ } . { x µ } is related to { t, r, θ, ϕ } as usual:\nx 0 = t, x 1 = r sin θ cos ϕ, x 2 = r sin θ sin ϕ, x 3 = r cos θ.\nIt could be proved [15, 25, 28] that γ ab and S c ab have only these dependent components in the static spherical coordinate system:\nγ 00 = -2 φ ( r ) , γ rr = -2 ψ ( r ) , (15)\n S 0 0 r = f ( r ) , S r 0 r = h ( r ) , S θ rθ = g ( r ) , S θ 0 θ = -k ( r ) , S ϕ rϕ = g ( r ) , S ϕ 0 ϕ = -k ( r ) , (16)\n where φ plays the role of the Newtonian gravitational potential [1-3, 25, 29] and ψ is an unknown function. It can be shown that components of γ ab and S c ab in { x µ } are as follows:\nγ 00 = -2 φ, γ 0 i = 0 , γ ij = ( -2 ψ ) x i x j /r 2 , (17)\n S 0 0 i = fx i /r, S 0 ij = 0 , S i 0 j = ( h + k ) x i x j /r 2 -kδ i j , S i jk = ( -g/r )( δ i j x k -δ i k x j ) . (18)\nFor this case the contorsion tensor is related to the torsion tensor by\nK abc = S cba . (19)\nLet Γ c ab = Γ σ µν ∂ σ c ( dx µ ) a ( dx ν ) b , where Γ σ µν is the connection coefficient in { x µ } . Γ c ab and the curvature tensor have the following first order approximate expressions:\nΓ c ab = 1 2 ( ∂ a γ b c + ∂ b γ a c -∂ c γ ab ) -K c ab , (20)\nR abc d = -( ∂ c ∂ [ a γ b ] d -∂ d ∂ [ a γ b ] c ) + 2 ∂ [ a K d | c | b ] , (21)\nK c ab = 1 2 ( S c ab + S ab c + S ba c ) (22)\nwhere\nis the contorsion tensor. In the case with Σ ab = ρ ( r )( dt ) a ( dt ) b , the equations for the first order approximate g ab and S c ab are as follows:\n| R | 2 η ab -4 R acde R b cde = 0 , (23)\nR + ∂ c S bc b +( l 2 / 8 κ ) ρ = 0 , (24)\nR [ ab ] + ∂ c S [ ab ] c = 0 , (25)\n∂ d R da bc = 0 . (26)\nThe first order approximation of Eq. (9) is an identity. Here Eq. (23) is the second order approximation of Eq. (9). It should be considered for the reason that it is still an equation for the first order approximate g ab and S c ab .\nNow we are going to solve the above weak field equations. Applying Eq. (21) to Eq. (26), we have\n∂ d ( ∂ [ d ∂ [ c γ b ] a ] + ∂ [ d K cb a ] ) = 0 . (27)\nThe 00 i ( abc ) component of Eq. (27) is\n∂ d ( ∂ d ∂ i γ 00 +2 ∂ d K i 00 ) = 0 ,\nwhich gives\n/triangle [( φ ' + f ) x i /r ] = 0 , i.e. ( φ ' + f ) '' /r +2( φ ' + f ) ' /r 2 -2( φ ' + f ) /r 3 = 0 .\nSolving this equation we get that\nφ ' + f = Cr + D/r 2 . (28)\nThe 0 ij component of Eq. (27) is an identity. The i 0 j component of Eq. (27) is\n∂ d ∂ d K j 0 i -∂ d ∂ i K j 0 d = 0 ,\nwhich gives\nδ ij ( -/triangle k -h ' /r ) + ( x i x j /r 2 )[ /triangle k + h ' /r -2 k ' /r -2( h + k ) /r 2 ] = 0 , i.e. /triangle k + h ' /r = 0 , /triangle k + h ' /r -2 k ' /r -2( h + k ) /r 2 = 0 ,\nor equivalently\nh + k + rk ' = 0 . (29)\nThe ijk component of Eq. (27) is\n∂ d ∂ d ∂ k γ ji -∂ d ∂ d ∂ j γ ki -∂ d ∂ i ∂ k γ jd + ∂ d ∂ i ∂ j γ kd +2 ∂ d ∂ d K kji -2 ∂ d ∂ i K kjd = 0 ,\nwhich gives\n/triangle [(2 ψ/r 2 -2 g/r )( δ ik x j -δ ij x k )] = 0 , i.e. (2 ψ/r 2 -2 g/r ) '' +(4 /r )(2 ψ/r 2 -2 g/r ) ' = 0 .\nSolving this equation we get that\nψ/r 2 -g/r = B/r 3 + A. (30)\nFrom Eqs. (21), (17) and (18) the components of R abcd in { x µ } could be attained as follows:\n R 0 i 0 j = ( φ '' + f ' ) x i x j /r 2 +( φ ' + f )( δ ij r 2 -x i x j ) /r 3 , R 0 ijk = 0 , R ijk 0 = (2 /r 2 )( h + k + rk ' ) x [ i δ j ] k , R ijkl = ( ψ/r 2 -g/r ) ' (2 /r ) x [ i ( δ j ] k x l -δ j ] l x k ) -4( ψ/r 2 -g/r ) δ i [ k δ l ] j . (31)\nSubstituting Eqs. (28), (29) and (30) into the above equation, we get that\nThen\n R 0 i 0 j = ( Cr + D/r 2 ) ' x i x j /r 2 +( Cr + D/r 2 )( δ ij r 2 -x i x j ) /r 3 , R 0 ijk = 0 , R ijk 0 = 0 , R ijkl = ( B/r 3 + A ) ' (2 /r ) x [ i ( δ j ] k x l -δ j ] l x k ) -4( B/r 3 + A ) δ i [ k δ l ] j . (32)\n| R | 2 η 00 -4 R 0 cde R 0 cde = 12( C 2 -4 A 2 ) + 24( D 2 -B 2 ) /r 6 , | R | 2 η 0 i -4 R 0 cde R i cde = 0 , | R | 2 η ij -4 R icde R j cde = (4 C 2 -16 A 2 -16 CD/r 3 -32 AB/r 3 +16 D 2 /r 6 -16 B 2 /r 6 ) δ ij +(48 CD/r 3 +96 AB/r 3 -24 D 2 /r 6 +24 B 2 /r 6 ) x i x j /r 2 , (33)\nR 00 = 3 C, R 0 i = R i 0 = 0 , R ij = -( C + D/r 3 +4 A + B/r 3 ) δ ij +[3( B + D ) /r 3 ] x i x j /r 2 , R = -6( C +2 A ) , (34)\nApplying Eq. (33), the symmetric trace-free equation (23) could be solved, resulting in the following relations:\nC = ± 2 A, B = ± D, CD +2 AB = 0 . (35)\nFrom Eq. (34) one could see that R [ ab ] = 0 and thus the antisymmetric equation (25) gives ∂ c S [ ab ] c = 0. Components of ∂ c S ab c are as follows:\n∂ c S 00 c = -f ' -2 f/r, ∂ c S 0 i c = 0 , ∂ c S i 0 c = x i [ h ' /r +2( h + k ) /r 2 ] , ∂ c S ij c = [ -2( g/r ) -r ( g/r ) ' ] δ ij +( g/r ) ' x i x j /r. (36)\nTherefore, ∂ c S [ ab ] c = 0 results in\nh ' /r +2( h + k ) /r 2 = 0 . (37)\nCombining Eqs. (29) and (37) we have\n( h -2 k ) ' = 0 , h + k = -r ( h + k ) ' / 3 , h = 2 k + C 1 , h + k = C 2 /r 3 . (38)\nNow we turn to the trace equation (24). From Eqs. (36), (28) and (30) we have\n∂ c S bc b = -f ' -2 f/r +2 r ( g/r ) ' +6( g/r ) = 2 ψ ' /r +2 ψ/r 2 + /triangle φ -3(2 A + C ) . (39)\nSubstituting Eqs. (34) and (39) into Eq. (24) results in\n-( /triangle φ +2 ψ ' /r +2 ψ/r 2 ) + 9(2 A + C ) = ( l 2 / 8 κ ) ρ. (40)\nEquation. (40) is an underdetermined equation for φ and ψ . To solve it, more conditions are needed. Suppose that the external solution is the weak Schwarzschild field, i.e., φ = ψ = -GM/r and the internal solution is regular and satisfies /triangle φ = 4 πGρ . Also, it is assumed that the internal solution could be linked to the external solution smoothly at r = R S , resulting in a complete solution. For this complete solution, there would be C = -2 A ,\nwith\nand\nψ = [ -Gm ( r ) /r ]( l 2 / 64 πGκ +1 / 2) .\nNote that ψ ( R S ) = -Gm ( R S ) /R S , thus,\nψ = -Gm ( r ) /r, (42)\nκ = l 2 / 32 πG. (43)\nEquation. (42) is just the same as the corresponding case in GR. The result C = -2 A is in accordance with Eq. (35). The torsion solutions will be given later in the more general case.\nActually, Eq. (40) can also be solved with other supplementary conditions. For example, instead of assuming /triangle φ = 4 πGρ , we may let\n/triangle φ = 4 πG ( ρ + ˜ ρ ) , (44)\nwhere ˜ ρ is an arbitrarily given function and does not contribute to the energy-momentumstress tensors of matter fields. Fixing κ by Eq. (43), then from Eqs. (35), (40) and (44) we have\nφ = G ∫ r 0 { [ m ( r ) + ˜ m ( r )] /r 2 } dr + φ (0) , (45)\nψ = -G r [ m ( r ) + ˜ m ( r ) / 2] + 3 2 (2 A + C ) r 2 (46)\n˜ m ( r ) = ∫ B 3 ( r ) ˜ ρ = ∫ r 0 4 π ˜ ρr 2 dr, C = ± 2 A.\nwith\nAs the internal solutions are regular, from Eqs. (28), (30) and (38), there should be B = D = 0, C 2 = 0. Therefore, the torsion solutions corresponding to Eqs. (45) and (46) are as follows:\nf = Cr -G [ m ( r ) + ˜ m ( r )] /r 2 , (47)\ng = (4 A +3 C ) r/ 2 -G [ m ( r ) + ˜ m ( r ) / 2] /r 2 , (48)\nh = -k = 1 3 C 1 . (49)\nφ = ∫ r 0 [ Gm ( r ) /r 2 ] dr + φ (0) (41)\nm ( r ) = ∫ B 3 ( r ) ρ = ∫ r 0 4 πρr 2 dr,\nφ (0) = -GM/R S -∫ R S 0 [ Gm ( r ) /r 2 ] dr,\nThe former case which is compatible with the Schwarzschild solutions corresponds to the special choice with C = -2 A and ˜ ρ = 0. In fact, another choice of ˜ ρ could deduce the galactic rotation curves without invoking dark matter. To fit the galactic rotation curves, the dark matter density profile ρ DM has been given for many spiral galaxies, for example, see Refs. [30, 31], where the following choice is made:\nρ DM = σ 2 2 πG ( r 2 + a 2 ) . (50)\nIn Refs. [30, 31], the mass distribution of the galaxies is modeled as the sum of the bulge and disk stellar components and a halo of dark matter. The rotation curves are used to determine the two halo parameters σ and a . In our model, we may just let the gravitational contribution ˜ ρ to take the same form as the dark matter density profile and suitably choose the integration constants, i.e., ˜ ρ = ρ DM and C = -2 A , without the inclusion of any real dark matter. For this case, Eqs. (45) and (46) is almost equivalent to the corresponding case in GR with dark matter. The parameters σ and a can be determined in the same way as that in Refs. [30, 31] and, therefore, with the same values. For example, for the galaxy NGC 2841, σ = 232 km/s and a = 11 . 6 kpc fit the rotation curve well, for the galaxy NGC 3031, σ = 86 km/s and a = 2 . 0 kpc fit the rotation curve well, and so on. To say 'almost equivalent' but not 'equivalent', is because the term ˜ m/ 2 in Eq. (46) is different from ˜ m , which should be the case in GR with dark matter. Fortunately, ψ would not affect the rotation curves in the leading order of approximation, since the rotation velocity v c in a galaxy at a radius r in the approximation is given by\nv 2 c ( r ) = r ( ∂φ/∂r ) . (51)\nFor higher order approximations, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results.\nOne may argue that ˜ ρ can not be specified a priori and could only be determined from observation. Actually, such kinds of functions also appear in other models which attempt to explain the galactic rotation curves without involving dark matter, such as Milgrom's modification of Newtonian dynamics (MOND) [21, 22] and the modified Newton's gravity in Finsler space [24]. What we can do now is to point out the geometrical meaning of ˜ ρ . From Eqs. (47) and (48), there is the relation:\n4 πG ˜ ρ = -2 r 2 [ r 2 ( f -g )] ' -3(4 A + C ) , (52)\nwhich shows that the dark matter density could be directly related to the spacetime torsion.\nWhen l →∞ , l 2 /κ should tend to a finite value, as was mentioned before. Obviously Eq. (43) satisfies this requirement. In [1-3, 8], the coupling constant is chosen to be -l 2 / 64 πG , which is different from Eq. (43). For this case, there exists no regular internal solution which satisfies /triangle φ = 4 πGρ and has a smooth junction to the Schwarzschild solutions. In fact, with this choice, the ratio of the coefficient of the Einstein term G ab to that of the matter term Σ ab in Eq. (7) would be 1 : ( -8 πG ), just like the case in GR. But the role of the Einstein term in our model is different from that of GR. Actually, from Eq. (34), the Einstein term only contributes a constant term to Eq. (24), while the torsion term plays an important role in that equation.\nGenerally, the torsion tensor can be decomposed [32, 33] into three irreducible parts with respect to the Lorentz group: the tensor part, trace-vector part, and the axial vector part. For static and O (3)-symmetric torsion, the axial vector part vanishes automatically, the tensor part satisfies f = 2 g , h = 2 k and the trace-vector part satisfies f = -g , h = -k . By Eqs. (47) and (48), if the torsion field only contains the tensor part, the matter density should be a constant:\nρ = 3(2 A + C ) / 2 πG. (53)\nIf the torsion field only contains the trace-vector part, then\n4 ρ +3˜ ρ = 3(4 A +5 C ) / 4 πG. (54)\nWhen ˜ ρ = 0, the matter density has to be a constant, too.\n4 Remarks\nThe weak field approximation of the Λ → 0 limit of the dS gravity model has been calculated in the static and spherically symmetric case. The matter field is assumed to be a smoothly distributed dust sphere with finite radius. It comes out that if and only if κ = l 2 / 32 πG , there exist regular internal solutions which satisfy /triangle φ = 4 πGρ and have a smooth junction to the weak Schwarzschild fields. Recall that the main part of the action is the quadratic curvature term, not the Einstein-Hilbert term. The existence of the above solutions is of significance. The choice of the coupling constant here is different from that of [1-3, 8], where κ = -l 2 / 64 πG . The choice in [1-3, 8] may due to a comparison between the dS gravity model and GR. But the Einstein term in the dS gravity model plays a different role from that of GR, as it only contributes to a constant term in the weak field approximate equations. Actually, the metric components and torsion components are closely related by Eqs. (28) and (30), such that the curvature tensor has to take a special form (32). Moreover, one may let C = A = 0 and B = D = 0, then R abcd = 0, i.e., the Weizenbock spacetime [34, 35] would be attained. On the other hand, the torsion tensor plays an important role in this model. In the weak field approximate solutions, if the torsion tensor only contains the tensor part, the matter density should be a constant; if it only contains the trace-vector part, Eq. (54) should be upheld. In particular, the matter density should be a constant in the torsion-free case.\nThe trace equation (24) results in an underdetermined equation for the metric components φ and ψ in the weak field approximation. Solutions with /triangle φ = 4 πG ( ρ +˜ ρ ) could be attained, which can explain the galactic rotation curves without the help of introducing dark matter. The geometrical meaning of ˜ ρ has been given by Eq. (52). It is a geometric quantity related to the spacetime torsion and can play the role of dark matter density though it is irrelevant to the energy-momentum-stress tensors of matter fields. To see the higher order behavior of the model, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results.\n/negationslash\nFinally, it should be remarked that all the above results need to be reexamined in the case with Λ = 0. But we can conclude, at least, that if there exist regular internal solutions which are in accordance with the Newtonian gravitational law and could be smoothly extended to the weak S-dS fields, the coupling constant should be chosen as κ = l 2 / 32 πG .\nAcknowledgments\nOne of us (Lu) would like to thank Prof. Zhi-Bing Li, Xi-Ping Zhu, and thank the late Prof. Han-Ying Guo for their sincere help. He also expresses his appreciation for hospitality during his stay at the Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences. This work is supported by the National Natural Science Foundation of China under Grant Nos. 10975141, 10831008, 11275207, and the oriented projects of CAS under Grant No. KJCX2-EW-W01.\nReferences\n\n[1] Wu, Y.-S., Li, G.-D., Guo, H.-Y.: Gravitational Lagrangian and local de Sitter invariance. Kexue Tongbao. (Chin. Sci. Bull.) 19 , 509-512 (1974) (in Chinese)\n[2] An, Y., Chen, S., Zou, Z.-L., Guo, H.-Y.: A new theory of gravity - a theory with local de Sitter invariance. ibid 21 , 379-382 (1976) (in Chinese)\n[3] Guo, H.-Y.: On de Sitter gauge theory of gravity. ibid 24, 202-207 (1979) (in Chinese)\n[4] Townsend, P.K.: Small-scale structure of spacetime as the origin of the gravitational constant. Phys. Rev. D 15 , 2795-2801 (1977)\n[5] Bennett, C.L., et al.: First year Wilkinson microwave anisotropy probe (WMAP) observations: preliminary maps and basic results. Astrophys. J. Suppl. 148 , 1 (2003). astroph/0302207\n[6] Tegmark, M., et al.: Cosmological parameters from SDSS and WMAP. Phys. Rev. D 69 , 103501 (2004). astroph/0310723\n[7] Peebles, P.J.E., Ratra, B.: The cosmological constant and dark energy. Rev. Mod. Phys. 75 , 559-606 (2003)\n[8] Guo, H.-Y., Huang, C.-G., Tian, Y., Wu, H.-T., Xu, Z., Zhou, B.: Snyder's model de Sitter special relativity duality and de Sitter gravity. Class. Quantum Grav. 24 , 4009-4035 (2007)\n[9] Huang, C.-G., Zhang, H.-Q., Guo, H.-Y.: Cosmological solutions with torsion in a model of the de Sitter gauge theory of gravity. JCAP 10 , 010 (2008)\n[10] Huang, C.-G., Zhang, H.-Q., Guo, H.-Y.: A new gravitational model for dark energy. Chin. Phys. C (High Energ. Phys. Nucl. Phys.) 32 , 687-691 (2008)\n[11] Huang, C.-G., Tian, Y., Wu, X.-N., Guo, H.-Y.: On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity. Front. Phys. China 2 , 191-194 (2008)\n[12] Huang, C.-G., Ma, M.-S.: On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity (II). Front. Phys. China 4 , 525-529 (2009)\n[13] Huang, C.-G., Ma, M.-S.: de Sitter spacetimes with torsion in the model of de Sitter gauge theory of gravity. Phys. Rev. D 80 , 084033 (2009)\n\n\n[14] Huang, C.-G., Ma, M.-S.: A new solution with torsion in model of dS gauge theory of gravity. Commun. Theor. Phys. 55 , 65-68 (2011)\n[15] Chen, C.-M., Chern, D.-C., Nester, J.M., Zhytnikov, P., Vadim, V.: Poincar'e gauge theory Schwarzschild-de Sitter solutions with long range spherically symmetric torsion. Chin. J. Phys. 32 , 29-40 (1994)\n[16] Lenzen, H.-J.: On spherically symmetric fields with dynamic torsion in gauge theories of gravitation. Gen. Relativ. Gravit. 17 , 1137-1151 (1985)\n[17] Hayashi, K., Shirafuji, T.: Gravity from Poincar'e gauge theory of the fundamental particles. III weak field approximation. Prog. Theor. Phys. 64 , 1435-1452 (1980)\n[18] Zhang, Y.-Z.: Approximate solutions for general Riemann-Cartan-type R + R 2 theories of gravitation. Phys. Rev. D 28 , 1866-1871 (1983)\n[19] Ma, M.-S.: Doctoral Dissertation. Institute of High Energy Physics, Chinese Academy of Sciences (2011)\n[20] Rubin, V.C., Ford, W.K., Thonnard, N.: Astrophys. J. 238 , 471-487 (1980)\n[21] Milgrom, M.: A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270 , 365-370 (1983)\n[22] Milgrom, M.: A modification of the Newtonian dynamics - Implications for galaxies. Astrophys. J. 270 , 371-389 (1983)\n[23] Xu, C., et al.: The problem of dark matter and higher-order gravitational theory. S. Afr. J. Phys. 15 , 5 (1992)\n[24] Chang, Z., Li, X.: Modified Newton's gravity in Finsler space as a possible alternative to dark matter hypothesis. Phys. Lett. B. 668 , 453-456 (2008)\n[25] Liang, C.-B., Zhou, B.: Introduction to Differential Geometry and General Relativity. Science press, Beijing (2006). (in Chinese)\n[26] Wald, R.M.: General Relativity. The University of Chicago Press, Chicago (1984)\n[27] Wise, D.K.: MacDowell-Mansouri gravity and Cartan geometry. Class. Quantum Grav. 27 , 155010 (2010)\n[28] Wheeler, J.T.: Symmetric solutions to themaximally Gauss-Bonnet extentded Einstein equations.Nucl. Phys. B 273 , 732-748 (1986)\n[29] Zhang, Y.-Z.: Newtonian limit in the Poincar'e gauge field theory of gravitation. Sci. Sin. A 4 , 399-404 (1985)\n[30] Kent, S.M.: Dark matter in spiral galaxies. I. Galaxies with optical rotation curves. Astron. J. 91 , 1301-1327 (1986)\n[31] Kent, S.M.: Dark matter in spiral galaxies. II. Galaxies with H riptsize I rotation curves. Astron. J. 93 , 816-832 (1987)\n\n\n[32] Hayashi, K., Shirafuji, T.: Gravity from Poincar'e gauge theory of the fundamental particles. I. General formulation. Prog. Theor. Phys. 64 , 866-882 (1980)\n[33] Hehl, F.W., McCrea, J.D., Mielke, E.W., Neeman, Y.: Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance. Phys. Rep. 258 , 1-171 (1995)\n[34] R. Weitzenbock, Invarianten Theorie. Nordhoff, Groningen, 1923\n[35] Hayashi, K., Shirafuji, T.: New general relativity. Phys. Rev. D 19 , 3524-3553 (1979)\n\n"},"sections":{"kind":"list like","value":[{"title":"Weak field approximation in a model of de Sitter gravity: Schwarzschild solutions and galactic rotation curves","content":"Jia-An Lu a ∗ and Chao-Guang Huang b †","pages":[1]},{"title":"Abstract","content":"Weak field approximate solutions in the Λ → 0 limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotation curves without invoking dark matter. Keywords: de Sitter gravity, Schwarzschild solutions, torsion, dark matter","pages":[1]},{"title":"1 Introduction","content":"In the 1970s a model of de Sitter (dS) gravity had been proposed [1-4]. In this model the Einstein-Hilbert action with a cosmological term could be deduced from a gauge-like action besides two quadratic terms of the curvature and torsion. The astronomical observation [5, 6] on the asymptotically dS behavior of our universe has increased interest in the model as it may offer a way to deal with the dark energy problem [7]. If the EinsteinHilbert term is required to be the main part of the gauge-like action, the cosmological constant should be large. The large cosmological constant may be canceled out by the vacuum energy density, leaving a small cosmological constant [4]. But it is difficult to explain why the large cosmological constant and the vacuum energy density are so close, but not exactly equal, to each other. On the other hand, if the cosmological constant is required to be small [1-3, 8], the quadratic curvature term would become the main part of the action. Note that in one of the field equations, the quadratic curvature term only contributes to the symmetric trace-free part. It is worth checking carefully whether the model under this case could explain the experimental observations. Actually it has been shown [9, 10] that the model with a small cosmological constant may explain the accelerating expansion of the universe and supply a natural transit from decelerating expansion to accelerating expansion without the help of introducing matter fields in addition to dust. It has also been shown [11, 12] that all torsion-free vacuum solutions of this model are the vacuum solutions of Einstein's field equation with the same cosmological constant, and vise versa. Therefore, one may expect that the model with a small cosmological constant may pass all solar-system-scale experimental tests for general relativity (GR). However, it has been pointed out [9] that the energy-momentum-stress tensor of a spinless fluid in the torsion-free case of this model should be with a constant trace. Questions would then appear such as, could the torsion-free Schwarzschild-dS (S-dS) solution be smoothly connected to internal solutions with nonzero torsion, or are there any S-dS solutions with nonzero torsion? In fact, the different dS spacetimes with nonzero torsion in this model have been obtained in [13, 14], but they are sill not the S-dS solutions. On the other hand, S-dS solutions with long-range spherically symmetric torsion have been given [15] in some special cases (not necessarily under the double duality ansatz [16]) of quadratic models of Poincar'e gauge theory of gravity, but our model does not fall into those special cases. We would like to firstly check the existence of the S-dS solutions with nonzero torsion in the weak field approximation. The Newtonian limit of general quadratic models in Poincar'e gauge theory of gravity has been calculated [17, 18] in the 1980's. In those calculations, quadratic terms in the field equations have been thrown away as usual. However, in the weak field approximation of our model, the quadratic curvature terms could not be easily thrown away, for the reason that they are the main parts of one of the field equations. In fact, we may let the cosmological constant be Λ → 0, then only those quadratic curvature terms would appear in the limit of the field equation which contains the energy-momentum-stress tensor of the matter field. On the other hand, as those quadratic curvature terms are symmetric and trace-free, they would not appear in the trace part and the antisymmetric part of the field equations. The Newtonian limit of the trace equations has been recently analyzed [19], but a more complete analysis of all components of the field equations is needed. As was well known, Newton's theory of gravity meets great difficulties in the explanation of the flat rotation curves [20] of spiral galaxies. The most widely adopted way to resolve this problem is the dark matter hypothesis. But up to now, all of the possible candidates of dark matter (such as neutralino, axion, etc.) are either undetected or unsatisfactory. In the meanwhile, there also exist some models [21-24] which could deduce the galactic rotation curves without involving dark matter. We would like to explore the possibility of a new explanation for the galactic rotation curves from the dS gravity model. The paper is arranged as follows. We first briefly review the model of the dS gravity in section 2. In the third section, after dividing a field equation into its trace part, symmetric trace-free part and antisymmetric part, we attain the Λ → 0 limit of the model and calculate its weak field approximation in the static and spherically symmetric case. The weak field approximate solutions contain the weak Schwarzschild fields with nonzero torsion, which could be smoothly linked to regular internal solutions obeying the Newtonian gravitational law. The coupling constant is determined by the existence of such solutions. Moreover, solutions that could deduce the galactic rotation curves without invoking dark matter are also attained. Finally we end with some remarks in the last section.","pages":[1,2,3]},{"title":"2 A model of dS gravity","content":"A model of dS gravity has been constructed with a gauge-like action [1-4] in the units of /planckover2pi1 = c = 1, where κ is a dimensionless coupling constant to be determined, and or explicitly is a dS algebra-valued 2-form and is a dS algebra-valued 1-form. Here A, B... = 0 , 1 , 2 , 3 , 4 stand for matrix indices (internal indices) and the trace in Eq. (1) is taken for those indices. In addition, { e α a } is some local orthonormal frame field on the spacetime manifold and Γ α βa is the connection 1-form in this frame field, where a, b... stand for abstract indices [25, 26] and α, β... = 0 , 1 , 2 , 3 are concrete indices related to the frame field mentioned above. The curvature 2-form R ab α β and torsion 2-form S α ab are related to the connection 1-form Γ α βa as follows: Moreover, In fact, if spacetime is an umbilical submanifold of some (1+4)-dimensional ambient manifold and with positive normal curvature, then A a and F ab could be viewed [8] as the connection 1-form and curvature 2-form (in the dS-Lorentz frame) of the ambient manifold restricted to spacetime. Here, an umbilical submanifold means a submanifold with constant normal curvature, such as the dS spacetime which could be seen as an umbilical submanifold of a 5d Minkowski spacetime with positive normal curvature. A a could also be seen [27] as the Cartan connection of a Cartan geometry modeled on the dS spacetime and based on the spacetime manifold, with F ab the corresponding curvature 2-form. The Cartan geometry is a generalization of homogenous spaces with fibre bundle language, and one may refer to [27] for more details. In addition, it should be noted that 3 /l 2 is identified [8] with a small cosmological constant Λ here, which is very different from the viewpoint of [4] where l is identified with the Planck length. The signature is chosen such that the metric coefficients are η αβ = diag( -1 , 1 , 1 , 1). The total action is S = S M + S G , where S M is the action of the matter fields and the field equations can be given via the variational principle with respect to e α a , Γ α βa : where and the variational derivatives are defined as follows: if then","pages":[3,4]},{"title":"3 Weak field approximation in the case with Λ → 0","content":"As Λ is very small, it is interesting to see the case with Λ → 0 ( l → ∞ ). If Λ → 0 is directly set in the first field equation, then only the quadratic curvature terms are left, which are symmetric and trace-free. Thus, we would like to perform the following procedure. Divide the first field equation into its symmetric trace-free part, trace part, and antisymmetric part, then let l tend to infinity ( l →∞ ) in the above three parts and in the second field equation. The limiting equations are: When l → ∞ , l 2 /κ should tend to a finite value, otherwise Eqs. (10) and (11) would give Σ = 0 and Σ [ ab ] = 0, which are unreasonable. In the torsion-free case, the scalar curvature would be a constant from Eq. (12), and, therefore, Σ = const from Eq. (10). This property has been pointed out by [9]. Now we are going to consider the week field approximation of the above equations. It would be assumed that where s is a dimensionless parameter, called the weak field parameter. We will restrict ourselves to the static and O (3)-symmetric case, with the static spherical coordinate system { t, r, θ, ϕ } . η ab could be defined by its components η µν = diag( -1 , 1 , 1 , 1) in the approximate inertial coordinate system { x µ } . { x µ } is related to { t, r, θ, ϕ } as usual: It could be proved [15, 25, 28] that γ ab and S c ab have only these dependent components in the static spherical coordinate system: where φ plays the role of the Newtonian gravitational potential [1-3, 25, 29] and ψ is an unknown function. It can be shown that components of γ ab and S c ab in { x µ } are as follows: For this case the contorsion tensor is related to the torsion tensor by Let Γ c ab = Γ σ µν ∂ σ c ( dx µ ) a ( dx ν ) b , where Γ σ µν is the connection coefficient in { x µ } . Γ c ab and the curvature tensor have the following first order approximate expressions: where is the contorsion tensor. In the case with Σ ab = ρ ( r )( dt ) a ( dt ) b , the equations for the first order approximate g ab and S c ab are as follows: The first order approximation of Eq. (9) is an identity. Here Eq. (23) is the second order approximation of Eq. (9). It should be considered for the reason that it is still an equation for the first order approximate g ab and S c ab . Now we are going to solve the above weak field equations. Applying Eq. (21) to Eq. (26), we have The 00 i ( abc ) component of Eq. (27) is which gives Solving this equation we get that The 0 ij component of Eq. (27) is an identity. The i 0 j component of Eq. (27) is which gives or equivalently The ijk component of Eq. (27) is which gives Solving this equation we get that From Eqs. (21), (17) and (18) the components of R abcd in { x µ } could be attained as follows: Substituting Eqs. (28), (29) and (30) into the above equation, we get that Then Applying Eq. (33), the symmetric trace-free equation (23) could be solved, resulting in the following relations: From Eq. (34) one could see that R [ ab ] = 0 and thus the antisymmetric equation (25) gives ∂ c S [ ab ] c = 0. Components of ∂ c S ab c are as follows: Therefore, ∂ c S [ ab ] c = 0 results in Combining Eqs. (29) and (37) we have Now we turn to the trace equation (24). From Eqs. (36), (28) and (30) we have Substituting Eqs. (34) and (39) into Eq. (24) results in Equation. (40) is an underdetermined equation for φ and ψ . To solve it, more conditions are needed. Suppose that the external solution is the weak Schwarzschild field, i.e., φ = ψ = -GM/r and the internal solution is regular and satisfies /triangle φ = 4 πGρ . Also, it is assumed that the internal solution could be linked to the external solution smoothly at r = R S , resulting in a complete solution. For this complete solution, there would be C = -2 A , with and Note that ψ ( R S ) = -Gm ( R S ) /R S , thus, Equation. (42) is just the same as the corresponding case in GR. The result C = -2 A is in accordance with Eq. (35). The torsion solutions will be given later in the more general case. Actually, Eq. (40) can also be solved with other supplementary conditions. For example, instead of assuming /triangle φ = 4 πGρ , we may let where ˜ ρ is an arbitrarily given function and does not contribute to the energy-momentumstress tensors of matter fields. Fixing κ by Eq. (43), then from Eqs. (35), (40) and (44) we have with As the internal solutions are regular, from Eqs. (28), (30) and (38), there should be B = D = 0, C 2 = 0. Therefore, the torsion solutions corresponding to Eqs. (45) and (46) are as follows: The former case which is compatible with the Schwarzschild solutions corresponds to the special choice with C = -2 A and ˜ ρ = 0. In fact, another choice of ˜ ρ could deduce the galactic rotation curves without invoking dark matter. To fit the galactic rotation curves, the dark matter density profile ρ DM has been given for many spiral galaxies, for example, see Refs. [30, 31], where the following choice is made: In Refs. [30, 31], the mass distribution of the galaxies is modeled as the sum of the bulge and disk stellar components and a halo of dark matter. The rotation curves are used to determine the two halo parameters σ and a . In our model, we may just let the gravitational contribution ˜ ρ to take the same form as the dark matter density profile and suitably choose the integration constants, i.e., ˜ ρ = ρ DM and C = -2 A , without the inclusion of any real dark matter. For this case, Eqs. (45) and (46) is almost equivalent to the corresponding case in GR with dark matter. The parameters σ and a can be determined in the same way as that in Refs. [30, 31] and, therefore, with the same values. For example, for the galaxy NGC 2841, σ = 232 km/s and a = 11 . 6 kpc fit the rotation curve well, for the galaxy NGC 3031, σ = 86 km/s and a = 2 . 0 kpc fit the rotation curve well, and so on. To say 'almost equivalent' but not 'equivalent', is because the term ˜ m/ 2 in Eq. (46) is different from ˜ m , which should be the case in GR with dark matter. Fortunately, ψ would not affect the rotation curves in the leading order of approximation, since the rotation velocity v c in a galaxy at a radius r in the approximation is given by For higher order approximations, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results. One may argue that ˜ ρ can not be specified a priori and could only be determined from observation. Actually, such kinds of functions also appear in other models which attempt to explain the galactic rotation curves without involving dark matter, such as Milgrom's modification of Newtonian dynamics (MOND) [21, 22] and the modified Newton's gravity in Finsler space [24]. What we can do now is to point out the geometrical meaning of ˜ ρ . From Eqs. (47) and (48), there is the relation: which shows that the dark matter density could be directly related to the spacetime torsion. When l →∞ , l 2 /κ should tend to a finite value, as was mentioned before. Obviously Eq. (43) satisfies this requirement. In [1-3, 8], the coupling constant is chosen to be -l 2 / 64 πG , which is different from Eq. (43). For this case, there exists no regular internal solution which satisfies /triangle φ = 4 πGρ and has a smooth junction to the Schwarzschild solutions. In fact, with this choice, the ratio of the coefficient of the Einstein term G ab to that of the matter term Σ ab in Eq. (7) would be 1 : ( -8 πG ), just like the case in GR. But the role of the Einstein term in our model is different from that of GR. Actually, from Eq. (34), the Einstein term only contributes a constant term to Eq. (24), while the torsion term plays an important role in that equation. Generally, the torsion tensor can be decomposed [32, 33] into three irreducible parts with respect to the Lorentz group: the tensor part, trace-vector part, and the axial vector part. For static and O (3)-symmetric torsion, the axial vector part vanishes automatically, the tensor part satisfies f = 2 g , h = 2 k and the trace-vector part satisfies f = -g , h = -k . By Eqs. (47) and (48), if the torsion field only contains the tensor part, the matter density should be a constant: If the torsion field only contains the trace-vector part, then When ˜ ρ = 0, the matter density has to be a constant, too.","pages":[4,5,6,7,8,9,10]},{"title":"4 Remarks","content":"The weak field approximation of the Λ → 0 limit of the dS gravity model has been calculated in the static and spherically symmetric case. The matter field is assumed to be a smoothly distributed dust sphere with finite radius. It comes out that if and only if κ = l 2 / 32 πG , there exist regular internal solutions which satisfy /triangle φ = 4 πGρ and have a smooth junction to the weak Schwarzschild fields. Recall that the main part of the action is the quadratic curvature term, not the Einstein-Hilbert term. The existence of the above solutions is of significance. The choice of the coupling constant here is different from that of [1-3, 8], where κ = -l 2 / 64 πG . The choice in [1-3, 8] may due to a comparison between the dS gravity model and GR. But the Einstein term in the dS gravity model plays a different role from that of GR, as it only contributes to a constant term in the weak field approximate equations. Actually, the metric components and torsion components are closely related by Eqs. (28) and (30), such that the curvature tensor has to take a special form (32). Moreover, one may let C = A = 0 and B = D = 0, then R abcd = 0, i.e., the Weizenbock spacetime [34, 35] would be attained. On the other hand, the torsion tensor plays an important role in this model. In the weak field approximate solutions, if the torsion tensor only contains the tensor part, the matter density should be a constant; if it only contains the trace-vector part, Eq. (54) should be upheld. In particular, the matter density should be a constant in the torsion-free case. The trace equation (24) results in an underdetermined equation for the metric components φ and ψ in the weak field approximation. Solutions with /triangle φ = 4 πG ( ρ +˜ ρ ) could be attained, which can explain the galactic rotation curves without the help of introducing dark matter. The geometrical meaning of ˜ ρ has been given by Eq. (52). It is a geometric quantity related to the spacetime torsion and can play the role of dark matter density though it is irrelevant to the energy-momentum-stress tensors of matter fields. To see the higher order behavior of the model, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results. /negationslash Finally, it should be remarked that all the above results need to be reexamined in the case with Λ = 0. But we can conclude, at least, that if there exist regular internal solutions which are in accordance with the Newtonian gravitational law and could be smoothly extended to the weak S-dS fields, the coupling constant should be chosen as κ = l 2 / 32 πG .","pages":[10]},{"title":"Acknowledgments","content":"One of us (Lu) would like to thank Prof. Zhi-Bing Li, Xi-Ping Zhu, and thank the late Prof. Han-Ying Guo for their sincere help. He also expresses his appreciation for hospitality during his stay at the Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences. This work is supported by the National Natural Science Foundation of China under Grant Nos. 10975141, 10831008, 11275207, and the oriented projects of CAS under Grant No. KJCX2-EW-W01.","pages":[11]}],"string":"[\n {\n \"title\": \"Weak field approximation in a model of de Sitter gravity: Schwarzschild solutions and galactic rotation curves\",\n \"content\": \"Jia-An Lu a ∗ and Chao-Guang Huang b †\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Abstract\",\n \"content\": \"Weak field approximate solutions in the Λ → 0 limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotation curves without invoking dark matter. Keywords: de Sitter gravity, Schwarzschild solutions, torsion, dark matter\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1 Introduction\",\n \"content\": \"In the 1970s a model of de Sitter (dS) gravity had been proposed [1-4]. In this model the Einstein-Hilbert action with a cosmological term could be deduced from a gauge-like action besides two quadratic terms of the curvature and torsion. The astronomical observation [5, 6] on the asymptotically dS behavior of our universe has increased interest in the model as it may offer a way to deal with the dark energy problem [7]. If the EinsteinHilbert term is required to be the main part of the gauge-like action, the cosmological constant should be large. The large cosmological constant may be canceled out by the vacuum energy density, leaving a small cosmological constant [4]. But it is difficult to explain why the large cosmological constant and the vacuum energy density are so close, but not exactly equal, to each other. On the other hand, if the cosmological constant is required to be small [1-3, 8], the quadratic curvature term would become the main part of the action. Note that in one of the field equations, the quadratic curvature term only contributes to the symmetric trace-free part. It is worth checking carefully whether the model under this case could explain the experimental observations. Actually it has been shown [9, 10] that the model with a small cosmological constant may explain the accelerating expansion of the universe and supply a natural transit from decelerating expansion to accelerating expansion without the help of introducing matter fields in addition to dust. It has also been shown [11, 12] that all torsion-free vacuum solutions of this model are the vacuum solutions of Einstein's field equation with the same cosmological constant, and vise versa. Therefore, one may expect that the model with a small cosmological constant may pass all solar-system-scale experimental tests for general relativity (GR). However, it has been pointed out [9] that the energy-momentum-stress tensor of a spinless fluid in the torsion-free case of this model should be with a constant trace. Questions would then appear such as, could the torsion-free Schwarzschild-dS (S-dS) solution be smoothly connected to internal solutions with nonzero torsion, or are there any S-dS solutions with nonzero torsion? In fact, the different dS spacetimes with nonzero torsion in this model have been obtained in [13, 14], but they are sill not the S-dS solutions. On the other hand, S-dS solutions with long-range spherically symmetric torsion have been given [15] in some special cases (not necessarily under the double duality ansatz [16]) of quadratic models of Poincar'e gauge theory of gravity, but our model does not fall into those special cases. We would like to firstly check the existence of the S-dS solutions with nonzero torsion in the weak field approximation. The Newtonian limit of general quadratic models in Poincar'e gauge theory of gravity has been calculated [17, 18] in the 1980's. In those calculations, quadratic terms in the field equations have been thrown away as usual. However, in the weak field approximation of our model, the quadratic curvature terms could not be easily thrown away, for the reason that they are the main parts of one of the field equations. In fact, we may let the cosmological constant be Λ → 0, then only those quadratic curvature terms would appear in the limit of the field equation which contains the energy-momentum-stress tensor of the matter field. On the other hand, as those quadratic curvature terms are symmetric and trace-free, they would not appear in the trace part and the antisymmetric part of the field equations. The Newtonian limit of the trace equations has been recently analyzed [19], but a more complete analysis of all components of the field equations is needed. As was well known, Newton's theory of gravity meets great difficulties in the explanation of the flat rotation curves [20] of spiral galaxies. The most widely adopted way to resolve this problem is the dark matter hypothesis. But up to now, all of the possible candidates of dark matter (such as neutralino, axion, etc.) are either undetected or unsatisfactory. In the meanwhile, there also exist some models [21-24] which could deduce the galactic rotation curves without involving dark matter. We would like to explore the possibility of a new explanation for the galactic rotation curves from the dS gravity model. The paper is arranged as follows. We first briefly review the model of the dS gravity in section 2. In the third section, after dividing a field equation into its trace part, symmetric trace-free part and antisymmetric part, we attain the Λ → 0 limit of the model and calculate its weak field approximation in the static and spherically symmetric case. The weak field approximate solutions contain the weak Schwarzschild fields with nonzero torsion, which could be smoothly linked to regular internal solutions obeying the Newtonian gravitational law. The coupling constant is determined by the existence of such solutions. Moreover, solutions that could deduce the galactic rotation curves without invoking dark matter are also attained. Finally we end with some remarks in the last section.\",\n \"pages\": [\n 1,\n 2,\n 3\n ]\n },\n {\n \"title\": \"2 A model of dS gravity\",\n \"content\": \"A model of dS gravity has been constructed with a gauge-like action [1-4] in the units of /planckover2pi1 = c = 1, where κ is a dimensionless coupling constant to be determined, and or explicitly is a dS algebra-valued 2-form and is a dS algebra-valued 1-form. Here A, B... = 0 , 1 , 2 , 3 , 4 stand for matrix indices (internal indices) and the trace in Eq. (1) is taken for those indices. In addition, { e α a } is some local orthonormal frame field on the spacetime manifold and Γ α βa is the connection 1-form in this frame field, where a, b... stand for abstract indices [25, 26] and α, β... = 0 , 1 , 2 , 3 are concrete indices related to the frame field mentioned above. The curvature 2-form R ab α β and torsion 2-form S α ab are related to the connection 1-form Γ α βa as follows: Moreover, In fact, if spacetime is an umbilical submanifold of some (1+4)-dimensional ambient manifold and with positive normal curvature, then A a and F ab could be viewed [8] as the connection 1-form and curvature 2-form (in the dS-Lorentz frame) of the ambient manifold restricted to spacetime. Here, an umbilical submanifold means a submanifold with constant normal curvature, such as the dS spacetime which could be seen as an umbilical submanifold of a 5d Minkowski spacetime with positive normal curvature. A a could also be seen [27] as the Cartan connection of a Cartan geometry modeled on the dS spacetime and based on the spacetime manifold, with F ab the corresponding curvature 2-form. The Cartan geometry is a generalization of homogenous spaces with fibre bundle language, and one may refer to [27] for more details. In addition, it should be noted that 3 /l 2 is identified [8] with a small cosmological constant Λ here, which is very different from the viewpoint of [4] where l is identified with the Planck length. The signature is chosen such that the metric coefficients are η αβ = diag( -1 , 1 , 1 , 1). The total action is S = S M + S G , where S M is the action of the matter fields and the field equations can be given via the variational principle with respect to e α a , Γ α βa : where and the variational derivatives are defined as follows: if then\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"3 Weak field approximation in the case with Λ → 0\",\n \"content\": \"As Λ is very small, it is interesting to see the case with Λ → 0 ( l → ∞ ). If Λ → 0 is directly set in the first field equation, then only the quadratic curvature terms are left, which are symmetric and trace-free. Thus, we would like to perform the following procedure. Divide the first field equation into its symmetric trace-free part, trace part, and antisymmetric part, then let l tend to infinity ( l →∞ ) in the above three parts and in the second field equation. The limiting equations are: When l → ∞ , l 2 /κ should tend to a finite value, otherwise Eqs. (10) and (11) would give Σ = 0 and Σ [ ab ] = 0, which are unreasonable. In the torsion-free case, the scalar curvature would be a constant from Eq. (12), and, therefore, Σ = const from Eq. (10). This property has been pointed out by [9]. Now we are going to consider the week field approximation of the above equations. It would be assumed that where s is a dimensionless parameter, called the weak field parameter. We will restrict ourselves to the static and O (3)-symmetric case, with the static spherical coordinate system { t, r, θ, ϕ } . η ab could be defined by its components η µν = diag( -1 , 1 , 1 , 1) in the approximate inertial coordinate system { x µ } . { x µ } is related to { t, r, θ, ϕ } as usual: It could be proved [15, 25, 28] that γ ab and S c ab have only these dependent components in the static spherical coordinate system: where φ plays the role of the Newtonian gravitational potential [1-3, 25, 29] and ψ is an unknown function. It can be shown that components of γ ab and S c ab in { x µ } are as follows: For this case the contorsion tensor is related to the torsion tensor by Let Γ c ab = Γ σ µν ∂ σ c ( dx µ ) a ( dx ν ) b , where Γ σ µν is the connection coefficient in { x µ } . Γ c ab and the curvature tensor have the following first order approximate expressions: where is the contorsion tensor. In the case with Σ ab = ρ ( r )( dt ) a ( dt ) b , the equations for the first order approximate g ab and S c ab are as follows: The first order approximation of Eq. (9) is an identity. Here Eq. (23) is the second order approximation of Eq. (9). It should be considered for the reason that it is still an equation for the first order approximate g ab and S c ab . Now we are going to solve the above weak field equations. Applying Eq. (21) to Eq. (26), we have The 00 i ( abc ) component of Eq. (27) is which gives Solving this equation we get that The 0 ij component of Eq. (27) is an identity. The i 0 j component of Eq. (27) is which gives or equivalently The ijk component of Eq. (27) is which gives Solving this equation we get that From Eqs. (21), (17) and (18) the components of R abcd in { x µ } could be attained as follows: Substituting Eqs. (28), (29) and (30) into the above equation, we get that Then Applying Eq. (33), the symmetric trace-free equation (23) could be solved, resulting in the following relations: From Eq. (34) one could see that R [ ab ] = 0 and thus the antisymmetric equation (25) gives ∂ c S [ ab ] c = 0. Components of ∂ c S ab c are as follows: Therefore, ∂ c S [ ab ] c = 0 results in Combining Eqs. (29) and (37) we have Now we turn to the trace equation (24). From Eqs. (36), (28) and (30) we have Substituting Eqs. (34) and (39) into Eq. (24) results in Equation. (40) is an underdetermined equation for φ and ψ . To solve it, more conditions are needed. Suppose that the external solution is the weak Schwarzschild field, i.e., φ = ψ = -GM/r and the internal solution is regular and satisfies /triangle φ = 4 πGρ . Also, it is assumed that the internal solution could be linked to the external solution smoothly at r = R S , resulting in a complete solution. For this complete solution, there would be C = -2 A , with and Note that ψ ( R S ) = -Gm ( R S ) /R S , thus, Equation. (42) is just the same as the corresponding case in GR. The result C = -2 A is in accordance with Eq. (35). The torsion solutions will be given later in the more general case. Actually, Eq. (40) can also be solved with other supplementary conditions. For example, instead of assuming /triangle φ = 4 πGρ , we may let where ˜ ρ is an arbitrarily given function and does not contribute to the energy-momentumstress tensors of matter fields. Fixing κ by Eq. (43), then from Eqs. (35), (40) and (44) we have with As the internal solutions are regular, from Eqs. (28), (30) and (38), there should be B = D = 0, C 2 = 0. Therefore, the torsion solutions corresponding to Eqs. (45) and (46) are as follows: The former case which is compatible with the Schwarzschild solutions corresponds to the special choice with C = -2 A and ˜ ρ = 0. In fact, another choice of ˜ ρ could deduce the galactic rotation curves without invoking dark matter. To fit the galactic rotation curves, the dark matter density profile ρ DM has been given for many spiral galaxies, for example, see Refs. [30, 31], where the following choice is made: In Refs. [30, 31], the mass distribution of the galaxies is modeled as the sum of the bulge and disk stellar components and a halo of dark matter. The rotation curves are used to determine the two halo parameters σ and a . In our model, we may just let the gravitational contribution ˜ ρ to take the same form as the dark matter density profile and suitably choose the integration constants, i.e., ˜ ρ = ρ DM and C = -2 A , without the inclusion of any real dark matter. For this case, Eqs. (45) and (46) is almost equivalent to the corresponding case in GR with dark matter. The parameters σ and a can be determined in the same way as that in Refs. [30, 31] and, therefore, with the same values. For example, for the galaxy NGC 2841, σ = 232 km/s and a = 11 . 6 kpc fit the rotation curve well, for the galaxy NGC 3031, σ = 86 km/s and a = 2 . 0 kpc fit the rotation curve well, and so on. To say 'almost equivalent' but not 'equivalent', is because the term ˜ m/ 2 in Eq. (46) is different from ˜ m , which should be the case in GR with dark matter. Fortunately, ψ would not affect the rotation curves in the leading order of approximation, since the rotation velocity v c in a galaxy at a radius r in the approximation is given by For higher order approximations, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results. One may argue that ˜ ρ can not be specified a priori and could only be determined from observation. Actually, such kinds of functions also appear in other models which attempt to explain the galactic rotation curves without involving dark matter, such as Milgrom's modification of Newtonian dynamics (MOND) [21, 22] and the modified Newton's gravity in Finsler space [24]. What we can do now is to point out the geometrical meaning of ˜ ρ . From Eqs. (47) and (48), there is the relation: which shows that the dark matter density could be directly related to the spacetime torsion. When l →∞ , l 2 /κ should tend to a finite value, as was mentioned before. Obviously Eq. (43) satisfies this requirement. In [1-3, 8], the coupling constant is chosen to be -l 2 / 64 πG , which is different from Eq. (43). For this case, there exists no regular internal solution which satisfies /triangle φ = 4 πGρ and has a smooth junction to the Schwarzschild solutions. In fact, with this choice, the ratio of the coefficient of the Einstein term G ab to that of the matter term Σ ab in Eq. (7) would be 1 : ( -8 πG ), just like the case in GR. But the role of the Einstein term in our model is different from that of GR. Actually, from Eq. (34), the Einstein term only contributes a constant term to Eq. (24), while the torsion term plays an important role in that equation. Generally, the torsion tensor can be decomposed [32, 33] into three irreducible parts with respect to the Lorentz group: the tensor part, trace-vector part, and the axial vector part. For static and O (3)-symmetric torsion, the axial vector part vanishes automatically, the tensor part satisfies f = 2 g , h = 2 k and the trace-vector part satisfies f = -g , h = -k . By Eqs. (47) and (48), if the torsion field only contains the tensor part, the matter density should be a constant: If the torsion field only contains the trace-vector part, then When ˜ ρ = 0, the matter density has to be a constant, too.\",\n \"pages\": [\n 4,\n 5,\n 6,\n 7,\n 8,\n 9,\n 10\n ]\n },\n {\n \"title\": \"4 Remarks\",\n \"content\": \"The weak field approximation of the Λ → 0 limit of the dS gravity model has been calculated in the static and spherically symmetric case. The matter field is assumed to be a smoothly distributed dust sphere with finite radius. It comes out that if and only if κ = l 2 / 32 πG , there exist regular internal solutions which satisfy /triangle φ = 4 πGρ and have a smooth junction to the weak Schwarzschild fields. Recall that the main part of the action is the quadratic curvature term, not the Einstein-Hilbert term. The existence of the above solutions is of significance. The choice of the coupling constant here is different from that of [1-3, 8], where κ = -l 2 / 64 πG . The choice in [1-3, 8] may due to a comparison between the dS gravity model and GR. But the Einstein term in the dS gravity model plays a different role from that of GR, as it only contributes to a constant term in the weak field approximate equations. Actually, the metric components and torsion components are closely related by Eqs. (28) and (30), such that the curvature tensor has to take a special form (32). Moreover, one may let C = A = 0 and B = D = 0, then R abcd = 0, i.e., the Weizenbock spacetime [34, 35] would be attained. On the other hand, the torsion tensor plays an important role in this model. In the weak field approximate solutions, if the torsion tensor only contains the tensor part, the matter density should be a constant; if it only contains the trace-vector part, Eq. (54) should be upheld. In particular, the matter density should be a constant in the torsion-free case. The trace equation (24) results in an underdetermined equation for the metric components φ and ψ in the weak field approximation. Solutions with /triangle φ = 4 πG ( ρ +˜ ρ ) could be attained, which can explain the galactic rotation curves without the help of introducing dark matter. The geometrical meaning of ˜ ρ has been given by Eq. (52). It is a geometric quantity related to the spacetime torsion and can play the role of dark matter density though it is irrelevant to the energy-momentum-stress tensors of matter fields. To see the higher order behavior of the model, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results. /negationslash Finally, it should be remarked that all the above results need to be reexamined in the case with Λ = 0. But we can conclude, at least, that if there exist regular internal solutions which are in accordance with the Newtonian gravitational law and could be smoothly extended to the weak S-dS fields, the coupling constant should be chosen as κ = l 2 / 32 πG .\",\n \"pages\": [\n 10\n ]\n },\n {\n \"title\": \"Acknowledgments\",\n \"content\": \"One of us (Lu) would like to thank Prof. Zhi-Bing Li, Xi-Ping Zhu, and thank the late Prof. Han-Ying Guo for their sincere help. He also expresses his appreciation for hospitality during his stay at the Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences. This work is supported by the National Natural Science Foundation of China under Grant Nos. 10975141, 10831008, 11275207, and the oriented projects of CAS under Grant No. KJCX2-EW-W01.\",\n \"pages\": [\n 11\n ]\n }\n]"}}},{"rowIdx":91,"cells":{"bibcode":{"kind":"string","value":"2013GReGr..45.2143M"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1307.4371.pdf"},"content":{"kind":"string","value":"\nReview on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results\nMarc Mars ∗ , Filipe C. Mena † and Ra¨ul Vera ‡\n∗ Instituto de F´ısica Fundamental y Matem´aticas, Universidad de Salamanca,\nPlaza de la Merced s/n, 37008 Salamanca, Spain\n† Centro de Matem´atica, Universidade do Minho, 4710-057 Braga, Portugal ‡ Dept. of Theoretical Physics and History of Science,\nUniversity of the Basque Country UPV/EHU, 644 PK, Bilbao 48080, Basque Country, Spain\nAbstract\nThe Einstein-Straus model consists of a Schwarzschild spherical vacuole in a Friedman-Lemaˆıtre-Robertson-Walker (FLRW) dust spacetime (with or without Λ). It constitutes the most widely accepted model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model is that there is no influence from the cosmic background, since the spherical vacuole is static. Spherical generalizations to other interior matter models are commonly used in the construction of lumpy inhomogeneous cosmological models. On the other hand, the model has proven to be reluctant to admit non-spherical generalizations. In this review, we summarize the known uniqueness results for this model. These seem to indicate that the only reasonable and realistic nonspherical deformations of the Einstein-Straus model require perturbing the FLRW background. We review results about linear perturbations of the Einstein-Straus model, where the perturbations in the vacuole are assumed to be stationary and axially symmetric so as to describe regions (voids in particular) in which the matter has reached an equilibrium regime.\n1 Introduction\nDuring a meal in the 19th Jena Meeting on Relativity, in September 1996, Bill Bonnor provocatively asked Jos'e Senovilla if the table could be expanding with the Universe. Not surprisingly, Bonnor later took the question seriously and wrote a paper about how the hydrogen atom is affected by the cosmic expansion [11], which is well worth reading.\nAbout five decades before, Einstein and Straus asked a similar question, on a bigger scale, which led them to investigate the influence of the expansion of space on the gravitational fields surrounding individual stars [19]. They took the Schwarzschild solution representing the vacuole surrounding a star located in the centre and the FriedmanLemaitre-Robertson-Walker (FLRW) solution as the cosmological model. At the core of their model was the matching of the two solutions across a spherical surface with constant cosmological radius. Since the expansion kept the vacuole symmetry and time independence, their conclusion was that it does not affect the gravitational fields surrounding\nstars and, in particular, it does not affect the solar system dynamics. A previous attempt to address the issue of whether the planetary orbits expand with the Universe was made by McVittie [44] who found a smooth model describing a spherically symmetric mass embedded in a flat FLRW.\nSince then the research about this problem was scarce, although some alternatives to the McVittie model were suggested, e.g. in [22], and difficulties of the global meaning of the model were also pointed out [48, 49, 50, 51] (see also [15]). Concerning the Einstein-Straus model itself, it was revisited in [2, 8] and stability issues were raised in [57], [32] cf. also the discussion in [30]. However, the Einstein-Straus model has never stopped being considered as the correct answer to the lack of influence of the cosmological expansion on local systems. Moreover, since the vacuole can be inserted anywhere due to the homogeneity of FLRW, the Einstein-Straus model led to the original Swiss cheese model of a lumpy inhomogeneous universe (see e.g. [20]).\nBonnor's question, that 1996 afternoon, raised a totally new issue for the EinsteinStraus models, namely whether spherical symmetry was a crucial ingredient of the model and, therefore, for the existence of time-invariant bounded systems embedded in a FLRW universe. Indeed, the question triggered research by Senovilla and Vera [59], that led to the result about the impossibility of the Einstein-Straus model in cylindrical symmetry. In turn, this important result was the origin of over fifteen years of research about the rigidity, in the sense of uniqueness, of the model. The aim of this paper is to review these results on rigidity both for exact models and from a perturbative perspective.\nCrucial to this endeavour was the development of a general mathematical theory of spacetime matching [41] and of its perturbative version [4, 47, 35]. This allowed to achieve quite general results about the possibility of generalizing both the shape of the cavity and the cosmological setting of the original Einstein-Straus model. As an example, described below in some detail, uniqueness of the static Λ-vacuum spherical region embedded in a non-static FLRW cosmological model has been proved [34].\nThe scope of the Einstein-Straus model has been taken well beyond both the physical scale originally considered and the physical problems for which the model was conceived. In fact, the model has been used not only at the solar system scale, but also on galaxy [27] and galaxy clusters' scales [27, 54]. On the other hand, the vacuole of the (original) Einstein-Straus model has been replaced by other spherically symmetric geometries, generally Lemaˆıtre-Tolman-Bondi (LTB), also spherically shaped regions of Szekeres, in order to construct 'generalized' Einstein-Straus models for describing extra-galactic scale and cosmic voids (we refer to the reviews in [30, 20]). Lumpy inhomogeneous cosmological models based on the generalized Einstein-Straus Swiss cheese models are being used in the search of possible explanations to the accelerated expansion of the Universe by the study of lensing effects at cosmic scales produced by the voids (see e.g. [20]).\nSo far, all these generalized Einstein-Straus (and the corresponding Swiss cheese) models have assumed spherically shaped inhomogeneities (voids). One of themes of the research we will review here is how far can one push the Einstein-Straus model towards non-spherical generalizations. The fundamental ingredient we want to keep is that the bound system remains stationary, so as to keep the absence of influence of the cosmic dynamics on astrophysical scales. We will use the term Einstein-Straus problem to the problem of finding the most general stationary regions (vacuum or not) one can embed in a realistic cosmological model in a broad sense.\nThe Einstein-Straus model has also been taken beyond the exact solutions' settings\nto include metric perturbations. Perturbation theory in General Relativity (GR) is a natural framework to study small departures from symmetric configurations and thus to perform stability analysis. For instance, it allows to include simultaneously density, rotational and gravitational wave perturbation modes into an, otherwise, spatially homogeneous and isotropic cosmological model. Most interestingly, it allows a priori to perturb independently the interior and exterior spacetimes as well as the matching boundary. Furthermore, although the three perturbation modes are decoupled on a FLRW background, they may couple at a matching boundary. In this context, an important question is how general can the perturbations be in each model.\nInherent to perturbation theory is the issue of gauge freedom. In perturbed spacetime matchings, this can be complicated by the fact that three independent perturbation gauges may be in use. For the sake of completeness, we include a short review of linearized matching, where these issues are discussed, see also [47] for further details, including the definition of the so-called doubly gauge invariant variables .\nPerturbations in the FLRW background are customarily split in scalar, vector and tensor modes, and the later are generically viewed as cosmological gravitational waves. Given that the gravitational wave detectors are already active, and gravitational waves are expected to be detected within the next five years (see e.g. [6, 55] for recent accounts and the review [56]), it would be interesting to investigate their inclusion in the models. One now certainly has the necessary mathematical machinery to do so, and preliminary results indicate the possibility of having, for instance, a stationary axially symmetric vacuole embedded in an expanding cosmological model containing tensor modes [38]. Even more, the linearized matching links the rotational and tensor modes degrees of freedom in the perturbation variables [38].\nThis is therefore an interesting timing to revise the state-of-the-art and point out potentially interesting directions of research about the Einstein-Straus problem, in the sense pointed out above.\nThe plan of the review is the following. In Section 2, the Einstein-Straus model is briefly presented. Similar summaries with different degrees of detail can be found in many places in the literature, see e.g. [20]. We include it here for the sake of completeness and in order to fix our notation. Section 3 is devoted to describing in some detail the uniqueness results concerning both general static regions and stationary and axisymmetric regions (irrespective of any symmetry consideration and/or matter content) embeddable in a FLRW expanding cosmology. Section 3.1 is devoted to the static case. The main conclusion here is that the only static vacuum region that can be embedded to an expanding FLRW is a spherically shaped region of Schwarzschild (i.e. the Einstein-Straus model). Similar uniqueness results hold for other matter models, such as vacuum with cosmological constant. Section 3.2 deals, in turn, with the uniqueness results for stationary and axially symmetric regions in FLRW expanding universes. The main result is that the stationary region must, in fact, be static, so that the previous conclusions on static regions apply. The uniqueness result thus states that the only way of having a stationary and axially symmetric or static region in an expanding FLRW is the Einstein-Straus model. Following the uniqueness results, the robustness of the Einstein-Straus model is further analyzed by considering alternative exact cosmological models. In Section 4 the replacement of the FLRW region by more general anisotropic cosmologies, i.e. the Bianchi models, is studied for static locally cylindrically symmetric interiors, leading to severe restrictions and no-go results for reasonable evolving cosmologies. The final part of the paper is devoted to\nthe generalization of the Einstein-Straus model from a perturbative perspective. After a brief overview of perturbative matching theory in Section 5, and the use of the Hodge decomposition on the sphere instead of the usual spherical harmonic decomposition in Section 6, the linearized matching between stationary and axisymmetric perturbations of Schwarzschild and general perturbed FLRW is reviewed in Section 7. We finish with some conclusions in Section 8, pointing out some ongoing research, prospects for future work on the perturbed Einstein-Straus model and its possible implications on the relationship between astrophysical bounded systems and cosmological dynamics in the form of cosmic gravitational waves.\n2 The Einstein-Straus model\nThis model consists of a spherically symmetric (both in shape and intrinsic geometry) Ricci-flat region embedded in a FLRW universe without cosmological constant. Recall that two spacetimes can be matched across their boundary if and only if the first fundamental forms q and second fundamental forms K agree on the matching hypersurface. A consequence of this are the well-known Israel conditions, which restrict the jump of the energy-momentum tensor across the boundary. In the present context, they imply that the cosmological fluid must be dust and the vacuole must be comoving with the cosmological fluid. Writing the FLRW metric in cosmic time coordinates\ng RW = -dt 2 + a 2 ( t ) g M , with g M = dR 2 +Σ 2 ( R,glyph[epsilon1] ) d Ω 2 , (1)\nwhere glyph[epsilon1] = {-1 , 0 , +1 } , Σ ' 2 = 1 -glyph[epsilon1] Σ 2 with prime denoting derivative with respect to R , in units G = c = 1 the Friedman equation reads\n˙ a 2 + glyph[epsilon1] = 8 πρ 0 3 a ,\nwhere the dot denotes derivative with respect to t and ρ 0 is a constant such that the cosmological energy-density ρ satisfies ρ = ρ 0 /a 3 . The boundary of the vacuole can be parametrized by { t = t, R = R 0 } (we ignore the angular variables as they behave trivially, and use t both as spacetime coordinate and intrinsic coordinate on the hypersurface, the precise meaning will be clear from the context). For the matching one needs the induced metric q RW and the second fundamental form K RW . Using the outward unit normal n RW = a ( t ) dR these objects read, with Σ c := Σ | R = R 0 , and Σ ' c := Σ ' | R = R 0 ,\nq RW = -dt 2 + a 2 ( t )Σ 2 c d Ω 2 , K RW = a ( t )Σ c Σ ' c d Ω 2 .\nFrom Birkhoff's theorem, the geometry of the vacuole is Kruskal. Assuming that the boundary is away from the Schwarzschild horizon (this happens sufficiently away from the big bang or big crunch) the interior metric can be written in Schwarzschild coordinates\ng Sch = -( 1 -2 m r ) 2 dT 2 + dr 2 1 -2 m r + r 2 d Ω 2 . (2)\nThe boundary can be parametrized as { T = T 0 ( t ) , r = r 0 ( t ) } and, given the time inversion symmetry of Schwarzschild, we can assume ˙ T 0 > 0 without loss of generality. The induced metric on the boundary is\nq Sch = -N 2 ( t ) dt 2 + r 2 0 ( t ) d Ω 2 , N 2 = ( 1 -2 m r 0 ) ˙ T 2 0 -˙ r 2 0 1 -2 m r 0 .\nUsing the unit normal n Sch = 1 N ( ˙ T 0 dr -˙ r 0 dT ) (note that the global sign of N is kept free at this stage), the second fundamental form is\nK Sch = 1 N ( -˙ T 0 r 0 + T 0 ˙ r 0 + 3 m ˙ r 2 0 ˙ T 0 r 0 ( r 0 -2 m ) -m r 2 0 ( 1 -2 m r 0 ) ˙ T 3 0 ) dt 2 + ˙ T 0 ( r 0 -2 m ) N d Ω 2 .\nEquality of the t -component of the induced metric requires N 2 = 1. Then, equality of the angular parts of the first and second fundamental forms imposes N = 1 and\nr 0 ( t ) = Σ c a ( t ) , ˙ T 0 = a ( t )Σ c Σ ' c a ( t )Σ c -2 m . (3)\nA straightforward computation shows that the equality of the t -component of the induced metric and second fundamental forms are satisfied provided the values of ρ 0 and m are linked by\nm = 4 π 3 ρ 0 Σ 3 c ,\nwhich has a clear interpretation in terms of (Misner-Sharp)-mass conservation. This is the Einstein-Straus model [19].\nA natural generalization consists in adding a cosmological constant Λ both to the FLRW and to the interior part (originally considered in [25] and fully solved in [2]). The Israel matching conditions on the energy-momentum tensor now impose the FLRW matter model to be dust with Λ, so that the Friedman equation is now\n˙ a 2 + glyph[epsilon1] = 8 πρ 0 3 a + Λ 3 a 2 .\nBy Birkhoff's theorem, the interior metric is the Kottler solution (also known as 'Schwarzschild(anti) de Sitter'), which away from the horizons is\ng K = -( 1 -2 m r -Λ r 2 3 ) 2 dT 2 + dr 2 1 -2 m r -Λ r 2 3 + r 2 d Ω 2 .\nIn this case, the matching conditions are\nr 0 ( t ) = Σ c a ( t ) , ˙ T 0 = a ( t )Σ c Σ ' c a ( t )Σ c -2 m -Λ 3 Σ 3 c a ( t ) 3 , m = 4 π 3 ρ 0 Σ 3 c .\nWe emphasize that any matching of two spacetimes immediately leads to a complementary matching, at least locally, where the 'interior' and 'exterior' regions on each spacetime reverse their roles (see [21] for details). In the matching above, this leads to the Oppenheimer-Snyder collapse model [53].\n3 Rigidity of the Einstein-Straus model\nThe Einstein-Straus model is such that, for a given total mass inside the vacuole and a given energy density in the cosmological background, the radius of the static region is uniquely fixed. This already poses difficulties for the model since it is often the case that the size of the vacuole does not match the observed sizes of clustered matter in the\nuniverse, such as stars or galaxies. This fact indicates that the Einstein-Straus model may be lacking flexibility to accommodate the various situations present in cosmology (cf. [58] and [10]). In fact, the Einstein-Straus vacuole was found to be radially unstable in a certain sense [30]. The other main restriction of the model is its exact spherical symmetry. It is clear that vacuoles in the universe are not exactly spherically symmetric so a natural question is how robust is the model to non-spherical generalizations.\nThe first thing to consider is which fundamental ingredients of the model should be kept. The main motivation of the Einstein-Straus model was its ability to combine cosmological expansion at large scales with no observable effects on the local physics. Thus, the fundamental ingredient to keep is the absence of influence of the cosmic expansion inside the region. The simplest and most natural way to achieve this is imposing that the interior geometry is stationary, because then no dynamical effects whatsoever from the surrounding evolving cosmology would affect the local physics. Among stationary interiors, the simplest case corresponds to static situations, so it is natural to start with this case (note that the Einstein-Straus model is itself static).\nThe question is then how rigid or flexible is the possibility of having stationary/static regions embedded in an otherwise expanding FLRW universe. Ideally, one would like to make no further assumptions and find the most general model with these properties. The matter model inside may also be kept arbitrary, and see what are the possibilities allowed by the coexistence of a stationary/static region inside an expanding FLRW universe. This coexistence has been sometimes called the Einstein-Straus problem in the literature (see e.g. [2]). The first indication that the Einstein-Straus model might be very rigid came from a seminal work by Senovilla and Vera [59] who considered the possibility of matching a static and cylindrically symmetric region (with no restriction on the matter model) with a FLRW dynamical cosmology. The matching hypersurface was taken to be locally a cylinder, in the sense of being tangent in an open set to the two (commuting) generators of two spatial local isometries. No global consideration was needed. The result was a no-go theorem: no such model exists.\nWith the impossibility of generalizing the Einstein-Straus model to a cylindrical setting, it became of interest to study the problem in as much generality as possible. The static case was treated in complete generality in [33], [34] and it is by now well-understood. The more complicated stationary situation has been studied [52] under the additional assumptions of axisymmetry and a group action orthogonally transitive. The motivation to study this simplified problem lies in the fact that one expects equilibrium configurations to also exhibit an axial symmetry. It is worth to mention that one step in the black hole uniqueness theorems corresponds to showing that the domain of outer communications must be axially symmetric [26].\nWe devote the following Section 3.1 to describing the main results in the static setting, and Section 3.2 to review the uniqueness results in the stationary and axially symmetric setting.\n3.1 Uniqueness results in the static case\nThis case was first considered in [33] under the additional assumption of axial symmetry, and one extra technical assumption relating cosmic and static times on the matching hypersurfaces. Both assumptions were dropped in [34] where a satisfactory uniqueness result for static region in FLRW was obtained.\nThe setup consists on a spacetime ( V , g ) composed by two regions ( W ST , g ST ) and ( W RW , g RW ) matched in absence of surface layers across their boundaries, denoted by Ω ST and Ω RW respectively, which once identified conform to a hypersurface Ω in ( V , g ). The region ( W ST , g ST ) is strictly static, i.e. admits a Killing vector ξ which is timelike and orthogonal to hypersurfaces everywhere. ( W RW , g RW ) is a codimension-zero submanifold with smooth boundary Ω RW of the FLRW spacetime ( V RW , g RW ), by which we mean the manifold V RW = I ×M , where I ⊂ R is an open interval, M is either E 3 ( glyph[epsilon1] = 0), S 3 ( glyph[epsilon1] = 1) or H 3 ( glyph[epsilon1] = -1) and the FLRW metric g RW takes the form (1). We call any coordinate system { R,θ, φ } in which the metric takes this form a spherical coordinate system . Note that since ( M , g M ) is homogeneous, there exist spherical coordinate systems centered at any point p ∈ M , and this will be used below.\nThe function a ( t ) is positive and smooth (in fact C 3 suffices). We assume that ˙ a does not vanish on any open set (this excludes uninteresting situations where the FRLW does not evolve). Define the 'geometric' energy-density ρ RW and pressure p RW by\n8 πρ RW := 3(˙ a 2 + glyph[epsilon1] ) /a 2 , 8 πp RW := ( -2 a a -˙ a 2 -glyph[epsilon1] ) /a 2 , (4)\nglyph[negationslash]\nso that, if the spacetime has a cosmological constant Λ, the energy-density and pressure of the cosmic fluid is ρ = ρ RW -Λ 8 π , p = p RW + Λ 8 π . We make the assumption that ρ RW + p RW = 0 so that we do have a non-trivial cosmic fluid (this allows us to define t unambiguously). Concerning the boundary Ω RW it is assumed to be connected (this is irrelevant because the matching conditions are local, the assumption is made merely for notational convenience), and nowhere tangential to a hypersurface of constant cosmic time t . This assumption is physically reasonable and automatically satisfied if the boundary is causal. In fact, dropping this assumption would only make the presentation more involved, but would not spoil any of the results (see [34] for a discussion). Finally, we assume that Ω RW is spatially compact. A sufficient condition for this is the 'energy condition' ρ RW ≥ 0, see [33], and this is in fact the assumption made in [33]. However, it can be proved that spatial compactness suffices for the validity of all the results below. Note finally, that spatial compactness is indeed an assumption: allowing for non-compact boundaries, additional configurations not covered by the uniqueness results do arise, as shown in [45] (see also references therein), where configurations with planar and hyperbolic symmetries were found and analized. It would be interesting to analyze how far can one extend uniqueness without any compactness assumption on the boundary. Nevertheless, for the purposes of the Einstein-Straus problem, compactness is a completely natural assumption, as we want the local physics unaffected by the cosmological expansion be spatially confined.\nBy a detailed analysis of the matching conditions, the following restrictions on the boundary Ω RW are obtained [34]. First of all, the intersection S RW t of Ω RW with a hypersurface of constant cosmic time t is a sphere. More precisely, for any t ∈ I , there exists a point c ( t ) ∈ M so that S RW t is a coordinate sphere of radius R ( t ) in a spherical coordinate system centered at c ( t ). The radius R ( t ) is restricted to satisfy the bound\nΣ ' 2 -Σ 2 ˙ a 2 | R = R ( t ) > 0 . (5)\nThis inequality means that the surface S RW t is non-trapped (i.e. has a mean curvature vector spacelike everywhere). The necessity of this condition can be understood from the fact that no closed spacelike surface in a static spacetime can have a future (or past) causal and not-identically zero mean curvature vector [42]. The spherical symmetry of\nthe surface S RW t and the fact that the matching conditions force the mean curvature vector to be continuous across the matching hypersurface implies that S RW t must be nontrapped, which is precisely (5). Note also that if the static Killing vector ξ admits Killing horizons and hence changes causal character, then the bound (5) is no longer necessary. This behaviour occurs in the Einstein-Straus model when a ( t ) is sufficiently small so that Σ c a ( t ) = 2 m . The breakdown of the ODE (3) in the Einstein-Straus model is just a manifestation of the breakdown of the the static coordinate system in the interior region. In Kruskal coordinates, the matching would continue across Σ c a ( t ) = 2 m without problem. Something similar would occur in the general setting if we allowed the static Killing to change causal character.\nReturning to the shape of Ω RW , the center point c ( t ) follows a geodesic in ( M , g M ) (which may degenerate to a point). The parameter t is not in general an affine parameter for the geodesic, so the center c ( t ) is a priori allowed to move at any speed (in fact the trajectory can have turning points along the curve). In order to describe the matching hypersurface, choose any point c 0 along this geodesic and let c ' 0 be its tangent vector. We can choose a spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 so that the axis of symmetry ˆ θ = 0 is along the tangent vector c ' 0 . In this coordinate system, the center c ( t ) will have coordinates\nc ( t ) = { ˆ R = σ ( t ) , | cos ˆ θ | = 1 }\n(the value of ˆ θ can be 0 or π depending on whether c ( t ) lies after or before c 0 along the geodesic). The function σ ( t ) describes the motion of c ( t ) along the curve. The relationship between the spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 and a spherical coordinate system { R,θ, φ } centered at c ( t ) with parallel axis (i.e. with coincident lines | cos θ | = 1 and | cos ˆ θ | = 1) is easily found to be\nΣ( ˆ R ) sin ˆ θ = Σ( R ) sin θ Σ( ˆ R ) cos ˆ θ = Σ ' ( σ ( t ))Σ( R ) cos θ +Σ( σ ( t ))Σ ' ( R ) ˆ φ = φ . (6)\nThus, the matching hypersurface Ω RW in the spherical coordinates centered at c 0 can be parametrized by coordinates t, θ, φ as\nΣ( ˆ R ( t, θ )) = √ sin 2 θ Σ 2 | R ( t ) + ( cos θ Σ ' | σ ( t ) Σ | R ( t ) +Σ | σ ( t ) Σ ' | R ( t ) ) 2 cotan( ˆ θ ( t, θ )) = cotan( θ ) Σ ' | σ ( t ) + Σ | σ ( t ) Σ ' | R ( t ) sin θ Σ | R ( t ) ˆ φ = φ ,\nwhich is a rather complicated form for the matching hypersurface. A useful alternative is to use a coordinate system { t, R, θ, φ } in ( W RW , g RW ) such that, for each t , { R,θ, φ } is the spherical coordinate system centered at c ( t ). Applying the coordinate transformation (6) to the metric\ng RW = -dt 2 + a 2 ( t ) ( d ˆ R 2 +Σ 2 ( ˆ R ) ( d ˆ θ 2 +sin 2 ˆ θd ˆ φ 2 ))\ngives\nds 2 = -dt 2 + a 2 ( t ) [ ( dR + f ( t ) cos θdt ) 2 +(Σ( R ) dθ -f ( t )Σ ' ( R ) sin θdt ) 2 + + Σ 2 ( R ) sin 2 θdφ 2 ] . (7)\nwhere f ( t ) = ˙ σ ( t ). The explicit calculation leading to (7) is somewhat long, a much more elegant method of obtaining this form of the metric is discussed in the Appendix of [34]. In these coordinates, the matching hypersurface Ω RW is simply { R = R ( t ) } .\nThe matching conditions in the FLRW part are supplemented with a differential equation relating the trajectory of the center σ ( t ) with the radius R ( t ). To write it down, define a function β ( t ) via\ntanh β ( t ) = glyph[epsilon1] 1 Σ˙ a Σ ' ∣ ∣ ∣ ∣ R = R ( t ) , (8)\nwhere glyph[epsilon1] 1 = ± 1 depending on whether the FLRW region to be matched is R > R ( t ) or R < R ( t ) (more specifically, the manifold with boundary W RW is { glyph[epsilon1] 1 R ≥ glyph[epsilon1] 1 R ( t ) } ). Note that β ( t ) is well-defined because of (5). The ODE relating R ( t ) and σ ( t ) is conveniently written using an auxiliary function ∆( t ) = 0 as the following pair of differential equations\nglyph[negationslash]\n˙ f = ( 2 glyph[epsilon1] 1 ˙ a ˙ R tanh β + ˙ ∆ ∆ -2 cosh β sinh β ˙ β ) f, f 2 Σ ' Σ ∣ ∣ ∣ ∣ R = R ( t ) -R + glyph[epsilon1] 1 ˙ a ˙ R 2 tanh β + ˙ ∆ ∆ ( ˙ R + glyph[epsilon1] 1 a tanh β ) -2 ( glyph[epsilon1] 1 a + ˙ R tanh β ) ˙ β = 0 . (9)\nIn summary, the static domain embedded in the FLRW regions consists of a sphere with time dependent radius R ( t ) and with center moving across the FLRW spacetime along a geodesic. Speed along the geodesic and radius R ( t ) are linked by (9). The model is not spherically symmetric because the center of the sphere is allowed to move. However, it is very close to spherically symmetric and it turns out that the center of the sphere must be at rest for several relevant matter models in the static domain, as we discuss next.\nAn important consequence of the matching procedure (cf. Lemma 1 in [34]) is that the Killing vector field ξ is everywhere transverse to the matching hypersurface Ω ST in the static region. Combining this with the fact that the static geometry is invariant along ξ it follows that the static metric in the spacetime region obtained by dragging Ω ST with the static Killing vector can be fully determined in terms of hypersurface geometry of Ω ST . Since, in turn, the geometry on Ω ST is related to the geometry of Ω RW via the matching conditions, it follows that the spacetime geometry of the static region becomes completely determined [34] in a neighbourhood of its matching hypersurface in terms of the FLRW geometry and the functions R ( t ) , σ ( t ) and ∆( t ) (see Theorem 1 in [34] for details). Specifically, there exist coordinates { T, t, θ, φ } so that the metric g ST takes the form (note that t is a spacelike coordinate in the static domain)\ng ST = -(cosh β + µ sinh β ) 2 ∆ 2 dT 2 +( µ cosh β +sinh β ) 2 dt 2 + + a 2 ( t )Σ 2 ( R ( t )) ( dθ -f ( t ) Σ ' Σ ∣ ∣ ∣ ∣ R = R ( t ) sin θdt ) 2 +sin 2 θdφ 2 , (10)\nwhere µ := glyph[epsilon1]a ( t )( ˙ R ( t ) + f ( t ) cos θ ). The matching hypersurface Ω ST is defined by the embedding { t, θ, φ } → { T = T ( t ) , t, θ, φ } , where T ( t ) satisfies ˙ T ( t ) = ∆( t ) and the portion of the static spacetime to be matched to the exterior region is { T ≥ T ( t ) } . The metric (10) is foliated by round spheres { T = const , t = const } but it is not spherically\nsymmetric in general (unless f ( t ) = 0 and R ( t ) = 0). To complete the picture, we review the energy-momentum tensor in the static part. Introduce two one-forms and one symmetric two-tensor h by\nθ 0 = (cosh β + µ sinh β ) ∆ dT, θ 1 = ( µ cosh β +sinh β ) dt, h = a 2 ( t )Σ 2 ( R ( t )) ( dθ -f ( t ) Σ ' Σ ∣ ∣ ∣ ∣ R = R ( t ) sin θdt ) 2 +sin 2 θdφ 2 ,\nThe Einstein tensor of ( W ST , g ST ) is (cf. Proposition 1 in [34])\n1 8 π G ST = ρ ST θ 0 ⊗ θ 0 + p ST r θ 1 ⊗ θ 1 + p ST t h\nwhere ρ ST , p ST r and p ST t read\nρ ST = ρ RW µ -p RW tanh β µ +tanh β , ρ ST + p ST r = ( ρ RW + p RW ) µ ( µ sinh β +cosh β ) (sinh β + µ cosh β ) , (11) p ST t = 3 p RW -ρ RW 6 + tanh β ( 2 f 2 sin 2 θ -Σ 2 ( R ( t )) ( ρ + p ) ( µ 2 -1) ) 16 π Σ 2 ( R ( t )) ( µ +tanh β ) (1 + µ tanh β ) + + [ -¨ β + ˙ ∆ ∆ ( ˙ a a 1 tanh β + ˙ β ) -2 ˙ β ˙ a a ( 1 + µ tanh β ) + µ ( a a + µ ˙ a 2 a 2 tanh β )] 8 π cosh 2 β ( µ +tanh β ) (1 + µ tanh β ) ,\nand ρ RW and p RW were defined in (4). Several consequences of (11) can be drawn [33, 34]. Concerning the uniqueness of the Einstein-Straus model, under the assumption ρ ST + p ST = 0 (which includes vacuum with or without cosmological constant or a non-singular electromagnetic field) it follows that µ = 0 and hence f ( t ) = 0 and R ( t ) = 0. The second equation in (9) gives (with an appropriate but still completely general choice of integration constant),\n˙ T ( t ) = ∆( t ) = 1 Σ ' c cosh 2 β ( t ) = Σ ' c Σ ' c 2 -Σ 2 c ˙ a 2 ,\nwhere (8) and the definitions of Σ c and Σ ' c in Section 2 have been used. The static metric simplifies to\ng ST = -( Σ ' c 2 -Σ 2 c ˙ a 2 ) dT 2 + Σ 2 c ˙ a 2 Σ ' c 2 -Σ 2 c ˙ a 2 dt 2 +Σ 2 c a 2 ( t ) d Ω 2 .\nFrom this metric, uniqueness of the Einstein-Straus model as the unique static vacuum (with or without cosmological constant) region embedded in a FRLW cosmological model follows easily. So, static vacuoles in a FLRW model must be spherically symmetric both in shape and interior geometry.\nIt is an open problem to analyze whether there are any physically realistic matter models in the interior static region for which the motion of the static domain inside FLRW has interesting properties. Note that a priori nothing prevents the geodesic c ( t ) from being spacelike, so the motion of the static domain can in principle be superluminal for the cosmic observers. This is of course reminiscent to the superluminal warp drive discovered by Alcubierre [1].\n3.2 Uniqueness results in the stationary and axisymmetric case\nThe study of axially symmetric equilibrium regions in FLRW universe was dealt with in [52], and, in short, the main result found was that those stationary regions must, in fact, be static, and therefore the results of the previous section apply.\nWith the same definitions and assumptions concerning the FLRW region ( W RW , g RW ) and its boundary Ω RW as in the previous section, we assume now that the interior region ( W SX , g SX ) is (strictly) stationary and axisymmetric. More specifically, we demand that (i) the spacetime admits a two-dimensional group of isometries G 2 acting simply-transitively on timelike surfaces T 2 and containing a (spacelike) cyclic subgroup, so that G 2 = R × S 1 , and (ii) that the set of fixed points of the cyclic group is not empty. Consequences of the definition are that the G 2 group has to be Abelian [17, 14, 3], and that the set of fixed points must form a timelike two-surface [40], which is the axis. The axial Killing η is then intrinsically defined by normalizing it demanding ∂ α η 2 ∂ α η 2 / 4 η 2 → 1 at the axis. See also [61] and [13]. In addition, we demand that the isometry group is orthogonally transitively (OT), i.e. that the two planes orthogonal to the orbits of the isometry group are surface forming. This assumption is also known as the 'circularity condition', and in many cases of interest it follows as a consequence of the Einstein field equations. Indeed, the G 2 on T 2 group must act orthogonally transitively in a region that intersects the axis of symmetry whenever the Ricci tensor has an invariant 2-plane spanned by the tangents to the orbits of the G 2 on T 2 group [16]. By the Einstein field equations, this includes Λ-term type matter (i.e. vacuum with or without cosmological constant), perfect fluids without convective motions, and also stationary and axisymmetric electrovacuum [61].\nAn OT stationary and axisymmetric spacetime ( V SX , g SX ) is locally characterized by the existence of a coordinate system { T, Φ , x M } ( M,N,... = 2 , 3) in which the line-element for the metric g SX outside the axis reads [61]\ng SX = -e 2 U ( dT + Ad Φ) 2 + e -2 U W 2 d Φ 2 + g MN dx M dx N , (12)\nwhere U , A , W and g MN are functions of x M , the axial Killing vector field is given by η = ∂ Φ , and a timelike (future-pointing) Killing vector field is given by ξ = ∂ T . Although useful for the sake of clarity, the use of coordinates is not essential for the results below, which only depend on the intrinsic geometric properties of of ( W SX , g SX ).\nAs before, no specific matter content is assumed in the stationary and axisymmetric region. Regarding the matching hypersurface Ω, besides those in the previous Section 3.1, we make the only extra assumption that it preserves the axial symmetry [62] of ( W SX , g SX ) and of ( W RW , g RW ). This means that Ω SX is assumed to be invariant under the axial symmetry of ( W SX , g SX ) and that there is an axial Killing vector η RW in the Killing algebra of ( W RW , g RW ) tangent to Ω RW .\nWith these assumptions at hand, in [52], it is proven, first, that the stationary (timelike) Killing vector field ξ is nowhere tangent to Ω SX . As explained in the previous section, this serves in particular to construct a neighbourhood of Ω SX by dragging it along the orbits of ξ , in which the geometry is thus fully determined by the information in Ω SX . The main result in [52] is that if a OT stationary and axisymmetric region ( W SX , g SX ) can be matched to a FLRW region through a hypersurface Ω SX preserving the axial symmetry, then the region ( W SX , g SX ) must be, in fact, static on a neighbourhood of Ω SX .\nAll in all, in that neighbourhood of the matching hypersurface the OT stationary axisymmetric region ( W SX , g SX ) thus becomes a static axisymmetric region ( W ST , g ST ), and therefore the results of the previous Section 3.1 (cf. [34]) apply.\nSo far, no explicit condition on the matter content of the stationary region has been used. When conditions on the matter content on the (OT) stationary and axisymmetric (and hence static) region are imposed, the functions that determine the matching hypersurface and the static geometry are determined by the results reviewed in Section 3.1.\nIn particular, and for completeness, let us consider a vacuum (with or without a cosmological constant) stationary and axisymmetric region ( W SX , g SX ) matched to FLRW preserving the axial symmetry. As mentioned above, a vacuum matter content forces the axial symmetry and stationary group G 2 on T 2 to act orthogonal transitively. On the other hand, a region of FLRW ( W RW , g RW ) matched to a vacuum region must satisfy the assumptions made and, in particular, have a causal Ω RW (in fact tangent to the fluid flow). The above result implies then that the vacuum region must be static. The results of Section 3.1 thus apply, and imply, in turn, that the whole region (not just its boundary) has to be spherically symmetric, and hence Schwarzschild.\nTo sum up, this means that the only stationary and axially symmetric vacuum region that can be matched to FLRW is a spherically symmetric piece of Schwarzschild. This constitutes still another uniqueness result of the Einstein-Straus model when the vacuum region lies inside FLRW.\nThe complementary result, when the vacuum region lies outside FLRW, constitutes a uniqueness result of the Oppenheimer-Snyder model [53]. It is worth noticing that this result can also be interpreted as a no-go result for the possible interiors of Kerr. Indeed, this result states that an axially symmetric region of (an evolving) FLRW, irrespective of its relative rotation with the exterior, cannot be the source of a stationary and axisymmetric vacuum region, in particular, Kerr.\n4 Robustness of Einstein-Straus: Generalized exact cosmologies\nIn the previous sections, the robustness of the Einstein-Straus model has been discussed by considering generalizations of the interior vacuole and keeping the FLRW model as the exterior cosmological model. The question arises as to what happens if these symmetry assumptions concerning the exterior metric are relaxed. There are two different ways to study departures from the spherical FLRW: either perturbatively or using exact solutions. In this section, we concentrate on the later possibility and, in particular, we review the results found in [46] for spatially homogeneous (but anisotropic) cosmologies.\nA step in the direction of generalising the exterior was taken by Bonnor, who considered the embedding of a Schwarzschild region in an expanding spherically symmetric inhomogeneous Lemaˆıtre-Tolman-Bondi (LTB) exterior. He found that such a matching is possible in general, and that it allows the average density of the Schwarzschild interior to be chosen independently of the exterior LTB density [12]. So, clearly, if the spherical symmetry is kept, the exterior can be readily generalized to the case of inhomogeneous dust cosmologies. An interesting review about physical aspects of spherically symmetric Einstein-Straus and McVittie type models can be found in [15].\nWhile keeping the spherical symmetry of the cavity allows for straightforward generalizations of Einstein-Straus, breaking this symmetry brings in unexpected complications, as we have seen in the previous section. The same seems to hold if we consider exact\ngeneralizations of the FLRW cylindrical symmetry exterior to spatially homogeneous but anisotropic spacetimes. This problem was considered in [46] and we summarize it next:\nConsider the problem of matching, across a hypersurface Ω which is spatially a topological sphere 1 , of an interior locally cylindrically symmetric (LCS) static spacetime ( W ST , g ST ), which represents a spatially compact region, to a spatially homogeneous anisotropic exterior ( W HOM , g HOM ) having a Lie group G 3 acting on S 3 surfaces. Once more, we make no assumptions a priori on the matter contents, so the main results are purely geometric. Only at the end of the section, assumptions on the matter content will lead to a final no-go result.\nWe wish to preserve globally the axial symmetry and thus we need to impose first the existence of a group of cyclic symmetries in the exterior region. This, combined with the assumption of a spacelike spherical topological shaped 2 Ω ST , implies the existence of an exterior axis. Thus, the cyclic symmetry in the exterior must really be an axial symmetry (see the discussion in Section 3.2). Moreover, we require that the cylindrical symmetry is preserved (in the sense of [62]) at least on a non-empty open subset of Ω. This has the consequence that ( W HOM , g HOM ) must admit a G 4 on S 3 group of isometries, so that it is locally rotationally symmetric (LRS). In [46], it is shown how all the LRS spatially homogeneous metrics can be written in the form adapted to the two commuting Killing vectors defining the cylindrical symmetry ∂ ϕ and ∂ z , where ∂ ϕ is axial with axis at r = 0:\ng HOM = -dt 2 + b 2 ( t ) dr 2 -2 glyph[epsilon1]r b 2 ( t ) drdz + ˆ C 2 dϕ 2 +2 ˆ Edzdϕ + ˆ D 2 dz 2 (13)\nwith\nˆ C 2 = b 2 ( t )Σ 2 ( r, k ) + na 2 ( t )( F ( r, k ) + k ) 2 , ˆ D 2 = a 2 ( t ) + glyph[epsilon1]r 2 b 2 ( t ) , ˆ E = na 2 ( t )( F ( r, k ) + k ) , (14)\nwhere the functions Σ and F are given by\nΣ( r, k ) = sin r, k = +1 r, k = 0 sinh r, k = -1 and F ( r, k ) = -cos r, k = +1 r 2 / 2 , k = 0 cosh r, k = -1 ,\nand where glyph[epsilon1] and n are given such that glyph[epsilon1] = 0 , 1; n = 0 , 1; glyph[epsilon1]n = glyph[epsilon1]k = 0 3 . The metrics are classified according to these constants in Table 1.\nThe matching conditions are then investigated and a crucial step was to observe that they lead to the following necessary relations involving only exterior metric functions:\nˆ D ,t ˆ C ,r -ˆ D ,r ˆ C ,t Ω = 0 , ˆ E ,t ˆ D ,r -ˆ E ,r ˆ D ,t Ω = 0 , ˆ E ,t ˆ C ,r -ˆ E ,r ˆ C ,t Ω = 0 , (15)\n2 This implies the existence of north and south poles on Ω ST where the axial killing vector in the interior vanishes and, therefore, also the generator of the cyclic symmetry in the exterior region on Ω HOM by construction.\n3 Let us note that the case glyph[epsilon1] = n = 0 with k = 1 is special, since it corresponds to the Kantowski-Sachs (KS) class of metrics, which do not admit a G 3 on S 3 subgroup [61]. It was included in the study for completeness.\n
\n\n
Table 1: Classification of possible G 3 on S 3 subgroup types according to the values of { glyph[epsilon1], k, n } for the metric given by (13).
\n
\nwhich, for non-static exteriors, imply n = 0 and thus exclude Bianchi types II, III, VIII and IX.\nBy inserting (15) back in the matching conditions one is able to prove a series of results that lead to the following conclusion: The only expanding spatially homogeneous spacetimes which can be matched to a locally cylindrically symmetric static interior region preserving the (cylindrical) symmetry, across a non-spacelike hypersurface which is spatially a topological sphere, are given by\nds 2 = -dt 2 + β 2 dz 2 + b 2 ( t ) [ ( dr -glyph[epsilon1]r dz ) 2 +Σ 2 ( r, k ) dϕ 2 ] , (16)\nwhere β is constant. This metric for k = 1 belongs to the Kantowski-Sachs class, when k = -1 admits a G 3 on S 3 of Bianchi type III, and when k = 0 of Bianchi types I,V,VII 0 ,VII h .\nThe metrics (16) are very special, partly due to the fact that condition a ,t = 0 (see (13)-(14)) imposes a strong constraint, implying that there cannot be any time (nor space) evolution along the direction orthogonal to the orbits of the subgroup G 3 on S 2 of the LRS. There are also constraints imposed through the matching in the interior region and the interested reader can find those in [46]. Note that the no-go result found in [59] is trivially recovered, since FLRW is included in the LRS class for b ( t ) = a ( t ), and the above would imply a static FLRW metric.\nIf one specifies a particular class of matter fields, then one gets further constraints on the cosmological dynamics. For example, if the matter in the static region is not specified but the dynamical (cosmological) region is assumed to contain a perfect fluid with pressure p and energy-density ρ satisfying the dominant energy condition everywhere, then glyph[epsilon1] = 0 necessarily, which corresponds to a stiff fluid equation of state ρ = p = α 2 / (4 t 2 ( α -kt ) 2 ), with b ( t ) = √ αt -kt 2 , where α > 0. On the other hand, if the interior is vacuum then the exterior must be also vacuum.\nThe overall no-go results, in this case, can be seen in two ways: either as a consequence of the assumption that the interior metric is static and cylindrically symmetric, which seems to prohibit time dependence along one direction, or as a consequence of the particular exterior metrics we are considering, which are homogeneous then prohibiting the coefficients along this direction to be space dependent. The perturbative approach described in the next sections can help to clarify this question.\nTo conclude this section we remark that there exists an example of a Einstein-Straus model with exact non-spherical inhomogeneous cosmologies. This is provided by the Szekeres dust solution which has no Killing vectors, in general, but contains intrinsic symmetries on 2-spaces of constant curvature: The Szekeres solution is divided into class\nI, which generalizes the LTB solution having non-concentric spheres of constant mass, and class II which includes the Kantowski-Sachs solution. Class I solutions have been proved to be interiors to the Schwarzschild solution [9] and this result has been generalized to include the cosmological constant [31, 45]. As mentioned before, one can invert the roles of the two spacetimes involved and hence construct an Einstein-Straus type model with a Schwarzschild or Kottler cavity within a class I Szekeres' cosmology. Let us remark that the Szekeres class has been used recently in Swiss cheese models as interiors to FLRW (see [7] and references therein).\nClass II Szekeres dust metrics are less known, but contain curious inhomogeneous solutions with cylindrical symmetry [60]. In this case, it seems harder to be able to get a physically reasonable Einstein-Straus model considering what we have described above.\n5 Brief overview of perturbative matching theory\nA perturbed spacetime consists of a symmetric two-covariant tensor (the 'perturbation metric') defined on a fixed spacetime (the 'background'). From a structural point of view, spacetime perturbation theory is a gauge theory in the sense that many perturbation metrics describe the same physical situation (i.e. they are gauge related). The underlying geometrical reason for this gauge freedom can be understood from the following intuitive picture of perturbation theory. We imagine a one-parameter family of spacetimes ( V ε , g ε ) such that all the manifolds are diffeomorphic to each other. This allows one to pull back g ε onto a single manifold in the family (say V 0 := V ε =0 ) and work with a one-parameter family of metrics on a single manifold. If all the construction is smooth in ε , derivatives with respect to this parameter can be taken. The perturbation metric g (1) is simply the derivative at ε = 0 of this family of metrics. However, the identification of points in the different manifolds (the diffeomorphism above) is highly non-unique. Any other choice of identification would lead to a different, but geometrically equivalent, perturbation metric. This is the gauge freedom of the theory. Intuitively, it is clear that the gauge freedom will consist of a vector field on the background, because this measures the shift of the new identification with respect to the previous one, and an initial direction (in ε ) is all what is required to compute derivatives with respect to ε at ε = 0.\nWhen two spacetimes with boundary are matched, an identification of the boundaries is required. As already mentioned before, if the boundaries are nowhere null, the matching conditions require the equality of the induced metric and second fundamental form (with appropriate choices of orientation). To compare the tensors it is necessary to pull them back to a single manifold and this is done via the identification of boundaries. Contrarily than before, the matching theory is strongly dependent on the identification of the boundaries. In fact, the matching conditions demand the existence of one such identification for which the first and second fundamental forms agree.\nAssume now that we are studying perturbation theory on a background spacetime constructed from the matching of two spacetimes. The question then arises of what are the conditions that the metric perturbation tensors on each side must satisfy to have a perturbed matching spacetime. This issue is somewhat more involved than one may think a priori and it was solved in a complete manner for the first time by Battye and Carter [4] and independently by Mukohyama [47] (this has been extended to second order in [35]). Previous attempts [24, 23, 43] did not take into account all the subtleties of\nthe interplay between two completely different gauge freedoms inherent to this problem. Indeed, in the picture above of perturbation theory in terms of a collection of spacetimes ( V ε , g ε ), each one of them arises now as the matching of two spacetimes with boundary W ± ε across their respective boundaries Ω ± ε . For better visualization, assume that each one of W ± ε is a submanifold with boundary of a larger boundary-less manifold ̂ W ± ε and assume that the { ̂ W + ε } manifolds are identified among themselves (say with ̂ W + 0 := ̂ W + ε =0 ) via an ε -dependent diffeomorphism. The hypersurface Ω + ε projects down to ̂ W + 0 as a hypersurface ̂ Ω + ε . Now we have a collection of hypersurfaces in one single manifold, and one can think of taking ε -derivatives of geometric quantities intrinsic to the hypersurface. The important point is that, given a point p ∈ Ω + ε =0 , we do not know how this point maps into ̂ Ω + ε . For that, it is necessary to prescribe first how p is mapped into Ω + ε . The identification of { Ω + ε } among themselves is an additional gauge freedom. It is fully independent of the standard gauge freedom in perturbation theory (called 'spacetime gauge freedom' from now on) and is referred to as hypersurface gauge freedom [47]. The composition of both identifications gives, as ε varies, and for any p ∈ Ω + ε =0 , a path γ p ( ε ) in ̂ W + 0 starting at p . Since everything is smooth in ε , the tangent vector to this path at ε = 0 defines a vector field Z + on Ω + 0 := Ω + ε =0 (= ̂ Ω ε =0 ). This vector field is not necessarily tangent (nor normal) to Ω + 0 and it depends on both gauge freedoms. A schematic figure for the definition of Z + and how it depends on the gauges is given in Figure 5. If we let n (0) + be a unit normal vector to Ω + 0 , we can decompose Z + = Q + n (0) + + T + , where T + is tangent to Ω + 0 . From the discussion above, it should be clear that Q + is independent of the hypersurface gauge while T + strongly depends on it. In fact, it can always be made zero by an appropriate choice of gauge. However, doing this is not usually a good idea because the matching has two regions and, at each value of ε , the matching requires an identification between Ω + ε and Ω -ε . After a choice of hypersurface gauge to identify Ω + ε with Ω + 0 we have no freedom left to choose a hypersurface gauge to identity Ω -ε and Ω -0 . The matching conditions will tell us how this identification must be done. So, had we chosen T + = 0, we would still have to leave T -free and let the linearized matching theory determine its value. Further details on the double gauge freedom of linearized perturbation theory can be found in the paper of Mukohyama [47] and in [37], where the issue is discussed in depth including a critical analysis of previous attempts to formulate a consistent perturbative matching theory.\nAfter this brief discussion on gauge issues for linearized matching theory, let us describe the actual perturbative matching conditions (for details see [4, 47, 35]). The matching theory involves the equality of the first and second fundamental forms of the boundaries. To compare them they are pulled-back into a single boundary via the identification. In perturbative matching theory everything occurs on the abstract hypersurface Ω 0 diffeomorphic to Ω + 0 and Ω -0 of the background spacetime. On Ω ± 0 we attach two vector fields Z ± = Q ± n (0) ± + T ± whose geometric meaning has been discussed above. They are not know a priori, firstly, because of the hypersurface gauge freedom, and secondly, because the identification of the boundaries Ω + ε and Ω -ε is not known a priori. To the unknowns Z ± we add four symmetric tensors q (1) ± and K (1) ± intrinsic to Ω 0 which arise as the ε -derivative at ε = 0 of the first fundamental form q ± ε and second fundamental form K ± ε of Ω ± ε . These tensors are intrinsic to Ω ± ε , so before taking ε -derivatives they must be pulled back onto Ω 0 via the hypersurface gauges (on each side). Thus, q (1) ± and K (1) ± are hypersurface gaugedependent by construction. On the other hand, their construction is fully independent of\n\n\n
Figure 1: The different spacetimes ̂ W ε are represented by horizontal sheets, with ̂ W 0 at the bottom. On each ̂ W ε there is a hypersurface Ω ε . The hypersurfaces Ω ε for all ε span a manifold transverse to V ε (the blue sheet in the figure). The choice of spacetime gauge is represented by big dots on each ̂ W ε linked by green curves, while the choice of hypersurface gauge is represented by the grey curves on the blue sheet. The point p is mapped first to q ε through the hypersurface gauge and back to p ε ∈ ̂ W 0 through the spacetime gauge. The points p ε define on ̂ W 0 the path γ p ( ε ). The vector Z is the tangent of γ p ( ε ) at p .
\n\nthe spacetime gauge freedom.\nIn order to write down their explicit expression, let g (1) ± be the perturbed metric (i.e. the fundamental unknown in metric perturbation theory) on each side of the background spacetime. Let also Ψ ± 0 : Ω 0 → W ± 0 be the embedding of the matching hypersurface on each region of the background spacetime. Let y i ( i, j, . . . = 1 , . . . , n -1) be a local coordinate system on Ω 0 and define tangent vectors e ± i = Ψ ± 0 glyph[star] ( ∂ y i ). There are also unique (up to orientation) unit one-forms n (0) ± normal to the boundaries. We choose them so that the corresponding vector n (0) + points towards W + 0 and n (0) -points outside of W -0 or viceversa. The first and second fundamental forms of the background are simply q (0) ± := Ψ ± 0 glyph[star] ( g (0) ± ) , K (0) ± := Ψ ± 0 glyph[star] ( ∇ ± n (0) ± ), where ∇ ± is the covariant derivative in ( W ± 0 , g (0) ± ). Given that the background configuration is already composed of the matching of V + 0 and V -0 through Ω + 0 := Ω 0 , we already have q (0)+ = q (0) -and K (0)+ = K (0) -. Then q (1) ± and K (1) ± are defined as follows [47]\nq (1) ij ± = L T ± q (0) ij ± +2 Q ± K (0) ij ± + e ± α i e ± β j g (1) αβ ± , (17) K (1) ij ± = L T ± K (0) ij ± -σD i D j Q ± + Q ± ( -n (0) ± µ n (0) ± ν R (0) ± αµβν e ± α i e ± β j + K (0) il ± K (0) l j ± ) + σ g (1) αβ ± n (0) ± α n (0) ± β K (0) ij ± -n (0) ± µ S (1) ± µ αβ e ± α i e ± β j , (18)\n2\nwhere σ := g (0) ± ( n (0) ± , n (0) ± ), D is the covariant derivative of (Ω 0 , q (0) ± ), R (0) ± αµβν is the Riemann tensor of ( W ± 0 , g (0) ± ) and S (1) ± α βγ := 1 2 ( ∇ ± β g (1) ± α γ + ∇ ± γ g (1) ± α β -∇ ± α g (1) ± βγ ). The first order matching conditions (in the absence of shells) require the equalities\nq (1)+ = q (1) -, K (1)+ = K (1) -. (19)\nWe emphasize that Q ± and T ± are a priori unknown quantities and fulfilling the matching conditions requires showing that two vectors Z ± exist such that (19) are satisfied. The spacetime gauge freedom can be exploited to fix either or both vectors Z ± a priori, but this should be avoided (or at least carefully analyzed) if additional spacetime gauge choices are made, in order not to restrict a priori the possible matchings. Regarding the hypersurface gauge, this can be used to fix one of the vectors T + or T -, but not both. Note also that the linearized matching conditions are, by construction, spacetime gauge invariant because, as discussed above, the tensors q (1) ± , K (1) ± are necessarily spacetime gauge invariant. In fact, it is straightforward to check explicitly that the right-hands sides of (17) and (18) are spacetime gauge invariant (the individual terms are not, and it is precisely the spacetime gauge dependence in Z ± which makes these objects spacetime gauge invariant). Moreover, the set of conditions (19) are hypersurface gauge invariant, provided the background is properly matched, since, as shown in [47], under such a hypersurface gauge transformation given by the vector ζ in Ω 0 , q (1) transforms as q (1) + L ζ q (0) , and similarly for K (1) .\n6 Spherical symmetry: Hodge decomposition\nAfter the previous summary on linearized matching, in this section we introduce the second main ingredient for the linearized Einstein-Straus model reviewed in the following sections: the Hodge decomposition on the sphere [38].\nIn order to exploit the underlying spherical symmetry of the background configuration it is common practice to decompose the perturbations, and their related objects and equations, in terms of scalar, vector and tensor harmonics on the sphere. That was the procedure used in the seminal work on perturbations around spherical matched background configurations, due to Gerlach and Sengupta (GS) in [23] and [24], revisited and improved by Mart'ın-Garc'ıa and Gundlach in [43].\nThe aim in [38] was to use an alternative method, based on the Hodge decomposition on the sphere in terms of scalars, in order to avoid the need to deal with infinite series of objects. In particular, the whole set of matching conditions for the linearized EinsteinStraus model was presented in [38] as a finite number of equations involving scalars that depend on the three coordinates in the matching hypersurface Ω 0 , in contrast with an infinite number of equations for an infinite set of functions of one variable. It is clear that one can always go from the Hodge scalars to the spherical harmonics decomposition in a straightforward way. However, it is not always easy to rewrite the infinite number of expressions appearing in a spectral decomposition in terms of Hodge scalars.\nConsider the round unit metric Ω AB dx A dx B = dϑ 2 +sin 2 ϑdϕ 2 , with η AB and D A denoting the corresponding volume form and covariant derivative respectively, and ( glyph[star]dG ) A = η C A D C G the Hodge dual with respect to Ω AB . Let us recall that the usual Hodge decomposition on ( S 2 , Ω AB ) states that any one-form V A can be canonically decomposed as V A = D A F +( glyph[star]dG ) A , where F and G are functions on S 2 , and any symmetric tensor T AB\nas T AB = D A U B + D B U A + H Ω AB , for some U A on S 2 , which can be in turn decomposed in terms of scalars.\nBased on this, it is convenient to define the following two functionals. Given three scalars X tr , X 1 and X 2 on ( S 2 , Ω AB ) we define the functional one form V A ( X 1 , X 2 ) as\nV A ( X 1 , X 2 ) = D A X 1 +( glyph[star]d X 2 ) A ,\nand the functional symmetric tensor T AB ( X tr , X 1 , X 2 ) as\nT AB ( X tr , X 1 , X 2 ) = D A V B ( X 1 , X 2 ) + D B V A ( X 1 , X 2 ) + X tr Ω AB .\nLet us recall that the decomposition defines these X 's on S 2 up to the kernels of the operators V A and T AB . We allowed for the appearance of all these kernels in [38], where their relevance (or their lack of) was already discussed. In order to avoid spurious information and present a more concise review -and also to ease the translation and comparison with the quantities used in the previous literature in terms of the harmonic decompositions,we use the reformulation already presented in [39] where the Hodge decomposition is, in fact, unique.\nIndeed, in order to fix the Hodge decomposition uniquely we define a canonical dual decomposition by demanding that the functions X 1 , X 2 in V A ( X 1 , X 2 ) are always orthogonal (in the L 2 sense on S 2 ) to 1, and the functions X 1 , X 2 in T AB ( X tr , X 1 , X 2 ) are orthogonal to 1 and to the l = 1 spherical harmonics. Schematically, we may use\nW A S 2 →X 1 , X 2 to indicate W A = V A ( X 1 , X 2 )\nand\nW AB S 2 →X tr , X 1 , X 2 when W AB = T AB ( X tr , X 1 , X 2 ) .\nWe will use the following notation: given any function f on S 2 we define\nf || 0 := Y 0 ∫ S 2 f Y 0 d Ω 2 , f || 1 := Y 1 ∫ S 2 f Y 1 d Ω 2 ( = ∑ m Y m 1 ∫ S 2 f Y m 1 d Ω 2 ) ,\nso that f -f || 0 is orthogonal to the l = 0 harmonics Y 0 and f -f || 1 is orthogonal to the l = 1 harmonics Y m 1 .\nNote finally that the Hodge decomposition in terms of scalars involves two types of objects depending on their behaviour under reflection on the sphere. The scalars with subscripts 1 and tr remain unchanged under reflection, and are typically called longitudinal, even or polar quantities, while those with subscripts 2 change, and correspond to the transversal, odd or axial quantities.\nLet us consider now the general spherically symmetric spacetime V = M 2 × S 2 with metric g αβ = ω IJ ⊕ r 2 Ω AB , so that ( M 2 , ω IJ ) is a 2-dim Lorentzian space and r > 0 a function on M 2 . The dual in ( M 2 , ω IJ ) will be indicated by ∗ and the covariant derivative by ∇ .\nWe can now proceed to decompose any one-form (vector) or symmetric two-tensor on V by first taking the part orthogonal to the sphere and then apply the Hodge canonical decomposition to the part tangent to the sphere. In particular, given a normalized timelike one-form u α orthogonal to the spheres, its corresponding one-form u I on ( M 2 , ω IJ ) (defined by u α = ( u I , 0)) can be used to construct a convenient orthonormal basis { u I , m I }\nso that ω IJ = -u I u J + m I m J (this is u I u I = -1 and m I := ∗ u I ), and consider then the one-form on V defined by m α := ( m I , 0). Given any vector V I we will simply denote by V u and V m the contractions u I V I and m I V I respectively.\nWe apply now this decomposition to encode the objects that will describe the (first order) perturbation of a background consisting of two spherically symmetric regions ( W + , g (0)+ ) and ( W -, g (0) -) matched across corresponding spherically symmetric boundaries Ω + 0 and Ω -0 . At each side ± (we avoid the use of ± just now for clarity) the metric perturbation tensor g (1) αβ gets thus decomposed as\ng (1) IJ = Z IJ , g (1) IA S 2 →Z I 1 , Z I 2 , g (1) AB S 2 →Z S 2 tr , Z S 2 1 , Z S 2 2 , (20)\nwhere Z I 1 and Z I 2 are two one-forms defined on M 2 , and analogously for any symmetric tensor. The deformation vector Z α , defined on M at points on Ω, is decomposed as\nZ α → { Z I → Q,T } ⊕ { Z A S 2 →T 1 , T 2 } ,\nwhereby the part Z I gets decomposed, in turn, onto the normal and tangential parts to Ω 0 , Q and T respectively. Given the (first order) perturbation tensor and the deformation vector at either ± side of the matching hypersurface, one can calculate the symmetric tensors q (1) ij and K (1) ij , i.e. the 'perturbed first and second fundamental forms', using (17)-(18). Recalling now that q (1) ij and K (1) ij are defined on (Ω 0 , q (0) ij ) and that Ω 0 at either side are tangent to the spheres { θ, φ } , let us denote by λ the parameter that follows the direction on Ω 0 orthogonal to the spheres in order to decompose q (1) ij and K (1) ij into q (1) λλ , K (1) λλ , plus\nq (1) λA S 2 → F q , G q , q (1) AB S 2 → H q , P q , R q , (21)\nand\nK (1) λA S 2 → F k , G k , K (1) AB S 2 → H k , P k , R k . (22)\nNote that all these functions are scalars on the sphere that depend only on λ . The first order matching conditions (19) are therefore equivalent to\nq (1) λλ + = q (1) λλ -, F q + = F q -, G q + = G q -, H q + = H q -, P q + = P q -, R q + = R q -, K (1) λλ + = K (1) λλ -, F k + = F k -, G k + = G k -, H k + = H k -, P k + = P k -, R k + = R k -. (23)\nExcept for the simplification of the kernels by the canonical decomposition, these are the linearized matching conditions presented in [38].\n6.1 Gerlach and Sengupta (GS) 2+2 formalism\nLet us emphasize again that the conditions (19), and thus (23), concern quantities defined on Ω 0 and are therefore independent on the coordinates used in W + and W -for their computation. These quantities are thus, on the one hand, spacetime gauge independent by construction. Moreover, as discussed in Section 5, the equations are also hypersurface gauge independent. All this makes it unnecessary the use of gauge invariant quantities\nin order to establish the perturbed matching conditions. Having said that, however, the use of gauge independent quantities turns out to be convenient in the end, mostly when one eventually wants to impose the Einstein field equations. As shown in the works [23], [24], [43], the use of spacetime gauge invariants is very convenient in order to combine the Einstein field equations with the perturbed matching conditions.\nOne can proceed by constructing gauge invariants in terms of Hodge scalars using analogous expressions to those in the harmonic decomposition constructed in [24, 23, 43].\nLet us now concentrate on the odd (axial) sector. The odd gauge invariant quantities are encoded in the vector [36] (cf. [24])\nK I := Z I 2 -∇ I Z S 2 2 +2 Z S 2 2 r -1 ∇ I r.\nNote that K I , as defined above, contains l = 1 harmonics, from Z I 2 , but only the l ≥ 2 sector is gauge invariant. In other words, the part of K I orthogonal to Y 1 (i.e. K I -K I || 1 in the notation above) is the gauge invariant part. Once the orthonormal basis { u I , m I } has been identified at both sides, the odd sector of the linearized matching, which corresponds to the set of equations\nG q + = G q -, R q + = R q -, G k + = G k -, R k + = R k -, (24)\nin (23), is equivalent in the l ≥ 2 sector (the part orthogonal to l = 0 and l = 1) to [36] (cf. [24])\nK + u Ω 0 = K -u , K + m Ω 0 = K -m , ∗ d ( r -2 K + ) Ω 0 = ∗ d ( r -2 K -) (25)\nplus an equation for T + 2 -T -2 .\n7 Linearized Einstein-Straus model: matching conditions\nWe are ready to consider the linearized matching of the perturbed Schwarzschild and FLRW spacetimes, as it was analyzed in [38]. Take the Einstein-Straus model as described in Section 2: the FLRW geometry in cosmic time coordinates (1), the Schwarzschild in standard coordinates (2), and the background matching hypersurface Ω 0 described by Ω RW 0 : { t = t, R = R 0 } and Ω ST 0 : { T = T 0 ( t ) , r = r 0 ( t ) } respectively, where T 0 ( t ) and r 0 ( t ) satisfy (3) and the angular part is again ignored.\nThe orthonormal basis we take on the Lorentzian space orthogonal to the spheres is formed by u = dt , m = adR . Note that this choice corresponds to the tangent and normal forms to Ω 0 at Ω 0 , respectively. More precisely, m is chosen to be n (0) at points on Ω 0 . On the Schwarzschild side we have u | Ω 0 = ˙ T 0 ∂ T + ˙ r 0 ∂ r and m | Ω 0 := n (0) = -˙ r 0 dT + ˙ T 0 dr .\nTake the first order perturbations of FLRW, in no specific gauge, formally decomposed into the usual scalar, vector and tensor (SVT) modes, i.e. 4 (Latin indices a, b, c are used for tensors on ( M , g M ))\ng (1) tt + = -2Ψ g (1) ta + = aW a g (1) ab + = a 2 ( -2Φ γ ab + χ ab )\nwith\nW a = ∂ a W + ˜ W a , χ ab = ( ∇ a ∇ b -1 3 γ ab ∇ 2 ) χ +2 ∇ ( a Y b ) +Π ab\nsatisfying the constraints\n∇ a Y a = Π a a = 0 , ∇ a Π ab = 0 , ∇ a ˜ W a = 0 .\nThe canonical Hodge decomposition is then used to encode the part tangent to the spheres into S 2 scalars in the following schematic way [38]: vector\n˜ W a → ˜ W R ⊕{ ˜ W A S 2 →W 1 , W 2 } , Y a → Y R ⊕{ Y A S 2 →Y 1 , Y 2 } ,\nΠ RA S 2 →Q 1 , Q 2 , Π AB S 2 →H , U 1 , U 2 .\nAll in all, encoding g (1)+ using the SVT modes together with the Hodge decomposition leaves us with 15 SVT-Hodge quantities, corresponding to the scalar modes { Ψ , Φ , W, χ } , vector modes { ˜ W R , W 1 , W 2 , Y R , Y 1 , Y 2 } and tensor modes {Q 1 , Q 2 , H , U 1 , U 2 } , all scalars on S 2 , not all independent due to the previous constraints, and, on the other hand, not unique . Consider, in particular, the only 4 scalars we have in the odd sector; vector modes {W 2 , Y 2 } and tensor modes {Q 2 , U 2 } . As discussed in the previous section, only two gauge invariant quantities exist in the odd sector. These correspond to the two components of the gauge invariant odd vector (and for l ≥ 2), K + I , which given the above construction in terms of the SVT-Hodge quantities, read [39, 36]\nK + u = a ( W 2 -a ( ˙ U 2 + ˙ Y 2 ) ) , K + m = a ( Q 2 -U 2 ' +2 U 2 Σ ' Σ -1 ) .\nConsider now the stationary and axially symmetric vacuum perturbations in the Weyl gauge. They can be described in terms of two functions U (1) ( r, θ ) and A (1) ( r, θ ), which correspond, basically, to the perturbation of the gravitational Newtonian potential and the rotational perturbation, respectively. The perturbation tensor reads [38]\ng (1) Sch = -2 ( 1 -2 m r ) ( U (1) dt 2 + A (1) dtdφ ) -2 r 2 sin 2 θU (1) dφ 2 +2 ( k (1) -U (1) ) [ ( 1 -2 m r ) -1 dr 2 + r 2 dθ 2 ] . (26)\nNote that, when using the full set of the Einstein field equations for vacuum, the function k (1) is determined up to quadratures once U (1) ( r, θ ) and A (1) ( r, θ ) are found. We stress, however, that the vacuum equations, although indicated, were not imposed in the perturbed Schwarzschild region (nor in the perturbed FLRW region) in [38], and therefore the results found there are purely geometric.\nInstead of working with A (1) ( r, θ ), it is convenient to use an auxiliary function, G , defined by A (1) := sin θ∂ θ G . In terms of the Hodge decomposition of the perturbation tensor (20), applied to (26), we have G = -( 1 -2 M r ) -1 Z -T 2 . Another auxiliary function P can be introduced for k (1) .\nThe whole set of matching conditions (23) for the linearized Einstein-Straus model, both in the odd and even sectors, were found in [38] in terms of these functions U (1) ( r, θ ) , G\ntensor\nand P in the Schwarzschild side together with the above 15 SVT-Hodge scalars describing the FLRW perturbation. The whole set is too long to be included here, but in order to review the main results in [38] only the odd sector of the linearized matching is needed.\nThe odd sector of the linearized matching (24) projected to the part orthogonal to the l = 0 and l = 1 harmonics can be rewritten as the following three relations [38]\nW 2 -a [ ˙ U 2 + ˙ Y 2 ] Ω 0 = -G Σ ' c a -1 , (27)\nQ 2 -U 2 ' +2Σ -1 c Σ ' c U 2 Ω 0 = -G a -1 ˙ a Σ c , (28)\nW 2 ' -a d dt [( U 2 ' + Y 2 ' ) | Ω 0 ] Ω 0 = G Σ 3 c aglyph[epsilon1] -3 M Σ 2 c a 2 + ∂ G ∂r (Σ 2 c glyph[epsilon1] -1) , (29)\nplus an equation for the difference T RW 2 -T Sch 2 . The three equations above can be shown [36] to correspond indeed to (25), taking into account that K Sch = -( 1 -2 M r ) G dT . These equations were presented in [38] in full, including the parts lying on the l = 0 and l = 1 harmonics. There, a series of kernels inherent to the usual Hodge decomposition where the responsible for the usual freedom found in the l = 0 and l = 1 sectors when using harmonic decompositions. By using the canonical Hodge decomposition introduced in Section 6, we can have a better control of that freedom, and understand its nature, getting rid of the spurious terms. Indeed, by doing that it can be shown [36] that the projection of the linearized matching on the l = 1 harmonics -on the l = 0 it is trivial, since all scalars in the odd sector are orthogonal to l = 0- gives\n˙ aa 2 Σ 2 c [ W ' 2 -a d dt Y ' 2 | Ω 0 -2Σ -1 c Σ ' c ( W 2 -a d dt Y 2 )] || 1 Ω 0 = a (2 M -a Σ c ) ˙ G || 1 +2˙ a ( a Σ c -3 M ) G || 1 (30)\nwhile ( T RW 2 -T Sch 2 ) || 1 is free.\nThe first consequence of the above equations is that if the FLRW remains unperturbed then the stationary region must be static in the range of variation of r 0 ( t ): equations (27)-(29) imply that the part of G orthogonal to l = 1 vanishes, and (30) implies that G || 1 = Ca 3 / (2 M -a Σ c ) , where C is a constant. Therefore G = Ca 3 / (2 M -a Σ c ) cos θ , and thus 5\nA (1) | Ω 0 = C sin 2 θa 3 / (2 M -a Σ c ) .\nAs shown in [38], this implies that the perturbed spacetime is static in the range of variation of r 0 ( t ).\nThis result generalizes that in [52] because now the matching hypersurface does not necessarily keep the axial symmetry. Therefore, the only way of having a stationary and axisymmetric vacuum arbitrarily shaped (at the linear level) region in FLRW is to have the Einstein-Straus model. Let us remark again that by the interior/exterior duality, this result also implies that a piece of FLRW, irrespective of its shape and its relative rotation with the exterior, cannot describe the interior of Kerr.\n7.1 Constraint on FLRW\nAnother interesting consequence of the matching conditions is that the combination of (27) and (28) produces one equation that involves only quantities in FLRW [38]\n˙ a Σ c a Σ ' c ( W 2 -a [ ˙ U 2 + ˙ Y 2 ] ) Ω 0 = Q 2 -U 2 ' +2Σ -1 c Σ ' c U 2 ,\nand thus constitutes a constraint in FLRW. Recalling that this equation is meant to be orthogonal to l = 1 (and vanishes identically if projected on l = 0), this constraint implies that if the perturbed FLRW contains vector modes with l ≥ 2 harmonics on Ω 0 , then it must contain also tensor modes there. Since, as we have just seen above, the existence of a rotation in the stationary region implies the existence of, at least, vector perturbations in FLRW, then both vector and tensor modes must exist on Ω 0 .\nIt must be stressed that, as demonstrated in [5] (and references therein), there exist configurations of FLRW linear perturbations containing only vector perturbations which vanish identically inside a spherical surface. Such configurations are compatible with the results reviewed here, since that interior region is FLRW and the above constraints do not apply. A completely different matter is the embedding of a Schwarzschild spherical cavity (or a vacuum perturbation thereof) into any such model: the Schwarzschild cavity cannot reach the perturbed FLRW region, as otherwise the constraints above would require that tensor perturbations are also present (at least near the boundary of the Schwarzschild cavity).\nThere also exists a Einstein-Straus perturbative model by Chamorro [18] consisting on small rotation Kerr vacuole within a perturbed FLRW. Again, the constraint above does not apply to this model because there are no l ≥ 2 modes there.\nThe fact that tensor modes must exist near Ω 0 once some rotation with l ≥ 2, whatever small, exists in the stationary region, may indicate the existence of some kind of gravitational waves on FLRW near Ω 0 . In order to analyze further this issue one needs to take the Einstein field equations into consideration. That is the purpose of our work in preparation [36], some result of which will appear in the proceedings of the ERE2012 meeting.\n8 Conclusions and outlook\nThis paper is concerned with the difficulties that the Einstein-Straus model encounters. A fundamental one refers to its high level of rigidity and the impossible generalization to non-spherical symmetry if the bound system is required to be time independent so as to retain the property that cosmic expansion does not affect the local systems. Moreover, if one views the model within the LTB class with a step function density profile, the model is unstable to perturbations [57], [32], cf. also the discussion in [30]. The rigidity result so far requires either stationarity and axial symmetry or staticity. An interesting open problem would be to relax the conditions and assume only stationarity.\nDespite these difficulties, the Einstein-Straus model has played and plays a very important role in cosmology in different areas or research, most notably on the influence (or lack thereof) of the cosmic expansion on local systems, or in the problem of averaging in cosmology at least on an observational level (see e.g. [20]). The model is still widely used as textbook explanation of the lack of influence of the cosmic expansion on astrophysical\nsystems and, in fact, there are not many known alternatives (a notable exception is the McVittie model [44], [28], [29] which is also spherically symmetric and mimics the geometry of Schwarzschild at small scales while approaching a FLRW model at long distances, and which has been studied thoroughly, see [15] and references therein). Concerning the use of the Einstein-Straus model on observational cosmology, mainly by studying lensing effects, its generalizations have systematically consisted in keeping spherical symmetry and allowing for some dynamics in the interior. The prominent example here consists of LTB regions inside a FLRW universe (see references in [20]).\nAn important ingredient for the rigidity of the Einstein-Straus model is the large symmetry of the FLRW background. It is therefore an interesting problem to analyze how the model gets modified in the presence of cosmic perturbations. In a conservative approach, one still wants to keep the main properties (stationarity of a region inside a cosmological model) as far as possible and analyze the possible departures from the model in more realistic situations. Moreover, by studying perturbed Einstein-Straus models one seeks going beyond the problem of the influence of cosmic expansion on local systems, and tackle the problem of the influence of general cosmic dynamics. Surprisingly, it turns out that the existence of static (stationary) regions does impose conditions on the cosmic perturbations, at least near the boundary. Whether this is a real effect or simply an indication that the interior region should not be kept stationary remains to be seen.\nAnother implication of the perturbed Einstein-Straus model is that extra care is required in the standard decomposition of metric perturbations in terms of scalar, vector and tensor modes. As discussed above, any rotation in the vacuole implies necessarily the presence of both vector and tensor modes in the cosmic perturbations. It is interesting to analyze whether these tensor modes could represent cosmic gravitational waves. Some preliminary results along these lines have already been presented in [39]. A detailed and more complete approach will appear elsewhere.\nAnother interesting future line of research is to allow for non-stationary perturbations in the vacuole and study the transmission of gravitational waves from the cosmic region to the bound system.\n9 Acknowledgements\nMM acknowledges financial support under the projects FIS2012-30926 (MICINN) and P09-FQM-4496 (J. Andaluc'ıa-FEDER).\nFM thanks the warm hospitality from Instituto de F'ısica, UERJ, Rio de Janeiro, Brasil, projects PTDC/MAT/108921/2008 and CERN/FP/123609/2011 from Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT), as well as CMAT, Univ. Minho, for support through FEDER funds Programa Operacional Factores de Competitividade (COMPETE) and Portuguese Funds from FCT within the project PEst-C/MAT/UI0013/2011.\nRV thanks the kind hospitality from the Universidad de Salamanca, where parts of this work have been produced, and financial support from project IT592-13 of the Basque Government, and FIS2010-15492 from the MICINN.\nReferences\n\n[1] M. Alcubierre (1994) The warp drive: hyper-fast travel within general relativity . Class. Quantum Grav. 11 L73-L77.\n[2] R. Balbinot, R. Bergamini and A. Comastri (1988) Solution of the Einstein-Strauss problem with a Λ term . Phys. Rev. D 38 2415-2418.\n[3] A. Barnes (2000) A comment on a paper by Carot et al . Class. Quantum Grav. 17 2605-2609.\n[4] R. A. Battye and B. Carter (2001) Generic junction conditions in brane-world scenarios . Phys. Lett. B 509 331-336.\n[5] J. Bicak, J. Katz and D. Lynden-Bell (2007) Cosmological perturbation theory, instantaneous gauges, and local inertial frames . Phys. Rev. D 76 063501.\n[6] M. A. Bizouard and M. A. Papa (2013) Searching for gravitational waves with the LIGO and Virgo interferometers . C. R. Phys. 14 352-365.\n[7] K. Bolejko (2009) The Szekeres Swiss Cheese model and the CMB observations . Gen. Rel. Grav. 41 1737-1755.\n[8] C. Bona and J. Stela (1987) 'Swiss cheese' models with pressure . Phys. Rev. D 36 2915-2918.\n[9] W. B. Bonnor (1976) Non-radiative solutions of Einstein's equations for dust . Comm. Math. Phys. 51 191-199.\n[10] W. B. Bonnor (1996) The cosmic expansion and local dynamics . Mon. Not. Roy. Astr. Soc. 282 1467-1469.\n[11] W. B. Bonnor (1999) Size of a hydrogen atom in the expanding universe . Class. Quantum Grav. 16 1313-1323.\n[12] W. B. Bonnor (2000) A generalization of the Einstein-Straus vacuole . Class. Quantum Grav. 17 2739-2748.\n[13] J. Carot (2000) Some developments on axial symmetry . Class. Quantum Grav. 17 2675-2690.\n[14] J. Carot, J. M. M. Senovilla and R. Vera (1999) On the definition of cylindrical symmetry . Class. Quantum Grav. 16 3025-3034.\n[15] M. Carrera and D. Giulini (2010) Influence of global cosmological expansion on local dynamics and kinematics . Rev. Mod. Phys. 82 169-208.\n[16] B. Carter (1969) Killing horizons and orthogonally transitive groups in space-time . J. Math. Phys. 10 70-81.\n[17] B. Carter (1970) The commutation property of a stationary, axisymmetric system . Comm. Math. Phys. 17 233-238.\n\n
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\n\n[35] M. Mars (2005) First- and second-order perturbations of hypersurfaces . Class. Quantum Grav. 22 3325-3347.\n[36] M. Mars, F. C. Mena and R. Vera in preparation.\n[37] M. Mars, F. C. Mena and R. Vera (2007) Linear perturbations of matched spacetimes: the gauge problem and background symmetries . Class. Quantum Grav. 24 3673-3689.\n[38] M. Mars, F. C. Mena and R. Vera (2008) First order perturbations of the EinsteinStraus and Oppenheimer-Snyder models . Phys. Rev. D 78 084022.\n[39] M. Mars, F. C. Mena and R. Vera (2013) Cosmological gravitational waves and Einstein-Straus voids . to appear in 'Progress in Mathematical Relativity, Gravitation and Cosmology - Proceedings of the Spanish Relativity Meeting in Portugal (ERE2012)', Springer Proceedings in Mathematics, 2013.\n[40] M. Mars and J. M. M. Senovilla (1999) Axial symmetry and conformal Killing vectors . Class. Quantum Grav. 10 1633-1647.\n[41] M. Mars and J. M. M. Senovilla (1999) Geometry of general hypersurfaces in spacetime: junction conditions . Class. Quantum Grav. 10 1865-1897.\n[42] M. Mars and J. M. M. Senovilla (2003) Trapped surfaces and symmetries . Class. Quantum Grav. 20 L293-L300.\n[43] J. Mart'ın-Garc'ıa and C. Gundlach (2001) Gauge-invariant and coordinateindependent perturbations of stellar collapse. II. Matching to the exterior . Phys. Rev. D 64 024012.\n[44] G. McVittie (1933) The mass-particle in an expanding universe . Mon. Not. Roy. Astr. Soc. 93 325-339.\n[45] F. Mena, J. Nat'ario and P. Tod (2008) Gravitational Collapse to Toroidal and Higher Genus Asymptotically AdS Black Holes . Adv. Theor. Math. Phys. 12 1163-1181.\n[46] F. Mena, R. Tavakol and R. Vera (2002) Generalization of the Einstein-Straus model to anisotropic settings . Phys. Rev. D 66 044004.\n[47] S. Mukohyama (2000) Perturbation of the junction condition and doubly gaugeinvariant variables . Class. Quantum Grav. 17 4777-4798.\n[48] B. Nolan (1993) Sources for McVittie's mass particle in an expanding universe . J. Math. Phys. 34 178-185.\n[49] B. C. Nolan (1998) A point mass in an isotropic universe: Existence, uniqueness, and basic properties . Phys. Rev. D 58 064006.\n[50] B. C. Nolan (1999) A point mass in an isotropic universe: II. Global properties . Class. Quantum Grav. 16 1227-1254.\n[51] B. C. Nolan (1999) A point mass in an isotropic universe: III. The region R ≤ 2 m . Class. Quantum Grav. 16 3183-3191.\n\n
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\n"},"sections":{"kind":"list like","value":[{"title":"Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results","content":"Marc Mars ∗ , Filipe C. Mena † and Ra¨ul Vera ‡ ∗ Instituto de F´ısica Fundamental y Matem´aticas, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca, Spain † Centro de Matem´atica, Universidade do Minho, 4710-057 Braga, Portugal ‡ Dept. of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 644 PK, Bilbao 48080, Basque Country, Spain","pages":[1]},{"title":"Abstract","content":"The Einstein-Straus model consists of a Schwarzschild spherical vacuole in a Friedman-Lemaˆıtre-Robertson-Walker (FLRW) dust spacetime (with or without Λ). It constitutes the most widely accepted model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model is that there is no influence from the cosmic background, since the spherical vacuole is static. Spherical generalizations to other interior matter models are commonly used in the construction of lumpy inhomogeneous cosmological models. On the other hand, the model has proven to be reluctant to admit non-spherical generalizations. In this review, we summarize the known uniqueness results for this model. These seem to indicate that the only reasonable and realistic nonspherical deformations of the Einstein-Straus model require perturbing the FLRW background. We review results about linear perturbations of the Einstein-Straus model, where the perturbations in the vacuole are assumed to be stationary and axially symmetric so as to describe regions (voids in particular) in which the matter has reached an equilibrium regime.","pages":[1]},{"title":"1 Introduction","content":"During a meal in the 19th Jena Meeting on Relativity, in September 1996, Bill Bonnor provocatively asked Jos'e Senovilla if the table could be expanding with the Universe. Not surprisingly, Bonnor later took the question seriously and wrote a paper about how the hydrogen atom is affected by the cosmic expansion [11], which is well worth reading. About five decades before, Einstein and Straus asked a similar question, on a bigger scale, which led them to investigate the influence of the expansion of space on the gravitational fields surrounding individual stars [19]. They took the Schwarzschild solution representing the vacuole surrounding a star located in the centre and the FriedmanLemaitre-Robertson-Walker (FLRW) solution as the cosmological model. At the core of their model was the matching of the two solutions across a spherical surface with constant cosmological radius. Since the expansion kept the vacuole symmetry and time independence, their conclusion was that it does not affect the gravitational fields surrounding stars and, in particular, it does not affect the solar system dynamics. A previous attempt to address the issue of whether the planetary orbits expand with the Universe was made by McVittie [44] who found a smooth model describing a spherically symmetric mass embedded in a flat FLRW. Since then the research about this problem was scarce, although some alternatives to the McVittie model were suggested, e.g. in [22], and difficulties of the global meaning of the model were also pointed out [48, 49, 50, 51] (see also [15]). Concerning the Einstein-Straus model itself, it was revisited in [2, 8] and stability issues were raised in [57], [32] cf. also the discussion in [30]. However, the Einstein-Straus model has never stopped being considered as the correct answer to the lack of influence of the cosmological expansion on local systems. Moreover, since the vacuole can be inserted anywhere due to the homogeneity of FLRW, the Einstein-Straus model led to the original Swiss cheese model of a lumpy inhomogeneous universe (see e.g. [20]). Bonnor's question, that 1996 afternoon, raised a totally new issue for the EinsteinStraus models, namely whether spherical symmetry was a crucial ingredient of the model and, therefore, for the existence of time-invariant bounded systems embedded in a FLRW universe. Indeed, the question triggered research by Senovilla and Vera [59], that led to the result about the impossibility of the Einstein-Straus model in cylindrical symmetry. In turn, this important result was the origin of over fifteen years of research about the rigidity, in the sense of uniqueness, of the model. The aim of this paper is to review these results on rigidity both for exact models and from a perturbative perspective. Crucial to this endeavour was the development of a general mathematical theory of spacetime matching [41] and of its perturbative version [4, 47, 35]. This allowed to achieve quite general results about the possibility of generalizing both the shape of the cavity and the cosmological setting of the original Einstein-Straus model. As an example, described below in some detail, uniqueness of the static Λ-vacuum spherical region embedded in a non-static FLRW cosmological model has been proved [34]. The scope of the Einstein-Straus model has been taken well beyond both the physical scale originally considered and the physical problems for which the model was conceived. In fact, the model has been used not only at the solar system scale, but also on galaxy [27] and galaxy clusters' scales [27, 54]. On the other hand, the vacuole of the (original) Einstein-Straus model has been replaced by other spherically symmetric geometries, generally Lemaˆıtre-Tolman-Bondi (LTB), also spherically shaped regions of Szekeres, in order to construct 'generalized' Einstein-Straus models for describing extra-galactic scale and cosmic voids (we refer to the reviews in [30, 20]). Lumpy inhomogeneous cosmological models based on the generalized Einstein-Straus Swiss cheese models are being used in the search of possible explanations to the accelerated expansion of the Universe by the study of lensing effects at cosmic scales produced by the voids (see e.g. [20]). So far, all these generalized Einstein-Straus (and the corresponding Swiss cheese) models have assumed spherically shaped inhomogeneities (voids). One of themes of the research we will review here is how far can one push the Einstein-Straus model towards non-spherical generalizations. The fundamental ingredient we want to keep is that the bound system remains stationary, so as to keep the absence of influence of the cosmic dynamics on astrophysical scales. We will use the term Einstein-Straus problem to the problem of finding the most general stationary regions (vacuum or not) one can embed in a realistic cosmological model in a broad sense. The Einstein-Straus model has also been taken beyond the exact solutions' settings to include metric perturbations. Perturbation theory in General Relativity (GR) is a natural framework to study small departures from symmetric configurations and thus to perform stability analysis. For instance, it allows to include simultaneously density, rotational and gravitational wave perturbation modes into an, otherwise, spatially homogeneous and isotropic cosmological model. Most interestingly, it allows a priori to perturb independently the interior and exterior spacetimes as well as the matching boundary. Furthermore, although the three perturbation modes are decoupled on a FLRW background, they may couple at a matching boundary. In this context, an important question is how general can the perturbations be in each model. Inherent to perturbation theory is the issue of gauge freedom. In perturbed spacetime matchings, this can be complicated by the fact that three independent perturbation gauges may be in use. For the sake of completeness, we include a short review of linearized matching, where these issues are discussed, see also [47] for further details, including the definition of the so-called doubly gauge invariant variables . Perturbations in the FLRW background are customarily split in scalar, vector and tensor modes, and the later are generically viewed as cosmological gravitational waves. Given that the gravitational wave detectors are already active, and gravitational waves are expected to be detected within the next five years (see e.g. [6, 55] for recent accounts and the review [56]), it would be interesting to investigate their inclusion in the models. One now certainly has the necessary mathematical machinery to do so, and preliminary results indicate the possibility of having, for instance, a stationary axially symmetric vacuole embedded in an expanding cosmological model containing tensor modes [38]. Even more, the linearized matching links the rotational and tensor modes degrees of freedom in the perturbation variables [38]. This is therefore an interesting timing to revise the state-of-the-art and point out potentially interesting directions of research about the Einstein-Straus problem, in the sense pointed out above. The plan of the review is the following. In Section 2, the Einstein-Straus model is briefly presented. Similar summaries with different degrees of detail can be found in many places in the literature, see e.g. [20]. We include it here for the sake of completeness and in order to fix our notation. Section 3 is devoted to describing in some detail the uniqueness results concerning both general static regions and stationary and axisymmetric regions (irrespective of any symmetry consideration and/or matter content) embeddable in a FLRW expanding cosmology. Section 3.1 is devoted to the static case. The main conclusion here is that the only static vacuum region that can be embedded to an expanding FLRW is a spherically shaped region of Schwarzschild (i.e. the Einstein-Straus model). Similar uniqueness results hold for other matter models, such as vacuum with cosmological constant. Section 3.2 deals, in turn, with the uniqueness results for stationary and axially symmetric regions in FLRW expanding universes. The main result is that the stationary region must, in fact, be static, so that the previous conclusions on static regions apply. The uniqueness result thus states that the only way of having a stationary and axially symmetric or static region in an expanding FLRW is the Einstein-Straus model. Following the uniqueness results, the robustness of the Einstein-Straus model is further analyzed by considering alternative exact cosmological models. In Section 4 the replacement of the FLRW region by more general anisotropic cosmologies, i.e. the Bianchi models, is studied for static locally cylindrically symmetric interiors, leading to severe restrictions and no-go results for reasonable evolving cosmologies. The final part of the paper is devoted to the generalization of the Einstein-Straus model from a perturbative perspective. After a brief overview of perturbative matching theory in Section 5, and the use of the Hodge decomposition on the sphere instead of the usual spherical harmonic decomposition in Section 6, the linearized matching between stationary and axisymmetric perturbations of Schwarzschild and general perturbed FLRW is reviewed in Section 7. We finish with some conclusions in Section 8, pointing out some ongoing research, prospects for future work on the perturbed Einstein-Straus model and its possible implications on the relationship between astrophysical bounded systems and cosmological dynamics in the form of cosmic gravitational waves.","pages":[1,2,3,4]},{"title":"2 The Einstein-Straus model","content":"This model consists of a spherically symmetric (both in shape and intrinsic geometry) Ricci-flat region embedded in a FLRW universe without cosmological constant. Recall that two spacetimes can be matched across their boundary if and only if the first fundamental forms q and second fundamental forms K agree on the matching hypersurface. A consequence of this are the well-known Israel conditions, which restrict the jump of the energy-momentum tensor across the boundary. In the present context, they imply that the cosmological fluid must be dust and the vacuole must be comoving with the cosmological fluid. Writing the FLRW metric in cosmic time coordinates where glyph[epsilon1] = {-1 , 0 , +1 } , Σ ' 2 = 1 -glyph[epsilon1] Σ 2 with prime denoting derivative with respect to R , in units G = c = 1 the Friedman equation reads where the dot denotes derivative with respect to t and ρ 0 is a constant such that the cosmological energy-density ρ satisfies ρ = ρ 0 /a 3 . The boundary of the vacuole can be parametrized by { t = t, R = R 0 } (we ignore the angular variables as they behave trivially, and use t both as spacetime coordinate and intrinsic coordinate on the hypersurface, the precise meaning will be clear from the context). For the matching one needs the induced metric q RW and the second fundamental form K RW . Using the outward unit normal n RW = a ( t ) dR these objects read, with Σ c := Σ | R = R 0 , and Σ ' c := Σ ' | R = R 0 , From Birkhoff's theorem, the geometry of the vacuole is Kruskal. Assuming that the boundary is away from the Schwarzschild horizon (this happens sufficiently away from the big bang or big crunch) the interior metric can be written in Schwarzschild coordinates The boundary can be parametrized as { T = T 0 ( t ) , r = r 0 ( t ) } and, given the time inversion symmetry of Schwarzschild, we can assume ˙ T 0 > 0 without loss of generality. The induced metric on the boundary is Using the unit normal n Sch = 1 N ( ˙ T 0 dr -˙ r 0 dT ) (note that the global sign of N is kept free at this stage), the second fundamental form is Equality of the t -component of the induced metric requires N 2 = 1. Then, equality of the angular parts of the first and second fundamental forms imposes N = 1 and A straightforward computation shows that the equality of the t -component of the induced metric and second fundamental forms are satisfied provided the values of ρ 0 and m are linked by which has a clear interpretation in terms of (Misner-Sharp)-mass conservation. This is the Einstein-Straus model [19]. A natural generalization consists in adding a cosmological constant Λ both to the FLRW and to the interior part (originally considered in [25] and fully solved in [2]). The Israel matching conditions on the energy-momentum tensor now impose the FLRW matter model to be dust with Λ, so that the Friedman equation is now By Birkhoff's theorem, the interior metric is the Kottler solution (also known as 'Schwarzschild(anti) de Sitter'), which away from the horizons is In this case, the matching conditions are We emphasize that any matching of two spacetimes immediately leads to a complementary matching, at least locally, where the 'interior' and 'exterior' regions on each spacetime reverse their roles (see [21] for details). In the matching above, this leads to the Oppenheimer-Snyder collapse model [53].","pages":[4,5]},{"title":"3 Rigidity of the Einstein-Straus model","content":"The Einstein-Straus model is such that, for a given total mass inside the vacuole and a given energy density in the cosmological background, the radius of the static region is uniquely fixed. This already poses difficulties for the model since it is often the case that the size of the vacuole does not match the observed sizes of clustered matter in the universe, such as stars or galaxies. This fact indicates that the Einstein-Straus model may be lacking flexibility to accommodate the various situations present in cosmology (cf. [58] and [10]). In fact, the Einstein-Straus vacuole was found to be radially unstable in a certain sense [30]. The other main restriction of the model is its exact spherical symmetry. It is clear that vacuoles in the universe are not exactly spherically symmetric so a natural question is how robust is the model to non-spherical generalizations. The first thing to consider is which fundamental ingredients of the model should be kept. The main motivation of the Einstein-Straus model was its ability to combine cosmological expansion at large scales with no observable effects on the local physics. Thus, the fundamental ingredient to keep is the absence of influence of the cosmic expansion inside the region. The simplest and most natural way to achieve this is imposing that the interior geometry is stationary, because then no dynamical effects whatsoever from the surrounding evolving cosmology would affect the local physics. Among stationary interiors, the simplest case corresponds to static situations, so it is natural to start with this case (note that the Einstein-Straus model is itself static). The question is then how rigid or flexible is the possibility of having stationary/static regions embedded in an otherwise expanding FLRW universe. Ideally, one would like to make no further assumptions and find the most general model with these properties. The matter model inside may also be kept arbitrary, and see what are the possibilities allowed by the coexistence of a stationary/static region inside an expanding FLRW universe. This coexistence has been sometimes called the Einstein-Straus problem in the literature (see e.g. [2]). The first indication that the Einstein-Straus model might be very rigid came from a seminal work by Senovilla and Vera [59] who considered the possibility of matching a static and cylindrically symmetric region (with no restriction on the matter model) with a FLRW dynamical cosmology. The matching hypersurface was taken to be locally a cylinder, in the sense of being tangent in an open set to the two (commuting) generators of two spatial local isometries. No global consideration was needed. The result was a no-go theorem: no such model exists. With the impossibility of generalizing the Einstein-Straus model to a cylindrical setting, it became of interest to study the problem in as much generality as possible. The static case was treated in complete generality in [33], [34] and it is by now well-understood. The more complicated stationary situation has been studied [52] under the additional assumptions of axisymmetry and a group action orthogonally transitive. The motivation to study this simplified problem lies in the fact that one expects equilibrium configurations to also exhibit an axial symmetry. It is worth to mention that one step in the black hole uniqueness theorems corresponds to showing that the domain of outer communications must be axially symmetric [26]. We devote the following Section 3.1 to describing the main results in the static setting, and Section 3.2 to review the uniqueness results in the stationary and axially symmetric setting.","pages":[5,6]},{"title":"3.1 Uniqueness results in the static case","content":"This case was first considered in [33] under the additional assumption of axial symmetry, and one extra technical assumption relating cosmic and static times on the matching hypersurfaces. Both assumptions were dropped in [34] where a satisfactory uniqueness result for static region in FLRW was obtained. The setup consists on a spacetime ( V , g ) composed by two regions ( W ST , g ST ) and ( W RW , g RW ) matched in absence of surface layers across their boundaries, denoted by Ω ST and Ω RW respectively, which once identified conform to a hypersurface Ω in ( V , g ). The region ( W ST , g ST ) is strictly static, i.e. admits a Killing vector ξ which is timelike and orthogonal to hypersurfaces everywhere. ( W RW , g RW ) is a codimension-zero submanifold with smooth boundary Ω RW of the FLRW spacetime ( V RW , g RW ), by which we mean the manifold V RW = I ×M , where I ⊂ R is an open interval, M is either E 3 ( glyph[epsilon1] = 0), S 3 ( glyph[epsilon1] = 1) or H 3 ( glyph[epsilon1] = -1) and the FLRW metric g RW takes the form (1). We call any coordinate system { R,θ, φ } in which the metric takes this form a spherical coordinate system . Note that since ( M , g M ) is homogeneous, there exist spherical coordinate systems centered at any point p ∈ M , and this will be used below. The function a ( t ) is positive and smooth (in fact C 3 suffices). We assume that ˙ a does not vanish on any open set (this excludes uninteresting situations where the FRLW does not evolve). Define the 'geometric' energy-density ρ RW and pressure p RW by glyph[negationslash] so that, if the spacetime has a cosmological constant Λ, the energy-density and pressure of the cosmic fluid is ρ = ρ RW -Λ 8 π , p = p RW + Λ 8 π . We make the assumption that ρ RW + p RW = 0 so that we do have a non-trivial cosmic fluid (this allows us to define t unambiguously). Concerning the boundary Ω RW it is assumed to be connected (this is irrelevant because the matching conditions are local, the assumption is made merely for notational convenience), and nowhere tangential to a hypersurface of constant cosmic time t . This assumption is physically reasonable and automatically satisfied if the boundary is causal. In fact, dropping this assumption would only make the presentation more involved, but would not spoil any of the results (see [34] for a discussion). Finally, we assume that Ω RW is spatially compact. A sufficient condition for this is the 'energy condition' ρ RW ≥ 0, see [33], and this is in fact the assumption made in [33]. However, it can be proved that spatial compactness suffices for the validity of all the results below. Note finally, that spatial compactness is indeed an assumption: allowing for non-compact boundaries, additional configurations not covered by the uniqueness results do arise, as shown in [45] (see also references therein), where configurations with planar and hyperbolic symmetries were found and analized. It would be interesting to analyze how far can one extend uniqueness without any compactness assumption on the boundary. Nevertheless, for the purposes of the Einstein-Straus problem, compactness is a completely natural assumption, as we want the local physics unaffected by the cosmological expansion be spatially confined. By a detailed analysis of the matching conditions, the following restrictions on the boundary Ω RW are obtained [34]. First of all, the intersection S RW t of Ω RW with a hypersurface of constant cosmic time t is a sphere. More precisely, for any t ∈ I , there exists a point c ( t ) ∈ M so that S RW t is a coordinate sphere of radius R ( t ) in a spherical coordinate system centered at c ( t ). The radius R ( t ) is restricted to satisfy the bound This inequality means that the surface S RW t is non-trapped (i.e. has a mean curvature vector spacelike everywhere). The necessity of this condition can be understood from the fact that no closed spacelike surface in a static spacetime can have a future (or past) causal and not-identically zero mean curvature vector [42]. The spherical symmetry of the surface S RW t and the fact that the matching conditions force the mean curvature vector to be continuous across the matching hypersurface implies that S RW t must be nontrapped, which is precisely (5). Note also that if the static Killing vector ξ admits Killing horizons and hence changes causal character, then the bound (5) is no longer necessary. This behaviour occurs in the Einstein-Straus model when a ( t ) is sufficiently small so that Σ c a ( t ) = 2 m . The breakdown of the ODE (3) in the Einstein-Straus model is just a manifestation of the breakdown of the the static coordinate system in the interior region. In Kruskal coordinates, the matching would continue across Σ c a ( t ) = 2 m without problem. Something similar would occur in the general setting if we allowed the static Killing to change causal character. Returning to the shape of Ω RW , the center point c ( t ) follows a geodesic in ( M , g M ) (which may degenerate to a point). The parameter t is not in general an affine parameter for the geodesic, so the center c ( t ) is a priori allowed to move at any speed (in fact the trajectory can have turning points along the curve). In order to describe the matching hypersurface, choose any point c 0 along this geodesic and let c ' 0 be its tangent vector. We can choose a spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 so that the axis of symmetry ˆ θ = 0 is along the tangent vector c ' 0 . In this coordinate system, the center c ( t ) will have coordinates (the value of ˆ θ can be 0 or π depending on whether c ( t ) lies after or before c 0 along the geodesic). The function σ ( t ) describes the motion of c ( t ) along the curve. The relationship between the spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 and a spherical coordinate system { R,θ, φ } centered at c ( t ) with parallel axis (i.e. with coincident lines | cos θ | = 1 and | cos ˆ θ | = 1) is easily found to be Thus, the matching hypersurface Ω RW in the spherical coordinates centered at c 0 can be parametrized by coordinates t, θ, φ as which is a rather complicated form for the matching hypersurface. A useful alternative is to use a coordinate system { t, R, θ, φ } in ( W RW , g RW ) such that, for each t , { R,θ, φ } is the spherical coordinate system centered at c ( t ). Applying the coordinate transformation (6) to the metric gives where f ( t ) = ˙ σ ( t ). The explicit calculation leading to (7) is somewhat long, a much more elegant method of obtaining this form of the metric is discussed in the Appendix of [34]. In these coordinates, the matching hypersurface Ω RW is simply { R = R ( t ) } . The matching conditions in the FLRW part are supplemented with a differential equation relating the trajectory of the center σ ( t ) with the radius R ( t ). To write it down, define a function β ( t ) via where glyph[epsilon1] 1 = ± 1 depending on whether the FLRW region to be matched is R > R ( t ) or R < R ( t ) (more specifically, the manifold with boundary W RW is { glyph[epsilon1] 1 R ≥ glyph[epsilon1] 1 R ( t ) } ). Note that β ( t ) is well-defined because of (5). The ODE relating R ( t ) and σ ( t ) is conveniently written using an auxiliary function ∆( t ) = 0 as the following pair of differential equations glyph[negationslash] In summary, the static domain embedded in the FLRW regions consists of a sphere with time dependent radius R ( t ) and with center moving across the FLRW spacetime along a geodesic. Speed along the geodesic and radius R ( t ) are linked by (9). The model is not spherically symmetric because the center of the sphere is allowed to move. However, it is very close to spherically symmetric and it turns out that the center of the sphere must be at rest for several relevant matter models in the static domain, as we discuss next. An important consequence of the matching procedure (cf. Lemma 1 in [34]) is that the Killing vector field ξ is everywhere transverse to the matching hypersurface Ω ST in the static region. Combining this with the fact that the static geometry is invariant along ξ it follows that the static metric in the spacetime region obtained by dragging Ω ST with the static Killing vector can be fully determined in terms of hypersurface geometry of Ω ST . Since, in turn, the geometry on Ω ST is related to the geometry of Ω RW via the matching conditions, it follows that the spacetime geometry of the static region becomes completely determined [34] in a neighbourhood of its matching hypersurface in terms of the FLRW geometry and the functions R ( t ) , σ ( t ) and ∆( t ) (see Theorem 1 in [34] for details). Specifically, there exist coordinates { T, t, θ, φ } so that the metric g ST takes the form (note that t is a spacelike coordinate in the static domain) where µ := glyph[epsilon1]a ( t )( ˙ R ( t ) + f ( t ) cos θ ). The matching hypersurface Ω ST is defined by the embedding { t, θ, φ } → { T = T ( t ) , t, θ, φ } , where T ( t ) satisfies ˙ T ( t ) = ∆( t ) and the portion of the static spacetime to be matched to the exterior region is { T ≥ T ( t ) } . The metric (10) is foliated by round spheres { T = const , t = const } but it is not spherically symmetric in general (unless f ( t ) = 0 and R ( t ) = 0). To complete the picture, we review the energy-momentum tensor in the static part. Introduce two one-forms and one symmetric two-tensor h by The Einstein tensor of ( W ST , g ST ) is (cf. Proposition 1 in [34]) where ρ ST , p ST r and p ST t read and ρ RW and p RW were defined in (4). Several consequences of (11) can be drawn [33, 34]. Concerning the uniqueness of the Einstein-Straus model, under the assumption ρ ST + p ST = 0 (which includes vacuum with or without cosmological constant or a non-singular electromagnetic field) it follows that µ = 0 and hence f ( t ) = 0 and R ( t ) = 0. The second equation in (9) gives (with an appropriate but still completely general choice of integration constant), where (8) and the definitions of Σ c and Σ ' c in Section 2 have been used. The static metric simplifies to From this metric, uniqueness of the Einstein-Straus model as the unique static vacuum (with or without cosmological constant) region embedded in a FRLW cosmological model follows easily. So, static vacuoles in a FLRW model must be spherically symmetric both in shape and interior geometry. It is an open problem to analyze whether there are any physically realistic matter models in the interior static region for which the motion of the static domain inside FLRW has interesting properties. Note that a priori nothing prevents the geodesic c ( t ) from being spacelike, so the motion of the static domain can in principle be superluminal for the cosmic observers. This is of course reminiscent to the superluminal warp drive discovered by Alcubierre [1].","pages":[6,7,8,9,10]},{"title":"3.2 Uniqueness results in the stationary and axisymmetric case","content":"The study of axially symmetric equilibrium regions in FLRW universe was dealt with in [52], and, in short, the main result found was that those stationary regions must, in fact, be static, and therefore the results of the previous section apply. With the same definitions and assumptions concerning the FLRW region ( W RW , g RW ) and its boundary Ω RW as in the previous section, we assume now that the interior region ( W SX , g SX ) is (strictly) stationary and axisymmetric. More specifically, we demand that (i) the spacetime admits a two-dimensional group of isometries G 2 acting simply-transitively on timelike surfaces T 2 and containing a (spacelike) cyclic subgroup, so that G 2 = R × S 1 , and (ii) that the set of fixed points of the cyclic group is not empty. Consequences of the definition are that the G 2 group has to be Abelian [17, 14, 3], and that the set of fixed points must form a timelike two-surface [40], which is the axis. The axial Killing η is then intrinsically defined by normalizing it demanding ∂ α η 2 ∂ α η 2 / 4 η 2 → 1 at the axis. See also [61] and [13]. In addition, we demand that the isometry group is orthogonally transitively (OT), i.e. that the two planes orthogonal to the orbits of the isometry group are surface forming. This assumption is also known as the 'circularity condition', and in many cases of interest it follows as a consequence of the Einstein field equations. Indeed, the G 2 on T 2 group must act orthogonally transitively in a region that intersects the axis of symmetry whenever the Ricci tensor has an invariant 2-plane spanned by the tangents to the orbits of the G 2 on T 2 group [16]. By the Einstein field equations, this includes Λ-term type matter (i.e. vacuum with or without cosmological constant), perfect fluids without convective motions, and also stationary and axisymmetric electrovacuum [61]. An OT stationary and axisymmetric spacetime ( V SX , g SX ) is locally characterized by the existence of a coordinate system { T, Φ , x M } ( M,N,... = 2 , 3) in which the line-element for the metric g SX outside the axis reads [61] where U , A , W and g MN are functions of x M , the axial Killing vector field is given by η = ∂ Φ , and a timelike (future-pointing) Killing vector field is given by ξ = ∂ T . Although useful for the sake of clarity, the use of coordinates is not essential for the results below, which only depend on the intrinsic geometric properties of of ( W SX , g SX ). As before, no specific matter content is assumed in the stationary and axisymmetric region. Regarding the matching hypersurface Ω, besides those in the previous Section 3.1, we make the only extra assumption that it preserves the axial symmetry [62] of ( W SX , g SX ) and of ( W RW , g RW ). This means that Ω SX is assumed to be invariant under the axial symmetry of ( W SX , g SX ) and that there is an axial Killing vector η RW in the Killing algebra of ( W RW , g RW ) tangent to Ω RW . With these assumptions at hand, in [52], it is proven, first, that the stationary (timelike) Killing vector field ξ is nowhere tangent to Ω SX . As explained in the previous section, this serves in particular to construct a neighbourhood of Ω SX by dragging it along the orbits of ξ , in which the geometry is thus fully determined by the information in Ω SX . The main result in [52] is that if a OT stationary and axisymmetric region ( W SX , g SX ) can be matched to a FLRW region through a hypersurface Ω SX preserving the axial symmetry, then the region ( W SX , g SX ) must be, in fact, static on a neighbourhood of Ω SX . All in all, in that neighbourhood of the matching hypersurface the OT stationary axisymmetric region ( W SX , g SX ) thus becomes a static axisymmetric region ( W ST , g ST ), and therefore the results of the previous Section 3.1 (cf. [34]) apply. So far, no explicit condition on the matter content of the stationary region has been used. When conditions on the matter content on the (OT) stationary and axisymmetric (and hence static) region are imposed, the functions that determine the matching hypersurface and the static geometry are determined by the results reviewed in Section 3.1. In particular, and for completeness, let us consider a vacuum (with or without a cosmological constant) stationary and axisymmetric region ( W SX , g SX ) matched to FLRW preserving the axial symmetry. As mentioned above, a vacuum matter content forces the axial symmetry and stationary group G 2 on T 2 to act orthogonal transitively. On the other hand, a region of FLRW ( W RW , g RW ) matched to a vacuum region must satisfy the assumptions made and, in particular, have a causal Ω RW (in fact tangent to the fluid flow). The above result implies then that the vacuum region must be static. The results of Section 3.1 thus apply, and imply, in turn, that the whole region (not just its boundary) has to be spherically symmetric, and hence Schwarzschild. To sum up, this means that the only stationary and axially symmetric vacuum region that can be matched to FLRW is a spherically symmetric piece of Schwarzschild. This constitutes still another uniqueness result of the Einstein-Straus model when the vacuum region lies inside FLRW. The complementary result, when the vacuum region lies outside FLRW, constitutes a uniqueness result of the Oppenheimer-Snyder model [53]. It is worth noticing that this result can also be interpreted as a no-go result for the possible interiors of Kerr. Indeed, this result states that an axially symmetric region of (an evolving) FLRW, irrespective of its relative rotation with the exterior, cannot be the source of a stationary and axisymmetric vacuum region, in particular, Kerr.","pages":[11,12]},{"title":"4 Robustness of Einstein-Straus: Generalized exact cosmologies","content":"In the previous sections, the robustness of the Einstein-Straus model has been discussed by considering generalizations of the interior vacuole and keeping the FLRW model as the exterior cosmological model. The question arises as to what happens if these symmetry assumptions concerning the exterior metric are relaxed. There are two different ways to study departures from the spherical FLRW: either perturbatively or using exact solutions. In this section, we concentrate on the later possibility and, in particular, we review the results found in [46] for spatially homogeneous (but anisotropic) cosmologies. A step in the direction of generalising the exterior was taken by Bonnor, who considered the embedding of a Schwarzschild region in an expanding spherically symmetric inhomogeneous Lemaˆıtre-Tolman-Bondi (LTB) exterior. He found that such a matching is possible in general, and that it allows the average density of the Schwarzschild interior to be chosen independently of the exterior LTB density [12]. So, clearly, if the spherical symmetry is kept, the exterior can be readily generalized to the case of inhomogeneous dust cosmologies. An interesting review about physical aspects of spherically symmetric Einstein-Straus and McVittie type models can be found in [15]. While keeping the spherical symmetry of the cavity allows for straightforward generalizations of Einstein-Straus, breaking this symmetry brings in unexpected complications, as we have seen in the previous section. The same seems to hold if we consider exact generalizations of the FLRW cylindrical symmetry exterior to spatially homogeneous but anisotropic spacetimes. This problem was considered in [46] and we summarize it next: Consider the problem of matching, across a hypersurface Ω which is spatially a topological sphere 1 , of an interior locally cylindrically symmetric (LCS) static spacetime ( W ST , g ST ), which represents a spatially compact region, to a spatially homogeneous anisotropic exterior ( W HOM , g HOM ) having a Lie group G 3 acting on S 3 surfaces. Once more, we make no assumptions a priori on the matter contents, so the main results are purely geometric. Only at the end of the section, assumptions on the matter content will lead to a final no-go result. We wish to preserve globally the axial symmetry and thus we need to impose first the existence of a group of cyclic symmetries in the exterior region. This, combined with the assumption of a spacelike spherical topological shaped 2 Ω ST , implies the existence of an exterior axis. Thus, the cyclic symmetry in the exterior must really be an axial symmetry (see the discussion in Section 3.2). Moreover, we require that the cylindrical symmetry is preserved (in the sense of [62]) at least on a non-empty open subset of Ω. This has the consequence that ( W HOM , g HOM ) must admit a G 4 on S 3 group of isometries, so that it is locally rotationally symmetric (LRS). In [46], it is shown how all the LRS spatially homogeneous metrics can be written in the form adapted to the two commuting Killing vectors defining the cylindrical symmetry ∂ ϕ and ∂ z , where ∂ ϕ is axial with axis at r = 0: with where the functions Σ and F are given by and where glyph[epsilon1] and n are given such that glyph[epsilon1] = 0 , 1; n = 0 , 1; glyph[epsilon1]n = glyph[epsilon1]k = 0 3 . The metrics are classified according to these constants in Table 1. The matching conditions are then investigated and a crucial step was to observe that they lead to the following necessary relations involving only exterior metric functions: 2 This implies the existence of north and south poles on Ω ST where the axial killing vector in the interior vanishes and, therefore, also the generator of the cyclic symmetry in the exterior region on Ω HOM by construction. 3 Let us note that the case glyph[epsilon1] = n = 0 with k = 1 is special, since it corresponds to the Kantowski-Sachs (KS) class of metrics, which do not admit a G 3 on S 3 subgroup [61]. It was included in the study for completeness. which, for non-static exteriors, imply n = 0 and thus exclude Bianchi types II, III, VIII and IX. By inserting (15) back in the matching conditions one is able to prove a series of results that lead to the following conclusion: The only expanding spatially homogeneous spacetimes which can be matched to a locally cylindrically symmetric static interior region preserving the (cylindrical) symmetry, across a non-spacelike hypersurface which is spatially a topological sphere, are given by where β is constant. This metric for k = 1 belongs to the Kantowski-Sachs class, when k = -1 admits a G 3 on S 3 of Bianchi type III, and when k = 0 of Bianchi types I,V,VII 0 ,VII h . The metrics (16) are very special, partly due to the fact that condition a ,t = 0 (see (13)-(14)) imposes a strong constraint, implying that there cannot be any time (nor space) evolution along the direction orthogonal to the orbits of the subgroup G 3 on S 2 of the LRS. There are also constraints imposed through the matching in the interior region and the interested reader can find those in [46]. Note that the no-go result found in [59] is trivially recovered, since FLRW is included in the LRS class for b ( t ) = a ( t ), and the above would imply a static FLRW metric. If one specifies a particular class of matter fields, then one gets further constraints on the cosmological dynamics. For example, if the matter in the static region is not specified but the dynamical (cosmological) region is assumed to contain a perfect fluid with pressure p and energy-density ρ satisfying the dominant energy condition everywhere, then glyph[epsilon1] = 0 necessarily, which corresponds to a stiff fluid equation of state ρ = p = α 2 / (4 t 2 ( α -kt ) 2 ), with b ( t ) = √ αt -kt 2 , where α > 0. On the other hand, if the interior is vacuum then the exterior must be also vacuum. The overall no-go results, in this case, can be seen in two ways: either as a consequence of the assumption that the interior metric is static and cylindrically symmetric, which seems to prohibit time dependence along one direction, or as a consequence of the particular exterior metrics we are considering, which are homogeneous then prohibiting the coefficients along this direction to be space dependent. The perturbative approach described in the next sections can help to clarify this question. To conclude this section we remark that there exists an example of a Einstein-Straus model with exact non-spherical inhomogeneous cosmologies. This is provided by the Szekeres dust solution which has no Killing vectors, in general, but contains intrinsic symmetries on 2-spaces of constant curvature: The Szekeres solution is divided into class I, which generalizes the LTB solution having non-concentric spheres of constant mass, and class II which includes the Kantowski-Sachs solution. Class I solutions have been proved to be interiors to the Schwarzschild solution [9] and this result has been generalized to include the cosmological constant [31, 45]. As mentioned before, one can invert the roles of the two spacetimes involved and hence construct an Einstein-Straus type model with a Schwarzschild or Kottler cavity within a class I Szekeres' cosmology. Let us remark that the Szekeres class has been used recently in Swiss cheese models as interiors to FLRW (see [7] and references therein). Class II Szekeres dust metrics are less known, but contain curious inhomogeneous solutions with cylindrical symmetry [60]. In this case, it seems harder to be able to get a physically reasonable Einstein-Straus model considering what we have described above.","pages":[12,13,14,15]},{"title":"5 Brief overview of perturbative matching theory","content":"A perturbed spacetime consists of a symmetric two-covariant tensor (the 'perturbation metric') defined on a fixed spacetime (the 'background'). From a structural point of view, spacetime perturbation theory is a gauge theory in the sense that many perturbation metrics describe the same physical situation (i.e. they are gauge related). The underlying geometrical reason for this gauge freedom can be understood from the following intuitive picture of perturbation theory. We imagine a one-parameter family of spacetimes ( V ε , g ε ) such that all the manifolds are diffeomorphic to each other. This allows one to pull back g ε onto a single manifold in the family (say V 0 := V ε =0 ) and work with a one-parameter family of metrics on a single manifold. If all the construction is smooth in ε , derivatives with respect to this parameter can be taken. The perturbation metric g (1) is simply the derivative at ε = 0 of this family of metrics. However, the identification of points in the different manifolds (the diffeomorphism above) is highly non-unique. Any other choice of identification would lead to a different, but geometrically equivalent, perturbation metric. This is the gauge freedom of the theory. Intuitively, it is clear that the gauge freedom will consist of a vector field on the background, because this measures the shift of the new identification with respect to the previous one, and an initial direction (in ε ) is all what is required to compute derivatives with respect to ε at ε = 0. When two spacetimes with boundary are matched, an identification of the boundaries is required. As already mentioned before, if the boundaries are nowhere null, the matching conditions require the equality of the induced metric and second fundamental form (with appropriate choices of orientation). To compare the tensors it is necessary to pull them back to a single manifold and this is done via the identification of boundaries. Contrarily than before, the matching theory is strongly dependent on the identification of the boundaries. In fact, the matching conditions demand the existence of one such identification for which the first and second fundamental forms agree. Assume now that we are studying perturbation theory on a background spacetime constructed from the matching of two spacetimes. The question then arises of what are the conditions that the metric perturbation tensors on each side must satisfy to have a perturbed matching spacetime. This issue is somewhat more involved than one may think a priori and it was solved in a complete manner for the first time by Battye and Carter [4] and independently by Mukohyama [47] (this has been extended to second order in [35]). Previous attempts [24, 23, 43] did not take into account all the subtleties of the interplay between two completely different gauge freedoms inherent to this problem. Indeed, in the picture above of perturbation theory in terms of a collection of spacetimes ( V ε , g ε ), each one of them arises now as the matching of two spacetimes with boundary W ± ε across their respective boundaries Ω ± ε . For better visualization, assume that each one of W ± ε is a submanifold with boundary of a larger boundary-less manifold ̂ W ± ε and assume that the { ̂ W + ε } manifolds are identified among themselves (say with ̂ W + 0 := ̂ W + ε =0 ) via an ε -dependent diffeomorphism. The hypersurface Ω + ε projects down to ̂ W + 0 as a hypersurface ̂ Ω + ε . Now we have a collection of hypersurfaces in one single manifold, and one can think of taking ε -derivatives of geometric quantities intrinsic to the hypersurface. The important point is that, given a point p ∈ Ω + ε =0 , we do not know how this point maps into ̂ Ω + ε . For that, it is necessary to prescribe first how p is mapped into Ω + ε . The identification of { Ω + ε } among themselves is an additional gauge freedom. It is fully independent of the standard gauge freedom in perturbation theory (called 'spacetime gauge freedom' from now on) and is referred to as hypersurface gauge freedom [47]. The composition of both identifications gives, as ε varies, and for any p ∈ Ω + ε =0 , a path γ p ( ε ) in ̂ W + 0 starting at p . Since everything is smooth in ε , the tangent vector to this path at ε = 0 defines a vector field Z + on Ω + 0 := Ω + ε =0 (= ̂ Ω ε =0 ). This vector field is not necessarily tangent (nor normal) to Ω + 0 and it depends on both gauge freedoms. A schematic figure for the definition of Z + and how it depends on the gauges is given in Figure 5. If we let n (0) + be a unit normal vector to Ω + 0 , we can decompose Z + = Q + n (0) + + T + , where T + is tangent to Ω + 0 . From the discussion above, it should be clear that Q + is independent of the hypersurface gauge while T + strongly depends on it. In fact, it can always be made zero by an appropriate choice of gauge. However, doing this is not usually a good idea because the matching has two regions and, at each value of ε , the matching requires an identification between Ω + ε and Ω -ε . After a choice of hypersurface gauge to identify Ω + ε with Ω + 0 we have no freedom left to choose a hypersurface gauge to identity Ω -ε and Ω -0 . The matching conditions will tell us how this identification must be done. So, had we chosen T + = 0, we would still have to leave T -free and let the linearized matching theory determine its value. Further details on the double gauge freedom of linearized perturbation theory can be found in the paper of Mukohyama [47] and in [37], where the issue is discussed in depth including a critical analysis of previous attempts to formulate a consistent perturbative matching theory. After this brief discussion on gauge issues for linearized matching theory, let us describe the actual perturbative matching conditions (for details see [4, 47, 35]). The matching theory involves the equality of the first and second fundamental forms of the boundaries. To compare them they are pulled-back into a single boundary via the identification. In perturbative matching theory everything occurs on the abstract hypersurface Ω 0 diffeomorphic to Ω + 0 and Ω -0 of the background spacetime. On Ω ± 0 we attach two vector fields Z ± = Q ± n (0) ± + T ± whose geometric meaning has been discussed above. They are not know a priori, firstly, because of the hypersurface gauge freedom, and secondly, because the identification of the boundaries Ω + ε and Ω -ε is not known a priori. To the unknowns Z ± we add four symmetric tensors q (1) ± and K (1) ± intrinsic to Ω 0 which arise as the ε -derivative at ε = 0 of the first fundamental form q ± ε and second fundamental form K ± ε of Ω ± ε . These tensors are intrinsic to Ω ± ε , so before taking ε -derivatives they must be pulled back onto Ω 0 via the hypersurface gauges (on each side). Thus, q (1) ± and K (1) ± are hypersurface gaugedependent by construction. On the other hand, their construction is fully independent of the spacetime gauge freedom. In order to write down their explicit expression, let g (1) ± be the perturbed metric (i.e. the fundamental unknown in metric perturbation theory) on each side of the background spacetime. Let also Ψ ± 0 : Ω 0 → W ± 0 be the embedding of the matching hypersurface on each region of the background spacetime. Let y i ( i, j, . . . = 1 , . . . , n -1) be a local coordinate system on Ω 0 and define tangent vectors e ± i = Ψ ± 0 glyph[star] ( ∂ y i ). There are also unique (up to orientation) unit one-forms n (0) ± normal to the boundaries. We choose them so that the corresponding vector n (0) + points towards W + 0 and n (0) -points outside of W -0 or viceversa. The first and second fundamental forms of the background are simply q (0) ± := Ψ ± 0 glyph[star] ( g (0) ± ) , K (0) ± := Ψ ± 0 glyph[star] ( ∇ ± n (0) ± ), where ∇ ± is the covariant derivative in ( W ± 0 , g (0) ± ). Given that the background configuration is already composed of the matching of V + 0 and V -0 through Ω + 0 := Ω 0 , we already have q (0)+ = q (0) -and K (0)+ = K (0) -. Then q (1) ± and K (1) ± are defined as follows [47] where σ := g (0) ± ( n (0) ± , n (0) ± ), D is the covariant derivative of (Ω 0 , q (0) ± ), R (0) ± αµβν is the Riemann tensor of ( W ± 0 , g (0) ± ) and S (1) ± α βγ := 1 2 ( ∇ ± β g (1) ± α γ + ∇ ± γ g (1) ± α β -∇ ± α g (1) ± βγ ). The first order matching conditions (in the absence of shells) require the equalities We emphasize that Q ± and T ± are a priori unknown quantities and fulfilling the matching conditions requires showing that two vectors Z ± exist such that (19) are satisfied. The spacetime gauge freedom can be exploited to fix either or both vectors Z ± a priori, but this should be avoided (or at least carefully analyzed) if additional spacetime gauge choices are made, in order not to restrict a priori the possible matchings. Regarding the hypersurface gauge, this can be used to fix one of the vectors T + or T -, but not both. Note also that the linearized matching conditions are, by construction, spacetime gauge invariant because, as discussed above, the tensors q (1) ± , K (1) ± are necessarily spacetime gauge invariant. In fact, it is straightforward to check explicitly that the right-hands sides of (17) and (18) are spacetime gauge invariant (the individual terms are not, and it is precisely the spacetime gauge dependence in Z ± which makes these objects spacetime gauge invariant). Moreover, the set of conditions (19) are hypersurface gauge invariant, provided the background is properly matched, since, as shown in [47], under such a hypersurface gauge transformation given by the vector ζ in Ω 0 , q (1) transforms as q (1) + L ζ q (0) , and similarly for K (1) .","pages":[15,16,17,18]},{"title":"6 Spherical symmetry: Hodge decomposition","content":"After the previous summary on linearized matching, in this section we introduce the second main ingredient for the linearized Einstein-Straus model reviewed in the following sections: the Hodge decomposition on the sphere [38]. In order to exploit the underlying spherical symmetry of the background configuration it is common practice to decompose the perturbations, and their related objects and equations, in terms of scalar, vector and tensor harmonics on the sphere. That was the procedure used in the seminal work on perturbations around spherical matched background configurations, due to Gerlach and Sengupta (GS) in [23] and [24], revisited and improved by Mart'ın-Garc'ıa and Gundlach in [43]. The aim in [38] was to use an alternative method, based on the Hodge decomposition on the sphere in terms of scalars, in order to avoid the need to deal with infinite series of objects. In particular, the whole set of matching conditions for the linearized EinsteinStraus model was presented in [38] as a finite number of equations involving scalars that depend on the three coordinates in the matching hypersurface Ω 0 , in contrast with an infinite number of equations for an infinite set of functions of one variable. It is clear that one can always go from the Hodge scalars to the spherical harmonics decomposition in a straightforward way. However, it is not always easy to rewrite the infinite number of expressions appearing in a spectral decomposition in terms of Hodge scalars. Consider the round unit metric Ω AB dx A dx B = dϑ 2 +sin 2 ϑdϕ 2 , with η AB and D A denoting the corresponding volume form and covariant derivative respectively, and ( glyph[star]dG ) A = η C A D C G the Hodge dual with respect to Ω AB . Let us recall that the usual Hodge decomposition on ( S 2 , Ω AB ) states that any one-form V A can be canonically decomposed as V A = D A F +( glyph[star]dG ) A , where F and G are functions on S 2 , and any symmetric tensor T AB as T AB = D A U B + D B U A + H Ω AB , for some U A on S 2 , which can be in turn decomposed in terms of scalars. Based on this, it is convenient to define the following two functionals. Given three scalars X tr , X 1 and X 2 on ( S 2 , Ω AB ) we define the functional one form V A ( X 1 , X 2 ) as and the functional symmetric tensor T AB ( X tr , X 1 , X 2 ) as Let us recall that the decomposition defines these X 's on S 2 up to the kernels of the operators V A and T AB . We allowed for the appearance of all these kernels in [38], where their relevance (or their lack of) was already discussed. In order to avoid spurious information and present a more concise review -and also to ease the translation and comparison with the quantities used in the previous literature in terms of the harmonic decompositions,we use the reformulation already presented in [39] where the Hodge decomposition is, in fact, unique. Indeed, in order to fix the Hodge decomposition uniquely we define a canonical dual decomposition by demanding that the functions X 1 , X 2 in V A ( X 1 , X 2 ) are always orthogonal (in the L 2 sense on S 2 ) to 1, and the functions X 1 , X 2 in T AB ( X tr , X 1 , X 2 ) are orthogonal to 1 and to the l = 1 spherical harmonics. Schematically, we may use and We will use the following notation: given any function f on S 2 we define so that f -f || 0 is orthogonal to the l = 0 harmonics Y 0 and f -f || 1 is orthogonal to the l = 1 harmonics Y m 1 . Note finally that the Hodge decomposition in terms of scalars involves two types of objects depending on their behaviour under reflection on the sphere. The scalars with subscripts 1 and tr remain unchanged under reflection, and are typically called longitudinal, even or polar quantities, while those with subscripts 2 change, and correspond to the transversal, odd or axial quantities. Let us consider now the general spherically symmetric spacetime V = M 2 × S 2 with metric g αβ = ω IJ ⊕ r 2 Ω AB , so that ( M 2 , ω IJ ) is a 2-dim Lorentzian space and r > 0 a function on M 2 . The dual in ( M 2 , ω IJ ) will be indicated by ∗ and the covariant derivative by ∇ . We can now proceed to decompose any one-form (vector) or symmetric two-tensor on V by first taking the part orthogonal to the sphere and then apply the Hodge canonical decomposition to the part tangent to the sphere. In particular, given a normalized timelike one-form u α orthogonal to the spheres, its corresponding one-form u I on ( M 2 , ω IJ ) (defined by u α = ( u I , 0)) can be used to construct a convenient orthonormal basis { u I , m I } so that ω IJ = -u I u J + m I m J (this is u I u I = -1 and m I := ∗ u I ), and consider then the one-form on V defined by m α := ( m I , 0). Given any vector V I we will simply denote by V u and V m the contractions u I V I and m I V I respectively. We apply now this decomposition to encode the objects that will describe the (first order) perturbation of a background consisting of two spherically symmetric regions ( W + , g (0)+ ) and ( W -, g (0) -) matched across corresponding spherically symmetric boundaries Ω + 0 and Ω -0 . At each side ± (we avoid the use of ± just now for clarity) the metric perturbation tensor g (1) αβ gets thus decomposed as where Z I 1 and Z I 2 are two one-forms defined on M 2 , and analogously for any symmetric tensor. The deformation vector Z α , defined on M at points on Ω, is decomposed as whereby the part Z I gets decomposed, in turn, onto the normal and tangential parts to Ω 0 , Q and T respectively. Given the (first order) perturbation tensor and the deformation vector at either ± side of the matching hypersurface, one can calculate the symmetric tensors q (1) ij and K (1) ij , i.e. the 'perturbed first and second fundamental forms', using (17)-(18). Recalling now that q (1) ij and K (1) ij are defined on (Ω 0 , q (0) ij ) and that Ω 0 at either side are tangent to the spheres { θ, φ } , let us denote by λ the parameter that follows the direction on Ω 0 orthogonal to the spheres in order to decompose q (1) ij and K (1) ij into q (1) λλ , K (1) λλ , plus and Note that all these functions are scalars on the sphere that depend only on λ . The first order matching conditions (19) are therefore equivalent to Except for the simplification of the kernels by the canonical decomposition, these are the linearized matching conditions presented in [38].","pages":[18,19,20]},{"title":"6.1 Gerlach and Sengupta (GS) 2+2 formalism","content":"Let us emphasize again that the conditions (19), and thus (23), concern quantities defined on Ω 0 and are therefore independent on the coordinates used in W + and W -for their computation. These quantities are thus, on the one hand, spacetime gauge independent by construction. Moreover, as discussed in Section 5, the equations are also hypersurface gauge independent. All this makes it unnecessary the use of gauge invariant quantities in order to establish the perturbed matching conditions. Having said that, however, the use of gauge independent quantities turns out to be convenient in the end, mostly when one eventually wants to impose the Einstein field equations. As shown in the works [23], [24], [43], the use of spacetime gauge invariants is very convenient in order to combine the Einstein field equations with the perturbed matching conditions. One can proceed by constructing gauge invariants in terms of Hodge scalars using analogous expressions to those in the harmonic decomposition constructed in [24, 23, 43]. Let us now concentrate on the odd (axial) sector. The odd gauge invariant quantities are encoded in the vector [36] (cf. [24]) Note that K I , as defined above, contains l = 1 harmonics, from Z I 2 , but only the l ≥ 2 sector is gauge invariant. In other words, the part of K I orthogonal to Y 1 (i.e. K I -K I || 1 in the notation above) is the gauge invariant part. Once the orthonormal basis { u I , m I } has been identified at both sides, the odd sector of the linearized matching, which corresponds to the set of equations in (23), is equivalent in the l ≥ 2 sector (the part orthogonal to l = 0 and l = 1) to [36] (cf. [24]) plus an equation for T + 2 -T -2 .","pages":[20,21]},{"title":"7 Linearized Einstein-Straus model: matching conditions","content":"We are ready to consider the linearized matching of the perturbed Schwarzschild and FLRW spacetimes, as it was analyzed in [38]. Take the Einstein-Straus model as described in Section 2: the FLRW geometry in cosmic time coordinates (1), the Schwarzschild in standard coordinates (2), and the background matching hypersurface Ω 0 described by Ω RW 0 : { t = t, R = R 0 } and Ω ST 0 : { T = T 0 ( t ) , r = r 0 ( t ) } respectively, where T 0 ( t ) and r 0 ( t ) satisfy (3) and the angular part is again ignored. The orthonormal basis we take on the Lorentzian space orthogonal to the spheres is formed by u = dt , m = adR . Note that this choice corresponds to the tangent and normal forms to Ω 0 at Ω 0 , respectively. More precisely, m is chosen to be n (0) at points on Ω 0 . On the Schwarzschild side we have u | Ω 0 = ˙ T 0 ∂ T + ˙ r 0 ∂ r and m | Ω 0 := n (0) = -˙ r 0 dT + ˙ T 0 dr . Take the first order perturbations of FLRW, in no specific gauge, formally decomposed into the usual scalar, vector and tensor (SVT) modes, i.e. 4 (Latin indices a, b, c are used for tensors on ( M , g M )) with satisfying the constraints The canonical Hodge decomposition is then used to encode the part tangent to the spheres into S 2 scalars in the following schematic way [38]: vector All in all, encoding g (1)+ using the SVT modes together with the Hodge decomposition leaves us with 15 SVT-Hodge quantities, corresponding to the scalar modes { Ψ , Φ , W, χ } , vector modes { ˜ W R , W 1 , W 2 , Y R , Y 1 , Y 2 } and tensor modes {Q 1 , Q 2 , H , U 1 , U 2 } , all scalars on S 2 , not all independent due to the previous constraints, and, on the other hand, not unique . Consider, in particular, the only 4 scalars we have in the odd sector; vector modes {W 2 , Y 2 } and tensor modes {Q 2 , U 2 } . As discussed in the previous section, only two gauge invariant quantities exist in the odd sector. These correspond to the two components of the gauge invariant odd vector (and for l ≥ 2), K + I , which given the above construction in terms of the SVT-Hodge quantities, read [39, 36] Consider now the stationary and axially symmetric vacuum perturbations in the Weyl gauge. They can be described in terms of two functions U (1) ( r, θ ) and A (1) ( r, θ ), which correspond, basically, to the perturbation of the gravitational Newtonian potential and the rotational perturbation, respectively. The perturbation tensor reads [38] Note that, when using the full set of the Einstein field equations for vacuum, the function k (1) is determined up to quadratures once U (1) ( r, θ ) and A (1) ( r, θ ) are found. We stress, however, that the vacuum equations, although indicated, were not imposed in the perturbed Schwarzschild region (nor in the perturbed FLRW region) in [38], and therefore the results found there are purely geometric. Instead of working with A (1) ( r, θ ), it is convenient to use an auxiliary function, G , defined by A (1) := sin θ∂ θ G . In terms of the Hodge decomposition of the perturbation tensor (20), applied to (26), we have G = -( 1 -2 M r ) -1 Z -T 2 . Another auxiliary function P can be introduced for k (1) . The whole set of matching conditions (23) for the linearized Einstein-Straus model, both in the odd and even sectors, were found in [38] in terms of these functions U (1) ( r, θ ) , G tensor and P in the Schwarzschild side together with the above 15 SVT-Hodge scalars describing the FLRW perturbation. The whole set is too long to be included here, but in order to review the main results in [38] only the odd sector of the linearized matching is needed. The odd sector of the linearized matching (24) projected to the part orthogonal to the l = 0 and l = 1 harmonics can be rewritten as the following three relations [38] plus an equation for the difference T RW 2 -T Sch 2 . The three equations above can be shown [36] to correspond indeed to (25), taking into account that K Sch = -( 1 -2 M r ) G dT . These equations were presented in [38] in full, including the parts lying on the l = 0 and l = 1 harmonics. There, a series of kernels inherent to the usual Hodge decomposition where the responsible for the usual freedom found in the l = 0 and l = 1 sectors when using harmonic decompositions. By using the canonical Hodge decomposition introduced in Section 6, we can have a better control of that freedom, and understand its nature, getting rid of the spurious terms. Indeed, by doing that it can be shown [36] that the projection of the linearized matching on the l = 1 harmonics -on the l = 0 it is trivial, since all scalars in the odd sector are orthogonal to l = 0- gives while ( T RW 2 -T Sch 2 ) || 1 is free. The first consequence of the above equations is that if the FLRW remains unperturbed then the stationary region must be static in the range of variation of r 0 ( t ): equations (27)-(29) imply that the part of G orthogonal to l = 1 vanishes, and (30) implies that G || 1 = Ca 3 / (2 M -a Σ c ) , where C is a constant. Therefore G = Ca 3 / (2 M -a Σ c ) cos θ , and thus 5 As shown in [38], this implies that the perturbed spacetime is static in the range of variation of r 0 ( t ). This result generalizes that in [52] because now the matching hypersurface does not necessarily keep the axial symmetry. Therefore, the only way of having a stationary and axisymmetric vacuum arbitrarily shaped (at the linear level) region in FLRW is to have the Einstein-Straus model. Let us remark again that by the interior/exterior duality, this result also implies that a piece of FLRW, irrespective of its shape and its relative rotation with the exterior, cannot describe the interior of Kerr.","pages":[21,22,23]},{"title":"7.1 Constraint on FLRW","content":"Another interesting consequence of the matching conditions is that the combination of (27) and (28) produces one equation that involves only quantities in FLRW [38] and thus constitutes a constraint in FLRW. Recalling that this equation is meant to be orthogonal to l = 1 (and vanishes identically if projected on l = 0), this constraint implies that if the perturbed FLRW contains vector modes with l ≥ 2 harmonics on Ω 0 , then it must contain also tensor modes there. Since, as we have just seen above, the existence of a rotation in the stationary region implies the existence of, at least, vector perturbations in FLRW, then both vector and tensor modes must exist on Ω 0 . It must be stressed that, as demonstrated in [5] (and references therein), there exist configurations of FLRW linear perturbations containing only vector perturbations which vanish identically inside a spherical surface. Such configurations are compatible with the results reviewed here, since that interior region is FLRW and the above constraints do not apply. A completely different matter is the embedding of a Schwarzschild spherical cavity (or a vacuum perturbation thereof) into any such model: the Schwarzschild cavity cannot reach the perturbed FLRW region, as otherwise the constraints above would require that tensor perturbations are also present (at least near the boundary of the Schwarzschild cavity). There also exists a Einstein-Straus perturbative model by Chamorro [18] consisting on small rotation Kerr vacuole within a perturbed FLRW. Again, the constraint above does not apply to this model because there are no l ≥ 2 modes there. The fact that tensor modes must exist near Ω 0 once some rotation with l ≥ 2, whatever small, exists in the stationary region, may indicate the existence of some kind of gravitational waves on FLRW near Ω 0 . In order to analyze further this issue one needs to take the Einstein field equations into consideration. That is the purpose of our work in preparation [36], some result of which will appear in the proceedings of the ERE2012 meeting.","pages":[24]},{"title":"8 Conclusions and outlook","content":"This paper is concerned with the difficulties that the Einstein-Straus model encounters. A fundamental one refers to its high level of rigidity and the impossible generalization to non-spherical symmetry if the bound system is required to be time independent so as to retain the property that cosmic expansion does not affect the local systems. Moreover, if one views the model within the LTB class with a step function density profile, the model is unstable to perturbations [57], [32], cf. also the discussion in [30]. The rigidity result so far requires either stationarity and axial symmetry or staticity. An interesting open problem would be to relax the conditions and assume only stationarity. Despite these difficulties, the Einstein-Straus model has played and plays a very important role in cosmology in different areas or research, most notably on the influence (or lack thereof) of the cosmic expansion on local systems, or in the problem of averaging in cosmology at least on an observational level (see e.g. [20]). The model is still widely used as textbook explanation of the lack of influence of the cosmic expansion on astrophysical systems and, in fact, there are not many known alternatives (a notable exception is the McVittie model [44], [28], [29] which is also spherically symmetric and mimics the geometry of Schwarzschild at small scales while approaching a FLRW model at long distances, and which has been studied thoroughly, see [15] and references therein). Concerning the use of the Einstein-Straus model on observational cosmology, mainly by studying lensing effects, its generalizations have systematically consisted in keeping spherical symmetry and allowing for some dynamics in the interior. The prominent example here consists of LTB regions inside a FLRW universe (see references in [20]). An important ingredient for the rigidity of the Einstein-Straus model is the large symmetry of the FLRW background. It is therefore an interesting problem to analyze how the model gets modified in the presence of cosmic perturbations. In a conservative approach, one still wants to keep the main properties (stationarity of a region inside a cosmological model) as far as possible and analyze the possible departures from the model in more realistic situations. Moreover, by studying perturbed Einstein-Straus models one seeks going beyond the problem of the influence of cosmic expansion on local systems, and tackle the problem of the influence of general cosmic dynamics. Surprisingly, it turns out that the existence of static (stationary) regions does impose conditions on the cosmic perturbations, at least near the boundary. Whether this is a real effect or simply an indication that the interior region should not be kept stationary remains to be seen. Another implication of the perturbed Einstein-Straus model is that extra care is required in the standard decomposition of metric perturbations in terms of scalar, vector and tensor modes. As discussed above, any rotation in the vacuole implies necessarily the presence of both vector and tensor modes in the cosmic perturbations. It is interesting to analyze whether these tensor modes could represent cosmic gravitational waves. Some preliminary results along these lines have already been presented in [39]. A detailed and more complete approach will appear elsewhere. Another interesting future line of research is to allow for non-stationary perturbations in the vacuole and study the transmission of gravitational waves from the cosmic region to the bound system.","pages":[24,25]},{"title":"9 Acknowledgements","content":"MM acknowledges financial support under the projects FIS2012-30926 (MICINN) and P09-FQM-4496 (J. Andaluc'ıa-FEDER). FM thanks the warm hospitality from Instituto de F'ısica, UERJ, Rio de Janeiro, Brasil, projects PTDC/MAT/108921/2008 and CERN/FP/123609/2011 from Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT), as well as CMAT, Univ. Minho, for support through FEDER funds Programa Operacional Factores de Competitividade (COMPETE) and Portuguese Funds from FCT within the project PEst-C/MAT/UI0013/2011. RV thanks the kind hospitality from the Universidad de Salamanca, where parts of this work have been produced, and financial support from project IT592-13 of the Basque Government, and FIS2010-15492 from the MICINN.","pages":[25]}],"string":"[\n {\n \"title\": \"Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results\",\n \"content\": \"Marc Mars ∗ , Filipe C. Mena † and Ra¨ul Vera ‡ ∗ Instituto de F´ısica Fundamental y Matem´aticas, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca, Spain † Centro de Matem´atica, Universidade do Minho, 4710-057 Braga, Portugal ‡ Dept. of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 644 PK, Bilbao 48080, Basque Country, Spain\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Abstract\",\n \"content\": \"The Einstein-Straus model consists of a Schwarzschild spherical vacuole in a Friedman-Lemaˆıtre-Robertson-Walker (FLRW) dust spacetime (with or without Λ). It constitutes the most widely accepted model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model is that there is no influence from the cosmic background, since the spherical vacuole is static. Spherical generalizations to other interior matter models are commonly used in the construction of lumpy inhomogeneous cosmological models. On the other hand, the model has proven to be reluctant to admit non-spherical generalizations. In this review, we summarize the known uniqueness results for this model. These seem to indicate that the only reasonable and realistic nonspherical deformations of the Einstein-Straus model require perturbing the FLRW background. We review results about linear perturbations of the Einstein-Straus model, where the perturbations in the vacuole are assumed to be stationary and axially symmetric so as to describe regions (voids in particular) in which the matter has reached an equilibrium regime.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1 Introduction\",\n \"content\": \"During a meal in the 19th Jena Meeting on Relativity, in September 1996, Bill Bonnor provocatively asked Jos'e Senovilla if the table could be expanding with the Universe. Not surprisingly, Bonnor later took the question seriously and wrote a paper about how the hydrogen atom is affected by the cosmic expansion [11], which is well worth reading. About five decades before, Einstein and Straus asked a similar question, on a bigger scale, which led them to investigate the influence of the expansion of space on the gravitational fields surrounding individual stars [19]. They took the Schwarzschild solution representing the vacuole surrounding a star located in the centre and the FriedmanLemaitre-Robertson-Walker (FLRW) solution as the cosmological model. At the core of their model was the matching of the two solutions across a spherical surface with constant cosmological radius. Since the expansion kept the vacuole symmetry and time independence, their conclusion was that it does not affect the gravitational fields surrounding stars and, in particular, it does not affect the solar system dynamics. A previous attempt to address the issue of whether the planetary orbits expand with the Universe was made by McVittie [44] who found a smooth model describing a spherically symmetric mass embedded in a flat FLRW. Since then the research about this problem was scarce, although some alternatives to the McVittie model were suggested, e.g. in [22], and difficulties of the global meaning of the model were also pointed out [48, 49, 50, 51] (see also [15]). Concerning the Einstein-Straus model itself, it was revisited in [2, 8] and stability issues were raised in [57], [32] cf. also the discussion in [30]. However, the Einstein-Straus model has never stopped being considered as the correct answer to the lack of influence of the cosmological expansion on local systems. Moreover, since the vacuole can be inserted anywhere due to the homogeneity of FLRW, the Einstein-Straus model led to the original Swiss cheese model of a lumpy inhomogeneous universe (see e.g. [20]). Bonnor's question, that 1996 afternoon, raised a totally new issue for the EinsteinStraus models, namely whether spherical symmetry was a crucial ingredient of the model and, therefore, for the existence of time-invariant bounded systems embedded in a FLRW universe. Indeed, the question triggered research by Senovilla and Vera [59], that led to the result about the impossibility of the Einstein-Straus model in cylindrical symmetry. In turn, this important result was the origin of over fifteen years of research about the rigidity, in the sense of uniqueness, of the model. The aim of this paper is to review these results on rigidity both for exact models and from a perturbative perspective. Crucial to this endeavour was the development of a general mathematical theory of spacetime matching [41] and of its perturbative version [4, 47, 35]. This allowed to achieve quite general results about the possibility of generalizing both the shape of the cavity and the cosmological setting of the original Einstein-Straus model. As an example, described below in some detail, uniqueness of the static Λ-vacuum spherical region embedded in a non-static FLRW cosmological model has been proved [34]. The scope of the Einstein-Straus model has been taken well beyond both the physical scale originally considered and the physical problems for which the model was conceived. In fact, the model has been used not only at the solar system scale, but also on galaxy [27] and galaxy clusters' scales [27, 54]. On the other hand, the vacuole of the (original) Einstein-Straus model has been replaced by other spherically symmetric geometries, generally Lemaˆıtre-Tolman-Bondi (LTB), also spherically shaped regions of Szekeres, in order to construct 'generalized' Einstein-Straus models for describing extra-galactic scale and cosmic voids (we refer to the reviews in [30, 20]). Lumpy inhomogeneous cosmological models based on the generalized Einstein-Straus Swiss cheese models are being used in the search of possible explanations to the accelerated expansion of the Universe by the study of lensing effects at cosmic scales produced by the voids (see e.g. [20]). So far, all these generalized Einstein-Straus (and the corresponding Swiss cheese) models have assumed spherically shaped inhomogeneities (voids). One of themes of the research we will review here is how far can one push the Einstein-Straus model towards non-spherical generalizations. The fundamental ingredient we want to keep is that the bound system remains stationary, so as to keep the absence of influence of the cosmic dynamics on astrophysical scales. We will use the term Einstein-Straus problem to the problem of finding the most general stationary regions (vacuum or not) one can embed in a realistic cosmological model in a broad sense. The Einstein-Straus model has also been taken beyond the exact solutions' settings to include metric perturbations. Perturbation theory in General Relativity (GR) is a natural framework to study small departures from symmetric configurations and thus to perform stability analysis. For instance, it allows to include simultaneously density, rotational and gravitational wave perturbation modes into an, otherwise, spatially homogeneous and isotropic cosmological model. Most interestingly, it allows a priori to perturb independently the interior and exterior spacetimes as well as the matching boundary. Furthermore, although the three perturbation modes are decoupled on a FLRW background, they may couple at a matching boundary. In this context, an important question is how general can the perturbations be in each model. Inherent to perturbation theory is the issue of gauge freedom. In perturbed spacetime matchings, this can be complicated by the fact that three independent perturbation gauges may be in use. For the sake of completeness, we include a short review of linearized matching, where these issues are discussed, see also [47] for further details, including the definition of the so-called doubly gauge invariant variables . Perturbations in the FLRW background are customarily split in scalar, vector and tensor modes, and the later are generically viewed as cosmological gravitational waves. Given that the gravitational wave detectors are already active, and gravitational waves are expected to be detected within the next five years (see e.g. [6, 55] for recent accounts and the review [56]), it would be interesting to investigate their inclusion in the models. One now certainly has the necessary mathematical machinery to do so, and preliminary results indicate the possibility of having, for instance, a stationary axially symmetric vacuole embedded in an expanding cosmological model containing tensor modes [38]. Even more, the linearized matching links the rotational and tensor modes degrees of freedom in the perturbation variables [38]. This is therefore an interesting timing to revise the state-of-the-art and point out potentially interesting directions of research about the Einstein-Straus problem, in the sense pointed out above. The plan of the review is the following. In Section 2, the Einstein-Straus model is briefly presented. Similar summaries with different degrees of detail can be found in many places in the literature, see e.g. [20]. We include it here for the sake of completeness and in order to fix our notation. Section 3 is devoted to describing in some detail the uniqueness results concerning both general static regions and stationary and axisymmetric regions (irrespective of any symmetry consideration and/or matter content) embeddable in a FLRW expanding cosmology. Section 3.1 is devoted to the static case. The main conclusion here is that the only static vacuum region that can be embedded to an expanding FLRW is a spherically shaped region of Schwarzschild (i.e. the Einstein-Straus model). Similar uniqueness results hold for other matter models, such as vacuum with cosmological constant. Section 3.2 deals, in turn, with the uniqueness results for stationary and axially symmetric regions in FLRW expanding universes. The main result is that the stationary region must, in fact, be static, so that the previous conclusions on static regions apply. The uniqueness result thus states that the only way of having a stationary and axially symmetric or static region in an expanding FLRW is the Einstein-Straus model. Following the uniqueness results, the robustness of the Einstein-Straus model is further analyzed by considering alternative exact cosmological models. In Section 4 the replacement of the FLRW region by more general anisotropic cosmologies, i.e. the Bianchi models, is studied for static locally cylindrically symmetric interiors, leading to severe restrictions and no-go results for reasonable evolving cosmologies. The final part of the paper is devoted to the generalization of the Einstein-Straus model from a perturbative perspective. After a brief overview of perturbative matching theory in Section 5, and the use of the Hodge decomposition on the sphere instead of the usual spherical harmonic decomposition in Section 6, the linearized matching between stationary and axisymmetric perturbations of Schwarzschild and general perturbed FLRW is reviewed in Section 7. We finish with some conclusions in Section 8, pointing out some ongoing research, prospects for future work on the perturbed Einstein-Straus model and its possible implications on the relationship between astrophysical bounded systems and cosmological dynamics in the form of cosmic gravitational waves.\",\n \"pages\": [\n 1,\n 2,\n 3,\n 4\n ]\n },\n {\n \"title\": \"2 The Einstein-Straus model\",\n \"content\": \"This model consists of a spherically symmetric (both in shape and intrinsic geometry) Ricci-flat region embedded in a FLRW universe without cosmological constant. Recall that two spacetimes can be matched across their boundary if and only if the first fundamental forms q and second fundamental forms K agree on the matching hypersurface. A consequence of this are the well-known Israel conditions, which restrict the jump of the energy-momentum tensor across the boundary. In the present context, they imply that the cosmological fluid must be dust and the vacuole must be comoving with the cosmological fluid. Writing the FLRW metric in cosmic time coordinates where glyph[epsilon1] = {-1 , 0 , +1 } , Σ ' 2 = 1 -glyph[epsilon1] Σ 2 with prime denoting derivative with respect to R , in units G = c = 1 the Friedman equation reads where the dot denotes derivative with respect to t and ρ 0 is a constant such that the cosmological energy-density ρ satisfies ρ = ρ 0 /a 3 . The boundary of the vacuole can be parametrized by { t = t, R = R 0 } (we ignore the angular variables as they behave trivially, and use t both as spacetime coordinate and intrinsic coordinate on the hypersurface, the precise meaning will be clear from the context). For the matching one needs the induced metric q RW and the second fundamental form K RW . Using the outward unit normal n RW = a ( t ) dR these objects read, with Σ c := Σ | R = R 0 , and Σ ' c := Σ ' | R = R 0 , From Birkhoff's theorem, the geometry of the vacuole is Kruskal. Assuming that the boundary is away from the Schwarzschild horizon (this happens sufficiently away from the big bang or big crunch) the interior metric can be written in Schwarzschild coordinates The boundary can be parametrized as { T = T 0 ( t ) , r = r 0 ( t ) } and, given the time inversion symmetry of Schwarzschild, we can assume ˙ T 0 > 0 without loss of generality. The induced metric on the boundary is Using the unit normal n Sch = 1 N ( ˙ T 0 dr -˙ r 0 dT ) (note that the global sign of N is kept free at this stage), the second fundamental form is Equality of the t -component of the induced metric requires N 2 = 1. Then, equality of the angular parts of the first and second fundamental forms imposes N = 1 and A straightforward computation shows that the equality of the t -component of the induced metric and second fundamental forms are satisfied provided the values of ρ 0 and m are linked by which has a clear interpretation in terms of (Misner-Sharp)-mass conservation. This is the Einstein-Straus model [19]. A natural generalization consists in adding a cosmological constant Λ both to the FLRW and to the interior part (originally considered in [25] and fully solved in [2]). The Israel matching conditions on the energy-momentum tensor now impose the FLRW matter model to be dust with Λ, so that the Friedman equation is now By Birkhoff's theorem, the interior metric is the Kottler solution (also known as 'Schwarzschild(anti) de Sitter'), which away from the horizons is In this case, the matching conditions are We emphasize that any matching of two spacetimes immediately leads to a complementary matching, at least locally, where the 'interior' and 'exterior' regions on each spacetime reverse their roles (see [21] for details). In the matching above, this leads to the Oppenheimer-Snyder collapse model [53].\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"3 Rigidity of the Einstein-Straus model\",\n \"content\": \"The Einstein-Straus model is such that, for a given total mass inside the vacuole and a given energy density in the cosmological background, the radius of the static region is uniquely fixed. This already poses difficulties for the model since it is often the case that the size of the vacuole does not match the observed sizes of clustered matter in the universe, such as stars or galaxies. This fact indicates that the Einstein-Straus model may be lacking flexibility to accommodate the various situations present in cosmology (cf. [58] and [10]). In fact, the Einstein-Straus vacuole was found to be radially unstable in a certain sense [30]. The other main restriction of the model is its exact spherical symmetry. It is clear that vacuoles in the universe are not exactly spherically symmetric so a natural question is how robust is the model to non-spherical generalizations. The first thing to consider is which fundamental ingredients of the model should be kept. The main motivation of the Einstein-Straus model was its ability to combine cosmological expansion at large scales with no observable effects on the local physics. Thus, the fundamental ingredient to keep is the absence of influence of the cosmic expansion inside the region. The simplest and most natural way to achieve this is imposing that the interior geometry is stationary, because then no dynamical effects whatsoever from the surrounding evolving cosmology would affect the local physics. Among stationary interiors, the simplest case corresponds to static situations, so it is natural to start with this case (note that the Einstein-Straus model is itself static). The question is then how rigid or flexible is the possibility of having stationary/static regions embedded in an otherwise expanding FLRW universe. Ideally, one would like to make no further assumptions and find the most general model with these properties. The matter model inside may also be kept arbitrary, and see what are the possibilities allowed by the coexistence of a stationary/static region inside an expanding FLRW universe. This coexistence has been sometimes called the Einstein-Straus problem in the literature (see e.g. [2]). The first indication that the Einstein-Straus model might be very rigid came from a seminal work by Senovilla and Vera [59] who considered the possibility of matching a static and cylindrically symmetric region (with no restriction on the matter model) with a FLRW dynamical cosmology. The matching hypersurface was taken to be locally a cylinder, in the sense of being tangent in an open set to the two (commuting) generators of two spatial local isometries. No global consideration was needed. The result was a no-go theorem: no such model exists. With the impossibility of generalizing the Einstein-Straus model to a cylindrical setting, it became of interest to study the problem in as much generality as possible. The static case was treated in complete generality in [33], [34] and it is by now well-understood. The more complicated stationary situation has been studied [52] under the additional assumptions of axisymmetry and a group action orthogonally transitive. The motivation to study this simplified problem lies in the fact that one expects equilibrium configurations to also exhibit an axial symmetry. It is worth to mention that one step in the black hole uniqueness theorems corresponds to showing that the domain of outer communications must be axially symmetric [26]. We devote the following Section 3.1 to describing the main results in the static setting, and Section 3.2 to review the uniqueness results in the stationary and axially symmetric setting.\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"3.1 Uniqueness results in the static case\",\n \"content\": \"This case was first considered in [33] under the additional assumption of axial symmetry, and one extra technical assumption relating cosmic and static times on the matching hypersurfaces. Both assumptions were dropped in [34] where a satisfactory uniqueness result for static region in FLRW was obtained. The setup consists on a spacetime ( V , g ) composed by two regions ( W ST , g ST ) and ( W RW , g RW ) matched in absence of surface layers across their boundaries, denoted by Ω ST and Ω RW respectively, which once identified conform to a hypersurface Ω in ( V , g ). The region ( W ST , g ST ) is strictly static, i.e. admits a Killing vector ξ which is timelike and orthogonal to hypersurfaces everywhere. ( W RW , g RW ) is a codimension-zero submanifold with smooth boundary Ω RW of the FLRW spacetime ( V RW , g RW ), by which we mean the manifold V RW = I ×M , where I ⊂ R is an open interval, M is either E 3 ( glyph[epsilon1] = 0), S 3 ( glyph[epsilon1] = 1) or H 3 ( glyph[epsilon1] = -1) and the FLRW metric g RW takes the form (1). We call any coordinate system { R,θ, φ } in which the metric takes this form a spherical coordinate system . Note that since ( M , g M ) is homogeneous, there exist spherical coordinate systems centered at any point p ∈ M , and this will be used below. The function a ( t ) is positive and smooth (in fact C 3 suffices). We assume that ˙ a does not vanish on any open set (this excludes uninteresting situations where the FRLW does not evolve). Define the 'geometric' energy-density ρ RW and pressure p RW by glyph[negationslash] so that, if the spacetime has a cosmological constant Λ, the energy-density and pressure of the cosmic fluid is ρ = ρ RW -Λ 8 π , p = p RW + Λ 8 π . We make the assumption that ρ RW + p RW = 0 so that we do have a non-trivial cosmic fluid (this allows us to define t unambiguously). Concerning the boundary Ω RW it is assumed to be connected (this is irrelevant because the matching conditions are local, the assumption is made merely for notational convenience), and nowhere tangential to a hypersurface of constant cosmic time t . This assumption is physically reasonable and automatically satisfied if the boundary is causal. In fact, dropping this assumption would only make the presentation more involved, but would not spoil any of the results (see [34] for a discussion). Finally, we assume that Ω RW is spatially compact. A sufficient condition for this is the 'energy condition' ρ RW ≥ 0, see [33], and this is in fact the assumption made in [33]. However, it can be proved that spatial compactness suffices for the validity of all the results below. Note finally, that spatial compactness is indeed an assumption: allowing for non-compact boundaries, additional configurations not covered by the uniqueness results do arise, as shown in [45] (see also references therein), where configurations with planar and hyperbolic symmetries were found and analized. It would be interesting to analyze how far can one extend uniqueness without any compactness assumption on the boundary. Nevertheless, for the purposes of the Einstein-Straus problem, compactness is a completely natural assumption, as we want the local physics unaffected by the cosmological expansion be spatially confined. By a detailed analysis of the matching conditions, the following restrictions on the boundary Ω RW are obtained [34]. First of all, the intersection S RW t of Ω RW with a hypersurface of constant cosmic time t is a sphere. More precisely, for any t ∈ I , there exists a point c ( t ) ∈ M so that S RW t is a coordinate sphere of radius R ( t ) in a spherical coordinate system centered at c ( t ). The radius R ( t ) is restricted to satisfy the bound This inequality means that the surface S RW t is non-trapped (i.e. has a mean curvature vector spacelike everywhere). The necessity of this condition can be understood from the fact that no closed spacelike surface in a static spacetime can have a future (or past) causal and not-identically zero mean curvature vector [42]. The spherical symmetry of the surface S RW t and the fact that the matching conditions force the mean curvature vector to be continuous across the matching hypersurface implies that S RW t must be nontrapped, which is precisely (5). Note also that if the static Killing vector ξ admits Killing horizons and hence changes causal character, then the bound (5) is no longer necessary. This behaviour occurs in the Einstein-Straus model when a ( t ) is sufficiently small so that Σ c a ( t ) = 2 m . The breakdown of the ODE (3) in the Einstein-Straus model is just a manifestation of the breakdown of the the static coordinate system in the interior region. In Kruskal coordinates, the matching would continue across Σ c a ( t ) = 2 m without problem. Something similar would occur in the general setting if we allowed the static Killing to change causal character. Returning to the shape of Ω RW , the center point c ( t ) follows a geodesic in ( M , g M ) (which may degenerate to a point). The parameter t is not in general an affine parameter for the geodesic, so the center c ( t ) is a priori allowed to move at any speed (in fact the trajectory can have turning points along the curve). In order to describe the matching hypersurface, choose any point c 0 along this geodesic and let c ' 0 be its tangent vector. We can choose a spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 so that the axis of symmetry ˆ θ = 0 is along the tangent vector c ' 0 . In this coordinate system, the center c ( t ) will have coordinates (the value of ˆ θ can be 0 or π depending on whether c ( t ) lies after or before c 0 along the geodesic). The function σ ( t ) describes the motion of c ( t ) along the curve. The relationship between the spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 and a spherical coordinate system { R,θ, φ } centered at c ( t ) with parallel axis (i.e. with coincident lines | cos θ | = 1 and | cos ˆ θ | = 1) is easily found to be Thus, the matching hypersurface Ω RW in the spherical coordinates centered at c 0 can be parametrized by coordinates t, θ, φ as which is a rather complicated form for the matching hypersurface. A useful alternative is to use a coordinate system { t, R, θ, φ } in ( W RW , g RW ) such that, for each t , { R,θ, φ } is the spherical coordinate system centered at c ( t ). Applying the coordinate transformation (6) to the metric gives where f ( t ) = ˙ σ ( t ). The explicit calculation leading to (7) is somewhat long, a much more elegant method of obtaining this form of the metric is discussed in the Appendix of [34]. In these coordinates, the matching hypersurface Ω RW is simply { R = R ( t ) } . The matching conditions in the FLRW part are supplemented with a differential equation relating the trajectory of the center σ ( t ) with the radius R ( t ). To write it down, define a function β ( t ) via where glyph[epsilon1] 1 = ± 1 depending on whether the FLRW region to be matched is R > R ( t ) or R < R ( t ) (more specifically, the manifold with boundary W RW is { glyph[epsilon1] 1 R ≥ glyph[epsilon1] 1 R ( t ) } ). Note that β ( t ) is well-defined because of (5). The ODE relating R ( t ) and σ ( t ) is conveniently written using an auxiliary function ∆( t ) = 0 as the following pair of differential equations glyph[negationslash] In summary, the static domain embedded in the FLRW regions consists of a sphere with time dependent radius R ( t ) and with center moving across the FLRW spacetime along a geodesic. Speed along the geodesic and radius R ( t ) are linked by (9). The model is not spherically symmetric because the center of the sphere is allowed to move. However, it is very close to spherically symmetric and it turns out that the center of the sphere must be at rest for several relevant matter models in the static domain, as we discuss next. An important consequence of the matching procedure (cf. Lemma 1 in [34]) is that the Killing vector field ξ is everywhere transverse to the matching hypersurface Ω ST in the static region. Combining this with the fact that the static geometry is invariant along ξ it follows that the static metric in the spacetime region obtained by dragging Ω ST with the static Killing vector can be fully determined in terms of hypersurface geometry of Ω ST . Since, in turn, the geometry on Ω ST is related to the geometry of Ω RW via the matching conditions, it follows that the spacetime geometry of the static region becomes completely determined [34] in a neighbourhood of its matching hypersurface in terms of the FLRW geometry and the functions R ( t ) , σ ( t ) and ∆( t ) (see Theorem 1 in [34] for details). Specifically, there exist coordinates { T, t, θ, φ } so that the metric g ST takes the form (note that t is a spacelike coordinate in the static domain) where µ := glyph[epsilon1]a ( t )( ˙ R ( t ) + f ( t ) cos θ ). The matching hypersurface Ω ST is defined by the embedding { t, θ, φ } → { T = T ( t ) , t, θ, φ } , where T ( t ) satisfies ˙ T ( t ) = ∆( t ) and the portion of the static spacetime to be matched to the exterior region is { T ≥ T ( t ) } . The metric (10) is foliated by round spheres { T = const , t = const } but it is not spherically symmetric in general (unless f ( t ) = 0 and R ( t ) = 0). To complete the picture, we review the energy-momentum tensor in the static part. Introduce two one-forms and one symmetric two-tensor h by The Einstein tensor of ( W ST , g ST ) is (cf. Proposition 1 in [34]) where ρ ST , p ST r and p ST t read and ρ RW and p RW were defined in (4). Several consequences of (11) can be drawn [33, 34]. Concerning the uniqueness of the Einstein-Straus model, under the assumption ρ ST + p ST = 0 (which includes vacuum with or without cosmological constant or a non-singular electromagnetic field) it follows that µ = 0 and hence f ( t ) = 0 and R ( t ) = 0. The second equation in (9) gives (with an appropriate but still completely general choice of integration constant), where (8) and the definitions of Σ c and Σ ' c in Section 2 have been used. The static metric simplifies to From this metric, uniqueness of the Einstein-Straus model as the unique static vacuum (with or without cosmological constant) region embedded in a FRLW cosmological model follows easily. So, static vacuoles in a FLRW model must be spherically symmetric both in shape and interior geometry. It is an open problem to analyze whether there are any physically realistic matter models in the interior static region for which the motion of the static domain inside FLRW has interesting properties. Note that a priori nothing prevents the geodesic c ( t ) from being spacelike, so the motion of the static domain can in principle be superluminal for the cosmic observers. This is of course reminiscent to the superluminal warp drive discovered by Alcubierre [1].\",\n \"pages\": [\n 6,\n 7,\n 8,\n 9,\n 10\n ]\n },\n {\n \"title\": \"3.2 Uniqueness results in the stationary and axisymmetric case\",\n \"content\": \"The study of axially symmetric equilibrium regions in FLRW universe was dealt with in [52], and, in short, the main result found was that those stationary regions must, in fact, be static, and therefore the results of the previous section apply. With the same definitions and assumptions concerning the FLRW region ( W RW , g RW ) and its boundary Ω RW as in the previous section, we assume now that the interior region ( W SX , g SX ) is (strictly) stationary and axisymmetric. More specifically, we demand that (i) the spacetime admits a two-dimensional group of isometries G 2 acting simply-transitively on timelike surfaces T 2 and containing a (spacelike) cyclic subgroup, so that G 2 = R × S 1 , and (ii) that the set of fixed points of the cyclic group is not empty. Consequences of the definition are that the G 2 group has to be Abelian [17, 14, 3], and that the set of fixed points must form a timelike two-surface [40], which is the axis. The axial Killing η is then intrinsically defined by normalizing it demanding ∂ α η 2 ∂ α η 2 / 4 η 2 → 1 at the axis. See also [61] and [13]. In addition, we demand that the isometry group is orthogonally transitively (OT), i.e. that the two planes orthogonal to the orbits of the isometry group are surface forming. This assumption is also known as the 'circularity condition', and in many cases of interest it follows as a consequence of the Einstein field equations. Indeed, the G 2 on T 2 group must act orthogonally transitively in a region that intersects the axis of symmetry whenever the Ricci tensor has an invariant 2-plane spanned by the tangents to the orbits of the G 2 on T 2 group [16]. By the Einstein field equations, this includes Λ-term type matter (i.e. vacuum with or without cosmological constant), perfect fluids without convective motions, and also stationary and axisymmetric electrovacuum [61]. An OT stationary and axisymmetric spacetime ( V SX , g SX ) is locally characterized by the existence of a coordinate system { T, Φ , x M } ( M,N,... = 2 , 3) in which the line-element for the metric g SX outside the axis reads [61] where U , A , W and g MN are functions of x M , the axial Killing vector field is given by η = ∂ Φ , and a timelike (future-pointing) Killing vector field is given by ξ = ∂ T . Although useful for the sake of clarity, the use of coordinates is not essential for the results below, which only depend on the intrinsic geometric properties of of ( W SX , g SX ). As before, no specific matter content is assumed in the stationary and axisymmetric region. Regarding the matching hypersurface Ω, besides those in the previous Section 3.1, we make the only extra assumption that it preserves the axial symmetry [62] of ( W SX , g SX ) and of ( W RW , g RW ). This means that Ω SX is assumed to be invariant under the axial symmetry of ( W SX , g SX ) and that there is an axial Killing vector η RW in the Killing algebra of ( W RW , g RW ) tangent to Ω RW . With these assumptions at hand, in [52], it is proven, first, that the stationary (timelike) Killing vector field ξ is nowhere tangent to Ω SX . As explained in the previous section, this serves in particular to construct a neighbourhood of Ω SX by dragging it along the orbits of ξ , in which the geometry is thus fully determined by the information in Ω SX . The main result in [52] is that if a OT stationary and axisymmetric region ( W SX , g SX ) can be matched to a FLRW region through a hypersurface Ω SX preserving the axial symmetry, then the region ( W SX , g SX ) must be, in fact, static on a neighbourhood of Ω SX . All in all, in that neighbourhood of the matching hypersurface the OT stationary axisymmetric region ( W SX , g SX ) thus becomes a static axisymmetric region ( W ST , g ST ), and therefore the results of the previous Section 3.1 (cf. [34]) apply. So far, no explicit condition on the matter content of the stationary region has been used. When conditions on the matter content on the (OT) stationary and axisymmetric (and hence static) region are imposed, the functions that determine the matching hypersurface and the static geometry are determined by the results reviewed in Section 3.1. In particular, and for completeness, let us consider a vacuum (with or without a cosmological constant) stationary and axisymmetric region ( W SX , g SX ) matched to FLRW preserving the axial symmetry. As mentioned above, a vacuum matter content forces the axial symmetry and stationary group G 2 on T 2 to act orthogonal transitively. On the other hand, a region of FLRW ( W RW , g RW ) matched to a vacuum region must satisfy the assumptions made and, in particular, have a causal Ω RW (in fact tangent to the fluid flow). The above result implies then that the vacuum region must be static. The results of Section 3.1 thus apply, and imply, in turn, that the whole region (not just its boundary) has to be spherically symmetric, and hence Schwarzschild. To sum up, this means that the only stationary and axially symmetric vacuum region that can be matched to FLRW is a spherically symmetric piece of Schwarzschild. This constitutes still another uniqueness result of the Einstein-Straus model when the vacuum region lies inside FLRW. The complementary result, when the vacuum region lies outside FLRW, constitutes a uniqueness result of the Oppenheimer-Snyder model [53]. It is worth noticing that this result can also be interpreted as a no-go result for the possible interiors of Kerr. Indeed, this result states that an axially symmetric region of (an evolving) FLRW, irrespective of its relative rotation with the exterior, cannot be the source of a stationary and axisymmetric vacuum region, in particular, Kerr.\",\n \"pages\": [\n 11,\n 12\n ]\n },\n {\n \"title\": \"4 Robustness of Einstein-Straus: Generalized exact cosmologies\",\n \"content\": \"In the previous sections, the robustness of the Einstein-Straus model has been discussed by considering generalizations of the interior vacuole and keeping the FLRW model as the exterior cosmological model. The question arises as to what happens if these symmetry assumptions concerning the exterior metric are relaxed. There are two different ways to study departures from the spherical FLRW: either perturbatively or using exact solutions. In this section, we concentrate on the later possibility and, in particular, we review the results found in [46] for spatially homogeneous (but anisotropic) cosmologies. A step in the direction of generalising the exterior was taken by Bonnor, who considered the embedding of a Schwarzschild region in an expanding spherically symmetric inhomogeneous Lemaˆıtre-Tolman-Bondi (LTB) exterior. He found that such a matching is possible in general, and that it allows the average density of the Schwarzschild interior to be chosen independently of the exterior LTB density [12]. So, clearly, if the spherical symmetry is kept, the exterior can be readily generalized to the case of inhomogeneous dust cosmologies. An interesting review about physical aspects of spherically symmetric Einstein-Straus and McVittie type models can be found in [15]. While keeping the spherical symmetry of the cavity allows for straightforward generalizations of Einstein-Straus, breaking this symmetry brings in unexpected complications, as we have seen in the previous section. The same seems to hold if we consider exact generalizations of the FLRW cylindrical symmetry exterior to spatially homogeneous but anisotropic spacetimes. This problem was considered in [46] and we summarize it next: Consider the problem of matching, across a hypersurface Ω which is spatially a topological sphere 1 , of an interior locally cylindrically symmetric (LCS) static spacetime ( W ST , g ST ), which represents a spatially compact region, to a spatially homogeneous anisotropic exterior ( W HOM , g HOM ) having a Lie group G 3 acting on S 3 surfaces. Once more, we make no assumptions a priori on the matter contents, so the main results are purely geometric. Only at the end of the section, assumptions on the matter content will lead to a final no-go result. We wish to preserve globally the axial symmetry and thus we need to impose first the existence of a group of cyclic symmetries in the exterior region. This, combined with the assumption of a spacelike spherical topological shaped 2 Ω ST , implies the existence of an exterior axis. Thus, the cyclic symmetry in the exterior must really be an axial symmetry (see the discussion in Section 3.2). Moreover, we require that the cylindrical symmetry is preserved (in the sense of [62]) at least on a non-empty open subset of Ω. This has the consequence that ( W HOM , g HOM ) must admit a G 4 on S 3 group of isometries, so that it is locally rotationally symmetric (LRS). In [46], it is shown how all the LRS spatially homogeneous metrics can be written in the form adapted to the two commuting Killing vectors defining the cylindrical symmetry ∂ ϕ and ∂ z , where ∂ ϕ is axial with axis at r = 0: with where the functions Σ and F are given by and where glyph[epsilon1] and n are given such that glyph[epsilon1] = 0 , 1; n = 0 , 1; glyph[epsilon1]n = glyph[epsilon1]k = 0 3 . The metrics are classified according to these constants in Table 1. The matching conditions are then investigated and a crucial step was to observe that they lead to the following necessary relations involving only exterior metric functions: 2 This implies the existence of north and south poles on Ω ST where the axial killing vector in the interior vanishes and, therefore, also the generator of the cyclic symmetry in the exterior region on Ω HOM by construction. 3 Let us note that the case glyph[epsilon1] = n = 0 with k = 1 is special, since it corresponds to the Kantowski-Sachs (KS) class of metrics, which do not admit a G 3 on S 3 subgroup [61]. It was included in the study for completeness. which, for non-static exteriors, imply n = 0 and thus exclude Bianchi types II, III, VIII and IX. By inserting (15) back in the matching conditions one is able to prove a series of results that lead to the following conclusion: The only expanding spatially homogeneous spacetimes which can be matched to a locally cylindrically symmetric static interior region preserving the (cylindrical) symmetry, across a non-spacelike hypersurface which is spatially a topological sphere, are given by where β is constant. This metric for k = 1 belongs to the Kantowski-Sachs class, when k = -1 admits a G 3 on S 3 of Bianchi type III, and when k = 0 of Bianchi types I,V,VII 0 ,VII h . The metrics (16) are very special, partly due to the fact that condition a ,t = 0 (see (13)-(14)) imposes a strong constraint, implying that there cannot be any time (nor space) evolution along the direction orthogonal to the orbits of the subgroup G 3 on S 2 of the LRS. There are also constraints imposed through the matching in the interior region and the interested reader can find those in [46]. Note that the no-go result found in [59] is trivially recovered, since FLRW is included in the LRS class for b ( t ) = a ( t ), and the above would imply a static FLRW metric. If one specifies a particular class of matter fields, then one gets further constraints on the cosmological dynamics. For example, if the matter in the static region is not specified but the dynamical (cosmological) region is assumed to contain a perfect fluid with pressure p and energy-density ρ satisfying the dominant energy condition everywhere, then glyph[epsilon1] = 0 necessarily, which corresponds to a stiff fluid equation of state ρ = p = α 2 / (4 t 2 ( α -kt ) 2 ), with b ( t ) = √ αt -kt 2 , where α > 0. On the other hand, if the interior is vacuum then the exterior must be also vacuum. The overall no-go results, in this case, can be seen in two ways: either as a consequence of the assumption that the interior metric is static and cylindrically symmetric, which seems to prohibit time dependence along one direction, or as a consequence of the particular exterior metrics we are considering, which are homogeneous then prohibiting the coefficients along this direction to be space dependent. The perturbative approach described in the next sections can help to clarify this question. To conclude this section we remark that there exists an example of a Einstein-Straus model with exact non-spherical inhomogeneous cosmologies. This is provided by the Szekeres dust solution which has no Killing vectors, in general, but contains intrinsic symmetries on 2-spaces of constant curvature: The Szekeres solution is divided into class I, which generalizes the LTB solution having non-concentric spheres of constant mass, and class II which includes the Kantowski-Sachs solution. Class I solutions have been proved to be interiors to the Schwarzschild solution [9] and this result has been generalized to include the cosmological constant [31, 45]. As mentioned before, one can invert the roles of the two spacetimes involved and hence construct an Einstein-Straus type model with a Schwarzschild or Kottler cavity within a class I Szekeres' cosmology. Let us remark that the Szekeres class has been used recently in Swiss cheese models as interiors to FLRW (see [7] and references therein). Class II Szekeres dust metrics are less known, but contain curious inhomogeneous solutions with cylindrical symmetry [60]. In this case, it seems harder to be able to get a physically reasonable Einstein-Straus model considering what we have described above.\",\n \"pages\": [\n 12,\n 13,\n 14,\n 15\n ]\n },\n {\n \"title\": \"5 Brief overview of perturbative matching theory\",\n \"content\": \"A perturbed spacetime consists of a symmetric two-covariant tensor (the 'perturbation metric') defined on a fixed spacetime (the 'background'). From a structural point of view, spacetime perturbation theory is a gauge theory in the sense that many perturbation metrics describe the same physical situation (i.e. they are gauge related). The underlying geometrical reason for this gauge freedom can be understood from the following intuitive picture of perturbation theory. We imagine a one-parameter family of spacetimes ( V ε , g ε ) such that all the manifolds are diffeomorphic to each other. This allows one to pull back g ε onto a single manifold in the family (say V 0 := V ε =0 ) and work with a one-parameter family of metrics on a single manifold. If all the construction is smooth in ε , derivatives with respect to this parameter can be taken. The perturbation metric g (1) is simply the derivative at ε = 0 of this family of metrics. However, the identification of points in the different manifolds (the diffeomorphism above) is highly non-unique. Any other choice of identification would lead to a different, but geometrically equivalent, perturbation metric. This is the gauge freedom of the theory. Intuitively, it is clear that the gauge freedom will consist of a vector field on the background, because this measures the shift of the new identification with respect to the previous one, and an initial direction (in ε ) is all what is required to compute derivatives with respect to ε at ε = 0. When two spacetimes with boundary are matched, an identification of the boundaries is required. As already mentioned before, if the boundaries are nowhere null, the matching conditions require the equality of the induced metric and second fundamental form (with appropriate choices of orientation). To compare the tensors it is necessary to pull them back to a single manifold and this is done via the identification of boundaries. Contrarily than before, the matching theory is strongly dependent on the identification of the boundaries. In fact, the matching conditions demand the existence of one such identification for which the first and second fundamental forms agree. Assume now that we are studying perturbation theory on a background spacetime constructed from the matching of two spacetimes. The question then arises of what are the conditions that the metric perturbation tensors on each side must satisfy to have a perturbed matching spacetime. This issue is somewhat more involved than one may think a priori and it was solved in a complete manner for the first time by Battye and Carter [4] and independently by Mukohyama [47] (this has been extended to second order in [35]). Previous attempts [24, 23, 43] did not take into account all the subtleties of the interplay between two completely different gauge freedoms inherent to this problem. Indeed, in the picture above of perturbation theory in terms of a collection of spacetimes ( V ε , g ε ), each one of them arises now as the matching of two spacetimes with boundary W ± ε across their respective boundaries Ω ± ε . For better visualization, assume that each one of W ± ε is a submanifold with boundary of a larger boundary-less manifold ̂ W ± ε and assume that the { ̂ W + ε } manifolds are identified among themselves (say with ̂ W + 0 := ̂ W + ε =0 ) via an ε -dependent diffeomorphism. The hypersurface Ω + ε projects down to ̂ W + 0 as a hypersurface ̂ Ω + ε . Now we have a collection of hypersurfaces in one single manifold, and one can think of taking ε -derivatives of geometric quantities intrinsic to the hypersurface. The important point is that, given a point p ∈ Ω + ε =0 , we do not know how this point maps into ̂ Ω + ε . For that, it is necessary to prescribe first how p is mapped into Ω + ε . The identification of { Ω + ε } among themselves is an additional gauge freedom. It is fully independent of the standard gauge freedom in perturbation theory (called 'spacetime gauge freedom' from now on) and is referred to as hypersurface gauge freedom [47]. The composition of both identifications gives, as ε varies, and for any p ∈ Ω + ε =0 , a path γ p ( ε ) in ̂ W + 0 starting at p . Since everything is smooth in ε , the tangent vector to this path at ε = 0 defines a vector field Z + on Ω + 0 := Ω + ε =0 (= ̂ Ω ε =0 ). This vector field is not necessarily tangent (nor normal) to Ω + 0 and it depends on both gauge freedoms. A schematic figure for the definition of Z + and how it depends on the gauges is given in Figure 5. If we let n (0) + be a unit normal vector to Ω + 0 , we can decompose Z + = Q + n (0) + + T + , where T + is tangent to Ω + 0 . From the discussion above, it should be clear that Q + is independent of the hypersurface gauge while T + strongly depends on it. In fact, it can always be made zero by an appropriate choice of gauge. However, doing this is not usually a good idea because the matching has two regions and, at each value of ε , the matching requires an identification between Ω + ε and Ω -ε . After a choice of hypersurface gauge to identify Ω + ε with Ω + 0 we have no freedom left to choose a hypersurface gauge to identity Ω -ε and Ω -0 . The matching conditions will tell us how this identification must be done. So, had we chosen T + = 0, we would still have to leave T -free and let the linearized matching theory determine its value. Further details on the double gauge freedom of linearized perturbation theory can be found in the paper of Mukohyama [47] and in [37], where the issue is discussed in depth including a critical analysis of previous attempts to formulate a consistent perturbative matching theory. After this brief discussion on gauge issues for linearized matching theory, let us describe the actual perturbative matching conditions (for details see [4, 47, 35]). The matching theory involves the equality of the first and second fundamental forms of the boundaries. To compare them they are pulled-back into a single boundary via the identification. In perturbative matching theory everything occurs on the abstract hypersurface Ω 0 diffeomorphic to Ω + 0 and Ω -0 of the background spacetime. On Ω ± 0 we attach two vector fields Z ± = Q ± n (0) ± + T ± whose geometric meaning has been discussed above. They are not know a priori, firstly, because of the hypersurface gauge freedom, and secondly, because the identification of the boundaries Ω + ε and Ω -ε is not known a priori. To the unknowns Z ± we add four symmetric tensors q (1) ± and K (1) ± intrinsic to Ω 0 which arise as the ε -derivative at ε = 0 of the first fundamental form q ± ε and second fundamental form K ± ε of Ω ± ε . These tensors are intrinsic to Ω ± ε , so before taking ε -derivatives they must be pulled back onto Ω 0 via the hypersurface gauges (on each side). Thus, q (1) ± and K (1) ± are hypersurface gaugedependent by construction. On the other hand, their construction is fully independent of the spacetime gauge freedom. In order to write down their explicit expression, let g (1) ± be the perturbed metric (i.e. the fundamental unknown in metric perturbation theory) on each side of the background spacetime. Let also Ψ ± 0 : Ω 0 → W ± 0 be the embedding of the matching hypersurface on each region of the background spacetime. Let y i ( i, j, . . . = 1 , . . . , n -1) be a local coordinate system on Ω 0 and define tangent vectors e ± i = Ψ ± 0 glyph[star] ( ∂ y i ). There are also unique (up to orientation) unit one-forms n (0) ± normal to the boundaries. We choose them so that the corresponding vector n (0) + points towards W + 0 and n (0) -points outside of W -0 or viceversa. The first and second fundamental forms of the background are simply q (0) ± := Ψ ± 0 glyph[star] ( g (0) ± ) , K (0) ± := Ψ ± 0 glyph[star] ( ∇ ± n (0) ± ), where ∇ ± is the covariant derivative in ( W ± 0 , g (0) ± ). Given that the background configuration is already composed of the matching of V + 0 and V -0 through Ω + 0 := Ω 0 , we already have q (0)+ = q (0) -and K (0)+ = K (0) -. Then q (1) ± and K (1) ± are defined as follows [47] where σ := g (0) ± ( n (0) ± , n (0) ± ), D is the covariant derivative of (Ω 0 , q (0) ± ), R (0) ± αµβν is the Riemann tensor of ( W ± 0 , g (0) ± ) and S (1) ± α βγ := 1 2 ( ∇ ± β g (1) ± α γ + ∇ ± γ g (1) ± α β -∇ ± α g (1) ± βγ ). The first order matching conditions (in the absence of shells) require the equalities We emphasize that Q ± and T ± are a priori unknown quantities and fulfilling the matching conditions requires showing that two vectors Z ± exist such that (19) are satisfied. The spacetime gauge freedom can be exploited to fix either or both vectors Z ± a priori, but this should be avoided (or at least carefully analyzed) if additional spacetime gauge choices are made, in order not to restrict a priori the possible matchings. Regarding the hypersurface gauge, this can be used to fix one of the vectors T + or T -, but not both. Note also that the linearized matching conditions are, by construction, spacetime gauge invariant because, as discussed above, the tensors q (1) ± , K (1) ± are necessarily spacetime gauge invariant. In fact, it is straightforward to check explicitly that the right-hands sides of (17) and (18) are spacetime gauge invariant (the individual terms are not, and it is precisely the spacetime gauge dependence in Z ± which makes these objects spacetime gauge invariant). Moreover, the set of conditions (19) are hypersurface gauge invariant, provided the background is properly matched, since, as shown in [47], under such a hypersurface gauge transformation given by the vector ζ in Ω 0 , q (1) transforms as q (1) + L ζ q (0) , and similarly for K (1) .\",\n \"pages\": [\n 15,\n 16,\n 17,\n 18\n ]\n },\n {\n \"title\": \"6 Spherical symmetry: Hodge decomposition\",\n \"content\": \"After the previous summary on linearized matching, in this section we introduce the second main ingredient for the linearized Einstein-Straus model reviewed in the following sections: the Hodge decomposition on the sphere [38]. In order to exploit the underlying spherical symmetry of the background configuration it is common practice to decompose the perturbations, and their related objects and equations, in terms of scalar, vector and tensor harmonics on the sphere. That was the procedure used in the seminal work on perturbations around spherical matched background configurations, due to Gerlach and Sengupta (GS) in [23] and [24], revisited and improved by Mart'ın-Garc'ıa and Gundlach in [43]. The aim in [38] was to use an alternative method, based on the Hodge decomposition on the sphere in terms of scalars, in order to avoid the need to deal with infinite series of objects. In particular, the whole set of matching conditions for the linearized EinsteinStraus model was presented in [38] as a finite number of equations involving scalars that depend on the three coordinates in the matching hypersurface Ω 0 , in contrast with an infinite number of equations for an infinite set of functions of one variable. It is clear that one can always go from the Hodge scalars to the spherical harmonics decomposition in a straightforward way. However, it is not always easy to rewrite the infinite number of expressions appearing in a spectral decomposition in terms of Hodge scalars. Consider the round unit metric Ω AB dx A dx B = dϑ 2 +sin 2 ϑdϕ 2 , with η AB and D A denoting the corresponding volume form and covariant derivative respectively, and ( glyph[star]dG ) A = η C A D C G the Hodge dual with respect to Ω AB . Let us recall that the usual Hodge decomposition on ( S 2 , Ω AB ) states that any one-form V A can be canonically decomposed as V A = D A F +( glyph[star]dG ) A , where F and G are functions on S 2 , and any symmetric tensor T AB as T AB = D A U B + D B U A + H Ω AB , for some U A on S 2 , which can be in turn decomposed in terms of scalars. Based on this, it is convenient to define the following two functionals. Given three scalars X tr , X 1 and X 2 on ( S 2 , Ω AB ) we define the functional one form V A ( X 1 , X 2 ) as and the functional symmetric tensor T AB ( X tr , X 1 , X 2 ) as Let us recall that the decomposition defines these X 's on S 2 up to the kernels of the operators V A and T AB . We allowed for the appearance of all these kernels in [38], where their relevance (or their lack of) was already discussed. In order to avoid spurious information and present a more concise review -and also to ease the translation and comparison with the quantities used in the previous literature in terms of the harmonic decompositions,we use the reformulation already presented in [39] where the Hodge decomposition is, in fact, unique. Indeed, in order to fix the Hodge decomposition uniquely we define a canonical dual decomposition by demanding that the functions X 1 , X 2 in V A ( X 1 , X 2 ) are always orthogonal (in the L 2 sense on S 2 ) to 1, and the functions X 1 , X 2 in T AB ( X tr , X 1 , X 2 ) are orthogonal to 1 and to the l = 1 spherical harmonics. Schematically, we may use and We will use the following notation: given any function f on S 2 we define so that f -f || 0 is orthogonal to the l = 0 harmonics Y 0 and f -f || 1 is orthogonal to the l = 1 harmonics Y m 1 . Note finally that the Hodge decomposition in terms of scalars involves two types of objects depending on their behaviour under reflection on the sphere. The scalars with subscripts 1 and tr remain unchanged under reflection, and are typically called longitudinal, even or polar quantities, while those with subscripts 2 change, and correspond to the transversal, odd or axial quantities. Let us consider now the general spherically symmetric spacetime V = M 2 × S 2 with metric g αβ = ω IJ ⊕ r 2 Ω AB , so that ( M 2 , ω IJ ) is a 2-dim Lorentzian space and r > 0 a function on M 2 . The dual in ( M 2 , ω IJ ) will be indicated by ∗ and the covariant derivative by ∇ . We can now proceed to decompose any one-form (vector) or symmetric two-tensor on V by first taking the part orthogonal to the sphere and then apply the Hodge canonical decomposition to the part tangent to the sphere. In particular, given a normalized timelike one-form u α orthogonal to the spheres, its corresponding one-form u I on ( M 2 , ω IJ ) (defined by u α = ( u I , 0)) can be used to construct a convenient orthonormal basis { u I , m I } so that ω IJ = -u I u J + m I m J (this is u I u I = -1 and m I := ∗ u I ), and consider then the one-form on V defined by m α := ( m I , 0). Given any vector V I we will simply denote by V u and V m the contractions u I V I and m I V I respectively. We apply now this decomposition to encode the objects that will describe the (first order) perturbation of a background consisting of two spherically symmetric regions ( W + , g (0)+ ) and ( W -, g (0) -) matched across corresponding spherically symmetric boundaries Ω + 0 and Ω -0 . At each side ± (we avoid the use of ± just now for clarity) the metric perturbation tensor g (1) αβ gets thus decomposed as where Z I 1 and Z I 2 are two one-forms defined on M 2 , and analogously for any symmetric tensor. The deformation vector Z α , defined on M at points on Ω, is decomposed as whereby the part Z I gets decomposed, in turn, onto the normal and tangential parts to Ω 0 , Q and T respectively. Given the (first order) perturbation tensor and the deformation vector at either ± side of the matching hypersurface, one can calculate the symmetric tensors q (1) ij and K (1) ij , i.e. the 'perturbed first and second fundamental forms', using (17)-(18). Recalling now that q (1) ij and K (1) ij are defined on (Ω 0 , q (0) ij ) and that Ω 0 at either side are tangent to the spheres { θ, φ } , let us denote by λ the parameter that follows the direction on Ω 0 orthogonal to the spheres in order to decompose q (1) ij and K (1) ij into q (1) λλ , K (1) λλ , plus and Note that all these functions are scalars on the sphere that depend only on λ . The first order matching conditions (19) are therefore equivalent to Except for the simplification of the kernels by the canonical decomposition, these are the linearized matching conditions presented in [38].\",\n \"pages\": [\n 18,\n 19,\n 20\n ]\n },\n {\n \"title\": \"6.1 Gerlach and Sengupta (GS) 2+2 formalism\",\n \"content\": \"Let us emphasize again that the conditions (19), and thus (23), concern quantities defined on Ω 0 and are therefore independent on the coordinates used in W + and W -for their computation. These quantities are thus, on the one hand, spacetime gauge independent by construction. Moreover, as discussed in Section 5, the equations are also hypersurface gauge independent. All this makes it unnecessary the use of gauge invariant quantities in order to establish the perturbed matching conditions. Having said that, however, the use of gauge independent quantities turns out to be convenient in the end, mostly when one eventually wants to impose the Einstein field equations. As shown in the works [23], [24], [43], the use of spacetime gauge invariants is very convenient in order to combine the Einstein field equations with the perturbed matching conditions. One can proceed by constructing gauge invariants in terms of Hodge scalars using analogous expressions to those in the harmonic decomposition constructed in [24, 23, 43]. Let us now concentrate on the odd (axial) sector. The odd gauge invariant quantities are encoded in the vector [36] (cf. [24]) Note that K I , as defined above, contains l = 1 harmonics, from Z I 2 , but only the l ≥ 2 sector is gauge invariant. In other words, the part of K I orthogonal to Y 1 (i.e. K I -K I || 1 in the notation above) is the gauge invariant part. Once the orthonormal basis { u I , m I } has been identified at both sides, the odd sector of the linearized matching, which corresponds to the set of equations in (23), is equivalent in the l ≥ 2 sector (the part orthogonal to l = 0 and l = 1) to [36] (cf. [24]) plus an equation for T + 2 -T -2 .\",\n \"pages\": [\n 20,\n 21\n ]\n },\n {\n \"title\": \"7 Linearized Einstein-Straus model: matching conditions\",\n \"content\": \"We are ready to consider the linearized matching of the perturbed Schwarzschild and FLRW spacetimes, as it was analyzed in [38]. Take the Einstein-Straus model as described in Section 2: the FLRW geometry in cosmic time coordinates (1), the Schwarzschild in standard coordinates (2), and the background matching hypersurface Ω 0 described by Ω RW 0 : { t = t, R = R 0 } and Ω ST 0 : { T = T 0 ( t ) , r = r 0 ( t ) } respectively, where T 0 ( t ) and r 0 ( t ) satisfy (3) and the angular part is again ignored. The orthonormal basis we take on the Lorentzian space orthogonal to the spheres is formed by u = dt , m = adR . Note that this choice corresponds to the tangent and normal forms to Ω 0 at Ω 0 , respectively. More precisely, m is chosen to be n (0) at points on Ω 0 . On the Schwarzschild side we have u | Ω 0 = ˙ T 0 ∂ T + ˙ r 0 ∂ r and m | Ω 0 := n (0) = -˙ r 0 dT + ˙ T 0 dr . Take the first order perturbations of FLRW, in no specific gauge, formally decomposed into the usual scalar, vector and tensor (SVT) modes, i.e. 4 (Latin indices a, b, c are used for tensors on ( M , g M )) with satisfying the constraints The canonical Hodge decomposition is then used to encode the part tangent to the spheres into S 2 scalars in the following schematic way [38]: vector All in all, encoding g (1)+ using the SVT modes together with the Hodge decomposition leaves us with 15 SVT-Hodge quantities, corresponding to the scalar modes { Ψ , Φ , W, χ } , vector modes { ˜ W R , W 1 , W 2 , Y R , Y 1 , Y 2 } and tensor modes {Q 1 , Q 2 , H , U 1 , U 2 } , all scalars on S 2 , not all independent due to the previous constraints, and, on the other hand, not unique . Consider, in particular, the only 4 scalars we have in the odd sector; vector modes {W 2 , Y 2 } and tensor modes {Q 2 , U 2 } . As discussed in the previous section, only two gauge invariant quantities exist in the odd sector. These correspond to the two components of the gauge invariant odd vector (and for l ≥ 2), K + I , which given the above construction in terms of the SVT-Hodge quantities, read [39, 36] Consider now the stationary and axially symmetric vacuum perturbations in the Weyl gauge. They can be described in terms of two functions U (1) ( r, θ ) and A (1) ( r, θ ), which correspond, basically, to the perturbation of the gravitational Newtonian potential and the rotational perturbation, respectively. The perturbation tensor reads [38] Note that, when using the full set of the Einstein field equations for vacuum, the function k (1) is determined up to quadratures once U (1) ( r, θ ) and A (1) ( r, θ ) are found. We stress, however, that the vacuum equations, although indicated, were not imposed in the perturbed Schwarzschild region (nor in the perturbed FLRW region) in [38], and therefore the results found there are purely geometric. Instead of working with A (1) ( r, θ ), it is convenient to use an auxiliary function, G , defined by A (1) := sin θ∂ θ G . In terms of the Hodge decomposition of the perturbation tensor (20), applied to (26), we have G = -( 1 -2 M r ) -1 Z -T 2 . Another auxiliary function P can be introduced for k (1) . The whole set of matching conditions (23) for the linearized Einstein-Straus model, both in the odd and even sectors, were found in [38] in terms of these functions U (1) ( r, θ ) , G tensor and P in the Schwarzschild side together with the above 15 SVT-Hodge scalars describing the FLRW perturbation. The whole set is too long to be included here, but in order to review the main results in [38] only the odd sector of the linearized matching is needed. The odd sector of the linearized matching (24) projected to the part orthogonal to the l = 0 and l = 1 harmonics can be rewritten as the following three relations [38] plus an equation for the difference T RW 2 -T Sch 2 . The three equations above can be shown [36] to correspond indeed to (25), taking into account that K Sch = -( 1 -2 M r ) G dT . These equations were presented in [38] in full, including the parts lying on the l = 0 and l = 1 harmonics. There, a series of kernels inherent to the usual Hodge decomposition where the responsible for the usual freedom found in the l = 0 and l = 1 sectors when using harmonic decompositions. By using the canonical Hodge decomposition introduced in Section 6, we can have a better control of that freedom, and understand its nature, getting rid of the spurious terms. Indeed, by doing that it can be shown [36] that the projection of the linearized matching on the l = 1 harmonics -on the l = 0 it is trivial, since all scalars in the odd sector are orthogonal to l = 0- gives while ( T RW 2 -T Sch 2 ) || 1 is free. The first consequence of the above equations is that if the FLRW remains unperturbed then the stationary region must be static in the range of variation of r 0 ( t ): equations (27)-(29) imply that the part of G orthogonal to l = 1 vanishes, and (30) implies that G || 1 = Ca 3 / (2 M -a Σ c ) , where C is a constant. Therefore G = Ca 3 / (2 M -a Σ c ) cos θ , and thus 5 As shown in [38], this implies that the perturbed spacetime is static in the range of variation of r 0 ( t ). This result generalizes that in [52] because now the matching hypersurface does not necessarily keep the axial symmetry. Therefore, the only way of having a stationary and axisymmetric vacuum arbitrarily shaped (at the linear level) region in FLRW is to have the Einstein-Straus model. Let us remark again that by the interior/exterior duality, this result also implies that a piece of FLRW, irrespective of its shape and its relative rotation with the exterior, cannot describe the interior of Kerr.\",\n \"pages\": [\n 21,\n 22,\n 23\n ]\n },\n {\n \"title\": \"7.1 Constraint on FLRW\",\n \"content\": \"Another interesting consequence of the matching conditions is that the combination of (27) and (28) produces one equation that involves only quantities in FLRW [38] and thus constitutes a constraint in FLRW. Recalling that this equation is meant to be orthogonal to l = 1 (and vanishes identically if projected on l = 0), this constraint implies that if the perturbed FLRW contains vector modes with l ≥ 2 harmonics on Ω 0 , then it must contain also tensor modes there. Since, as we have just seen above, the existence of a rotation in the stationary region implies the existence of, at least, vector perturbations in FLRW, then both vector and tensor modes must exist on Ω 0 . It must be stressed that, as demonstrated in [5] (and references therein), there exist configurations of FLRW linear perturbations containing only vector perturbations which vanish identically inside a spherical surface. Such configurations are compatible with the results reviewed here, since that interior region is FLRW and the above constraints do not apply. A completely different matter is the embedding of a Schwarzschild spherical cavity (or a vacuum perturbation thereof) into any such model: the Schwarzschild cavity cannot reach the perturbed FLRW region, as otherwise the constraints above would require that tensor perturbations are also present (at least near the boundary of the Schwarzschild cavity). There also exists a Einstein-Straus perturbative model by Chamorro [18] consisting on small rotation Kerr vacuole within a perturbed FLRW. Again, the constraint above does not apply to this model because there are no l ≥ 2 modes there. The fact that tensor modes must exist near Ω 0 once some rotation with l ≥ 2, whatever small, exists in the stationary region, may indicate the existence of some kind of gravitational waves on FLRW near Ω 0 . In order to analyze further this issue one needs to take the Einstein field equations into consideration. That is the purpose of our work in preparation [36], some result of which will appear in the proceedings of the ERE2012 meeting.\",\n \"pages\": [\n 24\n ]\n },\n {\n \"title\": \"8 Conclusions and outlook\",\n \"content\": \"This paper is concerned with the difficulties that the Einstein-Straus model encounters. A fundamental one refers to its high level of rigidity and the impossible generalization to non-spherical symmetry if the bound system is required to be time independent so as to retain the property that cosmic expansion does not affect the local systems. Moreover, if one views the model within the LTB class with a step function density profile, the model is unstable to perturbations [57], [32], cf. also the discussion in [30]. The rigidity result so far requires either stationarity and axial symmetry or staticity. An interesting open problem would be to relax the conditions and assume only stationarity. Despite these difficulties, the Einstein-Straus model has played and plays a very important role in cosmology in different areas or research, most notably on the influence (or lack thereof) of the cosmic expansion on local systems, or in the problem of averaging in cosmology at least on an observational level (see e.g. [20]). The model is still widely used as textbook explanation of the lack of influence of the cosmic expansion on astrophysical systems and, in fact, there are not many known alternatives (a notable exception is the McVittie model [44], [28], [29] which is also spherically symmetric and mimics the geometry of Schwarzschild at small scales while approaching a FLRW model at long distances, and which has been studied thoroughly, see [15] and references therein). Concerning the use of the Einstein-Straus model on observational cosmology, mainly by studying lensing effects, its generalizations have systematically consisted in keeping spherical symmetry and allowing for some dynamics in the interior. The prominent example here consists of LTB regions inside a FLRW universe (see references in [20]). An important ingredient for the rigidity of the Einstein-Straus model is the large symmetry of the FLRW background. It is therefore an interesting problem to analyze how the model gets modified in the presence of cosmic perturbations. In a conservative approach, one still wants to keep the main properties (stationarity of a region inside a cosmological model) as far as possible and analyze the possible departures from the model in more realistic situations. Moreover, by studying perturbed Einstein-Straus models one seeks going beyond the problem of the influence of cosmic expansion on local systems, and tackle the problem of the influence of general cosmic dynamics. Surprisingly, it turns out that the existence of static (stationary) regions does impose conditions on the cosmic perturbations, at least near the boundary. Whether this is a real effect or simply an indication that the interior region should not be kept stationary remains to be seen. Another implication of the perturbed Einstein-Straus model is that extra care is required in the standard decomposition of metric perturbations in terms of scalar, vector and tensor modes. As discussed above, any rotation in the vacuole implies necessarily the presence of both vector and tensor modes in the cosmic perturbations. It is interesting to analyze whether these tensor modes could represent cosmic gravitational waves. Some preliminary results along these lines have already been presented in [39]. A detailed and more complete approach will appear elsewhere. Another interesting future line of research is to allow for non-stationary perturbations in the vacuole and study the transmission of gravitational waves from the cosmic region to the bound system.\",\n \"pages\": [\n 24,\n 25\n ]\n },\n {\n \"title\": \"9 Acknowledgements\",\n \"content\": \"MM acknowledges financial support under the projects FIS2012-30926 (MICINN) and P09-FQM-4496 (J. Andaluc'ıa-FEDER). FM thanks the warm hospitality from Instituto de F'ısica, UERJ, Rio de Janeiro, Brasil, projects PTDC/MAT/108921/2008 and CERN/FP/123609/2011 from Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT), as well as CMAT, Univ. Minho, for support through FEDER funds Programa Operacional Factores de Competitividade (COMPETE) and Portuguese Funds from FCT within the project PEst-C/MAT/UI0013/2011. RV thanks the kind hospitality from the Universidad de Salamanca, where parts of this work have been produced, and financial support from project IT592-13 of the Basque Government, and FIS2010-15492 from the MICINN.\",\n \"pages\": [\n 25\n ]\n }\n]"}}},{"rowIdx":92,"cells":{"bibcode":{"kind":"string","value":"2013Ge&Ae..53..813K"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1307.7960.pdf"},"content":{"kind":"string","value":"\nLONG-TERM VARIATIONS OF GEOMAGNETIC ACTIVITY AND THEIR SOLAR SOURCES\nKirov B. 1 , Obridko V.N. 2 , Georgieva K. 1 , Nepomnyashtaya E.V. 2 ,\nShelting B.D. 2\n1 - Space Research ant Technologies Institute - BAS, Sofia, Bulgaria 2 - IZMIRAN, Russia\nemail: bkirov@space.bas.bg\nAbstract\nGeomagnetic activity in each phase of the solar cycle consists of 3 parts: (1) a 'floor' below which the geomagnetic activity cannot fall even in the absence of sunspots, related to moderate graduate commencement storms; (2) sunspot-related activity due to sudden commencement storms caused by coronal mass ejections; (3) graduate commencement storms due to high speed solar wind from solar coronal holes. We find that the changes in the 'floor' depend on the global magnetic moment of the Sun, and on the other side, from the height of the 'floor' we can judge about the amplitude of the sunspot cycle.\n1. Introduction\nAs early as in 1852 it was noted that geomagnetic disturbances are related to solar activity [Sabine, 1852], and in 1982 it was found that geomagnetic activity is caused by two types of solar agents, the first one related to sunspots and caused by coronal mass ejections (CMEs), and the other one -not related to sunspots and caused by high speed solar wind from solar coronal holes [Feynman, 1982]. CME-caused geomagnetic disturbances have a maximum in sunspot maximum, and coronal holes-related disturbances - on the descending phase of sunspots. In the present study we aim to determine how these two components of geomagnetic activity vary from cycle to cycle, and the variations of which solar agents cause these changes.\n2. Components of geomagnetic activity\nFeynman [1982] noted that if a geomagnetic activity index (e.g. aa -index) is plotted as a function of the sunspot number R (Fig.1), all aa -index values lie above a line given by the equation aaR=a0 + b.R . Feynman [1982] suggested that aaR is the geomagnetic activity caused by sunspot-related solar activity, and the aa values above this line represent the geomagnetic activity caused by high speed solar wind: ааP = aa - aaR .\n\n\n\n\n\n
Fig.1. Dependence of аа-index on R in the period 1878-1912 (left) and 1954-1985 (right)
\n\nFeynman [1982] determined that aa R = 5.38 + 0.12. R . We calculated the values of a0 and b in consecutive periods of around 30 years, each including 3 sunspot cycles (cycles 9-11, 10-12 and so on). The calculated values of the coefficients demonstrate a clear quasi-secular cycle (Fig. 2).\n\n\n
Fig. 2 . Cyclic variations of the coefficients a0 and b
\n\nActually, geomagnetic activity can be divided into 3 rather than 2 components. The first one is the 'floor', equal to the а0 coefficient which represents the geomagnetic activity in the absence of sunspots. It is practically determined by the activity in the cycle minimum and varies smoothly from cycle to cycle. The second component is the geomagnetic activity caused by sunspot-related solar activity which is described by the straight line aaT = b.R so that aaR = а0 + aaT . The slope b of this line also changes cyclically. The third component ааP (the value above aaR ) is caused by high speed solar wind. It can be seen that when the coefficient а0 is big (high 'floor' of the geomagnetic activity), the geomagnetic activity is almost independent on the sunspot number (small coefficient b ), and when the 'floor' is low, the geomagnetic activity quickly grows with growing sunspot number.\nFig.3 demonstrates that both the 'floor' of the geomagnetic activity а0 and the slope b don't depend on the phase of the sunspot cycle (upward or downward branch), but are different in different intervals. Besides, the scatter of values above aaR in any interval is much bigger during the downward branch which has to be expected because of the strong influence of high speed solar wind streams on the geomagnetic activity in this phase of the sunspot cycle [Georgieva, K., Kirov, B, 2005].\n\n\n
Fig. 3. Dependence of aa on R in the upward (upper panel) and in the downward branch (lower panel) of the sunspot cycle in the period 1844 - 1957 (left) and in the period 1955 1985 (right)
\n\nThe question now is which solar agents cause the nonzero values of the geomagnetic activity 'floor', and which factors lead to the changes in the coefficients а0 and b .\n3. Types of geomagnetic storms\nThe geomagnetic storms differ in intensity as well as in characteristics. The intensity of the storm is determined by the parameters D, H и Z - the magnetic declination, change of the horizontal and vertical components of the Earth's magnetic field, respectively, measured in nT (Table 1), and the storm can be with a sudden or gradual commencement. In order to determine the origin of different storms, [Шельтинг, Обридко , 2011] compared the occurrence frequency of all, strong, moderate and weak storms with sudden and with gradual commencement to the number of sunspots. They found that the occurrence frequency of the sudden commencement storms correlates with the sunspot number, with correlation coefficient 0.872 +/- 0.06. In contrast, the correlation coefficient of the occurrence frequency of the gradual commencement storms and the sunspot number is practically zero (0.014 +/0.13), and their maximum is shifted by 1-3 years after the sunspot maximum. Further analysis shows that there is high correlation among storms of different intensity inside each of the\ngroups, and absolutely no correlation between the two groups of storms. From there the authors make the conclusion that these two types of storms have different origin. Sudden commencement storms are caused by coronal mass ejections (CMEs). As the solar coronal mass ejections are associated with active areas, that is with local magnetic fields, a high correlation is observed between the occurrence frequency of sudden commencement storms and the number of sunspots.\nGradual commencement storms are caused by high speed solar wind. It originates from solar coronal holes whose maximum is on the downward branch of the sunspot cycle. This leads to two maxima in geomagnetic activity in the course of the sunspot cycle, the second one being due mainly to the occurrence of many gradual commencement storms [Tsurutani, et al. 2006].\n4. Geomagnetic activity 'floor'\nThe geomagnetic activity 'floor' is the geomagnetic activity in the absence of any sunspots. Practically it is determined by the geomagnetic activity in the sunspot minimum. As seen in Fig.4, during the whole investigated period, the geomagnetic activity with aa -index between 10 and 30 is caused by gradual commencement storms, but this is especially well pronounced in sunspot minimum periods.\n\n\n
Fig.4 . Annual number of weak sudden commencement storms (solid line) and gradual commencement storms (dotted line).
\n\nWe can conclude that the geomagnetic activity 'floor' is determined by non sunspot-related solar activity. Fig.5 demonstrates that the variations in the geomagnetic activity floor follow, with the exception of cycle 13, the variations in the number of 30hour intervals with aa -index between 10 and 30 in the minimum of the respective cycle. Moreover, from cycle 14 to 21 (around 1985), an increase is observed in both the number of 3-hour intervals with 10< аа <30, and of the geomagnetic activity floor, after which they both begin decreasing. The correlation between the two quantities is 0.85 with p<0.01.\n\n\n
Fig.5. Number of 3-hour intervals with aa between 10 and 30 (solid line) and the geomagnetic activity floor а0 (dotted line), in consecutive sunspot cycle minima.
\n\nIt is seen that the geomagnetic activity floor in each cycle is determined by the geomagnetic activity in the range 10<аа<30 in the cycle minimum, and as far as this geomagnetic activity, especially in the cycle minimum, is related as shown above to gradual commencement storms, the floor is determined by the high speed solar wind streams causing gradual commencement storms. Therefore, the reason for the changing geomagnetic activity floor is the changing high speed solar wind reaching the Earth during sunspot minimum.\nIt is interesting to note that at the same time as the increase in the floor changed to decrease (cycle 21), the increase in the solar global magnetic moment changed to a sharp decrease[Обридко, Шельтинг, 2009 ] - (Fig.6). It seems that the change in the solar global magnetic moment is reflected in the geomagnetic activity caused by the high speed solar wind during the sunspot minimum through its effects on the thickness of the heliospheric current sheet [Simon and Legrand, 1987].\n\n\n
Fig.6. Evolution of the solar magnetic moment from 1918 to 2006.
\n\n5. Coefficient b (slope)\nThe sunspot-related geoeffective solar agents are the CMEs. It is known that the geoeffectiveness of CMEs vary little in the course of the sunspot cycle; considerably changes the geoeffectiveness of magnetic clouds (a subclass of CMEs with high and smoothly rotating magnetic field), but their number is negligible compared to the total number of CMEs except around sunspot minimum when their geoeffectiveness is low. Therefore, the varying contribution of CMEs to geomagnetic activity from year to year depends on their varying number. [Georgieva and Kirov, 2005]. Fig.7 presents the ratio of CMEs to the number of sunspots for the period 1996-2012. For the number of CMEs, the SOHO/LASCO CME catalog is used (http://cdaw.gsfc.nasa.gov/CME_list/) as it provides a fairly homogenous data set.\n\n\n
Fig. 7 . Ratio of the number of CMEs to the sunspot number (monthly averages).
\n\nIt can be seen that the ratio is almost constant during the greater part of the sunspot cycle, with the exception of the periods of sunspot minima, especially in the minimum between cycles 23 and 24 which is known to be very peculiar. In 2007, 2008, and 2009 we had total annuals of 20, 70, and 60 CMEs, respectively, with the average annual number of sunspots between 3 and 7. A small change in the correlation between the sunspot number and the number of CMEs is observed in the previous sunspot minimum also, but it is only due to CMEs in a few single months. We can conclude that the increasing geomagnetic activity with increasing sunspot number (the coefficient b ) is due to the increasing number of CMEs with increasing number of sunspots.\n6. Forecasting the following cycle\nFig.8 demonstrates that the sunspot number in the cycle maximum is related to the geomagnetic activity floor in the same cycle. The correlation between the two variables is 0,792 with p=0.001.\n\n\n
Fig.8. Geomagnetic activity floor (solid line) and sunspot number in the cycle maximum (dotted line)
\n\nFrom this it follows that the characteristics of the whole cycle are set already at its beginning, and measuring the geomagnetic activity we can forecast to a great extend its maximum. On the other hand, given that the evolution of the Sun's magnetic moment is indicative of the changes in а0 , we can evaluate in advance the direction of change of the geomagnetic activity 'floor'.\n6. Summary and conclusions\nThe geomagnetic activity consists of three components: (1) a0 - the geomagnetic activity 'floor', theoretically equal to the activity at zero number of sunspots. Practically this activity is determined by the gradual commencement geomagnetic disturbances with 10< аа <30 in the beginning of the sunspot cycle; (2) aaT - the geomagnetic activity caused by CMEs whose number linearly increases with increasing number of sunspots aaT = b.R , so that aaR = a0 + b.R ; (3) ааP - the values of aa above aaR , caused by high speed solar wind streams from solar coronal holes. We have found that the variations of a0 have a quasi-secular cycle, with the direction of variation following the variation of the global magnetic moment of the Sun. On the other hand, we have found that a0 determined by the geomagnetic activity in the beginning\nof a cycle is directly related to the sunspot maximum in the same cycle. Therefore, if we know the direction of change (increasing or decreasing) of the global magnetic moment, we can forecast the increase or decrease of a0 in the next cycle, and from there - the increase or decrease of the sunspot maximum. Moreover, during the sunspot minimum we can quite accurately forecast the following sunspot minimum.\n
\n\n
Table 1
\n
\nReferences\nОбридко В.Н., Шельтинг Б.Д. Некоторые аномалии эволюции глобальных и крупномасштабных магнитных полей на Солнце как предвестники нескольких предстоящих невысоких циклов// Письма в астрономический журнал. Т. 35. №3, С. 3844. 2009.\nШельтинг Б.Д., Обридко В.Н. Магнитные бури с внезапным и постепенным началом как индексы солнечной активности// Всероссийская ежегодная конференция по физике Солнца. Пулково Русия. 2011.\nFeynman J. Geomagnetic and solar wind cycles, 1900-1975// J. Geophys. Res. 87, 6153-6162 (1982)\nGeorgieva K., Kirov B. Helicity of magnetic clouds and solar cycle variations of their geoeffectiveness// Proceedings IAU Symposium 226 Coronal and Stellar Mass Ejections, Oxford University Press. P.470-472, 2005.\nSabine E. On Periodical Laws Discoverable in the Mean Effects of the Larger Magnetic Disturbances// Phil. Trans. R. Soc. Lond. January 1, 1852 142 103-124; doi:10.1098/rstl.1852.0009.\nSimon P.A., Legrand J.P. : Some solar cycle phenomena related to the geomagnetic activity from 1868 to 1980. III - Quiet-days, fluctuating activity or the solar equatorial belt as the main origin of the solar wind flowing in the ecliptic plane// Astron. Astrophys. V. 182, P. 329-336, 1987.\nTsurutani B.T., Gonzalez W. D., Gonzalez A.L.C. et al. , Corotating solar wind streams and recurrent geomagnetic activity: A review // J. Geophys. Res., V. 111, No A07S01, P. 1110711132, 2006.\n"},"sections":{"kind":"list like","value":[{"title":"Kirov B. 1 , Obridko V.N. 2 , Georgieva K. 1 , Nepomnyashtaya E.V. 2 ,","content":"Shelting B.D. 2 1 - Space Research ant Technologies Institute - BAS, Sofia, Bulgaria 2 - IZMIRAN, Russia email: bkirov@space.bas.bg","pages":[1]},{"title":"Abstract","content":"Geomagnetic activity in each phase of the solar cycle consists of 3 parts: (1) a 'floor' below which the geomagnetic activity cannot fall even in the absence of sunspots, related to moderate graduate commencement storms; (2) sunspot-related activity due to sudden commencement storms caused by coronal mass ejections; (3) graduate commencement storms due to high speed solar wind from solar coronal holes. We find that the changes in the 'floor' depend on the global magnetic moment of the Sun, and on the other side, from the height of the 'floor' we can judge about the amplitude of the sunspot cycle.","pages":[1]},{"title":"1. Introduction","content":"As early as in 1852 it was noted that geomagnetic disturbances are related to solar activity [Sabine, 1852], and in 1982 it was found that geomagnetic activity is caused by two types of solar agents, the first one related to sunspots and caused by coronal mass ejections (CMEs), and the other one -not related to sunspots and caused by high speed solar wind from solar coronal holes [Feynman, 1982]. CME-caused geomagnetic disturbances have a maximum in sunspot maximum, and coronal holes-related disturbances - on the descending phase of sunspots. In the present study we aim to determine how these two components of geomagnetic activity vary from cycle to cycle, and the variations of which solar agents cause these changes.","pages":[1]},{"title":"2. Components of geomagnetic activity","content":"Feynman [1982] noted that if a geomagnetic activity index (e.g. aa -index) is plotted as a function of the sunspot number R (Fig.1), all aa -index values lie above a line given by the equation aaR=a0 + b.R . Feynman [1982] suggested that aaR is the geomagnetic activity caused by sunspot-related solar activity, and the aa values above this line represent the geomagnetic activity caused by high speed solar wind: ааP = aa - aaR . Feynman [1982] determined that aa R = 5.38 + 0.12. R . We calculated the values of a0 and b in consecutive periods of around 30 years, each including 3 sunspot cycles (cycles 9-11, 10-12 and so on). The calculated values of the coefficients demonstrate a clear quasi-secular cycle (Fig. 2). Actually, geomagnetic activity can be divided into 3 rather than 2 components. The first one is the 'floor', equal to the а0 coefficient which represents the geomagnetic activity in the absence of sunspots. It is practically determined by the activity in the cycle minimum and varies smoothly from cycle to cycle. The second component is the geomagnetic activity caused by sunspot-related solar activity which is described by the straight line aaT = b.R so that aaR = а0 + aaT . The slope b of this line also changes cyclically. The third component ааP (the value above aaR ) is caused by high speed solar wind. It can be seen that when the coefficient а0 is big (high 'floor' of the geomagnetic activity), the geomagnetic activity is almost independent on the sunspot number (small coefficient b ), and when the 'floor' is low, the geomagnetic activity quickly grows with growing sunspot number. Fig.3 demonstrates that both the 'floor' of the geomagnetic activity а0 and the slope b don't depend on the phase of the sunspot cycle (upward or downward branch), but are different in different intervals. Besides, the scatter of values above aaR in any interval is much bigger during the downward branch which has to be expected because of the strong influence of high speed solar wind streams on the geomagnetic activity in this phase of the sunspot cycle [Georgieva, K., Kirov, B, 2005]. The question now is which solar agents cause the nonzero values of the geomagnetic activity 'floor', and which factors lead to the changes in the coefficients а0 and b .","pages":[1,2,3]},{"title":"3. Types of geomagnetic storms","content":"The geomagnetic storms differ in intensity as well as in characteristics. The intensity of the storm is determined by the parameters D, H и Z - the magnetic declination, change of the horizontal and vertical components of the Earth's magnetic field, respectively, measured in nT (Table 1), and the storm can be with a sudden or gradual commencement. In order to determine the origin of different storms, [Шельтинг, Обридко , 2011] compared the occurrence frequency of all, strong, moderate and weak storms with sudden and with gradual commencement to the number of sunspots. They found that the occurrence frequency of the sudden commencement storms correlates with the sunspot number, with correlation coefficient 0.872 +/- 0.06. In contrast, the correlation coefficient of the occurrence frequency of the gradual commencement storms and the sunspot number is practically zero (0.014 +/0.13), and their maximum is shifted by 1-3 years after the sunspot maximum. Further analysis shows that there is high correlation among storms of different intensity inside each of the groups, and absolutely no correlation between the two groups of storms. From there the authors make the conclusion that these two types of storms have different origin. Sudden commencement storms are caused by coronal mass ejections (CMEs). As the solar coronal mass ejections are associated with active areas, that is with local magnetic fields, a high correlation is observed between the occurrence frequency of sudden commencement storms and the number of sunspots. Gradual commencement storms are caused by high speed solar wind. It originates from solar coronal holes whose maximum is on the downward branch of the sunspot cycle. This leads to two maxima in geomagnetic activity in the course of the sunspot cycle, the second one being due mainly to the occurrence of many gradual commencement storms [Tsurutani, et al. 2006].","pages":[3,4]},{"title":"4. Geomagnetic activity 'floor'","content":"The geomagnetic activity 'floor' is the geomagnetic activity in the absence of any sunspots. Practically it is determined by the geomagnetic activity in the sunspot minimum. As seen in Fig.4, during the whole investigated period, the geomagnetic activity with aa -index between 10 and 30 is caused by gradual commencement storms, but this is especially well pronounced in sunspot minimum periods. We can conclude that the geomagnetic activity 'floor' is determined by non sunspot-related solar activity. Fig.5 demonstrates that the variations in the geomagnetic activity floor follow, with the exception of cycle 13, the variations in the number of 30hour intervals with aa -index between 10 and 30 in the minimum of the respective cycle. Moreover, from cycle 14 to 21 (around 1985), an increase is observed in both the number of 3-hour intervals with 10< аа <30, and of the geomagnetic activity floor, after which they both begin decreasing. The correlation between the two quantities is 0.85 with p<0.01. It is seen that the geomagnetic activity floor in each cycle is determined by the geomagnetic activity in the range 10<аа<30 in the cycle minimum, and as far as this geomagnetic activity, especially in the cycle minimum, is related as shown above to gradual commencement storms, the floor is determined by the high speed solar wind streams causing gradual commencement storms. Therefore, the reason for the changing geomagnetic activity floor is the changing high speed solar wind reaching the Earth during sunspot minimum. It is interesting to note that at the same time as the increase in the floor changed to decrease (cycle 21), the increase in the solar global magnetic moment changed to a sharp decrease[Обридко, Шельтинг, 2009 ] - (Fig.6). It seems that the change in the solar global magnetic moment is reflected in the geomagnetic activity caused by the high speed solar wind during the sunspot minimum through its effects on the thickness of the heliospheric current sheet [Simon and Legrand, 1987].","pages":[4,5]},{"title":"5. Coefficient b (slope)","content":"The sunspot-related geoeffective solar agents are the CMEs. It is known that the geoeffectiveness of CMEs vary little in the course of the sunspot cycle; considerably changes the geoeffectiveness of magnetic clouds (a subclass of CMEs with high and smoothly rotating magnetic field), but their number is negligible compared to the total number of CMEs except around sunspot minimum when their geoeffectiveness is low. Therefore, the varying contribution of CMEs to geomagnetic activity from year to year depends on their varying number. [Georgieva and Kirov, 2005]. Fig.7 presents the ratio of CMEs to the number of sunspots for the period 1996-2012. For the number of CMEs, the SOHO/LASCO CME catalog is used (http://cdaw.gsfc.nasa.gov/CME_list/) as it provides a fairly homogenous data set. It can be seen that the ratio is almost constant during the greater part of the sunspot cycle, with the exception of the periods of sunspot minima, especially in the minimum between cycles 23 and 24 which is known to be very peculiar. In 2007, 2008, and 2009 we had total annuals of 20, 70, and 60 CMEs, respectively, with the average annual number of sunspots between 3 and 7. A small change in the correlation between the sunspot number and the number of CMEs is observed in the previous sunspot minimum also, but it is only due to CMEs in a few single months. We can conclude that the increasing geomagnetic activity with increasing sunspot number (the coefficient b ) is due to the increasing number of CMEs with increasing number of sunspots.","pages":[6]},{"title":"6. Forecasting the following cycle","content":"Fig.8 demonstrates that the sunspot number in the cycle maximum is related to the geomagnetic activity floor in the same cycle. The correlation between the two variables is 0,792 with p=0.001. From this it follows that the characteristics of the whole cycle are set already at its beginning, and measuring the geomagnetic activity we can forecast to a great extend its maximum. On the other hand, given that the evolution of the Sun's magnetic moment is indicative of the changes in а0 , we can evaluate in advance the direction of change of the geomagnetic activity 'floor'.","pages":[7]},{"title":"6. Summary and conclusions","content":"The geomagnetic activity consists of three components: (1) a0 - the geomagnetic activity 'floor', theoretically equal to the activity at zero number of sunspots. Practically this activity is determined by the gradual commencement geomagnetic disturbances with 10< аа <30 in the beginning of the sunspot cycle; (2) aaT - the geomagnetic activity caused by CMEs whose number linearly increases with increasing number of sunspots aaT = b.R , so that aaR = a0 + b.R ; (3) ааP - the values of aa above aaR , caused by high speed solar wind streams from solar coronal holes. We have found that the variations of a0 have a quasi-secular cycle, with the direction of variation following the variation of the global magnetic moment of the Sun. On the other hand, we have found that a0 determined by the geomagnetic activity in the beginning of a cycle is directly related to the sunspot maximum in the same cycle. Therefore, if we know the direction of change (increasing or decreasing) of the global magnetic moment, we can forecast the increase or decrease of a0 in the next cycle, and from there - the increase or decrease of the sunspot maximum. Moreover, during the sunspot minimum we can quite accurately forecast the following sunspot minimum.","pages":[7,8]},{"title":"References","content":"Обридко В.Н., Шельтинг Б.Д. Некоторые аномалии эволюции глобальных и крупномасштабных магнитных полей на Солнце как предвестники нескольких предстоящих невысоких циклов// Письма в астрономический журнал. Т. 35. №3, С. 3844. 2009. Шельтинг Б.Д., Обридко В.Н. Магнитные бури с внезапным и постепенным началом как индексы солнечной активности// Всероссийская ежегодная конференция по физике Солнца. Пулково Русия. 2011. Feynman J. Geomagnetic and solar wind cycles, 1900-1975// J. Geophys. Res. 87, 6153-6162 (1982) Georgieva K., Kirov B. Helicity of magnetic clouds and solar cycle variations of their geoeffectiveness// Proceedings IAU Symposium 226 Coronal and Stellar Mass Ejections, Oxford University Press. P.470-472, 2005. Sabine E. On Periodical Laws Discoverable in the Mean Effects of the Larger Magnetic Disturbances// Phil. Trans. R. Soc. Lond. January 1, 1852 142 103-124; doi:10.1098/rstl.1852.0009. Simon P.A., Legrand J.P. : Some solar cycle phenomena related to the geomagnetic activity from 1868 to 1980. III - Quiet-days, fluctuating activity or the solar equatorial belt as the main origin of the solar wind flowing in the ecliptic plane// Astron. Astrophys. V. 182, P. 329-336, 1987. Tsurutani B.T., Gonzalez W. D., Gonzalez A.L.C. et al. , Corotating solar wind streams and recurrent geomagnetic activity: A review // J. Geophys. Res., V. 111, No A07S01, P. 1110711132, 2006.","pages":[8]}],"string":"[\n {\n \"title\": \"Kirov B. 1 , Obridko V.N. 2 , Georgieva K. 1 , Nepomnyashtaya E.V. 2 ,\",\n \"content\": \"Shelting B.D. 2 1 - Space Research ant Technologies Institute - BAS, Sofia, Bulgaria 2 - IZMIRAN, Russia email: bkirov@space.bas.bg\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Abstract\",\n \"content\": \"Geomagnetic activity in each phase of the solar cycle consists of 3 parts: (1) a 'floor' below which the geomagnetic activity cannot fall even in the absence of sunspots, related to moderate graduate commencement storms; (2) sunspot-related activity due to sudden commencement storms caused by coronal mass ejections; (3) graduate commencement storms due to high speed solar wind from solar coronal holes. We find that the changes in the 'floor' depend on the global magnetic moment of the Sun, and on the other side, from the height of the 'floor' we can judge about the amplitude of the sunspot cycle.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"As early as in 1852 it was noted that geomagnetic disturbances are related to solar activity [Sabine, 1852], and in 1982 it was found that geomagnetic activity is caused by two types of solar agents, the first one related to sunspots and caused by coronal mass ejections (CMEs), and the other one -not related to sunspots and caused by high speed solar wind from solar coronal holes [Feynman, 1982]. CME-caused geomagnetic disturbances have a maximum in sunspot maximum, and coronal holes-related disturbances - on the descending phase of sunspots. In the present study we aim to determine how these two components of geomagnetic activity vary from cycle to cycle, and the variations of which solar agents cause these changes.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"2. Components of geomagnetic activity\",\n \"content\": \"Feynman [1982] noted that if a geomagnetic activity index (e.g. aa -index) is plotted as a function of the sunspot number R (Fig.1), all aa -index values lie above a line given by the equation aaR=a0 + b.R . Feynman [1982] suggested that aaR is the geomagnetic activity caused by sunspot-related solar activity, and the aa values above this line represent the geomagnetic activity caused by high speed solar wind: ааP = aa - aaR . Feynman [1982] determined that aa R = 5.38 + 0.12. R . We calculated the values of a0 and b in consecutive periods of around 30 years, each including 3 sunspot cycles (cycles 9-11, 10-12 and so on). The calculated values of the coefficients demonstrate a clear quasi-secular cycle (Fig. 2). Actually, geomagnetic activity can be divided into 3 rather than 2 components. The first one is the 'floor', equal to the а0 coefficient which represents the geomagnetic activity in the absence of sunspots. It is practically determined by the activity in the cycle minimum and varies smoothly from cycle to cycle. The second component is the geomagnetic activity caused by sunspot-related solar activity which is described by the straight line aaT = b.R so that aaR = а0 + aaT . The slope b of this line also changes cyclically. The third component ааP (the value above aaR ) is caused by high speed solar wind. It can be seen that when the coefficient а0 is big (high 'floor' of the geomagnetic activity), the geomagnetic activity is almost independent on the sunspot number (small coefficient b ), and when the 'floor' is low, the geomagnetic activity quickly grows with growing sunspot number. Fig.3 demonstrates that both the 'floor' of the geomagnetic activity а0 and the slope b don't depend on the phase of the sunspot cycle (upward or downward branch), but are different in different intervals. Besides, the scatter of values above aaR in any interval is much bigger during the downward branch which has to be expected because of the strong influence of high speed solar wind streams on the geomagnetic activity in this phase of the sunspot cycle [Georgieva, K., Kirov, B, 2005]. The question now is which solar agents cause the nonzero values of the geomagnetic activity 'floor', and which factors lead to the changes in the coefficients а0 and b .\",\n \"pages\": [\n 1,\n 2,\n 3\n ]\n },\n {\n \"title\": \"3. Types of geomagnetic storms\",\n \"content\": \"The geomagnetic storms differ in intensity as well as in characteristics. The intensity of the storm is determined by the parameters D, H и Z - the magnetic declination, change of the horizontal and vertical components of the Earth's magnetic field, respectively, measured in nT (Table 1), and the storm can be with a sudden or gradual commencement. In order to determine the origin of different storms, [Шельтинг, Обридко , 2011] compared the occurrence frequency of all, strong, moderate and weak storms with sudden and with gradual commencement to the number of sunspots. They found that the occurrence frequency of the sudden commencement storms correlates with the sunspot number, with correlation coefficient 0.872 +/- 0.06. In contrast, the correlation coefficient of the occurrence frequency of the gradual commencement storms and the sunspot number is practically zero (0.014 +/0.13), and their maximum is shifted by 1-3 years after the sunspot maximum. Further analysis shows that there is high correlation among storms of different intensity inside each of the groups, and absolutely no correlation between the two groups of storms. From there the authors make the conclusion that these two types of storms have different origin. Sudden commencement storms are caused by coronal mass ejections (CMEs). As the solar coronal mass ejections are associated with active areas, that is with local magnetic fields, a high correlation is observed between the occurrence frequency of sudden commencement storms and the number of sunspots. Gradual commencement storms are caused by high speed solar wind. It originates from solar coronal holes whose maximum is on the downward branch of the sunspot cycle. This leads to two maxima in geomagnetic activity in the course of the sunspot cycle, the second one being due mainly to the occurrence of many gradual commencement storms [Tsurutani, et al. 2006].\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"4. Geomagnetic activity 'floor'\",\n \"content\": \"The geomagnetic activity 'floor' is the geomagnetic activity in the absence of any sunspots. Practically it is determined by the geomagnetic activity in the sunspot minimum. As seen in Fig.4, during the whole investigated period, the geomagnetic activity with aa -index between 10 and 30 is caused by gradual commencement storms, but this is especially well pronounced in sunspot minimum periods. We can conclude that the geomagnetic activity 'floor' is determined by non sunspot-related solar activity. Fig.5 demonstrates that the variations in the geomagnetic activity floor follow, with the exception of cycle 13, the variations in the number of 30hour intervals with aa -index between 10 and 30 in the minimum of the respective cycle. Moreover, from cycle 14 to 21 (around 1985), an increase is observed in both the number of 3-hour intervals with 10< аа <30, and of the geomagnetic activity floor, after which they both begin decreasing. The correlation between the two quantities is 0.85 with p<0.01. It is seen that the geomagnetic activity floor in each cycle is determined by the geomagnetic activity in the range 10<аа<30 in the cycle minimum, and as far as this geomagnetic activity, especially in the cycle minimum, is related as shown above to gradual commencement storms, the floor is determined by the high speed solar wind streams causing gradual commencement storms. Therefore, the reason for the changing geomagnetic activity floor is the changing high speed solar wind reaching the Earth during sunspot minimum. It is interesting to note that at the same time as the increase in the floor changed to decrease (cycle 21), the increase in the solar global magnetic moment changed to a sharp decrease[Обридко, Шельтинг, 2009 ] - (Fig.6). It seems that the change in the solar global magnetic moment is reflected in the geomagnetic activity caused by the high speed solar wind during the sunspot minimum through its effects on the thickness of the heliospheric current sheet [Simon and Legrand, 1987].\",\n \"pages\": [\n 4,\n 5\n ]\n },\n {\n \"title\": \"5. Coefficient b (slope)\",\n \"content\": \"The sunspot-related geoeffective solar agents are the CMEs. It is known that the geoeffectiveness of CMEs vary little in the course of the sunspot cycle; considerably changes the geoeffectiveness of magnetic clouds (a subclass of CMEs with high and smoothly rotating magnetic field), but their number is negligible compared to the total number of CMEs except around sunspot minimum when their geoeffectiveness is low. Therefore, the varying contribution of CMEs to geomagnetic activity from year to year depends on their varying number. [Georgieva and Kirov, 2005]. Fig.7 presents the ratio of CMEs to the number of sunspots for the period 1996-2012. For the number of CMEs, the SOHO/LASCO CME catalog is used (http://cdaw.gsfc.nasa.gov/CME_list/) as it provides a fairly homogenous data set. It can be seen that the ratio is almost constant during the greater part of the sunspot cycle, with the exception of the periods of sunspot minima, especially in the minimum between cycles 23 and 24 which is known to be very peculiar. In 2007, 2008, and 2009 we had total annuals of 20, 70, and 60 CMEs, respectively, with the average annual number of sunspots between 3 and 7. A small change in the correlation between the sunspot number and the number of CMEs is observed in the previous sunspot minimum also, but it is only due to CMEs in a few single months. We can conclude that the increasing geomagnetic activity with increasing sunspot number (the coefficient b ) is due to the increasing number of CMEs with increasing number of sunspots.\",\n \"pages\": [\n 6\n ]\n },\n {\n \"title\": \"6. Forecasting the following cycle\",\n \"content\": \"Fig.8 demonstrates that the sunspot number in the cycle maximum is related to the geomagnetic activity floor in the same cycle. The correlation between the two variables is 0,792 with p=0.001. From this it follows that the characteristics of the whole cycle are set already at its beginning, and measuring the geomagnetic activity we can forecast to a great extend its maximum. On the other hand, given that the evolution of the Sun's magnetic moment is indicative of the changes in а0 , we can evaluate in advance the direction of change of the geomagnetic activity 'floor'.\",\n \"pages\": [\n 7\n ]\n },\n {\n \"title\": \"6. Summary and conclusions\",\n \"content\": \"The geomagnetic activity consists of three components: (1) a0 - the geomagnetic activity 'floor', theoretically equal to the activity at zero number of sunspots. Practically this activity is determined by the gradual commencement geomagnetic disturbances with 10< аа <30 in the beginning of the sunspot cycle; (2) aaT - the geomagnetic activity caused by CMEs whose number linearly increases with increasing number of sunspots aaT = b.R , so that aaR = a0 + b.R ; (3) ааP - the values of aa above aaR , caused by high speed solar wind streams from solar coronal holes. We have found that the variations of a0 have a quasi-secular cycle, with the direction of variation following the variation of the global magnetic moment of the Sun. On the other hand, we have found that a0 determined by the geomagnetic activity in the beginning of a cycle is directly related to the sunspot maximum in the same cycle. Therefore, if we know the direction of change (increasing or decreasing) of the global magnetic moment, we can forecast the increase or decrease of a0 in the next cycle, and from there - the increase or decrease of the sunspot maximum. Moreover, during the sunspot minimum we can quite accurately forecast the following sunspot minimum.\",\n \"pages\": [\n 7,\n 8\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Обридко В.Н., Шельтинг Б.Д. Некоторые аномалии эволюции глобальных и крупномасштабных магнитных полей на Солнце как предвестники нескольких предстоящих невысоких циклов// Письма в астрономический журнал. Т. 35. №3, С. 3844. 2009. Шельтинг Б.Д., Обридко В.Н. Магнитные бури с внезапным и постепенным началом как индексы солнечной активности// Всероссийская ежегодная конференция по физике Солнца. Пулково Русия. 2011. Feynman J. Geomagnetic and solar wind cycles, 1900-1975// J. Geophys. Res. 87, 6153-6162 (1982) Georgieva K., Kirov B. Helicity of magnetic clouds and solar cycle variations of their geoeffectiveness// Proceedings IAU Symposium 226 Coronal and Stellar Mass Ejections, Oxford University Press. P.470-472, 2005. Sabine E. On Periodical Laws Discoverable in the Mean Effects of the Larger Magnetic Disturbances// Phil. Trans. R. Soc. Lond. January 1, 1852 142 103-124; doi:10.1098/rstl.1852.0009. Simon P.A., Legrand J.P. : Some solar cycle phenomena related to the geomagnetic activity from 1868 to 1980. III - Quiet-days, fluctuating activity or the solar equatorial belt as the main origin of the solar wind flowing in the ecliptic plane// Astron. Astrophys. V. 182, P. 329-336, 1987. Tsurutani B.T., Gonzalez W. D., Gonzalez A.L.C. et al. , Corotating solar wind streams and recurrent geomagnetic activity: A review // J. Geophys. Res., V. 111, No A07S01, P. 1110711132, 2006.\",\n \"pages\": [\n 8\n ]\n }\n]"}}},{"rowIdx":93,"cells":{"bibcode":{"kind":"string","value":"2013IAUS..288..239M"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1209.3837.pdf"},"content":{"kind":"string","value":"\nNext Generation Deep 2 µ Survey\nJeremy Mould\nCentre for Astrophysics and Supercomputing, Swinburne University, Hawthorn 3122, Australia\n2 ARC Centre of Excellence for All-sky Astrophysics (CAASTRO) email: jmould@swin.edu.au\nAbstract.\nThere is a major opportunity for the KDUST 2.5m telescope to carry out the next generation IR survey. A resolution of 0.2 arcsec is obtainable from Dome A over a wide field. This opens a unique discovery space during the 2015-2025 decade.\nA next generation 2 µ survey will feed JWST with serendipitous targets for spectroscopy, including spectra and images of the first galaxies.\nKeywords. infrared, survey, galaxies\n1. Introduction: the state of the art of infrared surveys\nUKIDSS † has surveyed 7500 square degrees of the Northern sky, extending over both high and low Galactic latitudes, in the JHK bandpasses to K=18.3. This is three magnitudes deeper than 2MASS. UKIDSS has provided a near-infrared SDSS and a panoramic atlas of the Galactic plane. UKIDSS is actually five surveys, including two deep extragalactic elements, one covering 35 sq deg to K = 21, and the other reaching K = 23 over 0.77 sq deg.\nVIKING-VISTA ‡ is a kilo-degree infrared galaxy survey. The VIKING survey will image 1500 sq deg in Z, Y, J, H, and Ks to a limiting magnitude 1.4 mag beyond the UKIDSS Large Area Survey. It will furnish very accurate photometric redshifts, especially at z > 1, an important step in weak lensing analysis and observation of baryon acoustic oscillations. Other science drivers include the hunt for high redshift quasars, galaxy clusters, and the study of galaxy stellar masses.\nMould (2011) offers a summary of the prospects for improving on these surveys using the KDUST 2.5m telescope.\n2. KDUST camera architecture\nThe simplest option for a focal plane array is a Teledyne HgCdTe 2048 2 . A better option is 4096 2 or 2 x 2 (8.5 arcmin field). ANU has delivered two such cameras to the Gemini Observatory (McGregor et al. 2004, McGregor et al. 1999). The KDUST focal plane scale is appropriate without change. JHK and Kdark filters would be required.\nPlan B is for a Sofradir SATURN SW HgCdTe SWIR. However, these detectors have 150 electrons read noise and would require long exposures to overcome readout noise. Nevertheless they are feasible Plan B detectors for broadband survey work. Mosaicing many detectors is also acceptable for survey work, and, after mosaicing the focal plane, plan A and plan B detectors are fairly similar in cost.\n† www.ukidss.org ‡ www.astro-wise/projects/VIKING\n1\n3. The Antarctic advantage\nAbove the ground layer turbulence one obtains almost diffraction limited images over a wide field with low 2 µ background. This combination is only available from the Antarctic plateau, high altitude balloons and space. The competition, then, is space. We confine ourselves to WFIRST, since the ESA Euclid mission observes at H band, but not at K.\nAdvantages of WFIRST\n\n· Top ranked in ASTRO 2010 (Blandford 2009)\n· Broader band possible, e.g. 1.6-3.6 µ .\n· No clouds\n\nDisadvantages of WFIRST\n\n· 3 year mission lifetime\n· Earliest launch 2025\n· Order of magnitude higher cost\n\nProvided the US NRO supplies a 2.5m mirror, the following Astro2010-era disadvan-\ntages are no longer in effect.\n\n· Smaller aperture, 1.5 metre\n· Lower resolution\n· 200 nJy limit vs 70 nJy with KDUST\n\n4. Science case\nAn excellent science case for a 2.5m Antarctic telescope is presented by Burton et al. (2007).\nA further science case is that of WFIRST (Green et al. 2012)\n\n· Kuiper Belt census and properties\n· Cluster and Star-Forming-Region IMFs to planetary mass\n· The H 2 kink in star cluster CMDs\n· The most distant Star-Forming-Regions in the Milky Way\n· Quasars as a Reference Frame for Proper Motion Studies\n· Proper Motions and parallaxes of disk and bulge Stars\n· Cool white dwarfs as Galactic chronometers\n· Planetary transits\n· Evolution of massive Galaxies: formation of red sequence galaxies\n· Finding and weighing distant, high mass clusters of galaxies\n· Obscured quasars\n· Strongly lensed quasars\n· High-redshift quasars and Reionization\n· Faint end of the quasar luminosity function\n· Probing Epoch of Reionization with Lyman α emitters\n· Shapes of galaxy haloes from gravitational flexion\n\nTo focus on one of these areas, it is interesting to note the discovery space in the investigation of the epoch of reionization:\n\n· 1 µ band dropouts at z = 1.1/0.09 -1 = 11\n· J band dropouts at z = 1.4/0.09 -1 = 14\n· Galaxies with 10 8 year old stellar pops at z = 6\n· Pair production SNe (massive stars) at M K = -23\n· Activity from the progenitors of supermassive black holes\n· Dark stars, see Ilie et al. (2012)\n\n\n· Young globular clusters with 10 6 year free fall times and M/L approaching 10 -4\n· Rare bright objects requiring wide field survey, then JWST, TMT, EELT or GMT spectra.\n\n5. The next steps\nThe first question is whether this project is compatible with KDUST 2.5 (Cui 2010, Zhao et al. 2011). Assuming it is, we need to finalize the IR camera configuration, find IR camera partners, such as U. Tasmania, Swinburne University, UNSW, AAO/Macquarie University, Texas A&M, ANU and University of Melbourne. We then need to flowdown the science to camera requirements.\nTo maximize advantage over VISTA, the speed of a survey to a given magnitude (inverse of the number of years to complete 1 sr) is a factor of ∼ 9. The goal is to increase this and get a full order of magnitude (or better). Perhaps we should move from K to Kdark, when we have accurate measurements of the relevant backgrounds. We could consider adding a reimager to KDUST and undersample a bit. Alternatively a slightly faster secondary on KDUST could be entertained. For Sofradir chips the minimum exposure time is larger to overcome readout noise. For a background of 0.1 mJy/sq arcsec, the photon rate is half a photon per sec. This requires > 2000 sec exposures for photon noise to double the Sofradir readout noise. (70% QE assumed.)\nA construction and operations schedule tentatively would be:\n\n· January 2015 ARC LIEF funding, followed by Preliminary Design Review\n·\n2016 Texas A & M purchases Teledyne arrays; ANU purchases dewar and filters\n· 2016 Integrate and test focal plane at ANU or AAO\n· January 2017 Integrate telescope/ camera in Fremantle\n· 2018-2021 operations (within the international antarctic science region) at Kunlun\n\nStation\n\n· 2022 return of focal plane to the USA.\n\nThis schedule is set by the time to manufacture and test the KDUST telescope in China. If it slipped a year or two, so could the instrument schedule, although we do have the precedent of GSAOI, where the camera was ready years before the adaptive optics. The Centre for All-Sky Astrophysics in Australia and the proposed Joint Australia-China research centre would provide a very appropriate context for this collaboration. At Dome A astronomy can have another world class astrophysics enterprise in Antarctica yielding major results.\nAcknowledgements\nI would like to thank our Chinese colleagues for hosting a workshop at the Institute of High Energy Physics of the Chinese Academy of Sciences in Beijing in November 2011, where a number of these ideas were developed. Survey astronomy is supported by the Australian Research Council through CAASTRO † . The Centre for All-sky Astrophysics is an Australian Research Council Centre of Excellence, funded by grant CE11001020.\nReferences\nBlandford, R. 2009, AAS, 213, 21301\nBurton, M. et al. 2007, PASA 22, 199.\n† www.caastro.org\nCui, Xiangqun 2010, Highlights of Astronomy, 15, 639 Green, J. et al. 2012, astro-ph 1208.4012 Ilie, C., Freese, K., Valluri, M., Iliev, I., & Shapiro, P. 2012, MNRAS, 422, 2164 McGregor, P., Hart, J., Stevanovic, D., Bloxham, G., Jones, D., Van Harmelen, J., Griesbach, J., Dawson, M., Young, P., & Jarnyk, M. 2004, SPIE, 5492, 1033 McGregor, P. J., Conroy, P., Bloxham, G., & van Harmelen, J. 1999 PASA, 16, 273 Mould, J. 2011, PASA, 28, 266 Thompson, R. et al. 2007, ApJ, 657, 669\nZhao, Gong-Bo, Zhan, Hu, Wang, Lifan, Fan, Zuhui, Zhang, Xinmin 2011, PASP, 123, 725\nDiscussion\nCharling Tao: There are problems with the persistence of Sofradir arrays.\nJeremy Mould: There are strategies for dealing with the persistence. But, thank you, this will need to be investigated for the Plan B detectors.\nHans Zinnecker: What about L and M band?\nJeremy Mould: This is feasible. However, even in the Antarctic the thermal background comes roaring up and one becomes uncompetitive with space for broadband.\n\n\n
Figure 1. The proposed survey will reach to within a magnitude of the NICMOS deep field (Thompson et al. 2007) with similar resolution, but cover many steradians. The field shown here is a few arc minutes. Image courtesy NASA, Hubble Space Telescope, University of Arizona .
\n\n"},"sections":{"kind":"list like","value":[{"title":"Jeremy Mould","content":"Centre for Astrophysics and Supercomputing, Swinburne University, Hawthorn 3122, Australia 2 ARC Centre of Excellence for All-sky Astrophysics (CAASTRO) email: jmould@swin.edu.au","pages":[1]},{"title":"Abstract.","content":"There is a major opportunity for the KDUST 2.5m telescope to carry out the next generation IR survey. A resolution of 0.2 arcsec is obtainable from Dome A over a wide field. This opens a unique discovery space during the 2015-2025 decade. A next generation 2 µ survey will feed JWST with serendipitous targets for spectroscopy, including spectra and images of the first galaxies. Keywords. infrared, survey, galaxies","pages":[1]},{"title":"1. Introduction: the state of the art of infrared surveys","content":"UKIDSS † has surveyed 7500 square degrees of the Northern sky, extending over both high and low Galactic latitudes, in the JHK bandpasses to K=18.3. This is three magnitudes deeper than 2MASS. UKIDSS has provided a near-infrared SDSS and a panoramic atlas of the Galactic plane. UKIDSS is actually five surveys, including two deep extragalactic elements, one covering 35 sq deg to K = 21, and the other reaching K = 23 over 0.77 sq deg. VIKING-VISTA ‡ is a kilo-degree infrared galaxy survey. The VIKING survey will image 1500 sq deg in Z, Y, J, H, and Ks to a limiting magnitude 1.4 mag beyond the UKIDSS Large Area Survey. It will furnish very accurate photometric redshifts, especially at z > 1, an important step in weak lensing analysis and observation of baryon acoustic oscillations. Other science drivers include the hunt for high redshift quasars, galaxy clusters, and the study of galaxy stellar masses. Mould (2011) offers a summary of the prospects for improving on these surveys using the KDUST 2.5m telescope.","pages":[1]},{"title":"2. KDUST camera architecture","content":"The simplest option for a focal plane array is a Teledyne HgCdTe 2048 2 . A better option is 4096 2 or 2 x 2 (8.5 arcmin field). ANU has delivered two such cameras to the Gemini Observatory (McGregor et al. 2004, McGregor et al. 1999). The KDUST focal plane scale is appropriate without change. JHK and Kdark filters would be required. Plan B is for a Sofradir SATURN SW HgCdTe SWIR. However, these detectors have 150 electrons read noise and would require long exposures to overcome readout noise. Nevertheless they are feasible Plan B detectors for broadband survey work. Mosaicing many detectors is also acceptable for survey work, and, after mosaicing the focal plane, plan A and plan B detectors are fairly similar in cost. † www.ukidss.org ‡ www.astro-wise/projects/VIKING 1","pages":[1]},{"title":"3. The Antarctic advantage","content":"Above the ground layer turbulence one obtains almost diffraction limited images over a wide field with low 2 µ background. This combination is only available from the Antarctic plateau, high altitude balloons and space. The competition, then, is space. We confine ourselves to WFIRST, since the ESA Euclid mission observes at H band, but not at K.","pages":[2]},{"title":"Disadvantages of WFIRST","content":"Provided the US NRO supplies a 2.5m mirror, the following Astro2010-era disadvan- tages are no longer in effect.","pages":[2]},{"title":"4. Science case","content":"An excellent science case for a 2.5m Antarctic telescope is presented by Burton et al. (2007). A further science case is that of WFIRST (Green et al. 2012) To focus on one of these areas, it is interesting to note the discovery space in the investigation of the epoch of reionization:","pages":[2]},{"title":"5. The next steps","content":"The first question is whether this project is compatible with KDUST 2.5 (Cui 2010, Zhao et al. 2011). Assuming it is, we need to finalize the IR camera configuration, find IR camera partners, such as U. Tasmania, Swinburne University, UNSW, AAO/Macquarie University, Texas A&M, ANU and University of Melbourne. We then need to flowdown the science to camera requirements. To maximize advantage over VISTA, the speed of a survey to a given magnitude (inverse of the number of years to complete 1 sr) is a factor of ∼ 9. The goal is to increase this and get a full order of magnitude (or better). Perhaps we should move from K to Kdark, when we have accurate measurements of the relevant backgrounds. We could consider adding a reimager to KDUST and undersample a bit. Alternatively a slightly faster secondary on KDUST could be entertained. For Sofradir chips the minimum exposure time is larger to overcome readout noise. For a background of 0.1 mJy/sq arcsec, the photon rate is half a photon per sec. This requires > 2000 sec exposures for photon noise to double the Sofradir readout noise. (70% QE assumed.) A construction and operations schedule tentatively would be:","pages":[3]},{"title":"Station","content":"This schedule is set by the time to manufacture and test the KDUST telescope in China. If it slipped a year or two, so could the instrument schedule, although we do have the precedent of GSAOI, where the camera was ready years before the adaptive optics. The Centre for All-Sky Astrophysics in Australia and the proposed Joint Australia-China research centre would provide a very appropriate context for this collaboration. At Dome A astronomy can have another world class astrophysics enterprise in Antarctica yielding major results.","pages":[3]},{"title":"Acknowledgements","content":"I would like to thank our Chinese colleagues for hosting a workshop at the Institute of High Energy Physics of the Chinese Academy of Sciences in Beijing in November 2011, where a number of these ideas were developed. Survey astronomy is supported by the Australian Research Council through CAASTRO † . The Centre for All-sky Astrophysics is an Australian Research Council Centre of Excellence, funded by grant CE11001020.","pages":[3]},{"title":"References","content":"Blandford, R. 2009, AAS, 213, 21301 Burton, M. et al. 2007, PASA 22, 199. † www.caastro.org Cui, Xiangqun 2010, Highlights of Astronomy, 15, 639 Green, J. et al. 2012, astro-ph 1208.4012 Ilie, C., Freese, K., Valluri, M., Iliev, I., & Shapiro, P. 2012, MNRAS, 422, 2164 McGregor, P., Hart, J., Stevanovic, D., Bloxham, G., Jones, D., Van Harmelen, J., Griesbach, J., Dawson, M., Young, P., & Jarnyk, M. 2004, SPIE, 5492, 1033 McGregor, P. J., Conroy, P., Bloxham, G., & van Harmelen, J. 1999 PASA, 16, 273 Mould, J. 2011, PASA, 28, 266 Thompson, R. et al. 2007, ApJ, 657, 669 Zhao, Gong-Bo, Zhan, Hu, Wang, Lifan, Fan, Zuhui, Zhang, Xinmin 2011, PASP, 123, 725","pages":[3,4]},{"title":"Discussion","content":"Charling Tao: There are problems with the persistence of Sofradir arrays. Jeremy Mould: There are strategies for dealing with the persistence. But, thank you, this will need to be investigated for the Plan B detectors. Hans Zinnecker: What about L and M band? Jeremy Mould: This is feasible. However, even in the Antarctic the thermal background comes roaring up and one becomes uncompetitive with space for broadband.","pages":[4]}],"string":"[\n {\n \"title\": \"Jeremy Mould\",\n \"content\": \"Centre for Astrophysics and Supercomputing, Swinburne University, Hawthorn 3122, Australia 2 ARC Centre of Excellence for All-sky Astrophysics (CAASTRO) email: jmould@swin.edu.au\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Abstract.\",\n \"content\": \"There is a major opportunity for the KDUST 2.5m telescope to carry out the next generation IR survey. A resolution of 0.2 arcsec is obtainable from Dome A over a wide field. This opens a unique discovery space during the 2015-2025 decade. A next generation 2 µ survey will feed JWST with serendipitous targets for spectroscopy, including spectra and images of the first galaxies. Keywords. infrared, survey, galaxies\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction: the state of the art of infrared surveys\",\n \"content\": \"UKIDSS † has surveyed 7500 square degrees of the Northern sky, extending over both high and low Galactic latitudes, in the JHK bandpasses to K=18.3. This is three magnitudes deeper than 2MASS. UKIDSS has provided a near-infrared SDSS and a panoramic atlas of the Galactic plane. UKIDSS is actually five surveys, including two deep extragalactic elements, one covering 35 sq deg to K = 21, and the other reaching K = 23 over 0.77 sq deg. VIKING-VISTA ‡ is a kilo-degree infrared galaxy survey. The VIKING survey will image 1500 sq deg in Z, Y, J, H, and Ks to a limiting magnitude 1.4 mag beyond the UKIDSS Large Area Survey. It will furnish very accurate photometric redshifts, especially at z > 1, an important step in weak lensing analysis and observation of baryon acoustic oscillations. Other science drivers include the hunt for high redshift quasars, galaxy clusters, and the study of galaxy stellar masses. Mould (2011) offers a summary of the prospects for improving on these surveys using the KDUST 2.5m telescope.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"2. KDUST camera architecture\",\n \"content\": \"The simplest option for a focal plane array is a Teledyne HgCdTe 2048 2 . A better option is 4096 2 or 2 x 2 (8.5 arcmin field). ANU has delivered two such cameras to the Gemini Observatory (McGregor et al. 2004, McGregor et al. 1999). The KDUST focal plane scale is appropriate without change. JHK and Kdark filters would be required. Plan B is for a Sofradir SATURN SW HgCdTe SWIR. However, these detectors have 150 electrons read noise and would require long exposures to overcome readout noise. Nevertheless they are feasible Plan B detectors for broadband survey work. Mosaicing many detectors is also acceptable for survey work, and, after mosaicing the focal plane, plan A and plan B detectors are fairly similar in cost. † www.ukidss.org ‡ www.astro-wise/projects/VIKING 1\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"3. The Antarctic advantage\",\n \"content\": \"Above the ground layer turbulence one obtains almost diffraction limited images over a wide field with low 2 µ background. This combination is only available from the Antarctic plateau, high altitude balloons and space. The competition, then, is space. We confine ourselves to WFIRST, since the ESA Euclid mission observes at H band, but not at K.\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"Disadvantages of WFIRST\",\n \"content\": \"Provided the US NRO supplies a 2.5m mirror, the following Astro2010-era disadvan- tages are no longer in effect.\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"4. Science case\",\n \"content\": \"An excellent science case for a 2.5m Antarctic telescope is presented by Burton et al. (2007). A further science case is that of WFIRST (Green et al. 2012) To focus on one of these areas, it is interesting to note the discovery space in the investigation of the epoch of reionization:\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"5. The next steps\",\n \"content\": \"The first question is whether this project is compatible with KDUST 2.5 (Cui 2010, Zhao et al. 2011). Assuming it is, we need to finalize the IR camera configuration, find IR camera partners, such as U. Tasmania, Swinburne University, UNSW, AAO/Macquarie University, Texas A&M, ANU and University of Melbourne. We then need to flowdown the science to camera requirements. To maximize advantage over VISTA, the speed of a survey to a given magnitude (inverse of the number of years to complete 1 sr) is a factor of ∼ 9. The goal is to increase this and get a full order of magnitude (or better). Perhaps we should move from K to Kdark, when we have accurate measurements of the relevant backgrounds. We could consider adding a reimager to KDUST and undersample a bit. Alternatively a slightly faster secondary on KDUST could be entertained. For Sofradir chips the minimum exposure time is larger to overcome readout noise. For a background of 0.1 mJy/sq arcsec, the photon rate is half a photon per sec. This requires > 2000 sec exposures for photon noise to double the Sofradir readout noise. (70% QE assumed.) A construction and operations schedule tentatively would be:\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"Station\",\n \"content\": \"This schedule is set by the time to manufacture and test the KDUST telescope in China. If it slipped a year or two, so could the instrument schedule, although we do have the precedent of GSAOI, where the camera was ready years before the adaptive optics. The Centre for All-Sky Astrophysics in Australia and the proposed Joint Australia-China research centre would provide a very appropriate context for this collaboration. At Dome A astronomy can have another world class astrophysics enterprise in Antarctica yielding major results.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"Acknowledgements\",\n \"content\": \"I would like to thank our Chinese colleagues for hosting a workshop at the Institute of High Energy Physics of the Chinese Academy of Sciences in Beijing in November 2011, where a number of these ideas were developed. Survey astronomy is supported by the Australian Research Council through CAASTRO † . The Centre for All-sky Astrophysics is an Australian Research Council Centre of Excellence, funded by grant CE11001020.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Blandford, R. 2009, AAS, 213, 21301 Burton, M. et al. 2007, PASA 22, 199. † www.caastro.org Cui, Xiangqun 2010, Highlights of Astronomy, 15, 639 Green, J. et al. 2012, astro-ph 1208.4012 Ilie, C., Freese, K., Valluri, M., Iliev, I., & Shapiro, P. 2012, MNRAS, 422, 2164 McGregor, P., Hart, J., Stevanovic, D., Bloxham, G., Jones, D., Van Harmelen, J., Griesbach, J., Dawson, M., Young, P., & Jarnyk, M. 2004, SPIE, 5492, 1033 McGregor, P. J., Conroy, P., Bloxham, G., & van Harmelen, J. 1999 PASA, 16, 273 Mould, J. 2011, PASA, 28, 266 Thompson, R. et al. 2007, ApJ, 657, 669 Zhao, Gong-Bo, Zhan, Hu, Wang, Lifan, Fan, Zuhui, Zhang, Xinmin 2011, PASP, 123, 725\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"Discussion\",\n \"content\": \"Charling Tao: There are problems with the persistence of Sofradir arrays. Jeremy Mould: There are strategies for dealing with the persistence. But, thank you, this will need to be investigated for the Plan B detectors. Hans Zinnecker: What about L and M band? Jeremy Mould: This is feasible. However, even in the Antarctic the thermal background comes roaring up and one becomes uncompetitive with space for broadband.\",\n \"pages\": [\n 4\n ]\n }\n]"}}},{"rowIdx":94,"cells":{"bibcode":{"kind":"string","value":"2013IAUS..291..141D"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1210.6981.pdf"},"content":{"kind":"string","value":"\nA peculiar thermonuclear X-ray burst from the transiently accreting neutron star SAX J1810.8-2609\nN. Degenaar 1 † and R. Wijnands 2\n1 University of Michigan, Dept. of Astronomy, 500 Church St, Ann Arbor, MI 48109, USA email: degenaar@umich.edu\n2 Astronomical Institute 'Anton Pannekoek', University of Amsterdam Postbus 94249, 1090 GE Amsterdam, The Netherlands email: r.a.d.wijnands@uva.nl\nAbstract. We report on a thermonuclear (type-I) X-ray burst that was detected from the neutron star low-mass X-ray binary SAX J1810.8-2609 in 2007 with Swift . This event was longer ( /similarequal 20 min) and more energetic (a radiated energy of E b /similarequal 6 . 5 × 10 39 erg) than other X-ray bursts observed from this source. A possible explanation for the peculiar properties is that the X-ray burst occurred during the early stage of the outburst when the neutron star was relatively cold, which allows for the accumulation of a thicker layer of fuel. We also report on a new accretion outburst of SAX J1810.8-2609 that was observed with MAXI and Swift in 2012. The outburst had a duration of /similarequal 17 days and reached a 2-10 keV peak luminosity of L X /similarequal 3 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . This is a factor > 10 more luminous than the two previous outbursts observed from the source, and classifies it as a bright rather than a faint X-ray transient.\nKeywords. stars: neutron, X-rays: binaries, X-rays: bursts, X-rays: individual (SAX J1810.82609)\n1. Introduction\nSAX J1810.8-2609 is a transient neutron star LMXB that was discovered by BeppoSAX on 1998 March 10 when it exhibited an accretion outburst (Ubertini et al. 1998). BeppoSAX and ROSAT observations detected the source at a luminosity of L X /similarequal (0 . 2 -1) × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 (2-10 keV), and suggest that the outburst had a duration of /greaterorsimilar 13 days (Greiner et al. 1999; Natalucci et al. 2000).\nSoon after its discovery, a type-I X-ray burst was detected from SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000). These thermonuclear explosions occur on the surface of accreting neutron stars due to unstable burning of helium/hydrogen. The majority of observed X-ray bursts have a duration of /similarequal 10-100 s and generate a radiated energy output of E b /similarequal 10 39 erg (e.g., Galloway et al. 2008; Chelovekov & Grebenev 2011). Occasionally intermediately-long X-ray bursts are observed, which are more energetic ( E b /similarequal 10 40 -41 erg) and longer (tens of minutes) than normal X-ray bursts (e.g., in 't Zand et al. 2008; Falanga et al. 2008; Linares et al. 2009; Degenaar et al. 2010, 2011).\nRenewed activity was detected from SAX J1810.8-2609 with Swift , INTEGRAL and RXTE in 2007 August (Parsons et al. 2007; Degenaar et al. 2007; Haymoz et al. 2007; Fiocchi et al. 2009). During this outburst INTEGRAL detected 17 X-ray bursts, which had an observed duration of /similarequal 10-30 s (3-25 keV; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The brightest event reached a bolometric peak flux of F peak /similarequal 1 × 10 -7 erg cm -2 s -1 , implying a distance of D /lessorequalslant 5.7 kpc (Fiocchi et al. 2009).\n\n\n
Figure 1. Swift /XRT light curve showing the decay of the X-ray burst detected from SAX J1810.8-2609 on 2007 August 5 (BAT trigger 287042). The black and grey data points indicate WT and PC mode data, respectively. The dashed curve shows a fit to a power-law decay with an index of α = -1 . 43, and the solid line a fit to an exponential function with a decay time of τ = 129 s. The dotted horizontal line indicates the persistent emission level.
\n\n2. A long thermonuclear X-ray burst detected with Swift in 2007\nOn 2007 August 5 at 11:27:26 UT, the Swift /BAT was triggered by SAX J1810.8-2609 (trigger 287042; Parsons et al. 2007). We investigated the trigger data and follow-up XRT observations, and conclude that the BAT triggered on a type-I X-ray burst. For the details on the reduction and analysis procedures we refer to Degenaar et al. (2012a). We carried out exactly the same analysis for SAX J1810.8-2609.\nThe BAT light curve shows a single /similarequal 10-s long peak. The average spectrum can be described by a black body model with a temperature of kT bb /similarequal 3 . 0 keV and an emitting radius of R bb /similarequal 7 km (Table 1), which is typical for the peak emission of X-ray bursts. We estimate a bolometric peak flux of F peak /similarequal 7 × 10 -8 erg cm -2 s -1 (0.01-100 keV), which is similar to that observed for other X-ray bursts of SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011).\nAutomated follow-up XRT observations commenced /similarequal 65 s after the BAT trigger. The XRT light curve shows a continuous decay in count rate until it settles at a constant level /similarequal 1200 s after the BAT trigger (Figure 1). The light curve can be described by an exponential with a decay time of τ /similarequal 129 s, but a power law with a decay index of α /similarequal -1 . 43 provides a better fit (Figure 1). The XRT data can be described by a black body model that cools along the decay (Table 1), a typical signature of X-ray bursts.\nThe total estimated fluence of the X-ray burst inferred from the BAT and XRT data is f b /similarequal 1 . 6 × 10 -6 erg cm -2 . For an assumed distance of D = 5 . 7 kpc, this translates into a total radiated energy of E b /similarequal 6 . 5 × 10 39 erg. We use /similarequal 2 ks of XRT PC mode data obtained between /similarequal 4000-6000 s after the BAT trigger to characterize the persistent accretion emission at the time of the X-ray burst (Figure 1). This data can be described by a simple absorbed power law model with N H = (6 . 2 ± 0 . 1) × 10 21 cm -2 and Γ = 2 . 4 ± 0 . 3. We estimate a bolometric accretion luminosity of L acc /similarequal 5 × 10 35 ( D/ 5 . 7 kpc) 2 erg s -1 . The characteristics of the X-ray burst and persistent emission are summarized in Table 1.\nSAX J1810.8-2609 was covered by the RXTE /PCA Galactic bulge scan project between 1999 February 5 and 2011 October 30 (Swank & Markwardt 2001), which reveals one outburst from the source (in 2007). The source was detected above the background level ( L X /greaterorsimilar 3 × 10 35 erg s -1 ) between 2007 August 4 and October 28 at an average 2-10 keV luminosity of L X /similarequal 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 . Non-detections on August 1 and November 1, suggest an outburst duration of /similarequal 85-92 days.\n
\n\n
Table 1. Time-resolved spectral analysis of the X-ray burst.
\n
\nNote. Quoted errors refer to 90% confidence levels. ∆ t indicates the time since the BAT trigger and F bol the estimated bolometric flux over the interval. The simultaneous fit resulted in N H = (2 . 2 ± 0 . 3) × 10 21 cm -2 ( χ 2 ν = 0 . 93 for 281 d.o.f.) and we assumed D = 5 . 7 kpc.\n3. A new accretion outburst in 2012 seen with MAXI and Swift\nMAXI monitoring observations show that SAX J1810.8-2609 was again active between 2012 May 7-24. We estimate an average 2-20 keV luminosity of L X /similarequal 6 . 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 , peaking at L X /similarequal 2 . 0 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . The MAXI data suggests that the source intensity was L X /greaterorsimilar 10 36 erg s -1 for /similarequal 17 days.\nA pointed Swift /XRT observation was performed on 2012 May 12 (Obs ID 32459001). The WT spectrum is best described by a combined power law and black body model with N H = (0 . 51 ± 0 . 02) × 10 21 cm -2 , Γ = 1 . 67 ± 0 . 05, kT bb = 0 . 74 ± 0 . 03 keV, and R bb = 13 . 4 ± 1 . 4 km ( χ 2 ν = 1 . 09 for 721 d.o.f.). The resulting unabsorbed 2-10 keV model flux of F X /similarequal 6 . 9 × 10 -9 erg cm -2 s -1 implies a luminosity of L X /similarequal 2 . 7 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 .\nSimultaneously obtained UVOT observations using the uw 1 filter ( λ 0 = 2600 ˚ A) reveal an object at R.A. = 18 h 10 m 44.487 s , decl. = -26 · 09 ' 01.30 '' , with an uncertainty of 0 . 61 '' . This coincides exactly with the Chandra position of SAX J1810.8-2609 (Jonker et al. 2004) and suggests that this is the UV counterpart of the LMXB. We determine (Vega) magnitudes of uw 1 = 18 . 80 ± 0 . 12 and 18 . 57 ± 0 . 22 mag for the two separate exposures.\n4. Discussion\nThe X-ray burst from SAX J1810.8-2609 observed with Swift is both longer and more energetic than others observed from the source (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The duration is similar to that of intermediately long X-ray bursts, but the radiated energy output is an order of magnitude lower. This suggests that the X-ray burst observed from SAX J1810.8-2609 was a normal X-ray burst, albeit with an unusual long duration. There are different explanations for such peculiar X-ray bursts (see Degenaar et al. 2012a, and references therein).\nThe long X-ray burst occurred within a few days after the onset of the 2007 accretion outburst. This implies that the neutron star crust had likely not yet been significantly heated due to accretion, and hence the heat flux from the crust towards the surface was small. Combined with a low accretion rate ( /similarequal 0.1% of Eddington), this suggests that the temperature in the accreted envelop was likely low. This allows for the accumulation of a relatively thick layer of fuel before the ignition conditions are met, and may have caused its unusual properties compared to other X-ray bursts observed from the source.\nThe X-ray flux observed with MAXI and Swift during the 2012 outburst of SAX J1810.8-2609 is a factor of > 10 higher than seen during its 1998 and 2007 outbursts. Although the previous activity of the source classified it as a faint LMXB (Natalucci et al. 2000; Jonker et al. 2004; Fiocchi et al. 2009), this demonstrates that it is actually a bright\n
\n\n
Table 2. Characteristics of the X-ray burst and the post-burst persistent emission.
\n
\nNote. The quoted peak flux is unabsorbed and for the 0.01-100 keV energy range. The quoted accretion luminosity and mass-accretion rates were inferred from fitting /similarequal 2 ks of post-burst persistent emission. We assumed a distance of D = 5 . 7 kpc.\ntransient (cf. Wijnands et al. 2006). It is not uncommon for bright X-ray transients to exhibit faint outbursts (e.g., Degenaar & Wijnands 2009; Degenaar et al. 2012b).\nAcknowledgements\nND is supported by NASA through Hubble Postdoctoral Fellowship grant number HSTHF-51287.01-A from the Space Telescope Science Institute. RW is supported by a European Research Council starting grant. This work made use of Swift data supplied by the UK Swift Science Data Centre at the University of Leicester, MAXI data provided by RIKEN, JAXA and the MAXI team, and publicly available RXTE /PCA bulge scan light curves maintained by C. Markwardt.\nReferences\nChelovekov, I. V. & Grebenev, S. A. 2011, Astronomy Letters , 37, 597\nCocchi, M., Bazzano, A., Natalucci, L., et al. 1999, Astrophysical Letters and Communications ,\n38, 133\nDegenaar, N., Jonker, P. G., Torres, M. A. P., et al. 2010, MNRAS , 404, 1591\nDegenaar, N., Klein-Wolt, M., & Wijnands, R. 2007, The Astronomer's Telegram , 1175\nDegenaar, N., Linares, M., Altamirano, D., & Wijnands, R. 2012a, ApJ , 759, 8\nDegenaar, N. & Wijnands, R. 2009, A&A , 495, 547\nDegenaar, N., Wijnands, R., Cackett, E. M., et al. 2012b, A&A , 545, A49\nDegenaar, N., Wijnands, R., & Kaur, R. 2011, MNRAS , 414, L104\nFalanga, M., Chenevez, J., Cumming, A., et al. 2008, A&A , 484, 43\nFiocchi, M., Natalucci, L., Chenevez, J., et al. 2009, ApJ , 693, 333\nGalloway, D. K., Muno, M. P., Hartman, J. M., et al. 2008, ApJS , 179, 360\nGreiner, J., Castro-Tirado, A. J., Boller, T., et al. 1999, MNRAS , 308, L17\nHaymoz, P., Eckert, D., Shaw, S., & Kuulkers, E. 2007, The Astronomer's Telegram , 1185, 1\nin 't Zand, J. J. M., Bassa, C. G., Jonker, P. G., et al. 2008, A&A , 485, 183\nJonker, P. G., Galloway, D. K., McClintock, J. E., et al. 2004, MNRAS , 354, 666\nLinares, M., Watts, A. L., Wijnands, R., et al. 2009, MNRAS , 392, L11\nNatalucci, L., Bazzano, A., Cocchi, M., et al. 2000, ApJ , 536, 891\nParsons, A. M., Barthelmy, S. D., Gehrels, N., et al. 2007, GRB Coordinates Network , 6706\nSwank, J. & Markwardt, C. 2001, in ASP Conf. Series , Vol. 251, New Century of X-ray Astron- omy, ed. H. Inoue & H. Kunieda, 94\nUbertini, P., in 't Zand, J., Tesseri, A., Ricci, D., & Piro, L. 1998, IAU Circ. , 6838, 1\nWijnands, R., in 't Zand, J. J. M., Rupen, M., et al. 2006, A&A , 449, 1117\n"},"sections":{"kind":"list like","value":[{"title":"N. Degenaar 1 † and R. Wijnands 2","content":"1 University of Michigan, Dept. of Astronomy, 500 Church St, Ann Arbor, MI 48109, USA email: degenaar@umich.edu 2 Astronomical Institute 'Anton Pannekoek', University of Amsterdam Postbus 94249, 1090 GE Amsterdam, The Netherlands email: r.a.d.wijnands@uva.nl Abstract. We report on a thermonuclear (type-I) X-ray burst that was detected from the neutron star low-mass X-ray binary SAX J1810.8-2609 in 2007 with Swift . This event was longer ( /similarequal 20 min) and more energetic (a radiated energy of E b /similarequal 6 . 5 × 10 39 erg) than other X-ray bursts observed from this source. A possible explanation for the peculiar properties is that the X-ray burst occurred during the early stage of the outburst when the neutron star was relatively cold, which allows for the accumulation of a thicker layer of fuel. We also report on a new accretion outburst of SAX J1810.8-2609 that was observed with MAXI and Swift in 2012. The outburst had a duration of /similarequal 17 days and reached a 2-10 keV peak luminosity of L X /similarequal 3 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . This is a factor > 10 more luminous than the two previous outbursts observed from the source, and classifies it as a bright rather than a faint X-ray transient. Keywords. stars: neutron, X-rays: binaries, X-rays: bursts, X-rays: individual (SAX J1810.82609)","pages":[1]},{"title":"1. Introduction","content":"SAX J1810.8-2609 is a transient neutron star LMXB that was discovered by BeppoSAX on 1998 March 10 when it exhibited an accretion outburst (Ubertini et al. 1998). BeppoSAX and ROSAT observations detected the source at a luminosity of L X /similarequal (0 . 2 -1) × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 (2-10 keV), and suggest that the outburst had a duration of /greaterorsimilar 13 days (Greiner et al. 1999; Natalucci et al. 2000). Soon after its discovery, a type-I X-ray burst was detected from SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000). These thermonuclear explosions occur on the surface of accreting neutron stars due to unstable burning of helium/hydrogen. The majority of observed X-ray bursts have a duration of /similarequal 10-100 s and generate a radiated energy output of E b /similarequal 10 39 erg (e.g., Galloway et al. 2008; Chelovekov & Grebenev 2011). Occasionally intermediately-long X-ray bursts are observed, which are more energetic ( E b /similarequal 10 40 -41 erg) and longer (tens of minutes) than normal X-ray bursts (e.g., in 't Zand et al. 2008; Falanga et al. 2008; Linares et al. 2009; Degenaar et al. 2010, 2011). Renewed activity was detected from SAX J1810.8-2609 with Swift , INTEGRAL and RXTE in 2007 August (Parsons et al. 2007; Degenaar et al. 2007; Haymoz et al. 2007; Fiocchi et al. 2009). During this outburst INTEGRAL detected 17 X-ray bursts, which had an observed duration of /similarequal 10-30 s (3-25 keV; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The brightest event reached a bolometric peak flux of F peak /similarequal 1 × 10 -7 erg cm -2 s -1 , implying a distance of D /lessorequalslant 5.7 kpc (Fiocchi et al. 2009).","pages":[1]},{"title":"2. A long thermonuclear X-ray burst detected with Swift in 2007","content":"On 2007 August 5 at 11:27:26 UT, the Swift /BAT was triggered by SAX J1810.8-2609 (trigger 287042; Parsons et al. 2007). We investigated the trigger data and follow-up XRT observations, and conclude that the BAT triggered on a type-I X-ray burst. For the details on the reduction and analysis procedures we refer to Degenaar et al. (2012a). We carried out exactly the same analysis for SAX J1810.8-2609. The BAT light curve shows a single /similarequal 10-s long peak. The average spectrum can be described by a black body model with a temperature of kT bb /similarequal 3 . 0 keV and an emitting radius of R bb /similarequal 7 km (Table 1), which is typical for the peak emission of X-ray bursts. We estimate a bolometric peak flux of F peak /similarequal 7 × 10 -8 erg cm -2 s -1 (0.01-100 keV), which is similar to that observed for other X-ray bursts of SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). Automated follow-up XRT observations commenced /similarequal 65 s after the BAT trigger. The XRT light curve shows a continuous decay in count rate until it settles at a constant level /similarequal 1200 s after the BAT trigger (Figure 1). The light curve can be described by an exponential with a decay time of τ /similarequal 129 s, but a power law with a decay index of α /similarequal -1 . 43 provides a better fit (Figure 1). The XRT data can be described by a black body model that cools along the decay (Table 1), a typical signature of X-ray bursts. The total estimated fluence of the X-ray burst inferred from the BAT and XRT data is f b /similarequal 1 . 6 × 10 -6 erg cm -2 . For an assumed distance of D = 5 . 7 kpc, this translates into a total radiated energy of E b /similarequal 6 . 5 × 10 39 erg. We use /similarequal 2 ks of XRT PC mode data obtained between /similarequal 4000-6000 s after the BAT trigger to characterize the persistent accretion emission at the time of the X-ray burst (Figure 1). This data can be described by a simple absorbed power law model with N H = (6 . 2 ± 0 . 1) × 10 21 cm -2 and Γ = 2 . 4 ± 0 . 3. We estimate a bolometric accretion luminosity of L acc /similarequal 5 × 10 35 ( D/ 5 . 7 kpc) 2 erg s -1 . The characteristics of the X-ray burst and persistent emission are summarized in Table 1. SAX J1810.8-2609 was covered by the RXTE /PCA Galactic bulge scan project between 1999 February 5 and 2011 October 30 (Swank & Markwardt 2001), which reveals one outburst from the source (in 2007). The source was detected above the background level ( L X /greaterorsimilar 3 × 10 35 erg s -1 ) between 2007 August 4 and October 28 at an average 2-10 keV luminosity of L X /similarequal 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 . Non-detections on August 1 and November 1, suggest an outburst duration of /similarequal 85-92 days. Note. Quoted errors refer to 90% confidence levels. ∆ t indicates the time since the BAT trigger and F bol the estimated bolometric flux over the interval. The simultaneous fit resulted in N H = (2 . 2 ± 0 . 3) × 10 21 cm -2 ( χ 2 ν = 0 . 93 for 281 d.o.f.) and we assumed D = 5 . 7 kpc.","pages":[2,3]},{"title":"3. A new accretion outburst in 2012 seen with MAXI and Swift","content":"MAXI monitoring observations show that SAX J1810.8-2609 was again active between 2012 May 7-24. We estimate an average 2-20 keV luminosity of L X /similarequal 6 . 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 , peaking at L X /similarequal 2 . 0 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . The MAXI data suggests that the source intensity was L X /greaterorsimilar 10 36 erg s -1 for /similarequal 17 days. A pointed Swift /XRT observation was performed on 2012 May 12 (Obs ID 32459001). The WT spectrum is best described by a combined power law and black body model with N H = (0 . 51 ± 0 . 02) × 10 21 cm -2 , Γ = 1 . 67 ± 0 . 05, kT bb = 0 . 74 ± 0 . 03 keV, and R bb = 13 . 4 ± 1 . 4 km ( χ 2 ν = 1 . 09 for 721 d.o.f.). The resulting unabsorbed 2-10 keV model flux of F X /similarequal 6 . 9 × 10 -9 erg cm -2 s -1 implies a luminosity of L X /similarequal 2 . 7 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . Simultaneously obtained UVOT observations using the uw 1 filter ( λ 0 = 2600 ˚ A) reveal an object at R.A. = 18 h 10 m 44.487 s , decl. = -26 · 09 ' 01.30 '' , with an uncertainty of 0 . 61 '' . This coincides exactly with the Chandra position of SAX J1810.8-2609 (Jonker et al. 2004) and suggests that this is the UV counterpart of the LMXB. We determine (Vega) magnitudes of uw 1 = 18 . 80 ± 0 . 12 and 18 . 57 ± 0 . 22 mag for the two separate exposures.","pages":[3]},{"title":"4. Discussion","content":"The X-ray burst from SAX J1810.8-2609 observed with Swift is both longer and more energetic than others observed from the source (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The duration is similar to that of intermediately long X-ray bursts, but the radiated energy output is an order of magnitude lower. This suggests that the X-ray burst observed from SAX J1810.8-2609 was a normal X-ray burst, albeit with an unusual long duration. There are different explanations for such peculiar X-ray bursts (see Degenaar et al. 2012a, and references therein). The long X-ray burst occurred within a few days after the onset of the 2007 accretion outburst. This implies that the neutron star crust had likely not yet been significantly heated due to accretion, and hence the heat flux from the crust towards the surface was small. Combined with a low accretion rate ( /similarequal 0.1% of Eddington), this suggests that the temperature in the accreted envelop was likely low. This allows for the accumulation of a relatively thick layer of fuel before the ignition conditions are met, and may have caused its unusual properties compared to other X-ray bursts observed from the source. The X-ray flux observed with MAXI and Swift during the 2012 outburst of SAX J1810.8-2609 is a factor of > 10 higher than seen during its 1998 and 2007 outbursts. Although the previous activity of the source classified it as a faint LMXB (Natalucci et al. 2000; Jonker et al. 2004; Fiocchi et al. 2009), this demonstrates that it is actually a bright Note. The quoted peak flux is unabsorbed and for the 0.01-100 keV energy range. The quoted accretion luminosity and mass-accretion rates were inferred from fitting /similarequal 2 ks of post-burst persistent emission. We assumed a distance of D = 5 . 7 kpc. transient (cf. Wijnands et al. 2006). It is not uncommon for bright X-ray transients to exhibit faint outbursts (e.g., Degenaar & Wijnands 2009; Degenaar et al. 2012b).","pages":[3,4]},{"title":"Acknowledgements","content":"ND is supported by NASA through Hubble Postdoctoral Fellowship grant number HSTHF-51287.01-A from the Space Telescope Science Institute. RW is supported by a European Research Council starting grant. This work made use of Swift data supplied by the UK Swift Science Data Centre at the University of Leicester, MAXI data provided by RIKEN, JAXA and the MAXI team, and publicly available RXTE /PCA bulge scan light curves maintained by C. Markwardt.","pages":[4]},{"title":"References","content":"Chelovekov, I. V. & Grebenev, S. A. 2011, Astronomy Letters , 37, 597 Cocchi, M., Bazzano, A., Natalucci, L., et al. 1999, Astrophysical Letters and Communications , 38, 133 Degenaar, N., Jonker, P. G., Torres, M. A. P., et al. 2010, MNRAS , 404, 1591 Degenaar, N., Klein-Wolt, M., & Wijnands, R. 2007, The Astronomer's Telegram , 1175 Degenaar, N., Linares, M., Altamirano, D., & Wijnands, R. 2012a, ApJ , 759, 8 Degenaar, N. & Wijnands, R. 2009, A&A , 495, 547 Degenaar, N., Wijnands, R., Cackett, E. M., et al. 2012b, A&A , 545, A49 Degenaar, N., Wijnands, R., & Kaur, R. 2011, MNRAS , 414, L104 Falanga, M., Chenevez, J., Cumming, A., et al. 2008, A&A , 484, 43 Fiocchi, M., Natalucci, L., Chenevez, J., et al. 2009, ApJ , 693, 333 Galloway, D. K., Muno, M. P., Hartman, J. M., et al. 2008, ApJS , 179, 360 Greiner, J., Castro-Tirado, A. J., Boller, T., et al. 1999, MNRAS , 308, L17 Haymoz, P., Eckert, D., Shaw, S., & Kuulkers, E. 2007, The Astronomer's Telegram , 1185, 1 in 't Zand, J. J. M., Bassa, C. G., Jonker, P. G., et al. 2008, A&A , 485, 183 Jonker, P. G., Galloway, D. K., McClintock, J. E., et al. 2004, MNRAS , 354, 666 Linares, M., Watts, A. L., Wijnands, R., et al. 2009, MNRAS , 392, L11 Natalucci, L., Bazzano, A., Cocchi, M., et al. 2000, ApJ , 536, 891 Parsons, A. M., Barthelmy, S. D., Gehrels, N., et al. 2007, GRB Coordinates Network , 6706 Swank, J. & Markwardt, C. 2001, in ASP Conf. Series , Vol. 251, New Century of X-ray Astron- omy, ed. H. Inoue & H. Kunieda, 94 Ubertini, P., in 't Zand, J., Tesseri, A., Ricci, D., & Piro, L. 1998, IAU Circ. , 6838, 1 Wijnands, R., in 't Zand, J. J. M., Rupen, M., et al. 2006, A&A , 449, 1117","pages":[4]}],"string":"[\n {\n \"title\": \"N. Degenaar 1 † and R. Wijnands 2\",\n \"content\": \"1 University of Michigan, Dept. of Astronomy, 500 Church St, Ann Arbor, MI 48109, USA email: degenaar@umich.edu 2 Astronomical Institute 'Anton Pannekoek', University of Amsterdam Postbus 94249, 1090 GE Amsterdam, The Netherlands email: r.a.d.wijnands@uva.nl Abstract. We report on a thermonuclear (type-I) X-ray burst that was detected from the neutron star low-mass X-ray binary SAX J1810.8-2609 in 2007 with Swift . This event was longer ( /similarequal 20 min) and more energetic (a radiated energy of E b /similarequal 6 . 5 × 10 39 erg) than other X-ray bursts observed from this source. A possible explanation for the peculiar properties is that the X-ray burst occurred during the early stage of the outburst when the neutron star was relatively cold, which allows for the accumulation of a thicker layer of fuel. We also report on a new accretion outburst of SAX J1810.8-2609 that was observed with MAXI and Swift in 2012. The outburst had a duration of /similarequal 17 days and reached a 2-10 keV peak luminosity of L X /similarequal 3 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . This is a factor > 10 more luminous than the two previous outbursts observed from the source, and classifies it as a bright rather than a faint X-ray transient. Keywords. stars: neutron, X-rays: binaries, X-rays: bursts, X-rays: individual (SAX J1810.82609)\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"SAX J1810.8-2609 is a transient neutron star LMXB that was discovered by BeppoSAX on 1998 March 10 when it exhibited an accretion outburst (Ubertini et al. 1998). BeppoSAX and ROSAT observations detected the source at a luminosity of L X /similarequal (0 . 2 -1) × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 (2-10 keV), and suggest that the outburst had a duration of /greaterorsimilar 13 days (Greiner et al. 1999; Natalucci et al. 2000). Soon after its discovery, a type-I X-ray burst was detected from SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000). These thermonuclear explosions occur on the surface of accreting neutron stars due to unstable burning of helium/hydrogen. The majority of observed X-ray bursts have a duration of /similarequal 10-100 s and generate a radiated energy output of E b /similarequal 10 39 erg (e.g., Galloway et al. 2008; Chelovekov & Grebenev 2011). Occasionally intermediately-long X-ray bursts are observed, which are more energetic ( E b /similarequal 10 40 -41 erg) and longer (tens of minutes) than normal X-ray bursts (e.g., in 't Zand et al. 2008; Falanga et al. 2008; Linares et al. 2009; Degenaar et al. 2010, 2011). Renewed activity was detected from SAX J1810.8-2609 with Swift , INTEGRAL and RXTE in 2007 August (Parsons et al. 2007; Degenaar et al. 2007; Haymoz et al. 2007; Fiocchi et al. 2009). During this outburst INTEGRAL detected 17 X-ray bursts, which had an observed duration of /similarequal 10-30 s (3-25 keV; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The brightest event reached a bolometric peak flux of F peak /similarequal 1 × 10 -7 erg cm -2 s -1 , implying a distance of D /lessorequalslant 5.7 kpc (Fiocchi et al. 2009).\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"2. A long thermonuclear X-ray burst detected with Swift in 2007\",\n \"content\": \"On 2007 August 5 at 11:27:26 UT, the Swift /BAT was triggered by SAX J1810.8-2609 (trigger 287042; Parsons et al. 2007). We investigated the trigger data and follow-up XRT observations, and conclude that the BAT triggered on a type-I X-ray burst. For the details on the reduction and analysis procedures we refer to Degenaar et al. (2012a). We carried out exactly the same analysis for SAX J1810.8-2609. The BAT light curve shows a single /similarequal 10-s long peak. The average spectrum can be described by a black body model with a temperature of kT bb /similarequal 3 . 0 keV and an emitting radius of R bb /similarequal 7 km (Table 1), which is typical for the peak emission of X-ray bursts. We estimate a bolometric peak flux of F peak /similarequal 7 × 10 -8 erg cm -2 s -1 (0.01-100 keV), which is similar to that observed for other X-ray bursts of SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). Automated follow-up XRT observations commenced /similarequal 65 s after the BAT trigger. The XRT light curve shows a continuous decay in count rate until it settles at a constant level /similarequal 1200 s after the BAT trigger (Figure 1). The light curve can be described by an exponential with a decay time of τ /similarequal 129 s, but a power law with a decay index of α /similarequal -1 . 43 provides a better fit (Figure 1). The XRT data can be described by a black body model that cools along the decay (Table 1), a typical signature of X-ray bursts. The total estimated fluence of the X-ray burst inferred from the BAT and XRT data is f b /similarequal 1 . 6 × 10 -6 erg cm -2 . For an assumed distance of D = 5 . 7 kpc, this translates into a total radiated energy of E b /similarequal 6 . 5 × 10 39 erg. We use /similarequal 2 ks of XRT PC mode data obtained between /similarequal 4000-6000 s after the BAT trigger to characterize the persistent accretion emission at the time of the X-ray burst (Figure 1). This data can be described by a simple absorbed power law model with N H = (6 . 2 ± 0 . 1) × 10 21 cm -2 and Γ = 2 . 4 ± 0 . 3. We estimate a bolometric accretion luminosity of L acc /similarequal 5 × 10 35 ( D/ 5 . 7 kpc) 2 erg s -1 . The characteristics of the X-ray burst and persistent emission are summarized in Table 1. SAX J1810.8-2609 was covered by the RXTE /PCA Galactic bulge scan project between 1999 February 5 and 2011 October 30 (Swank & Markwardt 2001), which reveals one outburst from the source (in 2007). The source was detected above the background level ( L X /greaterorsimilar 3 × 10 35 erg s -1 ) between 2007 August 4 and October 28 at an average 2-10 keV luminosity of L X /similarequal 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 . Non-detections on August 1 and November 1, suggest an outburst duration of /similarequal 85-92 days. Note. Quoted errors refer to 90% confidence levels. ∆ t indicates the time since the BAT trigger and F bol the estimated bolometric flux over the interval. The simultaneous fit resulted in N H = (2 . 2 ± 0 . 3) × 10 21 cm -2 ( χ 2 ν = 0 . 93 for 281 d.o.f.) and we assumed D = 5 . 7 kpc.\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"3. A new accretion outburst in 2012 seen with MAXI and Swift\",\n \"content\": \"MAXI monitoring observations show that SAX J1810.8-2609 was again active between 2012 May 7-24. We estimate an average 2-20 keV luminosity of L X /similarequal 6 . 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 , peaking at L X /similarequal 2 . 0 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . The MAXI data suggests that the source intensity was L X /greaterorsimilar 10 36 erg s -1 for /similarequal 17 days. A pointed Swift /XRT observation was performed on 2012 May 12 (Obs ID 32459001). The WT spectrum is best described by a combined power law and black body model with N H = (0 . 51 ± 0 . 02) × 10 21 cm -2 , Γ = 1 . 67 ± 0 . 05, kT bb = 0 . 74 ± 0 . 03 keV, and R bb = 13 . 4 ± 1 . 4 km ( χ 2 ν = 1 . 09 for 721 d.o.f.). The resulting unabsorbed 2-10 keV model flux of F X /similarequal 6 . 9 × 10 -9 erg cm -2 s -1 implies a luminosity of L X /similarequal 2 . 7 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . Simultaneously obtained UVOT observations using the uw 1 filter ( λ 0 = 2600 ˚ A) reveal an object at R.A. = 18 h 10 m 44.487 s , decl. = -26 · 09 ' 01.30 '' , with an uncertainty of 0 . 61 '' . This coincides exactly with the Chandra position of SAX J1810.8-2609 (Jonker et al. 2004) and suggests that this is the UV counterpart of the LMXB. We determine (Vega) magnitudes of uw 1 = 18 . 80 ± 0 . 12 and 18 . 57 ± 0 . 22 mag for the two separate exposures.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"4. Discussion\",\n \"content\": \"The X-ray burst from SAX J1810.8-2609 observed with Swift is both longer and more energetic than others observed from the source (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The duration is similar to that of intermediately long X-ray bursts, but the radiated energy output is an order of magnitude lower. This suggests that the X-ray burst observed from SAX J1810.8-2609 was a normal X-ray burst, albeit with an unusual long duration. There are different explanations for such peculiar X-ray bursts (see Degenaar et al. 2012a, and references therein). The long X-ray burst occurred within a few days after the onset of the 2007 accretion outburst. This implies that the neutron star crust had likely not yet been significantly heated due to accretion, and hence the heat flux from the crust towards the surface was small. Combined with a low accretion rate ( /similarequal 0.1% of Eddington), this suggests that the temperature in the accreted envelop was likely low. This allows for the accumulation of a relatively thick layer of fuel before the ignition conditions are met, and may have caused its unusual properties compared to other X-ray bursts observed from the source. The X-ray flux observed with MAXI and Swift during the 2012 outburst of SAX J1810.8-2609 is a factor of > 10 higher than seen during its 1998 and 2007 outbursts. Although the previous activity of the source classified it as a faint LMXB (Natalucci et al. 2000; Jonker et al. 2004; Fiocchi et al. 2009), this demonstrates that it is actually a bright Note. The quoted peak flux is unabsorbed and for the 0.01-100 keV energy range. The quoted accretion luminosity and mass-accretion rates were inferred from fitting /similarequal 2 ks of post-burst persistent emission. We assumed a distance of D = 5 . 7 kpc. transient (cf. Wijnands et al. 2006). It is not uncommon for bright X-ray transients to exhibit faint outbursts (e.g., Degenaar & Wijnands 2009; Degenaar et al. 2012b).\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"Acknowledgements\",\n \"content\": \"ND is supported by NASA through Hubble Postdoctoral Fellowship grant number HSTHF-51287.01-A from the Space Telescope Science Institute. RW is supported by a European Research Council starting grant. This work made use of Swift data supplied by the UK Swift Science Data Centre at the University of Leicester, MAXI data provided by RIKEN, JAXA and the MAXI team, and publicly available RXTE /PCA bulge scan light curves maintained by C. Markwardt.\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Chelovekov, I. V. & Grebenev, S. A. 2011, Astronomy Letters , 37, 597 Cocchi, M., Bazzano, A., Natalucci, L., et al. 1999, Astrophysical Letters and Communications , 38, 133 Degenaar, N., Jonker, P. G., Torres, M. A. P., et al. 2010, MNRAS , 404, 1591 Degenaar, N., Klein-Wolt, M., & Wijnands, R. 2007, The Astronomer's Telegram , 1175 Degenaar, N., Linares, M., Altamirano, D., & Wijnands, R. 2012a, ApJ , 759, 8 Degenaar, N. & Wijnands, R. 2009, A&A , 495, 547 Degenaar, N., Wijnands, R., Cackett, E. M., et al. 2012b, A&A , 545, A49 Degenaar, N., Wijnands, R., & Kaur, R. 2011, MNRAS , 414, L104 Falanga, M., Chenevez, J., Cumming, A., et al. 2008, A&A , 484, 43 Fiocchi, M., Natalucci, L., Chenevez, J., et al. 2009, ApJ , 693, 333 Galloway, D. K., Muno, M. P., Hartman, J. M., et al. 2008, ApJS , 179, 360 Greiner, J., Castro-Tirado, A. J., Boller, T., et al. 1999, MNRAS , 308, L17 Haymoz, P., Eckert, D., Shaw, S., & Kuulkers, E. 2007, The Astronomer's Telegram , 1185, 1 in 't Zand, J. J. M., Bassa, C. G., Jonker, P. G., et al. 2008, A&A , 485, 183 Jonker, P. G., Galloway, D. K., McClintock, J. E., et al. 2004, MNRAS , 354, 666 Linares, M., Watts, A. L., Wijnands, R., et al. 2009, MNRAS , 392, L11 Natalucci, L., Bazzano, A., Cocchi, M., et al. 2000, ApJ , 536, 891 Parsons, A. M., Barthelmy, S. D., Gehrels, N., et al. 2007, GRB Coordinates Network , 6706 Swank, J. & Markwardt, C. 2001, in ASP Conf. Series , Vol. 251, New Century of X-ray Astron- omy, ed. H. Inoue & H. Kunieda, 94 Ubertini, P., in 't Zand, J., Tesseri, A., Ricci, D., & Piro, L. 1998, IAU Circ. , 6838, 1 Wijnands, R., in 't Zand, J. J. M., Rupen, M., et al. 2006, A&A , 449, 1117\",\n \"pages\": [\n 4\n ]\n }\n]"}}},{"rowIdx":95,"cells":{"bibcode":{"kind":"string","value":"2013IAUS..294..289A"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1305.5282.pdf"},"content":{"kind":"string","value":"\nFractal multi-scale nature of solar/stellar magnetic field\nValentina I. Abramenko\nBig Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314, USA\nABSTRACT\nAn abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy release events, conditions for turbulent dynamo action, nature of turbulent magnetic diffusivity, and even the dual nature of solar dynamo. In this talk, I will briefly outline how the ideas of multi-fractality are used to explore the above mentioned aspects of solar magnetism.\n1. Introduction: Why Fractals?\nA mathematical fractal is a self-similar object on all possible spatial and time scales. It means that when we proceed from large to smaller scales, we will see exactly the same picture. From mathematical standpoint this means that a unique scaling law holds for all scales. A fractal (or, more rigorously, a mono-fractal) is a deterministic, predictable system. Mathematical monofractals differ drastically from what we observe in nature: fractal-like structures in nature are multi-fractals - a superposition of infinite number of mono-fractals.\nThe transition from mono-fractals to multi-fractals turns an amusing mathematical toy into a powerful tool to study real processes in nature. The matter is that multi-fractals posses the same properties in both the spatial and temporal domains. This means that if we see a very complex, jagged shape in space (multi-fractal in space), then we will observe a violent, burst-like behavior in time (multi-fractal in time). For such systems, any small perturbation can cause an avalanche of any possible size.\nTherefore, revealing the fact that a system under study is a fractal does not allow us to make inferences about its nature and essential properties of its behavior. We need something\nmore, namely, to know of how many mono-fractals our system is made of. Numerous examples of fractals and multi-fractals can be found (e.g., Feder 1989; Schroeder 2000, Internet).\nMathematical details of the fractal calculus are well described as well (e.g., Baumann 2005; McAteer et al. 2007). Historically, when analyzing spatial objects, their capability to be organized into very jagged structures with extended voids and sharp peaks is addressed as a property of multi-fractality. At the sate time, while analyzing time series, we address the same property as intermittency. Thus, multi-fractality and intermittency are two terms for the same physical property of a system. I will use both of them in this talk.\nSeveral approaches were elaborated during a couple of last decades to probe the properties of multi-fractality in different fields of science. In a brief review below, I will focus on multi-fractality techniques applied in astrophysics. Thus, multi-fractal systems are capable of self-organization (i.e., formation of larger entities from smaller ones via inverse cascade), and of self-organized criticality (SOC) when burst-like energy release events of any scale are possible at any moment (e.g., Charbonneau et al. 2001; Longcope & Noonan 2000; Aschwanden 2011).\nA theory of catastrophes is also based on the multi-fractal nature of astrophysical phenomena (Priest & Forbes 2002; Isenberg & Forbes 2007). Percolating clusters (Balke et al. 1993; Seiden & Wentzel 1996; Pustil'nik 1999; Schatten 2007) are also fractals and multi-fractals.\nDirect calculations of fractal dimensions and spectra of multi-fractality is one of the most popular tool to explore astrophysical multi-fractals (e.g., Lawrence et al. 1993; Meunier 1999; Lepreti et al. 1999; McAteer et al. 2007; Dimitropoulou et al. 2009; Abramenko & Yurchyshyn 2010a; Aschwanden 2011).\nAnother possibility to study multi-fractality is to analyze high statistical moments by means of distribution functions (Bogdan et al. 1988; Parnell et al. 2009), or structure functions (Consolini et al. 1999; Abramenko et al. 2002; Abramenko 2005; Uritsky et al. 2007; Abramenko & Yurchyshyn 2010b; Abramenko et al. 2012).\nEssential physical properties of multi-fractals can be formulated as follows.\n\n(i) Scaling laws change with scale, i.e., no unique power law index can be valid for all scales;\n(ii) Large fluctuations (in both time and space domains) are not rare and contribute significantly to high statistical moments, which grow as the data set expands;\n(iii) Direct and inverse cascades along scales are possible (fragmentation and aggregation), which results in capability to form larger features from smaller ones, i.e., self-organization and SOC state.\n\nThese properties can help us to diagnose the presence and degree of multi-fractality of various\nastrophysical phenomena. Meanwhile, keeping in mind that in astrophysical magnetism we deal with a specific type of a multi-fractal medium, namely, intermittent turbulence in an electroconductive flow , we can take advantage of it and incorporate other very important properties and tools. So our list of properties can be extended:\n\n(iv) Intermittent turbulent magnetized plasma is capable of amplifying a seed magnetic field, i.e., local fast dynamo is at work (Zeldovich et al. 1987; Biskamp 1993; Vogler & Schussler 2007; Pietarila Graham et al. 2010), see also a recent review by Brandenburg et al. (2012);\n(v) Turbulent plasma at high Reynolds number displays properties of multi-fractality and intermittency in spatial/temporal structures of temperatures, velocities, density, etc. (see, e.g., Zeldovich et al. 1987; Frisch 1995);\n(vi) The regime of diffusivity on multi-fractals is expected to be an anomalous diffusion.\n\nBased on these properties of multi-fractal systems, I will discuss below how exploration of these properties can help us in understanding of solar and stellar magnetism. It is impossible in the framework of this invited talk to discuss all aforementioned approaches and tools in great details, so I will concentrate on the analysis of structure functions, which are used in my research.\n2. Structure functions approach to study multi-fractality\nSince Kolmogorov's study (Kolmogorov 1941), various models have been proposed to describe the statistical behavior of fully developed turbulence. In these studies, the flow is modeled using statistically averaged quantities, and structure functions play a significant role. They are defined as statistical moments of the q -powers of the increment of a field. The definition can be applied to different fields (e.g., velocity, temperature, magnetic field, etc). Here, in the most of the cases, I will refer to the line-of-sight component of the magnetic field, B l , for which the structure function can be written as\nS q ( r ) = 〈| B l ( x + r ) -B l ( x ) | q 〉 , (1)\nwhere x is the current pixel on a magnetogram, r is the separation vector between any two points used to measure the increment (see the lower right panel in Figure 1, and q is the order of a statistical moment, which takes on real values. The angular brackets denote averaging over the magnetogram, and the vector r is allowed to adopt all possible orientations, θ , on the magnetogram. The next step is to calculate the scaling of the structure functions, which is defined as the slope, ζ ( q ) , measured inside some range of scales where the S q ( r ) -function is linear and the field is intermittent. The function ζ ( q ) is shown in the upper right panel in Figure 1.\nA weak point in the above technique is the determination of the range, ∆ r , where the slopes\n\n\n
Fig. 1.- Structure functions S q ( r ) ( upper left ) calculated from a magnetogram of active region NOAA 0501 ( lower right ) according to Eq. (1). Lower left - flatness function F ( r ) derived from the structure functions using Eq. (2). Vertical dotted lines in both left panels mark the interval of intermittency, ∆ r , where flatness grows as power law when r decreases. The index κ is the power index of the flatness function determined within ∆ r . The slopes of S q ( r ), defined for each q within ∆ r , constitute ζ ( q ) function ( upper right ), which is concave (straight) for a multi-fractal/intermittent (mono-fractal/non-intermittent) field. An example of a separation vector r and the corresponding directional angle θ are shown on the magnetogram.
\n\nof the structure functions are to be calculated. To visualize the range of intermittency, ∆ r , we suggest to use the flatness function (Abramenko 2005), which is determined as the ratio of the fourth statistical moment to the square of the second statistical moment. To better identify the effect of intermittency, we reinforced the definition of the flatness function and calculated the hyper-flatness function, namely, the ratio of the sixth moment to the cube of the second moment:\nF ( r ) = S 6 ( r ) / ( S 2 ( r )) 3 ∼ k -κ . (2)\nFor simplicity, we will refer to F ( r ) as the flatness function, or multi-fractality/intermittency spectrum. For a non-intermittent structure, the flatness function is not dependent on the scale, r . On the contrary, for an intermittent/multi-fractal structure, the flatness grows as power-law, when the scale decreases. The slope of flatness function, κ , and the width of ∆ r characterize the degree of multi-fractality and intermittency.\nApplication of this technique to two hundred of solar active regions observed with SOHO/MDI in the high resolution mode (Abramenko & Yurchyshyn 2010a) demonstrated that active regions of high flare productivity display steeper and broader multifractality spectra, F ( r ) . The inference agrees with the formulated above statement that multi-fractality in spatial domain is accompanied by intermittency (burst-like behavior) in time. Moreover, for any multi-fractal system, individual bursts cannot be precisely predicted in advance. So, the exact prediction of the location and the onset moment of a flare (of any size), strictly speaking, is a hopeless task. Based on different indirect indications, one may only hope to provide a probabilistic estimate for ongoing flaring.\nMulti-fractality of time series of X-ray emission from an individual solar flare was discussed in McAteer et al. (2007), where an inference on the fractal nature of the flaring current sheet was made.\nI will focus below on a solar surface outside active regions, which occupy usually more than 80% of the entire solar surface. Many important aspects of solar magnetism are rooted there.\n3. Multi-fractality in the solar surface\nExamples of line-of-sight (LOS) magnetograms recorded in coronal holes (CHs) using different solar instruments are shown in Figure 2. The left panel shows data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO, Scherrer et al. 2012), the middle panel shows LOS magnetic field provided by Hinode Solar Optical Telescope SpectroPolarimeter (SOT/SP, Tsuneta et al. 2008), and the right panel presents a magnetogram from the New Solar Telescope (NST) (Goode et al. 2010) operating at the Big Bear Solar Observatory (BBSO). Note that the NST data were obtained at a near-infrared spectral line (1.56 µm ) and\nrepresent the magnetic field in the deep photosphere at depths of about 50 km below the τ 500 = 1 level. Figure 2 clearly demonstrates that with improved telescope resolution more mixed polarity magnetic elements become visible inside a CH. In spite of the fact that the three magnetograms refer to different CHs, this tendency is well defined.\n\n\n
Fig. 2.- Examples of LOS magnetograms recorded inside CHs with three solar instruments (from left to right): SDO/HMI magnetogram (Aug 12, 2011, spatial sampling of 0. '' 5); SOT/SP magnetogram (Mar 10, 2007, spatial sampling of 0. '' 16); BBSO/NST magnetogram (Jun 2, 2012, spatial sampling of 0. '' 098). Red boxes and arrows outline areas of the same size.
\n\nFlatness functions calculated from the three above mentioned magnetograms are shown in Figure 3. The HMI data show only a hint of multi-fractality on scales above 1500 km and a very shallow slope of F ( r ) ( κ = -0 . 07 ). The HMI resolution of 1 '' obviously is not sufficient to clearly reveal multi-fractality in quiet Sun. Meanwhile, the SOT/SP data show a much broader scale range of multi-fractality down to approximately 630 km and a steeper slope ( κ = -0 . 107 ). The HMI result refers to the height of 280-360 km (the effective line formation level of the FeI 617.3 nm spectral line, Gurtovenko & R.I.Kostyk (1989)), whereas the SOT/NBF data refer to a level of 400-700 km in the photosphere (the line formation height of the NaI 589.6 nm spectral line is discussed in Sheminova (1998)). The flatness function obtained from NST data clearly reveal (at the deeper layer) strong intermittency and multi-fractality on scales down to ∼ 400 km.\n\n\n
Fig. 3.- Flatness functions calculated from the magnetograms shown in Fig.2. Dashed lines show best linear fits to the data points inside intervals starting above the small-scale cutoff, r /star . For better compatison, the curves are shifted along the vertical axis.
\n\nThus, the multi-fractal nature of small-scale magnetic fields becomes better pronounced with depth and improvement of spatial resolution, which leads us to conclude that intermittency and multi-fractality is an intrinsic property of the near-surface magnetic fields in the quiet Sun.\nMagnetic elements against granulation inside a CH are shown in Figure 4, where the background is an NST solar granulation image overplotted with NST LOS and transverse magnetic features and Hinode SOT Narrow Band Filter (NBF) LOS magnetic field.\nIn the upper right corner of the image, a fragment of bright points (BPs) filigree corresponding to the super-granular boundary is visible. The rest of the image shows the intra-network area, where nine isolated magnetic elements were detected by the SOT/NBF. All of them are co-spatial with BPs and with the LOS signal from the NST. In six cases there are neither opposite polarity nor transverse magnetic field features in the closest vicinity. This may indicate that these mag-\n\n\n
Fig. 4.- Background - NST/TiO image of 26.6 '' 0 × 20.1 '' in size recorded in a CH at 18:20:32 UT on Aug 12, 2011. Blue (red) contours show the line-of-sight positive (negative) component measured with NST and correspond to 90, 210, 300 G. Green contours represent the signal from the transverse magnetic field component from NST, ( Q 2 + U 2 ) 1 / 2 , corresponding to 100 and 200 G. Yellow and turquoise contours outline the Hinode SOT/NBF magnetic elements of negative (-50, -100, -300 G) and positive (50 G) polarities for the same day and time.
\n\nnetic elements are footpoints of open magnetic flux tubes representing the skeleton of the CH. The presence of BPs indicates that they might be produced via the convective collapse (Parker 1978; Spruit 1979).\nAt the same time, a significant part of the intra-network population is composed of magnetic features, which are not related to BPs and scattered over granules and inter-granular lanes. These magnetic elements were not detected by SOT/NBF and they are not necessarily very weak. On the contrary, they are quite compatible (by size and intensity) with those detected by the both instruments, they are simply not visible in NBF magnetograms. A simplest explanation could be the difference in heights. As I mentioned above, the NST measures the magnetic signal formed very deep in the photosphere, precisely, at the depth of 50 km below the τ 500 = 1 level, while the\nmagnetic signal measured with SOT/NBF is formed at the hight of approximately 400-700 km. If magnetic elements associated with granules are predominantly small (200-500 km in length) closed loops anchored at a depth of about -50 km, they might not be visible at the altitude of 400-700 km. This speculation is supported by the inspection of mutual location of Stokes V features (blue and red contours) and the transverse magnetic field features (green contours) in Figure 4. Indeed, the V-signal is co-spatial with the ( Q 2 + U 2 ) signal for the granules-associated magnetic elements, which supports the idea of closed loops (or bunches of loops) rather than presence of singular footpoints of extended, high loops or open field lines.\nAs for the magnetic elements associated with BPs and visible with the both instruments, they seem to be the best candidates for the roots of the open field lines, as we mentioned above. This can explain why they are visible on different heights.\nThus, the data allows us to speculate that the BPs-associated magnetic elements are related to the advection and convective collapse, whereas the numerous granule-associated intra-network elements are situated deeper in the photosphere and might be produced (at least, part of them) by local turbulent dynamo (see the talk by Dr. Tsuneta in this Symposium).\nMulti-fractality of granulation . To drive local turbulent dynamo, the environment should be a highly turbulent medium, i.e., to be a multi-fractal. Is the solar granulation pattern a multi-fractal? To explore the question, Abramenko et al. (2012) used a NST data set of solar granulation images obtained for the quiet Sun area on the solar disk center recorded under excellent seeing conditions. Flatness functions for 36 independent snapshots and their average are shown in Figure 5 a .\nThe flatness functions indicate that solar granulation is non-intermittent (a mono-fractal) on scales exceeding approximately 600 km, and it becomes highly intermittent and multi-fractal on scales below 600 km. Thus, a random, Gaussian-like distribution of granule size holds down to 600 km only. On smaller scales, the multi-fractal spatial organization of solar granulation takes over.\nA distribution function of granular size (Figure 5 b ) further confirms this inference. On scales of approximately 600 and 1300 km, the averaged probability distribution function (PDF) rapidly changes its slope. This varying power law PDF is suggestive that the observed ensemble of granules may consist of two populations with distinct properties: regular granules and minigranules. Decomposition of the observed PDF showed that the best fit is achieved with a combination of a log-normal function, f 1 , representing mini-granules, and a Gaussian function, f 2 , representing regular granules. Their sum perfectly fits to the observational data.\nUntil now it was thought that solar convection produces convection cells, visible on the solar surface as granules, of characteristic ('dominant') spatial scale of about 1000 km and\n\n\n
Fig. 5.a - Flatness functions calculated from 36 granulation images (gray) and their average (turquoise). The dashed segments show the best linear fits to the data points. The blue arrow divides the multi-fractality range where the flatness function varies as a power law from the Gaussian range where the flatness function is scale independent. b - decomposition of the observed averaged probability distribution function (red line) into two components: a log-normal approximation, ( f 1 , green line) and a Gaussian approximation ( f 2 , blue). Their sum is plotted with the turquoise line.
\n\na Gaussian (normal) distribution of granule sizes. In this case, the mechanism that produces granules is 'programmed' to churn up convection cells of a typical size, without much freedom in size variation. Mini-granules do not display any characteristic ('dominant') scale, their size distribution is continuous and can be described by a decreasing log-normal (Gaussian distribution does not work any longer here). A majority (about 80%) of mini-granules are smaller than 600 km and about 50% are smaller than 300 km in diameter. This non-Gaussian distribution of sizes implies that a much more sophisticated mechanism, with much more degrees of freedom may be at work, where any very small fluctuation in density, pressure, velocity and magnetic fields may have significant impact and affect the resulting dynamics. Physical differences between the log-normal and Gaussian distributions are discussed by, e.g., Abramenko & Longcope (2005).\nAn important inference from the above discussion reads that a necessary condition for the seed magnetic field to be amplified is met. So, local turbulent dynamo in the near-surface layer is quite a possibility.\nRegime of turbulent magnetic diffusion in the photosphere . As we saw in Introduction, the anomalous diffusivity is another hallmark of multi-fractality. The dispersal process embedded\nin a multi-fractal cannot follow the random walk with normal diffusion. For example, in the case of solar photosphere, the multi-fractal plasma cannot ensure an arbitrary displacement in an arbitrary direction for all magnetic elements. A discussion of differences between the normal and anomalous diffusion can be found, e.g., in Lawrence & Schrijver (1993); Vlahos et al. (2008).\nThe coefficient of magnetic diffusivity is an essential input parameter for meridional flux transport models and global dynamo models. Therefore, magnetic flux dispersal on the solar surface was studies extensively (e.g., Lawrence & Schrijver 1993; Schrijver et al. 1996; Berger et al. 1998a,b; Cadavid et al. 1999; Hagenaar et al. 1999; Lawrence et al. 2001; Utz et al. 2009, 2010; Crockett et al. 2010; Abramenko et al. 2011).\nIn the most of these studies, observational data were interpreted in the framework of normal diffusion, and variety of estimates for the magnetic diffusivity coefficient, η , were reported: from 50 km 2 s -1 (Berger et al. 1998b) to 350 km 2 s -1 (Utz et al. 2010). Numerical simulations of the isotropic turbulence with magnetic field (Brandenburg et al. 2008) showed that the turbulent magnetic diffusivity increases with increasing scale. Combination of MHD modeling with observations allowed Chae et al. (2008) to conclude that the turbulent diffusivity changes with scale and is smallest (about 1 km 2 s -1 ) on smallest available scale of approximately 200 km.\nPhotospheric BPs, as tracers of kilo-gauss magnetic flux tubes, were utilized to probe photospheric flux dispersal (e.g., Berger et al. 1998a,b; Utz et al. 2010; Crockett et al. 2010). Recently, the high resolution power of the NST allowed Abramenko et al. (2011) to explore the regime of diffusion in the photosphere down to scales of 10 sec in time and 25 km in space. Magnetic BPs detected from NST/TiO images were tracked, and their squared displacements (from the initial position of a given BP) were calculated as a function of a time lag, τ . Later, the routine was repeated for HMI magnetic flux concentrations in a quiet Sun area on the disk center. Figure 6 a summarizes results.\nRecall that for normal diffusion (Brownian motions), the squared displacements of tracers are directly proportional to time, i.e., the power law index, γ , of the displacement spectrum is a unity (an example of the normal diffusion regime is illustrated in Figure 6 with thick black dashed lines). When γ > 1 ( γ < 1 ), a regime of super-diffusion (sub-diffusion) dominates. The squared displacements (∆ l ) 2 ( τ ) can be approximated, at a given range of scales, as\n(∆ l ) 2 ( τ ) = cτ γ , (3)\nwhere c = 10 y sect and γ and y sect are derived from the best linear lit to the data points plotted in a double-logarithmic plot. Then the diffusion coefficient can be written as (Abramenko et al. 2011):\nη ( τ ) = cγ 4 τ γ -1 , (4)\n\n\n
Fig. 6.a - Squared displacements of magnetic BPs detected from a 2-hour data set from the NST/BBSO ( blue ) and squared displacements of magnetic elements detected from 9-hour data set from SDO/HMI magnetograms recorded in a quiet Sun area on the solar disk center ( red ). Dash-dot lines are the best linear fit to the data points inside ranges of linearity; the slopes of the fits, γ , are indicated. b - The turbulent magnetic diffusivity, η , as a function of linear scale derived by Eq. (5) from linear fits for the NST (blue) and HMI (red) data shown in panel a . The thick dashed lines in both panels show an example of scaling for the normal diffusion regime with γ = 1.
\n\n10\n1\nη\n~ (<\n2\n10\n∆\nl\n2\n3\n∆\n10\nSpatial Scale,\n-1)/\nγ\n10\nl, km\nη (∆ l ) = cγ 4 ((∆ l ) 2 /c ) ( γ -1) /γ . (5)\nAs if follows from Figure 6, for both data sets we observe the super-diffusion regime. The coefficient of magnetic turbulent diffusivity, η (∆ l ) , derived by Eq. (5) for both data sets is shown in Figure 6 b . Two essential things should be mentioned here: first, the diffusion coefficient grows as the scale increases (the same is true for a time scale, too, see Eq. (4). Second, the slope of the power law varies with scale (which is a characteristic feature of intrinsic multi-fractality). On the minimal spatial (25 km) and temporal (10 sec) scales considered in Abramenko et al. (2011), the diffusion coefficient in QS area was found to be 19 km 2 s -1 . The HMI data provided a value of approximately 220 km 2 s -1 on the largest available scale of 4 Mm.\nThe observed tendency of the turbulent magnetic diffusivity to decrease with decreasing scales leads us to expect that the turbulent diffusivity might be close to the magnitudes of diffusivity adopted in the numerical simulations of small-scale dynamo (0.01 - 10 km 2 s -1 , e.g., Boldyrev & Cattaneo (2004); Vogler & Schussler (2007); Pietarila Graham et al. (2010)). This\n1000\n100\n10\n1\n0\n10\n(\n>)\nγ\n4\nb\n5\n10\nmakes the simulations even more realistic.\nIn summary, a super-diffusion regime on very small scales is very favorable for pictures assuming turbulent dynamo action since it assumes decreasing diffusivity with decreasing scales.\n4. Concluding remarks\nContinuously varying magnetic fields are the main reason for the solar/stellar activity. The 11-year solar cycle is one of the most astonishing and widely known examples of the self-organized generation of the magnetic field. Although we know that there is no two absolutely similar solar cycles, yet, persistency and regularity of the solar periodicity through thousands of years remains impressive. A drastically different picture arises when one looks on the photosphere: chaos of mixed-polarity magnetic elements of all sizes until the resolution limits of modern instruments, continuously renewing during 1-2 days - the magnetic carpet.\nDualism of the solar magnetism is usually explained by a simultaneous action of two dynamos: a global dynamo operating in the convective zone and responsible for the 11-year solar cycle, and local, or turbulent dynamo, which might operate inside the near-surface layer and to be responsible for generation of small-scale magnetic fields forming the magnetic carpet. The explanation seems to oversimplify the reality because resent studies of distribution of the magnetic flux accumulated in magnetic flux tubes showed the non-interrupted power law for many decades (Parnell et al. 2009) thus supposing a common (for all scales) mechanism for the magnetic field generation. One of promising ways to handle the problem is to consider the solar dynamo process as a non-linear dynamical system (NDS), with intrinsic properties of multi-fractality and intermittency.\nLike any NDS, the solar dynamo is then capable to self-organization on all scales (including large scales) and display a chaotic nature on small scales. Self-organization, in turn, provides for a magnetic complex a way to reach a SOC state, when burst-like energy release events of any size are possible at any time instant. The concept is very important for our understanding of flaring and heating processes in solar/stellar atmospheres.\nFurther, multi-fractal nature on the magnetic field provides a necessary condition for the local turbulent dynamo operation in the near-surface layer of the convective zone. Observational evidences for local dynamo operation are still under strong debates, e.g., compare the talks by Drs. Tsuneta and Stenflo presented at this symposium.\nOne pragmatic advise for researchers could be inferred form the observed multi-fractal nature of magnetized solar plasma. Namely, observed power laws should not be extrapolated over neighboring scales, a frequent mistake for power laws studies in various fields.\nIn summary, the paradigm of multi-fractal and highly intermittent structure of solar magnetized plasma offers new approaches to understand the solar and stellar magnetism.\nREFERENCES\nAbramenko, V., & Yurchyshyn, V. 2010a, ApJ , 722, 122 -. 2010b, ApJ , 722, 122 Abramenko, V. 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The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy release events, conditions for turbulent dynamo action, nature of turbulent magnetic diffusivity, and even the dual nature of solar dynamo. In this talk, I will briefly outline how the ideas of multi-fractality are used to explore the above mentioned aspects of solar magnetism.","pages":[1]},{"title":"Fractal multi-scale nature of solar/stellar magnetic field","content":"Valentina I. Abramenko Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314, USA","pages":[1]},{"title":"1. Introduction: Why Fractals?","content":"A mathematical fractal is a self-similar object on all possible spatial and time scales. It means that when we proceed from large to smaller scales, we will see exactly the same picture. From mathematical standpoint this means that a unique scaling law holds for all scales. A fractal (or, more rigorously, a mono-fractal) is a deterministic, predictable system. Mathematical monofractals differ drastically from what we observe in nature: fractal-like structures in nature are multi-fractals - a superposition of infinite number of mono-fractals. The transition from mono-fractals to multi-fractals turns an amusing mathematical toy into a powerful tool to study real processes in nature. The matter is that multi-fractals posses the same properties in both the spatial and temporal domains. This means that if we see a very complex, jagged shape in space (multi-fractal in space), then we will observe a violent, burst-like behavior in time (multi-fractal in time). For such systems, any small perturbation can cause an avalanche of any possible size. Therefore, revealing the fact that a system under study is a fractal does not allow us to make inferences about its nature and essential properties of its behavior. We need something more, namely, to know of how many mono-fractals our system is made of. Numerous examples of fractals and multi-fractals can be found (e.g., Feder 1989; Schroeder 2000, Internet). Mathematical details of the fractal calculus are well described as well (e.g., Baumann 2005; McAteer et al. 2007). Historically, when analyzing spatial objects, their capability to be organized into very jagged structures with extended voids and sharp peaks is addressed as a property of multi-fractality. At the sate time, while analyzing time series, we address the same property as intermittency. Thus, multi-fractality and intermittency are two terms for the same physical property of a system. I will use both of them in this talk. Several approaches were elaborated during a couple of last decades to probe the properties of multi-fractality in different fields of science. In a brief review below, I will focus on multi-fractality techniques applied in astrophysics. Thus, multi-fractal systems are capable of self-organization (i.e., formation of larger entities from smaller ones via inverse cascade), and of self-organized criticality (SOC) when burst-like energy release events of any scale are possible at any moment (e.g., Charbonneau et al. 2001; Longcope & Noonan 2000; Aschwanden 2011). A theory of catastrophes is also based on the multi-fractal nature of astrophysical phenomena (Priest & Forbes 2002; Isenberg & Forbes 2007). Percolating clusters (Balke et al. 1993; Seiden & Wentzel 1996; Pustil'nik 1999; Schatten 2007) are also fractals and multi-fractals. Direct calculations of fractal dimensions and spectra of multi-fractality is one of the most popular tool to explore astrophysical multi-fractals (e.g., Lawrence et al. 1993; Meunier 1999; Lepreti et al. 1999; McAteer et al. 2007; Dimitropoulou et al. 2009; Abramenko & Yurchyshyn 2010a; Aschwanden 2011). Another possibility to study multi-fractality is to analyze high statistical moments by means of distribution functions (Bogdan et al. 1988; Parnell et al. 2009), or structure functions (Consolini et al. 1999; Abramenko et al. 2002; Abramenko 2005; Uritsky et al. 2007; Abramenko & Yurchyshyn 2010b; Abramenko et al. 2012). Essential physical properties of multi-fractals can be formulated as follows. These properties can help us to diagnose the presence and degree of multi-fractality of various astrophysical phenomena. Meanwhile, keeping in mind that in astrophysical magnetism we deal with a specific type of a multi-fractal medium, namely, intermittent turbulence in an electroconductive flow , we can take advantage of it and incorporate other very important properties and tools. So our list of properties can be extended: Based on these properties of multi-fractal systems, I will discuss below how exploration of these properties can help us in understanding of solar and stellar magnetism. It is impossible in the framework of this invited talk to discuss all aforementioned approaches and tools in great details, so I will concentrate on the analysis of structure functions, which are used in my research.","pages":[1,2,3]},{"title":"2. Structure functions approach to study multi-fractality","content":"Since Kolmogorov's study (Kolmogorov 1941), various models have been proposed to describe the statistical behavior of fully developed turbulence. In these studies, the flow is modeled using statistically averaged quantities, and structure functions play a significant role. They are defined as statistical moments of the q -powers of the increment of a field. The definition can be applied to different fields (e.g., velocity, temperature, magnetic field, etc). Here, in the most of the cases, I will refer to the line-of-sight component of the magnetic field, B l , for which the structure function can be written as where x is the current pixel on a magnetogram, r is the separation vector between any two points used to measure the increment (see the lower right panel in Figure 1, and q is the order of a statistical moment, which takes on real values. The angular brackets denote averaging over the magnetogram, and the vector r is allowed to adopt all possible orientations, θ , on the magnetogram. The next step is to calculate the scaling of the structure functions, which is defined as the slope, ζ ( q ) , measured inside some range of scales where the S q ( r ) -function is linear and the field is intermittent. The function ζ ( q ) is shown in the upper right panel in Figure 1. A weak point in the above technique is the determination of the range, ∆ r , where the slopes of the structure functions are to be calculated. To visualize the range of intermittency, ∆ r , we suggest to use the flatness function (Abramenko 2005), which is determined as the ratio of the fourth statistical moment to the square of the second statistical moment. To better identify the effect of intermittency, we reinforced the definition of the flatness function and calculated the hyper-flatness function, namely, the ratio of the sixth moment to the cube of the second moment: For simplicity, we will refer to F ( r ) as the flatness function, or multi-fractality/intermittency spectrum. For a non-intermittent structure, the flatness function is not dependent on the scale, r . On the contrary, for an intermittent/multi-fractal structure, the flatness grows as power-law, when the scale decreases. The slope of flatness function, κ , and the width of ∆ r characterize the degree of multi-fractality and intermittency. Application of this technique to two hundred of solar active regions observed with SOHO/MDI in the high resolution mode (Abramenko & Yurchyshyn 2010a) demonstrated that active regions of high flare productivity display steeper and broader multifractality spectra, F ( r ) . The inference agrees with the formulated above statement that multi-fractality in spatial domain is accompanied by intermittency (burst-like behavior) in time. Moreover, for any multi-fractal system, individual bursts cannot be precisely predicted in advance. So, the exact prediction of the location and the onset moment of a flare (of any size), strictly speaking, is a hopeless task. Based on different indirect indications, one may only hope to provide a probabilistic estimate for ongoing flaring. Multi-fractality of time series of X-ray emission from an individual solar flare was discussed in McAteer et al. (2007), where an inference on the fractal nature of the flaring current sheet was made. I will focus below on a solar surface outside active regions, which occupy usually more than 80% of the entire solar surface. Many important aspects of solar magnetism are rooted there.","pages":[3,5]},{"title":"3. Multi-fractality in the solar surface","content":"Examples of line-of-sight (LOS) magnetograms recorded in coronal holes (CHs) using different solar instruments are shown in Figure 2. The left panel shows data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO, Scherrer et al. 2012), the middle panel shows LOS magnetic field provided by Hinode Solar Optical Telescope SpectroPolarimeter (SOT/SP, Tsuneta et al. 2008), and the right panel presents a magnetogram from the New Solar Telescope (NST) (Goode et al. 2010) operating at the Big Bear Solar Observatory (BBSO). Note that the NST data were obtained at a near-infrared spectral line (1.56 µm ) and represent the magnetic field in the deep photosphere at depths of about 50 km below the τ 500 = 1 level. Figure 2 clearly demonstrates that with improved telescope resolution more mixed polarity magnetic elements become visible inside a CH. In spite of the fact that the three magnetograms refer to different CHs, this tendency is well defined. Flatness functions calculated from the three above mentioned magnetograms are shown in Figure 3. The HMI data show only a hint of multi-fractality on scales above 1500 km and a very shallow slope of F ( r ) ( κ = -0 . 07 ). The HMI resolution of 1 '' obviously is not sufficient to clearly reveal multi-fractality in quiet Sun. Meanwhile, the SOT/SP data show a much broader scale range of multi-fractality down to approximately 630 km and a steeper slope ( κ = -0 . 107 ). The HMI result refers to the height of 280-360 km (the effective line formation level of the FeI 617.3 nm spectral line, Gurtovenko & R.I.Kostyk (1989)), whereas the SOT/NBF data refer to a level of 400-700 km in the photosphere (the line formation height of the NaI 589.6 nm spectral line is discussed in Sheminova (1998)). The flatness function obtained from NST data clearly reveal (at the deeper layer) strong intermittency and multi-fractality on scales down to ∼ 400 km. Thus, the multi-fractal nature of small-scale magnetic fields becomes better pronounced with depth and improvement of spatial resolution, which leads us to conclude that intermittency and multi-fractality is an intrinsic property of the near-surface magnetic fields in the quiet Sun. Magnetic elements against granulation inside a CH are shown in Figure 4, where the background is an NST solar granulation image overplotted with NST LOS and transverse magnetic features and Hinode SOT Narrow Band Filter (NBF) LOS magnetic field. In the upper right corner of the image, a fragment of bright points (BPs) filigree corresponding to the super-granular boundary is visible. The rest of the image shows the intra-network area, where nine isolated magnetic elements were detected by the SOT/NBF. All of them are co-spatial with BPs and with the LOS signal from the NST. In six cases there are neither opposite polarity nor transverse magnetic field features in the closest vicinity. This may indicate that these mag- netic elements are footpoints of open magnetic flux tubes representing the skeleton of the CH. The presence of BPs indicates that they might be produced via the convective collapse (Parker 1978; Spruit 1979). At the same time, a significant part of the intra-network population is composed of magnetic features, which are not related to BPs and scattered over granules and inter-granular lanes. These magnetic elements were not detected by SOT/NBF and they are not necessarily very weak. On the contrary, they are quite compatible (by size and intensity) with those detected by the both instruments, they are simply not visible in NBF magnetograms. A simplest explanation could be the difference in heights. As I mentioned above, the NST measures the magnetic signal formed very deep in the photosphere, precisely, at the depth of 50 km below the τ 500 = 1 level, while the magnetic signal measured with SOT/NBF is formed at the hight of approximately 400-700 km. If magnetic elements associated with granules are predominantly small (200-500 km in length) closed loops anchored at a depth of about -50 km, they might not be visible at the altitude of 400-700 km. This speculation is supported by the inspection of mutual location of Stokes V features (blue and red contours) and the transverse magnetic field features (green contours) in Figure 4. Indeed, the V-signal is co-spatial with the ( Q 2 + U 2 ) signal for the granules-associated magnetic elements, which supports the idea of closed loops (or bunches of loops) rather than presence of singular footpoints of extended, high loops or open field lines. As for the magnetic elements associated with BPs and visible with the both instruments, they seem to be the best candidates for the roots of the open field lines, as we mentioned above. This can explain why they are visible on different heights. Thus, the data allows us to speculate that the BPs-associated magnetic elements are related to the advection and convective collapse, whereas the numerous granule-associated intra-network elements are situated deeper in the photosphere and might be produced (at least, part of them) by local turbulent dynamo (see the talk by Dr. Tsuneta in this Symposium). Multi-fractality of granulation . To drive local turbulent dynamo, the environment should be a highly turbulent medium, i.e., to be a multi-fractal. Is the solar granulation pattern a multi-fractal? To explore the question, Abramenko et al. (2012) used a NST data set of solar granulation images obtained for the quiet Sun area on the solar disk center recorded under excellent seeing conditions. Flatness functions for 36 independent snapshots and their average are shown in Figure 5 a . The flatness functions indicate that solar granulation is non-intermittent (a mono-fractal) on scales exceeding approximately 600 km, and it becomes highly intermittent and multi-fractal on scales below 600 km. Thus, a random, Gaussian-like distribution of granule size holds down to 600 km only. On smaller scales, the multi-fractal spatial organization of solar granulation takes over. A distribution function of granular size (Figure 5 b ) further confirms this inference. On scales of approximately 600 and 1300 km, the averaged probability distribution function (PDF) rapidly changes its slope. This varying power law PDF is suggestive that the observed ensemble of granules may consist of two populations with distinct properties: regular granules and minigranules. Decomposition of the observed PDF showed that the best fit is achieved with a combination of a log-normal function, f 1 , representing mini-granules, and a Gaussian function, f 2 , representing regular granules. Their sum perfectly fits to the observational data. Until now it was thought that solar convection produces convection cells, visible on the solar surface as granules, of characteristic ('dominant') spatial scale of about 1000 km and a Gaussian (normal) distribution of granule sizes. In this case, the mechanism that produces granules is 'programmed' to churn up convection cells of a typical size, without much freedom in size variation. Mini-granules do not display any characteristic ('dominant') scale, their size distribution is continuous and can be described by a decreasing log-normal (Gaussian distribution does not work any longer here). A majority (about 80%) of mini-granules are smaller than 600 km and about 50% are smaller than 300 km in diameter. This non-Gaussian distribution of sizes implies that a much more sophisticated mechanism, with much more degrees of freedom may be at work, where any very small fluctuation in density, pressure, velocity and magnetic fields may have significant impact and affect the resulting dynamics. Physical differences between the log-normal and Gaussian distributions are discussed by, e.g., Abramenko & Longcope (2005). An important inference from the above discussion reads that a necessary condition for the seed magnetic field to be amplified is met. So, local turbulent dynamo in the near-surface layer is quite a possibility. Regime of turbulent magnetic diffusion in the photosphere . As we saw in Introduction, the anomalous diffusivity is another hallmark of multi-fractality. The dispersal process embedded in a multi-fractal cannot follow the random walk with normal diffusion. For example, in the case of solar photosphere, the multi-fractal plasma cannot ensure an arbitrary displacement in an arbitrary direction for all magnetic elements. A discussion of differences between the normal and anomalous diffusion can be found, e.g., in Lawrence & Schrijver (1993); Vlahos et al. (2008). The coefficient of magnetic diffusivity is an essential input parameter for meridional flux transport models and global dynamo models. Therefore, magnetic flux dispersal on the solar surface was studies extensively (e.g., Lawrence & Schrijver 1993; Schrijver et al. 1996; Berger et al. 1998a,b; Cadavid et al. 1999; Hagenaar et al. 1999; Lawrence et al. 2001; Utz et al. 2009, 2010; Crockett et al. 2010; Abramenko et al. 2011). In the most of these studies, observational data were interpreted in the framework of normal diffusion, and variety of estimates for the magnetic diffusivity coefficient, η , were reported: from 50 km 2 s -1 (Berger et al. 1998b) to 350 km 2 s -1 (Utz et al. 2010). Numerical simulations of the isotropic turbulence with magnetic field (Brandenburg et al. 2008) showed that the turbulent magnetic diffusivity increases with increasing scale. Combination of MHD modeling with observations allowed Chae et al. (2008) to conclude that the turbulent diffusivity changes with scale and is smallest (about 1 km 2 s -1 ) on smallest available scale of approximately 200 km. Photospheric BPs, as tracers of kilo-gauss magnetic flux tubes, were utilized to probe photospheric flux dispersal (e.g., Berger et al. 1998a,b; Utz et al. 2010; Crockett et al. 2010). Recently, the high resolution power of the NST allowed Abramenko et al. (2011) to explore the regime of diffusion in the photosphere down to scales of 10 sec in time and 25 km in space. Magnetic BPs detected from NST/TiO images were tracked, and their squared displacements (from the initial position of a given BP) were calculated as a function of a time lag, τ . Later, the routine was repeated for HMI magnetic flux concentrations in a quiet Sun area on the disk center. Figure 6 a summarizes results. Recall that for normal diffusion (Brownian motions), the squared displacements of tracers are directly proportional to time, i.e., the power law index, γ , of the displacement spectrum is a unity (an example of the normal diffusion regime is illustrated in Figure 6 with thick black dashed lines). When γ > 1 ( γ < 1 ), a regime of super-diffusion (sub-diffusion) dominates. The squared displacements (∆ l ) 2 ( τ ) can be approximated, at a given range of scales, as where c = 10 y sect and γ and y sect are derived from the best linear lit to the data points plotted in a double-logarithmic plot. Then the diffusion coefficient can be written as (Abramenko et al. 2011): 10 1 η ~ (< 2 10 ∆ l 2 3 ∆ 10 Spatial Scale, -1)/ γ 10 l, km As if follows from Figure 6, for both data sets we observe the super-diffusion regime. The coefficient of magnetic turbulent diffusivity, η (∆ l ) , derived by Eq. (5) for both data sets is shown in Figure 6 b . Two essential things should be mentioned here: first, the diffusion coefficient grows as the scale increases (the same is true for a time scale, too, see Eq. (4). Second, the slope of the power law varies with scale (which is a characteristic feature of intrinsic multi-fractality). On the minimal spatial (25 km) and temporal (10 sec) scales considered in Abramenko et al. (2011), the diffusion coefficient in QS area was found to be 19 km 2 s -1 . The HMI data provided a value of approximately 220 km 2 s -1 on the largest available scale of 4 Mm. The observed tendency of the turbulent magnetic diffusivity to decrease with decreasing scales leads us to expect that the turbulent diffusivity might be close to the magnitudes of diffusivity adopted in the numerical simulations of small-scale dynamo (0.01 - 10 km 2 s -1 , e.g., Boldyrev & Cattaneo (2004); Vogler & Schussler (2007); Pietarila Graham et al. (2010)). This 1000 100 10 1 0 10 ( >) γ 4 b 5 10 makes the simulations even more realistic. In summary, a super-diffusion regime on very small scales is very favorable for pictures assuming turbulent dynamo action since it assumes decreasing diffusivity with decreasing scales.","pages":[5,6,7,8,9,10,11,12,13]},{"title":"4. Concluding remarks","content":"Continuously varying magnetic fields are the main reason for the solar/stellar activity. The 11-year solar cycle is one of the most astonishing and widely known examples of the self-organized generation of the magnetic field. Although we know that there is no two absolutely similar solar cycles, yet, persistency and regularity of the solar periodicity through thousands of years remains impressive. A drastically different picture arises when one looks on the photosphere: chaos of mixed-polarity magnetic elements of all sizes until the resolution limits of modern instruments, continuously renewing during 1-2 days - the magnetic carpet. Dualism of the solar magnetism is usually explained by a simultaneous action of two dynamos: a global dynamo operating in the convective zone and responsible for the 11-year solar cycle, and local, or turbulent dynamo, which might operate inside the near-surface layer and to be responsible for generation of small-scale magnetic fields forming the magnetic carpet. The explanation seems to oversimplify the reality because resent studies of distribution of the magnetic flux accumulated in magnetic flux tubes showed the non-interrupted power law for many decades (Parnell et al. 2009) thus supposing a common (for all scales) mechanism for the magnetic field generation. One of promising ways to handle the problem is to consider the solar dynamo process as a non-linear dynamical system (NDS), with intrinsic properties of multi-fractality and intermittency. Like any NDS, the solar dynamo is then capable to self-organization on all scales (including large scales) and display a chaotic nature on small scales. Self-organization, in turn, provides for a magnetic complex a way to reach a SOC state, when burst-like energy release events of any size are possible at any time instant. The concept is very important for our understanding of flaring and heating processes in solar/stellar atmospheres. Further, multi-fractal nature on the magnetic field provides a necessary condition for the local turbulent dynamo operation in the near-surface layer of the convective zone. Observational evidences for local dynamo operation are still under strong debates, e.g., compare the talks by Drs. Tsuneta and Stenflo presented at this symposium. One pragmatic advise for researchers could be inferred form the observed multi-fractal nature of magnetized solar plasma. Namely, observed power laws should not be extrapolated over neighboring scales, a frequent mistake for power laws studies in various fields. In summary, the paradigm of multi-fractal and highly intermittent structure of solar magnetized plasma offers new approaches to understand the solar and stellar magnetism.","pages":[13,14]},{"title":"REFERENCES","content":"Abramenko, V., & Yurchyshyn, V. 2010a, ApJ , 722, 122 -. 2010b, ApJ , 722, 122 Abramenko, V. I. 2005, Sol. Phys. , 228, 29 Abramenko, V. 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J. 1993, ApJ , 411, 402 Lepreti, F., et al. 1999, in ESA Special Publication, Vol. 448, Magnetic Fields and Solar Processes, ed. A. Wilson & et al., 327 Longcope, D. W., & Noonan, E. J. 2000, ApJ , 542, 1088 Zeldovich, Y. B., Molchanov, S. A., Ruzmaikin, A. A., & Sokoloff, D. D. 1987, Sov. Phys. Usp., 30, 353","pages":[14,15,17]}],"string":"[\n {\n \"title\": \"ABSTRACT\",\n \"content\": \"An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy release events, conditions for turbulent dynamo action, nature of turbulent magnetic diffusivity, and even the dual nature of solar dynamo. In this talk, I will briefly outline how the ideas of multi-fractality are used to explore the above mentioned aspects of solar magnetism.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Fractal multi-scale nature of solar/stellar magnetic field\",\n \"content\": \"Valentina I. Abramenko Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314, USA\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction: Why Fractals?\",\n \"content\": \"A mathematical fractal is a self-similar object on all possible spatial and time scales. It means that when we proceed from large to smaller scales, we will see exactly the same picture. From mathematical standpoint this means that a unique scaling law holds for all scales. A fractal (or, more rigorously, a mono-fractal) is a deterministic, predictable system. Mathematical monofractals differ drastically from what we observe in nature: fractal-like structures in nature are multi-fractals - a superposition of infinite number of mono-fractals. The transition from mono-fractals to multi-fractals turns an amusing mathematical toy into a powerful tool to study real processes in nature. The matter is that multi-fractals posses the same properties in both the spatial and temporal domains. This means that if we see a very complex, jagged shape in space (multi-fractal in space), then we will observe a violent, burst-like behavior in time (multi-fractal in time). For such systems, any small perturbation can cause an avalanche of any possible size. Therefore, revealing the fact that a system under study is a fractal does not allow us to make inferences about its nature and essential properties of its behavior. We need something more, namely, to know of how many mono-fractals our system is made of. Numerous examples of fractals and multi-fractals can be found (e.g., Feder 1989; Schroeder 2000, Internet). Mathematical details of the fractal calculus are well described as well (e.g., Baumann 2005; McAteer et al. 2007). Historically, when analyzing spatial objects, their capability to be organized into very jagged structures with extended voids and sharp peaks is addressed as a property of multi-fractality. At the sate time, while analyzing time series, we address the same property as intermittency. Thus, multi-fractality and intermittency are two terms for the same physical property of a system. I will use both of them in this talk. Several approaches were elaborated during a couple of last decades to probe the properties of multi-fractality in different fields of science. In a brief review below, I will focus on multi-fractality techniques applied in astrophysics. Thus, multi-fractal systems are capable of self-organization (i.e., formation of larger entities from smaller ones via inverse cascade), and of self-organized criticality (SOC) when burst-like energy release events of any scale are possible at any moment (e.g., Charbonneau et al. 2001; Longcope & Noonan 2000; Aschwanden 2011). A theory of catastrophes is also based on the multi-fractal nature of astrophysical phenomena (Priest & Forbes 2002; Isenberg & Forbes 2007). Percolating clusters (Balke et al. 1993; Seiden & Wentzel 1996; Pustil'nik 1999; Schatten 2007) are also fractals and multi-fractals. Direct calculations of fractal dimensions and spectra of multi-fractality is one of the most popular tool to explore astrophysical multi-fractals (e.g., Lawrence et al. 1993; Meunier 1999; Lepreti et al. 1999; McAteer et al. 2007; Dimitropoulou et al. 2009; Abramenko & Yurchyshyn 2010a; Aschwanden 2011). Another possibility to study multi-fractality is to analyze high statistical moments by means of distribution functions (Bogdan et al. 1988; Parnell et al. 2009), or structure functions (Consolini et al. 1999; Abramenko et al. 2002; Abramenko 2005; Uritsky et al. 2007; Abramenko & Yurchyshyn 2010b; Abramenko et al. 2012). Essential physical properties of multi-fractals can be formulated as follows. These properties can help us to diagnose the presence and degree of multi-fractality of various astrophysical phenomena. Meanwhile, keeping in mind that in astrophysical magnetism we deal with a specific type of a multi-fractal medium, namely, intermittent turbulence in an electroconductive flow , we can take advantage of it and incorporate other very important properties and tools. So our list of properties can be extended: Based on these properties of multi-fractal systems, I will discuss below how exploration of these properties can help us in understanding of solar and stellar magnetism. It is impossible in the framework of this invited talk to discuss all aforementioned approaches and tools in great details, so I will concentrate on the analysis of structure functions, which are used in my research.\",\n \"pages\": [\n 1,\n 2,\n 3\n ]\n },\n {\n \"title\": \"2. Structure functions approach to study multi-fractality\",\n \"content\": \"Since Kolmogorov's study (Kolmogorov 1941), various models have been proposed to describe the statistical behavior of fully developed turbulence. In these studies, the flow is modeled using statistically averaged quantities, and structure functions play a significant role. They are defined as statistical moments of the q -powers of the increment of a field. The definition can be applied to different fields (e.g., velocity, temperature, magnetic field, etc). Here, in the most of the cases, I will refer to the line-of-sight component of the magnetic field, B l , for which the structure function can be written as where x is the current pixel on a magnetogram, r is the separation vector between any two points used to measure the increment (see the lower right panel in Figure 1, and q is the order of a statistical moment, which takes on real values. The angular brackets denote averaging over the magnetogram, and the vector r is allowed to adopt all possible orientations, θ , on the magnetogram. The next step is to calculate the scaling of the structure functions, which is defined as the slope, ζ ( q ) , measured inside some range of scales where the S q ( r ) -function is linear and the field is intermittent. The function ζ ( q ) is shown in the upper right panel in Figure 1. A weak point in the above technique is the determination of the range, ∆ r , where the slopes of the structure functions are to be calculated. To visualize the range of intermittency, ∆ r , we suggest to use the flatness function (Abramenko 2005), which is determined as the ratio of the fourth statistical moment to the square of the second statistical moment. To better identify the effect of intermittency, we reinforced the definition of the flatness function and calculated the hyper-flatness function, namely, the ratio of the sixth moment to the cube of the second moment: For simplicity, we will refer to F ( r ) as the flatness function, or multi-fractality/intermittency spectrum. For a non-intermittent structure, the flatness function is not dependent on the scale, r . On the contrary, for an intermittent/multi-fractal structure, the flatness grows as power-law, when the scale decreases. The slope of flatness function, κ , and the width of ∆ r characterize the degree of multi-fractality and intermittency. Application of this technique to two hundred of solar active regions observed with SOHO/MDI in the high resolution mode (Abramenko & Yurchyshyn 2010a) demonstrated that active regions of high flare productivity display steeper and broader multifractality spectra, F ( r ) . The inference agrees with the formulated above statement that multi-fractality in spatial domain is accompanied by intermittency (burst-like behavior) in time. Moreover, for any multi-fractal system, individual bursts cannot be precisely predicted in advance. So, the exact prediction of the location and the onset moment of a flare (of any size), strictly speaking, is a hopeless task. Based on different indirect indications, one may only hope to provide a probabilistic estimate for ongoing flaring. Multi-fractality of time series of X-ray emission from an individual solar flare was discussed in McAteer et al. (2007), where an inference on the fractal nature of the flaring current sheet was made. I will focus below on a solar surface outside active regions, which occupy usually more than 80% of the entire solar surface. Many important aspects of solar magnetism are rooted there.\",\n \"pages\": [\n 3,\n 5\n ]\n },\n {\n \"title\": \"3. Multi-fractality in the solar surface\",\n \"content\": \"Examples of line-of-sight (LOS) magnetograms recorded in coronal holes (CHs) using different solar instruments are shown in Figure 2. The left panel shows data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO, Scherrer et al. 2012), the middle panel shows LOS magnetic field provided by Hinode Solar Optical Telescope SpectroPolarimeter (SOT/SP, Tsuneta et al. 2008), and the right panel presents a magnetogram from the New Solar Telescope (NST) (Goode et al. 2010) operating at the Big Bear Solar Observatory (BBSO). Note that the NST data were obtained at a near-infrared spectral line (1.56 µm ) and represent the magnetic field in the deep photosphere at depths of about 50 km below the τ 500 = 1 level. Figure 2 clearly demonstrates that with improved telescope resolution more mixed polarity magnetic elements become visible inside a CH. In spite of the fact that the three magnetograms refer to different CHs, this tendency is well defined. Flatness functions calculated from the three above mentioned magnetograms are shown in Figure 3. The HMI data show only a hint of multi-fractality on scales above 1500 km and a very shallow slope of F ( r ) ( κ = -0 . 07 ). The HMI resolution of 1 '' obviously is not sufficient to clearly reveal multi-fractality in quiet Sun. Meanwhile, the SOT/SP data show a much broader scale range of multi-fractality down to approximately 630 km and a steeper slope ( κ = -0 . 107 ). The HMI result refers to the height of 280-360 km (the effective line formation level of the FeI 617.3 nm spectral line, Gurtovenko & R.I.Kostyk (1989)), whereas the SOT/NBF data refer to a level of 400-700 km in the photosphere (the line formation height of the NaI 589.6 nm spectral line is discussed in Sheminova (1998)). The flatness function obtained from NST data clearly reveal (at the deeper layer) strong intermittency and multi-fractality on scales down to ∼ 400 km. Thus, the multi-fractal nature of small-scale magnetic fields becomes better pronounced with depth and improvement of spatial resolution, which leads us to conclude that intermittency and multi-fractality is an intrinsic property of the near-surface magnetic fields in the quiet Sun. Magnetic elements against granulation inside a CH are shown in Figure 4, where the background is an NST solar granulation image overplotted with NST LOS and transverse magnetic features and Hinode SOT Narrow Band Filter (NBF) LOS magnetic field. In the upper right corner of the image, a fragment of bright points (BPs) filigree corresponding to the super-granular boundary is visible. The rest of the image shows the intra-network area, where nine isolated magnetic elements were detected by the SOT/NBF. All of them are co-spatial with BPs and with the LOS signal from the NST. In six cases there are neither opposite polarity nor transverse magnetic field features in the closest vicinity. This may indicate that these mag- netic elements are footpoints of open magnetic flux tubes representing the skeleton of the CH. The presence of BPs indicates that they might be produced via the convective collapse (Parker 1978; Spruit 1979). At the same time, a significant part of the intra-network population is composed of magnetic features, which are not related to BPs and scattered over granules and inter-granular lanes. These magnetic elements were not detected by SOT/NBF and they are not necessarily very weak. On the contrary, they are quite compatible (by size and intensity) with those detected by the both instruments, they are simply not visible in NBF magnetograms. A simplest explanation could be the difference in heights. As I mentioned above, the NST measures the magnetic signal formed very deep in the photosphere, precisely, at the depth of 50 km below the τ 500 = 1 level, while the magnetic signal measured with SOT/NBF is formed at the hight of approximately 400-700 km. If magnetic elements associated with granules are predominantly small (200-500 km in length) closed loops anchored at a depth of about -50 km, they might not be visible at the altitude of 400-700 km. This speculation is supported by the inspection of mutual location of Stokes V features (blue and red contours) and the transverse magnetic field features (green contours) in Figure 4. Indeed, the V-signal is co-spatial with the ( Q 2 + U 2 ) signal for the granules-associated magnetic elements, which supports the idea of closed loops (or bunches of loops) rather than presence of singular footpoints of extended, high loops or open field lines. As for the magnetic elements associated with BPs and visible with the both instruments, they seem to be the best candidates for the roots of the open field lines, as we mentioned above. This can explain why they are visible on different heights. Thus, the data allows us to speculate that the BPs-associated magnetic elements are related to the advection and convective collapse, whereas the numerous granule-associated intra-network elements are situated deeper in the photosphere and might be produced (at least, part of them) by local turbulent dynamo (see the talk by Dr. Tsuneta in this Symposium). Multi-fractality of granulation . To drive local turbulent dynamo, the environment should be a highly turbulent medium, i.e., to be a multi-fractal. Is the solar granulation pattern a multi-fractal? To explore the question, Abramenko et al. (2012) used a NST data set of solar granulation images obtained for the quiet Sun area on the solar disk center recorded under excellent seeing conditions. Flatness functions for 36 independent snapshots and their average are shown in Figure 5 a . The flatness functions indicate that solar granulation is non-intermittent (a mono-fractal) on scales exceeding approximately 600 km, and it becomes highly intermittent and multi-fractal on scales below 600 km. Thus, a random, Gaussian-like distribution of granule size holds down to 600 km only. On smaller scales, the multi-fractal spatial organization of solar granulation takes over. A distribution function of granular size (Figure 5 b ) further confirms this inference. On scales of approximately 600 and 1300 km, the averaged probability distribution function (PDF) rapidly changes its slope. This varying power law PDF is suggestive that the observed ensemble of granules may consist of two populations with distinct properties: regular granules and minigranules. Decomposition of the observed PDF showed that the best fit is achieved with a combination of a log-normal function, f 1 , representing mini-granules, and a Gaussian function, f 2 , representing regular granules. Their sum perfectly fits to the observational data. Until now it was thought that solar convection produces convection cells, visible on the solar surface as granules, of characteristic ('dominant') spatial scale of about 1000 km and a Gaussian (normal) distribution of granule sizes. In this case, the mechanism that produces granules is 'programmed' to churn up convection cells of a typical size, without much freedom in size variation. Mini-granules do not display any characteristic ('dominant') scale, their size distribution is continuous and can be described by a decreasing log-normal (Gaussian distribution does not work any longer here). A majority (about 80%) of mini-granules are smaller than 600 km and about 50% are smaller than 300 km in diameter. This non-Gaussian distribution of sizes implies that a much more sophisticated mechanism, with much more degrees of freedom may be at work, where any very small fluctuation in density, pressure, velocity and magnetic fields may have significant impact and affect the resulting dynamics. Physical differences between the log-normal and Gaussian distributions are discussed by, e.g., Abramenko & Longcope (2005). An important inference from the above discussion reads that a necessary condition for the seed magnetic field to be amplified is met. So, local turbulent dynamo in the near-surface layer is quite a possibility. Regime of turbulent magnetic diffusion in the photosphere . As we saw in Introduction, the anomalous diffusivity is another hallmark of multi-fractality. The dispersal process embedded in a multi-fractal cannot follow the random walk with normal diffusion. For example, in the case of solar photosphere, the multi-fractal plasma cannot ensure an arbitrary displacement in an arbitrary direction for all magnetic elements. A discussion of differences between the normal and anomalous diffusion can be found, e.g., in Lawrence & Schrijver (1993); Vlahos et al. (2008). The coefficient of magnetic diffusivity is an essential input parameter for meridional flux transport models and global dynamo models. Therefore, magnetic flux dispersal on the solar surface was studies extensively (e.g., Lawrence & Schrijver 1993; Schrijver et al. 1996; Berger et al. 1998a,b; Cadavid et al. 1999; Hagenaar et al. 1999; Lawrence et al. 2001; Utz et al. 2009, 2010; Crockett et al. 2010; Abramenko et al. 2011). In the most of these studies, observational data were interpreted in the framework of normal diffusion, and variety of estimates for the magnetic diffusivity coefficient, η , were reported: from 50 km 2 s -1 (Berger et al. 1998b) to 350 km 2 s -1 (Utz et al. 2010). Numerical simulations of the isotropic turbulence with magnetic field (Brandenburg et al. 2008) showed that the turbulent magnetic diffusivity increases with increasing scale. Combination of MHD modeling with observations allowed Chae et al. (2008) to conclude that the turbulent diffusivity changes with scale and is smallest (about 1 km 2 s -1 ) on smallest available scale of approximately 200 km. Photospheric BPs, as tracers of kilo-gauss magnetic flux tubes, were utilized to probe photospheric flux dispersal (e.g., Berger et al. 1998a,b; Utz et al. 2010; Crockett et al. 2010). Recently, the high resolution power of the NST allowed Abramenko et al. (2011) to explore the regime of diffusion in the photosphere down to scales of 10 sec in time and 25 km in space. Magnetic BPs detected from NST/TiO images were tracked, and their squared displacements (from the initial position of a given BP) were calculated as a function of a time lag, τ . Later, the routine was repeated for HMI magnetic flux concentrations in a quiet Sun area on the disk center. Figure 6 a summarizes results. Recall that for normal diffusion (Brownian motions), the squared displacements of tracers are directly proportional to time, i.e., the power law index, γ , of the displacement spectrum is a unity (an example of the normal diffusion regime is illustrated in Figure 6 with thick black dashed lines). When γ > 1 ( γ < 1 ), a regime of super-diffusion (sub-diffusion) dominates. The squared displacements (∆ l ) 2 ( τ ) can be approximated, at a given range of scales, as where c = 10 y sect and γ and y sect are derived from the best linear lit to the data points plotted in a double-logarithmic plot. Then the diffusion coefficient can be written as (Abramenko et al. 2011): 10 1 η ~ (< 2 10 ∆ l 2 3 ∆ 10 Spatial Scale, -1)/ γ 10 l, km As if follows from Figure 6, for both data sets we observe the super-diffusion regime. The coefficient of magnetic turbulent diffusivity, η (∆ l ) , derived by Eq. (5) for both data sets is shown in Figure 6 b . Two essential things should be mentioned here: first, the diffusion coefficient grows as the scale increases (the same is true for a time scale, too, see Eq. (4). Second, the slope of the power law varies with scale (which is a characteristic feature of intrinsic multi-fractality). On the minimal spatial (25 km) and temporal (10 sec) scales considered in Abramenko et al. (2011), the diffusion coefficient in QS area was found to be 19 km 2 s -1 . The HMI data provided a value of approximately 220 km 2 s -1 on the largest available scale of 4 Mm. The observed tendency of the turbulent magnetic diffusivity to decrease with decreasing scales leads us to expect that the turbulent diffusivity might be close to the magnitudes of diffusivity adopted in the numerical simulations of small-scale dynamo (0.01 - 10 km 2 s -1 , e.g., Boldyrev & Cattaneo (2004); Vogler & Schussler (2007); Pietarila Graham et al. (2010)). This 1000 100 10 1 0 10 ( >) γ 4 b 5 10 makes the simulations even more realistic. In summary, a super-diffusion regime on very small scales is very favorable for pictures assuming turbulent dynamo action since it assumes decreasing diffusivity with decreasing scales.\",\n \"pages\": [\n 5,\n 6,\n 7,\n 8,\n 9,\n 10,\n 11,\n 12,\n 13\n ]\n },\n {\n \"title\": \"4. Concluding remarks\",\n \"content\": \"Continuously varying magnetic fields are the main reason for the solar/stellar activity. The 11-year solar cycle is one of the most astonishing and widely known examples of the self-organized generation of the magnetic field. Although we know that there is no two absolutely similar solar cycles, yet, persistency and regularity of the solar periodicity through thousands of years remains impressive. A drastically different picture arises when one looks on the photosphere: chaos of mixed-polarity magnetic elements of all sizes until the resolution limits of modern instruments, continuously renewing during 1-2 days - the magnetic carpet. Dualism of the solar magnetism is usually explained by a simultaneous action of two dynamos: a global dynamo operating in the convective zone and responsible for the 11-year solar cycle, and local, or turbulent dynamo, which might operate inside the near-surface layer and to be responsible for generation of small-scale magnetic fields forming the magnetic carpet. The explanation seems to oversimplify the reality because resent studies of distribution of the magnetic flux accumulated in magnetic flux tubes showed the non-interrupted power law for many decades (Parnell et al. 2009) thus supposing a common (for all scales) mechanism for the magnetic field generation. One of promising ways to handle the problem is to consider the solar dynamo process as a non-linear dynamical system (NDS), with intrinsic properties of multi-fractality and intermittency. Like any NDS, the solar dynamo is then capable to self-organization on all scales (including large scales) and display a chaotic nature on small scales. Self-organization, in turn, provides for a magnetic complex a way to reach a SOC state, when burst-like energy release events of any size are possible at any time instant. The concept is very important for our understanding of flaring and heating processes in solar/stellar atmospheres. Further, multi-fractal nature on the magnetic field provides a necessary condition for the local turbulent dynamo operation in the near-surface layer of the convective zone. Observational evidences for local dynamo operation are still under strong debates, e.g., compare the talks by Drs. Tsuneta and Stenflo presented at this symposium. One pragmatic advise for researchers could be inferred form the observed multi-fractal nature of magnetized solar plasma. Namely, observed power laws should not be extrapolated over neighboring scales, a frequent mistake for power laws studies in various fields. In summary, the paradigm of multi-fractal and highly intermittent structure of solar magnetized plasma offers new approaches to understand the solar and stellar magnetism.\",\n \"pages\": [\n 13,\n 14\n ]\n },\n {\n \"title\": \"REFERENCES\",\n \"content\": \"Abramenko, V., & Yurchyshyn, V. 2010a, ApJ , 722, 122 -. 2010b, ApJ , 722, 122 Abramenko, V. I. 2005, Sol. Phys. , 228, 29 Abramenko, V. I., Carbone, V., Yurchyshyn, V., Goode, P. R., Stein, R. F., Lepreti, F., Capparelli, V., & Vecchio, A. 2011, ApJ , 743, 133 Abramenko, V. I., & Longcope, D. W. 2005, ApJ , 619, 1160 Abramenko, V. I., Yurchyshyn, V. B., Goode, P. R., Kitiashvili, I. N., & Kosovichev, A. G. 2012, ApJ , 756, L27 Abramenko, V. I., Yurchyshyn, V. B., Wang, H., Spirock, T. J., & Goode, P. 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Usp., 30, 353\",\n \"pages\": [\n 14,\n 15,\n 17\n ]\n }\n]"}}},{"rowIdx":96,"cells":{"bibcode":{"kind":"string","value":"2013IAUS..295..225C"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1211.1023.pdf"},"content":{"kind":"string","value":"\nFurther evidence for large central mass-to-light ratios in massive early-type galaxies\nE. M. Corsini 1 , 2 , G. A. Wegner 3 , J. Thomas 4 , R. P. Saglia 4 , R. Bender 4 , 5 and S. B. Pu 6\n1 Dipartimento di Fisica e Astronomia, Universit'a di Padova, Padova, Italy email: enricomaria.corsini@unipd.it\n2\nINAF-Osservatorio Astronomico di Padova, Padova, Italy 3 Department of Physics and Astronomy, Dartmouth College, Hanover, NH, USA 4 Max-Planck-Institut fur extraterrestrische Physik, Garching, Germany 5 Universitats-Sternwarte Munchen, Munchen, Germany 6 The Beijing No. 12 High School, Beijing, China\nAbstract. We studied the stellar populations, distribution of dark matter, and dynamical structure of a sample of 25 early-type galaxies in the Coma and Abell 262 clusters. We derived dynamical mass-to-light ratios and dark matter densities from orbit-based dynamical models, complemented by the ages, metallicities, and α -elements abundances of the galaxies from single stellar population models. Most of the galaxies have a significant detection of dark matter and their halos are about 10 times denser than in spirals of the same stellar mass. Calibrating dark matter densities to cosmological simulations we find assembly redshifts z DM ≈ 1 -3. The dynamical mass that follows the light is larger than expected for a Kroupa stellar initial mass function, especially in galaxies with high velocity dispersion σ eff inside the effective radius r eff . We now have 5 of 25 galaxies where mass follows light to 1 -3 r eff , the dynamical mass-to-light ratio of all the mass that follows the light is large ( ≈ 8 -10 in the Kron-Cousins R band), the dark matter fraction is negligible to 1 -3 r eff . This could indicate a 'massive' initial mass function in massive early-type galaxies. Alternatively, some of the dark matter in massive galaxies could follow the light very closely suggesting a significant degeneracy between luminous and dark matter.\nKeywords. galaxies: abundances, galaxies: elliptical and lenticular, cD, galaxies: formation, galaxies: kinematics and dynamics, galaxies: stellar content.\n1. Introduction\nIn the past years we studied the stellar populations, mass distribution, and orbital structure of a sample of early-type galaxies in the Coma cluster with the aim of constraining the epoch and mechanism of their assembly.\nThe surface-brightness distribution was obtained from ground-based and HST data. The stellar rotation, velocity dispersion, and the H 3 and H 4 coefficients of the line-of-sight velocity distribution were measured along the major axis, minor axis, and an intermediate axis. In addition, the line index profiles of Mg, Fe and H β were derived (Mehlert et al. 2000; Wegner et al. 2002; Corsini et al. 2008). Axisymmetric orbit-based dynamical models were used to derive the mass-to-light ratio Υ ∗ of all the mass that follows the light and the dark matter (DM) halo parameters in 17 galaxies (Thomas et al. 2005, 2007a,b, 2009a,b). The comparison with masses derived through strong gravitational lensing for early-type galaxies with similar velocity dispersion and the analysis of the ionized-gas\nkinematics gave valuable consistency checks for the total mass distribution predicted by dynamical modeling (Thomas et al. 2011). The line-strength indices were analyzed by single stellar-population models to derive the age, metallicity, α -elements abundance, and mass-to-light ratio Υ Kroupa (or Υ Salpeter depending on the adopted initial mass function, IMF) of the galaxies (Mehlert et al. 2003).\nMore recently, we have performed the same dynamical analysis for 8 early-type galaxies of the nearby cluster Abell 262 (Wegner et al. 2012). The latter is far less densely populated than Coma cluster and it is comparable to the Virgo cluster. Moreover, while the Coma galaxies were selected to be mostly flattened, the Abell 262 galaxies we measured appear predominantly round on the sky.\n2. Results\n2.1. Evidence for halo mass not associated to the light\nIn the Coma galaxy sample the statistical significance for DM halos is over 95% for 8 (out of 17) galaxies (Thomas et al. 2007b), whereas the Abell 262 sample reveals 4 (out of 8) galaxies of this kind (Wegner et al. 2012). In Coma, we found only one galaxy (GMP 1990) with f halo ≈ 0, i.e., with a negligible halo-mass fraction of the total mass inside r eff . This is also the case of 4 galaxies in Abell 262 (NGC 703, NGC 708, NGC 712, and UGC 1308). The evidence for a DM component in addition mass that follows light is not directly connected to the spatial extent of the kinematic data, degree of rotation, or flattening of the system. There is no relationship with the age, metallicity, and α -elements abundance of the stellar populations.\nWe can not discriminate between cuspy and logarithmic halos based on the quality of the kinematic fits, except for NGC 703 where the logarithmic halo fits better. Still the majority of cluster early-type galaxies have 2 -10 times denser halos than local spirals (e.g., Persic et al. 1996), implying a 1 . 3 -2 . 2 times higher (1 + z DM ) assuming 〈 ρ DM 〉 ∼ (1 + z DM ) 3 , where z DM is the formation redshift of the DM halos. Thus, if spirals typically formed at z DM ≈ 1, then cluster early-type galaxies assembled at z DM ≈ 1 . 6 -3 . 4.\nAveraging over all galaxies, we find that a fraction of 〈 f halo 〉 = 0 . 2 of the total mass inside r eff is in a DM halo distinct from the light. Similar fractions come from other dynamical studies employing spherical models (e.g., Gerhard et al. 2001). The Coma and Abell 262 galaxies show an anti-correlation between Υ ∗ / Υ Kroupa , i.e. the ratio between the dynamical and stellar population mass-to-light ratios, and f halo (Fig. 1, left panel). Galaxies where the dynamical mass following the light exceeds the Kroupa value by far (Υ ∗ / Υ Kroupa > 3) seem to lack matter following the halo distribution inside r eff ( 〈 f halo 〉 ≈ 0). Not so in galaxies near the Kroupa limit (Υ ∗ / Υ Kroupa < 1 . 4), where the dark-halo mass fraction is at its maximum ( 〈 f halo 〉 = 0 . 3).\n2.2. Mass that follows the light\nAs far as the mass-to-light ratios are concerned, the galaxies of Coma and Abell 262 follow a similar trend. While the dynamically determined Υ ∗ increases strongly with σ eff , i.e., the velocity dispersion averaged within r eff (Fig. 1, right top panel), the stellar population models indicate almost constant Υ Kroupa (Fig. 1, right middle panel). This implies that the ratio Υ ∗ / Υ Kroupa increases with σ eff (Fig. 1, right bottom panel). Around σ eff ≈ 200 km s -1 the distribution of Υ ∗ / Υ Kroupa has a sharp cutoff with almost no galaxy below Υ ∗ / Υ Kroupa = 1. For σ eff /greaterorsimilar 250 km s -1 the lower bound of Υ ∗ / Υ Kroupa increases to Υ ∗ / Υ Kroupa /greaterorsimilar 2 at σ eff ≈ 300 km s -1 . Similar trends are also observed in the SAURON sample with dynamical models lacking a separate DM halo (Cappellari\n\n\n
Figure 1. Left: Ratio of dynamical Υ ∗ to stellar-population Υ Kroupa as a function of f halo , i.e., the halo-mass fraction of the total mass inside r eff , for galaxies in Coma (open circles, Thomas et al. 2011) and Abell 262 (filled circles, Wegner et al. 2012). r eff . Υ ∗ / Υ Kroupa = 1 . 6 corresponds to a Salpeter IMF. Right: Dynamical Υ ∗ (upper panel), stellar-population Υ Kroupa (middle panel), and their ratio (bottom panel) as a function of the effective velocity dispersion, σ eff . In the bottom panel, Coma and Abell 262 galaxies are compared to SLACS (open squares, Treu et al. 2010) and SAURON galaxies (open triangles, Cappellari et al. 2006).
\n\net al. 2006), in SLACS galaxies with combined dynamical and lensing analysis (Treu et al. 2010) and, recently, in the ATLAS3d survey with dynamical models including a DM halo (Cappellari et al. 2012).\n3. Discussion\nFig. 1 provides strong evidence for large central Υ ∗ in massive early-type galaxies. However, in all gravity-based methods there is a fundamental degeneracy concerning the interpretation of mass-to-light ratios. Such methods can not uniquely discriminate between luminous and dark matter once they follow similar radial distributions. The distinction is always based on the assumption that the mass density profile of the DM differs from that of the luminous matter.\nOne extreme point of view is the assumption that the stellar masses in early-type galaxies are maximal and correspond to Υ ∗ . The immediate consequence is that the stellar IMF in early-type galaxies is not universal, varying from Kroupa-like at low velocity dispersions to Salpeter (or steeper) in the most massive galaxies (see Auger et al. 2010, Thomas et al. 2011, and Cappellari et al. 2012, for a detailed discussion). Recent attempts to measure the stellar IMF directly from near-infrared observations point in the same direction (see Conroy & van Dokkum 2012, and references therein). However, we also find the galaxies with the largest Υ ∗ / Υ Kroupa have the lowest halo-mass fractions inside r eff and vice versa. A possible explanation for this finding is a DM distribution that follows the light very closely in massive galaxies and contaminates the measured Υ ∗ , while it is\nmore distinct from the light in lower-mass systems. This has been suggested elsewhere as a signature of violent relaxation.\nOne option to further constrain the mass-decomposition of gravity-based models is to incorporate predictions from cosmological simulations that confine the maximum amount of DM that can be plausibly attached to a galaxy of a given stellar mass. Since adiabatic contraction increases the amount of DM in the galaxy center, it could be in principle a viable mechanism to lower the required stellar masses towards a Kroupa IMF (Napolitano et al. 2010, but see also Cappellari et al. 2012). An immediate consequence is that some of the mass that follows the light is actually DM, increasing the DM fraction to about 50% of the total mass inside r eff .\nSince the (decontracted) average halo density scales with the mean density of the universe at the assembly epoch, we derived the dark-halo assembly redshift z DM for Coma (Thomas et al. 2011) and Abell 262 galaxies (Wegner et al. 2012). We compared the values of z DM to the star-formation redshifts z ∗ calculated from the stellar-population ages. For the majority of galaxies z DM ≈ z ∗ and their assembly seems to have stopped before z DM ≈ 1. The stars of some galaxies appear to be younger than the halo, which indicates a secondary star-formation episode after the main halo assembly. The photometric and kinematic properties of the remaining galaxies suggest they are the remnants of gas-poor binary mergers and their progenitors formed close to the z DM = z ∗ relation. Without trying to overinterpret the result given the assumptions, it seems that Kroupa IMF allows us to explain the formation redshifts of our galaxies. In addition, galaxies in Coma and Abell 262 where the dynamical mass that follows the light is in excess of a Kroupa stellar population do not differ in terms of their stellar population ages, metallicities and α -elements abundances from galaxies where this is not the case.\nTaken at face value, our dynamical mass models are therefore as consistent with a universal IMF, as they are with a variable IMF. If the IMF indeed varies from galaxy to galaxy according to the average star-formation rate (Conroy & van Dokkum 2012) then the assumption of a constant stellar mass-to-light ratio inside a galaxy should be relaxed in future dynamical and lensing models.\nReferences\nAuger, M. W., Treu, T., Bolton, A. S. et al. 2009, ApJ , 705, 1099\nCappellari, M., Bacon, R., Bureau, M. et al. 2006, MNRAS , 366, 1126\nCappellari, M., McDermid, R. M., Alatalo, K. et al. 2012, Nature , 484, 485\nConroy, C., & van Dokkum, P. 2012, ApJ , submitted, arXiv:1205.6473\nCorsini, E. M., Wegner, G. A., Saglia, R. P. et al. 2008, ApJS , 175, 462\nGerhard , O., Kronawitter, A., Saglia, R. P., & Bender, R. 2001, AJ , 121, 1936\nMehlert, D., Saglia, R. P., Bender, R., & Wegner, G. A. 2000, A&AS , 141, 449\nMehlert, D., Thomas, D., Saglia, R. P., Bender, R., & Wegner, G. A. 2000, A&A , 407, 423\nNapolitano, N. R., Romanowsky, A. J., & Tortora, C. 2010, MNRAS , 405, 2351\nPersic, M., Salucci, P., & Stel, F. 1996, MNRAS , 283, 1102\nThomas, J., Jesseit, R., Naab, T. et al. 2007a, MNRAS , 381, 1672\nThomas, J., Jesseit, R., Saglia, R. P. et al. 2009a, MNRAS , 393, 641\nThomas, J., Saglia, R. P., Bender, R. et al. 2005, MNRAS , 360, 1355\nThomas, J., Saglia, R. P., Bender, R. et al. 2007b, MNRAS , 382, 657\nThomas, J., Saglia, R. P., Bender, R.\net al.\n2009b,\nApJ\n, 691, 770\nThomas, J., Saglia, R. P., Bender, R. et al. 2011, MNRAS , 415, 545\nTreu, T., Auger, M. W., Koopmans, L. V. E. et al. 2010, ApJ , 709, 1195\nWegner, G. A., Corsini, E. M., Saglia, R. P. et al. 2002, A&A , 395, 753\nWegner, G. A., Corsini, E. M., Thomas, J. et al. 2012, AJ , 144, 78\n"},"sections":{"kind":"list like","value":[{"title":"E. M. Corsini 1 , 2 , G. A. Wegner 3 , J. Thomas 4 , R. P. Saglia 4 , R. Bender 4 , 5 and S. B. Pu 6","content":"1 Dipartimento di Fisica e Astronomia, Universit'a di Padova, Padova, Italy email: enricomaria.corsini@unipd.it 2 INAF-Osservatorio Astronomico di Padova, Padova, Italy 3 Department of Physics and Astronomy, Dartmouth College, Hanover, NH, USA 4 Max-Planck-Institut fur extraterrestrische Physik, Garching, Germany 5 Universitats-Sternwarte Munchen, Munchen, Germany 6 The Beijing No. 12 High School, Beijing, China Abstract. We studied the stellar populations, distribution of dark matter, and dynamical structure of a sample of 25 early-type galaxies in the Coma and Abell 262 clusters. We derived dynamical mass-to-light ratios and dark matter densities from orbit-based dynamical models, complemented by the ages, metallicities, and α -elements abundances of the galaxies from single stellar population models. Most of the galaxies have a significant detection of dark matter and their halos are about 10 times denser than in spirals of the same stellar mass. Calibrating dark matter densities to cosmological simulations we find assembly redshifts z DM ≈ 1 -3. The dynamical mass that follows the light is larger than expected for a Kroupa stellar initial mass function, especially in galaxies with high velocity dispersion σ eff inside the effective radius r eff . We now have 5 of 25 galaxies where mass follows light to 1 -3 r eff , the dynamical mass-to-light ratio of all the mass that follows the light is large ( ≈ 8 -10 in the Kron-Cousins R band), the dark matter fraction is negligible to 1 -3 r eff . This could indicate a 'massive' initial mass function in massive early-type galaxies. Alternatively, some of the dark matter in massive galaxies could follow the light very closely suggesting a significant degeneracy between luminous and dark matter. Keywords. galaxies: abundances, galaxies: elliptical and lenticular, cD, galaxies: formation, galaxies: kinematics and dynamics, galaxies: stellar content.","pages":[1]},{"title":"1. Introduction","content":"In the past years we studied the stellar populations, mass distribution, and orbital structure of a sample of early-type galaxies in the Coma cluster with the aim of constraining the epoch and mechanism of their assembly. The surface-brightness distribution was obtained from ground-based and HST data. The stellar rotation, velocity dispersion, and the H 3 and H 4 coefficients of the line-of-sight velocity distribution were measured along the major axis, minor axis, and an intermediate axis. In addition, the line index profiles of Mg, Fe and H β were derived (Mehlert et al. 2000; Wegner et al. 2002; Corsini et al. 2008). Axisymmetric orbit-based dynamical models were used to derive the mass-to-light ratio Υ ∗ of all the mass that follows the light and the dark matter (DM) halo parameters in 17 galaxies (Thomas et al. 2005, 2007a,b, 2009a,b). The comparison with masses derived through strong gravitational lensing for early-type galaxies with similar velocity dispersion and the analysis of the ionized-gas kinematics gave valuable consistency checks for the total mass distribution predicted by dynamical modeling (Thomas et al. 2011). The line-strength indices were analyzed by single stellar-population models to derive the age, metallicity, α -elements abundance, and mass-to-light ratio Υ Kroupa (or Υ Salpeter depending on the adopted initial mass function, IMF) of the galaxies (Mehlert et al. 2003). More recently, we have performed the same dynamical analysis for 8 early-type galaxies of the nearby cluster Abell 262 (Wegner et al. 2012). The latter is far less densely populated than Coma cluster and it is comparable to the Virgo cluster. Moreover, while the Coma galaxies were selected to be mostly flattened, the Abell 262 galaxies we measured appear predominantly round on the sky.","pages":[1,2]},{"title":"2.1. Evidence for halo mass not associated to the light","content":"In the Coma galaxy sample the statistical significance for DM halos is over 95% for 8 (out of 17) galaxies (Thomas et al. 2007b), whereas the Abell 262 sample reveals 4 (out of 8) galaxies of this kind (Wegner et al. 2012). In Coma, we found only one galaxy (GMP 1990) with f halo ≈ 0, i.e., with a negligible halo-mass fraction of the total mass inside r eff . This is also the case of 4 galaxies in Abell 262 (NGC 703, NGC 708, NGC 712, and UGC 1308). The evidence for a DM component in addition mass that follows light is not directly connected to the spatial extent of the kinematic data, degree of rotation, or flattening of the system. There is no relationship with the age, metallicity, and α -elements abundance of the stellar populations. We can not discriminate between cuspy and logarithmic halos based on the quality of the kinematic fits, except for NGC 703 where the logarithmic halo fits better. Still the majority of cluster early-type galaxies have 2 -10 times denser halos than local spirals (e.g., Persic et al. 1996), implying a 1 . 3 -2 . 2 times higher (1 + z DM ) assuming 〈 ρ DM 〉 ∼ (1 + z DM ) 3 , where z DM is the formation redshift of the DM halos. Thus, if spirals typically formed at z DM ≈ 1, then cluster early-type galaxies assembled at z DM ≈ 1 . 6 -3 . 4. Averaging over all galaxies, we find that a fraction of 〈 f halo 〉 = 0 . 2 of the total mass inside r eff is in a DM halo distinct from the light. Similar fractions come from other dynamical studies employing spherical models (e.g., Gerhard et al. 2001). The Coma and Abell 262 galaxies show an anti-correlation between Υ ∗ / Υ Kroupa , i.e. the ratio between the dynamical and stellar population mass-to-light ratios, and f halo (Fig. 1, left panel). Galaxies where the dynamical mass following the light exceeds the Kroupa value by far (Υ ∗ / Υ Kroupa > 3) seem to lack matter following the halo distribution inside r eff ( 〈 f halo 〉 ≈ 0). Not so in galaxies near the Kroupa limit (Υ ∗ / Υ Kroupa < 1 . 4), where the dark-halo mass fraction is at its maximum ( 〈 f halo 〉 = 0 . 3).","pages":[2]},{"title":"2.2. Mass that follows the light","content":"As far as the mass-to-light ratios are concerned, the galaxies of Coma and Abell 262 follow a similar trend. While the dynamically determined Υ ∗ increases strongly with σ eff , i.e., the velocity dispersion averaged within r eff (Fig. 1, right top panel), the stellar population models indicate almost constant Υ Kroupa (Fig. 1, right middle panel). This implies that the ratio Υ ∗ / Υ Kroupa increases with σ eff (Fig. 1, right bottom panel). Around σ eff ≈ 200 km s -1 the distribution of Υ ∗ / Υ Kroupa has a sharp cutoff with almost no galaxy below Υ ∗ / Υ Kroupa = 1. For σ eff /greaterorsimilar 250 km s -1 the lower bound of Υ ∗ / Υ Kroupa increases to Υ ∗ / Υ Kroupa /greaterorsimilar 2 at σ eff ≈ 300 km s -1 . Similar trends are also observed in the SAURON sample with dynamical models lacking a separate DM halo (Cappellari et al. 2006), in SLACS galaxies with combined dynamical and lensing analysis (Treu et al. 2010) and, recently, in the ATLAS3d survey with dynamical models including a DM halo (Cappellari et al. 2012).","pages":[2,3]},{"title":"3. Discussion","content":"Fig. 1 provides strong evidence for large central Υ ∗ in massive early-type galaxies. However, in all gravity-based methods there is a fundamental degeneracy concerning the interpretation of mass-to-light ratios. Such methods can not uniquely discriminate between luminous and dark matter once they follow similar radial distributions. The distinction is always based on the assumption that the mass density profile of the DM differs from that of the luminous matter. One extreme point of view is the assumption that the stellar masses in early-type galaxies are maximal and correspond to Υ ∗ . The immediate consequence is that the stellar IMF in early-type galaxies is not universal, varying from Kroupa-like at low velocity dispersions to Salpeter (or steeper) in the most massive galaxies (see Auger et al. 2010, Thomas et al. 2011, and Cappellari et al. 2012, for a detailed discussion). Recent attempts to measure the stellar IMF directly from near-infrared observations point in the same direction (see Conroy & van Dokkum 2012, and references therein). However, we also find the galaxies with the largest Υ ∗ / Υ Kroupa have the lowest halo-mass fractions inside r eff and vice versa. A possible explanation for this finding is a DM distribution that follows the light very closely in massive galaxies and contaminates the measured Υ ∗ , while it is more distinct from the light in lower-mass systems. This has been suggested elsewhere as a signature of violent relaxation. One option to further constrain the mass-decomposition of gravity-based models is to incorporate predictions from cosmological simulations that confine the maximum amount of DM that can be plausibly attached to a galaxy of a given stellar mass. Since adiabatic contraction increases the amount of DM in the galaxy center, it could be in principle a viable mechanism to lower the required stellar masses towards a Kroupa IMF (Napolitano et al. 2010, but see also Cappellari et al. 2012). An immediate consequence is that some of the mass that follows the light is actually DM, increasing the DM fraction to about 50% of the total mass inside r eff . Since the (decontracted) average halo density scales with the mean density of the universe at the assembly epoch, we derived the dark-halo assembly redshift z DM for Coma (Thomas et al. 2011) and Abell 262 galaxies (Wegner et al. 2012). We compared the values of z DM to the star-formation redshifts z ∗ calculated from the stellar-population ages. For the majority of galaxies z DM ≈ z ∗ and their assembly seems to have stopped before z DM ≈ 1. The stars of some galaxies appear to be younger than the halo, which indicates a secondary star-formation episode after the main halo assembly. The photometric and kinematic properties of the remaining galaxies suggest they are the remnants of gas-poor binary mergers and their progenitors formed close to the z DM = z ∗ relation. Without trying to overinterpret the result given the assumptions, it seems that Kroupa IMF allows us to explain the formation redshifts of our galaxies. In addition, galaxies in Coma and Abell 262 where the dynamical mass that follows the light is in excess of a Kroupa stellar population do not differ in terms of their stellar population ages, metallicities and α -elements abundances from galaxies where this is not the case. Taken at face value, our dynamical mass models are therefore as consistent with a universal IMF, as they are with a variable IMF. If the IMF indeed varies from galaxy to galaxy according to the average star-formation rate (Conroy & van Dokkum 2012) then the assumption of a constant stellar mass-to-light ratio inside a galaxy should be relaxed in future dynamical and lensing models.","pages":[3,4]},{"title":"References","content":"Auger, M. W., Treu, T., Bolton, A. S. et al. 2009, ApJ , 705, 1099 Cappellari, M., Bacon, R., Bureau, M. et al. 2006, MNRAS , 366, 1126 Cappellari, M., McDermid, R. M., Alatalo, K. et al. 2012, Nature , 484, 485 Conroy, C., & van Dokkum, P. 2012, ApJ , submitted, arXiv:1205.6473 Corsini, E. M., Wegner, G. A., Saglia, R. P. et al. 2008, ApJS , 175, 462 Gerhard , O., Kronawitter, A., Saglia, R. P., & Bender, R. 2001, AJ , 121, 1936 Mehlert, D., Saglia, R. P., Bender, R., & Wegner, G. A. 2000, A&AS , 141, 449 Mehlert, D., Thomas, D., Saglia, R. P., Bender, R., & Wegner, G. A. 2000, A&A , 407, 423 Napolitano, N. R., Romanowsky, A. J., & Tortora, C. 2010, MNRAS , 405, 2351 Persic, M., Salucci, P., & Stel, F. 1996, MNRAS , 283, 1102 Thomas, J., Jesseit, R., Naab, T. et al. 2007a, MNRAS , 381, 1672 Thomas, J., Jesseit, R., Saglia, R. P. et al. 2009a, MNRAS , 393, 641 Thomas, J., Saglia, R. P., Bender, R. et al. 2005, MNRAS , 360, 1355 Thomas, J., Saglia, R. P., Bender, R. et al. 2007b, MNRAS , 382, 657 Thomas, J., Saglia, R. P., Bender, R. et al. 2009b, ApJ , 691, 770 Thomas, J., Saglia, R. P., Bender, R. et al. 2011, MNRAS , 415, 545 Treu, T., Auger, M. W., Koopmans, L. V. E. et al. 2010, ApJ , 709, 1195 Wegner, G. A., Corsini, E. M., Saglia, R. P. et al. 2002, A&A , 395, 753 Wegner, G. A., Corsini, E. M., Thomas, J. et al. 2012, AJ , 144, 78","pages":[4]}],"string":"[\n {\n \"title\": \"E. M. Corsini 1 , 2 , G. A. Wegner 3 , J. Thomas 4 , R. P. Saglia 4 , R. Bender 4 , 5 and S. B. Pu 6\",\n \"content\": \"1 Dipartimento di Fisica e Astronomia, Universit'a di Padova, Padova, Italy email: enricomaria.corsini@unipd.it 2 INAF-Osservatorio Astronomico di Padova, Padova, Italy 3 Department of Physics and Astronomy, Dartmouth College, Hanover, NH, USA 4 Max-Planck-Institut fur extraterrestrische Physik, Garching, Germany 5 Universitats-Sternwarte Munchen, Munchen, Germany 6 The Beijing No. 12 High School, Beijing, China Abstract. We studied the stellar populations, distribution of dark matter, and dynamical structure of a sample of 25 early-type galaxies in the Coma and Abell 262 clusters. We derived dynamical mass-to-light ratios and dark matter densities from orbit-based dynamical models, complemented by the ages, metallicities, and α -elements abundances of the galaxies from single stellar population models. Most of the galaxies have a significant detection of dark matter and their halos are about 10 times denser than in spirals of the same stellar mass. Calibrating dark matter densities to cosmological simulations we find assembly redshifts z DM ≈ 1 -3. The dynamical mass that follows the light is larger than expected for a Kroupa stellar initial mass function, especially in galaxies with high velocity dispersion σ eff inside the effective radius r eff . We now have 5 of 25 galaxies where mass follows light to 1 -3 r eff , the dynamical mass-to-light ratio of all the mass that follows the light is large ( ≈ 8 -10 in the Kron-Cousins R band), the dark matter fraction is negligible to 1 -3 r eff . This could indicate a 'massive' initial mass function in massive early-type galaxies. Alternatively, some of the dark matter in massive galaxies could follow the light very closely suggesting a significant degeneracy between luminous and dark matter. Keywords. galaxies: abundances, galaxies: elliptical and lenticular, cD, galaxies: formation, galaxies: kinematics and dynamics, galaxies: stellar content.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"In the past years we studied the stellar populations, mass distribution, and orbital structure of a sample of early-type galaxies in the Coma cluster with the aim of constraining the epoch and mechanism of their assembly. The surface-brightness distribution was obtained from ground-based and HST data. The stellar rotation, velocity dispersion, and the H 3 and H 4 coefficients of the line-of-sight velocity distribution were measured along the major axis, minor axis, and an intermediate axis. In addition, the line index profiles of Mg, Fe and H β were derived (Mehlert et al. 2000; Wegner et al. 2002; Corsini et al. 2008). Axisymmetric orbit-based dynamical models were used to derive the mass-to-light ratio Υ ∗ of all the mass that follows the light and the dark matter (DM) halo parameters in 17 galaxies (Thomas et al. 2005, 2007a,b, 2009a,b). The comparison with masses derived through strong gravitational lensing for early-type galaxies with similar velocity dispersion and the analysis of the ionized-gas kinematics gave valuable consistency checks for the total mass distribution predicted by dynamical modeling (Thomas et al. 2011). The line-strength indices were analyzed by single stellar-population models to derive the age, metallicity, α -elements abundance, and mass-to-light ratio Υ Kroupa (or Υ Salpeter depending on the adopted initial mass function, IMF) of the galaxies (Mehlert et al. 2003). More recently, we have performed the same dynamical analysis for 8 early-type galaxies of the nearby cluster Abell 262 (Wegner et al. 2012). The latter is far less densely populated than Coma cluster and it is comparable to the Virgo cluster. Moreover, while the Coma galaxies were selected to be mostly flattened, the Abell 262 galaxies we measured appear predominantly round on the sky.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2.1. Evidence for halo mass not associated to the light\",\n \"content\": \"In the Coma galaxy sample the statistical significance for DM halos is over 95% for 8 (out of 17) galaxies (Thomas et al. 2007b), whereas the Abell 262 sample reveals 4 (out of 8) galaxies of this kind (Wegner et al. 2012). In Coma, we found only one galaxy (GMP 1990) with f halo ≈ 0, i.e., with a negligible halo-mass fraction of the total mass inside r eff . This is also the case of 4 galaxies in Abell 262 (NGC 703, NGC 708, NGC 712, and UGC 1308). The evidence for a DM component in addition mass that follows light is not directly connected to the spatial extent of the kinematic data, degree of rotation, or flattening of the system. There is no relationship with the age, metallicity, and α -elements abundance of the stellar populations. We can not discriminate between cuspy and logarithmic halos based on the quality of the kinematic fits, except for NGC 703 where the logarithmic halo fits better. Still the majority of cluster early-type galaxies have 2 -10 times denser halos than local spirals (e.g., Persic et al. 1996), implying a 1 . 3 -2 . 2 times higher (1 + z DM ) assuming 〈 ρ DM 〉 ∼ (1 + z DM ) 3 , where z DM is the formation redshift of the DM halos. Thus, if spirals typically formed at z DM ≈ 1, then cluster early-type galaxies assembled at z DM ≈ 1 . 6 -3 . 4. Averaging over all galaxies, we find that a fraction of 〈 f halo 〉 = 0 . 2 of the total mass inside r eff is in a DM halo distinct from the light. Similar fractions come from other dynamical studies employing spherical models (e.g., Gerhard et al. 2001). The Coma and Abell 262 galaxies show an anti-correlation between Υ ∗ / Υ Kroupa , i.e. the ratio between the dynamical and stellar population mass-to-light ratios, and f halo (Fig. 1, left panel). Galaxies where the dynamical mass following the light exceeds the Kroupa value by far (Υ ∗ / Υ Kroupa > 3) seem to lack matter following the halo distribution inside r eff ( 〈 f halo 〉 ≈ 0). Not so in galaxies near the Kroupa limit (Υ ∗ / Υ Kroupa < 1 . 4), where the dark-halo mass fraction is at its maximum ( 〈 f halo 〉 = 0 . 3).\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"2.2. Mass that follows the light\",\n \"content\": \"As far as the mass-to-light ratios are concerned, the galaxies of Coma and Abell 262 follow a similar trend. While the dynamically determined Υ ∗ increases strongly with σ eff , i.e., the velocity dispersion averaged within r eff (Fig. 1, right top panel), the stellar population models indicate almost constant Υ Kroupa (Fig. 1, right middle panel). This implies that the ratio Υ ∗ / Υ Kroupa increases with σ eff (Fig. 1, right bottom panel). Around σ eff ≈ 200 km s -1 the distribution of Υ ∗ / Υ Kroupa has a sharp cutoff with almost no galaxy below Υ ∗ / Υ Kroupa = 1. For σ eff /greaterorsimilar 250 km s -1 the lower bound of Υ ∗ / Υ Kroupa increases to Υ ∗ / Υ Kroupa /greaterorsimilar 2 at σ eff ≈ 300 km s -1 . Similar trends are also observed in the SAURON sample with dynamical models lacking a separate DM halo (Cappellari et al. 2006), in SLACS galaxies with combined dynamical and lensing analysis (Treu et al. 2010) and, recently, in the ATLAS3d survey with dynamical models including a DM halo (Cappellari et al. 2012).\",\n \"pages\": [\n 2,\n 3\n ]\n },\n {\n \"title\": \"3. Discussion\",\n \"content\": \"Fig. 1 provides strong evidence for large central Υ ∗ in massive early-type galaxies. However, in all gravity-based methods there is a fundamental degeneracy concerning the interpretation of mass-to-light ratios. Such methods can not uniquely discriminate between luminous and dark matter once they follow similar radial distributions. The distinction is always based on the assumption that the mass density profile of the DM differs from that of the luminous matter. One extreme point of view is the assumption that the stellar masses in early-type galaxies are maximal and correspond to Υ ∗ . The immediate consequence is that the stellar IMF in early-type galaxies is not universal, varying from Kroupa-like at low velocity dispersions to Salpeter (or steeper) in the most massive galaxies (see Auger et al. 2010, Thomas et al. 2011, and Cappellari et al. 2012, for a detailed discussion). Recent attempts to measure the stellar IMF directly from near-infrared observations point in the same direction (see Conroy & van Dokkum 2012, and references therein). However, we also find the galaxies with the largest Υ ∗ / Υ Kroupa have the lowest halo-mass fractions inside r eff and vice versa. A possible explanation for this finding is a DM distribution that follows the light very closely in massive galaxies and contaminates the measured Υ ∗ , while it is more distinct from the light in lower-mass systems. This has been suggested elsewhere as a signature of violent relaxation. One option to further constrain the mass-decomposition of gravity-based models is to incorporate predictions from cosmological simulations that confine the maximum amount of DM that can be plausibly attached to a galaxy of a given stellar mass. Since adiabatic contraction increases the amount of DM in the galaxy center, it could be in principle a viable mechanism to lower the required stellar masses towards a Kroupa IMF (Napolitano et al. 2010, but see also Cappellari et al. 2012). An immediate consequence is that some of the mass that follows the light is actually DM, increasing the DM fraction to about 50% of the total mass inside r eff . Since the (decontracted) average halo density scales with the mean density of the universe at the assembly epoch, we derived the dark-halo assembly redshift z DM for Coma (Thomas et al. 2011) and Abell 262 galaxies (Wegner et al. 2012). We compared the values of z DM to the star-formation redshifts z ∗ calculated from the stellar-population ages. For the majority of galaxies z DM ≈ z ∗ and their assembly seems to have stopped before z DM ≈ 1. The stars of some galaxies appear to be younger than the halo, which indicates a secondary star-formation episode after the main halo assembly. The photometric and kinematic properties of the remaining galaxies suggest they are the remnants of gas-poor binary mergers and their progenitors formed close to the z DM = z ∗ relation. Without trying to overinterpret the result given the assumptions, it seems that Kroupa IMF allows us to explain the formation redshifts of our galaxies. In addition, galaxies in Coma and Abell 262 where the dynamical mass that follows the light is in excess of a Kroupa stellar population do not differ in terms of their stellar population ages, metallicities and α -elements abundances from galaxies where this is not the case. Taken at face value, our dynamical mass models are therefore as consistent with a universal IMF, as they are with a variable IMF. If the IMF indeed varies from galaxy to galaxy according to the average star-formation rate (Conroy & van Dokkum 2012) then the assumption of a constant stellar mass-to-light ratio inside a galaxy should be relaxed in future dynamical and lensing models.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Auger, M. W., Treu, T., Bolton, A. S. et al. 2009, ApJ , 705, 1099 Cappellari, M., Bacon, R., Bureau, M. et al. 2006, MNRAS , 366, 1126 Cappellari, M., McDermid, R. M., Alatalo, K. et al. 2012, Nature , 484, 485 Conroy, C., & van Dokkum, P. 2012, ApJ , submitted, arXiv:1205.6473 Corsini, E. M., Wegner, G. A., Saglia, R. P. et al. 2008, ApJS , 175, 462 Gerhard , O., Kronawitter, A., Saglia, R. P., & Bender, R. 2001, AJ , 121, 1936 Mehlert, D., Saglia, R. P., Bender, R., & Wegner, G. A. 2000, A&AS , 141, 449 Mehlert, D., Thomas, D., Saglia, R. P., Bender, R., & Wegner, G. A. 2000, A&A , 407, 423 Napolitano, N. R., Romanowsky, A. J., & Tortora, C. 2010, MNRAS , 405, 2351 Persic, M., Salucci, P., & Stel, F. 1996, MNRAS , 283, 1102 Thomas, J., Jesseit, R., Naab, T. et al. 2007a, MNRAS , 381, 1672 Thomas, J., Jesseit, R., Saglia, R. P. et al. 2009a, MNRAS , 393, 641 Thomas, J., Saglia, R. P., Bender, R. et al. 2005, MNRAS , 360, 1355 Thomas, J., Saglia, R. P., Bender, R. et al. 2007b, MNRAS , 382, 657 Thomas, J., Saglia, R. P., Bender, R. et al. 2009b, ApJ , 691, 770 Thomas, J., Saglia, R. P., Bender, R. et al. 2011, MNRAS , 415, 545 Treu, T., Auger, M. W., Koopmans, L. V. E. et al. 2010, ApJ , 709, 1195 Wegner, G. A., Corsini, E. M., Saglia, R. P. et al. 2002, A&A , 395, 753 Wegner, G. A., Corsini, E. M., Thomas, J. et al. 2012, AJ , 144, 78\",\n \"pages\": [\n 4\n ]\n }\n]"}}},{"rowIdx":97,"cells":{"bibcode":{"kind":"string","value":"2013ICRC...33.2330F"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1309.3391.pdf"},"content":{"kind":"string","value":"\n\n\n\nCosMO - A Cosmic Muon Observer Experiment for Students\nR. FRANKE, M. HOLLER, B. KAMINSKY, T. KARG, H. PROKOPH, A. SCH ONWALD, C. SCHWERDT, A. ST OSSL, M. WALTER\nDESY, Platanenallee 6, 15738 Zeuthen, Germany\ncarolin.schwerdt@desy.de\nAbstract: What are cosmic particles and where do they come from? These are questions which are not only fascinating for scientists in astrophysics. With the CosMO experiment (Cosmic Muon Observer) students can autonomously study these particles. They can perform their own hands-on experiments to become familiar with modern scientific working methods and to obtain a direct insight into astroparticle physics. In this contribution we present the experimental setup and possible measurements. The detector consists of three scintillator boxes. Events are triggered and readout by a data acquisition board developed for the QuarkNet Project. With a Python program running on a netbook under Linux, the trigger and data taking conditions can be defined. The program displays the particle rates in real-time and stores the data for offline analysis. Possible student experiments are the measurement of cosmic particle rates dependent on the zenith angle, the distribution of geometrical size of particle showers, and the lifetime of muons. Twenty CosMO detectors have been built at DESY. They are used within the German outreach network Netzwerk Teilchenwelt at 15 astroparticle-research institutes and universities for project work with students.\nKeywords: atmospheric muons, scintillation detector, education, outreach.\n1 Introduction\nCosmic particles of various types reach the Earth. They rain down constantly, some of them with energies much higher than the LHC reaches. Cosmic rays contribute to natural background radiation and produce the beautiful light of the auroras. Perhaps they also influence the formation of clouds and even the evolution of live. Although hundreds of these particles pass through us every second, most people do not know about this. Within Netzwerk Teilchenwelt [1, 2] we have developed the CosMO experiment to provide insights into this fascinating field.\nCosMO is a scintillation counter experiment based on detector components that are used in particle and astroparticle physics. It can be operated by students on their own and brings the current topic of astroparticle physics to pupils who are interested in physics, astronomy, or computing. The project allows autonomous investigation and gets students involved in research. They are given the opportunity to experience hands-on science with the help of modern measurement techniques, as well as analysis methods in particle physics and in close collaboration with scientists. CosMO can be used in outreach projects at research institutes or within school teaching. Teachers receive training so that they are enabled to incorporate the CosMO experiment into their classes.\nDESY and other partner institutes within Netzwerk Teilchenwelt lend the CosMO experiments for student projects and provide advise and support.\n2 Detector Setup\nThe design goal of the CosMO detector was to develop an astroparticle-physics experiment that can be operated by students and that is easily transportable to be used at schools. The detector consists of three plastic scintillators. The scintillator tiles are connected to a data acquisition (DAQ)\ncard with software-adjustable thresholds and coincidence conditions. A netbook computer is used to control the DAQ readout and to visualize the data. Figure 1 shows the full setup during operation.\nScintillator. We use plastic scintillator 1 tiles with a size of 20 × 20 × 1 . 2 cm 3 . The tiles are read out with 9 optical fibres each, which are connected to a multi-pixel photon counter 2 (MPPC), a type of silicon photomultiplier. The operating voltage of about 70 V for the MPPC is generated from a 5 V input voltage using an adjustable DC-DC converter 3 . The MPPC has the advantage that only low voltages are required for operation which are considered safe for students. The scintillator material and MPPC are housed in a lightproof aluminium box with connectors for the voltage supply and coaxial cable for the analogue MPPC output signal. The layout of the scintillator boxes is shown in Figure 2.\nDAQ card. The DAQ card used is the version 2.5 data acquisition board [3] developed by a team of Fermilab, University of Nebraska, and University of Washington for the Cosmic Ray e-Lab [4] of the QuarkNet [5] project. Up to four analogue input signals are processed by discriminators with a software-adjustable thresholds. Each crossing of the discriminator threshold is\n\n· recorded by a time-to-digital converter with a resolution of 1 . 25 ns (rising and falling edge),\n· processed in a complex programmable logic device (CPLD) which forms a multiplicity trigger decision,\n\n\n\n\n\n\n
Figure 1 : Overview of the CosMO setup in operation with three scintillator boxes (right), the DAQ card (center), and the readout netbook with the graphical user interface (left).
\n\n\n\n
Figure 2 : Overview of an open scintillator box: 1. plastic scintillator wrapped in paper, 2. optical fibers, 3. MPPC mounting, 4. voltage converter, 5. resistor for voltage adjustment, 6. connector for power supply, 7. analogue output for MPPC signal.
\n\n· counted in scalers for each channel.\nThe required multiplicity and the trigger time window can both be set in software. If the trigger condition is fulfilled an event is generated that contains a global timestamp and all threshold crossing times. In addition, a GPS module can be connected to the DAQ card that allows recording the global timestamp in UTC with a precision of 50 ns [6].\nThe DAQ card is powered with 5 V DC and offers the possibility to distribute its input voltage to the scintillator boxes so that the whole setup can be operated with a single main power supply.\nReadout. The DAQ card provides a virtual serial port via a standard USB interface that makes it possible to access the data from a variety of different operating systems and programming languages. We developed software (cf. Sec. 3)\nspecifically tailored to the CosMO project and running on a lightweight netbook computer.\nThe complete CosMO setup has a weight of about 5 kg and can be transported in a single briefcase, making it well usable in lectures, labs and outreach projects as well as in school projects. The detector can also be operated with a small 5 V battery pack, independent of the power grid.\n3 Data Processing and Visualisation\nOnce connected with the netbook, DAQ communications are managed via a simple text protocol. The discriminator threshold crossing information is transmitted together with GPS and timing information via the USB interface. Commands can be issued to the DAQ card via the same interface.\nTo manage DAQ communications and visualize the data, we developed the software muonic [7]. As the main purpose of CosMO is the use for student experiments, the focus during the development of the software was to provide an easy-to-use interface. Muonic was developed entirely in Python, using PyQt4 for the graphical user interface (GUI). The software is written in a modular way, and can be extended easily. It is open-source and does not depend on closed source libraries. Muonic runs platform-independent and does not need an internet connection, which allows its operation in remote locations.\nWith muonic the user can set the DAQ configuration, like thresholds or trigger conditions by manipulating typical GUI elements. The software queries the DAQ for scaler information in a given time interval and displays this data as a simple rate per channel over time plot. Also the mean rate is calculated. The width of PMT pulses is displayed in a histogram for debugging and maintenance. The data stream from the DAQ can be stored in its raw format or as tab-separated values that can be imported into a spreadsheet. A screen shot of the GUI during a typical rate measurement is shown in Fig. 3.\n\n\n\n\n\n
Figure 3 : Screen shot of the muonic graphical user interface during a typical rate measurement.
\n\n4 Projects for Students\n4.1 Calibration\nWith muonic students can perform calibration measurements of the scintillation detectors themselves and thus gain deeper understanding of the physical principles involved. Evaluating the trigger rate vs. averaging time students can explore the influence of statistical fluctuations and determine the measurement time necessary to get a robust rate estimate. Analysing the single channel trigger rate vs. threshold will reveal the desired plateau of stable rates due to cosmic muons, bound by electronic noise towards too low thresholds and the absence of muon signals at too high thresholds. A typical calibration measurement is shown in Fig. 4. For each threshold setting approx. 5 minutes of data were collected.\n4.2 Zenith Angle Dependence\nA simple project for students to become familiar with the CosMO experiment is the measurement of the rate of coincidences as a function of the zenith angle, i.e. the suppression of the atmospheric muon flux with increasing atmospheric depth. At least two scintillation detectors are used in coincidence to suppress electronic noise and are placed in parallel to each other at a mutual distance d , which defines the solid angle from which particles are accepted. It has been shown that distances between 20 and 30 cm give a good compromise between restriction to direction of arrival and too low rates. The coincidence rate is measured using the muonic software and the measurement is repeated at different zenith angles. The students can be tasked to construct a setup that allows the rotation to well defined zenith angles while keeping the scintillator plates parallel to each other and at constant distance. The resulting rate as a function of zenith angle q can be described by a cos 2 q dependence [8]. Figure 5 shows a typical result plot for a scintillator tile distance of d = 20 cm and a measurement time of 1 h at each zenith angle.\n4.3 Muon Lifetime\nThe CosMO detector allows a measurement of the mean lifetime of muons. Three scintillator boxes are stacked on top of each other. Decaying muons leave a characteristic signature in one of the channels, which are two pulses in a time interval, typically in the microsecond range. The first of these pulses is induced by the stopping muon, the second one by the electron created in the muon decay. To suppress coincident muon events, the downmost channel can be used as a veto.\nTo enhance the stopping power of the detector, students can test the influence of different absorber materials between the scintillation detectors. A histogram of the recorded time intervals can be fitted with an exponential function by the use of muonic , and the measured mean lifetime is displayed by the software. To gather enough statistics to be confident in the fit, a measurement time of about one week is required. However, the results of the measurement must be inspected carefully, since for some scintillators the results are affected by electronic noise. To suppress this noise contribution, very short time intervals can be excluded from the fit. The values of these time intervals can be set via a GUI element within muonic . The measurement of muon decay gives students insights into coincidence and veto techniques typically used in particle physics. This experiment illustrates also the measurement of statistically fluctuating quantities as well as the law of exponential decay. The measurement of muon lifetime also provides a good introduction into discussions about special relativity, because muons are only able to reach Earth's surface due to relativistic effects.\n4.4 Further Possibilities\nThe CosMO detector further allows the study of absorption of air shower particles in different materials and to measure the velocity of muons. With three detectors in coincidence and arranged in a plane, extended particle showers can be measured. The versatility of the setup enables students to\n\n\n
Figure 4 : Single channel trigger rate as a function of threshold. The operating threshold for each scintillator is chosen on the plateau between 250 and 350 mV.
\n\nlearn about the acceptance of different detector geometries. With the stored data students can learn about statistical methods for analysing large data sets.\n5 Netzwerk Teilchenwelt\nNetzwerk Teilchenwelt [2] is a network of 24 German research institutes of astroparticle and particle physics with the goal to enable students to authentically experience modern physics research. More than 100 young scientists are active in the network and provide students and teachers with insights into their research in astroparticle and particle physics. Students and teachers experience the world of quarks, electrons and cosmic rays firsthand at workshops in schools, student laboratories, or museums all over Germany. As a scientist for one day, they analyse real LHC data in a masterclass. Within cosmic particle projects they perform own measurements. Netzwerk Teilchenwelt encourages discussion with scientists and diving into the world of smallest particles and the big questions about the origin and structure of the universe.\n6 Conclusions and Outlook\nThe CosMO experiment enables students and teachers to explore the physics of cosmic rays in outreach projects or at workshops in school. They develop their own research project, analyse their own data, and discuss their results with professional scientists. This introduces students to the world of the smallest particles and to questions about the origin and structure of our universe. The hands-on experiments are currently extended by projects where the scintillation counters are installed at the German Antarctic research station Neumayer III [9] and on the German research icebreaker Polarstern [10] of the Alfred-Wegner Institute for Polar and Marine Research. These detectors take data continuously, thus enabling analyses over long time ranges with sufficient statistics. The major goal of the Polarstern project is to measure the dependence of the rate of cosmic rays on the geographical latitude, i.e. the geomagnetic cutoff. Furthermore, the influence of atmospheric pressure and temperature on the rate of atmospheric muons can be studied. On the Polarstern and at the Neumayer station\n\n\n\n\n\n
Figure 5 : Measured muon rate as a function of zenith angle. To guide the eye, the curve indicates the expected [8] cos 2 q dependence (including an offset for random noise).
\n\nadditional neutron monitors are installed. All data will be made available on the internet to interested students and teachers and can be analysed together with the data from the CosMO detectors.\nAll these activities are implemented in and supported by Netzwerk Teilchenwelt . Everybody, no matter whether scientist, teacher, or student, is encouraged to become active and join us at Netzwerk Teilchenwelt .\nAcknowledgment: We would like to thank the DESY mechanical and electronics workshops for the machining and production of the detector components. The authors acknowledge the support from Netzwerk Teilchenwelt which is managed by the Technical University Dresden under the auspices of the German Physical Society (DPG). We also gratefully acknowledge the financial support of the German Ministry for Education and Research (BMBF).\nReferences\n\n[1] M. Hawner, S. Schmeling, C. Schwerdt et al., PhyDid B (2012) DD 15.44.\n[2] http://www.teilchenwelt.de/ [3] S. Hansen, T. Jordan, T. Kiper et al., IEEE Nuclear Science Symposium Conference Record 1 (2003) 130-133 doi:10.1109/NSSMIC.2003.1352014.\n[4] http://www.i2u2.org/elab/cosmic/home/ ; http: //quarknet.fnal.gov/toolkits/ati/fnaldet.html\n[5] http://quarknet.fnal.gov/ [6] H.-G. Berns, T. H. Burnett, R. Gran et al., IEEE Nuclear Science Symposium Conference Record 2 (2003) 789-792 doi:10.1109/NSSMIC.2003.1351816.\n[7] https://code.google.com/p/muonic/\n[8] J. Beringer, J.-F. Arguin, R.M. Barnett et al., Phys. Rev. D 86 (2012) 010001 doi:10.1103/PhysRevD.86.010001.\n[9] http://www.awi.de/en/infrastructure/stations/ neumayer_station/\n[10] http://www.awi.de/en/infrastructure/ships/ polarstern/\n"},"sections":{"kind":"list like","value":[{"title":"CosMO - A Cosmic Muon Observer Experiment for Students","content":"R. FRANKE, M. HOLLER, B. KAMINSKY, T. KARG, H. PROKOPH, A. SCH ONWALD, C. SCHWERDT, A. ST OSSL, M. WALTER DESY, Platanenallee 6, 15738 Zeuthen, Germany carolin.schwerdt@desy.de Abstract: What are cosmic particles and where do they come from? These are questions which are not only fascinating for scientists in astrophysics. With the CosMO experiment (Cosmic Muon Observer) students can autonomously study these particles. They can perform their own hands-on experiments to become familiar with modern scientific working methods and to obtain a direct insight into astroparticle physics. In this contribution we present the experimental setup and possible measurements. The detector consists of three scintillator boxes. Events are triggered and readout by a data acquisition board developed for the QuarkNet Project. With a Python program running on a netbook under Linux, the trigger and data taking conditions can be defined. The program displays the particle rates in real-time and stores the data for offline analysis. Possible student experiments are the measurement of cosmic particle rates dependent on the zenith angle, the distribution of geometrical size of particle showers, and the lifetime of muons. Twenty CosMO detectors have been built at DESY. They are used within the German outreach network Netzwerk Teilchenwelt at 15 astroparticle-research institutes and universities for project work with students. Keywords: atmospheric muons, scintillation detector, education, outreach.","pages":[1]},{"title":"1 Introduction","content":"Cosmic particles of various types reach the Earth. They rain down constantly, some of them with energies much higher than the LHC reaches. Cosmic rays contribute to natural background radiation and produce the beautiful light of the auroras. Perhaps they also influence the formation of clouds and even the evolution of live. Although hundreds of these particles pass through us every second, most people do not know about this. Within Netzwerk Teilchenwelt [1, 2] we have developed the CosMO experiment to provide insights into this fascinating field. CosMO is a scintillation counter experiment based on detector components that are used in particle and astroparticle physics. It can be operated by students on their own and brings the current topic of astroparticle physics to pupils who are interested in physics, astronomy, or computing. The project allows autonomous investigation and gets students involved in research. They are given the opportunity to experience hands-on science with the help of modern measurement techniques, as well as analysis methods in particle physics and in close collaboration with scientists. CosMO can be used in outreach projects at research institutes or within school teaching. Teachers receive training so that they are enabled to incorporate the CosMO experiment into their classes. DESY and other partner institutes within Netzwerk Teilchenwelt lend the CosMO experiments for student projects and provide advise and support.","pages":[1]},{"title":"2 Detector Setup","content":"The design goal of the CosMO detector was to develop an astroparticle-physics experiment that can be operated by students and that is easily transportable to be used at schools. The detector consists of three plastic scintillators. The scintillator tiles are connected to a data acquisition (DAQ) card with software-adjustable thresholds and coincidence conditions. A netbook computer is used to control the DAQ readout and to visualize the data. Figure 1 shows the full setup during operation. Scintillator. We use plastic scintillator 1 tiles with a size of 20 × 20 × 1 . 2 cm 3 . The tiles are read out with 9 optical fibres each, which are connected to a multi-pixel photon counter 2 (MPPC), a type of silicon photomultiplier. The operating voltage of about 70 V for the MPPC is generated from a 5 V input voltage using an adjustable DC-DC converter 3 . The MPPC has the advantage that only low voltages are required for operation which are considered safe for students. The scintillator material and MPPC are housed in a lightproof aluminium box with connectors for the voltage supply and coaxial cable for the analogue MPPC output signal. The layout of the scintillator boxes is shown in Figure 2. DAQ card. The DAQ card used is the version 2.5 data acquisition board [3] developed by a team of Fermilab, University of Nebraska, and University of Washington for the Cosmic Ray e-Lab [4] of the QuarkNet [5] project. Up to four analogue input signals are processed by discriminators with a software-adjustable thresholds. Each crossing of the discriminator threshold is","pages":[1]},{"title":"· counted in scalers for each channel.","content":"The required multiplicity and the trigger time window can both be set in software. If the trigger condition is fulfilled an event is generated that contains a global timestamp and all threshold crossing times. In addition, a GPS module can be connected to the DAQ card that allows recording the global timestamp in UTC with a precision of 50 ns [6]. The DAQ card is powered with 5 V DC and offers the possibility to distribute its input voltage to the scintillator boxes so that the whole setup can be operated with a single main power supply. Readout. The DAQ card provides a virtual serial port via a standard USB interface that makes it possible to access the data from a variety of different operating systems and programming languages. We developed software (cf. Sec. 3) specifically tailored to the CosMO project and running on a lightweight netbook computer. The complete CosMO setup has a weight of about 5 kg and can be transported in a single briefcase, making it well usable in lectures, labs and outreach projects as well as in school projects. The detector can also be operated with a small 5 V battery pack, independent of the power grid.","pages":[2]},{"title":"3 Data Processing and Visualisation","content":"Once connected with the netbook, DAQ communications are managed via a simple text protocol. The discriminator threshold crossing information is transmitted together with GPS and timing information via the USB interface. Commands can be issued to the DAQ card via the same interface. To manage DAQ communications and visualize the data, we developed the software muonic [7]. As the main purpose of CosMO is the use for student experiments, the focus during the development of the software was to provide an easy-to-use interface. Muonic was developed entirely in Python, using PyQt4 for the graphical user interface (GUI). The software is written in a modular way, and can be extended easily. It is open-source and does not depend on closed source libraries. Muonic runs platform-independent and does not need an internet connection, which allows its operation in remote locations. With muonic the user can set the DAQ configuration, like thresholds or trigger conditions by manipulating typical GUI elements. The software queries the DAQ for scaler information in a given time interval and displays this data as a simple rate per channel over time plot. Also the mean rate is calculated. The width of PMT pulses is displayed in a histogram for debugging and maintenance. The data stream from the DAQ can be stored in its raw format or as tab-separated values that can be imported into a spreadsheet. A screen shot of the GUI during a typical rate measurement is shown in Fig. 3.","pages":[2]},{"title":"4.1 Calibration","content":"With muonic students can perform calibration measurements of the scintillation detectors themselves and thus gain deeper understanding of the physical principles involved. Evaluating the trigger rate vs. averaging time students can explore the influence of statistical fluctuations and determine the measurement time necessary to get a robust rate estimate. Analysing the single channel trigger rate vs. threshold will reveal the desired plateau of stable rates due to cosmic muons, bound by electronic noise towards too low thresholds and the absence of muon signals at too high thresholds. A typical calibration measurement is shown in Fig. 4. For each threshold setting approx. 5 minutes of data were collected.","pages":[3]},{"title":"4.2 Zenith Angle Dependence","content":"A simple project for students to become familiar with the CosMO experiment is the measurement of the rate of coincidences as a function of the zenith angle, i.e. the suppression of the atmospheric muon flux with increasing atmospheric depth. At least two scintillation detectors are used in coincidence to suppress electronic noise and are placed in parallel to each other at a mutual distance d , which defines the solid angle from which particles are accepted. It has been shown that distances between 20 and 30 cm give a good compromise between restriction to direction of arrival and too low rates. The coincidence rate is measured using the muonic software and the measurement is repeated at different zenith angles. The students can be tasked to construct a setup that allows the rotation to well defined zenith angles while keeping the scintillator plates parallel to each other and at constant distance. The resulting rate as a function of zenith angle q can be described by a cos 2 q dependence [8]. Figure 5 shows a typical result plot for a scintillator tile distance of d = 20 cm and a measurement time of 1 h at each zenith angle.","pages":[3]},{"title":"4.3 Muon Lifetime","content":"The CosMO detector allows a measurement of the mean lifetime of muons. Three scintillator boxes are stacked on top of each other. Decaying muons leave a characteristic signature in one of the channels, which are two pulses in a time interval, typically in the microsecond range. The first of these pulses is induced by the stopping muon, the second one by the electron created in the muon decay. To suppress coincident muon events, the downmost channel can be used as a veto. To enhance the stopping power of the detector, students can test the influence of different absorber materials between the scintillation detectors. A histogram of the recorded time intervals can be fitted with an exponential function by the use of muonic , and the measured mean lifetime is displayed by the software. To gather enough statistics to be confident in the fit, a measurement time of about one week is required. However, the results of the measurement must be inspected carefully, since for some scintillators the results are affected by electronic noise. To suppress this noise contribution, very short time intervals can be excluded from the fit. The values of these time intervals can be set via a GUI element within muonic . The measurement of muon decay gives students insights into coincidence and veto techniques typically used in particle physics. This experiment illustrates also the measurement of statistically fluctuating quantities as well as the law of exponential decay. The measurement of muon lifetime also provides a good introduction into discussions about special relativity, because muons are only able to reach Earth's surface due to relativistic effects.","pages":[3]},{"title":"4.4 Further Possibilities","content":"The CosMO detector further allows the study of absorption of air shower particles in different materials and to measure the velocity of muons. With three detectors in coincidence and arranged in a plane, extended particle showers can be measured. The versatility of the setup enables students to learn about the acceptance of different detector geometries. With the stored data students can learn about statistical methods for analysing large data sets.","pages":[3,4]},{"title":"5 Netzwerk Teilchenwelt","content":"Netzwerk Teilchenwelt [2] is a network of 24 German research institutes of astroparticle and particle physics with the goal to enable students to authentically experience modern physics research. More than 100 young scientists are active in the network and provide students and teachers with insights into their research in astroparticle and particle physics. Students and teachers experience the world of quarks, electrons and cosmic rays firsthand at workshops in schools, student laboratories, or museums all over Germany. As a scientist for one day, they analyse real LHC data in a masterclass. Within cosmic particle projects they perform own measurements. Netzwerk Teilchenwelt encourages discussion with scientists and diving into the world of smallest particles and the big questions about the origin and structure of the universe.","pages":[4]},{"title":"6 Conclusions and Outlook","content":"The CosMO experiment enables students and teachers to explore the physics of cosmic rays in outreach projects or at workshops in school. They develop their own research project, analyse their own data, and discuss their results with professional scientists. This introduces students to the world of the smallest particles and to questions about the origin and structure of our universe. The hands-on experiments are currently extended by projects where the scintillation counters are installed at the German Antarctic research station Neumayer III [9] and on the German research icebreaker Polarstern [10] of the Alfred-Wegner Institute for Polar and Marine Research. These detectors take data continuously, thus enabling analyses over long time ranges with sufficient statistics. The major goal of the Polarstern project is to measure the dependence of the rate of cosmic rays on the geographical latitude, i.e. the geomagnetic cutoff. Furthermore, the influence of atmospheric pressure and temperature on the rate of atmospheric muons can be studied. On the Polarstern and at the Neumayer station additional neutron monitors are installed. All data will be made available on the internet to interested students and teachers and can be analysed together with the data from the CosMO detectors. All these activities are implemented in and supported by Netzwerk Teilchenwelt . Everybody, no matter whether scientist, teacher, or student, is encouraged to become active and join us at Netzwerk Teilchenwelt . Acknowledgment: We would like to thank the DESY mechanical and electronics workshops for the machining and production of the detector components. The authors acknowledge the support from Netzwerk Teilchenwelt which is managed by the Technical University Dresden under the auspices of the German Physical Society (DPG). We also gratefully acknowledge the financial support of the German Ministry for Education and Research (BMBF).","pages":[4]}],"string":"[\n {\n \"title\": \"CosMO - A Cosmic Muon Observer Experiment for Students\",\n \"content\": \"R. FRANKE, M. HOLLER, B. KAMINSKY, T. KARG, H. PROKOPH, A. SCH ONWALD, C. SCHWERDT, A. ST OSSL, M. WALTER DESY, Platanenallee 6, 15738 Zeuthen, Germany carolin.schwerdt@desy.de Abstract: What are cosmic particles and where do they come from? These are questions which are not only fascinating for scientists in astrophysics. With the CosMO experiment (Cosmic Muon Observer) students can autonomously study these particles. They can perform their own hands-on experiments to become familiar with modern scientific working methods and to obtain a direct insight into astroparticle physics. In this contribution we present the experimental setup and possible measurements. The detector consists of three scintillator boxes. Events are triggered and readout by a data acquisition board developed for the QuarkNet Project. With a Python program running on a netbook under Linux, the trigger and data taking conditions can be defined. The program displays the particle rates in real-time and stores the data for offline analysis. Possible student experiments are the measurement of cosmic particle rates dependent on the zenith angle, the distribution of geometrical size of particle showers, and the lifetime of muons. Twenty CosMO detectors have been built at DESY. They are used within the German outreach network Netzwerk Teilchenwelt at 15 astroparticle-research institutes and universities for project work with students. Keywords: atmospheric muons, scintillation detector, education, outreach.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1 Introduction\",\n \"content\": \"Cosmic particles of various types reach the Earth. They rain down constantly, some of them with energies much higher than the LHC reaches. Cosmic rays contribute to natural background radiation and produce the beautiful light of the auroras. Perhaps they also influence the formation of clouds and even the evolution of live. Although hundreds of these particles pass through us every second, most people do not know about this. Within Netzwerk Teilchenwelt [1, 2] we have developed the CosMO experiment to provide insights into this fascinating field. CosMO is a scintillation counter experiment based on detector components that are used in particle and astroparticle physics. It can be operated by students on their own and brings the current topic of astroparticle physics to pupils who are interested in physics, astronomy, or computing. The project allows autonomous investigation and gets students involved in research. They are given the opportunity to experience hands-on science with the help of modern measurement techniques, as well as analysis methods in particle physics and in close collaboration with scientists. CosMO can be used in outreach projects at research institutes or within school teaching. Teachers receive training so that they are enabled to incorporate the CosMO experiment into their classes. DESY and other partner institutes within Netzwerk Teilchenwelt lend the CosMO experiments for student projects and provide advise and support.\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"2 Detector Setup\",\n \"content\": \"The design goal of the CosMO detector was to develop an astroparticle-physics experiment that can be operated by students and that is easily transportable to be used at schools. The detector consists of three plastic scintillators. The scintillator tiles are connected to a data acquisition (DAQ) card with software-adjustable thresholds and coincidence conditions. A netbook computer is used to control the DAQ readout and to visualize the data. Figure 1 shows the full setup during operation. Scintillator. We use plastic scintillator 1 tiles with a size of 20 × 20 × 1 . 2 cm 3 . The tiles are read out with 9 optical fibres each, which are connected to a multi-pixel photon counter 2 (MPPC), a type of silicon photomultiplier. The operating voltage of about 70 V for the MPPC is generated from a 5 V input voltage using an adjustable DC-DC converter 3 . The MPPC has the advantage that only low voltages are required for operation which are considered safe for students. The scintillator material and MPPC are housed in a lightproof aluminium box with connectors for the voltage supply and coaxial cable for the analogue MPPC output signal. The layout of the scintillator boxes is shown in Figure 2. DAQ card. The DAQ card used is the version 2.5 data acquisition board [3] developed by a team of Fermilab, University of Nebraska, and University of Washington for the Cosmic Ray e-Lab [4] of the QuarkNet [5] project. Up to four analogue input signals are processed by discriminators with a software-adjustable thresholds. Each crossing of the discriminator threshold is\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"· counted in scalers for each channel.\",\n \"content\": \"The required multiplicity and the trigger time window can both be set in software. If the trigger condition is fulfilled an event is generated that contains a global timestamp and all threshold crossing times. In addition, a GPS module can be connected to the DAQ card that allows recording the global timestamp in UTC with a precision of 50 ns [6]. The DAQ card is powered with 5 V DC and offers the possibility to distribute its input voltage to the scintillator boxes so that the whole setup can be operated with a single main power supply. Readout. The DAQ card provides a virtual serial port via a standard USB interface that makes it possible to access the data from a variety of different operating systems and programming languages. We developed software (cf. Sec. 3) specifically tailored to the CosMO project and running on a lightweight netbook computer. The complete CosMO setup has a weight of about 5 kg and can be transported in a single briefcase, making it well usable in lectures, labs and outreach projects as well as in school projects. The detector can also be operated with a small 5 V battery pack, independent of the power grid.\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"3 Data Processing and Visualisation\",\n \"content\": \"Once connected with the netbook, DAQ communications are managed via a simple text protocol. The discriminator threshold crossing information is transmitted together with GPS and timing information via the USB interface. Commands can be issued to the DAQ card via the same interface. To manage DAQ communications and visualize the data, we developed the software muonic [7]. As the main purpose of CosMO is the use for student experiments, the focus during the development of the software was to provide an easy-to-use interface. Muonic was developed entirely in Python, using PyQt4 for the graphical user interface (GUI). The software is written in a modular way, and can be extended easily. It is open-source and does not depend on closed source libraries. Muonic runs platform-independent and does not need an internet connection, which allows its operation in remote locations. With muonic the user can set the DAQ configuration, like thresholds or trigger conditions by manipulating typical GUI elements. The software queries the DAQ for scaler information in a given time interval and displays this data as a simple rate per channel over time plot. Also the mean rate is calculated. The width of PMT pulses is displayed in a histogram for debugging and maintenance. The data stream from the DAQ can be stored in its raw format or as tab-separated values that can be imported into a spreadsheet. A screen shot of the GUI during a typical rate measurement is shown in Fig. 3.\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"4.1 Calibration\",\n \"content\": \"With muonic students can perform calibration measurements of the scintillation detectors themselves and thus gain deeper understanding of the physical principles involved. Evaluating the trigger rate vs. averaging time students can explore the influence of statistical fluctuations and determine the measurement time necessary to get a robust rate estimate. Analysing the single channel trigger rate vs. threshold will reveal the desired plateau of stable rates due to cosmic muons, bound by electronic noise towards too low thresholds and the absence of muon signals at too high thresholds. A typical calibration measurement is shown in Fig. 4. For each threshold setting approx. 5 minutes of data were collected.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"4.2 Zenith Angle Dependence\",\n \"content\": \"A simple project for students to become familiar with the CosMO experiment is the measurement of the rate of coincidences as a function of the zenith angle, i.e. the suppression of the atmospheric muon flux with increasing atmospheric depth. At least two scintillation detectors are used in coincidence to suppress electronic noise and are placed in parallel to each other at a mutual distance d , which defines the solid angle from which particles are accepted. It has been shown that distances between 20 and 30 cm give a good compromise between restriction to direction of arrival and too low rates. The coincidence rate is measured using the muonic software and the measurement is repeated at different zenith angles. The students can be tasked to construct a setup that allows the rotation to well defined zenith angles while keeping the scintillator plates parallel to each other and at constant distance. The resulting rate as a function of zenith angle q can be described by a cos 2 q dependence [8]. Figure 5 shows a typical result plot for a scintillator tile distance of d = 20 cm and a measurement time of 1 h at each zenith angle.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"4.3 Muon Lifetime\",\n \"content\": \"The CosMO detector allows a measurement of the mean lifetime of muons. Three scintillator boxes are stacked on top of each other. Decaying muons leave a characteristic signature in one of the channels, which are two pulses in a time interval, typically in the microsecond range. The first of these pulses is induced by the stopping muon, the second one by the electron created in the muon decay. To suppress coincident muon events, the downmost channel can be used as a veto. To enhance the stopping power of the detector, students can test the influence of different absorber materials between the scintillation detectors. A histogram of the recorded time intervals can be fitted with an exponential function by the use of muonic , and the measured mean lifetime is displayed by the software. To gather enough statistics to be confident in the fit, a measurement time of about one week is required. However, the results of the measurement must be inspected carefully, since for some scintillators the results are affected by electronic noise. To suppress this noise contribution, very short time intervals can be excluded from the fit. The values of these time intervals can be set via a GUI element within muonic . The measurement of muon decay gives students insights into coincidence and veto techniques typically used in particle physics. This experiment illustrates also the measurement of statistically fluctuating quantities as well as the law of exponential decay. The measurement of muon lifetime also provides a good introduction into discussions about special relativity, because muons are only able to reach Earth's surface due to relativistic effects.\",\n \"pages\": [\n 3\n ]\n },\n {\n \"title\": \"4.4 Further Possibilities\",\n \"content\": \"The CosMO detector further allows the study of absorption of air shower particles in different materials and to measure the velocity of muons. With three detectors in coincidence and arranged in a plane, extended particle showers can be measured. The versatility of the setup enables students to learn about the acceptance of different detector geometries. With the stored data students can learn about statistical methods for analysing large data sets.\",\n \"pages\": [\n 3,\n 4\n ]\n },\n {\n \"title\": \"5 Netzwerk Teilchenwelt\",\n \"content\": \"Netzwerk Teilchenwelt [2] is a network of 24 German research institutes of astroparticle and particle physics with the goal to enable students to authentically experience modern physics research. More than 100 young scientists are active in the network and provide students and teachers with insights into their research in astroparticle and particle physics. Students and teachers experience the world of quarks, electrons and cosmic rays firsthand at workshops in schools, student laboratories, or museums all over Germany. As a scientist for one day, they analyse real LHC data in a masterclass. Within cosmic particle projects they perform own measurements. Netzwerk Teilchenwelt encourages discussion with scientists and diving into the world of smallest particles and the big questions about the origin and structure of the universe.\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"6 Conclusions and Outlook\",\n \"content\": \"The CosMO experiment enables students and teachers to explore the physics of cosmic rays in outreach projects or at workshops in school. They develop their own research project, analyse their own data, and discuss their results with professional scientists. This introduces students to the world of the smallest particles and to questions about the origin and structure of our universe. The hands-on experiments are currently extended by projects where the scintillation counters are installed at the German Antarctic research station Neumayer III [9] and on the German research icebreaker Polarstern [10] of the Alfred-Wegner Institute for Polar and Marine Research. These detectors take data continuously, thus enabling analyses over long time ranges with sufficient statistics. The major goal of the Polarstern project is to measure the dependence of the rate of cosmic rays on the geographical latitude, i.e. the geomagnetic cutoff. Furthermore, the influence of atmospheric pressure and temperature on the rate of atmospheric muons can be studied. On the Polarstern and at the Neumayer station additional neutron monitors are installed. All data will be made available on the internet to interested students and teachers and can be analysed together with the data from the CosMO detectors. All these activities are implemented in and supported by Netzwerk Teilchenwelt . Everybody, no matter whether scientist, teacher, or student, is encouraged to become active and join us at Netzwerk Teilchenwelt . Acknowledgment: We would like to thank the DESY mechanical and electronics workshops for the machining and production of the detector components. The authors acknowledge the support from Netzwerk Teilchenwelt which is managed by the Technical University Dresden under the auspices of the German Physical Society (DPG). We also gratefully acknowledge the financial support of the German Ministry for Education and Research (BMBF).\",\n \"pages\": [\n 4\n ]\n }\n]"}}},{"rowIdx":98,"cells":{"bibcode":{"kind":"string","value":"2013Icar..222..766T"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1206.1185.pdf"},"content":{"kind":"string","value":"\nActivity of comet 103P / Hartley 2 at the time of the EPOXI mission fly-by 1\nGian Paolo Tozzi a , Elena Mazzotta Epifani b , Olivier R. Hainaut c , Patrizio Patriarchi a , Luisa Lara d , John Robert Brucato a , Hermann Boehnhardt e , Marco Del B'o f , Javier Licandro g , Karen Meech h , Paolo Tanga f\na\nINAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50 125 Firenze, Italy b INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80 131 Napoli, Italy c European Southern Observatory - Karl-Schwarzschild-Straße 2, D-85 748 Garching bei Mnchen, Germany d Instituto de Astrofis'ıca de Andaluc'ıa (IAA-CSIC) C / Glorieta de la Astronom'ıa,s / n 18008 Granada, Spain e Max-Planck Institut fur Sonnensystemforschung, D-37 191Katlenburg-Lindau, Germany f UNS-CNRS-Observatoire de la Cˆote d'Azur, Laboratoire Cassiop'ee, BP 4229, 06 304 Nice cedex 04, France g Instituto de Astrof'ısica de Canarias, V'ıa L'actea s / n, 38 200 La Laguna, Tenerife, Spain h Institute for Astronomy - University of Hawai'i, 2680 Woodlawn Drive, Honolulu, HI 96 822, USA\nAbstract\nComet 103P / Hartley 2 was observed on Nov. 1-6, 2010, coinciding with the fly-by of the space probe EPOXI. The goal was to connect the large scale phenomena observed from the ground, with those at small scale observed from the spacecraft. The comet showed strong activity correlated with the rotation of its nucleus, also observed by the spacecraft. We report here the characterization of the solid component produced by this activity, via observations of the emission in two spectral regions where only grain scattering of the solar radiation is present. We show that the grains produced by this activity had a lifetime of the order of 5 hours, compatible with the spacecraft observations of the large icy chunks. Moreover, the grains produced by one of the active regions have a very red color. This suggests an organic component mixed with the ice in the grains.\nKeywords: Comets, Comets, dust, Comets, coma\n1. Introduction\nComet 103P / Hartley 2 (hereafter 103P) was discovered in March 1986 by M. Hartley (1986) with the UK Schmidt Telescope at Siding Spring (Australia). Its dynamical history (Carusi et al., 1985, and following electronic updates) shows that its orbit has been quite unstable over the last 150 years, with a perihelion distance oscillating between 1 and 2.5 AU. 103P is one of the few comets that have become an Earth crosser in the recent past.\n103P has been frequently observed over the 20 years following its discovery, both by ground-based and space telescopes. The portrait that emerged from this harvest of ground-based data ( e.g. Licandro et al., 2000; Lowry & Fitzsimmons, 2001; Lowry et al., 2003; Snodgrass et al., 2006, 2008; Mazzotta Epifani et al., 2008) is that of a highly active comet, even at large heliocentric distance (5 AU, Snodgrass et al., 2008). In October 2007, 103P was selected as the target for the NASA Deep Impact extended mission EPOXI (A'Hearn et al., 2005); consequently, an intense world-wide observation campaign has been devoted to characterize its nucleus and coma properties in order to prepare for the spacecraft fly-by, occurring in November 2010.\nthan the nucleus to the total water production rate ( > 90% at perihelion). The presence of large grains was already inferred during the 1998 perihelion passage: analysis and modeling of ISOCAM (Cesarski et al., 1996) infrared images of the dust coma and tail (Epifani et al., 2001) implied an evolution of the dust production rate from 10 kg s -1 at 3.25 AU to 100 kg s -1 at 1.04 AU, with grains up to centimeters in size. This dust environment of 103P seems consistent with a trail structure (Lisse et al., 2009), presumably associated with millimeter-sized debris.\nThe main results of this campaign are summarized in Meech et al. (2011): the comet has a small, sub-km, nucleus, with a rotation period of 16.4 hrs when inactive, slowly increasing with activity. This possibly indicates that the rotation rate is slowed by out-gassing from the (irregular) surface.\nThe campaign data also showed that the active fraction of the nucleus' surface is, as typical, about 2%, but that it is surrounded by a large halo of (icy?) grains that contribute more\nOn UT 4.583 November 2010, the NASA mission spacecraft EPOXI flew by 103P. The closest approach was 694 km, when the comet was at 1.064 AU from the Sun. The main results of the in-situ measurements are described in A'Hearn et al. (2011): the nucleus showed a bi-lobed morphology, with a maximum length of 2.33 km and a mean radius of 0 . 58 ± 0 . 02 km. The rotation period at the time of the closest approach was measured to be 18 . 34 ± 0 . 04 h. Images obtained during the fly-by confirmed the presence of individual, 'large' chunks near the nucleus, moving at 1-2 m s -1 . Large grains had already been detected via radar observations just before the close encounter (Harmon et al., 2011): decimeter-sized grains (or possibly even larger), moving at 20-30 m s -1 , and ejected into free trajectories rather than circum-nuclear orbits were modeled to fit the grain-coma echo from 103P. A'Hearn et al. (2011) argued that the largest chunks they detected from EPOXI were icy, with radii up to 10-20 cm, dragged out by super-volatiles (specifically, CO2) and then sublimating to provide a large fraction of\n
\n\n
Table 2: Narrow band continuum cometary filters: central wavelength and FWHM
\n
\nthe total H2O gaseous output of the comet.\nHere we report observations done during 5 (half) nights around the time of the space probe fly-by. The observations were obtained with narrow band filters centered in regions with continuum emission, i.e. due to the scattering of solar radiation by the grains present in the coma.\n2. Observations and data reduction\nAll the observations were performed with EFOSC 2 at the ESO 3.56 m New Technology Telescope (NTT), in La Silla (Chile). The observation epoch, geometry and conditions are listed in Table 1.\nMost of the observations consisted in images of the comet obtained through Narrow Band (NB) cometary filters (similar to those described in Farnham et al., 2000). The NB filters included blue and red continuum ( Bc and Rc ), CN (0-0) Violet band, C 3 1 Π u -1 Σ + g and the C 2 Swan ( ∆ ν = 0) bands. In this paper we focus on the solid component of the coma, i.e. the data obtained with the two continuum filters. Table 2 lists their central wavelengths and full widths at half maximum.\nTo minimize the contamination by background stars and to evaluate the sky background, each comet observation sequence consisted of 5 or 8 exposures on target, moving the telescope by few tens of arcseconds in between, and one additional exposure obtained /similarequal 8 ' o ff the comet, to record the sky uncontaminated by the comet.\nBias and twilight sky flat-field exposures were also obtained in order to correct for the instrumental signature. Spectrophotometric standard stars and solar analog stars were observed spectroscopically and also in imaging mode, with the same filters at about the same airmass as the comet, to calibrate in flux the comet images.\nAt the beginning of the run, some images of the comet were acquired through the standard broad band filters V , R and i . They were not used in this analysis, because their pass-bands contain non negligible gas emission lines. This was verified a posteriori with the spectra.\nAll the images and spectra were at first corrected for bias and flat-field, using the appropriate ancillary frames in the customary manner. To calibrate the images in Af (see below) we computed the 'theoretical' filter color indexes ( Bc -V and Rc -V) of the observed spectrophotometric standard and solar analog stars. By using the tabulated spectra, we compared stellar\nfluxes measured through the NB and V filters to that of a star of A0V spectral type that, by definition, has a color index equal to 0. The knowledge of the V magnitude of the observed stars allowed us to recover the NB magnitudes and hence, from the observations, the photometric zero point (ZP) of each NB filter for each night.\nFor the extinction correction, we adopted the standard extinction of La Silla 3 . Since the standard stars were observed at about the same airmass as at least one of the comet sequences, the errors introduced by possible di ff erences in the extinctions are negligible. When more than one sequence with the same filter was observed, the resulting calibrated images were in agreement within 10%. The same agreement was found also for calibrated images from consecutive photometric nights, in regions of the coma where the signature produced by periodic change of activity (see below) was not yet present. All the frames with the same filter were then inter-calibrated (see below).\nThe level of the sky contribution was then evaluated for each comet sequence, measuring the median level of the sky frame acquired through the same filter 8 ' away from the comet. This value was subtracted from each frame.\nThesky-subtracted frames then were re-centered on the comet photometric center, and a composite comet image was obtained through a median average of the 5 or 8 frames of the sequence.\nThe use of a median combination significantly reduces the contamination produced by background stars. The background was then refined and subtracted with a trial and error procedure using the Σ Af function (see below), by making this function independent of the projected nucleo-centric distance ( ρ ) for distances greater than 150 pixels (corresponding to /similarequal 15000 km at the comet distance) from the photometric center. The resulting continuum images were then calibrated in Af (A'Hearn et al., 1984).\n3. Analysis\n3.1. 1D analysis: background activity\nAs shown by the spacecraft observations (A'Hearn et al., 2011) and as already noticed at the telescope during the observations, the comet showed a strong variability with nucleus rotation. By studying the CN features in the coma, Samarasinha et al. (2011) found that rotation period varied from 17.1 h in September to 18.8 h in November 2010. Thus for this study we assume a rotation period of 18.8 h. We arbitrarily use as a starting point for the rotation phase the time of the first observation (not used here because it was recorded with a broad band filter). This point was Nov. 1, UT = 7:39.\nTo check how the emission of the continuum varied with the rotation period, we first characterized the constant background coma, which was estimated from the epoch of minimal activity.\nA'Hearn et al. (1984) introduced the function Af ρ as a proxy for production of the solid component. A is the geometric albedo of the grains and f the filling factor, defined as the percentage of the area that is covered by the grains, and ρ the projected\n
\n\n
Table 1: Log of Observations through narrow band continuum cometary filters in the visible.
\n
\nUT str refers to the beginning of the observations; rh and ∆ are the helio- and geocentric distances; Phase is the Sun-Target-Observer angle; PA is the position angle of the extended Sun-Target vector. The sky conditions are listed: Pht is for photometric, Clr is for clear. Filt. is the identifier of the filter; Texp the is the sequence exposure time on target, in second; the airmass ( airm ) is listed for the beginning of each observations\n\n\n
Figure 1: Σ Af ( ρ ) functions for all the observations obtained with Bc (a) and Rc (b) filters. The functions have been vertically shifted by 10 cm for clarity. The plots are ordered (from bottom to top) in observational sequence, as in Table 1
\n\nnucleo-centric distance of the aperture. Typically, the filling factor, f , is proportional to 1 /ρ , while A is, at first approximation, independent of ρ . Since from the observations we get the product Af ( ρ ), it is not possible to disentangle these two parameters without additional observations in the thermal IR or without making assumptions.\nHere we used another function derived by the above one, i.e. Σ Af ( ρ ), that is proportional to the average column density of the solid component at the projected nucleo-centric distance ρ . It is equal to 2 πρ Af ( ρ ). As shown by Tozzi et al. (2007), Σ Af should be constant with respect to the projected nuclear distance, ρ , for a comet with a dust outflow of constant velocity and production rate, and if sublimation or fragmentation of the grains are excluded. The solar radiation pressure introduces a small linear dependence with ρ , but normally its e ff ects are only noticeable at large distances from the nucleus, larger than the field of view (FoV) of EFOSC.\nThe final calibrated images were analyzed by computing their Σ Af ( ρ ) function. In Fig. 1 some examples of the Σ Af function are shown. The solid component production rate was clearly not constant, as it can be noticed by comparing the regions with ρ < 500-1000 km. However, excluding the region with ρ smaller than about 3000-5000 km, the profiles are very\n\n\n
Figure 2: Σ Af profiles corresponding to the comet at minimum activity. The solid line is for filter Bc , and the dashed line for Rc .
\n\nsimilar, and the signatures of the change of activity seems to overlap that of a typical, constant profile.\nPlotting all the Σ Af profiles together, as shown in Fig. 1, we can see that they have the same behavior for ρ greater that 30005000 km and the values of Σ Af in that region are within ± 10%. These di ff erences are comparable to the uncertainty of the absolute calibration. We therefore assumed that the average value of Σ Af over ρ in the 6000-8000 km range was constant over the observations, and made small corrections to the Zero Points to adjust the profiles so they have the same average value over that range. This assumption is equivalent to considering that any change in grains production did not reach ρ = 6000 km from one day to the next. The validity of this hypothesis will be verified later. Note that using this method, the data acquired during the non-photometric night (Nov. 4) have been also calibrated to the same system as the others.\nAll the Σ Af profiles are very similar except in the region very close to the nucleus ( ρ < 2000 km) where the signature of the activity seems confined. In order to characterize the periodic emissions, a Σ Af profile corresponding to the minimum of cometary activity -what we call the 'quiet comet'- was determined for each filter as follows: for the regions with ρ > 6000 km as a median of all the profiles, and for that with ρ < 6000 km as the minimum envelope of all the profiles (excluding the region with ρ < 200 km). The median was used to reduce signatures of possible background stars, still present in the single Σ Af profiles; the minimum envelope allowed us to discard the peaks produced by the activity. However, the always present activity in the regions with ρ < 100-200 km (see below) was visually removed by spline interpolation. The Σ Af profiles, corresponding to the constant level of activity, are shown in Fig. 2 for both filters.\nFrom the measurements of Σ Af , the values of Af ρ for ρ in the 6000-8000km range corresponded to 80 ± 3 cm and 91 ± 3 cm in Bc and Rc , respectively. The errors were obtained from the standard deviation of the values of the Σ Af function, with the re-normalization described above.\nFrom the above values of Af ρ , it is possible to derive the\n\n\n
Figure 3: Example of Σ Af profiles produced by the periodic activity: the profile corresponding to the minimum activity was subtracted from an individual profile, leaving only the profile for additional activity. The solid line is for the observations through the Bc filter, the dashed line for observations through the Rc filter.
\n\nslope of the reflectivity spectrum for the solid component coma of the 'quiet comet'. Assuming a linear variation with lambda, the Af ρ at λ = 5550 Å would be 85 ± 3 cm and the corresponding spectral slope would be 5.2 ± 1.5 % / 1000 Å.\nAs seen in Fig. 2, the Σ Af profiles of the minimum activity are not completely constant with ρ , but they systematically increase in the inner region of the coma up to ρ equal to 20002500 km. Note that this behavior cannot be due to a residual background, because this would produce a linear variation with ρ . A profile like that means that the total grain cross-section increases with ρ in a systematic way. The only possible explanation is the fragmentation of large grains, with dimensions much larger than the observation wavelength, as they move away from the nucleus. In that way, the total grain cross-sections would increase with ρ . It is important to notice that the behavior of the quiet coma can be found in all the profiles, even though, it is partially hidden by the periodic activity\n3.2. Periodic activity\nBy subtracting the minimum profile for Bc or Rc from the individual Σ Af profiles, we found the signature of the clouds of grains periodically ejected by the nucleus. Typical Σ Af profiles of the those clouds are shown in Figure 3. All profiles are similar, with a very strong increase towards the nucleus. There is no evidence of any motion of the clouds, as it has been seen for other outbursts (see for instance Tozzi and Licandro, 2002).\nIt would be interesting to determine the colors of the clouds of grains produced by the periodic activity, and to compare them to that of the coma at minimum activity. This measurement is complicated by the rapid evolution of the cloud and by the fact that the observations in Bc and Rc are taken at di ff erent times. To measure the color of the material produced by the activity, we have first to characterize its evolution with time.\nWe determined then the time when the comet was closer to the minimum activity, by checking the individual Σ Af profiles and then selecting the minimum ones. They were those\nrecorded on November 6 at UT 5:10 and 5:58 for the Bc and Rc filters, respectively. Their Σ Af profiles are very similar to the minimum profiles derived above: only a narrow and faint peak is present in the region with ρ < 100-200 km, indicating that the periodic activity was starting again. By chance those two observations are very close to the rotation phase equal to 0 as defined in the previous section.\nTo map the emission produced by the periodic activity, we subtract these images corresponding to the minimum of activity from the individual images.\nAs pointed out above, those two images were not acquired at the exact minimum of activity: the inner part already shows the signs of the periodic activity emission. Nevertheless, these signs are limited to the very inner coma ( ρ /lessorsimilar 200 km) and it is easy to take them into account in the following analysis.\nThe activity maps are shown as a function of the rotation phase in Figures 4 and 5 for the Bc and Rc filters, respectively. For clarity, the figures cover a limited FoV, equivalent to a projected area of 2000 × 2000 km 2 centered on the comet. The FoV actually covered by the observations is more than 10 times larger. The grains released by the periodic activity are clearly visible in both filters. They are particularly evident in two preferred directions. The first one points to the East at position angle PA ∼ 90 · and is active from a rotation phase of about 90 · to 200 · . The second one points to PA ∼ 140 · and is active from the rotation phase greater than 200 · . They don't seem produced by the same active region on the rotating nucleus, because in such a case we should see the produced grains spiraling around the nucleus.\nWe have then analyzed the two directions independently, to check whether the active regions have di ff erent origins, as found by the spacecraft (A'Hearn et al., 2011). The maps have been transformed to polar coordinates, and the profiles of the emission with respect to the nucleo-centric distance ρ have been obtained by integrating between PA = 40 · and 117 · for the first cloud, and between PA = 118 · to 165 · for the second one. The profiles have been transformed in equivalent Σ Af units (accounting for the limited angular range, as the standard definition of Σ Af implies an integration over 2 π ). Typical equivalent Σ Af profiles of the cloud during a phase of high activity are shown in Fig. 6.\nThe Σ Af profiles for the active regions are very similar to those presented earlier for the 1D analysis -only the peak intensity and signal-to-noise ratio (SNR) are di ff erent. Excluding the region with ρ /lessorsimilar 200 km, which is dominated by the seeing of the image and contaminated by the near-nucleus activity in the reference image of the 'quiet' comet, the profiles are very well represented by a constant plus an exponential function,\nΣ Af ( ρ ) = Σ Af 0 + Σ Af 1 exp ( -ρ L 1 ) ,\nwhere L 1 is the scale length of the cloud released by the activity (in km), and Σ Af 1 the peak intensity (in cm). The fit residuals are very small, with errors less than 10% even for profiles with medium / high activity, i.e. with high SNR.\nThe variation of L 1 with time gives the projected expansion velocity of the grains located at ρ = L 1. Of course grains\n\n\n
1105
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11021106
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1104 8:48 Ph-320 PA_S-284
\n\n\n\n
Figure 4: Maps of the material released by the periodic activity of the comet as observed with the Bc filter. The images are di ff erences of the comet images minus that of Nov. 5, 5:10 UT, the one with the minimum periodic activity. Each sub-image covers a projected area FoV of 2000 × 2000 km 2 , with the comet at the center. North is up, East to the left. The sub-images have been ordered with the rotation phase (marked Ph). PA S is the position angle of the projected Sun direction. The look-up table is logarithmic.
\n\n\n\n\n\n\n
Bc NB filter
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1101 8+18 Ph-12 PA_S-280
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1106 5;27 Ph-96 PA_S-286
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Figure 5: Maps of the material released by the periodic activity of the comet as observed with the Rc filter. The images are di ff erences of the comet images minus that of Nov. 5, 5:58 UT, the one with minimum periodic activity. Each sub-image covers a projected area FoV of 2000 × 2000 km 2 , with the comet at the center. North is up, East to the left. The sub-images have been ordered with the rotation phase (marked Ph). PA S is the position angle of the projected Sun direction. The look-up table is logarithmic.
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Rc NB filter Ima 1105 5.58 Phase=6
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Figure 6: Example of equivalent Σ Af profiles produced by the cloud of particles released by the activity at PA ∼ 90 · : Solid and dashed lines are for observations in Bc and Rc , respectively.
\n\nlocated at ρ > L 1 have larger projected velocities and those at smaller distances have smaller velocities. Since the direction of the emission of the cloud of particles in space is not known, the projected velocities are a lower limit of the real expansion velocities. To get the projected velocity we used the observations from November 6, that are most numerous and that were obtained when the level of activity was relatively high. The resulting dL 1 / dt is ≈ 15-20 m s -1 for both clouds, which is comparable to the velocity of the grains measured by radar (Harmon et al., 2011). Note that they measured radial velocities, while we measured projected velocities.\nThose low projected velocities imply that the cloud of grains produced by periodic activity cannot move to distances greater than about 1700 km in 24 hours. This implies the grains must still be well within the FoV for observations recorded during the following night. The assumption we had made before, that the grains had not reached a projected distance larger than 6000 km from one night to the next, is therefore valid, justifying our inter-normalization of the outer part of the profiles.\nThe equivalent Σ Af ( ρ ) functions are always peaked at ρ close to 0, as can be seen in Fig. 3. A motion of the cloud away from the nucleus was never detected (apart the small increase of L 1 mentioned above) contrary to other comets, e.g. C / 1999 S4 before its breakup (Tozzi and Licandro, 2002) or 9P / Tempel 1 after the impact (Tozzi et al., 2007), for which a similar analysis revealed a clear motion of the ejecta with a Maxwellian profile.\nThe product Σ Af 1 × L 1 gives the cross-sections, S A , of the released clouds, i.e. the total surface ( S ) covered by the grains multiplied by their geometric albedo ( A ).\nThe values of S A together with those of the scale-length are reported in Table 3 for both filters. S A as function of the rotation phase is shown in Fig. 7.\n3.2.1. PA ∼ 90 ·\nFor the activity cloud released at PA ∼ 90 · the variations of S A for Bc and Rc filters with the phase have similar behaviors, with the values for Bc lower than those of Rc . By interpolating\na.\nb.\n\n\n
Figure 7: Cross-section S A in km 2 of the cloud emitted toward East (a.) and South-East directions (b.), as a function of the nucleus rotation phase. Squares are derived from observations through the Bc filter, and crossed through the Rc filter. For the cloud released into the East direction, the Bc cross-sections have been multiplied by 1.36 (see text). All the other values are plotted without multiplications. Note that the error bars are 3 times the value given in Table 3
\n\n
\n\n
Table 3: Fitting parameters for the profiles of the clouds produced by the periodic activity. L is the scalelength and SA is the cross section, as explained in the text.
\n
\nthe points obtained with di ff erent phases, we see that, multiplying the Bc intensities by 1.36, the two profiles overlap. As long as the grains are bigger than the wavelength, this is simply the variation of the albedo from Bc to Rc , i.e. the color of the grains. Note that in such a way those measurements of color are independent from any temporal change due to the variability of the emission. The error in the color of the grains has been evaluated as the standard deviation of the data with respect to an interpolating curve. It results of the order of 0.026 km 2 .\nThe albedo of the grains in Rc is then 36% higher than in Bc . Assuming a linear dependence with wavelength, the albedo at λ = 5550 Å is 20% higher than that at Bc and the spectral slope is (14.7 ± 1.1) % / 1000 Å. This value is more than 3 times larger than that of the background dust emission of the 'quiet comet' obtained in the previous section.\nIn Fig. 7 (a), the S A derived from the observations with the Bc filters have been multiplied by 1.36 to take into account the di ff erent albedos, in order to check how the crosssections change with the rotation phase. The points from consecutive nights interleave nicely, suggesting the repeatability of the emission period after period. However, we cannot firmly prove this asserting. In fact, for example, the data at phase around 200 · come from observations of Nov. 3 at UT 8-9, while the data for phase of 300 · come from observations taken the day after, more or less at the same UT (see tables 3). That means that the nucleus had rotated by one full turn plus 100 · .\nAssuming a typical grain albedo of A = 0 . 04, the maximum area covered by them is of the order of 5 km 2 . The variations of S A illustrated in Fig. 7 are very large: it varies from almost 0.04 km 2 , at phase close to 0, to more than 0.2 km 2 at phase ∼ 150-200 · , with an increase of at least a factor of 5. The increases of S A between phase 0 · to 200 · can be simply explained with an increase of the production in the grains as the active area moves into sunlight.\nInstead the factor of four decrease passing from phase 200 · to phase 300 · (see Fig. 7, a), corresponding to about 5 h if the periodicity can be trusted (or 24 h actual elapsed time), is more di ffi cult to explain: the cloud must still be well within the FoV of the observations because of the low projected velocity. This strongly supports the hypothesis that grains sublimated away, with a lifetime surely shorter than 24 h and probably of the order of 5 h. If they are transformed into gas, they will contribute no longer to the observations in the continuum bands.\nThe color of the grains ejected at this PA is similar to that of the surface of short period comets, Centaurs and scattered disk TNOs (see online MBOSS color database Hainaut & Delsanti, 2002). This color cannot be explained by pure ice; they could be ice particles with a large amount of organic material or just organic grains that sublimate under the solar radiation.\n3.2.2. PA ∼ 140 ·\nThe clouds of particles released at PA ∼ 140 · are much fainter and the data therefore are more noisy than the other ones. However the data taken through the Bc filter overlap with those through the Rc filter, within the errors. The estimated error is here about 0.05 km 2 . The corresponding spectral slope is then 0 ± 2.4 % / 1000 Å.\nThis cloud appears during a short range of rotation period, at a phase ∼ 200 · . The S A changes by a factor 6-7 during the whole rotation. As for the other cloud, it decreases by a factor 4 passing from rotation phase of 300 · to (360 + )20 · , suggesting sublimating grains for this cloud as well.\nHowever, these grains seem to have a gray color, in contrast to those released at PA ∼ 90 · . The appearance of the two clouds at di ff erent rotation phases indicates that they are produced by di ff erent active regions of the nucleus, and the great di ff erence in their color, suggest that these regions produce different kind of grains. Those at PA ∼ 140 · are more similar to the icy chunks discovered by the spacecraft, because ice should have gray color. Also those grains cannot be pure ices, since their lifetimes should be much longer that the /similarequal 5 hours indicated here (see for example Beer et al. (2006)). So also these grains should have some impurities of gray color, as for example silicates.\n4. Conclusions\nFrom the analysis of images recorded in the blue and red continuum regions of the visible spectra, we have separated the solid state emission produced by the periodic activity from the normal dust cometary coma of the 'quiet' comet.\nWe have found that the coma of the 'quiet' comet shows a peculiar behavior: its Σ Af function is not constant, but shows an increase with nucleo-centric distances ρ , for ρ < 2000-2500 km, that is not typical of a comet with constant outflow velocity and without fragmentation or sublimation. The Σ Af profiles of the 'quiet coma' obtained over the 5 nights of observations have a very similar behavior. Of course this is true for the observations where the emission due to the periodic activity does not hide completely the inner coma. This kind of profile is an indication that the scattering of the grains increases as they move away from the nucleus. Since this behavior is the same during a long period of time (5 nights), the only explanation is that the grains present in the coma of the 'quiet' comet fragment with the time, increasing their scattering area with the nucleo-centric distance.\nThe color of the solid state coma of the 'quiet' comet is red, with a spectral slope of 4.6 ± 1.5 % / 1000 Å, assuming a linear variation with wavelength.\nBy analyzing the grains produced by the periodic activity we have shown that the released clouds have two privileged projected directions: one at PA ∼ 90 · and the other at ∼ 140 · . The profiles of the equivalent Σ Af function with ρ of the clouds released in the two direction can be fitted with a constant plus an exponential function. The cross-sections S A of the two clouds vary strongly with the rotation phase of the nucleus. They move very slowly, with projected velocities of the order of 20 m / s, for both PAs. One of the two clouds (the one with PA ∼ 90 · ) has a very red color, of the order of 15 ± 3 % / 1000 Å, while the other seems to have a gray color. Assuming a periodic emission with the rotation, both sublimate with lifetimes of the order of 5 h.\nDuring the flyby, the spacecraft has observed for the first time some large chunks around the nucleus, that are supposed\nto be icy ice particles. The gray cloud can be then constituted by those chunks. However, to explain their relatively short lifetimes, those particles also need to have some impurities, gray in color, as for example silicates. The clouds released in the other direction are very red and sublimate as well with a lifetime of the order of few hours. So these grains should have lot of organics embedded in them, or they are pure organic grains that sublimate. It is important to notice that, within ρ equal to 4000 km, i.e. where most of the activity takes place, the cross section of the clouds produced by the activity is at most 6% of that of the quiet comet. This is of the same order of magnitude of the 4% contribution of the icy chunks measured by the spacecraft (A'Hearn et al., 2011).\nOnce the full geometrical analysis of the jets observed by the spacecraft becomes available, it will be interesting to connect them with the two clouds described here, and to investigate whether their di ff erent characteristics can be traced to di ff erent natures of the sublimating area.\n\nMazzotta Epifani E., Palumbo P., Capria M.T., Cremonese G., Fulle M., Colangeli L., 2008. The distant activity of Short Period Comets. II. MNRAS 390, 265-280\nMeech K.J., A'Hearn M.F., Adams J.A. et al., 2011. EPOXI: comet 103P / Hartley 2 observations from a worldwide campaign. ApJ 734, L1-l9 Samarasinha N.H., Mueller B.E.A., A'Hearn M.F., Farnham T.L., Gersch, A. 2011. Rotation of Comet Hartley2 from Structures in the Coma. ApJ letters, 734, L3-L6\nSnodgrass C., Lowry S.C., Fitzsimmons A., 2006. Photometry of cometary nuclei: Rotation rates, colors and a comparison with Kuiper Belt Objects. MNRAS 373, 1590-1602\nSnodgrass C., Lowry S.C., Fitzsimmons A., 2008. Optical observations of 23 distant Jupiter Family Comets, including 36P / Whipple at multiple phase angles. MNRAS 385, 737-756\nTozzi, G. P., and Licandro, J., 2002, Icarus. Visible and Infrared Images of C / 1999 S4 (LINEAR) during the Disruption of Its Nucleus. 157, 187-192\n\nTozzi, G. P., Boehnhardt, H., Kolokolova, L., et al., 2007, A&A. Dust observa-\n\ntions of Comet 9P / Tempel 1 at the time of the Deep Impact. 476, 979-988\n\n5. Acknowledgments\nBased on Observations performed at the European Southern Observatory, La Silla, Progr. 086.C-0375. This work has been partially funded by MIUR - Ministero dell'Istruzione, dell'Universit'a e della Ricerca (Italy), under the PRIN 2008 funding.\n6. References\nReferences\n\nA'Hearn, M.F., Schleicher, D.G., Feldman, P.D, Millis R.L., & Thompson, D.T. 1984. Comet Bowell 1980b.0 AJ, 89, 579-591\nA'Hearn M.F., Belton M.J.S., Delamere W.A. et al., 2005. Deep Impact: Excavating Comet Tempel 1. Science 310, 258-264\nA'Hearn M.F., Belton M.J.S., Delamere W.A. et al., 2011. EPOXI at comet Hartley 2. Science 332, 1396-1400\nBeer, E. H., Podolack, M. Prialnik, D., 2006. The contribution of icy grains to the activity of comets I. Grain lifetime and distribution, Icarus, 180, 473-486 Carusi A., Kresak L., Perozzi E., Valsecchi G.B., 1985. Long-term Evolution of Short-period Comets. Text book, Adam Hilger, Bristol\n\nCesarsky C.J. and 65 colleagues, 1996. ISOCAM in flight. A&A 315, L32-L37 Epifani E., Colangeli L., Fulle M., Brucato J.R., Bussoletti E., De Sanctis M.C., Mennella V., Palomba E., Palumbo P., Rotundi A., 2001. ISOCAM imaging of comets 103P / Hartley 2 and 2P / Encke. Icarus 149, 339-350\nFarnham, T. L. and Schleicher, D. G. and A'Hearn, M. F., 2000.The HB Narrowband Comet Filters: Standard Stars and Calibrations. Icarus, 147, 180204\nHainaut, O.R. and Delsanti, A.C., 2002. Colors of Minor Bodies in the Outer Solar System - a Statistical Analysis. A&A 389, 641-664\n\nHarmon J.K., Nolan M.C., Howell E.S., Giorgini J.D., Taylor P.A., 2011. Radar observations of comet 103P / Hartley 2. ApJ 734, L2-L4\n\nHartley M., 1986. Comet Hartley (1986c). IAU Circ. 4197\nLicandro J., Tancredi G., Lindgren M., Rickman H., Hutton R. G., 2000. CCD Photometry of Cometary Nuclei, I: Observations from 1990-1995. Icarus 147, 161-179\nLisse C.M., Fernadez Y.R., Reach W.T., Bauer J.M., A'Hearn M.F., Farnham T.L., Groussin O., Belton M.J., Meech K.J., Snodgrass C.D., 2009. Spizer Space Telescope Observations of the Nucleus of Comet 103P / Hartley 2. PASP 121, 968-975\nLowry S.C. & Fitzsimmons A., 2001.CCD photometry of distant comets. II. A&A 365, 204-213\n\nLowry S.C., Fitzsimmons A., Collander-Brown S., 2003. CCD photometry of distant comets. III - Ensemble properties of Jupiter-family comets. A&A 397, 329-343\n\n"},"sections":{"kind":"list like","value":[{"title":"Activity of comet 103P / Hartley 2 at the time of the EPOXI mission fly-by 1","content":"Gian Paolo Tozzi a , Elena Mazzotta Epifani b , Olivier R. Hainaut c , Patrizio Patriarchi a , Luisa Lara d , John Robert Brucato a , Hermann Boehnhardt e , Marco Del B'o f , Javier Licandro g , Karen Meech h , Paolo Tanga f a INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50 125 Firenze, Italy b INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80 131 Napoli, Italy c European Southern Observatory - Karl-Schwarzschild-Straße 2, D-85 748 Garching bei Mnchen, Germany d Instituto de Astrofis'ıca de Andaluc'ıa (IAA-CSIC) C / Glorieta de la Astronom'ıa,s / n 18008 Granada, Spain e Max-Planck Institut fur Sonnensystemforschung, D-37 191Katlenburg-Lindau, Germany f UNS-CNRS-Observatoire de la Cˆote d'Azur, Laboratoire Cassiop'ee, BP 4229, 06 304 Nice cedex 04, France g Instituto de Astrof'ısica de Canarias, V'ıa L'actea s / n, 38 200 La Laguna, Tenerife, Spain h Institute for Astronomy - University of Hawai'i, 2680 Woodlawn Drive, Honolulu, HI 96 822, USA","pages":[1]},{"title":"Abstract","content":"Comet 103P / Hartley 2 was observed on Nov. 1-6, 2010, coinciding with the fly-by of the space probe EPOXI. The goal was to connect the large scale phenomena observed from the ground, with those at small scale observed from the spacecraft. The comet showed strong activity correlated with the rotation of its nucleus, also observed by the spacecraft. We report here the characterization of the solid component produced by this activity, via observations of the emission in two spectral regions where only grain scattering of the solar radiation is present. We show that the grains produced by this activity had a lifetime of the order of 5 hours, compatible with the spacecraft observations of the large icy chunks. Moreover, the grains produced by one of the active regions have a very red color. This suggests an organic component mixed with the ice in the grains. Keywords: Comets, Comets, dust, Comets, coma","pages":[1]},{"title":"1. Introduction","content":"Comet 103P / Hartley 2 (hereafter 103P) was discovered in March 1986 by M. Hartley (1986) with the UK Schmidt Telescope at Siding Spring (Australia). Its dynamical history (Carusi et al., 1985, and following electronic updates) shows that its orbit has been quite unstable over the last 150 years, with a perihelion distance oscillating between 1 and 2.5 AU. 103P is one of the few comets that have become an Earth crosser in the recent past. 103P has been frequently observed over the 20 years following its discovery, both by ground-based and space telescopes. The portrait that emerged from this harvest of ground-based data ( e.g. Licandro et al., 2000; Lowry & Fitzsimmons, 2001; Lowry et al., 2003; Snodgrass et al., 2006, 2008; Mazzotta Epifani et al., 2008) is that of a highly active comet, even at large heliocentric distance (5 AU, Snodgrass et al., 2008). In October 2007, 103P was selected as the target for the NASA Deep Impact extended mission EPOXI (A'Hearn et al., 2005); consequently, an intense world-wide observation campaign has been devoted to characterize its nucleus and coma properties in order to prepare for the spacecraft fly-by, occurring in November 2010. than the nucleus to the total water production rate ( > 90% at perihelion). The presence of large grains was already inferred during the 1998 perihelion passage: analysis and modeling of ISOCAM (Cesarski et al., 1996) infrared images of the dust coma and tail (Epifani et al., 2001) implied an evolution of the dust production rate from 10 kg s -1 at 3.25 AU to 100 kg s -1 at 1.04 AU, with grains up to centimeters in size. This dust environment of 103P seems consistent with a trail structure (Lisse et al., 2009), presumably associated with millimeter-sized debris. The main results of this campaign are summarized in Meech et al. (2011): the comet has a small, sub-km, nucleus, with a rotation period of 16.4 hrs when inactive, slowly increasing with activity. This possibly indicates that the rotation rate is slowed by out-gassing from the (irregular) surface. The campaign data also showed that the active fraction of the nucleus' surface is, as typical, about 2%, but that it is surrounded by a large halo of (icy?) grains that contribute more On UT 4.583 November 2010, the NASA mission spacecraft EPOXI flew by 103P. The closest approach was 694 km, when the comet was at 1.064 AU from the Sun. The main results of the in-situ measurements are described in A'Hearn et al. (2011): the nucleus showed a bi-lobed morphology, with a maximum length of 2.33 km and a mean radius of 0 . 58 ± 0 . 02 km. The rotation period at the time of the closest approach was measured to be 18 . 34 ± 0 . 04 h. Images obtained during the fly-by confirmed the presence of individual, 'large' chunks near the nucleus, moving at 1-2 m s -1 . Large grains had already been detected via radar observations just before the close encounter (Harmon et al., 2011): decimeter-sized grains (or possibly even larger), moving at 20-30 m s -1 , and ejected into free trajectories rather than circum-nuclear orbits were modeled to fit the grain-coma echo from 103P. A'Hearn et al. (2011) argued that the largest chunks they detected from EPOXI were icy, with radii up to 10-20 cm, dragged out by super-volatiles (specifically, CO2) and then sublimating to provide a large fraction of the total H2O gaseous output of the comet. Here we report observations done during 5 (half) nights around the time of the space probe fly-by. The observations were obtained with narrow band filters centered in regions with continuum emission, i.e. due to the scattering of solar radiation by the grains present in the coma.","pages":[1,2]},{"title":"2. Observations and data reduction","content":"All the observations were performed with EFOSC 2 at the ESO 3.56 m New Technology Telescope (NTT), in La Silla (Chile). The observation epoch, geometry and conditions are listed in Table 1. Most of the observations consisted in images of the comet obtained through Narrow Band (NB) cometary filters (similar to those described in Farnham et al., 2000). The NB filters included blue and red continuum ( Bc and Rc ), CN (0-0) Violet band, C 3 1 Π u -1 Σ + g and the C 2 Swan ( ∆ ν = 0) bands. In this paper we focus on the solid component of the coma, i.e. the data obtained with the two continuum filters. Table 2 lists their central wavelengths and full widths at half maximum. To minimize the contamination by background stars and to evaluate the sky background, each comet observation sequence consisted of 5 or 8 exposures on target, moving the telescope by few tens of arcseconds in between, and one additional exposure obtained /similarequal 8 ' o ff the comet, to record the sky uncontaminated by the comet. Bias and twilight sky flat-field exposures were also obtained in order to correct for the instrumental signature. Spectrophotometric standard stars and solar analog stars were observed spectroscopically and also in imaging mode, with the same filters at about the same airmass as the comet, to calibrate in flux the comet images. At the beginning of the run, some images of the comet were acquired through the standard broad band filters V , R and i . They were not used in this analysis, because their pass-bands contain non negligible gas emission lines. This was verified a posteriori with the spectra. All the images and spectra were at first corrected for bias and flat-field, using the appropriate ancillary frames in the customary manner. To calibrate the images in Af (see below) we computed the 'theoretical' filter color indexes ( Bc -V and Rc -V) of the observed spectrophotometric standard and solar analog stars. By using the tabulated spectra, we compared stellar fluxes measured through the NB and V filters to that of a star of A0V spectral type that, by definition, has a color index equal to 0. The knowledge of the V magnitude of the observed stars allowed us to recover the NB magnitudes and hence, from the observations, the photometric zero point (ZP) of each NB filter for each night. For the extinction correction, we adopted the standard extinction of La Silla 3 . Since the standard stars were observed at about the same airmass as at least one of the comet sequences, the errors introduced by possible di ff erences in the extinctions are negligible. When more than one sequence with the same filter was observed, the resulting calibrated images were in agreement within 10%. The same agreement was found also for calibrated images from consecutive photometric nights, in regions of the coma where the signature produced by periodic change of activity (see below) was not yet present. All the frames with the same filter were then inter-calibrated (see below). The level of the sky contribution was then evaluated for each comet sequence, measuring the median level of the sky frame acquired through the same filter 8 ' away from the comet. This value was subtracted from each frame. Thesky-subtracted frames then were re-centered on the comet photometric center, and a composite comet image was obtained through a median average of the 5 or 8 frames of the sequence. The use of a median combination significantly reduces the contamination produced by background stars. The background was then refined and subtracted with a trial and error procedure using the Σ Af function (see below), by making this function independent of the projected nucleo-centric distance ( ρ ) for distances greater than 150 pixels (corresponding to /similarequal 15000 km at the comet distance) from the photometric center. The resulting continuum images were then calibrated in Af (A'Hearn et al., 1984).","pages":[2]},{"title":"3.1. 1D analysis: background activity","content":"As shown by the spacecraft observations (A'Hearn et al., 2011) and as already noticed at the telescope during the observations, the comet showed a strong variability with nucleus rotation. By studying the CN features in the coma, Samarasinha et al. (2011) found that rotation period varied from 17.1 h in September to 18.8 h in November 2010. Thus for this study we assume a rotation period of 18.8 h. We arbitrarily use as a starting point for the rotation phase the time of the first observation (not used here because it was recorded with a broad band filter). This point was Nov. 1, UT = 7:39. To check how the emission of the continuum varied with the rotation period, we first characterized the constant background coma, which was estimated from the epoch of minimal activity. A'Hearn et al. (1984) introduced the function Af ρ as a proxy for production of the solid component. A is the geometric albedo of the grains and f the filling factor, defined as the percentage of the area that is covered by the grains, and ρ the projected UT str refers to the beginning of the observations; rh and ∆ are the helio- and geocentric distances; Phase is the Sun-Target-Observer angle; PA is the position angle of the extended Sun-Target vector. The sky conditions are listed: Pht is for photometric, Clr is for clear. Filt. is the identifier of the filter; Texp the is the sequence exposure time on target, in second; the airmass ( airm ) is listed for the beginning of each observations nucleo-centric distance of the aperture. Typically, the filling factor, f , is proportional to 1 /ρ , while A is, at first approximation, independent of ρ . Since from the observations we get the product Af ( ρ ), it is not possible to disentangle these two parameters without additional observations in the thermal IR or without making assumptions. Here we used another function derived by the above one, i.e. Σ Af ( ρ ), that is proportional to the average column density of the solid component at the projected nucleo-centric distance ρ . It is equal to 2 πρ Af ( ρ ). As shown by Tozzi et al. (2007), Σ Af should be constant with respect to the projected nuclear distance, ρ , for a comet with a dust outflow of constant velocity and production rate, and if sublimation or fragmentation of the grains are excluded. The solar radiation pressure introduces a small linear dependence with ρ , but normally its e ff ects are only noticeable at large distances from the nucleus, larger than the field of view (FoV) of EFOSC. The final calibrated images were analyzed by computing their Σ Af ( ρ ) function. In Fig. 1 some examples of the Σ Af function are shown. The solid component production rate was clearly not constant, as it can be noticed by comparing the regions with ρ < 500-1000 km. However, excluding the region with ρ smaller than about 3000-5000 km, the profiles are very similar, and the signatures of the change of activity seems to overlap that of a typical, constant profile. Plotting all the Σ Af profiles together, as shown in Fig. 1, we can see that they have the same behavior for ρ greater that 30005000 km and the values of Σ Af in that region are within ± 10%. These di ff erences are comparable to the uncertainty of the absolute calibration. We therefore assumed that the average value of Σ Af over ρ in the 6000-8000 km range was constant over the observations, and made small corrections to the Zero Points to adjust the profiles so they have the same average value over that range. This assumption is equivalent to considering that any change in grains production did not reach ρ = 6000 km from one day to the next. The validity of this hypothesis will be verified later. Note that using this method, the data acquired during the non-photometric night (Nov. 4) have been also calibrated to the same system as the others. All the Σ Af profiles are very similar except in the region very close to the nucleus ( ρ < 2000 km) where the signature of the activity seems confined. In order to characterize the periodic emissions, a Σ Af profile corresponding to the minimum of cometary activity -what we call the 'quiet comet'- was determined for each filter as follows: for the regions with ρ > 6000 km as a median of all the profiles, and for that with ρ < 6000 km as the minimum envelope of all the profiles (excluding the region with ρ < 200 km). The median was used to reduce signatures of possible background stars, still present in the single Σ Af profiles; the minimum envelope allowed us to discard the peaks produced by the activity. However, the always present activity in the regions with ρ < 100-200 km (see below) was visually removed by spline interpolation. The Σ Af profiles, corresponding to the constant level of activity, are shown in Fig. 2 for both filters. From the measurements of Σ Af , the values of Af ρ for ρ in the 6000-8000km range corresponded to 80 ± 3 cm and 91 ± 3 cm in Bc and Rc , respectively. The errors were obtained from the standard deviation of the values of the Σ Af function, with the re-normalization described above. From the above values of Af ρ , it is possible to derive the slope of the reflectivity spectrum for the solid component coma of the 'quiet comet'. Assuming a linear variation with lambda, the Af ρ at λ = 5550 Å would be 85 ± 3 cm and the corresponding spectral slope would be 5.2 ± 1.5 % / 1000 Å. As seen in Fig. 2, the Σ Af profiles of the minimum activity are not completely constant with ρ , but they systematically increase in the inner region of the coma up to ρ equal to 20002500 km. Note that this behavior cannot be due to a residual background, because this would produce a linear variation with ρ . A profile like that means that the total grain cross-section increases with ρ in a systematic way. The only possible explanation is the fragmentation of large grains, with dimensions much larger than the observation wavelength, as they move away from the nucleus. In that way, the total grain cross-sections would increase with ρ . It is important to notice that the behavior of the quiet coma can be found in all the profiles, even though, it is partially hidden by the periodic activity","pages":[2,3,4,5]},{"title":"3.2. Periodic activity","content":"By subtracting the minimum profile for Bc or Rc from the individual Σ Af profiles, we found the signature of the clouds of grains periodically ejected by the nucleus. Typical Σ Af profiles of the those clouds are shown in Figure 3. All profiles are similar, with a very strong increase towards the nucleus. There is no evidence of any motion of the clouds, as it has been seen for other outbursts (see for instance Tozzi and Licandro, 2002). It would be interesting to determine the colors of the clouds of grains produced by the periodic activity, and to compare them to that of the coma at minimum activity. This measurement is complicated by the rapid evolution of the cloud and by the fact that the observations in Bc and Rc are taken at di ff erent times. To measure the color of the material produced by the activity, we have first to characterize its evolution with time. We determined then the time when the comet was closer to the minimum activity, by checking the individual Σ Af profiles and then selecting the minimum ones. They were those recorded on November 6 at UT 5:10 and 5:58 for the Bc and Rc filters, respectively. Their Σ Af profiles are very similar to the minimum profiles derived above: only a narrow and faint peak is present in the region with ρ < 100-200 km, indicating that the periodic activity was starting again. By chance those two observations are very close to the rotation phase equal to 0 as defined in the previous section. To map the emission produced by the periodic activity, we subtract these images corresponding to the minimum of activity from the individual images. As pointed out above, those two images were not acquired at the exact minimum of activity: the inner part already shows the signs of the periodic activity emission. Nevertheless, these signs are limited to the very inner coma ( ρ /lessorsimilar 200 km) and it is easy to take them into account in the following analysis. The activity maps are shown as a function of the rotation phase in Figures 4 and 5 for the Bc and Rc filters, respectively. For clarity, the figures cover a limited FoV, equivalent to a projected area of 2000 × 2000 km 2 centered on the comet. The FoV actually covered by the observations is more than 10 times larger. The grains released by the periodic activity are clearly visible in both filters. They are particularly evident in two preferred directions. The first one points to the East at position angle PA ∼ 90 · and is active from a rotation phase of about 90 · to 200 · . The second one points to PA ∼ 140 · and is active from the rotation phase greater than 200 · . They don't seem produced by the same active region on the rotating nucleus, because in such a case we should see the produced grains spiraling around the nucleus. We have then analyzed the two directions independently, to check whether the active regions have di ff erent origins, as found by the spacecraft (A'Hearn et al., 2011). The maps have been transformed to polar coordinates, and the profiles of the emission with respect to the nucleo-centric distance ρ have been obtained by integrating between PA = 40 · and 117 · for the first cloud, and between PA = 118 · to 165 · for the second one. The profiles have been transformed in equivalent Σ Af units (accounting for the limited angular range, as the standard definition of Σ Af implies an integration over 2 π ). Typical equivalent Σ Af profiles of the cloud during a phase of high activity are shown in Fig. 6. The Σ Af profiles for the active regions are very similar to those presented earlier for the 1D analysis -only the peak intensity and signal-to-noise ratio (SNR) are di ff erent. Excluding the region with ρ /lessorsimilar 200 km, which is dominated by the seeing of the image and contaminated by the near-nucleus activity in the reference image of the 'quiet' comet, the profiles are very well represented by a constant plus an exponential function, where L 1 is the scale length of the cloud released by the activity (in km), and Σ Af 1 the peak intensity (in cm). The fit residuals are very small, with errors less than 10% even for profiles with medium / high activity, i.e. with high SNR. The variation of L 1 with time gives the projected expansion velocity of the grains located at ρ = L 1. Of course grains located at ρ > L 1 have larger projected velocities and those at smaller distances have smaller velocities. Since the direction of the emission of the cloud of particles in space is not known, the projected velocities are a lower limit of the real expansion velocities. To get the projected velocity we used the observations from November 6, that are most numerous and that were obtained when the level of activity was relatively high. The resulting dL 1 / dt is ≈ 15-20 m s -1 for both clouds, which is comparable to the velocity of the grains measured by radar (Harmon et al., 2011). Note that they measured radial velocities, while we measured projected velocities. Those low projected velocities imply that the cloud of grains produced by periodic activity cannot move to distances greater than about 1700 km in 24 hours. This implies the grains must still be well within the FoV for observations recorded during the following night. The assumption we had made before, that the grains had not reached a projected distance larger than 6000 km from one night to the next, is therefore valid, justifying our inter-normalization of the outer part of the profiles. The equivalent Σ Af ( ρ ) functions are always peaked at ρ close to 0, as can be seen in Fig. 3. A motion of the cloud away from the nucleus was never detected (apart the small increase of L 1 mentioned above) contrary to other comets, e.g. C / 1999 S4 before its breakup (Tozzi and Licandro, 2002) or 9P / Tempel 1 after the impact (Tozzi et al., 2007), for which a similar analysis revealed a clear motion of the ejecta with a Maxwellian profile. The product Σ Af 1 × L 1 gives the cross-sections, S A , of the released clouds, i.e. the total surface ( S ) covered by the grains multiplied by their geometric albedo ( A ). The values of S A together with those of the scale-length are reported in Table 3 for both filters. S A as function of the rotation phase is shown in Fig. 7.","pages":[5,8]},{"title":"3.2.1. PA ∼ 90 ·","content":"For the activity cloud released at PA ∼ 90 · the variations of S A for Bc and Rc filters with the phase have similar behaviors, with the values for Bc lower than those of Rc . By interpolating a. b. the points obtained with di ff erent phases, we see that, multiplying the Bc intensities by 1.36, the two profiles overlap. As long as the grains are bigger than the wavelength, this is simply the variation of the albedo from Bc to Rc , i.e. the color of the grains. Note that in such a way those measurements of color are independent from any temporal change due to the variability of the emission. The error in the color of the grains has been evaluated as the standard deviation of the data with respect to an interpolating curve. It results of the order of 0.026 km 2 . The albedo of the grains in Rc is then 36% higher than in Bc . Assuming a linear dependence with wavelength, the albedo at λ = 5550 Å is 20% higher than that at Bc and the spectral slope is (14.7 ± 1.1) % / 1000 Å. This value is more than 3 times larger than that of the background dust emission of the 'quiet comet' obtained in the previous section. In Fig. 7 (a), the S A derived from the observations with the Bc filters have been multiplied by 1.36 to take into account the di ff erent albedos, in order to check how the crosssections change with the rotation phase. The points from consecutive nights interleave nicely, suggesting the repeatability of the emission period after period. However, we cannot firmly prove this asserting. In fact, for example, the data at phase around 200 · come from observations of Nov. 3 at UT 8-9, while the data for phase of 300 · come from observations taken the day after, more or less at the same UT (see tables 3). That means that the nucleus had rotated by one full turn plus 100 · . Assuming a typical grain albedo of A = 0 . 04, the maximum area covered by them is of the order of 5 km 2 . The variations of S A illustrated in Fig. 7 are very large: it varies from almost 0.04 km 2 , at phase close to 0, to more than 0.2 km 2 at phase ∼ 150-200 · , with an increase of at least a factor of 5. The increases of S A between phase 0 · to 200 · can be simply explained with an increase of the production in the grains as the active area moves into sunlight. Instead the factor of four decrease passing from phase 200 · to phase 300 · (see Fig. 7, a), corresponding to about 5 h if the periodicity can be trusted (or 24 h actual elapsed time), is more di ffi cult to explain: the cloud must still be well within the FoV of the observations because of the low projected velocity. This strongly supports the hypothesis that grains sublimated away, with a lifetime surely shorter than 24 h and probably of the order of 5 h. If they are transformed into gas, they will contribute no longer to the observations in the continuum bands. The color of the grains ejected at this PA is similar to that of the surface of short period comets, Centaurs and scattered disk TNOs (see online MBOSS color database Hainaut & Delsanti, 2002). This color cannot be explained by pure ice; they could be ice particles with a large amount of organic material or just organic grains that sublimate under the solar radiation.","pages":[8,10]},{"title":"3.2.2. PA ∼ 140 ·","content":"The clouds of particles released at PA ∼ 140 · are much fainter and the data therefore are more noisy than the other ones. However the data taken through the Bc filter overlap with those through the Rc filter, within the errors. The estimated error is here about 0.05 km 2 . The corresponding spectral slope is then 0 ± 2.4 % / 1000 Å. This cloud appears during a short range of rotation period, at a phase ∼ 200 · . The S A changes by a factor 6-7 during the whole rotation. As for the other cloud, it decreases by a factor 4 passing from rotation phase of 300 · to (360 + )20 · , suggesting sublimating grains for this cloud as well. However, these grains seem to have a gray color, in contrast to those released at PA ∼ 90 · . The appearance of the two clouds at di ff erent rotation phases indicates that they are produced by di ff erent active regions of the nucleus, and the great di ff erence in their color, suggest that these regions produce different kind of grains. Those at PA ∼ 140 · are more similar to the icy chunks discovered by the spacecraft, because ice should have gray color. Also those grains cannot be pure ices, since their lifetimes should be much longer that the /similarequal 5 hours indicated here (see for example Beer et al. (2006)). So also these grains should have some impurities of gray color, as for example silicates.","pages":[10]},{"title":"4. Conclusions","content":"From the analysis of images recorded in the blue and red continuum regions of the visible spectra, we have separated the solid state emission produced by the periodic activity from the normal dust cometary coma of the 'quiet' comet. We have found that the coma of the 'quiet' comet shows a peculiar behavior: its Σ Af function is not constant, but shows an increase with nucleo-centric distances ρ , for ρ < 2000-2500 km, that is not typical of a comet with constant outflow velocity and without fragmentation or sublimation. The Σ Af profiles of the 'quiet coma' obtained over the 5 nights of observations have a very similar behavior. Of course this is true for the observations where the emission due to the periodic activity does not hide completely the inner coma. This kind of profile is an indication that the scattering of the grains increases as they move away from the nucleus. Since this behavior is the same during a long period of time (5 nights), the only explanation is that the grains present in the coma of the 'quiet' comet fragment with the time, increasing their scattering area with the nucleo-centric distance. The color of the solid state coma of the 'quiet' comet is red, with a spectral slope of 4.6 ± 1.5 % / 1000 Å, assuming a linear variation with wavelength. By analyzing the grains produced by the periodic activity we have shown that the released clouds have two privileged projected directions: one at PA ∼ 90 · and the other at ∼ 140 · . The profiles of the equivalent Σ Af function with ρ of the clouds released in the two direction can be fitted with a constant plus an exponential function. The cross-sections S A of the two clouds vary strongly with the rotation phase of the nucleus. They move very slowly, with projected velocities of the order of 20 m / s, for both PAs. One of the two clouds (the one with PA ∼ 90 · ) has a very red color, of the order of 15 ± 3 % / 1000 Å, while the other seems to have a gray color. Assuming a periodic emission with the rotation, both sublimate with lifetimes of the order of 5 h. During the flyby, the spacecraft has observed for the first time some large chunks around the nucleus, that are supposed to be icy ice particles. The gray cloud can be then constituted by those chunks. However, to explain their relatively short lifetimes, those particles also need to have some impurities, gray in color, as for example silicates. The clouds released in the other direction are very red and sublimate as well with a lifetime of the order of few hours. So these grains should have lot of organics embedded in them, or they are pure organic grains that sublimate. It is important to notice that, within ρ equal to 4000 km, i.e. where most of the activity takes place, the cross section of the clouds produced by the activity is at most 6% of that of the quiet comet. This is of the same order of magnitude of the 4% contribution of the icy chunks measured by the spacecraft (A'Hearn et al., 2011). Once the full geometrical analysis of the jets observed by the spacecraft becomes available, it will be interesting to connect them with the two clouds described here, and to investigate whether their di ff erent characteristics can be traced to di ff erent natures of the sublimating area. Tozzi, G. P., Boehnhardt, H., Kolokolova, L., et al., 2007, A&A. Dust observa-","pages":[10,11]},{"title":"5. Acknowledgments","content":"Based on Observations performed at the European Southern Observatory, La Silla, Progr. 086.C-0375. This work has been partially funded by MIUR - Ministero dell'Istruzione, dell'Universit'a e della Ricerca (Italy), under the PRIN 2008 funding.","pages":[11]},{"title":"References","content":"Cesarsky C.J. and 65 colleagues, 1996. ISOCAM in flight. A&A 315, L32-L37 Epifani E., Colangeli L., Fulle M., Brucato J.R., Bussoletti E., De Sanctis M.C., Mennella V., Palomba E., Palumbo P., Rotundi A., 2001. ISOCAM imaging of comets 103P / Hartley 2 and 2P / Encke. Icarus 149, 339-350 Farnham, T. L. and Schleicher, D. G. and A'Hearn, M. F., 2000.The HB Narrowband Comet Filters: Standard Stars and Calibrations. Icarus, 147, 180204 Hainaut, O.R. and Delsanti, A.C., 2002. Colors of Minor Bodies in the Outer Solar System - a Statistical Analysis. A&A 389, 641-664 Hartley M., 1986. Comet Hartley (1986c). IAU Circ. 4197 Licandro J., Tancredi G., Lindgren M., Rickman H., Hutton R. G., 2000. CCD Photometry of Cometary Nuclei, I: Observations from 1990-1995. Icarus 147, 161-179 Lisse C.M., Fernadez Y.R., Reach W.T., Bauer J.M., A'Hearn M.F., Farnham T.L., Groussin O., Belton M.J., Meech K.J., Snodgrass C.D., 2009. Spizer Space Telescope Observations of the Nucleus of Comet 103P / Hartley 2. PASP 121, 968-975 Lowry S.C. & Fitzsimmons A., 2001.CCD photometry of distant comets. II. A&A 365, 204-213","pages":[11]}],"string":"[\n {\n \"title\": \"Activity of comet 103P / Hartley 2 at the time of the EPOXI mission fly-by 1\",\n \"content\": \"Gian Paolo Tozzi a , Elena Mazzotta Epifani b , Olivier R. Hainaut c , Patrizio Patriarchi a , Luisa Lara d , John Robert Brucato a , Hermann Boehnhardt e , Marco Del B'o f , Javier Licandro g , Karen Meech h , Paolo Tanga f a INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50 125 Firenze, Italy b INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80 131 Napoli, Italy c European Southern Observatory - Karl-Schwarzschild-Straße 2, D-85 748 Garching bei Mnchen, Germany d Instituto de Astrofis'ıca de Andaluc'ıa (IAA-CSIC) C / Glorieta de la Astronom'ıa,s / n 18008 Granada, Spain e Max-Planck Institut fur Sonnensystemforschung, D-37 191Katlenburg-Lindau, Germany f UNS-CNRS-Observatoire de la Cˆote d'Azur, Laboratoire Cassiop'ee, BP 4229, 06 304 Nice cedex 04, France g Instituto de Astrof'ısica de Canarias, V'ıa L'actea s / n, 38 200 La Laguna, Tenerife, Spain h Institute for Astronomy - University of Hawai'i, 2680 Woodlawn Drive, Honolulu, HI 96 822, USA\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Abstract\",\n \"content\": \"Comet 103P / Hartley 2 was observed on Nov. 1-6, 2010, coinciding with the fly-by of the space probe EPOXI. The goal was to connect the large scale phenomena observed from the ground, with those at small scale observed from the spacecraft. The comet showed strong activity correlated with the rotation of its nucleus, also observed by the spacecraft. We report here the characterization of the solid component produced by this activity, via observations of the emission in two spectral regions where only grain scattering of the solar radiation is present. We show that the grains produced by this activity had a lifetime of the order of 5 hours, compatible with the spacecraft observations of the large icy chunks. Moreover, the grains produced by one of the active regions have a very red color. This suggests an organic component mixed with the ice in the grains. Keywords: Comets, Comets, dust, Comets, coma\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"1. Introduction\",\n \"content\": \"Comet 103P / Hartley 2 (hereafter 103P) was discovered in March 1986 by M. Hartley (1986) with the UK Schmidt Telescope at Siding Spring (Australia). Its dynamical history (Carusi et al., 1985, and following electronic updates) shows that its orbit has been quite unstable over the last 150 years, with a perihelion distance oscillating between 1 and 2.5 AU. 103P is one of the few comets that have become an Earth crosser in the recent past. 103P has been frequently observed over the 20 years following its discovery, both by ground-based and space telescopes. The portrait that emerged from this harvest of ground-based data ( e.g. Licandro et al., 2000; Lowry & Fitzsimmons, 2001; Lowry et al., 2003; Snodgrass et al., 2006, 2008; Mazzotta Epifani et al., 2008) is that of a highly active comet, even at large heliocentric distance (5 AU, Snodgrass et al., 2008). In October 2007, 103P was selected as the target for the NASA Deep Impact extended mission EPOXI (A'Hearn et al., 2005); consequently, an intense world-wide observation campaign has been devoted to characterize its nucleus and coma properties in order to prepare for the spacecraft fly-by, occurring in November 2010. than the nucleus to the total water production rate ( > 90% at perihelion). The presence of large grains was already inferred during the 1998 perihelion passage: analysis and modeling of ISOCAM (Cesarski et al., 1996) infrared images of the dust coma and tail (Epifani et al., 2001) implied an evolution of the dust production rate from 10 kg s -1 at 3.25 AU to 100 kg s -1 at 1.04 AU, with grains up to centimeters in size. This dust environment of 103P seems consistent with a trail structure (Lisse et al., 2009), presumably associated with millimeter-sized debris. The main results of this campaign are summarized in Meech et al. (2011): the comet has a small, sub-km, nucleus, with a rotation period of 16.4 hrs when inactive, slowly increasing with activity. This possibly indicates that the rotation rate is slowed by out-gassing from the (irregular) surface. The campaign data also showed that the active fraction of the nucleus' surface is, as typical, about 2%, but that it is surrounded by a large halo of (icy?) grains that contribute more On UT 4.583 November 2010, the NASA mission spacecraft EPOXI flew by 103P. The closest approach was 694 km, when the comet was at 1.064 AU from the Sun. The main results of the in-situ measurements are described in A'Hearn et al. (2011): the nucleus showed a bi-lobed morphology, with a maximum length of 2.33 km and a mean radius of 0 . 58 ± 0 . 02 km. The rotation period at the time of the closest approach was measured to be 18 . 34 ± 0 . 04 h. Images obtained during the fly-by confirmed the presence of individual, 'large' chunks near the nucleus, moving at 1-2 m s -1 . Large grains had already been detected via radar observations just before the close encounter (Harmon et al., 2011): decimeter-sized grains (or possibly even larger), moving at 20-30 m s -1 , and ejected into free trajectories rather than circum-nuclear orbits were modeled to fit the grain-coma echo from 103P. A'Hearn et al. (2011) argued that the largest chunks they detected from EPOXI were icy, with radii up to 10-20 cm, dragged out by super-volatiles (specifically, CO2) and then sublimating to provide a large fraction of the total H2O gaseous output of the comet. Here we report observations done during 5 (half) nights around the time of the space probe fly-by. The observations were obtained with narrow band filters centered in regions with continuum emission, i.e. due to the scattering of solar radiation by the grains present in the coma.\",\n \"pages\": [\n 1,\n 2\n ]\n },\n {\n \"title\": \"2. Observations and data reduction\",\n \"content\": \"All the observations were performed with EFOSC 2 at the ESO 3.56 m New Technology Telescope (NTT), in La Silla (Chile). The observation epoch, geometry and conditions are listed in Table 1. Most of the observations consisted in images of the comet obtained through Narrow Band (NB) cometary filters (similar to those described in Farnham et al., 2000). The NB filters included blue and red continuum ( Bc and Rc ), CN (0-0) Violet band, C 3 1 Π u -1 Σ + g and the C 2 Swan ( ∆ ν = 0) bands. In this paper we focus on the solid component of the coma, i.e. the data obtained with the two continuum filters. Table 2 lists their central wavelengths and full widths at half maximum. To minimize the contamination by background stars and to evaluate the sky background, each comet observation sequence consisted of 5 or 8 exposures on target, moving the telescope by few tens of arcseconds in between, and one additional exposure obtained /similarequal 8 ' o ff the comet, to record the sky uncontaminated by the comet. Bias and twilight sky flat-field exposures were also obtained in order to correct for the instrumental signature. Spectrophotometric standard stars and solar analog stars were observed spectroscopically and also in imaging mode, with the same filters at about the same airmass as the comet, to calibrate in flux the comet images. At the beginning of the run, some images of the comet were acquired through the standard broad band filters V , R and i . They were not used in this analysis, because their pass-bands contain non negligible gas emission lines. This was verified a posteriori with the spectra. All the images and spectra were at first corrected for bias and flat-field, using the appropriate ancillary frames in the customary manner. To calibrate the images in Af (see below) we computed the 'theoretical' filter color indexes ( Bc -V and Rc -V) of the observed spectrophotometric standard and solar analog stars. By using the tabulated spectra, we compared stellar fluxes measured through the NB and V filters to that of a star of A0V spectral type that, by definition, has a color index equal to 0. The knowledge of the V magnitude of the observed stars allowed us to recover the NB magnitudes and hence, from the observations, the photometric zero point (ZP) of each NB filter for each night. For the extinction correction, we adopted the standard extinction of La Silla 3 . Since the standard stars were observed at about the same airmass as at least one of the comet sequences, the errors introduced by possible di ff erences in the extinctions are negligible. When more than one sequence with the same filter was observed, the resulting calibrated images were in agreement within 10%. The same agreement was found also for calibrated images from consecutive photometric nights, in regions of the coma where the signature produced by periodic change of activity (see below) was not yet present. All the frames with the same filter were then inter-calibrated (see below). The level of the sky contribution was then evaluated for each comet sequence, measuring the median level of the sky frame acquired through the same filter 8 ' away from the comet. This value was subtracted from each frame. Thesky-subtracted frames then were re-centered on the comet photometric center, and a composite comet image was obtained through a median average of the 5 or 8 frames of the sequence. The use of a median combination significantly reduces the contamination produced by background stars. The background was then refined and subtracted with a trial and error procedure using the Σ Af function (see below), by making this function independent of the projected nucleo-centric distance ( ρ ) for distances greater than 150 pixels (corresponding to /similarequal 15000 km at the comet distance) from the photometric center. The resulting continuum images were then calibrated in Af (A'Hearn et al., 1984).\",\n \"pages\": [\n 2\n ]\n },\n {\n \"title\": \"3.1. 1D analysis: background activity\",\n \"content\": \"As shown by the spacecraft observations (A'Hearn et al., 2011) and as already noticed at the telescope during the observations, the comet showed a strong variability with nucleus rotation. By studying the CN features in the coma, Samarasinha et al. (2011) found that rotation period varied from 17.1 h in September to 18.8 h in November 2010. Thus for this study we assume a rotation period of 18.8 h. We arbitrarily use as a starting point for the rotation phase the time of the first observation (not used here because it was recorded with a broad band filter). This point was Nov. 1, UT = 7:39. To check how the emission of the continuum varied with the rotation period, we first characterized the constant background coma, which was estimated from the epoch of minimal activity. A'Hearn et al. (1984) introduced the function Af ρ as a proxy for production of the solid component. A is the geometric albedo of the grains and f the filling factor, defined as the percentage of the area that is covered by the grains, and ρ the projected UT str refers to the beginning of the observations; rh and ∆ are the helio- and geocentric distances; Phase is the Sun-Target-Observer angle; PA is the position angle of the extended Sun-Target vector. The sky conditions are listed: Pht is for photometric, Clr is for clear. Filt. is the identifier of the filter; Texp the is the sequence exposure time on target, in second; the airmass ( airm ) is listed for the beginning of each observations nucleo-centric distance of the aperture. Typically, the filling factor, f , is proportional to 1 /ρ , while A is, at first approximation, independent of ρ . Since from the observations we get the product Af ( ρ ), it is not possible to disentangle these two parameters without additional observations in the thermal IR or without making assumptions. Here we used another function derived by the above one, i.e. Σ Af ( ρ ), that is proportional to the average column density of the solid component at the projected nucleo-centric distance ρ . It is equal to 2 πρ Af ( ρ ). As shown by Tozzi et al. (2007), Σ Af should be constant with respect to the projected nuclear distance, ρ , for a comet with a dust outflow of constant velocity and production rate, and if sublimation or fragmentation of the grains are excluded. The solar radiation pressure introduces a small linear dependence with ρ , but normally its e ff ects are only noticeable at large distances from the nucleus, larger than the field of view (FoV) of EFOSC. The final calibrated images were analyzed by computing their Σ Af ( ρ ) function. In Fig. 1 some examples of the Σ Af function are shown. The solid component production rate was clearly not constant, as it can be noticed by comparing the regions with ρ < 500-1000 km. However, excluding the region with ρ smaller than about 3000-5000 km, the profiles are very similar, and the signatures of the change of activity seems to overlap that of a typical, constant profile. Plotting all the Σ Af profiles together, as shown in Fig. 1, we can see that they have the same behavior for ρ greater that 30005000 km and the values of Σ Af in that region are within ± 10%. These di ff erences are comparable to the uncertainty of the absolute calibration. We therefore assumed that the average value of Σ Af over ρ in the 6000-8000 km range was constant over the observations, and made small corrections to the Zero Points to adjust the profiles so they have the same average value over that range. This assumption is equivalent to considering that any change in grains production did not reach ρ = 6000 km from one day to the next. The validity of this hypothesis will be verified later. Note that using this method, the data acquired during the non-photometric night (Nov. 4) have been also calibrated to the same system as the others. All the Σ Af profiles are very similar except in the region very close to the nucleus ( ρ < 2000 km) where the signature of the activity seems confined. In order to characterize the periodic emissions, a Σ Af profile corresponding to the minimum of cometary activity -what we call the 'quiet comet'- was determined for each filter as follows: for the regions with ρ > 6000 km as a median of all the profiles, and for that with ρ < 6000 km as the minimum envelope of all the profiles (excluding the region with ρ < 200 km). The median was used to reduce signatures of possible background stars, still present in the single Σ Af profiles; the minimum envelope allowed us to discard the peaks produced by the activity. However, the always present activity in the regions with ρ < 100-200 km (see below) was visually removed by spline interpolation. The Σ Af profiles, corresponding to the constant level of activity, are shown in Fig. 2 for both filters. From the measurements of Σ Af , the values of Af ρ for ρ in the 6000-8000km range corresponded to 80 ± 3 cm and 91 ± 3 cm in Bc and Rc , respectively. The errors were obtained from the standard deviation of the values of the Σ Af function, with the re-normalization described above. From the above values of Af ρ , it is possible to derive the slope of the reflectivity spectrum for the solid component coma of the 'quiet comet'. Assuming a linear variation with lambda, the Af ρ at λ = 5550 Å would be 85 ± 3 cm and the corresponding spectral slope would be 5.2 ± 1.5 % / 1000 Å. As seen in Fig. 2, the Σ Af profiles of the minimum activity are not completely constant with ρ , but they systematically increase in the inner region of the coma up to ρ equal to 20002500 km. Note that this behavior cannot be due to a residual background, because this would produce a linear variation with ρ . A profile like that means that the total grain cross-section increases with ρ in a systematic way. The only possible explanation is the fragmentation of large grains, with dimensions much larger than the observation wavelength, as they move away from the nucleus. In that way, the total grain cross-sections would increase with ρ . It is important to notice that the behavior of the quiet coma can be found in all the profiles, even though, it is partially hidden by the periodic activity\",\n \"pages\": [\n 2,\n 3,\n 4,\n 5\n ]\n },\n {\n \"title\": \"3.2. Periodic activity\",\n \"content\": \"By subtracting the minimum profile for Bc or Rc from the individual Σ Af profiles, we found the signature of the clouds of grains periodically ejected by the nucleus. Typical Σ Af profiles of the those clouds are shown in Figure 3. All profiles are similar, with a very strong increase towards the nucleus. There is no evidence of any motion of the clouds, as it has been seen for other outbursts (see for instance Tozzi and Licandro, 2002). It would be interesting to determine the colors of the clouds of grains produced by the periodic activity, and to compare them to that of the coma at minimum activity. This measurement is complicated by the rapid evolution of the cloud and by the fact that the observations in Bc and Rc are taken at di ff erent times. To measure the color of the material produced by the activity, we have first to characterize its evolution with time. We determined then the time when the comet was closer to the minimum activity, by checking the individual Σ Af profiles and then selecting the minimum ones. They were those recorded on November 6 at UT 5:10 and 5:58 for the Bc and Rc filters, respectively. Their Σ Af profiles are very similar to the minimum profiles derived above: only a narrow and faint peak is present in the region with ρ < 100-200 km, indicating that the periodic activity was starting again. By chance those two observations are very close to the rotation phase equal to 0 as defined in the previous section. To map the emission produced by the periodic activity, we subtract these images corresponding to the minimum of activity from the individual images. As pointed out above, those two images were not acquired at the exact minimum of activity: the inner part already shows the signs of the periodic activity emission. Nevertheless, these signs are limited to the very inner coma ( ρ /lessorsimilar 200 km) and it is easy to take them into account in the following analysis. The activity maps are shown as a function of the rotation phase in Figures 4 and 5 for the Bc and Rc filters, respectively. For clarity, the figures cover a limited FoV, equivalent to a projected area of 2000 × 2000 km 2 centered on the comet. The FoV actually covered by the observations is more than 10 times larger. The grains released by the periodic activity are clearly visible in both filters. They are particularly evident in two preferred directions. The first one points to the East at position angle PA ∼ 90 · and is active from a rotation phase of about 90 · to 200 · . The second one points to PA ∼ 140 · and is active from the rotation phase greater than 200 · . They don't seem produced by the same active region on the rotating nucleus, because in such a case we should see the produced grains spiraling around the nucleus. We have then analyzed the two directions independently, to check whether the active regions have di ff erent origins, as found by the spacecraft (A'Hearn et al., 2011). The maps have been transformed to polar coordinates, and the profiles of the emission with respect to the nucleo-centric distance ρ have been obtained by integrating between PA = 40 · and 117 · for the first cloud, and between PA = 118 · to 165 · for the second one. The profiles have been transformed in equivalent Σ Af units (accounting for the limited angular range, as the standard definition of Σ Af implies an integration over 2 π ). Typical equivalent Σ Af profiles of the cloud during a phase of high activity are shown in Fig. 6. The Σ Af profiles for the active regions are very similar to those presented earlier for the 1D analysis -only the peak intensity and signal-to-noise ratio (SNR) are di ff erent. Excluding the region with ρ /lessorsimilar 200 km, which is dominated by the seeing of the image and contaminated by the near-nucleus activity in the reference image of the 'quiet' comet, the profiles are very well represented by a constant plus an exponential function, where L 1 is the scale length of the cloud released by the activity (in km), and Σ Af 1 the peak intensity (in cm). The fit residuals are very small, with errors less than 10% even for profiles with medium / high activity, i.e. with high SNR. The variation of L 1 with time gives the projected expansion velocity of the grains located at ρ = L 1. Of course grains located at ρ > L 1 have larger projected velocities and those at smaller distances have smaller velocities. Since the direction of the emission of the cloud of particles in space is not known, the projected velocities are a lower limit of the real expansion velocities. To get the projected velocity we used the observations from November 6, that are most numerous and that were obtained when the level of activity was relatively high. The resulting dL 1 / dt is ≈ 15-20 m s -1 for both clouds, which is comparable to the velocity of the grains measured by radar (Harmon et al., 2011). Note that they measured radial velocities, while we measured projected velocities. Those low projected velocities imply that the cloud of grains produced by periodic activity cannot move to distances greater than about 1700 km in 24 hours. This implies the grains must still be well within the FoV for observations recorded during the following night. The assumption we had made before, that the grains had not reached a projected distance larger than 6000 km from one night to the next, is therefore valid, justifying our inter-normalization of the outer part of the profiles. The equivalent Σ Af ( ρ ) functions are always peaked at ρ close to 0, as can be seen in Fig. 3. A motion of the cloud away from the nucleus was never detected (apart the small increase of L 1 mentioned above) contrary to other comets, e.g. C / 1999 S4 before its breakup (Tozzi and Licandro, 2002) or 9P / Tempel 1 after the impact (Tozzi et al., 2007), for which a similar analysis revealed a clear motion of the ejecta with a Maxwellian profile. The product Σ Af 1 × L 1 gives the cross-sections, S A , of the released clouds, i.e. the total surface ( S ) covered by the grains multiplied by their geometric albedo ( A ). The values of S A together with those of the scale-length are reported in Table 3 for both filters. S A as function of the rotation phase is shown in Fig. 7.\",\n \"pages\": [\n 5,\n 8\n ]\n },\n {\n \"title\": \"3.2.1. PA ∼ 90 ·\",\n \"content\": \"For the activity cloud released at PA ∼ 90 · the variations of S A for Bc and Rc filters with the phase have similar behaviors, with the values for Bc lower than those of Rc . By interpolating a. b. the points obtained with di ff erent phases, we see that, multiplying the Bc intensities by 1.36, the two profiles overlap. As long as the grains are bigger than the wavelength, this is simply the variation of the albedo from Bc to Rc , i.e. the color of the grains. Note that in such a way those measurements of color are independent from any temporal change due to the variability of the emission. The error in the color of the grains has been evaluated as the standard deviation of the data with respect to an interpolating curve. It results of the order of 0.026 km 2 . The albedo of the grains in Rc is then 36% higher than in Bc . Assuming a linear dependence with wavelength, the albedo at λ = 5550 Å is 20% higher than that at Bc and the spectral slope is (14.7 ± 1.1) % / 1000 Å. This value is more than 3 times larger than that of the background dust emission of the 'quiet comet' obtained in the previous section. In Fig. 7 (a), the S A derived from the observations with the Bc filters have been multiplied by 1.36 to take into account the di ff erent albedos, in order to check how the crosssections change with the rotation phase. The points from consecutive nights interleave nicely, suggesting the repeatability of the emission period after period. However, we cannot firmly prove this asserting. In fact, for example, the data at phase around 200 · come from observations of Nov. 3 at UT 8-9, while the data for phase of 300 · come from observations taken the day after, more or less at the same UT (see tables 3). That means that the nucleus had rotated by one full turn plus 100 · . Assuming a typical grain albedo of A = 0 . 04, the maximum area covered by them is of the order of 5 km 2 . The variations of S A illustrated in Fig. 7 are very large: it varies from almost 0.04 km 2 , at phase close to 0, to more than 0.2 km 2 at phase ∼ 150-200 · , with an increase of at least a factor of 5. The increases of S A between phase 0 · to 200 · can be simply explained with an increase of the production in the grains as the active area moves into sunlight. Instead the factor of four decrease passing from phase 200 · to phase 300 · (see Fig. 7, a), corresponding to about 5 h if the periodicity can be trusted (or 24 h actual elapsed time), is more di ffi cult to explain: the cloud must still be well within the FoV of the observations because of the low projected velocity. This strongly supports the hypothesis that grains sublimated away, with a lifetime surely shorter than 24 h and probably of the order of 5 h. If they are transformed into gas, they will contribute no longer to the observations in the continuum bands. The color of the grains ejected at this PA is similar to that of the surface of short period comets, Centaurs and scattered disk TNOs (see online MBOSS color database Hainaut & Delsanti, 2002). This color cannot be explained by pure ice; they could be ice particles with a large amount of organic material or just organic grains that sublimate under the solar radiation.\",\n \"pages\": [\n 8,\n 10\n ]\n },\n {\n \"title\": \"3.2.2. PA ∼ 140 ·\",\n \"content\": \"The clouds of particles released at PA ∼ 140 · are much fainter and the data therefore are more noisy than the other ones. However the data taken through the Bc filter overlap with those through the Rc filter, within the errors. The estimated error is here about 0.05 km 2 . The corresponding spectral slope is then 0 ± 2.4 % / 1000 Å. This cloud appears during a short range of rotation period, at a phase ∼ 200 · . The S A changes by a factor 6-7 during the whole rotation. As for the other cloud, it decreases by a factor 4 passing from rotation phase of 300 · to (360 + )20 · , suggesting sublimating grains for this cloud as well. However, these grains seem to have a gray color, in contrast to those released at PA ∼ 90 · . The appearance of the two clouds at di ff erent rotation phases indicates that they are produced by di ff erent active regions of the nucleus, and the great di ff erence in their color, suggest that these regions produce different kind of grains. Those at PA ∼ 140 · are more similar to the icy chunks discovered by the spacecraft, because ice should have gray color. Also those grains cannot be pure ices, since their lifetimes should be much longer that the /similarequal 5 hours indicated here (see for example Beer et al. (2006)). So also these grains should have some impurities of gray color, as for example silicates.\",\n \"pages\": [\n 10\n ]\n },\n {\n \"title\": \"4. Conclusions\",\n \"content\": \"From the analysis of images recorded in the blue and red continuum regions of the visible spectra, we have separated the solid state emission produced by the periodic activity from the normal dust cometary coma of the 'quiet' comet. We have found that the coma of the 'quiet' comet shows a peculiar behavior: its Σ Af function is not constant, but shows an increase with nucleo-centric distances ρ , for ρ < 2000-2500 km, that is not typical of a comet with constant outflow velocity and without fragmentation or sublimation. The Σ Af profiles of the 'quiet coma' obtained over the 5 nights of observations have a very similar behavior. Of course this is true for the observations where the emission due to the periodic activity does not hide completely the inner coma. This kind of profile is an indication that the scattering of the grains increases as they move away from the nucleus. Since this behavior is the same during a long period of time (5 nights), the only explanation is that the grains present in the coma of the 'quiet' comet fragment with the time, increasing their scattering area with the nucleo-centric distance. The color of the solid state coma of the 'quiet' comet is red, with a spectral slope of 4.6 ± 1.5 % / 1000 Å, assuming a linear variation with wavelength. By analyzing the grains produced by the periodic activity we have shown that the released clouds have two privileged projected directions: one at PA ∼ 90 · and the other at ∼ 140 · . The profiles of the equivalent Σ Af function with ρ of the clouds released in the two direction can be fitted with a constant plus an exponential function. The cross-sections S A of the two clouds vary strongly with the rotation phase of the nucleus. They move very slowly, with projected velocities of the order of 20 m / s, for both PAs. One of the two clouds (the one with PA ∼ 90 · ) has a very red color, of the order of 15 ± 3 % / 1000 Å, while the other seems to have a gray color. Assuming a periodic emission with the rotation, both sublimate with lifetimes of the order of 5 h. During the flyby, the spacecraft has observed for the first time some large chunks around the nucleus, that are supposed to be icy ice particles. The gray cloud can be then constituted by those chunks. However, to explain their relatively short lifetimes, those particles also need to have some impurities, gray in color, as for example silicates. The clouds released in the other direction are very red and sublimate as well with a lifetime of the order of few hours. So these grains should have lot of organics embedded in them, or they are pure organic grains that sublimate. It is important to notice that, within ρ equal to 4000 km, i.e. where most of the activity takes place, the cross section of the clouds produced by the activity is at most 6% of that of the quiet comet. This is of the same order of magnitude of the 4% contribution of the icy chunks measured by the spacecraft (A'Hearn et al., 2011). Once the full geometrical analysis of the jets observed by the spacecraft becomes available, it will be interesting to connect them with the two clouds described here, and to investigate whether their di ff erent characteristics can be traced to di ff erent natures of the sublimating area. Tozzi, G. P., Boehnhardt, H., Kolokolova, L., et al., 2007, A&A. Dust observa-\",\n \"pages\": [\n 10,\n 11\n ]\n },\n {\n \"title\": \"5. Acknowledgments\",\n \"content\": \"Based on Observations performed at the European Southern Observatory, La Silla, Progr. 086.C-0375. This work has been partially funded by MIUR - Ministero dell'Istruzione, dell'Universit'a e della Ricerca (Italy), under the PRIN 2008 funding.\",\n \"pages\": [\n 11\n ]\n },\n {\n \"title\": \"References\",\n \"content\": \"Cesarsky C.J. and 65 colleagues, 1996. ISOCAM in flight. A&A 315, L32-L37 Epifani E., Colangeli L., Fulle M., Brucato J.R., Bussoletti E., De Sanctis M.C., Mennella V., Palomba E., Palumbo P., Rotundi A., 2001. ISOCAM imaging of comets 103P / Hartley 2 and 2P / Encke. Icarus 149, 339-350 Farnham, T. L. and Schleicher, D. G. and A'Hearn, M. F., 2000.The HB Narrowband Comet Filters: Standard Stars and Calibrations. Icarus, 147, 180204 Hainaut, O.R. and Delsanti, A.C., 2002. Colors of Minor Bodies in the Outer Solar System - a Statistical Analysis. A&A 389, 641-664 Hartley M., 1986. Comet Hartley (1986c). IAU Circ. 4197 Licandro J., Tancredi G., Lindgren M., Rickman H., Hutton R. G., 2000. CCD Photometry of Cometary Nuclei, I: Observations from 1990-1995. Icarus 147, 161-179 Lisse C.M., Fernadez Y.R., Reach W.T., Bauer J.M., A'Hearn M.F., Farnham T.L., Groussin O., Belton M.J., Meech K.J., Snodgrass C.D., 2009. Spizer Space Telescope Observations of the Nucleus of Comet 103P / Hartley 2. PASP 121, 968-975 Lowry S.C. & Fitzsimmons A., 2001.CCD photometry of distant comets. II. A&A 365, 204-213\",\n \"pages\": [\n 11\n ]\n }\n]"}}},{"rowIdx":99,"cells":{"bibcode":{"kind":"string","value":"2013Icar..224..253N"},"pdf_url":{"kind":"string","value":"https://arxiv.org/pdf/1303.3023.pdf"},"content":{"kind":"string","value":"\nUpper limits for PH 3 and H 2 S in Titan's atmosphere from Cassini CIRS\nConor A. Nixon a , Nicholas A. Teanby b , Patrick G. J. Irwin c , Sarah M. Horst d\n\na Planetary Systems Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA b School of Earth Sciences, University of Bristol, Wills Memorial Building, Queen's Road, BS8 1RJ, Bristol, UK c Atmospheric, Oceanic and Planetary Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK Cooperative Institute for Research in Environmental Sciences, University of Colorado,\nd Boulder, CO 80309, USA\n\nAbstract\nWe have searched for the presence of simple P and S-bearing molecules in Titan's atmosphere, by looking for the characteristic signatures of phosphine and hydrogen sulfide in infrared spectra obtained by Cassini CIRS. As a result we have placed the first upper limits on the stratospheric abundances, which are 1 ppb (PH 3 ) and 330 ppb (H 2 S), at the 2σ significance level. Keywords: Titan, Titan, atmosphere, Abundances, atmospheres,\nAtmospheres, Composition, Saturn, satellites\n1. Introduction 1\n\nTo date, no molecules bearing the light elements phosphorus (P) and 2\nsulfur (S) have been detected in the atmosphere of Titan by either remote 3\nsensing or in-situ methods. However, from cosmological considerations both 4\nP and S must have been present in the icy planetesimals that formed Titan, 5\n\n\nand also delivered in trace quantities by later impacts. P in the form of PH 3 6\nis found in Jupiter's atmosphere at approximately solar abundance, while on 7\nSaturn its abundance is around 3 × solar (Owen and Encrenaz, 2003). This 8\nenrichment is in line with core-accretion models, which predict that Saturn 9\nhad a larger ice-to-gas fraction in its formation compared to Jupiter. Sulfur 10\nis enriched on Jupiter by 2.5 × solar (Niemann et al., 1998) (and not yet 11\ndetected on Saturn), perhaps due to easy formation of H 2 S clathrate hydrates 12\nOwen and Encrenaz (2003). Both P and S should therefore be present in 13\nTitan's bulk composition at fractions greater than those on Saturn, since the 14\nice to gas ratio must have been much higher. 15\nFortes et al. (2007) considered a possible role for sulfur compounds in Ti16 tan cryovolcanism, suggesting that ammonium sulfate could form a magma 17\nin Titan's mantle. Plumes of this magma could dissolve methane present in 18\ncrustal clathrates, allowing explosive release to the surface. One prediction 19\nof this model is that ammonium or other sulfates should be detectable spec20\ntroscopically on Titan's surface, as is the case on Europa and Ganymede. 21\nSuch a model would presumably also release trace amounts of sulfur into 22\nTitan's atmosphere, especially in the wake of eruptions. Pasek et al. (2011) 23\nfocused on the role of phosphorus in Titan, arguing that it could be delivered 24\nboth endogenously and exogenously to the surface. Phosphine is efficiently 25\ntrapped in clathrate hydrates, and Pasek et al. (2011) show that all clathrates 26\nthat trap H 2 S also trap at least as much PH 3 . Moreover, they show that PH 3 27\nis more soluble in organic liquids than in water, and therefore any phosphine 28\nreleased from melted clathrates could be dissolved in Titan's hydrocarbon 29\nlakes, and would participate in the hydrocarbon meteorological cycle. 30\n\n\nWe have therefore searched the infrared spectrum of Titan for the sig31 natures of the two most likely carriers of P and S: phosphine (PH 3 ) and 32 hydrogen sulfide (H 2 S). Our data is from the Composite Infrared Spectrome33 ter (CIRS, Flasar et al., 2004), carried onboard the Cassini spacecraft, which 34 has been making close flybys of Titan since attaining Saturn orbit in mid35 2004. Both gases have signatures in the 8-11 µ m (1250-900 cm -1 ) range, 36 which is largely free of the hydrocarbon emissions that dominate much of 37 Titan's infrared spectrum. We first model and subtract out the emissions of 38 known species including methane (CH 4 ), acetylene (C 2 H 2 ), ethylene (C 2 H 4 ) 39 and deuterated methane (CH 3 D). We then add H 2 S and PH 3 incrementally 40 to our spectral calculation using standard line lists from HITRAN (Rothman 41 et al., 2009), and compare the predictions to the remaining Titan spectrum. 42 By comparing the model predictions to the instrument noise level at the 43 1, 2, and 3σ levels, we have derived the first numerical upper limits on the 44 prevalence of H 2 S and PH 3 in Titan's stratosphere. We follow a report of our 45 results with a discussion of the implications for existing models, and finish 46 with some conclusions about the prospects for future searches. 47\n\n2. Method 48\n2.1. Instrument and Dataset 49\n\nThe Cassini CIRS instrument is a dual design, comprising mid-infrared 50 (1400-600 cm -1 ) and far-infrared (600-10 cm -1 ) spectrometers, both with a 51 FWHM (full-width to half-maximum) spectral resolution variable from 0.552 15.5 cm -1 after Hamming apodization. The mid-IR Michelson spectrometer 53 employs two 1 × 10 detector arrays: focal plane 3 (FP3, 600-1100 cm -1 ) 54\n\n\nand focal plane 4 (FP4, 1100-1400 cm -1 ). Both arrays have square pixels 55 with fields of view 0.3 mrad across. FP4 has the highest sensitivity (lowest 56 background noise) and least instrumental interferences, and was consequently 57 used in this study. 58\nThe observations were described in an earlier paper (Nixon et al., 2010). 59 The spectra were acquired during the 55 th Titan flyby (T55) of Cassini on 60 May 22 nd 2009, in a four-hour period when the spacecraft was at a range 61 of 116,000-177,000 km. The observation (known as 'MIRLMPAIR'-type) 62 was targeted at Titan's limb, with the two arrays above and parallel to the 63 horizon. FP4 was above FP3, with the pixels centered at an altitude of 247 64 km (0.27 mbar) and spanning approximately 44 km (just under one scale 65 height) in the vertical direction at the mid-point of the observation. Using 66 CIRS PAIR mode, all ten detectors simultaneously recorded data, paired into 67 five receiver channels. A total of 941 pair-mode spectra at 0.5 cm -1 resolution 68 were selected and then averaged to create a single, high signal-to-noise (S/N) 69\nratio spectrum. 70\n\n2.2. Spectral Modeling 71\n\nThe CIRS FP4 limb spectrum was then modeled to remove the signatures\n\n72 of known gas species. These included CH 4 ( ν 4 band at 1305 cm -1 ) and 73 CH 3 D ( ν 6 band at 1156 cm -1 ), plus some weaker contributions from the 74 hydrocarbons C 2 H 4 and C 2 H 2 . The modeling closely follows that described 75 in a recent paper (Nixon et al., 2012), and is briefly summarized here. 76\n\nAn initial vertical atmospheric model was created with 100 layers equally 77 spaced in log pressure from 1.45 bar to 0.05 µ bar, based on the temper78 ature profile and major gas abundances (N 2 , CH 4 , H 2 ) determined by the 79\n\n\nHuygens probe (Fulchignoni et al., 2005; Niemann et al., 2010). Other gas 80\nspecies (C 2 H 4 , C 2 H 2 ) were included with constant vertical abundances in the 81\nstratosphere, at initial values taken from previous CIRS measurements at 82\nlow latitudes (Coustenis et al., 2010). Similarly a uniformly mixed (constant 83\nparticles/g atmosphere) stratospheric haze was included with optical prop84\nerties from Khare et al. (1984). The forward radiative transfer model was 85\ncomputed using the NEMESIS code (Irwin et al., 2008) applied to the model 86\natmosphere and using the HITRAN gas line atlas (Rothman et al., 2009), 87\nand then convolved with the FP4 detector spatial response shapes (Nixon\n88 et al., 2009b) to generate a model spectrum. 89\n90\nAt this point the model was iterated to arrive at an optimum fit to the\nmeasured spectrum, by adjusting the model temperature profile (at each 91\nlayer) and uniform vertical gas abundances of C H and C H , to minimize 92\n100 wavelength calibration uncertainties. 101\n2 2 2 4 a cost function similar to a χ 2 figure of merit. This approach has been 93 successfully used to fit the T55 limb spectrum of Titan in previous work 94 (Nixon et al., 2009a, 2010). Fig .1 (a) shows the best fit to the data. Note 95 that a weak band of propane ( ν 7 at 1158 cm -1 ) was not included in the 96 model, as a line list for this band has yet to be produced, and shows clearly 97 in the data-model residual (Fig .1 (b)). The strong CH 4 ν 4 band is fitted 98 reasonably well, but also shows some residual mismatch, which may be due 99 to imperfect knowledge of the underlying haze (continuum) opacity and/or\n\n2.3. Determination of Abundance Upper Limits 102\nTo search for PH 3 and H 2 S, we avoided spectral regions that showed non103 random 'noise' residual: especially the C 3 H 8 ν 7 region (1140-1200 cm -1 ) and 104\nthe CH 4 region (˜ ν > 1250 cm -1 ). This permitted us to search for the ν 4 105 band of PH 3 around 1120 cm -1 , and for a portion of the weak H 2 S ν 2 band 106 at 1200-1250 cm -1 (see Fig .1 (c) and (d)). The summed line strengths in 107 these regions were 1 . 40 × 10 -18 cm molecule -1 for 1121 lines of PH 3 from 108 1080-1140 cm -1 , and 2 . 2 × 10 -20 cm molecule -1 for 130 lines of H 2 S at 1200109 1250 cm -1 , using line data from HITRAN (Rothman et al., 2009). Note that 110 the PH 3 band intensity was almost 100 × that of H 2 S in the spectral ranges 111 considered, so we expect 100 × greater sensitivity to PH 3 compared to H 2 S. 112\nThese two gas species were added to the best-fit atmospheric model at 113 fixed trial abundances of 1 ppb with other gases and temperature held con114 stant at the previously retrieved values, and NEMESIS was allowed to re115 trieve a 'best fit' abundance for the new species. In both cases, these retrievals 116 resulted in no statistically significant improvement to the model χ 2 , hereafter 117 designated χ 2 0 : the minimum χ 2 . We then proceeded to calculate upper lim118 its to the abundances, following the approach of Teanby et al. (2009) and 119 Nixon et al. (2010). Starting with very low trial gas abundances in the model, 120 these were increased incrementally, and at each value the forward spectral 121 model was calculated, without optimized fitting or inversion, and the data122 model χ 2 computed. As the trial gas abundances increase, so too does the 123 ∆ χ 2 = χ 2 -χ 2 0 . See Fig. .2. Following Press et al. (1992) the 1, 2 and 3σ 124 upper limits to the gas abundances occur at ∆ χ 2 = 1 , 4 , 9. 125\n3. Results and Discussion 126\nTable 1 shows our results. The derived 1, 2, 3σ maximum abundances for 127 PH 3 are 0.3, 1.1, 2.2 ppb respectively, while the corresponding values for H 2 S 128\nare 91, 330, 700 ppb. The H 2 S upper limits are some two orders of magnitude 129 higher than those of PH 3 as expected, due to the much weaker band inten130 sity in the spectral region considered, along with a higher 1σ NESR (Noise 131 Equivalent Spectral Radiance) level in the corresponding spectral interval 132 (0.6 versus 0.3 nW cm -2 sr -1 /cm -1 ). 133\nSulfur compounds have been suggested to play a role in Titan cryovol134 canism (Fortes et al., 2007), and therefore be present in trace amounts in 135 Titan's atmosphere. Phosphorus is also easily dissolved in organic solvents, 136 and as such could be a component of Titan's present-day methane-ethane 137 lakes, and participate in the hydrocarbon cycle (Pasek et al., 2011). A sim138 ple calculation tracing the saturation vapor pressure (data from public NIST 139 and CRC databases) up through Titan's troposphere using the Huygens tem140 perature profile, indicates that abundances of PH 3 and H 2 S that could reach 141 the stratosphere are 6 and 0.035 ppb respectively. Therefore, our 2σ upper 142 limit of 1 ppb for PH 3 provides some constraint on tropospheric PH 3 , while 143 our H 2 S limit of 330 ppb is four orders of magnitude greater than allowed in 144 this scenario and is not constraining. 145\nAt the present time, the lack of detection of P or S-bearing species any146 where in Titan's atmosphere has caused these elements to be omitted from 147 present photochemical models, so we have no predictions for comparison. In 148 future, it could be interesting for such models to allow for some injection 149 of P and S molecules into the atmosphere through a putative eruption, and 150 to investigate subsequent chemistry, for example, conversion of sulfates to 151 sulfides. 152\n4. Conclusions and Further Work 153\nIn this paper we have searched for simple compounds of phosphorus and 154 sulfur in Titan's infrared spectrum recorded by Cassini CIRS, placing the 155 first upper limits on the abundance of PH 3 and H 2 S. In the stratosphere 156 at 247 km we find that no more than 1 ppb of PH 3 and 330 ppb of H 2 S 157 can be present, at the 2σ level of significance. Some potential exists for 158 improving on these upper limits using CIRS, e.g. by future measurements 159 at a lower limb altitude where the atmospheric density is greater. The peak 160 sensitivity for weak trace gases is often near 10 mbar ( ∼ 100 km), at least at 161 low latitudes, so a repeat measurement in the lower stratosphere may yield 162 more stringent limits. 163\nSearching in the far-IR spectrum may prove helpful in the case of H 2 S, 164 which has rotational lines at 50-150 cm -1 that are some 100 × stronger than 165 the ν 2 considered here. However in this region the NESR of CIRS FP1 is 166 more than 10 × higher than that of the FP4 detectors used in this work, and 167 suffers from systematic noise artifacts. Nevertheless, the sub-mm range has 168 already proved productive for molecular line searches by instruments such 169 as Herschel and ground-based sub-mm telescopes, resulting in the detections 170 of CH 3 CN (Marten et al., 2002) and HNC (Moreno et al., 2011), and will 171 doubtless reveal further new species in due course. 172\nReferences 173\nCoustenis, A., Jennings, D.E., Nixon, C.A., Achterberg, R.K., Lavvas, P., 174 Vinatier, S., Teanby, N.A., Bjoraker, G.L., Carlson, R.C., Piani, L., Bam175 pasidis, G., Flasar, F.M., Romani, P.N., 2010. Titan trace gaseous compo176\nsition from CIRS at the end of the Cassini-Huygens prime mission. 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Journal of Geophysical Research (Planets) 115, 228 12006. 229\nNixon, C.A., Achterberg, R.K., Teanby, N.A., Irwin, P.G.J., Flaud, J.M., 230 Kleiner, I., Dehayem-Kamadjeu, A., Brown, L.R., Sams, R.L., B'ezard, 231 B., Coustenis, A., Ansty, T.M., Mamoutkine, A., Vinatier, S., Bjoraker, 232 G.L., Jennings, D.E., Romani, P.N., Flasar, F.M., 2010. Upper limits for 233 undetected trace species in the stratosphere of Titan. Faraday Discussions 234 147, 65. 1103.0297 . 235\nNixon, C.A., Jennings, D.E., Flaud, J.M., B'ezard, B., Teanby, N.A., Irwin, 236 P.G.J., Ansty, T.M., Coustenis, A., Vinatier, S., Flasar, F.M., 2009a. Ti237 tan's prolific propane: The Cassini CIRS perspective. Planetary and Space 238 Science 57, 1573-1585. 0909.1794 . 239\nNixon, C.A., Teanby, N.A., Calcutt, S.B., Aslam, S., Jennings, D.E., Kunde, 240 V.G., Flasar, F.M., Irwin, P.G., Taylor, F.W., Glenar, D.A., Smith, M.D., 241 2009b. Infrared limb sounding of Titan with the Cassini Composite In242 fraRed Spectrometer: effects of the mid-IR detector spatial responses. Ap243 plied Optics 48, 1912. 244\nNixon, C.A., Temelso, B., Vinatier, S., Teanby, N.A., B'ezard, B., Achterberg, 245 R.K., Mandt, K.E., Sherrill, C.D., Irwin, P.G.J., Jennings, D.E., Romani, 246\n\nP.N., Coustenis, A., Flasar, F.M., 2012. Isotopic ratios in Titan's methane: 247 measurements and modeling. Astrophys. J. 749, 159. 248\nOwen, T., Encrenaz, T., 2003. Element Abundances and Isotope Ratios in 249 the Giant Planets and Titan. Space Sci. Rev. 106, 121-138. 250\nPasek, M.A., Mousis, O., Lunine, J.I., 2011. Phosphorus chemistry on Titan. 251 Icarus 212, 751-761. 252\nPress, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Nu253 merical recipes in FORTRAN. The art of scientific computing. 254\n\nRothman, L.S., Gordon, I.E., Barbe, A., Benner, D.C., Bernath, P.F., 255 Birk, M., Boudon, V., Brown, L.R., Campargue, A., Champion, J.P., 256 Chance, K., Coudert, L.H., Dana, V., Devi, V.M., Fally, S., Flaud, J.M., 257 Gamache, R.R., Goldman, A., Jacquemart, D., Kleiner, I., Lacome, N., 258 Lafferty, W.J., Mandin, J.Y., Massie, S.T., Mikhailenko, S.N., Miller, 259 C.E., Moazzen-Ahmadi, N., Naumenko, O.V., Nikitin, A.V., Orphal, J., 260 Perevalov, V.I., Perrin, A., Predoi-Cross, A., Rinsland, C.P., Rotger, M., 261 ˇ Simeˇckov'a, M., Smith, M.A.H., Sung, K., Tashkun, S.A., Tennyson, J., 262 Toth, R.A., Vandaele, A.C., Vander Auwera, J., 2009. The HITRAN 2008 263 molecular spectroscopic database. J. Quant. Spectr. Rad. Trans. 110, 533264 572. 265\nTeanby, N.A., Irwin, P.G.J., de Kok, R., Jolly, A., B'ezard, B., Nixon, C.A., 266 Calcutt, S.B., 2009. Titan's stratospheric C 2 N 2 , C 3 H 4 , and C 4 H 2 abun267 dances from Cassini/CIRS far-infrared spectra. Icarus 202, 620-631. 268\n
\n\n
Table 1: Calculated abundance upper limits for PH 3 and H 2 S
\n
\n\n\n
Figure .1: (a): CIRS limb average spectrum of Titan from T55 flyby (black) and model fit (green). (b): data-model spectral residual. Note the ν 7 band of C 3 H 8 at 1158 cm -1 that is not included in our model (see text for details). (c) and (d) show the density and strengths of lines of PH 3 and H 2 S respectively in the interval considered.
\n\n\n\n
Figure .2: Calculation of upper limits for the abundances of H 2 S and PH 3 in Titan's stratosphere. (a) & (c): residual of fit to the CIRS Titan spectrum in each region, after the modeling and removal known gas species (black line). Over-plotted is a calculation with exaggerated trial gas abundances of the undetected species to show their spectral signature (colored line). (b) & (d): the curve of growth of ∆ χ 2 over a wide range of trial abundances. The 1, 2 and 3σ upper limits are indicated by the vertical dashed lines at ∆ χ 2 = 1, 4, 9 respectively.
\n\n"},"sections":{"kind":"list like","value":[{"title":"Upper limits for PH 3 and H 2 S in Titan's atmosphere from Cassini CIRS","content":"Conor A. Nixon a , Nicholas A. Teanby b , Patrick G. J. Irwin c , Sarah M. Horst d","pages":[1]},{"title":"Abstract","content":"We have searched for the presence of simple P and S-bearing molecules in Titan's atmosphere, by looking for the characteristic signatures of phosphine and hydrogen sulfide in infrared spectra obtained by Cassini CIRS. As a result we have placed the first upper limits on the stratospheric abundances, which are 1 ppb (PH 3 ) and 330 ppb (H 2 S), at the 2σ significance level. Keywords: Titan, Titan, atmosphere, Abundances, atmospheres, Atmospheres, Composition, Saturn, satellites","pages":[1]},{"title":"2.2. Spectral Modeling 71","content":"72 of known gas species. These included CH 4 ( ν 4 band at 1305 cm -1 ) and 73 CH 3 D ( ν 6 band at 1156 cm -1 ), plus some weaker contributions from the 74 hydrocarbons C 2 H 4 and C 2 H 2 . The modeling closely follows that described 75 in a recent paper (Nixon et al., 2012), and is briefly summarized here. 76","pages":[4]},{"title":"2.3. Determination of Abundance Upper Limits 102","content":"To search for PH 3 and H 2 S, we avoided spectral regions that showed non103 random 'noise' residual: especially the C 3 H 8 ν 7 region (1140-1200 cm -1 ) and 104 the CH 4 region (˜ ν > 1250 cm -1 ). This permitted us to search for the ν 4 105 band of PH 3 around 1120 cm -1 , and for a portion of the weak H 2 S ν 2 band 106 at 1200-1250 cm -1 (see Fig .1 (c) and (d)). The summed line strengths in 107 these regions were 1 . 40 × 10 -18 cm molecule -1 for 1121 lines of PH 3 from 108 1080-1140 cm -1 , and 2 . 2 × 10 -20 cm molecule -1 for 130 lines of H 2 S at 1200109 1250 cm -1 , using line data from HITRAN (Rothman et al., 2009). Note that 110 the PH 3 band intensity was almost 100 × that of H 2 S in the spectral ranges 111 considered, so we expect 100 × greater sensitivity to PH 3 compared to H 2 S. 112 These two gas species were added to the best-fit atmospheric model at 113 fixed trial abundances of 1 ppb with other gases and temperature held con114 stant at the previously retrieved values, and NEMESIS was allowed to re115 trieve a 'best fit' abundance for the new species. In both cases, these retrievals 116 resulted in no statistically significant improvement to the model χ 2 , hereafter 117 designated χ 2 0 : the minimum χ 2 . We then proceeded to calculate upper lim118 its to the abundances, following the approach of Teanby et al. (2009) and 119 Nixon et al. (2010). Starting with very low trial gas abundances in the model, 120 these were increased incrementally, and at each value the forward spectral 121 model was calculated, without optimized fitting or inversion, and the data122 model χ 2 computed. As the trial gas abundances increase, so too does the 123 ∆ χ 2 = χ 2 -χ 2 0 . See Fig. .2. Following Press et al. (1992) the 1, 2 and 3σ 124 upper limits to the gas abundances occur at ∆ χ 2 = 1 , 4 , 9. 125","pages":[5,6]},{"title":"3. Results and Discussion 126","content":"Table 1 shows our results. The derived 1, 2, 3σ maximum abundances for 127 PH 3 are 0.3, 1.1, 2.2 ppb respectively, while the corresponding values for H 2 S 128 are 91, 330, 700 ppb. The H 2 S upper limits are some two orders of magnitude 129 higher than those of PH 3 as expected, due to the much weaker band inten130 sity in the spectral region considered, along with a higher 1σ NESR (Noise 131 Equivalent Spectral Radiance) level in the corresponding spectral interval 132 (0.6 versus 0.3 nW cm -2 sr -1 /cm -1 ). 133 Sulfur compounds have been suggested to play a role in Titan cryovol134 canism (Fortes et al., 2007), and therefore be present in trace amounts in 135 Titan's atmosphere. Phosphorus is also easily dissolved in organic solvents, 136 and as such could be a component of Titan's present-day methane-ethane 137 lakes, and participate in the hydrocarbon cycle (Pasek et al., 2011). A sim138 ple calculation tracing the saturation vapor pressure (data from public NIST 139 and CRC databases) up through Titan's troposphere using the Huygens tem140 perature profile, indicates that abundances of PH 3 and H 2 S that could reach 141 the stratosphere are 6 and 0.035 ppb respectively. Therefore, our 2σ upper 142 limit of 1 ppb for PH 3 provides some constraint on tropospheric PH 3 , while 143 our H 2 S limit of 330 ppb is four orders of magnitude greater than allowed in 144 this scenario and is not constraining. 145 At the present time, the lack of detection of P or S-bearing species any146 where in Titan's atmosphere has caused these elements to be omitted from 147 present photochemical models, so we have no predictions for comparison. In 148 future, it could be interesting for such models to allow for some injection 149 of P and S molecules into the atmosphere through a putative eruption, and 150 to investigate subsequent chemistry, for example, conversion of sulfates to 151 sulfides. 152","pages":[6,7]},{"title":"4. Conclusions and Further Work 153","content":"In this paper we have searched for simple compounds of phosphorus and 154 sulfur in Titan's infrared spectrum recorded by Cassini CIRS, placing the 155 first upper limits on the abundance of PH 3 and H 2 S. In the stratosphere 156 at 247 km we find that no more than 1 ppb of PH 3 and 330 ppb of H 2 S 157 can be present, at the 2σ level of significance. Some potential exists for 158 improving on these upper limits using CIRS, e.g. by future measurements 159 at a lower limb altitude where the atmospheric density is greater. The peak 160 sensitivity for weak trace gases is often near 10 mbar ( ∼ 100 km), at least at 161 low latitudes, so a repeat measurement in the lower stratosphere may yield 162 more stringent limits. 163 Searching in the far-IR spectrum may prove helpful in the case of H 2 S, 164 which has rotational lines at 50-150 cm -1 that are some 100 × stronger than 165 the ν 2 considered here. However in this region the NESR of CIRS FP1 is 166 more than 10 × higher than that of the FP4 detectors used in this work, and 167 suffers from systematic noise artifacts. Nevertheless, the sub-mm range has 168 already proved productive for molecular line searches by instruments such 169 as Herschel and ground-based sub-mm telescopes, resulting in the detections 170 of CH 3 CN (Marten et al., 2002) and HNC (Moreno et al., 2011), and will 171 doubtless reveal further new species in due course. 172","pages":[8]},{"title":"References 173","content":"Coustenis, A., Jennings, D.E., Nixon, C.A., Achterberg, R.K., Lavvas, P., 174 Vinatier, S., Teanby, N.A., Bjoraker, G.L., Carlson, R.C., Piani, L., Bam175 pasidis, G., Flasar, F.M., Romani, P.N., 2010. Titan trace gaseous compo176 sition from CIRS at the end of the Cassini-Huygens prime mission. Icarus 177 207, 461-476. 178 Flasar, F.M., Kunde, V.G., Abbas, M.M., Achterberg, R.K., Ade, P., 179 Barucci, A., B'ezard, B., Bjoraker, G.L., Brasunas, J.C., Calcutt, S., 180 Carlson, R., C'esarsky, C.J., Conrath, B.J., Coradini, A., Courtin, R., 181 Coustenis, A., Edberg, S., Edgington, S., Ferrari, C., Fouchet, T., Gau182 tier, D., Gierasch, P.J., Grossman, K., Irwin, P., Jennings, D.E., Lel183 louch, E., Mamoutkine, A.A., Marten, A., Meyer, J.P., Nixon, C.A., Or184 ton, G.S., Owen, T.C., Pearl, J.C., Prang'e, R., Raulin, F., Read, P.L., 185 Romani, P.N., Samuelson, R.E., Segura, M.E., Showalter, M.R., Simon186 Miller, A.A., Smith, M.D., Spencer, J.R., Spilker, L.J., Taylor, F.W., 2004. 187 Exploring The Saturn System In The Thermal Infrared: The Composite 188 Infrared Spectrometer. Space Sci. Rev. 115, 169-297. 189 190 191 192 Fortes, A.D., Grindrod, P.M., Trickett, S.K., Voˇcadlo, L., 2007. Ammonium sulfate on Titan: Possible origin and role in cryovolcanism. Icarus 188, 139-153. Fulchignoni, M., Ferri, F., Angrilli, F., Ball, A.J., Bar-Nun, A., Barucci, 193 M.A., Bettanini, C., Bianchini, G., Borucki, W., Colombatti, G., Cora194 dini, M., Coustenis, A., Debei, S., Falkner, P., Fanti, G., Flamini, E., Ga195 borit, V., Grard, R., Hamelin, M., Harri, A.M., Hathi, B., Jernej, I., Leese, 196 M.R., Lehto, A., Lion Stoppato, P.F., L'opez-Moreno, J.J., Makinen, T., 197 McDonnell, J.A.M., McKay, C.P., Molina-Cuberos, G., Neubauer, F.M., 198 Pirronello, V., Rodrigo, R., Saggin, B., Schwingenschuh, K., Seiff, A., 199 Sim˜oes, F., Svedhem, H., Tokano, T., Towner, M.C., Trautner, R., With200 ers, P., Zarnecki, J.C., 2005. In situ measurements of the physical charac201 teristics of Titan's environment. Nature 438, 785-791. 202 Irwin, P.G.J., Teanby, N.A., de Kok, R., Fletcher, L.N., Howett, C.J.A., 203 Tsang, C.C.C., Wilson, C.F., Calcutt, S.B., Nixon, C.A., Parrish, P.D., 204 2008. The NEMESIS planetary atmosphere radiative transfer and retrieval 205 tool. J. Quant. Spectr. Rad. Trans. 109, 1136-1150. 206 Khare, B.N., Sagan, C., Arakawa, E.T., Suits, F., Callcott, T.A., Williams, 207 M.W., 1984. Optical constants of organic tholins produced in a simulated 208 Titanian atmosphere - From soft X-ray to microwave frequencies. Icarus 209 60, 127-137. 210 Marten, A., Hidayat, T., Biraud, Y., Moreno, R., 2002. New Millimeter 211 Heterodyne Observations of Titan: Vertical Distributions of Nitriles HCN, 212 HC 3 N, CH 3 CN, and the Isotopic Ratio 15 N/ 14 N in Its Atmosphere. Icarus 213 158, 532-544. 214 Moreno, R., Lellouch, E., Lara, L.M., Courtin, R., Bockel'ee-Morvan, D., 215 Hartogh, P., Rengel, M., Biver, N., Banaszkiewicz, M., Gonz'alez, A., 2011. 216 First detection of hydrogen isocyanide (HNC) in Titan's atmosphere. As217 tron. and Astrophys. 536, L12. 218 Niemann, H.B., Atreya, S.K., Carignan, G.R., Donahue, T.M., Haberman, 219 J.A., Harpold, D.N., Hartle, R.E., Hunten, D.M., Kasprzak, W.T., Ma220 haffy, P.R., Owen, T.C., Way, S.H., 1998. The composition of the Jovian 221 atmosphere as determined by the Galileo probe mass spectrometer. J. 222 Geophys. Res. 103, 22831-22846. 223 Niemann, H.B., Atreya, S.K., Demick, J.E., Gautier, D., Haberman, J.A., 224 Harpold, D.N., Kasprzak, W.T., Lunine, J.I., Owen, T.C., Raulin, F., 225 2010. Composition of Titan's lower atmosphere and simple surface volatiles 226 as measured by the Cassini-Huygens probe gas chromatograph mass spec227 trometer experiment. Journal of Geophysical Research (Planets) 115, 228 12006. 229 Nixon, C.A., Achterberg, R.K., Teanby, N.A., Irwin, P.G.J., Flaud, J.M., 230 Kleiner, I., Dehayem-Kamadjeu, A., Brown, L.R., Sams, R.L., B'ezard, 231 B., Coustenis, A., Ansty, T.M., Mamoutkine, A., Vinatier, S., Bjoraker, 232 G.L., Jennings, D.E., Romani, P.N., Flasar, F.M., 2010. Upper limits for 233 undetected trace species in the stratosphere of Titan. Faraday Discussions 234 147, 65. 1103.0297 . 235 Nixon, C.A., Jennings, D.E., Flaud, J.M., B'ezard, B., Teanby, N.A., Irwin, 236 P.G.J., Ansty, T.M., Coustenis, A., Vinatier, S., Flasar, F.M., 2009a. Ti237 tan's prolific propane: The Cassini CIRS perspective. Planetary and Space 238 Science 57, 1573-1585. 0909.1794 . 239 Nixon, C.A., Teanby, N.A., Calcutt, S.B., Aslam, S., Jennings, D.E., Kunde, 240 V.G., Flasar, F.M., Irwin, P.G., Taylor, F.W., Glenar, D.A., Smith, M.D., 241 2009b. Infrared limb sounding of Titan with the Cassini Composite In242 fraRed Spectrometer: effects of the mid-IR detector spatial responses. Ap243 plied Optics 48, 1912. 244 Nixon, C.A., Temelso, B., Vinatier, S., Teanby, N.A., B'ezard, B., Achterberg, 245 R.K., Mandt, K.E., Sherrill, C.D., Irwin, P.G.J., Jennings, D.E., Romani, 246 Rothman, L.S., Gordon, I.E., Barbe, A., Benner, D.C., Bernath, P.F., 255 Birk, M., Boudon, V., Brown, L.R., Campargue, A., Champion, J.P., 256 Chance, K., Coudert, L.H., Dana, V., Devi, V.M., Fally, S., Flaud, J.M., 257 Gamache, R.R., Goldman, A., Jacquemart, D., Kleiner, I., Lacome, N., 258 Lafferty, W.J., Mandin, J.Y., Massie, S.T., Mikhailenko, S.N., Miller, 259 C.E., Moazzen-Ahmadi, N., Naumenko, O.V., Nikitin, A.V., Orphal, J., 260 Perevalov, V.I., Perrin, A., Predoi-Cross, A., Rinsland, C.P., Rotger, M., 261 ˇ Simeˇckov'a, M., Smith, M.A.H., Sung, K., Tashkun, S.A., Tennyson, J., 262 Toth, R.A., Vandaele, A.C., Vander Auwera, J., 2009. The HITRAN 2008 263 molecular spectroscopic database. J. Quant. Spectr. Rad. Trans. 110, 533264 572. 265 Teanby, N.A., Irwin, P.G.J., de Kok, R., Jolly, A., B'ezard, B., Nixon, C.A., 266 Calcutt, S.B., 2009. Titan's stratospheric C 2 N 2 , C 3 H 4 , and C 4 H 2 abun267 dances from Cassini/CIRS far-infrared spectra. Icarus 202, 620-631. 268","pages":[8,9,10,11,12]}],"string":"[\n {\n \"title\": \"Upper limits for PH 3 and H 2 S in Titan's atmosphere from Cassini CIRS\",\n \"content\": \"Conor A. Nixon a , Nicholas A. Teanby b , Patrick G. J. Irwin c , Sarah M. Horst d\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"Abstract\",\n \"content\": \"We have searched for the presence of simple P and S-bearing molecules in Titan's atmosphere, by looking for the characteristic signatures of phosphine and hydrogen sulfide in infrared spectra obtained by Cassini CIRS. As a result we have placed the first upper limits on the stratospheric abundances, which are 1 ppb (PH 3 ) and 330 ppb (H 2 S), at the 2σ significance level. Keywords: Titan, Titan, atmosphere, Abundances, atmospheres, Atmospheres, Composition, Saturn, satellites\",\n \"pages\": [\n 1\n ]\n },\n {\n \"title\": \"2.2. Spectral Modeling 71\",\n \"content\": \"72 of known gas species. These included CH 4 ( ν 4 band at 1305 cm -1 ) and 73 CH 3 D ( ν 6 band at 1156 cm -1 ), plus some weaker contributions from the 74 hydrocarbons C 2 H 4 and C 2 H 2 . The modeling closely follows that described 75 in a recent paper (Nixon et al., 2012), and is briefly summarized here. 76\",\n \"pages\": [\n 4\n ]\n },\n {\n \"title\": \"2.3. Determination of Abundance Upper Limits 102\",\n \"content\": \"To search for PH 3 and H 2 S, we avoided spectral regions that showed non103 random 'noise' residual: especially the C 3 H 8 ν 7 region (1140-1200 cm -1 ) and 104 the CH 4 region (˜ ν > 1250 cm -1 ). This permitted us to search for the ν 4 105 band of PH 3 around 1120 cm -1 , and for a portion of the weak H 2 S ν 2 band 106 at 1200-1250 cm -1 (see Fig .1 (c) and (d)). The summed line strengths in 107 these regions were 1 . 40 × 10 -18 cm molecule -1 for 1121 lines of PH 3 from 108 1080-1140 cm -1 , and 2 . 2 × 10 -20 cm molecule -1 for 130 lines of H 2 S at 1200109 1250 cm -1 , using line data from HITRAN (Rothman et al., 2009). Note that 110 the PH 3 band intensity was almost 100 × that of H 2 S in the spectral ranges 111 considered, so we expect 100 × greater sensitivity to PH 3 compared to H 2 S. 112 These two gas species were added to the best-fit atmospheric model at 113 fixed trial abundances of 1 ppb with other gases and temperature held con114 stant at the previously retrieved values, and NEMESIS was allowed to re115 trieve a 'best fit' abundance for the new species. In both cases, these retrievals 116 resulted in no statistically significant improvement to the model χ 2 , hereafter 117 designated χ 2 0 : the minimum χ 2 . We then proceeded to calculate upper lim118 its to the abundances, following the approach of Teanby et al. (2009) and 119 Nixon et al. (2010). Starting with very low trial gas abundances in the model, 120 these were increased incrementally, and at each value the forward spectral 121 model was calculated, without optimized fitting or inversion, and the data122 model χ 2 computed. As the trial gas abundances increase, so too does the 123 ∆ χ 2 = χ 2 -χ 2 0 . See Fig. .2. Following Press et al. (1992) the 1, 2 and 3σ 124 upper limits to the gas abundances occur at ∆ χ 2 = 1 , 4 , 9. 125\",\n \"pages\": [\n 5,\n 6\n ]\n },\n {\n \"title\": \"3. Results and Discussion 126\",\n \"content\": \"Table 1 shows our results. The derived 1, 2, 3σ maximum abundances for 127 PH 3 are 0.3, 1.1, 2.2 ppb respectively, while the corresponding values for H 2 S 128 are 91, 330, 700 ppb. The H 2 S upper limits are some two orders of magnitude 129 higher than those of PH 3 as expected, due to the much weaker band inten130 sity in the spectral region considered, along with a higher 1σ NESR (Noise 131 Equivalent Spectral Radiance) level in the corresponding spectral interval 132 (0.6 versus 0.3 nW cm -2 sr -1 /cm -1 ). 133 Sulfur compounds have been suggested to play a role in Titan cryovol134 canism (Fortes et al., 2007), and therefore be present in trace amounts in 135 Titan's atmosphere. Phosphorus is also easily dissolved in organic solvents, 136 and as such could be a component of Titan's present-day methane-ethane 137 lakes, and participate in the hydrocarbon cycle (Pasek et al., 2011). A sim138 ple calculation tracing the saturation vapor pressure (data from public NIST 139 and CRC databases) up through Titan's troposphere using the Huygens tem140 perature profile, indicates that abundances of PH 3 and H 2 S that could reach 141 the stratosphere are 6 and 0.035 ppb respectively. Therefore, our 2σ upper 142 limit of 1 ppb for PH 3 provides some constraint on tropospheric PH 3 , while 143 our H 2 S limit of 330 ppb is four orders of magnitude greater than allowed in 144 this scenario and is not constraining. 145 At the present time, the lack of detection of P or S-bearing species any146 where in Titan's atmosphere has caused these elements to be omitted from 147 present photochemical models, so we have no predictions for comparison. In 148 future, it could be interesting for such models to allow for some injection 149 of P and S molecules into the atmosphere through a putative eruption, and 150 to investigate subsequent chemistry, for example, conversion of sulfates to 151 sulfides. 152\",\n \"pages\": [\n 6,\n 7\n ]\n },\n {\n \"title\": \"4. Conclusions and Further Work 153\",\n \"content\": \"In this paper we have searched for simple compounds of phosphorus and 154 sulfur in Titan's infrared spectrum recorded by Cassini CIRS, placing the 155 first upper limits on the abundance of PH 3 and H 2 S. In the stratosphere 156 at 247 km we find that no more than 1 ppb of PH 3 and 330 ppb of H 2 S 157 can be present, at the 2σ level of significance. Some potential exists for 158 improving on these upper limits using CIRS, e.g. by future measurements 159 at a lower limb altitude where the atmospheric density is greater. The peak 160 sensitivity for weak trace gases is often near 10 mbar ( ∼ 100 km), at least at 161 low latitudes, so a repeat measurement in the lower stratosphere may yield 162 more stringent limits. 163 Searching in the far-IR spectrum may prove helpful in the case of H 2 S, 164 which has rotational lines at 50-150 cm -1 that are some 100 × stronger than 165 the ν 2 considered here. However in this region the NESR of CIRS FP1 is 166 more than 10 × higher than that of the FP4 detectors used in this work, and 167 suffers from systematic noise artifacts. Nevertheless, the sub-mm range has 168 already proved productive for molecular line searches by instruments such 169 as Herschel and ground-based sub-mm telescopes, resulting in the detections 170 of CH 3 CN (Marten et al., 2002) and HNC (Moreno et al., 2011), and will 171 doubtless reveal further new species in due course. 172\",\n \"pages\": [\n 8\n ]\n },\n {\n \"title\": \"References 173\",\n \"content\": \"Coustenis, A., Jennings, D.E., Nixon, C.A., Achterberg, R.K., Lavvas, P., 174 Vinatier, S., Teanby, N.A., Bjoraker, G.L., Carlson, R.C., Piani, L., Bam175 pasidis, G., Flasar, F.M., Romani, P.N., 2010. Titan trace gaseous compo176 sition from CIRS at the end of the Cassini-Huygens prime mission. Icarus 177 207, 461-476. 178 Flasar, F.M., Kunde, V.G., Abbas, M.M., Achterberg, R.K., Ade, P., 179 Barucci, A., B'ezard, B., Bjoraker, G.L., Brasunas, J.C., Calcutt, S., 180 Carlson, R., C'esarsky, C.J., Conrath, B.J., Coradini, A., Courtin, R., 181 Coustenis, A., Edberg, S., Edgington, S., Ferrari, C., Fouchet, T., Gau182 tier, D., Gierasch, P.J., Grossman, K., Irwin, P., Jennings, D.E., Lel183 louch, E., Mamoutkine, A.A., Marten, A., Meyer, J.P., Nixon, C.A., Or184 ton, G.S., Owen, T.C., Pearl, J.C., Prang'e, R., Raulin, F., Read, P.L., 185 Romani, P.N., Samuelson, R.E., Segura, M.E., Showalter, M.R., Simon186 Miller, A.A., Smith, M.D., Spencer, J.R., Spilker, L.J., Taylor, F.W., 2004. 187 Exploring The Saturn System In The Thermal Infrared: The Composite 188 Infrared Spectrometer. Space Sci. Rev. 115, 169-297. 189 190 191 192 Fortes, A.D., Grindrod, P.M., Trickett, S.K., Voˇcadlo, L., 2007. Ammonium sulfate on Titan: Possible origin and role in cryovolcanism. Icarus 188, 139-153. Fulchignoni, M., Ferri, F., Angrilli, F., Ball, A.J., Bar-Nun, A., Barucci, 193 M.A., Bettanini, C., Bianchini, G., Borucki, W., Colombatti, G., Cora194 dini, M., Coustenis, A., Debei, S., Falkner, P., Fanti, G., Flamini, E., Ga195 borit, V., Grard, R., Hamelin, M., Harri, A.M., Hathi, B., Jernej, I., Leese, 196 M.R., Lehto, A., Lion Stoppato, P.F., L'opez-Moreno, J.J., Makinen, T., 197 McDonnell, J.A.M., McKay, C.P., Molina-Cuberos, G., Neubauer, F.M., 198 Pirronello, V., Rodrigo, R., Saggin, B., Schwingenschuh, K., Seiff, A., 199 Sim˜oes, F., Svedhem, H., Tokano, T., Towner, M.C., Trautner, R., With200 ers, P., Zarnecki, J.C., 2005. In situ measurements of the physical charac201 teristics of Titan's environment. Nature 438, 785-791. 202 Irwin, P.G.J., Teanby, N.A., de Kok, R., Fletcher, L.N., Howett, C.J.A., 203 Tsang, C.C.C., Wilson, C.F., Calcutt, S.B., Nixon, C.A., Parrish, P.D., 204 2008. The NEMESIS planetary atmosphere radiative transfer and retrieval 205 tool. J. Quant. Spectr. Rad. Trans. 109, 1136-1150. 206 Khare, B.N., Sagan, C., Arakawa, E.T., Suits, F., Callcott, T.A., Williams, 207 M.W., 1984. Optical constants of organic tholins produced in a simulated 208 Titanian atmosphere - From soft X-ray to microwave frequencies. Icarus 209 60, 127-137. 210 Marten, A., Hidayat, T., Biraud, Y., Moreno, R., 2002. New Millimeter 211 Heterodyne Observations of Titan: Vertical Distributions of Nitriles HCN, 212 HC 3 N, CH 3 CN, and the Isotopic Ratio 15 N/ 14 N in Its Atmosphere. Icarus 213 158, 532-544. 214 Moreno, R., Lellouch, E., Lara, L.M., Courtin, R., Bockel'ee-Morvan, D., 215 Hartogh, P., Rengel, M., Biver, N., Banaszkiewicz, M., Gonz'alez, A., 2011. 216 First detection of hydrogen isocyanide (HNC) in Titan's atmosphere. As217 tron. and Astrophys. 536, L12. 218 Niemann, H.B., Atreya, S.K., Carignan, G.R., Donahue, T.M., Haberman, 219 J.A., Harpold, D.N., Hartle, R.E., Hunten, D.M., Kasprzak, W.T., Ma220 haffy, P.R., Owen, T.C., Way, S.H., 1998. The composition of the Jovian 221 atmosphere as determined by the Galileo probe mass spectrometer. J. 222 Geophys. Res. 103, 22831-22846. 223 Niemann, H.B., Atreya, S.K., Demick, J.E., Gautier, D., Haberman, J.A., 224 Harpold, D.N., Kasprzak, W.T., Lunine, J.I., Owen, T.C., Raulin, F., 225 2010. Composition of Titan's lower atmosphere and simple surface volatiles 226 as measured by the Cassini-Huygens probe gas chromatograph mass spec227 trometer experiment. Journal of Geophysical Research (Planets) 115, 228 12006. 229 Nixon, C.A., Achterberg, R.K., Teanby, N.A., Irwin, P.G.J., Flaud, J.M., 230 Kleiner, I., Dehayem-Kamadjeu, A., Brown, L.R., Sams, R.L., B'ezard, 231 B., Coustenis, A., Ansty, T.M., Mamoutkine, A., Vinatier, S., Bjoraker, 232 G.L., Jennings, D.E., Romani, P.N., Flasar, F.M., 2010. Upper limits for 233 undetected trace species in the stratosphere of Titan. Faraday Discussions 234 147, 65. 1103.0297 . 235 Nixon, C.A., Jennings, D.E., Flaud, J.M., B'ezard, B., Teanby, N.A., Irwin, 236 P.G.J., Ansty, T.M., Coustenis, A., Vinatier, S., Flasar, F.M., 2009a. Ti237 tan's prolific propane: The Cassini CIRS perspective. Planetary and Space 238 Science 57, 1573-1585. 0909.1794 . 239 Nixon, C.A., Teanby, N.A., Calcutt, S.B., Aslam, S., Jennings, D.E., Kunde, 240 V.G., Flasar, F.M., Irwin, P.G., Taylor, F.W., Glenar, D.A., Smith, M.D., 241 2009b. Infrared limb sounding of Titan with the Cassini Composite In242 fraRed Spectrometer: effects of the mid-IR detector spatial responses. Ap243 plied Optics 48, 1912. 244 Nixon, C.A., Temelso, B., Vinatier, S., Teanby, N.A., B'ezard, B., Achterberg, 245 R.K., Mandt, K.E., Sherrill, C.D., Irwin, P.G.J., Jennings, D.E., Romani, 246 Rothman, L.S., Gordon, I.E., Barbe, A., Benner, D.C., Bernath, P.F., 255 Birk, M., Boudon, V., Brown, L.R., Campargue, A., Champion, J.P., 256 Chance, K., Coudert, L.H., Dana, V., Devi, V.M., Fally, S., Flaud, J.M., 257 Gamache, R.R., Goldman, A., Jacquemart, D., Kleiner, I., Lacome, N., 258 Lafferty, W.J., Mandin, J.Y., Massie, S.T., Mikhailenko, S.N., Miller, 259 C.E., Moazzen-Ahmadi, N., Naumenko, O.V., Nikitin, A.V., Orphal, J., 260 Perevalov, V.I., Perrin, A., Predoi-Cross, A., Rinsland, C.P., Rotger, M., 261 ˇ Simeˇckov'a, M., Smith, M.A.H., Sung, K., Tashkun, S.A., Tennyson, J., 262 Toth, R.A., Vandaele, A.C., Vander Auwera, J., 2009. The HITRAN 2008 263 molecular spectroscopic database. J. Quant. Spectr. Rad. Trans. 110, 533264 572. 265 Teanby, N.A., Irwin, P.G.J., de Kok, R., Jolly, A., B'ezard, B., Nixon, C.A., 266 Calcutt, S.B., 2009. Titan's stratospheric C 2 N 2 , C 3 H 4 , and C 4 H 2 abun267 dances from Cassini/CIRS far-infrared spectra. Icarus 202, 620-631. 268\",\n \"pages\": [\n 8,\n 9,\n 10,\n 11,\n 12\n ]\n }\n]"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":0,"numItemsPerPage":100,"numTotalItems":3838,"offset":0,"length":100}},"jwt":"eyJhbGciOiJFZERTQSJ9.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc0MTg2MzM3NSwic3ViIjoiL2RhdGFzZXRzL2FzaGlzaGtncGlhbi9hZHNwYXBlcnNfODBfODUiLCJleHAiOjE3NDE4NjY5NzUsImlzcyI6Imh0dHBzOi8vaHVnZ2luZ2ZhY2UuY28ifQ.ty2UZ-Xz3eaSd2KMJ-c5WeB5SMBpCi2riZ8Tk9AodWrp-p_0g227wY0REOMYYs-RqhYGtLLV_xszNSO3-A-kCw","displayUrls":true},"discussionsStats":{"closed":0,"open":0,"total":0},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false}">
<document>
<section_header_level_1><location><page_1><loc_26><loc_85><loc_76><loc_87></location>Heavy coronal ions in the heliosphere</section_header_level_1>
<section_header_level_1><location><page_1><loc_13><loc_82><loc_89><loc_83></location>II. Expected fluxes of energetic neutral He atoms from the heliosheath</section_header_level_1>
<text><location><page_1><loc_34><loc_80><loc_68><loc_81></location>S. Grzedzielski, P. Swaczyna, and M. Bzowski</text>
<text><location><page_1><loc_11><loc_77><loc_87><loc_78></location>Space Research Centre, Polish Academy of Sciences, Bartycka 18A, 00-716 Warsaw, Poland e-mail: [email protected]</text>
<text><location><page_1><loc_11><loc_74><loc_31><loc_75></location>Received [date] / Accepted [date]</text>
<section_header_level_1><location><page_1><loc_47><loc_72><loc_55><loc_73></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_66><loc_91><loc_71></location>Aims. A model of heliosheath density and energy spectra of GLYPH<11> -particles and He + ions carried by the solar wind is developed. Neutralization of heliosheath He ions, mainly by charge exchange (CX) with neutral interstellar H and He atoms, gives rise to GLYPH<24> 0.2 GLYPH<24> 100 keV fluxes of energetic neutral He atoms (He ENA). Such fluxes, if observed, would give information about plasmas in the heliosheath and heliospheric tail.</text>
<text><location><page_1><loc_11><loc_59><loc_91><loc_66></location>Methods. Helium ions crossing the termination shock (TS) constitute suprathermal (test) particles convected by (locally also di GLYPH<11> using through) hydrodynamically calculated background plasma flows (three versions of flows are employed). The He ions proceed from the TS towards heliopause (HP) and finally to the heliospheric tail (HT). Calculations of the evolution of GLYPH<11> - and He + particle densities and energy spectra include binary interactions with background plasma and interstellar atoms (radiative and dielectronic recombinations, single and double CX, stripping, photoionization and impact ionizations), adiabatic heating (cooling) resulting from flow compression (rarefaction), and Coulomb scattering on background plasma.</text>
<text><location><page_1><loc_11><loc_53><loc_91><loc_59></location>Results. Neutralization of suprathermal He ions leads to the emergence of He ENA fluxes with energy spectra modified by the Compton-Getting e GLYPH<11> ect at emission and ENA loss during flight to the Sun. Energy-integrated He ENA intensities are in the range GLYPH<24> 0.05 GLYPH<24> 50 cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 depending on spectra at the TS (assumed kappa-distributions), background plasma model, and look direction. The tail / apex intensity ratio varies between GLYPH<24> 1.8 and GLYPH<24> 800 depending on model assumptions. Energy spectra are broad with maxima in the GLYPH<24> 0.2 GLYPH<24> 3 keV range depending on the look direction and model.</text>
<text><location><page_1><loc_11><loc_50><loc_91><loc_53></location>Conclusions. Expected heliosheath He ENA fluxes may be measurable based on the capabilities of the IBEX spacecraft. Data could o GLYPH<11> er insight into the heliosheath structure and improve understanding of the post-TS solar wind plasmas. HT direction and extent could be assessed.</text>
<text><location><page_1><loc_11><loc_48><loc_85><loc_49></location>Key words. Sun: heliosphere - particle emission - Plasmas - Atomic processes - Accelerations of particles - ISM: atoms</text>
<section_header_level_1><location><page_1><loc_7><loc_43><loc_19><loc_45></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_20><loc_50><loc_42></location>Helium, as the second abundant ion species in the solar wind, should also be prominent in energetic neutral atom (ENA) fluxes from the heliosheath, resulting from the transcharge on neutral atom populations. Detection of these fluxes is contingent upon the energy of the He ENAs. It is known that He ions at interplanetary shocks do not equilibrate their downstream thermal energies with protons. SWICS experiment data obtained on board Ulysses s / c for 15 shocks at distances between 2.7 and 5.1 AU from the Sun indicate that the mean ratio of GLYPH<11> -to-protons downstream thermal velocities is 1 : 3 GLYPH<6> 0 : 3 (Berdichevsky et al. 1997). High thermal speeds of GLYPH<11> -particles (and pickup He + ) at shocks accompanied by enhanced high-energy power-law tails were also seen by Ulysses SWICS and HISCALE experiments in a reverse quasi-perpendicular CIR shock and also at the inbound pass of the quasi-parallel Jovian bow shock (Gloeckler et al. 2005). Instances of non-thermalization of He ions at Earth bowshock were reported and discussed by Liu et al. (2007).</text>
<text><location><page_1><loc_7><loc_10><loc_50><loc_20></location>All this suggests that the He ions in the heliosheath can be treated at injection, i.e. immediately upon crossing the TS, as thermally separate from the bulk of shocked solar wind plasma: the average post-shock energy should be close to the upstream energy in a solar frame, with tail distributions approximated by power laws in energy. The excess energy, compared to ideal gas dynamics, of the random motions of He ions in the heliosheath can probably persist for a long time. The Coulomb equilibra-</text>
<text><location><page_1><loc_52><loc_23><loc_95><loc_44></location>tion time for 1 keV / n GLYPH<11> -particles (i.e. bulk pre-TS He) with heliosheath thermal protons of number density GLYPH<24> 0.001 cm GLYPH<0> 3 and temperature GLYPH<24> 70 000 K (Richardson 2011) amounts to 5 GLYPH<2> 10 11 s, which is longer than the heliosheath residence time GLYPH<24> 10 9 s. Loss of energy through interaction with neutral H atoms in the heliosheath is also slow. For total stopping power for 1 keV / n GLYPH<11> -particles in H equal to 1120 MeVcm 2 g GLYPH<0> 1 (Berger et al. 2005) the characteristic time for GLYPH<11> -energy decay in neutral H density 0 : 2 cm GLYPH<0> 3 is GLYPH<24> 2 GLYPH<2> 10 11 s. All this suggests that He ions in the heliosheath will constitute a relatively hot particle population, with typical energies GLYPH<24> 0.5-1 keV / n, so well above the thermal proton plasma measured by Voyager, and with nonthermal tails reaching several keV / n. Neutralization of He ions, mainly by charge exchange with neutral interstellar H and He, should therefore lead to the emergence of fluxes of relatively energetic He ENAs. The aim of the present paper is to estimate the magnitude of theses fluxes and to look for the conditions for detection.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_20></location>Our approach is in part similar to the one used by Grzedzielski et al. (2010) to study the fate of solar-wind heavy ions in the heliosheath. The He ions are treated as test particles undergoing various binary interactions (BI), with other particle populations constituting the heliosheath plasma. This allows us to calculate (1) how the He ions change their charge states and energies, (2) what the emissivity of He ENA is as a function of energy for each point in the heliosheath, and (3) how many</text>
<text><location><page_2><loc_7><loc_91><loc_50><loc_93></location>of these ENAs, having survived losses on the way, will reach Earth's vicinity from a particular direction.</text>
<section_header_level_1><location><page_2><loc_7><loc_87><loc_22><loc_88></location>2. Physical model</section_header_level_1>
<text><location><page_2><loc_7><loc_71><loc_50><loc_86></location>In our model we follow the time evolution of charge states and energy of He ions in the heliosheath as solar wind plasma flows from the TS, towards the heliopause (HP), and finally to the heliospheric tail (HT). We treat GLYPH<11> -particles and He + ions as test particles, carried by the general flow, which undergo BI with background electrons and protons, with solar ionizing photons, and with neutral H and He atoms coming from interstellar space. In addition we take He ions energy changes into account due to (adiabatic) compression / decompression of the background flow, as well as energy change (in fact decrease) resulting from Coulomb scattering on plasma background and possible e GLYPH<11> ects of spatial di GLYPH<11> usion.</text>
<section_header_level_1><location><page_2><loc_7><loc_67><loc_38><loc_68></location>2.1. Evolution of helium ions in phase space</section_header_level_1>
<text><location><page_2><loc_7><loc_51><loc_50><loc_66></location>To describe the behavior of the two He ion species, GLYPH<11> -particles and He + ions, we calculate changes in the local velocity distribution functions f GLYPH<11> and f He + resulting from displacement of the considered plasma parcel along its flow line determined by the hydrodynamic time-independent solution for background plasma. The background flow is assumed to be stationary in time and axially symmetric, depending on distance r from the Sun and angle GLYPH<18> from the apex axis (cf. Sect. 2.3). The functions f GLYPH<11> and f He + are assumed to be isotropic in velocity space; that is, they are functions of the scalar momentum p . Their dependence on r and GLYPH<18> can be expressed as functions of the curvilinear coordinate s along the flow line or, equivalently, using</text>
<formula><location><page_2><loc_7><loc_48><loc_50><loc_50></location>d s = j v sw j d t ; (1)</formula>
<text><location><page_2><loc_7><loc_44><loc_50><loc_47></location>as functions of time t , i.e., the flow history of the parcel of background plasma. v sw describes the solar wind bulk velocity in the heliosheath.</text>
<text><location><page_2><loc_7><loc_40><loc_50><loc_44></location>The changes in f GLYPH<11> and f He + along the flow line are thus determined by coupled equations of the type used to describe the transport of cosmic rays (Jokipii 1987)</text>
<formula><location><page_2><loc_7><loc_34><loc_50><loc_39></location>v sw d d s f GLYPH<11> = 1 3 r GLYPH<1> v sw @ @ (ln p ) f GLYPH<11> + G BI ; He + ! GLYPH<11> GLYPH<0> L BI ;GLYPH<11> ! He + + GLYPH<0> L BI ;GLYPH<11> ! He GLYPH<0> L C ;GLYPH<23> GLYPH<11> n p GLYPH<15> GLYPH<0> L GLYPH<11>; H + r GLYPH<1> ( GLYPH<20> GLYPH<1> r f GLYPH<11> ) ; (2)</formula>
<formula><location><page_2><loc_7><loc_28><loc_50><loc_33></location>v sw d d s f He + = 1 3 r GLYPH<1> v sw @ @ (ln p ) f He + + G BI ;GLYPH<11> ! He + GLYPH<0> L BI ; He + ! GLYPH<11> + GLYPH<0> L BI ; He + ! He GLYPH<0> L C ;GLYPH<23> He + n p GLYPH<15> GLYPH<0> L He + ; H + r GLYPH<1> GLYPH<16> GLYPH<20> GLYPH<1> r f He + GLYPH<17> : (3)</formula>
<text><location><page_2><loc_7><loc_10><loc_50><loc_27></location>The successive terms on the righthand side of Eq. (2) describe changes in f GLYPH<11> due to adiabatic compression / rarefaction of the background flow, gain ( G BI ; He + ! GLYPH<11> ) from BI conversion of He + into GLYPH<11> , loss ( L BI ;GLYPH<11> ! He + ) from BI conversion of GLYPH<11> into He + , and loss ( L BI ;GLYPH<11> ! He) from BI conversion of GLYPH<11> into He, loss ( L C ;GLYPH<23> GLYPH<11> n p GLYPH<15> ) due to Coulomb scattering on background protons corresponding to energy loss rate GLYPH<23> GLYPH<11> n p GLYPH<15> as given by Huba (2002), and loss ( L GLYPH<11>; H) due to GLYPH<11> interaction with neutral hydrogen (Berger et al. 2005). The last term on the righthand side describes possible e GLYPH<11> ect of GLYPH<11> -particles spatial di GLYPH<11> usion, with corresponding tensorial di GLYPH<11> usion coe GLYPH<14> cient GLYPH<20> (cf. Sect. 2.4). Equation (3) is analogous to Eq. (2) with symbols GLYPH<11> and He + interchanged. Details on BI are given in Sect. 2.2.</text>
<text><location><page_2><loc_52><loc_80><loc_95><loc_93></location>Equations (2) and (3) do not contain Fokker-Planck type terms that would describe possible local stochastic acceleration. This acceleration is often invoked in the context of ACR populations, though its relevance - in view of the V1 and V2 data - is debatable (Florinski et al., 2011, 'The global heliosphere during the recent solar minimum' talk at the Solar Minimum Workshop, Boulder CO, May 17 - 19, 2011). Applying stochastic acceleration to the present context of GLYPH<24> keV ions would require a sound understanding of the small-scale magnetohydrodynamic turbulence in the heliosheath, which is lacking at present.</text>
<text><location><page_2><loc_52><loc_70><loc_95><loc_80></location>In numerical solution of Eqs. (2) and (3) we calculate the evolution of GLYPH<11> and He + spectra separately for each flow line. We set initial discretized spectra at the TS (cf. Sect. 2.5) and then calculate the evolution between adjacent points. Discretization is fixed at 500 bins between 0 km s GLYPH<0> 1 and 5000 km s GLYPH<0> 1 with a 10 km s GLYPH<0> 1 width each. As the plasma parcel proceeds along its flow line, particles are shu GLYPH<15> ed between bins as required by the interactions. This scheme is repeated for all flow lines.</text>
<text><location><page_2><loc_52><loc_56><loc_95><loc_69></location>To be able to calculate the righthand side of Eqs. (2) and (3), one should know, besides the relevant cross sections, the background solar plasma and neutral interstellar gas flows, e.g., the solar wind electron ( n e), proton ( n p) densities, the density distribution of interstellar neutral H and He ( n H, n He), as well as the corresponding bulk flow velocities of the heliosheath solar wind plasma ( v sw), interstellar gas ( v H), and the e GLYPH<11> ective relative velocities of particles at collisions ( v rel) resulting from local particle velocity distribution functions. Modeling of these functions is described in Sect. 2.3.</text>
<section_header_level_1><location><page_2><loc_52><loc_53><loc_83><loc_54></location>2.2. Binary interactions affecting the He ions</section_header_level_1>
<text><location><page_2><loc_52><loc_31><loc_95><loc_52></location>We assume that the He ions (test particles) are immersed in a substratum constituted by background heliosheath protons and electrons, background neutral H and He atoms of interstellar origin, and ionizing solar photons. The binary interactions include radiative and dielectronic recombinations, electron impact ionizations, photoionizations, double and single charge exchanges (also to upper levels), and electron stripping. The scheme of transitions between the charge states of He ions resulting from the interactions is shown in Fig. 1, in which the three levels describe He charge-states 0, + 1, + 2 and the arrows correspond to binary interactions denoted a, b, c, d, e, f, g, h, i, k, l, m (Table 1). As we look for He ENAs with velocities > 100 km s GLYPH<0> 1 (energy > 207 eV), we take the He + pickup ions born in the supersonic solar wind into account, while we disregard those originating in the heliosheath, where the relative velocity between heliosheath flow and interstellar neutral He atoms is rather low.</text>
<text><location><page_2><loc_52><loc_22><loc_95><loc_31></location>Interactions b, c, d, e, k, l, m shu GLYPH<15> e the ions between charge states 1 and 2. They preserve the total number of ionized He atoms. Interactions a, f, g, h, i convert He ions into He ENAs and are the source of presumed He ENA fluxes at Earth. Once a He ENA is born, it is assumed to be lost to the heliosheath He budget. Probability of reionization of a 1 keV He atom flying from 5000 AU in the tail to Earth is only 12%.</text>
<section_header_level_1><location><page_2><loc_52><loc_18><loc_78><loc_19></location>2.3. Heliosheath background plasma</section_header_level_1>
<text><location><page_2><loc_52><loc_10><loc_95><loc_17></location>The state of bulk solar wind plasma in the heliosheath is, at present, the subject of an intense debate brought about by unexpected results of the plasma experiment on board Voyager-2 (V2) (Richardson et al. 2008) during and after crossing(s) of the TS in Aug. / Sep. 2007. There is little doubt that the downwind (post-TS) plasma is in a very di GLYPH<11> erent state from what was</text>
<figure>
<location><page_3><loc_7><loc_81><loc_64><loc_93></location>
<caption>Table 1. Binary interactions determining charge-state changes of He ions in the heliosheath</caption>
</figure>
<table>
<location><page_3><loc_8><loc_58><loc_49><loc_73></location>
</table>
<text><location><page_3><loc_7><loc_51><loc_50><loc_55></location>Notes. e - electron, p - proton, GLYPH<11> -GLYPH<11> -particle, cx - charge exchange ( y ) A104 and similars symbols denote reactions as listed in (1) ( z ) (1) A88 for energy > 5 keV, excitation and / or emission involving upper levels includes (1) B90, B96, B102, B104</text>
<text><location><page_3><loc_7><loc_46><loc_50><loc_50></location>References. (1) Barnett (1990); (2) Arnaud & Rothenflug (1985); (3) Liu et al. (2003); (4) Aldrovandi & Pequignot (1973); (5) Bochsler et al. (2012); (6) Janev et al. (1987)</text>
<text><location><page_3><loc_7><loc_33><loc_50><loc_42></location>expected on the basis of standard Rankine-Hugoniot equations. The post-shock temperature of the majority (thermal) protons seems to be much lower ( GLYPH<24> 70 000 K) than expected in a singlefluid shock transition ( GLYPH<24> 10 6 K), and the bulk flow velocity starts to decrease well ahead of the shock with a much smaller velocity jump at the shock itself. Also the electron temperature seems to be quite low, T e < 10 eV (Richardson 2008).</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_33></location>In contrast, a relatively small fraction ( GLYPH<24> 10-30%) of postshock protons is endowed with energies of GLYPH<24> 1 to perhaps several keV. This nonthermal proton population, resulting presumably from ionized interstellar H atoms picked up by the supersonic solar wind, is thought to contain the bulk of total energy density (pressure) of the post-shock plasma. V2 data indicate such a situation seems to prevail deep into the post-shock plasma (Richardson 2011) with little spatial change observed in thermal proton density and temperature. Such conditions may exist in the frontal lobes and perhaps also in near tail of the heliosheath. Another important fact is a much faster than anticipated decline in heliosheath plasma bulk velocity derived from Voyager-1 (V1) data as the spacecraft receded from the TS in years 2005-2011 (Krimigis et al. 2011). In particular the simultaneous drastic decrease on Aug. 25, 2012 in the fluxes of ions of energies > 0 : 5 MeV / n observed by the LET telescopes of the cosmic ray subsystem instrument on board V1 and the accompanying increase in the magnetic field to about 0.41 nT</text>
<text><location><page_3><loc_66><loc_80><loc_95><loc_92></location>Fig. 1. Scheme of transitions between charge states of He resulting from the considered binary interaction with heliosheath background ion, electron, and neutral atom populations (cf. text). The heavy arrows denote transitions of greatest importance in most of heliosheath regions, the dashed arrow (crossed over) is the neglected production of low-energy He + ions. Emissivity (source funtion) of He ENA is determined by transitions a + f + g + h + i.</text>
<text><location><page_3><loc_52><loc_76><loc_95><loc_78></location>(ftp: // lepvgr.gsfc.nasa.gov / pub / voyager / ) seem to indicate that V1 might have crossed the heliopause around this date.</text>
<text><location><page_3><loc_52><loc_61><loc_95><loc_75></location>These results imply that the TS-HP stretch along V1 trajectory is only GLYPH<24> 121 : 5 GLYPH<0> 94 = GLYPH<24> 27 : 5 AU long; that is, the heliosheath is much narrower than GLYPH<24> 60 GLYPH<24> 100 AU obtained in gasdynamical modeling based on data available prior to V1 and V2 TS-crossings (e.g., in the Izmodenov & Alexashov (2003) model the distances Sun-TS and Sun-HP for ecliptic latitudes corresponding to the V2 trajectory are 110 AU and 208 AU, respectively). A narrow heliosheath of only 25 GLYPH<6> 8 AU thickness in the upwind region also comes out from the analysis of H ENA fluxes observed by the IBEX, SOHO / HSTOF, and Cassini / INCA spacecraft (Hsieh et al. 2010).</text>
<text><location><page_3><loc_52><loc_45><loc_95><loc_61></location>These new findings are at present not properly integrated and understood within a coherent physical picture. Despite the success of a realistic and time-varying description of the TS crossing positions by both Voyager spacecraft in a recent model by Washimi et al. (2011), the single-fluid MHD calculations employed therein are unable to render the nonthermal aspects of the particle distribution functions in the heliosheath that may be important for He ions physics. Therefore to numerically describe the background plasma flow conditions we employ three timeindependent, axisymmetric heliosheath models (denoted in the following: hydrodynamic, Parker, and ad hoc), corresponding to three simple variants of assumed heliosheath plasma.</text>
<text><location><page_3><loc_52><loc_16><loc_95><loc_45></location>The hydrodynamic model is the model developed by Izmodenov & Alexashov (2003) and used previously in Grzedzielski et al. (2010). The Parker and ad-hoc models, though not internally coherent in terms of physics, are 'tailored' in such a way as to approximately render the V2 suggested spatial distribution of variables decisive for the behavior of He ions: that is, thermal proton and electron densities ( n p, n e), temperatures ( T p, T e), as well as the main traits of the nonthermal plasma components. We also try to approximately render the common heliosheath bulk flow velocity ( v sw) along the V2 trajectory. For each variant, integration of Eqs. (2) and (3) is performed. In this way we follow the time evolution of the charge states, spatial distribution, and energy spectra of He ions in each fluid element carried by the background flow. This allows the local He ENA production rates to be calculated and - after accounting for He ENA energy losses and reionization on the way - we can construct expected He ENA spectra at Earth. The point is to test how sensitive the predicted He ENA fluxes are to the assumed widely discordant variants of plasma. We believe that if important common features of predicted He ENA fluxes appear in all considered cases, credence could be given to the results despite the partial inadequacy of the physical modeling employed.</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_16></location>In the hydrodynamic model , the background flow of solar plasma and neutral hydrogen atoms in the supersonic solar wind, inner heliosheath, and distant heliospheric tail is described as single-fluid, non-magnetic, gas-dynamical flow of heliospheric proton-electron plasma coupled by mass, momentum, and en-</text>
<text><location><page_4><loc_7><loc_83><loc_50><loc_93></location>ergy exchange with the neutral interstellar hydrogen atoms calculated kinetically (Monte-Carlo approach). The Sun as a source of solar wind and ionizing photons is assumed to be spherically symmetric, with the wind speed of 450 km s GLYPH<0> 1 , Mach number 10, and n p = 7 cm GLYPH<0> 3 at Earth orbit. At infinity, a uniform interstellar flow of 25 km s GLYPH<0> 1 with neutral hydrogen density n H ; LISM = 0 : 2 cm GLYPH<0> 3 , proton density n p ; LISM = 0 : 07 cm GLYPH<0> 3 , and temperature 6000 K was assumed.</text>
<text><location><page_4><loc_7><loc_68><loc_50><loc_82></location>Interstellar neutral He atoms are represented by a uniform substratum with density n He = 0 : 015 at : cm GLYPH<0> 3 (Gloeckler et al. 2004) flowing with velocity of 25 km s GLYPH<0> 1 . Because of axial symmetry, all variables depend on the radial distance r from the Sun and angle GLYPH<18> from the apex direction. The background flow is found in form of n p, n e, T p ( = T e) given as functions of distance s along individual flow lines. There are 180 flow lines, each starting at Earth's orbit. The flow lines are identified by the initial (1 AU) value of the angle GLYPH<18> . In this solution the TS and HP are, correspondingly, 102 and 177 AU distant from the Sun along the apex axis.</text>
<text><location><page_4><loc_7><loc_62><loc_50><loc_67></location>The shocked solar wind plasma is very hot immediately behind the TS ( T p = T e GLYPH<24> 10 6 K) and then cools down to about 20 000 K in the distant heliotail. The background plasma velocity distributions are always local Maxwellians.</text>
<text><location><page_4><loc_7><loc_31><loc_50><loc_61></location>The Parker model is the classical subsonic solution for a point source of incompressible fluid (stellar wind) in a uniform, incompressible external flow (Parker 1961). To be applicable, the model requires the TS radius much less than the distance Sun-HP. We assume that the solar wind mass source and the interstellar flow are the same as in the hydrodynamical model. The background velocities and shape of the flow lines are determined by the Parker analytical solution. Typical heliosheath velocities are in the range 120-250 km s GLYPH<0> 1 at GLYPH<24> 100 AU and tend to 170 km s GLYPH<0> 1 in the tail. We crudely approximate observed heliosheath plasma conditions by assuming constant heliosheath proton density to be constituted by two proton populations, the thermal one with n p ; th = 0 : 0015 cm GLYPH<0> 3 and another nonthermal one with n p ; nth = 0 : 0005 cm GLYPH<0> 3 . The proton energies are described by a Maxwellian with 70 000 K temperature and a monoenergetic population of 1.1 keV per proton, respectively. Electron temperature is set to T e = 3 eV. To conform to a smaller HP distance as presently envisaged (Krimigis et al. 2011) the Sun-HP stretch along the apex axis is set to 101 AU. The corresponding Sun-HP distance at the V2 ecliptic latitude is 83 : 7 + 27 : 5 = 111 : 2 AU. Comparison of proton density, bulk radial, and tangentional velocities measured in the heliosheath by V2 with the Parker model solution is shown in Fig. 2.</text>
<text><location><page_4><loc_7><loc_10><loc_50><loc_30></location>The ad hoc model was developed for this research. We include in it both the new (smaller) heliospheric scale and some of the new physical aspects of heliosheath plasmas. The solar wind mass source and the interstellar flow are again the same as in the hydrodynamic model. However, the background flow in the heliosheath is solved anew. We use the approximation that the flow along each of the flow lines is one-dimensional in a known channel of varying cross section A ( s ). The geometry of the channels is determined by the flow lines of the hydrodynamic model but linearly rescaled so as to place the termination shock (with shape conserved) at the observed distance of the V2 crossing, that is, at 83.7 AU from the Sun. In this rescaling, the heliopause is put at 111 : 2 AU (at V2 ecliptic latitude). The flow along the reshaped flow lines is found by integrating equations of conservation of mass, momentum, and energy with the appropriate source terms on the righthand side.</text>
<text><location><page_4><loc_54><loc_92><loc_90><loc_93></location>In a channel we have the mass conservation equation</text>
<formula><location><page_4><loc_52><loc_88><loc_95><loc_91></location>1 A d d s h A GLYPH<26> p v sw i = Q ; (4)</formula>
<text><location><page_4><loc_52><loc_77><loc_95><loc_87></location>where GLYPH<26> p is total (thermal + nonthermal) mass density of protons and v sw bulk plasma velocity in the heliosheath, and Q is the mass-loading term. We neglect the contribution of solar wind He ions and neutral interstellar He atoms to mass loading compared to the H contribution, and we also neglect electron impact ionization of H atoms because of low heliosheath electron temperature, T e = 3 eV. Mass loading results only from proton H-atom charge exchange and net Q = 0.</text>
<text><location><page_4><loc_52><loc_73><loc_95><loc_76></location>Momentum loading is nonvanishing, and we have in the equation of motion the frictional force (acting in direction s ) resulting from proton - H-atom charge exchange:</text>
<formula><location><page_4><loc_52><loc_69><loc_95><loc_71></location>1 A d d s h A GLYPH<26> p v 2 sw i = GLYPH<0> d d s p nth + GLYPH<27> ( v e GLYPH<11> ) v e GLYPH<11> n H GLYPH<26> p ( v H cos GLYPH<18> GLYPH<0> v sw) ; (5)</formula>
<text><location><page_4><loc_52><loc_55><loc_95><loc_68></location>where GLYPH<27> denotes the charge exchange cross section, and v e GLYPH<11> is the relative velocity between particles. In the energy equation we treat as small the kinetic energy of the bulk heliosheath flow, as well as the pressure of the thermal protons (kept at T p ; th = 70 000 K), and retain solely the terms proportional to the high pressure (energy) p nth, of the mono-energetic nonthermal proton population. We assume this energy (1) is convected with flow velocity v sw and (2) decays by charge exchange with interstellar H atoms on a time GLYPH<28> cx depending on particle energy. Then the equation takes the form</text>
<formula><location><page_4><loc_52><loc_51><loc_95><loc_54></location>1 A d d s GLYPH<2> Av sw GLYPH<13> p nth GLYPH<3> = ( GLYPH<13> GLYPH<0> 1) v sw d d s p nth GLYPH<0> p nth GLYPH<28> cx ; (6)</formula>
<text><location><page_4><loc_52><loc_36><loc_95><loc_50></location>where GLYPH<13> is the usual adiabatic exponent. In numerical calculations we assume the nonthermal population contains 25% of mass and average energy per proton at the TS is 1.1 keV (Giacalone & Decker 2010). This means that nonthermal protons contain 77% of the total energy associated with particle random motions. The bulk velocity on the TS downwind side is 150 km s GLYPH<0> 1 (Richardson et al. 2008) and the TS downwind density dependence on angle GLYPH<18> is like in the hydrodynamic model but rescaled to the new TS position. The fit of the ad hoc model solution to V2 measurements in the heliosheath for proton density, radial, and tangential velocities is shown in Fig. 3.</text>
<text><location><page_4><loc_52><loc_29><loc_95><loc_35></location>The density in the ad hoc model seems to be too high by a factor GLYPH<24> 2. A number of causes could be responsible, among them time-dependent e GLYPH<11> ects in the solar wind flow (our modeling always uses an 'average' solar wind model) and / or heliosheath asymmetry resulting from a skewed interstellar magnetic field.</text>
<section_header_level_1><location><page_4><loc_52><loc_26><loc_89><loc_27></location>2.4. Adiabatic heating/cooling versus spatial diffusion</section_header_level_1>
<text><location><page_4><loc_52><loc_13><loc_95><loc_25></location>Changes in background plasma density along the flow line induce He ion energy changes that can be treated as adiabatic if di GLYPH<11> usion is slow enough. We made an estimate of the possible role of di GLYPH<11> usion in the case of the hydrodynamic model. To find regions in the heliosheath in which di GLYPH<11> usion of GLYPH<11> -particles is negligible we use a simplified version of Eq. (2) treated as the transport equation for pressure p GLYPH<11> of the GLYPH<11> -particle cosmic ray gas (Drury & Voelk 1981). In this approximation Eq. (2) becomes</text>
<formula><location><page_4><loc_52><loc_9><loc_95><loc_12></location>d d t p GLYPH<11> GLYPH<13> GLYPH<0> 1 ! = r GLYPH<1> " GLYPH<20> r p GLYPH<11> GLYPH<13> GLYPH<0> 1 !# + GLYPH<13> GLYPH<13> GLYPH<0> 1 p GLYPH<11> GLYPH<26> d GLYPH<26> d t ; (7)</formula>
<figure>
<location><page_5><loc_8><loc_78><loc_94><loc_94></location>
<caption>Fig. 2. Comparison of heliosheath proton density (left panel), radial velocity (middle panel), and tangential velocity (right panel) in the Parker model with corresponding in situ measurements (Richardson 2011) along the orbit of Voyager 2.</caption>
</figure>
<figure>
<location><page_5><loc_8><loc_59><loc_94><loc_74></location>
<caption>Fig. 3. Comparison of heliosheath proton density (left panel), radial velocity (middle panel), and tangential velocity (right panel) in the ad hoc model with corresponding in situ measurements (Richardson 2011) along the orbit of Voyager 2.</caption>
</figure>
<text><location><page_5><loc_7><loc_35><loc_50><loc_53></location>in which GLYPH<26> is the background plasma density. We assume diffusion is negligible as long as the first term on the righthand side (e GLYPH<11> ect of di GLYPH<11> usion) is much less than the second term (adiabatic heating / cooling). The heliosheath di GLYPH<11> usion coe GLYPH<14> cient for low-energy GLYPH<11> -particles is in fact unknown. It depends most probably on heliosheath turbulence. Models for the superposition of slab and 2-D turbulence were developed for the solar wind (Zank et al. 2004), but it is unclear how the assumed (2:8) energy partition between the two modes of turbulence corresponds to real heliosheath conditions. Therefore we take simply two limiting formulae as crude guesses: (i) Bohm di GLYPH<11> usion, GLYPH<20> B, and (ii) phenomenological di GLYPH<11> usion by le Roux et al. (1996) originally developed for the ACR ions, GLYPH<20> ACR. We extrapolate them to our GLYPH<11> -particle energies. In both formulae we assume GLYPH<20> is scalar.</text>
<text><location><page_5><loc_7><loc_10><loc_50><loc_34></location>Because di GLYPH<11> usion coe GLYPH<14> cients (i) and (ii) di GLYPH<11> er, for the range of energies discussed ( GLYPH<24> 0.2 - 20 keV, cf. Sect. 3) by 4.5 to 5.5 orders of magnitudes, we also take for comparison (iii) an intermediary di GLYPH<11> usion coe GLYPH<14> cient equal to ( GLYPH<20> B GLYPH<20> ACR) 1 = 2 . In calculating the values of the first term on the righthand side of Eq. (7) along the flow line, one has to use the local value of the heliosheath magnetic field B hsh. As the detailed structure of B hsh is unknown, we calculate B hsh along the flow line assuming the field starts on the downwind side of the TS with a value of 0.1 nT as measured by Burlaga et al. (2005, 2008) (variation in the magnetic field along the TS surface was described by standard dependence on angle / distance). Further evolution of the field then followed from background plasma density variations. In this we assumed that the magnetic field is frozen to background plasma, its direction is randomly oriented and plasma compression / decompression is isotropic, i.e. B hsh / (background plasma density) 2 = 3 . In this way one can construct maps of the ratio of first-to-second terms on the righthand side of Eq. (7) in the heliosheath. The maps are shown for values of the said ratio equal to 1 / 100 and 1 / 10 in</text>
<text><location><page_5><loc_52><loc_44><loc_95><loc_53></location>Fig. 4. They correspond to GLYPH<20> = GLYPH<20> B and GLYPH<20> = ( GLYPH<20> B GLYPH<20> ACR) 1 = 2 and to GLYPH<11> -particle energies at injection, peaking at energy corresponding to 170 km s GLYPH<0> 1 (cf. Sect. 2.5). Figure 4 suggests that neglect of di GLYPH<11> usion is justified for both di GLYPH<11> usion versions (i) and (iii). For version (ii) di GLYPH<11> usion is a paramount e GLYPH<11> ect, but this case is hardly realistic for the low energies discussed here. Di GLYPH<11> usion e GLYPH<11> ects obtained for He + ions are similar.</text>
<text><location><page_5><loc_52><loc_32><loc_95><loc_43></location>In the Parker model di GLYPH<11> usion does not exist because of assumed uniform background plasma density. In the ad hoc model, the density distribution is quite flat (cf. Fig. 3, left panel), so diffusion is also negligible. In solving Eqs. (2) and (3) we therefore always consistently retain the adiabatic cooling / heating term (first on the righthand side). Energy variations due to these terms are moderate; for instance, energy increase along the flow line starting at GLYPH<18> = 5 GLYPH<14> at the TS from apex, does not exceed a factor 1.5 at its maximum.</text>
<section_header_level_1><location><page_5><loc_52><loc_27><loc_93><loc_29></location>2.5. Density distributions and energy spectra of GLYPH<11> -particles and He + ions in the heliosheath</section_header_level_1>
<text><location><page_5><loc_52><loc_10><loc_95><loc_25></location>The GLYPH<11> -particles ( n GLYPH<11> ) and He + ions ( n He + ) density distributions and energy spectra are calculated for the three background flow models (hydrodynamic, Parker, ad hoc, Sect. 2.3) by integrating Eqs. (2) and (3) along 180 flow lines. The approximations and procedures we adopted are described in Sects. 2.2, 2.3 and 2.4. Consistent treatment applies e GLYPH<11> ectively to the interval (100, 2000) km s GLYPH<0> 1 corresponding to energy range 0.207 - 82.9 keV for He ions. The initial values of n GLYPH<11> and n He + are stated at the TS for the hydrodynamic and ad hoc models, assuming that the total He content of the solar wind constitutes 5% of the local proton plasma (by number). For the Parker model they are stated at the distance fitted to TS crossing by V2.</text>
<text><location><page_6><loc_54><loc_93><loc_55><loc_93></location>1</text>
<text><location><page_6><loc_55><loc_93><loc_55><loc_93></location>/Slash1</text>
<text><location><page_6><loc_55><loc_93><loc_55><loc_93></location>2</text>
<figure>
<location><page_6><loc_7><loc_78><loc_65><loc_93></location>
<caption>Fig. 4. Heliosheath map of regions (light-gray areas) where in the hydrodynamic model the ratio of the 1st-to-2nd terms on the righthand side of. Eq. (7) is < 1 = 100 (lower panels) and < 1 = 10 (upper panels); that is, the role of diffusion is small. Left column is for Bohm diffusion, case (i); right column for ( GLYPH<20> B GLYPH<20> ACR) 1 = 2 , case(iii).</caption>
</figure>
<text><location><page_6><loc_7><loc_55><loc_50><loc_76></location>Two variants of injected (initial) GLYPH<11> -particle energy distributions at the TS were taken: one peaking at energy 0.6 keV, which corresponds to velocity 170 km s GLYPH<0> 1 (in the following we label this variant '170 km s GLYPH<0> 1 '), the other peaking at energy 2.1 keV, which corresponds to 320 km s GLYPH<0> 1 (we label this variant '320 kms GLYPH<0> 1 '). These energies were chosen because the first one could correspond to the case when excess post-TS energy of an GLYPH<11> -particle is coming from the bulk velocity jump at the TS, and the second to the case when excess energy is approximately equal to total bulk kinetic energy at the shock (Richardson et al. 2008) (cf. Sects. 1 and 2.3). In both variants the initial velocity distribution shape is the same: a kappa-distribution with GLYPH<20> = 2 : 5. This value was chosen because it corresponds to the borderline between the near-equilibrium region applicable to heavy solar wind ions and the far-equilibrium region corresponding to the inner heliosheath (Livadiotis & McComas 2011, cf. their Fig. 2).</text>
<text><location><page_6><loc_7><loc_42><loc_50><loc_55></location>The initial population of He + at the TS is made up of (a) solar wind GLYPH<11> -particles singly-decharged during their flight to the TS and (b) pickup He + produced by neutral interstellar He ionization in the supersonic solar wind region. Based on solar wind as in the hydrodynamic model, we estimated that group (a) amounts to 0.0005 (by number) of the proton content. For group (b) the corresponding number is 0.002 (Rucinski et al. 2003). Initial spectra for He + group (a) at the TS are the same as those for GLYPH<11> -particles. For He + group (b) we consistently use only one initial spectrum: a kappa( = 2.5)-distribution that peaks at 4 keV.</text>
<text><location><page_6><loc_7><loc_24><loc_50><loc_41></location>Energetic He ion heliosheath density distributions and energy spectra obtained from integration of Eqs. (2) and (3) are shown in Fig. 5 for variants '170 km s GLYPH<0> 1 ' and '320 km s GLYPH<0> 1 '. The lefthand column of panels corresponds to '170 km s GLYPH<0> 1 ', the righthand one to '320 km s GLYPH<0> 1 '. Each row corresponds to one of the three models employed (top to bottom: hydrodynamic, ad hoc, Parker). Upper (lower) half of each heliosphere map refers to GLYPH<11> -particles (He + ions). To give some feeling of the evolution of energy spectra, above and below each map we show four panels with ion energy spectra corresponding to spatial positions labeled I, II, III, IV. As indicated, all these points lie on the same flow line starting at the TS at a point 90 GLYPH<14> away from the apex as seen from the Sun.</text>
<text><location><page_6><loc_7><loc_15><loc_50><loc_24></location>Figure 5 illustrates some of the basic physics of He-ion behavior. First densities per energy interval are much lower for He + than for GLYPH<11> -particles. This reflects the di GLYPH<11> erences in the injection at the TS. However, second, while the GLYPH<11> -particles shift to lower energies when we go from point I to IV with monotonically decreasing spectra preserved, the He + ions often develop maxima at mid-energy range, even though they decline at high energy.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_15></location>This has two main causes. One is that, on the whole, energetic He ions lose energy on average because of Coulomb scattering on the plasma background. Though adiabatic compression may overturn this process, this happens only locally in the</text>
<text><location><page_6><loc_52><loc_67><loc_95><loc_76></location>upwind heliosheath. In the end, both Coulomb scattering and general decompression towards the tail have to take over. The other cause is related to the circumstance that conversion of GLYPH<11> s into He + is, in practice, a one-way process. This comes from the high ionization potential of He + . Therefore while locally heated GLYPH<11> s may later resupply the mid energies of the He + population, no similar process operates in the opposite direction.</text>
<text><location><page_6><loc_52><loc_56><loc_95><loc_66></location>Insight into the situation in the upwind heliosheath for the hydrodynamic model can be gathered from Fig. 6, which shows expanded maps of the frontal part of heliosphere in a similar format to Fig. 5. The points I to IV are now shown along a flow line starting at a TS point 15 GLYPH<14> away from the apex. The energy maxima of the He + ions are more pronounced here than in Fig. 5. This is due to more e GLYPH<11> ective heating by compression in the frontal heliosheath.</text>
<section_header_level_1><location><page_6><loc_52><loc_53><loc_92><loc_54></location>3. Expected He ENA fluxes from the heliosheath</section_header_level_1>
<text><location><page_6><loc_52><loc_38><loc_95><loc_52></location>The local emissivity (source function) j ENA (cm GLYPH<0> 3 s GLYPH<0> 1 keV GLYPH<0> 1 ) of He ENA is determined by the product of reagents' densities and reaction rates (i.e. relative velocity times cross section, cm 3 s GLYPH<0> 1 ) for BI a, f, g, h, i (Sect. 2.2). All these quantities can be found as functions of position in the three heliosheath models (hydrodynamic, Parker, ad hoc) by procedures described in Sects. 2.1, 2.2, 2.3, 2.4, and 2.5. The He ENA intensity I ENA( E ; GLYPH<18> ) (cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 keV GLYPH<0> 1 ) of particles of energy E coming from the direction at angle GLYPH<18> from the apex is expressed as a line-of-sight (LOS) integral of the source function from the TS to HP</text>
<formula><location><page_6><loc_65><loc_37><loc_66><loc_37></location>r</formula>
<formula><location><page_6><loc_52><loc_31><loc_95><loc_37></location>I ENA( E ; GLYPH<18> ) = L sw Z HP r TS j ENA( E ; r ;GLYPH<18> ) 4 GLYPH<25> F CG( E ; GLYPH<18>; v sw) GLYPH<2> exp " GLYPH<0> Z r r TS GLYPH<28> ext( r 0 ) v ENA d r 0 # d r : (8)</formula>
<text><location><page_6><loc_52><loc_12><loc_95><loc_30></location>Formula (8) contains corrections for re-ionization losses in the heliosheath and in the supersonic solar wind, as well as a correction ( F CG) for the Compton-Getting e GLYPH<11> ect. The losses in the heliosheath were calculated for BI as listed in Table 2. In Eq. (8) they are described by the e GLYPH<11> ective depth GLYPH<28> ext for extinction of He ENA with velocity v ENA. The main contributions to heliosheath losses come from reactions a, i, and s. In the hydrodynamic model, He ENA reionization by electron impact is also of some importance in view of the high electron temperature. The ionization losses in the supersonic solar wind ( L sw) are mainly due to reaction p (photoionization) in Table 2, with a small contribution from reaction q inside the orbit of Mars (Bzowski et al. 2012). On the whole, losses inside the supersonic solar wind are much less important than those in the heliosheath.</text>
<text><location><page_6><loc_52><loc_10><loc_95><loc_12></location>The value of F CG depends on He ENA energy E in the observer's frame and the velocity of the source carried by the back-</text>
<figure>
<location><page_7><loc_11><loc_23><loc_47><loc_93></location>
</figure>
<figure>
<location><page_7><loc_55><loc_23><loc_91><loc_93></location>
<caption>Fig. 5. Calculated density distributions and energy spectra of heliosheath energetic He ions for the hydrodynamic, Parker, and ad hoc models. Upper / middle / lower rows correspond to hydrodynamic / ad hoc / Parker models. Left column of the panels corresponds to the peak velocity of the initial kappa-distributions of GLYPH<11> -particles injected at TS equal to 170 km s GLYPH<0> 1 ; right column, correspondingly, to 320 km s GLYPH<0> 1 . He + injection as described in the text. In a given row, the upper (lower) half of each heliosphere map represents density distribution of GLYPH<11> -particles (He + ions). Distance scale is in AU. Density scales (equal for GLYPH<11> -particles and He + ions only in the two upper rows) are indicated on vertical strips on the right side of each half-heliosphere map. Small panels placed above (below) maps illustrate the evolution of energy spectra of GLYPH<11> -particles (He + ions) as the background plasma parcel is carried over points I, II, III, IV along the flow line. The line starting at the TS point 90 GLYPH<14> away from the apex is shown. Horizontal (vertical) axis in small panels describes ion energy in keV (ion density in cm GLYPH<0> 3 keV GLYPH<0> 1 ).</caption>
</figure>
<figure>
<location><page_8><loc_11><loc_70><loc_47><loc_93></location>
</figure>
<figure>
<location><page_8><loc_55><loc_70><loc_91><loc_93></location>
<caption>Fig. 6. Calculated heliosheath energetic He-ion density distributions and energy spectra for the frontal part of heliosphere (in the hydrodynamic model). Injection data in left panel correspond to '170 km s GLYPH<0> 1 ', right panel to '320 km s GLYPH<0> 1 '. Other details similar to Fig. 5, except that the flow line shown starts at a TS point 15 GLYPH<14> away from the apex.</caption>
</figure>
<table>
<location><page_8><loc_12><loc_47><loc_45><loc_58></location>
<caption>Table 2. Binary interactions determining He ENA losses in the heliosheath</caption>
</table>
<text><location><page_8><loc_7><loc_42><loc_50><loc_45></location>Notes. e - electron, p - proton, H - hydrogen atom, GLYPH<11> -GLYPH<11> -particle, cx charge exchange;</text>
<text><location><page_8><loc_7><loc_41><loc_20><loc_42></location>( z ) same as in Table 1</text>
<text><location><page_8><loc_7><loc_38><loc_50><loc_40></location>References. (1) Barnett (1990); (2) Cummings et al. (2002); (3) Janev et al. (1987)</text>
<text><location><page_8><loc_7><loc_27><loc_50><loc_36></location>ground relative to the Sun ( v sw) for a given model. F CG is a function of angular distance GLYPH<18> of the LOS from apex. It is calculated for an observer at rest, at 1 AU from the Sun in the direction of incoming ENA, with solar gravity neglected. F CG is particularly significant in reducing energy of He ENA coming from the upwind heliosheath in the ad hoc model, in which background flow recedes quickly from the Sun.</text>
<text><location><page_8><loc_7><loc_19><loc_50><loc_26></location>The dependence of total He ENA intensity (integrated over energy range 0.2 - 50 keV and with losses included) on angle GLYPH<18> from the apex is shown in Fig. 7 for the hydrodynamic, Parker, and ad hoc models for two assumed variants of GLYPH<11> -population injected at the TS ('170 km s GLYPH<0> 1 ' and '320 km s GLYPH<0> 1 ') and He + injection as in Sect. 2.5.</text>
<text><location><page_8><loc_7><loc_10><loc_50><loc_19></location>Results presented in Fig. 7 indicate that expected energyintegrated intensities of He ENA seem to depend more on the background model than to be sensitive to the energy of He ions injected to the inner heliosheath plasma at the TS. However, in all three models the intensity from the tail is greatest and ranges from a few ENA (cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 ) for the hydrodynamic and Parker models to a few tens of ENA (cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 ) for the ad hoc</text>
<text><location><page_8><loc_52><loc_51><loc_95><loc_62></location>model. The fluxes from upwind are smaller than those from the tail, but the di GLYPH<11> erence is marginal for the hydrodynamic model. The decrease is only by a factor GLYPH<24> 1.8. This is an e GLYPH<11> ect of the He ion decharging relatively close to the Sun in the hydrodynamic model compared to other models. On the other hand, the tail / upwind contrast is significant for the Parker and ad hoc models (ratios of GLYPH<24> 60 and GLYPH<24> 800, respectively). Detection from the tail should therefore be the easiest, and the contrast tail / upwind may tell something about background plasma conditions.</text>
<text><location><page_8><loc_52><loc_38><loc_95><loc_51></location>Details on the dependence of He ENA energy spectra on model and angle GLYPH<18> are given in Fig. 8 in which rows from top to bottom correspond to upwind ( GLYPH<18> = 10 GLYPH<14> ), crosswind ( GLYPH<18> = 90 GLYPH<14> ), and tail ( GLYPH<18> = 170 GLYPH<14> ) directions, for two variants of injection, '170 km s GLYPH<0> 1 ' (left panels) and '320 km s GLYPH<0> 1 ' (right panels). In all cases the spectra are broad in energy with maxima at < ' 1 keV for '170 km s GLYPH<0> 1 ' and between GLYPH<24> 0.5 to GLYPH<24> 5 keV for '320 km s GLYPH<0> 1 '. Most energetic tail spectra are obtained in the ad hoc model. On the whole, the spectral region GLYPH<24> 0.5 GLYPH<24> 5 keV seems to be the most promising for detecting He ENA.</text>
<section_header_level_1><location><page_8><loc_52><loc_34><loc_82><loc_35></location>4. Final discussion and conclusions</section_header_level_1>
<text><location><page_8><loc_52><loc_18><loc_95><loc_33></location>Calculating the heliosheath production of ENAs out of heavy solar ions that capture electrons from neutral interstellar atoms is basically a straightforward exercise, if ion densities are estimated, the flux of interstellar neutrals is measured, and particle collision velocities can be calculated based on simple assumptions. This would apply if the state of background plasma were determined by hydrodynamics and if heavy ions (treated as test particles) were heavy enough to be weakly coupled to the background and therefore were able to preserve energies they had at the TS. Such an approach has been used in the past (Grzedzielski et al. 2010) to follow de-ionization of multicharged coronal ions of C, O, N, Mg, Si, and S carried by the solar wind.</text>
<text><location><page_8><loc_52><loc_10><loc_95><loc_17></location>In the present paper that deals with light ions such as GLYPH<11> -particles and He + , we have been faced with the situation that, on one hand, the interaction with the background plasma can be more important and, on the other, the evidently non-single fluid state of the background (as established by Voyager) a GLYPH<11> ects various binary interactions to degrees that have not been assessed</text>
<figure>
<location><page_9><loc_9><loc_71><loc_93><loc_93></location>
<caption>Fig. 7. Total He ENA intensities (integrated over energy range 0.2 - 50 keV and with losses included) as a function of angle GLYPH<18> from the apex for the hydrodynamic, Parker, and ad hoc models, and two variants of GLYPH<11> -particle injection at the TS: '170 km s GLYPH<0> 1 ' - left panel and '320 km s GLYPH<0> 1 ' - right panel (Sect. 2.5). He + injection is as described in Sect. 2.5.</caption>
</figure>
<table>
<location><page_9><loc_7><loc_42><loc_50><loc_60></location>
<caption>Table 3. Expected energy-integrated He ENA intensities</caption>
</table>
<text><location><page_9><loc_7><loc_35><loc_50><loc_37></location>reliably. This can make the outcome very sensitive to details of heliosheath modeling.</text>
<text><location><page_9><loc_7><loc_28><loc_50><loc_34></location>In view of the present lack of understanding what goes on in heliosheath plasmas, we tried to explore the range of expected He ENA fluxes for some simple models covering a wide gamut of possibilities. If a feature has emerged in all models, one may presume it has some relevance.</text>
<text><location><page_9><loc_7><loc_10><loc_50><loc_28></location>As explained in Sect. 2.3, we employed three simple descriptions of heliosheath plasma background: hydrodynamic model by Izmodenov & Alexashov (2003); classical Parker model; ad hoc model attempting to partially render the V1 & V2 measured heliosheath data. These models cover a fairly wide range of possibilities. For all three models we followed the evolution of GLYPH<11> -particles and He + ions (isotropic) momentum distribution functions in phase space (Sects. 2.1, 2.2, 2.4), calculated heliosheath density distributions and energy spectra (Sect. 2.5), and estimated He ENA energy fluxes expected at Earth (Sect. 3). The last estimates are essentially the observables given in Table 3. The data are organized following assumed peak injection energy of He-ions at the TS (cases '170 km s GLYPH<0> 1 ' and '320 km s GLYPH<0> 1 ', cf. Sect. 2.5).</text>
<text><location><page_9><loc_52><loc_51><loc_95><loc_64></location>IBEX is the first mission dedicated to the astronomy of energetic neutral atoms (McComas 2009). It features two singlepixel, neutral atom cameras: IBEX-Hi (Funsten et al. 2009) and IBEX-Lo (Fuselier et al. 2009). Basically only IBEX-Lo has the capability of discerning species of the incoming atoms, including (indirectly) neutral He (Mobius et al. 2009), and IBEX-Hi was designed to observe neutral H. Allegrini et al. (2008) suggest an ingeneous technique by which some other species, including He, might also be registered owing to a special treatment of data from the IBEX-Hi anti-coincidence system.</text>
<text><location><page_9><loc_52><loc_19><loc_95><loc_50></location>Results of this paper suggest that detecting maximum predicted fluxes might be within the reach of IBEX instrumentation. The full possibilities of He ENAs measurements have not as yet been published, but the possibility of detection depends critically on the ratio of He ENA to H ENA fluxes (Allegrini et al. 2008). Based on published detection e GLYPH<14> ciencies (Allegrini et al. 2008, Fig. 2) and H ENA fluxes given by McComas et al. (2010) we preliminarily estimate that He ENA intensities predicted by our modeling could be measured from the heliospheric tail direction alone. For the ad hoc model predictions, the measurements should be possible in the IBEX-Hi energy channels 1.1, 2.7, and 4.3 keV, both for the '170 km s GLYPH<0> 1 ' and '320 km s GLYPH<0> 1 ' variants. For the hydrodynamic model predictions, the measurement might be marginally feasible at 2.7 keV for the '320 km s GLYPH<0> 1 ' variant. In all considered models, maximum He ENA flux should come from the tail, though the e GLYPH<11> ect may be only marginal for the hydrodynamic model (cf. fluxes given in Table 3). If an angular tail-upwind decrease in the ENA signal could be measured, this might help to better pinpoint the essential physics of interactions. Maximum signal from the tail should also be related to maximum tail extension, which could help determine the direction of heliosphere wake, independently of the IBEX hydrogen data as in McComas et al. (2012), with obvious inferences concerning the interstellar medium state.</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_17></location>Since the expected He ENA intensity at 1 AU from the Sun strongly depends on the conditions in the inner heliosheath, He ENAdetection, if accomplished, may become an important asset in diagnosing the physical state of the innner heliosheath plasma with embedded He ions, as a complement to diagnosing via H ENA currently performed by IBEX.</text>
<figure>
<location><page_10><loc_8><loc_28><loc_93><loc_93></location>
<caption>Fig. 8. Expected energy spectra of He ENA (cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 keV GLYPH<0> 1 ) from the heliosheath. Left / right column - TS injection variants '170 km s GLYPH<0> 1 ' / '320 km s GLYPH<0> 1 '. Upper / middle / lower row of panels - LOS angle GLYPH<18> from apex 10 GLYPH<14> / 90 GLYPH<14> / 170 GLYPH<14> . For hydrodynamic / Parker / ad hoc models, the result is denoted by a solid / dashed / dotted line.</caption>
</figure>
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[
{
"title": "ABSTRACT",
"content": "Aims. A model of heliosheath density and energy spectra of GLYPH<11> -particles and He + ions carried by the solar wind is developed. Neutralization of heliosheath He ions, mainly by charge exchange (CX) with neutral interstellar H and He atoms, gives rise to GLYPH<24> 0.2 GLYPH<24> 100 keV fluxes of energetic neutral He atoms (He ENA). Such fluxes, if observed, would give information about plasmas in the heliosheath and heliospheric tail. Methods. Helium ions crossing the termination shock (TS) constitute suprathermal (test) particles convected by (locally also di GLYPH<11> using through) hydrodynamically calculated background plasma flows (three versions of flows are employed). The He ions proceed from the TS towards heliopause (HP) and finally to the heliospheric tail (HT). Calculations of the evolution of GLYPH<11> - and He + particle densities and energy spectra include binary interactions with background plasma and interstellar atoms (radiative and dielectronic recombinations, single and double CX, stripping, photoionization and impact ionizations), adiabatic heating (cooling) resulting from flow compression (rarefaction), and Coulomb scattering on background plasma. Results. Neutralization of suprathermal He ions leads to the emergence of He ENA fluxes with energy spectra modified by the Compton-Getting e GLYPH<11> ect at emission and ENA loss during flight to the Sun. Energy-integrated He ENA intensities are in the range GLYPH<24> 0.05 GLYPH<24> 50 cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 depending on spectra at the TS (assumed kappa-distributions), background plasma model, and look direction. The tail / apex intensity ratio varies between GLYPH<24> 1.8 and GLYPH<24> 800 depending on model assumptions. Energy spectra are broad with maxima in the GLYPH<24> 0.2 GLYPH<24> 3 keV range depending on the look direction and model. Conclusions. Expected heliosheath He ENA fluxes may be measurable based on the capabilities of the IBEX spacecraft. Data could o GLYPH<11> er insight into the heliosheath structure and improve understanding of the post-TS solar wind plasmas. HT direction and extent could be assessed. Key words. Sun: heliosphere - particle emission - Plasmas - Atomic processes - Accelerations of particles - ISM: atoms",
"pages": [
1
]
},
{
"title": "II. Expected fluxes of energetic neutral He atoms from the heliosheath",
"content": "S. Grzedzielski, P. Swaczyna, and M. Bzowski Space Research Centre, Polish Academy of Sciences, Bartycka 18A, 00-716 Warsaw, Poland e-mail: [email protected] Received [date] / Accepted [date]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Helium, as the second abundant ion species in the solar wind, should also be prominent in energetic neutral atom (ENA) fluxes from the heliosheath, resulting from the transcharge on neutral atom populations. Detection of these fluxes is contingent upon the energy of the He ENAs. It is known that He ions at interplanetary shocks do not equilibrate their downstream thermal energies with protons. SWICS experiment data obtained on board Ulysses s / c for 15 shocks at distances between 2.7 and 5.1 AU from the Sun indicate that the mean ratio of GLYPH<11> -to-protons downstream thermal velocities is 1 : 3 GLYPH<6> 0 : 3 (Berdichevsky et al. 1997). High thermal speeds of GLYPH<11> -particles (and pickup He + ) at shocks accompanied by enhanced high-energy power-law tails were also seen by Ulysses SWICS and HISCALE experiments in a reverse quasi-perpendicular CIR shock and also at the inbound pass of the quasi-parallel Jovian bow shock (Gloeckler et al. 2005). Instances of non-thermalization of He ions at Earth bowshock were reported and discussed by Liu et al. (2007). All this suggests that the He ions in the heliosheath can be treated at injection, i.e. immediately upon crossing the TS, as thermally separate from the bulk of shocked solar wind plasma: the average post-shock energy should be close to the upstream energy in a solar frame, with tail distributions approximated by power laws in energy. The excess energy, compared to ideal gas dynamics, of the random motions of He ions in the heliosheath can probably persist for a long time. The Coulomb equilibra- tion time for 1 keV / n GLYPH<11> -particles (i.e. bulk pre-TS He) with heliosheath thermal protons of number density GLYPH<24> 0.001 cm GLYPH<0> 3 and temperature GLYPH<24> 70 000 K (Richardson 2011) amounts to 5 GLYPH<2> 10 11 s, which is longer than the heliosheath residence time GLYPH<24> 10 9 s. Loss of energy through interaction with neutral H atoms in the heliosheath is also slow. For total stopping power for 1 keV / n GLYPH<11> -particles in H equal to 1120 MeVcm 2 g GLYPH<0> 1 (Berger et al. 2005) the characteristic time for GLYPH<11> -energy decay in neutral H density 0 : 2 cm GLYPH<0> 3 is GLYPH<24> 2 GLYPH<2> 10 11 s. All this suggests that He ions in the heliosheath will constitute a relatively hot particle population, with typical energies GLYPH<24> 0.5-1 keV / n, so well above the thermal proton plasma measured by Voyager, and with nonthermal tails reaching several keV / n. Neutralization of He ions, mainly by charge exchange with neutral interstellar H and He, should therefore lead to the emergence of fluxes of relatively energetic He ENAs. The aim of the present paper is to estimate the magnitude of theses fluxes and to look for the conditions for detection. Our approach is in part similar to the one used by Grzedzielski et al. (2010) to study the fate of solar-wind heavy ions in the heliosheath. The He ions are treated as test particles undergoing various binary interactions (BI), with other particle populations constituting the heliosheath plasma. This allows us to calculate (1) how the He ions change their charge states and energies, (2) what the emissivity of He ENA is as a function of energy for each point in the heliosheath, and (3) how many of these ENAs, having survived losses on the way, will reach Earth's vicinity from a particular direction.",
"pages": [
1,
2
]
},
{
"title": "2. Physical model",
"content": "In our model we follow the time evolution of charge states and energy of He ions in the heliosheath as solar wind plasma flows from the TS, towards the heliopause (HP), and finally to the heliospheric tail (HT). We treat GLYPH<11> -particles and He + ions as test particles, carried by the general flow, which undergo BI with background electrons and protons, with solar ionizing photons, and with neutral H and He atoms coming from interstellar space. In addition we take He ions energy changes into account due to (adiabatic) compression / decompression of the background flow, as well as energy change (in fact decrease) resulting from Coulomb scattering on plasma background and possible e GLYPH<11> ects of spatial di GLYPH<11> usion.",
"pages": [
2
]
},
{
"title": "2.1. Evolution of helium ions in phase space",
"content": "To describe the behavior of the two He ion species, GLYPH<11> -particles and He + ions, we calculate changes in the local velocity distribution functions f GLYPH<11> and f He + resulting from displacement of the considered plasma parcel along its flow line determined by the hydrodynamic time-independent solution for background plasma. The background flow is assumed to be stationary in time and axially symmetric, depending on distance r from the Sun and angle GLYPH<18> from the apex axis (cf. Sect. 2.3). The functions f GLYPH<11> and f He + are assumed to be isotropic in velocity space; that is, they are functions of the scalar momentum p . Their dependence on r and GLYPH<18> can be expressed as functions of the curvilinear coordinate s along the flow line or, equivalently, using as functions of time t , i.e., the flow history of the parcel of background plasma. v sw describes the solar wind bulk velocity in the heliosheath. The changes in f GLYPH<11> and f He + along the flow line are thus determined by coupled equations of the type used to describe the transport of cosmic rays (Jokipii 1987) The successive terms on the righthand side of Eq. (2) describe changes in f GLYPH<11> due to adiabatic compression / rarefaction of the background flow, gain ( G BI ; He + ! GLYPH<11> ) from BI conversion of He + into GLYPH<11> , loss ( L BI ;GLYPH<11> ! He + ) from BI conversion of GLYPH<11> into He + , and loss ( L BI ;GLYPH<11> ! He) from BI conversion of GLYPH<11> into He, loss ( L C ;GLYPH<23> GLYPH<11> n p GLYPH<15> ) due to Coulomb scattering on background protons corresponding to energy loss rate GLYPH<23> GLYPH<11> n p GLYPH<15> as given by Huba (2002), and loss ( L GLYPH<11>; H) due to GLYPH<11> interaction with neutral hydrogen (Berger et al. 2005). The last term on the righthand side describes possible e GLYPH<11> ect of GLYPH<11> -particles spatial di GLYPH<11> usion, with corresponding tensorial di GLYPH<11> usion coe GLYPH<14> cient GLYPH<20> (cf. Sect. 2.4). Equation (3) is analogous to Eq. (2) with symbols GLYPH<11> and He + interchanged. Details on BI are given in Sect. 2.2. Equations (2) and (3) do not contain Fokker-Planck type terms that would describe possible local stochastic acceleration. This acceleration is often invoked in the context of ACR populations, though its relevance - in view of the V1 and V2 data - is debatable (Florinski et al., 2011, 'The global heliosphere during the recent solar minimum' talk at the Solar Minimum Workshop, Boulder CO, May 17 - 19, 2011). Applying stochastic acceleration to the present context of GLYPH<24> keV ions would require a sound understanding of the small-scale magnetohydrodynamic turbulence in the heliosheath, which is lacking at present. In numerical solution of Eqs. (2) and (3) we calculate the evolution of GLYPH<11> and He + spectra separately for each flow line. We set initial discretized spectra at the TS (cf. Sect. 2.5) and then calculate the evolution between adjacent points. Discretization is fixed at 500 bins between 0 km s GLYPH<0> 1 and 5000 km s GLYPH<0> 1 with a 10 km s GLYPH<0> 1 width each. As the plasma parcel proceeds along its flow line, particles are shu GLYPH<15> ed between bins as required by the interactions. This scheme is repeated for all flow lines. To be able to calculate the righthand side of Eqs. (2) and (3), one should know, besides the relevant cross sections, the background solar plasma and neutral interstellar gas flows, e.g., the solar wind electron ( n e), proton ( n p) densities, the density distribution of interstellar neutral H and He ( n H, n He), as well as the corresponding bulk flow velocities of the heliosheath solar wind plasma ( v sw), interstellar gas ( v H), and the e GLYPH<11> ective relative velocities of particles at collisions ( v rel) resulting from local particle velocity distribution functions. Modeling of these functions is described in Sect. 2.3.",
"pages": [
2
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},
{
"title": "2.2. Binary interactions affecting the He ions",
"content": "We assume that the He ions (test particles) are immersed in a substratum constituted by background heliosheath protons and electrons, background neutral H and He atoms of interstellar origin, and ionizing solar photons. The binary interactions include radiative and dielectronic recombinations, electron impact ionizations, photoionizations, double and single charge exchanges (also to upper levels), and electron stripping. The scheme of transitions between the charge states of He ions resulting from the interactions is shown in Fig. 1, in which the three levels describe He charge-states 0, + 1, + 2 and the arrows correspond to binary interactions denoted a, b, c, d, e, f, g, h, i, k, l, m (Table 1). As we look for He ENAs with velocities > 100 km s GLYPH<0> 1 (energy > 207 eV), we take the He + pickup ions born in the supersonic solar wind into account, while we disregard those originating in the heliosheath, where the relative velocity between heliosheath flow and interstellar neutral He atoms is rather low. Interactions b, c, d, e, k, l, m shu GLYPH<15> e the ions between charge states 1 and 2. They preserve the total number of ionized He atoms. Interactions a, f, g, h, i convert He ions into He ENAs and are the source of presumed He ENA fluxes at Earth. Once a He ENA is born, it is assumed to be lost to the heliosheath He budget. Probability of reionization of a 1 keV He atom flying from 5000 AU in the tail to Earth is only 12%.",
"pages": [
2
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},
{
"title": "2.3. Heliosheath background plasma",
"content": "The state of bulk solar wind plasma in the heliosheath is, at present, the subject of an intense debate brought about by unexpected results of the plasma experiment on board Voyager-2 (V2) (Richardson et al. 2008) during and after crossing(s) of the TS in Aug. / Sep. 2007. There is little doubt that the downwind (post-TS) plasma is in a very di GLYPH<11> erent state from what was Notes. e - electron, p - proton, GLYPH<11> -GLYPH<11> -particle, cx - charge exchange ( y ) A104 and similars symbols denote reactions as listed in (1) ( z ) (1) A88 for energy > 5 keV, excitation and / or emission involving upper levels includes (1) B90, B96, B102, B104 References. (1) Barnett (1990); (2) Arnaud & Rothenflug (1985); (3) Liu et al. (2003); (4) Aldrovandi & Pequignot (1973); (5) Bochsler et al. (2012); (6) Janev et al. (1987) expected on the basis of standard Rankine-Hugoniot equations. The post-shock temperature of the majority (thermal) protons seems to be much lower ( GLYPH<24> 70 000 K) than expected in a singlefluid shock transition ( GLYPH<24> 10 6 K), and the bulk flow velocity starts to decrease well ahead of the shock with a much smaller velocity jump at the shock itself. Also the electron temperature seems to be quite low, T e < 10 eV (Richardson 2008). In contrast, a relatively small fraction ( GLYPH<24> 10-30%) of postshock protons is endowed with energies of GLYPH<24> 1 to perhaps several keV. This nonthermal proton population, resulting presumably from ionized interstellar H atoms picked up by the supersonic solar wind, is thought to contain the bulk of total energy density (pressure) of the post-shock plasma. V2 data indicate such a situation seems to prevail deep into the post-shock plasma (Richardson 2011) with little spatial change observed in thermal proton density and temperature. Such conditions may exist in the frontal lobes and perhaps also in near tail of the heliosheath. Another important fact is a much faster than anticipated decline in heliosheath plasma bulk velocity derived from Voyager-1 (V1) data as the spacecraft receded from the TS in years 2005-2011 (Krimigis et al. 2011). In particular the simultaneous drastic decrease on Aug. 25, 2012 in the fluxes of ions of energies > 0 : 5 MeV / n observed by the LET telescopes of the cosmic ray subsystem instrument on board V1 and the accompanying increase in the magnetic field to about 0.41 nT Fig. 1. Scheme of transitions between charge states of He resulting from the considered binary interaction with heliosheath background ion, electron, and neutral atom populations (cf. text). The heavy arrows denote transitions of greatest importance in most of heliosheath regions, the dashed arrow (crossed over) is the neglected production of low-energy He + ions. Emissivity (source funtion) of He ENA is determined by transitions a + f + g + h + i. (ftp: // lepvgr.gsfc.nasa.gov / pub / voyager / ) seem to indicate that V1 might have crossed the heliopause around this date. These results imply that the TS-HP stretch along V1 trajectory is only GLYPH<24> 121 : 5 GLYPH<0> 94 = GLYPH<24> 27 : 5 AU long; that is, the heliosheath is much narrower than GLYPH<24> 60 GLYPH<24> 100 AU obtained in gasdynamical modeling based on data available prior to V1 and V2 TS-crossings (e.g., in the Izmodenov & Alexashov (2003) model the distances Sun-TS and Sun-HP for ecliptic latitudes corresponding to the V2 trajectory are 110 AU and 208 AU, respectively). A narrow heliosheath of only 25 GLYPH<6> 8 AU thickness in the upwind region also comes out from the analysis of H ENA fluxes observed by the IBEX, SOHO / HSTOF, and Cassini / INCA spacecraft (Hsieh et al. 2010). These new findings are at present not properly integrated and understood within a coherent physical picture. Despite the success of a realistic and time-varying description of the TS crossing positions by both Voyager spacecraft in a recent model by Washimi et al. (2011), the single-fluid MHD calculations employed therein are unable to render the nonthermal aspects of the particle distribution functions in the heliosheath that may be important for He ions physics. Therefore to numerically describe the background plasma flow conditions we employ three timeindependent, axisymmetric heliosheath models (denoted in the following: hydrodynamic, Parker, and ad hoc), corresponding to three simple variants of assumed heliosheath plasma. The hydrodynamic model is the model developed by Izmodenov & Alexashov (2003) and used previously in Grzedzielski et al. (2010). The Parker and ad-hoc models, though not internally coherent in terms of physics, are 'tailored' in such a way as to approximately render the V2 suggested spatial distribution of variables decisive for the behavior of He ions: that is, thermal proton and electron densities ( n p, n e), temperatures ( T p, T e), as well as the main traits of the nonthermal plasma components. We also try to approximately render the common heliosheath bulk flow velocity ( v sw) along the V2 trajectory. For each variant, integration of Eqs. (2) and (3) is performed. In this way we follow the time evolution of the charge states, spatial distribution, and energy spectra of He ions in each fluid element carried by the background flow. This allows the local He ENA production rates to be calculated and - after accounting for He ENA energy losses and reionization on the way - we can construct expected He ENA spectra at Earth. The point is to test how sensitive the predicted He ENA fluxes are to the assumed widely discordant variants of plasma. We believe that if important common features of predicted He ENA fluxes appear in all considered cases, credence could be given to the results despite the partial inadequacy of the physical modeling employed. In the hydrodynamic model , the background flow of solar plasma and neutral hydrogen atoms in the supersonic solar wind, inner heliosheath, and distant heliospheric tail is described as single-fluid, non-magnetic, gas-dynamical flow of heliospheric proton-electron plasma coupled by mass, momentum, and en- ergy exchange with the neutral interstellar hydrogen atoms calculated kinetically (Monte-Carlo approach). The Sun as a source of solar wind and ionizing photons is assumed to be spherically symmetric, with the wind speed of 450 km s GLYPH<0> 1 , Mach number 10, and n p = 7 cm GLYPH<0> 3 at Earth orbit. At infinity, a uniform interstellar flow of 25 km s GLYPH<0> 1 with neutral hydrogen density n H ; LISM = 0 : 2 cm GLYPH<0> 3 , proton density n p ; LISM = 0 : 07 cm GLYPH<0> 3 , and temperature 6000 K was assumed. Interstellar neutral He atoms are represented by a uniform substratum with density n He = 0 : 015 at : cm GLYPH<0> 3 (Gloeckler et al. 2004) flowing with velocity of 25 km s GLYPH<0> 1 . Because of axial symmetry, all variables depend on the radial distance r from the Sun and angle GLYPH<18> from the apex direction. The background flow is found in form of n p, n e, T p ( = T e) given as functions of distance s along individual flow lines. There are 180 flow lines, each starting at Earth's orbit. The flow lines are identified by the initial (1 AU) value of the angle GLYPH<18> . In this solution the TS and HP are, correspondingly, 102 and 177 AU distant from the Sun along the apex axis. The shocked solar wind plasma is very hot immediately behind the TS ( T p = T e GLYPH<24> 10 6 K) and then cools down to about 20 000 K in the distant heliotail. The background plasma velocity distributions are always local Maxwellians. The Parker model is the classical subsonic solution for a point source of incompressible fluid (stellar wind) in a uniform, incompressible external flow (Parker 1961). To be applicable, the model requires the TS radius much less than the distance Sun-HP. We assume that the solar wind mass source and the interstellar flow are the same as in the hydrodynamical model. The background velocities and shape of the flow lines are determined by the Parker analytical solution. Typical heliosheath velocities are in the range 120-250 km s GLYPH<0> 1 at GLYPH<24> 100 AU and tend to 170 km s GLYPH<0> 1 in the tail. We crudely approximate observed heliosheath plasma conditions by assuming constant heliosheath proton density to be constituted by two proton populations, the thermal one with n p ; th = 0 : 0015 cm GLYPH<0> 3 and another nonthermal one with n p ; nth = 0 : 0005 cm GLYPH<0> 3 . The proton energies are described by a Maxwellian with 70 000 K temperature and a monoenergetic population of 1.1 keV per proton, respectively. Electron temperature is set to T e = 3 eV. To conform to a smaller HP distance as presently envisaged (Krimigis et al. 2011) the Sun-HP stretch along the apex axis is set to 101 AU. The corresponding Sun-HP distance at the V2 ecliptic latitude is 83 : 7 + 27 : 5 = 111 : 2 AU. Comparison of proton density, bulk radial, and tangentional velocities measured in the heliosheath by V2 with the Parker model solution is shown in Fig. 2. The ad hoc model was developed for this research. We include in it both the new (smaller) heliospheric scale and some of the new physical aspects of heliosheath plasmas. The solar wind mass source and the interstellar flow are again the same as in the hydrodynamic model. However, the background flow in the heliosheath is solved anew. We use the approximation that the flow along each of the flow lines is one-dimensional in a known channel of varying cross section A ( s ). The geometry of the channels is determined by the flow lines of the hydrodynamic model but linearly rescaled so as to place the termination shock (with shape conserved) at the observed distance of the V2 crossing, that is, at 83.7 AU from the Sun. In this rescaling, the heliopause is put at 111 : 2 AU (at V2 ecliptic latitude). The flow along the reshaped flow lines is found by integrating equations of conservation of mass, momentum, and energy with the appropriate source terms on the righthand side. In a channel we have the mass conservation equation where GLYPH<26> p is total (thermal + nonthermal) mass density of protons and v sw bulk plasma velocity in the heliosheath, and Q is the mass-loading term. We neglect the contribution of solar wind He ions and neutral interstellar He atoms to mass loading compared to the H contribution, and we also neglect electron impact ionization of H atoms because of low heliosheath electron temperature, T e = 3 eV. Mass loading results only from proton H-atom charge exchange and net Q = 0. Momentum loading is nonvanishing, and we have in the equation of motion the frictional force (acting in direction s ) resulting from proton - H-atom charge exchange: where GLYPH<27> denotes the charge exchange cross section, and v e GLYPH<11> is the relative velocity between particles. In the energy equation we treat as small the kinetic energy of the bulk heliosheath flow, as well as the pressure of the thermal protons (kept at T p ; th = 70 000 K), and retain solely the terms proportional to the high pressure (energy) p nth, of the mono-energetic nonthermal proton population. We assume this energy (1) is convected with flow velocity v sw and (2) decays by charge exchange with interstellar H atoms on a time GLYPH<28> cx depending on particle energy. Then the equation takes the form where GLYPH<13> is the usual adiabatic exponent. In numerical calculations we assume the nonthermal population contains 25% of mass and average energy per proton at the TS is 1.1 keV (Giacalone & Decker 2010). This means that nonthermal protons contain 77% of the total energy associated with particle random motions. The bulk velocity on the TS downwind side is 150 km s GLYPH<0> 1 (Richardson et al. 2008) and the TS downwind density dependence on angle GLYPH<18> is like in the hydrodynamic model but rescaled to the new TS position. The fit of the ad hoc model solution to V2 measurements in the heliosheath for proton density, radial, and tangential velocities is shown in Fig. 3. The density in the ad hoc model seems to be too high by a factor GLYPH<24> 2. A number of causes could be responsible, among them time-dependent e GLYPH<11> ects in the solar wind flow (our modeling always uses an 'average' solar wind model) and / or heliosheath asymmetry resulting from a skewed interstellar magnetic field.",
"pages": [
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},
{
"title": "2.4. Adiabatic heating/cooling versus spatial diffusion",
"content": "Changes in background plasma density along the flow line induce He ion energy changes that can be treated as adiabatic if di GLYPH<11> usion is slow enough. We made an estimate of the possible role of di GLYPH<11> usion in the case of the hydrodynamic model. To find regions in the heliosheath in which di GLYPH<11> usion of GLYPH<11> -particles is negligible we use a simplified version of Eq. (2) treated as the transport equation for pressure p GLYPH<11> of the GLYPH<11> -particle cosmic ray gas (Drury & Voelk 1981). In this approximation Eq. (2) becomes in which GLYPH<26> is the background plasma density. We assume diffusion is negligible as long as the first term on the righthand side (e GLYPH<11> ect of di GLYPH<11> usion) is much less than the second term (adiabatic heating / cooling). The heliosheath di GLYPH<11> usion coe GLYPH<14> cient for low-energy GLYPH<11> -particles is in fact unknown. It depends most probably on heliosheath turbulence. Models for the superposition of slab and 2-D turbulence were developed for the solar wind (Zank et al. 2004), but it is unclear how the assumed (2:8) energy partition between the two modes of turbulence corresponds to real heliosheath conditions. Therefore we take simply two limiting formulae as crude guesses: (i) Bohm di GLYPH<11> usion, GLYPH<20> B, and (ii) phenomenological di GLYPH<11> usion by le Roux et al. (1996) originally developed for the ACR ions, GLYPH<20> ACR. We extrapolate them to our GLYPH<11> -particle energies. In both formulae we assume GLYPH<20> is scalar. Because di GLYPH<11> usion coe GLYPH<14> cients (i) and (ii) di GLYPH<11> er, for the range of energies discussed ( GLYPH<24> 0.2 - 20 keV, cf. Sect. 3) by 4.5 to 5.5 orders of magnitudes, we also take for comparison (iii) an intermediary di GLYPH<11> usion coe GLYPH<14> cient equal to ( GLYPH<20> B GLYPH<20> ACR) 1 = 2 . In calculating the values of the first term on the righthand side of Eq. (7) along the flow line, one has to use the local value of the heliosheath magnetic field B hsh. As the detailed structure of B hsh is unknown, we calculate B hsh along the flow line assuming the field starts on the downwind side of the TS with a value of 0.1 nT as measured by Burlaga et al. (2005, 2008) (variation in the magnetic field along the TS surface was described by standard dependence on angle / distance). Further evolution of the field then followed from background plasma density variations. In this we assumed that the magnetic field is frozen to background plasma, its direction is randomly oriented and plasma compression / decompression is isotropic, i.e. B hsh / (background plasma density) 2 = 3 . In this way one can construct maps of the ratio of first-to-second terms on the righthand side of Eq. (7) in the heliosheath. The maps are shown for values of the said ratio equal to 1 / 100 and 1 / 10 in Fig. 4. They correspond to GLYPH<20> = GLYPH<20> B and GLYPH<20> = ( GLYPH<20> B GLYPH<20> ACR) 1 = 2 and to GLYPH<11> -particle energies at injection, peaking at energy corresponding to 170 km s GLYPH<0> 1 (cf. Sect. 2.5). Figure 4 suggests that neglect of di GLYPH<11> usion is justified for both di GLYPH<11> usion versions (i) and (iii). For version (ii) di GLYPH<11> usion is a paramount e GLYPH<11> ect, but this case is hardly realistic for the low energies discussed here. Di GLYPH<11> usion e GLYPH<11> ects obtained for He + ions are similar. In the Parker model di GLYPH<11> usion does not exist because of assumed uniform background plasma density. In the ad hoc model, the density distribution is quite flat (cf. Fig. 3, left panel), so diffusion is also negligible. In solving Eqs. (2) and (3) we therefore always consistently retain the adiabatic cooling / heating term (first on the righthand side). Energy variations due to these terms are moderate; for instance, energy increase along the flow line starting at GLYPH<18> = 5 GLYPH<14> at the TS from apex, does not exceed a factor 1.5 at its maximum.",
"pages": [
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},
{
"title": "2.5. Density distributions and energy spectra of GLYPH<11> -particles and He + ions in the heliosheath",
"content": "The GLYPH<11> -particles ( n GLYPH<11> ) and He + ions ( n He + ) density distributions and energy spectra are calculated for the three background flow models (hydrodynamic, Parker, ad hoc, Sect. 2.3) by integrating Eqs. (2) and (3) along 180 flow lines. The approximations and procedures we adopted are described in Sects. 2.2, 2.3 and 2.4. Consistent treatment applies e GLYPH<11> ectively to the interval (100, 2000) km s GLYPH<0> 1 corresponding to energy range 0.207 - 82.9 keV for He ions. The initial values of n GLYPH<11> and n He + are stated at the TS for the hydrodynamic and ad hoc models, assuming that the total He content of the solar wind constitutes 5% of the local proton plasma (by number). For the Parker model they are stated at the distance fitted to TS crossing by V2. 1 /Slash1 2 Two variants of injected (initial) GLYPH<11> -particle energy distributions at the TS were taken: one peaking at energy 0.6 keV, which corresponds to velocity 170 km s GLYPH<0> 1 (in the following we label this variant '170 km s GLYPH<0> 1 '), the other peaking at energy 2.1 keV, which corresponds to 320 km s GLYPH<0> 1 (we label this variant '320 kms GLYPH<0> 1 '). These energies were chosen because the first one could correspond to the case when excess post-TS energy of an GLYPH<11> -particle is coming from the bulk velocity jump at the TS, and the second to the case when excess energy is approximately equal to total bulk kinetic energy at the shock (Richardson et al. 2008) (cf. Sects. 1 and 2.3). In both variants the initial velocity distribution shape is the same: a kappa-distribution with GLYPH<20> = 2 : 5. This value was chosen because it corresponds to the borderline between the near-equilibrium region applicable to heavy solar wind ions and the far-equilibrium region corresponding to the inner heliosheath (Livadiotis & McComas 2011, cf. their Fig. 2). The initial population of He + at the TS is made up of (a) solar wind GLYPH<11> -particles singly-decharged during their flight to the TS and (b) pickup He + produced by neutral interstellar He ionization in the supersonic solar wind region. Based on solar wind as in the hydrodynamic model, we estimated that group (a) amounts to 0.0005 (by number) of the proton content. For group (b) the corresponding number is 0.002 (Rucinski et al. 2003). Initial spectra for He + group (a) at the TS are the same as those for GLYPH<11> -particles. For He + group (b) we consistently use only one initial spectrum: a kappa( = 2.5)-distribution that peaks at 4 keV. Energetic He ion heliosheath density distributions and energy spectra obtained from integration of Eqs. (2) and (3) are shown in Fig. 5 for variants '170 km s GLYPH<0> 1 ' and '320 km s GLYPH<0> 1 '. The lefthand column of panels corresponds to '170 km s GLYPH<0> 1 ', the righthand one to '320 km s GLYPH<0> 1 '. Each row corresponds to one of the three models employed (top to bottom: hydrodynamic, ad hoc, Parker). Upper (lower) half of each heliosphere map refers to GLYPH<11> -particles (He + ions). To give some feeling of the evolution of energy spectra, above and below each map we show four panels with ion energy spectra corresponding to spatial positions labeled I, II, III, IV. As indicated, all these points lie on the same flow line starting at the TS at a point 90 GLYPH<14> away from the apex as seen from the Sun. Figure 5 illustrates some of the basic physics of He-ion behavior. First densities per energy interval are much lower for He + than for GLYPH<11> -particles. This reflects the di GLYPH<11> erences in the injection at the TS. However, second, while the GLYPH<11> -particles shift to lower energies when we go from point I to IV with monotonically decreasing spectra preserved, the He + ions often develop maxima at mid-energy range, even though they decline at high energy. This has two main causes. One is that, on the whole, energetic He ions lose energy on average because of Coulomb scattering on the plasma background. Though adiabatic compression may overturn this process, this happens only locally in the upwind heliosheath. In the end, both Coulomb scattering and general decompression towards the tail have to take over. The other cause is related to the circumstance that conversion of GLYPH<11> s into He + is, in practice, a one-way process. This comes from the high ionization potential of He + . Therefore while locally heated GLYPH<11> s may later resupply the mid energies of the He + population, no similar process operates in the opposite direction. Insight into the situation in the upwind heliosheath for the hydrodynamic model can be gathered from Fig. 6, which shows expanded maps of the frontal part of heliosphere in a similar format to Fig. 5. The points I to IV are now shown along a flow line starting at a TS point 15 GLYPH<14> away from the apex. The energy maxima of the He + ions are more pronounced here than in Fig. 5. This is due to more e GLYPH<11> ective heating by compression in the frontal heliosheath.",
"pages": [
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},
{
"title": "3. Expected He ENA fluxes from the heliosheath",
"content": "The local emissivity (source function) j ENA (cm GLYPH<0> 3 s GLYPH<0> 1 keV GLYPH<0> 1 ) of He ENA is determined by the product of reagents' densities and reaction rates (i.e. relative velocity times cross section, cm 3 s GLYPH<0> 1 ) for BI a, f, g, h, i (Sect. 2.2). All these quantities can be found as functions of position in the three heliosheath models (hydrodynamic, Parker, ad hoc) by procedures described in Sects. 2.1, 2.2, 2.3, 2.4, and 2.5. The He ENA intensity I ENA( E ; GLYPH<18> ) (cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 keV GLYPH<0> 1 ) of particles of energy E coming from the direction at angle GLYPH<18> from the apex is expressed as a line-of-sight (LOS) integral of the source function from the TS to HP Formula (8) contains corrections for re-ionization losses in the heliosheath and in the supersonic solar wind, as well as a correction ( F CG) for the Compton-Getting e GLYPH<11> ect. The losses in the heliosheath were calculated for BI as listed in Table 2. In Eq. (8) they are described by the e GLYPH<11> ective depth GLYPH<28> ext for extinction of He ENA with velocity v ENA. The main contributions to heliosheath losses come from reactions a, i, and s. In the hydrodynamic model, He ENA reionization by electron impact is also of some importance in view of the high electron temperature. The ionization losses in the supersonic solar wind ( L sw) are mainly due to reaction p (photoionization) in Table 2, with a small contribution from reaction q inside the orbit of Mars (Bzowski et al. 2012). On the whole, losses inside the supersonic solar wind are much less important than those in the heliosheath. The value of F CG depends on He ENA energy E in the observer's frame and the velocity of the source carried by the back- Notes. e - electron, p - proton, H - hydrogen atom, GLYPH<11> -GLYPH<11> -particle, cx charge exchange; ( z ) same as in Table 1 References. (1) Barnett (1990); (2) Cummings et al. (2002); (3) Janev et al. (1987) ground relative to the Sun ( v sw) for a given model. F CG is a function of angular distance GLYPH<18> of the LOS from apex. It is calculated for an observer at rest, at 1 AU from the Sun in the direction of incoming ENA, with solar gravity neglected. F CG is particularly significant in reducing energy of He ENA coming from the upwind heliosheath in the ad hoc model, in which background flow recedes quickly from the Sun. The dependence of total He ENA intensity (integrated over energy range 0.2 - 50 keV and with losses included) on angle GLYPH<18> from the apex is shown in Fig. 7 for the hydrodynamic, Parker, and ad hoc models for two assumed variants of GLYPH<11> -population injected at the TS ('170 km s GLYPH<0> 1 ' and '320 km s GLYPH<0> 1 ') and He + injection as in Sect. 2.5. Results presented in Fig. 7 indicate that expected energyintegrated intensities of He ENA seem to depend more on the background model than to be sensitive to the energy of He ions injected to the inner heliosheath plasma at the TS. However, in all three models the intensity from the tail is greatest and ranges from a few ENA (cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 ) for the hydrodynamic and Parker models to a few tens of ENA (cm GLYPH<0> 2 s GLYPH<0> 1 sr GLYPH<0> 1 ) for the ad hoc model. The fluxes from upwind are smaller than those from the tail, but the di GLYPH<11> erence is marginal for the hydrodynamic model. The decrease is only by a factor GLYPH<24> 1.8. This is an e GLYPH<11> ect of the He ion decharging relatively close to the Sun in the hydrodynamic model compared to other models. On the other hand, the tail / upwind contrast is significant for the Parker and ad hoc models (ratios of GLYPH<24> 60 and GLYPH<24> 800, respectively). Detection from the tail should therefore be the easiest, and the contrast tail / upwind may tell something about background plasma conditions. Details on the dependence of He ENA energy spectra on model and angle GLYPH<18> are given in Fig. 8 in which rows from top to bottom correspond to upwind ( GLYPH<18> = 10 GLYPH<14> ), crosswind ( GLYPH<18> = 90 GLYPH<14> ), and tail ( GLYPH<18> = 170 GLYPH<14> ) directions, for two variants of injection, '170 km s GLYPH<0> 1 ' (left panels) and '320 km s GLYPH<0> 1 ' (right panels). In all cases the spectra are broad in energy with maxima at < ' 1 keV for '170 km s GLYPH<0> 1 ' and between GLYPH<24> 0.5 to GLYPH<24> 5 keV for '320 km s GLYPH<0> 1 '. Most energetic tail spectra are obtained in the ad hoc model. On the whole, the spectral region GLYPH<24> 0.5 GLYPH<24> 5 keV seems to be the most promising for detecting He ENA.",
"pages": [
6,
8
]
},
{
"title": "4. Final discussion and conclusions",
"content": "Calculating the heliosheath production of ENAs out of heavy solar ions that capture electrons from neutral interstellar atoms is basically a straightforward exercise, if ion densities are estimated, the flux of interstellar neutrals is measured, and particle collision velocities can be calculated based on simple assumptions. This would apply if the state of background plasma were determined by hydrodynamics and if heavy ions (treated as test particles) were heavy enough to be weakly coupled to the background and therefore were able to preserve energies they had at the TS. Such an approach has been used in the past (Grzedzielski et al. 2010) to follow de-ionization of multicharged coronal ions of C, O, N, Mg, Si, and S carried by the solar wind. In the present paper that deals with light ions such as GLYPH<11> -particles and He + , we have been faced with the situation that, on one hand, the interaction with the background plasma can be more important and, on the other, the evidently non-single fluid state of the background (as established by Voyager) a GLYPH<11> ects various binary interactions to degrees that have not been assessed reliably. This can make the outcome very sensitive to details of heliosheath modeling. In view of the present lack of understanding what goes on in heliosheath plasmas, we tried to explore the range of expected He ENA fluxes for some simple models covering a wide gamut of possibilities. If a feature has emerged in all models, one may presume it has some relevance. As explained in Sect. 2.3, we employed three simple descriptions of heliosheath plasma background: hydrodynamic model by Izmodenov & Alexashov (2003); classical Parker model; ad hoc model attempting to partially render the V1 & V2 measured heliosheath data. These models cover a fairly wide range of possibilities. For all three models we followed the evolution of GLYPH<11> -particles and He + ions (isotropic) momentum distribution functions in phase space (Sects. 2.1, 2.2, 2.4), calculated heliosheath density distributions and energy spectra (Sect. 2.5), and estimated He ENA energy fluxes expected at Earth (Sect. 3). The last estimates are essentially the observables given in Table 3. The data are organized following assumed peak injection energy of He-ions at the TS (cases '170 km s GLYPH<0> 1 ' and '320 km s GLYPH<0> 1 ', cf. Sect. 2.5). IBEX is the first mission dedicated to the astronomy of energetic neutral atoms (McComas 2009). It features two singlepixel, neutral atom cameras: IBEX-Hi (Funsten et al. 2009) and IBEX-Lo (Fuselier et al. 2009). Basically only IBEX-Lo has the capability of discerning species of the incoming atoms, including (indirectly) neutral He (Mobius et al. 2009), and IBEX-Hi was designed to observe neutral H. Allegrini et al. (2008) suggest an ingeneous technique by which some other species, including He, might also be registered owing to a special treatment of data from the IBEX-Hi anti-coincidence system. Results of this paper suggest that detecting maximum predicted fluxes might be within the reach of IBEX instrumentation. The full possibilities of He ENAs measurements have not as yet been published, but the possibility of detection depends critically on the ratio of He ENA to H ENA fluxes (Allegrini et al. 2008). Based on published detection e GLYPH<14> ciencies (Allegrini et al. 2008, Fig. 2) and H ENA fluxes given by McComas et al. (2010) we preliminarily estimate that He ENA intensities predicted by our modeling could be measured from the heliospheric tail direction alone. For the ad hoc model predictions, the measurements should be possible in the IBEX-Hi energy channels 1.1, 2.7, and 4.3 keV, both for the '170 km s GLYPH<0> 1 ' and '320 km s GLYPH<0> 1 ' variants. For the hydrodynamic model predictions, the measurement might be marginally feasible at 2.7 keV for the '320 km s GLYPH<0> 1 ' variant. In all considered models, maximum He ENA flux should come from the tail, though the e GLYPH<11> ect may be only marginal for the hydrodynamic model (cf. fluxes given in Table 3). If an angular tail-upwind decrease in the ENA signal could be measured, this might help to better pinpoint the essential physics of interactions. Maximum signal from the tail should also be related to maximum tail extension, which could help determine the direction of heliosphere wake, independently of the IBEX hydrogen data as in McComas et al. (2012), with obvious inferences concerning the interstellar medium state. Since the expected He ENA intensity at 1 AU from the Sun strongly depends on the conditions in the inner heliosheath, He ENAdetection, if accomplished, may become an important asset in diagnosing the physical state of the innner heliosheath plasma with embedded He ions, as a complement to diagnosing via H ENA currently performed by IBEX.",
"pages": [
8,
9
]
},
{
"title": "References",
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"pages": [
10,
11
]
}
]
2013A&A...550A..10L
https://arxiv.org/pdf/1211.3554.pdf
<document>
<section_header_level_1><location><page_1><loc_15><loc_82><loc_87><loc_87></location>The distribution of warm gas in the G327.3-0.6 massive star-forming region</section_header_level_1>
<text><location><page_1><loc_16><loc_80><loc_86><loc_81></location>S. Leurini 1 , F. Wyrowski 1 , F. Herpin 2 , 3 , F. van der Tak 4 , 5 , R. Gusten 1 , and E.F. van Dishoeck 6 , 7</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_76><loc_64><loc_78></location>1 Max-Planck-Institut fur Radioastronomie, Auf dem Hugel69, 53121 Bonn, Germany e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_50><loc_76></location>2 Univ. de Bordeaux, LAB, UMR 5804, F-33270 Floirac, France</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_43><loc_74></location>3 CNRS, LAB, UMR 5804, F-33270 Floirac, France</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_73><loc_73></location>4 SRON Netherlands Institute for Space Research, PO Box 800, 9700 AV, Groningen, The Netherlands</list_item>
<list_item><location><page_1><loc_11><loc_71><loc_79><loc_72></location>5 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV, Groningen, The Netherlands</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_66><loc_71></location>6 Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands</list_item>
<list_item><location><page_1><loc_11><loc_69><loc_72><loc_70></location>7 Max Planck Institut fur Extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_66><loc_23><loc_67></location>September 16, 2018</text>
<section_header_level_1><location><page_1><loc_47><loc_64><loc_55><loc_65></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_59><loc_91><loc_63></location>Aims. Most studies of high-mass star formation focus on massive and / or luminous clumps, but the physical properties of their larger scale environment are poorly known. In this work, we aim at characterising the e ff ects of clustered star formation and feedback of massive stars on the surrounding medium by studying the distribution of warm gas through midJ 12 CO and 13 CO observations.</text>
<text><location><page_1><loc_11><loc_56><loc_91><loc_59></location>Methods. We present APEX 12 CO(6-5), (7-6), 13 CO(6-5), (8-7) and HIFI 13 CO(10-9) maps of the star forming region G327.36-0.6 with a linear size of ∼ 3 pc × 4 pc. We infer the physical properties of the emitting gas on large scales through a local thermodynamic equilibrium analysis, while we apply a more sophisticated large velocity gradient approach on selected positions.</text>
<text><location><page_1><loc_11><loc_44><loc_91><loc_56></location>Results. Maps of all lines are dominated in intensity by the photon dominated region around the H ii region G327.3-0.5. MidJ 12 CO emission is detected over the whole extent of the maps with excitation temperatures ranging from 20 K up to 80 K in the gas around the H ii region, and H2 column densities from few 10 21 cm -2 in the inter-clump gas to 3 × 10 22 cm -2 towards the hot core G327.30.6. The warm gas (traced by 12 and 13 CO(6-5) emission) is only a small percentage ( ∼ 10%) of the total gas in the infrared dark cloud, while it reaches values up to ∼ 35% of the total gas in the ring surrounding the H ii region. The 12 CO ladders are qualitatively compatible with photon dominated region models for high density gas, but the much weaker than predicted 13 CO emission suggests that it comes from a large number of clumps along the line of sight. All lines are detected in the inter-clump gas when averaged over a large region with an equivalent radius of 50 '' ( ∼ 0.8 pc), implying that the midJ 12 CO and 13 CO inter-clump emission is due to high density components with low filling factor. Finally, the detection of the 13 CO(10-9) line allows to disentangle the e ff ects of gas temperature and gas density on the CO emission, which are degenerate in the APEX observations alone.</text>
<text><location><page_1><loc_11><loc_42><loc_64><loc_43></location>Key words. Stars: formation - ISM: H ii regions - ISM: individual objects: G327.36-0.6</text>
<section_header_level_1><location><page_1><loc_7><loc_38><loc_19><loc_39></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_23><loc_50><loc_37></location>The influence of high-mass stars on the interstellar medium is tremendous. During their process of formation, they are sources of powerful, bipolar outflows (e.g., Beuther et al., 2002), their strong ultraviolet and far-ultraviolet radiation fields give rise to bright H ii and photon dominated regions (PDRs) and during their whole lifetime powerful stellar winds interact with the surroundings. Finally, their short life ends in a violent supernova explosion, injecting heavy elements into the interstellar medium and possibly triggering further star formation with the accompanying shocks. These are also the type of regions that dominate farinfrared observations of starburst galaxies.</text>
<text><location><page_1><loc_7><loc_10><loc_50><loc_22></location>Most studies of massive star formation focus on emission peaks at infrared or submillimetre wavelengths, which correspond to peaks in the temperature and / or mass distribution. The aim of our work is to characterise the e ff ects of clustered star formation and feedback of massive stars on the surrounding medium. We have made APEX maps of three cluster-forming regions (G327.3-0.6, NGC6334 and W51) in midJ 12 CO ((65) and (7-6)) and 13 CO transitions ((6-5) and (8-7)) in order to have a direct measure of the excitation of the warm extended inter-clump gas between dense cores in the cluster (see for ex-</text>
<text><location><page_1><loc_52><loc_31><loc_95><loc_39></location>ample Blitz & Stark, 1986; Stutzki & Gusten, 1990). Our sample of sources was chosen among six nearby cluster-forming clouds mapped in water and in the 13 CO(10-9) transition as part of the Water in Star-Forming Regions with Herschel (WISH) (van Dishoeck et al., 2011) guaranteed time key program (GTKP) for the Herschel Space Observatory (Pilbratt et al., 2010).</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_29></location>In this paper, we present the 12 CO and 13 CO maps of the star-forming region G327.3-0.6 at a distance of 3.3 kpc (Urquhart et al., 2011, based on H I absorption). G327.3-0.6 is well suited to study cluster-forming clouds because of its relatively close distance and because several sources in di ff erent evolutionary phases coexist in a small region, as found by Wyrowski et al. (2006). Our maps (with a linear extension of ∼ 3 pc × 4 pc) cover the H ii region G327.3-0.5 (Goss & Shaver, 1970) associated with a luminous PDR, and an infrared dark cloud (IRDC) (Wyrowski et al., 2006) hosting the bright hot core G327.3-0.6 (Gibb et al., 2000) and the extended green object (EGO) candidate G327.30-0.58 (Cyganowski et al., 2008). EGOs are identified through their extended 4.5 µ m emission in the Spitzer IRAC2 band, which is believed to trace outflows from massive young stellar objects (YSOs) (Cyganowski et al., 2008).</text>
<figure>
<location><page_2><loc_8><loc_73><loc_44><loc_93></location>
<caption>Fig. 1. Spitzer infrared colour image of the region G327.3-0.6 with red representing 8.0 µ m, green 4.5 µ m and blue 3.6 µ m. The blue contours represent the integrated intensity of the 12 CO(6-5) line (thin contours are 15%, 45% and 70% of the peak emission, thick contours 30%, 60% and 90% of the peak emission). The sources discussed in this paper (the IRDC, the EGO, the hot core G327.3-0.6, the SMM6 position and the H ii region G327.3-0.5) are also marked with crosses. The white and yellow boxes mark the regions mapped with APEX and Herschel , respectively.</caption>
</figure>
<table>
<location><page_2><loc_7><loc_47><loc_51><loc_55></location>
<caption>Table 1. Observational parameters.</caption>
</table>
<text><location><page_2><loc_7><loc_35><loc_50><loc_44></location>This paper is organised as follows: in Sect. 2 we present the APEX and Herschel 1 observations of G327.3-0.6, in Sect. 3 we discuss the morphology and kinematics of the 12 CO and 13 CO emission, in Sect. 4 we investigate the physical conditions of the emitting gas. Finally, in Sect. 5 we discuss our results and compare to similar observations performed towards low- and highmass star forming regions. Our results are summarised in Sect. 6.</text>
<section_header_level_1><location><page_2><loc_7><loc_31><loc_20><loc_32></location>2. Observations</section_header_level_1>
<section_header_level_1><location><page_2><loc_7><loc_29><loc_22><loc_30></location>2.1. APEXtelescope</section_header_level_1>
<text><location><page_2><loc_7><loc_19><loc_50><loc_28></location>The CHAMP + (Kasemann et al., 2006; Gusten et al., 2008) dual colour heterodyne array receiver of 7 pixels per frequency channel on the APEX telescope 2 was used in September 2008 to simultaneously map the star-forming region G327.3-0.6 in the 12 CO (6-5) and (7-6) lines and, in a second coverage, the 13 CO (6-5) and (8-7) transitions. The region from the hot core in G327.3-006 to the H ii region G327.3-0.5 (Fig. 1) was covered</text>
<text><location><page_2><loc_52><loc_91><loc_95><loc_93></location>with on-the-fly maps of 200 '' × 240 '' spaced by 4 '' in declination and right ascension.</text>
<text><location><page_2><loc_52><loc_82><loc_95><loc_89></location>We used the Fast Fourier Transform Spectrometer (FFTS, Klein et al., 2006) as backend with two units of fixed bandwidth of 1.5 GHz and 8192 channels per pixel. We used the two IF groups of the FFTS with an o ff set of ± 460 MHz between them. The original resolution of the dataset is 0 . 3 km s -1 ; the spectra were smoothed to 1 km s -1 for a better signal-to-noise ratio.</text>
<text><location><page_2><loc_52><loc_60><loc_95><loc_81></location>The observations were performed under good weather conditions with a precipitable water vapour level between 0.5 and 0.7 mm. Typical single side band system temperatures during the observations were around 1600 K and 5200 K, for the low and high frequency channel respectively. The conversion from antenna temperature units to brightness temperatures was done assuming a forward e ffi ciency of 0.95 for all channels, and a main beam e ffi ciency of 0.48 for the 12 CO and 13 CO (6-5) observations, 0.45 for the 12 CO(7-6) data, and 0.44 for 13 CO(8-7), as measured on Jupiter in September 2008 3 . The pointing was checked on the continuum of the hot core G327.3-0.6 ( α J2000 = 15 h 53 m 07 s . 8 , δ J2000 = -54 · 36 ' 06 . '' 4). The maps were produced with the XY MAP task of CLASS90 4 , which convolves the data with a Gaussian of one third of the beam: the final angular resolution is 9 . '' 4 for the low frequency data, 8 . '' 1 for the high frequency.</text>
<section_header_level_1><location><page_2><loc_52><loc_56><loc_75><loc_57></location>2.2. Herschel SpaceObservatory</section_header_level_1>
<text><location><page_2><loc_52><loc_23><loc_95><loc_54></location>The 13 CO (10-9) line (see Table 1) was mapped (size = 210 '' × 270 '' ) with the HIFI instrument (de Graauw et al., 2010) towards G327.3-0.6 on February, 18th, 2011 (observing day (OD) 645, observing identification number (OBSID) 1342214421. The centre of the map is α J2000 = 15 h 53 m 05 s . 48 , δ J2000 = -54 · 36 ' 06 . '' 2. The observations are part of the WISH GT-KP (van Dishoeck et al., 2011). Data were taken simultaneously in H and V polarisations using both the acousto-optical WideBand Spectrometer (WBS) with 1.1 MHz resolution and the correlator-based High-Resolution Spectrometer (HRS) with 250 kHz nominal resolution. In this paper we present only the WBS data. We used the on-the-fly mapping mode with Nyquist sampling. HIFI receivers are double sideband with a sideband ratio close to unity. The double side band system temperatures and total integration times are respectively 384 K and 3482 s. The rms noise level at 1 km s -1 spectral resolution is ∼ 0.1 K. Calibration of the raw data onto TA scale was performed by the in-orbit system (Roelfsema et al., 2012); conversion to Tmb was done with a beam e ffi ciency of 0.74 and a forward e ffi ciency of 0.96. The flux scale accuracy is estimated to be around 15% for band 3. Data calibration was performed in the Herschel Interactive Processing Environment(HIPE, Ott, 2010) version 6.0. Further analysis was done within the CLASS90 package. After inspection, data from the two polarisations were averaged together.</text>
<text><location><page_2><loc_52><loc_18><loc_95><loc_22></location>The original angular resolution of the data is 19 . '' 0. The final maps were produced with the XY MAP task of CLASS90 and have an angular resolution of 21 . '' 1.</text>
<figure>
<location><page_3><loc_8><loc_70><loc_93><loc_92></location>
<caption>Fig. 2. Maps of the integrated intensity of the 12 CO(3-2), (6-5) and (7-6) lines in the velocity range vLSR = [ -54 , -40] km s -1 (colour scale). Solid contours are the integrated intensity of the 12 CO(6-5) line from 20% of the peak emission in steps of 10%. In each panel, the positions analysed in Sect. 4.2 (the hot core, the IRDC position, and the centre of the H ii region) are marked with black triangles. The red star labels the position of the EGO. SMM6 (left panel) is one of the submillimetre sources detected by Minier et al. (2009).</caption>
</figure>
<figure>
<location><page_3><loc_9><loc_33><loc_92><loc_60></location>
<caption>Fig. 3. Maps of the integrated intensity of the 13 CO(6-5), (8-7) and (10-9) transitions in the velocity range vLSR = [ -54 , -40] km s -1 (colour scale). The solid contours in the left panel represent the LABOCA continuum emission at 870 µ m from 5% of the peak emission in steps of 10% (Schuller et al., 2009). In the middle and right panels, the solid contours are the integrated intensity of the 13 CO(6-5) from 20% of the peak emission in steps of 10%. In each panel, the positions analysed in Sect. 4.2 (the hot core, the IRDC position, and the centre of the H ii region) are marked with black triangles (except in the left panel, where the hot core is shown by a white triangle). The red star labels the position of the EGO.</caption>
</figure>
<section_header_level_1><location><page_3><loc_7><loc_20><loc_27><loc_21></location>3. Observational results</section_header_level_1>
<section_header_level_1><location><page_3><loc_7><loc_17><loc_19><loc_18></location>3.1. Morphology</section_header_level_1>
<text><location><page_3><loc_7><loc_10><loc_50><loc_16></location>Figure 1 shows the 12 CO(6-5) integrated intensity map overlaid on the composite image of the IRAC Spitzer 3.6, 4.5 and 8.0 µ m bands of the region. The 12 CO emission traces the distribution of the 8.0 µ memission, but it is also associated with the infrared dark cloud found on the east of the hot core. The EGO candi-</text>
<text><location><page_3><loc_52><loc_11><loc_95><loc_21></location>te G327.30-0.58 identified by Cyganowski et al. (2008) and clearly visible in Fig. 1, is also detected in the 12 CO data as secondary peak of emission (Fig. 2). The map of the integrated intensities of the 12 CO(7-6) line is also presented in Fig. 2 together with the integrated intensity of the 12 CO(3-2) line from Wyrowski et al. (2006). Figure 3 shows the distribution of the 13 CO(6-5), (8-7) and (10-9) emissions. The accuracy of the relative pointings was checked on the hot core G327.3-0.6. For this</text>
<table>
<location><page_4><loc_16><loc_83><loc_41><loc_89></location>
<caption>Table 2. Coordinates of the main sources in the G327.3-0.6 massive star-forming region</caption>
</table>
<unordered_list>
<list_item><location><page_4><loc_8><loc_81><loc_21><loc_82></location>a Minier et al. (2009)</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_4><loc_8><loc_77><loc_25><loc_78></location>c Cyganowski et al. (2008)</list_item>
<list_item><location><page_4><loc_8><loc_75><loc_50><loc_77></location>d peak of the centimetre continuum emission from ATCA archival data at 2.3 GHz, project number C772</list_item>
</unordered_list>
<text><location><page_4><loc_7><loc_62><loc_50><loc_71></location>purpose, we derived integrated intensity maps of lines detected only towards this position, which are close in frequency to the 12 CO(6-5), 13 CO(6-5) and 13 CO(8-7) transitions, and therefore were observed simultaneously to the current dataset. From these data, we infer a position for the hot core in agreement with interferometric measurements at 3 mm (Wyrowski et al., 2008, and Table 2) within ∼ 1 . '' 5.</text>
<text><location><page_4><loc_7><loc_49><loc_50><loc_62></location>All observed 12 CO transitions trace the H ii region G327.30.5 as well as the infrared dark cloud which hosts the hot core G327.3-0.6. Moreover, the 12 CO(6-5), (7-6) and 13 CO(6-5) lines show extended emission along a ridge running approximately N-S that matches very well with the distribution of the CO(3-2) transition. The hourglass shape hole to the west of the H ii region G327.3-0.5 where the 12 CO(3-2) emission is strongly reduced (see Wyrowski et al., 2006) is seen also in the 12 CO(65) and (7-6) lines which, although much weaker than in the rest of the map, are still detected at this position.</text>
<text><location><page_4><loc_7><loc_33><loc_50><loc_49></location>All transitions peak towards the H ii region G327.3-0.5 where the main isotopologue lines have intensities up to 6065 K. The integrated intensities of the CO isotopologues show a distribution along a ring-like structure around the peak of the cm continuum emission (Goss & Shaver, 1970). The centre of the ring also coincides with the massive young stellar object number 87 identified in the near-infrared by Mois'es et al. (2011). Since the ring is detected also in highJ transitions of 13 CO, it is plausible that this morphology is true and not due to optical depth e ff ects. This structure likely coincides with the limb brightening of the hot surface of a PDR around G327.3-0.5 and could trace an expanding shell. We will investigate this scenario in Sect. 3.2.</text>
<text><location><page_4><loc_7><loc_14><loc_50><loc_33></location>The hot core G327.3-0.6 shows up as a secondary peak in the integrated intensity maps of the 13 CO transitions, while the main CO isotopologue peaks to its north-west, probably because of optical depth e ff ects. Strong self-absorption profiles are indeed detected in all 12 CO lines towards the hot core (see Sect. 3.2). The submillimetre source SMM6 (seen in the continuum emission at 450 µ m by Minier et al., 2009) is detected as a peak of emission in all integrated intensity maps of 12 COandin 13 CO(65), although at the edge of the mapped region. The other submillimetre sources are also marked in Figs. 2. The EGO candidate G327.30-0.58 is also detected in the 13 CO(6-5) map (Fig. 3). The 13 CO(6-5) traces the whole IRDC and not only the active site of star formation where the EGO is detected. The continuum emission due to dust (seen for example at 870 µ min Fig. 3) follows the distribution of the 13 CO lines.</text>
<text><location><page_4><loc_7><loc_10><loc_50><loc_13></location>In Fig. 4 we show the ratio of the integrated intensity of the 12 CO(6-5) transition (convolved to the 18 '' resolution of the 12 CO(3-2) data) to that of the 12 CO(3-2) line. This ratio ranges</text>
<figure>
<location><page_4><loc_52><loc_67><loc_95><loc_92></location>
<caption>Fig. 4. Distribution of the line ratio of the 12 CO(6-5) transition to the 12 CO(3-2) line. Solid contours show the 12 CO(6-5) integrated intensity in the velocity range vLSR = [ -54 , -40] km s -1 from 20% of the peak value in steps of 10%. The black triangles are as in Fig. 2.</caption>
</figure>
<text><location><page_4><loc_52><loc_44><loc_95><loc_55></location>between 0.3 and 1.8; it has values slightly larger than one towards the H ii region (1.2 at its centre), while it is about unity towards the hot core. The peak is found south-west of the H ii region G327.3-0.5, where both lines are detected with a high confidence level. However, these results could be biased by the strong self absorption in both 12 CO lines (see Sect. 3.2). For this reason, we computed the ratio between the two transitions in four velocity ranges to cross-check the results of Fig. 4. The inferred values, however, do not change significantly.</text>
<section_header_level_1><location><page_4><loc_52><loc_41><loc_76><loc_42></location>3.2. Lineprofilesandvelocityfield</section_header_level_1>
<text><location><page_4><loc_52><loc_25><loc_95><loc_40></location>The widespread 12 CO(6-5) emission shows line profiles with a typical width of ∼ 8 km s -1 in the gas between G327.3-0.5 and the infrared dark cloud. Broader profiles are detected in the infrared dark cloud and in the northern part of the H ii region G327.3-0.5. Figure 5 shows the distribution of the line width of the 12 CO(6-5) transition: the 12 CO(6-5) line width follows an arc-like structure that connects the H ii region G327.3-0.5 to the infrared dark cloud where the hot core is. Interestingly, the same morphology is seen in the LABOCA map of the region (Schuller et al., 2009). Line widths are similar for all 12 COlines, while they are consistently narrower in the 13 CO transitions.</text>
<text><location><page_4><loc_52><loc_10><loc_95><loc_25></location>Representative spectra of all 12 CO transitions analysed in this study are presented in Fig. 6 towards the hot core, the IRDC position ((30 '' , 30 '' ) from the centre of the APEX maps, see Sect. 4.2 and Figs. 2-3) and the peak of the cm continuum emission in G327.3-0.5. Spectra of the 13 CO transitions are shown in Fig. 7. Red- and blue-shifted wings are detected in the 12 COlines in a velocity range between -71 and -24 km s -1 (in 12 CO(6-5)) towards G327.3-0.6 probably due to outflow motions. However, no sign of bipolar outflows is found when inspecting the integrated intensity maps of the blue- and red-shifted wings nor in position-velocity diagrams (Fig. 8). Moreover, very similar broad lines are detected along the whole extent of the infrared</text>
<figure>
<location><page_5><loc_8><loc_64><loc_49><loc_92></location>
<caption>Fig. 5. Distribution of the second moment of the 12 CO(6-5) line. The black solid contours represent the LABOCA continuum emission at 870 µ m from 5% of the peak emission in steps of 5%. The peak of the continuum emission corresponds to the hot core position.</caption>
</figure>
<text><location><page_5><loc_7><loc_40><loc_50><loc_53></location>dark cloud, as shown in the top panel of Fig. 8. At the IRDC position, the wings in 12 CO(6-5) range from -60 to -31 km s -1 . All main isotopologue transitions analysed in this paper are a ff ected by self-absorption (see Fig. 6 for reference spectra towards the hot core, the IRDC position and the H ii region); moreover, even the 13 CO(6-5) line shows weak evidence of self-absorbed profile towards the hot core. Figure 9 shows the 12 CO(7-6) spectra overlaid on the continuum emission at 870 µ m: the self-reversed profile is spread over a large area and seems to follow the thermal dust continuum emission.</text>
<text><location><page_5><loc_7><loc_22><loc_50><loc_40></location>Finally, the velocity field of the 12 CO transitions may help us to understand the nature of the ring detected towards the H ii region G327.3-0.5. We therefore used the task KSHELL built in the visualisation software package KARMA (Gooch, 1996). KSHELLcomputes an average brightness temperature on annuli about a user defined centre. A spherically symmetric expanding shell will look like a half ellipse in a (rv) diagram with the axis in the v direction twice the expansion velocity. Figure 10 shows the resulting (rv) diagram obtained with the 12 CO(6-5) data cube using the peak of the cm continuum emission as centre. The emission does not follow a perfect spherical shell. This is likely due to inhomogeneities in the distribution of the gas, as already seen in Fig. 11 where the distribution of the optical depth of 13 CO is not symmetric.</text>
<section_header_level_1><location><page_5><loc_7><loc_18><loc_39><loc_19></location>4. Physical conditions of the warm gas</section_header_level_1>
<section_header_level_1><location><page_5><loc_7><loc_16><loc_19><loc_17></location>4.1. LTEanalysis</section_header_level_1>
<text><location><page_5><loc_7><loc_10><loc_50><loc_15></location>From the line ratio of the 12 CO(6-5) to 13 CO(6-5) transitions we can derive the optical depth of the 12 CO(6-5) line emission, which can be then used to infer the excitation temperature of the line and the column density of 12 CO in the region.</text>
<figure>
<location><page_5><loc_58><loc_57><loc_88><loc_92></location>
<caption>Fig. 6. Mean spectra over a beam of 18 '' (to match the resolution of the 12 CO(3-2) data) of the 12 CO isotopologue transitions analysed in the paper. The top panel shows spectra at the centre of G327.3-0.5, the middle panel spectra at the IRDC position, the bottom panel spectra at the hot core position.</caption>
</figure>
<text><location><page_5><loc_52><loc_45><loc_95><loc_47></location>The line intensity in a given velocity channel of a given transition is</text>
<formula><location><page_5><loc_52><loc_41><loc_95><loc_44></location>T L = η × [ F ν ( T ex) -F ν ( T cbg)] × ( 1 -e -τν ) (1)</formula>
<text><location><page_5><loc_52><loc_22><loc_95><loc_41></location>where η is the beam filling factor (assumed to be 1 in the following analysis), F ν = h ν/ k × [exp(h ν/ kT) -1] -1 , T cbg = 2 . 7 K, and τν is the optical depth. Under the local thermodynamic equilibrium (LTE) assumption, Tex is assumed to be equal to the kinetic temperature of the gas and equal for all transitions. In the following analysis, we study the peak intensities of the 12 CO(6-5) and 13 CO(6-5) lines, and include only the cosmic background as background radiation and neglect, for example, any contribution from infrared dust emission since we do not have any map of the distribution of the dust temperature. This most likely a ff ects only our estimates at the hot core position and possibly towards the H ii region G327.3-0.5 where SABOCA continuum emission at 350 µ mis also detected (Wyrowski et al., in prep.). For an appropriate analysis of the emission from the hot core, see Rol ff s et al. (2011).</text>
<text><location><page_5><loc_52><loc_17><loc_95><loc_22></location>Assuming that the 12 CO(6-5) emission is optically thick and that the 12 CO(6-5) and 13 CO(6-5) lines have the same excitation temperatures, the optical depth of the 13 CO(6-5) transition, τ 13 CO , is</text>
<formula><location><page_5><loc_52><loc_13><loc_95><loc_16></location>τ 13 CO = -ln ( 1 -TL ( 13 CO) TL ( 12 CO) ) (2)</formula>
<text><location><page_5><loc_52><loc_10><loc_95><loc_12></location>The optical depth of the 12 CO(6-5) transition can then be obtained by multiplying for the abundance of 12 CO relative to</text>
<figure>
<location><page_6><loc_12><loc_55><loc_43><loc_93></location>
<caption>Fig. 8. Top panel: Colour scale and contours show the P-V diagram of the CO(6-5) transition computed along the cut indicated by the white arrow in the bottom panel. O ff set positions increase along the direction of the arrow shown in the bottom panel. Bottom panel: distribution of the integrated intensity of the 13 CO(6-5) transition towards the hot core G327.3-0.6. Solid contours show the continuum emission at 350 µ m (Wyrowski et al., in prep.) from 3 σ in steps of 10 σ ( σ ∼ 3 Jy / beam). Symbols are as in Fig. 2.</caption>
</figure>
<figure>
<location><page_6><loc_55><loc_53><loc_90><loc_92></location>
<caption>Fig. 7. Mean spectra over a beam of 21 . '' 1 (to match the resolution of the 13 CO(10-9) data) of the 13 CO isotopologue transitions. The selected positions are those discussed in Sect. 4.2.</caption>
</figure>
<text><location><page_6><loc_7><loc_19><loc_50><loc_44></location>13 CO, X 12 CO / 13 CO ∼ 60 (Wilson & Rood, 1994). From the optical depth of the 12 CO(6-5) line, one can also derive its excitation temperature using Eq. 1. Figure 11 shows the distribution of the optical depth of the 13 CO(6-5) line and of the excitation temperature of 12 CO(6-5). The 13 CO(6-5) emission is moderately optically thick (0.6-0.7) at the H ii region and at the infrared dark cloud, while it reaches values of ∼ 1.2 at the hot core position and in a small part of ring around the H ii region. The map distribution of the excitation temperature of the 12 CO(6-5) line is shown in the bottom panel of Fig. 11. The map is dominated by the H ii region, where T ex reaches values of 80 K in the ring around the H ii region and then decreases with increasing distance from it. The hot core and the rest of the infrared dark cloud have values around 30-35 K. The excitation temperature increases to the south west of the hot core, in a region where there is also 8 µ memission, and to the north-east of the H ii along a layer of gas also visible in the 12 CO(6-5) integrated intensity map (see Fig. 2), but more prominent in the T ex map and in the 8 µ memission map (see Fig. 1).</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_19></location>From the optical depth and the excitation temperature of the 12 CO(6-5) line, we derived the H2 column density assuming a relative abundance of 12 CO relative to H2 of 2 . 7 × 10 -4 (Lacy et al., 1994). Results are shown in Fig. 12. The largest column density is found towards the hot core ( ∼ 3 × 10 22 cm -2 in the 9 . '' 4 beam of the 13 CO(6-5) data) and decreases along the infrared dark cloud with a distribution similar to that of the 870 µ m</text>
<text><location><page_6><loc_52><loc_33><loc_95><loc_36></location>continuum emission. Three peaks around 10 22 cm -2 are found in the H ii region.</text>
<text><location><page_6><loc_52><loc_18><loc_95><loc_33></location>We cross-checked our results by computing the H2 column density under the assumption that the 13 CO emission is optically thin. The results are consistent with those presented in Fig. 12; the largest di ff erences (of the order of 30%) are found towards those positions where the optical depth of the 13 CO(65) transition (Fig. 11) exceeds ∼ 0.7. The assumption of optically thin emission for 13 CO may be particularly useful for the inter-clump medium (arbitrarily defined as the region in the map where the 13 CO lines are not detected on individual spectra), towards which we infer H2 column densities of ∼ 2 × 10 21 cm -2 corresponding to a 13 COcolumndensity of ∼ 10 16 cm -2 (see also Sect. 5.1).</text>
<text><location><page_6><loc_52><loc_10><loc_95><loc_17></location>We also computed column densities and rotational temperatures in the region using the rotational diagram technique applied to the 13 CO data. We did not include the 12 CO lines in the analysis because of their complex line profiles and high optical depths. Given the optical depth previously derived for the 13 CO(6-5) line, we did not apply any correction due to optical depth e ff ects</text>
<figure>
<location><page_7><loc_10><loc_68><loc_47><loc_93></location>
<caption>Fig. 9. Map of the 12 CO(7-6) line overlaid on the continuum emission at 870 µ m from LABOCA. The velocity axis ranges from -60 to -25 km s -1 , the temperature axis from -1 to 15 K. The 12 CO(7-6) data were smoothed to a resolution of 18 '' to match the resolution of the 12 CO(3-2) data and of the LABOCA emission. The centre of the map is that of the APEX data (see Sect. 2.1). The triangles and the green star are as in Fig. 2.</caption>
</figure>
<text><location><page_7><loc_7><loc_36><loc_50><loc_55></location>to the 13 CO data. Results are consistent with the estimates based on equation 1. The main di ff erences between the two analyses are found towards the hot core, where the rotational temperature is higher than the excitation derived with equation 1 ( T rot ∼ 70 K and T ex ∼ 32 K) and the H2 column density lower (10 22 cm -2 versus 3 × 10 22 cm -2 obtained with the first method). The differences between the two methods are likely influenced by the self-absorption profile detected in the 12 CO(6-5) line which results in lower line intensities towards the regions of large column densities. In particular, while the first approach overestimates the optical depths (and hence column density) because of the self absorption, the column density derived with the rotational diagram analysis is likely underestimated towards the hot core because of the optically thin emission assumption, and should be corrected by a factor τ LTE / (1 -exp( τ LTE) -) ∼ 1.7.</text>
<text><location><page_7><loc_7><loc_24><loc_50><loc_36></location>Finally, we computed the ratio between the amount of warm gas (traced by 12 CO and 13 CO(6-5) and shown in Fig. 12) and the total amount of gas (traced by the continuum emission at 870 µ m) as derived assuming a dust temperature equal to the excitation temperature of 12 CO(6-5) and a dust opacity of 0.0182 cm 2 g 1 (Kau ff mann et al., 2008). The results are shown in Fig. 13: the warm gas is only a small percentage ( ∼ 10%) of the total gas in the infrared dark cloud, while it reaches values up to ∼ 35% of the total gas in the ring surrounding the H ii region.</text>
<section_header_level_1><location><page_7><loc_7><loc_21><loc_19><loc_22></location>4.2. 13 COladder</section_header_level_1>
<text><location><page_7><loc_7><loc_10><loc_50><loc_20></location>Since the G327.3-0.6 region was mapped in three di ff erent transitions of the 13 CO molecule, we can perform a multi-line analysis towards selected positions and infer the parameter of the gas. The advantage of 13 CO compared to the main isotopologue is in the lower opacities of the lines and in the less complex line profiles. For this analysis, we used the RADEX program (van der Tak et al., 2007) with expanding sphere geometry. The molecular dataset comes from the LAMDA database</text>
<figure>
<location><page_7><loc_62><loc_61><loc_86><loc_92></location>
<caption>Fig. 10. (rv) diagram of the H ii region G327.3-0.5 obtained from the 12 CO(6-5) data cube. The radius axis is the distance to the shell expansion centre, chosen to be the peak of the cm continuum emission. The half ellipse represents an ideal shell in (rv) diagram with an expansion velocity of 5 km s -1 .</caption>
</figure>
<table>
<location><page_7><loc_55><loc_31><loc_91><loc_48></location>
<caption>Table 3. Line parameters of the 13 CO lines</caption>
</table>
<text><location><page_7><loc_52><loc_23><loc_95><loc_28></location>(Schoier et al., 2005) and includes collisional rates adapted from Yang et al. (2010). We ran models with temperatures from 20 to 200 K, densities in the range 10 4 -5 × 10 7 cm -3 , and 13 CO column densities between 10 14 and 10 19 cm -2 .</text>
<text><location><page_7><loc_52><loc_10><loc_95><loc_23></location>All data were smoothed to the resolution of the 13 CO(10-9) map. We selected three positions for the analysis: the hot core, the IRDC position ((30 '' , 30 '' ) from the centre of the APEX maps), and the centre of the H ii region. The IRDC position was selected to be a position associated with high column density in the infrared dark cloud (see Figs. 2, 3 and 12) but without IR emission. However, it is only 10 '' to the north of the EGO candidate (Cyganowski et al., 2008, see Figs. 2-3), and therefore, given the beam of the observations, contamination from the embedded YSO may still be possible. Table 3 reports the measured</text>
<figure>
<location><page_8><loc_11><loc_51><loc_45><loc_91></location>
<caption>Fig. 11. Distribution of the optical depth of the 13 CO(6-5) line ( τ 13 CO , top panel) and of the excitation temperature of 12 CO(6-5) transition ( T exCO, bottom panel). Black contours are the 13 CO(65) integrated intensity as in Fig. 3.</caption>
</figure>
<text><location><page_8><loc_7><loc_33><loc_50><loc_41></location>line parameters of the 13 CO transitions obtained with Gaussian fits; based on these values, we adopt line widths of 6, 3 and 7, for the hot core, the IRDC and the H ii respectively, in agreement with values reported by San Jos'e-Garc'ıa et al. (2012) for the 13 CO(10-9) line towards a sample of intermediate- and highmass sources. The spectra are shown in Fig. 7.</text>
<text><location><page_8><loc_7><loc_10><loc_50><loc_33></location>The results of the RADEX analysis are listed in Table 4 and shown in Fig. 14. For the IRDC position, the 13 CO(10-9) line intensity is not well fitted by our one-temperature model. This likely reflects the fact that the 13 CO(10-9) spectrum is dominated by the embedded source while the other two lines sample colder gas in the envelope. We considered a 20% calibration error for the 13 CO(6-5) and (8-7) observations and a 15% error for the 13 CO(10-9) data. Wyrowski et al. (2006) mapped the region with the APEX telescope in the C 18 O(3-2) line. Therefore, since no observations were performed in the 13 CO(3-2) transition, we included the C 18 O(3-2) data in Fig. 14. Note however, that the C 18 O(3-2) fluxes are not included in the fitting procedure, but that they are simply used to cross-check results. Since the C 18 O(3-2) flux corresponds to a lower limit to the flux of 13 CO(3-2) line, we also plotted the C 18 O(3-2) flux corrected for the abundance ratio of 13 CO to C 18 O, X 13 CO / C 18 O ∼ 8 (Wilson & Rood, 1994). This value is likely an upper limit to the flux of the 13 CO(3-2) line due to opacity e ff ects.</text>
<figure>
<location><page_8><loc_52><loc_66><loc_93><loc_93></location>
<caption>Fig. 12. Distribution of the H2 column density in the G327.3-0.6 star-forming region based on equation 1. Black contours are the 13 CO(6-5) integrated intensity as in Fig. 3.</caption>
</figure>
<figure>
<location><page_8><loc_52><loc_30><loc_93><loc_57></location>
<caption>Fig. 13. Distribution of the ratio between the column density of warm gas (traced by 12 CO and 13 CO(6-5)) and the total H2 column density (traced by the continuum emission at 870 µ m) in the G327.3-0.6 star-forming region. Black contours are the 13 CO(65) integrated intensity as in Fig. 3.</caption>
</figure>
<text><location><page_8><loc_52><loc_10><loc_95><loc_19></location>An example of the χ 2 distribution projected on to the T -n plane is shown in Fig. 15 for the HII position, where the reduced χ 2 at the best fit position is 3. Figure 15 shows the typical inverse n -T relationship often seen in χ 2 distributions and due to the fact that density and temperature are, in the case of the CO molecule, not independent parameters (see Appendix C of van der Tak et al., 2007).</text>
<figure>
<location><page_9><loc_7><loc_63><loc_48><loc_93></location>
<caption>Fig. 14. Distribution of the 13 CO peak line intensities. Full black triangles correspond to 13 CO(6-5), (8-7) and (10-9) observed intensities. The circle represents the observed C 18 O(3-2) flux, the empty black triangle the flux of the C 18 O(3-2) line multiplied by X 13 CO / C 18 O ∼ 8. The red triangles are the best model fit results. The error bars include only calibration uncertainties. The dashed lines represent the best fit 13 CO ladder.</caption>
</figure>
<text><location><page_9><loc_7><loc_40><loc_50><loc_48></location>Wenote here that the detection of the 13 CO(10-9) line breaks the degeneracy between density and temperature typical of 12 CO analyses (e.g., Kramer et al., 2004; van der Tak et al., 2007) and help to give stronger constraints: indeed, with the exception of the hot core, at least the temperature of the gas is well determined at all positions.</text>
<text><location><page_9><loc_7><loc_20><loc_50><loc_40></location>The results of the RADEX analysis confirm that the LTE assumption used in Sect. 4.1 is reasonable since the inferred densities are much larger than the critical densities (a few 10 4 cm -3 for all three analysed transitions). Assuming X 12 CO / 13 CO ∼ 60 and an abundance of 12 COrelative to H2 of 2 . 7 × 10 -4 , the derived 13 CO column densities listed in Table 4 correspond to H2 column densities of some 10 22 cm -2 for the hot core and the IRDC position, and of 2 × 10 22 cm -2 for the H ii position. The derived column densities and temperatures are in agreement with those derived in Sect. 4.1 through rotational diagrams of the 13 CO emission. The 13 CO(6-5) optical depths are also in agreement with those estimated in Sect. 4.1 through the 13 CO and 12 CO(6-5) line ratio, with the exception of the hot core position: τ LTE ∼ 1.2 and τ RADEX ∼ 0.3 for the hot core, 0.6 and 0.5 for the H ii region, and 0.6 and 0.7 for the IRDC position.</text>
<text><location><page_9><loc_7><loc_10><loc_50><loc_20></location>Wefinally stress that the results obtained with the LTE analysis (Sect. 4.1) and with the RADEX code (this section) are based on the assumptions that 1) all lines have a beam filling factor of one, and 2) that the emitting gas is homogeneous, whereas selfabsorption profiles in the 12 COlines indicate an excitation gradient along the line of sights. For optically thin lines ( 13 CO in the current case), a beam filling factor less than one (but equal for all transitions) would mostly a ff ect the column density and result in</text>
<figure>
<location><page_9><loc_55><loc_67><loc_91><loc_93></location>
<caption>Fig. 15. Projection of the 3-dimensional (T-n-N) distribution of the χ 2 on the T -n plane for the H ii position. The contours show the 1, 2 and 3 σ confidence levels for two degrees of freedom. The triangle marks the best fit position.</caption>
</figure>
<table>
<location><page_9><loc_56><loc_49><loc_91><loc_56></location>
<caption>Table 4. Best fit parameters of the 13 CO line modelling</caption>
</table>
<text><location><page_9><loc_52><loc_45><loc_95><loc_48></location>The errors represent the 3 σ confidence levels in the temperature-density plane or 3 σ lower (shown in brackets) limit when no stronger constraints can be inferred.</text>
<text><location><page_9><loc_52><loc_40><loc_95><loc_42></location>larger values of N ; for optically thick lines, a smaller value of η would imply larger values of density and / or temperature.</text>
<text><location><page_9><loc_52><loc_33><loc_95><loc_40></location>The uncertainties on the derived parameters due to the assumption of a homogeneous medium are of less immediate interpretation, and more complex radiative transfer codes (e.g., Hogerheijde & van der Tak, 2000) should be used to reproduce the observed line velocity profiles.</text>
<section_header_level_1><location><page_9><loc_52><loc_29><loc_63><loc_31></location>5. Discussion</section_header_level_1>
<section_header_level_1><location><page_9><loc_52><loc_27><loc_77><loc_29></location>5.1. Total 12 COand 13 COemission</section_header_level_1>
<text><location><page_9><loc_52><loc_10><loc_95><loc_27></location>Figure 16 shows the 12 CO and 13 CO ladders obtained by averaging the emission of the di ff erent observed transitions, smoothed to the resolution of the HIFI data, over four regions: the total map, the H ii region G327.3-0.5, the IRDC hosting the hot core (the selected region does include the hot core), and finally the inter-clump gas, which was defined as the region in the map where the 13 CO lines are not detected on individual spectra. This region has an equivalent radius of 50 '' (corresponding to ∼ 0.8 pc at the distance of the source). Examples of 12 CO line profiles towards the inter-clump gas are shown in Fig. 17. The C 18 O(3-2) cannot be used in this analysis because the observations cover a much smaller region than that mapped in 13 CO. The total mass of the mapped region can be computed using the excitation tem-</text>
<figure>
<location><page_10><loc_9><loc_62><loc_92><loc_92></location>
<caption>Fig. 16. CO (left) and 13 CO (right) ladders for the whole mapped region (black), the H ii region G327.3-0.5 (red), the IRDC including the hot core (blue) and the inter-clump gas (magenta). Error bars include only calibration uncertainties. In both panels, the dashed and dotted curves represent the predicted intensities for model B from Koester et al. (1994) for a density of 10 7 cm -3 , incident UV fields of 10 3 and 10 4 relative to the average interstellar field</caption>
</figure>
<text><location><page_10><loc_20><loc_54><loc_81><loc_55></location>, a visual extinction of 10, and a Doppler broadening of 3 (dashed curve) and 1 km s -1 (dotted curve).</text>
<figure>
<location><page_10><loc_10><loc_29><loc_47><loc_52></location>
<caption>Fig. 17. CO(6-5) (solid line) and 12 CO(7-6) (dashed line) spectra towards some positions in the inter-clump gas. The o ff set position from the centre of the APEX 12 CO maps (Sect. 2.1) is shown for each spectrum in the top right corner.</caption>
</figure>
<text><location><page_10><loc_7><loc_16><loc_50><loc_19></location>perature and H2 column density distributions shown in Figs. 11 and 12. This corresponds to ∼ 700 M /circledot .</text>
<text><location><page_10><loc_7><loc_10><loc_50><loc_16></location>The four regions have similar 12 CO and 13 CO ladders. In order to correct for self-absorption, integrated fluxes were obtained for each of the four regions from line fitting of the CO spectra with one Gaussian component. While this works fine for the spectra of the IRDC hosting the hot core and for the inter-</text>
<text><location><page_10><loc_52><loc_10><loc_95><loc_52></location>clump gas, the line profiles of the total map and of H ii region are red-skewed and therefore the fluxes derived with this method are likely underestimated. For the main isotopologue, the flux of the (7-6) and (6-5) transitions is very similar, although for the IRDC + HCand the inter-clump the flux of the (7-6) line is lower than that of the (6-5) line. On the other hand, in the 13 CO ladder the peak flux decreases with increasing energy level. For all transitions presented in this paper, the spectra are dominated in intensity by the H ii region, whose flux is of the order of 60% of the total flux for the main isotopologue lines, and ranging from ∼ 49% of the total flux in the (6-5) line to ∼ 85% in the (10-9) transition for 13 CO (see Table 5). The main di ff erence between the 12 CO spectra and those of 13 CO lies in the emission from the inter-clump gas: for all 12 CO lines, the intensity is relatively strong, 10% of the flux from the whole region. On the other hand, the flux of the 13 CO lines coming from the inter-clump gas decreases with increasing J, from ∼ 7% of the total flux for J = 6 to ∼ 2% for J = 10. The general behaviour of the 12 CO and 13 CO ladders is qualitatively compatible with PDR models from Koester et al. (1994) for high density (10 6 -10 7 cm -3 ) clouds illuminated on one side by a UV radiation field (their model B). In Fig. 16, we show the predicted CO and 13 CO line intensities for models with a density of 10 7 cm -3 , incident UV fields with strength 10 3 and 10 4 relative to the average interstellar field (Draine, 1978), a visual extinction of 10, and a Doppler broadening of 3 and 1 km s -1 . High densities ( n > 10 6 cm -3 , in agreement with our results from Sect. 4.2) are needed to locate the peak of the CO ladders at mid-, highJ transitions (see Figs. 9-10, 12-13 of Koester et al. 1994). Stronger UV radiation fields also shift the peak of the CO ladders to higher J transitions than observed. In Fig. 16, the 12 CO model intensities are corrected by a factor 0.2 and 0.25 to correct for di ff erent line-</text>
<table>
<location><page_11><loc_19><loc_79><loc_38><loc_88></location>
<caption>Table 5. Percentage of integrated fluxes from the H ii region G327.3-0.5 and from the inter-clump gas respect to the total integrated flux in the map.</caption>
</table>
<text><location><page_11><loc_7><loc_62><loc_50><loc_76></location>etween the model and the observations, and possibly for beam dilution e ff ects. On the other hand, the 13 CO results of Fig. 16 are not scaled down by any factor as they are far too weak to match the observations. Koester et al. (1994) already noticed that the predicted line intensities of midJ 13 CO transitions in their models are much weaker than observed in star-forming regions. They proposed that midJ 13 CO emission comes from a large number of filamentary structures, or clumps, along the line of sight. In this way, the modelled line intensity of midJ 13 CO lines would increase significantly as the lines are optically thin, while it would not change for optically thick transitions.</text>
<text><location><page_11><loc_7><loc_46><loc_50><loc_62></location>Rotational diagrams of the 13 CO emission applied to the spectra of the H ii region, of the IRDC and of the inter-clump gas infer rotational temperatures of 66 K, 47 K and 44 K, respectively, and 13 CO column densities of 6 × 10 15 cm -2 for the H ii region and the IRDC, and of 2 × 10 15 cm -2 for the inter-clump gas. Since the inter-clump gas has physical parameters very similar to those of the IRDC region, but a much lower column density, we suggest that it is composed of high-density clumps with low filling factors. This is again in agreement with PDR models (e.g., Koester et al., 1994; Cubick et al., 2008) which predict strong emission at midJ 13 COand highJ 12 CO lines in the case of small, low mass, high density clumps.</text>
<text><location><page_11><loc_7><loc_24><loc_50><loc_46></location>Cubick et al. (2008) suggested that the COBE 12 CO ladder of the Milky Way can be reproduced by a clumpy PDR model, and that the bulk of the Galactic FIR line emission comes from PDRs around the Galactic population of massive stars. Our observations seem to confirm this result, since the CO emission of the G327.3-0.6 region is dominated by the PDR around the H ii region. Our results are also consistent with the findings from Davies et al. (2011) and Mottram et al. (2011). These authors studied the properties of massive YSOs and compact H ii regions in the RMS survey (Hoare et al., 2005), and found that there is no significant population of massive YSOs above ∼ 10 5 L /circledot , while compact H ii regions are detected up to ∼ 10 6 L /circledot . Since highJ CO lines are among the most important cooling lines in PDR, they reflect the luminosity of their heating sources: if the luminosity distribution of massive stars in the Galaxy is dominated by H ii regions and not by younger massive stars, then we also expect that the CO distribution follows the same rule.</text>
<section_header_level_1><location><page_11><loc_7><loc_21><loc_42><loc_22></location>5.2. Comparisonswithotherstarformingregions</section_header_level_1>
<text><location><page_11><loc_7><loc_10><loc_50><loc_20></location>Large-scale mapping of some low- and high-mass star forming regions was performed in several 12 CO transitions. However, given the di ff erent critical densities of the lines, we prefer to compare our results with studies carried on with J > 3 CO lines. Excitation temperatures around 8-30 K are found in extended di ff use emission and towards the brightest positions, respectively, in low-mass star forming regions (e.g., Davis et al., 2010; Curtis et al., 2010), while massive star-forming regions are usu-</text>
<text><location><page_11><loc_52><loc_84><loc_95><loc_93></location>ally warmer as confirmed by our findings (see also Wilson et al., 2001; Jakob et al., 2007; Kirk et al., 2010; Wilson et al., 2011; Peng et al., 2012). The CO column densities (10 17 -10 18 cm -2 from the LTE analysis) found in G327 are also comparable with values obtained in other massive star-forming regions (Wilson et al., 2001; Jakob et al., 2007; White et al., 2010; Wilson et al., 2011).</text>
<text><location><page_11><loc_52><loc_59><loc_95><loc_84></location>Comparison with 12 CO large maps of other high-mass star forming regions would be important to verify whether our result that the 12 CO distribution is dominated by the H ii region is a common feature or not. However, most studies do not cover di ff erent evolutionary phases as in our case. For OMC1, Peng et al. (2012) confirmed that the peak of the integrated intensity of several CO isotopologue lines is close to the OrionKL hot core (although Orion-south and the Orion Bar PDR are also very prominent). One should notice however, that Orion is roughly six times closer to the Sun than G327.3-0.6, and therefore the Orion Bar and Orion-KL would be much closer on sky ( ∼ 30 '' ) if one would place them at the distance of G327.30.6. Moreover, Orion-KL likely represents a special case since it hosts a very powerful outflow (e.g., Kwan & Scoville, 1976; Snell et al., 1984), which could alter the distribution of 12 CO in the region. Indeed, Marrone et al. (2004) show that broad velocity emission arises mainly from the Orion-KL region, while much of the narrower emission arises from the PDR excited by the M42 H ii region.</text>
<section_header_level_1><location><page_11><loc_52><loc_56><loc_72><loc_57></location>5.3. Self-absorptionprofiles</section_header_level_1>
<text><location><page_11><loc_52><loc_23><loc_95><loc_54></location>As noted in Sect. 3.2, all 12 CO transitions analysed in this paper are a ff ected by self-absorption, which is likely to be due to cold gas surrounding a warmer component (Phillips et al., 1981). In particular along the infrared dark cloud (Fig. 8), the 12 CO(6-5) line has blue-skewed profiles in the north-east (towards the EGO and the IRDC positions) and the red-skewed ones towards the south-west (the hot core). Blue- and red-skewed profiles (e.g., Mardones et al., 1997) are commonly interpreted as due to rotation or outflow motions (which should produce equal numbers of red and blue profiles, and could therefore explain the profiles detected towards the EGO and IRDC position, the hot core and the H ii region, Fig. 6) or to infall (which should produce profiles which are skewed towards the blue, e.g. towards the EGO and IRDC position) or to expansion (which should produce profiles skewed towards the red and could be responsible for the 12 CO spectra of the hot core and the H ii region). From the PV diagram of the 12 CO(6-5) line, we do not have any evidence of global rotation towards the hot core and the red-skewed profile can be interpreted in terms of expansion or outflow motion. Similarly, from Fig. 10 we see that the emission does not follow a perfect expanding spherical shell which might imply that the rotation is on the origin of the self-absorbed profile seen towards the H ii region. Finally, the blue-skewed line profile detected toward the EGO and IRDC positions are typical of infall motion.</text>
<section_header_level_1><location><page_11><loc_52><loc_18><loc_64><loc_20></location>6. Conclusions</section_header_level_1>
<text><location><page_11><loc_52><loc_10><loc_95><loc_17></location>To study the e ff ect of feedback from massive star forming regions in their surrounding environment, we selected the region G327.3-0.6 for large scale mapping of several midJ 12 CO and 13 COlines with the APEX telescope and of the highJ 13 CO(109) transition with the Herschel satellite. Our results can be summarised as follows:</text>
<unordered_list>
<list_item><location><page_12><loc_8><loc_89><loc_50><loc_93></location>1. Maps of all transitions are dominated by the PDR associated with the H ii region G327.3-0.5; midJ 12 COand 13 COemission is detected along the whole extent of the IRDC;</list_item>
<list_item><location><page_12><loc_8><loc_85><loc_50><loc_89></location>2. MidJ transitions show rather extended emission with typical excitation temperatures of ∼ 30 K and column densities of some 10 21 cm -2 ;</list_item>
<list_item><location><page_12><loc_8><loc_78><loc_50><loc_85></location>3. All observed transitions are detected also in the inter-clump gas when averaged over large regions. The inter-clump emission is compatible with LTE emission from a gas at 44 K, and with a 13 CO column density of 2 × 10 15 cm -2 , thus suggesting that the inter-clump is composed of high-density clumps with low filling factors;</list_item>
<list_item><location><page_12><loc_8><loc_72><loc_50><loc_78></location>4. The warm gas traced by 12 and 13 CO(6-5) is only a small percentage ( ∼ 10%) of the total gas in the infrared dark cloud, while it reaches values up to ∼ 35%of the total gas in the ring surrounding the H ii region;</list_item>
<list_item><location><page_12><loc_8><loc_67><loc_50><loc_72></location>5. The 12 CO and 13 CO ladders are qualitatively compatible with PDR models for high density gas ( n > 10 6 cm -3 ) and, in the case of 13 CO, suggest that the emission comes from a large number of clumps;</list_item>
<list_item><location><page_12><loc_8><loc_61><loc_50><loc_67></location>6. The detection of the 13 CO(10-9) line allows to give stronger constraints on the physics of the gas by breaking the degeneracy between density and temperature (typical of 12 CO and 13 CO transitions) in the high temperature-low density part of the T -n plane.</list_item>
</unordered_list>
<text><location><page_12><loc_7><loc_57><loc_50><loc_59></location>Acknowledgements. The authors thank Dr. Joe Mottram for a careful review of the manuscript and an anonymous referee for useful comments and suggestions.</text>
<text><location><page_12><loc_7><loc_41><loc_50><loc_57></location>Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. HIFI has been designed and built by a consortium of institutes and university departments from across Europe, Canada and the United States under the leadership of SRON Netherlands Institute for Space Research, Groningen, The Netherlands and with major contributions from Germany, France and the US. Consortium members are: Canada: CSA, U.Waterloo; France: CESR, LAB, LERMA, IRAM; Germany: KOSMA, MPIfR, MPS; Ireland, NUI Maynooth; Italy: ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri- INAF; Netherlands: SRON, TUD; Poland: CAMK, CBK; Spain: Observatorio Astron'omico Nacional (IGN), Centro de Astrobiolog'ıa (CSIC-INTA). Sweden: Chalmers University of Technology - MC2, RSS & GARD; Onsala Space Observatory; Swedish National Space Board, Stockholm University - Stockholm Observatory; Switzerland: ETH Zurich, FHNW; USA: Caltech, JPL, NHSC.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Aims. Most studies of high-mass star formation focus on massive and / or luminous clumps, but the physical properties of their larger scale environment are poorly known. In this work, we aim at characterising the e ff ects of clustered star formation and feedback of massive stars on the surrounding medium by studying the distribution of warm gas through midJ 12 CO and 13 CO observations. Methods. We present APEX 12 CO(6-5), (7-6), 13 CO(6-5), (8-7) and HIFI 13 CO(10-9) maps of the star forming region G327.36-0.6 with a linear size of ∼ 3 pc × 4 pc. We infer the physical properties of the emitting gas on large scales through a local thermodynamic equilibrium analysis, while we apply a more sophisticated large velocity gradient approach on selected positions. Results. Maps of all lines are dominated in intensity by the photon dominated region around the H ii region G327.3-0.5. MidJ 12 CO emission is detected over the whole extent of the maps with excitation temperatures ranging from 20 K up to 80 K in the gas around the H ii region, and H2 column densities from few 10 21 cm -2 in the inter-clump gas to 3 × 10 22 cm -2 towards the hot core G327.30.6. The warm gas (traced by 12 and 13 CO(6-5) emission) is only a small percentage ( ∼ 10%) of the total gas in the infrared dark cloud, while it reaches values up to ∼ 35% of the total gas in the ring surrounding the H ii region. The 12 CO ladders are qualitatively compatible with photon dominated region models for high density gas, but the much weaker than predicted 13 CO emission suggests that it comes from a large number of clumps along the line of sight. All lines are detected in the inter-clump gas when averaged over a large region with an equivalent radius of 50 '' ( ∼ 0.8 pc), implying that the midJ 12 CO and 13 CO inter-clump emission is due to high density components with low filling factor. Finally, the detection of the 13 CO(10-9) line allows to disentangle the e ff ects of gas temperature and gas density on the CO emission, which are degenerate in the APEX observations alone. Key words. Stars: formation - ISM: H ii regions - ISM: individual objects: G327.36-0.6",
"pages": [
1
]
},
{
"title": "The distribution of warm gas in the G327.3-0.6 massive star-forming region",
"content": "S. Leurini 1 , F. Wyrowski 1 , F. Herpin 2 , 3 , F. van der Tak 4 , 5 , R. Gusten 1 , and E.F. van Dishoeck 6 , 7 September 16, 2018",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The influence of high-mass stars on the interstellar medium is tremendous. During their process of formation, they are sources of powerful, bipolar outflows (e.g., Beuther et al., 2002), their strong ultraviolet and far-ultraviolet radiation fields give rise to bright H ii and photon dominated regions (PDRs) and during their whole lifetime powerful stellar winds interact with the surroundings. Finally, their short life ends in a violent supernova explosion, injecting heavy elements into the interstellar medium and possibly triggering further star formation with the accompanying shocks. These are also the type of regions that dominate farinfrared observations of starburst galaxies. Most studies of massive star formation focus on emission peaks at infrared or submillimetre wavelengths, which correspond to peaks in the temperature and / or mass distribution. The aim of our work is to characterise the e ff ects of clustered star formation and feedback of massive stars on the surrounding medium. We have made APEX maps of three cluster-forming regions (G327.3-0.6, NGC6334 and W51) in midJ 12 CO ((65) and (7-6)) and 13 CO transitions ((6-5) and (8-7)) in order to have a direct measure of the excitation of the warm extended inter-clump gas between dense cores in the cluster (see for ex- ample Blitz & Stark, 1986; Stutzki & Gusten, 1990). Our sample of sources was chosen among six nearby cluster-forming clouds mapped in water and in the 13 CO(10-9) transition as part of the Water in Star-Forming Regions with Herschel (WISH) (van Dishoeck et al., 2011) guaranteed time key program (GTKP) for the Herschel Space Observatory (Pilbratt et al., 2010). In this paper, we present the 12 CO and 13 CO maps of the star-forming region G327.3-0.6 at a distance of 3.3 kpc (Urquhart et al., 2011, based on H I absorption). G327.3-0.6 is well suited to study cluster-forming clouds because of its relatively close distance and because several sources in di ff erent evolutionary phases coexist in a small region, as found by Wyrowski et al. (2006). Our maps (with a linear extension of ∼ 3 pc × 4 pc) cover the H ii region G327.3-0.5 (Goss & Shaver, 1970) associated with a luminous PDR, and an infrared dark cloud (IRDC) (Wyrowski et al., 2006) hosting the bright hot core G327.3-0.6 (Gibb et al., 2000) and the extended green object (EGO) candidate G327.30-0.58 (Cyganowski et al., 2008). EGOs are identified through their extended 4.5 µ m emission in the Spitzer IRAC2 band, which is believed to trace outflows from massive young stellar objects (YSOs) (Cyganowski et al., 2008). This paper is organised as follows: in Sect. 2 we present the APEX and Herschel 1 observations of G327.3-0.6, in Sect. 3 we discuss the morphology and kinematics of the 12 CO and 13 CO emission, in Sect. 4 we investigate the physical conditions of the emitting gas. Finally, in Sect. 5 we discuss our results and compare to similar observations performed towards low- and highmass star forming regions. Our results are summarised in Sect. 6.",
"pages": [
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},
{
"title": "2.1. APEXtelescope",
"content": "The CHAMP + (Kasemann et al., 2006; Gusten et al., 2008) dual colour heterodyne array receiver of 7 pixels per frequency channel on the APEX telescope 2 was used in September 2008 to simultaneously map the star-forming region G327.3-0.6 in the 12 CO (6-5) and (7-6) lines and, in a second coverage, the 13 CO (6-5) and (8-7) transitions. The region from the hot core in G327.3-006 to the H ii region G327.3-0.5 (Fig. 1) was covered with on-the-fly maps of 200 '' × 240 '' spaced by 4 '' in declination and right ascension. We used the Fast Fourier Transform Spectrometer (FFTS, Klein et al., 2006) as backend with two units of fixed bandwidth of 1.5 GHz and 8192 channels per pixel. We used the two IF groups of the FFTS with an o ff set of ± 460 MHz between them. The original resolution of the dataset is 0 . 3 km s -1 ; the spectra were smoothed to 1 km s -1 for a better signal-to-noise ratio. The observations were performed under good weather conditions with a precipitable water vapour level between 0.5 and 0.7 mm. Typical single side band system temperatures during the observations were around 1600 K and 5200 K, for the low and high frequency channel respectively. The conversion from antenna temperature units to brightness temperatures was done assuming a forward e ffi ciency of 0.95 for all channels, and a main beam e ffi ciency of 0.48 for the 12 CO and 13 CO (6-5) observations, 0.45 for the 12 CO(7-6) data, and 0.44 for 13 CO(8-7), as measured on Jupiter in September 2008 3 . The pointing was checked on the continuum of the hot core G327.3-0.6 ( α J2000 = 15 h 53 m 07 s . 8 , δ J2000 = -54 · 36 ' 06 . '' 4). The maps were produced with the XY MAP task of CLASS90 4 , which convolves the data with a Gaussian of one third of the beam: the final angular resolution is 9 . '' 4 for the low frequency data, 8 . '' 1 for the high frequency.",
"pages": [
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},
{
"title": "2.2. Herschel SpaceObservatory",
"content": "The 13 CO (10-9) line (see Table 1) was mapped (size = 210 '' × 270 '' ) with the HIFI instrument (de Graauw et al., 2010) towards G327.3-0.6 on February, 18th, 2011 (observing day (OD) 645, observing identification number (OBSID) 1342214421. The centre of the map is α J2000 = 15 h 53 m 05 s . 48 , δ J2000 = -54 · 36 ' 06 . '' 2. The observations are part of the WISH GT-KP (van Dishoeck et al., 2011). Data were taken simultaneously in H and V polarisations using both the acousto-optical WideBand Spectrometer (WBS) with 1.1 MHz resolution and the correlator-based High-Resolution Spectrometer (HRS) with 250 kHz nominal resolution. In this paper we present only the WBS data. We used the on-the-fly mapping mode with Nyquist sampling. HIFI receivers are double sideband with a sideband ratio close to unity. The double side band system temperatures and total integration times are respectively 384 K and 3482 s. The rms noise level at 1 km s -1 spectral resolution is ∼ 0.1 K. Calibration of the raw data onto TA scale was performed by the in-orbit system (Roelfsema et al., 2012); conversion to Tmb was done with a beam e ffi ciency of 0.74 and a forward e ffi ciency of 0.96. The flux scale accuracy is estimated to be around 15% for band 3. Data calibration was performed in the Herschel Interactive Processing Environment(HIPE, Ott, 2010) version 6.0. Further analysis was done within the CLASS90 package. After inspection, data from the two polarisations were averaged together. The original angular resolution of the data is 19 . '' 0. The final maps were produced with the XY MAP task of CLASS90 and have an angular resolution of 21 . '' 1.",
"pages": [
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},
{
"title": "3.1. Morphology",
"content": "Figure 1 shows the 12 CO(6-5) integrated intensity map overlaid on the composite image of the IRAC Spitzer 3.6, 4.5 and 8.0 µ m bands of the region. The 12 CO emission traces the distribution of the 8.0 µ memission, but it is also associated with the infrared dark cloud found on the east of the hot core. The EGO candi- te G327.30-0.58 identified by Cyganowski et al. (2008) and clearly visible in Fig. 1, is also detected in the 12 CO data as secondary peak of emission (Fig. 2). The map of the integrated intensities of the 12 CO(7-6) line is also presented in Fig. 2 together with the integrated intensity of the 12 CO(3-2) line from Wyrowski et al. (2006). Figure 3 shows the distribution of the 13 CO(6-5), (8-7) and (10-9) emissions. The accuracy of the relative pointings was checked on the hot core G327.3-0.6. For this purpose, we derived integrated intensity maps of lines detected only towards this position, which are close in frequency to the 12 CO(6-5), 13 CO(6-5) and 13 CO(8-7) transitions, and therefore were observed simultaneously to the current dataset. From these data, we infer a position for the hot core in agreement with interferometric measurements at 3 mm (Wyrowski et al., 2008, and Table 2) within ∼ 1 . '' 5. All observed 12 CO transitions trace the H ii region G327.30.5 as well as the infrared dark cloud which hosts the hot core G327.3-0.6. Moreover, the 12 CO(6-5), (7-6) and 13 CO(6-5) lines show extended emission along a ridge running approximately N-S that matches very well with the distribution of the CO(3-2) transition. The hourglass shape hole to the west of the H ii region G327.3-0.5 where the 12 CO(3-2) emission is strongly reduced (see Wyrowski et al., 2006) is seen also in the 12 CO(65) and (7-6) lines which, although much weaker than in the rest of the map, are still detected at this position. All transitions peak towards the H ii region G327.3-0.5 where the main isotopologue lines have intensities up to 6065 K. The integrated intensities of the CO isotopologues show a distribution along a ring-like structure around the peak of the cm continuum emission (Goss & Shaver, 1970). The centre of the ring also coincides with the massive young stellar object number 87 identified in the near-infrared by Mois'es et al. (2011). Since the ring is detected also in highJ transitions of 13 CO, it is plausible that this morphology is true and not due to optical depth e ff ects. This structure likely coincides with the limb brightening of the hot surface of a PDR around G327.3-0.5 and could trace an expanding shell. We will investigate this scenario in Sect. 3.2. The hot core G327.3-0.6 shows up as a secondary peak in the integrated intensity maps of the 13 CO transitions, while the main CO isotopologue peaks to its north-west, probably because of optical depth e ff ects. Strong self-absorption profiles are indeed detected in all 12 CO lines towards the hot core (see Sect. 3.2). The submillimetre source SMM6 (seen in the continuum emission at 450 µ m by Minier et al., 2009) is detected as a peak of emission in all integrated intensity maps of 12 COandin 13 CO(65), although at the edge of the mapped region. The other submillimetre sources are also marked in Figs. 2. The EGO candidate G327.30-0.58 is also detected in the 13 CO(6-5) map (Fig. 3). The 13 CO(6-5) traces the whole IRDC and not only the active site of star formation where the EGO is detected. The continuum emission due to dust (seen for example at 870 µ min Fig. 3) follows the distribution of the 13 CO lines. In Fig. 4 we show the ratio of the integrated intensity of the 12 CO(6-5) transition (convolved to the 18 '' resolution of the 12 CO(3-2) data) to that of the 12 CO(3-2) line. This ratio ranges between 0.3 and 1.8; it has values slightly larger than one towards the H ii region (1.2 at its centre), while it is about unity towards the hot core. The peak is found south-west of the H ii region G327.3-0.5, where both lines are detected with a high confidence level. However, these results could be biased by the strong self absorption in both 12 CO lines (see Sect. 3.2). For this reason, we computed the ratio between the two transitions in four velocity ranges to cross-check the results of Fig. 4. The inferred values, however, do not change significantly.",
"pages": [
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},
{
"title": "3.2. Lineprofilesandvelocityfield",
"content": "The widespread 12 CO(6-5) emission shows line profiles with a typical width of ∼ 8 km s -1 in the gas between G327.3-0.5 and the infrared dark cloud. Broader profiles are detected in the infrared dark cloud and in the northern part of the H ii region G327.3-0.5. Figure 5 shows the distribution of the line width of the 12 CO(6-5) transition: the 12 CO(6-5) line width follows an arc-like structure that connects the H ii region G327.3-0.5 to the infrared dark cloud where the hot core is. Interestingly, the same morphology is seen in the LABOCA map of the region (Schuller et al., 2009). Line widths are similar for all 12 COlines, while they are consistently narrower in the 13 CO transitions. Representative spectra of all 12 CO transitions analysed in this study are presented in Fig. 6 towards the hot core, the IRDC position ((30 '' , 30 '' ) from the centre of the APEX maps, see Sect. 4.2 and Figs. 2-3) and the peak of the cm continuum emission in G327.3-0.5. Spectra of the 13 CO transitions are shown in Fig. 7. Red- and blue-shifted wings are detected in the 12 COlines in a velocity range between -71 and -24 km s -1 (in 12 CO(6-5)) towards G327.3-0.6 probably due to outflow motions. However, no sign of bipolar outflows is found when inspecting the integrated intensity maps of the blue- and red-shifted wings nor in position-velocity diagrams (Fig. 8). Moreover, very similar broad lines are detected along the whole extent of the infrared dark cloud, as shown in the top panel of Fig. 8. At the IRDC position, the wings in 12 CO(6-5) range from -60 to -31 km s -1 . All main isotopologue transitions analysed in this paper are a ff ected by self-absorption (see Fig. 6 for reference spectra towards the hot core, the IRDC position and the H ii region); moreover, even the 13 CO(6-5) line shows weak evidence of self-absorbed profile towards the hot core. Figure 9 shows the 12 CO(7-6) spectra overlaid on the continuum emission at 870 µ m: the self-reversed profile is spread over a large area and seems to follow the thermal dust continuum emission. Finally, the velocity field of the 12 CO transitions may help us to understand the nature of the ring detected towards the H ii region G327.3-0.5. We therefore used the task KSHELL built in the visualisation software package KARMA (Gooch, 1996). KSHELLcomputes an average brightness temperature on annuli about a user defined centre. A spherically symmetric expanding shell will look like a half ellipse in a (rv) diagram with the axis in the v direction twice the expansion velocity. Figure 10 shows the resulting (rv) diagram obtained with the 12 CO(6-5) data cube using the peak of the cm continuum emission as centre. The emission does not follow a perfect spherical shell. This is likely due to inhomogeneities in the distribution of the gas, as already seen in Fig. 11 where the distribution of the optical depth of 13 CO is not symmetric.",
"pages": [
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},
{
"title": "4.1. LTEanalysis",
"content": "From the line ratio of the 12 CO(6-5) to 13 CO(6-5) transitions we can derive the optical depth of the 12 CO(6-5) line emission, which can be then used to infer the excitation temperature of the line and the column density of 12 CO in the region. The line intensity in a given velocity channel of a given transition is where η is the beam filling factor (assumed to be 1 in the following analysis), F ν = h ν/ k × [exp(h ν/ kT) -1] -1 , T cbg = 2 . 7 K, and τν is the optical depth. Under the local thermodynamic equilibrium (LTE) assumption, Tex is assumed to be equal to the kinetic temperature of the gas and equal for all transitions. In the following analysis, we study the peak intensities of the 12 CO(6-5) and 13 CO(6-5) lines, and include only the cosmic background as background radiation and neglect, for example, any contribution from infrared dust emission since we do not have any map of the distribution of the dust temperature. This most likely a ff ects only our estimates at the hot core position and possibly towards the H ii region G327.3-0.5 where SABOCA continuum emission at 350 µ mis also detected (Wyrowski et al., in prep.). For an appropriate analysis of the emission from the hot core, see Rol ff s et al. (2011). Assuming that the 12 CO(6-5) emission is optically thick and that the 12 CO(6-5) and 13 CO(6-5) lines have the same excitation temperatures, the optical depth of the 13 CO(6-5) transition, τ 13 CO , is The optical depth of the 12 CO(6-5) transition can then be obtained by multiplying for the abundance of 12 CO relative to 13 CO, X 12 CO / 13 CO ∼ 60 (Wilson & Rood, 1994). From the optical depth of the 12 CO(6-5) line, one can also derive its excitation temperature using Eq. 1. Figure 11 shows the distribution of the optical depth of the 13 CO(6-5) line and of the excitation temperature of 12 CO(6-5). The 13 CO(6-5) emission is moderately optically thick (0.6-0.7) at the H ii region and at the infrared dark cloud, while it reaches values of ∼ 1.2 at the hot core position and in a small part of ring around the H ii region. The map distribution of the excitation temperature of the 12 CO(6-5) line is shown in the bottom panel of Fig. 11. The map is dominated by the H ii region, where T ex reaches values of 80 K in the ring around the H ii region and then decreases with increasing distance from it. The hot core and the rest of the infrared dark cloud have values around 30-35 K. The excitation temperature increases to the south west of the hot core, in a region where there is also 8 µ memission, and to the north-east of the H ii along a layer of gas also visible in the 12 CO(6-5) integrated intensity map (see Fig. 2), but more prominent in the T ex map and in the 8 µ memission map (see Fig. 1). From the optical depth and the excitation temperature of the 12 CO(6-5) line, we derived the H2 column density assuming a relative abundance of 12 CO relative to H2 of 2 . 7 × 10 -4 (Lacy et al., 1994). Results are shown in Fig. 12. The largest column density is found towards the hot core ( ∼ 3 × 10 22 cm -2 in the 9 . '' 4 beam of the 13 CO(6-5) data) and decreases along the infrared dark cloud with a distribution similar to that of the 870 µ m continuum emission. Three peaks around 10 22 cm -2 are found in the H ii region. We cross-checked our results by computing the H2 column density under the assumption that the 13 CO emission is optically thin. The results are consistent with those presented in Fig. 12; the largest di ff erences (of the order of 30%) are found towards those positions where the optical depth of the 13 CO(65) transition (Fig. 11) exceeds ∼ 0.7. The assumption of optically thin emission for 13 CO may be particularly useful for the inter-clump medium (arbitrarily defined as the region in the map where the 13 CO lines are not detected on individual spectra), towards which we infer H2 column densities of ∼ 2 × 10 21 cm -2 corresponding to a 13 COcolumndensity of ∼ 10 16 cm -2 (see also Sect. 5.1). We also computed column densities and rotational temperatures in the region using the rotational diagram technique applied to the 13 CO data. We did not include the 12 CO lines in the analysis because of their complex line profiles and high optical depths. Given the optical depth previously derived for the 13 CO(6-5) line, we did not apply any correction due to optical depth e ff ects to the 13 CO data. Results are consistent with the estimates based on equation 1. The main di ff erences between the two analyses are found towards the hot core, where the rotational temperature is higher than the excitation derived with equation 1 ( T rot ∼ 70 K and T ex ∼ 32 K) and the H2 column density lower (10 22 cm -2 versus 3 × 10 22 cm -2 obtained with the first method). The differences between the two methods are likely influenced by the self-absorption profile detected in the 12 CO(6-5) line which results in lower line intensities towards the regions of large column densities. In particular, while the first approach overestimates the optical depths (and hence column density) because of the self absorption, the column density derived with the rotational diagram analysis is likely underestimated towards the hot core because of the optically thin emission assumption, and should be corrected by a factor τ LTE / (1 -exp( τ LTE) -) ∼ 1.7. Finally, we computed the ratio between the amount of warm gas (traced by 12 CO and 13 CO(6-5) and shown in Fig. 12) and the total amount of gas (traced by the continuum emission at 870 µ m) as derived assuming a dust temperature equal to the excitation temperature of 12 CO(6-5) and a dust opacity of 0.0182 cm 2 g 1 (Kau ff mann et al., 2008). The results are shown in Fig. 13: the warm gas is only a small percentage ( ∼ 10%) of the total gas in the infrared dark cloud, while it reaches values up to ∼ 35% of the total gas in the ring surrounding the H ii region.",
"pages": [
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},
{
"title": "4.2. 13 COladder",
"content": "Since the G327.3-0.6 region was mapped in three di ff erent transitions of the 13 CO molecule, we can perform a multi-line analysis towards selected positions and infer the parameter of the gas. The advantage of 13 CO compared to the main isotopologue is in the lower opacities of the lines and in the less complex line profiles. For this analysis, we used the RADEX program (van der Tak et al., 2007) with expanding sphere geometry. The molecular dataset comes from the LAMDA database (Schoier et al., 2005) and includes collisional rates adapted from Yang et al. (2010). We ran models with temperatures from 20 to 200 K, densities in the range 10 4 -5 × 10 7 cm -3 , and 13 CO column densities between 10 14 and 10 19 cm -2 . All data were smoothed to the resolution of the 13 CO(10-9) map. We selected three positions for the analysis: the hot core, the IRDC position ((30 '' , 30 '' ) from the centre of the APEX maps), and the centre of the H ii region. The IRDC position was selected to be a position associated with high column density in the infrared dark cloud (see Figs. 2, 3 and 12) but without IR emission. However, it is only 10 '' to the north of the EGO candidate (Cyganowski et al., 2008, see Figs. 2-3), and therefore, given the beam of the observations, contamination from the embedded YSO may still be possible. Table 3 reports the measured line parameters of the 13 CO transitions obtained with Gaussian fits; based on these values, we adopt line widths of 6, 3 and 7, for the hot core, the IRDC and the H ii respectively, in agreement with values reported by San Jos'e-Garc'ıa et al. (2012) for the 13 CO(10-9) line towards a sample of intermediate- and highmass sources. The spectra are shown in Fig. 7. The results of the RADEX analysis are listed in Table 4 and shown in Fig. 14. For the IRDC position, the 13 CO(10-9) line intensity is not well fitted by our one-temperature model. This likely reflects the fact that the 13 CO(10-9) spectrum is dominated by the embedded source while the other two lines sample colder gas in the envelope. We considered a 20% calibration error for the 13 CO(6-5) and (8-7) observations and a 15% error for the 13 CO(10-9) data. Wyrowski et al. (2006) mapped the region with the APEX telescope in the C 18 O(3-2) line. Therefore, since no observations were performed in the 13 CO(3-2) transition, we included the C 18 O(3-2) data in Fig. 14. Note however, that the C 18 O(3-2) fluxes are not included in the fitting procedure, but that they are simply used to cross-check results. Since the C 18 O(3-2) flux corresponds to a lower limit to the flux of 13 CO(3-2) line, we also plotted the C 18 O(3-2) flux corrected for the abundance ratio of 13 CO to C 18 O, X 13 CO / C 18 O ∼ 8 (Wilson & Rood, 1994). This value is likely an upper limit to the flux of the 13 CO(3-2) line due to opacity e ff ects. An example of the χ 2 distribution projected on to the T -n plane is shown in Fig. 15 for the HII position, where the reduced χ 2 at the best fit position is 3. Figure 15 shows the typical inverse n -T relationship often seen in χ 2 distributions and due to the fact that density and temperature are, in the case of the CO molecule, not independent parameters (see Appendix C of van der Tak et al., 2007). Wenote here that the detection of the 13 CO(10-9) line breaks the degeneracy between density and temperature typical of 12 CO analyses (e.g., Kramer et al., 2004; van der Tak et al., 2007) and help to give stronger constraints: indeed, with the exception of the hot core, at least the temperature of the gas is well determined at all positions. The results of the RADEX analysis confirm that the LTE assumption used in Sect. 4.1 is reasonable since the inferred densities are much larger than the critical densities (a few 10 4 cm -3 for all three analysed transitions). Assuming X 12 CO / 13 CO ∼ 60 and an abundance of 12 COrelative to H2 of 2 . 7 × 10 -4 , the derived 13 CO column densities listed in Table 4 correspond to H2 column densities of some 10 22 cm -2 for the hot core and the IRDC position, and of 2 × 10 22 cm -2 for the H ii position. The derived column densities and temperatures are in agreement with those derived in Sect. 4.1 through rotational diagrams of the 13 CO emission. The 13 CO(6-5) optical depths are also in agreement with those estimated in Sect. 4.1 through the 13 CO and 12 CO(6-5) line ratio, with the exception of the hot core position: τ LTE ∼ 1.2 and τ RADEX ∼ 0.3 for the hot core, 0.6 and 0.5 for the H ii region, and 0.6 and 0.7 for the IRDC position. Wefinally stress that the results obtained with the LTE analysis (Sect. 4.1) and with the RADEX code (this section) are based on the assumptions that 1) all lines have a beam filling factor of one, and 2) that the emitting gas is homogeneous, whereas selfabsorption profiles in the 12 COlines indicate an excitation gradient along the line of sights. For optically thin lines ( 13 CO in the current case), a beam filling factor less than one (but equal for all transitions) would mostly a ff ect the column density and result in The errors represent the 3 σ confidence levels in the temperature-density plane or 3 σ lower (shown in brackets) limit when no stronger constraints can be inferred. larger values of N ; for optically thick lines, a smaller value of η would imply larger values of density and / or temperature. The uncertainties on the derived parameters due to the assumption of a homogeneous medium are of less immediate interpretation, and more complex radiative transfer codes (e.g., Hogerheijde & van der Tak, 2000) should be used to reproduce the observed line velocity profiles.",
"pages": [
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},
{
"title": "5.1. Total 12 COand 13 COemission",
"content": "Figure 16 shows the 12 CO and 13 CO ladders obtained by averaging the emission of the di ff erent observed transitions, smoothed to the resolution of the HIFI data, over four regions: the total map, the H ii region G327.3-0.5, the IRDC hosting the hot core (the selected region does include the hot core), and finally the inter-clump gas, which was defined as the region in the map where the 13 CO lines are not detected on individual spectra. This region has an equivalent radius of 50 '' (corresponding to ∼ 0.8 pc at the distance of the source). Examples of 12 CO line profiles towards the inter-clump gas are shown in Fig. 17. The C 18 O(3-2) cannot be used in this analysis because the observations cover a much smaller region than that mapped in 13 CO. The total mass of the mapped region can be computed using the excitation tem- , a visual extinction of 10, and a Doppler broadening of 3 (dashed curve) and 1 km s -1 (dotted curve). perature and H2 column density distributions shown in Figs. 11 and 12. This corresponds to ∼ 700 M /circledot . The four regions have similar 12 CO and 13 CO ladders. In order to correct for self-absorption, integrated fluxes were obtained for each of the four regions from line fitting of the CO spectra with one Gaussian component. While this works fine for the spectra of the IRDC hosting the hot core and for the inter- clump gas, the line profiles of the total map and of H ii region are red-skewed and therefore the fluxes derived with this method are likely underestimated. For the main isotopologue, the flux of the (7-6) and (6-5) transitions is very similar, although for the IRDC + HCand the inter-clump the flux of the (7-6) line is lower than that of the (6-5) line. On the other hand, in the 13 CO ladder the peak flux decreases with increasing energy level. For all transitions presented in this paper, the spectra are dominated in intensity by the H ii region, whose flux is of the order of 60% of the total flux for the main isotopologue lines, and ranging from ∼ 49% of the total flux in the (6-5) line to ∼ 85% in the (10-9) transition for 13 CO (see Table 5). The main di ff erence between the 12 CO spectra and those of 13 CO lies in the emission from the inter-clump gas: for all 12 CO lines, the intensity is relatively strong, 10% of the flux from the whole region. On the other hand, the flux of the 13 CO lines coming from the inter-clump gas decreases with increasing J, from ∼ 7% of the total flux for J = 6 to ∼ 2% for J = 10. The general behaviour of the 12 CO and 13 CO ladders is qualitatively compatible with PDR models from Koester et al. (1994) for high density (10 6 -10 7 cm -3 ) clouds illuminated on one side by a UV radiation field (their model B). In Fig. 16, we show the predicted CO and 13 CO line intensities for models with a density of 10 7 cm -3 , incident UV fields with strength 10 3 and 10 4 relative to the average interstellar field (Draine, 1978), a visual extinction of 10, and a Doppler broadening of 3 and 1 km s -1 . High densities ( n > 10 6 cm -3 , in agreement with our results from Sect. 4.2) are needed to locate the peak of the CO ladders at mid-, highJ transitions (see Figs. 9-10, 12-13 of Koester et al. 1994). Stronger UV radiation fields also shift the peak of the CO ladders to higher J transitions than observed. In Fig. 16, the 12 CO model intensities are corrected by a factor 0.2 and 0.25 to correct for di ff erent line- etween the model and the observations, and possibly for beam dilution e ff ects. On the other hand, the 13 CO results of Fig. 16 are not scaled down by any factor as they are far too weak to match the observations. Koester et al. (1994) already noticed that the predicted line intensities of midJ 13 CO transitions in their models are much weaker than observed in star-forming regions. They proposed that midJ 13 CO emission comes from a large number of filamentary structures, or clumps, along the line of sight. In this way, the modelled line intensity of midJ 13 CO lines would increase significantly as the lines are optically thin, while it would not change for optically thick transitions. Rotational diagrams of the 13 CO emission applied to the spectra of the H ii region, of the IRDC and of the inter-clump gas infer rotational temperatures of 66 K, 47 K and 44 K, respectively, and 13 CO column densities of 6 × 10 15 cm -2 for the H ii region and the IRDC, and of 2 × 10 15 cm -2 for the inter-clump gas. Since the inter-clump gas has physical parameters very similar to those of the IRDC region, but a much lower column density, we suggest that it is composed of high-density clumps with low filling factors. This is again in agreement with PDR models (e.g., Koester et al., 1994; Cubick et al., 2008) which predict strong emission at midJ 13 COand highJ 12 CO lines in the case of small, low mass, high density clumps. Cubick et al. (2008) suggested that the COBE 12 CO ladder of the Milky Way can be reproduced by a clumpy PDR model, and that the bulk of the Galactic FIR line emission comes from PDRs around the Galactic population of massive stars. Our observations seem to confirm this result, since the CO emission of the G327.3-0.6 region is dominated by the PDR around the H ii region. Our results are also consistent with the findings from Davies et al. (2011) and Mottram et al. (2011). These authors studied the properties of massive YSOs and compact H ii regions in the RMS survey (Hoare et al., 2005), and found that there is no significant population of massive YSOs above ∼ 10 5 L /circledot , while compact H ii regions are detected up to ∼ 10 6 L /circledot . Since highJ CO lines are among the most important cooling lines in PDR, they reflect the luminosity of their heating sources: if the luminosity distribution of massive stars in the Galaxy is dominated by H ii regions and not by younger massive stars, then we also expect that the CO distribution follows the same rule.",
"pages": [
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},
{
"title": "5.2. Comparisonswithotherstarformingregions",
"content": "Large-scale mapping of some low- and high-mass star forming regions was performed in several 12 CO transitions. However, given the di ff erent critical densities of the lines, we prefer to compare our results with studies carried on with J > 3 CO lines. Excitation temperatures around 8-30 K are found in extended di ff use emission and towards the brightest positions, respectively, in low-mass star forming regions (e.g., Davis et al., 2010; Curtis et al., 2010), while massive star-forming regions are usu- ally warmer as confirmed by our findings (see also Wilson et al., 2001; Jakob et al., 2007; Kirk et al., 2010; Wilson et al., 2011; Peng et al., 2012). The CO column densities (10 17 -10 18 cm -2 from the LTE analysis) found in G327 are also comparable with values obtained in other massive star-forming regions (Wilson et al., 2001; Jakob et al., 2007; White et al., 2010; Wilson et al., 2011). Comparison with 12 CO large maps of other high-mass star forming regions would be important to verify whether our result that the 12 CO distribution is dominated by the H ii region is a common feature or not. However, most studies do not cover di ff erent evolutionary phases as in our case. For OMC1, Peng et al. (2012) confirmed that the peak of the integrated intensity of several CO isotopologue lines is close to the OrionKL hot core (although Orion-south and the Orion Bar PDR are also very prominent). One should notice however, that Orion is roughly six times closer to the Sun than G327.3-0.6, and therefore the Orion Bar and Orion-KL would be much closer on sky ( ∼ 30 '' ) if one would place them at the distance of G327.30.6. Moreover, Orion-KL likely represents a special case since it hosts a very powerful outflow (e.g., Kwan & Scoville, 1976; Snell et al., 1984), which could alter the distribution of 12 CO in the region. Indeed, Marrone et al. (2004) show that broad velocity emission arises mainly from the Orion-KL region, while much of the narrower emission arises from the PDR excited by the M42 H ii region.",
"pages": [
11
]
},
{
"title": "5.3. Self-absorptionprofiles",
"content": "As noted in Sect. 3.2, all 12 CO transitions analysed in this paper are a ff ected by self-absorption, which is likely to be due to cold gas surrounding a warmer component (Phillips et al., 1981). In particular along the infrared dark cloud (Fig. 8), the 12 CO(6-5) line has blue-skewed profiles in the north-east (towards the EGO and the IRDC positions) and the red-skewed ones towards the south-west (the hot core). Blue- and red-skewed profiles (e.g., Mardones et al., 1997) are commonly interpreted as due to rotation or outflow motions (which should produce equal numbers of red and blue profiles, and could therefore explain the profiles detected towards the EGO and IRDC position, the hot core and the H ii region, Fig. 6) or to infall (which should produce profiles which are skewed towards the blue, e.g. towards the EGO and IRDC position) or to expansion (which should produce profiles skewed towards the red and could be responsible for the 12 CO spectra of the hot core and the H ii region). From the PV diagram of the 12 CO(6-5) line, we do not have any evidence of global rotation towards the hot core and the red-skewed profile can be interpreted in terms of expansion or outflow motion. Similarly, from Fig. 10 we see that the emission does not follow a perfect expanding spherical shell which might imply that the rotation is on the origin of the self-absorbed profile seen towards the H ii region. Finally, the blue-skewed line profile detected toward the EGO and IRDC positions are typical of infall motion.",
"pages": [
11
]
},
{
"title": "6. Conclusions",
"content": "To study the e ff ect of feedback from massive star forming regions in their surrounding environment, we selected the region G327.3-0.6 for large scale mapping of several midJ 12 CO and 13 COlines with the APEX telescope and of the highJ 13 CO(109) transition with the Herschel satellite. Our results can be summarised as follows: Acknowledgements. The authors thank Dr. Joe Mottram for a careful review of the manuscript and an anonymous referee for useful comments and suggestions. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. HIFI has been designed and built by a consortium of institutes and university departments from across Europe, Canada and the United States under the leadership of SRON Netherlands Institute for Space Research, Groningen, The Netherlands and with major contributions from Germany, France and the US. Consortium members are: Canada: CSA, U.Waterloo; France: CESR, LAB, LERMA, IRAM; Germany: KOSMA, MPIfR, MPS; Ireland, NUI Maynooth; Italy: ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri- INAF; Netherlands: SRON, TUD; Poland: CAMK, CBK; Spain: Observatorio Astron'omico Nacional (IGN), Centro de Astrobiolog'ıa (CSIC-INTA). Sweden: Chalmers University of Technology - MC2, RSS & GARD; Onsala Space Observatory; Swedish National Space Board, Stockholm University - Stockholm Observatory; Switzerland: ETH Zurich, FHNW; USA: Caltech, JPL, NHSC.",
"pages": [
11,
12
]
},
{
"title": "References",
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"pages": [
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}
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2013A&A...550A..84K
https://arxiv.org/pdf/1301.1680.pdf
<document>
<section_header_level_1><location><page_1><loc_15><loc_85><loc_84><loc_87></location>Magnetic field topology of the RS CVn star II Pegasi ?</section_header_level_1>
<text><location><page_1><loc_28><loc_82><loc_72><loc_84></location>O. Kochukhov 1 , M.J. Mantere 2 , T. Hackman 2 ; 3 , and I. Ilyin 4</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_78><loc_71><loc_80></location>1 Department of Physics and Astronomy, Uppsala University, Box 516, Uppsala SE-751 20, Sweden e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_10><loc_77><loc_79><loc_78></location>2 Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Box 64, Helsinki FI-00014, Finland</list_item>
<list_item><location><page_1><loc_10><loc_76><loc_80><loc_77></location>3 Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, Piikkiö FI-21500, Finland</list_item>
<list_item><location><page_1><loc_10><loc_74><loc_73><loc_75></location>4 Leibniz Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, Potsdam D-14482, Germany</list_item>
</unordered_list>
<text><location><page_1><loc_10><loc_72><loc_46><loc_73></location>Received 24 September 2012 / Accepted 10 December 2012</text>
<section_header_level_1><location><page_1><loc_46><loc_69><loc_54><loc_70></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_10><loc_63><loc_90><loc_68></location>Context. The dynamo processes in cool active stars generate complex magnetic fields responsible for prominent surface stellar activity and variability at di GLYPH<11> erent time scales. For a small number of cool stars magnetic field topologies were reconstructed from the time series of spectropolarimetric observations using the Zeeman Doppler imaging (ZDI) method, often yielding surprising and controversial results.</text>
<text><location><page_1><loc_10><loc_61><loc_90><loc_63></location>Aims. In this study we follow a long-term evolution of the magnetic field topology of the RS CVn binary star II Peg using a more self-consistent and physically more meaningful modelling approach compared to previous ZDI studies.</text>
<text><location><page_1><loc_10><loc_56><loc_90><loc_61></location>Methods. We collected high-resolution circular polarisation observations of II Peg using the SOFIN spectropolarimeter at the Nordic Optical Telescope. These data cover 12 epochs spread over 7 years, comprising one of the most comprehensive spectropolarimetric data sets acquired for a cool active star. A multi-line diagnostic technique in combination with a new ZDI code is applied to interpret these observations.</text>
<text><location><page_1><loc_10><loc_46><loc_90><loc_56></location>Results. Wehave succeeded in detecting clear magnetic field signatures in average Stokes V profiles for all 12 data sets. These profiles typically have complex shapes and amplitudes of GLYPH<24> 10 GLYPH<0> 3 of the unpolarised continuum, corresponding to mean longitudinal fields of 50-100 G. Magnetic inversions using these data reveals evolving magnetic fields with typical local strengths of 0.5-1.0 kG and complex topologies. Despite using a self-consistent magnetic and temperature mapping technique, we do not find a clear correlation between magnetic and temperature features in the ZDI maps. Neither do we confirm the presence of persistent azimuthal field rings found in other RS CVn stars. Reconstruction of the magnetic field topology of II Peg reveals significant evolution of both the surface magnetic field structure and the extended magnetospheric field geometry on the time scale covered by our observations. From 2004 to 2010 the total field energy drastically declined and the field became less axisymmetric. This also coincided with the transition from predominantly poloidal to mainly toroidal field topology.</text>
<text><location><page_1><loc_10><loc_42><loc_90><loc_45></location>Conclusions. A qualitative comparison of the ZDI maps of II Peg with the prediction of dynamo theory suggests that the magnetic field in this star is produced mainly by the turbulent GLYPH<11> 2 dynamo rather than the solar GLYPH<11> GLYPH<10> dynamo. Our results do not show a clear active longitude system, nor is there an evidence of the presence of an azimuthal dynamo wave.</text>
<text><location><page_1><loc_10><loc_40><loc_77><loc_41></location>Key words. polarisation - stars: activity - stars: atmospheres - stars: magnetic fields - stars: individual: II Peg</text>
<section_header_level_1><location><page_1><loc_6><loc_36><loc_18><loc_37></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_6><loc_16><loc_49><loc_35></location>Direct, spatially-resolved observations of the solar disk demonstrate the ubiquitous presence of magnetic fields and their key role in driving time-dependent, energetic processes. It is believed that magnetic fields are generated in the solar interior, due to a complex interplay between the non-uniformities in the internal rotation profile, large-scale flows, and vigorous turbulence due to convective motions (Ossendrijver 2003). Although the rotation profile, with two prominent regions of high radial shear near the bottom and top of the solar convection zone, is known rather reliably from helioseismic observations (e.g. Thompson et al. 2003), measurements of the potentially very important meridional flow pattern, especially deeper in the convection zone, are highly uncertain (Gough & Hindman 2010). A variety of models of the solar dynamo exists (e.g. Dikpati & Charbonneau 1999; Käpylä et al. 2006; Kitchatinov & Olemskoy</text>
<text><location><page_1><loc_51><loc_24><loc_94><loc_37></location>2012), but none of them is capable of fully reproducing the observed characteristics of the solar magnetic cycle. Direct numerical simulations aiming at including all the relevant physics in a single model, with the expectation being that all the observable features from the flow patterns up to the magnetic cycle would emerge self-consistently, have so far been only marginally successful (Ghizaru et al. 2010; Racine et al. 2011; Käpylä et al. 2012a). Therefore, it is fair to say that the solar cycle remains a theoretical challenge, with some key information on the largescale flow patterns yet to be supplied by observations.</text>
<text><location><page_1><loc_51><loc_10><loc_94><loc_24></location>Compared to the Sun, many cool stars exhibit enhanced activity levels, suggesting the presence of stronger surface magnetic fields produced by more e GLYPH<14> cient dynamos. Observations of such active stars o GLYPH<11> er possibilities to constrain theoretical models by examining the e GLYPH<14> ciency of dynamo mechanisms as a function of stellar mass, age, and rotation rate. However, direct magnetic field analysis of cool active stars is impeded by the weakness of polarisation signatures in the spatially-unresolved stellar spectra. Furthermore, dynamos in cool stars usually give rise to topologically complex magnetic fields which cannot be meaningfully characterised using observational techniques sen-</text>
<text><location><page_2><loc_6><loc_91><loc_49><loc_93></location>sitive only to the global magnetic field component (Borra & Landstreet 1980; Vogt 1980).</text>
<text><location><page_2><loc_6><loc_76><loc_49><loc_90></location>A major breakthrough in studying the magnetism of cool stars was achieved by combining multi-line polarisation diagnostic techniques (Donati et al. 1997) applied to high-resolution spectropolarimetric observations with the inversion procedure of Zeeman Doppler imaging (ZDI, Brown et al. 1991; Donati & Brown 1997). This approach, capable of providing spatiallyresolved information about stellar magnetic field topologies, was applied to a number of late-type stars (e.g. Donati et al. 2003; Petit et al. 2004), but only three objects - AB Dor, LQ Hya, and HR1099 - were systematically followed with multiple magnetic maps on the time scales of five to ten years.</text>
<text><location><page_2><loc_6><loc_48><loc_49><loc_75></location>The results of ZDI mapping are often spectacular in their ability to resolve fine details of stellar magnetic field geometries, but also controversial in several aspects. First, analysis of stellar spectra is limited to only circular polarisation because, being roughly ten times weaker, the linear polarisation signatures are not readily detectable at the moderate signal-to-noise (S / N) ratios used for the circular polarisation monitoring (Kochukhov et al. 2011). Supplying inversion algorithms with such incomplete Stokes vector data is known to lead to spurious features in the reconstructed magnetic maps (Donati & Brown 1997; Kochukhov & Piskunov 2002). Second, interpretation of the mean-line shapes constructed by averaging thousands of lines is inevitably inferior to modelling individual spectral lines because of the di GLYPH<14> culty in choosing appropriate mean-line parameters (Kochukhov et al. 2010). Finally, and most importantly, nearly all magnetic field maps reconstructed from the Stokes V observations of cool active stars were obtained separately and inconsistently from the mapping of brightness distributions from Stokes I , raising questions about the validity of magnetic maps and preventing direct analysis of the spatial relation between magnetic and temperature inhomogeneities.</text>
<text><location><page_2><loc_6><loc_34><loc_49><loc_48></location>These considerations suggest that substantial progress in understanding cool-star magnetism through ZDI requires continuing research in several directions. On the one hand, the sample of active stars studied with multiple-epoch magnetic images has to be expanded to justify the far-reaching conclusions previously inferred from the analysis of a few objects. On the other hand, ZDI studies must re-examine key methodological limitations of this technique and strive to employ physically realistic modelling approaches whenever possible. This paper addresses both of these aspects in a detailed ZDI analysis of the RS CVn binary II Peg.</text>
<text><location><page_2><loc_6><loc_10><loc_49><loc_33></location>The source of the most powerful stellar flares ever observed (Osten et al. 2007) and the brightest X-ray object within 50 pc (Makarov 2003), II Peg (HD 224085, HIP 117915) is one of the most prominent active cool stars in the solar neighbourhood. This star is an RS CVn-type, single-line spectroscopic binary (SB1) with an orbital period of GLYPH<25> 6.72 days, consisting of a K2IV primary and a low-mass (M0-M3V) secondary. The primary star exhibits copious manifestations of the magnetically-driven surface activity, including a strong non-thermal emission in the UV and optical chromospheric lines and in the X-ray and radio wavelength regions. It also shows powerful flares as well as regular photometric and spectroscopic variations due to evolving cool spots. Berdyugina et al. (1998b) studied the orbital motion of the massive component and provided a comprehensive summary of the physical properties of II Peg. Many studies examined photometric variations of this star (e.g. Siwak et al. 2010; Roettenbacher et al. 2011, and references therein), aiming to explore long-term activity cycles and, in particular, to investigate</text>
<text><location><page_2><loc_51><loc_91><loc_94><loc_93></location>the role of active longitudes (Berdyugina et al. 1999; Rodonò et al. 2000).</text>
<text><location><page_2><loc_51><loc_72><loc_94><loc_90></location>Other studies targeted II Peg with high-resolution spectroscopic observations with the goal to constrain the spot temperatures using TiO absorption bands (O'Neal et al. 1998; Berdyugina et al. 1998b) and to analyse configurations of the surface temperature inhomogeneities with the Doppler imaging technique (Berdyugina et al. 1998a; Gu et al. 2003; Lindborg et al. 2011; Hackman et al. 2012). Early DI images corresponding to the period between 1994 and 2002 suggested persistent presence of a pair of active longitudes and showed major changes in the surface structure on a time-scale of less than a year (Berdyugina et al. 1998a, 1999; Lindborg et al. 2011). More recent DI maps covering the years from 2004 to 2010 revealed the star entering a low-activity state characterised by a more random distribution of cool spots (Hackman et al. 2012).</text>
<text><location><page_2><loc_51><loc_62><loc_94><loc_72></location>The underlying cause of the remarkable surface activity of II Peg - the dynamo-generated magnetic field - was first detected in this star by Donati et al. (1992) with four circular polarisation observations of a few magnetically sensitive lines. The presence of the Stokes V signatures in spectral lines was subsequently confirmed by Donati et al. (1997) using a multi-line polarimetric analysis, but no systematic phase-resolved investigation of the magnetic field topology of II Peg has ever been undertaken.</text>
<text><location><page_2><loc_51><loc_45><loc_94><loc_62></location>Since 2004 we have been monitoring the magnetic field in II Peg using the SOFIN spectropolarimeter at the Nordic Optical Telescope. We have acquired a unique collection of highresolution Stokes I and V spectra covering GLYPH<25> 5.5 years or almost 300 stellar rotations. In this paper we present a comprehensive analysis of these polarisation data, focusing on the selfconsistent ZDI mapping of stellar magnetic field topology. The accompanying study by Hackman et al. (2012) obtained temperature maps from the same SOFIN Stokes I spectra. Preliminary attempts to map the magnetic field geometry of II Peg, using about 10% of the spectropolarimetric data analysed here, were presented first by Carroll et al. (2007), and then by Carroll et al. (2009b) and Kochukhov et al. (2009).</text>
<text><location><page_2><loc_51><loc_32><loc_94><loc_45></location>This paper is organised as follows. In Sect. 2 we describe the acquisition and reduction of the spectropolarimetric observations of II Peg. Detection of the magnetic signatures in spectral lines with the help of a multi-line analysis is presented in Sect. 3. The methodology of the self-consistent ZDI and the choice of stellar parameters required for mapping is described in Sect. 4. Results of the magnetic and temperature inversions of II Peg are presented and analysed in Sect. 5. The outcome of our investigation is discussed in the context of previous observational and theoretical studies in Sect. 6.</text>
<section_header_level_1><location><page_2><loc_51><loc_29><loc_81><loc_30></location>2. Spectropolarimetric observations</section_header_level_1>
<text><location><page_2><loc_51><loc_12><loc_94><loc_28></location>The spectropolarimetric observations of II Peg analysed here were carried out during the period from Jul. 2004 to Jan. 2010 using the SOFIN echelle spectrograph (Tuominen et al. 1999) at the 2.56-m Nordic Optical Telescope. The spectrograph, which is mounted at the Cassegrain focus and is equipped with a 2048 GLYPH<2> 2048 pixel CCD detector, was configured to use its second camera yielding resolving power of R GLYPH<25> 70000. For ZDI analysis we used 12 echelle orders, each covering 40-50 Å in the wavelength region between 4600 and 6135 Å. The data for II Peg were obtained during 12 individual epochs, for which from 3 to 12 observations were recorded over the time span ranging from 3 to 14 nights. The spectra have typical S / N ratio of 200-300.</text>
<text><location><page_2><loc_51><loc_10><loc_94><loc_12></location>The circular polarisation observations were obtained with the Zeeman analyser, consisting of a calcite plate used as a beam</text>
<text><location><page_3><loc_6><loc_76><loc_49><loc_93></location>splitter and an achromatic rotating quarter-wave plate. At least two exposures with the quarter-wave retarder angles separated by 90 GLYPH<14> is required to obtain the Stokes V spectrum. Rotation of the quarter-wave plate has the e GLYPH<11> ect of exchanging positions of the right- and left-hand circularly polarised beams on the detector. The beam exchange procedure (Semel et al. 1993) facilitates an accurate polarisation analysis because possible instrumental artefacts change sign when the quarter-wave plate is rotated and then cancel out when all sub-exposures are combined. To accumulate su GLYPH<14> cient signal-to-noise ratio, a sequence of 2 or 3 double exposures was obtained in this way. The length of individual sub-exposures varied between 15 and 25 min, depending on seeing and weather conditions.</text>
<text><location><page_3><loc_6><loc_62><loc_49><loc_76></location>The data were reduced with the help of the 4A software package (Ilyin 2000). Specific details of the SOFIN polarimeter design and corresponding data reduction methods are given by Ilyin (2012). The spectral processing included standard reduction steps, such as bias subtraction, flat field correction, removal of the scattered light, and optimal extraction of the spectra. Wavelength calibration used ThAr exposures obtained before and after each single exposure to account for environmental variations and gravitational bending of a Cassegrain mounted spectrograph by means of a global fit of the two ThAr wavelength solutions versus time.</text>
<text><location><page_3><loc_6><loc_49><loc_49><loc_62></location>Spectropolarimetric observations of strongly magnetic Ap stars are frequently performed with SOFIN in a configuration similar to the one used for II Peg. These measurements agree closely with the results obtained for the same stars at other telescopes (e.g. Ryabchikova et al. 2007; Ilyin 2012). Repeated observations of a very slowly rotating Ap star GLYPH<13> Equ reveals no systematic di GLYPH<11> erences in the Stokes V profiles during the entire period of our observations of II Peg. This confirms the robustness and accuracy of the employed instrument calibration and data reduction methods.</text>
<text><location><page_3><loc_6><loc_42><loc_49><loc_49></location>The log of all 88 SOFIN Stokes V observations of II Peg is given in Table 1. The rotation of the primary component of II Peg is synchronised with the orbital motion. Therefore, we calculated rotational phases using the orbital ephemeris from Berdyugina et al. (1998b)</text>
<formula><location><page_3><loc_6><loc_40><loc_49><loc_41></location>T = 2449582 : 9268 + 6 : 724333 GLYPH<2> E (1)</formula>
<text><location><page_3><loc_6><loc_36><loc_49><loc_39></location>which refers to the time of orbital conjunction. The orbital solution from the same study was applied to correct the radial velocity variation caused by the orbital motion.</text>
<text><location><page_3><loc_6><loc_23><loc_49><loc_35></location>Our 12 sets of spectropolarimetric observations of II Peg comprise 3 to 12 distinct rotational phases, whereas GLYPH<24> 10 evenly distributed phases are needed for an optimal ZDI reconstruction (Kochukhov & Piskunov 2002). Assuming that each observation provides a coverage of 10% of the rotational period, we quantified the phase coverage of each data set as a fraction f of the full rotational cycle (see Table 1). Our SOFIN observations yield from f = 30% (epoch 2005.0) to f = 87% (epoch 2009.7). The three epochs with the best phase-coverage are 2004.6 (75%), 2007.6 (81%), and 2009.7 (87%).</text>
<text><location><page_3><loc_6><loc_10><loc_49><loc_22></location>The quality of ZDI mapping is reduced for the data sets with an insu GLYPH<14> cient phase-coverage. Yet, as demonstrated by numerical experiments (Donati & Brown 1997; Kochukhov & Piskunov 2002) and ZDI studies based on observations with poor phasecoverage (Donati 1999; Hussain et al. 2009), it is still possible to extract useful information about the stellar surface features from just a few spectra and from observations covering only half of the stellar rotation cycle. Aiming to maintain consistency in our long-term ZDI analysis of II Peg, we performed magnetic inversions for all 12 epochs. At the same time, we kept in mind the</text>
<text><location><page_3><loc_51><loc_91><loc_94><loc_93></location>di GLYPH<11> erence in data quality during the assessment of the inversion results.</text>
<section_header_level_1><location><page_3><loc_51><loc_87><loc_78><loc_88></location>3. Multi-line polarisation analysis</section_header_level_1>
<section_header_level_1><location><page_3><loc_51><loc_85><loc_74><loc_86></location>3.1. Least-squares deconvolution</section_header_level_1>
<text><location><page_3><loc_51><loc_70><loc_94><loc_84></location>Even the most active late-type stars exhibit a relatively low amplitude of the circular polarisation signal in spectral lines, rarely exceeding 1% of the Stokes V continuum intensity. Given the moderate quality of the SOFIN spectropolarimetric observations of II Peg, we were able to detect Stokes V signatures at the 23 GLYPH<27> confidence level in only a few of the strongest spectral lines (Fig. 1). This makes it challenging to model the magnetic field of II Peg using a direct analysis of individual line profiles. A widely-used approach to overcome this di GLYPH<14> culty is to employ a multi-line technique, combining information from hundreds or thousands of individual metal lines.</text>
<text><location><page_3><loc_51><loc_46><loc_94><loc_70></location>In this study of II Peg we applied the least-squares deconvolution (LSD) technique (Donati et al. 1997) using the code and methodology described by Kochukhov et al. (2010). The LSD technique extracts information from all available lines by assuming that the Stokes I and V spectra can be represented by a superposition of corresponding scaled mean profiles. The scaling factors, established under the weak-line and weak-field approximations, are equal to the central line depth d for Stokes I and to the product of the line depth, laboratory wavelength of the transition GLYPH<21> , and its e GLYPH<11> ective Landé factor z for Stokes V , respectively. A linear superposition of scaled profiles is mathematically equivalent to a convolution of the average profile with a line mask. This simple stellar spectrum model can be inverted, obtaining a high-quality mean profile for a given line mask and observational data. Kochukhov et al. (2010) showed that, for the magnetic fields below GLYPH<25> 2 kG, the LSD Stokes V profiles derived in this way can be interpreted as a real Zeeman triplet line with an average Landé factor.</text>
<text><location><page_3><loc_51><loc_31><loc_94><loc_46></location>The atomic line data required for the application of LSD to observations of II Peg were obtained from the vald database (Kupka et al. 1999). We extracted a total of 1580 spectral lines with the central depth larger than 10% of the continuum. The line intensities were calculated for a marcs model atmosphere (Gustafsson et al. 2008) with the e GLYPH<11> ective temperature T e GLYPH<11> = 4750 K, surface gravity log g = 3.5, and metallicity [ M = H ] = GLYPH<0> 0 : 25. The mean parameters of the resulting line mask are GLYPH<21> 0 = 5067 Å, z 0 = 1 : 21, and d 0 = 0 : 46. The same parameters were used for normalising the Stokes I and V LSD weights. The LSD profiles were calculated with a 1.2 km s GLYPH<0> 1 step for the velocity range GLYPH<6> 60 km s GLYPH<0> 1 .</text>
<text><location><page_3><loc_51><loc_20><loc_94><loc_30></location>The LSD analysis of the SOFIN observations of II Peg allowed us to achieve a S = N gain of 30-40, obtaining a definite detection (false alarm probability < 10 GLYPH<0> 5 ) of the circular polarisation signatures for all but one Stokes V spectrum (phase 0.035 for epoch 2008.7). The resulting mean Stokes V profiles are compatible with the marginal polarisation seen in individual lines (see Fig. 1), but have a much higher quality, making them suitable for detailed modelling.</text>
<section_header_level_1><location><page_3><loc_51><loc_17><loc_77><loc_18></location>3.2. Mean longitudinal magnetic field</section_header_level_1>
<text><location><page_3><loc_51><loc_10><loc_94><loc_16></location>In Table 1 we report the maximum amplitude of the LSD Stokes V profiles and the mean longitudinal magnetic field h B z i determined from their first moment. We found typical LSD Stokes V amplitudes of the order of 0.1% and h B z i in the range 30250 G, determined with the precision of GLYPH<25> 5 G. These results are</text>
<figure>
<location><page_4><loc_6><loc_64><loc_27><loc_94></location>
</figure>
<figure>
<location><page_4><loc_28><loc_64><loc_49><loc_94></location>
<caption>Fig. 1. Comparison of the Stokes V profiles of the Ca i 6122.2 Å line ( left panel ) with the scaled LSD V profiles ( right panel ) at epoch 2004.6. The spectra for di GLYPH<11> erent rotational phases are shifted vertically. The 1GLYPH<27> error bars are indicated on the left side of each panel.</caption>
</figure>
<text><location><page_4><loc_6><loc_53><loc_49><loc_56></location>compatible with the previous longitudinal field measurements by Vogt (1980), which had an accuracy of 100-160 G and did not yield a convincing detection of magnetic field in II Peg.</text>
<text><location><page_4><loc_6><loc_28><loc_49><loc_52></location>Despite the ubiquitous definite detections of the circular polarisation signatures, 16 out of 88 LSD profiles of II Peg do not exhibit a significant mean longitudinal magnetic field. A comparison of h B z i measurements with the maximum LSD Stokes V amplitude (Fig. 2) shows no obvious correlation. This indicates that, with a few exceptions (e.g. phase 0.531 at epoch 2004.6 illustrated in Fig. 1), the Stokes V profiles of II Peg are generally complex and cannot be fully characterised by their first-order moment. Nevertheless, analysis of the longitudinal magnetic field measurements does reveal an intriguing long-term behaviour. As illustrated in Fig. 3, the range of the longitudinal field variation with rotational phase systematically decreased from 2004 to 2010. Furthermore, it appears that the phaseaveraged value of the longitudinal magnetic field was significantly deviating from 0 during the period from the beginning of our monitoring until the epoch 2006.9. This suggests the presence of large areas of positive magnetic polarity on the visible hemisphere of the star before that epoch and a more symmetric distribution of the field orientation at later epochs.</text>
<section_header_level_1><location><page_4><loc_6><loc_23><loc_43><loc_26></location>4. Self-consistent magnetic and temperature mapping</section_header_level_1>
<section_header_level_1><location><page_4><loc_6><loc_21><loc_38><loc_22></location>4.1. Zeeman Doppler imaging code I nvers 13</section_header_level_1>
<text><location><page_4><loc_6><loc_10><loc_49><loc_20></location>Reconstruction of the distribution of magnetic field and temperature on the surface of II Peg was carried out with the help of our new ZDI code I nvers 13. This inversion software represents a further development of the I nvers 10 code (Piskunov & Kochukhov 2002; Kochukhov & Piskunov 2002), previously applied for mapping magnetic geometries and chemical spots on Ap stars (Kochukhov et al. 2004; Kochukhov & Wade 2010; Lüftinger et al. 2010). Both codes incorporate full treatment of</text>
<figure>
<location><page_4><loc_52><loc_73><loc_93><loc_94></location>
<caption>Fig. 2. Maximum amplitude of the LSD Stokes V profiles as a function of the absolute value of the mean longitudinal magnetic field. The observations for which a polarisation signal is definitely detected and h B z i is measured at > 3GLYPH<27> significance are shown with squares. Circles correspond to the observations for which h B z i is not significant, but polarisation signal is still detected. The triangle in the lower-left corner corresponds to a single non-detection of the polarisation signal in the LSD Stokes V profile.</caption>
</figure>
<figure>
<location><page_4><loc_52><loc_40><loc_93><loc_61></location>
<caption>Fig. 3. Range of longitudinal field variation with rotational phase for di GLYPH<11> erent epochs of II Peg observations. The line thickness is proportional to the phase coverage f . The squares show longitudinal field averaged over rotational phase.</caption>
</figure>
<text><location><page_4><loc_51><loc_10><loc_94><loc_32></location>the polarised radiative transfer using a modified Diagonal Element Lambda-Operator (DELO) algorithm (Rees et al. 1989; Piskunov & Kochukhov 2002). All four Stokes parameters are calculated simultaneously and fully self-consistently, taking into account Zeeman broadening and splitting of spectral lines in the intensity spectra on the one hand, and attenuation of the polarised profiles due to temperature spots on the other hand. Some aspects of this approach have already been incorporated in the ZDI of cool stars in the preliminary studies of II Peg (Carroll et al. 2007, 2009b; Kochukhov et al. 2009). However, the majority of recent applications of ZDI (e.g. Skelly et al. 2010; Waite et al. 2011; Marsden et al. 2011) still systematically neglect effects of temperature spots in the magnetic inversions. As demonstrated by the numerical tests of Rosén & Kochukhov (2012), the lack of self-consistency in temperature and magnetic mapping can lead to severe artefacts if cool spots coincide with major concentrations of the magnetic flux.</text>
<text><location><page_5><loc_6><loc_74><loc_49><loc_93></location>Calculation of the local Stokes parameter profiles by I n -vers 13 is based on a prescribed line list of atomic and molecular lines, normally obtained from the vald and marcs databases, and a grid of model atmospheres. In the present study of II Peg we employed a grid consisting of 18 marcs model atmospheres covering a T e GLYPH<11> range of 3000-5750 K with a 100-250 K step in temperature. The Stokes IQUV profiles and continuum intensities I c are calculated for the temperature of a given stellar surface element by quadratic interpolation between three sets of model spectra corresponding to the nearest points in the model atmosphere grid. This allows an accurate semi-analytical computation of the derivatives with respect to temperature. On the other hand, the derivatives with respect to the three magnetic field vector components are evaluated numerically, using a simple one-sided di GLYPH<11> erence scheme.</text>
<text><location><page_5><loc_6><loc_49><loc_49><loc_73></location>The local profiles are convolved with a Gaussian function to take into account instrumental and radial-tangential macroturbulent broadening, Doppler shifted, and summed for each rotational phase on the wavelength grid of observed spectra. The resulting Stokes parameter profiles are normalised by the phasedependent continuum flux and compared with observations. In calculating the goodness of the fit we approximately balance the contributions of each Stokes parameter by scaling the respective chi-square terms by the inverse of the mean amplitude of the corresponding Stokes profiles. Test inversions by Kochukhov & Piskunov (2002) and Rosén & Kochukhov (2012) verified simultaneous reconstruction of the magnetic and starspot maps using this weighting scheme. This approach is also routinely used in the reconstruction of Ap-star magnetic fields from four Stokes parameter observations (Kochukhov et al. 2004; Kochukhov & Wade 2010). In the study of II Peg the contributions of the Stokes I and V spectra were weighted as 1:30. Inversion results are not sensitive to the exact choice of the relative weighting of Stokes I and V .</text>
<text><location><page_5><loc_6><loc_37><loc_49><loc_49></location>The iterative adjustment of the surface maps for matching available observations is accomplished by means of the Levenberg-Marquardt optimisation algorithm, which enables convergence in typically 10-20 iterations starting from a homogeneous temperature distribution and zero magnetic field. The I nvers 13 code is optimised for execution on massivelyparallel computers using MPI libraries. We refer the reader to Kochukhov et al. (2012) for further details on the numerical methods and computational techniques employed in I nvers 13.</text>
<text><location><page_5><loc_6><loc_23><loc_49><loc_37></location>As shown numerically by Donati & Brown (1997) and Piskunov & Kochukhov (2002), and analytically by Piskunov (2005), ZDI with only Stokes I and V spectra is an intrinsically ill-posed problem, requiring the use of a regularisation or penalty function to reach a stable and unique solution. The reconstruction of temperature in I nvers 13 is regularised using the Tikhonov method, very similar to many previous DI studies of cool active stars (e.g. Piskunov & Rice 1993) and our recent temperature mapping of II Peg with the same SOFIN data (Hackman et al. 2012). In this approach the code seeks a surface distribution with a minimum contrast between adjacent surface elements.</text>
<text><location><page_5><loc_6><loc_10><loc_49><loc_22></location>For the magnetic field reconstruction, I nvers 13 o GLYPH<11> ers a choice of either directly mapping the three magnetic vector components and applying the Tikhonov regularisation individually to the radial, meridional, and azimuthal magnetic component maps (Piskunov & Kochukhov 2002), or expanding the field into a spherical harmonic series (Donati et al. 2006). In the latter formulation of the magnetic inversion problem, the free parameters optimised by the code are the spherical harmonic coe GLYPH<14> cients GLYPH<11>' m , GLYPH<12>' m , and GLYPH<13>' m , giving the amplitudes of the poloidal and toroidal terms for a given angular degree ' and azimuthal num-</text>
<text><location><page_5><loc_51><loc_80><loc_94><loc_93></location>ber m (see Eqs. 2-8 in Donati et al. 2006). In particular, the radial field is determined entirely by the poloidal contribution (coe GLYPH<14> cient GLYPH<11> ), whereas both poloidal and toroidal components (coe GLYPH<14> cients GLYPH<12> and GLYPH<13> , respectively) are contributing to the meridional and azimuthal field. In this description of the stellar magnetic field topology through a spherical harmonic expansion, the role of regularisation is played by a penalty function equal to the sum of squares (magnetic energies) of the harmonic coe GLYPH<14> -cients weighted by ' 2 . This prevents the code from introducing high-order modes not justified by the observational data.</text>
<text><location><page_5><loc_51><loc_68><loc_94><loc_80></location>Expansion in spherical harmonics has the advantage of automatically satisfying the divergence-free condition for a magnetic field. It also allows us to conveniently characterise the relative contributions of di GLYPH<11> erent components to the stellar magnetic field topology and to study the evolution of these contributions with time. Therefore, for the magnetic mapping of II Peg we adopted the spherical harmonic approach, choosing ' max = 10 which corresponds to a total of 360 independent magnetic field parameters.</text>
<text><location><page_5><loc_51><loc_55><loc_94><loc_68></location>Similar to other quantities obtained by solving a regularised ill-posed problem, the spherical harmonic coe GLYPH<14> cients cannot be attributed formal error bars because, in addition to the observational data, the individual modes are constrained by the penalty function. Therefore, their formal error bars are strongly dependent on the choice of regularisation parameter, especially for the high-' modes. This is why here, as well as in all previous ZDI studies employing spherical harmonic expansion (e.g. Donati et al. 2006; Skelly et al. 2010; Fares et al. 2012), no formal uncertainty estimates are derived for the harmonic coe GLYPH<14> cients.</text>
<text><location><page_5><loc_51><loc_36><loc_94><loc_55></location>As inferred from the previous numerical tests of ZDI inversions (Donati & Brown 1997; Kochukhov & Piskunov 2002; Rosén & Kochukhov 2012), reconstruction of the magnetic field distributions from the Stokes I and V data alone su GLYPH<11> ers from some ambiguities. The most important problem is a cross-talk between the radial and meridional field components at low latitudes (i.e. for the regions below the stellar equator for the rotational geometry of II Peg). On the other hand, the harmonic regularisation or parameterisation of the magnetic field maps partly alleviates this problem (Donati 2001; Kochukhov & Piskunov 2002), because in this case the inversion code is not allowed to vary the three magnetic vector components arbitrarily. Instead, the meridional and azimuthal components are coupled via the GLYPH<12> and GLYPH<13> harmonic coe GLYPH<14> cients which avoids the cross-talk between the radial and meridional fields, at least for the low-' values.</text>
<section_header_level_1><location><page_5><loc_51><loc_33><loc_91><loc_34></location>4.2. Reconstructing temperature spots from LSD profiles</section_header_level_1>
<text><location><page_5><loc_51><loc_20><loc_94><loc_32></location>Most previous ZDI modelling of the Stokes I and V LSDprofiles of late-type active stars relied on simple analytical formulas, often a Gaussian approximation, to represent the local intensity and polarisation profiles. These coarse line-profile models have either entirely neglected dependence of the local line intensity on temperature (e.g. Petit et al. 2004) or used disk-integrated spectra of suitably chosen cool and hot slowly rotating template stars to represent local contribution of the spot and photosphere, respectively (e.g. Donati et al. 2003).</text>
<text><location><page_5><loc_51><loc_10><loc_94><loc_20></location>Here we develop a more sophisticated approach to interpret the LSD profile time series. We aim to describe the LSD Stokes I and V spectra with self-consistent polarised radiative transfer calculations, based on realistic model atmospheres, for a fictitious spectral line with average atomic parameters. Comprehensive investigation of the properties of LSD profiles by Kochukhov et al. (2010) showed that this approach yields an accurate description of the mean circular polarisation line shapes</text>
<figure>
<location><page_6><loc_9><loc_63><loc_46><loc_93></location>
<caption>Fig. 4. Comparison of temperature mapping from a real line and from LSD profiles. a) True temperature distribution. b) DI map reconstructed from the simulated observations of a real spectral line. c) Temperature reconstruction from the simulated LSD profiles assuming mean-line parameters.</caption>
</figure>
<text><location><page_6><loc_6><loc_40><loc_49><loc_53></location>for the magnetic field strengths below GLYPH<25> 2 kG. For stronger fields, details of the LSD Stokes V profile shape cannot be reproduced, although the LSD profile moments still yield correct longitudinal magnetic field. According to previous studies, magnetic fields found on the surfaces of RS CVn- and BY Dra-type active stars are safely within this limit. On the other hand, analyses of Ap / Bp stars hosting much stronger fields (e.g. Wade et al. 2000; Silvester et al. 2012) proves that the LSD line-averaging method itself does not systematically underestimate magnetic field strength even beyond the weak-field regime.</text>
<text><location><page_6><loc_6><loc_14><loc_49><loc_40></location>At the same time, Kochukhov et al. (2010) found that a response of the LSD Stokes I profile to the variation of chemical composition di GLYPH<11> ers from that of any real spectral line, which prevents an accurate mapping of the chemical spots in Ap stars using LSD profiles (Folsom et al. 2008). One might suspect that reconstruction of the temperature inhomogeneities from the LSD spectra is similarly limited. It is clear that the temperature sensitivity of an average profile, composed of an essentially random mixture of thousands of lines with diverse temperature responses, cannot be known as well as the one for a set of judiciously chosen individual spectral lines with accurate atomic parameters. On the other hand, typical Stokes I atomic line profile variations in active stars are dominated by the continuum brightness e GLYPH<11> ect, which influences all lines in a similar way (Vogt & Penrod 1983; Unruh & Collier Cameron 1995). Adding to this a greatly enhanced S = N of the LSD spectra, one might hope to achieve a reasonable reconstruction of temperature spots treating the LSD intensity profiles as a real spectral line. To clarify whether this is indeed possible, we have carried out numerical tests of temperature inversions based on simulated LSD spectra.</text>
<text><location><page_6><loc_6><loc_10><loc_49><loc_13></location>First, we established mean-line parameters appropriate for the LSD line mask applied to the SOFIN observations of II Peg. Among the 1580 spectral lines included in this mask, Fe i is the</text>
<text><location><page_6><loc_51><loc_72><loc_94><loc_93></location>most common ion (about 40% of all lines). Thus, we adopted the Fe i identification for a fictitious line representing LSD profiles and obtained the preliminary set of atomic parameters necessary for spectrum synthesis by combining the average excitation energy of the lower level, oscillator strength, and broadening constants for this ion with the mean wavelength and Landé factor (5067 Å and 1.21, respectively) for the entire line list. Then we adjusted the oscillator strength and van der Waals damping constant by fitting the synthetic LSD profiles derived from a theoretical spectrum covering the same wavelength interval as real observations. These calculations adopted the stellar atmospheric parameters discussed below (Sect. 4.3) and were performed for the v e sin i of II Peg and for the non-rotating star with the same parameters. In both cases we found that single-line calculations provide an excellent fit to the LSD profiles obtained from the synthetic spectra.</text>
<text><location><page_6><loc_51><loc_52><loc_94><loc_70></location>At the next step, we simulated spectra of a star with temperature inhomogeneities, using a photospheric temperature of 4750 K and a spot temperature of 3700 K. The Stokes I spectra for the entire SOFIN wavelength range were computed for 10 equidistant rotational phases, assuming i = 60 GLYPH<14> , v e sin i = 23 kms GLYPH<0> 1 , and no magnetic field. A surface temperature map consisting of four circular spots located at di GLYPH<11> erent latitudes (see Fig. 4a) was employed in these calculations. These theoretical spectra were processed with our LSD code in exactly the same way as real stellar observations. The resulting set of synthetic LSD profiles was interpreted with I nvers 13 using the line parameters established above. For comparison, we also reconstructed a temperature map from the direct forward calculations for the same spectral line.</text>
<text><location><page_6><loc_51><loc_26><loc_94><loc_49></location>A comparison of the DI maps inferred from the simulated data with the true temperature distribution is presented in Fig. 4. The reconstructions from the simulated observations of the real spectral line and from the simulated LSD profiles are generally successful in recovering the properties of cool spots. However, the temperature DI using LSD profiles shows a tendency to produce spurious hot surface features in which the temperature is overestimated by 200-300 K. We emphasise that this problem appears entirely due to a loss of information about real temperature sensitivity of the local profiles of individual spectral lines. Fortunately, this bias does not significantly interfere with the reconstruction of large low-temperature spots, although their contrast seems to be systematically underestimated. Thus, we conclude that the temperature DI based on a single-line radiative transfer approximation of the LSD profiles is a viable approach to mapping the distribution of cool spots on the surfaces of active stars. At the same time, the reliability of hot features recovered with this method is questionable.</text>
<text><location><page_6><loc_51><loc_10><loc_94><loc_24></location>Limitations of LSD-based temperature inversions partly explain why some of the temperature maps presented here di GLYPH<11> er from those in our previous analysis (Hackman et al. 2012). The di GLYPH<11> erences are mainly caused by the use here of LSD profiles, while our previous analysis was based on individual lines. While individual lines will give a more accurate result, this approach su GLYPH<11> ers from a lower S / N. At the same time, neglect of the Zeeman broadening and intensification in earlier temperature inversions may also contribute to the discrepancy with the present results. In general, both of these e GLYPH<11> ects will influence the spot temperatures and latitudes.</text>
<section_header_level_1><location><page_7><loc_6><loc_92><loc_22><loc_93></location>4.3. Stellar parameters</section_header_level_1>
<text><location><page_7><loc_6><loc_66><loc_49><loc_91></location>Di GLYPH<11> erent sets of atmospheric parameters have been deduced in previous studies of II Peg. The most thorough model atmosphere analyses were those by Berdyugina et al. (1998b) and Ottmann et al. (1998). The first paper suggested T e GLYPH<11> = 4600 K, log g = 3.2, and [ M = H ] = GLYPH<0> 0 : 4, whereas the second paper has inferred T e GLYPH<11> = 4800 K, log g = 3.65, and [ Fe = H ] = GLYPH<0> 0 : 24. A comparison of the average SOFIN observations with the theoretical spectra computed using the synth 3 code (Kochukhov 2007) and marcs model atmospheres supports the latter set of stellar parameters. Therefore, we adopted a marcs model atmosphere with T e GLYPH<11> = 4750 K, log g = 3.5, and [ M = H ] = GLYPH<0> 0 : 25 to represent an unspotted star. This temperature was also used as a starting guess for DI. All spectrum synthesis calculations assumed a microturbulent velocity of GLYPH<24> t = 2 kms GLYPH<0> 1 and a radial-tangential macroturbulent broadening of GLYPH<16> t = 4 kms GLYPH<0> 1 . These parameters are compatible with the values determined in previous studies. We note that the synthetic Fe i line approximating the LSD profiles of II Peg is weak ( W GLYPH<21> = 40 mÅ) and, therefore, relatively insensitive to the choice of GLYPH<24> t.</text>
<text><location><page_7><loc_6><loc_55><loc_49><loc_66></location>Based on previous studies (Berdyugina et al. 1998b; Frasca et al. 2008), we adopted an inclination of the stellar rotational axis i = 60 GLYPH<14> . Using the three data sets with the best phasecoverage (epochs 2004.6, 2007.6, and 2009.7), we found that the best fit to the Stokes I LSD profiles is achieved for v e sin i = 23 GLYPH<6> 0 : 5 km s GLYPH<0> 1 . This value of the projected rotational velocity is consistent with v e sin i = 22 : 6 GLYPH<6> 0 : 5 km s GLYPH<0> 1 determined by Berdyugina et al. (1998b) and used in the recent DI studies by Lindborg et al. (2011) and Hackman et al. (2012).</text>
<text><location><page_7><loc_6><loc_34><loc_49><loc_54></location>A latitude-dependent di GLYPH<11> erential rotation can be incorporated in the ZDI with I nvers 13. This e GLYPH<11> ect was ignored by previous spectroscopic DI investigations of II Peg and was theoretically predicted to be negligible in the rapidly rotating stars with deep convective envelopes (Kitchatinov & Rüdiger 1999). On the other hand, photometric analyses occasionally claimed detection of the di GLYPH<11> erential rotation in II Peg (Henry et al. 1995; Siwak et al. 2010; Roettenbacher et al. 2011), yet giving contradictory results, mainly because of the di GLYPH<14> culty of constraining the spot latitudes in light curve modelling. However, even the largest value of the di GLYPH<11> erential rotation coe GLYPH<14> cient reported in the literature k = 0 : 0245 (Siwak et al. 2010) is substantially smaller than the solar value of k = 0 : 19 and corresponds to an insignificant surface shearing for the time span of most of our SOFIN data sets. Therefore, ZDI analysis of II Peg was carried out assuming no di GLYPH<11> erential rotation.</text>
<section_header_level_1><location><page_7><loc_6><loc_30><loc_35><loc_31></location>5. Magnetic field topology of II Peg</section_header_level_1>
<text><location><page_7><loc_6><loc_14><loc_49><loc_29></location>Results of the simultaneous reconstruction of magnetic field topology and temperature distribution for II Peg are illustrated for the four data sets with best phase-coverage in Figs. 5 and 6 and for the remaining epochs in the online Figs. 7-9. For each data set we present four rectangular maps, showing the distribution of temperature as well as the radial, meridional, and azimuthal field components. A comparison between observed and computed LSD Stokes I and V profiles is illustrated next to the corresponding surface images. The model profiles generally achieve an adequate fit to observations, with median mean deviations of 0.15% and 0.01% for the Stokes I and V LSD profiles, respectively.</text>
<text><location><page_7><loc_6><loc_10><loc_49><loc_13></location>The maximum local magnetic field intensity inferred by our ZDI code reaches 1 kG for 2004.6 data set, but is typically on the order of 400-500 G for the later magnetic images. Judging</text>
<text><location><page_7><loc_51><loc_84><loc_94><loc_93></location>from these results, the field strength on the surface of II Peg was steadily decreasing from our first observations to later epochs. The field topology appears to be rather complex in 2004-2005, with many localised magnetic spots in all three magnetic vector component maps. As the field became weaker, this configuration evolved into a simpler topology, often dominated by large regions of common field polarity (e.g. epoch 2007.6).</text>
<text><location><page_7><loc_51><loc_76><loc_94><loc_84></location>The temperature maps of II Peg reconstructed from LSD profiles show cool spots with an 800-1000 K contrast relative to the photospheric T = 4750 K. Occasionally, the inversion code reconstructed spots which are a few hundred K hotter than the photosphere. However, the numerical experiments discussed in Sect. 4.2 suggest that these features are not reliable.</text>
<text><location><page_7><loc_51><loc_70><loc_94><loc_76></location>Inversions were carried out for all epochs, including the three data sets (2005.0, 2005.9, and 2008.7) with a poor phasecoverage. Temperature maps for these three data sets are dominated by a strong axisymmetric component, which should be regarded as spurious.</text>
<section_header_level_1><location><page_7><loc_51><loc_66><loc_72><loc_68></location>5.1. Average field parameters</section_header_level_1>
<text><location><page_7><loc_51><loc_51><loc_94><loc_65></location>The two independent ZDI reconstructions obtained for the epochs 2006.7 and 2006.9 allow us to investigate short-term changes of the surface distributions. The temperature maps inferred from the observations separated by three months are very similar. Both images are dominated by a large low-latitude cool spot at 180 GLYPH<14> longitude and an extended high-latitude spot group in the longitude interval 300 GLYPH<14> to 60 GLYPH<14> . The azimuthal field maps, representing the dominant magnetic component for both epochs, are also fairly similar. At the same time, distributions of the weaker radial and meridional field components exhibit significant di GLYPH<11> erences, suggesting field evolution.</text>
<text><location><page_7><loc_51><loc_28><loc_94><loc_51></location>Next, to detect possible systematic changes either in the phases of the surface magnetic field distribution or in the total magnetic field strength, we calculated di GLYPH<11> erent types of averages of the ZDI maps. First, we averaged over the visible latitude range in each map, to obtain magnetic field profiles that depend on longitude (or phase) only. The profiles shown in Fig. 11 are averaged over the latitude interval from GLYPH<0> 60 GLYPH<14> to 90 GLYPH<14> for the di GLYPH<11> erent magnetic field components as function of time. This procedure can reveal azimuthal dynamo waves, that were visible in the surface temperature maps of this object during 1994-2002 (see Lindborg et al. 2011). There is no evidence for this type of dynamo wave from the ZDI maps. This agrees with the results of Hackman et al. (2012), who reported the disappearance of the clear drift pattern in the surface temperature maps during these years. The radial field plot, on the other hand, reveals a rather abrupt appearance and disappearance of spots of opposite polarities at a certain phase which are, however, irregular with time.</text>
<text><location><page_7><loc_51><loc_10><loc_94><loc_28></location>Finally, we calculated the root-mean-square values of the magnetic field over each ZDI map, characterising the overall magnetic field strength (shown in Fig. 12). Interestingly, all the magnetic field components are of comparable strength, immediately hinting, from basic dynamo theory, towards an GLYPH<11> 2 dynamo operational in the object - the presence of di GLYPH<11> erential rotation would lead to the e GLYPH<14> cient shearing of the poloidal field into a toroidal field, in which case the azimuthal component would be observed to dominate over the other components. The radial and meridional components are clearly decreasing monotonically with time, reaching a minimum at around the year 2009. After that, the radial field possibly starts rising again. The azimuthal field shows a somewhat di GLYPH<11> erent trend in time: at first it is somewhat weaker than the other components, slightly increas-</text>
<figure>
<location><page_8><loc_9><loc_37><loc_91><loc_91></location>
<caption>Fig. 5. Magnetic field topology and temperature distribution of II Peg at epochs 2004.6 and 2006.7. For each epoch the two columns on the left compare the observed Stokes I and V LSD profiles ( symbols ) and the theoretical spectrum synthesis fit ( solid lines ). Spectra corresponding to di GLYPH<11> erent rotational phases are shifted vertically. The scale is given in % for Stokes V and in units of the continuum intensity for Stokes I . The four rectangular maps represent surface distributions of the radial, meridional, and azimuthal magnetic field components and corresponding temperature reconstructed for each epoch. The contours are plotted with a step of 0.2 kG over the magnetic maps and with a step of 200 K over the temperature distributions. The thick contour lines indicate where the field changes sign in the magnetic maps. The vertical bars above each rectangular panel indicate rotational phases of individual observations. The rotational phase runs from right to left on all maps.</caption>
</figure>
<text><location><page_8><loc_6><loc_16><loc_49><loc_25></location>ing during 2004-2007, after which it also shows a decreasing trend. Similar to the radial component, it seems to start rising again after 2010. Therefore, judging from the magnetic field strength, it seems plausible that the magnetic activity level of the star has been declining during the epoch 2004-2009, while the signs of rising activity can be seen at least in the rms field strength for later epochs.</text>
<section_header_level_1><location><page_8><loc_6><loc_13><loc_37><loc_14></location>5.2. Evolution of harmonic field components</section_header_level_1>
<text><location><page_8><loc_6><loc_10><loc_49><loc_12></location>Magnetic field maps reconstructed by our ZDI code are parameterised in terms of the spherical harmonic coe GLYPH<14> cients corre-</text>
<text><location><page_8><loc_51><loc_20><loc_94><loc_25></location>sponding to the poloidal and toroidal field components. In addition to the analysis of 2D maps, this representation provides another convenient possibility to characterise the field topology and its long-term evolution.</text>
<text><location><page_8><loc_51><loc_10><loc_94><loc_20></location>The sum of the spherical harmonic coe GLYPH<14> cients squared is proportional to the total energy contained in the stellar magnetic field. Figure 13a illustrates how this parameter has changed for II Peg between 2004 and 2010. Consistently with the results discussed above, we find a noticeable decrease of the total field energy in the period between 2004 and 2008, with a possible reversal of this trend afterwards. One can note that the total magnetic energy recovered from the data sets containing only a few</text>
<figure>
<location><page_9><loc_9><loc_37><loc_91><loc_92></location>
<caption>Fig. 6. Same as Fig. 5 for epochs 2007.6 and 2009.7.</caption>
</figure>
<text><location><page_9><loc_6><loc_27><loc_49><loc_32></location>spectra (e.g. 2005.0, 2005.9) is systematically underestimated compared to the trend defined by other maps. It is reassuring that the analysis of these data sets does not result in spurious strong magnetic field features.</text>
<text><location><page_9><loc_6><loc_15><loc_49><loc_27></location>The time dependence of the relative contributions of the poloidal and toroidal field components is illustrated in Fig. 13b. It appears that our observations of II Peg reveal a cyclic change of the field topology on the time scale of a few years. Ignoring magnetic maps corresponding to epochs with a partial phasecoverage, one can conclude that II Peg exhibited a predominantly poloidal field before 2007.6 and a mainly toroidal field afterwards. However, the di GLYPH<11> erence between the energies of the two components is never much larger than 20-30%.</text>
<text><location><page_9><loc_6><loc_10><loc_49><loc_15></location>Finally, Fig. 13c assesses relative contribution of the axisymmetric and non-axisymmetric field components as a function of time. Here we define axisymmetric harmonic components as those with m < '= 2 and non-axisymmetric ones as m GLYPH<21> '= 2 (e.g.</text>
<paragraph><location><page_9><loc_51><loc_30><loc_94><loc_32></location>Fares et al. 2009). With this definition, non-axisymmetric field dominates all the time, except for the last two observing epochs.</paragraph>
<text><location><page_9><loc_51><loc_10><loc_94><loc_24></location>As mentioned in Sect. 4.1, formal error bars cannot provide a realistic estimate of uncertainties of the spherical harmonic coe GLYPH<14> cients recovered in a regularised least-squares problem. Instead, the scatter of points corresponding to close observational epochs gives an idea of the uncertainties. We can see that in Figs. 12 and 13 the points inferred from the poor phase-coverage data sets often deviate significantly from the general trends. On the other hand, there are only a few cases when results obtained from the good phase-coverage data exhibit abrupt changes. This suggests that the trends examined in this and the previous sections are real and are not dominated by random inversion errors.</text>
<figure>
<location><page_10><loc_10><loc_36><loc_46><loc_93></location>
<caption>Fig. 11. Magnetic field components (top: radial field, middle: meridional field, bottom: azimuthal field) averaged over the latitude interval GLYPH<0> 60 GLYPH<14> to 90 GLYPH<14> from each ZDI map. Each stripe represents the average field from one ZDI map, extended over the time axis to help the visualisation. The stripes are organised as function of time, according to their observational epoch, running from top to bottom. Dark colours represent negative polarities, bright colours positive ones; in all figures a linear colour table with minimum of GLYPH<0> 300 G and maximum of 300 G has been used.</caption>
</figure>
<section_header_level_1><location><page_10><loc_6><loc_20><loc_35><loc_21></location>5.3. Extended magnetospheric structure</section_header_level_1>
<text><location><page_10><loc_6><loc_10><loc_49><loc_19></location>The results of ZDI calculations are commonly used to investigate an extended stellar magnetospheric structure (Donati et al. 2008; Jardine et al. 2008; Gregory et al. 2008; Fares et al. 2012). The knowledge of the field topology above the stellar surface and in the immediate circumstellar environment allows photospheric magnetic field measurements to be connected with the studies of stellar coronas, X-ray emission, and prominences and the inter-</text>
<text><location><page_10><loc_51><loc_78><loc_94><loc_93></location>action between the mass loss and magnetic field to be investigated. To determine the structure of the circumstellar magnetic field, one can use the potential field source surface (PFSS) extrapolation method developed for the solar magnetic field by van Ballegooijen et al. (1998) and adapted for stellar magnetic fields by Jardine et al. (2002). In this method the extended stellar magnetic field is represented as the gradient of a scalar potential expanded in a spherical harmonic series. The boundary condition for the radial field component at the stellar surface is provided by the empirical magnetic field maps. The outer boundary condition is given by a source surface of radius R s beyond which the field is assumed to be purely radial.</text>
<text><location><page_10><loc_51><loc_67><loc_94><loc_77></location>We reconstructed the extended magnetospheric structure of II Peg with the help of an independently developed PFSS code. This software was applied to all our ZDI maps. The source surface is placed at R s = 3 R ? , which is plausible given the mean value of the solar source surface radius of 2 : 5 R GLYPH<12> . Previous potential field extrapolation studies adopted similar R s values for other cool active stars (e.g. Jardine et al. 2002; Hussain et al. 2002).</text>
<text><location><page_10><loc_51><loc_45><loc_94><loc_67></location>The magnetospheric structure of II Peg predicted by our ZDI maps is illustrated in Fig. 14 for the four epochs with best phasecoverage. The stellar magnetosphere is shown at four distinct rotational phases, with di GLYPH<11> erent colours highlighting open and closed magnetic field lines. The evolution of the large-scale field is evident from this figure. Since the contribution of the small-scale (and hence less reliably reconstructed) field structures decays more rapidly with radius, this potential field extrapolation essentially presents a distilled view of the radial component of the ZDI maps, in which only the most robust large-scale information is retained. We find that during the first two epochs (2004.6 and 2006.7) the global field is nearly axisymmetric and is reminiscent of a dipole aligned with the stellar rotational axis. Adrastic change of the large-scale magnetic topology occurs between epochs 2006.7 and 2007.6. Simultaneously with a sharp decline in the total magnetic field energy, the field becomes more complex and decidedly non-axisymmetric.</text>
<section_header_level_1><location><page_10><loc_51><loc_40><loc_62><loc_41></location>6. Discussion</section_header_level_1>
<section_header_level_1><location><page_10><loc_51><loc_38><loc_81><loc_39></location>6.1. Comparison with previous ZDI studies</section_header_level_1>
<text><location><page_10><loc_51><loc_25><loc_94><loc_37></location>The only other RS CVn system repeatedly studied with ZDI is HR 1099 (V711 Tau). The papers by Donati (1999), Donati et al. (2003), and Petit et al. (2004) presented magnetic field and brightness distributions recovered for about five epochs each, spanning the period from 1991 to 2002. In all these studies magnetic field reconstruction was carried out assuming an immaculate photosphere and the local line profiles were treated with a Gaussian approximation or using LSD profiles of slowly rotating inactive standards.</text>
<text><location><page_10><loc_51><loc_10><loc_94><loc_25></location>The observed LSD Stokes V profiles of HR 1099 have a typical peak-to-peak amplitude of 0.15%, whereas the reconstructed field intensities are of the order of a few hundred G on average and reach up to GLYPH<24> 1 kG locally. This is comparable to our observational data and inversion results for II Peg. The ZDI studies of HR1099 revealed dominant azimuthal magnetic fields, often arranged in unipolar rings encircling the star at a certain latitude. Repeated magnetic inversions suggested stability of these structures on the time scales of several years. The authors attributed these horizontal fields to a global toroidal magnetic component produced by a non-solar dynamo mechanism distributed throughout the stellar convection zone.</text>
<figure>
<location><page_11><loc_8><loc_35><loc_47><loc_93></location>
<caption>Fig. 12. Root-mean-square values of the di GLYPH<11> erent magnetic field components calculated over each ZDI map: a) radial field, b) meridional field, c) azimuthal field, d) total field. The relative sizes of symbols and their colours correspond to the phase coverage of individual data sets, similar to Fig. 3.</caption>
</figure>
<text><location><page_11><loc_6><loc_12><loc_49><loc_25></location>Compared to these studies of HR 1099, our ZDI maps of II Peg show a considerably smaller relative contribution of azimuthal fields. We still find a dominant toroidal component; however, these results are not fully equivalent nor easily comparable to those of, for example, Donati (1999) because here we use a harmonic representation of the magnetic field topology and hence are able to disentangle toroidal and poloidal contributions to the azimuthal field, whereas previous studies of HR 1099 completely ignored the poloidal contribution to the azimuthal field.</text>
<text><location><page_11><loc_6><loc_10><loc_49><loc_12></location>It is clear that our data contain no evidence of the persistent unipolar azimuthal ring-like magnetic structures similar to</text>
<figure>
<location><page_11><loc_53><loc_47><loc_92><loc_93></location>
<caption>Fig. 13. Long-term evolution of di GLYPH<11> erent contributions to the magnetic field topology of II Peg. The panels show: a) variation of the total magnetic energy, b) the relative contributions of the poloidal ( filled symbols ) and toroidal ( open symbols ) harmonic components, and c) the relative contributions of the axisymmetric ( filled symbols ) and nonaxisymmetric ( open symbols ) components. The relative sizes of symbols and their colours correspond to the phase coverage of individual data sets, similar to Fig. 3.</caption>
</figure>
<text><location><page_11><loc_51><loc_10><loc_94><loc_30></location>those reported for HR 1099. Thus, either the dynamo mechanism operates di GLYPH<11> erently in the two RS CVn stars with nearly identical fundamental parameters, or azimuthal fields may represent an artefact owing to a simplified ZDI approach adopted for HR 1099 (Carroll et al. 2009a). To this end, we note that any axially-symmetric structure appearing in stellar DI maps must be carefully examined to exclude possible systematic biases and, at least, must be connected to the stationary features in the observed profiles to prove its reality. Neither was done for HR1099. Faced with this discrepancy between major features of the magnetic maps of II Peg and HR 1099, we conclude that a definite confirmation of the dominant ring-like azimuthal fields in the latter star and associated inferences about field generation mechanisms must await improved inversion methodologies and observations in all four Stokes parameters (Kochukhov et al. 2011).</text>
<figure>
<location><page_12><loc_9><loc_39><loc_90><loc_93></location>
<caption>Fig. 14. Extended magnetosphere of II Peg determined using potential field extrapolation from the radial component of ZDI maps. The star is shown at four equidistant rotation phases ( columns ) for the four epochs with best phase-coverage ( rows ). The underlying spherical map corresponds to the radial magnetic field component. The open and closed magnetic field lines are shown in di GLYPH<11> erent colour.</caption>
</figure>
<section_header_level_1><location><page_12><loc_6><loc_31><loc_48><loc_32></location>6.2. Relation between temperature and magnetic field maps</section_header_level_1>
<text><location><page_12><loc_6><loc_10><loc_49><loc_29></location>Throughout the entire series of ZDI images reconstructed for II Peg we see no obvious spatial correlation between the lowtemperature spots and the strongest magnetic field features. This suggests that a significant fraction of magnetic flux is not associated with cool spots. Although a similar conclusion has been reached by previous studies (Donati & Collier Cameron 1997; Donati 1999), it was unclear whether this represented a genuine characteristic of an active-star stellar surface structure or an inversion artefact coming from an inconsistent modelling of the magnetic and temperature spots. Our work confirms the lack of the field-spot correlation based on a self-consistent and physically realistic analysis of the circular polarisation in spectral lines. Using a similar approach, Carroll et al. (2007) also failed to detect a strong correlation between magnetic and temperature features on the surface of II Peg. These results may be inter-</text>
<text><location><page_12><loc_51><loc_23><loc_94><loc_32></location>preted as evidence that current ZDI maps are mostly sensitive to magnetic fields at photospheric temperature and entirely miss the very strong fields inside cool spots. Instead, numerical experiments predict that self-consistent ZDI should be capable of recovering fields inside cool spots even if the temperature contrast is as large as 1500 K (Kochukhov & Piskunov 2009; Rosén &Kochukhov 2012).</text>
<text><location><page_12><loc_51><loc_10><loc_94><loc_22></location>A limited spatial resolution of the ZDI maps may be another reason for not seeing a link between fields and cool spots. Both the magnetic and temperature distributions obtained using a spectral inversion technique reveal only the largest-scale structures, which are probably not monolithic but consist of many smaller spots with di GLYPH<11> erent geometries and field polarities. Then a local correlation between low-temperature spots and magnetic fields may be washed out in the current generation of ZDI maps. One can note that the presence of a substantial unresolved smallscale magnetic flux implies a much stronger average magnetic</text>
<text><location><page_13><loc_6><loc_87><loc_49><loc_93></location>field strength than the one inferred from the ZDI analysis of circular polarisation. Highly inconsistent results of ZDI and Zeeman splitting studies of low-mass stars represent an example of this situation for a di GLYPH<11> erent dynamo regime (Reiners & Basri 2009).</text>
<text><location><page_13><loc_6><loc_62><loc_49><loc_86></location>At the same time, it is not entirely obvious from a theoretical standpoint that a one-to-one relation between the cool spots and magnetic fields stemming from the solar paradigm can be universally extended to other types of cool active stars. There is an increasing amount of theoretical evidence (e.g. Chan 2007; Käpylä et al. 2011b; Mantere et al. 2011) of a pure hydrodynamical instability leading to the generation of large-scale vortices in the rapid rotation regime. These structures have so far been found only in local Cartesian simulations of turbulent convection, the sizes of the vortices always being very close to the box size, suggesting that these structures may have globally significant spatial extents. Depending on the rotation rate, either cool, cyclonic vortices for intermediate rotation, or warm anticyclonic vortices are excited, the temperature contrast being of the order of ten percent. This instability might contribute to the generation of magnetic fields independent from temperature structures in rapid rotators. So far, however, these structures have been detected neither in more realistic spherical geometry nor in the magnetohydrodynamic regime (see e.g. Käpylä et al. 2012b).</text>
<section_header_level_1><location><page_13><loc_6><loc_59><loc_38><loc_60></location>6.3. Interpretation in terms of dynamo theory</section_header_level_1>
<text><location><page_13><loc_6><loc_20><loc_49><loc_58></location>The picture arising from an extensive set of previous photometric and spectroscopic observations of II Peg suggests that the surface magnetic field of this object concentrates on one or two active longitudes, i.e. is highly non-axisymmetric, and that these active longitudes evolve dynamically over time. During the epoch 1994-2002, a persistent drift of the active longitude has been confirmed (Berdyugina et al. 1998a, 1999; Lindborg et al. 2011). It is not detectable during 2004-2010 (Hackman et al. 2012) which is supported by the ZDI maps presented in this paper. Furthermore, our new results give an indication that the strength of the magnetic field has been monotonically decreasing, at least during 2004-2009; it seems that a minimum was reached at about 2009, after which the magnetic field strength started increasing again. The analysis of the energy contained in the poloidal and toroidal components as function of time shows that while in the beginning of the dataset the field was predominantly poloidal, the portion of the toroidal field is increasing nearly linearly with time, and is dominating at the end of the dataset. This is also reflected by the increasing contribution of the non-axisymmetric component exceeding the energy contained in the axisymmetric modes for 2009-2010. All these findings together hint towards a possible minimum in the star's magnetic activity cycle, during which the magnetic field tends to be more poloidal and axisymmetric, accompanied with the signature of the non-axisymmetric drifting dynamo wave getting too weak to be detectable. Unfortunately, the datasets, especially the series of ZDI maps, are too short to make decisive conclusions on the cyclic nature of the magnetic field. In any case it seems evident that the magnetic field on global scale is far from static.</text>
<text><location><page_13><loc_6><loc_10><loc_49><loc_20></location>How can this be understood in terms of dynamo theory? In the solar case, the internal rotation and its non-uniformities are known from helioseismic inversions, while in the case of other stars, photometric period variations, interpreted as indirect proxies of stellar surface di GLYPH<11> erential rotation, are normally much smaller than the solar value. Theoretically this is conceivable, as it has been predicted that the faster the star rotates, the smaller the non-uniformities in its rotation rate will be (see e.g.</text>
<text><location><page_13><loc_51><loc_54><loc_94><loc_93></location>Küker & Rüdiger 2005). This means that in the rapidly rotating late-type stars the operation of the dynamo should rely more strongly on the collective inductive action of convective turbulence (called the GLYPH<11> e GLYPH<11> ect), and less on the non-uniformities of the rotational velocity (called the GLYPH<10> e GLYPH<11> ect), the dynamo therefore being more of the GLYPH<11> 2 type than the GLYPH<11> GLYPH<10> solar dynamo. The simplest of these systems (see e.g. Krause & Raedler 1980) excite dynamo modes that are non-axisymmetric but show no oscillations, although drifts of the magnetic structure, i.e. azimuthal dynamo waves, are typical. As more and more observational evidence on dynamically changing magnetic fields is being gathered, it has become evident that this simple picture is not adequate. It has been suggested that either these objects have more di GLYPH<11> erential rotation than predicted by theory (e.g. Elstner & Korhonen 2005), or that the mean-field transport coe GLYPH<14> cients describing the convective turbulence are far too simple. Indeed, oscillating dynamo solutions in the GLYPH<11> 2 regime have been found with more complex profiles (Baryshnikova & Shukurov 1987; Mitra et al. 2010; Käpylä et al. 2012b). We also note that some observational evidence exists supporting the idea of stars showing a larger amount of di GLYPH<11> erential rotation than actually predicted by the theoretical models, although the discrepancy between observations and theory appears to be quite small (Hall 1991; Collier Cameron 2007). Direct numerical simulations in spherical geometry also show results consistent with the quenching of relative di GLYPH<11> erential rotation with increasing rotation rate (Käpylä et al. 2011a), although it is still challenging to relate these models to real stars. Therefore, we cannot completely rule out the existence of enough di GLYPH<11> erential rotation in rapid rotators to be significant for the dynamo mechanism.</text>
<text><location><page_13><loc_51><loc_24><loc_94><loc_54></location>For our purposes, it is relevant to compare our observational results with direct numerical simulations of turbulent convection. Extensive parameter studies have been performed particularly in Cartesian geometry (Käpylä et al. 2012b), while such studies in global spherical geometry remain challenging (Miesch & Toomre 2009). One clear shortcoming of the local Cartesian models is that the di GLYPH<11> erential rotation cannot self-consistently emerge as a result of the modelling but needs to be imposed. The global spherical models can grasp this aspect, but only a few are successful in reproducing the solar rotation profile (see Miesch et al. 2006). The Cartesian studies clearly indicate that oscillatory GLYPH<11> 2 dynamos are quite natural in the rotation-dominated regime. Typical solutions (e.g. Käpylä et al. 2012b) show radial and azimuthal components of nearly equal strengths, with a rough GLYPH<25>= 2 phase separation in the cycle. Inclusion of shear into such a system has two principal e GLYPH<11> ects. Firstly, the azimuthal component grows in strength versus the radial component, and quite often the components are in anti-phase, the sign changes and minima occur simultaneously. The ZDI data indicates that the azimuthal field component is not completely synchronised with the radial and meridional fields, i.e. they do not seem to grow / decline simultaneously. This, again, is more consistent with the GLYPH<11> 2 scenario than the GLYPH<11> GLYPH<10> picture.</text>
<text><location><page_13><loc_51><loc_10><loc_94><loc_24></location>The dominating non-axisymmetric topology, azimuthal dynamo waves, and even the time dependence of the magnetic fields in rapid rotators can be quite readily understood in terms of dynamo theory relying only on the GLYPH<11> mechanism; GLYPH<11> GLYPH<10> dynamos, in contrast, produce latitudinal dynamo waves (such as the solar butterfly diagram), mostly axisymmetric fields, and oscillatory solutions are the preferentially excited ones (see e.g. Steenbeck & Krause 1969). The presence of a significant axisymmetric contribution, as was found in the case of II Peg in this study, is di GLYPH<14> cult to explain with a pure GLYPH<11> 2 dynamo mechanism. To 'axisymmetrise' some part of the dynamo solution, some di GLYPH<11> eren-</text>
<text><location><page_14><loc_6><loc_89><loc_49><loc_93></location>tial rotation will probably be needed; therefore our ZDI results most reasonably point towards an GLYPH<11> 2 GLYPH<10> dynamo operating on the object under study.</text>
<text><location><page_14><loc_6><loc_81><loc_49><loc_88></location>Acknowledgements. Doppler imaging calculations presented in this paper were carried out at the supercomputer facility provided to the Uppsala Astronomical Observatory by the Knut and Alice Wallenberg Foundation and at the UPPMAX supercomputer center at Uppsala University. OK is a Royal Swedish Academy of Sciences Research Fellow supported by grants from the Knut and Alice Wallenberg Foundation and from the Swedish Research Council. TH was funded by the research programme 'Active Suns' at the University of Helsinki.</text>
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<table>
<location><page_15><loc_16><loc_10><loc_84><loc_91></location>
<caption>Table 1. The journal of spectropolarimetric observations of II Peg.</caption>
</table>
<table>
<location><page_16><loc_16><loc_58><loc_84><loc_91></location>
<caption>Table 1. Continued.</caption>
</table>
<figure>
<location><page_17><loc_9><loc_36><loc_91><loc_91></location>
<caption>Fig. 7. Same as Fig. 5 for epochs 2005.0 and 2005.6.</caption>
</figure>
<figure>
<location><page_18><loc_9><loc_36><loc_91><loc_91></location>
<caption>Fig. 8. Same as Fig. 5 for epochs 2005.9 and 2006.9.</caption>
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<location><page_19><loc_9><loc_37><loc_91><loc_91></location>
<caption>Fig. 9. Same as Fig. 5 for epochs 2007.9 and 2008.7.</caption>
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<caption>Fig. 10. Same as Fig. 5 for epochs 2008.9 and 2010.0.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "Context. The dynamo processes in cool active stars generate complex magnetic fields responsible for prominent surface stellar activity and variability at di GLYPH<11> erent time scales. For a small number of cool stars magnetic field topologies were reconstructed from the time series of spectropolarimetric observations using the Zeeman Doppler imaging (ZDI) method, often yielding surprising and controversial results. Aims. In this study we follow a long-term evolution of the magnetic field topology of the RS CVn binary star II Peg using a more self-consistent and physically more meaningful modelling approach compared to previous ZDI studies. Methods. We collected high-resolution circular polarisation observations of II Peg using the SOFIN spectropolarimeter at the Nordic Optical Telescope. These data cover 12 epochs spread over 7 years, comprising one of the most comprehensive spectropolarimetric data sets acquired for a cool active star. A multi-line diagnostic technique in combination with a new ZDI code is applied to interpret these observations. Results. Wehave succeeded in detecting clear magnetic field signatures in average Stokes V profiles for all 12 data sets. These profiles typically have complex shapes and amplitudes of GLYPH<24> 10 GLYPH<0> 3 of the unpolarised continuum, corresponding to mean longitudinal fields of 50-100 G. Magnetic inversions using these data reveals evolving magnetic fields with typical local strengths of 0.5-1.0 kG and complex topologies. Despite using a self-consistent magnetic and temperature mapping technique, we do not find a clear correlation between magnetic and temperature features in the ZDI maps. Neither do we confirm the presence of persistent azimuthal field rings found in other RS CVn stars. Reconstruction of the magnetic field topology of II Peg reveals significant evolution of both the surface magnetic field structure and the extended magnetospheric field geometry on the time scale covered by our observations. From 2004 to 2010 the total field energy drastically declined and the field became less axisymmetric. This also coincided with the transition from predominantly poloidal to mainly toroidal field topology. Conclusions. A qualitative comparison of the ZDI maps of II Peg with the prediction of dynamo theory suggests that the magnetic field in this star is produced mainly by the turbulent GLYPH<11> 2 dynamo rather than the solar GLYPH<11> GLYPH<10> dynamo. Our results do not show a clear active longitude system, nor is there an evidence of the presence of an azimuthal dynamo wave. Key words. polarisation - stars: activity - stars: atmospheres - stars: magnetic fields - stars: individual: II Peg",
"pages": [
1
]
},
{
"title": "Magnetic field topology of the RS CVn star II Pegasi ?",
"content": "O. Kochukhov 1 , M.J. Mantere 2 , T. Hackman 2 ; 3 , and I. Ilyin 4 Received 24 September 2012 / Accepted 10 December 2012",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Direct, spatially-resolved observations of the solar disk demonstrate the ubiquitous presence of magnetic fields and their key role in driving time-dependent, energetic processes. It is believed that magnetic fields are generated in the solar interior, due to a complex interplay between the non-uniformities in the internal rotation profile, large-scale flows, and vigorous turbulence due to convective motions (Ossendrijver 2003). Although the rotation profile, with two prominent regions of high radial shear near the bottom and top of the solar convection zone, is known rather reliably from helioseismic observations (e.g. Thompson et al. 2003), measurements of the potentially very important meridional flow pattern, especially deeper in the convection zone, are highly uncertain (Gough & Hindman 2010). A variety of models of the solar dynamo exists (e.g. Dikpati & Charbonneau 1999; Käpylä et al. 2006; Kitchatinov & Olemskoy 2012), but none of them is capable of fully reproducing the observed characteristics of the solar magnetic cycle. Direct numerical simulations aiming at including all the relevant physics in a single model, with the expectation being that all the observable features from the flow patterns up to the magnetic cycle would emerge self-consistently, have so far been only marginally successful (Ghizaru et al. 2010; Racine et al. 2011; Käpylä et al. 2012a). Therefore, it is fair to say that the solar cycle remains a theoretical challenge, with some key information on the largescale flow patterns yet to be supplied by observations. Compared to the Sun, many cool stars exhibit enhanced activity levels, suggesting the presence of stronger surface magnetic fields produced by more e GLYPH<14> cient dynamos. Observations of such active stars o GLYPH<11> er possibilities to constrain theoretical models by examining the e GLYPH<14> ciency of dynamo mechanisms as a function of stellar mass, age, and rotation rate. However, direct magnetic field analysis of cool active stars is impeded by the weakness of polarisation signatures in the spatially-unresolved stellar spectra. Furthermore, dynamos in cool stars usually give rise to topologically complex magnetic fields which cannot be meaningfully characterised using observational techniques sen- sitive only to the global magnetic field component (Borra & Landstreet 1980; Vogt 1980). A major breakthrough in studying the magnetism of cool stars was achieved by combining multi-line polarisation diagnostic techniques (Donati et al. 1997) applied to high-resolution spectropolarimetric observations with the inversion procedure of Zeeman Doppler imaging (ZDI, Brown et al. 1991; Donati & Brown 1997). This approach, capable of providing spatiallyresolved information about stellar magnetic field topologies, was applied to a number of late-type stars (e.g. Donati et al. 2003; Petit et al. 2004), but only three objects - AB Dor, LQ Hya, and HR1099 - were systematically followed with multiple magnetic maps on the time scales of five to ten years. The results of ZDI mapping are often spectacular in their ability to resolve fine details of stellar magnetic field geometries, but also controversial in several aspects. First, analysis of stellar spectra is limited to only circular polarisation because, being roughly ten times weaker, the linear polarisation signatures are not readily detectable at the moderate signal-to-noise (S / N) ratios used for the circular polarisation monitoring (Kochukhov et al. 2011). Supplying inversion algorithms with such incomplete Stokes vector data is known to lead to spurious features in the reconstructed magnetic maps (Donati & Brown 1997; Kochukhov & Piskunov 2002). Second, interpretation of the mean-line shapes constructed by averaging thousands of lines is inevitably inferior to modelling individual spectral lines because of the di GLYPH<14> culty in choosing appropriate mean-line parameters (Kochukhov et al. 2010). Finally, and most importantly, nearly all magnetic field maps reconstructed from the Stokes V observations of cool active stars were obtained separately and inconsistently from the mapping of brightness distributions from Stokes I , raising questions about the validity of magnetic maps and preventing direct analysis of the spatial relation between magnetic and temperature inhomogeneities. These considerations suggest that substantial progress in understanding cool-star magnetism through ZDI requires continuing research in several directions. On the one hand, the sample of active stars studied with multiple-epoch magnetic images has to be expanded to justify the far-reaching conclusions previously inferred from the analysis of a few objects. On the other hand, ZDI studies must re-examine key methodological limitations of this technique and strive to employ physically realistic modelling approaches whenever possible. This paper addresses both of these aspects in a detailed ZDI analysis of the RS CVn binary II Peg. The source of the most powerful stellar flares ever observed (Osten et al. 2007) and the brightest X-ray object within 50 pc (Makarov 2003), II Peg (HD 224085, HIP 117915) is one of the most prominent active cool stars in the solar neighbourhood. This star is an RS CVn-type, single-line spectroscopic binary (SB1) with an orbital period of GLYPH<25> 6.72 days, consisting of a K2IV primary and a low-mass (M0-M3V) secondary. The primary star exhibits copious manifestations of the magnetically-driven surface activity, including a strong non-thermal emission in the UV and optical chromospheric lines and in the X-ray and radio wavelength regions. It also shows powerful flares as well as regular photometric and spectroscopic variations due to evolving cool spots. Berdyugina et al. (1998b) studied the orbital motion of the massive component and provided a comprehensive summary of the physical properties of II Peg. Many studies examined photometric variations of this star (e.g. Siwak et al. 2010; Roettenbacher et al. 2011, and references therein), aiming to explore long-term activity cycles and, in particular, to investigate the role of active longitudes (Berdyugina et al. 1999; Rodonò et al. 2000). Other studies targeted II Peg with high-resolution spectroscopic observations with the goal to constrain the spot temperatures using TiO absorption bands (O'Neal et al. 1998; Berdyugina et al. 1998b) and to analyse configurations of the surface temperature inhomogeneities with the Doppler imaging technique (Berdyugina et al. 1998a; Gu et al. 2003; Lindborg et al. 2011; Hackman et al. 2012). Early DI images corresponding to the period between 1994 and 2002 suggested persistent presence of a pair of active longitudes and showed major changes in the surface structure on a time-scale of less than a year (Berdyugina et al. 1998a, 1999; Lindborg et al. 2011). More recent DI maps covering the years from 2004 to 2010 revealed the star entering a low-activity state characterised by a more random distribution of cool spots (Hackman et al. 2012). The underlying cause of the remarkable surface activity of II Peg - the dynamo-generated magnetic field - was first detected in this star by Donati et al. (1992) with four circular polarisation observations of a few magnetically sensitive lines. The presence of the Stokes V signatures in spectral lines was subsequently confirmed by Donati et al. (1997) using a multi-line polarimetric analysis, but no systematic phase-resolved investigation of the magnetic field topology of II Peg has ever been undertaken. Since 2004 we have been monitoring the magnetic field in II Peg using the SOFIN spectropolarimeter at the Nordic Optical Telescope. We have acquired a unique collection of highresolution Stokes I and V spectra covering GLYPH<25> 5.5 years or almost 300 stellar rotations. In this paper we present a comprehensive analysis of these polarisation data, focusing on the selfconsistent ZDI mapping of stellar magnetic field topology. The accompanying study by Hackman et al. (2012) obtained temperature maps from the same SOFIN Stokes I spectra. Preliminary attempts to map the magnetic field geometry of II Peg, using about 10% of the spectropolarimetric data analysed here, were presented first by Carroll et al. (2007), and then by Carroll et al. (2009b) and Kochukhov et al. (2009). This paper is organised as follows. In Sect. 2 we describe the acquisition and reduction of the spectropolarimetric observations of II Peg. Detection of the magnetic signatures in spectral lines with the help of a multi-line analysis is presented in Sect. 3. The methodology of the self-consistent ZDI and the choice of stellar parameters required for mapping is described in Sect. 4. Results of the magnetic and temperature inversions of II Peg are presented and analysed in Sect. 5. The outcome of our investigation is discussed in the context of previous observational and theoretical studies in Sect. 6.",
"pages": [
1,
2
]
},
{
"title": "2. Spectropolarimetric observations",
"content": "The spectropolarimetric observations of II Peg analysed here were carried out during the period from Jul. 2004 to Jan. 2010 using the SOFIN echelle spectrograph (Tuominen et al. 1999) at the 2.56-m Nordic Optical Telescope. The spectrograph, which is mounted at the Cassegrain focus and is equipped with a 2048 GLYPH<2> 2048 pixel CCD detector, was configured to use its second camera yielding resolving power of R GLYPH<25> 70000. For ZDI analysis we used 12 echelle orders, each covering 40-50 Å in the wavelength region between 4600 and 6135 Å. The data for II Peg were obtained during 12 individual epochs, for which from 3 to 12 observations were recorded over the time span ranging from 3 to 14 nights. The spectra have typical S / N ratio of 200-300. The circular polarisation observations were obtained with the Zeeman analyser, consisting of a calcite plate used as a beam splitter and an achromatic rotating quarter-wave plate. At least two exposures with the quarter-wave retarder angles separated by 90 GLYPH<14> is required to obtain the Stokes V spectrum. Rotation of the quarter-wave plate has the e GLYPH<11> ect of exchanging positions of the right- and left-hand circularly polarised beams on the detector. The beam exchange procedure (Semel et al. 1993) facilitates an accurate polarisation analysis because possible instrumental artefacts change sign when the quarter-wave plate is rotated and then cancel out when all sub-exposures are combined. To accumulate su GLYPH<14> cient signal-to-noise ratio, a sequence of 2 or 3 double exposures was obtained in this way. The length of individual sub-exposures varied between 15 and 25 min, depending on seeing and weather conditions. The data were reduced with the help of the 4A software package (Ilyin 2000). Specific details of the SOFIN polarimeter design and corresponding data reduction methods are given by Ilyin (2012). The spectral processing included standard reduction steps, such as bias subtraction, flat field correction, removal of the scattered light, and optimal extraction of the spectra. Wavelength calibration used ThAr exposures obtained before and after each single exposure to account for environmental variations and gravitational bending of a Cassegrain mounted spectrograph by means of a global fit of the two ThAr wavelength solutions versus time. Spectropolarimetric observations of strongly magnetic Ap stars are frequently performed with SOFIN in a configuration similar to the one used for II Peg. These measurements agree closely with the results obtained for the same stars at other telescopes (e.g. Ryabchikova et al. 2007; Ilyin 2012). Repeated observations of a very slowly rotating Ap star GLYPH<13> Equ reveals no systematic di GLYPH<11> erences in the Stokes V profiles during the entire period of our observations of II Peg. This confirms the robustness and accuracy of the employed instrument calibration and data reduction methods. The log of all 88 SOFIN Stokes V observations of II Peg is given in Table 1. The rotation of the primary component of II Peg is synchronised with the orbital motion. Therefore, we calculated rotational phases using the orbital ephemeris from Berdyugina et al. (1998b) which refers to the time of orbital conjunction. The orbital solution from the same study was applied to correct the radial velocity variation caused by the orbital motion. Our 12 sets of spectropolarimetric observations of II Peg comprise 3 to 12 distinct rotational phases, whereas GLYPH<24> 10 evenly distributed phases are needed for an optimal ZDI reconstruction (Kochukhov & Piskunov 2002). Assuming that each observation provides a coverage of 10% of the rotational period, we quantified the phase coverage of each data set as a fraction f of the full rotational cycle (see Table 1). Our SOFIN observations yield from f = 30% (epoch 2005.0) to f = 87% (epoch 2009.7). The three epochs with the best phase-coverage are 2004.6 (75%), 2007.6 (81%), and 2009.7 (87%). The quality of ZDI mapping is reduced for the data sets with an insu GLYPH<14> cient phase-coverage. Yet, as demonstrated by numerical experiments (Donati & Brown 1997; Kochukhov & Piskunov 2002) and ZDI studies based on observations with poor phasecoverage (Donati 1999; Hussain et al. 2009), it is still possible to extract useful information about the stellar surface features from just a few spectra and from observations covering only half of the stellar rotation cycle. Aiming to maintain consistency in our long-term ZDI analysis of II Peg, we performed magnetic inversions for all 12 epochs. At the same time, we kept in mind the di GLYPH<11> erence in data quality during the assessment of the inversion results.",
"pages": [
2,
3
]
},
{
"title": "3.1. Least-squares deconvolution",
"content": "Even the most active late-type stars exhibit a relatively low amplitude of the circular polarisation signal in spectral lines, rarely exceeding 1% of the Stokes V continuum intensity. Given the moderate quality of the SOFIN spectropolarimetric observations of II Peg, we were able to detect Stokes V signatures at the 23 GLYPH<27> confidence level in only a few of the strongest spectral lines (Fig. 1). This makes it challenging to model the magnetic field of II Peg using a direct analysis of individual line profiles. A widely-used approach to overcome this di GLYPH<14> culty is to employ a multi-line technique, combining information from hundreds or thousands of individual metal lines. In this study of II Peg we applied the least-squares deconvolution (LSD) technique (Donati et al. 1997) using the code and methodology described by Kochukhov et al. (2010). The LSD technique extracts information from all available lines by assuming that the Stokes I and V spectra can be represented by a superposition of corresponding scaled mean profiles. The scaling factors, established under the weak-line and weak-field approximations, are equal to the central line depth d for Stokes I and to the product of the line depth, laboratory wavelength of the transition GLYPH<21> , and its e GLYPH<11> ective Landé factor z for Stokes V , respectively. A linear superposition of scaled profiles is mathematically equivalent to a convolution of the average profile with a line mask. This simple stellar spectrum model can be inverted, obtaining a high-quality mean profile for a given line mask and observational data. Kochukhov et al. (2010) showed that, for the magnetic fields below GLYPH<25> 2 kG, the LSD Stokes V profiles derived in this way can be interpreted as a real Zeeman triplet line with an average Landé factor. The atomic line data required for the application of LSD to observations of II Peg were obtained from the vald database (Kupka et al. 1999). We extracted a total of 1580 spectral lines with the central depth larger than 10% of the continuum. The line intensities were calculated for a marcs model atmosphere (Gustafsson et al. 2008) with the e GLYPH<11> ective temperature T e GLYPH<11> = 4750 K, surface gravity log g = 3.5, and metallicity [ M = H ] = GLYPH<0> 0 : 25. The mean parameters of the resulting line mask are GLYPH<21> 0 = 5067 Å, z 0 = 1 : 21, and d 0 = 0 : 46. The same parameters were used for normalising the Stokes I and V LSD weights. The LSD profiles were calculated with a 1.2 km s GLYPH<0> 1 step for the velocity range GLYPH<6> 60 km s GLYPH<0> 1 . The LSD analysis of the SOFIN observations of II Peg allowed us to achieve a S = N gain of 30-40, obtaining a definite detection (false alarm probability < 10 GLYPH<0> 5 ) of the circular polarisation signatures for all but one Stokes V spectrum (phase 0.035 for epoch 2008.7). The resulting mean Stokes V profiles are compatible with the marginal polarisation seen in individual lines (see Fig. 1), but have a much higher quality, making them suitable for detailed modelling.",
"pages": [
3
]
},
{
"title": "3.2. Mean longitudinal magnetic field",
"content": "In Table 1 we report the maximum amplitude of the LSD Stokes V profiles and the mean longitudinal magnetic field h B z i determined from their first moment. We found typical LSD Stokes V amplitudes of the order of 0.1% and h B z i in the range 30250 G, determined with the precision of GLYPH<25> 5 G. These results are compatible with the previous longitudinal field measurements by Vogt (1980), which had an accuracy of 100-160 G and did not yield a convincing detection of magnetic field in II Peg. Despite the ubiquitous definite detections of the circular polarisation signatures, 16 out of 88 LSD profiles of II Peg do not exhibit a significant mean longitudinal magnetic field. A comparison of h B z i measurements with the maximum LSD Stokes V amplitude (Fig. 2) shows no obvious correlation. This indicates that, with a few exceptions (e.g. phase 0.531 at epoch 2004.6 illustrated in Fig. 1), the Stokes V profiles of II Peg are generally complex and cannot be fully characterised by their first-order moment. Nevertheless, analysis of the longitudinal magnetic field measurements does reveal an intriguing long-term behaviour. As illustrated in Fig. 3, the range of the longitudinal field variation with rotational phase systematically decreased from 2004 to 2010. Furthermore, it appears that the phaseaveraged value of the longitudinal magnetic field was significantly deviating from 0 during the period from the beginning of our monitoring until the epoch 2006.9. This suggests the presence of large areas of positive magnetic polarity on the visible hemisphere of the star before that epoch and a more symmetric distribution of the field orientation at later epochs.",
"pages": [
3,
4
]
},
{
"title": "4.1. Zeeman Doppler imaging code I nvers 13",
"content": "Reconstruction of the distribution of magnetic field and temperature on the surface of II Peg was carried out with the help of our new ZDI code I nvers 13. This inversion software represents a further development of the I nvers 10 code (Piskunov & Kochukhov 2002; Kochukhov & Piskunov 2002), previously applied for mapping magnetic geometries and chemical spots on Ap stars (Kochukhov et al. 2004; Kochukhov & Wade 2010; Lüftinger et al. 2010). Both codes incorporate full treatment of the polarised radiative transfer using a modified Diagonal Element Lambda-Operator (DELO) algorithm (Rees et al. 1989; Piskunov & Kochukhov 2002). All four Stokes parameters are calculated simultaneously and fully self-consistently, taking into account Zeeman broadening and splitting of spectral lines in the intensity spectra on the one hand, and attenuation of the polarised profiles due to temperature spots on the other hand. Some aspects of this approach have already been incorporated in the ZDI of cool stars in the preliminary studies of II Peg (Carroll et al. 2007, 2009b; Kochukhov et al. 2009). However, the majority of recent applications of ZDI (e.g. Skelly et al. 2010; Waite et al. 2011; Marsden et al. 2011) still systematically neglect effects of temperature spots in the magnetic inversions. As demonstrated by the numerical tests of Rosén & Kochukhov (2012), the lack of self-consistency in temperature and magnetic mapping can lead to severe artefacts if cool spots coincide with major concentrations of the magnetic flux. Calculation of the local Stokes parameter profiles by I n -vers 13 is based on a prescribed line list of atomic and molecular lines, normally obtained from the vald and marcs databases, and a grid of model atmospheres. In the present study of II Peg we employed a grid consisting of 18 marcs model atmospheres covering a T e GLYPH<11> range of 3000-5750 K with a 100-250 K step in temperature. The Stokes IQUV profiles and continuum intensities I c are calculated for the temperature of a given stellar surface element by quadratic interpolation between three sets of model spectra corresponding to the nearest points in the model atmosphere grid. This allows an accurate semi-analytical computation of the derivatives with respect to temperature. On the other hand, the derivatives with respect to the three magnetic field vector components are evaluated numerically, using a simple one-sided di GLYPH<11> erence scheme. The local profiles are convolved with a Gaussian function to take into account instrumental and radial-tangential macroturbulent broadening, Doppler shifted, and summed for each rotational phase on the wavelength grid of observed spectra. The resulting Stokes parameter profiles are normalised by the phasedependent continuum flux and compared with observations. In calculating the goodness of the fit we approximately balance the contributions of each Stokes parameter by scaling the respective chi-square terms by the inverse of the mean amplitude of the corresponding Stokes profiles. Test inversions by Kochukhov & Piskunov (2002) and Rosén & Kochukhov (2012) verified simultaneous reconstruction of the magnetic and starspot maps using this weighting scheme. This approach is also routinely used in the reconstruction of Ap-star magnetic fields from four Stokes parameter observations (Kochukhov et al. 2004; Kochukhov & Wade 2010). In the study of II Peg the contributions of the Stokes I and V spectra were weighted as 1:30. Inversion results are not sensitive to the exact choice of the relative weighting of Stokes I and V . The iterative adjustment of the surface maps for matching available observations is accomplished by means of the Levenberg-Marquardt optimisation algorithm, which enables convergence in typically 10-20 iterations starting from a homogeneous temperature distribution and zero magnetic field. The I nvers 13 code is optimised for execution on massivelyparallel computers using MPI libraries. We refer the reader to Kochukhov et al. (2012) for further details on the numerical methods and computational techniques employed in I nvers 13. As shown numerically by Donati & Brown (1997) and Piskunov & Kochukhov (2002), and analytically by Piskunov (2005), ZDI with only Stokes I and V spectra is an intrinsically ill-posed problem, requiring the use of a regularisation or penalty function to reach a stable and unique solution. The reconstruction of temperature in I nvers 13 is regularised using the Tikhonov method, very similar to many previous DI studies of cool active stars (e.g. Piskunov & Rice 1993) and our recent temperature mapping of II Peg with the same SOFIN data (Hackman et al. 2012). In this approach the code seeks a surface distribution with a minimum contrast between adjacent surface elements. For the magnetic field reconstruction, I nvers 13 o GLYPH<11> ers a choice of either directly mapping the three magnetic vector components and applying the Tikhonov regularisation individually to the radial, meridional, and azimuthal magnetic component maps (Piskunov & Kochukhov 2002), or expanding the field into a spherical harmonic series (Donati et al. 2006). In the latter formulation of the magnetic inversion problem, the free parameters optimised by the code are the spherical harmonic coe GLYPH<14> cients GLYPH<11>' m , GLYPH<12>' m , and GLYPH<13>' m , giving the amplitudes of the poloidal and toroidal terms for a given angular degree ' and azimuthal num- ber m (see Eqs. 2-8 in Donati et al. 2006). In particular, the radial field is determined entirely by the poloidal contribution (coe GLYPH<14> cient GLYPH<11> ), whereas both poloidal and toroidal components (coe GLYPH<14> cients GLYPH<12> and GLYPH<13> , respectively) are contributing to the meridional and azimuthal field. In this description of the stellar magnetic field topology through a spherical harmonic expansion, the role of regularisation is played by a penalty function equal to the sum of squares (magnetic energies) of the harmonic coe GLYPH<14> -cients weighted by ' 2 . This prevents the code from introducing high-order modes not justified by the observational data. Expansion in spherical harmonics has the advantage of automatically satisfying the divergence-free condition for a magnetic field. It also allows us to conveniently characterise the relative contributions of di GLYPH<11> erent components to the stellar magnetic field topology and to study the evolution of these contributions with time. Therefore, for the magnetic mapping of II Peg we adopted the spherical harmonic approach, choosing ' max = 10 which corresponds to a total of 360 independent magnetic field parameters. Similar to other quantities obtained by solving a regularised ill-posed problem, the spherical harmonic coe GLYPH<14> cients cannot be attributed formal error bars because, in addition to the observational data, the individual modes are constrained by the penalty function. Therefore, their formal error bars are strongly dependent on the choice of regularisation parameter, especially for the high-' modes. This is why here, as well as in all previous ZDI studies employing spherical harmonic expansion (e.g. Donati et al. 2006; Skelly et al. 2010; Fares et al. 2012), no formal uncertainty estimates are derived for the harmonic coe GLYPH<14> cients. As inferred from the previous numerical tests of ZDI inversions (Donati & Brown 1997; Kochukhov & Piskunov 2002; Rosén & Kochukhov 2012), reconstruction of the magnetic field distributions from the Stokes I and V data alone su GLYPH<11> ers from some ambiguities. The most important problem is a cross-talk between the radial and meridional field components at low latitudes (i.e. for the regions below the stellar equator for the rotational geometry of II Peg). On the other hand, the harmonic regularisation or parameterisation of the magnetic field maps partly alleviates this problem (Donati 2001; Kochukhov & Piskunov 2002), because in this case the inversion code is not allowed to vary the three magnetic vector components arbitrarily. Instead, the meridional and azimuthal components are coupled via the GLYPH<12> and GLYPH<13> harmonic coe GLYPH<14> cients which avoids the cross-talk between the radial and meridional fields, at least for the low-' values.",
"pages": [
4,
5
]
},
{
"title": "4.2. Reconstructing temperature spots from LSD profiles",
"content": "Most previous ZDI modelling of the Stokes I and V LSDprofiles of late-type active stars relied on simple analytical formulas, often a Gaussian approximation, to represent the local intensity and polarisation profiles. These coarse line-profile models have either entirely neglected dependence of the local line intensity on temperature (e.g. Petit et al. 2004) or used disk-integrated spectra of suitably chosen cool and hot slowly rotating template stars to represent local contribution of the spot and photosphere, respectively (e.g. Donati et al. 2003). Here we develop a more sophisticated approach to interpret the LSD profile time series. We aim to describe the LSD Stokes I and V spectra with self-consistent polarised radiative transfer calculations, based on realistic model atmospheres, for a fictitious spectral line with average atomic parameters. Comprehensive investigation of the properties of LSD profiles by Kochukhov et al. (2010) showed that this approach yields an accurate description of the mean circular polarisation line shapes for the magnetic field strengths below GLYPH<25> 2 kG. For stronger fields, details of the LSD Stokes V profile shape cannot be reproduced, although the LSD profile moments still yield correct longitudinal magnetic field. According to previous studies, magnetic fields found on the surfaces of RS CVn- and BY Dra-type active stars are safely within this limit. On the other hand, analyses of Ap / Bp stars hosting much stronger fields (e.g. Wade et al. 2000; Silvester et al. 2012) proves that the LSD line-averaging method itself does not systematically underestimate magnetic field strength even beyond the weak-field regime. At the same time, Kochukhov et al. (2010) found that a response of the LSD Stokes I profile to the variation of chemical composition di GLYPH<11> ers from that of any real spectral line, which prevents an accurate mapping of the chemical spots in Ap stars using LSD profiles (Folsom et al. 2008). One might suspect that reconstruction of the temperature inhomogeneities from the LSD spectra is similarly limited. It is clear that the temperature sensitivity of an average profile, composed of an essentially random mixture of thousands of lines with diverse temperature responses, cannot be known as well as the one for a set of judiciously chosen individual spectral lines with accurate atomic parameters. On the other hand, typical Stokes I atomic line profile variations in active stars are dominated by the continuum brightness e GLYPH<11> ect, which influences all lines in a similar way (Vogt & Penrod 1983; Unruh & Collier Cameron 1995). Adding to this a greatly enhanced S = N of the LSD spectra, one might hope to achieve a reasonable reconstruction of temperature spots treating the LSD intensity profiles as a real spectral line. To clarify whether this is indeed possible, we have carried out numerical tests of temperature inversions based on simulated LSD spectra. First, we established mean-line parameters appropriate for the LSD line mask applied to the SOFIN observations of II Peg. Among the 1580 spectral lines included in this mask, Fe i is the most common ion (about 40% of all lines). Thus, we adopted the Fe i identification for a fictitious line representing LSD profiles and obtained the preliminary set of atomic parameters necessary for spectrum synthesis by combining the average excitation energy of the lower level, oscillator strength, and broadening constants for this ion with the mean wavelength and Landé factor (5067 Å and 1.21, respectively) for the entire line list. Then we adjusted the oscillator strength and van der Waals damping constant by fitting the synthetic LSD profiles derived from a theoretical spectrum covering the same wavelength interval as real observations. These calculations adopted the stellar atmospheric parameters discussed below (Sect. 4.3) and were performed for the v e sin i of II Peg and for the non-rotating star with the same parameters. In both cases we found that single-line calculations provide an excellent fit to the LSD profiles obtained from the synthetic spectra. At the next step, we simulated spectra of a star with temperature inhomogeneities, using a photospheric temperature of 4750 K and a spot temperature of 3700 K. The Stokes I spectra for the entire SOFIN wavelength range were computed for 10 equidistant rotational phases, assuming i = 60 GLYPH<14> , v e sin i = 23 kms GLYPH<0> 1 , and no magnetic field. A surface temperature map consisting of four circular spots located at di GLYPH<11> erent latitudes (see Fig. 4a) was employed in these calculations. These theoretical spectra were processed with our LSD code in exactly the same way as real stellar observations. The resulting set of synthetic LSD profiles was interpreted with I nvers 13 using the line parameters established above. For comparison, we also reconstructed a temperature map from the direct forward calculations for the same spectral line. A comparison of the DI maps inferred from the simulated data with the true temperature distribution is presented in Fig. 4. The reconstructions from the simulated observations of the real spectral line and from the simulated LSD profiles are generally successful in recovering the properties of cool spots. However, the temperature DI using LSD profiles shows a tendency to produce spurious hot surface features in which the temperature is overestimated by 200-300 K. We emphasise that this problem appears entirely due to a loss of information about real temperature sensitivity of the local profiles of individual spectral lines. Fortunately, this bias does not significantly interfere with the reconstruction of large low-temperature spots, although their contrast seems to be systematically underestimated. Thus, we conclude that the temperature DI based on a single-line radiative transfer approximation of the LSD profiles is a viable approach to mapping the distribution of cool spots on the surfaces of active stars. At the same time, the reliability of hot features recovered with this method is questionable. Limitations of LSD-based temperature inversions partly explain why some of the temperature maps presented here di GLYPH<11> er from those in our previous analysis (Hackman et al. 2012). The di GLYPH<11> erences are mainly caused by the use here of LSD profiles, while our previous analysis was based on individual lines. While individual lines will give a more accurate result, this approach su GLYPH<11> ers from a lower S / N. At the same time, neglect of the Zeeman broadening and intensification in earlier temperature inversions may also contribute to the discrepancy with the present results. In general, both of these e GLYPH<11> ects will influence the spot temperatures and latitudes.",
"pages": [
5,
6
]
},
{
"title": "4.3. Stellar parameters",
"content": "Di GLYPH<11> erent sets of atmospheric parameters have been deduced in previous studies of II Peg. The most thorough model atmosphere analyses were those by Berdyugina et al. (1998b) and Ottmann et al. (1998). The first paper suggested T e GLYPH<11> = 4600 K, log g = 3.2, and [ M = H ] = GLYPH<0> 0 : 4, whereas the second paper has inferred T e GLYPH<11> = 4800 K, log g = 3.65, and [ Fe = H ] = GLYPH<0> 0 : 24. A comparison of the average SOFIN observations with the theoretical spectra computed using the synth 3 code (Kochukhov 2007) and marcs model atmospheres supports the latter set of stellar parameters. Therefore, we adopted a marcs model atmosphere with T e GLYPH<11> = 4750 K, log g = 3.5, and [ M = H ] = GLYPH<0> 0 : 25 to represent an unspotted star. This temperature was also used as a starting guess for DI. All spectrum synthesis calculations assumed a microturbulent velocity of GLYPH<24> t = 2 kms GLYPH<0> 1 and a radial-tangential macroturbulent broadening of GLYPH<16> t = 4 kms GLYPH<0> 1 . These parameters are compatible with the values determined in previous studies. We note that the synthetic Fe i line approximating the LSD profiles of II Peg is weak ( W GLYPH<21> = 40 mÅ) and, therefore, relatively insensitive to the choice of GLYPH<24> t. Based on previous studies (Berdyugina et al. 1998b; Frasca et al. 2008), we adopted an inclination of the stellar rotational axis i = 60 GLYPH<14> . Using the three data sets with the best phasecoverage (epochs 2004.6, 2007.6, and 2009.7), we found that the best fit to the Stokes I LSD profiles is achieved for v e sin i = 23 GLYPH<6> 0 : 5 km s GLYPH<0> 1 . This value of the projected rotational velocity is consistent with v e sin i = 22 : 6 GLYPH<6> 0 : 5 km s GLYPH<0> 1 determined by Berdyugina et al. (1998b) and used in the recent DI studies by Lindborg et al. (2011) and Hackman et al. (2012). A latitude-dependent di GLYPH<11> erential rotation can be incorporated in the ZDI with I nvers 13. This e GLYPH<11> ect was ignored by previous spectroscopic DI investigations of II Peg and was theoretically predicted to be negligible in the rapidly rotating stars with deep convective envelopes (Kitchatinov & Rüdiger 1999). On the other hand, photometric analyses occasionally claimed detection of the di GLYPH<11> erential rotation in II Peg (Henry et al. 1995; Siwak et al. 2010; Roettenbacher et al. 2011), yet giving contradictory results, mainly because of the di GLYPH<14> culty of constraining the spot latitudes in light curve modelling. However, even the largest value of the di GLYPH<11> erential rotation coe GLYPH<14> cient reported in the literature k = 0 : 0245 (Siwak et al. 2010) is substantially smaller than the solar value of k = 0 : 19 and corresponds to an insignificant surface shearing for the time span of most of our SOFIN data sets. Therefore, ZDI analysis of II Peg was carried out assuming no di GLYPH<11> erential rotation.",
"pages": [
7
]
},
{
"title": "5. Magnetic field topology of II Peg",
"content": "Results of the simultaneous reconstruction of magnetic field topology and temperature distribution for II Peg are illustrated for the four data sets with best phase-coverage in Figs. 5 and 6 and for the remaining epochs in the online Figs. 7-9. For each data set we present four rectangular maps, showing the distribution of temperature as well as the radial, meridional, and azimuthal field components. A comparison between observed and computed LSD Stokes I and V profiles is illustrated next to the corresponding surface images. The model profiles generally achieve an adequate fit to observations, with median mean deviations of 0.15% and 0.01% for the Stokes I and V LSD profiles, respectively. The maximum local magnetic field intensity inferred by our ZDI code reaches 1 kG for 2004.6 data set, but is typically on the order of 400-500 G for the later magnetic images. Judging from these results, the field strength on the surface of II Peg was steadily decreasing from our first observations to later epochs. The field topology appears to be rather complex in 2004-2005, with many localised magnetic spots in all three magnetic vector component maps. As the field became weaker, this configuration evolved into a simpler topology, often dominated by large regions of common field polarity (e.g. epoch 2007.6). The temperature maps of II Peg reconstructed from LSD profiles show cool spots with an 800-1000 K contrast relative to the photospheric T = 4750 K. Occasionally, the inversion code reconstructed spots which are a few hundred K hotter than the photosphere. However, the numerical experiments discussed in Sect. 4.2 suggest that these features are not reliable. Inversions were carried out for all epochs, including the three data sets (2005.0, 2005.9, and 2008.7) with a poor phasecoverage. Temperature maps for these three data sets are dominated by a strong axisymmetric component, which should be regarded as spurious.",
"pages": [
7
]
},
{
"title": "5.1. Average field parameters",
"content": "The two independent ZDI reconstructions obtained for the epochs 2006.7 and 2006.9 allow us to investigate short-term changes of the surface distributions. The temperature maps inferred from the observations separated by three months are very similar. Both images are dominated by a large low-latitude cool spot at 180 GLYPH<14> longitude and an extended high-latitude spot group in the longitude interval 300 GLYPH<14> to 60 GLYPH<14> . The azimuthal field maps, representing the dominant magnetic component for both epochs, are also fairly similar. At the same time, distributions of the weaker radial and meridional field components exhibit significant di GLYPH<11> erences, suggesting field evolution. Next, to detect possible systematic changes either in the phases of the surface magnetic field distribution or in the total magnetic field strength, we calculated di GLYPH<11> erent types of averages of the ZDI maps. First, we averaged over the visible latitude range in each map, to obtain magnetic field profiles that depend on longitude (or phase) only. The profiles shown in Fig. 11 are averaged over the latitude interval from GLYPH<0> 60 GLYPH<14> to 90 GLYPH<14> for the di GLYPH<11> erent magnetic field components as function of time. This procedure can reveal azimuthal dynamo waves, that were visible in the surface temperature maps of this object during 1994-2002 (see Lindborg et al. 2011). There is no evidence for this type of dynamo wave from the ZDI maps. This agrees with the results of Hackman et al. (2012), who reported the disappearance of the clear drift pattern in the surface temperature maps during these years. The radial field plot, on the other hand, reveals a rather abrupt appearance and disappearance of spots of opposite polarities at a certain phase which are, however, irregular with time. Finally, we calculated the root-mean-square values of the magnetic field over each ZDI map, characterising the overall magnetic field strength (shown in Fig. 12). Interestingly, all the magnetic field components are of comparable strength, immediately hinting, from basic dynamo theory, towards an GLYPH<11> 2 dynamo operational in the object - the presence of di GLYPH<11> erential rotation would lead to the e GLYPH<14> cient shearing of the poloidal field into a toroidal field, in which case the azimuthal component would be observed to dominate over the other components. The radial and meridional components are clearly decreasing monotonically with time, reaching a minimum at around the year 2009. After that, the radial field possibly starts rising again. The azimuthal field shows a somewhat di GLYPH<11> erent trend in time: at first it is somewhat weaker than the other components, slightly increas- ing during 2004-2007, after which it also shows a decreasing trend. Similar to the radial component, it seems to start rising again after 2010. Therefore, judging from the magnetic field strength, it seems plausible that the magnetic activity level of the star has been declining during the epoch 2004-2009, while the signs of rising activity can be seen at least in the rms field strength for later epochs.",
"pages": [
7,
8
]
},
{
"title": "5.2. Evolution of harmonic field components",
"content": "Magnetic field maps reconstructed by our ZDI code are parameterised in terms of the spherical harmonic coe GLYPH<14> cients corre- sponding to the poloidal and toroidal field components. In addition to the analysis of 2D maps, this representation provides another convenient possibility to characterise the field topology and its long-term evolution. The sum of the spherical harmonic coe GLYPH<14> cients squared is proportional to the total energy contained in the stellar magnetic field. Figure 13a illustrates how this parameter has changed for II Peg between 2004 and 2010. Consistently with the results discussed above, we find a noticeable decrease of the total field energy in the period between 2004 and 2008, with a possible reversal of this trend afterwards. One can note that the total magnetic energy recovered from the data sets containing only a few spectra (e.g. 2005.0, 2005.9) is systematically underestimated compared to the trend defined by other maps. It is reassuring that the analysis of these data sets does not result in spurious strong magnetic field features. The time dependence of the relative contributions of the poloidal and toroidal field components is illustrated in Fig. 13b. It appears that our observations of II Peg reveal a cyclic change of the field topology on the time scale of a few years. Ignoring magnetic maps corresponding to epochs with a partial phasecoverage, one can conclude that II Peg exhibited a predominantly poloidal field before 2007.6 and a mainly toroidal field afterwards. However, the di GLYPH<11> erence between the energies of the two components is never much larger than 20-30%. Finally, Fig. 13c assesses relative contribution of the axisymmetric and non-axisymmetric field components as a function of time. Here we define axisymmetric harmonic components as those with m < '= 2 and non-axisymmetric ones as m GLYPH<21> '= 2 (e.g. As mentioned in Sect. 4.1, formal error bars cannot provide a realistic estimate of uncertainties of the spherical harmonic coe GLYPH<14> cients recovered in a regularised least-squares problem. Instead, the scatter of points corresponding to close observational epochs gives an idea of the uncertainties. We can see that in Figs. 12 and 13 the points inferred from the poor phase-coverage data sets often deviate significantly from the general trends. On the other hand, there are only a few cases when results obtained from the good phase-coverage data exhibit abrupt changes. This suggests that the trends examined in this and the previous sections are real and are not dominated by random inversion errors.",
"pages": [
8,
9
]
},
{
"title": "5.3. Extended magnetospheric structure",
"content": "The results of ZDI calculations are commonly used to investigate an extended stellar magnetospheric structure (Donati et al. 2008; Jardine et al. 2008; Gregory et al. 2008; Fares et al. 2012). The knowledge of the field topology above the stellar surface and in the immediate circumstellar environment allows photospheric magnetic field measurements to be connected with the studies of stellar coronas, X-ray emission, and prominences and the inter- action between the mass loss and magnetic field to be investigated. To determine the structure of the circumstellar magnetic field, one can use the potential field source surface (PFSS) extrapolation method developed for the solar magnetic field by van Ballegooijen et al. (1998) and adapted for stellar magnetic fields by Jardine et al. (2002). In this method the extended stellar magnetic field is represented as the gradient of a scalar potential expanded in a spherical harmonic series. The boundary condition for the radial field component at the stellar surface is provided by the empirical magnetic field maps. The outer boundary condition is given by a source surface of radius R s beyond which the field is assumed to be purely radial. We reconstructed the extended magnetospheric structure of II Peg with the help of an independently developed PFSS code. This software was applied to all our ZDI maps. The source surface is placed at R s = 3 R ? , which is plausible given the mean value of the solar source surface radius of 2 : 5 R GLYPH<12> . Previous potential field extrapolation studies adopted similar R s values for other cool active stars (e.g. Jardine et al. 2002; Hussain et al. 2002). The magnetospheric structure of II Peg predicted by our ZDI maps is illustrated in Fig. 14 for the four epochs with best phasecoverage. The stellar magnetosphere is shown at four distinct rotational phases, with di GLYPH<11> erent colours highlighting open and closed magnetic field lines. The evolution of the large-scale field is evident from this figure. Since the contribution of the small-scale (and hence less reliably reconstructed) field structures decays more rapidly with radius, this potential field extrapolation essentially presents a distilled view of the radial component of the ZDI maps, in which only the most robust large-scale information is retained. We find that during the first two epochs (2004.6 and 2006.7) the global field is nearly axisymmetric and is reminiscent of a dipole aligned with the stellar rotational axis. Adrastic change of the large-scale magnetic topology occurs between epochs 2006.7 and 2007.6. Simultaneously with a sharp decline in the total magnetic field energy, the field becomes more complex and decidedly non-axisymmetric.",
"pages": [
10
]
},
{
"title": "6.1. Comparison with previous ZDI studies",
"content": "The only other RS CVn system repeatedly studied with ZDI is HR 1099 (V711 Tau). The papers by Donati (1999), Donati et al. (2003), and Petit et al. (2004) presented magnetic field and brightness distributions recovered for about five epochs each, spanning the period from 1991 to 2002. In all these studies magnetic field reconstruction was carried out assuming an immaculate photosphere and the local line profiles were treated with a Gaussian approximation or using LSD profiles of slowly rotating inactive standards. The observed LSD Stokes V profiles of HR 1099 have a typical peak-to-peak amplitude of 0.15%, whereas the reconstructed field intensities are of the order of a few hundred G on average and reach up to GLYPH<24> 1 kG locally. This is comparable to our observational data and inversion results for II Peg. The ZDI studies of HR1099 revealed dominant azimuthal magnetic fields, often arranged in unipolar rings encircling the star at a certain latitude. Repeated magnetic inversions suggested stability of these structures on the time scales of several years. The authors attributed these horizontal fields to a global toroidal magnetic component produced by a non-solar dynamo mechanism distributed throughout the stellar convection zone. Compared to these studies of HR 1099, our ZDI maps of II Peg show a considerably smaller relative contribution of azimuthal fields. We still find a dominant toroidal component; however, these results are not fully equivalent nor easily comparable to those of, for example, Donati (1999) because here we use a harmonic representation of the magnetic field topology and hence are able to disentangle toroidal and poloidal contributions to the azimuthal field, whereas previous studies of HR 1099 completely ignored the poloidal contribution to the azimuthal field. It is clear that our data contain no evidence of the persistent unipolar azimuthal ring-like magnetic structures similar to those reported for HR 1099. Thus, either the dynamo mechanism operates di GLYPH<11> erently in the two RS CVn stars with nearly identical fundamental parameters, or azimuthal fields may represent an artefact owing to a simplified ZDI approach adopted for HR 1099 (Carroll et al. 2009a). To this end, we note that any axially-symmetric structure appearing in stellar DI maps must be carefully examined to exclude possible systematic biases and, at least, must be connected to the stationary features in the observed profiles to prove its reality. Neither was done for HR1099. Faced with this discrepancy between major features of the magnetic maps of II Peg and HR 1099, we conclude that a definite confirmation of the dominant ring-like azimuthal fields in the latter star and associated inferences about field generation mechanisms must await improved inversion methodologies and observations in all four Stokes parameters (Kochukhov et al. 2011).",
"pages": [
10,
11
]
},
{
"title": "6.2. Relation between temperature and magnetic field maps",
"content": "Throughout the entire series of ZDI images reconstructed for II Peg we see no obvious spatial correlation between the lowtemperature spots and the strongest magnetic field features. This suggests that a significant fraction of magnetic flux is not associated with cool spots. Although a similar conclusion has been reached by previous studies (Donati & Collier Cameron 1997; Donati 1999), it was unclear whether this represented a genuine characteristic of an active-star stellar surface structure or an inversion artefact coming from an inconsistent modelling of the magnetic and temperature spots. Our work confirms the lack of the field-spot correlation based on a self-consistent and physically realistic analysis of the circular polarisation in spectral lines. Using a similar approach, Carroll et al. (2007) also failed to detect a strong correlation between magnetic and temperature features on the surface of II Peg. These results may be inter- preted as evidence that current ZDI maps are mostly sensitive to magnetic fields at photospheric temperature and entirely miss the very strong fields inside cool spots. Instead, numerical experiments predict that self-consistent ZDI should be capable of recovering fields inside cool spots even if the temperature contrast is as large as 1500 K (Kochukhov & Piskunov 2009; Rosén &Kochukhov 2012). A limited spatial resolution of the ZDI maps may be another reason for not seeing a link between fields and cool spots. Both the magnetic and temperature distributions obtained using a spectral inversion technique reveal only the largest-scale structures, which are probably not monolithic but consist of many smaller spots with di GLYPH<11> erent geometries and field polarities. Then a local correlation between low-temperature spots and magnetic fields may be washed out in the current generation of ZDI maps. One can note that the presence of a substantial unresolved smallscale magnetic flux implies a much stronger average magnetic field strength than the one inferred from the ZDI analysis of circular polarisation. Highly inconsistent results of ZDI and Zeeman splitting studies of low-mass stars represent an example of this situation for a di GLYPH<11> erent dynamo regime (Reiners & Basri 2009). At the same time, it is not entirely obvious from a theoretical standpoint that a one-to-one relation between the cool spots and magnetic fields stemming from the solar paradigm can be universally extended to other types of cool active stars. There is an increasing amount of theoretical evidence (e.g. Chan 2007; Käpylä et al. 2011b; Mantere et al. 2011) of a pure hydrodynamical instability leading to the generation of large-scale vortices in the rapid rotation regime. These structures have so far been found only in local Cartesian simulations of turbulent convection, the sizes of the vortices always being very close to the box size, suggesting that these structures may have globally significant spatial extents. Depending on the rotation rate, either cool, cyclonic vortices for intermediate rotation, or warm anticyclonic vortices are excited, the temperature contrast being of the order of ten percent. This instability might contribute to the generation of magnetic fields independent from temperature structures in rapid rotators. So far, however, these structures have been detected neither in more realistic spherical geometry nor in the magnetohydrodynamic regime (see e.g. Käpylä et al. 2012b).",
"pages": [
12,
13
]
},
{
"title": "6.3. Interpretation in terms of dynamo theory",
"content": "The picture arising from an extensive set of previous photometric and spectroscopic observations of II Peg suggests that the surface magnetic field of this object concentrates on one or two active longitudes, i.e. is highly non-axisymmetric, and that these active longitudes evolve dynamically over time. During the epoch 1994-2002, a persistent drift of the active longitude has been confirmed (Berdyugina et al. 1998a, 1999; Lindborg et al. 2011). It is not detectable during 2004-2010 (Hackman et al. 2012) which is supported by the ZDI maps presented in this paper. Furthermore, our new results give an indication that the strength of the magnetic field has been monotonically decreasing, at least during 2004-2009; it seems that a minimum was reached at about 2009, after which the magnetic field strength started increasing again. The analysis of the energy contained in the poloidal and toroidal components as function of time shows that while in the beginning of the dataset the field was predominantly poloidal, the portion of the toroidal field is increasing nearly linearly with time, and is dominating at the end of the dataset. This is also reflected by the increasing contribution of the non-axisymmetric component exceeding the energy contained in the axisymmetric modes for 2009-2010. All these findings together hint towards a possible minimum in the star's magnetic activity cycle, during which the magnetic field tends to be more poloidal and axisymmetric, accompanied with the signature of the non-axisymmetric drifting dynamo wave getting too weak to be detectable. Unfortunately, the datasets, especially the series of ZDI maps, are too short to make decisive conclusions on the cyclic nature of the magnetic field. In any case it seems evident that the magnetic field on global scale is far from static. How can this be understood in terms of dynamo theory? In the solar case, the internal rotation and its non-uniformities are known from helioseismic inversions, while in the case of other stars, photometric period variations, interpreted as indirect proxies of stellar surface di GLYPH<11> erential rotation, are normally much smaller than the solar value. Theoretically this is conceivable, as it has been predicted that the faster the star rotates, the smaller the non-uniformities in its rotation rate will be (see e.g. Küker & Rüdiger 2005). This means that in the rapidly rotating late-type stars the operation of the dynamo should rely more strongly on the collective inductive action of convective turbulence (called the GLYPH<11> e GLYPH<11> ect), and less on the non-uniformities of the rotational velocity (called the GLYPH<10> e GLYPH<11> ect), the dynamo therefore being more of the GLYPH<11> 2 type than the GLYPH<11> GLYPH<10> solar dynamo. The simplest of these systems (see e.g. Krause & Raedler 1980) excite dynamo modes that are non-axisymmetric but show no oscillations, although drifts of the magnetic structure, i.e. azimuthal dynamo waves, are typical. As more and more observational evidence on dynamically changing magnetic fields is being gathered, it has become evident that this simple picture is not adequate. It has been suggested that either these objects have more di GLYPH<11> erential rotation than predicted by theory (e.g. Elstner & Korhonen 2005), or that the mean-field transport coe GLYPH<14> cients describing the convective turbulence are far too simple. Indeed, oscillating dynamo solutions in the GLYPH<11> 2 regime have been found with more complex profiles (Baryshnikova & Shukurov 1987; Mitra et al. 2010; Käpylä et al. 2012b). We also note that some observational evidence exists supporting the idea of stars showing a larger amount of di GLYPH<11> erential rotation than actually predicted by the theoretical models, although the discrepancy between observations and theory appears to be quite small (Hall 1991; Collier Cameron 2007). Direct numerical simulations in spherical geometry also show results consistent with the quenching of relative di GLYPH<11> erential rotation with increasing rotation rate (Käpylä et al. 2011a), although it is still challenging to relate these models to real stars. Therefore, we cannot completely rule out the existence of enough di GLYPH<11> erential rotation in rapid rotators to be significant for the dynamo mechanism. For our purposes, it is relevant to compare our observational results with direct numerical simulations of turbulent convection. Extensive parameter studies have been performed particularly in Cartesian geometry (Käpylä et al. 2012b), while such studies in global spherical geometry remain challenging (Miesch & Toomre 2009). One clear shortcoming of the local Cartesian models is that the di GLYPH<11> erential rotation cannot self-consistently emerge as a result of the modelling but needs to be imposed. The global spherical models can grasp this aspect, but only a few are successful in reproducing the solar rotation profile (see Miesch et al. 2006). The Cartesian studies clearly indicate that oscillatory GLYPH<11> 2 dynamos are quite natural in the rotation-dominated regime. Typical solutions (e.g. Käpylä et al. 2012b) show radial and azimuthal components of nearly equal strengths, with a rough GLYPH<25>= 2 phase separation in the cycle. Inclusion of shear into such a system has two principal e GLYPH<11> ects. Firstly, the azimuthal component grows in strength versus the radial component, and quite often the components are in anti-phase, the sign changes and minima occur simultaneously. The ZDI data indicates that the azimuthal field component is not completely synchronised with the radial and meridional fields, i.e. they do not seem to grow / decline simultaneously. This, again, is more consistent with the GLYPH<11> 2 scenario than the GLYPH<11> GLYPH<10> picture. The dominating non-axisymmetric topology, azimuthal dynamo waves, and even the time dependence of the magnetic fields in rapid rotators can be quite readily understood in terms of dynamo theory relying only on the GLYPH<11> mechanism; GLYPH<11> GLYPH<10> dynamos, in contrast, produce latitudinal dynamo waves (such as the solar butterfly diagram), mostly axisymmetric fields, and oscillatory solutions are the preferentially excited ones (see e.g. Steenbeck & Krause 1969). The presence of a significant axisymmetric contribution, as was found in the case of II Peg in this study, is di GLYPH<14> cult to explain with a pure GLYPH<11> 2 dynamo mechanism. To 'axisymmetrise' some part of the dynamo solution, some di GLYPH<11> eren- tial rotation will probably be needed; therefore our ZDI results most reasonably point towards an GLYPH<11> 2 GLYPH<10> dynamo operating on the object under study. Acknowledgements. Doppler imaging calculations presented in this paper were carried out at the supercomputer facility provided to the Uppsala Astronomical Observatory by the Knut and Alice Wallenberg Foundation and at the UPPMAX supercomputer center at Uppsala University. OK is a Royal Swedish Academy of Sciences Research Fellow supported by grants from the Knut and Alice Wallenberg Foundation and from the Swedish Research Council. TH was funded by the research programme 'Active Suns' at the University of Helsinki.",
"pages": [
13,
14
]
},
{
"title": "References",
"content": "Fares, R., Donati, J.-F., Moutou, C., et al. 2009, MNRAS, 398, 1383 Gu, S.-H., Tan, H.-S., Wang, X.-B., & Shan, H.-G. 2003, A&A, 405, 763 Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951 Hackman, T., Mantere, M. J., Lindborg, M., et al. 2012, A&A, 538, A126 Hall, D. S. 1991, in Lecture Notes in Physics, Berlin Springer Verlag, Vol. 380, Jardine, M., Collier Cameron, A., & Donati, J.-F. 2002, MNRAS, 333, 339 Jardine, M. M., Gregory, S. G., & Donati, J.-F. 2008, MNRAS, 386, 688 Lüftinger, T., Kochukhov, O., Ryabchikova, T., et al. 2010, A&A, 509, A71 Makarov, V. V. 2003, AJ, 126, 1996 Mitra, D., Tavakol, R., Käpylä, P. J., & Brandenburg, A. 2010, ApJ, 719, L1 O'Neal, D., Saar, S. M., & Ne GLYPH<11> , J. E. 1998, ApJ, 501, L73 Silvester, J., Wade, G. A., Kochukhov, O., et al. 2012, MNRAS, 426, 1003 Skelly, M. B., Donati, J.-F., Bouvier, J., et al. 2010, MNRAS, 403, 159 Unruh, Y. C. & Collier Cameron, A. 1995, MNRAS, 273, 1",
"pages": [
14
]
}
]
2013A&A...551A..54V
https://arxiv.org/pdf/1301.1147.pdf
<document>
<section_header_level_1><location><page_1><loc_7><loc_82><loc_95><loc_87></location>Flux Modulation from the Rossby Wave Instability in microquasars' accretion disks: toward a HFQPO model</section_header_level_1>
<text><location><page_1><loc_29><loc_80><loc_73><loc_82></location>F. H. Vincent 1 , H. Meheut 2 ; 3 , P. Varniere 1 , and T. Paumard 4</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_76><loc_88><loc_78></location>1 AstroParticule et Cosmologie (APC), Universit'e Paris Diderot, 10 rue A. Domon et L. Duquet, 75205 Paris Cedex 13, France e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_51><loc_76></location>2 Physikalisches Institut, Universitat Bern, 3012 Bern, Switzerland</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_52><loc_75></location>3 CEA, Irfu, SAp, Centre de Saclay, F-91191 Gif-sur-Yvette, France e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_91><loc_72></location>4 LESIA, Observatoire de Paris, CNRS, Universit'e Pierre et Marie Curie, Universit'e Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_67><loc_20><loc_68></location>April 19, 2022</text>
<section_header_level_1><location><page_1><loc_47><loc_65><loc_55><loc_65></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_59><loc_91><loc_63></location>Context. There have been a long string of e GLYPH<11> orts to understand the source of the variability observed in microquasars, especially concerning the elusive High-Frequency Quasi-Periodic Oscillation. These oscillations are among the fastest phenomena that a GLYPH<11> ect matter in the vicinity of stellar black holes and therefore could be used as probes of strong-field general relativity. Nevertheless, no model has yet gained wide acceptance.</text>
<text><location><page_1><loc_11><loc_55><loc_91><loc_58></location>Aims. The aim of this article is to investigate the model derived from the occurrence of the Rossby wave instability at the inner edge of the accretion disk. In particular, our goal here is to demonstrate the capacity of this instability to modulate the observed flux in agreement with the observed results.</text>
<text><location><page_1><loc_11><loc_53><loc_91><loc_55></location>Methods. We use the AMRVAC hydrodynamical code to model the instability in a 3D optically thin disk. The GYOTO ray-tracing code is then used to compute the associated light curve.</text>
<text><location><page_1><loc_11><loc_48><loc_91><loc_52></location>Results. We show that the 3D Rossby wave instability is able to modulate the flux well within the observed limits.We highlight that 2D simulations allow us to obtain the same general characteristics of the light curve as 3D calculations. With the time resolution we adopted in this work, three dimensional simulations do not give rise to any new observable features that could be detected by current instrumentation or archive data.</text>
<text><location><page_1><loc_11><loc_46><loc_80><loc_47></location>Key words. Accretion, accretion disks - Hydrodynamics - Instabilities - Radiative transfer - Methods: numerical</text>
<section_header_level_1><location><page_1><loc_7><loc_42><loc_19><loc_43></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_10><loc_50><loc_38></location>Black hole binary systems exhibit a wide range of variability patterns. Among these, the high frequency quasi-periodic oscillations (HFQPOs) appear as small narrow peaks in the power density spectrum. Their frequencies, of several tens to a few hundred Hertz, correspond to the rotation frequency in the inner part of the disk surrounding the black hole (see more details in the review of van der Klis 2006) making them an interesting tool to study strong-field gravity. Even though they are the fastest phenomena observed in the vicinity of black holes, HFQPOs are also extremely elusive, especially when compared to the lower frequency quasi-periodic oscillations (LFQPO). For this reason, we do not have a rich domain of observations from which to draw constraints for the models. This has led to a wide variety of models (see e.g. Lai & Tsang 2009 for a very brief review) focusing on one or another of the observed characteristics of the HFQPOs. As more and more data are obtained, especially with the next generation telescopes such as LOFT (Bozzo et al. 2011), we will be able to gain a better picture of what a model must explain. Nevertheless, we already can make a stringent list of constraints based on the eight objects with recurrent HFQPOs (see for example the review by Remillard & McClintock 2006). Among the most important of those constraints we note:</text>
<unordered_list>
<list_item><location><page_1><loc_52><loc_38><loc_95><loc_43></location>1- The emitted flux is modulated at a level of a few percent in X-ray and this modulation increases with energy. This first and fundamental point, often not discussed by models, is the aim of this paper.</list_item>
<list_item><location><page_1><loc_52><loc_35><loc_95><loc_38></location>2- The frequency of the modulation has a small but significant range that must be explained.</list_item>
<list_item><location><page_1><loc_52><loc_31><loc_95><loc_35></location>3- The HFQPOs occur sometimes, but not always, in pairs close to a 2:3 ratio. Those occurrences, and not just the close ratio, need to be elucidated.</list_item>
<list_item><location><page_1><loc_52><loc_27><loc_95><loc_31></location>4- Another point often neglected in models for HFQPOs is the fact that, sometimes, they co-exist with the more ubiquitous LFQPOs.</list_item>
</unordered_list>
<text><location><page_1><loc_52><loc_10><loc_95><loc_26></location>The model we are investigating here is based on the existence of the Rossby wave instability (RWI) at the inner edge of the disk as was discussed in Tagger & Varniere (2006). Indeed, it was shown that the existence of an innermost stable circular orbit (ISCO) around a black hole makes the disk prone to the RWI because the vorticity profile has a natural extremum. This dynamic instability results in the formation of large-scale spiral density waves and Rossby waves that can reach high amplitudes. Depending on the disk's physical parameters, di GLYPH<11> erent modes of this instability will be selected, most often with azimuthal mode number m = 2 or 3 (Tagger & Varniere 2006) which gives a natural explanation for some of the observed characteristics of HFQPOs. Nevertheless, the important step of computing the ac-</text>
<text><location><page_2><loc_7><loc_79><loc_50><loc_93></location>tual flux modulation one would observe when such an instability occurs in a disk was still missing. Here we focus on this point and therefore restrict ourselves to the case of the HFQPO alone. Indeed, we are trying to explore the capacity of one particular HFQPO model to modulate the X-ray flux and having only one instability in the disk makes the results more conspicuous. To this end we will use the purely hydrodynamic version of the Rossby wave instability (RWI, Lovelace et al. 1999), without the extra destabilizing e GLYPH<11> ect provided by a poloidal magnetic field (Tagger & Varniere 2006) or the extra stabilizing e GLYPH<11> ect of a toroidal magnetic field (Yu & Li 2009).</text>
<text><location><page_2><loc_7><loc_68><loc_50><loc_79></location>This is the continuation of the long string of studies on the impact of the RWI in disks such as was done in the context of protoplanetary disks (Reg'aly et al. 2012) and the galactic centre (Falanga et al. 2007). Whereas the first case is highly di GLYPH<11> erent from ours, the second is more comparable and we use similar tools, but Falanga et al. (2007) restricted themselves to the 2D case and to the special context of the galactic centre source Sgr A*.</text>
<text><location><page_2><loc_7><loc_44><loc_50><loc_68></location>Our main interest here will thus be to answer the key question: is the RWI able to modulate the flux of a microquasar at a level coherent with observations? In a more practical manner, we will also address the question of the necessity of full 3D simulations of the RWI, and to what extent it is su GLYPH<14> cient to restrict oneself to 2D simulations. Those 2D simulations are more accessible in terms of computing and storage resources, therefore allowing us to do much larger parameter studies and with a higher time resolution that could be compared with future LOFT observations. These questions will be addressed by computing the light curve of a microquasar subject to the RWI, as observed by a distant observer. This computation will be performed by means of a general relativistic ray-tracing code (Vincent et al. 2011). The main general relativistic e GLYPH<11> ect that a GLYPH<11> ects the RWI being the existence of an ISCO, we use a pseudo-Newtonian potential in order to model this in the hydrodynamical simulations, instead of considering the full general relativistic case. This simplifying assumption is su GLYPH<14> cient in order to derive a proof of principle of the ability of the RWI to modulate the flux of microquasars.</text>
<text><location><page_2><loc_7><loc_36><loc_50><loc_43></location>Sect. 2 briefly presents the RWI and then develops the hydrodynamical simulations that allow us to model the unstable accretion structure. The following section is focused on the raytracing procedure used to compute observable quantities. Sect. 4 presents the light curves that were obtained and Sect. 5 gives conclusions and prospects.</text>
<section_header_level_1><location><page_2><loc_7><loc_32><loc_41><loc_33></location>2. Hydrodynamical simulation of the RWI</section_header_level_1>
<text><location><page_2><loc_7><loc_22><loc_50><loc_31></location>The RWI has been discussed in multiple astrophysical contexts, from the galactic centre to protoplanetary disks. It can be seen as the form the Kelvin-Helmholtz instability takes in di GLYPH<11> erentially rotating disks, and has a similar instability criterion. For twodimensional (vertically integrated) barotropic disks, the RWI can be triggered provided an extremum exists in a quantity L which is the inverse vortensity 1 :</text>
<formula><location><page_2><loc_7><loc_18><loc_50><loc_20></location>L = GLYPH<6>GLYPH<10> 2 GLYPH<20> 2 p GLYPH<6> GLYPH<13> ; (1)</formula>
<text><location><page_2><loc_7><loc_12><loc_50><loc_16></location>where p is the pressure, GLYPH<6> is the surface density, GLYPH<10> is the rotation frequency, GLYPH<20> 2 = 2 GLYPH<10> = r d = d r GLYPH<16> r 2 GLYPH<10> GLYPH<17> is the squared epicyclic frequency and GLYPH<13> is the adiabatic index. An extremum of vortensity</text>
<text><location><page_2><loc_52><loc_84><loc_95><loc_93></location>can thus typically arise from an extremum of the epicyclic frequency, as is the case close to the ISCO, or from an extremum in the density profile which gives rise to the RWI in the disk. Once it is triggered, it leads to large scale spiral density waves and Rossby vortices. The dominant mode (i.e. the number of vortices) is dependent on the disk conditions (Tagger & Varniere 2006).</text>
<section_header_level_1><location><page_2><loc_52><loc_81><loc_81><loc_82></location>2.1. The RWI as a model for the HFQPO</section_header_level_1>
<text><location><page_2><loc_52><loc_70><loc_95><loc_80></location>Due to general relativistic e GLYPH<11> ects, the epicyclic frequency profile will show a maximum in the vicinity of the black hole's ISCO, creating a vortensity extremum . Tagger & Varniere (2006) showed that it would lead to the growth of the RWI at the inner edge of black hole binaries when the disk nears its ISCO. From these facts, it seems natural that the RWI model may be capable of accounting for points 2- to 4- in the Introduction above (that will not be investigated in detail here).</text>
<unordered_list>
<list_item><location><page_2><loc_52><loc_58><loc_95><loc_68></location>2- The frequency range: the exact location of the resulting vortensity extremum will depend on the density profile of the disk on top of the epicyclic frequency. Thus the location of the launching of the instability can vary depending on the disk properties. As the Rossby vortices will orbit around the central black hole with the disk's rotation frequency at the radius of launching, this variation of the disk properties gives rise to a range of di GLYPH<11> erent possible frequencies of the signal.</list_item>
<list_item><location><page_2><loc_52><loc_50><loc_95><loc_58></location>3- Pairs of frequencies: di GLYPH<11> erent modes can dominate the signal depending on the physical state of the disk. This was adressed in Tagger & Varniere (2006) and more recently in Varniere et al. (2012b). The 2:3 frequency pairs can be naturally explained by a superposition of azimuthal modes m = 2 and m = 3.</list_item>
<list_item><location><page_2><loc_52><loc_42><loc_95><loc_50></location>4- Coexistence of HF- and LFQPO: we have tackled this point by showing the ability of the RWI to co-exist with another instability that we proposed to be at the origin of the LFQPO (Varniere et al. 2012a), the Accretion Ejection Instability (AEI). A disk giving rise to both AEI and RWI will thus naturally show both types of QPOs.</list_item>
</unordered_list>
<text><location><page_2><loc_52><loc_37><loc_95><loc_41></location>It seems therefore natural to address in more detail if the RWI is strong enough to give rise to a modulation that could explain the observations.</text>
<section_header_level_1><location><page_2><loc_52><loc_34><loc_67><loc_35></location>2.2. Numerical setup</section_header_level_1>
<text><location><page_2><loc_52><loc_22><loc_95><loc_33></location>To perform the hydrodynamical simulation of the RWI we use the Message Passing Interface-Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC) developed by Keppens et al. (2011). The numerical scheme is the same for all refinement levels, namely the Total Variation Diminishing Lax-Friedrich scheme (see T'oth & Odstrˇcil 1996) with a third order accurate Koren limiter (Koren 1993) on the primitive variables.</text>
<text><location><page_2><loc_52><loc_19><loc_95><loc_22></location>We consider a geometrically thin disk and neglect selfgravity. The Euler equations in cylindrical coordinates ( r ; '; z ) read:</text>
<formula><location><page_2><loc_63><loc_16><loc_95><loc_17></location>@ t GLYPH<26> + r GLYPH<1> ( v GLYPH<26> ) = 0 ; (2)</formula>
<formula><location><page_2><loc_52><loc_14><loc_95><loc_16></location>@ t ( GLYPH<26> v ) + r GLYPH<1> ( v GLYPH<26> v ) + r p = GLYPH<0> GLYPH<26> r GLYPH<8> G ; (3)</formula>
<text><location><page_2><loc_52><loc_10><loc_95><loc_13></location>where GLYPH<26> is the mass density of the fluid, v its velocity, and p its pressure. We consider a barotropic flow, i.e. the entropy is constant in the entire system. The pressure is then p = S GLYPH<26> GLYPH<13> ,</text>
<text><location><page_3><loc_7><loc_85><loc_50><loc_93></location>with the adiabatic index GLYPH<13> = 5 = 3 and the constant S related to entropy. The sound speed is given by c 2 s = GLYPH<13> p =GLYPH<26> = S GLYPH<13>GLYPH<26> GLYPH<13> GLYPH<0> 1 and the temperature by T / p =GLYPH<26> / S GLYPH<26> GLYPH<13> GLYPH<0> 1 . All the distances are normalized by the ISCO radius r 0. The same applies for temperatures normalized at ISCO by: T 0 = 10 7 K , while all times are in units of the ISCO period t ISCO.</text>
<text><location><page_3><loc_7><loc_74><loc_50><loc_84></location>The general relativistic e GLYPH<11> ects have to be taken into account to study the innermost region of the black hole disk. In order to provide a proof of principle of the ability of the 3D RWI to modulate the flux of microquasars, we use the minimum model necessary to mimic some of these general relativistic e GLYPH<11> ects by using a pseudo-Newtonian potential GLYPH<8> G . For our simulations, we use the common Paczy'nsky & Wiita (1980) gravitational potential:</text>
<formula><location><page_3><loc_7><loc_70><loc_50><loc_73></location>GLYPH<8> G = GLYPH<0> GM GLYPH<3> p r 2 + z 2 GLYPH<0> 2 rg (4)</formula>
<text><location><page_3><loc_7><loc_52><loc_50><loc_69></location>where rg = GM GLYPH<3> c 2 is the gravitational radius, G the gravitational constant, M GLYPH<3> the black hole mass, c the speed of light in vacuum. With this gravitational potential, one can define the inner limit below which there is no stable circular orbit, the ISCO, located at r 0 = 6 rg . Let us stress the fact that this choice of potential allows us to mimic only some aspects of the Schwarzschild metric. The e GLYPH<11> ect of the black hole spin is not taken into account. It is also important to keep in mind that this pseudo-Newtonian potential, although widely used, is far from giving an exact description of general relativity. However, the only characteristic of the Schwarzschild metric that is of primordial importance as far as RWI is concerned is the existence of an ISCO, and this is correctly modeled by Eq. 4.</text>
<text><location><page_3><loc_7><loc_42><loc_50><loc_51></location>Let us mention that we have also developed 2D RWI simulations with alternative pseudo-Newtonian potentials that take into account the rotation of the black hole. These alternative potentials were taken from Artemova et al. (1996). The RWI also develops well in these potentials, and future works will be dedicated to studying the e GLYPH<11> ect of the black hole's rotation on the observables.</text>
<section_header_level_1><location><page_3><loc_7><loc_39><loc_36><loc_40></location>2.3. Disk setup and boundary conditions</section_header_level_1>
<text><location><page_3><loc_7><loc_24><loc_50><loc_38></location>The grid is cylindrical with the unit length defined as the ISCO radius r 0. The radial coordinate r is in the range [0 : 8 ; 6], the full azimuthal coordinate spans [0 ; 2 GLYPH<25> ] and the vertical coordinate z lies in the range [0 ; 0 : 2] for the 3D simulations. For the fluid simulations, we considered only the upper part of the disk as the mid-plane is a symmetry plane for the RWI (Meheut et al. 2010, 2012). For the ray-tracing computations, the full disk is considered by symmetrizing the upper part. We used a fixed and homogeneous grid with a resolution nr GLYPH<2> n ' = (384 ; 72) in 2D and nr GLYPH<2> n ' GLYPH<2> nz = (384 ; 72 ; 72) in 3D, which is slightly higher than the resolution used in Meheut et al. (2010).</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_24></location>As we describe gravitation by the pseudo-Newtonian potential in Eq. 4, the epicyclic frequency will show a maximum at a radius slightly higher than the ISCO radius r 0. This epicyclic frequency maximum gives rise to an extremum of the initial vortensity profile, which is shown in Fig. 1. The existence of this vortensity extremum does not depend on the choice of initial density profile even though it does influence its precise location in the disk. Considering the density, we choose a typical power-law profile with a slope of GLYPH<0> 3 = 2. This choice, while reasonable, allows us to obtain a steeper vortensity extremum and hence a stronger instability. Note that the precise value of the</text>
<figure>
<location><page_3><loc_55><loc_73><loc_91><loc_93></location>
<caption>Fig. 1. Inverse vortensity profile, normalized to its extremum value. The instability is triggered at the location of the extremum, i.e. at r GLYPH<25> 1 : 4 r 0.</caption>
</figure>
<text><location><page_3><loc_52><loc_58><loc_95><loc_66></location>rms of the modulation depends on this choice of slope. However, we are here only interested in proving the existence of the flux modulation, not comparing a precise value of modulation to observations. If future instruments give better data on the rise of the HFQPO we might be able to use these to constrain the disk model that could reproduce the observed data.</text>
<text><location><page_3><loc_54><loc_57><loc_79><loc_58></location>The initial density profile then reads:</text>
<formula><location><page_3><loc_52><loc_53><loc_95><loc_56></location>GLYPH<26> M GLYPH<17> GLYPH<26> ( r ; '; z = 0) = GLYPH<26> 0 2 GLYPH<20> 1 + tanh GLYPH<16> r GLYPH<0> rB GLYPH<27> GLYPH<17> GLYPH<21> r r 0 ! GLYPH<11> ; (5)</formula>
<text><location><page_3><loc_52><loc_49><loc_95><loc_52></location>the hydrostatic equilibrium gives the vertical profile of the density</text>
<formula><location><page_3><loc_52><loc_45><loc_95><loc_48></location>GLYPH<26> ( r ; '; z ) = GLYPH<26> M GLYPH<18> 1 GLYPH<0> GLYPH<13> GLYPH<0> 1 GLYPH<13> S GLYPH<26> GLYPH<13> GLYPH<0> 1 M " GM GLYPH<3> r GLYPH<0> 2 rg GLYPH<0> GM GLYPH<3> p r 2 + z 2 GLYPH<0> 2 rg GLYPH<21> ! 1 GLYPH<13> GLYPH<0> 1 (6)</formula>
<text><location><page_3><loc_52><loc_27><loc_95><loc_44></location>where rB = 1 : 3 r 0 gives the position of the density maximum (its value was choosen to fit the simulations of Tagger & Varniere 2006), rg = r 0 = 6 is the gravitational radius, GLYPH<27> = 0 : 05 r 0 gives the width of the plunging region, GLYPH<11> = GLYPH<0> 3 = 2 is the density slope, and GLYPH<26> 0 is the minimum density of the simulation. These parameters, and mainly the choice of density slope, can modify the structure and characteristics of the RWI. In our case, the existence of an extremum in GLYPH<20> limits the impact of the density power-law index and any reasonable choice will exhibit the instability. The detailed e GLYPH<11> ect of the initial density profile on the growth rate of the instability and its saturation level will be studied in a forthcoming paper (Meheut, Lovelace, Lai, 2013) but will not influence its ability to modulate the flux.</text>
<text><location><page_3><loc_52><loc_22><loc_95><loc_27></location>We also considered a 2D disk with the surface density defined as GLYPH<6> / r GLYPH<0> 3 = 2 in the outer region. The initial conditions of the 2D and 3D simulations are then highly di GLYPH<11> erent. In both cases, the azimuthal velocity is determined by force balance:</text>
<formula><location><page_3><loc_52><loc_17><loc_95><loc_21></location>v ' = s GM GLYPH<3> r ( r GLYPH<0> 2 rg ) 2 + GLYPH<11> S GLYPH<13>GLYPH<26> GLYPH<13> GLYPH<0> 1 M + S GLYPH<13>GLYPH<26> GLYPH<13> GLYPH<0> 2 M ( r = r 0) GLYPH<11> + 1 GLYPH<26> 0 2 GLYPH<27> cosh 2 r GLYPH<0> rB GLYPH<27> : (7)</formula>
<text><location><page_3><loc_52><loc_10><loc_95><loc_16></location>The density and velocity profiles given in Eqs. 6-7 include high amplitude gradients and do not give exact numerical equilibrium. For this reason, the initial conditions of our simulations are numerically computed from this pseudo-equilibrium. This means that a first simulation is done without any perturbations</text>
<figure>
<location><page_4><loc_16><loc_74><loc_45><loc_93></location>
<caption>Fig. 2. Midplane density map of the 3D simulation when the m = 1 mode dominates. The axes are in units of the ISCO radius.</caption>
</figure>
<text><location><page_4><loc_7><loc_63><loc_50><loc_68></location>and is run until the disk has reached a permanent stage which is chosen as the initial conditions. This disk is then perturbed with small amplitude ( GLYPH<24> 10 GLYPH<0> 3 v ' ) random perturbations on the radial velocity which act as seeds for the instability.</text>
<text><location><page_4><loc_7><loc_48><loc_50><loc_63></location>The inner boundary condition is a no-inflow condition and the outer boundary condition is a null radial velocity condition. Meheut et al. (2012) have shown that the boundary conditions do not change significantly the growth rate of the RWI due to its confinement in the vortensity bump. Moreover the inner edge of the simulation being inside the ISCO, any reflected wave would not reach the region of interest for the instability. Therefore, the boundary conditions are not determinant for these simulations. For the 3D simulations, symmetric boundary conditions are implemented at the mid-plane, and we use a null vertical velocity at the grid upper boundary limit, situated outside of the disk.</text>
<section_header_level_1><location><page_4><loc_7><loc_45><loc_28><loc_46></location>2.4. Time evolution of the RWI</section_header_level_1>
<text><location><page_4><loc_7><loc_39><loc_50><loc_44></location>Fig. 2 shows the density map of the z = 0 plane of a 3D RWI simulation, when the instability is completely developed. This section presents the time evolution of the instability (at 2D and 3D) from its launch to its complete development.</text>
<text><location><page_4><loc_7><loc_25><loc_50><loc_39></location>At first, the disk is assumed to be 2D and the vertical structure of the disk is neglected. The growth of the instability is shown on Fig. 3 where the time evolution of the perturbation of density is plotted on a logarithmic scale. This allows the identification of the linear phase of the instability when the amplitude of the perturbations grows exponentially (thus linearly in logarithm), as well as the saturation which is due to non-linearities. In the 2D case, the initial conditions give rise to a rapid growth of the instability on a time scale of a few periods at ISCO as can be seen in Fig. 3. During the linear phase, the perturbations can be separated in the di GLYPH<11> erent azimuthal modes:</text>
<formula><location><page_4><loc_7><loc_21><loc_50><loc_24></location>X = X m 2 N Xm sin( m ! t GLYPH<0> m GLYPH<30> ) exp GLYPH<13> mt (8)</formula>
<text><location><page_4><loc_7><loc_10><loc_50><loc_20></location>where X = GLYPH<6> for 2D simulations and X = GLYPH<26> for 3D. The quantities GLYPH<13> m are the growth rates of each mode, ! the characteristic frequency of the instability depending on the position of the extremum of L , m the azimuthal mode number, and Xm the amplitude of mode m . Therefore, Xm = 0 corresponds to the axisymmetric part of the density and the frequency of the mode m is the multiple m ! of the frequency of the fundamental mode. Fig. 3 also shows the time evolution of the amplitude of the</text>
<figure>
<location><page_4><loc_53><loc_70><loc_96><loc_90></location>
<caption>Fig. 3. Amplitude of the surface density perturbation in logarithmic scale (solid line) for the 2D simulation. The amplitudes of the strongest modes are also plotted in dotted and dashed lines. The vertical dashed lines show the changes of dominant modes, indicated in italic at the top of the figure. The fundamental mode m = 1 eventually dominates.</caption>
</figure>
<figure>
<location><page_4><loc_53><loc_38><loc_96><loc_57></location>
<caption>Fig. 4. Same as Fig. 3 for 3D simulations. However, mind the di GLYPH<11> erent time scale.</caption>
</figure>
<text><location><page_4><loc_52><loc_23><loc_95><loc_30></location>strongest modes. During the linear phase, the dominant mode is m = 3, and later on the disk is dominated by the fundamental mode m = 1 with important contributions from the modes m = 2 and 3. This evolution of the oscillation modes depends on the disk's astrophysical properties: di GLYPH<11> erent modes dominate for di GLYPH<11> erent initial disk conditions.</text>
<text><location><page_4><loc_52><loc_10><loc_95><loc_21></location>This fact is illustrated in the 3D simulations. Indeed, the initial conditions di GLYPH<11> er largely between the 2D and 3D simulations, with a di GLYPH<11> erent surface density radial profile and absolute value. The characteristic velocity of the waves is then di GLYPH<11> erent. This modifies the timescale for the growth of the instability as can be seen in Fig. 4. This di GLYPH<11> erence is not due to the dimensionality (Meheut et al. 2012; Lin 2012). Nevertheless, the RWI is triggered and saturation of the 3D instability is reached after a few tens of periods at ISCO. The dominant modes are also di GLYPH<11> er-</text>
<text><location><page_5><loc_7><loc_91><loc_50><loc_93></location>ent during the linear phase, but non-linearities still tend to favour the lowest azimuthal mode.</text>
<text><location><page_5><loc_7><loc_81><loc_50><loc_90></location>Let us note that, as the epicyclic frequency profile is not evolving with time, the location of the extremum of vortensity will stay the same. Moreover the vortices grow in a density extremum where they cannot migrate due to the two density slopes of opposite sign. As a consequence, the Rossby vortices will not migrate during the simulation (for more details see Meheut et al. 2012).</text>
<text><location><page_5><loc_7><loc_72><loc_50><loc_81></location>From the hydrodynamical simulations we obtain the density and velocity at every point of our grid with a su GLYPH<14> cient time sampling (of 40 frames in 2D and 6 frames in 3D per orbit at the ISCO) to follow the RWI in the disk from its rise to its saturation. In the next step those will be used as input for the ray-tracing code in order to trace the impact of the RWI on the observed emission.</text>
<section_header_level_1><location><page_5><loc_7><loc_69><loc_38><loc_70></location>3. Ray-tracing of the RWI with GYOTO</section_header_level_1>
<section_header_level_1><location><page_5><loc_7><loc_67><loc_31><loc_68></location>3.1. Ray-tracing the accretion disk</section_header_level_1>
<text><location><page_5><loc_7><loc_52><loc_50><loc_66></location>In order to obtain images, and especially lightcurves, that could be compared with observations we used the general relativistic ray-tracing code GYOTO (Vincent et al. 2011). Null geodesics are computed backward in time in the Schwarzschild metric from a distant observer to the emitting disk. The coordinates used by GYOTO are spherical-like and denoted (¯ r ; GLYPH<18>; ' ), where ¯ r is used to di GLYPH<11> erentiate the GYOTO spherical radius from the fluid simulations cylindrical radius r . Once a backward integrated geodesic hits the disk, the density and 3-velocity at the point of emission is linearly interpolated at the time of emission from the results of the MPI-AMRVAC computations.</text>
<section_header_level_1><location><page_5><loc_7><loc_49><loc_38><loc_50></location>3.1.1. Radiative processes at 2D: blackbody</section_header_level_1>
<text><location><page_5><loc_7><loc_42><loc_50><loc_48></location>The 2D disk is assumed to be optically thick, so the integration is stopped at the first encounter of the disk. The emission is supposed to follow the Planck law: the only parameter needed is thus the temperature which can be easily derived from the density according to the following computations.</text>
<text><location><page_5><loc_10><loc_40><loc_29><loc_41></location>The gas being assumed ideal:</text>
<formula><location><page_5><loc_7><loc_37><loc_50><loc_39></location>p = GLYPH<26> GLYPH<22> mu k T (9)</formula>
<text><location><page_5><loc_7><loc_29><loc_50><loc_37></location>where GLYPH<22> is the mean molecular weight, mu is the atomic mass constant and k is the Boltzmann constant. Assuming that the plasma is made of pure hydrogen, GLYPH<22> = 1. Using the relation R = NA k between the ideal gas contant R , the Avogadro number NA and the Boltzmann constant together with the expression of the sound speed this yields:</text>
<formula><location><page_5><loc_7><loc_26><loc_50><loc_28></location>T = NA mu GLYPH<13> c 2 s R : (10)</formula>
<text><location><page_5><loc_7><loc_23><loc_50><loc_25></location>This allows the computation of the emitted specific intensity at the surface of a 2D disk:</text>
<formula><location><page_5><loc_7><loc_21><loc_50><loc_22></location>I GLYPH<23> = B GLYPH<23> ( T ) (11)</formula>
<text><location><page_5><loc_7><loc_19><loc_29><loc_20></location>where B GLYPH<23> is the Planck function.</text>
<section_header_level_1><location><page_5><loc_7><loc_16><loc_42><loc_17></location>3.1.2. Radiative processes at 3D: Bremsstrahlung</section_header_level_1>
<text><location><page_5><loc_7><loc_10><loc_50><loc_15></location>For the three dimensional computations, the only radiative process considered is Bremsstrahlung. As the disk is purely hydrodynamic, there is no synchrotron emission, and Compton scattering is neglected as we are only interested here in a proof of</text>
<text><location><page_5><loc_52><loc_88><loc_95><loc_93></location>principle, not in a detailed study of emission processes. The Bremsstrahlung emission is assumed to be thermal, so that the emission coe GLYPH<14> cient j GLYPH<23> and absorption coe GLYPH<14> cient GLYPH<11>GLYPH<23> are related via Kirchho GLYPH<11> 's law:</text>
<formula><location><page_5><loc_52><loc_86><loc_95><loc_87></location>j GLYPH<23> = GLYPH<11>GLYPH<23> B GLYPH<23> : (12)</formula>
<text><location><page_5><loc_52><loc_82><loc_95><loc_84></location>The emission coe GLYPH<14> cient for thermal Bremsstrahlung is given by (Rybicki & Lightman 1979):</text>
<formula><location><page_5><loc_52><loc_78><loc_95><loc_81></location>j GLYPH<23> = 1 4 GLYPH<25> 2 5 GLYPH<25> e 6 3 m e c 3 2 GLYPH<25> 3 km e ! 1 = 2 T GLYPH<0> 1 = 2 GLYPH<26> m u ! 2 exp GLYPH<0> h GLYPH<23> kT ! (13)</formula>
<text><location><page_5><loc_52><loc_69><loc_95><loc_77></location>where e is the electron charge, m e is the electron mass and h is the Planck constant. Here, we assume that the disk is made of pure hydrogen, and that the emission is isotropic in the emitter's frame (hence the 1 = 4 GLYPH<25> initial factor). Moreover, the Gaunt factor is neglected as most of the radiation arises from locations in the disk where h GLYPH<23> GLYPH<25> kT .</text>
<text><location><page_5><loc_52><loc_66><loc_95><loc_69></location>Once the emission coe GLYPH<14> cient is computed, the absorption coe GLYPH<14> cient is derived by using Eq. 12.</text>
<section_header_level_1><location><page_5><loc_52><loc_63><loc_86><loc_64></location>3.1.3. Dependency on temperature at 2D and 3D</section_header_level_1>
<text><location><page_5><loc_52><loc_51><loc_95><loc_62></location>Let us investigate the dependency on temperature of the 3D emission process (Bremsstrahlung) as compared to the 2D case (blackbody). For temperatures around 10 7 K, from where most of the flux arises, the 3D emission coe GLYPH<14> cient follows j Br GLYPH<23> / T 2 : 5 exp ( GLYPH<0> h GLYPH<23>= kT ) whereas the 2D specific intensity follows I BB GLYPH<23> / exp ( GLYPH<0> h GLYPH<23>= kT ). The dependency on temperature is thus much more important in 3D, and the emission arises only from the hottest parts of the disk, whereas the emission is more spread out in the 2D case.</text>
<text><location><page_5><loc_52><loc_40><loc_95><loc_49></location>All these computations allow us to determine the specific intensity in the emitter's frame, I GLYPH<23> em . In order to compute the specific intensity in the observer's frame I GLYPH<23> obs , the frame invariant quantity I GLYPH<23> =GLYPH<23> 3 is used: I GLYPH<23> obs = GLYPH<23> 3 obs =GLYPH<23> 3 em I GLYPH<23> em . The quantity GLYPH<23> em can be related to the emitter's 4-velocity. The 3-velocity computed by the fluid simulations is used to determine the emitter's 4-velocity, and the observed specific intensity is thus at hand.</text>
<section_header_level_1><location><page_5><loc_52><loc_36><loc_87><loc_38></location>3.2. Computing the disk image and the light curve</section_header_level_1>
<text><location><page_5><loc_52><loc_10><loc_95><loc_35></location>Before producing an image of the disk, one needs to compute the relativistic time delay for each point of the disk in order to take into account the multiple time steps of the fluid simulations that will correspond to the same observed time. Fig. 5 shows the emission date of photons for two extreme inclinations (5 GLYPH<14> and 85 GLYPH<14> ). Fig. 5 shows that the emission points are spread di GLYPH<11> erently along the disk depending on the inclination. The distribution is homogeneous and isotropic for low inclinations, but is very inhomogeneous and anisotropic for high inclinations. This anisotropy is due to the projection e GLYPH<11> ect due to the mapping of the observer's screen onto a very inclined disk, resulting in the emission points being aligned preferentially along the direction perpendicular to the line of sight. The inhomogeneity is due to the lensing e GLYPH<11> ect of the black hole that concentrates emission points on the side of the black hole opposite to the observer. Fig. 5 also clearly shows that the higher the inclination, the more time slices of data will be required. The respective di GLYPH<11> erence between the maximal and minimal emission dates on the primary image are approximately 0 : 1 t ISCO (left panel) and 0 : 9 t ISCO (right panel). However, due to the strong beaming e GLYPH<11> ect at high</text>
<figure>
<location><page_6><loc_10><loc_73><loc_91><loc_94></location>
<caption>Fig. 5. Emission dates of photons at the footpoint of null geodesics connected to the observer's screen, plotted with the same color scale for an inclination of 5 GLYPH<14> (left) and 85 GLYPH<14> (right). The grid of emission positions is projected onto the plane of the accretion disk. The color bar is expressed in units of the ISCO orbital time t ISCO. The lensing e GLYPH<11> ect of the black hole is clear for an inclination of 85 GLYPH<14> on the right panel, leading to a higher concentration of emission points on the side of the black hole opposite to the observer.</caption>
</figure>
<text><location><page_6><loc_7><loc_56><loc_50><loc_65></location>inclination, the bulk of the total specific intensity in one image comes from a small part of the disk. Thus, the emission dates of the photons reaching this small part of the disk are close to each other, and the final e GLYPH<11> ect of time delay is only marginal on the light curve. We have checked that the di GLYPH<11> erence between the exact light curve and a light curve computed without taking into account the time delay is at the level of one to a few percent only.</text>
<text><location><page_6><loc_7><loc_39><loc_50><loc_54></location>Fig. 6 shows the image (i.e. the map of specific intensity) of the accretion disk at an inclination 2 of 85 GLYPH<14> , approximately at the time when the fundamental mode of the RWI dominates. Each pixel of the image is obtained by interpolating between the set of simulated data at the time of emission of the photon, as stressed in Sect. 3. Here, around 40 di GLYPH<11> erent data time slices are used for computing the image. The instability has started to grow and one can identify the spiral density waves of the RWI. On top of this modulation due to the instability, there is a clear beaming e GLYPH<11> ect: matter moving towards the observer is brighter (here, on the left side of the image). The secondary image of the disk is visible as a semicircle at the centre of the primary image.</text>
<text><location><page_6><loc_7><loc_23><loc_50><loc_38></location>Fig. 7 depicts the image of a 3D disk subject to the RWI, approximately at the time when the fundamental mode of the RWI dominates. Here, around 6 di GLYPH<11> erent data time slices are used for computing the image: the time sampling has been reduced as 3D data are much heavier than 2D data. We checked at 2D that this reduced sampling still allows us to retrieve similar results. As compared to Fig. 6, the 3D disk's emission is much more concentrated on the inner parts of the disk. This is due to the much stronger dependency of the 3D emission on temperature as compared to the 2D case, as explained in Sect. 3.1.3. As the hottest parts of the disk are concentrated close to the radius of launching of the instability (see Fig. 2), only these inner regions are seen.</text>
<section_header_level_1><location><page_6><loc_7><loc_19><loc_42><loc_20></location>4. Modulation of the light curve by the RWI</section_header_level_1>
<text><location><page_6><loc_7><loc_14><loc_50><loc_17></location>This section presents and analyzes the light curves obtained by ray-tracing the RWI hydrodynamical simulations. These are computed by summing the specific intensities over all solid an-</text>
<figure>
<location><page_6><loc_56><loc_41><loc_90><loc_65></location>
<caption>Fig. 6. Image of a 2D optically thick disk emitting blackbody radiation with an inclination of 85 GLYPH<14> and in the presence of the RWI . The first order image (the distorted complete ring) clearly shows the spiral shape of the emitting region. The beaming e GLYPH<11> ect makes the emission brighter on the approaching side of the disk (here, on the left of the image). The second order image is the portion of ring at the bottom of the image. It is due to photon swirling around the black hole before reaching the observer. The third order image is the thin ring of illuminated pixels at the center of the image, due to photons orbiting around the black hole very close to the event horizon before reaching the observer. This ring is the so-called black hole silhouette, it is truncated here due to optical thickness.</caption>
</figure>
<text><location><page_6><loc_52><loc_17><loc_95><loc_19></location>gles on the observer's sky. This boils down to summing the disk images over all pixels, for all observation times.</text>
<section_header_level_1><location><page_6><loc_52><loc_13><loc_76><loc_14></location>4.1. 2D case: high time resolution</section_header_level_1>
<text><location><page_6><loc_52><loc_10><loc_95><loc_12></location>We first analyze the main characteristics of the light curve modulation in the 2D case where we can have a much better</text>
<figure>
<location><page_7><loc_12><loc_70><loc_45><loc_93></location>
<caption>Fig. 7. Image of a 3D disk emitting Bremsstrahlung radiation with an inclination of 85 GLYPH<14> and in the presence of the RWI. The overall emission is much more concentrated in the vicinity of the Rossby vortex as compared to Fig. 6.</caption>
</figure>
<text><location><page_7><loc_7><loc_43><loc_50><loc_61></location>time resolution between the hydrodynamical snapshots 3 . In order to catch the details of the light curve evolution, 40 frames of fluid simulations are computed during each period of rotation at ISCO. The ray-tracing code then interpolates between these fluid simulation results in order to compute the specific intensity map at di GLYPH<11> erent times of observation. We compared the results obtained with the one from a higher (80 frames) and smaller (20 frames and 6 frames) time resolution. While the overall behaviour was similar, 40 frames allow us to get a more detailed light curve, similar to that with 80 frames. We therefore decided to do all the runs in 2D at 40 frames per period of rotation at ISCO. We computed the light curve from the moment the RWI started to grow in the disk until it reaches its non-linear states as shown by the amplitude evolution in Fig. 3.</text>
<text><location><page_7><loc_7><loc_22><loc_50><loc_42></location>At zero inclination, the light curve will slowly drift towards smaller values due to the black hole's accretion during the simulation. In order to determine the flux fluctuation that is only due to the RWI, it is important to subtract this continuous drift from the light curve. This is done by simply subtracting the light curve obtained at 1 GLYPH<14> of inclination from every other light curve. As the GYOTO code uses Boyer-Lindquist spherical-like coordinates, the z -axis is singular, and it is not possible to derive a light curve at exactly zero inclination. However, the light curve is only marginally impacted by beaming at 1 GLYPH<14> as compared to exactly 0 GLYPH<14> . The error introduced by subtracting the light curve at 1 GLYPH<14> of inclination is a small underestimation of the amplitude of the modulation that does not impact our result here. Indeed, we are only looking for a proof of principle that the RWI could modulate the flux at a level compatible with the observed HFQPO.</text>
<text><location><page_7><loc_7><loc_13><loc_50><loc_22></location>Fig. 8 shows the light curves obtained for di GLYPH<11> erent values of the inclination parameter at two di GLYPH<11> erent values of the energy of the observed photon: 1 and 2 keV. Initially when the instability has a very low amplitude, the modulation of the flux is very low. After a few ISCO rotations, the instability is growing exponentially and modulates the flux at a detectable level. The period T mod of the modulation equals the period of rotation of</text>
<text><location><page_7><loc_52><loc_90><loc_95><loc_93></location>the Rossby vortices, i.e. the period of rotation at r GLYPH<25> 1 : 4 r 0 (see Fig. 1), that is to say T mod GLYPH<25> 1 : 6 t ISCO.</text>
<text><location><page_7><loc_52><loc_67><loc_95><loc_90></location>Due to the general relativistic beaming e GLYPH<11> ect, when the Rossby vortex is on the approaching side of the disk, the resulting flux is boosted at high inclination, the opposite being true for the receding side of the disk. This beaming e GLYPH<11> ect is also visible in the light curve substructures that can be observed at high inclination. For instance, an m = 2 mode will lead to two sharp peaks in the light curve at high inclination, related to the passage of the Rossby vortices at the approaching side of the disk. If the inclination is low, this e GLYPH<11> ect is much fainter, leading to smaller substructures in the light curve. The oscillation frequency of the light curve evolves during the simulation with a high frequency after a few rotations. After 5 rotations, a mixture of modes between one frequency and twice this frequency, can be identified. Whereas at the end of the simulation the mode with the lowest frequency dominates. This evolution corresponds to the evolution of modes seen in Fig. 3: the dominant mode has initially a frequency 3 ! , then 2 ! and eventually the fundamental mode dominates.</text>
<text><location><page_7><loc_52><loc_59><loc_95><loc_67></location>The comparison between the two values of energy of the observed photon shows that similar shapes are obtained for the two cases, but a higher modulation amplitude is reached for higher energy as expected due to the Planck law. Indeed, the ISCO temperature being 10 7 K, the maximum frequency of the Planck law is closer to 2 keV that to 1 keV.</text>
<text><location><page_7><loc_52><loc_44><loc_95><loc_59></location>Fig. 9 shows the light curve rms computed with a sliding window with a width of two orbital periods. The amplitude of the modulation is growing linearly with a change of slope at around 5 t ISCO, corresponding to the saturation of the instability (see Fig. 3). The maximum level of modulation is of around 4% at 1 keV and 8% at 2 keV. This is somewhat higher than most observations of HFQPOs. However, the maximum's exact value is influenced by the initial L profile (see Eq. 1 and Fig. 1). Here we are only interested in seeing if a reasonable setup can modulate the flux to a level similar to the one observed. We keep the detailed study of the growth rate and saturation level for a forthcoming paper (Meheut, Lovelace, Lai, 2013)</text>
<section_header_level_1><location><page_7><loc_52><loc_40><loc_64><loc_41></location>4.2. Full 3D case</section_header_level_1>
<text><location><page_7><loc_52><loc_28><loc_95><loc_39></location>We then turned to 3D simulation to see if there was any di GLYPH<11> erence in the observables. There, we could not get a similar time resolution as in 2D because of the hydrodynamical data size. We therefore used the 40 frames per orbit resolution for only one period for confirmation while we made a longer term lightcurve at the much lower time resolution of 6 frames per orbit at the ISCO. As we will see below, this lower resolution is still able to catch the broad aspects of the light curve, although it will not allow us to obtain the finest details.</text>
<text><location><page_7><loc_52><loc_19><loc_95><loc_28></location>Fig. 10 depicts the light curve and its rms for a 3D disk subject to the RWI, for photons of observed energy equal to 2 keV, and for three di GLYPH<11> erent values of inclination. The first important result is that the RWI is capable of modulating the light curve, similar to what had already been shown in the 2D case, with a modulation of a few percent. This is a strong argument that makes the RWI a reliable model of microquasars HFQPOs.</text>
<text><location><page_7><loc_52><loc_10><loc_95><loc_19></location>The domination of the di GLYPH<11> erent modes is also easily seen in Fig. 10, with the mode m = 2 dominating at the beginning of the simulation, and eventually the mode m = 1. Here, the mode m = 1 dominates after around 15 ISCO periods, whereas it dominates after around 30 periods in Fig. 4. This di GLYPH<11> erence is due to the fact that the ray-tracing simulations are initiated when the instability is already strong enough to give a non negligible rms.</text>
<figure>
<location><page_8><loc_15><loc_70><loc_48><loc_94></location>
</figure>
<figure>
<location><page_8><loc_53><loc_70><loc_87><loc_94></location>
<caption>Fig. 8. Light curves of a microquasar subject to the 2D RWI at 1 keV (left) and 2 keV (right) at di GLYPH<11> erent inclinations. The flux is normalized to its initial value. The inclination is 5 GLYPH<14> (dash-dotted black), 45 GLYPH<14> (dashed blue), or 85 GLYPH<14> (solid red).</caption>
</figure>
<figure>
<location><page_8><loc_15><loc_41><loc_48><loc_65></location>
</figure>
<figure>
<location><page_8><loc_53><loc_41><loc_87><loc_65></location>
<caption>Fig. 9. Dispersion of the light curve points in Fig. 8 at 1 keV (left) and 2 keV (right). Each point is obtained by computing the dispersion of the light curve points over two orbital periods. The inclination is 5 GLYPH<14> (black triangles), 45 GLYPH<14> (blue diamonds), or 85 GLYPH<14> (red crosses).</caption>
</figure>
<text><location><page_8><loc_7><loc_30><loc_50><loc_34></location>As a consequence, the 15 first ISCO periods of the 3D hydrodynamics computations where not used as their rms is extremely low.</text>
<text><location><page_8><loc_7><loc_25><loc_50><loc_30></location>The right panel of Fig. 10 shows the same characteristics as in the equivalent 2D Fig. 9. The rms shows a linear profile with a clear change of slope around t GLYPH<25> 7 t ISCO. This is linked to mode m = 1 starting to dominate over mode m = 2.</text>
<text><location><page_8><loc_7><loc_23><loc_50><loc_25></location>This being given, there are two main di GLYPH<11> erences between the 2D and 3D results:</text>
<unordered_list>
<list_item><location><page_8><loc_7><loc_19><loc_50><loc_21></location>1- The 3D modulation grows more slowly than its 2D counterpart.</list_item>
</unordered_list>
<text><location><page_8><loc_10><loc_10><loc_50><loc_19></location>This is comes from the di GLYPH<11> erences in initial disk conditions, i.e. mainly to the choice of the density profile: di GLYPH<11> erent density profiles give di GLYPH<11> erent shapes for the extremum of L which in turns give di GLYPH<11> erent growths of the instability. Figs. 3 and 4 already showed that the 3D growth rate is slower than its 2D counterpart. This translates directly to the light curve (moreover, as stated above, the 3D light curve</text>
<text><location><page_8><loc_54><loc_32><loc_95><loc_34></location>initial point is 15 ISCO periods after the launch of the instability).</text>
<text><location><page_8><loc_54><loc_27><loc_95><loc_32></location>Let us stress that the index of the density profile is not constrained by observations. As the di GLYPH<11> erence of growth time depends on the choice of the power-law index, it cannot not be taken as an intrinsic di GLYPH<11> erence between 2D and 3D RWI.</text>
<unordered_list>
<list_item><location><page_8><loc_52><loc_23><loc_95><loc_26></location>2- The light curve exhibits a slight asymmetry in the 3D case (the oscillation is not exactly centered on the initial flux value).</list_item>
</unordered_list>
<text><location><page_8><loc_54><loc_15><loc_95><loc_22></location>This could be explained by the strong dependency on temperature of the 3D emission, as explained in Sect. 3.1.3. During the simulation, the temperature of the Rossby vortex increases by a few %, due to accretion. Its emission thus becomes greater and greater. This translates to a slight drift of the light curve maxima towards higher values.</text>
<figure>
<location><page_9><loc_15><loc_70><loc_48><loc_94></location>
</figure>
<figure>
<location><page_9><loc_53><loc_70><loc_87><loc_94></location>
<caption>Fig. 10. Left : Light curves of a microquasar subject to the 3D RWI at 2 keV at an inclination of 5 GLYPH<14> (dash-dotted black), 45 GLYPH<14> (dashed blue) or 85 GLYPH<14> (solid red). Right : Dispersion of the light curve points of the left panel. Each point is obtained by computing the dispersion of the light curve points over two orbital periods. The inclination is 5 GLYPH<14> (black triangles), 45 GLYPH<14> (blue diamonds) or 85 GLYPH<14> (red crosses). For both panels, mind the di GLYPH<11> erent time scale as compared to Figs. 8 and 9.</caption>
</figure>
<section_header_level_1><location><page_9><loc_7><loc_59><loc_43><loc_61></location>4.3. Are 3D simulations necessary to compare with observations?</section_header_level_1>
<text><location><page_9><loc_7><loc_46><loc_50><loc_57></location>Comparing Figs. 8 to 10, it appears first that the light curve is modulated both in 2D and 3D, which is the main result of this paper. The dependency of the light curve as a function of the inclination parameter and frequency of the radiation is also very similar. As these general features of the 2D and 3D computations are alike, an interesting conclusion is that 2D results are su GLYPH<14> cient in order to analyze the general observable characteristics of the RWI, at least until we get a better constraint on the profiles in the disk.</text>
<text><location><page_9><loc_7><loc_36><loc_50><loc_45></location>This is particularly interesting when considering the di GLYPH<11> erence in terms of computing time and memory resources between a 2D and 3D simulation. The hydrodynamical data at a given time is around 100 times heavier at 3D than 2D (typically respectively 50 Mo and 0 : 5 Mo).The time needed to compute an image from 3D data is typically 15 times what is needed for a 2D computation.</text>
<text><location><page_9><loc_7><loc_17><loc_50><loc_35></location>However, let us stress that the present work does not allow us to compare the detailed time evolution of the 3D RWI with the 2D case, due to our choice of time sampling in the ray-tracing computations (this choice being dictated by the computing time and memory resources needed for the 3D simulations). As the 3D RWI displays specific features in the z direction (Meheut et al. 2010), it may be that specific observable characteristics could be obtained only by resorting to high time resolution 3D simulations. Nevertheless, these features would be small corrections to the general trend that stays close to the 2D results, and would not be within reach of current instruments. Indeed the 2D time sampling of 40 frames per ISCO period implies a time resolution of around 10 GLYPH<0> 4 s for the observed light curve. This is far beyond current instrumental capabilities.</text>
<text><location><page_9><loc_7><loc_10><loc_50><loc_16></location>Moreover, let us stress that the radiative processes and radiative transfer are treated in a very simplified way in this study for the 3D case. The 2D simulations are thus su GLYPH<14> cient only when one is not interested in studying precisely the radiative properties of the disk.</text>
<section_header_level_1><location><page_9><loc_52><loc_60><loc_63><loc_61></location>5. Conclusion</section_header_level_1>
<text><location><page_9><loc_52><loc_49><loc_95><loc_59></location>The RWI has been previously proposed as a model for HFQPOs and we have now demonstrated its ability to modulate the flux coming from the disk. Using 2D and 3D hydrodynamical simulations we have also been able to study how the amplitude of this modulation evolves as a function of the source inclination and of the radiation frequency. The 2D simulations have been shown to be su GLYPH<14> cient in order to recover the broad characteristics of the light curve.</text>
<text><location><page_9><loc_52><loc_32><loc_95><loc_49></location>By using hydrodynamical simulations we were able to focus only on the RWI and its e GLYPH<11> ects on the light curve. If this can be considered for the case where HFQPOs occur alone in a softer state, as is the case for the 67Hz modulation of GRS 1915 + 105 for example (Morgan et al. 1997), HFQPOs are more commonly observed in the steep power law or hard intermediate state simultaneously with a LFQPO. In Varniere et al. (2012a) we have demonstrated, in 2D, the ability of the RWI to co-exist with another instability that could give rise to the LFQPO. Our future work will be devoted to that particular case and in particular how it influences the observables. Indeed, this state is much more frequent during microquasar outbursts than the softer state we studied here.</text>
<text><location><page_9><loc_52><loc_28><loc_95><loc_31></location>Acknowledgements. This work has been financially supported by the French GdR PCHE and Campus Spatial Paris Diderot. Some of the simulations were performed using HPC resources from GENCI-CINES (Grant 2012046810).</text>
<section_header_level_1><location><page_9><loc_52><loc_24><loc_61><loc_25></location>References</section_header_level_1>
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</document>
[
{
"title": "ABSTRACT",
"content": "Context. There have been a long string of e GLYPH<11> orts to understand the source of the variability observed in microquasars, especially concerning the elusive High-Frequency Quasi-Periodic Oscillation. These oscillations are among the fastest phenomena that a GLYPH<11> ect matter in the vicinity of stellar black holes and therefore could be used as probes of strong-field general relativity. Nevertheless, no model has yet gained wide acceptance. Aims. The aim of this article is to investigate the model derived from the occurrence of the Rossby wave instability at the inner edge of the accretion disk. In particular, our goal here is to demonstrate the capacity of this instability to modulate the observed flux in agreement with the observed results. Methods. We use the AMRVAC hydrodynamical code to model the instability in a 3D optically thin disk. The GYOTO ray-tracing code is then used to compute the associated light curve. Results. We show that the 3D Rossby wave instability is able to modulate the flux well within the observed limits.We highlight that 2D simulations allow us to obtain the same general characteristics of the light curve as 3D calculations. With the time resolution we adopted in this work, three dimensional simulations do not give rise to any new observable features that could be detected by current instrumentation or archive data. Key words. Accretion, accretion disks - Hydrodynamics - Instabilities - Radiative transfer - Methods: numerical",
"pages": [
1
]
},
{
"title": "Flux Modulation from the Rossby Wave Instability in microquasars' accretion disks: toward a HFQPO model",
"content": "F. H. Vincent 1 , H. Meheut 2 ; 3 , P. Varniere 1 , and T. Paumard 4 April 19, 2022",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Black hole binary systems exhibit a wide range of variability patterns. Among these, the high frequency quasi-periodic oscillations (HFQPOs) appear as small narrow peaks in the power density spectrum. Their frequencies, of several tens to a few hundred Hertz, correspond to the rotation frequency in the inner part of the disk surrounding the black hole (see more details in the review of van der Klis 2006) making them an interesting tool to study strong-field gravity. Even though they are the fastest phenomena observed in the vicinity of black holes, HFQPOs are also extremely elusive, especially when compared to the lower frequency quasi-periodic oscillations (LFQPO). For this reason, we do not have a rich domain of observations from which to draw constraints for the models. This has led to a wide variety of models (see e.g. Lai & Tsang 2009 for a very brief review) focusing on one or another of the observed characteristics of the HFQPOs. As more and more data are obtained, especially with the next generation telescopes such as LOFT (Bozzo et al. 2011), we will be able to gain a better picture of what a model must explain. Nevertheless, we already can make a stringent list of constraints based on the eight objects with recurrent HFQPOs (see for example the review by Remillard & McClintock 2006). Among the most important of those constraints we note: The model we are investigating here is based on the existence of the Rossby wave instability (RWI) at the inner edge of the disk as was discussed in Tagger & Varniere (2006). Indeed, it was shown that the existence of an innermost stable circular orbit (ISCO) around a black hole makes the disk prone to the RWI because the vorticity profile has a natural extremum. This dynamic instability results in the formation of large-scale spiral density waves and Rossby waves that can reach high amplitudes. Depending on the disk's physical parameters, di GLYPH<11> erent modes of this instability will be selected, most often with azimuthal mode number m = 2 or 3 (Tagger & Varniere 2006) which gives a natural explanation for some of the observed characteristics of HFQPOs. Nevertheless, the important step of computing the ac- tual flux modulation one would observe when such an instability occurs in a disk was still missing. Here we focus on this point and therefore restrict ourselves to the case of the HFQPO alone. Indeed, we are trying to explore the capacity of one particular HFQPO model to modulate the X-ray flux and having only one instability in the disk makes the results more conspicuous. To this end we will use the purely hydrodynamic version of the Rossby wave instability (RWI, Lovelace et al. 1999), without the extra destabilizing e GLYPH<11> ect provided by a poloidal magnetic field (Tagger & Varniere 2006) or the extra stabilizing e GLYPH<11> ect of a toroidal magnetic field (Yu & Li 2009). This is the continuation of the long string of studies on the impact of the RWI in disks such as was done in the context of protoplanetary disks (Reg'aly et al. 2012) and the galactic centre (Falanga et al. 2007). Whereas the first case is highly di GLYPH<11> erent from ours, the second is more comparable and we use similar tools, but Falanga et al. (2007) restricted themselves to the 2D case and to the special context of the galactic centre source Sgr A*. Our main interest here will thus be to answer the key question: is the RWI able to modulate the flux of a microquasar at a level coherent with observations? In a more practical manner, we will also address the question of the necessity of full 3D simulations of the RWI, and to what extent it is su GLYPH<14> cient to restrict oneself to 2D simulations. Those 2D simulations are more accessible in terms of computing and storage resources, therefore allowing us to do much larger parameter studies and with a higher time resolution that could be compared with future LOFT observations. These questions will be addressed by computing the light curve of a microquasar subject to the RWI, as observed by a distant observer. This computation will be performed by means of a general relativistic ray-tracing code (Vincent et al. 2011). The main general relativistic e GLYPH<11> ect that a GLYPH<11> ects the RWI being the existence of an ISCO, we use a pseudo-Newtonian potential in order to model this in the hydrodynamical simulations, instead of considering the full general relativistic case. This simplifying assumption is su GLYPH<14> cient in order to derive a proof of principle of the ability of the RWI to modulate the flux of microquasars. Sect. 2 briefly presents the RWI and then develops the hydrodynamical simulations that allow us to model the unstable accretion structure. The following section is focused on the raytracing procedure used to compute observable quantities. Sect. 4 presents the light curves that were obtained and Sect. 5 gives conclusions and prospects.",
"pages": [
1,
2
]
},
{
"title": "2. Hydrodynamical simulation of the RWI",
"content": "The RWI has been discussed in multiple astrophysical contexts, from the galactic centre to protoplanetary disks. It can be seen as the form the Kelvin-Helmholtz instability takes in di GLYPH<11> erentially rotating disks, and has a similar instability criterion. For twodimensional (vertically integrated) barotropic disks, the RWI can be triggered provided an extremum exists in a quantity L which is the inverse vortensity 1 : where p is the pressure, GLYPH<6> is the surface density, GLYPH<10> is the rotation frequency, GLYPH<20> 2 = 2 GLYPH<10> = r d = d r GLYPH<16> r 2 GLYPH<10> GLYPH<17> is the squared epicyclic frequency and GLYPH<13> is the adiabatic index. An extremum of vortensity can thus typically arise from an extremum of the epicyclic frequency, as is the case close to the ISCO, or from an extremum in the density profile which gives rise to the RWI in the disk. Once it is triggered, it leads to large scale spiral density waves and Rossby vortices. The dominant mode (i.e. the number of vortices) is dependent on the disk conditions (Tagger & Varniere 2006).",
"pages": [
2
]
},
{
"title": "2.1. The RWI as a model for the HFQPO",
"content": "Due to general relativistic e GLYPH<11> ects, the epicyclic frequency profile will show a maximum in the vicinity of the black hole's ISCO, creating a vortensity extremum . Tagger & Varniere (2006) showed that it would lead to the growth of the RWI at the inner edge of black hole binaries when the disk nears its ISCO. From these facts, it seems natural that the RWI model may be capable of accounting for points 2- to 4- in the Introduction above (that will not be investigated in detail here). It seems therefore natural to address in more detail if the RWI is strong enough to give rise to a modulation that could explain the observations.",
"pages": [
2
]
},
{
"title": "2.2. Numerical setup",
"content": "To perform the hydrodynamical simulation of the RWI we use the Message Passing Interface-Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC) developed by Keppens et al. (2011). The numerical scheme is the same for all refinement levels, namely the Total Variation Diminishing Lax-Friedrich scheme (see T'oth & Odstrˇcil 1996) with a third order accurate Koren limiter (Koren 1993) on the primitive variables. We consider a geometrically thin disk and neglect selfgravity. The Euler equations in cylindrical coordinates ( r ; '; z ) read: where GLYPH<26> is the mass density of the fluid, v its velocity, and p its pressure. We consider a barotropic flow, i.e. the entropy is constant in the entire system. The pressure is then p = S GLYPH<26> GLYPH<13> , with the adiabatic index GLYPH<13> = 5 = 3 and the constant S related to entropy. The sound speed is given by c 2 s = GLYPH<13> p =GLYPH<26> = S GLYPH<13>GLYPH<26> GLYPH<13> GLYPH<0> 1 and the temperature by T / p =GLYPH<26> / S GLYPH<26> GLYPH<13> GLYPH<0> 1 . All the distances are normalized by the ISCO radius r 0. The same applies for temperatures normalized at ISCO by: T 0 = 10 7 K , while all times are in units of the ISCO period t ISCO. The general relativistic e GLYPH<11> ects have to be taken into account to study the innermost region of the black hole disk. In order to provide a proof of principle of the ability of the 3D RWI to modulate the flux of microquasars, we use the minimum model necessary to mimic some of these general relativistic e GLYPH<11> ects by using a pseudo-Newtonian potential GLYPH<8> G . For our simulations, we use the common Paczy'nsky & Wiita (1980) gravitational potential: where rg = GM GLYPH<3> c 2 is the gravitational radius, G the gravitational constant, M GLYPH<3> the black hole mass, c the speed of light in vacuum. With this gravitational potential, one can define the inner limit below which there is no stable circular orbit, the ISCO, located at r 0 = 6 rg . Let us stress the fact that this choice of potential allows us to mimic only some aspects of the Schwarzschild metric. The e GLYPH<11> ect of the black hole spin is not taken into account. It is also important to keep in mind that this pseudo-Newtonian potential, although widely used, is far from giving an exact description of general relativity. However, the only characteristic of the Schwarzschild metric that is of primordial importance as far as RWI is concerned is the existence of an ISCO, and this is correctly modeled by Eq. 4. Let us mention that we have also developed 2D RWI simulations with alternative pseudo-Newtonian potentials that take into account the rotation of the black hole. These alternative potentials were taken from Artemova et al. (1996). The RWI also develops well in these potentials, and future works will be dedicated to studying the e GLYPH<11> ect of the black hole's rotation on the observables.",
"pages": [
2,
3
]
},
{
"title": "2.3. Disk setup and boundary conditions",
"content": "The grid is cylindrical with the unit length defined as the ISCO radius r 0. The radial coordinate r is in the range [0 : 8 ; 6], the full azimuthal coordinate spans [0 ; 2 GLYPH<25> ] and the vertical coordinate z lies in the range [0 ; 0 : 2] for the 3D simulations. For the fluid simulations, we considered only the upper part of the disk as the mid-plane is a symmetry plane for the RWI (Meheut et al. 2010, 2012). For the ray-tracing computations, the full disk is considered by symmetrizing the upper part. We used a fixed and homogeneous grid with a resolution nr GLYPH<2> n ' = (384 ; 72) in 2D and nr GLYPH<2> n ' GLYPH<2> nz = (384 ; 72 ; 72) in 3D, which is slightly higher than the resolution used in Meheut et al. (2010). As we describe gravitation by the pseudo-Newtonian potential in Eq. 4, the epicyclic frequency will show a maximum at a radius slightly higher than the ISCO radius r 0. This epicyclic frequency maximum gives rise to an extremum of the initial vortensity profile, which is shown in Fig. 1. The existence of this vortensity extremum does not depend on the choice of initial density profile even though it does influence its precise location in the disk. Considering the density, we choose a typical power-law profile with a slope of GLYPH<0> 3 = 2. This choice, while reasonable, allows us to obtain a steeper vortensity extremum and hence a stronger instability. Note that the precise value of the rms of the modulation depends on this choice of slope. However, we are here only interested in proving the existence of the flux modulation, not comparing a precise value of modulation to observations. If future instruments give better data on the rise of the HFQPO we might be able to use these to constrain the disk model that could reproduce the observed data. The initial density profile then reads: the hydrostatic equilibrium gives the vertical profile of the density where rB = 1 : 3 r 0 gives the position of the density maximum (its value was choosen to fit the simulations of Tagger & Varniere 2006), rg = r 0 = 6 is the gravitational radius, GLYPH<27> = 0 : 05 r 0 gives the width of the plunging region, GLYPH<11> = GLYPH<0> 3 = 2 is the density slope, and GLYPH<26> 0 is the minimum density of the simulation. These parameters, and mainly the choice of density slope, can modify the structure and characteristics of the RWI. In our case, the existence of an extremum in GLYPH<20> limits the impact of the density power-law index and any reasonable choice will exhibit the instability. The detailed e GLYPH<11> ect of the initial density profile on the growth rate of the instability and its saturation level will be studied in a forthcoming paper (Meheut, Lovelace, Lai, 2013) but will not influence its ability to modulate the flux. We also considered a 2D disk with the surface density defined as GLYPH<6> / r GLYPH<0> 3 = 2 in the outer region. The initial conditions of the 2D and 3D simulations are then highly di GLYPH<11> erent. In both cases, the azimuthal velocity is determined by force balance: The density and velocity profiles given in Eqs. 6-7 include high amplitude gradients and do not give exact numerical equilibrium. For this reason, the initial conditions of our simulations are numerically computed from this pseudo-equilibrium. This means that a first simulation is done without any perturbations and is run until the disk has reached a permanent stage which is chosen as the initial conditions. This disk is then perturbed with small amplitude ( GLYPH<24> 10 GLYPH<0> 3 v ' ) random perturbations on the radial velocity which act as seeds for the instability. The inner boundary condition is a no-inflow condition and the outer boundary condition is a null radial velocity condition. Meheut et al. (2012) have shown that the boundary conditions do not change significantly the growth rate of the RWI due to its confinement in the vortensity bump. Moreover the inner edge of the simulation being inside the ISCO, any reflected wave would not reach the region of interest for the instability. Therefore, the boundary conditions are not determinant for these simulations. For the 3D simulations, symmetric boundary conditions are implemented at the mid-plane, and we use a null vertical velocity at the grid upper boundary limit, situated outside of the disk.",
"pages": [
3,
4
]
},
{
"title": "2.4. Time evolution of the RWI",
"content": "Fig. 2 shows the density map of the z = 0 plane of a 3D RWI simulation, when the instability is completely developed. This section presents the time evolution of the instability (at 2D and 3D) from its launch to its complete development. At first, the disk is assumed to be 2D and the vertical structure of the disk is neglected. The growth of the instability is shown on Fig. 3 where the time evolution of the perturbation of density is plotted on a logarithmic scale. This allows the identification of the linear phase of the instability when the amplitude of the perturbations grows exponentially (thus linearly in logarithm), as well as the saturation which is due to non-linearities. In the 2D case, the initial conditions give rise to a rapid growth of the instability on a time scale of a few periods at ISCO as can be seen in Fig. 3. During the linear phase, the perturbations can be separated in the di GLYPH<11> erent azimuthal modes: where X = GLYPH<6> for 2D simulations and X = GLYPH<26> for 3D. The quantities GLYPH<13> m are the growth rates of each mode, ! the characteristic frequency of the instability depending on the position of the extremum of L , m the azimuthal mode number, and Xm the amplitude of mode m . Therefore, Xm = 0 corresponds to the axisymmetric part of the density and the frequency of the mode m is the multiple m ! of the frequency of the fundamental mode. Fig. 3 also shows the time evolution of the amplitude of the strongest modes. During the linear phase, the dominant mode is m = 3, and later on the disk is dominated by the fundamental mode m = 1 with important contributions from the modes m = 2 and 3. This evolution of the oscillation modes depends on the disk's astrophysical properties: di GLYPH<11> erent modes dominate for di GLYPH<11> erent initial disk conditions. This fact is illustrated in the 3D simulations. Indeed, the initial conditions di GLYPH<11> er largely between the 2D and 3D simulations, with a di GLYPH<11> erent surface density radial profile and absolute value. The characteristic velocity of the waves is then di GLYPH<11> erent. This modifies the timescale for the growth of the instability as can be seen in Fig. 4. This di GLYPH<11> erence is not due to the dimensionality (Meheut et al. 2012; Lin 2012). Nevertheless, the RWI is triggered and saturation of the 3D instability is reached after a few tens of periods at ISCO. The dominant modes are also di GLYPH<11> er- ent during the linear phase, but non-linearities still tend to favour the lowest azimuthal mode. Let us note that, as the epicyclic frequency profile is not evolving with time, the location of the extremum of vortensity will stay the same. Moreover the vortices grow in a density extremum where they cannot migrate due to the two density slopes of opposite sign. As a consequence, the Rossby vortices will not migrate during the simulation (for more details see Meheut et al. 2012). From the hydrodynamical simulations we obtain the density and velocity at every point of our grid with a su GLYPH<14> cient time sampling (of 40 frames in 2D and 6 frames in 3D per orbit at the ISCO) to follow the RWI in the disk from its rise to its saturation. In the next step those will be used as input for the ray-tracing code in order to trace the impact of the RWI on the observed emission.",
"pages": [
4,
5
]
},
{
"title": "3.1. Ray-tracing the accretion disk",
"content": "In order to obtain images, and especially lightcurves, that could be compared with observations we used the general relativistic ray-tracing code GYOTO (Vincent et al. 2011). Null geodesics are computed backward in time in the Schwarzschild metric from a distant observer to the emitting disk. The coordinates used by GYOTO are spherical-like and denoted (¯ r ; GLYPH<18>; ' ), where ¯ r is used to di GLYPH<11> erentiate the GYOTO spherical radius from the fluid simulations cylindrical radius r . Once a backward integrated geodesic hits the disk, the density and 3-velocity at the point of emission is linearly interpolated at the time of emission from the results of the MPI-AMRVAC computations.",
"pages": [
5
]
},
{
"title": "3.1.1. Radiative processes at 2D: blackbody",
"content": "The 2D disk is assumed to be optically thick, so the integration is stopped at the first encounter of the disk. The emission is supposed to follow the Planck law: the only parameter needed is thus the temperature which can be easily derived from the density according to the following computations. The gas being assumed ideal: where GLYPH<22> is the mean molecular weight, mu is the atomic mass constant and k is the Boltzmann constant. Assuming that the plasma is made of pure hydrogen, GLYPH<22> = 1. Using the relation R = NA k between the ideal gas contant R , the Avogadro number NA and the Boltzmann constant together with the expression of the sound speed this yields: This allows the computation of the emitted specific intensity at the surface of a 2D disk: where B GLYPH<23> is the Planck function.",
"pages": [
5
]
},
{
"title": "3.1.2. Radiative processes at 3D: Bremsstrahlung",
"content": "For the three dimensional computations, the only radiative process considered is Bremsstrahlung. As the disk is purely hydrodynamic, there is no synchrotron emission, and Compton scattering is neglected as we are only interested here in a proof of principle, not in a detailed study of emission processes. The Bremsstrahlung emission is assumed to be thermal, so that the emission coe GLYPH<14> cient j GLYPH<23> and absorption coe GLYPH<14> cient GLYPH<11>GLYPH<23> are related via Kirchho GLYPH<11> 's law: The emission coe GLYPH<14> cient for thermal Bremsstrahlung is given by (Rybicki & Lightman 1979): where e is the electron charge, m e is the electron mass and h is the Planck constant. Here, we assume that the disk is made of pure hydrogen, and that the emission is isotropic in the emitter's frame (hence the 1 = 4 GLYPH<25> initial factor). Moreover, the Gaunt factor is neglected as most of the radiation arises from locations in the disk where h GLYPH<23> GLYPH<25> kT . Once the emission coe GLYPH<14> cient is computed, the absorption coe GLYPH<14> cient is derived by using Eq. 12.",
"pages": [
5
]
},
{
"title": "3.1.3. Dependency on temperature at 2D and 3D",
"content": "Let us investigate the dependency on temperature of the 3D emission process (Bremsstrahlung) as compared to the 2D case (blackbody). For temperatures around 10 7 K, from where most of the flux arises, the 3D emission coe GLYPH<14> cient follows j Br GLYPH<23> / T 2 : 5 exp ( GLYPH<0> h GLYPH<23>= kT ) whereas the 2D specific intensity follows I BB GLYPH<23> / exp ( GLYPH<0> h GLYPH<23>= kT ). The dependency on temperature is thus much more important in 3D, and the emission arises only from the hottest parts of the disk, whereas the emission is more spread out in the 2D case. All these computations allow us to determine the specific intensity in the emitter's frame, I GLYPH<23> em . In order to compute the specific intensity in the observer's frame I GLYPH<23> obs , the frame invariant quantity I GLYPH<23> =GLYPH<23> 3 is used: I GLYPH<23> obs = GLYPH<23> 3 obs =GLYPH<23> 3 em I GLYPH<23> em . The quantity GLYPH<23> em can be related to the emitter's 4-velocity. The 3-velocity computed by the fluid simulations is used to determine the emitter's 4-velocity, and the observed specific intensity is thus at hand.",
"pages": [
5
]
},
{
"title": "3.2. Computing the disk image and the light curve",
"content": "Before producing an image of the disk, one needs to compute the relativistic time delay for each point of the disk in order to take into account the multiple time steps of the fluid simulations that will correspond to the same observed time. Fig. 5 shows the emission date of photons for two extreme inclinations (5 GLYPH<14> and 85 GLYPH<14> ). Fig. 5 shows that the emission points are spread di GLYPH<11> erently along the disk depending on the inclination. The distribution is homogeneous and isotropic for low inclinations, but is very inhomogeneous and anisotropic for high inclinations. This anisotropy is due to the projection e GLYPH<11> ect due to the mapping of the observer's screen onto a very inclined disk, resulting in the emission points being aligned preferentially along the direction perpendicular to the line of sight. The inhomogeneity is due to the lensing e GLYPH<11> ect of the black hole that concentrates emission points on the side of the black hole opposite to the observer. Fig. 5 also clearly shows that the higher the inclination, the more time slices of data will be required. The respective di GLYPH<11> erence between the maximal and minimal emission dates on the primary image are approximately 0 : 1 t ISCO (left panel) and 0 : 9 t ISCO (right panel). However, due to the strong beaming e GLYPH<11> ect at high inclination, the bulk of the total specific intensity in one image comes from a small part of the disk. Thus, the emission dates of the photons reaching this small part of the disk are close to each other, and the final e GLYPH<11> ect of time delay is only marginal on the light curve. We have checked that the di GLYPH<11> erence between the exact light curve and a light curve computed without taking into account the time delay is at the level of one to a few percent only. Fig. 6 shows the image (i.e. the map of specific intensity) of the accretion disk at an inclination 2 of 85 GLYPH<14> , approximately at the time when the fundamental mode of the RWI dominates. Each pixel of the image is obtained by interpolating between the set of simulated data at the time of emission of the photon, as stressed in Sect. 3. Here, around 40 di GLYPH<11> erent data time slices are used for computing the image. The instability has started to grow and one can identify the spiral density waves of the RWI. On top of this modulation due to the instability, there is a clear beaming e GLYPH<11> ect: matter moving towards the observer is brighter (here, on the left side of the image). The secondary image of the disk is visible as a semicircle at the centre of the primary image. Fig. 7 depicts the image of a 3D disk subject to the RWI, approximately at the time when the fundamental mode of the RWI dominates. Here, around 6 di GLYPH<11> erent data time slices are used for computing the image: the time sampling has been reduced as 3D data are much heavier than 2D data. We checked at 2D that this reduced sampling still allows us to retrieve similar results. As compared to Fig. 6, the 3D disk's emission is much more concentrated on the inner parts of the disk. This is due to the much stronger dependency of the 3D emission on temperature as compared to the 2D case, as explained in Sect. 3.1.3. As the hottest parts of the disk are concentrated close to the radius of launching of the instability (see Fig. 2), only these inner regions are seen.",
"pages": [
5,
6
]
},
{
"title": "4. Modulation of the light curve by the RWI",
"content": "This section presents and analyzes the light curves obtained by ray-tracing the RWI hydrodynamical simulations. These are computed by summing the specific intensities over all solid an- gles on the observer's sky. This boils down to summing the disk images over all pixels, for all observation times.",
"pages": [
6
]
},
{
"title": "4.1. 2D case: high time resolution",
"content": "We first analyze the main characteristics of the light curve modulation in the 2D case where we can have a much better time resolution between the hydrodynamical snapshots 3 . In order to catch the details of the light curve evolution, 40 frames of fluid simulations are computed during each period of rotation at ISCO. The ray-tracing code then interpolates between these fluid simulation results in order to compute the specific intensity map at di GLYPH<11> erent times of observation. We compared the results obtained with the one from a higher (80 frames) and smaller (20 frames and 6 frames) time resolution. While the overall behaviour was similar, 40 frames allow us to get a more detailed light curve, similar to that with 80 frames. We therefore decided to do all the runs in 2D at 40 frames per period of rotation at ISCO. We computed the light curve from the moment the RWI started to grow in the disk until it reaches its non-linear states as shown by the amplitude evolution in Fig. 3. At zero inclination, the light curve will slowly drift towards smaller values due to the black hole's accretion during the simulation. In order to determine the flux fluctuation that is only due to the RWI, it is important to subtract this continuous drift from the light curve. This is done by simply subtracting the light curve obtained at 1 GLYPH<14> of inclination from every other light curve. As the GYOTO code uses Boyer-Lindquist spherical-like coordinates, the z -axis is singular, and it is not possible to derive a light curve at exactly zero inclination. However, the light curve is only marginally impacted by beaming at 1 GLYPH<14> as compared to exactly 0 GLYPH<14> . The error introduced by subtracting the light curve at 1 GLYPH<14> of inclination is a small underestimation of the amplitude of the modulation that does not impact our result here. Indeed, we are only looking for a proof of principle that the RWI could modulate the flux at a level compatible with the observed HFQPO. Fig. 8 shows the light curves obtained for di GLYPH<11> erent values of the inclination parameter at two di GLYPH<11> erent values of the energy of the observed photon: 1 and 2 keV. Initially when the instability has a very low amplitude, the modulation of the flux is very low. After a few ISCO rotations, the instability is growing exponentially and modulates the flux at a detectable level. The period T mod of the modulation equals the period of rotation of the Rossby vortices, i.e. the period of rotation at r GLYPH<25> 1 : 4 r 0 (see Fig. 1), that is to say T mod GLYPH<25> 1 : 6 t ISCO. Due to the general relativistic beaming e GLYPH<11> ect, when the Rossby vortex is on the approaching side of the disk, the resulting flux is boosted at high inclination, the opposite being true for the receding side of the disk. This beaming e GLYPH<11> ect is also visible in the light curve substructures that can be observed at high inclination. For instance, an m = 2 mode will lead to two sharp peaks in the light curve at high inclination, related to the passage of the Rossby vortices at the approaching side of the disk. If the inclination is low, this e GLYPH<11> ect is much fainter, leading to smaller substructures in the light curve. The oscillation frequency of the light curve evolves during the simulation with a high frequency after a few rotations. After 5 rotations, a mixture of modes between one frequency and twice this frequency, can be identified. Whereas at the end of the simulation the mode with the lowest frequency dominates. This evolution corresponds to the evolution of modes seen in Fig. 3: the dominant mode has initially a frequency 3 ! , then 2 ! and eventually the fundamental mode dominates. The comparison between the two values of energy of the observed photon shows that similar shapes are obtained for the two cases, but a higher modulation amplitude is reached for higher energy as expected due to the Planck law. Indeed, the ISCO temperature being 10 7 K, the maximum frequency of the Planck law is closer to 2 keV that to 1 keV. Fig. 9 shows the light curve rms computed with a sliding window with a width of two orbital periods. The amplitude of the modulation is growing linearly with a change of slope at around 5 t ISCO, corresponding to the saturation of the instability (see Fig. 3). The maximum level of modulation is of around 4% at 1 keV and 8% at 2 keV. This is somewhat higher than most observations of HFQPOs. However, the maximum's exact value is influenced by the initial L profile (see Eq. 1 and Fig. 1). Here we are only interested in seeing if a reasonable setup can modulate the flux to a level similar to the one observed. We keep the detailed study of the growth rate and saturation level for a forthcoming paper (Meheut, Lovelace, Lai, 2013)",
"pages": [
6,
7
]
},
{
"title": "4.2. Full 3D case",
"content": "We then turned to 3D simulation to see if there was any di GLYPH<11> erence in the observables. There, we could not get a similar time resolution as in 2D because of the hydrodynamical data size. We therefore used the 40 frames per orbit resolution for only one period for confirmation while we made a longer term lightcurve at the much lower time resolution of 6 frames per orbit at the ISCO. As we will see below, this lower resolution is still able to catch the broad aspects of the light curve, although it will not allow us to obtain the finest details. Fig. 10 depicts the light curve and its rms for a 3D disk subject to the RWI, for photons of observed energy equal to 2 keV, and for three di GLYPH<11> erent values of inclination. The first important result is that the RWI is capable of modulating the light curve, similar to what had already been shown in the 2D case, with a modulation of a few percent. This is a strong argument that makes the RWI a reliable model of microquasars HFQPOs. The domination of the di GLYPH<11> erent modes is also easily seen in Fig. 10, with the mode m = 2 dominating at the beginning of the simulation, and eventually the mode m = 1. Here, the mode m = 1 dominates after around 15 ISCO periods, whereas it dominates after around 30 periods in Fig. 4. This di GLYPH<11> erence is due to the fact that the ray-tracing simulations are initiated when the instability is already strong enough to give a non negligible rms. As a consequence, the 15 first ISCO periods of the 3D hydrodynamics computations where not used as their rms is extremely low. The right panel of Fig. 10 shows the same characteristics as in the equivalent 2D Fig. 9. The rms shows a linear profile with a clear change of slope around t GLYPH<25> 7 t ISCO. This is linked to mode m = 1 starting to dominate over mode m = 2. This being given, there are two main di GLYPH<11> erences between the 2D and 3D results: This is comes from the di GLYPH<11> erences in initial disk conditions, i.e. mainly to the choice of the density profile: di GLYPH<11> erent density profiles give di GLYPH<11> erent shapes for the extremum of L which in turns give di GLYPH<11> erent growths of the instability. Figs. 3 and 4 already showed that the 3D growth rate is slower than its 2D counterpart. This translates directly to the light curve (moreover, as stated above, the 3D light curve initial point is 15 ISCO periods after the launch of the instability). Let us stress that the index of the density profile is not constrained by observations. As the di GLYPH<11> erence of growth time depends on the choice of the power-law index, it cannot not be taken as an intrinsic di GLYPH<11> erence between 2D and 3D RWI. This could be explained by the strong dependency on temperature of the 3D emission, as explained in Sect. 3.1.3. During the simulation, the temperature of the Rossby vortex increases by a few %, due to accretion. Its emission thus becomes greater and greater. This translates to a slight drift of the light curve maxima towards higher values.",
"pages": [
7,
8
]
},
{
"title": "4.3. Are 3D simulations necessary to compare with observations?",
"content": "Comparing Figs. 8 to 10, it appears first that the light curve is modulated both in 2D and 3D, which is the main result of this paper. The dependency of the light curve as a function of the inclination parameter and frequency of the radiation is also very similar. As these general features of the 2D and 3D computations are alike, an interesting conclusion is that 2D results are su GLYPH<14> cient in order to analyze the general observable characteristics of the RWI, at least until we get a better constraint on the profiles in the disk. This is particularly interesting when considering the di GLYPH<11> erence in terms of computing time and memory resources between a 2D and 3D simulation. The hydrodynamical data at a given time is around 100 times heavier at 3D than 2D (typically respectively 50 Mo and 0 : 5 Mo).The time needed to compute an image from 3D data is typically 15 times what is needed for a 2D computation. However, let us stress that the present work does not allow us to compare the detailed time evolution of the 3D RWI with the 2D case, due to our choice of time sampling in the ray-tracing computations (this choice being dictated by the computing time and memory resources needed for the 3D simulations). As the 3D RWI displays specific features in the z direction (Meheut et al. 2010), it may be that specific observable characteristics could be obtained only by resorting to high time resolution 3D simulations. Nevertheless, these features would be small corrections to the general trend that stays close to the 2D results, and would not be within reach of current instruments. Indeed the 2D time sampling of 40 frames per ISCO period implies a time resolution of around 10 GLYPH<0> 4 s for the observed light curve. This is far beyond current instrumental capabilities. Moreover, let us stress that the radiative processes and radiative transfer are treated in a very simplified way in this study for the 3D case. The 2D simulations are thus su GLYPH<14> cient only when one is not interested in studying precisely the radiative properties of the disk.",
"pages": [
9
]
},
{
"title": "5. Conclusion",
"content": "The RWI has been previously proposed as a model for HFQPOs and we have now demonstrated its ability to modulate the flux coming from the disk. Using 2D and 3D hydrodynamical simulations we have also been able to study how the amplitude of this modulation evolves as a function of the source inclination and of the radiation frequency. The 2D simulations have been shown to be su GLYPH<14> cient in order to recover the broad characteristics of the light curve. By using hydrodynamical simulations we were able to focus only on the RWI and its e GLYPH<11> ects on the light curve. If this can be considered for the case where HFQPOs occur alone in a softer state, as is the case for the 67Hz modulation of GRS 1915 + 105 for example (Morgan et al. 1997), HFQPOs are more commonly observed in the steep power law or hard intermediate state simultaneously with a LFQPO. In Varniere et al. (2012a) we have demonstrated, in 2D, the ability of the RWI to co-exist with another instability that could give rise to the LFQPO. Our future work will be devoted to that particular case and in particular how it influences the observables. Indeed, this state is much more frequent during microquasar outbursts than the softer state we studied here. Acknowledgements. This work has been financially supported by the French GdR PCHE and Campus Spatial Paris Diderot. Some of the simulations were performed using HPC resources from GENCI-CINES (Grant 2012046810).",
"pages": [
9
]
},
{
"title": "References",
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"pages": [
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2013A&A...551A.142D
https://arxiv.org/pdf/1302.7113.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_85><loc_90><loc_87></location>The seven year Swift-XRT point source catalog (1SWXRT) /star</section_header_level_1>
<text><location><page_1><loc_7><loc_81><loc_95><loc_84></location>V. D'Elia 1 , 2 , M. Perri 1 , 2 , S. Puccetti 1 , 2 , M. Capalbi 1 , 2 , P. Giommi 1 , D. N. Burrows 3 , S. Campana 4 , G. Tagliaferri 4 , G. Cusumano 5 , P. Evans 6 , N. Gehrels 7 , J. Kennea 3 , A. Moretti 4 , J. A. Nousek 3 , J.P. Osborne 6 , P. Romano 5 and G. Stratta 1 , 2</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_78><loc_53><loc_79></location>1 ASI-Science Data Centre, Via Galileo Galilei, I-00044 Frascati, Italy;</list_item>
<list_item><location><page_1><loc_11><loc_76><loc_69><loc_77></location>2 INAF-Osservatorio Astronomico di Roma, Via Frascati 33, I-00040 Monteporzio Catone, Italy;</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_84><loc_76></location>3 Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802, USA;</list_item>
<list_item><location><page_1><loc_11><loc_74><loc_64><loc_75></location>4 INAF-Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate (LC), Italy;</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_80><loc_74></location>5 INAF-Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo, Via U. La Malfa 153, I-90146, Palermo, Italy;</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_62><loc_73></location>6 Dept. of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH, UK.</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_56><loc_72></location>7 NASA-Goddard Space Flight Center, Greenbelt, Maryland, 20771, USA;</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_67><loc_35><loc_68></location>Preprint online version: October 9, 2018</text>
<section_header_level_1><location><page_1><loc_47><loc_65><loc_55><loc_66></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_59><loc_91><loc_63></location>Context. The Swift satellite is a multi-wavelength observatory specifically designed for gamma-ray burst (GRB) astronomy that is operational since 2004. Swift is also a very flexible multi-purpose facility that supports a wide range of scientific fields such as active galactic nuclei, supernovae, cataclysmic variables, Galactic transients, active stars and comets. The Swift X-ray Telescope (XRT) has collected more than 150 Ms of observations in its first seven years of operations.</text>
<text><location><page_1><loc_11><loc_55><loc_91><loc_59></location>Aims. The purpose of this work is to present to the scientific community the list of all the X-ray point sources detected in XRT imaging data taken in photon counting mode during the first seven years of Swift operations. All these point-like sources, excluding the Gamma-Ray Bursts (GRB), will be stored in a catalog publicly available (1SWXRT).</text>
<text><location><page_1><loc_11><loc_51><loc_91><loc_55></location>Methods. We consider all the XRT observations with exposure time longer than 500 s taken in the period 2005-2011. Data were reduced and analyzed with standard techniques and a list of detected sources for each observation was produced. A careful visual inspection was performed to remove extended, spurious and piled-up sources. Finally, positions, count rates, fluxes and the corresponding uncertainties were computed.</text>
<text><location><page_1><loc_11><loc_41><loc_91><loc_50></location>Results. We have analyzed more than 35,000 XRT fields, with exposures ranging between 500 s and 100 ks, for a total exposure time of almost 140 Ms. The catalog includes approximately 89,000 entries, of which almost 85,000 are not a ff ected by pile-up and are not GRBs. Considering that many XRT fields were observed several times, we have a total of ∼ 36,000 distinct celestial sources. We computed count rates in three energy bands: 0 . 3 -10 keV (Full, or F), 0 . 3 -3 keV (Soft, or S) and 2 -10 keV (Hard, or H). Each entry has a detection in at least one of these bands. In particular, we detect ∼ 80,000, ∼ 70,000 and ∼ 25 , 500 in the F, S and H band, respectively. Count rates were converted into fluxes in the 0 . 5 -10, 0 . 5 -2 and 2 -10 keV bands. The flux interval sampled by the detected sources is 7 . 4 × 10 -15 -9 . 1 × 10 -11 , 3 . 1 × 10 -15 -1 . 1 × 10 -11 and 1 . 3 × 10 -14 -9 . 1 × 10 -11 erg cm -2 s -1 for the F, S and H band, respectively. Some possible scientific uses of the catalog are also highlighted.</text>
<text><location><page_1><loc_11><loc_39><loc_47><loc_40></location>Key words. gamma rays: bursts - cosmology: observations</text>
<section_header_level_1><location><page_1><loc_7><loc_35><loc_19><loc_36></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_21><loc_50><loc_34></location>The Swift Gamma-Ray Burst Explorer (Gehrels et al. 2004) is a NASA mission, successfully launched on 2004 Nov. 20. The hardware and software were built by an international team involving US, United Kingdom and Italy, with contributions from Germany and Japan. The main scientific driver of the Swift mission is to detect gamma-ray bursts (GRBs) in the hard Xray band with the Burst Alert Telescope (BAT, Barthelmy et al. 2005) and quickly follow-up their emission at longer wavelength with the X-Ray Telescope (XRT, Burrows et al. 2005) and Ultraviolet / Optical Telescope (UVOT, Roming et al. 2005).</text>
<text><location><page_1><loc_7><loc_15><loc_50><loc_21></location>Despite being specifically designed to address GRB science topics, Swift is also an e ff ective multi-purpose multi-frequency observatory. The Swift team expertise in following up GRBs has grown during the satellite operations, leading to an evolution of the observing time share between GRBs and other cos-</text>
<text><location><page_1><loc_52><loc_19><loc_95><loc_36></location>mic sources. At the beginning of the satellite operations (up to 2006, Romano 2012), approximately 56% of the Swift observing time was dedicated to GRB observations, and ∼ 26% divided up between target of opportunity (ToO, ∼ 8%) and 'fill-in' observations (that are short exposures of a variety of X-ray sources taken when Swift was not engaged in GRB science, ∼ 18%). After 2006, it became evident that there was no need to follow up all GRBs for a very long time. Thus, without losing too much relevant scientific information, in 2010 the GRB dedicated time dropped to ∼ 27%while ∼ 29%and ∼ 26%was allocated to ToO and Fill-in observations, respectively. In the remaining ∼ 18%of the time the satellite flies through the South Atlantic Anomaly or is devoted to calibration issues.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_19></location>The Swift mission is currently producing data at a pace of about ∼ 500 observations per month, contributing to most areas of astronomy. Apart from GRBs, the Swift instruments are observing extragalactic targets, such as active galactic nuclei, clusters of galaxies, nearby galaxies, and Galactic sources, such as binaries, microquasars, pulsars, and all Galactic variable sources in general.</text>
<figure>
<location><page_2><loc_9><loc_75><loc_50><loc_90></location>
<caption>Table 1. Observations and exposure times in 2005 -2011 1 , 2Fig. 1. The Aito ff projection in Galactic coordinates of the Swift -XRT fields analyzed in this paper.</caption>
</figure>
<text><location><page_2><loc_7><loc_45><loc_50><loc_64></location>The Swift -XRT utilizes a mirror set built for JET-X and an XMM / EPIC MOS CCD detector to provide a sensitive broadband (0.2-10 keV) X-ray imager with e ff ective area of > 120 cm 2 at 1 . 5 keV, field of view of 23 . 6 × 23 . 6 arcmin, and angular resolution of 18 arcsec. The detection sensitivity is 2 × 10 -14 erg cm -2 s -1 in 10 4 s. The instrument can work in three di ff erent modes (Hill et al. 2004): Photodiode (PD), Windowed-Timing (WT) and Photon-Counting (PC) modes. Due to a micrometeorite hit on May 27 2005, the PD mode has been disabled because of the very high background rate from hot pixels which cannot be avoided during read-out in this mode (Abbey et al. 2006). While the first two modes are built to produce a high time resolution at the expense of losing all (PD) or part (WT) of the spatial information, the latter one retains full imaging resolution and will be the only mode exploited here.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_45></location>This paper presents the 1SWXRT catalog, which consists of all the point-like sources detected by the XRT in its first seven years of operations (2005 -2011). Updated versions of the catalog, containing observations performed from 2012, are foreseen on timescales of about two years. Similar catalogs have already been produced for the first eight years of Chandra operations (Evans et al. 2010) and for the first seven years of XMMNewton operations (Watson et al. 2009). The reduction and analysis method is very similar to that adopted for the production of the ' Swift Serendipitous Survey in deep XRT GRB fields' (Puccetti et al. 2011), which comprises a list of sources detected in all Swift -XRT GRB fields with exposure times longer than 10 ks, observed by Swift between 2004 and 2008. Our goal is complementary to that of Puccetti et al. (2011). Instead of summing all the observations related to the same field, we keep them separated, in order to build a catalog which retains information about the variability of our sources. In addition, we analyzed all the XRT observations, and not only the fields centered on GRBs. A future work (Evans et al., in prep) will consider all XRT fields, combined where the same field is observed multiple times. A first catalog of extended sources has been published (Tundo et al. 2012), and further updates are in preparation. Our paper is organized as follows. In Sect. 2 we briefly describe our catalog. In Sect. 3 and 4 we present the data reduction and analysis method, respectively. In Sect. 5 we briefly discuss the scientific issues that can be tackled using our catalog. Finally, in Sect. 6 we draw our conclusions.</text>
<table>
<location><page_2><loc_52><loc_59><loc_97><loc_90></location>
</table>
<unordered_list>
<list_item><location><page_2><loc_52><loc_57><loc_95><loc_58></location>1 The first number of each entry shows the total observations per month.</list_item>
<list_item><location><page_2><loc_52><loc_54><loc_95><loc_57></location>2 The second number of each entry shows the total exposure time per month, in units of Ms.</list_item>
</unordered_list>
<section_header_level_1><location><page_2><loc_52><loc_50><loc_92><loc_51></location>2. The seven year Swift -XRT point source catalog</section_header_level_1>
<text><location><page_2><loc_52><loc_32><loc_95><loc_49></location>The seven year Swift -XRT point source catalog (1SWXRT) is built using all the observations performed by Swift -XRT in PC observing mode between 2005 and 2011. We consider in our analysis all the XRT fields, including 'safe pointings', that are sky positions used by the satellite as safe positions in case there are troubles during the slew from one target to another. The only constraint for a field to be analyzed is on the exposure time, which is required to be longer than 500 s. Di ff erent observations are not merged, but analyzed separately, thus retaining information about the variability of the catalogued sources. Here and in the following we define as 'observation' the total exposure time per target for a given day, identified by an unambiguous sequence number.</text>
<text><location><page_2><loc_52><loc_10><loc_95><loc_32></location>The total number of observations considered is 35 , 011, for an overall exposure time of ∼ 140 Ms. Fig. 1 shows the Aito ff projection in Galactic coordinates of these XRT observations. Table 1 collects the number of observations per month in the period 2005 -2011, together with the corresponding exposure time. Fig. 2 shows the number of observations as a function of the month in which they were performed. It is interesting to note how this number increased with time, reflecting the evolution of the Swift observing policy. Fig. 3 displays the number of observations grouped in bins of exposure time (500 s binning). Most of the observations have short exposures. In fact, ∼ 18% have texp < 1 ks and ∼ 77% have texp < 5 ks. Only 7% of the observations have an exposure time > 10 ks, which are mostly (but not exclusively) fields associated with GRBs. A bump at about 10 ks is evident in Fig. 3. This happens because GRBs are typically observed for 10 ks per day, so that a lot of observations have that exposure duration.</text>
<figure>
<location><page_3><loc_8><loc_62><loc_50><loc_92></location>
<caption>Fig. 2. The number of Swift -XRT observations with exposure time longer than 500 s acquired every month from January 1 st 2005.</caption>
</figure>
<text><location><page_3><loc_7><loc_42><loc_50><loc_54></location>Many of the ∼ 35,000 fields analyzed are repeated pointings centered on the same sky position. To estimate the total sky coverage of our data set, when fields were observed more than once, we considered only the deepest exposure. This leaves us with 8,644 distinct fields, whose geometrical sky coverage as a function of the exposure time is plotted in Fig. 4. The cumulative sky coverage of all our distinct fields, which by definition have exposure times texp > 500 s is 1300 square degrees. A full list of the observations analyzed in this work is available online at the ASI Science Data Centre (ASDC) website www.asdc.asi.it.</text>
<text><location><page_3><loc_7><loc_38><loc_50><loc_41></location>In the next sections we will discuss how these raw observations have been reduced and analyzed, to detect and gather information on the sources that make up the XRT catalog.</text>
<section_header_level_1><location><page_3><loc_7><loc_34><loc_25><loc_35></location>3. XRT data reduction</section_header_level_1>
<text><location><page_3><loc_7><loc_20><loc_50><loc_33></location>The XRT data were processed using the XRTDAS software (v. 2.7.0, Capalbi et al. 2005) developed at the ASI Science Data Centre and included in the HEAsoft package (v. 6.11) distributed by HEASARC. For each observation of the sample, calibrated and cleaned PC mode event files were produced with the xrtpipeline task. In addition to the screening criteria used by the standard pipeline processing, we applied two further, more restrictive screening criteria to the data, in order to improve the signal to noise ratio of the faintest, background dominated, serendipitous sources.</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_20></location>First, we selected only time intervals with CCD temperature less than -50 o C (instead of the standard limit of -47 o C) since the contamination by dark current and hot pixels, which increase the low energy background, is strongly temperature dependent. Second, background spikes can occur in some cases, when the angle between the pointing direction of the satellite and the bright Earth limb is low. In order to eliminate this socalled bright Earth e ff ect, due to the scattered optical light that</text>
<figure>
<location><page_3><loc_52><loc_62><loc_96><loc_92></location>
<caption>Fig. 3. The exposure time distribution for the XRT sources analyzed in this work. The time bin is 500 s.</caption>
</figure>
<figure>
<location><page_3><loc_52><loc_34><loc_95><loc_57></location>
<caption>Fig. 4. The sky coverage of the Swift -XRT fields as a function of the exposure time (cumulative distribution).</caption>
</figure>
<text><location><page_3><loc_52><loc_19><loc_95><loc_28></location>usually occurs towards the beginning or the end of each orbit, we monitored the count rate in four regions of 70 × 350 physical pixels, located along the four sides of the CCD. Then, through the xselect package, we excluded time intervals when the count rate is greater than 40 counts / s. This is enough to remove the bright Earth contamination from most (but not all, see next section) of the XRT observations.</text>
<text><location><page_3><loc_52><loc_9><loc_95><loc_19></location>We produced exposure maps of the individual observations, using the task xrtexpomap . Exposure maps were produced at three energies: 1.0 keV, 4.5 keV, and 1.5 keV. These correspond to the mean values for a power-law spectrum of photon index Γ = 1 . 8 (see Sec. 4.3) weighted by the XRT e ffi ciency over the three energy ranges considered here: 0 . 3 -3 keV (soft band S), 2 -10 keV (hard band H), 0 . 3 -10 keV (full band F). For each ob-</text>
<figure>
<location><page_4><loc_7><loc_62><loc_50><loc_92></location>
<caption>Fig. 5. The distribution of the mean background counts / sec / arcmin 2 for our XRT observations, in the F band (black-shaded histogram), S band (red-shaded histogram) and H band (blue histogram).</caption>
</figure>
<text><location><page_4><loc_7><loc_48><loc_50><loc_53></location>ervation we also produced a background map, using XIMAGE, by eliminating the detected sources and calculating the mean background in box cells of size 32 × 32 pixels.</text>
<text><location><page_4><loc_7><loc_37><loc_50><loc_49></location>Fig. 5 shows the distribution of the mean background counts / s / arcmin 2 in the F, S and H energy bands. The median values of background and their interquartile ranges are 0 . 45 + 0 . 25 -0 . 10 counts / ks / arcmin 2 , 0 . 31 + 0 . 09 -0 . 08 counts / ks / arcmin 2 and 0 . 19 + 0 . 31 -0 . 03 counts / ks / arcmin 2 for the F, S and H band, respectively. These median values correspond to a level of 1 . 1, 0 . 77 and 0 . 47 counts in the F, S, and H band, respectively, over a typical source detection cell (see Sec. 4) and an exposure of 100 ks, which is the highest exposure time for all our observations.</text>
<section_header_level_1><location><page_4><loc_7><loc_33><loc_20><loc_34></location>4. Data analysis</section_header_level_1>
<section_header_level_1><location><page_4><loc_7><loc_31><loc_33><loc_32></location>4.1. Detectionandfilteringprocedure</section_header_level_1>
<text><location><page_4><loc_7><loc_12><loc_50><loc_30></location>The point source catalog was produced by running the detection algorithm detect , a tool of the XIMAGE package version 4.4.1 1 . Detect locates the point sources using a sliding-cell method. The average background intensity is estimated in several small square boxes uniformly located within the image. The position and intensity of each detected source are calculated in a box whose size maximizes the signal-to-noise ratio. The net counts are corrected for dead times and vignetting using the input exposure maps, and for the fraction of source counts that fall outside the box where the net counts are estimated, using the PSF calibration. Count rate statistical and systematic uncertainties are added quadratically. Detect was set to work in bright mode, which is recommended for crowded fields and fields containing bright sources, since it can reconstruct the centroids of very</text>
<text><location><page_4><loc_52><loc_76><loc_95><loc_93></location>nearby sources (see the XIMAGE help). While producing the deep Swift -XRT catalog, Puccetti et al. (2011) found that background is well evaluated for all exposure times using a box size of 32 × 32 original detector pixels, and that the optimized size of the search cell that minimizes source confusion, is 4 × 4 original detector pixels. The background adopted by XIMAGE for each observation is an average of the background evaluated in all the 32 × 32 individual cells. We adopted these cell sizes and backgroundestimation method too, and we also set the signal-tonoise acceptance threshold to 2.5. We produced a catalog using a corresponding Poisson probability threshold of 4 × 10 -4 . We applied detect on the XRT image using the original pixel size, and in the three energy bands: F, S and H (see Sec. 3).</text>
<text><location><page_4><loc_52><loc_42><loc_95><loc_76></location>The catalog was cleaned from spurious and extended sources by visual inspection of all the observations. Spurious sources arise on the the wings of the PSF of extremely bright sources, or near the edges of the XRT CCD (where the exposure map drastically drops out), or as fluctuations on extended sources and in some cases as residual bright Earth contamination not completely eliminated by our screening criteria. To deal with this last source of spurious detections, we run the detect algorithm on the observations a ff ected by bright Earth, lowering the count rate threshold value on the corners of the detector, as defined in Sect 3. In a few cases, to avoid lowering the threshold excessively, and thus exclude too many time intervals from the analysis, we decided to manually remove the spurious sources associated with residual bright Earth contamination even after the adopted cleaning criteria described in Sect. 3. About 200 observations out of the entire sample of ∼ 35,000 ( ∼ 0 . 6%) needed a manual removal of spurious sources induced by bright Earth background. Extended sources have also been eliminated from the final point-like catalog, because detect is not optimized to detect this type of sources, not being calibrated to correct for the background and PSF loss in case of extended sources. In order to clean the catalog from extended sources, we compare their brightness profile with the XRT PSF at the source position on the detector, using XIMAGE. In total, ∼ 3 , 700 observations needed a manual removal of spurious and / or extended sources, which is ∼ 10% of the total fields analyzed.</text>
<section_header_level_1><location><page_4><loc_52><loc_39><loc_67><loc_40></location>4.2. Sourcestatistics</section_header_level_1>
<text><location><page_4><loc_52><loc_30><loc_95><loc_38></location>The above procedure resulted in 89 , 053 point-like objects detected in at least one of the three bands. Of these, 1 , 947 are a ff ected by pile-up, i.e., feature more than 0 . 6 counts in the full band, while 2 , 166 are GRBs, which will not appear in this catalog. After removing GRBs and piled-up sources, we are left with 84 , 992 entries, which define a 'good' sample.</text>
<text><location><page_4><loc_52><loc_10><loc_95><loc_30></location>As explained before, not all these detections represent distinct sources, since observations of some fields are repeated many times. To obtain an estimate of the number of independent celestial sources, we compress our catalog over a radius of 12 arcsec. In other words, all entries within 12 arcsec of each other are counted once. The choice of the compressing radius is not straightforward. In fact, too large a radius would lead to the compression of sources that are really di ff erent, while too small a value would result in counting the same source more than once, as it could have a slightly di ff erent position in di ff erent observations due to statistical and systematic uncertainties. We tried di ff erent compressing radii, and we noted that the number of compressed sources increases slightly while reducing the radius up to 12 arcsec, while this increment is huge with a further reduction of the compressing parameter. This means that below 12 arcsec we are beginning to count the same sources more than</text>
<figure>
<location><page_5><loc_7><loc_62><loc_50><loc_92></location>
<caption>Fig. 6. The distribution of the detected sources per field. Each source in this plot is detected in at least one of the three bands. Fields with more than 40 sources have high exposure times.</caption>
</figure>
<text><location><page_5><loc_7><loc_45><loc_50><loc_54></location>once. This number is close to twice the typical uncertainty of the weakest sources in the XRT fields, which is roughly of 6-7 arcsec. The estimated number of independent celestial sources obtained in this way is ∼ 36,000. In this section, however, we will consider every one of the 84,992 entries of the catalog, because of the observation-by-observation analysis we decided to perform to build our database.</text>
<table>
<location><page_5><loc_16><loc_32><loc_40><loc_39></location>
<caption>Table 2. Number of sources detected in each band and any combination of them.</caption>
</table>
<text><location><page_5><loc_7><loc_16><loc_50><loc_28></location>Table 2 shows the detections in each of the three bands and in all possible combinations of them. In particular, 80,123 sources are detected in the F band, 70,018, in the S band and 25,437 in the H band. Fig. 6 plots the histogram of the number of sources detected per field. Most of the observations present few sources, with ∼ 51%of the fields having just one or no detections and less than 5% showing more than 10 sources. This is a consequence of the features of our sample, composed by many observations with a low exposure time.</text>
<section_header_level_1><location><page_5><loc_7><loc_13><loc_26><loc_14></location>4.3. Countratesandfluxes</section_header_level_1>
<text><location><page_5><loc_7><loc_10><loc_50><loc_12></location>As explained in section 4.1, the count rates are estimated through the detect algorithm in the F, S, H bands and corrected using</text>
<figure>
<location><page_5><loc_52><loc_62><loc_95><loc_92></location>
<caption>Fig. 7. The distribution of the count rates in the full (black), soft (red) and hard (blue) bands.</caption>
</figure>
<text><location><page_5><loc_52><loc_37><loc_95><loc_56></location>proper exposure maps (i.e., taking into account bad columns and vignetting) and PSF. To assess the reliability of the count rates evaluated with detect , Puccetti et al. (2011) selected a sample of 20 sources at di ff erent o ff -axis angles, and compared the detect results with that obtained by extracting the source spectra in a region of 20 arcsec. The average ratio between the count rates estimated using the two methods resulted to be 1 . 1 ± 0 . 2, confirming the reliability of our method. Fig. 7 shows the distribution of the count rates in the three energy bands. The median values of the count rates are 3 . 86 × 10 -3 , 3 . 85 × 10 -3 and 6 . 89 × 10 -3 cts s -1 in the F, S and H band, respectively. The faintest objects have been detected in the longest exposure time observations. The lowest count rate values estimated are ∼ 2 . 1 × 10 -4 , ∼ 1 . 8 × 10 -4 and ∼ 1 . 5 × 10 -4 cts s -1 in the F, S and H band, respectively.</text>
<text><location><page_5><loc_52><loc_13><loc_95><loc_38></location>Count rates in the F, S and H bands were converted to 0 . 5 -10, 0 . 5 -2 and 2 -10 keV observed fluxes, respectively. We adopted these flux bands to be consistent with previously published works (e.g., Watson et al. 2009; Evans et al. 2010). The conversion was made under the assumption that the spectral shape of each source is described by an absorbed power-law. The Hydrogen column density (N H ) in the direction of our target is assumed to be the Galactic one, while the photon spectral index Γ has been estimated through the hardness ratio 2 . The latter quantity is defined, for each source, as HR = ( cH -cS ) / ( cH + cS ), cS and cH being the count rates in the S and H band, respectively. Fig. 8 plots the hardness ratio distribution of our sources and their spectral indices. The median value of the hardness ratio is HRM = -0 . 38, while the distribution peaks at HRP = -0 . 50. However, HR can be evaluated only for objects with a detection in both the S and H bands, which are 21,097 out of a total of 84,992, i.e., ∼ 25% of our sample (see Table 2). For sources which miss the detection in one of these two bands, the Γ slope must be chosen somehow. One way would be to compute the av-</text>
<text><location><page_6><loc_7><loc_66><loc_50><loc_93></location>e or the median of all the Γ values of our sources. However, this is not the best strategy, because Γ strongly depends on the source type, and our sample is highly heterogeneous. Thus, we decide to fix the photon index of the sources with a missing S or H count rate to Γ ≡ 1 . 8, following Puccetti et al. (2011). In fact, they computed the most probable hardness ratio value ( HR = -0 . 5) in a subsample of their catalog comprising all the high Galactic-latitude ( | b | > 20 deg) sources. This HR value, combined with the median of the Galactic Hydrogen column density ( NH = 3 . 3 × 10 20 cm -2 , Kalberla et al. 2005), corresponds to Γ = 1 . 8. This choice should provide a reliable flux estimate for our extragalactic sources, which constitute most of our catalog. However, the reader must be aware that the flux computed this way may represent just a rough estimate for other type of sources (see also next sub-section for a more detailed description about the flux uncertainties). The faintest fluxes sampled by our survey belong to the sources detected in the deepest observations. In detail, we find that the flux interval sampled by the detected sources is in the range 7 . 4 × 10 -15 -9 . 1 × 10 -11 , 3 . 1 × 10 -15 -1 . 1 × 10 -11 and 1 . 3 × 10 -14 -9 . 1 × 10 -11 erg cm -2 s -1 for the F, S and H band, respectively.</text>
<text><location><page_6><loc_7><loc_57><loc_50><loc_66></location>We provide 90% count rate and flux upper limits every time a source is not detected in one or two of the considered bands. The 90% count upper limit for a given background is defined as the number of counts necessary to be interpreted as a background fluctuation with a probability of 10% or less, according to a Poissonian distribution. In other words, if the background of our field is B , we are searching the upper limit X for which</text>
<formula><location><page_6><loc_16><loc_52><loc_50><loc_55></location>PPoisson ≡ e -( X + B ) M ∑ i = 0 ( X + B ) i ! ≤ 0 . 1 , (1)</formula>
<text><location><page_6><loc_7><loc_32><loc_50><loc_51></location>where M is the number of counts measured at the position of each source in a region of 16 . 5 arcsec radius, which corresponds to a fraction of the point spread function of ∼ 68%. Eq. (1) does not take into account possible background fluctuations that may arise close to the considered source. The correction factor has been evaluated by Puccetti et al. (2011) following the recipe in Bevington and Robinson (1992). They found that the factor 1 . 282 × σ (with σ ( B ) = √ B describing the Poissonian background fluctuations) must be added to the count upper limits. The count rate upper limits are finally evaluated from these counts (which are corrected for the non-included PSF fraction of the cell), by dividing them for the net exposure, which takes into account the vignetting at the source position. Flux upper limits are computed from count rate upper limits, adopting the appropriate N H and assuming Γ = 1 . 8, as explained before.</text>
<section_header_level_1><location><page_6><loc_7><loc_29><loc_35><loc_30></location>4.4. Uncertaintiesandsourcereliability</section_header_level_1>
<text><location><page_6><loc_7><loc_12><loc_50><loc_28></location>Detect count rates are associated with their statistical (Poissonian) uncertainties. These errors are propagated to the flux estimates, but here the main uncertainty is the variety of the spectral behaviour of di ff erent sources. In order to determine the flux variation with the spectral parameters, we estimate the count rate-to-flux conversion factors for a wide range of spectral slopes ( Γ = 0 -2) and Hydrogen column densities ( NH = 10 19 -10 22 cm -2 ). The conversion factors are in the range (2 . 9 -15) × 10 -11 , (0 . 9 -1 . 5) × 10 -11 and (8 . 1 -17) × 10 -11 erg cm -2 s -1 for the F, S and H band, respectively. The conversion factor for the F band is more sensitive to the spectral shape than for the S and H bands, because this band is wider.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_12></location>Concerning the source positions, their errors are both statistical and systematic, with the total positional uncertainty being:</text>
<figure>
<location><page_6><loc_52><loc_62><loc_95><loc_92></location>
</figure>
<figure>
<location><page_6><loc_52><loc_30><loc_95><loc_60></location>
<caption>Fig. 8. Top panel: the hardness ratio distribution of our sample. Bottom panel: the distribution of the X-ray spectral indices for our sample. These plots include only sources with a detection in both the S and H bands.</caption>
</figure>
<formula><location><page_6><loc_66><loc_18><loc_95><loc_20></location>σ pos = √ σ 2 stat + σ 2 sys . (2)</formula>
<text><location><page_6><loc_52><loc_10><loc_95><loc_17></location>The systematic error σ sys is due to the uncertainty on the XRT aspect solution. This quantity has been estimated by Puccetti et al. (2011) by cross-correlating a sub-sample of bright sources of their XRT-deep catalog with the SDSS optical galaxy catalog. They found that the mean σ sys at the 68% confidence level is 2 . 05 arcsec, a value consistent with previous results by</text>
<table>
<location><page_7><loc_8><loc_51><loc_94><loc_91></location>
<caption>Table 3. Source parameters in the catalog.</caption>
</table>
<text><location><page_7><loc_7><loc_42><loc_50><loc_47></location>Moretti et al. (2006). This value represents the number we will adopt in estimating the positional error in Eq. 2. The statistical variance σ 2 stat is instead inversely proportional to the source number counts.</text>
<text><location><page_7><loc_7><loc_32><loc_50><loc_42></location>To assess the reliability of our detections we must address the possibility of source confusion. The source confusion issue arises when two close sources are detected as a single one. This problem may be important if the distances between two objects is of the order of the cell detection of the algorithm detect . To evaluate the possibility of source confusion, we compute the probability of finding two sources with a X-ray flux higher than a certain threshold Flim , lying at a distance smaller than θ min :</text>
<formula><location><page_7><loc_20><loc_27><loc_50><loc_30></location>P ( < θ min ) = 1 -e -π N θ 2 min . (3)</formula>
<text><location><page_7><loc_7><loc_9><loc_50><loc_26></location>Here we adopt as θ min twice the typical size of the cell detection box (4 pixels or 9 . 44 arcsec), while N is the number counts corresponding to Flim , which can be evaluated, e.g., from the CCOSMOS survey (Elvis et al. 2009). Our deepest field has an exposure of ∼ 100 ks. Using the Flim corresponding to the count rates of the faintest sources detected in this field ( ∼ 1 . 7 × 10 -4 and ∼ 1 . 5 × 10 -4 cts / s in the S and H band, respectively), we find that the source confusion probability is less than 3% in both the S and H band. This is of course the field in which the source confusion probability is highest. For fields of ∼ 10 ks ( ∼ 93% of our sample has exposures < 10 ks) the flux limits are shallower by a factor of ∼ 3. Applying Eq. (3) to these fields results in a probability of source confusion of ∼ 0 . 9% and ∼ 0 . 3% in the</text>
<text><location><page_7><loc_52><loc_45><loc_95><loc_47></location>S and H band, respectively. This means that source confusion is negligible in our sample.</text>
<section_header_level_1><location><page_7><loc_52><loc_42><loc_70><loc_43></location>4.5. 1SWXRTdescription</section_header_level_1>
<text><location><page_7><loc_52><loc_33><loc_95><loc_40></location>The final catalog comprises 32 field parameters for each entry. Source name, position, count rates and fluxes, exposure, hardness ratio and galactic NH are reported, together with the corresponding uncertainties and / or reliabilities. A full description of all the parameters is presented in Table 3. Table 4 gives instead the first ten entries of the catalog as an example.</text>
<section_header_level_1><location><page_7><loc_52><loc_29><loc_77><loc_30></location>5. Scientific use of the catalog</section_header_level_1>
<text><location><page_7><loc_52><loc_23><loc_95><loc_28></location>A full exploitation of the scientific data presented in this work is far beyond the scope of the present paper. Nevertheless, we would like to draw the reader's attention to some of the scientific topics that can be addressed using 1SWXRT.</text>
<section_header_level_1><location><page_7><loc_52><loc_20><loc_70><loc_21></location>5.1. Short-termvariability</section_header_level_1>
<text><location><page_7><loc_52><loc_12><loc_95><loc_19></location>As stated in the previous section, in our analysis we do not merge observations pointing to the same field, so we can study the variability of sources observed more than once. Since many observations are often performed consecutively, this enables to determine short-term variability for the involved sources.</text>
<text><location><page_7><loc_52><loc_10><loc_95><loc_12></location>Our database comprises 12,908 sources observed at least twice. Among these, we select all sources detected in each obser-</text>
<figure>
<location><page_8><loc_8><loc_29><loc_94><loc_91></location>
<caption>Table 4. 1SWXRT catalog template</caption>
</figure>
<table>
<location><page_8><loc_8><loc_29><loc_94><loc_91></location>
</table>
<text><location><page_8><loc_7><loc_10><loc_50><loc_25></location>vation in the soft or hard band. 7,936 and 2,113 sources are detected in the soft and hard band, respectively. Fig. 9 plots the distribution of the number of sources observed many times, while Fig. 10 displays the histogram for the variability as a function of the σ significance. The number of sources in the soft band with a variation larger than 3 σ and 5 σ is 1,774 and 623, respectively, i.e., a fraction of 22% and 7 . 7% of the total soft sources. Similarly, the number of sources in the hard band with a variation larger than 3 σ and 5 σ is 447 and 148, respectively, i.e., a fraction of 23% and 7 . 6% of the total hard sources. Thus, variability is observed in both bands, and with similar trends. However, some tens of sources show extreme variability (Fig.</text>
<text><location><page_8><loc_52><loc_18><loc_95><loc_25></location>10). The ratio of such extreme variable sources with respect to the total number grows stronger in the hard band with respect to the soft one as the significance of the variability increases. For example, the fraction of sources which vary at more than 10 σ is 1 . 7% and 1 . 9% in the soft and hard band, respectively, while at the 20 σ level, the fractions become 0 . 4%(soft) and 0 . 7%(hard).</text>
<text><location><page_8><loc_52><loc_10><loc_95><loc_17></location>We then select all the sources observed at least 5 times. Fig. 11 shows the cumulative distribution of the statistical significance of the variability for sources with five observations or more. This variability significance has been computed with respect both to the maximum and to the minimum fluxes. It interesting to note that the variability is more pronounced when</text>
<figure>
<location><page_9><loc_7><loc_65><loc_54><loc_92></location>
<caption>Fig. 11. The cumulative distribution of the statistical significance of the variability for sources with five observations or more. Red (Blue) lines refer to the soft (hard) band. Solid (dotted) lines refer to the variability significance of the minimum (maximum) flux values with respect to the average ones.</caption>
</figure>
<figure>
<location><page_9><loc_55><loc_65><loc_95><loc_92></location>
<caption>Fig. 9. The distribution of the number of sources observed more than once. Red line refers to the soft band, blue line to the hard one.</caption>
</figure>
<figure>
<location><page_9><loc_7><loc_31><loc_50><loc_58></location>
<caption>Fig. 10. The distribution of the source variability expressed as a function of the σ significance. Red line refers to the soft band, blue line to the hard one.</caption>
</figure>
<text><location><page_9><loc_7><loc_17><loc_50><loc_23></location>considering the maximum fluxes. In other words, the average fluxes are in general closer to the minimum values than to the maximum ones. This could be a possible indication that we are observing short-duration flares in some sources, with the normal state being close to the minimum value observed.</text>
<section_header_level_1><location><page_9><loc_7><loc_13><loc_19><loc_14></location>5.2. Softsources</section_header_level_1>
<text><location><page_9><loc_7><loc_10><loc_50><loc_12></location>We can use our dataset to study sources showing emission in the soft band only. Among these, one important class is rep-</text>
<text><location><page_9><loc_52><loc_53><loc_95><loc_55></location>resented by isolated neutron stars (INS, see, e.g., Treves et al. 2000; Haberl et al. 2003; Haberl 2004).</text>
<text><location><page_9><loc_52><loc_27><loc_95><loc_53></location>INS are blank field sources, i.e., X-ray sources with no or very faint counterparts in other wavelength domains. Concerning the X-ray-to-optical flux ratio, values of fX / fopt > 10 3 define the INS class, but in some cases values as high as 10 5 have been reported. The X-ray emission is supposed to be produced by some residual internal energy (coolers) or because they are interacting with the interstellar medium (accretors). The INS X-ray spectrum is well fitted by a soft blackbody, with temperatures of ∼ 100 eV. This means that basically no X-ray emission above ∼ 2 keV is expected. Given the low column densities measured for these objects, the emission is consistent with being produced from the neutron star surface (see, e.g., Walter & Lattimer 2002). Other characteristics often exhibited by these sources (coolers) are a periodicity of ∼ 5 -10 s, absorption features below 1 keV and closeness. These elusive sources are of extreme importance, because they could represent ∼ 1% of the total number of stars in our Galaxy. To pinpoint their properties means to understand the end-point of the evolution of a large class of stars. To date, only 8 -10 objects of this class have been identified.</text>
<text><location><page_9><loc_52><loc_16><loc_95><loc_28></location>In order to check our catalog for the presence of INS, and in general to categorize the soft objects, we selected all sources that do not show emission in the full and hard band. When considering objects observed more than once, we excluded from our analysis all sources in which there is a detection in the full or hard band in at least one observation. This helps us to include in our sample just genuine soft emitters, and to exclude part of the sources that are possibly not detected in the hard band due to low exposure times.</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_16></location>We selected 2087 objects following the above criteria. Fig. 12 displays the 0 . 5 -2 keV flux distribution for these sources. The histogram bin size is set to 0 . 05 dex. Since the soft band is in general more sensitive than the hard one, the faint part of this distribution can still comprise normal sources that are not detected</text>
<figure>
<location><page_10><loc_8><loc_65><loc_50><loc_92></location>
<caption>Fig. 12. The distribution of the 0 . 5 -2 keV flux for the sources detected in the soft band only.</caption>
</figure>
<text><location><page_10><loc_7><loc_50><loc_50><loc_57></location>in the 2 -10 keV range due to a flux level below the sensitivity threshold. However, we determined the number of XRT sources featuring at least 50 or 100 counts in the 0 . 5 -2 keV band, without detection in the 2 -10 one. We obtain 7 sources with at least 50 counts. Of these, 3 have more than 100 counts. These seven objects are good INS candidates.</text>
<section_header_level_1><location><page_10><loc_7><loc_46><loc_20><loc_47></location>5.3. Hardsources</section_header_level_1>
<text><location><page_10><loc_7><loc_24><loc_50><loc_45></location>In a similar way to what described in the previous sub-section, we can search our dataset for sources which show emission in the hard band only. To categorize the hard objects, we selected all sources that do not show emission in the full and soft band. When considering objects observed more than once, we excluded from our analysis all sources in which there is a detection in the full or soft band in at least one observation. This helps us to include in our sample just genuine hard emitters, and to exclude part of the sources that are possibly not detected in the soft band due to a low exposure time coupled with an unusual background level. 308 objects in our dataset fulfill the above criteria. Fig. 13 displays the 2 -10 keV flux distribution for these sources. The histogram bin dimension is set to 0 . 1 dex. The hard band is less sensitive than the soft one. Thus, contrary to the case of the soft sources, we are confident that this sub-sample contains genuine hard sources only.</text>
<text><location><page_10><loc_7><loc_10><loc_50><loc_24></location>The main type of objects contributing to this sub-sample are expected to be obscured Active Galactic Nuclei (AGN), whose discovery and study is very important both to study the properties and evolution of the accretion process onto supermassive black holes residing at the center of galaxies and to determine their contribution to the X-ray background, in particular to its peak emission in the 20-30 keV band that still remains largely unexplained (see, e.g., Gilli et al. 2007; Treister et al. 2009, and references therein). In future works we will investigate on the nature of these sources in order to determine their properties and nature.</text>
<figure>
<location><page_10><loc_54><loc_65><loc_95><loc_92></location>
<caption>Fig. 13. The distribution of the 2 -10 keV flux for the sources detected in the hard band only.</caption>
</figure>
<section_header_level_1><location><page_10><loc_52><loc_58><loc_89><loc_59></location>5.4. Cross-correlationwithmulti-wavelengthcatalogs</section_header_level_1>
<text><location><page_10><loc_52><loc_48><loc_95><loc_56></location>Our catalog can be cross-correlated with multi-wavelength ones, to obtain statistical information about specific class of sources. Here, we cross-correlated the XRT catalog with BZCAT, a multifrequency catalogue of blazars (Massaro et al. 2009). We stress that this is just an example, and that many more crosscorrelations with other catalogs can be performed to fully exploit 1SWXRT.</text>
<text><location><page_10><loc_52><loc_26><loc_95><loc_47></location>Blazars are radio loud AGN pointing their jets in the direction of the observer (see e.g. Urry & Padovani 1995). They come in two main subclasses, the Flat Spectrum Radio Quasars (FSRQs), which show strong, broad emission lines in their optical spectrum, just like radio quiet QSOs, and BL Lacs, which are instead characterized by an optical spectrum, which at most shows weak emission lines or is completely featureless. The strong non-thermal radiation is composed of two basic parts forming two broad humps in the ν vs. ν F ν plane, the low-energy one attributed to synchrotron radiation, and the high-energy one, usually thought to be due to inverse Compton radiation (Abdo et al. 2010). The peak of the synchrotron hump ( ν S peak ) can occur at di ff erent frequencies. In FSRQs ν S peak never reaches very high values ( ν S peak < ∼ 10 14 . 5 Hz), whereas the ν S peak of BL Lacs can reach values as high as ν S peak > ∼ 10 18 Hz (e.g. Giommi et al. 2012).</text>
<text><location><page_10><loc_52><loc_10><loc_95><loc_26></location>The cross-correlation between the BZCAT and 1SWXRT catalogs has been performed by matching the coordinates over an error radius of 0 . 2 arcmins. We found 938 sources in 1SWXRT with a BZCAT counterpart. Of these, 524 are FSRQs and 414 are BL Lacs. Fig. 14 shows the X-ray spectral index distribution for these sources. It is evident that BL Lac distribution is softer than FSRQ one. This is because the X-ray 0 . 5 -10 keV band samples on average the high energy tail of the synchrotron emission in BL Lacs, where ν F ν is decreasing. On the other hand, the same energy band describes, on average, the low energy tail of the inverse Compton emission in FSRQs, where ν F ν is instead increasing. For comparison, Fig. 14 plots also the Xray spectral index of the stars, obtained by cross-correlating the</text>
<figure>
<location><page_11><loc_8><loc_61><loc_49><loc_93></location>
<caption>Fig. 14. The distribution of the X-ray spectral index for specific source types in our catalog.</caption>
</figure>
<text><location><page_11><loc_7><loc_53><loc_50><loc_55></location>XRT catalog with the Smithsonian Astrophysical Observatory Star Catalog (SAO), and that of the unidentified sources.</text>
<section_header_level_1><location><page_11><loc_7><loc_49><loc_31><loc_51></location>6. Summary and conclusions</section_header_level_1>
<text><location><page_11><loc_7><loc_39><loc_50><loc_48></location>We have reduced and analyzed all the observations performed by Swift -XRT in PC mode with an exposure time longer than 500 s, during its first seven years of operations, i.e., between 2005 and 2011. Approximately 35,000 XRT fields have been analyzed, with net exposures (after screening and filtering criteria being applied) ranging from 500 s to 100 ks. The total, net exposure time is ∼ 140 Ms.</text>
<text><location><page_11><loc_7><loc_10><loc_50><loc_19></location>For all the entries of 1SWXRT, we determined the position, the detection probability and the signal-to-noise ratio. Count rates were estimated in the 0 . 3 -10, 0 . 3 -3 and 2 -10 keV bands. Each source has a detection in at least one of these bands, with ∼ 80,000, ∼ 70,000 and ∼ 25,500 sources detected in the full, soft and hard band, respectively. 90% upper limits were provided in case of missing detection in one or two of these bands.</text>
<text><location><page_11><loc_7><loc_18><loc_50><loc_39></location>The purpose of this work was to create a catalog (1SWXRT) of all the point like sources detected in these observations. To this purpose, we run the XIMAGE detect algorithm to all our fields, and then removed spurious and extended sources through visual inspection of the XRT observations. The total number of point-like objects detected is 89 , 053, of which 2 , 166 are GRB detections (so transient sources by definition) and 1 , 947 are sources a ff ected by pile-up. Thus, our final version of the catalog comprises 84 , 992 entries, which define the 'good' sample. Many entries represent the same sources, since several portions of the sky have been observed many times by XRT. To estimate an approximate number of distinct, celestial sources, we compress our catalog over a radius of 12 arcsec, a typical positional uncertainty value in faint XRT sources. In other words, all entries closer than 12 arcsec are counted once, and the result of this procedure is ∼ 36,000 distinct sources.</text>
<text><location><page_11><loc_52><loc_81><loc_95><loc_93></location>The count rates were converted into fluxes in the 0 . 5 -10, 0 . 5 -2 and 2 -10 keV X-ray bands. The flux interval sampled by the detected sources is 7 . 4 × 10 -15 -9 . 1 × 10 -11 , 3 . 1 × 10 -15 -1 . 1 × 10 -11 and 1 . 3 × 10 -14 -9 . 1 × 10 -11 erg cm -2 s -1 for the full, soft and hard band, respectively. Among the possible scientific uses of 1SWXRT, we discussed the possibility to study short-term variability, the identification of sources emitting in the soft or hard band only, and the cross correlation of our catalogue to multiwavelength ones.</text>
<text><location><page_11><loc_52><loc_77><loc_95><loc_80></location>Acknowledgements. We thank the referee for a quick and careful reading of the manuscript. This work has been supported by ASI grant I / 004 / 11 / 0. JPO acknowledges financial support from the UK Space Agency</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Context. The Swift satellite is a multi-wavelength observatory specifically designed for gamma-ray burst (GRB) astronomy that is operational since 2004. Swift is also a very flexible multi-purpose facility that supports a wide range of scientific fields such as active galactic nuclei, supernovae, cataclysmic variables, Galactic transients, active stars and comets. The Swift X-ray Telescope (XRT) has collected more than 150 Ms of observations in its first seven years of operations. Aims. The purpose of this work is to present to the scientific community the list of all the X-ray point sources detected in XRT imaging data taken in photon counting mode during the first seven years of Swift operations. All these point-like sources, excluding the Gamma-Ray Bursts (GRB), will be stored in a catalog publicly available (1SWXRT). Methods. We consider all the XRT observations with exposure time longer than 500 s taken in the period 2005-2011. Data were reduced and analyzed with standard techniques and a list of detected sources for each observation was produced. A careful visual inspection was performed to remove extended, spurious and piled-up sources. Finally, positions, count rates, fluxes and the corresponding uncertainties were computed. Results. We have analyzed more than 35,000 XRT fields, with exposures ranging between 500 s and 100 ks, for a total exposure time of almost 140 Ms. The catalog includes approximately 89,000 entries, of which almost 85,000 are not a ff ected by pile-up and are not GRBs. Considering that many XRT fields were observed several times, we have a total of ∼ 36,000 distinct celestial sources. We computed count rates in three energy bands: 0 . 3 -10 keV (Full, or F), 0 . 3 -3 keV (Soft, or S) and 2 -10 keV (Hard, or H). Each entry has a detection in at least one of these bands. In particular, we detect ∼ 80,000, ∼ 70,000 and ∼ 25 , 500 in the F, S and H band, respectively. Count rates were converted into fluxes in the 0 . 5 -10, 0 . 5 -2 and 2 -10 keV bands. The flux interval sampled by the detected sources is 7 . 4 × 10 -15 -9 . 1 × 10 -11 , 3 . 1 × 10 -15 -1 . 1 × 10 -11 and 1 . 3 × 10 -14 -9 . 1 × 10 -11 erg cm -2 s -1 for the F, S and H band, respectively. Some possible scientific uses of the catalog are also highlighted. Key words. gamma rays: bursts - cosmology: observations",
"pages": [
1
]
},
{
"title": "The seven year Swift-XRT point source catalog (1SWXRT) /star",
"content": "V. D'Elia 1 , 2 , M. Perri 1 , 2 , S. Puccetti 1 , 2 , M. Capalbi 1 , 2 , P. Giommi 1 , D. N. Burrows 3 , S. Campana 4 , G. Tagliaferri 4 , G. Cusumano 5 , P. Evans 6 , N. Gehrels 7 , J. Kennea 3 , A. Moretti 4 , J. A. Nousek 3 , J.P. Osborne 6 , P. Romano 5 and G. Stratta 1 , 2 Preprint online version: October 9, 2018",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The Swift Gamma-Ray Burst Explorer (Gehrels et al. 2004) is a NASA mission, successfully launched on 2004 Nov. 20. The hardware and software were built by an international team involving US, United Kingdom and Italy, with contributions from Germany and Japan. The main scientific driver of the Swift mission is to detect gamma-ray bursts (GRBs) in the hard Xray band with the Burst Alert Telescope (BAT, Barthelmy et al. 2005) and quickly follow-up their emission at longer wavelength with the X-Ray Telescope (XRT, Burrows et al. 2005) and Ultraviolet / Optical Telescope (UVOT, Roming et al. 2005). Despite being specifically designed to address GRB science topics, Swift is also an e ff ective multi-purpose multi-frequency observatory. The Swift team expertise in following up GRBs has grown during the satellite operations, leading to an evolution of the observing time share between GRBs and other cos- mic sources. At the beginning of the satellite operations (up to 2006, Romano 2012), approximately 56% of the Swift observing time was dedicated to GRB observations, and ∼ 26% divided up between target of opportunity (ToO, ∼ 8%) and 'fill-in' observations (that are short exposures of a variety of X-ray sources taken when Swift was not engaged in GRB science, ∼ 18%). After 2006, it became evident that there was no need to follow up all GRBs for a very long time. Thus, without losing too much relevant scientific information, in 2010 the GRB dedicated time dropped to ∼ 27%while ∼ 29%and ∼ 26%was allocated to ToO and Fill-in observations, respectively. In the remaining ∼ 18%of the time the satellite flies through the South Atlantic Anomaly or is devoted to calibration issues. The Swift mission is currently producing data at a pace of about ∼ 500 observations per month, contributing to most areas of astronomy. Apart from GRBs, the Swift instruments are observing extragalactic targets, such as active galactic nuclei, clusters of galaxies, nearby galaxies, and Galactic sources, such as binaries, microquasars, pulsars, and all Galactic variable sources in general. The Swift -XRT utilizes a mirror set built for JET-X and an XMM / EPIC MOS CCD detector to provide a sensitive broadband (0.2-10 keV) X-ray imager with e ff ective area of > 120 cm 2 at 1 . 5 keV, field of view of 23 . 6 × 23 . 6 arcmin, and angular resolution of 18 arcsec. The detection sensitivity is 2 × 10 -14 erg cm -2 s -1 in 10 4 s. The instrument can work in three di ff erent modes (Hill et al. 2004): Photodiode (PD), Windowed-Timing (WT) and Photon-Counting (PC) modes. Due to a micrometeorite hit on May 27 2005, the PD mode has been disabled because of the very high background rate from hot pixels which cannot be avoided during read-out in this mode (Abbey et al. 2006). While the first two modes are built to produce a high time resolution at the expense of losing all (PD) or part (WT) of the spatial information, the latter one retains full imaging resolution and will be the only mode exploited here. This paper presents the 1SWXRT catalog, which consists of all the point-like sources detected by the XRT in its first seven years of operations (2005 -2011). Updated versions of the catalog, containing observations performed from 2012, are foreseen on timescales of about two years. Similar catalogs have already been produced for the first eight years of Chandra operations (Evans et al. 2010) and for the first seven years of XMMNewton operations (Watson et al. 2009). The reduction and analysis method is very similar to that adopted for the production of the ' Swift Serendipitous Survey in deep XRT GRB fields' (Puccetti et al. 2011), which comprises a list of sources detected in all Swift -XRT GRB fields with exposure times longer than 10 ks, observed by Swift between 2004 and 2008. Our goal is complementary to that of Puccetti et al. (2011). Instead of summing all the observations related to the same field, we keep them separated, in order to build a catalog which retains information about the variability of our sources. In addition, we analyzed all the XRT observations, and not only the fields centered on GRBs. A future work (Evans et al., in prep) will consider all XRT fields, combined where the same field is observed multiple times. A first catalog of extended sources has been published (Tundo et al. 2012), and further updates are in preparation. Our paper is organized as follows. In Sect. 2 we briefly describe our catalog. In Sect. 3 and 4 we present the data reduction and analysis method, respectively. In Sect. 5 we briefly discuss the scientific issues that can be tackled using our catalog. Finally, in Sect. 6 we draw our conclusions.",
"pages": [
1,
2
]
},
{
"title": "2. The seven year Swift -XRT point source catalog",
"content": "The seven year Swift -XRT point source catalog (1SWXRT) is built using all the observations performed by Swift -XRT in PC observing mode between 2005 and 2011. We consider in our analysis all the XRT fields, including 'safe pointings', that are sky positions used by the satellite as safe positions in case there are troubles during the slew from one target to another. The only constraint for a field to be analyzed is on the exposure time, which is required to be longer than 500 s. Di ff erent observations are not merged, but analyzed separately, thus retaining information about the variability of the catalogued sources. Here and in the following we define as 'observation' the total exposure time per target for a given day, identified by an unambiguous sequence number. The total number of observations considered is 35 , 011, for an overall exposure time of ∼ 140 Ms. Fig. 1 shows the Aito ff projection in Galactic coordinates of these XRT observations. Table 1 collects the number of observations per month in the period 2005 -2011, together with the corresponding exposure time. Fig. 2 shows the number of observations as a function of the month in which they were performed. It is interesting to note how this number increased with time, reflecting the evolution of the Swift observing policy. Fig. 3 displays the number of observations grouped in bins of exposure time (500 s binning). Most of the observations have short exposures. In fact, ∼ 18% have texp < 1 ks and ∼ 77% have texp < 5 ks. Only 7% of the observations have an exposure time > 10 ks, which are mostly (but not exclusively) fields associated with GRBs. A bump at about 10 ks is evident in Fig. 3. This happens because GRBs are typically observed for 10 ks per day, so that a lot of observations have that exposure duration. Many of the ∼ 35,000 fields analyzed are repeated pointings centered on the same sky position. To estimate the total sky coverage of our data set, when fields were observed more than once, we considered only the deepest exposure. This leaves us with 8,644 distinct fields, whose geometrical sky coverage as a function of the exposure time is plotted in Fig. 4. The cumulative sky coverage of all our distinct fields, which by definition have exposure times texp > 500 s is 1300 square degrees. A full list of the observations analyzed in this work is available online at the ASI Science Data Centre (ASDC) website www.asdc.asi.it. In the next sections we will discuss how these raw observations have been reduced and analyzed, to detect and gather information on the sources that make up the XRT catalog.",
"pages": [
2,
3
]
},
{
"title": "3. XRT data reduction",
"content": "The XRT data were processed using the XRTDAS software (v. 2.7.0, Capalbi et al. 2005) developed at the ASI Science Data Centre and included in the HEAsoft package (v. 6.11) distributed by HEASARC. For each observation of the sample, calibrated and cleaned PC mode event files were produced with the xrtpipeline task. In addition to the screening criteria used by the standard pipeline processing, we applied two further, more restrictive screening criteria to the data, in order to improve the signal to noise ratio of the faintest, background dominated, serendipitous sources. First, we selected only time intervals with CCD temperature less than -50 o C (instead of the standard limit of -47 o C) since the contamination by dark current and hot pixels, which increase the low energy background, is strongly temperature dependent. Second, background spikes can occur in some cases, when the angle between the pointing direction of the satellite and the bright Earth limb is low. In order to eliminate this socalled bright Earth e ff ect, due to the scattered optical light that usually occurs towards the beginning or the end of each orbit, we monitored the count rate in four regions of 70 × 350 physical pixels, located along the four sides of the CCD. Then, through the xselect package, we excluded time intervals when the count rate is greater than 40 counts / s. This is enough to remove the bright Earth contamination from most (but not all, see next section) of the XRT observations. We produced exposure maps of the individual observations, using the task xrtexpomap . Exposure maps were produced at three energies: 1.0 keV, 4.5 keV, and 1.5 keV. These correspond to the mean values for a power-law spectrum of photon index Γ = 1 . 8 (see Sec. 4.3) weighted by the XRT e ffi ciency over the three energy ranges considered here: 0 . 3 -3 keV (soft band S), 2 -10 keV (hard band H), 0 . 3 -10 keV (full band F). For each ob- ervation we also produced a background map, using XIMAGE, by eliminating the detected sources and calculating the mean background in box cells of size 32 × 32 pixels. Fig. 5 shows the distribution of the mean background counts / s / arcmin 2 in the F, S and H energy bands. The median values of background and their interquartile ranges are 0 . 45 + 0 . 25 -0 . 10 counts / ks / arcmin 2 , 0 . 31 + 0 . 09 -0 . 08 counts / ks / arcmin 2 and 0 . 19 + 0 . 31 -0 . 03 counts / ks / arcmin 2 for the F, S and H band, respectively. These median values correspond to a level of 1 . 1, 0 . 77 and 0 . 47 counts in the F, S, and H band, respectively, over a typical source detection cell (see Sec. 4) and an exposure of 100 ks, which is the highest exposure time for all our observations.",
"pages": [
3,
4
]
},
{
"title": "4.1. Detectionandfilteringprocedure",
"content": "The point source catalog was produced by running the detection algorithm detect , a tool of the XIMAGE package version 4.4.1 1 . Detect locates the point sources using a sliding-cell method. The average background intensity is estimated in several small square boxes uniformly located within the image. The position and intensity of each detected source are calculated in a box whose size maximizes the signal-to-noise ratio. The net counts are corrected for dead times and vignetting using the input exposure maps, and for the fraction of source counts that fall outside the box where the net counts are estimated, using the PSF calibration. Count rate statistical and systematic uncertainties are added quadratically. Detect was set to work in bright mode, which is recommended for crowded fields and fields containing bright sources, since it can reconstruct the centroids of very nearby sources (see the XIMAGE help). While producing the deep Swift -XRT catalog, Puccetti et al. (2011) found that background is well evaluated for all exposure times using a box size of 32 × 32 original detector pixels, and that the optimized size of the search cell that minimizes source confusion, is 4 × 4 original detector pixels. The background adopted by XIMAGE for each observation is an average of the background evaluated in all the 32 × 32 individual cells. We adopted these cell sizes and backgroundestimation method too, and we also set the signal-tonoise acceptance threshold to 2.5. We produced a catalog using a corresponding Poisson probability threshold of 4 × 10 -4 . We applied detect on the XRT image using the original pixel size, and in the three energy bands: F, S and H (see Sec. 3). The catalog was cleaned from spurious and extended sources by visual inspection of all the observations. Spurious sources arise on the the wings of the PSF of extremely bright sources, or near the edges of the XRT CCD (where the exposure map drastically drops out), or as fluctuations on extended sources and in some cases as residual bright Earth contamination not completely eliminated by our screening criteria. To deal with this last source of spurious detections, we run the detect algorithm on the observations a ff ected by bright Earth, lowering the count rate threshold value on the corners of the detector, as defined in Sect 3. In a few cases, to avoid lowering the threshold excessively, and thus exclude too many time intervals from the analysis, we decided to manually remove the spurious sources associated with residual bright Earth contamination even after the adopted cleaning criteria described in Sect. 3. About 200 observations out of the entire sample of ∼ 35,000 ( ∼ 0 . 6%) needed a manual removal of spurious sources induced by bright Earth background. Extended sources have also been eliminated from the final point-like catalog, because detect is not optimized to detect this type of sources, not being calibrated to correct for the background and PSF loss in case of extended sources. In order to clean the catalog from extended sources, we compare their brightness profile with the XRT PSF at the source position on the detector, using XIMAGE. In total, ∼ 3 , 700 observations needed a manual removal of spurious and / or extended sources, which is ∼ 10% of the total fields analyzed.",
"pages": [
4
]
},
{
"title": "4.2. Sourcestatistics",
"content": "The above procedure resulted in 89 , 053 point-like objects detected in at least one of the three bands. Of these, 1 , 947 are a ff ected by pile-up, i.e., feature more than 0 . 6 counts in the full band, while 2 , 166 are GRBs, which will not appear in this catalog. After removing GRBs and piled-up sources, we are left with 84 , 992 entries, which define a 'good' sample. As explained before, not all these detections represent distinct sources, since observations of some fields are repeated many times. To obtain an estimate of the number of independent celestial sources, we compress our catalog over a radius of 12 arcsec. In other words, all entries within 12 arcsec of each other are counted once. The choice of the compressing radius is not straightforward. In fact, too large a radius would lead to the compression of sources that are really di ff erent, while too small a value would result in counting the same source more than once, as it could have a slightly di ff erent position in di ff erent observations due to statistical and systematic uncertainties. We tried di ff erent compressing radii, and we noted that the number of compressed sources increases slightly while reducing the radius up to 12 arcsec, while this increment is huge with a further reduction of the compressing parameter. This means that below 12 arcsec we are beginning to count the same sources more than once. This number is close to twice the typical uncertainty of the weakest sources in the XRT fields, which is roughly of 6-7 arcsec. The estimated number of independent celestial sources obtained in this way is ∼ 36,000. In this section, however, we will consider every one of the 84,992 entries of the catalog, because of the observation-by-observation analysis we decided to perform to build our database. Table 2 shows the detections in each of the three bands and in all possible combinations of them. In particular, 80,123 sources are detected in the F band, 70,018, in the S band and 25,437 in the H band. Fig. 6 plots the histogram of the number of sources detected per field. Most of the observations present few sources, with ∼ 51%of the fields having just one or no detections and less than 5% showing more than 10 sources. This is a consequence of the features of our sample, composed by many observations with a low exposure time.",
"pages": [
4,
5
]
},
{
"title": "4.3. Countratesandfluxes",
"content": "As explained in section 4.1, the count rates are estimated through the detect algorithm in the F, S, H bands and corrected using proper exposure maps (i.e., taking into account bad columns and vignetting) and PSF. To assess the reliability of the count rates evaluated with detect , Puccetti et al. (2011) selected a sample of 20 sources at di ff erent o ff -axis angles, and compared the detect results with that obtained by extracting the source spectra in a region of 20 arcsec. The average ratio between the count rates estimated using the two methods resulted to be 1 . 1 ± 0 . 2, confirming the reliability of our method. Fig. 7 shows the distribution of the count rates in the three energy bands. The median values of the count rates are 3 . 86 × 10 -3 , 3 . 85 × 10 -3 and 6 . 89 × 10 -3 cts s -1 in the F, S and H band, respectively. The faintest objects have been detected in the longest exposure time observations. The lowest count rate values estimated are ∼ 2 . 1 × 10 -4 , ∼ 1 . 8 × 10 -4 and ∼ 1 . 5 × 10 -4 cts s -1 in the F, S and H band, respectively. Count rates in the F, S and H bands were converted to 0 . 5 -10, 0 . 5 -2 and 2 -10 keV observed fluxes, respectively. We adopted these flux bands to be consistent with previously published works (e.g., Watson et al. 2009; Evans et al. 2010). The conversion was made under the assumption that the spectral shape of each source is described by an absorbed power-law. The Hydrogen column density (N H ) in the direction of our target is assumed to be the Galactic one, while the photon spectral index Γ has been estimated through the hardness ratio 2 . The latter quantity is defined, for each source, as HR = ( cH -cS ) / ( cH + cS ), cS and cH being the count rates in the S and H band, respectively. Fig. 8 plots the hardness ratio distribution of our sources and their spectral indices. The median value of the hardness ratio is HRM = -0 . 38, while the distribution peaks at HRP = -0 . 50. However, HR can be evaluated only for objects with a detection in both the S and H bands, which are 21,097 out of a total of 84,992, i.e., ∼ 25% of our sample (see Table 2). For sources which miss the detection in one of these two bands, the Γ slope must be chosen somehow. One way would be to compute the av- e or the median of all the Γ values of our sources. However, this is not the best strategy, because Γ strongly depends on the source type, and our sample is highly heterogeneous. Thus, we decide to fix the photon index of the sources with a missing S or H count rate to Γ ≡ 1 . 8, following Puccetti et al. (2011). In fact, they computed the most probable hardness ratio value ( HR = -0 . 5) in a subsample of their catalog comprising all the high Galactic-latitude ( | b | > 20 deg) sources. This HR value, combined with the median of the Galactic Hydrogen column density ( NH = 3 . 3 × 10 20 cm -2 , Kalberla et al. 2005), corresponds to Γ = 1 . 8. This choice should provide a reliable flux estimate for our extragalactic sources, which constitute most of our catalog. However, the reader must be aware that the flux computed this way may represent just a rough estimate for other type of sources (see also next sub-section for a more detailed description about the flux uncertainties). The faintest fluxes sampled by our survey belong to the sources detected in the deepest observations. In detail, we find that the flux interval sampled by the detected sources is in the range 7 . 4 × 10 -15 -9 . 1 × 10 -11 , 3 . 1 × 10 -15 -1 . 1 × 10 -11 and 1 . 3 × 10 -14 -9 . 1 × 10 -11 erg cm -2 s -1 for the F, S and H band, respectively. We provide 90% count rate and flux upper limits every time a source is not detected in one or two of the considered bands. The 90% count upper limit for a given background is defined as the number of counts necessary to be interpreted as a background fluctuation with a probability of 10% or less, according to a Poissonian distribution. In other words, if the background of our field is B , we are searching the upper limit X for which where M is the number of counts measured at the position of each source in a region of 16 . 5 arcsec radius, which corresponds to a fraction of the point spread function of ∼ 68%. Eq. (1) does not take into account possible background fluctuations that may arise close to the considered source. The correction factor has been evaluated by Puccetti et al. (2011) following the recipe in Bevington and Robinson (1992). They found that the factor 1 . 282 × σ (with σ ( B ) = √ B describing the Poissonian background fluctuations) must be added to the count upper limits. The count rate upper limits are finally evaluated from these counts (which are corrected for the non-included PSF fraction of the cell), by dividing them for the net exposure, which takes into account the vignetting at the source position. Flux upper limits are computed from count rate upper limits, adopting the appropriate N H and assuming Γ = 1 . 8, as explained before.",
"pages": [
5,
6
]
},
{
"title": "4.4. Uncertaintiesandsourcereliability",
"content": "Detect count rates are associated with their statistical (Poissonian) uncertainties. These errors are propagated to the flux estimates, but here the main uncertainty is the variety of the spectral behaviour of di ff erent sources. In order to determine the flux variation with the spectral parameters, we estimate the count rate-to-flux conversion factors for a wide range of spectral slopes ( Γ = 0 -2) and Hydrogen column densities ( NH = 10 19 -10 22 cm -2 ). The conversion factors are in the range (2 . 9 -15) × 10 -11 , (0 . 9 -1 . 5) × 10 -11 and (8 . 1 -17) × 10 -11 erg cm -2 s -1 for the F, S and H band, respectively. The conversion factor for the F band is more sensitive to the spectral shape than for the S and H bands, because this band is wider. Concerning the source positions, their errors are both statistical and systematic, with the total positional uncertainty being: The systematic error σ sys is due to the uncertainty on the XRT aspect solution. This quantity has been estimated by Puccetti et al. (2011) by cross-correlating a sub-sample of bright sources of their XRT-deep catalog with the SDSS optical galaxy catalog. They found that the mean σ sys at the 68% confidence level is 2 . 05 arcsec, a value consistent with previous results by Moretti et al. (2006). This value represents the number we will adopt in estimating the positional error in Eq. 2. The statistical variance σ 2 stat is instead inversely proportional to the source number counts. To assess the reliability of our detections we must address the possibility of source confusion. The source confusion issue arises when two close sources are detected as a single one. This problem may be important if the distances between two objects is of the order of the cell detection of the algorithm detect . To evaluate the possibility of source confusion, we compute the probability of finding two sources with a X-ray flux higher than a certain threshold Flim , lying at a distance smaller than θ min : Here we adopt as θ min twice the typical size of the cell detection box (4 pixels or 9 . 44 arcsec), while N is the number counts corresponding to Flim , which can be evaluated, e.g., from the CCOSMOS survey (Elvis et al. 2009). Our deepest field has an exposure of ∼ 100 ks. Using the Flim corresponding to the count rates of the faintest sources detected in this field ( ∼ 1 . 7 × 10 -4 and ∼ 1 . 5 × 10 -4 cts / s in the S and H band, respectively), we find that the source confusion probability is less than 3% in both the S and H band. This is of course the field in which the source confusion probability is highest. For fields of ∼ 10 ks ( ∼ 93% of our sample has exposures < 10 ks) the flux limits are shallower by a factor of ∼ 3. Applying Eq. (3) to these fields results in a probability of source confusion of ∼ 0 . 9% and ∼ 0 . 3% in the S and H band, respectively. This means that source confusion is negligible in our sample.",
"pages": [
6,
7
]
},
{
"title": "4.5. 1SWXRTdescription",
"content": "The final catalog comprises 32 field parameters for each entry. Source name, position, count rates and fluxes, exposure, hardness ratio and galactic NH are reported, together with the corresponding uncertainties and / or reliabilities. A full description of all the parameters is presented in Table 3. Table 4 gives instead the first ten entries of the catalog as an example.",
"pages": [
7
]
},
{
"title": "5. Scientific use of the catalog",
"content": "A full exploitation of the scientific data presented in this work is far beyond the scope of the present paper. Nevertheless, we would like to draw the reader's attention to some of the scientific topics that can be addressed using 1SWXRT.",
"pages": [
7
]
},
{
"title": "5.1. Short-termvariability",
"content": "As stated in the previous section, in our analysis we do not merge observations pointing to the same field, so we can study the variability of sources observed more than once. Since many observations are often performed consecutively, this enables to determine short-term variability for the involved sources. Our database comprises 12,908 sources observed at least twice. Among these, we select all sources detected in each obser- vation in the soft or hard band. 7,936 and 2,113 sources are detected in the soft and hard band, respectively. Fig. 9 plots the distribution of the number of sources observed many times, while Fig. 10 displays the histogram for the variability as a function of the σ significance. The number of sources in the soft band with a variation larger than 3 σ and 5 σ is 1,774 and 623, respectively, i.e., a fraction of 22% and 7 . 7% of the total soft sources. Similarly, the number of sources in the hard band with a variation larger than 3 σ and 5 σ is 447 and 148, respectively, i.e., a fraction of 23% and 7 . 6% of the total hard sources. Thus, variability is observed in both bands, and with similar trends. However, some tens of sources show extreme variability (Fig. 10). The ratio of such extreme variable sources with respect to the total number grows stronger in the hard band with respect to the soft one as the significance of the variability increases. For example, the fraction of sources which vary at more than 10 σ is 1 . 7% and 1 . 9% in the soft and hard band, respectively, while at the 20 σ level, the fractions become 0 . 4%(soft) and 0 . 7%(hard). We then select all the sources observed at least 5 times. Fig. 11 shows the cumulative distribution of the statistical significance of the variability for sources with five observations or more. This variability significance has been computed with respect both to the maximum and to the minimum fluxes. It interesting to note that the variability is more pronounced when considering the maximum fluxes. In other words, the average fluxes are in general closer to the minimum values than to the maximum ones. This could be a possible indication that we are observing short-duration flares in some sources, with the normal state being close to the minimum value observed.",
"pages": [
7,
8,
9
]
},
{
"title": "5.2. Softsources",
"content": "We can use our dataset to study sources showing emission in the soft band only. Among these, one important class is rep- resented by isolated neutron stars (INS, see, e.g., Treves et al. 2000; Haberl et al. 2003; Haberl 2004). INS are blank field sources, i.e., X-ray sources with no or very faint counterparts in other wavelength domains. Concerning the X-ray-to-optical flux ratio, values of fX / fopt > 10 3 define the INS class, but in some cases values as high as 10 5 have been reported. The X-ray emission is supposed to be produced by some residual internal energy (coolers) or because they are interacting with the interstellar medium (accretors). The INS X-ray spectrum is well fitted by a soft blackbody, with temperatures of ∼ 100 eV. This means that basically no X-ray emission above ∼ 2 keV is expected. Given the low column densities measured for these objects, the emission is consistent with being produced from the neutron star surface (see, e.g., Walter & Lattimer 2002). Other characteristics often exhibited by these sources (coolers) are a periodicity of ∼ 5 -10 s, absorption features below 1 keV and closeness. These elusive sources are of extreme importance, because they could represent ∼ 1% of the total number of stars in our Galaxy. To pinpoint their properties means to understand the end-point of the evolution of a large class of stars. To date, only 8 -10 objects of this class have been identified. In order to check our catalog for the presence of INS, and in general to categorize the soft objects, we selected all sources that do not show emission in the full and hard band. When considering objects observed more than once, we excluded from our analysis all sources in which there is a detection in the full or hard band in at least one observation. This helps us to include in our sample just genuine soft emitters, and to exclude part of the sources that are possibly not detected in the hard band due to low exposure times. We selected 2087 objects following the above criteria. Fig. 12 displays the 0 . 5 -2 keV flux distribution for these sources. The histogram bin size is set to 0 . 05 dex. Since the soft band is in general more sensitive than the hard one, the faint part of this distribution can still comprise normal sources that are not detected in the 2 -10 keV range due to a flux level below the sensitivity threshold. However, we determined the number of XRT sources featuring at least 50 or 100 counts in the 0 . 5 -2 keV band, without detection in the 2 -10 one. We obtain 7 sources with at least 50 counts. Of these, 3 have more than 100 counts. These seven objects are good INS candidates.",
"pages": [
9,
10
]
},
{
"title": "5.3. Hardsources",
"content": "In a similar way to what described in the previous sub-section, we can search our dataset for sources which show emission in the hard band only. To categorize the hard objects, we selected all sources that do not show emission in the full and soft band. When considering objects observed more than once, we excluded from our analysis all sources in which there is a detection in the full or soft band in at least one observation. This helps us to include in our sample just genuine hard emitters, and to exclude part of the sources that are possibly not detected in the soft band due to a low exposure time coupled with an unusual background level. 308 objects in our dataset fulfill the above criteria. Fig. 13 displays the 2 -10 keV flux distribution for these sources. The histogram bin dimension is set to 0 . 1 dex. The hard band is less sensitive than the soft one. Thus, contrary to the case of the soft sources, we are confident that this sub-sample contains genuine hard sources only. The main type of objects contributing to this sub-sample are expected to be obscured Active Galactic Nuclei (AGN), whose discovery and study is very important both to study the properties and evolution of the accretion process onto supermassive black holes residing at the center of galaxies and to determine their contribution to the X-ray background, in particular to its peak emission in the 20-30 keV band that still remains largely unexplained (see, e.g., Gilli et al. 2007; Treister et al. 2009, and references therein). In future works we will investigate on the nature of these sources in order to determine their properties and nature.",
"pages": [
10
]
},
{
"title": "5.4. Cross-correlationwithmulti-wavelengthcatalogs",
"content": "Our catalog can be cross-correlated with multi-wavelength ones, to obtain statistical information about specific class of sources. Here, we cross-correlated the XRT catalog with BZCAT, a multifrequency catalogue of blazars (Massaro et al. 2009). We stress that this is just an example, and that many more crosscorrelations with other catalogs can be performed to fully exploit 1SWXRT. Blazars are radio loud AGN pointing their jets in the direction of the observer (see e.g. Urry & Padovani 1995). They come in two main subclasses, the Flat Spectrum Radio Quasars (FSRQs), which show strong, broad emission lines in their optical spectrum, just like radio quiet QSOs, and BL Lacs, which are instead characterized by an optical spectrum, which at most shows weak emission lines or is completely featureless. The strong non-thermal radiation is composed of two basic parts forming two broad humps in the ν vs. ν F ν plane, the low-energy one attributed to synchrotron radiation, and the high-energy one, usually thought to be due to inverse Compton radiation (Abdo et al. 2010). The peak of the synchrotron hump ( ν S peak ) can occur at di ff erent frequencies. In FSRQs ν S peak never reaches very high values ( ν S peak < ∼ 10 14 . 5 Hz), whereas the ν S peak of BL Lacs can reach values as high as ν S peak > ∼ 10 18 Hz (e.g. Giommi et al. 2012). The cross-correlation between the BZCAT and 1SWXRT catalogs has been performed by matching the coordinates over an error radius of 0 . 2 arcmins. We found 938 sources in 1SWXRT with a BZCAT counterpart. Of these, 524 are FSRQs and 414 are BL Lacs. Fig. 14 shows the X-ray spectral index distribution for these sources. It is evident that BL Lac distribution is softer than FSRQ one. This is because the X-ray 0 . 5 -10 keV band samples on average the high energy tail of the synchrotron emission in BL Lacs, where ν F ν is decreasing. On the other hand, the same energy band describes, on average, the low energy tail of the inverse Compton emission in FSRQs, where ν F ν is instead increasing. For comparison, Fig. 14 plots also the Xray spectral index of the stars, obtained by cross-correlating the XRT catalog with the Smithsonian Astrophysical Observatory Star Catalog (SAO), and that of the unidentified sources.",
"pages": [
10,
11
]
},
{
"title": "6. Summary and conclusions",
"content": "We have reduced and analyzed all the observations performed by Swift -XRT in PC mode with an exposure time longer than 500 s, during its first seven years of operations, i.e., between 2005 and 2011. Approximately 35,000 XRT fields have been analyzed, with net exposures (after screening and filtering criteria being applied) ranging from 500 s to 100 ks. The total, net exposure time is ∼ 140 Ms. For all the entries of 1SWXRT, we determined the position, the detection probability and the signal-to-noise ratio. Count rates were estimated in the 0 . 3 -10, 0 . 3 -3 and 2 -10 keV bands. Each source has a detection in at least one of these bands, with ∼ 80,000, ∼ 70,000 and ∼ 25,500 sources detected in the full, soft and hard band, respectively. 90% upper limits were provided in case of missing detection in one or two of these bands. The purpose of this work was to create a catalog (1SWXRT) of all the point like sources detected in these observations. To this purpose, we run the XIMAGE detect algorithm to all our fields, and then removed spurious and extended sources through visual inspection of the XRT observations. The total number of point-like objects detected is 89 , 053, of which 2 , 166 are GRB detections (so transient sources by definition) and 1 , 947 are sources a ff ected by pile-up. Thus, our final version of the catalog comprises 84 , 992 entries, which define the 'good' sample. Many entries represent the same sources, since several portions of the sky have been observed many times by XRT. To estimate an approximate number of distinct, celestial sources, we compress our catalog over a radius of 12 arcsec, a typical positional uncertainty value in faint XRT sources. In other words, all entries closer than 12 arcsec are counted once, and the result of this procedure is ∼ 36,000 distinct sources. The count rates were converted into fluxes in the 0 . 5 -10, 0 . 5 -2 and 2 -10 keV X-ray bands. The flux interval sampled by the detected sources is 7 . 4 × 10 -15 -9 . 1 × 10 -11 , 3 . 1 × 10 -15 -1 . 1 × 10 -11 and 1 . 3 × 10 -14 -9 . 1 × 10 -11 erg cm -2 s -1 for the full, soft and hard band, respectively. Among the possible scientific uses of 1SWXRT, we discussed the possibility to study short-term variability, the identification of sources emitting in the soft or hard band only, and the cross correlation of our catalogue to multiwavelength ones. Acknowledgements. We thank the referee for a quick and careful reading of the manuscript. This work has been supported by ASI grant I / 004 / 11 / 0. JPO acknowledges financial support from the UK Space Agency",
"pages": [
11
]
},
{
"title": "References",
"content": "Abbey T., Carpenter J., Read A. et al. 2006, The X-Ray Universe 2005, 604, 943 Abdo A.A., Ackermann M., Agudo I. et al. 2010, 2010, ApJ, 716, 30, Bevington P.R. & Robinson K. 1992, Data Reduction and Error Analysis for the Physical Sciences (the McGraw-Hill Companies, Inc.) Barthelmy S.D., Barbier L.M., Cummings, J. R. et al. 2005, SSR, 120, 143 Burrows D.N., Hill J.E., Nousek J.A. et al. 2005, SSR 120, 165 Capalbi M., Perri M. Saija B. Tamburelli F. & Angelini L. 2005, http: // heasarc.nasa.gov / docs / swift / analysis / xrt swguide v1 2.pdf Elvis M., Civano F., Vignali C., et al. 2009, ApJS, 184, 158 Evans I.N., Primini F.A., Glotfelthy K.J et al. 2010, ApJ, 189, 37 437, 845 Gehrels N., Chincarini G., Giommi P., et al. 2004, ApJ 621, 558 Gilli, R., Comastri, A., Hasinger, G. 2007, A&A, 463, 79 Giommi P., et al., 2012, A&A, 514, 160 Haberl F, Schwope A.D., Hambaryan V., Hasinger G. & Motch C. 2003, A&A,",
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{
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"content": "Haberl F 2004, MemSAIt, 75, 454 Hill J.E., Burrows D.N., Nousek J.A. et al. 2004, SPIE, 5165, 217 Kalberla P.M.W., Burton W.B., Hartmann D. et al. 2005, A&A, 440, 775 Massaro E, Giommi P., Leto C., Marchegiani P., Maselli A., Perri M., Piranomonte S., Sclavi S. 2009, A&A, 495, 691 Moretti A, Perri M., Capalbi M., et al. 2006, A&A, 448, L9 Puccetti S., Capalbi M., Giommi P. et al. 2011, A&A, 528, 122 Romano P 2012, Mem SAIt, 19, 306 Sari R. & Piran T. 1998, MNRAS, 287, 110 Tundo E., Moretti A., Tozzi P., Teng L., Rosati P., Tagliaferri G., Campana S. 2012, A&A, 547, 57 Urry M. & Padovani P. 1995, PASP, 107, 83 Nature 461, 1254 Treister E., Urry C.M., Virani S. 2009, ApJ, 696, 110 Treves A., Turolla R., Zane S. & Colpi M. 2000, PASP, 112, 297 468, 83 Walter F.M. & Lattimer J.M. 2002, ApJ, 576, 145 Watson M.G., Schroder A.C., Fyfe D. et al. 2009, A&A, 493, 339",
"pages": [
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}
]
2013A&A...552A...1P
https://arxiv.org/pdf/1303.3653.pdf
<document>
<section_header_level_1><location><page_1><loc_9><loc_85><loc_93><loc_87></location>Size and disk-like shape of the broad-line region of ESO399-IG20</section_header_level_1>
<text><location><page_1><loc_7><loc_81><loc_94><loc_84></location>Francisco Pozo Nu˜nez 1 , Christian Westhues 1 , Michael Ramolla 1 , Christoph Bruckmann 1 , Martin Haas 1 , Rolf Chini 1 ; 2 , Katrien Steenbrugge 2 ; 3 , Roland Lemke 1 , and Miguel Murphy 2</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_78><loc_74><loc_79></location>1 Astronomisches Institut, Ruhr-Universitat Bochum, Universitatsstraße 150, 44801 Bochum, Germany</list_item>
<list_item><location><page_1><loc_11><loc_77><loc_81><loc_78></location>2 Instituto de Astronomia, Universidad Cat'olica del Norte, Avenida Angamos 0610, Casilla 1280 Antofagasta, Chile</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_62><loc_76></location>3 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_72><loc_44><loc_73></location>Received January 6, 2013; Accepted February 5, 2013</text>
<section_header_level_1><location><page_1><loc_47><loc_70><loc_55><loc_71></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_58><loc_91><loc_68></location>We present photometric reverberation mapping of the narrow-line Seyfert 1 galaxy ESO399-IG20 performed with the robotic 15 cm telescope VYSOS-6 at the Cerro Armazones Observatory. Through the combination of broad- and narrow-band filters we determine the size of the broad-line emitting region (BLR) by measuring the time delay between the variability of the continuum and the H GLYPH<11> emission line. We use the flux variation gradient method to separate the host galaxy contribution from that of the active galactic nucleus (AGN), and to calculate the 5100Å luminosity L AGN of the AGN. Both measurements permit us to derive the position of ESO399-IG20 in the BLR size - AGN luminosity R BLR / L 0 : 5 AGN diagram. We infer the basic geometry of the BLR through modelling of the light curves. The pronounced sharp variability patterns in both the continuum and the emission line light curves allow us to reject a spherical BLR geometry. The light curves are best fitted by a disk-like BLR seen nearly face-on with an inclination angle of 6 GLYPH<14> GLYPH<6> 3 GLYPH<14> and with an extension from 16 to 20 light days.</text>
<text><location><page_1><loc_11><loc_55><loc_91><loc_57></location>Key words. galaxies: active -galaxies: Seyfert -quasars: emission lines -galaxies: distances and redshifts -galaxies: individual: ESO399-IG20</text>
<section_header_level_1><location><page_1><loc_7><loc_51><loc_19><loc_52></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_16><loc_50><loc_48></location>The physical properties of the broad line region (BLR) in active galactic nuclei (AGN) have been extensively studied during the last three decades. Consensus has been reached that the luminosity variations of the continuum emitting region of the hot accretion disk produce variations of the broad emission lines with a delay due to the light travel time across the BLR. To date, the only method independent on spatial resolution is reverberation mapping (Blandford & McKee 1982; Peterson 1993), in which one measures the time delay or 'echo' between the continuum variability and the variability observed in the broad emission lines. This method has been used successfully for determining the BLR size, kinematics and black hole mass ( MBH ) of several Type-1 AGNs. RM provides basic MBH estimates through the virial product MBH = f GLYPH<1> RBLR GLYPH<1> GLYPH<27> 2 V = G , where G is the gravitational constant, RBLR = c GLYPH<1> GLYPH<28> is the BLR size, GLYPH<27> V is the emissionline velocity dispersion of the BLR gas and the factor f depends on the - so far unknown - geometry and kinematics of the BLR (Peterson et al. 2004 and references therein). Furthermore, as a widely used extrapolation of locally obtained RM results to higher redshift data, MBH has be estimated using the BLR Size-Luminosity R BLR / L 0 : 5 AGN relationship (Koratkar & Gaskell 1991; Kaspi et al. 1996, Kaspi et al. 2000; Wandel et al. 1999; McGill et al. 2008; Vestergaard et al. 2011). However, a reliable MBH estimation from the luminosity requires a considerable reduction of the R GLYPH<0> L dispersion present.</text>
<text><location><page_1><loc_7><loc_10><loc_50><loc_15></location>As the size of the BLR ranges from a few to several hundred light days, it is necessary to perform observational monitoring campaigns ranging from months to years in order to su GLYPH<14> ciently sample the time domain of the echo. Most observational RM</text>
<text><location><page_1><loc_52><loc_49><loc_95><loc_52></location>campaigns have used spectroscopic monitoring of the sources, which however requires large amounts of telescope time.</text>
<text><location><page_1><loc_52><loc_36><loc_95><loc_49></location>Recently, Haas et al. (2011) proposed photometric reverberation mapping (PRM) as an e GLYPH<14> cient method to determine the BLR size through the use of broad band filters to trace the AGN continuum variations and narrow-band filters to catch the BLR emission line response. Because the narrow-band collects both the emission line flux and the underlying continuum, the challenge is to extract the pure emission line light curve. In the dedicated case study of 3C120, Pozo Nu˜nez et al. (2012) demonstrated that PRM reaches an accuracy similar to spectroscopic RM(Grier et al. 2012).</text>
<text><location><page_1><loc_52><loc_15><loc_95><loc_36></location>Another e GLYPH<14> cient approach to determine the BLR size has been proposed by Chelouche & Daniel (2012), through the analysis of the di GLYPH<11> erence between the cross-correlation (CCF) and the auto-correlation (ACF) functions for suitably chosen broad band filters, one filter covering a bright emission line and one covering only the continuum. While this method does not place a strict requirement on the object's redshift such that the emission line falls into the narrow-band filter (as in the case proposed by Haas et al. 2011), the use of broad band filters only (as proposed by Chelouche & Daniel 2012) limits the application of PRM to cases with a su GLYPH<14> ciently strong emission line contribution in the respective filter used. Despite of this handicap, this method has been successfully applied to determine the BLR size for one low-luminosity AGN NGC4395 (Edri et al. 2012) and one highz luminous MACHO quasar (Chelouche et al. 2012) consistent with previous spectroscopic RM results.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_15></location>A fundamental issue in both these methods is to separate the host-galaxy contribution from the total luminosity to calculate the AGN luminosity. An incorrect determination of the nuclear AGN luminosity (due to the contamination of the host compo-</text>
<text><location><page_2><loc_7><loc_70><loc_50><loc_93></location>nent) causes an overestimation of the linear regression slope GLYPH<11> . This has been demonstrated by Bentz et al. (2009a), who presented the most recent compilation of host-subtracted AGN luminosities for several reverberation-mapped Seyfert 1 galaxies obtained through host-galaxy modeling of high-resolution Hubble Space Telescope (HST) images. Compared to the previous slope of GLYPH<11> = 0 : 7 they determined an improved slope of GLYPH<11> = 0.519 0 : 063 GLYPH<0> 0 : 066 close to GLYPH<11> = 0 : 5 expected from photo-ionization models of the BLR (Davidson & Netzer 1979). A di GLYPH<11> erent approach to estimate the host galaxy contribution is the flux variation gradient method (FVG, Choloniewski 1981; Winkler 1997). An advantage is that it does not require high spatial resolution imaging and can be applied directly to the monitoring data. Recently, FVG has been tested on PRM data (Haas et al. 2011; Pozo Nu˜nez et al. 2012). These tests show that by using a well defined range for the host galaxy slope (Sakata et al. 2010) it is possible to separate the AGN contribution at the time of the monitoring campaigns.</text>
<text><location><page_2><loc_7><loc_44><loc_50><loc_69></location>ESO399-IG20 has been classified as a Narrow-Line Seyfert 1 (NLS1) galaxy (V'eron-Cetty & V'eron 2010). It has often been speculated that the lack of broad emission lines of - at least - part of the NLS1 population can be explained by face-on disk-like BLR geometries. Single-epoch spectroscopic investigations by Dietrich et al. (2005) show high-ionized gas orbiting at high velocities, producing strong broad profiles (FWHM(H GLYPH<12> ) = 2425 GLYPH<6> 121 km / s, see their Table 3 and Figures 2-5) like in Broad-Line Seyfert 1 (BLS1) galaxies. Furthermore, they find a strong host-galaxy contribution with respect to the total observed 5100Å continuum flux ( GLYPH<24> 50%). Here, we present the first measurement of the BLR size and the host-subtracted AGN 5100Å luminosity for ESO399-IG20. Both results allow us to infer its position in the BLR size-Luminosity R BLR / L 0 : 5 AGN diagram. Additionally, pure broad-band PRM (Chelouche & Daniel 2012) is applied and compared with the broad- and narrow-band PRM technique (Haas et al. 2011). Finally, the geometry of the BLR, whether spherical or an inclined disk, is inferred via light curve modeling.</text>
<section_header_level_1><location><page_2><loc_7><loc_36><loc_36><loc_37></location>2. Observations and data reduction</section_header_level_1>
<text><location><page_2><loc_7><loc_25><loc_50><loc_34></location>Broad-band Johnson B (4330 Å), Sloan-band r (6230 Å) and the redshifted H GLYPH<11> (SII 6721 GLYPH<6> 30 Å at z = 0.0249) images were obtained with the robotic 15 cm VYSOS6 telescope of the Universitatssternwarte Bochum, located near Cerro Armazones, future location of the ESO Extreme Large Telescope (ELT) in Chile. Monitoring occurred between May 5 and November 18 of 2011, with a median sampling of 3 days.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_24></location>ESO399-IG20 lies at redshift z = 0 : 0249, therefore the H GLYPH<11> emission line falls into the SII 6721 GLYPH<6> 30Å narrow-band filter. Figure 1 shows the position of the narrow-band with respect to the H GLYPH<11> emission line together with the e GLYPH<11> ective transmission of the other filters used. The H GLYPH<11> line is broader than the SII filter, however, simulations with di GLYPH<11> erent asymmetric and perfect symmetric cutting of the high-velocity line wings show negligible systematic e GLYPH<11> ect introduced in the time delay ( GLYPH<24> 2%), even considering the fact of only using one part of the wing profile. This e GLYPH<11> ect will be discussed in depth in a forthcoming contribution (Bruckmann et al. 2012., in preparation).</text>
<figure>
<location><page_2><loc_55><loc_74><loc_93><loc_92></location>
</figure>
<figure>
<location><page_2><loc_55><loc_53><loc_93><loc_72></location>
<caption>Fig. 1. E GLYPH<11> ective transmission of the VYSOS6 filters convolved with the quantum e GLYPH<14> ciency of the ALTA U16M CCD camera (top). The position of the narrow-band [SII] 6721Å filter (red line) and the simulated redshifted gaussian-shaped H GLYPH<11> emission line using the parameters obtained by Dietrich et al. (2005) (black line) are shown in the bottom panel.</caption>
</figure>
<text><location><page_2><loc_52><loc_30><loc_95><loc_42></location>Data reduction was performed using IRAF 1 , in combination with SCAMP (Bertin 2006) and SWARP (Bertin et al. 2002) routines, in the same manner as described by Haas et al. (2012). Light curves were extracted using di GLYPH<11> erent apertures (5', 7 : 00 5, 15' and 25') in order to compare and trace the host and AGN contribution. The light curves for the di GLYPH<11> erent apertures are shown in Figure 2. Additionally, for each aperture we determined the level of variability using the fractional flux variation introduced by Rodriguez-Pascual et al. (1997):</text>
<formula><location><page_2><loc_52><loc_26><loc_95><loc_29></location>F var = p GLYPH<27> 2 GLYPH<0> GLYPH<1> 2 h f i (1)</formula>
<text><location><page_2><loc_52><loc_16><loc_95><loc_25></location>where GLYPH<27> 2 is the flux variance of the observations, GLYPH<1> 2 is the mean square uncertainty, and h f i is the mean observed flux. The variability statistics is listed in Table 2. Selecting a small aperture (5') we are only considering a small portion of the total flux, which remains heavily dependent on the quality of the PSF, whereas bigger apertures (15' and 25'), enclose more contribution of the host-galaxy and the results are more sensitive to</text>
<figure>
<location><page_3><loc_11><loc_64><loc_49><loc_92></location>
</figure>
<figure>
<location><page_3><loc_11><loc_33><loc_49><loc_62></location>
</figure>
<figure>
<location><page_3><loc_54><loc_64><loc_92><loc_92></location>
</figure>
<figure>
<location><page_3><loc_54><loc_33><loc_92><loc_62></location>
<caption>Fig. 2. B , r -Sloan and SII-bands light curves for di GLYPH<11> erent apertures (5' upper left, 7.5' lower left, 15' upper right and 25' lower right). The light curves have been corrected for foreground galactic extinction using the values given in Table 1.</caption>
</figure>
<text><location><page_3><loc_7><loc_10><loc_50><loc_27></location>sky background contamination resulting in larger uncertainties. We found that 7 : 00 5 around the nucleus is the right size aperture which maximizes the signal-to-noise ratio (S / N) and delivers the lowest absolute scatter for the fluxes. Thus, we use this aperture for the further analysis of the BLR size and AGN luminosity. Although the light curves in Figure 2 have not yet been corrected for the host galaxy contribution, one can see that the fractional variation ( Fvar ) and the ratio of the maximum to minimum fluxes ( Rmax ) are higher in the B -band than in the r -band for which the host-galaxy present a greater contribution. A di GLYPH<11> erent case can be seen in the SII light curves, which are mostly dominated by the contribution of the H GLYPH<11> emission line resulting in a higher amplitude of variability. As expected, for bigger apertures the B</text>
<text><location><page_3><loc_52><loc_24><loc_95><loc_27></location>and r light curves become flatter with Fvar and Rmax smaller due to the larger contribution from the host-galaxy.</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_22></location>Non-variable reference stars located on the same field and with similar brightness as the AGN were used to create the relative light curves in normalized flux units. For the absolute photometry calibration we used reference stars from Landolt (2009) observed on the same nights as the AGN, considering the atmospheric extinction for the nearby site Paranal by Patat et al. (2011) and the recalibrated galactic foreground extinction presented by Schlafly & Finkbeiner (2011) obtained from the Schlegel et al. (1998) dust extinction maps. In Table 1, we give the characteristics of ESO399-IG20. A summary of the photo-</text>
<table>
<location><page_4><loc_24><loc_87><loc_78><loc_91></location>
<caption>Table 1. Characteristics of ESO399-IG20</caption>
</table>
<table>
<location><page_4><loc_10><loc_71><loc_92><loc_80></location>
<caption>Table 2. Light Curve Variability Statistics.</caption>
</table>
<text><location><page_4><loc_7><loc_66><loc_95><loc_70></location>Note. Column 1 list the aperture in arc-seconds, Columns 2-5 list the mean flux, the standard deviation, the normalized excess variance and the ratio of the maximum to minimum fluxes for the continuum light curve. Similarly, columns 6-13 list the variability for the r and SII bands respectively. The standard deviation and the mean fluxes are expressed in units of mJy.</text>
<table>
<location><page_4><loc_25><loc_57><loc_77><loc_61></location>
<caption>Table 3. Summary of the photometry results for 7 : 00 5 aperture.</caption>
</table>
<text><location><page_4><loc_7><loc_50><loc_50><loc_52></location>metric results and the fluxes in all bands are listed in Table 3 and Table 4, respectively.</text>
<section_header_level_1><location><page_4><loc_7><loc_46><loc_29><loc_47></location>3. Results and discussion</section_header_level_1>
<section_header_level_1><location><page_4><loc_7><loc_44><loc_29><loc_45></location>3.1. Light curves and BLR size</section_header_level_1>
<text><location><page_4><loc_7><loc_20><loc_50><loc_43></location>The B -band, which is dominated by the AGN continuum, shows a strong flux increase (about 35%) between the beginning and the end of May. Afterwards, the two measurements obtained in June reflect a more gradual increase until a maximum is reached at the end of July. After this maximum, the fluxes decreases gradually (about 20%) until the end of September, and then the light curves become more constant until middle of November. Likewise, the r -band, which is dominated by the continuum but also contains a contribution from the strong H GLYPH<11> emission line, follows the sames features as the B -band light curve, although with a lower amplitude. In contrast to the continuum dominated broad-band light curves, the narrow SII-band light curve exhibits a flux increase which is stretched. For instance the prominent maximum in the B - and r - band at the end of July occurs in the SII-band in August, giving a first approximation for the H GLYPH<11> time delay of 15-20 days. Note that the visual inspection of the r - and B -band light curves does not allow an approximation for the time delay.</text>
<text><location><page_4><loc_7><loc_10><loc_50><loc_20></location>As already discussed in previous PRM studies, the narrowband contains a contribution of the varying continuum, which must be removed before applying cross correlation techniques (Haas et al. 2011; Pozo Nu˜nez et al. 2012). In order to determine this contribution, we used the SII and r -band fluxes, previously calibrated to mJy, as is shown with the flux-flux diagram in Figure 3. The H GLYPH<11> line is strong contributing, on average, about 70% of the total flux enclose in the SII-band, while the con-</text>
<figure>
<location><page_4><loc_56><loc_27><loc_92><loc_51></location>
<caption>Fig. 3. Flux-flux diagram for the SII and r band measured using 7.5' aperture. Black dots denote the measurement pair of each night. The straight red and green lines represents the average flux in the SII and r band respectively. The data are as observed and not corrected for galactic foreground extinction.</caption>
</figure>
<text><location><page_4><loc_52><loc_10><loc_95><loc_16></location>inuum contribution ( r -band) is about 30%. Following the usual practice of PRM, we construct a synthetic H GLYPH<11> light curve by subtracting a third of the r -band flux (H GLYPH<11> = SII GLYPH<0> 0.3 r ). The H GLYPH<11> light curve was used afterwards to estimate the time delay. For this purpose, we used the discrete correlation function (DCF,</text>
<table>
<location><page_5><loc_24><loc_46><loc_77><loc_91></location>
<caption>Table 4. B , r , S II and H GLYPH<11> Fluxes corrected by extinction.</caption>
</table>
<text><location><page_5><loc_7><loc_14><loc_50><loc_43></location>Edelson & Krolik 1988) to cross-correlate the continuum and the synthetic H GLYPH<11> emission line, taking into account possible bin size dependency (Rodriguez-Pascual et al. 1989). The centroid in the cross-correlation of B -band and H GLYPH<11> show a time delay of 18.1 days, while the centroid in the cross-correlation between B -band and SII-band yields a time delay of 15.8 days. However, this is an expected result because of the more pronounced peak at zero lag due to the contamination by the continuum emission in the narrow-band filter. Both cross-correlation functions are shown in Figure 4. Uncertainties in the time delay were calculated using the flux randomization and random subset selection method (FR / RSS, Peterson et al. 1998b; Peterson et al. 2004). From the observed light curves we create 2000 randomly selected subset light curves, each containing 63% of the original data points (the other fraction of points are unselected according to Poisson probability). The flux value of each data point was randomly altered consistent with its (normal-distributed) measurement error. We calculated the DCF for the 2000 pairs of subset light curves and the corresponding centroid (Figure 5). From this cross-correlation error analysis, we measure a median lag of GLYPH<28> cent = 18.7 + 2 : 5 GLYPH<0> 2 : 2 . Correcting for the time dilation factor (1 + z = 1 : 0249) we obtain a rest frame lag of 18 : 2 GLYPH<6> 2 : 29 days.</text>
<text><location><page_5><loc_7><loc_10><loc_50><loc_13></location>An alternative method to estimate the time delay, called Stochastic Process Estimation for AGN Reverberation (SPEAR), has been worked out recently by Zu et al. (2011).</text>
<text><location><page_5><loc_52><loc_31><loc_95><loc_43></location>Through the modeling of the AGN light curves as a damped random walk (DRW) (Zu et al. 2011; Zu et al. 2012 and reference therein), this method appears to be consistent with previous cross-correlation techniques (e.g. Grier et al. (2012) for spectroscopic reverberation data). Using the SPEAR code 2 on our light curves, we obtain a time delay of GLYPH<28> spear = 18.4 + 1 : 2 GLYPH<0> 1 : 0 . After correction for time dilation the rest frame lag GLYPH<28> rest = 17.9 GLYPH<6> 1 : 1 days, in agreement with the results from the DCF method. Figure 6 shows the SPEAR light curve models.</text>
<section_header_level_1><location><page_5><loc_52><loc_28><loc_87><loc_29></location>3.2. Broad-band reverberation mapping approach</section_header_level_1>
<text><location><page_5><loc_52><loc_13><loc_95><loc_27></location>Recently, pure broad-band photometric RM has been introduced as an e GLYPH<14> cient alternative to measure the BLR size in quasars (Chelouche & Daniel 2012). In this method, the emission line is also measured using a broad-band filter, and the removal of the underlying continuum is performed in the correlation domain. The centroid of the lag is obtained by the subtraction of the auto-correlation function ( ACF ) between the continuum (represented by one broad band filter enclosing only continuum emission) from the cross-correlation function ( CCF ) between the continuum and the emission line (represented by one broadband filter that contains a su GLYPH<14> ciently strong emission line con-</text>
<figure>
<location><page_6><loc_10><loc_73><loc_47><loc_91></location>
<caption>Fig. 4. Cross correlation of B and SII light curves (dotted line) and of B and H GLYPH<11> light curves (dashed line). The error range ( GLYPH<6> 1 GLYPH<27> ) around the cross correlation was omitted for better viewing. The red and black shaded areas marks the range used to calculate the centroid of the lag (vertical red and black straight lines).</caption>
</figure>
<figure>
<location><page_6><loc_10><loc_38><loc_48><loc_61></location>
<caption>Fig. 5. Results of the lag error analysis. The histogram shows the distribution of the centroid lag obtained by cross correlating 2000 flux randomized and randomly selected subset light curves (FR / RSS method). The black area marks the 68% confidence range used to calculate the errors of the centroid (red line).</caption>
</figure>
<text><location><page_6><loc_7><loc_15><loc_50><loc_26></location>tribution). This method has been applied for two objects; the low-luminosity AGN NGC4395 (Edri et al. 2012) and the highredshift ( z = 1 : 72) luminous MACHO quasar (13.6805.324) (Chelouche et al. 2012); in both cases a successful recovery of the time delay has been reported. Our ESO399-IG20 has a strong H GLYPH<11> emission line contributing to about 20% to the r -band flux (Fig. 3) and the light curves are well sampled. This makes ESO399-IG20 an ideal object to perform a further test of the pure broad-band PRM method.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_15></location>The B -band is mostly dominated by the continuum, and the r -band contains a strong H GLYPH<11> emission line. This allows us to calculate the line-continuum cross-correlation function CCF ( GLYPH<28> ) = CCFBr ( GLYPH<28> ) GLYPH<0> ACFB ( GLYPH<28> ) and to obtain the time delay (centroid). As</text>
<figure>
<location><page_6><loc_55><loc_64><loc_92><loc_92></location>
<caption>Fig. 6. Synthetic H GLYPH<11> and continuum light curves. The solid red and blue lines show the H GLYPH<11> and continuum models estimated by SPEAR respectively. The red and blue area (enclosed by the dashed line) represent the expected variance about the mean light curve model. The original H GLYPH<11> light curve is computed by subtracting a scaled r curve from the SII curve and re-normalizing it to mean = 1 (red dots). The H GLYPH<11> light curve is vertically shifted by 0.2 with respect to the continuum light curve (blue dots) for clarity.</caption>
</figure>
<figure>
<location><page_6><loc_52><loc_27><loc_95><loc_47></location>
<caption>Fig. 7. Broad-band RM results. Top: The B -band ACF (dotted line) show a well defined centroid at zero lag (vertical blue line), while the B = r -band CCF shows the same peak at zero lag, a secondary peak at 3 days is also visible (vertical black line). In the same case as the B -band ACF, the r -band ACF (red line) show a peak at zero lag, however, one additionally faint peak is clearly visible between 10-20 days, in comparison with the ACF of the B -band. Bottom: The cross-correlation yields a centroid lag of 15.0 days (vertical black line). The red shaded area marks the range used to calculate the centroid.</caption>
</figure>
<figure>
<location><page_7><loc_10><loc_69><loc_48><loc_92></location>
<caption>Fig. 9. BLR disk / sphere-model. Simulated H GLYPH<11> light curves for a disk-like BLR geometry and di GLYPH<11> erent inclinations (4 GLYPH<20> i GLYPH<20> 30 GLYPH<14> ) are shown in di GLYPH<11> erent colors for illustration. The black dotted line is the H GLYPH<11> simulated light curve for a spherical BLR model. A disk-like BLR model with inclination of 6 GLYPH<14> is able to reproduce the features of the original H GLYPH<11> light curve (black crosses).</caption>
</figure>
<figure>
<location><page_7><loc_55><loc_71><loc_97><loc_91></location>
<caption>Fig. 8. Results of the lag error analysis of CCFBr ( GLYPH<28> ) GLYPH<0> ACFB ( GLYPH<28> ). The histogram shows the distribution of the centroid lag obtained by cross correlating 2000 flux randomized and randomly selected subset light curves (FR / RSS method). The black shaded area marks the 68% confidence range used to calculate the errors of the centroid (red line).</caption>
</figure>
<text><location><page_7><loc_7><loc_31><loc_50><loc_56></location>shown in Figure 7, the B = r cross-correlation exhibits two di GLYPH<11> erent peaks, one peak at zero lag (from the auto-correlation of the continuum) and one peak at lag GLYPH<24> 3 days. Furthermore, a small but extended enhancement can be seen in the auto-correlation of the r -band at about 10-20 days, in comparison with the ACF of the B -band. This feature can be interpreted as a clear contribution from the H GLYPH<11> emission line to the broad r -band filter. In fact, the cross-correlation shows a broad peak with a lag of 15.0 days as defined by the centroid in Figure 7. To determine the lag uncertainties, we applied the FR / RSS method. Again from the observed light curves we created 2000 randomly selected subset light curves, each containing 63% of the original data points, and randomly altering the flux value of each data point consistent with its (normal-distributed) measurement error. We calculated the DCF for the 2000 pairs of subset light curves and the corresponding centroid (Figure 8). This yields a median lag GLYPH<28> cent = 17.9 + 2 : 9 GLYPH<0> 3 : 2 days. Correcting for time dilation we obtain a rest frame lag GLYPH<28> rest = 17.5 GLYPH<6> 3 : 1 days. This nicely agrees with the results from narrow-band PRM (18 : 2 GLYPH<6> 2 : 3 days for the DCF, and 17.9 GLYPH<6> 1 : 1 days for SPEAR)</text>
<section_header_level_1><location><page_7><loc_7><loc_27><loc_45><loc_28></location>3.3. Modeling the geometry of the Broad-Line Region</section_header_level_1>
<text><location><page_7><loc_7><loc_21><loc_50><loc_26></location>We have inferred the geometry of the BLR through the direct modeling of the results obtained from PRM. Following Welsh & Horne (1991), the time delay function for a spherically symmetric geometry of the BLR is:</text>
<formula><location><page_7><loc_7><loc_17><loc_50><loc_20></location>GLYPH<1> ( GLYPH<28> ) = r c (1 + sin GLYPH<30> GLYPH<1> cos GLYPH<18> ) (2)</formula>
<text><location><page_7><loc_7><loc_13><loc_50><loc_16></location>where r is the radius of the spherical shell, GLYPH<30> and GLYPH<18> the respectives angles in the spherical coordinates. While for a Keplerian ring / disk structure the time delay function is:</text>
<formula><location><page_7><loc_7><loc_9><loc_50><loc_12></location>GLYPH<1> ( GLYPH<28> ) = r c (1 GLYPH<0> sin i GLYPH<1> cos GLYPH<30> ) (3)</formula>
<text><location><page_7><loc_52><loc_47><loc_95><loc_58></location>where r is the radius of the ring, i is the inclination (0 GLYPH<20> i GLYPH<20> 90 GLYPH<14> ) of the axis of the disk with respect to the observer line of sight (0 = face-on, 90 = edge-on) and GLYPH<30> is the azimuthal angle between a point on the disk and the projection of the line of sight onto the disk. The observed continuum light curve (previously interpolated by SPEAR) was convolved with the time-delay function for the respective disk and sphere geometry to simulate the expected H GLYPH<11> light curve. The results of the simulation are shown in Figure 9.</text>
<text><location><page_7><loc_52><loc_33><loc_95><loc_46></location>The H GLYPH<11> light curve for a spherical BLR configuration does not reproduce the observations, however a nearly face-on disklike BLR geometry with an inclination between 4 to 10 GLYPH<14> provides an acceptable fit to the original data. To estimate the disk inclination, we performed the GLYPH<31> 2 minimizing fitting procedure for a range of inclination angles (Fig 9). The best fit yields a value of i = 6 GLYPH<14> GLYPH<6> 3 GLYPH<14> for a disk-like BLR model with an extension from 16 to 20 light days. For such a nearly face-on BLR the velocity of orbiting broad line gas clouds will appear about a factor ten smaller, mimicking a NLS1.</text>
<section_header_level_1><location><page_7><loc_52><loc_30><loc_90><loc_31></location>3.4. AGN luminosity and the Host-subtraction process</section_header_level_1>
<text><location><page_7><loc_52><loc_10><loc_95><loc_29></location>To determine the AGN luminosity free of host galaxy contributions, we applied the flux variation gradient (FVG) method, originally proposed by Choloniewski (1981) and later modified by Winkler et al. (1992). A detailed description of the FVG method on PRM data is presented in Pozo Nu˜nez et al. (2012), and here we give a brief outline. In this method the fluxes obtained through di GLYPH<11> erent filters and same apertures are plotted in a flux-flux diagram. The fluxes follow a linear slope representing the AGN color, while the slope of the nuclear host galaxy contribution (including the contribution from the narrow line region (NLR)) lies in a well defined range (0 : 4 < GLYPH<0> host BV < 0 : 53, for 8 : 00 3 aperture and redshift z < 0 : 03, Sakata et al. 2010). The AGN slope is determined through linear regression analysis. The intersection of the AGN slope with the host galaxy range yields the actual host galaxy contribution at the time of</text>
<table>
<location><page_8><loc_13><loc_86><loc_88><loc_91></location>
<caption>Table 5. Total, host galaxy and AGN fluxes of ESO399-IG20</caption>
</table>
<figure>
<location><page_8><loc_12><loc_55><loc_48><loc_79></location>
<caption>Fig. 10. Flux variation gradient diagram of ESO399-IG20 for 7 : 00 5 aperture. The solid lines delineate the ordinary least square bisector regression model yielding the range of the AGN slope. The dashed lines indicate the interpolated range of host slopes obtained from Sakata et al. (2010) for 11 nearby AGN. The intersection between the host galaxy and AGN slope (red area) gives the host galaxy flux in both bands. The dash-dotted blue lines represent the range of the AGN flux in both filters.</caption>
</figure>
<text><location><page_8><loc_7><loc_23><loc_50><loc_40></location>the monitoring campaign. Figure 10 shows the FVG diagram for the B and r fluxes (corrected for galactic foreground extinction) obtained during the same nights and through 7 : 00 5 aperture. Additionally, FVGs were evaluated for di GLYPH<11> erent apertures, as shown in Figure 11. As already noted in Section 2, a big fraction of the total flux is lost in the small 5' aperture, hence, the results are more sensitive to a possible underestimation of the real AGN and host galaxy contribution. Furthermore, one may expect that for larger apertures the fluxes will lie closer to the range for the host galaxy slope, however, it appears that the host galaxy is intrinsically strong and very blue, closer to the nucleus and in the outer parts. As for the analysis of the light curves we here use the results for the 7 : 00 5 aperture.</text>
<text><location><page_8><loc_7><loc_10><loc_50><loc_23></location>Averaging over the intersection area between the AGN and the host galaxy slopes, we obtain a mean host galaxy flux of (0 : 95 GLYPH<6> 0 : 18) mJy in B and (2 : 51 GLYPH<6> 0 : 20) mJy in r . During our monitoring campaign the host galaxy subtracted AGN fluxes range between 2.29 and 2.71 and between 2.14 and 2.58 mJy in the B and r band, respectively. These fluxes are represented by the blue dotted lines in Figure 10. From this range we interpolate the host-subtracted monochromatic AGN flux at restframe 5100Å F 5100 = 2 : 66 GLYPH<6> 0 : 22 GLYPH<1> 10 GLYPH<0> 15 ergs GLYPH<0> 1 cm GLYPH<0> 2 Å GLYPH<0> 1 . For the interpolation we assumed a power law spectral en-</text>
<figure>
<location><page_8><loc_56><loc_55><loc_92><loc_79></location>
<caption>Fig. 11. Flux variation gradient diagram of ESO399-IG20 for di GLYPH<11> erent apertures. The fluxes obtained through 7 : 00 5 show an strong correlation, with a correlation coe GLYPH<14> cient of rc = 0 : 94. While for 5', 15' and 25' the correlation coe GLYPH<14> cients are equal to 0.81, 0.90 and 0.89 respectively. This significant decrease in the correlation supports once again our choice of 7 : 00 5 as the best aperture.</caption>
</figure>
<figure>
<location><page_8><loc_56><loc_20><loc_93><loc_41></location>
<caption>Fig. 12. RBLR versus L , using data from Bentz et al. (2009a), Denney et al. (2010), Doroshenko et al. (2012) and Grier et al. (2012). As a red dot we included our results for ESO399-IG20. Shown is a zoomed portion containing ESO399-IG20. The solid dotted line show a fitted slope GLYPH<11> = 0 : 519. ESO399-IG20 lies close to the expected slope.</caption>
</figure>
<text><location><page_9><loc_7><loc_83><loc_50><loc_93></location>gy distribution (SED) ( F GLYPH<23> / GLYPH<23> GLYPH<11> ) with an spectral index GLYPH<11> = log( f BAGN = f rAGN ) = log( GLYPH<23> B =GLYPH<23> r ), where GLYPH<23> B and GLYPH<23> r are the e GLYPH<11> ective frequencies in the B and r bands, respectively. The error was determined by interpolation between the ranges of the AGN fluxes GLYPH<6> GLYPH<27> in both filters. At the distance of 102 Mpc this yields a hostsubtracted AGN luminosity at 5100Å L AGN = (1 : 69 GLYPH<6> 0 : 25) GLYPH<2> 10 43 ergs GLYPH<0> 1 . The total fluxes, host galaxy subtracted AGN fluxes and the AGN luminosity are listed in Table 5.</text>
<section_header_level_1><location><page_9><loc_7><loc_79><loc_36><loc_80></location>3.5. The BLR size-luminosity relationship</section_header_level_1>
<text><location><page_9><loc_7><loc_50><loc_50><loc_78></location>Estimates of the BLR size and host-galaxy subtracted AGN luminosity in the literature have been derived from several spectroscopic RM campaigns and through host-galaxy modeling using high-resolution images from HST . In consequence, the relationship between the H GLYPH<12> BLR size and the luminosity (5100Å) R BLR / L GLYPH<11> (Kaspi et al. 2000) has been improved considerably with the most recent slope of GLYPH<11> = 0.519 0 : 063 GLYPH<0> 0 : 066 (Bentz et al. 2009a). Although to date this relationship has been corroborated for 38 AGNs, still there exist objects with large uncertainties in both measurements. In order to improve the statistic, it is of interest to see the position for this new Seyfert 1 galaxy on the BLR-Luminosity relationship. In order to obtain the H GLYPH<12> BLR radius, we used the weighted mean ratio for the time lag GLYPH<28> ( H GLYPH<11> ) : GLYPH<28> ( H GLYPH<12> ) : 1 : 54 : 1 : 00, obtained recently by Bentz et al. (2010) from the Lick AGN Monitoring Program of 11 lowluminosity AGN. Therefore, the H GLYPH<11> lag of 18 : 2 days translates into an H GLYPH<12> lag of 11 : 8 days. Figure 12 shows the position of ESO399-IG20 on the R BLRLAGN diagram. The data are taken from Bentz et al. (2009a) and here we include the most recent results for particular objects obtained from spectroscopic RM by Denney et al. (2010), Doroshenko et al. (2012) and Grier et al. (2012) respectively.</text>
<section_header_level_1><location><page_9><loc_7><loc_46><loc_31><loc_48></location>4. Summary and conclusions</section_header_level_1>
<text><location><page_9><loc_7><loc_40><loc_50><loc_45></location>Wepresented new photometric reverberation mapping results for the Seyfert 1 galaxy ESO399-IG20. We determined the broad line region size, the basic geometry of the BLR and the hostsubtracted AGN luminosity. The results are:</text>
<unordered_list>
<list_item><location><page_9><loc_7><loc_27><loc_50><loc_39></location>1. The cross-correlation of the H GLYPH<11> emission line measured in a narrow-band filter with the optical continuum light curve yields a rest-frame time delay GLYPH<28> rest = 18.2 GLYPH<6> 2.29 days. We explored the SPEAR method, and - given that H GLYPH<11> contributes about 15-20% to the r -band - also the capabilities of pure broad-band photometric reverberation mapping. The SPEAR method yields a rest-frame time delay of GLYPH<28> rest = 17.9 GLYPH<6> 1.1 days, while the pure broad-band PRM method yields GLYPH<28> rest = 17.5 GLYPH<6> 3.1 days. The results indicate that, within the errors, the three methods are in good agreement.</list_item>
<list_item><location><page_9><loc_7><loc_15><loc_50><loc_26></location>2. We constrained the basic geometry of the BLR by comparing simulated light curves, using the size determined for the BLR, to the observed H GLYPH<11> light curve. The pronounced and sharp variability features in both the continuum and emission line light curves allow us to exclude a spherical BLR geometry. We found that the BLR has a disk-like shape with an inclination of i = 6 GLYPH<6> 3 GLYPH<14> and an extension from 16 to 20 light days. This nearly face-on BLR can explain the appearance of ESO399-IG20 as a narrow-line Seyfert-1 galaxy.</list_item>
<list_item><location><page_9><loc_7><loc_10><loc_50><loc_15></location>3. We successfully separated the host-galaxy contribution from the total flux through the flux variation gradient method (FVG). The average host-galaxy subtracted AGN luminosity of ESO399-IG20 at the time of our monitoring campaign</list_item>
</unordered_list>
<text><location><page_9><loc_54><loc_89><loc_95><loc_93></location>is L AGN = (1 : 69 GLYPH<6> 0 : 25) GLYPH<2> 10 43 ergs GLYPH<0> 1 . In the BLR size - AGN luminosity diagram ESO399-IG20 lies close to the best fit of the relation.</text>
<text><location><page_9><loc_52><loc_83><loc_95><loc_88></location>These results document the e GLYPH<14> ciency and accuracy of photometric reverberation mapping for determining the AGN luminosity, the BLR size and the potential to constrain even the BLR geometry.</text>
<text><location><page_9><loc_52><loc_78><loc_95><loc_82></location>Acknowledgements. This publication is supported as a project of the NordrheinWestfalische Akademie der Wissenschaften und der Kunste in the framework of the academy program by the Federal Republic of Germany and the state Nordrhein-Westfalen.</text>
<text><location><page_9><loc_52><loc_75><loc_95><loc_77></location>The observations on Cerro Armazones benefitted from the care of the guardians Hector Labra, Gerardo Pino, Roberto Munoz, and Francisco Arraya.</text>
<text><location><page_9><loc_52><loc_69><loc_95><loc_75></location>This research has made use of the NASA / IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. We thank the anonymous referee for his comments and careful review of the manuscript.</text>
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[
{
"title": "ABSTRACT",
"content": "We present photometric reverberation mapping of the narrow-line Seyfert 1 galaxy ESO399-IG20 performed with the robotic 15 cm telescope VYSOS-6 at the Cerro Armazones Observatory. Through the combination of broad- and narrow-band filters we determine the size of the broad-line emitting region (BLR) by measuring the time delay between the variability of the continuum and the H GLYPH<11> emission line. We use the flux variation gradient method to separate the host galaxy contribution from that of the active galactic nucleus (AGN), and to calculate the 5100Å luminosity L AGN of the AGN. Both measurements permit us to derive the position of ESO399-IG20 in the BLR size - AGN luminosity R BLR / L 0 : 5 AGN diagram. We infer the basic geometry of the BLR through modelling of the light curves. The pronounced sharp variability patterns in both the continuum and the emission line light curves allow us to reject a spherical BLR geometry. The light curves are best fitted by a disk-like BLR seen nearly face-on with an inclination angle of 6 GLYPH<14> GLYPH<6> 3 GLYPH<14> and with an extension from 16 to 20 light days. Key words. galaxies: active -galaxies: Seyfert -quasars: emission lines -galaxies: distances and redshifts -galaxies: individual: ESO399-IG20",
"pages": [
1
]
},
{
"title": "Size and disk-like shape of the broad-line region of ESO399-IG20",
"content": "Francisco Pozo Nu˜nez 1 , Christian Westhues 1 , Michael Ramolla 1 , Christoph Bruckmann 1 , Martin Haas 1 , Rolf Chini 1 ; 2 , Katrien Steenbrugge 2 ; 3 , Roland Lemke 1 , and Miguel Murphy 2 Received January 6, 2013; Accepted February 5, 2013",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The physical properties of the broad line region (BLR) in active galactic nuclei (AGN) have been extensively studied during the last three decades. Consensus has been reached that the luminosity variations of the continuum emitting region of the hot accretion disk produce variations of the broad emission lines with a delay due to the light travel time across the BLR. To date, the only method independent on spatial resolution is reverberation mapping (Blandford & McKee 1982; Peterson 1993), in which one measures the time delay or 'echo' between the continuum variability and the variability observed in the broad emission lines. This method has been used successfully for determining the BLR size, kinematics and black hole mass ( MBH ) of several Type-1 AGNs. RM provides basic MBH estimates through the virial product MBH = f GLYPH<1> RBLR GLYPH<1> GLYPH<27> 2 V = G , where G is the gravitational constant, RBLR = c GLYPH<1> GLYPH<28> is the BLR size, GLYPH<27> V is the emissionline velocity dispersion of the BLR gas and the factor f depends on the - so far unknown - geometry and kinematics of the BLR (Peterson et al. 2004 and references therein). Furthermore, as a widely used extrapolation of locally obtained RM results to higher redshift data, MBH has be estimated using the BLR Size-Luminosity R BLR / L 0 : 5 AGN relationship (Koratkar & Gaskell 1991; Kaspi et al. 1996, Kaspi et al. 2000; Wandel et al. 1999; McGill et al. 2008; Vestergaard et al. 2011). However, a reliable MBH estimation from the luminosity requires a considerable reduction of the R GLYPH<0> L dispersion present. As the size of the BLR ranges from a few to several hundred light days, it is necessary to perform observational monitoring campaigns ranging from months to years in order to su GLYPH<14> ciently sample the time domain of the echo. Most observational RM campaigns have used spectroscopic monitoring of the sources, which however requires large amounts of telescope time. Recently, Haas et al. (2011) proposed photometric reverberation mapping (PRM) as an e GLYPH<14> cient method to determine the BLR size through the use of broad band filters to trace the AGN continuum variations and narrow-band filters to catch the BLR emission line response. Because the narrow-band collects both the emission line flux and the underlying continuum, the challenge is to extract the pure emission line light curve. In the dedicated case study of 3C120, Pozo Nu˜nez et al. (2012) demonstrated that PRM reaches an accuracy similar to spectroscopic RM(Grier et al. 2012). Another e GLYPH<14> cient approach to determine the BLR size has been proposed by Chelouche & Daniel (2012), through the analysis of the di GLYPH<11> erence between the cross-correlation (CCF) and the auto-correlation (ACF) functions for suitably chosen broad band filters, one filter covering a bright emission line and one covering only the continuum. While this method does not place a strict requirement on the object's redshift such that the emission line falls into the narrow-band filter (as in the case proposed by Haas et al. 2011), the use of broad band filters only (as proposed by Chelouche & Daniel 2012) limits the application of PRM to cases with a su GLYPH<14> ciently strong emission line contribution in the respective filter used. Despite of this handicap, this method has been successfully applied to determine the BLR size for one low-luminosity AGN NGC4395 (Edri et al. 2012) and one highz luminous MACHO quasar (Chelouche et al. 2012) consistent with previous spectroscopic RM results. A fundamental issue in both these methods is to separate the host-galaxy contribution from the total luminosity to calculate the AGN luminosity. An incorrect determination of the nuclear AGN luminosity (due to the contamination of the host compo- nent) causes an overestimation of the linear regression slope GLYPH<11> . This has been demonstrated by Bentz et al. (2009a), who presented the most recent compilation of host-subtracted AGN luminosities for several reverberation-mapped Seyfert 1 galaxies obtained through host-galaxy modeling of high-resolution Hubble Space Telescope (HST) images. Compared to the previous slope of GLYPH<11> = 0 : 7 they determined an improved slope of GLYPH<11> = 0.519 0 : 063 GLYPH<0> 0 : 066 close to GLYPH<11> = 0 : 5 expected from photo-ionization models of the BLR (Davidson & Netzer 1979). A di GLYPH<11> erent approach to estimate the host galaxy contribution is the flux variation gradient method (FVG, Choloniewski 1981; Winkler 1997). An advantage is that it does not require high spatial resolution imaging and can be applied directly to the monitoring data. Recently, FVG has been tested on PRM data (Haas et al. 2011; Pozo Nu˜nez et al. 2012). These tests show that by using a well defined range for the host galaxy slope (Sakata et al. 2010) it is possible to separate the AGN contribution at the time of the monitoring campaigns. ESO399-IG20 has been classified as a Narrow-Line Seyfert 1 (NLS1) galaxy (V'eron-Cetty & V'eron 2010). It has often been speculated that the lack of broad emission lines of - at least - part of the NLS1 population can be explained by face-on disk-like BLR geometries. Single-epoch spectroscopic investigations by Dietrich et al. (2005) show high-ionized gas orbiting at high velocities, producing strong broad profiles (FWHM(H GLYPH<12> ) = 2425 GLYPH<6> 121 km / s, see their Table 3 and Figures 2-5) like in Broad-Line Seyfert 1 (BLS1) galaxies. Furthermore, they find a strong host-galaxy contribution with respect to the total observed 5100Å continuum flux ( GLYPH<24> 50%). Here, we present the first measurement of the BLR size and the host-subtracted AGN 5100Å luminosity for ESO399-IG20. Both results allow us to infer its position in the BLR size-Luminosity R BLR / L 0 : 5 AGN diagram. Additionally, pure broad-band PRM (Chelouche & Daniel 2012) is applied and compared with the broad- and narrow-band PRM technique (Haas et al. 2011). Finally, the geometry of the BLR, whether spherical or an inclined disk, is inferred via light curve modeling.",
"pages": [
1,
2
]
},
{
"title": "2. Observations and data reduction",
"content": "Broad-band Johnson B (4330 Å), Sloan-band r (6230 Å) and the redshifted H GLYPH<11> (SII 6721 GLYPH<6> 30 Å at z = 0.0249) images were obtained with the robotic 15 cm VYSOS6 telescope of the Universitatssternwarte Bochum, located near Cerro Armazones, future location of the ESO Extreme Large Telescope (ELT) in Chile. Monitoring occurred between May 5 and November 18 of 2011, with a median sampling of 3 days. ESO399-IG20 lies at redshift z = 0 : 0249, therefore the H GLYPH<11> emission line falls into the SII 6721 GLYPH<6> 30Å narrow-band filter. Figure 1 shows the position of the narrow-band with respect to the H GLYPH<11> emission line together with the e GLYPH<11> ective transmission of the other filters used. The H GLYPH<11> line is broader than the SII filter, however, simulations with di GLYPH<11> erent asymmetric and perfect symmetric cutting of the high-velocity line wings show negligible systematic e GLYPH<11> ect introduced in the time delay ( GLYPH<24> 2%), even considering the fact of only using one part of the wing profile. This e GLYPH<11> ect will be discussed in depth in a forthcoming contribution (Bruckmann et al. 2012., in preparation). Data reduction was performed using IRAF 1 , in combination with SCAMP (Bertin 2006) and SWARP (Bertin et al. 2002) routines, in the same manner as described by Haas et al. (2012). Light curves were extracted using di GLYPH<11> erent apertures (5', 7 : 00 5, 15' and 25') in order to compare and trace the host and AGN contribution. The light curves for the di GLYPH<11> erent apertures are shown in Figure 2. Additionally, for each aperture we determined the level of variability using the fractional flux variation introduced by Rodriguez-Pascual et al. (1997): where GLYPH<27> 2 is the flux variance of the observations, GLYPH<1> 2 is the mean square uncertainty, and h f i is the mean observed flux. The variability statistics is listed in Table 2. Selecting a small aperture (5') we are only considering a small portion of the total flux, which remains heavily dependent on the quality of the PSF, whereas bigger apertures (15' and 25'), enclose more contribution of the host-galaxy and the results are more sensitive to sky background contamination resulting in larger uncertainties. We found that 7 : 00 5 around the nucleus is the right size aperture which maximizes the signal-to-noise ratio (S / N) and delivers the lowest absolute scatter for the fluxes. Thus, we use this aperture for the further analysis of the BLR size and AGN luminosity. Although the light curves in Figure 2 have not yet been corrected for the host galaxy contribution, one can see that the fractional variation ( Fvar ) and the ratio of the maximum to minimum fluxes ( Rmax ) are higher in the B -band than in the r -band for which the host-galaxy present a greater contribution. A di GLYPH<11> erent case can be seen in the SII light curves, which are mostly dominated by the contribution of the H GLYPH<11> emission line resulting in a higher amplitude of variability. As expected, for bigger apertures the B and r light curves become flatter with Fvar and Rmax smaller due to the larger contribution from the host-galaxy. Non-variable reference stars located on the same field and with similar brightness as the AGN were used to create the relative light curves in normalized flux units. For the absolute photometry calibration we used reference stars from Landolt (2009) observed on the same nights as the AGN, considering the atmospheric extinction for the nearby site Paranal by Patat et al. (2011) and the recalibrated galactic foreground extinction presented by Schlafly & Finkbeiner (2011) obtained from the Schlegel et al. (1998) dust extinction maps. In Table 1, we give the characteristics of ESO399-IG20. A summary of the photo- Note. Column 1 list the aperture in arc-seconds, Columns 2-5 list the mean flux, the standard deviation, the normalized excess variance and the ratio of the maximum to minimum fluxes for the continuum light curve. Similarly, columns 6-13 list the variability for the r and SII bands respectively. The standard deviation and the mean fluxes are expressed in units of mJy. metric results and the fluxes in all bands are listed in Table 3 and Table 4, respectively.",
"pages": [
2,
3,
4
]
},
{
"title": "3.1. Light curves and BLR size",
"content": "The B -band, which is dominated by the AGN continuum, shows a strong flux increase (about 35%) between the beginning and the end of May. Afterwards, the two measurements obtained in June reflect a more gradual increase until a maximum is reached at the end of July. After this maximum, the fluxes decreases gradually (about 20%) until the end of September, and then the light curves become more constant until middle of November. Likewise, the r -band, which is dominated by the continuum but also contains a contribution from the strong H GLYPH<11> emission line, follows the sames features as the B -band light curve, although with a lower amplitude. In contrast to the continuum dominated broad-band light curves, the narrow SII-band light curve exhibits a flux increase which is stretched. For instance the prominent maximum in the B - and r - band at the end of July occurs in the SII-band in August, giving a first approximation for the H GLYPH<11> time delay of 15-20 days. Note that the visual inspection of the r - and B -band light curves does not allow an approximation for the time delay. As already discussed in previous PRM studies, the narrowband contains a contribution of the varying continuum, which must be removed before applying cross correlation techniques (Haas et al. 2011; Pozo Nu˜nez et al. 2012). In order to determine this contribution, we used the SII and r -band fluxes, previously calibrated to mJy, as is shown with the flux-flux diagram in Figure 3. The H GLYPH<11> line is strong contributing, on average, about 70% of the total flux enclose in the SII-band, while the con- inuum contribution ( r -band) is about 30%. Following the usual practice of PRM, we construct a synthetic H GLYPH<11> light curve by subtracting a third of the r -band flux (H GLYPH<11> = SII GLYPH<0> 0.3 r ). The H GLYPH<11> light curve was used afterwards to estimate the time delay. For this purpose, we used the discrete correlation function (DCF, Edelson & Krolik 1988) to cross-correlate the continuum and the synthetic H GLYPH<11> emission line, taking into account possible bin size dependency (Rodriguez-Pascual et al. 1989). The centroid in the cross-correlation of B -band and H GLYPH<11> show a time delay of 18.1 days, while the centroid in the cross-correlation between B -band and SII-band yields a time delay of 15.8 days. However, this is an expected result because of the more pronounced peak at zero lag due to the contamination by the continuum emission in the narrow-band filter. Both cross-correlation functions are shown in Figure 4. Uncertainties in the time delay were calculated using the flux randomization and random subset selection method (FR / RSS, Peterson et al. 1998b; Peterson et al. 2004). From the observed light curves we create 2000 randomly selected subset light curves, each containing 63% of the original data points (the other fraction of points are unselected according to Poisson probability). The flux value of each data point was randomly altered consistent with its (normal-distributed) measurement error. We calculated the DCF for the 2000 pairs of subset light curves and the corresponding centroid (Figure 5). From this cross-correlation error analysis, we measure a median lag of GLYPH<28> cent = 18.7 + 2 : 5 GLYPH<0> 2 : 2 . Correcting for the time dilation factor (1 + z = 1 : 0249) we obtain a rest frame lag of 18 : 2 GLYPH<6> 2 : 29 days. An alternative method to estimate the time delay, called Stochastic Process Estimation for AGN Reverberation (SPEAR), has been worked out recently by Zu et al. (2011). Through the modeling of the AGN light curves as a damped random walk (DRW) (Zu et al. 2011; Zu et al. 2012 and reference therein), this method appears to be consistent with previous cross-correlation techniques (e.g. Grier et al. (2012) for spectroscopic reverberation data). Using the SPEAR code 2 on our light curves, we obtain a time delay of GLYPH<28> spear = 18.4 + 1 : 2 GLYPH<0> 1 : 0 . After correction for time dilation the rest frame lag GLYPH<28> rest = 17.9 GLYPH<6> 1 : 1 days, in agreement with the results from the DCF method. Figure 6 shows the SPEAR light curve models.",
"pages": [
4,
5
]
},
{
"title": "3.2. Broad-band reverberation mapping approach",
"content": "Recently, pure broad-band photometric RM has been introduced as an e GLYPH<14> cient alternative to measure the BLR size in quasars (Chelouche & Daniel 2012). In this method, the emission line is also measured using a broad-band filter, and the removal of the underlying continuum is performed in the correlation domain. The centroid of the lag is obtained by the subtraction of the auto-correlation function ( ACF ) between the continuum (represented by one broad band filter enclosing only continuum emission) from the cross-correlation function ( CCF ) between the continuum and the emission line (represented by one broadband filter that contains a su GLYPH<14> ciently strong emission line con- tribution). This method has been applied for two objects; the low-luminosity AGN NGC4395 (Edri et al. 2012) and the highredshift ( z = 1 : 72) luminous MACHO quasar (13.6805.324) (Chelouche et al. 2012); in both cases a successful recovery of the time delay has been reported. Our ESO399-IG20 has a strong H GLYPH<11> emission line contributing to about 20% to the r -band flux (Fig. 3) and the light curves are well sampled. This makes ESO399-IG20 an ideal object to perform a further test of the pure broad-band PRM method. The B -band is mostly dominated by the continuum, and the r -band contains a strong H GLYPH<11> emission line. This allows us to calculate the line-continuum cross-correlation function CCF ( GLYPH<28> ) = CCFBr ( GLYPH<28> ) GLYPH<0> ACFB ( GLYPH<28> ) and to obtain the time delay (centroid). As shown in Figure 7, the B = r cross-correlation exhibits two di GLYPH<11> erent peaks, one peak at zero lag (from the auto-correlation of the continuum) and one peak at lag GLYPH<24> 3 days. Furthermore, a small but extended enhancement can be seen in the auto-correlation of the r -band at about 10-20 days, in comparison with the ACF of the B -band. This feature can be interpreted as a clear contribution from the H GLYPH<11> emission line to the broad r -band filter. In fact, the cross-correlation shows a broad peak with a lag of 15.0 days as defined by the centroid in Figure 7. To determine the lag uncertainties, we applied the FR / RSS method. Again from the observed light curves we created 2000 randomly selected subset light curves, each containing 63% of the original data points, and randomly altering the flux value of each data point consistent with its (normal-distributed) measurement error. We calculated the DCF for the 2000 pairs of subset light curves and the corresponding centroid (Figure 8). This yields a median lag GLYPH<28> cent = 17.9 + 2 : 9 GLYPH<0> 3 : 2 days. Correcting for time dilation we obtain a rest frame lag GLYPH<28> rest = 17.5 GLYPH<6> 3 : 1 days. This nicely agrees with the results from narrow-band PRM (18 : 2 GLYPH<6> 2 : 3 days for the DCF, and 17.9 GLYPH<6> 1 : 1 days for SPEAR)",
"pages": [
5,
6,
7
]
},
{
"title": "3.3. Modeling the geometry of the Broad-Line Region",
"content": "We have inferred the geometry of the BLR through the direct modeling of the results obtained from PRM. Following Welsh & Horne (1991), the time delay function for a spherically symmetric geometry of the BLR is: where r is the radius of the spherical shell, GLYPH<30> and GLYPH<18> the respectives angles in the spherical coordinates. While for a Keplerian ring / disk structure the time delay function is: where r is the radius of the ring, i is the inclination (0 GLYPH<20> i GLYPH<20> 90 GLYPH<14> ) of the axis of the disk with respect to the observer line of sight (0 = face-on, 90 = edge-on) and GLYPH<30> is the azimuthal angle between a point on the disk and the projection of the line of sight onto the disk. The observed continuum light curve (previously interpolated by SPEAR) was convolved with the time-delay function for the respective disk and sphere geometry to simulate the expected H GLYPH<11> light curve. The results of the simulation are shown in Figure 9. The H GLYPH<11> light curve for a spherical BLR configuration does not reproduce the observations, however a nearly face-on disklike BLR geometry with an inclination between 4 to 10 GLYPH<14> provides an acceptable fit to the original data. To estimate the disk inclination, we performed the GLYPH<31> 2 minimizing fitting procedure for a range of inclination angles (Fig 9). The best fit yields a value of i = 6 GLYPH<14> GLYPH<6> 3 GLYPH<14> for a disk-like BLR model with an extension from 16 to 20 light days. For such a nearly face-on BLR the velocity of orbiting broad line gas clouds will appear about a factor ten smaller, mimicking a NLS1.",
"pages": [
7
]
},
{
"title": "3.4. AGN luminosity and the Host-subtraction process",
"content": "To determine the AGN luminosity free of host galaxy contributions, we applied the flux variation gradient (FVG) method, originally proposed by Choloniewski (1981) and later modified by Winkler et al. (1992). A detailed description of the FVG method on PRM data is presented in Pozo Nu˜nez et al. (2012), and here we give a brief outline. In this method the fluxes obtained through di GLYPH<11> erent filters and same apertures are plotted in a flux-flux diagram. The fluxes follow a linear slope representing the AGN color, while the slope of the nuclear host galaxy contribution (including the contribution from the narrow line region (NLR)) lies in a well defined range (0 : 4 < GLYPH<0> host BV < 0 : 53, for 8 : 00 3 aperture and redshift z < 0 : 03, Sakata et al. 2010). The AGN slope is determined through linear regression analysis. The intersection of the AGN slope with the host galaxy range yields the actual host galaxy contribution at the time of the monitoring campaign. Figure 10 shows the FVG diagram for the B and r fluxes (corrected for galactic foreground extinction) obtained during the same nights and through 7 : 00 5 aperture. Additionally, FVGs were evaluated for di GLYPH<11> erent apertures, as shown in Figure 11. As already noted in Section 2, a big fraction of the total flux is lost in the small 5' aperture, hence, the results are more sensitive to a possible underestimation of the real AGN and host galaxy contribution. Furthermore, one may expect that for larger apertures the fluxes will lie closer to the range for the host galaxy slope, however, it appears that the host galaxy is intrinsically strong and very blue, closer to the nucleus and in the outer parts. As for the analysis of the light curves we here use the results for the 7 : 00 5 aperture. Averaging over the intersection area between the AGN and the host galaxy slopes, we obtain a mean host galaxy flux of (0 : 95 GLYPH<6> 0 : 18) mJy in B and (2 : 51 GLYPH<6> 0 : 20) mJy in r . During our monitoring campaign the host galaxy subtracted AGN fluxes range between 2.29 and 2.71 and between 2.14 and 2.58 mJy in the B and r band, respectively. These fluxes are represented by the blue dotted lines in Figure 10. From this range we interpolate the host-subtracted monochromatic AGN flux at restframe 5100Å F 5100 = 2 : 66 GLYPH<6> 0 : 22 GLYPH<1> 10 GLYPH<0> 15 ergs GLYPH<0> 1 cm GLYPH<0> 2 Å GLYPH<0> 1 . For the interpolation we assumed a power law spectral en- gy distribution (SED) ( F GLYPH<23> / GLYPH<23> GLYPH<11> ) with an spectral index GLYPH<11> = log( f BAGN = f rAGN ) = log( GLYPH<23> B =GLYPH<23> r ), where GLYPH<23> B and GLYPH<23> r are the e GLYPH<11> ective frequencies in the B and r bands, respectively. The error was determined by interpolation between the ranges of the AGN fluxes GLYPH<6> GLYPH<27> in both filters. At the distance of 102 Mpc this yields a hostsubtracted AGN luminosity at 5100Å L AGN = (1 : 69 GLYPH<6> 0 : 25) GLYPH<2> 10 43 ergs GLYPH<0> 1 . The total fluxes, host galaxy subtracted AGN fluxes and the AGN luminosity are listed in Table 5.",
"pages": [
7,
8,
9
]
},
{
"title": "3.5. The BLR size-luminosity relationship",
"content": "Estimates of the BLR size and host-galaxy subtracted AGN luminosity in the literature have been derived from several spectroscopic RM campaigns and through host-galaxy modeling using high-resolution images from HST . In consequence, the relationship between the H GLYPH<12> BLR size and the luminosity (5100Å) R BLR / L GLYPH<11> (Kaspi et al. 2000) has been improved considerably with the most recent slope of GLYPH<11> = 0.519 0 : 063 GLYPH<0> 0 : 066 (Bentz et al. 2009a). Although to date this relationship has been corroborated for 38 AGNs, still there exist objects with large uncertainties in both measurements. In order to improve the statistic, it is of interest to see the position for this new Seyfert 1 galaxy on the BLR-Luminosity relationship. In order to obtain the H GLYPH<12> BLR radius, we used the weighted mean ratio for the time lag GLYPH<28> ( H GLYPH<11> ) : GLYPH<28> ( H GLYPH<12> ) : 1 : 54 : 1 : 00, obtained recently by Bentz et al. (2010) from the Lick AGN Monitoring Program of 11 lowluminosity AGN. Therefore, the H GLYPH<11> lag of 18 : 2 days translates into an H GLYPH<12> lag of 11 : 8 days. Figure 12 shows the position of ESO399-IG20 on the R BLRLAGN diagram. The data are taken from Bentz et al. (2009a) and here we include the most recent results for particular objects obtained from spectroscopic RM by Denney et al. (2010), Doroshenko et al. (2012) and Grier et al. (2012) respectively.",
"pages": [
9
]
},
{
"title": "4. Summary and conclusions",
"content": "Wepresented new photometric reverberation mapping results for the Seyfert 1 galaxy ESO399-IG20. We determined the broad line region size, the basic geometry of the BLR and the hostsubtracted AGN luminosity. The results are: is L AGN = (1 : 69 GLYPH<6> 0 : 25) GLYPH<2> 10 43 ergs GLYPH<0> 1 . In the BLR size - AGN luminosity diagram ESO399-IG20 lies close to the best fit of the relation. These results document the e GLYPH<14> ciency and accuracy of photometric reverberation mapping for determining the AGN luminosity, the BLR size and the potential to constrain even the BLR geometry. Acknowledgements. This publication is supported as a project of the NordrheinWestfalische Akademie der Wissenschaften und der Kunste in the framework of the academy program by the Federal Republic of Germany and the state Nordrhein-Westfalen. The observations on Cerro Armazones benefitted from the care of the guardians Hector Labra, Gerardo Pino, Roberto Munoz, and Francisco Arraya. This research has made use of the NASA / IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. We thank the anonymous referee for his comments and careful review of the manuscript.",
"pages": [
9
]
},
{
"title": "References",
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"pages": [
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}
]
2013A&A...552A..69V
https://arxiv.org/pdf/1302.7181.pdf
<document>
<section_header_level_1><location><page_1><loc_17><loc_82><loc_85><loc_87></location>Population synthesis of ultracompact X-ray binaries in the Galactic Bulge</section_header_level_1>
<text><location><page_1><loc_12><loc_78><loc_89><loc_82></location>L. M. van Haaften 1 , G. Nelemans 1 ; 2 , R. Voss 1 , S. Toonen 1 , S. F. Portegies Zwart 3 , L. R. Yungelson 4 , and M. V. van der Sluys 1</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_74><loc_91><loc_77></location>1 Department of Astrophysics / IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands, e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_62><loc_74></location>2 Institute for Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium</list_item>
<list_item><location><page_1><loc_11><loc_71><loc_73><loc_72></location>4 Institute of Astronomy, Russian Academy of Sciences, 48 Pyatnitskaya Str., 119017 Moscow, Russia</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_67><loc_73></location>3 Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_68><loc_38><loc_70></location>Preprint online version: September 10, 2018</text>
<section_header_level_1><location><page_1><loc_48><loc_66><loc_54><loc_67></location>Abstract</section_header_level_1>
<text><location><page_1><loc_11><loc_61><loc_91><loc_65></location>Aims. We model the present-day number and properties of ultracompact X-ray binaries (UCXBs) in the Galactic Bulge. The main objective is to compare the results to the known UCXB population as well as to data from the Galactic Bulge Survey, in order to learn about the formation of UCXBs and their evolution, such as the onset of mass transfer and late-time behavior.</text>
<text><location><page_1><loc_11><loc_58><loc_91><loc_61></location>Methods. The binary population synthesis code SeBa and detailed stellar evolutionary tracks have been used to model the UCXB population in the Bulge. The luminosity behavior of UCXBs has been predicted using long-term X-ray observations of the known UCXBs as well as the thermal-viscous disk instability model.</text>
<text><location><page_1><loc_11><loc_51><loc_91><loc_58></location>Results. In our model, the majority of UCXBs initially have a helium burning star donor. Of the white dwarf donors, most have helium composition. In the absence of a mechanism that destroys old UCXBs, we predict (0 : 2 GLYPH<0> 1 : 9) GLYPH<2> 10 5 UCXBs in the Galactic Bulge, depending on assumptions, mostly at orbital periods longer than 60 min (a large number of long-period systems also follows from the observed short-period UCXB population). About 5 GLYPH<0> 50 UCXBs should be brighter than 10 35 erg s GLYPH<0> 1 , mostly persistent sources with orbital periods shorter than about 30 min and with degenerate helium and carbon-oxygen donors. This is about one order of magnitude more than the observed number of (probably) three.</text>
<text><location><page_1><loc_11><loc_42><loc_91><loc_51></location>Conclusions. This overprediction of short-period UCXBs by roughly one order of magnitude implies that fewer systems are formed, or that a super-Eddington mass transfer rate is more di GLYPH<14> cult to survive than we assumed. The very small number of observed longperiod UCXBs with respect to short-period UCXBs, the surprisingly high luminosity of the observed UCXBs with orbital periods around 50 min, and the properties of the PSR J1719-1438 system all point to much faster UCXB evolution than expected from angular momentum loss via gravitational wave radiation alone. Old UCXBs, if they still exist, probably have orbital periods longer than 2 h and have become very faint due to either reduced accretion or quiescence, or have become detached. UCXBs are promising candidate progenitors of isolated millisecond radio pulsars.</text>
<text><location><page_1><loc_11><loc_41><loc_70><loc_42></location>Key words. binaries: close - stars: evolution - Galaxy: bulge - X-rays: binaries - pulsars: general</text>
<section_header_level_1><location><page_1><loc_7><loc_36><loc_19><loc_37></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_21><loc_50><loc_35></location>Ultracompact X-ray binaries (UCXBs) are low-mass X-ray binaries with observed orbital periods shorter than GLYPH<24> 1 h, indicating a compact, hydrogen deficient donor star (Vila 1971; Paczy'nski 1981; Sienkiewicz 1984). The donor overflows its Roche lobe, and lost matter is partially accreted by a neutron star or black hole companion. Because of the compact orbit, mass transfer is driven by orbital angular momentum loss via gravitational wave radiation (e.g. Kraft et al. 1962; Paczy'nski 1967; Faulkner 1971; Pringle & Webbink 1975; Tutukov & Yungelson 1979). For an overview of the relevance of studying UCXBs, see e.g. Nelemans & Jonker (2010).</text>
<text><location><page_1><loc_7><loc_10><loc_50><loc_20></location>The Galactic Bulge is a suitable environment to discover UCXBs because of the high local star concentration. Furthermore, the Bulge is an old stellar population that contains few young X-ray sources such as high-mass X-ray binaries and core-collapse supernova remnants. Due to their rarity, UCXBs are not found nearby in the Galaxy. Also, while observable in X-rays, they are too faint to be identified in other galaxies (e.g. Voss & Gilfanov 2007).</text>
<text><location><page_1><loc_52><loc_30><loc_95><loc_38></location>The Galactic Bulge Survey (GBS) (Jonker et al. 2011) is an X-ray and optical survey focused on two 6 GLYPH<14> GLYPH<2> 1 GLYPH<14> regions centered 1 : 5 GLYPH<14> to the North and South of the Galactic Center. One of the goals of the GBS is to investigate the properties of populations of X-ray binaries in order to constrain their formation scenarios, especially the common-envelope phase(s).</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_29></location>The present study aims to predict and explain GBS results regarding the number and luminosities of UCXBs by means of binary population synthesis and UCXB evolutionary tracks, thereby contributing to a better understanding of the formation and evolution of UCXBs. We also compare our results to the orbital periods and chemical compositions of the known UCXB population. In Sect. 2 we describe our assumptions on the star formation, stellar and binary evolution, and the observable characteristics of evolved UCXBs. The results follow in Sect. 3, where we present the modeled present-day population and its observational properties. In Sect. 4, we compare our results with the population synthesis studies by Belczynski & Taam (2004a), Zhu et al. (2012a), and Zhu et al. (2012b), as well as to observations, and we discuss various implications. We conclude in Sect. 5.</text>
<section_header_level_1><location><page_2><loc_7><loc_92><loc_15><loc_93></location>2. Method</section_header_level_1>
<text><location><page_2><loc_7><loc_65><loc_50><loc_91></location>The study of the evolution of the UCXB population consists of several steps. First, the star formation history of the Galactic Bulge and the binary initial mass function prescribe which types of zero-age main sequence binaries form in the Bulge, and when they form. The binary population synthesis code SeBa (Portegies Zwart & Verbunt 1996; Nelemans et al. 2001; Toonen et al. 2012) is used to simulate the evolution of this population of zero-age main sequence binaries. During the evolution of the population, all UCXB progenitors are selected at a certain moment after the supernova explosion that leaves behind the neutron star or black hole. More detailed evolutionary tracks are used to trace the subsequent evolution. This yields the present-day number and intrinsic parameters of the UCXBs in the Galactic Bulge. Finally, using long-term observations by the Rossi X-ray Timing Explorer All-Sky Monitor ( RXTE ASM) (Bradt et al. 1993; Levine et al. 1996) as well as the accretion disk instability model, the modeled UCXB parameters are translated into observational parameters using the results of van Haaften et al. (2012c). The result is a prediction of the presentday observable population.</text>
<section_header_level_1><location><page_2><loc_7><loc_62><loc_25><loc_63></location>2.1. Population synthesis</section_header_level_1>
<text><location><page_2><loc_7><loc_48><loc_50><loc_61></location>The binary population synthesis code SeBa models the evolutionary transformations of a population of binary stars based on a distribution of initial binary parameters. It follows the evolution of stellar components using analytic formulas by Hurley et al. (2000), taking into account circularization due to tidal interaction, magnetic braking, gravitational wave radiation, mass exchange via Roche-lobe overflow, common envelopes, and empirical parameterizations of wind mass loss. For a more extensive description of SeBa we refer to Portegies Zwart & Verbunt (1996), Nelemans et al. (2001), and Toonen et al. (2012).</text>
<text><location><page_2><loc_7><loc_19><loc_50><loc_48></location>As is common, we use parameterizations to describe the common-envelope process. In this study, the density profile of the donor envelope is parametrized by GLYPH<21> = 1 = 2, the e GLYPH<14> ciency with which orbital energy is used on unbinding the common envelope by GLYPH<11> CE = 4 (justified by explosive shell burning in massive stars during the common-envelope phase, Podsiadlowski et al. 2010) and the specific angular momentum of the envelope after it has left the system, relative to the specific angular momentum of the pre-common-envelope binary, by GLYPH<13> = 7 = 4. In choosing a value of GLYPH<11> CE GLYPH<21> = 2 for massive stars we follow Portegies Zwart & Yungelson (1998); Yungelson et al. (2006); Yungelson & Lasota (2008). The GLYPH<13> - and GLYPH<11> CE-prescriptions are used as described in Toonen et al. (2012). A metallicity Z = 0 : 02 has been used (Zoccali et al. 2003). The metallicity is held constant in the population synthesis simulations as well as the subsequent tracks because of the relatively short episode of star formation (Sect. 2.2). For the kicks acquired by nascent neutron stars we use the velocity distribution suggested by Paczy'nski (1990) with a dispersion of 270 km s GLYPH<0> 1 . Because these parameters are very uncertain, in Sect. 4 we will consider the e GLYPH<11> ect of varying the common-envelope parameters and the supernova kick velocity distribution from our standard values.</text>
<section_header_level_1><location><page_2><loc_7><loc_16><loc_46><loc_17></location>2.2. Star formation history and initial binary parameters</section_header_level_1>
<text><location><page_2><loc_7><loc_9><loc_50><loc_15></location>The star formation history of the Galactic Bulge can be approximated by a Gaussian distribution with a mean GLYPH<22> = GLYPH<0> 10 Gyr and a standard deviation GLYPH<27> = 0 : 5 GLYPH<0> 2 : 5 Gyr, where the total mass of stars that are formed is 1 GLYPH<2> 10 10 M GLYPH<12> (Clarkson & Rich 2009;</text>
<text><location><page_2><loc_56><loc_90><loc_57><loc_92></location>10</text>
<figure>
<location><page_2><loc_52><loc_71><loc_91><loc_91></location>
<caption>Figure 1. Star formation history of the Galactic Bulge as a Gaussian distribution for mean GLYPH<22> = GLYPH<0> 10 Gyr and two values of the standard deviation GLYPH<27> . The total mass of the stars formed is 1 GLYPH<2> 10 10 M GLYPH<12> . Time = 0 corresponds to the present. Star formation is assumed to start at Time = GLYPH<0> 13 Gyr.</caption>
</figure>
<text><location><page_2><loc_52><loc_52><loc_95><loc_61></location>Wyse 2009). Star formation is assumed to start 13 Gyr before present. For a narrow distribution the star formation is concentrated around 10 Gyr in the past, but the GLYPH<27> = 2 : 5 Gyr distribution has an important tail of recent star formation. In this paper we consider GLYPH<27> = 0 : 5 Gyr and GLYPH<27> = 2 : 5 Gyr (Fig. 1), representing a relatively instantaneous burst of star formation, and additional recent star formation, respectively.</text>
<text><location><page_2><loc_52><loc_29><loc_95><loc_52></location>We find the initial binary parameters by primary-constrained pairing (Kouwenhoven et al. 2008). We derive the initial mass function for the primary components by combining the initial mass function for stellar systems by Kroupa (2001) with an estimate of the binary fraction as a function of mass. The mass ratio of the secondary and the primary is drawn from a flat distribution between 0 and 1. The 1 GLYPH<2> 10 10 M GLYPH<12> of stellar mass is found to contain 5 : 2 GLYPH<2> 10 9 binary systems. We simulated 1 million binaries with a lower primary mass limit of 4 M GLYPH<12> (because systems with a lower primary mass do not produce a supernova event in either component), and another 4 : 3 million binaries with a lower primary mass limit of 8 M GLYPH<12> , after it became clear that systems with lower primary masses do not produce UCXBs. Using the binary initial mass function we calculated to how many binaries in the full mass range of primaries (0 : 08 GLYPH<0> 100 M GLYPH<12> ) this simulation corresponds. The resulting population was then multiplied by a factor (of 14 : 45) to scale to the entire Bulge population.</text>
<text><location><page_2><loc_52><loc_27><loc_95><loc_29></location>For an analytic derivation of the binary initial mass function we refer to Appendix A.</text>
<section_header_level_1><location><page_2><loc_52><loc_23><loc_70><loc_25></location>2.3. Formation scenarios</section_header_level_1>
<text><location><page_2><loc_52><loc_19><loc_95><loc_23></location>Weconsider three UCXB-progenitor classes, each defined by the stellar type of the donor at the time it fills, or will fill, its Roche lobe:</text>
<text><location><page_2><loc_52><loc_11><loc_95><loc_15></location>Class 2. Helium burning star with a neutron star or black hole companion (Savonije et al. 1986; Iben & Tutukov 1987; Yungelson 2008),</text>
<text><location><page_2><loc_52><loc_15><loc_95><loc_19></location>Class 1. White dwarf with a neutron star or black hole companion (Tutukov & Yungelson 1993; Iben et al. 1995; Yungelson et al. 2002),</text>
<text><location><page_2><loc_52><loc_9><loc_95><loc_11></location>Class 3. Evolved main sequence star of about 1 M GLYPH<12> with a neu-</text>
<text><location><page_3><loc_7><loc_88><loc_50><loc_93></location>tron star or black hole companion (Tutukov et al. 1985; Nelson et al. 1986; Fedorova & Ergma 1989; Pylyser & Savonije 1989; Podsiadlowski et al. 2002; Nelson & Rappaport 2003; van der Sluys et al. 2005a; Lin et al. 2011).</text>
<text><location><page_3><loc_7><loc_63><loc_50><loc_67></location>The initial system parameters (component masses and orbital periods) and major events during the evolution towards an UCXB are described below for each class.</text>
<text><location><page_3><loc_7><loc_67><loc_50><loc_88></location>These classes include all the binary systems that may eventually evolve into an UCXB (Belczynski & Taam 2004a; van der Sluys et al. 2005a; Nelemans et al. 2010) - in some models involving accretion-induced collapse of a white dwarf or a neutron star, the donor star has already transferred mass before the formation of the eventual accretor, a neutron star or a black hole, respectively. The detailed tracks follow the evolution of the helium burning donor starting immediately after its formation, and the main sequence donor immediately after the supernova event. The white dwarf donor tracks start at the onset of Roche-lobe overflow. In each of the detailed tracks the mass transfer is conservative as long as the mass transfer rate does not exceed the Eddington limit. If the mass transfer is faster than that, accretion at the Eddington limit is assumed, and the mass that is lost from the system carries the specific angular momentum of the accretor.</text>
<section_header_level_1><location><page_3><loc_7><loc_60><loc_31><loc_61></location>2.3.1. White dwarf donor systems</section_header_level_1>
<text><location><page_3><loc_7><loc_31><loc_50><loc_59></location>The evolution of UCXBs with a white dwarf donor can be divided into two main categories based on whether the primary (initially more massive star) or secondary component becomes a supernova. A supernova explosion of the secondary star is possible when it gains mass by hydrogen accretion from the primary (e.g. Tutukov & Yungelson 1993; Portegies Zwart & Verbunt 1996; van Kerkwijk & Kulkarni 1999; Portegies Zwart & Yungelson 1999; Tauris & Sennels 2000). A supernova explosion of the secondary probably never produces a black hole, neither does the primary turn into a helium white dwarf after the supernova, because it starts out too massive. Thus, all secondarysupernova systems have a carbon-oxygen or oxygen-neon white dwarf donor and a neutron star accretor. Because the high stellar mass required for a supernova explosion of the primary is relatively rare due to the steep initial mass function, in our simulations a significant fraction of the systems (13% of the carbonoxygen white dwarf systems and 36% of the oxygen-neon white dwarf systems) experience their supernova in the secondary star. Systems with a black hole accretor are rare, about 0 : 2% of all white dwarf systems. All black holes form from the primary and have a GLYPH<24> 0 : 6 GLYPH<0> 0 : 8 M GLYPH<12> carbon-oxygen white dwarf companion.</text>
<text><location><page_3><loc_7><loc_27><loc_50><loc_32></location>Carbon-oxygen white dwarf systems 1 are 1 : 5 times more prevalent than oxygen-neon white dwarf systems in our simulations, and GLYPH<24> 30 times more prevalent than helium white dwarf systems (combining primary and secondary supernovae).</text>
<text><location><page_3><loc_7><loc_21><loc_50><loc_25></location>Supernova explosion of the primary This category can be subdivided by the predominant white dwarf composition: helium, carbon-oxygen or oxygen-neon.</text>
<text><location><page_3><loc_7><loc_14><loc_50><loc_21></location>Evolution starts with a zero-age main sequence binary in which the primary is a massive star ( M & 8 M GLYPH<12> if the secondary is to become a helium or carbon-oxygen white dwarf, and M & 10 M GLYPH<12> in the case of an oxygen-neon white dwarf companion) that evolves o GLYPH<11> the main sequence first. Systems</text>
<text><location><page_3><loc_52><loc_70><loc_95><loc_93></location>that eventually produce a helium white dwarf donor have initial orbital periods ranging mainly from 1 to 100 yr. For systems that produce a carbon-oxygen or oxygen-neon white dwarf donor the orbital periods lie mostly between 0 : 1 and 1000 yr. In the case of neutron star accretors, the primary expands during the Hertzsprung gap or as a giant and fills its Roche lobe, followed by mass transfer to the companion. The secondary cannot accrete all of this mass and is engulfed in a common envelope (Paczy'nski 1976). The envelope is expelled before the two components merge and the exposed helium core and the main sequence secondary are left behind with an orbital separation several tens of times smaller than before. After a few 10 Myr, the helium star turns into a giant (which may lead to a subsequent phase of Roche-lobe overflow) and explodes as a core-collapse supernova, leaving behind a neutron star. Black hole progenitors are Wolf-Rayet stars, which lose a large fraction of their mass before evolving into a helium giant, and then collapse to form a black hole.</text>
<text><location><page_3><loc_52><loc_39><loc_95><loc_69></location>Secondary stars that eventually become a helium white dwarf donor had a zero-age main sequence mass between 1 : 4 and 2 : 3 M GLYPH<12> , whereas for carbon-oxygen white dwarf donors this range is 2 : 3 GLYPH<0> 7 M GLYPH<12> , where 2 : 3 M GLYPH<12> is the maximum mass of single stars that undergo the helium flash. A small fraction started with a higher initial mass. Progenitors of oxygen-neon white dwarf secondaries have a mass between 7 and 11 M GLYPH<12> on the zero-age main sequence and do not become a supernova due to severe mass loss (e.g. Gil-Pons & Garc'ıa-Berro 2001). (There is some overlap with the progenitor mass range of carbon-oxygen white dwarfs - the end product depends on whether burning stops before of after carbon ignition.) After the supernova explosion has occurred, the secondary evolves o GLYPH<11> the main sequence. As a subgiant, it initiates a common envelope with the neutron star, shrinking the orbit by another factor of a few tens. The core cools into a helium white dwarf ( . 0 : 35 M GLYPH<12> ) or, after a helium burning and helium giant stage, a carbon-oxygen white dwarf (0 : 35 GLYPH<0> 1 : 1 M GLYPH<12> ), or even, after carbon burning, an oxygen-neon white dwarf ( & 1 : 1 M GLYPH<12> , Gil-Pons & Garc'ıa-Berro 2001). Orbital angular momentum loss via gravitational wave radiation further shrinks the orbit until the white dwarf eventually overfills its Roche lobe, which happens at an orbital period of a few minutes.</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_37></location>Supernova explosion of the secondary In this scenario, the total binary mass needs to be at least 9 M GLYPH<12> if the primary becomes a carbon-oxygen white dwarf and 12 M GLYPH<12> if the primary becomes an oxygen-neon white dwarf. The primary transfers several solar masses to the secondary in a stable manner (avoiding a common envelope - initially the secondary must have a mass of at least 0 : 55 times the primary mass) while ascending the red giant branch (e.g. Tauris & Sennels 2000). Eventually the core becomes a helium star, or a carbon-oxygen or oxygen-neon white dwarf. The secondary, which becomes the more massive component of the system, evolves o GLYPH<11> the main sequence and initiates a common envelope. The orbit shrinks, and 30 GLYPH<0> 70 Myr after the binary formation the secondary explodes as a supernova and produces a neutron star. In systems which remain bound after the supernova explosion, the primary will eventually reach Rochelobe overflow as a relatively massive ( & 0 : 7 M GLYPH<12> ) carbon-oxygen white dwarf or an oxygen-neon white dwarf ( & 1 : 1 M GLYPH<12> ). The relatively high initial mass of the primary precludes less massive carbon-oxygen white dwarfs. The initial orbital period in this scenario can be much shorter than in the primary-supernova scenarios, down to a few days. The initial stellar masses lie be-</text>
<text><location><page_4><loc_7><loc_88><loc_50><loc_93></location>tween 4 : 5 and GLYPH<24> 10 M GLYPH<12> for the primary and 4 GLYPH<0> 9 M GLYPH<12> for the secondary (if the former becomes a carbon-oxygen white dwarf) and about 5 GLYPH<0> 12 M GLYPH<12> for both the primary and secondary (if the former becomes an oxygen-neon white dwarf).</text>
<text><location><page_4><loc_7><loc_45><loc_50><loc_86></location>The onset of mass transfer from the white dwarf Most white dwarf-neutron star systems merge upon the onset of mass transfer. For a 1 : 4 M GLYPH<12> neutron star companion, white dwarfs with a mass higher than GLYPH<24> 0 : 83 M GLYPH<12> experience dynamically unstable mass transfer, assuming a zero-temperature (completely degenerate) mass-radius relation for the donor (e.g. Yungelson et al. 2002; van Haaften et al. 2012b). This assumption implies that these white dwarfs have cooled considerably by the time they eventually fill their Roche lobe, although tidal heating and irradiation before the onset of mass transfer may counteract this for a short time. 2 This leads to runaway mass loss on the dynamical timescale of the donor, followed by accretion of part of the disrupted white dwarf via a disk around the neutron star (see e.g. van den Heuvel & Bonsema 1984; Fryer et al. 1999; Paschalidis et al. 2011; Metzger 2012). Furthermore, in systems with a donor mass larger than GLYPH<24> 0 : 38 M GLYPH<12> (Yungelson et al. 2002; van Haaften et al. 2012b) (this value is only weakly sensitive to accretor mass) the accretor will be unable to eject enough transferred matter from the system by isotropic re-emission, where most arriving matter leaves the vicinity of the accretor in a fast, isotropic wind powered by accretion (Soberman et al. 1997; Tauris & Savonije 1999). This also leads to a merger. Therefore, systems that are unstable due to either a dynamical instability or insu GLYPH<14> cient isotropic re-emission have been removed from the sample. These instabilities only occur in systems with a white dwarf donor, because of the negative donor mass-radius exponent and the small donor size (hence, small orbit) at the onset of mass transfer. Dynamical instabilities may occur in systems with helium or main sequence donors if they have masses considerably higher than considered in this study (see e.g. Pols & Marinus 1994).</text>
<text><location><page_4><loc_7><loc_34><loc_50><loc_46></location>In our simulation 97 : 4% of all white dwarf systems have a donor with a mass higher than 0 : 38 M GLYPH<12> and do not survive the onset of mass transfer. This includes 99 : 1% of carbon-oxygen (solid line in Fig. 2) and all oxygen-neon (dashed line in Fig. 2) white dwarf systems. In about 80% of the surviving white dwarf donor systems, the donor is a helium white dwarf (dotted line in Fig. 2), in the remainder it is a carbon-oxygen white dwarf. All surviving systems experienced the supernova explosion in the primary star and host a neutron star.</text>
<text><location><page_4><loc_7><loc_28><loc_50><loc_34></location>If a white dwarf donor with a mass higher than the 0 : 38 M GLYPH<12> isotropic re-emission limit has a non-degenerate surface layer, the system may not merge immediately upon the onset of mass transfer, but it will once this layer has been lost.</text>
<text><location><page_4><loc_7><loc_19><loc_50><loc_28></location>Two thirds of the white dwarf donor systems start to transfer mass to the neutron star within 2 Gyr, but some systems take much longer (Fig. 3). This is the case for all white dwarf types. White dwarfs can take very long to start mass transfer depending on the width of the initial orbit, since the orbital decay of binaries consisting of a neutron star and a white dwarf is caused by gravitational wave radiation only.</text>
<text><location><page_4><loc_7><loc_15><loc_50><loc_17></location>Evolutionary tracks For each donor composition, the evolution after the stage described in Sect. 2.3.1 follows the tracks de-</text>
<figure>
<location><page_4><loc_54><loc_71><loc_90><loc_91></location>
</figure>
<text><location><page_4><loc_87><loc_70><loc_88><loc_72></location>/circledot</text>
<figure>
<location><page_4><loc_52><loc_40><loc_91><loc_60></location>
<caption>Figure 2. Total time-integrated number of UCXBs with a helium (dotted line), carbon-oxygen (solid line) or oxygen-neon (dashed line) white dwarf donor at the onset of mass transfer to a neutron star (including merging systems).Figure 3. Delay time distribution between the zero-age main sequence (ZAMS) and the onset of mass transfer to a neutron star for UCXBs with a white dwarf (excluding merging systems, solid line), helium star (dashed line) and main sequence (dotted line) donor.</caption>
</figure>
<text><location><page_4><loc_52><loc_10><loc_95><loc_27></location>scribed in van Haaften et al. (2012b). Initially, the white dwarf donor has not yet cooled and therefore is larger than a zerotemperature white dwarf of the same mass. While the donor loses mass, its radius is held constant until it equals the zerotemperature radius of the same mass (this is justified by the rapid mass loss the donor initially experiences). From this point on, the zero-temperature radius (Zapolsky & Salpeter 1969; Rappaport et al. 1987) is used, which increases with further mass loss. The initial neutron star mass is taken to be 1 : 4 M GLYPH<12> and its radius 12 km (Guillot et al. 2011; Steiner et al. 2013). The evolution of UCXBs with degenerate donor stars is governed by angular momentum loss through gravitational wave radiation, which forces mass transfer via Roche-lobe overflow.</text>
<text><location><page_5><loc_11><loc_90><loc_12><loc_92></location>6</text>
<section_header_level_1><location><page_5><loc_52><loc_92><loc_78><loc_93></location>2.3.3. Main sequence donor systems</section_header_level_1>
<figure>
<location><page_5><loc_8><loc_71><loc_46><loc_91></location>
<caption>Figure 4. Sample of helium star-neutron star UCXB tracks, for initial helium star mass range 0 : 35 GLYPH<0> 1 : 0 M GLYPH<12> and initial orbital period range 20 GLYPH<0> 200 min by Nelemans et al. (2010) (solid lines), and our white dwarf donor track extensions (dashed lines).</caption>
</figure>
<section_header_level_1><location><page_5><loc_7><loc_58><loc_33><loc_59></location>2.3.2. Helium burning donor systems</section_header_level_1>
<text><location><page_5><loc_7><loc_38><loc_50><loc_57></location>The supernova in low-mass helium burning star systems occurs in the primary, which has an initial mass M & 8 M GLYPH<12> . Most systems start out with an orbital period between 0 : 1 and 100 yr. Most of the helium stars form less than 500 Myr after the zeroage main sequence when the secondaries, with initial masses of 2 : 3 GLYPH<0> 5 M GLYPH<12> experience hydrogen shell burning (Savonije et al. 1986) and lose their hydrogen envelope in case B mass transfer (Kippenhahn & Weigert 1967). They fill their Roche lobes within another GLYPH<24> 200 Myr, which is much earlier than UCXBs with white dwarf donors. In part this is due to the requirement that the helium star has not yet turned into a white dwarf before the onset of mass transfer (thereby disqualifying itself from the helium burning donor sample) which constrains the size of the initial orbit. We do not find systems with a black hole accretor.</text>
<text><location><page_5><loc_7><loc_16><loc_50><loc_38></location>We have used stellar evolutionary tracks for systems with an 0 : 35 GLYPH<0> 1 : 0 M GLYPH<12> helium star and a 1 : 4 M GLYPH<12> neutron star at initial orbital periods 3 between 20 and 200 min (Nelemans et al. 2010, table in electronic article), part of which is shown in Fig. 4. These tracks were made in the same way as the tracks for systems with white dwarf accretors in Yungelson (2008). The donor metallicity Z = 0 : 02. Because the donors at the end of the tracks are degenerate, we have extended these tracks by making a smooth transition to the zero-temperature white dwarf evolution. The tracks describe the orbital period, mass transfer rate, donor mass, and core and surface compositions as a function of time. In Fig. 4, the helium stars live up to 400 Myr. After the onset of mass transfer (vertical part of the tracks), the orbits shrink until the period minimums, then expand towards the bottom right of the figure. For each individual 'zero-age' UCXB system produced by SeBa , the track that best matches its donor mass and orbital period has been used.</text>
<text><location><page_5><loc_52><loc_71><loc_95><loc_90></location>Main sequence donors have mostly evolved from 1 : 0 GLYPH<0> 1 : 2 M GLYPH<12> secondaries that started transferring mass after orbital decay due to magnetic braking (van der Sluys et al. 2005a). After the magnetic field disappears (because the star becomes fully convective as a result of mass loss), gravitational wave radiation becomes the dominating angular momentum loss mechanism, continuing the orbital shrinking. In this scenario, the initial period and donor mass need to fall within relatively narrow ranges in order to sufficiently evolve the main sequence star. Moreover, the magnetic braking must be su GLYPH<14> ciently e GLYPH<14> cient (van der Sluys et al. 2005b) which it probably is not (Queloz et al. 1998). Depending on the extent of hydrogen depletion in the stellar center, systems can reach a minimum orbital period between 10 and 80 min, where GLYPH<24> 80 min is the lower limit for hydrogen-rich donors (Paczy'nski 1981).</text>
<text><location><page_5><loc_52><loc_62><loc_95><loc_70></location>We have used stellar evolutionary tracks by van der Sluys et al. (2005a) for binaries with an 0 : 7 GLYPH<0> 1 : 5 M GLYPH<12> main sequence star and a 1 : 4 M GLYPH<12> neutron star at initial orbital periods between 0 : 50 and 2 : 75 days. The donor metallicity Z = 0 : 01. These tracks describe the orbital period and mass transfer rate as a function of time, as well as the core and surface compositions.</text>
<section_header_level_1><location><page_5><loc_52><loc_58><loc_71><loc_59></location>2.4. Behavior of old UCXBs</section_header_level_1>
<text><location><page_5><loc_52><loc_18><loc_95><loc_56></location>Figure 4 suggests that once the donor has become degenerate, UCXBs 'uneventfully' reach long orbital periods and very low mass transfer rates. This is probably not the case. Instead, at low mass transfer rate a thermal-viscous instability in the accretion disk (Osaki 1974; Lasota 2001) can cause UCXBs with a sufficiently low mass transfer rate to become transient (Deloye & Bildsten 2003). This usually implies that these systems are visible only during outbursts when the disk is in a hot state, which is only a small fraction of the time, and not during the quiescent state when the disk is cold and gaining mass. Furthermore, due to accretion of angular momentum, a neutron star accretor in an UCXB can be recycled to a spin period between one and a few ms (Bisnovatyi-Kogan & Komberg 1974; Alpar et al. 1982; Radhakrishnan & Srinivasan 1982). Combined with a low mass transfer rate, the magnetosphere may transfer angular momentum from the neutron star to the accretion disk, thereby accelerating orbiting disk matter and counteracting accretion, known as the 'propeller e GLYPH<11> ect' (Davidson & Ostriker 1973; Illarionov & Sunyaev 1975). As a result, the inner accretion disk, source of most X-ray radiation, can become disrupted by the magnetosphere. See van Haaften et al. (2012b) for more details on the thermal-viscous disk instability and propeller e GLYPH<11> ect in UCXBs. Finally, at low donor mass, high-energy radiation from the neutron star, the magnetosphere and the accretion disk may evaporate the donor, or detach it from its Roche lobe (Klu'zniak et al. 1988; van den Heuvel & van Paradijs 1988; Ruderman et al. 1989a; Rasio et al. 1989). Hot, low-mass donors may su GLYPH<11> er from a dynamical instability caused by a minimum value of their mass in the case of a constant core temperature (Bildsten 2002).</text>
<text><location><page_5><loc_52><loc_10><loc_95><loc_18></location>Each of these mechanisms can potentially diminish the visibility of UCXBs. Because it is impossible to precisely quantify at which stage of the evolution (if at all) these mechanisms become important, and to what degree, we do not remove UCXBs from the sample, instead we will discuss the implications on the population of old UCXBs in the Discussion (Sect. 4).</text>
<section_header_level_1><location><page_6><loc_7><loc_92><loc_27><loc_93></location>2.5. Present-day population</section_header_level_1>
<text><location><page_6><loc_7><loc_66><loc_50><loc_91></location>The present-day number and system parameters of UCXBs in the Galactic Bulge can be found by evaluating the evolutionary stage of all simulated systems at the present time. The most interesting parameters are the orbital period, mass transfer rate and surface composition, because these can be inferred from observations. The orbital periods of observed systems can be found from periodic modulations in the light curve or spectrum, although this is usually very di GLYPH<14> cult for UCXBs (e.g. Nelemans et al. 2006; in't Zand et al. 2007). Since the transferred matter originates from the surface of the donor, the occurrence and relative abundance of elements in the donor can be inferred from X-ray (Schulz et al. 2001), ultraviolet (Homer et al. 2002), and optical (Nelemans et al. 2004) spectra, and more indirectly, typeI X-ray bursts (in't Zand et al. 2005). The mass transfer rate cannot be directly determined observationally. However, because the energy output of an X-ray binary is for a large part provided by the gravitational energy release of the accreted matter, the mass transfer rate strongly influences the luminosity of the system, which can be observed.</text>
<section_header_level_1><location><page_6><loc_7><loc_62><loc_27><loc_63></location>2.5.1. Bolometric luminosity</section_header_level_1>
<text><location><page_6><loc_7><loc_59><loc_50><loc_61></location>We employ two methods of converting the modeled mass transfer rate to bolometric luminosity.</text>
<text><location><page_6><loc_7><loc_28><loc_50><loc_58></location>An observational method is to match the modeled systems to real systems and assume that the modeled system behaves similar to the real system in terms of emission. We match a modeled UCXB to the real UCXB with the nearest orbital period. The relevant parameter of the emission behavior is the fraction of the time a source radiates at a given bolometric luminosity, measured over a su GLYPH<14> ciently long timespan. We use 16-year observations by the RXTE ASM to determine this behavior for the 14 known UCXBs (including two candidates) for which ASM data is available. Figure 5 shows this behavior for sources when they are visible well above the noise level (van Haaften et al. 2012c). ASM X-ray luminosity was converted to bolometric luminosity using an estimate by in't Zand et al. (2007). At a given time, the luminosity of an UCXB is randomly drawn from either the individual ASM observations that make up this time-luminosity curve, or (most of the time) from the faint-end extrapolations of the curves in Fig. 5 (van Haaften et al. 2012c). These extrapolations are constructed in such a way that the average luminosity of the luminosity distribution is equal to the time-averaged luminosity of the source as observed by the ASM. The amount of time that a given source spends at a particular luminosity translates into the number of sources in a population at the same luminosity.</text>
<text><location><page_6><loc_7><loc_15><loc_50><loc_28></location>The second method, of a more theoretical nature, is to convert a system's modeled mass transfer rate to luminosity, using predictions by the disk instability model (Sect. 2.4) in the case of long-period UCXBs. According to this model the mass transfer rate must exceed a critical value in order to be stable and the source to be persistent, i.e., visible at a relatively high luminosity (almost) all the time. A crude estimate for the critical mass transfer rate in the case of an irradiated disk is given by in't Zand et al. (2007), based on Dubus et al. (1999); Lasota (2001); Menou et al. (2002)</text>
<formula><location><page_6><loc_12><loc_9><loc_50><loc_13></location>˙ M crit GLYPH<25> 5 : 3 GLYPH<2> 10 GLYPH<0> 11 f M a M GLYPH<12> ! 0 : 3 GLYPH<18> P orb h GLYPH<19> 1 : 4 M GLYPH<12> yr GLYPH<0> 1 (1)</formula>
<text><location><page_6><loc_56><loc_91><loc_57><loc_92></location>0</text>
<figure>
<location><page_6><loc_53><loc_71><loc_92><loc_91></location>
<caption>Figure 5. UCXB variability: fraction of time that a source emits above a given luminosity for 14 UCXBs, including two candidates with tentative orbital periods, adapted from van Haaften et al. (2012c). The numbers associated with the curves indicate the orbital periods in minutes.</caption>
</figure>
<text><location><page_6><loc_52><loc_56><loc_95><loc_61></location>with M a the accretor mass, P orb the orbital period, and f is a factor accounting for the disk composition; f GLYPH<25> 1 for carbonoxygen disks and f GLYPH<25> 6 for helium disks.</text>
<formula><location><page_6><loc_69><loc_50><loc_95><loc_54></location>L = GM a ˙ M a 2 R a ; (2)</formula>
<text><location><page_6><loc_52><loc_53><loc_95><loc_57></location>When the time-averaged mass transfer rate exceeds the critical value, the bolometric luminosity L is assumed to be constant at</text>
<text><location><page_6><loc_52><loc_49><loc_92><loc_50></location>with G the gravitational constant and R a the accretor radius.</text>
<formula><location><page_6><loc_68><loc_37><loc_95><loc_40></location>DC = L avg L outburst ; (3)</formula>
<text><location><page_6><loc_52><loc_40><loc_95><loc_49></location>Sources with a time-averaged mass transfer rate below the critical value are assumed to be visible only during outburst stages. The predictions by the thermal-viscous disk instability model regarding the degree of variability of sources is supported by observations (van Paradijs 1996; Ramsay et al. 2012; Coriat et al. 2012). The duty cycle (fraction of the time the source is in outburst) is</text>
<text><location><page_6><loc_52><loc_32><loc_95><loc_36></location>where L avg is the time-averaged luminosity based on the theoretical mass transfer rate, (Eq. 2), and L outburst is the luminosity during outburst, derived by Lasota et al. (2008)</text>
<formula><location><page_6><loc_60><loc_28><loc_95><loc_32></location>L outburst GLYPH<25> 3 : 5 GLYPH<2> 10 37 GLYPH<18> P orb h GLYPH<19> 1 : 67 erg s GLYPH<0> 1 ; (4)</formula>
<text><location><page_6><loc_52><loc_20><loc_95><loc_28></location>which is consistent with observations of outbursts in UCXBs (e.g. Wu et al. 2010). The period of this cycle is not relevant here. We neglect the decay in the light curve after an outburst. Furthermore, we do not predict the luminosity of systems that are in quiescence, which in fact has been assumed to be zero in the above method.</text>
<text><location><page_6><loc_52><loc_10><loc_95><loc_20></location>Both methods have advantages and shortcomings. The ASM observations have a rather high lower limit in converted bolometric luminosity, of GLYPH<24> 10 37 erg s GLYPH<0> 1 at 8 : 3 kpc, the estimated distance to the Galactic Center (Gillessen et al. 2009). Below this luminosity, we have to rely on extrapolations. Also, variability on a timescale longer than 16 yr cannot have been observed by the ASM. On the other hand, the data do not strongly rely on uncertainties in models, as is the case for the disk instability</text>
<text><location><page_7><loc_7><loc_80><loc_50><loc_93></location>model method. The ASM data show that UCXBs with a similar orbital period can behave rather di GLYPH<11> erently, for instance XTE J1751-305 (42 : 4 min orbital period) and XTE J0929-314 (43 : 6 min), or 4U 0513-40 (17 : 0 min) and 2S 0918-549 (17 : 4 min). Equation (1), however, shows that in the disk instability model the critical mass transfer rate and hence luminosity is largely determined by the orbital period and composition. A longer orbital period does not automatically imply a lower luminosity, as evidenced by M 15 X-2 (20 : 6 min orbital period) and 4U 1916-05 (49 : 5 min).</text>
<text><location><page_7><loc_7><loc_66><loc_50><loc_80></location>In general, the ASM data show that a clear distinction between persistent and transient behavior is not justified (van Haaften et al. 2012c). Almost all systems are visible above the ASM detection limit only sporadically. Still, short orbital period systems are typically visible more often at a given luminosity, i.e., they have a (slightly) higher time-averaged luminosity. Even though the available sample is small, individual unusual behavior is expected to partially cancel out for the population as a whole, because some modeled UCXBs will be matched to a real UCXB that is brighter than typical for its orbital period, while others will be matched to one that is fainter than typical.</text>
<section_header_level_1><location><page_7><loc_7><loc_63><loc_25><loc_64></location>2.5.2. Donor composition</section_header_level_1>
<text><location><page_7><loc_7><loc_30><loc_50><loc_62></location>The donor surface compositions of the modeled UCXBs are predicted using the helium-star donor and main sequence donor tracks, as well as the white dwarf types from the population synthesis model. These predicted compositions can be compared to observations of real systems, in the Bulge and elsewhere. Donors that start mass transfer as a white dwarf can be helium and carbon-oxygen white dwarfs (Sect. 2.3.1). In the latter case we assume 30% carbon and 70% oxygen by mass, based on the most common eventual compositions in the helium burning donors (Sect. 3.4). Donors that start mass transfer as a helium burning star can also produce helium-carbon-oxygen donors due to an interrupted helium burning stage. For the subsequent tracks for these systems, we use the mass-radius relation for degenerate donors composed of a mixture of 60% helium, 30% carbon and 10% oxygen, a choice based on the dominant tracks by Nelemans et al. (2010) as will be discussed in Sect. 3.4. We note that the degenerate tracks are not very sensitive to the composition (as long as there is no hydrogen), so these simplifications are justified. Matter processed in the CNO cycle has a high nitrogento-carbon abundance ratio, whereas helium burning converts this to a low ratio. Consequently, the nitrogen-to-oxygen ratio is a good test for the formation channel because it can discriminate between a history as a helium white dwarf donor or a helium burning donor (Nelemans et al. 2010).</text>
<text><location><page_7><loc_7><loc_19><loc_50><loc_31></location>Based on the overview in van Haaften et al. (2012c), the compositions of observed UCXBs can be summarized as being roughly equally distributed over helium and carbon-oxygen compositions. There is no clear dependency on the orbital period, although helium composition may be more common among systems with a long orbital period ( & 40 min) (van Haaften et al. 2012c). The surface composition of very low-mass donors corresponds to the (inner) core composition of the object before it started transferring mass.</text>
<section_header_level_1><location><page_7><loc_7><loc_15><loc_15><loc_16></location>3. Results</section_header_level_1>
<section_header_level_1><location><page_7><loc_7><loc_13><loc_38><loc_14></location>3.1. Birth rates and total number of systems</section_header_level_1>
<text><location><page_7><loc_7><loc_10><loc_50><loc_12></location>Convolving the star formation history (Fig. 1) with the delay times of the onset of mass transfer (Fig. 3) yields the birth rate</text>
<figure>
<location><page_7><loc_53><loc_71><loc_91><loc_91></location>
<caption>Figure 6. Birth rate of systems reaching Roche-lobe overflow against time for UCXBs from the white dwarf donor channel (solid lines), helium-star donor channel (dashed lines) and main sequence donor channel (dotted lines). Time = 0 corresponds to the present. Black lines correspond to a star formation history width GLYPH<27> = 0 : 5 Gyr, gray lines to GLYPH<27> = 2 : 5 Gyr.</caption>
</figure>
<text><location><page_7><loc_52><loc_37><loc_95><loc_59></location>distributions, shown in Fig. 6 for burst-like (black) and extended (gray) star formation epochs. Except for part of the white dwarf channel and the main sequence channel, the delay times are much shorter than the age of the Bulge (Sect. 2.2). In the case of GLYPH<27> = 0 : 5 Gyr, 98% of the white dwarf donor systems have started Roche-lobe overflow before the present, whereas 100% of the helium-star donor and 84% of the main sequence donor systems have. In the case of GLYPH<27> = 2 : 5, these percentages are 97%, 100% and 77%, respectively. The main distinguishing feature between the three classes (Sect. 2.3) is the most recent time at which mass transfer can begin. Initially wide systems from the white dwarf donor channel can still start mass transfer at the present, whereas main sequence donor systems and especially helium-star donor systems cannot, unless they have formed relatively recently (star formation history width GLYPH<27> = 2 : 5 Gyr). The rate of helium burning donor systems reaching Roche-lobe overflow closely follows the star formation history.</text>
<text><location><page_7><loc_52><loc_21><loc_95><loc_37></location>Upon the onset of mass loss, the donor radius increases immediately for fully degenerate white dwarf donors, and after approximately 100 Myr for helium burning donors, once the donor has become su GLYPH<14> ciently degenerate following the extinction of nuclear fusion (this happens some time after the period minimum). The orbital period decreases in the case of helium burning or main sequence donors, whereas the period increases with mass loss for systems with degenerate donors (in each channel). If main sequence donor systems become ultracompact, this typically happens GLYPH<24> 3 Gyr after the onset of mass transfer, and mass transfer starts after 2 GLYPH<0> 6 Gyr after the formation of the binary (van der Sluys et al. 2005a).</text>
<text><location><page_7><loc_52><loc_10><loc_95><loc_21></location>The total number of UCXBs with a white dwarf or heliumstar donor, shown as the solid and dashed lines in Fig. 7, initially follows the star formation rate and later on approaches an upper limit as star formation slows down. The number of systems below a given orbital period initially resembles the instantaneous star formation rate more closely for short orbital periods. After the peak in star formation rate, the number of systems below a given period keeps increasing as long as more new systems form than old systems are removed from the given sample due</text>
<figure>
<location><page_8><loc_9><loc_71><loc_46><loc_91></location>
<caption>all Figure 7. Number of UCXBs from the white dwarf donor channel (solid lines), helium-star donor channel (dashed lines) and main sequence donor channel (dotted lines). Time = 0 corresponds to the present. For each line style, the three lines represent the full population (upper) and the systems with orbital periods shorter than 60 min (middle) and shorter than 20 min (lower). A star formation history width GLYPH<27> = 0 : 5 Gyr has been used.</caption>
</figure>
<text><location><page_8><loc_7><loc_53><loc_50><loc_57></location>to their increasing orbital periods. The numbers of systems from the three di GLYPH<11> erent classes decline at di GLYPH<11> erent rates corresponding to their respective recent birth rates (Fig. 6).</text>
<section_header_level_1><location><page_8><loc_7><loc_50><loc_27><loc_51></location>3.2. Present-day population</section_header_level_1>
<text><location><page_8><loc_7><loc_27><loc_50><loc_49></location>While the evolution of the population is interesting in itself, the population today can be used to validate the results. In the case of a star formation history distribution width GLYPH<27> = 0 : 5 Gyr, shown in Fig. 8, most systems at the present are old, and have expanded to an orbital period of GLYPH<24> 80 min. Since evolution slows down at longer periods, systems tend to 'pile up'. 4 Di GLYPH<11> erences in donor composition lead to di GLYPH<11> erent present-day orbital periods. This is the case even among hydrogen-deficient compositions because during most of the evolution, the donor mass is low enough for Coulomb physics to be important to the stellar structure, or even dominating degeneracy pressure. Coulomb interactions cause a donor that is composed of 'heavy' elements such as carbon and oxygen to have a smaller radius than donors with lighter composition, such as helium, of the same mass (Zapolsky & Salpeter 1969). A larger donor radius (at each mass) results in a longer orbital period at each mass, but also at each age (because less time is spent at a given orbital period). 5</text>
<text><location><page_8><loc_7><loc_15><loc_50><loc_27></location>For GLYPH<27> = 0 : 5 Gyr, all UCXBs with orbital periods shorter than 1 h started Roche-lobe overflow from a white dwarf donor (Fig. 8), long after the formation of the system. Most of these systems host a helium white dwarf. The main sequence channel contributes a negligible number of UCXBs and can only be distinguishable (in principle) via donor compositions. For GLYPH<27> = 2 : 5 Gyr, shown in Fig. 9, there is also recent star formation. This produces a population of young UCXBs that descended from helium burning donor systems (or still have a helium burning</text>
<figure>
<location><page_8><loc_53><loc_71><loc_92><loc_92></location>
<caption>Figure 8. Present-day orbital period distribution for UCXBs from the white dwarf donor channel (solid lines), helium-star donor channel (dashed lines) and main sequence donor channel (dotted lines). The elements next to the lines indicate the most abundant element(s) at the surface of the donor, hence in the transferred matter. The star formation history has width GLYPH<27> = 0 : 5 Gyr.</caption>
</figure>
<figure>
<location><page_8><loc_53><loc_36><loc_92><loc_57></location>
<caption>Figure 9. Same as Fig. 8 except GLYPH<27> = 2 : 5 Gyr.</caption>
</figure>
<text><location><page_8><loc_52><loc_24><loc_95><loc_28></location>donor), with orbital periods shorter than 1 h. The steep cut-o GLYPH<11> at the long-period end of several curves is due to the assumption that star formation suddenly starts 13 Gyr before present.</text>
<text><location><page_8><loc_52><loc_10><loc_95><loc_24></location>Combining all donor compositions, the result is a current GLYPH<24> 1 : 9 GLYPH<2> 10 5 population of UCXBs, mostly at long orbital period (60 GLYPH<0> 90 min). The total number of UCXBs in each class is 3 : 5 GLYPH<2> 10 4 (18%) with white dwarf donors, 1 : 56 GLYPH<2> 10 5 (81%) with helium-star donors, and 5 : 1 GLYPH<2> 10 2 (0 : 3%) with main sequence donors. The number of modeled systems with orbital periods shorter than 60 min is 1 : 5 GLYPH<2> 10 3 for GLYPH<27> = 0 : 5 Gyr, and 7 : 4 GLYPH<2> 10 3 for GLYPH<27> = 2 : 5 Gyr (0 : 8%and 3 : 8%of the population, respectively). We note that these numbers are rather sensitive to assumptions in the model, and could be lower by an order of magnitude, as will be discussed in Sect. 4.</text>
<figure>
<location><page_9><loc_8><loc_71><loc_47><loc_91></location>
<caption>Figure 10. Present-day luminosity distribution of UCXBs in the Bulge based on Rossi XTE All-Sky Monitor observations, after incorporating the accelerated evolution of the systems (Sect. 3.3.1). The star formation history has width GLYPH<27> = 0 : 5 Gyr (solid line) and GLYPH<27> = 2 : 5 Gyr (dashed line).</caption>
</figure>
<section_header_level_1><location><page_9><loc_7><loc_59><loc_26><loc_60></location>3.3. Observable population</section_header_level_1>
<text><location><page_9><loc_7><loc_54><loc_50><loc_58></location>As described in Sect. 2.5.1, in order to determine what we can observe at high luminosity we have to convert the modeled population to luminosities.</text>
<section_header_level_1><location><page_9><loc_7><loc_51><loc_27><loc_52></location>3.3.1. RXTE All-Sky Monitor</section_header_level_1>
<text><location><page_9><loc_7><loc_25><loc_50><loc_50></location>In the first method, we apply the observations of known UCXBs by the RXTE ASM (Fig. 5, Sect. 2.5.1) to the modeled population (Figs. 8 and 9, Sect. 3.2). Modeled UCXBs with an orbital period longer than 60 min are left out because of the absence of known real systems with such periods (i.e., they are assumed never to reach luminosities above GLYPH<24> 10 34 erg s GLYPH<0> 1 ). The timeaveraged luminosity of most UCXBs with orbital periods longer than 40 min is approximately two orders of magnitude higher than expected from the gravitational-wave model (van Haaften et al. 2012c). This implies that either the observed sources are atypically bright, or that they show normal behavior, but evolve much faster than if driven only by gravitational wave losses (the implications will be discussed in Sect. 4.2). In each case, due to energy conservation, we need to reduce the number of bright sources at each orbital period by a factor that corresponds to the ratio between the gravitational-wave luminosity and the actual observed luminosity, given by van Haaften et al. (2012c, their Fig. 3). Figure 10 shows the resulting number of bright UCXBs predicted by the ASM data.</text>
<text><location><page_9><loc_7><loc_10><loc_50><loc_25></location>For star formation history width GLYPH<27> = 0 : 5 Gyr, about 40 systems are expected to be visible as bright sources at a given time. For GLYPH<27> = 2 : 5 Gyr, this number is larger, GLYPH<24> 80, because recent star formation causes more young systems to exist, which have not yet reached orbital periods of 60 min. The cut-o GLYPH<11> at the faint end of the histogram is an artifact of the assumed linear extrapolation to the faint behavior. This also results in a relatively high minimum luminosity. In reality, especially sources with orbital periods longer than GLYPH<24> 40 min are expected to be very faint (i.e., much fainter than suggested by a linear extrapolation) at least some fraction of the time, which means the cumulative luminosity distribution flattens at faint luminosities, causing a tail at the</text>
<figure>
<location><page_9><loc_53><loc_71><loc_92><loc_91></location>
<caption>Figure 11. Present-day luminosity distribution of UCXBs in the Bulge based on the disk instability model (Sect. 2.5.1). Line color distinguishes between helium (thick black lines), carbonoxygen (thick gray and thin black lines) and helium-carbonoxygen (thin gray lines) donor compositions. The thick lines correspond to the white dwarf donor channel, the thin lines to the helium burning channel. The star formation history has width GLYPH<27> = 0 : 5 Gyr (solid lines) and GLYPH<27> = 2 : 5 Gyr (dashed lines).</caption>
</figure>
<text><location><page_9><loc_52><loc_53><loc_95><loc_57></location>low-luminosity end of Fig. 10. The distribution decreases with increasing luminosity in a similar way as the luminosity distribution of the representative individual observed UCXBs (Fig. 5).</text>
<section_header_level_1><location><page_9><loc_52><loc_50><loc_71><loc_51></location>3.3.2. Disk instability model</section_header_level_1>
<text><location><page_9><loc_52><loc_32><loc_95><loc_49></location>The second method relies on converting theoretical mass transfer rates to luminosities using the disk instability model (Sect. 2.5.1), the result of which is shown in Figs. 11 and 12. The total number of bright ( & 10 35 erg s GLYPH<0> 1 ) sources (either persistent or in outburst) is 34 for GLYPH<27> = 0 : 5 Gyr and 51 for GLYPH<27> = 2 : 5 Gyr. The vast majority of these are persistent (short-period) sources, and therefore the number is larger in the case of recent star formation. For the same reason, the white dwarf donor channel (Sect. 2.3.1) dominates this population, and most should have helium or carbon-oxygen donors. The helium burning channel is expected to contribute at most a couple of bright sources, in outburst at long orbital period (60 GLYPH<0> 80 min).</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_33></location>Figure 11 shows the luminosity distribution of bright sources. UCXBs with a luminosity between GLYPH<24> 10 36 GLYPH<0> 37 erg s GLYPH<0> 1 are the ones with the shortest orbital periods, below GLYPH<24> 20 min. From here, the number of sources at a given luminosity increases towards fainter luminosities because these sources have longer period derivatives and lower time-averaged mass transfer rates, until a sharp cut-o GLYPH<11> defined by the longest orbital period at which sources are still considered persistent. Carbon-oxygen dominated sources are persistent to longer periods and lower luminosities because accretion disks composed of carbon-oxygen are more stable than helium dominated disks, see Eq. (1). For GLYPH<27> = 0 : 5 Gyr the number of short-period, persistent, systems is negligible. At longer periods ( & 40 min), the duty cycle (Eq. 3) determines the number of sources in outburst. The duty cycle decreases below 10 GLYPH<0> 4 at orbital periods longer than 60 GLYPH<0> 70 min, depending on donor composition. During their rare outbursts, sources are temporarily bright at GLYPH<24> 10 37 GLYPH<0> 38 erg s GLYPH<0> 1 , as follows from Eq. (4). Their peak luminosities are used in Fig. 11.</text>
<figure>
<location><page_10><loc_8><loc_71><loc_47><loc_91></location>
<caption>Figure 12. Orbital period distribution of the predicted bright population of UCXBs in the Bulge at the present based on the disk instability model. For details see Fig. 11.</caption>
</figure>
<text><location><page_10><loc_7><loc_48><loc_50><loc_63></location>Two peaks can be distinguished in the lines representing the white dwarf channel in Fig. 11 (thick lines). The peak at GLYPH<24> 10 37 erg s GLYPH<0> 1 consists of systems with orbital periods just longer than the critical period because these still have a relatively high duty cycle. The second peak at GLYPH<24> 10 37 : 6 erg s GLYPH<0> 1 consists of longperiod systems because these are very numerous and distributed over a relatively narrow interval of orbital periods. The duty cycle at a given orbital period is higher for helium burning systems owing to their larger size and, because their average density is set by the orbital period, correspondingly larger mass. Hence, their time-averaged mass transfer rate at a given orbital period is also higher.</text>
<text><location><page_10><loc_7><loc_27><loc_50><loc_48></location>In Fig. 12 the orbital period distribution is shown for the same population of bright sources as in Fig. 11. The jumps of these distributions correspond to the respective low-luminosity ends of the distribution in Fig. 11. The cut-o GLYPH<11> period of persistent sources (at 30 GLYPH<0> 40 min) lies at a longer orbital period for the systems with a helium burning donor origin compared with systems with a white dwarf origin. The reason is that these donors have a higher temperature than originally white dwarf donors, and therefore the time-averaged mass transfer rate is higher at the same period. This causes the disk to remain stable (and the sources to be persistent) up to a longer period. Again we see that carbon-oxygen donor systems are persistent up to a longer orbital period than helium-dominated donor systems. Transient systems with orbital periods longer than GLYPH<24> 40 min are rarely in outburst and at most a handful have a high luminosity at a given time.</text>
<section_header_level_1><location><page_10><loc_7><loc_23><loc_29><loc_25></location>3.4. Donor surface composition</section_header_level_1>
<text><location><page_10><loc_7><loc_10><loc_50><loc_23></location>The helium-star donors have partially turned into carbon-oxygen white dwarfs during their evolution, depending on their mass and evolutionary stage at the onset of Roche-lobe overflow (determined by the initial mass and orbital period). When the star starts mass transfer after filling its Roche lobe, burning is extinguished quickly (Savonije et al. 1986), and at this stage the core mass fraction of helium varies between a few percent to almost 100% (Nelemans et al. 2010). Figure 13 shows the surface abundances at the present day, assuming a narrow star formation history ( GLYPH<27> = 0 : 5 Gyr). Two thirds of the systems end up</text>
<figure>
<location><page_10><loc_53><loc_71><loc_91><loc_91></location>
<caption>Figure 13. Surface abundances of helium versus carbon (black squares) and oxygen (white triangles) for donors in the heliumstar channel at the present time in the case of a su GLYPH<14> ciently narrow star formation history. These correspond to the core abundances at the end of the tracks by Nelemans et al. (2010). The surface area of a symbol is proportional to the number of systems in the corresponding track.</caption>
</figure>
<text><location><page_10><loc_52><loc_46><loc_95><loc_58></location>with less than 10% helium on their surface. Systems that started out with a short orbital period generally have a higher helium mass fraction, because these had less time to burn helium before the onset of mass transfer. The abundances depend on the temperature at which helium and carbon burning takes place. A higher temperature causes a higher helium burning rate, producing more carbon. Later, the carbon abundance reduces in favor of oxygen. The scatter in Fig. 13 is therefore due to di GLYPH<11> erences in core burning temperature caused by di GLYPH<11> erent stellar masses.</text>
<text><location><page_10><loc_52><loc_37><loc_95><loc_46></location>UCXBs produced via the white dwarf donor channel have donors mostly composed of either helium material (produced in the CNO cycle), or carbon-oxygen. The ratio between both types is about 3:1 but strongly depends on the e GLYPH<14> ciency of isotropic re-emission, which strongly a GLYPH<11> ects the number of carbon-oxygen white dwarf donor systems that survive the onset of mass transfer (Sect. 2.3.1).</text>
<text><location><page_10><loc_52><loc_31><loc_95><loc_37></location>Evolved main sequence donors with an initial mass of 1 : 0 GLYPH<0> 1 : 2 M GLYPH<12> reach a helium surface abundance Y GLYPH<25> 0 : 9 once they become ultracompact, the remaining part being hydrogen and a metallicity Z = 0 : 01, which has been present from the start (van der Sluys et al. 2005a).</text>
<text><location><page_10><loc_52><loc_23><loc_95><loc_31></location>Because the core material is exposed early on (e.g., at an orbital period shorter than GLYPH<24> 20 min for the helium burning systems, Nelemans et al. 2010), and the core is homogeneous due to convection during its burning stages, the chemical composition is expected not to change with increasing orbital period, and therefore the same for the total and the observable population.</text>
<section_header_level_1><location><page_10><loc_52><loc_20><loc_88><loc_21></location>3.5. Collective emission as function of orbital period</section_header_level_1>
<text><location><page_10><loc_52><loc_10><loc_95><loc_19></location>Even though variability behavior determines the number of UCXBs in outburst and their luminosity, the collective luminosity of all UCXBs at a given orbital period is in principle not dependent on variability, because the time-averaged mass transfer rate of an UCXB is a relatively straightforward function of orbital period. During the evolution of an UCXB, its evolutionary timescale increases with age and orbital period. This means that</text>
<figure>
<location><page_11><loc_9><loc_71><loc_47><loc_92></location>
<caption>Figure 14. Energy released per unit interval of orbital period for an UCXB with a zero-temperature helium white dwarf donor and a 1 : 4 M GLYPH<12> neutron star accretor or a 10 M GLYPH<12> black hole accretor. Note that the quantity on the vertical axis should not be interpreted as a luminosity; the time unit represents change in orbital period rather than passing time.</caption>
</figure>
<text><location><page_11><loc_7><loc_51><loc_50><loc_60></location>there exist many more systems at longer orbital period. On the other hand the time-averaged mass transfer rate decreases with age and orbital period, so a long-period source has a lower timeaveraged luminosity. The total energy output of a source, or of the population as a whole (under the assumption of a constant star formation rate), at a given orbital period is an indication of at which orbital periods systems are likely to be observed.</text>
<text><location><page_11><loc_7><loc_48><loc_50><loc_51></location>The amount of energy emitted by an UCXB per unit orbital period is given by</text>
<formula><location><page_11><loc_19><loc_44><loc_50><loc_47></location>d E d P orb = L ˙ P orb = GLYPH<0> GM a 2 R a d M d d P orb (5)</formula>
<text><location><page_11><loc_7><loc_25><loc_50><loc_43></location>where E is the emitted energy and M d the donor mass. This relation is illustrated in Fig. 14. The donor mass decreases much faster at shorter orbital periods ( M d / P GLYPH<0> 1 : 3 orb (van Haaften et al. 2012b), i.e., d M d = d P orb / P GLYPH<0> 2 : 3 orb ), and since the donor mass is the fuel for the luminosity, systems emit much more energy at short orbital periods, not only per time interval (their luminosity) but also per orbital period interval. For instance, an UCXB will emit GLYPH<24> 12 times as much energy during its evolution from 20 to 21 min as it does between 60 and 61 min. The consequence is that the short-period systems dominate the collective X-ray output of an UCXB population, unless the star formation rate decreases very fast. Depending on the variability of systems and the sensitivity of the instrument used, this could very well result in short-period systems dominating the visible population. 6</text>
<section_header_level_1><location><page_11><loc_7><loc_21><loc_18><loc_23></location>4. Discussion</section_header_level_1>
<text><location><page_11><loc_7><loc_15><loc_50><loc_21></location>Wepredict GLYPH<24> 1 : 9 GLYPH<2> 10 5 of UCXBs in the Galactic Bulge, predominantly at orbital periods of & 70 min, but also a few thousand systems with orbital periods shorter than 60 min (but mostly longer than 40 min). Based on RXTE ASM observations, about</text>
<table>
<location><page_11><loc_55><loc_83><loc_91><loc_89></location>
<caption>Table 1. Size of the modeled UCXB population in the Galactic Bulge for di GLYPH<11> erent model parameters.</caption>
</table>
<text><location><page_11><loc_52><loc_72><loc_95><loc_80></location>40 GLYPH<0> 80 of these sub-hour UCXBs should be visible at high luminosities of & 10 35 erg s GLYPH<0> 1 (Fig. 10), depending on the star formation history. Also, GLYPH<24> 35 GLYPH<0> 50 bright UCXBs with orbital periods . 30 min (i.e., persistent) should be visible above such a luminosity based on gravitational energy release and the disk instability model (Figs. 11 and 12). 7</text>
<text><location><page_11><loc_52><loc_48><loc_95><loc_72></location>The combined common-envelope parameter GLYPH<11> CE GLYPH<21> for massive stars may be lower than the value of 2 that we used (Voss & Tauris 2003). Decreasing this value to 0 : 2, as well as using a Maxwellian kick velocity distribution with a dispersion of 450 km s GLYPH<0> 1 , rather than the distribution by Paczy'nski (1990), would reduce the number of UCXBs formed by a factor of GLYPH<24> 8, as fewer systems will survive the common-envelope stage or the supernova explosion. In that case, the total number of UCXBs in the Bulge we predict is GLYPH<24> 2 GLYPH<2> 10 4 , and the number of bright systems becomes GLYPH<24> 5 GLYPH<0> 10. Table 1 shows the number of UCXBs in our model for various combinations of common-envelope efficiency and neutron star kick velocity distribution. Furthermore, the slope of the initial mass function at high stellar mass is also uncertain. A steeper slope (resulting from earlier studies such as Kroupa et al. 1993) leads to a smaller fraction of massive stars and therefore fewer UCXBs. A di GLYPH<11> erent choice for the initial component mass pairing may also reduce the number of UCXBs by an order of magnitude (Belczynski & Taam 2004a).</text>
<text><location><page_11><loc_52><loc_35><loc_95><loc_48></location>We can distinguish several disagreements with observations. First, no UCXBs with orbital periods longer than 60 min have been discovered, faint or bright, in the Bulge or elsewhere. Second, no bright UCXBs with a short orbital period ( . 30 min) have been identified in the Galactic Bulge. Third, only three UCXBs with orbital periods between 40 and 55 min, XTE J1807-294 (Markwardt et al. 2003), XTE J1751-305 (Markwardt et al. 2002) and SWIFT J1756.9-2508 (Krimm et al. 2007), are presumably located in the Bulge, based on their positions in the sky, as their distances are not known.</text>
<text><location><page_11><loc_52><loc_22><loc_95><loc_35></location>As for the predicted GLYPH<24> 1 : 9 GLYPH<2> 10 5 long-period systems, the probable existence of three observed UCXBs with orbital periods shorter than 55 min in the Bulge can be used to calibrate the formation rate of UCXBs, independent of population synthesis . This yields a much larger number of UCXBs than three for systems with a period longer than 55 min, based only on the rapid increase of the evolutionary timescale (set by gravitational wave radiation) with orbital period. For instance, UCXBs are expected to reach an orbital period of 55 min within GLYPH<24> 2 Gyr after the onset of mass transfer (van Haaften et al. 2012b).</text>
<text><location><page_11><loc_52><loc_18><loc_95><loc_22></location>Even though the disk instability model predicts these longperiod systems to be in outburst so rarely that few are expected to be bright, in quiescence they would still be detectable by sen-</text>
<text><location><page_12><loc_7><loc_91><loc_50><loc_93></location>sitive instruments at GLYPH<24> 10 31 GLYPH<0> 33 erg s GLYPH<0> 1 (e.g. Bildsten & Rutledge 2001; Heinke et al. 2003; Belczynski & Taam 2004b).</text>
<text><location><page_12><loc_7><loc_81><loc_50><loc_89></location>The three observed UCXBs that are located in the direction of the Bulge have undetermined donor compositions, though SWIFT J1756.9-2508 is thought to have helium composition (Krimm et al. 2007). This cannot be used to constrain the star formation history, as UCXBs with helium white dwarf donors can form with a wide range of delay times.</text>
<section_header_level_1><location><page_12><loc_7><loc_77><loc_34><loc_78></location>4.1. Comparison with previous studies</section_header_level_1>
<text><location><page_12><loc_7><loc_25><loc_50><loc_75></location>Belczynski & Taam (2004a) performed a population synthesis study of (primordial) UCXBs in the Galactic disk. The main difference between their and our results is that they found a total of 478 UCXBs with orbital periods shorter than 80 min in the disk at the present epoch, about three orders of magnitude fewer than our result, per unit star forming mass. It is not clear what causes this discrepancy, although these authors use di GLYPH<11> erent initial binary parameters than we do (Appendix A), for example a steeper high-mass slope in the initial mass function that leads to fewer massive stars, relatively. Also, their initial primary masses leading to UCXBs span a narrower range. Of all UCXBs in their simulation, about 20% have a black hole accretor, all of which form via the accretion-induced collapse of a neutron star. This percentage strongly depends on the assumed upper mass of a neutron star (2 M GLYPH<12> ), the mass retention e GLYPH<14> ciency of the accreting neutron star and the evolutionary stage at which the common envelope happens. As in our study, these authors did not find any (surviving) UCXBs with a black hole that was formed directly in the collapse of a massive star. They found that about 90% of the neutron star accretors form via the accretion-induced collapse of an oxygen-neon-magnesium white dwarf, a scenario our model does not produce. In our simulations, 81% of the UCXBs start mass transfer from a helium burning donor, compared to 40% in Belczynski & Taam (2004a) for the Galactic field. This is not unreasonable given the uncertainties in e.g. the onset of mass transfer from a white dwarf, and di GLYPH<11> erences in assumptions between both studies. The number of persistent sources predicted by the disk instability model depends sensitively on the orbital period separating the persistent and transient sources, because most of the predicted persistent sources have orbital periods only slightly shorter than this critical period. Details in accretion disk models (e.g. X-ray irradiation) and composition can make a large difference. We predict about 0 : 02% of the UCXBs to be persistent (Sect. 3.3.2), a much smaller fraction than found by Belczynski &Taam (2004a) (2 : 2%), but their number applies to the Galactic disk, which has a several orders of magnitude higher ongoing star formation rate, and therefore more young UCXBs, which have short orbital periods.</text>
<text><location><page_12><loc_7><loc_9><loc_50><loc_24></location>Our number of persistently bright UCXBs (35 GLYPH<0> 50 from the disk instability model, using our standard parameters) can also be compared with the number of persistent UCXBs with white dwarf donors (600 GLYPH<0> 900) predicted by Zhu et al. (2012a) for the whole Galaxy, if one takes into account the di GLYPH<11> erence in adopted cut-o GLYPH<11> donor mass for persistent behavior. These authors found that UCXBs with donor masses lower than 0 : 03 M GLYPH<12> are transient whereas our limit lies around 0 : 02 M GLYPH<12> . Using their limit, our estimate would reduce to roughly ten, which scales within a factor of a few with their number given the stellar mass ratio between Bulge (1 GLYPH<2> 10 10 M GLYPH<12> ) and Galaxy (an additional 4 GLYPH<0> 6 GLYPH<2> 10 10 M GLYPH<12></text>
<text><location><page_12><loc_52><loc_91><loc_95><loc_93></location>in the Disk, Klypin et al. 2002). 8 The overprediction of bright, persistent UCXBs is therefore not unique to our study.</text>
<text><location><page_12><loc_52><loc_80><loc_95><loc_91></location>Recently, Zhu et al. (2012b) performed a population synthesis study of Galactic UCXBs with neutron star accretors, and predicted 5 GLYPH<0> 10 GLYPH<2> 10 3 systems in the Galaxy, depending on neutron star birth kicks. As in our study, the helium burning donor channel was the most common. Notable di GLYPH<11> erences with our work are that these authors found a large number of UCXBs with a carbon-oxygen white dwarf origin, and a peak in the orbital period distribution near 40 min.</text>
<section_header_level_1><location><page_12><loc_52><loc_77><loc_89><loc_78></location>4.2. Overprediction of UCXBs with long orbital period</section_header_level_1>
<text><location><page_12><loc_52><loc_38><loc_95><loc_76></location>An important clue towards what may happen at long periods comes from the long-term ASM data. The reason for the difference in predictions by the ASM and disk instability model (Sect. 3.3) lies in the ASM observations that the UCXBs with orbital periods 40 GLYPH<0> 55 min are approximately two orders of magnitude brighter than theoretically expected from the timeaveraged mass transfer rate, assuming mass transfer is driven exclusively by gravitational wave radiation in a binary with a (semi-)degenerate donor (van Haaften et al. 2012c). 9 Assuming that the observed systems have been displaying normal behavior during the 16 years of RXTE observations, additional angular momentum loss besides that from gravitational wave radiation would cause a higher mass transfer rate at the same orbital period, and therefore a higher time-averaged luminosity (see also Ruderman et al. 1989b). As mentioned in Sect. 2.4, an e GLYPH<14> cient physical mechanism for additional loss of angular momentum from the system is a wind from the donor, induced by irradiation from the accretion disk or millisecond pulsar. In black widow systems, which host a millisecond pulsar and a low-mass ( . 0 : 2 M GLYPH<12> ) companion in a < 10 h orbit (King et al. 2005), such donor evaporation has been observed (e.g. Fruchter et al. 1988). This scenario has also been proposed to be happening to the unusually light ( GLYPH<24> 10 GLYPH<0> 3 M GLYPH<12> ) detached companion to the millisecond pulsar PSR J1719-1438 (Bailes et al. 2011) via either the white dwarf or helium burning donor channels (van Haaften et al. 2012a) or the evolved main sequence donor channel (with an orbital period minimum at GLYPH<24> 45 min, Benvenuto et al. 2012), though the latter scenario does not produce a carbon-oxygen rich donor.</text>
<text><location><page_12><loc_52><loc_25><loc_95><loc_38></location>The recently discovered spin-powered millisecond gammaray pulsar PSR J1311-3430 system (Pletsch et al. 2012), with an orbital period of 93 : 8 min (Romani 2012; Kataoka et al. 2012) and an evaporating helium donor (Romani et al. 2012) supports the hypothesis that UCXB evolution is strongly influenced by donor evaporation. Given the low hydrogen abundance, donor evaporation, orbital period, pulsar spin period, and minimum companion mass, PSR J1311-3430 could very well be an UCXB descendant on its way to becoming a millisecond radio pulsar system like PSR J1719-1438.</text>
<text><location><page_12><loc_52><loc_17><loc_95><loc_25></location>The non-detection of UCXBs with periods longer than GLYPH<24> 60 min, when the donor is still expected to be much more massive than the companion in PSR J1719-1438, suggests the existence of another mechanism that hides UCXBs with low donor masses and low mass transfer rates (the 60 min limit is uncertain due to the small observed sample). The propeller e GLYPH<11> ect (Sect. 2.4)</text>
<text><location><page_13><loc_7><loc_78><loc_50><loc_93></location>is the most promising mechanism to explain this non-detection. The rotational energy of the millisecond pulsar is su GLYPH<14> cient to make long-period UCXBs with very low mass transfer rates ( GLYPH<24> 10 GLYPH<0> 13 M GLYPH<12> yr GLYPH<0> 1 ) much fainter, since it causes arriving matter to be unbound (van Haaften et al. 2012b). The propeller e GLYPH<11> ect could still allow for a (very) low rate of accretion that would prevent radio emission and make the sources visible in the ultraviolet (owing to their low disk temperatures and possibly disturbed inner accretion disks). Furthermore, radio emission from a millisecond pulsar itself, once switched on after an interruption in mass transfer, is capable of preventing accretion (Burderi et al. 2001; Fu & Li 2011).</text>
<text><location><page_13><loc_7><loc_54><loc_50><loc_78></location>Using the Chandra X-Ray Observatory (Weisskopf et al. 2002), the Galactic Bulge Survey has found 1234 X-ray sources in 8 : 3 deg 2 (Jonker et al. 2011) so far, most of which have not yet been identified. Although many are expected to be foreground Cataclysmic Variables or non-ultracompact X-ray binaries, this number of systems found in approximately 5% of the total area of the Bulge on the sky is at least consistent with a large population of faint X-ray binaries. Also, a potentially large population of sub-luminous X-ray transients with neutron star accretors exists near the Galactic Center (Sakano et al. 2005; Wijnands et al. 2006; Degenaar & Wijnands 2009, 2010). These systems have (intrinsic) peak luminosities near GLYPH<24> 10 34 GLYPH<0> 35 erg s GLYPH<0> 1 (in the 2 GLYPH<0> 10 keV range), and may include UCXBs, although the disk instability model predicts peak luminosities & 10 37 erg s GLYPH<0> 1 for UCXBs. King & Wijnands (2006) found that the luminosities of some very faint X-ray transients imply mass transfer rates of GLYPH<24> 10 GLYPH<0> 13 M GLYPH<12> yr GLYPH<0> 1 , which is consistent with the behavior of old UCXBs.</text>
<text><location><page_13><loc_7><loc_48><loc_50><loc_54></location>The additional angular momentum loss increases the time derivative of the orbital period, and as a result the actual number of systems at long periods in our prediction based on only gravitational wave radiation (Figs. 8 and 9) should be reduced by two orders of magnitude.</text>
<section_header_level_1><location><page_13><loc_7><loc_44><loc_45><loc_45></location>4.3. Overprediction of UCXBs with short orbital period</section_header_level_1>
<text><location><page_13><loc_7><loc_33><loc_50><loc_44></location>Since UCXBs with an orbital period shorter than GLYPH<24> 30 min are expected to be persistently bright, our overprediction of these binaries ( GLYPH<24> 5 GLYPH<0> 50 systems based on the disk instability model, depending on assumptions in the model, is about one order of magnitude more than the three observed Bulge UCXBs) can have several causes: the population synthesis model produces too many UCXBs, fewer UCXBs survive the onset of mass transfer, or short-period UCXBs are bright less than 100% of the time.</text>
<text><location><page_13><loc_7><loc_10><loc_50><loc_33></location>It is uncertain whether the white dwarf donor mass limit of 0 : 38 M GLYPH<12> for isotropic re-emission (based on the zerotemperature mass-radius relation and a consideration of the energy necessary to eject matter) should be used as the threshold for the survival of a system. A di GLYPH<11> erent assumption in the details of the hydrodynamics of the onset of mass transfer could result in either a lower or a higher limit. However, the number of surviving white dwarf donors is not very sensitive to small changes in the isotropic re-emission limit because of the small number of donors around this value (Fig. 2). On the other hand, due to the sensitivity of this donor mass limit to the actual and critical mass transfer rates (van Haaften et al. 2012b), the number of surviving UCXBs could be significantly smaller if the isotropic re-emission e GLYPH<14> ciently is less than unity, which seems plausible. However, systems could survive a mass transfer rate exceeding the isotropic re-emission limit if an UCXB with a GLYPH<24> 2 min orbital period is able to survive a few hundred years ( GLYPH<24> 10 8 orbits) with a significant amount of matter orbiting in and around the bi-</text>
<text><location><page_13><loc_52><loc_80><loc_95><loc_93></location>nary, perhaps in a circumbinary ring (Soberman et al. 1997; Ma & Li 2009) that would be removed at a later stage. The value of isotropic re-emission limit can be tested only using shortperiod UCXBs, because for those the white dwarf donor channel is expected to dominate. In the total population (mostly longperiod systems), the helium donor channel is more important. This channel does not experience the high mass transfer rates that characterize the onset of mass transfer from a white dwarf donor. Near the period minimum the mass transfer rate remains below approximately three times the Eddington limit (Fig. 4)</text>
<text><location><page_13><loc_52><loc_71><loc_95><loc_80></location>Even though Fig. 7 shows that the contribution of the heliumstar channel dominates, its importance has not been established observationally yet, as no detached (short orbital period) helium star-neutron star binaries have been discovered so far (Nelemans et al. 2010). If helium burning stars would turn into white dwarfs before the onset of Roche-lobe overflow, over 90% would be unable to survive as a binary system.</text>
<text><location><page_13><loc_52><loc_64><loc_95><loc_71></location>Given these uncertainties, our overprediction by approximately one order of magnitude may simply be a consequence of poorly known parameters in our simulation, and in this case no problematic discrepancy between our results and X-ray observations would remain.</text>
<section_header_level_1><location><page_13><loc_52><loc_60><loc_92><loc_62></location>4.4. Consequences for the population of millisecond radio pulsars</section_header_level_1>
<text><location><page_13><loc_52><loc_26><loc_95><loc_59></location>If mass transfer would cease completely in most old UCXBs as suggested by the existence of PSR J1719-1438, then a fraction of the neutron stars they harbor would become visible to us as (binary) millisecond radio pulsars for several billion years. The same is probably true for UCXBs in environments closer to us than the Bulge. The number of isolated or binary millisecond radio pulsars in the Bulge suggested by the number of UCXBs with & 70 min periods we predict in our standard model, after correcting for the factor of ten overestimation in the UCXB birth rate identified above, is about 2 GLYPH<2> 10 4 , assuming the pulsars have not yet turned o GLYPH<11> as a result of spinning down. The estimated Galactic population of millisecond pulsars, based on the observed population, is 4 GLYPH<2> 10 4 (Lorimer 2008). Of the known Galactic Disk population (i.e., excluding globular clusters) of GLYPH<24> 100 radio pulsars with spin periods shorter than 10 ms, about 60% have a companion too massive to be consistent with latetime UCXB evolution, based on the ATNFPulsar Catalogue 10 in January 2013 (Manchester et al. 2005). (These have descended from hydrogen-rich low-mass and intermediate-mass X-ray binaries, Bhattacharya & van den Heuvel 1991; Tauris 2011.) Extrapolating this to the estimated Galactic population, GLYPH<24> 2 GLYPH<2> 10 4 millisecond pulsars are left that have no or a very low-mass companion, roughly the same number we predict from UCXBs for the Bulge alone (after normalizing the number of short-period UCXBs).</text>
<text><location><page_13><loc_52><loc_12><loc_95><loc_26></location>It seems likely that millisecond pulsars have evaporated their companion entirely and are left as isolated millisecond pulsars given the reasonable match between the predicted number of old UCXBs and the number of isolated millisecond radio pulsars, combined with the very small number of observed millisecond radio pulsars with companions with masses lower than 0 : 01 M GLYPH<12> . Alternative formation channels for isolated millisecond pulsars are spin up of a neutron star by a disrupted white dwarf companion (van den Heuvel 1984), and disruption of a millisecond pulsar binary during the supernova explosion of the donor star in a high-mass X-ray binary (e.g. Camilo et al. 1993). The num-</text>
<text><location><page_14><loc_7><loc_77><loc_50><loc_93></location>ber of neutron star-white dwarf mergers, however, seems too high to be consistent with the number of isolated millisecond pulsars that have formed. Based on Fig. 2, merging systems are much more common than surviving UCXBs, also after including UCXBs from the helium burning donor channel (see also Iben et al. 1995). On the other hand, the number of millisecond pulsars that lose their companions when it explodes as a supernova seems too small to be responsible for a large fraction of the isolated millisecond pulsars (Burgay et al. 2003; Belczynski et al. 2010) - moreover the high-mass donor star may not live long enough to spin up the neutron star to a spin period shorter than GLYPH<24> 10 ms.</text>
<section_header_level_1><location><page_14><loc_7><loc_74><loc_31><loc_75></location>5. Summary and conclusions</section_header_level_1>
<text><location><page_14><loc_7><loc_55><loc_50><loc_73></location>We modeled the present-day population of primordial ultracompact X-ray binaries in the Galactic Bulge with the purpose of gaining insight in their formation and evolution. Both binary evolution and accretion physics determine the observable population, and we attempted to disentangle these in this study. We considered three main formation channels: systems that start Roche-lobe overflow by a white dwarf donor, a helium burning donor or an evolved main sequence donor. Our simulations have not produced UCXBs containing a black hole, because most systems with a very massive primary merge during unstable mass transfer, and the small number that remains is expected to merge during the onset of mass transfer from a relatively massive white dwarf to the black hole. Thus, all UCXB systems in our simulations have a neutron star accretor.</text>
<text><location><page_14><loc_7><loc_28><loc_50><loc_41></location>The size and characteristics of the present-day population are only marginally dependent on the assumed width, GLYPH<27> , of the Gaussian distribution describing the star formation history if this value is . 1 Gyr. This is because these values of GLYPH<27> are small compared to the age of a 10 Gyr old system. A broad star formation history allows for recent star formation and short orbital period UCXBs with a helium burning donor origin, because of their short delay time. With a narrow star formation history, shortperiod UCXBs must have a white dwarf origin and therefore can have helium composition.</text>
<text><location><page_14><loc_7><loc_41><loc_50><loc_55></location>The vast majority of UCXBs form via the helium burning donor channel (81%) or the white dwarf donor channel (18%), and therefore their exposed cores are expected to show either carbon and oxygen in their spectra, or helium, as well as small amounts of other reaction products. These two channels di GLYPH<11> er in the delay time between the zero-age main sequence and the onset of Roche-lobe overflow to the neutron star. In the white dwarf channel this delay can be as long as the age of the Universe or more (though for most systems it is less than a few billion years), whereas in the helium burning channel the delay is less than 1 Gyr.</text>
<text><location><page_14><loc_7><loc_23><loc_50><loc_28></location>Very short period UCXBs can have a helium or carbonoxygen white dwarf donor, since these must have formed recently. Recent UCXB formation is dominated by the white dwarf donor channel, even for GLYPH<27> = 2 : 5 Gyr.</text>
<text><location><page_14><loc_7><loc_10><loc_50><loc_23></location>The number of predicted systems with orbital periods shorter than GLYPH<24> 30 min is particularly important, since those systems are probably observable as persistently bright sources, and therefore well suited to test and calibrate the simulations. We predict about 40 bright sources, mostly of helium and carbon-oxygen composition and with orbital periods shorter than 30 min. The UCXBs with the shortest periods ( . 20 min) are more likely to have helium composition. The observed number of bright UCXBs is about ten times smaller than suggested by our model, which reflects the uncertainties in the adopted star formation history,</text>
<text><location><page_14><loc_52><loc_89><loc_95><loc_93></location>initial binary parameters, natal kick velocities of neutron stars, common-envelope parameters and the onset of mass transfer to a neutron star accretor.</text>
<text><location><page_14><loc_52><loc_77><loc_95><loc_89></location>We predict about (0 : 2 GLYPH<0> 1 : 9) GLYPH<2> 10 5 UCXBs in the Galactic Bulge, and we stress that such a large population is necessary based on the simple argument that the evolutionary timescale of UCXBs increases rapidly towards longer orbital periods, and therefore the observed number of short-period UCXBs, in the Bulge and also in the Galactic Disk, implies several orders of magnitude more UCXBs at long orbital periods ( > 60 min). With di GLYPH<11> erent model assumptions, this number could be up to an order of magnitude lower.</text>
<text><location><page_14><loc_52><loc_56><loc_95><loc_77></location>Irradiation of the donor star by the neutron star and accretion disk strongly influences UCXB evolution, at least at orbital periods longer than 40 min. These systems evolve much faster , probably by GLYPH<24> 100 times, than they would if their evolution was driven exclusively by angular momentum loss via gravitational wave radiation, as assumed in this paper. UCXBs with orbital periods longer than 1 h have not been detected yet, which implies that, if existent, these systems are very faint in all electromagnetic bands (and therefore cannot be considered true X-ray binaries). We suggest that the majority of these systems have orbital periods on the order of 1 : 5 GLYPH<0> 2 : 5 h rather than the GLYPH<24> 1 : 3 h expected from gravitational wave driven evolution. Furthermore we expect that the neutron stars have companions with masses much lower than 0 : 01 M GLYPH<12> , and could very well have evaporated their companions entirely, being left as isolated millisecond pulsars.</text>
<text><location><page_14><loc_52><loc_53><loc_95><loc_56></location>In a forthcoming paper we will model the population of hydrogen-rich low-mass X-ray binaries in the Galactic Bulge.</text>
<text><location><page_14><loc_52><loc_42><loc_95><loc_50></location>Acknowledgements. LMvH, GN, RV, and SFPZ are supported by the Netherlands Organisation for Scientific Research (NWO). GN and RV are supported by NWO Vidi grant #016 : 093 : 305 to GN. SFPZ is supported by NWO grants #639 : 073 : 803 (Vici) and #614 : 061 : 608, and the Netherlands Research School for Astronomy (NOVA). LRY is supported by RFBR grant #10-0200231 and the Program P-21 of the Praesidium of Russian Academy of Sciences. This research has made use of NASA's Astrophysics Data System Bibliographic Services (ADS).</text>
<section_header_level_1><location><page_14><loc_52><loc_35><loc_89><loc_37></location>Appendix A: Binary initial mass function and normalization of the simulation</section_header_level_1>
<text><location><page_14><loc_52><loc_13><loc_95><loc_34></location>In the initial binary system, the more massive component is called the primary. We use primary-constrained pairing to construct 'zero-age' binaries (Kouwenhoven et al. 2008). The primary masses M primary of the zero-age main sequence binaries are drawn from the stellar initial mass function (IMF) of primaries in massive star clusters that we derive from the results by Kroupa (2001), where M is the stellar mass and 0 : 08 GLYPH<20> M = M GLYPH<12> GLYPH<20> 100. The mass ratio 0 < M secondary = M primary GLYPH<20> 1 of the components is subsequently drawn from a constant distribution (Kraicheva et al. 1989; Hogeveen 1992) - secondary masses lower than 0 : 08 M GLYPH<12> are accepted. The eccentricity e distribution is proportional to e between 0 and 1, and the semi-major axis a distribution is inversely proportional to a (Popova et al. 1982; Abt 1983), up to 10 6 R GLYPH<12> (Duquennoy & Mayor 1991) - the lower limit is set by the requirement that the initial stellar radii fit inside the circularized orbit.</text>
<text><location><page_14><loc_52><loc_10><loc_95><loc_12></location>The specific binary fraction as a function of M is given by the observationally practical definition (Reipurth & Zinnecker</text>
<text><location><page_15><loc_7><loc_92><loc_29><loc_93></location>1993; Kouwenhoven et al. 2009)</text>
<formula><location><page_15><loc_12><loc_85><loc_50><loc_92></location>B ( M ) GLYPH<17> N binary( M primary = M ) N single( M ) + N binary( M primary = M ) = N binary( M primary = M ) IMF ( M ) (A.1)</formula>
<text><location><page_15><loc_7><loc_76><loc_50><loc_85></location>where N single( M ) is the distribution of single stars of mass M , N binary( M primary = M ) the distribution of binary systems containing a primary of mass M , and IMF ( M ) the IMF of systems (single stars and multiple systems combined) by Kroupa (2001). Based on observations summarized in Kouwenhoven et al. (2009); Kraus & Hillenbrand (2009); Sana et al. (2012) we approximate</text>
<formula><location><page_15><loc_9><loc_72><loc_50><loc_75></location>B ( M ) = 1 2 + 1 4 log 10 ( M ) (0 : 08 GLYPH<20> M = M GLYPH<12> GLYPH<20> 100) (A.2)</formula>
<text><location><page_15><loc_7><loc_69><loc_50><loc_72></location>where we assume all multiple systems to be binaries. Equation (A.1) can be separated as</text>
<formula><location><page_15><loc_12><loc_65><loc_50><loc_69></location>N binary( M primary = M ) / B ( M ) IMF ( M ) ; N single( M ) / [1 GLYPH<0> B ( M )] IMF ( M ) : (A.3)</formula>
<text><location><page_15><loc_7><loc_60><loc_50><loc_65></location>It follows that single stars are more common than binary systems; there are 1 : 6 single stars for each binary system. The mass per binary system including the corresponding single stars (which can be a fractional number) is given by</text>
<formula><location><page_15><loc_16><loc_56><loc_50><loc_60></location>M T = 1 B ( M primary) M primary + M secondary ; (A.4)</formula>
<text><location><page_15><loc_7><loc_53><loc_50><loc_56></location>and the average star forming mass for each binary system formed (i.e., including mass from single stars) by</text>
<formula><location><page_15><loc_9><loc_49><loc_50><loc_53></location>¯ M T = Z 100 M GLYPH<12> 0 : 08 M GLYPH<12> 1 + B ( M ) 2 ! IMF ( M ) M d M GLYPH<25> 1 : 9 M GLYPH<12> (A.5)</formula>
<text><location><page_15><loc_7><loc_36><loc_50><loc_49></location>(the factor 1 = 2 appears because the average secondary mass is equal to half of the average primary mass for the chosen constant mass ratio distribution). This number is the sum of the average primary mass (0 : 86 M GLYPH<12> ), 11 the average secondary mass (0 : 43 M GLYPH<12> ) and the corresponding average mass in single stars per binary system (0 : 64 M GLYPH<12> ). A lower limit of 0 : 1 M GLYPH<12> increases the average mass per binary by GLYPH<24> 12%. Overall two-thirds of the star-forming mass is in binaries. The total number of binaries that forms in the Galactic Bulge is normalized using the total number of stars</text>
<formula><location><page_15><loc_9><loc_32><loc_50><loc_36></location>Z 100 M GLYPH<12> 0 : 08 M GLYPH<12> N binary( M ) d M = 1 GLYPH<2> 10 10 M GLYPH<12> ¯ M T GLYPH<25> 5 : 2 GLYPH<2> 10 9 : (A.6)</formula>
<text><location><page_15><loc_7><loc_17><loc_50><loc_32></location>Of all primaries, 1 : 3% have a mass higher than 8 M GLYPH<12> . For these masses, the power-law slope of the primary IMF (defined over linear mass intervals), from which we draw primary masses, varies between GLYPH<0> 2 : 15 (for M = 8 M GLYPH<12> ) and GLYPH<0> 2 : 2 ( M = 100 M GLYPH<12> ), compared to the estimate of GLYPH<0> 2 : 3 by Kroupa (2001) for the combined IMF of single stars and primary components. The IMF of primary components N binary( M primary = M ) is flatter than the IMF of systems IMF ( M ) because Eq. (A.2) is an increasing function (most low-mass stars are single whereas massive stars are usually in binaries). 12 The IMF for single stars only is steeper than GLYPH<0> 2 : 3 and steepens towards high mass.</text>
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</document>
[
{
"title": "Population synthesis of ultracompact X-ray binaries in the Galactic Bulge",
"content": "L. M. van Haaften 1 , G. Nelemans 1 ; 2 , R. Voss 1 , S. Toonen 1 , S. F. Portegies Zwart 3 , L. R. Yungelson 4 , and M. V. van der Sluys 1 Preprint online version: September 10, 2018",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "Aims. We model the present-day number and properties of ultracompact X-ray binaries (UCXBs) in the Galactic Bulge. The main objective is to compare the results to the known UCXB population as well as to data from the Galactic Bulge Survey, in order to learn about the formation of UCXBs and their evolution, such as the onset of mass transfer and late-time behavior. Methods. The binary population synthesis code SeBa and detailed stellar evolutionary tracks have been used to model the UCXB population in the Bulge. The luminosity behavior of UCXBs has been predicted using long-term X-ray observations of the known UCXBs as well as the thermal-viscous disk instability model. Results. In our model, the majority of UCXBs initially have a helium burning star donor. Of the white dwarf donors, most have helium composition. In the absence of a mechanism that destroys old UCXBs, we predict (0 : 2 GLYPH<0> 1 : 9) GLYPH<2> 10 5 UCXBs in the Galactic Bulge, depending on assumptions, mostly at orbital periods longer than 60 min (a large number of long-period systems also follows from the observed short-period UCXB population). About 5 GLYPH<0> 50 UCXBs should be brighter than 10 35 erg s GLYPH<0> 1 , mostly persistent sources with orbital periods shorter than about 30 min and with degenerate helium and carbon-oxygen donors. This is about one order of magnitude more than the observed number of (probably) three. Conclusions. This overprediction of short-period UCXBs by roughly one order of magnitude implies that fewer systems are formed, or that a super-Eddington mass transfer rate is more di GLYPH<14> cult to survive than we assumed. The very small number of observed longperiod UCXBs with respect to short-period UCXBs, the surprisingly high luminosity of the observed UCXBs with orbital periods around 50 min, and the properties of the PSR J1719-1438 system all point to much faster UCXB evolution than expected from angular momentum loss via gravitational wave radiation alone. Old UCXBs, if they still exist, probably have orbital periods longer than 2 h and have become very faint due to either reduced accretion or quiescence, or have become detached. UCXBs are promising candidate progenitors of isolated millisecond radio pulsars. Key words. binaries: close - stars: evolution - Galaxy: bulge - X-rays: binaries - pulsars: general",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Ultracompact X-ray binaries (UCXBs) are low-mass X-ray binaries with observed orbital periods shorter than GLYPH<24> 1 h, indicating a compact, hydrogen deficient donor star (Vila 1971; Paczy'nski 1981; Sienkiewicz 1984). The donor overflows its Roche lobe, and lost matter is partially accreted by a neutron star or black hole companion. Because of the compact orbit, mass transfer is driven by orbital angular momentum loss via gravitational wave radiation (e.g. Kraft et al. 1962; Paczy'nski 1967; Faulkner 1971; Pringle & Webbink 1975; Tutukov & Yungelson 1979). For an overview of the relevance of studying UCXBs, see e.g. Nelemans & Jonker (2010). The Galactic Bulge is a suitable environment to discover UCXBs because of the high local star concentration. Furthermore, the Bulge is an old stellar population that contains few young X-ray sources such as high-mass X-ray binaries and core-collapse supernova remnants. Due to their rarity, UCXBs are not found nearby in the Galaxy. Also, while observable in X-rays, they are too faint to be identified in other galaxies (e.g. Voss & Gilfanov 2007). The Galactic Bulge Survey (GBS) (Jonker et al. 2011) is an X-ray and optical survey focused on two 6 GLYPH<14> GLYPH<2> 1 GLYPH<14> regions centered 1 : 5 GLYPH<14> to the North and South of the Galactic Center. One of the goals of the GBS is to investigate the properties of populations of X-ray binaries in order to constrain their formation scenarios, especially the common-envelope phase(s). The present study aims to predict and explain GBS results regarding the number and luminosities of UCXBs by means of binary population synthesis and UCXB evolutionary tracks, thereby contributing to a better understanding of the formation and evolution of UCXBs. We also compare our results to the orbital periods and chemical compositions of the known UCXB population. In Sect. 2 we describe our assumptions on the star formation, stellar and binary evolution, and the observable characteristics of evolved UCXBs. The results follow in Sect. 3, where we present the modeled present-day population and its observational properties. In Sect. 4, we compare our results with the population synthesis studies by Belczynski & Taam (2004a), Zhu et al. (2012a), and Zhu et al. (2012b), as well as to observations, and we discuss various implications. We conclude in Sect. 5.",
"pages": [
1
]
},
{
"title": "2. Method",
"content": "The study of the evolution of the UCXB population consists of several steps. First, the star formation history of the Galactic Bulge and the binary initial mass function prescribe which types of zero-age main sequence binaries form in the Bulge, and when they form. The binary population synthesis code SeBa (Portegies Zwart & Verbunt 1996; Nelemans et al. 2001; Toonen et al. 2012) is used to simulate the evolution of this population of zero-age main sequence binaries. During the evolution of the population, all UCXB progenitors are selected at a certain moment after the supernova explosion that leaves behind the neutron star or black hole. More detailed evolutionary tracks are used to trace the subsequent evolution. This yields the present-day number and intrinsic parameters of the UCXBs in the Galactic Bulge. Finally, using long-term observations by the Rossi X-ray Timing Explorer All-Sky Monitor ( RXTE ASM) (Bradt et al. 1993; Levine et al. 1996) as well as the accretion disk instability model, the modeled UCXB parameters are translated into observational parameters using the results of van Haaften et al. (2012c). The result is a prediction of the presentday observable population.",
"pages": [
2
]
},
{
"title": "2.1. Population synthesis",
"content": "The binary population synthesis code SeBa models the evolutionary transformations of a population of binary stars based on a distribution of initial binary parameters. It follows the evolution of stellar components using analytic formulas by Hurley et al. (2000), taking into account circularization due to tidal interaction, magnetic braking, gravitational wave radiation, mass exchange via Roche-lobe overflow, common envelopes, and empirical parameterizations of wind mass loss. For a more extensive description of SeBa we refer to Portegies Zwart & Verbunt (1996), Nelemans et al. (2001), and Toonen et al. (2012). As is common, we use parameterizations to describe the common-envelope process. In this study, the density profile of the donor envelope is parametrized by GLYPH<21> = 1 = 2, the e GLYPH<14> ciency with which orbital energy is used on unbinding the common envelope by GLYPH<11> CE = 4 (justified by explosive shell burning in massive stars during the common-envelope phase, Podsiadlowski et al. 2010) and the specific angular momentum of the envelope after it has left the system, relative to the specific angular momentum of the pre-common-envelope binary, by GLYPH<13> = 7 = 4. In choosing a value of GLYPH<11> CE GLYPH<21> = 2 for massive stars we follow Portegies Zwart & Yungelson (1998); Yungelson et al. (2006); Yungelson & Lasota (2008). The GLYPH<13> - and GLYPH<11> CE-prescriptions are used as described in Toonen et al. (2012). A metallicity Z = 0 : 02 has been used (Zoccali et al. 2003). The metallicity is held constant in the population synthesis simulations as well as the subsequent tracks because of the relatively short episode of star formation (Sect. 2.2). For the kicks acquired by nascent neutron stars we use the velocity distribution suggested by Paczy'nski (1990) with a dispersion of 270 km s GLYPH<0> 1 . Because these parameters are very uncertain, in Sect. 4 we will consider the e GLYPH<11> ect of varying the common-envelope parameters and the supernova kick velocity distribution from our standard values.",
"pages": [
2
]
},
{
"title": "2.2. Star formation history and initial binary parameters",
"content": "The star formation history of the Galactic Bulge can be approximated by a Gaussian distribution with a mean GLYPH<22> = GLYPH<0> 10 Gyr and a standard deviation GLYPH<27> = 0 : 5 GLYPH<0> 2 : 5 Gyr, where the total mass of stars that are formed is 1 GLYPH<2> 10 10 M GLYPH<12> (Clarkson & Rich 2009; 10 Wyse 2009). Star formation is assumed to start 13 Gyr before present. For a narrow distribution the star formation is concentrated around 10 Gyr in the past, but the GLYPH<27> = 2 : 5 Gyr distribution has an important tail of recent star formation. In this paper we consider GLYPH<27> = 0 : 5 Gyr and GLYPH<27> = 2 : 5 Gyr (Fig. 1), representing a relatively instantaneous burst of star formation, and additional recent star formation, respectively. We find the initial binary parameters by primary-constrained pairing (Kouwenhoven et al. 2008). We derive the initial mass function for the primary components by combining the initial mass function for stellar systems by Kroupa (2001) with an estimate of the binary fraction as a function of mass. The mass ratio of the secondary and the primary is drawn from a flat distribution between 0 and 1. The 1 GLYPH<2> 10 10 M GLYPH<12> of stellar mass is found to contain 5 : 2 GLYPH<2> 10 9 binary systems. We simulated 1 million binaries with a lower primary mass limit of 4 M GLYPH<12> (because systems with a lower primary mass do not produce a supernova event in either component), and another 4 : 3 million binaries with a lower primary mass limit of 8 M GLYPH<12> , after it became clear that systems with lower primary masses do not produce UCXBs. Using the binary initial mass function we calculated to how many binaries in the full mass range of primaries (0 : 08 GLYPH<0> 100 M GLYPH<12> ) this simulation corresponds. The resulting population was then multiplied by a factor (of 14 : 45) to scale to the entire Bulge population. For an analytic derivation of the binary initial mass function we refer to Appendix A.",
"pages": [
2
]
},
{
"title": "2.3. Formation scenarios",
"content": "Weconsider three UCXB-progenitor classes, each defined by the stellar type of the donor at the time it fills, or will fill, its Roche lobe: Class 2. Helium burning star with a neutron star or black hole companion (Savonije et al. 1986; Iben & Tutukov 1987; Yungelson 2008), Class 1. White dwarf with a neutron star or black hole companion (Tutukov & Yungelson 1993; Iben et al. 1995; Yungelson et al. 2002), Class 3. Evolved main sequence star of about 1 M GLYPH<12> with a neu- tron star or black hole companion (Tutukov et al. 1985; Nelson et al. 1986; Fedorova & Ergma 1989; Pylyser & Savonije 1989; Podsiadlowski et al. 2002; Nelson & Rappaport 2003; van der Sluys et al. 2005a; Lin et al. 2011). The initial system parameters (component masses and orbital periods) and major events during the evolution towards an UCXB are described below for each class. These classes include all the binary systems that may eventually evolve into an UCXB (Belczynski & Taam 2004a; van der Sluys et al. 2005a; Nelemans et al. 2010) - in some models involving accretion-induced collapse of a white dwarf or a neutron star, the donor star has already transferred mass before the formation of the eventual accretor, a neutron star or a black hole, respectively. The detailed tracks follow the evolution of the helium burning donor starting immediately after its formation, and the main sequence donor immediately after the supernova event. The white dwarf donor tracks start at the onset of Roche-lobe overflow. In each of the detailed tracks the mass transfer is conservative as long as the mass transfer rate does not exceed the Eddington limit. If the mass transfer is faster than that, accretion at the Eddington limit is assumed, and the mass that is lost from the system carries the specific angular momentum of the accretor.",
"pages": [
2,
3
]
},
{
"title": "2.3.1. White dwarf donor systems",
"content": "The evolution of UCXBs with a white dwarf donor can be divided into two main categories based on whether the primary (initially more massive star) or secondary component becomes a supernova. A supernova explosion of the secondary star is possible when it gains mass by hydrogen accretion from the primary (e.g. Tutukov & Yungelson 1993; Portegies Zwart & Verbunt 1996; van Kerkwijk & Kulkarni 1999; Portegies Zwart & Yungelson 1999; Tauris & Sennels 2000). A supernova explosion of the secondary probably never produces a black hole, neither does the primary turn into a helium white dwarf after the supernova, because it starts out too massive. Thus, all secondarysupernova systems have a carbon-oxygen or oxygen-neon white dwarf donor and a neutron star accretor. Because the high stellar mass required for a supernova explosion of the primary is relatively rare due to the steep initial mass function, in our simulations a significant fraction of the systems (13% of the carbonoxygen white dwarf systems and 36% of the oxygen-neon white dwarf systems) experience their supernova in the secondary star. Systems with a black hole accretor are rare, about 0 : 2% of all white dwarf systems. All black holes form from the primary and have a GLYPH<24> 0 : 6 GLYPH<0> 0 : 8 M GLYPH<12> carbon-oxygen white dwarf companion. Carbon-oxygen white dwarf systems 1 are 1 : 5 times more prevalent than oxygen-neon white dwarf systems in our simulations, and GLYPH<24> 30 times more prevalent than helium white dwarf systems (combining primary and secondary supernovae). Supernova explosion of the primary This category can be subdivided by the predominant white dwarf composition: helium, carbon-oxygen or oxygen-neon. Evolution starts with a zero-age main sequence binary in which the primary is a massive star ( M & 8 M GLYPH<12> if the secondary is to become a helium or carbon-oxygen white dwarf, and M & 10 M GLYPH<12> in the case of an oxygen-neon white dwarf companion) that evolves o GLYPH<11> the main sequence first. Systems that eventually produce a helium white dwarf donor have initial orbital periods ranging mainly from 1 to 100 yr. For systems that produce a carbon-oxygen or oxygen-neon white dwarf donor the orbital periods lie mostly between 0 : 1 and 1000 yr. In the case of neutron star accretors, the primary expands during the Hertzsprung gap or as a giant and fills its Roche lobe, followed by mass transfer to the companion. The secondary cannot accrete all of this mass and is engulfed in a common envelope (Paczy'nski 1976). The envelope is expelled before the two components merge and the exposed helium core and the main sequence secondary are left behind with an orbital separation several tens of times smaller than before. After a few 10 Myr, the helium star turns into a giant (which may lead to a subsequent phase of Roche-lobe overflow) and explodes as a core-collapse supernova, leaving behind a neutron star. Black hole progenitors are Wolf-Rayet stars, which lose a large fraction of their mass before evolving into a helium giant, and then collapse to form a black hole. Secondary stars that eventually become a helium white dwarf donor had a zero-age main sequence mass between 1 : 4 and 2 : 3 M GLYPH<12> , whereas for carbon-oxygen white dwarf donors this range is 2 : 3 GLYPH<0> 7 M GLYPH<12> , where 2 : 3 M GLYPH<12> is the maximum mass of single stars that undergo the helium flash. A small fraction started with a higher initial mass. Progenitors of oxygen-neon white dwarf secondaries have a mass between 7 and 11 M GLYPH<12> on the zero-age main sequence and do not become a supernova due to severe mass loss (e.g. Gil-Pons & Garc'ıa-Berro 2001). (There is some overlap with the progenitor mass range of carbon-oxygen white dwarfs - the end product depends on whether burning stops before of after carbon ignition.) After the supernova explosion has occurred, the secondary evolves o GLYPH<11> the main sequence. As a subgiant, it initiates a common envelope with the neutron star, shrinking the orbit by another factor of a few tens. The core cools into a helium white dwarf ( . 0 : 35 M GLYPH<12> ) or, after a helium burning and helium giant stage, a carbon-oxygen white dwarf (0 : 35 GLYPH<0> 1 : 1 M GLYPH<12> ), or even, after carbon burning, an oxygen-neon white dwarf ( & 1 : 1 M GLYPH<12> , Gil-Pons & Garc'ıa-Berro 2001). Orbital angular momentum loss via gravitational wave radiation further shrinks the orbit until the white dwarf eventually overfills its Roche lobe, which happens at an orbital period of a few minutes. Supernova explosion of the secondary In this scenario, the total binary mass needs to be at least 9 M GLYPH<12> if the primary becomes a carbon-oxygen white dwarf and 12 M GLYPH<12> if the primary becomes an oxygen-neon white dwarf. The primary transfers several solar masses to the secondary in a stable manner (avoiding a common envelope - initially the secondary must have a mass of at least 0 : 55 times the primary mass) while ascending the red giant branch (e.g. Tauris & Sennels 2000). Eventually the core becomes a helium star, or a carbon-oxygen or oxygen-neon white dwarf. The secondary, which becomes the more massive component of the system, evolves o GLYPH<11> the main sequence and initiates a common envelope. The orbit shrinks, and 30 GLYPH<0> 70 Myr after the binary formation the secondary explodes as a supernova and produces a neutron star. In systems which remain bound after the supernova explosion, the primary will eventually reach Rochelobe overflow as a relatively massive ( & 0 : 7 M GLYPH<12> ) carbon-oxygen white dwarf or an oxygen-neon white dwarf ( & 1 : 1 M GLYPH<12> ). The relatively high initial mass of the primary precludes less massive carbon-oxygen white dwarfs. The initial orbital period in this scenario can be much shorter than in the primary-supernova scenarios, down to a few days. The initial stellar masses lie be- tween 4 : 5 and GLYPH<24> 10 M GLYPH<12> for the primary and 4 GLYPH<0> 9 M GLYPH<12> for the secondary (if the former becomes a carbon-oxygen white dwarf) and about 5 GLYPH<0> 12 M GLYPH<12> for both the primary and secondary (if the former becomes an oxygen-neon white dwarf). The onset of mass transfer from the white dwarf Most white dwarf-neutron star systems merge upon the onset of mass transfer. For a 1 : 4 M GLYPH<12> neutron star companion, white dwarfs with a mass higher than GLYPH<24> 0 : 83 M GLYPH<12> experience dynamically unstable mass transfer, assuming a zero-temperature (completely degenerate) mass-radius relation for the donor (e.g. Yungelson et al. 2002; van Haaften et al. 2012b). This assumption implies that these white dwarfs have cooled considerably by the time they eventually fill their Roche lobe, although tidal heating and irradiation before the onset of mass transfer may counteract this for a short time. 2 This leads to runaway mass loss on the dynamical timescale of the donor, followed by accretion of part of the disrupted white dwarf via a disk around the neutron star (see e.g. van den Heuvel & Bonsema 1984; Fryer et al. 1999; Paschalidis et al. 2011; Metzger 2012). Furthermore, in systems with a donor mass larger than GLYPH<24> 0 : 38 M GLYPH<12> (Yungelson et al. 2002; van Haaften et al. 2012b) (this value is only weakly sensitive to accretor mass) the accretor will be unable to eject enough transferred matter from the system by isotropic re-emission, where most arriving matter leaves the vicinity of the accretor in a fast, isotropic wind powered by accretion (Soberman et al. 1997; Tauris & Savonije 1999). This also leads to a merger. Therefore, systems that are unstable due to either a dynamical instability or insu GLYPH<14> cient isotropic re-emission have been removed from the sample. These instabilities only occur in systems with a white dwarf donor, because of the negative donor mass-radius exponent and the small donor size (hence, small orbit) at the onset of mass transfer. Dynamical instabilities may occur in systems with helium or main sequence donors if they have masses considerably higher than considered in this study (see e.g. Pols & Marinus 1994). In our simulation 97 : 4% of all white dwarf systems have a donor with a mass higher than 0 : 38 M GLYPH<12> and do not survive the onset of mass transfer. This includes 99 : 1% of carbon-oxygen (solid line in Fig. 2) and all oxygen-neon (dashed line in Fig. 2) white dwarf systems. In about 80% of the surviving white dwarf donor systems, the donor is a helium white dwarf (dotted line in Fig. 2), in the remainder it is a carbon-oxygen white dwarf. All surviving systems experienced the supernova explosion in the primary star and host a neutron star. If a white dwarf donor with a mass higher than the 0 : 38 M GLYPH<12> isotropic re-emission limit has a non-degenerate surface layer, the system may not merge immediately upon the onset of mass transfer, but it will once this layer has been lost. Two thirds of the white dwarf donor systems start to transfer mass to the neutron star within 2 Gyr, but some systems take much longer (Fig. 3). This is the case for all white dwarf types. White dwarfs can take very long to start mass transfer depending on the width of the initial orbit, since the orbital decay of binaries consisting of a neutron star and a white dwarf is caused by gravitational wave radiation only. Evolutionary tracks For each donor composition, the evolution after the stage described in Sect. 2.3.1 follows the tracks de- /circledot scribed in van Haaften et al. (2012b). Initially, the white dwarf donor has not yet cooled and therefore is larger than a zerotemperature white dwarf of the same mass. While the donor loses mass, its radius is held constant until it equals the zerotemperature radius of the same mass (this is justified by the rapid mass loss the donor initially experiences). From this point on, the zero-temperature radius (Zapolsky & Salpeter 1969; Rappaport et al. 1987) is used, which increases with further mass loss. The initial neutron star mass is taken to be 1 : 4 M GLYPH<12> and its radius 12 km (Guillot et al. 2011; Steiner et al. 2013). The evolution of UCXBs with degenerate donor stars is governed by angular momentum loss through gravitational wave radiation, which forces mass transfer via Roche-lobe overflow. 6",
"pages": [
3,
4,
5
]
},
{
"title": "2.3.2. Helium burning donor systems",
"content": "The supernova in low-mass helium burning star systems occurs in the primary, which has an initial mass M & 8 M GLYPH<12> . Most systems start out with an orbital period between 0 : 1 and 100 yr. Most of the helium stars form less than 500 Myr after the zeroage main sequence when the secondaries, with initial masses of 2 : 3 GLYPH<0> 5 M GLYPH<12> experience hydrogen shell burning (Savonije et al. 1986) and lose their hydrogen envelope in case B mass transfer (Kippenhahn & Weigert 1967). They fill their Roche lobes within another GLYPH<24> 200 Myr, which is much earlier than UCXBs with white dwarf donors. In part this is due to the requirement that the helium star has not yet turned into a white dwarf before the onset of mass transfer (thereby disqualifying itself from the helium burning donor sample) which constrains the size of the initial orbit. We do not find systems with a black hole accretor. We have used stellar evolutionary tracks for systems with an 0 : 35 GLYPH<0> 1 : 0 M GLYPH<12> helium star and a 1 : 4 M GLYPH<12> neutron star at initial orbital periods 3 between 20 and 200 min (Nelemans et al. 2010, table in electronic article), part of which is shown in Fig. 4. These tracks were made in the same way as the tracks for systems with white dwarf accretors in Yungelson (2008). The donor metallicity Z = 0 : 02. Because the donors at the end of the tracks are degenerate, we have extended these tracks by making a smooth transition to the zero-temperature white dwarf evolution. The tracks describe the orbital period, mass transfer rate, donor mass, and core and surface compositions as a function of time. In Fig. 4, the helium stars live up to 400 Myr. After the onset of mass transfer (vertical part of the tracks), the orbits shrink until the period minimums, then expand towards the bottom right of the figure. For each individual 'zero-age' UCXB system produced by SeBa , the track that best matches its donor mass and orbital period has been used. Main sequence donors have mostly evolved from 1 : 0 GLYPH<0> 1 : 2 M GLYPH<12> secondaries that started transferring mass after orbital decay due to magnetic braking (van der Sluys et al. 2005a). After the magnetic field disappears (because the star becomes fully convective as a result of mass loss), gravitational wave radiation becomes the dominating angular momentum loss mechanism, continuing the orbital shrinking. In this scenario, the initial period and donor mass need to fall within relatively narrow ranges in order to sufficiently evolve the main sequence star. Moreover, the magnetic braking must be su GLYPH<14> ciently e GLYPH<14> cient (van der Sluys et al. 2005b) which it probably is not (Queloz et al. 1998). Depending on the extent of hydrogen depletion in the stellar center, systems can reach a minimum orbital period between 10 and 80 min, where GLYPH<24> 80 min is the lower limit for hydrogen-rich donors (Paczy'nski 1981). We have used stellar evolutionary tracks by van der Sluys et al. (2005a) for binaries with an 0 : 7 GLYPH<0> 1 : 5 M GLYPH<12> main sequence star and a 1 : 4 M GLYPH<12> neutron star at initial orbital periods between 0 : 50 and 2 : 75 days. The donor metallicity Z = 0 : 01. These tracks describe the orbital period and mass transfer rate as a function of time, as well as the core and surface compositions.",
"pages": [
5
]
},
{
"title": "2.4. Behavior of old UCXBs",
"content": "Figure 4 suggests that once the donor has become degenerate, UCXBs 'uneventfully' reach long orbital periods and very low mass transfer rates. This is probably not the case. Instead, at low mass transfer rate a thermal-viscous instability in the accretion disk (Osaki 1974; Lasota 2001) can cause UCXBs with a sufficiently low mass transfer rate to become transient (Deloye & Bildsten 2003). This usually implies that these systems are visible only during outbursts when the disk is in a hot state, which is only a small fraction of the time, and not during the quiescent state when the disk is cold and gaining mass. Furthermore, due to accretion of angular momentum, a neutron star accretor in an UCXB can be recycled to a spin period between one and a few ms (Bisnovatyi-Kogan & Komberg 1974; Alpar et al. 1982; Radhakrishnan & Srinivasan 1982). Combined with a low mass transfer rate, the magnetosphere may transfer angular momentum from the neutron star to the accretion disk, thereby accelerating orbiting disk matter and counteracting accretion, known as the 'propeller e GLYPH<11> ect' (Davidson & Ostriker 1973; Illarionov & Sunyaev 1975). As a result, the inner accretion disk, source of most X-ray radiation, can become disrupted by the magnetosphere. See van Haaften et al. (2012b) for more details on the thermal-viscous disk instability and propeller e GLYPH<11> ect in UCXBs. Finally, at low donor mass, high-energy radiation from the neutron star, the magnetosphere and the accretion disk may evaporate the donor, or detach it from its Roche lobe (Klu'zniak et al. 1988; van den Heuvel & van Paradijs 1988; Ruderman et al. 1989a; Rasio et al. 1989). Hot, low-mass donors may su GLYPH<11> er from a dynamical instability caused by a minimum value of their mass in the case of a constant core temperature (Bildsten 2002). Each of these mechanisms can potentially diminish the visibility of UCXBs. Because it is impossible to precisely quantify at which stage of the evolution (if at all) these mechanisms become important, and to what degree, we do not remove UCXBs from the sample, instead we will discuss the implications on the population of old UCXBs in the Discussion (Sect. 4).",
"pages": [
5
]
},
{
"title": "2.5. Present-day population",
"content": "The present-day number and system parameters of UCXBs in the Galactic Bulge can be found by evaluating the evolutionary stage of all simulated systems at the present time. The most interesting parameters are the orbital period, mass transfer rate and surface composition, because these can be inferred from observations. The orbital periods of observed systems can be found from periodic modulations in the light curve or spectrum, although this is usually very di GLYPH<14> cult for UCXBs (e.g. Nelemans et al. 2006; in't Zand et al. 2007). Since the transferred matter originates from the surface of the donor, the occurrence and relative abundance of elements in the donor can be inferred from X-ray (Schulz et al. 2001), ultraviolet (Homer et al. 2002), and optical (Nelemans et al. 2004) spectra, and more indirectly, typeI X-ray bursts (in't Zand et al. 2005). The mass transfer rate cannot be directly determined observationally. However, because the energy output of an X-ray binary is for a large part provided by the gravitational energy release of the accreted matter, the mass transfer rate strongly influences the luminosity of the system, which can be observed.",
"pages": [
6
]
},
{
"title": "2.5.1. Bolometric luminosity",
"content": "We employ two methods of converting the modeled mass transfer rate to bolometric luminosity. An observational method is to match the modeled systems to real systems and assume that the modeled system behaves similar to the real system in terms of emission. We match a modeled UCXB to the real UCXB with the nearest orbital period. The relevant parameter of the emission behavior is the fraction of the time a source radiates at a given bolometric luminosity, measured over a su GLYPH<14> ciently long timespan. We use 16-year observations by the RXTE ASM to determine this behavior for the 14 known UCXBs (including two candidates) for which ASM data is available. Figure 5 shows this behavior for sources when they are visible well above the noise level (van Haaften et al. 2012c). ASM X-ray luminosity was converted to bolometric luminosity using an estimate by in't Zand et al. (2007). At a given time, the luminosity of an UCXB is randomly drawn from either the individual ASM observations that make up this time-luminosity curve, or (most of the time) from the faint-end extrapolations of the curves in Fig. 5 (van Haaften et al. 2012c). These extrapolations are constructed in such a way that the average luminosity of the luminosity distribution is equal to the time-averaged luminosity of the source as observed by the ASM. The amount of time that a given source spends at a particular luminosity translates into the number of sources in a population at the same luminosity. The second method, of a more theoretical nature, is to convert a system's modeled mass transfer rate to luminosity, using predictions by the disk instability model (Sect. 2.4) in the case of long-period UCXBs. According to this model the mass transfer rate must exceed a critical value in order to be stable and the source to be persistent, i.e., visible at a relatively high luminosity (almost) all the time. A crude estimate for the critical mass transfer rate in the case of an irradiated disk is given by in't Zand et al. (2007), based on Dubus et al. (1999); Lasota (2001); Menou et al. (2002) 0 with M a the accretor mass, P orb the orbital period, and f is a factor accounting for the disk composition; f GLYPH<25> 1 for carbonoxygen disks and f GLYPH<25> 6 for helium disks. When the time-averaged mass transfer rate exceeds the critical value, the bolometric luminosity L is assumed to be constant at with G the gravitational constant and R a the accretor radius. Sources with a time-averaged mass transfer rate below the critical value are assumed to be visible only during outburst stages. The predictions by the thermal-viscous disk instability model regarding the degree of variability of sources is supported by observations (van Paradijs 1996; Ramsay et al. 2012; Coriat et al. 2012). The duty cycle (fraction of the time the source is in outburst) is where L avg is the time-averaged luminosity based on the theoretical mass transfer rate, (Eq. 2), and L outburst is the luminosity during outburst, derived by Lasota et al. (2008) which is consistent with observations of outbursts in UCXBs (e.g. Wu et al. 2010). The period of this cycle is not relevant here. We neglect the decay in the light curve after an outburst. Furthermore, we do not predict the luminosity of systems that are in quiescence, which in fact has been assumed to be zero in the above method. Both methods have advantages and shortcomings. The ASM observations have a rather high lower limit in converted bolometric luminosity, of GLYPH<24> 10 37 erg s GLYPH<0> 1 at 8 : 3 kpc, the estimated distance to the Galactic Center (Gillessen et al. 2009). Below this luminosity, we have to rely on extrapolations. Also, variability on a timescale longer than 16 yr cannot have been observed by the ASM. On the other hand, the data do not strongly rely on uncertainties in models, as is the case for the disk instability model method. The ASM data show that UCXBs with a similar orbital period can behave rather di GLYPH<11> erently, for instance XTE J1751-305 (42 : 4 min orbital period) and XTE J0929-314 (43 : 6 min), or 4U 0513-40 (17 : 0 min) and 2S 0918-549 (17 : 4 min). Equation (1), however, shows that in the disk instability model the critical mass transfer rate and hence luminosity is largely determined by the orbital period and composition. A longer orbital period does not automatically imply a lower luminosity, as evidenced by M 15 X-2 (20 : 6 min orbital period) and 4U 1916-05 (49 : 5 min). In general, the ASM data show that a clear distinction between persistent and transient behavior is not justified (van Haaften et al. 2012c). Almost all systems are visible above the ASM detection limit only sporadically. Still, short orbital period systems are typically visible more often at a given luminosity, i.e., they have a (slightly) higher time-averaged luminosity. Even though the available sample is small, individual unusual behavior is expected to partially cancel out for the population as a whole, because some modeled UCXBs will be matched to a real UCXB that is brighter than typical for its orbital period, while others will be matched to one that is fainter than typical.",
"pages": [
6,
7
]
},
{
"title": "2.5.2. Donor composition",
"content": "The donor surface compositions of the modeled UCXBs are predicted using the helium-star donor and main sequence donor tracks, as well as the white dwarf types from the population synthesis model. These predicted compositions can be compared to observations of real systems, in the Bulge and elsewhere. Donors that start mass transfer as a white dwarf can be helium and carbon-oxygen white dwarfs (Sect. 2.3.1). In the latter case we assume 30% carbon and 70% oxygen by mass, based on the most common eventual compositions in the helium burning donors (Sect. 3.4). Donors that start mass transfer as a helium burning star can also produce helium-carbon-oxygen donors due to an interrupted helium burning stage. For the subsequent tracks for these systems, we use the mass-radius relation for degenerate donors composed of a mixture of 60% helium, 30% carbon and 10% oxygen, a choice based on the dominant tracks by Nelemans et al. (2010) as will be discussed in Sect. 3.4. We note that the degenerate tracks are not very sensitive to the composition (as long as there is no hydrogen), so these simplifications are justified. Matter processed in the CNO cycle has a high nitrogento-carbon abundance ratio, whereas helium burning converts this to a low ratio. Consequently, the nitrogen-to-oxygen ratio is a good test for the formation channel because it can discriminate between a history as a helium white dwarf donor or a helium burning donor (Nelemans et al. 2010). Based on the overview in van Haaften et al. (2012c), the compositions of observed UCXBs can be summarized as being roughly equally distributed over helium and carbon-oxygen compositions. There is no clear dependency on the orbital period, although helium composition may be more common among systems with a long orbital period ( & 40 min) (van Haaften et al. 2012c). The surface composition of very low-mass donors corresponds to the (inner) core composition of the object before it started transferring mass.",
"pages": [
7
]
},
{
"title": "3.1. Birth rates and total number of systems",
"content": "Convolving the star formation history (Fig. 1) with the delay times of the onset of mass transfer (Fig. 3) yields the birth rate distributions, shown in Fig. 6 for burst-like (black) and extended (gray) star formation epochs. Except for part of the white dwarf channel and the main sequence channel, the delay times are much shorter than the age of the Bulge (Sect. 2.2). In the case of GLYPH<27> = 0 : 5 Gyr, 98% of the white dwarf donor systems have started Roche-lobe overflow before the present, whereas 100% of the helium-star donor and 84% of the main sequence donor systems have. In the case of GLYPH<27> = 2 : 5, these percentages are 97%, 100% and 77%, respectively. The main distinguishing feature between the three classes (Sect. 2.3) is the most recent time at which mass transfer can begin. Initially wide systems from the white dwarf donor channel can still start mass transfer at the present, whereas main sequence donor systems and especially helium-star donor systems cannot, unless they have formed relatively recently (star formation history width GLYPH<27> = 2 : 5 Gyr). The rate of helium burning donor systems reaching Roche-lobe overflow closely follows the star formation history. Upon the onset of mass loss, the donor radius increases immediately for fully degenerate white dwarf donors, and after approximately 100 Myr for helium burning donors, once the donor has become su GLYPH<14> ciently degenerate following the extinction of nuclear fusion (this happens some time after the period minimum). The orbital period decreases in the case of helium burning or main sequence donors, whereas the period increases with mass loss for systems with degenerate donors (in each channel). If main sequence donor systems become ultracompact, this typically happens GLYPH<24> 3 Gyr after the onset of mass transfer, and mass transfer starts after 2 GLYPH<0> 6 Gyr after the formation of the binary (van der Sluys et al. 2005a). The total number of UCXBs with a white dwarf or heliumstar donor, shown as the solid and dashed lines in Fig. 7, initially follows the star formation rate and later on approaches an upper limit as star formation slows down. The number of systems below a given orbital period initially resembles the instantaneous star formation rate more closely for short orbital periods. After the peak in star formation rate, the number of systems below a given period keeps increasing as long as more new systems form than old systems are removed from the given sample due to their increasing orbital periods. The numbers of systems from the three di GLYPH<11> erent classes decline at di GLYPH<11> erent rates corresponding to their respective recent birth rates (Fig. 6).",
"pages": [
7,
8
]
},
{
"title": "3.2. Present-day population",
"content": "While the evolution of the population is interesting in itself, the population today can be used to validate the results. In the case of a star formation history distribution width GLYPH<27> = 0 : 5 Gyr, shown in Fig. 8, most systems at the present are old, and have expanded to an orbital period of GLYPH<24> 80 min. Since evolution slows down at longer periods, systems tend to 'pile up'. 4 Di GLYPH<11> erences in donor composition lead to di GLYPH<11> erent present-day orbital periods. This is the case even among hydrogen-deficient compositions because during most of the evolution, the donor mass is low enough for Coulomb physics to be important to the stellar structure, or even dominating degeneracy pressure. Coulomb interactions cause a donor that is composed of 'heavy' elements such as carbon and oxygen to have a smaller radius than donors with lighter composition, such as helium, of the same mass (Zapolsky & Salpeter 1969). A larger donor radius (at each mass) results in a longer orbital period at each mass, but also at each age (because less time is spent at a given orbital period). 5 For GLYPH<27> = 0 : 5 Gyr, all UCXBs with orbital periods shorter than 1 h started Roche-lobe overflow from a white dwarf donor (Fig. 8), long after the formation of the system. Most of these systems host a helium white dwarf. The main sequence channel contributes a negligible number of UCXBs and can only be distinguishable (in principle) via donor compositions. For GLYPH<27> = 2 : 5 Gyr, shown in Fig. 9, there is also recent star formation. This produces a population of young UCXBs that descended from helium burning donor systems (or still have a helium burning donor), with orbital periods shorter than 1 h. The steep cut-o GLYPH<11> at the long-period end of several curves is due to the assumption that star formation suddenly starts 13 Gyr before present. Combining all donor compositions, the result is a current GLYPH<24> 1 : 9 GLYPH<2> 10 5 population of UCXBs, mostly at long orbital period (60 GLYPH<0> 90 min). The total number of UCXBs in each class is 3 : 5 GLYPH<2> 10 4 (18%) with white dwarf donors, 1 : 56 GLYPH<2> 10 5 (81%) with helium-star donors, and 5 : 1 GLYPH<2> 10 2 (0 : 3%) with main sequence donors. The number of modeled systems with orbital periods shorter than 60 min is 1 : 5 GLYPH<2> 10 3 for GLYPH<27> = 0 : 5 Gyr, and 7 : 4 GLYPH<2> 10 3 for GLYPH<27> = 2 : 5 Gyr (0 : 8%and 3 : 8%of the population, respectively). We note that these numbers are rather sensitive to assumptions in the model, and could be lower by an order of magnitude, as will be discussed in Sect. 4.",
"pages": [
8
]
},
{
"title": "3.3. Observable population",
"content": "As described in Sect. 2.5.1, in order to determine what we can observe at high luminosity we have to convert the modeled population to luminosities.",
"pages": [
9
]
},
{
"title": "3.3.1. RXTE All-Sky Monitor",
"content": "In the first method, we apply the observations of known UCXBs by the RXTE ASM (Fig. 5, Sect. 2.5.1) to the modeled population (Figs. 8 and 9, Sect. 3.2). Modeled UCXBs with an orbital period longer than 60 min are left out because of the absence of known real systems with such periods (i.e., they are assumed never to reach luminosities above GLYPH<24> 10 34 erg s GLYPH<0> 1 ). The timeaveraged luminosity of most UCXBs with orbital periods longer than 40 min is approximately two orders of magnitude higher than expected from the gravitational-wave model (van Haaften et al. 2012c). This implies that either the observed sources are atypically bright, or that they show normal behavior, but evolve much faster than if driven only by gravitational wave losses (the implications will be discussed in Sect. 4.2). In each case, due to energy conservation, we need to reduce the number of bright sources at each orbital period by a factor that corresponds to the ratio between the gravitational-wave luminosity and the actual observed luminosity, given by van Haaften et al. (2012c, their Fig. 3). Figure 10 shows the resulting number of bright UCXBs predicted by the ASM data. For star formation history width GLYPH<27> = 0 : 5 Gyr, about 40 systems are expected to be visible as bright sources at a given time. For GLYPH<27> = 2 : 5 Gyr, this number is larger, GLYPH<24> 80, because recent star formation causes more young systems to exist, which have not yet reached orbital periods of 60 min. The cut-o GLYPH<11> at the faint end of the histogram is an artifact of the assumed linear extrapolation to the faint behavior. This also results in a relatively high minimum luminosity. In reality, especially sources with orbital periods longer than GLYPH<24> 40 min are expected to be very faint (i.e., much fainter than suggested by a linear extrapolation) at least some fraction of the time, which means the cumulative luminosity distribution flattens at faint luminosities, causing a tail at the low-luminosity end of Fig. 10. The distribution decreases with increasing luminosity in a similar way as the luminosity distribution of the representative individual observed UCXBs (Fig. 5).",
"pages": [
9
]
},
{
"title": "3.3.2. Disk instability model",
"content": "The second method relies on converting theoretical mass transfer rates to luminosities using the disk instability model (Sect. 2.5.1), the result of which is shown in Figs. 11 and 12. The total number of bright ( & 10 35 erg s GLYPH<0> 1 ) sources (either persistent or in outburst) is 34 for GLYPH<27> = 0 : 5 Gyr and 51 for GLYPH<27> = 2 : 5 Gyr. The vast majority of these are persistent (short-period) sources, and therefore the number is larger in the case of recent star formation. For the same reason, the white dwarf donor channel (Sect. 2.3.1) dominates this population, and most should have helium or carbon-oxygen donors. The helium burning channel is expected to contribute at most a couple of bright sources, in outburst at long orbital period (60 GLYPH<0> 80 min). Figure 11 shows the luminosity distribution of bright sources. UCXBs with a luminosity between GLYPH<24> 10 36 GLYPH<0> 37 erg s GLYPH<0> 1 are the ones with the shortest orbital periods, below GLYPH<24> 20 min. From here, the number of sources at a given luminosity increases towards fainter luminosities because these sources have longer period derivatives and lower time-averaged mass transfer rates, until a sharp cut-o GLYPH<11> defined by the longest orbital period at which sources are still considered persistent. Carbon-oxygen dominated sources are persistent to longer periods and lower luminosities because accretion disks composed of carbon-oxygen are more stable than helium dominated disks, see Eq. (1). For GLYPH<27> = 0 : 5 Gyr the number of short-period, persistent, systems is negligible. At longer periods ( & 40 min), the duty cycle (Eq. 3) determines the number of sources in outburst. The duty cycle decreases below 10 GLYPH<0> 4 at orbital periods longer than 60 GLYPH<0> 70 min, depending on donor composition. During their rare outbursts, sources are temporarily bright at GLYPH<24> 10 37 GLYPH<0> 38 erg s GLYPH<0> 1 , as follows from Eq. (4). Their peak luminosities are used in Fig. 11. Two peaks can be distinguished in the lines representing the white dwarf channel in Fig. 11 (thick lines). The peak at GLYPH<24> 10 37 erg s GLYPH<0> 1 consists of systems with orbital periods just longer than the critical period because these still have a relatively high duty cycle. The second peak at GLYPH<24> 10 37 : 6 erg s GLYPH<0> 1 consists of longperiod systems because these are very numerous and distributed over a relatively narrow interval of orbital periods. The duty cycle at a given orbital period is higher for helium burning systems owing to their larger size and, because their average density is set by the orbital period, correspondingly larger mass. Hence, their time-averaged mass transfer rate at a given orbital period is also higher. In Fig. 12 the orbital period distribution is shown for the same population of bright sources as in Fig. 11. The jumps of these distributions correspond to the respective low-luminosity ends of the distribution in Fig. 11. The cut-o GLYPH<11> period of persistent sources (at 30 GLYPH<0> 40 min) lies at a longer orbital period for the systems with a helium burning donor origin compared with systems with a white dwarf origin. The reason is that these donors have a higher temperature than originally white dwarf donors, and therefore the time-averaged mass transfer rate is higher at the same period. This causes the disk to remain stable (and the sources to be persistent) up to a longer period. Again we see that carbon-oxygen donor systems are persistent up to a longer orbital period than helium-dominated donor systems. Transient systems with orbital periods longer than GLYPH<24> 40 min are rarely in outburst and at most a handful have a high luminosity at a given time.",
"pages": [
9,
10
]
},
{
"title": "3.4. Donor surface composition",
"content": "The helium-star donors have partially turned into carbon-oxygen white dwarfs during their evolution, depending on their mass and evolutionary stage at the onset of Roche-lobe overflow (determined by the initial mass and orbital period). When the star starts mass transfer after filling its Roche lobe, burning is extinguished quickly (Savonije et al. 1986), and at this stage the core mass fraction of helium varies between a few percent to almost 100% (Nelemans et al. 2010). Figure 13 shows the surface abundances at the present day, assuming a narrow star formation history ( GLYPH<27> = 0 : 5 Gyr). Two thirds of the systems end up with less than 10% helium on their surface. Systems that started out with a short orbital period generally have a higher helium mass fraction, because these had less time to burn helium before the onset of mass transfer. The abundances depend on the temperature at which helium and carbon burning takes place. A higher temperature causes a higher helium burning rate, producing more carbon. Later, the carbon abundance reduces in favor of oxygen. The scatter in Fig. 13 is therefore due to di GLYPH<11> erences in core burning temperature caused by di GLYPH<11> erent stellar masses. UCXBs produced via the white dwarf donor channel have donors mostly composed of either helium material (produced in the CNO cycle), or carbon-oxygen. The ratio between both types is about 3:1 but strongly depends on the e GLYPH<14> ciency of isotropic re-emission, which strongly a GLYPH<11> ects the number of carbon-oxygen white dwarf donor systems that survive the onset of mass transfer (Sect. 2.3.1). Evolved main sequence donors with an initial mass of 1 : 0 GLYPH<0> 1 : 2 M GLYPH<12> reach a helium surface abundance Y GLYPH<25> 0 : 9 once they become ultracompact, the remaining part being hydrogen and a metallicity Z = 0 : 01, which has been present from the start (van der Sluys et al. 2005a). Because the core material is exposed early on (e.g., at an orbital period shorter than GLYPH<24> 20 min for the helium burning systems, Nelemans et al. 2010), and the core is homogeneous due to convection during its burning stages, the chemical composition is expected not to change with increasing orbital period, and therefore the same for the total and the observable population.",
"pages": [
10
]
},
{
"title": "3.5. Collective emission as function of orbital period",
"content": "Even though variability behavior determines the number of UCXBs in outburst and their luminosity, the collective luminosity of all UCXBs at a given orbital period is in principle not dependent on variability, because the time-averaged mass transfer rate of an UCXB is a relatively straightforward function of orbital period. During the evolution of an UCXB, its evolutionary timescale increases with age and orbital period. This means that there exist many more systems at longer orbital period. On the other hand the time-averaged mass transfer rate decreases with age and orbital period, so a long-period source has a lower timeaveraged luminosity. The total energy output of a source, or of the population as a whole (under the assumption of a constant star formation rate), at a given orbital period is an indication of at which orbital periods systems are likely to be observed. The amount of energy emitted by an UCXB per unit orbital period is given by where E is the emitted energy and M d the donor mass. This relation is illustrated in Fig. 14. The donor mass decreases much faster at shorter orbital periods ( M d / P GLYPH<0> 1 : 3 orb (van Haaften et al. 2012b), i.e., d M d = d P orb / P GLYPH<0> 2 : 3 orb ), and since the donor mass is the fuel for the luminosity, systems emit much more energy at short orbital periods, not only per time interval (their luminosity) but also per orbital period interval. For instance, an UCXB will emit GLYPH<24> 12 times as much energy during its evolution from 20 to 21 min as it does between 60 and 61 min. The consequence is that the short-period systems dominate the collective X-ray output of an UCXB population, unless the star formation rate decreases very fast. Depending on the variability of systems and the sensitivity of the instrument used, this could very well result in short-period systems dominating the visible population. 6",
"pages": [
10,
11
]
},
{
"title": "4. Discussion",
"content": "Wepredict GLYPH<24> 1 : 9 GLYPH<2> 10 5 of UCXBs in the Galactic Bulge, predominantly at orbital periods of & 70 min, but also a few thousand systems with orbital periods shorter than 60 min (but mostly longer than 40 min). Based on RXTE ASM observations, about 40 GLYPH<0> 80 of these sub-hour UCXBs should be visible at high luminosities of & 10 35 erg s GLYPH<0> 1 (Fig. 10), depending on the star formation history. Also, GLYPH<24> 35 GLYPH<0> 50 bright UCXBs with orbital periods . 30 min (i.e., persistent) should be visible above such a luminosity based on gravitational energy release and the disk instability model (Figs. 11 and 12). 7 The combined common-envelope parameter GLYPH<11> CE GLYPH<21> for massive stars may be lower than the value of 2 that we used (Voss & Tauris 2003). Decreasing this value to 0 : 2, as well as using a Maxwellian kick velocity distribution with a dispersion of 450 km s GLYPH<0> 1 , rather than the distribution by Paczy'nski (1990), would reduce the number of UCXBs formed by a factor of GLYPH<24> 8, as fewer systems will survive the common-envelope stage or the supernova explosion. In that case, the total number of UCXBs in the Bulge we predict is GLYPH<24> 2 GLYPH<2> 10 4 , and the number of bright systems becomes GLYPH<24> 5 GLYPH<0> 10. Table 1 shows the number of UCXBs in our model for various combinations of common-envelope efficiency and neutron star kick velocity distribution. Furthermore, the slope of the initial mass function at high stellar mass is also uncertain. A steeper slope (resulting from earlier studies such as Kroupa et al. 1993) leads to a smaller fraction of massive stars and therefore fewer UCXBs. A di GLYPH<11> erent choice for the initial component mass pairing may also reduce the number of UCXBs by an order of magnitude (Belczynski & Taam 2004a). We can distinguish several disagreements with observations. First, no UCXBs with orbital periods longer than 60 min have been discovered, faint or bright, in the Bulge or elsewhere. Second, no bright UCXBs with a short orbital period ( . 30 min) have been identified in the Galactic Bulge. Third, only three UCXBs with orbital periods between 40 and 55 min, XTE J1807-294 (Markwardt et al. 2003), XTE J1751-305 (Markwardt et al. 2002) and SWIFT J1756.9-2508 (Krimm et al. 2007), are presumably located in the Bulge, based on their positions in the sky, as their distances are not known. As for the predicted GLYPH<24> 1 : 9 GLYPH<2> 10 5 long-period systems, the probable existence of three observed UCXBs with orbital periods shorter than 55 min in the Bulge can be used to calibrate the formation rate of UCXBs, independent of population synthesis . This yields a much larger number of UCXBs than three for systems with a period longer than 55 min, based only on the rapid increase of the evolutionary timescale (set by gravitational wave radiation) with orbital period. For instance, UCXBs are expected to reach an orbital period of 55 min within GLYPH<24> 2 Gyr after the onset of mass transfer (van Haaften et al. 2012b). Even though the disk instability model predicts these longperiod systems to be in outburst so rarely that few are expected to be bright, in quiescence they would still be detectable by sen- sitive instruments at GLYPH<24> 10 31 GLYPH<0> 33 erg s GLYPH<0> 1 (e.g. Bildsten & Rutledge 2001; Heinke et al. 2003; Belczynski & Taam 2004b). The three observed UCXBs that are located in the direction of the Bulge have undetermined donor compositions, though SWIFT J1756.9-2508 is thought to have helium composition (Krimm et al. 2007). This cannot be used to constrain the star formation history, as UCXBs with helium white dwarf donors can form with a wide range of delay times.",
"pages": [
11,
12
]
},
{
"title": "4.1. Comparison with previous studies",
"content": "Belczynski & Taam (2004a) performed a population synthesis study of (primordial) UCXBs in the Galactic disk. The main difference between their and our results is that they found a total of 478 UCXBs with orbital periods shorter than 80 min in the disk at the present epoch, about three orders of magnitude fewer than our result, per unit star forming mass. It is not clear what causes this discrepancy, although these authors use di GLYPH<11> erent initial binary parameters than we do (Appendix A), for example a steeper high-mass slope in the initial mass function that leads to fewer massive stars, relatively. Also, their initial primary masses leading to UCXBs span a narrower range. Of all UCXBs in their simulation, about 20% have a black hole accretor, all of which form via the accretion-induced collapse of a neutron star. This percentage strongly depends on the assumed upper mass of a neutron star (2 M GLYPH<12> ), the mass retention e GLYPH<14> ciency of the accreting neutron star and the evolutionary stage at which the common envelope happens. As in our study, these authors did not find any (surviving) UCXBs with a black hole that was formed directly in the collapse of a massive star. They found that about 90% of the neutron star accretors form via the accretion-induced collapse of an oxygen-neon-magnesium white dwarf, a scenario our model does not produce. In our simulations, 81% of the UCXBs start mass transfer from a helium burning donor, compared to 40% in Belczynski & Taam (2004a) for the Galactic field. This is not unreasonable given the uncertainties in e.g. the onset of mass transfer from a white dwarf, and di GLYPH<11> erences in assumptions between both studies. The number of persistent sources predicted by the disk instability model depends sensitively on the orbital period separating the persistent and transient sources, because most of the predicted persistent sources have orbital periods only slightly shorter than this critical period. Details in accretion disk models (e.g. X-ray irradiation) and composition can make a large difference. We predict about 0 : 02% of the UCXBs to be persistent (Sect. 3.3.2), a much smaller fraction than found by Belczynski &Taam (2004a) (2 : 2%), but their number applies to the Galactic disk, which has a several orders of magnitude higher ongoing star formation rate, and therefore more young UCXBs, which have short orbital periods. Our number of persistently bright UCXBs (35 GLYPH<0> 50 from the disk instability model, using our standard parameters) can also be compared with the number of persistent UCXBs with white dwarf donors (600 GLYPH<0> 900) predicted by Zhu et al. (2012a) for the whole Galaxy, if one takes into account the di GLYPH<11> erence in adopted cut-o GLYPH<11> donor mass for persistent behavior. These authors found that UCXBs with donor masses lower than 0 : 03 M GLYPH<12> are transient whereas our limit lies around 0 : 02 M GLYPH<12> . Using their limit, our estimate would reduce to roughly ten, which scales within a factor of a few with their number given the stellar mass ratio between Bulge (1 GLYPH<2> 10 10 M GLYPH<12> ) and Galaxy (an additional 4 GLYPH<0> 6 GLYPH<2> 10 10 M GLYPH<12> in the Disk, Klypin et al. 2002). 8 The overprediction of bright, persistent UCXBs is therefore not unique to our study. Recently, Zhu et al. (2012b) performed a population synthesis study of Galactic UCXBs with neutron star accretors, and predicted 5 GLYPH<0> 10 GLYPH<2> 10 3 systems in the Galaxy, depending on neutron star birth kicks. As in our study, the helium burning donor channel was the most common. Notable di GLYPH<11> erences with our work are that these authors found a large number of UCXBs with a carbon-oxygen white dwarf origin, and a peak in the orbital period distribution near 40 min.",
"pages": [
12
]
},
{
"title": "4.2. Overprediction of UCXBs with long orbital period",
"content": "An important clue towards what may happen at long periods comes from the long-term ASM data. The reason for the difference in predictions by the ASM and disk instability model (Sect. 3.3) lies in the ASM observations that the UCXBs with orbital periods 40 GLYPH<0> 55 min are approximately two orders of magnitude brighter than theoretically expected from the timeaveraged mass transfer rate, assuming mass transfer is driven exclusively by gravitational wave radiation in a binary with a (semi-)degenerate donor (van Haaften et al. 2012c). 9 Assuming that the observed systems have been displaying normal behavior during the 16 years of RXTE observations, additional angular momentum loss besides that from gravitational wave radiation would cause a higher mass transfer rate at the same orbital period, and therefore a higher time-averaged luminosity (see also Ruderman et al. 1989b). As mentioned in Sect. 2.4, an e GLYPH<14> cient physical mechanism for additional loss of angular momentum from the system is a wind from the donor, induced by irradiation from the accretion disk or millisecond pulsar. In black widow systems, which host a millisecond pulsar and a low-mass ( . 0 : 2 M GLYPH<12> ) companion in a < 10 h orbit (King et al. 2005), such donor evaporation has been observed (e.g. Fruchter et al. 1988). This scenario has also been proposed to be happening to the unusually light ( GLYPH<24> 10 GLYPH<0> 3 M GLYPH<12> ) detached companion to the millisecond pulsar PSR J1719-1438 (Bailes et al. 2011) via either the white dwarf or helium burning donor channels (van Haaften et al. 2012a) or the evolved main sequence donor channel (with an orbital period minimum at GLYPH<24> 45 min, Benvenuto et al. 2012), though the latter scenario does not produce a carbon-oxygen rich donor. The recently discovered spin-powered millisecond gammaray pulsar PSR J1311-3430 system (Pletsch et al. 2012), with an orbital period of 93 : 8 min (Romani 2012; Kataoka et al. 2012) and an evaporating helium donor (Romani et al. 2012) supports the hypothesis that UCXB evolution is strongly influenced by donor evaporation. Given the low hydrogen abundance, donor evaporation, orbital period, pulsar spin period, and minimum companion mass, PSR J1311-3430 could very well be an UCXB descendant on its way to becoming a millisecond radio pulsar system like PSR J1719-1438. The non-detection of UCXBs with periods longer than GLYPH<24> 60 min, when the donor is still expected to be much more massive than the companion in PSR J1719-1438, suggests the existence of another mechanism that hides UCXBs with low donor masses and low mass transfer rates (the 60 min limit is uncertain due to the small observed sample). The propeller e GLYPH<11> ect (Sect. 2.4) is the most promising mechanism to explain this non-detection. The rotational energy of the millisecond pulsar is su GLYPH<14> cient to make long-period UCXBs with very low mass transfer rates ( GLYPH<24> 10 GLYPH<0> 13 M GLYPH<12> yr GLYPH<0> 1 ) much fainter, since it causes arriving matter to be unbound (van Haaften et al. 2012b). The propeller e GLYPH<11> ect could still allow for a (very) low rate of accretion that would prevent radio emission and make the sources visible in the ultraviolet (owing to their low disk temperatures and possibly disturbed inner accretion disks). Furthermore, radio emission from a millisecond pulsar itself, once switched on after an interruption in mass transfer, is capable of preventing accretion (Burderi et al. 2001; Fu & Li 2011). Using the Chandra X-Ray Observatory (Weisskopf et al. 2002), the Galactic Bulge Survey has found 1234 X-ray sources in 8 : 3 deg 2 (Jonker et al. 2011) so far, most of which have not yet been identified. Although many are expected to be foreground Cataclysmic Variables or non-ultracompact X-ray binaries, this number of systems found in approximately 5% of the total area of the Bulge on the sky is at least consistent with a large population of faint X-ray binaries. Also, a potentially large population of sub-luminous X-ray transients with neutron star accretors exists near the Galactic Center (Sakano et al. 2005; Wijnands et al. 2006; Degenaar & Wijnands 2009, 2010). These systems have (intrinsic) peak luminosities near GLYPH<24> 10 34 GLYPH<0> 35 erg s GLYPH<0> 1 (in the 2 GLYPH<0> 10 keV range), and may include UCXBs, although the disk instability model predicts peak luminosities & 10 37 erg s GLYPH<0> 1 for UCXBs. King & Wijnands (2006) found that the luminosities of some very faint X-ray transients imply mass transfer rates of GLYPH<24> 10 GLYPH<0> 13 M GLYPH<12> yr GLYPH<0> 1 , which is consistent with the behavior of old UCXBs. The additional angular momentum loss increases the time derivative of the orbital period, and as a result the actual number of systems at long periods in our prediction based on only gravitational wave radiation (Figs. 8 and 9) should be reduced by two orders of magnitude.",
"pages": [
12,
13
]
},
{
"title": "4.3. Overprediction of UCXBs with short orbital period",
"content": "Since UCXBs with an orbital period shorter than GLYPH<24> 30 min are expected to be persistently bright, our overprediction of these binaries ( GLYPH<24> 5 GLYPH<0> 50 systems based on the disk instability model, depending on assumptions in the model, is about one order of magnitude more than the three observed Bulge UCXBs) can have several causes: the population synthesis model produces too many UCXBs, fewer UCXBs survive the onset of mass transfer, or short-period UCXBs are bright less than 100% of the time. It is uncertain whether the white dwarf donor mass limit of 0 : 38 M GLYPH<12> for isotropic re-emission (based on the zerotemperature mass-radius relation and a consideration of the energy necessary to eject matter) should be used as the threshold for the survival of a system. A di GLYPH<11> erent assumption in the details of the hydrodynamics of the onset of mass transfer could result in either a lower or a higher limit. However, the number of surviving white dwarf donors is not very sensitive to small changes in the isotropic re-emission limit because of the small number of donors around this value (Fig. 2). On the other hand, due to the sensitivity of this donor mass limit to the actual and critical mass transfer rates (van Haaften et al. 2012b), the number of surviving UCXBs could be significantly smaller if the isotropic re-emission e GLYPH<14> ciently is less than unity, which seems plausible. However, systems could survive a mass transfer rate exceeding the isotropic re-emission limit if an UCXB with a GLYPH<24> 2 min orbital period is able to survive a few hundred years ( GLYPH<24> 10 8 orbits) with a significant amount of matter orbiting in and around the bi- nary, perhaps in a circumbinary ring (Soberman et al. 1997; Ma & Li 2009) that would be removed at a later stage. The value of isotropic re-emission limit can be tested only using shortperiod UCXBs, because for those the white dwarf donor channel is expected to dominate. In the total population (mostly longperiod systems), the helium donor channel is more important. This channel does not experience the high mass transfer rates that characterize the onset of mass transfer from a white dwarf donor. Near the period minimum the mass transfer rate remains below approximately three times the Eddington limit (Fig. 4) Even though Fig. 7 shows that the contribution of the heliumstar channel dominates, its importance has not been established observationally yet, as no detached (short orbital period) helium star-neutron star binaries have been discovered so far (Nelemans et al. 2010). If helium burning stars would turn into white dwarfs before the onset of Roche-lobe overflow, over 90% would be unable to survive as a binary system. Given these uncertainties, our overprediction by approximately one order of magnitude may simply be a consequence of poorly known parameters in our simulation, and in this case no problematic discrepancy between our results and X-ray observations would remain.",
"pages": [
13
]
},
{
"title": "4.4. Consequences for the population of millisecond radio pulsars",
"content": "If mass transfer would cease completely in most old UCXBs as suggested by the existence of PSR J1719-1438, then a fraction of the neutron stars they harbor would become visible to us as (binary) millisecond radio pulsars for several billion years. The same is probably true for UCXBs in environments closer to us than the Bulge. The number of isolated or binary millisecond radio pulsars in the Bulge suggested by the number of UCXBs with & 70 min periods we predict in our standard model, after correcting for the factor of ten overestimation in the UCXB birth rate identified above, is about 2 GLYPH<2> 10 4 , assuming the pulsars have not yet turned o GLYPH<11> as a result of spinning down. The estimated Galactic population of millisecond pulsars, based on the observed population, is 4 GLYPH<2> 10 4 (Lorimer 2008). Of the known Galactic Disk population (i.e., excluding globular clusters) of GLYPH<24> 100 radio pulsars with spin periods shorter than 10 ms, about 60% have a companion too massive to be consistent with latetime UCXB evolution, based on the ATNFPulsar Catalogue 10 in January 2013 (Manchester et al. 2005). (These have descended from hydrogen-rich low-mass and intermediate-mass X-ray binaries, Bhattacharya & van den Heuvel 1991; Tauris 2011.) Extrapolating this to the estimated Galactic population, GLYPH<24> 2 GLYPH<2> 10 4 millisecond pulsars are left that have no or a very low-mass companion, roughly the same number we predict from UCXBs for the Bulge alone (after normalizing the number of short-period UCXBs). It seems likely that millisecond pulsars have evaporated their companion entirely and are left as isolated millisecond pulsars given the reasonable match between the predicted number of old UCXBs and the number of isolated millisecond radio pulsars, combined with the very small number of observed millisecond radio pulsars with companions with masses lower than 0 : 01 M GLYPH<12> . Alternative formation channels for isolated millisecond pulsars are spin up of a neutron star by a disrupted white dwarf companion (van den Heuvel 1984), and disruption of a millisecond pulsar binary during the supernova explosion of the donor star in a high-mass X-ray binary (e.g. Camilo et al. 1993). The num- ber of neutron star-white dwarf mergers, however, seems too high to be consistent with the number of isolated millisecond pulsars that have formed. Based on Fig. 2, merging systems are much more common than surviving UCXBs, also after including UCXBs from the helium burning donor channel (see also Iben et al. 1995). On the other hand, the number of millisecond pulsars that lose their companions when it explodes as a supernova seems too small to be responsible for a large fraction of the isolated millisecond pulsars (Burgay et al. 2003; Belczynski et al. 2010) - moreover the high-mass donor star may not live long enough to spin up the neutron star to a spin period shorter than GLYPH<24> 10 ms.",
"pages": [
13,
14
]
},
{
"title": "5. Summary and conclusions",
"content": "We modeled the present-day population of primordial ultracompact X-ray binaries in the Galactic Bulge with the purpose of gaining insight in their formation and evolution. Both binary evolution and accretion physics determine the observable population, and we attempted to disentangle these in this study. We considered three main formation channels: systems that start Roche-lobe overflow by a white dwarf donor, a helium burning donor or an evolved main sequence donor. Our simulations have not produced UCXBs containing a black hole, because most systems with a very massive primary merge during unstable mass transfer, and the small number that remains is expected to merge during the onset of mass transfer from a relatively massive white dwarf to the black hole. Thus, all UCXB systems in our simulations have a neutron star accretor. The size and characteristics of the present-day population are only marginally dependent on the assumed width, GLYPH<27> , of the Gaussian distribution describing the star formation history if this value is . 1 Gyr. This is because these values of GLYPH<27> are small compared to the age of a 10 Gyr old system. A broad star formation history allows for recent star formation and short orbital period UCXBs with a helium burning donor origin, because of their short delay time. With a narrow star formation history, shortperiod UCXBs must have a white dwarf origin and therefore can have helium composition. The vast majority of UCXBs form via the helium burning donor channel (81%) or the white dwarf donor channel (18%), and therefore their exposed cores are expected to show either carbon and oxygen in their spectra, or helium, as well as small amounts of other reaction products. These two channels di GLYPH<11> er in the delay time between the zero-age main sequence and the onset of Roche-lobe overflow to the neutron star. In the white dwarf channel this delay can be as long as the age of the Universe or more (though for most systems it is less than a few billion years), whereas in the helium burning channel the delay is less than 1 Gyr. Very short period UCXBs can have a helium or carbonoxygen white dwarf donor, since these must have formed recently. Recent UCXB formation is dominated by the white dwarf donor channel, even for GLYPH<27> = 2 : 5 Gyr. The number of predicted systems with orbital periods shorter than GLYPH<24> 30 min is particularly important, since those systems are probably observable as persistently bright sources, and therefore well suited to test and calibrate the simulations. We predict about 40 bright sources, mostly of helium and carbon-oxygen composition and with orbital periods shorter than 30 min. The UCXBs with the shortest periods ( . 20 min) are more likely to have helium composition. The observed number of bright UCXBs is about ten times smaller than suggested by our model, which reflects the uncertainties in the adopted star formation history, initial binary parameters, natal kick velocities of neutron stars, common-envelope parameters and the onset of mass transfer to a neutron star accretor. We predict about (0 : 2 GLYPH<0> 1 : 9) GLYPH<2> 10 5 UCXBs in the Galactic Bulge, and we stress that such a large population is necessary based on the simple argument that the evolutionary timescale of UCXBs increases rapidly towards longer orbital periods, and therefore the observed number of short-period UCXBs, in the Bulge and also in the Galactic Disk, implies several orders of magnitude more UCXBs at long orbital periods ( > 60 min). With di GLYPH<11> erent model assumptions, this number could be up to an order of magnitude lower. Irradiation of the donor star by the neutron star and accretion disk strongly influences UCXB evolution, at least at orbital periods longer than 40 min. These systems evolve much faster , probably by GLYPH<24> 100 times, than they would if their evolution was driven exclusively by angular momentum loss via gravitational wave radiation, as assumed in this paper. UCXBs with orbital periods longer than 1 h have not been detected yet, which implies that, if existent, these systems are very faint in all electromagnetic bands (and therefore cannot be considered true X-ray binaries). We suggest that the majority of these systems have orbital periods on the order of 1 : 5 GLYPH<0> 2 : 5 h rather than the GLYPH<24> 1 : 3 h expected from gravitational wave driven evolution. Furthermore we expect that the neutron stars have companions with masses much lower than 0 : 01 M GLYPH<12> , and could very well have evaporated their companions entirely, being left as isolated millisecond pulsars. In a forthcoming paper we will model the population of hydrogen-rich low-mass X-ray binaries in the Galactic Bulge. Acknowledgements. LMvH, GN, RV, and SFPZ are supported by the Netherlands Organisation for Scientific Research (NWO). GN and RV are supported by NWO Vidi grant #016 : 093 : 305 to GN. SFPZ is supported by NWO grants #639 : 073 : 803 (Vici) and #614 : 061 : 608, and the Netherlands Research School for Astronomy (NOVA). LRY is supported by RFBR grant #10-0200231 and the Program P-21 of the Praesidium of Russian Academy of Sciences. This research has made use of NASA's Astrophysics Data System Bibliographic Services (ADS).",
"pages": [
14
]
},
{
"title": "Appendix A: Binary initial mass function and normalization of the simulation",
"content": "In the initial binary system, the more massive component is called the primary. We use primary-constrained pairing to construct 'zero-age' binaries (Kouwenhoven et al. 2008). The primary masses M primary of the zero-age main sequence binaries are drawn from the stellar initial mass function (IMF) of primaries in massive star clusters that we derive from the results by Kroupa (2001), where M is the stellar mass and 0 : 08 GLYPH<20> M = M GLYPH<12> GLYPH<20> 100. The mass ratio 0 < M secondary = M primary GLYPH<20> 1 of the components is subsequently drawn from a constant distribution (Kraicheva et al. 1989; Hogeveen 1992) - secondary masses lower than 0 : 08 M GLYPH<12> are accepted. The eccentricity e distribution is proportional to e between 0 and 1, and the semi-major axis a distribution is inversely proportional to a (Popova et al. 1982; Abt 1983), up to 10 6 R GLYPH<12> (Duquennoy & Mayor 1991) - the lower limit is set by the requirement that the initial stellar radii fit inside the circularized orbit. The specific binary fraction as a function of M is given by the observationally practical definition (Reipurth & Zinnecker 1993; Kouwenhoven et al. 2009) where N single( M ) is the distribution of single stars of mass M , N binary( M primary = M ) the distribution of binary systems containing a primary of mass M , and IMF ( M ) the IMF of systems (single stars and multiple systems combined) by Kroupa (2001). Based on observations summarized in Kouwenhoven et al. (2009); Kraus & Hillenbrand (2009); Sana et al. (2012) we approximate where we assume all multiple systems to be binaries. Equation (A.1) can be separated as It follows that single stars are more common than binary systems; there are 1 : 6 single stars for each binary system. The mass per binary system including the corresponding single stars (which can be a fractional number) is given by and the average star forming mass for each binary system formed (i.e., including mass from single stars) by (the factor 1 = 2 appears because the average secondary mass is equal to half of the average primary mass for the chosen constant mass ratio distribution). This number is the sum of the average primary mass (0 : 86 M GLYPH<12> ), 11 the average secondary mass (0 : 43 M GLYPH<12> ) and the corresponding average mass in single stars per binary system (0 : 64 M GLYPH<12> ). A lower limit of 0 : 1 M GLYPH<12> increases the average mass per binary by GLYPH<24> 12%. Overall two-thirds of the star-forming mass is in binaries. The total number of binaries that forms in the Galactic Bulge is normalized using the total number of stars Of all primaries, 1 : 3% have a mass higher than 8 M GLYPH<12> . For these masses, the power-law slope of the primary IMF (defined over linear mass intervals), from which we draw primary masses, varies between GLYPH<0> 2 : 15 (for M = 8 M GLYPH<12> ) and GLYPH<0> 2 : 2 ( M = 100 M GLYPH<12> ), compared to the estimate of GLYPH<0> 2 : 3 by Kroupa (2001) for the combined IMF of single stars and primary components. The IMF of primary components N binary( M primary = M ) is flatter than the IMF of systems IMF ( M ) because Eq. (A.2) is an increasing function (most low-mass stars are single whereas massive stars are usually in binaries). 12 The IMF for single stars only is steeper than GLYPH<0> 2 : 3 and steepens towards high mass.",
"pages": [
14,
15
]
},
{
"title": "References",
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2013A&A...552A.111P
https://arxiv.org/pdf/1302.2861.pdf
<document>
<section_header_level_1><location><page_1><loc_16><loc_85><loc_86><loc_87></location>The evolution of the AGN content in groups up to z ∼ 1</section_header_level_1>
<text><location><page_1><loc_8><loc_81><loc_94><loc_84></location>L. Pentericci 1 , M. Castellano 1 , N. Menci 1 , S. Salimbeni 2 , T. Dahlen 3 , A. Galametz 1 , P. Santini 1 , A. Grazian 1 and A. Fontana 1</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_78><loc_71><loc_79></location>1 INAF - Osservatorio Astronomico di Roma, Via Frascati 33, I-00040, Monte Porzio Catone, Italy</list_item>
<list_item><location><page_1><loc_11><loc_77><loc_62><loc_78></location>2 Astronomy Department, University of Massachusetts, Amherst, MA, 01003, USA</list_item>
<list_item><location><page_1><loc_11><loc_76><loc_64><loc_77></location>3 Space Telescope Science Institute 3700 San Martin Drive Baltimore, MD 21218 USA</list_item>
</unordered_list>
<section_header_level_1><location><page_1><loc_47><loc_72><loc_55><loc_73></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_69><loc_91><loc_71></location>Context. We explore the AGN content in groups in the two GOODS fields (North and South), exploiting the ultra-deep 2 and 4 Msec Chandra data and the deep multiwavelength observations from optical to mid IR available for both fields.</text>
<text><location><page_1><loc_11><loc_66><loc_91><loc_68></location>Aims. Determining the AGN content in structures of di ff erent mass / velocity dispersion and comparing them to higher mass / lower redshift analogs is important to understand how the AGN formation process is related to environmental properties.</text>
<text><location><page_1><loc_11><loc_58><loc_91><loc_66></location>Methods. We use our well-tested cluster finding algorithm to identify structures in the two GOODS fields, exploiting the available spectroscopic redshifts as well as accurate photometric redshifts. We identify 9 structures in GOODS-south (already presented in a previous paper) and 8 new structures in the GOODS-north field. We only consider structures where at least 2 / 3 of the members brighter than MR = -20 have a spectroscopic redshift. We then check if any of the group members coincides with X-ray sources that belong to the 4 and 2 Msec source catalogs respectively, and with a simple classification based on total rest-frame hard luminosity and hardness ratio we determine if the X-ray emission originates from AGN activity or it is more probably related to the galaxies' star-formation activity.</text>
<text><location><page_1><loc_11><loc_49><loc_91><loc_58></location>Results. We find that the fraction of AGN with LogLH > 42 ergs -1 in galaxies with MR < -20 varies from less than 5% to 22% with an average value of 6 . 3 ± 1 . 3%, i.e. much higher than the value found for lower redshift groups of similar mass, which is just 1%. It is also more than double the fraction found for massive clusters at a similar high redshift ( z ∼ 1). We then explore the spatial distribution of AGN in the structures and find that they preferentially populate the outer regions rather than the center. The colors of AGN host galaxies in structures tend to be confined to the green valley, thus avoiding the blue cloud and partially also the red-sequence, contrary to what happens in the field. We finally compare our results to the predictions of two sets of semi analytic models to investigate the evolution of AGN and evaluate potential triggering and fueling mechanisms. The outcome of this comparison attests the importance of galaxy encounters, not necessarily leading to mergers, as an e ffi cient AGN triggering mechanism.</text>
<section_header_level_1><location><page_1><loc_7><loc_44><loc_19><loc_45></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_19><loc_50><loc_42></location>The frequency and properties of active galactic nuclei (AGN) in the field, groups and clusters can provide information about how these objects are triggered and fueled. In fact, one of the possible mechanisms that trigger AGN activity is the interaction and merging of galaxies (Barnes & Hernquist 1996), enabling the creation of a central super-massive black hole and the matter to fuel it. In this context the AGN fraction would be heavily influenced by the environment providing the opportunities for interaction and the supply of fuel, and should therefore strongly depend on the local density. In addition to a comparison between the AGN fraction in di ff erent environments, measurements of the evolution of the AGN population in clusters can constrain the formation time of their super-massive black holes and the extent of their co-evolution with the cluster galaxy population (Martini et al. 2009). Indeed the external conditions are likely to heavily depend on the cluster evolutionary stage, and can be very di ff erent in structures that have recently merged compared to massive virialized clusters (van Breukelen & Clewley 2009).</text>
<text><location><page_1><loc_7><loc_13><loc_50><loc_19></location>X-ray observations are essential in the study of active galaxies since a considerable fraction of X-ray selected AGN do not show in their spectra the emission lines characteristic of optically selected AGN (Martini et al. 2002). This suggests the existence of a large population of obscured, or at least optically</text>
<text><location><page_1><loc_52><loc_19><loc_95><loc_45></location>unremarkable AGN. This result is attributed to the higher sensitivity of X-ray observations to lower-luminosity AGN relative to visible-wavelength emission-line diagnostics. In particular, deep X-ray observations can probe also the relatively faint AGN population, associated to more 'normal' galaxies and not just to the extremely massive ones. The Chandra Deep Field North and South are currently the areas with the deepest available X-ray observations, having a total of 2 and 4 Ms of data respectively. They are therefore the ideal locations to study AGN with moderate luminosity up to relative high redshifts. Although the AGN population in the CDFS has been extensively studied (e.g. Mainieri et al. 2005; Trevese et al. 2007), our project is focused on the association between AGN (relatively faint ones) with groups and small clusters that have been detected in the two fields at intermediate redshifts. Both fields were the subjects of very extensive observational campaigns at practically all wavelengths, from optical to near and mid-IR (including deep Spitzer data). Last but not least, about 2000 spectra were obtained on each area from several groups (Vanzella et al. 2006, 2008; Popesso et al. 2009; Balestra et al. 2010).</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_19></location>In this paper we will assess the fraction of AGN in groups from z ∼ 0 . 5 to z ∼ 1 . 1. The paper is organized as follows: in Section 2 we present the detection of the structures using a 3D algorithm based on photometric redshifts. In Section 3 we present the identification of group members with the X-ray sources; in Section 4 we determine the fraction of AGN in each of our structures and discuss the dependence of this fraction on both red-</text>
<text><location><page_2><loc_7><loc_87><loc_50><loc_93></location>t and velocity dispersion, using complementary data from the literature on lower redshift / more massive systems. We also determine the colors and spatial distribution of AGN. Finally in Section 5 we compare our results to the prediction of di ff erent semi-analytic models and discuss their implications.</text>
<text><location><page_2><loc_7><loc_84><loc_50><loc_86></location>Throughout the paper all magnitudes are in the AB system, and we adopt H 0 = 70 km / s / Mpc, Ω M = 0 . 3 and ΩΛ = 0 . 7.</text>
<section_header_level_1><location><page_2><loc_7><loc_79><loc_45><loc_82></location>2. Structures and groups in GOODS North and South fields</section_header_level_1>
<section_header_level_1><location><page_2><loc_7><loc_77><loc_17><loc_78></location>2.1. Detection</section_header_level_1>
<text><location><page_2><loc_7><loc_63><loc_50><loc_76></location>It has been shown (Eisenhardt et al. 2008; Salimbeni et al. 2009; van Breukelen & Clewley 2009) that high quality photometric redshifts can be e ff ectively used to find and study clusters at redshift above 1, where X-ray detection techniques become progressively less e ffi cient, due to surface brightness dimming and SZ surveys are only just beginning to give preliminary detections (Vanderlinde et al. 2010). Other methods rely on assumptions that are not necessarily fulfilled at these early epochs, such as the presence of a well defined red sequence (Gladders & Yee 2000; Andreon et al. 2009).</text>
<text><location><page_2><loc_7><loc_38><loc_50><loc_63></location>In this context, we have developed the '(2 + 1)D algorithm' providing an adaptive estimate of the 3D density field, using positions and photometric redshifts (Trevese et al. 2007) that can be used in an e ffi cient way to detect candidate galaxy clusters and groups. On the basis of accurate simulations we have shown that our algorithm can individuate groups and clusters with a very low spurious detection rate and a high completeness up to redshift ∼ 2 (for a detailed description of these simulations see Sect. 3 in Salimbeni et al. 2009). This algorithm has been extensively applied to the GOODS-North and South fields (Giavalisco et al. 2004), where extremely accurate photometric redshifts can be determined thanks to the deep multiwavelength photometry available in many bands (Grazian et al. 2006). In particular the z 850-selected catalogue of the GOODSSouth field includes photometric redshifts for ∼ 10000 galaxies with an r.m.s. ∆ z / (1 + z ) ∼ 0 . 03 up to redshift 2 (Santini et al. 2009). The GOODS-North field includes photometric redshifts for ∼ 10000 galaxies with an r.m.s. ∆ z / (1 + z ) ∼ 0 . 045 up to redshift 2 (Dahlen et al. in prep).</text>
<text><location><page_2><loc_7><loc_27><loc_50><loc_38></location>Despite the fact that the areas studied are not very large (each field is approximately 10 ' × 15 ' for a total of about 300 arcmin 2 ), and therefore we do not expect to find rare massive clusters, we identify several structures, that we characterize as groups and small clusters. Indeed, one of the most distant clusters known to date, CL0332-2742 at z = 1.61 was found by our group using this algorithm (Castellano et al. 2007) and was then spectroscopically confirmed with independent follow up observations by the GMASS collaboration (Kurk et al. 2009).</text>
<section_header_level_1><location><page_2><loc_7><loc_23><loc_35><loc_24></location>2.2. Groupsandclusterscharacteristics</section_header_level_1>
<text><location><page_2><loc_7><loc_12><loc_50><loc_22></location>In the GOODS-south field we find several structures up to z ∼ 2 that have been extensively described in Salimbeni et al. (2009). Of these, two are classified as small clusters and the rest as groups based on the masses derived from the galaxy over-density and / or from the velocity dispersion. We will consider only the structures up to redshift ∼ 1, for consistency with the GOODSNorth field where the larger photometric redshift uncertainty does not allow us to reach a similar accuracy at z > 1.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_12></location>In the GOODS-North field we find 8 structures up to redshift ∼ 1. In Table 1 we report the groups and cluster characteris-</text>
<text><location><page_2><loc_52><loc_70><loc_95><loc_93></location>cs derived from the algorithm, namely the peak position of the over-density, the mean redshift. We report the mass determined from the over-density value and the radius, assuming a bias parameter 1 and 2. In particular, the mass M 200 is defined as the mass inside the radius corresponding to a density contrast δ m = deltagal / b ∼ 200 (Carlberg et al. 1997), where b is the bias factor (see Salimbeni et al. 2009 for more details). In the Table we also report the number of spectroscopically confirmed galaxies. Briefly, of the new structures in GOODSnorth, CIG1236 + 6215 (GN 5) at z = 0.85 was originally identified by Dawson et al. (2001) with 8 spectroscopic members and was then reported by Bauer et al. (2002) as a possibly underluminous X-ray cluster, using the then available 1 Msec Chandra observation. We now assign 37 spectroscopic members to this cluster. While nobody specifically reported on the other structures in the GOODS-north field, Barger et al. (2008) and Elbaz et al. (2007) both noticed the presence of large scale structures at z = 0.85 and z = 1 from the spectroscopic redshift distribution.</text>
<text><location><page_2><loc_52><loc_53><loc_95><loc_69></location>In this work, we restrict our analysis to the structures that have a large fraction of member galaxies with accurate spectroscopic redshifts, the main reason being the need to determine the total number of group / cluster members to derive the AGN fraction as accurately as possible. Specifically we select groups / clusters that have an accurate spectroscopic redshift for at least 65% of the members brighter than MR < -20 (the limit that will be used to determine the AGN fraction). In total, 5 structures from GOODS-South and 6 from GOODS-North comply with this requirement. This does not mean that the other structures are unreal, but only that the fraction of AGN determined would be more uncertain due to the unknown number of real bright cluster members.</text>
<text><location><page_2><loc_52><loc_34><loc_95><loc_52></location>We use all spectroscopic galaxies (including in some cases objects with a magnitude below the considered limit) to determine the structure spectroscopic center and the velocity dispersion: we apply a clipping in velocity of ± 2000 kms -1 from the center. If the redshift is farther than 2000 kms -1 from the spectroscopic center, the galaxy is considered as an interloper. The number of interlopers is typically very low (1-4 per structure). For groups containing less than 15 spectroscopic members, the velocity dispersion is derived using the Gapper sigma statistics (Beers et al. 1990), while for the others we use the normal statistics. The dispersions obtained are in the range 370 to 640 km s -1 and the masses are of the order of 0.5 to few times 10 14 M /circledot (Salimbeni et al. 2009): these values confirm that we are observing structures that range from groups to small-sized clusters.</text>
<text><location><page_2><loc_52><loc_10><loc_95><loc_34></location>It is not trivial to evaluate the status of our groups and clusters as fully formed and virialized structures, given that for some we only have few spectroscopic redshift. For the two most massive structures, where the number of redshifts is su ffi ciently high, we assessed two of the most important cluster characteristics, i.e. the presence of the red-sequence and the virialization status. In Figure 1 (lower panel) we present the color magnitude relation for the most massive structure in GOODS-North (GN 5) for both spectroscopic and photometric cluster members. The presence of the red-sequence is clear. To check if the cluster has reached a relaxed status (virial equilibrium) we analyse the velocity distribution of the spectroscopic members. Indeed this status, which is acquired through the process of violent relaxation (Lynden-Bell 1967), is characterised by a Gaussian galaxy velocity distribution (e.g. Nakamura 2000) and, as shown by N-body simulations, by a low mass fraction included in substructures (e.g. Shaw et al. 2006). In the upper left panel of Figure 1 we show the binned velocity distribution of the spectroscopic members, compared to Gaussians with dispersion obtained through the biweight esti-</text>
<table>
<location><page_3><loc_7><loc_81><loc_58><loc_93></location>
</table>
<text><location><page_3><loc_7><loc_62><loc_50><loc_76></location>mate (red) and considering the jackknife uncertainties (blue and green lines). We then performed five one-dimensional statistical tests to investigate whether the velocity distribution of the galaxy members is consistent with being Gaussian: the KolmogorovSmirnov test (as implemented in the ROSTAT package of Beers et al. 1990), two classical normality tests (skewness and kurtosis) and the two more robust asymmetry index (A.I.) and tail index (T.I.) described in Bird & Beers (1993). We find consistency with a Gaussian in all cases. We then performed the twodimensional -test of Dressler & Shectman (1988) to look for substructures and found no evidence.</text>
<text><location><page_3><loc_7><loc_53><loc_50><loc_62></location>The observed color magnitude diagram and the results of the tests for Gaussianity and substructures for one of the most massive structure in GOODS-South (GS 4) have been presented and discussed in Castellano et al. (2011). In that paper there are also additional details on the tests performed. For the other structures it is not possible to carry out such tests since the number of spectroscopic members is too low to give meaningful results.</text>
<text><location><page_3><loc_7><loc_40><loc_50><loc_53></location>Figure 2 shows the density isosurfaces for the structures in GOODS-North superimposed on the ACS z850 band images of the field. Figure 3 shows the positions of the overdensities over the photometric redshift distribution of the entire GOODS-North sample. The overdensities are also traced by the distribution of the spectroscopically confirmed AGN in our catalogue, as shown in the lower panel of this Figure (note that AGN are not included in the sample used for the density estimation ). The analogous figures for GOODS-South were presented in Salimbeni et al. (2009).</text>
<section_header_level_1><location><page_3><loc_7><loc_37><loc_42><loc_38></location>2.3. X-rayemissionfromtheclustersandgroups</section_header_level_1>
<text><location><page_3><loc_7><loc_10><loc_50><loc_35></location>An inspection of the Chandra images at each cluster / group position shows that only two of the structures have significant extended X-ray emission due to the hot IGM. These are cluster GS 5 and cluster GN 8. The emission from Cluster GS 5 can be modeled with a Raymond Smith model with a best fit temperature 2.6 keV and metallicity 0.2 Z /circledot : the resulting X-ray luminosity is 9 . 56 × 10 42 ergs -1 in the 0.1-2.4 keV rest-frame band (Castellano et al. in preparation). For GN 8 we can not estimate a temperature from the data: in this case the X-ray luminosities in the 0.1-2.4 keV rest-frame band is 4.1 × 10 42 ergs -1 , assuming a Raymond Smith model with temperature 1 keV and metallicity 0.2 Z /circledot . All other structures, including the most massive ones, are undetected: as argued by Salimbeni et al. (2009), this lack of X-ray emission possibly indicates that optically selected structures are X-ray under-luminous, at least when compared to X-ray selected ones. This is for example the case of GS 4 (or CIG 0332-2747) at z = 0.734, which was extensively discussed in Castellano et al. (2011), where we showed also a tentative ∼ 3 σ detection of the X-ray emission, corresponding to a luminosity of 2 × 10 42 ergs -1 .</text>
<figure>
<location><page_3><loc_52><loc_46><loc_95><loc_75></location>
<caption>Fig. 1. Upper left panel: binned velocity distribution of the spectroscopic members, compared to Gaussians with dispersion obtained through the biweight estimate (red) and considering the jackknife uncertainties (blue and green). All distributions are normalized to 1.0. Upper right panel: cumulative velocity distributions, colour code as in the left panel. Lower panel: observed colour magnitude diagram of GN 5 of all spectroscopic (black circles) and photometric (crosses) members of the cluster within 1 Mpc from the center.</caption>
</figure>
<text><location><page_3><loc_94><loc_47><loc_95><loc_47></location>28</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_29></location>To further check the reality of our groups we performed a stack of the X-ray emission for all the new structures found in GOODS-North. We first measured the count rates in the soft band, within a square of side of ∼ 30 '' centred on the position of the peak of each structure, as given by our algorithm. This aperture was used to be consistent with Salimbeni et al. (2009) and corresponds approximately to a 1Mpc radius (of course depending slightly on redshift), which is similar to the R 200 reported in Table 1. We then masked all X-ray sources present within this area. We finally subtracted the soft-band background which was calculated from the total exposure map, by taking the total integration time at the position of each group and multiplying it by the average background count rate of 0.056 counts Ms -1 pixel -1 (Alexander et al. 2003). Alternatively for each group we calculated the average background count-rate in an annulus around</text>
<figure>
<location><page_4><loc_7><loc_66><loc_50><loc_93></location>
<caption>Fig. 2. Density isosurfaces for structures at z ∼ 0 . 45 -0 . 48 a), at z ∼ 0 . 64 b), z ∼ 0 . 85 c) and at z ∼ 0 . 97 -1 . 01 d) (average, average + 2 σ , average + 3 σ to average + 10 σ ) superimposed on the ACS z850 band image of the GOODS-North field. Yellow crosses indicate the density peak of each structure, the number is the ID of the structure in Table 1.</caption>
</figure>
<text><location><page_4><loc_7><loc_52><loc_50><loc_55></location>the source where no other sources were present. The two values in general agreed to within 1%.</text>
<text><location><page_4><loc_7><loc_35><loc_50><loc_52></location>For the combination of the 7 groups / clusters in GOODS-North that are individually undetected (all but GN 8) we get an average of 310 ± 60 counts ( ∼ 5 . 2 σ ); if we only include the 5 groups that are used in this work, the result is 220 ± 50 ( ∼ 4 . 4 σ ). We convert the measured count rate to rest frame total Lx in the 0.1-2.4 keV band, assuming a metallicity Z = 0 . 3 Z /circledot and a temperature kT = 1 keV. This temperature is typical for low redshift groups with similar velocity dispersion (e.g. Osmond & Ponman 2004). We obtain a luminosity of the order 1-2 10 42 ergs -1 . Compared to the typical luminosities of X-ray selected groups with similar velocity dispersion in the local Universe, the value we have found is on the low side, but still within the range of the X-ray luminosities of these structures (Osman & Ponman 2004).</text>
<text><location><page_4><loc_7><loc_25><loc_50><loc_35></location>We conclude that given the low mass of most of our structures and their high redshift, the lack of significant X-ray emission is still consistent in most cases with the Lx -σ relation, especially if one considers the larger scatter that is found for optically selected structures (e.g. Ryko ff et al. 2008). We caution that, although the results from the X-ray stacking are encouraging, it is impossible with the present data to test the virialization status of the individual groups.</text>
<section_header_level_1><location><page_4><loc_7><loc_20><loc_40><loc_22></location>3. X-ray point sources identification and classification</section_header_level_1>
<text><location><page_4><loc_7><loc_10><loc_50><loc_19></location>Given the sensitivity of the 2 Msec observations with a typical total flux limit of 7 × 10 -17 ergs -1 cm 2 , we are able to detect AGN with LH > 10 42 at all redshifts up to 1.1 (the most distant structure in the present study) also in the shallower GOODSNorth field. We cross correlate the group / cluster member lists with the Chandra deep field north and south source catalogs derived respectively by Alexander et al. (2003) and Luo et al.</text>
<figure>
<location><page_4><loc_53><loc_64><loc_93><loc_92></location>
<caption>Fig. 3. Upper panel: photometric redshift distribution of our sample (continuous line). The vertical red lines mark the redshifts of the detected structures. Lower panel: redshift distribution of spectroscopically selected AGN in the GOODS-North</caption>
</figure>
<text><location><page_4><loc_52><loc_47><loc_95><loc_54></location>(2008). The cross correlation was performed using a radius of 2 arcsec, which can be considered the nominal relative uncertainty of the astrometric solution. In all cases there is no ambiguity in the identification of the Chandra X-ray source with its optical counterpart.</text>
<text><location><page_4><loc_52><loc_21><loc_95><loc_47></location>In Table 2 we present the group / cluster members with an absolute magnitude MR < -20 which coincide with an X-ray source. AGN in galaxies fainter than this limit are not considered for consistency with previous works (e.g. Arnold et al. 2009). We find a total of 31 sources that are also members of our groups / clusters. In the Table we report their ID from the GOODS-MUSIC catalog for the southern field (Santini et al. 2009) and from Dahlen et al. (in preparation) for the northern field; the positions; the spectroscopic redshift; the total hard (28 keV) and soft band (0.5-2 keV) fluxes from the catalogs; the derived hardness ratio HR = (H-S) / (H + S), where H and S are the soft and hard band counts; the total inferred luminosity in the rest-frame hard band (2-10 KeV) obtained extrapolating the observed hard band flux and assuming a power law with photon index Γ = 1 . 8. For those AGN which are undetected in the hard band, but are detected in the total band, this last value was used. For those few that are detected only in the soft band (and have upper limits both in the total and in the hard-band), we infer an upper limit for the total rest-frame hard band luminosity. Note that all these X-ray sources have a spectroscopic redshift.</text>
<text><location><page_4><loc_52><loc_10><loc_95><loc_21></location>The characterization of sources is not entirely trivial since we are probing deep enough X-ray luminosities that some of the detected X-ray emission might be due to star-burst rather than related to AGN activity (especially in the deeper GOODS-South field). We will employ a very simple classification according to the total luminosity and to the hardness ratio of the X-ray emission. X-ray sources are classified as type 2 AGN if they have a hardness ratio HR ≥ -0 . 2, regardless of their total luminosity. They are classified as Type 1 AGN if they have HS ≤ -0 . 2</text>
<table>
<location><page_5><loc_7><loc_51><loc_100><loc_93></location>
<caption>L. Pentericci et al.: The evolution of the AGN content in groups and small clusters up to z ∼ 1</caption>
</table>
<text><location><page_5><loc_7><loc_43><loc_95><loc_51></location>Table 2. X-ray sources associated to galaxies brighter than MB = -20; the Xray properties of the sources have been derived from the Chandra Deep Field South 4-Megasecond Catalog (http: // heasarc.gsfc.nasa.gov / W3Browse / chandra / chandfs4ms.html) and the Chandra Deep Field North 2-Megasecond Catalog (http: // heasarc.gsfc.nasa.gov / W3Browse / all / chandfn2ms.html). The tipical onaxis 3 σ flux limits are 3 . 2 × 10 -17 , 9 . 1 × 10 -18 , and 5 . 5 × 10 -17 ergcm -2 s -1 for the full, soft, and hard bands, respectively for the GOODS-South sources; 7 . 1 × 10 -17 , 2 . 5 × 10 -17 and 1 . 4 × 10 -16 ergscm -2 s -1 for the full, soft and hard bands for the GOODS-North sources. We refer to the linked table for individual flux uncertainties.</text>
<table>
<location><page_5><loc_19><loc_25><loc_83><loc_41></location>
<caption>Table 3. Cluster properties and AGN fraction; the velocity dispersion σ is in km s -1 : 'g' indicates that is was determined using gaussian statistics, while 'cl' indicates that it was computed using the Gapper sigma statistics.</caption>
</table>
<text><location><page_5><loc_7><loc_11><loc_50><loc_18></location>but a total X-ray luminosity exceeding 10 42 ergs -1 . Sources with lower luminosity and soft emission, are classified as star-burst galaxies. In some case only a limit in available for the HR, so the classification becomes ambiguous: in this cases we further considered the X-ray-to-optical ratio ( log ( fx / fo )), which is defined as the ratio between the total X-ray flux and the B band flux (as</text>
<text><location><page_5><loc_52><loc_11><loc_95><loc_18></location>in Georgakakis et al. 2004). AGN broadly have log ( fx / fo ) in the range -1 to 1, so if log ( fx / fo ) < -1, sources are considered starburst. In Table 2 we report this ratio for all sources. We finally checked, whenever available in the literature, the optical spectra of the X-ray sources, or a classification based on these spectra (e.g. Szokoly et al. 2004, Trouille et al. 2008, Mignoli et al.</text>
<text><location><page_6><loc_7><loc_89><loc_50><loc_93></location>2004). Most of the sources are classified as emission line galaxies or high excitation emitters. None of the sources we could check were classified as broad line AGN.</text>
<text><location><page_6><loc_7><loc_80><loc_50><loc_89></location>In conclusion, of the total sample of X-ray sources, 9 are classified as star-burst galaxies, 15 are Type 2 AGN, 5 are Type 1 AGN, and one is associated to the di ff use emission from the hot cluster gas (although there could be a component associated to the BC galaxy). In some cases the classification maybe border line, however the AGN that we will use in the rest of the analysis (those with L > 10 42 ergs -1 cm -2 ) all have a solid classification.</text>
<section_header_level_1><location><page_6><loc_7><loc_77><loc_29><loc_78></location>4. Results and discussion</section_header_level_1>
<section_header_level_1><location><page_6><loc_7><loc_74><loc_36><loc_75></location>4.1. AGNfractionsinclustersandgroups</section_header_level_1>
<text><location><page_6><loc_7><loc_58><loc_50><loc_73></location>We determine the fraction fA of AGN in clusters and groups, by dividing the number of AGN (regardless of type) by the total number of members down to an absolute magnitude limit MR = -20. All AGN have a spectroscopic redshift, but cluster / group members include also some galaxies with only a photometric redshift. While it is possible that some of the galaxies included are interlopers, we also expect that galaxies belonging to the structure could be placed out of the structures due to a wrong photometric redshift. We will assume that these two effects more or less compensate each other; in any case since we include only structures with at least 65% of spectroscopic members, we estimate that this uncertainty is minimal.</text>
<text><location><page_6><loc_7><loc_49><loc_50><loc_58></location>Another way to estimate the global structure population is from the velocity dispersion, using the correlation between this quantity and the total number of galaxies within R 200 found by Koester et al. (2007) which is ln σ = 5 . 52 + 0 . 31 lnNR 200. We derive the N 200 using this relation and it is in general agreement with the total number of cluster / group members derived from our photometric plus spectroscopic redshifts.</text>
<text><location><page_6><loc_7><loc_33><loc_50><loc_49></location>In Table 3 we report the fraction of AGN with luminosity larger than LH = 10 42 ergs -1 and the fraction of AGN with luminosity higher than LH = 10 43 ergs -1 , hosted by galaxies with rest-frame magnitude brighter than MR = -20. When no AGN are identified the upper limits are evaluated using the low number statistics estimators by Gehrels (1986). Overall, we find an average fraction of 6 . 3% for AGN with LH > 10 42 ergs -1 with a very large range (from less than 5% to 22%). For the most luminous AGN with LH > 10 43 ergs -1 , we find a global fraction of 2 . 1%. In Figure 4 we plot these individual fractions (for LH > 10 42 ergs -1 ) or upper limits for our groups and small clusters (as green symbols).</text>
<section_header_level_1><location><page_6><loc_7><loc_29><loc_45><loc_31></location>4.2. ThedependenceofAGNfractionsonredshiftand velocitydispersion</section_header_level_1>
<text><location><page_6><loc_7><loc_10><loc_50><loc_28></location>Our results can be immediately compared to the analogous analysis of low redshift groups and clusters by Arnold et al. (2009). They selected structures with a range of velocity dispersions (and richness) similar to ours and extended to groups with σ s as low as 250 km / s and, on the other side, to few more massive clusters with σ up to 900 kms -1 . For a more accurate comparison we restrict their study to the same range of velocity dispersion probed by our sample, which is approximately between 350 and 700 km / s , thus including six of their structures. The result is a fraction of AGN with LH > 10 42 ergs -1 of ∼ 1% at an average redshift z = 0.045. No AGN brighter than LH = 10 43 ergs -1 are hosted by groups and small clusters in the local universe in the sample of Arnold et al. (2009), implying a limit of < 0 . 9%. In Figure 4 we report the values derived by Arnold et al. for</text>
<text><location><page_6><loc_52><loc_75><loc_95><loc_93></location>these six groups (represented as blue symbols); we also include few more relevant results from the literature, in particular the small clusters presented in Martini et al. (2009) at slightly higher redshift (Abell 1240 at z = 0 . 159 and MS1512 at z = 0 . 37, black symbols) and one of the structures studied in Eastman et al (2007) (Abell 0848 at z = 0.67, red symbol), with a velocity dispersion that is within our range. The trend for increasing AGN fraction with redshift is clear: most of the low redshift groups have no AGN (and are plotted as upper limits), while at z > 0 . 5 many have fA ∼ 5 -10% amongst bright galaxies. Note that in some cases, the luminosity of AGN in the above papers was reported in di ff erent rest-frame bands: we convert it to 2-10 KeV rest-frame, always assuming that the spectrum is represented by a power-law with photon index Γ = 1 . 8 as above.</text>
<text><location><page_6><loc_52><loc_52><loc_95><loc_75></location>The same trend we observe in groups / small clusters has already been noted in more massive clusters: Eastman et al. (2007) compared the AGN content in clusters at z ∼ 0.6-0,7 to the analogous structures in the local Universe analysed by Martini et al. (2007) and found a factor of 10 increase. In Figure 4 (right panel) we also plot a collection of results from the literature on more massive structures (i.e. clusters with σ > 700 kms -1 ): these include the three more massive clusters in Eastman et al. (2007) at z ∼ 0.60.7 (red symbols), the low redshift structures with σ > 700 km / s from Arnold et al. (2009) (blue symbols) and the intermediate redshift clusters analysed by Martini et al. (2006) (black symbols). Although several results have been published on massive clusters at redshift above 0.7, we do not include them in this plot mainly because the available X-ray observations are not sensitive to AGN with luminosities of LX = 10 42 at these very high redshifts. We remind that for AGN with L > LH = 10 43 ergs -1 in clusters, Martini et al. (2009) found a considerable evolution from 0.2% at z < 0 . 3 to 1.2 % at z ∼ 1.</text>
<text><location><page_6><loc_52><loc_46><loc_95><loc_51></location>We conclude that groups behave like their more massive counterparts, in terms of AGN content and its evolution with time, and there is a net trend for an increasing AGN fraction hosted by galaxies brighter than a fixed limit ( MR = -20 in our case).</text>
<text><location><page_6><loc_52><loc_23><loc_95><loc_46></location>From a comparison between the two panels of Figure 4 we see that groups contain comparatively many more AGN that more massive clusters. To test if the fraction of AGN depends significantly on the velocity dispersion of the systems at a fixed redshift, we run a Spearman rank correlation: we first apply the test to our own sample and the result is a rank coe ffi cient r = -0.58 with a probability of no correlation of P = 0.06. So there are indications of some anti-correlation between the velocity dispersion of a structure and its AGN fraction, although with a large scatter. We then add the four structures studied by Eastman et al. (2007) at z ∼ 0.6 which include three higher velocity dispersion systems (see above). We repeated the Spearman rank correlation test with the total sample of 15 groups and clusters and found a higher coe ffi cient (r = -0.64) with a much higher significance (P = 0.010). We therefore conclude that, at a given redshift, the lower dispersion systems have comparatively more AGN at a fixed luminosity threshold, compared to the more massive structures.</text>
<section_header_level_1><location><page_6><loc_52><loc_20><loc_94><loc_21></location>4.3. TheAGNspatialandvelocitydistributionwithingroups</section_header_level_1>
<text><location><page_6><loc_52><loc_10><loc_95><loc_19></location>The distribution of the AGN within the clusters and groups in terms of spatial position and relative velocity, can potentially offer clues on the triggering of the active phase, its lifetime, and the fueling mechanisms. If AGN are mainly fueled by galaxygalaxy interactions, one expects that they should be more prevalent in the outskirts of clusters / groups. If gas-rich mergers are the primary mechanism for activating and fueling AGN, one ex-</text>
<figure>
<location><page_7><loc_10><loc_71><loc_51><loc_93></location>
</figure>
<figure>
<location><page_7><loc_55><loc_71><loc_97><loc_93></location>
<caption>Fig. 4. Left panel: the fraction of AGN with LH > 10 42 ergs -1 in groups and small clusters with velocity dispersion 350 < σ < 700 kms -1 . Green symbols are structures from the present work, blue symbols are from Arnold et al. (2009), black symbols from Martini et al. (2009), red symbol from Eastman et al. (2007). Right panel: the same for clusters with σ > 700 kms -1 . In both plots, to determine the upper limits and to estimate the uncertainties on the fractions we used the low number statistics estimators (at 1 σ ) by Gehrels (1986). The red solid lines are the predictions from the Millenium simulation (Guo et al. 2011), the black solid and dash-dotted lines are the nominal and maximal predictions using the Menci et al. (2006) model, see text for more details.</caption>
</figure>
<text><location><page_7><loc_7><loc_41><loc_50><loc_59></location>pects higher AGN fractions in environments where galaxies have an abundant supply of gas: in this case galaxies in the centers of rich clusters should host less AGN since there is proportionally less cold gas (e.g. Giovanelli & Haynes 1985). However, a significant fraction of early type galaxies, which tend to lie in the centers of richest clusters, are known to harbour AGN and LINERs. A relation between AGN and early-type galaxies could dilute or even reverse the trends predicted by gas-rich mergers or galaxy harassment. A further e ff ect that can trigger AGN is the interaction with the central brightest cluster galaxy, which is itself often a powerful AGN (e.g. Ruderman & Ebeling 2005). The relative importance of all these e ff ects could also vary from very massive structures (where the velocity di ff erences are more marked) to groups and smaller clusters.</text>
<text><location><page_7><loc_7><loc_18><loc_50><loc_41></location>Martini et al. (2002) were amongst the first to study the spatial distribution of X-ray selected AGN in clusters of galaxies at z ∼ 0.06-0.31 and found that the AGN with LX > 10 42 ergs -1 and MR < -20 were located more centrally compared to inactive galaxies, although they had comparable velocity and substructure distributions to other cluster members. Ruderman & Ebeling (2005) studied the spatial distribution of X-ray point sources in 51 massive galaxy clusters at 0 . 3 < z < 0 . 7, and concluded that they lie predominantly in the central 0.5 Mpc. Similarly Martel et al. (2007) showed that the surface density of the X-ray sources in five massive X-ray clusters at z ∼ 0 . 8 -1 . 2 is highest in the inner regions and relatively flat at larger radii, although AGN tend to avoid the very inner cores of clusters, i.e. regions of ∼ 200 kpc . The same was found by Galametz et al. (2009) for bright X-ray AGN for 0 . 5 < z < 1 . 5 galaxy clusters and by Bignamini et al. (2008) for RCS clusters at z ∼ 0 . 6 -1 also showing a significant excess of medium luminosity X-ray AGN close to the centroid of the Xray emission.</text>
<text><location><page_7><loc_7><loc_10><loc_50><loc_17></location>At variance with the above works, Gilmour et al. (2009) analysed a sample of 148 galaxy clusters at 0 . 1 < z < 0 . 9 finding that the X-ray sources are quite evenly distributed over the central 1 Mpc, while Johnson et al. (2003) found that in the z = 0.83 cluster MS 10540321, the excess of X-ray AGN is at much larger radial distances, suggesting that they may be associated with infalling</text>
<figure>
<location><page_7><loc_56><loc_39><loc_94><loc_59></location>
<caption>Fig. 5. The solid line shows the radial distribution of all galaxies brighter than MR = -20 in the 11 structures (normalized by the maximum radius of each structure); the dashed line is the same distribution for AGN</caption>
</figure>
<text><location><page_7><loc_52><loc_21><loc_95><loc_29></location>galaxies. Finally we mention the recent work of Fassbender et al. (2012) in high redshift massive clusters, indicated significant excess of low luminosity AGN in the inner (1Mpc) regions as well as an excess of brighter soft band sources at much larger distances suggesting perhaps the idea of two di ff erent AGN populations and triggering mechanisms of nuclear activity.</text>
<text><location><page_7><loc_52><loc_10><loc_95><loc_21></location>A big caveat to the above studies (with the exception of Martini et al. 2002, 2007) is the lack the spectroscopic redshift confirmation for most or all X-ray AGN. Moreover a lot of the analysis reported are limited to very luminous AGN: testing the distribution of more 'normal' AGN can probe whether the AGN activity is more related to the host galaxy properties, or to the environment. We therefore analysed the spatial distribution of active and inactive galaxies in our structures; we used as cluster / group centers the position given by the search algorithm, un-</text>
<text><location><page_8><loc_7><loc_70><loc_50><loc_93></location>less a clearer center is given by the presence of extended X-ray emission (as in the case of GS 5) or by the position of a dominant brightest galaxy. We then determined the distance of the AGN and inactive galaxies from the center and normalized it by the extent of each system. The resulting distribution for normal and active galaxies is presented in Figure 5. We see no indication for a concentration of AGN towards the cluster / group center compared to the entire galaxy population. The distribution of AGN is actually flatter than that of the underling population, i.e. there are comparatively more AGN in the outer parts of the structures. To determine whether the AGN sample is consistent with being randomly drawn from the parent sample of galaxies or not, we run a non parametric K-S test. We find that the probability of this event is very low P = 0.055, so most probably the AGN are distributed di ff erently from the underling global population. Our conclusion is therefore that moderately luminous AGN tend to preferentially reside in the outskirts of structures compared to normal galaxies.</text>
<text><location><page_8><loc_7><loc_58><loc_50><loc_70></location>One possibility is that these AGN might have just entered in the cluster / group potential: in this case we also expect that they would be on more radial orbits compared to the rest of the population. Following, e.g., Martini et al. (2009) we determine the cumulative velocity distribution for all AGN, normalised by the cluster velocity dispersion in each case ( v -vc /σ ). We find that the distribution agrees well with a Gaussian, thus there is no evidence that the AGN have a larger velocity dispersion than the rest of inactive galaxies.</text>
<text><location><page_8><loc_7><loc_44><loc_50><loc_58></location>In conclusion we find that our AGN are preferentially located in the outskirts of the structures but have the same velocity distribution as the rest of the galaxy population. This would support to the idea that mergers and tidal interactions are one of the main instigators of AGN activity; AGN are preferentially located in intermediate density regions (outskirts of groups and clusters) which are the most conducive to galaxy-galaxy interactions because of the elevated densities, compared to the field, but the relatively low velocities compared to cluster cores. However given the many discrepant results in the literature, this scenario has to be tested further with larger, high redshift group samples.</text>
<section_header_level_1><location><page_8><loc_7><loc_39><loc_43><loc_41></location>4.4. Thecolor-magnituderelationofAGNindense environment</section_header_level_1>
<text><location><page_8><loc_7><loc_19><loc_50><loc_38></location>It has been proposed that AGN may be responsible for the moderation of star-formation activity, either by sweeping up the gas from the galaxy thus stripping star-formation, or by inhibiting further gas from cooling and infalling (e.g., Maiolino et al. 2012, Croton et al. 2006). In this context one can predict the AGN hosts to be located in distinct regions of the color-magnitude diagram for galaxies. In particular the color distribution of AGN compared to those of the general (inactive) galaxy population can place constraints on the relative timing of the physical processes that take place in the galaxies: for example, if the nuclear activity timescale is longer than the timescales on which star formation activity is quenched, or if there are dynamical delays between star-burst and AGN activity in galaxy nuclei, AGN hosts will tend to be preferentially red compared to the general inactive galaxy population.</text>
<text><location><page_8><loc_7><loc_10><loc_50><loc_19></location>We therefore investigated the colors of our AGN host galaxies compared to the underling galaxy population: we remark that our AGN are all of modest luminosities hence we expect that their optical light is dominated by host galaxy contribution and not influenced in a significant way by the AGN, therefore the colors we determine correspond to the stellar population. We further checked this issue by exploiting the fitting made by Santini</text>
<text><location><page_8><loc_52><loc_81><loc_95><loc_93></location>et al. (2012) for X-ray sources in Goods-North and South. Here the spectral energy distribution (SED) of galaxies hosting Xray sources was fitted with a double component, one for the AGN and one for the stars (see for example Figure 2 of that paper, for two cases, a type 1 and a type 2 AGN). As a result we get for the best-fit solution the relative contribution to the total luminosity of the two components at a rest-frame wavelength 6500 Å(Rband). We have verified that for our sources the contribution of the AGN component is not significant in all cases.</text>
<text><location><page_8><loc_52><loc_72><loc_95><loc_81></location>The color-magnitude diagram for the X-ray sources and of the general galaxy population is shown in Figure 6: the galaxies show the well-established bimodality of colors at this redshift, while it is clear that X-ray sources are not randomly distributed over the same region as the galaxies. All AGN hosts have colors redder than U -B > 0 . 5 and tend to reside mostly in the green valley, on the red sequence or the top of the blue cloud.</text>
<text><location><page_8><loc_52><loc_49><loc_95><loc_72></location>This plot can be immediately compared to an analogous one by Nandra et al. (2007, Figure 1 of their paper) who analysed the Color-Magnitude Relation for X-Ray selected AGN in the AEGIS field at a similar redshift (0 . 6 < z < 1 . 4). If we neglect the brightest of their AGN, which are actually QSOs and have very blue colors, we see that in their case AGN tend to populate the entire color magnitude diagram; there are also AGN in the blue cloud, although they are a relative minority. The fraction of galaxies which are also X-ray sources in the red sequence, green valley and blue cloud are 3.4, 4.2 and 0.9% respectively. Silverman et al. (2008) also showed that the fraction of galaxies hosting AGN peaks in the 'green valley' (0 . 5 < U -V < 1 . 0) especially in the presence of large scale structures. They further showed that at z > 0 . 8, a distinct, blue population of host AGN galaxies is prevalent, with colors similar to the star-forming galaxies. More recently, Rumbaugh et al. (2012) confirmed that in clusters and superclusters many AGN are located in the green valley, consistent with being a transition population.</text>
<text><location><page_8><loc_52><loc_31><loc_95><loc_49></location>From the comparison of the color-magnitude diagram of AGN in groups / clusters (our work Figure 6) with the CMD of AGN in the field (Nandra et al., Silverman et al.) we can see that in groups / cluster the AGN basically avoid the blue cloud, while in the field, AGN are also present in the blue cloud. If merger-induced AGN activity is associated with the process that quenches star formation in massive galaxies (e.g. di Matteo et al. 2005), causing the migration of blue cloud galaxies to the red sequence (Croton et al. 2006; Hopkins et al. 2006b), then the di ff erent color-distribution of AGN in the field and in groups indicates that these phenomena are more rapid in dense environments. Galaxies hosting AGN abandon the blue cloud more rapidly in clusters and groups, as inferred from our data, compared to what happens in the field.</text>
<section_header_level_1><location><page_8><loc_52><loc_27><loc_82><loc_28></location>5. Comparison to model predictions</section_header_level_1>
<text><location><page_8><loc_52><loc_10><loc_95><loc_26></location>A comparison between the observed results and the predictions of semi-analytic models (SAM) that include AGN growth, can help us understand what are the main physical processes that drive the formation and the fueling of black holes. In the previous section we have derived that the frequency and colors of AGN depend quite strongly on the environmental density, with marked di ff erences between field, groups and massive clusters. We will therefore compare our results to models that analyse the processes of AGN triggering and fuelling within a fully cosmological framework. Broadly, there are two main modes of AGN growth in these models: the so called 'radio mode' and the 'quasars mode'. The quasar mode applies to black hole growth during gas-rich mergers where the central black hole of</text>
<figure>
<location><page_9><loc_7><loc_67><loc_50><loc_91></location>
<caption>Fig. 6. The color magnitude diagram for all galaxies in the clusters and groups (small black dots) with the positions of the AGN marked by the red diamonds.</caption>
</figure>
<figure>
<location><page_9><loc_8><loc_19><loc_51><loc_57></location>
<caption>Fig. 7. The predicted color magnitude relation for all galaxies (top panel) and active galaxies (lower panel) with a hard X-ray luminosity larger than 10 42 ergs -1 from the M04 model: contours are number densities. In the lower panel we overplot the AGN observed in our sample as red diamonds.</caption>
</figure>
<text><location><page_9><loc_52><loc_84><loc_95><loc_93></location>the major progenitor grows both by absorbing the central black hole of the minor progenitor and by accreting the cold gas. In the radio mode, quiescent hot gas is accreted onto the central super-massive black hole; this accretion comes from the surrounding hot halo and is typically well below the Eddington rate. This model captures the mean behaviour of the black hole over timescales much longer than the duty cycle.</text>
<text><location><page_9><loc_52><loc_57><loc_95><loc_84></location>We will employ two di ff erent semi-analytic models, one that implements only the quasar mode and one that implements both. The model of Menci et al. (2004 M04 in the following) falls in the first category and is particularly tailored to follow the evolution of AGN. In this model the accretion of gas in the central black holes, is triggered by galaxy encounters, not necessarily leading to bound mergers, in common host structures such as clusters and especially groups; these events destabilize part of the galactic cold gas and hence feed the central BH, following the physical modeling developed by Cavaliere & Vittorini (2000). The amount of cold gas available, the interaction rates, and the properties of the host galaxies are derived as in Menci et al. (2002). As a result, at high redshift the proto-galaxies grow rapidly by hierarchical merging; meanwhile fresh gas is imported and the BHs are fueled at their full Eddington rates. At lower redshift, the dominant dynamical events are galaxy encounters in hierarchically growing groups; at this point refueling diminishes as the residual gas is exhausted, and the destabilizing encounters also decrease. This model successfully reproduces the observed properties of both galaxies and AGN across a wide redshift range (e.g. Fontana et al. 2006; Menci et al. 2008b;</text>
<text><location><page_9><loc_52><loc_55><loc_82><loc_56></location>Calura & Menci 2009; Lamastra et al. 2010).</text>
<text><location><page_9><loc_52><loc_38><loc_95><loc_55></location>We further compare our results to the output of a SAM model implemented in the Milleniumn simulations (MS in the following) as in Guo et al. (2011). For black hole growth and AGN feedback they follow Croton et al. (2006), who implement both quasar mode and radio mode. In the 'quasars mode' black hole accretion is allowed during both major and minor mergers, but the e ffi ciency in the latter is lower because the mass accreted during a merger depends, among the other factors, on the ratio msat / mcentral (eq. 8 in Croton et al. 2006). In the 'radio mode', the growth of the super-massive black hole is the result of continuous hot gas accretion once a static hot halo has formed around the host galaxy of the black hole. This accretion is assumed to be continual and quiescent (see Croton et al. 2006 for more details).</text>
<text><location><page_9><loc_52><loc_19><loc_95><loc_38></location>From the two SAMs, we select all galaxies residing in massive halos (on the scale of groups and clusters), with rest-frame magnitudes brighter than MR = -20 as in our observations. As for the real clusters and groups, we divide the simulated structures into those with a velocity dispersion between 400 and 700 kms -1 (i.e., groups and small clusters) and those with sigma above 700 kms -1 (massive clusters). From the simulations we actually know the total mass of the corresponding dark matter halos, which is related to the velocity dispersion via vc 3 = ( M / f ( z )) ∗ ( h / 0 . 235), where f ( z ) = H ( z ) / H 0, with halo mass in unity of 10 12 M /circledot and v is in unity of 100 kms -1 . The SAMs provide the total bolometric luminosity of each AGN; to convert this into observed X-ray luminosity in the 2-10keV rest-frame band, we follow the relations found by Marconi et. al. (2004) applied to our luminosity limits ( LH > 10 42 and LH > 10 43 )</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_19></location>For all galaxies, the model computes the total stellar mass (M*): at each redshift we determine the mass corresponding to MR = -20 from the relation between stellar mass and MR derived from the GOODS-South catalog (Grazian et al. 2006). We then use this mass to select mock galaxies brighter than MR = -20. Since the mass-magnitude relation has a scatter we make two di ff erent predictions. In one case we use the best fit value of</text>
<text><location><page_10><loc_7><loc_44><loc_50><loc_93></location>the mass-magnitude relation to determine MR and then select galaxies (filled curve in Figure 4, nominal prediction). In the second case we use the maximum stellar mass M* corresponding to MR = -20 as a selection threshold. In this second way we select more massive galaxies and therefore the probability to find an AGN in the galaxies is higher. This is the upper envelope of our prediction (dashed curve in Figure 4, maximal prediction).The MS model gives directly the R magnitude of the mock galaxies so for this model we have only the nominal prediction. The resulting fractions of AGN with LH > 10 42 in groups and clusters hosted by galaxies brighter than MR = -20 found in the two models are presented in Figure 4, along with the observed data. The MS model tends to over-predict the fraction of AGN, especially for massive structures and at high redshift, while is it more in agreement with the data for groups. It also predicts a very marked increase of the AGN fraction with redshift, more pronounced than what is observed in the data. This steep increment is linked to the marked rise of major mergers (the only mergers considered for the quasar mode) towards high redshift. This model predicts a modest dependence of the AGN fraction on the velocity dispersion of the systems: for example at z ∼ 0 . 6 simulated groups contain only ∼ 20% more AGN than the more massive structures, while the observed di ff erence is much larger. The M04 model predicts a milder increase of AGN fraction with redshift, both for massive and smaller systems: this is due to the fact that in this model minor mergers and close encounters are also very important and their frequency does not depend so strongly on redshift, since the small Dark Matter halos continue to merge frequently until low redshift. The M04 model tend to under-predict slightly the observed AGN fractions at all redshifts: the observed o ff set between the data and the predictions is approximately a factor of 3, both for clusters and for groups. This can be explained by the known problems of semi-analytic model that tend to overestimate the number of galaxies at the faint end of the luminosity function. In particular for the M04 model this discrepancy at the faint end was extensively discussed in Salimbeni et al. (2008) and is clearly observed at the magnitude limit that we are using in this study ( MR = -20).</text>
<text><location><page_10><loc_7><loc_27><loc_50><loc_43></location>The M04 model predicts a marked di ff erence between groups and clusters: for example at z ∼ 0.6 groups / small systems contain a factor of 5 more AGN compared to massive clusters, in agreement with what is observed on the data. Indeed, in this model the fraction of gas accreted during mergers and fly-by is inversely proportional to the velocity dispersion of the structures, therefore for clusters it is lower than in groups. This e ff ect is in addition to the increased merger rate between galaxies in groups, as compared to clusters, due to the lower encounter velocities in these small systems. In this sense, the agreement between the observational and predicted trends with velocity dispersion and with redshift validates the implemented mode of AGN growth in the M04 models.</text>
<text><location><page_10><loc_7><loc_10><loc_50><loc_26></location>We further check if the models can reproduce the colors of the AGN in dense environments. To this aim, we find that the MS model has problem in reproducing the colors of the general galaxy population in clusters and groups. Guo et al. (2011) already remarked clear di ff erences between SDSS observations and model predictions in the slope of the red sequence and in the number of fainter red-sequence galaxies. The same was also noticed by de la Torre et al. (2011), who found that the De Lucia & Blazoit (2007) implementation on the Millenium Simulation does not reproduce quantitatively the observed intrinsic colour distributions of galaxies, with much fewer very blue galaxies and many more green valley galaxies in the model than in the observations, at redshifts 0 . 2 < z < 2 . 1. In addition, the model predicts</text>
<text><location><page_10><loc_52><loc_83><loc_95><loc_93></location>an excess of red galaxies at low redshift. We therefore decided to employ only the M04 model for this comparison: this model does a good job in reproducing the color bimodality of galaxies up to high redshift, as shown in the upper panel of Figure 7 where we plot the predicted color magnitude relation for all mock galaxies. The galaxies are located in a clear red-sequence and blue cloud and are well matched to the colors of the observed galaxies (Figure 6).</text>
<text><location><page_10><loc_52><loc_75><loc_95><loc_83></location>In the lower panel we plot the predicted colors of active galaxies which are selected as objects with a total rest-frame magnitude brighter than MR = -20, hosting an AGN with luminosity exceeding 10 42 ergs -1 , and included in halos of mass comparable to our small clusters and groups. Here we also plot the colors of our observed AGN.</text>
<text><location><page_10><loc_52><loc_53><loc_95><loc_75></location>The U-B color range of the predicted AGN is well matched to the observations, most AGN having 0 . 5 < U -B < 1, like the observed ones. The model predicts the presence of a small fraction of extremely red AGN, that reside on top of the red sequence, i.e., that are even redder than the typical red-sequence galaxies. We do not observe these extremely red AGN but this might be just due to lack of statistics. The model also predicts AGN in galaxies brighter than MUV = -22 that we do not observe. Again this could be due to lack of statistics, since these extremely luminous galaxies are quite rare in our observed sample (see Figure 6). Alternatively it might be that mock galaxies hosting AGN of L ∼ 10 42 ergs -1 become too bright. Indeed in the M04 model each encounter / merger that triggers AGN activity also triggers star-formation, thus enhancing the UV luminosity of the host galaxy; the relative proportion of gas that feeds AGN and star formation, which is now fixed to approximately 1 to 4 (see Menci et al. 2006) might need to be revised.</text>
<section_header_level_1><location><page_10><loc_52><loc_49><loc_76><loc_51></location>6. Summary and conclusions</section_header_level_1>
<text><location><page_10><loc_52><loc_10><loc_95><loc_48></location>We have explored the AGN content in small clusters and groups in the two GOODS fields, exploiting the ultra-deep 2 and 4 Msec Chandra data and the deep multiwavelength observations available. We have used our previously tested cluster-finding algorithm to identify structures, exploiting the available spectroscopic redshifts as well as accurate photometric redshifts. We identified 9 structures in GOODS-south (already presented in Salimbeni et al. 2009) and 8 new structures in the GOODS-north field. To have a reliable estimate of AGN fraction, we restrict our study to structures where at least 2 / 3 of the galaxies brighter than MR = -20 have a spectroscopic redshift. We identified those clusters members that coincide with X-ray sources in the 4 and 2 Msec source catalogs (Luo et al. 2011 and Alexander et al. 2003 respectively), and with a simple classification based on total restframe hard luminosity and hardness ratio we determined if the X-ray emission originates from AGN activity or it is related to the galaxies'star-formation activity. We then computed the frequency of AGN in each group: we found that at z ∼ 0 . 6 -1 . 0 the average fraction of AGN with LogLH > 42 in galaxies with MR < -20 is 6 . 3 ± 1 . 3%, i.e. much higher than the value found in lower redshift groups, which is just 1%. This fraction is also more than double the fraction found in more massive clusters at a similar redshift. We have then explored the AGN spatial distribution within the structures and found that they tend to populate the outer regions rather than the central cluster galaxies. The colors of AGN in structures are confined to the green valley and red-sequence, avoiding the blue-cloud, whereas in the field AGNare also present in the blue cloud (e.g. Nandra et al. 2007). If the AGN activity is associated with the process that quenches star formation in massive galaxies (e.g. di Matteo et al. 2005),</text>
<text><location><page_11><loc_7><loc_88><loc_50><loc_93></location>causing the migration of blue cloud galaxies to the red sequence (Croton et al. 2006; Hopkins et al. 2006), we conclude that these phenomena are more rapid in dense environment compared to what happens in the field.</text>
<text><location><page_11><loc_7><loc_71><loc_50><loc_88></location>We finally compared our results to the predictions of two sets of semi analytic models: the M04 model (Menci et al. 2006) and one implemented on the Millenium Simulation by Guo et al. (2011). The MS model predicts a dependence of AGN content with redshift (both for clusters and groups) that is much steeper than what observed and a very modest di ff erence between massive and less massive structures. The MS04 does a good job in predicting the redshift dependence of the AGN fractions, and the marked di ff erence that is observed between groups and massive clusters. This agreement validates the implemented mode of AGN growth in the model and in particular stresses the importance of galaxy encounters, not necessarily leading to mergers, as an e ffi cient AGN triggering mechanism.</text>
<text><location><page_11><loc_7><loc_50><loc_50><loc_71></location>The M04 model also reproduces accurately the range of observed AGN colors and their position in the color-magnitude diagram, although it tends to find AGN in galaxies that are on average slightly more luminous than the observed ones. It also predicts the presence of a small fraction of extremely red AGN, residing on top of the red sequence. We do not observe these extremely red AGN but this might be due to lack of statistics: we therefore plan to expand our analysis to other fields, with similar multiwavelength data and deep X-ray observations to study the AGNcontent. In particular we are currently working on the UDS field, thus more than doubling the area (and the statistics) presented of this paper. In this way we will be able to test, amongst other things, if the predicted extremely red AGN exist, and we will be able to place more stringent constrains on the relative timing of AGN activity and the quenching of star formation at high redshift.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Context. We explore the AGN content in groups in the two GOODS fields (North and South), exploiting the ultra-deep 2 and 4 Msec Chandra data and the deep multiwavelength observations from optical to mid IR available for both fields. Aims. Determining the AGN content in structures of di ff erent mass / velocity dispersion and comparing them to higher mass / lower redshift analogs is important to understand how the AGN formation process is related to environmental properties. Methods. We use our well-tested cluster finding algorithm to identify structures in the two GOODS fields, exploiting the available spectroscopic redshifts as well as accurate photometric redshifts. We identify 9 structures in GOODS-south (already presented in a previous paper) and 8 new structures in the GOODS-north field. We only consider structures where at least 2 / 3 of the members brighter than MR = -20 have a spectroscopic redshift. We then check if any of the group members coincides with X-ray sources that belong to the 4 and 2 Msec source catalogs respectively, and with a simple classification based on total rest-frame hard luminosity and hardness ratio we determine if the X-ray emission originates from AGN activity or it is more probably related to the galaxies' star-formation activity. Results. We find that the fraction of AGN with LogLH > 42 ergs -1 in galaxies with MR < -20 varies from less than 5% to 22% with an average value of 6 . 3 ± 1 . 3%, i.e. much higher than the value found for lower redshift groups of similar mass, which is just 1%. It is also more than double the fraction found for massive clusters at a similar high redshift ( z ∼ 1). We then explore the spatial distribution of AGN in the structures and find that they preferentially populate the outer regions rather than the center. The colors of AGN host galaxies in structures tend to be confined to the green valley, thus avoiding the blue cloud and partially also the red-sequence, contrary to what happens in the field. We finally compare our results to the predictions of two sets of semi analytic models to investigate the evolution of AGN and evaluate potential triggering and fueling mechanisms. The outcome of this comparison attests the importance of galaxy encounters, not necessarily leading to mergers, as an e ffi cient AGN triggering mechanism.",
"pages": [
1
]
},
{
"title": "The evolution of the AGN content in groups up to z ∼ 1",
"content": "L. Pentericci 1 , M. Castellano 1 , N. Menci 1 , S. Salimbeni 2 , T. Dahlen 3 , A. Galametz 1 , P. Santini 1 , A. Grazian 1 and A. Fontana 1",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The frequency and properties of active galactic nuclei (AGN) in the field, groups and clusters can provide information about how these objects are triggered and fueled. In fact, one of the possible mechanisms that trigger AGN activity is the interaction and merging of galaxies (Barnes & Hernquist 1996), enabling the creation of a central super-massive black hole and the matter to fuel it. In this context the AGN fraction would be heavily influenced by the environment providing the opportunities for interaction and the supply of fuel, and should therefore strongly depend on the local density. In addition to a comparison between the AGN fraction in di ff erent environments, measurements of the evolution of the AGN population in clusters can constrain the formation time of their super-massive black holes and the extent of their co-evolution with the cluster galaxy population (Martini et al. 2009). Indeed the external conditions are likely to heavily depend on the cluster evolutionary stage, and can be very di ff erent in structures that have recently merged compared to massive virialized clusters (van Breukelen & Clewley 2009). X-ray observations are essential in the study of active galaxies since a considerable fraction of X-ray selected AGN do not show in their spectra the emission lines characteristic of optically selected AGN (Martini et al. 2002). This suggests the existence of a large population of obscured, or at least optically unremarkable AGN. This result is attributed to the higher sensitivity of X-ray observations to lower-luminosity AGN relative to visible-wavelength emission-line diagnostics. In particular, deep X-ray observations can probe also the relatively faint AGN population, associated to more 'normal' galaxies and not just to the extremely massive ones. The Chandra Deep Field North and South are currently the areas with the deepest available X-ray observations, having a total of 2 and 4 Ms of data respectively. They are therefore the ideal locations to study AGN with moderate luminosity up to relative high redshifts. Although the AGN population in the CDFS has been extensively studied (e.g. Mainieri et al. 2005; Trevese et al. 2007), our project is focused on the association between AGN (relatively faint ones) with groups and small clusters that have been detected in the two fields at intermediate redshifts. Both fields were the subjects of very extensive observational campaigns at practically all wavelengths, from optical to near and mid-IR (including deep Spitzer data). Last but not least, about 2000 spectra were obtained on each area from several groups (Vanzella et al. 2006, 2008; Popesso et al. 2009; Balestra et al. 2010). In this paper we will assess the fraction of AGN in groups from z ∼ 0 . 5 to z ∼ 1 . 1. The paper is organized as follows: in Section 2 we present the detection of the structures using a 3D algorithm based on photometric redshifts. In Section 3 we present the identification of group members with the X-ray sources; in Section 4 we determine the fraction of AGN in each of our structures and discuss the dependence of this fraction on both red- t and velocity dispersion, using complementary data from the literature on lower redshift / more massive systems. We also determine the colors and spatial distribution of AGN. Finally in Section 5 we compare our results to the prediction of di ff erent semi-analytic models and discuss their implications. Throughout the paper all magnitudes are in the AB system, and we adopt H 0 = 70 km / s / Mpc, Ω M = 0 . 3 and ΩΛ = 0 . 7.",
"pages": [
1,
2
]
},
{
"title": "2.1. Detection",
"content": "It has been shown (Eisenhardt et al. 2008; Salimbeni et al. 2009; van Breukelen & Clewley 2009) that high quality photometric redshifts can be e ff ectively used to find and study clusters at redshift above 1, where X-ray detection techniques become progressively less e ffi cient, due to surface brightness dimming and SZ surveys are only just beginning to give preliminary detections (Vanderlinde et al. 2010). Other methods rely on assumptions that are not necessarily fulfilled at these early epochs, such as the presence of a well defined red sequence (Gladders & Yee 2000; Andreon et al. 2009). In this context, we have developed the '(2 + 1)D algorithm' providing an adaptive estimate of the 3D density field, using positions and photometric redshifts (Trevese et al. 2007) that can be used in an e ffi cient way to detect candidate galaxy clusters and groups. On the basis of accurate simulations we have shown that our algorithm can individuate groups and clusters with a very low spurious detection rate and a high completeness up to redshift ∼ 2 (for a detailed description of these simulations see Sect. 3 in Salimbeni et al. 2009). This algorithm has been extensively applied to the GOODS-North and South fields (Giavalisco et al. 2004), where extremely accurate photometric redshifts can be determined thanks to the deep multiwavelength photometry available in many bands (Grazian et al. 2006). In particular the z 850-selected catalogue of the GOODSSouth field includes photometric redshifts for ∼ 10000 galaxies with an r.m.s. ∆ z / (1 + z ) ∼ 0 . 03 up to redshift 2 (Santini et al. 2009). The GOODS-North field includes photometric redshifts for ∼ 10000 galaxies with an r.m.s. ∆ z / (1 + z ) ∼ 0 . 045 up to redshift 2 (Dahlen et al. in prep). Despite the fact that the areas studied are not very large (each field is approximately 10 ' × 15 ' for a total of about 300 arcmin 2 ), and therefore we do not expect to find rare massive clusters, we identify several structures, that we characterize as groups and small clusters. Indeed, one of the most distant clusters known to date, CL0332-2742 at z = 1.61 was found by our group using this algorithm (Castellano et al. 2007) and was then spectroscopically confirmed with independent follow up observations by the GMASS collaboration (Kurk et al. 2009).",
"pages": [
2
]
},
{
"title": "2.2. Groupsandclusterscharacteristics",
"content": "In the GOODS-south field we find several structures up to z ∼ 2 that have been extensively described in Salimbeni et al. (2009). Of these, two are classified as small clusters and the rest as groups based on the masses derived from the galaxy over-density and / or from the velocity dispersion. We will consider only the structures up to redshift ∼ 1, for consistency with the GOODSNorth field where the larger photometric redshift uncertainty does not allow us to reach a similar accuracy at z > 1. In the GOODS-North field we find 8 structures up to redshift ∼ 1. In Table 1 we report the groups and cluster characteris- cs derived from the algorithm, namely the peak position of the over-density, the mean redshift. We report the mass determined from the over-density value and the radius, assuming a bias parameter 1 and 2. In particular, the mass M 200 is defined as the mass inside the radius corresponding to a density contrast δ m = deltagal / b ∼ 200 (Carlberg et al. 1997), where b is the bias factor (see Salimbeni et al. 2009 for more details). In the Table we also report the number of spectroscopically confirmed galaxies. Briefly, of the new structures in GOODSnorth, CIG1236 + 6215 (GN 5) at z = 0.85 was originally identified by Dawson et al. (2001) with 8 spectroscopic members and was then reported by Bauer et al. (2002) as a possibly underluminous X-ray cluster, using the then available 1 Msec Chandra observation. We now assign 37 spectroscopic members to this cluster. While nobody specifically reported on the other structures in the GOODS-north field, Barger et al. (2008) and Elbaz et al. (2007) both noticed the presence of large scale structures at z = 0.85 and z = 1 from the spectroscopic redshift distribution. In this work, we restrict our analysis to the structures that have a large fraction of member galaxies with accurate spectroscopic redshifts, the main reason being the need to determine the total number of group / cluster members to derive the AGN fraction as accurately as possible. Specifically we select groups / clusters that have an accurate spectroscopic redshift for at least 65% of the members brighter than MR < -20 (the limit that will be used to determine the AGN fraction). In total, 5 structures from GOODS-South and 6 from GOODS-North comply with this requirement. This does not mean that the other structures are unreal, but only that the fraction of AGN determined would be more uncertain due to the unknown number of real bright cluster members. We use all spectroscopic galaxies (including in some cases objects with a magnitude below the considered limit) to determine the structure spectroscopic center and the velocity dispersion: we apply a clipping in velocity of ± 2000 kms -1 from the center. If the redshift is farther than 2000 kms -1 from the spectroscopic center, the galaxy is considered as an interloper. The number of interlopers is typically very low (1-4 per structure). For groups containing less than 15 spectroscopic members, the velocity dispersion is derived using the Gapper sigma statistics (Beers et al. 1990), while for the others we use the normal statistics. The dispersions obtained are in the range 370 to 640 km s -1 and the masses are of the order of 0.5 to few times 10 14 M /circledot (Salimbeni et al. 2009): these values confirm that we are observing structures that range from groups to small-sized clusters. It is not trivial to evaluate the status of our groups and clusters as fully formed and virialized structures, given that for some we only have few spectroscopic redshift. For the two most massive structures, where the number of redshifts is su ffi ciently high, we assessed two of the most important cluster characteristics, i.e. the presence of the red-sequence and the virialization status. In Figure 1 (lower panel) we present the color magnitude relation for the most massive structure in GOODS-North (GN 5) for both spectroscopic and photometric cluster members. The presence of the red-sequence is clear. To check if the cluster has reached a relaxed status (virial equilibrium) we analyse the velocity distribution of the spectroscopic members. Indeed this status, which is acquired through the process of violent relaxation (Lynden-Bell 1967), is characterised by a Gaussian galaxy velocity distribution (e.g. Nakamura 2000) and, as shown by N-body simulations, by a low mass fraction included in substructures (e.g. Shaw et al. 2006). In the upper left panel of Figure 1 we show the binned velocity distribution of the spectroscopic members, compared to Gaussians with dispersion obtained through the biweight esti- mate (red) and considering the jackknife uncertainties (blue and green lines). We then performed five one-dimensional statistical tests to investigate whether the velocity distribution of the galaxy members is consistent with being Gaussian: the KolmogorovSmirnov test (as implemented in the ROSTAT package of Beers et al. 1990), two classical normality tests (skewness and kurtosis) and the two more robust asymmetry index (A.I.) and tail index (T.I.) described in Bird & Beers (1993). We find consistency with a Gaussian in all cases. We then performed the twodimensional -test of Dressler & Shectman (1988) to look for substructures and found no evidence. The observed color magnitude diagram and the results of the tests for Gaussianity and substructures for one of the most massive structure in GOODS-South (GS 4) have been presented and discussed in Castellano et al. (2011). In that paper there are also additional details on the tests performed. For the other structures it is not possible to carry out such tests since the number of spectroscopic members is too low to give meaningful results. Figure 2 shows the density isosurfaces for the structures in GOODS-North superimposed on the ACS z850 band images of the field. Figure 3 shows the positions of the overdensities over the photometric redshift distribution of the entire GOODS-North sample. The overdensities are also traced by the distribution of the spectroscopically confirmed AGN in our catalogue, as shown in the lower panel of this Figure (note that AGN are not included in the sample used for the density estimation ). The analogous figures for GOODS-South were presented in Salimbeni et al. (2009).",
"pages": [
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},
{
"title": "2.3. X-rayemissionfromtheclustersandgroups",
"content": "An inspection of the Chandra images at each cluster / group position shows that only two of the structures have significant extended X-ray emission due to the hot IGM. These are cluster GS 5 and cluster GN 8. The emission from Cluster GS 5 can be modeled with a Raymond Smith model with a best fit temperature 2.6 keV and metallicity 0.2 Z /circledot : the resulting X-ray luminosity is 9 . 56 × 10 42 ergs -1 in the 0.1-2.4 keV rest-frame band (Castellano et al. in preparation). For GN 8 we can not estimate a temperature from the data: in this case the X-ray luminosities in the 0.1-2.4 keV rest-frame band is 4.1 × 10 42 ergs -1 , assuming a Raymond Smith model with temperature 1 keV and metallicity 0.2 Z /circledot . All other structures, including the most massive ones, are undetected: as argued by Salimbeni et al. (2009), this lack of X-ray emission possibly indicates that optically selected structures are X-ray under-luminous, at least when compared to X-ray selected ones. This is for example the case of GS 4 (or CIG 0332-2747) at z = 0.734, which was extensively discussed in Castellano et al. (2011), where we showed also a tentative ∼ 3 σ detection of the X-ray emission, corresponding to a luminosity of 2 × 10 42 ergs -1 . 28 To further check the reality of our groups we performed a stack of the X-ray emission for all the new structures found in GOODS-North. We first measured the count rates in the soft band, within a square of side of ∼ 30 '' centred on the position of the peak of each structure, as given by our algorithm. This aperture was used to be consistent with Salimbeni et al. (2009) and corresponds approximately to a 1Mpc radius (of course depending slightly on redshift), which is similar to the R 200 reported in Table 1. We then masked all X-ray sources present within this area. We finally subtracted the soft-band background which was calculated from the total exposure map, by taking the total integration time at the position of each group and multiplying it by the average background count rate of 0.056 counts Ms -1 pixel -1 (Alexander et al. 2003). Alternatively for each group we calculated the average background count-rate in an annulus around the source where no other sources were present. The two values in general agreed to within 1%. For the combination of the 7 groups / clusters in GOODS-North that are individually undetected (all but GN 8) we get an average of 310 ± 60 counts ( ∼ 5 . 2 σ ); if we only include the 5 groups that are used in this work, the result is 220 ± 50 ( ∼ 4 . 4 σ ). We convert the measured count rate to rest frame total Lx in the 0.1-2.4 keV band, assuming a metallicity Z = 0 . 3 Z /circledot and a temperature kT = 1 keV. This temperature is typical for low redshift groups with similar velocity dispersion (e.g. Osmond & Ponman 2004). We obtain a luminosity of the order 1-2 10 42 ergs -1 . Compared to the typical luminosities of X-ray selected groups with similar velocity dispersion in the local Universe, the value we have found is on the low side, but still within the range of the X-ray luminosities of these structures (Osman & Ponman 2004). We conclude that given the low mass of most of our structures and their high redshift, the lack of significant X-ray emission is still consistent in most cases with the Lx -σ relation, especially if one considers the larger scatter that is found for optically selected structures (e.g. Ryko ff et al. 2008). We caution that, although the results from the X-ray stacking are encouraging, it is impossible with the present data to test the virialization status of the individual groups.",
"pages": [
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},
{
"title": "3. X-ray point sources identification and classification",
"content": "Given the sensitivity of the 2 Msec observations with a typical total flux limit of 7 × 10 -17 ergs -1 cm 2 , we are able to detect AGN with LH > 10 42 at all redshifts up to 1.1 (the most distant structure in the present study) also in the shallower GOODSNorth field. We cross correlate the group / cluster member lists with the Chandra deep field north and south source catalogs derived respectively by Alexander et al. (2003) and Luo et al. (2008). The cross correlation was performed using a radius of 2 arcsec, which can be considered the nominal relative uncertainty of the astrometric solution. In all cases there is no ambiguity in the identification of the Chandra X-ray source with its optical counterpart. In Table 2 we present the group / cluster members with an absolute magnitude MR < -20 which coincide with an X-ray source. AGN in galaxies fainter than this limit are not considered for consistency with previous works (e.g. Arnold et al. 2009). We find a total of 31 sources that are also members of our groups / clusters. In the Table we report their ID from the GOODS-MUSIC catalog for the southern field (Santini et al. 2009) and from Dahlen et al. (in preparation) for the northern field; the positions; the spectroscopic redshift; the total hard (28 keV) and soft band (0.5-2 keV) fluxes from the catalogs; the derived hardness ratio HR = (H-S) / (H + S), where H and S are the soft and hard band counts; the total inferred luminosity in the rest-frame hard band (2-10 KeV) obtained extrapolating the observed hard band flux and assuming a power law with photon index Γ = 1 . 8. For those AGN which are undetected in the hard band, but are detected in the total band, this last value was used. For those few that are detected only in the soft band (and have upper limits both in the total and in the hard-band), we infer an upper limit for the total rest-frame hard band luminosity. Note that all these X-ray sources have a spectroscopic redshift. The characterization of sources is not entirely trivial since we are probing deep enough X-ray luminosities that some of the detected X-ray emission might be due to star-burst rather than related to AGN activity (especially in the deeper GOODS-South field). We will employ a very simple classification according to the total luminosity and to the hardness ratio of the X-ray emission. X-ray sources are classified as type 2 AGN if they have a hardness ratio HR ≥ -0 . 2, regardless of their total luminosity. They are classified as Type 1 AGN if they have HS ≤ -0 . 2 Table 2. X-ray sources associated to galaxies brighter than MB = -20; the Xray properties of the sources have been derived from the Chandra Deep Field South 4-Megasecond Catalog (http: // heasarc.gsfc.nasa.gov / W3Browse / chandra / chandfs4ms.html) and the Chandra Deep Field North 2-Megasecond Catalog (http: // heasarc.gsfc.nasa.gov / W3Browse / all / chandfn2ms.html). The tipical onaxis 3 σ flux limits are 3 . 2 × 10 -17 , 9 . 1 × 10 -18 , and 5 . 5 × 10 -17 ergcm -2 s -1 for the full, soft, and hard bands, respectively for the GOODS-South sources; 7 . 1 × 10 -17 , 2 . 5 × 10 -17 and 1 . 4 × 10 -16 ergscm -2 s -1 for the full, soft and hard bands for the GOODS-North sources. We refer to the linked table for individual flux uncertainties. but a total X-ray luminosity exceeding 10 42 ergs -1 . Sources with lower luminosity and soft emission, are classified as star-burst galaxies. In some case only a limit in available for the HR, so the classification becomes ambiguous: in this cases we further considered the X-ray-to-optical ratio ( log ( fx / fo )), which is defined as the ratio between the total X-ray flux and the B band flux (as in Georgakakis et al. 2004). AGN broadly have log ( fx / fo ) in the range -1 to 1, so if log ( fx / fo ) < -1, sources are considered starburst. In Table 2 we report this ratio for all sources. We finally checked, whenever available in the literature, the optical spectra of the X-ray sources, or a classification based on these spectra (e.g. Szokoly et al. 2004, Trouille et al. 2008, Mignoli et al. 2004). Most of the sources are classified as emission line galaxies or high excitation emitters. None of the sources we could check were classified as broad line AGN. In conclusion, of the total sample of X-ray sources, 9 are classified as star-burst galaxies, 15 are Type 2 AGN, 5 are Type 1 AGN, and one is associated to the di ff use emission from the hot cluster gas (although there could be a component associated to the BC galaxy). In some cases the classification maybe border line, however the AGN that we will use in the rest of the analysis (those with L > 10 42 ergs -1 cm -2 ) all have a solid classification.",
"pages": [
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},
{
"title": "4.1. AGNfractionsinclustersandgroups",
"content": "We determine the fraction fA of AGN in clusters and groups, by dividing the number of AGN (regardless of type) by the total number of members down to an absolute magnitude limit MR = -20. All AGN have a spectroscopic redshift, but cluster / group members include also some galaxies with only a photometric redshift. While it is possible that some of the galaxies included are interlopers, we also expect that galaxies belonging to the structure could be placed out of the structures due to a wrong photometric redshift. We will assume that these two effects more or less compensate each other; in any case since we include only structures with at least 65% of spectroscopic members, we estimate that this uncertainty is minimal. Another way to estimate the global structure population is from the velocity dispersion, using the correlation between this quantity and the total number of galaxies within R 200 found by Koester et al. (2007) which is ln σ = 5 . 52 + 0 . 31 lnNR 200. We derive the N 200 using this relation and it is in general agreement with the total number of cluster / group members derived from our photometric plus spectroscopic redshifts. In Table 3 we report the fraction of AGN with luminosity larger than LH = 10 42 ergs -1 and the fraction of AGN with luminosity higher than LH = 10 43 ergs -1 , hosted by galaxies with rest-frame magnitude brighter than MR = -20. When no AGN are identified the upper limits are evaluated using the low number statistics estimators by Gehrels (1986). Overall, we find an average fraction of 6 . 3% for AGN with LH > 10 42 ergs -1 with a very large range (from less than 5% to 22%). For the most luminous AGN with LH > 10 43 ergs -1 , we find a global fraction of 2 . 1%. In Figure 4 we plot these individual fractions (for LH > 10 42 ergs -1 ) or upper limits for our groups and small clusters (as green symbols).",
"pages": [
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},
{
"title": "4.2. ThedependenceofAGNfractionsonredshiftand velocitydispersion",
"content": "Our results can be immediately compared to the analogous analysis of low redshift groups and clusters by Arnold et al. (2009). They selected structures with a range of velocity dispersions (and richness) similar to ours and extended to groups with σ s as low as 250 km / s and, on the other side, to few more massive clusters with σ up to 900 kms -1 . For a more accurate comparison we restrict their study to the same range of velocity dispersion probed by our sample, which is approximately between 350 and 700 km / s , thus including six of their structures. The result is a fraction of AGN with LH > 10 42 ergs -1 of ∼ 1% at an average redshift z = 0.045. No AGN brighter than LH = 10 43 ergs -1 are hosted by groups and small clusters in the local universe in the sample of Arnold et al. (2009), implying a limit of < 0 . 9%. In Figure 4 we report the values derived by Arnold et al. for these six groups (represented as blue symbols); we also include few more relevant results from the literature, in particular the small clusters presented in Martini et al. (2009) at slightly higher redshift (Abell 1240 at z = 0 . 159 and MS1512 at z = 0 . 37, black symbols) and one of the structures studied in Eastman et al (2007) (Abell 0848 at z = 0.67, red symbol), with a velocity dispersion that is within our range. The trend for increasing AGN fraction with redshift is clear: most of the low redshift groups have no AGN (and are plotted as upper limits), while at z > 0 . 5 many have fA ∼ 5 -10% amongst bright galaxies. Note that in some cases, the luminosity of AGN in the above papers was reported in di ff erent rest-frame bands: we convert it to 2-10 KeV rest-frame, always assuming that the spectrum is represented by a power-law with photon index Γ = 1 . 8 as above. The same trend we observe in groups / small clusters has already been noted in more massive clusters: Eastman et al. (2007) compared the AGN content in clusters at z ∼ 0.6-0,7 to the analogous structures in the local Universe analysed by Martini et al. (2007) and found a factor of 10 increase. In Figure 4 (right panel) we also plot a collection of results from the literature on more massive structures (i.e. clusters with σ > 700 kms -1 ): these include the three more massive clusters in Eastman et al. (2007) at z ∼ 0.60.7 (red symbols), the low redshift structures with σ > 700 km / s from Arnold et al. (2009) (blue symbols) and the intermediate redshift clusters analysed by Martini et al. (2006) (black symbols). Although several results have been published on massive clusters at redshift above 0.7, we do not include them in this plot mainly because the available X-ray observations are not sensitive to AGN with luminosities of LX = 10 42 at these very high redshifts. We remind that for AGN with L > LH = 10 43 ergs -1 in clusters, Martini et al. (2009) found a considerable evolution from 0.2% at z < 0 . 3 to 1.2 % at z ∼ 1. We conclude that groups behave like their more massive counterparts, in terms of AGN content and its evolution with time, and there is a net trend for an increasing AGN fraction hosted by galaxies brighter than a fixed limit ( MR = -20 in our case). From a comparison between the two panels of Figure 4 we see that groups contain comparatively many more AGN that more massive clusters. To test if the fraction of AGN depends significantly on the velocity dispersion of the systems at a fixed redshift, we run a Spearman rank correlation: we first apply the test to our own sample and the result is a rank coe ffi cient r = -0.58 with a probability of no correlation of P = 0.06. So there are indications of some anti-correlation between the velocity dispersion of a structure and its AGN fraction, although with a large scatter. We then add the four structures studied by Eastman et al. (2007) at z ∼ 0.6 which include three higher velocity dispersion systems (see above). We repeated the Spearman rank correlation test with the total sample of 15 groups and clusters and found a higher coe ffi cient (r = -0.64) with a much higher significance (P = 0.010). We therefore conclude that, at a given redshift, the lower dispersion systems have comparatively more AGN at a fixed luminosity threshold, compared to the more massive structures.",
"pages": [
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},
{
"title": "4.3. TheAGNspatialandvelocitydistributionwithingroups",
"content": "The distribution of the AGN within the clusters and groups in terms of spatial position and relative velocity, can potentially offer clues on the triggering of the active phase, its lifetime, and the fueling mechanisms. If AGN are mainly fueled by galaxygalaxy interactions, one expects that they should be more prevalent in the outskirts of clusters / groups. If gas-rich mergers are the primary mechanism for activating and fueling AGN, one ex- pects higher AGN fractions in environments where galaxies have an abundant supply of gas: in this case galaxies in the centers of rich clusters should host less AGN since there is proportionally less cold gas (e.g. Giovanelli & Haynes 1985). However, a significant fraction of early type galaxies, which tend to lie in the centers of richest clusters, are known to harbour AGN and LINERs. A relation between AGN and early-type galaxies could dilute or even reverse the trends predicted by gas-rich mergers or galaxy harassment. A further e ff ect that can trigger AGN is the interaction with the central brightest cluster galaxy, which is itself often a powerful AGN (e.g. Ruderman & Ebeling 2005). The relative importance of all these e ff ects could also vary from very massive structures (where the velocity di ff erences are more marked) to groups and smaller clusters. Martini et al. (2002) were amongst the first to study the spatial distribution of X-ray selected AGN in clusters of galaxies at z ∼ 0.06-0.31 and found that the AGN with LX > 10 42 ergs -1 and MR < -20 were located more centrally compared to inactive galaxies, although they had comparable velocity and substructure distributions to other cluster members. Ruderman & Ebeling (2005) studied the spatial distribution of X-ray point sources in 51 massive galaxy clusters at 0 . 3 < z < 0 . 7, and concluded that they lie predominantly in the central 0.5 Mpc. Similarly Martel et al. (2007) showed that the surface density of the X-ray sources in five massive X-ray clusters at z ∼ 0 . 8 -1 . 2 is highest in the inner regions and relatively flat at larger radii, although AGN tend to avoid the very inner cores of clusters, i.e. regions of ∼ 200 kpc . The same was found by Galametz et al. (2009) for bright X-ray AGN for 0 . 5 < z < 1 . 5 galaxy clusters and by Bignamini et al. (2008) for RCS clusters at z ∼ 0 . 6 -1 also showing a significant excess of medium luminosity X-ray AGN close to the centroid of the Xray emission. At variance with the above works, Gilmour et al. (2009) analysed a sample of 148 galaxy clusters at 0 . 1 < z < 0 . 9 finding that the X-ray sources are quite evenly distributed over the central 1 Mpc, while Johnson et al. (2003) found that in the z = 0.83 cluster MS 10540321, the excess of X-ray AGN is at much larger radial distances, suggesting that they may be associated with infalling galaxies. Finally we mention the recent work of Fassbender et al. (2012) in high redshift massive clusters, indicated significant excess of low luminosity AGN in the inner (1Mpc) regions as well as an excess of brighter soft band sources at much larger distances suggesting perhaps the idea of two di ff erent AGN populations and triggering mechanisms of nuclear activity. A big caveat to the above studies (with the exception of Martini et al. 2002, 2007) is the lack the spectroscopic redshift confirmation for most or all X-ray AGN. Moreover a lot of the analysis reported are limited to very luminous AGN: testing the distribution of more 'normal' AGN can probe whether the AGN activity is more related to the host galaxy properties, or to the environment. We therefore analysed the spatial distribution of active and inactive galaxies in our structures; we used as cluster / group centers the position given by the search algorithm, un- less a clearer center is given by the presence of extended X-ray emission (as in the case of GS 5) or by the position of a dominant brightest galaxy. We then determined the distance of the AGN and inactive galaxies from the center and normalized it by the extent of each system. The resulting distribution for normal and active galaxies is presented in Figure 5. We see no indication for a concentration of AGN towards the cluster / group center compared to the entire galaxy population. The distribution of AGN is actually flatter than that of the underling population, i.e. there are comparatively more AGN in the outer parts of the structures. To determine whether the AGN sample is consistent with being randomly drawn from the parent sample of galaxies or not, we run a non parametric K-S test. We find that the probability of this event is very low P = 0.055, so most probably the AGN are distributed di ff erently from the underling global population. Our conclusion is therefore that moderately luminous AGN tend to preferentially reside in the outskirts of structures compared to normal galaxies. One possibility is that these AGN might have just entered in the cluster / group potential: in this case we also expect that they would be on more radial orbits compared to the rest of the population. Following, e.g., Martini et al. (2009) we determine the cumulative velocity distribution for all AGN, normalised by the cluster velocity dispersion in each case ( v -vc /σ ). We find that the distribution agrees well with a Gaussian, thus there is no evidence that the AGN have a larger velocity dispersion than the rest of inactive galaxies. In conclusion we find that our AGN are preferentially located in the outskirts of the structures but have the same velocity distribution as the rest of the galaxy population. This would support to the idea that mergers and tidal interactions are one of the main instigators of AGN activity; AGN are preferentially located in intermediate density regions (outskirts of groups and clusters) which are the most conducive to galaxy-galaxy interactions because of the elevated densities, compared to the field, but the relatively low velocities compared to cluster cores. However given the many discrepant results in the literature, this scenario has to be tested further with larger, high redshift group samples.",
"pages": [
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},
{
"title": "4.4. Thecolor-magnituderelationofAGNindense environment",
"content": "It has been proposed that AGN may be responsible for the moderation of star-formation activity, either by sweeping up the gas from the galaxy thus stripping star-formation, or by inhibiting further gas from cooling and infalling (e.g., Maiolino et al. 2012, Croton et al. 2006). In this context one can predict the AGN hosts to be located in distinct regions of the color-magnitude diagram for galaxies. In particular the color distribution of AGN compared to those of the general (inactive) galaxy population can place constraints on the relative timing of the physical processes that take place in the galaxies: for example, if the nuclear activity timescale is longer than the timescales on which star formation activity is quenched, or if there are dynamical delays between star-burst and AGN activity in galaxy nuclei, AGN hosts will tend to be preferentially red compared to the general inactive galaxy population. We therefore investigated the colors of our AGN host galaxies compared to the underling galaxy population: we remark that our AGN are all of modest luminosities hence we expect that their optical light is dominated by host galaxy contribution and not influenced in a significant way by the AGN, therefore the colors we determine correspond to the stellar population. We further checked this issue by exploiting the fitting made by Santini et al. (2012) for X-ray sources in Goods-North and South. Here the spectral energy distribution (SED) of galaxies hosting Xray sources was fitted with a double component, one for the AGN and one for the stars (see for example Figure 2 of that paper, for two cases, a type 1 and a type 2 AGN). As a result we get for the best-fit solution the relative contribution to the total luminosity of the two components at a rest-frame wavelength 6500 Å(Rband). We have verified that for our sources the contribution of the AGN component is not significant in all cases. The color-magnitude diagram for the X-ray sources and of the general galaxy population is shown in Figure 6: the galaxies show the well-established bimodality of colors at this redshift, while it is clear that X-ray sources are not randomly distributed over the same region as the galaxies. All AGN hosts have colors redder than U -B > 0 . 5 and tend to reside mostly in the green valley, on the red sequence or the top of the blue cloud. This plot can be immediately compared to an analogous one by Nandra et al. (2007, Figure 1 of their paper) who analysed the Color-Magnitude Relation for X-Ray selected AGN in the AEGIS field at a similar redshift (0 . 6 < z < 1 . 4). If we neglect the brightest of their AGN, which are actually QSOs and have very blue colors, we see that in their case AGN tend to populate the entire color magnitude diagram; there are also AGN in the blue cloud, although they are a relative minority. The fraction of galaxies which are also X-ray sources in the red sequence, green valley and blue cloud are 3.4, 4.2 and 0.9% respectively. Silverman et al. (2008) also showed that the fraction of galaxies hosting AGN peaks in the 'green valley' (0 . 5 < U -V < 1 . 0) especially in the presence of large scale structures. They further showed that at z > 0 . 8, a distinct, blue population of host AGN galaxies is prevalent, with colors similar to the star-forming galaxies. More recently, Rumbaugh et al. (2012) confirmed that in clusters and superclusters many AGN are located in the green valley, consistent with being a transition population. From the comparison of the color-magnitude diagram of AGN in groups / clusters (our work Figure 6) with the CMD of AGN in the field (Nandra et al., Silverman et al.) we can see that in groups / cluster the AGN basically avoid the blue cloud, while in the field, AGN are also present in the blue cloud. If merger-induced AGN activity is associated with the process that quenches star formation in massive galaxies (e.g. di Matteo et al. 2005), causing the migration of blue cloud galaxies to the red sequence (Croton et al. 2006; Hopkins et al. 2006b), then the di ff erent color-distribution of AGN in the field and in groups indicates that these phenomena are more rapid in dense environments. Galaxies hosting AGN abandon the blue cloud more rapidly in clusters and groups, as inferred from our data, compared to what happens in the field.",
"pages": [
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},
{
"title": "5. Comparison to model predictions",
"content": "A comparison between the observed results and the predictions of semi-analytic models (SAM) that include AGN growth, can help us understand what are the main physical processes that drive the formation and the fueling of black holes. In the previous section we have derived that the frequency and colors of AGN depend quite strongly on the environmental density, with marked di ff erences between field, groups and massive clusters. We will therefore compare our results to models that analyse the processes of AGN triggering and fuelling within a fully cosmological framework. Broadly, there are two main modes of AGN growth in these models: the so called 'radio mode' and the 'quasars mode'. The quasar mode applies to black hole growth during gas-rich mergers where the central black hole of the major progenitor grows both by absorbing the central black hole of the minor progenitor and by accreting the cold gas. In the radio mode, quiescent hot gas is accreted onto the central super-massive black hole; this accretion comes from the surrounding hot halo and is typically well below the Eddington rate. This model captures the mean behaviour of the black hole over timescales much longer than the duty cycle. We will employ two di ff erent semi-analytic models, one that implements only the quasar mode and one that implements both. The model of Menci et al. (2004 M04 in the following) falls in the first category and is particularly tailored to follow the evolution of AGN. In this model the accretion of gas in the central black holes, is triggered by galaxy encounters, not necessarily leading to bound mergers, in common host structures such as clusters and especially groups; these events destabilize part of the galactic cold gas and hence feed the central BH, following the physical modeling developed by Cavaliere & Vittorini (2000). The amount of cold gas available, the interaction rates, and the properties of the host galaxies are derived as in Menci et al. (2002). As a result, at high redshift the proto-galaxies grow rapidly by hierarchical merging; meanwhile fresh gas is imported and the BHs are fueled at their full Eddington rates. At lower redshift, the dominant dynamical events are galaxy encounters in hierarchically growing groups; at this point refueling diminishes as the residual gas is exhausted, and the destabilizing encounters also decrease. This model successfully reproduces the observed properties of both galaxies and AGN across a wide redshift range (e.g. Fontana et al. 2006; Menci et al. 2008b; Calura & Menci 2009; Lamastra et al. 2010). We further compare our results to the output of a SAM model implemented in the Milleniumn simulations (MS in the following) as in Guo et al. (2011). For black hole growth and AGN feedback they follow Croton et al. (2006), who implement both quasar mode and radio mode. In the 'quasars mode' black hole accretion is allowed during both major and minor mergers, but the e ffi ciency in the latter is lower because the mass accreted during a merger depends, among the other factors, on the ratio msat / mcentral (eq. 8 in Croton et al. 2006). In the 'radio mode', the growth of the super-massive black hole is the result of continuous hot gas accretion once a static hot halo has formed around the host galaxy of the black hole. This accretion is assumed to be continual and quiescent (see Croton et al. 2006 for more details). From the two SAMs, we select all galaxies residing in massive halos (on the scale of groups and clusters), with rest-frame magnitudes brighter than MR = -20 as in our observations. As for the real clusters and groups, we divide the simulated structures into those with a velocity dispersion between 400 and 700 kms -1 (i.e., groups and small clusters) and those with sigma above 700 kms -1 (massive clusters). From the simulations we actually know the total mass of the corresponding dark matter halos, which is related to the velocity dispersion via vc 3 = ( M / f ( z )) ∗ ( h / 0 . 235), where f ( z ) = H ( z ) / H 0, with halo mass in unity of 10 12 M /circledot and v is in unity of 100 kms -1 . The SAMs provide the total bolometric luminosity of each AGN; to convert this into observed X-ray luminosity in the 2-10keV rest-frame band, we follow the relations found by Marconi et. al. (2004) applied to our luminosity limits ( LH > 10 42 and LH > 10 43 ) For all galaxies, the model computes the total stellar mass (M*): at each redshift we determine the mass corresponding to MR = -20 from the relation between stellar mass and MR derived from the GOODS-South catalog (Grazian et al. 2006). We then use this mass to select mock galaxies brighter than MR = -20. Since the mass-magnitude relation has a scatter we make two di ff erent predictions. In one case we use the best fit value of the mass-magnitude relation to determine MR and then select galaxies (filled curve in Figure 4, nominal prediction). In the second case we use the maximum stellar mass M* corresponding to MR = -20 as a selection threshold. In this second way we select more massive galaxies and therefore the probability to find an AGN in the galaxies is higher. This is the upper envelope of our prediction (dashed curve in Figure 4, maximal prediction).The MS model gives directly the R magnitude of the mock galaxies so for this model we have only the nominal prediction. The resulting fractions of AGN with LH > 10 42 in groups and clusters hosted by galaxies brighter than MR = -20 found in the two models are presented in Figure 4, along with the observed data. The MS model tends to over-predict the fraction of AGN, especially for massive structures and at high redshift, while is it more in agreement with the data for groups. It also predicts a very marked increase of the AGN fraction with redshift, more pronounced than what is observed in the data. This steep increment is linked to the marked rise of major mergers (the only mergers considered for the quasar mode) towards high redshift. This model predicts a modest dependence of the AGN fraction on the velocity dispersion of the systems: for example at z ∼ 0 . 6 simulated groups contain only ∼ 20% more AGN than the more massive structures, while the observed di ff erence is much larger. The M04 model predicts a milder increase of AGN fraction with redshift, both for massive and smaller systems: this is due to the fact that in this model minor mergers and close encounters are also very important and their frequency does not depend so strongly on redshift, since the small Dark Matter halos continue to merge frequently until low redshift. The M04 model tend to under-predict slightly the observed AGN fractions at all redshifts: the observed o ff set between the data and the predictions is approximately a factor of 3, both for clusters and for groups. This can be explained by the known problems of semi-analytic model that tend to overestimate the number of galaxies at the faint end of the luminosity function. In particular for the M04 model this discrepancy at the faint end was extensively discussed in Salimbeni et al. (2008) and is clearly observed at the magnitude limit that we are using in this study ( MR = -20). The M04 model predicts a marked di ff erence between groups and clusters: for example at z ∼ 0.6 groups / small systems contain a factor of 5 more AGN compared to massive clusters, in agreement with what is observed on the data. Indeed, in this model the fraction of gas accreted during mergers and fly-by is inversely proportional to the velocity dispersion of the structures, therefore for clusters it is lower than in groups. This e ff ect is in addition to the increased merger rate between galaxies in groups, as compared to clusters, due to the lower encounter velocities in these small systems. In this sense, the agreement between the observational and predicted trends with velocity dispersion and with redshift validates the implemented mode of AGN growth in the M04 models. We further check if the models can reproduce the colors of the AGN in dense environments. To this aim, we find that the MS model has problem in reproducing the colors of the general galaxy population in clusters and groups. Guo et al. (2011) already remarked clear di ff erences between SDSS observations and model predictions in the slope of the red sequence and in the number of fainter red-sequence galaxies. The same was also noticed by de la Torre et al. (2011), who found that the De Lucia & Blazoit (2007) implementation on the Millenium Simulation does not reproduce quantitatively the observed intrinsic colour distributions of galaxies, with much fewer very blue galaxies and many more green valley galaxies in the model than in the observations, at redshifts 0 . 2 < z < 2 . 1. In addition, the model predicts an excess of red galaxies at low redshift. We therefore decided to employ only the M04 model for this comparison: this model does a good job in reproducing the color bimodality of galaxies up to high redshift, as shown in the upper panel of Figure 7 where we plot the predicted color magnitude relation for all mock galaxies. The galaxies are located in a clear red-sequence and blue cloud and are well matched to the colors of the observed galaxies (Figure 6). In the lower panel we plot the predicted colors of active galaxies which are selected as objects with a total rest-frame magnitude brighter than MR = -20, hosting an AGN with luminosity exceeding 10 42 ergs -1 , and included in halos of mass comparable to our small clusters and groups. Here we also plot the colors of our observed AGN. The U-B color range of the predicted AGN is well matched to the observations, most AGN having 0 . 5 < U -B < 1, like the observed ones. The model predicts the presence of a small fraction of extremely red AGN, that reside on top of the red sequence, i.e., that are even redder than the typical red-sequence galaxies. We do not observe these extremely red AGN but this might be just due to lack of statistics. The model also predicts AGN in galaxies brighter than MUV = -22 that we do not observe. Again this could be due to lack of statistics, since these extremely luminous galaxies are quite rare in our observed sample (see Figure 6). Alternatively it might be that mock galaxies hosting AGN of L ∼ 10 42 ergs -1 become too bright. Indeed in the M04 model each encounter / merger that triggers AGN activity also triggers star-formation, thus enhancing the UV luminosity of the host galaxy; the relative proportion of gas that feeds AGN and star formation, which is now fixed to approximately 1 to 4 (see Menci et al. 2006) might need to be revised.",
"pages": [
8,
9,
10
]
},
{
"title": "6. Summary and conclusions",
"content": "We have explored the AGN content in small clusters and groups in the two GOODS fields, exploiting the ultra-deep 2 and 4 Msec Chandra data and the deep multiwavelength observations available. We have used our previously tested cluster-finding algorithm to identify structures, exploiting the available spectroscopic redshifts as well as accurate photometric redshifts. We identified 9 structures in GOODS-south (already presented in Salimbeni et al. 2009) and 8 new structures in the GOODS-north field. To have a reliable estimate of AGN fraction, we restrict our study to structures where at least 2 / 3 of the galaxies brighter than MR = -20 have a spectroscopic redshift. We identified those clusters members that coincide with X-ray sources in the 4 and 2 Msec source catalogs (Luo et al. 2011 and Alexander et al. 2003 respectively), and with a simple classification based on total restframe hard luminosity and hardness ratio we determined if the X-ray emission originates from AGN activity or it is related to the galaxies'star-formation activity. We then computed the frequency of AGN in each group: we found that at z ∼ 0 . 6 -1 . 0 the average fraction of AGN with LogLH > 42 in galaxies with MR < -20 is 6 . 3 ± 1 . 3%, i.e. much higher than the value found in lower redshift groups, which is just 1%. This fraction is also more than double the fraction found in more massive clusters at a similar redshift. We have then explored the AGN spatial distribution within the structures and found that they tend to populate the outer regions rather than the central cluster galaxies. The colors of AGN in structures are confined to the green valley and red-sequence, avoiding the blue-cloud, whereas in the field AGNare also present in the blue cloud (e.g. Nandra et al. 2007). If the AGN activity is associated with the process that quenches star formation in massive galaxies (e.g. di Matteo et al. 2005), causing the migration of blue cloud galaxies to the red sequence (Croton et al. 2006; Hopkins et al. 2006), we conclude that these phenomena are more rapid in dense environment compared to what happens in the field. We finally compared our results to the predictions of two sets of semi analytic models: the M04 model (Menci et al. 2006) and one implemented on the Millenium Simulation by Guo et al. (2011). The MS model predicts a dependence of AGN content with redshift (both for clusters and groups) that is much steeper than what observed and a very modest di ff erence between massive and less massive structures. The MS04 does a good job in predicting the redshift dependence of the AGN fractions, and the marked di ff erence that is observed between groups and massive clusters. This agreement validates the implemented mode of AGN growth in the model and in particular stresses the importance of galaxy encounters, not necessarily leading to mergers, as an e ffi cient AGN triggering mechanism. The M04 model also reproduces accurately the range of observed AGN colors and their position in the color-magnitude diagram, although it tends to find AGN in galaxies that are on average slightly more luminous than the observed ones. It also predicts the presence of a small fraction of extremely red AGN, residing on top of the red sequence. We do not observe these extremely red AGN but this might be due to lack of statistics: we therefore plan to expand our analysis to other fields, with similar multiwavelength data and deep X-ray observations to study the AGNcontent. In particular we are currently working on the UDS field, thus more than doubling the area (and the statistics) presented of this paper. In this way we will be able to test, amongst other things, if the predicted extremely red AGN exist, and we will be able to place more stringent constrains on the relative timing of AGN activity and the quenching of star formation at high redshift.",
"pages": [
10,
11
]
},
{
"title": "References",
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"pages": [
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}
]
2013A&A...554A..40C
https://arxiv.org/pdf/1304.5470.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_82><loc_91><loc_87></location>Impact of internal gravity waves on the rotation profile inside pre-main sequence low-mass stars</section_header_level_1>
<text><location><page_1><loc_25><loc_80><loc_77><loc_81></location>C. Charbonnel 1 , 2 , T.Decressin 1 , L.Amard 1 , 3 , A.Palacios 3 , and S.Talon 4</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_77><loc_71><loc_78></location>1 Geneva Observatory, University of Geneva, Chemin des Maillettes 51, 1290 Versoix, Switzerland</list_item>
<list_item><location><page_1><loc_11><loc_76><loc_67><loc_77></location>2 IRAP, CNRS UMR 5277, Université de Toulouse, 14, Av. E.Belin, 31400 Toulouse, France</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_73><loc_76></location>3 LUPM, Université Montpellier II, CNRS, UMR 5299, Place E. Bataillon, 34095, Montpellier, France</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_79><loc_74></location>4 Calcul Québec, Université de Montréal (DGTIC), C.P. 6128, succ. Centre-ville, Montréal (Québec) H3C 3J7</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_71><loc_38><loc_72></location>Accepted for publication in A&A (Section 7)</text>
<section_header_level_1><location><page_1><loc_47><loc_69><loc_55><loc_70></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_65><loc_91><loc_67></location>Aims. We study the impact of internal gravity waves (IGW), meridional circulation, shear turbulence, and stellar contraction on the internal rotation profile and surface velocity evolution of solar metallicity low-mass pre-main sequence stars.</text>
<text><location><page_1><loc_11><loc_59><loc_91><loc_65></location>Methods. We compute a grid of rotating stellar evolution models with masses between 0.6 and 2.0 M /circledot taking these processes into account for the transport of angular momentum, as soon as the radiative core appears and assuming no more disk-locking from that moment on. IGW generation along the PMS is computed taking Reynolds-stress and buoyancy into account in the bulk of the stellar convective envelope and convective core (when present). Redistribution of angular momentum within the radiative layers accounts for damping of prograde and retrograde IGW by thermal di ff usivity and viscosity in corotation resonance.</text>
<text><location><page_1><loc_11><loc_56><loc_91><loc_59></location>Results. Over the whole mass range considered, IGW are found to be e ffi ciently generated by the convective envelope and to slow down the stellar core early on the PMS. In stars more massive than ∼ 1.6 M /circledot , IGW produced by the convective core also contribute to angular momentum redistribution close to the ZAMS.</text>
<text><location><page_1><loc_11><loc_55><loc_79><loc_56></location>Conclusions. Overall, IGW are found to significantly change the internal rotation profile of PMS low-mass stars.</text>
<text><location><page_1><loc_11><loc_53><loc_70><loc_54></location>Key words. stars: evolution - stars: rotation - stars: interior - hydrodynamics - waves - turbulence</text>
<section_header_level_1><location><page_1><loc_7><loc_49><loc_19><loc_50></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_22><loc_50><loc_47></location>The evolution of the surface rotation of low-mass stars along the pre-main sequence (hereafter PMS) follows a specific path as shown by the data, both rotation periods and v sin i measurements, collected in young stellar clusters (e.g. Irwin & Bouvier 2009, and references therein for a review). The rotational properties of young stars appear to result from an intricate interplay between several physical processes that a ff ect the angular momentumgains, losses, and redistribution as the stars evolve along the PMS towards the zero age main sequence (hereafter ZAMS). These mechanisms can be roughly divided into two classes. The first ones result from the connection of the stars to their environment (magnetic and dynamic coupling to a circumstellar disk, accretion, jets, stellar and disk winds, etc.), and are particularly crucial during the T-Tauri phase, when star-disk interaction is observed and expected to be strong (see, for instance, Shu et al. 1994; Matt & Pudritz 2005; Zanni & Ferreira 2012). The broad variety of possible star-environment configurations may, in particular, explain part of the large dispersion in rotation rates of solar-type stars observed along the PMS and at the arrival on the ZAMS (e.g., Stau ff er et al. 1985; Irwin & Bouvier 2009).</text>
<text><location><page_1><loc_7><loc_14><loc_50><loc_21></location>The second class is related to stellar secular evolution and consists of the (magneto-) hydrodynamical transport mechanisms that contribute to redistributing angular momentum inside the stars themselves. In the present paper we focus on exploring these internal mechanisms once the disk has dissipated and the accretion process is over, which occurs after 3-10</text>
<text><location><page_1><loc_7><loc_10><loc_30><loc_11></location>email: [email protected]</text>
<text><location><page_1><loc_52><loc_30><loc_95><loc_50></location>Myr (e.g., Haisch et al. 2001; Hartmann 2005; Hernández et al. 2008), i.e., roughly at the time when a radiative core appears in the contracting PMS stars. Our aim is to evaluate, in particular and for the first time, the interplay between internal gravity waves (hereafter IGW), meridional circulation, turbulent shear, and stellar contraction during the PMS, considering that IGW are one of the best candidate mechanisms to explain the flat angular velocity profile inside the Sun as revealed by helioseismology (Charbonnel & Talon 2005). This work is also motivated by the results of Talon & Charbonnel (2008, hereafter TC08), who showed that IGW are e ffi ciently excited inside intermediatemass PMS stars and suggested that waves should e ffi ciently transport angular momentum during the PMS evolution, which should a ff ect the angular velocity profile at this phase and at the arrival on the ZAMS.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_26></location>In §2 we introduce the formalism for IGW excitation and for the transport of angular momentum through the various mechanisms considered. We describe in §3 the basic assumptions for the present grid of PMS models for low-mass (0.6 to 2 M /circledot ), solar-metallicity stars. In §4 we examine IGW generation by the convective envelope and the convective core (when present) along the PMS evolution for the whole mass range covered by the grid. In § 5 we describe the impact of the various interacting transport mechanisms on the evolution of the internal rotation profile for the various stellar masses, and in § 6 we briefly discuss their influence on the surface rotation velocity and lithium abundance, as well as on global stellar properties. Conclusions are presented in § 7.</text>
<section_header_level_1><location><page_2><loc_7><loc_92><loc_18><loc_93></location>2. Formalism</section_header_level_1>
<text><location><page_2><loc_7><loc_66><loc_50><loc_91></location>We follow Talon & Charbonnel (2005, hereafter TC05) for the treatment of both the excitation of IGW and the transport of angular momentum and chemicals by waves, meridional circulation, and shear turbulence in hydrodynamical stellar models. We, however, underline three main improvements over TC05 paper. First, we consider IGW generated both by the external and central convective regions (when present), while only those excited by the convective envelope were considered in our previous work. Second, the important variations in the stellar structure and of the IGW properties along the pre-main sequence (see § 4 and TC08) require that we then compute the wave spectra at each evolution time step, while the main sequence computation presented in TC05 was based on the wave spectrum of the stellar model on the ZAMS. Finally, we account here for both prograde and retrograde waves in the whole radiative interior, while only the latter ones were considered previously. We recall below the formalism (i.e., relevant equations and assumptions) that is included in the evolution code STAREVOL (see TC05, TC08, and Mathis et al. 2013).</text>
<section_header_level_1><location><page_2><loc_7><loc_63><loc_22><loc_64></location>2.1. IGWgeneration</section_header_level_1>
<text><location><page_2><loc_7><loc_45><loc_50><loc_62></location>In this exploratory work we apply the Goldreich et al. (1994) formalism as adapted by Kumar & Quataert (1997) to calculate the spectrum of IGW excited by Reynolds stress and buoyancy in the bulk of convective regions (see e.g. Zahn et al. 1997). We do not consider the possible e ff ects of IGWs generated by convective overshooting plumes, since no analytical prescription is available to describe this excitation mechanism (see details and discussion in TC05). However as we see in § 2.3.1, we multiply the IGW flux by a factor 2 in the transport equation in order to account for the recent results by Lecoanet & Quataert (2012). We treat the waves by assuming that they are pure gravity waves (i.e., not modified by the Coriolis acceleration) that only feel the entrainment by di ff erential rotation.</text>
<text><location><page_2><loc_10><loc_44><loc_39><loc_45></location>The kinetic energy flux per unit frequency is</text>
<formula><location><page_2><loc_7><loc_35><loc_50><loc_43></location>F E ( /lscript, ω ) = ω 2 4 π ∫ dr ρ 2 r 2 ( ∂ξ r ∂ r ) 2 + /lscript ( /lscript + 1) ( ∂ξ h ∂ r ) 2 × exp [ -h 2 ω /lscript ( /lscript + 1) / 2 r 2 ] v 3 c L 4 1 + ( ωτ L ) 15 / 2 (1)</formula>
<text><location><page_2><loc_7><loc_23><loc_50><loc_35></location>with ξ r and [ /lscript ( /lscript + 1)] 1 / 2 ξ h the radial and horizontal displacement wave functions normalized to unit energy flux at the edge of the considered convection zone, vc the convective velocity, L = α MLT HP the radial size of an energy bearing turbulent eddy, τ L ≈ L / vc the characteristic convective time, HP the pressure scale height P /ρ g , and h ω the radial size of the largest eddy at depth r with characteristic frequency of ω or higher ( h ω = L min { 1 , (2 ωτ L ) -3 / 2 } ). The radial and horizontal wave numbers (respectively kr and kh ) are related by</text>
<formula><location><page_2><loc_16><loc_18><loc_50><loc_22></location>k 2 r = ( N 2 ω 2 -1 ) k 2 h = ( N 2 ω 2 -1 ) /lscript ( /lscript + 1) r 2 (2)</formula>
<text><location><page_2><loc_7><loc_16><loc_36><loc_17></location>where N 2 is the Brunt-Väisälä frequency 1 .</text>
<text><location><page_2><loc_52><loc_87><loc_95><loc_93></location>At the considered convective edge (located at radius rcz ), the mean flux of angular momentum carried by a monochromatic wave of spherical order /lscript and local (i.e., emission) frequency ω ( m being the azimutal order), i.e., the momentum flux per unit frequency, is related to the kinetic energy flux by</text>
<formula><location><page_2><loc_64><loc_82><loc_95><loc_85></location>F J , rcz ( m , /lscript, ω ) = 2 m ω F E ( /lscript, ω ) (3)</formula>
<text><location><page_2><loc_52><loc_77><loc_95><loc_81></location>(Goldreich & Nicholson 1989; Zahn et al. 1997). The so-called angular momentum luminosity at the considered convective edge (envelope or core) is obtained after horizontal integration</text>
<formula><location><page_2><loc_65><loc_74><loc_95><loc_76></location>L J /lscript, m ( r cz) = 4 π r 2 cz F J , rcz . (4)</formula>
<section_header_level_1><location><page_2><loc_52><loc_71><loc_65><loc_72></location>2.2. IGWdamping</section_header_level_1>
<text><location><page_2><loc_52><loc_57><loc_95><loc_70></location>Deposition of angular momentum (positive or negative) within the radiative layers occurs at the depth where individual monochromatic waves are eventually damped by thermal di ff usivity and viscosity in corotation resonance (Goldreich & Nicholson 1989; Schatzman 1993; Zahn et al. 1997). In the present study the local momentum luminosity at a given radius r within the radiative region accounts for prograde and retrograde waves (i.e., with respectively positive and negative m values) generated by both the convective envelope and the convective core (if present), i.e.,</text>
<formula><location><page_2><loc_65><loc_54><loc_95><loc_55></location>L J ( r ) = L J ,env + L J , core , (5)</formula>
<text><location><page_2><loc_52><loc_51><loc_75><loc_52></location>where each component is given by</text>
<formula><location><page_2><loc_63><loc_46><loc_95><loc_50></location>∑ σ,/lscript, m L J /lscript, m ( r cz) exp [ -τ ( r , σ, /lscript )] , (6)</formula>
<text><location><page_2><loc_52><loc_43><loc_95><loc_45></location>where 'cz' refers to the interface between the radiative region and the corresponding convection zone (i.e., envelope or core).</text>
<text><location><page_2><loc_54><loc_41><loc_70><loc_42></location>The local damping rate</text>
<formula><location><page_2><loc_53><loc_35><loc_95><loc_40></location>τ ( r , σ, /lscript ) = [ /lscript ( /lscript + 1)] 3 2 ∫ rcz r ( KT + ν v ) NNT 2 σ 4 ( N 2 N 2 -σ 2 ) 1 2 d r r 3 (7)</formula>
<text><location><page_2><loc_52><loc_29><loc_95><loc_35></location>takes the mean molecular weight stratification into account (Goldreich & Nicholson 1989; Schatzman 1993; Zahn et al. 1997), as well as the thermal and the (vertical) turbulent viscosity ( KT and ν v respectively). Here, σ is the local Doppler-shifted frequency</text>
<formula><location><page_2><loc_64><loc_27><loc_95><loc_28></location>σ ( r ) = ω -m [ Ω ( r ) -Ω cz] (8)</formula>
<text><location><page_2><loc_52><loc_22><loc_95><loc_25></location>with ω the wave frequency in the reference frame of the corresponding emitting convection zone that rotates with the angular velocity Ω cz.</text>
<text><location><page_2><loc_52><loc_10><loc_95><loc_21></location>As can be seen from these expressions, angular momentum redistribution by IGW within the radiative region is dominated by low-frequency ( σ /lessmuch N ), low-degree waves; indeed, those penetrate deeper, and their prograde and retrograde components experience strong di ff erential damping, as required to produce a net momentum deposition. In contrast, high-degree waves are damped closer to the convection zone (since damping ∝ [ /lscript ( /lscript + 1)] 3 2 ), and high-frequency waves experience less di ff erential damping.</text>
<section_header_level_1><location><page_3><loc_7><loc_91><loc_44><loc_93></location>2.3. GlobaltransportofangularmomentumbyIGW, meridionalcirculation,andshearturbulence</section_header_level_1>
<section_header_level_1><location><page_3><loc_7><loc_89><loc_25><loc_90></location>2.3.1. General equations</section_header_level_1>
<text><location><page_3><loc_7><loc_81><loc_50><loc_87></location>We assume solid-body rotation in the convective regions. In the stellar radiative regions, the evolution of angular momentum through advection by meridional circulation, di ff usion by shear turbulence, and deposit or extraction by IGW follows the general expression below (e.g., Talon & Zahn 1998):</text>
<formula><location><page_3><loc_7><loc_74><loc_50><loc_80></location>ρ d d t [ r 2 Ω ] = 1 5 r 2 ∂ ∂ r [ ρ r 4 Ω U ] + 1 r 2 ∂ ∂ r [ ρν vr 4 ∂ Ω ∂ r ] -2 3 8 π 1 r 2 ∂ ∂ r L J ( r ) , (9)</formula>
<text><location><page_3><loc_7><loc_63><loc_50><loc_73></location>where U is the radial meridional circulation velocity, ν v the turbulent viscosity due to di ff erential rotation, and ρ the density. We have added a factor 2 in the last term to account for the study by Lecoanet & Quataert (2012), who predict the IGW flux due to turbulent convection to be a few to five times larger than in previous estimates by, e.g., Goldreich & Kumar (1990) and Goldreich et al. (1994). However as we see in § 5.1.2, our conclusions are not sensitive to this multiplication factor.</text>
<text><location><page_3><loc_7><loc_58><loc_50><loc_63></location>Following Decressin et al. (2009) and Mathis et al. (2013) we integrate Eq. 9 over an isobar enclosing the mass m ( r ) to obtain the expression of the total flux (loss or gain) of angular momentum carried by the considered transport processes:</text>
<formula><location><page_3><loc_7><loc_53><loc_49><loc_57></location>Γ ( m ) = 1 4 π d d t [∫ m ( r ) 0 r ' 2 Ω d m ' ] = -F MC ( r ) -F S ( r ) + F IGW ( r )</formula>
<text><location><page_3><loc_7><loc_50><loc_50><loc_52></location>where the fluxes driven by meridional circulation, vertical shearinduced turbulence, and IGWs are, respectively,</text>
<formula><location><page_3><loc_21><loc_46><loc_50><loc_49></location>F MC ( r ) = -1 5 ρ r 4 Ω U 2 (10)</formula>
<formula><location><page_3><loc_22><loc_43><loc_50><loc_45></location>F S ( r ) = -ρ r 4 ν v ∂ r Ω (11)</formula>
<formula><location><page_3><loc_22><loc_40><loc_50><loc_43></location>F IGW ( r ) = 3 8 π L J ( r ) . (12)</formula>
<section_header_level_1><location><page_3><loc_7><loc_37><loc_27><loc_38></location>2.3.2. Meridional circulation</section_header_level_1>
<text><location><page_3><loc_7><loc_30><loc_50><loc_36></location>As can be seen in Eq. 9 the transport of angular momentum through meridional circulation is treated as an advective process. As in our previous studies we apply the formalism developed by Zahn (1992), Maeder & Zahn (1998) and Mathis & Zahn (2004, see also Decressin et al. 2009).</text>
<section_header_level_1><location><page_3><loc_7><loc_26><loc_30><loc_27></location>2.3.3. Shear-induced turbulence</section_header_level_1>
<text><location><page_3><loc_7><loc_20><loc_50><loc_25></location>Shear-induced turbulence is assumed to be highly anisotropic. Following TC05 we assume that the turbulent di ff usion coe ffi -cient equals turbulent viscosity and use the corresponding expression given by Talon & Zahn (1997), i.e.,</text>
<formula><location><page_3><loc_16><loc_16><loc_50><loc_19></location>Dv = ν v = 8 5 Ri crit( r d Ω / d r ) 2 N 2 T / ( K + Dh ) + N 2 µ / Dh (13)</formula>
<text><location><page_3><loc_7><loc_10><loc_50><loc_15></location>that considers the weakening e ff ect of thermal di ff usivity ( KT ) on the thermal stratification and of horizontal turbulence ( Dh , see below) on both the thermal and mean molecular weight stratifications.</text>
<text><location><page_3><loc_52><loc_91><loc_95><loc_93></location>For the treatment of horizontal turbulent viscosity, we follow Zahn (1992), again as in TC05:</text>
<formula><location><page_3><loc_52><loc_83><loc_95><loc_89></location>Dh = ν h = r Ch √ ∣ ∣ ∣ ∣ ∣ ∣ 1 3 ρ r d( ρ r 2 U ) d r -U 2 d ln r 2 Ω d ln r ∣ ∣ ∣ ∣ ∣ ∣ 2 + U 2 (14) with Ch = 1.</formula>
<text><location><page_3><loc_52><loc_81><loc_95><loc_83></location>The influence of the prescriptions assumed for Dv and Dh will be investigated in a future paper.</text>
<section_header_level_1><location><page_3><loc_52><loc_77><loc_71><loc_78></location>2.4. Transportofchemicals</section_header_level_1>
<text><location><page_3><loc_52><loc_71><loc_95><loc_76></location>Wetreat the transport of chemical species in the radiative regions as a di ff usive process through the combined action of meridional circulation and shear-induced turbulence (Chaboyer & Zahn 1992). The e ff ective di ff usion coe ffi cient is written</text>
<formula><location><page_3><loc_68><loc_67><loc_95><loc_70></location>D e ff = | rU ( r ) | 2 30 Dh (15)</formula>
<text><location><page_3><loc_52><loc_63><loc_95><loc_66></location>where Dh is the horizontal component of the turbulent di ff usivity (see Eq. 14).</text>
<text><location><page_3><loc_52><loc_54><loc_95><loc_63></location>In the present study we neglect atomic di ff usion, whose effects require much longer timescales to develop compared to the very short duration of the pre-main sequence phase. We also neglect possible wave-induced turbulence. Therefore the expression for the transport of chemicals (here, the mass fraction X of the element i ) in the stellar radiative region writes as (see e.g. Meynet & Maeder 2000):</text>
<formula><location><page_3><loc_52><loc_49><loc_95><loc_53></location>( d Xi d t ) Mr = ∂ ∂ Mr [ (4 π r 2 ρ ) 2 ( DV + D e ff ) ∂ Xi ∂ Mr ] + ( d Xi d t ) nucl , (16)</formula>
<text><location><page_3><loc_52><loc_46><loc_95><loc_49></location>where dMr = 4 πρ r 2 dr , and the last term accounts for nuclear destruction or production of the considered element.</text>
<section_header_level_1><location><page_3><loc_52><loc_42><loc_66><loc_44></location>3. Stellar models</section_header_level_1>
<section_header_level_1><location><page_3><loc_52><loc_40><loc_81><loc_41></location>3.1. Inputphysicsandbasicassumptions</section_header_level_1>
<text><location><page_3><loc_52><loc_25><loc_95><loc_39></location>We focus on the pre-main sequence evolution of solarmetallicity stars in the mass range between 0.6 and 2.0 M /circledot . We adopt the solar composition of Asplund et al. (2009). Opacity tables are updated accordingly both at high and low temperature respectively from OPAL and Wichita websites 2 (see e.g. Iglesias & Rogers 1996; Ferguson et al. 2005). The mixing length parameter α MLT = 1 . 63 is calibrated so that our standard (i.e., non rotating) 1 M /circledot , Z /circledot model fits the solar radius, e ff ective temperature, and luminosity at the age of the sun. Convection zone bounderies are defined by the Schwarzschild criterion, and we do not account for convective overshoot.</text>
<text><location><page_3><loc_52><loc_13><loc_95><loc_25></location>Computations are performed with the stellar evolution code STAREVOL(see e.g. TC05, Lagarde et al. 2012). Initial models are totally convective polytropic stars, with central temperature lower than 10 6 K (i.e., deuterium burning has not yet occurred). We follow the PMS evolution along the Hayashi track up to the arrival on the ZAMS that we define as the point where the ratio between central and surface hydrogen abundance reaches 0.998. The stellar mass is assumed to be constant during that phase (i.e., no accretion nor mass loss). For each stellar mass we compute</text>
<figure>
<location><page_4><loc_6><loc_32><loc_95><loc_93></location>
<caption>Fig. 1. PMStracks in the Hertzsprung-Russel diagram for solar metallicity stars with initial masses between 0.6 and 2.0 M /circledot (classical models are shown here) and properties of the external convective layers. Colors indicate the radial extent of the convective envelope (top left panel), the temperature at its bottom (top right panel), the maximal convective flux (bottom left panel), and the thermal di ff usivity below the envelope (bottom right panel). Dashed lines connect points with similar values for these quantities, and the colored axes are in cgs units. The dotted parts of the tracks correspond to the phase when the stars are still fully convective</caption>
</figure>
<text><location><page_4><loc_7><loc_15><loc_50><loc_22></location>classical models (i.e., without any transport of angular momentum nor of chemicals) as well as rotating models with and without IGW. We neglect the hydrostatic e ff ects of the centrifugal force in all our rotating models but two; we discuss the impact of this simplification in § 5. The evolution tracks of the classical models in the Hertzsprung-Russel diagram are shown in Fig.1.</text>
<section_header_level_1><location><page_4><loc_52><loc_21><loc_79><loc_22></location>3.2. Initialinternalandsurfacerotation</section_header_level_1>
<text><location><page_4><loc_52><loc_10><loc_95><loc_20></location>We assume solid-body rotation while stars are fully convective (which corresponds to the dotted part of the tracks in Fig. 1) and we start computing the evolution of surface and internal rotation under the action of stellar contraction, meridional circulation, turbulence, and IGW when the radiative core appears, which happens at ages between ∼ 0.5 and 7.5 Myr for the mass range considered (see τ (core) in Table 1), and at ∼ 2.5 Myr for the 1.0 M /circledot model. At that time, most or even all low-mass</text>
<figure>
<location><page_5><loc_7><loc_31><loc_95><loc_93></location>
<caption>Fig. 2. Same as Fig. 1, but for the properties of the convective core. Here dotted parts on the tracks indicate the phase when the convective core is not yet present</caption>
</figure>
<text><location><page_5><loc_7><loc_10><loc_50><loc_25></location>stars have already lost their disks as shown by observations in very young clusters (e.g. Haisch et al. 2001; Hartmann 2005; Hernández et al. 2008). For all stellar masses, we choose the initial rotation velocity at the moment when the radiative zone appears to be equal to 5% of the critical velocity of the corresponding model (V crit = √ 2 3 GM R ; see Table 1). This corresponds approximately to the median of the observed distribution in young open clusters (see Fig. 13 and § 6 for discussion). We assume that there is no more coupling between the star and a potential disk beyond that evolution point. The surface of the star is then free to spin up, and we do not apply any magnetic braking. The</text>
<text><location><page_5><loc_52><loc_19><loc_95><loc_25></location>influence of the initial rotation velocity, of the disk lifetime that a ff ects the moment when a PMS star starts spinning up, as well as that of magnetic wind braking that may a ff ect the rotation rate at the arrival on the ZAMS, will be investigated in a forthcoming paper.</text>
<section_header_level_1><location><page_5><loc_52><loc_14><loc_93><loc_17></location>4. IGW generation along the PMS evolution for all grid models</section_header_level_1>
<text><location><page_5><loc_52><loc_10><loc_95><loc_13></location>The internal structure strongly changes as low-mass stars evolve along the PMS. This implies strong variations in the quantities that are relevant to IGW generation and momentum transport, as</text>
<table>
<location><page_6><loc_7><loc_53><loc_98><loc_84></location>
<caption>Table 1. Properties of the di ff erent models computed without rotation (std), with rotation but without IGW (rot), and with rotation taking into account IGW (igw); for the 1.0 M /circledot star a couple of models were computed taking into account the hydrostatic e ff ects of rotation (rot + hydro and igw + hydro). For each model we give: lifetime on the PMS, age at which the radiative core appears, initial rotation velocity, surface rotation rate and rotation period when the radiative core appears (taken at 5% of critical rotation velocity of the corresponding model), and surface rotation velocity, surface rotation rate, rotation period, surface lithium abundance, e ff ective temperature, and luminosity at the arrival on the ZAMS</caption>
</table>
<text><location><page_6><loc_7><loc_48><loc_50><loc_50></location>depicted in Figs. 1 for the properties of the convective envelope and 2 for the core. All quantities are given in cgs units.</text>
<text><location><page_6><loc_7><loc_39><loc_50><loc_47></location>Stars are first fully convective and a radiative core appears along the Hayashi track as they contract and heat (Fig. 1). The thickness of the convective envelope decreases, and the temperature at its base increases as the stars move towards higher e ff ective temperatures. Due to central CNO-burning ignition on the final approach towards the ZAMS a convective core develops (Fig.2).</text>
<text><location><page_6><loc_7><loc_14><loc_50><loc_38></location>One can follow the evolution along the tracks of the maximum convective flux ( Fc = Cp ρ vc ∆ T ) inside the external and central convective regions, which directly a ff ects the energy flux associated to a given frequency (see Eq.1). Wave excitation is stronger when the convective length scale ( /lscript c = 2 π rcz /α Hp ) is larger, but decreases when the turnover timescale ( τ c = α MLT Hp / vc ) becomes too large. The combination of these two factors induces large di ff erences in the overall e ffi ciency of wave generation as the internal structure evolves. This is well illustrated in Fig. 3 that shows the luminosity spectrum of IGW generated by the external convection zone in the 1 M /circledot model at four ages on the PMS. One sees clearly that wave-induced transport is dominated by low-frequency waves (i.e., < 3 . 5 µ Hz). High degree waves at low frequencies do not contribute much to the transport of angular momentum even though their excitation flux is important : indeed they are essentially damped near the convective envelope edge. In Fig. 4 colors along the tracks indicate the net momentum luminosity L J (see Eq. 4) of IGWs generated by the external and internal convective regions.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_13></location>In the case of external convection, the net momentum luminosity L J , sur f rapidly increases as the excitation of IGW strengthens up when stars evolve towards higher e ff ective tem-</text>
<text><location><page_6><loc_52><loc_35><loc_95><loc_50></location>perature, and reaches maximum values as high as 10 39 g.cm 2 s 2 around T e ff ∼ 6200 K. Stars with initial masses lower than 1.3 M /circledot never reach this e ff ective temperature and the corresponding L J , sur f remains always below this maximum and shows only a monotonic increase along the PMS. On the other hand in the more massive models the convective envelope keeps shrinking in size and L J , sur f decreases when T e f f increases above 6200 K. This behavior confirms TC08 findings for intermediate-mass PMS stars, and is very similar to the L J plateau we found for Pop I and Pop II main sequence stars (Talon & Charbonnel 2003, 2004), which share very similar convective properties with PMS stars in the same T e f f range.</text>
<text><location><page_6><loc_52><loc_10><loc_95><loc_28></location>IGW are also emitted from the convective core at the end of the PMS. The more massive the star, the more the convective core expands, and the stronger the corresponding wave excitation. We note however from Fig. 4 that wave excitation by the convective core (when present) is generally much less e ffi cient than that of the convective envelope. The ratio between L J , core and L J , sur f is shown in Fig. 5 as a function of T e f f for the various models. For stars with masses below 1.4 M /circledot , L J , core is always ∼ 5-6 order of magnitude lower than L J , sur f . These two quantities reach similar orders of magnitude only very close from the ZAMSfor stars more massive than 1.6 M /circledot . Therefore and as we shall see below, the impact of IGW on the internal rotation profile along the PMS will be dominated by the waves emitted by the convective envelope.</text>
<figure>
<location><page_7><loc_7><loc_32><loc_94><loc_93></location>
<caption>Fig. 3. Angular momentum luminosity at the base of the convective envelope of IGW generated by Reynolds-stress in the external convective layers as a function of emission frequency ω and degree /lscript . The color axis is in log and white areas correspond to log L J , sur f < 22. The plots are shown for the 1 M /circledot model at four ages along the PMS (5.8, 14, 35, and 55 Myr from top left to bottom right; the corresponding values of T e f f are 4277, 4357, 5560, and 5612 K).</caption>
</figure>
<section_header_level_1><location><page_7><loc_7><loc_22><loc_42><loc_23></location>5. Evolution of the internal rotation profile</section_header_level_1>
<section_header_level_1><location><page_7><loc_7><loc_19><loc_28><loc_20></location>5.1. Thecaseofthe1M /circledot star</section_header_level_1>
<text><location><page_7><loc_7><loc_10><loc_50><loc_17></location>Figure 6 depicts the evolution along the PMS of the rotation profile inside the 1 M /circledot star for two cases: when angular momentum transport is operated solely by meridional circulation and shear turbulence (bottom panels), and when angular momentum deposition by internal gravity waves is taken into account in addition to the hydrodynamic processes (top panels); the rotation profile</text>
<text><location><page_7><loc_52><loc_11><loc_95><loc_23></location>is shown at di ff erent ages as a function of both relative mass fraction and reduced radius (left and right panels respectively). The decomposition of the total flux of angular momentum into the various components driven by meridional circulation, shear turbulence, and IGW (when accounted for; see Eqs. 10, 11, and 12 respectively) is shown in Fig. 7 at three ages along the PMS. Meridional circulation currents are shown at the same ages in Fig.8; clockwise currents (matter flowing from the equator to the pole and resulting in deposition of angular momentum in-</text>
<figure>
<location><page_8><loc_7><loc_63><loc_95><loc_93></location>
<caption>Fig. 4. Same as Fig. 1, but with colors indicating the total momentum flux carried by IGW generated by the convective envelope (left) and the convective core (right). Dotted lines indicate the region where the stars are fully convective (left) or have no convective core (right) so that no IGW can be generated. In the left panel the vertical dashed lines connect models where the excitation has the same value: log ( Σ |F J ( ω, l , m ) | ) = 28, 30, 32, 34, 36, 38.</caption>
</figure>
<figure>
<location><page_8><loc_7><loc_26><loc_51><loc_55></location>
<caption>Fig. 5. Ratio of the total momentum luminosity carried by IGW generated by the convective core and the convective envelope for the PMS models of various masses</caption>
</figure>
<text><location><page_8><loc_7><loc_10><loc_50><loc_12></location>wards) and counterclockwise ones (carrying angular momentum outwards) are drawn in blue and red respectively.</text>
<section_header_level_1><location><page_8><loc_52><loc_52><loc_89><loc_54></location>5.1.1. Transport of angular momentum by meridional circulation and shear turbulence only</section_header_level_1>
<text><location><page_8><loc_52><loc_42><loc_95><loc_51></location>When only meridional circulation and shear turbulence are accounted for, di ff erential rotation rapidly develops inside the radiative region as the surface rotation velocity increases due to stellar contraction (Fig. 6, bottom plots). This behavior as well as the rotation profile at the arrival on the ZAMS are similar to the results of Eggenberger et al. (2012) for their rotating 1 M /circledot model computed with similar assumptions.</text>
<text><location><page_8><loc_52><loc_23><loc_95><loc_41></location>As can be seen in Fig.7 (right plots) for this model without IGW, the transport of angular momentum is dominated by meridional circulation all along the PMS, while the contribution of shear turbulence is negligible (the flux of angular momentum by turbulence FV is indeed ∼ 2 orders of magnitude lower than the flux driven by meridional circulation FMC ). The number of circulation loops evolves with time (Fig.8, bottom plots; see also Fig. 7): In the early stages (14.9 Myrs, left panel), the circulation consists of a single counterclockwise current that transports matter inward along the rotational axis and outward in the equatorial plane; later on (33.5 Myrs, middle panel) a clockwise loop appears in the central regions; finally an additional counterclockwise loop shows up when the convective core develops (55 Myrs, right panel).</text>
<section_header_level_1><location><page_8><loc_52><loc_20><loc_79><loc_21></location>5.1.2. Impact of internal gravity waves</section_header_level_1>
<text><location><page_8><loc_52><loc_10><loc_95><loc_19></location>The evolution of the internal rotation profile changes drastically when IGW are taken into account in conjunction with meridional circulation and shear turbulence, as can be seen in Fig. 6 (top plots). As already discussed in § 4, the emitted wave spectrum strongly evolves with the stellar structure along the PMS. IGW are first emitted by the receding convective envelope, and much later by the convective core when it appears during the final ap-</text>
<figure>
<location><page_9><loc_11><loc_39><loc_90><loc_94></location>
<caption>Fig. 6. Evolution along the PMS of the rotation profile in the 1 M /circledot models computed with and without IGW (top and bottom respectively) as a function of relative mass fraction and radius in solar units (left and right respectively). The curves are labeled according to age. On each plot the left and right scales give Ω in µ Hz and in solar units respectively</caption>
</figure>
<text><location><page_9><loc_7><loc_25><loc_50><loc_32></location>roach towards the zams. In the case of the 1 M /circledot model, IGW emitted by the convective core play actually no role since their luminosity is extremely low (see Fig. 5 and discussion in § 4). Therefore the following discussion refers only to those emitted by the envelope.</text>
<text><location><page_9><loc_7><loc_10><loc_50><loc_25></location>In order to understand wave-induced transport, we must also focus on the important quantities for wave damping in the radiative layers, namely the Brunt-Väisälä frequency N 2 and the thermal di ff usivity KT : For a given di ff erential rotation within the radiative layers, low-frequency (i.e., with ω < 3.5 µ Hz) and / or large degree waves that dominate the angular momentum transport are damped very e ffi ciently close to the convective edges when N 2 T is too small or when KT is too large (see Eq. 7). Fig.9 and 14 show the radial profiles of these two quantities in the radiative layers of the 1 M /circledot model at various ages (see also Fig. 1 and 2 that show the variations along the evolution track of the value of KT just below the convective envelope and above the</text>
<text><location><page_9><loc_52><loc_11><loc_95><loc_32></location>convective core). At all ages N 2 drops near the stellar center and the convective edges; in addition its value at a given depth increases with time along the PMS as a result of the stellar contraction that leads to an increase of gravity and a decrease of the pressure scale height as the star evolves. On the other hand the value of KT just below the convective envelope also increases as the star contracts and move towards higher e ff ective temperature; this implies stronger damping of all the waves (independently of their properties) closer to the convective envelope; note that KT at a given depth within the star increases only slightly during the evolution. Besides, the build up of di ff erential rotation with time within the star induces a change in the local Doppler shift frequency, which allows a di ff erent damping for waves with different frequencies and m through the term σ -4 ( N 2 -σ 2 ) -0 . 5 .</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_12></location>Let us see what these general considerations imply for the 1.0 M /circledot model. We start with initial solid body rotation and then</text>
<figure>
<location><page_10><loc_7><loc_66><loc_46><loc_93></location>
</figure>
<figure>
<location><page_10><loc_48><loc_65><loc_89><loc_93></location>
<caption>Fig. 7. Decomposition of the total flux of angular momentum (solid black) into meridional circulation (long-dashed magenta), shear turbulence (dotted blue), and IGW (short-dashed red) in the 1 M /circledot models computed with and without IGW (left and right panels respectively). Bold lines indicate negative values for the fluxes F MC ( r ), F S ( r ), or F IGW ( r ), when angular momentum is transported towards the central regions by the corresponding mechanism; in the case of meridional circulation and of shear turbulence this corresponds respectively to clockwise currents ( U 2 > 0) and to a positive Ω gradient. The profiles are shown at three di ff erent ages along the PMS. Shaded areas correspond to convective regions</caption>
</figure>
<text><location><page_10><loc_7><loc_29><loc_50><loc_54></location>follow the transport of angular momentum when the radiative layers appear. At that moment di ff erential rotation has not yet developed, and the local frequency σ of individual waves in the very thin radiative zone is similar to their emission frequency ω at the base of the convective envelope. However slight differential rotation soon builds up as a result of stellar contraction along the Hayashi track, which induces a Doppler shift between the emission and local IGW spectra. As a consequence, low-frequency low-degree waves, which undergo the largest differential damping between retrogade and prograde components, soon penetrate all the way to the central regions where they deposit their negative momentum and very e ffi ciently spin down the core whose amount of angular momentum is minute (see Fig. 6). This explains the strong positive gradient in the profile of Ω below ∼ 0 . 2 R /circledot , while the negative gradient of Ω in the external layers results from ongoing stellar contraction. As a consequence a peak builds up in the internal rotation profile with a core spinning at lower rate than the stellar surface all along the PMS.</text>
<text><location><page_10><loc_7><loc_10><loc_50><loc_28></location>We show in Fig.7 the total flux of angular momentum carried by the waves as a function of depth within the 1 M /circledot model, and compare it to the contribution of meridional circulation and shear turbulence at di ff erent evolution stages. We note first that the transport of angular momentum is generally dominated by the waves in the radiative layers where they can propagate, except in the early times when meridional circulation dominates in the most external regions below the convective envelope (upper panel at 14 Myr). Since downward propagating waves are totally damped as soon as the condition Ω ( r ) = ω/ m + Ω cz is fulfilled near the corotation radius, the total flux F IGW drops and remains negligible below the Ω peak. This can be clearly seen in the middle and lower panels in Fig.7 at 35 and 55 Myrs; at that time meridional circulation dominates in the regions below</text>
<text><location><page_10><loc_52><loc_45><loc_95><loc_54></location>∼ 0.15 and 0.2 M /circledot respectively, while IGW are dominant in the outer regions. Note that the total flux of angular momentum is dominated by IGW when they are accounted for and is larger by two orders of magnitude compared to the case without IGW. Overall, IGW do shape the circulation patterns, leading to the appearance of several loops in the whole radiative region as can be seen in Figs. 7 and 8.</text>
<text><location><page_10><loc_52><loc_30><loc_95><loc_44></location>Let us add a final remark. As explained in § 2.3.1, we have increased by a factor 2 the IGW luminosity in order to account for the results by Lecoanet & Quataert (2012) who predict the IGW flux due to turbulent convection to be a few to five times larger than in previous estimates by e.g. Goldreich & Kumar (1990) and Goldreich et al. (1994). In order to test the impact of this assumption, we have computed two additional models for the 1 M /circledot rotating star with multiplying factors of 1 and 5. We find that this has no impact on the conclusions, as can be seen in Fig. 10 where we plot the corresponding rotation profiles at the arrival on the ZAMS.</text>
<section_header_level_1><location><page_10><loc_52><loc_27><loc_73><loc_28></location>5.2. Impactofthestellarmass</section_header_level_1>
<text><location><page_10><loc_52><loc_14><loc_95><loc_25></location>For all the stars within the considered mass range, strong differential rotation with a fast rotating core is obtained under the combined action of stellar contraction and meridional circulation when IGW are not accounted for. Besides, in all cases IGW do break-up the stellar core, which results in a peak in Ω at r ∼ 0.250.3R ∗ as in the 1 M /circledot case. This can be seen in Fig. 10 where we show the rotation profiles at the arrival on the ZAMS for all our models (black and red lines correspond respectively to the models computed without or with IGW).</text>
<text><location><page_10><loc_52><loc_10><loc_95><loc_13></location>Let us note however that the impact of IGW is slightly different in stars more massive than ∼ 1 . 6 M /circledot . This is illustrated for the 2 M /circledot star in Fig. 11 where we decompose the total flux</text>
<figure>
<location><page_11><loc_10><loc_49><loc_91><loc_92></location>
<caption>Fig. 8. Meridional circulation currents in the 1 M /circledot models computed with and without IGW (top and bottom respectively) at three di ff erent evolution ages along the PMS (14, 35, and 55Myrs from left to right)). Blue and red lines indicate clockwise ( U 2 > 0) and counterclockwise ( U 2 < 0) circulation respectively. Hatched areas correspond to convective regions</caption>
</figure>
<text><location><page_11><loc_7><loc_14><loc_50><loc_41></location>of angular momentum within the model according to the various transport processes at three di ff erent ages, and in Fig. 12 where we follow the corresponding evolution of the radial profile of Ω . For this more massive star, IGW emitted by the convective envelope dominate during the first part of the PMS and manage to slow down the most central regions as in the 1 M /circledot case (top panel, Fig. 11). However those waves fade away when the convective envelope becomes too thin and are supplanted by those emitted by the convective core at the approach of the ZAMS (see Fig. 4). During that transition period (middle panel in Fig. 11), meridional circulation dominates the transport of angular momentum although shear turbulence also contributes more e ffi ciently near the most central regions (between 0.05 and 0.1 M /circledot ) and in the most external layers; as a result, the core slightly accelerates and eventually manages to rotate faster than the outer radiative layers, although not fast enough for the peak to be erased. Once the convective core has su ffi ciently developed (lower panel, Fig. 11), the IGW emitted in the central regions will start conveying angular momentum very e ffi ciently towards the core; at that time meridional circulation remains however the dominant process in the most external radiative layers.</text>
<section_header_level_1><location><page_11><loc_52><loc_38><loc_92><loc_41></location>6. Global stellar properties, surface rotation and lithium abundance</section_header_level_1>
<text><location><page_11><loc_52><loc_10><loc_95><loc_37></location>We summarize in Table 1 the main properties of our models computed under various assumptions. We also include the predictions for two additional models of 1 M /circledot that account for the hydrostatic e ff ects of rotation (i.e., the e ff ects of centrifugal acceleration on e ff ective gravity) and show in Fig. 15 all the corresponding evolution tracks for this star. We see that the rotating tracks without hydrostatic e ff ects are hardly modified compared to the standard case, the main shift to slightly lower e ff ective temperature and luminosity (that implies slightly longer PMS lifetime) being due to the e ff ects of the centrifugal force and not to rotation-induced mixing. This is in agreement with the predictions by Eggenberger et al. (2012) (see also Pinsonneault et al. 1989; Martin & Claret 1996; Mendes et al. 1999). However the hydrostatic e ff ects are modest and our general conclusions on the evolution of the internal rotation profile and on the impact of IGW are not a ff ected by this simplification. We can also note in Table 1 that the models computed with IGW have longer PMS lifetimes than the others. This simply results from the higher total di ff usion coe ffi cient for chemicals in the deep radiative layers close to the convective core when central H-burning sets in close to the ZAMS (see Fig. 14).</text>
<figure>
<location><page_12><loc_8><loc_66><loc_46><loc_92></location>
</figure>
<figure>
<location><page_12><loc_49><loc_66><loc_87><loc_92></location>
<caption>Fig. 9. Evolution of the Brunt-Väisälä frequency in the 1 M /circledot PMS star as a function of relative mass fraction and radius (left and right respectively). The colours correspond to the same ages as in Fig. 6. On the right plot the vertical lines indicate the total stellar radius at the corresponding ages</caption>
</figure>
<figure>
<location><page_12><loc_7><loc_31><loc_45><loc_59></location>
</figure>
<figure>
<location><page_12><loc_47><loc_31><loc_85><loc_59></location>
<caption>Fig. 12. Same as Fig.6 for the 2 M /circledot model computed with IGW</caption>
</figure>
<text><location><page_12><loc_7><loc_15><loc_50><loc_27></location>As shown in Fig. 13, the evolution of surface rotation for the models with IGW accounts well for the mean rotation rates collected by Gallet & Bouvier (2013) for PMS stars in young open clusters in the considered mass range. The rotation velocity at the arrival on the ZAMS is slightly higher (by a few %; see Table 1) in this case than in rotating models without IGW, due to the different e ffi ciency of the redistribution of angular momentum by the various transport mechanisms within the star as discussed previously. Again, the hydrostatic e ff ects are negligible.</text>
<text><location><page_12><loc_7><loc_10><loc_50><loc_15></location>The surface lithium abundance at the ZAMS is not significantly di ff erent in the rotating models without and with IGW, as can be seen from Table 1. Indeed this quantity mostly depends, on one hand, on the temperature at the base of the con-</text>
<text><location><page_12><loc_52><loc_11><loc_95><loc_27></location>vective envelope, which is una ff ected since the evolution tracks almost superpose, and on the other hand, on the di ff usion coefficient Def f (Eq. 15) in the external radiative layers shown in Fig. 14. Since the gradient of Ω in the outer part of the star is dominated by stellar contraction and is very similar in the cases with and without IGW (see Figs. 6 and 12), the resulting Li abundance at the ZAMS is una ff ected. The rotating models including the hydrostatic e ff ects have slightly higher lithium abundance on the ZAMS, in agreement with the behavior found by Eggenberger et al. (2012). In a future work we will revisit PMS Li depletion taking the influence of the disk lifetime, of the initial rotation velocity, and of magnetic braking into account .</text>
<figure>
<location><page_13><loc_7><loc_63><loc_51><loc_93></location>
</figure>
<figure>
<location><page_13><loc_52><loc_63><loc_95><loc_94></location>
<caption>Fig. 13. Evolution of the surface rotation rate as a function of time for the models computed with IGW. Stellar masses are indicated on the tracks. In the left panel, the theoretical predictions for the 0.9, 1, and 1.2 M /circledot models are compared with the observed rotational distribution for stars with estimated masses between ∼ 0.9 and 1.1 M /circledot in young open clusters from Gallet & Bouvier (2013)</caption>
</figure>
<figure>
<location><page_13><loc_9><loc_30><loc_46><loc_56></location>
</figure>
<figure>
<location><page_13><loc_50><loc_30><loc_87><loc_56></location>
<caption>Fig. 14. Di ff usion coe ffi cients associated to meridional circulation (red), horizontal and vertical turbulence (black and blue respectively). The total di ff usion coe ffi cient for the chemicals (magenta) and thermal di ff usivity (cyan) are also shown. The figures correspond to the 1 M /circledot models with and without IGW (left and right respectively) at di ff erent evolution ages along the PMS. Hatched areas indicate the convective regions</caption>
</figure>
<section_header_level_1><location><page_13><loc_7><loc_19><loc_20><loc_20></location>7. Conclusions</section_header_level_1>
<text><location><page_13><loc_7><loc_10><loc_50><loc_17></location>In this paper we have analyzed the transport of angular momentum during the PMS for solar-metallicity, low-mass stars (with masses between 0.6 and 2.0 M /circledot ) through the combined action of structural changes, meridional circulation, shear turbulence, and internal gravity waves generated by Reynold-stress and buoyancy in the stellar convective envelope and core (when present).</text>
<text><location><page_13><loc_52><loc_10><loc_95><loc_20></location>For all the stellar masses considered, IGW are e ffi ciently generated by the convective envelope with a momentum luminosity that peaks around Tef f ∼ 6200 K, as in the case of main sequence stars. These waves soon become an e ffi cient agent for angular momentum redistribution because they spin down the stellar core early on the PMS, while structural changes lead to a negative di ff erential rotation in the outer stellar layers as the star contracts. On the other hand, IGW generated by the con-</text>
<figure>
<location><page_14><loc_7><loc_63><loc_49><loc_92></location>
<caption>Fig. 10. Rotation profile on the ZAMS for all the stellar masses between 0.6 and 2.0 M /circledot in the cases without and with IGW (full black and red dotted lines respectively). In the 1 M /circledot panel, the blue long-dashed and the green dashed lines correspond to computations made with multiplication factors for IGW luminosity of one and five respectively, all the other models with IGW being computed with a multiplication factor of two (see Eq. 9)</caption>
</figure>
<figure>
<location><page_14><loc_7><loc_21><loc_49><loc_50></location>
<caption>Fig. 11. Same as Fig. 7 for the 2 M /circledot model computed with IGW</caption>
</figure>
<text><location><page_14><loc_7><loc_10><loc_50><loc_15></location>ctive core close to the arrival on the ZAMS carry much less energy, except in the case of stars more massive than ∼ 1.6 M /circledot . Over the whole considered mass range, IGW were found to significantly modify the internal rotation profile of PMS stars and</text>
<figure>
<location><page_14><loc_52><loc_66><loc_91><loc_92></location>
<caption>Fig. 15. Impact of rotation, IGW, and of the hydrostatic e ff ects on the evolution track of the 1 M /circledot star. The square indicates the point where the radiative zone appears and internal transport of angular momentum starts</caption>
</figure>
<text><location><page_14><loc_52><loc_52><loc_95><loc_55></location>lead to slightly higher surface rotation velocity compared to the case where only meridional circulation and shear turbulence are accounted for.</text>
<text><location><page_14><loc_52><loc_37><loc_95><loc_51></location>The exploratory results presented in this paper show the ability of IGW to e ffi ciently extract angular momentum in the early phases of stellar evolution, as anticipated by Talon & Charbonnel (2008) and as shown by Charbonnel & Talon (2005) and Talon & Charbonnel (2005) for solar-type main sequence stars. We now plan to investigate the influence of the disk lifetime, of the initial rotation velocity, and of magnetic braking during the PMS over a broader mass domain in order to compare model predictions with large data sets that are currently being collected to trace the rotational properties of young stars.</text>
<text><location><page_14><loc_52><loc_27><loc_95><loc_36></location>Acknowledgements. We thank F.Gallet and J.Bouvier for kindly providing data before publication and for fruitful discussions, as well as P.Eggenberger for detailed model comparisons. We thank the referee J.P.Zahn for suggestions that helped improve the manuscript. We acknowledge financial support from the Swiss National Science Foundation (FNS), from the french Programme National de Physique Stellaire (PNPS) of CNRS / INSU, and from the Agence Nationale de la Recherche (ANR) for the project TOUPIES (Towards Understanding the sPIn Evolution of Stars).</text>
<section_header_level_1><location><page_14><loc_52><loc_23><loc_61><loc_24></location>References</section_header_level_1>
<text><location><page_14><loc_52><loc_10><loc_95><loc_22></location>Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481 Chaboyer, B. & Zahn, J.-P. 1992, A&A, 253, 173 Charbonnel, C. & Talon, S. 2005, Science, 309, 2189 Decressin, T., Mathis, S., Palacios, A., et al. 2009, A&A, 495, 271 Eggenberger, P., Haemmerlé, L., Meynet, G., & Maeder, A. 2012, A&A, 539, A70 Ferguson, J. W., Alexander, D. R., Allard, F., et al. 2005, ApJ, 623, 585 Gallet, F. & Bouvier, J. 2013, A&A, tbc Goldreich, P. & Kumar, P. 1990, ApJ, 363, 694 Goldreich, P., Murray, N., & Kumar, P. 1994, ApJ, 424, 466 Goldreich, P. & Nicholson, P. D. 1989, ApJ, 342, 1079 Haisch, Jr., K. E., Lada, E. A., & Lada, C. J. 2001, ApJ, 553, L153</text>
<text><location><page_15><loc_7><loc_92><loc_50><loc_93></location>Hartmann, L. 2005, in Astronomical Society of the Pacific Conference Series,</text>
<text><location><page_15><loc_7><loc_59><loc_50><loc_92></location>Vol. 341, Chondrites and the Protoplanetary Disk, ed. A. N. Krot, E. R. D. Scott, & B. Reipurth, 131 Hernández, J., Hartmann, L., Calvet, N., et al. 2008, ApJ, 686, 1195 Iglesias, C. A. & Rogers, F. J. 1996, ApJ, 464, 943 Irwin, J. & Bouvier, J. 2009, in IAU Symposium, Vol. 258, IAU Symposium, ed. E. E. Mamajek, D. R. Soderblom, & R. F. G. Wyse, 363-374 Kumar, P. & Quataert, E. J. 1997, ApJ, 475, L143 Lagarde, N., Decressin, T., Charbonnel, C., et al. 2012, A&A, 543, A108 Lecoanet, D. & Quataert, E. 2012, ArXiv e-prints Maeder, A. & Zahn, J.-P. 1998, A&A, 334, 1000 Martin, E. L. & Claret, A. 1996, A&A, 306, 408 Mathis, S., Decressin, T., Eggenberger, P., & Charbonnel, C. 2013, A&A, in preparation Mathis, S. & Zahn, J.-P. 2004, A&A, 425, 229 Matt, S. & Pudritz, R. E. 2005, ApJ, 632, L135 Mendes, L. T. S., D'Antona, F., & Mazzitelli, I. 1999, A&A, 341, 174 Meynet, G. & Maeder, A. 2000, A&A, 361, 101 Pinsonneault, M. H., Kawaler, S. D., Sofia, S., & Demarque, P. 1989, ApJ, 338, 424 Schatzman, E. 1993, A&A, 279, 431 Shu, F., Najita, J., Ostriker, E., et al. 1994, ApJ, 429, 781 Stau ff er, J. R., Hartmann, L. W., Burnham, J. N., & Jones, B. F. 1985, ApJ, 289, 247 Talon, S. & Charbonnel, C. 2003, A&A, 405, 1025 Talon, S. & Charbonnel, C. 2004, A&A, 418, 1051 Talon, S. & Charbonnel, C. 2005, A&A, 440, 981 (TC05) Talon, S. & Charbonnel, C. 2008, A&A, 482, 597 (TC08) Talon, S. & Zahn, J.-P. 1997, A&A, 317, 749 Talon, S. & Zahn, J.-P. 1998, A&A, 329, 315 Zahn, J.-P. 1992, A&A, 265, 115 Zahn, J.-P., Talon, S., & Matias, J. 1997, A&A, 322, 320</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Aims. We study the impact of internal gravity waves (IGW), meridional circulation, shear turbulence, and stellar contraction on the internal rotation profile and surface velocity evolution of solar metallicity low-mass pre-main sequence stars. Methods. We compute a grid of rotating stellar evolution models with masses between 0.6 and 2.0 M /circledot taking these processes into account for the transport of angular momentum, as soon as the radiative core appears and assuming no more disk-locking from that moment on. IGW generation along the PMS is computed taking Reynolds-stress and buoyancy into account in the bulk of the stellar convective envelope and convective core (when present). Redistribution of angular momentum within the radiative layers accounts for damping of prograde and retrograde IGW by thermal di ff usivity and viscosity in corotation resonance. Results. Over the whole mass range considered, IGW are found to be e ffi ciently generated by the convective envelope and to slow down the stellar core early on the PMS. In stars more massive than ∼ 1.6 M /circledot , IGW produced by the convective core also contribute to angular momentum redistribution close to the ZAMS. Conclusions. Overall, IGW are found to significantly change the internal rotation profile of PMS low-mass stars. Key words. stars: evolution - stars: rotation - stars: interior - hydrodynamics - waves - turbulence",
"pages": [
1
]
},
{
"title": "Impact of internal gravity waves on the rotation profile inside pre-main sequence low-mass stars",
"content": "C. Charbonnel 1 , 2 , T.Decressin 1 , L.Amard 1 , 3 , A.Palacios 3 , and S.Talon 4 Accepted for publication in A&A (Section 7)",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The evolution of the surface rotation of low-mass stars along the pre-main sequence (hereafter PMS) follows a specific path as shown by the data, both rotation periods and v sin i measurements, collected in young stellar clusters (e.g. Irwin & Bouvier 2009, and references therein for a review). The rotational properties of young stars appear to result from an intricate interplay between several physical processes that a ff ect the angular momentumgains, losses, and redistribution as the stars evolve along the PMS towards the zero age main sequence (hereafter ZAMS). These mechanisms can be roughly divided into two classes. The first ones result from the connection of the stars to their environment (magnetic and dynamic coupling to a circumstellar disk, accretion, jets, stellar and disk winds, etc.), and are particularly crucial during the T-Tauri phase, when star-disk interaction is observed and expected to be strong (see, for instance, Shu et al. 1994; Matt & Pudritz 2005; Zanni & Ferreira 2012). The broad variety of possible star-environment configurations may, in particular, explain part of the large dispersion in rotation rates of solar-type stars observed along the PMS and at the arrival on the ZAMS (e.g., Stau ff er et al. 1985; Irwin & Bouvier 2009). The second class is related to stellar secular evolution and consists of the (magneto-) hydrodynamical transport mechanisms that contribute to redistributing angular momentum inside the stars themselves. In the present paper we focus on exploring these internal mechanisms once the disk has dissipated and the accretion process is over, which occurs after 3-10 email: [email protected] Myr (e.g., Haisch et al. 2001; Hartmann 2005; Hernández et al. 2008), i.e., roughly at the time when a radiative core appears in the contracting PMS stars. Our aim is to evaluate, in particular and for the first time, the interplay between internal gravity waves (hereafter IGW), meridional circulation, turbulent shear, and stellar contraction during the PMS, considering that IGW are one of the best candidate mechanisms to explain the flat angular velocity profile inside the Sun as revealed by helioseismology (Charbonnel & Talon 2005). This work is also motivated by the results of Talon & Charbonnel (2008, hereafter TC08), who showed that IGW are e ffi ciently excited inside intermediatemass PMS stars and suggested that waves should e ffi ciently transport angular momentum during the PMS evolution, which should a ff ect the angular velocity profile at this phase and at the arrival on the ZAMS. In §2 we introduce the formalism for IGW excitation and for the transport of angular momentum through the various mechanisms considered. We describe in §3 the basic assumptions for the present grid of PMS models for low-mass (0.6 to 2 M /circledot ), solar-metallicity stars. In §4 we examine IGW generation by the convective envelope and the convective core (when present) along the PMS evolution for the whole mass range covered by the grid. In § 5 we describe the impact of the various interacting transport mechanisms on the evolution of the internal rotation profile for the various stellar masses, and in § 6 we briefly discuss their influence on the surface rotation velocity and lithium abundance, as well as on global stellar properties. Conclusions are presented in § 7.",
"pages": [
1
]
},
{
"title": "2. Formalism",
"content": "We follow Talon & Charbonnel (2005, hereafter TC05) for the treatment of both the excitation of IGW and the transport of angular momentum and chemicals by waves, meridional circulation, and shear turbulence in hydrodynamical stellar models. We, however, underline three main improvements over TC05 paper. First, we consider IGW generated both by the external and central convective regions (when present), while only those excited by the convective envelope were considered in our previous work. Second, the important variations in the stellar structure and of the IGW properties along the pre-main sequence (see § 4 and TC08) require that we then compute the wave spectra at each evolution time step, while the main sequence computation presented in TC05 was based on the wave spectrum of the stellar model on the ZAMS. Finally, we account here for both prograde and retrograde waves in the whole radiative interior, while only the latter ones were considered previously. We recall below the formalism (i.e., relevant equations and assumptions) that is included in the evolution code STAREVOL (see TC05, TC08, and Mathis et al. 2013).",
"pages": [
2
]
},
{
"title": "2.1. IGWgeneration",
"content": "In this exploratory work we apply the Goldreich et al. (1994) formalism as adapted by Kumar & Quataert (1997) to calculate the spectrum of IGW excited by Reynolds stress and buoyancy in the bulk of convective regions (see e.g. Zahn et al. 1997). We do not consider the possible e ff ects of IGWs generated by convective overshooting plumes, since no analytical prescription is available to describe this excitation mechanism (see details and discussion in TC05). However as we see in § 2.3.1, we multiply the IGW flux by a factor 2 in the transport equation in order to account for the recent results by Lecoanet & Quataert (2012). We treat the waves by assuming that they are pure gravity waves (i.e., not modified by the Coriolis acceleration) that only feel the entrainment by di ff erential rotation. The kinetic energy flux per unit frequency is with ξ r and [ /lscript ( /lscript + 1)] 1 / 2 ξ h the radial and horizontal displacement wave functions normalized to unit energy flux at the edge of the considered convection zone, vc the convective velocity, L = α MLT HP the radial size of an energy bearing turbulent eddy, τ L ≈ L / vc the characteristic convective time, HP the pressure scale height P /ρ g , and h ω the radial size of the largest eddy at depth r with characteristic frequency of ω or higher ( h ω = L min { 1 , (2 ωτ L ) -3 / 2 } ). The radial and horizontal wave numbers (respectively kr and kh ) are related by where N 2 is the Brunt-Väisälä frequency 1 . At the considered convective edge (located at radius rcz ), the mean flux of angular momentum carried by a monochromatic wave of spherical order /lscript and local (i.e., emission) frequency ω ( m being the azimutal order), i.e., the momentum flux per unit frequency, is related to the kinetic energy flux by (Goldreich & Nicholson 1989; Zahn et al. 1997). The so-called angular momentum luminosity at the considered convective edge (envelope or core) is obtained after horizontal integration",
"pages": [
2
]
},
{
"title": "2.2. IGWdamping",
"content": "Deposition of angular momentum (positive or negative) within the radiative layers occurs at the depth where individual monochromatic waves are eventually damped by thermal di ff usivity and viscosity in corotation resonance (Goldreich & Nicholson 1989; Schatzman 1993; Zahn et al. 1997). In the present study the local momentum luminosity at a given radius r within the radiative region accounts for prograde and retrograde waves (i.e., with respectively positive and negative m values) generated by both the convective envelope and the convective core (if present), i.e., where each component is given by where 'cz' refers to the interface between the radiative region and the corresponding convection zone (i.e., envelope or core). The local damping rate takes the mean molecular weight stratification into account (Goldreich & Nicholson 1989; Schatzman 1993; Zahn et al. 1997), as well as the thermal and the (vertical) turbulent viscosity ( KT and ν v respectively). Here, σ is the local Doppler-shifted frequency with ω the wave frequency in the reference frame of the corresponding emitting convection zone that rotates with the angular velocity Ω cz. As can be seen from these expressions, angular momentum redistribution by IGW within the radiative region is dominated by low-frequency ( σ /lessmuch N ), low-degree waves; indeed, those penetrate deeper, and their prograde and retrograde components experience strong di ff erential damping, as required to produce a net momentum deposition. In contrast, high-degree waves are damped closer to the convection zone (since damping ∝ [ /lscript ( /lscript + 1)] 3 2 ), and high-frequency waves experience less di ff erential damping.",
"pages": [
2
]
},
{
"title": "2.3.1. General equations",
"content": "We assume solid-body rotation in the convective regions. In the stellar radiative regions, the evolution of angular momentum through advection by meridional circulation, di ff usion by shear turbulence, and deposit or extraction by IGW follows the general expression below (e.g., Talon & Zahn 1998): where U is the radial meridional circulation velocity, ν v the turbulent viscosity due to di ff erential rotation, and ρ the density. We have added a factor 2 in the last term to account for the study by Lecoanet & Quataert (2012), who predict the IGW flux due to turbulent convection to be a few to five times larger than in previous estimates by, e.g., Goldreich & Kumar (1990) and Goldreich et al. (1994). However as we see in § 5.1.2, our conclusions are not sensitive to this multiplication factor. Following Decressin et al. (2009) and Mathis et al. (2013) we integrate Eq. 9 over an isobar enclosing the mass m ( r ) to obtain the expression of the total flux (loss or gain) of angular momentum carried by the considered transport processes: where the fluxes driven by meridional circulation, vertical shearinduced turbulence, and IGWs are, respectively,",
"pages": [
3
]
},
{
"title": "2.3.2. Meridional circulation",
"content": "As can be seen in Eq. 9 the transport of angular momentum through meridional circulation is treated as an advective process. As in our previous studies we apply the formalism developed by Zahn (1992), Maeder & Zahn (1998) and Mathis & Zahn (2004, see also Decressin et al. 2009).",
"pages": [
3
]
},
{
"title": "2.3.3. Shear-induced turbulence",
"content": "Shear-induced turbulence is assumed to be highly anisotropic. Following TC05 we assume that the turbulent di ff usion coe ffi -cient equals turbulent viscosity and use the corresponding expression given by Talon & Zahn (1997), i.e., that considers the weakening e ff ect of thermal di ff usivity ( KT ) on the thermal stratification and of horizontal turbulence ( Dh , see below) on both the thermal and mean molecular weight stratifications. For the treatment of horizontal turbulent viscosity, we follow Zahn (1992), again as in TC05: The influence of the prescriptions assumed for Dv and Dh will be investigated in a future paper.",
"pages": [
3
]
},
{
"title": "2.4. Transportofchemicals",
"content": "Wetreat the transport of chemical species in the radiative regions as a di ff usive process through the combined action of meridional circulation and shear-induced turbulence (Chaboyer & Zahn 1992). The e ff ective di ff usion coe ffi cient is written where Dh is the horizontal component of the turbulent di ff usivity (see Eq. 14). In the present study we neglect atomic di ff usion, whose effects require much longer timescales to develop compared to the very short duration of the pre-main sequence phase. We also neglect possible wave-induced turbulence. Therefore the expression for the transport of chemicals (here, the mass fraction X of the element i ) in the stellar radiative region writes as (see e.g. Meynet & Maeder 2000): where dMr = 4 πρ r 2 dr , and the last term accounts for nuclear destruction or production of the considered element.",
"pages": [
3
]
},
{
"title": "3.1. Inputphysicsandbasicassumptions",
"content": "We focus on the pre-main sequence evolution of solarmetallicity stars in the mass range between 0.6 and 2.0 M /circledot . We adopt the solar composition of Asplund et al. (2009). Opacity tables are updated accordingly both at high and low temperature respectively from OPAL and Wichita websites 2 (see e.g. Iglesias & Rogers 1996; Ferguson et al. 2005). The mixing length parameter α MLT = 1 . 63 is calibrated so that our standard (i.e., non rotating) 1 M /circledot , Z /circledot model fits the solar radius, e ff ective temperature, and luminosity at the age of the sun. Convection zone bounderies are defined by the Schwarzschild criterion, and we do not account for convective overshoot. Computations are performed with the stellar evolution code STAREVOL(see e.g. TC05, Lagarde et al. 2012). Initial models are totally convective polytropic stars, with central temperature lower than 10 6 K (i.e., deuterium burning has not yet occurred). We follow the PMS evolution along the Hayashi track up to the arrival on the ZAMS that we define as the point where the ratio between central and surface hydrogen abundance reaches 0.998. The stellar mass is assumed to be constant during that phase (i.e., no accretion nor mass loss). For each stellar mass we compute classical models (i.e., without any transport of angular momentum nor of chemicals) as well as rotating models with and without IGW. We neglect the hydrostatic e ff ects of the centrifugal force in all our rotating models but two; we discuss the impact of this simplification in § 5. The evolution tracks of the classical models in the Hertzsprung-Russel diagram are shown in Fig.1.",
"pages": [
3,
4
]
},
{
"title": "3.2. Initialinternalandsurfacerotation",
"content": "We assume solid-body rotation while stars are fully convective (which corresponds to the dotted part of the tracks in Fig. 1) and we start computing the evolution of surface and internal rotation under the action of stellar contraction, meridional circulation, turbulence, and IGW when the radiative core appears, which happens at ages between ∼ 0.5 and 7.5 Myr for the mass range considered (see τ (core) in Table 1), and at ∼ 2.5 Myr for the 1.0 M /circledot model. At that time, most or even all low-mass stars have already lost their disks as shown by observations in very young clusters (e.g. Haisch et al. 2001; Hartmann 2005; Hernández et al. 2008). For all stellar masses, we choose the initial rotation velocity at the moment when the radiative zone appears to be equal to 5% of the critical velocity of the corresponding model (V crit = √ 2 3 GM R ; see Table 1). This corresponds approximately to the median of the observed distribution in young open clusters (see Fig. 13 and § 6 for discussion). We assume that there is no more coupling between the star and a potential disk beyond that evolution point. The surface of the star is then free to spin up, and we do not apply any magnetic braking. The influence of the initial rotation velocity, of the disk lifetime that a ff ects the moment when a PMS star starts spinning up, as well as that of magnetic wind braking that may a ff ect the rotation rate at the arrival on the ZAMS, will be investigated in a forthcoming paper.",
"pages": [
4,
5
]
},
{
"title": "4. IGW generation along the PMS evolution for all grid models",
"content": "The internal structure strongly changes as low-mass stars evolve along the PMS. This implies strong variations in the quantities that are relevant to IGW generation and momentum transport, as depicted in Figs. 1 for the properties of the convective envelope and 2 for the core. All quantities are given in cgs units. Stars are first fully convective and a radiative core appears along the Hayashi track as they contract and heat (Fig. 1). The thickness of the convective envelope decreases, and the temperature at its base increases as the stars move towards higher e ff ective temperatures. Due to central CNO-burning ignition on the final approach towards the ZAMS a convective core develops (Fig.2). One can follow the evolution along the tracks of the maximum convective flux ( Fc = Cp ρ vc ∆ T ) inside the external and central convective regions, which directly a ff ects the energy flux associated to a given frequency (see Eq.1). Wave excitation is stronger when the convective length scale ( /lscript c = 2 π rcz /α Hp ) is larger, but decreases when the turnover timescale ( τ c = α MLT Hp / vc ) becomes too large. The combination of these two factors induces large di ff erences in the overall e ffi ciency of wave generation as the internal structure evolves. This is well illustrated in Fig. 3 that shows the luminosity spectrum of IGW generated by the external convection zone in the 1 M /circledot model at four ages on the PMS. One sees clearly that wave-induced transport is dominated by low-frequency waves (i.e., < 3 . 5 µ Hz). High degree waves at low frequencies do not contribute much to the transport of angular momentum even though their excitation flux is important : indeed they are essentially damped near the convective envelope edge. In Fig. 4 colors along the tracks indicate the net momentum luminosity L J (see Eq. 4) of IGWs generated by the external and internal convective regions. In the case of external convection, the net momentum luminosity L J , sur f rapidly increases as the excitation of IGW strengthens up when stars evolve towards higher e ff ective tem- perature, and reaches maximum values as high as 10 39 g.cm 2 s 2 around T e ff ∼ 6200 K. Stars with initial masses lower than 1.3 M /circledot never reach this e ff ective temperature and the corresponding L J , sur f remains always below this maximum and shows only a monotonic increase along the PMS. On the other hand in the more massive models the convective envelope keeps shrinking in size and L J , sur f decreases when T e f f increases above 6200 K. This behavior confirms TC08 findings for intermediate-mass PMS stars, and is very similar to the L J plateau we found for Pop I and Pop II main sequence stars (Talon & Charbonnel 2003, 2004), which share very similar convective properties with PMS stars in the same T e f f range. IGW are also emitted from the convective core at the end of the PMS. The more massive the star, the more the convective core expands, and the stronger the corresponding wave excitation. We note however from Fig. 4 that wave excitation by the convective core (when present) is generally much less e ffi cient than that of the convective envelope. The ratio between L J , core and L J , sur f is shown in Fig. 5 as a function of T e f f for the various models. For stars with masses below 1.4 M /circledot , L J , core is always ∼ 5-6 order of magnitude lower than L J , sur f . These two quantities reach similar orders of magnitude only very close from the ZAMSfor stars more massive than 1.6 M /circledot . Therefore and as we shall see below, the impact of IGW on the internal rotation profile along the PMS will be dominated by the waves emitted by the convective envelope.",
"pages": [
5,
6
]
},
{
"title": "5.1. Thecaseofthe1M /circledot star",
"content": "Figure 6 depicts the evolution along the PMS of the rotation profile inside the 1 M /circledot star for two cases: when angular momentum transport is operated solely by meridional circulation and shear turbulence (bottom panels), and when angular momentum deposition by internal gravity waves is taken into account in addition to the hydrodynamic processes (top panels); the rotation profile is shown at di ff erent ages as a function of both relative mass fraction and reduced radius (left and right panels respectively). The decomposition of the total flux of angular momentum into the various components driven by meridional circulation, shear turbulence, and IGW (when accounted for; see Eqs. 10, 11, and 12 respectively) is shown in Fig. 7 at three ages along the PMS. Meridional circulation currents are shown at the same ages in Fig.8; clockwise currents (matter flowing from the equator to the pole and resulting in deposition of angular momentum in- wards) and counterclockwise ones (carrying angular momentum outwards) are drawn in blue and red respectively.",
"pages": [
7,
8
]
},
{
"title": "5.1.1. Transport of angular momentum by meridional circulation and shear turbulence only",
"content": "When only meridional circulation and shear turbulence are accounted for, di ff erential rotation rapidly develops inside the radiative region as the surface rotation velocity increases due to stellar contraction (Fig. 6, bottom plots). This behavior as well as the rotation profile at the arrival on the ZAMS are similar to the results of Eggenberger et al. (2012) for their rotating 1 M /circledot model computed with similar assumptions. As can be seen in Fig.7 (right plots) for this model without IGW, the transport of angular momentum is dominated by meridional circulation all along the PMS, while the contribution of shear turbulence is negligible (the flux of angular momentum by turbulence FV is indeed ∼ 2 orders of magnitude lower than the flux driven by meridional circulation FMC ). The number of circulation loops evolves with time (Fig.8, bottom plots; see also Fig. 7): In the early stages (14.9 Myrs, left panel), the circulation consists of a single counterclockwise current that transports matter inward along the rotational axis and outward in the equatorial plane; later on (33.5 Myrs, middle panel) a clockwise loop appears in the central regions; finally an additional counterclockwise loop shows up when the convective core develops (55 Myrs, right panel).",
"pages": [
8
]
},
{
"title": "5.1.2. Impact of internal gravity waves",
"content": "The evolution of the internal rotation profile changes drastically when IGW are taken into account in conjunction with meridional circulation and shear turbulence, as can be seen in Fig. 6 (top plots). As already discussed in § 4, the emitted wave spectrum strongly evolves with the stellar structure along the PMS. IGW are first emitted by the receding convective envelope, and much later by the convective core when it appears during the final ap- roach towards the zams. In the case of the 1 M /circledot model, IGW emitted by the convective core play actually no role since their luminosity is extremely low (see Fig. 5 and discussion in § 4). Therefore the following discussion refers only to those emitted by the envelope. In order to understand wave-induced transport, we must also focus on the important quantities for wave damping in the radiative layers, namely the Brunt-Väisälä frequency N 2 and the thermal di ff usivity KT : For a given di ff erential rotation within the radiative layers, low-frequency (i.e., with ω < 3.5 µ Hz) and / or large degree waves that dominate the angular momentum transport are damped very e ffi ciently close to the convective edges when N 2 T is too small or when KT is too large (see Eq. 7). Fig.9 and 14 show the radial profiles of these two quantities in the radiative layers of the 1 M /circledot model at various ages (see also Fig. 1 and 2 that show the variations along the evolution track of the value of KT just below the convective envelope and above the convective core). At all ages N 2 drops near the stellar center and the convective edges; in addition its value at a given depth increases with time along the PMS as a result of the stellar contraction that leads to an increase of gravity and a decrease of the pressure scale height as the star evolves. On the other hand the value of KT just below the convective envelope also increases as the star contracts and move towards higher e ff ective temperature; this implies stronger damping of all the waves (independently of their properties) closer to the convective envelope; note that KT at a given depth within the star increases only slightly during the evolution. Besides, the build up of di ff erential rotation with time within the star induces a change in the local Doppler shift frequency, which allows a di ff erent damping for waves with different frequencies and m through the term σ -4 ( N 2 -σ 2 ) -0 . 5 . Let us see what these general considerations imply for the 1.0 M /circledot model. We start with initial solid body rotation and then follow the transport of angular momentum when the radiative layers appear. At that moment di ff erential rotation has not yet developed, and the local frequency σ of individual waves in the very thin radiative zone is similar to their emission frequency ω at the base of the convective envelope. However slight differential rotation soon builds up as a result of stellar contraction along the Hayashi track, which induces a Doppler shift between the emission and local IGW spectra. As a consequence, low-frequency low-degree waves, which undergo the largest differential damping between retrogade and prograde components, soon penetrate all the way to the central regions where they deposit their negative momentum and very e ffi ciently spin down the core whose amount of angular momentum is minute (see Fig. 6). This explains the strong positive gradient in the profile of Ω below ∼ 0 . 2 R /circledot , while the negative gradient of Ω in the external layers results from ongoing stellar contraction. As a consequence a peak builds up in the internal rotation profile with a core spinning at lower rate than the stellar surface all along the PMS. We show in Fig.7 the total flux of angular momentum carried by the waves as a function of depth within the 1 M /circledot model, and compare it to the contribution of meridional circulation and shear turbulence at di ff erent evolution stages. We note first that the transport of angular momentum is generally dominated by the waves in the radiative layers where they can propagate, except in the early times when meridional circulation dominates in the most external regions below the convective envelope (upper panel at 14 Myr). Since downward propagating waves are totally damped as soon as the condition Ω ( r ) = ω/ m + Ω cz is fulfilled near the corotation radius, the total flux F IGW drops and remains negligible below the Ω peak. This can be clearly seen in the middle and lower panels in Fig.7 at 35 and 55 Myrs; at that time meridional circulation dominates in the regions below ∼ 0.15 and 0.2 M /circledot respectively, while IGW are dominant in the outer regions. Note that the total flux of angular momentum is dominated by IGW when they are accounted for and is larger by two orders of magnitude compared to the case without IGW. Overall, IGW do shape the circulation patterns, leading to the appearance of several loops in the whole radiative region as can be seen in Figs. 7 and 8. Let us add a final remark. As explained in § 2.3.1, we have increased by a factor 2 the IGW luminosity in order to account for the results by Lecoanet & Quataert (2012) who predict the IGW flux due to turbulent convection to be a few to five times larger than in previous estimates by e.g. Goldreich & Kumar (1990) and Goldreich et al. (1994). In order to test the impact of this assumption, we have computed two additional models for the 1 M /circledot rotating star with multiplying factors of 1 and 5. We find that this has no impact on the conclusions, as can be seen in Fig. 10 where we plot the corresponding rotation profiles at the arrival on the ZAMS.",
"pages": [
8,
9,
10
]
},
{
"title": "5.2. Impactofthestellarmass",
"content": "For all the stars within the considered mass range, strong differential rotation with a fast rotating core is obtained under the combined action of stellar contraction and meridional circulation when IGW are not accounted for. Besides, in all cases IGW do break-up the stellar core, which results in a peak in Ω at r ∼ 0.250.3R ∗ as in the 1 M /circledot case. This can be seen in Fig. 10 where we show the rotation profiles at the arrival on the ZAMS for all our models (black and red lines correspond respectively to the models computed without or with IGW). Let us note however that the impact of IGW is slightly different in stars more massive than ∼ 1 . 6 M /circledot . This is illustrated for the 2 M /circledot star in Fig. 11 where we decompose the total flux of angular momentum within the model according to the various transport processes at three di ff erent ages, and in Fig. 12 where we follow the corresponding evolution of the radial profile of Ω . For this more massive star, IGW emitted by the convective envelope dominate during the first part of the PMS and manage to slow down the most central regions as in the 1 M /circledot case (top panel, Fig. 11). However those waves fade away when the convective envelope becomes too thin and are supplanted by those emitted by the convective core at the approach of the ZAMS (see Fig. 4). During that transition period (middle panel in Fig. 11), meridional circulation dominates the transport of angular momentum although shear turbulence also contributes more e ffi ciently near the most central regions (between 0.05 and 0.1 M /circledot ) and in the most external layers; as a result, the core slightly accelerates and eventually manages to rotate faster than the outer radiative layers, although not fast enough for the peak to be erased. Once the convective core has su ffi ciently developed (lower panel, Fig. 11), the IGW emitted in the central regions will start conveying angular momentum very e ffi ciently towards the core; at that time meridional circulation remains however the dominant process in the most external radiative layers.",
"pages": [
10,
11
]
},
{
"title": "6. Global stellar properties, surface rotation and lithium abundance",
"content": "We summarize in Table 1 the main properties of our models computed under various assumptions. We also include the predictions for two additional models of 1 M /circledot that account for the hydrostatic e ff ects of rotation (i.e., the e ff ects of centrifugal acceleration on e ff ective gravity) and show in Fig. 15 all the corresponding evolution tracks for this star. We see that the rotating tracks without hydrostatic e ff ects are hardly modified compared to the standard case, the main shift to slightly lower e ff ective temperature and luminosity (that implies slightly longer PMS lifetime) being due to the e ff ects of the centrifugal force and not to rotation-induced mixing. This is in agreement with the predictions by Eggenberger et al. (2012) (see also Pinsonneault et al. 1989; Martin & Claret 1996; Mendes et al. 1999). However the hydrostatic e ff ects are modest and our general conclusions on the evolution of the internal rotation profile and on the impact of IGW are not a ff ected by this simplification. We can also note in Table 1 that the models computed with IGW have longer PMS lifetimes than the others. This simply results from the higher total di ff usion coe ffi cient for chemicals in the deep radiative layers close to the convective core when central H-burning sets in close to the ZAMS (see Fig. 14). As shown in Fig. 13, the evolution of surface rotation for the models with IGW accounts well for the mean rotation rates collected by Gallet & Bouvier (2013) for PMS stars in young open clusters in the considered mass range. The rotation velocity at the arrival on the ZAMS is slightly higher (by a few %; see Table 1) in this case than in rotating models without IGW, due to the different e ffi ciency of the redistribution of angular momentum by the various transport mechanisms within the star as discussed previously. Again, the hydrostatic e ff ects are negligible. The surface lithium abundance at the ZAMS is not significantly di ff erent in the rotating models without and with IGW, as can be seen from Table 1. Indeed this quantity mostly depends, on one hand, on the temperature at the base of the con- vective envelope, which is una ff ected since the evolution tracks almost superpose, and on the other hand, on the di ff usion coefficient Def f (Eq. 15) in the external radiative layers shown in Fig. 14. Since the gradient of Ω in the outer part of the star is dominated by stellar contraction and is very similar in the cases with and without IGW (see Figs. 6 and 12), the resulting Li abundance at the ZAMS is una ff ected. The rotating models including the hydrostatic e ff ects have slightly higher lithium abundance on the ZAMS, in agreement with the behavior found by Eggenberger et al. (2012). In a future work we will revisit PMS Li depletion taking the influence of the disk lifetime, of the initial rotation velocity, and of magnetic braking into account .",
"pages": [
11,
12
]
},
{
"title": "7. Conclusions",
"content": "In this paper we have analyzed the transport of angular momentum during the PMS for solar-metallicity, low-mass stars (with masses between 0.6 and 2.0 M /circledot ) through the combined action of structural changes, meridional circulation, shear turbulence, and internal gravity waves generated by Reynold-stress and buoyancy in the stellar convective envelope and core (when present). For all the stellar masses considered, IGW are e ffi ciently generated by the convective envelope with a momentum luminosity that peaks around Tef f ∼ 6200 K, as in the case of main sequence stars. These waves soon become an e ffi cient agent for angular momentum redistribution because they spin down the stellar core early on the PMS, while structural changes lead to a negative di ff erential rotation in the outer stellar layers as the star contracts. On the other hand, IGW generated by the con- ctive core close to the arrival on the ZAMS carry much less energy, except in the case of stars more massive than ∼ 1.6 M /circledot . Over the whole considered mass range, IGW were found to significantly modify the internal rotation profile of PMS stars and lead to slightly higher surface rotation velocity compared to the case where only meridional circulation and shear turbulence are accounted for. The exploratory results presented in this paper show the ability of IGW to e ffi ciently extract angular momentum in the early phases of stellar evolution, as anticipated by Talon & Charbonnel (2008) and as shown by Charbonnel & Talon (2005) and Talon & Charbonnel (2005) for solar-type main sequence stars. We now plan to investigate the influence of the disk lifetime, of the initial rotation velocity, and of magnetic braking during the PMS over a broader mass domain in order to compare model predictions with large data sets that are currently being collected to trace the rotational properties of young stars. Acknowledgements. We thank F.Gallet and J.Bouvier for kindly providing data before publication and for fruitful discussions, as well as P.Eggenberger for detailed model comparisons. We thank the referee J.P.Zahn for suggestions that helped improve the manuscript. We acknowledge financial support from the Swiss National Science Foundation (FNS), from the french Programme National de Physique Stellaire (PNPS) of CNRS / INSU, and from the Agence Nationale de la Recherche (ANR) for the project TOUPIES (Towards Understanding the sPIn Evolution of Stars).",
"pages": [
13,
14
]
},
{
"title": "References",
"content": "Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481 Chaboyer, B. & Zahn, J.-P. 1992, A&A, 253, 173 Charbonnel, C. & Talon, S. 2005, Science, 309, 2189 Decressin, T., Mathis, S., Palacios, A., et al. 2009, A&A, 495, 271 Eggenberger, P., Haemmerlé, L., Meynet, G., & Maeder, A. 2012, A&A, 539, A70 Ferguson, J. W., Alexander, D. R., Allard, F., et al. 2005, ApJ, 623, 585 Gallet, F. & Bouvier, J. 2013, A&A, tbc Goldreich, P. & Kumar, P. 1990, ApJ, 363, 694 Goldreich, P., Murray, N., & Kumar, P. 1994, ApJ, 424, 466 Goldreich, P. & Nicholson, P. D. 1989, ApJ, 342, 1079 Haisch, Jr., K. E., Lada, E. A., & Lada, C. J. 2001, ApJ, 553, L153 Hartmann, L. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 341, Chondrites and the Protoplanetary Disk, ed. A. N. Krot, E. R. D. Scott, & B. Reipurth, 131 Hernández, J., Hartmann, L., Calvet, N., et al. 2008, ApJ, 686, 1195 Iglesias, C. A. & Rogers, F. J. 1996, ApJ, 464, 943 Irwin, J. & Bouvier, J. 2009, in IAU Symposium, Vol. 258, IAU Symposium, ed. E. E. Mamajek, D. R. Soderblom, & R. F. G. Wyse, 363-374 Kumar, P. & Quataert, E. J. 1997, ApJ, 475, L143 Lagarde, N., Decressin, T., Charbonnel, C., et al. 2012, A&A, 543, A108 Lecoanet, D. & Quataert, E. 2012, ArXiv e-prints Maeder, A. & Zahn, J.-P. 1998, A&A, 334, 1000 Martin, E. L. & Claret, A. 1996, A&A, 306, 408 Mathis, S., Decressin, T., Eggenberger, P., & Charbonnel, C. 2013, A&A, in preparation Mathis, S. & Zahn, J.-P. 2004, A&A, 425, 229 Matt, S. & Pudritz, R. E. 2005, ApJ, 632, L135 Mendes, L. T. S., D'Antona, F., & Mazzitelli, I. 1999, A&A, 341, 174 Meynet, G. & Maeder, A. 2000, A&A, 361, 101 Pinsonneault, M. H., Kawaler, S. D., Sofia, S., & Demarque, P. 1989, ApJ, 338, 424 Schatzman, E. 1993, A&A, 279, 431 Shu, F., Najita, J., Ostriker, E., et al. 1994, ApJ, 429, 781 Stau ff er, J. R., Hartmann, L. W., Burnham, J. N., & Jones, B. F. 1985, ApJ, 289, 247 Talon, S. & Charbonnel, C. 2003, A&A, 405, 1025 Talon, S. & Charbonnel, C. 2004, A&A, 418, 1051 Talon, S. & Charbonnel, C. 2005, A&A, 440, 981 (TC05) Talon, S. & Charbonnel, C. 2008, A&A, 482, 597 (TC08) Talon, S. & Zahn, J.-P. 1997, A&A, 317, 749 Talon, S. & Zahn, J.-P. 1998, A&A, 329, 315 Zahn, J.-P. 1992, A&A, 265, 115 Zahn, J.-P., Talon, S., & Matias, J. 1997, A&A, 322, 320 Zanni, C. & Ferreira, J. 2012, ArXiv e-prints",
"pages": [
14,
15
]
}
]
2013A&A...554A..41M
https://arxiv.org/pdf/1302.7211.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_82><loc_88><loc_87></location>Speckle temporal stability in XAO coronagraphic images (ResearchNote)</section_header_level_1>
<section_header_level_1><location><page_1><loc_10><loc_81><loc_92><loc_82></location>II. Refine model for quasi-static speckle temporal evolution for VLT/SPHERE</section_header_level_1>
<text><location><page_1><loc_17><loc_78><loc_85><loc_80></location>P. Martinez 1 , M. Kasper 2 , A. Costille 3 , J.F. Sauvage 4 , K. Dohlen 5 , P. Puget 3 , and J.L. Beuzit 3</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_74><loc_91><loc_76></location>1 Laboratoire Lagrange, UMR7293, Universit'e de Nice Sophia-Antipolis, CNRS, Observatoire de la Cˆote d'Azur, Bd. de l'Observatoire, 06304 Nice, France</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_68><loc_74></location>2 European Southern Observatory, Karl-Schwarzschild-Straße 2, D-85748, Garching, Germany</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_89><loc_73></location>3 UJF-Grenoble 1 / CNRS-INSU, Institut de Plan'etologie et d'Astrophysique de Grenoble UMR 5274, Grenoble, F-38041, France</list_item>
<list_item><location><page_1><loc_11><loc_69><loc_91><loc_71></location>4 Laboratoire d'Astrophysique de Marseille, UMR 7326, CNRS, Universit'e de Provence, 38 rue Fr'ed'eric Joliot-Curie, 1 3388, Marseille Cedex 13, France</list_item>
<list_item><location><page_1><loc_11><loc_68><loc_90><loc_69></location>5 O ffi ce National d'Etudes et de Recherches Aerospatiales (ONERA), Optics Department, BP 72, F-92322 Chatillon cedex, France</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_66><loc_35><loc_67></location>Preprint online version: October 9, 2018</text>
<section_header_level_1><location><page_1><loc_47><loc_64><loc_55><loc_64></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_59><loc_91><loc_62></location>Context. Observing sequences have shown that the major noise source limitation in high-contrast imaging is due to the presence of quasi-static speckles. The timescale on which quasi-static speckles evolve, is determined by various factors, among others mechanical or thermal deformations.</text>
<text><location><page_1><loc_11><loc_54><loc_91><loc_59></location>Aims. Understanding of these time-variable instrumental speckles, and especially their interaction with other aberrations, referred to as the pinning e ff ect, is paramount for the search of faint stellar companions. The temporal evolution of quasi-static speckles is for instance required for a quantification of the gain expected when using angular di ff erential imaging (ADI), and to determine the interval on which speckle nulling techniques must be carried out.</text>
<text><location><page_1><loc_11><loc_48><loc_91><loc_54></location>Methods. Following an early analysis of a time series of adaptively corrected, coronagraphic images obtained in a laboratory condition with the High-Order Test bench (HOT) at ESO Headquarters, we confirm our results with new measurements carried out with the SPHERE instrument during its final test phase in Europe. The analysis of the residual speckle pattern in both direct and di ff erential coronagraphic images enables the characterization of the temporal stability of quasi-static speckles. Data were obtained in a thermally actively controlled environment reproducing realistic conditions encountered at the telescope.</text>
<text><location><page_1><loc_11><loc_42><loc_91><loc_48></location>Results. The temporal evolution of the quasi-static wavefront error exhibits linear power law, which can be used to model quasi-static speckle evolution in the context of forthcoming high-contrast imaging instruments, with implications for instrumentation (design, observing strategies, data reduction). Such a model can be used for instance to derive the timescale on which non-common path aberrations must be sensed and corrected. We found in our data that quasi-static wavefront error increases with ∼ 0.7Å per minute.</text>
<text><location><page_1><loc_11><loc_41><loc_74><loc_42></location>Key words. Techniques: high angular resolution -Instrumentation: high angular resolution -Telescopes</text>
<section_header_level_1><location><page_1><loc_7><loc_36><loc_19><loc_37></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_12><loc_50><loc_35></location>Observing sequences have shown that the major noise source limitation in high-contrast imaging is due to the presence of instrumental speckles, and more precisely to quasi-static speckles (Marois et al. 2003; Boccaletti et al. 2003, 2004; Hinkley et al. 2007). Speckle noise originates from wavefront errors caused by various independent sources, and evolves on di ff erent timescales pending to their nature. The first class of speckle to overcome comes from the large, dynamical wavefront error that the atmosphere generates, but real-time adaptive optics systems measure and correct it down to fundamental limitations. The fast-varying speckle noise floor left uncorrected by such systems would average out over time, as it consists in a random and uncorrelated noise for which the intensity variance converges to null contribution for an infinitely long exposure. For a non-photon noise limited observing run, speckle noise associated to wavefront aberrations introduced in the optical train are fundamental to tackle. In this context, instrumental speckles can be divided into two di ff erent flavors: long-timescale wavefront errors present in the</text>
<text><location><page_1><loc_52><loc_28><loc_95><loc_37></location>optical train (e.g., optical quality, misalignment errors) that generate static speckles that constitute a deterministic contribution to the noise variance, and slowly-varying instrumental wavefront aberrations, amplitude and phase errors, originating from various causes, among others mechanical or thermal deformations. The latest evolve on a shorter timescale than long-lived aberrations, and are the so-called quasi-static speckles.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_28></location>Instrumental speckles average to form a fixed pattern, which can be calibrated to a certain extent. A deterministic contribution to the noise variance such as static speckles can easily be calibrated, while using a reference image, time-variable quasistatic noise can be subtracted as well, but its temporal evolution ultimately limit this possibility. In particular it is understood that some timescales have a larger impact than others. This is especially true as quasi-static speckles interact with other aberrations, referred to as the pinning e ff ect , or speckle cross terms. The timescale of quasi-static speckles evolution is essential to understand and predict the performance of the new generation of instruments such as SPHERE (Beuzit et al. 2008), GPI (Macintosh et al. 2008), HiCIAO (Hodapp et al. 2008), and Project 1640 (Hinkley et al. 2011). The temporal evolution of</text>
<text><location><page_2><loc_7><loc_75><loc_50><loc_93></location>these quasi-static speckles is in particular needed for the quantification of the gain expected with angular di ff erential imaging (ADI, Marois et al. 2006), as well as to determine the timescale on which speckle nulling techniques should be carried out. For instance, a typical hour-long ADI observing sequence provides a partial self-calibration of the residuals after a rotation of ∼ 1 λ/ D at a given angular separation, which generally requires less than few minutes (e.g., 5 to 7 mn at 1 '' on a 8-m class telescope for stars near the meridian in H -band), though it depends on wavelength, telescope latitude, and object declination. Residual speckles with decorrelation times faster than the time needed to obtain the ADI reference image cannot then be removed, while quasi-static speckles associated with larger timescales can largely be subtracted.</text>
<text><location><page_2><loc_7><loc_36><loc_50><loc_75></location>In this context, several authors have investigated the decorrelation timescale of quasi-static residuals in the particular context of ADI but at moderate 20-40 % Strehl levels (Marois et al. 2006; Lafreni'ere et al. 2007; Hinkley et al. 2007), while in a former paper (Martinez et al. 2012, hereafter Paper I), we explored the realm of very high Strehl ratios (extreme adaptive optic systems, XAO). In paper I, we analyzed a time series of adaptively corrected, coronagraphic images recorded in the laboratory with the High-Order Test bench, a versatile high-contrast imaging, adaptive optics bench developed at ESO. We shown that quasi-static aberrations exhibit a linear power law with time and are interacting through the pinning e ff ect with static speckles. We examined and discussed this e ff ect using the statistical model of the noise variance in high-contrast imaging proposed by Soummer et al. (2007). In particular, we found that quasistatic speckles, fast-evolving on the level of a few angstroms to nanometers over a timescale of few seconds, explained the evolution of our sensitivity through amplification of the systematics. It is believed that this e ff ect is a consequence of thermal and mechanical instabilities of the optical bench. The HOT bench is indeed localized in a classical laboratory setting, and was not initially designed to guarantee stability, nor mechanical stability at the level that would be required / expected for an actual highcontrast imaging instrument. Indeed Paper I emphasizes the importance of such stability for the next generation of high-contrast instruments, but the estimates found in this former analysis (amplitude, and slope of the temporal evolution) could not fairly be considered as representative of a realistic situation in order to a ff ect operational aspects or designs of nowadays / future real instruments.</text>
<text><location><page_2><loc_7><loc_25><loc_50><loc_35></location>In this paper, we confirm the results presented in Paper I with more representative measurements. We analyze a time series of adaptively corrected, coronagraphic images with the SPHERE instrument in a thermally actively controlled environment reproducing realistic conditions encountered at the telescope. In this context, we propose a refine model of quasi-static speckle evolution that can be used for forthcoming high-contrast imaging instrument classes that SPHERE represents.</text>
<text><location><page_2><loc_7><loc_17><loc_50><loc_25></location>The paper reads as follow: in Sect. 2, we briefly recall the formalism of the statistical model of the noise variance in highcontrast imaging proposed by Soummer et al. (2007) and used in Paper I to discuss our former results, in Sect. 3, the experimental conditions are described, and in Sect. 4 we analyze and discuss the results. Finally, in Sect. 5, we draw conclusions.</text>
<section_header_level_1><location><page_2><loc_7><loc_13><loc_39><loc_14></location>2. Speckle noise and dynamical range</section_header_level_1>
<text><location><page_2><loc_7><loc_10><loc_50><loc_12></location>In Paper I, we examined and discussed our data using the statistical model of the noise variance in high-contrast imaging pro-</text>
<text><location><page_2><loc_52><loc_91><loc_95><loc_93></location>posed by Soummer et al. (2007). Following the same formalism as for Paper I, we briefly recall here the main equations.</text>
<text><location><page_2><loc_52><loc_84><loc_95><loc_90></location>Soummer et al. (2007) proposed the following analytical expression for the variance of the intensity, including speckle and photon noise in the presence of static, quasi-static, and fast varying aberrations, in the context of a propagation through a coronagraph:</text>
<formula><location><page_2><loc_54><loc_80><loc_95><loc_83></location>σ 2 I = N ( I 2 s 1 + NI 2 s 2 + 2 IcIs 1 + 2 NIcIs 2 + 2 Is 1 Is 2 ) + σ 2 p , (1)</formula>
<text><location><page_2><loc_52><loc_59><loc_95><loc_81></location>where I denotes the intensity, σ 2 p is the variance of the photon noise, and N is the ratio of fast-speckle and slow-speckle lifetimes. The intensity produced by the deterministic part of the wavefront, including static aberrations, is denoted by Ic , while the Is terms corresponds to the halo produced by random intensity variations, i.e. atmospheric ( Is 1) and quasi-static contributions ( Is 2). In this generalized expression of the variance, several contributions can be identified by order of appearance: (1 / ) the atmospheric halo, (2 / ) the quasi-static halo, (3 / ) the atmospheric pinning term, the speckle pinning of the static aberrations by the fast evolving atmospheric speckles, (4 / ) the speckle pinning of the static by quasi-static speckles, and finally (5 / ) the speckle pinning of the atmospheric speckles by quasi-static speckles. Equation 1 provides useful insights in the understanding of the impact of quasi-static speckles and their interactions through the pinning phenomenon with other aberrations present in a real instrument.</text>
<text><location><page_2><loc_52><loc_47><loc_95><loc_59></location>As for Paper I, we focus our analysis on contribution (4 / ) to this noise budget in XAO coronagraphic images. In particular, we are interested in the speckle pinning of the static by the quasistatic speckles when no atmospheric contribution is present (dynamical speckles), i.e., when the contribution of Is 1 to Eq. 1 can be neglected. Furthermore, our study concerns a situation where the photon noise is not limiting, so that the contribution σ 2 p from the noise variance can be neglected. In such conditions, Eq. 1 can be simplified such that:</text>
<formula><location><page_2><loc_67><loc_43><loc_95><loc_46></location>σ 2 I /similarequal ( I 2 s 2 + 2 IcIs 2 ) , (2)</formula>
<text><location><page_2><loc_52><loc_39><loc_95><loc_44></location>and the present study focuses on the e ff ect of the cross-term IcIs 2. Since we can fairly assume that Is 2 /lessmuch Ic , Is 2 can be neglected except in the cross-term, and the noise variance in the raw coronagraphic image finally becomes:</text>
<formula><location><page_2><loc_69><loc_36><loc_95><loc_38></location>σ 2 I /similarequal 2 IcIs 2 . (3)</formula>
<text><location><page_2><loc_52><loc_27><loc_95><loc_36></location>Ultimately, very deep dynamic range imager, such as SPHERE, or GPI, aim to calibrate static speckles ( Ic ) such that Ic ≈ Is 2, which would largely reduce speckle pinning. Speckle nulling techniques to correct for remnant quasi-static aberrations would be a must to access deeper contrast level, nonetheless, the temporal characteristic of Is 2 remains a key parameter in these circumstances (Eq. 2).</text>
<text><location><page_2><loc_52><loc_12><loc_95><loc_27></location>From Eq. 3 a breakdown of this pinning e ff ect can be carried out at the level of di ff erential images. Raw coronagraphic images are dominated by static speckle noise. This means that the interaction between the quasi-static terms of Eq. 3, being timedependent, and static terms, assumed time-independent, can be studied through di ff erential imaging from a time series of raw coronagraphic images, which simply refers to the di ff erence in intensity between an image recorded at time t 0 +∆ t and the reference image registered at t 0. In this situation, a similar expression of the noise variance for the di ff erential images ( σ DI ) can be derived as the di ff erence of Eq. 3 evaluated at t 0 +∆ t , to that of the reference, at t 0, and reads:</text>
<formula><location><page_2><loc_68><loc_9><loc_95><loc_11></location>σ 2 DI /similarequal 2 Ic ∆ Is 2 , (4)</formula>
<text><location><page_3><loc_7><loc_89><loc_50><loc_93></location>where ∆ Is 2 represents the quasi-static evolution between the two successive images. Therefore, the quasi-static contribution can be expressed as:</text>
<formula><location><page_3><loc_24><loc_86><loc_50><loc_89></location>∆ Is 2 /similarequal σ 2 DI 2 Ic . (5)</formula>
<text><location><page_3><loc_7><loc_83><loc_50><loc_85></location>A general expression of the speckle intensity (Racine et al. 1999) is:</text>
<formula><location><page_3><loc_23><loc_80><loc_50><loc_83></location>Ispeckle ≈ (1 -S ) 0 . 34 , (6)</formula>
<text><location><page_3><loc_7><loc_77><loc_50><loc_80></location>where S can be related to the wavefront error φ using Mar'echal's approximation (Born & Wolf 1993):</text>
<formula><location><page_3><loc_23><loc_73><loc_50><loc_76></location>S ≈ 1 -( 2 πφ λ ) 2 , (7)</formula>
<text><location><page_3><loc_7><loc_69><loc_50><loc_72></location>and the contribution from static speckles to the wavefront error ( φ s 2 /lessmuch φ c , and φ s 1 neglected) can be expressed as:</text>
<formula><location><page_3><loc_22><loc_65><loc_50><loc_69></location>φ c /similarequal λ π √ 6 × √ Ic . (8)</formula>
<text><location><page_3><loc_7><loc_62><loc_50><loc_65></location>Similarly, the contribution from quasi-static speckles to the wavefront error in the di ff erential images can be expressed as:</text>
<formula><location><page_3><loc_21><loc_58><loc_50><loc_61></location>∆ φ s 2 /similarequal λ 2 π √ 6 × σ DI √ Ic . (9)</formula>
<text><location><page_3><loc_7><loc_49><loc_50><loc_57></location>Using Eqs. 8 and 9, the analysis of both direct and di ff erential images allows to characterize the temporal properties of static and quasi-static aberrations. We note that both Eq. 8 and 9 are approximated expressions relying on simple rule of thumbs / assumptions (e.g., general expression of speckle intensity, low phase aberration regime) to provide wavefront estimation per Fourier component.</text>
<section_header_level_1><location><page_3><loc_7><loc_45><loc_29><loc_46></location>3. Experimental conditions</section_header_level_1>
<section_header_level_1><location><page_3><loc_7><loc_43><loc_20><loc_44></location>3.1. Opticalsetup</section_header_level_1>
<text><location><page_3><loc_7><loc_21><loc_50><loc_42></location>SPHERE which stands for Spectro-Polarimetric High-contrast Exoplanet REsearch, is a second generation instrument for the Very Large Telescope, aiming at direct detection and spectral characterization of extrasolar planets. The instrument is now nearing completion in its final integration stage in Europe, before shipping to Chile. Being in its final test phase, it o ff ers a unique opportunity to carried out research on static and quasistatic speckles. SPHERE is a unique instrument, with first light in 2013, including a powerful extreme adaptive optics system (SAXO), an infrared di ff erential imaging camera (IRDIS), an integral field spectrograph (IFS), and a visible di ff erential polarimeter (ZIMPOL). The time series of adaptively corrected, coronagraphic images that will be discussed through this paper have been obtained using SPHERE with the IRDIS instrument, so that for the sake of clarity only the systems that have been used and are relevant will be further described.</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_21></location>The SPHERE adaptive optics for exoplanet observation (SAXO) uses a 41 × 41 actuator deformable mirror (DM) of 180 mmdiameterwith inter-actuator stroke > ± 1 µ mandamaximum stroke > ± 3.5 µ m, and a 2-axis tip-tilt mirror (TTM) with ± 0.5 mas resolution. The wavefront sensor is a 40 × 40 sub-apertures Shack-Hartmann sensor equipped with a spatial filter for aliasing minimization. During the test, no dynamical turbulence was present in the system, except the low internal turbulence (optical elements are installed inside an hermetical enclosure). Hence,</text>
<text><location><page_3><loc_52><loc_74><loc_95><loc_93></location>SAXO is used to correct for internal turbulence, static aberrations, and guarantee image and pupil stability. As image and pupil stability are essential in high-contrast imaging, di ff erential image movements due to thermo-mechanical e ff ects are measured in real-time using an auxiliary NIR tip-tilt sensor located close to the coronagraph focus plan, and corrected with a di ff erential tip-tilt mirror in the wavefront sensor arm. Similarly, pupil runout is accounted for and corrected by a pupil tip-tilt mirror at the entrance of the instrument. The near-IR Strehl ratio is > 95 %. In particular, non-common path aberrations (from the DM to the detector) are measured o ff -line using a phase diversity algorithm and compensated by reference slopes adjustment. In these conditions, static wavefront errors left uncorrected in the system are estimated at the level of ∼ 6 nm rms.</text>
<text><location><page_3><loc_52><loc_70><loc_95><loc_75></location>SPHERE o ff ers various coronagraphic possibilities (classical Lyot coronagraphs, apodized Lyot coronagraphs - ALC -, and achromatic four quadrants phase masks). During the experiment, a 5.2 λ/ D ALC has been used.</text>
<text><location><page_3><loc_52><loc_50><loc_95><loc_69></location>The infra-red dual beam imaging and spectroscopy (IRDIS) sub-system includes a spectral range from 950 to 2320 nm and an image scale of 12.25 mas per pixel (Nyquist sampling at 950nm). The field of view is greater than 11 '' square, with a 2kx2k Hawaii-II-RG detector. The main mode of IRDIS is the dual band imaging (DBI), providing images in two neighboring spectral channels with minimized di ff erential aberrations. Ten di ff erent filter couples are defined corresponding to di ff erent spectral features in modeled exoplanet spectra. During the experiment the narrow H -band couple filters have been used (centered around 1593 nm, and 1667 nm, R = 30). The DBI mode is not of the interest of the present study as we are interested in the temporal evolution of aberrations, nevertheless it allows a simulatenous characterization of quasi-static speckles at two di ff erent wavelengths for comparison / confirmation purpose.</text>
<text><location><page_3><loc_52><loc_47><loc_95><loc_50></location>Finally, the SPHERE instrument is installed on an active tripod damping system, and fully covered by an hermetic enclosure.</text>
<section_header_level_1><location><page_3><loc_52><loc_44><loc_69><loc_45></location>3.2. Thermalfunctioning</section_header_level_1>
<text><location><page_3><loc_52><loc_22><loc_95><loc_43></location>The SPHERE instrument must conform to several environmental specifications. In particular, it shall operate under a temperature range from 5 to 18 · C, while the highest gradient of temperature at the VLT is -0.9 · C / h and -1.4 · C / h for respectively 80% and 95%of the nights. In order to validate that SPHERE is compliant with such conditions, cold tests have been set up for functional and performance evaluation at di ff erent ambient temperatures within the operational range, and with realistic transient conditions reflecting situations encountered at the VLT. The whole SPHERE instrument has been installed in a cold tent (150 m 3 ) and cooled down with an e ffi cient air conditioning system. The cooling system allows to reduce by ∼ 10 · C the temperature inside the tent compared to the outside (in the integration hall). Numerous temperature probes have been installed at several critical locations in the instrument to accurately monitored the evolution inside / outside the SPHERE enclosure.</text>
<section_header_level_1><location><page_3><loc_52><loc_18><loc_79><loc_19></location>3.3. Observingrunanddatareduction</section_header_level_1>
<text><location><page_3><loc_52><loc_10><loc_95><loc_17></location>The observing run consists in recording a time series of AO close-loop IRDIS coronagraphic images. Each coronagraphic image of the time series corresponds to a series of 3 s short exposure images, averaged out over ∼ 3 mn. During the experiment, the temperature outside the enclosure (inside the cold tent) was monitored and programmed to decrease from 15 · Cwith a rate of</text>
<figure>
<location><page_4><loc_10><loc_74><loc_37><loc_93></location>
<caption>Figure 1 presents three coronagraphic images extracted from the time series: the coronagraphic image recorded at t 0 (the reference), t 0 + 10mn, and t 0 + 100mn. In Fig. 2, the corresponding differential images are shown: the di ff erence of the t 0 + 10 mn image to the reference t 0 (left), and the di ff erence of the t 0 + 100 mn image to the reference t 0 (right). The corresponding profiles for both raw and di ff erential images are presented in Fig. 3.</caption>
</figure>
<figure>
<location><page_4><loc_38><loc_74><loc_64><loc_93></location>
</figure>
<figure>
<location><page_4><loc_65><loc_74><loc_91><loc_93></location>
<caption>Fig. 1. Coronagraphic images recorded at t 0, t 0 + 10 mn, and t 0 + 100 mn. The Strehl ratio is ∼ 95 %. The arbitrary color scale and dynamic range (identical for the three images) were chosen to enhance the contrast for the sake of clarity. The field covered in the images is ∼ 2 '' square.</caption>
</figure>
<figure>
<location><page_4><loc_10><loc_40><loc_51><loc_68></location>
</figure>
<figure>
<location><page_4><loc_51><loc_40><loc_92><loc_68></location>
<caption>Fig. 2. Di ff erential coronagraphic images. Left: di ff erence of the t 0 + 10 mn image to the reference t 0. Right: di ff erence of the t 0 + 100 mn image to the reference t 0. The increase in the strength of residuals can be qualitatively observed here (the intensity range is similar in both images).</caption>
</figure>
<text><location><page_4><loc_7><loc_12><loc_50><loc_33></location>2 · C per hour. The total duration of the experiment was 100 mn. The gradient inside the enclosure was estimated at the level of 0.2 · C / h. The data-reduction process corrects for bad pixels and background, and normalizes the images with respect to exposure time and flux. Before subtraction, a fine, sub-pixel correction of the residual tip-tilt component is performed on the raw images. The analysis has been done on the two H -band filters data set available and converge to similar results, so that only one data set is presented here. Depending on the nature of the image analyzed, we applied di ff erent metrics. The contrast refers to the ratio of intensity in the raw coronagraphic image, averaged azimuthally at a given angular separation, to the peak intensity of the direct flux. When studying a di ff erential image, implying the subtraction of a reference image, the average contrast is no longer suited. The detectability is used then, which stands for the azimuthal standard deviation measured in a ring of width λ/ D .</text>
<text><location><page_4><loc_52><loc_30><loc_95><loc_32></location>It quantifies the ability to distinguish a companion at a given angular distance.</text>
<section_header_level_1><location><page_4><loc_52><loc_26><loc_76><loc_27></location>4. Analysis and interpretation</section_header_level_1>
<text><location><page_4><loc_52><loc_10><loc_95><loc_16></location>Qualitatively, the raw coronagraphic images (Fig. 1) demonstrate starlight attenuation, and exhibit static speckles with lower intensity in the AO-correction domain (from the second or third wing of the coronagraphic image to the rise of the AO cut-o ff frequency). A radial trend in speckle intensity is observable in the</text>
<figure>
<location><page_5><loc_10><loc_73><loc_49><loc_93></location>
<caption>Fig. 4. Time variability of wavefront error due to quasi-static speckles, evaluated at various angular separations (observational data).</caption>
</figure>
<figure>
<location><page_5><loc_54><loc_73><loc_93><loc_92></location>
<caption>Fig. 3. Contrast profiles of a time series of coronagraphic images (top) and detectability (1 σ ) of the di ff erential images (subtraction of the time series of coronagraphic images to the reference one, bottom)</caption>
</figure>
<text><location><page_5><loc_7><loc_51><loc_50><loc_64></location>image: speckles closer to the center of the image are brighter. The central part of the coronagraphic image is dominated by di ff raction residuals. The AO cut-o ff frequency can be readily seen in the image owing to the slope of intensity in the speckle field at 0.8 '' (20 λ / D) from the center, as expected. Outside the inner-domain defined by the AO cut-o ff frequency, the AO system cannot measure or correct the corresponding spatial frequencies. Various bright spots are observable at ∼ 40 λ/ D (twice the AO cut-o ff frequency) and correspond to the inter-actuator pitch spatial frequency.</text>
<text><location><page_5><loc_7><loc_36><loc_50><loc_51></location>As observed in Fig. 1 and presented in Fig. 3 (top curves), raw coronagraphic images are dominated by the static contribution, for which contrast profiles are stable over time at any angular separation. Raw coronagraphic images are dominated by static speckle noise, as no evolution in the speckle field is visually detectable over the three images presented that cover the temporal duration of the experiment. This is consistent with the fact that the interaction between the quasi-static terms of Eq. 3, being time-dependent, and static terms, assumed timeindependent, can be studied through di ff erential imaging from a time series of raw coronagraphic images, and not directly at the level of raw images.</text>
<text><location><page_5><loc_7><loc_10><loc_50><loc_35></location>The static wavefront error amplitude has been evaluated on the raw coronagraphic images using Eq. 8, and converges to the value of ∼ 5 nm rms, though it might be slightly underestimated (see Sect. 3.1). This is basically a factor of 10 lower than the estimation obtained on the HOT bench, and contribute to the increase of dynamic range of the instrument to that of the performance obtained with the HOT bench in both classical and differential imaging (virtually by an order of magnitude). By contrast to raw images, an evolution in the speckle field is seen in the di ff erential images. The profiles presented in Fig. 3 (bottom curves) clearly indicate that the detectability level degrades with time. These profiles demonstrate that raw coronagraphic images evolve temporally, being less and less correlated with the reference over time, even though such an evolution cannot be readily seen in raw images. Further, this degradation of the detectability is e ff ective at all angular separations. This result is compliant with observations formally reported in Paper I. From the time series of di ff erential images, using Eq. 9, we derive the quasistatic wavefront error contribution per Fourier component, of the pinning e ff ect at several angular separations. Figure 4 shows</text>
<text><location><page_5><loc_52><loc_39><loc_95><loc_65></location>the temporal evolution of φ s 2 at 3, and 10 λ/ D , i.e. the quasistatic wavefront error (rms) as function of time at several angular separations. It clearly indicates that φ s 2 is time-dependent and increases with time, justifying the constant degradation of detectability observed in Fig. 3 (bottom curves). This is true for all angular separations, and the shorter the separation the higher the amplitude. Quantitatively, the level of quasi-static wavefront error that limits the sensitivity in the di ff erential images ( ∼ 10 -7 to ∼ 10 -8 , 1 σ ) is found to be in the regime of ∼ 0.1Å to 1Å. The power law of the temporal evolution of the quasi-static wavefront error is derived and exhibits a similar tendency whatever the angular position in the field. It can be fitted by a linear function of time. The parameters for the linear fits are presented in the legend of Fig. 4, and can be used to extrapolate a model for quasistatic speckle evolution in the context of high-contrast imaging instruments. From the linear fits derived at various angular separations, and considering that the di ff erence in amplitude is not significant , we attempt to generalize the expression of the power law for any angular position in the field, which reads as the following approximation:</text>
<formula><location><page_5><loc_64><loc_36><loc_95><loc_38></location>∆ φ s 2( t ) /similarequal 0 . 065 + 0 . 001 × t , (10)</formula>
<text><location><page_5><loc_52><loc_34><loc_95><loc_36></location>where t is the time in minutes, and ∆ φ 2 is expressed in nm rms.</text>
<text><location><page_5><loc_52><loc_10><loc_95><loc_35></location>s In Paper I, the parameters found for the fit were 0.250 for the value at the origin, and a slope of 0.012. This means that SPHERE is definitely more stable in term of thermo-mechanical variations than the HOT bench, though this was expected (a slope reduced by at least an order of magnitude, since data were not recorded a transient regime as performed here, but in stabilized temperature environment). While scaling the fit parameters to model quasi-static temporal evolution observed with the HOT bench to real instrument was highly non-trivial as it significantly dependents on the instrument environment (temperature or pressure changes, mechanical flexures, etc...), we believe that the estimates found with SPHERE and presented in Eq. 10 are representative of the new high-contrast imaging instrument generation that SPHERE represents, and can be used as such. In our data we found that quasi-static wavefront error increases with ∼ 0.7Å per minute. Quasi-static speckles, fast-evolving on the level of a few angstroms over a timescale of few seconds, explained the evolution of our sensitivity through amplification of the systematics. It is believed that this e ff ect is a consequence</text>
<figure>
<location><page_6><loc_9><loc_73><loc_48><loc_92></location>
<caption>Fig. 5. Quasi-static aberrations power spectral density at various timescales (using Eq. 5).</caption>
</figure>
<text><location><page_6><loc_7><loc_58><loc_50><loc_67></location>of thermal and mechanical instabilities (pressure changes, mechanical flexures...) of the optical bench. This is qualitatively supported by the fact that outside the AO control radius, a characteristic 'butterfly shape' drawn by the speckle pattern in the di ff erential image at t 0 + 100 mn is observable (Fig. 2, right). This indicates that a beam-shift is at work, though it is di ffi cult to obtained quantitative information on it.</text>
<text><location><page_6><loc_7><loc_32><loc_50><loc_58></location>I functions described in Sect. 2 essentially represent power spectral densities (PSD). While Ic symbolizes the PSD of the static wavefront, ∆ Is 2 stands for the PSD of the di ff erential aberrations, which is calculated by Eq. 5. Plotting Eq. 5 gives access to the quasi-static aberration PSD as function of time (Fig. 5). From the DSPs presented in Fig. 5, we can observe that: (1 / ) at very low frequencies (from 0.1 to 3 cycles per pupil) the PSD is temporally roughly stable and exhibits a f 0 power law, where f is the spatial frequency, while it must be pointed out that in this frequency domain, Eq. 5 might not be entirely valid, (2 / ) at low frequencies (from 3 to 8 cycles per pupil) the PSD exhibits a f -5 power law, (3 / ) at intermediate frequencies (from 8 to 20 cycles per pupil) the PSD exhibits a f 0 power law, then essentially dominated by a white noise, (4 / ) at high frequencies (outside the AO control domain, from 20 to 30 cycles per pupil, noise dominated at farther spatial frequencies) the power law is again f -5 . From Fig. 5 it is di ffi cult to extract further unambiguous informations, or initiate preliminary explanations, such as the f -5 power law being in contradiction with the generally adopted and standard PSD slope of f -2 for surface optics (static aberrations).</text>
<section_header_level_1><location><page_6><loc_7><loc_29><loc_19><loc_30></location>5. Conclusion</section_header_level_1>
<text><location><page_6><loc_7><loc_10><loc_50><loc_28></location>In this paper, we confirm the results formerly reported in Paper I with new measurements, and derive a practical and generalized expression to model quasi-static speckles temporal evolution for any angular position in the field (Eq.10), in the context of the forthcoming high-contrast planet imagers. Quasi-static aberrations observed in a time series of extreme adaptive opticscorrected coronagraphic images exhibit a linear power law with time and are interacting through the pinning e ff ect with static aberrations. We examine and discuss this e ff ect using the statistical model of the noise variance in high-contrast imaging proposed by Soummer et al. (2007), where the e ff ect of pinning quasi-static to static speckles as described by the expression for the variance (Eq. 9) is found to reflect the situation in our data set fairly well.</text>
<text><location><page_6><loc_52><loc_79><loc_95><loc_93></location>We found that quasi-static wavefront error increases with a rate of ∼ 0.7Å per minute. In this context, Eq. 10 is meant to feed complex system analysis for timescale specifications and impact assessments in the context of calibration / operational strategies for high-contrast imaging class instruments. In addition, Eq. 5 provides a useful insight in the PSD of quasi-static aberrations in the system, and at first glance to identify what moves in the system. The proposed model of quasi-static speckles temporal evolution can be used to derive timescales for calibration / operational aspects, such as ADI, or non-common path aberrations correction.</text>
<text><location><page_6><loc_52><loc_71><loc_95><loc_79></location>The case considered in this present paper represents a static system subject to a thermal gradient. The foreseen impact of rotating components in the instrument, such as, e.g., the atmospheric dispersion compensators (ADCs, not seen by the AO system), or the derotator (seen by AO system) will be treated in a separated study.</text>
<text><location><page_6><loc_52><loc_66><loc_95><loc_70></location>Acknowledgements. SPHERE is an instrument designed and built by a consortium consisting of IPAG, MPIA, LAM, LESIA, Laboratoire Lagrange, INAF, Observatoire de Gen'eve, ETH, NOVA, ONERA, and ASTRON in collaboration with ESO.</text>
<section_header_level_1><location><page_6><loc_52><loc_62><loc_61><loc_63></location>References</section_header_level_1>
<text><location><page_6><loc_52><loc_59><loc_95><loc_61></location>Beuzit, J.-L., Feldt, M., Dohlen, K., et al. 2008, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7014</text>
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<list_item><location><page_6><loc_52><loc_57><loc_95><loc_59></location>Boccaletti, A., Chauvin, G., Lagrange, A.-M., & Marchis, F. 2003, A&A, 410, 283</list_item>
<list_item><location><page_6><loc_52><loc_56><loc_87><loc_57></location>Boccaletti, A., Riaud, P., Baudoz, P., et al. 2004, PASP, 116, 1061</list_item>
<list_item><location><page_6><loc_52><loc_55><loc_82><loc_56></location>Born, M. & Wolf, E. 1993, Cambridge University Press</list_item>
<list_item><location><page_6><loc_52><loc_54><loc_92><loc_55></location>Hinkley, S., Oppenheimer, B. R., Soummer, R., et al. 2007, ApJ, 654, 633</list_item>
<list_item><location><page_6><loc_52><loc_53><loc_93><loc_54></location>Hinkley, S., Oppenheimer, B. R., Zimmerman, N., et al. 2011, PASP, 123, 74</list_item>
<list_item><location><page_6><loc_52><loc_51><loc_95><loc_52></location>Hodapp, K. W., Suzuki, R., Tamura, M., et al. 2008, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7014</list_item>
<list_item><location><page_6><loc_52><loc_48><loc_95><loc_51></location>Lafreni'ere, D., Marois, C., Doyon, R., Nadeau, D., & Artigau, ' E. 2007, ApJ, 660, 770</list_item>
<list_item><location><page_6><loc_52><loc_44><loc_95><loc_48></location>Macintosh, B. A., Graham, J. R., Palmer, D. W., et al. 2008, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7015, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series</list_item>
<list_item><location><page_6><loc_52><loc_42><loc_95><loc_44></location>Marois, C., Lafreni'ere, D., Doyon, R., Macintosh, B., & Nadeau, D. 2006, ApJ, 641, 556</list_item>
<list_item><location><page_6><loc_52><loc_40><loc_95><loc_42></location>Marois, C., Nadeau, D., Doyon, R., Racine, R., & Walker, G. A. H. 2003, in IAU Symposium, Vol. 211, Brown Dwarfs, ed. E. Mart'ın, 275-+</list_item>
<list_item><location><page_6><loc_52><loc_38><loc_95><loc_40></location>Martinez, P., Loose, C., Aller Carpentier, E., & Kasper, M. 2012, A&A, 541, A136</list_item>
<list_item><location><page_6><loc_52><loc_36><loc_95><loc_38></location>Racine, R., Walker, G. A. H., Nadeau, D., Doyon, R., & Marois, C. 1999, PASP, 111, 587</list_item>
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<text><location><page_6><loc_52><loc_35><loc_91><loc_35></location>Soummer, R., Ferrari, A., Aime, C., & Jolissaint, L. 2007, ApJ, 669, 642</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Context. Observing sequences have shown that the major noise source limitation in high-contrast imaging is due to the presence of quasi-static speckles. The timescale on which quasi-static speckles evolve, is determined by various factors, among others mechanical or thermal deformations. Aims. Understanding of these time-variable instrumental speckles, and especially their interaction with other aberrations, referred to as the pinning e ff ect, is paramount for the search of faint stellar companions. The temporal evolution of quasi-static speckles is for instance required for a quantification of the gain expected when using angular di ff erential imaging (ADI), and to determine the interval on which speckle nulling techniques must be carried out. Methods. Following an early analysis of a time series of adaptively corrected, coronagraphic images obtained in a laboratory condition with the High-Order Test bench (HOT) at ESO Headquarters, we confirm our results with new measurements carried out with the SPHERE instrument during its final test phase in Europe. The analysis of the residual speckle pattern in both direct and di ff erential coronagraphic images enables the characterization of the temporal stability of quasi-static speckles. Data were obtained in a thermally actively controlled environment reproducing realistic conditions encountered at the telescope. Results. The temporal evolution of the quasi-static wavefront error exhibits linear power law, which can be used to model quasi-static speckle evolution in the context of forthcoming high-contrast imaging instruments, with implications for instrumentation (design, observing strategies, data reduction). Such a model can be used for instance to derive the timescale on which non-common path aberrations must be sensed and corrected. We found in our data that quasi-static wavefront error increases with ∼ 0.7Å per minute. Key words. Techniques: high angular resolution -Instrumentation: high angular resolution -Telescopes",
"pages": [
1
]
},
{
"title": "II. Refine model for quasi-static speckle temporal evolution for VLT/SPHERE",
"content": "P. Martinez 1 , M. Kasper 2 , A. Costille 3 , J.F. Sauvage 4 , K. Dohlen 5 , P. Puget 3 , and J.L. Beuzit 3 Preprint online version: October 9, 2018",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Observing sequences have shown that the major noise source limitation in high-contrast imaging is due to the presence of instrumental speckles, and more precisely to quasi-static speckles (Marois et al. 2003; Boccaletti et al. 2003, 2004; Hinkley et al. 2007). Speckle noise originates from wavefront errors caused by various independent sources, and evolves on di ff erent timescales pending to their nature. The first class of speckle to overcome comes from the large, dynamical wavefront error that the atmosphere generates, but real-time adaptive optics systems measure and correct it down to fundamental limitations. The fast-varying speckle noise floor left uncorrected by such systems would average out over time, as it consists in a random and uncorrelated noise for which the intensity variance converges to null contribution for an infinitely long exposure. For a non-photon noise limited observing run, speckle noise associated to wavefront aberrations introduced in the optical train are fundamental to tackle. In this context, instrumental speckles can be divided into two di ff erent flavors: long-timescale wavefront errors present in the optical train (e.g., optical quality, misalignment errors) that generate static speckles that constitute a deterministic contribution to the noise variance, and slowly-varying instrumental wavefront aberrations, amplitude and phase errors, originating from various causes, among others mechanical or thermal deformations. The latest evolve on a shorter timescale than long-lived aberrations, and are the so-called quasi-static speckles. Instrumental speckles average to form a fixed pattern, which can be calibrated to a certain extent. A deterministic contribution to the noise variance such as static speckles can easily be calibrated, while using a reference image, time-variable quasistatic noise can be subtracted as well, but its temporal evolution ultimately limit this possibility. In particular it is understood that some timescales have a larger impact than others. This is especially true as quasi-static speckles interact with other aberrations, referred to as the pinning e ff ect , or speckle cross terms. The timescale of quasi-static speckles evolution is essential to understand and predict the performance of the new generation of instruments such as SPHERE (Beuzit et al. 2008), GPI (Macintosh et al. 2008), HiCIAO (Hodapp et al. 2008), and Project 1640 (Hinkley et al. 2011). The temporal evolution of these quasi-static speckles is in particular needed for the quantification of the gain expected with angular di ff erential imaging (ADI, Marois et al. 2006), as well as to determine the timescale on which speckle nulling techniques should be carried out. For instance, a typical hour-long ADI observing sequence provides a partial self-calibration of the residuals after a rotation of ∼ 1 λ/ D at a given angular separation, which generally requires less than few minutes (e.g., 5 to 7 mn at 1 '' on a 8-m class telescope for stars near the meridian in H -band), though it depends on wavelength, telescope latitude, and object declination. Residual speckles with decorrelation times faster than the time needed to obtain the ADI reference image cannot then be removed, while quasi-static speckles associated with larger timescales can largely be subtracted. In this context, several authors have investigated the decorrelation timescale of quasi-static residuals in the particular context of ADI but at moderate 20-40 % Strehl levels (Marois et al. 2006; Lafreni'ere et al. 2007; Hinkley et al. 2007), while in a former paper (Martinez et al. 2012, hereafter Paper I), we explored the realm of very high Strehl ratios (extreme adaptive optic systems, XAO). In paper I, we analyzed a time series of adaptively corrected, coronagraphic images recorded in the laboratory with the High-Order Test bench, a versatile high-contrast imaging, adaptive optics bench developed at ESO. We shown that quasi-static aberrations exhibit a linear power law with time and are interacting through the pinning e ff ect with static speckles. We examined and discussed this e ff ect using the statistical model of the noise variance in high-contrast imaging proposed by Soummer et al. (2007). In particular, we found that quasistatic speckles, fast-evolving on the level of a few angstroms to nanometers over a timescale of few seconds, explained the evolution of our sensitivity through amplification of the systematics. It is believed that this e ff ect is a consequence of thermal and mechanical instabilities of the optical bench. The HOT bench is indeed localized in a classical laboratory setting, and was not initially designed to guarantee stability, nor mechanical stability at the level that would be required / expected for an actual highcontrast imaging instrument. Indeed Paper I emphasizes the importance of such stability for the next generation of high-contrast instruments, but the estimates found in this former analysis (amplitude, and slope of the temporal evolution) could not fairly be considered as representative of a realistic situation in order to a ff ect operational aspects or designs of nowadays / future real instruments. In this paper, we confirm the results presented in Paper I with more representative measurements. We analyze a time series of adaptively corrected, coronagraphic images with the SPHERE instrument in a thermally actively controlled environment reproducing realistic conditions encountered at the telescope. In this context, we propose a refine model of quasi-static speckle evolution that can be used for forthcoming high-contrast imaging instrument classes that SPHERE represents. The paper reads as follow: in Sect. 2, we briefly recall the formalism of the statistical model of the noise variance in highcontrast imaging proposed by Soummer et al. (2007) and used in Paper I to discuss our former results, in Sect. 3, the experimental conditions are described, and in Sect. 4 we analyze and discuss the results. Finally, in Sect. 5, we draw conclusions.",
"pages": [
1,
2
]
},
{
"title": "2. Speckle noise and dynamical range",
"content": "In Paper I, we examined and discussed our data using the statistical model of the noise variance in high-contrast imaging pro- posed by Soummer et al. (2007). Following the same formalism as for Paper I, we briefly recall here the main equations. Soummer et al. (2007) proposed the following analytical expression for the variance of the intensity, including speckle and photon noise in the presence of static, quasi-static, and fast varying aberrations, in the context of a propagation through a coronagraph: where I denotes the intensity, σ 2 p is the variance of the photon noise, and N is the ratio of fast-speckle and slow-speckle lifetimes. The intensity produced by the deterministic part of the wavefront, including static aberrations, is denoted by Ic , while the Is terms corresponds to the halo produced by random intensity variations, i.e. atmospheric ( Is 1) and quasi-static contributions ( Is 2). In this generalized expression of the variance, several contributions can be identified by order of appearance: (1 / ) the atmospheric halo, (2 / ) the quasi-static halo, (3 / ) the atmospheric pinning term, the speckle pinning of the static aberrations by the fast evolving atmospheric speckles, (4 / ) the speckle pinning of the static by quasi-static speckles, and finally (5 / ) the speckle pinning of the atmospheric speckles by quasi-static speckles. Equation 1 provides useful insights in the understanding of the impact of quasi-static speckles and their interactions through the pinning phenomenon with other aberrations present in a real instrument. As for Paper I, we focus our analysis on contribution (4 / ) to this noise budget in XAO coronagraphic images. In particular, we are interested in the speckle pinning of the static by the quasistatic speckles when no atmospheric contribution is present (dynamical speckles), i.e., when the contribution of Is 1 to Eq. 1 can be neglected. Furthermore, our study concerns a situation where the photon noise is not limiting, so that the contribution σ 2 p from the noise variance can be neglected. In such conditions, Eq. 1 can be simplified such that: and the present study focuses on the e ff ect of the cross-term IcIs 2. Since we can fairly assume that Is 2 /lessmuch Ic , Is 2 can be neglected except in the cross-term, and the noise variance in the raw coronagraphic image finally becomes: Ultimately, very deep dynamic range imager, such as SPHERE, or GPI, aim to calibrate static speckles ( Ic ) such that Ic ≈ Is 2, which would largely reduce speckle pinning. Speckle nulling techniques to correct for remnant quasi-static aberrations would be a must to access deeper contrast level, nonetheless, the temporal characteristic of Is 2 remains a key parameter in these circumstances (Eq. 2). From Eq. 3 a breakdown of this pinning e ff ect can be carried out at the level of di ff erential images. Raw coronagraphic images are dominated by static speckle noise. This means that the interaction between the quasi-static terms of Eq. 3, being timedependent, and static terms, assumed time-independent, can be studied through di ff erential imaging from a time series of raw coronagraphic images, which simply refers to the di ff erence in intensity between an image recorded at time t 0 +∆ t and the reference image registered at t 0. In this situation, a similar expression of the noise variance for the di ff erential images ( σ DI ) can be derived as the di ff erence of Eq. 3 evaluated at t 0 +∆ t , to that of the reference, at t 0, and reads: where ∆ Is 2 represents the quasi-static evolution between the two successive images. Therefore, the quasi-static contribution can be expressed as: A general expression of the speckle intensity (Racine et al. 1999) is: where S can be related to the wavefront error φ using Mar'echal's approximation (Born & Wolf 1993): and the contribution from static speckles to the wavefront error ( φ s 2 /lessmuch φ c , and φ s 1 neglected) can be expressed as: Similarly, the contribution from quasi-static speckles to the wavefront error in the di ff erential images can be expressed as: Using Eqs. 8 and 9, the analysis of both direct and di ff erential images allows to characterize the temporal properties of static and quasi-static aberrations. We note that both Eq. 8 and 9 are approximated expressions relying on simple rule of thumbs / assumptions (e.g., general expression of speckle intensity, low phase aberration regime) to provide wavefront estimation per Fourier component.",
"pages": [
2,
3
]
},
{
"title": "3.1. Opticalsetup",
"content": "SPHERE which stands for Spectro-Polarimetric High-contrast Exoplanet REsearch, is a second generation instrument for the Very Large Telescope, aiming at direct detection and spectral characterization of extrasolar planets. The instrument is now nearing completion in its final integration stage in Europe, before shipping to Chile. Being in its final test phase, it o ff ers a unique opportunity to carried out research on static and quasistatic speckles. SPHERE is a unique instrument, with first light in 2013, including a powerful extreme adaptive optics system (SAXO), an infrared di ff erential imaging camera (IRDIS), an integral field spectrograph (IFS), and a visible di ff erential polarimeter (ZIMPOL). The time series of adaptively corrected, coronagraphic images that will be discussed through this paper have been obtained using SPHERE with the IRDIS instrument, so that for the sake of clarity only the systems that have been used and are relevant will be further described. The SPHERE adaptive optics for exoplanet observation (SAXO) uses a 41 × 41 actuator deformable mirror (DM) of 180 mmdiameterwith inter-actuator stroke > ± 1 µ mandamaximum stroke > ± 3.5 µ m, and a 2-axis tip-tilt mirror (TTM) with ± 0.5 mas resolution. The wavefront sensor is a 40 × 40 sub-apertures Shack-Hartmann sensor equipped with a spatial filter for aliasing minimization. During the test, no dynamical turbulence was present in the system, except the low internal turbulence (optical elements are installed inside an hermetical enclosure). Hence, SAXO is used to correct for internal turbulence, static aberrations, and guarantee image and pupil stability. As image and pupil stability are essential in high-contrast imaging, di ff erential image movements due to thermo-mechanical e ff ects are measured in real-time using an auxiliary NIR tip-tilt sensor located close to the coronagraph focus plan, and corrected with a di ff erential tip-tilt mirror in the wavefront sensor arm. Similarly, pupil runout is accounted for and corrected by a pupil tip-tilt mirror at the entrance of the instrument. The near-IR Strehl ratio is > 95 %. In particular, non-common path aberrations (from the DM to the detector) are measured o ff -line using a phase diversity algorithm and compensated by reference slopes adjustment. In these conditions, static wavefront errors left uncorrected in the system are estimated at the level of ∼ 6 nm rms. SPHERE o ff ers various coronagraphic possibilities (classical Lyot coronagraphs, apodized Lyot coronagraphs - ALC -, and achromatic four quadrants phase masks). During the experiment, a 5.2 λ/ D ALC has been used. The infra-red dual beam imaging and spectroscopy (IRDIS) sub-system includes a spectral range from 950 to 2320 nm and an image scale of 12.25 mas per pixel (Nyquist sampling at 950nm). The field of view is greater than 11 '' square, with a 2kx2k Hawaii-II-RG detector. The main mode of IRDIS is the dual band imaging (DBI), providing images in two neighboring spectral channels with minimized di ff erential aberrations. Ten di ff erent filter couples are defined corresponding to di ff erent spectral features in modeled exoplanet spectra. During the experiment the narrow H -band couple filters have been used (centered around 1593 nm, and 1667 nm, R = 30). The DBI mode is not of the interest of the present study as we are interested in the temporal evolution of aberrations, nevertheless it allows a simulatenous characterization of quasi-static speckles at two di ff erent wavelengths for comparison / confirmation purpose. Finally, the SPHERE instrument is installed on an active tripod damping system, and fully covered by an hermetic enclosure.",
"pages": [
3
]
},
{
"title": "3.2. Thermalfunctioning",
"content": "The SPHERE instrument must conform to several environmental specifications. In particular, it shall operate under a temperature range from 5 to 18 · C, while the highest gradient of temperature at the VLT is -0.9 · C / h and -1.4 · C / h for respectively 80% and 95%of the nights. In order to validate that SPHERE is compliant with such conditions, cold tests have been set up for functional and performance evaluation at di ff erent ambient temperatures within the operational range, and with realistic transient conditions reflecting situations encountered at the VLT. The whole SPHERE instrument has been installed in a cold tent (150 m 3 ) and cooled down with an e ffi cient air conditioning system. The cooling system allows to reduce by ∼ 10 · C the temperature inside the tent compared to the outside (in the integration hall). Numerous temperature probes have been installed at several critical locations in the instrument to accurately monitored the evolution inside / outside the SPHERE enclosure.",
"pages": [
3
]
},
{
"title": "3.3. Observingrunanddatareduction",
"content": "The observing run consists in recording a time series of AO close-loop IRDIS coronagraphic images. Each coronagraphic image of the time series corresponds to a series of 3 s short exposure images, averaged out over ∼ 3 mn. During the experiment, the temperature outside the enclosure (inside the cold tent) was monitored and programmed to decrease from 15 · Cwith a rate of 2 · C per hour. The total duration of the experiment was 100 mn. The gradient inside the enclosure was estimated at the level of 0.2 · C / h. The data-reduction process corrects for bad pixels and background, and normalizes the images with respect to exposure time and flux. Before subtraction, a fine, sub-pixel correction of the residual tip-tilt component is performed on the raw images. The analysis has been done on the two H -band filters data set available and converge to similar results, so that only one data set is presented here. Depending on the nature of the image analyzed, we applied di ff erent metrics. The contrast refers to the ratio of intensity in the raw coronagraphic image, averaged azimuthally at a given angular separation, to the peak intensity of the direct flux. When studying a di ff erential image, implying the subtraction of a reference image, the average contrast is no longer suited. The detectability is used then, which stands for the azimuthal standard deviation measured in a ring of width λ/ D . It quantifies the ability to distinguish a companion at a given angular distance.",
"pages": [
3,
4
]
},
{
"title": "4. Analysis and interpretation",
"content": "Qualitatively, the raw coronagraphic images (Fig. 1) demonstrate starlight attenuation, and exhibit static speckles with lower intensity in the AO-correction domain (from the second or third wing of the coronagraphic image to the rise of the AO cut-o ff frequency). A radial trend in speckle intensity is observable in the image: speckles closer to the center of the image are brighter. The central part of the coronagraphic image is dominated by di ff raction residuals. The AO cut-o ff frequency can be readily seen in the image owing to the slope of intensity in the speckle field at 0.8 '' (20 λ / D) from the center, as expected. Outside the inner-domain defined by the AO cut-o ff frequency, the AO system cannot measure or correct the corresponding spatial frequencies. Various bright spots are observable at ∼ 40 λ/ D (twice the AO cut-o ff frequency) and correspond to the inter-actuator pitch spatial frequency. As observed in Fig. 1 and presented in Fig. 3 (top curves), raw coronagraphic images are dominated by the static contribution, for which contrast profiles are stable over time at any angular separation. Raw coronagraphic images are dominated by static speckle noise, as no evolution in the speckle field is visually detectable over the three images presented that cover the temporal duration of the experiment. This is consistent with the fact that the interaction between the quasi-static terms of Eq. 3, being time-dependent, and static terms, assumed timeindependent, can be studied through di ff erential imaging from a time series of raw coronagraphic images, and not directly at the level of raw images. The static wavefront error amplitude has been evaluated on the raw coronagraphic images using Eq. 8, and converges to the value of ∼ 5 nm rms, though it might be slightly underestimated (see Sect. 3.1). This is basically a factor of 10 lower than the estimation obtained on the HOT bench, and contribute to the increase of dynamic range of the instrument to that of the performance obtained with the HOT bench in both classical and differential imaging (virtually by an order of magnitude). By contrast to raw images, an evolution in the speckle field is seen in the di ff erential images. The profiles presented in Fig. 3 (bottom curves) clearly indicate that the detectability level degrades with time. These profiles demonstrate that raw coronagraphic images evolve temporally, being less and less correlated with the reference over time, even though such an evolution cannot be readily seen in raw images. Further, this degradation of the detectability is e ff ective at all angular separations. This result is compliant with observations formally reported in Paper I. From the time series of di ff erential images, using Eq. 9, we derive the quasistatic wavefront error contribution per Fourier component, of the pinning e ff ect at several angular separations. Figure 4 shows the temporal evolution of φ s 2 at 3, and 10 λ/ D , i.e. the quasistatic wavefront error (rms) as function of time at several angular separations. It clearly indicates that φ s 2 is time-dependent and increases with time, justifying the constant degradation of detectability observed in Fig. 3 (bottom curves). This is true for all angular separations, and the shorter the separation the higher the amplitude. Quantitatively, the level of quasi-static wavefront error that limits the sensitivity in the di ff erential images ( ∼ 10 -7 to ∼ 10 -8 , 1 σ ) is found to be in the regime of ∼ 0.1Å to 1Å. The power law of the temporal evolution of the quasi-static wavefront error is derived and exhibits a similar tendency whatever the angular position in the field. It can be fitted by a linear function of time. The parameters for the linear fits are presented in the legend of Fig. 4, and can be used to extrapolate a model for quasistatic speckle evolution in the context of high-contrast imaging instruments. From the linear fits derived at various angular separations, and considering that the di ff erence in amplitude is not significant , we attempt to generalize the expression of the power law for any angular position in the field, which reads as the following approximation: where t is the time in minutes, and ∆ φ 2 is expressed in nm rms. s In Paper I, the parameters found for the fit were 0.250 for the value at the origin, and a slope of 0.012. This means that SPHERE is definitely more stable in term of thermo-mechanical variations than the HOT bench, though this was expected (a slope reduced by at least an order of magnitude, since data were not recorded a transient regime as performed here, but in stabilized temperature environment). While scaling the fit parameters to model quasi-static temporal evolution observed with the HOT bench to real instrument was highly non-trivial as it significantly dependents on the instrument environment (temperature or pressure changes, mechanical flexures, etc...), we believe that the estimates found with SPHERE and presented in Eq. 10 are representative of the new high-contrast imaging instrument generation that SPHERE represents, and can be used as such. In our data we found that quasi-static wavefront error increases with ∼ 0.7Å per minute. Quasi-static speckles, fast-evolving on the level of a few angstroms over a timescale of few seconds, explained the evolution of our sensitivity through amplification of the systematics. It is believed that this e ff ect is a consequence of thermal and mechanical instabilities (pressure changes, mechanical flexures...) of the optical bench. This is qualitatively supported by the fact that outside the AO control radius, a characteristic 'butterfly shape' drawn by the speckle pattern in the di ff erential image at t 0 + 100 mn is observable (Fig. 2, right). This indicates that a beam-shift is at work, though it is di ffi cult to obtained quantitative information on it. I functions described in Sect. 2 essentially represent power spectral densities (PSD). While Ic symbolizes the PSD of the static wavefront, ∆ Is 2 stands for the PSD of the di ff erential aberrations, which is calculated by Eq. 5. Plotting Eq. 5 gives access to the quasi-static aberration PSD as function of time (Fig. 5). From the DSPs presented in Fig. 5, we can observe that: (1 / ) at very low frequencies (from 0.1 to 3 cycles per pupil) the PSD is temporally roughly stable and exhibits a f 0 power law, where f is the spatial frequency, while it must be pointed out that in this frequency domain, Eq. 5 might not be entirely valid, (2 / ) at low frequencies (from 3 to 8 cycles per pupil) the PSD exhibits a f -5 power law, (3 / ) at intermediate frequencies (from 8 to 20 cycles per pupil) the PSD exhibits a f 0 power law, then essentially dominated by a white noise, (4 / ) at high frequencies (outside the AO control domain, from 20 to 30 cycles per pupil, noise dominated at farther spatial frequencies) the power law is again f -5 . From Fig. 5 it is di ffi cult to extract further unambiguous informations, or initiate preliminary explanations, such as the f -5 power law being in contradiction with the generally adopted and standard PSD slope of f -2 for surface optics (static aberrations).",
"pages": [
4,
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6
]
},
{
"title": "5. Conclusion",
"content": "In this paper, we confirm the results formerly reported in Paper I with new measurements, and derive a practical and generalized expression to model quasi-static speckles temporal evolution for any angular position in the field (Eq.10), in the context of the forthcoming high-contrast planet imagers. Quasi-static aberrations observed in a time series of extreme adaptive opticscorrected coronagraphic images exhibit a linear power law with time and are interacting through the pinning e ff ect with static aberrations. We examine and discuss this e ff ect using the statistical model of the noise variance in high-contrast imaging proposed by Soummer et al. (2007), where the e ff ect of pinning quasi-static to static speckles as described by the expression for the variance (Eq. 9) is found to reflect the situation in our data set fairly well. We found that quasi-static wavefront error increases with a rate of ∼ 0.7Å per minute. In this context, Eq. 10 is meant to feed complex system analysis for timescale specifications and impact assessments in the context of calibration / operational strategies for high-contrast imaging class instruments. In addition, Eq. 5 provides a useful insight in the PSD of quasi-static aberrations in the system, and at first glance to identify what moves in the system. The proposed model of quasi-static speckles temporal evolution can be used to derive timescales for calibration / operational aspects, such as ADI, or non-common path aberrations correction. The case considered in this present paper represents a static system subject to a thermal gradient. The foreseen impact of rotating components in the instrument, such as, e.g., the atmospheric dispersion compensators (ADCs, not seen by the AO system), or the derotator (seen by AO system) will be treated in a separated study. Acknowledgements. SPHERE is an instrument designed and built by a consortium consisting of IPAG, MPIA, LAM, LESIA, Laboratoire Lagrange, INAF, Observatoire de Gen'eve, ETH, NOVA, ONERA, and ASTRON in collaboration with ESO.",
"pages": [
6
]
},
{
"title": "References",
"content": "Beuzit, J.-L., Feldt, M., Dohlen, K., et al. 2008, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7014 Soummer, R., Ferrari, A., Aime, C., & Jolissaint, L. 2007, ApJ, 669, 642",
"pages": [
6
]
}
]
2013A&A...554A.127M
https://arxiv.org/pdf/1303.3803.pdf
<document>
<section_header_level_1><location><page_1><loc_13><loc_85><loc_88><loc_87></location>HAWK-I infrared supernova search in starburst galaxies /star</section_header_level_1>
<text><location><page_1><loc_10><loc_81><loc_92><loc_83></location>M. Miluzio 1 , E. Cappellaro 2 , M.T. Botticella 3 , G. Cresci 4 , L. Greggio 2 , F. Mannucci 4 , S. Benetti 2 , Bufano, F. 5 , Elias-Rosa, N. 6 , A. Pastorello 2 , M. Turatto 2 , Zampieri, L. 2</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_76><loc_71><loc_79></location>1 Department of Astronomy, Padova University, Vicolo dell'Osservatorio 3, I-35122, Padova, Italy e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_68><loc_76></location>2 INAF, Osservatorio Astronomico di Padova, vicolo dell'Osservatorio 5, Padova, 35122 Italy</list_item>
<list_item><location><page_1><loc_11><loc_74><loc_68><loc_75></location>3 INAF, Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, Napoli, 80131 Italy</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_64><loc_74></location>4 INAF, Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, Firenze, 50125 Italy</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_71><loc_73></location>5 Departamento de Ciencias Fisicas, Universidad Andr'es Bello, Av. Rep'ublica 252, Santiago, Chile</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_76><loc_72></location>6 Institut de Ci'encies de l'Espai (IEEC-CSIC), Facultat de Ci'encies, Campus UAB, Bellaterra, 08193 Spain</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_68><loc_41><loc_69></location>Received: ????; Revised: ??????; Accepted: ?????</text>
<section_header_level_1><location><page_1><loc_47><loc_66><loc_55><loc_67></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_61><loc_91><loc_65></location>Context. The use of SN rates to probe explosion scenarios and to trace the cosmic star formation history received a boost from a number of synoptic surveys. There has been a recent claim of a mismatch by a factor of two between star formation and core collapse SN rates, and di ff erent explanations have been proposed for this discrepancy.</text>
<text><location><page_1><loc_11><loc_59><loc_91><loc_61></location>Aims. We attempted an independent test of the relation between star formation and supernova rates in the extreme environment of starburst galaxies, where both star formation and extinction are extremely high.</text>
<text><location><page_1><loc_11><loc_53><loc_91><loc_59></location>Methods. To this aim we conducted an infrared supernova search in a sample of local starburts galaxies. The rational to search in the infrared is to reduce the bias due to extinction, which is one of the putative reasons for the observed discrepancy between star formation and supernova rates. To evaluate the outcome of the search we developed a MonteCarlo simulation tool that is used to predict the number and properties of the expected supernovae based on the search characteristics and the current understanding of starburst galaxies and supernovae.</text>
<text><location><page_1><loc_11><loc_51><loc_91><loc_53></location>Results. During the search we discovered 6 supernovae (4 with spectroscopic classification) which is in excellent agreement with the prediction of the MonteCarlo simulation tool that is, on average, 5 . 3 ± 2 . 3 events.</text>
<text><location><page_1><loc_11><loc_47><loc_91><loc_50></location>Conclusions. The number of supernovae detected in starburst galaxies is consistent with that predicted from their high star formation rate when we recognize that a major fraction ( ∼ 60%) of the events remains hidden in the unaccessible, high density nuclear regions because of a combination of reduced search e ffi ciency and high extinction.</text>
<text><location><page_1><loc_11><loc_45><loc_84><loc_46></location>Key words. Stars: supernovae: general - Galaxies: starburst - Galaxies: star formation - Infrared: galaxies - Infrared: stars</text>
<section_header_level_1><location><page_1><loc_7><loc_41><loc_19><loc_42></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_18><loc_50><loc_40></location>The rate of supernovae (SNe) is a key quantity in astrophysics that provides a crucial test for stellar evolution theory and an input for the modeling of galaxy evolution with direct impact on the chemical enrichment and the feedback mechanism. Corecollapse SNe (SN CC), because of their short-lived progenitors, trace the current star formation rate (SFR). Conversely, for an adopted SFR, measurements of the SN CC rates give information on the mass range of their progenitors as well as the slope of the initial mass function at the high mass end. SN Ia, resulting from the thermonuclear explosion of a white dwarf in a binary system, show a wide range of delay times from star formation to explosion. Therefore, the SN Ia rate reflects the long-term star formation history of the parent stellar system. Recently, it has been claimed that a significant fraction of SN Ia have a short delay time, possibly as short as 10 7 years (Mannucci et al. 2006). Like for CC SN, the rate of such prompt SN Ia events is expected to be proportional to the current SFR.</text>
<text><location><page_1><loc_7><loc_14><loc_50><loc_17></location>In one of the early attempts to compare the SN and SF rates, Cappellaro et al. (1999) found that the SN CC rate in galaxies with di ff erent U -V color matches the predicted SFR when</text>
<text><location><page_1><loc_52><loc_40><loc_95><loc_42></location>adopting a mass range 10 M /circledot < M < 40 M /circledot for the SN CC progenitors.</text>
<text><location><page_1><loc_52><loc_31><loc_95><loc_39></location>In the last decade there was a enormous improvement in the measurement of the cosmic SFR with the careful combination of many di ff erent probes (eg. Hopkins & Beacom 2006). A most relevant feature is that the SFR reaches a maximum at a redshift z ∼ 1 and hereafter begins to decrease down to the current rate which is over one order of magnitude lower than at peak.</text>
<text><location><page_1><loc_52><loc_13><loc_95><loc_31></location>A significant e ff ort was also devoted to the measurement of the cosmic SN rate: although much of the focus was for type SN Ia, a few estimates of the SN CC rates were also published both for the local Universe (Li et al. 2011a) and at high redshifts (Dahlen et al. 2004; Cappellaro et al. 2005; Botticella et al. 2008; Bazin et al. 2009; Graur et al. 2011; Melinder et al. 2012; Dahlen et al. 2012). While the new local SN CC rate confirms previous results, with a much better statistics and lower systematic errors, the evolution with redshift was found to track very well the SFR evolution, considering the large uncertainties in the extinction corrections. Again, to best match the observed SN and SF rates it was argued that the lower limit for SN CC progenitor had to be ∼ 10 M /circledot (Botticella et al. 2008; Blanc & Greggio 2008).</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_12></location>At about the same time, following a di ff erent line of research, the analysis of archival images allowed the identification of the</text>
<text><location><page_2><loc_7><loc_72><loc_50><loc_93></location>precursors for a number of nearby SN CC. From the often very scanty but precious photometry, and using stellar evolution models, one can estimate the SN precursor mass. The uncertainties are in general quite large, as confirmed from the discrepancy in the mass estimates from di ff erent groups, but this analysis suggests a lower limit for SN CC progenitors of 8 ± 1 M /circledot (Smartt 2009). If this value is adopted, the observed SN rates would result a factor two smaller than those expected from the observed SFR. This was identified by some authors as a 'SN rate problem' (e.g. Horiuchi et al. 2011. While one should remind that the uncertainties on SFR rate calibrations are still large (Botticella et al. 2012; Kennicutt & Evans 2012), it also true that there is a number of possible biases in the SN rate estimates. The two most severe are the possible underestimate of a large population of faint SN CC and / or the underestimate of the correction for extinction (Horiuchi et al. 2011; Mattila et al. 2012).</text>
<text><location><page_2><loc_7><loc_50><loc_50><loc_72></location>In particular, Mannucci et al. (2007); Cresci et al. (2007) and, more recently, Mattila et al. (2012) argued that a significant fraction of SN CC remains hidden in the nuclear region of starburst galaxies, with a loss of up to ∼ 70-90% in the highly dustenshrouded environments of (ultra-)luminous infrared galaxies( U / LIRGs). This e ff ect is expected to be more important at high redshift because of the larger fraction of starburst galaxies. Indeed, when a correction for this hidden SN fraction is included in the rate calculation the discrepancy between SN and SF rates at high redshifts seems to disappear (Melinder et al. 2012; Dahlen et al. 2012; the 'missing fraction' correction adopted in these works was from Mattila et al. (2012). It is currently unclear if this e ff ect is large enough to explain also the discrepancy observed in the local Universe with somewhat conflicting evidences from the statistics of SNe in the Local Group galaxies (Botticella et al. 2012; Mattila et al. 2012) and large sample SN searches (Li et al. 2011a).</text>
<text><location><page_2><loc_7><loc_42><loc_50><loc_50></location>Entering in this debate, we planned for an infrared SN search in a sample of local starburst galaxies (SBs). The idea was to verify the link between SN and SF rates in an environment where star formation is very high, 1-2 order of magnitude higher than in normal star-forming galaxies. By observing in the K-band we were aiming to reduce the bias due to extinction (AK ∼ 0 . 1AV).</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_42></location>The idea is not new. A first attempt of a dedicated SN search in SBs was performed in the optical band by Richmond et al. (1998). During the search only a handful of events were detected leading the authors to conclude that the rate of (unobscured) SNe in SBs is the same as in quiescent galaxies. A similar conclusion was reached by Navasardyan et al. (2001), again based on optical data. As for infrared SN search, after a few unsuccessful attempts (Grossan et al. 1999; Bregman et al. 2000), the first results of a systematic search in SBs were reported by Maiolino et al. (2002) and Mannucci et al. (2003). They found that the observed SN rate in SBs was indeed one order of magnitude higher then expected for the galaxy blue luminosities but still 3-10 times lower than would be expected from the far infrared (FIR) luminosity. Among the possible explanation for the remaining discrepancy, they suggested extreme extinction in the galaxy nuclear regions (AV > 25mag), which would dim SNe even in the near-IR, and insu ffi cient spatial resolution to probe the very nuclear regions. The reliability of the use of NIR search for obscured SNe in the nuclear and circumnuclear regions of active starburst galaxies was also investigated by Mattila & Meikle (2001) taking into account in particular the problem of extinction. They conclude that with a modest investment of observational time it may be possible to discover a number of nuclear SNe. A negative search for transients in NICMOS images retrieved from the Hubble Space Telescope archive suggests that</text>
<text><location><page_2><loc_52><loc_91><loc_95><loc_93></location>the same biases likely a ff ect also space-based, high spatial resolution observations (Cresci et al. 2007).</text>
<text><location><page_2><loc_52><loc_84><loc_95><loc_90></location>The same approach was used by Mattila et al. (2007b) but with ground based, adaptive optics (AO) assisted observations. The application of this technique led to the discovery of a handful of SNe (Kankare et al. 2008, 2012) but not yet to an estimate of the SN CC rate.</text>
<text><location><page_2><loc_52><loc_74><loc_95><loc_84></location>Until now, about a dozen SNe have been discovered by IR SN searches, not all with spectroscopic confirmation. The number is higher if we include also events first detected in the optical and re-discovered by the IR searches. Therefore the statistics is still very low and many of the original questions are still unanswered. This gave us the motivations to make a new attempt exploiting the opportunity o ff ered by HAWK-I, the infrared camera mounted at the ESO VLT telescope.</text>
<text><location><page_2><loc_52><loc_59><loc_95><loc_73></location>The paper is divided in two parts: the first part describe the observing program, namely the galaxy sample and the search strategy in Sect. 2.1, the data reduction in Sect. 2.3, the SN discoveries and classification in Sect. 2.4 while in Sect. 2.5 we detail the procedure to estimate the search detection e ffi ciency. The second part is devoted to the description of a simulation tool which is used to predict, based on our current knowledge of SBs properties and on the specific features of our SN search, the number of expected SNdetections (Sect. 3). Finally, we compare the number and properties of the expected and observed events (Sect. 4) and draw our conclusions (Sect. 5).</text>
<text><location><page_2><loc_52><loc_55><loc_95><loc_59></location>Throughout this paper we assume the following cosmological parameters: H 0 = 72 kms -1 Mpc -1 , ΩΛ = 0 . 73 and Ω M = 0 . 27.</text>
<section_header_level_1><location><page_2><loc_52><loc_51><loc_74><loc_53></location>2. The SN search program</section_header_level_1>
<section_header_level_1><location><page_2><loc_52><loc_49><loc_66><loc_50></location>2.1. Galaxysample</section_header_level_1>
<text><location><page_2><loc_52><loc_31><loc_95><loc_48></location>Starbursts are galaxies with very high star formation rate, of the order of 10-100 M /circledot yr -1 compared to the few M /circledot yr -1 of normal star forming galaxies in the local universe. Given that in a typical galaxy the very high SFR will rapidly consume the gas reservoir, it is thought that the starburst is a temporary phase in the galaxy evolution. The fact that many SBs are in close pairs or have disturbed morphologies point to the interaction as a dominant, although possibly not unique, reason of the phenomena (Gallagher 1993). The ultra-violet radiation from young, massive stars heats the surrounding dust and is re-emitted in the far infrared. Indeed the most luminous SBs in the local Universe are LIRGs , with 11 < log( LIR / L /circledot ) < 12, and ULIRGs, with log( LIR / L /circledot ) > 12 (Sanders & Mirabel 1996).</text>
<text><location><page_2><loc_52><loc_22><loc_95><loc_31></location>For our project we selected from the IRAS Revised Bright Galaxy Sample (Sanders et al. 2003) a sample of SBs with total infrared (TIR) luminosity log( LTIR / L /circledot ) > 11 and redshift z < 0 . 07. With the additional requirement that the targets are accessible from Paranal in the April to September observing season (to fit in one of the ESO allocation period) we retrieved a sample of 30 SBs.</text>
<text><location><page_2><loc_52><loc_15><loc_95><loc_22></location>The list of SBs is reported in Tab. 1. Along with the galaxy name and equatorial coordinates (cols. 1-3) we report the heliocentric redshift (col. 4), log LTIR and log LB (cols. 5 and 6; cf. Sect. 3.1.1), the Hubble type (col. 7), the SFR and the expected SNrates (cols 8, 9) derived from LTIR as described in Sect. 3.1.1. Galaxy data have been retrieved from NED 1 . In the last column</text>
<text><location><page_3><loc_33><loc_62><loc_35><loc_64></location>⊙</text>
<figure>
<location><page_3><loc_11><loc_63><loc_47><loc_90></location>
<caption>Fig. 1: Distribution of the B and FIR luminosities for the SB galaxies of our sample.</caption>
</figure>
<text><location><page_3><loc_7><loc_40><loc_50><loc_55></location>we listed (in boldface) the designation of the SNe discovered in our search which are the basis for our analysis. For completeness we also list (in italics) the SNe discovered by other SN searches outside our monitoring period. The distribution of LB and LTIR are compared in Fig. 1 showing that, as typical for SBs, LTIR is on average a factor ten higher than LB , whereas for normal star forming galaxies LTIR ∼ LB . We notice that almost all galaxies are LIRGs and only two are ULIRGS. Most galaxies of the sample are isolated ( ∼ 60 -70%) while the remaining are double / interacting galaxies or contain double nuclei, signature of a recent merger. Several galaxies of the sample are asymmetrical, disturbed, or show warps, bars and tidal tails.</text>
<section_header_level_1><location><page_3><loc_7><loc_37><loc_22><loc_38></location>2.2. Searchstrategy</section_header_level_1>
<text><location><page_3><loc_7><loc_27><loc_50><loc_36></location>To search SNe in the selected SB sample we used the HAWK-I instrument installed at the ESO VLT telescope at Cerro Paranal (Chile). HAWK-I is a NIR (0 . 85 -2 . 5 µ m ) wide-field imager with a mosaic of four Hawaii-2RG detectors. The total field of view is 7 . 5 ' × 7 . 5 ' with a scale of 0 . 106 '' / pix. Even in poor seeing conditions ( > 1 . 5 arcsec) the instrument allows to achieve S / N ∼ 10 for a K = 20 magnitude star with a 15 min exposure.</text>
<text><location><page_3><loc_7><loc_12><loc_50><loc_26></location>The infrared light curves of SNe evolve relatively slowly, remaining within one / two magnitudes from maximum for two / three months (Mattila & Meikle 2001) and therefore an IR SN search does not require frequent monitoring. We planned for an average of three visits per galaxy per semester, for a total of 80-100 visits. The monitoring campaign was scheduled in service mode and we did not set tight constraints for the sky conditions. This and the relatively short duration of the observing blocks made the program well suited as filler. We notice that we had no influence on the actual scheduling of the observations which followed the rules of the ESO service mode scheduler.</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_12></location>Eventually, the fraction of useful observing time was 100% of the allocated time in the first season, and 70% in the second</text>
<text><location><page_3><loc_52><loc_83><loc_95><loc_93></location>and third semesters. The log of the observations is reported in Tab. 2 where for each galaxy we list the epoch of observations (MJD), the seeing (FWHM in arcsec), and the minimum and maximum magnitude limit for SN detection across the image (cf. Sec. 2.5). In total, we obtained 210 K-band exposures (exposure time 15min), with an average of about 3 visits per galaxy per semester. Because of the time loss, three galaxies were not monitored in the last two seasons.</text>
<text><location><page_3><loc_52><loc_79><loc_95><loc_82></location>It turned out that the average image quality was quite good: for ∼ 90 % of the exposures the seeing was less than 1 . 0 '' , with an average FWHM across the whole program of 0 . 6 '' .</text>
<section_header_level_1><location><page_3><loc_52><loc_75><loc_75><loc_77></location>2.3. Datareductionandanalysis</section_header_level_1>
<text><location><page_3><loc_52><loc_71><loc_95><loc_74></location>For data reduction and mining of the HAWK-I mosaic images we developed a custom pipeline that integrates di ff erent, publicly available, recipes and tools in a Python environment.</text>
<text><location><page_3><loc_54><loc_69><loc_80><loc_70></location>The pipeline consists of four sections:</text>
<unordered_list>
<list_item><location><page_3><loc_52><loc_63><loc_95><loc_68></location>1. pre-reduction, astrometric calibration and production of the stacked mosaic image. For these steps we use the ESO HAWK-I pipeline recipes in EsoRex , the ESO Recipe Execution Tool 2 ;</list_item>
<list_item><location><page_3><loc_52><loc_60><loc_95><loc_63></location>2. subtraction of images taken at di ff erent epochs using ISIS (Alard 2000) for the PSF matching;</list_item>
<list_item><location><page_3><loc_52><loc_54><loc_95><loc_60></location>3. search for transient candidates in the di ff erence image using Sextractor (Bertin & Arnouts 1996). The candidates were ranked based on their Sextractor measured parameters and submitted to the operator for visual inspection and validation;</list_item>
<list_item><location><page_3><loc_52><loc_50><loc_95><loc_54></location>4. estimate of the detection e ffi ciency through artificial star experiments performed for each of the search images (details in Sect.2.5).</list_item>
</unordered_list>
<text><location><page_3><loc_52><loc_45><loc_95><loc_48></location>The raw images were retrieved from the ESO archive as soon as they became available, and immediately reduced to allow for activation of follow-up spectroscopy of transient candidates.</text>
<text><location><page_3><loc_52><loc_29><loc_95><loc_44></location>For the pre-reduction, we followed the reduction cascade described in the HAWK-I pipeline manual 3 including dark subtraction, flat field and illumination corrections, background subtraction, distortion correction, astrometric o ff set refinement, combination of the di ff erent exposures and stitch of the 4 detectors in a single mosaic image. Actually, it turned out that the ESO pipeline recipes for background subtraction and o ff set refinement do not provide satisfactory results for our images. The main reason is the extended size of our sources and the consequent large dithering we had adopted. To address this issue we implemented custom recipes for the two afore mentioned reduction steps.</text>
<text><location><page_3><loc_52><loc_15><loc_95><loc_29></location>The most critical step of the data reduction is the image subtraction, in particular in the proximity of the nuclear regions of the galaxies. First of all we need to choose a proper reference image, usually the image with the best seeing obtained at least three month before (or in some case after) the image to be searched. We also need to choose the proper parameters for the image di ff erence procedure (see Melinder et al. 2012 for an extensive discussion). An additional problems arises because in the distributed version of ISIS , the program automatically selects the reference sources for the computation of the convolution kernel. Owing to the small number of sources in our extragalactic fields,</text>
<table>
<location><page_4><loc_7><loc_51><loc_88><loc_90></location>
<caption>Table 1: The SB galaxy sample. The last column report our 6 SNe (in bold) with other SNe discovered previously in the galaxy sample.</caption>
</table>
<text><location><page_4><loc_7><loc_39><loc_50><loc_49></location>the reference source list in general includes the bright galaxy nucleus which, being very bright, has a significant weight in the determination of the kernel. This may cause some problems because if at one epoch a SN occurs very close to the galaxy nucleus it can be included in the convolution kernel and e ff ectively cancelled in the di ff erence image. We therefore modified the ISIS selection procedure to allow for exclusion of specific sources, in particular the galaxy nuclei, from the reference list.</text>
<text><location><page_4><loc_7><loc_27><loc_50><loc_38></location>Despite the e ff orts in many cases the di ff erence image shows significant spurious residuals in correspondence to the galaxy nuclear regions. The problem is most severe in case of images with poor seeing ( FWHM > 1 '' ) and / or reduced transparency. This is illustrated in Fig. 2 where we show two examples of image di ff erence one for a search image with poor seeing ( FWHM = 1 . 5 '' , left panel) and the other for a case with excellent seeing ( FWHM = 0 . 4 '' ). In both cases, the reference image was the same and had excellent seeing ( FWHM = 0 . 4 '' ).</text>
<text><location><page_4><loc_7><loc_23><loc_50><loc_27></location>False detections due to residuals of the image subtraction were largely removed by the requirement that the candidate had to be visible at least in two consecutive epochs.</text>
<section_header_level_1><location><page_4><loc_7><loc_20><loc_41><loc_21></location>2.4. Supernovadiscoveriesandcharacterization</section_header_level_1>
<text><location><page_4><loc_7><loc_10><loc_50><loc_19></location>During our monitoring campaign 6 transients were detected in at least two consecutive epochs separated by at least one month (finding charts are in Fig. 3). Four of them were spectroscopically confirmed as SNe (three SN-CC and one SN Ia) and we will argue in the following that also the other two transients, labeled as probable SN (PSN), are likely SN CC (Tab. 3). SNe 2010bt and 2010gp were discovered and announced before our</text>
<figure>
<location><page_4><loc_52><loc_35><loc_96><loc_49></location>
<caption>Fig. 2: Left panel : example of poor subtraction of images of NGC 7130 with large seeing di ff erences ( FWHM = 1 . 5 '' , with FWHM = 0 . 4 ''' for the reference). Right panel : optimal subtraction for two images with similar, good seeing ( FWHM = 0 . 4 '' ). In both panels the source in the lower left quadrant is SN 2010bt (cf. Fig. 3). The FOV in both panel is about 2' × 2'.</caption>
</figure>
<text><location><page_4><loc_52><loc_21><loc_95><loc_24></location>detection by optical searches but have been independently rediscovered by us.</text>
<text><location><page_4><loc_52><loc_15><loc_95><loc_21></location>The objects are listed in Tab. 3 along with the host galaxy name, distance modulus (computed from the galactocentric redshift and the adopted cosmology), SN coordinates, o ff sets from the galaxy nucleus and projected linear distances from the galaxy nucleus.</text>
<text><location><page_4><loc_52><loc_10><loc_95><loc_15></location>For all transients K-band magnitudes were measured through aperture photometry on the di ff erence images and calibrated with respect to 2MASS stars in the field. Upper limits measured on pre-discovery images were also estimated. For all transients,</text>
<table>
<location><page_5><loc_7><loc_8><loc_91><loc_90></location>
<caption>Table 2: The log of the observations with the epoch of observations (MJD), the seeing (FWHM in arcsec), and the minimum and maximum magnitude limit for SN detection across the image (cf. Sec. 2.5).</caption>
</table>
<section_header_level_1><location><page_6><loc_39><loc_95><loc_62><loc_95></location>M. Miluzio et al.: HAWK-I SN search</section_header_level_1>
<table>
<location><page_6><loc_10><loc_72><loc_92><loc_91></location>
<caption>Table 3: Information for the detected SNe.</caption>
</table>
<text><location><page_6><loc_7><loc_57><loc_50><loc_68></location>but PSN2010 in IC4687, we obtained some follow-up imaging in the optical or near-infrared domains. These observations were reduced using standard procedures in IRAF . When a reference image was not available, the SN magnitude was measured using the PSF fitting technique. Optical band magnitudes were calibrated with respect to Landolt's standard fields. Our photometry for the six transients is reported in Tab.4. For the two transients with no spectroscopic confirmation, the photometry will be used to assess their nature.</text>
<text><location><page_6><loc_7><loc_37><loc_50><loc_57></location>Spectroscopic observations were obtained for four candidates: epoch, spectral range and instruments are reported in Tab.5. Data were reduced using standard procedure in IRAF but for the X-Shooter spectra which were reduced using version 1.0.0 of the ESO X-shooter pipeline (Goldoni et al. 2006) with the calibration frames (biases, darks, arc lamps, and flat fields) taken during daytime. The extracted spectra, after wavelength and flux calibration, were compared with a library of template spectra using the GELATO SN spectra comparison tool (https: // gelato.tng.iac.es / , Harutyunyan et al. 2008). The best fit template SN, the SN type and phase are reported in Tab.5. Spectroscopic classification for PSN2010 in IC4687 was attempted, but the observed spectrum resulted too noisy for a safe classification. The table includes the result of the spectroscopic observations of SN 2010gp from Folatelli et al. (2010).</text>
<text><location><page_6><loc_7><loc_32><loc_50><loc_37></location>We have used the available photometry and spectroscopy to put some constraints to the amount of extinction su ff ered by the SNe. Hereafter we will describe in some details the sparse information available for each transient.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_30></location>SN 2010bt was discovered on 2010 April 17.10 UT by Monard (2010). A spectrum taken on April 18.39 UT (Turatto et al. 2010) shows strong resemblance to several type-IIn SNe, in particular SN 1996L (Benetti et al. 1999) shortly after explosion (Fig. 4). A broad H α component is present indicating an expansion velocity of about 3500 km s -1 (half width at zero intensity). SN 2010bt was independently rediscovered by us on May 25 and was observed in other 2 epochs. The object was not visible on a HAWK-I image taken in 2009 July 26 (limit K = 19 . 0 mag). While the analysis of the light curve and spectral evolution of this SN will be presented elsewhere (Elias-Rosa et al. 2013), a preliminary analysis shows that to match the color of SN 2010bt to that of the type IIn SN 1998S requires a significant amount of extinction ( AB = 1 . 7 ± 0 . 5 mag). This extinction improves also the matching of the spectra of SN 2010bt to SN 1996L.</text>
<unordered_list>
<list_item><location><page_6><loc_52><loc_54><loc_95><loc_68></location>SN 2010gp was discovered on 2010 July 14.10 UT by Maza et al. (2010) with the 0.41-m PROMPT1 telescope located at Cerro Tololo. Folatelli et al. (2010) reported the spectroscopic classification as a type-Ia SN around maximum light and with high expansion velocity of the ejecta. SN 2010gp was rediscovered independently by us on July 21 and was observed in other 2 epochs. The object was not visible on a HAWK-I image taken on 2010 May 26 (limit K = 18 . 5 mag). The available colors compared to that of standard SN Ia suggest a small reddening inside the host galaxy, AB = 0 . 2 mag.</list_item>
<list_item><location><page_6><loc_52><loc_36><loc_95><loc_54></location>SN 2010hp was discovered on a HAWK-I image taken on 2010 July 21.3 UT (Miluzio & Cappellaro 2010). The object was not detected on 2009 Aug. 25 (limit K = 19 . 0 mag). Based on a spectrum taken on 2010 Sept 8, the SN was classified as a type II event more than 30 days past maximum light (Marion et al. 2010). We obtained a follow-up spectrum on 2010 Sept 15 with EFOSC2 at the NTT showing the typical features of type II SN, that is H Balmer lines, NaI D doublet, the NIR CaII emission triplet along with a number of FeII lines in the blue region. The GELATO spectral comparison tool found a best match with the type IIP SN 1999em (Elmhamdi et al. 2003) at about + 60 days, adopting a reddening of about AB = 0 . 5 mag (Fig.4). This is fully consistent with the color curves comparison between the two SNe.</list_item>
<list_item><location><page_6><loc_52><loc_18><loc_95><loc_36></location>SN 2011ee was discovered on 2011 June 27.3 UT (Miluzio et al. 2011). The object was not detected on a K-band image taken on 2010 September 7 ( K > 19 . 0 mag). An optical spectrum was obtained with X-Shooter at the VLT on 2011 July 17.3 UT showing that the transient is a type Ic SN. The GELATO code finds a best match with SN 2007gr (Hunter et al. 2009) at maximum (Fig. 4). Because the classification of type Ic SNe near maximum is sometimes ambiguous we obtained a followup spectrum about two months later (2011 Sept 20) using OSIRIS at the GTC. Again the spectrum is very similar to SN 2007gr at corresponding phase (Fig. 4 bottom panel). The color comparison and the spectral match are consistent with a negligible host galaxy extinction.</list_item>
</unordered_list>
<text><location><page_6><loc_52><loc_10><loc_95><loc_18></location>PSN2010 in IC 4687 was discovered on 2010 May 21.3 UT in the northern component of a galaxy triplet that include also IC 4686 and, 1 arcmin to the south of IC 4687, IC 4689. IC 4687 has a chaotic structure formed byf stars, gas and dust and a large curly tail. The transient was not detected on a K-band image taken on 2009 Aug. 8.1 ( K > 19 . 0 mag).</text>
<figure>
<location><page_7><loc_15><loc_69><loc_50><loc_93></location>
<caption>(a) SN 2010bt</caption>
</figure>
<figure>
<location><page_7><loc_15><loc_41><loc_50><loc_66></location>
<caption>(c) SN 2010hp</caption>
</figure>
<figure>
<location><page_7><loc_15><loc_13><loc_50><loc_38></location>
<caption>Fig. 3: K-band finding charts for the SNe of our list. The inserts show the transients as they appear in the di ff erence image.</caption>
</figure>
<text><location><page_7><loc_28><loc_12><loc_36><loc_13></location>(e) SN 2011ee</text>
<figure>
<location><page_7><loc_53><loc_69><loc_88><loc_93></location>
<caption>(b) SN 2010gp</caption>
</figure>
<figure>
<location><page_7><loc_53><loc_41><loc_88><loc_66></location>
<caption>(d) PSN2010 in IC 4687</caption>
</figure>
<figure>
<location><page_7><loc_53><loc_13><loc_88><loc_38></location>
</figure>
<text><location><page_7><loc_62><loc_12><loc_78><loc_13></location>(f) PSN 2011 in IC1623A</text>
<section_header_level_1><location><page_8><loc_39><loc_95><loc_62><loc_95></location>M. Miluzio et al.: HAWK-I SN search</section_header_level_1>
<table>
<location><page_8><loc_14><loc_41><loc_88><loc_91></location>
<caption>Table 4: Transient photometry. Estimated errors are given in parentheses.</caption>
</table>
<text><location><page_8><loc_18><loc_40><loc_84><loc_41></location>H = HAWK-I@VLT, E = EFOSC2@NTT, S = SOFI@NTT, L = RATCam@Liverpool, D = Dolores@TNG</text>
<table>
<location><page_8><loc_16><loc_27><loc_85><loc_36></location>
<caption>Table 5: Log of spectroscopic observations.</caption>
</table>
<text><location><page_8><loc_10><loc_11><loc_50><loc_24></location>We obtained an optical / infrared spectrum with X-Shooter at VLT on 2010 June 5. However, because of its very low S / N, we could not derive a convincing classification and therefore we had to rely on the K-band photometry. Comparing the K band absolute light curve of PSN2010 ( AB (host) = 0) with template light curves of di ff erent SN types we found a good match with SN 2005cs a prototype of under-luminous type IIP SN (Pastorello et al. 2009), assuming that the detection of PSN2010 was 2 months after the explosion. However, lacking color measurements, we could not constraint the ex-</text>
<text><location><page_8><loc_54><loc_19><loc_95><loc_24></location>tinction and indeed, assuming a high extinction AB ∼ 8 mag, we found an alternative good match with the light curve of SN 1999em (Fig. 5). Intermediate values may also be adopted by fitting other SN II.</text>
<text><location><page_8><loc_52><loc_11><loc_95><loc_18></location>PSN2011 in IC 1623 was discovered on 2011 July 21.4 UT in the western component of a galaxy pair. The object was not detected on a K-band image taken on 2010 Sept. 5 ( K > 19 . 0 mag). Unfortunately, due to bad weather in the scheduled nights, we could not obtain a spectroscopic observation of the transients. We have to rely on three epochs of photome-</text>
<figure>
<location><page_9><loc_12><loc_72><loc_43><loc_91></location>
<caption>(a) The spectrum of 2010bt, dereddened by AB = 1 . 7 mag (see text) is compared with that of the type IIn SN 1996L.</caption>
</figure>
<figure>
<location><page_9><loc_12><loc_46><loc_43><loc_66></location>
<caption>(b) The spectrum of 2010hp, dereddened by AB = 0 , 5 mag (see text) is compared with that of the type IIP SN 1999em.</caption>
</figure>
<figure>
<location><page_9><loc_13><loc_14><loc_43><loc_39></location>
<caption>(c) The spectrum of 2011ee is compared to that of the SN Ic 2007gr at the maximum (top panel) and 60 days after the maximum.</caption>
</figure>
<figure>
<location><page_9><loc_54><loc_67><loc_91><loc_92></location>
<caption>Fig. 4: Spectra of SN 2010bt, 2010hp, and 2011ee are shown along with the best fitting templates.Fig. 5: K band absolute light curve of the PSN2010 (black dots), compared with those of template SNe. The empty circles show the same data but assuming an extinction AB = 8 mag.</caption>
</figure>
<text><location><page_9><loc_54><loc_47><loc_95><loc_58></location>try, in K complemented by two epochs in the optical R and I bands. A simultaneous comparison of the absolute observed luminosity with template SNe give a best fit with the SN Ic 2007gr one month after maximum (Fig. 6). Assuming this classification, from the colors we can constrain the extinction to be AB = 0 . 5 ± 0 . 5 mag. However, we have to admit that, within the errors, the photometry of PSN2011 can be consistent also with a type IIP at about 3 months after explosion.</text>
<text><location><page_9><loc_52><loc_38><loc_95><loc_46></location>To recap, during the search we discovered 6 SNe. Four received a spectroscopic classifications: one as a type Ia and three as core collapse events, a type IIn, a type IIP and a type Ic. For the other two, based on the sparse photometry, we argue that most likely they are core collapse SNe, with a best fit as type IIP and type Ic, respectively.</text>
<section_header_level_1><location><page_9><loc_52><loc_35><loc_71><loc_36></location>2.5. Searchdetectionlimit</section_header_level_1>
<text><location><page_9><loc_52><loc_25><loc_95><loc_34></location>In order to derive the SN rate from the number of detected events it is crucial to obtain an accurate estimate of the magnitude detection limit for each of the search images and for di ff erent locations in the images. As it has been shown in Fig. 2, the detection e ffi ciency is influenced by the sky conditions at the time of observations (namely seeing and transparency) and by the transient position inside the host galaxy.</text>
<text><location><page_9><loc_52><loc_21><loc_95><loc_25></location>The magnitude limit for SN detection has been estimated through artificial star experiments. The procedure we adopted was the following:</text>
<unordered_list>
<list_item><location><page_9><loc_52><loc_17><loc_95><loc_20></location>1. fake SNe of di ff erent magnitudes are simulated with the PSF derived from isolated field stars;</list_item>
<list_item><location><page_9><loc_52><loc_12><loc_95><loc_17></location>2. the image is segmented in a number of intensity contour levels. We took denser contours in the nuclear regions because the magnitude limit changes rapidly with background intensity;</list_item>
<list_item><location><page_9><loc_52><loc_10><loc_95><loc_12></location>3. one fake SN of specific magnitude is randomly placed inside a chosen intensity contour;</list_item>
</unordered_list>
<figure>
<location><page_10><loc_9><loc_62><loc_44><loc_91></location>
<caption>Fig. 6: K and R-I colours of PSN 2011, compared with those of template SNe. For this plot we adopted AB = 0 . 5 mag, which improves the fit of the R band photometry ( ∆ R = 0 . 3 mag).</caption>
</figure>
<unordered_list>
<list_item><location><page_10><loc_8><loc_52><loc_50><loc_54></location>4. the image with the fake SN is processed through the image di ff erence and transient detection pipeline;</list_item>
<list_item><location><page_10><loc_8><loc_45><loc_50><loc_51></location>5. if the fake SN results in a detected transient, the experiment is repeated with a fainter artificial star until we have a null detection. The fainter magnitude for which the fake SN is detected defines the magnitude limit for the given background intensity level;</list_item>
<list_item><location><page_10><loc_8><loc_39><loc_50><loc_45></location>6. Steps 2 to 5 were repeated for each contour level three times to enhance the statistical significance of the results. The average value for each contour level has been adopted as the magnitude discovery limit for the given background intensity.</list_item>
</unordered_list>
<text><location><page_10><loc_7><loc_30><loc_50><loc_37></location>To illustrate the results, a plot of the magnitude limit versus background counts for four observations of the galaxy NGC7130isshownin Fig. 7. Each epoch is labelled with the image seeing, while the errorbar shows the range of limiting magnitudes for the three experiments. The top x-axis shows the linear distance in Kpc from the galaxy center.</text>
<text><location><page_10><loc_7><loc_20><loc_50><loc_29></location>It can be seen that, as expected, the magnitude limit is lower in the nuclear regions which, for a typical galaxy, correspond to 1.5-2.0 kpc. Epochs with di ff erent seeing have similar magnitude limits in the galaxy outskirts (typically K ∼ 19 mag), while in the nuclear region when seeing is poorer the magnitude limit is brighter (in the worst case even 5-6 mag brighter than in the galaxy outskirts).</text>
<section_header_level_1><location><page_10><loc_7><loc_17><loc_27><loc_18></location>3. SN search simulation</section_header_level_1>
<text><location><page_10><loc_7><loc_10><loc_50><loc_16></location>To evaluate the significance of the detected events we elaborated a simulation tool that returns the number and properties of expected events based on specific features of our SN search, a number of parameters describing our current knowledge of SBs and SN properties. The tool uses a MonteCarlo approach which</text>
<figure>
<location><page_10><loc_54><loc_74><loc_92><loc_93></location>
<caption>Fig. 7: Magnitude limit vs. background intensity for four di ff erent observations of NGC 7130. The points are labeled with the respective image seeing. Errorbars show the range of the magnitude limits from the three di ff erent experiments.</caption>
</figure>
<text><location><page_10><loc_52><loc_57><loc_95><loc_65></location>simulates the stochastic nature of SN explosions. By collecting a number of MonteCarlo experiments with the same input parameters, we can test whether the observed events are within the expected distribution. On the other hand by varying some of the input parameters, we can test the influence of specific assumptions.</text>
<section_header_level_1><location><page_10><loc_52><loc_54><loc_69><loc_55></location>3.1. Thesimulationtool</section_header_level_1>
<text><location><page_10><loc_52><loc_47><loc_95><loc_53></location>Our MonteCarlo (MC) simulation tool is built in a Python environment and makes use, for the di ff erent inputs, of standard values taken from the literature. For those that are more controversial, we will give references with some discussion. The basic ingredients of the simulation are:</text>
<unordered_list>
<list_item><location><page_10><loc_53><loc_39><loc_95><loc_45></location>-relevant data for the selected SBs, namely: redshift, galactic extinction, infrared fluxes from IRAS catalogues at 25, 60 and 100 µ , B magnitude corrected for internal extinction 4 , Hubble morphological type. These data were retrieved from NED;</list_item>
<list_item><location><page_10><loc_53><loc_20><loc_95><loc_39></location>-information describing the SN properties for each of the SN types considered here: SNe Ia and core collapse events, including SNe IIP, IIL, IIn and Ib / c. K band template light curves were constructed starting from B template light curves (Cappellaro et al. 1997) and B -K k-corrections for the given galaxy redshift (Botticella et al. 2008). We note that the results of this procedure are in close agreement with the K template light curves of Mattila & Meikle (2001). For the SN luminosity functions we adopted as reference those of Li et al. (2011b), but we also tested for the possible presence of a significant population of faint core collapse which may be suggested by the analysis of very nearby SNe (Horiuchi et al. 2011). From the LOSS project we adopted also the relative rates for the di ff erent SN types (Li et al. 2011a);</list_item>
<list_item><location><page_10><loc_53><loc_16><loc_95><loc_19></location>-details of the search campaign: log of observations, magnitude detection limit for each observation as a function of the host galaxy background intensity;</list_item>
<list_item><location><page_10><loc_53><loc_13><loc_95><loc_15></location>-the number of SNe expected from a given star formation episode. For core collapse SNe, this is determined only by</list_item>
</unordered_list>
<text><location><page_11><loc_10><loc_84><loc_50><loc_93></location>the adopted mass range of the progenitors and IMF slope. In fact, for our purposes, we can neglect the very short time delay from CC progenitor formation to explosion. For type Ia SNe we need to consider the realization factor, that is the fraction of events in the proper mass range which occurs in suitable close binary systems and the delay time distribution (Sect. 3.1.2).;</text>
<unordered_list>
<list_item><location><page_11><loc_8><loc_81><loc_50><loc_84></location>-the depth and distribution of the extinction by dust inside the parent galaxies (cf. Sect. 3.1.3);</list_item>
<list_item><location><page_11><loc_8><loc_79><loc_50><loc_81></location>-the star formation spatial distribution in the parent galaxies (cf. Sect. 3.1.4).</list_item>
</unordered_list>
<text><location><page_11><loc_7><loc_75><loc_50><loc_78></location>Hereafter, we discuss our assumptions about the parameters of the simulation.</text>
<section_header_level_1><location><page_11><loc_7><loc_72><loc_47><loc_73></location>3.1.1. From IRAS measurements to Star Formation Rate</section_header_level_1>
<text><location><page_11><loc_7><loc_65><loc_50><loc_71></location>The SFR in SBs can be estimated on the basis of the galaxy total infrared luminosity (L TIR ) under the assumption that dust re-radiates a major fraction of the UV luminosity, and after calibration with stellar synthesis models. In turn the TIR luminosity can be estimated from FIR flux measurements.</text>
<text><location><page_11><loc_7><loc_62><loc_50><loc_64></location>Helou et al. (1988) provided a prescription for deriving the FIR emission from IRAS measurements:</text>
<formula><location><page_11><loc_12><loc_58><loc_45><loc_60></location>FIR = 1 . 26 × 10 -14 [2 . 58 f ν (60 µ m ) + f ν (100 µ m )]</formula>
<text><location><page_11><loc_7><loc_54><loc_50><loc_57></location>where FIR is in W m -2 and f ν are in Jansky. FIR fluxes are converted into TIR fluxes by using the relation of Dale et al. (2001)</text>
<formula><location><page_11><loc_15><loc_50><loc_42><loc_52></location>log TIR FIR = a 0 + a 1 x + a 2 x 2 + a 3 x 3 + a 4 x 4</formula>
<text><location><page_11><loc_7><loc_46><loc_49><loc_49></location>where x = log f ν (60 µ m ) f ν (100 µ m ) and [ a ( z = 0)] /similarequal [0 . 2378 , -0 . 0282 , 0 . 7281 , 0 . 6208 , 0 . 9118]</text>
<text><location><page_11><loc_7><loc_42><loc_50><loc_45></location>TIR fluxes are converted in luminosities using the adopted distances:</text>
<formula><location><page_11><loc_23><loc_40><loc_34><loc_41></location>LTIR = 4 π D 2 TIR</formula>
<text><location><page_11><loc_7><loc_34><loc_50><loc_39></location>Finally, the relation between the SFR ( ψ ), and L TIR was derived by Kennicutt (1998) from SB galaxy spectral synthesis model adopting 10-100 Myr continuous bursts and a Salpeter IMF as:</text>
<formula><location><page_11><loc_11><loc_29><loc_46><loc_32></location>ψ [M /circledot yr -1 ] = LTIR 2 . 2 × 10 43 [erg s -1 ] = LTIR 5 . 8 × 10 9 [L /circledot ]</formula>
<section_header_level_1><location><page_11><loc_7><loc_26><loc_22><loc_27></location>3.1.2. SNR and SFR</section_header_level_1>
<text><location><page_11><loc_7><loc_17><loc_50><loc_25></location>In general, the rate of SNe expected at a specific time, ˙ nSN ( t ), for a stellar population depends on the star formation history, the number of SNe per unit mass from one stellar generation (labelled as SN productivity) and the distribution of delay time from star formation to explosion for the specific SN type. Following the notation of Greggio (2005, 2010):</text>
<formula><location><page_11><loc_7><loc_13><loc_50><loc_16></location>˙ nSN ( t ) = ∫ t 0 ψ ( t -τ ) kSN fSN ( τ ) d τ (1)</formula>
<text><location><page_11><loc_7><loc_10><loc_50><loc_12></location>where ψ ( t ) is the star formation rate, fS N is the distribution of the delay times τ and kSN is the supernova productivity. The</text>
<text><location><page_11><loc_52><loc_88><loc_95><loc_93></location>equation shows that at a fixed epoch t since the beginning of star formation, the rate of SNe is obtained by adding the contribution of all past stellar generations, each of them weighted with the SFR at the appropriate time.</text>
<section_header_level_1><location><page_11><loc_52><loc_85><loc_66><loc_86></location>Core Collapse SNe</section_header_level_1>
<text><location><page_11><loc_52><loc_76><loc_95><loc_84></location>For core collapse SNe the delay time from star formation to explosion (2.5 Myr for 120 M /circledot stars up to 40 Myr for 8 M /circledot stars) is short compared with the typical SBs duration (200 -400 Myr, McQuinn et al. 2009). Assuming that the SFR in the SB was constant during the past 40 Myr, the expected CC SN rate, ˙ nCC , is proportional to the current SFR:</text>
<formula><location><page_11><loc_68><loc_73><loc_78><loc_74></location>˙ nCC = kCC × ψ</formula>
<text><location><page_11><loc_52><loc_69><loc_95><loc_72></location>The supernova productivity kCC is derived by integrating the IMF, φ ( m ), and assuming a CC progenitor mass ( MCC ) range:</text>
<formula><location><page_11><loc_66><loc_62><loc_80><loc_68></location>kCC = ∫ M U CC M L CC φ ( m ) dm ∫ MU ML m φ ( m ) dm</formula>
<text><location><page_11><loc_52><loc_57><loc_95><loc_62></location>where M L CC and M U CC are respectively the lower and upper mass limits for SN CC progenitors and ML , MU are the lower and upper stellar mass limit. To be consistent with the Kennicutt's SFR calibration we adopted a Salpeter IMF, that is:</text>
<formula><location><page_11><loc_54><loc_53><loc_92><loc_54></location>φ ( m ) ∝ m -α with α = 2 . 35 and 0 . 1 M /circledot < M < 100 M /circledot</formula>
<text><location><page_11><loc_52><loc_41><loc_95><loc_51></location>Assuming 8 < MCC < 50 M /circledot for the CC progenitor mass range, kCC = 0 . 007 M -1 . This number changes significantly if we adopt a di ff erent IMF, e.g. kCC = 0 . 011 for a Kroupa IMF or kCC = 0 . 039 for an extreme Starburst IMF (Dwek et al. 2011). We soon note however that, because the IMF enters also in the conversion from LTIR to ψ , the expected rate of SN events is almost independent on the selected IMF (cf. Sect. 4.1) provided the choice is consistent.</text>
<text><location><page_11><loc_52><loc_32><loc_95><loc_41></location>More important is the assumption on the mass range for CC progenitors which is not well constrained. Actually, while changing the upper limit of the progenitor mass from 40 to 100 M /circledot makes a modest 10% increase in the CC SN productivity, the lower mass limit is crucial, with kCC decreasing by 30% if we adopted M L CC = 10 M /circledot instead of the favored value of 8 M /circledot (Smartt 2009).</text>
<section_header_level_1><location><page_11><loc_52><loc_29><loc_56><loc_30></location>SN Ia</section_header_level_1>
<text><location><page_11><loc_52><loc_10><loc_95><loc_28></location>Estimating the expected rate of SN Ia is complicated because the delay time distribution fIa , while still uncertain, certainly ranges from short to very long time. In particular it has been suggested that SN Ia can be divided into two classes, one with a short delay time whose rate scales with the current SFR (also called prompt ), and a second with a long delay time ( tardy ), whose rate scales with the average of the SFR along the entire galactic evolution (Scannapieco & Bildsten 2005; Mannucci et al. 2006). While stellar evolution arguments (Greggio 2010, 2005; Greggio & Renzini 1983) and more recent data (Maoz et al. 2012; Totani et al. 2008) suggest a continuous distribution of the delay time instead of two distinct classes, the schematization is still a fair approximation that help in simplifying the problem of predicting the expected SN Ia rate in SBs.</text>
<text><location><page_12><loc_7><loc_89><loc_50><loc_93></location>In general, for a galaxy of the local Universe, ∼ 13 Gyr after the beginning of SFR, we can identify the contribution of the two components as follows (Greggio 2010):</text>
<formula><location><page_12><loc_7><loc_84><loc_50><loc_87></location>˙ nIa (13) = kIa × ( ψ C ∫ 0 . 1 0 fIa ( τ ) d τ + ψ P ∫ 13 0 . 1 fIa ( τ ) d τ ) (2)</formula>
<text><location><page_12><loc_7><loc_64><loc_50><loc_82></location>where ψ C and ψ P are the average SFR over, respectively, the last 0.1 Gyr (current SFR) and from 0.1 to 13 Gyr ago (past SFR). The SN productivity kIa is the product of the number of stars per unit mass in the adopted progenitor mass range (0.021 for a Salpeter IMF and a mass range 3M /circledot < M < 8 M /circledot ) and the realization fraction, the actual fraction of systems which make a successful explosion ( ∼ 5% according to the most recent estimate) (Maoz & Mannucci 2012). We assume that SF history in SBs can be described schematically with two components: a constant SFR during the galaxy evolution which created the galaxy stellar mass, and an on-going episode of intense SFR which is the source of the strong TIR emission. Neglecting the contribution of the ongoing SB to the galaxy stellar mass, we can approximate ψ P /similarequal M / 13 × 10 9 , and write Eq. 2 as follows:</text>
<formula><location><page_12><loc_16><loc_59><loc_41><loc_62></location>˙ nIa (13) /similarequal kIa ( ψ CF p Ia + M 13 × 10 9 F t Ia )</formula>
<text><location><page_12><loc_7><loc_50><loc_50><loc_58></location>where F p Ia = < f p Ia > × 0 . 1 and F t Ia = < f t Ia > × 13 /similarequal 1 -F p Ia are the relative fraction of prompt and tardy events derived by integrating the delay time distribution in the relevant time range. In our approximation ψ C can be derived from the observed LTIR and the galaxy mass from the K magnitude and B -K colors (cf. Mannucci et al. 2005).</text>
<text><location><page_12><loc_7><loc_43><loc_50><loc_50></location>The relative contribution of the two SN Ia components has been a very debated issue in the last few years, ranging from F p Ia ∼ 50% (Mannucci et al. 2006) to F p Ia ∼ 10% from standard stellar evolution scenarios (Greggio 2010). In our simulation we adopted as reference an intermediate value, F p Ia ∼ 30%.</text>
<section_header_level_1><location><page_12><loc_7><loc_40><loc_19><loc_41></location>3.1.3. Extinction</section_header_level_1>
<text><location><page_12><loc_7><loc_27><loc_50><loc_38></location>Dust extinction in SBs is very high, especially in the nuclear regions. For instance, Shioya et al. (2001) found that fitting the spectral energy distribution of the nuclear region of Arp 220 requires a visual extinction AV > 30 mag. Actually, according to Engel et al. (2011), 'over most of the disk the near-infrared obscuration is moderate, but increases dramatically in the central tens of parsecs of each nucleus'. Similar high extinction, AV ∼ 20, was found for the SB region of Zw 096 (Inami et al. 2010).</text>
<text><location><page_12><loc_7><loc_12><loc_50><loc_27></location>As a first order approximation, for our simulation we assumed that the extinction has the same distribution of the SF (see next section) with a maximum value AV = 30 mag corresponding to the SFR peak and scaled linearly in the other regions. While this is a crude approximation, it turns out that the actual choice of extinction correction has little impact for our simulation. In the nuclear, high extinction regions the SN detection is limited by the reduced performance of the image subtraction algorithm in these high surface brightness regions. At the same time, our IR search is largely insensitive to variation in the (moderate) extinction of the outer galaxy regions.</text>
<text><location><page_12><loc_7><loc_10><loc_50><loc_12></location>For the wavelength dependence of extinction we adopted the Calzetti's law with RV = 4 . 05 ± 0 . 8 (Calzetti et al. 2000).</text>
<section_header_level_1><location><page_12><loc_52><loc_92><loc_75><loc_93></location>3.1.4. Star Formation Distribution</section_header_level_1>
<text><location><page_12><loc_52><loc_79><loc_95><loc_91></location>The spatial distribution of the SFR is a key ingredient of the simulation. This is because we expect that SNe occur more frequently in the high SF regions where, on the other hand, our detection e ffi ciency is lower. In principle, the FIR emission which is used to estimate the SFR would also be a good tracer of its spatial distribution. However, it turned out that the available MIR imaging for the galaxies of our sample (mainly obtained with the Spitzer observatory) do not have enough spatial resolution for mapping the compact SB structures.</text>
<text><location><page_12><loc_52><loc_71><loc_95><loc_79></location>Selected K-band images from our survey can have excellent resolution but, as is well-known, the near IR emission better traces the old star population, that is the galaxy mass distribution more than the SFR distribution. Therefore for an estimate of the SFR concentration, we are forced to an indirect, statistical approach.</text>
<text><location><page_12><loc_52><loc_50><loc_95><loc_71></location>Our starting point is the SB classification by Hattori et al. (2004), who derived a correlation between the global SBs properties, such as FIR colors, and the compactness of the SF regions. These range from very compact ( ≤ 100 pc) nuclear starbursts with almost no star-forming activity in the outer regions (type 1), to extended starbursts with relatively faint nuclei (type 4), with type 2 and 3 as intermediate cases. In addition, they found a trend for galaxies with more compact SF region showing a higher star formation e ffi ciency and hotter far-infrared color. They also found that the compactness of SF regions is weakly correlated with the galaxy morphology, with disturbed objects showing preferentially more concentrated SF. On the other hand, an appreciable fraction ( ∼ 50%) of their galaxy sample was dominated by extended starbursts (type 4). The significant variations in the degree of concentration of the SB SF regions has been recently confirmed by McQuinn et al. (2012).</text>
<text><location><page_12><loc_52><loc_36><loc_95><loc_50></location>In an attempt to characterize the SF spatial distribution for the SBs of our sample we derived estimates of their morphological class and FIR colors. In particular, following Hattori et al. (2004), SBs with strong tidal features and a single nucleus were classified as 'mergers' (M), galaxy pairs with an overlapping disk or a connecting bridge were classified as 'close pairs' (CP) if the projected separation is < 20 Kpc and galaxies that have a nearby ( < 100 Kpc) companion at the same redshift were classified as 'pairs' (P). The remaining objects were classified as 'single' (S). The classification of the SBs of our sample is listed in Tab. 6 along with the galaxy FIR colors, log f 60 / f 100, log f 25 / f 60.</text>
<text><location><page_12><loc_52><loc_28><loc_95><loc_36></location>We attributed to each galaxy a compactness class on the basis of its correlation with the FIR colors as shown in Fig. 4 of Hattori et al. (2004) that for the object of our sample corresponds to our Fig. 8. As it can be seen, we also confirmed their claim of a (weak) relation of FIR color and, as a consequence, compactness class with SB morphology.</text>
<text><location><page_12><loc_52><loc_10><loc_95><loc_28></location>The next step is based on Soifer et al. (2000, 2001). For a number of SBs galaxies they plotted the MIR and NIR emission curve of growth finding that in general the MIR emission is more concentrated, while only for few galaxies the MIR and NIR curves of growth show a similar trend. Actually we found that, to a first order approximation, the MIR emission profile of a given galaxy can be matched by NIR profile powered to an exponent α which ranges between 1, when the two profiles are similar, to 2, when the MIR emission is strongly concentrated. When we classify the same galaxies with the compactness criteria of Hattori et al. (2004), we found that (as expected) the galaxies with compact SF regions (type 1 -2) are characterized by more concentrated MIR emission ( α = 2 . 0 -1 . 5, respectively), while galaxies with extended SF region (type 3-4) have similar MIR</text>
<table>
<location><page_13><loc_7><loc_49><loc_50><loc_87></location>
<caption>Table 6: Morphological classification, FIR colors and compactness classification for the SBs of our sample. Following Hattori et al. (2004), type 1 have SF region < 500 pc, type 2 < 1 Kpc, type 3 > 1 Kpc and type 4 have extranuclear star formation.</caption>
</table>
<figure>
<location><page_13><loc_10><loc_21><loc_44><loc_44></location>
<caption>Fig. 8: FIR color of the SBs of our sample. The di ff erent symbols identify the compactness class (Hattori et al. 2004) while the label show the morphological type.</caption>
</figure>
<text><location><page_13><loc_52><loc_88><loc_95><loc_93></location>vs. NIR profiles ( α = 1 . 25 -1 . 0, respectively). As a reference, we notice that in the typical case of NGC 6240, assuming α = 1 corresponds to locate 50% of the SFR within 1.5 Kpc, whereas for α = 2 the same SFR fraction is enclosed within 500 pc.</text>
<text><location><page_13><loc_52><loc_83><loc_95><loc_88></location>As a result of this discussion we have a prescription to estimate the SF distribution based on the observed LK map, and adopting a power index α appropriate for the compactness class of the given SB galaxy (Tab. 7).</text>
<section_header_level_1><location><page_13><loc_52><loc_79><loc_76><loc_80></location>3.1.5. Flow chart of the simulation</section_header_level_1>
<text><location><page_13><loc_52><loc_75><loc_95><loc_78></location>Having defined all the ingredients of the simulation, we can now describe how this proceeds. The simulation flowchart can be summarized as follows:</text>
<unordered_list>
<list_item><location><page_13><loc_52><loc_69><loc_95><loc_73></location>1. for each galaxy of the sample, based on the estimated total SFR and adopted progenitor scenarios, we compute the expected number of SNe per year;</list_item>
<list_item><location><page_13><loc_52><loc_58><loc_95><loc_69></location>2. a time interval is chosen so that 100 SNe are expected to explode in the given galaxy in that period. The time interval ends with the last observations of the galaxy. Given the expected SN rates it is for all galaxies much longer than the duration of our monitoring campaign. The reason to simulate 100 events is to avoid having to deal with fractional SN numbers for the di ff erent subtypes. We assign to each event a random epoch of explosion chosen within the defined time interval;</list_item>
<list_item><location><page_13><loc_52><loc_55><loc_95><loc_57></location>3. each SN is assigned to a random explosion site inside the parent galaxy according to the SFR spatial distribution;</list_item>
<list_item><location><page_13><loc_52><loc_47><loc_95><loc_55></location>4. a peak magnitude is also assigned to each SN, with a random value derived from the adopted SN luminosity function for the specific subtype. We also associate to the event an extinction value randomly extracted from a gaussian distribution whose mean value depends on the position of the SN, and σ = 1 / 3 of the mean value;</list_item>
<list_item><location><page_13><loc_52><loc_39><loc_95><loc_47></location>5. the apparent magnitude is thereafter calculated at the epochs of available observations, knowing the galaxy distance modulus and SN epoch of explosion. This is compared with the search magnitude detection limit for the given position and, when brighter, the SN is added to the simulated discovery list.</list_item>
</unordered_list>
<text><location><page_13><loc_52><loc_29><loc_95><loc_38></location>The process, iterated for all the galaxies of the sample, defines a single simulation run. Outcomes of the simulation are the expected number of SN discoveries, their types, magnitudes, extinctions and positions inside the host galaxies. To explore the distribution of the outcomes from the random process, a complete experiment is made by collecting a minimum of a hundred single simulation runs.</text>
<text><location><page_13><loc_52><loc_25><loc_95><loc_29></location>For the reference simulation we used theinput parameters summarized in Tab. 7. In the next section we will compare the prediction of the simulation with the current SN discoveries.</text>
<section_header_level_1><location><page_13><loc_52><loc_20><loc_94><loc_22></location>4. Comparison between observed and expected SN discoveries</section_header_level_1>
<text><location><page_13><loc_52><loc_10><loc_95><loc_19></location>As we outlined above, from a large number of MonteCarlo simulation runs we obtain the distribution of the expected SN discoveries. This is shown in Fig. 9, where each bin of the histogram is the predicted probability of observing the specific number of SN discoveries whereas the dashed line marks the number of actual SNe discovered and the shaded area shows its 1σ Poissonian uncertainty range.</text>
<table>
<location><page_14><loc_10><loc_74><loc_47><loc_91></location>
<caption>Table 7: Input parameters for the reference simulation</caption>
</table>
<figure>
<location><page_14><loc_9><loc_45><loc_46><loc_70></location>
<caption>Fig. 9: Histogram of the number of expected SNe from our MonteCarlo experiments. The dashed vertical line indicates the number of observed events and the grey area its 1 σ -Poissonian uncertainty.</caption>
</figure>
<text><location><page_14><loc_7><loc_28><loc_50><loc_34></location>Wefoundthat with the adopted simulation scenario and input parameters we should have expected, on average, the discovery of 5 . 3 ± 2 . 3 SNe. In 68% of the experiments (1σ ) the expected number is in the range 4-8 which is in excellent agreement with the observed number of 6 events.</text>
<text><location><page_14><loc_7><loc_23><loc_50><loc_28></location>The prediction of the simulation is that almost all SNe are CC(5.1 SN CC vs. 0.2 SN Ia), though in 10% of the experiments at least one type Ia is found (that is what we have from the real SN search).</text>
<text><location><page_14><loc_7><loc_16><loc_50><loc_22></location>The distributions of some of the expected and observed SN properties are compared in Fig. 10. For the simulation, we show the distribution across a large number of experiments (line-only histogram) while the grey shaded histogram represents the actual observations.</text>
<text><location><page_14><loc_7><loc_10><loc_50><loc_16></location>The top panel in Fig. 10 shows the distribution of the apparent magnitudes at the discovery. The good agreement between simulations and observations is a crucial consistency check of our estimates of the magnitude detection limit: if the discovered SNe were systematically fainter / brighter then expected, this</text>
<figure>
<location><page_14><loc_58><loc_73><loc_87><loc_93></location>
<caption>(a) Expected (line-only) and observed (grey) K magnitude distribution at the discovery</caption>
</figure>
<figure>
<location><page_14><loc_59><loc_47><loc_87><loc_67></location>
<caption>(b) Expected (line-only) and observed (grey) extinction distribution. In light grey we indicate the allowed range for the extinction of PSN2010 (see text).</caption>
</figure>
<figure>
<location><page_14><loc_59><loc_18><loc_87><loc_38></location>
<caption>(c) Radial distribution of expected (line-only) and detected (dark grey) SNe. For regular galaxies the surface brightness decrease monotonically with radial distance (the upper axis shows this correspondence for one of the galaxy of our sample). In light grey we show the distribution of injected artificial SNe (see text).</caption>
</figure>
<text><location><page_15><loc_7><loc_91><loc_50><loc_93></location>would indicate, respectively, an underestimate / overestimate of the search detection e ffi ciency.</text>
<text><location><page_15><loc_7><loc_70><loc_50><loc_90></location>A comparison of the simulated vs observed extinction distribution is shown in the middle panel of Fig. 10. For the observed distribution the case of PSN2010 for which extinction is ambiguous is shown in light grey. Again the simulation is in good agreement with the observations. This argues in favor of the consistency of the input assumptions. The fact that, in our IR search we expect that most of detected SNe have low extinction ( ∼ 75% with AV < 1 mag) is a consequence of our assumption that the extinction is very high in the nucleus and rapidly decreases with the galaxy radius, following the same trend of the SFR. This does not means that extinguished SN are intrinsically rare but that they are confined to the galaxy nuclear regions where extinction is extremely high even in the IR (see next). At the same time we can exclude the presence of a significant population of SNe with intermediate extinctions: we would easily detect them in our infrared search.</text>
<text><location><page_15><loc_7><loc_61><loc_50><loc_69></location>Mattila & Meikle (2001) found an average value of AV = 30 mag for the extinction towards the SN remnants of M82. Confirming the presence of high extinction (about AV ∼ 15-45 mag) in the innermost 300 pc regions. On the other hand, Kankare et al. (2008) found an host galaxy extinction of AV ∼ 16 mag for the SN 2008cs, located at about 1.5 Kpc, relatively far from the galaxy nucleus.</text>
<text><location><page_15><loc_7><loc_41><loc_50><loc_60></location>Finally, in the bottom panel of Fig. 10 we compare the distribution of locations inside the host galaxy for the expected (lineonly) vs observed (dark grey) SNe. The di ff erent location are identified by the K band pixel counts: in general high counts occurs in the nuclear regions while low counts are in the outskirts (we use pixel counts instead of radial distances because the latter is di ffi cult to be defined for galaxies with irregular morphology or double nuclei. However a indicative correspondence from pixel count to radial distance is shown it the top axis of the figure for a galaxy with regular morphology. There is a mild indication of a deficiency of observed events in regions with high pixel counts. Taken to face value this may suggest a minor overestimate of the detection magnitude limit in the nuclear regions. Given the poor statistics we cannot derive definite conclusions and therefore we will not elaborate further this issue.</text>
<text><location><page_15><loc_7><loc_30><loc_50><loc_41></location>In the same figure we show also (in light grey) the distribution of locations of the expected events for an ideal case where the magnitude detection limit in the nuclear regions is as deep as in the outskirts, and extinction is negligible. The experiment shows that the fraction of events that remains hidden to our search in the galaxy nuclear regions due to the combined e ff ect of reduced search e ffi ciency and high extinction is very high, being about 60% (cf. Mattila et al. 2012).</text>
<section_header_level_1><location><page_15><loc_7><loc_27><loc_45><loc_28></location>4.1. Uncertaintiesandeffectofdifferentassumptions</section_header_level_1>
<section_header_level_1><location><page_15><loc_7><loc_25><loc_25><loc_26></location>Magnitude detection limit</section_header_level_1>
<text><location><page_15><loc_7><loc_14><loc_50><loc_24></location>One of the main source of uncertainty for the simulation is related to the estimate of the magnitude detection limit, ma g lim . For the reference simulation, we adopted as ma g lim the mean value out of three artificial star experiments conducted for a number of selected positions inside the host galaxy (cf. 2.5). The dispersion of measurements, that is the uncertainty on ma g lim , is quite large with a typical range of ∼ 0 . 5 mag but, in more extreme di ffi cult cases, it can be as large as 2 mag.</text>
<text><location><page_15><loc_7><loc_10><loc_50><loc_13></location>To test the propagation of this uncertainty, we performed MonteCarlo experiments assuming alternatively the lower and higher ma g lim out of the three experiments. We found that the</text>
<text><location><page_15><loc_52><loc_87><loc_95><loc_93></location>predicted number of SNe is respectively 6 . 2 ± 2 . 5 and 4 . 7 ± 2 . 2, that are + 17% and -11% with respect to the numbers from the reference simulation. The fact that the error is significant is the reason why we spent a significant e ff ort for a detailed estimate of the detection limit.</text>
<section_header_level_1><location><page_15><loc_52><loc_83><loc_69><loc_84></location>SN Luminosity Function</section_header_level_1>
<text><location><page_15><loc_52><loc_60><loc_95><loc_82></location>In the reference simulation we use a gaussian distribution for the SN luminosity function (SN-LF) with a mean value and dispersion taken from Li et al. (2011b). However, Horiuchi et al. (2011), based on a small sample of very nearby SNe, claimed that the faint end of the SN-LF is underestimated and SN CC fainter than mag /similarequal -16 could made up to 50% of the distribution, to be compared with 20% of the sample of Li et al. (2011b). On the other hand, Mattila et al. (2012) argued that Horiuchi et al. (2011) overestimated the fraction of intrisically faint CCSNe since they neglect the host galaxy extinction for their SN absolute magnitudes. We performed a MonteCarlo experiment adopting the Horiuchi's SN-LF and found that in this case the expected number of events would be low, only 3.3 on average. This is because most faint events are expected to fall below the search detection limit. The fact that the actual discoveries are twice this number argues against a large fraction of faint SN-CC (cf. Botticella et al. 2012)</text>
<section_header_level_1><location><page_15><loc_52><loc_57><loc_79><loc_58></location>IMF and SN CC progenitor mass range</section_header_level_1>
<text><location><page_15><loc_52><loc_30><loc_95><loc_56></location>The IMF enters both in the estimate of the number of SN progenitors and in the calibration of TIR luminosity in terms of SFR relation. However, the expected rate of CC SNe in our sample is virtually independent of the IMF slope. Indeed, for a given total mass of the parent stellar population, top heavy IMFs imply both a higher number of CC progenitors as well as a larger luminosity. Following Dwek et al. (2011) the number of CC progenitors per unit mass is kCC = 0 . 007 , 0 . 011 and 0.039 M /circledot -1 respectively for a Salpeter, a Kroupa and a Starburst IMF , assuming that the progenitors range from 8 to 50 M /circledot . At the same time the total luminosity of a SB forming stars with a SFR of 1 M /circledot yr -1 over a period of 10 Myr (i.e. a 10 7 M /circledot stellar population) is 4 . 71 × 10 9 , 7 . 33 × 10 9 and 2 . 55 × 10 10 L /circledot again for a Salpeter, a Kroupa and a Starburst IMF, respectively. The M / L ratio of such SB is then 0.0021, 0.0014 and 0.0004 (solar units) for the three IMFs, and the expected number CC SNe originating from it is /similarequal 1 . 5 every 10 5 L -1 /circledot for all the three IMFs. Working out the numbers, it turns out that the SN CC rates from a population with a given LTIR is almost independent on the IMF, provided a consistent choice is made.</text>
<text><location><page_15><loc_52><loc_19><loc_95><loc_29></location>Crucial is instead the assumption of the SN CC progenitor mass range, in particular the lower limit. Indeed if we adopted an upper limit of 100 M /circledot instead of the reference value of 50 M /circledot the expected number of SNe would be 5 . 5 ± 2 . 1, only ∼ 5% higher then the reference simulation. On the other hand assuming a lower limit of 10 M /circledot (instead of 8 M /circledot ) results in an expected number of SNe of 3.9 ± 2.1, which is ∼ 30%lower than the expected rate obtained in the reference case.</text>
<section_header_level_1><location><page_15><loc_52><loc_16><loc_59><loc_17></location>Extinction</section_header_level_1>
<text><location><page_15><loc_52><loc_10><loc_95><loc_15></location>For the reference case we assumed that the extinction scales with the SFR with a maximum value corresponding to the SFR peak AV = 30 mag. To test the uncertainty related to this assumption we made two di ff erent tests. In one experiment we maintained</text>
<text><location><page_16><loc_7><loc_84><loc_50><loc_93></location>the relation of AV with SFR but taking, alternatively, a peak extinction value AV = 10 and AV = 100 mag. The experiment gave as expected number of SNe 5 . 5 ± 2 . 7 and 4 . 7 ± 2 . 3, respectively. In the second experiment we assume that the extinction is constant through the galaxy and is AV = 3 . 0 mag. In this case the expected number is 5 . 3 ± 2 . 3 identical to the value of the reference simulation.</text>
<text><location><page_16><loc_7><loc_80><loc_50><loc_84></location>The conclusion is that the uncertainty on the extinction does not a ff ect significantly the simulation or, conversely, that our experiment we cannot probe the extinction distribution.</text>
<section_header_level_1><location><page_16><loc_7><loc_77><loc_26><loc_78></location>Star Formation Distribution</section_header_level_1>
<text><location><page_16><loc_7><loc_66><loc_50><loc_76></location>The spatial distribution of SFR is an important, and the most uncertain, ingredient of the simulation. For instance, if we assume that the SFR is confined in the very inner regions, say in the inner 3 -500 pc, the resulting SNe will remain unaccessible to our search. On the other hand, the fact that in some SBs the SFR is extended has been confirmed by di ff erent studies (eg. McQuinn et al. 2012), not to mention that many of the SNe we have discovered are at significant radial distances (cf. Tab. 3).</text>
<text><location><page_16><loc_7><loc_54><loc_50><loc_65></location>As we described in Sect. 3.1.4 as proxy of the SFR distribution we use L α K where α range from 1 to 2 depending on the galaxy compactness class (Tab. 6). To test for the uncertainties of this assumption we performed two simulations assuming that for all galaxy α is either 1 or 2. We obtained in the first case an expected rate of 8 . 8 ± 3 . 0 and in the second case a value of 3 . 0 ± 1 . 7. The latter occurs because when the SFR is more concentrated, a large number of SNe remain hidden to our search due to the low search detection e ffi ciency in the nuclear regions.</text>
<text><location><page_16><loc_7><loc_47><loc_50><loc_54></location>The conclusion is that the uncertainty in the adopted SF distribution propagates with an error of ∼ 50% on the expected SN number. We may consider that the actual good match of observations with the reference simulation argues in favor of the adopted prescription.</text>
<section_header_level_1><location><page_16><loc_7><loc_44><loc_32><loc_45></location>5. Summary and Conclusions</section_header_level_1>
<text><location><page_16><loc_7><loc_36><loc_50><loc_43></location>We have presented the analysis of an infrared SN search in a sample of 30 nearby SB galaxies, conducted between 2009 and 2011, with the goal to verify the link between star formation and SN rate. During our search we collected in total about 240 observations discovering 6 SNe, 4 of them with spectroscopic confirmation.</text>
<text><location><page_16><loc_10><loc_34><loc_47><loc_35></location>How does this number compares with the expectation ?</text>
<text><location><page_16><loc_7><loc_25><loc_50><loc_34></location>Answering this question requires a detailed characterization of the SN search detection e ffi ciency, the galaxy properties (in particular SF rate and spatial distribution) and the SN properties and progenitor scenarios. We included all these ingredients in a MonteCarlo simulation tool that, allowing for the stochastic nature of SN events, can be used to explore the distribution of the expected SN number and properties.</text>
<text><location><page_16><loc_7><loc_10><loc_50><loc_25></location>First of all, we may remark that by itself the number of detected SNe is a proof of the high SFR in SBs. In fact if we compute the expected number of SNe in our survey based on the average SN rate per unit B luminosity or mass (Li et al. 2011a), we would predict the discovery of 0.5 events (or more precisely, 50% of the simulation predict the discovery of one event and none is expected in the other 50%). The observed number is one order of magnitude higher, which is consistent with the fact that the TIR emission of SBs is about ten times higher than for normal SF galaxies with the same B luminosity. Indeed, it is wellknown that the TIR luminosity is an excellent tracer for SFR, in particular in SBs.</text>
<text><location><page_16><loc_52><loc_79><loc_95><loc_93></location>When we adopt the SFR from LTIR as input for the MonteCarlo experiment, we find that the expected number of SNe in our search is 5 . 3 ± 2 . 3, SNe in excellent agreement with observations. In most cases we predict that only SN CC should be discovered while in the actual search we did detect one type Ia SN. Given that there is a sizable fraction of experiments (10%) when this is predicted to occur we do not elaborate further this issue. Also, allowing for the low statistics, we find an excellent agreement between the predicted and observed SN properties, namely apparent magnitude at discovery, extinction and location inside the host galaxies.</text>
<text><location><page_16><loc_52><loc_49><loc_95><loc_79></location>We performed a number of tests to verify the dependence of the simulation outcomes from the input parameters. For the SN search characterization we show that an accurate estimate of the magnitude limit for SN detection is crucial. This is why we spend a considerable e ff ort in artificial star experiments (possibly the single most expensive task of our project). For the galaxy characterization the most uncertain input is the SF spatial distribution. With some creativity, we devised a prescription that seems to work, but it is certain that this is a place for improvements when new, high resolution SB maps will become available. Instead, we found that our results are not sensitive to the uncertainty on the amount of extinction because where extinction is very high (the dense SB regions) our search is limited by the bright magnitude detection limit. SNe in these regions remain hidden to our search almost independently on the amount of extinction. Based on our simulation we estimated that the fraction of hidden SNe is very significant, that is ∼ 60% with an upper limit of 75% if we account for the poissonian uncertainties in the number of detected events. Finally, for the SN progenitor scenarios the larger uncertainty is the lower limit of the progenitor mass range. If we adopt a lower limit M L CC = 10 M /circledot instead of 8 M /circledot as in the reference simulation, the expected number of SNe would be 30% lower than observed.</text>
<text><location><page_16><loc_52><loc_33><loc_95><loc_49></location>Our results appear in good agreement with those of previous similar searches (Mannucci et al. 2003; Cresci et al. 2007; Mattila et al. 2007a, 2012, cf. Sect. 1). In broad terms, the overall conclusion of all these studies can be expressed as follows: the number of (CC) SNe found in SBs galaxies is consistent with that predicted from the high SFR (and the canonical mass range for the progenitors) when we recognize that a major fraction of the events remains hidden in the unaccessible SB regions. As stressed by Mattila et al. (2012), this has important consequences for the use of SN CC as probe of the cosmic SFR, because the fraction of SBs is expected to increase with redshifts (cf. Melinder et al. 2012; Dahlen et al. 2012)</text>
<text><location><page_16><loc_52><loc_29><loc_95><loc_33></location>While continuing to search for SNe in SBs, in optical and infrared, can certainly help to improve the still low statistics, one may argue at this point for a change of strategy.</text>
<text><location><page_16><loc_52><loc_10><loc_95><loc_29></location>In this respect good example is the attempt to reveal some of the hidden SN CC through infrared SN searches which exploits adaptive optics at large telescopes, eg. Gemini or VLT. The results are encouraging with the discovery of two SNe with very high extinction, namely SN 2004ip with AV between 5 and 40 mag (Mattila et al. 2007b) and SN 2008cs with AV 16 mag (Kankare et al. 2008), though we may notice that both objects were too faint for spectroscopic confirmation. Other two SNe were discovered very close to the galaxy nucleus, namely SN 2010cu at a radial distance of 180 pc and SN 2011hi at 380 pc (Kankare et al. 2012), though in these cases the low extinction suggests that the low radial distance is a projection e ff ect (also in these cases no spectroscopic classification was obtained). The extinction towards SN 2011hi was revised by Romero-Ca˜nizales et al. (2012) using Gemini-N data. They</text>
<text><location><page_17><loc_7><loc_87><loc_50><loc_93></location>demonstrate that this is most likely a SN IIP with AV of 5-7 mag. Because of the need to monitor one galaxy at the time and to access heavily subscribed large telescopes, this approach will not result in large statistics though even a few events may be molstly valuable to explore the very obscured nuclear regions.</text>
<text><location><page_17><loc_7><loc_79><loc_50><loc_86></location>On the other hand, a new opportunity that should be explored is the piggy-back on wide field extragalactic surveys of the next generation infrared facilities, in particular EUCLID. This would allow for the first time to perform IR SN searches on large sample of galaxies exploring a range of SF activity and, by monitoring galaxies at di ff erent redshifts, probe the cosmic evolution.</text>
<text><location><page_17><loc_7><loc_76><loc_50><loc_78></location>Acknowledgements. Wethank the referee, Seppo Mattila, for the careful reading and the very useful comments.</text>
<text><location><page_17><loc_7><loc_71><loc_50><loc_75></location>We particular thank Anna Feltre (ESO), for her help inestimating the possible contribution by AGNs to the FIR luminosity of the galaxies and to Barbara Lo Faro (Astronomy Department of Padova) for helpful discussions and suggestions.</text>
<text><location><page_17><loc_7><loc_69><loc_50><loc_71></location>We acknowledge the support of the PRIN-INAF 2009 with the project 'Supernovae Variety and Nucleosynthesis Yields'.</text>
<text><location><page_17><loc_7><loc_67><loc_50><loc_69></location>E.C., L.G., S.B., A.P. and M.T. are partially supported by the PRIN-INAF 2011 with the project 'Transient Universe: from ESO Large to PESSTO'.</text>
<text><location><page_17><loc_7><loc_64><loc_50><loc_67></location>N.E.R. acknowledges financial support by the MICINN grant AYA08-1839 / ESP, AYA2011-24704 / ESP, and by the ESF EUROCORES Program EUROGENESIS (MINECO grants EUI2009-04170).</text>
<text><location><page_17><loc_7><loc_60><loc_50><loc_64></location>F.B. acknowledges support from FONDECYT through Postdoctoral grant 3120227 and from the Millennium Center for Supernova Science through grant P10-064-F (funded by 'Programa Bicentenario de Ciencia y Tecnologa de CONICYT' and 'Programa Iniciativa Cientiffica Milenio de MIDEPLAN').</text>
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[
{
"title": "ABSTRACT",
"content": "Context. The use of SN rates to probe explosion scenarios and to trace the cosmic star formation history received a boost from a number of synoptic surveys. There has been a recent claim of a mismatch by a factor of two between star formation and core collapse SN rates, and di ff erent explanations have been proposed for this discrepancy. Aims. We attempted an independent test of the relation between star formation and supernova rates in the extreme environment of starburst galaxies, where both star formation and extinction are extremely high. Methods. To this aim we conducted an infrared supernova search in a sample of local starburts galaxies. The rational to search in the infrared is to reduce the bias due to extinction, which is one of the putative reasons for the observed discrepancy between star formation and supernova rates. To evaluate the outcome of the search we developed a MonteCarlo simulation tool that is used to predict the number and properties of the expected supernovae based on the search characteristics and the current understanding of starburst galaxies and supernovae. Results. During the search we discovered 6 supernovae (4 with spectroscopic classification) which is in excellent agreement with the prediction of the MonteCarlo simulation tool that is, on average, 5 . 3 ± 2 . 3 events. Conclusions. The number of supernovae detected in starburst galaxies is consistent with that predicted from their high star formation rate when we recognize that a major fraction ( ∼ 60%) of the events remains hidden in the unaccessible, high density nuclear regions because of a combination of reduced search e ffi ciency and high extinction. Key words. Stars: supernovae: general - Galaxies: starburst - Galaxies: star formation - Infrared: galaxies - Infrared: stars",
"pages": [
1
]
},
{
"title": "HAWK-I infrared supernova search in starburst galaxies /star",
"content": "M. Miluzio 1 , E. Cappellaro 2 , M.T. Botticella 3 , G. Cresci 4 , L. Greggio 2 , F. Mannucci 4 , S. Benetti 2 , Bufano, F. 5 , Elias-Rosa, N. 6 , A. Pastorello 2 , M. Turatto 2 , Zampieri, L. 2 Received: ????; Revised: ??????; Accepted: ?????",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The rate of supernovae (SNe) is a key quantity in astrophysics that provides a crucial test for stellar evolution theory and an input for the modeling of galaxy evolution with direct impact on the chemical enrichment and the feedback mechanism. Corecollapse SNe (SN CC), because of their short-lived progenitors, trace the current star formation rate (SFR). Conversely, for an adopted SFR, measurements of the SN CC rates give information on the mass range of their progenitors as well as the slope of the initial mass function at the high mass end. SN Ia, resulting from the thermonuclear explosion of a white dwarf in a binary system, show a wide range of delay times from star formation to explosion. Therefore, the SN Ia rate reflects the long-term star formation history of the parent stellar system. Recently, it has been claimed that a significant fraction of SN Ia have a short delay time, possibly as short as 10 7 years (Mannucci et al. 2006). Like for CC SN, the rate of such prompt SN Ia events is expected to be proportional to the current SFR. In one of the early attempts to compare the SN and SF rates, Cappellaro et al. (1999) found that the SN CC rate in galaxies with di ff erent U -V color matches the predicted SFR when adopting a mass range 10 M /circledot < M < 40 M /circledot for the SN CC progenitors. In the last decade there was a enormous improvement in the measurement of the cosmic SFR with the careful combination of many di ff erent probes (eg. Hopkins & Beacom 2006). A most relevant feature is that the SFR reaches a maximum at a redshift z ∼ 1 and hereafter begins to decrease down to the current rate which is over one order of magnitude lower than at peak. A significant e ff ort was also devoted to the measurement of the cosmic SN rate: although much of the focus was for type SN Ia, a few estimates of the SN CC rates were also published both for the local Universe (Li et al. 2011a) and at high redshifts (Dahlen et al. 2004; Cappellaro et al. 2005; Botticella et al. 2008; Bazin et al. 2009; Graur et al. 2011; Melinder et al. 2012; Dahlen et al. 2012). While the new local SN CC rate confirms previous results, with a much better statistics and lower systematic errors, the evolution with redshift was found to track very well the SFR evolution, considering the large uncertainties in the extinction corrections. Again, to best match the observed SN and SF rates it was argued that the lower limit for SN CC progenitor had to be ∼ 10 M /circledot (Botticella et al. 2008; Blanc & Greggio 2008). At about the same time, following a di ff erent line of research, the analysis of archival images allowed the identification of the precursors for a number of nearby SN CC. From the often very scanty but precious photometry, and using stellar evolution models, one can estimate the SN precursor mass. The uncertainties are in general quite large, as confirmed from the discrepancy in the mass estimates from di ff erent groups, but this analysis suggests a lower limit for SN CC progenitors of 8 ± 1 M /circledot (Smartt 2009). If this value is adopted, the observed SN rates would result a factor two smaller than those expected from the observed SFR. This was identified by some authors as a 'SN rate problem' (e.g. Horiuchi et al. 2011. While one should remind that the uncertainties on SFR rate calibrations are still large (Botticella et al. 2012; Kennicutt & Evans 2012), it also true that there is a number of possible biases in the SN rate estimates. The two most severe are the possible underestimate of a large population of faint SN CC and / or the underestimate of the correction for extinction (Horiuchi et al. 2011; Mattila et al. 2012). In particular, Mannucci et al. (2007); Cresci et al. (2007) and, more recently, Mattila et al. (2012) argued that a significant fraction of SN CC remains hidden in the nuclear region of starburst galaxies, with a loss of up to ∼ 70-90% in the highly dustenshrouded environments of (ultra-)luminous infrared galaxies( U / LIRGs). This e ff ect is expected to be more important at high redshift because of the larger fraction of starburst galaxies. Indeed, when a correction for this hidden SN fraction is included in the rate calculation the discrepancy between SN and SF rates at high redshifts seems to disappear (Melinder et al. 2012; Dahlen et al. 2012; the 'missing fraction' correction adopted in these works was from Mattila et al. (2012). It is currently unclear if this e ff ect is large enough to explain also the discrepancy observed in the local Universe with somewhat conflicting evidences from the statistics of SNe in the Local Group galaxies (Botticella et al. 2012; Mattila et al. 2012) and large sample SN searches (Li et al. 2011a). Entering in this debate, we planned for an infrared SN search in a sample of local starburst galaxies (SBs). The idea was to verify the link between SN and SF rates in an environment where star formation is very high, 1-2 order of magnitude higher than in normal star-forming galaxies. By observing in the K-band we were aiming to reduce the bias due to extinction (AK ∼ 0 . 1AV). The idea is not new. A first attempt of a dedicated SN search in SBs was performed in the optical band by Richmond et al. (1998). During the search only a handful of events were detected leading the authors to conclude that the rate of (unobscured) SNe in SBs is the same as in quiescent galaxies. A similar conclusion was reached by Navasardyan et al. (2001), again based on optical data. As for infrared SN search, after a few unsuccessful attempts (Grossan et al. 1999; Bregman et al. 2000), the first results of a systematic search in SBs were reported by Maiolino et al. (2002) and Mannucci et al. (2003). They found that the observed SN rate in SBs was indeed one order of magnitude higher then expected for the galaxy blue luminosities but still 3-10 times lower than would be expected from the far infrared (FIR) luminosity. Among the possible explanation for the remaining discrepancy, they suggested extreme extinction in the galaxy nuclear regions (AV > 25mag), which would dim SNe even in the near-IR, and insu ffi cient spatial resolution to probe the very nuclear regions. The reliability of the use of NIR search for obscured SNe in the nuclear and circumnuclear regions of active starburst galaxies was also investigated by Mattila & Meikle (2001) taking into account in particular the problem of extinction. They conclude that with a modest investment of observational time it may be possible to discover a number of nuclear SNe. A negative search for transients in NICMOS images retrieved from the Hubble Space Telescope archive suggests that the same biases likely a ff ect also space-based, high spatial resolution observations (Cresci et al. 2007). The same approach was used by Mattila et al. (2007b) but with ground based, adaptive optics (AO) assisted observations. The application of this technique led to the discovery of a handful of SNe (Kankare et al. 2008, 2012) but not yet to an estimate of the SN CC rate. Until now, about a dozen SNe have been discovered by IR SN searches, not all with spectroscopic confirmation. The number is higher if we include also events first detected in the optical and re-discovered by the IR searches. Therefore the statistics is still very low and many of the original questions are still unanswered. This gave us the motivations to make a new attempt exploiting the opportunity o ff ered by HAWK-I, the infrared camera mounted at the ESO VLT telescope. The paper is divided in two parts: the first part describe the observing program, namely the galaxy sample and the search strategy in Sect. 2.1, the data reduction in Sect. 2.3, the SN discoveries and classification in Sect. 2.4 while in Sect. 2.5 we detail the procedure to estimate the search detection e ffi ciency. The second part is devoted to the description of a simulation tool which is used to predict, based on our current knowledge of SBs properties and on the specific features of our SN search, the number of expected SNdetections (Sect. 3). Finally, we compare the number and properties of the expected and observed events (Sect. 4) and draw our conclusions (Sect. 5). Throughout this paper we assume the following cosmological parameters: H 0 = 72 kms -1 Mpc -1 , ΩΛ = 0 . 73 and Ω M = 0 . 27.",
"pages": [
1,
2
]
},
{
"title": "2.1. Galaxysample",
"content": "Starbursts are galaxies with very high star formation rate, of the order of 10-100 M /circledot yr -1 compared to the few M /circledot yr -1 of normal star forming galaxies in the local universe. Given that in a typical galaxy the very high SFR will rapidly consume the gas reservoir, it is thought that the starburst is a temporary phase in the galaxy evolution. The fact that many SBs are in close pairs or have disturbed morphologies point to the interaction as a dominant, although possibly not unique, reason of the phenomena (Gallagher 1993). The ultra-violet radiation from young, massive stars heats the surrounding dust and is re-emitted in the far infrared. Indeed the most luminous SBs in the local Universe are LIRGs , with 11 < log( LIR / L /circledot ) < 12, and ULIRGs, with log( LIR / L /circledot ) > 12 (Sanders & Mirabel 1996). For our project we selected from the IRAS Revised Bright Galaxy Sample (Sanders et al. 2003) a sample of SBs with total infrared (TIR) luminosity log( LTIR / L /circledot ) > 11 and redshift z < 0 . 07. With the additional requirement that the targets are accessible from Paranal in the April to September observing season (to fit in one of the ESO allocation period) we retrieved a sample of 30 SBs. The list of SBs is reported in Tab. 1. Along with the galaxy name and equatorial coordinates (cols. 1-3) we report the heliocentric redshift (col. 4), log LTIR and log LB (cols. 5 and 6; cf. Sect. 3.1.1), the Hubble type (col. 7), the SFR and the expected SNrates (cols 8, 9) derived from LTIR as described in Sect. 3.1.1. Galaxy data have been retrieved from NED 1 . In the last column ⊙ we listed (in boldface) the designation of the SNe discovered in our search which are the basis for our analysis. For completeness we also list (in italics) the SNe discovered by other SN searches outside our monitoring period. The distribution of LB and LTIR are compared in Fig. 1 showing that, as typical for SBs, LTIR is on average a factor ten higher than LB , whereas for normal star forming galaxies LTIR ∼ LB . We notice that almost all galaxies are LIRGs and only two are ULIRGS. Most galaxies of the sample are isolated ( ∼ 60 -70%) while the remaining are double / interacting galaxies or contain double nuclei, signature of a recent merger. Several galaxies of the sample are asymmetrical, disturbed, or show warps, bars and tidal tails.",
"pages": [
2,
3
]
},
{
"title": "2.2. Searchstrategy",
"content": "To search SNe in the selected SB sample we used the HAWK-I instrument installed at the ESO VLT telescope at Cerro Paranal (Chile). HAWK-I is a NIR (0 . 85 -2 . 5 µ m ) wide-field imager with a mosaic of four Hawaii-2RG detectors. The total field of view is 7 . 5 ' × 7 . 5 ' with a scale of 0 . 106 '' / pix. Even in poor seeing conditions ( > 1 . 5 arcsec) the instrument allows to achieve S / N ∼ 10 for a K = 20 magnitude star with a 15 min exposure. The infrared light curves of SNe evolve relatively slowly, remaining within one / two magnitudes from maximum for two / three months (Mattila & Meikle 2001) and therefore an IR SN search does not require frequent monitoring. We planned for an average of three visits per galaxy per semester, for a total of 80-100 visits. The monitoring campaign was scheduled in service mode and we did not set tight constraints for the sky conditions. This and the relatively short duration of the observing blocks made the program well suited as filler. We notice that we had no influence on the actual scheduling of the observations which followed the rules of the ESO service mode scheduler. Eventually, the fraction of useful observing time was 100% of the allocated time in the first season, and 70% in the second and third semesters. The log of the observations is reported in Tab. 2 where for each galaxy we list the epoch of observations (MJD), the seeing (FWHM in arcsec), and the minimum and maximum magnitude limit for SN detection across the image (cf. Sec. 2.5). In total, we obtained 210 K-band exposures (exposure time 15min), with an average of about 3 visits per galaxy per semester. Because of the time loss, three galaxies were not monitored in the last two seasons. It turned out that the average image quality was quite good: for ∼ 90 % of the exposures the seeing was less than 1 . 0 '' , with an average FWHM across the whole program of 0 . 6 '' .",
"pages": [
3
]
},
{
"title": "2.3. Datareductionandanalysis",
"content": "For data reduction and mining of the HAWK-I mosaic images we developed a custom pipeline that integrates di ff erent, publicly available, recipes and tools in a Python environment. The pipeline consists of four sections: The raw images were retrieved from the ESO archive as soon as they became available, and immediately reduced to allow for activation of follow-up spectroscopy of transient candidates. For the pre-reduction, we followed the reduction cascade described in the HAWK-I pipeline manual 3 including dark subtraction, flat field and illumination corrections, background subtraction, distortion correction, astrometric o ff set refinement, combination of the di ff erent exposures and stitch of the 4 detectors in a single mosaic image. Actually, it turned out that the ESO pipeline recipes for background subtraction and o ff set refinement do not provide satisfactory results for our images. The main reason is the extended size of our sources and the consequent large dithering we had adopted. To address this issue we implemented custom recipes for the two afore mentioned reduction steps. The most critical step of the data reduction is the image subtraction, in particular in the proximity of the nuclear regions of the galaxies. First of all we need to choose a proper reference image, usually the image with the best seeing obtained at least three month before (or in some case after) the image to be searched. We also need to choose the proper parameters for the image di ff erence procedure (see Melinder et al. 2012 for an extensive discussion). An additional problems arises because in the distributed version of ISIS , the program automatically selects the reference sources for the computation of the convolution kernel. Owing to the small number of sources in our extragalactic fields, the reference source list in general includes the bright galaxy nucleus which, being very bright, has a significant weight in the determination of the kernel. This may cause some problems because if at one epoch a SN occurs very close to the galaxy nucleus it can be included in the convolution kernel and e ff ectively cancelled in the di ff erence image. We therefore modified the ISIS selection procedure to allow for exclusion of specific sources, in particular the galaxy nuclei, from the reference list. Despite the e ff orts in many cases the di ff erence image shows significant spurious residuals in correspondence to the galaxy nuclear regions. The problem is most severe in case of images with poor seeing ( FWHM > 1 '' ) and / or reduced transparency. This is illustrated in Fig. 2 where we show two examples of image di ff erence one for a search image with poor seeing ( FWHM = 1 . 5 '' , left panel) and the other for a case with excellent seeing ( FWHM = 0 . 4 '' ). In both cases, the reference image was the same and had excellent seeing ( FWHM = 0 . 4 '' ). False detections due to residuals of the image subtraction were largely removed by the requirement that the candidate had to be visible at least in two consecutive epochs.",
"pages": [
3,
4
]
},
{
"title": "2.4. Supernovadiscoveriesandcharacterization",
"content": "During our monitoring campaign 6 transients were detected in at least two consecutive epochs separated by at least one month (finding charts are in Fig. 3). Four of them were spectroscopically confirmed as SNe (three SN-CC and one SN Ia) and we will argue in the following that also the other two transients, labeled as probable SN (PSN), are likely SN CC (Tab. 3). SNe 2010bt and 2010gp were discovered and announced before our detection by optical searches but have been independently rediscovered by us. The objects are listed in Tab. 3 along with the host galaxy name, distance modulus (computed from the galactocentric redshift and the adopted cosmology), SN coordinates, o ff sets from the galaxy nucleus and projected linear distances from the galaxy nucleus. For all transients K-band magnitudes were measured through aperture photometry on the di ff erence images and calibrated with respect to 2MASS stars in the field. Upper limits measured on pre-discovery images were also estimated. For all transients,",
"pages": [
4
]
},
{
"title": "M. Miluzio et al.: HAWK-I SN search",
"content": "H = HAWK-I@VLT, E = EFOSC2@NTT, S = SOFI@NTT, L = RATCam@Liverpool, D = Dolores@TNG We obtained an optical / infrared spectrum with X-Shooter at VLT on 2010 June 5. However, because of its very low S / N, we could not derive a convincing classification and therefore we had to rely on the K-band photometry. Comparing the K band absolute light curve of PSN2010 ( AB (host) = 0) with template light curves of di ff erent SN types we found a good match with SN 2005cs a prototype of under-luminous type IIP SN (Pastorello et al. 2009), assuming that the detection of PSN2010 was 2 months after the explosion. However, lacking color measurements, we could not constraint the ex- tinction and indeed, assuming a high extinction AB ∼ 8 mag, we found an alternative good match with the light curve of SN 1999em (Fig. 5). Intermediate values may also be adopted by fitting other SN II. PSN2011 in IC 1623 was discovered on 2011 July 21.4 UT in the western component of a galaxy pair. The object was not detected on a K-band image taken on 2010 Sept. 5 ( K > 19 . 0 mag). Unfortunately, due to bad weather in the scheduled nights, we could not obtain a spectroscopic observation of the transients. We have to rely on three epochs of photome- try, in K complemented by two epochs in the optical R and I bands. A simultaneous comparison of the absolute observed luminosity with template SNe give a best fit with the SN Ic 2007gr one month after maximum (Fig. 6). Assuming this classification, from the colors we can constrain the extinction to be AB = 0 . 5 ± 0 . 5 mag. However, we have to admit that, within the errors, the photometry of PSN2011 can be consistent also with a type IIP at about 3 months after explosion. To recap, during the search we discovered 6 SNe. Four received a spectroscopic classifications: one as a type Ia and three as core collapse events, a type IIn, a type IIP and a type Ic. For the other two, based on the sparse photometry, we argue that most likely they are core collapse SNe, with a best fit as type IIP and type Ic, respectively.",
"pages": [
8,
9
]
},
{
"title": "2.5. Searchdetectionlimit",
"content": "In order to derive the SN rate from the number of detected events it is crucial to obtain an accurate estimate of the magnitude detection limit for each of the search images and for di ff erent locations in the images. As it has been shown in Fig. 2, the detection e ffi ciency is influenced by the sky conditions at the time of observations (namely seeing and transparency) and by the transient position inside the host galaxy. The magnitude limit for SN detection has been estimated through artificial star experiments. The procedure we adopted was the following: To illustrate the results, a plot of the magnitude limit versus background counts for four observations of the galaxy NGC7130isshownin Fig. 7. Each epoch is labelled with the image seeing, while the errorbar shows the range of limiting magnitudes for the three experiments. The top x-axis shows the linear distance in Kpc from the galaxy center. It can be seen that, as expected, the magnitude limit is lower in the nuclear regions which, for a typical galaxy, correspond to 1.5-2.0 kpc. Epochs with di ff erent seeing have similar magnitude limits in the galaxy outskirts (typically K ∼ 19 mag), while in the nuclear region when seeing is poorer the magnitude limit is brighter (in the worst case even 5-6 mag brighter than in the galaxy outskirts).",
"pages": [
9,
10
]
},
{
"title": "3. SN search simulation",
"content": "To evaluate the significance of the detected events we elaborated a simulation tool that returns the number and properties of expected events based on specific features of our SN search, a number of parameters describing our current knowledge of SBs and SN properties. The tool uses a MonteCarlo approach which simulates the stochastic nature of SN explosions. By collecting a number of MonteCarlo experiments with the same input parameters, we can test whether the observed events are within the expected distribution. On the other hand by varying some of the input parameters, we can test the influence of specific assumptions.",
"pages": [
10
]
},
{
"title": "3.1. Thesimulationtool",
"content": "Our MonteCarlo (MC) simulation tool is built in a Python environment and makes use, for the di ff erent inputs, of standard values taken from the literature. For those that are more controversial, we will give references with some discussion. The basic ingredients of the simulation are: the adopted mass range of the progenitors and IMF slope. In fact, for our purposes, we can neglect the very short time delay from CC progenitor formation to explosion. For type Ia SNe we need to consider the realization factor, that is the fraction of events in the proper mass range which occurs in suitable close binary systems and the delay time distribution (Sect. 3.1.2).; Hereafter, we discuss our assumptions about the parameters of the simulation.",
"pages": [
10,
11
]
},
{
"title": "3.1.1. From IRAS measurements to Star Formation Rate",
"content": "The SFR in SBs can be estimated on the basis of the galaxy total infrared luminosity (L TIR ) under the assumption that dust re-radiates a major fraction of the UV luminosity, and after calibration with stellar synthesis models. In turn the TIR luminosity can be estimated from FIR flux measurements. Helou et al. (1988) provided a prescription for deriving the FIR emission from IRAS measurements: where FIR is in W m -2 and f ν are in Jansky. FIR fluxes are converted into TIR fluxes by using the relation of Dale et al. (2001) where x = log f ν (60 µ m ) f ν (100 µ m ) and [ a ( z = 0)] /similarequal [0 . 2378 , -0 . 0282 , 0 . 7281 , 0 . 6208 , 0 . 9118] TIR fluxes are converted in luminosities using the adopted distances: Finally, the relation between the SFR ( ψ ), and L TIR was derived by Kennicutt (1998) from SB galaxy spectral synthesis model adopting 10-100 Myr continuous bursts and a Salpeter IMF as:",
"pages": [
11
]
},
{
"title": "3.1.2. SNR and SFR",
"content": "In general, the rate of SNe expected at a specific time, ˙ nSN ( t ), for a stellar population depends on the star formation history, the number of SNe per unit mass from one stellar generation (labelled as SN productivity) and the distribution of delay time from star formation to explosion for the specific SN type. Following the notation of Greggio (2005, 2010): where ψ ( t ) is the star formation rate, fS N is the distribution of the delay times τ and kSN is the supernova productivity. The equation shows that at a fixed epoch t since the beginning of star formation, the rate of SNe is obtained by adding the contribution of all past stellar generations, each of them weighted with the SFR at the appropriate time.",
"pages": [
11
]
},
{
"title": "Core Collapse SNe",
"content": "For core collapse SNe the delay time from star formation to explosion (2.5 Myr for 120 M /circledot stars up to 40 Myr for 8 M /circledot stars) is short compared with the typical SBs duration (200 -400 Myr, McQuinn et al. 2009). Assuming that the SFR in the SB was constant during the past 40 Myr, the expected CC SN rate, ˙ nCC , is proportional to the current SFR: The supernova productivity kCC is derived by integrating the IMF, φ ( m ), and assuming a CC progenitor mass ( MCC ) range: where M L CC and M U CC are respectively the lower and upper mass limits for SN CC progenitors and ML , MU are the lower and upper stellar mass limit. To be consistent with the Kennicutt's SFR calibration we adopted a Salpeter IMF, that is: Assuming 8 < MCC < 50 M /circledot for the CC progenitor mass range, kCC = 0 . 007 M -1 . This number changes significantly if we adopt a di ff erent IMF, e.g. kCC = 0 . 011 for a Kroupa IMF or kCC = 0 . 039 for an extreme Starburst IMF (Dwek et al. 2011). We soon note however that, because the IMF enters also in the conversion from LTIR to ψ , the expected rate of SN events is almost independent on the selected IMF (cf. Sect. 4.1) provided the choice is consistent. More important is the assumption on the mass range for CC progenitors which is not well constrained. Actually, while changing the upper limit of the progenitor mass from 40 to 100 M /circledot makes a modest 10% increase in the CC SN productivity, the lower mass limit is crucial, with kCC decreasing by 30% if we adopted M L CC = 10 M /circledot instead of the favored value of 8 M /circledot (Smartt 2009).",
"pages": [
11
]
},
{
"title": "SN Ia",
"content": "Estimating the expected rate of SN Ia is complicated because the delay time distribution fIa , while still uncertain, certainly ranges from short to very long time. In particular it has been suggested that SN Ia can be divided into two classes, one with a short delay time whose rate scales with the current SFR (also called prompt ), and a second with a long delay time ( tardy ), whose rate scales with the average of the SFR along the entire galactic evolution (Scannapieco & Bildsten 2005; Mannucci et al. 2006). While stellar evolution arguments (Greggio 2010, 2005; Greggio & Renzini 1983) and more recent data (Maoz et al. 2012; Totani et al. 2008) suggest a continuous distribution of the delay time instead of two distinct classes, the schematization is still a fair approximation that help in simplifying the problem of predicting the expected SN Ia rate in SBs. In general, for a galaxy of the local Universe, ∼ 13 Gyr after the beginning of SFR, we can identify the contribution of the two components as follows (Greggio 2010): where ψ C and ψ P are the average SFR over, respectively, the last 0.1 Gyr (current SFR) and from 0.1 to 13 Gyr ago (past SFR). The SN productivity kIa is the product of the number of stars per unit mass in the adopted progenitor mass range (0.021 for a Salpeter IMF and a mass range 3M /circledot < M < 8 M /circledot ) and the realization fraction, the actual fraction of systems which make a successful explosion ( ∼ 5% according to the most recent estimate) (Maoz & Mannucci 2012). We assume that SF history in SBs can be described schematically with two components: a constant SFR during the galaxy evolution which created the galaxy stellar mass, and an on-going episode of intense SFR which is the source of the strong TIR emission. Neglecting the contribution of the ongoing SB to the galaxy stellar mass, we can approximate ψ P /similarequal M / 13 × 10 9 , and write Eq. 2 as follows: where F p Ia = < f p Ia > × 0 . 1 and F t Ia = < f t Ia > × 13 /similarequal 1 -F p Ia are the relative fraction of prompt and tardy events derived by integrating the delay time distribution in the relevant time range. In our approximation ψ C can be derived from the observed LTIR and the galaxy mass from the K magnitude and B -K colors (cf. Mannucci et al. 2005). The relative contribution of the two SN Ia components has been a very debated issue in the last few years, ranging from F p Ia ∼ 50% (Mannucci et al. 2006) to F p Ia ∼ 10% from standard stellar evolution scenarios (Greggio 2010). In our simulation we adopted as reference an intermediate value, F p Ia ∼ 30%.",
"pages": [
11,
12
]
},
{
"title": "3.1.3. Extinction",
"content": "Dust extinction in SBs is very high, especially in the nuclear regions. For instance, Shioya et al. (2001) found that fitting the spectral energy distribution of the nuclear region of Arp 220 requires a visual extinction AV > 30 mag. Actually, according to Engel et al. (2011), 'over most of the disk the near-infrared obscuration is moderate, but increases dramatically in the central tens of parsecs of each nucleus'. Similar high extinction, AV ∼ 20, was found for the SB region of Zw 096 (Inami et al. 2010). As a first order approximation, for our simulation we assumed that the extinction has the same distribution of the SF (see next section) with a maximum value AV = 30 mag corresponding to the SFR peak and scaled linearly in the other regions. While this is a crude approximation, it turns out that the actual choice of extinction correction has little impact for our simulation. In the nuclear, high extinction regions the SN detection is limited by the reduced performance of the image subtraction algorithm in these high surface brightness regions. At the same time, our IR search is largely insensitive to variation in the (moderate) extinction of the outer galaxy regions. For the wavelength dependence of extinction we adopted the Calzetti's law with RV = 4 . 05 ± 0 . 8 (Calzetti et al. 2000).",
"pages": [
12
]
},
{
"title": "3.1.4. Star Formation Distribution",
"content": "The spatial distribution of the SFR is a key ingredient of the simulation. This is because we expect that SNe occur more frequently in the high SF regions where, on the other hand, our detection e ffi ciency is lower. In principle, the FIR emission which is used to estimate the SFR would also be a good tracer of its spatial distribution. However, it turned out that the available MIR imaging for the galaxies of our sample (mainly obtained with the Spitzer observatory) do not have enough spatial resolution for mapping the compact SB structures. Selected K-band images from our survey can have excellent resolution but, as is well-known, the near IR emission better traces the old star population, that is the galaxy mass distribution more than the SFR distribution. Therefore for an estimate of the SFR concentration, we are forced to an indirect, statistical approach. Our starting point is the SB classification by Hattori et al. (2004), who derived a correlation between the global SBs properties, such as FIR colors, and the compactness of the SF regions. These range from very compact ( ≤ 100 pc) nuclear starbursts with almost no star-forming activity in the outer regions (type 1), to extended starbursts with relatively faint nuclei (type 4), with type 2 and 3 as intermediate cases. In addition, they found a trend for galaxies with more compact SF region showing a higher star formation e ffi ciency and hotter far-infrared color. They also found that the compactness of SF regions is weakly correlated with the galaxy morphology, with disturbed objects showing preferentially more concentrated SF. On the other hand, an appreciable fraction ( ∼ 50%) of their galaxy sample was dominated by extended starbursts (type 4). The significant variations in the degree of concentration of the SB SF regions has been recently confirmed by McQuinn et al. (2012). In an attempt to characterize the SF spatial distribution for the SBs of our sample we derived estimates of their morphological class and FIR colors. In particular, following Hattori et al. (2004), SBs with strong tidal features and a single nucleus were classified as 'mergers' (M), galaxy pairs with an overlapping disk or a connecting bridge were classified as 'close pairs' (CP) if the projected separation is < 20 Kpc and galaxies that have a nearby ( < 100 Kpc) companion at the same redshift were classified as 'pairs' (P). The remaining objects were classified as 'single' (S). The classification of the SBs of our sample is listed in Tab. 6 along with the galaxy FIR colors, log f 60 / f 100, log f 25 / f 60. We attributed to each galaxy a compactness class on the basis of its correlation with the FIR colors as shown in Fig. 4 of Hattori et al. (2004) that for the object of our sample corresponds to our Fig. 8. As it can be seen, we also confirmed their claim of a (weak) relation of FIR color and, as a consequence, compactness class with SB morphology. The next step is based on Soifer et al. (2000, 2001). For a number of SBs galaxies they plotted the MIR and NIR emission curve of growth finding that in general the MIR emission is more concentrated, while only for few galaxies the MIR and NIR curves of growth show a similar trend. Actually we found that, to a first order approximation, the MIR emission profile of a given galaxy can be matched by NIR profile powered to an exponent α which ranges between 1, when the two profiles are similar, to 2, when the MIR emission is strongly concentrated. When we classify the same galaxies with the compactness criteria of Hattori et al. (2004), we found that (as expected) the galaxies with compact SF regions (type 1 -2) are characterized by more concentrated MIR emission ( α = 2 . 0 -1 . 5, respectively), while galaxies with extended SF region (type 3-4) have similar MIR vs. NIR profiles ( α = 1 . 25 -1 . 0, respectively). As a reference, we notice that in the typical case of NGC 6240, assuming α = 1 corresponds to locate 50% of the SFR within 1.5 Kpc, whereas for α = 2 the same SFR fraction is enclosed within 500 pc. As a result of this discussion we have a prescription to estimate the SF distribution based on the observed LK map, and adopting a power index α appropriate for the compactness class of the given SB galaxy (Tab. 7).",
"pages": [
12,
13
]
},
{
"title": "3.1.5. Flow chart of the simulation",
"content": "Having defined all the ingredients of the simulation, we can now describe how this proceeds. The simulation flowchart can be summarized as follows: The process, iterated for all the galaxies of the sample, defines a single simulation run. Outcomes of the simulation are the expected number of SN discoveries, their types, magnitudes, extinctions and positions inside the host galaxies. To explore the distribution of the outcomes from the random process, a complete experiment is made by collecting a minimum of a hundred single simulation runs. For the reference simulation we used theinput parameters summarized in Tab. 7. In the next section we will compare the prediction of the simulation with the current SN discoveries.",
"pages": [
13
]
},
{
"title": "4. Comparison between observed and expected SN discoveries",
"content": "As we outlined above, from a large number of MonteCarlo simulation runs we obtain the distribution of the expected SN discoveries. This is shown in Fig. 9, where each bin of the histogram is the predicted probability of observing the specific number of SN discoveries whereas the dashed line marks the number of actual SNe discovered and the shaded area shows its 1σ Poissonian uncertainty range. Wefoundthat with the adopted simulation scenario and input parameters we should have expected, on average, the discovery of 5 . 3 ± 2 . 3 SNe. In 68% of the experiments (1σ ) the expected number is in the range 4-8 which is in excellent agreement with the observed number of 6 events. The prediction of the simulation is that almost all SNe are CC(5.1 SN CC vs. 0.2 SN Ia), though in 10% of the experiments at least one type Ia is found (that is what we have from the real SN search). The distributions of some of the expected and observed SN properties are compared in Fig. 10. For the simulation, we show the distribution across a large number of experiments (line-only histogram) while the grey shaded histogram represents the actual observations. The top panel in Fig. 10 shows the distribution of the apparent magnitudes at the discovery. The good agreement between simulations and observations is a crucial consistency check of our estimates of the magnitude detection limit: if the discovered SNe were systematically fainter / brighter then expected, this would indicate, respectively, an underestimate / overestimate of the search detection e ffi ciency. A comparison of the simulated vs observed extinction distribution is shown in the middle panel of Fig. 10. For the observed distribution the case of PSN2010 for which extinction is ambiguous is shown in light grey. Again the simulation is in good agreement with the observations. This argues in favor of the consistency of the input assumptions. The fact that, in our IR search we expect that most of detected SNe have low extinction ( ∼ 75% with AV < 1 mag) is a consequence of our assumption that the extinction is very high in the nucleus and rapidly decreases with the galaxy radius, following the same trend of the SFR. This does not means that extinguished SN are intrinsically rare but that they are confined to the galaxy nuclear regions where extinction is extremely high even in the IR (see next). At the same time we can exclude the presence of a significant population of SNe with intermediate extinctions: we would easily detect them in our infrared search. Mattila & Meikle (2001) found an average value of AV = 30 mag for the extinction towards the SN remnants of M82. Confirming the presence of high extinction (about AV ∼ 15-45 mag) in the innermost 300 pc regions. On the other hand, Kankare et al. (2008) found an host galaxy extinction of AV ∼ 16 mag for the SN 2008cs, located at about 1.5 Kpc, relatively far from the galaxy nucleus. Finally, in the bottom panel of Fig. 10 we compare the distribution of locations inside the host galaxy for the expected (lineonly) vs observed (dark grey) SNe. The di ff erent location are identified by the K band pixel counts: in general high counts occurs in the nuclear regions while low counts are in the outskirts (we use pixel counts instead of radial distances because the latter is di ffi cult to be defined for galaxies with irregular morphology or double nuclei. However a indicative correspondence from pixel count to radial distance is shown it the top axis of the figure for a galaxy with regular morphology. There is a mild indication of a deficiency of observed events in regions with high pixel counts. Taken to face value this may suggest a minor overestimate of the detection magnitude limit in the nuclear regions. Given the poor statistics we cannot derive definite conclusions and therefore we will not elaborate further this issue. In the same figure we show also (in light grey) the distribution of locations of the expected events for an ideal case where the magnitude detection limit in the nuclear regions is as deep as in the outskirts, and extinction is negligible. The experiment shows that the fraction of events that remains hidden to our search in the galaxy nuclear regions due to the combined e ff ect of reduced search e ffi ciency and high extinction is very high, being about 60% (cf. Mattila et al. 2012).",
"pages": [
13,
14,
15
]
},
{
"title": "Magnitude detection limit",
"content": "One of the main source of uncertainty for the simulation is related to the estimate of the magnitude detection limit, ma g lim . For the reference simulation, we adopted as ma g lim the mean value out of three artificial star experiments conducted for a number of selected positions inside the host galaxy (cf. 2.5). The dispersion of measurements, that is the uncertainty on ma g lim , is quite large with a typical range of ∼ 0 . 5 mag but, in more extreme di ffi cult cases, it can be as large as 2 mag. To test the propagation of this uncertainty, we performed MonteCarlo experiments assuming alternatively the lower and higher ma g lim out of the three experiments. We found that the predicted number of SNe is respectively 6 . 2 ± 2 . 5 and 4 . 7 ± 2 . 2, that are + 17% and -11% with respect to the numbers from the reference simulation. The fact that the error is significant is the reason why we spent a significant e ff ort for a detailed estimate of the detection limit.",
"pages": [
15
]
},
{
"title": "SN Luminosity Function",
"content": "In the reference simulation we use a gaussian distribution for the SN luminosity function (SN-LF) with a mean value and dispersion taken from Li et al. (2011b). However, Horiuchi et al. (2011), based on a small sample of very nearby SNe, claimed that the faint end of the SN-LF is underestimated and SN CC fainter than mag /similarequal -16 could made up to 50% of the distribution, to be compared with 20% of the sample of Li et al. (2011b). On the other hand, Mattila et al. (2012) argued that Horiuchi et al. (2011) overestimated the fraction of intrisically faint CCSNe since they neglect the host galaxy extinction for their SN absolute magnitudes. We performed a MonteCarlo experiment adopting the Horiuchi's SN-LF and found that in this case the expected number of events would be low, only 3.3 on average. This is because most faint events are expected to fall below the search detection limit. The fact that the actual discoveries are twice this number argues against a large fraction of faint SN-CC (cf. Botticella et al. 2012)",
"pages": [
15
]
},
{
"title": "IMF and SN CC progenitor mass range",
"content": "The IMF enters both in the estimate of the number of SN progenitors and in the calibration of TIR luminosity in terms of SFR relation. However, the expected rate of CC SNe in our sample is virtually independent of the IMF slope. Indeed, for a given total mass of the parent stellar population, top heavy IMFs imply both a higher number of CC progenitors as well as a larger luminosity. Following Dwek et al. (2011) the number of CC progenitors per unit mass is kCC = 0 . 007 , 0 . 011 and 0.039 M /circledot -1 respectively for a Salpeter, a Kroupa and a Starburst IMF , assuming that the progenitors range from 8 to 50 M /circledot . At the same time the total luminosity of a SB forming stars with a SFR of 1 M /circledot yr -1 over a period of 10 Myr (i.e. a 10 7 M /circledot stellar population) is 4 . 71 × 10 9 , 7 . 33 × 10 9 and 2 . 55 × 10 10 L /circledot again for a Salpeter, a Kroupa and a Starburst IMF, respectively. The M / L ratio of such SB is then 0.0021, 0.0014 and 0.0004 (solar units) for the three IMFs, and the expected number CC SNe originating from it is /similarequal 1 . 5 every 10 5 L -1 /circledot for all the three IMFs. Working out the numbers, it turns out that the SN CC rates from a population with a given LTIR is almost independent on the IMF, provided a consistent choice is made. Crucial is instead the assumption of the SN CC progenitor mass range, in particular the lower limit. Indeed if we adopted an upper limit of 100 M /circledot instead of the reference value of 50 M /circledot the expected number of SNe would be 5 . 5 ± 2 . 1, only ∼ 5% higher then the reference simulation. On the other hand assuming a lower limit of 10 M /circledot (instead of 8 M /circledot ) results in an expected number of SNe of 3.9 ± 2.1, which is ∼ 30%lower than the expected rate obtained in the reference case.",
"pages": [
15
]
},
{
"title": "Extinction",
"content": "For the reference case we assumed that the extinction scales with the SFR with a maximum value corresponding to the SFR peak AV = 30 mag. To test the uncertainty related to this assumption we made two di ff erent tests. In one experiment we maintained the relation of AV with SFR but taking, alternatively, a peak extinction value AV = 10 and AV = 100 mag. The experiment gave as expected number of SNe 5 . 5 ± 2 . 7 and 4 . 7 ± 2 . 3, respectively. In the second experiment we assume that the extinction is constant through the galaxy and is AV = 3 . 0 mag. In this case the expected number is 5 . 3 ± 2 . 3 identical to the value of the reference simulation. The conclusion is that the uncertainty on the extinction does not a ff ect significantly the simulation or, conversely, that our experiment we cannot probe the extinction distribution.",
"pages": [
15,
16
]
},
{
"title": "Star Formation Distribution",
"content": "The spatial distribution of SFR is an important, and the most uncertain, ingredient of the simulation. For instance, if we assume that the SFR is confined in the very inner regions, say in the inner 3 -500 pc, the resulting SNe will remain unaccessible to our search. On the other hand, the fact that in some SBs the SFR is extended has been confirmed by di ff erent studies (eg. McQuinn et al. 2012), not to mention that many of the SNe we have discovered are at significant radial distances (cf. Tab. 3). As we described in Sect. 3.1.4 as proxy of the SFR distribution we use L α K where α range from 1 to 2 depending on the galaxy compactness class (Tab. 6). To test for the uncertainties of this assumption we performed two simulations assuming that for all galaxy α is either 1 or 2. We obtained in the first case an expected rate of 8 . 8 ± 3 . 0 and in the second case a value of 3 . 0 ± 1 . 7. The latter occurs because when the SFR is more concentrated, a large number of SNe remain hidden to our search due to the low search detection e ffi ciency in the nuclear regions. The conclusion is that the uncertainty in the adopted SF distribution propagates with an error of ∼ 50% on the expected SN number. We may consider that the actual good match of observations with the reference simulation argues in favor of the adopted prescription.",
"pages": [
16
]
},
{
"title": "5. Summary and Conclusions",
"content": "We have presented the analysis of an infrared SN search in a sample of 30 nearby SB galaxies, conducted between 2009 and 2011, with the goal to verify the link between star formation and SN rate. During our search we collected in total about 240 observations discovering 6 SNe, 4 of them with spectroscopic confirmation. How does this number compares with the expectation ? Answering this question requires a detailed characterization of the SN search detection e ffi ciency, the galaxy properties (in particular SF rate and spatial distribution) and the SN properties and progenitor scenarios. We included all these ingredients in a MonteCarlo simulation tool that, allowing for the stochastic nature of SN events, can be used to explore the distribution of the expected SN number and properties. First of all, we may remark that by itself the number of detected SNe is a proof of the high SFR in SBs. In fact if we compute the expected number of SNe in our survey based on the average SN rate per unit B luminosity or mass (Li et al. 2011a), we would predict the discovery of 0.5 events (or more precisely, 50% of the simulation predict the discovery of one event and none is expected in the other 50%). The observed number is one order of magnitude higher, which is consistent with the fact that the TIR emission of SBs is about ten times higher than for normal SF galaxies with the same B luminosity. Indeed, it is wellknown that the TIR luminosity is an excellent tracer for SFR, in particular in SBs. When we adopt the SFR from LTIR as input for the MonteCarlo experiment, we find that the expected number of SNe in our search is 5 . 3 ± 2 . 3, SNe in excellent agreement with observations. In most cases we predict that only SN CC should be discovered while in the actual search we did detect one type Ia SN. Given that there is a sizable fraction of experiments (10%) when this is predicted to occur we do not elaborate further this issue. Also, allowing for the low statistics, we find an excellent agreement between the predicted and observed SN properties, namely apparent magnitude at discovery, extinction and location inside the host galaxies. We performed a number of tests to verify the dependence of the simulation outcomes from the input parameters. For the SN search characterization we show that an accurate estimate of the magnitude limit for SN detection is crucial. This is why we spend a considerable e ff ort in artificial star experiments (possibly the single most expensive task of our project). For the galaxy characterization the most uncertain input is the SF spatial distribution. With some creativity, we devised a prescription that seems to work, but it is certain that this is a place for improvements when new, high resolution SB maps will become available. Instead, we found that our results are not sensitive to the uncertainty on the amount of extinction because where extinction is very high (the dense SB regions) our search is limited by the bright magnitude detection limit. SNe in these regions remain hidden to our search almost independently on the amount of extinction. Based on our simulation we estimated that the fraction of hidden SNe is very significant, that is ∼ 60% with an upper limit of 75% if we account for the poissonian uncertainties in the number of detected events. Finally, for the SN progenitor scenarios the larger uncertainty is the lower limit of the progenitor mass range. If we adopt a lower limit M L CC = 10 M /circledot instead of 8 M /circledot as in the reference simulation, the expected number of SNe would be 30% lower than observed. Our results appear in good agreement with those of previous similar searches (Mannucci et al. 2003; Cresci et al. 2007; Mattila et al. 2007a, 2012, cf. Sect. 1). In broad terms, the overall conclusion of all these studies can be expressed as follows: the number of (CC) SNe found in SBs galaxies is consistent with that predicted from the high SFR (and the canonical mass range for the progenitors) when we recognize that a major fraction of the events remains hidden in the unaccessible SB regions. As stressed by Mattila et al. (2012), this has important consequences for the use of SN CC as probe of the cosmic SFR, because the fraction of SBs is expected to increase with redshifts (cf. Melinder et al. 2012; Dahlen et al. 2012) While continuing to search for SNe in SBs, in optical and infrared, can certainly help to improve the still low statistics, one may argue at this point for a change of strategy. In this respect good example is the attempt to reveal some of the hidden SN CC through infrared SN searches which exploits adaptive optics at large telescopes, eg. Gemini or VLT. The results are encouraging with the discovery of two SNe with very high extinction, namely SN 2004ip with AV between 5 and 40 mag (Mattila et al. 2007b) and SN 2008cs with AV 16 mag (Kankare et al. 2008), though we may notice that both objects were too faint for spectroscopic confirmation. Other two SNe were discovered very close to the galaxy nucleus, namely SN 2010cu at a radial distance of 180 pc and SN 2011hi at 380 pc (Kankare et al. 2012), though in these cases the low extinction suggests that the low radial distance is a projection e ff ect (also in these cases no spectroscopic classification was obtained). The extinction towards SN 2011hi was revised by Romero-Ca˜nizales et al. (2012) using Gemini-N data. They demonstrate that this is most likely a SN IIP with AV of 5-7 mag. Because of the need to monitor one galaxy at the time and to access heavily subscribed large telescopes, this approach will not result in large statistics though even a few events may be molstly valuable to explore the very obscured nuclear regions. On the other hand, a new opportunity that should be explored is the piggy-back on wide field extragalactic surveys of the next generation infrared facilities, in particular EUCLID. This would allow for the first time to perform IR SN searches on large sample of galaxies exploring a range of SF activity and, by monitoring galaxies at di ff erent redshifts, probe the cosmic evolution. Acknowledgements. Wethank the referee, Seppo Mattila, for the careful reading and the very useful comments. We particular thank Anna Feltre (ESO), for her help inestimating the possible contribution by AGNs to the FIR luminosity of the galaxies and to Barbara Lo Faro (Astronomy Department of Padova) for helpful discussions and suggestions. We acknowledge the support of the PRIN-INAF 2009 with the project 'Supernovae Variety and Nucleosynthesis Yields'. E.C., L.G., S.B., A.P. and M.T. are partially supported by the PRIN-INAF 2011 with the project 'Transient Universe: from ESO Large to PESSTO'. N.E.R. acknowledges financial support by the MICINN grant AYA08-1839 / ESP, AYA2011-24704 / ESP, and by the ESF EUROCORES Program EUROGENESIS (MINECO grants EUI2009-04170). F.B. acknowledges support from FONDECYT through Postdoctoral grant 3120227 and from the Millennium Center for Supernova Science through grant P10-064-F (funded by 'Programa Bicentenario de Ciencia y Tecnologa de CONICYT' and 'Programa Iniciativa Cientiffica Milenio de MIDEPLAN').",
"pages": [
16,
17
]
},
{
"title": "References",
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"pages": [
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}
]
2013A&A...555A.113B
https://arxiv.org/pdf/1306.0390.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_82><loc_90><loc_87></location>Enhanced H GLYPH<11> activity at periastron in the young and massive spectroscopic binary HD 200775 ?</section_header_level_1>
<text><location><page_1><loc_10><loc_77><loc_92><loc_81></location>M. Benisty 1 ; 2 , K. Perraut 1 , D. Mourard 3 , P. Stee 3 , G.H.R.A. Lima 1 , J.B. Le Bouquin 1 , M. Borges Fernandes 4 , O. Chesneau 3 , N. Nardetto 3 , I. Tallon-Bosc 5 , H. McAlister 6 ; 7 , T. Ten Brummelaar 7 , S. Ridgway 8 , J. Sturmann 7 , L. Sturmann 7 , N. Turner 7 , C. Farrington 7 , P.J. Goldfinger 7</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_73><loc_91><loc_75></location>1 Institut d'Astrophysique et de Plan'etologie de Grenoble, CNRS-UJF UMR 5571, 414 rue de la Piscine, 38400 St Martin d'H'eres, France</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_61><loc_73></location>2 Max Planck Institut fur Astronomie, Konigstuhl 17, 69117 Heidelberg, Germany</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_88><loc_71></location>3 Laboratoire Lagrange, UMR 7293 UNS-CNRS-OCA, Boulevard de l'Observatoire, B.P. 4229 F, 06304 NICE Cedex 4, France</list_item>
<list_item><location><page_1><loc_11><loc_69><loc_75><loc_70></location>4 Observatorio Nacional, Rua General Jos'e Cristino, 77, 20921-400, Sao Cristovao, Rio de Janeiro, Brazil</list_item>
<list_item><location><page_1><loc_11><loc_67><loc_91><loc_69></location>5 Universit'e de Lyon, 69003 Lyon, France; Universit'e Lyon 1, Observatoire de Lyon, 9 avenue Charles Andr'e, 69230 Saint Genis Laval; CNRS, UMR 5574, Centre de Recherche Astrophysique de Lyon; Ecole Normale Sup'erieure, 69007 Lyon, France</list_item>
<list_item><location><page_1><loc_11><loc_66><loc_55><loc_67></location>6 Georgia State University, PO Box 3969, Atlanta GA 30302-3969, USA</list_item>
<list_item><location><page_1><loc_11><loc_64><loc_58><loc_66></location>7 CHARA Array, Mount Wilson Observatory, 91023 Mount Wilson CA, USA</list_item>
<list_item><location><page_1><loc_11><loc_63><loc_63><loc_64></location>8 National Optical Astronomy Observatory, PO Box 26732, Tucson, AZ 85726, USA</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_60><loc_39><loc_61></location>Received 26 June 2012 / Accepted 7 May 2013</text>
<section_header_level_1><location><page_1><loc_47><loc_58><loc_55><loc_59></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_53><loc_91><loc_56></location>Context. Young close binaries clear central cavities in their surrounding circumbinary disk from which the stars can still accrete material. This process takes place within the very first astronomical units, and is still not well constrained as the observational evidence has been gathered, until now, only by means of spectroscopy.</text>
<text><location><page_1><loc_11><loc_49><loc_91><loc_53></location>Aims. The young object HD 200775 (MWC 361) is a massive spectroscopic binary (separation of GLYPH<24> 15.9 mas, GLYPH<24> 5.0 AU), with uncertain classification (early / late Be), that shows a strong and variable H GLYPH<11> emission. We aim to study the mechanisms that produce the H GLYPH<11> line at the AU-scale.</text>
<text><location><page_1><loc_11><loc_46><loc_91><loc_49></location>Methods. Combining the radial velocity measurements and astrometric data available in the literature, we determined new orbital parameters. With the VEGA instrument on the CHARA array, we spatially and spectrally resolved the H GLYPH<11> emission of HD 200775 on a scale of a few milliarcseconds, at low and medium spectral resolutions (R GLYPH<24> 1600 and 5000) over a full orbital period ( GLYPH<24> 3.6 years).</text>
<text><location><page_1><loc_11><loc_37><loc_91><loc_46></location>Results. We observe that the H GLYPH<11> equivalent width varies with the orbital phase, and increases close to periastron, as expected from theoretical models that predict an increase of the mass transfer from the circumbinary disk to the primary disk. In addition, using spectral visibilities and di GLYPH<11> erential phases, we find marginal variations of the typical extent of the H GLYPH<11> emission (at 1 to 2 GLYPH<27> level) and location (at 1 to 5 GLYPH<27> level). The spatial extent of the H GLYPH<11> emission, as probed by a Gaussian FWHM, is minimum at the ascending node (0.67 GLYPH<6> 0.20 mas, i.e., 0.22 GLYPH<6> 0.06 AU), and more than doubles at periastron. In addition, the Gaussian photocenter is slightly displaced in the direction opposite to the secondary, ruling out the scenario in which all or most of the H GLYPH<11> emission is due to accretion onto the secondary. These findings, together with the wide H GLYPH<11> line profile, may be due to a non-spherical wind enhanced at periastron.</text>
<text><location><page_1><loc_11><loc_33><loc_91><loc_37></location>Conclusions. For the first time in a system of this kind, we spatially resolve the H GLYPH<11> line and estimate that it is emitted in a region larger than the one usually inferred in accretion processes. The H GLYPH<11> line could be emitted in a stellar or disk-wind, enhanced at periastron as a result of gravitational perturbation, after a period of increased mass accretion rate. Our results suggest a strong connection between accretion and ejection in these massive objects, consistent with the predictions for lower-mass close binaries.</text>
<text><location><page_1><loc_11><loc_30><loc_91><loc_32></location>Key words. Methods: observational Techniques: high angular resolution - Techniques: interferometric - Stars: binary (HD 200775) Stars: emission-line - Stars: circumstellar matter</text>
<section_header_level_1><location><page_1><loc_7><loc_26><loc_19><loc_27></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_13><loc_50><loc_25></location>Herbig AeBe (HAeBe) stars are pre-main-sequence objects of intermediate mass, with spectral types from B to F. They are surrounded by protoplanetary disks of gas and dust, responsible for the observed excess emission from the infrared to the submillimeter (e.g., Alonso-Albi et al. 2009). Their spectra display many emission lines, which are signatures of accretion and outflow (Mundt & Ray 1994). These objects are of particular interest as they lie between solar-mass young stars, thought to form through gravitational collapse of a molecular cloud, and the mas-</text>
<text><location><page_1><loc_7><loc_11><loc_45><loc_12></location>Send o GLYPH<11> print requests to : [email protected]</text>
<text><location><page_1><loc_52><loc_24><loc_95><loc_27></location>sive young stars for which the process of formation is still matter of debate.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_24></location>Like their lower mass counterparts (e.g., Duchˆene et al. 2007), a large fraction of Herbig AeBe stars is found in multiple systems (up to 68 GLYPH<6> 11%, Baines et al. (2006)). Once formed, close binary stars are thought to accrete mass from an envelope through a circumbinary disk. However, it is not clear what e GLYPH<11> ect preferential mass accretion will have on the evolution of the two components. Observations have shown that a number of close T Tauri star binaries (e.g., DQ Tau, Basri et al. 1997) show enhanced emission line activity close to periastron, indicating that the accretion is non-axisymmetric. Numerical studies of young close binary systems have shown that an inner cavity forms in-</text>
<text><location><page_2><loc_7><loc_83><loc_50><loc_93></location>ide the 2:1 resonance and that accretion streamers can still feed the stars inside the circumbinary disk, producing the observed periodic line changes (Artymowicz & Lubow 1996; Gunther & Kley 2002; de Val-Borro et al. 2011). This interaction between the circumbinary disk and the stars occurs at (sub-)AU scales and, until now, only spatially unresolved observations have been published. Being able to directly probe the disk-binary interaction is crucial to test models of young binary evolution.</text>
<text><location><page_2><loc_7><loc_67><loc_50><loc_82></location>The object HD 200775 (MWC361) is a triple system consisting of a spectroscopic binary (SB) at GLYPH<24> 18 milliseconds of arc (mas) separation (Millan-Gabet et al. 2001), and a third companion at 6' (Li et al. 1994). Based on the analysis of the H GLYPH<11> line, a radial velocity (RV) orbit with a period of 1341 days was reported for the SB (Pogodin et al. 2004). From their analysis of 33 spectral features, Hern'andez et al. (2004) classified the SB as a Herbig Be star with a luminosity of 15000-L GLYPH<12> . However, because of the large uncertainty on the age of the system, the fundamental parameters of the individual sources remain highly uncertain, although it is likely that at least one of the two is an early Herbig Be star that dominates the spectrum.</text>
<text><location><page_2><loc_7><loc_49><loc_50><loc_66></location>Various terminologies and criteria have been used to distinguish one star from the other in the literature, generating some confusion. Using H-band interferometric measurements, Monnier et al. (2006) determined an astrometric orbit with a projected separation of 15.14 GLYPH<6> 0.70 mas and an inclination of i GLYPH<24> 65 GLYPH<14> GLYPH<6> 8 GLYPH<14> . They defined as primary target, the brightest near infrared (NIR) source, and found an H-band brightness ratio of 6.5 GLYPH<6> 0.5. They modeled the NIR visibilities around the primary star, assuming that the secondary was unresolved in the NIR, i.e., it did not possess any extended disk at their angular resolution ( GLYPH<24> 4.3 mas). Using analytical models, they found a uniform disk diameter of 3.6 GLYPH<6> 0.5 mas, i.e., 1.3 GLYPH<6> 0.2 AU, at a distance of 360 + 120 GLYPH<0> 70 pc.</text>
<text><location><page_2><loc_7><loc_23><loc_50><loc_49></location>HD 200775 was later observed during an extensive spectropolarimetric campaign (Alecian et al. 2008). Two individual components were found in the photospheric line profiles. The authors defined as the primary target the one that emits the sharper lines: the secondary was determined to be the one responsible for the broader, shallower lines. Based on the RV of the lines, the authors provided orbital parameters in overall agreement with Pogodin et al. (2004) and Monnier et al. (2006), and a mass ratio primary / secondary of 0.81 GLYPH<6> 0.22, indicating that the star considered as secondary is in practice the most massive one. The H GLYPH<11> bisector velocities computed at a line intensity of 1.5 times the continuum were found to trace the RV of the secondary, suggesting that the line emission is dominated by this star. Their observations revealed a strongly inclined dipolar magnetic field (1000 GLYPH<6> 150 G), found to have been stable for more than 2 years, and related to the object considered as the primary. Although the authors derive similar masses and e GLYPH<11> ective temperatures ( GLYPH<24> 10 M GLYPH<12> and 18600 K, respectively), the discrepancy between the observational properties suggests that the two stellar components must have grown and evolved di GLYPH<11> erently.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_22></location>It seems very likely that the component defined as secondary in Alecian et al. (2008) is actually the one defined as primary in Monnier et al. (2006), the most massive component. The RV mass estimate and the dominant H GLYPH<11> activity is consistent with the presence of a circumstellar dusty disk as invoked in Monnier et al. (2006) around the most massive component. In this paper, we consider the primary to be the most massive component, i.e., the one that possesses a circumstellar dusty disk and dominates the H GLYPH<11> emission. The secondary is the least massive component that possesses a strong magnetic field.</text>
<text><location><page_2><loc_52><loc_72><loc_95><loc_93></location>Mid-infrared (MIR) images obtained with the Keck segmenttilting experiment indicated a large halo containing 45% of 10.7 GLYPH<22> mflux with a north-south elongation (Monnier et al. 2009) consistent with the orientation of the binary orbit measured by Monnier et al. (2006). This suggests that the halo is the remnant of a circumbinary disk. This was confirmed by Subaru MIR images that showed a di GLYPH<11> use emission with an elliptical shape, suggesting an inclined flared disk (i = 54.5 GLYPH<14> GLYPH<6> 1.2 GLYPH<14> ; Okamoto et al. 2009). The MIR emission extends up to 20 times the semi-major axis of the binary, which indicates a large gap in the system. Furthermore, the system lies in a large scale biconical cavity that has very likely been excavated by an extended bipolar outflow inclined by GLYPH<24> 70 GLYPH<14> (Fuente et al. 1998; Watt et al. 1986), a value also close to the orbital plane inclination. These results support the presence of a circumbinary disk in the same plane as the orbit.</text>
<text><location><page_2><loc_52><loc_58><loc_95><loc_72></location>The H GLYPH<11> and H GLYPH<12> emission lines show great variations over time, indicating changes in activity with a period of 3.68 years, in agreement with the binary period (Pogodin et al. 2004). In low states, the lines are double-peaked. In active states, the line intensities and equivalent widths (EW) increase, while their profiles show a complicated multi-component structure, including a doubling of the central absorption feature with a new, variable, blue-shifted component in addition to the pre-existing redshifted one. The EW is found to be at its maximum right after periastron, indicating that the line activity is indeed related to the binarity.</text>
<text><location><page_2><loc_52><loc_36><loc_95><loc_58></location>The hot gas, responsible for the Hydrogen line, can be involved in accretion and ejection flows close to the source and can be used to probe the corresponding physical conditions. These phenomena, however, occur in a small region of a few AU around the star, corresponding to a few mas. With the recent advent of spectro-interferometric instruments, it has been possible to achieve such a resolution, and to spatially and spectrally resolve some of these lines. The first studies of the kind showed that the Br GLYPH<13> emission line was probably tracing winds or gas in a rotating disk (Malbet et al. 2007; Kraus et al. 2008). One of the challenging goals is to study the launching points of the jets and discriminate between the various theoretical models, Xwind (Shu et al. 1994) and disk-wind (Casse & Ferreira 2000). Inspired by the magneto-centrifugal scenario for the acceleration of jets, Rousselet-Perraut et al. (2010) and Weigelt et al. (2011) provided realistic solutions to account for the line emission in disk winds.</text>
<text><location><page_2><loc_52><loc_25><loc_95><loc_36></location>From 2008 to 2011, we led an observing campaign over an entire orbit of HD 200775 with the optical spectrointerferometer VEGA installed at the CHARA Array. The paper is organized as follows: in Sect. 2 we describe the observations and the data processing. We present the new orbital solution, spectra, and interferometric observables in Sects. 3 and 4, and describe our modeling in Sect. 5. We discuss our results in Sect. 6 and conclude in Sect. 7.</text>
<section_header_level_1><location><page_2><loc_52><loc_22><loc_82><loc_23></location>2. Observations and data processing</section_header_level_1>
<section_header_level_1><location><page_2><loc_52><loc_20><loc_69><loc_21></location>2.1. VEGA observations</section_header_level_1>
<text><location><page_2><loc_52><loc_10><loc_95><loc_19></location>The data were collected at the CHARA array (ten Brummelaar et al. 2005), with the VEGA instrument (Mourard et al. 2009). Our datasets were obtained with two telescopes (S1S2) and cover the period from July 2008 to October 2011, i.e., an orbital period. The average projected baseline length (Bp) is about 27 m, and the average baseline position angles (PAB) are given in Table 1. The angular resolution ( GLYPH<21> / 2Bp) of our observations</text>
<table>
<location><page_3><loc_15><loc_71><loc_87><loc_91></location>
<caption>Table 1. Log of the observations. GLYPH<30> is the orbital phase (zero at periastron). Italics indicate that only spectra were retrieved.</caption>
</table>
<text><location><page_3><loc_7><loc_65><loc_50><loc_69></location>is GLYPH<24> 2.5 mas. We therefore fully resolve the spectroscopic binary. The interferometric field of view is GLYPH<6> 2' in the slit direction and excludes the third object of the system (at 6').</text>
<text><location><page_3><loc_7><loc_58><loc_50><loc_65></location>The first dataset was recorded with the lowest spectral resolution of VEGA (R GLYPH<24> 1600, hereafter LR), as the target is at the instrumental sensitivity limit ( mV = 7.4). Instrumental improvements allowed us to later record data in medium spectral resolution (R GLYPH<24> 5000, hereafter MR).</text>
<text><location><page_3><loc_7><loc_48><loc_50><loc_58></location>Each observation followed a calibrator-star-calibrator sequence, with 40 files of 1000 short exposures (15 ms) per observation. The calibrators were chosen to be close to the target both in distance and in spectral type, to be small enough at visible wavelengths, and to have an angular diameter known to an accuracy of a few percentage points. Using the SearchCal JMMC tool, we selected HD 204770 and HD 197950 (uniform disk diameters of GLYPH<24> 0.17 GLYPH<6> 0.01 mas and GLYPH<24> 0.33 GLYPH<6> 0.02 mas, respectively).</text>
<section_header_level_1><location><page_3><loc_7><loc_45><loc_22><loc_46></location>2.2. Data processing</section_header_level_1>
<text><location><page_3><loc_7><loc_33><loc_50><loc_43></location>Spectra: the spectra were extracted using a classical scheme of collapsing the 2D flux in one spectrum, calibrating the pixel-wavelength relation using a Thorium-Argon lamp, and normalizing the continuum by a polynomial fit. We used the H GLYPH<11> absorption lines of the calibrators to check the spectral calibration at medium resolution. The accuracy of the spectral calibration is 0.13 nm (i.e., 60 km / s) in MR, and 0.39 nm (i.e., 178 km / s) in LR.</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_32></location>Visibilities and di GLYPH<11> erential phases: The standard routines of the VEGA data reduction pipeline were used (Mourard et al. 2009). We computed visibilities and di GLYPH<11> erential phases in individual spectral channels, using the cross-spectrum method between two spectral channels [1] and [2] (for more details, see Berio et al. 1999). To reach a su GLYPH<14> cient signal-to-noise ratio (SNR) (at least 1 photon per speckle, spectral channel and single exposure), we considered the spectral band [1] to be as wide as the entire spectral range (32 nm, i.e., a broad band measurement), and [2], to be 4 nm-wide. This method first led to the determination of the di GLYPH<11> erential phase between [1] and [2], and of the product of the visibility amplitude V1*V2. The dataset was calibrated from the residual atmospheric piston and chromatic optical path di GLYPH<11> erence with the model described in Mourard et al. (2009). V 1 2 were estimated using the integration of the spectral densities of the short exposures over the entire spectral range [1] and calibrated from the instrumental transfer function estimated on the</text>
<table>
<location><page_3><loc_52><loc_55><loc_90><loc_64></location>
<caption>Table 2. Detection level of the V and GLYPH<1> GLYPH<30> change in H GLYPH<11> . GLYPH<27> cont and GLYPH<27> H GLYPH<11> are the errors in the continuum and in the line, respectively (computed as in Sect. 2.2).</caption>
</table>
<text><location><page_3><loc_52><loc_40><loc_95><loc_53></location>calibrators. Using an estimate of V1 and of the transfer function, we deduced the calibrated visibility V2 for the narrow spectral channel [2]. By sliding the narrow spectral channel [2] with steps of 2 nm across the entire spectral range [1], we obtained a set of 13 visibilities V2 and di GLYPH<11> erential phases, GLYPH<1> GLYPH<30> = GLYPH<30> 2 GLYPH<0> GLYPH<30> 1, with a final spectral resolution of GLYPH<24> 160. We considered GLYPH<1> GLYPH<30> equal to 0 in the continuum part of the spectrum, which means that the di GLYPH<11> erential phases measured in the H GLYPH<11> line correspond to astrometric o GLYPH<11> sets along the baseline direction, with the photocenter in the continuum as a reference point.</text>
<text><location><page_3><loc_52><loc_23><loc_95><loc_39></location>The data reduction pipeline provided individual errors for each spectral channel, that account for photon noise only. To account for other sources of noise, we adopted conservative errors by considering the largest value between the rms in the continuum and the error computed by the pipeline. As the number of photons NH GLYPH<11> is much higher in the H GLYPH<11> spectral channel than in the continuum, we estimated the error in the H GLYPH<11> visibility by dividing the continuum error by p NH GLYPH<11> = N cont. Finally, as HD 200775 is a faint target compared to the VEGA limiting magnitude, excellent weather conditions are required to obtain good quality data. As a consequence, only 6 observations over our 14 attempts have led to a su GLYPH<14> cient SNR to produce interferometric observables.</text>
<section_header_level_1><location><page_3><loc_52><loc_17><loc_69><loc_18></location>3. Orbital parameters</section_header_level_1>
<text><location><page_3><loc_52><loc_10><loc_95><loc_16></location>Several determinations of the binary orbit exist in the literature. However, the SB2 radial velocities (Alecian et al. 2008) and resolved astrometric observations (Monnier et al. 2006) have never been fitted conjointly. Consequently, we revisit these works with the goal of determining the dynamical distance of the system</text>
<figure>
<location><page_4><loc_14><loc_69><loc_87><loc_94></location>
<caption>Fig. 1. Left: H GLYPH<11> VEGA spectra obtained at R = 1600 (LR). Right: Additional VEGA spectra obtained at R = 5000 (MR).</caption>
</figure>
<figure>
<location><page_4><loc_8><loc_26><loc_97><loc_65></location>
<caption>Fig. 3. Variation of the line profile measured with VEGA at R GLYPH<24> 5000, with the orbital phase. In each panel, the astrometric orbit is shown, with a full black circle indicating the corresponding orbital phase. The thick part is oriented towards the observer.</caption>
</figure>
<text><location><page_4><loc_7><loc_11><loc_50><loc_19></location>and the individual masses of the components. We combined the available datasets following the formalism detailed in Le Bouquin et al. (2013) and performed a Levenberg-Marquardt least-square fit of the data. We are confident in our orbital determination, as the convergence toward a single and deep GLYPH<31> 2 minimumis fast and robust for a wide range of initial guesses. The error bars on the parameters were obtained by bootstrapping. The</text>
<text><location><page_4><loc_52><loc_13><loc_95><loc_19></location>best-fit parameters are provided in Table 3. We note that the dynamical distance is out of the confidence interval of the new reduction of the Hipparcos data (520 GLYPH<6> 150 pc, Van Leeuwen 2007) and the individual masses are smaller by a factor of 2 than the ones derived in Alecian et al. (2008).</text>
<figure>
<location><page_5><loc_11><loc_69><loc_46><loc_93></location>
<caption>Fig. 2. Equivalent widths of the H GLYPH<11> line over the orbit for all the spectra.</caption>
</figure>
<table>
<location><page_5><loc_8><loc_38><loc_49><loc_61></location>
<caption>Table 3. Best fit orbital elements and related physical parameters</caption>
</table>
<section_header_level_1><location><page_5><loc_7><loc_34><loc_28><loc_35></location>4. Spectro-interferometry</section_header_level_1>
<section_header_level_1><location><page_5><loc_7><loc_31><loc_20><loc_33></location>4.1. Spectroscopy</section_header_level_1>
<text><location><page_5><loc_7><loc_10><loc_50><loc_30></location>Figure 1 presents 14 di GLYPH<11> erent H GLYPH<11> spectra that show a drastic change of intensity with time as well as slight changes in the full width at half maximum (FWHM) of the line. With these measurements, we confirm that the equivalent width (EW) of the line (Fig. 2) varies with the orbital phase, and reaches its maximum close to the periastron. In the following, we refer to 'active phase or state' when the system is close to the periastron, otherwise to 'quiescent phase or state'. In the quiescent state, we measure an EW of GLYPH<24> 35-40 Å, about twice as much as in the active phase which is in agreement with previous studies (Miroshnichenko et al. 1998; Alecian et al. 2008). For the sake of clarity, Fig. 3 shows six of the spectra obtained at medium spectral resolution, with a schematic of the system at the corresponding orbital epoch. The line is double peaked in the quiescent state with peak-velocities of GLYPH<24> 75-80 km / s, FWHM GLYPH<24> 450 km / s and broad wings at very high velocities ( GLYPH<24> 800 km / s), as deter-</text>
<text><location><page_5><loc_52><loc_81><loc_95><loc_93></location>ined through Gaussian fitting of the profiles. The profile is almost symmetric close to the ascending node ( GLYPH<30> GLYPH<24> 0 : 5), and slightly asymmetric as the system gets closer to the periastron ( GLYPH<30> GLYPH<24> 0.8), with more blue-shifted emission. At periastron ( GLYPH<30> GLYPH<24> 0), the line is single peaked, and shows a slight asymmetry with more redshifted emission. There is no variability in the broad wings. These results support the idea that the binarity is at the origin of the line profile and intensity variations, as expected and observed in other close binaries.</text>
<section_header_level_1><location><page_5><loc_52><loc_78><loc_65><loc_79></location>4.2. Interferometry</section_header_level_1>
<text><location><page_5><loc_52><loc_74><loc_95><loc_76></location>Figure 4 presents the visibilities and di GLYPH<11> erential phases, as well as the corresponding spectra at a resolution of 1600.</text>
<text><location><page_5><loc_52><loc_64><loc_95><loc_72></location>Change in the spectral shape of the visibility. By comparing the interferometric quantities in the continuum to the ones in the spectral channel centred on H GLYPH<11> , we detect a marginal visibility drop in the line during the active states ( GLYPH<30> GLYPH<24> 0 and 0.8; Table 2). This means that at least at these dates, the bulk of the H GLYPH<11> emission is spatially resolved and extended.</text>
<text><location><page_5><loc_52><loc_41><loc_95><loc_63></location>Change in the spectral shape of the di GLYPH<11> erential phases. We find that within large error bars, the di GLYPH<11> erential phase in the line is consistent with zero for all measurements, except for GLYPH<30> GLYPH<24> 0.5 and 0.8. The di GLYPH<11> erential phase signals can be translated into a photocenter displacement in the plane of the sky along the direction of the projected baseline. For the S1S2 baseline used for the observations, a positive phase corresponds to a photocenter displacement towards the south, and a negative phase corresponds to the displacement towards the north, as detailed in Mourard et al. (2012). Therefore, the measured non-zero di GLYPH<11> erential phases trace for all epochs a photocenter displacement in the direction opposite to the secondary. As the measured differential phases are low ( GLYPH<1> GLYPH<30> GLYPH<20> 20 GLYPH<14> ), the photocenter of the H GLYPH<11> emission is rather close to the continuum / binary photocenter. Detection levels are defined using the errors in the continuum and in the line ( GLYPH<27> cont and GLYPH<27> H GLYPH<11> , respectively, computed as in Sect. 2.2) and are reported in Table 2.</text>
<text><location><page_5><loc_52><loc_26><loc_95><loc_41></location>Change in the absolute level of the visibility. We notice that the level of the continuum visibility varies with the orbital phase, even if the measurements were obtained at similar angular resolutions ( GLYPH<24> 2.5 mas). This behavior is expected since the continuum emission is due to the binary that is spatially resolved by the interferometer. Therefore, any change in binary separation, position angle and / or flux ratio strongly a GLYPH<11> ects the visibilities. Close to the ascending node (2009 dataset), we measure a continuum visibility close to 1, corresponding to an unresolved emission along the baseline position angle, while in the active state, the continuum visibility can be as low as GLYPH<24> 0.76.</text>
<section_header_level_1><location><page_5><loc_52><loc_20><loc_60><loc_21></location>5. Results</section_header_level_1>
<text><location><page_5><loc_52><loc_10><loc_95><loc_19></location>The goal of the analysis is to derive the basic properties of the H GLYPH<11> emitting region. This requires a proper subtraction of the continuum emission that is only due to the binary stars. To do so, we first fit a binary model to the continuum visibilities, with fixed orbital parameters (Table 3), in order to determine the flux ratio (FR) between the two stars. This flux ratio will set our model in the continuum for both the visibilities and di GLYPH<11> erential phases.</text>
<table>
<location><page_6><loc_11><loc_77><loc_90><loc_87></location>
<caption>Table 4. Orbital phase ( GLYPH<30> ), angular separation ( GLYPH<1> GLYPH<11> , GLYPH<1> GLYPH<14> ), and position angle (PAbin) of the SB at the date of the interferometric observations. PAB is the baseline position angle, FR the binary flux ratio in the continuum, GLYPH<2> H GLYPH<11> and GLYPH<26> H GLYPH<11> the H GLYPH<11> FWHM and displacements resulting from the best fit of a face-on Gaussian model, in mas and AU at 320 pc. The displacements are counted positive towards the secondary.</caption>
</table>
<section_header_level_1><location><page_6><loc_7><loc_73><loc_21><loc_74></location>5.1. Binary flux ratio</section_header_level_1>
<text><location><page_6><loc_7><loc_62><loc_50><loc_72></location>In the spectral range of our observations, we assume that the only emitters in the continuum are the two stellar components. Their relative flux ratios, separations, and position angles have a strong impact on the visibility in the continuum. Assuming that the relative stellar fluxes vary over the orbit, we can use our continuum visibilities to retrieve the flux ratio at di GLYPH<11> erent epochs, assuming that the individual stars are unresolved, and using a simple analytical formula for the binary visibility.</text>
<text><location><page_6><loc_7><loc_32><loc_50><loc_62></location>We first compute the position angle and separation for each epoch, using the orbital parameters determined in Tab. 3. We then compute a large grid of GLYPH<24> 1000 binary models, and minimize a GLYPH<31> 2 . Individual fits to each data set provide flux ratios from 0.07 + 0 : 05 GLYPH<0> 0 : 06 to 0.29 + 0 : 18 GLYPH<0> 0 : 11 ( GLYPH<31> 2 = 1.5 at most). This suggests that the secondary is the dimmer object in the continuum. At the ascending node GLYPH<30> GLYPH<24> 0.26 where V GLYPH<24> 1 and the binary is unresolved, all flux ratio values below 0.06 provide an equally good fit ( GLYPH<31> 2 = 1.1), while for GLYPH<30> GLYPH<24> 0.81 all possible flux ratio values surprisingly provide a bad fit ( GLYPH<31> 2 = 3.3). The second dataset shows a large intrinsic scatter in the continuum (rms GLYPH<24> 10%), and seems to su GLYPH<11> er from calibration problems that prevent us from determining a good absolute value for the visibility. Because we cannot determine a flux ratio for this measurement, we scale the average continuum visibilities, for this dataset only, to the binary model predictions with FR = 0.10, which corresponds to the best-fit model assuming a constant flux ratio over the entire orbit ( GLYPH<31> 2 = 3.8). The scaling factor is GLYPH<24> 25%, as shown in Fig. A.1, together with the best fit of the binary model for each dataset. Values of flux ratios are given in Table 4. Because of the large error bars, we cannot determine whether the change in FR with the orbital period is significant and expect that further high SNR observations would answer this question.</text>
<section_header_level_1><location><page_6><loc_7><loc_28><loc_39><loc_30></location>5.2. Size and photocenter of the H GLYPH<11> emission</section_header_level_1>
<text><location><page_6><loc_7><loc_21><loc_50><loc_27></location>To model the H GLYPH<11> circumstellar emission, we consider the contribution of the binary to the measured visibilities and di GLYPH<11> erential phases using the complex visibilities. Assuming that the binary is at the photocenter of the continuum emission (i.e., GLYPH<1> GLYPH<30> = 0 in the continuum), we find that for each spectral channel k</text>
<formula><location><page_6><loc_7><loc_16><loc_50><loc_19></location>Vke i GLYPH<1> GLYPH<30> k = Fcont ; kVcont ; k + FH GLYPH<11> ; kVH GLYPH<11> ; ke i GLYPH<1> GLYPH<30> H GLYPH<11> ; k Fcont ; k + FH GLYPH<11> ; k ; (1)</formula>
<text><location><page_6><loc_7><loc_10><loc_50><loc_15></location>where the indices cont and H GLYPH<11> refer to the continuum (binary) and circumstellar emission, GLYPH<1> GLYPH<30> k is the measured di GLYPH<11> erential phases in the spectral channel k , and GLYPH<1> GLYPH<30> H GLYPH<11> is the di GLYPH<11> erential phase due to the H GLYPH<11> emitting region. The real and imaginary</text>
<text><location><page_6><loc_52><loc_72><loc_95><loc_74></location>parts of Eq. 1 lead to two equations that can be solved for VH GLYPH<11> and GLYPH<1> GLYPH<30> H (see, eg., Weigelt et al. 2007; Eisner et al. 2010).</text>
<text><location><page_6><loc_58><loc_72><loc_58><loc_72></location>GLYPH<11></text>
<text><location><page_6><loc_52><loc_49><loc_95><loc_71></location>With the best binary model, and the line to continuum ratio determined from the spectra after subtraction of the photospheric H GLYPH<11> absorption, we fit our model for the H GLYPH<11> emission to VH GLYPH<11> and GLYPH<1> GLYPH<30> H GLYPH<11> , in the two spectral channels that contain most or all of the line. Considering the low quality of our datasets, we limit ourselves to a simplistic analytical approach with a face-on Gaussian model, which FWHM (considered as a typical size) and location can vary. We restrict the Gaussian displacement along the binary axis only, since our measurements have been obtained along a single baseline orientation at a time, which prevents us from determining a full 2-D position. The reference is taken to be the primary and displacements are counted positive towards the secondary. We vary the Gaussian FWHM from 0 to 6 mas, and since the sign of the di GLYPH<11> erential phases indicates a displacement in the direction opposite to the secondary, we vary the Gaussian location from -4 to 0 mas, and minimize a GLYPH<31> 2 to find the best model parameters.</text>
<text><location><page_6><loc_52><loc_40><loc_95><loc_49></location>Figure 5 shows the best-fit to the H GLYPH<11> visibilities and di GLYPH<11> erential phases, and Fig. 6 presents the model parameters as they vary with the orbital phase (values are in Table 4). Our model fits the observations well, with a reduced GLYPH<31> 2 of 2.7 (at most) in the line + continuum (1.1 in the H GLYPH<11> spectral channels only). Conservative error bars have been obtained by considering the extreme values of the visibilities and FR within their error bars.</text>
<text><location><page_6><loc_52><loc_28><loc_95><loc_40></location>We find that the spatial extent of the emission changes over the orbit. In the quiescent state, the Gaussian FWHM is 0.67 GLYPH<6> 0.20 mas (i.e., GLYPH<24> 0.22 AU) and increases up to GLYPH<24> 1.95 GLYPH<6> 0.20 mas (i.e., GLYPH<24> 0.62 AU), close to periastron. The displacements towards the opposite direction than the secondary appear to be quasi constant along the orbit, with absolute values close to 0.10 GLYPH<6> 0.03 mas (i.e., 0.03 GLYPH<6> 0.01 AU). The errors on the displacement are dominated by the errors on the binary flux ratio, hence are very large for GLYPH<30> GLYPH<24> 0.81.</text>
<text><location><page_6><loc_52><loc_11><loc_95><loc_28></location>Because our measurements only probe one direction at a time, we are not able to determine an inclination and a position angle for the H GLYPH<11> emitting region, and leave this for a detailed radiative transfer modeling combined with additional simultaneous multi-baseline interferometric observations. Thus, we would like to stress that the obtained parameter values are model-dependent and di GLYPH<11> erent geometries (e.g., ring, uniform disk) lead to slightly larger values of typical size, as expected with such simple prescriptions. In addition, the values of the displacement strongly depend on the binary flux ratio that set the phase values in the continuum. However, the variations of the H GLYPH<11> characteristic size along the orbit and the negative photocenter displacements still hold.</text>
<figure>
<location><page_7><loc_7><loc_52><loc_51><loc_94></location>
<caption>Fig. 5. Best-fit continuum and H GLYPH<11> line model (dashed line). The first two lines give the visibilities, the following two, the differential phases. We recall that the visibilities for GLYPH<30> = 0.806 have been scaled to the binary model with FR = 0.10.</caption>
</figure>
<section_header_level_1><location><page_7><loc_7><loc_43><loc_18><loc_44></location>6. Discussion</section_header_level_1>
<section_header_level_1><location><page_7><loc_7><loc_40><loc_35><loc_42></location>6.1. Characteristic spatial extents in H GLYPH<11></section_header_level_1>
<text><location><page_7><loc_7><loc_24><loc_50><loc_39></location>It is useful to compare the H GLYPH<11> size estimates to typical radii in the close circumstellar regions probed by our measurements. If we consider the extreme values of luminosities found in the literature ( GLYPH<24> 3000 and GLYPH<24> 15000 L GLYPH<12> from Alecian et al. (2008); Hern'andez et al. (2004)), we derive an estimate of the location of the dust sublimation radius of the circumprimary disk to be between 3.7 and 8.4 AU (e.g., Dullemond & Monnier 2010). These estimates are larger than the dust inner radius ( GLYPH<24> 1.73 mas, i.e., 0.55 AU at 320 pc) measured by Monnier et al. (2006). This apparent discrepancy can be explained with optically thick material inside the dust sublimation radius that e GLYPH<14> ciently shields the dust from the stellar light (Monnier & Millan-Gabet 2002).</text>
<text><location><page_7><loc_7><loc_10><loc_50><loc_24></location>Considering the vsin(i) estimate and stellar properties from Alecian et al. (2008), we find that the corotation radius should be GLYPH<24> 0.30 GLYPH<6> 0.15 AU. This estimate su GLYPH<11> ers from the large uncertainties on the stellar parameters inferred in the literature. Nonetheless, our Gaussian fit seems to indicate that the bulk of the H GLYPH<11> emission as described by a Gaussian model is most likely located between the corotation radius and the dust sublimation radius, and is more extended than the typical regions involved in accretion processes onto the star. In the case of a low mass star, the truncation radius is set by the interaction of the stellar magnetic field and the gaseous disk in a region very close to the</text>
<figure>
<location><page_7><loc_55><loc_60><loc_91><loc_93></location>
<caption>Fig. 6. Best-fit model parameters, Gaussian FWHM (top) and displacement (bottom), over the orbit.</caption>
</figure>
<text><location><page_7><loc_52><loc_51><loc_95><loc_53></location>star. In a massive star, although this is still a matter of debate, the accretion is thought to occur through a boundary layer.</text>
<text><location><page_7><loc_52><loc_43><loc_95><loc_50></location>Similar extents for Hydrogen line emission have been found in other Herbig Be stars, in the Br GLYPH<13> line, and interpreted as originating in a stellar or disk wind (e.g., Kraus et al. 2012; Weigelt et al. 2011; Benisty et al. 2010), in contrast with the findings of Eisner et al. (2010) on a survey of lower mass young stars that are consistent with accretion.</text>
<text><location><page_7><loc_52><loc_30><loc_95><loc_42></location>It also seems unlikely that the bulk of the H GLYPH<11> emission is due to a rotating disk, even in the quiescent state, where the H GLYPH<11> line profile shows a double peak at low velocities ( GLYPH<24> 75 km / s). If we consider a mass of GLYPH<24> 10 M GLYPH<12> , and the velocity field of a disk in Keplerian rotation ( v = p GM GLYPH<3> = R / sin(i)), the H GLYPH<11> double peak in the quiescent state could result in a rotating disk with a minimum outer radius of R GLYPH<24> 1.2 AU, a much larger value than our estimates (Table 4). The disk region responsible for the broad H GLYPH<11> wings would be located very close to or inside the stellar surface ( GLYPH<24> 7.6 R GLYPH<12> ).</text>
<section_header_level_1><location><page_7><loc_52><loc_26><loc_70><loc_27></location>6.2. Origin of the H GLYPH<11> burst</section_header_level_1>
<text><location><page_7><loc_52><loc_10><loc_95><loc_25></location>The results given in the previous section can be interpreted in the context of mass ejection. The extended H GLYPH<11> emission together with the increase of the H GLYPH<11> line intensity may trace a period of enhanced mass loss in a strong wind emitted by the primary. Such an event could follow a period of enhanced mass accretion from the circumbinary disk to the primary disk, triggered at periastron as predicted by numerical models. The photocenter displacements in the direction opposite to the secondary indicate that if a wind is responsible for the H GLYPH<11> emission, the emission should be enhanced along this direction. The wind therefore could not be fully spherical, as the consequent emission would be symmetric.</text>
<text><location><page_8><loc_7><loc_65><loc_50><loc_93></location>Figure 1 shows that the H GLYPH<11> broad line wings ( GLYPH<24> 800 km / s) are very stable, and can be due to outflowing matter, as such velocities are often seen in wind tracers. The additional emission at periastron is produced only at very low projected velocities, probably coming from a plane close to perpendicular to our line of sight. The lack of P Cygni absorption indicates that the wind is not self-absorbing along our line of sight. This would support a wind with a higher density towards low latitudes, close to the equatorial plane, in agreement with the model predictions of poorly collimated winds in massive stars (Vaidya et al. 2011). With a non-zero inclination, an outflow can also produce the double peaked profile observed in quiescent state, as shown in Stee & de Araujo (1994) for Be stars, and more recently in Weigelt et al. (2011) for a Herbig Be star of similar mass. However, complex line opacity e GLYPH<11> ects can come into play, as suggested by Elitzur et al. (2012) who showed that it is in practice impossible to disentangle e GLYPH<11> ects of kinematics and line opacity e GLYPH<11> ects in double peaked lines and that proper radiative transfer is needed. In addition, we note that spectra obtained at high spectral resolution (Alecian et al. 2008) show that the line profile is extremely complex with variable features, which seem to indicate a combination of various variable mechanisms.</text>
<text><location><page_8><loc_7><loc_28><loc_50><loc_64></location>The additional emission at periastron could, in principle, come from either the primary, the secondary, or a combination of both. However, the low di GLYPH<11> erential phases indicate that the photocenter of the H GLYPH<11> emitting region is close to the continuum photocenter, which is located close to the primary (since the binary best-fit flux ratio is 0.10). The displacement values found by our simple analytical model fitting therefore rule out a scenario in which all of the additional H GLYPH<11> emission at periastron comes from the secondary. It seems therefore very unlikely that accretion onto the secondary or wind-enhancement on the secondary is the key-mechanism at periastron or that both objects are equally responsible for the increase. On the contrary, because the displacements are in the opposite direction to the secondary, the burst of activity at periastron seems to be connected to the primary. Although the variation of photocenter with the orbital phase is marginal, a smaller displacement at the ascending node is consistent with a smaller emitting region and a lower line intensity. An almost-constant displacement at all other phases is also in agreement with the derivation of a similar extent at these dates. This is supported by recent numerical simulations of accretion flows in close binaries done at high resolution (de ValBorro et al. 2011). These models suggested that accretion from the circumbinary disk onto the primary is favored at periastron. In that scenario, it is expected that most or all of the additional H GLYPH<11> emission in the active state comes from the primary star, as our data seem to indicate. We note, however, that with our single-baseline measurements, we are not able to disentangle more complex scenarios.</text>
<text><location><page_8><loc_7><loc_10><loc_50><loc_28></location>Whatever the mechanism favored to enhance the H GLYPH<11> emission at periastron, additional mass has to be fed into the innermost regions at these active stages. If mass is transferred through accretion streamers from the circumbinary disk to the primary disk, there should be a consequent time delay to allow matter to flow through the primary disk and reach the innermost AU. The viscous time is proportional to GLYPH<24> R / ( GLYPH<11> cs H / R), with R the radius, H the disk scale height, and GLYPH<11> the turbulence parameter (proportional to the viscosity; Shakura & Sunyaev (1973)). Considering a maximum outer disk radius for the circumprimary disk of 2 AU (because the binary separation at periastron is GLYPH<24> 4 AU, (Monnier et al. 2006)), GLYPH<11> = 0.01, and H / R = 0.05, the viscous time needed for the mass flow to propagate is of the order of a few ten thousand years, much larger than the binary period. An alternative</text>
<text><location><page_8><loc_52><loc_84><loc_95><loc_93></location>scenario is that the secondary induces gravitational instabilities in the primary disk as it approaches. In fact, tidal e GLYPH<11> ects could induce strong waves all over the disk spatial range and produce instabilities, which would in turn enhance the mass accretion in the inner AU and result in a higher mass loss. The exact physical process that leads to the H GLYPH<11> increase still remains to be understood.</text>
<text><location><page_8><loc_52><loc_75><loc_95><loc_84></location>The comparison of Fig. 2 and Fig. 6 seems to suggest that the variations in H GLYPH<11> EW and sizes are slightly shifted in time, as the size appears to increase faster than the absolute EW. This delay is di GLYPH<14> cult to interpret as we would expect a larger emitting area to produce a stronger H GLYPH<11> emission, but considering the large error bars on our size estimate and the sparse time sampling of the orbit, we cannot determine whether it is a real feature or not.</text>
<section_header_level_1><location><page_8><loc_52><loc_72><loc_75><loc_73></location>7. Summary and conclusion</section_header_level_1>
<text><location><page_8><loc_52><loc_55><loc_95><loc_71></location>In this paper, we report the first spatially and spectrally resolved observations of the H GLYPH<11> line emitting region in a close binary system using the VEGA spectrometer on the CHARA array. As previous authors have already pointed out (Pogodin et al. 2004; Alecian et al. 2008), we find that HD 200775 shows a variation of the H GLYPH<11> EW with the orbital phase. We use a simple Gaussian model located along the binary axis to fit the H GLYPH<11> visibilities and di GLYPH<11> erential phases, and find marginal evidence for a change in spatial extent during the orbit that is minimum in quiescent state (close to the ascending node). The H GLYPH<11> Gaussian photocenter is at all epochs located in the direction opposite to the secondary, supporting a dominant emission by the primary.</text>
<text><location><page_8><loc_52><loc_44><loc_95><loc_55></location>We find typical H GLYPH<11> extents within the sublimation radius. These H GLYPH<11> spatial extents do not support an accretion origin for the bulk of the line emission, as it would involve smaller scales. Instead, we interpret these results in the context of an enhanced mass-loss event, triggered by the gravitational influence of the secondary. Such a scenario would suggest a strong connection between accretion and ejection in this Herbig Be star, as already noted in other massive objects (e.g., Ellerbroek et al. 2011; Benisty et al. 2010).</text>
<text><location><page_8><loc_52><loc_28><loc_95><loc_43></location>Adominant contribution to the H GLYPH<11> line by the primary is supported by our results and by the analysis of Alecian et al. (2008) and Monnier et al. (2006). However, although the stellar parameters are still highly uncertain, it is puzzling that only the primary has a circumstellar disk which accretes from the circumbinary disk. In particular, the kilo-Gauss magnetic field detected on the secondary should induce the formation of a gaseous disk which should in turn emit H GLYPH<11> . The circumstellar environments of the two objects must either have evolved di GLYPH<11> erently, or the secondary could itself be an unknown spectroscopic binary of lower mass which would more easily explain the strong magnetic field, an uncommon feature in Herbig Be stars.</text>
<text><location><page_8><loc_52><loc_10><loc_95><loc_28></location>We find that the binary flux ratio in the continuum is GLYPH<24> 0.10 (from GLYPH<24> 0.07 to GLYPH<24> 0.29, Tab. 4). Because of large error bars on the visibilities, we are not able to retrieve a precise flux ratio at each orbital phase and to determine whether the change in H GLYPH<11> EW is correlated with some change in the amount of reprocessed and scattered light as observed in other young close binaries (van Boekel et al. 2010). We notice a discrepancy between our flux ratio estimates in the continuum and the estimate of Alecian et al. (2008), based on an analysis of spectral lines ( GLYPH<24> 0.67). These estimates are di GLYPH<14> cult to reconcile, unless one invokes variable extinction on one of the two objects, or if one of the two (most likely the magnetic secondary) is already chemically peculiar. Besides, the large uncertainties on the individual masses, the distance, and age of the system prevents the nature</text>
<text><location><page_9><loc_7><loc_80><loc_50><loc_93></location>of the individual objects from being assessed precisely. As noted by Alecian et al. (2008), photometric observations of each component separately are necessary. In addition, a regular and full coverage of the orbit is required to answer a number of open questions, such as a possible time delay between periastron passage and maximum activity. More detailed modeling, as well as an intensive high SNR spectro-interferometric campaign with additional baselines at various orientations are also expected to properly constrain the complex interplay between accretion and ejection in such massive close binary systems.</text>
<section_header_level_1><location><page_9><loc_7><loc_75><loc_26><loc_76></location>Appendix A: Appendix</section_header_level_1>
<figure>
<location><page_9><loc_10><loc_55><loc_46><loc_73></location>
<caption>Fig. A.1. Best-fit binary models in the continuum (dashed blue line). The red dotted line in the lower right panel is the prediction of a binary model with flux ratio of FR = 0.10 to which the continuum visibilities measured for GLYPH<30> = 0.806 were re-scaled.</caption>
</figure>
<text><location><page_9><loc_7><loc_35><loc_50><loc_45></location>Acknowledgements. We acknowledge the anonymous referee for the constructive report that helped improve the manuscript. We thank E. Alecian, J. Bouvier, P. Garcia, A. M'erand, J.L. Monin and J. Monnier for fruitful discussions. We acknowledge all the great observers at the CHARA Array who helped to gather this large dataset. The CHARA Array is operated with support from the National Science Foundation through Grant AST-0908253, the W. M. Keck Foundation, the NASA Exoplanet Science Institute, and from Georgia State University. GHRAL acknowledges CAPES for the support. This research has made use of the Jean-Marie Mariotti Center SearchCal service 1 co-developped by FIZEAU and IPAG, and of CDS Astronomical Databases SIMBAD and VIZIER 2 .</text>
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<caption>Fig. 4. VEGA spectro-interferometric measurements over the orbit.</caption>
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</document>
[
{
"title": "ABSTRACT",
"content": "Context. Young close binaries clear central cavities in their surrounding circumbinary disk from which the stars can still accrete material. This process takes place within the very first astronomical units, and is still not well constrained as the observational evidence has been gathered, until now, only by means of spectroscopy. Aims. The young object HD 200775 (MWC 361) is a massive spectroscopic binary (separation of GLYPH<24> 15.9 mas, GLYPH<24> 5.0 AU), with uncertain classification (early / late Be), that shows a strong and variable H GLYPH<11> emission. We aim to study the mechanisms that produce the H GLYPH<11> line at the AU-scale. Methods. Combining the radial velocity measurements and astrometric data available in the literature, we determined new orbital parameters. With the VEGA instrument on the CHARA array, we spatially and spectrally resolved the H GLYPH<11> emission of HD 200775 on a scale of a few milliarcseconds, at low and medium spectral resolutions (R GLYPH<24> 1600 and 5000) over a full orbital period ( GLYPH<24> 3.6 years). Results. We observe that the H GLYPH<11> equivalent width varies with the orbital phase, and increases close to periastron, as expected from theoretical models that predict an increase of the mass transfer from the circumbinary disk to the primary disk. In addition, using spectral visibilities and di GLYPH<11> erential phases, we find marginal variations of the typical extent of the H GLYPH<11> emission (at 1 to 2 GLYPH<27> level) and location (at 1 to 5 GLYPH<27> level). The spatial extent of the H GLYPH<11> emission, as probed by a Gaussian FWHM, is minimum at the ascending node (0.67 GLYPH<6> 0.20 mas, i.e., 0.22 GLYPH<6> 0.06 AU), and more than doubles at periastron. In addition, the Gaussian photocenter is slightly displaced in the direction opposite to the secondary, ruling out the scenario in which all or most of the H GLYPH<11> emission is due to accretion onto the secondary. These findings, together with the wide H GLYPH<11> line profile, may be due to a non-spherical wind enhanced at periastron. Conclusions. For the first time in a system of this kind, we spatially resolve the H GLYPH<11> line and estimate that it is emitted in a region larger than the one usually inferred in accretion processes. The H GLYPH<11> line could be emitted in a stellar or disk-wind, enhanced at periastron as a result of gravitational perturbation, after a period of increased mass accretion rate. Our results suggest a strong connection between accretion and ejection in these massive objects, consistent with the predictions for lower-mass close binaries. Key words. Methods: observational Techniques: high angular resolution - Techniques: interferometric - Stars: binary (HD 200775) Stars: emission-line - Stars: circumstellar matter",
"pages": [
1
]
},
{
"title": "Enhanced H GLYPH<11> activity at periastron in the young and massive spectroscopic binary HD 200775 ?",
"content": "M. Benisty 1 ; 2 , K. Perraut 1 , D. Mourard 3 , P. Stee 3 , G.H.R.A. Lima 1 , J.B. Le Bouquin 1 , M. Borges Fernandes 4 , O. Chesneau 3 , N. Nardetto 3 , I. Tallon-Bosc 5 , H. McAlister 6 ; 7 , T. Ten Brummelaar 7 , S. Ridgway 8 , J. Sturmann 7 , L. Sturmann 7 , N. Turner 7 , C. Farrington 7 , P.J. Goldfinger 7 Received 26 June 2012 / Accepted 7 May 2013",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Herbig AeBe (HAeBe) stars are pre-main-sequence objects of intermediate mass, with spectral types from B to F. They are surrounded by protoplanetary disks of gas and dust, responsible for the observed excess emission from the infrared to the submillimeter (e.g., Alonso-Albi et al. 2009). Their spectra display many emission lines, which are signatures of accretion and outflow (Mundt & Ray 1994). These objects are of particular interest as they lie between solar-mass young stars, thought to form through gravitational collapse of a molecular cloud, and the mas- Send o GLYPH<11> print requests to : [email protected] sive young stars for which the process of formation is still matter of debate. Like their lower mass counterparts (e.g., Duchˆene et al. 2007), a large fraction of Herbig AeBe stars is found in multiple systems (up to 68 GLYPH<6> 11%, Baines et al. (2006)). Once formed, close binary stars are thought to accrete mass from an envelope through a circumbinary disk. However, it is not clear what e GLYPH<11> ect preferential mass accretion will have on the evolution of the two components. Observations have shown that a number of close T Tauri star binaries (e.g., DQ Tau, Basri et al. 1997) show enhanced emission line activity close to periastron, indicating that the accretion is non-axisymmetric. Numerical studies of young close binary systems have shown that an inner cavity forms in- ide the 2:1 resonance and that accretion streamers can still feed the stars inside the circumbinary disk, producing the observed periodic line changes (Artymowicz & Lubow 1996; Gunther & Kley 2002; de Val-Borro et al. 2011). This interaction between the circumbinary disk and the stars occurs at (sub-)AU scales and, until now, only spatially unresolved observations have been published. Being able to directly probe the disk-binary interaction is crucial to test models of young binary evolution. The object HD 200775 (MWC361) is a triple system consisting of a spectroscopic binary (SB) at GLYPH<24> 18 milliseconds of arc (mas) separation (Millan-Gabet et al. 2001), and a third companion at 6' (Li et al. 1994). Based on the analysis of the H GLYPH<11> line, a radial velocity (RV) orbit with a period of 1341 days was reported for the SB (Pogodin et al. 2004). From their analysis of 33 spectral features, Hern'andez et al. (2004) classified the SB as a Herbig Be star with a luminosity of 15000-L GLYPH<12> . However, because of the large uncertainty on the age of the system, the fundamental parameters of the individual sources remain highly uncertain, although it is likely that at least one of the two is an early Herbig Be star that dominates the spectrum. Various terminologies and criteria have been used to distinguish one star from the other in the literature, generating some confusion. Using H-band interferometric measurements, Monnier et al. (2006) determined an astrometric orbit with a projected separation of 15.14 GLYPH<6> 0.70 mas and an inclination of i GLYPH<24> 65 GLYPH<14> GLYPH<6> 8 GLYPH<14> . They defined as primary target, the brightest near infrared (NIR) source, and found an H-band brightness ratio of 6.5 GLYPH<6> 0.5. They modeled the NIR visibilities around the primary star, assuming that the secondary was unresolved in the NIR, i.e., it did not possess any extended disk at their angular resolution ( GLYPH<24> 4.3 mas). Using analytical models, they found a uniform disk diameter of 3.6 GLYPH<6> 0.5 mas, i.e., 1.3 GLYPH<6> 0.2 AU, at a distance of 360 + 120 GLYPH<0> 70 pc. HD 200775 was later observed during an extensive spectropolarimetric campaign (Alecian et al. 2008). Two individual components were found in the photospheric line profiles. The authors defined as the primary target the one that emits the sharper lines: the secondary was determined to be the one responsible for the broader, shallower lines. Based on the RV of the lines, the authors provided orbital parameters in overall agreement with Pogodin et al. (2004) and Monnier et al. (2006), and a mass ratio primary / secondary of 0.81 GLYPH<6> 0.22, indicating that the star considered as secondary is in practice the most massive one. The H GLYPH<11> bisector velocities computed at a line intensity of 1.5 times the continuum were found to trace the RV of the secondary, suggesting that the line emission is dominated by this star. Their observations revealed a strongly inclined dipolar magnetic field (1000 GLYPH<6> 150 G), found to have been stable for more than 2 years, and related to the object considered as the primary. Although the authors derive similar masses and e GLYPH<11> ective temperatures ( GLYPH<24> 10 M GLYPH<12> and 18600 K, respectively), the discrepancy between the observational properties suggests that the two stellar components must have grown and evolved di GLYPH<11> erently. It seems very likely that the component defined as secondary in Alecian et al. (2008) is actually the one defined as primary in Monnier et al. (2006), the most massive component. The RV mass estimate and the dominant H GLYPH<11> activity is consistent with the presence of a circumstellar dusty disk as invoked in Monnier et al. (2006) around the most massive component. In this paper, we consider the primary to be the most massive component, i.e., the one that possesses a circumstellar dusty disk and dominates the H GLYPH<11> emission. The secondary is the least massive component that possesses a strong magnetic field. Mid-infrared (MIR) images obtained with the Keck segmenttilting experiment indicated a large halo containing 45% of 10.7 GLYPH<22> mflux with a north-south elongation (Monnier et al. 2009) consistent with the orientation of the binary orbit measured by Monnier et al. (2006). This suggests that the halo is the remnant of a circumbinary disk. This was confirmed by Subaru MIR images that showed a di GLYPH<11> use emission with an elliptical shape, suggesting an inclined flared disk (i = 54.5 GLYPH<14> GLYPH<6> 1.2 GLYPH<14> ; Okamoto et al. 2009). The MIR emission extends up to 20 times the semi-major axis of the binary, which indicates a large gap in the system. Furthermore, the system lies in a large scale biconical cavity that has very likely been excavated by an extended bipolar outflow inclined by GLYPH<24> 70 GLYPH<14> (Fuente et al. 1998; Watt et al. 1986), a value also close to the orbital plane inclination. These results support the presence of a circumbinary disk in the same plane as the orbit. The H GLYPH<11> and H GLYPH<12> emission lines show great variations over time, indicating changes in activity with a period of 3.68 years, in agreement with the binary period (Pogodin et al. 2004). In low states, the lines are double-peaked. In active states, the line intensities and equivalent widths (EW) increase, while their profiles show a complicated multi-component structure, including a doubling of the central absorption feature with a new, variable, blue-shifted component in addition to the pre-existing redshifted one. The EW is found to be at its maximum right after periastron, indicating that the line activity is indeed related to the binarity. The hot gas, responsible for the Hydrogen line, can be involved in accretion and ejection flows close to the source and can be used to probe the corresponding physical conditions. These phenomena, however, occur in a small region of a few AU around the star, corresponding to a few mas. With the recent advent of spectro-interferometric instruments, it has been possible to achieve such a resolution, and to spatially and spectrally resolve some of these lines. The first studies of the kind showed that the Br GLYPH<13> emission line was probably tracing winds or gas in a rotating disk (Malbet et al. 2007; Kraus et al. 2008). One of the challenging goals is to study the launching points of the jets and discriminate between the various theoretical models, Xwind (Shu et al. 1994) and disk-wind (Casse & Ferreira 2000). Inspired by the magneto-centrifugal scenario for the acceleration of jets, Rousselet-Perraut et al. (2010) and Weigelt et al. (2011) provided realistic solutions to account for the line emission in disk winds. From 2008 to 2011, we led an observing campaign over an entire orbit of HD 200775 with the optical spectrointerferometer VEGA installed at the CHARA Array. The paper is organized as follows: in Sect. 2 we describe the observations and the data processing. We present the new orbital solution, spectra, and interferometric observables in Sects. 3 and 4, and describe our modeling in Sect. 5. We discuss our results in Sect. 6 and conclude in Sect. 7.",
"pages": [
1,
2
]
},
{
"title": "2.1. VEGA observations",
"content": "The data were collected at the CHARA array (ten Brummelaar et al. 2005), with the VEGA instrument (Mourard et al. 2009). Our datasets were obtained with two telescopes (S1S2) and cover the period from July 2008 to October 2011, i.e., an orbital period. The average projected baseline length (Bp) is about 27 m, and the average baseline position angles (PAB) are given in Table 1. The angular resolution ( GLYPH<21> / 2Bp) of our observations is GLYPH<24> 2.5 mas. We therefore fully resolve the spectroscopic binary. The interferometric field of view is GLYPH<6> 2' in the slit direction and excludes the third object of the system (at 6'). The first dataset was recorded with the lowest spectral resolution of VEGA (R GLYPH<24> 1600, hereafter LR), as the target is at the instrumental sensitivity limit ( mV = 7.4). Instrumental improvements allowed us to later record data in medium spectral resolution (R GLYPH<24> 5000, hereafter MR). Each observation followed a calibrator-star-calibrator sequence, with 40 files of 1000 short exposures (15 ms) per observation. The calibrators were chosen to be close to the target both in distance and in spectral type, to be small enough at visible wavelengths, and to have an angular diameter known to an accuracy of a few percentage points. Using the SearchCal JMMC tool, we selected HD 204770 and HD 197950 (uniform disk diameters of GLYPH<24> 0.17 GLYPH<6> 0.01 mas and GLYPH<24> 0.33 GLYPH<6> 0.02 mas, respectively).",
"pages": [
2,
3
]
},
{
"title": "2.2. Data processing",
"content": "Spectra: the spectra were extracted using a classical scheme of collapsing the 2D flux in one spectrum, calibrating the pixel-wavelength relation using a Thorium-Argon lamp, and normalizing the continuum by a polynomial fit. We used the H GLYPH<11> absorption lines of the calibrators to check the spectral calibration at medium resolution. The accuracy of the spectral calibration is 0.13 nm (i.e., 60 km / s) in MR, and 0.39 nm (i.e., 178 km / s) in LR. Visibilities and di GLYPH<11> erential phases: The standard routines of the VEGA data reduction pipeline were used (Mourard et al. 2009). We computed visibilities and di GLYPH<11> erential phases in individual spectral channels, using the cross-spectrum method between two spectral channels [1] and [2] (for more details, see Berio et al. 1999). To reach a su GLYPH<14> cient signal-to-noise ratio (SNR) (at least 1 photon per speckle, spectral channel and single exposure), we considered the spectral band [1] to be as wide as the entire spectral range (32 nm, i.e., a broad band measurement), and [2], to be 4 nm-wide. This method first led to the determination of the di GLYPH<11> erential phase between [1] and [2], and of the product of the visibility amplitude V1*V2. The dataset was calibrated from the residual atmospheric piston and chromatic optical path di GLYPH<11> erence with the model described in Mourard et al. (2009). V 1 2 were estimated using the integration of the spectral densities of the short exposures over the entire spectral range [1] and calibrated from the instrumental transfer function estimated on the calibrators. Using an estimate of V1 and of the transfer function, we deduced the calibrated visibility V2 for the narrow spectral channel [2]. By sliding the narrow spectral channel [2] with steps of 2 nm across the entire spectral range [1], we obtained a set of 13 visibilities V2 and di GLYPH<11> erential phases, GLYPH<1> GLYPH<30> = GLYPH<30> 2 GLYPH<0> GLYPH<30> 1, with a final spectral resolution of GLYPH<24> 160. We considered GLYPH<1> GLYPH<30> equal to 0 in the continuum part of the spectrum, which means that the di GLYPH<11> erential phases measured in the H GLYPH<11> line correspond to astrometric o GLYPH<11> sets along the baseline direction, with the photocenter in the continuum as a reference point. The data reduction pipeline provided individual errors for each spectral channel, that account for photon noise only. To account for other sources of noise, we adopted conservative errors by considering the largest value between the rms in the continuum and the error computed by the pipeline. As the number of photons NH GLYPH<11> is much higher in the H GLYPH<11> spectral channel than in the continuum, we estimated the error in the H GLYPH<11> visibility by dividing the continuum error by p NH GLYPH<11> = N cont. Finally, as HD 200775 is a faint target compared to the VEGA limiting magnitude, excellent weather conditions are required to obtain good quality data. As a consequence, only 6 observations over our 14 attempts have led to a su GLYPH<14> cient SNR to produce interferometric observables.",
"pages": [
3
]
},
{
"title": "3. Orbital parameters",
"content": "Several determinations of the binary orbit exist in the literature. However, the SB2 radial velocities (Alecian et al. 2008) and resolved astrometric observations (Monnier et al. 2006) have never been fitted conjointly. Consequently, we revisit these works with the goal of determining the dynamical distance of the system and the individual masses of the components. We combined the available datasets following the formalism detailed in Le Bouquin et al. (2013) and performed a Levenberg-Marquardt least-square fit of the data. We are confident in our orbital determination, as the convergence toward a single and deep GLYPH<31> 2 minimumis fast and robust for a wide range of initial guesses. The error bars on the parameters were obtained by bootstrapping. The best-fit parameters are provided in Table 3. We note that the dynamical distance is out of the confidence interval of the new reduction of the Hipparcos data (520 GLYPH<6> 150 pc, Van Leeuwen 2007) and the individual masses are smaller by a factor of 2 than the ones derived in Alecian et al. (2008).",
"pages": [
3,
4
]
},
{
"title": "4.1. Spectroscopy",
"content": "Figure 1 presents 14 di GLYPH<11> erent H GLYPH<11> spectra that show a drastic change of intensity with time as well as slight changes in the full width at half maximum (FWHM) of the line. With these measurements, we confirm that the equivalent width (EW) of the line (Fig. 2) varies with the orbital phase, and reaches its maximum close to the periastron. In the following, we refer to 'active phase or state' when the system is close to the periastron, otherwise to 'quiescent phase or state'. In the quiescent state, we measure an EW of GLYPH<24> 35-40 Å, about twice as much as in the active phase which is in agreement with previous studies (Miroshnichenko et al. 1998; Alecian et al. 2008). For the sake of clarity, Fig. 3 shows six of the spectra obtained at medium spectral resolution, with a schematic of the system at the corresponding orbital epoch. The line is double peaked in the quiescent state with peak-velocities of GLYPH<24> 75-80 km / s, FWHM GLYPH<24> 450 km / s and broad wings at very high velocities ( GLYPH<24> 800 km / s), as deter- ined through Gaussian fitting of the profiles. The profile is almost symmetric close to the ascending node ( GLYPH<30> GLYPH<24> 0 : 5), and slightly asymmetric as the system gets closer to the periastron ( GLYPH<30> GLYPH<24> 0.8), with more blue-shifted emission. At periastron ( GLYPH<30> GLYPH<24> 0), the line is single peaked, and shows a slight asymmetry with more redshifted emission. There is no variability in the broad wings. These results support the idea that the binarity is at the origin of the line profile and intensity variations, as expected and observed in other close binaries.",
"pages": [
5
]
},
{
"title": "4.2. Interferometry",
"content": "Figure 4 presents the visibilities and di GLYPH<11> erential phases, as well as the corresponding spectra at a resolution of 1600. Change in the spectral shape of the visibility. By comparing the interferometric quantities in the continuum to the ones in the spectral channel centred on H GLYPH<11> , we detect a marginal visibility drop in the line during the active states ( GLYPH<30> GLYPH<24> 0 and 0.8; Table 2). This means that at least at these dates, the bulk of the H GLYPH<11> emission is spatially resolved and extended. Change in the spectral shape of the di GLYPH<11> erential phases. We find that within large error bars, the di GLYPH<11> erential phase in the line is consistent with zero for all measurements, except for GLYPH<30> GLYPH<24> 0.5 and 0.8. The di GLYPH<11> erential phase signals can be translated into a photocenter displacement in the plane of the sky along the direction of the projected baseline. For the S1S2 baseline used for the observations, a positive phase corresponds to a photocenter displacement towards the south, and a negative phase corresponds to the displacement towards the north, as detailed in Mourard et al. (2012). Therefore, the measured non-zero di GLYPH<11> erential phases trace for all epochs a photocenter displacement in the direction opposite to the secondary. As the measured differential phases are low ( GLYPH<1> GLYPH<30> GLYPH<20> 20 GLYPH<14> ), the photocenter of the H GLYPH<11> emission is rather close to the continuum / binary photocenter. Detection levels are defined using the errors in the continuum and in the line ( GLYPH<27> cont and GLYPH<27> H GLYPH<11> , respectively, computed as in Sect. 2.2) and are reported in Table 2. Change in the absolute level of the visibility. We notice that the level of the continuum visibility varies with the orbital phase, even if the measurements were obtained at similar angular resolutions ( GLYPH<24> 2.5 mas). This behavior is expected since the continuum emission is due to the binary that is spatially resolved by the interferometer. Therefore, any change in binary separation, position angle and / or flux ratio strongly a GLYPH<11> ects the visibilities. Close to the ascending node (2009 dataset), we measure a continuum visibility close to 1, corresponding to an unresolved emission along the baseline position angle, while in the active state, the continuum visibility can be as low as GLYPH<24> 0.76.",
"pages": [
5
]
},
{
"title": "5. Results",
"content": "The goal of the analysis is to derive the basic properties of the H GLYPH<11> emitting region. This requires a proper subtraction of the continuum emission that is only due to the binary stars. To do so, we first fit a binary model to the continuum visibilities, with fixed orbital parameters (Table 3), in order to determine the flux ratio (FR) between the two stars. This flux ratio will set our model in the continuum for both the visibilities and di GLYPH<11> erential phases.",
"pages": [
5
]
},
{
"title": "5.1. Binary flux ratio",
"content": "In the spectral range of our observations, we assume that the only emitters in the continuum are the two stellar components. Their relative flux ratios, separations, and position angles have a strong impact on the visibility in the continuum. Assuming that the relative stellar fluxes vary over the orbit, we can use our continuum visibilities to retrieve the flux ratio at di GLYPH<11> erent epochs, assuming that the individual stars are unresolved, and using a simple analytical formula for the binary visibility. We first compute the position angle and separation for each epoch, using the orbital parameters determined in Tab. 3. We then compute a large grid of GLYPH<24> 1000 binary models, and minimize a GLYPH<31> 2 . Individual fits to each data set provide flux ratios from 0.07 + 0 : 05 GLYPH<0> 0 : 06 to 0.29 + 0 : 18 GLYPH<0> 0 : 11 ( GLYPH<31> 2 = 1.5 at most). This suggests that the secondary is the dimmer object in the continuum. At the ascending node GLYPH<30> GLYPH<24> 0.26 where V GLYPH<24> 1 and the binary is unresolved, all flux ratio values below 0.06 provide an equally good fit ( GLYPH<31> 2 = 1.1), while for GLYPH<30> GLYPH<24> 0.81 all possible flux ratio values surprisingly provide a bad fit ( GLYPH<31> 2 = 3.3). The second dataset shows a large intrinsic scatter in the continuum (rms GLYPH<24> 10%), and seems to su GLYPH<11> er from calibration problems that prevent us from determining a good absolute value for the visibility. Because we cannot determine a flux ratio for this measurement, we scale the average continuum visibilities, for this dataset only, to the binary model predictions with FR = 0.10, which corresponds to the best-fit model assuming a constant flux ratio over the entire orbit ( GLYPH<31> 2 = 3.8). The scaling factor is GLYPH<24> 25%, as shown in Fig. A.1, together with the best fit of the binary model for each dataset. Values of flux ratios are given in Table 4. Because of the large error bars, we cannot determine whether the change in FR with the orbital period is significant and expect that further high SNR observations would answer this question.",
"pages": [
6
]
},
{
"title": "5.2. Size and photocenter of the H GLYPH<11> emission",
"content": "To model the H GLYPH<11> circumstellar emission, we consider the contribution of the binary to the measured visibilities and di GLYPH<11> erential phases using the complex visibilities. Assuming that the binary is at the photocenter of the continuum emission (i.e., GLYPH<1> GLYPH<30> = 0 in the continuum), we find that for each spectral channel k where the indices cont and H GLYPH<11> refer to the continuum (binary) and circumstellar emission, GLYPH<1> GLYPH<30> k is the measured di GLYPH<11> erential phases in the spectral channel k , and GLYPH<1> GLYPH<30> H GLYPH<11> is the di GLYPH<11> erential phase due to the H GLYPH<11> emitting region. The real and imaginary parts of Eq. 1 lead to two equations that can be solved for VH GLYPH<11> and GLYPH<1> GLYPH<30> H (see, eg., Weigelt et al. 2007; Eisner et al. 2010). GLYPH<11> With the best binary model, and the line to continuum ratio determined from the spectra after subtraction of the photospheric H GLYPH<11> absorption, we fit our model for the H GLYPH<11> emission to VH GLYPH<11> and GLYPH<1> GLYPH<30> H GLYPH<11> , in the two spectral channels that contain most or all of the line. Considering the low quality of our datasets, we limit ourselves to a simplistic analytical approach with a face-on Gaussian model, which FWHM (considered as a typical size) and location can vary. We restrict the Gaussian displacement along the binary axis only, since our measurements have been obtained along a single baseline orientation at a time, which prevents us from determining a full 2-D position. The reference is taken to be the primary and displacements are counted positive towards the secondary. We vary the Gaussian FWHM from 0 to 6 mas, and since the sign of the di GLYPH<11> erential phases indicates a displacement in the direction opposite to the secondary, we vary the Gaussian location from -4 to 0 mas, and minimize a GLYPH<31> 2 to find the best model parameters. Figure 5 shows the best-fit to the H GLYPH<11> visibilities and di GLYPH<11> erential phases, and Fig. 6 presents the model parameters as they vary with the orbital phase (values are in Table 4). Our model fits the observations well, with a reduced GLYPH<31> 2 of 2.7 (at most) in the line + continuum (1.1 in the H GLYPH<11> spectral channels only). Conservative error bars have been obtained by considering the extreme values of the visibilities and FR within their error bars. We find that the spatial extent of the emission changes over the orbit. In the quiescent state, the Gaussian FWHM is 0.67 GLYPH<6> 0.20 mas (i.e., GLYPH<24> 0.22 AU) and increases up to GLYPH<24> 1.95 GLYPH<6> 0.20 mas (i.e., GLYPH<24> 0.62 AU), close to periastron. The displacements towards the opposite direction than the secondary appear to be quasi constant along the orbit, with absolute values close to 0.10 GLYPH<6> 0.03 mas (i.e., 0.03 GLYPH<6> 0.01 AU). The errors on the displacement are dominated by the errors on the binary flux ratio, hence are very large for GLYPH<30> GLYPH<24> 0.81. Because our measurements only probe one direction at a time, we are not able to determine an inclination and a position angle for the H GLYPH<11> emitting region, and leave this for a detailed radiative transfer modeling combined with additional simultaneous multi-baseline interferometric observations. Thus, we would like to stress that the obtained parameter values are model-dependent and di GLYPH<11> erent geometries (e.g., ring, uniform disk) lead to slightly larger values of typical size, as expected with such simple prescriptions. In addition, the values of the displacement strongly depend on the binary flux ratio that set the phase values in the continuum. However, the variations of the H GLYPH<11> characteristic size along the orbit and the negative photocenter displacements still hold.",
"pages": [
6
]
},
{
"title": "6.1. Characteristic spatial extents in H GLYPH<11>",
"content": "It is useful to compare the H GLYPH<11> size estimates to typical radii in the close circumstellar regions probed by our measurements. If we consider the extreme values of luminosities found in the literature ( GLYPH<24> 3000 and GLYPH<24> 15000 L GLYPH<12> from Alecian et al. (2008); Hern'andez et al. (2004)), we derive an estimate of the location of the dust sublimation radius of the circumprimary disk to be between 3.7 and 8.4 AU (e.g., Dullemond & Monnier 2010). These estimates are larger than the dust inner radius ( GLYPH<24> 1.73 mas, i.e., 0.55 AU at 320 pc) measured by Monnier et al. (2006). This apparent discrepancy can be explained with optically thick material inside the dust sublimation radius that e GLYPH<14> ciently shields the dust from the stellar light (Monnier & Millan-Gabet 2002). Considering the vsin(i) estimate and stellar properties from Alecian et al. (2008), we find that the corotation radius should be GLYPH<24> 0.30 GLYPH<6> 0.15 AU. This estimate su GLYPH<11> ers from the large uncertainties on the stellar parameters inferred in the literature. Nonetheless, our Gaussian fit seems to indicate that the bulk of the H GLYPH<11> emission as described by a Gaussian model is most likely located between the corotation radius and the dust sublimation radius, and is more extended than the typical regions involved in accretion processes onto the star. In the case of a low mass star, the truncation radius is set by the interaction of the stellar magnetic field and the gaseous disk in a region very close to the star. In a massive star, although this is still a matter of debate, the accretion is thought to occur through a boundary layer. Similar extents for Hydrogen line emission have been found in other Herbig Be stars, in the Br GLYPH<13> line, and interpreted as originating in a stellar or disk wind (e.g., Kraus et al. 2012; Weigelt et al. 2011; Benisty et al. 2010), in contrast with the findings of Eisner et al. (2010) on a survey of lower mass young stars that are consistent with accretion. It also seems unlikely that the bulk of the H GLYPH<11> emission is due to a rotating disk, even in the quiescent state, where the H GLYPH<11> line profile shows a double peak at low velocities ( GLYPH<24> 75 km / s). If we consider a mass of GLYPH<24> 10 M GLYPH<12> , and the velocity field of a disk in Keplerian rotation ( v = p GM GLYPH<3> = R / sin(i)), the H GLYPH<11> double peak in the quiescent state could result in a rotating disk with a minimum outer radius of R GLYPH<24> 1.2 AU, a much larger value than our estimates (Table 4). The disk region responsible for the broad H GLYPH<11> wings would be located very close to or inside the stellar surface ( GLYPH<24> 7.6 R GLYPH<12> ).",
"pages": [
7
]
},
{
"title": "6.2. Origin of the H GLYPH<11> burst",
"content": "The results given in the previous section can be interpreted in the context of mass ejection. The extended H GLYPH<11> emission together with the increase of the H GLYPH<11> line intensity may trace a period of enhanced mass loss in a strong wind emitted by the primary. Such an event could follow a period of enhanced mass accretion from the circumbinary disk to the primary disk, triggered at periastron as predicted by numerical models. The photocenter displacements in the direction opposite to the secondary indicate that if a wind is responsible for the H GLYPH<11> emission, the emission should be enhanced along this direction. The wind therefore could not be fully spherical, as the consequent emission would be symmetric. Figure 1 shows that the H GLYPH<11> broad line wings ( GLYPH<24> 800 km / s) are very stable, and can be due to outflowing matter, as such velocities are often seen in wind tracers. The additional emission at periastron is produced only at very low projected velocities, probably coming from a plane close to perpendicular to our line of sight. The lack of P Cygni absorption indicates that the wind is not self-absorbing along our line of sight. This would support a wind with a higher density towards low latitudes, close to the equatorial plane, in agreement with the model predictions of poorly collimated winds in massive stars (Vaidya et al. 2011). With a non-zero inclination, an outflow can also produce the double peaked profile observed in quiescent state, as shown in Stee & de Araujo (1994) for Be stars, and more recently in Weigelt et al. (2011) for a Herbig Be star of similar mass. However, complex line opacity e GLYPH<11> ects can come into play, as suggested by Elitzur et al. (2012) who showed that it is in practice impossible to disentangle e GLYPH<11> ects of kinematics and line opacity e GLYPH<11> ects in double peaked lines and that proper radiative transfer is needed. In addition, we note that spectra obtained at high spectral resolution (Alecian et al. 2008) show that the line profile is extremely complex with variable features, which seem to indicate a combination of various variable mechanisms. The additional emission at periastron could, in principle, come from either the primary, the secondary, or a combination of both. However, the low di GLYPH<11> erential phases indicate that the photocenter of the H GLYPH<11> emitting region is close to the continuum photocenter, which is located close to the primary (since the binary best-fit flux ratio is 0.10). The displacement values found by our simple analytical model fitting therefore rule out a scenario in which all of the additional H GLYPH<11> emission at periastron comes from the secondary. It seems therefore very unlikely that accretion onto the secondary or wind-enhancement on the secondary is the key-mechanism at periastron or that both objects are equally responsible for the increase. On the contrary, because the displacements are in the opposite direction to the secondary, the burst of activity at periastron seems to be connected to the primary. Although the variation of photocenter with the orbital phase is marginal, a smaller displacement at the ascending node is consistent with a smaller emitting region and a lower line intensity. An almost-constant displacement at all other phases is also in agreement with the derivation of a similar extent at these dates. This is supported by recent numerical simulations of accretion flows in close binaries done at high resolution (de ValBorro et al. 2011). These models suggested that accretion from the circumbinary disk onto the primary is favored at periastron. In that scenario, it is expected that most or all of the additional H GLYPH<11> emission in the active state comes from the primary star, as our data seem to indicate. We note, however, that with our single-baseline measurements, we are not able to disentangle more complex scenarios. Whatever the mechanism favored to enhance the H GLYPH<11> emission at periastron, additional mass has to be fed into the innermost regions at these active stages. If mass is transferred through accretion streamers from the circumbinary disk to the primary disk, there should be a consequent time delay to allow matter to flow through the primary disk and reach the innermost AU. The viscous time is proportional to GLYPH<24> R / ( GLYPH<11> cs H / R), with R the radius, H the disk scale height, and GLYPH<11> the turbulence parameter (proportional to the viscosity; Shakura & Sunyaev (1973)). Considering a maximum outer disk radius for the circumprimary disk of 2 AU (because the binary separation at periastron is GLYPH<24> 4 AU, (Monnier et al. 2006)), GLYPH<11> = 0.01, and H / R = 0.05, the viscous time needed for the mass flow to propagate is of the order of a few ten thousand years, much larger than the binary period. An alternative scenario is that the secondary induces gravitational instabilities in the primary disk as it approaches. In fact, tidal e GLYPH<11> ects could induce strong waves all over the disk spatial range and produce instabilities, which would in turn enhance the mass accretion in the inner AU and result in a higher mass loss. The exact physical process that leads to the H GLYPH<11> increase still remains to be understood. The comparison of Fig. 2 and Fig. 6 seems to suggest that the variations in H GLYPH<11> EW and sizes are slightly shifted in time, as the size appears to increase faster than the absolute EW. This delay is di GLYPH<14> cult to interpret as we would expect a larger emitting area to produce a stronger H GLYPH<11> emission, but considering the large error bars on our size estimate and the sparse time sampling of the orbit, we cannot determine whether it is a real feature or not.",
"pages": [
7,
8
]
},
{
"title": "7. Summary and conclusion",
"content": "In this paper, we report the first spatially and spectrally resolved observations of the H GLYPH<11> line emitting region in a close binary system using the VEGA spectrometer on the CHARA array. As previous authors have already pointed out (Pogodin et al. 2004; Alecian et al. 2008), we find that HD 200775 shows a variation of the H GLYPH<11> EW with the orbital phase. We use a simple Gaussian model located along the binary axis to fit the H GLYPH<11> visibilities and di GLYPH<11> erential phases, and find marginal evidence for a change in spatial extent during the orbit that is minimum in quiescent state (close to the ascending node). The H GLYPH<11> Gaussian photocenter is at all epochs located in the direction opposite to the secondary, supporting a dominant emission by the primary. We find typical H GLYPH<11> extents within the sublimation radius. These H GLYPH<11> spatial extents do not support an accretion origin for the bulk of the line emission, as it would involve smaller scales. Instead, we interpret these results in the context of an enhanced mass-loss event, triggered by the gravitational influence of the secondary. Such a scenario would suggest a strong connection between accretion and ejection in this Herbig Be star, as already noted in other massive objects (e.g., Ellerbroek et al. 2011; Benisty et al. 2010). Adominant contribution to the H GLYPH<11> line by the primary is supported by our results and by the analysis of Alecian et al. (2008) and Monnier et al. (2006). However, although the stellar parameters are still highly uncertain, it is puzzling that only the primary has a circumstellar disk which accretes from the circumbinary disk. In particular, the kilo-Gauss magnetic field detected on the secondary should induce the formation of a gaseous disk which should in turn emit H GLYPH<11> . The circumstellar environments of the two objects must either have evolved di GLYPH<11> erently, or the secondary could itself be an unknown spectroscopic binary of lower mass which would more easily explain the strong magnetic field, an uncommon feature in Herbig Be stars. We find that the binary flux ratio in the continuum is GLYPH<24> 0.10 (from GLYPH<24> 0.07 to GLYPH<24> 0.29, Tab. 4). Because of large error bars on the visibilities, we are not able to retrieve a precise flux ratio at each orbital phase and to determine whether the change in H GLYPH<11> EW is correlated with some change in the amount of reprocessed and scattered light as observed in other young close binaries (van Boekel et al. 2010). We notice a discrepancy between our flux ratio estimates in the continuum and the estimate of Alecian et al. (2008), based on an analysis of spectral lines ( GLYPH<24> 0.67). These estimates are di GLYPH<14> cult to reconcile, unless one invokes variable extinction on one of the two objects, or if one of the two (most likely the magnetic secondary) is already chemically peculiar. Besides, the large uncertainties on the individual masses, the distance, and age of the system prevents the nature of the individual objects from being assessed precisely. As noted by Alecian et al. (2008), photometric observations of each component separately are necessary. In addition, a regular and full coverage of the orbit is required to answer a number of open questions, such as a possible time delay between periastron passage and maximum activity. More detailed modeling, as well as an intensive high SNR spectro-interferometric campaign with additional baselines at various orientations are also expected to properly constrain the complex interplay between accretion and ejection in such massive close binary systems.",
"pages": [
8,
9
]
},
{
"title": "Appendix A: Appendix",
"content": "Acknowledgements. We acknowledge the anonymous referee for the constructive report that helped improve the manuscript. We thank E. Alecian, J. Bouvier, P. Garcia, A. M'erand, J.L. Monin and J. Monnier for fruitful discussions. We acknowledge all the great observers at the CHARA Array who helped to gather this large dataset. The CHARA Array is operated with support from the National Science Foundation through Grant AST-0908253, the W. M. Keck Foundation, the NASA Exoplanet Science Institute, and from Georgia State University. GHRAL acknowledges CAPES for the support. This research has made use of the Jean-Marie Mariotti Center SearchCal service 1 co-developped by FIZEAU and IPAG, and of CDS Astronomical Databases SIMBAD and VIZIER 2 .",
"pages": [
9
]
},
{
"title": "References",
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"pages": [
9
]
}
]
2013A&A...555A.147W
https://arxiv.org/pdf/1307.3734.pdf
<document>
<section_header_level_1><location><page_1><loc_10><loc_82><loc_90><loc_87></location>Probing the evolution of the substructure frequency in galaxy clusters up to z ∼ 1</section_header_level_1>
<text><location><page_1><loc_35><loc_80><loc_65><loc_81></location>A. Weißmann 1 , H. Böhringer 1 , G. Chon 1</text>
<text><location><page_1><loc_10><loc_76><loc_77><loc_78></location>1 Max-Planck-Institut für extraterrestrische Physik, Postfach 1312, Giessenbachstr., 85741 Garching, Germany email: [email protected]</text>
<text><location><page_1><loc_10><loc_73><loc_40><loc_74></location>Received 18 March 2013 / Accepted 4 June 2013</text>
<section_header_level_1><location><page_1><loc_46><loc_70><loc_54><loc_71></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_10><loc_66><loc_90><loc_69></location>Context. Galaxy clusters are the last and largest objects to form in the standard hierarchical structure formation scenario through merging of smaller systems. The substructure frequency in the past and present epoch provides excellent means for studying the underlying cosmological model.</text>
<text><location><page_1><loc_10><loc_62><loc_90><loc_65></location>Aims. Using X-ray observations, we study the substructure frequency as a function of redshift by quantifying and comparing the fraction of dynamically young clusters at di ff erent redshifts up to z = 1 . 08. We are especially interested in possible biases due to the inconsistent data quality of the low-z and high-z samples.</text>
<text><location><page_1><loc_10><loc_60><loc_90><loc_62></location>Methods. Two well-studied morphology estimators, power ratio P 3 / P 0 and center shift w , were used to quantify the dynamical state of 129 galaxy clusters, taking into account the di ff erent observational depth and noise levels of the observations.</text>
<text><location><page_1><loc_10><loc_55><loc_90><loc_60></location>Results. Owing to the sensitivity of P 3 / P 0 to Poisson noise, it is essential to use datasets with similar photon statistics when studying the P 3 / P 0-z relation. We degraded the high-quality data of the low-redshift sample to the low data quality of the high-z observations and found a shallow positive slope that is, however, not significant, indicating a slightly larger fraction of dynamically young objects at higher redshift. The w -z relation shows no significant dependence on the data quality and gives a similar result.</text>
<text><location><page_1><loc_10><loc_53><loc_90><loc_55></location>Conclusions. We find a similar trend for P 3 / P 0 and w , namely a very mild increase of the disturbed cluster fraction with increasing redshifts. Within the significance limits, our findings are also consistent with no evolution.</text>
<text><location><page_1><loc_10><loc_51><loc_59><loc_52></location>Key words. X-rays: galaxies: clusters - Galaxies: clusters: Intracluster medium</text>
<section_header_level_1><location><page_1><loc_6><loc_46><loc_18><loc_48></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_6><loc_13><loc_49><loc_45></location>The standard theory of structure formation predicts hierarchical growth from positive fluctuations in the primordial density field. Subgalactic scale objects decouple first, then collapse and virialize due to the greater amplitudes of the density fluctuations on small scales. They grow through merging, finally forming galaxy clusters, which are considered the largest virialized objects in the Universe. Galaxy cluster growth probes the evolution of density perturbations and directly traces the process of structure formation in the Universe. Galaxy clusters are thus important laboratories for studying and testing the underlying cosmological model (e.g. Borgani 2008; Voit 2005). Especially important in this context is the study of the cluster mass function, whose evolution provides constraints on the linear growth rate of density perturbations. Using X-rays and analyzing the hot intracluster medium (ICM) that resides in the deep potential well of galaxy clusters, mass determination is based on the assumptions of hydrostatic equilibrium and spherical shape. These assumptions may be unsatisfactory for dynamically young objects showing multiple surface brightness peaks in the distribution of the ICM, however (e.g. Nelson et al. 2012; Rasia et al. 2012; Zhang et al. 2008). In addition, the influence of dynamical activity such as merging on L X, T X etc. needs to be known in detail to explain possible deviations from scaling relations for disturbed clusters (e.g. Pratt et al. 2009; Rowley et al. 2004; Chon et al. 2012) with the aim to reduce the errors in cosmological studies.</text>
<text><location><page_1><loc_6><loc_10><loc_49><loc_12></location>Observations of substructure and disturbed morphologies in the optical (see e.g. Girardi & Biviano 2002; West & Bothun</text>
<text><location><page_1><loc_51><loc_40><loc_94><loc_48></location>1990, and references therein) and X-ray band (for a review see e.g. Buote 2002) indicate that a large fraction of clusters is dynamically young and has not reached a relaxed state yet. It is therefore essential to quantify the fraction of disturbed clusters that reflects the formation rate and to probe higher redshifts to constrain cosmological parameters.</text>
<text><location><page_1><loc_51><loc_18><loc_94><loc_40></location>X-ray observations provide excellent probes for studying the dynamical state of clusters because the ICM traces their deep potential well. Over the years, X-ray studies became very e ffi cient in quantifying cluster structure, and a variety of X-ray morphology estimators was introduced (for a review see Rasia 2013). However, only recently, larger samples of high-z observations of galaxy clusters became available and allowed statistical studies of the evolution of the substructure frequency up to z ∼ 1. Since then, several observational X-ray studies have shown a larger fraction of dynamically relaxed clusters at lower redshift than at z > 0 . 5 (e.g. Mann & Ebeling 2012; Andersson et al. 2009; Maughan et al. 2008; Hashimoto et al. 2007; Bauer et al. 2005; Jeltema et al. 2005; Plionis 2002; Melott et al. 2001). A less clear evolution was found in hydrodynamical simulations, but higher merger rates at high redshift support the observational results (e.g. Burns et al. 2008; Jeltema et al. 2008; Kay et al. 2007; Rahman et al. 2006; Cohn & White 2005).</text>
<text><location><page_1><loc_51><loc_10><loc_94><loc_17></location>Opening the window toward higher-redshift clusters is accompanied by the problem of the insu ffi cient data quality of Xray images in terms of net photon counts and background contribution. Exploring a broad redshift range directly translates into probing data with quite substantial quality di ff erences. It is therefore not only essential to use well-studied morphology estima-</text>
<text><location><page_2><loc_6><loc_91><loc_49><loc_93></location>tors but also to understand possible biases caused by uneven data quality.</text>
<text><location><page_2><loc_6><loc_67><loc_49><loc_90></location>In this work, we used two common X-ray substructure estimators, power ratio P 3 / P 0 (Buote & Tsai 1995) and center shift w (Mohr et al. 1993), to study the relation between cluster structure and redshift up to z = 1 . 08. To do so, we took advantage of the detailed study of the influence of net photon counts and background on the computation of P 3 / P 0 and w in our recently published work (Weißmann et al. 2013). Jeltema et al. (2005) presented the first analysis of the P 3 / P 0-z relation using 40 X-ray selected luminous clusters in the redshift range 0 . 1 < z < 0 . 89. Using di ff erent statistical measures, they reported on average higher P 3 / P 0 for clusters with z > 0 . 5 than for low-z objects. While they accounted for the bias caused by photon noise and background, they did not fully consider the strong decrease of data quality at higher redshifts and overestimated the P 3 / P 0-z relation. In addition to using a larger sample, we explored possible biases caused by di ff erent observational depths in the lowz and high-z samples and determined how to account for them when analyzing the P 3 / P 0-z and w -z relation.</text>
<text><location><page_2><loc_6><loc_53><loc_49><loc_67></location>The paper is organized as follows. We characterize the sample and briefly discuss the data reduction process in Sect. 2. In Sect. 3 we introduce the morphology estimators P 3 / P 0 and w used in this work. Sect. 4 summarizes how we degraded the high-quality data of the low-z sample to match the high-z observations. We give results in Sect. 5, including a detailed study of the influence of the di ff erent data quality in samples. Previous studies and the e ff ect of cool cores are discussed in Sect. 6. We finally conclude with Sect. 7. Throughout the paper, the standard Λ CDM cosmology was assumed: H 0 = 70 km s -1 Mpc -1 , ΩΛ= 0.7, Ω M = 0.3.</text>
<section_header_level_1><location><page_2><loc_6><loc_49><loc_35><loc_50></location>2. Observations and data reduction</section_header_level_1>
<text><location><page_2><loc_6><loc_21><loc_49><loc_48></location>In this section we discuss the three samples used for our study: the low-z sample and the high-z subsamples of the 400SD and SPT surveys. An overview of the redshift distribution is shown in Fig. 1. Table 1 summarizes the sample statistics including the number of clusters, the redshift range, the mean net photon counts within r 500, and the mean net- (signal-)to-background photon counts ratio S / B. This table is discussed in more detail in Sect. 4, where we concentrate on the problem of the data quality. Details of the galaxy clusters and observational properties are given in Table 5. r 500 was calculated for all clusters using the formula given by Arnaud et al. (2005). The temperature and redshift values were taken from previous works as indicated in Table 5. For a full gallery of the X-ray images of the galaxy clusters used in this study we refer to Weißmann et al. (2013) for the lowz sample, the website of the 400d 2 cluster survey 1 for the highz 400SD objects, and to Andersson et al. (2011) for the high-z SPT clusters. To give an impression of the substructure values and the data quality, we provide a few examples of backgroundincluded, point-source-corrected smoothed X-ray images in Fig. 2 (left panels) for the low-z sample and in Fig. 3 for the high-z samples.</text>
<section_header_level_1><location><page_2><loc_6><loc_18><loc_25><loc_19></location>2.1. Low-zclustersample</section_header_level_1>
<text><location><page_2><loc_6><loc_12><loc_49><loc_17></location>The low-redshift sample (short: low-z) was previously used and discussed in detail in Weißmann et al. (2013, W13 hereafter). For our current work, we excluded two clusters that were part of the W13 sample: RXJ1347-1145 and RXCJ0516-5430.</text>
<figure>
<location><page_2><loc_55><loc_72><loc_92><loc_92></location>
<caption>Fig. 1. Redshift distribution of the low-z (red filled histogram), high-z 400SD (green filled histogram), and high-z SPT sample (black dashed histogram) .</caption>
</figure>
<text><location><page_2><loc_51><loc_55><loc_94><loc_63></location>RXJ1347-1145 was omitted because of its high redshift of z = 0 . 45 and because we did not want to add this cluster to the high-z samples with defined origin. RXCJ0516-5430 or SPT-CLJ05165430 ( z = 0 . 29) was already part of the high-z SPT sample. We thus excluded it from the low-z sample because of its high redshift.</text>
<text><location><page_2><loc_51><loc_27><loc_94><loc_55></location>The low-z sample now comprises 78 archival XMM-Newton observations of galaxy clusters covering redshifts between 0.05 and 0.31, with 〈 z 〉 = 0 . 15. The clusters were drawn from several well-known samples observed with XMMNewton (for details see Table 5): REXCESS (Böhringer et al. 2007), LoCuSS (Smith et al., Zhang et al. 2008), the Snowden Catalog (Snowden et al. 2008), the REFLEX-DXL sample (Zhang et al. 2006), and Buote & Tsai (1996). The clusters were chosen to be well-studied, nearby (0 . 05 < z < 0 . 31), and publicly available (in 2009) in the XMM-Newton science archive 2 . In addition, we required r 500 to fit on the detector. The calculation of r 500 using the formula of Arnaud et al. (2005) led to slightly di ff erent r 500 and hence P 3 / P 0 and w values to those quoted in W13. The di ff erences are small, however. This merged low-z sample has no unique selection function, but a wide spread in luminosity, temperature, and mass. A large part of the clusters comes from representative samples such as REXCESS and LoCuSS and we therefore expect the sample to have a very roughly representative character. To check in more detail that no bias e ff ect is introduced by the merged sample, we also performed all tests with the 31 REXCESS clusters only. The results are consistent with the full low-z sample and we therefore do not quote them in detail.</text>
<section_header_level_1><location><page_2><loc_51><loc_23><loc_70><loc_24></location>2.2. High-zclustersamples</section_header_level_1>
<text><location><page_2><loc_51><loc_14><loc_94><loc_22></location>In the high-redshift range, we used two samples to account for possible selection e ff ects and performed our analysis on each sample individually: the X-ray-selected high-z subsample from the 400SD survey (Burenin et al. 2007; Vikhlinin et al. 2009) and the SZ-selected subsample from SPT discussed in Andersson et al. (2011).</text>
<figure>
<location><page_3><loc_7><loc_83><loc_27><loc_93></location>
<caption>Fig. 2. Examples of the background-included, point-source-corrected smoothed X-ray images of the low-z sample. Left: high-quality (undegraded) images. Right: degraded images (for details see Sect. 4.1). Top panels: A963 - relaxed galaxy cluster at z = 0 . 21 with P 3 / P 0 = (1 . 77 ± 1 . 42) × 10 -8 and w = (4 . 40 ± 0 . 30) × 10 -3 , non-significant detection after degrading. Bottom panels: A115 - merging cluster at z = 0 . 20 with P 3 / P 0 = (5 . 33 ± 0 . 19) × 10 -6 and w = (8 . 54 ± 0 . 05) × 10 -2 , significant detection after degrading. The circle indicates r 500.</caption>
</figure>
<figure>
<location><page_3><loc_73><loc_83><loc_93><loc_93></location>
</figure>
<text><location><page_3><loc_7><loc_83><loc_7><loc_83></location>-0.0</text>
<text><location><page_3><loc_9><loc_83><loc_9><loc_83></location>0.1</text>
<text><location><page_3><loc_11><loc_83><loc_11><loc_83></location>0.4</text>
<text><location><page_3><loc_13><loc_83><loc_13><loc_83></location>1.1</text>
<text><location><page_3><loc_15><loc_83><loc_15><loc_83></location>2.3</text>
<text><location><page_3><loc_17><loc_83><loc_17><loc_83></location>4.8</text>
<text><location><page_3><loc_19><loc_83><loc_19><loc_83></location>9.7</text>
<text><location><page_3><loc_21><loc_83><loc_21><loc_83></location>19.5</text>
<text><location><page_3><loc_23><loc_83><loc_23><loc_83></location>39.2</text>
<text><location><page_3><loc_25><loc_83><loc_25><loc_83></location>78.3</text>
<text><location><page_3><loc_26><loc_83><loc_27><loc_83></location>156.1</text>
<text><location><page_3><loc_28><loc_83><loc_28><loc_83></location>0</text>
<text><location><page_3><loc_30><loc_83><loc_31><loc_83></location>0.005</text>
<text><location><page_3><loc_32><loc_83><loc_33><loc_83></location>0.015</text>
<text><location><page_3><loc_34><loc_83><loc_35><loc_83></location>0.035</text>
<text><location><page_3><loc_36><loc_83><loc_37><loc_83></location>0.074</text>
<text><location><page_3><loc_38><loc_83><loc_39><loc_83></location>0.15</text>
<text><location><page_3><loc_40><loc_83><loc_41><loc_83></location>0.31</text>
<text><location><page_3><loc_42><loc_83><loc_43><loc_83></location>0.62</text>
<text><location><page_3><loc_44><loc_83><loc_45><loc_83></location>1.3</text>
<text><location><page_3><loc_46><loc_83><loc_47><loc_83></location>2.5</text>
<text><location><page_3><loc_48><loc_83><loc_48><loc_83></location>5</text>
<figure>
<location><page_3><loc_7><loc_72><loc_27><loc_82></location>
</figure>
<text><location><page_3><loc_7><loc_72><loc_7><loc_72></location>-0</text>
<text><location><page_3><loc_9><loc_72><loc_9><loc_72></location>0</text>
<text><location><page_3><loc_11><loc_72><loc_11><loc_72></location>1</text>
<text><location><page_3><loc_13><loc_72><loc_13><loc_72></location>2</text>
<text><location><page_3><loc_15><loc_72><loc_15><loc_72></location>4</text>
<text><location><page_3><loc_17><loc_72><loc_17><loc_72></location>9</text>
<text><location><page_3><loc_19><loc_72><loc_19><loc_72></location>17</text>
<text><location><page_3><loc_21><loc_72><loc_21><loc_72></location>35</text>
<text><location><page_3><loc_23><loc_72><loc_23><loc_72></location>70</text>
<text><location><page_3><loc_25><loc_72><loc_25><loc_72></location>141</text>
<text><location><page_3><loc_27><loc_72><loc_27><loc_72></location>280</text>
<text><location><page_3><loc_28><loc_72><loc_29><loc_72></location>3.6e-10</text>
<text><location><page_3><loc_30><loc_72><loc_31><loc_72></location>0.005</text>
<text><location><page_3><loc_32><loc_72><loc_33><loc_72></location>0.015</text>
<text><location><page_3><loc_34><loc_72><loc_35><loc_72></location>0.035</text>
<text><location><page_3><loc_36><loc_72><loc_37><loc_72></location>0.074</text>
<text><location><page_3><loc_38><loc_72><loc_39><loc_72></location>0.15</text>
<text><location><page_3><loc_40><loc_72><loc_41><loc_72></location>0.31</text>
<text><location><page_3><loc_42><loc_72><loc_43><loc_72></location>0.62</text>
<text><location><page_3><loc_44><loc_72><loc_45><loc_72></location>1.3</text>
<text><location><page_3><loc_46><loc_72><loc_47><loc_72></location>2.5</text>
<text><location><page_3><loc_48><loc_72><loc_48><loc_72></location>5</text>
<text><location><page_3><loc_6><loc_38><loc_49><loc_57></location>The high-z 400SD sample (short: 400SD) forms a complete subsample of the z > 0 . 35 clusters from the 400SD survey. It is composed of 36 objects in the 0 . 35 < z < 0 . 89 range and was selected as a quasi-mass-limited sample at z > 0 . 5. This was done by requiring a luminosity above a threshold of L X , min = 4 . 8 × 10 43 (1 + z ) 1 . 8 erg s -1 . All 36 400SD clusters were observed with CHANDRA and are publically available in the CHANDRA archive 3 . Several authors (e.g. Santos et al. 2010) have raised the question whether there might be a possible bias in the 400SD sample due to the detection algorithm. This may result in a lack of concentrated clusters compared with other high-redshift samples such as the Rosat Deep Cluster Survey (RDCS, Rosati et al. 1998) or the Wide Angle ROSAT Pointed Survey (WARPS, Jones et al. 1998). We accounted for these e ff ects by using the high-z SPT sample for comparison.</text>
<text><location><page_3><loc_6><loc_19><loc_49><loc_37></location>The high-z SPT sample (short: SPT) is a subsample of the first SZ-selected cluster catalog, obtained from observations of 178 deg 2 of sky surveyed by the South Pole Telescope (SPT). Vanderlinde et al. (2010) presented a significance-limited catalog of 21 SZ-detected galaxy clusters of which 15 objects with SZ-detection-significance above 5.4 were selected for an X-ray follow-up program. This subsample covers the redshift range 0 . 29 < z < 1 . 08. The majority of the clusters was observed with CHANDRA, but for three objects we used XMM-Newton data because no CHANDRA data are available (SPT-CLJ23325358 and SPT-CLJ0559-5249) or because of the better photon statistics of the XMM-Newton observation (SPT-CLJ05165430). This results in 12 CHANDRA and 3 XMM-Newton observations (for details see Table 5, Column 9).</text>
<section_header_level_1><location><page_3><loc_6><loc_15><loc_20><loc_16></location>2.3. Datareduction</section_header_level_1>
<text><location><page_3><loc_6><loc_12><loc_49><loc_14></location>The 78 low-z and additional 3 high-z SPT XMMNewton observations (SPT-CLJ2332-5358, SPT-CLJ0559-5249 and</text>
<figure>
<location><page_3><loc_28><loc_72><loc_48><loc_82></location>
</figure>
<figure>
<location><page_3><loc_28><loc_83><loc_48><loc_93></location>
</figure>
<figure>
<location><page_3><loc_51><loc_83><loc_72><loc_93></location>
</figure>
<text><location><page_3><loc_52><loc_83><loc_52><loc_83></location>0</text>
<text><location><page_3><loc_53><loc_83><loc_54><loc_83></location>0.005</text>
<text><location><page_3><loc_55><loc_83><loc_56><loc_83></location>0.015</text>
<text><location><page_3><loc_57><loc_83><loc_58><loc_83></location>0.035</text>
<text><location><page_3><loc_59><loc_83><loc_60><loc_83></location>0.074</text>
<text><location><page_3><loc_61><loc_83><loc_62><loc_83></location>0.15</text>
<text><location><page_3><loc_63><loc_83><loc_64><loc_83></location>0.31</text>
<text><location><page_3><loc_65><loc_83><loc_66><loc_83></location>0.62</text>
<text><location><page_3><loc_67><loc_83><loc_68><loc_83></location>1.3</text>
<text><location><page_3><loc_69><loc_83><loc_70><loc_83></location>2.5</text>
<text><location><page_3><loc_72><loc_83><loc_72><loc_83></location>5</text>
<text><location><page_3><loc_73><loc_83><loc_73><loc_83></location>0</text>
<text><location><page_3><loc_75><loc_83><loc_76><loc_83></location>0.005</text>
<text><location><page_3><loc_77><loc_83><loc_78><loc_83></location>0.015</text>
<text><location><page_3><loc_79><loc_83><loc_80><loc_83></location>0.035</text>
<text><location><page_3><loc_81><loc_83><loc_82><loc_83></location>0.074</text>
<text><location><page_3><loc_83><loc_83><loc_84><loc_83></location>0.15</text>
<text><location><page_3><loc_85><loc_83><loc_86><loc_83></location>0.31</text>
<text><location><page_3><loc_87><loc_83><loc_87><loc_83></location>0.62</text>
<text><location><page_3><loc_89><loc_83><loc_89><loc_83></location>1.3</text>
<text><location><page_3><loc_91><loc_83><loc_91><loc_83></location>2.5</text>
<text><location><page_3><loc_93><loc_83><loc_93><loc_83></location>5</text>
<table>
<location><page_3><loc_51><loc_46><loc_95><loc_71></location>
<caption>Fig. 3. Examples of the background-included, point-source-corrected smoothed X-ray images of the high-z samples. Left: 0152-1358 - very structured cluster at z = 0 . 83 with P 3 / P 0 = (5 . 76 ± 0 . 95) × 10 -5 and w = (6 . 64 ± 0 . 57) × 10 -2 . This 400SD cluster has the highest P 3 / P 0 value and is marked by a circle in Figs. 5-7. Right: SPT-CLJ0509-5342 - rather relaxed SPT cluster at z = 0 . 46 with a non-significant detection in P 3 / P 0 and w = (3 . 13 ± 1 . 33) × 10 -3 . The circle indicates r 500.Table 1. Overview of the data quality of the samples. Mean net photon counts and mean S / B calculated within r 500 of the reduced and point source corrected X-ray image. S / B gives the ratio of net photon counts (signal) to background photon counts. P 3 / P 0 and w are computed in the r 500 aperture. P 3 / P 0 > 0 and w > 0 include all clusters with positive corrected substructure values, including positive non-significant detections. For clusters with non-significant results, we quote upper limits, which are taken as the sum of the non-significant result (or zero for a neg. corrected P 3 / P 0 or w ) and the 1σ error (for details see Sect. 3). The significance S is computed as the ratio of P 3 / P 0 or w with respect to its error. This table is discussed in more detail in Sect. 4.</caption>
</table>
<text><location><page_3><loc_51><loc_12><loc_94><loc_27></location>SPT-CLJ0516-5430) were taken from the public XMM-Newton Science archive and were analyzed with the XMMNewton SAS 4 in the well-established standard 0.5-2 keV band, which covers most of the cluster signal. The low-z clusters and SPT-CLJ0516-5430 were reduced prior to this study using SAS v. 9.0.0, while we used v. 12.0.1 for the other two SPT objects. In both cases we followed the data reduction recipe described in detail in Böhringer et al. (2010, 2007), except for the point source removal. Point sources were detected with the SAS task ewavelet in the combined image from all three detectors to increase the sensitivity of the point source detection. However, we removed the point sources from each detector</text>
<text><location><page_4><loc_6><loc_84><loc_49><loc_93></location>image in the 0.5-2 keV band individually and refilled the gaps using the CIAO 5 task dmfilth . In the next step we subtracted the background, which was obtained from a vignetting model fit to a source-excised, hard-band-scaled blank sky field from the point-source-corrected images and combined them. This method yields point-source-corrected images without visible artifacts of the cutting regions.</text>
<text><location><page_4><loc_6><loc_50><loc_49><loc_83></location>The high-z CHANDRA observations of the 400SD and SPT sample were treated as follows. A standard data reduction in the 0.5-2 keV band was performed using the CIAO software package v4.4 and CALDB v4.4.7. This band was chosen to match the XMMNewton data. For each observation, the level = 1 event file was reprocessed using chandra_repro , including amongst others the detection of afterglows, the generation of a new bad pixel file and corrections for di ff ering gains across the CCDs, timedependent gain, and charge transfer ine ffi ciencies (CTIs). For observations taken in the VFAINT mode, we applied the additional background cleaning using the task acis_process_events while setting check_vf_pha = yes . This procedure uses the outer 5 x 5 pixel (instead of 3 x 3 for FAINT) event island to search for potential cosmic-ray background events. Flared periods were excluded from the level = 2 event file using lc_clean . We created images in the 0.5-2 keV range and used fluximage to generate monochromatic 1 keV exposure maps. Point sources were detected and removed using dmfilth , which also refills the excised regions. For the background, blank-sky event files were reprojected, scaled to the exposure time of the flare-cleaned observation, restricted to the 0.5-2 keV range and binned with a factor of 4 to match the observations. When there were several pointings per cluster, we reduced the observations individually, but detected point sources on the merged 0.5-2 keV image. Images and exposure maps were merged using reproject_image .</text>
<section_header_level_1><location><page_4><loc_6><loc_47><loc_27><loc_48></location>3. Morphological analysis</section_header_level_1>
<text><location><page_4><loc_6><loc_13><loc_49><loc_45></location>We used power ratios and center shifts as morphology estimators for our analysis. The power ratio method was introduced by Buote & Tsai (1995) to quantify the amount of substructure in a cluster and its dynamical state. The powers are based on a 2D multipole expansion of the cluster's gravitational potential and are evaluated within a certain aperture radius (e.g. r 500). It is already well established that the normalized hexapole of the X-ray surface brightness, P 3 / P 0, is sensitive to asymmetries on scales of the aperture radius and provides a useful measure of the dynamical state of a cluster (e.g. Jeltema et al. 2005; Buote & Tsai 1995; Böhringer et al. 2010; Chon et al. 2012, W13). Moreover, the center shift parameter w (e.g. O'Hara et al. 2006; Mohr et al. 1993; Böhringer et al. 2010; Chon et al. 2012, W13) characterizes the morphology of the cluster X-ray surface brightness. It measures the shift of the centroid, defined as the center of mass of the X-ray surface brightness, with respect to the X-ray peak in di ff erent apertures. The X-ray peak was determined from an image smoothed with a Gaussian with σ of 8 arcseconds. The o ff set of the X-ray peak from the centroid was then calculated for ten aperture sizes (0.1-1 r 500) and the final parameter w obtained as the standard deviation of the di ff erent center shifts in units of r 500. Unless stated otherwise, all presented P 3 / P 0 and w values were calculated within an aperture of r 500 and including the central region. However, we exclude the central 0.1 r 500 region when we calculated the X-ray</text>
<text><location><page_4><loc_51><loc_91><loc_94><loc_93></location>centroid for the discussion in Sect. 6.2 to study possible e ff ects of cool cores.</text>
<text><location><page_4><loc_51><loc_55><loc_94><loc_89></location>Both morphology estimators were discussed in our previous paper W13, where we studied the influence of background and shot noise on P 3 / P 0 and w as a function of photon counts and presented a method to correct for these e ff ects. In short, we first subtract the moments of the background image from those of the full (background-included) image to obtain a background-corrected power ratio. In a second step, we correct the bias caused by shot noise using repoissonized realizations of the cluster image. For w we subtract the background pixel values before calculating the position of the X-ray peak and centroid and estimate the shot noise bias analogous to the power ratios. For very regular clusters or observations highly influenced by noise, we sometimes overestimate the bias and obtain negative corrected P 3 / P 0 and w values with errors exceeding the negative value. We call such results non-significant detections. Substructure values that are positive after the bias correction, but have a 1σ error σ ( P 3 / P 0) that exceeds the P 3 / P 0 or w value by more than a factor of 3 are also considered as non-significant detections. For a more conservative factor of 1, hence taking values with σ ( P 3 / P 0) > P 3 / P 0 or σ ( w ) > w as non-significant detections, we find consistent results within the errors. For non-significant detections, we use upper limits (UL) in the analysis, where UL = σ ( P 3 / P 0) + P 3 / P 0non -significant for positive and UL = σ ( P 3 / P 0) for negative corrected P 3 / P 0 values. The definition is analogous for w . All presented P 3 / P 0 and w values are background and bias corrected.</text>
<text><location><page_4><loc_51><loc_35><loc_94><loc_54></location>During our discussion we will refer to di ff erent thresholds for P 3 / P 0 and w to divide the sample according to the dynamical state of the clusters. These dividing boundaries are taken from our previous work W13, where we also defined the significance S of a P 3 / P 0 or w value as the ratio of the biascorrected signal with respect to the obtained error. For highquality data ( S > 3) we established two morphological P3 / P0 boundaries to divide the sample into relaxed ( P 3 / P 0 < 10 -8 ), mildly disturbed (10 -8 < P 3 / P 0 < 5 × 10 -7 ), and disturbed objects ( P 3 / P 0 > 5 × 10 -7 ). High S values down to 10 -8 allow for this detailed classification. When dealing with low count observations, we reach S = 1 around 10 -7 and use this value as simple P 3 / P 0 boundary to separate disturbed and relaxed clusters. Owing to the data quality of the high-z samples (see Table 1), we only used the P 3 / P 0 boundary at 10 -7 for our analysis.</text>
<text><location><page_4><loc_51><loc_28><loc_94><loc_34></location>For the center shift parameter, we used w = 0 . 01 to split the sample. Since w is only severly a ff ected by Poisson noise for considerably less than 1 000 net photon counts within r 500 for a reasonably low background, this threshold can be used for highand low-quality data.</text>
<section_header_level_1><location><page_4><loc_51><loc_25><loc_63><loc_26></location>4. Data quality</section_header_level_1>
<text><location><page_4><loc_51><loc_10><loc_94><loc_24></location>The strongest potential disadvantage when dealing with a combination of low- and high-z observations is the di ff erence in the photon statistics of the observations, as can be seen by comparing Figs. 2 (left) and 3. Details of the sample statistics are given in Table 1, which shows that the low-z sample is not only larger in numbers but also in terms of higher photon statistics and a higher ratio of net (signal) to background photon counts (S / B). This results in a significant di ff erence between the two samples in the extent and importance of photon shot noise. As we have shown in our previous work W13, photon shot noise can have a severe e ff ect on the determination of the cluster morphology.</text>
<section_header_level_1><location><page_5><loc_51><loc_92><loc_86><loc_93></location>4.1. Degradingofhigh-qualitylow-zobservations</section_header_level_1>
<figure>
<location><page_5><loc_9><loc_72><loc_47><loc_92></location>
<caption>Fig. 4. Overview of the net photon counts distribution within r 500 of the low-z (red filled histogram), high-z 400SD (green filled histogram) and high-z SPT sample (black dashed histogram). The dotted line indicates the net photon counts of the degraded data.</caption>
</figure>
<text><location><page_5><loc_6><loc_34><loc_49><loc_61></location>We studied and quantified these e ff ects and the influence of the background as a function of photon counts and S / B ratio for P 3 / P 0 and w . We found that the center shift parameter can be determined with a small error even below the w = 0 . 01 threshold for low photon statistics ( < 1 000 net photon counts) and a reasonable S / B of e.g. ∼ 2. We can therefore obtain reasonable results for all morphologies, partly with relative large errors for very relaxed objects. The power ratio method needs su ffi cient photon counts to overcome the influence of Poisson noise, however. We showed that this problem is not important for disturbed objects, which do not su ff er severly from shot noise and thus enable an accurate estimation even for low-quality data. For decreasing photon counts, however, mildly disturbed and relaxed objects undergo a boost of their signal due to an underestimation of the bias contribution that yields substructure parameters that are too high. In the case of excessive noise, we obtain a non-significant result. High-quality data therefore enable a more reliable determination of P 3 / P 0 ( w ) and better statistics, including a higher number of clusters with P 3 / P 0 > 0 ( w > 0) and a higher mean significance 〈 S 〉 . A direct comparison between lowand high-quality data may thus not be conclusive.</text>
<text><location><page_5><loc_6><loc_11><loc_49><loc_33></location>Fig. 4 shows that the low-z data have more than su ffi cient photon counts with a mean of ∼ 97 000 net photon counts within r 500 to give P 3 / P 0 and w values with very good error properties and large S . The high-z objects, however, peak just above 1000 net photon counts with a mean of ∼ 1 200 for 400SD and ∼ 1700 for SPT. According to simulations presented in W13, these high-z observations meet the criteria to roughly separate the sample into disturbed clusters with high and accurately determined substructure parameters and relaxed ones with parameters below the P 3 / P 0 ( w ) threshold with large errors or non-significant detections. High-z observations contain a higher contribution from the background with a mean S / B of ∼ 3 . 5. This causes additional uncertainties due to the extra noise from the background and results in the low number of objects with S > 1. To obtain conclusive results we need to establish the influence of noise and the possible boost of the P 3 / P 0 ( w ) signal due to the lower data quality in the high-z sample.</text>
<text><location><page_5><loc_51><loc_61><loc_94><loc_91></location>To test how robust our results are to the di ff erence in the data quality of the samples, we first performed our analysis using the high-quality or so-called undegraded low-z data. In addition, we created a degraded low-z sample by aligning the data quality of the low-z observations to that of the high-z objects. This was done by degrading the high-quality low-z observations to the photon statistics (1 200 net photon counts and S / B = 3.7 within r 500) of the 400SD high-z sample (see Table 1). The degrading was done in several steps, taking care of the di ff erent net and background photon counts and the increased Poisson noise. Two examples of degraded cluster images are given in Fig. 2 (right panels), compared with the undegraded images (left panels). The undegraded cluster image ( IM 0) is not background subtracted. In the following recipe we denote images with capital letters and photon counts with lowercase letters. The recipe to obtain a low-z cluster and background image with the same photon statistics as the average high-z cluster is outlined in steps 1-4. However, observations with low photon statistics do not only lack the su ffi cient number of photon counts, but also su ff er from a considerable amount of Poisson noise. This is included by adding additional Poisson noise to the degraded image using the zhtools 6 task poisson . In steps 5-7 we summarize the statistical analysis using the Poissonized realizations of these images.</text>
<unordered_list>
<list_item><location><page_5><loc_51><loc_54><loc_94><loc_59></location>1. Extract total photon counts ( im 0) and background photon counts ( bkg 0) within r 500 from the undegraded cluster ( IM 0) and background image ( BKG 0). Obtain net photon counts of the cluster as cl 0 = im 0 -bkg 0 and the S / B as cl 0 / bkg 0.</list_item>
<list_item><location><page_5><loc_51><loc_48><loc_94><loc_53></location>2. Calculate the additional background photon counts needed to obtain an S / B = 3.7: bkgadd = ( cl 0 / 3 . 7) -bkg 0. Rescale the undegradedbackground image by bkgadd : BKGadd = BKG 0 ∗ bkgadd / bkg 0</list_item>
<list_item><location><page_5><loc_51><loc_45><loc_94><loc_48></location>3. Add the additional background image to the undegraded cluster image: IM 1 = IM 0 + BKGadd . This image has the desired S / B of 3.7.</list_item>
<list_item><location><page_5><loc_51><loc_37><loc_94><loc_44></location>4. Rescale IM 1 to 1530 total photon counts within r 500: IMdeg = IM 1 ∗ (1530 / im 1). Due to its S / B of 3.7, this degraded cluster image IMdeg comprises 330 background and 1200 net photon counts. Rescale BKG 0 to 330 photon counts within r 500: BKGdeg = BKG 0 ∗ (330 / bkg 0) to obtain the degraded background image.</list_item>
<list_item><location><page_5><loc_51><loc_32><loc_94><loc_37></location>5. Create 100 Poissonized realizations of the degraded cluster image IMdeg . Calculate background- and bias-corrected power ratios and center shifts including their errors for all 100 realizations of the cluster as described in W13.</list_item>
<list_item><location><page_5><loc_51><loc_28><loc_94><loc_31></location>6. Randomly select one realization per cluster to create a new sample of 78 degraded low-z observations and obtain statistical measures like BCES fits or mean values.</list_item>
<list_item><location><page_5><loc_51><loc_24><loc_94><loc_28></location>7. Repeat the previous step 100 times for statistical purposes and obtain the mean values. These are quoted when discussing our results including the mean errors.</list_item>
</unordered_list>
<section_header_level_1><location><page_5><loc_51><loc_20><loc_59><loc_22></location>5. Results</section_header_level_1>
<text><location><page_5><loc_51><loc_12><loc_94><loc_19></location>We studied the evolution of the substructure frequency up to z = 1 . 08 using di ff erent statistical measures on the morphology estimators P 3 / P 0 and w : i) fitting the data in the P 3 / P 0-z and w -z plane with the linear relation log ( Y ) = A × log ( z / 0 . 25) + B for Y = P 3 / P 0 and w respectively, ii) calculating mean values for the di ff erent redshift intervals and iii) analyzing the fraction of</text>
<text><location><page_6><loc_6><loc_83><loc_49><loc_93></location>relaxed and disturbed objects using P 3 / P 0 and w boundaries. For non-significant detections, we used upper limits as discussed in Sect. 3. These are not included in the BCES fits given in Table 2 and Figs. 5-7. All analyses were performed on the log-distribution of P 3 / P 0 and w to take into account very low P 3 / P 0 and w values. Fitting parameters were calculated using the BCES (Y | X) fitting method (Akritas & Bershady 1996), which minimizes the residuals in Y.</text>
<text><location><page_6><loc_6><loc_66><loc_49><loc_83></location>To study the P 3 / P 0-z and w -z relation we formed two samples to study possible selection e ff ects of the high-z samples: i) sample I - low-z sample and high-z subsample of 400SD sample, ii) sample II - low-z sample and high-z subsample of SPT sample. We argue that using the degraded low-z data might be essential to obtain reliable and conclusive results. We therefore performed the identical analysis on sample I / II and the degraded sample I / II, where we used the degraded low-z data. We point out that only the high-quality low-z observations are degraded and thus are di ff erent in sample I / II and degraded sample I / II. The high-z data remains unchanged. In the following we focus on the heavily noise-a ff ected P 3 / P 0 parameter and then consider the more robust w parameter.</text>
<text><location><page_6><loc_6><loc_49><loc_49><loc_64></location>During our analysis, we tried to include the information given by the upper limits in the P 3 / P 0-z and w -z fits and tested the ASURV (Feigelson & Nelson 1985; Isobe et al. 1986) and the LINMIX_ERR (Kelly 2007) routine. For upper limits, both methods use estimated data points for fitting that are computed from the input upper limit and the distribution of the detected data points. Several tests using simulated images showed that the estimated data points are strongly coupled to the fit obtained from the detected data points and do not reflect the true P 3 / P 0 values. Since the censorship in our data is due to low counts and dependent on P 3 / P 0 itself, we conclude that our data do not fulfill the requirements for these routines to work properly.</text>
<table>
<location><page_6><loc_8><loc_26><loc_47><loc_42></location>
<caption>Table 2. Overview of the BCES (Y | z) fits in the log-log plane using the linear relation log ( Y ) = A × log ( z / 0 . 25) + B for Y = P 3 / P 0 and w , respectively. Upper limits are omitted for these fits.</caption>
</table>
<section_header_level_1><location><page_6><loc_6><loc_20><loc_21><loc_21></location>5.1. P 3 / P 0 -zrelation</section_header_level_1>
<text><location><page_6><loc_6><loc_10><loc_49><loc_19></location>We first discuss the structure parameter P 3 / P 0 as a function of redshift for sample I and II using Fig. 5. On the left side we show only the significant data points, while we include non-significant results as upper limits (arrows) on the right. For illustration, we show the P 3 / P 0 boundary at 10 -7 to separate relaxed and disturbed objects. When looking at this figure, one immediately notices the lack of significant detections of high-z</text>
<text><location><page_6><loc_51><loc_80><loc_94><loc_93></location>clusters with P 3 / P 0 < 10 -7 . In addition, essentially all upper limits are found above this P 3 / P 0 boundary. We quantified the P 3 / P 0-z relation using the undegraded low-z data and di ff erent statistical measures. On the left of Fig. 5 we show the linear BCES fit. For sample I we obtained a more than 3 σ significant slope with A = 1 . 01 ± 0 . 31, for sample II we found a somewhat shallower slope of A = 0 . 59 ± 0 . 36. We then tested the influence of the very structured 400SD cluster 0152-1358 ( z ∼ 0 . 8) with P 3 / P 0 > 10 -5 on the fit, finding a shallower, but consistent slope when excluding it from the fit.</text>
<text><location><page_6><loc_51><loc_54><loc_94><loc_79></location>Another way of quantifying the observed relation is computing the fraction of relaxed and disturbed objects in comparison to upper limits, which are shown in Table 3. Because of the high data quality of the undegraded low-z observations, the fraction of upper limits is small. All these objects can be considered as relaxed clusters because P 3 / P 0 can detect significant signals well below 10 -7 for such good data quality. Their non-significant signals or upper limits are consistent with P 3 / P 0 << 10 -7 . In addition, we find 45% of the low-z objects to be relaxed. The majority of clusters in this sample is found below the P 3 / P 0 threshold of 10 -7 with a mean of the log P 3 / P 0 distribution of -7 . 1 ± 0 . 8. The high-z samples yield a higher mean of -5 . 9 ± 0 . 6 ( -6 . 1 ± 0 . 5) for 400SD (SPT). The mean values are given in Table 4 and are denoted as mean data for the significant data points and mean UL for the upper limits. We plot the mean data values in Fig. 5 on the right side to illustrate this o ff set. In addition, we add the mean UL values to emphasize again the di ff erence in the location of upper limits for the high- and low-quality data.</text>
<text><location><page_6><loc_51><loc_29><loc_94><loc_52></location>All statistical measures used on this dataset so far give a clear trend of a larger fraction of disturbed clusters at higher redshift. This conclusion should not be drawn without caution, however, since we are comparing very di ff erent datasets. We already argued that P 3 / P 0 is heavily influenced by noise for observations with low net photon counts and / or high background. The computation of substructure parameters for the high-z objects therefore su ff ers severely from noise. According to results presented in W13, we can obtain significant P 3 / P 0 values for the majority of the disturbed clusters even with fewer than 1 000 net photon counts within r 500. Mildly disturbed and relaxed objects will mostly either yield non-significant detections or undergo a boost of the P 3 / P 0 signal. Except for some mildly disturbed objects whose P 3 / P 0 values are just below the 10 -7 boundary in the undegraded case, this boost will not result in P 3 / P 0 > 10 -7 . We should thus be able to very roughly separate the sample into disturbed ( P 3 / P 0 > 10 -7 ) and relaxed ( P 3 / P 0 < 10 -7 and upper limits) objects.</text>
<text><location><page_6><loc_51><loc_11><loc_94><loc_29></location>We repeated the analysis using the degraded low-z data and show the results in Fig. 6. We found significantly shallower slopes of A = 0 . 24 ± 0 . 28 ( A = 0 . 17 ± 0 . 24) and higher intercepts B for the degarded sample I (II). This is due to the apparent loss of data points with P 3 / P 0 < 10 -7 and large errors on the detected P 3 / P 0 signals after degrading. We find a significant increase of the upper limit fraction to 72% while the fraction of relaxed clusters decreases from 45% to on average 0% (Table 3). The fraction of disturbed objects stays roughly the same, showing that we can detect a signal for the majority of structured objects while only a small number gives upper limits. With these low-quality data, we cannot measure a significant P 3 / P 0 value for mildly disturbed or relaxed clusters anymore, but only detect disturbed objects.</text>
<text><location><page_6><loc_51><loc_10><loc_94><loc_11></location>For the high-z samples, we found no objects with P 3 / P 0 < 10 -7</text>
<text><location><page_7><loc_6><loc_79><loc_49><loc_93></location>but a large number of upper limits (Table 3) and a disturbed cluster fraction of 42% for 400SD and 47% for SPT. Assuming that the majority of the disturbed objects yield significant detections, we found a slightly higher fraction of disturbed objects in the high-z samples than in the degraded low-z sample. We performed more tests by varying the degree of degradation of the low-z data. We found that the larger the disagreement between the net photon counts and S / B of the samples, the more biased the obtained slope or mean value. It is therefore of extreme importance to take this issue into account when analyzing the P 3 / P 0-z relation.</text>
<table>
<location><page_7><loc_6><loc_56><loc_49><loc_72></location>
<caption>Table 3. Fraction of relaxed and disturbed objects using P 3 / P 0 and w boundaries taken from W13 (see Sect. 3). Upper limits (UL) are given for non-significant detections.</caption>
</table>
<text><location><page_7><loc_6><loc_53><loc_41><loc_54></location>Notes. (a) mean values of 100 randomly selected samples.</text>
<section_header_level_1><location><page_7><loc_6><loc_48><loc_18><loc_49></location>5.2. w -zrelation</section_header_level_1>
<text><location><page_7><loc_6><loc_31><loc_49><loc_47></location>Analogously to P 3 / P 0, we used the same statistical measures on the w parameter to probe its behavior as a function of redshift. Fig. 7 shows the w distribution for sample I and II, including upper limits on the right and the w = 0 . 01 boundary to seperate relaxed and disturbed objects. We performed a linear BCES fit and give the fitting parameters in Table 2. The fits are illustrated on the left side of Fig. 7, with slope A = 0 . 18 ± 0 . 14 ( A = 0 . 02 ± 0 . 13) for sample I (II). These slopes are both positive, but not significant and consistent with zero within 1σ . In contrast to P 3 / P 0, low- and high-z clusters populate the full w range. This is reflected in the very similar mean values of the samples and their upper limits. We show these values in Table 4 and Fig. 7 on the right side.</text>
<text><location><page_7><loc_6><loc_10><loc_49><loc_30></location>Because the w parameter is not very sensitive to noise when dealing with > 1 000 net photon counts and a background that is not too high - as is the case with the high-z observations -, degrading the low-z observations to match the data quality of the 400SD clusters shows little e ff ect. All statistical measures show very similar results when using the degraded low-z sample (Tables 2-4). The slopes stay well within the errors, and the mean data value does not change either. Only the mean upper limit value increases slightly, because the undegraded low-z data contains only one upper limit, but the degraded sample contains a few more. This is reflected in the slight increase of the upper limit fraction from 1% to 6%, which is very similar to those of the 400SD (8%) and SPT (7%) sample. The fraction of relaxed objects decreases slightly for the degraded data from 58% to 52%, while it increases for disturbed objects from 41% to 43%. These changes are within the errors and again show the robustness of</text>
<text><location><page_7><loc_51><loc_88><loc_94><loc_93></location>w against noise. Comapring the low-z fractions with those of the high-z samples, we see a very similar behavior of the SPT clusters, but the 400SD sample shows a larger fraction of objects with w > 0 . 01.</text>
<table>
<location><page_7><loc_51><loc_69><loc_94><loc_81></location>
<caption>Table 4. Mean log( P 3 / P 0) and log( w ) values for the low- and highredshift samples. We give the mean of the significant data points (mean data) and the upper limits (mean UL) including their 1σ errors.</caption>
</table>
<section_header_level_1><location><page_7><loc_51><loc_63><loc_62><loc_64></location>6. Discussion</section_header_level_1>
<text><location><page_7><loc_51><loc_37><loc_94><loc_62></location>Assessing the dynamical state of a galaxy cluster calls for a well-studied method for detecting and quantifying substructure in the ICM. Well-understood error properties are of great importance, especially when dealing with high-z observations and thus low photon statistics. The two applied methods, power ratios and center shifts, fulfill these requirements. A strong correlation with a large scatter between P 3 / P 0 and w is known from previous studies (e.g. Böhringer et al. 2010) and therefore a similar trend in both relations is expected. Comparing the results obtained from applying P 3 / P 0 and w on sample I / II shows a very large discrepancy. While P 3 / P 0 shows a significant increase with redshift in all statistical measures used, w shows a positive but non-significant slope and no trend in the mean values either. We claim that the discrepancy between these results is caused by the inconsistent data quality of the full sample, which a ff ects P 3 / P 0 more than w . Taking into account the slopes, mean values, and fractions, one can conclude that w is not sensitive to di ff erent data quality since the results hardly change.</text>
<text><location><page_7><loc_51><loc_24><loc_94><loc_37></location>For of P 3 / P 0, degrading the high-quality low-z observations to the net photon counts and background of the high-z objects yields very di ff erent results. The slope flattens significantly, yielding a similar result to w - a positive but non-significant slope. The fraction of upper limits increases dramatically, because all relaxed objects yield non-significant detections. The fraction of low-z disturbed object is therefore only slightly smaller than those of the 400SD and SPT sample. Moreover, the mean data and mean UL values match those of the high-z samples when using equal data quality.</text>
<text><location><page_7><loc_51><loc_11><loc_94><loc_22></location>The results using P 3 / P 0 and w on this particular dataset show a similar trend. We found a very mild positive evolution, which is also consistent with no change with redshift within the significance limits. We excluded a strong increase of the disturbed cluster fraction with redshift and set an upper limit with the shallow slopes of the BCES fits. For the lower limit, we found no indication of a negative evolution because all statistical measures show an increase of P 3 / P 0 and w with redshift, but with low significance.</text>
<figure>
<location><page_8><loc_9><loc_73><loc_48><loc_92></location>
</figure>
<figure>
<location><page_8><loc_53><loc_73><loc_91><loc_92></location>
<caption>Fig. 5. Undegraded P 3 / P 0-z relation. Low-z (black circles), 400SD (red triangles), and SPT (green crosses) sample. Left: The BCES fit to sample I is shown as a red line while the green line indicates the fit to sample II. The dashed areas show the 1σ error of best-fitting values. Fitting parameters are given in Table 2. The very structured 400SD cluster 0152-1358 at z ∼ 0 . 8 with P 3 / P 0 > 10 -5 is marked by a black circle. Excluding this cluster from sample I gives consistent results. In addition we show the P 3 / P 0 boundary at 10 -7 (dashed line). Right: Same data points as on the left, but including upper limits as downward arrows. For all three samples the solid lines give the mean of the log distribution of the significant data points including the 1σ errors, while the dotted lines show the mean of the upper limits.</caption>
</figure>
<figure>
<location><page_8><loc_9><loc_41><loc_48><loc_60></location>
</figure>
<figure>
<location><page_8><loc_53><loc_41><loc_91><loc_60></location>
<caption>Fig. 6. Degraded P 3 / P 0-z relation. Details are the same as in Fig. 5.</caption>
</figure>
<figure>
<location><page_8><loc_8><loc_14><loc_48><loc_33></location>
</figure>
<figure>
<location><page_8><loc_51><loc_14><loc_91><loc_33></location>
<caption>Fig. 7. Undegraded w -z relation. Details are the same as in Fig. 5, except for the w boundary at 10 -2 (dashed line).</caption>
</figure>
<text><location><page_8><loc_6><loc_7><loc_24><loc_8></location>Article number, page 8 of 14</text>
<section_header_level_1><location><page_9><loc_6><loc_92><loc_33><loc_93></location>6.1. Comparisonwithpreviousstudies</section_header_level_1>
<text><location><page_9><loc_6><loc_44><loc_49><loc_91></location>In the light of our finding that the di ff erent data quality between the low-z and high-z sample can severly bias the results, we compared our work with previous studies that did not take this problem into account. Jeltema et al. (2005) presented the first analysis of the P 3 / P 0-z relation using 40 X-ray-selected luminous clusters in the 0 . 1 < z < 0 . 89 range and a fixed physical aperture of 0.5 Mpc. They found the slope of the linear P 3 / P 0-z relation to be 4 . 1 × 10 -7 , but did not provide an intercept. We argue that a linear fit is not sensitive enough when working with a P 3 / P 0 range of 10 -9 -10 -5 . High P 3 / P 0 values like that of the 400SD cluster 0152-1358 ( P 3 / P 0 > 10 -5 at z ∼ 0.8) dominate a linear fit, while low P 3 / P 0 values are not adequately taken into account. We therefore did not include this result in Fig. 8, which compares our findings with previous studies. Jeltema et al. (2005) also provided mean P 3 / P 0 values for z < 0 . 5 and z > 0 . 5 objects. For a fair comparison, we calculated P 3 / P 0 in the same 0.5 Mpc aperture, since r 500 is typically larger than 1 Mpc for the low-z sample and on average 0.8 Mpc for high-z objects. A fixed aperture of 0.5 Mpc probes the cluster structure on a di ff erent scale than r 500. For the 0.5 Mpc aperture, the slopes of the fits are steeper and the intercepts higher with A = 1 . 52 ± 0 . 30 ( A = 1 . 08 ± 0 . 39) and B = -6 . 61 ± 0 . 07 ( B = -6 . 75 ± 0 . 10) for sample I (II). After degrading, the P 3 / P 0-z fits flatten significantly to A = 0 . 42 ± 0 . 18 ( A = 0 . 08 ± 0 . 31) with B = -5 . 96 ± 0 . 06 ( B = -6 . 09 ± 0 . 10) for the degraded sample I (II) and agree well with the degraded results when using r 500 as aperture. The general impression of a very mild increase of the disturbed cluster fraction with redshift thus holds also for the 0.5 Mpc aperture. We show the fits for sample I and the degraded sample I using the 0.5 Mpc aperture in Fig. 8. The discrepancy between our fit of the degraded sample I and the mean values of Jeltema et al. (2005) is apparent. While Jeltema et al. (2005) took general noise properties into account, they did not address the problem of the data quality di ff erence, which results in an overestimation of the slope and a large o ff set between the mean low-z and high-z sample.</text>
<text><location><page_9><loc_6><loc_36><loc_49><loc_44></location>Another study was performed by Andersson et al. (2009), who also calculated P 3 / P 0 in an 0.5 Mpc aperture for 101 galaxy clusters in the range 0 . 07 < z < 0 . 89. They reported an increase in P 3 / P 0 and provided average P 3 / P 0 values given for three redshift bins (0 . 069 < z < 0 . 1, 0 . 1 < z < 0 . 3 and z > 0 . 3). We see an o ff set to our degraded fits here as well.</text>
<text><location><page_9><loc_6><loc_14><loc_49><loc_34></location>Several studies using both simulations (e.g. Ho et al. 2006) and observations (e.g. Maughan et al. 2008; Plionis 2002; Melott et al. 2001) explored the evolution of ellipticity with redshift. The asymmetry in the X-ray surface brightness distribution was studied by Hashimoto et al. (2007), reporting no significant di ff erence regarding ellipticity and o ff -center between the low- and high-z sample, but a hint of a weak evolution for the concentration and asymmetry parameter. Recently, Mann & Ebeling (2012) presented a study of the evolution of the cluster merger fraction using 108 of the most X-ray-luminous galaxy clusters at 0 . 15 < z < 0 . 7. They used optical and X-ray data and classified mergers according to their morphological class, X-ray centroid - BCG separation and X-ray peak - BCG separation. They reported an increase of the fraction of disturbed clusters with redshift, starting around z = 0 . 4.</text>
<text><location><page_9><loc_6><loc_10><loc_49><loc_13></location>In addition to observational studies, we compared our findings with those of Jeltema et al. (2008), who studied the evolution of cluster structure with P 3 / P 0 and w in hydrodynamical sim-</text>
<figure>
<location><page_9><loc_53><loc_73><loc_92><loc_92></location>
<caption>Fig. 8. Comparison with previous studies. From Jeltema et al. (2005) we show the mean P 3 / P 0 values for z < 0 . 5 and z > 0 . 5 objects (black). Errors on these values are not provided. In addition, we plot the mean P 3 / P 0 of Andersson et al. (2009) for three redshift bins (0 . 069 < z < 0 . 1, 0 . 1 < z < 0 . 3 and z > 0 . 3) in red. We provide our slope of the P 3 / P 0-z plane calculated using an aperture of 0.5 Mpc for sample I (blue line) and the degraded sample I (green line) including the 1σ errors as dashed area. The dashed line indicates the P 3 / P 0 boundary at 10 -7 .</caption>
</figure>
<text><location><page_9><loc_51><loc_41><loc_94><loc_57></location>ulations performed with Enzo, a hybrid Eulerian adaptive mesh refinement / N-body code. Their simulations did not include the e ff ect of noise or instrumental response, therefore only a broad comparison to low-z observed data with high singal-to-noise is possible. They reported a dependence of the evolution of P 3 / P 0 with redshift on the selection criterium and on the radius chosen. While for w they found a significant increase with redshift for a mass as well as a luminosity cut, P 3 / P 0 showed an evolution only for a luminosity-limited sample. In agreement with our results, they stated that the evolution of cluster structure is mild compared with the variety of cluster morphologies seen at all redshifts.</text>
<section_header_level_1><location><page_9><loc_51><loc_37><loc_68><loc_38></location>6.2. Effectofcoolcores</section_header_level_1>
<text><location><page_9><loc_51><loc_23><loc_94><loc_36></location>Several studies showed that cool cores are preferentially found in relaxed systems. Santos et al. (2010) and Andersson et al. (2009) found a negative evolution of the fraction of cool-core clusters, reporting that the number of cooling core clusters appears to decrease with redshift. This suggests a higher fraction of relaxed clusters at low than at high redshift. They also argued that the evolution is significantly less pronounced than previously claimed. Bauer et al. (2005) used the high-z end of the BCS sample and concluded that the fraction of cool-cores does not significantly evolve up to z ∼ 0 . 4.</text>
<text><location><page_9><loc_51><loc_10><loc_94><loc_21></location>It is therefore an interesting exercise to study whether the P 3 / P 0-z and w -z relation is driven by the presence of a cool core or by the overall dynamical state of the cluster. To do this, we excluded the 0.1 r 500 region when calculating the centroid, but kept it to determine the X-ray peak. For an aperture of r 500 we found very similar slopes for both relations. For w the slope becomes somewhat shallower but remains well within the 1σ error with A = 0 . 10 ± 0 . 14 ( A = -0 . 07 ± 0 . 13) and B = -1 . 97 ± 0 . 04 ( B = -2 . 02 ± 0 . 04). As expected, degrading</text>
<text><location><page_10><loc_6><loc_85><loc_49><loc_93></location>has no real e ff ect on the center-excised w -z relation, and the mean values also stay well within the errors. Contrary to our findings, Maughan et al. (2008) reported a significant absence of relaxed clusters at high redshift using a sample of 115 galaxy clusters in the 0 . 1 < z < 1 . 3 range and center shifts with the central 30 kpc excised as morphology estimator.</text>
<text><location><page_10><loc_6><loc_67><loc_49><loc_85></location>P 3 / P 0, on the other hand, yields slightly higher values on averge when excluding the center, which results in a very similar slope of A = 0 . 97 ± 0 . 29 ( A = 0 . 58 ± 0 . 32), but in a higher intercept of B = -6 . 53 ± 0 . 09 ( B = -6 . 68 ± 0 . 10) and higher mean values for sample I (II). The same e ff ects are seen when using the degraded low-z sample. The analysis was repeated using the fixed 0.5 Mpc aperture. We found a larger di ff erence between the core-included and excised P 3 / P 0-z relation for this aperture, because it is more sensitive to substructure in the inner region of the cluster. The obtained results are comparable with the r 500 case, however. We conclude that based on the method to obtain P 3 / P 0 and w , the P 3 / P 0-z and w -z relations seem to be mainly driven by the dynamical state of the cluster on the scale of the aperture radius.</text>
<section_header_level_1><location><page_10><loc_6><loc_63><loc_19><loc_64></location>7. Conclusions</section_header_level_1>
<text><location><page_10><loc_6><loc_50><loc_49><loc_62></location>We studied the evolution of the substructure frequency by comparing a merged sample of 78 low-z observations of galaxy clusters with the high-z subsample of the 400SD and SPT sample. The analysis was performed on two samples individually to exclude possible selection e ff ects of the high-z samples: i) sample I: 78 low-z and 36 400SD, ii) sample II: 78 low-z and 15 SPT clusters. Power ratios P 3 / P 0 and the center shift parameter w were used to quantify the amount of substructure in the cluster X-ray images.</text>
<text><location><page_10><loc_6><loc_46><loc_49><loc_49></location>We found that directly comparing high-quality low-z and low-quality high-z observations using P 3 / P 0</text>
<unordered_list>
<list_item><location><page_10><loc_7><loc_43><loc_49><loc_45></location>· yields a very steep P 3 / P 0-z relation with slopes of 1 . 01 ± 0 . 31 (0 . 59 ± 0 . 36) for sample I (II),</list_item>
<list_item><location><page_10><loc_7><loc_40><loc_49><loc_43></location>· gives a significant di ff erence in the mean P 3 / P 0 values of the low-z and high-z samples, and</list_item>
<list_item><location><page_10><loc_7><loc_38><loc_49><loc_40></location>· returns a very large fraction of relaxed objects at low-z (45%), but none at high-z.</list_item>
</unordered_list>
<text><location><page_10><loc_6><loc_23><loc_49><loc_37></location>However, as was shown in our previous work (Weißmann et al. 2013), P 3 / P 0 is very sensitive to noise and thus to the depth and quality of the observation. We corrected for the noise bias, but uncertainties in the results of low-quality data remained. Since there is a significant di ff erence in the data quality of the samples, this problem needed to be considered during the analysis. We therefore degraded the high-quality low-z observations to the photon statistics of the high-z 400SD observations. This enabled a comparison of data with similar quality and thus more reliable results. Using equal data quality and P 3 / P 0, we found</text>
<unordered_list>
<list_item><location><page_10><loc_7><loc_18><loc_49><loc_22></location>· a weak, but not very significant evolution in the P 3 / P 0-z relation with slopes of 0 . 24 ± 0 . 28(0 . 17 ± 0 . 24) for the degraded sample I (II),</list_item>
<list_item><location><page_10><loc_7><loc_16><loc_49><loc_18></location>· no di ff erence in the mean P 3 / P 0 value of the low-z and highz samples,</list_item>
<list_item><location><page_10><loc_7><loc_13><loc_49><loc_16></location>· that all relaxed ( P 3 / P 0 < 10 -7 ) low-z clusters yield nonsignificant detections after degradation, and</list_item>
<list_item><location><page_10><loc_7><loc_10><loc_49><loc_13></location>· a slightly larger fraction of disturbed clusters in the high-z samples (42% for 400SD, 47% for SPT) than in the degraded low-z sample (31%).</list_item>
</unordered_list>
<text><location><page_10><loc_51><loc_87><loc_94><loc_93></location>We performed the same analysis using the center shift parameter w as morphology estimator. w is more robust against Poisson noise and not very sensitive to the data quality di ff erence of the samples. We therefore found very similar results using the undegraded and degraded low-z data, namely</text>
<unordered_list>
<list_item><location><page_10><loc_52><loc_82><loc_94><loc_86></location>· a very shallow slope of the w -z relation: 0 . 18 ± 0 . 14 (0 . 02 ± 0 . 13) for sample I (II), 0 . 23 ± 0 . 12 (0 . 07 ± 0 . 11) for the degraded sample I (II),</list_item>
<list_item><location><page_10><loc_52><loc_79><loc_94><loc_82></location>· no di ff erence in the mean w value of the low-z and high-z samples, and</list_item>
<list_item><location><page_10><loc_52><loc_77><loc_94><loc_79></location>· no significant di ff erence in the fraction of relaxed and disturbed objects.</list_item>
</unordered_list>
<text><location><page_10><loc_51><loc_67><loc_94><loc_76></location>Considering that the 400SD high-z sample may contain an unrepresentatively large number of disturbed clusters, the slopes obtained using this dataset should be taken as upper limits. They are consistent with the results when using the SPT clusters as high-z sample, however. In summary, we agree with previous findings, which indicate an evolution of the substructure frequency with redshift.</text>
<text><location><page_10><loc_51><loc_51><loc_94><loc_65></location>We conclude that the results using P 3 / P 0 and w on this particular dataset show a similar and very mild positive evolution of the substructure frequency with redshift. However, within the significance limits, our findings are also consistent with no evolution. A strong increase of the disturbed cluster fraction is excluded and the BCES fits are taken as upper limits. For the lower limit, we found no indication of a negative evolution. All statistical measures show a slight increase of P 3 / P 0 and w with redshift, but with low significance. Larger samples of deep observations of z > 0 . 3 galaxy clusters would provide a better way to quantify these relations and allow unambiguous conclusions.</text>
<text><location><page_10><loc_51><loc_35><loc_94><loc_50></location>Acknowledgements. Wewould like to thank the anonymous referee for constructive comments and suggestions. This work is based on observations obtained with XMMNewton and CHANDRA. XMMNewton is an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. The XMMNewton project is supported by the Bundesministerium für Wirtschaft und Technologie / Deutsches Zentrum für Luft- und Raumfahrt (BMWI / DLR, FKZ 50 OX 0001), the Max-Planck Society and the HeidenhainStiftung. A part of the scientific results reported in this article is based on data obtained from the Chandra Data Archive. AW acknowledges the support from and participation in the International Max-Planck Research School on Astrophysics at the Ludwig-Maximilians University. GC acknowledges the support from Deutsches Zentrum für Luft- und Raumfahrt (DLR) with the program ID 50 R 1004. HB and GC acknowledge support from the DfG Transregio Program TR33 and the Munich Excellence Cluster 'Structure and Evolution of the Universe'.</text>
<section_header_level_1><location><page_10><loc_51><loc_30><loc_60><loc_31></location>References</section_header_level_1>
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<table>
<location><page_12><loc_7><loc_11><loc_92><loc_91></location>
<caption>Table 5. Details of the individual galaxy clusters including structure parameters.</caption>
</table>
<table>
<location><page_13><loc_8><loc_11><loc_92><loc_91></location>
<caption>Table 5. continued.</caption>
</table>
<table>
<location><page_14><loc_8><loc_55><loc_92><loc_91></location>
<caption>Table 5. continued.</caption>
</table>
<text><location><page_14><loc_6><loc_48><loc_94><loc_53></location>Notes. Column 2: cluster redshift; Column 3: r 500 in Mpc estimated from the formula given by Arnaud et al. (2005); Column 4 / 6: bias- and background-corrected P 3 / P 0 and w values calculated in an aperture of r 500 including the central region. Errors are 1σ uncertainties; Column 5 / 7: flags for upper limits where 0 indicates a significant detection and 1 an upper limit. For flag 1 P 3 / P 0 / w and its error are the same. The upper limit is calculated as described in Sect. 3; Column 8: Reference. In case of multiple references, * indicates the temperature source for the r 500 calculation; Column 9: Flag indicating whether an XMM-Newton (X) or CHANDRA (C) image was used in the analysis.</text>
<text><location><page_14><loc_6><loc_44><loc_94><loc_47></location>References. (1) LoCuSS: Zhang et al. (2008); (2) REFLEX-DXL: Zhang et al. (2006); (3) Snowden et al. (2008); (4) Arnaud et al. (2005); (5) Buote & Tsai (1996); (6) REXCESS: Böhringer et al. (2010); (7) high-z 400SD sample: Vikhlinin et al. (2009); (8) high-z SPT sample: Andersson et al. (2011).</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Context. Galaxy clusters are the last and largest objects to form in the standard hierarchical structure formation scenario through merging of smaller systems. The substructure frequency in the past and present epoch provides excellent means for studying the underlying cosmological model. Aims. Using X-ray observations, we study the substructure frequency as a function of redshift by quantifying and comparing the fraction of dynamically young clusters at di ff erent redshifts up to z = 1 . 08. We are especially interested in possible biases due to the inconsistent data quality of the low-z and high-z samples. Methods. Two well-studied morphology estimators, power ratio P 3 / P 0 and center shift w , were used to quantify the dynamical state of 129 galaxy clusters, taking into account the di ff erent observational depth and noise levels of the observations. Results. Owing to the sensitivity of P 3 / P 0 to Poisson noise, it is essential to use datasets with similar photon statistics when studying the P 3 / P 0-z relation. We degraded the high-quality data of the low-redshift sample to the low data quality of the high-z observations and found a shallow positive slope that is, however, not significant, indicating a slightly larger fraction of dynamically young objects at higher redshift. The w -z relation shows no significant dependence on the data quality and gives a similar result. Conclusions. We find a similar trend for P 3 / P 0 and w , namely a very mild increase of the disturbed cluster fraction with increasing redshifts. Within the significance limits, our findings are also consistent with no evolution. Key words. X-rays: galaxies: clusters - Galaxies: clusters: Intracluster medium",
"pages": [
1
]
},
{
"title": "Probing the evolution of the substructure frequency in galaxy clusters up to z ∼ 1",
"content": "A. Weißmann 1 , H. Böhringer 1 , G. Chon 1 1 Max-Planck-Institut für extraterrestrische Physik, Postfach 1312, Giessenbachstr., 85741 Garching, Germany email: [email protected] Received 18 March 2013 / Accepted 4 June 2013",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The standard theory of structure formation predicts hierarchical growth from positive fluctuations in the primordial density field. Subgalactic scale objects decouple first, then collapse and virialize due to the greater amplitudes of the density fluctuations on small scales. They grow through merging, finally forming galaxy clusters, which are considered the largest virialized objects in the Universe. Galaxy cluster growth probes the evolution of density perturbations and directly traces the process of structure formation in the Universe. Galaxy clusters are thus important laboratories for studying and testing the underlying cosmological model (e.g. Borgani 2008; Voit 2005). Especially important in this context is the study of the cluster mass function, whose evolution provides constraints on the linear growth rate of density perturbations. Using X-rays and analyzing the hot intracluster medium (ICM) that resides in the deep potential well of galaxy clusters, mass determination is based on the assumptions of hydrostatic equilibrium and spherical shape. These assumptions may be unsatisfactory for dynamically young objects showing multiple surface brightness peaks in the distribution of the ICM, however (e.g. Nelson et al. 2012; Rasia et al. 2012; Zhang et al. 2008). In addition, the influence of dynamical activity such as merging on L X, T X etc. needs to be known in detail to explain possible deviations from scaling relations for disturbed clusters (e.g. Pratt et al. 2009; Rowley et al. 2004; Chon et al. 2012) with the aim to reduce the errors in cosmological studies. Observations of substructure and disturbed morphologies in the optical (see e.g. Girardi & Biviano 2002; West & Bothun 1990, and references therein) and X-ray band (for a review see e.g. Buote 2002) indicate that a large fraction of clusters is dynamically young and has not reached a relaxed state yet. It is therefore essential to quantify the fraction of disturbed clusters that reflects the formation rate and to probe higher redshifts to constrain cosmological parameters. X-ray observations provide excellent probes for studying the dynamical state of clusters because the ICM traces their deep potential well. Over the years, X-ray studies became very e ffi cient in quantifying cluster structure, and a variety of X-ray morphology estimators was introduced (for a review see Rasia 2013). However, only recently, larger samples of high-z observations of galaxy clusters became available and allowed statistical studies of the evolution of the substructure frequency up to z ∼ 1. Since then, several observational X-ray studies have shown a larger fraction of dynamically relaxed clusters at lower redshift than at z > 0 . 5 (e.g. Mann & Ebeling 2012; Andersson et al. 2009; Maughan et al. 2008; Hashimoto et al. 2007; Bauer et al. 2005; Jeltema et al. 2005; Plionis 2002; Melott et al. 2001). A less clear evolution was found in hydrodynamical simulations, but higher merger rates at high redshift support the observational results (e.g. Burns et al. 2008; Jeltema et al. 2008; Kay et al. 2007; Rahman et al. 2006; Cohn & White 2005). Opening the window toward higher-redshift clusters is accompanied by the problem of the insu ffi cient data quality of Xray images in terms of net photon counts and background contribution. Exploring a broad redshift range directly translates into probing data with quite substantial quality di ff erences. It is therefore not only essential to use well-studied morphology estima- tors but also to understand possible biases caused by uneven data quality. In this work, we used two common X-ray substructure estimators, power ratio P 3 / P 0 (Buote & Tsai 1995) and center shift w (Mohr et al. 1993), to study the relation between cluster structure and redshift up to z = 1 . 08. To do so, we took advantage of the detailed study of the influence of net photon counts and background on the computation of P 3 / P 0 and w in our recently published work (Weißmann et al. 2013). Jeltema et al. (2005) presented the first analysis of the P 3 / P 0-z relation using 40 X-ray selected luminous clusters in the redshift range 0 . 1 < z < 0 . 89. Using di ff erent statistical measures, they reported on average higher P 3 / P 0 for clusters with z > 0 . 5 than for low-z objects. While they accounted for the bias caused by photon noise and background, they did not fully consider the strong decrease of data quality at higher redshifts and overestimated the P 3 / P 0-z relation. In addition to using a larger sample, we explored possible biases caused by di ff erent observational depths in the lowz and high-z samples and determined how to account for them when analyzing the P 3 / P 0-z and w -z relation. The paper is organized as follows. We characterize the sample and briefly discuss the data reduction process in Sect. 2. In Sect. 3 we introduce the morphology estimators P 3 / P 0 and w used in this work. Sect. 4 summarizes how we degraded the high-quality data of the low-z sample to match the high-z observations. We give results in Sect. 5, including a detailed study of the influence of the di ff erent data quality in samples. Previous studies and the e ff ect of cool cores are discussed in Sect. 6. We finally conclude with Sect. 7. Throughout the paper, the standard Λ CDM cosmology was assumed: H 0 = 70 km s -1 Mpc -1 , ΩΛ= 0.7, Ω M = 0.3.",
"pages": [
1,
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},
{
"title": "2. Observations and data reduction",
"content": "In this section we discuss the three samples used for our study: the low-z sample and the high-z subsamples of the 400SD and SPT surveys. An overview of the redshift distribution is shown in Fig. 1. Table 1 summarizes the sample statistics including the number of clusters, the redshift range, the mean net photon counts within r 500, and the mean net- (signal-)to-background photon counts ratio S / B. This table is discussed in more detail in Sect. 4, where we concentrate on the problem of the data quality. Details of the galaxy clusters and observational properties are given in Table 5. r 500 was calculated for all clusters using the formula given by Arnaud et al. (2005). The temperature and redshift values were taken from previous works as indicated in Table 5. For a full gallery of the X-ray images of the galaxy clusters used in this study we refer to Weißmann et al. (2013) for the lowz sample, the website of the 400d 2 cluster survey 1 for the highz 400SD objects, and to Andersson et al. (2011) for the high-z SPT clusters. To give an impression of the substructure values and the data quality, we provide a few examples of backgroundincluded, point-source-corrected smoothed X-ray images in Fig. 2 (left panels) for the low-z sample and in Fig. 3 for the high-z samples.",
"pages": [
2
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},
{
"title": "2.1. Low-zclustersample",
"content": "The low-redshift sample (short: low-z) was previously used and discussed in detail in Weißmann et al. (2013, W13 hereafter). For our current work, we excluded two clusters that were part of the W13 sample: RXJ1347-1145 and RXCJ0516-5430. RXJ1347-1145 was omitted because of its high redshift of z = 0 . 45 and because we did not want to add this cluster to the high-z samples with defined origin. RXCJ0516-5430 or SPT-CLJ05165430 ( z = 0 . 29) was already part of the high-z SPT sample. We thus excluded it from the low-z sample because of its high redshift. The low-z sample now comprises 78 archival XMM-Newton observations of galaxy clusters covering redshifts between 0.05 and 0.31, with 〈 z 〉 = 0 . 15. The clusters were drawn from several well-known samples observed with XMMNewton (for details see Table 5): REXCESS (Böhringer et al. 2007), LoCuSS (Smith et al., Zhang et al. 2008), the Snowden Catalog (Snowden et al. 2008), the REFLEX-DXL sample (Zhang et al. 2006), and Buote & Tsai (1996). The clusters were chosen to be well-studied, nearby (0 . 05 < z < 0 . 31), and publicly available (in 2009) in the XMM-Newton science archive 2 . In addition, we required r 500 to fit on the detector. The calculation of r 500 using the formula of Arnaud et al. (2005) led to slightly di ff erent r 500 and hence P 3 / P 0 and w values to those quoted in W13. The di ff erences are small, however. This merged low-z sample has no unique selection function, but a wide spread in luminosity, temperature, and mass. A large part of the clusters comes from representative samples such as REXCESS and LoCuSS and we therefore expect the sample to have a very roughly representative character. To check in more detail that no bias e ff ect is introduced by the merged sample, we also performed all tests with the 31 REXCESS clusters only. The results are consistent with the full low-z sample and we therefore do not quote them in detail.",
"pages": [
2
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},
{
"title": "2.2. High-zclustersamples",
"content": "In the high-redshift range, we used two samples to account for possible selection e ff ects and performed our analysis on each sample individually: the X-ray-selected high-z subsample from the 400SD survey (Burenin et al. 2007; Vikhlinin et al. 2009) and the SZ-selected subsample from SPT discussed in Andersson et al. (2011). -0.0 0.1 0.4 1.1 2.3 4.8 9.7 19.5 39.2 78.3 156.1 0 0.005 0.015 0.035 0.074 0.15 0.31 0.62 1.3 2.5 5 -0 0 1 2 4 9 17 35 70 141 280 3.6e-10 0.005 0.015 0.035 0.074 0.15 0.31 0.62 1.3 2.5 5 The high-z 400SD sample (short: 400SD) forms a complete subsample of the z > 0 . 35 clusters from the 400SD survey. It is composed of 36 objects in the 0 . 35 < z < 0 . 89 range and was selected as a quasi-mass-limited sample at z > 0 . 5. This was done by requiring a luminosity above a threshold of L X , min = 4 . 8 × 10 43 (1 + z ) 1 . 8 erg s -1 . All 36 400SD clusters were observed with CHANDRA and are publically available in the CHANDRA archive 3 . Several authors (e.g. Santos et al. 2010) have raised the question whether there might be a possible bias in the 400SD sample due to the detection algorithm. This may result in a lack of concentrated clusters compared with other high-redshift samples such as the Rosat Deep Cluster Survey (RDCS, Rosati et al. 1998) or the Wide Angle ROSAT Pointed Survey (WARPS, Jones et al. 1998). We accounted for these e ff ects by using the high-z SPT sample for comparison. The high-z SPT sample (short: SPT) is a subsample of the first SZ-selected cluster catalog, obtained from observations of 178 deg 2 of sky surveyed by the South Pole Telescope (SPT). Vanderlinde et al. (2010) presented a significance-limited catalog of 21 SZ-detected galaxy clusters of which 15 objects with SZ-detection-significance above 5.4 were selected for an X-ray follow-up program. This subsample covers the redshift range 0 . 29 < z < 1 . 08. The majority of the clusters was observed with CHANDRA, but for three objects we used XMM-Newton data because no CHANDRA data are available (SPT-CLJ23325358 and SPT-CLJ0559-5249) or because of the better photon statistics of the XMM-Newton observation (SPT-CLJ05165430). This results in 12 CHANDRA and 3 XMM-Newton observations (for details see Table 5, Column 9).",
"pages": [
2,
3
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},
{
"title": "2.3. Datareduction",
"content": "The 78 low-z and additional 3 high-z SPT XMMNewton observations (SPT-CLJ2332-5358, SPT-CLJ0559-5249 and 0 0.005 0.015 0.035 0.074 0.15 0.31 0.62 1.3 2.5 5 0 0.005 0.015 0.035 0.074 0.15 0.31 0.62 1.3 2.5 5 SPT-CLJ0516-5430) were taken from the public XMM-Newton Science archive and were analyzed with the XMMNewton SAS 4 in the well-established standard 0.5-2 keV band, which covers most of the cluster signal. The low-z clusters and SPT-CLJ0516-5430 were reduced prior to this study using SAS v. 9.0.0, while we used v. 12.0.1 for the other two SPT objects. In both cases we followed the data reduction recipe described in detail in Böhringer et al. (2010, 2007), except for the point source removal. Point sources were detected with the SAS task ewavelet in the combined image from all three detectors to increase the sensitivity of the point source detection. However, we removed the point sources from each detector image in the 0.5-2 keV band individually and refilled the gaps using the CIAO 5 task dmfilth . In the next step we subtracted the background, which was obtained from a vignetting model fit to a source-excised, hard-band-scaled blank sky field from the point-source-corrected images and combined them. This method yields point-source-corrected images without visible artifacts of the cutting regions. The high-z CHANDRA observations of the 400SD and SPT sample were treated as follows. A standard data reduction in the 0.5-2 keV band was performed using the CIAO software package v4.4 and CALDB v4.4.7. This band was chosen to match the XMMNewton data. For each observation, the level = 1 event file was reprocessed using chandra_repro , including amongst others the detection of afterglows, the generation of a new bad pixel file and corrections for di ff ering gains across the CCDs, timedependent gain, and charge transfer ine ffi ciencies (CTIs). For observations taken in the VFAINT mode, we applied the additional background cleaning using the task acis_process_events while setting check_vf_pha = yes . This procedure uses the outer 5 x 5 pixel (instead of 3 x 3 for FAINT) event island to search for potential cosmic-ray background events. Flared periods were excluded from the level = 2 event file using lc_clean . We created images in the 0.5-2 keV range and used fluximage to generate monochromatic 1 keV exposure maps. Point sources were detected and removed using dmfilth , which also refills the excised regions. For the background, blank-sky event files were reprojected, scaled to the exposure time of the flare-cleaned observation, restricted to the 0.5-2 keV range and binned with a factor of 4 to match the observations. When there were several pointings per cluster, we reduced the observations individually, but detected point sources on the merged 0.5-2 keV image. Images and exposure maps were merged using reproject_image .",
"pages": [
3,
4
]
},
{
"title": "3. Morphological analysis",
"content": "We used power ratios and center shifts as morphology estimators for our analysis. The power ratio method was introduced by Buote & Tsai (1995) to quantify the amount of substructure in a cluster and its dynamical state. The powers are based on a 2D multipole expansion of the cluster's gravitational potential and are evaluated within a certain aperture radius (e.g. r 500). It is already well established that the normalized hexapole of the X-ray surface brightness, P 3 / P 0, is sensitive to asymmetries on scales of the aperture radius and provides a useful measure of the dynamical state of a cluster (e.g. Jeltema et al. 2005; Buote & Tsai 1995; Böhringer et al. 2010; Chon et al. 2012, W13). Moreover, the center shift parameter w (e.g. O'Hara et al. 2006; Mohr et al. 1993; Böhringer et al. 2010; Chon et al. 2012, W13) characterizes the morphology of the cluster X-ray surface brightness. It measures the shift of the centroid, defined as the center of mass of the X-ray surface brightness, with respect to the X-ray peak in di ff erent apertures. The X-ray peak was determined from an image smoothed with a Gaussian with σ of 8 arcseconds. The o ff set of the X-ray peak from the centroid was then calculated for ten aperture sizes (0.1-1 r 500) and the final parameter w obtained as the standard deviation of the di ff erent center shifts in units of r 500. Unless stated otherwise, all presented P 3 / P 0 and w values were calculated within an aperture of r 500 and including the central region. However, we exclude the central 0.1 r 500 region when we calculated the X-ray centroid for the discussion in Sect. 6.2 to study possible e ff ects of cool cores. Both morphology estimators were discussed in our previous paper W13, where we studied the influence of background and shot noise on P 3 / P 0 and w as a function of photon counts and presented a method to correct for these e ff ects. In short, we first subtract the moments of the background image from those of the full (background-included) image to obtain a background-corrected power ratio. In a second step, we correct the bias caused by shot noise using repoissonized realizations of the cluster image. For w we subtract the background pixel values before calculating the position of the X-ray peak and centroid and estimate the shot noise bias analogous to the power ratios. For very regular clusters or observations highly influenced by noise, we sometimes overestimate the bias and obtain negative corrected P 3 / P 0 and w values with errors exceeding the negative value. We call such results non-significant detections. Substructure values that are positive after the bias correction, but have a 1σ error σ ( P 3 / P 0) that exceeds the P 3 / P 0 or w value by more than a factor of 3 are also considered as non-significant detections. For a more conservative factor of 1, hence taking values with σ ( P 3 / P 0) > P 3 / P 0 or σ ( w ) > w as non-significant detections, we find consistent results within the errors. For non-significant detections, we use upper limits (UL) in the analysis, where UL = σ ( P 3 / P 0) + P 3 / P 0non -significant for positive and UL = σ ( P 3 / P 0) for negative corrected P 3 / P 0 values. The definition is analogous for w . All presented P 3 / P 0 and w values are background and bias corrected. During our discussion we will refer to di ff erent thresholds for P 3 / P 0 and w to divide the sample according to the dynamical state of the clusters. These dividing boundaries are taken from our previous work W13, where we also defined the significance S of a P 3 / P 0 or w value as the ratio of the biascorrected signal with respect to the obtained error. For highquality data ( S > 3) we established two morphological P3 / P0 boundaries to divide the sample into relaxed ( P 3 / P 0 < 10 -8 ), mildly disturbed (10 -8 < P 3 / P 0 < 5 × 10 -7 ), and disturbed objects ( P 3 / P 0 > 5 × 10 -7 ). High S values down to 10 -8 allow for this detailed classification. When dealing with low count observations, we reach S = 1 around 10 -7 and use this value as simple P 3 / P 0 boundary to separate disturbed and relaxed clusters. Owing to the data quality of the high-z samples (see Table 1), we only used the P 3 / P 0 boundary at 10 -7 for our analysis. For the center shift parameter, we used w = 0 . 01 to split the sample. Since w is only severly a ff ected by Poisson noise for considerably less than 1 000 net photon counts within r 500 for a reasonably low background, this threshold can be used for highand low-quality data.",
"pages": [
4
]
},
{
"title": "4. Data quality",
"content": "The strongest potential disadvantage when dealing with a combination of low- and high-z observations is the di ff erence in the photon statistics of the observations, as can be seen by comparing Figs. 2 (left) and 3. Details of the sample statistics are given in Table 1, which shows that the low-z sample is not only larger in numbers but also in terms of higher photon statistics and a higher ratio of net (signal) to background photon counts (S / B). This results in a significant di ff erence between the two samples in the extent and importance of photon shot noise. As we have shown in our previous work W13, photon shot noise can have a severe e ff ect on the determination of the cluster morphology.",
"pages": [
4
]
},
{
"title": "4.1. Degradingofhigh-qualitylow-zobservations",
"content": "We studied and quantified these e ff ects and the influence of the background as a function of photon counts and S / B ratio for P 3 / P 0 and w . We found that the center shift parameter can be determined with a small error even below the w = 0 . 01 threshold for low photon statistics ( < 1 000 net photon counts) and a reasonable S / B of e.g. ∼ 2. We can therefore obtain reasonable results for all morphologies, partly with relative large errors for very relaxed objects. The power ratio method needs su ffi cient photon counts to overcome the influence of Poisson noise, however. We showed that this problem is not important for disturbed objects, which do not su ff er severly from shot noise and thus enable an accurate estimation even for low-quality data. For decreasing photon counts, however, mildly disturbed and relaxed objects undergo a boost of their signal due to an underestimation of the bias contribution that yields substructure parameters that are too high. In the case of excessive noise, we obtain a non-significant result. High-quality data therefore enable a more reliable determination of P 3 / P 0 ( w ) and better statistics, including a higher number of clusters with P 3 / P 0 > 0 ( w > 0) and a higher mean significance 〈 S 〉 . A direct comparison between lowand high-quality data may thus not be conclusive. Fig. 4 shows that the low-z data have more than su ffi cient photon counts with a mean of ∼ 97 000 net photon counts within r 500 to give P 3 / P 0 and w values with very good error properties and large S . The high-z objects, however, peak just above 1000 net photon counts with a mean of ∼ 1 200 for 400SD and ∼ 1700 for SPT. According to simulations presented in W13, these high-z observations meet the criteria to roughly separate the sample into disturbed clusters with high and accurately determined substructure parameters and relaxed ones with parameters below the P 3 / P 0 ( w ) threshold with large errors or non-significant detections. High-z observations contain a higher contribution from the background with a mean S / B of ∼ 3 . 5. This causes additional uncertainties due to the extra noise from the background and results in the low number of objects with S > 1. To obtain conclusive results we need to establish the influence of noise and the possible boost of the P 3 / P 0 ( w ) signal due to the lower data quality in the high-z sample. To test how robust our results are to the di ff erence in the data quality of the samples, we first performed our analysis using the high-quality or so-called undegraded low-z data. In addition, we created a degraded low-z sample by aligning the data quality of the low-z observations to that of the high-z objects. This was done by degrading the high-quality low-z observations to the photon statistics (1 200 net photon counts and S / B = 3.7 within r 500) of the 400SD high-z sample (see Table 1). The degrading was done in several steps, taking care of the di ff erent net and background photon counts and the increased Poisson noise. Two examples of degraded cluster images are given in Fig. 2 (right panels), compared with the undegraded images (left panels). The undegraded cluster image ( IM 0) is not background subtracted. In the following recipe we denote images with capital letters and photon counts with lowercase letters. The recipe to obtain a low-z cluster and background image with the same photon statistics as the average high-z cluster is outlined in steps 1-4. However, observations with low photon statistics do not only lack the su ffi cient number of photon counts, but also su ff er from a considerable amount of Poisson noise. This is included by adding additional Poisson noise to the degraded image using the zhtools 6 task poisson . In steps 5-7 we summarize the statistical analysis using the Poissonized realizations of these images.",
"pages": [
5
]
},
{
"title": "5. Results",
"content": "We studied the evolution of the substructure frequency up to z = 1 . 08 using di ff erent statistical measures on the morphology estimators P 3 / P 0 and w : i) fitting the data in the P 3 / P 0-z and w -z plane with the linear relation log ( Y ) = A × log ( z / 0 . 25) + B for Y = P 3 / P 0 and w respectively, ii) calculating mean values for the di ff erent redshift intervals and iii) analyzing the fraction of relaxed and disturbed objects using P 3 / P 0 and w boundaries. For non-significant detections, we used upper limits as discussed in Sect. 3. These are not included in the BCES fits given in Table 2 and Figs. 5-7. All analyses were performed on the log-distribution of P 3 / P 0 and w to take into account very low P 3 / P 0 and w values. Fitting parameters were calculated using the BCES (Y | X) fitting method (Akritas & Bershady 1996), which minimizes the residuals in Y. To study the P 3 / P 0-z and w -z relation we formed two samples to study possible selection e ff ects of the high-z samples: i) sample I - low-z sample and high-z subsample of 400SD sample, ii) sample II - low-z sample and high-z subsample of SPT sample. We argue that using the degraded low-z data might be essential to obtain reliable and conclusive results. We therefore performed the identical analysis on sample I / II and the degraded sample I / II, where we used the degraded low-z data. We point out that only the high-quality low-z observations are degraded and thus are di ff erent in sample I / II and degraded sample I / II. The high-z data remains unchanged. In the following we focus on the heavily noise-a ff ected P 3 / P 0 parameter and then consider the more robust w parameter. During our analysis, we tried to include the information given by the upper limits in the P 3 / P 0-z and w -z fits and tested the ASURV (Feigelson & Nelson 1985; Isobe et al. 1986) and the LINMIX_ERR (Kelly 2007) routine. For upper limits, both methods use estimated data points for fitting that are computed from the input upper limit and the distribution of the detected data points. Several tests using simulated images showed that the estimated data points are strongly coupled to the fit obtained from the detected data points and do not reflect the true P 3 / P 0 values. Since the censorship in our data is due to low counts and dependent on P 3 / P 0 itself, we conclude that our data do not fulfill the requirements for these routines to work properly.",
"pages": [
5,
6
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},
{
"title": "5.1. P 3 / P 0 -zrelation",
"content": "We first discuss the structure parameter P 3 / P 0 as a function of redshift for sample I and II using Fig. 5. On the left side we show only the significant data points, while we include non-significant results as upper limits (arrows) on the right. For illustration, we show the P 3 / P 0 boundary at 10 -7 to separate relaxed and disturbed objects. When looking at this figure, one immediately notices the lack of significant detections of high-z clusters with P 3 / P 0 < 10 -7 . In addition, essentially all upper limits are found above this P 3 / P 0 boundary. We quantified the P 3 / P 0-z relation using the undegraded low-z data and di ff erent statistical measures. On the left of Fig. 5 we show the linear BCES fit. For sample I we obtained a more than 3 σ significant slope with A = 1 . 01 ± 0 . 31, for sample II we found a somewhat shallower slope of A = 0 . 59 ± 0 . 36. We then tested the influence of the very structured 400SD cluster 0152-1358 ( z ∼ 0 . 8) with P 3 / P 0 > 10 -5 on the fit, finding a shallower, but consistent slope when excluding it from the fit. Another way of quantifying the observed relation is computing the fraction of relaxed and disturbed objects in comparison to upper limits, which are shown in Table 3. Because of the high data quality of the undegraded low-z observations, the fraction of upper limits is small. All these objects can be considered as relaxed clusters because P 3 / P 0 can detect significant signals well below 10 -7 for such good data quality. Their non-significant signals or upper limits are consistent with P 3 / P 0 << 10 -7 . In addition, we find 45% of the low-z objects to be relaxed. The majority of clusters in this sample is found below the P 3 / P 0 threshold of 10 -7 with a mean of the log P 3 / P 0 distribution of -7 . 1 ± 0 . 8. The high-z samples yield a higher mean of -5 . 9 ± 0 . 6 ( -6 . 1 ± 0 . 5) for 400SD (SPT). The mean values are given in Table 4 and are denoted as mean data for the significant data points and mean UL for the upper limits. We plot the mean data values in Fig. 5 on the right side to illustrate this o ff set. In addition, we add the mean UL values to emphasize again the di ff erence in the location of upper limits for the high- and low-quality data. All statistical measures used on this dataset so far give a clear trend of a larger fraction of disturbed clusters at higher redshift. This conclusion should not be drawn without caution, however, since we are comparing very di ff erent datasets. We already argued that P 3 / P 0 is heavily influenced by noise for observations with low net photon counts and / or high background. The computation of substructure parameters for the high-z objects therefore su ff ers severely from noise. According to results presented in W13, we can obtain significant P 3 / P 0 values for the majority of the disturbed clusters even with fewer than 1 000 net photon counts within r 500. Mildly disturbed and relaxed objects will mostly either yield non-significant detections or undergo a boost of the P 3 / P 0 signal. Except for some mildly disturbed objects whose P 3 / P 0 values are just below the 10 -7 boundary in the undegraded case, this boost will not result in P 3 / P 0 > 10 -7 . We should thus be able to very roughly separate the sample into disturbed ( P 3 / P 0 > 10 -7 ) and relaxed ( P 3 / P 0 < 10 -7 and upper limits) objects. We repeated the analysis using the degraded low-z data and show the results in Fig. 6. We found significantly shallower slopes of A = 0 . 24 ± 0 . 28 ( A = 0 . 17 ± 0 . 24) and higher intercepts B for the degarded sample I (II). This is due to the apparent loss of data points with P 3 / P 0 < 10 -7 and large errors on the detected P 3 / P 0 signals after degrading. We find a significant increase of the upper limit fraction to 72% while the fraction of relaxed clusters decreases from 45% to on average 0% (Table 3). The fraction of disturbed objects stays roughly the same, showing that we can detect a signal for the majority of structured objects while only a small number gives upper limits. With these low-quality data, we cannot measure a significant P 3 / P 0 value for mildly disturbed or relaxed clusters anymore, but only detect disturbed objects. For the high-z samples, we found no objects with P 3 / P 0 < 10 -7 but a large number of upper limits (Table 3) and a disturbed cluster fraction of 42% for 400SD and 47% for SPT. Assuming that the majority of the disturbed objects yield significant detections, we found a slightly higher fraction of disturbed objects in the high-z samples than in the degraded low-z sample. We performed more tests by varying the degree of degradation of the low-z data. We found that the larger the disagreement between the net photon counts and S / B of the samples, the more biased the obtained slope or mean value. It is therefore of extreme importance to take this issue into account when analyzing the P 3 / P 0-z relation. Notes. (a) mean values of 100 randomly selected samples.",
"pages": [
6,
7
]
},
{
"title": "5.2. w -zrelation",
"content": "Analogously to P 3 / P 0, we used the same statistical measures on the w parameter to probe its behavior as a function of redshift. Fig. 7 shows the w distribution for sample I and II, including upper limits on the right and the w = 0 . 01 boundary to seperate relaxed and disturbed objects. We performed a linear BCES fit and give the fitting parameters in Table 2. The fits are illustrated on the left side of Fig. 7, with slope A = 0 . 18 ± 0 . 14 ( A = 0 . 02 ± 0 . 13) for sample I (II). These slopes are both positive, but not significant and consistent with zero within 1σ . In contrast to P 3 / P 0, low- and high-z clusters populate the full w range. This is reflected in the very similar mean values of the samples and their upper limits. We show these values in Table 4 and Fig. 7 on the right side. Because the w parameter is not very sensitive to noise when dealing with > 1 000 net photon counts and a background that is not too high - as is the case with the high-z observations -, degrading the low-z observations to match the data quality of the 400SD clusters shows little e ff ect. All statistical measures show very similar results when using the degraded low-z sample (Tables 2-4). The slopes stay well within the errors, and the mean data value does not change either. Only the mean upper limit value increases slightly, because the undegraded low-z data contains only one upper limit, but the degraded sample contains a few more. This is reflected in the slight increase of the upper limit fraction from 1% to 6%, which is very similar to those of the 400SD (8%) and SPT (7%) sample. The fraction of relaxed objects decreases slightly for the degraded data from 58% to 52%, while it increases for disturbed objects from 41% to 43%. These changes are within the errors and again show the robustness of w against noise. Comapring the low-z fractions with those of the high-z samples, we see a very similar behavior of the SPT clusters, but the 400SD sample shows a larger fraction of objects with w > 0 . 01.",
"pages": [
7
]
},
{
"title": "6. Discussion",
"content": "Assessing the dynamical state of a galaxy cluster calls for a well-studied method for detecting and quantifying substructure in the ICM. Well-understood error properties are of great importance, especially when dealing with high-z observations and thus low photon statistics. The two applied methods, power ratios and center shifts, fulfill these requirements. A strong correlation with a large scatter between P 3 / P 0 and w is known from previous studies (e.g. Böhringer et al. 2010) and therefore a similar trend in both relations is expected. Comparing the results obtained from applying P 3 / P 0 and w on sample I / II shows a very large discrepancy. While P 3 / P 0 shows a significant increase with redshift in all statistical measures used, w shows a positive but non-significant slope and no trend in the mean values either. We claim that the discrepancy between these results is caused by the inconsistent data quality of the full sample, which a ff ects P 3 / P 0 more than w . Taking into account the slopes, mean values, and fractions, one can conclude that w is not sensitive to di ff erent data quality since the results hardly change. For of P 3 / P 0, degrading the high-quality low-z observations to the net photon counts and background of the high-z objects yields very di ff erent results. The slope flattens significantly, yielding a similar result to w - a positive but non-significant slope. The fraction of upper limits increases dramatically, because all relaxed objects yield non-significant detections. The fraction of low-z disturbed object is therefore only slightly smaller than those of the 400SD and SPT sample. Moreover, the mean data and mean UL values match those of the high-z samples when using equal data quality. The results using P 3 / P 0 and w on this particular dataset show a similar trend. We found a very mild positive evolution, which is also consistent with no change with redshift within the significance limits. We excluded a strong increase of the disturbed cluster fraction with redshift and set an upper limit with the shallow slopes of the BCES fits. For the lower limit, we found no indication of a negative evolution because all statistical measures show an increase of P 3 / P 0 and w with redshift, but with low significance. Article number, page 8 of 14",
"pages": [
7,
8
]
},
{
"title": "6.1. Comparisonwithpreviousstudies",
"content": "In the light of our finding that the di ff erent data quality between the low-z and high-z sample can severly bias the results, we compared our work with previous studies that did not take this problem into account. Jeltema et al. (2005) presented the first analysis of the P 3 / P 0-z relation using 40 X-ray-selected luminous clusters in the 0 . 1 < z < 0 . 89 range and a fixed physical aperture of 0.5 Mpc. They found the slope of the linear P 3 / P 0-z relation to be 4 . 1 × 10 -7 , but did not provide an intercept. We argue that a linear fit is not sensitive enough when working with a P 3 / P 0 range of 10 -9 -10 -5 . High P 3 / P 0 values like that of the 400SD cluster 0152-1358 ( P 3 / P 0 > 10 -5 at z ∼ 0.8) dominate a linear fit, while low P 3 / P 0 values are not adequately taken into account. We therefore did not include this result in Fig. 8, which compares our findings with previous studies. Jeltema et al. (2005) also provided mean P 3 / P 0 values for z < 0 . 5 and z > 0 . 5 objects. For a fair comparison, we calculated P 3 / P 0 in the same 0.5 Mpc aperture, since r 500 is typically larger than 1 Mpc for the low-z sample and on average 0.8 Mpc for high-z objects. A fixed aperture of 0.5 Mpc probes the cluster structure on a di ff erent scale than r 500. For the 0.5 Mpc aperture, the slopes of the fits are steeper and the intercepts higher with A = 1 . 52 ± 0 . 30 ( A = 1 . 08 ± 0 . 39) and B = -6 . 61 ± 0 . 07 ( B = -6 . 75 ± 0 . 10) for sample I (II). After degrading, the P 3 / P 0-z fits flatten significantly to A = 0 . 42 ± 0 . 18 ( A = 0 . 08 ± 0 . 31) with B = -5 . 96 ± 0 . 06 ( B = -6 . 09 ± 0 . 10) for the degraded sample I (II) and agree well with the degraded results when using r 500 as aperture. The general impression of a very mild increase of the disturbed cluster fraction with redshift thus holds also for the 0.5 Mpc aperture. We show the fits for sample I and the degraded sample I using the 0.5 Mpc aperture in Fig. 8. The discrepancy between our fit of the degraded sample I and the mean values of Jeltema et al. (2005) is apparent. While Jeltema et al. (2005) took general noise properties into account, they did not address the problem of the data quality di ff erence, which results in an overestimation of the slope and a large o ff set between the mean low-z and high-z sample. Another study was performed by Andersson et al. (2009), who also calculated P 3 / P 0 in an 0.5 Mpc aperture for 101 galaxy clusters in the range 0 . 07 < z < 0 . 89. They reported an increase in P 3 / P 0 and provided average P 3 / P 0 values given for three redshift bins (0 . 069 < z < 0 . 1, 0 . 1 < z < 0 . 3 and z > 0 . 3). We see an o ff set to our degraded fits here as well. Several studies using both simulations (e.g. Ho et al. 2006) and observations (e.g. Maughan et al. 2008; Plionis 2002; Melott et al. 2001) explored the evolution of ellipticity with redshift. The asymmetry in the X-ray surface brightness distribution was studied by Hashimoto et al. (2007), reporting no significant di ff erence regarding ellipticity and o ff -center between the low- and high-z sample, but a hint of a weak evolution for the concentration and asymmetry parameter. Recently, Mann & Ebeling (2012) presented a study of the evolution of the cluster merger fraction using 108 of the most X-ray-luminous galaxy clusters at 0 . 15 < z < 0 . 7. They used optical and X-ray data and classified mergers according to their morphological class, X-ray centroid - BCG separation and X-ray peak - BCG separation. They reported an increase of the fraction of disturbed clusters with redshift, starting around z = 0 . 4. In addition to observational studies, we compared our findings with those of Jeltema et al. (2008), who studied the evolution of cluster structure with P 3 / P 0 and w in hydrodynamical sim- ulations performed with Enzo, a hybrid Eulerian adaptive mesh refinement / N-body code. Their simulations did not include the e ff ect of noise or instrumental response, therefore only a broad comparison to low-z observed data with high singal-to-noise is possible. They reported a dependence of the evolution of P 3 / P 0 with redshift on the selection criterium and on the radius chosen. While for w they found a significant increase with redshift for a mass as well as a luminosity cut, P 3 / P 0 showed an evolution only for a luminosity-limited sample. In agreement with our results, they stated that the evolution of cluster structure is mild compared with the variety of cluster morphologies seen at all redshifts.",
"pages": [
9
]
},
{
"title": "6.2. Effectofcoolcores",
"content": "Several studies showed that cool cores are preferentially found in relaxed systems. Santos et al. (2010) and Andersson et al. (2009) found a negative evolution of the fraction of cool-core clusters, reporting that the number of cooling core clusters appears to decrease with redshift. This suggests a higher fraction of relaxed clusters at low than at high redshift. They also argued that the evolution is significantly less pronounced than previously claimed. Bauer et al. (2005) used the high-z end of the BCS sample and concluded that the fraction of cool-cores does not significantly evolve up to z ∼ 0 . 4. It is therefore an interesting exercise to study whether the P 3 / P 0-z and w -z relation is driven by the presence of a cool core or by the overall dynamical state of the cluster. To do this, we excluded the 0.1 r 500 region when calculating the centroid, but kept it to determine the X-ray peak. For an aperture of r 500 we found very similar slopes for both relations. For w the slope becomes somewhat shallower but remains well within the 1σ error with A = 0 . 10 ± 0 . 14 ( A = -0 . 07 ± 0 . 13) and B = -1 . 97 ± 0 . 04 ( B = -2 . 02 ± 0 . 04). As expected, degrading has no real e ff ect on the center-excised w -z relation, and the mean values also stay well within the errors. Contrary to our findings, Maughan et al. (2008) reported a significant absence of relaxed clusters at high redshift using a sample of 115 galaxy clusters in the 0 . 1 < z < 1 . 3 range and center shifts with the central 30 kpc excised as morphology estimator. P 3 / P 0, on the other hand, yields slightly higher values on averge when excluding the center, which results in a very similar slope of A = 0 . 97 ± 0 . 29 ( A = 0 . 58 ± 0 . 32), but in a higher intercept of B = -6 . 53 ± 0 . 09 ( B = -6 . 68 ± 0 . 10) and higher mean values for sample I (II). The same e ff ects are seen when using the degraded low-z sample. The analysis was repeated using the fixed 0.5 Mpc aperture. We found a larger di ff erence between the core-included and excised P 3 / P 0-z relation for this aperture, because it is more sensitive to substructure in the inner region of the cluster. The obtained results are comparable with the r 500 case, however. We conclude that based on the method to obtain P 3 / P 0 and w , the P 3 / P 0-z and w -z relations seem to be mainly driven by the dynamical state of the cluster on the scale of the aperture radius.",
"pages": [
9,
10
]
},
{
"title": "7. Conclusions",
"content": "We studied the evolution of the substructure frequency by comparing a merged sample of 78 low-z observations of galaxy clusters with the high-z subsample of the 400SD and SPT sample. The analysis was performed on two samples individually to exclude possible selection e ff ects of the high-z samples: i) sample I: 78 low-z and 36 400SD, ii) sample II: 78 low-z and 15 SPT clusters. Power ratios P 3 / P 0 and the center shift parameter w were used to quantify the amount of substructure in the cluster X-ray images. We found that directly comparing high-quality low-z and low-quality high-z observations using P 3 / P 0 However, as was shown in our previous work (Weißmann et al. 2013), P 3 / P 0 is very sensitive to noise and thus to the depth and quality of the observation. We corrected for the noise bias, but uncertainties in the results of low-quality data remained. Since there is a significant di ff erence in the data quality of the samples, this problem needed to be considered during the analysis. We therefore degraded the high-quality low-z observations to the photon statistics of the high-z 400SD observations. This enabled a comparison of data with similar quality and thus more reliable results. Using equal data quality and P 3 / P 0, we found We performed the same analysis using the center shift parameter w as morphology estimator. w is more robust against Poisson noise and not very sensitive to the data quality di ff erence of the samples. We therefore found very similar results using the undegraded and degraded low-z data, namely Considering that the 400SD high-z sample may contain an unrepresentatively large number of disturbed clusters, the slopes obtained using this dataset should be taken as upper limits. They are consistent with the results when using the SPT clusters as high-z sample, however. In summary, we agree with previous findings, which indicate an evolution of the substructure frequency with redshift. We conclude that the results using P 3 / P 0 and w on this particular dataset show a similar and very mild positive evolution of the substructure frequency with redshift. However, within the significance limits, our findings are also consistent with no evolution. A strong increase of the disturbed cluster fraction is excluded and the BCES fits are taken as upper limits. For the lower limit, we found no indication of a negative evolution. All statistical measures show a slight increase of P 3 / P 0 and w with redshift, but with low significance. Larger samples of deep observations of z > 0 . 3 galaxy clusters would provide a better way to quantify these relations and allow unambiguous conclusions. Acknowledgements. Wewould like to thank the anonymous referee for constructive comments and suggestions. This work is based on observations obtained with XMMNewton and CHANDRA. XMMNewton is an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. The XMMNewton project is supported by the Bundesministerium für Wirtschaft und Technologie / Deutsches Zentrum für Luft- und Raumfahrt (BMWI / DLR, FKZ 50 OX 0001), the Max-Planck Society and the HeidenhainStiftung. A part of the scientific results reported in this article is based on data obtained from the Chandra Data Archive. AW acknowledges the support from and participation in the International Max-Planck Research School on Astrophysics at the Ludwig-Maximilians University. GC acknowledges the support from Deutsches Zentrum für Luft- und Raumfahrt (DLR) with the program ID 50 R 1004. HB and GC acknowledge support from the DfG Transregio Program TR33 and the Munich Excellence Cluster 'Structure and Evolution of the Universe'.",
"pages": [
10
]
},
{
"title": "References",
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"pages": [
10,
11,
14
]
}
]
2013A&A...556A..40M
https://arxiv.org/pdf/1307.6720.pdf
<document>
<section_header_level_1><location><page_1><loc_13><loc_82><loc_89><loc_87></location>Non-symmetric magnetohydrostatic equilibria: a multigrid approach</section_header_level_1>
<text><location><page_1><loc_25><loc_80><loc_76><loc_81></location>D. MacTaggart 1 , A. Elsheikh 1 , J. A. McLaughlin 2 and R. D. Simitev 3</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_76><loc_91><loc_78></location>1 School of Engineering, Computing and Applied Mathematics, University of Abertay Dundee, Kydd Building, Dundee, DD1 1HG, Scotland, UK</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_89><loc_76></location>2 Department of Mathematics and Information Sciences, Northumbria University, Newcastle Upon Tyne, NE1 8ST, England, UK</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_71><loc_74></location>3 School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, Scotland, UK</list_item>
</unordered_list>
<section_header_level_1><location><page_1><loc_47><loc_70><loc_55><loc_71></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_65><loc_91><loc_69></location>Aims. Linear magnetohydrostatic (MHS) models of solar magnetic fields balance plasma pressure gradients, gravity and Lorentz forces where the current density is composed of a linear force-free component and a cross-field component that depends on gravitational stratification. In this paper, we investigate an e ffi cient numerical procedure for calculating such equilibria.</text>
<text><location><page_1><loc_11><loc_61><loc_91><loc_65></location>Methods. The MHS equations are reduced to two scalar elliptic equations - one on the lower boundary and the other within the interior of the computational domain. The normal component of the magnetic field is prescribed on the lower boundary and a multigrid method is applied on both this boundary and within the domain to find the poloidal scalar potential. Once solved to a desired accuracy, the magnetic field, plasma pressure and density are found using a finite di ff erence method.</text>
<text><location><page_1><loc_11><loc_57><loc_91><loc_60></location>Results. We investigate the e ff ects of the cross-field currents on the linear MHS equilibria. Force-free and non-force-free examples are given to demonstrate the numerical scheme and an analysis of speed-up due to parallelization on a graphics processing unit (GPU) is presented. It is shown that speed-ups of × 30 are readily achievable.</text>
<text><location><page_1><loc_11><loc_55><loc_65><loc_56></location>Key words. Sun: magnetic fields - Magnetohydrodynamics (MHD) - Methods: numerical</text>
<section_header_level_1><location><page_1><loc_7><loc_51><loc_19><loc_52></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_40><loc_50><loc_50></location>The calculation of three-dimensional non-linear magnetohydrostatic (MHS) equilibria is a non-trivial subject. In the solar physics context, progress has been made by considering linear subclasses of MHS equilibria. One such class, known as laminated equilibria, makes use of an Euler potential representation of the magnetic field (e.g. Low (1982)). On each lamina, a 2D magnetic field is calculated and the 3D field comprises of the union of these laminas.</text>
<text><location><page_1><loc_7><loc_16><loc_50><loc_39></location>Another approach is to model the current density as a linear combination of field-aligned and cross-field currents (Low (1991), Low (1992)). Here, the field-aligned current is that of a linear force-free field and the cross-field current depends on the variation of the magnetic field with height. Details of this will be presented in the next section. Neukirch & Rastatter (1999) (NR99 hereafter) present a new formulation of Low's model by writing the magnetic field in terms of poloidal and toroidal components. This has the advantage that the calculation of the magnetic field only involves one scalar function whereas, previously, one was forced to operate with all three components of the magnetic field independently. Petrie & Neukirch (2000) use the representation of NR99 and find closed-form solutions for MHSequilibria via Green's functions. The price paid for finding closed-form solutions, however, is that they are forced to choose a simple term for the cross-field current. To date, the authors are unaware of any closed-form solutions using Green's functions, other than those presented in Petrie & Neukirch (2000).</text>
<text><location><page_1><loc_7><loc_13><loc_50><loc_16></location>Although more detailed analytical solutions may prove di ffi -cult with the representation of NR99, it is, however, set up per-</text>
<text><location><page_1><loc_7><loc_11><loc_50><loc_12></location>Send o ff print requests to : D. MacTaggart, e-mail:</text>
<text><location><page_1><loc_52><loc_40><loc_95><loc_52></location>fectly for an e ffi cient numerical treatment. In this paper, we outline a simple and fast numerical procedure for calculating MHS equilibria based on the NR99 representation. The details of this are given in the next section. This is followed by some examples of force-free and linear MHS equilibria. For the linear MHS case, we investigate the e ff ects of the cross-field currents on the equilibria. We then highlight how the scheme can be parallelized simply and e ff ectively on a graphics processing unit (GPU). The paper concludes with a summary.</text>
<section_header_level_1><location><page_1><loc_52><loc_37><loc_85><loc_38></location>2. Model equations and solution method</section_header_level_1>
<text><location><page_1><loc_52><loc_32><loc_95><loc_36></location>Firstly, we shall outline where the equations to be solved come from. Fuller details can be found in NR99. This will be followed by an algorithm for the numerical solution.</text>
<section_header_level_1><location><page_1><loc_52><loc_29><loc_70><loc_30></location>2.1. Themodelequations</section_header_level_1>
<text><location><page_1><loc_52><loc_27><loc_81><loc_28></location>The MHS equations that we shall solve are</text>
<formula><location><page_1><loc_52><loc_24><loc_95><loc_26></location>µ -1 0 ( ∇× B ) × B - ∇ p -ρ g ˆ e z = 0 , (1)</formula>
<formula><location><page_1><loc_52><loc_22><loc_95><loc_23></location>∇ × B = µ 0 j , (2)</formula>
<text><location><page_1><loc_52><loc_20><loc_59><loc_21></location>∇ · B = 0 ,</text>
<text><location><page_1><loc_93><loc_20><loc_95><loc_21></location>(3)</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_19></location>where B is the magnetic induction (commonly referred to as the magnetic field), j is the current density, p is the plasma presure, ρ is the density, g is the (constant) gravitational acceleration and µ 0 is the permeability of free space. To complete the problem, boundary conditions must be specified. This choice is problem-dependentbut will, at least, require B to be specified on the boundaries of the domain through Dirichlet or von Neuman</text>
<text><location><page_2><loc_7><loc_89><loc_50><loc_93></location>conditions. In this paper we will consider a Cartesian domain. Following Low (1992), we assume the current density takes the following form</text>
<formula><location><page_2><loc_7><loc_87><loc_50><loc_88></location>µ 0 j = α B + ∇ ( gF ) × ˆ e z , (4)</formula>
<text><location><page_2><loc_7><loc_80><loc_50><loc_86></location>where α is a constant and F is an arbitrary function. The first term on the right-hand-side is the aligned current associated with a linear force-free field. The second term is the non-force-free cross current due to the gravitational stratification. The magnetic induction can be written as</text>
<formula><location><page_2><loc_7><loc_77><loc_50><loc_78></location>B = ∇ × [ ∇× ( P ˆ e z ) + T ˆ e z ] , (5)</formula>
<text><location><page_2><loc_7><loc_73><loc_50><loc_76></location>where P and T are scalar functions corresponding to the poloidal and toroidal components respectively. This form satisfies equation (3). Using this in equation (2) with equation (4) gives</text>
<formula><location><page_2><loc_7><loc_70><loc_50><loc_71></location>T = α P , (6)</formula>
<formula><location><page_2><loc_7><loc_68><loc_50><loc_69></location>∇ 2 P + α 2 P + gF = 0 . (7)</formula>
<text><location><page_2><loc_7><loc_65><loc_35><loc_67></location>Following NR99 and Low (1992), we set</text>
<text><location><page_2><loc_7><loc_63><loc_8><loc_64></location>F</text>
<text><location><page_2><loc_9><loc_63><loc_10><loc_64></location>=</text>
<text><location><page_2><loc_10><loc_63><loc_11><loc_64></location>g</text>
<text><location><page_2><loc_11><loc_64><loc_12><loc_65></location>-</text>
<text><location><page_2><loc_12><loc_64><loc_12><loc_65></location>1</text>
<text><location><page_2><loc_12><loc_63><loc_13><loc_64></location>ξ</text>
<text><location><page_2><loc_13><loc_63><loc_14><loc_64></location>(</text>
<text><location><page_2><loc_14><loc_63><loc_14><loc_64></location>z</text>
<text><location><page_2><loc_14><loc_63><loc_15><loc_64></location>)</text>
<text><location><page_2><loc_15><loc_63><loc_17><loc_64></location>Bz</text>
<text><location><page_2><loc_17><loc_63><loc_17><loc_64></location>.</text>
<text><location><page_2><loc_7><loc_61><loc_34><loc_62></location>With this identity, equation (7) becomes</text>
<formula><location><page_2><loc_7><loc_57><loc_50><loc_60></location>[1 -ξ ( z )] ( ∂ 2 P ∂ x 2 + ∂ 2 P ∂ y 2 ) + ∂ 2 P ∂ z 2 + α 2 P = 0 . (8)</formula>
<text><location><page_2><loc_7><loc_52><loc_50><loc_56></location>For ξ ( z ) < 1, equation (8) is elliptic. Now the magnetic field can be found by solving this for the poloidal scalar potential P and then using equations (5) and (6).</text>
<text><location><page_2><loc_7><loc_50><loc_50><loc_52></location>Once the magnetic field is found, the plasma pressure and density are given by</text>
<formula><location><page_2><loc_7><loc_46><loc_50><loc_49></location>p = pb ( z ) -ξ ( z ) B 2 z 2 µ 0 (9)</formula>
<text><location><page_2><loc_7><loc_44><loc_10><loc_45></location>and</text>
<formula><location><page_2><loc_7><loc_40><loc_50><loc_43></location>ρ = ρ b ( z ) + 1 g ( d ξ d z B 2 z 2 µ 0 + 1 µ 0 ξ B · ∇ Bz ) . (10)</formula>
<text><location><page_2><loc_7><loc_35><loc_50><loc_39></location>pb and ρ b are the background equilibrium plasma pressure and density respectively. A derivation of these formulae is given in NR99.</text>
<section_header_level_1><location><page_2><loc_7><loc_32><loc_28><loc_33></location>2.2. Thenumericalprocedure</section_header_level_1>
<text><location><page_2><loc_7><loc_27><loc_50><loc_31></location>An e ffi cient numerical solution of this class of the MHS equations rests on reducing the equations to a set of linear, scalar elliptic problems. i.e. those of the form</text>
<formula><location><page_2><loc_7><loc_25><loc_31><loc_26></location>a ( x ) ∇ 2 u + b ( x ) u = c ( x ) , x ∈ D ,</formula>
<text><location><page_2><loc_7><loc_20><loc_50><loc_24></location>with u defined on ∂ D . Here the Laplacian operator can be twodimensional (for boundaries) or three-dimensional (for the interior) and a , b and c are known scalar functions.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_20></location>There exists a wide variety of techniques to solve such problems e ffi ciently, from Krylov subspace methods to multigrid methods. Although solution methods are problem-dependent, the multigrid method is often an optimal solver for discrete Poisson problems (Elman et al. (2005)), i.e. its convergence rate is independent of the problem mesh size. It can also be parallelized e ffi ciently, and for these reasons we adopt it in this work. The multigrid method, in a di ff erent representation to the one of</text>
<text><location><page_2><loc_52><loc_91><loc_95><loc_93></location>this paper, was used successfully for MHS models of flux tubes bounded by current sheets (Henning & Cally (2001)).</text>
<text><location><page_2><loc_52><loc_80><loc_95><loc_90></location>As mentioned above, the MHS equations are reduced to a set of linear elliptic problems defined on the boundaries and in the interior. Equation (8) is the three-dimensional elliptic problem for the poloidal scalar potential P defined in the interior of the domain. The other elliptic equations required to be solved depend on the boundary conditions. On the lower boundary, the vertical component of the magnetic field, Bz , is prescribed. From equation (5), it is clear that, on the lower boundary,</text>
<formula><location><page_2><loc_52><loc_76><loc_95><loc_79></location>( ∂ 2 P ∂ x 2 + ∂ 2 P ∂ y 2 ) = -Bz ( x , y ) . (11)</formula>
<text><location><page_2><loc_52><loc_64><loc_95><loc_75></location>In principle other elliptic equtions can be defined on the other boundaries of the Cartesian domain. For simplicity, however, we shall assume the B = 0 on these boundaries. For the scalar elliptic problem, this translates to P = 0 on top and side boundaries. This boundary condition also applies to the sides of the 2D domain (the lower boundary) where equation (11) is solved. In short, the numerical procedure to determine the poloidal scalar potential P involves:</text>
<unordered_list>
<list_item><location><page_2><loc_52><loc_62><loc_84><loc_63></location>1. Set P = 0 everywhere, initially, on the grid.</list_item>
<list_item><location><page_2><loc_52><loc_59><loc_95><loc_62></location>2. Use the multigrid method to solve equation (11) on the lower boundary with P = 0 on the sides.</list_item>
<list_item><location><page_2><loc_52><loc_54><loc_95><loc_59></location>3. Use the multigrid method to solve equation (8) within the domain, using P = 0 on the top and side boundaries and the distribution of P on the lower boundary determined from the previous step.</list_item>
</unordered_list>
<text><location><page_2><loc_52><loc_49><loc_95><loc_53></location>After these steps are completed, the magnetic field B can be calculated. From equation (5), the other components of the magnetic field are given by</text>
<formula><location><page_2><loc_52><loc_45><loc_64><loc_48></location>Bx = α ∂ P ∂ y + ∂ 2 P ∂ x ∂ z</formula>
<text><location><page_2><loc_52><loc_43><loc_54><loc_44></location>and</text>
<formula><location><page_2><loc_52><loc_39><loc_66><loc_42></location>By = -α ∂ P ∂ x + ∂ 2 P ∂ y ∂ z .</formula>
<text><location><page_2><loc_52><loc_33><loc_95><loc_38></location>These, together with equation (11), can be approximated using finite di ff erences, giving Bx , By and Bz on the grid to a required accuracy. In this paper, we use second-order accurate central finite di ff erences.</text>
<text><location><page_2><loc_52><loc_26><loc_95><loc_32></location>All that remains now is the calculation of the pressure p and the density ρ . Once Bz is determined on the grid, it is clear from equation (9) that p can be evaluated directly. In equation (10) the derivatives must be dealt with using finite di ff erences. After this, ρ is determined on the grid.</text>
<section_header_level_1><location><page_2><loc_52><loc_22><loc_62><loc_23></location>3. Examples</section_header_level_1>
<text><location><page_2><loc_52><loc_18><loc_95><loc_21></location>Here we present examples of equilibria to demonstrate the effectiveness of our numerical scheme. Details of computational aspects and parallelization are discussed in Section 4.</text>
<text><location><page_2><loc_52><loc_10><loc_95><loc_17></location>For the cases under consideration we non-dimensionalize equations (1) to (3) with respect to photospheric values. The variables are plasma pressure, p 0 = 1 . 4 × 10 4 Pa; density, ρ 0 = 3 × 10 -4 kg / m 3 ; scale height H 0 = 340 km; magnetic induction B 0 = (2 µ 0 p 0) 1 / 2 = 1 . 3 × 10 3 G and temperature, T 0 = p 0 / ( R ρ 0) = 5 . 6 × 10 3 K. Here, R is the gas constant.</text>
<text><location><page_3><loc_10><loc_92><loc_48><loc_93></location>We assume a background temperature profile of the form</text>
<formula><location><page_3><loc_7><loc_85><loc_28><loc_91></location>Tb ( z ) = 1 , 0 ≤ z ≤ 5 , T ( z -5) / 5 cor , 5 < z ≤ 10 , T cor , z > 10 .</formula>
<text><location><page_3><loc_7><loc_81><loc_50><loc_88></location> T cor = 150 is the non-dimensional coronal temperature. The model photosphere / chromosphere ranges from 0 ≤ z ≤ 5, the transition region ranges from 5 < z ≤ 10 and the corona is in z > 10. With an ideal gas equation</text>
<formula><location><page_3><loc_7><loc_79><loc_14><loc_80></location>pb = ρ bTb ,</formula>
<text><location><page_3><loc_7><loc_77><loc_38><loc_78></location>hydrostatic pressure balance can be written as</text>
<formula><location><page_3><loc_7><loc_74><loc_16><loc_76></location>d pb d z = -pbg Tb .</formula>
<text><location><page_3><loc_7><loc_64><loc_50><loc_73></location>The equation is solved for pb and then ρ b follows from the ideal gas law. The non-dimensionalization and atmospheric model presented here are similar to those in flux emergence studies (e.g. MacTaggart (2011), Hood et al. (2012), McLaughlin et al. (2012)). For the following cases, we set B = 0 on the side and top boundaries. The size of the domain is [ -5 . 5 , 5 . 5] 2 × [0 , 12] and we use a resolution of 128 3 .</text>
<section_header_level_1><location><page_3><loc_7><loc_61><loc_22><loc_62></location>3.1. Force-freecase</section_header_level_1>
<text><location><page_3><loc_7><loc_53><loc_50><loc_60></location>For a force-free field, ξ = 0. This, of course, means that p = pb and ρ = ρ b . In this example we take α = 0 . 4. We model a magnetic configuration with three sources, similar to that in R'egnier et al. (2005). For each source, we define a Gaussian profile for Bz , on the lower boundary, of the form</text>
<formula><location><page_3><loc_7><loc_51><loc_23><loc_53></location>Bz ( r ) = B 0 exp( -r 2 / l 2 ) .</formula>
<text><location><page_3><loc_7><loc_40><loc_50><loc_50></location>B 0 is the field strength at the centre of the source, l is source width and r 2 = ( x -x 0) 2 + ( y -y 0) 2 with source centre ( x 0 , y 0). Here we take l = 0 . 3 for all the sources. There is one positive source with Bz = 1 and two negative sources with Bz = -0 . 5. The position of the positive source is (1.5,1.5). The two negative sources have positions (-1.5,-1.5) and (1.5,-1.5). Figure 1 shows some field lines of the calculated region, with a magnetogram of Bz displayed at the base.</text>
<text><location><page_3><loc_7><loc_32><loc_50><loc_40></location>Between the two negative polarities, there is a rapid divergence in the field lines as they connect down to the positive polarity. This indicates the presence of a null point at the base of the domain. Further evidence for this can found by looking at the distribution of | B | near the base of the domain. Figure 2 displays this at z = 0 . 1.</text>
<section_header_level_1><location><page_3><loc_7><loc_29><loc_24><loc_30></location>3.2. Non-force-freecase</section_header_level_1>
<text><location><page_3><loc_7><loc_23><loc_50><loc_28></location>Having demonstrated that our multigrid scheme can successfully compute linear force-free equilibria with rapidly changing field lines and null points, we now turn our attention to the linear MHS case. For this we examine two profiles for ξ :</text>
<text><location><page_3><loc_7><loc_21><loc_23><loc_22></location>ξ 1( z ) = 0 . 7 exp( -0 . 2 z ) ,</text>
<text><location><page_3><loc_47><loc_21><loc_50><loc_22></location>(12)</text>
<formula><location><page_3><loc_7><loc_19><loc_50><loc_21></location>ξ 2( z ) = [0 . 7 + 0 . 3 sin( π z )] exp( -0 . 1 z ) . (13)</formula>
<text><location><page_3><loc_7><loc_10><loc_50><loc_19></location>These profiles are displayed in Figure 3. ξ 1( z ) is a simple exponential decay which models the fact the magnetic field becomes more force-free as one moves from the photosphere to the corona. ξ 2( z ) is also exponentially decaying but has the additional complexity of a sine wave superimposed on it. Note that both of these profiles satisfy the condition ξ ( z ) < 1 to ensure that equation (8) is elliptic.</text>
<figure>
<location><page_3><loc_52><loc_71><loc_95><loc_93></location>
<caption>Fig. 1. Magnetic field lines of the linear force-free region are displayed in orange. A magnetogram of Bz is given at the base to indicate the positions of the sources.</caption>
</figure>
<figure>
<location><page_3><loc_52><loc_55><loc_58><loc_61></location>
</figure>
<figure>
<location><page_3><loc_60><loc_41><loc_93><loc_63></location>
<caption>Fig. 2. A map of | B | , within the range given on the scale, at z = 0 . 1. The null point is clearly highlighted between the two negative polarities.</caption>
</figure>
<section_header_level_1><location><page_3><loc_52><loc_30><loc_75><loc_31></location>3.2.1. Magnetic field and current</section_header_level_1>
<text><location><page_3><loc_52><loc_25><loc_95><loc_29></location>The sigmoidal magnetic field for profile ξ 1 is displayed in Figure 4. That for ξ 2 is in Figure 5. In both figures, a magnetogram of Bz is placed at z = 0 and the field lines are shaded with |∇ × B | .</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_25></location>The magnetic field of ξ 2 is the more twisted of the two. The current is stronger at the footpoints and this is due to the initial increase in the ξ 2 profile. Although the magnetic fields for both profiles look similar, superficially at least, the structure of the current density is di ff erent. Figure 6 displays an isosurface of | j | for the ξ 1 profile field. Here, the current density is concentrated at the footpoints. Figure 7 displays the corresponding isosurface for the ξ 2-profile field. The oscillating ξ 2-profile allows for additional structure within the current density, as evidenced by an additional bridging arch in Figure 7. As one moves higher into the corona, the current density becomes weaker and the magnetic field becomes close to potential.</text>
<figure>
<location><page_4><loc_11><loc_69><loc_46><loc_92></location>
<caption>Fig. 3. The profiles of ξ ( z ) from the cross-field current.</caption>
</figure>
<figure>
<location><page_4><loc_7><loc_35><loc_50><loc_65></location>
<caption>Fig. 4. Magnetic field lines for the MHS case with ξ 1. The field lines are coloured with |∇ × B | .</caption>
</figure>
<section_header_level_1><location><page_4><loc_7><loc_27><loc_27><loc_28></location>3.2.2. Pressure and density</section_header_level_1>
<text><location><page_4><loc_7><loc_10><loc_50><loc_26></location>As is evident from equations (9) and (10), the plasma pressure and density are highly dependent on the magnetic field and the ξ -profile. Although the ξ -profiles are decreasing with height (on average for ξ 2), they are always positive. From equation (9) it is clear that the e ff ect of a positive ξ -profile is to introduce a pressure deficit where there is strong vertical magnetic field. Since the temperature is constant in the region near the photosphere, the geometrical depression, as measured from the pressure p , corresponds approximately to the Wilson depression (Spruit (1976)). For the linear MHS equilibria of this paper, a source of size ≈ 300km produces a Wilson depression of ≈ 100km. These values lie within the same order of magnitude as those given in Spruit (1976).</text>
<figure>
<location><page_4><loc_52><loc_63><loc_95><loc_93></location>
<caption>Fig. 5. Magnetic field lines for the MHS case with ξ 2. The field lines are coloured with |∇ × B | .</caption>
</figure>
<figure>
<location><page_4><loc_52><loc_33><loc_95><loc_58></location>
<caption>Fig. 6. An isosurface of | j | = 0 . 03 for the MHS solution with ξ 1.</caption>
</figure>
<text><location><page_4><loc_52><loc_10><loc_95><loc_26></location>Equation (10) demonstrates that the density enhancement or depletion is due to the competition of a magnetic pressure term combined with ξ ' ( z ) and a magnetic tension term. Considering the ξ 1-profile first, ξ ' 1 ( z ) < 0 for all z . Hence, the 'pressure' term is negative. The 'tension' term is also negative due to the fast drop in field strength of Bz with height. For the ξ 2-profile the situation is slightly more complex as ξ ' 2 ( z ) is zero, positive and negative at di ff erent heights. This means that the 'pressure' term changes sign with height. For the numerical values chosen in this paper, however, the 'tension' term dominates in magnitude. This results in two density deficits over the locations of the footpoints, as shown in Figure 8. If one chooses a 'pressure' term that is greater in magnitude than the 'tension' term, then one</text>
<figure>
<location><page_5><loc_7><loc_68><loc_50><loc_93></location>
<caption>Fig. 7. An isosurface of | j | = 0 . 03 for the MHS solution with ξ 2.</caption>
</figure>
<figure>
<location><page_5><loc_9><loc_42><loc_46><loc_63></location>
<caption>Fig. 8. The non-dimensional density along a diagonal cut through the domain at z = 0 . 46875. The two troughs correspond to the locations of the magnetic footpoints. This profile is for the linear MHS equilibrium with ξ 2.</caption>
</figure>
<text><location><page_5><loc_7><loc_31><loc_50><loc_33></location>could produce a linear MHS model with density enhancements at di ff erent heights.</text>
<section_header_level_1><location><page_5><loc_7><loc_27><loc_47><loc_28></location>4. Computational aspects of the implementation</section_header_level_1>
<text><location><page_5><loc_7><loc_10><loc_50><loc_26></location>The scheme outlined in this paper reduces the problem of solving the full linear MHS equations to a finite set of scalar elliptic problems. We have implemented a multigrid method as an efficient solver of such problems. To reduce the time taken for calculations, we have made use of the massive parallelization capabilities of graphical processing units (GPUs). The development of GPUs has been driven by the computer games industry. In the last few years, however, general purpose GPU computing (GPGPU) has grown due to the development of APIs such as CUDA (for NVIDIA GPUs) and OpenCL. The use of these languages is now an important part of scientific computing. Within solar physics, GPUs have not been exploited greatly yet. This is likely to change, however, as they give scientists the capability of</text>
<text><location><page_5><loc_52><loc_91><loc_95><loc_93></location>parallelizing their codes with hundreds or thousands of threads without having to completely redesign them.</text>
<text><location><page_5><loc_52><loc_78><loc_95><loc_90></location>For the problem in hand, the multigrid method involves various stages that can be treated in parallel. The relaxation steps (Gauss-Jacobi), the calculation of the residual and the interpolations between grids (reduction and prolongation) can each be treated in a parallel fashion. To perform this, one has to map the computational grid onto the GPU's grid of threads that can be run in parallel. We demonstrate this below with an example of how to perform Gauss-Jacobi iteration on a GPU. For an introduction to GPUs and programming in CUDA, we recommend Sanders & Kandrot (2011).</text>
<text><location><page_5><loc_52><loc_74><loc_95><loc_77></location>Subroutines that are run on the GPU are known as kernels. Below is pseudocode showing the key elements of a GaussJacobi kernel used in the multigrid evaluation of equation (11).</text>
<text><location><page_5><loc_52><loc_69><loc_88><loc_73></location>ix = threadIdx.x + blockIdx.x*blockDim.x; iy = threadIdx.y + blockIdx.y*blockDim.y; off = ix + iy * blockDim.x * gridDim.x;</text>
<text><location><page_5><loc_52><loc_66><loc_58><loc_67></location>io = 1;</text>
<text><location><page_5><loc_52><loc_65><loc_60><loc_66></location>jo = DIM;</text>
<text><location><page_5><loc_52><loc_63><loc_70><loc_64></location>invdx2 = 1.0/(dx*dx);</text>
<text><location><page_5><loc_52><loc_61><loc_70><loc_62></location>invdy2 = 1.0/(dy*dy);</text>
<text><location><page_5><loc_52><loc_59><loc_68><loc_60></location>if ( on boundary )</text>
<text><location><page_5><loc_52><loc_57><loc_53><loc_58></location>{</text>
<text><location><page_5><loc_52><loc_56><loc_69><loc_57></location>set d_P2[off] here;</text>
<text><location><page_5><loc_52><loc_55><loc_53><loc_56></location>}</text>
<text><location><page_5><loc_52><loc_53><loc_57><loc_54></location>else {</text>
<text><location><page_5><loc_52><loc_52><loc_96><loc_53></location>d_P2[off] = ( (d_P1[off+io] + d_P1[off-io])*invdx2</text>
<text><location><page_5><loc_62><loc_51><loc_96><loc_52></location>+ (d_P1[off+jo] + d_P1[off-jo])*invdy2</text>
<text><location><page_5><loc_62><loc_50><loc_95><loc_51></location>+ Bz[off] ) / (2.0*(invdx2+invdy2) );</text>
<text><location><page_5><loc_52><loc_48><loc_53><loc_49></location>}</text>
<text><location><page_5><loc_52><loc_32><loc_95><loc_46></location>The first three lines of pseudocode link the node positions of the computational grid to that of the GPU, which consists of blocks that are divided into threads. Here we have one thread per node. In the x -direction, threadIdx.x is the thread index, blockIdx.x is the block index and blockDim.x is the number of threads per block. This combination gives the ix position. The iy position is found similarly. The third line of pseudocode calculates an o ff set that allows one to write all the positions on a 2D grid within a 1D array. Here, gridDim.x is the number of blocks in the x -direction. In this example, it is the same number as in the y -direction.</text>
<text><location><page_5><loc_52><loc_24><loc_95><loc_32></location>Now that a thread is linked to every node, we must be able to perform calculations involving nodes at di ff erent positions. To move to a neighbouring node in the x -direction, io=1 is added to or taken from off . Similarly, to move to a neighbouring node in the y -direction, jo=DIM is added to or taken from off . Here, DIM is the dimension of the grid in the x -direction.</text>
<text><location><page_5><loc_52><loc_14><loc_95><loc_24></location>With the grid set up, and the ability to move through it, the finite di ff erence implementation of one iteration of Gauss-Jacobi relaxation is simple to implement. In the pseudocode, there is one command for points on the boundary and another for points in the interior. Values from the previous iteration are read from d_P1[] . The new values of the Gauss-Jacobi iteration are written to d_P2[] . Both variables begin with d to highlight that they are on the device (GPU) as opposed to the host (CPU).</text>
<text><location><page_5><loc_52><loc_10><loc_95><loc_13></location>This example demonstrates how one can parallelize a finite di ff erence scheme simply. Edits to codes can be made function by function, rather than having to redesign from scratch. The</text>
<text><location><page_6><loc_7><loc_81><loc_50><loc_93></location>purpose of this endeavour is, of course, to achieve a sizeable speed-up in the running of a code. Figure 9 compares the run times of the serial and parallel versions of the multigrid code for di ff erent resolutions. For these calculations, we use the same parameters as for the MHS case described in the paper but set ξ = 0. i.e. we solve the force-free case. As the resolution increases, the benefits of the parallel code run on the GPU become obvious. For resolutions of 128 3 and 256 3 , impressive speed-ups of × 32.418 and × 29.632 are achieved respectively.</text>
<section_header_level_1><location><page_6><loc_7><loc_78><loc_17><loc_79></location>5. Summary</section_header_level_1>
<text><location><page_6><loc_7><loc_73><loc_50><loc_77></location>In this paper we calculate linear MHS equilibria with an e ffi -cient numerical scheme based on the representation of NR99. The outline algorithm of this scheme is as follows:</text>
<unordered_list>
<list_item><location><page_6><loc_8><loc_70><loc_50><loc_72></location>· Calculate the background equilibrium plasma plasma pressure pb and density ρ b .</list_item>
<list_item><location><page_6><loc_8><loc_66><loc_50><loc_70></location>· Prescribe Bz on the lower boundary and find the poloidal scalar potential P on this boundary by solving, using a multigrid method, the Poisson equation</list_item>
</unordered_list>
<formula><location><page_6><loc_10><loc_62><loc_22><loc_65></location>∂ 2 P ∂ x 2 + ∂ 2 P ∂ y 2 = -Bz ,</formula>
<text><location><page_6><loc_10><loc_60><loc_35><loc_62></location>with P defined on the side boundaries.</text>
<unordered_list>
<list_item><location><page_6><loc_8><loc_58><loc_50><loc_60></location>· Define the other boundary conditions for P , choose ξ < 1 and α , and solve, using a multigrid method,</list_item>
</unordered_list>
<formula><location><page_6><loc_10><loc_54><loc_38><loc_57></location>[1 -ξ ( z )] ( ∂ 2 P ∂ x 2 + ∂ 2 P ∂ y 2 ) + ∂ 2 P ∂ z 2 + α 2 P = 0 .</formula>
<unordered_list>
<list_item><location><page_6><loc_8><loc_52><loc_50><loc_53></location>· Calculate the magnetic field by applying finite di ff erences to</list_item>
</unordered_list>
<formula><location><page_6><loc_10><loc_50><loc_29><loc_51></location>B = ∇× [ ∇× ( P ˆ e z ) + α P ˆ e z ] .</formula>
<unordered_list>
<list_item><location><page_6><loc_8><loc_48><loc_34><loc_49></location>· Calculate the pressure directly using</list_item>
</unordered_list>
<formula><location><page_6><loc_10><loc_44><loc_24><loc_47></location>p = pb ( z ) -ξ ( z ) B 2 z 2 µ 0 .</formula>
<unordered_list>
<list_item><location><page_6><loc_8><loc_42><loc_43><loc_43></location>· Use finite di ff erences to calculate the density with</list_item>
</unordered_list>
<formula><location><page_6><loc_10><loc_38><loc_36><loc_41></location>ρ = ρ b ( z ) + 1 g ( d ξ d z B 2 z 2 µ 0 + 1 µ 0 ξ B · ∇ Bz ) .</formula>
<text><location><page_6><loc_7><loc_23><loc_50><loc_37></location>The elegance of the NR99 formulation allows for an e ffi cient numerical solution. We demonstrate the above scheme by calculating linear force-free and linear MHS equilibria. For the forcefree case, we calculate an equilibrium with three footpoints and a null point. For the linear MHS case, we consider a region with two footpoints and investigate the e ff ects of changing ξ . We consider profiles that cannot be treated, in the NR99 formalism, analytically and demonstrate how these can change the structure of the current distribution within the domain. We also show that the linear MHS equilibria are consistent with the Wilson e ff ect for the size of the regions considered.</text>
<text><location><page_6><loc_7><loc_13><loc_50><loc_23></location>As well as demonstrating the scheme to be accurate, we show that the calculation time can be significantly reduced through parallelization on a GPU. This is achieved function by function and speed-ups of × 30 are realized. This result is significant as GPUs are inexpensive and readily available, unlike compute clusters and supercomputers. This fast and accurate scheme could be used for calculating equilibria in their own right or as input to MHD codes.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_12></location>Acknowledgements. DM would like to thank the Royal Astronomical Society for financial support. JM acknowledges IDL support provided by STFC.</text>
<section_header_level_1><location><page_6><loc_52><loc_92><loc_60><loc_93></location>References</section_header_level_1>
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<text><location><page_6><loc_52><loc_82><loc_69><loc_82></location>Low, B.C. 1991, ApJ, 370, 427</text>
<text><location><page_6><loc_52><loc_81><loc_69><loc_81></location>Low, B.C. 1992, ApJ, 399, 300</text>
<text><location><page_6><loc_52><loc_79><loc_73><loc_80></location>MacTaggart, D. 2011, A&A, 531, A108</text>
<text><location><page_6><loc_52><loc_78><loc_90><loc_79></location>McLaughlin, J.A., Verth. G., Fedun, V., Erd´elyi, R. 2012, ApJ, 749, 30</text>
<text><location><page_6><loc_52><loc_77><loc_80><loc_78></location>Neukirch, T. & Rast¨atter, L. 1999, A&A, 348, 1000</text>
<text><location><page_6><loc_52><loc_76><loc_80><loc_77></location>Petrie, G.J.D. & Neukirch, T. 2000, A&A, 356, 735</text>
<text><location><page_6><loc_52><loc_75><loc_85><loc_76></location>R´egnier, S., Amari, T. & Canfield, R.C. 2005, A&A, 442, 345</text>
<text><location><page_6><loc_52><loc_74><loc_95><loc_75></location>Sanders, J. & Kandrot, E. 2011, CUDA by Example: An Introduction to General</text>
<text><location><page_6><loc_54><loc_73><loc_79><loc_74></location>Purpose GPU Programming, Addison-Wesley</text>
<text><location><page_6><loc_52><loc_72><loc_72><loc_73></location>Spruit, H.C. 1976, Sol. Phys., 50, 269</text>
<figure>
<location><page_7><loc_16><loc_65><loc_87><loc_93></location>
<caption>Fig. 9. The run times for the serial (blue) and parallel (green) versions of the multigrid code plotted against resolution. Each run time corresponds to the combined time for a 2D multigrid method calculation on the base of the domain and a 3D multigrid method calculation within the domain.</caption>
</figure>
<text><location><page_8><loc_16><loc_53><loc_19><loc_54></location>ρ</text>
<figure>
<location><page_8><loc_17><loc_34><loc_77><loc_71></location>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "Aims. Linear magnetohydrostatic (MHS) models of solar magnetic fields balance plasma pressure gradients, gravity and Lorentz forces where the current density is composed of a linear force-free component and a cross-field component that depends on gravitational stratification. In this paper, we investigate an e ffi cient numerical procedure for calculating such equilibria. Methods. The MHS equations are reduced to two scalar elliptic equations - one on the lower boundary and the other within the interior of the computational domain. The normal component of the magnetic field is prescribed on the lower boundary and a multigrid method is applied on both this boundary and within the domain to find the poloidal scalar potential. Once solved to a desired accuracy, the magnetic field, plasma pressure and density are found using a finite di ff erence method. Results. We investigate the e ff ects of the cross-field currents on the linear MHS equilibria. Force-free and non-force-free examples are given to demonstrate the numerical scheme and an analysis of speed-up due to parallelization on a graphics processing unit (GPU) is presented. It is shown that speed-ups of × 30 are readily achievable. Key words. Sun: magnetic fields - Magnetohydrodynamics (MHD) - Methods: numerical",
"pages": [
1
]
},
{
"title": "Non-symmetric magnetohydrostatic equilibria: a multigrid approach",
"content": "D. MacTaggart 1 , A. Elsheikh 1 , J. A. McLaughlin 2 and R. D. Simitev 3",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The calculation of three-dimensional non-linear magnetohydrostatic (MHS) equilibria is a non-trivial subject. In the solar physics context, progress has been made by considering linear subclasses of MHS equilibria. One such class, known as laminated equilibria, makes use of an Euler potential representation of the magnetic field (e.g. Low (1982)). On each lamina, a 2D magnetic field is calculated and the 3D field comprises of the union of these laminas. Another approach is to model the current density as a linear combination of field-aligned and cross-field currents (Low (1991), Low (1992)). Here, the field-aligned current is that of a linear force-free field and the cross-field current depends on the variation of the magnetic field with height. Details of this will be presented in the next section. Neukirch & Rastatter (1999) (NR99 hereafter) present a new formulation of Low's model by writing the magnetic field in terms of poloidal and toroidal components. This has the advantage that the calculation of the magnetic field only involves one scalar function whereas, previously, one was forced to operate with all three components of the magnetic field independently. Petrie & Neukirch (2000) use the representation of NR99 and find closed-form solutions for MHSequilibria via Green's functions. The price paid for finding closed-form solutions, however, is that they are forced to choose a simple term for the cross-field current. To date, the authors are unaware of any closed-form solutions using Green's functions, other than those presented in Petrie & Neukirch (2000). Although more detailed analytical solutions may prove di ffi -cult with the representation of NR99, it is, however, set up per- Send o ff print requests to : D. MacTaggart, e-mail: fectly for an e ffi cient numerical treatment. In this paper, we outline a simple and fast numerical procedure for calculating MHS equilibria based on the NR99 representation. The details of this are given in the next section. This is followed by some examples of force-free and linear MHS equilibria. For the linear MHS case, we investigate the e ff ects of the cross-field currents on the equilibria. We then highlight how the scheme can be parallelized simply and e ff ectively on a graphics processing unit (GPU). The paper concludes with a summary.",
"pages": [
1
]
},
{
"title": "2. Model equations and solution method",
"content": "Firstly, we shall outline where the equations to be solved come from. Fuller details can be found in NR99. This will be followed by an algorithm for the numerical solution.",
"pages": [
1
]
},
{
"title": "2.1. Themodelequations",
"content": "The MHS equations that we shall solve are ∇ · B = 0 , (3) where B is the magnetic induction (commonly referred to as the magnetic field), j is the current density, p is the plasma presure, ρ is the density, g is the (constant) gravitational acceleration and µ 0 is the permeability of free space. To complete the problem, boundary conditions must be specified. This choice is problem-dependentbut will, at least, require B to be specified on the boundaries of the domain through Dirichlet or von Neuman conditions. In this paper we will consider a Cartesian domain. Following Low (1992), we assume the current density takes the following form where α is a constant and F is an arbitrary function. The first term on the right-hand-side is the aligned current associated with a linear force-free field. The second term is the non-force-free cross current due to the gravitational stratification. The magnetic induction can be written as where P and T are scalar functions corresponding to the poloidal and toroidal components respectively. This form satisfies equation (3). Using this in equation (2) with equation (4) gives Following NR99 and Low (1992), we set F = g - 1 ξ ( z ) Bz . With this identity, equation (7) becomes For ξ ( z ) < 1, equation (8) is elliptic. Now the magnetic field can be found by solving this for the poloidal scalar potential P and then using equations (5) and (6). Once the magnetic field is found, the plasma pressure and density are given by and pb and ρ b are the background equilibrium plasma pressure and density respectively. A derivation of these formulae is given in NR99.",
"pages": [
1,
2
]
},
{
"title": "2.2. Thenumericalprocedure",
"content": "An e ffi cient numerical solution of this class of the MHS equations rests on reducing the equations to a set of linear, scalar elliptic problems. i.e. those of the form with u defined on ∂ D . Here the Laplacian operator can be twodimensional (for boundaries) or three-dimensional (for the interior) and a , b and c are known scalar functions. There exists a wide variety of techniques to solve such problems e ffi ciently, from Krylov subspace methods to multigrid methods. Although solution methods are problem-dependent, the multigrid method is often an optimal solver for discrete Poisson problems (Elman et al. (2005)), i.e. its convergence rate is independent of the problem mesh size. It can also be parallelized e ffi ciently, and for these reasons we adopt it in this work. The multigrid method, in a di ff erent representation to the one of this paper, was used successfully for MHS models of flux tubes bounded by current sheets (Henning & Cally (2001)). As mentioned above, the MHS equations are reduced to a set of linear elliptic problems defined on the boundaries and in the interior. Equation (8) is the three-dimensional elliptic problem for the poloidal scalar potential P defined in the interior of the domain. The other elliptic equations required to be solved depend on the boundary conditions. On the lower boundary, the vertical component of the magnetic field, Bz , is prescribed. From equation (5), it is clear that, on the lower boundary, In principle other elliptic equtions can be defined on the other boundaries of the Cartesian domain. For simplicity, however, we shall assume the B = 0 on these boundaries. For the scalar elliptic problem, this translates to P = 0 on top and side boundaries. This boundary condition also applies to the sides of the 2D domain (the lower boundary) where equation (11) is solved. In short, the numerical procedure to determine the poloidal scalar potential P involves: After these steps are completed, the magnetic field B can be calculated. From equation (5), the other components of the magnetic field are given by and These, together with equation (11), can be approximated using finite di ff erences, giving Bx , By and Bz on the grid to a required accuracy. In this paper, we use second-order accurate central finite di ff erences. All that remains now is the calculation of the pressure p and the density ρ . Once Bz is determined on the grid, it is clear from equation (9) that p can be evaluated directly. In equation (10) the derivatives must be dealt with using finite di ff erences. After this, ρ is determined on the grid.",
"pages": [
2
]
},
{
"title": "3. Examples",
"content": "Here we present examples of equilibria to demonstrate the effectiveness of our numerical scheme. Details of computational aspects and parallelization are discussed in Section 4. For the cases under consideration we non-dimensionalize equations (1) to (3) with respect to photospheric values. The variables are plasma pressure, p 0 = 1 . 4 × 10 4 Pa; density, ρ 0 = 3 × 10 -4 kg / m 3 ; scale height H 0 = 340 km; magnetic induction B 0 = (2 µ 0 p 0) 1 / 2 = 1 . 3 × 10 3 G and temperature, T 0 = p 0 / ( R ρ 0) = 5 . 6 × 10 3 K. Here, R is the gas constant. We assume a background temperature profile of the form T cor = 150 is the non-dimensional coronal temperature. The model photosphere / chromosphere ranges from 0 ≤ z ≤ 5, the transition region ranges from 5 < z ≤ 10 and the corona is in z > 10. With an ideal gas equation hydrostatic pressure balance can be written as The equation is solved for pb and then ρ b follows from the ideal gas law. The non-dimensionalization and atmospheric model presented here are similar to those in flux emergence studies (e.g. MacTaggart (2011), Hood et al. (2012), McLaughlin et al. (2012)). For the following cases, we set B = 0 on the side and top boundaries. The size of the domain is [ -5 . 5 , 5 . 5] 2 × [0 , 12] and we use a resolution of 128 3 .",
"pages": [
2,
3
]
},
{
"title": "3.1. Force-freecase",
"content": "For a force-free field, ξ = 0. This, of course, means that p = pb and ρ = ρ b . In this example we take α = 0 . 4. We model a magnetic configuration with three sources, similar to that in R'egnier et al. (2005). For each source, we define a Gaussian profile for Bz , on the lower boundary, of the form B 0 is the field strength at the centre of the source, l is source width and r 2 = ( x -x 0) 2 + ( y -y 0) 2 with source centre ( x 0 , y 0). Here we take l = 0 . 3 for all the sources. There is one positive source with Bz = 1 and two negative sources with Bz = -0 . 5. The position of the positive source is (1.5,1.5). The two negative sources have positions (-1.5,-1.5) and (1.5,-1.5). Figure 1 shows some field lines of the calculated region, with a magnetogram of Bz displayed at the base. Between the two negative polarities, there is a rapid divergence in the field lines as they connect down to the positive polarity. This indicates the presence of a null point at the base of the domain. Further evidence for this can found by looking at the distribution of | B | near the base of the domain. Figure 2 displays this at z = 0 . 1.",
"pages": [
3
]
},
{
"title": "3.2. Non-force-freecase",
"content": "Having demonstrated that our multigrid scheme can successfully compute linear force-free equilibria with rapidly changing field lines and null points, we now turn our attention to the linear MHS case. For this we examine two profiles for ξ : ξ 1( z ) = 0 . 7 exp( -0 . 2 z ) , (12) These profiles are displayed in Figure 3. ξ 1( z ) is a simple exponential decay which models the fact the magnetic field becomes more force-free as one moves from the photosphere to the corona. ξ 2( z ) is also exponentially decaying but has the additional complexity of a sine wave superimposed on it. Note that both of these profiles satisfy the condition ξ ( z ) < 1 to ensure that equation (8) is elliptic.",
"pages": [
3
]
},
{
"title": "3.2.1. Magnetic field and current",
"content": "The sigmoidal magnetic field for profile ξ 1 is displayed in Figure 4. That for ξ 2 is in Figure 5. In both figures, a magnetogram of Bz is placed at z = 0 and the field lines are shaded with |∇ × B | . The magnetic field of ξ 2 is the more twisted of the two. The current is stronger at the footpoints and this is due to the initial increase in the ξ 2 profile. Although the magnetic fields for both profiles look similar, superficially at least, the structure of the current density is di ff erent. Figure 6 displays an isosurface of | j | for the ξ 1 profile field. Here, the current density is concentrated at the footpoints. Figure 7 displays the corresponding isosurface for the ξ 2-profile field. The oscillating ξ 2-profile allows for additional structure within the current density, as evidenced by an additional bridging arch in Figure 7. As one moves higher into the corona, the current density becomes weaker and the magnetic field becomes close to potential.",
"pages": [
3
]
},
{
"title": "3.2.2. Pressure and density",
"content": "As is evident from equations (9) and (10), the plasma pressure and density are highly dependent on the magnetic field and the ξ -profile. Although the ξ -profiles are decreasing with height (on average for ξ 2), they are always positive. From equation (9) it is clear that the e ff ect of a positive ξ -profile is to introduce a pressure deficit where there is strong vertical magnetic field. Since the temperature is constant in the region near the photosphere, the geometrical depression, as measured from the pressure p , corresponds approximately to the Wilson depression (Spruit (1976)). For the linear MHS equilibria of this paper, a source of size ≈ 300km produces a Wilson depression of ≈ 100km. These values lie within the same order of magnitude as those given in Spruit (1976). Equation (10) demonstrates that the density enhancement or depletion is due to the competition of a magnetic pressure term combined with ξ ' ( z ) and a magnetic tension term. Considering the ξ 1-profile first, ξ ' 1 ( z ) < 0 for all z . Hence, the 'pressure' term is negative. The 'tension' term is also negative due to the fast drop in field strength of Bz with height. For the ξ 2-profile the situation is slightly more complex as ξ ' 2 ( z ) is zero, positive and negative at di ff erent heights. This means that the 'pressure' term changes sign with height. For the numerical values chosen in this paper, however, the 'tension' term dominates in magnitude. This results in two density deficits over the locations of the footpoints, as shown in Figure 8. If one chooses a 'pressure' term that is greater in magnitude than the 'tension' term, then one could produce a linear MHS model with density enhancements at di ff erent heights.",
"pages": [
4,
5
]
},
{
"title": "4. Computational aspects of the implementation",
"content": "The scheme outlined in this paper reduces the problem of solving the full linear MHS equations to a finite set of scalar elliptic problems. We have implemented a multigrid method as an efficient solver of such problems. To reduce the time taken for calculations, we have made use of the massive parallelization capabilities of graphical processing units (GPUs). The development of GPUs has been driven by the computer games industry. In the last few years, however, general purpose GPU computing (GPGPU) has grown due to the development of APIs such as CUDA (for NVIDIA GPUs) and OpenCL. The use of these languages is now an important part of scientific computing. Within solar physics, GPUs have not been exploited greatly yet. This is likely to change, however, as they give scientists the capability of parallelizing their codes with hundreds or thousands of threads without having to completely redesign them. For the problem in hand, the multigrid method involves various stages that can be treated in parallel. The relaxation steps (Gauss-Jacobi), the calculation of the residual and the interpolations between grids (reduction and prolongation) can each be treated in a parallel fashion. To perform this, one has to map the computational grid onto the GPU's grid of threads that can be run in parallel. We demonstrate this below with an example of how to perform Gauss-Jacobi iteration on a GPU. For an introduction to GPUs and programming in CUDA, we recommend Sanders & Kandrot (2011). Subroutines that are run on the GPU are known as kernels. Below is pseudocode showing the key elements of a GaussJacobi kernel used in the multigrid evaluation of equation (11). ix = threadIdx.x + blockIdx.x*blockDim.x; iy = threadIdx.y + blockIdx.y*blockDim.y; off = ix + iy * blockDim.x * gridDim.x; io = 1; jo = DIM; invdx2 = 1.0/(dx*dx); invdy2 = 1.0/(dy*dy); if ( on boundary ) { set d_P2[off] here; } else { d_P2[off] = ( (d_P1[off+io] + d_P1[off-io])*invdx2 + (d_P1[off+jo] + d_P1[off-jo])*invdy2 + Bz[off] ) / (2.0*(invdx2+invdy2) ); } The first three lines of pseudocode link the node positions of the computational grid to that of the GPU, which consists of blocks that are divided into threads. Here we have one thread per node. In the x -direction, threadIdx.x is the thread index, blockIdx.x is the block index and blockDim.x is the number of threads per block. This combination gives the ix position. The iy position is found similarly. The third line of pseudocode calculates an o ff set that allows one to write all the positions on a 2D grid within a 1D array. Here, gridDim.x is the number of blocks in the x -direction. In this example, it is the same number as in the y -direction. Now that a thread is linked to every node, we must be able to perform calculations involving nodes at di ff erent positions. To move to a neighbouring node in the x -direction, io=1 is added to or taken from off . Similarly, to move to a neighbouring node in the y -direction, jo=DIM is added to or taken from off . Here, DIM is the dimension of the grid in the x -direction. With the grid set up, and the ability to move through it, the finite di ff erence implementation of one iteration of Gauss-Jacobi relaxation is simple to implement. In the pseudocode, there is one command for points on the boundary and another for points in the interior. Values from the previous iteration are read from d_P1[] . The new values of the Gauss-Jacobi iteration are written to d_P2[] . Both variables begin with d to highlight that they are on the device (GPU) as opposed to the host (CPU). This example demonstrates how one can parallelize a finite di ff erence scheme simply. Edits to codes can be made function by function, rather than having to redesign from scratch. The purpose of this endeavour is, of course, to achieve a sizeable speed-up in the running of a code. Figure 9 compares the run times of the serial and parallel versions of the multigrid code for di ff erent resolutions. For these calculations, we use the same parameters as for the MHS case described in the paper but set ξ = 0. i.e. we solve the force-free case. As the resolution increases, the benefits of the parallel code run on the GPU become obvious. For resolutions of 128 3 and 256 3 , impressive speed-ups of × 32.418 and × 29.632 are achieved respectively.",
"pages": [
5,
6
]
},
{
"title": "5. Summary",
"content": "In this paper we calculate linear MHS equilibria with an e ffi -cient numerical scheme based on the representation of NR99. The outline algorithm of this scheme is as follows: with P defined on the side boundaries. The elegance of the NR99 formulation allows for an e ffi cient numerical solution. We demonstrate the above scheme by calculating linear force-free and linear MHS equilibria. For the forcefree case, we calculate an equilibrium with three footpoints and a null point. For the linear MHS case, we consider a region with two footpoints and investigate the e ff ects of changing ξ . We consider profiles that cannot be treated, in the NR99 formalism, analytically and demonstrate how these can change the structure of the current distribution within the domain. We also show that the linear MHS equilibria are consistent with the Wilson e ff ect for the size of the regions considered. As well as demonstrating the scheme to be accurate, we show that the calculation time can be significantly reduced through parallelization on a GPU. This is achieved function by function and speed-ups of × 30 are realized. This result is significant as GPUs are inexpensive and readily available, unlike compute clusters and supercomputers. This fast and accurate scheme could be used for calculating equilibria in their own right or as input to MHD codes. Acknowledgements. DM would like to thank the Royal Astronomical Society for financial support. JM acknowledges IDL support provided by STFC.",
"pages": [
6
]
},
{
"title": "References",
"content": "Aulanier, G., D'emoulin, P., Schmieder, B., Fang, C. & Tang, Y.H. 1998, Sol. Phys., 183, 369 Elman, H.C., Silvester, D.J., Wathen, A.J. 2005, Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, Oxford University Press Henning, B.S. & Cally, P.S. 2001, Sol. Phys., 201, 289 Hood, A.W., Archontis, V. & MacTaggart, D. 2012, Sol. Phys., 278, 3 Low, B.C. 1982, ApJ, 263, 952 Low, B.C. 1991, ApJ, 370, 427 Low, B.C. 1992, ApJ, 399, 300 MacTaggart, D. 2011, A&A, 531, A108 McLaughlin, J.A., Verth. G., Fedun, V., Erd´elyi, R. 2012, ApJ, 749, 30 Neukirch, T. & Rast¨atter, L. 1999, A&A, 348, 1000 Petrie, G.J.D. & Neukirch, T. 2000, A&A, 356, 735 R´egnier, S., Amari, T. & Canfield, R.C. 2005, A&A, 442, 345 Sanders, J. & Kandrot, E. 2011, CUDA by Example: An Introduction to General Purpose GPU Programming, Addison-Wesley Spruit, H.C. 1976, Sol. Phys., 50, 269 ρ",
"pages": [
6,
8
]
}
]
2013A&A...556A..96V
https://arxiv.org/pdf/1305.4050.pdf
<document>
<section_header_level_1><location><page_1><loc_20><loc_82><loc_82><loc_87></location>An approach for the detection of point sources in very high-resolution microwave maps</section_header_level_1>
<text><location><page_1><loc_16><loc_80><loc_85><loc_81></location>Roberto Vio 1 , Paola Andreani 2 Elsa Patr'ıcia R. G. Ramos 2 , 3 , 4 , and Antonio da Silva 3</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_76><loc_80><loc_78></location>1 Chip Computers Consulting s.r.l., Viale Don L. Sturzo 82, S.Liberale di Marcon, 30020 Venice, Italy e-mail: [email protected] ,</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_54><loc_76></location>2 ESO, Karl Schwarzschild strasse 2, 85748 Garching, Germany</list_item>
<list_item><location><page_1><loc_12><loc_73><loc_30><loc_74></location>e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_73><loc_73></location>3 Centro de Astrof'ısica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal e-mail: [email protected] e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_68><loc_91><loc_70></location>4 Departamento de F'ısica e Astronomia, Faculdade de Ciˆencias, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_65><loc_37><loc_66></location>Received .............; accepted ................</text>
<section_header_level_1><location><page_1><loc_47><loc_63><loc_55><loc_64></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_36><loc_91><loc_62></location>This paper deals with the detection problem of extragalactic point sources in multi-frequency, microwave sky maps that will be obtainable in future cosmic microwave background radiation (CMB) experiments with instruments capable of very high spatial resolution. With spatial resolutions that can be 0 . 1-1 . 0 arcsec or better, the extragalactic point sources will appear isolated. The same also holds for the compact structures due to the Sunyaev-Zeldovich (SZ) effect (both thermal and kinetic). This situation is different from the maps obtainable with instruments such as WMAP or PLANCK where, because of the lower spatial resolution ( ≈ 5-30 arcmin), the point sources and the compact structures due to the SZ effect form a uniform noisy background (' confusion noise '). The point source detection techniques developed in the past are therefore based on the assumption that all the emissions that contribute to the microwave background can be modeled with homogeneous and isotropic (often Gaussian) random fields and make use of the corresponding spatial power spectra. In the case of very high-resolution observations, such an assumption cannot be adopted since it still holds only for the CMB. Here, we propose an approach based on the assumption that the diffuse emissions that contribute to the microwave background can be locally approximated by two-dimensional low-order polynomials. In particular, two sets of numerical techniques are presented that contain two different algorithms each. The first set makes use of the a-priori information about the spectral properties of CMB and SZ and is suited to detecting an extragalactic point source with a different spectrum for these emissions. In this set, one algorithm is a modification of the internal linear combination (ILC) method, which is widely used in cosmology to extract the component of interest from a mixture of signals, and it is appropriate for extragalactic point sources with a known spectrum. The other one does not make use of this piece of information. The second set is tailored to detecting of extragalactic point sources with a similar spectrum to that of the CMB or SZ. Also in this set one algorithm is specific for extragalactic point sources with known spectrum whereas the other does not make use of this information. The performance of the algorithms is tested with numerical experiments that mimic the physical scenario expected for high Galactic latitude observations with the Atacama Large Millimeter/Submillimeter Array (ALMA).</text>
<text><location><page_1><loc_11><loc_34><loc_80><loc_35></location>Key words. Methods: data analysis - Methods: statistical - Cosmology: cosmic microwave background</text>
<section_header_level_1><location><page_1><loc_7><loc_30><loc_20><loc_31></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_10><loc_50><loc_28></location>The detection of extragalactic point sources in experimental microwave maps is a critical step in analyzing of the cosmic microwave background (CMB) maps. Besides the specific interest related to constructing of dedicated catalogs, these sources can, if not properly removed, have adverse effects on the estimation of the power spectrum and/or the test of Gaussianity of the CMB component. Much effort has been dedicated to multiple frequency maps of the same sky area, and many algorithms have been proposed (see Herranz and Sanz 2008; Herranz et al. 2012, and references therein). Apart from a recent Bayesian approach (Carvalho et al. 2009), most of them belong to two broad classes of techniques. The first class, suited to the extragalactic point sources with known spectra, is based on the</text>
<text><location><page_1><loc_52><loc_11><loc_95><loc_31></location>Neyman-Pearson (NP) criterion that consists in maximizing the probability of detection P D under the constraint that the probability of false alarm P FA (i.e., the probability of a false detection) does not exceed a fixed value α (Kay 1998). The resulting algorithms are extensions of the classic matched filter (MF) (Herranz et al. 2002; Ramos et al. 2011). The second class, appropriated to the extragalactic point sources with unknown spectra, is based on maximizing of the ' signal-to-noise ratio ' (S / N) of the source intensity with respect to the underlying background (Herranz et al. 2009; Lanz et al. 2010). Both classes require the spatial power spectrum of the emitting components and therefore are based on the assumption that the emissions contributing to the microwave sky can be modeled by means of homogeneous and isotropic random fields.</text>
<text><location><page_2><loc_7><loc_70><loc_50><loc_93></location>With a spatial resolution worse than 5 arcmin typical of Planck and WMAP experiments, such an assumption is excellent for the CMB, good for the confusion noise due to the point sources and the Sunyaev-Zeldovich (SZ) effect component, and locally barely acceptable for the diffuse Galactic emission. In the case of observation at very high spatial resolution, of order of 0 . 1-1 . 0 arcsec (that will be possible, for instance, with instruments as ALMA), this is no longer true. Indeed, since almost all of the extragalactic point sources but also of the compact structures due to the SZ effect will appear isolated, they can be thought of as the realization of (not necessarily stationary) shot-noise processes. Moreover, on small observing areas, it is realistic to expect that any other additional diffuse component (e.g. due to the Galactic emissions) is almost constant or slowly changing. This experimental scenario is different from the past or ongoing CMB experiments. New techniques of point source detection are therefore necessary.</text>
<text><location><page_2><loc_7><loc_38><loc_50><loc_69></location>From the consideration that the detection of extragalactic point sources is typically done on very small areas of the sky, where the contribution of the diffuse components can be approximated well by means of low-degree, twodimensional polynomials, we propose an approach based on two sets of algorithms. The first set makes use of the a-priori information about the spectral properties of CMB and SZ, and the second one does not exploit this piece of information. Each set contains two algorithms that are suited to detecting point sources with known and unknown spectra, respectively. The reason for two different sets of algorithms is that the use of the spectral properties of the CMB and SZ permits removal of the contribution from these components. As a consequence, the knowledge of their spatial power spectrum is no longer necessary, and at the same time it is possible to unambiguously distinguish between true extragalactic point sources and the compact structures due to SZ. The price is a reduced, or even null, detection capability for the point sources with spectra that are similar, or even identical, to that of CMB, SZ, or to a linear combination of these. The algorithms that do no make use of this piece of information do not suffer this limitation, but they cannot distinguish the true extragalactic point sources from the compact structures due to SZ.</text>
<text><location><page_2><loc_7><loc_12><loc_50><loc_38></location>The reason for two algorithms within each set is that those specialized for the extragalactic point sources with a specific spectrum are characterized by a greater detection capability. They are obtained by modifying the internal linear combination (ILC) method that in cosmology is used to extract a component of interest from the mixture of signals that contribute to the microwave sky emission (Eriksen et al. 2004; Hinshaw et al. 2007; Vio and Andreani 2008). Their main limitation is the necessity of multiple applications for detecting point sources with different spectra. Such a necessity is avoided by the algorithms that do not exploit this piece of information but at the price of less detection capability. The combined use of a couple of these algorithms belonging to different sets permits the detection of extragalactic point sources independently of their spectral emission and reduced contamination due to the SZ compact structures. The performances of both sets of algorithms is tested via numerical experiments based on simulated maps of high Galactic latitude that might be the area of interest of CMB high spatial resolution observations.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_12></location>The paper is organized as follows. Section 2 introduces the mathematical framework and explains the algorithms</text>
<text><location><page_2><loc_52><loc_88><loc_95><loc_93></location>used. Section 3 discusses practical problems related to the choice of the experimental parameters. Numerical experiments are reported in section 4, while conclusions are summarized in section 5.</text>
<section_header_level_1><location><page_2><loc_52><loc_84><loc_89><loc_85></location>2. Formalization and solution of the problem</section_header_level_1>
<text><location><page_2><loc_52><loc_77><loc_95><loc_83></location>By searching for a single extragalactic point source in a small area of sky, the microwave emission can be modeled with bidimensional discrete patches { X i } N f i =1 , each of them containing N p = N p 1 × N p 2 pixels, corresponding to N f different observing frequencies (channels), with the form</text>
<formula><location><page_2><loc_62><loc_74><loc_95><loc_75></location>X i = S i + C i + Z i + G i + N i . (1)</formula>
<text><location><page_2><loc_52><loc_64><loc_95><loc_73></location>Here, S i is the contribution of the extragalactic point source at the i th frequency, C i , Z i , and G i are the backgrounds due to CMB, extragalactic emission, and some other possible diffuse component (e.g. Galactic emission), respectively, and N i is the instrumental noise. In this model, the contribution of the extragalactic point sources is assumed in the form</text>
<formula><location><page_2><loc_70><loc_61><loc_95><loc_62></location>S i = a i F , (2)</formula>
<text><location><page_2><loc_52><loc_51><loc_95><loc_60></location>with ' a i ' the intensity of the source at the i th channel. According to Eq. (2), and without loss of generality, all the sources are assumed to have the same profile F independently of the observing frequency. In practical applications, this is not true. However, it is possible to meet this condition by convolving the images with an appropriate kernel (see below).</text>
<text><location><page_2><loc_52><loc_47><loc_95><loc_51></location>For computational reasons that soon will become evident, it is useful to convert the two-dimensional model (1) into the one-dimensional form</text>
<formula><location><page_2><loc_63><loc_44><loc_95><loc_46></location>x i = s i + c i + z i + g i + n i . (3)</formula>
<text><location><page_2><loc_52><loc_38><loc_95><loc_43></location>Here, x i = VEC[ X i ], with VEC[ H ] the operator that transforms a matrix H into a vector by stacking its columns one underneath the other. Something similar holds for the other quantities.</text>
<section_header_level_1><location><page_2><loc_52><loc_35><loc_83><loc_36></location>2.1. Detection with ILC background removal</section_header_level_1>
<text><location><page_2><loc_52><loc_28><loc_95><loc_34></location>One classical solution to deal with many maps of the same sky area taken at different observing frequencies consists in a linear composition by means a set of weights w = [ w 1 , w 2 , . . . , w N f ] T . In this way it is possible to work with a single map given by</text>
<formula><location><page_2><loc_70><loc_25><loc_95><loc_26></location>x = Xw , (4)</formula>
<text><location><page_2><loc_52><loc_21><loc_95><loc_24></location>where X = ( x 1 , x 2 , . . . , x N f ) is an N p × N f matrix. The obvious question is how to fix such weights.</text>
<text><location><page_2><loc_52><loc_17><loc_95><loc_21></location>Before proceeding, it is necessary to take into account that there is an a-priori information about the various components in Eq. (1). In particular,</text>
<unordered_list>
<list_item><location><page_2><loc_53><loc_11><loc_95><loc_16></location>-For each observing frequency i , the spectra of C i and Z i are known with good accuracy. Moreover, the spatial distribution of these components is independent of the observing frequency;</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_3><loc_8><loc_88><loc_50><loc_93></location>-C i has a diffuse spatial distribution with a coherence scale of about 10 arcmin, which is much greater than that of the point sources. It is reasonable to expect that something similar could hold for G i ;</list_item>
<list_item><location><page_3><loc_8><loc_83><loc_50><loc_87></location>-Noises N i can be reasonably assumed as given by the realization of independent Gaussian white-noise processes with standard deviation σ N i .</list_item>
</unordered_list>
<text><location><page_3><loc_7><loc_73><loc_50><loc_82></location>The first point implies that, for a given observing frequency, the emission due to the CMB and the SZ components can be obtained from a rescaled linear mixture of two templates (i.e., maps that do not depend on frequency) c and z , respectively. This implies that the cumulative contribution b i = c i + z i of these components is given by the i th column of matrix</text>
<formula><location><page_3><loc_23><loc_71><loc_50><loc_72></location>B = ( c , z ) M , (5)</formula>
<text><location><page_3><loc_7><loc_55><loc_50><loc_70></location>where M is an N e × N f matrix usually indicated with the term of mixing matrix . In the present context, the number of emission mechanisms is N e = 2 since the kinetic SZ emission has the same spectrum as for the CMB. For this reason, with c i we indicate the CMB plus the kinetic SZ emission from now on. The second point implies that within a small area centered on an extragalactic point source, the CMB and any other diffuse emission vary very little. This suggests that, for any patch X i ( j, k ) with -N j ≤ j ≤ N j and -N k ≤ k ≤ N k ( N p 1 = 2 N j +1, N p 2 = 2 N k +1), these emissions can be safely approximated by a low-degree, twodimensional polynomial of degree m</text>
<formula><location><page_3><loc_14><loc_50><loc_50><loc_54></location>P m ( j, k ) = m ∑ l =0 α l ( j q k r ); q + r ≤ l, (6)</formula>
<text><location><page_3><loc_7><loc_47><loc_50><loc_49></location>where { α l } are real coefficients, whereas q and r are integer numbers permuted accordingly.</text>
<section_header_level_1><location><page_3><loc_7><loc_43><loc_36><loc_45></location>2.1.1. Point sources with known spectrum</section_header_level_1>
<text><location><page_3><loc_7><loc_35><loc_50><loc_42></location>Starting from these considerations and adopting the criterion of the S/N maximization for a given extragalactic point source with emission spectrum a = a ̂ a , where ' a ' is to be estimated and ̂ a = [ ̂ a 1 , ̂ a 2 , . . . , ̂ a N f ] T is fixed, the weights w can be computed through the maximization of the quantity</text>
<formula><location><page_3><loc_20><loc_32><loc_50><loc_35></location>SNR = ( ̂ a T w ) 2 ‖ ( Xw -Lq ) ‖ 2 ; (7)</formula>
<text><location><page_3><loc_7><loc_30><loc_46><loc_31></location>with ' ‖ . ‖ ' the Euclidean norm, under the constraints</text>
<formula><location><page_3><loc_23><loc_27><loc_50><loc_29></location>̂ a T w = 1; (8)</formula>
<formula><location><page_3><loc_23><loc_24><loc_50><loc_27></location>Mw = ( 0 0 ) . (9)</formula>
<text><location><page_3><loc_7><loc_10><loc_50><loc_22></location>Because of the constraint (8), which forces weights w to preserve the intensity a , the numerator of Eq. (7) is a constant. Therefore, the maximization of SNR is obtained by the minimization of the denominator. The rationale behind this approach is that if each of the maps x i contains the contribution of a point source with shape F and of smooth component g i , approximable by means of a two-dimensional polynomial, then the same has to hold for their linear combination x = Xw . The denominator x -Lq thus represents the residuals of the least-squares fit to the composite map x</text>
<text><location><page_3><loc_52><loc_72><loc_95><loc_93></location>of a model where a central point spread function (PSF) is superimposed to a bivariate polynomial background. The weights w are computed in such a way as to minimize the standard deviation of these residuals under the constraints (8) and (9). In Eq. (7), q = ( a, α T ) T is an array with size N c = [( m +1)( m +2) / 2] + 1, α the coefficients of the two-dimensional polynomial, whereas L is an N p × N c matrix with the form L = [ f , P ] with f = VEC[ F ] and P the N p × ( N c -1) design matrix corresponding to the least-squares fit of a two-dimensional polynomial 1 . The constraint (9) forces the contribution of the CMB and SZ components to the final map x to zero, whereas the contamination g is removed by means of the two-dimensional polynomial. The quantities w and q are unknown and have to be estimated. The maximization of SNR with the constraints (8)-(9) can be written in the form</text>
<formula><location><page_3><loc_55><loc_67><loc_95><loc_71></location>R ( w , q , λ ) = arg min w , q , λ [ ‖ ( Xw -Lq ) ‖ 2 + λ T ( M T a w -e 1 ) ] , (10)</formula>
<text><location><page_3><loc_52><loc_62><loc_95><loc_66></location>with M a = ( ̂ a , M T ) , λ an N e +1 array of Lagrange multipliers , and e 1 an N e +1 array of zeros except for the first element, which is '1'.</text>
<text><location><page_3><loc_52><loc_53><loc_95><loc_62></location>This method is a modification of the constrained ILC by Remazeilles et al. (2010). We call it modified multiple ILC (MMILC). The basic idea is that, if in the center of the selected patch there is a point source, then the value of ' a ' should exceed a threshold due to noise. After some algebra, one obtains that the solution of problem (10) is given by the system of equations</text>
<formula><location><page_3><loc_55><loc_48><loc_95><loc_52></location> +2 C XX -2 C XL M a -2 C XL +2 C LL 0 M T a 0 0 ( w q λ ) = ( 0 0 e 1 ) , (11)</formula>
<text><location><page_3><loc_52><loc_44><loc_95><loc_47></location>C XX = X T X , C XL = X T L and C LL = L T L , which provides</text>
<formula><location><page_3><loc_59><loc_42><loc_95><loc_43></location>w = H -1 C -1 XX M a ( M T a C -1 XX M a ) -1 e 1 , (12)</formula>
<formula><location><page_3><loc_59><loc_40><loc_95><loc_41></location>q = C -1 LL C T XL w , (13)</formula>
<text><location><page_3><loc_52><loc_38><loc_56><loc_39></location>where</text>
<formula><location><page_3><loc_53><loc_35><loc_95><loc_37></location>H = [ I -C + C -1 XX M a ( M T a C -1 XX M a ) -1 M T a C ] , (14)</formula>
<text><location><page_3><loc_52><loc_33><loc_75><loc_34></location>with I the identity matrix, and</text>
<formula><location><page_3><loc_64><loc_31><loc_95><loc_32></location>C = C -1 XX C XL C -1 LL C T XL . (15)</formula>
<text><location><page_3><loc_52><loc_26><loc_95><loc_30></location>One interesting characteristic of solution (11) is that it does not require knowing the noise level of each map, a quantity that often can only be roughly estimated.</text>
<text><location><page_3><loc_52><loc_24><loc_95><loc_26></location>Auseful insight into how MMILC works can be obtained if problem (10) is recast in the form 2</text>
<formula><location><page_3><loc_53><loc_20><loc_95><loc_23></location>R ( w ) = arg min w ‖ Aw ‖ 2 subject to: ( M T a w -e 1 ) (16)</formula>
<text><location><page_3><loc_52><loc_11><loc_95><loc_19></location>1 If the degree is one, P = [ δ 1 , δ 2 , 1 ], whereas for a degree two P = [ δ 1 glyph[circledot] δ 1 , δ 2 glyph[circledot] δ 2 , δ 1 glyph[circledot] δ 2 , δ 1 , δ 2 , 1 ], where ' glyph[circledot] ' represents the element-wise matrix multiplication (Hadamard product), 1 is a vector of ones, and δ 1 = VEC[ ∆ 1 ], δ 2 = VEC[ ∆ 2 ], where ∆ 1 is a matrix with 2 N j + 1 identical columns [ -N k , -N k + 1 , . . . , 0 , . . . , N k -1 , N k ] T , whereas ∆ 2 is a matrix with 2 N k +1 identical rows [ -N j , -N j +1 , . . . , 0 , . . . , N j -1 , N j ].</text>
<text><location><page_3><loc_53><loc_10><loc_82><loc_11></location>2 We thank the referee for this suggestion.</text>
<text><location><page_4><loc_7><loc_85><loc_50><loc_93></location>where A = ( I -L ( L T L ) -1 L T ) X . Since matrix A is the orthogonal projection of X onto the nullspace of L T , MMILC can be seen to sequentially perform a least-squares fit of the PSF overlapping a two-dimensional polynomial background on the original data for each frequency, followed by a constrained ILC on the residuals.</text>
<section_header_level_1><location><page_4><loc_7><loc_82><loc_38><loc_83></location>2.1.2. Point sources with unknown spectrum</section_header_level_1>
<text><location><page_4><loc_7><loc_74><loc_50><loc_81></location>The main limitation of MMILC is that it only works optimally for a specific emission spectrum ̂ a . This assumption can be relaxed by converting the maximization of SNR with the constraints (8)-(9) in the least-squares minimization of the quantity</text>
<formula><location><page_4><loc_22><loc_73><loc_50><loc_74></location>S = ‖ Xw -Lq ‖ 2 , (17)</formula>
<text><location><page_4><loc_7><loc_71><loc_22><loc_72></location>with the constraints</text>
<formula><location><page_4><loc_23><loc_68><loc_50><loc_70></location>w T w = 1; (18)</formula>
<formula><location><page_4><loc_23><loc_65><loc_50><loc_68></location>Mw = ( 0 0 ) . (19)</formula>
<text><location><page_4><loc_7><loc_61><loc_50><loc_63></location>The constraint (18) is set to avoid the trivial solution w = 0 . In this way, problem (10) is converted into</text>
<formula><location><page_4><loc_8><loc_55><loc_50><loc_59></location>S ( w , q , λ ) = arg min w , q , λ [ ‖ ( Xw -Lq ) ‖ 2 +2 λ T M + γ ( w T w -1) ] . (20)</formula>
<text><location><page_4><loc_7><loc_50><loc_50><loc_54></location>After some algebra, it is possible to see that q is again given by Eq. (13) but with w the solution of the eigenvalue problem</text>
<formula><location><page_4><loc_24><loc_49><loc_50><loc_50></location>Hw = γ w , (21)</formula>
<text><location><page_4><loc_7><loc_46><loc_11><loc_47></location>where</text>
<formula><location><page_4><loc_9><loc_44><loc_50><loc_45></location>H = ( I -M T C -1 MM M )( C XX -C XL C -1 LL C T XL ) , (22)</formula>
<text><location><page_4><loc_7><loc_28><loc_50><loc_42></location>and C MM = MM T . The searched for w is given by the eigenvector of H that minimizes quantity S . Presently, the only method that we can suggest is to insert each eigenvector in Eq. (17) and to check numerically which of them provides the smallest S . This is because we have ascertained that there are situations where the eigenvector corresponding to the lowest eigenvalue of H (a criterion typical of the least-squares problems) does not work. Indeed, matrix H is not symmetric, and it cannot be expected to have any particular property. We call this method nonparametric MMILC (NP-MMILC).</text>
<text><location><page_4><loc_7><loc_10><loc_50><loc_28></location>Although not specifically optimized for a particular ̂ a , the results provided by NP-MMILC depend on the emission spectrum of the point source. Indeed, if like MILC, this method too is interpreted as a sequential least-squares fits followed by a constrained ILC, it can be understood that, in the case of a point source with a large amplitude in maps with a low S / N and a small amplitude in maps with a high S / N, this results in a reduced detection capability. A simple procedure for avoiding this problem consists of applying NP-MMILC not to all maps but only to those for which the best S / N for the point source is expected. The choice can be based on ̂ a . This means to use the a priori information on the emission spectrum in a different way from MMILC.</text>
<section_header_level_1><location><page_4><loc_52><loc_92><loc_70><loc_93></location>2.1.3. Detection procedure</section_header_level_1>
<text><location><page_4><loc_52><loc_77><loc_95><loc_91></location>When searching for extragalactic point sources with MMILC or NP-MMILC in a given set of maps, the procedure consists in fixing the size (2 N j +1) × (2 N k +1) of a window that is made to slide, pixel by pixel, across the area of interest. At the end of this procedure a single map is obtained containing the estimated values of ' a ' for each pixel. Now, the question is to fix the detection threshold below which a given value of ' a ' is supposed to be only due to noise. In this respect, the direct use of solutions (12)-(14) and (21) is difficult. For this reason, two different procedures are suggested,</text>
<unordered_list>
<list_item><location><page_4><loc_52><loc_56><loc_95><loc_76></location>1. For MMILC it is set a = 0 if a ≤ kσ L , where k is a constant factor (typically k = 4 , 5), σ L = ‖ σ T n w ‖ √ ( L T L ) -1 1 , 1 , σ n = ( σ n 1 , σ n 2 , . . . , σ n N f ) T , and ( L T L ) -1 1 , 1 is the first entry of matrix ( L T L ) -1 . This operation corresponds to estimating the standard deviation σ a of ' a ' for a fixed w . Such an approach has the advantage that matrix ( L T L ) -1 can be computed only once since it is the same for all the patches. But, it has the disadvantage that the standard deviations of the noises { n i } have to be known in advance. In the case of NP-MMILC, a similar procedure holds, but it is necessary to take the absolute value of a . Indeed, it is readily verified that, with q given by Eq. (13), a change of sign of w does not modify the value of S ;</list_item>
<list_item><location><page_4><loc_52><loc_46><loc_95><loc_55></location>2. It is set a = 0 if a ≤ kσ map , for MMILC, and | a | ≤ kσ map , for NP-MMILC. Again, k is a constant factor and σ map is the standard deviation of the entries in the final map. This is an unsophisticated approach, but it does have the advantage of not requiring the standard deviation of the noise in each patch, a quantity usually known only roughly.</list_item>
</unordered_list>
<text><location><page_4><loc_52><loc_21><loc_95><loc_45></location>Before concluding this section, we underline that the number of rows N e = 2 of the mixing matrix M comes from our interest in exploring the situation in which the extragalactic component Z i consists of secondary anisotropies of the CMB. In particular, we have only considered the SZ effect (both thermal and kinetic), which is the strongest one in galaxy clusters, groups of galaxies, and in protoclusters (i.e., Birkinshaw, 1999). However, if the information is available for one or more additional components, then it is sufficient to update M and the same solutions (12)-(14) and (21) and hold for N e = 3 or greater. Similarly, if one decides to remove only one component via ILC, either CMB or SZ, then it is sufficient to eliminate the appropriate row from matrix M and set N e = 1 in the solution. In this way, however, the drawback is that the remaining component has to be removed by means of the two-dimensional polynomial. This could be a necessary operation in the case of noisy maps (see below).</text>
<section_header_level_1><location><page_4><loc_52><loc_18><loc_85><loc_19></location>2.2. Detection without ILC background removal</section_header_level_1>
<text><location><page_4><loc_52><loc_13><loc_95><loc_17></location>The MMILC and NP-MMILC detection techniques are potentially quite effective, however they suffer from two main drawbacks:</text>
<unordered_list>
<list_item><location><page_4><loc_52><loc_10><loc_95><loc_12></location>1. To remove the CMB and SZ components, one or more of the weights in w have to be negative. As a consequence,</list_item>
</unordered_list>
<text><location><page_5><loc_10><loc_83><loc_50><loc_93></location>since in the final map a = a T w and σ map = ‖ σ T n w ‖ , ' a ' is given by the sum of both positive and negative values whereas, σ map is given by the sum of positive values alone. In other words, the background subtraction reduces the S / N with respect to a simple sum of the maps. The situation worsens when the emission of an extragalactic point source has a spectrum similar to that of the CMB or of the SZ since ' a ' will tend to zero;</text>
<unordered_list>
<list_item><location><page_5><loc_7><loc_72><loc_50><loc_81></location>2. If ̂ a is an array such that M ̂ a = 0 , i.e. ̂ a belongs to the nullspace of M (i.e., it is given by the linear combination of the column of M ), then the system (11) does not have any useful solution since, when w = ̂ a / ‖ ̂ a ‖ 2 , both constraints ̂ a T w = 1 and Mw = 0 are satisfied, but it happens that the estimate a is such that its expected value is zero.</list_item>
</unordered_list>
<text><location><page_5><loc_7><loc_65><loc_50><loc_71></location>For this reason, to detect extragalactic point sources with ̂ a belonging to the nullspace of M , the above procedures have to be adapted to work without the ILC removal of the CMB and the SZ components. Again, two different algorithms are presented.</text>
<section_header_level_1><location><page_5><loc_7><loc_62><loc_36><loc_63></location>2.2.1. Point sources with known spectrum</section_header_level_1>
<text><location><page_5><loc_7><loc_57><loc_50><loc_61></location>The case of point sources with known spectra can be easily obtained from problem (10) through the substitutions M a = ̂ a and e 1 = 1:</text>
<formula><location><page_5><loc_9><loc_53><loc_50><loc_56></location>R ( w , q , λ ) = arg min w , q ,λ [ ‖ ( Xw -Lq ) ‖ 2 + λ ( ̂ a T w -1) ] , (23)</formula>
<text><location><page_5><loc_7><loc_51><loc_23><loc_52></location>with solution given by</text>
<formula><location><page_5><loc_12><loc_46><loc_50><loc_51></location> +2 C XX -2 C XL ̂ a -2 C XL +2 C LL 0 ̂ a T 0 T 0 ( w q λ ) = ( 0 0 1 ) . (24)</formula>
<text><location><page_5><loc_7><loc_22><loc_50><loc_45></location>The explicit solution for w and q is given by Eqs. (12)-(14) with M a = ̂ a . Detection is still carried out as explained in Sec. 2.1.3. With this method, which we call modified ILC (MILC), the CMB and SZ emissions are not removed through the use of the mixing matrix M , but rather by exploiting that the CMB, part of the SZ, and any other component with a diffuse spatial distribution can be removed through the polynomial approximation. As a consequence, the only contribution in the final map beyond that of the extragalactic point sources is the compact component of the SZ (both thermal and kinetic), and this is an unavoidable problem. Without additional information, it is impossible to separate an SZ emission with point-like spatial distribution from a genuine extragalactic point source. In the case of SZ emission with more extended structures, a possible solution consists of checking if their spatial distribution is compatible with the PSF F . This issue, however, is beyond the scope of the present work.</text>
<section_header_level_1><location><page_5><loc_7><loc_19><loc_38><loc_20></location>2.2.2. Point sources with unknown spectrum</section_header_level_1>
<text><location><page_5><loc_7><loc_12><loc_50><loc_18></location>If in the minimization of the quantity S as given in Eq. (17) the constraint (19) is relaxed, the nonparametric version of MILC is obtained (NP-MILC). It is easily verified that for this problem too, q is given by Eq. (13), but now w is the solution of the eigenvalue problem Hw = γ w with</text>
<formula><location><page_5><loc_17><loc_9><loc_50><loc_11></location>H = ( C XX -C XL C -1 LL C T XL ) . (25)</formula>
<text><location><page_5><loc_52><loc_88><loc_95><loc_93></location>As for NP-MMILC, the searched w is given by the eigenvector of H that minimizes quantity S , and detection is carried out as explained in Sec. 2.1.3. Also, NP-MILC suffers the same dependence on ̂ a as NP-MMILC.</text>
<section_header_level_1><location><page_5><loc_52><loc_84><loc_66><loc_85></location>3. Practical uses</section_header_level_1>
<text><location><page_5><loc_52><loc_45><loc_95><loc_82></location>In this section we discuss some practical problems and how they can be addressed. The first is related to the degree m of the polynomial used to approximate the background. Obviously, the smaller the sky area of interest the lower the degree of the polynomial. For example, considering that the CMB has a coherence scale of about 10 arcmin, it can be reasonably expected that with a resolution of 0 . 1-1 . 0 arcsec a first-degree polynomial is a good choice. The second question is related to the sizes N j and N k of the patch for testing for the presence of a point source. Two competing requirements arise: on the one hand, N j and N k must be as large as possible to reduce errors in estimating the polynomial parameters, on the other, a small size implies that the approximation of the background with a low-degree polynomial is a more reliable operation and, at the same time, that the probability two or more sources being in the same patch X is low. For illustrative purposes, Fig. 1 shows the standard deviation σ a of the estimated intensity a as provided by MILC in the case of a point source with a Gaussian profile and a dispersion σ psf equal to three pixels. A single map is considered where the background is given by a twodimensional one-degree polynomial, instrumental noise is Gaussian and white with standard deviation σ n , and N p 1 and N p 2 are progressively increased. The true value of a is one in unit of σ n . The decrease in σ a is evident. Figure 2 shows the relationship between P D and P FA for different values of the ratio a/σ n . These figures clearly show that N j and N k lying in the range 3 σ psf -5 σ psf is a reasonable compromise.</text>
<text><location><page_5><loc_52><loc_10><loc_95><loc_45></location>As shown in the appendix A, that the exact PSF F could not be known or that some of the point sources could be overlapping and/or could have an extended shape, have no important consequences. However, another issue arises because the shape of the PFSs changes with observing frequency in practical applications. Widespread practice is to convolve maps with a suited kernel function in order to get a common spatial PSF F for all the frequencies. This operation has the beneficial effect of reducing the standard deviation of the instrumental noise, but at the same time it introduces a spurious spatial correlation in it. Actually, even if neglected, this is not expected to be critical since both MILC and MMILC are linear techniques, and the only consequence is a reduction of the efficiency of the leastsquares estimate of the coefficients q (i.e., the estimate is unbiased but with greater variance). Something similar is also expected for NP-MILC and NP-MMILC that represent the solution of a linear least-squares problem with a quadratic constraint (i.e., both the quantity to minimize and the constraint are smooth functions). In other words, given the above-mentioned reduction in the standard deviation of the noise, this spurious correlation is not expected to have critical consequences. This is especially true if one takes into account that there are other and more important approximations that make the analysis of data less rigorous (e.g., often the level of instrumental noise is only roughly known).</text>
<text><location><page_6><loc_7><loc_58><loc_50><loc_93></location>A final question regards whether in practical applications it is more convenient to use the MILC and MMILC algorithms or the NP-MILC and NP-MMILC ones. Indeed, MILC and MMILC work optimally only for a specific emission spectrum ̂ a , a feature common to other detection techniques such as the matched multifilter (Herranz et al. 2012). In principle, this is not a critical question. It is sufficient to apply the detection algorithm to a set of prefixed ̂ a obtained by grouping sources in broad families - radio flat, radio steep, dusty galaxies of a certain type, etc - and defining average spectral laws ̂ a for each family (Ramos et al. 2011; Herranz et al. 2012). Such an approach is viable since MILC and MMILC are fast algorithms, and they require the numerical solution of linear systems containing no more than a few of tens of linear equations. Moreover, as shown in Ramos et al. (2011), where a version of MMILC without background subtraction is applied to high-Galactic latitude WMAP maps, strong degradation of the detection capability has to be expected only if the spectrum of the point sources is quite different from the one for which the MMILC algorithm has been optimized. Of course, this kind of problem can be avoided using NP-MILC and NPMMILC. However, since they are not optimized for specific emission characteristics, the price is a lower detection capability for specific spectra. Given the inexpensive computational cost of the four algorithms, the best choice is to try all of them and check the results.</text>
<section_header_level_1><location><page_6><loc_7><loc_55><loc_28><loc_56></location>4. Numerical experiments</section_header_level_1>
<text><location><page_6><loc_7><loc_45><loc_50><loc_54></location>To support the arguments presented above, we present some numerical experiments here with simulated maps at high Galactic latitude (where the Galactic contamination is negligible) that is the region of interest for future CMB experiments. Since realistic experimental conditions are not yet available, such simulations are only presented for illustration.</text>
<text><location><page_6><loc_7><loc_27><loc_50><loc_45></location>We produced small sky patches of 0 . 86 deg 2 at 3 '' angular resolution with several components, namely, the CMB and the Sunyaev-Zel'dovich effects (SZ), both kinetic and thermal. To produce these maps we used hydrodynamic/Nbody simulations with cosmological parameters that are consistent with WMAP parameters for a flat Universe and standard ΛCDM model, with an equation of state for the dark energy component of w = -1. The adopted present time density parameters expressed in terms of the critical density are (Ω cdm , Ω Λ , Ω b ) = (0 . 256 , 0 . 7 , 0 . 044), a dimensionless Hubble constant of h = 0 . 71, and a mean CMB temperature of T =2.725 K. Adiabatic initial conditions are assumed, a spectral index of n s = 1, and full reionization at redshift 7.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_26></location>For the present epoch, we considered a normalization power spectrum of σ 8 = 0 . 9 and a shape parameter of Γ = 0 . 17. The CMB component is produced with the CAMB code (Lewis et al. 2000) to obtain the linear CMB power spectrum. The full-sky CMB temperature anisotropy map was generated with the HEALPix software (G'orski et al. 2005) with Nside = 8192. From this map a small sky region was extracted with an area of about 0.86 deg 2 around the equator, projected on a squared map. Details about the simulations of the SZ effect components can be found in da Silva et al. (2001) and Ramos et al. (2012). The frequencies chosen were 90, 150, 250, 330, 440, 675, and 950 GHz, which correspond to the ALMA receiver bands.</text>
<text><location><page_6><loc_52><loc_75><loc_95><loc_93></location>All components were co-added, resulting in a final map, ∆ I CMB+SZ /I , with a pixel size of 3 arcsec. We use the central part of the maps (300 × 300 pixels) and convolve them for each frequency with a Gaussian PSF with a dispersion of three pixels. To each map a white-noise process has also been added with standard deviations σ n i set to 0 . 12 time the standard deviation of the values of map itself. Finally, 20 randomly distributed point sources were included with a i = 1 . 7 σ n i . In this way, maps with the same S/N are obtained. The values of σ n i and a i have been arbitrarily chosen to test algorithms under very bad operational conditions, but at the same time to obtain stable results (i.e. with different realizations of the noise process almost all the sources are correctly detected with no false detections).</text>
<text><location><page_6><loc_52><loc_49><loc_95><loc_75></location>The simulated experimental scenario corresponds to an adverse situation of rather low S/N and, since σ n i increases with frequency, with a spectrum ̂ a (see curve a 1 in Fig. 3) that mimics that of the CMB plus SZ background (i.e. ̂ a is close to the nullspace of M , or M ̂ a ≈ 0 ). Figure 4 displays the simulated maps. We note that the point sources are not even visible, and they are by far exceeded by the SZ pointlike emission. Figure 5 shows the results obtained with the four algorithms presented above. For MILC, MMILC, and NP-MILC the detection threshold has been set to 4 σ L whereas a value of 3 . 5 σ L has been used for NP-MMILC. Background has been approximated by a two-dimensional first-degree polynomial. A sliding square window of 19 × 19 pixels has been adopted for the local search of point sources. As expected, the MMILC and NP-MMILC do not work. On the other hand, MILC and NP-MILC have effectively removed the CMB, as well as the SZ diffuse components, and correctly detected all the point sources in the map (see Fig. 8). However, many of the SZ point-like emissions are also present.</text>
<text><location><page_6><loc_76><loc_44><loc_76><loc_45></location>glyph[negationslash]</text>
<text><location><page_6><loc_52><loc_22><loc_95><loc_49></location>The situation greatly improves if { a i } = [2 . 00 , 1 . 00 , 0 . 60 , 0 . 40 , 0 . 20 , 0 . 06 , 0 . 02] T glyph[circledot] σ n which simulates an emission spectrum decreasing with frequency (see curve a 2 in Fig. 3). In this way M ̂ a = 0 . Figure 6 shows the maps corresponding to this case. As is visible in Fig. 7, now both MMILC and NP-MMILC are able to correctly detect all the point sources except one, as well to completely remove the CMB and SZ contamination. We note the detection of two couples of overlapping point sources in the bottom right hand and middle right hand parts of the map. However, as expected, the NP-MMILC map presents various false detections due to noise (the detection threshold has been set to 3 . 5 σ L in order to obtain the same number of true detections as MMILC). A point to stress is that, in the present high Galactic latitude experiment, the diffuse components { g i } can be set to zero. As a result, in models (10) and (20) it should have been possible to set L = f . (i.e., to avoid the polynomial approximation of the background). However, the use of the general model permits the stability of MMILC and NP-MMILC to be tested for high level of noise.</text>
<section_header_level_1><location><page_6><loc_52><loc_18><loc_76><loc_19></location>5. Summary and conclusions</section_header_level_1>
<text><location><page_6><loc_52><loc_10><loc_95><loc_17></location>In this paper four algorithms, the modified ILC (MILC), the modified multiple ILC (MMILC), the nonparametric -MILC (NP-MILC), and the nonparametric -MMILC (NPMMILC), have been presented for detection of extragalactic point sources in multifrequency, very high-resolution CMB maps. In particular, MMILC and NP-MMILC make use of</text>
<text><location><page_7><loc_7><loc_71><loc_50><loc_93></location>the a-priori information about the spectral properties of the CMB and SZ with MMILC tailored to detecting extragalactic point sources with a given spectrum that has to be different from that of these emissions. The other two algorithms are suited to detecting the extragalactic point sources with similar spectra to the CMB or SZ with MILC tailored to the specific spectra. The main property of the proposed algorithms is that they do not require any a-priori knowledge of the statistical characteristics of spatial distribution of the diffuse emissions that contribute to the microwave background. Indeed, these can be locally approximated with a low-degree, two-dimensional polynomial. The two proposed sets of algorithms used in conjunction are effective in detecting extragalactic point sources independently of the spectral characteristics of their emission. Their potential performance has been illustrated with some numerical experiments.</text>
<text><location><page_7><loc_7><loc_66><loc_50><loc_70></location>Acknowledgements. E. P. Ramos is supported by grant POPHQREN-SFRH/BD/45613/2008, from FCT (Portugal). E. P. Ramos and R. Vio thank ESO for its hospitality and support through the DGDF funding program.</text>
<section_header_level_1><location><page_7><loc_7><loc_62><loc_16><loc_63></location>References</section_header_level_1>
<text><location><page_7><loc_7><loc_59><loc_49><loc_61></location>Birkinshaw M., 1999, Phys. Rep., 310, 97 Carvalho, P., Rocha, G. and Hobson, M.P. 2009, MNRAS, 393, 681</text>
<text><location><page_7><loc_7><loc_35><loc_50><loc_59></location>da Silva A. J. C., Barbosa D., Liddle A. R., & Thomas, P. A. 2001, MNRAS, 326, 155 Herranz, D. et al. 2002, MNRAS, 336, 1057 Herranz, D. and Sanz, J.L. 2008, IEEE Journal of Selected Topics in Signal Processing, 5, 727 Herranz, D., L'opez-Caniego, M., Sanz, J.L., & Gonz'alez-Nuevo, J. 2009, MNRAS, 394, 510 Herranz, D., Argueso, F. and Carvalho, P. 2012, Advances in Astronomy, in print Eriksen, H.K., Banday, A.J., G'orski, K.M., & Lilje, P.B. 2004, ApJ, 612, 633 G'orski, K. M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K., Reinecke, M., & Bartelmann, M. 2005, ApJ, 622, 759 Hinshaw, G., et al. 2007, ApJS, 170, 288 Kay, S. M. 1998, Fundamentals of Statistical Signal Processing: Detection Theory (London: Prentice Hall) Lanz, L.F., Herranz, D., Sanz, J.L., Gonzalez-Nuevo, J. and LopezCaniego, M. 2010, MNRAS, 403, 212 Lewis, A., Challinor, A., & Lasenby, A. 2000, ApJ, 538, 473 Ramos, E.P.R.G., Vio, R. and Andreani, P. 2011, A&A, 528, A75 Ramos, E. P. R. G., da Silva, A., J. C., Liu, G.C., 2012, ApJ, in preparation Remazeilles, M., Delabrouille, J. and Cardoso, J.F. 2011, MNRAS,</text>
<text><location><page_7><loc_9><loc_34><loc_14><loc_35></location>418, 467</text>
<text><location><page_7><loc_7><loc_33><loc_36><loc_33></location>Vio, R. and Andreani, P. 2008, A&A, 487, 775</text>
<figure>
<location><page_8><loc_8><loc_43><loc_94><loc_92></location>
<caption>Fig. 1. Standard deviation σ a of the estimated intensity a as provided by MILC in the case of a point source, with a Gaussian profile with dispersion σ psf equal to 3 pixels, as a function of the sizes N j = N k of the searching patch. Here, a single map is considered with a background given by a two-dimensional, one-degree polynomial. Instrumental noise is Gaussian and white with standard deviation σ n , The true value of ' a ' is 1 in units of σ n .</caption>
</figure>
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<text><location><page_9><loc_27><loc_65><loc_29><loc_66></location>a/</text>
<text><location><page_9><loc_29><loc_65><loc_30><loc_67></location>σ</text>
<text><location><page_9><loc_30><loc_65><loc_31><loc_66></location>n</text>
<text><location><page_9><loc_31><loc_65><loc_35><loc_66></location>= 0.5</text>
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<text><location><page_9><loc_41><loc_42><loc_43><loc_43></location>FA</text>
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<location><page_9><loc_56><loc_42><loc_94><loc_66></location>
<caption>Fig. 2. Relationship between the probability of detection , P D , vs. the probability of false alarm , P FA for the case shown in Fig. 1 but for different values of the ratio a/σ n . Note the different scale used for the abscissa in the bottom-right panel.</caption>
</figure>
<text><location><page_9><loc_75><loc_65><loc_76><loc_67></location>σ</text>
<figure>
<location><page_10><loc_7><loc_45><loc_94><loc_92></location>
<caption>Fig. 3. Comparison of the spectrum of the point sources used in the numerical experiments of Figs. 4-7 with that of CMB and the thermal SZ. All spectra have been normalized in such a way to have absolute intensity equal to 1 at 90 GHz. Here, a 1 and a 2 indicate the point source with spectrum, respectively, similar to and unlike that of CMB used in the numerical experiment (see next figures).</caption>
</figure>
<paragraph><location><page_11><loc_13><loc_91><loc_20><loc_92></location>90 GHz</paragraph>
<paragraph><location><page_11><loc_46><loc_91><loc_54><loc_92></location>150 GHz</paragraph>
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<caption>250 GHz</caption>
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<location><page_11><loc_73><loc_77><loc_91><loc_90></location>
<caption>330 GHz</caption>
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<paragraph><location><page_11><loc_46><loc_72><loc_54><loc_74></location>440 GHz</paragraph>
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<caption>675 GHz</caption>
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<caption>950 GHz</caption>
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<paragraph><location><page_11><loc_43><loc_54><loc_56><loc_55></location>Point sources</paragraph>
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<location><page_11><loc_7><loc_40><loc_26><loc_53></location>
<caption>950 GHz + point sources</caption>
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<text><location><page_11><loc_89><loc_40><loc_90><loc_41></location>+</text>
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<location><page_11><loc_40><loc_77><loc_59><loc_90></location>
<caption>Fig. 4. Simulations of a sky region at high Galactic declination at the ALMA observing frequencies. 20 randomly distributed point sources with the same intensity have been added. Here, the point sources have a spectrum similar to that of CMB (see text and curve a 1 in Fig. 3). The PSFs are assumed to be Gaussian with a standard deviation of 3 pixels. Noise is Gaussian-white with standard deviation set to 0 . 12 time the standard deviation of the values in the corresponding noise-free maps. All of the point sources have the same intensity set to 1 . 7 times the standard deviation of the noise. The two bottom-right panels show the simulated point sources and their position on the 950 GHz map.</caption>
</figure>
<section_header_level_1><location><page_12><loc_13><loc_91><loc_35><loc_92></location>Detection map: MMILC</section_header_level_1>
<section_header_level_1><location><page_12><loc_68><loc_91><loc_88><loc_92></location>Detection map: MILC</section_header_level_1>
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<section_header_level_1><location><page_12><loc_11><loc_60><loc_36><loc_61></location>Detection map: NP-MMILC</section_header_level_1>
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<location><page_12><loc_8><loc_36><loc_40><loc_59></location>
<caption>Detection map: NP-MILC</caption>
</figure>
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<location><page_12><loc_62><loc_37><loc_94><loc_59></location>
<caption>Fig. 5. Results provided by MILC, MMILC, NP-MILC, and NP-MMILC when applied to the maps in Fig. 4. The detection threshold has been set to 4 σ L for all algorithms except for NP-MMILC for which a value of 3 . 5 σ L has been adopted (see text) and the background has been approximated by a two-dimensional polynomial of degree one. The top and bottom left panels clearly show that both MMILC and NP-MMILC are not able to retrieve point sources in this case. This happens because the spectrum of the point sources has a frequency-dependence similar to the CMB and SZ, and therefore the subtraction process gets rid of all of them. The top and bottom right panels show that both MILC and NP-MILC, on the contrary, retrieve all sources and the SZ point-like emissions, because it subtracts the underlying diffuse component with the polynomial approximation. For NP-MILC a greater noise contamination of the detection map is evident. Also notice the detection of two couples of overlapping point sources in the bottom-right and middle-right part of the map.</caption>
</figure>
<paragraph><location><page_13><loc_13><loc_91><loc_20><loc_92></location>90 GHz</paragraph>
<paragraph><location><page_13><loc_46><loc_91><loc_54><loc_92></location>150 GHz</paragraph>
<figure>
<location><page_13><loc_7><loc_77><loc_26><loc_90></location>
<caption>250 GHz</caption>
</figure>
<figure>
<location><page_13><loc_73><loc_77><loc_91><loc_90></location>
<caption>330 GHz</caption>
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<paragraph><location><page_13><loc_46><loc_72><loc_54><loc_74></location>440 GHz</paragraph>
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<location><page_13><loc_7><loc_59><loc_26><loc_72></location>
<caption>675 GHz</caption>
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<caption>950 GHz</caption>
</figure>
<paragraph><location><page_13><loc_43><loc_54><loc_56><loc_55></location>Point sources</paragraph>
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<location><page_13><loc_7><loc_40><loc_26><loc_53></location>
<caption>950 GHz + point sources</caption>
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<location><page_13><loc_73><loc_40><loc_91><loc_53></location>
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<text><location><page_13><loc_89><loc_40><loc_90><loc_41></location>+</text>
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<location><page_13><loc_40><loc_77><loc_59><loc_90></location>
<caption>Fig. 6. Simulations of a sky region at high Galactic declination at the ALMA observing frequencies, with 20 randomly distributed point sources with the same intensity added. In this case the point sources have a spectrum given by curve a 2 in Fig. 3. The PSFs are assumed to be Gaussian with a standard deviation of 3 pixels. Noise is Gaussian-white with standard deviation set to 0 . 12 times the standard deviation of the values in the corresponding noise-free maps. The PSFs are assumed to be Gaussian with a standard deviation of 3 pixels. The two bottom-right panels show the simulated point sources and their position on the 950 GHz map.</caption>
</figure>
<section_header_level_1><location><page_14><loc_13><loc_91><loc_35><loc_92></location>Detection map: MMILC</section_header_level_1>
<section_header_level_1><location><page_14><loc_68><loc_91><loc_88><loc_92></location>Detection map: MILC</section_header_level_1>
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<section_header_level_1><location><page_14><loc_11><loc_60><loc_36><loc_61></location>Detection map: NP-MMILC</section_header_level_1>
<section_header_level_1><location><page_14><loc_66><loc_60><loc_90><loc_61></location>Detection map: NP-MILC</section_header_level_1>
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<caption>Fig. 7. Results provided by MILC, MMILC, NP-MILC and NP-MMILC when applied to the maps in Fig. 6. The detection threshold has been set to 4 σ L for all algorithms except for NP-MMILC for which a value of 3 . 5 σ L has been adopted (see text), and the background has been approximated by a two-dimensional polynomial of degree one. The top and bottom left panels clearly show that in this case both MMILC and NP-MMILC miss only one point source and get rid of the SZ point-like emissions. A greater noise contamination in the detection map of NP-MMILC is also evident. The top and bottom right panels show that MILC and NP-MILC retrieve all point sources but also the SZ point-like emissions. This is a consequence of subtracting the underlying diffuse component with the polynomial approximation. Also for NP-MILC a greater noise contamination of the detection map is evident, and notice the detection of two couples of overlapping point sources in the bottom-right and middle-right part of the map.</caption>
</figure>
<text><location><page_15><loc_13><loc_91><loc_35><loc_92></location>Detection map: MMILC</text>
<text><location><page_15><loc_68><loc_91><loc_88><loc_92></location>Detection map: MILC</text>
<figure>
<location><page_15><loc_8><loc_67><loc_40><loc_90></location>
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<text><location><page_15><loc_11><loc_60><loc_36><loc_61></location>Detection map: NP-MMILC</text>
<text><location><page_15><loc_66><loc_60><loc_90><loc_61></location>Detection map: NP-MILC</text>
<figure>
<location><page_15><loc_8><loc_36><loc_40><loc_59></location>
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<figure>
<location><page_15><loc_62><loc_37><loc_94><loc_59></location>
<caption>Fig. 8. As in Fig. 7 with the difference that maps has not been thresholded. This is only to show that the CMB and the extended SZ components have been effectively removed by the polynomial approximation of the background.</caption>
</figure>
<figure>
<location><page_15><loc_62><loc_67><loc_94><loc_90></location>
</figure>
<section_header_level_1><location><page_16><loc_7><loc_92><loc_40><loc_93></location>Appendix A: Some additional questions</section_header_level_1>
<text><location><page_16><loc_7><loc_73><loc_50><loc_91></location>The detection techniques presented in Sec. 2 are based on the assumptions that a) the true PSF F is known; b) all the sources have a point-like shape (i.e. the shape of the PSF); c) all the sources are isolated. In practical applications, however, the PSF has to be estimated, some sources can have an extended shape, and overlapping is possible. Here, we show that all this can be expected to have only secondary consequences. In this respect, for sake of ease in the formalism, we start by considering an experimental one-dimensional signal x = a f + n . Here, f is the onedimensional PSF and n an additional white noise. In practice, x is due to a point source with amplitude a embedded in noise. As is well known, the least-squares fit estimate of a provides the solution</text>
<formula><location><page_16><loc_25><loc_69><loc_50><loc_72></location>̂ a = f T x f T f . (A.1)</formula>
<text><location><page_16><loc_7><loc_45><loc_50><loc_67></location>At this point, we point out that in detection problems the test statistic T ( x ) = f T x (e.g. see Kay 1998) is used where f is the well known matched filter (MF). In other words, unless of a constant factor, the estimate ̂ a is identical to the test statistic T ( x ). Indeed, the rhs of Eq. (A.1) is nothing else that the normalized correlation of x with f . This means that in the present context, the least squares fit and the matched filter are two equivalent techniques. This allows us to analyze the characteristic of the least-squares fit using the body of the theory of the linear filters. Therefore, f can be interpreted as a linear, typically low-pass, discrete filter with N p entries that is made to slide across an array x ≡ { x i } N x i =1 with N x glyph[greatermuch] N p . In this way, for each element x i one can obtain the quantity ̂ a i = T ( x i ) / ( f T f ), where x i ≡ { x j } i + N p -1 j = i . By means of the discrete Fourier transform (DFT) it is possible to compute ̂ a ≡ { ̂ a i } n x i =1 via</text>
<formula><location><page_16><loc_21><loc_41><loc_50><loc_45></location>̂ a = IDFT[˜ x glyph[circledot] ˜ f ∗ ] f T f , (A.2)</formula>
<text><location><page_16><loc_7><loc_31><loc_50><loc_40></location>with ˜ x and ˜ f the DFT of x and the zero padded version of f , IDFT[ . ] the inverse DFT operator and symbols ' ∗ ', ' glyph[circledot] ' indicating the complex conjugate and the point-wise multiplication , respectively. This implies that the statistical characteristics of ̂ a can be analyzed by means of the spectral properties of f . These considerations can be trivially extended to the two-dimensional case.</text>
<text><location><page_16><loc_7><loc_10><loc_50><loc_31></location>Here, it is useful to present some simple examples to see that the three facts above are actually not important. Concerning point a), Fig. A.1 shows a central slice P ( ν ) = | ˜ f | of the spectrum of three two-dimensional, circularly symmetric, Gaussian PSFs with dispersion σ G = 3 and 4 pixels, respectively. It is clearly visible that the value of σ G determines the bandwidth of ˜ f in the sense that the larger σ G , the stronger the filtering action. This means that, if a point source with σ G = 4 pixels is filtered assuming a PSF with σ G = 3 (i.e. with an error of 25%), the only consequence is a slighter reduction of the noise with respect to what is obtainable with the correct PSF. In contrast, if the point source has σ G = 3 and a PSF with σ G = 4 is assumed (i.e. with an error of 33%), a stronger reduction of the noise is obtained. In this case, however, part of the signal of interest is also filtered out, again with a slighter</text>
<text><location><page_16><loc_52><loc_89><loc_95><loc_93></location>reduction of the detection capability with respect to what is obtainable with the correct PSF. These two examples are shown in Figs. A.2-A.3.</text>
<text><location><page_16><loc_52><loc_79><loc_95><loc_89></location>Similar arguments hold for the point b) when the source has an extended shape. In this case, however, since the PSF is much ' narrower ' than the source, the noise filtering will be much less effective. However, as shown by the example in Fig. A.4, where an extended object with Gaussian shape, σ G = 10, and a Gaussian PSF with σ G = 3 pixels are considered, this does not mean that detection is not possible, but rather that it is less effective.</text>
<text><location><page_16><loc_52><loc_72><loc_95><loc_79></location>Finally, concerning point c), i.e. the case of two close point sources, the situation does not change very much. The only consequence is that the filtered point sources will appear more overlapped than the unfiltered ones (see Fig. A.5).</text>
<text><location><page_16><loc_52><loc_67><loc_95><loc_72></location>In the cases examined above, the presence of a smooth background p has not been considered. However, again, things can be expected not to change very much. Indeed, Eq. (A.1) becomes</text>
<formula><location><page_16><loc_67><loc_63><loc_95><loc_66></location>̂ a = f T ( x -p ) f T f . (A.3)</formula>
<text><location><page_16><loc_52><loc_59><loc_95><loc_62></location>Now, if instead of p the result of a least-squares polynomial fit ̂ p is used, then one obtains</text>
<formula><location><page_16><loc_67><loc_55><loc_95><loc_58></location>̂ a = f T x f T f + f T ̂ d f T f . (A.4)</formula>
<text><location><page_16><loc_52><loc_45><loc_95><loc_54></location>with ̂ d = ̂ p -p a smooth function. In other words, a map is produced where a smoothed point source is superimposed to a smoothed (presumably weak) background and noise is reduced. This is visible in Fig A.6, which shows the results obtained for a situation similar to that of Fig. A.5 when a first-degree, two-dimensional polynomial background is present.</text>
<text><location><page_16><loc_52><loc_23><loc_95><loc_45></location>To understand why it is reasonable to assume that these facts are not critical for MMILC, it is useful to interpret this method as done in Sec. 2.1.1; i.e, a sequential least-squares fit of a point spread function (PSF) overlapped to a twodimensional polynomial background on the original data for each frequency, followed by a constrained ILC on the residuals. Since, each of the fits is not very sensitive to the issues mentioned above, it is reasonable to assume that the same is valid for their linear combination. Something similar holds for MILC, NP-MILC, and NP-MMILC. These arguments can also be extended with very good approximation to the case that, as in Sec. 2, the background is computed for each position of the sliding detection window. Indeed, since the window is made to slide one pixel at a time, for close pixels the least-squares fit is done using essentially the same data. The experiments concerning MILC and NP-MILC in Figs. 4-7 confirm this.</text>
<figure>
<location><page_17><loc_8><loc_45><loc_94><loc_93></location>
<caption>Fig. A.1. Central slice of the spectrum P ( ν ) of three bivariate, circularly symmetric, Gaussian PSFs with dispersion σ G = 3 , 4 , 10, respectively. Frequency ν is in Nyquist units .</caption>
</figure>
<section_header_level_1><location><page_18><loc_16><loc_90><loc_35><loc_92></location>Point souce ( σ G = 4 )</section_header_level_1>
<figure>
<location><page_18><loc_7><loc_66><loc_41><loc_89></location>
<caption>Incorrect MF ( σ G = 3 )</caption>
</figure>
<figure>
<location><page_18><loc_7><loc_35><loc_41><loc_59></location>
</figure>
<section_header_level_1><location><page_18><loc_69><loc_90><loc_88><loc_91></location>Point source + noise</section_header_level_1>
<figure>
<location><page_18><loc_60><loc_66><loc_94><loc_90></location>
<caption>Correct MF ( σ G = 4 )</caption>
</figure>
<figure>
<location><page_18><loc_60><loc_35><loc_94><loc_59></location>
<caption>Fig. A.2. Upper left panel: image of the original point source when the PSF is a bivariate, circularly symmetric, Gaussian PSF with dispersion σ G = 4 pixels. Upper right panel: original point source added with a white-noise with standard deviation equal to half the peak value of the source itself; noisy image filtered with an improper matched filter (MF) which has a Gaussian shape and σ G = 3 pixels; bottom right panel: noisy image filtered with the correct MF.</caption>
</figure>
<section_header_level_1><location><page_19><loc_16><loc_90><loc_35><loc_92></location>Point souce ( σ G = 3 )</section_header_level_1>
<figure>
<location><page_19><loc_7><loc_66><loc_41><loc_89></location>
<caption>Incorrect MF ( σ G = 4 )</caption>
</figure>
<figure>
<location><page_19><loc_7><loc_35><loc_41><loc_59></location>
</figure>
<section_header_level_1><location><page_19><loc_69><loc_90><loc_88><loc_91></location>Point source + noise</section_header_level_1>
<figure>
<location><page_19><loc_60><loc_66><loc_94><loc_90></location>
<caption>Correct MF ( σ G = 3 )</caption>
</figure>
<figure>
<location><page_19><loc_60><loc_35><loc_94><loc_59></location>
<caption>Fig. A.3. Upper left panel: image of the original point source when the PSF is a bivariate, circularly symmetric, Gaussian PSF with dispersion σ G = 3 pixels. Upper right panel: original point source added with a white noise with standard deviation equal to half the peak value of the source itself. Bottom left panel: noisy image filtered with an improper matched filter (MF) that has a Gaussian shape and σ G = 4 pixels. Bottom right panel: noisy image filtered with the correct MF.</caption>
</figure>
<section_header_level_1><location><page_20><loc_13><loc_90><loc_38><loc_92></location>Extended source ( σ G = 10 )</section_header_level_1>
<figure>
<location><page_20><loc_7><loc_66><loc_41><loc_89></location>
<caption>Incorrect MF ( σ G = 3 )</caption>
</figure>
<figure>
<location><page_20><loc_7><loc_35><loc_41><loc_59></location>
</figure>
<section_header_level_1><location><page_20><loc_67><loc_90><loc_90><loc_91></location>Extended source + noise</section_header_level_1>
<figure>
<location><page_20><loc_60><loc_66><loc_94><loc_90></location>
<caption>Correct MF ( σ G = 10 )</caption>
</figure>
<figure>
<location><page_20><loc_60><loc_35><loc_94><loc_59></location>
<caption>Fig. A.4. Upper left panel: image of an extended point source with a circularly symmetric bivariate Gaussian shape with dispersion σ g = 10 pixels. Upper right panel: original point source added with a white noise with standard deviation equal to half the peak value of the source itself. Bottom left panel: noisy image filtered with an improper matched filter (MF), which has a Gaussian shape and σ G = 3 pixels. Bottom right panel: noisy image filtered with the correct MF.</caption>
</figure>
<section_header_level_1><location><page_21><loc_10><loc_91><loc_33><loc_93></location>Point souces ( ∆ x = 6 pixels)</section_header_level_1>
<figure>
<location><page_21><loc_7><loc_72><loc_33><loc_91></location>
</figure>
<section_header_level_1><location><page_21><loc_10><loc_64><loc_33><loc_65></location>Point souces ( ∆ x = 9 pixels)</section_header_level_1>
<figure>
<location><page_21><loc_7><loc_45><loc_33><loc_63></location>
</figure>
<section_header_level_1><location><page_21><loc_37><loc_91><loc_67><loc_93></location>Point souces + noise ( ∆ x = 6 pixels)</section_header_level_1>
<figure>
<location><page_21><loc_38><loc_72><loc_64><loc_90></location>
<caption>Point souces + noise ( ∆ x = 6 pixels)</caption>
</figure>
<figure>
<location><page_21><loc_38><loc_45><loc_64><loc_63></location>
<caption>MF ( ∆ x = 6 pixels)</caption>
</figure>
<figure>
<location><page_21><loc_68><loc_72><loc_94><loc_90></location>
<caption>MF ( ∆ x = 9 pixels)</caption>
</figure>
<figure>
<location><page_21><loc_68><loc_45><loc_94><loc_63></location>
<caption>Fig. A.5. Results obtainable with the matched filter (MF) in the case of two identical overlapping point sources with shape given by a bivariate, circularly symmetric, Gaussian PSF with σ G = 3 pixels, when their peaks are 6 and 9 pixels apart. A white noise is added with standard deviation equal to half the peak value of the sources.</caption>
</figure>
<section_header_level_1><location><page_22><loc_10><loc_91><loc_33><loc_93></location>Point souces ( ∆ x = 6 pixels)</section_header_level_1>
<figure>
<location><page_22><loc_7><loc_72><loc_33><loc_90></location>
</figure>
<section_header_level_1><location><page_22><loc_10><loc_64><loc_33><loc_65></location>Point souces ( ∆ x = 9 pixels)</section_header_level_1>
<figure>
<location><page_22><loc_7><loc_45><loc_33><loc_63></location>
</figure>
<section_header_level_1><location><page_22><loc_37><loc_91><loc_67><loc_93></location>Point souces + noise ( ∆ x = 6 pixels)</section_header_level_1>
<figure>
<location><page_22><loc_38><loc_72><loc_64><loc_90></location>
<caption>Point souces + noise ( ∆ x = 6 pixels)</caption>
</figure>
<figure>
<location><page_22><loc_38><loc_45><loc_64><loc_63></location>
<caption>MF ( ∆ x = 6 pixels)</caption>
</figure>
<figure>
<location><page_22><loc_68><loc_72><loc_94><loc_90></location>
<caption>MF ( ∆ x = 9 pixels)</caption>
</figure>
<figure>
<location><page_22><loc_68><loc_45><loc_94><loc_63></location>
<caption>Fig. A.6. Results obtainable with the matched filter (MF) in the case of two identical overlapping point sources with shape given by a bivariate, circularly symmetric, Gaussian PSF with σ G = 3 pixels, when their peaks are 6 and 9 pixels apart. A first-degree, two-dimensional polynomial background and a white noise with standard deviation equal to half the peak value of the sources are added.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "This paper deals with the detection problem of extragalactic point sources in multi-frequency, microwave sky maps that will be obtainable in future cosmic microwave background radiation (CMB) experiments with instruments capable of very high spatial resolution. With spatial resolutions that can be 0 . 1-1 . 0 arcsec or better, the extragalactic point sources will appear isolated. The same also holds for the compact structures due to the Sunyaev-Zeldovich (SZ) effect (both thermal and kinetic). This situation is different from the maps obtainable with instruments such as WMAP or PLANCK where, because of the lower spatial resolution ( ≈ 5-30 arcmin), the point sources and the compact structures due to the SZ effect form a uniform noisy background (' confusion noise '). The point source detection techniques developed in the past are therefore based on the assumption that all the emissions that contribute to the microwave background can be modeled with homogeneous and isotropic (often Gaussian) random fields and make use of the corresponding spatial power spectra. In the case of very high-resolution observations, such an assumption cannot be adopted since it still holds only for the CMB. Here, we propose an approach based on the assumption that the diffuse emissions that contribute to the microwave background can be locally approximated by two-dimensional low-order polynomials. In particular, two sets of numerical techniques are presented that contain two different algorithms each. The first set makes use of the a-priori information about the spectral properties of CMB and SZ and is suited to detecting an extragalactic point source with a different spectrum for these emissions. In this set, one algorithm is a modification of the internal linear combination (ILC) method, which is widely used in cosmology to extract the component of interest from a mixture of signals, and it is appropriate for extragalactic point sources with a known spectrum. The other one does not make use of this piece of information. The second set is tailored to detecting of extragalactic point sources with a similar spectrum to that of the CMB or SZ. Also in this set one algorithm is specific for extragalactic point sources with known spectrum whereas the other does not make use of this information. The performance of the algorithms is tested with numerical experiments that mimic the physical scenario expected for high Galactic latitude observations with the Atacama Large Millimeter/Submillimeter Array (ALMA). Key words. Methods: data analysis - Methods: statistical - Cosmology: cosmic microwave background",
"pages": [
1
]
},
{
"title": "An approach for the detection of point sources in very high-resolution microwave maps",
"content": "Roberto Vio 1 , Paola Andreani 2 Elsa Patr'ıcia R. G. Ramos 2 , 3 , 4 , and Antonio da Silva 3 Received .............; accepted ................",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The detection of extragalactic point sources in experimental microwave maps is a critical step in analyzing of the cosmic microwave background (CMB) maps. Besides the specific interest related to constructing of dedicated catalogs, these sources can, if not properly removed, have adverse effects on the estimation of the power spectrum and/or the test of Gaussianity of the CMB component. Much effort has been dedicated to multiple frequency maps of the same sky area, and many algorithms have been proposed (see Herranz and Sanz 2008; Herranz et al. 2012, and references therein). Apart from a recent Bayesian approach (Carvalho et al. 2009), most of them belong to two broad classes of techniques. The first class, suited to the extragalactic point sources with known spectra, is based on the Neyman-Pearson (NP) criterion that consists in maximizing the probability of detection P D under the constraint that the probability of false alarm P FA (i.e., the probability of a false detection) does not exceed a fixed value α (Kay 1998). The resulting algorithms are extensions of the classic matched filter (MF) (Herranz et al. 2002; Ramos et al. 2011). The second class, appropriated to the extragalactic point sources with unknown spectra, is based on maximizing of the ' signal-to-noise ratio ' (S / N) of the source intensity with respect to the underlying background (Herranz et al. 2009; Lanz et al. 2010). Both classes require the spatial power spectrum of the emitting components and therefore are based on the assumption that the emissions contributing to the microwave sky can be modeled by means of homogeneous and isotropic random fields. With a spatial resolution worse than 5 arcmin typical of Planck and WMAP experiments, such an assumption is excellent for the CMB, good for the confusion noise due to the point sources and the Sunyaev-Zeldovich (SZ) effect component, and locally barely acceptable for the diffuse Galactic emission. In the case of observation at very high spatial resolution, of order of 0 . 1-1 . 0 arcsec (that will be possible, for instance, with instruments as ALMA), this is no longer true. Indeed, since almost all of the extragalactic point sources but also of the compact structures due to the SZ effect will appear isolated, they can be thought of as the realization of (not necessarily stationary) shot-noise processes. Moreover, on small observing areas, it is realistic to expect that any other additional diffuse component (e.g. due to the Galactic emissions) is almost constant or slowly changing. This experimental scenario is different from the past or ongoing CMB experiments. New techniques of point source detection are therefore necessary. From the consideration that the detection of extragalactic point sources is typically done on very small areas of the sky, where the contribution of the diffuse components can be approximated well by means of low-degree, twodimensional polynomials, we propose an approach based on two sets of algorithms. The first set makes use of the a-priori information about the spectral properties of CMB and SZ, and the second one does not exploit this piece of information. Each set contains two algorithms that are suited to detecting point sources with known and unknown spectra, respectively. The reason for two different sets of algorithms is that the use of the spectral properties of the CMB and SZ permits removal of the contribution from these components. As a consequence, the knowledge of their spatial power spectrum is no longer necessary, and at the same time it is possible to unambiguously distinguish between true extragalactic point sources and the compact structures due to SZ. The price is a reduced, or even null, detection capability for the point sources with spectra that are similar, or even identical, to that of CMB, SZ, or to a linear combination of these. The algorithms that do no make use of this piece of information do not suffer this limitation, but they cannot distinguish the true extragalactic point sources from the compact structures due to SZ. The reason for two algorithms within each set is that those specialized for the extragalactic point sources with a specific spectrum are characterized by a greater detection capability. They are obtained by modifying the internal linear combination (ILC) method that in cosmology is used to extract a component of interest from the mixture of signals that contribute to the microwave sky emission (Eriksen et al. 2004; Hinshaw et al. 2007; Vio and Andreani 2008). Their main limitation is the necessity of multiple applications for detecting point sources with different spectra. Such a necessity is avoided by the algorithms that do not exploit this piece of information but at the price of less detection capability. The combined use of a couple of these algorithms belonging to different sets permits the detection of extragalactic point sources independently of their spectral emission and reduced contamination due to the SZ compact structures. The performances of both sets of algorithms is tested via numerical experiments based on simulated maps of high Galactic latitude that might be the area of interest of CMB high spatial resolution observations. The paper is organized as follows. Section 2 introduces the mathematical framework and explains the algorithms used. Section 3 discusses practical problems related to the choice of the experimental parameters. Numerical experiments are reported in section 4, while conclusions are summarized in section 5.",
"pages": [
1,
2
]
},
{
"title": "2. Formalization and solution of the problem",
"content": "By searching for a single extragalactic point source in a small area of sky, the microwave emission can be modeled with bidimensional discrete patches { X i } N f i =1 , each of them containing N p = N p 1 × N p 2 pixels, corresponding to N f different observing frequencies (channels), with the form Here, S i is the contribution of the extragalactic point source at the i th frequency, C i , Z i , and G i are the backgrounds due to CMB, extragalactic emission, and some other possible diffuse component (e.g. Galactic emission), respectively, and N i is the instrumental noise. In this model, the contribution of the extragalactic point sources is assumed in the form with ' a i ' the intensity of the source at the i th channel. According to Eq. (2), and without loss of generality, all the sources are assumed to have the same profile F independently of the observing frequency. In practical applications, this is not true. However, it is possible to meet this condition by convolving the images with an appropriate kernel (see below). For computational reasons that soon will become evident, it is useful to convert the two-dimensional model (1) into the one-dimensional form Here, x i = VEC[ X i ], with VEC[ H ] the operator that transforms a matrix H into a vector by stacking its columns one underneath the other. Something similar holds for the other quantities.",
"pages": [
2
]
},
{
"title": "2.1. Detection with ILC background removal",
"content": "One classical solution to deal with many maps of the same sky area taken at different observing frequencies consists in a linear composition by means a set of weights w = [ w 1 , w 2 , . . . , w N f ] T . In this way it is possible to work with a single map given by where X = ( x 1 , x 2 , . . . , x N f ) is an N p × N f matrix. The obvious question is how to fix such weights. Before proceeding, it is necessary to take into account that there is an a-priori information about the various components in Eq. (1). In particular, The first point implies that, for a given observing frequency, the emission due to the CMB and the SZ components can be obtained from a rescaled linear mixture of two templates (i.e., maps that do not depend on frequency) c and z , respectively. This implies that the cumulative contribution b i = c i + z i of these components is given by the i th column of matrix where M is an N e × N f matrix usually indicated with the term of mixing matrix . In the present context, the number of emission mechanisms is N e = 2 since the kinetic SZ emission has the same spectrum as for the CMB. For this reason, with c i we indicate the CMB plus the kinetic SZ emission from now on. The second point implies that within a small area centered on an extragalactic point source, the CMB and any other diffuse emission vary very little. This suggests that, for any patch X i ( j, k ) with -N j ≤ j ≤ N j and -N k ≤ k ≤ N k ( N p 1 = 2 N j +1, N p 2 = 2 N k +1), these emissions can be safely approximated by a low-degree, twodimensional polynomial of degree m where { α l } are real coefficients, whereas q and r are integer numbers permuted accordingly.",
"pages": [
2,
3
]
},
{
"title": "2.1.1. Point sources with known spectrum",
"content": "Starting from these considerations and adopting the criterion of the S/N maximization for a given extragalactic point source with emission spectrum a = a ̂ a , where ' a ' is to be estimated and ̂ a = [ ̂ a 1 , ̂ a 2 , . . . , ̂ a N f ] T is fixed, the weights w can be computed through the maximization of the quantity with ' ‖ . ‖ ' the Euclidean norm, under the constraints Because of the constraint (8), which forces weights w to preserve the intensity a , the numerator of Eq. (7) is a constant. Therefore, the maximization of SNR is obtained by the minimization of the denominator. The rationale behind this approach is that if each of the maps x i contains the contribution of a point source with shape F and of smooth component g i , approximable by means of a two-dimensional polynomial, then the same has to hold for their linear combination x = Xw . The denominator x -Lq thus represents the residuals of the least-squares fit to the composite map x of a model where a central point spread function (PSF) is superimposed to a bivariate polynomial background. The weights w are computed in such a way as to minimize the standard deviation of these residuals under the constraints (8) and (9). In Eq. (7), q = ( a, α T ) T is an array with size N c = [( m +1)( m +2) / 2] + 1, α the coefficients of the two-dimensional polynomial, whereas L is an N p × N c matrix with the form L = [ f , P ] with f = VEC[ F ] and P the N p × ( N c -1) design matrix corresponding to the least-squares fit of a two-dimensional polynomial 1 . The constraint (9) forces the contribution of the CMB and SZ components to the final map x to zero, whereas the contamination g is removed by means of the two-dimensional polynomial. The quantities w and q are unknown and have to be estimated. The maximization of SNR with the constraints (8)-(9) can be written in the form with M a = ( ̂ a , M T ) , λ an N e +1 array of Lagrange multipliers , and e 1 an N e +1 array of zeros except for the first element, which is '1'. This method is a modification of the constrained ILC by Remazeilles et al. (2010). We call it modified multiple ILC (MMILC). The basic idea is that, if in the center of the selected patch there is a point source, then the value of ' a ' should exceed a threshold due to noise. After some algebra, one obtains that the solution of problem (10) is given by the system of equations C XX = X T X , C XL = X T L and C LL = L T L , which provides where with I the identity matrix, and One interesting characteristic of solution (11) is that it does not require knowing the noise level of each map, a quantity that often can only be roughly estimated. Auseful insight into how MMILC works can be obtained if problem (10) is recast in the form 2 1 If the degree is one, P = [ δ 1 , δ 2 , 1 ], whereas for a degree two P = [ δ 1 glyph[circledot] δ 1 , δ 2 glyph[circledot] δ 2 , δ 1 glyph[circledot] δ 2 , δ 1 , δ 2 , 1 ], where ' glyph[circledot] ' represents the element-wise matrix multiplication (Hadamard product), 1 is a vector of ones, and δ 1 = VEC[ ∆ 1 ], δ 2 = VEC[ ∆ 2 ], where ∆ 1 is a matrix with 2 N j + 1 identical columns [ -N k , -N k + 1 , . . . , 0 , . . . , N k -1 , N k ] T , whereas ∆ 2 is a matrix with 2 N k +1 identical rows [ -N j , -N j +1 , . . . , 0 , . . . , N j -1 , N j ]. 2 We thank the referee for this suggestion. where A = ( I -L ( L T L ) -1 L T ) X . Since matrix A is the orthogonal projection of X onto the nullspace of L T , MMILC can be seen to sequentially perform a least-squares fit of the PSF overlapping a two-dimensional polynomial background on the original data for each frequency, followed by a constrained ILC on the residuals.",
"pages": [
3,
4
]
},
{
"title": "2.1.2. Point sources with unknown spectrum",
"content": "The main limitation of MMILC is that it only works optimally for a specific emission spectrum ̂ a . This assumption can be relaxed by converting the maximization of SNR with the constraints (8)-(9) in the least-squares minimization of the quantity with the constraints The constraint (18) is set to avoid the trivial solution w = 0 . In this way, problem (10) is converted into After some algebra, it is possible to see that q is again given by Eq. (13) but with w the solution of the eigenvalue problem where and C MM = MM T . The searched for w is given by the eigenvector of H that minimizes quantity S . Presently, the only method that we can suggest is to insert each eigenvector in Eq. (17) and to check numerically which of them provides the smallest S . This is because we have ascertained that there are situations where the eigenvector corresponding to the lowest eigenvalue of H (a criterion typical of the least-squares problems) does not work. Indeed, matrix H is not symmetric, and it cannot be expected to have any particular property. We call this method nonparametric MMILC (NP-MMILC). Although not specifically optimized for a particular ̂ a , the results provided by NP-MMILC depend on the emission spectrum of the point source. Indeed, if like MILC, this method too is interpreted as a sequential least-squares fits followed by a constrained ILC, it can be understood that, in the case of a point source with a large amplitude in maps with a low S / N and a small amplitude in maps with a high S / N, this results in a reduced detection capability. A simple procedure for avoiding this problem consists of applying NP-MMILC not to all maps but only to those for which the best S / N for the point source is expected. The choice can be based on ̂ a . This means to use the a priori information on the emission spectrum in a different way from MMILC.",
"pages": [
4
]
},
{
"title": "2.1.3. Detection procedure",
"content": "When searching for extragalactic point sources with MMILC or NP-MMILC in a given set of maps, the procedure consists in fixing the size (2 N j +1) × (2 N k +1) of a window that is made to slide, pixel by pixel, across the area of interest. At the end of this procedure a single map is obtained containing the estimated values of ' a ' for each pixel. Now, the question is to fix the detection threshold below which a given value of ' a ' is supposed to be only due to noise. In this respect, the direct use of solutions (12)-(14) and (21) is difficult. For this reason, two different procedures are suggested, Before concluding this section, we underline that the number of rows N e = 2 of the mixing matrix M comes from our interest in exploring the situation in which the extragalactic component Z i consists of secondary anisotropies of the CMB. In particular, we have only considered the SZ effect (both thermal and kinetic), which is the strongest one in galaxy clusters, groups of galaxies, and in protoclusters (i.e., Birkinshaw, 1999). However, if the information is available for one or more additional components, then it is sufficient to update M and the same solutions (12)-(14) and (21) and hold for N e = 3 or greater. Similarly, if one decides to remove only one component via ILC, either CMB or SZ, then it is sufficient to eliminate the appropriate row from matrix M and set N e = 1 in the solution. In this way, however, the drawback is that the remaining component has to be removed by means of the two-dimensional polynomial. This could be a necessary operation in the case of noisy maps (see below).",
"pages": [
4
]
},
{
"title": "2.2. Detection without ILC background removal",
"content": "The MMILC and NP-MMILC detection techniques are potentially quite effective, however they suffer from two main drawbacks: since in the final map a = a T w and σ map = ‖ σ T n w ‖ , ' a ' is given by the sum of both positive and negative values whereas, σ map is given by the sum of positive values alone. In other words, the background subtraction reduces the S / N with respect to a simple sum of the maps. The situation worsens when the emission of an extragalactic point source has a spectrum similar to that of the CMB or of the SZ since ' a ' will tend to zero; For this reason, to detect extragalactic point sources with ̂ a belonging to the nullspace of M , the above procedures have to be adapted to work without the ILC removal of the CMB and the SZ components. Again, two different algorithms are presented.",
"pages": [
4,
5
]
},
{
"title": "2.2.1. Point sources with known spectrum",
"content": "The case of point sources with known spectra can be easily obtained from problem (10) through the substitutions M a = ̂ a and e 1 = 1: with solution given by The explicit solution for w and q is given by Eqs. (12)-(14) with M a = ̂ a . Detection is still carried out as explained in Sec. 2.1.3. With this method, which we call modified ILC (MILC), the CMB and SZ emissions are not removed through the use of the mixing matrix M , but rather by exploiting that the CMB, part of the SZ, and any other component with a diffuse spatial distribution can be removed through the polynomial approximation. As a consequence, the only contribution in the final map beyond that of the extragalactic point sources is the compact component of the SZ (both thermal and kinetic), and this is an unavoidable problem. Without additional information, it is impossible to separate an SZ emission with point-like spatial distribution from a genuine extragalactic point source. In the case of SZ emission with more extended structures, a possible solution consists of checking if their spatial distribution is compatible with the PSF F . This issue, however, is beyond the scope of the present work.",
"pages": [
5
]
},
{
"title": "2.2.2. Point sources with unknown spectrum",
"content": "If in the minimization of the quantity S as given in Eq. (17) the constraint (19) is relaxed, the nonparametric version of MILC is obtained (NP-MILC). It is easily verified that for this problem too, q is given by Eq. (13), but now w is the solution of the eigenvalue problem Hw = γ w with As for NP-MMILC, the searched w is given by the eigenvector of H that minimizes quantity S , and detection is carried out as explained in Sec. 2.1.3. Also, NP-MILC suffers the same dependence on ̂ a as NP-MMILC.",
"pages": [
5
]
},
{
"title": "3. Practical uses",
"content": "In this section we discuss some practical problems and how they can be addressed. The first is related to the degree m of the polynomial used to approximate the background. Obviously, the smaller the sky area of interest the lower the degree of the polynomial. For example, considering that the CMB has a coherence scale of about 10 arcmin, it can be reasonably expected that with a resolution of 0 . 1-1 . 0 arcsec a first-degree polynomial is a good choice. The second question is related to the sizes N j and N k of the patch for testing for the presence of a point source. Two competing requirements arise: on the one hand, N j and N k must be as large as possible to reduce errors in estimating the polynomial parameters, on the other, a small size implies that the approximation of the background with a low-degree polynomial is a more reliable operation and, at the same time, that the probability two or more sources being in the same patch X is low. For illustrative purposes, Fig. 1 shows the standard deviation σ a of the estimated intensity a as provided by MILC in the case of a point source with a Gaussian profile and a dispersion σ psf equal to three pixels. A single map is considered where the background is given by a twodimensional one-degree polynomial, instrumental noise is Gaussian and white with standard deviation σ n , and N p 1 and N p 2 are progressively increased. The true value of a is one in unit of σ n . The decrease in σ a is evident. Figure 2 shows the relationship between P D and P FA for different values of the ratio a/σ n . These figures clearly show that N j and N k lying in the range 3 σ psf -5 σ psf is a reasonable compromise. As shown in the appendix A, that the exact PSF F could not be known or that some of the point sources could be overlapping and/or could have an extended shape, have no important consequences. However, another issue arises because the shape of the PFSs changes with observing frequency in practical applications. Widespread practice is to convolve maps with a suited kernel function in order to get a common spatial PSF F for all the frequencies. This operation has the beneficial effect of reducing the standard deviation of the instrumental noise, but at the same time it introduces a spurious spatial correlation in it. Actually, even if neglected, this is not expected to be critical since both MILC and MMILC are linear techniques, and the only consequence is a reduction of the efficiency of the leastsquares estimate of the coefficients q (i.e., the estimate is unbiased but with greater variance). Something similar is also expected for NP-MILC and NP-MMILC that represent the solution of a linear least-squares problem with a quadratic constraint (i.e., both the quantity to minimize and the constraint are smooth functions). In other words, given the above-mentioned reduction in the standard deviation of the noise, this spurious correlation is not expected to have critical consequences. This is especially true if one takes into account that there are other and more important approximations that make the analysis of data less rigorous (e.g., often the level of instrumental noise is only roughly known). A final question regards whether in practical applications it is more convenient to use the MILC and MMILC algorithms or the NP-MILC and NP-MMILC ones. Indeed, MILC and MMILC work optimally only for a specific emission spectrum ̂ a , a feature common to other detection techniques such as the matched multifilter (Herranz et al. 2012). In principle, this is not a critical question. It is sufficient to apply the detection algorithm to a set of prefixed ̂ a obtained by grouping sources in broad families - radio flat, radio steep, dusty galaxies of a certain type, etc - and defining average spectral laws ̂ a for each family (Ramos et al. 2011; Herranz et al. 2012). Such an approach is viable since MILC and MMILC are fast algorithms, and they require the numerical solution of linear systems containing no more than a few of tens of linear equations. Moreover, as shown in Ramos et al. (2011), where a version of MMILC without background subtraction is applied to high-Galactic latitude WMAP maps, strong degradation of the detection capability has to be expected only if the spectrum of the point sources is quite different from the one for which the MMILC algorithm has been optimized. Of course, this kind of problem can be avoided using NP-MILC and NPMMILC. However, since they are not optimized for specific emission characteristics, the price is a lower detection capability for specific spectra. Given the inexpensive computational cost of the four algorithms, the best choice is to try all of them and check the results.",
"pages": [
5,
6
]
},
{
"title": "4. Numerical experiments",
"content": "To support the arguments presented above, we present some numerical experiments here with simulated maps at high Galactic latitude (where the Galactic contamination is negligible) that is the region of interest for future CMB experiments. Since realistic experimental conditions are not yet available, such simulations are only presented for illustration. We produced small sky patches of 0 . 86 deg 2 at 3 '' angular resolution with several components, namely, the CMB and the Sunyaev-Zel'dovich effects (SZ), both kinetic and thermal. To produce these maps we used hydrodynamic/Nbody simulations with cosmological parameters that are consistent with WMAP parameters for a flat Universe and standard ΛCDM model, with an equation of state for the dark energy component of w = -1. The adopted present time density parameters expressed in terms of the critical density are (Ω cdm , Ω Λ , Ω b ) = (0 . 256 , 0 . 7 , 0 . 044), a dimensionless Hubble constant of h = 0 . 71, and a mean CMB temperature of T =2.725 K. Adiabatic initial conditions are assumed, a spectral index of n s = 1, and full reionization at redshift 7. For the present epoch, we considered a normalization power spectrum of σ 8 = 0 . 9 and a shape parameter of Γ = 0 . 17. The CMB component is produced with the CAMB code (Lewis et al. 2000) to obtain the linear CMB power spectrum. The full-sky CMB temperature anisotropy map was generated with the HEALPix software (G'orski et al. 2005) with Nside = 8192. From this map a small sky region was extracted with an area of about 0.86 deg 2 around the equator, projected on a squared map. Details about the simulations of the SZ effect components can be found in da Silva et al. (2001) and Ramos et al. (2012). The frequencies chosen were 90, 150, 250, 330, 440, 675, and 950 GHz, which correspond to the ALMA receiver bands. All components were co-added, resulting in a final map, ∆ I CMB+SZ /I , with a pixel size of 3 arcsec. We use the central part of the maps (300 × 300 pixels) and convolve them for each frequency with a Gaussian PSF with a dispersion of three pixels. To each map a white-noise process has also been added with standard deviations σ n i set to 0 . 12 time the standard deviation of the values of map itself. Finally, 20 randomly distributed point sources were included with a i = 1 . 7 σ n i . In this way, maps with the same S/N are obtained. The values of σ n i and a i have been arbitrarily chosen to test algorithms under very bad operational conditions, but at the same time to obtain stable results (i.e. with different realizations of the noise process almost all the sources are correctly detected with no false detections). The simulated experimental scenario corresponds to an adverse situation of rather low S/N and, since σ n i increases with frequency, with a spectrum ̂ a (see curve a 1 in Fig. 3) that mimics that of the CMB plus SZ background (i.e. ̂ a is close to the nullspace of M , or M ̂ a ≈ 0 ). Figure 4 displays the simulated maps. We note that the point sources are not even visible, and they are by far exceeded by the SZ pointlike emission. Figure 5 shows the results obtained with the four algorithms presented above. For MILC, MMILC, and NP-MILC the detection threshold has been set to 4 σ L whereas a value of 3 . 5 σ L has been used for NP-MMILC. Background has been approximated by a two-dimensional first-degree polynomial. A sliding square window of 19 × 19 pixels has been adopted for the local search of point sources. As expected, the MMILC and NP-MMILC do not work. On the other hand, MILC and NP-MILC have effectively removed the CMB, as well as the SZ diffuse components, and correctly detected all the point sources in the map (see Fig. 8). However, many of the SZ point-like emissions are also present. glyph[negationslash] The situation greatly improves if { a i } = [2 . 00 , 1 . 00 , 0 . 60 , 0 . 40 , 0 . 20 , 0 . 06 , 0 . 02] T glyph[circledot] σ n which simulates an emission spectrum decreasing with frequency (see curve a 2 in Fig. 3). In this way M ̂ a = 0 . Figure 6 shows the maps corresponding to this case. As is visible in Fig. 7, now both MMILC and NP-MMILC are able to correctly detect all the point sources except one, as well to completely remove the CMB and SZ contamination. We note the detection of two couples of overlapping point sources in the bottom right hand and middle right hand parts of the map. However, as expected, the NP-MMILC map presents various false detections due to noise (the detection threshold has been set to 3 . 5 σ L in order to obtain the same number of true detections as MMILC). A point to stress is that, in the present high Galactic latitude experiment, the diffuse components { g i } can be set to zero. As a result, in models (10) and (20) it should have been possible to set L = f . (i.e., to avoid the polynomial approximation of the background). However, the use of the general model permits the stability of MMILC and NP-MMILC to be tested for high level of noise.",
"pages": [
6
]
},
{
"title": "5. Summary and conclusions",
"content": "In this paper four algorithms, the modified ILC (MILC), the modified multiple ILC (MMILC), the nonparametric -MILC (NP-MILC), and the nonparametric -MMILC (NPMMILC), have been presented for detection of extragalactic point sources in multifrequency, very high-resolution CMB maps. In particular, MMILC and NP-MMILC make use of the a-priori information about the spectral properties of the CMB and SZ with MMILC tailored to detecting extragalactic point sources with a given spectrum that has to be different from that of these emissions. The other two algorithms are suited to detecting the extragalactic point sources with similar spectra to the CMB or SZ with MILC tailored to the specific spectra. The main property of the proposed algorithms is that they do not require any a-priori knowledge of the statistical characteristics of spatial distribution of the diffuse emissions that contribute to the microwave background. Indeed, these can be locally approximated with a low-degree, two-dimensional polynomial. The two proposed sets of algorithms used in conjunction are effective in detecting extragalactic point sources independently of the spectral characteristics of their emission. Their potential performance has been illustrated with some numerical experiments. Acknowledgements. E. P. Ramos is supported by grant POPHQREN-SFRH/BD/45613/2008, from FCT (Portugal). E. P. Ramos and R. Vio thank ESO for its hospitality and support through the DGDF funding program.",
"pages": [
6,
7
]
},
{
"title": "References",
"content": "Birkinshaw M., 1999, Phys. Rep., 310, 97 Carvalho, P., Rocha, G. and Hobson, M.P. 2009, MNRAS, 393, 681 da Silva A. J. C., Barbosa D., Liddle A. R., & Thomas, P. A. 2001, MNRAS, 326, 155 Herranz, D. et al. 2002, MNRAS, 336, 1057 Herranz, D. and Sanz, J.L. 2008, IEEE Journal of Selected Topics in Signal Processing, 5, 727 Herranz, D., L'opez-Caniego, M., Sanz, J.L., & Gonz'alez-Nuevo, J. 2009, MNRAS, 394, 510 Herranz, D., Argueso, F. and Carvalho, P. 2012, Advances in Astronomy, in print Eriksen, H.K., Banday, A.J., G'orski, K.M., & Lilje, P.B. 2004, ApJ, 612, 633 G'orski, K. M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K., Reinecke, M., & Bartelmann, M. 2005, ApJ, 622, 759 Hinshaw, G., et al. 2007, ApJS, 170, 288 Kay, S. M. 1998, Fundamentals of Statistical Signal Processing: Detection Theory (London: Prentice Hall) Lanz, L.F., Herranz, D., Sanz, J.L., Gonzalez-Nuevo, J. and LopezCaniego, M. 2010, MNRAS, 403, 212 Lewis, A., Challinor, A., & Lasenby, A. 2000, ApJ, 538, 473 Ramos, E.P.R.G., Vio, R. and Andreani, P. 2011, A&A, 528, A75 Ramos, E. P. R. G., da Silva, A., J. C., Liu, G.C., 2012, ApJ, in preparation Remazeilles, M., Delabrouille, J. and Cardoso, J.F. 2011, MNRAS, 418, 467 Vio, R. and Andreani, P. 2008, A&A, 487, 775 a/ σ n = 0.5 FA σ +",
"pages": [
7,
9,
11
]
},
{
"title": "Detection map: NP-MMILC",
"content": "+",
"pages": [
13
]
},
{
"title": "Detection map: NP-MILC",
"content": "Detection map: MMILC Detection map: MILC Detection map: NP-MMILC Detection map: NP-MILC",
"pages": [
15
]
},
{
"title": "Appendix A: Some additional questions",
"content": "The detection techniques presented in Sec. 2 are based on the assumptions that a) the true PSF F is known; b) all the sources have a point-like shape (i.e. the shape of the PSF); c) all the sources are isolated. In practical applications, however, the PSF has to be estimated, some sources can have an extended shape, and overlapping is possible. Here, we show that all this can be expected to have only secondary consequences. In this respect, for sake of ease in the formalism, we start by considering an experimental one-dimensional signal x = a f + n . Here, f is the onedimensional PSF and n an additional white noise. In practice, x is due to a point source with amplitude a embedded in noise. As is well known, the least-squares fit estimate of a provides the solution At this point, we point out that in detection problems the test statistic T ( x ) = f T x (e.g. see Kay 1998) is used where f is the well known matched filter (MF). In other words, unless of a constant factor, the estimate ̂ a is identical to the test statistic T ( x ). Indeed, the rhs of Eq. (A.1) is nothing else that the normalized correlation of x with f . This means that in the present context, the least squares fit and the matched filter are two equivalent techniques. This allows us to analyze the characteristic of the least-squares fit using the body of the theory of the linear filters. Therefore, f can be interpreted as a linear, typically low-pass, discrete filter with N p entries that is made to slide across an array x ≡ { x i } N x i =1 with N x glyph[greatermuch] N p . In this way, for each element x i one can obtain the quantity ̂ a i = T ( x i ) / ( f T f ), where x i ≡ { x j } i + N p -1 j = i . By means of the discrete Fourier transform (DFT) it is possible to compute ̂ a ≡ { ̂ a i } n x i =1 via with ˜ x and ˜ f the DFT of x and the zero padded version of f , IDFT[ . ] the inverse DFT operator and symbols ' ∗ ', ' glyph[circledot] ' indicating the complex conjugate and the point-wise multiplication , respectively. This implies that the statistical characteristics of ̂ a can be analyzed by means of the spectral properties of f . These considerations can be trivially extended to the two-dimensional case. Here, it is useful to present some simple examples to see that the three facts above are actually not important. Concerning point a), Fig. A.1 shows a central slice P ( ν ) = | ˜ f | of the spectrum of three two-dimensional, circularly symmetric, Gaussian PSFs with dispersion σ G = 3 and 4 pixels, respectively. It is clearly visible that the value of σ G determines the bandwidth of ˜ f in the sense that the larger σ G , the stronger the filtering action. This means that, if a point source with σ G = 4 pixels is filtered assuming a PSF with σ G = 3 (i.e. with an error of 25%), the only consequence is a slighter reduction of the noise with respect to what is obtainable with the correct PSF. In contrast, if the point source has σ G = 3 and a PSF with σ G = 4 is assumed (i.e. with an error of 33%), a stronger reduction of the noise is obtained. In this case, however, part of the signal of interest is also filtered out, again with a slighter reduction of the detection capability with respect to what is obtainable with the correct PSF. These two examples are shown in Figs. A.2-A.3. Similar arguments hold for the point b) when the source has an extended shape. In this case, however, since the PSF is much ' narrower ' than the source, the noise filtering will be much less effective. However, as shown by the example in Fig. A.4, where an extended object with Gaussian shape, σ G = 10, and a Gaussian PSF with σ G = 3 pixels are considered, this does not mean that detection is not possible, but rather that it is less effective. Finally, concerning point c), i.e. the case of two close point sources, the situation does not change very much. The only consequence is that the filtered point sources will appear more overlapped than the unfiltered ones (see Fig. A.5). In the cases examined above, the presence of a smooth background p has not been considered. However, again, things can be expected not to change very much. Indeed, Eq. (A.1) becomes Now, if instead of p the result of a least-squares polynomial fit ̂ p is used, then one obtains with ̂ d = ̂ p -p a smooth function. In other words, a map is produced where a smoothed point source is superimposed to a smoothed (presumably weak) background and noise is reduced. This is visible in Fig A.6, which shows the results obtained for a situation similar to that of Fig. A.5 when a first-degree, two-dimensional polynomial background is present. To understand why it is reasonable to assume that these facts are not critical for MMILC, it is useful to interpret this method as done in Sec. 2.1.1; i.e, a sequential least-squares fit of a point spread function (PSF) overlapped to a twodimensional polynomial background on the original data for each frequency, followed by a constrained ILC on the residuals. Since, each of the fits is not very sensitive to the issues mentioned above, it is reasonable to assume that the same is valid for their linear combination. Something similar holds for MILC, NP-MILC, and NP-MMILC. These arguments can also be extended with very good approximation to the case that, as in Sec. 2, the background is computed for each position of the sliding detection window. Indeed, since the window is made to slide one pixel at a time, for close pixels the least-squares fit is done using essentially the same data. The experiments concerning MILC and NP-MILC in Figs. 4-7 confirm this.",
"pages": [
16
]
}
]
2013A&A...557A...9M
https://arxiv.org/pdf/1306.5561.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_82><loc_91><loc_87></location>Estimation and correction of wavefront aberrations using the self-coherent camera: laboratory results</section_header_level_1>
<text><location><page_1><loc_24><loc_80><loc_77><loc_81></location>J. Mazoyer 1 , P. Baudoz 1 , R. Galicher 1 , M. Mas 2 , and G. Rousset 1</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_76><loc_91><loc_78></location>1 LESIA, Observatoire de Paris, CNRS, UPMC Paris 6 and Denis Diderot Paris 7, Meudon, France. e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_72><loc_76></location>2 Laboratoire d'Astrophysique de Marseille, CNRS, Aix-Marseille Univ., Marseille, France</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_72><loc_39><loc_73></location>Preprint online version: November 6, 2021</text>
<section_header_level_1><location><page_1><loc_48><loc_70><loc_54><loc_71></location>Abstract</section_header_level_1>
<text><location><page_1><loc_11><loc_65><loc_91><loc_69></location>Context. Direct imaging of exoplanets requires very high contrast levels, which are obtained using coronagraphs. But residual quasi-static aberrations create speckles in the focal plane downstream of the coronagraph which mask the planet. This problem appears in ground-based instruments as well as in space-based telescopes.</text>
<text><location><page_1><loc_11><loc_62><loc_91><loc_65></location>Aims. An active correction of these wavefront errors using a deformable mirror upstream of the coronagraph is mandatory, but conventional adaptive optics are limited by differential path aberrations. Dedicated techniques have to be implemented to measure phase and amplitude errors directly in the science focal plane.</text>
<text><location><page_1><loc_11><loc_56><loc_91><loc_62></location>Methods. First, we propose a method for estimating phase and amplitude aberrations upstream of a coronagraph from the speckle complex field in the downstream focal plane. Then, we present the self-coherent camera, which uses the coherence of light to spatially encode the focal plane speckles and retrieve the associated complex field. This enable us to estimate and compensate in a closed loop for the aberrations upstream of the coronagraph. We conducted numerical simulations as well as laboratory tests using a four-quadrant phase mask and a 32x32 actuator deformable mirror.</text>
<text><location><page_1><loc_11><loc_50><loc_91><loc_56></location>Results. We demonstrated in the laboratory our capability to achieve a stable closed loop and compensate for phase and amplitude quasi-static aberrations. We determined the best-suited parameter values to implement our technique. Contrasts better than 10 -6 between 2 and 12 λ/D and even 3 . 10 -7 (RMS) between 7 and 11 λ/D were reached in the focal plane. It seems that the contrast level is mainly limited by amplitude defects created by the surface of the deformable mirror and by the dynamic of the detector.</text>
<text><location><page_1><loc_11><loc_48><loc_91><loc_50></location>Conclusions. These results are promising for a future application to a dedicated space mission for exoplanet characterization. A number of possible improvements have been identified.</text>
<text><location><page_1><loc_11><loc_45><loc_91><loc_47></location>Key words. instrumentation: high angular resolution - instrumentation: adaptive optics - techniques: high angular resolution</text>
<section_header_level_1><location><page_1><loc_7><loc_40><loc_20><loc_42></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_23><loc_50><loc_39></location>Direct imaging is crucial to increase our knowledge of extrasolar planetary systems. On the one hand, it can detect long-orbit planets that are inaccessible for other methods (transits, radial velocities). On the other hand, it allows the full spectroscopic characterization of the surface and atmosphere of exoplanets. In a few favorable cases, direct imaging has already enabled the detection of exoplanets (Kalas et al. 2008; Lagrange et al. 2009) and even of planetary systems (Marois et al. 2008, 2010). However, the main difficulties of this method are the high contrast and small separation between the star and its planet. Indeed, a contrast level of 10 -10 has to be reached within a separation of ∼ 0 . 1 '' or lower to allow the detection of rocky planets.</text>
<text><location><page_1><loc_7><loc_10><loc_50><loc_22></location>To reduce the star light in the focal plane of a telescope, several coronagraphs have been developed, such as the fourquadrant phase mask (FQPM) coronograph (Rouan et al. 2000), the vortex coronograph (Mawet et al. 2005) and the phase-induced amplitude apodization coronograph (Guyon et al. 2005). However, the performance of these instruments is drastically limited by phase and amplitude errors. Indeed, these wavefront aberrations induce stellar speckles in the image, which are leaks of the star light in the focal plane downstream of the coronagraph. When classical adaptive</text>
<text><location><page_1><loc_52><loc_31><loc_95><loc_42></location>optics (AO) systems correct for most of the dynamic wavefront errors that are caused by to atmosphere, they use a dedicated optical channel for the wavefront sensing. Thus, they cannot detect quasi-static non-common path aberrations (NCPA) created in the differential optical paths by the instrument optics themselves. These NCPA have to be compensated for using dedicated techniques, for groundbased telescopes as well as for space-based instruments.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_29></location>Two strategies have been implemented to overcome the quasi-static speckle limitation. First, one can use differential imaging techniques to calibrate the speckle noise in the focal plane. Theses methods can use either the spectral signature and polarization state of the planet or differential rotation in the image (Marois et al. 2004, 2006). Second, even before applying these post-processing techniques, an active suppression of speckles (Malbet et al. 1995) has to be implemented to reach very high contrasts. It uses a deformable mirror (DM) controlled by a specific wavefront sensor that is immune against NCPA. The techniques developed for this purpose include dedicated instrumental designs (Guyon et al. 2009; Wallace et al. 2010), or creating of known phases on the DM (Bord'e & Traub 2006; Give'on et al. 2007) to estimate the complex speckle field.</text>
<text><location><page_2><loc_7><loc_83><loc_50><loc_93></location>Ground-based instruments that combine these two strategies are currently being developed, such as SPHERE (Beuzit et al. 2008) and GPI (Macintosh et al. 2008), to detect young Jupiter-like planets with an expected contrast performance of 10 -6 at 0 . 5 '' . Better contrasts might be achieved to reach the rocky planet level with instruments using dedicated active correction techniques embedded in space telescopes (Trauger & Traub 2007).</text>
<text><location><page_2><loc_7><loc_62><loc_50><loc_82></location>In this context, we study a technique of wavefront sensing in the focal plane that allows an active correction in a closed loop. This paper has two main objectives. First we give an overview of how the amplitude and phase errors upstream of a coronagraph can be retrieved from the complex amplitude of the speckle field (Section 2) and how they can be compensated for using a DM (Section 3). In Section 4, we introduce the self-coherent camera (Baudoz et al. 2006; Galicher et al. 2008). This instrument uses the coherence of the stellar light to generate Fizeau fringes in the focal plane and spatially encode the speckles. Using both the aberration estimator and the self-coherent camera (SCC), we are able to correct phase and amplitude aberrations. The second objective of the paper is a laboratory demonstration of the active correction and an experimental parametric study of the SCC (Section 5).</text>
<section_header_level_1><location><page_2><loc_7><loc_56><loc_46><loc_59></location>2. Wavefront estimator in the focal plane of a coronagraph</section_header_level_1>
<text><location><page_2><loc_7><loc_38><loc_50><loc_55></location>In this section, we aim to prove that one can retrieve the wavefront upstream of the coronagraph using the measured complex amplitude of the electric field in the focal plane downstream of the coronagraph. We assume in the whole section that we can measure this complex amplitude without error using an undetermined method. We describe one type of this method (the SCC) in Section 4. In Section 2.1, we express the complex electric field that is associated to the speckles as a function of the wavefront errors in the pupil upstream of a phase mask coronagraph. From this expression, we propose an estimator of the wavefront errors from the speckle electric field (Section 2.2) and analyze its accuracy for an FQPM (Section 2.3).</text>
<section_header_level_1><location><page_2><loc_7><loc_33><loc_49><loc_36></location>2.1. Expression of the complex amplitude of speckles in the focal plane as a function of the initial wavefront</section_header_level_1>
<text><location><page_2><loc_7><loc_17><loc_50><loc_32></location>We consider here a model of a phase mask coronagraph using Fourier optics. Figure 1 (top) presents the principle of a coronagraph. We assume that the star is a spatially unresolved monochromatic source centered on the optical axis. The stellar light moves through the entrance pupil P . Behind this pupil, the beam is focused on the mask M in the focal plane, which diffracts the light. Hence, the non aberrated part of the stellar light is rejected outside of the imaged pupil in the next pupil plane and is stopped by the Lyot stop diaphragm L . The aberrated part of the beam goes through the Lyot stop, producing speckles on the detector in the final focal plane (Figure 1, bottom).</text>
<text><location><page_2><loc_7><loc_13><loc_50><loc_16></location>We note whith α and φ the amplitude and phase aberrations in the entrance pupil plane and define the complex wavefront aberrations Φ as</text>
<formula><location><page_2><loc_24><loc_10><loc_50><loc_11></location>Φ = φ + iα. (1)</formula>
<figure>
<location><page_2><loc_52><loc_73><loc_94><loc_93></location>
<caption>Figure 1. Principle of a coronagraph (top). Aberrations in the entrance pupil plane induce speckles in the focal plane (bottom).</caption>
</figure>
<text><location><page_2><loc_52><loc_62><loc_95><loc_64></location>The complex amplitude of the star in the entrance pupil plane ψ ' S can be written as</text>
<formula><location><page_2><loc_62><loc_59><loc_95><loc_61></location>ψ ' S ( ξ , λ ) = ψ 0 P ( ξ ) exp ( i Φ( ξ )) , (2)</formula>
<text><location><page_2><loc_52><loc_53><loc_95><loc_58></location>where ψ 0 is the mean amplitude of the field over the pupil P, ξ the coordinate in the pupil plane and λ the wavelength. We assume that the aberrations are small and defined in the pupil P ( P Φ = Φ), thus</text>
<formula><location><page_2><loc_64><loc_49><loc_95><loc_52></location>ψ ' S ( ξ , λ ) ψ 0 glyph[similarequal] P ( ξ ) + i Φ( ξ ) . (3)</formula>
<text><location><page_2><loc_52><loc_46><loc_95><loc_48></location>The complex amplitude of the electric field A ' S behind the coronagraphic mask M in the first focal plane is</text>
<formula><location><page_2><loc_68><loc_43><loc_95><loc_45></location>A ' S = F [ ψ ' S ] M, (4)</formula>
<text><location><page_2><loc_52><loc_39><loc_95><loc_42></location>where F is the Fourier transform. Using Equation 3, we can write the electric field F -1 ( A ' S ) before the Lyot stop</text>
<formula><location><page_2><loc_59><loc_35><loc_95><loc_38></location>F -1 [ A ' S ] ψ 0 = P ∗ F -1 [ M ] + i Φ ∗ F -1 [ M ] , (5)</formula>
<text><location><page_2><loc_52><loc_32><loc_95><loc_34></location>where ∗ is the convolution product. We call Φ M the aberrated part of the field after the coronagraph:</text>
<formula><location><page_2><loc_61><loc_30><loc_95><loc_31></location>Φ M = φ M + iα M = Φ ∗ F -1 [ M ] . (6)</formula>
<text><location><page_2><loc_52><loc_27><loc_85><loc_28></location>After the Lyot stop L , the electric field ψ S is</text>
<formula><location><page_2><loc_61><loc_23><loc_95><loc_26></location>ψ S ψ 0 = ( P ∗ F -1 [ M ]) .L + i Φ M .L. (7)</formula>
<text><location><page_2><loc_52><loc_12><loc_95><loc_22></location>We assume a coronagraph for which the non aberrated part of the electric field is null inside the imaged pupil. This property of the perfect coronagraph (Cavarroc et al. 2006) has also been demonstrated analytically for several phase coronagraphs such as FQPM coronagraphs (Abe et al. 2003) and vortex coronagraphs (Mawet et al. 2005). The remaining part Φ L of the normalized electric field after the Lyot stop reads</text>
<formula><location><page_2><loc_57><loc_10><loc_95><loc_11></location>Φ L = φ L + iα L = Φ M .L = (Φ ∗ F -1 [ M ]) .L. (8)</formula>
<figure>
<location><page_3><loc_7><loc_86><loc_50><loc_93></location>
<caption>Figure 2. Simulations of an aberrated phase in the entrance pupil plane ( φ ), and the real part of the field in the next pupil plane before ( φ M ) or after ( φ L ) the Lyot pupil. We also show the estimate ( φ est ) and the difference between φ est and φ . L = P in this case.</caption>
</figure>
<text><location><page_3><loc_7><loc_74><loc_46><loc_75></location>In the final focal plane, the complex amplitude A S is</text>
<formula><location><page_3><loc_18><loc_68><loc_50><loc_72></location>A S = ψ 0 F [ i Φ L ] , A S = ψ 0 F [ i (Φ ∗ F -1 [ M ]) .L ] , A S = iψ 0 ( F [Φ] .M ) ∗ F [ L ] . (9)</formula>
<text><location><page_3><loc_7><loc_62><loc_50><loc_67></location>This complex amplitude is directly related to the wavefront aberrations in the entrance pupil. If one can measure A S , we can invert Equation 9 and retrieve the complex wavefront errors Φ in the entrance pupil.</text>
<section_header_level_1><location><page_3><loc_7><loc_59><loc_25><loc_60></location>2.2. Wavefront estimator</section_header_level_1>
<text><location><page_3><loc_7><loc_52><loc_50><loc_57></location>We still assume in this section that an undefined method provides access to A S . Using this complex amplitude A S as the measurement, we therefore propose the following estimator Φ est for the wavefront:</text>
<formula><location><page_3><loc_20><loc_48><loc_50><loc_51></location>Φ est = i F -1 [ A S Mψ 0 ] .P. (10)</formula>
<text><location><page_3><loc_7><loc_41><loc_50><loc_47></location>This estimator can be used for any phase mask coronograph (for which M is nonzero over the full focal plane). To justify the pertinence of this estimator, we can re-write it using the variables of our model. Using Equation 9, in a noise-free measurement case, this estimator reads</text>
<formula><location><page_3><loc_11><loc_36><loc_50><loc_39></location>Φ est = [ ((Φ ∗ F -1 [ M ]) .L ) ∗ F -1 [ 1 M ]] .P. (11)</formula>
<text><location><page_3><loc_7><loc_24><loc_50><loc_35></location>Theoretically, if no Lyot stop is applied ( L = 1), Equation 11 becomes Φ est = P Φ = Φ. We propose this estimator based on the assumption that most of the information about the aberrations is not diffracted outside of the imaged pupil by the coronagraphic mask. Therefore, using this assumption, we intuit that for L glyph[similarequal] P , we still have Φ est glyph[similarequal] Φ. This assumption is verified by the simulation in Section 2.3, and by the experiment described in Section 5.</text>
<text><location><page_3><loc_7><loc_19><loc_50><loc_24></location>For a symmetrical phase mask such as the FQPM, either F -1 [ M ] and F -1 [ 1 M ] are real. Thus, in the estimator we can separate the real ( φ est ) and imaginary part ( α est ) of the estimator in Equation 11:</text>
<formula><location><page_3><loc_11><loc_15><loc_50><loc_18></location>{ φ est = [ (( φ ∗ F -1 [ M ]) .L ) ∗ F -1 [ 1 M ]] .P α est = [ (( α ∗ F -1 [ M ]) .L ) ∗ F -1 [ 1 M ]] .P. (12)</formula>
<text><location><page_3><loc_7><loc_10><loc_50><loc_13></location>This relation ensures that within the limits of our model, this estimator independently provides estimates of the phase and amplitude aberrations.</text>
<section_header_level_1><location><page_3><loc_52><loc_92><loc_76><loc_93></location>2.3. Performance of the estimation</section_header_level_1>
<text><location><page_3><loc_52><loc_72><loc_95><loc_91></location>In this section we test the accuracy of the estimation φ est for a phase aberration φ and no amplitude aberrations ( α = 0). In the following numerical simulations, we assumed an FQPM coronagraph. It induces a phase shift of π in two quadrants with respect to the two others quadrants. We simulated FQPM coronagraphs in this paper using the method described in Mas et al. (2012). This coronagraph is completely insensitive to some aberrations, for instance to one of the astigmatism aberrations (Galicher 2009; Galicher et al. 2010). Because these aberrations introduce no aberration inside the Lyot pupil, we are unable to estimate them. We assumed an initial phase with aberrations of 30 nm root mean square (RMS) over the pupil at λ = 635 nm , with a power spectral density (PSD) in f -2 , where f is the spatial frequency.</text>
<text><location><page_3><loc_52><loc_65><loc_95><loc_71></location>In these simulations, we studied two cases. First, we used a Lyot pupil of the same diameter as the entrance pupil ( L = P ). Then, we studied the case of a reduced Lyot ( D L < D P , where D L and D P are the diameters of the Lyot and entrance pupil, respectively).</text>
<section_header_level_1><location><page_3><loc_52><loc_62><loc_65><loc_63></location>2.3.1. Case L = P</section_header_level_1>
<text><location><page_3><loc_52><loc_50><loc_95><loc_61></location>Figure 2 shows the effect of phase-only aberrations φ in different planes of the coronagraph. Starting from the left, we represent the initial phase φ , the real part of the amplitude due to the aberrations φ M ( φ L ) before the Lyot stop (after the Lyot stop), derived from Equation 6 (Equation 8) for phase-only aberrations. The last two images are the estimator φ est and the difference between the estimate and the entrance phase aberrations ( φ -φ est ).</text>
<text><location><page_3><loc_52><loc_37><loc_95><loc_50></location>The estimate φ est is very close to the initial phase φ . For initial phase aberrations of 30 nm RMS, the difference φ -φ est presents a level of 10 nm RMS in the entire pupil. The vertical and horizontal structures in this difference are due to the cut-off by the Lyot stop of the light diffracted by the FQPM (the light removed between φ M and φ L ), which leads to an imperfect estimate of the defects on the pupil edges. Aberrations to which the FQPM coronagraph is not sensitive (such as astigmatism) are also present in this difference.</text>
<text><location><page_3><loc_52><loc_23><loc_95><loc_37></location>Assuming a perfect DM, we can directly subtract φ est from φ in the entrance pupil. Then, we can estimate the residual error once again, and iterate the process. The aberrations in the Lyot pupil φ L converge toward zero (0.2 nm in ten iterations). This is important because these aberrations are directly linked to the speckle intensity in the focal plane downstream of the coronagraph. However, the difference φ -φ est does not converge toward zero in the entrance pupil. The fact that φ L converges toward zero proves that the residual phase is only composed of aberrations unseen by the FQPM.</text>
<section_header_level_1><location><page_3><loc_52><loc_19><loc_67><loc_21></location>2.3.2. Case D L < D P</section_header_level_1>
<text><location><page_3><loc_52><loc_10><loc_95><loc_19></location>In a more realistic case, we aim to remove all the light diffracted by the coronagraphic mask, even for unavoidable misalignments of the Lyot stop. For this reason, the Lyot stop is often chosen to be slightly smaller than the imaged pupil. We consider here a Lyot stop pupil L 95% whose diameter is D L = 95% D P . In a first part, we show below that phase defects at the edge of the entrance pupil can be</text>
<figure>
<location><page_4><loc_7><loc_86><loc_50><loc_93></location>
<caption>Figure 3. Simulations of an aberrated phase with a localized default in the entrance pupil plane ( φ ), and in the next pupil plane ( φ M , φ L ). We represent the entrance pupil size by a dark ring around φ L . We show the estimate ( φ est ) and the difference between φ est and φ in the last two images. D L = 95% D P in this case.</caption>
</figure>
<text><location><page_4><loc_7><loc_72><loc_50><loc_74></location>partially retrieved, then we study the convergence of the estimator in this case.</text>
<text><location><page_4><loc_7><loc_49><loc_50><loc_71></location>As in Figure 2, Figure 3 corresponds to the simulation of the consecutive steps of the model ( φ , φ M before Lyot stops, φ L after Lyot stop, then estimated phase φ est and difference with initial phase). We added a small localized phase default, indicated by the black arrow, inside the entrance pupil P , but outside of the Lyot stop L 95% (Figure 3, left). Around φ L , the complex amplitude after the Lyot stop, we drew a circle corresponding to the entrance pupil, slightly larger than L 95% . For an FQPM, the additional defect is diffracted in the Lyot stop plane ( φ M ). After applying the Lyot stop of 95% ( φ L ), most of the default disappears, but we can still see its signature. As the estimator φ est deconvolves by the phase mask, it partially retrieves the default, as seen in the estimate (indicated by the black arrow). In the error ( φ -φ est ), we notice a remarkable cross issued from this defect, which is due to the information lost during the filtering by the Lyot stop.</text>
<text><location><page_4><loc_7><loc_39><loc_50><loc_49></location>The wavefront estimation is limited when compared to the D L = D P case. Because of the light filtered by the Lyot stop, some information about the wavefront aberrations close to the border of the entrance pupil is inevitably lost. Due to these unseen aberrations, φ -φ est does not converge toward zero. However, the residual aberrations in the Lyot pupil φ L still converge toward zero, practically as quick as in the L = P case.</text>
<text><location><page_4><loc_7><loc_28><loc_50><loc_39></location>By this first rough analysis, we see that we can estimate phase aberrations upstream of a coronagraph using the complex amplitude A S of the speckle field and Equation 10. The same conclusion can be drawn for amplitude aberrations and, because the estimation is linear, for a complex entrance wavefront. In the next section, we demonstrate that one can compensate for the wavefront errors in the entrance pupil.</text>
<section_header_level_1><location><page_4><loc_7><loc_25><loc_39><loc_26></location>3. Entrance pupil wavefront correction</section_header_level_1>
<text><location><page_4><loc_7><loc_19><loc_50><loc_24></location>In this section, we use the estimator Φ est to numerically simulate the correction of phase and amplitude aberrations in a closed loop. In the loop, we can remove constant factors in the estimator, which can be adjusted with a gain g</text>
<formula><location><page_4><loc_20><loc_15><loc_50><loc_17></location>Φ est = gi F -1 [ A S M ] .P. (13)</formula>
<text><location><page_4><loc_7><loc_10><loc_50><loc_13></location>We still assume that we have a perfect sensor that measures the complex amplitude A S in the focal plane downstream of the coronagraph. We used a deformable mirror (DM)</text>
<text><location><page_4><loc_52><loc_88><loc_95><loc_93></location>of NxN actuators upstream of the coronagraph, in the entrance pupil plane. We started with phase-only correction. We explain how to correct for the effects of phase and amplitude aberrations with only one DM in Section 3.3.</text>
<text><location><page_4><loc_52><loc_85><loc_95><loc_88></location>We define the correction iterative loop by the expression of the residual phase φ j +1 at iteration j +1:</text>
<formula><location><page_4><loc_55><loc_80><loc_95><loc_84></location>φ j +1 = φ -φ j +1 DM = φ -[ φ j DM + N 2 -1 ∑ i =0 k j +1 i f i ] , (14)</formula>
<text><location><page_4><loc_52><loc_69><loc_95><loc_79></location>where φ j DM is the shape of the DM at iteration j , k j +1 i is the incremental command of the DM actuator i at iteration j + 1, and f i is the DM influence function, i.e., the WF deformation when only poking the actuator i . Note that φ j is the phase to be estimated at iteration j +1. The objective is now to determine the command vector { k j +1 i } from the phase estimator φ j +1 est .</text>
<section_header_level_1><location><page_4><loc_52><loc_66><loc_79><loc_67></location>3.1. Wavefront aberration minimization</section_header_level_1>
<text><location><page_4><loc_52><loc_58><loc_95><loc_65></location>To derivate the command vector { k j +1 i } , we minimize the distance between the measurements and the measurements that accounts for the parameters to be estimated. Ideally, we would like to find the { k i } minimizing the distance d j { k i } between the residual phase and the DM shape:</text>
<formula><location><page_4><loc_63><loc_53><loc_95><loc_57></location>d j { k i } = ‖ φ j -N 2 -1 ∑ i =0 k j +1 i f i ‖ 2 . (15)</formula>
<text><location><page_4><loc_52><loc_48><loc_95><loc_52></location>As presented in the previous section, a possible estimator of φ j is given by Equation 13, allowing us to compute Φ j +1 est from A j S (directly related to φ j ). So we minimize</text>
<formula><location><page_4><loc_61><loc_45><loc_95><loc_47></location>d j { k i } = ‖glyph[Rfractur] [ Φ j +1 est ] -D { k j +1 i }‖ 2 , (16)</formula>
<text><location><page_4><loc_52><loc_34><loc_95><loc_43></location>where D is the interaction matrix because we are using a linear model. This matrix is calibrated off-line directly using the wavefront sensor (Boyer et al. 1990). As in the conventional least-squares approach, we derived the pseudo inverse of D , denoted D † , by the singular value decomposition (SVD) method. Therefore, the command vector solution of Equation 16 is given by</text>
<formula><location><page_4><loc_65><loc_31><loc_95><loc_33></location>{ k j +1 i } = D † glyph[Rfractur] [ Φ j +1 est ] . (17)</formula>
<text><location><page_4><loc_52><loc_16><loc_95><loc_30></location>Equation 17 is applicable for different estimators (only D † changes). To create the interaction matrix, we poked one by one the actuators while the others remain flat, as shown in Figure 4. Each estimated phase vector obtained hence gives the column of the interaction matrix corresponding to the moved actuator. The influence function (which we simulated as a Gaussian function) is at the left, the estimator given by Equation 13 at the right. At the center, we also plot another estimator of the wavefront that does not include the deconvolution by the coronagraph mask. It is defined by</text>
<formula><location><page_4><loc_65><loc_14><loc_95><loc_16></location>Φ est, 2 = gi F -1 [ A S ] .P. (18)</formula>
<text><location><page_4><loc_52><loc_10><loc_95><loc_13></location>The chosen estimator applied to the influence function must be as spatially localized as possible: we have to filter the noise and it is far more efficient if the relevant information</text>
<figure>
<location><page_5><loc_8><loc_84><loc_48><loc_94></location>
<caption>Figure 4. Simulations of the influence function f i in the pupil plane (left), and the effect using the two different estimators: we deconvolve by the mask ( Φ est , right) or not ( Φ est, 2 , center)</caption>
</figure>
<text><location><page_5><loc_7><loc_58><loc_50><loc_74></location>is gathered around one point. For this reason, it is preferable to use Φ est (Figure 4, right) instead of Φ est, 2 (Figure 4, center). We notice in Figure 4 that even after deconvolution by the FQPM, the estimate (right) shows a negative cross centered on the poked actuator, whereas it is not present in the initial phase (left). This artifact is generated to the transitions of the quadrants, which diffract the light outside of the Lyot stop. This cross can be a problem for two reasons. First, it is difficult to properly retrieve it in a noisy image. Then, because it enhances the cross-talk between the actuator estimates, it may lead to unstable corrections (see Section 4.4).</text>
<text><location><page_5><loc_7><loc_54><loc_50><loc_58></location>For these reasons, we chose to create a synthetic interaction matrix, i.e. , use a slightly different model for the estimation.</text>
<section_header_level_1><location><page_5><loc_7><loc_51><loc_30><loc_52></location>3.2. Synthetic interaction matrix</section_header_level_1>
<text><location><page_5><loc_7><loc_29><loc_50><loc_50></location>One interest of interaction matrices is to calibrate the misregistration between the DM and the wavefront sensor when considering a complex optical system. It also allows us to calibrate the shape and magnitude of each actuator response. Since the cross in Figure 4 (right) is 40 times less intense than the poke actuator in the center, it may be only partially retrieved in noisy images, which may lead to an unstable loop. To avoid this problem, we decided to build a synthetic interaction matrix based on the measured position and shape of each actuator. Because we considered an iterative measurement and correction loop, we finally discarded the magnitude calibration of each actuator, which lead to a slight increase of the required iteration number for convergence. We decided to only adjust the mis-registration and estimation shape of the actuator set in the output pupil on the measured interaction matrix, as seen by the sensor.</text>
<text><location><page_5><loc_7><loc_10><loc_50><loc_29></location>Out of the NxN actuators of the square array in the DM, we chose to limit the response adjustment on the 12x12 actuators centered on the entrance pupil. These actuators were alternately pushed and pulled using known electrical voltages and we recorded A S for both positions. Assuming the complex amplitude A S is a linear function of the wavefront errors in the entrance pupil plane and that other aberrations of the optical path remain unchanged between two consecutive movements (the same pushed and pulled actuator), the difference between these two movements leads to the estimate ˆ f i of the influence function of a single poked actuator using Equation 13. For each estimate, we adjusted a Gaussian function defined by its width and position in the output pupil. From these 144 Gaussian fits, we can build the actuator grid as observed in the plane, where aberrations</text>
<text><location><page_5><loc_52><loc_85><loc_95><loc_93></location>are estimated and determine the inter-actuator distance in each direction and the orientation of this grid. We also determined the median width of the adjusted Gaussian functions and computed a synthetic Gaussian function, which was translated onto the adjusted actuator grid to create a new set of NxN synthetic estimates ˆ f i synth .</text>
<text><location><page_5><loc_52><loc_77><loc_95><loc_85></location>From these synthetic estimates, we built the synthetic interaction matrix D synth . Some of the actuators are outside of the entrance pupil, and their impact inside the pupil is negligible. We excluded these actuators from D synth . For any wavefront estimate, the distance to be minimized is now</text>
<formula><location><page_5><loc_60><loc_75><loc_95><loc_77></location>d j { k i } = ‖glyph[Rfractur] [ Φ j +1 est ] -D synth { k j +1 i }‖ 2 . (19)</formula>
<text><location><page_5><loc_52><loc_71><loc_95><loc_74></location>The solution is given by the pseudo-inverse of the interaction matrix D synth using the SVD method.</text>
<section_header_level_1><location><page_5><loc_52><loc_68><loc_88><loc_69></location>3.3. Phase and amplitude correction using one DM</section_header_level_1>
<text><location><page_5><loc_52><loc_59><loc_95><loc_67></location>As explained in Bord'e & Traub (2006), a complex wavefront Φ = φ + iα can be corrected for on half of the focal plane with only one DM. The idea is to apply a real phase on the DM to correct for the phase and amplitude on half of the focal plane. Because the Fourier transform of a Hermitian function is real, we define A hermi S as</text>
<formula><location><page_5><loc_59><loc_53><loc_95><loc_57></location> ∀ x ∈ R × R + , A hermi S ( x ) = A S ( x ) ∀ x ∈ R × R -, A hermi S ( x ) = A ∗ S ( -x ) , (20)</formula>
<text><location><page_5><loc_52><loc_47><loc_95><loc_52></location>where A ∗ S is the complex conjugated of A S and introduce it into the estimator of Equation 13. The resulting estimated wavefront is real, which allows its correction with only one DM.</text>
<text><location><page_5><loc_52><loc_40><loc_95><loc_46></location>Now we have a solution to correct for the wavefront aberrations upstream of the coronagraph when the complex amplitude in focal plane is known. We introduce in Section 4 a technique to measure A S : the self-coherent camera.</text>
<section_header_level_1><location><page_5><loc_52><loc_34><loc_90><loc_37></location>4. Self-coherent camera: a complex amplitude sensor in focal plane</section_header_level_1>
<text><location><page_5><loc_52><loc_31><loc_95><loc_33></location>The self-coherent camera (SCC) is an instrument that allows complex electric field estimations in the focal plane.</text>
<section_header_level_1><location><page_5><loc_52><loc_27><loc_64><loc_29></location>4.1. SCC principle</section_header_level_1>
<text><location><page_5><loc_52><loc_10><loc_95><loc_26></location>Figure 5 (top) is a schematic representation of the SCC combined with a focal phase mask coronagraph and a DM. We added a small pupil R , called reference pupil, in the Lyot stop plane of a classical coronagraph. R selects part of the stellar light that is diffracted by the focal coronagraphic mask. The two beams are recombined in the focal plane, forming Fizeau fringes, which spatially modulate the speckles. In the following, we call the SCC image the image of the encoded speckles (Figure 5, bottom). In this section, we briefly demonstrate that this spatial modulation allows us to retrieve the complex amplitude A S . A more complete description of the instrument can be found in Baudoz et al. (2006), Galicher et al. (2008, 2010).</text>
<figure>
<location><page_6><loc_7><loc_68><loc_49><loc_93></location>
<caption>Figure 5. Principle of the SCC combined with a coronagraph and a DM (top). A small hole is added in the Lyot stop plane to create a reference channel. In the final focal plane (bottom), the SCC image is formed by speckles encoded with Fizeau fringes</caption>
</figure>
<text><location><page_6><loc_7><loc_55><loc_50><loc_57></location>The electric field ψ in the pupil plane (Equation 7) after the modified Lyot stop is</text>
<formula><location><page_6><loc_11><loc_50><loc_50><loc_54></location>ψ ( ξ , λ ) ψ 0 = [ ( P ( ξ ) + i Φ( ξ , λ )) ∗ F -1 [ M ]( ξ ) ] . ( L ( ξ ) + R ( ξ ) ∗ δ ( ξ -ξ 0 )) , (21)</formula>
<text><location><page_6><loc_7><loc_45><loc_50><loc_49></location>where ξ 0 is the separation between the two pupils in the Lyot stop, and δ is the Kronecker delta. ψ can also be written as</text>
<formula><location><page_6><loc_13><loc_43><loc_50><loc_44></location>ψ ( ξ , λ ) = ψ S ( ξ , λ ) + ψ R ( ξ , λ ) ∗ δ ( ξ -ξ 0 ) , (22)</formula>
<text><location><page_6><loc_7><loc_33><loc_50><loc_42></location>where ψ S is the complex amplitude in the Lyot stop, defined in Equation 8, and ψ R is the complex amplitude in the reference pupil. We denote with A R its Fourier transform, the complex amplitude in the focal plane, of the light issued from the reference pupil. In monochromatic light, the intensity I = |F [ ψ ] | 2 recorded on the detector in the final focal plane can then be written as</text>
<formula><location><page_6><loc_17><loc_26><loc_50><loc_32></location>I ( x ) = | A S ( x ) | 2 + | A R ( x ) | 2 + A ∗ S ( x ) A R ( x ) exp ( -2 iπ x . ξ 0 λ ) + A S ( x ) A ∗ R ( x ) exp ( 2 iπ x . ξ 0 λ ) , (23)</formula>
<text><location><page_6><loc_7><loc_17><loc_50><loc_25></location>where A ∗ is the conjugate of A and x the coordinate in the focal plane. The two first terms are the intensities issued from Lyot and reference pupils, and provide access only to the square modulus of the complex amplitudes. The two correlation terms that create the fringes directly depend on A S and A R .</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_17></location>When an off-axis source (planet) is in the field of view, its light is not diffracted by the coronagraphic mask. Thus, it does not go through the reference pupil. Because the lights of the off-axis and in-axis sources are not coherent, the off-axis light amplitude in the focal plane does not appear in the correlation terms ( i.e. , its image is not fringed).</text>
<section_header_level_1><location><page_6><loc_52><loc_92><loc_82><loc_93></location>4.2. Complex amplitude of the speckle field</section_header_level_1>
<text><location><page_6><loc_52><loc_86><loc_95><loc_91></location>In this section, we demonstrate that we can use the SCC image to estimate the complex amplitude of the speckle field. We first apply a numerical inverse Fourier transform to the recorded SCC image (Equation 23),</text>
<formula><location><page_6><loc_53><loc_79><loc_95><loc_84></location>F -1 [ I ]( u ) = F -1 [ I S + I R ] + F -1 [ A ∗ S A R ] ∗ δ ( u -ξ 0 λ ) + F -1 [ A S A ∗ R ] ∗ δ ( u + ξ 0 λ ) , (24)</formula>
<text><location><page_6><loc_52><loc_75><loc_95><loc_79></location>where I S = | A S | 2 and I R = | A R | 2 are the intensities of the speckles and reference pupil, and u is the coordinate in the Fourier plane.</text>
<figure>
<location><page_6><loc_59><loc_52><loc_87><loc_73></location>
<caption>Figure 6. Correlation peaks in the Fourier transform of the focal plane. The inverse Fourier transform of I S + I R is circled in blue. The inverse Fourier transform of I -= A S A ∗ R is circled in red.</caption>
</figure>
<text><location><page_6><loc_52><loc_31><loc_95><loc_43></location>F -1 [ I ] is composed of three peaks centered at u = [ -ξ 0 /λ, 0 , + ξ 0 /λ ] (Figure 6). We denote with D L the diameter of the Lyot pupil and with D L /γ the diameter of the reference pupil ( γ > 1). The central peak is the sum of the autocorrelation of the Lyot and reference pupils F -1 [ I S + I R ]. Its radius is D L because we assume γ > 1. The lateral peaks of the correlation ( F -1 [ I -] and F -1 [ I + ] hereafter) have a radius ( D L + D L /γ ) / 2. Thus the three peaks do not overlap only if (Galicher et al. 2010)</text>
<formula><location><page_6><loc_65><loc_27><loc_95><loc_30></location>|| ξ 0 || > D L 2 ( 3 + 1 γ ) , (25)</formula>
<text><location><page_6><loc_52><loc_18><loc_95><loc_25></location>which puts a condition on the smallest pupil separation. The lateral peaks are conjugated and contain information only on the complex amplitude of the stellar speckles that are spatially modulated on the detector. When we shift one of these lateral peaks to the center of the correlation plane ( u = 0 ), its expression can be derived from Equation 24:</text>
<formula><location><page_6><loc_64><loc_15><loc_95><loc_16></location>F -1 [ I -] = F -1 [ A S A ∗ R ] . (26)</formula>
<text><location><page_6><loc_52><loc_10><loc_95><loc_13></location>Assuming γ glyph[greatermuch] 1, we can consider that the complex amplitude in the reference pupil is uniform and that A ∗ R is the complex amplitude of an Airy pattern. Therefore,</text>
<figure>
<location><page_7><loc_7><loc_75><loc_50><loc_93></location>
<caption>Figure 7. Steps followed to estimate the phase and amplitude from SCC images.</caption>
</figure>
<text><location><page_7><loc_7><loc_65><loc_50><loc_68></location>knowing A R , we can to retrieve the complex amplitude A S in the focal plane using the SCC (where A ∗ R is not zero):</text>
<formula><location><page_7><loc_25><loc_61><loc_50><loc_64></location>A S = I -A ∗ R . (27)</formula>
<section_header_level_1><location><page_7><loc_7><loc_58><loc_28><loc_59></location>4.3. SCC wavefront estimation</section_header_level_1>
<text><location><page_7><loc_7><loc_51><loc_50><loc_57></location>Equation 13 shows how to estimate the wavefront upstream of a coronagraph is estimated using the complex amplitude of the speckle field in the focal plane. Combining Equations 10 and 27, we have an estimator of the wavefront aberrations Φ as a function of I -:</text>
<formula><location><page_7><loc_18><loc_47><loc_50><loc_50></location>Φ est = [ i F -1 [ I -A ∗ R ψ 0 M ]] .P. (28)</formula>
<text><location><page_7><loc_7><loc_36><loc_50><loc_46></location>This estimator is only limited in frequency by the size of the reference pupil. Indeed, where the reference flux is null, the speckles are not fringed and their estimate cannot be achieved. Small reference pupils produce large point spread functions ( i.e. , with a first dark ring at large separation) and allow estimating A S in a large area of the focal plane. The influence of the reference pupil size is detailed in Section 5.5.</text>
<text><location><page_7><loc_7><loc_28><loc_50><loc_35></location>Figure 7 summarizes the steps followed to estimate the phase and amplitude aberrations with the SCC. From the fringed focal plane, we used a Fourier transform to retrieve I -, from which we deduced the complex amplitude of the speckle field A S . Using the estimator, we measured the phase and amplitude aberrations.</text>
<section_header_level_1><location><page_7><loc_7><loc_25><loc_21><loc_26></location>4.4. Correction loop</section_header_level_1>
<text><location><page_7><loc_7><loc_13><loc_50><loc_23></location>We can use this wavefront estimator to control a DM and correct for the speckle field in the focal plane as explained in Section 3. The DM has a finite number of degrees of freedom and thus can only correct for the focal plane in a limited zone. If the reference pupil is small enough ( γ glyph[greatermuch] 1), the point spread function (PSF) | A R | 2 is uniform over the correction zone ( A ∗ R glyph[similarequal] A 0 ). We discuss this assumption in Section 5.5. Under this assumption, Equation 28 becomes</text>
<formula><location><page_7><loc_10><loc_9><loc_50><loc_12></location>Φ est glyph[similarequal] i F -1 [ I -A 0 ψ 0 M ] .P = gi F -1 [ I -M ] .P. (29)</formula>
<figure>
<location><page_7><loc_55><loc_69><loc_92><loc_92></location>
<caption>Figure 8. Singular values, normalized to their respective maximum, issued from the inversion of the interaction matrices D , obtained using the two estimators Φ est (red,dotted) and Φ est, 2 (black, solid) and the synthetic matrix (blue, dashed) for γ = 40 .</caption>
</figure>
<text><location><page_7><loc_52><loc_52><loc_95><loc_58></location>As described in Section 3, we removed the constant terms in the estimation and put them into the gain g. From Φ est , we created a synthetic matrix, as explained in Section 3.2. Similarly, the other estimator Φ est, 2 introduced in Equation 18, becomes</text>
<formula><location><page_7><loc_65><loc_49><loc_95><loc_51></location>Φ est, 2 = gi F -1 [ I -] .P. (30)</formula>
<text><location><page_7><loc_52><loc_38><loc_95><loc_48></location>Using the interaction matrices deduced from these estimators (Φ est , Φ est, 2 ) and the synthetic one, we studied the correction loop. We simulated a DM with 27 actuators across the entrance pupil. To build these matrices, we only selected the actuators with a high influence in the pupil (633 actuators were selected for this number of actuators in the pupil). Lyot stop and entrance pupil have the same radius, and we chose γ = 40 for the reference pupil size.</text>
<text><location><page_7><loc_52><loc_34><loc_95><loc_38></location>In Figure 8, we plot the singular values (SV), normalized to their highest values, derived from the inversion of the matrices D obtained using the estimators Φ est and Φ est, 2</text>
<text><location><page_7><loc_52><loc_19><loc_95><loc_34></location>and of the interaction matrix built from ˆ f i synth . As already underlined, the cross in Φ est or Φ est, 2 (Figure 4, center and right) correlates the estimates of different actuators and therefore leads to lower SV (up to five times lower for the lowest SV). When inverted in D † , low SV lead to higher values (in absolute values) and amplify the noise in Equation 17. Applied to noisy data, such D † matrices may lead to an unstable correction. Even in a noise-free case, simulations of the correction with the three methods and the same number of actuators used (633) showed that only the synthetic matrix leads to a stable correction.</text>
<section_header_level_1><location><page_7><loc_52><loc_16><loc_71><loc_17></location>4.5. Optical path difference</section_header_level_1>
<text><location><page_7><loc_52><loc_10><loc_95><loc_15></location>Between the Lyot stop and the detector, the beam is split into two paths (image and reference), which encounter different areas in the optics. Thus, differential aberrations exist Galicher et al. (2010). However, because the reference</text>
<text><location><page_8><loc_7><loc_88><loc_50><loc_93></location>pupil is small ( γ glyph[greatermuch] 1), the main aberration is an optical path difference (OPD) between the two channels. In this section we study how this OPD impacts the SCC performance.</text>
<section_header_level_1><location><page_8><loc_7><loc_85><loc_38><loc_86></location>4.5.1. Influence of an OPD on the correction</section_header_level_1>
<text><location><page_8><loc_7><loc_80><loc_50><loc_84></location>Given an OPD d op , we can define phase difference φ op = 2 πd op /λ . This phase difference modifies the I -originally defined in Equation 26:</text>
<formula><location><page_8><loc_20><loc_77><loc_50><loc_79></location>I -= A S A ∗ R exp( iφ op ) . (31)</formula>
<text><location><page_8><loc_7><loc_72><loc_50><loc_76></location>The phase and amplitude estimate φ est,op and α est,op can be expressed as a function of the estimates made without an OPD ( d op = 0):</text>
<formula><location><page_8><loc_12><loc_70><loc_50><loc_71></location>φ est,op + iα est,op = ( φ est + iα est ) exp( iφ op ) , (32)</formula>
<text><location><page_8><loc_7><loc_68><loc_13><loc_69></location>and thus</text>
<formula><location><page_8><loc_11><loc_64><loc_50><loc_67></location>{ φ est,op = φ est cos( φ op ) -α est sin( φ op ) α est,op = φ est sin( φ op ) + α est cos( φ op ) . (33)</formula>
<text><location><page_8><loc_7><loc_52><loc_50><loc_63></location>Hence, even phase-only aberrations (such as the movements of the DM) have an influence on the estimated amplitude ( i.e. , the imaginary part of the estimator Φ est ) for a nonzero OPD. In this section, we make two assumptions. First, that the DM is perfect and we can correct for any desired phase in the pupil plane. Second, that the only error in the estimator is due to the OPD: if d op = 0, the estimator retrieves the exact phase and amplitude (Φ est = φ + iα ).</text>
<text><location><page_8><loc_7><loc_45><loc_50><loc_52></location>We started the loop with a phase φ 0 and an amplitude α . After j iterations the phase in the pupil plane φ j is the difference between the previous phase φ j -1 , and the estimate of this previous phase φ j -1 est,op . Under the previous assumptions, we have α est = α and φ est = φ j -1 , and</text>
<formula><location><page_8><loc_8><loc_43><loc_50><loc_44></location>φ j = φ j -1 -φ j -1 est,op = φ j -1 (1 -cos( φ op ))+ α sin( φ op ) . (34)</formula>
<text><location><page_8><loc_7><loc_35><loc_50><loc_42></location>Because the OPD biases the estimation, the correction introduces an error at each iteration. This sequence converges if | 1 -cos( φ op ) | < 1. This assumption ( -π/ 2 < φ op < π/ 2) is always satisfied in real cases. Its limit φ end satisfies the equation</text>
<formula><location><page_8><loc_15><loc_32><loc_50><loc_34></location>φ end = φ end (1 -cos( φ op )) + α sin( φ op ) φ end = α tan( φ op ) . (35)</formula>
<text><location><page_8><loc_7><loc_27><loc_50><loc_30></location>Therefore, for a nonzero OPD and a phase-only correction, the SCC correction converges, but the errors on the final phase depend on the uncorrected amplitude aberrations α .</text>
<text><location><page_8><loc_7><loc_10><loc_50><loc_26></location>To estimate the OPD effect on the level of the focal plane intensity, we considered the complex amplitude in the focal plane as a linear function of the phase and amplitude aberrations in the entrance pupil plane. We can thus evaluate the energy in the focal plane as a linear function of | φ | 2 + | α | 2 . Without an OPD, a perfect phase-only correction would leave a level of speckles only dependent on the entrance amplitude aberrations | α | 2 . With an OPD, this level is slightly higher: | α | 2 (1 + tan( φ op ) 2 ). For a realistic phase difference of 0 . 1 radians, the difference in intensity in the speckle field between the case with and without an OPD would be 1%. The impact on the correction is only weak.</text>
<text><location><page_8><loc_52><loc_83><loc_95><loc_93></location>The problem occurs when we try to correct phase and amplitude at the same time with one DM. We explained how to do this in Section 3.3. For φ op = 0, numerical simulations as well as tests on an optical bench show that the correction is unstable: at each iteration, we raised the phase aberrations by trying to correct for the amplitude aberrations and vice versa . Thus, we need an estimate of the OPD to stabilize the correction.</text>
<text><location><page_8><loc_80><loc_89><loc_80><loc_90></location>glyph[negationslash]</text>
<section_header_level_1><location><page_8><loc_52><loc_79><loc_83><loc_80></location>4.5.2. Estimation and correction of the OPD</section_header_level_1>
<text><location><page_8><loc_52><loc_59><loc_95><loc_78></location>In the construction of the synthetic matrix, (Section 3.2), we studied the difference of two SCC images produced by wavefronts that only differ by a movement of an actuator. Because the DM is in the pupil plane, the estimator applied to this difference is real for of an OPD equal to zero. However, for a nonzero OPD d op and using Equation 31 with α = 0, we deduce Φ i est,op = Φ i est (sin( d op ) + i cos( d op )). For each of the 12x12 actuators used to build the synthetic matrix, the arctangent of the ratio of the imaginary part on the real part of Φ i est,op leads to an estimate of the OPD. Due to the noise in the image, small differences in the OPD estimate can appear from one actuator to another. Calculating the median of the estimated OPDs, we obtain the measured phase difference φ mes op . We modified I -accounting for this OPD and our estimator (Equation 29) becomes</text>
<formula><location><page_8><loc_59><loc_55><loc_95><loc_57></location>Φ est,op = gi F -1 [ I -exp( -iφ mes op ) M ] .P. (36)</formula>
<text><location><page_8><loc_52><loc_52><loc_81><loc_53></location>We use this new estimator from now on.</text>
<text><location><page_8><loc_52><loc_39><loc_95><loc_52></location>The OPD variations during the correction are a problem that has to be carefully considered for a telescope application. In the current installation (bench under a hood, room temperature stabilized) these variations are much slower than the time of a correction loop. Moreover, one can change the value of φ op directly during the correction to compensate for slight changes. However, in an operational instrument, this problem will be taken into account by design to comply with the stability requirements (Macintosh et al. 2008).</text>
<section_header_level_1><location><page_8><loc_52><loc_34><loc_92><loc_36></location>5. Correction in the focal plane using the self-coherent camera: laboratory performance</section_header_level_1>
<section_header_level_1><location><page_8><loc_52><loc_31><loc_70><loc_32></location>5.1. Laboratory test bench</section_header_level_1>
<text><location><page_8><loc_52><loc_24><loc_95><loc_30></location>We tested the SCC on a laboratory bench at the Observatoire de Paris. A thorough description of this optical bench is given in Mas et al. (2010). We briefly present the main components used in the experiments of the current paper:</text>
<unordered_list>
<list_item><location><page_8><loc_52><loc_21><loc_95><loc_22></location>1. A quasi-monochromatic laser diode emitting at 635nm.</list_item>
<list_item><location><page_8><loc_52><loc_16><loc_95><loc_21></location>2. A tip-tilt mirror built at LESIA, used to center the beam on the coronagraphic mask (Mas et al. 2012). The tiptilt mirror can also be used in the closed-loop as an off-load for the DM.</list_item>
<list_item><location><page_8><loc_52><loc_11><loc_95><loc_16></location>3. A Boston Micromachines DM of 32x32 actuators on a square array. Each actuator has a size of 300 µm . We currently use an entrance pupil of 8.1mm and thus 27 actuators across the pupil.</list_item>
<list_item><location><page_8><loc_52><loc_10><loc_78><loc_11></location>4. An FQPM optimized for 635nm.</list_item>
</unordered_list>
<figure>
<location><page_9><loc_7><loc_83><loc_50><loc_93></location>
<caption>Figure 9. Dark holes recorded on the laboratory bench for correction with two different sizes of square mask S q : K S q = 20 . 8 λ/D L (left) and K S q = 24 . 5 λ/D L (center). The dark hole recorded on the laboratory bench for a correction in phase and amplitude with a square mask of size K S q = 24 . 5 λ/D L (right). These images use a different intensity scale but the same space scale</caption>
</figure>
<unordered_list>
<list_item><location><page_9><loc_7><loc_63><loc_50><loc_69></location>5. A Lyot stop with a diameter of 8mm for an entrance pupil of 8.1mm (98 . 7% filtering) and in the same plane, reference pupils of variable diameters: 0.3mm ( γ = 26 . 6), 0.35mm ( γ = 22 . 8), 0.4mm ( γ = 20) and 0.5mm ( γ = 16) and 0.8mm ( γ = 10).</list_item>
<list_item><location><page_9><loc_7><loc_59><loc_50><loc_63></location>6. A CCD camera of 400x400 pixels with a readout noise of 16 electrons/pixel and a full well capacity of 13,000 electrons/pixel.</list_item>
</unordered_list>
<text><location><page_9><loc_7><loc_55><loc_50><loc_58></location>We used the Labview software to control the bench and the DM and applied the closed-loop correction at 20 Hz.</text>
<section_header_level_1><location><page_9><loc_7><loc_52><loc_18><loc_53></location>5.2. Dark holes</section_header_level_1>
<text><location><page_9><loc_7><loc_32><loc_50><loc_51></location>Owing to the limited number of actuators on the DM, only spatial frequencies lower than the DM cut-off can be corrected for. For a given diameter D L of the Lyot pupil, the highest frequency attainable for a NxN actuators DM (N actuators across the pupil diameter) is Nλ/ (2 D L ) in one of the principal directions of the mirror and √ 2 Nλ/ (2 D L ) in the diagonal. The largest correction zone, called dark hole ( DH ) in Malbet et al. (1995) is the zone DH max = [ -Nλ/ (2 D P ) , Nλ/ (2 D P )] × [ -Nλ/ (2 D P ) , Nλ/ (2 D P )] in the image plane. During the numerical process of the SCC image (Figure 7), we can decide to reduce the correction to a smaller zone than the one allowed by the number of actuators of the DM. This can be implemented in the SCC correction by multiplying I -by a square mask S q . Modifying Equation 36, the estimation becomes</text>
<formula><location><page_9><loc_14><loc_28><loc_50><loc_31></location>Φ est = gi F -1 [ S q .I -exp( -iφ mes op ) M ] .P, (37)</formula>
<text><location><page_9><loc_7><loc_24><loc_50><loc_26></location>where S q equals 1 on a square area of K S q λ/D L x K S q λ/D L in the center of the image and 0 everywhere else.</text>
<text><location><page_9><loc_7><loc_10><loc_50><loc_24></location>Using an SCC with a reference pupil of 0.5 mm ( γ = 16), we applied Equation 37 to estimate the upstream wavefront. We used a square zone to restrain the correction zone to 24 . 5 λ/D L to optimize the correction of the DM. We built a synthetic interaction matrix as described in Section 3.2. The pseudo inverse of D synth was used to control the DM in a closed loop using Equation 14. The correction loop was closed at 20 Hz for the laboratory conditions and ran for a number of iterations large enough ( j > 10) for the DM to converge to a stable shape. We recorded focal plane images during the control loop. The typical result obtained on the</text>
<text><location><page_9><loc_52><loc_78><loc_95><loc_93></location>optical bench for this reference and square zone sizes and for phase-only correction is shown in Figure 9 (center). We also show an image of a DH obtained with a correction with a square zone of size K S q = 20 . 8 λ/D L (Figure 9, left). A specific study of the size of the correction zone is made in Section 5.4. In Figure 9, dark zones represent low intensities. The eight bright peaks at the edges are caused by high spatial frequencies due to the print-through of the actuators on the DM surface. These peaks are uncorrectable by nature, but probably do not strongly alter the correction because they are situated at more than 20 λ/D L from the center.</text>
<text><location><page_9><loc_52><loc_60><loc_95><loc_77></location>As explained in Section 3.1, the correction of phase and amplitude with only one DM is possible by replacing A S by A hermi S in Equation 13. With Equation 20, we similarly define the hermitian function I hermi -from I -. Using Equation 27 and the assumption that | A ∗ R | 2 is an Airy pattern, a phase and amplitude correction is therefore possible by replacing I -by I hermi -in Equation 37. This correction allows one to go deeper in contrast but limits the largest possible dark hole to half of the focal plane: DH + max = [0 , Nλ/ (2 D L )] × [ -Nλ/ (2 D L ) , Nλ/ (2 D L )]. On this half plane, we can also choose to reduce the correction to a smaller zone. A resulting dark hole is presented in Figure 9 (right) for K S q = 20 . 8 λ/D L .</text>
<section_header_level_1><location><page_9><loc_52><loc_57><loc_67><loc_58></location>5.3. SCC performance</section_header_level_1>
<text><location><page_9><loc_52><loc_48><loc_95><loc_56></location>In this section, we present contrast results obtained on the laboratory bench for phase-only correction and for amplitude and phase correction. We used a reference pupil of 0.5 mm ( γ = 16) to estimate the upstream wavefront and a square zone of size K S q = 24 . 5 λ/D L to optimize the correction of the DM.</text>
<section_header_level_1><location><page_9><loc_52><loc_45><loc_71><loc_46></location>5.3.1. Phase-only correction</section_header_level_1>
<text><location><page_9><loc_52><loc_35><loc_95><loc_44></location>The speckles near the FQPM transitions are brighter than those in other parts of the DH . Moreover, the contrast in these region is not relevant, because the image of a planet located on a transition would be distorted and strongly attenuated. Therefore, for phase-only correction, we chose to measure the radial profile of the SCC image only on the points (x,y) which verify</text>
<formula><location><page_9><loc_54><loc_31><loc_95><loc_34></location>{ x ∈ [ -20 λ/D L ; -1 λ/D L ] ∪ [1 λ/D L ; 20 λ/D L ] y ∈ [ -20 λ/D L ; -1 λ/D L ] ∪ [1 λ/D L ; 20 λ/D L ] . (38)</formula>
<text><location><page_9><loc_52><loc_12><loc_95><loc_30></location>We calculated the profiles by normalizing the intensities by the highest value of the PSF measured through the Lyot pupil and without coronagraphic mask. In practice, we moved the source away from the coronagraph transitions to measure this PSF. In the following figures, the distances to the center are measured in λ/D L . Figure 10 shows the radial profile of the azimuthal standard deviation of the intensities obtained in phase-only correction in the focal plane zone described in Equation 38. The detection level reaches a contrast level of 10 -6 between 6 and 12 λ/D L and 3 . 10 -7 at 11 λ/D L . As shown in Figure 9 (center), speckles are still present in the dark area. Since we only corrected for the phase, we can suspect amplitude effects.</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_12></location>To estimate the amplitude aberration level, we recorded the pupil illumination on the optical bench without coron-</text>
<figure>
<location><page_10><loc_11><loc_70><loc_46><loc_92></location>
<caption>Figure 10. Radial profiles of the azimuthal standard deviation (in RMS) of the intensities in the focal plane typically obtained with this method for phase-only correction, for simulation (blue dashed line) and laboratory bench result (red solid line), for γ = 16 and a square zone of size K S q = 24 . 5 λ/D L . We also plot in this graph the simulation of the focal plane obtained using the amplitude aberrations recorded and no phase aberrations (black dash-dotted line).</caption>
</figure>
<figure>
<location><page_10><loc_19><loc_42><loc_38><loc_55></location>
<caption>Figure 11. Pupil illumination recorded on the laboratory bench.</caption>
</figure>
<text><location><page_10><loc_7><loc_18><loc_50><loc_34></location>agraph, shown in Figure 11. The amplitude defect level is estimated to be about 10% RMS in intensity. The period of the actuator pitch clearly appears in this pupil image. Due to vignetting effects by the focal coronagraphic mask, these high-frequency structures of the DM surface create illumination variations across the pupil. The first effect of these high-frequency aberrations are bright speckles outside the corrected zone (mostly on the eight bright peaks). The second effect is more critical for our purpose. Because the level of high-frequency amplitude errors varies across the pupil, it creates low-frequency amplitude aberrations, which induce bright speckles in the center of the correction zone.</text>
<text><location><page_10><loc_7><loc_10><loc_50><loc_17></location>To compare the level of the recorded speckles with the one expected using amplitude and phase errors, we simulated the expected focal plane image. We used the amplitude aberrations deduced from the intensity measurement on the laboratory bench (Figure 11). From these amplitude aberrations, we first simulated the the focal plane without</text>
<text><location><page_10><loc_52><loc_75><loc_95><loc_93></location>phase errors (just amplitude errors). The profile of this focal plane is plotted in Figure 10 with a black dot-dashed line. We then simulated a phase-only correction, assuming initial phase aberrations of 16 nm RMS over the pupil, and a power spectral density (PSD) in f -2 where f is the spatial frequency. These simulation results (blue dashed line) are compared to the experimental measurement (red line) in Figure 10. The level and shape of the two curves are very similar. They show the same structure around 27 λ/D L , due to the eight bright peaks created by amplitude aberrations. These curves inside the DH match the simulation of the focal plane without amplitude aberrations. It seems that in phase-only correction, we corrected all phase aberrations and that we are only limited by amplitude errors.</text>
<section_header_level_1><location><page_10><loc_52><loc_72><loc_78><loc_73></location>5.3.2. Phase and amplitude correction</section_header_level_1>
<text><location><page_10><loc_52><loc_60><loc_95><loc_71></location>The simulation without amplitude errors (only phase aberrations) shows that a contrast level of 10 -10 can be reached, as previously shown in Galicher et al. (2010). Since the amplitude errors set the limits of our phase-only corrections, we aim to correct both phase and amplitude at the same time. However, with only one DM, the corrected zone is smaller by half, as shown in Figure 9 (right). Therefore, the radial profile measurement zone becomes</text>
<formula><location><page_10><loc_54><loc_57><loc_95><loc_59></location>{ x ∈ [1 λ/D L ; 20 λ/D L ] y ∈ [ -20 λ/D L ; -1 λ/D L ] ∪ [1 λ/D L ; 20 λ/D L ] . (39)</formula>
<text><location><page_10><loc_52><loc_44><loc_95><loc_55></location>The results for this correction are plotted in Figure 12 as a dashed blue line for the simulations and as a red line for the laboratory bench results. When correcting for the phase and amplitude aberrations, we obtain contrasts better than 10 -6 between 2 λ/D L and 12 λ/D L , and better than 3 . 10 -7 between 7 λ/D L and 11 λ/D L . This is an improvement compared to the phase-only correction. The simulated profiles match the laboratory results from 0 to 8 λ/D L and outside of the DH .</text>
<text><location><page_10><loc_52><loc_29><loc_95><loc_43></location>Between 8 and 12 λ/D L , the experimental correction shows a plateau at 3 . 10 -7 , while the simulation correction goes deeper. This plateau is a distinctive feature of a limitation caused by the low dynamic range of the detector (our CCD camera has a full well capacity of 13,000 electrons/pixels for a readout noise of 16 electrons/pixels). This is confirmed by the last images of the loop which show speckle levels below the readout noise between 8 and 12 λ/D L : the speckles beyond the readout noise are not visible and thus beyond correction. However, this problem can be solved by using a detector with a better dynamic range.</text>
<text><location><page_10><loc_52><loc_15><loc_95><loc_29></location>The number of incoming photons from the observed source is a critical problem of any speckle-correction technique: the speckles can only be corrected for to a certain level of contrast if the source is bright enough for them to be detected above photon and detector noise at these levels. Although we can correct in a closed loop at 20 Hz in the laboratory, the correction rate in a real telescope observation will be limited by the shortest exposure time necessary. This shortest exposure time depends on several parameters such as stellar magnitude, observational wavelengths, telescope diameter, or dynamic range of the camera.</text>
<text><location><page_10><loc_52><loc_10><loc_95><loc_15></location>The contrast level in the numerical simulation is limited to 10 -7 . This is due to the high-amplitude defects (10% in intensity) introduced by the DM in the pupil. Indeed, the bright speckles of the uncorrected half-area diffract their</text>
<figure>
<location><page_11><loc_11><loc_69><loc_46><loc_92></location>
<caption>Figure 12. Radial profiles of the azimuthal standard deviation (in RMS) of the intensities in the focal plane typically obtained with this method for phase and amplitude correction, for simulation (blue dashed line) and laboratory bench result (red solid line), for γ = 16 and a square zone of size K S q = 24 . 5 λ/D L .</caption>
</figure>
<text><location><page_11><loc_7><loc_52><loc_50><loc_57></location>light into the corrected half-area. This limit, independent of the estimation method (Give'on et al. 2006; Galicher et al. 2010), may be lowered by the introduction of a second DM on the optical bench (Pueyo et al. 2010).</text>
<text><location><page_11><loc_7><loc_49><loc_50><loc_51></location>In the next sections (Section 5.4 and 5.5), we study the influence of different parameters on the SCC performance.</text>
<section_header_level_1><location><page_11><loc_7><loc_46><loc_28><loc_47></location>5.4. Size of the corrected zone</section_header_level_1>
<text><location><page_11><loc_7><loc_24><loc_50><loc_45></location>In this section, we compare the performance for different sizes of the square zone S q . Using the modified estimator introduced in Equation 37, and for different square zone sizes K S q , we experimentally closed the loop and recorded images after convergence. In these tests, we used N = 27 actuators across the pupil diameter and γ = 16, with phase-only correction. As explained in Section 5.2, for this number of actuators, we have DH max = [ -26 . 6 λ/ (2 D L ) , 26 . 6 λ/ (2 D L )] × [ -26 . 6 λ/ (2 D L ) , 26 . 6 λ/ (2 D L )] (as D L /D P = 8 / 8 . 1). We tested the case ( K S q = ∞ ) and three others: K S q = 26 . 4 λ/D L , which is only slightly smaller than size of the largest DH and two smaller square zones ( K S q = 20 . 8 λ/D L and K S q = 24 . 5 λ/D L ). The images obtained in the last two cases can be seen in Figure 9: K S q = 20 . 8 λ/D L (left) and K S q = 24 . 5 λ/D L (center).</text>
<text><location><page_11><loc_7><loc_20><loc_50><loc_24></location>Figure 13 presents the radial profiles of the focal planes obtained on the laboratory bench, normalized by the highest value of the PSF obtained without coronagraphic mask.</text>
<text><location><page_11><loc_7><loc_10><loc_50><loc_19></location>The red, solid curve shows the result for K S q = ∞ , without square zone. The blue dotted line represents the result of a square mask of size K S q = 26 . 4 λ/D L , which is only slightly smaller than the actual cut-off frequency of the DM. In this case, we prevented the correction of speckles outside of the DH and obtained a great improvement inside the DH (0 to 13.5 λ/D L ) and a small depreciation</text>
<figure>
<location><page_11><loc_56><loc_69><loc_91><loc_92></location>
<caption>Figure 13. Experimental radial profile comparison of dark holes obtained on the test bench without square zone (directly using the estimator described in Equation 36) (red, solid) and with square zones of different side lengths: K S q = 26 . 4 λ/D L (blue, dotted), K S q = 24 . 5 λ/D L (green, dashed) and K S q = 20 . 8 λ/D L (black, dot-dashed). These phase-only corrections were achieved with a γ = 16 reference pupil. The intensities are normalized by the highest value of the PSF obtained without coronagraphic mask.</caption>
</figure>
<text><location><page_11><loc_52><loc_41><loc_95><loc_48></location>outside (13.5 to 15.5 λ/D L ). Using a smaller correction zone ( K S q = 24 . 5 λ/D L green dashed line) still improves the correction but to the detriment of the size of the DH (the contrast starts to rise around 12 λ/D L ). Finally, we see that a smaller square zone ( K S q = 20 . 8 λ/D L , black, dot-dashed) produces a smaller but not shallower DH .</text>
<text><location><page_11><loc_52><loc_25><loc_95><loc_40></location>Going from K S q = ∞ to K S q = 24 . 5 λ/D L , the contrast in the DH progressively deepens. This is because correcting fewer of the highest frequencies with a constant number of actuators, we free degrees of freedom. However, for K S q < 25 . 5 λ/D L , the contrast level does not improve because we reach the level of the speckles created by the amplitude aberrations. Additional shrinking would only reduce the size of the DH . Thus, the reduction of the corrected zone in the wavefront estimation greatly improves the correction performance (up to a factor 10) with only a small reduction of the DH size. This effect was described in Bord'e & Traub (2006) using 1D simulations.</text>
<text><location><page_11><loc_52><loc_10><loc_95><loc_24></location>It is important to note that this improvement does not come from the phenomenon of aliasing in the estimation (Poyneer & Macintosh 2004). Indeed, only the correction is enhanced by this process, because the estimation remained unchanged. The wavefront estimation with the SCC is only limited in frequency by the size of the reference PSF: we can estimate speckles as long as the reference flux is not null, i.e. , as long as the speckles are fringed. In most cases (see next section), the first dark ring of the reference PSF is larger than the correction zone and the frequencies inside the PSF's first dark ring are well estimated.</text>
<figure>
<location><page_12><loc_11><loc_70><loc_46><loc_92></location>
<caption>Figure 14. Experimental radial profiles of the PSFs for reference pupils from γ = 10 to γ = 22 . 8 recorded on the optical bench. The distance to the center is in λ/D L . These reference PSFs are normalized by the highest value of the Lyot PSF obtained without coronagraphic mask. The vertical line correspond to the frequency cut-off for N = 27 actuators in the entrance pupil ( √ 2 Nλ/ (2 D L ) )</caption>
</figure>
<section_header_level_1><location><page_12><loc_7><loc_54><loc_28><loc_55></location>5.5. Size of the reference pupil</section_header_level_1>
<text><location><page_12><loc_7><loc_33><loc_50><loc_53></location>In this section, we study the effect of the size of the reference pupil on the performance of the SCC. In the previous sections, we used two assumptions on the size of the reference pupil. First, in Section 4.2, we assumed a reference pupil small enough to consider that the influence of the aberrations inside such a reference pupil is negligible. Simulations showed that even for small γ , the level of aberrations in the reference pupil is very low and uncorrelated to the level of aberrations in the entrance pupil. Second, in Section 4, we assumed a reference pupil small enough to consider A ∗ R constant over the correction zone in the focal plane. As previously mentioned, the highest frequency attainable by the DM is √ 2 Nλ/ (2 D L ). Using the first assumption, | A ∗ R | 2 is a perfect PSF whose first dark ring is located at 1 . 22 λγ/D L . Thus, A ∗ R is roughly constant over the DH if</text>
<formula><location><page_12><loc_23><loc_31><loc_50><loc_33></location>1 . 22 γ > N/ √ 2 . (40)</formula>
<text><location><page_12><loc_7><loc_16><loc_50><loc_29></location>For N = 27 actuators in the entrance pupil, Equation 40 reads γ > 15 . 6. In Figure 14, we plot the radial profiles of | A R | 2 recorded on the optical bench for γ from 10 to 22 . 8. We observe a wide range of intensity levels for different reference pupils (from 10 -6 for γ = 10 to 3 . 10 -8 for γ = 22 . 8). A reference pupil with γ = 10 (blue, solid) does not satisfy Equation 40, and the first ring of its PSF is inside the correction zone (vertical orange dashed line). We test this case independently in Section 5.5.2. The other reference pupils are studied in Section 5.5.1.</text>
<section_header_level_1><location><page_12><loc_7><loc_13><loc_34><loc_14></location>5.5.1. Impact of small reference pupils</section_header_level_1>
<text><location><page_12><loc_7><loc_10><loc_50><loc_12></location>The size of the reference pupil can influence the correction in two different ways: it changes the signal-to-noise ratio</text>
<text><location><page_12><loc_52><loc_89><loc_95><loc_93></location>(S/N) on the fringes and modifies the flatness of the reference PSF over the correction zone. We develop these effects in this order in this section.</text>
<text><location><page_12><loc_52><loc_80><loc_95><loc_89></location>The S/N on the fringes is critical, because I -can only be retrieved with well-contrasted fringes. The S/N is directly related to the reference pupil size. Using Equation 23, we deduce that the peak-to-peak amplitude of the fringes in the focal plane is 2 | A S || A R | . Thus, if | A S | and | A R | are expressed in photons, and assuming only photon and read-out noise, the S/N can be written as</text>
<formula><location><page_12><loc_62><loc_76><loc_95><loc_79></location>S/N glyph[similarequal] 2 | A S || A R | √ | A S | 2 + | A R | 2 + σ 2 cam , (41)</formula>
<text><location><page_12><loc_52><loc_67><loc_95><loc_75></location>where σ cam is the standard deviation of the detector noise in photons. A higher S/N allows a better estimate of the speckle complex amplitude and thus, a better correction of the aberrations. One can notice that this S/N can be simplified depending on the relative values of its different terms. We quickly study the following cases:</text>
<unordered_list>
<list_item><location><page_12><loc_53><loc_64><loc_95><loc_66></location>-if | A S | ≈ | A R | glyph[lessmuch] σ cam , S/N → 0. In this case, the correction is limited by the dynamic range.</list_item>
<list_item><location><page_12><loc_53><loc_59><loc_95><loc_64></location>-if σ cam glyph[lessmuch] | A S | and | A R | glyph[lessmuch] | A S | , S/N ∼ 2 | A R | . Initial case, at the beginning of the correction, when the Lyot pupil is a lot brighter than the reference pupil. The S/N is only a function of | A R | .</list_item>
<list_item><location><page_12><loc_53><loc_55><loc_95><loc_59></location>-if σ cam glyph[lessmuch] | A R | and | A S | glyph[lessmuch] | A R | , S/N ∼ 2 | A S | . The S/N is decreasing with deepening correction. The reference brightness is not important.</list_item>
</unordered_list>
<text><location><page_12><loc_52><loc_50><loc_95><loc_54></location>Equation 41 shows that this S/N is an increasing function of | A R | , but for deep corrections ( | A S | glyph[lessmuch] | A R | ), the impact of the size of the reference is probably very weak.</text>
<text><location><page_12><loc_52><loc_38><loc_95><loc_50></location>The second effect is due to the assumption of a constant reference PSF over the correction zone. Variations of A ∗ R in the correction zone distort the wavefront estimation. This effect advocates for small reference pupils (large γ ): a reference pupil of γ = 16 generates an A ∗ R that varies from 1 to 0 . 03 inside a correction zone of 27x27 λ/D L . For this reference pupil, the fringe intensity is weaker at the edges of the DH . Therefore, the estimate is less accurate at these locations.</text>
<text><location><page_12><loc_52><loc_32><loc_95><loc_38></location>Using simulation tools, where we can change the camera and photon noise easily, we were able to isolate these two different effects and analyzed their influence on the performance of the instrument separately. A more detailed study has previously been presented in Mazoyer et al. (2012).</text>
<text><location><page_12><loc_52><loc_14><loc_95><loc_32></location>Here, we experimentally tested the influence of the reference size. We used 27 actuators across the pupil diameter and K S q = 24 . 5 λ/D L with phase-only correction. Figure 15 shows the radial profiles of the SCC image in RMS obtained on the laboratory bench for different reference pupils ( γ = 16 and γ = 22 . 8), normalized by the highest value of the PSF obtained without coronagraphic mask. These results show that a large reference pupil ( γ = 16) is preferable, even at the edge of the DH , where the reference PSF for γ = 16 is fainter than the reference PSF for γ = 22 . 8. Comparing the contrast levels obtained in this figure with those in Figure 14 for all reference pupils, we deduce that we are still in the case | A R | glyph[lessmuch] | A S | . Deeper corrections would normally depend less on the size of the reference pupil.</text>
<text><location><page_12><loc_52><loc_10><loc_95><loc_13></location>When we use the SCC as a planet finder there is another impact to consider: detection is possible only if the planet intensity is higher than the photon noise of the reference</text>
<figure>
<location><page_13><loc_11><loc_70><loc_47><loc_92></location>
<caption>Figure 15. Radial profiles obtained on the laboratory bench for two different reference pupils ( γ = 16 and γ = 22 . 8 ) with N = 27 actuators and K S q = 24 . 5 λ/D L for the size of the corrected zone. These contrasts are normalized by the highest value of the PSF obtained without coronagraphic mask.</caption>
</figure>
<text><location><page_13><loc_7><loc_51><loc_50><loc_57></location>pupil. This effect advocates for small reference pupils. A trade-off study of the reference size is needed depending on expected planet intensity and the actual contrast that can be achieved. A more complete study of the noise in the SCC estimation is given in Galicher et al. (2010).</text>
<section_header_level_1><location><page_13><loc_7><loc_47><loc_33><loc_48></location>5.5.2. Effect of large reference pupils</section_header_level_1>
<text><location><page_13><loc_7><loc_23><loc_50><loc_46></location>In this section, we experimentally prove that we can still achieve a correction inside the DH using a reference pupil that does not satisfy Equation 40 by modifying the phase estimator. This correction has previously been simulated in Galicher et al. (2010). A ∗ R is still considered as the complex amplitude of a perfect PSF, but we cannot consider it uniform anymore over the DH . First, the speckles in the first dark ring of this PSF are not fringed, because the reference PSF intensity is null at this location. The wavefront errors that produce these speckles are not estimated and are thus not corrected for. Second, the sign of glyph[Rfractur] [ A ∗ R ] and glyph[Ifractur] [ A ∗ R ] changes between the first and the second dark ring ( i.e. , between 1 . 22 and 2 . 23 λ/D L ). These speckles are fringed and we can estimate the wavefront errors that produce them when we consider the sign change. Hence, when Equation 40 is not satisfied, instead of A ∗ R constant, we assume | A ∗ R | constant and change the sign of A ∗ R over the correction zone. We now estimate</text>
<formula><location><page_13><loc_10><loc_20><loc_50><loc_23></location>Φ est = i F -1 [ Sign [ glyph[Rfractur] [ A ∗ R ]] .I -exp( -iφ mes op ) M ] .P, (42)</formula>
<text><location><page_13><loc_7><loc_16><loc_50><loc_19></location>where Sign [ glyph[Rfractur] [ A ∗ R ]], is the sign of the real part of A ∗ R . This function is represented in Figure 16 (center).</text>
<text><location><page_13><loc_7><loc_10><loc_50><loc_16></location>In practice, to achieve the correction with this reference pupil, we multiplied I -by the mask in Figure 16 (center), where the white zones (the black zones) are constant and equal to 1 ( -1). To build this mask, we recorded the reference PSF (Figure 16, left). From this PSF, we were able to</text>
<figure>
<location><page_13><loc_53><loc_84><loc_93><loc_93></location>
<caption>Figure 16. PSF of the 0.8mm reference pupil ( γ = 10 ) (right). From this PSF we constructed the sign mask (center). The white zones are uniform and equal to 1 and the black zones are equal to -1. Multiplying I -by this mask, the correction can be achieved (right) for this reference pupil.</caption>
</figure>
<text><location><page_13><loc_52><loc_70><loc_95><loc_73></location>find the dark rings of the complex amplitude. We were able to build the sign of the real part of the complex amplitude.</text>
<text><location><page_13><loc_52><loc_53><loc_95><loc_70></location>The tests on the optical bench were conducted using the 0.8mm reference pupil ( γ = 10) and the process described in Section 5.3. We used no square zone. The resulting DH is presented in Figure 16 (right). We distinctly see the first reference ring at 1 . 22 λ/D R . As expected, the speckles on this ring are not corrected for, because they are not fringed. Nevertheless, apart from this ring, the whole DH is corrected. Although correction with a large reference pupil is possible, the level of speckle suppression is much lower (better contrast) than with smaller reference pupils (higher γ ), because the speckles of the uncorrected dark ring diffract their light into the corrected zone (Galicher et al. 2010; Give'on et al. 2006).</text>
<text><location><page_13><loc_52><loc_39><loc_95><loc_53></location>We showed in Section 5.5.1 that the SCC used with a reference pupil that obeys Equation 40 shows a better performance. However, some cases (many aberrations due to an unknown initial position of the DM, for example) may require the use of large reference pupils that produce highly contrasted fringes even with very aberrated wavefronts. The correction can then be initiated by correcting for low spatial frequencies (usually dominating the wavefront errors). Finally, the large reference is replaced with a smaller reference (which satisfies Equation 40) to correct higher frequencies and reach better contrast levels.</text>
<section_header_level_1><location><page_13><loc_52><loc_35><loc_63><loc_36></location>6. Conclusion</section_header_level_1>
<text><location><page_13><loc_52><loc_24><loc_95><loc_34></location>In Section2.1, we used Fourier optics to model the propagation of light through a coronagraph. We then proposed a method for estimating phase and amplitude aberrations in the entrance pupil from the complex electric field measured in the focal plane after a four-quadrant phase mask coronagraph. We used this model to correct phase and amplitude aberrations in a closed loop using a DM in the pupil plane, even for a Lyot pupil smaller than the entrance pupil.</text>
<text><location><page_13><loc_52><loc_18><loc_95><loc_24></location>We implemented this technique, associated with a selfcoherent camera as a focal plane wavefront sensor. We corrected for phase and amplitude aberrations in a closed loop which led to speckle suppression in the central area of the focal plane (called dark hole).</text>
<text><location><page_13><loc_52><loc_10><loc_95><loc_17></location>We tested these methods on a laboratory bench where we were able to close the loop and obtain a stable correction at 20 Hz. When correcting for phase aberrations only , we obtained contrast levels (RMS) better than 10 -6 between 6 and 12 λ/D L and 3 . 10 -7 at 11 λ/D L . We proved that we corrected for most phase aberrations in the dark hole and</text>
<text><location><page_14><loc_7><loc_80><loc_50><loc_93></location>that the contrast is limited by high amplitude aberrations (10% RMS in intensity) induced by the DM. When correcting for the phase and amplitude aberrations using one DM, we obtained contrast level better than 10 -6 between 2 λ/D L and 12 λ/D L , and better than 3 . 10 -7 between 7 λ/D L and 11 λ/D L . The simulation performance was limited by the diffraction of the speckles of the uncorrected area in the focal plane created by the amplitude defects. In addition, in laboratory tests, the contrast is currently limited by the camera dynamics in the aberration estimation.</text>
<text><location><page_14><loc_7><loc_71><loc_50><loc_80></location>We experimentally proved that a small shrinking of the size of the correction zone can improve the contrast the contrast up to a factor 10. We analyzed the influence of the reference pupil radius on the performance of the SCC and proved that the reference of γ = 16 (the larger reference pupil possible with a nonzero reference flux inside the correction zone) provides the best correction in our case.</text>
<text><location><page_14><loc_7><loc_50><loc_50><loc_71></location>To enhance the performance of the self-coherent camera even more, we plan several improvements. First, one can directly minimize A S , the speckle complex field measured by the SCC and not the phase estimated in the pupil plane. This approach has started to show good results (Baudoz et al. 2012) for the simultaneous correction of amplitude and phase. The correction for the amplitude errors can probably also be improved by the use of two DMs. Moreover, solutions are considered to use the SCC with wider spectral bandwidths. First tests in polychromatic light have already been conducted and show promising results (Baudoz et al. 2012). A preliminary study of these effects has been published (Galicher et al. 2010). A forthcoming paper will present a new version of the SCC that will probably overcome the current chromatic limitation.</text>
<text><location><page_14><loc_7><loc_44><loc_50><loc_48></location>Acknowledgements. J. Mazoyer is grateful to the Centre National d'Etudes Spatiales (CNES, Toulouse, France) and Astrium (Toulouse, France) for supporting his PhD fellowship. SCC development is supported by CNES (Toulouse, France).</text>
<section_header_level_1><location><page_14><loc_7><loc_40><loc_16><loc_41></location>References</section_header_level_1>
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</document>
[
{
"title": "Estimation and correction of wavefront aberrations using the self-coherent camera: laboratory results",
"content": "J. Mazoyer 1 , P. Baudoz 1 , R. Galicher 1 , M. Mas 2 , and G. Rousset 1 Preprint online version: November 6, 2021",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "Context. Direct imaging of exoplanets requires very high contrast levels, which are obtained using coronagraphs. But residual quasi-static aberrations create speckles in the focal plane downstream of the coronagraph which mask the planet. This problem appears in ground-based instruments as well as in space-based telescopes. Aims. An active correction of these wavefront errors using a deformable mirror upstream of the coronagraph is mandatory, but conventional adaptive optics are limited by differential path aberrations. Dedicated techniques have to be implemented to measure phase and amplitude errors directly in the science focal plane. Methods. First, we propose a method for estimating phase and amplitude aberrations upstream of a coronagraph from the speckle complex field in the downstream focal plane. Then, we present the self-coherent camera, which uses the coherence of light to spatially encode the focal plane speckles and retrieve the associated complex field. This enable us to estimate and compensate in a closed loop for the aberrations upstream of the coronagraph. We conducted numerical simulations as well as laboratory tests using a four-quadrant phase mask and a 32x32 actuator deformable mirror. Results. We demonstrated in the laboratory our capability to achieve a stable closed loop and compensate for phase and amplitude quasi-static aberrations. We determined the best-suited parameter values to implement our technique. Contrasts better than 10 -6 between 2 and 12 λ/D and even 3 . 10 -7 (RMS) between 7 and 11 λ/D were reached in the focal plane. It seems that the contrast level is mainly limited by amplitude defects created by the surface of the deformable mirror and by the dynamic of the detector. Conclusions. These results are promising for a future application to a dedicated space mission for exoplanet characterization. A number of possible improvements have been identified. Key words. instrumentation: high angular resolution - instrumentation: adaptive optics - techniques: high angular resolution",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Direct imaging is crucial to increase our knowledge of extrasolar planetary systems. On the one hand, it can detect long-orbit planets that are inaccessible for other methods (transits, radial velocities). On the other hand, it allows the full spectroscopic characterization of the surface and atmosphere of exoplanets. In a few favorable cases, direct imaging has already enabled the detection of exoplanets (Kalas et al. 2008; Lagrange et al. 2009) and even of planetary systems (Marois et al. 2008, 2010). However, the main difficulties of this method are the high contrast and small separation between the star and its planet. Indeed, a contrast level of 10 -10 has to be reached within a separation of ∼ 0 . 1 '' or lower to allow the detection of rocky planets. To reduce the star light in the focal plane of a telescope, several coronagraphs have been developed, such as the fourquadrant phase mask (FQPM) coronograph (Rouan et al. 2000), the vortex coronograph (Mawet et al. 2005) and the phase-induced amplitude apodization coronograph (Guyon et al. 2005). However, the performance of these instruments is drastically limited by phase and amplitude errors. Indeed, these wavefront aberrations induce stellar speckles in the image, which are leaks of the star light in the focal plane downstream of the coronagraph. When classical adaptive optics (AO) systems correct for most of the dynamic wavefront errors that are caused by to atmosphere, they use a dedicated optical channel for the wavefront sensing. Thus, they cannot detect quasi-static non-common path aberrations (NCPA) created in the differential optical paths by the instrument optics themselves. These NCPA have to be compensated for using dedicated techniques, for groundbased telescopes as well as for space-based instruments. Two strategies have been implemented to overcome the quasi-static speckle limitation. First, one can use differential imaging techniques to calibrate the speckle noise in the focal plane. Theses methods can use either the spectral signature and polarization state of the planet or differential rotation in the image (Marois et al. 2004, 2006). Second, even before applying these post-processing techniques, an active suppression of speckles (Malbet et al. 1995) has to be implemented to reach very high contrasts. It uses a deformable mirror (DM) controlled by a specific wavefront sensor that is immune against NCPA. The techniques developed for this purpose include dedicated instrumental designs (Guyon et al. 2009; Wallace et al. 2010), or creating of known phases on the DM (Bord'e & Traub 2006; Give'on et al. 2007) to estimate the complex speckle field. Ground-based instruments that combine these two strategies are currently being developed, such as SPHERE (Beuzit et al. 2008) and GPI (Macintosh et al. 2008), to detect young Jupiter-like planets with an expected contrast performance of 10 -6 at 0 . 5 '' . Better contrasts might be achieved to reach the rocky planet level with instruments using dedicated active correction techniques embedded in space telescopes (Trauger & Traub 2007). In this context, we study a technique of wavefront sensing in the focal plane that allows an active correction in a closed loop. This paper has two main objectives. First we give an overview of how the amplitude and phase errors upstream of a coronagraph can be retrieved from the complex amplitude of the speckle field (Section 2) and how they can be compensated for using a DM (Section 3). In Section 4, we introduce the self-coherent camera (Baudoz et al. 2006; Galicher et al. 2008). This instrument uses the coherence of the stellar light to generate Fizeau fringes in the focal plane and spatially encode the speckles. Using both the aberration estimator and the self-coherent camera (SCC), we are able to correct phase and amplitude aberrations. The second objective of the paper is a laboratory demonstration of the active correction and an experimental parametric study of the SCC (Section 5).",
"pages": [
1,
2
]
},
{
"title": "2. Wavefront estimator in the focal plane of a coronagraph",
"content": "In this section, we aim to prove that one can retrieve the wavefront upstream of the coronagraph using the measured complex amplitude of the electric field in the focal plane downstream of the coronagraph. We assume in the whole section that we can measure this complex amplitude without error using an undetermined method. We describe one type of this method (the SCC) in Section 4. In Section 2.1, we express the complex electric field that is associated to the speckles as a function of the wavefront errors in the pupil upstream of a phase mask coronagraph. From this expression, we propose an estimator of the wavefront errors from the speckle electric field (Section 2.2) and analyze its accuracy for an FQPM (Section 2.3).",
"pages": [
2
]
},
{
"title": "2.1. Expression of the complex amplitude of speckles in the focal plane as a function of the initial wavefront",
"content": "We consider here a model of a phase mask coronagraph using Fourier optics. Figure 1 (top) presents the principle of a coronagraph. We assume that the star is a spatially unresolved monochromatic source centered on the optical axis. The stellar light moves through the entrance pupil P . Behind this pupil, the beam is focused on the mask M in the focal plane, which diffracts the light. Hence, the non aberrated part of the stellar light is rejected outside of the imaged pupil in the next pupil plane and is stopped by the Lyot stop diaphragm L . The aberrated part of the beam goes through the Lyot stop, producing speckles on the detector in the final focal plane (Figure 1, bottom). We note whith α and φ the amplitude and phase aberrations in the entrance pupil plane and define the complex wavefront aberrations Φ as The complex amplitude of the star in the entrance pupil plane ψ ' S can be written as where ψ 0 is the mean amplitude of the field over the pupil P, ξ the coordinate in the pupil plane and λ the wavelength. We assume that the aberrations are small and defined in the pupil P ( P Φ = Φ), thus The complex amplitude of the electric field A ' S behind the coronagraphic mask M in the first focal plane is where F is the Fourier transform. Using Equation 3, we can write the electric field F -1 ( A ' S ) before the Lyot stop where ∗ is the convolution product. We call Φ M the aberrated part of the field after the coronagraph: After the Lyot stop L , the electric field ψ S is We assume a coronagraph for which the non aberrated part of the electric field is null inside the imaged pupil. This property of the perfect coronagraph (Cavarroc et al. 2006) has also been demonstrated analytically for several phase coronagraphs such as FQPM coronagraphs (Abe et al. 2003) and vortex coronagraphs (Mawet et al. 2005). The remaining part Φ L of the normalized electric field after the Lyot stop reads In the final focal plane, the complex amplitude A S is This complex amplitude is directly related to the wavefront aberrations in the entrance pupil. If one can measure A S , we can invert Equation 9 and retrieve the complex wavefront errors Φ in the entrance pupil.",
"pages": [
2,
3
]
},
{
"title": "2.2. Wavefront estimator",
"content": "We still assume in this section that an undefined method provides access to A S . Using this complex amplitude A S as the measurement, we therefore propose the following estimator Φ est for the wavefront: This estimator can be used for any phase mask coronograph (for which M is nonzero over the full focal plane). To justify the pertinence of this estimator, we can re-write it using the variables of our model. Using Equation 9, in a noise-free measurement case, this estimator reads Theoretically, if no Lyot stop is applied ( L = 1), Equation 11 becomes Φ est = P Φ = Φ. We propose this estimator based on the assumption that most of the information about the aberrations is not diffracted outside of the imaged pupil by the coronagraphic mask. Therefore, using this assumption, we intuit that for L glyph[similarequal] P , we still have Φ est glyph[similarequal] Φ. This assumption is verified by the simulation in Section 2.3, and by the experiment described in Section 5. For a symmetrical phase mask such as the FQPM, either F -1 [ M ] and F -1 [ 1 M ] are real. Thus, in the estimator we can separate the real ( φ est ) and imaginary part ( α est ) of the estimator in Equation 11: This relation ensures that within the limits of our model, this estimator independently provides estimates of the phase and amplitude aberrations.",
"pages": [
3
]
},
{
"title": "2.3. Performance of the estimation",
"content": "In this section we test the accuracy of the estimation φ est for a phase aberration φ and no amplitude aberrations ( α = 0). In the following numerical simulations, we assumed an FQPM coronagraph. It induces a phase shift of π in two quadrants with respect to the two others quadrants. We simulated FQPM coronagraphs in this paper using the method described in Mas et al. (2012). This coronagraph is completely insensitive to some aberrations, for instance to one of the astigmatism aberrations (Galicher 2009; Galicher et al. 2010). Because these aberrations introduce no aberration inside the Lyot pupil, we are unable to estimate them. We assumed an initial phase with aberrations of 30 nm root mean square (RMS) over the pupil at λ = 635 nm , with a power spectral density (PSD) in f -2 , where f is the spatial frequency. In these simulations, we studied two cases. First, we used a Lyot pupil of the same diameter as the entrance pupil ( L = P ). Then, we studied the case of a reduced Lyot ( D L < D P , where D L and D P are the diameters of the Lyot and entrance pupil, respectively).",
"pages": [
3
]
},
{
"title": "2.3.1. Case L = P",
"content": "Figure 2 shows the effect of phase-only aberrations φ in different planes of the coronagraph. Starting from the left, we represent the initial phase φ , the real part of the amplitude due to the aberrations φ M ( φ L ) before the Lyot stop (after the Lyot stop), derived from Equation 6 (Equation 8) for phase-only aberrations. The last two images are the estimator φ est and the difference between the estimate and the entrance phase aberrations ( φ -φ est ). The estimate φ est is very close to the initial phase φ . For initial phase aberrations of 30 nm RMS, the difference φ -φ est presents a level of 10 nm RMS in the entire pupil. The vertical and horizontal structures in this difference are due to the cut-off by the Lyot stop of the light diffracted by the FQPM (the light removed between φ M and φ L ), which leads to an imperfect estimate of the defects on the pupil edges. Aberrations to which the FQPM coronagraph is not sensitive (such as astigmatism) are also present in this difference. Assuming a perfect DM, we can directly subtract φ est from φ in the entrance pupil. Then, we can estimate the residual error once again, and iterate the process. The aberrations in the Lyot pupil φ L converge toward zero (0.2 nm in ten iterations). This is important because these aberrations are directly linked to the speckle intensity in the focal plane downstream of the coronagraph. However, the difference φ -φ est does not converge toward zero in the entrance pupil. The fact that φ L converges toward zero proves that the residual phase is only composed of aberrations unseen by the FQPM.",
"pages": [
3
]
},
{
"title": "2.3.2. Case D L < D P",
"content": "In a more realistic case, we aim to remove all the light diffracted by the coronagraphic mask, even for unavoidable misalignments of the Lyot stop. For this reason, the Lyot stop is often chosen to be slightly smaller than the imaged pupil. We consider here a Lyot stop pupil L 95% whose diameter is D L = 95% D P . In a first part, we show below that phase defects at the edge of the entrance pupil can be partially retrieved, then we study the convergence of the estimator in this case. As in Figure 2, Figure 3 corresponds to the simulation of the consecutive steps of the model ( φ , φ M before Lyot stops, φ L after Lyot stop, then estimated phase φ est and difference with initial phase). We added a small localized phase default, indicated by the black arrow, inside the entrance pupil P , but outside of the Lyot stop L 95% (Figure 3, left). Around φ L , the complex amplitude after the Lyot stop, we drew a circle corresponding to the entrance pupil, slightly larger than L 95% . For an FQPM, the additional defect is diffracted in the Lyot stop plane ( φ M ). After applying the Lyot stop of 95% ( φ L ), most of the default disappears, but we can still see its signature. As the estimator φ est deconvolves by the phase mask, it partially retrieves the default, as seen in the estimate (indicated by the black arrow). In the error ( φ -φ est ), we notice a remarkable cross issued from this defect, which is due to the information lost during the filtering by the Lyot stop. The wavefront estimation is limited when compared to the D L = D P case. Because of the light filtered by the Lyot stop, some information about the wavefront aberrations close to the border of the entrance pupil is inevitably lost. Due to these unseen aberrations, φ -φ est does not converge toward zero. However, the residual aberrations in the Lyot pupil φ L still converge toward zero, practically as quick as in the L = P case. By this first rough analysis, we see that we can estimate phase aberrations upstream of a coronagraph using the complex amplitude A S of the speckle field and Equation 10. The same conclusion can be drawn for amplitude aberrations and, because the estimation is linear, for a complex entrance wavefront. In the next section, we demonstrate that one can compensate for the wavefront errors in the entrance pupil.",
"pages": [
3,
4
]
},
{
"title": "3. Entrance pupil wavefront correction",
"content": "In this section, we use the estimator Φ est to numerically simulate the correction of phase and amplitude aberrations in a closed loop. In the loop, we can remove constant factors in the estimator, which can be adjusted with a gain g We still assume that we have a perfect sensor that measures the complex amplitude A S in the focal plane downstream of the coronagraph. We used a deformable mirror (DM) of NxN actuators upstream of the coronagraph, in the entrance pupil plane. We started with phase-only correction. We explain how to correct for the effects of phase and amplitude aberrations with only one DM in Section 3.3. We define the correction iterative loop by the expression of the residual phase φ j +1 at iteration j +1: where φ j DM is the shape of the DM at iteration j , k j +1 i is the incremental command of the DM actuator i at iteration j + 1, and f i is the DM influence function, i.e., the WF deformation when only poking the actuator i . Note that φ j is the phase to be estimated at iteration j +1. The objective is now to determine the command vector { k j +1 i } from the phase estimator φ j +1 est .",
"pages": [
4
]
},
{
"title": "3.1. Wavefront aberration minimization",
"content": "To derivate the command vector { k j +1 i } , we minimize the distance between the measurements and the measurements that accounts for the parameters to be estimated. Ideally, we would like to find the { k i } minimizing the distance d j { k i } between the residual phase and the DM shape: As presented in the previous section, a possible estimator of φ j is given by Equation 13, allowing us to compute Φ j +1 est from A j S (directly related to φ j ). So we minimize where D is the interaction matrix because we are using a linear model. This matrix is calibrated off-line directly using the wavefront sensor (Boyer et al. 1990). As in the conventional least-squares approach, we derived the pseudo inverse of D , denoted D † , by the singular value decomposition (SVD) method. Therefore, the command vector solution of Equation 16 is given by Equation 17 is applicable for different estimators (only D † changes). To create the interaction matrix, we poked one by one the actuators while the others remain flat, as shown in Figure 4. Each estimated phase vector obtained hence gives the column of the interaction matrix corresponding to the moved actuator. The influence function (which we simulated as a Gaussian function) is at the left, the estimator given by Equation 13 at the right. At the center, we also plot another estimator of the wavefront that does not include the deconvolution by the coronagraph mask. It is defined by The chosen estimator applied to the influence function must be as spatially localized as possible: we have to filter the noise and it is far more efficient if the relevant information is gathered around one point. For this reason, it is preferable to use Φ est (Figure 4, right) instead of Φ est, 2 (Figure 4, center). We notice in Figure 4 that even after deconvolution by the FQPM, the estimate (right) shows a negative cross centered on the poked actuator, whereas it is not present in the initial phase (left). This artifact is generated to the transitions of the quadrants, which diffract the light outside of the Lyot stop. This cross can be a problem for two reasons. First, it is difficult to properly retrieve it in a noisy image. Then, because it enhances the cross-talk between the actuator estimates, it may lead to unstable corrections (see Section 4.4). For these reasons, we chose to create a synthetic interaction matrix, i.e. , use a slightly different model for the estimation.",
"pages": [
4,
5
]
},
{
"title": "3.2. Synthetic interaction matrix",
"content": "One interest of interaction matrices is to calibrate the misregistration between the DM and the wavefront sensor when considering a complex optical system. It also allows us to calibrate the shape and magnitude of each actuator response. Since the cross in Figure 4 (right) is 40 times less intense than the poke actuator in the center, it may be only partially retrieved in noisy images, which may lead to an unstable loop. To avoid this problem, we decided to build a synthetic interaction matrix based on the measured position and shape of each actuator. Because we considered an iterative measurement and correction loop, we finally discarded the magnitude calibration of each actuator, which lead to a slight increase of the required iteration number for convergence. We decided to only adjust the mis-registration and estimation shape of the actuator set in the output pupil on the measured interaction matrix, as seen by the sensor. Out of the NxN actuators of the square array in the DM, we chose to limit the response adjustment on the 12x12 actuators centered on the entrance pupil. These actuators were alternately pushed and pulled using known electrical voltages and we recorded A S for both positions. Assuming the complex amplitude A S is a linear function of the wavefront errors in the entrance pupil plane and that other aberrations of the optical path remain unchanged between two consecutive movements (the same pushed and pulled actuator), the difference between these two movements leads to the estimate ˆ f i of the influence function of a single poked actuator using Equation 13. For each estimate, we adjusted a Gaussian function defined by its width and position in the output pupil. From these 144 Gaussian fits, we can build the actuator grid as observed in the plane, where aberrations are estimated and determine the inter-actuator distance in each direction and the orientation of this grid. We also determined the median width of the adjusted Gaussian functions and computed a synthetic Gaussian function, which was translated onto the adjusted actuator grid to create a new set of NxN synthetic estimates ˆ f i synth . From these synthetic estimates, we built the synthetic interaction matrix D synth . Some of the actuators are outside of the entrance pupil, and their impact inside the pupil is negligible. We excluded these actuators from D synth . For any wavefront estimate, the distance to be minimized is now The solution is given by the pseudo-inverse of the interaction matrix D synth using the SVD method.",
"pages": [
5
]
},
{
"title": "3.3. Phase and amplitude correction using one DM",
"content": "As explained in Bord'e & Traub (2006), a complex wavefront Φ = φ + iα can be corrected for on half of the focal plane with only one DM. The idea is to apply a real phase on the DM to correct for the phase and amplitude on half of the focal plane. Because the Fourier transform of a Hermitian function is real, we define A hermi S as where A ∗ S is the complex conjugated of A S and introduce it into the estimator of Equation 13. The resulting estimated wavefront is real, which allows its correction with only one DM. Now we have a solution to correct for the wavefront aberrations upstream of the coronagraph when the complex amplitude in focal plane is known. We introduce in Section 4 a technique to measure A S : the self-coherent camera.",
"pages": [
5
]
},
{
"title": "4. Self-coherent camera: a complex amplitude sensor in focal plane",
"content": "The self-coherent camera (SCC) is an instrument that allows complex electric field estimations in the focal plane.",
"pages": [
5
]
},
{
"title": "4.1. SCC principle",
"content": "Figure 5 (top) is a schematic representation of the SCC combined with a focal phase mask coronagraph and a DM. We added a small pupil R , called reference pupil, in the Lyot stop plane of a classical coronagraph. R selects part of the stellar light that is diffracted by the focal coronagraphic mask. The two beams are recombined in the focal plane, forming Fizeau fringes, which spatially modulate the speckles. In the following, we call the SCC image the image of the encoded speckles (Figure 5, bottom). In this section, we briefly demonstrate that this spatial modulation allows us to retrieve the complex amplitude A S . A more complete description of the instrument can be found in Baudoz et al. (2006), Galicher et al. (2008, 2010). The electric field ψ in the pupil plane (Equation 7) after the modified Lyot stop is where ξ 0 is the separation between the two pupils in the Lyot stop, and δ is the Kronecker delta. ψ can also be written as where ψ S is the complex amplitude in the Lyot stop, defined in Equation 8, and ψ R is the complex amplitude in the reference pupil. We denote with A R its Fourier transform, the complex amplitude in the focal plane, of the light issued from the reference pupil. In monochromatic light, the intensity I = |F [ ψ ] | 2 recorded on the detector in the final focal plane can then be written as where A ∗ is the conjugate of A and x the coordinate in the focal plane. The two first terms are the intensities issued from Lyot and reference pupils, and provide access only to the square modulus of the complex amplitudes. The two correlation terms that create the fringes directly depend on A S and A R . When an off-axis source (planet) is in the field of view, its light is not diffracted by the coronagraphic mask. Thus, it does not go through the reference pupil. Because the lights of the off-axis and in-axis sources are not coherent, the off-axis light amplitude in the focal plane does not appear in the correlation terms ( i.e. , its image is not fringed).",
"pages": [
5,
6
]
},
{
"title": "4.2. Complex amplitude of the speckle field",
"content": "In this section, we demonstrate that we can use the SCC image to estimate the complex amplitude of the speckle field. We first apply a numerical inverse Fourier transform to the recorded SCC image (Equation 23), where I S = | A S | 2 and I R = | A R | 2 are the intensities of the speckles and reference pupil, and u is the coordinate in the Fourier plane. F -1 [ I ] is composed of three peaks centered at u = [ -ξ 0 /λ, 0 , + ξ 0 /λ ] (Figure 6). We denote with D L the diameter of the Lyot pupil and with D L /γ the diameter of the reference pupil ( γ > 1). The central peak is the sum of the autocorrelation of the Lyot and reference pupils F -1 [ I S + I R ]. Its radius is D L because we assume γ > 1. The lateral peaks of the correlation ( F -1 [ I -] and F -1 [ I + ] hereafter) have a radius ( D L + D L /γ ) / 2. Thus the three peaks do not overlap only if (Galicher et al. 2010) which puts a condition on the smallest pupil separation. The lateral peaks are conjugated and contain information only on the complex amplitude of the stellar speckles that are spatially modulated on the detector. When we shift one of these lateral peaks to the center of the correlation plane ( u = 0 ), its expression can be derived from Equation 24: Assuming γ glyph[greatermuch] 1, we can consider that the complex amplitude in the reference pupil is uniform and that A ∗ R is the complex amplitude of an Airy pattern. Therefore, knowing A R , we can to retrieve the complex amplitude A S in the focal plane using the SCC (where A ∗ R is not zero):",
"pages": [
6,
7
]
},
{
"title": "4.3. SCC wavefront estimation",
"content": "Equation 13 shows how to estimate the wavefront upstream of a coronagraph is estimated using the complex amplitude of the speckle field in the focal plane. Combining Equations 10 and 27, we have an estimator of the wavefront aberrations Φ as a function of I -: This estimator is only limited in frequency by the size of the reference pupil. Indeed, where the reference flux is null, the speckles are not fringed and their estimate cannot be achieved. Small reference pupils produce large point spread functions ( i.e. , with a first dark ring at large separation) and allow estimating A S in a large area of the focal plane. The influence of the reference pupil size is detailed in Section 5.5. Figure 7 summarizes the steps followed to estimate the phase and amplitude aberrations with the SCC. From the fringed focal plane, we used a Fourier transform to retrieve I -, from which we deduced the complex amplitude of the speckle field A S . Using the estimator, we measured the phase and amplitude aberrations.",
"pages": [
7
]
},
{
"title": "4.4. Correction loop",
"content": "We can use this wavefront estimator to control a DM and correct for the speckle field in the focal plane as explained in Section 3. The DM has a finite number of degrees of freedom and thus can only correct for the focal plane in a limited zone. If the reference pupil is small enough ( γ glyph[greatermuch] 1), the point spread function (PSF) | A R | 2 is uniform over the correction zone ( A ∗ R glyph[similarequal] A 0 ). We discuss this assumption in Section 5.5. Under this assumption, Equation 28 becomes As described in Section 3, we removed the constant terms in the estimation and put them into the gain g. From Φ est , we created a synthetic matrix, as explained in Section 3.2. Similarly, the other estimator Φ est, 2 introduced in Equation 18, becomes Using the interaction matrices deduced from these estimators (Φ est , Φ est, 2 ) and the synthetic one, we studied the correction loop. We simulated a DM with 27 actuators across the entrance pupil. To build these matrices, we only selected the actuators with a high influence in the pupil (633 actuators were selected for this number of actuators in the pupil). Lyot stop and entrance pupil have the same radius, and we chose γ = 40 for the reference pupil size. In Figure 8, we plot the singular values (SV), normalized to their highest values, derived from the inversion of the matrices D obtained using the estimators Φ est and Φ est, 2 and of the interaction matrix built from ˆ f i synth . As already underlined, the cross in Φ est or Φ est, 2 (Figure 4, center and right) correlates the estimates of different actuators and therefore leads to lower SV (up to five times lower for the lowest SV). When inverted in D † , low SV lead to higher values (in absolute values) and amplify the noise in Equation 17. Applied to noisy data, such D † matrices may lead to an unstable correction. Even in a noise-free case, simulations of the correction with the three methods and the same number of actuators used (633) showed that only the synthetic matrix leads to a stable correction.",
"pages": [
7
]
},
{
"title": "4.5. Optical path difference",
"content": "Between the Lyot stop and the detector, the beam is split into two paths (image and reference), which encounter different areas in the optics. Thus, differential aberrations exist Galicher et al. (2010). However, because the reference pupil is small ( γ glyph[greatermuch] 1), the main aberration is an optical path difference (OPD) between the two channels. In this section we study how this OPD impacts the SCC performance.",
"pages": [
7,
8
]
},
{
"title": "4.5.1. Influence of an OPD on the correction",
"content": "Given an OPD d op , we can define phase difference φ op = 2 πd op /λ . This phase difference modifies the I -originally defined in Equation 26: The phase and amplitude estimate φ est,op and α est,op can be expressed as a function of the estimates made without an OPD ( d op = 0): and thus Hence, even phase-only aberrations (such as the movements of the DM) have an influence on the estimated amplitude ( i.e. , the imaginary part of the estimator Φ est ) for a nonzero OPD. In this section, we make two assumptions. First, that the DM is perfect and we can correct for any desired phase in the pupil plane. Second, that the only error in the estimator is due to the OPD: if d op = 0, the estimator retrieves the exact phase and amplitude (Φ est = φ + iα ). We started the loop with a phase φ 0 and an amplitude α . After j iterations the phase in the pupil plane φ j is the difference between the previous phase φ j -1 , and the estimate of this previous phase φ j -1 est,op . Under the previous assumptions, we have α est = α and φ est = φ j -1 , and Because the OPD biases the estimation, the correction introduces an error at each iteration. This sequence converges if | 1 -cos( φ op ) | < 1. This assumption ( -π/ 2 < φ op < π/ 2) is always satisfied in real cases. Its limit φ end satisfies the equation Therefore, for a nonzero OPD and a phase-only correction, the SCC correction converges, but the errors on the final phase depend on the uncorrected amplitude aberrations α . To estimate the OPD effect on the level of the focal plane intensity, we considered the complex amplitude in the focal plane as a linear function of the phase and amplitude aberrations in the entrance pupil plane. We can thus evaluate the energy in the focal plane as a linear function of | φ | 2 + | α | 2 . Without an OPD, a perfect phase-only correction would leave a level of speckles only dependent on the entrance amplitude aberrations | α | 2 . With an OPD, this level is slightly higher: | α | 2 (1 + tan( φ op ) 2 ). For a realistic phase difference of 0 . 1 radians, the difference in intensity in the speckle field between the case with and without an OPD would be 1%. The impact on the correction is only weak. The problem occurs when we try to correct phase and amplitude at the same time with one DM. We explained how to do this in Section 3.3. For φ op = 0, numerical simulations as well as tests on an optical bench show that the correction is unstable: at each iteration, we raised the phase aberrations by trying to correct for the amplitude aberrations and vice versa . Thus, we need an estimate of the OPD to stabilize the correction. glyph[negationslash]",
"pages": [
8
]
},
{
"title": "4.5.2. Estimation and correction of the OPD",
"content": "In the construction of the synthetic matrix, (Section 3.2), we studied the difference of two SCC images produced by wavefronts that only differ by a movement of an actuator. Because the DM is in the pupil plane, the estimator applied to this difference is real for of an OPD equal to zero. However, for a nonzero OPD d op and using Equation 31 with α = 0, we deduce Φ i est,op = Φ i est (sin( d op ) + i cos( d op )). For each of the 12x12 actuators used to build the synthetic matrix, the arctangent of the ratio of the imaginary part on the real part of Φ i est,op leads to an estimate of the OPD. Due to the noise in the image, small differences in the OPD estimate can appear from one actuator to another. Calculating the median of the estimated OPDs, we obtain the measured phase difference φ mes op . We modified I -accounting for this OPD and our estimator (Equation 29) becomes We use this new estimator from now on. The OPD variations during the correction are a problem that has to be carefully considered for a telescope application. In the current installation (bench under a hood, room temperature stabilized) these variations are much slower than the time of a correction loop. Moreover, one can change the value of φ op directly during the correction to compensate for slight changes. However, in an operational instrument, this problem will be taken into account by design to comply with the stability requirements (Macintosh et al. 2008).",
"pages": [
8
]
},
{
"title": "5.1. Laboratory test bench",
"content": "We tested the SCC on a laboratory bench at the Observatoire de Paris. A thorough description of this optical bench is given in Mas et al. (2010). We briefly present the main components used in the experiments of the current paper: We used the Labview software to control the bench and the DM and applied the closed-loop correction at 20 Hz.",
"pages": [
8,
9
]
},
{
"title": "5.2. Dark holes",
"content": "Owing to the limited number of actuators on the DM, only spatial frequencies lower than the DM cut-off can be corrected for. For a given diameter D L of the Lyot pupil, the highest frequency attainable for a NxN actuators DM (N actuators across the pupil diameter) is Nλ/ (2 D L ) in one of the principal directions of the mirror and √ 2 Nλ/ (2 D L ) in the diagonal. The largest correction zone, called dark hole ( DH ) in Malbet et al. (1995) is the zone DH max = [ -Nλ/ (2 D P ) , Nλ/ (2 D P )] × [ -Nλ/ (2 D P ) , Nλ/ (2 D P )] in the image plane. During the numerical process of the SCC image (Figure 7), we can decide to reduce the correction to a smaller zone than the one allowed by the number of actuators of the DM. This can be implemented in the SCC correction by multiplying I -by a square mask S q . Modifying Equation 36, the estimation becomes where S q equals 1 on a square area of K S q λ/D L x K S q λ/D L in the center of the image and 0 everywhere else. Using an SCC with a reference pupil of 0.5 mm ( γ = 16), we applied Equation 37 to estimate the upstream wavefront. We used a square zone to restrain the correction zone to 24 . 5 λ/D L to optimize the correction of the DM. We built a synthetic interaction matrix as described in Section 3.2. The pseudo inverse of D synth was used to control the DM in a closed loop using Equation 14. The correction loop was closed at 20 Hz for the laboratory conditions and ran for a number of iterations large enough ( j > 10) for the DM to converge to a stable shape. We recorded focal plane images during the control loop. The typical result obtained on the optical bench for this reference and square zone sizes and for phase-only correction is shown in Figure 9 (center). We also show an image of a DH obtained with a correction with a square zone of size K S q = 20 . 8 λ/D L (Figure 9, left). A specific study of the size of the correction zone is made in Section 5.4. In Figure 9, dark zones represent low intensities. The eight bright peaks at the edges are caused by high spatial frequencies due to the print-through of the actuators on the DM surface. These peaks are uncorrectable by nature, but probably do not strongly alter the correction because they are situated at more than 20 λ/D L from the center. As explained in Section 3.1, the correction of phase and amplitude with only one DM is possible by replacing A S by A hermi S in Equation 13. With Equation 20, we similarly define the hermitian function I hermi -from I -. Using Equation 27 and the assumption that | A ∗ R | 2 is an Airy pattern, a phase and amplitude correction is therefore possible by replacing I -by I hermi -in Equation 37. This correction allows one to go deeper in contrast but limits the largest possible dark hole to half of the focal plane: DH + max = [0 , Nλ/ (2 D L )] × [ -Nλ/ (2 D L ) , Nλ/ (2 D L )]. On this half plane, we can also choose to reduce the correction to a smaller zone. A resulting dark hole is presented in Figure 9 (right) for K S q = 20 . 8 λ/D L .",
"pages": [
9
]
},
{
"title": "5.3. SCC performance",
"content": "In this section, we present contrast results obtained on the laboratory bench for phase-only correction and for amplitude and phase correction. We used a reference pupil of 0.5 mm ( γ = 16) to estimate the upstream wavefront and a square zone of size K S q = 24 . 5 λ/D L to optimize the correction of the DM.",
"pages": [
9
]
},
{
"title": "5.3.1. Phase-only correction",
"content": "The speckles near the FQPM transitions are brighter than those in other parts of the DH . Moreover, the contrast in these region is not relevant, because the image of a planet located on a transition would be distorted and strongly attenuated. Therefore, for phase-only correction, we chose to measure the radial profile of the SCC image only on the points (x,y) which verify We calculated the profiles by normalizing the intensities by the highest value of the PSF measured through the Lyot pupil and without coronagraphic mask. In practice, we moved the source away from the coronagraph transitions to measure this PSF. In the following figures, the distances to the center are measured in λ/D L . Figure 10 shows the radial profile of the azimuthal standard deviation of the intensities obtained in phase-only correction in the focal plane zone described in Equation 38. The detection level reaches a contrast level of 10 -6 between 6 and 12 λ/D L and 3 . 10 -7 at 11 λ/D L . As shown in Figure 9 (center), speckles are still present in the dark area. Since we only corrected for the phase, we can suspect amplitude effects. To estimate the amplitude aberration level, we recorded the pupil illumination on the optical bench without coron- agraph, shown in Figure 11. The amplitude defect level is estimated to be about 10% RMS in intensity. The period of the actuator pitch clearly appears in this pupil image. Due to vignetting effects by the focal coronagraphic mask, these high-frequency structures of the DM surface create illumination variations across the pupil. The first effect of these high-frequency aberrations are bright speckles outside the corrected zone (mostly on the eight bright peaks). The second effect is more critical for our purpose. Because the level of high-frequency amplitude errors varies across the pupil, it creates low-frequency amplitude aberrations, which induce bright speckles in the center of the correction zone. To compare the level of the recorded speckles with the one expected using amplitude and phase errors, we simulated the expected focal plane image. We used the amplitude aberrations deduced from the intensity measurement on the laboratory bench (Figure 11). From these amplitude aberrations, we first simulated the the focal plane without phase errors (just amplitude errors). The profile of this focal plane is plotted in Figure 10 with a black dot-dashed line. We then simulated a phase-only correction, assuming initial phase aberrations of 16 nm RMS over the pupil, and a power spectral density (PSD) in f -2 where f is the spatial frequency. These simulation results (blue dashed line) are compared to the experimental measurement (red line) in Figure 10. The level and shape of the two curves are very similar. They show the same structure around 27 λ/D L , due to the eight bright peaks created by amplitude aberrations. These curves inside the DH match the simulation of the focal plane without amplitude aberrations. It seems that in phase-only correction, we corrected all phase aberrations and that we are only limited by amplitude errors.",
"pages": [
9,
10
]
},
{
"title": "5.3.2. Phase and amplitude correction",
"content": "The simulation without amplitude errors (only phase aberrations) shows that a contrast level of 10 -10 can be reached, as previously shown in Galicher et al. (2010). Since the amplitude errors set the limits of our phase-only corrections, we aim to correct both phase and amplitude at the same time. However, with only one DM, the corrected zone is smaller by half, as shown in Figure 9 (right). Therefore, the radial profile measurement zone becomes The results for this correction are plotted in Figure 12 as a dashed blue line for the simulations and as a red line for the laboratory bench results. When correcting for the phase and amplitude aberrations, we obtain contrasts better than 10 -6 between 2 λ/D L and 12 λ/D L , and better than 3 . 10 -7 between 7 λ/D L and 11 λ/D L . This is an improvement compared to the phase-only correction. The simulated profiles match the laboratory results from 0 to 8 λ/D L and outside of the DH . Between 8 and 12 λ/D L , the experimental correction shows a plateau at 3 . 10 -7 , while the simulation correction goes deeper. This plateau is a distinctive feature of a limitation caused by the low dynamic range of the detector (our CCD camera has a full well capacity of 13,000 electrons/pixels for a readout noise of 16 electrons/pixels). This is confirmed by the last images of the loop which show speckle levels below the readout noise between 8 and 12 λ/D L : the speckles beyond the readout noise are not visible and thus beyond correction. However, this problem can be solved by using a detector with a better dynamic range. The number of incoming photons from the observed source is a critical problem of any speckle-correction technique: the speckles can only be corrected for to a certain level of contrast if the source is bright enough for them to be detected above photon and detector noise at these levels. Although we can correct in a closed loop at 20 Hz in the laboratory, the correction rate in a real telescope observation will be limited by the shortest exposure time necessary. This shortest exposure time depends on several parameters such as stellar magnitude, observational wavelengths, telescope diameter, or dynamic range of the camera. The contrast level in the numerical simulation is limited to 10 -7 . This is due to the high-amplitude defects (10% in intensity) introduced by the DM in the pupil. Indeed, the bright speckles of the uncorrected half-area diffract their light into the corrected half-area. This limit, independent of the estimation method (Give'on et al. 2006; Galicher et al. 2010), may be lowered by the introduction of a second DM on the optical bench (Pueyo et al. 2010). In the next sections (Section 5.4 and 5.5), we study the influence of different parameters on the SCC performance.",
"pages": [
10,
11
]
},
{
"title": "5.4. Size of the corrected zone",
"content": "In this section, we compare the performance for different sizes of the square zone S q . Using the modified estimator introduced in Equation 37, and for different square zone sizes K S q , we experimentally closed the loop and recorded images after convergence. In these tests, we used N = 27 actuators across the pupil diameter and γ = 16, with phase-only correction. As explained in Section 5.2, for this number of actuators, we have DH max = [ -26 . 6 λ/ (2 D L ) , 26 . 6 λ/ (2 D L )] × [ -26 . 6 λ/ (2 D L ) , 26 . 6 λ/ (2 D L )] (as D L /D P = 8 / 8 . 1). We tested the case ( K S q = ∞ ) and three others: K S q = 26 . 4 λ/D L , which is only slightly smaller than size of the largest DH and two smaller square zones ( K S q = 20 . 8 λ/D L and K S q = 24 . 5 λ/D L ). The images obtained in the last two cases can be seen in Figure 9: K S q = 20 . 8 λ/D L (left) and K S q = 24 . 5 λ/D L (center). Figure 13 presents the radial profiles of the focal planes obtained on the laboratory bench, normalized by the highest value of the PSF obtained without coronagraphic mask. The red, solid curve shows the result for K S q = ∞ , without square zone. The blue dotted line represents the result of a square mask of size K S q = 26 . 4 λ/D L , which is only slightly smaller than the actual cut-off frequency of the DM. In this case, we prevented the correction of speckles outside of the DH and obtained a great improvement inside the DH (0 to 13.5 λ/D L ) and a small depreciation outside (13.5 to 15.5 λ/D L ). Using a smaller correction zone ( K S q = 24 . 5 λ/D L green dashed line) still improves the correction but to the detriment of the size of the DH (the contrast starts to rise around 12 λ/D L ). Finally, we see that a smaller square zone ( K S q = 20 . 8 λ/D L , black, dot-dashed) produces a smaller but not shallower DH . Going from K S q = ∞ to K S q = 24 . 5 λ/D L , the contrast in the DH progressively deepens. This is because correcting fewer of the highest frequencies with a constant number of actuators, we free degrees of freedom. However, for K S q < 25 . 5 λ/D L , the contrast level does not improve because we reach the level of the speckles created by the amplitude aberrations. Additional shrinking would only reduce the size of the DH . Thus, the reduction of the corrected zone in the wavefront estimation greatly improves the correction performance (up to a factor 10) with only a small reduction of the DH size. This effect was described in Bord'e & Traub (2006) using 1D simulations. It is important to note that this improvement does not come from the phenomenon of aliasing in the estimation (Poyneer & Macintosh 2004). Indeed, only the correction is enhanced by this process, because the estimation remained unchanged. The wavefront estimation with the SCC is only limited in frequency by the size of the reference PSF: we can estimate speckles as long as the reference flux is not null, i.e. , as long as the speckles are fringed. In most cases (see next section), the first dark ring of the reference PSF is larger than the correction zone and the frequencies inside the PSF's first dark ring are well estimated.",
"pages": [
11
]
},
{
"title": "5.5. Size of the reference pupil",
"content": "In this section, we study the effect of the size of the reference pupil on the performance of the SCC. In the previous sections, we used two assumptions on the size of the reference pupil. First, in Section 4.2, we assumed a reference pupil small enough to consider that the influence of the aberrations inside such a reference pupil is negligible. Simulations showed that even for small γ , the level of aberrations in the reference pupil is very low and uncorrelated to the level of aberrations in the entrance pupil. Second, in Section 4, we assumed a reference pupil small enough to consider A ∗ R constant over the correction zone in the focal plane. As previously mentioned, the highest frequency attainable by the DM is √ 2 Nλ/ (2 D L ). Using the first assumption, | A ∗ R | 2 is a perfect PSF whose first dark ring is located at 1 . 22 λγ/D L . Thus, A ∗ R is roughly constant over the DH if For N = 27 actuators in the entrance pupil, Equation 40 reads γ > 15 . 6. In Figure 14, we plot the radial profiles of | A R | 2 recorded on the optical bench for γ from 10 to 22 . 8. We observe a wide range of intensity levels for different reference pupils (from 10 -6 for γ = 10 to 3 . 10 -8 for γ = 22 . 8). A reference pupil with γ = 10 (blue, solid) does not satisfy Equation 40, and the first ring of its PSF is inside the correction zone (vertical orange dashed line). We test this case independently in Section 5.5.2. The other reference pupils are studied in Section 5.5.1.",
"pages": [
12
]
},
{
"title": "5.5.1. Impact of small reference pupils",
"content": "The size of the reference pupil can influence the correction in two different ways: it changes the signal-to-noise ratio (S/N) on the fringes and modifies the flatness of the reference PSF over the correction zone. We develop these effects in this order in this section. The S/N on the fringes is critical, because I -can only be retrieved with well-contrasted fringes. The S/N is directly related to the reference pupil size. Using Equation 23, we deduce that the peak-to-peak amplitude of the fringes in the focal plane is 2 | A S || A R | . Thus, if | A S | and | A R | are expressed in photons, and assuming only photon and read-out noise, the S/N can be written as where σ cam is the standard deviation of the detector noise in photons. A higher S/N allows a better estimate of the speckle complex amplitude and thus, a better correction of the aberrations. One can notice that this S/N can be simplified depending on the relative values of its different terms. We quickly study the following cases: Equation 41 shows that this S/N is an increasing function of | A R | , but for deep corrections ( | A S | glyph[lessmuch] | A R | ), the impact of the size of the reference is probably very weak. The second effect is due to the assumption of a constant reference PSF over the correction zone. Variations of A ∗ R in the correction zone distort the wavefront estimation. This effect advocates for small reference pupils (large γ ): a reference pupil of γ = 16 generates an A ∗ R that varies from 1 to 0 . 03 inside a correction zone of 27x27 λ/D L . For this reference pupil, the fringe intensity is weaker at the edges of the DH . Therefore, the estimate is less accurate at these locations. Using simulation tools, where we can change the camera and photon noise easily, we were able to isolate these two different effects and analyzed their influence on the performance of the instrument separately. A more detailed study has previously been presented in Mazoyer et al. (2012). Here, we experimentally tested the influence of the reference size. We used 27 actuators across the pupil diameter and K S q = 24 . 5 λ/D L with phase-only correction. Figure 15 shows the radial profiles of the SCC image in RMS obtained on the laboratory bench for different reference pupils ( γ = 16 and γ = 22 . 8), normalized by the highest value of the PSF obtained without coronagraphic mask. These results show that a large reference pupil ( γ = 16) is preferable, even at the edge of the DH , where the reference PSF for γ = 16 is fainter than the reference PSF for γ = 22 . 8. Comparing the contrast levels obtained in this figure with those in Figure 14 for all reference pupils, we deduce that we are still in the case | A R | glyph[lessmuch] | A S | . Deeper corrections would normally depend less on the size of the reference pupil. When we use the SCC as a planet finder there is another impact to consider: detection is possible only if the planet intensity is higher than the photon noise of the reference pupil. This effect advocates for small reference pupils. A trade-off study of the reference size is needed depending on expected planet intensity and the actual contrast that can be achieved. A more complete study of the noise in the SCC estimation is given in Galicher et al. (2010).",
"pages": [
12,
13
]
},
{
"title": "5.5.2. Effect of large reference pupils",
"content": "In this section, we experimentally prove that we can still achieve a correction inside the DH using a reference pupil that does not satisfy Equation 40 by modifying the phase estimator. This correction has previously been simulated in Galicher et al. (2010). A ∗ R is still considered as the complex amplitude of a perfect PSF, but we cannot consider it uniform anymore over the DH . First, the speckles in the first dark ring of this PSF are not fringed, because the reference PSF intensity is null at this location. The wavefront errors that produce these speckles are not estimated and are thus not corrected for. Second, the sign of glyph[Rfractur] [ A ∗ R ] and glyph[Ifractur] [ A ∗ R ] changes between the first and the second dark ring ( i.e. , between 1 . 22 and 2 . 23 λ/D L ). These speckles are fringed and we can estimate the wavefront errors that produce them when we consider the sign change. Hence, when Equation 40 is not satisfied, instead of A ∗ R constant, we assume | A ∗ R | constant and change the sign of A ∗ R over the correction zone. We now estimate where Sign [ glyph[Rfractur] [ A ∗ R ]], is the sign of the real part of A ∗ R . This function is represented in Figure 16 (center). In practice, to achieve the correction with this reference pupil, we multiplied I -by the mask in Figure 16 (center), where the white zones (the black zones) are constant and equal to 1 ( -1). To build this mask, we recorded the reference PSF (Figure 16, left). From this PSF, we were able to find the dark rings of the complex amplitude. We were able to build the sign of the real part of the complex amplitude. The tests on the optical bench were conducted using the 0.8mm reference pupil ( γ = 10) and the process described in Section 5.3. We used no square zone. The resulting DH is presented in Figure 16 (right). We distinctly see the first reference ring at 1 . 22 λ/D R . As expected, the speckles on this ring are not corrected for, because they are not fringed. Nevertheless, apart from this ring, the whole DH is corrected. Although correction with a large reference pupil is possible, the level of speckle suppression is much lower (better contrast) than with smaller reference pupils (higher γ ), because the speckles of the uncorrected dark ring diffract their light into the corrected zone (Galicher et al. 2010; Give'on et al. 2006). We showed in Section 5.5.1 that the SCC used with a reference pupil that obeys Equation 40 shows a better performance. However, some cases (many aberrations due to an unknown initial position of the DM, for example) may require the use of large reference pupils that produce highly contrasted fringes even with very aberrated wavefronts. The correction can then be initiated by correcting for low spatial frequencies (usually dominating the wavefront errors). Finally, the large reference is replaced with a smaller reference (which satisfies Equation 40) to correct higher frequencies and reach better contrast levels.",
"pages": [
13
]
},
{
"title": "6. Conclusion",
"content": "In Section2.1, we used Fourier optics to model the propagation of light through a coronagraph. We then proposed a method for estimating phase and amplitude aberrations in the entrance pupil from the complex electric field measured in the focal plane after a four-quadrant phase mask coronagraph. We used this model to correct phase and amplitude aberrations in a closed loop using a DM in the pupil plane, even for a Lyot pupil smaller than the entrance pupil. We implemented this technique, associated with a selfcoherent camera as a focal plane wavefront sensor. We corrected for phase and amplitude aberrations in a closed loop which led to speckle suppression in the central area of the focal plane (called dark hole). We tested these methods on a laboratory bench where we were able to close the loop and obtain a stable correction at 20 Hz. When correcting for phase aberrations only , we obtained contrast levels (RMS) better than 10 -6 between 6 and 12 λ/D L and 3 . 10 -7 at 11 λ/D L . We proved that we corrected for most phase aberrations in the dark hole and that the contrast is limited by high amplitude aberrations (10% RMS in intensity) induced by the DM. When correcting for the phase and amplitude aberrations using one DM, we obtained contrast level better than 10 -6 between 2 λ/D L and 12 λ/D L , and better than 3 . 10 -7 between 7 λ/D L and 11 λ/D L . The simulation performance was limited by the diffraction of the speckles of the uncorrected area in the focal plane created by the amplitude defects. In addition, in laboratory tests, the contrast is currently limited by the camera dynamics in the aberration estimation. We experimentally proved that a small shrinking of the size of the correction zone can improve the contrast the contrast up to a factor 10. We analyzed the influence of the reference pupil radius on the performance of the SCC and proved that the reference of γ = 16 (the larger reference pupil possible with a nonzero reference flux inside the correction zone) provides the best correction in our case. To enhance the performance of the self-coherent camera even more, we plan several improvements. First, one can directly minimize A S , the speckle complex field measured by the SCC and not the phase estimated in the pupil plane. This approach has started to show good results (Baudoz et al. 2012) for the simultaneous correction of amplitude and phase. The correction for the amplitude errors can probably also be improved by the use of two DMs. Moreover, solutions are considered to use the SCC with wider spectral bandwidths. First tests in polychromatic light have already been conducted and show promising results (Baudoz et al. 2012). A preliminary study of these effects has been published (Galicher et al. 2010). A forthcoming paper will present a new version of the SCC that will probably overcome the current chromatic limitation. Acknowledgements. J. Mazoyer is grateful to the Centre National d'Etudes Spatiales (CNES, Toulouse, France) and Astrium (Toulouse, France) for supporting his PhD fellowship. SCC development is supported by CNES (Toulouse, France).",
"pages": [
13,
14
]
},
{
"title": "References",
"content": "Abe, L., Domiciano de Souza, Jr., A., Vakili, F., & Gay, J. 2003, A&A, 400, 385 Baudoz, P., Mazoyer, J., Mas, M., Galicher, R., & Rousset, G. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8446, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Beuzit, J.-L., Feldt, M., Dohlen, K., et al. 2008, in Society of PhotoOptical Instrumentation Engineers (SPIE) Conference Series, Vol. 7014, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Bord'e, P. J. & Traub, W. A. 2006, ApJ, 638, 488 Boyer, C., Michau, V., & Rousset, G. 1990, in Society of PhotoOptical Instrumentation Engineers (SPIE) Conference Series, Vol. 1237, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, ed. J. B. Breckinridge, 406-421 Cavarroc, C., Boccaletti, A., Baudoz, P., et al. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6271, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 15, 12338 Give'on, A., Kasdin, N. J., Vanderbei, R. J., & Avitzour, Y. 2006, J. Opt. Soc. Am. A, 23, 1063 Guyon, O., Matsuo, T., & Angel, R. 2009, ApJ, 693, 75 Lagrange, A., Kasper, M., Boccaletti, A., et al. 2009, A&A, 506, 927 Macintosh, B. A., Graham, J. R., Palmer, D. W., et al. 2008, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Instrumentation Mawet, D., Riaud, P., Absil, O., & Surdej, J. 2005, ApJ, 633, 1191 Mazoyer, J., Baudoz, P., Mas, M., Rousset, G., & Galicher, R. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8442, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Wallace, J. K., Burruss, R. S., Bartos, R. D., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7736, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series",
"pages": [
14
]
}
]
2013A&A...557A..13B
https://arxiv.org/pdf/1306.5482.pdf
<document>
<section_header_level_1><location><page_1><loc_32><loc_85><loc_70><loc_87></location>Eclipsing high-mass binaries</section_header_level_1>
<section_header_level_1><location><page_1><loc_10><loc_80><loc_91><loc_84></location>I. Light curves and system parameters for CPD GLYPH<0> 51 GLYPH<14> 8946, PISMIS24-1 and HD319702</section_header_level_1>
<text><location><page_1><loc_8><loc_78><loc_94><loc_79></location>A. Barr Dom'ınguez 1 , R. Chini 1 ; 2 , F. Pozo Nu˜nez 1 , M. Haas 1 , M. Hackstein 1 , H. Drass 1 R. Lemke 1 , and M. Murphy 2</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_75><loc_74><loc_76></location>1 Astronomisches Institut, Ruhr-Universitat Bochum, Universitatsstraße 150, 44801 Bochum, Germany</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_81><loc_75></location>2 Instituto de Astronomia, Universidad Cat'olica del Norte, Avenida Angamos 0610, Casilla 1280 Antofagasta, Chile</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_71><loc_23><loc_72></location>Received ; accepted</text>
<section_header_level_1><location><page_1><loc_47><loc_69><loc_55><loc_70></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_54><loc_91><loc_68></location>We present first results of a comprehensive photometric O-star survey performed with a robotic twin refractor at the Universitatssternwarte Bochum located near Cerro Armazones in Chile. For three high-mass stars, namely Pismis 24-1, CPD GLYPH<0> 51 GLYPH<14> 8946 and HD 319702, we determined the period through the Lafler-Kinman algorithm and model the light curves within the framework of the Roche geometry. For Pismis 24-1, a previously known eclipsing binary, we provide first light curves and determined a photometric period of 2.36 days together with an orbital inclination of 61 : 8 GLYPH<14> . The best-fitting model solution to the light curves suggest a detached configuration. With a primary temperature of T 1 = 42520 K we obtain the temperature of the secondary component as T 2 = 41500 K. CPD GLYPH<0> 51 GLYPH<14> 8946 is another known eclipsing binary for which we present a revised photometric period of 1.96 days with an orbital inclination of 58 : 4 GLYPH<14> . The system has likely a semi-detached configuration and a mass ratio q = M 1 = M 2 = 2 : 8. If we adopt a primary temperature of T 1 = 34550 K we obtain T 2 = 21500 K for the secondary component. HD 319702 is a newly discovered eclipsing binary member of the young open cluster NGC 6334. The system shows well-defined eclipses favouring a detached configuration with a period of 2.0 days and an orbital inclination of 67 : 5 GLYPH<14> . Combining our photometric result with the primary spectral type O8 III(f) ( T 1 = 34000 K) we derive a temperature of T 2 = 25200 K for the secondary component.</text>
<text><location><page_1><loc_11><loc_51><loc_91><loc_53></location>Key words. stars: fundamental parameters -stars: formation -binaries: eclipsing -binaries: spectroscopic -Galaxy: open clusters and associations: individual: NGC6334 -Galaxy: open clusters and associations: individual: NGC6357</text>
<section_header_level_1><location><page_1><loc_7><loc_46><loc_19><loc_47></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_14><loc_50><loc_45></location>The fundamental quantity of a star is its mass because it determines the energy production, the evolution and the final state; certainly there are other parameters like chemical composition and angular momentum that influence stellar evolution. At first glance, the easiest way to estimate stellar masses is by means of the mass-luminosity relation L / M GLYPH<11> which is well established by both theory and observation. However, the exponent GLYPH<11> itself is a function of mass: while GLYPH<11> GLYPH<24> 4 for solar-type stars it becomes smaller for stars of lower ( < 0 : 5 M GLYPH<12> ) and higher ( > 10 M GLYPH<12> ) mass. In practice there are many other parameters that influence the mass-luminosity relation. All stars increase their luminosity with age - on the other hand high-mass stars lose a considerable fraction of their mass during evolution. Observationally, the determination of the bolometric luminosity ( L bol) becomes more di GLYPH<14> cult for O- and early B-type stars because due to their high temperature most light is radiated in the UV . Likewise, distance, reddening and e GLYPH<11> ective temperature ( T e GLYPH<11> ) have to be known in order to calculate the absolute visual magnitude MV and to convert it into L bol. For high-mass stars one can circumvent the massluminosity relation and determine T e GLYPH<11> and L bol by modeling the optical spectra and by placing the star in the Hertzsprung-Russel diagram (HRD). Eventually evolutionary models yield the stellar mass which is obviously based on many assumptions and whose error is dominated by the uncertainties of theoretical models.</text>
<text><location><page_1><loc_7><loc_10><loc_50><loc_13></location>In contrast, binary stars allow the determination of fundamental stellar parameters through a combination of photometry, astrometry, and spectroscopy and by applying basic physical</text>
<text><location><page_1><loc_52><loc_42><loc_95><loc_47></location>laws. In case of an eclipsing binary (hereafter EB), radii, distance and, in favorable cases, T e GLYPH<11> also may be determined from a combined analysis of light curves and radial velocity (hereafter RV ) curves.</text>
<text><location><page_1><loc_52><loc_20><loc_95><loc_42></location>There is growing evidence that most high-mass stars occur as binaries and / or multiple systems (e.g., Preibisch et al. 1999; Mason et al. 2009; Sana & Evans 2011; Chini et al. 2012). Because properties such as binary fraction, period distribution, and mass-ratio distribution provide important constraints on models of star formation and dynamical evolution, precise knowledge of multiplicity characteristics and how they change within this exceptional mass region are important to understanding the formation of high-mass stars. The currently discussed high-mass star formation scenarios involve: i) the gravitational collapse of isolated massive cores and accretion disk (e.g., Myers 1991; Ward-Thompson 2002; Yorke & Sonnhalter 2002; Krumholz et al. 2005; Krumholz 2006), ii) competitive accretion in a clustered environment (Bonnell et al. 2003; Bonnell & Bate 2006; Bonnell 2008; Clark et al. 2008), and iii) stellar collisions in very dense clusters (Bonnell et al. 1998; Stahler et al. 2000; Vanbeveren et al. 2009).</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_20></location>Once a star has evolved to where it fills its Roche lobe, interaction with its companion through the transfer of mass is inevitable. The evolution of interacting binaries follows a significantly di GLYPH<11> erent path from that of single stars because of the mass flow outwards from one component, the mass gain by its companion and the mass loss from the entire system. The evolution of massive stars in binary systems may lead to exotic phenomena such as stellar mergers, X-ray binaries or gamma-ray bursts.</text>
<text><location><page_2><loc_7><loc_89><loc_50><loc_93></location>As recently claimed by Sana et al. (2012) more than 70% of all high-mass stars will exchange mass with a companion, leading to a binary merger in one-third of the cases.</text>
<text><location><page_2><loc_7><loc_72><loc_50><loc_89></location>While great progress has been made so far in a statistical sense, the system parameters like period ( P ), eccentricity ( e ) and mass for individual high-mass binaries are less known. To date, substantial parts of the observational material for binaries and multiple systems among high-mass stars comes from high-resolution spectroscopic monitoring campaigns performed for clusters e.g. Trumpler 14 and Trumpler 16 (Rauw et al. 2001), Cr 228 (Levato et al. 1990), IC 2944 (Sana et al. 2011), IC 1805 (De Becker et al. 2006), NGC 6231 (Sana et al. 2008), NGC 6611 (Sana 2009), NGC 2244 (Mahy et al. 2009), NGC6334 and NGC6357 (Russeil et al. 2012) or OB associations e.g. Monoceros OB2 (Mahy et al. 2009) and Cyg OB2 (Mahy et al. 2009).</text>
<text><location><page_2><loc_7><loc_62><loc_50><loc_72></location>Spectroscopic orbital parameters of individual binary systems have been reported for e.g. HD 166734 (O + O) (Conti et al. 1980), V382 Cyg (O + O), V448 Cyg (O + O), XZ Cep (O + O) (Harries et al. 1997), HD 93403 (O + O) (Rauw et al. 2000), HD149404 (O + O) (Rauw et al. 2001), HD 152248 (O + O) (Sana et al. 2001), HD 101131 (O + O) (Gies et al. 2002), HD 48099 (O + O) (Mahy et al. 2010), HD 152219 (O + B)(Sana et al. 2006), HD115071 (O + B) (Penny et al. 2002).</text>
<text><location><page_2><loc_7><loc_58><loc_50><loc_62></location>Photometric orbital parameters were reported e.g. by Davidge & Forbes (1988), Balona (1992), Terrell et al. (2003), and Sana et al. (2006).</text>
<text><location><page_2><loc_7><loc_50><loc_50><loc_58></location>There are only a few dozen EBs known among the O-type stars in the Galaxy, e.g. HD 167971 (O + O) (Davidge & Forbes 1988), V1182 Aqu (O + O) (Mayer et al. 2005), FO15 (O + O) (Niemela et al. 2006), and SZ Cam (O + B) (Lorenz et al. 1998). Further O-type EBs are desirable to increase the statistics on this exotic class of objects.</text>
<text><location><page_2><loc_7><loc_37><loc_50><loc_50></location>Currently, we are performing a photometric monitoring survey with the aim to detect all eclipsing O-type binaries in the southern hemisphere from two brightness limited samples. Our targets comprise a complete sample of about 250 O-type stars ( V < 8) taken from the Galactic O-Star Catalogue V.2.0 (Sota et al. 2008). Preliminary results indicate variability for about 24% of the objects (Chini et al. 2013). A second sample of fainter O stars comes from the Bochum Galactic disk Survey (Haas et al. 2012) where we are monitoring all stars with 10 < R ; I < 15 in a strip of GLYPH<1> b = GLYPH<6> 3 GLYPH<14> along the southern galactic plane.</text>
<text><location><page_2><loc_7><loc_29><loc_50><loc_37></location>In this paper we present a detailed photometric multiepoch study of three selected O-type stars, HD319702, CPD GLYPH<0> 51 GLYPH<14> 8946 and PISMIS24-1. We show the first light curve for Pismis 24-1, re-analyze the orbital period for CPD GLYPH<0> 51 GLYPH<14> 8946 and finally present the orbital parameters for a new high-mass EB system HD 319702.</text>
<section_header_level_1><location><page_2><loc_7><loc_25><loc_13><loc_27></location>2. Data</section_header_level_1>
<section_header_level_1><location><page_2><loc_7><loc_23><loc_20><loc_24></location>2.1. Observations</section_header_level_1>
<text><location><page_2><loc_7><loc_12><loc_50><loc_22></location>The photometric observations were conducted between May and October 2011 using the robotic 15 cm VYSOS-6 telescope of the Universitatssternwarte Bochum, located near Cerro Armazones, the future location of the ESO Extreme Large Telescope (ELT) in Chile 1 ; for instrumental details see Haas et al. (2012). The images were obtained simultaneously through Sloan r and i filters at 6230 Å and 7616 Å; each star was observed typically for about 40 epochs.</text>
<section_header_level_1><location><page_2><loc_52><loc_92><loc_62><loc_93></location>2.2. Reduction</section_header_level_1>
<text><location><page_2><loc_52><loc_75><loc_95><loc_91></location>The images were processed by standard IRAF 2 routines for image reduction, including bias, dark current and flatfield correction. Additionally, astrometry and astrometric distortion were calculated and properly corrected using SCAMP (Bertin 2006) in combination with SExtractor (Bertin & Arnouts 1996). To improve the image quality further we resampled the frames of an original pixel size of 2.4 00 to a new pixel size of 0.8 00 using the routine SWARP (Bertin et al. 2002). More information about the data reduction can be found in Haas et al. (2012). Photometry was performed using an aperture radius of 4 00 maximizing the signal-to-noise ratio ( S = N ) and delivering the lowest absolute scatter for the fluxes.</text>
<text><location><page_2><loc_52><loc_64><loc_95><loc_75></location>The light curves in normalized flux units are calculated relative to nearby non-variable reference stars located in the same field. The absolute photometric calibration was obtained using the fluxes of about 20 standard stars from Landolt (2009). The standard star fields have been observed during the same nights as the science targets. The photometry was corrected for airmass by using the extinction curve for the nearby site Cerro Paranal derived by Patat et al. (2011). The photometric errors are typically of the order of 0.05 mag at both wavelengths.</text>
<section_header_level_1><location><page_2><loc_52><loc_60><loc_69><loc_61></location>2.3. Light Curve analysis</section_header_level_1>
<text><location><page_2><loc_52><loc_41><loc_95><loc_59></location>The photometric light curves were analysed assuming a standard Roche geometry based on the Wilson-Devinney code (Wilson & Devinney 1971; Wilson 1979, Wilson 1990). Because Kurucz model atmospheres assume local thermodynamic equilibrium (LTE) for calculating the emergent fluxes from a star this approximation is insu GLYPH<14> cient in estimating the resultant light curves of high-mass stars, where non-LTE e GLYPH<11> ects alter the radiation field significantly from that of LTE. This is even more prominent in evolved stars, like Pismis 24-1, which is one of the objects investigated in the present study. For a more thorough analysis of these systems, after follow-up spectroscopy has been obtained, we will use a code that allows for input of model atmospheres that do not make the LTE assumption, such as the ELC code (Orosz & Hauschildt 2000).</text>
<text><location><page_2><loc_52><loc_24><loc_95><loc_41></location>For each model, the period P of the system and T e GLYPH<11> of one component were fixed. In the following we refer to the temperatures of the primary and secondary component as T 1 and T 2, respectively. Periods were determined independently through the Lafler-Kinman algorithm (Lafler & Kinman 1965) which was subsequently generalized and called Phase Dispersion Minimization (PDM) by Stellingwerf (1978). This method selects the period that yields the lowest dispersion of the phase light curve. The advantage of this algorithm compared to others (e.g. Analysis of Variance by Schwarzenberg-Czerny (1989), Schwarzenberg-Czerny (1999); Lomb-Scargle periodogram by Scargle (1982)) is that it works also reliably in cases where there are only a moderate number of data points ( GLYPH<24> 50).</text>
<text><location><page_2><loc_52><loc_16><loc_95><loc_24></location>E GLYPH<11> ective temperatures were adopted according to the spectral types of the stars. For cases where the mass ratio ( q = M 1 = M 2) of the stars was known, T e GLYPH<11> was also fixed accordingly. The best model was determined through several fits to the light curves until the minimum of the GLYPH<31> 2 was reached for each of the following free parameters adopted: the e GLYPH<11> ective temperature of</text>
<text><location><page_3><loc_7><loc_89><loc_50><loc_93></location>the secondary star, the Roche lobe filling factors and the inclination i . Because our light curves do not reveal any signs for spots, any further physical analysis was excluded.</text>
<text><location><page_3><loc_7><loc_79><loc_50><loc_89></location>A standard gravity-darkening law ( T e GLYPH<11> GLYPH<24> g GLYPH<12> ) with coe GLYPH<14> -cients GLYPH<12> 1 = GLYPH<12> 2 = 0 : 25 (von Zeipel 1924; Claret 2000; Djuraˇsevi'c et al. 2003) together with bolometric albedos A 1 = A 2 = 1 : 0 was assumed for early-type stars with radiative envelopes and hydrostatic equilibrium. We used a non-linear square-root limbdarkening law obtained at optical wavelengths (Diaz-Cordoves & Gimenez 1992) with limb darkening coe GLYPH<14> cients interpolated from tables of van Hamme (1993) at the given bandpass.</text>
<section_header_level_1><location><page_3><loc_7><loc_76><loc_15><loc_77></location>3. Results</section_header_level_1>
<text><location><page_3><loc_7><loc_71><loc_50><loc_75></location>In the following, we introduce the three multiple high-mass systems and describe their properties as obtained from our light curve analysis.</text>
<table>
<location><page_3><loc_7><loc_49><loc_50><loc_65></location>
<caption>Table 1. Pismis 24-1 orbital solution and system parameters. The reference time, T 0, refers to the time of the primary eclipse.</caption>
</table>
<section_header_level_1><location><page_3><loc_7><loc_44><loc_18><loc_45></location>3.1. Pismis 24-1</section_header_level_1>
<text><location><page_3><loc_7><loc_36><loc_50><loc_43></location>Pismis 24-1 is a triple system that belongs to the young open cluster Pismis 24 which resides within NGC 6357 in the Sagittarius spiral arm at a distance of 1.7 kpc (Fang et al. 2012). This well-studied region is known as a rich reservoir of young stars, containing several OB-type stars (Massey et al. 2001) and several shell-like H ii regions (Russeil et al. 2012).</text>
<text><location><page_3><loc_7><loc_23><loc_50><loc_35></location>As part of a multiplicity study at the high-mass end of the IMF, Pismis 24-1 (HDE 319718 A) has been investigated in depth by Ma'ız Apell'aniz et al. (2007) by means of highresolution images from the Hubble Space Telescope (HST). These observations resolved the system into two components - Pismis 24-1 SW and Pismis 24-1 NE separated by 0.36 00 (see Fig. 1 of Ma'ız Apell'aniz et al. 2007). Both components have similar absolute visual magnitudes ( MV = GLYPH<0> 6 : 28 for Pismis 241 SW and MV = GLYPH<0> 6 : 41 for Pismis 24-1 NE) and similar intrinsic colors.</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_22></location>High-resolution spectroscopy (Ma'ız Apell'aniz et al. 2007) yielded a spectral type O4 III(f + ) for Pismis 24-1 SW and confirmed the spectral type O3.5 If* for Pismis 24-1 NE as determined previously by Walborn (2002). Radial velocity variations from + 20 to GLYPH<0> 90 km s GLYPH<0> 1 for the absorption lines measured in eight spectra confirmed the variations reported previously by Lortet et al. (1984) and suggest that Pismis 24-1 NE is an unresolved spectroscopic binary. The estimated masses for Pismis 24-1 SW and Pismis 24-1 NE are 96 GLYPH<6> 10 M GLYPH<12> and 97 GLYPH<6> 10 M GLYPH<12> (Ma'ız Apell'aniz et al. 2007).</text>
<text><location><page_3><loc_52><loc_85><loc_95><loc_93></location>Phil Massey and collaborators have detected optical variability in the unresolved Pismis 24-1 NE + SW system with a peakto-peak amplitude of 0.07 mag and a period of 2.36088 days 3 . However, no light curve has been published to date. As a consequence, Pismis 24-1 is an excellent target to provide a decent light curve for this system and to test our photometric analysis.</text>
<text><location><page_3><loc_52><loc_81><loc_95><loc_85></location>The PDM analysis of our 32 data points yields a period of P = 2 : 36 days which is in excellent agreement with the result reported by Ma'ız Apell'aniz et al. (2007).</text>
<text><location><page_3><loc_52><loc_53><loc_95><loc_81></location>As already noted in Sect. 2, each final (reduced) image has a resolution of 0.8 00 which does not allow us to resolve both Pismis 24-1 NE + SW separately. In consequence, we expect that some amount of third light contribution could alter the properties of the system, reducing the depths of the eclipses resulting in temperature and inclination being underestimated. In order to estimate the third light contribution, we performed the analysis adopting l 3 as a free parameter. The analysis yields reasonable solutions for 0 : 05 GLYPH<20> l 3 GLYPH<20> 0 : 20 with the best-fitting model at l 3 = 0 : 15. An acceptable solution can be found without considering the third light component ( l 3 = 0), however, the uncertainty in the inclination and the temperature is large. Fig. 1 displays the observed Sloan r and Sloan i light curves together with the best-fitting model solution folded onto the orbital period. The light curves in both filters show nearly the same amplitude variations ( GLYPH<24> 7%) and both partial eclipses with the same duration of 0.174 in phase. The primary and secondary minimum eclipses, which are separated symmetrically by 0.5 in phase, show similar depths GLYPH<1> Dp = GLYPH<1> Dp ; min GLYPH<0> GLYPH<1> Dmax = 8% and GLYPH<1> Ds = GLYPH<1> Ds ; min GLYPH<0> GLYPH<1> Dmax = 7%, where p and s refer to the primary and secondary minimum, and max denotes to the global maximum of the light curve (Sandquist & Shetrone 2003).</text>
<text><location><page_3><loc_52><loc_23><loc_95><loc_52></location>We fixed T 1 = 42000 K according to the spectral type O3.5 If* reported by Ma'ız Apell'aniz et al. (2007) and used the observational Tef f calibration by Martins et al. (2005) (his Table 6). Additionally, we assumed equal masses for both components ( q = 1 : 0) as suggested by the spectroscopy (Ma'ız Apell'aniz et al. 2007). The best-fitting model favours a detached configuration with an inclination i = 61 : 8 GLYPH<14> and requires that both components fill up their Roche lobes at about 79% and 81%, respectively. A 3D graphic presentation of the Roche model of the system obtained at a orbital phase GLYPH<30> = 0 : 12 is shown in Fig. 1. Our calculations yield an e GLYPH<11> ective temperature of T 2 = 41500 K for the secondary star which is consistent with its spectral type designation. The spectral type O3.5 If* corresponds to the combined light of the two stars; hence spectroscopic follow-up is required to classify the individual components. Likewise, the similarity of the depths in the primary and secondary minimum agrees well with the derived temperature. The observed symmetrical separation of the primary and secondary minimum eclipses suggests that the system has a circular orbit compatible with the current spectroscopic knowledge of the system. In consequence, we assumed zero eccentricity and synchronous rotation for which the model provides the best fit to the system. A summary of the relevant parameters and the best-fitting values are listed in Table 1.</text>
<section_header_level_1><location><page_3><loc_52><loc_19><loc_66><loc_21></location>3.2. CPD GLYPH<0> 51 GLYPH<14> 8946</section_header_level_1>
<text><location><page_3><loc_52><loc_13><loc_95><loc_18></location>CPD GLYPH<0> 51 GLYPH<14> 8946 was classified as an OB-type star (Lynga 1964) and is part of a sample of about 700 OB stars observed by van Houten (2001) at the former Leiden Southern Station at Hartebeespoortdam, South Africa. The eclipsing nature of</text>
<figure>
<location><page_4><loc_9><loc_71><loc_49><loc_92></location>
<caption>Fig. 2 shown the light curves together with the best-fitting model solution corresponding to Sloan r and i filters. In addition, this figure shows the light curve obtained from the ASAS III catalogue with a period of 1.96 days. The light curves in both filters have similar amplitude variations of GLYPH<24> 16%. The primary and secondary minimum have di GLYPH<11> erent depths GLYPH<1> Dp = 16% and GLYPH<1> Ds = 10%, which can be interpreted through a di GLYPH<11> erence between the temperatures of the components. Both partial eclipses have the same duration (0.214 in phase) and their minima are</caption>
</figure>
<figure>
<location><page_4><loc_9><loc_47><loc_49><loc_69></location>
</figure>
<figure>
<location><page_4><loc_15><loc_29><loc_43><loc_46></location>
<caption>Fig. 1. Observed light curves of Pismis 24-1 with the best-fitting model obtained at l 3 = 0 : 15 (yellow solid line) in the Sloan r (top) and Sloan i (middle) bands, folded onto the orbital period of 2.36 days. The error bar in the bottom of the plot represents the average measurement uncertainty for the data set. The blue and black solid lines correspond to the solutions obtained at l 3 = 0 : 1 and l 3 = 0 : 2 respectively. Bottom: 3D view of the system Pismis 24-1 at an orbital phase of 0.12.</caption>
</figure>
<text><location><page_4><loc_7><loc_10><loc_50><loc_14></location>CPD GLYPH<0> 51 GLYPH<14> 8946 was established by Pojmanski & Maciejewski (2004) using the data obtained from the ASAS III (All Sky Automated Survey) catalogue of variable stars. The authors de-</text>
<table>
<location><page_4><loc_52><loc_72><loc_94><loc_88></location>
<caption>Table 2. CPD GLYPH<0> 51 GLYPH<14> 8946 orbital solution and system parameters.The reference time, T 0, refers to the time of the primary eclipse.Table 3. HD319702 orbital solution and system parameters. The reference time, T 0, refers to the time of the primary eclipse.</caption>
</table>
<table>
<location><page_4><loc_52><loc_51><loc_94><loc_67></location>
</table>
<text><location><page_4><loc_52><loc_46><loc_95><loc_48></location>termined a photometric period of 3.92 days and suggest an eclipsing detached binary configuration.</text>
<text><location><page_4><loc_52><loc_24><loc_95><loc_46></location>From 44 data points we obtain a photometric period of 1.96 days, which is exactly half the period reported by Pojmanski & Maciejewski (2004). To check this discrepancy, we performed a re-analysis of the light curves available from the ASAS photometric catalog 4 database. Firstly, we considered whether the difference maybe caused by the selection of the ASAS photometric data points, which are identified with the letters A to D according to the quality of the data. Using only the high-quality data available (marked with A) the PDM analysis yields a period P = 1 : 96 days which is exactly the same value obtained from our light curves. Second, we considered whether the discrepancy may be caused by the di GLYPH<11> erent algorithms used to calculate the period. However, using GLYPH<24> 50 light curves obtained from the ASAS catalogue and performing a PDM analysis yields 100% agreement with the values reported by Pojmanski & Maciejewski (2004). Therefore we assume that the entry in Table 2 from Pojmanski &Maciejewski (2004) must be erroneous.</text>
<figure>
<location><page_5><loc_9><loc_71><loc_49><loc_92></location>
</figure>
<figure>
<location><page_5><loc_9><loc_47><loc_49><loc_69></location>
</figure>
<figure>
<location><page_5><loc_9><loc_24><loc_49><loc_45></location>
<caption>Fig. 2. Observed (dots) and simulated (solid line) light curves in the r-Sloan (top) and i-Sloan (middle) bands, folded onto the orbital period (1 : 96 days) obtained from the PDM analysis. The error bar in the bottom of the plot represents the average measurement uncertainty for the data set. Bottom: The normalized V-band light curve obtained from the ASAS III catalogue folded with a period of 1 : 96 days.</caption>
</figure>
<figure>
<location><page_5><loc_55><loc_79><loc_91><loc_92></location>
<caption>Fig. 3. The graphical 3D view of the system CPD GLYPH<0> 51 GLYPH<14> 8946 when the secondary star fills up its Roche lobe (bottom) was obtained with the parameters estimated from the light curve analysis.</caption>
</figure>
<text><location><page_5><loc_52><loc_63><loc_95><loc_70></location>separated symmetrically (0.5 in phase). In consequence, we estimated the parameters of the system by assuming a circular orbit and a synchronous rotation. The primary component fills up its Roche lobe at about 95% while the secondary at about 99%, favouring a semi-detached configuration with an orbital inclination i = 58 : 4 GLYPH<14> .</text>
<text><location><page_5><loc_52><loc_55><loc_95><loc_62></location>We fixed the e GLYPH<11> ective temperature of the primary star T 1 = 34550 K according to the color-index B GLYPH<0> V = GLYPH<0> 0 : 32 obtained by van Houten (2001) 5 corresponding to the spectral type O8.5 V, reported originally by Boehm-Vitense (1981) and re-analyzed by Humphreys & McElroy (1984); this spectral designation is also consistent with recent investigations by Martins et al. (2005).</text>
<text><location><page_5><loc_52><loc_42><loc_95><loc_55></location>The best fit to the light curve yields a mass ratio q = M 1 = M 2 = 2 : 8 with a temperature of the secondary component T 2 = 21500 K corresponding to a spectral type B2 V (BoehmVitense 1981; Lefever et al. 2010; Nieva & Przybilla 2012). As displayed in Fig. 2, the 3D view Roche geometry of the system ( GLYPH<30> = 0 : 63) shows a transitional evolutionary state of the system for which both stars are close to filling their Roche Lobes. Most likely the future mass transfer will create a new contact binary system. A summary of the relevant parameters and the best-fitting values are listed in Table 2.</text>
<section_header_level_1><location><page_5><loc_52><loc_39><loc_63><loc_40></location>3.3. HD319702</section_header_level_1>
<text><location><page_5><loc_52><loc_25><loc_95><loc_37></location>Located at a distance of 1.75 kpc (Russeil et al. 2010; Russeil et al. 2012), HD 319702 is a member of the cluster NGC 6334. This region is considered as one of the most active regions of highmass star formation in our Galaxy (Tapia & Persi 2009; Russeil et al. 2012). The area contains evolved optical but also embedded compact H ii regions. HD 319702 has been classified originally as a B1 Ib by Neckel (1978); later measurements converted the spectral type into O8 III(f) (Walborn 1982; Ma'ız-Apell'aniz et al. 2004; Pinheiro et al. 2010). So far there was no hint for an eclipsing orbit.</text>
<text><location><page_5><loc_52><loc_16><loc_95><loc_24></location>As displayed in Fig. 4, the light curves constructed from 38 epochs show nearly identical amplitude variations with primary and secondary minimum eclipses at di GLYPH<11> erent depths ( GLYPH<1> Dp = 11%, GLYPH<1> Ds = 8%). This behaviour is characteristic for an eclipsing binary with di GLYPH<11> erent e GLYPH<11> ective temperatures; the primary minimum is due to the eclipse of the more luminous star by the less luminous companion. The eclipses are partial and symmet-</text>
<text><location><page_6><loc_7><loc_89><loc_50><loc_93></location>ric with the same duration of 0.189 in phase. The primary and secondary minimum are separated symmetrically by 0.5 in phase suggesting a circular orbit.</text>
<text><location><page_6><loc_7><loc_66><loc_50><loc_89></location>Our PDM analysis yields a period of P = 2 : 01 days. Again, we have assumed a zero eccentricity and synchronous rotation for which the model provides the best fit to the system. Based on the spectral type determination of the primary star we adopted a value of T 1 = 34000 K considering the observational Tef f calibration by Martins et al. (2005) (his Table 5). We computed a set of orbital solutions where the best-fitting model favours an orbital inclination of 67.5 GLYPH<14> with a mass ratio of q = M 1 = M 2 = 1 : 0. The system shows well-defined eclipses favouring a detached configuration, where both components fill up their Roche lobes at about 71%. The temperature of the secondary component is T 2 = 25200 K suggesting that this new system is most likely composed of an O8 III + a B0.5 V star if the calibration by Humphreys & McElroy (1984) is used for the secondary component. Considering the calibration reported by Boehm-Vitense (1981) and Harmanec (1988) the system would turn into O8 III + a B1 V. A summary of the relevant parameters and the bestfitting values are listed in Table 3.</text>
<section_header_level_1><location><page_6><loc_7><loc_63><loc_31><loc_64></location>4. Summary and conclusions</section_header_level_1>
<text><location><page_6><loc_7><loc_51><loc_50><loc_62></location>We have presented optical photometric observations for three high-mass eclipsing binaries performed during a six months monitoring campaign. A detailed analysis and modeling of the light curves was carried out within the framework of the Roche geometry. We find that all objects show light curve variations that occur on time-scales of less than 3 days and that the systems are well described by circular orbits (zero or negligible eccentricity). The individual results are:</text>
<unordered_list>
<list_item><location><page_6><loc_8><loc_46><loc_50><loc_51></location>-Pismis 24-1 is a detached system with an orbital inclination of 61 : 8 GLYPH<14> and an orbital period of 2.36 days. We can confirm that the eclipsing binary system of Pismis 24-1 is composed by at least one O + O pair.</list_item>
<list_item><location><page_6><loc_8><loc_40><loc_50><loc_45></location>-CPD GLYPH<0> 51 GLYPH<14> 8946 is a semi-detached system with an orbital inclination of 58 : 4 GLYPH<14> and an orbital period of 1.96 days. This system is most likely composed of an O8.5 V and a B2 V star and develops toward a contact system.</list_item>
<list_item><location><page_6><loc_8><loc_35><loc_50><loc_40></location>-HD319702 is a new high-mass eclipsing binary system with an detached configuration; its orbital inclination is 67 : 5 GLYPH<14> and the period is 2.01 days. The components are well described by the association of an O8 III and a B1 V star.</list_item>
</unordered_list>
<text><location><page_6><loc_7><loc_10><loc_50><loc_34></location>The current study has demonstrated that our photometric survey has the capability to detect O-type eclipsing binaries along the galactic plane in the brightness range 10 < R ; I < 15; more EB candidates will be presented in the future. Follow-up spectroscopic RV studies of this sample are essential to determine the absolute parameters and to track the evolutionary state of individual systems. On the other hand, for the complete sample from the Galactic O-Star Catalogue ( V < 8) we are currently monitoring all SB2 candidates (Chini et al. 2012) to detect further O-type EBs among this sample and to obtain precise light curves (Barr Dom'ınguez et al., in prep.). From the few results available so far - both in the literature and from our current study- it seems that the important mass ratio parameter q GLYPH<24> 1. However, there might be an observational bias since O stars have very high luminosities which prevent fainter companions from being detected. So far there are only four known high-mass binaries where q > 2 with the exceptional maximum of q GLYPH<24> 5 : 8: HD37022 (O5), HD53975 (B7Iab), HD199579 (O6 V), and HD 165246 (O8 V) (see Mayer et al. 2013 and references therein).</text>
<text><location><page_6><loc_52><loc_81><loc_95><loc_93></location>This strongly corroborates the view that high-mass binaries are generally created during the star formation process and are not a result of tidal capture. We expect that our study will increase the number of known O-type EBs substantially and that we can obtain a better census of the range of q = M 1 = M 2 in the high-mass regime. Likewise it will be interesting to see at which stellar primary mass q will significantly deviate from unity. For this reason we will extend our studies in the future also toward B-type binaries.</text>
<text><location><page_6><loc_52><loc_76><loc_95><loc_80></location>Acknowledgements. This publication is supported as a project of the NordrheinWestfalische Akademie der Wissenschaften und der Kunste in the framework of the academy program by the Federal Republic of Germany and the state Nordrhein-Westfalen.</text>
<text><location><page_6><loc_52><loc_73><loc_95><loc_76></location>The observations at Cerro Armazones benefitted from the continuous support of the Universidad Cat'olica del Norte and from the care of the guardians Hector Labra, Gerardo Pino, Roberto Munoz, and Francisco Arraya.</text>
<text><location><page_6><loc_52><loc_66><loc_95><loc_73></location>This research has made use of the NASA / IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. We thank the anonymous referee for his contructive comments and careful review of the manuscript.</text>
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<figure>
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</figure>
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<caption>Fig. 4. Observed (dots) and simulated (solid line) light curves in the Sloan r (top) and Sloan i (middle) bands, folded onto the orbital period (2 : 01 days) obtained from the PDM analysis. The error bar in the bottom of the plot represents the average measurement uncertainty for the data set. The graphical 3D view of the new detached binary system HD 319702 at an orbital phase 0.5 is displayed at the bottom.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "We present first results of a comprehensive photometric O-star survey performed with a robotic twin refractor at the Universitatssternwarte Bochum located near Cerro Armazones in Chile. For three high-mass stars, namely Pismis 24-1, CPD GLYPH<0> 51 GLYPH<14> 8946 and HD 319702, we determined the period through the Lafler-Kinman algorithm and model the light curves within the framework of the Roche geometry. For Pismis 24-1, a previously known eclipsing binary, we provide first light curves and determined a photometric period of 2.36 days together with an orbital inclination of 61 : 8 GLYPH<14> . The best-fitting model solution to the light curves suggest a detached configuration. With a primary temperature of T 1 = 42520 K we obtain the temperature of the secondary component as T 2 = 41500 K. CPD GLYPH<0> 51 GLYPH<14> 8946 is another known eclipsing binary for which we present a revised photometric period of 1.96 days with an orbital inclination of 58 : 4 GLYPH<14> . The system has likely a semi-detached configuration and a mass ratio q = M 1 = M 2 = 2 : 8. If we adopt a primary temperature of T 1 = 34550 K we obtain T 2 = 21500 K for the secondary component. HD 319702 is a newly discovered eclipsing binary member of the young open cluster NGC 6334. The system shows well-defined eclipses favouring a detached configuration with a period of 2.0 days and an orbital inclination of 67 : 5 GLYPH<14> . Combining our photometric result with the primary spectral type O8 III(f) ( T 1 = 34000 K) we derive a temperature of T 2 = 25200 K for the secondary component. Key words. stars: fundamental parameters -stars: formation -binaries: eclipsing -binaries: spectroscopic -Galaxy: open clusters and associations: individual: NGC6334 -Galaxy: open clusters and associations: individual: NGC6357",
"pages": [
1
]
},
{
"title": "I. Light curves and system parameters for CPD GLYPH<0> 51 GLYPH<14> 8946, PISMIS24-1 and HD319702",
"content": "A. Barr Dom'ınguez 1 , R. Chini 1 ; 2 , F. Pozo Nu˜nez 1 , M. Haas 1 , M. Hackstein 1 , H. Drass 1 R. Lemke 1 , and M. Murphy 2 Received ; accepted",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The fundamental quantity of a star is its mass because it determines the energy production, the evolution and the final state; certainly there are other parameters like chemical composition and angular momentum that influence stellar evolution. At first glance, the easiest way to estimate stellar masses is by means of the mass-luminosity relation L / M GLYPH<11> which is well established by both theory and observation. However, the exponent GLYPH<11> itself is a function of mass: while GLYPH<11> GLYPH<24> 4 for solar-type stars it becomes smaller for stars of lower ( < 0 : 5 M GLYPH<12> ) and higher ( > 10 M GLYPH<12> ) mass. In practice there are many other parameters that influence the mass-luminosity relation. All stars increase their luminosity with age - on the other hand high-mass stars lose a considerable fraction of their mass during evolution. Observationally, the determination of the bolometric luminosity ( L bol) becomes more di GLYPH<14> cult for O- and early B-type stars because due to their high temperature most light is radiated in the UV . Likewise, distance, reddening and e GLYPH<11> ective temperature ( T e GLYPH<11> ) have to be known in order to calculate the absolute visual magnitude MV and to convert it into L bol. For high-mass stars one can circumvent the massluminosity relation and determine T e GLYPH<11> and L bol by modeling the optical spectra and by placing the star in the Hertzsprung-Russel diagram (HRD). Eventually evolutionary models yield the stellar mass which is obviously based on many assumptions and whose error is dominated by the uncertainties of theoretical models. In contrast, binary stars allow the determination of fundamental stellar parameters through a combination of photometry, astrometry, and spectroscopy and by applying basic physical laws. In case of an eclipsing binary (hereafter EB), radii, distance and, in favorable cases, T e GLYPH<11> also may be determined from a combined analysis of light curves and radial velocity (hereafter RV ) curves. There is growing evidence that most high-mass stars occur as binaries and / or multiple systems (e.g., Preibisch et al. 1999; Mason et al. 2009; Sana & Evans 2011; Chini et al. 2012). Because properties such as binary fraction, period distribution, and mass-ratio distribution provide important constraints on models of star formation and dynamical evolution, precise knowledge of multiplicity characteristics and how they change within this exceptional mass region are important to understanding the formation of high-mass stars. The currently discussed high-mass star formation scenarios involve: i) the gravitational collapse of isolated massive cores and accretion disk (e.g., Myers 1991; Ward-Thompson 2002; Yorke & Sonnhalter 2002; Krumholz et al. 2005; Krumholz 2006), ii) competitive accretion in a clustered environment (Bonnell et al. 2003; Bonnell & Bate 2006; Bonnell 2008; Clark et al. 2008), and iii) stellar collisions in very dense clusters (Bonnell et al. 1998; Stahler et al. 2000; Vanbeveren et al. 2009). Once a star has evolved to where it fills its Roche lobe, interaction with its companion through the transfer of mass is inevitable. The evolution of interacting binaries follows a significantly di GLYPH<11> erent path from that of single stars because of the mass flow outwards from one component, the mass gain by its companion and the mass loss from the entire system. The evolution of massive stars in binary systems may lead to exotic phenomena such as stellar mergers, X-ray binaries or gamma-ray bursts. As recently claimed by Sana et al. (2012) more than 70% of all high-mass stars will exchange mass with a companion, leading to a binary merger in one-third of the cases. While great progress has been made so far in a statistical sense, the system parameters like period ( P ), eccentricity ( e ) and mass for individual high-mass binaries are less known. To date, substantial parts of the observational material for binaries and multiple systems among high-mass stars comes from high-resolution spectroscopic monitoring campaigns performed for clusters e.g. Trumpler 14 and Trumpler 16 (Rauw et al. 2001), Cr 228 (Levato et al. 1990), IC 2944 (Sana et al. 2011), IC 1805 (De Becker et al. 2006), NGC 6231 (Sana et al. 2008), NGC 6611 (Sana 2009), NGC 2244 (Mahy et al. 2009), NGC6334 and NGC6357 (Russeil et al. 2012) or OB associations e.g. Monoceros OB2 (Mahy et al. 2009) and Cyg OB2 (Mahy et al. 2009). Spectroscopic orbital parameters of individual binary systems have been reported for e.g. HD 166734 (O + O) (Conti et al. 1980), V382 Cyg (O + O), V448 Cyg (O + O), XZ Cep (O + O) (Harries et al. 1997), HD 93403 (O + O) (Rauw et al. 2000), HD149404 (O + O) (Rauw et al. 2001), HD 152248 (O + O) (Sana et al. 2001), HD 101131 (O + O) (Gies et al. 2002), HD 48099 (O + O) (Mahy et al. 2010), HD 152219 (O + B)(Sana et al. 2006), HD115071 (O + B) (Penny et al. 2002). Photometric orbital parameters were reported e.g. by Davidge & Forbes (1988), Balona (1992), Terrell et al. (2003), and Sana et al. (2006). There are only a few dozen EBs known among the O-type stars in the Galaxy, e.g. HD 167971 (O + O) (Davidge & Forbes 1988), V1182 Aqu (O + O) (Mayer et al. 2005), FO15 (O + O) (Niemela et al. 2006), and SZ Cam (O + B) (Lorenz et al. 1998). Further O-type EBs are desirable to increase the statistics on this exotic class of objects. Currently, we are performing a photometric monitoring survey with the aim to detect all eclipsing O-type binaries in the southern hemisphere from two brightness limited samples. Our targets comprise a complete sample of about 250 O-type stars ( V < 8) taken from the Galactic O-Star Catalogue V.2.0 (Sota et al. 2008). Preliminary results indicate variability for about 24% of the objects (Chini et al. 2013). A second sample of fainter O stars comes from the Bochum Galactic disk Survey (Haas et al. 2012) where we are monitoring all stars with 10 < R ; I < 15 in a strip of GLYPH<1> b = GLYPH<6> 3 GLYPH<14> along the southern galactic plane. In this paper we present a detailed photometric multiepoch study of three selected O-type stars, HD319702, CPD GLYPH<0> 51 GLYPH<14> 8946 and PISMIS24-1. We show the first light curve for Pismis 24-1, re-analyze the orbital period for CPD GLYPH<0> 51 GLYPH<14> 8946 and finally present the orbital parameters for a new high-mass EB system HD 319702.",
"pages": [
1,
2
]
},
{
"title": "2.1. Observations",
"content": "The photometric observations were conducted between May and October 2011 using the robotic 15 cm VYSOS-6 telescope of the Universitatssternwarte Bochum, located near Cerro Armazones, the future location of the ESO Extreme Large Telescope (ELT) in Chile 1 ; for instrumental details see Haas et al. (2012). The images were obtained simultaneously through Sloan r and i filters at 6230 Å and 7616 Å; each star was observed typically for about 40 epochs.",
"pages": [
2
]
},
{
"title": "2.2. Reduction",
"content": "The images were processed by standard IRAF 2 routines for image reduction, including bias, dark current and flatfield correction. Additionally, astrometry and astrometric distortion were calculated and properly corrected using SCAMP (Bertin 2006) in combination with SExtractor (Bertin & Arnouts 1996). To improve the image quality further we resampled the frames of an original pixel size of 2.4 00 to a new pixel size of 0.8 00 using the routine SWARP (Bertin et al. 2002). More information about the data reduction can be found in Haas et al. (2012). Photometry was performed using an aperture radius of 4 00 maximizing the signal-to-noise ratio ( S = N ) and delivering the lowest absolute scatter for the fluxes. The light curves in normalized flux units are calculated relative to nearby non-variable reference stars located in the same field. The absolute photometric calibration was obtained using the fluxes of about 20 standard stars from Landolt (2009). The standard star fields have been observed during the same nights as the science targets. The photometry was corrected for airmass by using the extinction curve for the nearby site Cerro Paranal derived by Patat et al. (2011). The photometric errors are typically of the order of 0.05 mag at both wavelengths.",
"pages": [
2
]
},
{
"title": "2.3. Light Curve analysis",
"content": "The photometric light curves were analysed assuming a standard Roche geometry based on the Wilson-Devinney code (Wilson & Devinney 1971; Wilson 1979, Wilson 1990). Because Kurucz model atmospheres assume local thermodynamic equilibrium (LTE) for calculating the emergent fluxes from a star this approximation is insu GLYPH<14> cient in estimating the resultant light curves of high-mass stars, where non-LTE e GLYPH<11> ects alter the radiation field significantly from that of LTE. This is even more prominent in evolved stars, like Pismis 24-1, which is one of the objects investigated in the present study. For a more thorough analysis of these systems, after follow-up spectroscopy has been obtained, we will use a code that allows for input of model atmospheres that do not make the LTE assumption, such as the ELC code (Orosz & Hauschildt 2000). For each model, the period P of the system and T e GLYPH<11> of one component were fixed. In the following we refer to the temperatures of the primary and secondary component as T 1 and T 2, respectively. Periods were determined independently through the Lafler-Kinman algorithm (Lafler & Kinman 1965) which was subsequently generalized and called Phase Dispersion Minimization (PDM) by Stellingwerf (1978). This method selects the period that yields the lowest dispersion of the phase light curve. The advantage of this algorithm compared to others (e.g. Analysis of Variance by Schwarzenberg-Czerny (1989), Schwarzenberg-Czerny (1999); Lomb-Scargle periodogram by Scargle (1982)) is that it works also reliably in cases where there are only a moderate number of data points ( GLYPH<24> 50). E GLYPH<11> ective temperatures were adopted according to the spectral types of the stars. For cases where the mass ratio ( q = M 1 = M 2) of the stars was known, T e GLYPH<11> was also fixed accordingly. The best model was determined through several fits to the light curves until the minimum of the GLYPH<31> 2 was reached for each of the following free parameters adopted: the e GLYPH<11> ective temperature of the secondary star, the Roche lobe filling factors and the inclination i . Because our light curves do not reveal any signs for spots, any further physical analysis was excluded. A standard gravity-darkening law ( T e GLYPH<11> GLYPH<24> g GLYPH<12> ) with coe GLYPH<14> -cients GLYPH<12> 1 = GLYPH<12> 2 = 0 : 25 (von Zeipel 1924; Claret 2000; Djuraˇsevi'c et al. 2003) together with bolometric albedos A 1 = A 2 = 1 : 0 was assumed for early-type stars with radiative envelopes and hydrostatic equilibrium. We used a non-linear square-root limbdarkening law obtained at optical wavelengths (Diaz-Cordoves & Gimenez 1992) with limb darkening coe GLYPH<14> cients interpolated from tables of van Hamme (1993) at the given bandpass.",
"pages": [
2,
3
]
},
{
"title": "3. Results",
"content": "In the following, we introduce the three multiple high-mass systems and describe their properties as obtained from our light curve analysis.",
"pages": [
3
]
},
{
"title": "3.1. Pismis 24-1",
"content": "Pismis 24-1 is a triple system that belongs to the young open cluster Pismis 24 which resides within NGC 6357 in the Sagittarius spiral arm at a distance of 1.7 kpc (Fang et al. 2012). This well-studied region is known as a rich reservoir of young stars, containing several OB-type stars (Massey et al. 2001) and several shell-like H ii regions (Russeil et al. 2012). As part of a multiplicity study at the high-mass end of the IMF, Pismis 24-1 (HDE 319718 A) has been investigated in depth by Ma'ız Apell'aniz et al. (2007) by means of highresolution images from the Hubble Space Telescope (HST). These observations resolved the system into two components - Pismis 24-1 SW and Pismis 24-1 NE separated by 0.36 00 (see Fig. 1 of Ma'ız Apell'aniz et al. 2007). Both components have similar absolute visual magnitudes ( MV = GLYPH<0> 6 : 28 for Pismis 241 SW and MV = GLYPH<0> 6 : 41 for Pismis 24-1 NE) and similar intrinsic colors. High-resolution spectroscopy (Ma'ız Apell'aniz et al. 2007) yielded a spectral type O4 III(f + ) for Pismis 24-1 SW and confirmed the spectral type O3.5 If* for Pismis 24-1 NE as determined previously by Walborn (2002). Radial velocity variations from + 20 to GLYPH<0> 90 km s GLYPH<0> 1 for the absorption lines measured in eight spectra confirmed the variations reported previously by Lortet et al. (1984) and suggest that Pismis 24-1 NE is an unresolved spectroscopic binary. The estimated masses for Pismis 24-1 SW and Pismis 24-1 NE are 96 GLYPH<6> 10 M GLYPH<12> and 97 GLYPH<6> 10 M GLYPH<12> (Ma'ız Apell'aniz et al. 2007). Phil Massey and collaborators have detected optical variability in the unresolved Pismis 24-1 NE + SW system with a peakto-peak amplitude of 0.07 mag and a period of 2.36088 days 3 . However, no light curve has been published to date. As a consequence, Pismis 24-1 is an excellent target to provide a decent light curve for this system and to test our photometric analysis. The PDM analysis of our 32 data points yields a period of P = 2 : 36 days which is in excellent agreement with the result reported by Ma'ız Apell'aniz et al. (2007). As already noted in Sect. 2, each final (reduced) image has a resolution of 0.8 00 which does not allow us to resolve both Pismis 24-1 NE + SW separately. In consequence, we expect that some amount of third light contribution could alter the properties of the system, reducing the depths of the eclipses resulting in temperature and inclination being underestimated. In order to estimate the third light contribution, we performed the analysis adopting l 3 as a free parameter. The analysis yields reasonable solutions for 0 : 05 GLYPH<20> l 3 GLYPH<20> 0 : 20 with the best-fitting model at l 3 = 0 : 15. An acceptable solution can be found without considering the third light component ( l 3 = 0), however, the uncertainty in the inclination and the temperature is large. Fig. 1 displays the observed Sloan r and Sloan i light curves together with the best-fitting model solution folded onto the orbital period. The light curves in both filters show nearly the same amplitude variations ( GLYPH<24> 7%) and both partial eclipses with the same duration of 0.174 in phase. The primary and secondary minimum eclipses, which are separated symmetrically by 0.5 in phase, show similar depths GLYPH<1> Dp = GLYPH<1> Dp ; min GLYPH<0> GLYPH<1> Dmax = 8% and GLYPH<1> Ds = GLYPH<1> Ds ; min GLYPH<0> GLYPH<1> Dmax = 7%, where p and s refer to the primary and secondary minimum, and max denotes to the global maximum of the light curve (Sandquist & Shetrone 2003). We fixed T 1 = 42000 K according to the spectral type O3.5 If* reported by Ma'ız Apell'aniz et al. (2007) and used the observational Tef f calibration by Martins et al. (2005) (his Table 6). Additionally, we assumed equal masses for both components ( q = 1 : 0) as suggested by the spectroscopy (Ma'ız Apell'aniz et al. 2007). The best-fitting model favours a detached configuration with an inclination i = 61 : 8 GLYPH<14> and requires that both components fill up their Roche lobes at about 79% and 81%, respectively. A 3D graphic presentation of the Roche model of the system obtained at a orbital phase GLYPH<30> = 0 : 12 is shown in Fig. 1. Our calculations yield an e GLYPH<11> ective temperature of T 2 = 41500 K for the secondary star which is consistent with its spectral type designation. The spectral type O3.5 If* corresponds to the combined light of the two stars; hence spectroscopic follow-up is required to classify the individual components. Likewise, the similarity of the depths in the primary and secondary minimum agrees well with the derived temperature. The observed symmetrical separation of the primary and secondary minimum eclipses suggests that the system has a circular orbit compatible with the current spectroscopic knowledge of the system. In consequence, we assumed zero eccentricity and synchronous rotation for which the model provides the best fit to the system. A summary of the relevant parameters and the best-fitting values are listed in Table 1.",
"pages": [
3
]
},
{
"title": "3.2. CPD GLYPH<0> 51 GLYPH<14> 8946",
"content": "CPD GLYPH<0> 51 GLYPH<14> 8946 was classified as an OB-type star (Lynga 1964) and is part of a sample of about 700 OB stars observed by van Houten (2001) at the former Leiden Southern Station at Hartebeespoortdam, South Africa. The eclipsing nature of CPD GLYPH<0> 51 GLYPH<14> 8946 was established by Pojmanski & Maciejewski (2004) using the data obtained from the ASAS III (All Sky Automated Survey) catalogue of variable stars. The authors de- termined a photometric period of 3.92 days and suggest an eclipsing detached binary configuration. From 44 data points we obtain a photometric period of 1.96 days, which is exactly half the period reported by Pojmanski & Maciejewski (2004). To check this discrepancy, we performed a re-analysis of the light curves available from the ASAS photometric catalog 4 database. Firstly, we considered whether the difference maybe caused by the selection of the ASAS photometric data points, which are identified with the letters A to D according to the quality of the data. Using only the high-quality data available (marked with A) the PDM analysis yields a period P = 1 : 96 days which is exactly the same value obtained from our light curves. Second, we considered whether the discrepancy may be caused by the di GLYPH<11> erent algorithms used to calculate the period. However, using GLYPH<24> 50 light curves obtained from the ASAS catalogue and performing a PDM analysis yields 100% agreement with the values reported by Pojmanski & Maciejewski (2004). Therefore we assume that the entry in Table 2 from Pojmanski &Maciejewski (2004) must be erroneous. separated symmetrically (0.5 in phase). In consequence, we estimated the parameters of the system by assuming a circular orbit and a synchronous rotation. The primary component fills up its Roche lobe at about 95% while the secondary at about 99%, favouring a semi-detached configuration with an orbital inclination i = 58 : 4 GLYPH<14> . We fixed the e GLYPH<11> ective temperature of the primary star T 1 = 34550 K according to the color-index B GLYPH<0> V = GLYPH<0> 0 : 32 obtained by van Houten (2001) 5 corresponding to the spectral type O8.5 V, reported originally by Boehm-Vitense (1981) and re-analyzed by Humphreys & McElroy (1984); this spectral designation is also consistent with recent investigations by Martins et al. (2005). The best fit to the light curve yields a mass ratio q = M 1 = M 2 = 2 : 8 with a temperature of the secondary component T 2 = 21500 K corresponding to a spectral type B2 V (BoehmVitense 1981; Lefever et al. 2010; Nieva & Przybilla 2012). As displayed in Fig. 2, the 3D view Roche geometry of the system ( GLYPH<30> = 0 : 63) shows a transitional evolutionary state of the system for which both stars are close to filling their Roche Lobes. Most likely the future mass transfer will create a new contact binary system. A summary of the relevant parameters and the best-fitting values are listed in Table 2.",
"pages": [
3,
4,
5
]
},
{
"title": "3.3. HD319702",
"content": "Located at a distance of 1.75 kpc (Russeil et al. 2010; Russeil et al. 2012), HD 319702 is a member of the cluster NGC 6334. This region is considered as one of the most active regions of highmass star formation in our Galaxy (Tapia & Persi 2009; Russeil et al. 2012). The area contains evolved optical but also embedded compact H ii regions. HD 319702 has been classified originally as a B1 Ib by Neckel (1978); later measurements converted the spectral type into O8 III(f) (Walborn 1982; Ma'ız-Apell'aniz et al. 2004; Pinheiro et al. 2010). So far there was no hint for an eclipsing orbit. As displayed in Fig. 4, the light curves constructed from 38 epochs show nearly identical amplitude variations with primary and secondary minimum eclipses at di GLYPH<11> erent depths ( GLYPH<1> Dp = 11%, GLYPH<1> Ds = 8%). This behaviour is characteristic for an eclipsing binary with di GLYPH<11> erent e GLYPH<11> ective temperatures; the primary minimum is due to the eclipse of the more luminous star by the less luminous companion. The eclipses are partial and symmet- ric with the same duration of 0.189 in phase. The primary and secondary minimum are separated symmetrically by 0.5 in phase suggesting a circular orbit. Our PDM analysis yields a period of P = 2 : 01 days. Again, we have assumed a zero eccentricity and synchronous rotation for which the model provides the best fit to the system. Based on the spectral type determination of the primary star we adopted a value of T 1 = 34000 K considering the observational Tef f calibration by Martins et al. (2005) (his Table 5). We computed a set of orbital solutions where the best-fitting model favours an orbital inclination of 67.5 GLYPH<14> with a mass ratio of q = M 1 = M 2 = 1 : 0. The system shows well-defined eclipses favouring a detached configuration, where both components fill up their Roche lobes at about 71%. The temperature of the secondary component is T 2 = 25200 K suggesting that this new system is most likely composed of an O8 III + a B0.5 V star if the calibration by Humphreys & McElroy (1984) is used for the secondary component. Considering the calibration reported by Boehm-Vitense (1981) and Harmanec (1988) the system would turn into O8 III + a B1 V. A summary of the relevant parameters and the bestfitting values are listed in Table 3.",
"pages": [
5,
6
]
},
{
"title": "4. Summary and conclusions",
"content": "We have presented optical photometric observations for three high-mass eclipsing binaries performed during a six months monitoring campaign. A detailed analysis and modeling of the light curves was carried out within the framework of the Roche geometry. We find that all objects show light curve variations that occur on time-scales of less than 3 days and that the systems are well described by circular orbits (zero or negligible eccentricity). The individual results are: The current study has demonstrated that our photometric survey has the capability to detect O-type eclipsing binaries along the galactic plane in the brightness range 10 < R ; I < 15; more EB candidates will be presented in the future. Follow-up spectroscopic RV studies of this sample are essential to determine the absolute parameters and to track the evolutionary state of individual systems. On the other hand, for the complete sample from the Galactic O-Star Catalogue ( V < 8) we are currently monitoring all SB2 candidates (Chini et al. 2012) to detect further O-type EBs among this sample and to obtain precise light curves (Barr Dom'ınguez et al., in prep.). From the few results available so far - both in the literature and from our current study- it seems that the important mass ratio parameter q GLYPH<24> 1. However, there might be an observational bias since O stars have very high luminosities which prevent fainter companions from being detected. So far there are only four known high-mass binaries where q > 2 with the exceptional maximum of q GLYPH<24> 5 : 8: HD37022 (O5), HD53975 (B7Iab), HD199579 (O6 V), and HD 165246 (O8 V) (see Mayer et al. 2013 and references therein). This strongly corroborates the view that high-mass binaries are generally created during the star formation process and are not a result of tidal capture. We expect that our study will increase the number of known O-type EBs substantially and that we can obtain a better census of the range of q = M 1 = M 2 in the high-mass regime. Likewise it will be interesting to see at which stellar primary mass q will significantly deviate from unity. For this reason we will extend our studies in the future also toward B-type binaries. Acknowledgements. This publication is supported as a project of the NordrheinWestfalische Akademie der Wissenschaften und der Kunste in the framework of the academy program by the Federal Republic of Germany and the state Nordrhein-Westfalen. The observations at Cerro Armazones benefitted from the continuous support of the Universidad Cat'olica del Norte and from the care of the guardians Hector Labra, Gerardo Pino, Roberto Munoz, and Francisco Arraya. This research has made use of the NASA / IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. We thank the anonymous referee for his contructive comments and careful review of the manuscript.",
"pages": [
6
]
},
{
"title": "References",
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"pages": [
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}
]
2013A&A...557A..38V
https://arxiv.org/pdf/1308.4505.pdf
<document>
<section_header_level_1><location><page_1><loc_13><loc_82><loc_89><loc_87></location>Spectropolarimetric observations of cool DQ white dwarfs (ResearchNote)</section_header_level_1>
<text><location><page_1><loc_31><loc_80><loc_70><loc_81></location>T. Vornanen 1 , S.V. Berdyugina 2 , 3 , and A. Berdyugin 4</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_76><loc_74><loc_78></location>1 Department of Physics and Astronomy, University of Turku, Vaisalantie 20, FI-21500 Piikkio, Finland e-mail: [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_63><loc_76></location>2 Kiepenheuer-Institut fur Sonnenphysik, Schoneckstr.6, D-79104 Freiburg, Germany</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_64><loc_74></location>3 NASA Astrobiology Institute, Institute for Astronomy, University of Hawaii, HI, USA</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_75><loc_73></location>4 Finnish Center for Astronomy with ESO, University of Turku, Vaisalantie 20, FI-21500 Piikkio, Finland</list_item>
</unordered_list>
<section_header_level_1><location><page_1><loc_47><loc_69><loc_55><loc_70></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_65><loc_91><loc_67></location>Aims. Following our recent discovery of a new magnetic DQ white dwarf (WD) with CH molecular features, we report the results for the rest of the DQ WDs from our survey.</text>
<text><location><page_1><loc_11><loc_64><loc_82><loc_65></location>Methods. We use high signal-to-noise spectropolarimetric data to search for magnetic fields in a sample of 11 objects.</text>
<text><location><page_1><loc_11><loc_61><loc_91><loc_64></location>Results. One object in our sample, WD1235 + 422, shows the signs of continuum circular polarization that is similar to some peculiar DQs with unidentified molecular absorption bands, but the low S / N and spectral resolution of these data make more observations necessary to reveal the true nature of this object.</text>
<text><location><page_1><loc_11><loc_59><loc_51><loc_60></location>Key words. magnetic fields - molecular processes - white dwarfs</text>
<section_header_level_1><location><page_1><loc_7><loc_54><loc_19><loc_56></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_31><loc_50><loc_53></location>White dwarfs that have carbon features in any part of the electromagnetic spectrum are classified as DQ white dwarfs (WDs). In these stars, carbon in either atomic or molecular form is the dominant and usually the only source of any spectral features. The carbon comes from convection induced dredge-up or the atmosphere is largely made up of carbon because of earlier stages of stellar evolution. The latter case is thought to be the origin of hot DQs (Dufour et al. 2008). Cooler members of the group get their carbon from dredge-up. In addition to the hot DQs, there are three other distinct groups of DQ WDs. Cool DQs show molecular absorption bands of C2 and in two cases CH. In peculiar DQs, unidentified molecular features are broader and deeper, and their spectra look very abnormal. Between the hot DQs that show atomic absorption lines of CII and the cool DQs, there are WDs that show absorption lines of CI. These could be called warm DQs to keep the same naming convention as the other groups.</text>
<text><location><page_1><loc_7><loc_13><loc_50><loc_31></location>Along with the mass of the star and chemical composition of its atmosphere, one important element of WD physics is magnetism. There have been extensive studies on the magnetic fields of hydrogen WDs (see Kulebi et al. 2009, for example), but the incidence of magnetism in carbon WDs is still unknown. There are currently six magnetic cool DQ WDs: LP790-29 (Liebert et al. 1978; Wickramasinghe & Bessell 1979; Bues 1999), LHS2229 (Schmidt et al. 1999), SDSS J1113 + 0146 (Schmidt et al. 2003), SDSS J1333 + 0016 (Schmidt et al. 2003), G99-37 (Angel & Landstreet 1974), and GJ841B (Vornanen et al. 2010, hereafter Paper I). However, four of these stars belong to the subclass of peculiar DQ WDs with broad, unidentified molecular bands, and only the last two are normal cool DQs.</text>
<text><location><page_1><loc_7><loc_10><loc_50><loc_12></location>As is often with negative results, there are very few reports on DQs that have been studied and found not to have polariza-</text>
<text><location><page_1><loc_52><loc_45><loc_95><loc_55></location>tion. Schmidt et al. (1999) mention three stars, LHS1126, G22568, and ESO 439-162, for which a search for circular polarization provided no results. However, the authors give upper limits of B = 3, 2, and 30 MG for the stars, respectively, which certainly do not exclude their magnetic nature. To understand magnetism, its origin, and evolution in WDs, it is important that we have information on non-magnetic WDs to compare their properties to the properties of their magnetic kin.</text>
<text><location><page_1><loc_52><loc_31><loc_95><loc_44></location>As an example of the importance of magnetic fields, we mention the subclass of hot DQs that has now 14 members. Five of them have been found to be magnetic, and another four might have a substantial magnetic field (Dufour et al. 2010). This gives an unusually high rate of magnetism (from 36 % to 64 %) for these WDs as compared to the average rate of 10-15 % for all WDs in the solar neighborhood (Liebert et al. 2003). Such a high fraction of magnetic objects in a class of stars is unusual. Coupled with the cool, carbon-rich atmosphere, this leads to questions about the role of magnetic fields in their evolution.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_29></location>In Paper I, we presented our results for GJ841B. In addition to G99-37, GJ841B is the second known DQ WD with circularly polarized spectral features of CH-molecules and the first one to apparently have polarized Swan bands of C2. Using the model of molecular polarization in strong magnetic fields by Berdyugina et al. (2007), and appliying it to the CH bands at 430nm and 390nm, we determined the field strength of 1.3 MG and the temperature of 6100 K for GJ841B. The discovery of this new magnetic WD came from a survey of cool DQs that we have carried out over the past four years. During this survey we have also observed ten other cool DQs that do not show circular polarization in optical wavelengths and thus can be considered as non-magnetic. We have also discovered circular polarization in WD1235 + 422, which is a clear indication of its magnetic nature.</text>
<section_header_level_1><location><page_2><loc_7><loc_92><loc_20><loc_93></location>2. Observations</section_header_level_1>
<text><location><page_2><loc_7><loc_79><loc_50><loc_91></location>In our survey of cool DQ WDs, we have observed thirteen DQ WDs using two di ff erent instruments at three di ff erent times: ALFOSC at the Nordic Optical Telescope (NOT) in February 2010, FORS at VLT / UT2 in November 2008, and FORS at VLT / UT1 in August 2009. Details of the observations are given in Table 1. In both VLT observing runs, we used Grism 600B + 12, which gives wavelength coverage from 330 nm to 621 nmwith a spectral resolution of R = 780. This wavelength interval includes several important molecular features of C2 and CH.</text>
<text><location><page_2><loc_7><loc_64><loc_50><loc_78></location>Our observations at the NOT were done with low resolution grism #10, which covers the wavelength region 330-1055 nm. We used this grism to get a spectral resolution as low as possible because our targets were faint for a 2.5 m telescope. The adopted strategy of a low resolution grism and a wide slit (1.8 '' ) resulted in a spectral resolution of only R = 70. This low resolution gave us a chance to observe our faint targets with spectropolarimetry, which normally requires a high S / N ratio as a technique. Our goal was to find polarization in molecular bands that are dozens of nanometers wide, so a low resolution was adequate for our purposes.</text>
<text><location><page_2><loc_7><loc_47><loc_50><loc_64></location>In the data reduction process, we subtracted the bias level from all images and also removed cosmic ray contamination. We skipped the flatfielding, because it did not improve the quality of data and sometimes even made it worse. Background was subtracted separately for the two beams, and the spectra were extracted. Wavelength calibration was done by using just one arclamp spectrum and not by using lamp spectra in di ff erent retarder plate positions. Finally, a dispersion correction was applied using the number of pixels in the dispersion direction of the raw image as the number of wavelength points. Spectra were normalized to the continuum level, because the model also produces normalized spectra. The intensity spectra of our targets are shown in Figs. 1 and 2.</text>
<text><location><page_2><loc_7><loc_32><loc_50><loc_47></location>In our survey, we have decided to concentrate on circular polarization (Stokes V ). From previous studies on G99-37 (Berdyugina et al. 2007), we expect a larger signal in circular than in linear polarization. Circular polarization observations require fewer measurements and calibrations. This allows us to dedicate more time for actual scientific exposures and reduce overheads. In observations made with VLT, our goal was to achieve a polarization accuracy of σ P = ± 0 . 2% (S / N ∼ 700). In the case of NOT observations, we could not get such a high accuracy, but nevertheless managed to attain approximately S / N = 300 ( σ P = ± 0 . 5%). The polarization spectra are shown in Fig. 3.</text>
<text><location><page_2><loc_7><loc_18><loc_50><loc_32></location>Additional observations of one of our targets, WD1235 + 422, were taken in service mode with the NOT on May 21st, 2011 and again on March 20th, 2013. The S / N of the 2011 measurement was better than in our 2010 observations (see Figures 2 and 4) due to the doubled exposure time with the 2013 measurement almost doubling the exposure time again. The resulting average spectrum is similar in all observing runs, but the poor spectral resolution does not allow us to make any conclusions about the magnetic properties, like field strength or geometry, of WD1235 + 422, apart from the conclusion that the star is indeed magnetic.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_17></location>The intensity spectra in Fig. 1 are normalized to continuum, but the absorption bands in WD1235 + 422 are overlapping, so there is no continuum to fit between 430 nm and 630 nm. For this reason we have flux calibrated the spectra and then normalized them to the value at 639.4 nm. In this way, some comparison to possible future observations and modelling can be done.</text>
<figure>
<location><page_2><loc_52><loc_52><loc_92><loc_92></location>
<caption>Fig. 1. Continuum normalized intensity spectra of the observed stars. Spectrum of GJ151 is at its actual value and the rest are shifted in intervals of 0.5. Horizontal lines denote the continuum level of each spectrum. See Fig. 2 for WD1235 + 422.</caption>
</figure>
<text><location><page_2><loc_52><loc_36><loc_95><loc_42></location>We note that the little emission peak at 410 nm in the objects observed with FORS1 (the first four in Figures 1 and 3) is not intrinsic to the objects. It is a spurious reflection signal in the optics, since it is present in the raw images of every object as a bright spot very close to the spectra.</text>
<section_header_level_1><location><page_2><loc_52><loc_33><loc_60><loc_34></location>3. Results</section_header_level_1>
<text><location><page_2><loc_52><loc_16><loc_95><loc_32></location>The intensity spectra of the objects in Table 1 are shown in Figure 1 and Stokes V / I in Figure 3. Our sample of DQ WDs shows a large variation in the depth of C2 features from 3 % to 30 % below the continuum level. The shape of the absorption features can be divided into two distinct categories. For example, see the ∆ v = 0 Swan band of GJ1037 at λ = 510 nm and compare it with the same band of GJ3306, where it is rounded and shows no internal structure. At high temperatures ( T ≥ 7000K), the higher energy vibrational bands with v ≥ 3 are visible as the individual dips within the Swan bands. We would like to stress that this di ff erence in appearance is real. All stars observed with VLT have a spectral resolution of about 0.7 nm.</text>
<text><location><page_2><loc_52><loc_10><loc_95><loc_16></location>For the objects observed with the NOT, the spectral resolution ranges from 5 nm to 15 nm across the observed wavelength region, which is too poor to reveal these features, but it is worth to note that one of these objects, GJ1117 (WD0856 + 331), shows lines of neutral carbon. The lines look very broad, but this is just</text>
<table>
<location><page_3><loc_12><loc_74><loc_89><loc_91></location>
<caption>Table 1. Observing log for our survey of cool DQ white dwarfs.</caption>
</table>
<figure>
<location><page_3><loc_7><loc_42><loc_47><loc_70></location>
<caption>Fig. 2. The spectra of WD1235 + 422 in three epochs are normalized to the flux value at 639.4 nm, and the horizontal lines denote this value. The bottom two spectra are shifted vertically.</caption>
</figure>
<text><location><page_3><loc_7><loc_28><loc_50><loc_34></location>an e ff ect of the low resolution (See Figure 7 from Dufour et al. 2005, for a higher resolution spectrum). These lines disappear at temperatures below 9000 K, so they provide an immediate temperature estimate for this star. The simultaneous existence of C2 gives an upper limit of 11000 K.</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_28></location>The Stokes V spectra of the survey targets, apart from GJ841B, show no signatures of polarization with one exception: WD1235 + 422 (See Figure 4) shows a large circular polarization signal of a few percent across the observed wavelength region in all sets of observations taken with the NOT over four years. It also has the strongest absorption bands of C2 among all stars presented in this paper. In addition, its molecular features are slightly shifted from the normal positions of Swan bands. This would make WD1235 + 422 related to the class of peculiar DQ WDs (Schmidt et al. 2003; Hall & Maxwell 2008). The Stokes V / I spectrum does not show any significant variations in the Swan bands at this resolution except for a slight decrease in the degree of polarization. Similar behaviour is shown by LP 790-29, one of the magnetic peculiar DQs (Schmidt et al.</text>
<figure>
<location><page_3><loc_52><loc_31><loc_92><loc_70></location>
<caption>Fig. 3. Stokes V / I spectra of the observed stars (in percents). Spectrum of GJ151 is at its real value, and the rest of the spectra are shifted in intervals of 4 %. See Fig. 4 for WD1235 + 422.</caption>
</figure>
<text><location><page_3><loc_52><loc_19><loc_95><loc_21></location>1999). Thus, we conclude that the 2-3% circular polarization in WD1235 + 422 is due to continuum polarization.</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_19></location>The white dwarf WD1235 + 422 seems to be an interesting link between normal and peculiar DQ WDs and thus deserves a more careful examination. Interestingly, the intensity spectrum of WD1235 + 422 looks similar to the simulated spectrum of a 10000 K purely carbon atmosphere DQ WD, as seen in Fig. 6 of Dufour et al. (2008). On the other hand, Koester & Knist (2006) modelled it as peculiar DQ WD with a temperature of 5846</text>
<figure>
<location><page_4><loc_7><loc_64><loc_48><loc_92></location>
<caption>Fig. 4. Stokes V / I spectra of WD125 + 422 from 2010, 2011, and 2013. Zero levels are marked with horizontal lines and the spectra have been displaced for clarity. Intensity spectrum in the bottom panel is for the comparison of feature wavelengths and clearly indicates that the polarization is of continuum origin.</caption>
</figure>
<text><location><page_4><loc_7><loc_46><loc_50><loc_54></location>K based on photometry. There are at least two other DQ WDs with similar spectra: GSC2U J131147.2 + 292348 (Carollo et al. 2003) and SDSS J090208.40 + 20104 (Limoges et al. 2013). We think that some attention needs to be given to these stars in the future because they might give new insight into the evolution of hot DQs.</text>
<text><location><page_4><loc_7><loc_31><loc_50><loc_46></location>We have tried to model the observed spectra of these WDs using the method by Berdyugina et al. (2007). This model is based on the Unno-Rachkovsky and Milne-Eddington approximations and is capable of inferring the temperature and magnetic field strength in a single-layer atmosphere. Using this model, we have encountered a problem to fit the C2 band strengths simultaneously with a single set of the parameters. We assume that this di ffi culty is related to the single-layer approximation and can be overcome with more realistic, stratified atmospheres of WDs, such as that by Dufour et al. (2005). We consider these atmospheres and address the modelling problems in a separate, forthcoming paper.</text>
<section_header_level_1><location><page_4><loc_7><loc_27><loc_20><loc_28></location>4. Conclusions</section_header_level_1>
<text><location><page_4><loc_7><loc_21><loc_50><loc_26></location>We have presented low resolution circular spectropolarimetric observations of 11 DQ WDs. Among these stars we found a circular polarization signal in only one, WD1235 + 422, with the addition of the previously reported GJ841B.</text>
<text><location><page_4><loc_7><loc_10><loc_50><loc_21></location>Although we did not find any other magnetic WDs in our sample apart from GJ841B and WD1235 + 422, the data are still valuable for the study of DQ WDs. At the moment, there are about 182 confirmed cool DQ WDs, and by including WD1235 + 422, only seven of them have been found to be magnetic. (There are also fourteen hot DQs of which at least five are magnetic.) This amounts to 4 % of the whole population, and the value is exactly what has been found for DA white dwarfs in the Sloan Digital Sky Survey (SDSS) (Kepler et al. 2013). The study</text>
<text><location><page_4><loc_52><loc_85><loc_95><loc_93></location>of Kepler et al. (2013) only concerns magnetic field strengths of over 2 MG, and these are also the values found for cool DQs so far. The authors note that there should be about as many low field WDs than these higher field dwarfs, but they are very di ffi cult to find. Landstreet et al. (2012) report results on a field of 10 kG on a DA white dwarf.</text>
<text><location><page_4><loc_52><loc_72><loc_95><loc_85></location>Magnetism seems to be a good way to study the connections between the di ff erent subclasses of DQ WDs. However, no one to our knowledge has made an extensive study of the magnetism of those DQ WDs that have absorption lines of neutral carbon. These might be called warm DQs, because they are between the hot DQs (CII lines) and cool DQs (molecular absorption) in temperature. One such object has been found recently (Williams et al. 2013). However, a lot still remains to be done, but we are hopefully moving in the right direction in solving the mystery of carbon atmosphere white dwarfs.</text>
<text><location><page_4><loc_52><loc_69><loc_95><loc_71></location>Acknowledgements. This work was supported by the Leibniz Association grant SAW-2011-KIS-7.</text>
<section_header_level_1><location><page_4><loc_52><loc_65><loc_61><loc_67></location>References</section_header_level_1>
<text><location><page_4><loc_52><loc_64><loc_81><loc_65></location>Angel, J. R. P. & Landstreet, J. D. 1974, ApJ, 191, 457</text>
<text><location><page_4><loc_52><loc_62><loc_95><loc_64></location>Berdyugina, S. V., Berdyugin, A. V., & Piirola, V. 2007, Physical Review Letters, 99, 091101</text>
<text><location><page_4><loc_52><loc_58><loc_95><loc_61></location>Bues, I. 1999, in Astronomical Society of the Pacific Conference Series, Vol. 169, 11th European Workshop on White Dwarfs, ed. S.-E. Solheim & E. G. Meistas, 240-+</text>
<text><location><page_4><loc_52><loc_56><loc_95><loc_58></location>Carollo, D., Koester, D., Spagna, A., Lattanzi, M. G., & Hodgkin, S. T. 2003, A&A, 400, L13</text>
<text><location><page_4><loc_52><loc_55><loc_84><loc_56></location>Dufour, P., Bergeron, P., & Fontaine, G. 2005, ApJ, 627, 404</text>
<text><location><page_4><loc_52><loc_52><loc_95><loc_55></location>Dufour, P., Fontaine, G., Bergeron, P., et al. 2010, in American Institute of Physics Conference Series, Vol. 1273, American Institute of Physics Conference Series, ed. K. Werner & T. Rauch, 64-69</text>
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<text><location><page_4><loc_52><loc_49><loc_79><loc_50></location>Hall, P. B. & Maxwell, A. J. 2008, ApJ, 678, 1292</text>
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<text><location><page_4><loc_52><loc_41><loc_95><loc_44></location>Landstreet, J. D., Bagnulo, S., Valyavin, G. G., et al. 2012, A&A, 545, A30 Liebert, J., Angel, J. R. P., Stockman, H. S., & Beaver, E. A. 1978, ApJ, 225, 181</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Aims. Following our recent discovery of a new magnetic DQ white dwarf (WD) with CH molecular features, we report the results for the rest of the DQ WDs from our survey. Methods. We use high signal-to-noise spectropolarimetric data to search for magnetic fields in a sample of 11 objects. Results. One object in our sample, WD1235 + 422, shows the signs of continuum circular polarization that is similar to some peculiar DQs with unidentified molecular absorption bands, but the low S / N and spectral resolution of these data make more observations necessary to reveal the true nature of this object. Key words. magnetic fields - molecular processes - white dwarfs",
"pages": [
1
]
},
{
"title": "Spectropolarimetric observations of cool DQ white dwarfs (ResearchNote)",
"content": "T. Vornanen 1 , S.V. Berdyugina 2 , 3 , and A. Berdyugin 4",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "White dwarfs that have carbon features in any part of the electromagnetic spectrum are classified as DQ white dwarfs (WDs). In these stars, carbon in either atomic or molecular form is the dominant and usually the only source of any spectral features. The carbon comes from convection induced dredge-up or the atmosphere is largely made up of carbon because of earlier stages of stellar evolution. The latter case is thought to be the origin of hot DQs (Dufour et al. 2008). Cooler members of the group get their carbon from dredge-up. In addition to the hot DQs, there are three other distinct groups of DQ WDs. Cool DQs show molecular absorption bands of C2 and in two cases CH. In peculiar DQs, unidentified molecular features are broader and deeper, and their spectra look very abnormal. Between the hot DQs that show atomic absorption lines of CII and the cool DQs, there are WDs that show absorption lines of CI. These could be called warm DQs to keep the same naming convention as the other groups. Along with the mass of the star and chemical composition of its atmosphere, one important element of WD physics is magnetism. There have been extensive studies on the magnetic fields of hydrogen WDs (see Kulebi et al. 2009, for example), but the incidence of magnetism in carbon WDs is still unknown. There are currently six magnetic cool DQ WDs: LP790-29 (Liebert et al. 1978; Wickramasinghe & Bessell 1979; Bues 1999), LHS2229 (Schmidt et al. 1999), SDSS J1113 + 0146 (Schmidt et al. 2003), SDSS J1333 + 0016 (Schmidt et al. 2003), G99-37 (Angel & Landstreet 1974), and GJ841B (Vornanen et al. 2010, hereafter Paper I). However, four of these stars belong to the subclass of peculiar DQ WDs with broad, unidentified molecular bands, and only the last two are normal cool DQs. As is often with negative results, there are very few reports on DQs that have been studied and found not to have polariza- tion. Schmidt et al. (1999) mention three stars, LHS1126, G22568, and ESO 439-162, for which a search for circular polarization provided no results. However, the authors give upper limits of B = 3, 2, and 30 MG for the stars, respectively, which certainly do not exclude their magnetic nature. To understand magnetism, its origin, and evolution in WDs, it is important that we have information on non-magnetic WDs to compare their properties to the properties of their magnetic kin. As an example of the importance of magnetic fields, we mention the subclass of hot DQs that has now 14 members. Five of them have been found to be magnetic, and another four might have a substantial magnetic field (Dufour et al. 2010). This gives an unusually high rate of magnetism (from 36 % to 64 %) for these WDs as compared to the average rate of 10-15 % for all WDs in the solar neighborhood (Liebert et al. 2003). Such a high fraction of magnetic objects in a class of stars is unusual. Coupled with the cool, carbon-rich atmosphere, this leads to questions about the role of magnetic fields in their evolution. In Paper I, we presented our results for GJ841B. In addition to G99-37, GJ841B is the second known DQ WD with circularly polarized spectral features of CH-molecules and the first one to apparently have polarized Swan bands of C2. Using the model of molecular polarization in strong magnetic fields by Berdyugina et al. (2007), and appliying it to the CH bands at 430nm and 390nm, we determined the field strength of 1.3 MG and the temperature of 6100 K for GJ841B. The discovery of this new magnetic WD came from a survey of cool DQs that we have carried out over the past four years. During this survey we have also observed ten other cool DQs that do not show circular polarization in optical wavelengths and thus can be considered as non-magnetic. We have also discovered circular polarization in WD1235 + 422, which is a clear indication of its magnetic nature.",
"pages": [
1
]
},
{
"title": "2. Observations",
"content": "In our survey of cool DQ WDs, we have observed thirteen DQ WDs using two di ff erent instruments at three di ff erent times: ALFOSC at the Nordic Optical Telescope (NOT) in February 2010, FORS at VLT / UT2 in November 2008, and FORS at VLT / UT1 in August 2009. Details of the observations are given in Table 1. In both VLT observing runs, we used Grism 600B + 12, which gives wavelength coverage from 330 nm to 621 nmwith a spectral resolution of R = 780. This wavelength interval includes several important molecular features of C2 and CH. Our observations at the NOT were done with low resolution grism #10, which covers the wavelength region 330-1055 nm. We used this grism to get a spectral resolution as low as possible because our targets were faint for a 2.5 m telescope. The adopted strategy of a low resolution grism and a wide slit (1.8 '' ) resulted in a spectral resolution of only R = 70. This low resolution gave us a chance to observe our faint targets with spectropolarimetry, which normally requires a high S / N ratio as a technique. Our goal was to find polarization in molecular bands that are dozens of nanometers wide, so a low resolution was adequate for our purposes. In the data reduction process, we subtracted the bias level from all images and also removed cosmic ray contamination. We skipped the flatfielding, because it did not improve the quality of data and sometimes even made it worse. Background was subtracted separately for the two beams, and the spectra were extracted. Wavelength calibration was done by using just one arclamp spectrum and not by using lamp spectra in di ff erent retarder plate positions. Finally, a dispersion correction was applied using the number of pixels in the dispersion direction of the raw image as the number of wavelength points. Spectra were normalized to the continuum level, because the model also produces normalized spectra. The intensity spectra of our targets are shown in Figs. 1 and 2. In our survey, we have decided to concentrate on circular polarization (Stokes V ). From previous studies on G99-37 (Berdyugina et al. 2007), we expect a larger signal in circular than in linear polarization. Circular polarization observations require fewer measurements and calibrations. This allows us to dedicate more time for actual scientific exposures and reduce overheads. In observations made with VLT, our goal was to achieve a polarization accuracy of σ P = ± 0 . 2% (S / N ∼ 700). In the case of NOT observations, we could not get such a high accuracy, but nevertheless managed to attain approximately S / N = 300 ( σ P = ± 0 . 5%). The polarization spectra are shown in Fig. 3. Additional observations of one of our targets, WD1235 + 422, were taken in service mode with the NOT on May 21st, 2011 and again on March 20th, 2013. The S / N of the 2011 measurement was better than in our 2010 observations (see Figures 2 and 4) due to the doubled exposure time with the 2013 measurement almost doubling the exposure time again. The resulting average spectrum is similar in all observing runs, but the poor spectral resolution does not allow us to make any conclusions about the magnetic properties, like field strength or geometry, of WD1235 + 422, apart from the conclusion that the star is indeed magnetic. The intensity spectra in Fig. 1 are normalized to continuum, but the absorption bands in WD1235 + 422 are overlapping, so there is no continuum to fit between 430 nm and 630 nm. For this reason we have flux calibrated the spectra and then normalized them to the value at 639.4 nm. In this way, some comparison to possible future observations and modelling can be done. We note that the little emission peak at 410 nm in the objects observed with FORS1 (the first four in Figures 1 and 3) is not intrinsic to the objects. It is a spurious reflection signal in the optics, since it is present in the raw images of every object as a bright spot very close to the spectra.",
"pages": [
2
]
},
{
"title": "3. Results",
"content": "The intensity spectra of the objects in Table 1 are shown in Figure 1 and Stokes V / I in Figure 3. Our sample of DQ WDs shows a large variation in the depth of C2 features from 3 % to 30 % below the continuum level. The shape of the absorption features can be divided into two distinct categories. For example, see the ∆ v = 0 Swan band of GJ1037 at λ = 510 nm and compare it with the same band of GJ3306, where it is rounded and shows no internal structure. At high temperatures ( T ≥ 7000K), the higher energy vibrational bands with v ≥ 3 are visible as the individual dips within the Swan bands. We would like to stress that this di ff erence in appearance is real. All stars observed with VLT have a spectral resolution of about 0.7 nm. For the objects observed with the NOT, the spectral resolution ranges from 5 nm to 15 nm across the observed wavelength region, which is too poor to reveal these features, but it is worth to note that one of these objects, GJ1117 (WD0856 + 331), shows lines of neutral carbon. The lines look very broad, but this is just an e ff ect of the low resolution (See Figure 7 from Dufour et al. 2005, for a higher resolution spectrum). These lines disappear at temperatures below 9000 K, so they provide an immediate temperature estimate for this star. The simultaneous existence of C2 gives an upper limit of 11000 K. The Stokes V spectra of the survey targets, apart from GJ841B, show no signatures of polarization with one exception: WD1235 + 422 (See Figure 4) shows a large circular polarization signal of a few percent across the observed wavelength region in all sets of observations taken with the NOT over four years. It also has the strongest absorption bands of C2 among all stars presented in this paper. In addition, its molecular features are slightly shifted from the normal positions of Swan bands. This would make WD1235 + 422 related to the class of peculiar DQ WDs (Schmidt et al. 2003; Hall & Maxwell 2008). The Stokes V / I spectrum does not show any significant variations in the Swan bands at this resolution except for a slight decrease in the degree of polarization. Similar behaviour is shown by LP 790-29, one of the magnetic peculiar DQs (Schmidt et al. 1999). Thus, we conclude that the 2-3% circular polarization in WD1235 + 422 is due to continuum polarization. The white dwarf WD1235 + 422 seems to be an interesting link between normal and peculiar DQ WDs and thus deserves a more careful examination. Interestingly, the intensity spectrum of WD1235 + 422 looks similar to the simulated spectrum of a 10000 K purely carbon atmosphere DQ WD, as seen in Fig. 6 of Dufour et al. (2008). On the other hand, Koester & Knist (2006) modelled it as peculiar DQ WD with a temperature of 5846 K based on photometry. There are at least two other DQ WDs with similar spectra: GSC2U J131147.2 + 292348 (Carollo et al. 2003) and SDSS J090208.40 + 20104 (Limoges et al. 2013). We think that some attention needs to be given to these stars in the future because they might give new insight into the evolution of hot DQs. We have tried to model the observed spectra of these WDs using the method by Berdyugina et al. (2007). This model is based on the Unno-Rachkovsky and Milne-Eddington approximations and is capable of inferring the temperature and magnetic field strength in a single-layer atmosphere. Using this model, we have encountered a problem to fit the C2 band strengths simultaneously with a single set of the parameters. We assume that this di ffi culty is related to the single-layer approximation and can be overcome with more realistic, stratified atmospheres of WDs, such as that by Dufour et al. (2005). We consider these atmospheres and address the modelling problems in a separate, forthcoming paper.",
"pages": [
2,
3,
4
]
},
{
"title": "4. Conclusions",
"content": "We have presented low resolution circular spectropolarimetric observations of 11 DQ WDs. Among these stars we found a circular polarization signal in only one, WD1235 + 422, with the addition of the previously reported GJ841B. Although we did not find any other magnetic WDs in our sample apart from GJ841B and WD1235 + 422, the data are still valuable for the study of DQ WDs. At the moment, there are about 182 confirmed cool DQ WDs, and by including WD1235 + 422, only seven of them have been found to be magnetic. (There are also fourteen hot DQs of which at least five are magnetic.) This amounts to 4 % of the whole population, and the value is exactly what has been found for DA white dwarfs in the Sloan Digital Sky Survey (SDSS) (Kepler et al. 2013). The study of Kepler et al. (2013) only concerns magnetic field strengths of over 2 MG, and these are also the values found for cool DQs so far. The authors note that there should be about as many low field WDs than these higher field dwarfs, but they are very di ffi cult to find. Landstreet et al. (2012) report results on a field of 10 kG on a DA white dwarf. Magnetism seems to be a good way to study the connections between the di ff erent subclasses of DQ WDs. However, no one to our knowledge has made an extensive study of the magnetism of those DQ WDs that have absorption lines of neutral carbon. These might be called warm DQs, because they are between the hot DQs (CII lines) and cool DQs (molecular absorption) in temperature. One such object has been found recently (Williams et al. 2013). However, a lot still remains to be done, but we are hopefully moving in the right direction in solving the mystery of carbon atmosphere white dwarfs. Acknowledgements. This work was supported by the Leibniz Association grant SAW-2011-KIS-7.",
"pages": [
4
]
},
{
"title": "References",
"content": "Angel, J. R. P. & Landstreet, J. D. 1974, ApJ, 191, 457 Berdyugina, S. V., Berdyugin, A. V., & Piirola, V. 2007, Physical Review Letters, 99, 091101 Bues, I. 1999, in Astronomical Society of the Pacific Conference Series, Vol. 169, 11th European Workshop on White Dwarfs, ed. S.-E. Solheim & E. G. Meistas, 240-+ Carollo, D., Koester, D., Spagna, A., Lattanzi, M. G., & Hodgkin, S. T. 2003, A&A, 400, L13 Dufour, P., Bergeron, P., & Fontaine, G. 2005, ApJ, 627, 404 Dufour, P., Fontaine, G., Bergeron, P., et al. 2010, in American Institute of Physics Conference Series, Vol. 1273, American Institute of Physics Conference Series, ed. K. Werner & T. Rauch, 64-69 Dufour, P., Fontaine, G., Liebert, J., Schmidt, G. D., & Behara, N. 2008, ApJ, 683, 978 Hall, P. B. & Maxwell, A. J. 2008, ApJ, 678, 1292 Koester, D. & Knist, S. 2006, A&A, 454, 951 Kulebi, B., Jordan, S., Euchner, F., Gansicke, B. T., & Hirsch, H. 2009, A&A, 506, 1341 Landstreet, J. D., Bagnulo, S., Valyavin, G. G., et al. 2012, A&A, 545, A30 Liebert, J., Angel, J. R. P., Stockman, H. S., & Beaver, E. A. 1978, ApJ, 225, 181 Liebert, J., Bergeron, P., & Holberg, J. B. 2003, AJ, 125, 348 Schmidt, G. D., Harris, H. C., Liebert, J., et al. 2003, ApJ, 595, 1101 Schmidt, G. D., Liebert, J., Harris, H. C., Dahn, C. C., & Leggett, S. K. 1999, ApJ, 512, 916 Vornanen, T., Berdyugina, S. V., Berdyugin, A. V., & Piirola, V. 2010, ApJ, 720, L52 Wickramasinghe, D. T. & Bessell, M. S. 1979, MNRAS, 188, 841 Williams, K. A., Winget, D. E., Montgomery, M. H., et al. 2013, ApJ, 769, 123",
"pages": [
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]
}
]
2013A&A...557A..45C
https://arxiv.org/pdf/1308.2053.pdf
<document>
<section_header_level_1><location><page_1><loc_16><loc_82><loc_86><loc_87></location>NIR and optical observations of the failed outbursts of black hole binary XTE J1550 -564 /star</section_header_level_1>
<text><location><page_1><loc_40><loc_80><loc_62><loc_81></location>P.A. Curran 1 , 2 and S. Chaty 2 , 3</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_77><loc_83><loc_78></location>1 International Centre for Radio Astronomy Research, Curtin University, GPO Box U1987, Perth, WA 6845, Australia</list_item>
<list_item><location><page_1><loc_11><loc_76><loc_91><loc_77></location>2 AIM (UMR-E 9005 CEA / DSM-CNRS-Universit'e Paris Diderot), Irfu / Service d'Astrophysique, Centre de Saclay, FR-91191 Gif-</list_item>
</unordered_list>
<text><location><page_1><loc_12><loc_75><loc_28><loc_76></location>sur-Yvette Cedex, France</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_73><loc_62><loc_74></location>3 Institut Universitaire de France, 103, boulevard Saint-Michel, 75005 Paris, France</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_71><loc_39><loc_72></location>Received 9 May 2013 / Accepted 17 July 2013</text>
<section_header_level_1><location><page_1><loc_47><loc_69><loc_55><loc_70></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_63><loc_91><loc_67></location>Context. A number of low mass X-ray binaries (LMXBs) undergo 'failed outbursts' in which, instead of evolving through the canonical states, they remain in a hard state throughout the outburst. While the sources of X-ray and radio emission in the hard state are relatively well understood, the origin of the near infrared (NIR) and optical emission is more complex though it likely stems from an amalgam of di ff erent emission processes, occurring as it does, at the intersecting wavelengths of those processes.</text>
<text><location><page_1><loc_11><loc_61><loc_91><loc_63></location>Aims. We aim to identify the NIR / optical emission region(s) during a number of failed outbursts of one such low mass X-ray binary and black hole candidate, XTE J1550 -564, in order to confirm or refute their classification as hard-state, failed outbursts.</text>
<text><location><page_1><loc_11><loc_57><loc_91><loc_60></location>Methods. We present unique NIR / optical images and spectra, obtained with the ESO-New Technology Telescope, during the failed outbursts of 2001 and 2000. We compare the NIR / optical photometric, timing, and spectral properties with those expected for the di ff erent emission mechanisms in the various LMXB states.</text>
<text><location><page_1><loc_11><loc_53><loc_91><loc_57></location>Results. The NIR / optical data are consistent with having come from reprocessing of X-rays in the accretion disk, with no evidence of direct thermal emission from the disk itself. However, the observed variability in high-cadence NIR light curves suggest that the radio jet extends and contributes to the NIR wavelengths.</text>
<text><location><page_1><loc_11><loc_51><loc_91><loc_53></location>Conclusions. We find that these failed outbursts did not transition to an intermediate state but remained in a true, hard state where there was no sign of jet quenching or deviation from the observed hard state correlations.</text>
<text><location><page_1><loc_11><loc_49><loc_63><loc_50></location>Key words. X-rays: binaries - infrared: stars - X-rays: individuals: XTE J1550 - 564</text>
<section_header_level_1><location><page_1><loc_7><loc_45><loc_19><loc_46></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_25><loc_50><loc_44></location>For the majority of their lifetimes, transient low mass X-ray binaries (LMXBs) are in a state of quiescence with faint or nondetected X-ray emission. In quiescence, near infrared (NIR) and optical emission, if detected, is dominated by the main-sequence companion star (with possibly significant contribution from the cold accretion disk). During outburst - on time scales of weeks, months or even longer - there is a dramatic increase in the Xray, NIR / optical, and radio flux, which is powered by an increased level of accretion onto the central, compact object (black hole or neutron star). Many of these sources are observed to undergo multiple, irregular outbursts (e.g., XTE J1550 -564 has displayed 5 outburst events in less than a decade) while others may remain in quiescence for decades after their initial discovery (e.g., V2107 Oph was detected in outburst in 1977 but has yet to repeat).</text>
<text><location><page_1><loc_7><loc_14><loc_50><loc_24></location>Black hole LMXB outbursts are usually divided into a number of states , based mainly on observable X-ray spectral and timing characteristics. The sources are initially observed in a, generally low intensity, hard state with spectra dominated by powerlaw emission. They then transition, via an intermediate state, to a soft or thermal-dominant state (so called because the spectrum is dominated by a thermal component). X-ray flux peaks in this state before decreasing and evolving, via a late hard state, back</text>
<text><location><page_1><loc_52><loc_27><loc_95><loc_46></location>into a quiescent state. For a fuller description of the various possible states and the associated X-ray timing properties, etc., see McClintock & Remillard 2006. While the majority of outbursts from LMXBs follow this standard evolution of X-ray defined states, a number of sources are observed to return to quiescence without displaying a soft state (e.g., 9 sources in Brocksopp et al. 2004 and references therein) and another four have been observed to proceed to an intermediate state before returning to the hard state and quiescence, without reaching the soft state (Capitanio et al., 2009; Ferrigno et al., 2012; Soleri et al., 2013; Wijnands & Miller, 2002). Despite being referred to as 'failed outbursts' (or 'Soft X-ray transient' outbursts which are not soft ; Brocksopp et al. 2004) these outbursts can in fact be quite luminous (e.g., V404 Cyg; Tanaka & Lewin 1995), though most are under-luminous.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_26></location>While the origin of X-ray emission in the di ff erent states is relatively well understood (e.g., McClintock & Remillard 2006), that of the NIR, optical, and ultraviolet (UV) is more complex as the optical wavelengths are at the intersection of a number of di ff erent emission mechanisms (for reviews of optical properties of LMXBs see e.g., van Paradijs & McClintock 1995; Charles & Coe 2006). Both intrinsic, thermal emission from the hot, outer accretion disk (e.g., Shakura & Sunyaev 1973; Frank et al. 2002) as well as reprocessing of X-rays in the same region of the disk (e.g., Cunningham 1976; van Paradijs & McClintock 1994) may contribute significant levels of flux at UV, optical, and NIR wavelengths. Recently, evidence has been mounting that the relativistic jet, usually detected</text>
<figure>
<location><page_2><loc_11><loc_65><loc_94><loc_93></location>
<caption>Fig. 1. The one-day averaged RXTE / ASM light curve for the period in question (count rate axes cut o ff at 50 counts / second for clarity but peaked at ≈ 490 counts / second during 1998 outburst). The epochs of our observations are marked with crosses on the zoomed inlays for the failed outbursts of 2001 and 2002.</caption>
</figure>
<text><location><page_2><loc_7><loc_51><loc_50><loc_58></location>in radio, also produces a significant contribution to the NIR - and possibly optical - flux, at least in the hard state (e.g., Jain et al. 2001a; Corbel & Fender 2002; Russell et al. 2006; Chaty et al. 2011), and it is possible that the power law component of the Xray emission extends to, and contributes at optical wavelengths.</text>
<text><location><page_2><loc_7><loc_25><loc_50><loc_51></location>XTEJ1550 -564 has undergone a number of weak, failed outbursts (in 2001 (Tomsick et al., 2001); 2002 (Belloni et al., 2002); and 2003 (Sturner & Shrader, 2005; Aref'ev et al., 2004)) as well as a number of complete (soft state) outbursts in 1998 / 99 (e.g., Sobczak et al. 2000) and 2000 (e.g., Jain et al. 2001a; see also figure 1). Even if these late time outbursts are considered as rebrightenings or reflarings of the original outburst, this source demonstrates conclusively that failed outbursts are not a separate class of object but are likely caused by differences in the accretion flow onto the black hole or by di ff erences in the systems' e ffi ciency in converting the accreted matter into observable flux. In this paper we present the only significant NIR / optical observations during the failed outbursts of 2001 and 2002, obtained by the ESO NTT (Table 1), and comprising of all the available unpublished, archived ESO data of the source. In section 2 we introduce the observations and reduction methods, while in section 3 we present the results of our photometric, timing and spectral analyses of the data. We discuss the interpretation of our findings in section 4 and summarise in section 5.</text>
<section_header_level_1><location><page_2><loc_7><loc_22><loc_31><loc_23></location>2. Observations & Reduction</section_header_level_1>
<section_header_level_1><location><page_2><loc_7><loc_20><loc_19><loc_21></location>2.1. Photometry</section_header_level_1>
<text><location><page_2><loc_7><loc_10><loc_50><loc_19></location>During the outbursts of 2001 and 2002 optical ( V , R , I ) data were obtained with the ESO Multi-Mode Instrument (EMMI; Dekker et al. 1986) and the Superb-Seeing Imager (SuSI2) on the 3 . 58m ESO - New Technology Telescope (NTT), as well as with the FOcal Reducer and low dispersion Spectrograph (FORS1) on the 8 . 2m UNIT 3 of the Very Large Telescope (VLT-UT3) (Table 1). Furthermore, during the same period NIR</text>
<table>
<location><page_2><loc_52><loc_29><loc_95><loc_55></location>
<caption>Table 1. Nights of observations.</caption>
</table>
<text><location><page_2><loc_54><loc_24><loc_95><loc_28></location>Notes. * Spectra; All NIR data were obtained by SofI while optical data were obtained by EMMI unless otherwise noted as s (SUSI2) or f (FORS1).</text>
<text><location><page_2><loc_52><loc_10><loc_95><loc_20></location>( J , H , KS ) data were obtained with the Son of ISAAC (SofI) infrared spectrograph and imaging camera on the NTT. These data were reduced using the IRAF package wherein crosstalk correction, bias-subtraction, flatfielding, sky subtraction, bad pixel correction and frame addition were carried out as necessary. The dither pattern, necessary for sky subtraction, was not applied to some of the J , H , and KS images obtained on MJD 52306 so those images underwent no further analysis.</text>
<figure>
<location><page_3><loc_7><loc_51><loc_50><loc_93></location>
<caption>Fig. 2. NTT 60 '' × 40 '' finding charts ( upper: 530s V image on MJD 52324; lower: 3240s KS image on MJD 52305) with the 0.3 '' radio positional uncertainty (Corbel et al., 2001) marked by a circle.</caption>
</figure>
<text><location><page_3><loc_7><loc_31><loc_50><loc_43></location>The images were astrometrically calibrated within the GAIA package, against the 2MASS (Skrutskie et al., 2006) or USNO-B1.0 (Monet et al., 2003) catalogues. The position of XTEJ1550 -564 was derived via the point spread function ( PSF ) of the source in the deep (3240s) KS -band image on January 30 (MJD 52305; seeing ≈ 0 . 8 '' ) as 15:50:58.67 -56:28:35.3, with a positional error 1 dominated by the 0.1 '' 2MASS systematic uncertainty (Figure 2). This is consistent with the radio position of Corbel et al. (2001) and the optical position of Jain et al. (1999).</text>
<text><location><page_3><loc_7><loc_12><loc_50><loc_31></location>Relative PSF photometry was carried out on the final images using the DAOPHOT package (Stetson, 1987) within IRAF. The NIR and V -band magnitudes (Table 2, Figure 3) were calibrated against the 2MASS and GSC 2.3 (Russell et al., 1990) catalogues using ≈ 100 -300 objects per image, after outliers and saturated objects were removed. R - and I -band magnitudes were calibrated against field stars observed by Jain et al. (2001b) and S'anchez-Fern'andez et al. (1999), noting that the publ ished positions of the latter are incorrect and using the transformation, i -I = (0 . 247 ± 0 . 003)( R -I ) (Jordi et al., 2006). V -band magnitudes were also estimated by this method, and were consistent with the GSC derived values. All derived magnitudes were comparable to magnitudes estimated via Persson et al. (1998) and Landolt (1992) photometric standards observed on some of the nights. Due to the small field of view (2 ' × 2 ' ) some V -band im-</text>
<table>
<location><page_3><loc_55><loc_43><loc_91><loc_91></location>
<caption>Table 2. Optical and NIR exposures and magnitudes.</caption>
</table>
<text><location><page_3><loc_52><loc_30><loc_95><loc_36></location>≈ 20 objects per image were available in these cases. The FORS1 images were heavily a ff ected by saturation of catalogue sources in the field so magnitudes were derived from 10 relatively isolated field stars, which were in turn derived from the catalogues on nights less a ff ected by saturation.</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_29></location>On a number of nights, data consisting of multiple ( ≥ 53) high-cadence, 'fast' photometry, images in KS - and V -band were obtained in order to investigate possible short-term variability of the source (see table 2). PSF photometry was carried out on each of these individual images, again using DAOPHOT. In each, the source magnitude was calculated relative to a number of field stars (12 in NIR and 10 in optical) and normalised so that the average is equal to zero. In addition, we also calculate (relative to the same field stars but normalised to a magnitude of one) the magnitudes of 5 comparison stars per band, of similar magnitude to XTE J1550 -564 (Table 3). The positions of those objects are derived via PSFs in the 530s V -band image on MJD 52324 or the 3240s KS -band image on MJD 52305 (Figure2; seeing of both ≈ 0 . 8 '' ) and are dominated by the 0.1 '' 2MASS systematic uncertainty.</text>
<figure>
<location><page_4><loc_9><loc_72><loc_49><loc_93></location>
<caption>Fig. 3. Optical and near-infrared light curves of XTE J1550 -564 during the failed outbursts of 2001 and 2002.</caption>
</figure>
<table>
<location><page_4><loc_12><loc_47><loc_45><loc_63></location>
<caption>Table 3. Positions and magnitudes of sources used for comparison against high-cadence photometry.</caption>
</table>
<text><location><page_4><loc_10><loc_43><loc_50><loc_46></location>Notes. V -band magnitudes are derived as described in section 2, while KS magnitudes are extracted directly from the 2MASS catalogue.</text>
<section_header_level_1><location><page_4><loc_7><loc_38><loc_31><loc_39></location>2.2. SpectralEnergyDistributions</section_header_level_1>
<text><location><page_4><loc_7><loc_19><loc_50><loc_37></location>For the purposes of fitting, the observed magnitudes (Table 2) were converted to flux densities, F ν , at frequency ν (Figure 4), and then to flux per filter, Ffilter in units of photons cm -2 s -1 . This is done via Ffilter = 1509 . 18896 F ν ( ∆ λ/λ ) where λ and ∆ λ are the e ff ective wavelength and full width at half maximum of the filter in question. XSPEC compatible files, for Spectral Energy Distribution (SED) fitting, were produced from the flux per filter value using the FTOOL , flx2xsp . Due to the time di ff erence between epochs of observations, we treat each night separately except for the data taken on the adjoining nights of MJD 52293 and MJD 52294. Due to the time di ff erence between the final I-band image (on MJD 52352) and the corresponding V - and R -band images (on MJD 52344) we do not consider these in our analysis, this results in 6 independent epochs (see table 4).</text>
<text><location><page_4><loc_7><loc_10><loc_50><loc_19></location>Our NIR / optical data were augmented with X-ray spectral data from the Rossi X-ray Timing Explorer (RXTE). Preprocessed Proportional Counter Array (PCA) and High Energy X-ray Timing Experiment (HEXTE; clusters 0 and 1) 'Standard Product' spectra were downloaded from the HEASARC archive for each of the seven nights where we had simultaneous optical or NIR data. All RXTE spectra were observed within 0.1-</text>
<figure>
<location><page_4><loc_55><loc_58><loc_94><loc_93></location>
<caption>Fig. 4. Flux versus frequency plot, at 6 di ff erent epochs, uncorrected (upper) and corrected (lower; Cardelli et al. 1989) for the derived extinction in the direction of the source of EB -V = 1 . 02 ± 0 . 05.</caption>
</figure>
<table>
<location><page_4><loc_64><loc_35><loc_83><loc_46></location>
<caption>Table 4. Unabsorbed X-ray fluxes, from 2-10 keV.</caption>
</table>
<text><location><page_4><loc_52><loc_26><loc_95><loc_32></location>1.0 days of our observations. PCA spectra were fit from 325keV while HEXTE were fit from 25-150keV. Unabsorbed X-ray fluxes, from 2-10 keV, (for comparison with correlations) were inferred from power-law fits to the spectra at each epoch (Table 4).</text>
<section_header_level_1><location><page_4><loc_52><loc_23><loc_65><loc_24></location>2.3. Spectroscopy</section_header_level_1>
<text><location><page_4><loc_52><loc_10><loc_95><loc_21></location>Spectral images were obtained on a number of nights (Tables 1, 2) with EMMI obtaining red (3,850-10,000Å), low-dispersio n spectra using Grism #1 ( RILD 1) and SofI obtaining blue ( GBF ; 9,500-16,400Å) and red ( GRF ; 15,300-25,200Å) low resolution spectra. The data were reduced using the IRAF package wherein crosstalk correction, flatfielding, and bias subtraction were carried out as necessary. To correct for NIR sky, the dithered NIR exposures were summed to create sky images which were subtracted.</text>
<text><location><page_5><loc_7><loc_68><loc_50><loc_93></location>Spectra were reduced and extracted within the IRAF package, noao.twodspec , and individual exposures of the same spectra were summed. Due to the crowded nature of the field and a lack of acquisition frames on some nights we were only able to extract spectra for the nights of MJDs 52302, 52305, and 52307. On nights when they were available, wavelength calibrations were performed against helium + argon (optical) or xenon (NIR) lamps whose spectra were extracted using the same parameters as for the relevant source. The (wavelength dependent) resolution of the final spectrum is 7-10 Å, with a wavelength calibra tion error of /lessorsimilar 20Å (optical) or /lessorsimilar 40Å (NIR). Atmospheric, telluric features significantly a ff ect the spectra and are corrected for by dividing the source spectrum by that of a telluric standard at a similar airmass, using the telluric tool within IRAF. This procedure often causes artefacts in the corrected spectra and in the case of the optical spectra, these artefacts are dominant so this procedure is not applied. Neither the optical nor the NIR spectra can be flux calibrated, due to a lack of standards, but they have been normalised.</text>
<text><location><page_5><loc_7><loc_62><loc_50><loc_68></location>No significant features which could not be associated to artefacts of the telluric correction are found in any of the extracted spectra. To increase the signal to noise, the NIR spectra from MJDs 52305 and 52307 (which exhibited consistent features) were summed but this did not exhibit any additional features.</text>
<section_header_level_1><location><page_5><loc_7><loc_58><loc_15><loc_59></location>3. Results</section_header_level_1>
<section_header_level_1><location><page_5><loc_7><loc_56><loc_29><loc_57></location>3.1. High-cadencephotometry</section_header_level_1>
<text><location><page_5><loc_7><loc_34><loc_50><loc_55></location>The high-cadence V -and KS -band light curves of XTEJ1550 -564 exhibit significant variability over the observations (see Figures 5 and 6 for examples on MJD 52323 and 51981, respectively), though this is much stronger in the NIR KS -band than the optical V -band. In all four KS -band light curves, the χ 2 ν of a constant fit to the data is inconsistent ( > 5 σ ) with being acceptable and is significantly greater than the χ 2 ν of a constant fit to the any of the five comparison objects of similar magnitude (Table 3), even in the worst case of poorest fit (Table 5). Likewise the scatter (standard deviation) of the magnitudes of the source are significantly greater than those of the comparison objects. For the two V -band light curves, the scatter of the source and the comparisons are more comparable, at least on MJD 52303, but the χ 2 ν of the constant fits to the source are again greater than those to the comparison objects and inconsistent with being an acceptable fit.</text>
<text><location><page_5><loc_7><loc_16><loc_50><loc_34></location>While the χ 2 ν of the constant fits to the V -band comparison objects are all consistent, at < 4 σ level, with those objects having constant magnitudes, the fits to the KS -band comparison stars are not consistent ( > 5 σ ) with that assumption. PSF photometry, particularly in the NIR, is prone to underestimating the actual errors on magnitude. This is due to the di ffi culty of accurately modelling the PSF from sources in a crowded field (more likely in NIR observations) and due to the di ffi culty of obtaining a representative PSF from images where the width is not significantly greater than 1 pixel, as is the case here. Even if we normalise the χ 2 ν of the source by that of the worst case comparison, we find that all the V - and KS -band light curves are inconsistent with a constant magnitude, though this should only be used as an approximate guide.</text>
<text><location><page_5><loc_7><loc_10><loc_50><loc_16></location>If we use the maximum standard deviation of the comparison sources on each epoch as an estimate of the 'background' noise we can calculate a corrected standard deviation of each source light curve and the root mean square variability of the light curve, as a percentage of flux (%RMS, Table 5). The error</text>
<figure>
<location><page_5><loc_54><loc_72><loc_95><loc_93></location>
<caption>Fig. 5. High-cadence V -band light curves of XTE J1550 -564 (normalised to a relative magnitude of 0) and of 5 comparison sources (normalised to relative magnitudes of 1) on MJD 52323.</caption>
</figure>
<figure>
<location><page_5><loc_54><loc_43><loc_95><loc_65></location>
<caption>Fig. 6. High-cadence KS -band light curves of XTE J1550 -564 (normalised to a relative magnitude of 0) and of 5 comparison sources (normalised to relative magnitudes of 1) on MJD 51981.</caption>
</figure>
<text><location><page_5><loc_52><loc_18><loc_95><loc_32></location>of the %RMS of the source is given as the %RMS of the background and the 3 σ upper limit to the variability is given as 3 times the background level. The calculated %RMSs imply that neither of the V -band light curves display significant variability, while in all but one case, the KS light curves display variability of ≈ 20%. While this is in contrast to the χ 2 ν analysis of the light curves, it is more robust as it is independent of any underestimate of the errors on individual points (assuming that any underestimate is similar for the source and for the comparison stars, which were chosen specifically to be of similar magnitude and hence, of a similar signal-to-noise ratio).</text>
<text><location><page_5><loc_52><loc_10><loc_95><loc_17></location>We used the IRAF task, pdm - an implementation of the phase dispersion minimisation method of Stellingwerf (1978) to test if any of the variability of the light curves displayed a periodicity. However, all tests returned Stellingwerf statistics, Θ ≈ 1 for all periods less than twice the duration of the observations, implying no periodic variability.</text>
<table>
<location><page_6><loc_24><loc_82><loc_78><loc_91></location>
<caption>Table 5. Optical and NIR variability of high-cadence photometry.</caption>
</table>
<text><location><page_6><loc_10><loc_78><loc_95><loc_81></location>Notes. The standard deviation of the magnitudes, STD, and the associated root mean square variability as percentage of the flux, %RMS, and the χ 2 ν (and number of degrees of freedom, dof) of a constant fit to the data are given for the source (and, in brakets, for the worst case of the comparison sources, or the upper %RMS limit implied from the comparison sources).</text>
<section_header_level_1><location><page_6><loc_7><loc_73><loc_31><loc_74></location>3.2. SpectralEnergyDistributions</section_header_level_1>
<text><location><page_6><loc_7><loc_67><loc_50><loc_72></location>In the following XSPEC fits, all 6 epochs of data are fit simultaneously, fixing the absorption ( redden) and extinction ( tbabs ), as well as other parameters on a case by case basis, across all epochs.</text>
<text><location><page_6><loc_7><loc_50><loc_50><loc_67></location>Given that the observed quiescent magnitudes (Russell et al., 2011) or the limits placed on those magnitudes by the 2MASS catalogue are magnitudes dimmer than we observe, we assume that the companion star makes no significant impact on our observed spectra. The NIR / optical data alone are poorly constrained but consistent with a single reddened power law ( F ν ∝ ν α ), of di ff erent normalisations, of spectral index α = -0 . 6 ± 0 . 2, and the extinction EB -V = 1 . 2 ± 0 . 1, but these parameters are highly degenerate and any values in the range -1 . 4 /lessorsimilar α /lessorsimilar 0 . 1 for 0 . 7 /lessorsimilar EB -V /lessorsimilar 1 . 7 will give acceptable fits. When we include the X-ray data a single power law is no longer an acceptable fit, as the extrapolation of the NIR / optical spectral index underestimates the X-ray flux.</text>
<text><location><page_6><loc_7><loc_17><loc_50><loc_50></location>Previous studies of the X-ray spectra of the 2002 outburst (Belloni et al., 2002) show that the system is in a hard state with the spectra being well described by a power-law of spectral index in the range of -0 . 4 to -0 . 5, without any thermal component. However, studies of other black hole sources (e.g., Miller et al. 2006; Ryko ff et al. 2007; Reis et al. 2010; Reynolds & Miller 2013) show that, even in the hard state, X-ray spectra can be fit by an irradiated disk model that can also describe emission at optical energies. We find that this model (implemented in XSPEC as diskir ; Gierli'nski et al. 2008, 2009) can well describe the broadband data from NIR to X-ray. However, due to the fact that the thermal component makes little contribution to the Xray flux above 3 keV in this state, as demonstrated by the pure power law models of Belloni et al. (2002), the model is underconstrained and many of the parameters related to the disk component cannot be estimated with much certainty. It is also true that the column density is under-constrained due to the relative weakness of X-ray absorption over the observed energies so we instead adopt that measured from Chandra data (Tomsick et al., 2001; Miller et al., 2003). The extinction is set to the value of EB -V = 1 . 02 ± 0 . 05, which is derived from a fit to the only epoch (MJD 52293 / 4) that includes both NIR and optical data which may best constrain extinction. This is consistent with that implied, via the relationship of Guver & Ozel (2009), from the X-ray absorption of this source.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_17></location>The fits to the irradiated disk model are poorly constrained but return photon indices of the power law component, Γ ∼ 1 . 5, and disk temperatures, kT disk ∼ 0 . 2keV, at all epochs. These values are in agreement with the photon indices derived for this source by Belloni et al. (2002) and the disk temperatures measured in the hard state of other LMXBs (e.g., Miller et al. 2006;</text>
<text><location><page_6><loc_52><loc_64><loc_95><loc_74></location>Ryko ff et al. 2007). The other parameters of the fit, even when fixed across epochs, are unconstrained but are in broad agreement with the underlying parameters of Gierli'nski et al. (2009). Given the poorly constrained nature of these spectra it is important to caution that the fit results should not be over interpreted, however we can state that the data are at least consistent with the irradiated disk model for a range of realistic, physical parameters and energies.</text>
<section_header_level_1><location><page_6><loc_52><loc_60><loc_63><loc_61></location>4. Discussion</section_header_level_1>
<text><location><page_6><loc_52><loc_34><loc_95><loc_59></location>X-ray observations of the 2001 and 2002 outbursts of XTEJ1550 -564 (Tomsick et al., 2001; Belloni et al., 2002) suggest that the source was in a hard state only, with no reports of a transition to a soft or intermediate state. Defining the state of an LMXB from NIR / optical observations is not as straight forward as from the X-ray due to the multiple emission mechanisms such as the accretion disk, radio jet, corona, reprocessing (see section 1) - that contribute at those wavelengths. However, variability, which is attributed to the non-thermal emission of the jet or corona, has been observed in the hard state, at least at NIR wavelengths (e.g., Casella et al. 2010; Chaty et al. 2011). In the past decade, a number of correlations have also been suggested that indicate which state the system is in without the need to know exactly which emission mechanism is contributing to the fluxes. This method uses the observed correlations between the X-ray luminosities and the NIR / optical (Russell et al., 2006) or radio (e.g., Corbel et al. 2000, 2003; Gallo et al. 2003; Fender et al. 2010; Coriat et al. 2011) luminosities in di ff erent states to imply which state the system is in.</text>
<text><location><page_6><loc_52><loc_10><loc_95><loc_34></location>Our detections of short term variability in the high-cadence KS -band light curves of ≈ 20%and non-detections in the V -band is consistent with the variabilities implied during the failed 2003 outburst of this source (Chaty et al., 2011). In that outburst, over a similar range of frequencies to ours ( ≈ 10 -4 -10 -1 Hz), KS -band variability was detected at a level of 7 . 2 ± 2 . 2% in contrast to a V -band upper limit of < 28 . 3%. These imply that the radio jet, or perhaps the high-energy corona, are making a significant contribution to the NIR flux. Compact radio jets are only observed in the hard state and while the corona can contribute in the soft state, it is usually weak, so any significant emission that can be associated with either implies that the source is in a hard state. Radio emission, consistent with optically thick emission from a compact jet, was observed from this source during the 2002 outburst (Corbel et al., 2002) and, given its flux of ≈ 2.5 mJy and spectral index of 0 . 07 ± 0 . 11, it is plausible that it contributed to the NIR flux. Unfortunately, while further radio observations of this source have been obtained with the same instrument during the 2001, 2002, and 2003 outbursts, they have yet to be pub-</text>
<text><location><page_7><loc_7><loc_85><loc_50><loc_93></location>nd it is beyond the scope of this paper to do so. Assuming that the observed variability is due to the radio jet implies that the jet's spectral break frequency is at NIR wavelengths - a result consistent with the previously implied break frequencies, both for this source in full outburst, and other LMXB systems (Russell et al., 2013).</text>
<text><location><page_7><loc_7><loc_63><loc_50><loc_85></location>The featureless spectra indicate that there is little direct emission from the accretion disk which would be expected in the soft state. While our SEDs are not well constrained, they are consistent (see section 3.2) with the flux being due to reprocessing of X-rays in a relatively cool ( ∼ 0 . 2keV) accretion disk, as expected in the hard state ( e.g., Miller et al. 2006; Ryko ff et al. 2007; a much higher disk temperature of ∼ 1keV is expected in the soft state, e.g., Sobczak et al. 2000). The absolute V -band magnitudes at the various epochs ( MV ≈ 1 -2, assuming a distance of 5 . 3 ± 2 . 3 kpc; Jonker & Nelemans 2004) are also consistent with observed correlation with Σ = ( L X / L Edd) 1 / 2 P 2 / 3 ≈ -0 . 3 (van Paradijs & McClintock, 1994; Deutsch et al., 2000) if we use the observed period, P = 1 . 5410 ± 0 . 009 days (Jain et al., 2001b), and an estimated mass of /similarequal 7 -10M /circledot (Orosz et al., 2002; Mu˜noz-Darias et al., 2008). This agreement of the observed magnitudes with this relationship is also consistent with those magnitudes being due to reprocessing.</text>
<text><location><page_7><loc_7><loc_40><loc_50><loc_63></location>Comparing our derived NIR / optical and X-ray luminosities (along with those from the failed 2003 outburst; Aref'ev et al. 2004; Chaty et al. 2011) with the observed values for other LMXBs (Russell et al., 2006) we find no significant deviation from the hard state correlation. It has been shown (Curran et al., 2012) that sources deviate from this correlation early in the intermediate state so this agreement adds further weight to the suggestion that the system was in the hard state at the time of the optical observations. During the 2001 outburst, our observations span most of the X-ray activity (see figure 1) without displaying any evidence of reaching a hard or intermediate state. Observations of the 2002 outburst and the single epoch of observations in the 2003 outburst (Chaty et al., 2011) were obtained only after the X-ray flux had already peaked and hence we cannot rule out that a transition to an intermediate state occurred; however, if a soft or intermediate state was reached, the transition back to the hard state would not be expected until late times when the accretion rate had dropped significantly.</text>
<section_header_level_1><location><page_7><loc_7><loc_36><loc_20><loc_38></location>5. Conclusions</section_header_level_1>
<text><location><page_7><loc_7><loc_10><loc_50><loc_35></location>The NIR / optical data of the black hole LMXB system, XTEJ1550 -564, while being consistent with having originated from reprocessing of X-rays in the accretion disk, display variability indicative of a contribution from the radio jet at NIR wavelengths. Hence, the NIR / optical likely combines both emission from the jet and reprocessing. The contribution of the radio jet at such high frequencies is consistent with both previous observations of this source in full outburst and other LMXB systems (Russell et al., 2013), and supports the hard state classification of the system at the time of observations. A comparison of the NIR / optical and X-ray luminosities with those of other LMXBs displays no deviation from the observed hard state correlations (Russell et al., 2006). This suggests that the failed outbursts of 2001, 2002, and 2003 did not transition to an intermediate state, or display signs of jet quenching, but remained in a true, hard state throughout the outburst. Failed outbursts seem only to di ff er from standard outbursts by their failure to quench the radio jet and reach accretion disk dominated emission and not in their underlying, time-independent, physical structure. Studying them at multiple wavelengths - to constrain physical parameters,</text>
<text><location><page_7><loc_52><loc_88><loc_95><loc_93></location>such as the frequency of the jet break, the accretion disk temperature and radius - is required to reveal how jet suppression and reactivation relates to accretion parameters in both failed and successful outbursts of LMXBs.</text>
<text><location><page_7><loc_52><loc_79><loc_95><loc_87></location>Acknowledgements. We thank the anonymous referee for their useful comments. This work was supported by the Australian Research Council's Discovery Projects funding scheme (project number DP120102393) and by the Centre National d'Etudes Spatiales (CNES). This work is based on observations obtained with MINE: the Multi-wavelength INTEGRAL NEtwork. This research has made use of NASA's Astrophysics Data System, the SIMBAD database, operated at CDS, Strasbourg, France and quick-look results provided by the ASM / RXTE team.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Context. A number of low mass X-ray binaries (LMXBs) undergo 'failed outbursts' in which, instead of evolving through the canonical states, they remain in a hard state throughout the outburst. While the sources of X-ray and radio emission in the hard state are relatively well understood, the origin of the near infrared (NIR) and optical emission is more complex though it likely stems from an amalgam of di ff erent emission processes, occurring as it does, at the intersecting wavelengths of those processes. Aims. We aim to identify the NIR / optical emission region(s) during a number of failed outbursts of one such low mass X-ray binary and black hole candidate, XTE J1550 -564, in order to confirm or refute their classification as hard-state, failed outbursts. Methods. We present unique NIR / optical images and spectra, obtained with the ESO-New Technology Telescope, during the failed outbursts of 2001 and 2000. We compare the NIR / optical photometric, timing, and spectral properties with those expected for the di ff erent emission mechanisms in the various LMXB states. Results. The NIR / optical data are consistent with having come from reprocessing of X-rays in the accretion disk, with no evidence of direct thermal emission from the disk itself. However, the observed variability in high-cadence NIR light curves suggest that the radio jet extends and contributes to the NIR wavelengths. Conclusions. We find that these failed outbursts did not transition to an intermediate state but remained in a true, hard state where there was no sign of jet quenching or deviation from the observed hard state correlations. Key words. X-rays: binaries - infrared: stars - X-rays: individuals: XTE J1550 - 564",
"pages": [
1
]
},
{
"title": "NIR and optical observations of the failed outbursts of black hole binary XTE J1550 -564 /star",
"content": "P.A. Curran 1 , 2 and S. Chaty 2 , 3 sur-Yvette Cedex, France Received 9 May 2013 / Accepted 17 July 2013",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "For the majority of their lifetimes, transient low mass X-ray binaries (LMXBs) are in a state of quiescence with faint or nondetected X-ray emission. In quiescence, near infrared (NIR) and optical emission, if detected, is dominated by the main-sequence companion star (with possibly significant contribution from the cold accretion disk). During outburst - on time scales of weeks, months or even longer - there is a dramatic increase in the Xray, NIR / optical, and radio flux, which is powered by an increased level of accretion onto the central, compact object (black hole or neutron star). Many of these sources are observed to undergo multiple, irregular outbursts (e.g., XTE J1550 -564 has displayed 5 outburst events in less than a decade) while others may remain in quiescence for decades after their initial discovery (e.g., V2107 Oph was detected in outburst in 1977 but has yet to repeat). Black hole LMXB outbursts are usually divided into a number of states , based mainly on observable X-ray spectral and timing characteristics. The sources are initially observed in a, generally low intensity, hard state with spectra dominated by powerlaw emission. They then transition, via an intermediate state, to a soft or thermal-dominant state (so called because the spectrum is dominated by a thermal component). X-ray flux peaks in this state before decreasing and evolving, via a late hard state, back into a quiescent state. For a fuller description of the various possible states and the associated X-ray timing properties, etc., see McClintock & Remillard 2006. While the majority of outbursts from LMXBs follow this standard evolution of X-ray defined states, a number of sources are observed to return to quiescence without displaying a soft state (e.g., 9 sources in Brocksopp et al. 2004 and references therein) and another four have been observed to proceed to an intermediate state before returning to the hard state and quiescence, without reaching the soft state (Capitanio et al., 2009; Ferrigno et al., 2012; Soleri et al., 2013; Wijnands & Miller, 2002). Despite being referred to as 'failed outbursts' (or 'Soft X-ray transient' outbursts which are not soft ; Brocksopp et al. 2004) these outbursts can in fact be quite luminous (e.g., V404 Cyg; Tanaka & Lewin 1995), though most are under-luminous. While the origin of X-ray emission in the di ff erent states is relatively well understood (e.g., McClintock & Remillard 2006), that of the NIR, optical, and ultraviolet (UV) is more complex as the optical wavelengths are at the intersection of a number of di ff erent emission mechanisms (for reviews of optical properties of LMXBs see e.g., van Paradijs & McClintock 1995; Charles & Coe 2006). Both intrinsic, thermal emission from the hot, outer accretion disk (e.g., Shakura & Sunyaev 1973; Frank et al. 2002) as well as reprocessing of X-rays in the same region of the disk (e.g., Cunningham 1976; van Paradijs & McClintock 1994) may contribute significant levels of flux at UV, optical, and NIR wavelengths. Recently, evidence has been mounting that the relativistic jet, usually detected in radio, also produces a significant contribution to the NIR - and possibly optical - flux, at least in the hard state (e.g., Jain et al. 2001a; Corbel & Fender 2002; Russell et al. 2006; Chaty et al. 2011), and it is possible that the power law component of the Xray emission extends to, and contributes at optical wavelengths. XTEJ1550 -564 has undergone a number of weak, failed outbursts (in 2001 (Tomsick et al., 2001); 2002 (Belloni et al., 2002); and 2003 (Sturner & Shrader, 2005; Aref'ev et al., 2004)) as well as a number of complete (soft state) outbursts in 1998 / 99 (e.g., Sobczak et al. 2000) and 2000 (e.g., Jain et al. 2001a; see also figure 1). Even if these late time outbursts are considered as rebrightenings or reflarings of the original outburst, this source demonstrates conclusively that failed outbursts are not a separate class of object but are likely caused by differences in the accretion flow onto the black hole or by di ff erences in the systems' e ffi ciency in converting the accreted matter into observable flux. In this paper we present the only significant NIR / optical observations during the failed outbursts of 2001 and 2002, obtained by the ESO NTT (Table 1), and comprising of all the available unpublished, archived ESO data of the source. In section 2 we introduce the observations and reduction methods, while in section 3 we present the results of our photometric, timing and spectral analyses of the data. We discuss the interpretation of our findings in section 4 and summarise in section 5.",
"pages": [
1,
2
]
},
{
"title": "2.1. Photometry",
"content": "During the outbursts of 2001 and 2002 optical ( V , R , I ) data were obtained with the ESO Multi-Mode Instrument (EMMI; Dekker et al. 1986) and the Superb-Seeing Imager (SuSI2) on the 3 . 58m ESO - New Technology Telescope (NTT), as well as with the FOcal Reducer and low dispersion Spectrograph (FORS1) on the 8 . 2m UNIT 3 of the Very Large Telescope (VLT-UT3) (Table 1). Furthermore, during the same period NIR Notes. * Spectra; All NIR data were obtained by SofI while optical data were obtained by EMMI unless otherwise noted as s (SUSI2) or f (FORS1). ( J , H , KS ) data were obtained with the Son of ISAAC (SofI) infrared spectrograph and imaging camera on the NTT. These data were reduced using the IRAF package wherein crosstalk correction, bias-subtraction, flatfielding, sky subtraction, bad pixel correction and frame addition were carried out as necessary. The dither pattern, necessary for sky subtraction, was not applied to some of the J , H , and KS images obtained on MJD 52306 so those images underwent no further analysis. The images were astrometrically calibrated within the GAIA package, against the 2MASS (Skrutskie et al., 2006) or USNO-B1.0 (Monet et al., 2003) catalogues. The position of XTEJ1550 -564 was derived via the point spread function ( PSF ) of the source in the deep (3240s) KS -band image on January 30 (MJD 52305; seeing ≈ 0 . 8 '' ) as 15:50:58.67 -56:28:35.3, with a positional error 1 dominated by the 0.1 '' 2MASS systematic uncertainty (Figure 2). This is consistent with the radio position of Corbel et al. (2001) and the optical position of Jain et al. (1999). Relative PSF photometry was carried out on the final images using the DAOPHOT package (Stetson, 1987) within IRAF. The NIR and V -band magnitudes (Table 2, Figure 3) were calibrated against the 2MASS and GSC 2.3 (Russell et al., 1990) catalogues using ≈ 100 -300 objects per image, after outliers and saturated objects were removed. R - and I -band magnitudes were calibrated against field stars observed by Jain et al. (2001b) and S'anchez-Fern'andez et al. (1999), noting that the publ ished positions of the latter are incorrect and using the transformation, i -I = (0 . 247 ± 0 . 003)( R -I ) (Jordi et al., 2006). V -band magnitudes were also estimated by this method, and were consistent with the GSC derived values. All derived magnitudes were comparable to magnitudes estimated via Persson et al. (1998) and Landolt (1992) photometric standards observed on some of the nights. Due to the small field of view (2 ' × 2 ' ) some V -band im- ≈ 20 objects per image were available in these cases. The FORS1 images were heavily a ff ected by saturation of catalogue sources in the field so magnitudes were derived from 10 relatively isolated field stars, which were in turn derived from the catalogues on nights less a ff ected by saturation. On a number of nights, data consisting of multiple ( ≥ 53) high-cadence, 'fast' photometry, images in KS - and V -band were obtained in order to investigate possible short-term variability of the source (see table 2). PSF photometry was carried out on each of these individual images, again using DAOPHOT. In each, the source magnitude was calculated relative to a number of field stars (12 in NIR and 10 in optical) and normalised so that the average is equal to zero. In addition, we also calculate (relative to the same field stars but normalised to a magnitude of one) the magnitudes of 5 comparison stars per band, of similar magnitude to XTE J1550 -564 (Table 3). The positions of those objects are derived via PSFs in the 530s V -band image on MJD 52324 or the 3240s KS -band image on MJD 52305 (Figure2; seeing of both ≈ 0 . 8 '' ) and are dominated by the 0.1 '' 2MASS systematic uncertainty. Notes. V -band magnitudes are derived as described in section 2, while KS magnitudes are extracted directly from the 2MASS catalogue.",
"pages": [
2,
3,
4
]
},
{
"title": "2.2. SpectralEnergyDistributions",
"content": "For the purposes of fitting, the observed magnitudes (Table 2) were converted to flux densities, F ν , at frequency ν (Figure 4), and then to flux per filter, Ffilter in units of photons cm -2 s -1 . This is done via Ffilter = 1509 . 18896 F ν ( ∆ λ/λ ) where λ and ∆ λ are the e ff ective wavelength and full width at half maximum of the filter in question. XSPEC compatible files, for Spectral Energy Distribution (SED) fitting, were produced from the flux per filter value using the FTOOL , flx2xsp . Due to the time di ff erence between epochs of observations, we treat each night separately except for the data taken on the adjoining nights of MJD 52293 and MJD 52294. Due to the time di ff erence between the final I-band image (on MJD 52352) and the corresponding V - and R -band images (on MJD 52344) we do not consider these in our analysis, this results in 6 independent epochs (see table 4). Our NIR / optical data were augmented with X-ray spectral data from the Rossi X-ray Timing Explorer (RXTE). Preprocessed Proportional Counter Array (PCA) and High Energy X-ray Timing Experiment (HEXTE; clusters 0 and 1) 'Standard Product' spectra were downloaded from the HEASARC archive for each of the seven nights where we had simultaneous optical or NIR data. All RXTE spectra were observed within 0.1- 1.0 days of our observations. PCA spectra were fit from 325keV while HEXTE were fit from 25-150keV. Unabsorbed X-ray fluxes, from 2-10 keV, (for comparison with correlations) were inferred from power-law fits to the spectra at each epoch (Table 4).",
"pages": [
4
]
},
{
"title": "2.3. Spectroscopy",
"content": "Spectral images were obtained on a number of nights (Tables 1, 2) with EMMI obtaining red (3,850-10,000Å), low-dispersio n spectra using Grism #1 ( RILD 1) and SofI obtaining blue ( GBF ; 9,500-16,400Å) and red ( GRF ; 15,300-25,200Å) low resolution spectra. The data were reduced using the IRAF package wherein crosstalk correction, flatfielding, and bias subtraction were carried out as necessary. To correct for NIR sky, the dithered NIR exposures were summed to create sky images which were subtracted. Spectra were reduced and extracted within the IRAF package, noao.twodspec , and individual exposures of the same spectra were summed. Due to the crowded nature of the field and a lack of acquisition frames on some nights we were only able to extract spectra for the nights of MJDs 52302, 52305, and 52307. On nights when they were available, wavelength calibrations were performed against helium + argon (optical) or xenon (NIR) lamps whose spectra were extracted using the same parameters as for the relevant source. The (wavelength dependent) resolution of the final spectrum is 7-10 Å, with a wavelength calibra tion error of /lessorsimilar 20Å (optical) or /lessorsimilar 40Å (NIR). Atmospheric, telluric features significantly a ff ect the spectra and are corrected for by dividing the source spectrum by that of a telluric standard at a similar airmass, using the telluric tool within IRAF. This procedure often causes artefacts in the corrected spectra and in the case of the optical spectra, these artefacts are dominant so this procedure is not applied. Neither the optical nor the NIR spectra can be flux calibrated, due to a lack of standards, but they have been normalised. No significant features which could not be associated to artefacts of the telluric correction are found in any of the extracted spectra. To increase the signal to noise, the NIR spectra from MJDs 52305 and 52307 (which exhibited consistent features) were summed but this did not exhibit any additional features.",
"pages": [
4,
5
]
},
{
"title": "3.1. High-cadencephotometry",
"content": "The high-cadence V -and KS -band light curves of XTEJ1550 -564 exhibit significant variability over the observations (see Figures 5 and 6 for examples on MJD 52323 and 51981, respectively), though this is much stronger in the NIR KS -band than the optical V -band. In all four KS -band light curves, the χ 2 ν of a constant fit to the data is inconsistent ( > 5 σ ) with being acceptable and is significantly greater than the χ 2 ν of a constant fit to the any of the five comparison objects of similar magnitude (Table 3), even in the worst case of poorest fit (Table 5). Likewise the scatter (standard deviation) of the magnitudes of the source are significantly greater than those of the comparison objects. For the two V -band light curves, the scatter of the source and the comparisons are more comparable, at least on MJD 52303, but the χ 2 ν of the constant fits to the source are again greater than those to the comparison objects and inconsistent with being an acceptable fit. While the χ 2 ν of the constant fits to the V -band comparison objects are all consistent, at < 4 σ level, with those objects having constant magnitudes, the fits to the KS -band comparison stars are not consistent ( > 5 σ ) with that assumption. PSF photometry, particularly in the NIR, is prone to underestimating the actual errors on magnitude. This is due to the di ffi culty of accurately modelling the PSF from sources in a crowded field (more likely in NIR observations) and due to the di ffi culty of obtaining a representative PSF from images where the width is not significantly greater than 1 pixel, as is the case here. Even if we normalise the χ 2 ν of the source by that of the worst case comparison, we find that all the V - and KS -band light curves are inconsistent with a constant magnitude, though this should only be used as an approximate guide. If we use the maximum standard deviation of the comparison sources on each epoch as an estimate of the 'background' noise we can calculate a corrected standard deviation of each source light curve and the root mean square variability of the light curve, as a percentage of flux (%RMS, Table 5). The error of the %RMS of the source is given as the %RMS of the background and the 3 σ upper limit to the variability is given as 3 times the background level. The calculated %RMSs imply that neither of the V -band light curves display significant variability, while in all but one case, the KS light curves display variability of ≈ 20%. While this is in contrast to the χ 2 ν analysis of the light curves, it is more robust as it is independent of any underestimate of the errors on individual points (assuming that any underestimate is similar for the source and for the comparison stars, which were chosen specifically to be of similar magnitude and hence, of a similar signal-to-noise ratio). We used the IRAF task, pdm - an implementation of the phase dispersion minimisation method of Stellingwerf (1978) to test if any of the variability of the light curves displayed a periodicity. However, all tests returned Stellingwerf statistics, Θ ≈ 1 for all periods less than twice the duration of the observations, implying no periodic variability. Notes. The standard deviation of the magnitudes, STD, and the associated root mean square variability as percentage of the flux, %RMS, and the χ 2 ν (and number of degrees of freedom, dof) of a constant fit to the data are given for the source (and, in brakets, for the worst case of the comparison sources, or the upper %RMS limit implied from the comparison sources).",
"pages": [
5,
6
]
},
{
"title": "3.2. SpectralEnergyDistributions",
"content": "In the following XSPEC fits, all 6 epochs of data are fit simultaneously, fixing the absorption ( redden) and extinction ( tbabs ), as well as other parameters on a case by case basis, across all epochs. Given that the observed quiescent magnitudes (Russell et al., 2011) or the limits placed on those magnitudes by the 2MASS catalogue are magnitudes dimmer than we observe, we assume that the companion star makes no significant impact on our observed spectra. The NIR / optical data alone are poorly constrained but consistent with a single reddened power law ( F ν ∝ ν α ), of di ff erent normalisations, of spectral index α = -0 . 6 ± 0 . 2, and the extinction EB -V = 1 . 2 ± 0 . 1, but these parameters are highly degenerate and any values in the range -1 . 4 /lessorsimilar α /lessorsimilar 0 . 1 for 0 . 7 /lessorsimilar EB -V /lessorsimilar 1 . 7 will give acceptable fits. When we include the X-ray data a single power law is no longer an acceptable fit, as the extrapolation of the NIR / optical spectral index underestimates the X-ray flux. Previous studies of the X-ray spectra of the 2002 outburst (Belloni et al., 2002) show that the system is in a hard state with the spectra being well described by a power-law of spectral index in the range of -0 . 4 to -0 . 5, without any thermal component. However, studies of other black hole sources (e.g., Miller et al. 2006; Ryko ff et al. 2007; Reis et al. 2010; Reynolds & Miller 2013) show that, even in the hard state, X-ray spectra can be fit by an irradiated disk model that can also describe emission at optical energies. We find that this model (implemented in XSPEC as diskir ; Gierli'nski et al. 2008, 2009) can well describe the broadband data from NIR to X-ray. However, due to the fact that the thermal component makes little contribution to the Xray flux above 3 keV in this state, as demonstrated by the pure power law models of Belloni et al. (2002), the model is underconstrained and many of the parameters related to the disk component cannot be estimated with much certainty. It is also true that the column density is under-constrained due to the relative weakness of X-ray absorption over the observed energies so we instead adopt that measured from Chandra data (Tomsick et al., 2001; Miller et al., 2003). The extinction is set to the value of EB -V = 1 . 02 ± 0 . 05, which is derived from a fit to the only epoch (MJD 52293 / 4) that includes both NIR and optical data which may best constrain extinction. This is consistent with that implied, via the relationship of Guver & Ozel (2009), from the X-ray absorption of this source. The fits to the irradiated disk model are poorly constrained but return photon indices of the power law component, Γ ∼ 1 . 5, and disk temperatures, kT disk ∼ 0 . 2keV, at all epochs. These values are in agreement with the photon indices derived for this source by Belloni et al. (2002) and the disk temperatures measured in the hard state of other LMXBs (e.g., Miller et al. 2006; Ryko ff et al. 2007). The other parameters of the fit, even when fixed across epochs, are unconstrained but are in broad agreement with the underlying parameters of Gierli'nski et al. (2009). Given the poorly constrained nature of these spectra it is important to caution that the fit results should not be over interpreted, however we can state that the data are at least consistent with the irradiated disk model for a range of realistic, physical parameters and energies.",
"pages": [
6
]
},
{
"title": "4. Discussion",
"content": "X-ray observations of the 2001 and 2002 outbursts of XTEJ1550 -564 (Tomsick et al., 2001; Belloni et al., 2002) suggest that the source was in a hard state only, with no reports of a transition to a soft or intermediate state. Defining the state of an LMXB from NIR / optical observations is not as straight forward as from the X-ray due to the multiple emission mechanisms such as the accretion disk, radio jet, corona, reprocessing (see section 1) - that contribute at those wavelengths. However, variability, which is attributed to the non-thermal emission of the jet or corona, has been observed in the hard state, at least at NIR wavelengths (e.g., Casella et al. 2010; Chaty et al. 2011). In the past decade, a number of correlations have also been suggested that indicate which state the system is in without the need to know exactly which emission mechanism is contributing to the fluxes. This method uses the observed correlations between the X-ray luminosities and the NIR / optical (Russell et al., 2006) or radio (e.g., Corbel et al. 2000, 2003; Gallo et al. 2003; Fender et al. 2010; Coriat et al. 2011) luminosities in di ff erent states to imply which state the system is in. Our detections of short term variability in the high-cadence KS -band light curves of ≈ 20%and non-detections in the V -band is consistent with the variabilities implied during the failed 2003 outburst of this source (Chaty et al., 2011). In that outburst, over a similar range of frequencies to ours ( ≈ 10 -4 -10 -1 Hz), KS -band variability was detected at a level of 7 . 2 ± 2 . 2% in contrast to a V -band upper limit of < 28 . 3%. These imply that the radio jet, or perhaps the high-energy corona, are making a significant contribution to the NIR flux. Compact radio jets are only observed in the hard state and while the corona can contribute in the soft state, it is usually weak, so any significant emission that can be associated with either implies that the source is in a hard state. Radio emission, consistent with optically thick emission from a compact jet, was observed from this source during the 2002 outburst (Corbel et al., 2002) and, given its flux of ≈ 2.5 mJy and spectral index of 0 . 07 ± 0 . 11, it is plausible that it contributed to the NIR flux. Unfortunately, while further radio observations of this source have been obtained with the same instrument during the 2001, 2002, and 2003 outbursts, they have yet to be pub- nd it is beyond the scope of this paper to do so. Assuming that the observed variability is due to the radio jet implies that the jet's spectral break frequency is at NIR wavelengths - a result consistent with the previously implied break frequencies, both for this source in full outburst, and other LMXB systems (Russell et al., 2013). The featureless spectra indicate that there is little direct emission from the accretion disk which would be expected in the soft state. While our SEDs are not well constrained, they are consistent (see section 3.2) with the flux being due to reprocessing of X-rays in a relatively cool ( ∼ 0 . 2keV) accretion disk, as expected in the hard state ( e.g., Miller et al. 2006; Ryko ff et al. 2007; a much higher disk temperature of ∼ 1keV is expected in the soft state, e.g., Sobczak et al. 2000). The absolute V -band magnitudes at the various epochs ( MV ≈ 1 -2, assuming a distance of 5 . 3 ± 2 . 3 kpc; Jonker & Nelemans 2004) are also consistent with observed correlation with Σ = ( L X / L Edd) 1 / 2 P 2 / 3 ≈ -0 . 3 (van Paradijs & McClintock, 1994; Deutsch et al., 2000) if we use the observed period, P = 1 . 5410 ± 0 . 009 days (Jain et al., 2001b), and an estimated mass of /similarequal 7 -10M /circledot (Orosz et al., 2002; Mu˜noz-Darias et al., 2008). This agreement of the observed magnitudes with this relationship is also consistent with those magnitudes being due to reprocessing. Comparing our derived NIR / optical and X-ray luminosities (along with those from the failed 2003 outburst; Aref'ev et al. 2004; Chaty et al. 2011) with the observed values for other LMXBs (Russell et al., 2006) we find no significant deviation from the hard state correlation. It has been shown (Curran et al., 2012) that sources deviate from this correlation early in the intermediate state so this agreement adds further weight to the suggestion that the system was in the hard state at the time of the optical observations. During the 2001 outburst, our observations span most of the X-ray activity (see figure 1) without displaying any evidence of reaching a hard or intermediate state. Observations of the 2002 outburst and the single epoch of observations in the 2003 outburst (Chaty et al., 2011) were obtained only after the X-ray flux had already peaked and hence we cannot rule out that a transition to an intermediate state occurred; however, if a soft or intermediate state was reached, the transition back to the hard state would not be expected until late times when the accretion rate had dropped significantly.",
"pages": [
6,
7
]
},
{
"title": "5. Conclusions",
"content": "The NIR / optical data of the black hole LMXB system, XTEJ1550 -564, while being consistent with having originated from reprocessing of X-rays in the accretion disk, display variability indicative of a contribution from the radio jet at NIR wavelengths. Hence, the NIR / optical likely combines both emission from the jet and reprocessing. The contribution of the radio jet at such high frequencies is consistent with both previous observations of this source in full outburst and other LMXB systems (Russell et al., 2013), and supports the hard state classification of the system at the time of observations. A comparison of the NIR / optical and X-ray luminosities with those of other LMXBs displays no deviation from the observed hard state correlations (Russell et al., 2006). This suggests that the failed outbursts of 2001, 2002, and 2003 did not transition to an intermediate state, or display signs of jet quenching, but remained in a true, hard state throughout the outburst. Failed outbursts seem only to di ff er from standard outbursts by their failure to quench the radio jet and reach accretion disk dominated emission and not in their underlying, time-independent, physical structure. Studying them at multiple wavelengths - to constrain physical parameters, such as the frequency of the jet break, the accretion disk temperature and radius - is required to reveal how jet suppression and reactivation relates to accretion parameters in both failed and successful outbursts of LMXBs. Acknowledgements. We thank the anonymous referee for their useful comments. This work was supported by the Australian Research Council's Discovery Projects funding scheme (project number DP120102393) and by the Centre National d'Etudes Spatiales (CNES). This work is based on observations obtained with MINE: the Multi-wavelength INTEGRAL NEtwork. This research has made use of NASA's Astrophysics Data System, the SIMBAD database, operated at CDS, Strasbourg, France and quick-look results provided by the ASM / RXTE team.",
"pages": [
7
]
},
{
"title": "References",
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"pages": [
7,
8
]
}
]
2013A&A...557A.123E
https://arxiv.org/pdf/1302.5329.pdf
<document>
<section_header_level_1><location><page_1><loc_21><loc_85><loc_81><loc_87></location>The XMM-NewtonWide Angle Survey (XWAS)</section_header_level_1>
<text><location><page_1><loc_7><loc_80><loc_95><loc_84></location>P. Esquej 1 , 2 , 3 , 4 , M. Page 5 , F. J. Carrera 3 , S. Mateos 3 , J. Tedds 2 , M. G. Watson 2 , A. Corral 6 , J. Ebrero 7 , M. Krumpe 8 , 9 , 10 , S. R. Rosen 2 , M. T. Ceballos 3 , A. Schwope 10 , C. Page 2 , A. Alonso-Herrero 3 /star , A. Caccianiga 6 , R. Della Ceca 6 , 11 10 6</text>
<text><location><page_1><loc_33><loc_79><loc_68><loc_80></location>O. Gonz'alez-Mart'ın , G. Lamer , P. Severgnini</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_76><loc_76><loc_77></location>1 Centro de Astrobiolog'ıa (INTA-CSIC), ESAC Campus, PO Box 78, 28691 Villanueva de la Ca˜nada, Spain</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_60><loc_76></location>2 Dept. of Physics and Astronomy, Leicester University, Leicester LE1 7RH, U.K.</list_item>
<list_item><location><page_1><loc_11><loc_74><loc_68><loc_75></location>3 Instituto de F'ısica de Cantabria (CSIC-UC), Avenida de los Castros, 39005 Santander, Spain</list_item>
<list_item><location><page_1><loc_11><loc_73><loc_79><loc_74></location>4 Departamento de F'ısica Moderna, Universidad de Cantabria, Avda. de Los Castros s / n, 39005 Santander, Spain</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_82><loc_73></location>5 Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_58><loc_71></location>6 INAF - Osservatorio Astronomico di Brera, via Brera 28, 20121 Milan, Italy</list_item>
<list_item><location><page_1><loc_11><loc_69><loc_74><loc_70></location>7 SRON - Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA, Utrecht, The Netherlands</list_item>
<list_item><location><page_1><loc_11><loc_68><loc_75><loc_69></location>8 European Southern Observatory, Karl-Schwarzschild-Stra β e 2, 85748 Garching bei Munchen, Germany</list_item>
<list_item><location><page_1><loc_11><loc_67><loc_86><loc_68></location>9 University of California, San Diego, Center for Astrophysics & Space Sciences, 9500 Gilman Drive, CA 92093-0424, USA</list_item>
<list_item><location><page_1><loc_11><loc_66><loc_72><loc_67></location>10 Leibniz-Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany</list_item>
<list_item><location><page_1><loc_11><loc_64><loc_71><loc_66></location>11 Instituto Astrof'ısico de Canarias, (IAC), C / V'ıa L'actea, s / n, E-38205, La Laguna, Tenerife, Spain</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_61><loc_37><loc_62></location>Preprint online version: November 15, 2021</text>
<section_header_level_1><location><page_1><loc_47><loc_59><loc_55><loc_60></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_53><loc_91><loc_57></location>Aims. This programme is aimed at obtaining one of the largest X-ray selected samples of identified active galactic nuclei to date in order to characterise such a population at intermediate fluxes, where most of the Universe's accretion power originates. We present the XMM-Newton Wide Angle Survey (XWAS), a new catalogue of almost a thousand X-ray sources spectroscopically identified through optical observations.</text>
<text><location><page_1><loc_11><loc_47><loc_91><loc_53></location>Methods. A sample of X-ray sources detected in 68 XMM-Newton pointed observations was selected for optical multi-fibre spectroscopy. Optical counterparts and corresponding photometry of the X-ray sources were obtained from the SuperCOSMOS Sky Survey. Candidates for spectroscopy were initially selected with magnitudes down to R ∼ 21, with preference for X-ray sources having a flux F 0 . 5 -4 . 5keV ≥ 10 -14 erg s -1 cm -2 . Optical spectroscopic observations performed at the Anglo Australian Telescope Two Degree Field were analysed, and the derived spectra were classified based on optical emission lines.</text>
<text><location><page_1><loc_11><loc_37><loc_91><loc_47></location>Results. We have identified through optical spectroscopy 940 X-ray sources over Ω ∼ 11.8 deg 2 of the sky. Source populations in our sample can be summarised as 65% broad line active galactic nuclei (BLAGN), 16% narrow emission line galaxies (NELGs), 6% absorption line galaxies (ALGs) and 13% stars. An active nucleus is likely to be present also in the large majority of the X-ray sources spectroscopically classified as NELGs or ALGs. Sources lie in high-galactic latitude ( | b | > 20 deg) XMM-Newton fields mainly in the southern hemisphere. Due to the large parameter space in redshift (0 ≤ z ≤ 4 . 25) and flux (10 -15 ≤ F 0 . 5 -4 . 5keV ≤ 10 -12 erg s -1 cm -2 ) covered by the XWAS this work provides an excellent resource to further study subsamples and particular cases. The overall properties of the extragalactic objects are presented in this paper. These include the redshift and luminosity distributions, optical and X-ray colours and X-ray-to-optical flux ratios.</text>
<text><location><page_1><loc_11><loc_36><loc_56><loc_37></location>Key words. X-ray: general - Surveys - X-rays: galaxies - Galaxies: active</text>
<section_header_level_1><location><page_1><loc_7><loc_31><loc_19><loc_32></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_15><loc_50><loc_30></location>According to synthesis models, the growth of supermassive black holes (SMBHs) by accretion over cosmic time is recorded in the X-ray source population which produces the cosmic X-ray background (CXB). Hence, X-ray surveys can be used to constrain the epochs and environments in which SMBHs formed and evolved (Alexander et al. 2003; Hasinger et al. 2005; Gilli et al. 2007). X-ray surveys with high sensitivities and good spatial and spectral resolution are essential for studying the properties of the bulk of X-ray sources. Deep pencil beam surveys are able to detect sources down to very faint fluxes, therefore allowing the detection of typical sources in the sky and contributing to the picture of the early Universe. Among these we can find</text>
<text><location><page_1><loc_52><loc_21><loc_95><loc_32></location>the Chandra deep field (CDF) surveys (e.g. Alexander et al. 2003; Tozzi et al. 2006; Luo et al. 2008; Xue et al. 2011), and the XMM-Newton deep surveys of the CDF-South (Ranalli et al. in prep.) and the Lockman Hole (Hasinger et al. 2001; Mainieri et al. 2002; Mateos et al. 2005). All-sky surveys like the ROSAT All-Sky Survey (Voges et al. 1999) with shallow exposures but with large sky coverage can observe rare objects with small surface number density, and are able to unveil the bright end of the luminosity function.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_20></location>Serendipitous surveys, covering X-ray fluxes between 10 -12 and 10 -15 erg s -1 cm -2 , fall in between especially designed all-sky programs and dedicated pointed observations. Sources at these intermediate fluxes are responsible for a large fraction of the X-ray background, as they sample the region around the break in the X-ray source counts (Carrera et al. 2007; Mateos et al. 2008). A number of campaigns have been dedicated to the optical-to-radio characterization of</text>
<text><location><page_2><loc_7><loc_83><loc_50><loc_93></location>X-ray sources selected at di ff erent X-ray depths like the XBootes survey (Murray et al. 2005; Brand et al. 2006), the Extended Groth strip Survey (EGS Georgakakis et al. 2006), the HELLAS2XMM survey (Cocchia et al. 2007; Fiore et al. 2003), the XMM-Newton and Chandra surveys in the COSMOS field (Hasinger et al. 2007; Elvis et al. 2009; Brusa et al. 2010) and the Bright Ultra-Hard XMM-Newton Survey (BUXS; Mateos et al. 2012).</text>
<text><location><page_2><loc_7><loc_53><loc_50><loc_83></location>Data from XMM-Newton observations have been used to create the largest X-ray catalogue ever produced, the 2XMMi-DR3 (Watson et al. 2009). Specific complete subsets of sources have already been used to investigate cosmological properties such as the X-ray log N - log S distributions and the angular clustering of X-ray sources (Mateos et al. 2008; Ebrero et al. 2009b). Optical imaging and spectroscopy of well-defined datasets from selected XMM-Newton fields have been obtained in order to characterise their X-ray source populations. The XMM-Newton Survey Science Centre (SSC) follow-up and identification (XID) programme is outlined in Watson et al. (2001). Their goals include the detailed characterisation of the dominant X-ray source populations and the discovery of new classes of probable rare sources. The outcome of these samples is currently being used to establish statistical identification criteria in order to characterise the complete XID database (Pineau et al. 2011). The XMMNewton Bright Serendipitous Survey (XBS; Della Ceca et al. 2004; Caccianiga et al. 2008) and X-ray luminosity function (Della Ceca et al. 2008; Ebrero et al. 2009a) have been published together with the XID Medium Survey catalogue (XMS; Barcons et al. 2007), the X-ray source counts and the angular clustering (Carrera et al. 2007), and the X-ray spectral analysis of the active galactic nuclei (Mateos et al. 2005).</text>
<text><location><page_2><loc_7><loc_37><loc_50><loc_53></location>The XMM-Newton Wide Angle Survey (XWAS) presented here is part of the follow-up programme conducted by the XMM-Newton collaboration. It complements previous surveys in providing a qualitative picture of the X-ray sky. It yields optical and X-ray characterisation of ∼ 1000 objects mainly in the southern hemisphere. Spectroscopic optical observations have been used to provide the redshift and classification of the sources. Published papers based on sources drawn from the XWAS sample include detailed X-ray spectral analysis of the identified broad line active galactic nuclei (BLAGN) (Mateos et al. 2010), stacking of all XID BLAGN spectra (Corral et al. 2008) and a study and X-ray stacking of type II QSOs (Krumpe et al. 2008).</text>
<text><location><page_2><loc_7><loc_27><loc_50><loc_37></location>This paper is structured as follows: in Sect. 2 we define the XWAS. In Sect. 3 we discuss the multi-band optical imaging and spectroscopic observations conducted on the XMM-Newton target fields. Sect. 4 gives details on the source spectroscopic classification scheme, followed by the counterpart selection procedure in Sect. 5. Section 6 presents the overall source populations. Section 7 describes the catalogue columns and how to obtain the data. Finally, Sect. 8 summarises our main results.</text>
<text><location><page_2><loc_7><loc_23><loc_50><loc_27></location>Throughout this paper a Λ CDM cosmology of ( Ω m, ΩΛ ) = (0.3, 0.7) and H 0 = 70 km s -1 Mpc -1 will be assumed. Optical magnitudes are given in the Vega system.</text>
<section_header_level_1><location><page_2><loc_7><loc_20><loc_19><loc_21></location>2. The sample</section_header_level_1>
<text><location><page_2><loc_7><loc_10><loc_50><loc_19></location>The XMM-Newton satellite features high spectral resolution and excellent sensitivity due to the large collecting area of its mirrors coupled with the high quantum e ffi ciency of the EPIC detectors (Jansen et al. 2001). It provides a significant detection of serendipitous sources in addition to the original target. The purpose of the XWAS project is to create a catalogue of X-ray sources detected by XMM-Newton with optical identifications</text>
<text><location><page_2><loc_52><loc_91><loc_95><loc_93></location>including redshift and classification based on our own optical multi-fibre spectroscopy.</text>
<text><location><page_2><loc_52><loc_78><loc_95><loc_90></location>The XMM-Newton field selection criteria for the XWAS prioritised those observations with adjacent or overlapping coverage, to take optimum advantage of the field of view of the spectrograph used for the optical observations. The Galactic latitude was restricted so only those fields with | b | > 20 deg were selected in order to avoid high Galactic absorption and source confusion in the Galactic plane. We also required that all XMM-Newton observations had total exposure times of > 10ks and that they were performed in Full Frame mode in the EPIC cameras with thin or medium filters.</text>
<text><location><page_2><loc_52><loc_63><loc_95><loc_77></location>With these properties, X-ray objects were originally selected from 68 spatially distinct pointing observations, carried out by XMM-Newton between June 2000 and May 2003. After the source selection, optical spectroscopic campaigns were performed. The Galactic absorbing column density along the line of sight for the selected observations is always < 2 × 10 21 cm -2 , which minimises non-uniformities introduced by large values of the Galactic N H. The median Galactic absorption is 3 × 10 20 cm -2 . Of the total 5675 serendipitous X-ray sources found in the 68 exposures, ∼ 3000 objects were selected for optical spectroscopy (see Sect. 3 for selection criteria).</text>
<text><location><page_2><loc_52><loc_46><loc_95><loc_63></location>To derive the X-ray selection function, we have estimated the sky coverage as a function of the X-ray flux using empirical sensitivity maps for every observation (Carrera et al. 2007; Mateos et al. 2008). For each observation, we have estimated the minimum detectable count rate at each position of the field of view (FOV) for a threshold in detection significance (we have selected L ≥ 6), taking into account the e ff ective exposure and background level across the field of view. For a full description please see Carrera et al. (2007); Mateos et al. (2008). For the count rate to flux conversion, which depends on the camera, observing mode, filter and spectral model we have used the energy conversion factors published in the 2XMMiDR3 documentation 1 .</text>
<text><location><page_2><loc_52><loc_31><loc_95><loc_46></location>The dependence of the sky coverage on the flux for the various cameras in the 0.5-4.5keV energy band is shown in Fig. 1. The individual cameras survey ∼ 9deg 2 and ∼ 8 deg 2 for the MOSs and pn respectively given that not all fields are observed by the three instruments. The fields targeted by the XWAScovera net sky area of Ω ∼ 11.3 deg 2 , calculated using all three EPIC cameras after correcting for overlaps. In calculating the source counts we have only used flux levels at which sources are detectable over at least 1 deg 2 of sky. This constraint has been imposed to prevent uncertainties in the source count distributions due to low count statistics, and to avoid inaccuracy in the sky coverage calculation at the very faint detection limits.</text>
<section_header_level_1><location><page_2><loc_52><loc_27><loc_71><loc_28></location>3. Source identification</section_header_level_1>
<section_header_level_1><location><page_2><loc_52><loc_25><loc_66><loc_26></location>3.1. Opticalimaging</section_header_level_1>
<text><location><page_2><loc_52><loc_12><loc_95><loc_24></location>Optical images are available for all our fields in the SuperCOSMOS Sky Survey (Hambly et al. 2001b). The SuperCOSMOS data primarily originate from scans of the UK Schmidt and Palomar POSS II blue, red and near-IR sky surveys. The ESO Schmidt R and Palomar POSS-I E surveys have also been scanned to provide an early epoch red measurement. The database hosting the SuperCOSMOS Science Archive (SSA) contains two main tables that hold the object catalogues. The Detection table contains a list of detected</text>
<figure>
<location><page_3><loc_7><loc_71><loc_51><loc_93></location>
<caption>Fig. 1. Distribution of the sky coverage as a function of X-ray flux in the 0.5-4.5keV energy band for the di ff erent cameras. The XWAS covers a total sky area of ∼ 11.3 deg 2 , calculated using all EPIC cameras after correcting for overlaps.</caption>
</figure>
<text><location><page_3><loc_7><loc_50><loc_50><loc_61></location>objects on each scanned plate. Detections on the di ff erent plates are merged into a single source catalogue, the Source table, that contains multi-colour data, given that each field is covered by four plates in passbands BJ , R and I (with R being covered twice at di ff erent times, namely R1 and R2 ). Extensive details on the surveys, the scanning process and the raw parameters extracted can be found under the SuperCOSMOS Sky Survey pages 2 and in Hambly et al. (2001b).</text>
<text><location><page_3><loc_7><loc_23><loc_50><loc_50></location>Our sample comprises both point-like and extended optical objects. The classMag SuperCOSMOS parameters have been used as magnitudes in the di ff erent bands all converted to the Vega magnitude scale, hereafter and in the published tables of XWAS data. The most accurate photometric measurement from the plates depends on image morphology, and two di ff erent calibrations are applied to extended and point-like sources. However, one should note that the image classifier is not perfect and sometimes classMag may not be the best photometric estimator for a given object. In the published XWAS catalogue we provide the SuperCOSMOS identifier so the user can return to the original tables and select either point-like or extended magnitudes if preferred. A 0.3 mag uncertainty can be adopted for SuperCOSMOS magnitudes (Hambly et al. 2001a). These uncertainties account for the photometric accuracy of the plates and the di ff erent photographic emulsions used at di ff erent epochs. However, BJ -R colours are expected to have an accuracy of ∼ 0.12 mag (for details, see Hambly et al. 2001b). Note that when using R band photometry, R2 has been preferred due to its higher signal-to-noise ratio and better calibration when compared to R1 as noted in the documentation.</text>
<text><location><page_3><loc_7><loc_12><loc_50><loc_23></location>Detections in the SuperCOSMOS BJ band have been primarily used for cross-correlation with the X-ray source positions due to their smaller position errors. Optical candidate counterparts were originally selected to be up to 10 arcsec from the X-ray position, although for the construction of the final catalogue a more stringent limit was imposed (see Sect. 5). If no match was found, R2 , R1 or I (in that hierarchical order) have been used for the counterpart selection. Further selection criteria imposed for</text>
<table>
<location><page_3><loc_52><loc_56><loc_95><loc_90></location>
<caption>Table 1. Optical spectroscopic observations. RA and Dec refer to the field centre of the 2dF observations.</caption>
</table>
<text><location><page_3><loc_52><loc_51><loc_95><loc_53></location>the spectroscopic observations will be detailed in the following section.</text>
<section_header_level_1><location><page_3><loc_52><loc_47><loc_70><loc_48></location>3.2. Opticalspectroscopy</section_header_level_1>
<text><location><page_3><loc_52><loc_31><loc_95><loc_46></location>We obtained optical multi-fibre spectroscopy of the X-ray sources with the Anglo Australian Telescope (AAT) Two Degree Field (2dF; Lewis et al. 2002). Sources with X-ray counterparts having a 0.5 -4.5keV flux ≥ 10 -14 erg s -1 cm -2 were prioritised ( ∼ 2500 sources). The selected energy range was chosen to maximise the XMM-Newton EPIC sensitivity. This band is a good compromise between a broad passband (to favour throughput) and a narrow passband (to minimize non-uniformities in the selection function due to di ff erent source spectra). The 0.5 keV threshold was imposed to reject very soft photons and reduce the strong bias against absorbed sources occurring when selecting at softer energies.</text>
<text><location><page_3><loc_52><loc_14><loc_95><loc_30></location>Candidates for spectroscopy were initially selected above R ∼ 21, excluding the targets of the XMM-Newton observations. About 1200 objects ( ∼ 21% of all sources in the 68 XMMNewton observations) fulfilled these criteria. The 2dF provides more fibres per field than required for this programme. A significant fraction of the spectroscopic fibres were placed on lower probability counterparts, allowing for lower X-ray fluxes and fainter optical magnitudes (up to R = 21 . 66) to be reached for a number of cases. Those X-ray sources with SuperCOSMOS counterpart o ff sets > 5 arcsec were entered with a low priority into the 2dF fibre positioning software, to allow for detection in case that they might be related to extended objects - e.g. galaxy clusters.</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_13></location>We obtained optical spectroscopic observations for 27 2dF fields for the potential counterparts of a total of ∼ 3000 Xray detections. General information for the observed fields</text>
<text><location><page_4><loc_7><loc_62><loc_50><loc_93></location>is presented on Table 1. Only one optical candidate per Xray source could be observed given that 2dF fibres cannot be positioned closer than 20 arcsec from each other. Fibres, with a diameter of ∼ 2.1 arcsec, were placed at the positions of the optical counterparts derived from SuperCOSMOS. Observations of one hour per field were typically performed, normally split into in 3 exposures of 1200 s to enable cosmic ray rejection. The XWAS 2dF spectroscopic observations provide an e ff ective resolution of λ/δλ ∼ 600 over a wavelength range ∼ 38508250 Å and reach a S / N of ∼ 5 at 5500 Å for V = 21mag. This is su ffi cient to provide a reliable object classification and redshift determination, together with a reasonable characterisation of the optical continuum shape for most of the objects. However, not all objects could be classified using this wavelength coverage and signal-to-noise ratio. Calibration lamp and flat-field exposures were taken before or after each science exposure, and observations of standards were performed in order to achieve the flux calibration of the targets. A number of exposures su ff ered from problems with the atmospheric dispersion corrector (ADC Lewis et al. 2002) or from non-optimal observing conditions such as cloud, poor seeing or the aurora. Spectra taken when the ADC was malfunctioning have distorted shapes due to wavelength-dependent light loss, particularly in the blue, but in many cases the spectra were still useful for identification.</text>
<text><location><page_4><loc_7><loc_45><loc_50><loc_62></location>The initial data reduction was carried out using the 2dF data reduction software 3 (2dfdr). This included bias and dark subtraction, flat fielding, tram-line mapping to the fibre locations on the CCD, fibre extraction, arc identification, wavelength calibration, fibre throughput calibration and sky subtraction. Flux calibration, removal of the telluric absorption features, and improvement of the sky subtraction were performed with the IRAF 4 software package. Wavelength calibration accuracy is always better than 0.5 Å in the residuals. However, the flux cali bration can only be considered as a calibration of the wavelengthdependence of the throughput, rather than as an absolute calibration, and even the relative flux calibration is not correct for spectra a ff ected by the ADC problem.</text>
<text><location><page_4><loc_7><loc_42><loc_50><loc_44></location>Henceforth, the fibre coordinates will be considered the reference position of our objects.</text>
<section_header_level_1><location><page_4><loc_7><loc_38><loc_26><loc_40></location>4. Source classification</section_header_level_1>
<text><location><page_4><loc_7><loc_32><loc_50><loc_37></location>Optical spectroscopy is crucial for determining the source type and redshift. Optical spectra have been screened and analysed in order to derive corresponding spectroscopic classification according to the following criteria.</text>
<text><location><page_4><loc_7><loc_18><loc_50><loc_32></location>Extragalactic sources are classified as broad-line active galactic nuclei (BLAGN) when their optical spectra are characterised by the presence of at least one emission line with FWHM > 1000 km s -1 , usually the H Balmer series, Mg ii , C iii ], C iv and / or Ly α . Those sources exhibiting emission lines which all have FWHM < 1000 km s -1 are classified as narrow emission line galaxies (NELGs). We did not attempt any intermediate classification, therefore types 1 to 1.5 Seyferts are included within the BLAGN category. NELG comprise type 1.8 to 2, H ii galaxies, starburst galaxies, narrow line Seyfert 1 galaxies and low ionisation nuclear emission-line regions</text>
<text><location><page_4><loc_52><loc_79><loc_95><loc_93></location>(LINERs). Counterparts with pure absorption line spectra and a spectral shape corresponding to a galaxy are classified as absorption line galaxies (ALGs). Optical images were screened to look for possible evidence of a galaxy concentration typical of clusters, although our final sample does not include any of these. This is due to several factors: (1) the centroid of the X-ray detection did not fulfil the criteria for counterpart selection probably due to the extended nature of the objects, and (2) the software for X-ray source detection is optimised for point-like sources and misses very extended or low surface brightness objects.</text>
<text><location><page_4><loc_52><loc_70><loc_95><loc_79></location>We note that we cannot apply emission line diagrams for source characterisation, as typical emission lines used for that purpose (e.g. H α ) are usually shifted out from the observing window due to the restricted wavelength coverage of the spectroscopic observations. In addition, in some cases the host galaxy H β absorption can mask any emission at that position and prevents us from using it as a useful AGN indicator.</text>
<text><location><page_4><loc_52><loc_60><loc_95><loc_69></location>Regarding the Galactic population, X-ray sources with a stellar optical spectrum are labelled as star . A detailed study of the stellar population of this survey is beyond the scope of this paper. Most of them are expected to be active coronal stars showing X-ray spectra generally peaking at ∼ 1 keV and dominated by soft X-ray line emission, as found in the XMMNewton Galactic Plane Survey (Motch et al. 2010).</text>
<text><location><page_4><loc_52><loc_54><loc_95><loc_60></location>We obtained identifiable spectra for 1250 fibres. 2dF identified sources previously classified according to NED 5 agree with our classification except for a few exceptions, some of them probably due to a di ff erent instrumental resolution or distinct criteria in the class determination (see Appendix A).</text>
<section_header_level_1><location><page_4><loc_52><loc_50><loc_72><loc_51></location>5. Counterpart selection</section_header_level_1>
<text><location><page_4><loc_52><loc_27><loc_95><loc_48></location>Given that sources were originally selected from an early epoch processing of the X-ray data, we have performed the correlation of our reference fibre positions for the identified objects with the most recent version of the XMM-Newton serendipitous source catalogue 6 , the 2XMMi-DR3. This has been done to take advantage of the significant improvements over the previous data processing system, so we can obtain a better parametrisation of the X-ray sources and the removal of possible spurious detections. Three XMM-Newton fields were excluded from the 2XMMi-DR3 catalogue because they were seriously a ff ected by high background flares, so the clean net exposure time was lower than the threshold used for the XMM-Newton pipeline. These were independently processed by us following the same recipe as in the pipeline, and were included here for cross correlation with sources with identified optical 2dF spectra. Fibre positions were also re-cross matched against SuperCOSMOS to obtain the final source photometry 7 .</text>
<text><location><page_4><loc_52><loc_17><loc_95><loc_26></location>Candidate counterparts derived from optical spectroscopy had to be either within 4 times the statistical error (at 90% confidence) on the X-ray position determination or within 4 arcsec from the position of the X-ray source. This last criterion was used to accommodate any residual in the astrometric calibration of the X-ray EPIC images. This coincides with the overall astrometric accuracy found for the 2XMM catalogue</text>
<text><location><page_5><loc_51><loc_79><loc_52><loc_87></location>Cumulative count</text>
<figure>
<location><page_5><loc_7><loc_71><loc_52><loc_94></location>
<caption>Fig. 2. Histogram of the o ff sets between the optical source (fibre position) and the X-ray source centroid for spectroscopically identified objects. Vertical lines mark 68%, 90% and 95% of the integration of the distribution.</caption>
</figure>
<text><location><page_5><loc_7><loc_58><loc_50><loc_61></location>(Watson et al. 2009), ensuring the X-ray / optical coincidence. A total of 963 sources fulfilled those restrictions.</text>
<text><location><page_5><loc_7><loc_37><loc_50><loc_58></location>After screening all spectroscopically identified sources, we concluded that for 14 cases the X-ray detection software detects a single source while several objects appear on the visual inspection of the X-ray image. These cases have been rejected so that the quality of the sample is not compromised. This is because the characterisation of such X-ray counterparts is ambiguous due to the contribution of emission from an additional object. In all cases the X-ray detection is extended and / or has low detection likelihood ( /lessorsimilar 20, which is the threshold used for X-ray sources in e.g. Mateos et al. (2010)). Other sources have been removed after further screening due to the following reasons: the recorded X-ray emission is contaminated by source photons from the target of the observation (2 sources), the centre of the X-ray emission is coincident with a di ff erent optical source (3), the fibre is located between two optical sources (3), the optical source is located close to a very bright optical object (1).</text>
<text><location><page_5><loc_7><loc_10><loc_50><loc_37></location>The final XWAS catalogue includes 940 objects. We assume that the di ff erence with the number of identified fibres (1250) is due to (a) our more restrictive assumptions in terms of opticalto-X-ray o ff set with respect to the original counterpart selection criteria, (b) di ff erences in the XMM-Newton software used for source determination as regards the version used for the original selection, and (c) the screening process. All these were needed in order to guarantee the highest possible quality catalogue. Fig. 2 shows the histogram of the X-ray to optical angular o ff sets for spectroscopically identified sources. The integration of this distribution shows that for 68%, 90% and 95% of the sample the optical counterpart lies closer than 1.2 arcsec, 2.7 arcsec and 4.0 arcsec respectively with respect to the X-ray position. Source populations in our sample can be summarised as 65% BLAGN, 16% NELGs, 6% ALGs and 13% stars. Fig. 3 shows examples of the di ff erent source types. We checked for spurious matches by cross-correlating almost 4000 random positions in the sky with SuperCosmos, the random positions obtained by shifting our source positions by ± 1 arcmin in RA and dec. We found contamination from spurious counterparts of only ∼ 5% within 4 times the statistical error or 4 arcsec.</text>
<figure>
<location><page_5><loc_53><loc_71><loc_96><loc_94></location>
<caption>Fig. 4. Cumulative count of X-ray sources as a function of flux in the 0.5-4.5 keV energy band. The total number of detections in the original 68 XMM-Newton observations (5675 sources) is represented by the solid line. Sources in the XWAS are shown by the dashed line.</caption>
</figure>
<figure>
<location><page_5><loc_52><loc_39><loc_95><loc_61></location>
<caption>Fig. 5. Distribution of the optical magnitude for all X-ray sources in the XWAS fields (solid line). The corresponding histogram of identified sources in the XWAS sample is shown by the dashed line).</caption>
</figure>
<text><location><page_5><loc_52><loc_16><loc_95><loc_29></location>We have estimated the completeness of our sample by deriving the number of identified matches with respect to the total number of sources in the XMM-Newton fields (see Fig. 4). In addition, we show our spectroscopic success rate as a function of the optical magnitude. In Fig. 5 we plot the distribution of BJ magnitudes for the counterparts of all X-ray sources in the XWAS fields in contrast to the distribution for objects successfully identified. There we can see that at magnitudes brighter than BJ = 20mag our spectroscopic identification rate is ∼ 80%, while this is ∼ 30% for 20 < BJ < 24.</text>
<text><location><page_5><loc_52><loc_10><loc_95><loc_16></location>We note that, given the SuperCOSMOS limiting optical magnitude, our sample could be biased towards bright objects. In order to check and quantify this limitation, we analysed additional observations in a few selected XWAS fields performed with the Wide Field Camera (WFC) on the Isaac Newton</text>
<figure>
<location><page_6><loc_8><loc_49><loc_93><loc_92></location>
<caption>Fig. 3. Optical spectra of the di ff erent source types identified in the XWAS. Top left: BLAGN at z = 0.152 - XWAS J231658.6423852. Top right: NELG at z = 0.043 - XWAS J033703.3-251456. Bottom left: ALG at z = 0.056 - XWAS J231756.3-421333. Bottom right: star - XWAS J015319.4-135552. The positions of prominent emission and absorption lines are marked on the spectra.</caption>
</figure>
<text><location><page_6><loc_7><loc_30><loc_50><loc_42></location>Telescope (INT). Typical exposure times of 600s were used for observations in the g ' and r ' Sloan Digital Sky Survey filters. This produced images with limiting magnitude for point-like sources down to r ' ∼ 23 -24 for ∼ 1 -1.5 arcsec seeing, typical in our observing runs. Data reduction was performed following the WFC pipeline procedures under the Cambridge Astronomy Survey Unit 8 (CASU). The WFC images were analysed using standard techniques including de-bias, non-linearity and flat field corrections (see Gonz'alez-Solares et al. 2011, for a full description). Errors in magnitudes are assumed to be of 0.2 mag.</text>
<text><location><page_6><loc_7><loc_16><loc_50><loc_28></location>Objects in the XWAS were cross-matched with detections in the WFC images. We used colour equations derived as in Gonz'alez-Solares et al. (2011) to obtain red WFC magnitudes in the Vega system that were compared with the corresponding SuperCosmos counterparts. Magnitudes of both observatories agree quite well, with a mean di ff erence of ∼ 0.1 mag. From the comparison, we expect up to 8% of sources having fainter magnitudes due to our limiting optical magnitude, which is the fraction of sources with SuperCosmos counterparts but having an additional viable fainter match in the WFC.</text>
<section_header_level_1><location><page_6><loc_52><loc_41><loc_94><loc_42></location>6. Overall characteristics of the source populations</section_header_level_1>
<text><location><page_6><loc_52><loc_16><loc_95><loc_40></location>To illustrate the overall population sampled in the XWAS, Fig. 6 shows the flux distribution of the XWAS sources in the 0.5 -4.5 keV band. We have used the EPIC fluxes appearing in the 2XMMi-DR3 catalogue. These are derived from the band count rates multiplied by a filter and camera-dependent energy factor (Mateos et al. 2009). This conversion assumes a spectral model consisting of a power-law with a continuum spectral slope Γ= 1.7 and a photoelectric absorption N H = 3 × 10 20 cm -2 (for a general description, see the XMM-Newton science survey centre memo, SSC-LUX TN-0059). Then, the EPIC flux in each band is the mean value of all cameras weighted by the errors. The model assumed in deriving the fluxes will be a fair representation for BLAGN, but less so for the other types of sources. We have included the correction for the Galactic column density using XSPEC simulations of a power-law model ( Γ= 1.7) and the Galactic N H of each individual source for the count rate to flux conversion. The estimated correction values are always less than a factor of 2. No attempt has been made to correct the fluxes for absorption of material intrinsic to the source.</text>
<figure>
<location><page_7><loc_7><loc_70><loc_50><loc_94></location>
<caption>Fig. 6. X-ray 0.5 -4.5 keV flux distribution of sources with spectroscopic optical identification in the XWAS. Blue solid line: BLAGN; red dotted line: NELG; green dashed line: ALG; black dash-dotted line: star.</caption>
</figure>
<section_header_level_1><location><page_7><loc_7><loc_61><loc_36><loc_62></location>6.1. Redshiftandluminositydistributions</section_header_level_1>
<text><location><page_7><loc_7><loc_30><loc_50><loc_60></location>The redshifts were obtained as follows. First, each spectrum was manually inspected, classified, and an approximate redshift was determined from the wavelengths of the most prominent features, usually either emission or absorption lines. Then, the redshift was refined by cross-correlating the spectrum with a suitable template. The redshift distribution of the XWAS sources for di ff erent source types is displayed in Fig. 7. From this histogram we can see that the distribution of BLAGN is broader than those of NELGs and ALGs. We derive the mean redshift of the BLAGN population to be 〈 z 〉 = 1 . 5, whereas the objects classified as NELGs and ALGs peak at lower redshift 〈 z 〉 = 0 . 3. Both values are comparable to those found in surveys with similar depths (e.g. Barcons et al. 2007), while deeper surveys tend to find higher peak values for the non-BLAGN population (e.g. Silverman et al. 2005; Mateos et al. 2005; Xue et al. 2011). We are able to detect BLAGN out to z ∼ 4 in these medium depth observations. However, the large majority of those sources which are not BLAGN (all except for 4 NELGs) have z < 0 . 6. The steep drop in the number of NELGs and ALGs above this redshift is almost certainly due to an optical selection bias, the combination of the optical faintness of these sources ( R /greaterorsimilar 21) and the redshifting of the most easily-identifiable features outside the observing window.</text>
<text><location><page_7><loc_7><loc_22><loc_50><loc_30></location>X-ray luminosities in the 0.5-4.5 keV energy band have been computed for the extragalactic objects of the sample using the redshifts obtained in our spectroscopic observations. In order to shift such values to a common rest-frame passband for all sources, a K-correction k ( z ) (Hogg et al. 2002) has been taken into account as</text>
<formula><location><page_7><loc_23><loc_20><loc_50><loc_21></location>k ( z ) = (1 + z ) Γ -2 (1)</formula>
<text><location><page_7><loc_7><loc_10><loc_50><loc_19></location>where Γ= 1.7 is the spectral photon index used for the count rate to flux conversion. X-ray luminosities (not corrected for intrinsic absorption) of the extragalactic sources as a function of redshift are presented in Fig. 8. The sample contains both Seyfert-like AGN and Quasi Stellar Objects (QSO). This is because the overall luminosity distribution is centred around 10 44 erg s -1 -which is the quantity commonly used to separate Seyferts and</text>
<table>
<location><page_7><loc_56><loc_82><loc_91><loc_88></location>
<caption>Table 2. General characteristics of the di ff erent spectroscopic types of extragalactic objects. Standard deviations are shown in brackets.</caption>
</table>
<figure>
<location><page_7><loc_52><loc_58><loc_95><loc_81></location>
<caption>Fig. 7. Redshift distribution of the XWAS objects coded by source type.</caption>
</figure>
<text><location><page_7><loc_52><loc_45><loc_95><loc_51></location>QSOs - where the bulk of the X-ray emission is produced as derived from the AGN X-ray luminosity function. Average properties of the extragalactic types are presented in Table 2. Note that the large standard deviations in the table are indicative of the large parameter space covered by the XWAS.</text>
<text><location><page_7><loc_52><loc_20><loc_95><loc_45></location>Given that many of the traditional optical signatures of AGN (i.e. evident emission lines in optical spectra) are not present in obscured sources, high X-ray luminosity becomes our single discriminant for supermassive black hole accretion in a number of cases. Sources optically classified as NELGs with X-ray luminosities exceeding 10 42 erg s -1 (73 % of the NELGs) are unlikely to be powered by star formation, and so this limit is placed in order to avoid objects dominated by star formation and X-ray binaries. Therefore they should be classified as type 2 AGN. In particular, the luminosity of the 3 NELGs exceed 10 44 erg s -1 , and therefore qualify as type 2 QSOs by standard X-ray astronomy definitions. Two XWAS sources have been included in the sample of type 2 QSOs of Krumpe et al. (2008) solely based on their optical spectra. It is worth mentioning that at the lower activity end L X < 10 42 erg s -1 , LINERs have been found to host active nuclei in a high number of cases (80%, e.g. Gonz'alez-Mart'ın et al. 2009). However, given t hat our classification lacks detail in that respect we cannot place further constraints on that particular class of activity.</text>
<text><location><page_7><loc_52><loc_10><loc_95><loc_20></location>There are 31 sources in the ALG class (52%) with luminosities beyond 10 42 erg s -1 . Sources with such properties are commonly identified as X-ray bright optically normal galaxies (XBONGs Fiore et al. 2000; Barger et al. 2001; Comastri et al. 2002; Georgantopoulos & Georgakakis 2005). They are usually found to host either heavily obscured or low luminosity AGN. The lack of emission lines in the optical spectra is commonly attributed to several factors, such as the</text>
<table>
<location><page_8><loc_11><loc_83><loc_46><loc_88></location>
<caption>Table 3. Mean optical colours and hardness ratios with their corresponding standard deviations (in brackets) for the di ff erent spectroscopic types of sources.</caption>
</table>
<text><location><page_8><loc_7><loc_71><loc_50><loc_80></location>faintness of the AGN with respect to the host galaxy or a non appropriate wavelength coverage of the optical spectrum (e.g. Moran et al. 2002; Severgnini et al. 2003; Caccianiga et al. 2007; Krumpe et al. 2007). Another argument that points to the presence of an active nucleus in NELGs and ALGs with luminosities higher than 10 42 erg s -1 is that they have X-rayto-optical flux ratios typical of AGN (see Sect. 6.4).</text>
<section_header_level_1><location><page_8><loc_7><loc_67><loc_29><loc_68></location>6.2. Opticalcolourdistributions</section_header_level_1>
<text><location><page_8><loc_7><loc_48><loc_50><loc_66></location>BLAGNare normally characterised by bluer optical colours than NELGs. This can also be seen in the average colours of our distributions, presented in Table 3, where the average 〈 Bj -R 〉 is 0.96 for the former and 1.44 for the latter. In Fig. 9 (left panel) we have plotted the Bj -R colour distribution for the di ff erent extragalactic source types. For the R -I colour histogram, shown in the right panel of Fig. 9, the average value for all populations is very similar, while a broader scatter on the distribution is seen for BLAGN in contrast to NELGs and ALGs. The KolmogorovSmirnov two-sample statistic has been estimated for the di ff erent colours. The small values of the significance level of the K-S test for the distinct populations (10 -11 and 0.04 for the Bj -R and R -I respectively) imply that the cumulative distribution of the two samples are significantly di ff erent.</text>
<section_header_level_1><location><page_8><loc_7><loc_45><loc_27><loc_46></location>6.3. X-raycolourdistribution</section_header_level_1>
<text><location><page_8><loc_7><loc_29><loc_50><loc_43></location>X-ray spectral analysis of sources in our sample can only be performed in a limited number of cases. A crude spectral determination is available through the source X-ray colour, known as hardness ratio (HR). This is obtained by combining corrected count rates from di ff erent energy bands. The HR used here is defined as HR = ( S h -S s) / ( S h + S s) where S h and S s are the count rates in the hard (2 -10keV) and soft (0.5 -2keV) bands respectively for a given source. By definition, -1 ≤ HR ≤ + 1. Values close to -1 indicate that the source has an extremely soft spectrum, while very hard or heavily absorbed sources are characterised by values close to + 1.</text>
<text><location><page_8><loc_7><loc_15><loc_50><loc_29></location>Fig. 10 shows the EPIC-pn hardness ratio distribution (90% of the total sample, i.e. sources observed with the EPIC-pn camera with detections in the individual soft and hard X-ray energy bands), where each population has been independently normalised. NELGs are expected to be absorbed sources, therefore we have simulated powerlaw spectra with X-ray slope of 1.7 and a variety of absorption values at the typical redshift of our sources 〈 z 〉 = 0.3. The hardness ratios corresponding to those spectra are shown as vertical lines in the figure. On average, the softest sources are the stars, followed by ALGs, BLAGN and NELGs (see also Table 3).</text>
<text><location><page_8><loc_7><loc_10><loc_50><loc_15></location>ALGs and NELGs have very similar redshift distribution, so one can directly compare the luminosity distributions of the two populations. On average, we find that ALGs are less luminous than NELGs for the same redshift range (3 × 10 42 vs</text>
<figure>
<location><page_8><loc_51><loc_70><loc_95><loc_93></location>
<caption>Fig. 10. Hardness ratio distribution of sources in the XWAS. Vertical lines show the hardness ratios corresponding to a source of z = 0.3 with a spectral slope of Γ= 1.7 subject to di ff erent absorption values.</caption>
</figure>
<text><location><page_8><loc_52><loc_52><loc_95><loc_61></location>9 × 10 42 erg s -1 ). This, in addition to the fact that ALGs are less absorbed than NELGs, is an indication that the non-active optical appearance of the ALGs is most likely due to a host galaxy e ff ect, i.e. the emission lines and AGN continnum are outshone by the stellar continuum as also found in Moran et al. (2002); Severgnini et al. (2003); Mateos et al. (2005); Page et al. (2006).</text>
<section_header_level_1><location><page_8><loc_52><loc_49><loc_72><loc_50></location>6.4. X-ray-to-opticalfluxratio</section_header_level_1>
<text><location><page_8><loc_52><loc_35><loc_95><loc_48></location>A classical approach extensively used in X-ray surveys as a proxy for detecting obscured sources is the so-called Xray-to-optical flux ratio ( f X / f opt ≡ X / O ) diagnostic diagram (Maccacaro et al. 1988). Previous analyses have shown that Xray selected unobscured AGN have typical X / O between 0.1 and 10 (Fiore et al. 2003, and references therein). Flux ratios below 0.1 are typical of stars and normal galaxies; and ratios higher than 10 would correspond to heavily obscured AGN (but not Compton-thick), high redshift galaxy clusters and extreme BL Lac objects.</text>
<text><location><page_8><loc_52><loc_30><loc_95><loc_35></location>Here, the X-ray flux is defined as the 0.5 -4.5 keV flux not corrected for Galactic absorption (the correction is not significant for our sources). For the optical flux we have used that in the red band, computed as</text>
<formula><location><page_8><loc_63><loc_27><loc_95><loc_28></location>log( f opt) = -0 . 4 R + log( fR 0 δλ ) (2)</formula>
<text><location><page_8><loc_52><loc_21><loc_95><loc_26></location>where fR 0 = 1 . 74 × 10 -9 erg s -1 cm -2 as the zero-point for R (Zombeck 1990) and δλ = 2200 Å as the FWHM of the red filter. We prefer to use R = R2 for SuperCOSMOS sources (or R 1 if there is not R 2 magnitude available). Therefore, we find</text>
<formula><location><page_8><loc_62><loc_18><loc_95><loc_19></location>log( X / O ) = log( f X) + 0 . 4 R + 5 . 42 (3)</formula>
<text><location><page_8><loc_52><loc_10><loc_95><loc_17></location>Fig. 11 shows the X-ray-to-optical flux ratio as a function of the 0.5 -4.5 keV X-ray luminosity for di ff erent extragalactic source types. The majority of sources detected in the 0.5 -4.5 keV band have X-ray-to-optical flux ratios of typical AGN. We note that only one source in our sample has X / O > 10. A small number was a priori expected given that the</text>
<figure>
<location><page_9><loc_7><loc_70><loc_95><loc_93></location>
<caption>Fig. 8. Observed X-ray luminosities in the 0.5 -4.5 keV energy band as a function of redshift for extragalactic sources. Left panel: BLAGN. Right panel: NELG (red squares) and ALG (green triangles).</caption>
</figure>
<figure>
<location><page_9><loc_7><loc_42><loc_50><loc_65></location>
<caption>Fig. 9. Histograms of the Bj -R and R -I colour distributions in the left and right panels respectively.</caption>
</figure>
<text><location><page_9><loc_58><loc_43><loc_61><loc_44></location>-0.5</text>
<text><location><page_9><loc_66><loc_43><loc_67><loc_44></location>0.0</text>
<text><location><page_9><loc_73><loc_43><loc_75><loc_44></location>0.5</text>
<text><location><page_9><loc_80><loc_43><loc_82><loc_44></location>1.0</text>
<text><location><page_9><loc_87><loc_43><loc_89><loc_44></location>1.5</text>
<text><location><page_9><loc_74><loc_42><loc_77><loc_43></location>R - I</text>
<text><location><page_9><loc_7><loc_16><loc_50><loc_37></location>initial threshold imposed on the optical flux of our sources was relatively high. The BLAGN distribution does not show any trend. Due to the absence of broad emission lines in NELGs and ALGs, we expect their optical R band emission to be dominated by the host galaxy given that the nuclear optical / UV emission is completely blocked (or strongly reduced). Therefore, X / O is roughly a flux ratio between the nuclear X-ray and the host galaxy light emissions. As can be seen in the plot, there is a correlation between X / O and the hard X-ray luminosity for non-BLAGN in such a way that higher luminosity sources tend to have higher X / O . The dashed diagonal line in Fig. 11 indicates the best linear regression only using detections between log ( X / O ) and log( L 0 . 5 -4 . 5 keV) for non-BLAGN with L 0 . 5 -4 . 5 keV > 10 42 erg s -1 (those expected to harbour a hidden AGN) and extrapolated to lower luminosities (similar to that found in Fiore et al. 2003).</text>
<section_header_level_1><location><page_9><loc_7><loc_13><loc_21><loc_14></location>7. The catalogue</section_header_level_1>
<text><location><page_9><loc_7><loc_10><loc_50><loc_12></location>The catalogue consists of 940 entries, one per object. It contains information about the X-ray detection, optical imaging and</text>
<text><location><page_9><loc_52><loc_29><loc_95><loc_37></location>optical spectroscopy for every object. Only a number of representative parameters of the 2XMM-DR3i and SuperCOSMOS archive appear in the XWAS. For additional information, we invite the user to search in the original tables. This can be done by looking for the IAUNAME and OBJID columns in the XMMNewton or SuperCOSMOS archives, respectively.</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_28></location>The XWASNAME column represents the name assigned to the XWAS sources. They start with the prefix, XWAS, and then encode the J2000 sky position of the X-ray object. Note that this coincides with the IAUNAME column in the 2XMM-DR3i aside from the prefix, except for the extra 50 sources not included in the XMM-Newton catalogue due to the high background flares (Sect. 5). For those extra objects, we release a separate table with data from the X-ray pipeline processing similar to that in the XMM-Newton catalogue. Some basic X-ray parameters directly extracted from the XMM-Newton survey are included in the released XWAS catalogue. These are the source name, coordinates, positional error and flux in the total 0.5-4.5 keV band. The X-ray luminosity has also been calculated using the redshift of the optical observations and included in the table.</text>
<text><location><page_9><loc_54><loc_64><loc_55><loc_65></location>7</text>
<text><location><page_9><loc_54><loc_61><loc_55><loc_62></location>6</text>
<text><location><page_9><loc_54><loc_59><loc_55><loc_60></location>5</text>
<text><location><page_9><loc_54><loc_56><loc_55><loc_57></location>4</text>
<text><location><page_9><loc_54><loc_53><loc_55><loc_54></location>3</text>
<text><location><page_9><loc_54><loc_50><loc_55><loc_51></location>2</text>
<text><location><page_9><loc_54><loc_47><loc_55><loc_48></location>1</text>
<text><location><page_9><loc_54><loc_44><loc_55><loc_45></location>0</text>
<text><location><page_9><loc_52><loc_50><loc_54><loc_59></location>Fractional count (%)</text>
<figure>
<location><page_10><loc_7><loc_70><loc_50><loc_94></location>
</figure>
<figure>
<location><page_10><loc_52><loc_70><loc_95><loc_94></location>
<caption>Fig. 11. X-ray-to-optical flux ratio (X / O) as a function of the 0.5 -4.5 keV X-ray luminosity for extragalactic sources. The horizontal dotted lines mark the level of X / O = 10, 1 and 0.1 from top to bottom. Left panel: BLAGN. Right panel: NELGs and ALGs. The dashed diagonal line is the best linear regression between log ( X / O ) and log( L 0 . 5 -4 . 5 keV) for NELGs and ALGs with L 0 . 5 -4 . 5 keV > 10 42 erg s -1 (see text for details).</caption>
</figure>
<text><location><page_10><loc_51><loc_63><loc_51><loc_64></location>.</text>
<text><location><page_10><loc_7><loc_45><loc_50><loc_60></location>For the optical information, we have an identifier derived from the 2dF observations, named OPTID. Fibre positioning and separation with respect to the X-ray position are also included, along with the object class and redshift derived from our analysis of the observations. From SuperCOSMOS we have included the OBJID, so the user can get all data from the original tables, plus the SuperCOSMOS magnitudes in the di ff erent bands when possible. When existing, we use the R2 magnitude in the R mag column, otherwise, sources are flagged and we quote the R1 magnitude instead. A subset of columns of the XWAS catalogue is presented in Table 4 and the complete catalogue will only be available in electronic form.</text>
<section_header_level_1><location><page_10><loc_7><loc_42><loc_20><loc_43></location>8. Conclusions</section_header_level_1>
<text><location><page_10><loc_7><loc_30><loc_50><loc_41></location>In this paper we have presented the strategy, production and overall characteristics of the new XMM-Newton Wide Angle Survey. With almost a thousand sources selected in the 0.5-4.5 keV energy band, this is one of the largest X-ray selected samples of spectroscopically identified AGN to date. The catalogue has a large scientific potential given the quality and high number of sources. It complements previous X-ray surveys to yield a qualitative picture of the X-ray sky.</text>
<text><location><page_10><loc_7><loc_21><loc_50><loc_30></location>The XWAS catalogue comprises 940 X-ray objects identified through optical observations performed by the 2dF multi-fibre spectrometer. Sources are distributed over Ω ∼ 11.8 deg 2 in highgalactic latitude XMM-Newton fields (-85 deg < b < -30deg). The large volume covered allows us to sample the bright end of the X-ray luminosity function. Source populations in our survey are 65% BLAGN, 16% NELGs, 6% ALGs and 13% stars.</text>
<text><location><page_10><loc_7><loc_12><loc_50><loc_21></location>Ahigh number of NELGs and ALGs are also presupposed to have an active nucleus given the X-ray luminosity and X-ray-tooptical flux ratios. NELGs are the most absorbed sources in the survey as shown by their X-ray colours. Extragalactic sources with luminosities lower than 10 42 erg s -1 could also have high absorption and host AGN. Indeed, some works suggest that they can include Compton-thick AGN.</text>
<text><location><page_10><loc_7><loc_10><loc_50><loc_12></location>The sample presented here spreads over a large parameter space, in a region of the redshift-luminosity diagram poorly</text>
<text><location><page_10><loc_52><loc_53><loc_95><loc_60></location>covered so far. The BLAGN sample extends out to redshift 4, with an average of 〈 z 〉 = 1.5. The average value for NELGs is 〈 z 〉 = 0.3, and 〈 z 〉 = 0.2 for ALGs. This is in agreement with previous surveys with similar depth. As expected, the BLAGN appear bluer than those galaxies with narrow or no spectral emission lines.</text>
<text><location><page_10><loc_52><loc_42><loc_95><loc_53></location>A similar survey in terms of sky coverage and X-ray flux limits is the XBootes survey, with optical spectroscopy from the AGN and Galaxy Evolution Survey (AGES; Hickox et al. 2009). The authors explore its multiwavelengh properties, but the radio, X-ray, and IR AGN samples only show a mild overlap. However, although it covers a similar X-ray luminosity range to the XWAS, the redshift sampling is quite limited 0 . 25 < z < 0 . 8.</text>
<text><location><page_10><loc_52><loc_35><loc_95><loc_42></location>Due to the large covered volume, one can also perform stacking analyses of the X-ray data to determine the mean X-ray properties of di ff erent populations. In that context, Mateos et al. (2010) derived he mean properties of BLAGN, and the corresponding characteristics of the Fe K α line were presented in Corral et al. (2008).</text>
<text><location><page_10><loc_52><loc_28><loc_95><loc_34></location>The catalogue table can be accessed by direct download or via searches in the major astronomical databases. The XID results database contains additional information including direct links to X-ray and optical thumbnails and optical spectra 9 that have been created for the present catalogue.</text>
<text><location><page_10><loc_52><loc_20><loc_95><loc_28></location>The results presented here can be an anticipation of what will be seen in future planned X-ray surveys. As an example, the XMM-XXL survey (Pierre et al. 2011) will cover two extragalactic regions of 25 deg 2 (at a depth of 5 × 10 -15 erg s -1 cm -2 ), and eROSITA (Predehl et al. 2010) will perform an all-sky survey at a limiting flux of 10 -14 erg s -1 cm -2 ).</text>
<text><location><page_10><loc_52><loc_12><loc_95><loc_19></location>Acknowledgements. XMM-Newton project is an ESA science mission with instruments and contributions directly funded by ESA member states and NASA. This project is based on data obtained with the Anglo Australian Telescope's 2dF multi-fibre spectrograph. PE and AAH acknowledge support from the Spanish Plan Nacional de Astronom'ıa y Astrof'ısica under grant AYA 2009-05705-E. PE, MP, SM, MW and JAT acknowledge support from the UK STFC research council. This work has been supported in part by the German DLR under contract</text>
<table>
<location><page_11><loc_7><loc_64><loc_93><loc_89></location>
<caption>Table 4. Subset of the XWAS including the first 20 sources of the catalogue, ordered by right ascension. Null values have been substituted by 99.99.</caption>
</table>
<unordered_list>
<list_item><location><page_11><loc_7><loc_63><loc_59><loc_64></location>(1) Absorbed X-ray flux in the 0.5-4.5 keV energy band, in units of 10 -14 erg s -1 cm -2 .</list_item>
<list_item><location><page_11><loc_7><loc_62><loc_61><loc_63></location>(2) Logarithm of the absorbed X-ray luminosity in the 0.5-4.5 keV energy band in erg s -1 .</list_item>
</unordered_list>
<text><location><page_11><loc_7><loc_51><loc_50><loc_59></location>numbers 50 OR 0404 and 50 OX 0201. The research leading to these results has received funding from the European Community's Seventh Framework Programme ( / FP7 / 2007-2013 / ) under grant agreement No 229517. MK thanks for the support by the Deutsches Zentrum fur Luft- und Raumfahrt (DLR) GmbH under contract No. FKZ 50 OR 0404. The Space Research Organisation of The Netherlands is supported financially by NWO, the Netherlands Organisation for Scientific Research. AC, RDC and PS acknowledge financial support from ASI (grant n. I / 088 / 06 / 0, COFIS contract and grant n. I 009 / 10 / 0).</text>
<section_header_level_1><location><page_11><loc_7><loc_47><loc_38><loc_48></location>Appendix A: Discrepancies with NED</section_header_level_1>
<text><location><page_11><loc_7><loc_34><loc_50><loc_46></location>A detailed literature search provided a source characterisation (i.e., optical spectral classification and redshift) for 225 XWAS candidate counterparts. We compared 2dF identified sources with those previously classified according to NED. They are considered the same object if both detections are located within 2.5 arcsec and the published redshift is the same ( ± 0.01) than that derived in our analysis. The majority of the NED classifications agree with ours except for a few exceptions, which are presented in Table A.1.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Aims. This programme is aimed at obtaining one of the largest X-ray selected samples of identified active galactic nuclei to date in order to characterise such a population at intermediate fluxes, where most of the Universe's accretion power originates. We present the XMM-Newton Wide Angle Survey (XWAS), a new catalogue of almost a thousand X-ray sources spectroscopically identified through optical observations. Methods. A sample of X-ray sources detected in 68 XMM-Newton pointed observations was selected for optical multi-fibre spectroscopy. Optical counterparts and corresponding photometry of the X-ray sources were obtained from the SuperCOSMOS Sky Survey. Candidates for spectroscopy were initially selected with magnitudes down to R ∼ 21, with preference for X-ray sources having a flux F 0 . 5 -4 . 5keV ≥ 10 -14 erg s -1 cm -2 . Optical spectroscopic observations performed at the Anglo Australian Telescope Two Degree Field were analysed, and the derived spectra were classified based on optical emission lines. Results. We have identified through optical spectroscopy 940 X-ray sources over Ω ∼ 11.8 deg 2 of the sky. Source populations in our sample can be summarised as 65% broad line active galactic nuclei (BLAGN), 16% narrow emission line galaxies (NELGs), 6% absorption line galaxies (ALGs) and 13% stars. An active nucleus is likely to be present also in the large majority of the X-ray sources spectroscopically classified as NELGs or ALGs. Sources lie in high-galactic latitude ( | b | > 20 deg) XMM-Newton fields mainly in the southern hemisphere. Due to the large parameter space in redshift (0 ≤ z ≤ 4 . 25) and flux (10 -15 ≤ F 0 . 5 -4 . 5keV ≤ 10 -12 erg s -1 cm -2 ) covered by the XWAS this work provides an excellent resource to further study subsamples and particular cases. The overall properties of the extragalactic objects are presented in this paper. These include the redshift and luminosity distributions, optical and X-ray colours and X-ray-to-optical flux ratios. Key words. X-ray: general - Surveys - X-rays: galaxies - Galaxies: active",
"pages": [
1
]
},
{
"title": "The XMM-NewtonWide Angle Survey (XWAS)",
"content": "P. Esquej 1 , 2 , 3 , 4 , M. Page 5 , F. J. Carrera 3 , S. Mateos 3 , J. Tedds 2 , M. G. Watson 2 , A. Corral 6 , J. Ebrero 7 , M. Krumpe 8 , 9 , 10 , S. R. Rosen 2 , M. T. Ceballos 3 , A. Schwope 10 , C. Page 2 , A. Alonso-Herrero 3 /star , A. Caccianiga 6 , R. Della Ceca 6 , 11 10 6 O. Gonz'alez-Mart'ın , G. Lamer , P. Severgnini Preprint online version: November 15, 2021",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "According to synthesis models, the growth of supermassive black holes (SMBHs) by accretion over cosmic time is recorded in the X-ray source population which produces the cosmic X-ray background (CXB). Hence, X-ray surveys can be used to constrain the epochs and environments in which SMBHs formed and evolved (Alexander et al. 2003; Hasinger et al. 2005; Gilli et al. 2007). X-ray surveys with high sensitivities and good spatial and spectral resolution are essential for studying the properties of the bulk of X-ray sources. Deep pencil beam surveys are able to detect sources down to very faint fluxes, therefore allowing the detection of typical sources in the sky and contributing to the picture of the early Universe. Among these we can find the Chandra deep field (CDF) surveys (e.g. Alexander et al. 2003; Tozzi et al. 2006; Luo et al. 2008; Xue et al. 2011), and the XMM-Newton deep surveys of the CDF-South (Ranalli et al. in prep.) and the Lockman Hole (Hasinger et al. 2001; Mainieri et al. 2002; Mateos et al. 2005). All-sky surveys like the ROSAT All-Sky Survey (Voges et al. 1999) with shallow exposures but with large sky coverage can observe rare objects with small surface number density, and are able to unveil the bright end of the luminosity function. Serendipitous surveys, covering X-ray fluxes between 10 -12 and 10 -15 erg s -1 cm -2 , fall in between especially designed all-sky programs and dedicated pointed observations. Sources at these intermediate fluxes are responsible for a large fraction of the X-ray background, as they sample the region around the break in the X-ray source counts (Carrera et al. 2007; Mateos et al. 2008). A number of campaigns have been dedicated to the optical-to-radio characterization of X-ray sources selected at di ff erent X-ray depths like the XBootes survey (Murray et al. 2005; Brand et al. 2006), the Extended Groth strip Survey (EGS Georgakakis et al. 2006), the HELLAS2XMM survey (Cocchia et al. 2007; Fiore et al. 2003), the XMM-Newton and Chandra surveys in the COSMOS field (Hasinger et al. 2007; Elvis et al. 2009; Brusa et al. 2010) and the Bright Ultra-Hard XMM-Newton Survey (BUXS; Mateos et al. 2012). Data from XMM-Newton observations have been used to create the largest X-ray catalogue ever produced, the 2XMMi-DR3 (Watson et al. 2009). Specific complete subsets of sources have already been used to investigate cosmological properties such as the X-ray log N - log S distributions and the angular clustering of X-ray sources (Mateos et al. 2008; Ebrero et al. 2009b). Optical imaging and spectroscopy of well-defined datasets from selected XMM-Newton fields have been obtained in order to characterise their X-ray source populations. The XMM-Newton Survey Science Centre (SSC) follow-up and identification (XID) programme is outlined in Watson et al. (2001). Their goals include the detailed characterisation of the dominant X-ray source populations and the discovery of new classes of probable rare sources. The outcome of these samples is currently being used to establish statistical identification criteria in order to characterise the complete XID database (Pineau et al. 2011). The XMMNewton Bright Serendipitous Survey (XBS; Della Ceca et al. 2004; Caccianiga et al. 2008) and X-ray luminosity function (Della Ceca et al. 2008; Ebrero et al. 2009a) have been published together with the XID Medium Survey catalogue (XMS; Barcons et al. 2007), the X-ray source counts and the angular clustering (Carrera et al. 2007), and the X-ray spectral analysis of the active galactic nuclei (Mateos et al. 2005). The XMM-Newton Wide Angle Survey (XWAS) presented here is part of the follow-up programme conducted by the XMM-Newton collaboration. It complements previous surveys in providing a qualitative picture of the X-ray sky. It yields optical and X-ray characterisation of ∼ 1000 objects mainly in the southern hemisphere. Spectroscopic optical observations have been used to provide the redshift and classification of the sources. Published papers based on sources drawn from the XWAS sample include detailed X-ray spectral analysis of the identified broad line active galactic nuclei (BLAGN) (Mateos et al. 2010), stacking of all XID BLAGN spectra (Corral et al. 2008) and a study and X-ray stacking of type II QSOs (Krumpe et al. 2008). This paper is structured as follows: in Sect. 2 we define the XWAS. In Sect. 3 we discuss the multi-band optical imaging and spectroscopic observations conducted on the XMM-Newton target fields. Sect. 4 gives details on the source spectroscopic classification scheme, followed by the counterpart selection procedure in Sect. 5. Section 6 presents the overall source populations. Section 7 describes the catalogue columns and how to obtain the data. Finally, Sect. 8 summarises our main results. Throughout this paper a Λ CDM cosmology of ( Ω m, ΩΛ ) = (0.3, 0.7) and H 0 = 70 km s -1 Mpc -1 will be assumed. Optical magnitudes are given in the Vega system.",
"pages": [
1,
2
]
},
{
"title": "2. The sample",
"content": "The XMM-Newton satellite features high spectral resolution and excellent sensitivity due to the large collecting area of its mirrors coupled with the high quantum e ffi ciency of the EPIC detectors (Jansen et al. 2001). It provides a significant detection of serendipitous sources in addition to the original target. The purpose of the XWAS project is to create a catalogue of X-ray sources detected by XMM-Newton with optical identifications including redshift and classification based on our own optical multi-fibre spectroscopy. The XMM-Newton field selection criteria for the XWAS prioritised those observations with adjacent or overlapping coverage, to take optimum advantage of the field of view of the spectrograph used for the optical observations. The Galactic latitude was restricted so only those fields with | b | > 20 deg were selected in order to avoid high Galactic absorption and source confusion in the Galactic plane. We also required that all XMM-Newton observations had total exposure times of > 10ks and that they were performed in Full Frame mode in the EPIC cameras with thin or medium filters. With these properties, X-ray objects were originally selected from 68 spatially distinct pointing observations, carried out by XMM-Newton between June 2000 and May 2003. After the source selection, optical spectroscopic campaigns were performed. The Galactic absorbing column density along the line of sight for the selected observations is always < 2 × 10 21 cm -2 , which minimises non-uniformities introduced by large values of the Galactic N H. The median Galactic absorption is 3 × 10 20 cm -2 . Of the total 5675 serendipitous X-ray sources found in the 68 exposures, ∼ 3000 objects were selected for optical spectroscopy (see Sect. 3 for selection criteria). To derive the X-ray selection function, we have estimated the sky coverage as a function of the X-ray flux using empirical sensitivity maps for every observation (Carrera et al. 2007; Mateos et al. 2008). For each observation, we have estimated the minimum detectable count rate at each position of the field of view (FOV) for a threshold in detection significance (we have selected L ≥ 6), taking into account the e ff ective exposure and background level across the field of view. For a full description please see Carrera et al. (2007); Mateos et al. (2008). For the count rate to flux conversion, which depends on the camera, observing mode, filter and spectral model we have used the energy conversion factors published in the 2XMMiDR3 documentation 1 . The dependence of the sky coverage on the flux for the various cameras in the 0.5-4.5keV energy band is shown in Fig. 1. The individual cameras survey ∼ 9deg 2 and ∼ 8 deg 2 for the MOSs and pn respectively given that not all fields are observed by the three instruments. The fields targeted by the XWAScovera net sky area of Ω ∼ 11.3 deg 2 , calculated using all three EPIC cameras after correcting for overlaps. In calculating the source counts we have only used flux levels at which sources are detectable over at least 1 deg 2 of sky. This constraint has been imposed to prevent uncertainties in the source count distributions due to low count statistics, and to avoid inaccuracy in the sky coverage calculation at the very faint detection limits.",
"pages": [
2
]
},
{
"title": "3.1. Opticalimaging",
"content": "Optical images are available for all our fields in the SuperCOSMOS Sky Survey (Hambly et al. 2001b). The SuperCOSMOS data primarily originate from scans of the UK Schmidt and Palomar POSS II blue, red and near-IR sky surveys. The ESO Schmidt R and Palomar POSS-I E surveys have also been scanned to provide an early epoch red measurement. The database hosting the SuperCOSMOS Science Archive (SSA) contains two main tables that hold the object catalogues. The Detection table contains a list of detected objects on each scanned plate. Detections on the di ff erent plates are merged into a single source catalogue, the Source table, that contains multi-colour data, given that each field is covered by four plates in passbands BJ , R and I (with R being covered twice at di ff erent times, namely R1 and R2 ). Extensive details on the surveys, the scanning process and the raw parameters extracted can be found under the SuperCOSMOS Sky Survey pages 2 and in Hambly et al. (2001b). Our sample comprises both point-like and extended optical objects. The classMag SuperCOSMOS parameters have been used as magnitudes in the di ff erent bands all converted to the Vega magnitude scale, hereafter and in the published tables of XWAS data. The most accurate photometric measurement from the plates depends on image morphology, and two di ff erent calibrations are applied to extended and point-like sources. However, one should note that the image classifier is not perfect and sometimes classMag may not be the best photometric estimator for a given object. In the published XWAS catalogue we provide the SuperCOSMOS identifier so the user can return to the original tables and select either point-like or extended magnitudes if preferred. A 0.3 mag uncertainty can be adopted for SuperCOSMOS magnitudes (Hambly et al. 2001a). These uncertainties account for the photometric accuracy of the plates and the di ff erent photographic emulsions used at di ff erent epochs. However, BJ -R colours are expected to have an accuracy of ∼ 0.12 mag (for details, see Hambly et al. 2001b). Note that when using R band photometry, R2 has been preferred due to its higher signal-to-noise ratio and better calibration when compared to R1 as noted in the documentation. Detections in the SuperCOSMOS BJ band have been primarily used for cross-correlation with the X-ray source positions due to their smaller position errors. Optical candidate counterparts were originally selected to be up to 10 arcsec from the X-ray position, although for the construction of the final catalogue a more stringent limit was imposed (see Sect. 5). If no match was found, R2 , R1 or I (in that hierarchical order) have been used for the counterpart selection. Further selection criteria imposed for the spectroscopic observations will be detailed in the following section.",
"pages": [
2,
3
]
},
{
"title": "3.2. Opticalspectroscopy",
"content": "We obtained optical multi-fibre spectroscopy of the X-ray sources with the Anglo Australian Telescope (AAT) Two Degree Field (2dF; Lewis et al. 2002). Sources with X-ray counterparts having a 0.5 -4.5keV flux ≥ 10 -14 erg s -1 cm -2 were prioritised ( ∼ 2500 sources). The selected energy range was chosen to maximise the XMM-Newton EPIC sensitivity. This band is a good compromise between a broad passband (to favour throughput) and a narrow passband (to minimize non-uniformities in the selection function due to di ff erent source spectra). The 0.5 keV threshold was imposed to reject very soft photons and reduce the strong bias against absorbed sources occurring when selecting at softer energies. Candidates for spectroscopy were initially selected above R ∼ 21, excluding the targets of the XMM-Newton observations. About 1200 objects ( ∼ 21% of all sources in the 68 XMMNewton observations) fulfilled these criteria. The 2dF provides more fibres per field than required for this programme. A significant fraction of the spectroscopic fibres were placed on lower probability counterparts, allowing for lower X-ray fluxes and fainter optical magnitudes (up to R = 21 . 66) to be reached for a number of cases. Those X-ray sources with SuperCOSMOS counterpart o ff sets > 5 arcsec were entered with a low priority into the 2dF fibre positioning software, to allow for detection in case that they might be related to extended objects - e.g. galaxy clusters. We obtained optical spectroscopic observations for 27 2dF fields for the potential counterparts of a total of ∼ 3000 Xray detections. General information for the observed fields is presented on Table 1. Only one optical candidate per Xray source could be observed given that 2dF fibres cannot be positioned closer than 20 arcsec from each other. Fibres, with a diameter of ∼ 2.1 arcsec, were placed at the positions of the optical counterparts derived from SuperCOSMOS. Observations of one hour per field were typically performed, normally split into in 3 exposures of 1200 s to enable cosmic ray rejection. The XWAS 2dF spectroscopic observations provide an e ff ective resolution of λ/δλ ∼ 600 over a wavelength range ∼ 38508250 Å and reach a S / N of ∼ 5 at 5500 Å for V = 21mag. This is su ffi cient to provide a reliable object classification and redshift determination, together with a reasonable characterisation of the optical continuum shape for most of the objects. However, not all objects could be classified using this wavelength coverage and signal-to-noise ratio. Calibration lamp and flat-field exposures were taken before or after each science exposure, and observations of standards were performed in order to achieve the flux calibration of the targets. A number of exposures su ff ered from problems with the atmospheric dispersion corrector (ADC Lewis et al. 2002) or from non-optimal observing conditions such as cloud, poor seeing or the aurora. Spectra taken when the ADC was malfunctioning have distorted shapes due to wavelength-dependent light loss, particularly in the blue, but in many cases the spectra were still useful for identification. The initial data reduction was carried out using the 2dF data reduction software 3 (2dfdr). This included bias and dark subtraction, flat fielding, tram-line mapping to the fibre locations on the CCD, fibre extraction, arc identification, wavelength calibration, fibre throughput calibration and sky subtraction. Flux calibration, removal of the telluric absorption features, and improvement of the sky subtraction were performed with the IRAF 4 software package. Wavelength calibration accuracy is always better than 0.5 Å in the residuals. However, the flux cali bration can only be considered as a calibration of the wavelengthdependence of the throughput, rather than as an absolute calibration, and even the relative flux calibration is not correct for spectra a ff ected by the ADC problem. Henceforth, the fibre coordinates will be considered the reference position of our objects.",
"pages": [
3,
4
]
},
{
"title": "4. Source classification",
"content": "Optical spectroscopy is crucial for determining the source type and redshift. Optical spectra have been screened and analysed in order to derive corresponding spectroscopic classification according to the following criteria. Extragalactic sources are classified as broad-line active galactic nuclei (BLAGN) when their optical spectra are characterised by the presence of at least one emission line with FWHM > 1000 km s -1 , usually the H Balmer series, Mg ii , C iii ], C iv and / or Ly α . Those sources exhibiting emission lines which all have FWHM < 1000 km s -1 are classified as narrow emission line galaxies (NELGs). We did not attempt any intermediate classification, therefore types 1 to 1.5 Seyferts are included within the BLAGN category. NELG comprise type 1.8 to 2, H ii galaxies, starburst galaxies, narrow line Seyfert 1 galaxies and low ionisation nuclear emission-line regions (LINERs). Counterparts with pure absorption line spectra and a spectral shape corresponding to a galaxy are classified as absorption line galaxies (ALGs). Optical images were screened to look for possible evidence of a galaxy concentration typical of clusters, although our final sample does not include any of these. This is due to several factors: (1) the centroid of the X-ray detection did not fulfil the criteria for counterpart selection probably due to the extended nature of the objects, and (2) the software for X-ray source detection is optimised for point-like sources and misses very extended or low surface brightness objects. We note that we cannot apply emission line diagrams for source characterisation, as typical emission lines used for that purpose (e.g. H α ) are usually shifted out from the observing window due to the restricted wavelength coverage of the spectroscopic observations. In addition, in some cases the host galaxy H β absorption can mask any emission at that position and prevents us from using it as a useful AGN indicator. Regarding the Galactic population, X-ray sources with a stellar optical spectrum are labelled as star . A detailed study of the stellar population of this survey is beyond the scope of this paper. Most of them are expected to be active coronal stars showing X-ray spectra generally peaking at ∼ 1 keV and dominated by soft X-ray line emission, as found in the XMMNewton Galactic Plane Survey (Motch et al. 2010). We obtained identifiable spectra for 1250 fibres. 2dF identified sources previously classified according to NED 5 agree with our classification except for a few exceptions, some of them probably due to a di ff erent instrumental resolution or distinct criteria in the class determination (see Appendix A).",
"pages": [
4
]
},
{
"title": "5. Counterpart selection",
"content": "Given that sources were originally selected from an early epoch processing of the X-ray data, we have performed the correlation of our reference fibre positions for the identified objects with the most recent version of the XMM-Newton serendipitous source catalogue 6 , the 2XMMi-DR3. This has been done to take advantage of the significant improvements over the previous data processing system, so we can obtain a better parametrisation of the X-ray sources and the removal of possible spurious detections. Three XMM-Newton fields were excluded from the 2XMMi-DR3 catalogue because they were seriously a ff ected by high background flares, so the clean net exposure time was lower than the threshold used for the XMM-Newton pipeline. These were independently processed by us following the same recipe as in the pipeline, and were included here for cross correlation with sources with identified optical 2dF spectra. Fibre positions were also re-cross matched against SuperCOSMOS to obtain the final source photometry 7 . Candidate counterparts derived from optical spectroscopy had to be either within 4 times the statistical error (at 90% confidence) on the X-ray position determination or within 4 arcsec from the position of the X-ray source. This last criterion was used to accommodate any residual in the astrometric calibration of the X-ray EPIC images. This coincides with the overall astrometric accuracy found for the 2XMM catalogue Cumulative count (Watson et al. 2009), ensuring the X-ray / optical coincidence. A total of 963 sources fulfilled those restrictions. After screening all spectroscopically identified sources, we concluded that for 14 cases the X-ray detection software detects a single source while several objects appear on the visual inspection of the X-ray image. These cases have been rejected so that the quality of the sample is not compromised. This is because the characterisation of such X-ray counterparts is ambiguous due to the contribution of emission from an additional object. In all cases the X-ray detection is extended and / or has low detection likelihood ( /lessorsimilar 20, which is the threshold used for X-ray sources in e.g. Mateos et al. (2010)). Other sources have been removed after further screening due to the following reasons: the recorded X-ray emission is contaminated by source photons from the target of the observation (2 sources), the centre of the X-ray emission is coincident with a di ff erent optical source (3), the fibre is located between two optical sources (3), the optical source is located close to a very bright optical object (1). The final XWAS catalogue includes 940 objects. We assume that the di ff erence with the number of identified fibres (1250) is due to (a) our more restrictive assumptions in terms of opticalto-X-ray o ff set with respect to the original counterpart selection criteria, (b) di ff erences in the XMM-Newton software used for source determination as regards the version used for the original selection, and (c) the screening process. All these were needed in order to guarantee the highest possible quality catalogue. Fig. 2 shows the histogram of the X-ray to optical angular o ff sets for spectroscopically identified sources. The integration of this distribution shows that for 68%, 90% and 95% of the sample the optical counterpart lies closer than 1.2 arcsec, 2.7 arcsec and 4.0 arcsec respectively with respect to the X-ray position. Source populations in our sample can be summarised as 65% BLAGN, 16% NELGs, 6% ALGs and 13% stars. Fig. 3 shows examples of the di ff erent source types. We checked for spurious matches by cross-correlating almost 4000 random positions in the sky with SuperCosmos, the random positions obtained by shifting our source positions by ± 1 arcmin in RA and dec. We found contamination from spurious counterparts of only ∼ 5% within 4 times the statistical error or 4 arcsec. We have estimated the completeness of our sample by deriving the number of identified matches with respect to the total number of sources in the XMM-Newton fields (see Fig. 4). In addition, we show our spectroscopic success rate as a function of the optical magnitude. In Fig. 5 we plot the distribution of BJ magnitudes for the counterparts of all X-ray sources in the XWAS fields in contrast to the distribution for objects successfully identified. There we can see that at magnitudes brighter than BJ = 20mag our spectroscopic identification rate is ∼ 80%, while this is ∼ 30% for 20 < BJ < 24. We note that, given the SuperCOSMOS limiting optical magnitude, our sample could be biased towards bright objects. In order to check and quantify this limitation, we analysed additional observations in a few selected XWAS fields performed with the Wide Field Camera (WFC) on the Isaac Newton Telescope (INT). Typical exposure times of 600s were used for observations in the g ' and r ' Sloan Digital Sky Survey filters. This produced images with limiting magnitude for point-like sources down to r ' ∼ 23 -24 for ∼ 1 -1.5 arcsec seeing, typical in our observing runs. Data reduction was performed following the WFC pipeline procedures under the Cambridge Astronomy Survey Unit 8 (CASU). The WFC images were analysed using standard techniques including de-bias, non-linearity and flat field corrections (see Gonz'alez-Solares et al. 2011, for a full description). Errors in magnitudes are assumed to be of 0.2 mag. Objects in the XWAS were cross-matched with detections in the WFC images. We used colour equations derived as in Gonz'alez-Solares et al. (2011) to obtain red WFC magnitudes in the Vega system that were compared with the corresponding SuperCosmos counterparts. Magnitudes of both observatories agree quite well, with a mean di ff erence of ∼ 0.1 mag. From the comparison, we expect up to 8% of sources having fainter magnitudes due to our limiting optical magnitude, which is the fraction of sources with SuperCosmos counterparts but having an additional viable fainter match in the WFC.",
"pages": [
4,
5,
6
]
},
{
"title": "6. Overall characteristics of the source populations",
"content": "To illustrate the overall population sampled in the XWAS, Fig. 6 shows the flux distribution of the XWAS sources in the 0.5 -4.5 keV band. We have used the EPIC fluxes appearing in the 2XMMi-DR3 catalogue. These are derived from the band count rates multiplied by a filter and camera-dependent energy factor (Mateos et al. 2009). This conversion assumes a spectral model consisting of a power-law with a continuum spectral slope Γ= 1.7 and a photoelectric absorption N H = 3 × 10 20 cm -2 (for a general description, see the XMM-Newton science survey centre memo, SSC-LUX TN-0059). Then, the EPIC flux in each band is the mean value of all cameras weighted by the errors. The model assumed in deriving the fluxes will be a fair representation for BLAGN, but less so for the other types of sources. We have included the correction for the Galactic column density using XSPEC simulations of a power-law model ( Γ= 1.7) and the Galactic N H of each individual source for the count rate to flux conversion. The estimated correction values are always less than a factor of 2. No attempt has been made to correct the fluxes for absorption of material intrinsic to the source.",
"pages": [
6
]
},
{
"title": "6.1. Redshiftandluminositydistributions",
"content": "The redshifts were obtained as follows. First, each spectrum was manually inspected, classified, and an approximate redshift was determined from the wavelengths of the most prominent features, usually either emission or absorption lines. Then, the redshift was refined by cross-correlating the spectrum with a suitable template. The redshift distribution of the XWAS sources for di ff erent source types is displayed in Fig. 7. From this histogram we can see that the distribution of BLAGN is broader than those of NELGs and ALGs. We derive the mean redshift of the BLAGN population to be 〈 z 〉 = 1 . 5, whereas the objects classified as NELGs and ALGs peak at lower redshift 〈 z 〉 = 0 . 3. Both values are comparable to those found in surveys with similar depths (e.g. Barcons et al. 2007), while deeper surveys tend to find higher peak values for the non-BLAGN population (e.g. Silverman et al. 2005; Mateos et al. 2005; Xue et al. 2011). We are able to detect BLAGN out to z ∼ 4 in these medium depth observations. However, the large majority of those sources which are not BLAGN (all except for 4 NELGs) have z < 0 . 6. The steep drop in the number of NELGs and ALGs above this redshift is almost certainly due to an optical selection bias, the combination of the optical faintness of these sources ( R /greaterorsimilar 21) and the redshifting of the most easily-identifiable features outside the observing window. X-ray luminosities in the 0.5-4.5 keV energy band have been computed for the extragalactic objects of the sample using the redshifts obtained in our spectroscopic observations. In order to shift such values to a common rest-frame passband for all sources, a K-correction k ( z ) (Hogg et al. 2002) has been taken into account as where Γ= 1.7 is the spectral photon index used for the count rate to flux conversion. X-ray luminosities (not corrected for intrinsic absorption) of the extragalactic sources as a function of redshift are presented in Fig. 8. The sample contains both Seyfert-like AGN and Quasi Stellar Objects (QSO). This is because the overall luminosity distribution is centred around 10 44 erg s -1 -which is the quantity commonly used to separate Seyferts and QSOs - where the bulk of the X-ray emission is produced as derived from the AGN X-ray luminosity function. Average properties of the extragalactic types are presented in Table 2. Note that the large standard deviations in the table are indicative of the large parameter space covered by the XWAS. Given that many of the traditional optical signatures of AGN (i.e. evident emission lines in optical spectra) are not present in obscured sources, high X-ray luminosity becomes our single discriminant for supermassive black hole accretion in a number of cases. Sources optically classified as NELGs with X-ray luminosities exceeding 10 42 erg s -1 (73 % of the NELGs) are unlikely to be powered by star formation, and so this limit is placed in order to avoid objects dominated by star formation and X-ray binaries. Therefore they should be classified as type 2 AGN. In particular, the luminosity of the 3 NELGs exceed 10 44 erg s -1 , and therefore qualify as type 2 QSOs by standard X-ray astronomy definitions. Two XWAS sources have been included in the sample of type 2 QSOs of Krumpe et al. (2008) solely based on their optical spectra. It is worth mentioning that at the lower activity end L X < 10 42 erg s -1 , LINERs have been found to host active nuclei in a high number of cases (80%, e.g. Gonz'alez-Mart'ın et al. 2009). However, given t hat our classification lacks detail in that respect we cannot place further constraints on that particular class of activity. There are 31 sources in the ALG class (52%) with luminosities beyond 10 42 erg s -1 . Sources with such properties are commonly identified as X-ray bright optically normal galaxies (XBONGs Fiore et al. 2000; Barger et al. 2001; Comastri et al. 2002; Georgantopoulos & Georgakakis 2005). They are usually found to host either heavily obscured or low luminosity AGN. The lack of emission lines in the optical spectra is commonly attributed to several factors, such as the faintness of the AGN with respect to the host galaxy or a non appropriate wavelength coverage of the optical spectrum (e.g. Moran et al. 2002; Severgnini et al. 2003; Caccianiga et al. 2007; Krumpe et al. 2007). Another argument that points to the presence of an active nucleus in NELGs and ALGs with luminosities higher than 10 42 erg s -1 is that they have X-rayto-optical flux ratios typical of AGN (see Sect. 6.4).",
"pages": [
7,
8
]
},
{
"title": "6.2. Opticalcolourdistributions",
"content": "BLAGNare normally characterised by bluer optical colours than NELGs. This can also be seen in the average colours of our distributions, presented in Table 3, where the average 〈 Bj -R 〉 is 0.96 for the former and 1.44 for the latter. In Fig. 9 (left panel) we have plotted the Bj -R colour distribution for the di ff erent extragalactic source types. For the R -I colour histogram, shown in the right panel of Fig. 9, the average value for all populations is very similar, while a broader scatter on the distribution is seen for BLAGN in contrast to NELGs and ALGs. The KolmogorovSmirnov two-sample statistic has been estimated for the di ff erent colours. The small values of the significance level of the K-S test for the distinct populations (10 -11 and 0.04 for the Bj -R and R -I respectively) imply that the cumulative distribution of the two samples are significantly di ff erent.",
"pages": [
8
]
},
{
"title": "6.3. X-raycolourdistribution",
"content": "X-ray spectral analysis of sources in our sample can only be performed in a limited number of cases. A crude spectral determination is available through the source X-ray colour, known as hardness ratio (HR). This is obtained by combining corrected count rates from di ff erent energy bands. The HR used here is defined as HR = ( S h -S s) / ( S h + S s) where S h and S s are the count rates in the hard (2 -10keV) and soft (0.5 -2keV) bands respectively for a given source. By definition, -1 ≤ HR ≤ + 1. Values close to -1 indicate that the source has an extremely soft spectrum, while very hard or heavily absorbed sources are characterised by values close to + 1. Fig. 10 shows the EPIC-pn hardness ratio distribution (90% of the total sample, i.e. sources observed with the EPIC-pn camera with detections in the individual soft and hard X-ray energy bands), where each population has been independently normalised. NELGs are expected to be absorbed sources, therefore we have simulated powerlaw spectra with X-ray slope of 1.7 and a variety of absorption values at the typical redshift of our sources 〈 z 〉 = 0.3. The hardness ratios corresponding to those spectra are shown as vertical lines in the figure. On average, the softest sources are the stars, followed by ALGs, BLAGN and NELGs (see also Table 3). ALGs and NELGs have very similar redshift distribution, so one can directly compare the luminosity distributions of the two populations. On average, we find that ALGs are less luminous than NELGs for the same redshift range (3 × 10 42 vs 9 × 10 42 erg s -1 ). This, in addition to the fact that ALGs are less absorbed than NELGs, is an indication that the non-active optical appearance of the ALGs is most likely due to a host galaxy e ff ect, i.e. the emission lines and AGN continnum are outshone by the stellar continuum as also found in Moran et al. (2002); Severgnini et al. (2003); Mateos et al. (2005); Page et al. (2006).",
"pages": [
8
]
},
{
"title": "6.4. X-ray-to-opticalfluxratio",
"content": "A classical approach extensively used in X-ray surveys as a proxy for detecting obscured sources is the so-called Xray-to-optical flux ratio ( f X / f opt ≡ X / O ) diagnostic diagram (Maccacaro et al. 1988). Previous analyses have shown that Xray selected unobscured AGN have typical X / O between 0.1 and 10 (Fiore et al. 2003, and references therein). Flux ratios below 0.1 are typical of stars and normal galaxies; and ratios higher than 10 would correspond to heavily obscured AGN (but not Compton-thick), high redshift galaxy clusters and extreme BL Lac objects. Here, the X-ray flux is defined as the 0.5 -4.5 keV flux not corrected for Galactic absorption (the correction is not significant for our sources). For the optical flux we have used that in the red band, computed as where fR 0 = 1 . 74 × 10 -9 erg s -1 cm -2 as the zero-point for R (Zombeck 1990) and δλ = 2200 Å as the FWHM of the red filter. We prefer to use R = R2 for SuperCOSMOS sources (or R 1 if there is not R 2 magnitude available). Therefore, we find Fig. 11 shows the X-ray-to-optical flux ratio as a function of the 0.5 -4.5 keV X-ray luminosity for di ff erent extragalactic source types. The majority of sources detected in the 0.5 -4.5 keV band have X-ray-to-optical flux ratios of typical AGN. We note that only one source in our sample has X / O > 10. A small number was a priori expected given that the -0.5 0.0 0.5 1.0 1.5 R - I initial threshold imposed on the optical flux of our sources was relatively high. The BLAGN distribution does not show any trend. Due to the absence of broad emission lines in NELGs and ALGs, we expect their optical R band emission to be dominated by the host galaxy given that the nuclear optical / UV emission is completely blocked (or strongly reduced). Therefore, X / O is roughly a flux ratio between the nuclear X-ray and the host galaxy light emissions. As can be seen in the plot, there is a correlation between X / O and the hard X-ray luminosity for non-BLAGN in such a way that higher luminosity sources tend to have higher X / O . The dashed diagonal line in Fig. 11 indicates the best linear regression only using detections between log ( X / O ) and log( L 0 . 5 -4 . 5 keV) for non-BLAGN with L 0 . 5 -4 . 5 keV > 10 42 erg s -1 (those expected to harbour a hidden AGN) and extrapolated to lower luminosities (similar to that found in Fiore et al. 2003).",
"pages": [
8,
9
]
},
{
"title": "7. The catalogue",
"content": "The catalogue consists of 940 entries, one per object. It contains information about the X-ray detection, optical imaging and optical spectroscopy for every object. Only a number of representative parameters of the 2XMM-DR3i and SuperCOSMOS archive appear in the XWAS. For additional information, we invite the user to search in the original tables. This can be done by looking for the IAUNAME and OBJID columns in the XMMNewton or SuperCOSMOS archives, respectively. The XWASNAME column represents the name assigned to the XWAS sources. They start with the prefix, XWAS, and then encode the J2000 sky position of the X-ray object. Note that this coincides with the IAUNAME column in the 2XMM-DR3i aside from the prefix, except for the extra 50 sources not included in the XMM-Newton catalogue due to the high background flares (Sect. 5). For those extra objects, we release a separate table with data from the X-ray pipeline processing similar to that in the XMM-Newton catalogue. Some basic X-ray parameters directly extracted from the XMM-Newton survey are included in the released XWAS catalogue. These are the source name, coordinates, positional error and flux in the total 0.5-4.5 keV band. The X-ray luminosity has also been calculated using the redshift of the optical observations and included in the table. 7 6 5 4 3 2 1 0 Fractional count (%) . For the optical information, we have an identifier derived from the 2dF observations, named OPTID. Fibre positioning and separation with respect to the X-ray position are also included, along with the object class and redshift derived from our analysis of the observations. From SuperCOSMOS we have included the OBJID, so the user can get all data from the original tables, plus the SuperCOSMOS magnitudes in the di ff erent bands when possible. When existing, we use the R2 magnitude in the R mag column, otherwise, sources are flagged and we quote the R1 magnitude instead. A subset of columns of the XWAS catalogue is presented in Table 4 and the complete catalogue will only be available in electronic form.",
"pages": [
9,
10
]
},
{
"title": "8. Conclusions",
"content": "In this paper we have presented the strategy, production and overall characteristics of the new XMM-Newton Wide Angle Survey. With almost a thousand sources selected in the 0.5-4.5 keV energy band, this is one of the largest X-ray selected samples of spectroscopically identified AGN to date. The catalogue has a large scientific potential given the quality and high number of sources. It complements previous X-ray surveys to yield a qualitative picture of the X-ray sky. The XWAS catalogue comprises 940 X-ray objects identified through optical observations performed by the 2dF multi-fibre spectrometer. Sources are distributed over Ω ∼ 11.8 deg 2 in highgalactic latitude XMM-Newton fields (-85 deg < b < -30deg). The large volume covered allows us to sample the bright end of the X-ray luminosity function. Source populations in our survey are 65% BLAGN, 16% NELGs, 6% ALGs and 13% stars. Ahigh number of NELGs and ALGs are also presupposed to have an active nucleus given the X-ray luminosity and X-ray-tooptical flux ratios. NELGs are the most absorbed sources in the survey as shown by their X-ray colours. Extragalactic sources with luminosities lower than 10 42 erg s -1 could also have high absorption and host AGN. Indeed, some works suggest that they can include Compton-thick AGN. The sample presented here spreads over a large parameter space, in a region of the redshift-luminosity diagram poorly covered so far. The BLAGN sample extends out to redshift 4, with an average of 〈 z 〉 = 1.5. The average value for NELGs is 〈 z 〉 = 0.3, and 〈 z 〉 = 0.2 for ALGs. This is in agreement with previous surveys with similar depth. As expected, the BLAGN appear bluer than those galaxies with narrow or no spectral emission lines. A similar survey in terms of sky coverage and X-ray flux limits is the XBootes survey, with optical spectroscopy from the AGN and Galaxy Evolution Survey (AGES; Hickox et al. 2009). The authors explore its multiwavelengh properties, but the radio, X-ray, and IR AGN samples only show a mild overlap. However, although it covers a similar X-ray luminosity range to the XWAS, the redshift sampling is quite limited 0 . 25 < z < 0 . 8. Due to the large covered volume, one can also perform stacking analyses of the X-ray data to determine the mean X-ray properties of di ff erent populations. In that context, Mateos et al. (2010) derived he mean properties of BLAGN, and the corresponding characteristics of the Fe K α line were presented in Corral et al. (2008). The catalogue table can be accessed by direct download or via searches in the major astronomical databases. The XID results database contains additional information including direct links to X-ray and optical thumbnails and optical spectra 9 that have been created for the present catalogue. The results presented here can be an anticipation of what will be seen in future planned X-ray surveys. As an example, the XMM-XXL survey (Pierre et al. 2011) will cover two extragalactic regions of 25 deg 2 (at a depth of 5 × 10 -15 erg s -1 cm -2 ), and eROSITA (Predehl et al. 2010) will perform an all-sky survey at a limiting flux of 10 -14 erg s -1 cm -2 ). Acknowledgements. XMM-Newton project is an ESA science mission with instruments and contributions directly funded by ESA member states and NASA. This project is based on data obtained with the Anglo Australian Telescope's 2dF multi-fibre spectrograph. PE and AAH acknowledge support from the Spanish Plan Nacional de Astronom'ıa y Astrof'ısica under grant AYA 2009-05705-E. PE, MP, SM, MW and JAT acknowledge support from the UK STFC research council. This work has been supported in part by the German DLR under contract numbers 50 OR 0404 and 50 OX 0201. The research leading to these results has received funding from the European Community's Seventh Framework Programme ( / FP7 / 2007-2013 / ) under grant agreement No 229517. MK thanks for the support by the Deutsches Zentrum fur Luft- und Raumfahrt (DLR) GmbH under contract No. FKZ 50 OR 0404. The Space Research Organisation of The Netherlands is supported financially by NWO, the Netherlands Organisation for Scientific Research. AC, RDC and PS acknowledge financial support from ASI (grant n. I / 088 / 06 / 0, COFIS contract and grant n. I 009 / 10 / 0).",
"pages": [
10,
11
]
},
{
"title": "Appendix A: Discrepancies with NED",
"content": "A detailed literature search provided a source characterisation (i.e., optical spectral classification and redshift) for 225 XWAS candidate counterparts. We compared 2dF identified sources with those previously classified according to NED. They are considered the same object if both detections are located within 2.5 arcsec and the published redshift is the same ( ± 0.01) than that derived in our analysis. The majority of the NED classifications agree with ours except for a few exceptions, which are presented in Table A.1.",
"pages": [
11
]
},
{
"title": "References",
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"pages": [
11,
12
]
}
]
2013A&A...558A..37C
https://arxiv.org/pdf/1310.1594.pdf
<document>
<section_header_level_1><location><page_1><loc_10><loc_82><loc_92><loc_87></location>Calibration of AGILE-GRID with In-Flight Data and Monte Carlo Simulations</section_header_level_1>
<text><location><page_1><loc_7><loc_70><loc_94><loc_82></location>A. W. Chen 1 ; 12 , A. Argan 2 , A. Bulgarelli 3 , P. W. Cattaneo 4 , T. Contessi 1 , A. Giuliani 1 , C. Pittori 5 ; 6 , G. Pucella 7 , M. Tavani 2 ; 8 ; 9 , A. Trois 10 , F. Verrecchia 5 ; 6 , G. Barbiellini 11 ; 9 , P. Caraveo 1 , S. Colafrancesco 6 ; 12 , E. Costa 2 , G. De Paris 2 , E. Del Monte 2 , G. Di Cocco 3 , I. Donnarumma 2 , Y. Evangelista 2 , A. Ferrari 13 ; 9 , M. Feroci 2 , V. Fioretti 3 , M. Fiorini 1 , F. Fuschino 3 , M. Galli 14 , F. Gianotti 3 , P. Giommi 5 ; 18 , M. Giusti 2 , C. Labanti 3 , I. Lapshov 2 , F. Lazzarotto 2 , P. Lipari 15 , F. Longo 11 , F. Lucarelli 5 ; 6 , M. Marisaldi 3 , S. Mereghetti 1 , E. Morelli 3 , E. Moretti 21 ; 22 , A. Morselli 16 , L. Pacciani 2 , A. Pellizzoni 10 , F. Perotti 1 , G. Piano 2 ; 16 ; 9 , P. Picozza 8 ; 16 , M. Pilia 10 ; 20 , M. Prest 17 , M. Rapisarda 7 , A. Rappoldi 4 , A. Rubini 2 , S. Sabatini 2 , P. Santolamazza 5 ; 6 , P. So GLYPH<14> tta 2 , E. Striani 2 , M. Trifoglio 3 , G. Valentini 18 , E. Vallazza 11 , S. Vercellone 19 , V. Vittorini 2 ; 8 , and D. Zanello 15</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_67><loc_50><loc_68></location>1 INAF / IASF-Milano, Via E. Bassini, 15 I-20133 Milano, Italy</list_item>
<list_item><location><page_1><loc_11><loc_66><loc_51><loc_67></location>2 INAF / IAPS, Via Fosso del Cavaliere, 100 I-00133 Roma, Italy</list_item>
<list_item><location><page_1><loc_11><loc_64><loc_50><loc_66></location>3 INAF / IASF-Bologna, Via Gobetti 101, I-40129 Bologna, Italy</list_item>
<list_item><location><page_1><loc_11><loc_63><loc_47><loc_64></location>4 INFN-Pavia, Via Agostino Bassi, 6, I-27100 Pavia, Italy</list_item>
<list_item><location><page_1><loc_11><loc_62><loc_59><loc_63></location>5 ASI Science Data Center, Via Galileo Galilei, I-00044 Frascati (Roma), Italy</list_item>
<list_item><location><page_1><loc_11><loc_61><loc_58><loc_62></location>6 INAF-OAR, Via di Frascati, 33 I-00040, Monteporzio Catone (Roma), Italy</list_item>
<list_item><location><page_1><loc_11><loc_60><loc_54><loc_61></location>7 ENEA Frascati, Via Enrico Fermi, 13 I-00044 Frascati (Roma), Italy</list_item>
<list_item><location><page_1><loc_11><loc_59><loc_64><loc_60></location>8 Dip. di Fisica, Univ. Tor Vergata, Via della Ricerca Scientifica, 1 I-00133 Roma, Italy</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_58><loc_12><loc_58></location>9</text>
<text><location><page_1><loc_13><loc_57><loc_53><loc_58></location>CIFS, Villa Gualino - v.le Settimio Severo 63, I-10133 Torino, Italy</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_56><loc_60><loc_57></location>10 INAF-OAC, localita' Poggio dei Pini, strada 54, I-09012 Capoterra (CA), Italy</list_item>
<list_item><location><page_1><loc_11><loc_55><loc_63><loc_56></location>11 Dip. Fisica, Univ. Trieste and INFN Trieste, Via A. Valerio, 2, I-34127 Trieste, Italy</list_item>
<list_item><location><page_1><loc_11><loc_54><loc_68><loc_55></location>12 School of Physics, University of the Witwatersrand, Johannesburg Wits 2050, South Africa</list_item>
<list_item><location><page_1><loc_11><loc_53><loc_55><loc_54></location>13 Dip. Fisica, Universit'a di Torino, Via Giuria, 1, I-10125, Torino, Italy</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_52><loc_12><loc_53></location>14</text>
<text><location><page_1><loc_13><loc_51><loc_52><loc_52></location>ENEA-Bologna, Via Martiri Montesole, 4 I-40129 Bologna, Italy</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_50><loc_51><loc_51></location>15 INFN-Roma La Sapienza, P.le A. Moro, 2 I-00185 Roma, Italy</list_item>
<list_item><location><page_1><loc_11><loc_49><loc_60><loc_50></location>16 INFN Roma Tor Vergata, Via della Ricerca Scientifica, 1 I-00133 Roma, Italy</list_item>
<list_item><location><page_1><loc_11><loc_48><loc_57><loc_49></location>17 Dip. di Fisica, Univ. Dell'Insubria, Via Valleggio 11, I-22100 Como, Italy</list_item>
<list_item><location><page_1><loc_11><loc_47><loc_50><loc_48></location>18 Agenzia Spaziale Italiana, Viale Liegi, 26 I-00198 Roma, Italy</list_item>
<list_item><location><page_1><loc_11><loc_46><loc_54><loc_47></location>19 INAF-IASF Palermo, Via Ugo La Malfa 153, I-90146 Palermo, Italy</list_item>
<list_item><location><page_1><loc_11><loc_44><loc_78><loc_45></location>20 ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands</list_item>
<list_item><location><page_1><loc_11><loc_43><loc_48><loc_44></location>21 Royal Institute of Technology (KTH), Stockholm, Sweden</list_item>
<list_item><location><page_1><loc_11><loc_42><loc_56><loc_43></location>22 The Oskar Klein Centre for Cosmoparticle Physics, Stockholm,Sweden</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_40><loc_23><loc_41></location>Received ; accepted</text>
<section_header_level_1><location><page_1><loc_47><loc_38><loc_55><loc_38></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_33><loc_91><loc_36></location>Context. AGILE is a GLYPH<13> -ray astrophysics mission which has been in orbit since 23 April 2007 and continues to operate reliably. The GLYPH<13> -ray detector, AGILE-GRID, has observed Galactic and extragalactic sources, many of which were collected in the first AGILE Catalog.</text>
<text><location><page_1><loc_11><loc_29><loc_91><loc_33></location>Aims. We present the calibration of the AGILE-GRID using in-flight data and Monte Carlo simulations, producing Instrument Response Functions (IRFs) for the e GLYPH<11> ective area ( A e GLYPH<11> ), Energy Dispersion Probability (EDP), and Point Spread Function (PSF), each as a function of incident direction in instrument coordinates and energy.</text>
<text><location><page_1><loc_11><loc_26><loc_91><loc_29></location>Methods. We performed Monte Carlo simulations at di GLYPH<11> erent GLYPH<13> -ray energies and incident angles, including background rejection filters and Kalman filter-based GLYPH<13> -ray reconstruction. Long integrations of in-flight observations of the Vela, Crab and Geminga sources in broad and narrow energy bands were used to validate and improve the accuracy of the instrument response functions.</text>
<text><location><page_1><loc_11><loc_24><loc_84><loc_25></location>Results. The weighted average PSFs as a function of spectra correspond well to the data for all sources and energy bands.</text>
<text><location><page_1><loc_11><loc_19><loc_91><loc_24></location>Conclusions. Changes in the interpolation of the PSF from Monte Carlo data and in the procedure for construction of the energyweighted e GLYPH<11> ective areas have improved the correspondence between predicted and observed fluxes and spectra of celestial calibration sources, reducing false positives and obviating the need for post-hoc energy-dependent scaling factors. The new IRFs have been publicly available from the Agile Science Data Centre since November 25, 2011, while the changes in the analysis software will be distributed in an upcoming release.</text>
<text><location><page_1><loc_11><loc_17><loc_91><loc_18></location>Key words. instrumentation: detectors - methods: data analysis - techniques: image processing - telescopes - gamma rays: general</text>
<section_header_level_1><location><page_1><loc_52><loc_12><loc_64><loc_14></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_52><loc_9><loc_95><loc_11></location>AGILE (Tavani et al. 2009) is an Italian Space Agency (ASI) Small Scientific Mission for high-energy astrophysics launched</text>
<text><location><page_2><loc_7><loc_80><loc_50><loc_93></location>on April 23, 2007, composed of a pair-production Gamma Ray Imager (GRID) sensitive in the energy range 30 MeV-50 GeV (Barbiellini et al. 2002; Prest et al. 2003), an X-ray Imager (Super-AGILE) sensitive in the energy range 18-60 keV (Feroci et al. 2007), and a Mini-Calorimeter sensitive to GLYPH<13> -rays and charged particles with energies between 300 keV and 100 MeV (Labanti et al. 2009). AGILE has detected both persistent and variable sources, many of which were collected in the first AGILE Catalog (Pittori et al. 2009) and in a recent study of bright sources variability (Verrecchia et al. A&A in press).</text>
<section_header_level_1><location><page_2><loc_7><loc_75><loc_42><loc_77></location>2. Pre-flight calibration of on-board trigger</section_header_level_1>
<text><location><page_2><loc_7><loc_52><loc_50><loc_74></location>The AGILE-GRID is a pair-production telescope with 12 planes of silicon strip detectors, the first 10 of which lie under a pairconversion tungsten layer (Bulgarelli et al. 2010). The size of the tungsten-silicon tracker is 38 : 06 GLYPH<2> 38 : 06 GLYPH<2> 21 : 078 cm 3 and its on-axis depth totals 0.8 radiation lengths. Monte Carlo simulations (Cocco et al. 2002; Longo et al. 2002) with GEANT3 (Brun & Carminati 1993) were used to determine which on-board filter strategy would produce the reduction in particle and albedo background required by telemetry constraints while maintaining an acceptable e GLYPH<11> ective area for GLYPH<13> -rays, resulting in hardware on-board triggers (Argan et al. 2008) and on-board simplified Kalman filter (Giuliani et al. 2006) for event reconstruction and albedo rejection. These simulations were validated with preflight tests with cosmic-ray muons in the clean rooms of Laben (Milan) and CGS (Tortona) (Argan et al. 2008) and with GLYPH<13> -rays at INFN Laboratori Nazionali di Frascati (Cattaneo et al. 2011, 2012).</text>
<section_header_level_1><location><page_2><loc_7><loc_48><loc_40><loc_49></location>3. On-ground background rejection filter</section_header_level_1>
<text><location><page_2><loc_7><loc_36><loc_50><loc_46></location>The e GLYPH<11> ective area ( A e GLYPH<11> ), the three-dimensional Point Spread Function (PSF), and the Energy Dispersion Probability (EDP) of AGILE-GRID, collectively referred to as the instrument response functions (IRFs), depend on the direction of the incoming GLYPH<13> -ray in instrument coordinates. Throughout this paper, we will refer to this direction by the angular coordinate GLYPH<10> = ( GLYPH<2> ; GLYPH<8> ), where GLYPH<2> is the o GLYPH<11> -axis (polar) angle and GLYPH<8> the azimuth angle in spherical coordinates (see also Pittori & Tavani 2002).</text>
<section_header_level_1><location><page_2><loc_7><loc_33><loc_18><loc_34></location>3.1. Description</section_header_level_1>
<text><location><page_2><loc_7><loc_10><loc_50><loc_32></location>Additional processing is required on-ground in order to further reduce the particle background. Detailed analysis of event morphology is used to distinguish GLYPH<13> -rays from charged particles. The first on-ground filter to be used with real flight data F4 , used a hard decision tree and severe cuts for GLYPH<13> -rays with GLYPH<2> > 40 GLYPH<14> to limit contamination by cosmic-ray electrons and positrons. Since AGILE Public Data Release v2.0 in October 6, 2009, F4 has been replaced by two new filters. A more permissive filter using multi-variate analysis, FT3ab , was developed. Further development of the multi-variate analysis technique combined with some of the F4 criteria produced a more advanced filter, FM3.119 (also known as FM ), which provides a good tradeo GLYPH<11> between e GLYPH<11> ective area and background rejection (Bulgarelli et al., in prep.). Each event is classified as a likely gamma-ray ( G ), uncertain ( L ), a particle ( P ) or a single-track event ( S ). In practice, all scientific analyses other than pulsar timing and gammaray bursts have used G events exclusively.</text>
<section_header_level_1><location><page_2><loc_52><loc_92><loc_72><loc_93></location>3.2. Monte Carlo simulations</section_header_level_1>
<text><location><page_2><loc_52><loc_79><loc_95><loc_91></location>In order to improve and extend the IRFs, we performed additional Monte Carlo simulations after the launch of AGILE. For each set of instrument coordinates ( GLYPH<2> = 1 ; 30 ; 35 ; 40 ; 45 ; 50 ; 60 GLYPH<14> and GLYPH<8> = 0 ; 45 GLYPH<14> ), C tot = 59 GLYPH<2> 10 6 events were generated from a source with a power-law spectrum whose spectral index is GLYPH<11> = GLYPH<0> 1 : 7, with energies ranging from 4 MeV to 50 GeV. The events were processed using both the onboard filter and the on-ground event reconstruction procedures, including the background rejection filters.</text>
<section_header_level_1><location><page_2><loc_52><loc_76><loc_65><loc_77></location>3.3. Effective area</section_header_level_1>
<text><location><page_2><loc_52><loc_66><loc_95><loc_75></location>For the e GLYPH<11> ective area matrix as a function of GLYPH<10> , the events for each event class were separated into Nm = 16 energy bins, whose boundaries are 10, 35, 50, 71, 100, 141, 200, 283, 400, 632, 1000, 1732, 3000, 5477, 10000, 20000, and 50000 MeV. For each energy bin i containing GLYPH<13> -rays with energies between Ei and Ei + 1, the number of events classified as event class V , is C ( i ; GLYPH<10> ; V ). The e GLYPH<11> ective area A e GLYPH<11> ( i ; GLYPH<10> ; V ) is then defined as</text>
<formula><location><page_2><loc_59><loc_61><loc_95><loc_64></location>A e GLYPH<11> ( i ; GLYPH<10> ; V ) = A geom C ( i ; GLYPH<10> ; V ) C tot E GLYPH<11> + 1 max GLYPH<0> E GLYPH<11> + 1 min E GLYPH<11> + 1 i + 1 GLYPH<0> E GLYPH<11> + 1 i (1)</formula>
<text><location><page_2><loc_52><loc_53><loc_95><loc_59></location>where A geom is the geometric area of the instrument, C tot is the total number of events as defined in Sect. 3.2, E max = EN m + 1 = 50 GeV and E min = E 1 = 10 MeV. Some results are shown in Fig. 1 and compared to the e GLYPH<11> ective area of Fermi-LAT in Fig. 2 (Ackermann et al. 2012).</text>
<section_header_level_1><location><page_2><loc_52><loc_50><loc_76><loc_51></location>3.4. Energy dispersion probability</section_header_level_1>
<text><location><page_2><loc_52><loc_10><loc_95><loc_48></location>The AGILE energy dispersion matrices use the same energy bins for the true and reconstructed energies. For each event class and set of instrument coordinates, the EDP is the fraction of events within a given true energy bin whose reconstructed energy lies within a given reconstructed energy bin. The EDPs for the G event class of the FM3.119 filter (hereafter referred to as FMG) for selected energy bins at GLYPH<2> = 30 GLYPH<14> are shown in Fig. 3. Note that a substantial fraction of GLYPH<13> -rays with true energy below 100 MeV have reconstructed energies above 100 MeV, implying that a substantial fraction of events with reconstructed energies above 100 MeV will have true energies below 100 MeV for most astrophysical GLYPH<13> -ray sources, which tend to have spectral indices GLYPH<11> GLYPH<25> GLYPH<0> 2. Any GLYPH<13> -ray source which emits primarily below 100 MeV will also be detected in the nominal E > 100 MeV band. Meanwhile, a majority of GLYPH<13> -rays with true energy above 1 GeV have reconstructed energies below 1 GeV. Any GLYPH<13> -ray source which emits primarily above 1 GeV will have most of its flux reconstructed in the 400 MeV < E < 1000 MeV band. Both of these e GLYPH<11> ects are due to the limitations of multiple scattering as the primary method of energy reconstruction; at lower energies, a certain fraction of events will nevertheless be scattered at small angles (where the peak of the angular distribution lies; see the description in the next section), while at high energies the pitch of the silicon microstrips, 121 GLYPH<22> m, is too coarse to measure the scattering angle and the Mini-Calorimeter reaches its saturation point. The relationship between true and observed energy is shown in Figs. 3 and 4. The AGILE-GRID analysis software takes these factors into account, but discrepancies may arise if the spectral index is fixed to the wrong value or if the spectrum diverges significantly from a power law.</text>
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<caption>Fig. 1. AGILE e GLYPH<11> ective areas as a function of energy. E GLYPH<11> ective area = geometric area GLYPH<2> fraction of surviving events. The top plot is for GLYPH<2> = 0 GLYPH<14> , the bottom plot for GLYPH<2> = 40 GLYPH<14> . AGILE curves are for filters FT3ab and FM3.119, event class G.</caption>
</figure>
<section_header_level_1><location><page_3><loc_7><loc_39><loc_25><loc_40></location>3.5. Point spread function</section_header_level_1>
<text><location><page_3><loc_7><loc_28><loc_50><loc_38></location>A series of GLYPH<13> -rays from the same direction in instrument coordinates will have a distribution of reconstructed directions, an e GLYPH<11> ect known as Point Spread Dispersion (PSD). The PSF, which also depends on the GLYPH<13> -ray energy and event class, is defined as the probability distribution of the angular distance GLYPH<18> between the reconstructed and the true direction. The PSF is estimated from Monte Carlo simulations. Some examples of PSFs are shown in Figs. 5 and 6.</text>
<section_header_level_1><location><page_3><loc_7><loc_24><loc_43><loc_25></location>4. Fluxes, spectra and PSFs of real sources</section_header_level_1>
<text><location><page_3><loc_7><loc_14><loc_50><loc_23></location>The flux and spectrum of any physical point source can be decomposed into a series of monoenergetic point sources whose fluxes are equal to the di GLYPH<11> erential flux of the point source at each energy. Each monoenergetic point source has a well-defined A e GLYPH<11> , EDP, and PSF. These quantities are used to calculate the composite e GLYPH<11> ective area and PSF of the physical source depending on its spectrum and coordinates in the instrument frame.</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_13></location>Several versions of the IRFs have been used for the AGILEGRID analysis. Version I0007, used internally since the beginning of 2009 and released publicly on May 22, 2009 in soft-</text>
<paragraph><location><page_3><loc_52><loc_39><loc_95><loc_49></location>Fig. 2. AGILE and Fermi e GLYPH<11> ective areas as a function of energy. The top plot is for GLYPH<2> = 0 GLYPH<14> , the bottom plot for GLYPH<2> = 40 GLYPH<14> . AGILE curves are for filters FT3ab and FM3.119, event class G. Fermi Pass 7 curves are for version 6, SOURCE event class, front and back events. Fermi IRFs are taken from the Fermi Science Tools, version v9r23p1. The current version is available for public download at http://fermi.gsfc.nasa.gov/ssc/ data/analysis/software/ .</paragraph>
<text><location><page_3><loc_52><loc_13><loc_95><loc_35></location>ware release 3.0 by the AGILE Data Center 1 , part of the ASI Science Data Center (ASDC), used histograms directly binned from Monte Carlo data for the PSFs, without fitting to any analytic function. Version I0010, used internally from August 2009 until the end of 2010 and never released in public software packages, used the same directly binned PSFs, but introduced correction factors into the e GLYPH<11> ective area matrices in a first attempt to account for energy dispersion when calculating the e GLYPH<11> ective area for real sources. Finally, the latest version (I0023), used internally by the AGILE team since the end of 2010, and publicly included in ASDC software release 5.0 on November 25, 2011, fills the PSFs with an analytic King function fit to the Monte Carlo data, while removing the e GLYPH<11> ective area correction factors introduced into I0010. A new exposure generation procedure which accounts for energy dispersion will be included in an upcoming software release. These characteristics are summarized in Table 1.</text>
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<caption>Fig. 3. EDPs for filter FMG at various energy bins (71-100, 100141, 400-632, and 3000-5477 MeV) at GLYPH<2> = 30 GLYPH<14> . Within each bin the true energy follows a power-law distribution (see Sect. 3.2). The solid vertical line is the lower boundary of the true energy bin, while the dotted lines are fixed at 100, 400, and 1000 MeV.</caption>
</figure>
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<caption>Fig. 4. EDP for filter FMG at GLYPH<2> = 30 GLYPH<14> . Note the deviations from linearity below 100 MeV and above 400 MeV.</caption>
</figure>
<table>
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<caption>Table 1. Versions of the AGILE-GRID IRFs.</caption>
</table>
<section_header_level_1><location><page_4><loc_52><loc_45><loc_65><loc_46></location>4.1. Effective area</section_header_level_1>
<text><location><page_4><loc_52><loc_42><loc_95><loc_44></location>Suppose that a GLYPH<13> -ray source has a power-law spectrum dN = dE = NE GLYPH<11> . Then the flux in the energy bin i is</text>
<formula><location><page_4><loc_59><loc_37><loc_95><loc_40></location>Fi = N Z Ei + 1 Ei E GLYPH<11> dE = N GLYPH<11> + 1 ( E GLYPH<11> + 1 i + 1 GLYPH<0> E GLYPH<11> + 1 i ) (2)</formula>
<text><location><page_4><loc_52><loc_35><loc_84><loc_36></location>and the total flux between energies Ea and Eb is</text>
<formula><location><page_4><loc_61><loc_29><loc_95><loc_33></location>Fab = b GLYPH<0> 1 X i = a Fi = N GLYPH<11> + 1 ( E GLYPH<11> + 1 b GLYPH<0> E GLYPH<11> + 1 a ) : (3)</formula>
<text><location><page_4><loc_52><loc_24><loc_95><loc_28></location>If an instrument with A e GLYPH<11> ( i ; GLYPH<10> ; V ) for GLYPH<13> -rays whose true energy lies within energy bin i is exposed to the source for time t , the number of counts in each energy bin is</text>
<formula><location><page_4><loc_64><loc_21><loc_95><loc_22></location>Ci ( GLYPH<10> ; V ) = FiA e GLYPH<11> ( i ; GLYPH<10> ; V ) t : (4)</formula>
<text><location><page_4><loc_52><loc_15><loc_95><loc_20></location>If EDP ( i ; j ; GLYPH<10> ; V ) is the fraction of GLYPH<13> -rays whose true energy lies in energy bin i which have reconstructed energy within energy bin j , the number of counts from the full source spectrum whose reconstructed energy lies in energy bin j is</text>
<formula><location><page_4><loc_62><loc_9><loc_95><loc_13></location>C 0 j ( GLYPH<10> ; V ) = Nm X i = 0 CiEDP ( i ; j ; GLYPH<10> ; V ) (5)</formula>
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<caption>Fig. 5. Monoenergetic PSFs at GLYPH<2> = 30 GLYPH<14> with filter FMG at 100, 400, and 1000 MeV. The I0007 PSF matrices were created by directly binning the Monte Carlo data, dividing the raw histogram by sin GLYPH<18> , and normalizing. The I0010 PSF matrices are identical to those of I0007.</caption>
</figure>
<text><location><page_5><loc_7><loc_23><loc_50><loc_26></location>with Nm defined as in Sect. 3.3. Therefore the total number of counts whose observed energies lie between Ea and Eb is</text>
<formula><location><page_5><loc_8><loc_14><loc_50><loc_22></location>C 0 ab ( GLYPH<10> ; V ) = b GLYPH<0> 1 X j = a C 0 j ( GLYPH<10> ; V ) = b GLYPH<0> 1 X j = a Nm X i = 0 N GLYPH<11> + 1 A e GLYPH<11> ( i ; GLYPH<10> ; V ) tEDP ( i ; j ; GLYPH<10> ; V )( E GLYPH<11> + 1 i + 1 GLYPH<0> E GLYPH<11> + 1 i ) (6)</formula>
<text><location><page_5><loc_7><loc_10><loc_50><loc_13></location>where both the e GLYPH<11> ective areas and EDPs for individual energy bins and the observed e GLYPH<11> ective areas are functions of the GLYPH<13> -ray direction GLYPH<10> in instrument coordinates and event type V .</text>
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<caption>Fig. 6. Monoenergetic PSFs at GLYPH<2> = 30 GLYPH<14> with filter FMG at 100, 400, and 1000 MeV. The I0023 PSF matrices were created by first fitting Eq. (11) to the Monte Carlo data, then binning the values of the King function and normalizing.</caption>
</figure>
<text><location><page_5><loc_52><loc_19><loc_95><loc_25></location>The e GLYPH<11> ective area with respect to an interval of observed energies Ea and Eb is defined as the number of counts whose observed energies lie between Ea and Eb (Eq. 6) divided by the true flux between Ea and Eb (Eq. 3) divided by the time of observation t as follows:</text>
<formula><location><page_5><loc_54><loc_10><loc_95><loc_17></location>A 0 ab ( GLYPH<10> ; V ) = C 0 ab ( GLYPH<10> ; V ) Fabt = P Nm i = 0 A e GLYPH<11> ( i ; GLYPH<10> ; V )( E GLYPH<11> + 1 i + 1 GLYPH<0> E GLYPH<11> + 1 i ) P b GLYPH<0> 1 j = a EDP ( i ; j ; GLYPH<10> ; V ) E GLYPH<11> + 1 b GLYPH<0> E GLYPH<11> + 1 a : (7)</formula>
<text><location><page_6><loc_7><loc_90><loc_50><loc_93></location>Note that A 0 ab can be expressed as a weighted sum of A e GLYPH<11> ( i ; GLYPH<10> ; V ) as follows:</text>
<formula><location><page_6><loc_10><loc_86><loc_50><loc_89></location>A 0 ab ( GLYPH<10> ; V ) = Nm X i = 0 A e GLYPH<11> ( i ; GLYPH<10> ; V ) E GLYPH<11> + 1 i + 1 GLYPH<0> E GLYPH<11> + 1 i E GLYPH<11> + 1 b GLYPH<0> E GLYPH<11> + 1 a w ab ( i ; GLYPH<10> ; V ) (8)</formula>
<text><location><page_6><loc_7><loc_84><loc_11><loc_85></location>where</text>
<formula><location><page_6><loc_17><loc_80><loc_50><loc_84></location>w ab ( i ; GLYPH<10> ; V ) = b GLYPH<0> 1 X j = a EDP ( i ; j ; GLYPH<10> ; V ) (9)</formula>
<text><location><page_6><loc_7><loc_70><loc_50><loc_79></location>As of this writing, a simpler formula for the energy weight, not taking into account the EDPs, has been used, where the scaling factors w ab ( i ; GLYPH<10> ; V ) were set equal to 1 for the first version of the IRFs (I0007), and determined post-hoc as a function of instrument coordinates GLYPH<10> according to the procedure in Sect. 5.1. These post-hoc scaling factors were incorporated directly into the e GLYPH<11> ective area matrices in version I0010 of the IRFs.</text>
<text><location><page_6><loc_7><loc_65><loc_50><loc_70></location>However, we have found too limited the range of spectral indices for which this simplified formula is applicable, and are implementing the correct formula in the soon-to-be-released BUILD 22 of the software.</text>
<section_header_level_1><location><page_6><loc_7><loc_62><loc_25><loc_63></location>4.2. Point spread function</section_header_level_1>
<text><location><page_6><loc_7><loc_49><loc_50><loc_61></location>The PSF for a physical source observed in an interval of reconstructed energies is the weighted average of the PSFs in individual energy bins, where the weight of each energy bin is proportional to the product of the e GLYPH<11> ective area, the flux in the energy bin (determined by the source spectrum), and the fraction of GLYPH<13> -rays from the energy bin whose reconstructed energy lies within the observed reconstructed energy interval (determined by the EDP). If the source has power-law index GLYPH<11> between energies Ea and Eb , the PSF is</text>
<formula><location><page_6><loc_13><loc_45><loc_50><loc_48></location>PSF 0 ab ( GLYPH<10> ; V ) = P Nm i = 0 qab ( i ; GLYPH<10> ; V ) PSF ( i ; GLYPH<10> ; V ) P Nm i = 0 qab ( i ; GLYPH<10> ; V ) (10)</formula>
<text><location><page_6><loc_7><loc_42><loc_11><loc_44></location>where</text>
<formula><location><page_6><loc_8><loc_38><loc_48><loc_41></location>qab ( i ; GLYPH<10> ; V ) = A e GLYPH<11> ( i ; GLYPH<10> ; V )( E GLYPH<11> + 1 i + 1 GLYPH<0> E GLYPH<11> + 1 i ) b X j = a EDP ( i ; j ; GLYPH<10> ; V ) :</formula>
<text><location><page_6><loc_7><loc_26><loc_50><loc_37></location>Earlier versions (I0007 / I0010) of the PSF matrices used histograms taken directly from the Monte Carlo simulations. The updated PSF matrices (I0023) contain values derived from a fit to the Monte Carlo data using a modified King function (King 1962) used to characterize high-energy PSFs (Kirsch et al. 2004; Read et al. 2011) f ( GLYPH<18> ), which has three parameters, B , the (arbitrary) normalization, GLYPH<14> , the characteristic width, and GLYPH<13> , which is related to the relative strength of the core vs. the tail, as follows:</text>
<formula><location><page_6><loc_11><loc_22><loc_50><loc_25></location>f ( GLYPH<18> ) sin GLYPH<18> d GLYPH<18> = B (1 GLYPH<0> 1 =GLYPH<13> ) 1 + ( GLYPH<18>=GLYPH<14> ) 2 2 GLYPH<13> ! GLYPH<0> GLYPH<13> sin GLYPH<18> d GLYPH<18> (11)</formula>
<text><location><page_6><loc_7><loc_19><loc_50><loc_21></location>The PSF matrices are then filled with the values derived from the King function with a bin size of 0 : 1 GLYPH<14> .</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_19></location>We compare the 68% GLYPH<13> -ray Containment Radii (CRs) of the PSFs in single, true energy bins (Table 2) with those of the composite PSFs in broad, reconstructed energy intervals (Table 3). Note that the CR for the reconstructed E > 1 GeV interval is broader than that of the true E = 1 GeV bin. This is because, as we showed in Sect. 3.4, the reconstructed E > 1 GeV interval is dominated by GLYPH<13> -rays whose true energy is actually below 1 GeV.</text>
<table>
<location><page_6><loc_63><loc_84><loc_84><loc_90></location>
<caption>Table 2. 68% GLYPH<13> -ray Containment Radii (CRs) of monoenergetic PSFs.</caption>
</table>
<text><location><page_6><loc_52><loc_81><loc_95><loc_83></location>Notes. Monoenergetic PSFs for three true energies at GLYPH<2> = 30 GLYPH<14> from Monte Carlo data.</text>
<table>
<location><page_6><loc_62><loc_71><loc_84><loc_76></location>
<caption>Table 3. 68% GLYPH<13> -ray Containment Radii (CRs) of composite PSFs.Notes. Composite PSFs for three reconstructed energy intervals at GLYPH<2> = 30 GLYPH<14> and spectral index GLYPH<11> = GLYPH<0> 1 : 66 from Monte Carlo data.</caption>
</table>
<section_header_level_1><location><page_6><loc_52><loc_63><loc_77><loc_64></location>5. Comparison to in-flight data</section_header_level_1>
<text><location><page_6><loc_52><loc_37><loc_95><loc_62></location>We generated long-term integrations of AGILE-GRID in-flight data in both pointing (2007 / 07 / 09 - 2009 / 10 / 15) and spinning (2009 / 11 / 04 - 2010 / 10 / 31) modes of the Vela and anti-center regions, generating counts and exposure maps with a bin size of 0 : 3 GLYPH<14> . The AGILE maximum likelihood analysis (Bulgarelli et al. 2012) was performed taking into account the Galactic diffuse emission and the isotropic background, and the following bright point sources: the Vela point source, which comprises both the pulsar and the pulsar wind nebula (PWN), and the Crab and Geminga point sources and IC443 in the anti-center region, where the Crab point source also comprises both the pulsar and the PWN, all with fixed source locations and fixed, power-law spectra. Model counts were compared to data to validate the PSF, while spectra and fluxes were compared to those published in the Third EGRET catalog (Hartman et al. 1999, hereafter 3EG) in order to determine the post-hoc scaling factors introduced in 4.1 that were incorporated into the I0010 e GLYPH<11> ective area matrices and calculated according to the procedure described in the following subsection.</text>
<section_header_level_1><location><page_6><loc_52><loc_34><loc_81><loc_35></location>5.1. Fluxes and spectra: correction factors</section_header_level_1>
<text><location><page_6><loc_52><loc_17><loc_95><loc_33></location>To create the I0010 version of the e GLYPH<11> ective area matrices, we compared the fluxes for E > 100 MeV obtained using the I0007 e GLYPH<11> ective areas with the AGILE likelihood analysis of the Vela pulsar at di GLYPH<11> erent o GLYPH<11> -axis angles with those expected from the fluxes and spectra reported in the Fermi Large Area Telescope First Source Catalog (Abdo et al. 2010, hereafter 1FGL). A linear fit was performed on the fluxes produced by the analysis (Fig. 7). The correction factors were set equal to the inverse of the ratio between the fluxes implied by the fit parameters and the 1FGL fluxes for GLYPH<2> < 60 GLYPH<14> and set equal to the value at 60 GLYPH<14> for GLYPH<2> GLYPH<21> 60 GLYPH<14> . These were applied to the original e GLYPH<11> ective areas to produce new e GLYPH<11> ective areas to be used in AGILE analysis.</text>
<text><location><page_6><loc_52><loc_10><loc_95><loc_17></location>However, when attempting to reproduce this procedure for the updated IRFs, we discovered that the fluxes and spectra of the softer spectrum of the Crab were overestimated. In fact, the likelihood analysis of the Crab pulsar using IRFs with no correction factors applied produces fluxes not far from the desired value, albeit with distortions in the spectrum.</text>
<figure>
<location><page_7><loc_9><loc_72><loc_48><loc_93></location>
<caption>Fig. 7. Observed flux of the source at the position of the Vela pulsar for E > 100 MeV as a function of GLYPH<2> with the I0007 IRFs. The linear fit to these fluxes were used to calculate the e GLYPH<11> ective area correction factors in the I0010 IRFs.</caption>
</figure>
<figure>
<location><page_7><loc_9><loc_43><loc_49><loc_64></location>
<caption>Fig. 8. Fluxes of the source at the position of the Vela pulsar found using the new e GLYPH<11> ective area calculation (I0023) and the new PSF (I0023) for long integrations in pointing (red diamonds) and spinning (blue squares) mode. The black curve represents the flux and spectrum listed in 1FGL. No curve fitting was performed.</caption>
</figure>
<section_header_level_1><location><page_7><loc_7><loc_26><loc_44><loc_29></location>5.2. Fluxes and spectra: a new routine for generating exposure</section_header_level_1>
<text><location><page_7><loc_7><loc_10><loc_50><loc_25></location>As a result, we concluded that scaling factors alone were unable to correct for the flux and spectra simultaneously for sources with both hard and soft spectra. We have revised the exposure generation routines to use the true e GLYPH<11> ective area formula in Eq. 7. We compare the results to the 1FGL spectra of Vela in Fig. 8 and the Crab in Fig. 9. In both cases, the AGILE analysis software assumes an unbroken power law with a single spectral index and is therefore unable to model the exponential cuto GLYPH<11> above 2.9 GeV in the case of Vela and 5.8 GeV in the case of the Crab. Also, because 1FGL and the AGILE observations cover slightly di GLYPH<11> erent epochs, the Crab flux and spectrum may be a GLYPH<11> ected by variability (Tavani et al. 2011; Abdo et al. 2011).</text>
<figure>
<location><page_7><loc_54><loc_72><loc_94><loc_93></location>
<caption>Fig. 9. Fluxes of the source at the position of the Crab pulsar found using the new e GLYPH<11> ective area calculation (I0023) and the new PSF (I0023) for long integrations in pointing (red diamonds) and spinning (blue squares) mode. The black curve represents the flux and spectrum listed in 1FGL. No curve fitting was performed.</caption>
</figure>
<section_header_level_1><location><page_7><loc_52><loc_60><loc_70><loc_61></location>5.3. Point spread function</section_header_level_1>
<text><location><page_7><loc_52><loc_43><loc_95><loc_58></location>The PSFs as calculated in Eq. 10 were compared to the count maps generated by the long integrations in pointing and spinning mode for all three pulsars, Vela, Crab, and Geminga, both as a function of energy bin and for the full energy range from 100 MeV to 50 GeV. The PSFs show varying levels of agreement with the data. Examples are shown in Figs. 10, 11, 12 and 13. In each of these figures, the number of counts were integrated within 10 GLYPH<14> GLYPH<2> 0 : 25 GLYPH<14> slices in galactic longitude and galactic latitude and compared to a model comprising an isotropic component, a galactic di GLYPH<11> use component, and a point source component (see Eq. 10). The coe GLYPH<14> cients of the components were determined using the AGILE analysis software.</text>
<text><location><page_7><loc_52><loc_41><loc_95><loc_43></location>To estimate the goodness of fit, we calculated the maximum likelihood ratio statistic (Baker & Cousins 1984),</text>
<formula><location><page_7><loc_62><loc_36><loc_95><loc_39></location>GLYPH<31> 2 GLYPH<21> = 2 N X i = 1 [ Mi GLYPH<0> Ci + Ci ln( Ci Mi )] ; (12)</formula>
<text><location><page_7><loc_52><loc_30><loc_95><loc_35></location>where Ci is the number of counts and Mi the number predicted by the model in each 10 GLYPH<14> GLYPH<2> 0 : 25 GLYPH<14> slice. The reduced GLYPH<31> 2 GLYPH<21> is found by dividing by the number of degrees of freedom, which in this case is 38 (43 slices GLYPH<0> 3 free parameters).</text>
<text><location><page_7><loc_52><loc_14><loc_95><loc_29></location>In some cases, the real PSF appears to be broader than the model predicts, particularly in spinning mode. One possible source of this broadening is systematic error in the measurement of the spacecraft orientation. For each AGILE observation in both pointing and spinning mode, we smoothed the two-dimensional model with a simple Gaussian and found the Gaussian width GLYPH<27> which minimized GLYPH<31> 2 GLYPH<21> . The di GLYPH<11> erence p TS = unreduced GLYPH<31> 2 GLYPH<21> ( GLYPH<27> ) GLYPH<0> unreduced GLYPH<31> 2 GLYPH<21> (0) should be distributed as GLYPH<31> 2 with one degree of freedom and therefore be statistically significant when it is greater than 5. Best fit Gaussian smoothed model PSFs are shown in Figs. 10, 11, 12 and 13. Figs. 14 and 15 show the reduced GLYPH<31> 2 with and without Gaussian smoothing.</text>
<text><location><page_7><loc_52><loc_10><loc_95><loc_14></location>GLYPH<21> Fig. 16 shows the best fit GLYPH<27> as a function of GLYPH<2> . The values of GLYPH<27> are roughly consistent with GLYPH<25> 0 : 3 GLYPH<14> . However, in Fig. 17, we see that p TS shows a statistically significant improvement only</text>
<figure>
<location><page_8><loc_12><loc_72><loc_49><loc_93></location>
</figure>
<figure>
<location><page_8><loc_12><loc_51><loc_48><loc_71></location>
<caption>Fig. 10. Observed counts vs. model with PSF at the Vela source, E > 100 MeV, pointing mode. The error bars are Poisson errors around the sum of the counts within 10 GLYPH<14> GLYPH<2> 0 : 25 GLYPH<14> slices in galactic longitude (top) and galactic latitude (bottom). The data are compared to a model (solid curve) composed of an isotropic component (dash-dot), a galactic di GLYPH<11> use component (dash), and a point source (dash-dot-dot-dot) with reduced GLYPH<31> 2 GLYPH<21> = 1 : 41 in longitude and 1.77 in latitude with 38 degrees of freedom. The composite PSF has a spectral index GLYPH<11> = GLYPH<0> 1 : 66, weighted by e GLYPH<11> ective area, spectrum, and EDP. Smoothing the model with a Gaussian (red dotted) yields GLYPH<27> = 0 : 31 and reduced GLYPH<31> 2 GLYPH<21> = 0 : 81 with 37 degrees of freedom in longitude and GLYPH<27> = 0 : 22 and reduced GLYPH<31> 2 GLYPH<21> = 1 : 62 in latitude, yielding likelihood ratios p TS = 4 : 9 and 2.7 respectively.</caption>
</figure>
<text><location><page_8><loc_7><loc_23><loc_50><loc_27></location>in the case of the observations in spinning mode. These results are consistent with the hypothesis of a systematic error in the measurement of the spacecraft orientation in spinning mode.</text>
<text><location><page_8><loc_7><loc_10><loc_50><loc_22></location>A refined attitude reconstruction method using Kalman filtering techniques, optimized for the AGILE spinning observation mode, has been recently developed by the Compagnia Generale per lo Spazio (CGS), in joint collaboration with the ASDC. CGS is the prime industrial contractor of the AGILE mission, being in charge of design development and integration of the complete satellite. Star Sensor data in spinning mode are noisier, and present short gaps due to occasional blinding. The new attitude reconstruction improves the e GLYPH<14> ciency and the quality of the attitude measurement. A new analysis of in-flight spin-</text>
<figure>
<location><page_8><loc_57><loc_72><loc_94><loc_93></location>
</figure>
<figure>
<location><page_8><loc_57><loc_51><loc_93><loc_71></location>
<caption>Fig. 11. Observed counts vs. model with PSF at the Vela source, E > 400 MeV, pointing mode. The error bars are Poisson errors around the sum of the counts within 10 GLYPH<14> GLYPH<2> 0 : 25 GLYPH<14> slices in galactic longitude (top) and galactic latitude (bottom). The data are compared to a model (solid curve) composed of an isotropic component (dash-dot), a galactic di GLYPH<11> use component (dash), and a point source (dash-dot-dot-dot) with reduced GLYPH<31> 2 GLYPH<21> = 1 : 75 in longitude and 1.68 in latitude with 38 degrees of freedom. The composite PSF has a spectral index GLYPH<11> = GLYPH<0> 1 : 66, weighted by e GLYPH<11> ective area, spectrum, and EDP. Smoothing the model with a Gaussian (red dotted) yields GLYPH<27> = 0 : 30 and reduced GLYPH<31> 2 GLYPH<21> = 1 : 27 with 37 degrees of freedom in longitude and GLYPH<27> = 0 : 23 and reduced GLYPH<31> 2 GLYPH<21> = 1 : 41 in latitude, yielding likelihood ratios p TS = 4 : 4 and 3.4 respectively.</caption>
</figure>
<text><location><page_8><loc_52><loc_26><loc_95><loc_28></location>ning data reprocessed with the new attitude reconstruction is in progress at ASDC, and the results will be presented elsewhere.</text>
<section_header_level_1><location><page_8><loc_52><loc_22><loc_64><loc_23></location>6. Conclusions</section_header_level_1>
<text><location><page_8><loc_52><loc_12><loc_95><loc_21></location>The on-ground background rejection filters used by AGILEGRID have been optimized a number of times to increase the e GLYPH<11> ective area while maintaining a reasonable level of instrumental and cosmic-ray background. To validate and keep pace with these changes, the monoenergetic PSFs and EDPs produced by Monte Carlo simulations and validated by pre-launch tests were compared to in-flight data.</text>
<text><location><page_8><loc_52><loc_10><loc_95><loc_12></location>The e GLYPH<11> ective area calculations in narrow and wide reconstructed energy bands show extreme sensitivity to the assumed</text>
<figure>
<location><page_9><loc_12><loc_72><loc_49><loc_93></location>
</figure>
<figure>
<location><page_9><loc_12><loc_51><loc_49><loc_71></location>
<caption>Fig. 12. Observed counts vs. model with PSF at the Vela source, E > 100 MeV, spinning mode. The error bars are Poisson errors around the sum of the counts within 10 GLYPH<14> GLYPH<2> 0 : 25 GLYPH<14> slices in galactic longitude (top) and galactic latitude (bottom). The data are compared to a model (solid curve) composed of an isotropic component (dash-dot), a galactic di GLYPH<11> use component (dash), and a point source (dash-dot-dot-dot) with reduced GLYPH<31> 2 GLYPH<21> = 3 : 42 in longitude and 2.69 in latitude with 38 degrees of freedom. The composite PSF has a spectral index GLYPH<11> = GLYPH<0> 1 : 66, weighted by e GLYPH<11> ective area, spectrum, and EDP. Smoothing the model with a Gaussian (red dotted) yields GLYPH<27> = 0 : 33 and reduced GLYPH<31> 2 GLYPH<21> = 1 : 96 with 37 degrees of freedom in longitude and GLYPH<27> = 0 : 33 and reduced GLYPH<31> 2 GLYPH<21> = 1 : 41 in latitude, yielding likelihood ratios p TS = 7 : 6 and 7.1 respectively.</caption>
</figure>
<text><location><page_9><loc_7><loc_23><loc_50><loc_28></location>spectral index due to the large energy dispersion. As a result, for day-to-day analysis, correction factors were calculated and introduced into the e GLYPH<11> ective area matrices as a substitute for the full energy dispersion calculation.</text>
<text><location><page_9><loc_7><loc_10><loc_50><loc_22></location>These correction factors produced valid results only for a limited range of source spectra. A new version of the analysis software, soon to be released by the ASDC, properly takes into account the energy dispersion when calculating the energydependent e GLYPH<11> ective area. The software may now be used to calculate the spectral index through simultaneous analysis of the data divided into energy intervals. By comparing the calculated index to the index initially assumed to generate the exposure files and PSFs and iterating, the true flux and spectral index of the source may then be found. Strong deviations from power-law</text>
<figure>
<location><page_9><loc_57><loc_73><loc_93><loc_93></location>
</figure>
<figure>
<location><page_9><loc_57><loc_51><loc_94><loc_71></location>
<caption>Fig. 13. Observed counts vs. model with PSF at the Vela source, E > 400 MeV, spinning mode. The error bars are Poisson errors around the sum of the counts within 10 GLYPH<14> GLYPH<2> 0 : 25 GLYPH<14> slices in galactic longitude (top) and galactic latitude (bottom). The data are compared to a model (solid curve) composed of an isotropic component (dash-dot), a galactic di GLYPH<11> use component (dash), and a point source (dash-dot-dot-dot) with reduced GLYPH<31> 2 GLYPH<21> = 2 : 82 in longitude and 1.96 in latitude with 38 degrees of freedom. The composite PSF has a spectral index GLYPH<11> = GLYPH<0> 1 : 66, weighted by e GLYPH<11> ective area, spectrum, and EDP. Smoothing the model with a Gaussian (red dotted) yields GLYPH<27> = 0 : 27 and reduced GLYPH<31> 2 GLYPH<21> = 1 : 75 with 37 degrees of freedom in longitude and GLYPH<27> = 0 : 21 and reduced GLYPH<31> 2 GLYPH<21> = 1 : 35 in latitude, yielding likelihood ratios p TS = 6 : 5 and 4.9 respectively.</caption>
</figure>
<text><location><page_9><loc_52><loc_24><loc_95><loc_28></location>spectral behavior are not implemented and may lead to distortions, particularly at low and high energies where a large portion of the flux may come from outside the nominal energy bins.</text>
<text><location><page_9><loc_52><loc_14><loc_95><loc_24></location>The in-flight PSFs for real sources in pointing mode agree with those predicted by the Monte Carlo simulations, while those in spinning mode di GLYPH<11> er significantly. This e GLYPH<11> ect is probably due to systematic error in the Star Sensor measurement of the spacecraft orientation in spinning mode. A new optimized attitude reconstruction method currently under testing at ASDC should be able to correct this systematic error, which broadens the PSF by GLYPH<25> 0 : 3 GLYPH<14> for spinning mode observations.</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_13></location>AGILE and Fermi have di GLYPH<11> erent pointing strategies and are sensitive to variability on di GLYPH<11> erent timescales. In addition, at any given time AGILE and Fermi pointed toward di GLYPH<11> erent areas on</text>
<figure>
<location><page_10><loc_11><loc_72><loc_48><loc_93></location>
</figure>
<figure>
<location><page_10><loc_11><loc_51><loc_48><loc_71></location>
<caption>Fig. 14. Reduced GLYPH<31> 2 GLYPH<21> for AGILE observations of E > 100 MeV (top) and E > 400 MeV (bottom) in pointing mode. Galactic longitude slices with (red dotted) and without (solid black) Gaussian smoothing of the model; Galactic latitude slices with (blue dot-dash) and without (magenta dashed) Gaussian smoothing. 38 degrees of freedom without and 37 with smoothing. The unsmoothed model shows good agreement and the fit is not significantly improved by Gaussian smoothing.</caption>
</figure>
<text><location><page_10><loc_7><loc_33><loc_50><loc_36></location>the sky. AGILE-GRID therefore remains a completely complementary instrument for the detection of rapid transient phenomena.</text>
<text><location><page_10><loc_7><loc_26><loc_50><loc_32></location>Acknowledgements. We would like to thank the Istituto Nazionale di Astrofisica, the Agenzia Spaziale Italiana, the Consorzio Interuniversitario per la Fisica Spaziale, and the Istituto Nazionale di Fisica Nucleare for their generous support of the AGILE mission and this research, including ASI contracts n. I / 042 / 10 / 1 and I / 028 / 12 / 0. We would also like to thank the journal referee, whose comments helped to substantially improve this paper.</text>
<section_header_level_1><location><page_10><loc_7><loc_22><loc_16><loc_23></location>References</section_header_level_1>
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<text><location><page_10><loc_7><loc_14><loc_50><loc_16></location>Baker, S. & Cousins, R. D. 1984, Nuclear Instruments and Methods in Physics Research, 221, 437</text>
<text><location><page_10><loc_7><loc_10><loc_50><loc_14></location>Barbiellini, G., Fedel, G., Liello, F., et al. 2002, Nucl. Instr. Meth. A, 490, 146 Brun, R. & Carminati, F. 1993, GEANT - Detector Description and Simulation Tool, CERN Program Library Long Writeup W5013, CERN Geneva, Switzerland, CH-1211 Geneva 23, Switzerland</text>
<figure>
<location><page_10><loc_56><loc_72><loc_93><loc_93></location>
</figure>
<figure>
<location><page_10><loc_56><loc_51><loc_93><loc_71></location>
<caption>Fig. 15. Reduced GLYPH<31> 2 GLYPH<21> for AGILE observations of E > 100 MeV (top) and E > 400 MeV (bottom) in spinning mode. Galactic longitude slices with (red dotted) and without (solid black) Gaussian smoothing of the model; Galactic latitude slices with (blue dot-dash) and without (magenta dashed) Gaussian smoothing. 38 degrees of freedom without and 37 with smoothing. In many cases, Gaussian smoothing significantly improves the goodness of fit.</caption>
</figure>
<text><location><page_10><loc_52><loc_33><loc_95><loc_35></location>Bulgarelli, A., Argan, A., Barbiellini, G., et al. 2010, Nucl. Instr. Meth. A, 614, 213</text>
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<list_item><location><page_10><loc_52><loc_29><loc_95><loc_33></location>Bulgarelli, A., Chen, A. W., Tavani, M., et al. 2012, A&A, 540, A79 Cattaneo, P. W., Argan, A., Bo GLYPH<11> elli, F., et al. 2012, Nucl. Instr. Meth. A, 674, 55 Cattaneo, P. W., Argan, A., Bo GLYPH<11> elli, F., et al. 2011, Nucl. Instr. Meth. A, 630, 251</list_item>
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<text><location><page_10><loc_52><loc_25><loc_95><loc_29></location>Cocco, V., Longo, F., & Tavani, M. 2002, Nucl. Instr. Meth. A, 486, 623 Feroci, M., Costa, E., So GLYPH<14> tta, P., et al. 2007, Nucl. Instr. Meth. A, 581, 728 Giuliani, A., Cocco, V., Mereghetti, S., Pittori, C., & Tavani, M. 2006, Nucl. Instr. Meth. A, 568, 692</text>
<text><location><page_10><loc_52><loc_22><loc_90><loc_24></location>Hartman, R. C., Bertsch, D. L., Bloom, S. D., et al. 1999, ApJS, 123, 79 King, I. 1962, AJ, 67, 471</text>
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<list_item><location><page_10><loc_52><loc_18><loc_95><loc_22></location>Kirsch, M. G. F., Altieri, B., Chen, B., et al. 2004, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 5488, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, ed. G. Hasinger & M. J. L. Turner, 103-114</list_item>
<list_item><location><page_10><loc_52><loc_16><loc_95><loc_18></location>Labanti, C., Marisaldi, M., Fuschino, F., et al. 2009, Nucl. Instr. Meth. A, 598, 470</list_item>
<list_item><location><page_10><loc_52><loc_15><loc_91><loc_16></location>Longo, F., Cocco, V., & Tavani, M. 2002, Nucl. Instr. Meth. A, 486, 610</list_item>
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<text><location><page_10><loc_52><loc_10><loc_94><loc_11></location>Read, A. M., Rosen, S. R., Saxton, R. D., & Ramirez, J. 2011, A&A, 534, A34</text>
<figure>
<location><page_11><loc_10><loc_72><loc_48><loc_93></location>
<caption>Fig. 17. Significance of improvement TS due to additional parameter GLYPH<27> for AGILE observations of E > 100 MeV (top) and E > 400 MeV (bottom). Galactic longitude slices in pointing (solid black) and spinning (red dotted) mode; Galactic latitude slices in pointing (magenta dashed) and spinning (blue dot-dash) mode. p TS > 5 only for observations in spinning mode.</caption>
</figure>
<figure>
<location><page_11><loc_10><loc_51><loc_48><loc_71></location>
<caption>Fig. 16. Best-fit Gaussian smoothing width GLYPH<27> for AGILE observations of E > 100 MeV (top) and E > 400 MeV (bottom). Galactic longitude slices in pointing (solid black) and spinning (red dotted) mode; Galactic latitude slices in pointing (magenta dashed) and spinning (blue dot-dash) mode. The widths are roughly consistent with GLYPH<25> 0 : 3 GLYPH<14> .</caption>
</figure>
<figure>
<location><page_11><loc_55><loc_72><loc_93><loc_93></location>
</figure>
<figure>
<location><page_11><loc_55><loc_51><loc_93><loc_71></location>
</figure>
<text><location><page_11><loc_77><loc_49><loc_78><loc_50></location>p</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Context. AGILE is a GLYPH<13> -ray astrophysics mission which has been in orbit since 23 April 2007 and continues to operate reliably. The GLYPH<13> -ray detector, AGILE-GRID, has observed Galactic and extragalactic sources, many of which were collected in the first AGILE Catalog. Aims. We present the calibration of the AGILE-GRID using in-flight data and Monte Carlo simulations, producing Instrument Response Functions (IRFs) for the e GLYPH<11> ective area ( A e GLYPH<11> ), Energy Dispersion Probability (EDP), and Point Spread Function (PSF), each as a function of incident direction in instrument coordinates and energy. Methods. We performed Monte Carlo simulations at di GLYPH<11> erent GLYPH<13> -ray energies and incident angles, including background rejection filters and Kalman filter-based GLYPH<13> -ray reconstruction. Long integrations of in-flight observations of the Vela, Crab and Geminga sources in broad and narrow energy bands were used to validate and improve the accuracy of the instrument response functions. Results. The weighted average PSFs as a function of spectra correspond well to the data for all sources and energy bands. Conclusions. Changes in the interpolation of the PSF from Monte Carlo data and in the procedure for construction of the energyweighted e GLYPH<11> ective areas have improved the correspondence between predicted and observed fluxes and spectra of celestial calibration sources, reducing false positives and obviating the need for post-hoc energy-dependent scaling factors. The new IRFs have been publicly available from the Agile Science Data Centre since November 25, 2011, while the changes in the analysis software will be distributed in an upcoming release. Key words. instrumentation: detectors - methods: data analysis - techniques: image processing - telescopes - gamma rays: general",
"pages": [
1
]
},
{
"title": "Calibration of AGILE-GRID with In-Flight Data and Monte Carlo Simulations",
"content": "A. W. Chen 1 ; 12 , A. Argan 2 , A. Bulgarelli 3 , P. W. Cattaneo 4 , T. Contessi 1 , A. Giuliani 1 , C. Pittori 5 ; 6 , G. Pucella 7 , M. Tavani 2 ; 8 ; 9 , A. Trois 10 , F. Verrecchia 5 ; 6 , G. Barbiellini 11 ; 9 , P. Caraveo 1 , S. Colafrancesco 6 ; 12 , E. Costa 2 , G. De Paris 2 , E. Del Monte 2 , G. Di Cocco 3 , I. Donnarumma 2 , Y. Evangelista 2 , A. Ferrari 13 ; 9 , M. Feroci 2 , V. Fioretti 3 , M. Fiorini 1 , F. Fuschino 3 , M. Galli 14 , F. Gianotti 3 , P. Giommi 5 ; 18 , M. Giusti 2 , C. Labanti 3 , I. Lapshov 2 , F. Lazzarotto 2 , P. Lipari 15 , F. Longo 11 , F. Lucarelli 5 ; 6 , M. Marisaldi 3 , S. Mereghetti 1 , E. Morelli 3 , E. Moretti 21 ; 22 , A. Morselli 16 , L. Pacciani 2 , A. Pellizzoni 10 , F. Perotti 1 , G. Piano 2 ; 16 ; 9 , P. Picozza 8 ; 16 , M. Pilia 10 ; 20 , M. Prest 17 , M. Rapisarda 7 , A. Rappoldi 4 , A. Rubini 2 , S. Sabatini 2 , P. Santolamazza 5 ; 6 , P. So GLYPH<14> tta 2 , E. Striani 2 , M. Trifoglio 3 , G. Valentini 18 , E. Vallazza 11 , S. Vercellone 19 , V. Vittorini 2 ; 8 , and D. Zanello 15 9 CIFS, Villa Gualino - v.le Settimio Severo 63, I-10133 Torino, Italy 14 ENEA-Bologna, Via Martiri Montesole, 4 I-40129 Bologna, Italy Received ; accepted",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "AGILE (Tavani et al. 2009) is an Italian Space Agency (ASI) Small Scientific Mission for high-energy astrophysics launched on April 23, 2007, composed of a pair-production Gamma Ray Imager (GRID) sensitive in the energy range 30 MeV-50 GeV (Barbiellini et al. 2002; Prest et al. 2003), an X-ray Imager (Super-AGILE) sensitive in the energy range 18-60 keV (Feroci et al. 2007), and a Mini-Calorimeter sensitive to GLYPH<13> -rays and charged particles with energies between 300 keV and 100 MeV (Labanti et al. 2009). AGILE has detected both persistent and variable sources, many of which were collected in the first AGILE Catalog (Pittori et al. 2009) and in a recent study of bright sources variability (Verrecchia et al. A&A in press).",
"pages": [
1,
2
]
},
{
"title": "2. Pre-flight calibration of on-board trigger",
"content": "The AGILE-GRID is a pair-production telescope with 12 planes of silicon strip detectors, the first 10 of which lie under a pairconversion tungsten layer (Bulgarelli et al. 2010). The size of the tungsten-silicon tracker is 38 : 06 GLYPH<2> 38 : 06 GLYPH<2> 21 : 078 cm 3 and its on-axis depth totals 0.8 radiation lengths. Monte Carlo simulations (Cocco et al. 2002; Longo et al. 2002) with GEANT3 (Brun & Carminati 1993) were used to determine which on-board filter strategy would produce the reduction in particle and albedo background required by telemetry constraints while maintaining an acceptable e GLYPH<11> ective area for GLYPH<13> -rays, resulting in hardware on-board triggers (Argan et al. 2008) and on-board simplified Kalman filter (Giuliani et al. 2006) for event reconstruction and albedo rejection. These simulations were validated with preflight tests with cosmic-ray muons in the clean rooms of Laben (Milan) and CGS (Tortona) (Argan et al. 2008) and with GLYPH<13> -rays at INFN Laboratori Nazionali di Frascati (Cattaneo et al. 2011, 2012).",
"pages": [
2
]
},
{
"title": "3. On-ground background rejection filter",
"content": "The e GLYPH<11> ective area ( A e GLYPH<11> ), the three-dimensional Point Spread Function (PSF), and the Energy Dispersion Probability (EDP) of AGILE-GRID, collectively referred to as the instrument response functions (IRFs), depend on the direction of the incoming GLYPH<13> -ray in instrument coordinates. Throughout this paper, we will refer to this direction by the angular coordinate GLYPH<10> = ( GLYPH<2> ; GLYPH<8> ), where GLYPH<2> is the o GLYPH<11> -axis (polar) angle and GLYPH<8> the azimuth angle in spherical coordinates (see also Pittori & Tavani 2002).",
"pages": [
2
]
},
{
"title": "3.1. Description",
"content": "Additional processing is required on-ground in order to further reduce the particle background. Detailed analysis of event morphology is used to distinguish GLYPH<13> -rays from charged particles. The first on-ground filter to be used with real flight data F4 , used a hard decision tree and severe cuts for GLYPH<13> -rays with GLYPH<2> > 40 GLYPH<14> to limit contamination by cosmic-ray electrons and positrons. Since AGILE Public Data Release v2.0 in October 6, 2009, F4 has been replaced by two new filters. A more permissive filter using multi-variate analysis, FT3ab , was developed. Further development of the multi-variate analysis technique combined with some of the F4 criteria produced a more advanced filter, FM3.119 (also known as FM ), which provides a good tradeo GLYPH<11> between e GLYPH<11> ective area and background rejection (Bulgarelli et al., in prep.). Each event is classified as a likely gamma-ray ( G ), uncertain ( L ), a particle ( P ) or a single-track event ( S ). In practice, all scientific analyses other than pulsar timing and gammaray bursts have used G events exclusively.",
"pages": [
2
]
},
{
"title": "3.2. Monte Carlo simulations",
"content": "In order to improve and extend the IRFs, we performed additional Monte Carlo simulations after the launch of AGILE. For each set of instrument coordinates ( GLYPH<2> = 1 ; 30 ; 35 ; 40 ; 45 ; 50 ; 60 GLYPH<14> and GLYPH<8> = 0 ; 45 GLYPH<14> ), C tot = 59 GLYPH<2> 10 6 events were generated from a source with a power-law spectrum whose spectral index is GLYPH<11> = GLYPH<0> 1 : 7, with energies ranging from 4 MeV to 50 GeV. The events were processed using both the onboard filter and the on-ground event reconstruction procedures, including the background rejection filters.",
"pages": [
2
]
},
{
"title": "3.3. Effective area",
"content": "For the e GLYPH<11> ective area matrix as a function of GLYPH<10> , the events for each event class were separated into Nm = 16 energy bins, whose boundaries are 10, 35, 50, 71, 100, 141, 200, 283, 400, 632, 1000, 1732, 3000, 5477, 10000, 20000, and 50000 MeV. For each energy bin i containing GLYPH<13> -rays with energies between Ei and Ei + 1, the number of events classified as event class V , is C ( i ; GLYPH<10> ; V ). The e GLYPH<11> ective area A e GLYPH<11> ( i ; GLYPH<10> ; V ) is then defined as where A geom is the geometric area of the instrument, C tot is the total number of events as defined in Sect. 3.2, E max = EN m + 1 = 50 GeV and E min = E 1 = 10 MeV. Some results are shown in Fig. 1 and compared to the e GLYPH<11> ective area of Fermi-LAT in Fig. 2 (Ackermann et al. 2012).",
"pages": [
2
]
},
{
"title": "3.4. Energy dispersion probability",
"content": "The AGILE energy dispersion matrices use the same energy bins for the true and reconstructed energies. For each event class and set of instrument coordinates, the EDP is the fraction of events within a given true energy bin whose reconstructed energy lies within a given reconstructed energy bin. The EDPs for the G event class of the FM3.119 filter (hereafter referred to as FMG) for selected energy bins at GLYPH<2> = 30 GLYPH<14> are shown in Fig. 3. Note that a substantial fraction of GLYPH<13> -rays with true energy below 100 MeV have reconstructed energies above 100 MeV, implying that a substantial fraction of events with reconstructed energies above 100 MeV will have true energies below 100 MeV for most astrophysical GLYPH<13> -ray sources, which tend to have spectral indices GLYPH<11> GLYPH<25> GLYPH<0> 2. Any GLYPH<13> -ray source which emits primarily below 100 MeV will also be detected in the nominal E > 100 MeV band. Meanwhile, a majority of GLYPH<13> -rays with true energy above 1 GeV have reconstructed energies below 1 GeV. Any GLYPH<13> -ray source which emits primarily above 1 GeV will have most of its flux reconstructed in the 400 MeV < E < 1000 MeV band. Both of these e GLYPH<11> ects are due to the limitations of multiple scattering as the primary method of energy reconstruction; at lower energies, a certain fraction of events will nevertheless be scattered at small angles (where the peak of the angular distribution lies; see the description in the next section), while at high energies the pitch of the silicon microstrips, 121 GLYPH<22> m, is too coarse to measure the scattering angle and the Mini-Calorimeter reaches its saturation point. The relationship between true and observed energy is shown in Figs. 3 and 4. The AGILE-GRID analysis software takes these factors into account, but discrepancies may arise if the spectral index is fixed to the wrong value or if the spectrum diverges significantly from a power law.",
"pages": [
2
]
},
{
"title": "3.5. Point spread function",
"content": "A series of GLYPH<13> -rays from the same direction in instrument coordinates will have a distribution of reconstructed directions, an e GLYPH<11> ect known as Point Spread Dispersion (PSD). The PSF, which also depends on the GLYPH<13> -ray energy and event class, is defined as the probability distribution of the angular distance GLYPH<18> between the reconstructed and the true direction. The PSF is estimated from Monte Carlo simulations. Some examples of PSFs are shown in Figs. 5 and 6.",
"pages": [
3
]
},
{
"title": "4. Fluxes, spectra and PSFs of real sources",
"content": "The flux and spectrum of any physical point source can be decomposed into a series of monoenergetic point sources whose fluxes are equal to the di GLYPH<11> erential flux of the point source at each energy. Each monoenergetic point source has a well-defined A e GLYPH<11> , EDP, and PSF. These quantities are used to calculate the composite e GLYPH<11> ective area and PSF of the physical source depending on its spectrum and coordinates in the instrument frame. Several versions of the IRFs have been used for the AGILEGRID analysis. Version I0007, used internally since the beginning of 2009 and released publicly on May 22, 2009 in soft- ware release 3.0 by the AGILE Data Center 1 , part of the ASI Science Data Center (ASDC), used histograms directly binned from Monte Carlo data for the PSFs, without fitting to any analytic function. Version I0010, used internally from August 2009 until the end of 2010 and never released in public software packages, used the same directly binned PSFs, but introduced correction factors into the e GLYPH<11> ective area matrices in a first attempt to account for energy dispersion when calculating the e GLYPH<11> ective area for real sources. Finally, the latest version (I0023), used internally by the AGILE team since the end of 2010, and publicly included in ASDC software release 5.0 on November 25, 2011, fills the PSFs with an analytic King function fit to the Monte Carlo data, while removing the e GLYPH<11> ective area correction factors introduced into I0010. A new exposure generation procedure which accounts for energy dispersion will be included in an upcoming software release. These characteristics are summarized in Table 1.",
"pages": [
3
]
},
{
"title": "4.1. Effective area",
"content": "Suppose that a GLYPH<13> -ray source has a power-law spectrum dN = dE = NE GLYPH<11> . Then the flux in the energy bin i is and the total flux between energies Ea and Eb is If an instrument with A e GLYPH<11> ( i ; GLYPH<10> ; V ) for GLYPH<13> -rays whose true energy lies within energy bin i is exposed to the source for time t , the number of counts in each energy bin is If EDP ( i ; j ; GLYPH<10> ; V ) is the fraction of GLYPH<13> -rays whose true energy lies in energy bin i which have reconstructed energy within energy bin j , the number of counts from the full source spectrum whose reconstructed energy lies in energy bin j is with Nm defined as in Sect. 3.3. Therefore the total number of counts whose observed energies lie between Ea and Eb is where both the e GLYPH<11> ective areas and EDPs for individual energy bins and the observed e GLYPH<11> ective areas are functions of the GLYPH<13> -ray direction GLYPH<10> in instrument coordinates and event type V . The e GLYPH<11> ective area with respect to an interval of observed energies Ea and Eb is defined as the number of counts whose observed energies lie between Ea and Eb (Eq. 6) divided by the true flux between Ea and Eb (Eq. 3) divided by the time of observation t as follows: Note that A 0 ab can be expressed as a weighted sum of A e GLYPH<11> ( i ; GLYPH<10> ; V ) as follows: where As of this writing, a simpler formula for the energy weight, not taking into account the EDPs, has been used, where the scaling factors w ab ( i ; GLYPH<10> ; V ) were set equal to 1 for the first version of the IRFs (I0007), and determined post-hoc as a function of instrument coordinates GLYPH<10> according to the procedure in Sect. 5.1. These post-hoc scaling factors were incorporated directly into the e GLYPH<11> ective area matrices in version I0010 of the IRFs. However, we have found too limited the range of spectral indices for which this simplified formula is applicable, and are implementing the correct formula in the soon-to-be-released BUILD 22 of the software.",
"pages": [
4,
5,
6
]
},
{
"title": "4.2. Point spread function",
"content": "The PSF for a physical source observed in an interval of reconstructed energies is the weighted average of the PSFs in individual energy bins, where the weight of each energy bin is proportional to the product of the e GLYPH<11> ective area, the flux in the energy bin (determined by the source spectrum), and the fraction of GLYPH<13> -rays from the energy bin whose reconstructed energy lies within the observed reconstructed energy interval (determined by the EDP). If the source has power-law index GLYPH<11> between energies Ea and Eb , the PSF is where Earlier versions (I0007 / I0010) of the PSF matrices used histograms taken directly from the Monte Carlo simulations. The updated PSF matrices (I0023) contain values derived from a fit to the Monte Carlo data using a modified King function (King 1962) used to characterize high-energy PSFs (Kirsch et al. 2004; Read et al. 2011) f ( GLYPH<18> ), which has three parameters, B , the (arbitrary) normalization, GLYPH<14> , the characteristic width, and GLYPH<13> , which is related to the relative strength of the core vs. the tail, as follows: The PSF matrices are then filled with the values derived from the King function with a bin size of 0 : 1 GLYPH<14> . We compare the 68% GLYPH<13> -ray Containment Radii (CRs) of the PSFs in single, true energy bins (Table 2) with those of the composite PSFs in broad, reconstructed energy intervals (Table 3). Note that the CR for the reconstructed E > 1 GeV interval is broader than that of the true E = 1 GeV bin. This is because, as we showed in Sect. 3.4, the reconstructed E > 1 GeV interval is dominated by GLYPH<13> -rays whose true energy is actually below 1 GeV. Notes. Monoenergetic PSFs for three true energies at GLYPH<2> = 30 GLYPH<14> from Monte Carlo data.",
"pages": [
6
]
},
{
"title": "5. Comparison to in-flight data",
"content": "We generated long-term integrations of AGILE-GRID in-flight data in both pointing (2007 / 07 / 09 - 2009 / 10 / 15) and spinning (2009 / 11 / 04 - 2010 / 10 / 31) modes of the Vela and anti-center regions, generating counts and exposure maps with a bin size of 0 : 3 GLYPH<14> . The AGILE maximum likelihood analysis (Bulgarelli et al. 2012) was performed taking into account the Galactic diffuse emission and the isotropic background, and the following bright point sources: the Vela point source, which comprises both the pulsar and the pulsar wind nebula (PWN), and the Crab and Geminga point sources and IC443 in the anti-center region, where the Crab point source also comprises both the pulsar and the PWN, all with fixed source locations and fixed, power-law spectra. Model counts were compared to data to validate the PSF, while spectra and fluxes were compared to those published in the Third EGRET catalog (Hartman et al. 1999, hereafter 3EG) in order to determine the post-hoc scaling factors introduced in 4.1 that were incorporated into the I0010 e GLYPH<11> ective area matrices and calculated according to the procedure described in the following subsection.",
"pages": [
6
]
},
{
"title": "5.1. Fluxes and spectra: correction factors",
"content": "To create the I0010 version of the e GLYPH<11> ective area matrices, we compared the fluxes for E > 100 MeV obtained using the I0007 e GLYPH<11> ective areas with the AGILE likelihood analysis of the Vela pulsar at di GLYPH<11> erent o GLYPH<11> -axis angles with those expected from the fluxes and spectra reported in the Fermi Large Area Telescope First Source Catalog (Abdo et al. 2010, hereafter 1FGL). A linear fit was performed on the fluxes produced by the analysis (Fig. 7). The correction factors were set equal to the inverse of the ratio between the fluxes implied by the fit parameters and the 1FGL fluxes for GLYPH<2> < 60 GLYPH<14> and set equal to the value at 60 GLYPH<14> for GLYPH<2> GLYPH<21> 60 GLYPH<14> . These were applied to the original e GLYPH<11> ective areas to produce new e GLYPH<11> ective areas to be used in AGILE analysis. However, when attempting to reproduce this procedure for the updated IRFs, we discovered that the fluxes and spectra of the softer spectrum of the Crab were overestimated. In fact, the likelihood analysis of the Crab pulsar using IRFs with no correction factors applied produces fluxes not far from the desired value, albeit with distortions in the spectrum.",
"pages": [
6
]
},
{
"title": "5.2. Fluxes and spectra: a new routine for generating exposure",
"content": "As a result, we concluded that scaling factors alone were unable to correct for the flux and spectra simultaneously for sources with both hard and soft spectra. We have revised the exposure generation routines to use the true e GLYPH<11> ective area formula in Eq. 7. We compare the results to the 1FGL spectra of Vela in Fig. 8 and the Crab in Fig. 9. In both cases, the AGILE analysis software assumes an unbroken power law with a single spectral index and is therefore unable to model the exponential cuto GLYPH<11> above 2.9 GeV in the case of Vela and 5.8 GeV in the case of the Crab. Also, because 1FGL and the AGILE observations cover slightly di GLYPH<11> erent epochs, the Crab flux and spectrum may be a GLYPH<11> ected by variability (Tavani et al. 2011; Abdo et al. 2011).",
"pages": [
7
]
},
{
"title": "5.3. Point spread function",
"content": "The PSFs as calculated in Eq. 10 were compared to the count maps generated by the long integrations in pointing and spinning mode for all three pulsars, Vela, Crab, and Geminga, both as a function of energy bin and for the full energy range from 100 MeV to 50 GeV. The PSFs show varying levels of agreement with the data. Examples are shown in Figs. 10, 11, 12 and 13. In each of these figures, the number of counts were integrated within 10 GLYPH<14> GLYPH<2> 0 : 25 GLYPH<14> slices in galactic longitude and galactic latitude and compared to a model comprising an isotropic component, a galactic di GLYPH<11> use component, and a point source component (see Eq. 10). The coe GLYPH<14> cients of the components were determined using the AGILE analysis software. To estimate the goodness of fit, we calculated the maximum likelihood ratio statistic (Baker & Cousins 1984), where Ci is the number of counts and Mi the number predicted by the model in each 10 GLYPH<14> GLYPH<2> 0 : 25 GLYPH<14> slice. The reduced GLYPH<31> 2 GLYPH<21> is found by dividing by the number of degrees of freedom, which in this case is 38 (43 slices GLYPH<0> 3 free parameters). In some cases, the real PSF appears to be broader than the model predicts, particularly in spinning mode. One possible source of this broadening is systematic error in the measurement of the spacecraft orientation. For each AGILE observation in both pointing and spinning mode, we smoothed the two-dimensional model with a simple Gaussian and found the Gaussian width GLYPH<27> which minimized GLYPH<31> 2 GLYPH<21> . The di GLYPH<11> erence p TS = unreduced GLYPH<31> 2 GLYPH<21> ( GLYPH<27> ) GLYPH<0> unreduced GLYPH<31> 2 GLYPH<21> (0) should be distributed as GLYPH<31> 2 with one degree of freedom and therefore be statistically significant when it is greater than 5. Best fit Gaussian smoothed model PSFs are shown in Figs. 10, 11, 12 and 13. Figs. 14 and 15 show the reduced GLYPH<31> 2 with and without Gaussian smoothing. GLYPH<21> Fig. 16 shows the best fit GLYPH<27> as a function of GLYPH<2> . The values of GLYPH<27> are roughly consistent with GLYPH<25> 0 : 3 GLYPH<14> . However, in Fig. 17, we see that p TS shows a statistically significant improvement only in the case of the observations in spinning mode. These results are consistent with the hypothesis of a systematic error in the measurement of the spacecraft orientation in spinning mode. A refined attitude reconstruction method using Kalman filtering techniques, optimized for the AGILE spinning observation mode, has been recently developed by the Compagnia Generale per lo Spazio (CGS), in joint collaboration with the ASDC. CGS is the prime industrial contractor of the AGILE mission, being in charge of design development and integration of the complete satellite. Star Sensor data in spinning mode are noisier, and present short gaps due to occasional blinding. The new attitude reconstruction improves the e GLYPH<14> ciency and the quality of the attitude measurement. A new analysis of in-flight spin- ning data reprocessed with the new attitude reconstruction is in progress at ASDC, and the results will be presented elsewhere.",
"pages": [
7,
8
]
},
{
"title": "6. Conclusions",
"content": "The on-ground background rejection filters used by AGILEGRID have been optimized a number of times to increase the e GLYPH<11> ective area while maintaining a reasonable level of instrumental and cosmic-ray background. To validate and keep pace with these changes, the monoenergetic PSFs and EDPs produced by Monte Carlo simulations and validated by pre-launch tests were compared to in-flight data. The e GLYPH<11> ective area calculations in narrow and wide reconstructed energy bands show extreme sensitivity to the assumed spectral index due to the large energy dispersion. As a result, for day-to-day analysis, correction factors were calculated and introduced into the e GLYPH<11> ective area matrices as a substitute for the full energy dispersion calculation. These correction factors produced valid results only for a limited range of source spectra. A new version of the analysis software, soon to be released by the ASDC, properly takes into account the energy dispersion when calculating the energydependent e GLYPH<11> ective area. The software may now be used to calculate the spectral index through simultaneous analysis of the data divided into energy intervals. By comparing the calculated index to the index initially assumed to generate the exposure files and PSFs and iterating, the true flux and spectral index of the source may then be found. Strong deviations from power-law spectral behavior are not implemented and may lead to distortions, particularly at low and high energies where a large portion of the flux may come from outside the nominal energy bins. The in-flight PSFs for real sources in pointing mode agree with those predicted by the Monte Carlo simulations, while those in spinning mode di GLYPH<11> er significantly. This e GLYPH<11> ect is probably due to systematic error in the Star Sensor measurement of the spacecraft orientation in spinning mode. A new optimized attitude reconstruction method currently under testing at ASDC should be able to correct this systematic error, which broadens the PSF by GLYPH<25> 0 : 3 GLYPH<14> for spinning mode observations. AGILE and Fermi have di GLYPH<11> erent pointing strategies and are sensitive to variability on di GLYPH<11> erent timescales. In addition, at any given time AGILE and Fermi pointed toward di GLYPH<11> erent areas on the sky. AGILE-GRID therefore remains a completely complementary instrument for the detection of rapid transient phenomena. Acknowledgements. We would like to thank the Istituto Nazionale di Astrofisica, the Agenzia Spaziale Italiana, the Consorzio Interuniversitario per la Fisica Spaziale, and the Istituto Nazionale di Fisica Nucleare for their generous support of the AGILE mission and this research, including ASI contracts n. I / 042 / 10 / 1 and I / 028 / 12 / 0. We would also like to thank the journal referee, whose comments helped to substantially improve this paper.",
"pages": [
8,
9,
10
]
},
{
"title": "References",
"content": "Abdo, A. A., Ackermann, M., Ajello, M., et al. 2010, ApJS, 188, 405 Abdo, A. A., Ackermann, M., Ajello, M., et al. 2011, Science, 331, 739 Ackermann, M., Ajello, M., Albert, A., et al. 2012, ApJS, 203, 4 Argan, A., Tavani, M., Trois, A., et al. 2008, in Nuclear Science Symposium Conference Record, 2008. NSS '08. IEEE (IEEE), 774-777 Baker, S. & Cousins, R. D. 1984, Nuclear Instruments and Methods in Physics Research, 221, 437 Barbiellini, G., Fedel, G., Liello, F., et al. 2002, Nucl. Instr. Meth. A, 490, 146 Brun, R. & Carminati, F. 1993, GEANT - Detector Description and Simulation Tool, CERN Program Library Long Writeup W5013, CERN Geneva, Switzerland, CH-1211 Geneva 23, Switzerland Bulgarelli, A., Argan, A., Barbiellini, G., et al. 2010, Nucl. Instr. Meth. A, 614, 213 Cocco, V., Longo, F., & Tavani, M. 2002, Nucl. Instr. Meth. A, 486, 623 Feroci, M., Costa, E., So GLYPH<14> tta, P., et al. 2007, Nucl. Instr. Meth. A, 581, 728 Giuliani, A., Cocco, V., Mereghetti, S., Pittori, C., & Tavani, M. 2006, Nucl. Instr. Meth. A, 568, 692 Hartman, R. C., Bertsch, D. L., Bloom, S. D., et al. 1999, ApJS, 123, 79 King, I. 1962, AJ, 67, 471 Read, A. M., Rosen, S. R., Saxton, R. D., & Ramirez, J. 2011, A&A, 534, A34 p",
"pages": [
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]
}
]
2013A&A...558A..44M
https://arxiv.org/pdf/1404.2539.pdf
<document>
<section_header_level_1><location><page_1><loc_9><loc_82><loc_93><loc_87></location>Mapping of interstellar clouds with infrared light scattered from dust: TMC-1N glyph[star]</section_header_level_1>
<text><location><page_1><loc_25><loc_80><loc_77><loc_82></location>J. Malinen 1 , M. Juvela 1 , V.-M. Pelkonen 2 , 1 , and M. G. Rawlings 3</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_77><loc_91><loc_78></location>1 Department of Physics, University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland; [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_76><loc_85><loc_77></location>2 Finnish Centre for Astronomy with ESO, University of Turku, Vaisalantie 20, FI-21500 PIIKKI O, Finland</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_76><loc_76></location>3 National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_73><loc_39><loc_74></location>Preprint online version: October 16, 2018</text>
<section_header_level_1><location><page_1><loc_47><loc_70><loc_55><loc_71></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_67><loc_91><loc_69></location>Context. Mapping of the near-infrared scattered light is a recent method for the study of interstellar clouds, complementing other, more commonly used methods, like dust emission and extinction.</text>
<text><location><page_1><loc_11><loc_63><loc_91><loc_67></location>Aims. Our goal is to study the usability of this method on larger scale, and compare the properties of a filamentary structure using infrared scattering and other methods. We also study the radiation field and differences in grain emissivity between diffuse and dense areas.</text>
<text><location><page_1><loc_11><loc_57><loc_91><loc_63></location>Methods. We have used scattered near-infrared (NIR) J , H , and K band surface brightness observations with WFCAM instrument to map a filament TMC-1N in Taurus Molecular Cloud, covering an area of 1 · × 1 · corresponding to ∼ (2.44 pc) 2 . We have converted the data into an optical depth map and compared the results with NIR extinction and Herschel observations of sub-mm dust emission. We have also modelled the filament with 3D radiative transfer calculations of scattered light.</text>
<text><location><page_1><loc_11><loc_47><loc_91><loc_57></location>Results. We see the filament in scattered light in all three NIR bands. We note that our WFCAM observations in TMC-1N show notably lower intensity than previous results in Corona Australis using the same method. We show that 3D radiative transfer simulations predict similar scattered surface brightness levels as seen in the observations. However, changing the assumptions about the background can change the results of simulations notably. We derive emissivity, the ratio of FIR dust emission to column density, by using optical depth in the J band, τ J , obtained from NIR extinction map as an independent tracer of column density. We obtain a value 0.0013 for the ratio τ 250 /τ Nicer J . This leads to opacity or dust emission cross-section σ e (250 µ m) values 1 . 7 -2 . 4 × 10 -25 cm 2 / H, depending on assumptions of the extinction curve, which can change the results by over 40%. These values are twice as high as obtained for diffuse areas, at the lower limit of earlier results for denser areas.</text>
<text><location><page_1><loc_11><loc_43><loc_91><loc_46></location>Conclusions. We show that NIR scattering can be a valuable tool in making high resolution maps. We conclude, however, that NIR scattering observations can be complicated, as the data can show comparatively low-level artefacts. This suggests caution when planning and interpreting the observations.</text>
<text><location><page_1><loc_11><loc_41><loc_89><loc_42></location>Key words. ISM: Clouds - Stars: formation - Infrared: ISM - Submillimeter: ISM - Scattering - Radiative transfer</text>
<section_header_level_1><location><page_1><loc_7><loc_37><loc_20><loc_38></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_28><loc_50><loc_36></location>The structure of molecular clouds can be studied via a number of methods. These include molecular line mapping, observations of dust emission at far-infrared/sub-millimetre wavelengths, star counts in the optical and near-infrared (NIR) wavelengths, and measurements of colour excesses of background stars.</text>
<text><location><page_1><loc_7><loc_15><loc_50><loc_28></location>All techniques have their own drawbacks. For example, line and continuum emission maps are subject to abundance variations (gas and dust, respectively) and variations in the physical conditions, most notably the excitation and kinetic temperatures. Mass estimates based on dust emission can also be biased because of line-of-sight temperature variations, especially in high density clouds where star formation is potential (see, e.g., Malinen et al. 2011). The colour excess method provides column density estimates for extremely narrow lines of sight toward background stars.</text>
<text><location><page_1><loc_52><loc_25><loc_95><loc_38></location>However, the intrinsic colours of the stars are usually unknown and this introduces significant noise, especially at low column densities. A full extinction map is obtained only after spatial averaging. This means that for all the listed methods the spatial resolution is usually some tens of arc seconds or worse. See, e.g., Juvela et al. (2006) for a more thorough review of the methods, Goodman et al. (2009) for a comparison of several methods, and Malinen et al. (2012) for a comparison of filament properties derived using NIR extinction and Herschel observations of dust emission.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_24></location>Surface brightness caused by scattered NIR light provides another means of studying cloud structure. The first observation of scattered NIR light from molecular clouds illuminated by the normal interstellar radiation field (ISRF) was by Lehtinen & Mattila (1996). Later the observations of Nakajima et al. (2003) and Foster & Goodman (2006) (who also named the phenomenon 'cloudshine') have shown that it is now possible to obtain large maps of the surface brightness of normal interstellar clouds illuminated by the normal ISRF. NIR scattering can therefore be a new, complementary tool for studying the structure of dark clouds. See,</text>
<text><location><page_2><loc_7><loc_91><loc_50><loc_93></location>e.g., Juvela et al. (2006) for a more complete review of the history of scattered light observations in dark clouds.</text>
<text><location><page_2><loc_7><loc_68><loc_50><loc_90></location>Padoan et al. (2006) presented a method to determine the cloud column density from the intensity of the nearinfrared scattered light. Juvela et al. (2006) analysed the method in more detail using simulations, and developed a method to combine the surface brightness with extinction, to reduce errors caused by wrong assumptions of radiation field or dust properties. Starting with the known properties of the interstellar dust and ISRF, the papers made predictions for the visibility of the cloudshine and for the accuracy of the resulting column density estimates. They also demonstrated, independently of the direct evidence given by the Foster & Goodman (2006) data, that such observations are well within the capabilities of modern wide-field infrared cameras. The main advantage of the new method is the potentially extremely good spatial resolution. When the J , H , and K bands are used, the method remains accurate in regions with A V even beyond 10 magnitudes.</text>
<text><location><page_2><loc_7><loc_45><loc_50><loc_68></location>The same NIR observations provide data for the colour excess method, which means that the results of the methods can be compared at lower spatial resolution. Although both methods depend on near-infrared dust properties, the main sources of error are different. Comparison of the results can be used to study the values and variation of nearinfrared dust properties (e.g., albedo and the shape of the extinction curve) and spatial variations in the strength of the local radiation field. Furthermore, correlations between wavelength bands give a direct way to estimate the point at which the contribution of dust emission from stochastically heated grains becomes significant. The level of the emission of these so-called Sellgren grains depends on the radiation field (Sellgren et al. 1996), but is still uncertain in normal interstellar clouds. On the other hand, the amount of the scattered light depends heavily on the grain size (Steinacker et al. 2010). These dependencies have implications for models of interstellar dust.</text>
<text><location><page_2><loc_7><loc_24><loc_50><loc_45></location>Juvela et al. (2008) used scattered NIR light to derive a column density map of a part of a filament in Corona Australis, and continued the analysis in a larger area in Juvela et al. (2009). They also compared the NIR data with Herschel sub-millimetre data in Juvela et al. (2012). Nakajima et al. (2008) applied a similar method to convert NIR scattered light to column density. They used the colour excess of individual background stars to calibrate an empirical relationship between surface brightness and column density, instead of an analytical formula, as used in Juvela et al. (2006, 2008). Scattered surface brightness from dense cores in the mid-infrared (MIR) was reported by Pagani et al. (2010) and Steinacker et al. (2010). Steinacker et al. (2010) named this phenomenon 'coreshine' as a counterpart to 'cloudshine', which is also observed in the outer parts of the clouds.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_24></location>In this paper, we study a filament in the Taurus molecular cloud using observations of NIR light of a 1 · × 1 · field observed with WFCAM instrument (Casali et al. 2007). Distance to the Taurus molecular cloud is ∼ 140 pc, making it one of the closest relatively high latitude clouds, and consequently one of the most studied star-forming regions (see, e.g., Cambr'esy 1999; Nutter et al. 2008; Kirk et al. 2013; Palmeirim et al. 2013). In Malinen et al. (2012), we compared the properties of this filament derived using NIR extinction and dust emission observed with Herschel . Here, we construct maps of the diffuse surface brightness, determine</text>
<text><location><page_2><loc_52><loc_80><loc_95><loc_93></location>the intensity of the NIR scattered light, and derive the optical depth based on scattered NIR light using the method presented in Padoan et al. (2006). We compare the scattered light images with the other tracers, NIR extinction and sub-millimetre dust emission and, using these results, draw some conclusions regarding the intensity and spectrum of the local ISRF. We also perform radiative transfer modelling to compare observations with the level of NIR and MIR scattered light that is expected using standard ISRF levels and standard dust models.</text>
<text><location><page_2><loc_52><loc_67><loc_95><loc_80></location>The contents of the article are the following: We present observations and data processing in Sect. 2. We describe the method for deriving optical depth from scattered NIR surface brightness in Sect. 3. We derive NIR surface brightness maps and optical depth maps based on observations of dust emission, NIR extinction, and NIR scattered surface brightness and compare the results in Sect. 4. We describe radiative transfer modelling of a filament seen in scattered light in Sect. 5. We discuss the results in Sect. 6 and present our conclusions in Sect. 7.</text>
<section_header_level_1><location><page_2><loc_52><loc_64><loc_82><loc_65></location>2. Observations and data processing</section_header_level_1>
<section_header_level_1><location><page_2><loc_52><loc_62><loc_61><loc_63></location>2.1. WFCAM</section_header_level_1>
<text><location><page_2><loc_52><loc_36><loc_95><loc_61></location>We have used the Wide Field CAMera (WFCAM) (Casali et al. 2007) of the United Kingdom InfraRed Telescope (UKIRT) to observe a 1 · × 1 · field in the NIR J , H , and K bands (1.25, 1.65, and 2.22 µm , respectively). The field, which we call TMC-1N (Malinen et al. 2012), is in the Taurus molecular cloud complex north of TMC-1. The central coordinates of this field are RA (J2000) 4h39m36s and Dec (J2000) +26 · 39 ' 32 '' . At a distance of 140 pc, this corresponds to an area of ∼ (2.44 pc) 2 . The Galactic latitude of this area is approximately -13 . 3 · . The target field was chosen based on the Taurus extinction maps of Cambr'esy (1999) and Padoan et al. (2002). According to Rebull et al. (2011), there are no strong young stellar objects (YSOs) in TMC-1N that could cause additional scattered light and therefore complicate the analysis. There is mainly just one continuous filament in the field. The A V range of the area is suitable for our method: there are some regions with A V ∼ 20 m , but the mean value remains well below 10 magnitudes, even in most parts of the filament.</text>
<text><location><page_2><loc_52><loc_14><loc_95><loc_36></location>We applied sky correction using offset fields to be able to measure faint surface brightness features. The observations were made during 13 nights between 2006-2008 using 2 × 2 pointings towards the selected field. Because WFCAM consists of four separate CCD arrays, the result is a 1 · × 1 · image consisting of 4 × 4 subimages. We used four separate OFF fields. The standard data reduction was conducted in accordance with the normal pipeline routine 1 , including, e.g., dark-correction, flatfielding (including internal gain correction), decurtaining, sky correction, and cross-talk. Standard decurtaining methods 2 were needed to remove the stripes caused by the instrument. The details of the observations are shown in Malinen et al. (2012) where we compared the filament properties derived using NIR extinction and sub-millimetre dust emission observed with Herschel . There, the NIR data were calibrated to magnitudes with the help of 2MASS catalogue stars to derive</text>
<text><location><page_3><loc_7><loc_88><loc_50><loc_93></location>an extinction map with the NICER method (Lombardi & Alves 2001). Here, in order to study the surface brightness, we calibrated the data from magnitudes to MJy/sr units using aperture photometry of several stars in each frame.</text>
<text><location><page_3><loc_7><loc_64><loc_50><loc_87></location>The reduced images contained residual gradients in each sub-image, shown as brightening of the signal towards the frame edges. These are probably of instrumental origin. The size of the gradients as a percentage of overall sky level varies, but is typically between 0.002-0.008. Dye et al. (2006) and Warren et al. (2007) report several types of artefacts in WFCAM data and note that removing sky subtraction residuals is a complex problem, especially when observing near the Moon. However, during our observations the Moon was always further than 40 degrees away. In addition, the moonlight artefacts that cause most problems are local scattered light from dust on the optics, not gradients. The master twilight flats may have low level gradients present in them, given the size of the WFCAM field-of-view. The dark correction can also leave low level reset anomalies, particularly near the detector edges. It is possible that our data are showing comparatively low-level residual issues that the general surveys have not encountered.</text>
<text><location><page_3><loc_7><loc_49><loc_50><loc_63></location>We first removed the stars using the Iraf Daophotpackage, masked the remaining bad pixels (noisy borders and residuals of bright or saturated stars) and performed the surface brightness calibration. We modelled the gradients with a method described in the following subsection (Sect. 2.1.1). We convolved the calibrated frames with a 2 '' Gaussian beam and resampled the data onto 0.8 '' pixels. The obtained gradients were then subtracted from the frames. The maximum intensity of the filament is a few times higher than the typical magnitude of the instrumental gradients.</text>
<text><location><page_3><loc_7><loc_34><loc_50><loc_49></location>We further median-filtered the images to ∼ 16.8 '' resolution to diminish the effect of residual stars and stellar artefacts, and finally convolved them to ∼ 40 '' resolution, for later comparison with Herschel observations at that resolution. We combined the frames to a full map using Montage 3 and resampled the data onto 8 '' pixels for the analysis. For comparisons with NICER data, we further convolved the intensity maps to 60 '' resolution. We subtracted the background from the maps, using an area of low column density outside the filament as a reference, see Fig. 9 (middle frame).</text>
<text><location><page_3><loc_7><loc_23><loc_50><loc_34></location>A map of visual extinction, A V , of the TMC-1N area was already derived and presented in Malinen et al. (2012), using a Cardelli et al. (1989) extinction curve with R V = 4 . 0. In this paper, we mainly use the J band optical depth τ J , which is in practice independent of the assumption of the R V value. For comparison, a Cardelli et al. (1989) extinction curve with R V = 4 . 0 gives the relation τ J = 0 . 2844 × A V .</text>
<text><location><page_3><loc_7><loc_14><loc_50><loc_23></location>Roy et al. (2013) discuss the effect of the finite width of the filters on the observed extinction. In their Fig. 10, they show the relation of colour excess E ( J -K S ) obtained with 2MASS filters to the corresponding monochromatic colour excess as a function of N H . In TMC-1N, having an A V of mostly less than 20 m , the effect is small (less than 5% even in the densest parts), and we have not made this correction.</text>
<section_header_level_1><location><page_3><loc_52><loc_92><loc_70><loc_93></location>2.1.1. Gradient modelling</section_header_level_1>
<text><location><page_3><loc_52><loc_70><loc_95><loc_91></location>During the data reduction, separate analysis was carried out to model and subtract the residual artefacts of the surface brightness data. To be able to model the large scale gradients, we first filtered the masked and calibrated data with a median filter to ∼ 40 '' resolution. The gradients were strongest near the borders, which meant that the overlap between the frames could not be reliably used to aid the gradient removal. To model the gradient, therefore, we assumed a similar relation between the column density and the surface brightness as the one described in Sect. 3. We used the Herschel column density map described in Sect. 2.2 as an independent tracer of the filament structure in the fitting of the gradients. In principle, the extinction map obtained from NIR reddening of background stars could also have been used, but we chose Herschel data because of its lower noise.</text>
<text><location><page_3><loc_52><loc_64><loc_95><loc_70></location>We modelled the gradients with a third order surface describing the artificial gradient in the image, with an additional column density dependent term. We used least squares fitting to minimize, separately for each band i in ( J , H , K ) and each frame, the residual</text>
<formula><location><page_3><loc_52><loc_61><loc_95><loc_63></location>Res = P + a i (1 -e -b i N ) -I i (1)</formula>
<text><location><page_3><loc_52><loc_55><loc_95><loc_60></location>where P is the complete third order polynomial for a 2dimensional surface (10 terms), I i is the observed intensity map in band i , and N the column density derived from Herschel data.</text>
<text><location><page_3><loc_52><loc_33><loc_95><loc_55></location>The parameter b describes the saturation of the relation between I and N , and it mainly depends on the grain properties (Juvela et al. 2006). If we presume that the dust grains in the cloud are similar as in the model of Juvela et al. (2006), the same b values should apply as long as the optical depth is not high. Therefore, we used the parameter values b J = 0.34, b H = 0.23, and b K = 0.15, (in 1/mag units, as the model used A V values instead of N ) taken from the model data. The parameter b does not depend on the strength of the incoming radiation, but in some amount on the direction distribution. The model was based on a large cloud with an inhomogeneous density distribution and an isotropic radiation field. TMC-1N, on the other hand, has a single, filamentary structure, and a larger part of the radiation comes in from the observer's side. We do not expect the model to describe the filament perfectly, but the model parameter values served as a good starting point.</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_33></location>The coefficients of the polynomial are free parameters and are used to describe the artificial gradients that will be removed in the subsequent analysis. The parameters a i are related to the actual signal from the cloud and are the same for all frames in the same band. They are also kept as free parameters to minimise the effect the cloud structure has on the gradient fits. The exponential term M = a i (1 -e -b i N ) is only an approximation of the column density dependence of the scattered light. However, because gradients are described only as third order surfaces over each frame and scattered light is visible only in some parts of each frame, the obtained gradient model is not expected to be strongly dependent on the reference map, here the column density derived from Herschel . In particular, the scaling between column density and the surface brightness is a free parameter and thus no assumption is made of the expected level of NIR surface brightness. Furthermore, the non-linear approximation represented by the term M becomes important</text>
<text><location><page_4><loc_7><loc_82><loc_50><loc_93></location>only at A V ∼ 10 m . To obtain a better fit for the central part of the frames used in the following analysis, the gradients were fitted excluding a 10% wide border in each frame. For comparison, we also performed a fit to the whole area of the frames, in order to better fit the borders of the frames. The fitting provides the model P (for each frame and band) of the gradients that we subtract from the original surface brightness images. Note that the exponential term M is not subtracted as that is not part of the artefact.</text>
<text><location><page_4><loc_7><loc_59><loc_50><loc_81></location>We tested the reliability of the gradient removal method in several ways. We calculated the residual between the used model and the corrected surface brightness map, S = I -P , with the function Res = a i (1 -e -b i N ) -S i , where b i are the constants used in the gradient modelling and a i are the values obtained from the fit. N is the map used in the gradient modelling. We used surface brightness maps in ∼ 2.2 '' resolution. The mean values for the residual are -0.0052, 0.00035, and 0.000074 MJy/sr for the J , H , and K bands, respectively. The standard deviation for the residuals of the same bands are 0.017, 0.031, and 0.021 MJy/sr. Noise, especially near the borders, increases the obtained standard deviation values. The absolute values for the mean residuals for all bands are less than 0.006 MJy/sr, indicating that the minimisation of the residual in Eq. 1 has been effective. The filament is not apparent in the residuals nor in the removed gradients.</text>
<text><location><page_4><loc_7><loc_41><loc_50><loc_59></location>We also compared the surface brightness maps derived using different areas for the fitting of the gradient, full area or excluding 10% wide borders of each frame. After the gradient removal, we compared the surface brightness maps (in 40 '' resolution) by calculating the difference between the maps in the final masked area shown in Fig. 2. The means of the difference of the final masked area are 0.0026, 0.0026, and -0.0014 MJy/sr for the J , H , and K bands, respectively. The standard deviations for the difference of the same bands are 0.0044, 0.0072, 0.0052 MJy/sr. This indicates that small differences in the fitting area do not cause a significant difference in the central parts of the corrected frames. Near the borders of the frames, the difference can be larger.</text>
<section_header_level_1><location><page_4><loc_7><loc_37><loc_16><loc_38></location>2.2. Herschel</section_header_level_1>
<text><location><page_4><loc_7><loc_23><loc_50><loc_36></location>The Taurus molecular cloud has been mapped with Herschel (Pilbratt et al. 2010) as part of the Gould Belt Survey 4 (Andr'e et al. 2010), see Kirk et al. (2013) and Palmeirim et al. (2013). We used SPIRE (Griffin et al. 2010) 250 µ m, 350 µ m, and 500 µ m maps of the TMC-1N field. We obtained the data from the Herschel Gould Belt Survey consortium. The observation identifiers of the data are 1342202252 and 1342202253. The details of the Herschel data and the derivation of column density map are presented in Malinen et al. (2012).</text>
<text><location><page_4><loc_7><loc_13><loc_50><loc_23></location>For easier comparison with other maps and to avoid the assumptions needed to make column density maps, we used optical depth τ 250 instead. We use the notation τ 250 to mean optical depth τ ν at wavelength 250 µ m ( ν =1200GHz). We derived τ 250 maps from Herschel intensity and colour temperature maps, using a value of 1.8 for the spectral index β . Recent studies with Planck (Planck Collaboration et al. 2011) show that this is a good estimate for Taurus. For</text>
<text><location><page_4><loc_52><loc_91><loc_95><loc_93></location>comparison, we also made the analysis with the commonly used value of β = 2 . 0.</text>
<section_header_level_1><location><page_4><loc_52><loc_87><loc_60><loc_88></location>2.3. Spitzer</section_header_level_1>
<text><location><page_4><loc_52><loc_72><loc_95><loc_86></location>The Taurus filament is covered by observations of the Spitzer IRAC instrument (Fazio et al. 2004). The IRAC data (observation numbers 11230976 and 11234816) are from the Taurus Spitzer legacy project (PI D. Padgett). The archival IRAC maps show some checkered pattern. We therefore started with the pipeline-reduced, artefactmitigated images (cbsd images). The residual offsets were corrected by subtracting the median value from each frame and by estimating the residual offsets with respect to the median of all frames 5 . The final mosaic image was then made with the MOPEX tool (Makovoz et al. 2006).</text>
<section_header_level_1><location><page_4><loc_52><loc_67><loc_90><loc_69></location>3. Deriving optical depth from scattered NIR surface brightness</section_header_level_1>
<text><location><page_4><loc_52><loc_59><loc_95><loc_66></location>Padoan et al. (2006) presented a method for converting scattered surface brightness into column density. Juvela et al. (2006, 2008) discussed the method and its reliability in more detail. We review the main points of the method given in these articles and formulate it to suit this study.</text>
<text><location><page_4><loc_52><loc_54><loc_95><loc_59></location>Based on the one-dimensional radiative transfer equation in a homogeneous medium, the relationship between surface brightness ( I ) and column density ( N ) can be approximated with the formula</text>
<formula><location><page_4><loc_52><loc_52><loc_95><loc_53></location>I = a (1 -e -bN ) (2)</formula>
<text><location><page_4><loc_52><loc_29><loc_95><loc_50></location>where the parameters a and b are positive constants defined separately for each band. The parameter b scales the column density to optical depth, τ . The function depicts the radiation coming from the cloud. We presume that the observed radiation is mainly caused by scattering. Also other tracers of cloud structure, such as extinction A V or optical depth τ can be used instead of column density N . In that case, the value and unit of the parameter b must be changed accordingly. The parameters b mainly depend on the NIR dust properties and the parameters a on the radiation field, although the interpretation is not this straightforward (Juvela et al. 2006). Equation 2 is exactly valid only for a homogeneous cloud. In real clouds it works only as an approximation. It is expected that both parameters change if the dust properties, radiation field or cloud geometry change. Both can, however, be treated just as empirical parameters.</text>
<text><location><page_4><loc_52><loc_25><loc_95><loc_28></location>In areas of low optical depth, the intensity of NIR scattered light is directly proportional to the column density as shown in the relation</text>
<formula><location><page_4><loc_52><loc_22><loc_95><loc_23></location>I = abN. (3)</formula>
<text><location><page_4><loc_52><loc_14><loc_95><loc_21></location>The product ab gives the scattered intensity per column density. With higher column densities ( A V ∼ 10 m ), the NIR intensity values begin to saturate, starting from the shorter wavelengths. Thus, the relation becomes more nonlinear with increasing column density.</text>
<text><location><page_5><loc_7><loc_74><loc_50><loc_93></location>Equation 2 can be considered as an empirical description of the relation between surface brightness and column density, and it is not necessarily the optimal functional form to describe this relation. However, as long as the data points follow this relation, it is possible to derive approximations for column density. Based on numerical simulations (Padoan et al. 2006; Juvela et al. 2006), this function is rather reliable in areas of low to medium visual extinction ( A V = 1 -15 m ), where the saturation is not strong. If no independent column density estimates are available, only the ratios between different bands can be derived from surface brightness observations. However, NIR observations also provide the colour excesses of background stars, and an extinction map can therefore be calculated and used to derive the necessary parameter values (Juvela et al. 2006).</text>
<text><location><page_5><loc_7><loc_55><loc_50><loc_73></location>To derive an optical depth τ SB J map from the surface brightness maps, we obtain a and b parameter values for each band from I ν /τ Nicer J correlations by fitting Eq. 2 to the data, using optical depth τ Nicer J instead of column density N in the exponential part. Thus, Eq. 2 is used to establish a non-linear scaling between the extinction that increases linearly with column density and the surface brightness for which the increase is non-linear. Once the parameters of this mapping have been determined, we can convert surface brightness observations directly to estimates of column density, possibly at a resolution higher than what is possible using background stars alone. Using the obtained parameter values, we calculate a value for each pixel of the τ SB J map by minimising the squared sum of residuals</text>
<formula><location><page_5><loc_7><loc_50><loc_50><loc_53></location>R 2 pixel = ∑ i = J,H,K ( I i -M i ) 2 pixel (4)</formula>
<text><location><page_5><loc_7><loc_48><loc_48><loc_49></location>where I i are the pixel values of the intensity maps, and</text>
<formula><location><page_5><loc_7><loc_44><loc_50><loc_46></location>M i = a i (1 . 0 -e -b i τ SB J ) (5)</formula>
<text><location><page_5><loc_7><loc_39><loc_50><loc_42></location>for each i in ( J , H , K ). Minimisation is needed, as the observed intensities do not follow Eq. 2 exactly due to noise and possible model errors.</text>
<section_header_level_1><location><page_5><loc_7><loc_34><loc_15><loc_35></location>4. Results</section_header_level_1>
<text><location><page_5><loc_7><loc_18><loc_50><loc_33></location>Surface brightness map in J band with 40 '' resolution is shown in Fig. 1. In this figure, the gradient removal is made using a fit to the whole area of each frame. In the analysis, bad pixels, border regions suffering from imperfect gradient removal, and the main artefacts remaining after star removal were all masked. We also limited the analysis to areas where Herschel column density values are above 1.0 × 10 21 cm -2 . The masked J map used in the analysis is shown in Fig. 2. We used the same mask for all maps ( J , H , K , NICER, and Herschel ) in the analysis. The reference area used for background subtraction is shown in Fig. 9 (middle frame). The median τ J in this area is ∼ 0.1.</text>
<text><location><page_5><loc_7><loc_10><loc_50><loc_17></location>A combined three-colour image of WFCAM J , H , and K band intensity maps with 40 '' resolution is shown in Fig. 3. Here, the removed gradients were fitted to the frames excluding 10% wide borders of each frame. The remaining gradients can most clearly be seen near the corners of the frames. Borders of the frames have been masked.</text>
<figure>
<location><page_5><loc_53><loc_67><loc_93><loc_91></location>
<caption>Fig. 2. J band intensity map with low column density areas (below 1.0 × 10 21 cm -2 ) and bad pixels masked. Only the shown unmasked data are used in the scatter plot analysis.</caption>
</figure>
<figure>
<location><page_5><loc_52><loc_33><loc_90><loc_60></location>
<caption>Fig. 3. Combined three-colour image of WFCAM J , H , and K band intensity maps with 40 '' resolution. J , H , and K bands are encoded in red, green, and blue, respectively. The removed gradients were fitted to the frames excluding 10% wide borders of each frame.</caption>
</figure>
<section_header_level_1><location><page_5><loc_52><loc_20><loc_94><loc_22></location>4.1. Correlations between NIR surface brightness and optical depth derived from extinction and dust emission</section_header_level_1>
<text><location><page_5><loc_52><loc_10><loc_95><loc_19></location>We show correlations between the NIR surface brightness in J , H , and K bands for the main filament area in Fig. 4. The main cloud of points is concentrated to values below 0.08 MJy/sr in I J , 0.17 MJy/sr in I H , and 0.12 MJy/sr in I K . The correlation between I J and I K is approximately linear up to I K ∼ 0.06 MJy/sr, after which I J starts to saturate. Similarly, the correlation between I H and I K is</text>
<text><location><page_5><loc_93><loc_78><loc_93><loc_78></location>✁</text>
<figure>
<location><page_6><loc_7><loc_76><loc_35><loc_91></location>
</figure>
<figure>
<location><page_6><loc_36><loc_76><loc_63><loc_91></location>
</figure>
<figure>
<location><page_6><loc_65><loc_76><loc_93><loc_91></location>
<caption>Fig. 1. J , H , and K band intensity maps observed with WFCAM and convolved to 40 '' resolution. Masked pixels are marked white.</caption>
</figure>
<text><location><page_6><loc_7><loc_67><loc_50><loc_70></location>approximately linear up to I K ∼ 0.08 MJy/sr, after which I H starts to saturate.</text>
<text><location><page_6><loc_7><loc_55><loc_50><loc_67></location>Compared to Fig. 3 in Juvela et al. (2008) for Corona Australis, our WFCAM data for TMC-1N show similar linear relations between I J and I K and between I H and I K in the low end of the intensity scale, although our data show slightly lower values. In TMC-1N, the main cloud of points is concentrated to I K values below 0.12 MJy/sr, whereas in Corona Australis there are also points up to I K ∼ 0.7 MJy/sr. In Corona Australis, the correlations turn to negative between I K ∼ 0.4-0.7 MJy/sr.</text>
<text><location><page_6><loc_7><loc_34><loc_50><loc_55></location>Correlations between surface brightness, I ν , and optical depth in J band derived from extinction, τ Nicer J , are shown for bands J , H , and K in Fig. 5. We fit Eq. 2 to the data, using optical depth τ Nicer J instead of column density N in the exponential part. As a result, we obtain for each band the a and b parameters needed for the derivation of the optical depth map. The fitted values are a J = 0 . 08, b J = 0 . 90, a H = 0 . 20, b H = 0 . 44, a K = 0 . 19, and b K = 0 . 21. For comparison, we plot in the same figures the data of Corona Australis from Juvela et al. (2008). We have scaled those data to I ν units (MJy/sr), as a function of τ J . Compared to Corona Australis, we obtain notably lower values for I ν as a function of τ J in all three bands. We also fit Eq. 2 to these data and show the obtained parameters in the figure. For comparison, we also show correlations between I ν and optical depth derived from Herschel maps, τ 250 , in Fig. 6.</text>
<text><location><page_6><loc_7><loc_19><loc_50><loc_34></location>We made error estimates for the a and b parameters obtained from the fitting of Eq. 2 using two different methods. First, we used a standard bootstrap method to estimate the errors caused by sampling. We made the fit using 100 different samples from the data, all samples having the size of the full dataset. The standard deviations for the a and b parameters and their product a × b , that is the slope of the linear part of the function, are shown in Table 1. The standard deviation for parameter a can be up to 0.004, and for parameter b up to ∼ 0.006, but for the slope the uncertainty is rather small, ∼ 0.0002 for K , ∼ 0.0003 for J , and ∼ 0.0004 for H band.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_19></location>Secondly, we tested the possible systematic effect of changing the upper limit of the fitted range between τ J values 1 . 5 -6 . 0. In Table 2 we show the relative change in the parameter values when the upper limit of the fitted range is changed from τ J = 2 . 0 to τ J = 6 . 0, as between these values the change is mainly systematic. Even though the change in the a parameter can be up to -33% and in the</text>
<table>
<location><page_6><loc_52><loc_61><loc_78><loc_66></location>
<caption>Table 1. Standard deviations ( σ ) for the a and b parameters and their product a × b .Table 2. Relative change in the a and b parameters and their product a × b when the upper limit of the fitted range is changed from τ J = 2 . 0 to τ J = 6 . 0.</caption>
</table>
<table>
<location><page_6><loc_52><loc_49><loc_75><loc_54></location>
</table>
<text><location><page_6><loc_52><loc_41><loc_95><loc_46></location>b parameter up to 61%, the change in the slope of the linear part is less than 10% for each band. Below a τ J value of 2.0, the parameter values can change in a more unpredictable way.</text>
<text><location><page_6><loc_52><loc_22><loc_95><loc_41></location>We derive emissivity, the ratio of FIR dust emission to column density, by using τ J obtained from NIR extinction map as an independent tracer of column density. Correlation between τ 250 and τ Nicer J with β = 1 . 8 is shown in Fig. 7 for the main filament area shown in Fig. 2. The slope of a straight line fitted to the range τ Nicer J =0-4 is ∼ 0.0013. We also tested the possible change of slope in the low and middle τ Nicer J range. The derived slope is 0.0013 for range 0-2, and 0.0015 (more precisely 0.00149) for range 2-4. If we change β from 1.8 to 2.0, the slope between 0-4 increases ∼ 32% to the value ∼ 0.0018. We also made a similar fit using all the data in the maps. The derived slope is 0.0013 for range 0-2, and 0.0014 (more precisely 0.00144) for range 2-4, indicating that there is no significant change when compared to the masked area.</text>
<text><location><page_6><loc_52><loc_18><loc_95><loc_22></location>For comparison with other studies, we convert our slope of τ 250 /τ J = 0 . 0013 to opacity or dust emission crosssection per H nucleon</text>
<formula><location><page_6><loc_52><loc_16><loc_95><loc_17></location>σ e ( ν ) = τ ν /N H = µm H κ ν [cm 2 / H] , (6)</formula>
<text><location><page_6><loc_52><loc_10><loc_95><loc_15></location>where τ ν is optical depth, N H is the total H column density (H in any form), µ is the mean molecular weight per H (1.4), m H is the mass of H atom, and κ ν is the mass absorption (or emission) coefficient (cm 2 /g) relative to gas</text>
<text><location><page_6><loc_36><loc_82><loc_37><loc_85></location>Dec (J2000)</text>
<text><location><page_6><loc_65><loc_82><loc_66><loc_85></location>Dec (J2000)</text>
<text><location><page_6><loc_35><loc_82><loc_35><loc_82></location>✂</text>
<text><location><page_6><loc_63><loc_82><loc_63><loc_82></location>✂</text>
<text><location><page_6><loc_93><loc_82><loc_93><loc_82></location>✂</text>
<text><location><page_7><loc_9><loc_57><loc_9><loc_57></location>✂</text>
<text><location><page_7><loc_9><loc_84><loc_9><loc_84></location>✁</text>
<text><location><page_7><loc_38><loc_93><loc_40><loc_94></location>0.5</text>
<text><location><page_7><loc_67><loc_93><loc_69><loc_94></location>0.7</text>
<figure>
<location><page_7><loc_7><loc_78><loc_94><loc_93></location>
</figure>
<text><location><page_7><loc_21><loc_78><loc_21><loc_78></location>J</text>
<text><location><page_7><loc_50><loc_78><loc_50><loc_78></location>J</text>
<text><location><page_7><loc_79><loc_78><loc_79><loc_78></location>J</text>
<figure>
<location><page_7><loc_7><loc_50><loc_94><loc_65></location>
<caption>Fig. 5. Observed NIR surface brightness I ν as the function of optical depth derived with NICER method τ Nicer J in J , H , and K bands. WFCAM data for TMC-1N are shown with a 2D histogram, the colour scale corresponding to the density of points. The black line shows the fitted Eq. 2 (using τ Nicer J instead of column density N ). For comparison, Corona Australis data from Juvela et al. (2008) are shown with black dots and the fitted function with a red line. The black dashed vertical line shows the upper limit used in the fitting of TMC-1N data in all frames and of Corona Australis data in left and middle frames. In the right frame ( K band), the red dashed vertical line shows the upper limit used in the fitting of Corona Australis data, as in this case higher upper limit was needed to make a better fit. The obtained parameter values are marked in the figures with black for TMC-1N and red for Corona Australis.Fig. 6. Observed NIR surface brightness I ν as the function of optical depth derived from Herschel maps τ 250 in J , H , and K bands. The data are at 40' resolution.</caption>
</figure>
<text><location><page_7><loc_7><loc_40><loc_50><loc_44></location>mass, also often called opacity. We again use wavelength instead of frequency in our notation: σ e (250) = σ e (250 µ m) = σ e (1200GHz).</text>
<text><location><page_7><loc_7><loc_15><loc_50><loc_40></location>We derive the τ 250 map directly from the Herschel observations, and use our WFCAM NIR extinction map as an independent tracer of the column density. We use the conversion factor for diffuse clouds N (HI + H 2 ) /E ( B -V ) = 5 . 8 × 10 21 cm -2 /mag of Bohlin et al. (1978). We derive the relation E ( B -V ) /E ( J -K ) from Cardelli et al. (1989) extinction curves, and obtain values 1.999 (with R V = 3 . 1) and 1.413 (with R V = 4 . 0), leading to relations N (H) = 11 . 59 × 10 21 E ( J -K ) (with R V = 3 . 1) and N (H) = 8 . 196 × 10 21 E ( J -K ) (with R V = 4 . 0). Martin et al. (2012) have observed a similar relation, N (H) ∼ 11 . 5 × 10 21 E ( J -K S ), for regions of moderate extinction in Vela. Cardelli et al. (1989) extinction curves also give the relation A J /E ( J -K ) ∼ 1 . 675 (with both R V values 3.1 and 4.0). Converting magnitudes to optical depths ( A = 2 . 5 lg ( e ) τ ∼ 1 . 086 τ ) gives the relation E ( J -K ) ∼ τ J / 1 . 54. This leads to the relations σ e (250) = 1 . 33 × 10 -22 τ 250 /τ J cm 2 /H (with R V = 3 . 1) and σ e (250) = 1 . 88 × 10 -22 τ 250 /τ J cm 2 /H (with R V = 4 . 0).</text>
<text><location><page_7><loc_7><loc_10><loc_50><loc_15></location>The value τ 250 /τ J = 0 . 0013 leads to values σ e (250) = 1 . 7 × 10 -25 cm 2 / H (with R V =3.1) or σ e (250) = 2 . 4 × 10 -25 cm 2 / H (with R V = 4 . 0). These can be converted to κ ν values 0.07 cm 2 /g or 0.10 cm 2 /g, respectively.</text>
<text><location><page_7><loc_52><loc_30><loc_95><loc_44></location>The map of the ratio τ 250 /τ Nicer J is shown in Fig. 8. The map shows no clear evidence for systematic increase of the ratio τ 250 /τ J with increasing density inside the densest filament. Some high value areas can be attributed to imperfections in the two maps, τ 250 and τ J . For instance, the high value area next to the densest part of the filament seems to be caused by the different shape of the filament in these two maps. There the value of the ratio is high, because the filament is slightly more narrow in τ J , possibly caused by the lack of background stars seen behind the densest filament.</text>
<section_header_level_1><location><page_7><loc_52><loc_27><loc_84><loc_28></location>4.2. Optical depth derived from scattered light</section_header_level_1>
<text><location><page_7><loc_52><loc_19><loc_95><loc_26></location>As described in Sect. 3, in order to derive an optical depth τ SB J map from the surface brightness maps, we obtain a and b parameter values for each band from correlations between I ν and τ Nicer J shown in Fig. 5. We calculate a value for each pixel of the τ SB J map by minimising Eq. 4.</text>
<text><location><page_7><loc_52><loc_13><loc_95><loc_19></location>We use 40 '' and 60 '' maps in the following analysis, but also show a higher resolution ( ∼ 2.2 '' ) τ SB J map in Fig. 9 (right frame). In the same figure, we also show maps of Herschel τ 250 and NICER τ Nicer J . In Fig. 10, we show closeups of the same maps.</text>
<text><location><page_7><loc_52><loc_9><loc_95><loc_12></location>Correlations between τ SB J /τ 250 (resolution 40 '' ) and τ SB J /τ Nicer J (resolution 60 '' ) are shown in Fig. 11. The ref-</text>
<text><location><page_7><loc_38><loc_56><loc_38><loc_56></location>✂</text>
<text><location><page_7><loc_67><loc_56><loc_67><loc_56></location>✂</text>
<text><location><page_7><loc_38><loc_84><loc_38><loc_84></location>✁</text>
<text><location><page_7><loc_67><loc_84><loc_67><loc_84></location>✁</text>
<text><location><page_8><loc_8><loc_80><loc_8><loc_80></location>✁</text>
<text><location><page_8><loc_8><loc_57><loc_8><loc_57></location>✁</text>
<figure>
<location><page_8><loc_7><loc_46><loc_50><loc_94></location>
<caption>Fig. 4. Surface brightness in J band, I J , as a function of the K band, I K , (upper frame) and I H as a function of I K (lower frame) for the main filament area shown in Fig. 2. The y = x function is denoted by a black line. The colour scale of the 2D histogram indicates the logarithmic density of the points, both here and in other figures. The data are convolved to 40 '' resolution.</caption>
</figure>
<text><location><page_8><loc_7><loc_22><loc_50><loc_34></location>erence area used for background subtraction is shown in Fig. 9 (middle frame). The fitted values for the slopes are 808 for τ SB J /τ 250 and 1.019 ∼ 1 for τ SB J /τ Nicer J . This is as expected, since τ SB J was derived based on the correlation between I ν and τ Nicer J . The correlations are linear up to τ Nicer J ∼ 4. Above that, the τ SB J values saturate strongly. The areas where τ Nicer J > 4 are marked with contours in Fig. 9 (middle frame), indicating that these form only a small area in the densest clumps inside the cloud.</text>
<section_header_level_1><location><page_8><loc_7><loc_18><loc_26><loc_19></location>4.3. Filament cross-sections</section_header_level_1>
<text><location><page_8><loc_7><loc_10><loc_50><loc_17></location>Median profiles of the filament are shown in Fig. 12, for bands J , H , and K (upper frame) and for τ Nicer J and τ SB J (lower frame). The cross-sections are taken from the area between the two red lines shown in Fig. 9 (middle frame), where we have continuous data in all WFCAM maps. This is not the densest part of the filament, but a moderately</text>
<figure>
<location><page_8><loc_52><loc_70><loc_95><loc_93></location>
<caption>Fig. 8. τ 250 /τ Nicer J map. τ 250 is derived from Herschel maps. τ 250 map is convolved to the same 60 '' resolution as τ Nicer J map. Areas where τ 250 < 0 . 0003 are masked. Contours for τ Nicer J = 4, 3, 1.5, and 0.75 are marked with red line. Contours for τ 250 = 0.0052, 0.0039, 0.0019, and 0.0010 are marked with black line.</caption>
</figure>
<text><location><page_8><loc_71><loc_70><loc_71><loc_70></location>J</text>
<paragraph><location><page_8><loc_52><loc_60><loc_95><loc_69></location>Fig. 7. Correlation between τ 250 and τ Nicer J with β = 1 . 8 for the main filament area shown in Fig. 2. τ 250 map is convolved to the same 60 '' resolution as τ Nicer J map. The data are fitted with a straight line, using data in the ranges τ J =0-2 (black line) and τ J =2-4 (red line). The values of the slopes, k , are indicated in the frame with corresponding colours.</paragraph>
<text><location><page_8><loc_90><loc_56><loc_93><loc_57></location>0.0030</text>
<figure>
<location><page_8><loc_53><loc_33><loc_94><loc_56></location>
</figure>
<text><location><page_8><loc_53><loc_43><loc_54><loc_47></location>Dec (J2000)</text>
<text><location><page_8><loc_52><loc_10><loc_95><loc_20></location>dense area next to it. The cross-sections show that the derived τ SB J gives rather similar results to the τ Nicer J map for the filament profile, except for an extra peak in the τ SB J profile. The profiles seen in J and K bands are rather similar, whereas the H band profile has approximately two times stronger peak than the other two bands. The filament width or FWHM is ∼ 3 ' ∼ 0 . 1 pc, as shown in Malinen et al. (2012).</text>
<text><location><page_8><loc_52><loc_82><loc_52><loc_82></location>✁</text>
<text><location><page_8><loc_94><loc_43><loc_94><loc_43></location>✁</text>
<text><location><page_8><loc_94><loc_45><loc_94><loc_45></location>✁</text>
<figure>
<location><page_9><loc_7><loc_76><loc_35><loc_91></location>
</figure>
<figure>
<location><page_9><loc_37><loc_76><loc_64><loc_91></location>
</figure>
<figure>
<location><page_9><loc_66><loc_76><loc_93><loc_91></location>
<caption>Fig. 9. Maps of optical depth τ : Herschel τ 250 (resolution 40 '' ), NICER τ Nicer J (resolution 60 '' ), and optical depth in J band, τ SB J , based on J , H , and K surface brightness maps (resolution ∼ 2.2 '' ). In the NICER map (middle frame) the densest areas where τ Nicer J > 4 are marked with a blue contour. The white rectangle marks the reference area used for background subtraction in the analysis. The profile cross-sections shown in Fig. 12 are taken as a median from the area between the two red lines.</caption>
</figure>
<figure>
<location><page_9><loc_7><loc_49><loc_35><loc_64></location>
</figure>
<figure>
<location><page_9><loc_36><loc_49><loc_63><loc_64></location>
</figure>
<figure>
<location><page_9><loc_66><loc_49><loc_92><loc_64></location>
<caption>Fig. 10. Maps of optical depth τ in a 10 × 10 arcmin area centered at 4h38m58s, +26 · 42 ' 24 '' (RA (J2000), Dec (J2000)): Herschel τ 250 (resolution 40 '' ), NICER τ Nicer J (resolution 60 '' ), and τ SB J (resolution ∼ 2.2 '' ).</caption>
</figure>
<section_header_level_1><location><page_9><loc_7><loc_41><loc_19><loc_42></location>4.4. Spitzer data</section_header_level_1>
<text><location><page_9><loc_7><loc_27><loc_50><loc_40></location>We compare the IRAC 3.6 µ m surface brightness with the Herschel optical depth τ 250 , to study also the correlations between MIR scattered light and sub-millimetre dust emission. The surface brightness at ∼ 3.6 µ m can still be dominated by light scattering, while at longer wavelengths, the scattering decreases and the signal is expected to be dominated by dust emission. Some contribution of dust emission cannot be excluded even around 3.6 µ m and we conservatively consider the Spitzer data only as an upper limit on the intensity of the scattered light.</text>
<text><location><page_9><loc_7><loc_10><loc_50><loc_26></location>The point sources are a major problem in estimating the level of the extended emission. Because the examined area is small, we can produce an extended MIR surface brightness map by manually masking all the visible point sources. The masks altogether cover 24 arcmin 2 . After the masking, we carry out median filtering. The filter calculates the 25% percentile of all unmasked pixels within a given radius that is fixed to 5 '' . If the area contains less than ten unmasked pixels, the value is left undefined. The images are then convolved with a Gaussian beam to produce final surface brightness maps at the resolution of 40 '' that corresponds to the resolution of the Herschel data. The convolution ignores the undefined values.</text>
<text><location><page_9><loc_52><loc_36><loc_95><loc_42></location>To reduce the noise (and because of the uncertainty of the fidelity of the large scale flat-fielding), data are correlated only around the main column density peak. The column density threshold of 4 × 10 21 cm -2 defines an area of ∼ 77 arcmin 2 .</text>
<text><location><page_9><loc_52><loc_22><loc_95><loc_35></location>The Spitzer 3.6 µ m map and the area used in the correlations are shown in Fig. 13. The resulting correlations between MIR surface brightness and optical depth τ 250 are shown in Fig. 14. In the figure, we also show the median surface brightness that is calculated for τ 250 bins with a width of 0.002. We fit a robust least squares line to the individual surface brightness values in pixels where τ 250 is between 0.0025-0.0065. The fit is performed iteratively, discarding points falling further than 2.5σ from the fitted line. The value of the fitted slope is 2.40 MJy/sr.</text>
<section_header_level_1><location><page_9><loc_52><loc_19><loc_75><loc_20></location>4.5. Spectral energy distributions</section_header_level_1>
<text><location><page_9><loc_52><loc_10><loc_95><loc_17></location>Spectral energy distributions are shown in Fig. 15. We calculate the values for I ν /τ J in TMC-1N with Eq. 3, using τ J instead of column density N . In areas of low optical depth, the product ab gives the ratio I ν /τ J . The obtained values for J , H and K bands are 0.074, 0.086, and 0.038 MJy/sr, respectively.</text>
<text><location><page_9><loc_62><loc_56><loc_63><loc_57></location>J</text>
<text><location><page_9><loc_35><loc_56><loc_35><loc_56></location>✁</text>
<text><location><page_9><loc_35><loc_83><loc_35><loc_83></location>✂</text>
<text><location><page_9><loc_63><loc_56><loc_63><loc_56></location>✁</text>
<text><location><page_9><loc_92><loc_56><loc_92><loc_56></location>✁</text>
<text><location><page_9><loc_92><loc_83><loc_92><loc_83></location>✂</text>
<text><location><page_10><loc_8><loc_82><loc_8><loc_82></location>✂</text>
<text><location><page_10><loc_8><loc_58><loc_8><loc_58></location>✁</text>
<figure>
<location><page_10><loc_7><loc_46><loc_50><loc_93></location>
<caption>Fig. 11. Correlations between τ SB and τ 250 with resolution 40 '' (upper frame) and between τ SB and τ Nicer J with resolution 60 '' (lower frame). The data are fitted with a straight line, marked with black line. The fitted values for the slope, k , are marked to the figures.</caption>
</figure>
<text><location><page_10><loc_26><loc_46><loc_26><loc_46></location>J</text>
<text><location><page_10><loc_7><loc_23><loc_50><loc_34></location>We compare our results with the values obtained for Corona Australis in Juvela et al. (2008) (filled squares in their Fig. 13). We have scaled the Corona Australis values to I ν /τ J units (with R V = 3 . 1). We have also marked Mathis ISRF (Interstellar Radiation Field) model (Mathis et al. 1983) values (with R V = 4 . 0) on the figure for comparison. The values are obtained by multiplying the Mathis intensities with the scattering cross-sections of the Draine (2003) dust model.</text>
<text><location><page_10><loc_7><loc_10><loc_50><loc_22></location>The values of J , H and K bands in TMC-1N are approximately one third of the values in Corona Australis. Mathis model values for H and K are ∼ 1.5 times as high as in TMC-1N. For J band, the Mathis model value is already ∼ 3 times as high as the TMC-1N values. The value we obtain for Spitzer 3.6 µ m is also only approximately one third of the value given by the Mathis model. In both TMC-1N and Corona Australis, I ν /τ J is lower in the J band than in the H band. However, in the Mathis model, the value for the J band is notably higher than for the H band.</text>
<figure>
<location><page_10><loc_52><loc_46><loc_95><loc_93></location>
<caption>Fig. 12. Median profile cross-sections of the filament, taken from the area between the two red lines shown in Fig. 9 (middle frame). (Upper frame) WFCAM maps in J , H , and K bands. (Lower frame) τ Nicer J is derived from NICER extinction map and τ SB J from WFCAM surface brightness maps, respectively.</caption>
</figure>
<section_header_level_1><location><page_10><loc_52><loc_31><loc_78><loc_32></location>5. Radiative transfer modelling</section_header_level_1>
<text><location><page_10><loc_52><loc_15><loc_95><loc_29></location>We carry out radiative transfer calculations of the ISRF light that is scattered from the cloud in the wavelength range 1.2-3.5 µ m. We construct a realistic threedimensional model of the density distribution of the densest part of the filament. Based on the density structure, we calculate predictions for the surface brightness using the Diffuse Infrared Background Experiment (DIRBE) observations on the Cosmic Background Explorer (COBE) as a template of the sky brightness. The radiative transfer calculations were carried out with a Monte Carlo radiative transfer program (Juvela & Padoan 2003).</text>
<text><location><page_10><loc_52><loc_10><loc_95><loc_15></location>The filament is illuminated by an anisotropic radiation field that, in conjunction with the scattering phase function, affects the strength and spatial distribution of the scattered intensity. We define the intensity of the incoming radiation</text>
<text><location><page_10><loc_53><loc_58><loc_53><loc_58></location>✁</text>
<text><location><page_10><loc_53><loc_81><loc_53><loc_81></location>✁</text>
<text><location><page_11><loc_8><loc_51><loc_8><loc_51></location>☎</text>
<text><location><page_11><loc_8><loc_46><loc_8><loc_46></location>✄</text>
<text><location><page_11><loc_9><loc_45><loc_9><loc_45></location>✂</text>
<text><location><page_11><loc_54><loc_92><loc_56><loc_94></location>0.25</text>
<figure>
<location><page_11><loc_52><loc_71><loc_95><loc_93></location>
<caption>Fig. 15. Spectral energy distribution shown as I ν /τ J . J, H, and K band data are shown with black circles (TMC-1N) and red squares (Corona Australis), and Spitzer 3.6 µm data with a black plus sign. Mathis ISRF model (Mathis et al. 1983) values are marked with blue crosses and a dashed line.</caption>
</figure>
<text><location><page_11><loc_52><loc_56><loc_95><loc_59></location>intensities themselves are ∼ 50% higher than in the Mathis et al. (1983) model.</text>
<text><location><page_11><loc_52><loc_43><loc_95><loc_56></location>The density distribution of the model cloud is based on the column density map that is derived from the Herschel sub-millimetre observations (see Malinen et al. 2012). This is based on the colour temperature of the emission and on the assumption that dust opacity follows the law 0.1 cm 2 /g ( ν /1000 GHz) β , with β = 2 . 0. The actual cloud model corresponds to 17 ' × 17 ' area that we cover with 68 × 68 pixels, 15 '' in size. Our three-dimensional cloud model is correspondingly a cube that consists of 68 3 cells and is viewed along one of its major axes.</text>
<text><location><page_11><loc_52><loc_37><loc_95><loc_43></location>The Herschel column density map constrains the mass distribution only in the plane of the sky. To construct a three-dimensional filament, we start with a cylindrical structure where the radial density profile follows the Plummer function</text>
<formula><location><page_11><loc_52><loc_33><loc_95><loc_36></location>ρ p ( r ) = ρ c [1 + ( r/R flat ) 2 ] p/ 2 . (7)</formula>
<text><location><page_11><loc_52><loc_12><loc_95><loc_32></location>with parameters ρ C = 4 × 10 4 cm -3 , R flat =0.03, and p =3.0. These are close to the values previously determined from the fitting of the Herschel observations (Malinen et al. 2012). This initial cylindrical structure therefore has properties close to those of the average filament. We modify this initial model by requiring that, for each line-of-sight, the column density of the model exactly matches that of the Herschel column density map. We calculate for each pixel the ratio of the Herschel column density and the initial column density in the model. The densities along the same line-of-sight are then multiplied by this value. The procedure modifies the filament so that it is no longer cylinder symmetric. However, the deformations remain relatively small so that the ratio of the major and minor axis of the 2D filament cross sections always remains below two.</text>
<text><location><page_11><loc_52><loc_10><loc_95><loc_12></location>The absolute value of the background affects the contrast between the cloud and the background. The surface</text>
<text><location><page_11><loc_49><loc_82><loc_49><loc_82></location>☎</text>
<text><location><page_11><loc_50><loc_78><loc_50><loc_78></location>✄</text>
<text><location><page_11><loc_50><loc_76><loc_50><loc_76></location>✂</text>
<figure>
<location><page_11><loc_8><loc_67><loc_50><loc_91></location>
<caption>Fig. 13. Spitzer 3.6 µ m intensity map of TMC-1N. The area with highest column density is shown with a contour and used in the scatter plot in Fig. 14. Pixels affected by point sources are masked and left empty in the figure.</caption>
</figure>
<figure>
<location><page_11><loc_7><loc_37><loc_50><loc_59></location>
<caption>Fig. 14. Spitzer 3.6 µ m surface brightness as the function of τ 250 derived from Herschel data. The black circles show the median surface brightness in τ 250 = 0.002 wide bands. The dashed red line is a robust least squares fit to the range τ 250 = 0.0025-0.0065, with the slope, k , given at the bottom of the frame. The zero point of the I ν (3.6 µ m) axis is arbitrary.</caption>
</figure>
<text><location><page_11><loc_7><loc_13><loc_50><loc_24></location>using the DIRBE all-sky maps 6 (Zodi-Subtracted Mission Average (ZSMA) Maps). The DIRBE bands 1, 2, and 3 can be used directly to specify the intensity at the corresponding wavelengths 1.2 µ m, 2.2 µ m, and 3.5 µ m. The H band intensity is obtained by multiplying the average of the J and K band intensities with the intensity ratio I H / < I J , I K > taken from the Mathis et al. (1983) ISRF model. Note that, averaged over the whole sky, the total</text>
<text><location><page_11><loc_8><loc_11><loc_9><loc_12></location>6</text>
<text><location><page_11><loc_10><loc_11><loc_12><loc_12></location>See</text>
<text><location><page_11><loc_17><loc_11><loc_22><loc_12></location>DIRBE</text>
<text><location><page_11><loc_28><loc_11><loc_36><loc_12></location>explanatory</text>
<text><location><page_11><loc_42><loc_11><loc_50><loc_12></location>supplement,</text>
<text><location><page_11><loc_7><loc_10><loc_51><loc_11></location>http://lambda.gsfc.nasa.gov/product/cobe/dirbe exsup.cfm</text>
<text><location><page_12><loc_7><loc_91><loc_50><loc_93></location>brightness relative to the brightness of the background sky is calculated as</text>
<formula><location><page_12><loc_7><loc_88><loc_50><loc_90></location>I = I sca + I bg e -τ -I bg , (8)</formula>
<text><location><page_12><loc_7><loc_77><loc_50><loc_88></location>where I is the total observed signal, I sca the scattered signal coming from the cloud, I bg e -τ the background signal coming directly (without scattering) through the cloud with optical depth τ , and I bg the background signal. The radiative transfer program takes into account the incoming ISRF and the absorption and scattering of those photons inside the cloud. I sca is the amount of light coming out of the cloud after this process.</text>
<text><location><page_12><loc_7><loc_57><loc_50><loc_77></location>The term I bg was estimated using WISE (Wright et al. 2010) and DIRBE data. The WISE map of a one degree diameter area around the column density peak was first adjusted to the absolute level indicated by the DIRBE data. We read the I bg value from the corrected WISE map, using the area that corresponds to the area where the model column density is approximately zero (corresponding to the upper part of Fig. 16). To exclude the effect of point sources in this area, we use the 40% percentile of pixels in this reference area. The values obtained for the background I bg are 0.122 MJy/sr ( J ), 0.0878 MJy/sr ( K ), and 0.0765 MJy/sr (3.4 µ m). We estimate a value 0.10 MJy/sr for the H band. The cosmic infrared background (CIB) between the J and 3.5 µ mbands is notably lower than these values, ∼ 0.01-0.02 MJy/sr (see, e.g., Cambr'esy et al. 2001; Wright & Reese 2000).</text>
<text><location><page_12><loc_7><loc_25><loc_50><loc_56></location>The dispersion of DIRBE values over the area used for comparison with WFCAM and WISE is ∼ 10% of the estimated I bg value. Because this includes not only noise but also real surface brightness variations, the statistical error of the mean DIRBE value is significantly lower. However, the dispersion is also a measure of the possible difference between the background value I bg derived for the reference area and the actual background at the position of the filament. The final I bg is calculated as 40% percentile of the reference area within WFCAM and WISE maps. The standard deviations of all pixels falling below the 40% value (assumed not to be significantly contaminated by point sources) are 0.011, 0.015, and 0.005 MJy sr -1 for J , K , and 3.4 µ m bands, respectively. The zero point uncertainty of the zodiacal light model subtracted in DIRBE ZSMA maps is ∼ 0.006 MJy sr -1 in the J band and less at longer wavelengths (Kelsall et al. 1998), but differences between zodiacal light models can be even larger (Wright 2001). Furthermore, Taurus is located at low ecliptic latitude and two thirds of the total signal observed by DIRBE consists of zodiacal light. A relative error of 10% in the zodiacal light model would therefore amount to ∼ 0.04, 0.03, and 0.02 MJy sr -1 for J , K , and 3.5 µ m, respectively, and could be the dominant source of error.</text>
<text><location><page_12><loc_7><loc_12><loc_50><loc_25></location>Diffuse emission that originates between the filament and observer does not contribute to Eq. 8, which describes the surface brightness contrast between the source and the background. In that equation, I bg corresponds to that part of the diffuse component that truly resides behind the filament. We can assume that most of the diffuse material is associated with the Taurus cloud but can reside either in front of or behind the filament. We therefore make the assumption that I bg corresponds to half of the values derived above.</text>
<text><location><page_12><loc_7><loc_10><loc_50><loc_12></location>If the diffuse component is closely associated with the filament, consistency requires that its effect is also taken</text>
<text><location><page_12><loc_52><loc_79><loc_95><loc_93></location>into account when calculating the component I sca . This term corresponds to photons scattered from the filament, excluding photons that may be scattered in some envelope around it. In this case, the filament (i.e., the densest part that is being modelled) is not illuminated by the full ISRF but by an ISRF that is attenuated by e -0 . 5 τ d , where τ d is the optical depth of the envelope. Similarly, when a photon scatters within the model, it must travel through a similar layer a second time (half of the full τ d ) before reaching the observer. Thus, the observed signal is reduced by a factor e -τ d .</text>
<text><location><page_12><loc_52><loc_70><loc_95><loc_79></location>We estimate that for the diffuse cloud τ J d = 0 . 5, and calculate values 0.34, 0.2, and 0.0998 for τ H d , τ K d , and τ 3 . 5 µ m d , respectively, using Cardelli et al. (1989) extinction curves. We compare three cases: (1) no background I bg , (2) with background I bg , and (3) with background I bg and attenuation of the scattered light in the envelope. We show the corrections in function</text>
<formula><location><page_12><loc_52><loc_67><loc_95><loc_69></location>I = I sca e -τ d + CI bg ( e -τ -1) , (9)</formula>
<text><location><page_12><loc_52><loc_62><loc_95><loc_66></location>where C is either 0 (case 1) or 0.5 (cases 2 and 3), indicating the amount of background, and use value 0 for τ d for cases 1 and 2, and the τ d values derived above for case 3.</text>
<text><location><page_12><loc_52><loc_52><loc_95><loc_62></location>In the calculations, we use the NIR dust properties of normal Milky Way dust (Draine 2003) and the tabulated scattering phase functions that are publicly available 7 . We do not seek a perfect match to the observations but explicitly assume the column density distribution and dust properties as described above. The comparison with the observations is thus a test for the consistency of these assumptions.</text>
<text><location><page_12><loc_52><loc_31><loc_95><loc_52></location>The τ J map of the model is shown in Fig. 16 and simulated scattered surface brightness maps in Fig. 17. Correlations of I ν and τ J from simulations are shown in Fig. 18 for intensity in bands J , H , and K , using the three cases for the background correction described above. For comparison, we plot in the same figures the data from our TMC-1N observations. We have subtracted the background from both the simulated and observed data using as reference area the area in which the model column density is lowest (corresponding to the upper part of Fig. 16). In the WFCAM data, the median τ J in this area is ∼ 0.5. Note the difference from Fig. 5, in which we used as reference area the low optical depth area marked in Fig. 9. We fit Eq. 2 to both of the data, using optical depth τ Nicer J instead of column density N in the exponential part. As a result, we obtain the a and b parameters for each band.</text>
<text><location><page_12><loc_52><loc_12><loc_95><loc_31></location>In the H band, the simulations give ∼ 1.5 times as high intensity values as the observations, without background (case 1). The observed values are mostly settled between the cases 2 and 3 in the simulations. In the K band, the simulations give nearly two times as high values to the observations, when no background is included (case 1). In case 3, with the background and attenuation in the envelope, the simulations give similar values as the observations. However, in the J band, the simulated values are approximately three times as high as in our observations, when no background is included (case 1). Even with background (case 2), the simulations still give approximately two times as high values. Only in case 3, with the attenuation in the envelope, the simulations give similar values to the observations. Even when the maximum intensities for observations</text>
<figure>
<location><page_13><loc_8><loc_67><loc_48><loc_91></location>
<caption>Fig. 16. Optical depth τ J of the model cloud.</caption>
</figure>
<text><location><page_13><loc_49><loc_40><loc_50><loc_41></location>9</text>
<figure>
<location><page_13><loc_7><loc_39><loc_50><loc_63></location>
<caption>Fig. 19. Simulated MIR surface brightness I ν in 3.5 µ m band as a function of τ J in the three test cases described in the text. The data are fitted with Eq. 2, and marked with the same notation as in Fig. 18. The black dashed line shows the upper limit for the data used in the fit. The obtained parameter values are marked in the figure.</caption>
</figure>
<text><location><page_13><loc_7><loc_24><loc_50><loc_28></location>and simulations are approximately the same, the form of the fitted Eq. 2 can be different, leading to notably different values for the parameters.</text>
<text><location><page_13><loc_7><loc_18><loc_50><loc_24></location>Correlation between I ν and τ J for the 3.5 µ m band is shown in Fig. 19, similarly using the three cases. At this wavelength, case 1 still gives two times as high values as case 2, but the difference between cases 2 and 3 is only ∼ 10%.</text>
<section_header_level_1><location><page_13><loc_7><loc_14><loc_18><loc_15></location>6. Discussion</section_header_level_1>
<text><location><page_13><loc_7><loc_10><loc_50><loc_13></location>We have studied a filament in the Taurus molecular cloud using NIR images of scattered light. The observations carried out with WFCAM instrument cover an area of 1 · × 1 ·</text>
<text><location><page_13><loc_52><loc_83><loc_95><loc_93></location>corresponding to ∼ (2.44 pc) 2 at the distance of 140 pc, making this, to our knowledge, the largest NIR map where the surface brightness is analysed in detail. We have analysed the faint surface brightness, determined its intensity (attributed to light scattering), and used it to derive an optical depth map based on the method of Padoan et al. (2006). We have compared the data derived from NIR scattering, NIR extinction and Herschel dust emission.</text>
<text><location><page_13><loc_52><loc_70><loc_95><loc_83></location>The signal-to-noise value, S/N, of our WFCAM data is lower than expected. There were significant artefacts, presumably of instrumental origin, namely the curtain effect and large scale gradients. It is possible that the excess noise is caused by these effects and the processes used to remove them. Due to this, the data could not be used at as high a resolution as expected. In principle, scattered light can be measured at arcsecond resolution. However, as shown here, it can be difficult to obtain reliable maps at the full resolution.</text>
<text><location><page_13><loc_52><loc_61><loc_95><loc_70></location>Correlations between I ν and τ Nicer J in Fig. 5 suggest that the radiation field in TMC-1N is notably lower in all three NIR bands when compared to similar observations of Corona Australis (Juvela et al. 2008). This reaffirms the results obtained with dust emission models of Juvela et al. (2012), suggesting that the radiation field in Corona Australis is at least three times that of the normal ISRF.</text>
<text><location><page_13><loc_52><loc_40><loc_95><loc_60></location>l o g 10 N p i x NIR intensity as a function of column density followed roughly the functional form assumed in Eq. 2. We have estimated the possible errors in obtaining the parameters a and b for each band from fitting Eq. 2 to the correlation between I ν and τ Nicer J . Errors caused by sampling are small, but changes to the fitting limit can cause up to ∼ 60% deviations in a single parameter. However, the change in the product a × b , that is the slope of the linear part of the Eq. 2, is only up to ∼ 10% for each band. As discussed in Sect. 3, Eq. 2 and the parameters a and b can be thought of as an empirical model that represents the relation between surface brightness and column density. The model may not be optimal and no direct physical interpretation can necessarily be attached to its parameters. Bias in the fitted parameter values could cause bias also when minimising the Eq. 4 to obtain an optical depth map.</text>
<text><location><page_13><loc_52><loc_29><loc_95><loc_40></location>We obtained the value 0.0013 for the slope τ 250 /τ Nicer J with β = 1 . 8, using values in the range τ J =0-2 (and the same for range 0-4), in Fig. 7. When we fit data in the range 2-4, the slope increased ∼ 15% to 0.0015, possibly suggesting a small increase in grain size in the denser areas, similarly to (Martin et al. 2012; Roy et al. 2013). With β = 2 . 0, and using range 0-4, the slope increased ∼ 38% to 0.0018.</text>
<text><location><page_13><loc_52><loc_10><loc_95><loc_29></location>For comparison with other studies, we convert our slope of τ 250 /τ Nicer J = 0 . 0013 to dust absorption cross-section per H nucleon, also called opacity. We use the conversion factor N (HI + H 2 ) /E ( B -V ) = 5 . 8 × 10 21 cm -2 /mag of Bohlin et al. (1978). In principle, this relation is valid only for diffuse areas, and can be used only as an approximation for the densest parts of our filament. We derive the extinction relations, E ( B -V ) /E ( J -K ) and A J /E ( J -K ), using the extinction curves of Cardelli et al. (1989), either with R V = 3 . 1 or R V = 4 . 0. This leads to σ e (250 µ m) values 1 . 7 × 10 -25 cm 2 / H (with R V =3.1) or 2 . 4 × 10 -25 cm 2 / H (with R V = 4 . 0). In terms of mass absorption (or emission) coefficient per gas mass, κ ν , the values are 0.07 cm 2 /g or 0.10 cm 2 /g, respectively. Changing the assumed R V value in E ( B -V ) /E ( J -K ) from 3.1 to 4.0 causes ∼ 40% increase</text>
<text><location><page_13><loc_47><loc_79><loc_47><loc_79></location>✁</text>
<text><location><page_14><loc_9><loc_45><loc_9><loc_45></location>✁</text>
<figure>
<location><page_14><loc_13><loc_77><loc_47><loc_94></location>
</figure>
<figure>
<location><page_14><loc_13><loc_57><loc_47><loc_74></location>
</figure>
<figure>
<location><page_14><loc_54><loc_77><loc_89><loc_93></location>
</figure>
<figure>
<location><page_14><loc_54><loc_57><loc_88><loc_74></location>
<caption>Fig. 17. Simulated maps of scattered surface brightness in J , H , K , and 3.5 µ m bands.</caption>
</figure>
<figure>
<location><page_14><loc_7><loc_38><loc_94><loc_54></location>
<caption>Fig. 18. Comparison of observed and simulated NIR surface brightness I ν in J , H , and K bands as the function of optical depth in J band, τ J . WFCAM data for TMC-1N are shown with a 2D histogram, the colour scale corresponding to the density of points, and a black line shows the fitted Eq. 2. For comparison, simulated data are shown in the same figures using the three test cases described in the text. We plot the simulated data points only for case 1 (black dots). The fitted function is marked with a green line (case 1: without background), blue line (case 2: with background), and red line (case 3: with background and attenuation of the scattered light in the envelope). In J band, black dashed vertical line shows the upper limit of fitting of both WFCAM and simulation data. In H and K bands, the black dashed vertical line shows the upper limit of fitting of WFCAM data, and green dashed vertical line the upper limit of fitting of simulated data (all three cases). To get a better fit, the limit for the observations is slightly higher. The obtained parameter values are marked in the figures with the same colours as the fitted lines.</caption>
</figure>
<text><location><page_14><loc_7><loc_17><loc_50><loc_22></location>in the obtained values. It is not obvious which assumptions can be made in areas having both diffuse and denser parts, but it is important to notice that the assumptions made will have notable differences in the results.</text>
<text><location><page_14><loc_7><loc_10><loc_50><loc_16></location>For high-latitude, diffuse ISM, the standard value for dust opacity is σ e (250 µ m) ∼ 1 . 0 × 10 -25 cm 2 / H (see, e.g., Boulanger et al. 1996; Planck Collaboration et al. 2011). In denser areas, 2-4 times larger values have been derived (see, e.g., Juvela et al. 2011; Planck Collaboration et al. 2011;</text>
<text><location><page_14><loc_52><loc_17><loc_95><loc_22></location>Martin et al. 2012; Roy et al. 2013). Our estimates for σ e (250 µ m) are ∼ 1 . 7 -2 . 4 times as large as the previous results for diffuse areas, at the lower limit of the values for denser areas.</text>
<text><location><page_14><loc_52><loc_9><loc_95><loc_16></location>As the width (or FWHM) of our filament is ∼ 0.1 pc, which for Taurus corresponds to ∼ 150 '' , we have enough resolution to look at the details of the filament. The τ 250 /τ Nicer J map shown in Fig. 8 gives no indication of systematic growth of the τ 250 /τ Nicer J towards the densest fil-</text>
<text><location><page_14><loc_38><loc_45><loc_38><loc_45></location>✁</text>
<text><location><page_14><loc_67><loc_45><loc_67><loc_45></location>✁</text>
<text><location><page_14><loc_47><loc_84><loc_47><loc_84></location>✁</text>
<text><location><page_14><loc_47><loc_65><loc_47><loc_65></location>✁</text>
<text><location><page_14><loc_88><loc_66><loc_88><loc_66></location>✂</text>
<text><location><page_14><loc_88><loc_63><loc_88><loc_63></location>✁</text>
<text><location><page_14><loc_89><loc_84><loc_89><loc_84></location>✁</text>
<text><location><page_15><loc_7><loc_84><loc_50><loc_93></location>ament. However, as discussed above, all the assumptions made in the process may not be valid in the densest part of the filament. As an additional confusing factor, some areas of high τ 250 /τ Nicer J ratio can be caused by small differences in the τ 250 and τ Nicer J maps, due to, e.g., the lack of background stars seen behind the densest filament, instead of real changes in the dust properties.</text>
<text><location><page_15><loc_7><loc_61><loc_50><loc_84></location>In Sect. 5, we constructed a realistic three-dimensional model of the density distribution of the densest part of the filament. We calculated predictions for the surface brightness using radiative transfer calculations of the ISRF light that is scattered from the cloud in the wavelength range 1.2-3.5 µ m. We used DIRBE observations as a model for the sky brightness. As the absolute value of the background affects the contrast between the cloud and the background, we calibrated our simulation data to the same absolute level with DIRBE. We also considered the role of a potential diffuse envelope that would affect the radiation impinging on the dense part of the filament, i.e., the part included in our model. We take into account that a scattered photon has to pass through the diffuse cloud twice. We compared three cases of using different background correction: (1) no background, (2) with background, and (3) with background and attenuation of the scattered light in the envelope surrounding the filament.</text>
<text><location><page_15><loc_7><loc_45><loc_50><loc_60></location>In the simulations, we have assumed that the filament is in the plane of the sky and is not prolate (long along the line-of-sight). If the filament is prolate, this will increase the short wavelength surface brightness relative to the longer wavelengths, and the saturation of the J band will be smaller. If the filament is not in the plane of the sky (i.e., our line-of-sight is not perpendicular to the filament axis), the effect is similar. The dust opacities used in the simulations are appropriate in high density environments (Hildebrand 1983; Beckwith et al. 1990) but could, in diffuse regions, overestimate κ (underestimate column density) by a factor of two (see Boulanger et al. 1996).</text>
<text><location><page_15><loc_7><loc_32><loc_50><loc_45></location>We find that the results change notably, especially for the J band, depending on what fraction of the background intensity is assumed to be really behind the filament and what fraction between the filament and the observer. In the J band, case 1 gives ∼ 1.5 times as high values to the relation between I ν and τ J as case 2, and ∼ 3 times as high values as case 3. In longer wavelengths the differences get smaller, but at 3.5 µ m, case 1 still gives ∼ 2 times as high values as case 2. At 3.5 µ m, the difference between cases 2 and 3 is only ∼ 10%.</text>
<text><location><page_15><loc_7><loc_18><loc_50><loc_32></location>In the H and K bands, the simulations give rather similar results to our observations in TMC-1N. However, in the J band, the simulations give over two times as high values as the observations, unless case 3 with the background correction and the correction for the scattered light is used. In the H band, case 3 also gives values that are lower than the observed values. The three test cases can be seen as rough error limits for the modelled cloud. Compared to the simulations, our observations do not suggest that there is any notable emission in the K band in addition to the scattered light.</text>
<section_header_level_1><location><page_15><loc_7><loc_14><loc_19><loc_15></location>7. Conclusions</section_header_level_1>
<text><location><page_15><loc_7><loc_10><loc_50><loc_13></location>We have used WFCAM NIR surface brightness observations to study scattered light in the TMC-1N filament in Taurus Molecular Cloud. We have presented a large NIR</text>
<text><location><page_15><loc_52><loc_85><loc_95><loc_93></location>surface brightness map (1 · × 1 · corresponding to ∼ (2.44 pc) 2 ) of this filament. We have converted the data into an optical depth map and compared the results with NIR extinction and Herschel observations of sub-mm dust emission. We have also modelled the filament by carrying out 3D radiative transfer calculations of light scattering.</text>
<unordered_list>
<list_item><location><page_15><loc_53><loc_81><loc_95><loc_84></location>-We see the filament in scattered light in all three NIR bands, J , H , and K .</list_item>
<list_item><location><page_15><loc_53><loc_73><loc_95><loc_81></location>-In all three NIR bands, our WFCAM observations in TMC-1N show lower intensity than previous results in Corona Australis, indicating a lower radiation field in this area. This reaffirms the previous findings, that the radiation field in Corona Australis is at least three times that of the normal ISRF.</list_item>
<list_item><location><page_15><loc_53><loc_64><loc_95><loc_73></location>-We derive a value 0.0013 for the ratio τ 250 /τ Nicer J . This leads to values σ e (250 µ m) ∼ 1 . 7 -2 . 4 × 10 -25 cm 2 / H, depending on the assumptions of the extinction curve ( R V = 3.1 or 4.0) which can change the results by over 40%. These σ e (250 µ m) values are twice the values reported for diffuse medium, at the lower limit of the values for denser areas.</list_item>
<list_item><location><page_15><loc_53><loc_61><loc_95><loc_64></location>-Changing β from 1.8 to 2.0 increases the ratio τ 250 /τ Nicer J by ∼ 30%.</list_item>
<list_item><location><page_15><loc_53><loc_51><loc_95><loc_61></location>-We see no indication of systematic growth of the τ 250 /τ Nicer J ratio towards the densest filament. However, all the assumptions made in the process may not be valid in the densest part of the filament. Also, some areas of high τ 250 /τ Nicer J ratio can be caused by imperfections in the τ 250 and τ Nicer J maps, due to, e.g., the lack of background stars seen behind the densest filament, instead of real changes in the dust properties.</list_item>
<list_item><location><page_15><loc_53><loc_42><loc_95><loc_51></location>-3D radiative transfer simulations predict surface brightness that is in intensity close to the observed values, especially in the H and K bands. In the J band, the model predictions can be over two times larger than observations, if no background correction is made. However, using background correction can change the results notably.</list_item>
<list_item><location><page_15><loc_53><loc_38><loc_95><loc_42></location>-We see no clear evidence for emission in the K band, in addition to the scattered light, based on the observations and simulations.</list_item>
<list_item><location><page_15><loc_53><loc_36><loc_95><loc_38></location>-NIR surface brightness can be a valuable tool in making high resolution maps, also at large scales.</list_item>
<list_item><location><page_15><loc_53><loc_29><loc_95><loc_35></location>-NIR surface brightness observations can be complicated, however, as the data can show comparatively low-level artefacts, that are still comparable to the faint surface brightness. This suggests caution when planning and interpreting the observations.</list_item>
<list_item><location><page_15><loc_53><loc_25><loc_95><loc_29></location>-It is possible to remove most of the effects of instrumental gradients, provided that they only affect large scales.</list_item>
</unordered_list>
<text><location><page_15><loc_52><loc_13><loc_95><loc_23></location>Acknowledgements. We thank the referee for useful comments. We thank CASA for carrying out the standard data reduction of the WFCAM data, and Mike Irwin for useful comments. JM and MJ acknowledge the support of the Academy of Finland Grants No. 250741 and 127015. MGR gratefully acknowledges support from the National Radio Astronomy Observatory (NRAO), the Joint ALMA Observatory and the Joint Astronomy Centre, Hawaii (UKIRT).The National Radio Astronomy Observatory is a facility of the NationalScience Foundation operated under cooperative agreement by AssociatedUniversities, Inc.</text>
<text><location><page_15><loc_52><loc_10><loc_95><loc_13></location>The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the U.K. This paper makes use of WFCAM observations</text>
<text><location><page_16><loc_7><loc_91><loc_50><loc_93></location>processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge.</text>
<text><location><page_16><loc_7><loc_84><loc_50><loc_91></location>This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.</text>
<text><location><page_16><loc_7><loc_78><loc_50><loc_84></location>This research made use of Montage, funded by the National Aeronautics and Space Administration's Earth Science Technology Office, Computation Technologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology. Montage is maintained by the NASA/IPAC Infrared Science Archive.</text>
<text><location><page_16><loc_7><loc_75><loc_50><loc_77></location>This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA.</text>
<text><location><page_16><loc_7><loc_69><loc_50><loc_74></location>This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Context. Mapping of the near-infrared scattered light is a recent method for the study of interstellar clouds, complementing other, more commonly used methods, like dust emission and extinction. Aims. Our goal is to study the usability of this method on larger scale, and compare the properties of a filamentary structure using infrared scattering and other methods. We also study the radiation field and differences in grain emissivity between diffuse and dense areas. Methods. We have used scattered near-infrared (NIR) J , H , and K band surface brightness observations with WFCAM instrument to map a filament TMC-1N in Taurus Molecular Cloud, covering an area of 1 · × 1 · corresponding to ∼ (2.44 pc) 2 . We have converted the data into an optical depth map and compared the results with NIR extinction and Herschel observations of sub-mm dust emission. We have also modelled the filament with 3D radiative transfer calculations of scattered light. Results. We see the filament in scattered light in all three NIR bands. We note that our WFCAM observations in TMC-1N show notably lower intensity than previous results in Corona Australis using the same method. We show that 3D radiative transfer simulations predict similar scattered surface brightness levels as seen in the observations. However, changing the assumptions about the background can change the results of simulations notably. We derive emissivity, the ratio of FIR dust emission to column density, by using optical depth in the J band, τ J , obtained from NIR extinction map as an independent tracer of column density. We obtain a value 0.0013 for the ratio τ 250 /τ Nicer J . This leads to opacity or dust emission cross-section σ e (250 µ m) values 1 . 7 -2 . 4 × 10 -25 cm 2 / H, depending on assumptions of the extinction curve, which can change the results by over 40%. These values are twice as high as obtained for diffuse areas, at the lower limit of earlier results for denser areas. Conclusions. We show that NIR scattering can be a valuable tool in making high resolution maps. We conclude, however, that NIR scattering observations can be complicated, as the data can show comparatively low-level artefacts. This suggests caution when planning and interpreting the observations. Key words. ISM: Clouds - Stars: formation - Infrared: ISM - Submillimeter: ISM - Scattering - Radiative transfer",
"pages": [
1
]
},
{
"title": "Mapping of interstellar clouds with infrared light scattered from dust: TMC-1N glyph[star]",
"content": "J. Malinen 1 , M. Juvela 1 , V.-M. Pelkonen 2 , 1 , and M. G. Rawlings 3 Preprint online version: October 16, 2018",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The structure of molecular clouds can be studied via a number of methods. These include molecular line mapping, observations of dust emission at far-infrared/sub-millimetre wavelengths, star counts in the optical and near-infrared (NIR) wavelengths, and measurements of colour excesses of background stars. All techniques have their own drawbacks. For example, line and continuum emission maps are subject to abundance variations (gas and dust, respectively) and variations in the physical conditions, most notably the excitation and kinetic temperatures. Mass estimates based on dust emission can also be biased because of line-of-sight temperature variations, especially in high density clouds where star formation is potential (see, e.g., Malinen et al. 2011). The colour excess method provides column density estimates for extremely narrow lines of sight toward background stars. However, the intrinsic colours of the stars are usually unknown and this introduces significant noise, especially at low column densities. A full extinction map is obtained only after spatial averaging. This means that for all the listed methods the spatial resolution is usually some tens of arc seconds or worse. See, e.g., Juvela et al. (2006) for a more thorough review of the methods, Goodman et al. (2009) for a comparison of several methods, and Malinen et al. (2012) for a comparison of filament properties derived using NIR extinction and Herschel observations of dust emission. Surface brightness caused by scattered NIR light provides another means of studying cloud structure. The first observation of scattered NIR light from molecular clouds illuminated by the normal interstellar radiation field (ISRF) was by Lehtinen & Mattila (1996). Later the observations of Nakajima et al. (2003) and Foster & Goodman (2006) (who also named the phenomenon 'cloudshine') have shown that it is now possible to obtain large maps of the surface brightness of normal interstellar clouds illuminated by the normal ISRF. NIR scattering can therefore be a new, complementary tool for studying the structure of dark clouds. See, e.g., Juvela et al. (2006) for a more complete review of the history of scattered light observations in dark clouds. Padoan et al. (2006) presented a method to determine the cloud column density from the intensity of the nearinfrared scattered light. Juvela et al. (2006) analysed the method in more detail using simulations, and developed a method to combine the surface brightness with extinction, to reduce errors caused by wrong assumptions of radiation field or dust properties. Starting with the known properties of the interstellar dust and ISRF, the papers made predictions for the visibility of the cloudshine and for the accuracy of the resulting column density estimates. They also demonstrated, independently of the direct evidence given by the Foster & Goodman (2006) data, that such observations are well within the capabilities of modern wide-field infrared cameras. The main advantage of the new method is the potentially extremely good spatial resolution. When the J , H , and K bands are used, the method remains accurate in regions with A V even beyond 10 magnitudes. The same NIR observations provide data for the colour excess method, which means that the results of the methods can be compared at lower spatial resolution. Although both methods depend on near-infrared dust properties, the main sources of error are different. Comparison of the results can be used to study the values and variation of nearinfrared dust properties (e.g., albedo and the shape of the extinction curve) and spatial variations in the strength of the local radiation field. Furthermore, correlations between wavelength bands give a direct way to estimate the point at which the contribution of dust emission from stochastically heated grains becomes significant. The level of the emission of these so-called Sellgren grains depends on the radiation field (Sellgren et al. 1996), but is still uncertain in normal interstellar clouds. On the other hand, the amount of the scattered light depends heavily on the grain size (Steinacker et al. 2010). These dependencies have implications for models of interstellar dust. Juvela et al. (2008) used scattered NIR light to derive a column density map of a part of a filament in Corona Australis, and continued the analysis in a larger area in Juvela et al. (2009). They also compared the NIR data with Herschel sub-millimetre data in Juvela et al. (2012). Nakajima et al. (2008) applied a similar method to convert NIR scattered light to column density. They used the colour excess of individual background stars to calibrate an empirical relationship between surface brightness and column density, instead of an analytical formula, as used in Juvela et al. (2006, 2008). Scattered surface brightness from dense cores in the mid-infrared (MIR) was reported by Pagani et al. (2010) and Steinacker et al. (2010). Steinacker et al. (2010) named this phenomenon 'coreshine' as a counterpart to 'cloudshine', which is also observed in the outer parts of the clouds. In this paper, we study a filament in the Taurus molecular cloud using observations of NIR light of a 1 · × 1 · field observed with WFCAM instrument (Casali et al. 2007). Distance to the Taurus molecular cloud is ∼ 140 pc, making it one of the closest relatively high latitude clouds, and consequently one of the most studied star-forming regions (see, e.g., Cambr'esy 1999; Nutter et al. 2008; Kirk et al. 2013; Palmeirim et al. 2013). In Malinen et al. (2012), we compared the properties of this filament derived using NIR extinction and dust emission observed with Herschel . Here, we construct maps of the diffuse surface brightness, determine the intensity of the NIR scattered light, and derive the optical depth based on scattered NIR light using the method presented in Padoan et al. (2006). We compare the scattered light images with the other tracers, NIR extinction and sub-millimetre dust emission and, using these results, draw some conclusions regarding the intensity and spectrum of the local ISRF. We also perform radiative transfer modelling to compare observations with the level of NIR and MIR scattered light that is expected using standard ISRF levels and standard dust models. The contents of the article are the following: We present observations and data processing in Sect. 2. We describe the method for deriving optical depth from scattered NIR surface brightness in Sect. 3. We derive NIR surface brightness maps and optical depth maps based on observations of dust emission, NIR extinction, and NIR scattered surface brightness and compare the results in Sect. 4. We describe radiative transfer modelling of a filament seen in scattered light in Sect. 5. We discuss the results in Sect. 6 and present our conclusions in Sect. 7.",
"pages": [
1,
2
]
},
{
"title": "2.1. WFCAM",
"content": "We have used the Wide Field CAMera (WFCAM) (Casali et al. 2007) of the United Kingdom InfraRed Telescope (UKIRT) to observe a 1 · × 1 · field in the NIR J , H , and K bands (1.25, 1.65, and 2.22 µm , respectively). The field, which we call TMC-1N (Malinen et al. 2012), is in the Taurus molecular cloud complex north of TMC-1. The central coordinates of this field are RA (J2000) 4h39m36s and Dec (J2000) +26 · 39 ' 32 '' . At a distance of 140 pc, this corresponds to an area of ∼ (2.44 pc) 2 . The Galactic latitude of this area is approximately -13 . 3 · . The target field was chosen based on the Taurus extinction maps of Cambr'esy (1999) and Padoan et al. (2002). According to Rebull et al. (2011), there are no strong young stellar objects (YSOs) in TMC-1N that could cause additional scattered light and therefore complicate the analysis. There is mainly just one continuous filament in the field. The A V range of the area is suitable for our method: there are some regions with A V ∼ 20 m , but the mean value remains well below 10 magnitudes, even in most parts of the filament. We applied sky correction using offset fields to be able to measure faint surface brightness features. The observations were made during 13 nights between 2006-2008 using 2 × 2 pointings towards the selected field. Because WFCAM consists of four separate CCD arrays, the result is a 1 · × 1 · image consisting of 4 × 4 subimages. We used four separate OFF fields. The standard data reduction was conducted in accordance with the normal pipeline routine 1 , including, e.g., dark-correction, flatfielding (including internal gain correction), decurtaining, sky correction, and cross-talk. Standard decurtaining methods 2 were needed to remove the stripes caused by the instrument. The details of the observations are shown in Malinen et al. (2012) where we compared the filament properties derived using NIR extinction and sub-millimetre dust emission observed with Herschel . There, the NIR data were calibrated to magnitudes with the help of 2MASS catalogue stars to derive an extinction map with the NICER method (Lombardi & Alves 2001). Here, in order to study the surface brightness, we calibrated the data from magnitudes to MJy/sr units using aperture photometry of several stars in each frame. The reduced images contained residual gradients in each sub-image, shown as brightening of the signal towards the frame edges. These are probably of instrumental origin. The size of the gradients as a percentage of overall sky level varies, but is typically between 0.002-0.008. Dye et al. (2006) and Warren et al. (2007) report several types of artefacts in WFCAM data and note that removing sky subtraction residuals is a complex problem, especially when observing near the Moon. However, during our observations the Moon was always further than 40 degrees away. In addition, the moonlight artefacts that cause most problems are local scattered light from dust on the optics, not gradients. The master twilight flats may have low level gradients present in them, given the size of the WFCAM field-of-view. The dark correction can also leave low level reset anomalies, particularly near the detector edges. It is possible that our data are showing comparatively low-level residual issues that the general surveys have not encountered. We first removed the stars using the Iraf Daophotpackage, masked the remaining bad pixels (noisy borders and residuals of bright or saturated stars) and performed the surface brightness calibration. We modelled the gradients with a method described in the following subsection (Sect. 2.1.1). We convolved the calibrated frames with a 2 '' Gaussian beam and resampled the data onto 0.8 '' pixels. The obtained gradients were then subtracted from the frames. The maximum intensity of the filament is a few times higher than the typical magnitude of the instrumental gradients. We further median-filtered the images to ∼ 16.8 '' resolution to diminish the effect of residual stars and stellar artefacts, and finally convolved them to ∼ 40 '' resolution, for later comparison with Herschel observations at that resolution. We combined the frames to a full map using Montage 3 and resampled the data onto 8 '' pixels for the analysis. For comparisons with NICER data, we further convolved the intensity maps to 60 '' resolution. We subtracted the background from the maps, using an area of low column density outside the filament as a reference, see Fig. 9 (middle frame). A map of visual extinction, A V , of the TMC-1N area was already derived and presented in Malinen et al. (2012), using a Cardelli et al. (1989) extinction curve with R V = 4 . 0. In this paper, we mainly use the J band optical depth τ J , which is in practice independent of the assumption of the R V value. For comparison, a Cardelli et al. (1989) extinction curve with R V = 4 . 0 gives the relation τ J = 0 . 2844 × A V . Roy et al. (2013) discuss the effect of the finite width of the filters on the observed extinction. In their Fig. 10, they show the relation of colour excess E ( J -K S ) obtained with 2MASS filters to the corresponding monochromatic colour excess as a function of N H . In TMC-1N, having an A V of mostly less than 20 m , the effect is small (less than 5% even in the densest parts), and we have not made this correction.",
"pages": [
2,
3
]
},
{
"title": "2.1.1. Gradient modelling",
"content": "During the data reduction, separate analysis was carried out to model and subtract the residual artefacts of the surface brightness data. To be able to model the large scale gradients, we first filtered the masked and calibrated data with a median filter to ∼ 40 '' resolution. The gradients were strongest near the borders, which meant that the overlap between the frames could not be reliably used to aid the gradient removal. To model the gradient, therefore, we assumed a similar relation between the column density and the surface brightness as the one described in Sect. 3. We used the Herschel column density map described in Sect. 2.2 as an independent tracer of the filament structure in the fitting of the gradients. In principle, the extinction map obtained from NIR reddening of background stars could also have been used, but we chose Herschel data because of its lower noise. We modelled the gradients with a third order surface describing the artificial gradient in the image, with an additional column density dependent term. We used least squares fitting to minimize, separately for each band i in ( J , H , K ) and each frame, the residual where P is the complete third order polynomial for a 2dimensional surface (10 terms), I i is the observed intensity map in band i , and N the column density derived from Herschel data. The parameter b describes the saturation of the relation between I and N , and it mainly depends on the grain properties (Juvela et al. 2006). If we presume that the dust grains in the cloud are similar as in the model of Juvela et al. (2006), the same b values should apply as long as the optical depth is not high. Therefore, we used the parameter values b J = 0.34, b H = 0.23, and b K = 0.15, (in 1/mag units, as the model used A V values instead of N ) taken from the model data. The parameter b does not depend on the strength of the incoming radiation, but in some amount on the direction distribution. The model was based on a large cloud with an inhomogeneous density distribution and an isotropic radiation field. TMC-1N, on the other hand, has a single, filamentary structure, and a larger part of the radiation comes in from the observer's side. We do not expect the model to describe the filament perfectly, but the model parameter values served as a good starting point. The coefficients of the polynomial are free parameters and are used to describe the artificial gradients that will be removed in the subsequent analysis. The parameters a i are related to the actual signal from the cloud and are the same for all frames in the same band. They are also kept as free parameters to minimise the effect the cloud structure has on the gradient fits. The exponential term M = a i (1 -e -b i N ) is only an approximation of the column density dependence of the scattered light. However, because gradients are described only as third order surfaces over each frame and scattered light is visible only in some parts of each frame, the obtained gradient model is not expected to be strongly dependent on the reference map, here the column density derived from Herschel . In particular, the scaling between column density and the surface brightness is a free parameter and thus no assumption is made of the expected level of NIR surface brightness. Furthermore, the non-linear approximation represented by the term M becomes important only at A V ∼ 10 m . To obtain a better fit for the central part of the frames used in the following analysis, the gradients were fitted excluding a 10% wide border in each frame. For comparison, we also performed a fit to the whole area of the frames, in order to better fit the borders of the frames. The fitting provides the model P (for each frame and band) of the gradients that we subtract from the original surface brightness images. Note that the exponential term M is not subtracted as that is not part of the artefact. We tested the reliability of the gradient removal method in several ways. We calculated the residual between the used model and the corrected surface brightness map, S = I -P , with the function Res = a i (1 -e -b i N ) -S i , where b i are the constants used in the gradient modelling and a i are the values obtained from the fit. N is the map used in the gradient modelling. We used surface brightness maps in ∼ 2.2 '' resolution. The mean values for the residual are -0.0052, 0.00035, and 0.000074 MJy/sr for the J , H , and K bands, respectively. The standard deviation for the residuals of the same bands are 0.017, 0.031, and 0.021 MJy/sr. Noise, especially near the borders, increases the obtained standard deviation values. The absolute values for the mean residuals for all bands are less than 0.006 MJy/sr, indicating that the minimisation of the residual in Eq. 1 has been effective. The filament is not apparent in the residuals nor in the removed gradients. We also compared the surface brightness maps derived using different areas for the fitting of the gradient, full area or excluding 10% wide borders of each frame. After the gradient removal, we compared the surface brightness maps (in 40 '' resolution) by calculating the difference between the maps in the final masked area shown in Fig. 2. The means of the difference of the final masked area are 0.0026, 0.0026, and -0.0014 MJy/sr for the J , H , and K bands, respectively. The standard deviations for the difference of the same bands are 0.0044, 0.0072, 0.0052 MJy/sr. This indicates that small differences in the fitting area do not cause a significant difference in the central parts of the corrected frames. Near the borders of the frames, the difference can be larger.",
"pages": [
3,
4
]
},
{
"title": "2.2. Herschel",
"content": "The Taurus molecular cloud has been mapped with Herschel (Pilbratt et al. 2010) as part of the Gould Belt Survey 4 (Andr'e et al. 2010), see Kirk et al. (2013) and Palmeirim et al. (2013). We used SPIRE (Griffin et al. 2010) 250 µ m, 350 µ m, and 500 µ m maps of the TMC-1N field. We obtained the data from the Herschel Gould Belt Survey consortium. The observation identifiers of the data are 1342202252 and 1342202253. The details of the Herschel data and the derivation of column density map are presented in Malinen et al. (2012). For easier comparison with other maps and to avoid the assumptions needed to make column density maps, we used optical depth τ 250 instead. We use the notation τ 250 to mean optical depth τ ν at wavelength 250 µ m ( ν =1200GHz). We derived τ 250 maps from Herschel intensity and colour temperature maps, using a value of 1.8 for the spectral index β . Recent studies with Planck (Planck Collaboration et al. 2011) show that this is a good estimate for Taurus. For comparison, we also made the analysis with the commonly used value of β = 2 . 0.",
"pages": [
4
]
},
{
"title": "2.3. Spitzer",
"content": "The Taurus filament is covered by observations of the Spitzer IRAC instrument (Fazio et al. 2004). The IRAC data (observation numbers 11230976 and 11234816) are from the Taurus Spitzer legacy project (PI D. Padgett). The archival IRAC maps show some checkered pattern. We therefore started with the pipeline-reduced, artefactmitigated images (cbsd images). The residual offsets were corrected by subtracting the median value from each frame and by estimating the residual offsets with respect to the median of all frames 5 . The final mosaic image was then made with the MOPEX tool (Makovoz et al. 2006).",
"pages": [
4
]
},
{
"title": "3. Deriving optical depth from scattered NIR surface brightness",
"content": "Padoan et al. (2006) presented a method for converting scattered surface brightness into column density. Juvela et al. (2006, 2008) discussed the method and its reliability in more detail. We review the main points of the method given in these articles and formulate it to suit this study. Based on the one-dimensional radiative transfer equation in a homogeneous medium, the relationship between surface brightness ( I ) and column density ( N ) can be approximated with the formula where the parameters a and b are positive constants defined separately for each band. The parameter b scales the column density to optical depth, τ . The function depicts the radiation coming from the cloud. We presume that the observed radiation is mainly caused by scattering. Also other tracers of cloud structure, such as extinction A V or optical depth τ can be used instead of column density N . In that case, the value and unit of the parameter b must be changed accordingly. The parameters b mainly depend on the NIR dust properties and the parameters a on the radiation field, although the interpretation is not this straightforward (Juvela et al. 2006). Equation 2 is exactly valid only for a homogeneous cloud. In real clouds it works only as an approximation. It is expected that both parameters change if the dust properties, radiation field or cloud geometry change. Both can, however, be treated just as empirical parameters. In areas of low optical depth, the intensity of NIR scattered light is directly proportional to the column density as shown in the relation The product ab gives the scattered intensity per column density. With higher column densities ( A V ∼ 10 m ), the NIR intensity values begin to saturate, starting from the shorter wavelengths. Thus, the relation becomes more nonlinear with increasing column density. Equation 2 can be considered as an empirical description of the relation between surface brightness and column density, and it is not necessarily the optimal functional form to describe this relation. However, as long as the data points follow this relation, it is possible to derive approximations for column density. Based on numerical simulations (Padoan et al. 2006; Juvela et al. 2006), this function is rather reliable in areas of low to medium visual extinction ( A V = 1 -15 m ), where the saturation is not strong. If no independent column density estimates are available, only the ratios between different bands can be derived from surface brightness observations. However, NIR observations also provide the colour excesses of background stars, and an extinction map can therefore be calculated and used to derive the necessary parameter values (Juvela et al. 2006). To derive an optical depth τ SB J map from the surface brightness maps, we obtain a and b parameter values for each band from I ν /τ Nicer J correlations by fitting Eq. 2 to the data, using optical depth τ Nicer J instead of column density N in the exponential part. Thus, Eq. 2 is used to establish a non-linear scaling between the extinction that increases linearly with column density and the surface brightness for which the increase is non-linear. Once the parameters of this mapping have been determined, we can convert surface brightness observations directly to estimates of column density, possibly at a resolution higher than what is possible using background stars alone. Using the obtained parameter values, we calculate a value for each pixel of the τ SB J map by minimising the squared sum of residuals where I i are the pixel values of the intensity maps, and for each i in ( J , H , K ). Minimisation is needed, as the observed intensities do not follow Eq. 2 exactly due to noise and possible model errors.",
"pages": [
4,
5
]
},
{
"title": "4. Results",
"content": "Surface brightness map in J band with 40 '' resolution is shown in Fig. 1. In this figure, the gradient removal is made using a fit to the whole area of each frame. In the analysis, bad pixels, border regions suffering from imperfect gradient removal, and the main artefacts remaining after star removal were all masked. We also limited the analysis to areas where Herschel column density values are above 1.0 × 10 21 cm -2 . The masked J map used in the analysis is shown in Fig. 2. We used the same mask for all maps ( J , H , K , NICER, and Herschel ) in the analysis. The reference area used for background subtraction is shown in Fig. 9 (middle frame). The median τ J in this area is ∼ 0.1. A combined three-colour image of WFCAM J , H , and K band intensity maps with 40 '' resolution is shown in Fig. 3. Here, the removed gradients were fitted to the frames excluding 10% wide borders of each frame. The remaining gradients can most clearly be seen near the corners of the frames. Borders of the frames have been masked.",
"pages": [
5
]
},
{
"title": "4.1. Correlations between NIR surface brightness and optical depth derived from extinction and dust emission",
"content": "We show correlations between the NIR surface brightness in J , H , and K bands for the main filament area in Fig. 4. The main cloud of points is concentrated to values below 0.08 MJy/sr in I J , 0.17 MJy/sr in I H , and 0.12 MJy/sr in I K . The correlation between I J and I K is approximately linear up to I K ∼ 0.06 MJy/sr, after which I J starts to saturate. Similarly, the correlation between I H and I K is ✁ approximately linear up to I K ∼ 0.08 MJy/sr, after which I H starts to saturate. Compared to Fig. 3 in Juvela et al. (2008) for Corona Australis, our WFCAM data for TMC-1N show similar linear relations between I J and I K and between I H and I K in the low end of the intensity scale, although our data show slightly lower values. In TMC-1N, the main cloud of points is concentrated to I K values below 0.12 MJy/sr, whereas in Corona Australis there are also points up to I K ∼ 0.7 MJy/sr. In Corona Australis, the correlations turn to negative between I K ∼ 0.4-0.7 MJy/sr. Correlations between surface brightness, I ν , and optical depth in J band derived from extinction, τ Nicer J , are shown for bands J , H , and K in Fig. 5. We fit Eq. 2 to the data, using optical depth τ Nicer J instead of column density N in the exponential part. As a result, we obtain for each band the a and b parameters needed for the derivation of the optical depth map. The fitted values are a J = 0 . 08, b J = 0 . 90, a H = 0 . 20, b H = 0 . 44, a K = 0 . 19, and b K = 0 . 21. For comparison, we plot in the same figures the data of Corona Australis from Juvela et al. (2008). We have scaled those data to I ν units (MJy/sr), as a function of τ J . Compared to Corona Australis, we obtain notably lower values for I ν as a function of τ J in all three bands. We also fit Eq. 2 to these data and show the obtained parameters in the figure. For comparison, we also show correlations between I ν and optical depth derived from Herschel maps, τ 250 , in Fig. 6. We made error estimates for the a and b parameters obtained from the fitting of Eq. 2 using two different methods. First, we used a standard bootstrap method to estimate the errors caused by sampling. We made the fit using 100 different samples from the data, all samples having the size of the full dataset. The standard deviations for the a and b parameters and their product a × b , that is the slope of the linear part of the function, are shown in Table 1. The standard deviation for parameter a can be up to 0.004, and for parameter b up to ∼ 0.006, but for the slope the uncertainty is rather small, ∼ 0.0002 for K , ∼ 0.0003 for J , and ∼ 0.0004 for H band. Secondly, we tested the possible systematic effect of changing the upper limit of the fitted range between τ J values 1 . 5 -6 . 0. In Table 2 we show the relative change in the parameter values when the upper limit of the fitted range is changed from τ J = 2 . 0 to τ J = 6 . 0, as between these values the change is mainly systematic. Even though the change in the a parameter can be up to -33% and in the b parameter up to 61%, the change in the slope of the linear part is less than 10% for each band. Below a τ J value of 2.0, the parameter values can change in a more unpredictable way. We derive emissivity, the ratio of FIR dust emission to column density, by using τ J obtained from NIR extinction map as an independent tracer of column density. Correlation between τ 250 and τ Nicer J with β = 1 . 8 is shown in Fig. 7 for the main filament area shown in Fig. 2. The slope of a straight line fitted to the range τ Nicer J =0-4 is ∼ 0.0013. We also tested the possible change of slope in the low and middle τ Nicer J range. The derived slope is 0.0013 for range 0-2, and 0.0015 (more precisely 0.00149) for range 2-4. If we change β from 1.8 to 2.0, the slope between 0-4 increases ∼ 32% to the value ∼ 0.0018. We also made a similar fit using all the data in the maps. The derived slope is 0.0013 for range 0-2, and 0.0014 (more precisely 0.00144) for range 2-4, indicating that there is no significant change when compared to the masked area. For comparison with other studies, we convert our slope of τ 250 /τ J = 0 . 0013 to opacity or dust emission crosssection per H nucleon where τ ν is optical depth, N H is the total H column density (H in any form), µ is the mean molecular weight per H (1.4), m H is the mass of H atom, and κ ν is the mass absorption (or emission) coefficient (cm 2 /g) relative to gas Dec (J2000) Dec (J2000) ✂ ✂ ✂ ✂ ✁ 0.5 0.7 J J J mass, also often called opacity. We again use wavelength instead of frequency in our notation: σ e (250) = σ e (250 µ m) = σ e (1200GHz). We derive the τ 250 map directly from the Herschel observations, and use our WFCAM NIR extinction map as an independent tracer of the column density. We use the conversion factor for diffuse clouds N (HI + H 2 ) /E ( B -V ) = 5 . 8 × 10 21 cm -2 /mag of Bohlin et al. (1978). We derive the relation E ( B -V ) /E ( J -K ) from Cardelli et al. (1989) extinction curves, and obtain values 1.999 (with R V = 3 . 1) and 1.413 (with R V = 4 . 0), leading to relations N (H) = 11 . 59 × 10 21 E ( J -K ) (with R V = 3 . 1) and N (H) = 8 . 196 × 10 21 E ( J -K ) (with R V = 4 . 0). Martin et al. (2012) have observed a similar relation, N (H) ∼ 11 . 5 × 10 21 E ( J -K S ), for regions of moderate extinction in Vela. Cardelli et al. (1989) extinction curves also give the relation A J /E ( J -K ) ∼ 1 . 675 (with both R V values 3.1 and 4.0). Converting magnitudes to optical depths ( A = 2 . 5 lg ( e ) τ ∼ 1 . 086 τ ) gives the relation E ( J -K ) ∼ τ J / 1 . 54. This leads to the relations σ e (250) = 1 . 33 × 10 -22 τ 250 /τ J cm 2 /H (with R V = 3 . 1) and σ e (250) = 1 . 88 × 10 -22 τ 250 /τ J cm 2 /H (with R V = 4 . 0). The value τ 250 /τ J = 0 . 0013 leads to values σ e (250) = 1 . 7 × 10 -25 cm 2 / H (with R V =3.1) or σ e (250) = 2 . 4 × 10 -25 cm 2 / H (with R V = 4 . 0). These can be converted to κ ν values 0.07 cm 2 /g or 0.10 cm 2 /g, respectively. The map of the ratio τ 250 /τ Nicer J is shown in Fig. 8. The map shows no clear evidence for systematic increase of the ratio τ 250 /τ J with increasing density inside the densest filament. Some high value areas can be attributed to imperfections in the two maps, τ 250 and τ J . For instance, the high value area next to the densest part of the filament seems to be caused by the different shape of the filament in these two maps. There the value of the ratio is high, because the filament is slightly more narrow in τ J , possibly caused by the lack of background stars seen behind the densest filament.",
"pages": [
5,
6,
7
]
},
{
"title": "4.2. Optical depth derived from scattered light",
"content": "As described in Sect. 3, in order to derive an optical depth τ SB J map from the surface brightness maps, we obtain a and b parameter values for each band from correlations between I ν and τ Nicer J shown in Fig. 5. We calculate a value for each pixel of the τ SB J map by minimising Eq. 4. We use 40 '' and 60 '' maps in the following analysis, but also show a higher resolution ( ∼ 2.2 '' ) τ SB J map in Fig. 9 (right frame). In the same figure, we also show maps of Herschel τ 250 and NICER τ Nicer J . In Fig. 10, we show closeups of the same maps. Correlations between τ SB J /τ 250 (resolution 40 '' ) and τ SB J /τ Nicer J (resolution 60 '' ) are shown in Fig. 11. The ref- ✂ ✂ ✁ ✁ ✁ ✁ erence area used for background subtraction is shown in Fig. 9 (middle frame). The fitted values for the slopes are 808 for τ SB J /τ 250 and 1.019 ∼ 1 for τ SB J /τ Nicer J . This is as expected, since τ SB J was derived based on the correlation between I ν and τ Nicer J . The correlations are linear up to τ Nicer J ∼ 4. Above that, the τ SB J values saturate strongly. The areas where τ Nicer J > 4 are marked with contours in Fig. 9 (middle frame), indicating that these form only a small area in the densest clumps inside the cloud.",
"pages": [
7,
8
]
},
{
"title": "4.3. Filament cross-sections",
"content": "Median profiles of the filament are shown in Fig. 12, for bands J , H , and K (upper frame) and for τ Nicer J and τ SB J (lower frame). The cross-sections are taken from the area between the two red lines shown in Fig. 9 (middle frame), where we have continuous data in all WFCAM maps. This is not the densest part of the filament, but a moderately J 0.0030 Dec (J2000) dense area next to it. The cross-sections show that the derived τ SB J gives rather similar results to the τ Nicer J map for the filament profile, except for an extra peak in the τ SB J profile. The profiles seen in J and K bands are rather similar, whereas the H band profile has approximately two times stronger peak than the other two bands. The filament width or FWHM is ∼ 3 ' ∼ 0 . 1 pc, as shown in Malinen et al. (2012). ✁ ✁ ✁",
"pages": [
8
]
},
{
"title": "4.4. Spitzer data",
"content": "We compare the IRAC 3.6 µ m surface brightness with the Herschel optical depth τ 250 , to study also the correlations between MIR scattered light and sub-millimetre dust emission. The surface brightness at ∼ 3.6 µ m can still be dominated by light scattering, while at longer wavelengths, the scattering decreases and the signal is expected to be dominated by dust emission. Some contribution of dust emission cannot be excluded even around 3.6 µ m and we conservatively consider the Spitzer data only as an upper limit on the intensity of the scattered light. The point sources are a major problem in estimating the level of the extended emission. Because the examined area is small, we can produce an extended MIR surface brightness map by manually masking all the visible point sources. The masks altogether cover 24 arcmin 2 . After the masking, we carry out median filtering. The filter calculates the 25% percentile of all unmasked pixels within a given radius that is fixed to 5 '' . If the area contains less than ten unmasked pixels, the value is left undefined. The images are then convolved with a Gaussian beam to produce final surface brightness maps at the resolution of 40 '' that corresponds to the resolution of the Herschel data. The convolution ignores the undefined values. To reduce the noise (and because of the uncertainty of the fidelity of the large scale flat-fielding), data are correlated only around the main column density peak. The column density threshold of 4 × 10 21 cm -2 defines an area of ∼ 77 arcmin 2 . The Spitzer 3.6 µ m map and the area used in the correlations are shown in Fig. 13. The resulting correlations between MIR surface brightness and optical depth τ 250 are shown in Fig. 14. In the figure, we also show the median surface brightness that is calculated for τ 250 bins with a width of 0.002. We fit a robust least squares line to the individual surface brightness values in pixels where τ 250 is between 0.0025-0.0065. The fit is performed iteratively, discarding points falling further than 2.5σ from the fitted line. The value of the fitted slope is 2.40 MJy/sr.",
"pages": [
9
]
},
{
"title": "4.5. Spectral energy distributions",
"content": "Spectral energy distributions are shown in Fig. 15. We calculate the values for I ν /τ J in TMC-1N with Eq. 3, using τ J instead of column density N . In areas of low optical depth, the product ab gives the ratio I ν /τ J . The obtained values for J , H and K bands are 0.074, 0.086, and 0.038 MJy/sr, respectively. J ✁ ✂ ✁ ✁ ✂ ✂ ✁ J We compare our results with the values obtained for Corona Australis in Juvela et al. (2008) (filled squares in their Fig. 13). We have scaled the Corona Australis values to I ν /τ J units (with R V = 3 . 1). We have also marked Mathis ISRF (Interstellar Radiation Field) model (Mathis et al. 1983) values (with R V = 4 . 0) on the figure for comparison. The values are obtained by multiplying the Mathis intensities with the scattering cross-sections of the Draine (2003) dust model. The values of J , H and K bands in TMC-1N are approximately one third of the values in Corona Australis. Mathis model values for H and K are ∼ 1.5 times as high as in TMC-1N. For J band, the Mathis model value is already ∼ 3 times as high as the TMC-1N values. The value we obtain for Spitzer 3.6 µ m is also only approximately one third of the value given by the Mathis model. In both TMC-1N and Corona Australis, I ν /τ J is lower in the J band than in the H band. However, in the Mathis model, the value for the J band is notably higher than for the H band.",
"pages": [
9,
10
]
},
{
"title": "5. Radiative transfer modelling",
"content": "We carry out radiative transfer calculations of the ISRF light that is scattered from the cloud in the wavelength range 1.2-3.5 µ m. We construct a realistic threedimensional model of the density distribution of the densest part of the filament. Based on the density structure, we calculate predictions for the surface brightness using the Diffuse Infrared Background Experiment (DIRBE) observations on the Cosmic Background Explorer (COBE) as a template of the sky brightness. The radiative transfer calculations were carried out with a Monte Carlo radiative transfer program (Juvela & Padoan 2003). The filament is illuminated by an anisotropic radiation field that, in conjunction with the scattering phase function, affects the strength and spatial distribution of the scattered intensity. We define the intensity of the incoming radiation ✁ ✁ ☎ ✄ ✂ 0.25 intensities themselves are ∼ 50% higher than in the Mathis et al. (1983) model. The density distribution of the model cloud is based on the column density map that is derived from the Herschel sub-millimetre observations (see Malinen et al. 2012). This is based on the colour temperature of the emission and on the assumption that dust opacity follows the law 0.1 cm 2 /g ( ν /1000 GHz) β , with β = 2 . 0. The actual cloud model corresponds to 17 ' × 17 ' area that we cover with 68 × 68 pixels, 15 '' in size. Our three-dimensional cloud model is correspondingly a cube that consists of 68 3 cells and is viewed along one of its major axes. The Herschel column density map constrains the mass distribution only in the plane of the sky. To construct a three-dimensional filament, we start with a cylindrical structure where the radial density profile follows the Plummer function with parameters ρ C = 4 × 10 4 cm -3 , R flat =0.03, and p =3.0. These are close to the values previously determined from the fitting of the Herschel observations (Malinen et al. 2012). This initial cylindrical structure therefore has properties close to those of the average filament. We modify this initial model by requiring that, for each line-of-sight, the column density of the model exactly matches that of the Herschel column density map. We calculate for each pixel the ratio of the Herschel column density and the initial column density in the model. The densities along the same line-of-sight are then multiplied by this value. The procedure modifies the filament so that it is no longer cylinder symmetric. However, the deformations remain relatively small so that the ratio of the major and minor axis of the 2D filament cross sections always remains below two. The absolute value of the background affects the contrast between the cloud and the background. The surface ☎ ✄ ✂ using the DIRBE all-sky maps 6 (Zodi-Subtracted Mission Average (ZSMA) Maps). The DIRBE bands 1, 2, and 3 can be used directly to specify the intensity at the corresponding wavelengths 1.2 µ m, 2.2 µ m, and 3.5 µ m. The H band intensity is obtained by multiplying the average of the J and K band intensities with the intensity ratio I H / < I J , I K > taken from the Mathis et al. (1983) ISRF model. Note that, averaged over the whole sky, the total 6 See DIRBE explanatory supplement, http://lambda.gsfc.nasa.gov/product/cobe/dirbe exsup.cfm brightness relative to the brightness of the background sky is calculated as where I is the total observed signal, I sca the scattered signal coming from the cloud, I bg e -τ the background signal coming directly (without scattering) through the cloud with optical depth τ , and I bg the background signal. The radiative transfer program takes into account the incoming ISRF and the absorption and scattering of those photons inside the cloud. I sca is the amount of light coming out of the cloud after this process. The term I bg was estimated using WISE (Wright et al. 2010) and DIRBE data. The WISE map of a one degree diameter area around the column density peak was first adjusted to the absolute level indicated by the DIRBE data. We read the I bg value from the corrected WISE map, using the area that corresponds to the area where the model column density is approximately zero (corresponding to the upper part of Fig. 16). To exclude the effect of point sources in this area, we use the 40% percentile of pixels in this reference area. The values obtained for the background I bg are 0.122 MJy/sr ( J ), 0.0878 MJy/sr ( K ), and 0.0765 MJy/sr (3.4 µ m). We estimate a value 0.10 MJy/sr for the H band. The cosmic infrared background (CIB) between the J and 3.5 µ mbands is notably lower than these values, ∼ 0.01-0.02 MJy/sr (see, e.g., Cambr'esy et al. 2001; Wright & Reese 2000). The dispersion of DIRBE values over the area used for comparison with WFCAM and WISE is ∼ 10% of the estimated I bg value. Because this includes not only noise but also real surface brightness variations, the statistical error of the mean DIRBE value is significantly lower. However, the dispersion is also a measure of the possible difference between the background value I bg derived for the reference area and the actual background at the position of the filament. The final I bg is calculated as 40% percentile of the reference area within WFCAM and WISE maps. The standard deviations of all pixels falling below the 40% value (assumed not to be significantly contaminated by point sources) are 0.011, 0.015, and 0.005 MJy sr -1 for J , K , and 3.4 µ m bands, respectively. The zero point uncertainty of the zodiacal light model subtracted in DIRBE ZSMA maps is ∼ 0.006 MJy sr -1 in the J band and less at longer wavelengths (Kelsall et al. 1998), but differences between zodiacal light models can be even larger (Wright 2001). Furthermore, Taurus is located at low ecliptic latitude and two thirds of the total signal observed by DIRBE consists of zodiacal light. A relative error of 10% in the zodiacal light model would therefore amount to ∼ 0.04, 0.03, and 0.02 MJy sr -1 for J , K , and 3.5 µ m, respectively, and could be the dominant source of error. Diffuse emission that originates between the filament and observer does not contribute to Eq. 8, which describes the surface brightness contrast between the source and the background. In that equation, I bg corresponds to that part of the diffuse component that truly resides behind the filament. We can assume that most of the diffuse material is associated with the Taurus cloud but can reside either in front of or behind the filament. We therefore make the assumption that I bg corresponds to half of the values derived above. If the diffuse component is closely associated with the filament, consistency requires that its effect is also taken into account when calculating the component I sca . This term corresponds to photons scattered from the filament, excluding photons that may be scattered in some envelope around it. In this case, the filament (i.e., the densest part that is being modelled) is not illuminated by the full ISRF but by an ISRF that is attenuated by e -0 . 5 τ d , where τ d is the optical depth of the envelope. Similarly, when a photon scatters within the model, it must travel through a similar layer a second time (half of the full τ d ) before reaching the observer. Thus, the observed signal is reduced by a factor e -τ d . We estimate that for the diffuse cloud τ J d = 0 . 5, and calculate values 0.34, 0.2, and 0.0998 for τ H d , τ K d , and τ 3 . 5 µ m d , respectively, using Cardelli et al. (1989) extinction curves. We compare three cases: (1) no background I bg , (2) with background I bg , and (3) with background I bg and attenuation of the scattered light in the envelope. We show the corrections in function where C is either 0 (case 1) or 0.5 (cases 2 and 3), indicating the amount of background, and use value 0 for τ d for cases 1 and 2, and the τ d values derived above for case 3. In the calculations, we use the NIR dust properties of normal Milky Way dust (Draine 2003) and the tabulated scattering phase functions that are publicly available 7 . We do not seek a perfect match to the observations but explicitly assume the column density distribution and dust properties as described above. The comparison with the observations is thus a test for the consistency of these assumptions. The τ J map of the model is shown in Fig. 16 and simulated scattered surface brightness maps in Fig. 17. Correlations of I ν and τ J from simulations are shown in Fig. 18 for intensity in bands J , H , and K , using the three cases for the background correction described above. For comparison, we plot in the same figures the data from our TMC-1N observations. We have subtracted the background from both the simulated and observed data using as reference area the area in which the model column density is lowest (corresponding to the upper part of Fig. 16). In the WFCAM data, the median τ J in this area is ∼ 0.5. Note the difference from Fig. 5, in which we used as reference area the low optical depth area marked in Fig. 9. We fit Eq. 2 to both of the data, using optical depth τ Nicer J instead of column density N in the exponential part. As a result, we obtain the a and b parameters for each band. In the H band, the simulations give ∼ 1.5 times as high intensity values as the observations, without background (case 1). The observed values are mostly settled between the cases 2 and 3 in the simulations. In the K band, the simulations give nearly two times as high values to the observations, when no background is included (case 1). In case 3, with the background and attenuation in the envelope, the simulations give similar values as the observations. However, in the J band, the simulated values are approximately three times as high as in our observations, when no background is included (case 1). Even with background (case 2), the simulations still give approximately two times as high values. Only in case 3, with the attenuation in the envelope, the simulations give similar values to the observations. Even when the maximum intensities for observations 9 and simulations are approximately the same, the form of the fitted Eq. 2 can be different, leading to notably different values for the parameters. Correlation between I ν and τ J for the 3.5 µ m band is shown in Fig. 19, similarly using the three cases. At this wavelength, case 1 still gives two times as high values as case 2, but the difference between cases 2 and 3 is only ∼ 10%.",
"pages": [
10,
11,
12,
13
]
},
{
"title": "6. Discussion",
"content": "We have studied a filament in the Taurus molecular cloud using NIR images of scattered light. The observations carried out with WFCAM instrument cover an area of 1 · × 1 · corresponding to ∼ (2.44 pc) 2 at the distance of 140 pc, making this, to our knowledge, the largest NIR map where the surface brightness is analysed in detail. We have analysed the faint surface brightness, determined its intensity (attributed to light scattering), and used it to derive an optical depth map based on the method of Padoan et al. (2006). We have compared the data derived from NIR scattering, NIR extinction and Herschel dust emission. The signal-to-noise value, S/N, of our WFCAM data is lower than expected. There were significant artefacts, presumably of instrumental origin, namely the curtain effect and large scale gradients. It is possible that the excess noise is caused by these effects and the processes used to remove them. Due to this, the data could not be used at as high a resolution as expected. In principle, scattered light can be measured at arcsecond resolution. However, as shown here, it can be difficult to obtain reliable maps at the full resolution. Correlations between I ν and τ Nicer J in Fig. 5 suggest that the radiation field in TMC-1N is notably lower in all three NIR bands when compared to similar observations of Corona Australis (Juvela et al. 2008). This reaffirms the results obtained with dust emission models of Juvela et al. (2012), suggesting that the radiation field in Corona Australis is at least three times that of the normal ISRF. l o g 10 N p i x NIR intensity as a function of column density followed roughly the functional form assumed in Eq. 2. We have estimated the possible errors in obtaining the parameters a and b for each band from fitting Eq. 2 to the correlation between I ν and τ Nicer J . Errors caused by sampling are small, but changes to the fitting limit can cause up to ∼ 60% deviations in a single parameter. However, the change in the product a × b , that is the slope of the linear part of the Eq. 2, is only up to ∼ 10% for each band. As discussed in Sect. 3, Eq. 2 and the parameters a and b can be thought of as an empirical model that represents the relation between surface brightness and column density. The model may not be optimal and no direct physical interpretation can necessarily be attached to its parameters. Bias in the fitted parameter values could cause bias also when minimising the Eq. 4 to obtain an optical depth map. We obtained the value 0.0013 for the slope τ 250 /τ Nicer J with β = 1 . 8, using values in the range τ J =0-2 (and the same for range 0-4), in Fig. 7. When we fit data in the range 2-4, the slope increased ∼ 15% to 0.0015, possibly suggesting a small increase in grain size in the denser areas, similarly to (Martin et al. 2012; Roy et al. 2013). With β = 2 . 0, and using range 0-4, the slope increased ∼ 38% to 0.0018. For comparison with other studies, we convert our slope of τ 250 /τ Nicer J = 0 . 0013 to dust absorption cross-section per H nucleon, also called opacity. We use the conversion factor N (HI + H 2 ) /E ( B -V ) = 5 . 8 × 10 21 cm -2 /mag of Bohlin et al. (1978). In principle, this relation is valid only for diffuse areas, and can be used only as an approximation for the densest parts of our filament. We derive the extinction relations, E ( B -V ) /E ( J -K ) and A J /E ( J -K ), using the extinction curves of Cardelli et al. (1989), either with R V = 3 . 1 or R V = 4 . 0. This leads to σ e (250 µ m) values 1 . 7 × 10 -25 cm 2 / H (with R V =3.1) or 2 . 4 × 10 -25 cm 2 / H (with R V = 4 . 0). In terms of mass absorption (or emission) coefficient per gas mass, κ ν , the values are 0.07 cm 2 /g or 0.10 cm 2 /g, respectively. Changing the assumed R V value in E ( B -V ) /E ( J -K ) from 3.1 to 4.0 causes ∼ 40% increase ✁ ✁ in the obtained values. It is not obvious which assumptions can be made in areas having both diffuse and denser parts, but it is important to notice that the assumptions made will have notable differences in the results. For high-latitude, diffuse ISM, the standard value for dust opacity is σ e (250 µ m) ∼ 1 . 0 × 10 -25 cm 2 / H (see, e.g., Boulanger et al. 1996; Planck Collaboration et al. 2011). In denser areas, 2-4 times larger values have been derived (see, e.g., Juvela et al. 2011; Planck Collaboration et al. 2011; Martin et al. 2012; Roy et al. 2013). Our estimates for σ e (250 µ m) are ∼ 1 . 7 -2 . 4 times as large as the previous results for diffuse areas, at the lower limit of the values for denser areas. As the width (or FWHM) of our filament is ∼ 0.1 pc, which for Taurus corresponds to ∼ 150 '' , we have enough resolution to look at the details of the filament. The τ 250 /τ Nicer J map shown in Fig. 8 gives no indication of systematic growth of the τ 250 /τ Nicer J towards the densest fil- ✁ ✁ ✁ ✁ ✂ ✁ ✁ ament. However, as discussed above, all the assumptions made in the process may not be valid in the densest part of the filament. As an additional confusing factor, some areas of high τ 250 /τ Nicer J ratio can be caused by small differences in the τ 250 and τ Nicer J maps, due to, e.g., the lack of background stars seen behind the densest filament, instead of real changes in the dust properties. In Sect. 5, we constructed a realistic three-dimensional model of the density distribution of the densest part of the filament. We calculated predictions for the surface brightness using radiative transfer calculations of the ISRF light that is scattered from the cloud in the wavelength range 1.2-3.5 µ m. We used DIRBE observations as a model for the sky brightness. As the absolute value of the background affects the contrast between the cloud and the background, we calibrated our simulation data to the same absolute level with DIRBE. We also considered the role of a potential diffuse envelope that would affect the radiation impinging on the dense part of the filament, i.e., the part included in our model. We take into account that a scattered photon has to pass through the diffuse cloud twice. We compared three cases of using different background correction: (1) no background, (2) with background, and (3) with background and attenuation of the scattered light in the envelope surrounding the filament. In the simulations, we have assumed that the filament is in the plane of the sky and is not prolate (long along the line-of-sight). If the filament is prolate, this will increase the short wavelength surface brightness relative to the longer wavelengths, and the saturation of the J band will be smaller. If the filament is not in the plane of the sky (i.e., our line-of-sight is not perpendicular to the filament axis), the effect is similar. The dust opacities used in the simulations are appropriate in high density environments (Hildebrand 1983; Beckwith et al. 1990) but could, in diffuse regions, overestimate κ (underestimate column density) by a factor of two (see Boulanger et al. 1996). We find that the results change notably, especially for the J band, depending on what fraction of the background intensity is assumed to be really behind the filament and what fraction between the filament and the observer. In the J band, case 1 gives ∼ 1.5 times as high values to the relation between I ν and τ J as case 2, and ∼ 3 times as high values as case 3. In longer wavelengths the differences get smaller, but at 3.5 µ m, case 1 still gives ∼ 2 times as high values as case 2. At 3.5 µ m, the difference between cases 2 and 3 is only ∼ 10%. In the H and K bands, the simulations give rather similar results to our observations in TMC-1N. However, in the J band, the simulations give over two times as high values as the observations, unless case 3 with the background correction and the correction for the scattered light is used. In the H band, case 3 also gives values that are lower than the observed values. The three test cases can be seen as rough error limits for the modelled cloud. Compared to the simulations, our observations do not suggest that there is any notable emission in the K band in addition to the scattered light.",
"pages": [
13,
14,
15
]
},
{
"title": "7. Conclusions",
"content": "We have used WFCAM NIR surface brightness observations to study scattered light in the TMC-1N filament in Taurus Molecular Cloud. We have presented a large NIR surface brightness map (1 · × 1 · corresponding to ∼ (2.44 pc) 2 ) of this filament. We have converted the data into an optical depth map and compared the results with NIR extinction and Herschel observations of sub-mm dust emission. We have also modelled the filament by carrying out 3D radiative transfer calculations of light scattering. Acknowledgements. We thank the referee for useful comments. We thank CASA for carrying out the standard data reduction of the WFCAM data, and Mike Irwin for useful comments. JM and MJ acknowledge the support of the Academy of Finland Grants No. 250741 and 127015. MGR gratefully acknowledges support from the National Radio Astronomy Observatory (NRAO), the Joint ALMA Observatory and the Joint Astronomy Centre, Hawaii (UKIRT).The National Radio Astronomy Observatory is a facility of the NationalScience Foundation operated under cooperative agreement by AssociatedUniversities, Inc. The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the U.K. This paper makes use of WFCAM observations processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This research made use of Montage, funded by the National Aeronautics and Space Administration's Earth Science Technology Office, Computation Technologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology. Montage is maintained by the NASA/IPAC Infrared Science Archive. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.",
"pages": [
15,
16
]
},
{
"title": "References",
"content": "Andr'e, P., Men'shchikov, A., Bontemps, S., et al. 2010, A&A, 518, L102 Beckwith, S. V. W., Sargent, A. I., Chini, R. S., & Guesten, R. 1990, AJ, 99, 924 Bohlin, R. C., Savage, B. D., & Drake, J. F. 1978, ApJ, 224, 132 Boulanger, F., Abergel, A., Bernard, J.-P., et al. 1996, A&A, 312, 256 Cambr'esy, L. 1999, A&A, 345, 965 Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245 Casali, M., Adamson, A., Alves de Oliveira, C., et al. 2007, A&A, 467, 777 Draine, B. T. 2003, ARA&A, 41, 241 Dye, S., Warren, S. J., Hambly, N. C., et al. 2006, MNRAS, 372, 1227 Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10 Foster, J. B. & Goodman, A. A. 2006, ApJ, 636, L105 Goodman, A. A., Pineda, J. E., & Schnee, S. L. 2009, ApJ, 692, 91 Griffin, M. J., Abergel, A., Abreu, A., et al. 2010, A&A, 518, L3 Hildebrand, R. H. 1983, QJRAS, 24, 267 Lehtinen, K. & Mattila, K. 1996, A&A, 309, 570 Lombardi, M. & Alves, J. 2001, A&A, 377, 1023 Makovoz, D., Roby, T., Khan, I., & Booth, H. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6274, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Malinen, J., Juvela, M., Collins, D. C., Lunttila, T., & Padoan, P. 2011, A&A, 530, A101 Mathis, J. S., Mezger, P. G., & Panagia, N. 1983, A&A, 128, 212 Nakajima, Y., Kandori, R., Tamura, M., et al. 2008, PASJ, 60, 731 Nakajima, Y., Nagata, T., Sato, S., et al. 2003, AJ, 125, 1407 Padoan, P., Cambr'esy, L., & Langer, W. 2002, ApJ, 580, L57 Padoan, P., Juvela, M., & Pelkonen, V.-M. 2006, ApJ, 636, L101 Pagani, L., Steinacker, J., Bacmann, A., Stutz, A., & Henning, T. 2010, Science, 329, 1622",
"pages": [
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}
]
2013A&A...558A.101S
https://arxiv.org/pdf/1308.1218.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_85><loc_91><loc_86></location>AGN behind the SMC selected from radio and X-ray surveys ?</section_header_level_1>
<text><location><page_1><loc_11><loc_81><loc_91><loc_84></location>R. Sturm 1 , D. Draˇskovi'c 2 , M. D. Filipovi'c 2 , F. Haberl 1 , J. Collier 2 , E. J. Crawford 2 , M. Ehle 3 , A. De Horta 2 , W. Pietsch 1 , N. F. H. Tothill 2 , and G. Wong 2</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_78><loc_70><loc_79></location>1 Max-Planck-Institut fur extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany</list_item>
<list_item><location><page_1><loc_11><loc_76><loc_67><loc_78></location>2 University of Western Sydney, Locked Bag 1797, Penrith South DC, NSW1797, Australia</list_item>
<list_item><location><page_1><loc_11><loc_75><loc_82><loc_76></location>3 XMM-Newton Science Operations Centre, ESAC, ESA, PO Box 78, 28691 Villanueva de la Ca˜nada, Madrid, Spain</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_73><loc_42><loc_74></location>Received 15 October 2012 / Accepted 20 July 2013</text>
<section_header_level_1><location><page_1><loc_47><loc_71><loc_55><loc_72></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_64><loc_91><loc_69></location>Context. The XMMNewton survey of the Small Magellanic Cloud (SMC) revealed 3053 X-ray sources with the majority expected to be active galactic nuclei (AGN) behind the SMC. However, the high stellar density in this field often does not allow assigning unique optical counterparts and hinders source classification. On the other hand, the association of X-ray point sources with radio emission can be used to select background AGN with high confidence, and to constrain other object classes like pulsar wind nebula. Aims. To classify X-ray and radio sources, we use clear correlations of X-ray sources found in the XMMNewton survey with radio-</text>
<text><location><page_1><loc_11><loc_62><loc_42><loc_63></location>continuum sources detected with ATCA and MOST.</text>
<text><location><page_1><loc_11><loc_60><loc_91><loc_62></location>Methods. Deep radio-continuum images were searched for correlations with X-ray sources of the XMMNewton SMC-survey pointsource catalogue as well as galaxy clusters seen with extended X-ray emission.</text>
<text><location><page_1><loc_11><loc_55><loc_91><loc_60></location>Results. Eighty eight discrete radio sources were found in common with the X-ray point-source catalogue in addition to six correlations with extended X-ray sources. One source is identified as a Galactic star and eight as galaxies. Eight radio sources likely originate in AGN that are associated with clusters of galaxies seen in X-rays. One source is a PWN candidate. We obtain 43 new candidates for background sources located behind the SMC. A total of 24 X-ray sources show jet-like radio structures.</text>
<text><location><page_1><loc_11><loc_53><loc_80><loc_54></location>Key words. galaxies: individual: Small Magellanic Cloud - radio continuum: general - X-rays: general - catalogs</text>
<section_header_level_1><location><page_1><loc_7><loc_49><loc_19><loc_50></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_31><loc_50><loc_48></location>Searching for background sources in fields with high stellar density like the Small Magellanic Cloud (SMC) can be intricate. Once background sources behind the SMC are identified, they constitute a valuable sample of sources. Besides studying these sources (e.g. Kelly et al. 2009), when multi-wavelength data from several epochs are available, they provide an ideal reference frame for astrometry as soon as their positions are known precisely. This is important for proper-motion studies of the SMC (e.g. Piatek et al. 2008), but also to reduce systematic uncertainties in the position of X-ray sources (e.g. Watson et al. 2009). Further, the interstellar medium of the SMC may be studied with the help of absorption lines in the spectra of illuminators in the background.</text>
<text><location><page_1><loc_7><loc_15><loc_50><loc_31></location>The first two quasars behind the SMC were reported by Mills et al. (1982) and Wilkes et al. (1983). Later on, Tinney et al. (1997) used optical spectroscopy to confirm additional eight candidates, selected from ROSAT X-ray sources. Dobrzycki et al. (2003a,b) added five X-ray selected candidates and five candidates chosen from their optical variability by Eyer (2002). Kozłowski & Kochanek (2009) selected 657 quasar candidates using Spitzer infrared and near-infrared photometry. Including also candidates selected from optical variability, Kozłowski et al. (2011, 2013) were able to confirm 193 of 766 observed candidates with followup spectroscopy, raising the number of confirmed background quasars to GLYPH<24> 200.</text>
<text><location><page_1><loc_52><loc_11><loc_95><loc_50></location>In this study, we search for sources with common X-ray and radio emission and classify them. The XMMNewton survey of the SMC (Haberl et al. 2012b), provides for the first time a complete coverage of the SMC main body with imaging Xray optics up to photon energies of 12 keV and with a sourcedetection sensitivity of GLYPH<24> 2 GLYPH<2> 10 GLYPH<0> 14 erg s GLYPH<0> 1 cm GLYPH<0> 2 . Compared to previous surveys with ROSAT in the (0.1 GLYPH<0> 2.0) keV band (Haberl et al. 2000; Sasaki et al. 2000), the sensitivity of XMMNewton at harder X-rays results in the detection of more background sources. The higher position accuracy allows a more unique correlation with radio counterparts. To identify X-ray and radio sources, we compare our X-ray point-source catalogue with deep merged Australia Telescope radio images of the SMC, having unprecedented sensitivity compared to earlier studies (e.g. Filipovi'c et al. 1997, 1998, 2002; Payne et al. 2004). Except for a few Galactic stars (such as young stellar objects (YSO) or binary stars) and rare SMC objects like pulsar wind nebulae (PWNe), the bulk of discrete sources emitting radio and X-rays are expected to originate in background objects. Active galactic nuclei (AGN) produce hard X-ray emission and relativistic jets visible in radio. In some cases emission can originate in nearby normal galaxies, with little or no contribution of an AGN. Also the AGN host galaxy can be part of a cluster of galaxies (ClG), where X-rays originate in the hot intracluster medium and radio-continuum emission from the AGN. Supernova remnants (SNRs) in the SMC also can show radio and X-ray emission. These sources have a significant extent at the distance of the SMC (10 00 translates to GLYPH<24> 3 pc) and can easily be excluded. They are not part of this study as these sources will be reviewed in a subsequent paper. Other X-ray and radio emitting sources like</text>
<figure>
<location><page_2><loc_13><loc_75><loc_40><loc_93></location>
</figure>
<figure>
<location><page_2><loc_57><loc_75><loc_84><loc_92></location>
</figure>
<figure>
<location><page_2><loc_13><loc_56><loc_39><loc_75></location>
</figure>
<figure>
<location><page_2><loc_51><loc_57><loc_94><loc_73></location>
<caption>Fig. 1. EPIC X-ray colour images with overlaid radio contours. Red / green / blue corresponds to intensities in the (0.2-1.0) keV, (1.0-2.0) keV and (2.0-4.5) keV band, respectively. Upper left: Three radio sources in the north-east of the SMC are presented in this image. Source No 14 is seen along SNR DEM S128 (the red structure). In the lower left of the image, source No 8 demonstrates an X-ray and radio point source. In the upper right, a ClG is visible in X-rays, containing a radio source in the centre. Contours are: 0.3, 0.6, 1.2, 2.5, 5, and 10 mJy beam GLYPH<0> 1 , beam = 7 : 00 05 GLYPH<2> 6 : 00 63, GLYPH<21> = 20 cm. Upper right: The upper radio source correlates with X-ray emission from source No 65. The lower source is a ClG and not included in our X-ray catalogue, due to the extended emission (Haberl et al. 2012b). Two radio jets are visible from one or possibly two AGN, presumably in the ClG. Contours are: 0.3, 0.6, 1, 2, 3, 5, 7, 10, 15, and 20 mJy beam GLYPH<0> 1 , beam = 6 : 00 56 GLYPH<2> 6 : 00 16, GLYPH<21> = 20 cm. Lower left: Source No 27 is a galaxy candidate showing soft X-ray emission and an extended radio structure. Contours are: 0.18, 0.3, 0.6, 1, 2, 3, 5 mJy beam GLYPH<0> 1 , beam = 6 : 00 56 GLYPH<2> 6 : 00 16, GLYPH<21> = 20 cm. Lower right: Source No 3 is a bright X-ray source in the centre of two radio lobes. Contours are: 2 to 50 mJy beam GLYPH<0> 1 in steps of 2 mJy beam GLYPH<0> 1 , beam = 17 : 00 8 GLYPH<2> 12 : 00 2, GLYPH<21> = 20 cm.</caption>
</figure>
<text><location><page_2><loc_7><loc_36><loc_50><loc_39></location>planetary nebulae are unlikely to be detected at SMC distance (Payne et al. 2004).</text>
<section_header_level_1><location><page_2><loc_7><loc_31><loc_36><loc_32></location>2. Observations and data reduction</section_header_level_1>
<section_header_level_1><location><page_2><loc_7><loc_29><loc_37><loc_30></location>2.1. The XMM-Newton survey of the SMC</section_header_level_1>
<text><location><page_2><loc_7><loc_10><loc_50><loc_28></location>The observatory XMMNewton (Jansen et al. 2001) is equipped with three X-ray telescopes (Aschenbach 2002), with EPIC CCD detectors (Struder et al. 2001; Turner et al. 2001) in their focal planes. XMMNewton performed a survey of the SMC (Haberl et al. 2012b), completely covering the main body with a field size of 5.58 deg 2 and a limiting sensitivity of GLYPH<24> 2 GLYPH<2> 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 in the (0.2-12.0) keV band. For each XMMNewton observation, a maximum-likelihood source detection was performed on X-ray images of various energy bands simultaneously, i.e. a similar method as used for the XMMNewton serendipitous source catalogue (Watson et al. 2009). This resulted in a catalogue of 3053 X-ray sources and includes additional outer fields, leading to a total area of 6.32 deg 2 . For the list of used observations and a detailed description of the X-ray point-source catalogue,</text>
<text><location><page_2><loc_52><loc_36><loc_95><loc_39></location>see Sturm et al. (2013). Extended X-ray sources can be found in Haberl et al. (2012b).</text>
<section_header_level_1><location><page_2><loc_52><loc_33><loc_77><loc_34></location>2.2. Radio observations of the SMC</section_header_level_1>
<text><location><page_2><loc_52><loc_20><loc_95><loc_32></location>Radio-continuum images used in this study (Table 1) were created by combining data from the Australia Telescope Compact Array (ATCA) with data obtained from Parkes radio studies (Filipovi'c et al. 2002; Crawford et al. 2011; Wong et al. 2011a,b, 2012a). We also used high-resolution images from Bojicic et al. (2010) and newly created images of the N 19 region (Wong et al. 2012b). To complement our study we included an image at 36 cm, which was obtained from the MOST survey (Ye & Turtle 1993).</text>
<section_header_level_1><location><page_2><loc_52><loc_17><loc_63><loc_18></location>2.3. Correlation</section_header_level_1>
<text><location><page_2><loc_52><loc_10><loc_95><loc_16></location>Radio-continuum emission of background sources can show spatial structures caused by jets emitted from the AGN. Examples from this work are shown in Fig. 1. In some cases, the X-ray source, which marks the position of the AGN candidate, is placed in between two radio jets. To find all such sources,</text>
<table>
<location><page_3><loc_8><loc_78><loc_93><loc_91></location>
<caption>Table 1. Details of radio-continuum data and surveys used in this study.</caption>
</table>
<text><location><page_3><loc_63><loc_75><loc_64><loc_76></location>12</text>
<text><location><page_3><loc_63><loc_73><loc_64><loc_73></location>11</text>
<text><location><page_3><loc_63><loc_70><loc_64><loc_71></location>10</text>
<text><location><page_3><loc_63><loc_46><loc_63><loc_47></location>0</text>
<figure>
<location><page_3><loc_8><loc_46><loc_64><loc_76></location>
<caption>Fig. 2. Spatial distribution of the X-ray sources with radio associations in the main field overplotted on the H i map of Stanimirovic et al. (1999). The colour scale indicates the column density in units of 10 21 cm GLYPH<0> 2 . The white line marks the XMMNewton main field of the SMC survey. Seven additional sources are located in outer fields, not shown here. Labels give the source number (Column 1 in Table 2). Radio sources in X-ray clusters of galaxies (Table 3) are labelled with C . X-ray radio correlations are shown by circles. If the source shows a jet-like structure in radio, it is shown by a boxed circle. Sources that are classified as galaxies are shown by boxes. Sources that are within ClGs are marked with diamonds. Radio sources with GLYPH<0> 0 : 3 < GLYPH<11> < 0 are plotted in cyan, others in white.</caption>
</figure>
<text><location><page_3><loc_7><loc_37><loc_50><loc_43></location>we visually inspected the radio images for counterparts of X-ray sources. We found 88 out of the 3053 sources from the X-ray point-source catalogue with a counterpart visible in at least one radio image. In Table 2, we list the radio sources with an X-ray match. The columns give the following parameters:</text>
<unordered_list>
<list_item><location><page_3><loc_7><loc_36><loc_43><loc_37></location>(1) Running number, No, of the sources in this study;</list_item>
<list_item><location><page_3><loc_7><loc_33><loc_50><loc_35></location>(2) Source number from the XMMNewton SMC point-source catalogue (Sturm et al. 2013);</list_item>
<list_item><location><page_3><loc_7><loc_28><loc_50><loc_33></location>(3) X-ray flux in the (0.2-4.5) keV band in 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 ; (4) Hardness ratio HR 2 = ( R 3 GLYPH<0> R 2) = ( R 3 + R 2) with R 2 and R 3 being the X-ray count rates in the (0.5 GLYPH<0> 1.0) and (1.0 GLYPH<0> 2.0) keV band;</list_item>
<list_item><location><page_3><loc_7><loc_20><loc_50><loc_28></location>(5-6) Sexagesimal J2000 coordinates as derived from radio. For point-like sources a Gaussian fit was used to determine the position, whereas for complex jet-like structures, the position of the peak flux is given. In the case of two radio detections obviously comprising two jets of the same source we list the apparent centre of the perceived origin of the jets;</list_item>
<list_item><location><page_3><loc_7><loc_17><loc_50><loc_20></location>(7) Estimated position uncertainty for the radio position in arcsec based on image resolution;</list_item>
<list_item><location><page_3><loc_7><loc_15><loc_50><loc_17></location>(8-14) Integrated flux densities S GLYPH<23> in mJy at various radio frequencies GLYPH<23> from the data described in Table 1;</list_item>
<list_item><location><page_3><loc_7><loc_12><loc_50><loc_15></location>(15) Radio spectral index GLYPH<11> according to S GLYPH<23> GLYPH<24> GLYPH<23> GLYPH<11> and uncertainty following Payne et al. (2004);</list_item>
<list_item><location><page_3><loc_7><loc_11><loc_35><loc_12></location>(16) Source classification from this work;</list_item>
</unordered_list>
<text><location><page_3><loc_52><loc_41><loc_95><loc_43></location>(17) Comments on individual sources and references to other catalogues. Jet-like radio structures are noted.</text>
<section_header_level_1><location><page_3><loc_52><loc_38><loc_73><loc_39></location>3. Results and discussion</section_header_level_1>
<text><location><page_3><loc_52><loc_10><loc_95><loc_37></location>The XMMNewton survey of the SMC provides a continuous coverage of the bar and eastern wing of the SMC and allowed the creation of the most comprehensive X-ray point-source catalogue. At the same time, deeper radio images reveal fainter sources in an even larger area. From the correlation of both datasets we derived a list of 88 discrete sources with X-ray and radio emission. In Fig. 2, we mark all X-ray sources with radio counterparts within the main field (5.58 deg 2 ) of the XMMNewton survey on an SMC H i image from Stanimirovic et al. (1999). The XMMNewton main field is indicated with a white contour. For a description of additional fields disconnected from the main field see Sturm et al. (2013). We do not see a particular correlation of the source density with the SMC H i intensity, which is consistent with the sources being mainly background objects. This is also evident when comparing the relative lineof-sight H i column density of our sources with the H i distribution in the XMMNewton field (Fig. 3). As expected, both show a similar distribution, i.e. we do not find more sources in regions with higher (or lower) H i as it would be the case for a correlation (or anti-correlation). Forty-five of our sources are located behind dense SMC regions with an H i column density of</text>
<figure>
<location><page_4><loc_10><loc_73><loc_49><loc_92></location>
<caption>Fig. 3. Cumulative distribution of H i column density in the XMMNewton field (black) and of the line-of-sight column densities of our X-ray radio correlations (red). Correlations with GLYPH<0> 0 : 3 < GLYPH<11> < 0 are plotted in green.</caption>
</figure>
<figure>
<location><page_4><loc_10><loc_38><loc_48><loc_64></location>
<caption>Fig. 4. Separation of X-ray and radio positions. Sources, which have some extent or jets in X-ray or radio are plotted with blue open circles, other sources with black filled circles. Error bars mark 1 GLYPH<27> confidence.</caption>
</figure>
<text><location><page_4><loc_7><loc_23><loc_50><loc_30></location>N SMC H > 4 GLYPH<2> 10 21 cm GLYPH<0> 2 , six sources have a N SMC H > 8 GLYPH<2> 10 21 cm GLYPH<0> 2 . Also no structure according to the bar of the SMC is seen, where sources of star-forming regions are found (e.g. compare compact H ii regions of Wong et al. (2012b, their Fig. 10) and YSO of Oliveira et al. (2013, their Fig. 1).</text>
<section_header_level_1><location><page_4><loc_7><loc_20><loc_25><loc_21></location>3.1. Correlation statistics</section_header_level_1>
<text><location><page_4><loc_7><loc_10><loc_50><loc_19></location>We show the angular separation between radio and X-ray positions in Fig. 4. Eighty-four of our 88 correlations have an angular separation of d GLYPH<20> 5 GLYPH<2> ( GLYPH<27> 2 r + GLYPH<27> 2 X ) 1 = 2 , where GLYPH<27> r and GLYPH<27> X are the position uncertainties of the radio and X-ray source. In some cases (e.g. source No 3, Fig. 1 lower right), the small errors and the radio extent cause larger separations as in these cases, the position of the central radio source had to be estimated. The</text>
<text><location><page_4><loc_52><loc_89><loc_95><loc_93></location>error-weighted average o GLYPH<11> set for point sources is GLYPH<1> RA = 0 : 00 14 and GLYPH<1> Dec = -0 : 00 07 with an uncertainty of 0 : 00 18. We do not see systematic deviations.</text>
<text><location><page_4><loc_52><loc_67><loc_95><loc_89></location>Since the source correlation was done manually, the determination of the fraction of chance coincidences is not straight forward. However, we can compare our result with the result of a simple angular-separation-based cross matching. We merged the radio catalogues of Wong et al. (2011b, GLYPH<21> = 13 ; 20 ; 36 cm) and Wong et al. (2012a, GLYPH<21> = 3 ; 6 cm), as well as the 13 cm sources of Filipovi'c et al. (2002). These catalogues are based on the same radio data, but omit the deep images and therefore contain only 60 of our 89 radio sources. Also, some sources with long jets were rejected for the radio point-source catalogues. We find 58 of our X-ray radio associations within d GLYPH<20> 3 : 439 GLYPH<2> ( GLYPH<27> 2 r + GLYPH<27> 2 X ) 1 = 2 . Additional 6 correlations were not selected in our manual correlation, as these were regarded as too uncertain, e.g. if a jet-like structure is not pointing towards the X-ray source. To check for chance coincidences, we shifted the coordinates of one catalogue by & 50 00 in di GLYPH<11> erent directions. This resulted in 2.5 GLYPH<6> 1.6 correlations indicating a chance coincidence rate of GLYPH<24> 5%.</text>
<section_header_level_1><location><page_4><loc_52><loc_64><loc_72><loc_65></location>3.2. Spectral characteristics</section_header_level_1>
<text><location><page_4><loc_52><loc_42><loc_95><loc_63></location>The spectral index GLYPH<11> of radio background sources covers a wide range, but is on average steeper for background sources than for SNRs or the thermal radio emission from H ii regions (c.f. Filipovi'c et al. 1998). For other rare source types, see the following sections. Because the possible GLYPH<11> values of AGN, SNRs, and H ii regions are overlapping, the classification of radio sources based only on GLYPH<11> is ambiguous, but with the detection of X-rays strongly points to a background object. The distribution of the spectral index GLYPH<11> as estimated from the radio images is shown in Fig. 5. As expected we find a relatively wide distribution in our sample. 60% of the 70 sources with determined spectral index have a steep spectrum ( GLYPH<11> < GLYPH<0> 0 : 45 with S GLYPH<23> GLYPH<24> GLYPH<23> GLYPH<11> ) and 16% show a flat spectrum ( GLYPH<11> > GLYPH<0> 0 : 2). Compared to an unbiased radio sample of background sources (Payne et al. 2004), we find more sources with flat spectrum due to the X-ray selection of our sample (Neumann et al. 1994).</text>
<text><location><page_4><loc_52><loc_32><loc_95><loc_42></location>Twenty-five sources (36%) have a very steep spectral index of GLYPH<11> < GLYPH<0> 0 : 8 and are excellent candidates for compact steep spectrum (CSS) sources (O'Dea 1998; Fanti 2009). CSS sources are believed to bridge the evolutionary phase between the early gigahertz peaked-spectrum (GPS) sources and later and larger Fanaro-Riley Type I and II (FR I / II) galaxies. Sources No 57 and 70 are perfect candidates for GPS sources, due to their curved spectral index.</text>
<text><location><page_4><loc_52><loc_21><loc_95><loc_32></location>Radio sources with a rather flat radio spectrum and no indication of a radio jet or extended structure in X-rays are good candidates for BL Lac objects. The nearly featureless spectrum of these sources makes them ideal background emitters to measure absorption e GLYPH<11> ects of the interstellar medium in the SMC. We find 22 compact radio sources that have an GLYPH<11> > GLYPH<0> 0 : 5 and are not classified as foreground object. These sources are good candidates for BL Lac objects.</text>
<text><location><page_4><loc_52><loc_16><loc_95><loc_21></location>The inverse spectral index ( GLYPH<11> > 0) of source No 28 can be explained by radio variability due to non-simultaneous measurements, as seen from the di GLYPH<11> erent flux densities measured at 20 cm. This can also be the case for sources No 26, 30, and 73.</text>
<text><location><page_4><loc_52><loc_10><loc_95><loc_16></location>In Fig. 6, we show the distribution of HR 2, defined by ( R 3 GLYPH<0> R 2) = ( R 3 + R 2), where R 2 and R 3 is the X-ray count rate in the (0.5 GLYPH<0> 1.0) keV and (1.0 GLYPH<0> 2.0) keV band, respectively. Hard X-ray sources, such as AGN or X-ray binaries, show higher HR 2 values than soft X-ray sources such as Galactic stars or SNRs.</text>
<figure>
<location><page_5><loc_8><loc_72><loc_49><loc_93></location>
<caption>Fig. 5. Histogram of all sources with determined radio spectral index GLYPH<11> . The bin width is 0.2.</caption>
</figure>
<figure>
<location><page_5><loc_8><loc_45><loc_49><loc_65></location>
<caption>Fig. 6. Histogram of the X-ray hardness ratio HR 2 distribution. The bin width is 0.2.</caption>
</figure>
<text><location><page_5><loc_7><loc_28><loc_50><loc_35></location>For AGN, typical values are HR 2 > 0 , whereas most foreground stars are found with HR 2 < 0 (e.g. Stiele et al. 2011). Normal galaxies can show soft and hard X-ray emission, depending on the contribution from X-ray binaries, hot interstellar medium and SNRs. As expected for background sources, the X-ray to radio correlations mainly show hard X-ray emission.</text>
<section_header_level_1><location><page_5><loc_7><loc_24><loc_16><loc_25></location>3.3. Galaxies</section_header_level_1>
<text><location><page_5><loc_7><loc_10><loc_50><loc_22></location>Six of our sources (No 17, 18, 24, 48, 79, and 87) have a counterpart in the 6dF galaxy survey with determined redshifts (Jones et al. 2009). Remarkably, all of the 6dF correlations with the 3053 X-ray sources show radio emission. No 17 is a known Seyfert 2 galaxy. All these sources have an entry in the 2MASS extended source catalogue (2MASX, Skrutskie et al. 2006). In addition we find 2MASX counterparts for sources No 27 and 86, pointing to a galaxy nature of these sources. The galaxy nature is further supported by a 2MASX galaxy score of 1.0 and a HR 2 < 0. Source No 27 is shown in Fig. 1, lower left.</text>
<section_header_level_1><location><page_5><loc_52><loc_92><loc_65><loc_93></location>3.4. Galactic stars</section_header_level_1>
<text><location><page_5><loc_52><loc_82><loc_95><loc_91></location>Galactic stars can show X-ray and radio emission. The correlation No 37 is identified with the Galactic star CF Tuc. This is an active RS CVn-type binary with known X-ray and radio emission (Kuerster & Schmitt 1996; Gunn et al. 1997). In addition to soft X-ray emission from coronal plasma, a bright (log ( F X = F opt) < GLYPH<0> 1) optical counterpart is expected for a foreground star (Maccacaro et al. 1988).</text>
<text><location><page_5><loc_52><loc_62><loc_95><loc_82></location>Eight of our sources show soft X-ray emission, compatible with the hardness-ratio criteria for stars of Pietsch et al. (2004) or Sturm et al. (2013) and have an appropriate optical counterpart in the Magellanic Cloud Photometric Survey (MCPS, Zaritsky et al. 2002). Five of these can be rejected as stars, because of a 2MASX counterpart (see Sec. 3.3). No 14 is along the SNR DEMS128, which causes a softer HR 2. However, in the X-ray image, a hard X-ray source is clearly seen. Because we are looking out of the Galactic plane we expect a low contribution of young Galactic stars and the jet-like structure of No 47 is more likely caused by a background AGN than by outflows of protostellar jets of a Galactic source. Source No 54 cannot be excluded as possible foreground star. All other sources show hard X-ray emission that is not expected from coronal stellar X-ray emission.</text>
<text><location><page_5><loc_52><loc_55><loc_95><loc_62></location>We do not expect a contribution of SMC stars in the X-ray sample, because the moderate X-ray emission of normal stars even during flares ( L X . 10 33 erg s GLYPH<0> 1 , Gudel & Naz'e 2009; Favata 2002) is below the detection limit of the XMMNewton survey. Further, only the brightest YSOs are detected in the radio observations (Oliveira et al. 2013).</text>
<section_header_level_1><location><page_5><loc_52><loc_51><loc_68><loc_52></location>3.5. Cluster of galaxies</section_header_level_1>
<text><location><page_5><loc_52><loc_33><loc_95><loc_50></location>Often, clusters of galaxies (ClGs), seen in X-rays, contain radio-continuum sources (e.g. Mittal et al. 2009, and references therein). In these cases, the X-ray emission is caused by the hot intracluster medium, whereas the radio-continuum emission originates in an AGN in or in the direction of the ClG. The sources No 34 and 72 were fitted with a significant extent in Xrays (11 : 00 9 GLYPH<6> 1 : 00 1 and 12 : 00 6 GLYPH<6> 1 : 00 6) and show hard X-ray emission, which points to a ClG nature of these sources. We found also strong radio jets in other cluster candidates, which have a larger extent and were therefore not included in the X-ray point-source catalogue. These cluster candidates can be found in Haberl et al. (2012b). The radio counterparts are listed in Table 3. Examples are given in both upper images of Fig. 1.</text>
<section_header_level_1><location><page_5><loc_52><loc_30><loc_65><loc_31></location>3.6. X-ray binaries</section_header_level_1>
<text><location><page_5><loc_52><loc_15><loc_95><loc_29></location>Because of the relatively small stellar mass of the SMC, only a few low-mass X-ray binaries (LMXBs) are expected and none is known to date (Coe et al. 2010). In the case of LMXBs, we would not expect to find an optical counterpart. Also no ultraluminous X-ray source (ULX) in the SMC is known and the measured X-ray luminosities are well below the ULX definition ( > 10 39 erg s GLYPH<0> 1 ). Therefore, the presence of a microquasar in our sample is unlikely, but cannot be ruled out. Redshift measurements of AGN candidates are needed, to further reduce the possibility of a microquasar in the SMC, that otherwise might only be recognised during a bright outburst.</text>
<text><location><page_5><loc_52><loc_10><loc_95><loc_15></location>The SMC hosts around one hundred known high-mass X-ray binaries (HMXB). Only one source in our sample has a proper optical counterpart in the MCPS that is compatible with an earlytype star of a HMXB. This source, No 5 = [SG2005] SMC34,</text>
<table>
<location><page_6><loc_17><loc_80><loc_85><loc_91></location>
<caption>Table 3. Radio sources in X-ray selected clusters of galaxies from Haberl et al. (2012b).</caption>
</table>
<text><location><page_6><loc_7><loc_78><loc_38><loc_79></location>Notes. Values and references analogous to Table 2.</text>
<text><location><page_6><loc_7><loc_46><loc_50><loc_76></location>was classified as 'HMXB candidate' from XMMNewton and optical data by Shtykovskiy & Gilfanov (2005, their source 34) and as 'new HMXB' from Chandra observations by Antoniou et al. (2009, source 4 4). Antoniou et al. (2009) also found additional possible optical counterparts from OGLE (Udalski et al. 1998) in agreement with the X-ray position. Kozłowski et al. (2011, see their Fig. 2) spectroscopically identified one of the fainter counterparts as a quasar with emission lines at redshift of z = 0 : 108. The Chandra source of Antoniou et al. (2009) has a similar angular separation to both OGLE sources, the star (SMCSC159896, 0.54 00 ) and the quasar (SMC-SC 159964, 0.53 00 ). Our radio source has an angular separation of 0.60 00 and 0.58 00 , respectively, with a position uncertainty of 1 00 . From a spectral analysis of the XMMNewton spectrum we could derive rough parameters for an absorbed power-law model. The photon index is between GLYPH<0> = (0 : 99 GLYPH<0> 1 : 97) and the source is highly absorbed with NH = (1 : 7 GLYPH<0> 3 : 9) GLYPH<2> 10 23 cm GLYPH<0> 2 . This is compatible with both AGN and HMXB, which have typical photon indices of 1.75 (Tozzi et al. 2006) and 1.0 (Haberl & Pietsch 2004), respectively, and can show high intrinsic absorption. Therefore, the radio emission is likely caused by the quasar and the X-ray emission can be caused by both, however a background object is more likely.</text>
<section_header_level_1><location><page_6><loc_7><loc_42><loc_25><loc_43></location>3.7. Pulsar wind nebulae</section_header_level_1>
<text><location><page_6><loc_7><loc_25><loc_50><loc_40></location>A rare but interesting source class are PWNe (e.g. Gaensler & Slane 2006). PWN candidates in the SMC are X-ray and radio emitting sources that are found within thermal SNR shells, like the central sources of HFPK 334 (Filipovi'c et al. 2008) and of IKT16 (Owen et al. 2011). In the Large Magellanic Cloud (LMC), five candidates for such composite SNRs are known (B0540-693, N157B, B0532-710, DEM L241, and SNRJ04536829, see Haberl et al. 2012a, and references therein). However, also PWNe without a thermal SNR shell, like the Crab Nebula or the PWN around the pulsar PSR B0540-69 in the LMC, are possible. The fact, that we do not know such a system in the SMC might be a selection e GLYPH<11> ect.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_24></location>The expected X-ray spectra of PWNe ( GLYPH<0> GLYPH<24> 2) will result in similar hardness ratios as for AGN ( GLYPH<0> GLYPH<24> 1 : 75) and hamper an Xray-based classification. Typical spectral radio indices of PWNe are GLYPH<0> 0 : 3 < GLYPH<11> < 0, where we find 15 sources in our sample. These sources might be taken as a flux limited sample of candidates for PWNe. However, the source distribution (plotted in cyan in Fig. 2 and green in Fig. 3) is not correlating with star-forming regions in the SMC, i.e. the bar of the SMC where we see most of the SNRs. Therefore, we expect that most of these sources are background objects and that there is no significant contribution of PWNe given the sensitivity of our observations.</text>
<text><location><page_6><loc_52><loc_56><loc_95><loc_76></location>A special case is source No 14, which is found along the SNR DEMS128 (upper left of Fig. 1) with a spectral index of GLYPH<11> = GLYPH<0> 0 : 21 GLYPH<6> 0 : 12, which is steeper than for the surrounding SNR ( GLYPH<11> = GLYPH<0> 0 : 48 GLYPH<6> 0 : 06, Filipovi'c et al. 2000). The type-Ia classification of the SNR (van der Heyden et al. 2004) and the o GLYPH<11> set of its X-ray bright centre from the point source suggest that both sources are not connected with each other. In the SAGE survey (Gordon et al. 2011) we find a mid-infrared Spitzer / IRAC counterpart (SSTISAGEMA J010530.69-721021.3) with colours that might be consistent with an AGN. However, in the deep Xray images, the emission from DEM S128 clearly extends further towards the north-west (compare also Haberl et al. 2012b, Fig 6.1). Therefore, we cannot exclude No 14 as a candidate for a PWN. DEMS128 will be discussed in more detail by Roper et al. (in prep.).</text>
<text><location><page_6><loc_52><loc_43><loc_95><loc_56></location>We can also roughly estimate the probability of finding a radio X-ray association within an SNR using our source list that contains 2.4 sources deg GLYPH<0> 2 with GLYPH<0> 0 : 3 < GLYPH<11> < 0. According to Haberl et al. (2012b), the area covered by known SNRs is GLYPH<24> 0.044 deg GLYPH<0> 2 . For a Poisson distribution, we would expect to find one source along an SNR with a likelihood of 9.4% and more than one source with a likelihood of 0.5%. So the DEM S128 correlation might still be by chance, but this is unlikely to be the case for all PWN candidates in the SMC (HFPK 334 and IKT 16, not included in this study).</text>
<section_header_level_1><location><page_6><loc_52><loc_40><loc_79><loc_41></location>3.8. Comparison with previous studies</section_header_level_1>
<text><location><page_6><loc_52><loc_19><loc_95><loc_38></location>For 17 of our sources, we find a counterpart in the ROSAT PSPC catalogue (Haberl et al. 2000). These are commented with H00 in Table 2. Twelve of these sources were already associated with radio sources at GLYPH<21> = 13 cm in that work. In addition, the ROSAT catalogue lists 39 sources with radio association. Of these, nine are outside the XMMNewton field ([HFP2000] 52, 124, 138, 347, 357, 522, 685, 687, and 692), four are now resolved as ClGs ([HFP2000] 101, 147, 317, and 410) and 18 are SNRs ([HFP2000] 45, 107, 125, 145, 148, 194, 217, 281, 285, 334, 401, 413, 414, 419, 437, 454, 461, and 530), where [HFP2000] 281 was probably detected as part of a bubble connected to the SNR DEMS68 (Filipovi'c et al. 2008). [HFP2000] 88 was not detected with XMMNewton . For [HFP2000] 49, 206, 249, 380, 440, 448, and 668, the improved X-ray positions with respect to ROSAT make an X-ray radio association unlikely.</text>
<text><location><page_6><loc_52><loc_10><loc_95><loc_19></location>Since the gain of the radio data is rather in sensitivity than in resolution, the comparison with Payne et al. (2004) is somewhat more straight forward. We find 32 of our sources in Payne et al. (2004), marked with P04 in Table 2. All sources but one were classified as background objects by these authors, but only 3 sources are noted as X-ray association. Only source No 22 ([FBR2002] J005254-720132) was classified as background ob-</text>
<text><location><page_7><loc_7><loc_76><loc_50><loc_93></location>ject or H ii region. The X-ray emission points to a background source in this case. Further, there are 37 sources for which Payne et al. (2004) give an X-ray luminosity or an X-ray comment. Of these, 13 were identified as SNRs, three are in ClGs, and 14 were classified as H ii regions where we do not find X-ray sources in our study, confirming the classification. From the remaining sources one is classified as 'XRB' (microquasar candidate), correlating with [HFP2000] 295. This X-ray radio association was rejected above. The other sources are candidate background objects, but we do not find X-ray counterparts in the XMMNewton catalogue ([FBR2002] J004552-731339, J004836-733056, J005218-722708, J005602-720908, J005610721833, and J010525-722525).</text>
<section_header_level_1><location><page_7><loc_7><loc_73><loc_19><loc_74></location>4. Conclusions</section_header_level_1>
<text><location><page_7><loc_7><loc_41><loc_50><loc_72></location>We inspect the positions of X-ray sources from the XMMNewton SMCsurvey in the corresponding deep radio-continuum images and found 88 X-ray sources associated with a unique radio counterpart. One source is identified with a foreground star, one is a confirmed quasar probably confused with a HMXB candidate, eight are identified or classified as galaxies, two radio sources are within clusters of galaxies, and one might be a PWN. The remaining 75 X-ray sources associated with a unique radio counterpart are classified as AGN behind the SMC. Due to the precise X-ray positions of our X-ray catalogue ( GLYPH<24> 1.5 00 ) and the low density of radio sources in the SMC field, chance correlations are unlikely and we derive a high purity for our sample. Weexpect the contribution of stars to our sample to be GLYPH<20> 2. From background source candidates, seven are infra-red-selected candidates of Kozłowski & Kochanek (2009), 31 were classified as background radio sources by Payne et al. (2004), and 11 as AGN candidates by Haberl et al. (2000). 40 associations are newly classified background objects behind the SMC, for the others, the X-ray radio association a GLYPH<14> rms the previous backgroundobject classification. For a total of 21 X-ray point sources, we find a jet like structure in radio, which points to the AGN character of the source. In addition, we list six radio sources inside ClGs with high X-ray extent, where three radio sources show a jet.</text>
<text><location><page_7><loc_7><loc_31><loc_50><loc_39></location>Acknowledgements. The XMM-Newton project is supported by the Bundesministerium fur Wirtschaft und Technologie / Deutsches Zentrum fur Luft- und Raumfahrt (BMWI / DLR, FKZ 50 OX 0001) and the Max-Planck Society. The ATCA is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. We used the karma and miriad software package developed by the ATNF. R.S. acknowledges support from the BMWI / DLR grant FKZ 50 OR 0907.</text>
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<section_header_level_1><location><page_9><loc_76><loc_12><loc_81><loc_95></location>Notes. F or a description of the T able, see Sec. 2.3. ( a ) Comments on indi vidual sources. F or details see te xt. Identifications with sources from other catalogues are mark ed as follo ws: Refer ences. (P04) P ayne et al. (2004); (H00) Haberl et al. (2000); (J09) Jones et al. (2009); (S06) Skrutskie et al. (2006); (S05) Shtyk o vskiy & Gilf ano v (2005); (K09) K ozło wski & K ochanek</section_header_level_1>
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</document>
[
{
"title": "ABSTRACT",
"content": "Context. The XMMNewton survey of the Small Magellanic Cloud (SMC) revealed 3053 X-ray sources with the majority expected to be active galactic nuclei (AGN) behind the SMC. However, the high stellar density in this field often does not allow assigning unique optical counterparts and hinders source classification. On the other hand, the association of X-ray point sources with radio emission can be used to select background AGN with high confidence, and to constrain other object classes like pulsar wind nebula. Aims. To classify X-ray and radio sources, we use clear correlations of X-ray sources found in the XMMNewton survey with radio- continuum sources detected with ATCA and MOST. Methods. Deep radio-continuum images were searched for correlations with X-ray sources of the XMMNewton SMC-survey pointsource catalogue as well as galaxy clusters seen with extended X-ray emission. Results. Eighty eight discrete radio sources were found in common with the X-ray point-source catalogue in addition to six correlations with extended X-ray sources. One source is identified as a Galactic star and eight as galaxies. Eight radio sources likely originate in AGN that are associated with clusters of galaxies seen in X-rays. One source is a PWN candidate. We obtain 43 new candidates for background sources located behind the SMC. A total of 24 X-ray sources show jet-like radio structures. Key words. galaxies: individual: Small Magellanic Cloud - radio continuum: general - X-rays: general - catalogs",
"pages": [
1
]
},
{
"title": "AGN behind the SMC selected from radio and X-ray surveys ?",
"content": "R. Sturm 1 , D. Draˇskovi'c 2 , M. D. Filipovi'c 2 , F. Haberl 1 , J. Collier 2 , E. J. Crawford 2 , M. Ehle 3 , A. De Horta 2 , W. Pietsch 1 , N. F. H. Tothill 2 , and G. Wong 2 Received 15 October 2012 / Accepted 20 July 2013",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Searching for background sources in fields with high stellar density like the Small Magellanic Cloud (SMC) can be intricate. Once background sources behind the SMC are identified, they constitute a valuable sample of sources. Besides studying these sources (e.g. Kelly et al. 2009), when multi-wavelength data from several epochs are available, they provide an ideal reference frame for astrometry as soon as their positions are known precisely. This is important for proper-motion studies of the SMC (e.g. Piatek et al. 2008), but also to reduce systematic uncertainties in the position of X-ray sources (e.g. Watson et al. 2009). Further, the interstellar medium of the SMC may be studied with the help of absorption lines in the spectra of illuminators in the background. The first two quasars behind the SMC were reported by Mills et al. (1982) and Wilkes et al. (1983). Later on, Tinney et al. (1997) used optical spectroscopy to confirm additional eight candidates, selected from ROSAT X-ray sources. Dobrzycki et al. (2003a,b) added five X-ray selected candidates and five candidates chosen from their optical variability by Eyer (2002). Kozłowski & Kochanek (2009) selected 657 quasar candidates using Spitzer infrared and near-infrared photometry. Including also candidates selected from optical variability, Kozłowski et al. (2011, 2013) were able to confirm 193 of 766 observed candidates with followup spectroscopy, raising the number of confirmed background quasars to GLYPH<24> 200. In this study, we search for sources with common X-ray and radio emission and classify them. The XMMNewton survey of the SMC (Haberl et al. 2012b), provides for the first time a complete coverage of the SMC main body with imaging Xray optics up to photon energies of 12 keV and with a sourcedetection sensitivity of GLYPH<24> 2 GLYPH<2> 10 GLYPH<0> 14 erg s GLYPH<0> 1 cm GLYPH<0> 2 . Compared to previous surveys with ROSAT in the (0.1 GLYPH<0> 2.0) keV band (Haberl et al. 2000; Sasaki et al. 2000), the sensitivity of XMMNewton at harder X-rays results in the detection of more background sources. The higher position accuracy allows a more unique correlation with radio counterparts. To identify X-ray and radio sources, we compare our X-ray point-source catalogue with deep merged Australia Telescope radio images of the SMC, having unprecedented sensitivity compared to earlier studies (e.g. Filipovi'c et al. 1997, 1998, 2002; Payne et al. 2004). Except for a few Galactic stars (such as young stellar objects (YSO) or binary stars) and rare SMC objects like pulsar wind nebulae (PWNe), the bulk of discrete sources emitting radio and X-rays are expected to originate in background objects. Active galactic nuclei (AGN) produce hard X-ray emission and relativistic jets visible in radio. In some cases emission can originate in nearby normal galaxies, with little or no contribution of an AGN. Also the AGN host galaxy can be part of a cluster of galaxies (ClG), where X-rays originate in the hot intracluster medium and radio-continuum emission from the AGN. Supernova remnants (SNRs) in the SMC also can show radio and X-ray emission. These sources have a significant extent at the distance of the SMC (10 00 translates to GLYPH<24> 3 pc) and can easily be excluded. They are not part of this study as these sources will be reviewed in a subsequent paper. Other X-ray and radio emitting sources like planetary nebulae are unlikely to be detected at SMC distance (Payne et al. 2004).",
"pages": [
1,
2
]
},
{
"title": "2.1. The XMM-Newton survey of the SMC",
"content": "The observatory XMMNewton (Jansen et al. 2001) is equipped with three X-ray telescopes (Aschenbach 2002), with EPIC CCD detectors (Struder et al. 2001; Turner et al. 2001) in their focal planes. XMMNewton performed a survey of the SMC (Haberl et al. 2012b), completely covering the main body with a field size of 5.58 deg 2 and a limiting sensitivity of GLYPH<24> 2 GLYPH<2> 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 in the (0.2-12.0) keV band. For each XMMNewton observation, a maximum-likelihood source detection was performed on X-ray images of various energy bands simultaneously, i.e. a similar method as used for the XMMNewton serendipitous source catalogue (Watson et al. 2009). This resulted in a catalogue of 3053 X-ray sources and includes additional outer fields, leading to a total area of 6.32 deg 2 . For the list of used observations and a detailed description of the X-ray point-source catalogue, see Sturm et al. (2013). Extended X-ray sources can be found in Haberl et al. (2012b).",
"pages": [
2
]
},
{
"title": "2.2. Radio observations of the SMC",
"content": "Radio-continuum images used in this study (Table 1) were created by combining data from the Australia Telescope Compact Array (ATCA) with data obtained from Parkes radio studies (Filipovi'c et al. 2002; Crawford et al. 2011; Wong et al. 2011a,b, 2012a). We also used high-resolution images from Bojicic et al. (2010) and newly created images of the N 19 region (Wong et al. 2012b). To complement our study we included an image at 36 cm, which was obtained from the MOST survey (Ye & Turtle 1993).",
"pages": [
2
]
},
{
"title": "2.3. Correlation",
"content": "Radio-continuum emission of background sources can show spatial structures caused by jets emitted from the AGN. Examples from this work are shown in Fig. 1. In some cases, the X-ray source, which marks the position of the AGN candidate, is placed in between two radio jets. To find all such sources, 12 11 10 0 we visually inspected the radio images for counterparts of X-ray sources. We found 88 out of the 3053 sources from the X-ray point-source catalogue with a counterpart visible in at least one radio image. In Table 2, we list the radio sources with an X-ray match. The columns give the following parameters: (17) Comments on individual sources and references to other catalogues. Jet-like radio structures are noted.",
"pages": [
2,
3
]
},
{
"title": "3. Results and discussion",
"content": "The XMMNewton survey of the SMC provides a continuous coverage of the bar and eastern wing of the SMC and allowed the creation of the most comprehensive X-ray point-source catalogue. At the same time, deeper radio images reveal fainter sources in an even larger area. From the correlation of both datasets we derived a list of 88 discrete sources with X-ray and radio emission. In Fig. 2, we mark all X-ray sources with radio counterparts within the main field (5.58 deg 2 ) of the XMMNewton survey on an SMC H i image from Stanimirovic et al. (1999). The XMMNewton main field is indicated with a white contour. For a description of additional fields disconnected from the main field see Sturm et al. (2013). We do not see a particular correlation of the source density with the SMC H i intensity, which is consistent with the sources being mainly background objects. This is also evident when comparing the relative lineof-sight H i column density of our sources with the H i distribution in the XMMNewton field (Fig. 3). As expected, both show a similar distribution, i.e. we do not find more sources in regions with higher (or lower) H i as it would be the case for a correlation (or anti-correlation). Forty-five of our sources are located behind dense SMC regions with an H i column density of N SMC H > 4 GLYPH<2> 10 21 cm GLYPH<0> 2 , six sources have a N SMC H > 8 GLYPH<2> 10 21 cm GLYPH<0> 2 . Also no structure according to the bar of the SMC is seen, where sources of star-forming regions are found (e.g. compare compact H ii regions of Wong et al. (2012b, their Fig. 10) and YSO of Oliveira et al. (2013, their Fig. 1).",
"pages": [
3,
4
]
},
{
"title": "3.1. Correlation statistics",
"content": "We show the angular separation between radio and X-ray positions in Fig. 4. Eighty-four of our 88 correlations have an angular separation of d GLYPH<20> 5 GLYPH<2> ( GLYPH<27> 2 r + GLYPH<27> 2 X ) 1 = 2 , where GLYPH<27> r and GLYPH<27> X are the position uncertainties of the radio and X-ray source. In some cases (e.g. source No 3, Fig. 1 lower right), the small errors and the radio extent cause larger separations as in these cases, the position of the central radio source had to be estimated. The error-weighted average o GLYPH<11> set for point sources is GLYPH<1> RA = 0 : 00 14 and GLYPH<1> Dec = -0 : 00 07 with an uncertainty of 0 : 00 18. We do not see systematic deviations. Since the source correlation was done manually, the determination of the fraction of chance coincidences is not straight forward. However, we can compare our result with the result of a simple angular-separation-based cross matching. We merged the radio catalogues of Wong et al. (2011b, GLYPH<21> = 13 ; 20 ; 36 cm) and Wong et al. (2012a, GLYPH<21> = 3 ; 6 cm), as well as the 13 cm sources of Filipovi'c et al. (2002). These catalogues are based on the same radio data, but omit the deep images and therefore contain only 60 of our 89 radio sources. Also, some sources with long jets were rejected for the radio point-source catalogues. We find 58 of our X-ray radio associations within d GLYPH<20> 3 : 439 GLYPH<2> ( GLYPH<27> 2 r + GLYPH<27> 2 X ) 1 = 2 . Additional 6 correlations were not selected in our manual correlation, as these were regarded as too uncertain, e.g. if a jet-like structure is not pointing towards the X-ray source. To check for chance coincidences, we shifted the coordinates of one catalogue by & 50 00 in di GLYPH<11> erent directions. This resulted in 2.5 GLYPH<6> 1.6 correlations indicating a chance coincidence rate of GLYPH<24> 5%.",
"pages": [
4
]
},
{
"title": "3.2. Spectral characteristics",
"content": "The spectral index GLYPH<11> of radio background sources covers a wide range, but is on average steeper for background sources than for SNRs or the thermal radio emission from H ii regions (c.f. Filipovi'c et al. 1998). For other rare source types, see the following sections. Because the possible GLYPH<11> values of AGN, SNRs, and H ii regions are overlapping, the classification of radio sources based only on GLYPH<11> is ambiguous, but with the detection of X-rays strongly points to a background object. The distribution of the spectral index GLYPH<11> as estimated from the radio images is shown in Fig. 5. As expected we find a relatively wide distribution in our sample. 60% of the 70 sources with determined spectral index have a steep spectrum ( GLYPH<11> < GLYPH<0> 0 : 45 with S GLYPH<23> GLYPH<24> GLYPH<23> GLYPH<11> ) and 16% show a flat spectrum ( GLYPH<11> > GLYPH<0> 0 : 2). Compared to an unbiased radio sample of background sources (Payne et al. 2004), we find more sources with flat spectrum due to the X-ray selection of our sample (Neumann et al. 1994). Twenty-five sources (36%) have a very steep spectral index of GLYPH<11> < GLYPH<0> 0 : 8 and are excellent candidates for compact steep spectrum (CSS) sources (O'Dea 1998; Fanti 2009). CSS sources are believed to bridge the evolutionary phase between the early gigahertz peaked-spectrum (GPS) sources and later and larger Fanaro-Riley Type I and II (FR I / II) galaxies. Sources No 57 and 70 are perfect candidates for GPS sources, due to their curved spectral index. Radio sources with a rather flat radio spectrum and no indication of a radio jet or extended structure in X-rays are good candidates for BL Lac objects. The nearly featureless spectrum of these sources makes them ideal background emitters to measure absorption e GLYPH<11> ects of the interstellar medium in the SMC. We find 22 compact radio sources that have an GLYPH<11> > GLYPH<0> 0 : 5 and are not classified as foreground object. These sources are good candidates for BL Lac objects. The inverse spectral index ( GLYPH<11> > 0) of source No 28 can be explained by radio variability due to non-simultaneous measurements, as seen from the di GLYPH<11> erent flux densities measured at 20 cm. This can also be the case for sources No 26, 30, and 73. In Fig. 6, we show the distribution of HR 2, defined by ( R 3 GLYPH<0> R 2) = ( R 3 + R 2), where R 2 and R 3 is the X-ray count rate in the (0.5 GLYPH<0> 1.0) keV and (1.0 GLYPH<0> 2.0) keV band, respectively. Hard X-ray sources, such as AGN or X-ray binaries, show higher HR 2 values than soft X-ray sources such as Galactic stars or SNRs. For AGN, typical values are HR 2 > 0 , whereas most foreground stars are found with HR 2 < 0 (e.g. Stiele et al. 2011). Normal galaxies can show soft and hard X-ray emission, depending on the contribution from X-ray binaries, hot interstellar medium and SNRs. As expected for background sources, the X-ray to radio correlations mainly show hard X-ray emission.",
"pages": [
4,
5
]
},
{
"title": "3.3. Galaxies",
"content": "Six of our sources (No 17, 18, 24, 48, 79, and 87) have a counterpart in the 6dF galaxy survey with determined redshifts (Jones et al. 2009). Remarkably, all of the 6dF correlations with the 3053 X-ray sources show radio emission. No 17 is a known Seyfert 2 galaxy. All these sources have an entry in the 2MASS extended source catalogue (2MASX, Skrutskie et al. 2006). In addition we find 2MASX counterparts for sources No 27 and 86, pointing to a galaxy nature of these sources. The galaxy nature is further supported by a 2MASX galaxy score of 1.0 and a HR 2 < 0. Source No 27 is shown in Fig. 1, lower left.",
"pages": [
5
]
},
{
"title": "3.4. Galactic stars",
"content": "Galactic stars can show X-ray and radio emission. The correlation No 37 is identified with the Galactic star CF Tuc. This is an active RS CVn-type binary with known X-ray and radio emission (Kuerster & Schmitt 1996; Gunn et al. 1997). In addition to soft X-ray emission from coronal plasma, a bright (log ( F X = F opt) < GLYPH<0> 1) optical counterpart is expected for a foreground star (Maccacaro et al. 1988). Eight of our sources show soft X-ray emission, compatible with the hardness-ratio criteria for stars of Pietsch et al. (2004) or Sturm et al. (2013) and have an appropriate optical counterpart in the Magellanic Cloud Photometric Survey (MCPS, Zaritsky et al. 2002). Five of these can be rejected as stars, because of a 2MASX counterpart (see Sec. 3.3). No 14 is along the SNR DEMS128, which causes a softer HR 2. However, in the X-ray image, a hard X-ray source is clearly seen. Because we are looking out of the Galactic plane we expect a low contribution of young Galactic stars and the jet-like structure of No 47 is more likely caused by a background AGN than by outflows of protostellar jets of a Galactic source. Source No 54 cannot be excluded as possible foreground star. All other sources show hard X-ray emission that is not expected from coronal stellar X-ray emission. We do not expect a contribution of SMC stars in the X-ray sample, because the moderate X-ray emission of normal stars even during flares ( L X . 10 33 erg s GLYPH<0> 1 , Gudel & Naz'e 2009; Favata 2002) is below the detection limit of the XMMNewton survey. Further, only the brightest YSOs are detected in the radio observations (Oliveira et al. 2013).",
"pages": [
5
]
},
{
"title": "3.5. Cluster of galaxies",
"content": "Often, clusters of galaxies (ClGs), seen in X-rays, contain radio-continuum sources (e.g. Mittal et al. 2009, and references therein). In these cases, the X-ray emission is caused by the hot intracluster medium, whereas the radio-continuum emission originates in an AGN in or in the direction of the ClG. The sources No 34 and 72 were fitted with a significant extent in Xrays (11 : 00 9 GLYPH<6> 1 : 00 1 and 12 : 00 6 GLYPH<6> 1 : 00 6) and show hard X-ray emission, which points to a ClG nature of these sources. We found also strong radio jets in other cluster candidates, which have a larger extent and were therefore not included in the X-ray point-source catalogue. These cluster candidates can be found in Haberl et al. (2012b). The radio counterparts are listed in Table 3. Examples are given in both upper images of Fig. 1.",
"pages": [
5
]
},
{
"title": "3.6. X-ray binaries",
"content": "Because of the relatively small stellar mass of the SMC, only a few low-mass X-ray binaries (LMXBs) are expected and none is known to date (Coe et al. 2010). In the case of LMXBs, we would not expect to find an optical counterpart. Also no ultraluminous X-ray source (ULX) in the SMC is known and the measured X-ray luminosities are well below the ULX definition ( > 10 39 erg s GLYPH<0> 1 ). Therefore, the presence of a microquasar in our sample is unlikely, but cannot be ruled out. Redshift measurements of AGN candidates are needed, to further reduce the possibility of a microquasar in the SMC, that otherwise might only be recognised during a bright outburst. The SMC hosts around one hundred known high-mass X-ray binaries (HMXB). Only one source in our sample has a proper optical counterpart in the MCPS that is compatible with an earlytype star of a HMXB. This source, No 5 = [SG2005] SMC34, Notes. Values and references analogous to Table 2. was classified as 'HMXB candidate' from XMMNewton and optical data by Shtykovskiy & Gilfanov (2005, their source 34) and as 'new HMXB' from Chandra observations by Antoniou et al. (2009, source 4 4). Antoniou et al. (2009) also found additional possible optical counterparts from OGLE (Udalski et al. 1998) in agreement with the X-ray position. Kozłowski et al. (2011, see their Fig. 2) spectroscopically identified one of the fainter counterparts as a quasar with emission lines at redshift of z = 0 : 108. The Chandra source of Antoniou et al. (2009) has a similar angular separation to both OGLE sources, the star (SMCSC159896, 0.54 00 ) and the quasar (SMC-SC 159964, 0.53 00 ). Our radio source has an angular separation of 0.60 00 and 0.58 00 , respectively, with a position uncertainty of 1 00 . From a spectral analysis of the XMMNewton spectrum we could derive rough parameters for an absorbed power-law model. The photon index is between GLYPH<0> = (0 : 99 GLYPH<0> 1 : 97) and the source is highly absorbed with NH = (1 : 7 GLYPH<0> 3 : 9) GLYPH<2> 10 23 cm GLYPH<0> 2 . This is compatible with both AGN and HMXB, which have typical photon indices of 1.75 (Tozzi et al. 2006) and 1.0 (Haberl & Pietsch 2004), respectively, and can show high intrinsic absorption. Therefore, the radio emission is likely caused by the quasar and the X-ray emission can be caused by both, however a background object is more likely.",
"pages": [
5,
6
]
},
{
"title": "3.7. Pulsar wind nebulae",
"content": "A rare but interesting source class are PWNe (e.g. Gaensler & Slane 2006). PWN candidates in the SMC are X-ray and radio emitting sources that are found within thermal SNR shells, like the central sources of HFPK 334 (Filipovi'c et al. 2008) and of IKT16 (Owen et al. 2011). In the Large Magellanic Cloud (LMC), five candidates for such composite SNRs are known (B0540-693, N157B, B0532-710, DEM L241, and SNRJ04536829, see Haberl et al. 2012a, and references therein). However, also PWNe without a thermal SNR shell, like the Crab Nebula or the PWN around the pulsar PSR B0540-69 in the LMC, are possible. The fact, that we do not know such a system in the SMC might be a selection e GLYPH<11> ect. The expected X-ray spectra of PWNe ( GLYPH<0> GLYPH<24> 2) will result in similar hardness ratios as for AGN ( GLYPH<0> GLYPH<24> 1 : 75) and hamper an Xray-based classification. Typical spectral radio indices of PWNe are GLYPH<0> 0 : 3 < GLYPH<11> < 0, where we find 15 sources in our sample. These sources might be taken as a flux limited sample of candidates for PWNe. However, the source distribution (plotted in cyan in Fig. 2 and green in Fig. 3) is not correlating with star-forming regions in the SMC, i.e. the bar of the SMC where we see most of the SNRs. Therefore, we expect that most of these sources are background objects and that there is no significant contribution of PWNe given the sensitivity of our observations. A special case is source No 14, which is found along the SNR DEMS128 (upper left of Fig. 1) with a spectral index of GLYPH<11> = GLYPH<0> 0 : 21 GLYPH<6> 0 : 12, which is steeper than for the surrounding SNR ( GLYPH<11> = GLYPH<0> 0 : 48 GLYPH<6> 0 : 06, Filipovi'c et al. 2000). The type-Ia classification of the SNR (van der Heyden et al. 2004) and the o GLYPH<11> set of its X-ray bright centre from the point source suggest that both sources are not connected with each other. In the SAGE survey (Gordon et al. 2011) we find a mid-infrared Spitzer / IRAC counterpart (SSTISAGEMA J010530.69-721021.3) with colours that might be consistent with an AGN. However, in the deep Xray images, the emission from DEM S128 clearly extends further towards the north-west (compare also Haberl et al. 2012b, Fig 6.1). Therefore, we cannot exclude No 14 as a candidate for a PWN. DEMS128 will be discussed in more detail by Roper et al. (in prep.). We can also roughly estimate the probability of finding a radio X-ray association within an SNR using our source list that contains 2.4 sources deg GLYPH<0> 2 with GLYPH<0> 0 : 3 < GLYPH<11> < 0. According to Haberl et al. (2012b), the area covered by known SNRs is GLYPH<24> 0.044 deg GLYPH<0> 2 . For a Poisson distribution, we would expect to find one source along an SNR with a likelihood of 9.4% and more than one source with a likelihood of 0.5%. So the DEM S128 correlation might still be by chance, but this is unlikely to be the case for all PWN candidates in the SMC (HFPK 334 and IKT 16, not included in this study).",
"pages": [
6
]
},
{
"title": "3.8. Comparison with previous studies",
"content": "For 17 of our sources, we find a counterpart in the ROSAT PSPC catalogue (Haberl et al. 2000). These are commented with H00 in Table 2. Twelve of these sources were already associated with radio sources at GLYPH<21> = 13 cm in that work. In addition, the ROSAT catalogue lists 39 sources with radio association. Of these, nine are outside the XMMNewton field ([HFP2000] 52, 124, 138, 347, 357, 522, 685, 687, and 692), four are now resolved as ClGs ([HFP2000] 101, 147, 317, and 410) and 18 are SNRs ([HFP2000] 45, 107, 125, 145, 148, 194, 217, 281, 285, 334, 401, 413, 414, 419, 437, 454, 461, and 530), where [HFP2000] 281 was probably detected as part of a bubble connected to the SNR DEMS68 (Filipovi'c et al. 2008). [HFP2000] 88 was not detected with XMMNewton . For [HFP2000] 49, 206, 249, 380, 440, 448, and 668, the improved X-ray positions with respect to ROSAT make an X-ray radio association unlikely. Since the gain of the radio data is rather in sensitivity than in resolution, the comparison with Payne et al. (2004) is somewhat more straight forward. We find 32 of our sources in Payne et al. (2004), marked with P04 in Table 2. All sources but one were classified as background objects by these authors, but only 3 sources are noted as X-ray association. Only source No 22 ([FBR2002] J005254-720132) was classified as background ob- ject or H ii region. The X-ray emission points to a background source in this case. Further, there are 37 sources for which Payne et al. (2004) give an X-ray luminosity or an X-ray comment. Of these, 13 were identified as SNRs, three are in ClGs, and 14 were classified as H ii regions where we do not find X-ray sources in our study, confirming the classification. From the remaining sources one is classified as 'XRB' (microquasar candidate), correlating with [HFP2000] 295. This X-ray radio association was rejected above. The other sources are candidate background objects, but we do not find X-ray counterparts in the XMMNewton catalogue ([FBR2002] J004552-731339, J004836-733056, J005218-722708, J005602-720908, J005610721833, and J010525-722525).",
"pages": [
6,
7
]
},
{
"title": "4. Conclusions",
"content": "We inspect the positions of X-ray sources from the XMMNewton SMCsurvey in the corresponding deep radio-continuum images and found 88 X-ray sources associated with a unique radio counterpart. One source is identified with a foreground star, one is a confirmed quasar probably confused with a HMXB candidate, eight are identified or classified as galaxies, two radio sources are within clusters of galaxies, and one might be a PWN. The remaining 75 X-ray sources associated with a unique radio counterpart are classified as AGN behind the SMC. Due to the precise X-ray positions of our X-ray catalogue ( GLYPH<24> 1.5 00 ) and the low density of radio sources in the SMC field, chance correlations are unlikely and we derive a high purity for our sample. Weexpect the contribution of stars to our sample to be GLYPH<20> 2. From background source candidates, seven are infra-red-selected candidates of Kozłowski & Kochanek (2009), 31 were classified as background radio sources by Payne et al. (2004), and 11 as AGN candidates by Haberl et al. (2000). 40 associations are newly classified background objects behind the SMC, for the others, the X-ray radio association a GLYPH<14> rms the previous backgroundobject classification. For a total of 21 X-ray point sources, we find a jet like structure in radio, which points to the AGN character of the source. In addition, we list six radio sources inside ClGs with high X-ray extent, where three radio sources show a jet. Acknowledgements. The XMM-Newton project is supported by the Bundesministerium fur Wirtschaft und Technologie / Deutsches Zentrum fur Luft- und Raumfahrt (BMWI / DLR, FKZ 50 OX 0001) and the Max-Planck Society. The ATCA is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. We used the karma and miriad software package developed by the ATNF. R.S. acknowledges support from the BMWI / DLR grant FKZ 50 OR 0907.",
"pages": [
7
]
},
{
"title": "References",
"content": "Antoniou, V., Zezas, A., Hatzidimitriou, D., & McDowell, J. C. 2009, ApJ, 697, 1695 O'Dea, C. P. 1998, PASP, 110, 493 Oliveira, J. M., van Loon, J. T., Sloan, G. C., et al. 2013, MNRAS, 428, 3001 Owen, R. A., Filipovi'c, M. D., Ballet, J., et al. 2011, A&A, 530, A132 Payne, J. L., Filipovi'c, M. D., Reid, W., et al. 2004, MNRAS, 355, 44 Piatek, S., Pryor, C., & Olszewski, E. W. 2008, AJ, 135, 1024 Pietsch, W., Misanovic, Z., Haberl, F., et al. 2004, A&A, 426, 11 Sasaki, M., Haberl, F., & Pietsch, W. 2000, A&AS, 147, 75 Shtykovskiy, P. & Gilfanov, M. 2005, MNRAS, 362, 879 Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stanimirovic, S., Staveley-Smith, L., Dickey, J. M., Sault, R. J., & Snowden, S. L. 1999, MNRAS, 302, 417 Stiele, H., Pietsch, W., Haberl, F., et al. 2011, A&A, 534, A55 Struder, L., Briel, U., Dennerl, K., et al. 2001, A&A, 365, L18 Sturm, R., Haberl, F., Pietsch, W., et al. 2013, A&A, accepted (arXiv1307.7594) Tinney, C. G., Da Costa, G. S., & Zinnecker, H. 1997, MNRAS, 285, 111 Tozzi, P., Gilli, R., Mainieri, V., et al. 2006, A&A, 451, 457 Turner, M. J. L., Abbey, A., Arnaud, M., et al. 2001, A&A, 365, L27 Udalski, A., Szymanski, M., Kubiak, M., et al. 1998, Acta Astron., 48, 147 van der Heyden, K. J., Bleeker, J. A. M., & Kaastra, J. S. . 2004, A&A, 421,",
"pages": [
7
]
},
{
"title": "Notes. F or a description of the T able, see Sec. 2.3. ( a ) Comments on indi vidual sources. F or details see te xt. Identifications with sources from other catalogues are mark ed as follo ws: Refer ences. (P04) P ayne et al. (2004); (H00) Haberl et al. (2000); (J09) Jones et al. (2009); (S06) Skrutskie et al. (2006); (S05) Shtyk o vskiy & Gilf ano v (2005); (K09) K ozło wski & K ochanek",
"content": "(2009).",
"pages": [
9
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}
]
2013A&A...558A.139V
https://arxiv.org/pdf/1309.3594.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_82><loc_91><loc_87></location>X Ray detection of GJ 581 and simultaneous UV observations (Research Note)</section_header_level_1>
<text><location><page_1><loc_37><loc_80><loc_65><loc_81></location>Vincenzo Vitale 1 ? and Kevin France 2</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_77><loc_83><loc_78></location>1 ASI Science Data Center & Istituto Nazionale di Fisica Nucleare, Via della Ricerca Scientifica, 1 00133 Roma - Italy</list_item>
<list_item><location><page_1><loc_11><loc_76><loc_78><loc_77></location>2 Center for Astrophysics and Space Astronomy, University of Colorado, 389 UCB, Boulder, CO 80309, USA</list_item>
</unordered_list>
<section_header_level_1><location><page_1><loc_47><loc_72><loc_55><loc_73></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_68><loc_91><loc_71></location>Context. The M3 dwarf GJ 581 hosts a rich system of exo-planets, some of which are potentially within or at the edge of the habitable zone (HZ). Nevertheless, the system habitability might be reduced by large and sterilizing high energy emission flares, if these are frequent.</text>
<text><location><page_1><loc_11><loc_65><loc_91><loc_67></location>Aims. The GJ 581 radiation environment was studied with simultaneous X-ray and UV observations, which were performed with the XRT and UVOT instruments, respectively, on board of the SWIFT satellite.</text>
<text><location><page_1><loc_11><loc_64><loc_59><loc_65></location>Methods. X-ray and UV data were analysed with the distributed standard tools.</text>
<text><location><page_1><loc_11><loc_58><loc_91><loc_64></location>Results. The dwarf GJ 581 was detected for the first time in the 0.210 keV range with an intensity of (8 GLYPH<6> 2) GLYPH<2> 10 GLYPH<0> 4 cts / s and a signal-tonoise ratio of 3.6. If black-body or APEC spectra are assumed, then the source X-ray flux is found to be between 1.8 and 3.3 GLYPH<2> 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 and log10(L X ) between 25.914 and 26.176. Despite hints of X-ray variability, better statistics are needed to establish robust evidence for this property. The UV measurements, obtained during 13 pointings, are also reported. A combination of these Swift X-ray and Hubble Space Telescope UV measurements (with Lyman-alpha) indicate a low X-ray to UV luminosity ratio of GLYPH<24> 4%.</text>
<text><location><page_1><loc_11><loc_56><loc_91><loc_58></location>Conclusions. Simultaneous X-ray and UV observations of GJ 581 are reported. These constitute an experimental view of the system radiation environment, which will be a useful input for the habitability studies of the GJ 581 planetary system.</text>
<text><location><page_1><loc_11><loc_54><loc_38><loc_55></location>Key words. GJ 581, star flares, astrobiology</text>
<section_header_level_1><location><page_1><loc_7><loc_50><loc_19><loc_51></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_25><loc_50><loc_49></location>Life 'as we know it' is found on a rocky planet surface, protected by an atmosphere, within the planetary system HZ (Kasting et al. 1993). For this reason the study of exo-planetary physical conditions, such as the radiation environment, has large relevance in the search for extra-terrestrial life. An important target for this search are M stars, because they are the most abundant in the solar neighbourhood (Miller and Scalo 1979) and likely also in the Galaxy. Concerns on the M dwarf systems habitability include: (i) tidal locking (Dole 1964), in which these planets should be to have liquid water within the conventional HZ. Nevertheless, this problem was subsequently reconsidered (Joshi 2003); (ii) large flare rates, which could give rise to relatively frequent episodes of very intense planetary irradiation with sterilizing X-ray and UV emissions, or originate long term atmosphere evaporation. Other e GLYPH<11> ects on the planetary atmospheric chemistry of a strong stellar flares, such as the ejection of energetic particles, also have been investigated (Segura et al. 2010).</text>
<text><location><page_1><loc_7><loc_19><loc_50><loc_25></location>Planetary irradiation is related to the large flares occurrence and to the atmosphere's capability of shielding. The energy distribution of coronal flares from late-type stars was investigated in Audard et al. (2000). According to these authors, the energy distributions are well described by power laws, such as</text>
<formula><location><page_1><loc_16><loc_16><loc_41><loc_18></location>dN dE = k 1 E GLYPH<0> GLYPH<11> with E > Emin ; GLYPH<11> > 1 ;</formula>
<text><location><page_1><loc_7><loc_12><loc_50><loc_15></location>where dN is the number of flares with energy within the dE energy range, E min is the minimum energy below which the distribution is not valid for example because of a large change in the</text>
<text><location><page_1><loc_52><loc_43><loc_95><loc_51></location>spectral index GLYPH<11> , and k1 is the normalization constant. They also considered the case when E min is below the instrument detection threshold. A large fraction the X-ray emission is then seen as a quiescent emission (90% in their case) but originates in a superposition of many undetectable small flares, while the rest is seen as individual detectable flares.</text>
<text><location><page_1><loc_52><loc_32><loc_95><loc_42></location>It was demonstrated in Smith et al. 2004 that thin atmospheres (below 100 g cm GLYPH<0> 2 ) can shield typical stellar X-rays fluxes and thick atmospheres ( > 100 g cm GLYPH<0> 2 ) can also e GLYPH<14> ciently shield GLYPH<13> -rays. A large fraction of the X-ray incident energy, up to the 10%, is redistributed into di GLYPH<11> use UV with consequences on the organic chemistry. For comparison, Earth's atmosphere allows 2 GLYPH<2> 10 GLYPH<0> 3 (up to 4 GLYPH<2> 10 GLYPH<0> 2 ) of the incident high energy radiation flux to reach the ground in the 200320 nm range.</text>
<text><location><page_1><loc_52><loc_23><loc_95><loc_31></location>The high energy radiation environment also determines the exo-planetary photochemistry. It has been shown in Segura et al. (2005) that the spectral distributions of the parent stars in the ultraviolet have significant influence on the presence of proposed bio-markers, such as CH4, N2O, and CH3Cl, in exo-planetary atmospheres.</text>
<text><location><page_1><loc_52><loc_10><loc_95><loc_22></location>In this note, we report X-ray and UV emission measurements of GJ 581, an M3 dwarf, which hosts a prominent planetary system with at least four confirmed planets and possibly two others. The planet GJ 581d is a super-earth with a mass of 5.6 GLYPH<6> 0.6M earth and is close to the outer edge of the HZ, within 0.11 and 0.21 AU (von Bloh et al. 2007, Selsis et al. 2007, Wordsworth et al. 2010, von Braun 2011). The dwarf GJ 581 was not detected in X-ray so far, at least to our knowledge. An upper limit of 26.89 erg / s on the X-ray luminosity in the range between 0.12.4 keV was obtained with ROSAT observations (Poppenhaeger</text>
<text><location><page_2><loc_7><loc_91><loc_50><loc_93></location>et al. 2010). UV observations were recently performed with the Hubble Space Telescope (France et al. 2013).</text>
<text><location><page_2><loc_7><loc_80><loc_50><loc_90></location>The note is organized as follows. In Section 2, the used data and the analysis procedures are described and the X-ray detection is reported. In Section 3, a short discussion of the reported measurements is given and is proposed an approximate bound to the large X-ray flares occurrence, which is valid only under certain assumptions. The X-ray to UV luminosity ratio is also derived as the X-ray and MgII surface fluxes and their implications on the source age are discussed.</text>
<section_header_level_1><location><page_2><loc_7><loc_75><loc_35><loc_76></location>2. Observations and data analysis</section_header_level_1>
<text><location><page_2><loc_7><loc_66><loc_50><loc_74></location>The source was observed with the XRT and UVOT telescopes on board of the Swift satellite (Gehrels et al. 2004) between December 2012 and March 2013. Twelve observations with exposures from 700s to 12ks were performed within the Fill-In Targets program at observation cycle 8. Observation logs are in Table 2.</text>
<section_header_level_1><location><page_2><loc_7><loc_63><loc_24><loc_64></location>2.1. XRT data reduction</section_header_level_1>
<text><location><page_2><loc_7><loc_58><loc_50><loc_62></location>Data were reduced with the HEASoft V6.12 package 1 and with the calibration files which were issued on March 2012 and January 2013 for the XRT and UVOT instruments, respectively.</text>
<text><location><page_2><loc_7><loc_30><loc_50><loc_57></location>The XRT observations were carried out using the photon counting readout mode. For XRT, the distributed level 2 cleaned event files were used with energy between 0.2 and 10 keV and grades from 0 to 12. Individual pointings were summed with the XSELECT tool to have a cumulative image with an exposure of 32798s. The X-ray image was subsequently analysed with the XIMAGEtool. An excess was detected at RA = 15 19 25.6 Dec = -07 43 21.5, which is compatible with the source location. It consisted of 27 GLYPH<6> 7 counts (which were obtained with the XIMAGE sosta tool, after correcting for various e GLYPH<11> ects) and an intensity of (8 GLYPH<6> 2) GLYPH<2> 10 GLYPH<0> 4 cts / s with a signal-to-noise ratio of 3.6. Individual pointings were grouped then into three datasets with similar exposure to investigate possible source variability. The obtained results are listed in Table 3. The source was detected only in the second period. The related X-ray image is shown in Fig 1. During period one and three, the count rate at the source position was 2.7 and 6.1 GLYPH<2> 10 GLYPH<0> 4 cts / s with a low signal-to-noise ratio in both cases. For these periods, the calculation of the count rate upper limit was then performed (XIMAGE uplim tool). For such a calculation the used source region was a circle with radius of 18'.</text>
<text><location><page_2><loc_7><loc_23><loc_50><loc_30></location>The background rates were measured as a function of the observation periods getting the number of events within a control region (with the XIMAGE counts tool) and dividing them by the exposure. The background rates are reported in Table 3, while the control region is shown in Fig. 1.</text>
<text><location><page_2><loc_7><loc_13><loc_50><loc_23></location>The average count rate was converted into an X-ray flux by means of the PIMMS v4.6 software. Very simple emission models were assumed to convert count rates to energy flux. These models were a black-body with temperatures of 3x10 6 K and 10 7 K, as those reported in Schmitt et al. 1990 for M dwarfs and an APEC model with an abundance parameter of 0.6. No further spectral studies were performed because of the limited statistics. The results are listed in Table 4.</text>
<table>
<location><page_2><loc_54><loc_72><loc_93><loc_86></location>
<caption>Table 1. GJ 581 parameters used for the analysis of the data. The position and proper motion parameters ( GLYPH<22>GLYPH<11> , GLYPH<22>GLYPH<14> ) are taken from the Hipparcos catalog (GJ 581 is HIP 74995). E GLYPH<11> ective temperatures T e f f are those estimated in von Paris et al. 2010. See references therein.Table 2. Swift Observations. The central wavelength(Å) and FWHM(Å) of the UVOT filters are 2600 and 693 for UVW1 , 2246 and 498 for UWM2 , 1928 and 657 for UVW2 (Poole et al. 2008 and Breeveld et al al. 2011)</caption>
</table>
<table>
<location><page_2><loc_54><loc_47><loc_92><loc_64></location>
</table>
<section_header_level_1><location><page_2><loc_52><loc_43><loc_87><loc_44></location>2.2. UVOT data reduction and UV variability study</section_header_level_1>
<text><location><page_2><loc_52><loc_19><loc_95><loc_42></location>Sources with a signal-to-noise ratio above 3 were searched for into the UVOT images with the UVOTDETECT tool. The dwarf GJ 581 was detected during all the observations at the expected location with the exception of the shortest one. Both a source region and background were defined on the basis of the UVOTDETECT tool results. The source region consisted of a circle with centre in RA = 229.85734 and Dec = -7.7267 (J2000.0) and with radius of 5', while the background region was composed with two annuli; the first annulus with a centre in RA = 229.85734 and Dec = -7.7267 (J2000.0) and with radii of 10 and 20', the second annulus with the same centre with radii of 80 and 110'. For each observation the source photometry was performed by means of the UVOTSOURCE tool. The tool was used with the option apercorr = CURVEOFGROWTH to apply an approximate aperture correction (0.02 to 0.05 mag systematic error) however, the source region is based on current standard photometric aperture equal to 5'. The photometry results are reported in Column 2 and 3 of Table 5.</text>
<text><location><page_2><loc_52><loc_10><loc_95><loc_19></location>The UVOT observations were performed with four di GLYPH<11> erent filters (UVW2,UVM2,UVW1 and U, see Poole et al. 2008 for details); the source count rates spanned a wide range from 0.05 to more than 80 cts / s. The results obtained with the same filter can be directly compared. The counts rate and associated uncertainties for each observation are reported in Table 5. The mean count rates and rms for the UVW2,UVM2, and UVW1 are, re-</text>
<table>
<location><page_3><loc_12><loc_82><loc_45><loc_90></location>
<caption>Table 3. X-Ray results. The control region is defined in subsection 2.1.Table 4. Unabsorbed X-Ray Flux and Luminosity. The used N(h) in the direction of GJ 581 was measured directly by France et al. 2013 to be 2.24 GLYPH<2> 10 18 cm GLYPH<0> 2 . The assumed APEC abundance was 0.6.</caption>
</table>
<table>
<location><page_3><loc_12><loc_67><loc_44><loc_74></location>
</table>
<figure>
<location><page_3><loc_8><loc_47><loc_48><loc_65></location>
<caption>Fig. 1. XRT sky map of observation 9. The smallest circle surrounds the source, which is detected with a signal-to-noise ratio above 3. The other two larger circles are the control region areas.</caption>
</figure>
<text><location><page_3><loc_7><loc_37><loc_50><loc_40></location>spectively: 3.17 and 0.046cts / s; 0.08 and 0.013 cts / s; and 9.4 and 0.6 cts / s.</text>
<text><location><page_3><loc_7><loc_31><loc_50><loc_37></location>The parameter k = R obs / R expected , which the ratio between the observed and the expected count rate, was introduced to compare the di GLYPH<11> erent filters observations. The expected count rate for each used filter was calculated, by folding a spectral model with the filter in-orbit e GLYPH<11> ective areas:</text>
<formula><location><page_3><loc_16><loc_27><loc_41><loc_30></location>Rexpected = m X i GLYPH<8> ( GLYPH<21> i ) GLYPH<2> Aef f ( GLYPH<21> i ) =GLYPH<15> ( GLYPH<21> i )</formula>
<text><location><page_3><loc_7><loc_20><loc_50><loc_25></location>where A e f f ( GLYPH<21> i ) is the e GLYPH<11> ective area of the current filter as a function of the wavelength, which is taken from the CALDB file in use, GLYPH<8> ( GLYPH<21> i ) is the energy flux, GLYPH<15> ( GLYPH<21> i ) is the photon energy, and the index i runs over m bins.</text>
<text><location><page_3><loc_7><loc_10><loc_50><loc_20></location>An arbitrary spectral model was made with (i) the experimental measurements of the ultraviolet spectral energy distribution of GJ 581, which were obtained with the Hubble Space Telescope during July 2011 and April 2012 (France et al. 2013), in the band between 1150 and 3140 Å and (ii) a black-body emission extrapolation in the range between 3140 and 6000 Å. This component was normalized to provide a flux of 3 GLYPH<2> 10 GLYPH<0> 15 erg cm GLYPH<0> 2 s GLYPH<0> 1 Å GLYPH<0> 1 at 3100Å for all the used temperatures. The count</text>
<figure>
<location><page_3><loc_53><loc_70><loc_93><loc_93></location>
<caption>Fig. 2. UVOT Lightcurve. The UVM2 rates (squares) were multiplied by 10, the UVW2 rates (circles) by 0.198, and UVW1 ones (triangles) by a factor 0.056. These two last factors are calculated by equalizing UVM2 and UVW2(UVW1) rates during observations 5 and 9, when two filters were used. For UVW1 and 2, error bars are often smaller than the data-point marker.</caption>
</figure>
<text><location><page_3><loc_52><loc_55><loc_95><loc_58></location>rate calculation was limited to e GLYPH<11> ective collection area values above 10 GLYPH<0> 2 cm 2 , given that the e GLYPH<11> ective area measurement had associated errors of 1% (Poole et al. 2008).</text>
<text><location><page_3><loc_52><loc_27><loc_95><loc_54></location>The expected count rates are sensitive to the spectral model parameters, such as the black-body temperature and normalization. In von Paris et al. 2010,, the range between T min = 3190K and T max = 3760K is reported as descriptive for the various e GLYPH<11> ective temperatures, which are found in literature. The di GLYPH<11> erence between the expected count rates obtained with T min = 3190K and T max = 3760K are 2%, 5% ,and 12% for the UVW1, UVM2, and UVW2 filters respectively . The average of the two expected count rates, obtained with these two extreme temperatures is assumed as the final expected count rate. In general, a systematic e GLYPH<11> ect on the parameter k is introduced by the choice of both e GLYPH<11> ective temperature and black-body normalization because of the di GLYPH<11> erent wavelength coverage of the filters. This e GLYPH<11> ect can be limited by minimizing the di GLYPH<11> erence of the ¯ k (W1), ¯ k (W2) and ¯ k (M2), which are the mean values of the k parameters obtained with the three UV filters. From Table 5 it can be seen that ¯ k (W1) = 0.95, ¯ k (W2) = 1.00 and ¯ k (M2) = 0.78, therefore a systematic error of at least 11% on the parameter k should be considered. The expected rates for UVW1,UVM2 and UVW2 are respectively: 9.85cts / s, 0.097.5cts / s and 3.15cts / s. The mean k parameter and rms are respectively 0.88 and 0.13.</text>
<section_header_level_1><location><page_3><loc_52><loc_24><loc_63><loc_25></location>3. Discussion</section_header_level_1>
<text><location><page_3><loc_52><loc_14><loc_95><loc_22></location>X-ray emission from GJ 581 was detected for the first time. The source detection is marginal as it is obtained with a signal consisting of 27 GLYPH<6> 7 counts with a cumulative signal-tonoise ratio of 3.6. If simple X-ray spectra are assumed then the source X-ray flux is found to be in the range between 1.8 and 3.3 GLYPH<2> 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 with an associated log10(L X ) between 25.914 and 26.176.</text>
<text><location><page_3><loc_52><loc_10><loc_95><loc_13></location>Data were divided into three periods with exposures as balanced as possible to search for variability. During the first period, a three standard deviation intensity upper limit of 8 GLYPH<2> 10 GLYPH<0> 4 cts / s</text>
<table>
<location><page_4><loc_9><loc_65><loc_48><loc_83></location>
<caption>Table 5. UV measurements. Observations with the U filter are not reported. The mean count rates and rms for the UVW2,UVM2 and UVW1 are respectively 3.167 and 0.046cts / s, 0.08 and 0.013 cts / s, 9.375 and 0.597 cts / s. The mean k parameter and rms are respectively 0.88 and 0.13. Only statistical errors are reported for the parameter k and a systematic error of at least 11% on this parameter should be considered.</caption>
</table>
<text><location><page_4><loc_7><loc_42><loc_50><loc_62></location>was obtained. The source was detected above a signal-to-noise ratio of 3 during the second period, while the third period again provided an upper limit but with weaker constraints due to the shorter exposure time. The results of the first period deviated about two standard deviations from the measurements of period two. Here, a main problem is the low statistics regime. During period one only a handful of counts were found within the source location, and the second period signal was at the edge of detectability. In both cases, small spurious e GLYPH<11> ects can have large impact on the results. A check was done with the background rate measurements as a function of the periods. They are found to be steady within the errors. Larger statistics are needed to establish robust evidence of X-ray variability. Furthermore, the single measurement would not allow one to sample the flares energy distribution.</text>
<text><location><page_4><loc_7><loc_24><loc_50><loc_42></location>Nevertheless, approximated bounds to the star X-ray activity can be obtained if the following hypotheses are assumed: (i) the X-ray emission, detected during observation window 9, is originated by a single flare; (ii) this flare is completely within the observation window; (iii) the flares have an energy distribution in the form of a power law with indices between 1.57 and 2.24, as reported in Audard et al. 2000 for the studied M dwarfs, GJ 411, AD Leo, EV Lac, and CN Leo during 1994 and 1995. Under these assumptions, the maximum duration of the detected flare would be GLYPH<28> = 12ks, and the maximum energy is E f = GLYPH<28> GLYPH<2> L X = 1.6 GLYPH<2> 10 30 erg. where a benchmark value of 1.3 GLYPH<2> 10 26 erg s GLYPH<0> 1 for L X has been used. Flares with an energy E f or larger would have an occurrence smaller than f0 = 3.3 GLYPH<2> 10 GLYPH<0> 5 s GLYPH<0> 1 , or one every 30ks period. For larger energies:</text>
<formula><location><page_4><loc_19><loc_21><loc_39><loc_23></location>f ( E > E 0 ) < f 0 GLYPH<2> ( E 0 = Ef ) GLYPH<0> GLYPH<11> + 1</formula>
<text><location><page_4><loc_7><loc_10><loc_50><loc_20></location>with GLYPH<11> = 2.24 (or 1.57). For the benchmark energy of E' = 10 32 erg the occurrence would be lower than 1.7 GLYPH<2> 10 GLYPH<0> 7 s GLYPH<0> 1 (or 3.1 GLYPH<2> 10 GLYPH<0> 6 s GLYPH<0> 1 ), respectively for the two indices, which translates to less than 6 (96) of such flares in a year. A linear correlation between the occurrence of 10 32 erg flares with the X-ray luminosity is also given in Audard et al. 2000. This relation indicates a flare occurence between 0.8 and 1.0 GLYPH<2> 10 GLYPH<0> 7 s GLYPH<0> 1 , with both estimates below the our proposed bounds.</text>
<text><location><page_4><loc_52><loc_87><loc_95><loc_93></location>It should be remarked that the proposed bounds are valid only under the assumed hypotheses and are linearly dependent on the considered maximum energy E f and the supposed flare time scale GLYPH<28> . A change of GLYPH<28> of a factor 10 implies a change of a factor 1 / 17(or 1 / 4 for the lower GLYPH<11> value) of the occurrence bound.</text>
<text><location><page_4><loc_52><loc_68><loc_95><loc_86></location>Relationships between age, rotation, and coronal activity for Mstars were proposed by Guinan and Engle (2009) and Stelzer et al. (2013). Guinan and Engle (2009) have found that L X < 1.5 GLYPH<2> 10 26 erg s GLYPH<0> 1 are related to an M dwarf with an age larger than 5 Gyr, which are older than Proxima Cen(M5) or IL Aqr (M4). Similarly, Engle and Guinan (2011) estimated that the age of GJ 581 is 5.7 GLYPH<6> 0.8 Gyr. This results was obtained with a rotation-age relation. Taking the X-ray luminosity-age relation presented by Stelzer et al. (2013) for M0-M3 stars, the X-ray luminosity of GJ 581 implies that the age of GJ 581 is larger than GLYPH<24> 4 Gyr (the last time value reported on their Fig. 15). In both cases, the coronal activity-age relations provide constraints that are consistent with the previous age estimates for GJ 581 ( > 2 Gyr; Bonfils et al. 2005.)</text>
<text><location><page_4><loc_52><loc_58><loc_95><loc_68></location>The UV normalized count-rates vs time are reported in Fig. 2. In the UV range, the largest flux variations are observed with the UVM2 filter, which most likely traces variability in the chromosphere MgII resonance doublet, the strongest emission feature in the UVM2 bandpass. For UVM2, the count rate rms is of the order of 16% of the average count rate. The UVW1 and UVW2 observations provide smaller variations as compared the UVM2.</text>
<text><location><page_4><loc_52><loc_42><loc_95><loc_58></location>France et al (2013) reported a total UV luminosity (including the FUV and NUV spectral band-passes) for GJ 581 of L UV = 27 GLYPH<2> 10 26 erg s GLYPH<0> 1 and a MgII doublet flux of F MgII = 2.13 GLYPH<6> 0.13 GLYPH<2> 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 obtained from Gaussian fits to both lines of the doublet. Comparing our Swift X-ray observations to the existing HST data, we find the L X / L UV ratio is 0.043 GLYPH<6> 0.012. However previous results argue for larger L X / L UV ratios. France et al (2013) have found a log10(L UV / L Bol ) GLYPH<25> -4 and Guinan and Engle (2007) log10(L X / L Bol ) GLYPH<25> -3. Therefore, we would have expected an L X / L UV ratio of greater than unity, and our finding of GLYPH<24> 4% suggests relatively weak coronal activity on GJ 581.</text>
<text><location><page_4><loc_52><loc_28><loc_95><loc_42></location>Using the interferometrically determined radius of GJ 581 (R = 0.29 GLYPH<6> 0.010R GLYPH<12> ; von Braun et al. 2011), we find an X-ray surface flux of (2.0 GLYPH<6> 0.7) GLYPH<2> 10 4 erg cm GLYPH<0> 2 s GLYPH<0> 1 and a MgII surface flux of (1.96 GLYPH<6> 0.11) GLYPH<2> 10 4 erg cm GLYPH<0> 2 s GLYPH<0> 1 . These surface fluxes can be compared with previously estimated values obtained by Rutten et al. 1991 (Figs. 1b and 1g). The found Mg II and X-ray surface fluxes are close to the basal flux limits, indicative of a relatively old main-sequence star (e.g., Hempelmann et al. 1995; Schrijver 1995; Cuntz et al. 1999); this finding is generally consistent with the deduced age of GJ 581, which has been found to be larger than GLYPH<24> 4 Gyr (Selsis et al. 2007).</text>
<text><location><page_4><loc_52><loc_16><loc_95><loc_28></location>Another approach pertaining to the relationship between the empirical Mg II surface flux and the stellar age has been given by Cardini & Cassatella 2007. Following their Eq. (8) with data from their Table 2, it is found that the implied age of GJ 581 is very large, possibly beyond 10 Gyr. For further comparison we considered the M dwarfs studied in Walkowicz et al. (2008). Compared to the MgII / X-ray ratios of other M dwarfs (e.g., Fig. 5 from Walkowicz et al. (2008)), we find that GJ 581 would be comparable to GJ 876(M4.0), GJ 273(M3.5), and GJ 191(M1.0).</text>
<text><location><page_4><loc_52><loc_10><loc_95><loc_16></location>GJ 876 has an estimated age between 0.1 and 5 Gyr (Correia et al. 2010), and despite has a low-to-intermediate activity level based on its optical spectrum has been shown to produce significant UV flux in its HZ. This source provides > 50% of the solar luminosity received at 1 AU in the FUV band-pass (1160 - 1790</text>
<text><location><page_5><loc_7><loc_88><loc_50><loc_93></location>Å, including Lyman-alpha; France et al. 2012). Therefore, the L X / L UV ratio is mainly indicative of the hard radiation content and does not rule out the possibility of strong UV emission in the HZ around GJ 581.</text>
<text><location><page_5><loc_7><loc_83><loc_50><loc_88></location>Wedid not attempt to discuss the habitability of GJ 581 planetary system because it would need a detailed planetary thermal evolution models which follows atmospheric and lithosperic phenomena, as this is beyond the scope of the present note.</text>
<section_header_level_1><location><page_5><loc_7><loc_79><loc_19><loc_80></location>4. Conclusions</section_header_level_1>
<text><location><page_5><loc_7><loc_69><loc_50><loc_78></location>We present the first X-ray detection of the exoplanet host star GJ 581. The observations performed were part of the Fill-In Targets program during SWIFT cycle 8. These simultaneous X-ray and UV observations provide an experimental view of the energetic radiation environment of the GJ 581 planetary system, which is an important input for habitability studies of the exo-planets orbiting this low mass star.</text>
<text><location><page_5><loc_7><loc_62><loc_50><loc_69></location>The low value of the found L X suggests that GJ 581 is older than 4 or 5 Gyr, assuming the coronal activity-age relations of Stelzer et al. (2013) or Guinan and Engle (2009). The data suggest that the X-ray emission may be variable; however, further observations with longer exposure times are required to establish robust evidence of X-ray variability.</text>
<text><location><page_5><loc_7><loc_51><loc_50><loc_61></location>Simultaneous UV photometric observations permitted monitoring of the UV variability during the X-ray observation. We find a low value of the X-ray to ultraviolet luminosity ratio (L X / L UVtotal ) when comparing the X-ray data to the MUSCLES M dwarf UV radiation field database. We detect evidence of chromospheric activity in the UV photometry, as seen by large amplitude variation in the SWIFT UVM2 count rates when compared to those from UVW1 and UVW2.</text>
<text><location><page_5><loc_7><loc_46><loc_50><loc_51></location>X-ray and MgII surface fluxes were derived, and they imply a stellar age ( > 4 Gyr), which is consistent with the age required by coronal activity-age relations and the previous estimates in literature.</text>
<section_header_level_1><location><page_5><loc_7><loc_42><loc_24><loc_43></location>5. Acknowledgments</section_header_level_1>
<text><location><page_5><loc_7><loc_25><loc_50><loc_41></location>The authors wish to thank the SWIFT team for the performed observations. We acknowledge the use of public data from the Swift data archive. This research has made use of the XRT Data Analysis Software (XRTDAS) developed under the responsibility of the ASI Science Data Center (ASDC), Italy. This work has made use of the MUSCLES M dwarf UV radiation field database. We are grateful to our anonymous reviewer for his / her constructive comments on our manuscript. V.V. is grateful to Dr. M. Capalbi and Dr V.D'Elia for help and support with the XRT data analysis, as also with the UVOT team and help-desk colleagues for the support with the UV observations. V.V. acknowledges the support of the ASI Science Data Center (ASDC), Prot. Agg. Convenzione Quadro ASI-INFN C / 011 / 11 / 1.</text>
<section_header_level_1><location><page_5><loc_7><loc_21><loc_16><loc_22></location>References</section_header_level_1>
<text><location><page_5><loc_7><loc_10><loc_42><loc_20></location>Audard M., et al 2000, ApJ 541, 396A Bonfils X., Forveille T., Delfosse X., et al. 2005, A&A 443, L15 Breeveld A. A., et al. 2011, arXiv:1102.4717 Cardini, D. and Cassatella, A. 2007, ApJ 666, 393C Correia A.C.M., et al 2010, A&A 511, 21 Cuntz M., et al. 1999, ApJ 522, 1053 Dole, S.H. 1964,Habitable Planets for Man, Blaisell, New York Engle S.G. and Guinan E.F. 2011, arXiv:1111.2872 France K., et al 2012, ApJ 750L, 32F France K., et al 2013, ApJ 763, 149F</text>
<text><location><page_5><loc_52><loc_91><loc_95><loc_93></location>Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ 611, 1005 Gray, D. F. 2005 'The observtion and Analysis of Stellar Photospheres', 2nd ed.</text>
<text><location><page_5><loc_52><loc_64><loc_92><loc_91></location>Cambridge: Cambridge Univ. Press Guinan E.F. and Engle S.G. 2007, arXiv0711.1530G Guinan E.F. and Engle S.G. 2009, arXiv0901.1860G Hempelmann, A., et al. 1995, A&A, 294, 515 Joshi, M. 2003, AsBio 3(2), 415427. Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993, Icarus, 101, 108 Miller, G.E. and Scalo, J.M. 1979, Astrophys. J. Suppl. 41, 513547. Perryman M.A.C.,et al. 1997, A&A 323L, 49P Poole T. S., et al 2008, MNRAS, 383, 627 Poppenhaeger K., et al. 2010, A&A 515, 98 Rutten R.G.M., et al. 1991, a&A 252, 203 Scalo J. et al. 2007, AsBio 7, 1 Schmitt, et al. 1990,ApJ 365, 704S Schrijver, C. J. 1995, A&A Rev., 6, 181 Segura A., et al. 2005, AsBio 5, 706S Segura A., et al. 2010,AsBio. 10, 751S Selsis et al. 2007 A&A 476, 1373 David S. Smith, John Scalo and J. Craig Wheeler 2004, Icarus 171, 229253 Stelzer B. et al. 2013, MNRAS 431, 20632079 Udry S., Bonfils X., Delfosse X., et al. 2007, A&A 469, L43 von Bloh W. et al. 2007 A&A 476, 1365 von Braun K. 2011, ApJ Letters 729, 26 von Paris P., et al. 2010, A&A 522, A23 Walkowicz L.M., et al. 2008 ApJ 677, 593 Wordsworth R. D., et al. 2010, A&A 522, 22W</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Context. The M3 dwarf GJ 581 hosts a rich system of exo-planets, some of which are potentially within or at the edge of the habitable zone (HZ). Nevertheless, the system habitability might be reduced by large and sterilizing high energy emission flares, if these are frequent. Aims. The GJ 581 radiation environment was studied with simultaneous X-ray and UV observations, which were performed with the XRT and UVOT instruments, respectively, on board of the SWIFT satellite. Methods. X-ray and UV data were analysed with the distributed standard tools. Results. The dwarf GJ 581 was detected for the first time in the 0.210 keV range with an intensity of (8 GLYPH<6> 2) GLYPH<2> 10 GLYPH<0> 4 cts / s and a signal-tonoise ratio of 3.6. If black-body or APEC spectra are assumed, then the source X-ray flux is found to be between 1.8 and 3.3 GLYPH<2> 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 and log10(L X ) between 25.914 and 26.176. Despite hints of X-ray variability, better statistics are needed to establish robust evidence for this property. The UV measurements, obtained during 13 pointings, are also reported. A combination of these Swift X-ray and Hubble Space Telescope UV measurements (with Lyman-alpha) indicate a low X-ray to UV luminosity ratio of GLYPH<24> 4%. Conclusions. Simultaneous X-ray and UV observations of GJ 581 are reported. These constitute an experimental view of the system radiation environment, which will be a useful input for the habitability studies of the GJ 581 planetary system. Key words. GJ 581, star flares, astrobiology",
"pages": [
1
]
},
{
"title": "X Ray detection of GJ 581 and simultaneous UV observations (Research Note)",
"content": "Vincenzo Vitale 1 ? and Kevin France 2",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Life 'as we know it' is found on a rocky planet surface, protected by an atmosphere, within the planetary system HZ (Kasting et al. 1993). For this reason the study of exo-planetary physical conditions, such as the radiation environment, has large relevance in the search for extra-terrestrial life. An important target for this search are M stars, because they are the most abundant in the solar neighbourhood (Miller and Scalo 1979) and likely also in the Galaxy. Concerns on the M dwarf systems habitability include: (i) tidal locking (Dole 1964), in which these planets should be to have liquid water within the conventional HZ. Nevertheless, this problem was subsequently reconsidered (Joshi 2003); (ii) large flare rates, which could give rise to relatively frequent episodes of very intense planetary irradiation with sterilizing X-ray and UV emissions, or originate long term atmosphere evaporation. Other e GLYPH<11> ects on the planetary atmospheric chemistry of a strong stellar flares, such as the ejection of energetic particles, also have been investigated (Segura et al. 2010). Planetary irradiation is related to the large flares occurrence and to the atmosphere's capability of shielding. The energy distribution of coronal flares from late-type stars was investigated in Audard et al. (2000). According to these authors, the energy distributions are well described by power laws, such as where dN is the number of flares with energy within the dE energy range, E min is the minimum energy below which the distribution is not valid for example because of a large change in the spectral index GLYPH<11> , and k1 is the normalization constant. They also considered the case when E min is below the instrument detection threshold. A large fraction the X-ray emission is then seen as a quiescent emission (90% in their case) but originates in a superposition of many undetectable small flares, while the rest is seen as individual detectable flares. It was demonstrated in Smith et al. 2004 that thin atmospheres (below 100 g cm GLYPH<0> 2 ) can shield typical stellar X-rays fluxes and thick atmospheres ( > 100 g cm GLYPH<0> 2 ) can also e GLYPH<14> ciently shield GLYPH<13> -rays. A large fraction of the X-ray incident energy, up to the 10%, is redistributed into di GLYPH<11> use UV with consequences on the organic chemistry. For comparison, Earth's atmosphere allows 2 GLYPH<2> 10 GLYPH<0> 3 (up to 4 GLYPH<2> 10 GLYPH<0> 2 ) of the incident high energy radiation flux to reach the ground in the 200320 nm range. The high energy radiation environment also determines the exo-planetary photochemistry. It has been shown in Segura et al. (2005) that the spectral distributions of the parent stars in the ultraviolet have significant influence on the presence of proposed bio-markers, such as CH4, N2O, and CH3Cl, in exo-planetary atmospheres. In this note, we report X-ray and UV emission measurements of GJ 581, an M3 dwarf, which hosts a prominent planetary system with at least four confirmed planets and possibly two others. The planet GJ 581d is a super-earth with a mass of 5.6 GLYPH<6> 0.6M earth and is close to the outer edge of the HZ, within 0.11 and 0.21 AU (von Bloh et al. 2007, Selsis et al. 2007, Wordsworth et al. 2010, von Braun 2011). The dwarf GJ 581 was not detected in X-ray so far, at least to our knowledge. An upper limit of 26.89 erg / s on the X-ray luminosity in the range between 0.12.4 keV was obtained with ROSAT observations (Poppenhaeger et al. 2010). UV observations were recently performed with the Hubble Space Telescope (France et al. 2013). The note is organized as follows. In Section 2, the used data and the analysis procedures are described and the X-ray detection is reported. In Section 3, a short discussion of the reported measurements is given and is proposed an approximate bound to the large X-ray flares occurrence, which is valid only under certain assumptions. The X-ray to UV luminosity ratio is also derived as the X-ray and MgII surface fluxes and their implications on the source age are discussed.",
"pages": [
1,
2
]
},
{
"title": "2. Observations and data analysis",
"content": "The source was observed with the XRT and UVOT telescopes on board of the Swift satellite (Gehrels et al. 2004) between December 2012 and March 2013. Twelve observations with exposures from 700s to 12ks were performed within the Fill-In Targets program at observation cycle 8. Observation logs are in Table 2.",
"pages": [
2
]
},
{
"title": "2.1. XRT data reduction",
"content": "Data were reduced with the HEASoft V6.12 package 1 and with the calibration files which were issued on March 2012 and January 2013 for the XRT and UVOT instruments, respectively. The XRT observations were carried out using the photon counting readout mode. For XRT, the distributed level 2 cleaned event files were used with energy between 0.2 and 10 keV and grades from 0 to 12. Individual pointings were summed with the XSELECT tool to have a cumulative image with an exposure of 32798s. The X-ray image was subsequently analysed with the XIMAGEtool. An excess was detected at RA = 15 19 25.6 Dec = -07 43 21.5, which is compatible with the source location. It consisted of 27 GLYPH<6> 7 counts (which were obtained with the XIMAGE sosta tool, after correcting for various e GLYPH<11> ects) and an intensity of (8 GLYPH<6> 2) GLYPH<2> 10 GLYPH<0> 4 cts / s with a signal-to-noise ratio of 3.6. Individual pointings were grouped then into three datasets with similar exposure to investigate possible source variability. The obtained results are listed in Table 3. The source was detected only in the second period. The related X-ray image is shown in Fig 1. During period one and three, the count rate at the source position was 2.7 and 6.1 GLYPH<2> 10 GLYPH<0> 4 cts / s with a low signal-to-noise ratio in both cases. For these periods, the calculation of the count rate upper limit was then performed (XIMAGE uplim tool). For such a calculation the used source region was a circle with radius of 18'. The background rates were measured as a function of the observation periods getting the number of events within a control region (with the XIMAGE counts tool) and dividing them by the exposure. The background rates are reported in Table 3, while the control region is shown in Fig. 1. The average count rate was converted into an X-ray flux by means of the PIMMS v4.6 software. Very simple emission models were assumed to convert count rates to energy flux. These models were a black-body with temperatures of 3x10 6 K and 10 7 K, as those reported in Schmitt et al. 1990 for M dwarfs and an APEC model with an abundance parameter of 0.6. No further spectral studies were performed because of the limited statistics. The results are listed in Table 4.",
"pages": [
2
]
},
{
"title": "2.2. UVOT data reduction and UV variability study",
"content": "Sources with a signal-to-noise ratio above 3 were searched for into the UVOT images with the UVOTDETECT tool. The dwarf GJ 581 was detected during all the observations at the expected location with the exception of the shortest one. Both a source region and background were defined on the basis of the UVOTDETECT tool results. The source region consisted of a circle with centre in RA = 229.85734 and Dec = -7.7267 (J2000.0) and with radius of 5', while the background region was composed with two annuli; the first annulus with a centre in RA = 229.85734 and Dec = -7.7267 (J2000.0) and with radii of 10 and 20', the second annulus with the same centre with radii of 80 and 110'. For each observation the source photometry was performed by means of the UVOTSOURCE tool. The tool was used with the option apercorr = CURVEOFGROWTH to apply an approximate aperture correction (0.02 to 0.05 mag systematic error) however, the source region is based on current standard photometric aperture equal to 5'. The photometry results are reported in Column 2 and 3 of Table 5. The UVOT observations were performed with four di GLYPH<11> erent filters (UVW2,UVM2,UVW1 and U, see Poole et al. 2008 for details); the source count rates spanned a wide range from 0.05 to more than 80 cts / s. The results obtained with the same filter can be directly compared. The counts rate and associated uncertainties for each observation are reported in Table 5. The mean count rates and rms for the UVW2,UVM2, and UVW1 are, re- spectively: 3.17 and 0.046cts / s; 0.08 and 0.013 cts / s; and 9.4 and 0.6 cts / s. The parameter k = R obs / R expected , which the ratio between the observed and the expected count rate, was introduced to compare the di GLYPH<11> erent filters observations. The expected count rate for each used filter was calculated, by folding a spectral model with the filter in-orbit e GLYPH<11> ective areas: where A e f f ( GLYPH<21> i ) is the e GLYPH<11> ective area of the current filter as a function of the wavelength, which is taken from the CALDB file in use, GLYPH<8> ( GLYPH<21> i ) is the energy flux, GLYPH<15> ( GLYPH<21> i ) is the photon energy, and the index i runs over m bins. An arbitrary spectral model was made with (i) the experimental measurements of the ultraviolet spectral energy distribution of GJ 581, which were obtained with the Hubble Space Telescope during July 2011 and April 2012 (France et al. 2013), in the band between 1150 and 3140 Å and (ii) a black-body emission extrapolation in the range between 3140 and 6000 Å. This component was normalized to provide a flux of 3 GLYPH<2> 10 GLYPH<0> 15 erg cm GLYPH<0> 2 s GLYPH<0> 1 Å GLYPH<0> 1 at 3100Å for all the used temperatures. The count rate calculation was limited to e GLYPH<11> ective collection area values above 10 GLYPH<0> 2 cm 2 , given that the e GLYPH<11> ective area measurement had associated errors of 1% (Poole et al. 2008). The expected count rates are sensitive to the spectral model parameters, such as the black-body temperature and normalization. In von Paris et al. 2010,, the range between T min = 3190K and T max = 3760K is reported as descriptive for the various e GLYPH<11> ective temperatures, which are found in literature. The di GLYPH<11> erence between the expected count rates obtained with T min = 3190K and T max = 3760K are 2%, 5% ,and 12% for the UVW1, UVM2, and UVW2 filters respectively . The average of the two expected count rates, obtained with these two extreme temperatures is assumed as the final expected count rate. In general, a systematic e GLYPH<11> ect on the parameter k is introduced by the choice of both e GLYPH<11> ective temperature and black-body normalization because of the di GLYPH<11> erent wavelength coverage of the filters. This e GLYPH<11> ect can be limited by minimizing the di GLYPH<11> erence of the ¯ k (W1), ¯ k (W2) and ¯ k (M2), which are the mean values of the k parameters obtained with the three UV filters. From Table 5 it can be seen that ¯ k (W1) = 0.95, ¯ k (W2) = 1.00 and ¯ k (M2) = 0.78, therefore a systematic error of at least 11% on the parameter k should be considered. The expected rates for UVW1,UVM2 and UVW2 are respectively: 9.85cts / s, 0.097.5cts / s and 3.15cts / s. The mean k parameter and rms are respectively 0.88 and 0.13.",
"pages": [
2,
3
]
},
{
"title": "3. Discussion",
"content": "X-ray emission from GJ 581 was detected for the first time. The source detection is marginal as it is obtained with a signal consisting of 27 GLYPH<6> 7 counts with a cumulative signal-tonoise ratio of 3.6. If simple X-ray spectra are assumed then the source X-ray flux is found to be in the range between 1.8 and 3.3 GLYPH<2> 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 with an associated log10(L X ) between 25.914 and 26.176. Data were divided into three periods with exposures as balanced as possible to search for variability. During the first period, a three standard deviation intensity upper limit of 8 GLYPH<2> 10 GLYPH<0> 4 cts / s was obtained. The source was detected above a signal-to-noise ratio of 3 during the second period, while the third period again provided an upper limit but with weaker constraints due to the shorter exposure time. The results of the first period deviated about two standard deviations from the measurements of period two. Here, a main problem is the low statistics regime. During period one only a handful of counts were found within the source location, and the second period signal was at the edge of detectability. In both cases, small spurious e GLYPH<11> ects can have large impact on the results. A check was done with the background rate measurements as a function of the periods. They are found to be steady within the errors. Larger statistics are needed to establish robust evidence of X-ray variability. Furthermore, the single measurement would not allow one to sample the flares energy distribution. Nevertheless, approximated bounds to the star X-ray activity can be obtained if the following hypotheses are assumed: (i) the X-ray emission, detected during observation window 9, is originated by a single flare; (ii) this flare is completely within the observation window; (iii) the flares have an energy distribution in the form of a power law with indices between 1.57 and 2.24, as reported in Audard et al. 2000 for the studied M dwarfs, GJ 411, AD Leo, EV Lac, and CN Leo during 1994 and 1995. Under these assumptions, the maximum duration of the detected flare would be GLYPH<28> = 12ks, and the maximum energy is E f = GLYPH<28> GLYPH<2> L X = 1.6 GLYPH<2> 10 30 erg. where a benchmark value of 1.3 GLYPH<2> 10 26 erg s GLYPH<0> 1 for L X has been used. Flares with an energy E f or larger would have an occurrence smaller than f0 = 3.3 GLYPH<2> 10 GLYPH<0> 5 s GLYPH<0> 1 , or one every 30ks period. For larger energies: with GLYPH<11> = 2.24 (or 1.57). For the benchmark energy of E' = 10 32 erg the occurrence would be lower than 1.7 GLYPH<2> 10 GLYPH<0> 7 s GLYPH<0> 1 (or 3.1 GLYPH<2> 10 GLYPH<0> 6 s GLYPH<0> 1 ), respectively for the two indices, which translates to less than 6 (96) of such flares in a year. A linear correlation between the occurrence of 10 32 erg flares with the X-ray luminosity is also given in Audard et al. 2000. This relation indicates a flare occurence between 0.8 and 1.0 GLYPH<2> 10 GLYPH<0> 7 s GLYPH<0> 1 , with both estimates below the our proposed bounds. It should be remarked that the proposed bounds are valid only under the assumed hypotheses and are linearly dependent on the considered maximum energy E f and the supposed flare time scale GLYPH<28> . A change of GLYPH<28> of a factor 10 implies a change of a factor 1 / 17(or 1 / 4 for the lower GLYPH<11> value) of the occurrence bound. Relationships between age, rotation, and coronal activity for Mstars were proposed by Guinan and Engle (2009) and Stelzer et al. (2013). Guinan and Engle (2009) have found that L X < 1.5 GLYPH<2> 10 26 erg s GLYPH<0> 1 are related to an M dwarf with an age larger than 5 Gyr, which are older than Proxima Cen(M5) or IL Aqr (M4). Similarly, Engle and Guinan (2011) estimated that the age of GJ 581 is 5.7 GLYPH<6> 0.8 Gyr. This results was obtained with a rotation-age relation. Taking the X-ray luminosity-age relation presented by Stelzer et al. (2013) for M0-M3 stars, the X-ray luminosity of GJ 581 implies that the age of GJ 581 is larger than GLYPH<24> 4 Gyr (the last time value reported on their Fig. 15). In both cases, the coronal activity-age relations provide constraints that are consistent with the previous age estimates for GJ 581 ( > 2 Gyr; Bonfils et al. 2005.) The UV normalized count-rates vs time are reported in Fig. 2. In the UV range, the largest flux variations are observed with the UVM2 filter, which most likely traces variability in the chromosphere MgII resonance doublet, the strongest emission feature in the UVM2 bandpass. For UVM2, the count rate rms is of the order of 16% of the average count rate. The UVW1 and UVW2 observations provide smaller variations as compared the UVM2. France et al (2013) reported a total UV luminosity (including the FUV and NUV spectral band-passes) for GJ 581 of L UV = 27 GLYPH<2> 10 26 erg s GLYPH<0> 1 and a MgII doublet flux of F MgII = 2.13 GLYPH<6> 0.13 GLYPH<2> 10 GLYPH<0> 14 erg cm GLYPH<0> 2 s GLYPH<0> 1 obtained from Gaussian fits to both lines of the doublet. Comparing our Swift X-ray observations to the existing HST data, we find the L X / L UV ratio is 0.043 GLYPH<6> 0.012. However previous results argue for larger L X / L UV ratios. France et al (2013) have found a log10(L UV / L Bol ) GLYPH<25> -4 and Guinan and Engle (2007) log10(L X / L Bol ) GLYPH<25> -3. Therefore, we would have expected an L X / L UV ratio of greater than unity, and our finding of GLYPH<24> 4% suggests relatively weak coronal activity on GJ 581. Using the interferometrically determined radius of GJ 581 (R = 0.29 GLYPH<6> 0.010R GLYPH<12> ; von Braun et al. 2011), we find an X-ray surface flux of (2.0 GLYPH<6> 0.7) GLYPH<2> 10 4 erg cm GLYPH<0> 2 s GLYPH<0> 1 and a MgII surface flux of (1.96 GLYPH<6> 0.11) GLYPH<2> 10 4 erg cm GLYPH<0> 2 s GLYPH<0> 1 . These surface fluxes can be compared with previously estimated values obtained by Rutten et al. 1991 (Figs. 1b and 1g). The found Mg II and X-ray surface fluxes are close to the basal flux limits, indicative of a relatively old main-sequence star (e.g., Hempelmann et al. 1995; Schrijver 1995; Cuntz et al. 1999); this finding is generally consistent with the deduced age of GJ 581, which has been found to be larger than GLYPH<24> 4 Gyr (Selsis et al. 2007). Another approach pertaining to the relationship between the empirical Mg II surface flux and the stellar age has been given by Cardini & Cassatella 2007. Following their Eq. (8) with data from their Table 2, it is found that the implied age of GJ 581 is very large, possibly beyond 10 Gyr. For further comparison we considered the M dwarfs studied in Walkowicz et al. (2008). Compared to the MgII / X-ray ratios of other M dwarfs (e.g., Fig. 5 from Walkowicz et al. (2008)), we find that GJ 581 would be comparable to GJ 876(M4.0), GJ 273(M3.5), and GJ 191(M1.0). GJ 876 has an estimated age between 0.1 and 5 Gyr (Correia et al. 2010), and despite has a low-to-intermediate activity level based on its optical spectrum has been shown to produce significant UV flux in its HZ. This source provides > 50% of the solar luminosity received at 1 AU in the FUV band-pass (1160 - 1790 Å, including Lyman-alpha; France et al. 2012). Therefore, the L X / L UV ratio is mainly indicative of the hard radiation content and does not rule out the possibility of strong UV emission in the HZ around GJ 581. Wedid not attempt to discuss the habitability of GJ 581 planetary system because it would need a detailed planetary thermal evolution models which follows atmospheric and lithosperic phenomena, as this is beyond the scope of the present note.",
"pages": [
3,
4,
5
]
},
{
"title": "4. Conclusions",
"content": "We present the first X-ray detection of the exoplanet host star GJ 581. The observations performed were part of the Fill-In Targets program during SWIFT cycle 8. These simultaneous X-ray and UV observations provide an experimental view of the energetic radiation environment of the GJ 581 planetary system, which is an important input for habitability studies of the exo-planets orbiting this low mass star. The low value of the found L X suggests that GJ 581 is older than 4 or 5 Gyr, assuming the coronal activity-age relations of Stelzer et al. (2013) or Guinan and Engle (2009). The data suggest that the X-ray emission may be variable; however, further observations with longer exposure times are required to establish robust evidence of X-ray variability. Simultaneous UV photometric observations permitted monitoring of the UV variability during the X-ray observation. We find a low value of the X-ray to ultraviolet luminosity ratio (L X / L UVtotal ) when comparing the X-ray data to the MUSCLES M dwarf UV radiation field database. We detect evidence of chromospheric activity in the UV photometry, as seen by large amplitude variation in the SWIFT UVM2 count rates when compared to those from UVW1 and UVW2. X-ray and MgII surface fluxes were derived, and they imply a stellar age ( > 4 Gyr), which is consistent with the age required by coronal activity-age relations and the previous estimates in literature.",
"pages": [
5
]
},
{
"title": "5. Acknowledgments",
"content": "The authors wish to thank the SWIFT team for the performed observations. We acknowledge the use of public data from the Swift data archive. This research has made use of the XRT Data Analysis Software (XRTDAS) developed under the responsibility of the ASI Science Data Center (ASDC), Italy. This work has made use of the MUSCLES M dwarf UV radiation field database. We are grateful to our anonymous reviewer for his / her constructive comments on our manuscript. V.V. is grateful to Dr. M. Capalbi and Dr V.D'Elia for help and support with the XRT data analysis, as also with the UVOT team and help-desk colleagues for the support with the UV observations. V.V. acknowledges the support of the ASI Science Data Center (ASDC), Prot. Agg. Convenzione Quadro ASI-INFN C / 011 / 11 / 1.",
"pages": [
5
]
},
{
"title": "References",
"content": "Audard M., et al 2000, ApJ 541, 396A Bonfils X., Forveille T., Delfosse X., et al. 2005, A&A 443, L15 Breeveld A. A., et al. 2011, arXiv:1102.4717 Cardini, D. and Cassatella, A. 2007, ApJ 666, 393C Correia A.C.M., et al 2010, A&A 511, 21 Cuntz M., et al. 1999, ApJ 522, 1053 Dole, S.H. 1964,Habitable Planets for Man, Blaisell, New York Engle S.G. and Guinan E.F. 2011, arXiv:1111.2872 France K., et al 2012, ApJ 750L, 32F France K., et al 2013, ApJ 763, 149F Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ 611, 1005 Gray, D. F. 2005 'The observtion and Analysis of Stellar Photospheres', 2nd ed. Cambridge: Cambridge Univ. Press Guinan E.F. and Engle S.G. 2007, arXiv0711.1530G Guinan E.F. and Engle S.G. 2009, arXiv0901.1860G Hempelmann, A., et al. 1995, A&A, 294, 515 Joshi, M. 2003, AsBio 3(2), 415427. Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993, Icarus, 101, 108 Miller, G.E. and Scalo, J.M. 1979, Astrophys. J. Suppl. 41, 513547. Perryman M.A.C.,et al. 1997, A&A 323L, 49P Poole T. S., et al 2008, MNRAS, 383, 627 Poppenhaeger K., et al. 2010, A&A 515, 98 Rutten R.G.M., et al. 1991, a&A 252, 203 Scalo J. et al. 2007, AsBio 7, 1 Schmitt, et al. 1990,ApJ 365, 704S Schrijver, C. J. 1995, A&A Rev., 6, 181 Segura A., et al. 2005, AsBio 5, 706S Segura A., et al. 2010,AsBio. 10, 751S Selsis et al. 2007 A&A 476, 1373 David S. Smith, John Scalo and J. Craig Wheeler 2004, Icarus 171, 229253 Stelzer B. et al. 2013, MNRAS 431, 20632079 Udry S., Bonfils X., Delfosse X., et al. 2007, A&A 469, L43 von Bloh W. et al. 2007 A&A 476, 1365 von Braun K. 2011, ApJ Letters 729, 26 von Paris P., et al. 2010, A&A 522, A23 Walkowicz L.M., et al. 2008 ApJ 677, 593 Wordsworth R. D., et al. 2010, A&A 522, 22W",
"pages": [
5
]
}
]
2013A&A...559A..18C
https://arxiv.org/pdf/1310.0615.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_80><loc_86><loc_87></location>Measuring galaxy [O ii ] emission line doublet with future ground-based wide-field spectroscopic surveys (Research Note)</section_header_level_1>
<text><location><page_1><loc_7><loc_76><loc_93><loc_79></location>Johan Comparat, 1 , Jean-Paul Kneib 2 ; 1 , Roland Bacon 3 , Nick J. Mostek 4 , Je GLYPH<11> rey A. Newman 5 , David J. Schlegel 4 , and Christophe Yèche 6</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_73><loc_85><loc_74></location>1 Aix Marseille Université, CNRS, LAM (Laboratoire d'Astrophysique de Marseille) UMR 7326, 13388, Marseille, France</list_item>
<list_item><location><page_1><loc_10><loc_69><loc_90><loc_72></location>2 Laboratoire d'astrophysique, École Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland</list_item>
<list_item><location><page_1><loc_10><loc_67><loc_79><loc_68></location>3 CRAL, Observatoire de Lyon, Université Lyon 1, 9 Avenue Ch. André, 69561 Saint Genis Laval Cedex, France</list_item>
<list_item><location><page_1><loc_10><loc_65><loc_64><loc_66></location>4 Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA</list_item>
<list_item><location><page_1><loc_10><loc_62><loc_88><loc_63></location>5 Department of Physics and Astronomy, University of Pittsburgh and PITT-PACC, 3941 O'Hara St., Pittsburgh, PA 15260, USA</list_item>
<list_item><location><page_1><loc_10><loc_60><loc_49><loc_61></location>6 CEA, Centre de Saclay, IRFU, F-91191 Gif-sur-Yvette, France</list_item>
</unordered_list>
<text><location><page_1><loc_10><loc_57><loc_33><loc_57></location>Accepted by A&A on sept. 20th 2013</text>
<section_header_level_1><location><page_1><loc_46><loc_53><loc_54><loc_54></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_10><loc_40><loc_90><loc_52></location>The next generation of wide-field spectroscopic redshift surveys will map the large-scale galaxy distribution in the redshift range 0 : 7 GLYPH<20> z GLYPH<20> 2 to measure baryonic acoustic oscillations (BAO). The primary optical signature used in this redshift range comes from the [O ii ] emission line doublet, which provides a unique redshift identification that can minimize confusion with other single emission lines. To derive the required spectrograph resolution for these redshift surveys, we simulate observations of the [O ii ] ( GLYPH<21>GLYPH<21> 3727,3729) doublet for various instrument resolutions, and line velocities. We foresee two strategies about the choice of the resolution for future spectrographs for BAO surveys. For bright [O ii ] emitter surveys ([O ii ] flux GLYPH<24> 30 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 like SDSS-IV / eBOSS), a resolution of R GLYPH<24> 3 300 allows the separation of 90 percent of the doublets. The impact of the sky lines on the completeness in redshift is less than 6 percent. For faint [O ii ] emitter surveys ([O ii ] flux GLYPH<24> 10 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 like DESi), the detection improves continuously with resolution, so we recommend the highest possible resolution, the limit being given by the number of pixels (4k by 4k) on the detector and the number of spectroscopic channels (2 or 3).</text>
<text><location><page_1><loc_10><loc_39><loc_80><loc_40></location>Key words. Instrumentation: spectroscopy, techniques: spectroscopy, cosmology: observations, galaxies: statistics.</text>
<section_header_level_1><location><page_1><loc_6><loc_34><loc_18><loc_35></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_6><loc_19><loc_49><loc_33></location>Following the successful baryonic acoustic oscillation (BAO) measurement in the galaxy clustering from SDSS (Eisenstein et al. 2005), 2dFGRS (Cole et al. 2005), Wiggle-Z (Blake et al. 2011), and the Baryonic Oscillation Spectroscopic Survey (BOSS) (Anderson et al. 2012), there is a strong motivation in the community to plan the next generation of spectroscopic redshift surveys for BAO. In particular, the future ground-based surveys plan to map the galaxy distribution in the redshift range 0 : 7 GLYPH<20> z GLYPH<20> 2 and use the galaxy power spectrum to precisely measure the BAO signature and constrain the cosmological parameters.</text>
<text><location><page_1><loc_6><loc_10><loc_49><loc_19></location>Two examples of this new paradigm are the following projects: SDSS-IV / eBOSS and DESi.The SDSS-IV / eBOSS dark energy experiment starts observing in 2014 with SDSSIII / BOSS infrastructure (1 000 fibers on GLYPH<24> 7 deg 2 ). This survey will measure about 1.5 million spectroscopic redshifts of QSOs in the redshift range 0 : 9 < z < 2 : 5 and galaxies with a redshift in 0 : 6 < z < 1 : 2. The DESi project plans to map 14 000 deg 2 of</text>
<text><location><page_1><loc_51><loc_30><loc_94><loc_36></location>sky using 5 000 motorized fibers over a 7 deg 2 field of view and to measure 22 million galaxy redshifts; see Schlegel et al. (2011) for a global survey description and Mostek et al. (2012) for the current survey parameters.</text>
<text><location><page_1><loc_51><loc_17><loc_94><loc_30></location>Galaxy redshifts will be mostly determined from the emission line features of star-forming galaxies between 0 : 7 GLYPH<20> z GLYPH<20> 2. Table 1 lists the primary emission lines that are available at optical and NIR wavelengths within this redshift range. Of these lines, the [O ii ] doublet at ( GLYPH<21> 3727 ; GLYPH<21> 3729) will provide the most consistently available feature. In order to avoid confusion with other prominent emission lines (H GLYPH<11> , H GLYPH<12> , [O iii ] ), the [O ii ] doublet should be resolved over the instrumented wavelength range where no other lines are available to make an unambiguous identification.</text>
<text><location><page_1><loc_51><loc_10><loc_94><loc_16></location>Previous emission line redshift surveys have had di GLYPH<11> erent strategies concerning the use of emission lines for measuring the redshift. Wiggle-Z with a spectral resolution of 1300 obtained 60% of reliable redshifts (18% based on the detection of the [O ii ] doublet i.e. the doublet is resolved or partially resolved), and</text>
<table>
<location><page_2><loc_9><loc_75><loc_46><loc_86></location>
<caption>Table 1. Emission lines available at optical and near-infrared wavelengths. Taken from Atomic Line List (from www.pa.uky.edu). GLYPH<21> vac is the wavelength emitted in vacuum in Å, the orbital transition is given under the column 'term', 'J-J' is the spin state. The last column gives the energy transition that occurs in electron-Volt.</caption>
</table>
<text><location><page_2><loc_6><loc_59><loc_49><loc_73></location>40% of unreliable redshifts; (Drinkwater et al. 2010). DEEP2 survey with a resolution of 6 000 obtained 71% of reliable redshifts (14.8% based on the detection of the [O ii ] doublet i.e. the doublet is resolved or partially resolved), 10% between reliable and unreliable, and 19% of unreliable redshifts (Newman et al. 2012). The di GLYPH<11> erence between these redshift e GLYPH<14> ciencies is related to the resolution of the spectrograph and the wavelength it covers. Indeed, if the [O ii ] emission is the only one available in the spectrum, at high resolution the doublet is split and the redshift is reliable. Whereas, at lower resolution the [O ii ] doublet is not always split and may be taken for another emission line.</text>
<text><location><page_2><loc_6><loc_52><loc_49><loc_58></location>In Section 2, we derive the minimum resolution necessary to resolve the doublet in the case of an observation without noise. In Section 3, we describe our simulation of [O ii ] doublet detections based on DEEP2 spectral observations. We discuss the results of our simulation in Section 4.</text>
<section_header_level_1><location><page_2><loc_6><loc_49><loc_30><loc_50></location>2. Instrumental requirements</section_header_level_1>
<text><location><page_2><loc_6><loc_39><loc_49><loc_48></location>First, let us define our notation. R = GLYPH<21>= FWHM GLYPH<21> is the resolution of the spectrograph, GLYPH<21> a = 3 727 : 092Å, GLYPH<21> b = 3 729 : 875Å are the individual [O ii ] emission wavelengths and GLYPH<21> [ O ii ] = ( GLYPH<21> a GLYPH<3> 3 : 326568 + GLYPH<21> b GLYPH<3> 3 : 324086) = (3 : 326568 + 3 : 324086) = 3 728 : 483Å is the energy-weighted mean [O ii ] wavelength. The observed wavelength separation between the emission lines depends on the redshift GLYPH<14> [ O ii ]( z ) = ( GLYPH<21> b GLYPH<0> GLYPH<21> a )(1 + z ) = 2 : 783(1 + z ) :</text>
<text><location><page_2><loc_6><loc_31><loc_49><loc_38></location>We can thus define the resolution, R [ O ii ], as the minimal resolution required to properly sample a theoretical [O ii ] doublet (with zero intrinsic width) without loss of information by R [ O ii ] = 2(1 + z ) GLYPH<21> [ O ii ] =GLYPH<14> [ O ii ]( z ) = 2 679 (Nyquist-Shannon sampling theorem, Shannon & Weaver 1975). Note that R [ O ii ] is independent of redshift.</text>
<text><location><page_2><loc_6><loc_23><loc_49><loc_31></location>However, a real galaxy has an intrinsic velocity dispersion, GLYPH<1> v , that broadens the emission lines from a theoretical Dirac GLYPH<14> -function profile. Assuming the line profile is dominated by thermal Doppler broadening in the host galaxy interstellar medium, the observed wavelength width, GLYPH<14>GLYPH<21>v , of the broadened [O ii ] line profiles is defined in Eq. 1 where c is the speed of light.</text>
<formula><location><page_2><loc_6><loc_19><loc_49><loc_22></location>GLYPH<14>GLYPH<21>v = GLYPH<21> [ O ii ] GLYPH<1> v c : (1)</formula>
<text><location><page_2><loc_6><loc_12><loc_49><loc_19></location>In this simplified case, the intrinsic velocity dispersion is equivalent to the standard deviation in a Gaussian profile. For example, a galaxy at z = 1 with GLYPH<1> v = 50 km s GLYPH<0> 1 has a line width of GLYPH<14>GLYPH<21>v GLYPH<24> 0 : 6Å, which represents GLYPH<24> 10% of the wavelength separation between the doublet peaks.</text>
<text><location><page_2><loc_6><loc_10><loc_49><loc_12></location>Furthermore, the spectral resolution of the instrument also broadens the width of the [O ii ] lines. The change in line width</text>
<text><location><page_2><loc_51><loc_87><loc_94><loc_93></location>due to resolution is given by GLYPH<14>GLYPH<21> R ( z ) defined in Eq. 2. Note that the broadening due to instrumental resolution depends on the redshift because the position of [O ii ] changes with redshift while the resolution element FWHM GLYPH<21> is roughly constant with the wavelength (for a grism spectrograph):</text>
<formula><location><page_2><loc_51><loc_83><loc_94><loc_85></location>GLYPH<14>GLYPH<21> R ( z ) = (1 + z ) GLYPH<21> [ O ii ] R : (2)</formula>
<text><location><page_2><loc_51><loc_78><loc_94><loc_82></location>By performing a squaring sum of the components in Eq. 1 and 2, we obtain the observed width, denoted w [ O ii ]( z ), of an individual line in the [O ii ] doublet:</text>
<formula><location><page_2><loc_51><loc_74><loc_94><loc_77></location>w [ O ii ]( z ) = GLYPH<21> [ O ii ] r (1 + z ) 2 R 2 + GLYPH<1> v 2 c 2 : (3)</formula>
<text><location><page_2><loc_51><loc_66><loc_94><loc_73></location>In order to Nyquist sample the observed [O ii ] doublet at redshift z , the individual line width of the doublet has to be at least twice the doublet separation, or w [ OII ]( z ) = 2 GLYPH<14> [ O ii ]( z ). Rewriting Eq. 3 in terms of this minimum sampling requirement gives the minimal resolution, denoted R ( z ; GLYPH<1> v ), required to split an [O ii ] doublet emitted at redshift z with a velocity dispersion GLYPH<1> v :</text>
<formula><location><page_2><loc_51><loc_61><loc_94><loc_64></location>R ( z ; GLYPH<1> v ) = 2 6 6 6 6 6 4 1 R 2 [ O ii ] GLYPH<0> GLYPH<1> v 2 (1 + z ) 2 c 2 3 7 7 7 7 7 5 GLYPH<0> 1 = 2 : (4)</formula>
<text><location><page_2><loc_51><loc_57><loc_94><loc_60></location>R ( z ; GLYPH<1> v ) decreases with redshift, increases with the velocity dispersion, and it converges asymptotically towards R [ O ii ].</text>
<text><location><page_2><loc_51><loc_45><loc_94><loc_57></location>For a galaxy at z = 1 ([O ii ] is observed at GLYPH<21> GLYPH<24> 7456Å) with GLYPH<1> v = 100 km s GLYPH<0> 1 , the minimum resolution required is Rmin = 3 000. For a galaxy at z = 1 with GLYPH<1> v = 70 km s GLYPH<0> 1 , it is Rmin = 2 800. The spectrograph currently used by SDSSIII / BOSS reaches R GLYPH<24> 2700 > R [ O ii ] at 9 320Å, and therefore it theoretically splits the [O ii ] doublet for galaxies with GLYPH<1> v < 50 km s GLYPH<0> 1 at z GLYPH<21> 1 : 5. With this spectrograph, the observation of the [O ii ] doublet of galaxies with GLYPH<1> v = 100 km s GLYPH<0> 1 will be highly-blended.</text>
<text><location><page_2><loc_51><loc_40><loc_94><loc_45></location>At low resolution, it is possible to actually see [O ii ] doublets when the lines peaks and valley falls exactly right opposite to the pixels. In the following, when we state 'the doublet is resolved', it is true wherever the emission line lands on the detector.</text>
<text><location><page_2><loc_51><loc_31><loc_94><loc_40></location>In classical spectrographs, the resolution element FWHM GLYPH<21> is roughly constant with wavelength, and therefore the spectral resolution R is a linear function of the observed wavelength GLYPH<21> . We must therefore define the minimum resolution requirement to be at the lowest redshift limit where [O ii ] becomes the only emission line available in the spectrum. The resolution requirement will automatically be satisfied for all higher redshifts.</text>
<text><location><page_2><loc_51><loc_28><loc_94><loc_31></location>In this study, we consider the more common case where the spectral range is limited to < 1 GLYPH<22> m .</text>
<section_header_level_1><location><page_2><loc_51><loc_25><loc_62><loc_26></location>3. Simulation</section_header_level_1>
<text><location><page_2><loc_51><loc_15><loc_94><loc_24></location>To confirm the theoretical considerations of Section 2, we simulate observations of [O ii ] doublets in the presence of Poisson noise. Future massive spectroscopic redshift surveys are primarily focused on obtaining redshifts with only emission lines, which is less demanding in terms of exposure time than requiring the detection of the continuum. For these applications, a Gaussian profile is su GLYPH<14> cient to simulate the resolution e GLYPH<11> ects.</text>
<text><location><page_2><loc_51><loc_10><loc_94><loc_15></location>Because spectrograph resolution increases with wavelength, the minimal resolution requirement is determined at the shortest wavelength where the [O ii ] doublet becomes the only major emission line feature in the spectrum. Assuming an instrumental</text>
<text><location><page_3><loc_6><loc_90><loc_49><loc_93></location>wavelength limit of 1 GLYPH<22> m, the resolution requirement for [O ii ] is therefore defined at GLYPH<21> obs ([ O ii ] ; z = 1) GLYPH<24> 7 450Å.</text>
<text><location><page_3><loc_6><loc_80><loc_49><loc_90></location>Of interest for this work, DEEP2 has obtained a complete spectroscopic sample of [O ii ] emitters at redshift z = 1. Its magnitude limit is r = 24 : 1 and its [O ii ] flux limit is 5 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 (Newman et al. 2012). These limits are deeper than the target selection limits for BAO surveys currently under development. DEEP2 used the DEIMOS grism spectrograph at Keck with a resolution R = 6 000 (Faber et al. 2003) and was limited by the galaxy continuum signal-to-noise.</text>
<text><location><page_3><loc_6><loc_73><loc_49><loc_79></location>The range of velocity dispersions used in our simulation is empirically determined by observations of z GLYPH<24> 1 [O ii ] emitters within the DEEP2 redshift survey. We set the lower (upper) limit of the investigated range at GLYPH<1> v = 20 km s GLYPH<0> 1 (120 km s GLYPH<0> 1 ), which encompasses most of the galaxies down to r < 24.</text>
<text><location><page_3><loc_6><loc_58><loc_49><loc_73></location>In terms of instrumental resolution, we explore the range of 2 500 < R < 6 000 sampled by steps of GLYPH<14> R = 3 in resolution. To avoid aliasing problems, for each doublets we add a random number smaller than 3 to the resolution, in order to sample correctly the complete resolution range. We use a sampling of 3 pixels per resolution element. Our results will span a meaningful range of resolutions for numerous spectrographs at GLYPH<21> obs ([ O ii ]) GLYPH<24> 7 500Å, including the current SDSS-III / BOSS spectrograph ( R GLYPH<24> 2 500, Smee et al. (2013)) and future spectrographs such as PFS-SUMIRE ( R GLYPH<24> 3 000 Vivès et al. (2012)) or DESi ( R GLYPH<24> 4 000 Jelinsky et al. (2012)).</text>
<text><location><page_3><loc_6><loc_42><loc_49><loc_58></location>Weuse a Gaussian function, to model the [O ii ] doublet, given by f gaussian( GLYPH<21>; GLYPH<21> 0 ; GLYPH<27>g ; F 0) = F 0 p 2 GLYPH<25>GLYPH<27>g Exp GLYPH<20> ( GLYPH<21> GLYPH<0> GLYPH<21> 0) 2 2 GLYPH<27> 2 g GLYPH<21> . This produces an emission line centered at GLYPH<21> 0 of total flux F 0. The profile width GLYPH<27>g is linked to the velocity dispersion by GLYPH<27>g = GLYPH<21> [ O ii ] GLYPH<1> v= c . The Gaussian profile has an exponential drop o GLYPH<11> from the emission peak value, and therefore it may not represent systematic e GLYPH<11> ects like scattered light within the spectrograph. A Mo GLYPH<11> at profile recovers the information in the wings of the emission line when GLYPH<12> is allowed to vary. However, the Mo GLYPH<11> at model is only attractive if the data has a high spectral resolution and high signal to noise ratio. Otherwise, the information in the wings will have low significance due to measurement noise.</text>
<text><location><page_3><loc_6><loc_26><loc_49><loc_41></location>We calibrate the flux f and the sky level to a recent emission line galaxy observational study performed at the SDSS Telescope (Comparat et al. 2013). This study showed the nominal observed total line flux is GLYPH<24> 30 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 and the nominal sky brightness is GLYPH<24> 3 GLYPH<2> 10 GLYPH<0> 18 erg cm GLYPH<0> 2 s GLYPH<0> 1 Å GLYPH<0> 1 arcsec GLYPH<0> 2 at GLYPH<24> 7400Å. This noise level corresponds to detections with a SNR above 7 which should be typical of observations in future BAO survey. In the simulation, we use fluxes f from a broader range, 6 < f < 100 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 . We determine the relative abundance of emission lines at a given flux with the [O ii ] luminosity function at z GLYPH<24> 1 measured by Zhu et al. (2009) on DEEP2 survey.</text>
<text><location><page_3><loc_6><loc_10><loc_49><loc_25></location>First, we first make a Gaussian doublet at GLYPH<21> obs ([ O ii ]) GLYPH<24> 7450Å for a given resolution R , velocity dispersion GLYPH<1> v , and flux f . The flux ratio between the two lines is fixed at 1, the impact of a varying flux ratio is discussed in the paragraph 4.3. Next, we sample the doublet spectrum at resolution R with 3 pixel per resolution element. We add Poisson sky noise on each pixel (this is the dominating contribution of the observed noise). This creates a mock observation of the [O ii ] emission doublet for the Gaussian profile. Finally, we fit two models to the simulated doublet: a single Gaussian profile, and a double Gaussian profile. From each fit, we compute the S NR and the GLYPH<31> 2 to compare the detections. GLYPH<31> 2 is defined as the usual 'reduced chi-square statistics'</text>
<text><location><page_3><loc_51><loc_91><loc_94><loc_93></location>by GLYPH<31> i = 1 or 2 = 1 ndof P k 2 pixels ( Ok GLYPH<0> M i k ) 2 N 2 k where ndof is the number of</text>
<text><location><page_3><loc_51><loc_85><loc_94><loc_91></location>degrees of freedom, O is the array of observed values, M 1 is the model with one line, M 2 is the model with 2 lines, and N is the noise. The number of degrees of freedom vary from 35 to 94 (depending on the spectral resolution used). The S NR is calculated with a Fisher matrix.</text>
<section_header_level_1><location><page_3><loc_51><loc_81><loc_59><loc_82></location>4. Results</section_header_level_1>
<text><location><page_3><loc_51><loc_77><loc_94><loc_80></location>The simulation contains GLYPH<24> 15 GLYPH<2> 10 6 simulated [O ii ] lines sampling the velocity dispersion, resolution, and flux range set in the above.</text>
<text><location><page_3><loc_51><loc_63><loc_94><loc_76></location>To statistically di GLYPH<11> erentiate whether an observation of [O ii ] is identified as a doublet or a single emission line (SEL), given that the numbers of degrees of freedom is high (35 < ndof < 94), we use the di GLYPH<11> erence GLYPH<1> GLYPH<31> 2 = GLYPH<31> 1 = ndof 1 GLYPH<0> GLYPH<31> 2 = ndof 2 of the normalized GLYPH<31> 2 . A GLYPH<1> GLYPH<31> 2 = 9 means the single line emission model is ruled out at 3 GLYPH<27> or with a 99.7% confidence level. We compute the share of emission line with r < 24 (convolved by the velocity dispersion distribution of DEEP2) detected as a doublet at the 3 GLYPH<27> confidence levels at redshift 1 as function of the resolution for di GLYPH<11> erent [O ii ] flux detection limit, see Fig. 1.</text>
<text><location><page_3><loc_51><loc_46><loc_94><loc_63></location>The main trend is that the percentage of doublets increases as a function of the resolution. We can distinguish two regimes. In the regime of low [O ii ] fluxes the gain is linear, i.e. for surveys with a lower limit of [O ii ] detection of 10 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 or below the increase of the share of doublet is linear as a function of the resolution (it corresponds to the line 10 of Fig. 1). For such survey, it indicates the resolution should be the highest possible. For higher [O ii ] fluxes, the marginal increase of the doublet share is large for low resolutions and small for higher resolution. For a survey aiming only to observe the brightest [O ii ] emitters (on Fig. 1), it is not necessary to aim for the highest resolution. R = 3 300 is su GLYPH<14> cient to obtain 90% of doublets. And for R > 3 300, the marginal cost of an extra percent of doublets decreases.</text>
<text><location><page_3><loc_51><loc_37><loc_94><loc_46></location>The DEEP 2 survey dealt with SEL using a neural network (Kirby et al. 2007). They showed that given a fair spectroscopic sample of an observed population with reliable redshifts, it is possible to infer correct redshifts to nearly 100% of the [O ii ] SEL. The H GLYPH<11> , H GLYPH<12> , and [O iii ] SEL cases are not as well handled by the neural network with e GLYPH<14> ciencies of GLYPH<24> 90%, GLYPH<24> 60%, and GLYPH<24> 60% respectively.</text>
<text><location><page_3><loc_51><loc_32><loc_94><loc_37></location>The combination of the two latter points shows it will be possible to derive robust [O ii ] redshifts where [O ii ] is the only emission line available in the spectrograph, even if the fraction of 3 GLYPH<27> doublet detections is small.</text>
<section_header_level_1><location><page_3><loc_51><loc_29><loc_82><loc_30></location>4.1. Higher redshift, sky lines, completeness</section_header_level_1>
<text><location><page_3><loc_51><loc_14><loc_94><loc_28></location>The sky lines have an observed width of one resolution element, therefore their width varies with the resolution. In the case of a single sky line located on a doublet, it is not a problem to subtract the sky line and obtain an accurate redshift. In the case of many contiguous sky lines, it can cover completely a doublet and prevent from getting any redshift in this zone. This causes the survey to have a varying [O ii ] flux limit as a function of the redshift. To quantify the impact of the sky lines obstruction as a function of redshift, we simulate at various resolutions the observation of a sky spectrum. The sky spectrum is taken from Hanuschik (2003).</text>
<text><location><page_3><loc_51><loc_10><loc_94><loc_13></location>At a given resolution, we convert the wavelength array of the sky into a redshift array corresponding to the [O ii ] redshift. We scan the redshift array by steps of 0.0005 (it corresponds to the</text>
<figure>
<location><page_4><loc_9><loc_75><loc_45><loc_93></location>
<caption>Fig. 1. Share of doublets at the 3 GLYPH<27> (confidence level of 99.7%) vs. resolution for r < 24 doublets at z = 1 for di GLYPH<11> erent flux bins and with a flux ratio between the lines of 1. Each line corresponds to a survey with a the flux detection limit given on the right end of each line in units of 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 . SDSS-IV / eBOSS corresponds to the line 30 and DESi to the line 10.</caption>
</figure>
<text><location><page_4><loc_6><loc_53><loc_49><loc_62></location>desired precision of a spectroscopic redshift). At each step, we compare the median value of the sky (we assume here a sky subtraction e GLYPH<14> cient at 90%) to the flux measured in the middle of an [O ii ] doublet with (where it is the lowest). If the median value of the sky is greater than the value of the doublet, we consider we cannot fit a redshift. Finally, we compute the percentage of the redshift range where we can fit spectroscopic redshifts.</text>
<text><location><page_4><loc_6><loc_36><loc_49><loc_53></location>We run this test for two settings. A bright survey with [O ii ] fluxes GLYPH<24> 30 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 and fibers of 2' diameter (SDSS-IV / eBOSS-like). A faint survey with [O ii ] fluxes GLYPH<24> 10 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 and fibers of 1.5' diameter (DESilike). It shows the impact of the sky lines on the completeness depends weakly on the resolution, the discrepancy between the di GLYPH<11> erent resolution settings is under a couple of percents. For the bright scenario the completeness is greater than 95%. For the faint survey case, the completeness is greater than 80%. This demonstrates how the sky lines impact the redshift completeness of an [O ii ] spectroscopic survey. It shows it is necessary to have the smallest fiber possible to diminish the impact of the sky. The increase in resolution is not useful to cope with this problem.</text>
<text><location><page_4><loc_6><loc_30><loc_49><loc_36></location>Finally the completeness in redshift is not driven by the resolution at the first order, but by the robustness of sky subtraction and the strength of the [O ii ] flux. To obtain a precise estimate of the impact of sky lines on the redshift distribution completeness, a full end-to-end simulation is needed.</text>
<section_header_level_1><location><page_4><loc_6><loc_26><loc_27><loc_27></location>4.2. Integrated velocity profile</section_header_level_1>
<text><location><page_4><loc_6><loc_16><loc_49><loc_25></location>In this study, the integrated velocity profile of each galaxy within a fiber is assumed to be Gaussian, although galaxy rotation may create complications. Current data is not su GLYPH<14> cient to explore this particular di GLYPH<14> culty. Nearby galaxies are not representative of the properties of these higher-redshift galaxies, and surveys like MASSIV are limited to a sample of only 50 galaxies in the redshift range 0 : 6 < z < 1 : 6 Epinat et al. (2012).</text>
<section_header_level_1><location><page_4><loc_6><loc_13><loc_25><loc_14></location>4.3. Emission line flux ratio</section_header_level_1>
<text><location><page_4><loc_6><loc_10><loc_49><loc_12></location>The flux ratio between the forbidden fine structure [O ii ] lines varies with the surrounding electronic density between 0.35</text>
<text><location><page_4><loc_51><loc_70><loc_94><loc_93></location>(high electron density limit) and 1.5 (low density limit) (Pradhan et al. 2006). A precise estimation of the distribution of this ratio at z GLYPH<24> 1 has not been measured, although observations show the ratio does not take the extreme values 0.35 or 1.5, but seems to stay around 1.A ratio of one is the best for separating the doublet. A di GLYPH<11> erent ratio can only decrease the e GLYPH<14> ciency at recognizing the doublet. Also this e GLYPH<11> ect is symmetric, a ratio of 0.7 or 1.4 implies the loss of the same amount of doublets. We quantify this e GLYPH<11> ect by varying the flux ratio of the lines simulated between 0.7 and 1. For emission lines with total flux of 10 GLYPH<0> 16 erg cm GLYPH<0> 2 s GLYPH<0> 1 (DESi-like), a flux ratio of 0.7 (or 1.4) induces a decrease in the amount of doublets seen of 8.3% at R GLYPH<24> 4 500. The total number of doublets detected at 3 GLYPH<27> goes from GLYPH<24> 25% to GLYPH<24> 22 : 9%. For emission lines with total flux of 3 GLYPH<2> 10 GLYPH<0> 16 erg cm GLYPH<0> 2 s GLYPH<0> 1 (SDSSIV / eBOSS-like), a flux ratio of 0.7 (or 1.4) induces a decrease in the amount of doublets seen of 9.1% at R GLYPH<24> 3 300. The total number of doublets detected at 3 GLYPH<27> diminishies from GLYPH<24> 90% to GLYPH<24> 81 : 8%.</text>
<section_header_level_1><location><page_4><loc_51><loc_66><loc_62><loc_67></location>5. Conclusion</section_header_level_1>
<text><location><page_4><loc_51><loc_55><loc_94><loc_65></location>Large spectroscopic redshift surveys are being designed to measure galaxy redshifts using the [O ii ] emission line doublet and trace the large-scale matter distribution. This study shows we should be optimistic regarding their feasibility. We have shown how the observation of the doublet evolves with the instrumental resolution and the line velocity dispersion. Also, we quantified the impact of sky lines on the redshift completeness of such a survey.</text>
<text><location><page_4><loc_51><loc_33><loc_94><loc_55></location>In light of the numbers obtained, we foresee two strategies about the choice of the resolution for future spectrographs: For bright [O ii ] emitter surveys (like SDSS-IV / eBOSS), a resolution of R GLYPH<24> 2 500 (current SDSS spectrograph) is su GLYPH<14> cient to obtain a fair sample of doublets (60%) in order to train the pipeline to recover all the [O ii ] redshifts. Increasing the resolution to 3 300 allows to get 90% of doublets. For a small increase in resolution, the redshift determination e GLYPH<14> ciency doubles. The impact of the sky lines on the completeness in redshift is smaller than 6%. For faint [O ii ] emitter surveys (like DESi), we recommend to push the resolution to the highest. Knowing there is a limited number of pixels on the detector (4k), and that the highest resolution possible on a three channel spectrograph is R GLYPH<24> 4 500 at 7 500Å, to go beyond, it is necessary to use a four channel spectrograph. Practically with a resolution of 4 500, one would obtain 25% of doublets, which is enough to train the pipeline to assign correct redshift.</text>
<text><location><page_4><loc_51><loc_28><loc_94><loc_32></location>Acknowledgements. JPK acknowledges support from the ERC advanced grant "LIDA". This work was supported by the United States Department of Energy Early Career program via grant de-sc0003960 and by the National Science Foundation via grant AST-0806732.</text>
<section_header_level_1><location><page_4><loc_51><loc_23><loc_60><loc_24></location>References</section_header_level_1>
<text><location><page_4><loc_51><loc_11><loc_94><loc_22></location>Anderson, L., Aubourg, E., Bailey, S., et al. 2012, MNRAS, 427, 3435 Blake, C., Kazin, E. A., Beutler, F., et al. 2011, MNRAS, 418, 1707 Cole, S., Percival, W. J., Peacock, J. A., et al. 2005, MNRAS, 362, 505 Comparat, J., Kneib, J.-P., Esco GLYPH<14> er, S., et al. 2013, MNRAS, 428, 1498 Drinkwater, M. J., Jurek, R. J., Blake, C., et al. 2010, MNRAS, 401, 1429 Eisenstein, D. J., Zehavi, I., Hogg, D. W., et al. 2005, ApJ, 633, 560 Epinat, B., Tasca, L., Amram, P., et al. 2012, A&A, 539, A92 Faber, S. M., Phillips, A. C., Kibrick, R. I., et al. 2003, in SPIE, Vol. 4841, SPIE Hanuschik, R. W. 2003, A&A, 407, 1157 Jelinsky, P., Bebek, C., Besuner, R., et al. 2012, in SPIE, Vol. 8446, SPIE Kirby, E. N., Guhathakurta, P., Faber, S. M., et al. 2007, ApJ, 660, 62</text>
<text><location><page_4><loc_51><loc_10><loc_91><loc_11></location>Mostek, N., Barbary, K., Bebek, C. J., et al. 2012, in SPIE, Vol. 8446, SPIE</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "The next generation of wide-field spectroscopic redshift surveys will map the large-scale galaxy distribution in the redshift range 0 : 7 GLYPH<20> z GLYPH<20> 2 to measure baryonic acoustic oscillations (BAO). The primary optical signature used in this redshift range comes from the [O ii ] emission line doublet, which provides a unique redshift identification that can minimize confusion with other single emission lines. To derive the required spectrograph resolution for these redshift surveys, we simulate observations of the [O ii ] ( GLYPH<21>GLYPH<21> 3727,3729) doublet for various instrument resolutions, and line velocities. We foresee two strategies about the choice of the resolution for future spectrographs for BAO surveys. For bright [O ii ] emitter surveys ([O ii ] flux GLYPH<24> 30 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 like SDSS-IV / eBOSS), a resolution of R GLYPH<24> 3 300 allows the separation of 90 percent of the doublets. The impact of the sky lines on the completeness in redshift is less than 6 percent. For faint [O ii ] emitter surveys ([O ii ] flux GLYPH<24> 10 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 like DESi), the detection improves continuously with resolution, so we recommend the highest possible resolution, the limit being given by the number of pixels (4k by 4k) on the detector and the number of spectroscopic channels (2 or 3). Key words. Instrumentation: spectroscopy, techniques: spectroscopy, cosmology: observations, galaxies: statistics.",
"pages": [
1
]
},
{
"title": "Measuring galaxy [O ii ] emission line doublet with future ground-based wide-field spectroscopic surveys (Research Note)",
"content": "Johan Comparat, 1 , Jean-Paul Kneib 2 ; 1 , Roland Bacon 3 , Nick J. Mostek 4 , Je GLYPH<11> rey A. Newman 5 , David J. Schlegel 4 , and Christophe Yèche 6 Accepted by A&A on sept. 20th 2013",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Following the successful baryonic acoustic oscillation (BAO) measurement in the galaxy clustering from SDSS (Eisenstein et al. 2005), 2dFGRS (Cole et al. 2005), Wiggle-Z (Blake et al. 2011), and the Baryonic Oscillation Spectroscopic Survey (BOSS) (Anderson et al. 2012), there is a strong motivation in the community to plan the next generation of spectroscopic redshift surveys for BAO. In particular, the future ground-based surveys plan to map the galaxy distribution in the redshift range 0 : 7 GLYPH<20> z GLYPH<20> 2 and use the galaxy power spectrum to precisely measure the BAO signature and constrain the cosmological parameters. Two examples of this new paradigm are the following projects: SDSS-IV / eBOSS and DESi.The SDSS-IV / eBOSS dark energy experiment starts observing in 2014 with SDSSIII / BOSS infrastructure (1 000 fibers on GLYPH<24> 7 deg 2 ). This survey will measure about 1.5 million spectroscopic redshifts of QSOs in the redshift range 0 : 9 < z < 2 : 5 and galaxies with a redshift in 0 : 6 < z < 1 : 2. The DESi project plans to map 14 000 deg 2 of sky using 5 000 motorized fibers over a 7 deg 2 field of view and to measure 22 million galaxy redshifts; see Schlegel et al. (2011) for a global survey description and Mostek et al. (2012) for the current survey parameters. Galaxy redshifts will be mostly determined from the emission line features of star-forming galaxies between 0 : 7 GLYPH<20> z GLYPH<20> 2. Table 1 lists the primary emission lines that are available at optical and NIR wavelengths within this redshift range. Of these lines, the [O ii ] doublet at ( GLYPH<21> 3727 ; GLYPH<21> 3729) will provide the most consistently available feature. In order to avoid confusion with other prominent emission lines (H GLYPH<11> , H GLYPH<12> , [O iii ] ), the [O ii ] doublet should be resolved over the instrumented wavelength range where no other lines are available to make an unambiguous identification. Previous emission line redshift surveys have had di GLYPH<11> erent strategies concerning the use of emission lines for measuring the redshift. Wiggle-Z with a spectral resolution of 1300 obtained 60% of reliable redshifts (18% based on the detection of the [O ii ] doublet i.e. the doublet is resolved or partially resolved), and 40% of unreliable redshifts; (Drinkwater et al. 2010). DEEP2 survey with a resolution of 6 000 obtained 71% of reliable redshifts (14.8% based on the detection of the [O ii ] doublet i.e. the doublet is resolved or partially resolved), 10% between reliable and unreliable, and 19% of unreliable redshifts (Newman et al. 2012). The di GLYPH<11> erence between these redshift e GLYPH<14> ciencies is related to the resolution of the spectrograph and the wavelength it covers. Indeed, if the [O ii ] emission is the only one available in the spectrum, at high resolution the doublet is split and the redshift is reliable. Whereas, at lower resolution the [O ii ] doublet is not always split and may be taken for another emission line. In Section 2, we derive the minimum resolution necessary to resolve the doublet in the case of an observation without noise. In Section 3, we describe our simulation of [O ii ] doublet detections based on DEEP2 spectral observations. We discuss the results of our simulation in Section 4.",
"pages": [
1,
2
]
},
{
"title": "2. Instrumental requirements",
"content": "First, let us define our notation. R = GLYPH<21>= FWHM GLYPH<21> is the resolution of the spectrograph, GLYPH<21> a = 3 727 : 092Å, GLYPH<21> b = 3 729 : 875Å are the individual [O ii ] emission wavelengths and GLYPH<21> [ O ii ] = ( GLYPH<21> a GLYPH<3> 3 : 326568 + GLYPH<21> b GLYPH<3> 3 : 324086) = (3 : 326568 + 3 : 324086) = 3 728 : 483Å is the energy-weighted mean [O ii ] wavelength. The observed wavelength separation between the emission lines depends on the redshift GLYPH<14> [ O ii ]( z ) = ( GLYPH<21> b GLYPH<0> GLYPH<21> a )(1 + z ) = 2 : 783(1 + z ) : We can thus define the resolution, R [ O ii ], as the minimal resolution required to properly sample a theoretical [O ii ] doublet (with zero intrinsic width) without loss of information by R [ O ii ] = 2(1 + z ) GLYPH<21> [ O ii ] =GLYPH<14> [ O ii ]( z ) = 2 679 (Nyquist-Shannon sampling theorem, Shannon & Weaver 1975). Note that R [ O ii ] is independent of redshift. However, a real galaxy has an intrinsic velocity dispersion, GLYPH<1> v , that broadens the emission lines from a theoretical Dirac GLYPH<14> -function profile. Assuming the line profile is dominated by thermal Doppler broadening in the host galaxy interstellar medium, the observed wavelength width, GLYPH<14>GLYPH<21>v , of the broadened [O ii ] line profiles is defined in Eq. 1 where c is the speed of light. In this simplified case, the intrinsic velocity dispersion is equivalent to the standard deviation in a Gaussian profile. For example, a galaxy at z = 1 with GLYPH<1> v = 50 km s GLYPH<0> 1 has a line width of GLYPH<14>GLYPH<21>v GLYPH<24> 0 : 6Å, which represents GLYPH<24> 10% of the wavelength separation between the doublet peaks. Furthermore, the spectral resolution of the instrument also broadens the width of the [O ii ] lines. The change in line width due to resolution is given by GLYPH<14>GLYPH<21> R ( z ) defined in Eq. 2. Note that the broadening due to instrumental resolution depends on the redshift because the position of [O ii ] changes with redshift while the resolution element FWHM GLYPH<21> is roughly constant with the wavelength (for a grism spectrograph): By performing a squaring sum of the components in Eq. 1 and 2, we obtain the observed width, denoted w [ O ii ]( z ), of an individual line in the [O ii ] doublet: In order to Nyquist sample the observed [O ii ] doublet at redshift z , the individual line width of the doublet has to be at least twice the doublet separation, or w [ OII ]( z ) = 2 GLYPH<14> [ O ii ]( z ). Rewriting Eq. 3 in terms of this minimum sampling requirement gives the minimal resolution, denoted R ( z ; GLYPH<1> v ), required to split an [O ii ] doublet emitted at redshift z with a velocity dispersion GLYPH<1> v : R ( z ; GLYPH<1> v ) decreases with redshift, increases with the velocity dispersion, and it converges asymptotically towards R [ O ii ]. For a galaxy at z = 1 ([O ii ] is observed at GLYPH<21> GLYPH<24> 7456Å) with GLYPH<1> v = 100 km s GLYPH<0> 1 , the minimum resolution required is Rmin = 3 000. For a galaxy at z = 1 with GLYPH<1> v = 70 km s GLYPH<0> 1 , it is Rmin = 2 800. The spectrograph currently used by SDSSIII / BOSS reaches R GLYPH<24> 2700 > R [ O ii ] at 9 320Å, and therefore it theoretically splits the [O ii ] doublet for galaxies with GLYPH<1> v < 50 km s GLYPH<0> 1 at z GLYPH<21> 1 : 5. With this spectrograph, the observation of the [O ii ] doublet of galaxies with GLYPH<1> v = 100 km s GLYPH<0> 1 will be highly-blended. At low resolution, it is possible to actually see [O ii ] doublets when the lines peaks and valley falls exactly right opposite to the pixels. In the following, when we state 'the doublet is resolved', it is true wherever the emission line lands on the detector. In classical spectrographs, the resolution element FWHM GLYPH<21> is roughly constant with wavelength, and therefore the spectral resolution R is a linear function of the observed wavelength GLYPH<21> . We must therefore define the minimum resolution requirement to be at the lowest redshift limit where [O ii ] becomes the only emission line available in the spectrum. The resolution requirement will automatically be satisfied for all higher redshifts. In this study, we consider the more common case where the spectral range is limited to < 1 GLYPH<22> m .",
"pages": [
2
]
},
{
"title": "3. Simulation",
"content": "To confirm the theoretical considerations of Section 2, we simulate observations of [O ii ] doublets in the presence of Poisson noise. Future massive spectroscopic redshift surveys are primarily focused on obtaining redshifts with only emission lines, which is less demanding in terms of exposure time than requiring the detection of the continuum. For these applications, a Gaussian profile is su GLYPH<14> cient to simulate the resolution e GLYPH<11> ects. Because spectrograph resolution increases with wavelength, the minimal resolution requirement is determined at the shortest wavelength where the [O ii ] doublet becomes the only major emission line feature in the spectrum. Assuming an instrumental wavelength limit of 1 GLYPH<22> m, the resolution requirement for [O ii ] is therefore defined at GLYPH<21> obs ([ O ii ] ; z = 1) GLYPH<24> 7 450Å. Of interest for this work, DEEP2 has obtained a complete spectroscopic sample of [O ii ] emitters at redshift z = 1. Its magnitude limit is r = 24 : 1 and its [O ii ] flux limit is 5 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 (Newman et al. 2012). These limits are deeper than the target selection limits for BAO surveys currently under development. DEEP2 used the DEIMOS grism spectrograph at Keck with a resolution R = 6 000 (Faber et al. 2003) and was limited by the galaxy continuum signal-to-noise. The range of velocity dispersions used in our simulation is empirically determined by observations of z GLYPH<24> 1 [O ii ] emitters within the DEEP2 redshift survey. We set the lower (upper) limit of the investigated range at GLYPH<1> v = 20 km s GLYPH<0> 1 (120 km s GLYPH<0> 1 ), which encompasses most of the galaxies down to r < 24. In terms of instrumental resolution, we explore the range of 2 500 < R < 6 000 sampled by steps of GLYPH<14> R = 3 in resolution. To avoid aliasing problems, for each doublets we add a random number smaller than 3 to the resolution, in order to sample correctly the complete resolution range. We use a sampling of 3 pixels per resolution element. Our results will span a meaningful range of resolutions for numerous spectrographs at GLYPH<21> obs ([ O ii ]) GLYPH<24> 7 500Å, including the current SDSS-III / BOSS spectrograph ( R GLYPH<24> 2 500, Smee et al. (2013)) and future spectrographs such as PFS-SUMIRE ( R GLYPH<24> 3 000 Vivès et al. (2012)) or DESi ( R GLYPH<24> 4 000 Jelinsky et al. (2012)). Weuse a Gaussian function, to model the [O ii ] doublet, given by f gaussian( GLYPH<21>; GLYPH<21> 0 ; GLYPH<27>g ; F 0) = F 0 p 2 GLYPH<25>GLYPH<27>g Exp GLYPH<20> ( GLYPH<21> GLYPH<0> GLYPH<21> 0) 2 2 GLYPH<27> 2 g GLYPH<21> . This produces an emission line centered at GLYPH<21> 0 of total flux F 0. The profile width GLYPH<27>g is linked to the velocity dispersion by GLYPH<27>g = GLYPH<21> [ O ii ] GLYPH<1> v= c . The Gaussian profile has an exponential drop o GLYPH<11> from the emission peak value, and therefore it may not represent systematic e GLYPH<11> ects like scattered light within the spectrograph. A Mo GLYPH<11> at profile recovers the information in the wings of the emission line when GLYPH<12> is allowed to vary. However, the Mo GLYPH<11> at model is only attractive if the data has a high spectral resolution and high signal to noise ratio. Otherwise, the information in the wings will have low significance due to measurement noise. We calibrate the flux f and the sky level to a recent emission line galaxy observational study performed at the SDSS Telescope (Comparat et al. 2013). This study showed the nominal observed total line flux is GLYPH<24> 30 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 and the nominal sky brightness is GLYPH<24> 3 GLYPH<2> 10 GLYPH<0> 18 erg cm GLYPH<0> 2 s GLYPH<0> 1 Å GLYPH<0> 1 arcsec GLYPH<0> 2 at GLYPH<24> 7400Å. This noise level corresponds to detections with a SNR above 7 which should be typical of observations in future BAO survey. In the simulation, we use fluxes f from a broader range, 6 < f < 100 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 . We determine the relative abundance of emission lines at a given flux with the [O ii ] luminosity function at z GLYPH<24> 1 measured by Zhu et al. (2009) on DEEP2 survey. First, we first make a Gaussian doublet at GLYPH<21> obs ([ O ii ]) GLYPH<24> 7450Å for a given resolution R , velocity dispersion GLYPH<1> v , and flux f . The flux ratio between the two lines is fixed at 1, the impact of a varying flux ratio is discussed in the paragraph 4.3. Next, we sample the doublet spectrum at resolution R with 3 pixel per resolution element. We add Poisson sky noise on each pixel (this is the dominating contribution of the observed noise). This creates a mock observation of the [O ii ] emission doublet for the Gaussian profile. Finally, we fit two models to the simulated doublet: a single Gaussian profile, and a double Gaussian profile. From each fit, we compute the S NR and the GLYPH<31> 2 to compare the detections. GLYPH<31> 2 is defined as the usual 'reduced chi-square statistics' by GLYPH<31> i = 1 or 2 = 1 ndof P k 2 pixels ( Ok GLYPH<0> M i k ) 2 N 2 k where ndof is the number of degrees of freedom, O is the array of observed values, M 1 is the model with one line, M 2 is the model with 2 lines, and N is the noise. The number of degrees of freedom vary from 35 to 94 (depending on the spectral resolution used). The S NR is calculated with a Fisher matrix.",
"pages": [
2,
3
]
},
{
"title": "4. Results",
"content": "The simulation contains GLYPH<24> 15 GLYPH<2> 10 6 simulated [O ii ] lines sampling the velocity dispersion, resolution, and flux range set in the above. To statistically di GLYPH<11> erentiate whether an observation of [O ii ] is identified as a doublet or a single emission line (SEL), given that the numbers of degrees of freedom is high (35 < ndof < 94), we use the di GLYPH<11> erence GLYPH<1> GLYPH<31> 2 = GLYPH<31> 1 = ndof 1 GLYPH<0> GLYPH<31> 2 = ndof 2 of the normalized GLYPH<31> 2 . A GLYPH<1> GLYPH<31> 2 = 9 means the single line emission model is ruled out at 3 GLYPH<27> or with a 99.7% confidence level. We compute the share of emission line with r < 24 (convolved by the velocity dispersion distribution of DEEP2) detected as a doublet at the 3 GLYPH<27> confidence levels at redshift 1 as function of the resolution for di GLYPH<11> erent [O ii ] flux detection limit, see Fig. 1. The main trend is that the percentage of doublets increases as a function of the resolution. We can distinguish two regimes. In the regime of low [O ii ] fluxes the gain is linear, i.e. for surveys with a lower limit of [O ii ] detection of 10 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 or below the increase of the share of doublet is linear as a function of the resolution (it corresponds to the line 10 of Fig. 1). For such survey, it indicates the resolution should be the highest possible. For higher [O ii ] fluxes, the marginal increase of the doublet share is large for low resolutions and small for higher resolution. For a survey aiming only to observe the brightest [O ii ] emitters (on Fig. 1), it is not necessary to aim for the highest resolution. R = 3 300 is su GLYPH<14> cient to obtain 90% of doublets. And for R > 3 300, the marginal cost of an extra percent of doublets decreases. The DEEP 2 survey dealt with SEL using a neural network (Kirby et al. 2007). They showed that given a fair spectroscopic sample of an observed population with reliable redshifts, it is possible to infer correct redshifts to nearly 100% of the [O ii ] SEL. The H GLYPH<11> , H GLYPH<12> , and [O iii ] SEL cases are not as well handled by the neural network with e GLYPH<14> ciencies of GLYPH<24> 90%, GLYPH<24> 60%, and GLYPH<24> 60% respectively. The combination of the two latter points shows it will be possible to derive robust [O ii ] redshifts where [O ii ] is the only emission line available in the spectrograph, even if the fraction of 3 GLYPH<27> doublet detections is small.",
"pages": [
3
]
},
{
"title": "4.1. Higher redshift, sky lines, completeness",
"content": "The sky lines have an observed width of one resolution element, therefore their width varies with the resolution. In the case of a single sky line located on a doublet, it is not a problem to subtract the sky line and obtain an accurate redshift. In the case of many contiguous sky lines, it can cover completely a doublet and prevent from getting any redshift in this zone. This causes the survey to have a varying [O ii ] flux limit as a function of the redshift. To quantify the impact of the sky lines obstruction as a function of redshift, we simulate at various resolutions the observation of a sky spectrum. The sky spectrum is taken from Hanuschik (2003). At a given resolution, we convert the wavelength array of the sky into a redshift array corresponding to the [O ii ] redshift. We scan the redshift array by steps of 0.0005 (it corresponds to the desired precision of a spectroscopic redshift). At each step, we compare the median value of the sky (we assume here a sky subtraction e GLYPH<14> cient at 90%) to the flux measured in the middle of an [O ii ] doublet with (where it is the lowest). If the median value of the sky is greater than the value of the doublet, we consider we cannot fit a redshift. Finally, we compute the percentage of the redshift range where we can fit spectroscopic redshifts. We run this test for two settings. A bright survey with [O ii ] fluxes GLYPH<24> 30 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 and fibers of 2' diameter (SDSS-IV / eBOSS-like). A faint survey with [O ii ] fluxes GLYPH<24> 10 GLYPH<2> 10 GLYPH<0> 17 erg cm GLYPH<0> 2 s GLYPH<0> 1 and fibers of 1.5' diameter (DESilike). It shows the impact of the sky lines on the completeness depends weakly on the resolution, the discrepancy between the di GLYPH<11> erent resolution settings is under a couple of percents. For the bright scenario the completeness is greater than 95%. For the faint survey case, the completeness is greater than 80%. This demonstrates how the sky lines impact the redshift completeness of an [O ii ] spectroscopic survey. It shows it is necessary to have the smallest fiber possible to diminish the impact of the sky. The increase in resolution is not useful to cope with this problem. Finally the completeness in redshift is not driven by the resolution at the first order, but by the robustness of sky subtraction and the strength of the [O ii ] flux. To obtain a precise estimate of the impact of sky lines on the redshift distribution completeness, a full end-to-end simulation is needed.",
"pages": [
3,
4
]
},
{
"title": "4.2. Integrated velocity profile",
"content": "In this study, the integrated velocity profile of each galaxy within a fiber is assumed to be Gaussian, although galaxy rotation may create complications. Current data is not su GLYPH<14> cient to explore this particular di GLYPH<14> culty. Nearby galaxies are not representative of the properties of these higher-redshift galaxies, and surveys like MASSIV are limited to a sample of only 50 galaxies in the redshift range 0 : 6 < z < 1 : 6 Epinat et al. (2012).",
"pages": [
4
]
},
{
"title": "4.3. Emission line flux ratio",
"content": "The flux ratio between the forbidden fine structure [O ii ] lines varies with the surrounding electronic density between 0.35 (high electron density limit) and 1.5 (low density limit) (Pradhan et al. 2006). A precise estimation of the distribution of this ratio at z GLYPH<24> 1 has not been measured, although observations show the ratio does not take the extreme values 0.35 or 1.5, but seems to stay around 1.A ratio of one is the best for separating the doublet. A di GLYPH<11> erent ratio can only decrease the e GLYPH<14> ciency at recognizing the doublet. Also this e GLYPH<11> ect is symmetric, a ratio of 0.7 or 1.4 implies the loss of the same amount of doublets. We quantify this e GLYPH<11> ect by varying the flux ratio of the lines simulated between 0.7 and 1. For emission lines with total flux of 10 GLYPH<0> 16 erg cm GLYPH<0> 2 s GLYPH<0> 1 (DESi-like), a flux ratio of 0.7 (or 1.4) induces a decrease in the amount of doublets seen of 8.3% at R GLYPH<24> 4 500. The total number of doublets detected at 3 GLYPH<27> goes from GLYPH<24> 25% to GLYPH<24> 22 : 9%. For emission lines with total flux of 3 GLYPH<2> 10 GLYPH<0> 16 erg cm GLYPH<0> 2 s GLYPH<0> 1 (SDSSIV / eBOSS-like), a flux ratio of 0.7 (or 1.4) induces a decrease in the amount of doublets seen of 9.1% at R GLYPH<24> 3 300. The total number of doublets detected at 3 GLYPH<27> diminishies from GLYPH<24> 90% to GLYPH<24> 81 : 8%.",
"pages": [
4
]
},
{
"title": "5. Conclusion",
"content": "Large spectroscopic redshift surveys are being designed to measure galaxy redshifts using the [O ii ] emission line doublet and trace the large-scale matter distribution. This study shows we should be optimistic regarding their feasibility. We have shown how the observation of the doublet evolves with the instrumental resolution and the line velocity dispersion. Also, we quantified the impact of sky lines on the redshift completeness of such a survey. In light of the numbers obtained, we foresee two strategies about the choice of the resolution for future spectrographs: For bright [O ii ] emitter surveys (like SDSS-IV / eBOSS), a resolution of R GLYPH<24> 2 500 (current SDSS spectrograph) is su GLYPH<14> cient to obtain a fair sample of doublets (60%) in order to train the pipeline to recover all the [O ii ] redshifts. Increasing the resolution to 3 300 allows to get 90% of doublets. For a small increase in resolution, the redshift determination e GLYPH<14> ciency doubles. The impact of the sky lines on the completeness in redshift is smaller than 6%. For faint [O ii ] emitter surveys (like DESi), we recommend to push the resolution to the highest. Knowing there is a limited number of pixels on the detector (4k), and that the highest resolution possible on a three channel spectrograph is R GLYPH<24> 4 500 at 7 500Å, to go beyond, it is necessary to use a four channel spectrograph. Practically with a resolution of 4 500, one would obtain 25% of doublets, which is enough to train the pipeline to assign correct redshift. Acknowledgements. JPK acknowledges support from the ERC advanced grant \"LIDA\". This work was supported by the United States Department of Energy Early Career program via grant de-sc0003960 and by the National Science Foundation via grant AST-0806732.",
"pages": [
4
]
},
{
"title": "References",
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"pages": [
4,
5
]
}
]
2013A&A...560A.113H
https://arxiv.org/pdf/1310.7879.pdf
<document>
<section_header_level_1><location><page_1><loc_21><loc_85><loc_81><loc_87></location>FIRST, a fibered aperture masking instrument</section_header_level_1>
<section_header_level_1><location><page_1><loc_14><loc_82><loc_88><loc_84></location>II. Spectroscopy of the Capella binary system at the diffraction limit</section_header_level_1>
<text><location><page_1><loc_8><loc_78><loc_94><loc_81></location>E. Huby 1 , G. Duchˆene 2 , 3 , F. Marchis 4 , S. Lacour 1 , G. Perrin 1 , T. Kotani 5 , ' E. Choquet 1 , 6 , E. L. Gates 7 , O. Lai 8 , 9 , and F. Allard 10</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_74><loc_91><loc_76></location>1 LESIA, Observatoire de Paris, CNRS, UPMC, Universit'e Paris-Diderot, Paris Sciences et Lettres, 5 place Jules Janssen, 92195 Meudon, France</list_item>
<list_item><location><page_1><loc_11><loc_72><loc_87><loc_73></location>2 Department of Astronomy, University of California at Berkeley, Hearst Field Annex, B-20, Berkeley CA 94720-3411, USA</list_item>
<list_item><location><page_1><loc_11><loc_71><loc_85><loc_72></location>3 UJF-Grenoble 1 / CNRS-INSU, Institut de Plan'etologie et d'Astrophysique (IPAG) UMR 5274, 38041 Grenoble, France</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_68><loc_71></location>4 Carl Sagan Center at the SETI Institute, 189 Bernardo Av., Mountain View CA 94043, USA</list_item>
<list_item><location><page_1><loc_11><loc_68><loc_91><loc_70></location>5 Extrasolar Planet Detection Project O ffi ce, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan</list_item>
<list_item><location><page_1><loc_11><loc_66><loc_66><loc_68></location>6 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA</list_item>
<list_item><location><page_1><loc_11><loc_65><loc_76><loc_66></location>7 University of California Observatories / Lick Observatory, P.O. Box 85, Mount Hamilton, CA 95140, USA</list_item>
<list_item><location><page_1><loc_11><loc_64><loc_57><loc_65></location>8 Gemini Observatory, 670 North A'ohoku Place Hilo, Hawaii 96720, USA</list_item>
<list_item><location><page_1><loc_11><loc_63><loc_56><loc_64></location>9 Subaru Telescope, 650 North A'ohoku Place, Hilo, Hawaii 96720, USA</list_item>
<list_item><location><page_1><loc_11><loc_62><loc_91><loc_63></location>10 CRAL UMR 5574: CNRS, Universit'e de Lyon, ' Ecole Normale Sup'erieure de Lyon, 46 all'ee d'Italie, 6936 4 Lyon Cedex 7, France</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_59><loc_36><loc_60></location>Preprint online version: January 17, 2021</text>
<section_header_level_1><location><page_1><loc_47><loc_57><loc_55><loc_58></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_11><loc_52><loc_91><loc_56></location>Aims. FIRST is a prototype instrument built to demonstrate the capabilities of the pupil remapping technique, using single-mode fibers and working at visible wavelengths. Our immediate objective is to demonstrate the high angular resolution capability of the instrument and to show that the spectral resolution of the instrument enables characterisation of stellar companions.</text>
<text><location><page_1><loc_11><loc_48><loc_91><loc_52></location>Methods. The FIRST-18 instrument is an improved version of FIRST-9, that simultaneously recombines two sets of nine fibers instead of one, thus greatly enhancing the ( u , v ) plane coverage. We report on observations of the binary system Capella at three epochs over a period of 14 months ( /greaterorsimilar 4 orbital periods) with FIRST-18 mounted on the 3-m Shane telescope at Lick Observatory. The binary separation during our observations ranges from 0.8 to 1.2 times the di ff raction limit of the telescope at the central wavelength of the</text>
<text><location><page_1><loc_11><loc_46><loc_19><loc_47></location>spectral band.</text>
<text><location><page_1><loc_11><loc_32><loc_91><loc_46></location>Results. We successfully resolved the Capella binary system at all epochs, with an astrometric precision as good as 1 mas under the best observing conditions. FIRST also gives access to the spectral flux ratio between the two components directly measured with an unprecedented spectral resolution of R ∼ 300 over the 600-850 nm range. In particular, our data allow to detect the well-known overall slope of the flux ratio spectrum, leading to an estimation of the 'pivot' wavelength of 0.64 ± 0.01 µ m, at which the cooler component becomes the brightest. Spectral features arising from the di ff erence in e ff ective temperature of the two components (specifically the H α line, TiO and CN bands) have been used to constrain the stellar parameters. The e ff ective temperatures we derive for both components are slightly lower (5-7%) than the well-established properties for this system. This di ff erence mainly originates from deeper molecular features than those predicted by state-of-the-art stellar atmospheric models, suggesting that molecular line lists used in the photospheric models are incomplete and / or oscillator strengths are underestimated, most likely concerning the CN molecule. Conclusions. These results demonstrate the power of FIRST, a fibered pupil remapping based instrument, in terms of high angular resolution and show that the direct measurement of the spectral flux ratio provides valuable information to characterize little known companions.</text>
<text><location><page_1><loc_11><loc_29><loc_91><loc_31></location>Key words. Instrumentation: high angular resolution - Techniques: interferometric - Binaries : close - Binaries : visual - Stars: fundamental parameters - Stars: individual: Capella</text>
<section_header_level_1><location><page_1><loc_7><loc_25><loc_19><loc_26></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_10><loc_50><loc_24></location>The objective of the FIRST (Fibered Imager foR a Single Telescope) prototype development is the detection of faint companions such as exoplanets. Many instruments currently being designed and manufactured are addressing this challenge, which requires high dynamic ranges at high angular resolution. Di ff erent solutions are implemented such as extreme adaptive optics systems, coronagraphic masks and interferometric techniques (or a combination thereof). FIRST belongs to the latter category since its principle relies on the aperture masking (Hani ff et al. 1987), in which a mask with small holes is put on the pupil of the telescope. In a traditional implementation,</text>
<text><location><page_1><loc_52><loc_11><loc_95><loc_26></location>these holes are organized in a non redundant manner in order to avoid the fringe blurring due to the atmospheric turbulence, which leads to the loss of most of the high spatial frequency information on the object. The image is thus the superimposition of all fringe patterns coded with as many spatial frequencies. Object visibilities corresponding to every subpupil pairs can therefore be retrieved. This technique has been established as a standard for di ff raction limited observations, up to dynamic ranges of a few hundreds, thanks to the routinely used Sparse Aperture Masking mode of the NACO instrument at the VLT (Lagrange et al. 2012; Sanchez-Bermudez et al. 2012; Grady et al. 2013; Cieza et al. 2013) and the Keck NIRC2</text>
<text><location><page_2><loc_7><loc_91><loc_50><loc_93></location>aperture masking experiment (Hinkley et al. 2011; Blasius et al. 2012; Evans et al. 2012).</text>
<text><location><page_2><loc_7><loc_65><loc_50><loc_90></location>FIRST is the implementation of the fibered pupil remapping technique as proposed by Chang & Buscher (1998) and then Perrin et al. (2006) at visible wavelengths. This technique can be seen as a variant of the aperture masking techniquethat aims at increasing the achievable dynamic range. As stated by Baldwin & Hani ff (2002), dynamic range directly depends on the number of sub-pupils and on the accuracy of the observable measurements (visibilities or closure phases for instance). In the FIRST instrument, single-mode fibers o ff er a way to improve these two aspects: (i) they allow to use the whole telescope pupil while their outputs can be non-redundantly recombined and (ii) they spatially filter the wavefront and thus avoid speckle noise. The spatial phase fluctuations due to the atmospheric turbulence are thus traded against flux fluctuations because of the imperfect coupling e ffi ciency into the fibers. However, these can be more easily handled during data reduction than phase fluctuations. A self-calibration algorithm has indeed been proposed to retrieve the complex visibilities without the need of specific photometric channels (Lacour et al. 2007).</text>
<text><location><page_2><loc_7><loc_49><loc_50><loc_65></location>The first light of the instrument was achieved in July 2010 at Lick Observatory with FIRST-9 mounted on the Cassegrain focus of the 3-m Shane telescope (Huby et al. 2012). The instrument has since been significantly improved to increase the number of sub-pupils and the accuracy on the closure phase measurements, and hence the achievable dynamic range. FIRST-9 has thus become FIRST-18, in which 18 sub-pupils are recombined, and has been mechanically enhanced to reach a higher stability. Four observing runs have been conducted between October 2011 and December 2012. Several binary systems have been observed, as these simple objects are particularly suited for testing the capabilities of the instrument.</text>
<text><location><page_2><loc_7><loc_10><loc_50><loc_48></location>Among these binaries, Capella ( α Aurigae, V = 0.08, R = -0.52) has been observed at three di ff erent epochs with FIRST18. Capella is a well-known nearby binary system, that has been studied for more than a hundred years, and its historical record is notably linked to the Lick Observatory and the first measurements with interferometers. The first announcement of discovery of this spectroscopic binary dates indeed from Campbell (1899) who used the Mills spectrograph installed on the 36inch Lick refractor to observe Capella (simultaneously Newall (1899) made the same discovery using the Cambridge spectroscope). Capella later was the first binary system whose astrometric orbit has been interferometrically measured with the 6m baseline Michelson interferometer on the 100-inch telescope at Mount Wilson (Anderson 1920; Merrill 1922). For decades, this friendly target has been observed with various interferometers and speckle imaging techniques. So far, the most accurate measurements of the astrometric orbit have been performed by Hummel et al. (1994) using the Mark III interferometer at Mount Wilson, using baselines from 3 m up to 23.6 m. Concerning the abundant bibliography about Capella, Torres et al. (2009) provide a very complete review of all spectroscopic, as well as interferometric measurements available at that time and they use them to derive the parameters of the system: e ff ective temperatures of 4920 ± 70K and 5680 ± 70K, radii of 11.87 ± 0.56 R /circledot and 8.75 ± 0.32 R /circledot , luminosities of 79.5 ± 4.8 L /circledot and 72.1 ± 3.6 L /circledot and the parameters of the relative orbit. The latest and most accurate masses have been determined by Weber & Strassmeier (2011) using the spectroscopic orbit combined with the inclination of the orbital plane derived from astrometry measurements: 2.573 ± 0.009 M /circledot and 2.488 ± 0.008 M /circledot .</text>
<text><location><page_2><loc_52><loc_63><loc_95><loc_93></location>With an angular separation varying from 41 mas to 56 mas, Capella is therefore an ideal target to probe the capabilities of FIRST-18 at the di ff raction limit, which ranges from 41 mas at 600nm to 58 mas at 850 nm for a 3-m telescope. In this paper, we report on the successful detection of Capella as a binary system at the di ff raction limit of the telescope using FIRST-18, which is described in Sect. 2, along with the data reduction procedure. The results are presented in Sect. 3. The spectrally-dispersed flux ratio measurement is of particular interest as it is the first time that it is directly measured with a R ∼ 300 spectral resolution. Higher-resolution spectra of the two components have been estimated by 'deblending' the composite spectrum of the binary using spectral templates to disentangle them (Barlow et al. 1993). Flux ratio measurements of the system, on the other hand, have been obtained in discrete broad- and narrow-band filters that are too sparsely distributed to provide fine spectral information (Torres et al. 2009). Thus, the FIRST data provide a unique insight into the Capella system and, by extension, all systems with separation as small as the di ff raction limit of a given telescope. In this work, we model our FIRST flux ratio spectrum to constrain the e ff ective temperatures of the Capella binary, thereby demonstrating the power of FIRST to study previously uncharacterized companions in the future.</text>
<section_header_level_1><location><page_2><loc_52><loc_60><loc_81><loc_61></location>2. Observations and data reduction</section_header_level_1>
<text><location><page_2><loc_52><loc_53><loc_95><loc_59></location>Observations were conducted with the 3-m Shane telescope at Lick Observatory from 2011 to 2012 (see Table 1). As in previous observations (Huby et al. 2012), the Shane adaptive optics system provided su ffi cient correction to stabilize the fringes, although it is optimized for the infrared wavelengths.</text>
<section_header_level_1><location><page_2><loc_52><loc_49><loc_62><loc_51></location>2.1. FIRST-18</section_header_level_1>
<text><location><page_2><loc_52><loc_37><loc_95><loc_48></location>After the first light of the instrument obtained in 2010 (Huby et al. 2012), e ff orts have been focused on improvements to the stability, sensitivity and dynamic range achievable with FIRST. The injection part of the instrument (including the pupil imager, the Iris AO segmented mirror used to precisely steer the beams on the fiber cores that are gathered in the fiber bundle, from Fiberguide Industries) is basically unchanged. However significant upgrades have been carried out in the recombination part of the instrument, as can be seen in Fig. 1.</text>
<text><location><page_2><loc_52><loc_10><loc_95><loc_37></location>Assuming that the noise is uncorrelated between the baselines - a reasonable assumption in the photon noise limited regime - the dynamic range increases with the number of visibility and closure phase measurements (Baldwin & Hani ff 2002; Lacour et al. 2011; Le Bouquin & Absil 2012). The main development was therefore aimed at increasing the number of sub-pupils, leading to the FIRST-18 instrument, in reference to the two sets of 9 sub-pupils that are recombined. The nonredundancy of the linear recombination configuration is a technical limit: standard V-groove chips o ff er 48 spaces where fibers can be positioned. The most compact 9-fiber configuration requires n max = 44 spaces, while the 10-fiber and 11-fiber ones require respectively 55 and 75 spaces. In addition, the 9-fiber configuration is also a compromise between the available space on the bench (defining the focal length f ' of the imaging lens), the di ff raction pattern width ( f ' λ/ D , with D corresponding to the V-groove pitch, and also to the collimated beam size at the fiber output) and the sampling of the highest frequency fringe pattern (of period T = f ' λ/ ( n max D )) that fits the detector dimensions. For these reasons, two sets of 9 fibers are recombined independently. Given the 30 available sub-pupils in the obstructed</text>
<figure>
<location><page_3><loc_8><loc_62><loc_50><loc_93></location>
<caption>Fig. 1. Set-up of the FIRST-18 instrument. The injection part of the set-up, up to the fiber bundle, is basically unchanged compared to the previous version of the instrument. The recombination part on the other hand has been duplicated. The EMCCD dedicated to the measurement of the transmitted flux during the optimization procedure has been also depicted. The mirrors drawn as gray lines (just after the V-grooves and microlens arrays) are removable from the light path. Inset a) illustrates the resulting beam shapes after the anamorphic system. Inset b) is a side view of the recombination of the beams (only three beams out of nine are represented). SM: Segmented mirror. PBS : Polarizing beam splitter. µ L : Microlens array. FB: Fiber bundle. VG: V-groove. P: Dispersing prism.</caption>
</figure>
<figure>
<location><page_3><loc_7><loc_27><loc_27><loc_41></location>
</figure>
<figure>
<location><page_3><loc_29><loc_27><loc_49><loc_41></location>
<caption>Fig. 2. Fiber configurations of the entrance pupil, the green and red colors corresponding to each of the two sets of nine fibers. The corresponding polychromatic ( u , v ) plane coverage is represented on the right panel. For clarity, the ( u , v ) plane coverage of each 9-fiber configuration is not symmetrized.</caption>
</figure>
<text><location><page_3><loc_7><loc_10><loc_50><loc_16></location>telescope pupil (see Fig. 2), our selected fiber configuration using 18 of them gives access to 73% of all possible independent baselines. As the instrument is mounted at the Cassegrain focus of the telescope, the ( u , v ) plane coverage does not rotate during the night and is stable in time. However, the ( u , v ) plane coverage</text>
<text><location><page_3><loc_52><loc_91><loc_95><loc_93></location>is significantly extended thanks to the broad wavelength range, as illustrated in Fig. 2.</text>
<text><location><page_3><loc_52><loc_68><loc_95><loc_90></location>Each recombination scheme of the beams is built on the same design as for the previous version. The collimated beams coming from the V-grooves are reshaped thanks to anamorphic systems that mimic the slit of a spectrometer consisting in dispersing prisms (see Fig. 1). The anamorphic system has been designed to satisfy the Nyquist-Shannon sampling condition for the highest frequency fringe pattern (for a given focal length of the imaging lens) on the one hand, and to reach a high spectral resolution on the other. This is achieved thanks to a 4-lens (2 spherical and 2 cylindrical lenses) afocal system performing a beam elongation of 20 in the direction of dispersion and a compression of 7 in the orthogonal direction. The two fringe patterns are imaged on the same detector side by side along the wavelength axis. Spectral filters have been inserted in each arm in order to avoid overlapping of the patterns. In the center of the detector, the fringe patterns are cut at 600 nm and 850 nm thereby defining the spectral range of the instrument.</text>
<text><location><page_3><loc_52><loc_58><loc_95><loc_68></location>Improvement of the data quality has also been provided by the use of a more e ffi cient detector, an Hamamatsu EMCCD camera, with maximal EM gain of 1200, quantum e ffi ciency of 90 %, 77 % and 54 % at 600, 700 and 800 nm, respectively, and 512 × 512 pixels 16 µ m wide. The overall mechanical stability has been enhanced too, allowing to observe objects up to 40 · from zenith without significant loss of flux due to mechanical flexures.</text>
<section_header_level_1><location><page_3><loc_52><loc_54><loc_71><loc_55></location>2.2. Acquisitionprocedure</section_header_level_1>
<text><location><page_3><loc_52><loc_45><loc_95><loc_53></location>Capella was observed in October 2011, July 2012 and December 2012 with FIRST-18 mounted on the 3-m Shane telescope at Lick Observatory. The observation log is reported in Table 1. Several bright (0 /lessorsimilar R /lessorsimilar 3) single stars were observed immediately before / after Capella so serve as calibrator for closure phase measurements and baseline calibration (see Sect. 3.2).</text>
<text><location><page_3><loc_52><loc_22><loc_95><loc_45></location>The acquisition procedure is similar to the description given in Huby et al. (2012). One data set comprises fringe sequences, fiber calibration files (every fiber di ff raction pattern is recorded individually), and background files. However, this procedure has been significantly shortened compared to the previous observations thanks to the implementation of a dedicated optimization path in the optical set-up. The injection of the flux into the fibers is indeed very sensitive and must be optimized at every target switch, to compensate for residual mechanical flexures occurring in the instrument but also in the AO system. While this optimization was done one fiber at a time in 2010 (by scanning the corresponding micro-segment and measuring the transmitted flux directly on the science camera), it is now done simultaneously for all fibers thanks to a motorized mirror system that allows to image all the output fibers on a dedicated detector. The 18 corresponding micro-segments can therefore be scanned at the same time. The optimization is now completed in less than two minutes leading to a substantial gain in time and stability.</text>
<section_header_level_1><location><page_3><loc_52><loc_18><loc_66><loc_19></location>2.3. Datareduction</section_header_level_1>
<text><location><page_3><loc_52><loc_10><loc_95><loc_17></location>The basic principles of the FIRST data analysis are based on the P2VM method ( Pixel to Visibility Matrix ), that was first developed for the AMBER instrument at the VLTI (Millour et al. 2004) and subsequently adapted to FIRST data, as described in more detail in Huby et al. (2012). The current data reduction process consists of the following steps:</text>
<table>
<location><page_4><loc_10><loc_49><loc_46><loc_84></location>
<caption>Table 1. Observation log, including the dates of observation, the type of target (AC stands for astrometric calibrator and C for closure phase calibrator), the number of images acquired with an integration time tint and an estimate of the r 0 parameter (evaluated thanks to the AO system occasionally once or twice during one sequence of observations).</caption>
</table>
<figure>
<location><page_4><loc_12><loc_26><loc_45><loc_48></location>
<caption>Spectral channel</caption>
</figure>
<paragraph><location><page_4><loc_7><loc_10><loc_50><loc_23></location>Fig. 3. Mean power spectral density computed from 5000 50 msimages for Capella on 2011 Oct. 16 using data from a single Vgroove. The color-scale has been adjusted discarding the zerofrequency peak (not visible on the image). The fitted peak positions are superposed as dashed white lines, only on the left part of the image for better visibility. The (telluric) absorption line appearing at spectral channel number 147 is exactly vertical, showing that the distortion in the image has been e ff ectively corrected. At least 27 di ff erent peaks are clearly visible out of the 36 expected ones.</paragraph>
<unordered_list>
<list_item><location><page_4><loc_53><loc_92><loc_87><loc_93></location>-background (including dark current) subtraction ;</list_item>
<list_item><location><page_4><loc_53><loc_91><loc_74><loc_92></location>-optical distortion correction ;</list_item>
<list_item><location><page_4><loc_53><loc_88><loc_95><loc_90></location>-spectral calibration based on the fitting of telluric absorption lines and features of the stellar spectrum ;</list_item>
<list_item><location><page_4><loc_53><loc_85><loc_95><loc_88></location>-fitting of the fringe spatial frequencies by adjusting the peak positions in the mean power spectral density ;</list_item>
<list_item><location><page_4><loc_53><loc_83><loc_95><loc_85></location>-calibration of the P2VM matrix from individual fiber profiles and spatial frequencies ;</list_item>
<list_item><location><page_4><loc_53><loc_80><loc_95><loc_83></location>-pseudo-inversion of the P2VM matrix and computation of the best parameter sets in the least-squares sense ;</list_item>
<list_item><location><page_4><loc_53><loc_79><loc_73><loc_80></location>-closure phase computation ;</list_item>
<list_item><location><page_4><loc_53><loc_76><loc_95><loc_79></location>-closure phase calibration by measurements obtained on an unresolved target.</list_item>
</unordered_list>
<text><location><page_4><loc_52><loc_68><loc_95><loc_75></location>The distortion mentioned in the second step of the reduction results from astigmatism introduced by the prism, and has an amplitude of about 10-15 pixels. The shape of this distortion is evaluated by detecting the position of the deepest telluric absorption line and is corrected by horizontally interpolating and shifting the image values.</text>
<text><location><page_4><loc_52><loc_49><loc_95><loc_67></location>The spectral calibration is done using the UVES sky emission atlas Hanuschik (2003). As the light is spectrally dispersed through an SF2-prism, there are two parameters defining the wavelength as a function of the pixel: the angle of incidence on the prism i , which a ff ects the spectral resolution, and the central wavelength λ 0. The continuum of the spectrum is fitted and subtracted, leaving only (stellar and telluric) absorption features. The same procedure is applied to the synthetic spectrum, and the parameters i and λ 0 are retrieved by maximizing the correlation product between the two spectra. A fine adjustment is then performed by fitting the peak positions of the power spectral density computed over all images. The results of this fit is shown in Fig. 3 where the fitted peak positions are superposed to the mean power spectral density.</text>
<text><location><page_4><loc_52><loc_39><loc_95><loc_49></location>After applying the P2VM method, the complex coherent fluxes are thus retrieved and their phases are combined to estimate closure phases. The data reduction output comprises 84 closure phase measurements for each of about 180 spectral channels from 600 nm to 850 nm. Since spatial frequency depends on wavelength, specific signal appears in the closure phase plotted as a function of wavelength, depending on the structure of the target.</text>
<section_header_level_1><location><page_4><loc_52><loc_36><loc_72><loc_37></location>2.4. Fittingofabinarymodel</section_header_level_1>
<text><location><page_4><loc_52><loc_27><loc_95><loc_35></location>The final step in the analysis consists of fitting the closure phase estimates with a binary model. Three parameters are optimized by minimizing the χ 2 function: two angular parameters defining the position of the companion, α and δ , and a flux ratio for each spectral channel, ρ ( λ ). The closure phase model function corresponding to a binary directly reads (Le Bouquin & Absil 2012):</text>
<formula><location><page_4><loc_52><loc_23><loc_95><loc_26></location>f ( α, δ, ρ ) = arg ( (1 + ρ e i α i j )(1 + ρ e i α jk )(1 + ρ e i α ki ) (1 + ρ ) 3 ) , (1)</formula>
<text><location><page_4><loc_52><loc_21><loc_55><loc_22></location>with</text>
<formula><location><page_4><loc_52><loc_17><loc_95><loc_20></location>α i j ( α, δ ) = 2 π ( α uij + δ vi j ) , (2)</formula>
<text><location><page_4><loc_52><loc_10><loc_95><loc_18></location>where uij and vi j are the projections of the spatial frequency vector -→ si j corresponding to the sub-pupils i and j , on two orthonormal axes defined by the segmented mirror reference frame (see Sect. 3.2 for details concerning the baseline calibration). This vector expresses as -→ si j = -→ Bij /λ with -→ Bij the baseline vector represented in the telescope pupil.</text>
<figure>
<location><page_5><loc_8><loc_57><loc_94><loc_93></location>
<caption>Fig. 4. Closure phase measurements obtained on 19 th October 2011 (black points with rescaled error bars such that the reduced χ 2 per spectral channel is unity) and best fit model (red points) computed from the best estimates of the binary parameters.</caption>
</figure>
<text><location><page_5><loc_7><loc_47><loc_50><loc_51></location>The χ 2 function is therefore 3 dimensional. For every spectral channel, the contributions of all n CP closure phases are added quadratically:</text>
<formula><location><page_5><loc_7><loc_43><loc_50><loc_46></location>χ 2 λ ( α, δ, ρ ) = n CP ∑ k ∆ CP k λ 2 σ k λ 2 , (3)</formula>
<text><location><page_5><loc_7><loc_40><loc_45><loc_42></location>with σ k λ the error on closure phase k at wavelength λ and</text>
<formula><location><page_5><loc_7><loc_38><loc_50><loc_39></location>∆ CP k λ = CP k λ -f k λ ( α, δ, ρ ) (mod 2 π ) , (4)</formula>
<text><location><page_5><loc_7><loc_35><loc_50><loc_37></location>is the phase di ff erence between the data and the model, defined modulo 2 π .</text>
<text><location><page_5><loc_7><loc_31><loc_50><loc_34></location>Under the assumption that the noise a ff ecting the data follows a Gaussian distribution, the likelihood function can be derived from the χ 2 function by:</text>
<formula><location><page_5><loc_7><loc_25><loc_50><loc_30></location>L λ ( α, δ, ρ ) ∝ exp -χ 2 λ ( α, δ, ρ ) 2 . (5)</formula>
<text><location><page_5><loc_7><loc_23><loc_50><loc_26></location>The proportional symbol is used as the likelihood function is normalized afterwards.</text>
<text><location><page_5><loc_7><loc_18><loc_50><loc_23></location>The optimal value for a given parameter can then be retrieved after marginalizing the likelihood function, i.e. by integrating over all other parameters. For the α parameter for instance, it is expressed as:</text>
<formula><location><page_5><loc_7><loc_15><loc_27><loc_17></location>L λ ( α ) = /iintegdisplay L λ ( α, δ, ρ )d δ d ρ.</formula>
<text><location><page_5><loc_7><loc_8><loc_50><loc_14></location>Similarly, a circular permutation over the set of parameters leads to L λ ( δ ) and L λ ( ρ ). For every spectral channel, the optimal parameter sets ( ˜ αλ, ˜ δλ, ˜ ρ ( λ ) ) are then determined by the median</text>
<text><location><page_5><loc_52><loc_49><loc_95><loc_51></location>value of these probability densities, and the associated error bars are defined as the 68% confidence interval.</text>
<text><location><page_5><loc_52><loc_38><loc_95><loc_48></location>The λ dependence has been noted di ff erently for the position parameters and the flux ratio since the position of the companion is achromatic. The ˜ αλ and ˜ δλ have therefore been averaged in order to determine the final position ( ˜ α, ˜ δ ) . Around 20 % of the data points with the worst error bars have not been taken into account to compute the averaged position, in order to discard aberrant points. The associated error bars on ˜ α and ˜ δ are computed from the standard deviation of the respective distributions.</text>
<section_header_level_1><location><page_5><loc_52><loc_35><loc_60><loc_36></location>3. Results</section_header_level_1>
<section_header_level_1><location><page_5><loc_52><loc_33><loc_69><loc_34></location>3.1. ThecaseofCapella</section_header_level_1>
<text><location><page_5><loc_52><loc_20><loc_95><loc_32></location>The calibrated closure phases of Capella are shown in Fig. 4. As is readily apparent, large deviations from the null closure phase are detected. Large phase changes of ∼ ± π indeed occur when the observed object is centrosymmetric, indicating here that the flux ratio between the two components is close to unity, as is expected for the Capella binary system at visible wavelengths. The fact that the transitions are smooth indicates that the flux ratio is not exactly equal to one. Thus these observations have clearly resolved the binary system.</text>
<text><location><page_5><loc_52><loc_10><loc_95><loc_20></location>However, some of these phase transitions occur in the opposite direction than expected by the best fit model (see the second closure phase graph in the first row of Fig. 4 for instance). This e ff ect is observed in around 6 % of all closure phase measurements (84 × 2 closure phases per date of observation). A possible explanation is that the measurements may be a ff ected by an uncalibrated bias on the imaginary part of the bispectrum. In this case, a sharp transition from 0 to ± π (imaginary part initially</text>
<table>
<location><page_6><loc_13><loc_77><loc_88><loc_85></location>
<caption>Table 2. Companion position measurements for the outer Algol system (C relative to A + B) converted into angular separation and position angle. The ratio between the measured and theoretical angular separations give an estimate of the corrective scaling factor. The di ff erences in position angle indicate the rotation of the segmented mirror reference frame relative to the North-East orientation. Horizontal lines separate the three observing runs considered here. Correction factors are assumed to be constant within a given observing run.Table 3. Angular parameter estimates for Capella at di ff erent observation dates. The reference axes are defined by the segmented mirror orientation which is actually rotated compared to the North-East orientation. The uncorrected estimates do not take the rotation of the image plane and the scaling factor into account, while the corrected ones are the final estimates. Horizontal lines separate the three observing runs considered here.</caption>
</table>
<table>
<location><page_6><loc_13><loc_57><loc_89><loc_67></location>
</table>
<text><location><page_6><loc_7><loc_51><loc_50><loc_54></location>equal to 0) can therefore be turned into a smoother transition from 0 to π or -π , depending on the sign of the bias o ff set.</text>
<text><location><page_6><loc_7><loc_42><loc_50><loc_51></location>This is most likely the reason why the minimum of the reduced χ 2 function is generally much larger than 1. It reaches up to ∼ 40 (for one spectral channel) in the worst cases. Therefore, prior to computing the likelihood functions, the statistical error bars are scaled such that the minimum of the reduced χ 2 function per spectral channel is 1 (error bars in the Fig. 4 are rescaled accordingly).</text>
<text><location><page_6><loc_7><loc_32><loc_50><loc_42></location>Another consequence of these transitions in the wrong direction is that it sharpens the transition when averaging closure phase datasets. The mean value of two transitions in opposite direction will indeed result in values globally closer to ± 180 · or 0 · . This can potentially translate into flux ratios that are biased towards unity. As detailed in the next section, the eventuality cannot be completely discarded when analyzing the spectral flux ratio.</text>
<text><location><page_6><loc_7><loc_19><loc_50><loc_32></location>It can be noted though, that averaging over the closure phase has been performed using complex phasors in order to take into account that the phase is known modulo 2 π . This is necessary to compute the correct phase, especially in the case of phases around ± 180 · , but that obviously does not prevent such bias effect. However, the final flux ratio estimates are assumed to be less a ff ected by this bias, as they result from the average over two independent measurements provided by the two sets of simultaneously recombined fibers, and also from the average over the di ff erent dates of observations.</text>
<text><location><page_6><loc_7><loc_10><loc_50><loc_19></location>Since the source of this bias is still unknown (photon bias only a ff ects the real part of the bispectrum as established by Wirnitzer 1985), this e ff ect becomes obvious only once the best fit model has been determined. There is thus no objective criterion that could allow to discriminate these biased data a priori . Nonetheless, closure phase error bars resulting from the average over all datasets corresponding to one date of observation are</text>
<text><location><page_6><loc_52><loc_49><loc_95><loc_54></location>necessary larger when there is an uncertainty on the transition direction. As can be seen in Fig. 4, error bars are much larger around phase transitions. As a consequence, these points are less weighted in the fit.</text>
<section_header_level_1><location><page_6><loc_52><loc_45><loc_59><loc_46></location>3.2. Orbit</section_header_level_1>
<text><location><page_6><loc_52><loc_32><loc_95><loc_44></location>The analysis of our results concerning the companion position requires a calibration of the ( u , v ) plane, that is a calibration of the baseline lengths and orientations (as explained by Woillez & Lacour 2013, under the imaging baseline section). For the fit, the baselines are conveniently defined by their theoretical lengths and orientation taken in a reference frame linked to the segmented mirror. However, to be scientifically useful, these need to be transformed into the angular separation of the binary and its position angle relative to North. Two aspects have to be considered for the calibration:</text>
<unordered_list>
<list_item><location><page_6><loc_53><loc_26><loc_95><loc_30></location>-the magnification factor between the telescope pupil and the pupil that is imaged in the FIRST instrument can vary with the alignment ;</list_item>
<list_item><location><page_6><loc_53><loc_23><loc_95><loc_26></location>-the rotation angle between the sky East-West / North-South orientation and the reference frame linked to the segmented mirror orientation.</list_item>
</unordered_list>
<text><location><page_6><loc_52><loc_15><loc_95><loc_21></location>The rotation of the pupil plane is due to the periscope sending the beam from the adaptive optics bench towards the hole through the FIRST bench. It uses a mirror combination working at angles di ff erent from 45 · that therefore induces an unknown rotation of the pupil relative to the sub-pupils.</text>
<text><location><page_6><loc_52><loc_10><loc_95><loc_15></location>The calibration over all baselines can thus be performed by estimating two parameters: a scaling factor and a rotation angle. This is done by measuring the position of another wellknown binary star, using the same data reduction pipeline as for</text>
<text><location><page_7><loc_7><loc_80><loc_50><loc_93></location>Capella. Among the binary systems observed at the same epochs as Capella, the triple system of Algol ( δ Per) is an ideal calibrator. The inner system (Algol A of type B8V and Algol B of type K2IV) of orbital period 2.87 days and semi-major axis of 2.3 mas is unresolved by a 3-m telescope. On the other hand, the outer system (Algol A + B and Algol C of type F1V) of orbital period ≈ 680days, semi-major axis of 93.8 mas and flux ratio estimated to 10 at visible wavelengths is well detected by FIRST-18. Its orbital period is much longer than the Capella period (104 days) and makes it a suitable target for the baseline calibration.</text>
<text><location><page_7><loc_7><loc_70><loc_50><loc_80></location>The relative positions of Algol A + B and C have therefore been estimated for several dates during the various runs, as shown in Table 1. The results are shown in Table 2. The position parameters have been converted into polar coordinates in order to derive the angle for the rotation to be applied to the field of view. The predicted positions are computed from the orbit resulting from the measurements with the CHARA interferometer fitted by Baron et al. (2012).</text>
<text><location><page_7><loc_7><loc_44><loc_50><loc_69></location>The Algol system was observed twice during both the October 2011 and December 2012 observing runs. In both cases, multiple observations of the systems within a given observing run yield consistent calibration factors at the 2 σ level or better (see Table 2). This confirms the expectation that the rotation of the pupil in comparison with the FIRST sub-pupils is stable over the duration of an observing run since the injection part of the set-up was not modified during the course of each run. In October 2011, uncertainties on the calibration factors are much larger on October 16 than on October 19, probably as a consequence of changes in r 0 (see Table 1) and short atmospheric coherence time. While the latter could not be measured, the shorter integration times used on October 16, which results from a compromise between sensitivity and fringe visibility, is indicative of a shorter timescale for atmospheric turbulence. We therefore use the estimated position of Algol C regarding Algol A + B on October 19 to correct for the pupil rotation and scaling factor for all three dates of observation in October 2011. For the December 2012 observing run, we use the weighted average of both observations of Algol since they have similar precision.</text>
<text><location><page_7><loc_7><loc_25><loc_50><loc_43></location>The final relative astrometry of the Capella system throughout our observations is shown in Fig. 5. The orbit computed from the model parameters fitted by Torres et al. (2009) is drawn for comparison. Table 3 presents both uncorrected and corrected (field rotation and scaling factor taken into account) estimates, along with their associated uncertainties. Most estimates are in agreement with the predicted positions within the 1σ range. However, the positions measured in 2011 seem to be a ff ected by a small systematic error of about 2 mas along the N-S direction (see Fig. 5, bottom). It is plausible that this results from the baseline calibration, since all three points have been calibrated by the same astrometric estimate for the Algol system. Ideally, the calibrator should have been observed with su ffi cient accuracy at the three di ff erent dates.</text>
<section_header_level_1><location><page_7><loc_7><loc_22><loc_21><loc_23></location>3.3. Spectralmodel</section_header_level_1>
<text><location><page_7><loc_7><loc_10><loc_50><loc_21></location>Along with the astrometry of the binary, our analysis also yields a 'spectrum' of the binary flux ratio, ρ ( λ ). We have inspected the quality of the flux ratio spectra from each individual night and each of the two separate V-grooves. As expected given seeing conditions, the flux ratios measured on December 2012 are of much worse quality than those from October 2011. Similarly, the July 2012 flux ratio spectrum is very noisy, owing to observations taken during early-morning twilight. While the astrometric position estimates from these epochs benefit from the av-</text>
<figure>
<location><page_7><loc_55><loc_68><loc_91><loc_93></location>
</figure>
<figure>
<location><page_7><loc_52><loc_56><loc_73><loc_67></location>
</figure>
<figure>
<location><page_7><loc_74><loc_56><loc_94><loc_67></location>
<caption>Fig. 5. Capella companion positions relative to the predicted orbit. Top: Measured positions at di ff erent epochs: red for October 2011, blue for July 2012 and green for December 2012. Expected companion positions are marked as black dots and measurement points are drawn with error bars. Bottom: Di ff erence between the estimated and expected values of the projection of the binary separation along the right ascension and declination axes. Each point corresponds to one observation date ranged in chronological order: 2011 October 16, 17 and 19, 2012 July 29 and 2012 December 19 and 20.</caption>
</figure>
<text><location><page_7><loc_52><loc_24><loc_95><loc_38></location>age over all spectral channels and are thus reasonably accurate, the flux ratio spectra obtained during the 2012 runs have been discarded for the spectral analysis. We therefore averaged all October 2011 datasets to produce a final flux ratio spectrum for the Capella binary system. The resulting final spectral resolution is about 1.5 pixel as determined from data taken using a monochromatic laser beam. Uncertainties on the flux ratio spectrum were estimated as the standard deviation of the mean over the datasets. These results are available at the CDS (column 1 lists the wavelengths in nm, column 2 and 3 give the flux ratio and their uncertainty, respectively).</text>
<text><location><page_7><loc_52><loc_10><loc_95><loc_24></location>The flux ratio spectrum obtained with FIRST agrees with historical measurements of the binary taken within our wavelength range at the /lessorsimilar 2 σ level. Furthermore, our spectrally dispersed observations reveal an overall slope that is consistent with data over a broader range and confirm that the cool component of the system is increasingly brighter at longer visible wavelengths. We find that the flux ratio reversal occurs at a wavelength of 0.64 ± 0.01 µ m. In addition to its general slope, the FIRST flux ratio spectrum reveals finer structures, such as a sharp peak at 0.655 µ m and two broad dips around 0.69-0.75 µ m and 0.780.84 µ m. Both can be traced to the di ff erence in e ff ective tem-</text>
<figure>
<location><page_8><loc_9><loc_65><loc_63><loc_92></location>
<caption>Fig. 6. Flux ratio for the Capella binary as a function of wavelength as measured with FIRST (gray diamonds). All curves represent predicted flux ratio spectra based on the PHOENIX grid of models and the set of solar abundances from Asplund et al. (2009). The blue dot-dashed curve shows the predicted flux ratio spectrum for the stellar parameters inferred by Torres et al. (2009), while the solid black curve represents the formal best fit (in the χ 2 sense) to the flux ratio spectrum from the solar metallicity model grid. The red dashed curve shows the best fit for the model grid for a metallicity of [ m / H] = + 0 . 5. Stellar parameters for all three models are listed in Table 4. The main atomic and molecular features that drive the model fitting are identified.</caption>
</figure>
<text><location><page_8><loc_7><loc_53><loc_50><loc_62></location>re between the two stars, which leads to photospheric features of di ff erent depths: the former is H α (the slight mismatch in wavelength results from a mild inaccuracy in our wavelength solution) while the latter two are molecular bands (most notably TiO and CN) that are characteristic of cool photospheres. These spectral features are a direct confirmation that the infrared-bright component is cooler than the visible-bright one.</text>
<text><location><page_8><loc_7><loc_31><loc_50><loc_53></location>To quantify the constraint on stellar properties provided by the FIRST flux ratio spectrum, we use the most recent BTSettl models 1 partially published in a review by (Allard et al. 2012a) and described by Allard et al. (2012b). These model atmospheres are computed with the PHOENIX multi-purpose atmosphere code version 15.5 Allard et al. (2001) solving the radiative transfer in 1D spherical symmetry, with the classical assumptions: hydrostatic equilibrium, convection using the mixing length theory, chemical equilibrium, and a sampling treatment of the opacities. The models use a mixing length as derived by the radiation hydrodynamic simulations of Ludwig et al. (2002, 2006) and Freytag et al. (2010, 2012) and a radius as determined by the Bara ff e et al. (1998) interior models as a function of the atmospheric parameters ( T e ff , log g , [ m / H]). The reference solar elemental abundances used in this version of the BT-Settl models are those defined by Asplund et al. (2009). For solar metallicity and higher, no α element enhancement is required.</text>
<text><location><page_8><loc_7><loc_12><loc_50><loc_30></location>The PHOENIX library includes stellar spectra with a 100 K and 0.5 sampling in T e ff and log g , respectively. We explored the parameter space as follows: each model consisted on two pairs of stellar parameters ( T e ff and log g for each component). The model flux ratio is computed using the same sampling and resolution as the FIRST data and normalized so as to match the observed median flux ratio. Since the PHOENIX emission spectra are given per unit surface area, this normalization is equivalent to setting the ratio of stellar radii to best match the median flux ratio in our spectral bandpass. In principle, our analysis could consider this ratio as a free parameter in the fit instead. However, since the FIRST flux ratios are in good agreement with previous flux ratio estimates of the binary, we do not expect to gain additional insight on the ratio of stellar radii. We therefore de-</text>
<text><location><page_8><loc_52><loc_50><loc_95><loc_62></location>cided to remove one free parameter from our fit by using this a priori normalization to ensure that the model fitting was primarily attempting at reproducing the global slope and finer spectral features, which depend only on the stellar e ff ective temperatures and surface gravities. We believe that our data are more apt at constraining the latter. Nonetheless, we note that our normalization for the best fit models is consistent at the 1 σ level with the stellar radii ratio of 0 . 737 ± 0 . 044 estimated by Torres et al. (2009).</text>
<text><location><page_8><loc_52><loc_31><loc_95><loc_50></location>We thus create a grid of flux ratio spectra that depends on four parameters, the e ff ective temperature and surface gravity of both components while approximately maintaining the average stellar luminosity ratio in the FIRST bandpass. By performing a wide grid search around the stellar parameters derived by Torres et al. (2009), the best fitting model has the following parameters: T hot e ff = 5300K, T cool e ff = 4700K, log g hot = log g cool = 2 . 0. This combination of stellar parameters yields a reasonably good match to the observed flux ratio spectrum (reduced χ 2 = 2 . 89, see Fig. 6 and Table 4). We note that there is another peak appearing in the likelihood distribution, corresponding to a model with T hot e ff = 5500K, T cool e ff = 4800K and leading to a marginally poorer χ 2 , which provides a sense for the uncertainties on the derived stellar e ff ective temperatures.</text>
<text><location><page_8><loc_52><loc_17><loc_95><loc_31></location>The stellar parameters derived here are significantly di ff erent from those estimated by Torres et al. (2009), although the e ff ective temperatures are only 4-7% smaller than their nominal values. As shown in Fig. 6, the higher e ff ective temperatures proposed by Torres et al. (2009) also result in detectable molecular features in the flux ratio spectrum, although they are less marked than in our data (this is particularly true for the 0.780.84 µ m feature). This issue can be partially alleviated by using synthetic stellar spectra corresponding to lower surface gravity strengths. However, the overall quality of the fit is much poorer (see Table 4).</text>
<text><location><page_8><loc_52><loc_10><loc_95><loc_16></location>One solution to improve the fit consists in using a metal-rich composition. Using the series of PHOENIX models computed for [ m / H] = + 0 . 5 (where elemental abundances are increased uniformly from the set of solar abundances), we find that the FIRST data are best fit using e ff ective temperatures of 5600 and 4900 K</text>
<text><location><page_9><loc_7><loc_83><loc_50><loc_93></location>and surface gravities of log g hot = 2 . 5 and log g hot = 2 . 5. This model is significantly better (reduced χ 2 = 2 . 31, see Fig. 6) than the best fit model at solar metallicity, and has stellar properties in good agreement with Torres et al. (2009). However, the super-solar metallicity is at odds with all estimates for the components of the system. We thus conclude that the observed flux ratio spectrum of the Capella binary does not conform perfectly to the prediction of stellar atmosphere models.</text>
<text><location><page_9><loc_7><loc_54><loc_50><loc_83></location>Breaking down the information provided by the FIRST flux ratio spectrum, it appears that the overall slope across the 0.60.85 µ m is reasonably well fit with both the nominal e ff ective temperatures and the lower values preferred by the model fitting above, so long as the di ff erence in e ff ective temperatures between the two components is about 10-12%. Thus it appears that the spectral features, specifically the depth of the molecular bands, represent the main culprit in forcing the fit away from the nominal stellar parameters. As mentioned in the previous section, we cannot exclude with certainty that a subtle bias in our data analysis is a ff ecting the resulting flux ratio spectrum, possibly because the system is close to a unity flux ratio. However, we find it extremely unlikely that this bias could a ff ect the wavelengths where molecular features are present but not the adjacent continuum. Indeed, such biases are expected to be present where the closure phases undergo large shift (from ± π to 0 for instance), as explained in the Section 3.1. This is therefore expected to be independent of spectral features, as the occurrence of these shifts only depends on the spatial frequencies ( ∝ B /λ , B corresponding to the baseline) involved in the closure triangle. We thus believe that the mismatch between observations and models is an astrophysical e ff ect instead.</text>
<text><location><page_9><loc_7><loc_19><loc_50><loc_54></location>Cooler e ff ective temperatures, lower surface gravities and / or higher metallicity are all factors that result in deeper molecular bands in each component and in an increased di ff erence in their strength, resulting in deeper features in the flux ratio spectrum as well. Since the stellar parameters of the Capella binary have been precisely determined, our FIRST flux ratio spectrum thus demonstrates that the molecular absorption bands in the spectra of each component are deeper than predicted by the models. One possible explanation for this shortcoming of the models is that the molecular opacities are underestimated in the models, because of incomplete line lists being used and / or underestimated oscillator strengths. Departures from local thermal equilibrium in stellar atmospheres can induce substantial e ff ects for A-type stars but are negligible in the range of e ff ective temperatures relevant to the Capella system. The two molecules that account for most of the opacity in the spectral features observed with FIRST are TiO and CN. For the former molecule, the version of the PHOENIX models used here are based on the line lists and oscillator strengths from Plez (1998). The CN line list and oscillator strengths are adopted from the SCAN database (Jorgensen & Larsson 1990). We believe that the TiO molecule, whose features are frequent in a broad range of cool stars, is much better calibrated and thus conclude that the reason for the under-prediction of these features by current atmospheric features most likely stems from the treatment of the CN molecule, either through the incompleteness of its line list or as a result of oscillator strengths that are too low.</text>
<section_header_level_1><location><page_9><loc_7><loc_16><loc_40><loc_17></location>4. Summary of findings and conclusion</section_header_level_1>
<text><location><page_9><loc_7><loc_10><loc_50><loc_15></location>In order to demonstrate the capabilities of a fibered aperture masking instrument like FIRST to provide valuable spectrallydispersed information on binary systems whose separation is on the order of the di ff raction limit, the results presented in this pa-</text>
<text><location><page_9><loc_52><loc_80><loc_95><loc_93></location>Table 4. Stellar parameters of the PHOENIX atmospheric models used in this analysis from Allard et al. (2012b) and assuming the set of solar abundances from Asplund et al. (2009). The first two models are at solar metallicity while the third one is assuming super-solar metallicity. All three models are shown in Fig. 6. The parameters adopted to mimic those from Torres et al. (2009) are slightly di ff erent from those given in their paper because of the discrete sampling of the PHOENIX model grid. The last line of the table gives the ratio of stellar radii derived from the scaling factor used to normalize the spectra as a first step of the modelling.</text>
<table>
<location><page_9><loc_57><loc_69><loc_90><loc_79></location>
<caption>References. 1 Torres et al. (2009).</caption>
</table>
<text><location><page_9><loc_52><loc_49><loc_95><loc_63></location>per are focused on the binary star Capella. Its separation is indeed comparable to the di ff raction limit and its flux ratio close to unity at visible wavelengths. Capella has been observed at three di ff erent epochs between 2011 and 2012 with FIRST-18 mounted on the 3-m Shane telescope of Lick Observatory (using its adaptive optics system as a fringe tracker). The secondary componenthas been detected at, or slightly below, the di ff raction limit of the telescope at visible wavelengths with an accuracy well below a tenth of the di ff raction limit. This first achievement illustrates the high angular resolution capability of the instrument.</text>
<text><location><page_9><loc_52><loc_27><loc_95><loc_49></location>Using FIRST, we have also directly measured, for the first time, the flux ratio of the binary system at a spectral resolution of R ∼ 300 between 600 and 850nm. This spectral range gives access to spectral features (H α line, TiO and CN bands) that are quite influential when comparing the observed flux ratio spectrum with predictions based on PHOENIX library of synthetic spectra. The e ff ective temperatures derived from this analysis are slightly o ff set (by 5-7%) from those estimated by Torres et al. (2009) based on the extensive literature on this system. While we cannot exclude a subtle bias a ff ecting our flux ratio measurements arising from the fact that the flux ratio is close to unity, this discrepancy probably indicates that the photospheric models used to predict the synthetic spectra are based on incomplete line lists and / or underestimated oscillator strengths for molecules commonly found in G- and K-type giants (most likely CN). This conclusion illustrates the power of FIRST in bringing valuable spectral information to characterize binary systems.</text>
<text><location><page_9><loc_52><loc_10><loc_95><loc_25></location>Acknowledgements. The authors would like to thank the sta ff from the Lick Observatory who provided an e ffi cient and friendly support, especially in the e ff ort of mounting the FIRST instrument and during the observing nights: Keith Baker, Bob Owen, Erik Kovacs, Kostas Chloros, Donnie Redel, Wayne Earthman, Paul Lynam and Pavl Zachary. They are also grateful to Dr. Bolte, Director of the University of California Observatories, for his commitment to the project and generous telescope time allocation. They also thank the students from UC Berkeley who helped during the observing runs: S. Goeble and K. J. Burns, or helped improve the data reduction software: B. Bordwell. Dr. Helmbrecht, President and Founder of Iris AO, is also greatly thanked for his precious support concerning the segmented mirror. E. Huby would like to thank Alain Delboulb for his valuable experience and recommendation concerning the optical bench dedicated to equalize the fiber lengths. Finally, we acknowledge financial support from Programme National de Physique Stellaire (PNPS) of CNRS / INSU, France and from a Small Research Grant of the American</text>
<text><location><page_10><loc_7><loc_90><loc_50><loc_93></location>Astronomical Society. F. Marchis contribution to this work was supported by NASA Grant NNX11AD62G and by the National Science Foundation under Award Number AAG-0807468.</text>
<section_header_level_1><location><page_10><loc_7><loc_86><loc_16><loc_87></location>References</section_header_level_1>
<table>
<location><page_10><loc_7><loc_30><loc_50><loc_85></location>
</table>
</document>
[
{
"title": "ABSTRACT",
"content": "Aims. FIRST is a prototype instrument built to demonstrate the capabilities of the pupil remapping technique, using single-mode fibers and working at visible wavelengths. Our immediate objective is to demonstrate the high angular resolution capability of the instrument and to show that the spectral resolution of the instrument enables characterisation of stellar companions. Methods. The FIRST-18 instrument is an improved version of FIRST-9, that simultaneously recombines two sets of nine fibers instead of one, thus greatly enhancing the ( u , v ) plane coverage. We report on observations of the binary system Capella at three epochs over a period of 14 months ( /greaterorsimilar 4 orbital periods) with FIRST-18 mounted on the 3-m Shane telescope at Lick Observatory. The binary separation during our observations ranges from 0.8 to 1.2 times the di ff raction limit of the telescope at the central wavelength of the spectral band. Results. We successfully resolved the Capella binary system at all epochs, with an astrometric precision as good as 1 mas under the best observing conditions. FIRST also gives access to the spectral flux ratio between the two components directly measured with an unprecedented spectral resolution of R ∼ 300 over the 600-850 nm range. In particular, our data allow to detect the well-known overall slope of the flux ratio spectrum, leading to an estimation of the 'pivot' wavelength of 0.64 ± 0.01 µ m, at which the cooler component becomes the brightest. Spectral features arising from the di ff erence in e ff ective temperature of the two components (specifically the H α line, TiO and CN bands) have been used to constrain the stellar parameters. The e ff ective temperatures we derive for both components are slightly lower (5-7%) than the well-established properties for this system. This di ff erence mainly originates from deeper molecular features than those predicted by state-of-the-art stellar atmospheric models, suggesting that molecular line lists used in the photospheric models are incomplete and / or oscillator strengths are underestimated, most likely concerning the CN molecule. Conclusions. These results demonstrate the power of FIRST, a fibered pupil remapping based instrument, in terms of high angular resolution and show that the direct measurement of the spectral flux ratio provides valuable information to characterize little known companions. Key words. Instrumentation: high angular resolution - Techniques: interferometric - Binaries : close - Binaries : visual - Stars: fundamental parameters - Stars: individual: Capella",
"pages": [
1
]
},
{
"title": "II. Spectroscopy of the Capella binary system at the diffraction limit",
"content": "E. Huby 1 , G. Duchˆene 2 , 3 , F. Marchis 4 , S. Lacour 1 , G. Perrin 1 , T. Kotani 5 , ' E. Choquet 1 , 6 , E. L. Gates 7 , O. Lai 8 , 9 , and F. Allard 10 Preprint online version: January 17, 2021",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The objective of the FIRST (Fibered Imager foR a Single Telescope) prototype development is the detection of faint companions such as exoplanets. Many instruments currently being designed and manufactured are addressing this challenge, which requires high dynamic ranges at high angular resolution. Di ff erent solutions are implemented such as extreme adaptive optics systems, coronagraphic masks and interferometric techniques (or a combination thereof). FIRST belongs to the latter category since its principle relies on the aperture masking (Hani ff et al. 1987), in which a mask with small holes is put on the pupil of the telescope. In a traditional implementation, these holes are organized in a non redundant manner in order to avoid the fringe blurring due to the atmospheric turbulence, which leads to the loss of most of the high spatial frequency information on the object. The image is thus the superimposition of all fringe patterns coded with as many spatial frequencies. Object visibilities corresponding to every subpupil pairs can therefore be retrieved. This technique has been established as a standard for di ff raction limited observations, up to dynamic ranges of a few hundreds, thanks to the routinely used Sparse Aperture Masking mode of the NACO instrument at the VLT (Lagrange et al. 2012; Sanchez-Bermudez et al. 2012; Grady et al. 2013; Cieza et al. 2013) and the Keck NIRC2 aperture masking experiment (Hinkley et al. 2011; Blasius et al. 2012; Evans et al. 2012). FIRST is the implementation of the fibered pupil remapping technique as proposed by Chang & Buscher (1998) and then Perrin et al. (2006) at visible wavelengths. This technique can be seen as a variant of the aperture masking techniquethat aims at increasing the achievable dynamic range. As stated by Baldwin & Hani ff (2002), dynamic range directly depends on the number of sub-pupils and on the accuracy of the observable measurements (visibilities or closure phases for instance). In the FIRST instrument, single-mode fibers o ff er a way to improve these two aspects: (i) they allow to use the whole telescope pupil while their outputs can be non-redundantly recombined and (ii) they spatially filter the wavefront and thus avoid speckle noise. The spatial phase fluctuations due to the atmospheric turbulence are thus traded against flux fluctuations because of the imperfect coupling e ffi ciency into the fibers. However, these can be more easily handled during data reduction than phase fluctuations. A self-calibration algorithm has indeed been proposed to retrieve the complex visibilities without the need of specific photometric channels (Lacour et al. 2007). The first light of the instrument was achieved in July 2010 at Lick Observatory with FIRST-9 mounted on the Cassegrain focus of the 3-m Shane telescope (Huby et al. 2012). The instrument has since been significantly improved to increase the number of sub-pupils and the accuracy on the closure phase measurements, and hence the achievable dynamic range. FIRST-9 has thus become FIRST-18, in which 18 sub-pupils are recombined, and has been mechanically enhanced to reach a higher stability. Four observing runs have been conducted between October 2011 and December 2012. Several binary systems have been observed, as these simple objects are particularly suited for testing the capabilities of the instrument. Among these binaries, Capella ( α Aurigae, V = 0.08, R = -0.52) has been observed at three di ff erent epochs with FIRST18. Capella is a well-known nearby binary system, that has been studied for more than a hundred years, and its historical record is notably linked to the Lick Observatory and the first measurements with interferometers. The first announcement of discovery of this spectroscopic binary dates indeed from Campbell (1899) who used the Mills spectrograph installed on the 36inch Lick refractor to observe Capella (simultaneously Newall (1899) made the same discovery using the Cambridge spectroscope). Capella later was the first binary system whose astrometric orbit has been interferometrically measured with the 6m baseline Michelson interferometer on the 100-inch telescope at Mount Wilson (Anderson 1920; Merrill 1922). For decades, this friendly target has been observed with various interferometers and speckle imaging techniques. So far, the most accurate measurements of the astrometric orbit have been performed by Hummel et al. (1994) using the Mark III interferometer at Mount Wilson, using baselines from 3 m up to 23.6 m. Concerning the abundant bibliography about Capella, Torres et al. (2009) provide a very complete review of all spectroscopic, as well as interferometric measurements available at that time and they use them to derive the parameters of the system: e ff ective temperatures of 4920 ± 70K and 5680 ± 70K, radii of 11.87 ± 0.56 R /circledot and 8.75 ± 0.32 R /circledot , luminosities of 79.5 ± 4.8 L /circledot and 72.1 ± 3.6 L /circledot and the parameters of the relative orbit. The latest and most accurate masses have been determined by Weber & Strassmeier (2011) using the spectroscopic orbit combined with the inclination of the orbital plane derived from astrometry measurements: 2.573 ± 0.009 M /circledot and 2.488 ± 0.008 M /circledot . With an angular separation varying from 41 mas to 56 mas, Capella is therefore an ideal target to probe the capabilities of FIRST-18 at the di ff raction limit, which ranges from 41 mas at 600nm to 58 mas at 850 nm for a 3-m telescope. In this paper, we report on the successful detection of Capella as a binary system at the di ff raction limit of the telescope using FIRST-18, which is described in Sect. 2, along with the data reduction procedure. The results are presented in Sect. 3. The spectrally-dispersed flux ratio measurement is of particular interest as it is the first time that it is directly measured with a R ∼ 300 spectral resolution. Higher-resolution spectra of the two components have been estimated by 'deblending' the composite spectrum of the binary using spectral templates to disentangle them (Barlow et al. 1993). Flux ratio measurements of the system, on the other hand, have been obtained in discrete broad- and narrow-band filters that are too sparsely distributed to provide fine spectral information (Torres et al. 2009). Thus, the FIRST data provide a unique insight into the Capella system and, by extension, all systems with separation as small as the di ff raction limit of a given telescope. In this work, we model our FIRST flux ratio spectrum to constrain the e ff ective temperatures of the Capella binary, thereby demonstrating the power of FIRST to study previously uncharacterized companions in the future.",
"pages": [
1,
2
]
},
{
"title": "2. Observations and data reduction",
"content": "Observations were conducted with the 3-m Shane telescope at Lick Observatory from 2011 to 2012 (see Table 1). As in previous observations (Huby et al. 2012), the Shane adaptive optics system provided su ffi cient correction to stabilize the fringes, although it is optimized for the infrared wavelengths.",
"pages": [
2
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},
{
"title": "2.1. FIRST-18",
"content": "After the first light of the instrument obtained in 2010 (Huby et al. 2012), e ff orts have been focused on improvements to the stability, sensitivity and dynamic range achievable with FIRST. The injection part of the instrument (including the pupil imager, the Iris AO segmented mirror used to precisely steer the beams on the fiber cores that are gathered in the fiber bundle, from Fiberguide Industries) is basically unchanged. However significant upgrades have been carried out in the recombination part of the instrument, as can be seen in Fig. 1. Assuming that the noise is uncorrelated between the baselines - a reasonable assumption in the photon noise limited regime - the dynamic range increases with the number of visibility and closure phase measurements (Baldwin & Hani ff 2002; Lacour et al. 2011; Le Bouquin & Absil 2012). The main development was therefore aimed at increasing the number of sub-pupils, leading to the FIRST-18 instrument, in reference to the two sets of 9 sub-pupils that are recombined. The nonredundancy of the linear recombination configuration is a technical limit: standard V-groove chips o ff er 48 spaces where fibers can be positioned. The most compact 9-fiber configuration requires n max = 44 spaces, while the 10-fiber and 11-fiber ones require respectively 55 and 75 spaces. In addition, the 9-fiber configuration is also a compromise between the available space on the bench (defining the focal length f ' of the imaging lens), the di ff raction pattern width ( f ' λ/ D , with D corresponding to the V-groove pitch, and also to the collimated beam size at the fiber output) and the sampling of the highest frequency fringe pattern (of period T = f ' λ/ ( n max D )) that fits the detector dimensions. For these reasons, two sets of 9 fibers are recombined independently. Given the 30 available sub-pupils in the obstructed telescope pupil (see Fig. 2), our selected fiber configuration using 18 of them gives access to 73% of all possible independent baselines. As the instrument is mounted at the Cassegrain focus of the telescope, the ( u , v ) plane coverage does not rotate during the night and is stable in time. However, the ( u , v ) plane coverage is significantly extended thanks to the broad wavelength range, as illustrated in Fig. 2. Each recombination scheme of the beams is built on the same design as for the previous version. The collimated beams coming from the V-grooves are reshaped thanks to anamorphic systems that mimic the slit of a spectrometer consisting in dispersing prisms (see Fig. 1). The anamorphic system has been designed to satisfy the Nyquist-Shannon sampling condition for the highest frequency fringe pattern (for a given focal length of the imaging lens) on the one hand, and to reach a high spectral resolution on the other. This is achieved thanks to a 4-lens (2 spherical and 2 cylindrical lenses) afocal system performing a beam elongation of 20 in the direction of dispersion and a compression of 7 in the orthogonal direction. The two fringe patterns are imaged on the same detector side by side along the wavelength axis. Spectral filters have been inserted in each arm in order to avoid overlapping of the patterns. In the center of the detector, the fringe patterns are cut at 600 nm and 850 nm thereby defining the spectral range of the instrument. Improvement of the data quality has also been provided by the use of a more e ffi cient detector, an Hamamatsu EMCCD camera, with maximal EM gain of 1200, quantum e ffi ciency of 90 %, 77 % and 54 % at 600, 700 and 800 nm, respectively, and 512 × 512 pixels 16 µ m wide. The overall mechanical stability has been enhanced too, allowing to observe objects up to 40 · from zenith without significant loss of flux due to mechanical flexures.",
"pages": [
2,
3
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},
{
"title": "2.2. Acquisitionprocedure",
"content": "Capella was observed in October 2011, July 2012 and December 2012 with FIRST-18 mounted on the 3-m Shane telescope at Lick Observatory. The observation log is reported in Table 1. Several bright (0 /lessorsimilar R /lessorsimilar 3) single stars were observed immediately before / after Capella so serve as calibrator for closure phase measurements and baseline calibration (see Sect. 3.2). The acquisition procedure is similar to the description given in Huby et al. (2012). One data set comprises fringe sequences, fiber calibration files (every fiber di ff raction pattern is recorded individually), and background files. However, this procedure has been significantly shortened compared to the previous observations thanks to the implementation of a dedicated optimization path in the optical set-up. The injection of the flux into the fibers is indeed very sensitive and must be optimized at every target switch, to compensate for residual mechanical flexures occurring in the instrument but also in the AO system. While this optimization was done one fiber at a time in 2010 (by scanning the corresponding micro-segment and measuring the transmitted flux directly on the science camera), it is now done simultaneously for all fibers thanks to a motorized mirror system that allows to image all the output fibers on a dedicated detector. The 18 corresponding micro-segments can therefore be scanned at the same time. The optimization is now completed in less than two minutes leading to a substantial gain in time and stability.",
"pages": [
3
]
},
{
"title": "2.3. Datareduction",
"content": "The basic principles of the FIRST data analysis are based on the P2VM method ( Pixel to Visibility Matrix ), that was first developed for the AMBER instrument at the VLTI (Millour et al. 2004) and subsequently adapted to FIRST data, as described in more detail in Huby et al. (2012). The current data reduction process consists of the following steps: The distortion mentioned in the second step of the reduction results from astigmatism introduced by the prism, and has an amplitude of about 10-15 pixels. The shape of this distortion is evaluated by detecting the position of the deepest telluric absorption line and is corrected by horizontally interpolating and shifting the image values. The spectral calibration is done using the UVES sky emission atlas Hanuschik (2003). As the light is spectrally dispersed through an SF2-prism, there are two parameters defining the wavelength as a function of the pixel: the angle of incidence on the prism i , which a ff ects the spectral resolution, and the central wavelength λ 0. The continuum of the spectrum is fitted and subtracted, leaving only (stellar and telluric) absorption features. The same procedure is applied to the synthetic spectrum, and the parameters i and λ 0 are retrieved by maximizing the correlation product between the two spectra. A fine adjustment is then performed by fitting the peak positions of the power spectral density computed over all images. The results of this fit is shown in Fig. 3 where the fitted peak positions are superposed to the mean power spectral density. After applying the P2VM method, the complex coherent fluxes are thus retrieved and their phases are combined to estimate closure phases. The data reduction output comprises 84 closure phase measurements for each of about 180 spectral channels from 600 nm to 850 nm. Since spatial frequency depends on wavelength, specific signal appears in the closure phase plotted as a function of wavelength, depending on the structure of the target.",
"pages": [
3,
4
]
},
{
"title": "2.4. Fittingofabinarymodel",
"content": "The final step in the analysis consists of fitting the closure phase estimates with a binary model. Three parameters are optimized by minimizing the χ 2 function: two angular parameters defining the position of the companion, α and δ , and a flux ratio for each spectral channel, ρ ( λ ). The closure phase model function corresponding to a binary directly reads (Le Bouquin & Absil 2012): with where uij and vi j are the projections of the spatial frequency vector -→ si j corresponding to the sub-pupils i and j , on two orthonormal axes defined by the segmented mirror reference frame (see Sect. 3.2 for details concerning the baseline calibration). This vector expresses as -→ si j = -→ Bij /λ with -→ Bij the baseline vector represented in the telescope pupil. The χ 2 function is therefore 3 dimensional. For every spectral channel, the contributions of all n CP closure phases are added quadratically: with σ k λ the error on closure phase k at wavelength λ and is the phase di ff erence between the data and the model, defined modulo 2 π . Under the assumption that the noise a ff ecting the data follows a Gaussian distribution, the likelihood function can be derived from the χ 2 function by: The proportional symbol is used as the likelihood function is normalized afterwards. The optimal value for a given parameter can then be retrieved after marginalizing the likelihood function, i.e. by integrating over all other parameters. For the α parameter for instance, it is expressed as: Similarly, a circular permutation over the set of parameters leads to L λ ( δ ) and L λ ( ρ ). For every spectral channel, the optimal parameter sets ( ˜ αλ, ˜ δλ, ˜ ρ ( λ ) ) are then determined by the median value of these probability densities, and the associated error bars are defined as the 68% confidence interval. The λ dependence has been noted di ff erently for the position parameters and the flux ratio since the position of the companion is achromatic. The ˜ αλ and ˜ δλ have therefore been averaged in order to determine the final position ( ˜ α, ˜ δ ) . Around 20 % of the data points with the worst error bars have not been taken into account to compute the averaged position, in order to discard aberrant points. The associated error bars on ˜ α and ˜ δ are computed from the standard deviation of the respective distributions.",
"pages": [
4,
5
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},
{
"title": "3.1. ThecaseofCapella",
"content": "The calibrated closure phases of Capella are shown in Fig. 4. As is readily apparent, large deviations from the null closure phase are detected. Large phase changes of ∼ ± π indeed occur when the observed object is centrosymmetric, indicating here that the flux ratio between the two components is close to unity, as is expected for the Capella binary system at visible wavelengths. The fact that the transitions are smooth indicates that the flux ratio is not exactly equal to one. Thus these observations have clearly resolved the binary system. However, some of these phase transitions occur in the opposite direction than expected by the best fit model (see the second closure phase graph in the first row of Fig. 4 for instance). This e ff ect is observed in around 6 % of all closure phase measurements (84 × 2 closure phases per date of observation). A possible explanation is that the measurements may be a ff ected by an uncalibrated bias on the imaginary part of the bispectrum. In this case, a sharp transition from 0 to ± π (imaginary part initially equal to 0) can therefore be turned into a smoother transition from 0 to π or -π , depending on the sign of the bias o ff set. This is most likely the reason why the minimum of the reduced χ 2 function is generally much larger than 1. It reaches up to ∼ 40 (for one spectral channel) in the worst cases. Therefore, prior to computing the likelihood functions, the statistical error bars are scaled such that the minimum of the reduced χ 2 function per spectral channel is 1 (error bars in the Fig. 4 are rescaled accordingly). Another consequence of these transitions in the wrong direction is that it sharpens the transition when averaging closure phase datasets. The mean value of two transitions in opposite direction will indeed result in values globally closer to ± 180 · or 0 · . This can potentially translate into flux ratios that are biased towards unity. As detailed in the next section, the eventuality cannot be completely discarded when analyzing the spectral flux ratio. It can be noted though, that averaging over the closure phase has been performed using complex phasors in order to take into account that the phase is known modulo 2 π . This is necessary to compute the correct phase, especially in the case of phases around ± 180 · , but that obviously does not prevent such bias effect. However, the final flux ratio estimates are assumed to be less a ff ected by this bias, as they result from the average over two independent measurements provided by the two sets of simultaneously recombined fibers, and also from the average over the di ff erent dates of observations. Since the source of this bias is still unknown (photon bias only a ff ects the real part of the bispectrum as established by Wirnitzer 1985), this e ff ect becomes obvious only once the best fit model has been determined. There is thus no objective criterion that could allow to discriminate these biased data a priori . Nonetheless, closure phase error bars resulting from the average over all datasets corresponding to one date of observation are necessary larger when there is an uncertainty on the transition direction. As can be seen in Fig. 4, error bars are much larger around phase transitions. As a consequence, these points are less weighted in the fit.",
"pages": [
5,
6
]
},
{
"title": "3.2. Orbit",
"content": "The analysis of our results concerning the companion position requires a calibration of the ( u , v ) plane, that is a calibration of the baseline lengths and orientations (as explained by Woillez & Lacour 2013, under the imaging baseline section). For the fit, the baselines are conveniently defined by their theoretical lengths and orientation taken in a reference frame linked to the segmented mirror. However, to be scientifically useful, these need to be transformed into the angular separation of the binary and its position angle relative to North. Two aspects have to be considered for the calibration: The rotation of the pupil plane is due to the periscope sending the beam from the adaptive optics bench towards the hole through the FIRST bench. It uses a mirror combination working at angles di ff erent from 45 · that therefore induces an unknown rotation of the pupil relative to the sub-pupils. The calibration over all baselines can thus be performed by estimating two parameters: a scaling factor and a rotation angle. This is done by measuring the position of another wellknown binary star, using the same data reduction pipeline as for Capella. Among the binary systems observed at the same epochs as Capella, the triple system of Algol ( δ Per) is an ideal calibrator. The inner system (Algol A of type B8V and Algol B of type K2IV) of orbital period 2.87 days and semi-major axis of 2.3 mas is unresolved by a 3-m telescope. On the other hand, the outer system (Algol A + B and Algol C of type F1V) of orbital period ≈ 680days, semi-major axis of 93.8 mas and flux ratio estimated to 10 at visible wavelengths is well detected by FIRST-18. Its orbital period is much longer than the Capella period (104 days) and makes it a suitable target for the baseline calibration. The relative positions of Algol A + B and C have therefore been estimated for several dates during the various runs, as shown in Table 1. The results are shown in Table 2. The position parameters have been converted into polar coordinates in order to derive the angle for the rotation to be applied to the field of view. The predicted positions are computed from the orbit resulting from the measurements with the CHARA interferometer fitted by Baron et al. (2012). The Algol system was observed twice during both the October 2011 and December 2012 observing runs. In both cases, multiple observations of the systems within a given observing run yield consistent calibration factors at the 2 σ level or better (see Table 2). This confirms the expectation that the rotation of the pupil in comparison with the FIRST sub-pupils is stable over the duration of an observing run since the injection part of the set-up was not modified during the course of each run. In October 2011, uncertainties on the calibration factors are much larger on October 16 than on October 19, probably as a consequence of changes in r 0 (see Table 1) and short atmospheric coherence time. While the latter could not be measured, the shorter integration times used on October 16, which results from a compromise between sensitivity and fringe visibility, is indicative of a shorter timescale for atmospheric turbulence. We therefore use the estimated position of Algol C regarding Algol A + B on October 19 to correct for the pupil rotation and scaling factor for all three dates of observation in October 2011. For the December 2012 observing run, we use the weighted average of both observations of Algol since they have similar precision. The final relative astrometry of the Capella system throughout our observations is shown in Fig. 5. The orbit computed from the model parameters fitted by Torres et al. (2009) is drawn for comparison. Table 3 presents both uncorrected and corrected (field rotation and scaling factor taken into account) estimates, along with their associated uncertainties. Most estimates are in agreement with the predicted positions within the 1σ range. However, the positions measured in 2011 seem to be a ff ected by a small systematic error of about 2 mas along the N-S direction (see Fig. 5, bottom). It is plausible that this results from the baseline calibration, since all three points have been calibrated by the same astrometric estimate for the Algol system. Ideally, the calibrator should have been observed with su ffi cient accuracy at the three di ff erent dates.",
"pages": [
6,
7
]
},
{
"title": "3.3. Spectralmodel",
"content": "Along with the astrometry of the binary, our analysis also yields a 'spectrum' of the binary flux ratio, ρ ( λ ). We have inspected the quality of the flux ratio spectra from each individual night and each of the two separate V-grooves. As expected given seeing conditions, the flux ratios measured on December 2012 are of much worse quality than those from October 2011. Similarly, the July 2012 flux ratio spectrum is very noisy, owing to observations taken during early-morning twilight. While the astrometric position estimates from these epochs benefit from the av- age over all spectral channels and are thus reasonably accurate, the flux ratio spectra obtained during the 2012 runs have been discarded for the spectral analysis. We therefore averaged all October 2011 datasets to produce a final flux ratio spectrum for the Capella binary system. The resulting final spectral resolution is about 1.5 pixel as determined from data taken using a monochromatic laser beam. Uncertainties on the flux ratio spectrum were estimated as the standard deviation of the mean over the datasets. These results are available at the CDS (column 1 lists the wavelengths in nm, column 2 and 3 give the flux ratio and their uncertainty, respectively). The flux ratio spectrum obtained with FIRST agrees with historical measurements of the binary taken within our wavelength range at the /lessorsimilar 2 σ level. Furthermore, our spectrally dispersed observations reveal an overall slope that is consistent with data over a broader range and confirm that the cool component of the system is increasingly brighter at longer visible wavelengths. We find that the flux ratio reversal occurs at a wavelength of 0.64 ± 0.01 µ m. In addition to its general slope, the FIRST flux ratio spectrum reveals finer structures, such as a sharp peak at 0.655 µ m and two broad dips around 0.69-0.75 µ m and 0.780.84 µ m. Both can be traced to the di ff erence in e ff ective tem- re between the two stars, which leads to photospheric features of di ff erent depths: the former is H α (the slight mismatch in wavelength results from a mild inaccuracy in our wavelength solution) while the latter two are molecular bands (most notably TiO and CN) that are characteristic of cool photospheres. These spectral features are a direct confirmation that the infrared-bright component is cooler than the visible-bright one. To quantify the constraint on stellar properties provided by the FIRST flux ratio spectrum, we use the most recent BTSettl models 1 partially published in a review by (Allard et al. 2012a) and described by Allard et al. (2012b). These model atmospheres are computed with the PHOENIX multi-purpose atmosphere code version 15.5 Allard et al. (2001) solving the radiative transfer in 1D spherical symmetry, with the classical assumptions: hydrostatic equilibrium, convection using the mixing length theory, chemical equilibrium, and a sampling treatment of the opacities. The models use a mixing length as derived by the radiation hydrodynamic simulations of Ludwig et al. (2002, 2006) and Freytag et al. (2010, 2012) and a radius as determined by the Bara ff e et al. (1998) interior models as a function of the atmospheric parameters ( T e ff , log g , [ m / H]). The reference solar elemental abundances used in this version of the BT-Settl models are those defined by Asplund et al. (2009). For solar metallicity and higher, no α element enhancement is required. The PHOENIX library includes stellar spectra with a 100 K and 0.5 sampling in T e ff and log g , respectively. We explored the parameter space as follows: each model consisted on two pairs of stellar parameters ( T e ff and log g for each component). The model flux ratio is computed using the same sampling and resolution as the FIRST data and normalized so as to match the observed median flux ratio. Since the PHOENIX emission spectra are given per unit surface area, this normalization is equivalent to setting the ratio of stellar radii to best match the median flux ratio in our spectral bandpass. In principle, our analysis could consider this ratio as a free parameter in the fit instead. However, since the FIRST flux ratios are in good agreement with previous flux ratio estimates of the binary, we do not expect to gain additional insight on the ratio of stellar radii. We therefore de- cided to remove one free parameter from our fit by using this a priori normalization to ensure that the model fitting was primarily attempting at reproducing the global slope and finer spectral features, which depend only on the stellar e ff ective temperatures and surface gravities. We believe that our data are more apt at constraining the latter. Nonetheless, we note that our normalization for the best fit models is consistent at the 1 σ level with the stellar radii ratio of 0 . 737 ± 0 . 044 estimated by Torres et al. (2009). We thus create a grid of flux ratio spectra that depends on four parameters, the e ff ective temperature and surface gravity of both components while approximately maintaining the average stellar luminosity ratio in the FIRST bandpass. By performing a wide grid search around the stellar parameters derived by Torres et al. (2009), the best fitting model has the following parameters: T hot e ff = 5300K, T cool e ff = 4700K, log g hot = log g cool = 2 . 0. This combination of stellar parameters yields a reasonably good match to the observed flux ratio spectrum (reduced χ 2 = 2 . 89, see Fig. 6 and Table 4). We note that there is another peak appearing in the likelihood distribution, corresponding to a model with T hot e ff = 5500K, T cool e ff = 4800K and leading to a marginally poorer χ 2 , which provides a sense for the uncertainties on the derived stellar e ff ective temperatures. The stellar parameters derived here are significantly di ff erent from those estimated by Torres et al. (2009), although the e ff ective temperatures are only 4-7% smaller than their nominal values. As shown in Fig. 6, the higher e ff ective temperatures proposed by Torres et al. (2009) also result in detectable molecular features in the flux ratio spectrum, although they are less marked than in our data (this is particularly true for the 0.780.84 µ m feature). This issue can be partially alleviated by using synthetic stellar spectra corresponding to lower surface gravity strengths. However, the overall quality of the fit is much poorer (see Table 4). One solution to improve the fit consists in using a metal-rich composition. Using the series of PHOENIX models computed for [ m / H] = + 0 . 5 (where elemental abundances are increased uniformly from the set of solar abundances), we find that the FIRST data are best fit using e ff ective temperatures of 5600 and 4900 K and surface gravities of log g hot = 2 . 5 and log g hot = 2 . 5. This model is significantly better (reduced χ 2 = 2 . 31, see Fig. 6) than the best fit model at solar metallicity, and has stellar properties in good agreement with Torres et al. (2009). However, the super-solar metallicity is at odds with all estimates for the components of the system. We thus conclude that the observed flux ratio spectrum of the Capella binary does not conform perfectly to the prediction of stellar atmosphere models. Breaking down the information provided by the FIRST flux ratio spectrum, it appears that the overall slope across the 0.60.85 µ m is reasonably well fit with both the nominal e ff ective temperatures and the lower values preferred by the model fitting above, so long as the di ff erence in e ff ective temperatures between the two components is about 10-12%. Thus it appears that the spectral features, specifically the depth of the molecular bands, represent the main culprit in forcing the fit away from the nominal stellar parameters. As mentioned in the previous section, we cannot exclude with certainty that a subtle bias in our data analysis is a ff ecting the resulting flux ratio spectrum, possibly because the system is close to a unity flux ratio. However, we find it extremely unlikely that this bias could a ff ect the wavelengths where molecular features are present but not the adjacent continuum. Indeed, such biases are expected to be present where the closure phases undergo large shift (from ± π to 0 for instance), as explained in the Section 3.1. This is therefore expected to be independent of spectral features, as the occurrence of these shifts only depends on the spatial frequencies ( ∝ B /λ , B corresponding to the baseline) involved in the closure triangle. We thus believe that the mismatch between observations and models is an astrophysical e ff ect instead. Cooler e ff ective temperatures, lower surface gravities and / or higher metallicity are all factors that result in deeper molecular bands in each component and in an increased di ff erence in their strength, resulting in deeper features in the flux ratio spectrum as well. Since the stellar parameters of the Capella binary have been precisely determined, our FIRST flux ratio spectrum thus demonstrates that the molecular absorption bands in the spectra of each component are deeper than predicted by the models. One possible explanation for this shortcoming of the models is that the molecular opacities are underestimated in the models, because of incomplete line lists being used and / or underestimated oscillator strengths. Departures from local thermal equilibrium in stellar atmospheres can induce substantial e ff ects for A-type stars but are negligible in the range of e ff ective temperatures relevant to the Capella system. The two molecules that account for most of the opacity in the spectral features observed with FIRST are TiO and CN. For the former molecule, the version of the PHOENIX models used here are based on the line lists and oscillator strengths from Plez (1998). The CN line list and oscillator strengths are adopted from the SCAN database (Jorgensen & Larsson 1990). We believe that the TiO molecule, whose features are frequent in a broad range of cool stars, is much better calibrated and thus conclude that the reason for the under-prediction of these features by current atmospheric features most likely stems from the treatment of the CN molecule, either through the incompleteness of its line list or as a result of oscillator strengths that are too low.",
"pages": [
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9
]
},
{
"title": "4. Summary of findings and conclusion",
"content": "In order to demonstrate the capabilities of a fibered aperture masking instrument like FIRST to provide valuable spectrallydispersed information on binary systems whose separation is on the order of the di ff raction limit, the results presented in this pa- Table 4. Stellar parameters of the PHOENIX atmospheric models used in this analysis from Allard et al. (2012b) and assuming the set of solar abundances from Asplund et al. (2009). The first two models are at solar metallicity while the third one is assuming super-solar metallicity. All three models are shown in Fig. 6. The parameters adopted to mimic those from Torres et al. (2009) are slightly di ff erent from those given in their paper because of the discrete sampling of the PHOENIX model grid. The last line of the table gives the ratio of stellar radii derived from the scaling factor used to normalize the spectra as a first step of the modelling. per are focused on the binary star Capella. Its separation is indeed comparable to the di ff raction limit and its flux ratio close to unity at visible wavelengths. Capella has been observed at three di ff erent epochs between 2011 and 2012 with FIRST-18 mounted on the 3-m Shane telescope of Lick Observatory (using its adaptive optics system as a fringe tracker). The secondary componenthas been detected at, or slightly below, the di ff raction limit of the telescope at visible wavelengths with an accuracy well below a tenth of the di ff raction limit. This first achievement illustrates the high angular resolution capability of the instrument. Using FIRST, we have also directly measured, for the first time, the flux ratio of the binary system at a spectral resolution of R ∼ 300 between 600 and 850nm. This spectral range gives access to spectral features (H α line, TiO and CN bands) that are quite influential when comparing the observed flux ratio spectrum with predictions based on PHOENIX library of synthetic spectra. The e ff ective temperatures derived from this analysis are slightly o ff set (by 5-7%) from those estimated by Torres et al. (2009) based on the extensive literature on this system. While we cannot exclude a subtle bias a ff ecting our flux ratio measurements arising from the fact that the flux ratio is close to unity, this discrepancy probably indicates that the photospheric models used to predict the synthetic spectra are based on incomplete line lists and / or underestimated oscillator strengths for molecules commonly found in G- and K-type giants (most likely CN). This conclusion illustrates the power of FIRST in bringing valuable spectral information to characterize binary systems. Acknowledgements. The authors would like to thank the sta ff from the Lick Observatory who provided an e ffi cient and friendly support, especially in the e ff ort of mounting the FIRST instrument and during the observing nights: Keith Baker, Bob Owen, Erik Kovacs, Kostas Chloros, Donnie Redel, Wayne Earthman, Paul Lynam and Pavl Zachary. They are also grateful to Dr. Bolte, Director of the University of California Observatories, for his commitment to the project and generous telescope time allocation. They also thank the students from UC Berkeley who helped during the observing runs: S. Goeble and K. J. Burns, or helped improve the data reduction software: B. Bordwell. Dr. Helmbrecht, President and Founder of Iris AO, is also greatly thanked for his precious support concerning the segmented mirror. E. Huby would like to thank Alain Delboulb for his valuable experience and recommendation concerning the optical bench dedicated to equalize the fiber lengths. Finally, we acknowledge financial support from Programme National de Physique Stellaire (PNPS) of CNRS / INSU, France and from a Small Research Grant of the American Astronomical Society. F. Marchis contribution to this work was supported by NASA Grant NNX11AD62G and by the National Science Foundation under Award Number AAG-0807468.",
"pages": [
9,
10
]
}
]
2013AIPC.1535...45C
https://arxiv.org/pdf/1307.1767.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_87><loc_89><loc_91></location>Measurement of a Phase of a Radio Wave Reflected from Rock Salt and Ice Irradiated by an Electron Beam for Detection of Ultra-High-Energy Neutrinos</section_header_level_1>
<text><location><page_1><loc_9><loc_80><loc_91><loc_83></location>Masami Chiba 1 , Toshio Kamijo 1 , Takahiro Tanikawa 1 , Hiroyuki Yano 1 , Fumiaki Yabuki 1 , Osamu Yasuda 1 , Yuichi Chikashige 2 , Tadashi Kon 2 , Yutaka Shimizu 2 , Souichirou Watanabe 2 , Michiaki Utsumi 3 , Masatoshi Fujii 4</text>
<unordered_list>
<list_item><location><page_1><loc_9><loc_75><loc_89><loc_78></location>1 Graduate School of Science and Engineering, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji-shi, Tokyo 192-0397, Japan</list_item>
<list_item><location><page_1><loc_9><loc_74><loc_71><loc_75></location>2 Faculty of Science and Technology, Seikei University, Musashino-shi, Tokyo 180-8633, Japan</list_item>
<list_item><location><page_1><loc_9><loc_70><loc_84><loc_74></location>3 Department of Applied Science and Energy Engineering, School of Engineering, Tokai University , Hiratsuka-shi, Kanagawa 259-1292, Japan</list_item>
</unordered_list>
<text><location><page_1><loc_9><loc_69><loc_61><loc_71></location>4 School of Medicine, Shimane University, Izumo-shi, Shimane 693-8501, Japan</text>
<text><location><page_1><loc_15><loc_46><loc_86><loc_66></location>We have found a radio-wave-reflection effect in rock salt for the detection of ultra-high energy neutrinos (UHEν's) which are expected to be generated in Greisen, Zatsepin, and Kuzmin (GZK) processes in the universe. When an UHEν interacts with rock salt or ice as a detection medium, a shower is generated. That shower is formed by hadronic and electromagnetic avalanche processes. The energy of the UHEν shower converts to thermal energy through ionization processes. Consequently, the temperature rises along the shower produced by the UHEν. The refractive index of the medium rises with temperature. The irregularity of the refractive index in the medium leads to a reflection of radio waves. This reflection effect combined with the long attenuation length of radio waves in rock salt and ice would yield a new method to detect UHEν's. We measured the phase of the reflected radio wave under irradiation with an electron beam on ice and rock salt powder. The measured phase showed excellent consistence with the power reflection fraction which was measured directly. A model taking into account the temperature change explained the phase and the amplitude of the reflected wave. Therefore the reflection mechanism was confirmed. The power reflection fraction was compared with that calculated with the Fresnel equations, the ratio between the measured result and that obtained with the Fresnel equations in ice was larger than that of rock salt.</text>
<text><location><page_1><loc_10><loc_43><loc_71><loc_44></location>Keywords: Neutrino detectors; ultra-high-energy cosmic rays; Rock salt; Antarctic ice sheet; Radar</text>
<section_header_level_1><location><page_1><loc_23><loc_38><loc_41><loc_39></location>I. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_12><loc_24><loc_49><loc_37></location>Ultra-high-energy neutrinos (UHEν's) were predicted to be produced at a collision of UHE-cosmic ray with the cosmic-microwave-radiation background by Berezinsky and Zatsepin [1] in Greisen, Zatsepin, and Kuzmin (GZK) processes in the universe [2, 3]. In order to detect them we had searched for and found a radio-wave-reflection effect in rock salt [4 - 6]. A gigantic detector is needed for the detection due to the expected ultra-low flux of about 1 km -2 d -1 . When an</text>
<section_header_level_1><location><page_1><loc_12><loc_22><loc_40><loc_24></location>Email: [email protected]</section_header_level_1>
<text><location><page_1><loc_12><loc_17><loc_49><loc_22></location>Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.</text>
<text><location><page_1><loc_12><loc_11><loc_49><loc_17></location>The following article appeared in (5 th International Workshop on Acoustic and Radio EeV Neutrino Detection Activities , AIP Conf. Proc. 1535, 45-50 (2013) ) and may be found at ( http://dx.doi.org/10.1063/1.4807519 ).</text>
<text><location><page_1><loc_52><loc_11><loc_88><loc_41></location>UHEν interacts with rock salt or ice as a detection medium, a shower is generated. That shower is formed by hadronic and electromagnetic avalanche processes. The energy of the UHEν shower converts finally to thermal energy through ionization processes. Consequently, the temperature rises along the shower produced by the UHEν. The refractive index rises as a function of the temperature. The irregularity of the refractive index in the medium for radio waves causes reflection. This reflection effect combined with long attenuation length of radio waves in rock salt and ice would yield a new method to detect UHEν's. We could find a huge amount of rock salt or ice of over 50 Gt in natural rock salt formations or the Antarctic ice sheet. The volume of the rock salt is 3 × 3 × 3 km 3 which is required for the detection of the neutrino flux. Radio waves transmitted into the medium generated by a radar system with a phased array antenna could be reflected by the shower. Receiving the reflected radio waves could be a method for the detection of the UHEν's.</text>
<text><location><page_1><loc_54><loc_9><loc_88><loc_11></location>We had carried out an experiment [4] previously to</text>
<text><location><page_2><loc_12><loc_71><loc_49><loc_91></location>the one described in this article to observe microwave reflection effects from a small rock-salt sample of 2 × 2 × 10 mm 3 irradiated by a synchrotron radiation Xray with a pulse width of 1.7 s. It was set in a 9.4 GHz waveguide [4] while microwaves were continuously injected to the waveguide. A null-detection method was employed to detect the feeble reflected signal in the waveguide circuit. Reflected microwaves were observed with a power reflection fraction of 1 × 10 -6 and a decay time of 8 s after the irradiation had stopped. The shape of the power reflection fraction with respect to time was similar to that of the temperature change in rock salt. The reflection fraction was proportional to the square of the X-ray intensity.</text>
<text><location><page_2><loc_12><loc_55><loc_49><loc_71></location>A larger rock salt sample of 10 cm 3 was irradiated by a 2 MeV electron beam with a duration of 60 s which was set in a free space without using a waveguide [5]. A continuous 435 MHz radio wave struck at the cube from a six-element Uda-Yagi antenna. The reflected power fraction increased as the temperature rose at the irradiated surface of the cube. The observation of the reflection excluded the possibility that the effect was due to a distortion of the waveguide heated by X-ray irradiation at the experiment [4].</text>
<text><location><page_2><loc_12><loc_37><loc_49><loc_55></location>A 435 MHz waveguide filled with rock salt powder was used to measure the radio wave reflection effect [6]. The 2 MeV electron beam was injected to rock salt powder through an aluminum-beam window of 20 × 20 cm 2 with a thickness of 0.5 mm. A continuous 435 MHz radio wave of 10 -4 W was emitted by a quarterwavelength antenna installed in the salt powder and the reflected radio wave was detected by the same antenna. The reflection fraction increased with the square of the temperature rise at the irradiated surface of the rock salt powder. The reflection fraction could be explained by the Fresnel equations.</text>
<section_header_level_1><location><page_2><loc_23><loc_34><loc_40><loc_36></location>II. EXPERIMENT</section_header_level_1>
<text><location><page_2><loc_12><loc_11><loc_49><loc_33></location>We report now on a new experiment using a coaxial tube (WX-20D) with a diameter of 20 mm and a length of 100 mm. An electron beam was injected into an open end of the coaxial tube set in a dry-ice cooling box. The coaxial tube was filled with rock salt powder or ice and was set in the cooling box as shown in Fig. 1. The temperature was measured by a chromel-alumel thermocouple positioned 2 mm from the surface of the open end. The refractive indices of rock salt powder and ice were measured by the reflection method from 0.4 MHz to 1 GHz in the coaxial tube yielding 1.79 0.01 at 22 and 1.76 0.01 at -60 , respectively. Then the diameter of the inner conductor was set to 4.5 mm in order to obtain an impedance of 50 when the tube was filled with the respective medium.</text>
<text><location><page_2><loc_14><loc_10><loc_48><loc_11></location>We utilized a 2 MeV electron beam produced by a</text>
<text><location><page_2><loc_52><loc_72><loc_88><loc_91></location>Cockcroft-Walton accelerator located at the Takasaki Advanced Radiation Research Institute (TARRI) of Japan Atomic Energy Agency (JAEA). The electron beam of 2 MeV was irradiated on the open end of the coaxial tube with a power of 4.2 J/s and a current of 1 mA. For the irradiation of a large target and to prevent damage of a titanium vacuum-beam window, the electron beam was swept over the target with a width of 1 m at 200Hz. Only a small part of the beam hit the open end of the coaxial tube. The increase of the refractive index with respect to the temperature gave rise to radio-wave reflection. We observed the reflection effect from ice as well as rock salt.</text>
<figure>
<location><page_2><loc_55><loc_52><loc_84><loc_70></location>
<caption>FIGURE 1. A coaxial tube with a diameter of 20 mm and a length of 100 mm was filled with rock salt power or ice. It was put in a cooling box of 300 × 300 ×100 mm 3 . The temperature in the medium was measured 2 mm under the open surface. An electron beam was injected into the open end.</caption>
</figure>
<text><location><page_2><loc_52><loc_11><loc_88><loc_40></location>As shown in Fig. 2, a 435 MHz continuous wave of 10 -4 W from an Oscillator (Rohde & Schwarz SMB100A) was split (Mini-Circuits ZMSC-2) into a signal ⃗ (expressed as a vector) sent to the coaxial tube through a circulator (MTC B115FFF) and reference signal ⃗ that could be phase shifted by a variable phase shifter (Mini-Circuits JSPHS-446). The reflected signal ⃗⃗ from the coaxial tube was sent to a combiner (Mini-Circuits ZMSC-2) through the circulator. The combined signal of ⃗ ⃗⃗ ⃗ was split into a real-time spectrum analyzer (Tektronix RSA3303B) and a detector (Power Detector, MiniCircuits ZX47-60-S+) for the power measurement. In order to reject noises due to the power source of 50 Hz, from the real-time spectrum analyzer (RSA), 1024 data samples within 128 ms in the time domain were fast-Fourier transformed to the frequency domain. The peak at 435 MHz was selected within 8 Hz to reject noise. In order to tune the frequency precisely between the oscillator and RSA, they were locked by the 10</text>
<text><location><page_3><loc_12><loc_88><loc_49><loc_91></location>MHz signal generated by a Rubidium-frequency standard (Stanford Research Systems FS725).</text>
<text><location><page_3><loc_12><loc_81><loc_49><loc_88></location>The output signal of the detector was routed to an Educational-Laboratory-Virtual-Instruments Suite (National Instruments NI ELVIS) based on an NI LabVIEW system where the signal was digitized by an ADC.</text>
<text><location><page_3><loc_12><loc_67><loc_49><loc_81></location>The digital output was converted to a value, such that the output of the combiner became zero, by a control program of LabVIEW and converted to an analog voltage by a DAC in the NI ELVIS. The analog signal was fed to the variable phase shifter as a control voltage where the phase of the reference signal ⃗ was shifted according to the voltage. The output of the phase shifter was fed to the combiner again. The feedback loop was repeated 13 Hz.</text>
<figure>
<location><page_3><loc_16><loc_43><loc_48><loc_66></location>
<caption>FIGURE 2. A 435MHz continuous wave of 10 -4 W from an Oscillator (Rohde & Schwarz SMB100A) was split (Mini-Circuits ZMSC-2) into a signal ⃗ sent to the coaxial tube through a circulator (MTC B115FFF) and another as a reference signal ⃗ that was phase shifted by a variable phase shifter (Mini-Circuits JSPHS-446). The reflected signal ⃗⃗ from the coaxial tube was sent to a combiner (Mini-Circuits ZMSC-2) through the circulator. The combined energy was measured by a real-time spectrum analyzer (Tektronix RSA3303B) and an ADC in NI ELVIS based on NI LabVIEW system through a detector, respectively. An output of the DAC in the NI ELVIS was fed to a variable phase shifter (Mini-Circuits JSPHS-446) to minimize | ⃗| , repeating a feedback in a loop.</caption>
</figure>
<text><location><page_3><loc_12><loc_10><loc_49><loc_21></location>A measurement of the power reflection fraction was done as follows. Before the electron beam irradiation, the vector of reflection signal was ⃗⃗ | ⃗⃗ | where a phase of was a constant without the irradiation. The phase of the reference signal was tuned to -so that the output of the combiner ⃗ ⃗⃗ ⃗ became close to zero. The amplitude of the reference signal was tuned</text>
<text><location><page_3><loc_52><loc_66><loc_88><loc_91></location>slightly by a variable attenuator (Mini-Circuits ZX732500-s) which was set just after the variable phase shifter so as to realize ⃗ | ⃗⃗ | . By simultaneously tuning the variable phase shifter and the variable attenuator in the feedback loop, the proper amplitude and phase of ⃗ was maintained. The control voltages of the variable phase shifter and the attenuator were recorded in each loop to know the phase shift and the attenuation. When the irradiation began, we stopped the feedback loop through the control program i.e. ⃗ | ⃗⃗ | was fixed. At the same time, the phase of the reflection signal began to change in ⃗⃗ | ⃗⃗ | . Consequently, the reflection combined amplitude of | ⃗| | ⃗⃗ ⃗ | began to increase and was measured by the RSA and the ADC of NI ELVIS.</text>
<text><location><page_3><loc_52><loc_55><loc_89><loc_66></location>In case of a measurement of the phase, we did not stop the feedback loop when the irradiation started. The phase was tuned automatically in the loop to get | ⃗| close to zero in the same way as the amplitude measurement. The reference signal was maintained as ⃗ | ⃗⃗ | . From the recorded phase of , we deduced of the reflected signal.</text>
<text><location><page_3><loc_52><loc_27><loc_89><loc_55></location>Figure 3 shows a result of the measurements for an ice target. The electron beam of 2 MeV with 2 mA was irradiating the target for 60 s. As the beam irradiated, the temperature increased from -60 to 35 over the time. The temperature was measured by the aforementioned thermocouple which was recorded by a NI CompactDAQ. The power reflection fraction measured by the RSA is plotted as small closed circles which is the reflection power fraction between the reflected wave and the wave injected to the coaxial tube. Five data points which were obtained by sampling over an interval of 128 ms are in 1 s. They increased from 0 to 8 ×10 -7 as the temperature rose and traced a curve without large fluctuations. The phase obtained from the variable phase shifter decreased from 0° to -0.2°. The relative refraction indices of n in ice [7] and the rock salt powder [8] increased with the temperature as in equations (1) and (2), respectively, where T is expressed in degrees Celsius.</text>
<formula><location><page_3><loc_61><loc_24><loc_88><loc_26></location>0.000260 1.786 n T (1)</formula>
<formula><location><page_3><loc_61><loc_21><loc_88><loc_23></location>0.000498 1.781 n T (2)</formula>
<text><location><page_3><loc_52><loc_11><loc_88><loc_19></location>Because the density of the rock salt powder is less than that of rock salt, the refractive index of rock salt powder is smaller than that of rock salt. We measured the refractive index of the rock salt powder and ice by a reflection method in a coaxial tube. The decrease of the phase in the measurement is explained by the</text>
<text><location><page_4><loc_12><loc_88><loc_48><loc_91></location>decrease of the velocity of the wave in the ice due to the increase of n .</text>
<text><location><page_4><loc_12><loc_82><loc_49><loc_88></location>The power of the reflected waves was calculated by Eq. (3) from the resulting vector ⃗ of a vector subtraction between two vectors with the length of | ⃗⃗ | and the rotation angle of :</text>
<formula><location><page_4><loc_19><loc_78><loc_49><loc_80></location> 2 2 2 1 ) c b cos (3)</formula>
<text><location><page_4><loc_12><loc_70><loc_49><loc_76></location>The power reflection fraction was obtained by a calculation using the phase difference and plotted as a short dash in Fig. 3. They are somewhat scattered but coincide very well with the RSA data.</text>
<text><location><page_4><loc_12><loc_55><loc_49><loc_70></location>A model calculation was done to confirm the cause of the radio wave reflection effect. We assumed that the temperature of the ice from the open end to 10 mm within the coaxial tube was the same as the measured temperature at 2 mm from the open end. We calculated the power reflection fraction based on the telegrapher's equations. The result was in agreement with the RSA value within 50 % during the irradiation and the shape was similar to the curve describing the temperature as a function of time.</text>
<figure>
<location><page_4><loc_13><loc_36><loc_48><loc_52></location>
<caption>FIGURE 3. During irradiation with the electron beam, the temperature of the ice target increased from -60 to -35 with time. The power reflection fraction measured by the RSA is plotted as small closed circles and increased from 0 to 8 × 10 -7 with the temperature. The phase obtained from by the variable phase shifter decreased from 0° to -0.2°. The power reflection fraction was got by a calculation using the phase and plotted as a short dash .</caption>
</figure>
<text><location><page_4><loc_12><loc_10><loc_49><loc_23></location>The power reflection fraction with respect to the square of the temperature rise is shown in Fig. 4. We compared the power reflection fractions at the irradiation time of 60 s for the beam currents of 1, 2 and 3 mA with the power reflection fraction of Fresnel equations as shown in Eq. (4). The refractive indices n1 and n2 are calculated from the measured temperatures before and during the irradiation, respectively.</text>
<figure>
<location><page_4><loc_52><loc_72><loc_84><loc_88></location>
<caption>1.E+01 1.E+02 1.E+03 1.E+05 Square of temperature rise (AT)?/K?</caption>
</figure>
<paragraph><location><page_4><loc_52><loc_58><loc_88><loc_66></location>FIGURE 4. Power reflection fraction with respective to the square of the temperature rise are shown. Calculated values and measured values of the salt powder or the ice are depicted as 'Salt (Fresnel)' or 'Ice(Fresnel)' by a line connected by dots and 'Salt' by closed triangles or 'Ice' by closed circles, respectively.</paragraph>
<formula><location><page_4><loc_63><loc_53><loc_88><loc_57></location> 2 2 1 2 2 1 n n n n (4)</formula>
<text><location><page_4><loc_52><loc_21><loc_88><loc_51></location>The values of , calculated by Eq. (4) using Eq. (1) and the measured values of the salt powder are depicted as 'Salt (Fresnel)' by a line connected by dots and the measured value 'Salt' by closed triangles, respectively. A line connected by dots of 'Ice (Fresnel)' is also calculated by Eq. (4). As can be seen, 'Salt (Fresnel)' is 3.6 times larger than 'Ice (Fresnel)', but the experimental data of 'Ice' of closed circles and 'Salt' of closed triangles are roughly the same with respect to the square of the temperature rise. The data of 'Salt' and 'Ice' are 16 and 54 % compared with 'Salt (Fresnel)' and 'Ice (Fresnel)', respectively. The loss of the reflection fraction was partly due to imperfect signal transmission of the coaxial tube and the partial measurement of the temperature. The higher power reflection fraction in 'Ice' compared to 'Salt' suggests that the ice was partly melted along an electron track locally. The refractive index of water at 0 is 5.3 times larger than that of ice. It might enhance the power reflection fraction.</text>
<section_header_level_1><location><page_4><loc_64><loc_16><loc_78><loc_18></location>III. SUMMARY</section_header_level_1>
<text><location><page_4><loc_52><loc_9><loc_88><loc_15></location>We found a radio wave reflection effect from ice as well as rock salt through irradiation with an electron beam. In addition to the amplitude measurement, we measured the phase of the reflected radio wave from</text>
<text><location><page_5><loc_12><loc_72><loc_49><loc_91></location>ice and rock salt by constructing an automatic feedback loop for the null detection method in which the variable phase shifter was tuned to get the null output. The fraction of the reflected power was calculated from the difference of two vectors with the same length and rotated with respect to each other by the rotation angle. Moreover we explained the reflection by a model in which the phase delay of the reflected wave was caused by the increase of the refractive index due to the temperature rise. The radio wave reflection effect is applicable to a radar method to detect GZKν in a huge amount of rock salt formation, Antarctic ice sheet and the moon crust.</text>
<text><location><page_5><loc_12><loc_50><loc_49><loc_72></location>Five types of radiation detectors using thermal effects are compared in Table 1. A 'Radar Chamber' as well as a 'Bolometer' detects a temperature rise due to an energy deposition of incident radiation. It receives the reflected radio wave (10 MHz - 1 GHz) from a heated portion emitted by a transmitter. It is appropriate to detect weakly interacting particle like neutrinos since the medium is a solid with a large density. The change of the refractive index of a medium is rather small due to the smaller temperature rise in the large volume of the shower. However the coherent reflection effect between the reflected waves from the many heated points distributed in the large volume of the shower might enhance the reflection fraction for wavelengths that are long compared to the</text>
<text><location><page_5><loc_52><loc_66><loc_88><loc_91></location>shower diameter. Even with a coherence effect the reflected radio wave is weak and a 'Radar Chamber' is suitable only for a large energy deposit. The detector size depends on the reflection fraction and the attenuation length of radio waves in the medium. The attenuation along the path could be compensated by a strong and narrow beam of radio waves generated artificially. We could detect GZKv's using radio waves with a peak power of 1 GW (Equivalent Isotropic Radiation Power) where the radio waves are supplied by a phased array antenna set on a surface of the medium. We do not need expensive boreholes for the installation of antennas. A 'Radar Chamber' has a long memory time and we could scan the effective volume by a radio wave beam within the memory time. So it could be operated as a stand-alone detector without a trigger detector system.</text>
<text><location><page_5><loc_52><loc_53><loc_88><loc_66></location>According to the elucidation of the radio wave reflection mechanism, a new radiation detector 'Radar Chamber' is applicable for all dielectric media where the refractive indices change with temperature. It is not only for radiation detection but also for other purposes using materials with inhomogeneous refractive index in space and time. An application for human-body imaging could be investigated at 10 MHz where the attenuation length is 5 cm.</text>
<table>
<location><page_5><loc_12><loc_18><loc_89><loc_47></location>
<caption>TABLE 1. Radiation detectors using heat effects.</caption>
</table>
<section_header_level_1><location><page_6><loc_17><loc_88><loc_41><loc_89></location>ACKNOWLEDGEMENTS</section_header_level_1>
<text><location><page_6><loc_9><loc_80><loc_49><loc_87></location>This work is partially supported by a Grant in Aid for Scientific Research for Ministry of Education, Science, Technology and Sports and Culture of Japan, and Funds of Tokutei Kenkyuhi and Tokubetsu Kenkyuhi at Tokyo Metropolitan University and Seikei University, respectively.</text>
<unordered_list>
<list_item><location><page_6><loc_9><loc_77><loc_45><loc_78></location>1. Berezinsky and Zatsepin, Phys. Lett.B 28 (1969)423.</list_item>
<list_item><location><page_6><loc_9><loc_75><loc_45><loc_77></location>2. K. Greisen, Phys. Rev. Lett. 16 (1966) pp. 748 - 750.</list_item>
<list_item><location><page_6><loc_9><loc_72><loc_48><loc_75></location>3. G.T. Zatsepin, V.A. Kuzmin, Zh. Eksp. Teor. Fiz. Pis'ma Red . 4 (1966) 114 ( Sov. Phys. JETP Lett. 4 (1966) 78).</list_item>
<list_item><location><page_6><loc_9><loc_62><loc_48><loc_72></location>4. M. Chiba et al., Proceedings of The 15 th international Conference on Supersymmetry and the Unification of fundamental Interactions , Volume I, pp. 850-853, Published by the University of Karlsruhe in collaboration with Tibun EU s.r.o. First Edition, Bruno 2008, ISBN978-80-7399-268-2. arXiv:0710.418v1 [astro-ph] 23 Oct 2007 .</list_item>
<list_item><location><page_6><loc_9><loc_56><loc_49><loc_62></location>5. M. Chiba et al., Nuclear Instr. and Meth., A604 (2009) pp. S233-S235. doi:10.1016/j.nima.2009.03.066. 6. M. Chiba et al., Nuclear Instr. and Meth, A662 (2012) pp. S222-S225. doi:10.1016/j.nima.2010.11.165 .</list_item>
<list_item><location><page_6><loc_9><loc_53><loc_48><loc_56></location>7. T. Matsuoka, S. Fujita and S. Mae, J. Appl. Phys. 80 (1996) pp. 5885 - 5890.</list_item>
<list_item><location><page_6><loc_9><loc_52><loc_38><loc_53></location>8. J. C. Owens, Phys. Rev. 181 (1969) 1228.</list_item>
</unordered_list>
<text><location><page_6><loc_52><loc_84><loc_92><loc_91></location>This work has been performed at the station of AR-NE5A, KEK under the approval of the Photon Factory Program Advisory Committee (Proposal No. 2004P009, 2005G121) and has been supported by the Inter-University Program for the Joint Use of JAEA Facilities.</text>
</document>
[
{
"title": "Measurement of a Phase of a Radio Wave Reflected from Rock Salt and Ice Irradiated by an Electron Beam for Detection of Ultra-High-Energy Neutrinos",
"content": "Masami Chiba 1 , Toshio Kamijo 1 , Takahiro Tanikawa 1 , Hiroyuki Yano 1 , Fumiaki Yabuki 1 , Osamu Yasuda 1 , Yuichi Chikashige 2 , Tadashi Kon 2 , Yutaka Shimizu 2 , Souichirou Watanabe 2 , Michiaki Utsumi 3 , Masatoshi Fujii 4 4 School of Medicine, Shimane University, Izumo-shi, Shimane 693-8501, Japan We have found a radio-wave-reflection effect in rock salt for the detection of ultra-high energy neutrinos (UHEν's) which are expected to be generated in Greisen, Zatsepin, and Kuzmin (GZK) processes in the universe. When an UHEν interacts with rock salt or ice as a detection medium, a shower is generated. That shower is formed by hadronic and electromagnetic avalanche processes. The energy of the UHEν shower converts to thermal energy through ionization processes. Consequently, the temperature rises along the shower produced by the UHEν. The refractive index of the medium rises with temperature. The irregularity of the refractive index in the medium leads to a reflection of radio waves. This reflection effect combined with the long attenuation length of radio waves in rock salt and ice would yield a new method to detect UHEν's. We measured the phase of the reflected radio wave under irradiation with an electron beam on ice and rock salt powder. The measured phase showed excellent consistence with the power reflection fraction which was measured directly. A model taking into account the temperature change explained the phase and the amplitude of the reflected wave. Therefore the reflection mechanism was confirmed. The power reflection fraction was compared with that calculated with the Fresnel equations, the ratio between the measured result and that obtained with the Fresnel equations in ice was larger than that of rock salt. Keywords: Neutrino detectors; ultra-high-energy cosmic rays; Rock salt; Antarctic ice sheet; Radar",
"pages": [
1
]
},
{
"title": "I. INTRODUCTION",
"content": "Ultra-high-energy neutrinos (UHEν's) were predicted to be produced at a collision of UHE-cosmic ray with the cosmic-microwave-radiation background by Berezinsky and Zatsepin [1] in Greisen, Zatsepin, and Kuzmin (GZK) processes in the universe [2, 3]. In order to detect them we had searched for and found a radio-wave-reflection effect in rock salt [4 - 6]. A gigantic detector is needed for the detection due to the expected ultra-low flux of about 1 km -2 d -1 . When an",
"pages": [
1
]
},
{
"title": "Email: [email protected]",
"content": "Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in (5 th International Workshop on Acoustic and Radio EeV Neutrino Detection Activities , AIP Conf. Proc. 1535, 45-50 (2013) ) and may be found at ( http://dx.doi.org/10.1063/1.4807519 ). UHEν interacts with rock salt or ice as a detection medium, a shower is generated. That shower is formed by hadronic and electromagnetic avalanche processes. The energy of the UHEν shower converts finally to thermal energy through ionization processes. Consequently, the temperature rises along the shower produced by the UHEν. The refractive index rises as a function of the temperature. The irregularity of the refractive index in the medium for radio waves causes reflection. This reflection effect combined with long attenuation length of radio waves in rock salt and ice would yield a new method to detect UHEν's. We could find a huge amount of rock salt or ice of over 50 Gt in natural rock salt formations or the Antarctic ice sheet. The volume of the rock salt is 3 × 3 × 3 km 3 which is required for the detection of the neutrino flux. Radio waves transmitted into the medium generated by a radar system with a phased array antenna could be reflected by the shower. Receiving the reflected radio waves could be a method for the detection of the UHEν's. We had carried out an experiment [4] previously to the one described in this article to observe microwave reflection effects from a small rock-salt sample of 2 × 2 × 10 mm 3 irradiated by a synchrotron radiation Xray with a pulse width of 1.7 s. It was set in a 9.4 GHz waveguide [4] while microwaves were continuously injected to the waveguide. A null-detection method was employed to detect the feeble reflected signal in the waveguide circuit. Reflected microwaves were observed with a power reflection fraction of 1 × 10 -6 and a decay time of 8 s after the irradiation had stopped. The shape of the power reflection fraction with respect to time was similar to that of the temperature change in rock salt. The reflection fraction was proportional to the square of the X-ray intensity. A larger rock salt sample of 10 cm 3 was irradiated by a 2 MeV electron beam with a duration of 60 s which was set in a free space without using a waveguide [5]. A continuous 435 MHz radio wave struck at the cube from a six-element Uda-Yagi antenna. The reflected power fraction increased as the temperature rose at the irradiated surface of the cube. The observation of the reflection excluded the possibility that the effect was due to a distortion of the waveguide heated by X-ray irradiation at the experiment [4]. A 435 MHz waveguide filled with rock salt powder was used to measure the radio wave reflection effect [6]. The 2 MeV electron beam was injected to rock salt powder through an aluminum-beam window of 20 × 20 cm 2 with a thickness of 0.5 mm. A continuous 435 MHz radio wave of 10 -4 W was emitted by a quarterwavelength antenna installed in the salt powder and the reflected radio wave was detected by the same antenna. The reflection fraction increased with the square of the temperature rise at the irradiated surface of the rock salt powder. The reflection fraction could be explained by the Fresnel equations.",
"pages": [
1,
2
]
},
{
"title": "II. EXPERIMENT",
"content": "We report now on a new experiment using a coaxial tube (WX-20D) with a diameter of 20 mm and a length of 100 mm. An electron beam was injected into an open end of the coaxial tube set in a dry-ice cooling box. The coaxial tube was filled with rock salt powder or ice and was set in the cooling box as shown in Fig. 1. The temperature was measured by a chromel-alumel thermocouple positioned 2 mm from the surface of the open end. The refractive indices of rock salt powder and ice were measured by the reflection method from 0.4 MHz to 1 GHz in the coaxial tube yielding 1.79 0.01 at 22 and 1.76 0.01 at -60 , respectively. Then the diameter of the inner conductor was set to 4.5 mm in order to obtain an impedance of 50 when the tube was filled with the respective medium. We utilized a 2 MeV electron beam produced by a Cockcroft-Walton accelerator located at the Takasaki Advanced Radiation Research Institute (TARRI) of Japan Atomic Energy Agency (JAEA). The electron beam of 2 MeV was irradiated on the open end of the coaxial tube with a power of 4.2 J/s and a current of 1 mA. For the irradiation of a large target and to prevent damage of a titanium vacuum-beam window, the electron beam was swept over the target with a width of 1 m at 200Hz. Only a small part of the beam hit the open end of the coaxial tube. The increase of the refractive index with respect to the temperature gave rise to radio-wave reflection. We observed the reflection effect from ice as well as rock salt. As shown in Fig. 2, a 435 MHz continuous wave of 10 -4 W from an Oscillator (Rohde & Schwarz SMB100A) was split (Mini-Circuits ZMSC-2) into a signal ⃗ (expressed as a vector) sent to the coaxial tube through a circulator (MTC B115FFF) and reference signal ⃗ that could be phase shifted by a variable phase shifter (Mini-Circuits JSPHS-446). The reflected signal ⃗⃗ from the coaxial tube was sent to a combiner (Mini-Circuits ZMSC-2) through the circulator. The combined signal of ⃗ ⃗⃗ ⃗ was split into a real-time spectrum analyzer (Tektronix RSA3303B) and a detector (Power Detector, MiniCircuits ZX47-60-S+) for the power measurement. In order to reject noises due to the power source of 50 Hz, from the real-time spectrum analyzer (RSA), 1024 data samples within 128 ms in the time domain were fast-Fourier transformed to the frequency domain. The peak at 435 MHz was selected within 8 Hz to reject noise. In order to tune the frequency precisely between the oscillator and RSA, they were locked by the 10 MHz signal generated by a Rubidium-frequency standard (Stanford Research Systems FS725). The output signal of the detector was routed to an Educational-Laboratory-Virtual-Instruments Suite (National Instruments NI ELVIS) based on an NI LabVIEW system where the signal was digitized by an ADC. The digital output was converted to a value, such that the output of the combiner became zero, by a control program of LabVIEW and converted to an analog voltage by a DAC in the NI ELVIS. The analog signal was fed to the variable phase shifter as a control voltage where the phase of the reference signal ⃗ was shifted according to the voltage. The output of the phase shifter was fed to the combiner again. The feedback loop was repeated 13 Hz. A measurement of the power reflection fraction was done as follows. Before the electron beam irradiation, the vector of reflection signal was ⃗⃗ | ⃗⃗ | where a phase of was a constant without the irradiation. The phase of the reference signal was tuned to -so that the output of the combiner ⃗ ⃗⃗ ⃗ became close to zero. The amplitude of the reference signal was tuned slightly by a variable attenuator (Mini-Circuits ZX732500-s) which was set just after the variable phase shifter so as to realize ⃗ | ⃗⃗ | . By simultaneously tuning the variable phase shifter and the variable attenuator in the feedback loop, the proper amplitude and phase of ⃗ was maintained. The control voltages of the variable phase shifter and the attenuator were recorded in each loop to know the phase shift and the attenuation. When the irradiation began, we stopped the feedback loop through the control program i.e. ⃗ | ⃗⃗ | was fixed. At the same time, the phase of the reflection signal began to change in ⃗⃗ | ⃗⃗ | . Consequently, the reflection combined amplitude of | ⃗| | ⃗⃗ ⃗ | began to increase and was measured by the RSA and the ADC of NI ELVIS. In case of a measurement of the phase, we did not stop the feedback loop when the irradiation started. The phase was tuned automatically in the loop to get | ⃗| close to zero in the same way as the amplitude measurement. The reference signal was maintained as ⃗ | ⃗⃗ | . From the recorded phase of , we deduced of the reflected signal. Figure 3 shows a result of the measurements for an ice target. The electron beam of 2 MeV with 2 mA was irradiating the target for 60 s. As the beam irradiated, the temperature increased from -60 to 35 over the time. The temperature was measured by the aforementioned thermocouple which was recorded by a NI CompactDAQ. The power reflection fraction measured by the RSA is plotted as small closed circles which is the reflection power fraction between the reflected wave and the wave injected to the coaxial tube. Five data points which were obtained by sampling over an interval of 128 ms are in 1 s. They increased from 0 to 8 ×10 -7 as the temperature rose and traced a curve without large fluctuations. The phase obtained from the variable phase shifter decreased from 0° to -0.2°. The relative refraction indices of n in ice [7] and the rock salt powder [8] increased with the temperature as in equations (1) and (2), respectively, where T is expressed in degrees Celsius. Because the density of the rock salt powder is less than that of rock salt, the refractive index of rock salt powder is smaller than that of rock salt. We measured the refractive index of the rock salt powder and ice by a reflection method in a coaxial tube. The decrease of the phase in the measurement is explained by the decrease of the velocity of the wave in the ice due to the increase of n . The power of the reflected waves was calculated by Eq. (3) from the resulting vector ⃗ of a vector subtraction between two vectors with the length of | ⃗⃗ | and the rotation angle of : The power reflection fraction was obtained by a calculation using the phase difference and plotted as a short dash in Fig. 3. They are somewhat scattered but coincide very well with the RSA data. A model calculation was done to confirm the cause of the radio wave reflection effect. We assumed that the temperature of the ice from the open end to 10 mm within the coaxial tube was the same as the measured temperature at 2 mm from the open end. We calculated the power reflection fraction based on the telegrapher's equations. The result was in agreement with the RSA value within 50 % during the irradiation and the shape was similar to the curve describing the temperature as a function of time. The power reflection fraction with respect to the square of the temperature rise is shown in Fig. 4. We compared the power reflection fractions at the irradiation time of 60 s for the beam currents of 1, 2 and 3 mA with the power reflection fraction of Fresnel equations as shown in Eq. (4). The refractive indices n1 and n2 are calculated from the measured temperatures before and during the irradiation, respectively. The values of , calculated by Eq. (4) using Eq. (1) and the measured values of the salt powder are depicted as 'Salt (Fresnel)' by a line connected by dots and the measured value 'Salt' by closed triangles, respectively. A line connected by dots of 'Ice (Fresnel)' is also calculated by Eq. (4). As can be seen, 'Salt (Fresnel)' is 3.6 times larger than 'Ice (Fresnel)', but the experimental data of 'Ice' of closed circles and 'Salt' of closed triangles are roughly the same with respect to the square of the temperature rise. The data of 'Salt' and 'Ice' are 16 and 54 % compared with 'Salt (Fresnel)' and 'Ice (Fresnel)', respectively. The loss of the reflection fraction was partly due to imperfect signal transmission of the coaxial tube and the partial measurement of the temperature. The higher power reflection fraction in 'Ice' compared to 'Salt' suggests that the ice was partly melted along an electron track locally. The refractive index of water at 0 is 5.3 times larger than that of ice. It might enhance the power reflection fraction.",
"pages": [
2,
3,
4
]
},
{
"title": "III. SUMMARY",
"content": "We found a radio wave reflection effect from ice as well as rock salt through irradiation with an electron beam. In addition to the amplitude measurement, we measured the phase of the reflected radio wave from ice and rock salt by constructing an automatic feedback loop for the null detection method in which the variable phase shifter was tuned to get the null output. The fraction of the reflected power was calculated from the difference of two vectors with the same length and rotated with respect to each other by the rotation angle. Moreover we explained the reflection by a model in which the phase delay of the reflected wave was caused by the increase of the refractive index due to the temperature rise. The radio wave reflection effect is applicable to a radar method to detect GZKν in a huge amount of rock salt formation, Antarctic ice sheet and the moon crust. Five types of radiation detectors using thermal effects are compared in Table 1. A 'Radar Chamber' as well as a 'Bolometer' detects a temperature rise due to an energy deposition of incident radiation. It receives the reflected radio wave (10 MHz - 1 GHz) from a heated portion emitted by a transmitter. It is appropriate to detect weakly interacting particle like neutrinos since the medium is a solid with a large density. The change of the refractive index of a medium is rather small due to the smaller temperature rise in the large volume of the shower. However the coherent reflection effect between the reflected waves from the many heated points distributed in the large volume of the shower might enhance the reflection fraction for wavelengths that are long compared to the shower diameter. Even with a coherence effect the reflected radio wave is weak and a 'Radar Chamber' is suitable only for a large energy deposit. The detector size depends on the reflection fraction and the attenuation length of radio waves in the medium. The attenuation along the path could be compensated by a strong and narrow beam of radio waves generated artificially. We could detect GZKv's using radio waves with a peak power of 1 GW (Equivalent Isotropic Radiation Power) where the radio waves are supplied by a phased array antenna set on a surface of the medium. We do not need expensive boreholes for the installation of antennas. A 'Radar Chamber' has a long memory time and we could scan the effective volume by a radio wave beam within the memory time. So it could be operated as a stand-alone detector without a trigger detector system. According to the elucidation of the radio wave reflection mechanism, a new radiation detector 'Radar Chamber' is applicable for all dielectric media where the refractive indices change with temperature. It is not only for radiation detection but also for other purposes using materials with inhomogeneous refractive index in space and time. An application for human-body imaging could be investigated at 10 MHz where the attenuation length is 5 cm.",
"pages": [
4,
5
]
},
{
"title": "ACKNOWLEDGEMENTS",
"content": "This work is partially supported by a Grant in Aid for Scientific Research for Ministry of Education, Science, Technology and Sports and Culture of Japan, and Funds of Tokutei Kenkyuhi and Tokubetsu Kenkyuhi at Tokyo Metropolitan University and Seikei University, respectively. This work has been performed at the station of AR-NE5A, KEK under the approval of the Photon Factory Program Advisory Committee (Proposal No. 2004P009, 2005G121) and has been supported by the Inter-University Program for the Joint Use of JAEA Facilities.",
"pages": [
6
]
}
]
2013AJ....145...88M
https://arxiv.org/pdf/1301.1086.pdf
<document>
<section_header_level_1><location><page_1><loc_27><loc_86><loc_73><loc_87></location>NEW UBVRI PHOTOMETRY OF 234 M33 STAR CLUSTERS</section_header_level_1>
<text><location><page_1><loc_46><loc_84><loc_53><loc_85></location>Jun Ma 1,2</text>
<text><location><page_1><loc_46><loc_83><loc_54><loc_84></location>AJ, in press</text>
<section_header_level_1><location><page_1><loc_45><loc_80><loc_55><loc_81></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_68><loc_86><loc_80></location>This is the second paper of our series. In this paper, we present UBVRI photometry for 234 star clusters in the field of M33. For most of these star clusters, there is photometry in only two bands in previous studies. The photometry of these star clusters is performed using archival images from the Local Group Galaxies Survey, which covers 0.8 deg 2 along the major axis of M33. Detailed comparisons show that, in general, our photometry is consistent with previous measurements, especially, our photometry is in good agreement with Zloczewski & Kaluzny. Combined with the star clusters' photometry in previous studies, we present some results: none of the M33 youngest clusters ( ∼ 10 7 yr) have masses approaching 10 5 M /circledot ; comparisons with models of simple stellar populations suggest a large range of ages of M33 star clusters, and some as old as the Galactic globular clusters.</text>
<text><location><page_1><loc_14><loc_64><loc_86><loc_67></location>Subject headings: catalogs - galaxies: individual (M33) - galaxies: spiral - galaxies: star clusters: general</text>
<section_header_level_1><location><page_1><loc_22><loc_61><loc_35><loc_62></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_54><loc_48><loc_60></location>Star clusters are an important tool for studying the star formation histories of galaxies. They represent, in distinct and luminous 'packets,' single-age and singleabundance points and encapsulate at least a partial history of the parent galaxy's evolution.</text>
<text><location><page_1><loc_8><loc_40><loc_48><loc_54></location>M33 is a small Scd Local Group galaxy. It is located ∼ 809 ± 24 kpc from us (distance modulus ( m -M ) 0 = 24 . 54 ± 0 . 06; McConnachie et al. 2004, 2005). M33 is interesting and important because it represents an intermediate morphological type between the largest 'earlytype' spirals and the dwarf irregulars in the Local Group. So, it can provide an important link between the star cluster populations of earlier-type spirals (Milky Way and M31) and the numerous nearby later-type dwarf galaxies.</text>
<text><location><page_1><loc_8><loc_15><loc_48><loc_40></location>In the pioneering work of M33 star clusters, Hiltner (1960) presented photometry for 23 M33 star cluster candidates and 23 M31 globular clusters in the UBV passbands using photographic plates taken with the Mt. Wilson 100-inch (2.5-m) telescope. And he found that, except for five of them, the star clusters in M33 are bluer and fainter than those in M31. At the same time, Kron & Mayall (1960) identified four M33 star clusters for which they gave PV photometry. Then, Melnick & D'Odorico (1978) detected 58 star cluster candidates in M33 based on a baked IIIa-J+GG385 plate covering a field of about 1 · in diameter, including B photometry of them. The most comprehensive catalog of nonstellar objects in M33 was compiled by Christian & Schommer (1982, 1988), who detected 250 nonstellar objects by visually examining a single photographic plate taken at the Ritchey-Chrestien focus of the 4-m telescope at Kitt Peak National Observatory. These authors obtained ground-based BVI photometry of 106</text>
<text><location><page_1><loc_10><loc_10><loc_48><loc_14></location>1 National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100012, China; [email protected]</text>
<text><location><page_1><loc_10><loc_7><loc_48><loc_10></location>2 Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China</text>
<text><location><page_1><loc_52><loc_58><loc_92><loc_62></location>of these objects, which they believe to be star clusters. However, the star cluster candidates detected by these authors are limited to the outer part of M33.</text>
<text><location><page_1><loc_52><loc_46><loc_92><loc_58></location>The first survey for M33 star clusters based on CCD imaging was performed by Mochejska et al. (1998), using the data collected in the DIRECT project (Kaluzny et al. 1998; Stanek et al. 1998). These authors detected 51 globular cluster candidates in M33, 32 of which were not previously cataloged. These globular cluster candidates covered the central region of M33. In addition, Mochejska et al. (1998) presented BVI photometry for these globular cluster candidates.</text>
<text><location><page_1><loc_52><loc_28><loc_92><loc_46></location>Since the pioneering work of Chandar et al. (1999a), the era of detecting and studying M33 star clusters based on the images taken with Hubble Space Telescope ( HST ) has begun (Chandar et al. 1999a,b,c, 2001, 2002; Bedin et al. 2005; Park & Lee 2007; Sarajedini et al. 2007, 1998, 2000; Stonkut˙e et al. 2008; Park et al. 2009; Huxor et al. 2009; San Roman et al. 2009; Zloczewski & Kaluzny 2009). The HST resolution makes it easy to distinguish individual stars from star clusters at the distance of M33. So, M33 star clusters identified with HST images are much less likely to be contaminated by other extended sources, such as a background galaxy or an HII region (see Park & Lee 2007, for details).</text>
<text><location><page_1><loc_52><loc_21><loc_92><loc_28></location>Ma et al. (2001, 2002a,b,c,d, 2004a,b) constructed spectral energy distributions in 13 intermediate filters of the Beijing-Arizona-Taiwan-Connecticut photometric system for known M33 star clusters and star cluster candidates, and estimated star cluster properties.</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_21></location>In order to construct a single master catalog incorporating the entries in all of the individual catalogs including all known properties of each star cluster, Sarajedini & Mancone (2007) merged all of the abovementioned catalogs before 2007, for a summary of the properties of all of these catalogs. This catalog contains 451 star cluster candidates, of which 255 are confirmed star clusters based on the HST and high-resolution ground-based imaging. The positions of the star clusters in Sarajedini & Mancone (2007) were transformed</text>
<text><location><page_2><loc_8><loc_89><loc_48><loc_92></location>to the J2000.0 epoch and refined using the Local Group Galaxies Survey (LGGS; Massey et al. 2006).</text>
<text><location><page_2><loc_8><loc_73><loc_48><loc_89></location>Very recently, some authors used the images observed with the MegaCam camera on the 3.6-m Canada-France-Hawaii Telescope (CFHT/MegaCam) to detect star clusters in M33 (Zloczewski et al. 2008; San Roman et al. 2010). Sharina et al. (2010) presented the evolutionary parameters of 15 GCs in M33 based on the results of medium-resolution spectroscopy obtained at the Special Astrophysical Observatory 6-m telescope. Most recently, Cockcroft et al. (2011) searched for outer halo star clusters in M33 based on CFHT/MegaCam imaging as part of the Pan-Andromeda Archaeological Survey.</text>
<text><location><page_2><loc_8><loc_65><loc_48><loc_73></location>Ma (2012) (Paper I) presented UBVRI photometry of 392 objects (277 star clusters and 115 star cluster candidates) in the field of M33, using the images of the LGGS (Massey et al. 2006). And he also provided properties of M33 star clusters such as their color-magnitude diagram and color-color diagram.</text>
<text><location><page_2><loc_8><loc_53><loc_48><loc_65></location>In this paper, we perform aperture photometry of 234 M33 star clusters based on the M33 images of the LGGS. These sample star clusters are selected from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). This paper is organized as follows. Section 2 describes the sample star cluster selection and UBVRI photometry. In Section 3, we present an analysis of the star cluster properties. Lastly, our conclusions are presented in Section 4.</text>
<section_header_level_1><location><page_2><loc_25><loc_51><loc_31><loc_52></location>2. DATA</section_header_level_1>
<section_header_level_1><location><page_2><loc_24><loc_49><loc_32><loc_50></location>2.1. Sample</section_header_level_1>
<text><location><page_2><loc_8><loc_7><loc_48><loc_48></location>In Paper I, we presented an updated UBVRI photometric catalog containing 392 star clusters and star cluster candidates in the field of M33 which were selected from the most recent star cluster catalog of Sarajedini & Mancone (2007). And we also provided properties of M33 star clusters such as their colormagnitude diagram (CMD) and color-color diagram combined with the photometry of M33 star clusters from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). However, we found that most of M33 star clusters from San Roman et al. (2009) and Zloczewski & Kaluzny (2009) have photometry in only two bands V and I . In the color-color diagram of Paper I, there are only ∼ 300 M33 star clusters, since ∼ 200 star clusters have no B -V data. So, integrated magnitudes of these star clusters in B and V bands are emergently needed for studying the properties of M33 star clusters. In this paper, we will provide UBVRI photometry of M33 star clusters from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). Park & Lee (2007) found 104 star clusters in the HST /WFPC 2 archive images of 24 fields that were not included in previous studies, of which 32 star clusters are newly detected. Zloczewski et al. (2008) presented a catalog of 4780 extended sources in a 1 deg 2 region around M33 including 3554 new star cluster candidates using the MegaCam camera on the CFHT. Zloczewski & Kaluzny (2009) used deep Advanced Camera for Surveys Wide Field Channel (ACS/WFC) images of M33 to check the nature of extended objects detected by Zloczewski et al. (2008),</text>
<text><location><page_2><loc_52><loc_7><loc_92><loc_92></location>and found that 24 star cluster candidates were confirmed to genuine compact star clusters. In addition, Zloczewski & Kaluzny (2009) detected 91 new star clusters based on these deep ASC/WFC images of M33, and provided integrated magnitudes and angular sizes for all these 115 star clusters. San Roman et al. (2009) presented integrated photometry and color-magnitude diagrams for 161 star clusters in M33 based on the ACS/WFC images, of which 115 were previously uncataloged. By cross-checking with the updated photometric catalog of M33 star cluster and candidate in Paper I, we found that, the photometry of 36 star clusters of Park & Lee (2007) was not presented in Paper I, of which the 32 star clusters were newly detected by Park & Lee (2007) and the remaining four were detected by previous studies. The three of the four star clusters were included in Sarajedini & Mancone (2007) and were classified as 'Stellar' (objects 69, 293 and 279 of Sarajedini & Mancone 2007 which being called star clusters 36, 195 and 197 in Park & Lee 2007, respectively), and the remaining one is star cluster 75 in Park & Lee (2007). The photometry of 118 star clusters of San Roman et al. (2009) was not presented in Paper I, of which 115 star clusters were newly detected by San Roman et al. (2009) based on the ACS/WFC images, and the remaining three star clusters were included in Sarajedini & Mancone (2007) which were classified as 'Galaxy' or 'Stellar' (objects 57, 62 and 69 of Sarajedini & Mancone 2007 which being called star clusters 27, 34 and 38 in San Roman et al. 2009). The photometry of all star clusters of Zloczewski & Kaluzny (2009) was not presented in Paper I, of which one star cluster was included in Sarajedini & Mancone (2007) and was classified as 'Galaxy' (object 57 of Sarajedini & Mancone 2007 which being called 33-3-021 in Zloczewski & Kaluzny 2009). So, in this paper, we will perform photometry for the M33 star clusters in Park & Lee (2007), Zloczewski & Kaluzny (2009) and San Roman et al. (2009) that were not presented in Paper I. Altogether, there are 269 star clusters combining the star clusters from Park & Lee (2007), Zloczewski & Kaluzny (2009) and San Roman et al. (2009). However, by cross-checking the coordinates of the star clusters of Park & Lee (2007), Zloczewski & Kaluzny (2009) and San Roman et al. (2009), and by checking the images of star clusters from the LGGS images, we found that, star clusters 7, 10, 14, and 18 of Park & Lee (2007) are the same objects with star clusters 33, 51, 59, and 64 of San Roman et al. (2009), respectively. In addition, there are 18 common star clusters between Zloczewski & Kaluzny (2009) and San Roman et al. (2009) (see Table 3 of San Roman et al. 2009). When we do photometry of the sample star clusters in this paper, we found that, there is nothing in the position of star cluster 195 of Park & Lee (2007) (i.e., no. 17 of Bedin et al. 2005), which was named object 293 in Sarajedini & Mancone (2007) and was classified as 'Stellar' by Sarajedini & Mancone (2007). We also found that, in the LGGS images of M33, (1) there are some bright objects near star cluster 12 of Park & Lee (2007); (2) there is a bright object near star clusters 23 and 32 of Park & Lee (2007), respectively; (3) there is a bright object very near star clusters 15, 114 and 141 of San Roman et al. (2009), respectively; (4) there are three bright objects near star cluster 143 of</text>
<text><location><page_3><loc_8><loc_81><loc_48><loc_92></location>San Roman et al. (2009); (5) there is a very close object to star clusters ZK-21, ZK-22, ZK-28, ZK-66 and ZK-72 of Zloczewski & Kaluzny (2009), respectively. The photometry of these 13 star clusters cannot be determined accurately in this paper. So, this paper will present homogeneous UBVRI photometries for 234 star clusters in M33 using the images of the LGGS (see details about the LGGS in Paper I).</text>
<section_header_level_1><location><page_3><loc_22><loc_79><loc_34><loc_80></location>2.2. Photometry</section_header_level_1>
<text><location><page_3><loc_8><loc_28><loc_48><loc_78></location>We used the LGGS archival images of M33 in the UBVRI bands to do photometry (see details in Paper I). We performed aperture photometry of the 234 M33 star clusters found in the LGGS images in all of the UBVRI bands to provide a comprehensive and homogeneous photometric catalog for them. The photometry routine we used is iraf/daophot (Stetson 1987). The photometric process used in this paper is the same as in Paper I. We have checked the aperture of every sample star cluster considered here by visual examination to make sure that it was not too large (to avoid contamination from other sources). The aperture photometry of star clusters was transformed to the standard system using transformation (constant offsets neglecting color term) derived based on aperture photometry of stars whose UBVRI magnitudes were published by Massey et al. (2006), who calibrated their photometry with standard stars of Landolt (1992). Finally, except for star cluster 27 of San Roman et al. (2009) (i.e., SR27, which was named 33-3-021 in Zloczewski & Kaluzny 2009) and ZK-82 of Zloczewski & Kaluzny (2009) in the I band, and ZK-90 of Zloczewski & Kaluzny (2009) in the U and I bands, we obtained photometry for 234 star clusters in the individual UBVRI bands. SR27 falls in the gap of the LGGS image in the I band, and ZK-82 and ZK-90 in the I band fall in the bleeding CCD column of a saturated star, and ZK-90 in the U band does not lie in the LGGS image. Table 1 lists our new UBVRI magnitudes and the aperture radii used (we adopted 0.258 '' pixel -1 from the image header), with errors given by iraf/daophot . The star cluster names follow the naming convention of Sarajedini & Mancone (2007) (i.e., SM ××× ), Park & Lee (2007) (i.e., PL ××× ), San Roman et al. (2009) (i.e., SR ××× ), and Zloczewski & Kaluzny (2009). In addition, we also list the reddening values of the sample star clusters in Table 1 (see Section 3.1 for details). In Table 1, R C and I C mean that RI magnitudes are on Johnson-Kron-Cousins system.</text>
<text><location><page_3><loc_8><loc_7><loc_48><loc_28></location>To examine the quality and reliability of our photometry, we compared the aperture magnitudes of the 234 star clusters obtained here with previous photometry of Park & Lee (2007), San Roman et al. (2009), and Zloczewski & Kaluzny (2009). There are eight star clusters, of which the magnitude scatters in the V band between this study and previous studies of Park & Lee (2007) and San Roman et al. (2009) are larger than 1.0 mag, i.e., our magnitudes are fainter than those obtained by Park & Lee (2007) and San Roman et al. (2009). We listed the comparison between this study and previous studies of V photometry for these eight star clusters in Table 2. We also plotted their images in Figure 2, in which the circles are photometric apertures adopted here. From this figure, we can see that nearly all these star clusters are close to one or more bright sources. If</text>
<text><location><page_3><loc_52><loc_52><loc_92><loc_92></location>photometric apertures are larger than the values adopted here, the light from these bright sources will not be excluded. As we know that, in Park & Lee (2007), the BVI integrated aperture photometry of M33 star clusters, which is included in 50 ' × 80 ' field of M33 based on CCD images taken with the CFH12k mosaic camera at the CFHT, is derived with an aperture of r = 4 . 0 '' for V magnitude measurement and an aperture of r = 2 . 0 '' for the measurement of color. San Roman et al. (2009) derived integrated photometry and color-magnitude diagrams (CMDs) for 161 star clusters in M33 using the ACS/WFC images. These authors adopted an aperture radius of r = 2 . 2 '' for V magnitude measurements and r = 1 . 5 '' for the colors. For these eight star clusters, a large scatter in the V photometric measurement between this study and previous studies (Park & Lee 2007; San Roman et al. 2009) mainly results from different photometric aperture sizes adopted by different authors (see Paper I for details). Figures 3-5 show the comparison of our photometry of the star clusters with previous photometry of Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). PL197 is not included in the figure of ∆ V comparison of Figure 3 because of too large value of ∆ V to be drawn in the figure. In addition, in Figure 5 (and Figures 6, 8 and 9 below), we have transformed the ACS/WFC magnitudes in F475W, F606W and F814W bands to the Johnson-Cousins B , V and I magnitudes using the colordependent synthetic transformations given by Sirianni et al. (2005).</text>
<text><location><page_3><loc_52><loc_7><loc_92><loc_52></location>From Figures 3-5, we can see that our measurements in the V band get systematically fainter than the photometric measurements in San Roman et al. (2009) for fainter sources ( V ≥ 19 mag). The ( V -I ) colors obtained here are in good agreement with those in Park & Lee (2007) and San Roman et al. (2009), however, the difference of ( B -V ) colors between San Roman et al. (2009) and this paper is large, which turned out to be 0 . 388 ± 0 . 040 with σ = 0 . 268. From Figure 5, we can see that both the ( B -V ) and ( V -I ) colors obtained here are in good agreement with those in Zloczewski & Kaluzny (2009), however, the V difference between this study and Zloczewski & Kaluzny (2009) turned out to be -0 . 103 ± 0 . 026 with σ = 0 . 262. By cross-identification, San Roman et al. (2009) provided 21 common star clusters in Zloczewski & Kaluzny (2009). We derived photometry for 18 of these 21 star clusters. We compared the photometry of these 18 star clusters with previous measurements in San Roman et al. (2009) and Zloczewski & Kaluzny (2009) for comparison. Figure 6 shows the comparison. From Figure 6, we can see that our measurements in V band get systematically fainter than the photometric measurements in San Roman et al. (2009) for fainter sources ( V ≥ 19 mag), however, this trend disappears between this study and Zloczewski & Kaluzny (2009). Both the ( B -V ) and ( V -I ) colors obtained here are in good agreement with those in San Roman et al. (2009) and Zloczewski & Kaluzny (2009). In Paper I, we has discussed the V difference between his study and previous studies in detail, and showed that the V difference resulted from different photometric apertures adopted in his study and previous studies. In Paper I, we showed that if the photometric apertures were adopted in our</text>
<figure>
<location><page_4><loc_15><loc_38><loc_84><loc_89></location>
<caption>Fig. 1.Spatial distribution of the 234 star clusters of M33 which were selected from Park & Lee (2007), San Roman et al. (2009), and Zloczewski & Kaluzny (2009) and their loci in the LGGS fields. We determined the photometry for these star clusters based on the LGGS archival images of M33 in the UBV RI bands. The large ellipse is the D 25 boundary of the M33 disk (de Vaucouleurs et al. 1991). The three large squares are the LGGS fields.</caption>
</figure>
<text><location><page_4><loc_8><loc_28><loc_48><loc_30></location>study to be the same as previous studies, the V difference disappeared.</text>
<section_header_level_1><location><page_4><loc_24><loc_26><loc_32><loc_27></location>3. RESULTS</section_header_level_1>
<text><location><page_4><loc_8><loc_7><loc_48><loc_25></location>In Paper I, we has presented some results for M33 star clusters including the CMD and color-color diagram. In addition, in Paper I, we pointed out that, before Zloczewski & Kaluzny (2009), none of M33 star clusters with V > 21 . 0 mag has been detected. And Zloczewski & Kaluzny (2009) emphasized that the faintest known globular cluster in the Milky Way has M V ∼ -1 mag comparing with M V ∼ -4 mag ( V ∼ 21 mag) observed for the faintest of the known M33 globular cluster candidates before Zloczewski & Kaluzny (2009). Zloczewski & Kaluzny (2009) provided integrated magnitudes for 115 M33 star clusters using the ACS/WFC images, of which nine have 21 . 0 mag < V < 22 . 0 mag corresponding to</text>
<text><location><page_4><loc_52><loc_9><loc_92><loc_30></location>-4 mag < M V < -3 mag. Although the faintest star cluster of M33 detected by Zloczewski & Kaluzny (2009) is 2.0 mag brighter than the faintest Galactic globular cluster, it will provide something unique to the analysis of M33 star clusters when including them. In fact, Paper I included the photometry of the M33 star clusters in Zloczewski & Kaluzny (2009) when we provided the results for M33 star clusters, however, most star clusters in Zloczewski & Kaluzny (2009) have photometry in only two bands ( V and I ). There are only 19 sample star clusters of Zloczewski & Kaluzny (2009) in the color-color diagram provided in Paper I. In addition, most star clusters in San Roman et al. (2009) also have photometry in only two bands ( V and I ). So, it is necessary that we re-provide a CMD and color-color diagram of M33 including photometry obtained in this paper.</text>
<figure>
<location><page_5><loc_17><loc_31><loc_85><loc_83></location>
<caption>Fig. 2.Finding charts of eight star clusters in the LGGS V band, of which the magnitude scatters in the V band between this and those studies of Park & Lee (2007) and San Roman et al. (2009) are larger than 1.0 mag, i.e., our measurements are fainter than those in Park & Lee (2007) and San Roman et al. (2009). The circles are photometric apertures adopted in this paper.</caption>
</figure>
<section_header_level_1><location><page_5><loc_17><loc_23><loc_39><loc_24></location>3.1. Color-Magnitude Diagram</section_header_level_1>
<text><location><page_5><loc_8><loc_8><loc_48><loc_22></location>The CMD can provide a qualitative modelindependent global indication of cluster-formation history that can be compared between galaxies because ( B -V ) 0 and ( V -I ) 0 are reasonably good age indicators, at least between young and old populations, with a secondary dependence on metallicity (Chandar et al. 1999b). CMDs of M33 star clusters have been previously discussed in the literature (Christian & Schommer 1982, 1988; Chandar et al. 1999b; Park & Lee 2007; Paper I). However, with a much larger star cluster sample in this paper, it is worth investigating them again. This</text>
<text><location><page_5><loc_52><loc_8><loc_92><loc_24></location>paper includes 523 star clusters of M33, of which the photometry of 234 and 277 is derived in this paper and in Paper I, respectively; and the photometry of the remaining 12 star clusters is from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009), since we cannot accurately derive the photometry for these 12 star clusters (see Section 2.2 for details). The 277 star clusters from Paper I are confirmed by Sarajedini & Mancone (2007) (254 star clusters), Park & Lee (2007) (7 star clusters), and San Roman et al. (2009) (16 star clusters) based on the HST and high-resolution ground-based imaging.</text>
<figure>
<location><page_6><loc_18><loc_55><loc_80><loc_92></location>
<caption>Fig. 3.Comparisons of our photometry of M33 star clusters in the UBVRI bands with previous photometry in Park & Lee (2007). The photometric offsets and rms scatter of the differences between their measurements and our new magnitudes are: ∆ V = 0 . 306 ± 0 . 089 with σ = 0 . 498, ∆( B -V ) = 0 . 126 ± 0 . 019 with σ = 0 . 102, and ∆( V -I ) = -0 . 023 ± 0 . 030 with σ = 0 . 162 (this study minus Park & Lee 2007).</caption>
</figure>
<text><location><page_6><loc_8><loc_7><loc_48><loc_47></location>We point out that the photometry of M33 star clusters obtained in Paper I and this study is homogeneous photometric data in the same photometric system. For completeness of data and readers' references, we list the photometry of 277 star clusters of Paper I in Table 3 including the reddening values from Park & Lee (2007) and San Roman et al. (2009) in column 9 of Table 3 (Table 3 includes E ( B -V ) missed in Paper I.). In Table 3, R C and I C mean that RI magnitudes are on Johnson-Kron-Cousins system. For the reddening values of the star clusters, we used those from Park & Lee (2007) or San Roman et al. (2009). For the star clusters, Park & Lee (2007) and San Roman et al. (2009) both presented their reddening values, we adopted their mean values. For the star clusters, Park & Lee (2007) and San Roman et al. (2009) did not present their reddening values, we adopted a uniform value of E ( B -V ) = 0 . 1 typical of the published values for the line-of-sight reddenings to M33 that Sarajedini & Mancone (2007) adopted. Figure 7 shows the spatial distribution of these 523 star clusters. The large ellipse is the D 25 boundary of the M33 disk (de Vaucouleurs et al. 1991). Figure 8 displays the integrated M V -( B -V ) 0 and M V -( V -I ) 0 CMDs of the sample star clusters of M33. The absolute magnitudes of the star clusters were derived for the adopted distance modulus of ( m -M ) 0 = 24 . 64 obtained by Galleti et al. (2004). The interstellar extinction curve, A λ , is taken from Schlegel et al. (1998). Below each CMD in Figure 8 we plotted the star cluster distribution in color space. To the right of each CMD</text>
<text><location><page_6><loc_52><loc_44><loc_92><loc_47></location>in Figure 8 we showed a histogram of the star clusters' absolute V magnitudes.</text>
<text><location><page_6><loc_52><loc_31><loc_92><loc_44></location>Sarajedini & Mancone (2007), Park & Lee (2007), and Paper I showed that the M33 star clusters are roughly separated into blue and red groups with a color boundary of ( B -V ) 0 /similarequal 0 . 5 in the M V -( B -V ) 0 based on a small star cluster sample. However, this feature did not clearly appear in Figure 8 as previous studies (Sarajedini & Mancone 2007; Park & Lee 2007; Paper I). Figure 8 shows that the star cluster luminosity function peaks near M V ∼ -6 . 0 mag, and nearly half of star clusters lies between M V = -5 . 5 and M V = -7 . 0 mag.</text>
<text><location><page_6><loc_52><loc_8><loc_92><loc_31></location>By adding models to the CMDs, we can obtain a more detailed history of star cluster formation. Three fading lines ( M V as a function of age) of Bruzual & Charlot (2003) for a metallicity of Z = 0 . 004 , Y = 0 . 24 which are thought to be appropriate for M33 star clusters (Chandar et al. 1999b), assuming a Salpeter initial mass function (IMF; Salpeter 1955) with lower and uppermass cut-offs of m L = 0 . 1 M /circledot and m U = 100 M /circledot , and using the Padova-1994 evolutionary tracks, are plotted on the CMDs of M33 star clusters for three different total initial masses: 10 5 , 10 4 , and 10 3 M /circledot . The majority of M33 star clusters fall between these three fading lines. From Figure 8, we note that none of the youngest clusters ( ∼ 10 7 yr) have masses approaching 10 5 M /circledot , which is consistent with the results of Chandar et al. (1999b) and Paper I. For ages older than 10 9 yr, some clusters with substantially higher masses are seen.</text>
<figure>
<location><page_7><loc_18><loc_55><loc_80><loc_92></location>
<caption>Fig. 4.Comparisons of our photometry of M33 star clusters in the UBVRI bands with previous photometry in San Roman et al. (2009). The photometric offsets and rms scatter of the differences between their measurements and our new magnitudes are: ∆ V = 0 . 363 ± 0 . 033 with σ = 0 . 352, ∆( B -V ) = 0 . 332 ± 0 . 052 with σ = 0 . 316, and ∆( V -I ) = -0 . 100 ± 0 . 021 with σ = 0 . 244 (this study minus San Roman et al. 2009).</caption>
</figure>
<section_header_level_1><location><page_7><loc_19><loc_46><loc_38><loc_47></location>3.2. Color-Color Diagram</section_header_level_1>
<text><location><page_7><loc_8><loc_30><loc_48><loc_45></location>Figure 9 shows the integrated ( B -V ) 0 versus ( V -I ) 0 color-color diagram for M33 star clusters. Galactic globular clusters from the online database of Harris (1996; 2010 update) are also plotted for comparison. We overplotted the theoretical evolutionary path for the single stellar population (SSP; Bruzual & Charlot 2003) for Z = 0 . 004 , Y = 0 . 24 that was appropriate for M33 (Chandar et al. 1999b). To identify different time periods, the different symbols correspond to 10 6 , 10 7 , 10 8 , 10 9 , and 10 10 yr. For comparison, the evolutionary path of the SSP for Z = 0 . 02 , Y = 0 . 28 is also overlaid.</text>
<text><location><page_7><loc_8><loc_8><loc_48><loc_30></location>In general, the star clusters in M33 are located along the sequence that is consistent with the theoretical evolutionary path for Z = 0 . 004 , Y = 0 . 24, while some are on the redder or bluer side in the ( V -I ) 0 color. The wide color range of M33 star clusters implies a large range of ages, suggesting a prolonged epoch of formation. From Figure 9, we find that the photometry is shifted below the SSP lines, i.e., the sample star clusters are on the redder side in the ( B -V ) 0 color, when the star clusters have the ( V -I ) 0 color between -0 . 5 and 0 . 4. In the same time, from Figure 9, we also find that the photometry for most of the Galactic globular clusters is also below the SSP lines but with much smaller range. Large scatter observed for M33 star clusters possibly results from large errors of colors. By comparing with SSP models, we can see that there are a large range of ages of M33 star clusters, of which some star clusters are as old as the</text>
<text><location><page_7><loc_52><loc_46><loc_70><loc_47></location>Galactic globular clusters.</text>
<section_header_level_1><location><page_7><loc_59><loc_43><loc_84><loc_44></location>4. SUMMARIES AND CONCLUSIONS</section_header_level_1>
<text><location><page_7><loc_52><loc_24><loc_92><loc_42></location>In this paper, we present UBVRI photometric measurements for 234 star clusters in the field of M33. These sample star clusters of M33 are from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). For most of these star clusters, there is photometry in only two bands ( V and I ) in previous studies. Photometry of these star clusters is performed using archival images from the LGGS (Massey et al. 2006). Detailed comparisons show that, in general, our photometry is consistent with previous measurements, especially, our photometry is in good agreement with that of Zloczewski & Kaluzny (2009). Combined with the star clusters' photometry in previous studies, we present some results:</text>
<unordered_list>
<list_item><location><page_7><loc_52><loc_21><loc_92><loc_24></location>1. None of the M33 youngest clusters ( ∼ 10 7 yr) have masses approaching 10 5 M /circledot .</list_item>
<list_item><location><page_7><loc_52><loc_14><loc_92><loc_21></location>2. The wide color range of M33 star clusters implies a large range of ages, suggesting a prolonged epoch of formation. And comparisons with SSP models suggest a large range of ages of M33 star clusters, and some as old as the Galactic globular clusters.</list_item>
</unordered_list>
<text><location><page_7><loc_52><loc_7><loc_92><loc_12></location>We would like to thank the anonymous referee for providing rapid and thoughtful report that helped improve the original manuscript greatly. This research was supported by the Chinese National Natural Science Founda-</text>
<figure>
<location><page_8><loc_18><loc_55><loc_80><loc_92></location>
<caption>Fig. 5.Comparisons of our photometry of M33 star clusters in the UBVRI bands with previous photometry in Zloczewski & Kaluzny (2009). The photometric offsets and rms scatter of the differences between their measurements and our new magnitudes are: ∆ V = -0 . 103 ± 0 . 026 with σ = 0 . 262, ∆( B -V ) = -0 . 028 ± 0 . 035 with σ = 0 . 149, and ∆( V -I ) = -0 . 032 ± 0 . 023 with σ = 0 . 234 (this study minus Zloczewski & Kaluzny 2009).</caption>
</figure>
<text><location><page_8><loc_8><loc_46><loc_48><loc_47></location>tion through grants 10873016 and 10633020, and by Na-</text>
<text><location><page_8><loc_52><loc_44><loc_92><loc_47></location>tional Basic Research Program of China (973 Program) under grant 2007CB815403.</text>
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<figure>
<location><page_9><loc_18><loc_55><loc_80><loc_92></location>
<caption>Fig. 6.Comparisons of our photometry of M33 star clusters in the UBVRI bands with previous measurements in San Roman et al. (2009) and Zloczewski & Kaluzny (2009). Crosses and circles represent the photometry difference between this study and previous study of San Roman et al. (2009), and the photometry difference between this study and previous study of Zloczewski & Kaluzny (2009), respectively. The photometric offsets and rms scatter of the differences between their measurements and our new magnitudes are: ∆ V = 0 . 517 ± 0 . 086 with σ = 0 . 353, ∆( B -V ) = -0 . 050 ± 0 . 079 with σ = 0 . 208, and ∆( V -I ) = -0 . 037 ± 0 . 040 with σ = 0 . 161 (this study minus San Roman et al. 2009); ∆ V = 0 . 006 ± 0 . 065 with σ = 0 . 268, ∆( B -V ) = -0 . 068 ± 0 . 045 with σ = 0 . 143, and ∆( V -I ) = 0 . 071 ± 0 . 045 with σ = 0 . 173 (this study minus Zloczewski & Kaluzny 2009).</caption>
</figure>
<text><location><page_9><loc_8><loc_41><loc_46><loc_43></location>Stanek, K. Z., Kaluzny, J., Krockenberger, M., et al. 1998, AJ, 115, 1894</text>
<text><location><page_9><loc_8><loc_40><loc_29><loc_41></location>Stetson, P. B. 1987, PASP, 99, 191</text>
<text><location><page_9><loc_52><loc_42><loc_91><loc_43></location>Stonkut˙e, R., Vansevi˘cius, V., Arimoto, N., et al. 2008, AJ, 135,</text>
<text><location><page_9><loc_52><loc_39><loc_90><loc_41></location>Zloczewski, K., & Kaluzny, J. 2009, Acta Astron., 59, 47 Zloczewski, K., Kaluzny, J., & Hartman, J. 2008, Acta Astron.,</text>
<text><location><page_9><loc_53><loc_38><loc_57><loc_42></location>1482 58, 23</text>
<figure>
<location><page_10><loc_15><loc_38><loc_84><loc_89></location>
<caption>Fig. 7.Spatial distribution of the 523 star clusters in M33. Crosses denote the star clusters, of which the photometry is obtained in Paper I and this study, and filled circles denote the star clusters, of which the photometry was obtained by Park & Lee (2007), San Roman et al. (2009), and Zloczewski & Kaluzny (2009). The large ellipse is the D 25 boundary of the M33 disk (de Vaucouleurs et al. 1991).</caption>
</figure>
<figure>
<location><page_11><loc_20><loc_20><loc_80><loc_91></location>
<caption>Fig. 8.Color-magnitude diagrams of M33 clusters. Crosses represent the star clusters in Ma (2012) and this study, filled circles represent the star clusters in Park & Lee (2007), San Roman et al. (2009), and Zloczewski & Kaluzny (2009). Fading lines are indicated for star clusters with total initial masses of 10 5 (upper dashed line), 10 4 , and 10 3 (lower dashed line) M /circledot , assuming a Salpeter IMF (see text). Stars along each fading line represent ages of 10 7 , 10 8 , 10 9 , and 10 10 yr, from top to bottom, respectively.</caption>
</figure>
<figure>
<location><page_12><loc_19><loc_44><loc_81><loc_92></location>
<caption>Fig. 9.-( B -V ) 0 vs. ( V -I ) 0 color-color diagram of star clusters in M33. Crosses represent the star clusters in Ma (2012) and this study, filled circles represent the star clusters in Park & Lee (2007), San Roman et al. (2009), and Zloczewski & Kaluzny (2009). Green squares are Galactic globular clusters from the online database of Harris (1996; 2010 update). Theoretical evolutionary paths from the SSP model (Bruzual & Charlot 2003) for Z = 0 . 004, Y = 0 . 24 (blue dashed line) and Z = 0 . 02, Y = 0 . 28 (red solid line) are drawn for every dex in age from 10 6 to 10 10 yr. The arrow represents the reddening direction.</caption>
</figure>
<text><location><page_13><loc_17><loc_84><loc_18><loc_85></location>p</text>
<text><location><page_13><loc_18><loc_85><loc_19><loc_85></location>)</text>
<text><location><page_13><loc_18><loc_84><loc_18><loc_85></location>'</text>
<text><location><page_13><loc_18><loc_84><loc_18><loc_84></location>'</text>
<text><location><page_13><loc_18><loc_84><loc_19><loc_84></location>(</text>
<text><location><page_13><loc_17><loc_84><loc_18><loc_84></location>a</text>
<text><location><page_13><loc_17><loc_84><loc_17><loc_84></location>r</text>
<text><location><page_13><loc_19><loc_85><loc_20><loc_85></location>8</text>
<text><location><page_13><loc_19><loc_84><loc_20><loc_85></location>3</text>
<text><location><page_13><loc_19><loc_84><loc_20><loc_84></location>8</text>
<text><location><page_13><loc_19><loc_84><loc_20><loc_84></location>.</text>
<text><location><page_13><loc_19><loc_83><loc_20><loc_84></location>2</text>
<text><location><page_13><loc_20><loc_85><loc_21><loc_85></location>4</text>
<text><location><page_13><loc_20><loc_84><loc_21><loc_85></location>6</text>
<text><location><page_13><loc_20><loc_84><loc_21><loc_84></location>0</text>
<text><location><page_13><loc_20><loc_84><loc_21><loc_84></location>.</text>
<text><location><page_13><loc_20><loc_83><loc_21><loc_84></location>2</text>
<text><location><page_13><loc_22><loc_85><loc_22><loc_85></location>4</text>
<text><location><page_13><loc_22><loc_84><loc_22><loc_85></location>6</text>
<text><location><page_13><loc_22><loc_84><loc_22><loc_84></location>0</text>
<text><location><page_13><loc_22><loc_84><loc_22><loc_84></location>.</text>
<text><location><page_13><loc_22><loc_83><loc_22><loc_84></location>2</text>
<text><location><page_13><loc_23><loc_85><loc_24><loc_85></location>4</text>
<text><location><page_13><loc_23><loc_84><loc_24><loc_85></location>5</text>
<text><location><page_13><loc_23><loc_84><loc_24><loc_84></location>3</text>
<text><location><page_13><loc_23><loc_84><loc_24><loc_84></location>.</text>
<text><location><page_13><loc_23><loc_83><loc_24><loc_84></location>3</text>
<text><location><page_13><loc_24><loc_85><loc_25><loc_85></location>2</text>
<text><location><page_13><loc_24><loc_84><loc_25><loc_85></location>2</text>
<text><location><page_13><loc_24><loc_84><loc_25><loc_84></location>3</text>
<text><location><page_13><loc_24><loc_84><loc_25><loc_84></location>.</text>
<text><location><page_13><loc_24><loc_83><loc_25><loc_84></location>2</text>
<text><location><page_13><loc_25><loc_85><loc_26><loc_85></location>8</text>
<text><location><page_13><loc_25><loc_84><loc_26><loc_85></location>2</text>
<text><location><page_13><loc_25><loc_84><loc_26><loc_84></location>1</text>
<text><location><page_13><loc_25><loc_84><loc_26><loc_84></location>.</text>
<text><location><page_13><loc_25><loc_83><loc_26><loc_84></location>4</text>
<text><location><page_13><loc_27><loc_85><loc_27><loc_85></location>2</text>
<text><location><page_13><loc_27><loc_84><loc_27><loc_85></location>2</text>
<text><location><page_13><loc_27><loc_84><loc_27><loc_84></location>3</text>
<text><location><page_13><loc_27><loc_84><loc_27><loc_84></location>.</text>
<text><location><page_13><loc_27><loc_83><loc_27><loc_84></location>2</text>
<text><location><page_13><loc_28><loc_85><loc_29><loc_85></location>4</text>
<text><location><page_13><loc_28><loc_84><loc_29><loc_85></location>6</text>
<text><location><page_13><loc_28><loc_84><loc_29><loc_84></location>0</text>
<text><location><page_13><loc_28><loc_84><loc_29><loc_84></location>.</text>
<text><location><page_13><loc_28><loc_83><loc_29><loc_84></location>2</text>
<text><location><page_13><loc_29><loc_85><loc_30><loc_85></location>6</text>
<text><location><page_13><loc_29><loc_84><loc_30><loc_85></location>9</text>
<text><location><page_13><loc_29><loc_84><loc_30><loc_84></location>0</text>
<text><location><page_13><loc_29><loc_84><loc_30><loc_84></location>.</text>
<text><location><page_13><loc_29><loc_83><loc_30><loc_84></location>3</text>
<text><location><page_13><loc_30><loc_85><loc_31><loc_85></location>0</text>
<text><location><page_13><loc_30><loc_84><loc_31><loc_85></location>7</text>
<text><location><page_13><loc_30><loc_84><loc_31><loc_84></location>8</text>
<text><location><page_13><loc_30><loc_84><loc_31><loc_84></location>.</text>
<text><location><page_13><loc_30><loc_83><loc_31><loc_84></location>3</text>
<text><location><page_13><loc_31><loc_85><loc_32><loc_85></location>4</text>
<text><location><page_13><loc_31><loc_84><loc_32><loc_85></location>6</text>
<text><location><page_13><loc_31><loc_84><loc_32><loc_84></location>0</text>
<text><location><page_13><loc_31><loc_84><loc_32><loc_84></location>.</text>
<text><location><page_13><loc_31><loc_83><loc_32><loc_84></location>2</text>
<text><location><page_13><loc_33><loc_85><loc_34><loc_85></location>0</text>
<text><location><page_13><loc_33><loc_84><loc_34><loc_85></location>8</text>
<text><location><page_13><loc_33><loc_84><loc_34><loc_84></location>5</text>
<text><location><page_13><loc_33><loc_84><loc_34><loc_84></location>.</text>
<text><location><page_13><loc_33><loc_83><loc_34><loc_84></location>2</text>
<text><location><page_13><loc_34><loc_85><loc_35><loc_85></location>0</text>
<text><location><page_13><loc_34><loc_84><loc_35><loc_85></location>8</text>
<text><location><page_13><loc_34><loc_84><loc_35><loc_84></location>5</text>
<text><location><page_13><loc_34><loc_84><loc_35><loc_84></location>.</text>
<text><location><page_13><loc_34><loc_83><loc_35><loc_84></location>2</text>
<text><location><page_13><loc_35><loc_85><loc_36><loc_85></location>4</text>
<text><location><page_13><loc_35><loc_84><loc_36><loc_85></location>5</text>
<text><location><page_13><loc_35><loc_84><loc_36><loc_84></location>3</text>
<text><location><page_13><loc_35><loc_84><loc_36><loc_84></location>.</text>
<text><location><page_13><loc_35><loc_83><loc_36><loc_84></location>3</text>
<text><location><page_13><loc_42><loc_93><loc_57><loc_94></location>Star clusters in M33</text>
<text><location><page_13><loc_90><loc_93><loc_92><loc_94></location>13</text>
<paragraph><location><page_13><loc_36><loc_84><loc_63><loc_85></location>5 4 6 4 8 0 8 0 8 0 9 6 9 6 8 0 8 0 6 4 2 2 8 0 5 4 6 4 3 8 8 0 8 0 3 2 9 0 6 4 9 0 0 6</paragraph>
<text><location><page_13><loc_36><loc_84><loc_37><loc_84></location>3</text>
<text><location><page_13><loc_36><loc_84><loc_37><loc_84></location>.</text>
<text><location><page_13><loc_36><loc_83><loc_37><loc_84></location>3</text>
<text><location><page_13><loc_38><loc_84><loc_38><loc_84></location>0</text>
<text><location><page_13><loc_38><loc_84><loc_38><loc_84></location>.</text>
<text><location><page_13><loc_38><loc_83><loc_38><loc_84></location>2</text>
<text><location><page_13><loc_39><loc_84><loc_40><loc_84></location>5</text>
<text><location><page_13><loc_39><loc_84><loc_40><loc_84></location>.</text>
<text><location><page_13><loc_39><loc_83><loc_40><loc_84></location>2</text>
<text><location><page_13><loc_40><loc_84><loc_41><loc_84></location>5</text>
<text><location><page_13><loc_40><loc_84><loc_41><loc_84></location>.</text>
<text><location><page_13><loc_40><loc_83><loc_41><loc_84></location>2</text>
<text><location><page_13><loc_41><loc_84><loc_42><loc_84></location>5</text>
<text><location><page_13><loc_41><loc_84><loc_42><loc_84></location>.</text>
<text><location><page_13><loc_41><loc_83><loc_42><loc_84></location>2</text>
<text><location><page_13><loc_43><loc_84><loc_43><loc_84></location>0</text>
<text><location><page_13><loc_43><loc_84><loc_43><loc_84></location>.</text>
<text><location><page_13><loc_43><loc_83><loc_43><loc_84></location>3</text>
<text><location><page_13><loc_44><loc_84><loc_45><loc_84></location>0</text>
<text><location><page_13><loc_44><loc_84><loc_45><loc_84></location>.</text>
<text><location><page_13><loc_44><loc_83><loc_45><loc_84></location>3</text>
<text><location><page_13><loc_45><loc_84><loc_46><loc_84></location>5</text>
<text><location><page_13><loc_45><loc_84><loc_46><loc_84></location>.</text>
<text><location><page_13><loc_45><loc_83><loc_46><loc_84></location>2</text>
<text><location><page_13><loc_46><loc_84><loc_47><loc_84></location>5</text>
<text><location><page_13><loc_46><loc_84><loc_47><loc_84></location>.</text>
<text><location><page_13><loc_46><loc_83><loc_47><loc_84></location>2</text>
<text><location><page_13><loc_47><loc_84><loc_48><loc_84></location>0</text>
<text><location><page_13><loc_47><loc_84><loc_48><loc_84></location>.</text>
<text><location><page_13><loc_47><loc_83><loc_48><loc_84></location>2</text>
<text><location><page_13><loc_49><loc_84><loc_49><loc_84></location>3</text>
<text><location><page_13><loc_49><loc_84><loc_49><loc_84></location>.</text>
<text><location><page_13><loc_49><loc_83><loc_49><loc_84></location>2</text>
<text><location><page_13><loc_50><loc_84><loc_51><loc_84></location>5</text>
<text><location><page_13><loc_50><loc_84><loc_51><loc_84></location>.</text>
<text><location><page_13><loc_50><loc_83><loc_51><loc_84></location>2</text>
<text><location><page_13><loc_51><loc_84><loc_52><loc_84></location>3</text>
<text><location><page_13><loc_51><loc_84><loc_52><loc_84></location>.</text>
<text><location><page_13><loc_51><loc_83><loc_52><loc_84></location>3</text>
<text><location><page_13><loc_52><loc_84><loc_53><loc_84></location>0</text>
<text><location><page_13><loc_52><loc_84><loc_53><loc_84></location>.</text>
<text><location><page_13><loc_52><loc_83><loc_53><loc_84></location>2</text>
<text><location><page_13><loc_54><loc_84><loc_54><loc_84></location>8</text>
<text><location><page_13><loc_54><loc_84><loc_54><loc_84></location>.</text>
<text><location><page_13><loc_54><loc_83><loc_54><loc_84></location>2</text>
<text><location><page_13><loc_55><loc_84><loc_56><loc_84></location>5</text>
<text><location><page_13><loc_55><loc_84><loc_56><loc_84></location>.</text>
<text><location><page_13><loc_55><loc_83><loc_56><loc_84></location>2</text>
<text><location><page_13><loc_56><loc_84><loc_57><loc_84></location>5</text>
<text><location><page_13><loc_56><loc_84><loc_57><loc_84></location>.</text>
<text><location><page_13><loc_56><loc_83><loc_57><loc_84></location>2</text>
<text><location><page_13><loc_57><loc_84><loc_58><loc_84></location>0</text>
<text><location><page_13><loc_57><loc_84><loc_58><loc_84></location>.</text>
<text><location><page_13><loc_57><loc_83><loc_58><loc_84></location>1</text>
<text><location><page_13><loc_58><loc_84><loc_59><loc_84></location>2</text>
<text><location><page_13><loc_58><loc_84><loc_59><loc_84></location>.</text>
<text><location><page_13><loc_58><loc_83><loc_59><loc_84></location>1</text>
<text><location><page_13><loc_60><loc_84><loc_61><loc_84></location>0</text>
<text><location><page_13><loc_60><loc_84><loc_61><loc_84></location>.</text>
<text><location><page_13><loc_60><loc_83><loc_61><loc_84></location>2</text>
<text><location><page_13><loc_61><loc_84><loc_62><loc_84></location>2</text>
<text><location><page_13><loc_61><loc_84><loc_62><loc_84></location>.</text>
<text><location><page_13><loc_61><loc_83><loc_62><loc_84></location>1</text>
<text><location><page_13><loc_62><loc_84><loc_63><loc_84></location>8</text>
<text><location><page_13><loc_62><loc_84><loc_63><loc_84></location>.</text>
<text><location><page_13><loc_62><loc_83><loc_63><loc_84></location>1</text>
<text><location><page_13><loc_63><loc_85><loc_64><loc_85></location>2</text>
<text><location><page_13><loc_63><loc_84><loc_64><loc_85></location>2</text>
<text><location><page_13><loc_63><loc_84><loc_64><loc_84></location>3</text>
<text><location><page_13><loc_63><loc_84><loc_64><loc_84></location>.</text>
<text><location><page_13><loc_63><loc_83><loc_64><loc_84></location>2</text>
<text><location><page_13><loc_65><loc_85><loc_65><loc_85></location>0</text>
<text><location><page_13><loc_65><loc_84><loc_65><loc_85></location>8</text>
<text><location><page_13><loc_65><loc_84><loc_65><loc_84></location>5</text>
<text><location><page_13><loc_65><loc_84><loc_65><loc_84></location>.</text>
<text><location><page_13><loc_65><loc_83><loc_65><loc_84></location>2</text>
<text><location><page_13><loc_66><loc_85><loc_67><loc_85></location>6</text>
<text><location><page_13><loc_66><loc_84><loc_67><loc_85></location>0</text>
<text><location><page_13><loc_66><loc_84><loc_67><loc_84></location>8</text>
<text><location><page_13><loc_66><loc_84><loc_67><loc_84></location>.</text>
<text><location><page_13><loc_66><loc_83><loc_67><loc_84></location>1</text>
<text><location><page_13><loc_67><loc_85><loc_68><loc_85></location>6</text>
<text><location><page_13><loc_67><loc_84><loc_68><loc_85></location>9</text>
<text><location><page_13><loc_67><loc_84><loc_68><loc_84></location>0</text>
<text><location><page_13><loc_67><loc_84><loc_68><loc_84></location>.</text>
<text><location><page_13><loc_67><loc_83><loc_68><loc_84></location>3</text>
<text><location><page_13><loc_68><loc_85><loc_69><loc_85></location>4</text>
<text><location><page_13><loc_68><loc_84><loc_69><loc_85></location>6</text>
<text><location><page_13><loc_68><loc_84><loc_69><loc_84></location>0</text>
<text><location><page_13><loc_68><loc_84><loc_69><loc_84></location>.</text>
<text><location><page_13><loc_68><loc_83><loc_69><loc_84></location>2</text>
<text><location><page_13><loc_70><loc_85><loc_70><loc_85></location>0</text>
<text><location><page_13><loc_70><loc_84><loc_70><loc_85></location>9</text>
<text><location><page_13><loc_70><loc_84><loc_70><loc_84></location>2</text>
<text><location><page_13><loc_70><loc_84><loc_70><loc_84></location>.</text>
<text><location><page_13><loc_70><loc_83><loc_70><loc_84></location>1</text>
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<text><location><page_13><loc_71><loc_84><loc_72><loc_85></location>8</text>
<text><location><page_13><loc_71><loc_84><loc_72><loc_84></location>5</text>
<text><location><page_13><loc_71><loc_84><loc_72><loc_84></location>.</text>
<text><location><page_13><loc_71><loc_83><loc_72><loc_84></location>2</text>
<text><location><page_13><loc_72><loc_85><loc_73><loc_85></location>6</text>
<text><location><page_13><loc_72><loc_84><loc_73><loc_85></location>9</text>
<text><location><page_13><loc_72><loc_84><loc_73><loc_84></location>0</text>
<text><location><page_13><loc_72><loc_84><loc_73><loc_84></location>.</text>
<text><location><page_13><loc_72><loc_83><loc_73><loc_84></location>3</text>
<text><location><page_13><loc_73><loc_85><loc_74><loc_85></location>0</text>
<text><location><page_13><loc_73><loc_84><loc_74><loc_85></location>8</text>
<text><location><page_13><loc_73><loc_84><loc_74><loc_84></location>5</text>
<text><location><page_13><loc_73><loc_84><loc_74><loc_84></location>.</text>
<text><location><page_13><loc_73><loc_83><loc_74><loc_84></location>2</text>
<text><location><page_13><loc_74><loc_85><loc_75><loc_85></location>0</text>
<text><location><page_13><loc_74><loc_84><loc_75><loc_85></location>8</text>
<text><location><page_13><loc_74><loc_84><loc_75><loc_84></location>5</text>
<text><location><page_13><loc_74><loc_84><loc_75><loc_84></location>.</text>
<text><location><page_13><loc_74><loc_83><loc_75><loc_84></location>2</text>
<text><location><page_13><loc_76><loc_85><loc_76><loc_85></location>2</text>
<text><location><page_13><loc_76><loc_84><loc_76><loc_85></location>2</text>
<text><location><page_13><loc_76><loc_84><loc_76><loc_84></location>3</text>
<text><location><page_13><loc_76><loc_84><loc_76><loc_84></location>.</text>
<text><location><page_13><loc_76><loc_83><loc_76><loc_84></location>2</text>
<text><location><page_13><loc_77><loc_85><loc_78><loc_85></location>8</text>
<text><location><page_13><loc_77><loc_84><loc_78><loc_85></location>3</text>
<text><location><page_13><loc_77><loc_84><loc_78><loc_84></location>8</text>
<text><location><page_13><loc_77><loc_84><loc_78><loc_84></location>.</text>
<text><location><page_13><loc_77><loc_83><loc_78><loc_84></location>2</text>
<text><location><page_13><loc_78><loc_85><loc_79><loc_85></location>0</text>
<text><location><page_13><loc_78><loc_84><loc_79><loc_85></location>8</text>
<text><location><page_13><loc_78><loc_84><loc_79><loc_84></location>5</text>
<text><location><page_13><loc_78><loc_84><loc_79><loc_84></location>.</text>
<text><location><page_13><loc_78><loc_83><loc_79><loc_84></location>2</text>
<text><location><page_13><loc_79><loc_85><loc_80><loc_85></location>6</text>
<text><location><page_13><loc_79><loc_84><loc_80><loc_85></location>9</text>
<text><location><page_13><loc_79><loc_84><loc_80><loc_84></location>0</text>
<text><location><page_13><loc_79><loc_84><loc_80><loc_84></location>.</text>
<text><location><page_13><loc_79><loc_83><loc_80><loc_84></location>3</text>
<text><location><page_13><loc_81><loc_85><loc_81><loc_85></location>2</text>
<text><location><page_13><loc_81><loc_84><loc_81><loc_85></location>2</text>
<text><location><page_13><loc_81><loc_84><loc_81><loc_84></location>3</text>
<text><location><page_13><loc_81><loc_84><loc_81><loc_84></location>.</text>
<text><location><page_13><loc_81><loc_83><loc_81><loc_84></location>2</text>
<text><location><page_13><loc_82><loc_85><loc_83><loc_85></location>0</text>
<text><location><page_13><loc_82><loc_84><loc_83><loc_85></location>8</text>
<text><location><page_13><loc_82><loc_84><loc_83><loc_84></location>5</text>
<text><location><page_13><loc_82><loc_84><loc_83><loc_84></location>.</text>
<text><location><page_13><loc_82><loc_83><loc_83><loc_84></location>2</text>
<text><location><page_13><loc_83><loc_85><loc_84><loc_85></location>0</text>
<text><location><page_13><loc_83><loc_84><loc_84><loc_85></location>7</text>
<text><location><page_13><loc_83><loc_84><loc_84><loc_84></location>8</text>
<text><location><page_13><loc_83><loc_84><loc_84><loc_84></location>.</text>
<text><location><page_13><loc_83><loc_83><loc_84><loc_84></location>3</text>
<text><location><page_13><loc_84><loc_85><loc_85><loc_85></location>2</text>
<text><location><page_13><loc_84><loc_84><loc_85><loc_85></location>1</text>
<text><location><page_13><loc_84><loc_84><loc_85><loc_84></location>6</text>
<text><location><page_13><loc_84><loc_84><loc_85><loc_84></location>.</text>
<text><location><page_13><loc_84><loc_83><loc_85><loc_84></location>3</text>
<text><location><page_13><loc_85><loc_85><loc_86><loc_85></location>6</text>
<text><location><page_13><loc_85><loc_84><loc_86><loc_85></location>9</text>
<text><location><page_13><loc_85><loc_84><loc_86><loc_84></location>0</text>
<text><location><page_13><loc_85><loc_84><loc_86><loc_84></location>.</text>
<text><location><page_13><loc_85><loc_83><loc_86><loc_84></location>3</text>
<text><location><page_13><loc_85><loc_81><loc_86><loc_81></location>2</text>
<text><location><page_13><loc_85><loc_80><loc_86><loc_81></location>1</text>
<text><location><page_13><loc_85><loc_80><loc_86><loc_80></location>.</text>
<text><location><page_13><loc_85><loc_79><loc_86><loc_80></location>0</text>
<text><location><page_13><loc_85><loc_77><loc_86><loc_77></location>6</text>
<text><location><page_13><loc_85><loc_76><loc_86><loc_77></location>3</text>
<text><location><page_13><loc_85><loc_76><loc_86><loc_76></location>0</text>
<text><location><page_13><loc_85><loc_75><loc_86><loc_76></location>.</text>
<text><location><page_13><loc_85><loc_75><loc_86><loc_75></location>0</text>
<text><location><page_13><loc_85><loc_74><loc_86><loc_75></location>±</text>
<text><location><page_13><loc_85><loc_73><loc_86><loc_74></location>8</text>
<text><location><page_13><loc_85><loc_73><loc_86><loc_73></location>3</text>
<text><location><page_13><loc_85><loc_72><loc_86><loc_73></location>4</text>
<text><location><page_13><loc_85><loc_72><loc_86><loc_72></location>.</text>
<text><location><page_13><loc_85><loc_72><loc_86><loc_72></location>8</text>
<text><location><page_13><loc_85><loc_71><loc_86><loc_72></location>1</text>
<text><location><page_13><loc_85><loc_70><loc_86><loc_70></location>9</text>
<text><location><page_13><loc_85><loc_69><loc_86><loc_70></location>4</text>
<text><location><page_13><loc_85><loc_69><loc_86><loc_69></location>0</text>
<text><location><page_13><loc_85><loc_69><loc_86><loc_69></location>.</text>
<text><location><page_13><loc_85><loc_68><loc_86><loc_69></location>0</text>
<text><location><page_13><loc_85><loc_67><loc_86><loc_68></location>±</text>
<text><location><page_13><loc_85><loc_66><loc_86><loc_67></location>2</text>
<text><location><page_13><loc_85><loc_66><loc_86><loc_66></location>9</text>
<text><location><page_13><loc_85><loc_66><loc_86><loc_66></location>1</text>
<text><location><page_13><loc_85><loc_65><loc_86><loc_66></location>.</text>
<text><location><page_13><loc_85><loc_65><loc_86><loc_65></location>9</text>
<text><location><page_13><loc_85><loc_64><loc_86><loc_65></location>1</text>
<text><location><page_13><loc_85><loc_63><loc_86><loc_63></location>4</text>
<text><location><page_13><loc_85><loc_62><loc_86><loc_63></location>6</text>
<text><location><page_13><loc_85><loc_62><loc_86><loc_62></location>0</text>
<text><location><page_13><loc_85><loc_62><loc_86><loc_62></location>.</text>
<text><location><page_13><loc_85><loc_61><loc_86><loc_62></location>0</text>
<text><location><page_13><loc_85><loc_60><loc_86><loc_61></location>±</text>
<text><location><page_13><loc_85><loc_60><loc_86><loc_60></location>4</text>
<text><location><page_13><loc_85><loc_59><loc_86><loc_60></location>5</text>
<text><location><page_13><loc_85><loc_59><loc_86><loc_59></location>8</text>
<text><location><page_13><loc_85><loc_58><loc_86><loc_59></location>.</text>
<text><location><page_13><loc_85><loc_58><loc_86><loc_58></location>9</text>
<text><location><page_13><loc_85><loc_58><loc_86><loc_58></location>1</text>
<text><location><page_13><loc_85><loc_56><loc_86><loc_56></location>5</text>
<text><location><page_13><loc_85><loc_55><loc_86><loc_56></location>9</text>
<text><location><page_13><loc_85><loc_55><loc_86><loc_55></location>0</text>
<text><location><page_13><loc_85><loc_55><loc_86><loc_55></location>.</text>
<text><location><page_13><loc_85><loc_54><loc_86><loc_55></location>0</text>
<text><location><page_13><loc_85><loc_53><loc_86><loc_54></location>±</text>
<text><location><page_13><loc_85><loc_53><loc_86><loc_53></location>6</text>
<text><location><page_13><loc_85><loc_52><loc_86><loc_53></location>7</text>
<text><location><page_13><loc_85><loc_52><loc_86><loc_52></location>6</text>
<text><location><page_13><loc_85><loc_52><loc_86><loc_52></location>.</text>
<text><location><page_13><loc_85><loc_51><loc_86><loc_52></location>0</text>
<text><location><page_13><loc_85><loc_51><loc_86><loc_51></location>2</text>
<text><location><page_13><loc_85><loc_49><loc_86><loc_49></location>5</text>
<text><location><page_13><loc_85><loc_49><loc_86><loc_49></location>6</text>
<text><location><page_13><loc_85><loc_48><loc_86><loc_49></location>0</text>
<text><location><page_13><loc_85><loc_48><loc_86><loc_48></location>.</text>
<text><location><page_13><loc_85><loc_47><loc_86><loc_48></location>0</text>
<text><location><page_13><loc_85><loc_46><loc_86><loc_47></location>±</text>
<text><location><page_13><loc_85><loc_46><loc_86><loc_46></location>9</text>
<text><location><page_13><loc_85><loc_45><loc_86><loc_46></location>7</text>
<text><location><page_13><loc_85><loc_45><loc_86><loc_45></location>2</text>
<text><location><page_13><loc_85><loc_45><loc_86><loc_45></location>.</text>
<text><location><page_13><loc_85><loc_44><loc_86><loc_45></location>0</text>
<text><location><page_13><loc_85><loc_44><loc_86><loc_44></location>2</text>
<text><location><page_13><loc_85><loc_42><loc_86><loc_43></location>0</text>
<text><location><page_13><loc_85><loc_42><loc_86><loc_42></location>3</text>
<text><location><page_13><loc_85><loc_41><loc_86><loc_42></location>.</text>
<text><location><page_13><loc_85><loc_41><loc_86><loc_41></location>0</text>
<text><location><page_13><loc_85><loc_41><loc_86><loc_41></location>2</text>
<text><location><page_13><loc_85><loc_40><loc_86><loc_40></location>0</text>
<text><location><page_13><loc_85><loc_39><loc_86><loc_40></location>3</text>
<text><location><page_13><loc_85><loc_39><loc_86><loc_39></location>0</text>
<text><location><page_13><loc_85><loc_38><loc_86><loc_39></location>3</text>
<text><location><page_13><loc_85><loc_37><loc_86><loc_37></location>8</text>
<text><location><page_13><loc_85><loc_36><loc_86><loc_37></location>1</text>
<text><location><page_13><loc_85><loc_36><loc_86><loc_36></location>9</text>
<text><location><page_13><loc_85><loc_35><loc_86><loc_36></location>.</text>
<text><location><page_13><loc_85><loc_35><loc_86><loc_35></location>9</text>
<text><location><page_13><loc_85><loc_35><loc_86><loc_35></location>1</text>
<text><location><page_13><loc_85><loc_34><loc_86><loc_34></location>3</text>
<text><location><page_13><loc_85><loc_33><loc_86><loc_34></location>3</text>
<text><location><page_13><loc_85><loc_33><loc_86><loc_33></location>1</text>
<text><location><page_13><loc_85><loc_32><loc_86><loc_33></location>0</text>
<text><location><page_13><loc_85><loc_19><loc_86><loc_19></location>8</text>
<text><location><page_13><loc_85><loc_19><loc_86><loc_19></location>2</text>
<text><location><page_13><loc_85><loc_18><loc_86><loc_19></location>R</text>
<text><location><page_13><loc_85><loc_18><loc_86><loc_18></location>S</text>
<text><location><page_13><loc_85><loc_16><loc_86><loc_16></location>.</text>
<text><location><page_13><loc_85><loc_16><loc_86><loc_16></location>.</text>
<text><location><page_13><loc_85><loc_15><loc_86><loc_16></location>.</text>
<text><location><page_13><loc_85><loc_15><loc_86><loc_15></location>.</text>
<text><location><page_13><loc_85><loc_15><loc_86><loc_15></location>.</text>
<text><location><page_13><loc_85><loc_15><loc_86><loc_15></location>.</text>
<text><location><page_13><loc_85><loc_14><loc_86><loc_15></location>5</text>
<text><location><page_13><loc_85><loc_14><loc_86><loc_14></location>5</text>
<table>
<location><page_13><loc_13><loc_12><loc_86><loc_83></location>
</table>
<text><location><page_13><loc_87><loc_85><loc_88><loc_85></location>6</text>
<text><location><page_13><loc_87><loc_84><loc_88><loc_85></location>9</text>
<text><location><page_13><loc_87><loc_84><loc_88><loc_84></location>0</text>
<text><location><page_13><loc_87><loc_84><loc_88><loc_84></location>.</text>
<text><location><page_13><loc_87><loc_83><loc_88><loc_84></location>3</text>
<text><location><page_13><loc_87><loc_81><loc_88><loc_81></location>5</text>
<text><location><page_13><loc_87><loc_80><loc_88><loc_81></location>0</text>
<text><location><page_13><loc_87><loc_80><loc_88><loc_80></location>.</text>
<text><location><page_13><loc_87><loc_79><loc_88><loc_80></location>0</text>
<text><location><page_13><loc_87><loc_77><loc_88><loc_77></location>3</text>
<text><location><page_13><loc_87><loc_76><loc_88><loc_77></location>1</text>
<text><location><page_13><loc_87><loc_76><loc_88><loc_76></location>0</text>
<text><location><page_13><loc_87><loc_75><loc_88><loc_76></location>.</text>
<text><location><page_13><loc_87><loc_75><loc_88><loc_75></location>0</text>
<text><location><page_13><loc_87><loc_74><loc_87><loc_75></location>±</text>
<text><location><page_13><loc_87><loc_73><loc_88><loc_74></location>3</text>
<text><location><page_13><loc_87><loc_73><loc_88><loc_73></location>8</text>
<text><location><page_13><loc_87><loc_72><loc_88><loc_73></location>8</text>
<text><location><page_13><loc_87><loc_72><loc_88><loc_72></location>.</text>
<text><location><page_13><loc_87><loc_72><loc_88><loc_72></location>7</text>
<text><location><page_13><loc_87><loc_71><loc_88><loc_72></location>1</text>
<text><location><page_13><loc_87><loc_70><loc_88><loc_70></location>0</text>
<text><location><page_13><loc_87><loc_69><loc_88><loc_70></location>1</text>
<text><location><page_13><loc_87><loc_69><loc_88><loc_69></location>0</text>
<text><location><page_13><loc_87><loc_69><loc_88><loc_69></location>.</text>
<text><location><page_13><loc_87><loc_68><loc_88><loc_69></location>0</text>
<text><location><page_13><loc_87><loc_67><loc_87><loc_68></location>±</text>
<text><location><page_13><loc_87><loc_66><loc_88><loc_67></location>5</text>
<text><location><page_13><loc_87><loc_66><loc_88><loc_66></location>7</text>
<text><location><page_13><loc_87><loc_66><loc_88><loc_66></location>1</text>
<text><location><page_13><loc_87><loc_65><loc_88><loc_66></location>.</text>
<text><location><page_13><loc_87><loc_65><loc_88><loc_65></location>8</text>
<text><location><page_13><loc_87><loc_64><loc_88><loc_65></location>1</text>
<text><location><page_13><loc_87><loc_63><loc_88><loc_63></location>9</text>
<text><location><page_13><loc_87><loc_62><loc_88><loc_63></location>0</text>
<text><location><page_13><loc_87><loc_62><loc_88><loc_62></location>0</text>
<text><location><page_13><loc_87><loc_62><loc_88><loc_62></location>.</text>
<text><location><page_13><loc_87><loc_61><loc_88><loc_62></location>0</text>
<text><location><page_13><loc_87><loc_60><loc_87><loc_61></location>±</text>
<text><location><page_13><loc_87><loc_60><loc_88><loc_60></location>2</text>
<text><location><page_13><loc_87><loc_59><loc_88><loc_60></location>1</text>
<text><location><page_13><loc_87><loc_59><loc_88><loc_59></location>3</text>
<text><location><page_13><loc_87><loc_58><loc_88><loc_59></location>.</text>
<text><location><page_13><loc_87><loc_58><loc_88><loc_58></location>8</text>
<text><location><page_13><loc_87><loc_58><loc_88><loc_58></location>1</text>
<text><location><page_13><loc_87><loc_56><loc_88><loc_56></location>9</text>
<text><location><page_13><loc_87><loc_55><loc_88><loc_56></location>0</text>
<text><location><page_13><loc_87><loc_55><loc_88><loc_55></location>0</text>
<text><location><page_13><loc_87><loc_55><loc_88><loc_55></location>.</text>
<text><location><page_13><loc_87><loc_54><loc_88><loc_55></location>0</text>
<text><location><page_13><loc_87><loc_53><loc_87><loc_54></location>±</text>
<text><location><page_13><loc_87><loc_53><loc_88><loc_53></location>8</text>
<text><location><page_13><loc_87><loc_52><loc_88><loc_53></location>5</text>
<text><location><page_13><loc_87><loc_52><loc_88><loc_52></location>5</text>
<text><location><page_13><loc_87><loc_52><loc_88><loc_52></location>.</text>
<text><location><page_13><loc_87><loc_51><loc_88><loc_52></location>8</text>
<text><location><page_13><loc_87><loc_51><loc_88><loc_51></location>1</text>
<text><location><page_13><loc_87><loc_49><loc_88><loc_49></location>7</text>
<text><location><page_13><loc_87><loc_49><loc_88><loc_49></location>0</text>
<text><location><page_13><loc_87><loc_48><loc_88><loc_49></location>0</text>
<text><location><page_13><loc_87><loc_48><loc_88><loc_48></location>.</text>
<text><location><page_13><loc_87><loc_47><loc_88><loc_48></location>0</text>
<text><location><page_13><loc_87><loc_46><loc_87><loc_47></location>±</text>
<text><location><page_13><loc_87><loc_46><loc_88><loc_46></location>7</text>
<text><location><page_13><loc_87><loc_45><loc_88><loc_46></location>8</text>
<text><location><page_13><loc_87><loc_45><loc_88><loc_45></location>3</text>
<text><location><page_13><loc_87><loc_45><loc_88><loc_45></location>.</text>
<text><location><page_13><loc_87><loc_44><loc_88><loc_45></location>8</text>
<text><location><page_13><loc_87><loc_44><loc_88><loc_44></location>1</text>
<text><location><page_13><loc_87><loc_42><loc_88><loc_43></location>5</text>
<text><location><page_13><loc_87><loc_42><loc_88><loc_42></location>0</text>
<text><location><page_13><loc_87><loc_41><loc_88><loc_42></location>.</text>
<text><location><page_13><loc_87><loc_41><loc_88><loc_41></location>2</text>
<text><location><page_13><loc_87><loc_41><loc_88><loc_41></location>3</text>
<text><location><page_13><loc_87><loc_40><loc_88><loc_40></location>0</text>
<text><location><page_13><loc_87><loc_39><loc_88><loc_40></location>2</text>
<text><location><page_13><loc_87><loc_39><loc_88><loc_39></location>0</text>
<text><location><page_13><loc_87><loc_38><loc_88><loc_39></location>3</text>
<text><location><page_13><loc_87><loc_37><loc_88><loc_37></location>9</text>
<text><location><page_13><loc_87><loc_36><loc_88><loc_37></location>9</text>
<text><location><page_13><loc_87><loc_36><loc_88><loc_36></location>2</text>
<text><location><page_13><loc_87><loc_35><loc_88><loc_36></location>.</text>
<text><location><page_13><loc_87><loc_35><loc_88><loc_35></location>1</text>
<text><location><page_13><loc_87><loc_35><loc_88><loc_35></location>2</text>
<text><location><page_13><loc_87><loc_34><loc_88><loc_34></location>3</text>
<text><location><page_13><loc_87><loc_33><loc_88><loc_34></location>3</text>
<text><location><page_13><loc_87><loc_33><loc_88><loc_33></location>1</text>
<text><location><page_13><loc_87><loc_32><loc_88><loc_33></location>0</text>
<text><location><page_13><loc_87><loc_31><loc_88><loc_31></location>0</text>
<text><location><page_13><loc_87><loc_30><loc_88><loc_31></location>2</text>
<text><location><page_13><loc_87><loc_30><loc_88><loc_30></location>0</text>
<text><location><page_13><loc_87><loc_29><loc_88><loc_30></location>-</text>
<text><location><page_13><loc_87><loc_29><loc_88><loc_29></location>3</text>
<text><location><page_13><loc_87><loc_29><loc_88><loc_29></location>-</text>
<text><location><page_13><loc_87><loc_28><loc_88><loc_29></location>3</text>
<text><location><page_13><loc_87><loc_28><loc_88><loc_28></location>3</text>
<text><location><page_13><loc_87><loc_19><loc_88><loc_19></location>0</text>
<text><location><page_13><loc_87><loc_19><loc_88><loc_19></location>3</text>
<text><location><page_13><loc_87><loc_18><loc_88><loc_19></location>R</text>
<text><location><page_13><loc_87><loc_18><loc_88><loc_18></location>S</text>
<text><location><page_13><loc_87><loc_16><loc_88><loc_16></location>.</text>
<text><location><page_13><loc_87><loc_16><loc_88><loc_16></location>.</text>
<text><location><page_13><loc_87><loc_15><loc_88><loc_16></location>.</text>
<text><location><page_13><loc_87><loc_15><loc_88><loc_15></location>.</text>
<text><location><page_13><loc_87><loc_15><loc_88><loc_15></location>.</text>
<text><location><page_13><loc_87><loc_15><loc_88><loc_15></location>.</text>
<text><location><page_13><loc_87><loc_14><loc_88><loc_15></location>6</text>
<text><location><page_13><loc_87><loc_14><loc_88><loc_14></location>5</text>
<text><location><page_14><loc_9><loc_93><loc_10><loc_94></location>14</text>
<text><location><page_14><loc_50><loc_93><loc_52><loc_94></location>Ma</text>
<paragraph><location><page_14><loc_47><loc_84><loc_52><loc_85></location>4 0 2 2 8</paragraph>
<text><location><page_14><loc_47><loc_84><loc_47><loc_84></location>5</text>
<text><location><page_14><loc_47><loc_84><loc_47><loc_84></location>3</text>
<text><location><page_14><loc_47><loc_83><loc_47><loc_84></location>.</text>
<text><location><page_14><loc_20><loc_84><loc_20><loc_85></location>6</text>
<text><location><page_14><loc_20><loc_84><loc_20><loc_84></location>9</text>
<text><location><page_14><loc_20><loc_84><loc_20><loc_84></location>0</text>
<text><location><page_14><loc_20><loc_83><loc_20><loc_84></location>.</text>
<text><location><page_14><loc_21><loc_84><loc_22><loc_85></location>2</text>
<text><location><page_14><loc_21><loc_84><loc_22><loc_84></location>2</text>
<text><location><page_14><loc_21><loc_84><loc_22><loc_84></location>3</text>
<text><location><page_14><loc_21><loc_83><loc_22><loc_84></location>.</text>
<text><location><page_14><loc_22><loc_84><loc_23><loc_85></location>8</text>
<text><location><page_14><loc_22><loc_84><loc_23><loc_84></location>3</text>
<text><location><page_14><loc_22><loc_84><loc_23><loc_84></location>8</text>
<text><location><page_14><loc_22><loc_83><loc_23><loc_84></location>.</text>
<text><location><page_14><loc_23><loc_84><loc_24><loc_85></location>8</text>
<text><location><page_14><loc_23><loc_84><loc_24><loc_84></location>3</text>
<text><location><page_14><loc_23><loc_84><loc_24><loc_84></location>8</text>
<text><location><page_14><loc_23><loc_83><loc_24><loc_84></location>.</text>
<text><location><page_14><loc_24><loc_84><loc_25><loc_85></location>4</text>
<text><location><page_14><loc_24><loc_84><loc_25><loc_84></location>4</text>
<text><location><page_14><loc_24><loc_84><loc_25><loc_84></location>6</text>
<text><location><page_14><loc_24><loc_83><loc_25><loc_84></location>.</text>
<text><location><page_14><loc_26><loc_84><loc_27><loc_85></location>8</text>
<text><location><page_14><loc_26><loc_84><loc_27><loc_84></location>3</text>
<text><location><page_14><loc_26><loc_84><loc_27><loc_84></location>8</text>
<text><location><page_14><loc_26><loc_83><loc_27><loc_84></location>.</text>
<text><location><page_14><loc_27><loc_84><loc_28><loc_85></location>2</text>
<text><location><page_14><loc_27><loc_84><loc_28><loc_84></location>2</text>
<text><location><page_14><loc_27><loc_84><loc_28><loc_84></location>3</text>
<text><location><page_14><loc_27><loc_83><loc_28><loc_84></location>.</text>
<text><location><page_14><loc_28><loc_84><loc_29><loc_85></location>4</text>
<text><location><page_14><loc_28><loc_84><loc_29><loc_84></location>6</text>
<text><location><page_14><loc_28><loc_84><loc_29><loc_84></location>0</text>
<text><location><page_14><loc_28><loc_83><loc_29><loc_84></location>.</text>
<text><location><page_14><loc_29><loc_84><loc_30><loc_85></location>8</text>
<text><location><page_14><loc_29><loc_84><loc_30><loc_84></location>3</text>
<text><location><page_14><loc_29><loc_84><loc_30><loc_84></location>8</text>
<text><location><page_14><loc_29><loc_83><loc_30><loc_84></location>.</text>
<text><location><page_14><loc_31><loc_84><loc_31><loc_85></location>8</text>
<text><location><page_14><loc_31><loc_84><loc_31><loc_84></location>4</text>
<text><location><page_14><loc_31><loc_84><loc_31><loc_84></location>5</text>
<text><location><page_14><loc_31><loc_83><loc_31><loc_84></location>.</text>
<text><location><page_14><loc_32><loc_84><loc_33><loc_85></location>0</text>
<text><location><page_14><loc_32><loc_84><loc_33><loc_84></location>8</text>
<text><location><page_14><loc_32><loc_84><loc_33><loc_84></location>5</text>
<text><location><page_14><loc_32><loc_83><loc_33><loc_84></location>.</text>
<text><location><page_14><loc_33><loc_84><loc_34><loc_85></location>8</text>
<text><location><page_14><loc_33><loc_84><loc_34><loc_84></location>4</text>
<text><location><page_14><loc_33><loc_84><loc_34><loc_84></location>5</text>
<text><location><page_14><loc_33><loc_83><loc_34><loc_84></location>.</text>
<text><location><page_14><loc_34><loc_84><loc_35><loc_85></location>4</text>
<text><location><page_14><loc_34><loc_84><loc_35><loc_84></location>6</text>
<text><location><page_14><loc_34><loc_84><loc_35><loc_84></location>0</text>
<text><location><page_14><loc_34><loc_83><loc_35><loc_84></location>.</text>
<text><location><page_14><loc_36><loc_84><loc_36><loc_85></location>8</text>
<text><location><page_14><loc_36><loc_84><loc_36><loc_84></location>3</text>
<text><location><page_14><loc_36><loc_84><loc_36><loc_84></location>8</text>
<text><location><page_14><loc_36><loc_83><loc_36><loc_84></location>.</text>
<text><location><page_14><loc_37><loc_84><loc_38><loc_85></location>0</text>
<text><location><page_14><loc_37><loc_84><loc_38><loc_84></location>8</text>
<text><location><page_14><loc_37><loc_84><loc_38><loc_84></location>5</text>
<text><location><page_14><loc_37><loc_83><loc_38><loc_84></location>.</text>
<text><location><page_14><loc_38><loc_84><loc_39><loc_85></location>6</text>
<text><location><page_14><loc_38><loc_84><loc_39><loc_84></location>9</text>
<text><location><page_14><loc_38><loc_84><loc_39><loc_84></location>0</text>
<text><location><page_14><loc_38><loc_83><loc_39><loc_84></location>.</text>
<text><location><page_14><loc_39><loc_84><loc_40><loc_85></location>6</text>
<text><location><page_14><loc_39><loc_84><loc_40><loc_84></location>9</text>
<text><location><page_14><loc_39><loc_84><loc_40><loc_84></location>0</text>
<text><location><page_14><loc_39><loc_83><loc_40><loc_84></location>.</text>
<text><location><page_14><loc_40><loc_84><loc_41><loc_85></location>6</text>
<text><location><page_14><loc_40><loc_84><loc_41><loc_84></location>0</text>
<text><location><page_14><loc_40><loc_84><loc_41><loc_84></location>8</text>
<text><location><page_14><loc_40><loc_83><loc_41><loc_84></location>.</text>
<text><location><page_14><loc_42><loc_84><loc_42><loc_85></location>4</text>
<text><location><page_14><loc_42><loc_84><loc_42><loc_84></location>6</text>
<text><location><page_14><loc_42><loc_84><loc_42><loc_84></location>0</text>
<text><location><page_14><loc_42><loc_83><loc_42><loc_84></location>.</text>
<text><location><page_14><loc_43><loc_84><loc_44><loc_85></location>0</text>
<text><location><page_14><loc_43><loc_84><loc_44><loc_84></location>8</text>
<text><location><page_14><loc_43><loc_84><loc_44><loc_84></location>5</text>
<text><location><page_14><loc_43><loc_83><loc_44><loc_84></location>.</text>
<text><location><page_14><loc_44><loc_84><loc_45><loc_85></location>8</text>
<text><location><page_14><loc_44><loc_84><loc_45><loc_84></location>4</text>
<text><location><page_14><loc_44><loc_84><loc_45><loc_84></location>5</text>
<text><location><page_14><loc_44><loc_83><loc_45><loc_84></location>.</text>
<text><location><page_14><loc_45><loc_84><loc_46><loc_85></location>2</text>
<text><location><page_14><loc_45><loc_84><loc_46><loc_84></location>2</text>
<text><location><page_14><loc_45><loc_84><loc_46><loc_84></location>3</text>
<text><location><page_14><loc_45><loc_83><loc_46><loc_84></location>.</text>
<text><location><page_14><loc_48><loc_84><loc_49><loc_84></location>8</text>
<text><location><page_14><loc_48><loc_84><loc_49><loc_84></location>5</text>
<text><location><page_14><loc_48><loc_83><loc_49><loc_84></location>.</text>
<text><location><page_14><loc_49><loc_84><loc_50><loc_84></location>2</text>
<text><location><page_14><loc_49><loc_84><loc_50><loc_84></location>3</text>
<text><location><page_14><loc_49><loc_83><loc_50><loc_84></location>.</text>
<text><location><page_14><loc_50><loc_84><loc_51><loc_84></location>2</text>
<text><location><page_14><loc_50><loc_84><loc_51><loc_84></location>3</text>
<text><location><page_14><loc_50><loc_83><loc_51><loc_84></location>.</text>
<text><location><page_14><loc_51><loc_84><loc_52><loc_84></location>3</text>
<text><location><page_14><loc_51><loc_84><loc_52><loc_84></location>8</text>
<text><location><page_14><loc_51><loc_83><loc_52><loc_84></location>.</text>
<text><location><page_14><loc_53><loc_84><loc_54><loc_85></location>0</text>
<text><location><page_14><loc_53><loc_84><loc_54><loc_84></location>7</text>
<text><location><page_14><loc_53><loc_84><loc_54><loc_84></location>8</text>
<text><location><page_14><loc_53><loc_83><loc_54><loc_84></location>.</text>
<text><location><page_14><loc_54><loc_84><loc_55><loc_85></location>0</text>
<text><location><page_14><loc_54><loc_84><loc_55><loc_84></location>8</text>
<text><location><page_14><loc_54><loc_84><loc_55><loc_84></location>5</text>
<text><location><page_14><loc_54><loc_83><loc_55><loc_84></location>.</text>
<text><location><page_14><loc_55><loc_84><loc_56><loc_85></location>0</text>
<text><location><page_14><loc_55><loc_84><loc_56><loc_84></location>8</text>
<text><location><page_14><loc_55><loc_84><loc_56><loc_84></location>5</text>
<text><location><page_14><loc_55><loc_83><loc_56><loc_84></location>.</text>
<text><location><page_14><loc_56><loc_84><loc_57><loc_85></location>0</text>
<text><location><page_14><loc_56><loc_84><loc_57><loc_84></location>9</text>
<text><location><page_14><loc_56><loc_84><loc_57><loc_84></location>2</text>
<text><location><page_14><loc_56><loc_83><loc_57><loc_84></location>.</text>
<text><location><page_14><loc_58><loc_84><loc_58><loc_85></location>6</text>
<text><location><page_14><loc_58><loc_84><loc_58><loc_84></location>0</text>
<text><location><page_14><loc_58><loc_84><loc_58><loc_84></location>8</text>
<text><location><page_14><loc_58><loc_83><loc_58><loc_84></location>.</text>
<text><location><page_14><loc_59><loc_84><loc_60><loc_85></location>8</text>
<text><location><page_14><loc_59><loc_84><loc_60><loc_84></location>4</text>
<text><location><page_14><loc_59><loc_84><loc_60><loc_84></location>5</text>
<text><location><page_14><loc_59><loc_83><loc_60><loc_84></location>.</text>
<text><location><page_14><loc_60><loc_84><loc_61><loc_85></location>0</text>
<text><location><page_14><loc_60><loc_84><loc_61><loc_84></location>8</text>
<text><location><page_14><loc_60><loc_84><loc_61><loc_84></location>5</text>
<text><location><page_14><loc_60><loc_83><loc_61><loc_84></location>.</text>
<text><location><page_14><loc_61><loc_84><loc_62><loc_85></location>4</text>
<text><location><page_14><loc_61><loc_84><loc_62><loc_84></location>6</text>
<text><location><page_14><loc_61><loc_84><loc_62><loc_84></location>0</text>
<text><location><page_14><loc_61><loc_83><loc_62><loc_84></location>.</text>
<text><location><page_14><loc_63><loc_84><loc_63><loc_85></location>2</text>
<text><location><page_14><loc_63><loc_84><loc_63><loc_84></location>2</text>
<text><location><page_14><loc_63><loc_84><loc_63><loc_84></location>3</text>
<text><location><page_14><loc_63><loc_83><loc_63><loc_84></location>.</text>
<text><location><page_14><loc_64><loc_84><loc_65><loc_85></location>6</text>
<text><location><page_14><loc_64><loc_84><loc_65><loc_84></location>9</text>
<text><location><page_14><loc_64><loc_84><loc_65><loc_84></location>0</text>
<text><location><page_14><loc_64><loc_83><loc_65><loc_84></location>.</text>
<text><location><page_14><loc_65><loc_84><loc_66><loc_85></location>4</text>
<text><location><page_14><loc_65><loc_84><loc_66><loc_84></location>5</text>
<text><location><page_14><loc_65><loc_84><loc_66><loc_84></location>3</text>
<text><location><page_14><loc_65><loc_83><loc_66><loc_84></location>.</text>
<text><location><page_14><loc_66><loc_84><loc_67><loc_85></location>6</text>
<text><location><page_14><loc_66><loc_84><loc_67><loc_84></location>9</text>
<text><location><page_14><loc_66><loc_84><loc_67><loc_84></location>0</text>
<text><location><page_14><loc_66><loc_83><loc_67><loc_84></location>.</text>
<text><location><page_14><loc_67><loc_84><loc_68><loc_85></location>4</text>
<text><location><page_14><loc_67><loc_84><loc_68><loc_84></location>4</text>
<text><location><page_14><loc_67><loc_84><loc_68><loc_84></location>6</text>
<text><location><page_14><loc_67><loc_83><loc_68><loc_84></location>.</text>
<text><location><page_14><loc_69><loc_84><loc_69><loc_85></location>6</text>
<text><location><page_14><loc_69><loc_84><loc_69><loc_84></location>9</text>
<text><location><page_14><loc_69><loc_84><loc_69><loc_84></location>0</text>
<text><location><page_14><loc_69><loc_83><loc_69><loc_84></location>.</text>
<text><location><page_14><loc_70><loc_84><loc_71><loc_85></location>0</text>
<text><location><page_14><loc_70><loc_84><loc_71><loc_84></location>8</text>
<text><location><page_14><loc_70><loc_84><loc_71><loc_84></location>5</text>
<text><location><page_14><loc_70><loc_83><loc_71><loc_84></location>.</text>
<text><location><page_14><loc_71><loc_84><loc_72><loc_85></location>4</text>
<text><location><page_14><loc_71><loc_84><loc_72><loc_84></location>5</text>
<text><location><page_14><loc_71><loc_84><loc_72><loc_84></location>3</text>
<text><location><page_14><loc_71><loc_83><loc_72><loc_84></location>.</text>
<text><location><page_14><loc_72><loc_84><loc_73><loc_85></location>4</text>
<text><location><page_14><loc_72><loc_84><loc_73><loc_84></location>5</text>
<text><location><page_14><loc_72><loc_84><loc_73><loc_84></location>3</text>
<text><location><page_14><loc_72><loc_83><loc_73><loc_84></location>.</text>
<text><location><page_14><loc_74><loc_84><loc_74><loc_85></location>0</text>
<text><location><page_14><loc_74><loc_84><loc_74><loc_84></location>8</text>
<text><location><page_14><loc_74><loc_84><loc_74><loc_84></location>5</text>
<text><location><page_14><loc_74><loc_83><loc_74><loc_84></location>.</text>
<text><location><page_14><loc_75><loc_84><loc_76><loc_85></location>2</text>
<text><location><page_14><loc_75><loc_84><loc_76><loc_84></location>1</text>
<text><location><page_14><loc_75><loc_84><loc_76><loc_84></location>6</text>
<text><location><page_14><loc_75><loc_83><loc_76><loc_84></location>.</text>
<text><location><page_14><loc_76><loc_84><loc_77><loc_85></location>0</text>
<text><location><page_14><loc_76><loc_84><loc_77><loc_84></location>8</text>
<text><location><page_14><loc_76><loc_84><loc_77><loc_84></location>5</text>
<text><location><page_14><loc_76><loc_83><loc_77><loc_84></location>.</text>
<text><location><page_14><loc_77><loc_84><loc_78><loc_85></location>2</text>
<text><location><page_14><loc_77><loc_84><loc_78><loc_84></location>2</text>
<text><location><page_14><loc_77><loc_84><loc_78><loc_84></location>3</text>
<text><location><page_14><loc_77><loc_83><loc_78><loc_84></location>.</text>
<text><location><page_14><loc_78><loc_84><loc_79><loc_85></location>8</text>
<text><location><page_14><loc_78><loc_84><loc_79><loc_84></location>3</text>
<text><location><page_14><loc_78><loc_84><loc_79><loc_84></location>8</text>
<text><location><page_14><loc_78><loc_83><loc_79><loc_84></location>.</text>
<text><location><page_14><loc_80><loc_84><loc_81><loc_85></location>0</text>
<text><location><page_14><loc_80><loc_84><loc_81><loc_84></location>8</text>
<text><location><page_14><loc_80><loc_84><loc_81><loc_84></location>5</text>
<text><location><page_14><loc_80><loc_83><loc_81><loc_84></location>.</text>
<text><location><page_14><loc_81><loc_84><loc_82><loc_85></location>0</text>
<text><location><page_14><loc_81><loc_84><loc_82><loc_84></location>8</text>
<text><location><page_14><loc_81><loc_84><loc_82><loc_84></location>5</text>
<text><location><page_14><loc_81><loc_83><loc_82><loc_84></location>.</text>
<text><location><page_14><loc_82><loc_84><loc_83><loc_85></location>6</text>
<text><location><page_14><loc_82><loc_84><loc_83><loc_84></location>0</text>
<text><location><page_14><loc_82><loc_84><loc_83><loc_84></location>8</text>
<text><location><page_14><loc_82><loc_83><loc_83><loc_84></location>.</text>
<text><location><page_14><loc_83><loc_84><loc_84><loc_85></location>2</text>
<text><location><page_14><loc_83><loc_84><loc_84><loc_84></location>1</text>
<text><location><page_14><loc_83><loc_84><loc_84><loc_84></location>6</text>
<text><location><page_14><loc_83><loc_83><loc_84><loc_84></location>.</text>
<text><location><page_14><loc_85><loc_84><loc_85><loc_85></location>4</text>
<text><location><page_14><loc_85><loc_84><loc_85><loc_84></location>6</text>
<text><location><page_14><loc_85><loc_84><loc_85><loc_84></location>0</text>
<text><location><page_14><loc_85><loc_83><loc_85><loc_84></location>.</text>
<table>
<location><page_14><loc_14><loc_12><loc_85><loc_83></location>
</table>
<text><location><page_14><loc_13><loc_51><loc_14><loc_52></location>1</text>
<text><location><page_14><loc_13><loc_50><loc_14><loc_51></location>E</text>
<text><location><page_14><loc_13><loc_50><loc_14><loc_50></location>L</text>
<text><location><page_14><loc_13><loc_48><loc_14><loc_50></location>AB</text>
<text><location><page_14><loc_13><loc_47><loc_14><loc_48></location>T</text>
<text><location><page_14><loc_17><loc_84><loc_18><loc_84></location>p</text>
<text><location><page_14><loc_18><loc_84><loc_19><loc_84></location>)</text>
<text><location><page_14><loc_18><loc_84><loc_19><loc_84></location>'</text>
<text><location><page_14><loc_18><loc_84><loc_19><loc_84></location>'</text>
<text><location><page_14><loc_18><loc_83><loc_19><loc_84></location>(</text>
<text><location><page_14><loc_17><loc_84><loc_18><loc_84></location>a</text>
<text><location><page_14><loc_17><loc_83><loc_18><loc_84></location>r</text>
<text><location><page_14><loc_86><loc_84><loc_87><loc_85></location>6</text>
<text><location><page_14><loc_86><loc_84><loc_87><loc_84></location>0</text>
<text><location><page_14><loc_86><loc_84><loc_87><loc_84></location>8</text>
<text><location><page_14><loc_86><loc_83><loc_87><loc_84></location>.</text>
<text><location><page_14><loc_86><loc_83><loc_87><loc_83></location>1</text>
<text><location><page_14><loc_86><loc_80><loc_87><loc_80></location>5</text>
<text><location><page_14><loc_86><loc_80><loc_87><loc_80></location>0</text>
<text><location><page_14><loc_86><loc_79><loc_87><loc_80></location>.</text>
<text><location><page_14><loc_86><loc_79><loc_87><loc_79></location>0</text>
<text><location><page_14><loc_86><loc_76><loc_87><loc_77></location>0</text>
<text><location><page_14><loc_86><loc_76><loc_87><loc_76></location>3</text>
<text><location><page_14><loc_86><loc_75><loc_87><loc_76></location>0</text>
<text><location><page_14><loc_86><loc_75><loc_87><loc_75></location>.</text>
<text><location><page_14><loc_86><loc_75><loc_87><loc_75></location>0</text>
<text><location><page_14><loc_86><loc_74><loc_87><loc_74></location>±</text>
<text><location><page_14><loc_86><loc_73><loc_87><loc_73></location>4</text>
<text><location><page_14><loc_86><loc_72><loc_87><loc_73></location>3</text>
<text><location><page_14><loc_86><loc_72><loc_87><loc_72></location>2</text>
<text><location><page_14><loc_86><loc_72><loc_87><loc_72></location>.</text>
<text><location><page_14><loc_86><loc_71><loc_87><loc_72></location>8</text>
<text><location><page_14><loc_86><loc_71><loc_87><loc_71></location>1</text>
<text><location><page_14><loc_86><loc_69><loc_87><loc_70></location>6</text>
<text><location><page_14><loc_86><loc_69><loc_87><loc_69></location>1</text>
<text><location><page_14><loc_86><loc_68><loc_87><loc_69></location>0</text>
<text><location><page_14><loc_86><loc_68><loc_87><loc_68></location>.</text>
<text><location><page_14><loc_86><loc_68><loc_87><loc_68></location>0</text>
<text><location><page_14><loc_86><loc_67><loc_87><loc_67></location>±</text>
<text><location><page_14><loc_86><loc_66><loc_87><loc_66></location>1</text>
<text><location><page_14><loc_86><loc_66><loc_87><loc_66></location>9</text>
<text><location><page_14><loc_86><loc_65><loc_87><loc_66></location>1</text>
<text><location><page_14><loc_86><loc_65><loc_87><loc_65></location>.</text>
<text><location><page_14><loc_86><loc_64><loc_87><loc_65></location>8</text>
<text><location><page_14><loc_86><loc_64><loc_87><loc_64></location>1</text>
<text><location><page_14><loc_86><loc_62><loc_87><loc_63></location>1</text>
<text><location><page_14><loc_86><loc_62><loc_87><loc_62></location>1</text>
<text><location><page_14><loc_86><loc_61><loc_87><loc_62></location>0</text>
<text><location><page_14><loc_86><loc_61><loc_87><loc_61></location>.</text>
<text><location><page_14><loc_86><loc_61><loc_87><loc_61></location>0</text>
<text><location><page_14><loc_86><loc_60><loc_87><loc_60></location>±</text>
<text><location><page_14><loc_86><loc_59><loc_87><loc_59></location>9</text>
<text><location><page_14><loc_86><loc_59><loc_87><loc_59></location>8</text>
<text><location><page_14><loc_86><loc_58><loc_87><loc_59></location>0</text>
<text><location><page_14><loc_86><loc_58><loc_87><loc_58></location>.</text>
<text><location><page_14><loc_86><loc_58><loc_87><loc_58></location>8</text>
<text><location><page_14><loc_86><loc_57><loc_87><loc_58></location>1</text>
<text><location><page_14><loc_86><loc_55><loc_87><loc_56></location>9</text>
<text><location><page_14><loc_86><loc_55><loc_87><loc_55></location>0</text>
<text><location><page_14><loc_86><loc_55><loc_87><loc_55></location>0</text>
<text><location><page_14><loc_86><loc_54><loc_87><loc_55></location>.</text>
<text><location><page_14><loc_86><loc_54><loc_87><loc_54></location>0</text>
<text><location><page_14><loc_86><loc_53><loc_87><loc_54></location>±</text>
<text><location><page_14><loc_86><loc_52><loc_87><loc_53></location>9</text>
<text><location><page_14><loc_86><loc_52><loc_87><loc_52></location>1</text>
<text><location><page_14><loc_86><loc_51><loc_87><loc_52></location>1</text>
<text><location><page_14><loc_86><loc_51><loc_87><loc_51></location>.</text>
<text><location><page_14><loc_86><loc_51><loc_87><loc_51></location>8</text>
<text><location><page_14><loc_86><loc_50><loc_87><loc_51></location>1</text>
<text><location><page_14><loc_86><loc_48><loc_87><loc_49></location>5</text>
<text><location><page_14><loc_86><loc_48><loc_87><loc_49></location>0</text>
<text><location><page_14><loc_86><loc_48><loc_87><loc_48></location>0</text>
<text><location><page_14><loc_86><loc_47><loc_87><loc_48></location>.</text>
<text><location><page_14><loc_86><loc_47><loc_87><loc_47></location>0</text>
<text><location><page_14><loc_86><loc_46><loc_87><loc_47></location>±</text>
<text><location><page_14><loc_86><loc_45><loc_87><loc_46></location>8</text>
<text><location><page_14><loc_86><loc_45><loc_87><loc_45></location>9</text>
<text><location><page_14><loc_86><loc_44><loc_87><loc_45></location>1</text>
<text><location><page_14><loc_86><loc_44><loc_87><loc_44></location>.</text>
<text><location><page_14><loc_86><loc_44><loc_87><loc_44></location>7</text>
<text><location><page_14><loc_86><loc_43><loc_87><loc_44></location>1</text>
<text><location><page_14><loc_86><loc_42><loc_87><loc_42></location>1</text>
<text><location><page_14><loc_86><loc_41><loc_87><loc_42></location>9</text>
<text><location><page_14><loc_86><loc_41><loc_87><loc_41></location>.</text>
<text><location><page_14><loc_86><loc_40><loc_87><loc_41></location>5</text>
<text><location><page_14><loc_86><loc_40><loc_87><loc_41></location>3</text>
<text><location><page_14><loc_86><loc_39><loc_87><loc_40></location>6</text>
<text><location><page_14><loc_86><loc_39><loc_87><loc_39></location>3</text>
<text><location><page_14><loc_86><loc_38><loc_87><loc_39></location>0</text>
<text><location><page_14><loc_86><loc_38><loc_87><loc_38></location>3</text>
<text><location><page_14><loc_86><loc_36><loc_87><loc_37></location>3</text>
<text><location><page_14><loc_86><loc_36><loc_87><loc_36></location>8</text>
<text><location><page_14><loc_86><loc_35><loc_87><loc_36></location>6</text>
<text><location><page_14><loc_86><loc_35><loc_87><loc_35></location>.</text>
<text><location><page_14><loc_86><loc_35><loc_87><loc_35></location>4</text>
<text><location><page_14><loc_86><loc_34><loc_87><loc_35></location>4</text>
<text><location><page_14><loc_86><loc_33><loc_87><loc_34></location>3</text>
<text><location><page_14><loc_86><loc_33><loc_87><loc_33></location>3</text>
<text><location><page_14><loc_86><loc_32><loc_87><loc_33></location>1</text>
<text><location><page_14><loc_86><loc_32><loc_87><loc_32></location>0</text>
<text><location><page_14><loc_86><loc_20><loc_87><loc_21></location>1</text>
<text><location><page_14><loc_86><loc_20><loc_87><loc_20></location>1</text>
<text><location><page_14><loc_86><loc_19><loc_87><loc_20></location>1</text>
<text><location><page_14><loc_86><loc_19><loc_87><loc_19></location>R</text>
<text><location><page_14><loc_86><loc_18><loc_87><loc_19></location>S</text>
<text><location><page_14><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_14><loc_86><loc_16><loc_87><loc_17></location>.</text>
<text><location><page_14><loc_86><loc_16><loc_87><loc_16></location>.</text>
<text><location><page_14><loc_86><loc_16><loc_87><loc_16></location>.</text>
<text><location><page_14><loc_86><loc_16><loc_87><loc_16></location>.</text>
<text><location><page_14><loc_86><loc_15><loc_87><loc_16></location>.</text>
<text><location><page_14><loc_86><loc_15><loc_87><loc_15></location>1</text>
<text><location><page_14><loc_86><loc_15><loc_87><loc_15></location>1</text>
<text><location><page_14><loc_86><loc_14><loc_87><loc_15></location>1</text>
<text><location><page_14><loc_87><loc_84><loc_88><loc_85></location>4</text>
<text><location><page_14><loc_87><loc_84><loc_88><loc_84></location>6</text>
<text><location><page_14><loc_87><loc_84><loc_88><loc_84></location>0</text>
<text><location><page_14><loc_87><loc_83><loc_88><loc_84></location>.</text>
<text><location><page_14><loc_87><loc_83><loc_88><loc_83></location>2</text>
<text><location><page_14><loc_87><loc_80><loc_88><loc_80></location>5</text>
<text><location><page_14><loc_87><loc_80><loc_88><loc_80></location>0</text>
<text><location><page_14><loc_87><loc_79><loc_88><loc_80></location>.</text>
<text><location><page_14><loc_87><loc_79><loc_88><loc_79></location>0</text>
<text><location><page_14><loc_87><loc_76><loc_88><loc_77></location>4</text>
<text><location><page_14><loc_87><loc_76><loc_88><loc_76></location>5</text>
<text><location><page_14><loc_87><loc_75><loc_88><loc_76></location>0</text>
<text><location><page_14><loc_87><loc_75><loc_88><loc_75></location>.</text>
<text><location><page_14><loc_87><loc_75><loc_88><loc_75></location>0</text>
<text><location><page_14><loc_87><loc_74><loc_88><loc_74></location>±</text>
<text><location><page_14><loc_87><loc_73><loc_88><loc_73></location>1</text>
<text><location><page_14><loc_87><loc_72><loc_88><loc_73></location>9</text>
<text><location><page_14><loc_87><loc_72><loc_88><loc_72></location>7</text>
<text><location><page_14><loc_87><loc_72><loc_88><loc_72></location>.</text>
<text><location><page_14><loc_87><loc_71><loc_88><loc_72></location>8</text>
<text><location><page_14><loc_87><loc_71><loc_88><loc_71></location>1</text>
<text><location><page_14><loc_87><loc_69><loc_88><loc_70></location>2</text>
<text><location><page_14><loc_87><loc_69><loc_88><loc_69></location>4</text>
<text><location><page_14><loc_87><loc_68><loc_88><loc_69></location>0</text>
<text><location><page_14><loc_87><loc_68><loc_88><loc_68></location>.</text>
<text><location><page_14><loc_87><loc_68><loc_88><loc_68></location>0</text>
<text><location><page_14><loc_87><loc_67><loc_88><loc_67></location>±</text>
<text><location><page_14><loc_87><loc_66><loc_88><loc_66></location>8</text>
<text><location><page_14><loc_87><loc_66><loc_88><loc_66></location>0</text>
<text><location><page_14><loc_87><loc_65><loc_88><loc_66></location>0</text>
<text><location><page_14><loc_87><loc_65><loc_88><loc_65></location>.</text>
<text><location><page_14><loc_87><loc_64><loc_88><loc_65></location>9</text>
<text><location><page_14><loc_87><loc_64><loc_88><loc_64></location>1</text>
<text><location><page_14><loc_87><loc_62><loc_88><loc_63></location>8</text>
<text><location><page_14><loc_87><loc_62><loc_88><loc_62></location>2</text>
<text><location><page_14><loc_87><loc_61><loc_88><loc_62></location>0</text>
<text><location><page_14><loc_87><loc_61><loc_88><loc_61></location>.</text>
<text><location><page_14><loc_87><loc_61><loc_88><loc_61></location>0</text>
<text><location><page_14><loc_87><loc_60><loc_88><loc_60></location>±</text>
<text><location><page_14><loc_87><loc_59><loc_88><loc_59></location>6</text>
<text><location><page_14><loc_87><loc_59><loc_88><loc_59></location>7</text>
<text><location><page_14><loc_87><loc_58><loc_88><loc_59></location>9</text>
<text><location><page_14><loc_87><loc_58><loc_88><loc_58></location>.</text>
<text><location><page_14><loc_87><loc_58><loc_88><loc_58></location>8</text>
<text><location><page_14><loc_87><loc_57><loc_88><loc_58></location>1</text>
<text><location><page_14><loc_87><loc_55><loc_88><loc_56></location>5</text>
<text><location><page_14><loc_87><loc_55><loc_88><loc_55></location>2</text>
<text><location><page_14><loc_87><loc_55><loc_88><loc_55></location>0</text>
<text><location><page_14><loc_87><loc_54><loc_88><loc_55></location>.</text>
<text><location><page_14><loc_87><loc_54><loc_88><loc_54></location>0</text>
<text><location><page_14><loc_87><loc_53><loc_88><loc_54></location>±</text>
<text><location><page_14><loc_87><loc_52><loc_88><loc_53></location>5</text>
<text><location><page_14><loc_87><loc_52><loc_88><loc_52></location>7</text>
<text><location><page_14><loc_87><loc_51><loc_88><loc_52></location>1</text>
<text><location><page_14><loc_87><loc_51><loc_88><loc_51></location>.</text>
<text><location><page_14><loc_87><loc_51><loc_88><loc_51></location>9</text>
<text><location><page_14><loc_87><loc_50><loc_88><loc_51></location>1</text>
<text><location><page_14><loc_87><loc_48><loc_88><loc_49></location>9</text>
<text><location><page_14><loc_87><loc_48><loc_88><loc_49></location>1</text>
<text><location><page_14><loc_87><loc_48><loc_88><loc_48></location>0</text>
<text><location><page_14><loc_87><loc_47><loc_88><loc_48></location>.</text>
<text><location><page_14><loc_87><loc_47><loc_88><loc_47></location>0</text>
<text><location><page_14><loc_87><loc_46><loc_88><loc_47></location>±</text>
<text><location><page_14><loc_87><loc_45><loc_88><loc_46></location>9</text>
<text><location><page_14><loc_87><loc_45><loc_88><loc_45></location>2</text>
<text><location><page_14><loc_87><loc_44><loc_88><loc_45></location>5</text>
<text><location><page_14><loc_87><loc_44><loc_88><loc_44></location>.</text>
<text><location><page_14><loc_87><loc_44><loc_88><loc_44></location>8</text>
<text><location><page_14><loc_87><loc_43><loc_88><loc_44></location>1</text>
<text><location><page_14><loc_87><loc_42><loc_88><loc_42></location>9</text>
<text><location><page_14><loc_87><loc_41><loc_88><loc_42></location>1</text>
<text><location><page_14><loc_87><loc_41><loc_88><loc_41></location>.</text>
<text><location><page_14><loc_87><loc_40><loc_88><loc_41></location>9</text>
<text><location><page_14><loc_87><loc_40><loc_88><loc_41></location>3</text>
<text><location><page_14><loc_87><loc_39><loc_88><loc_40></location>4</text>
<text><location><page_14><loc_87><loc_39><loc_88><loc_39></location>3</text>
<text><location><page_14><loc_87><loc_38><loc_88><loc_39></location>0</text>
<text><location><page_14><loc_87><loc_38><loc_88><loc_38></location>3</text>
<text><location><page_14><loc_87><loc_36><loc_88><loc_37></location>0</text>
<text><location><page_14><loc_87><loc_36><loc_88><loc_36></location>8</text>
<text><location><page_14><loc_87><loc_35><loc_88><loc_36></location>8</text>
<text><location><page_14><loc_87><loc_35><loc_88><loc_35></location>.</text>
<text><location><page_14><loc_87><loc_35><loc_88><loc_35></location>4</text>
<text><location><page_14><loc_87><loc_34><loc_88><loc_35></location>4</text>
<text><location><page_14><loc_87><loc_33><loc_88><loc_34></location>3</text>
<text><location><page_14><loc_87><loc_33><loc_88><loc_33></location>3</text>
<text><location><page_14><loc_87><loc_32><loc_88><loc_33></location>1</text>
<text><location><page_14><loc_87><loc_32><loc_88><loc_32></location>0</text>
<text><location><page_14><loc_87><loc_20><loc_88><loc_21></location>2</text>
<text><location><page_14><loc_87><loc_20><loc_88><loc_20></location>1</text>
<text><location><page_14><loc_87><loc_19><loc_88><loc_20></location>1</text>
<text><location><page_14><loc_87><loc_19><loc_88><loc_19></location>R</text>
<text><location><page_14><loc_87><loc_18><loc_88><loc_19></location>S</text>
<text><location><page_14><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_14><loc_87><loc_16><loc_88><loc_17></location>.</text>
<text><location><page_14><loc_87><loc_16><loc_88><loc_16></location>.</text>
<text><location><page_14><loc_87><loc_16><loc_88><loc_16></location>.</text>
<text><location><page_14><loc_87><loc_16><loc_88><loc_16></location>.</text>
<text><location><page_14><loc_87><loc_15><loc_88><loc_16></location>.</text>
<text><location><page_14><loc_87><loc_15><loc_88><loc_15></location>2</text>
<text><location><page_14><loc_87><loc_15><loc_88><loc_15></location>1</text>
<text><location><page_14><loc_87><loc_14><loc_88><loc_15></location>1</text>
<text><location><page_15><loc_13><loc_51><loc_14><loc_52></location>1</text>
<text><location><page_15><loc_13><loc_50><loc_14><loc_51></location>E</text>
<text><location><page_15><loc_13><loc_50><loc_14><loc_50></location>L</text>
<text><location><page_15><loc_13><loc_48><loc_14><loc_50></location>AB</text>
<text><location><page_15><loc_13><loc_47><loc_14><loc_48></location>T</text>
<text><location><page_15><loc_14><loc_52><loc_15><loc_53></location>)</text>
<text><location><page_15><loc_14><loc_52><loc_15><loc_52></location>.</text>
<text><location><page_15><loc_14><loc_52><loc_15><loc_52></location>d</text>
<text><location><page_15><loc_14><loc_51><loc_15><loc_52></location>e</text>
<text><location><page_15><loc_14><loc_50><loc_15><loc_51></location>u</text>
<text><location><page_15><loc_14><loc_50><loc_15><loc_50></location>n</text>
<text><location><page_15><loc_14><loc_49><loc_15><loc_50></location>i</text>
<text><location><page_15><loc_14><loc_49><loc_15><loc_49></location>t</text>
<text><location><page_15><loc_14><loc_48><loc_15><loc_49></location>n</text>
<text><location><page_15><loc_14><loc_48><loc_15><loc_48></location>o</text>
<text><location><page_15><loc_14><loc_47><loc_15><loc_48></location>C</text>
<text><location><page_15><loc_14><loc_46><loc_15><loc_47></location>(</text>
<text><location><page_15><loc_20><loc_83><loc_20><loc_84></location>4</text>
<text><location><page_15><loc_21><loc_83><loc_22><loc_84></location>8</text>
<text><location><page_15><loc_22><loc_83><loc_23><loc_84></location>8</text>
<text><location><page_15><loc_23><loc_83><loc_24><loc_84></location>8</text>
<text><location><page_15><loc_24><loc_83><loc_25><loc_84></location>0</text>
<text><location><page_15><loc_26><loc_83><loc_27><loc_84></location>4</text>
<text><location><page_15><loc_27><loc_83><loc_28><loc_84></location>2</text>
<text><location><page_15><loc_28><loc_83><loc_29><loc_84></location>6</text>
<text><location><page_15><loc_29><loc_83><loc_30><loc_84></location>8</text>
<text><location><page_15><loc_31><loc_83><loc_31><loc_84></location>6</text>
<text><location><page_15><loc_32><loc_83><loc_33><loc_84></location>4</text>
<text><location><page_15><loc_33><loc_83><loc_34><loc_84></location>8</text>
<text><location><page_15><loc_34><loc_83><loc_35><loc_84></location>8</text>
<text><location><page_15><loc_36><loc_83><loc_36><loc_84></location>4</text>
<text><location><page_15><loc_37><loc_83><loc_38><loc_84></location>4</text>
<text><location><page_15><loc_38><loc_83><loc_39><loc_84></location>4</text>
<text><location><page_15><loc_39><loc_83><loc_40><loc_84></location>2</text>
<text><location><page_15><loc_40><loc_83><loc_41><loc_84></location>2</text>
<text><location><page_15><loc_42><loc_83><loc_42><loc_84></location>8</text>
<text><location><page_15><loc_43><loc_83><loc_44><loc_84></location>6</text>
<text><location><page_15><loc_44><loc_83><loc_45><loc_84></location>0</text>
<text><location><page_15><loc_45><loc_83><loc_46><loc_84></location>8</text>
<text><location><page_15><loc_47><loc_83><loc_47><loc_84></location>0</text>
<text><location><page_15><loc_48><loc_83><loc_49><loc_84></location>4</text>
<text><location><page_15><loc_49><loc_83><loc_50><loc_84></location>6</text>
<text><location><page_15><loc_50><loc_83><loc_51><loc_84></location>0</text>
<text><location><page_15><loc_51><loc_83><loc_52><loc_84></location>0</text>
<text><location><page_15><loc_53><loc_83><loc_54><loc_84></location>4</text>
<text><location><page_15><loc_54><loc_83><loc_55><loc_84></location>2</text>
<text><location><page_15><loc_55><loc_83><loc_56><loc_84></location>0</text>
<text><location><page_15><loc_56><loc_83><loc_57><loc_84></location>4</text>
<text><location><page_15><loc_58><loc_83><loc_58><loc_84></location>6</text>
<text><location><page_15><loc_59><loc_83><loc_60><loc_84></location>4</text>
<text><location><page_15><loc_60><loc_83><loc_61><loc_84></location>8</text>
<text><location><page_15><loc_61><loc_83><loc_62><loc_84></location>2</text>
<text><location><page_15><loc_63><loc_83><loc_63><loc_84></location>0</text>
<text><location><page_15><loc_64><loc_83><loc_65><loc_84></location>4</text>
<text><location><page_15><loc_65><loc_83><loc_66><loc_84></location>0</text>
<text><location><page_15><loc_66><loc_83><loc_67><loc_84></location>6</text>
<text><location><page_15><loc_67><loc_83><loc_68><loc_84></location>4</text>
<text><location><page_15><loc_69><loc_83><loc_69><loc_84></location>8</text>
<text><location><page_15><loc_70><loc_83><loc_71><loc_84></location>8</text>
<text><location><page_15><loc_71><loc_83><loc_72><loc_84></location>6</text>
<text><location><page_15><loc_72><loc_83><loc_73><loc_84></location>8</text>
<text><location><page_15><loc_74><loc_83><loc_74><loc_84></location>8</text>
<text><location><page_15><loc_75><loc_83><loc_76><loc_84></location>4</text>
<text><location><page_15><loc_76><loc_83><loc_77><loc_84></location>2</text>
<text><location><page_15><loc_77><loc_83><loc_78><loc_84></location>6</text>
<text><location><page_15><loc_78><loc_83><loc_79><loc_84></location>4</text>
<text><location><page_15><loc_80><loc_83><loc_81><loc_84></location>4</text>
<text><location><page_15><loc_81><loc_83><loc_82><loc_84></location>8</text>
<text><location><page_15><loc_82><loc_83><loc_83><loc_84></location>4</text>
<text><location><page_15><loc_83><loc_83><loc_84><loc_84></location>0</text>
<text><location><page_15><loc_42><loc_93><loc_57><loc_94></location>Star clusters in M33</text>
<text><location><page_15><loc_90><loc_93><loc_92><loc_94></location>15</text>
<table>
<location><page_15><loc_15><loc_12><loc_84><loc_83></location>
</table>
<text><location><page_15><loc_85><loc_83><loc_85><loc_84></location>6</text>
<text><location><page_15><loc_85><loc_83><loc_85><loc_83></location>0</text>
<text><location><page_15><loc_85><loc_82><loc_85><loc_83></location>8</text>
<text><location><page_15><loc_85><loc_82><loc_85><loc_82></location>.</text>
<text><location><page_15><loc_85><loc_82><loc_85><loc_82></location>1</text>
<text><location><page_15><loc_85><loc_79><loc_85><loc_79></location>0</text>
<text><location><page_15><loc_85><loc_78><loc_85><loc_79></location>1</text>
<text><location><page_15><loc_85><loc_78><loc_85><loc_78></location>.</text>
<text><location><page_15><loc_85><loc_78><loc_85><loc_78></location>0</text>
<text><location><page_15><loc_85><loc_75><loc_85><loc_75></location>2</text>
<text><location><page_15><loc_85><loc_74><loc_85><loc_75></location>5</text>
<text><location><page_15><loc_85><loc_74><loc_85><loc_74></location>0</text>
<text><location><page_15><loc_85><loc_74><loc_85><loc_74></location>.</text>
<text><location><page_15><loc_85><loc_73><loc_85><loc_74></location>0</text>
<text><location><page_15><loc_85><loc_72><loc_85><loc_73></location>±</text>
<text><location><page_15><loc_85><loc_72><loc_85><loc_72></location>2</text>
<text><location><page_15><loc_85><loc_71><loc_85><loc_72></location>8</text>
<text><location><page_15><loc_85><loc_71><loc_85><loc_71></location>7</text>
<text><location><page_15><loc_85><loc_70><loc_85><loc_71></location>.</text>
<text><location><page_15><loc_85><loc_70><loc_85><loc_70></location>9</text>
<text><location><page_15><loc_85><loc_70><loc_85><loc_70></location>1</text>
<text><location><page_15><loc_85><loc_68><loc_85><loc_68></location>2</text>
<text><location><page_15><loc_85><loc_67><loc_85><loc_68></location>5</text>
<text><location><page_15><loc_85><loc_67><loc_85><loc_67></location>0</text>
<text><location><page_15><loc_85><loc_67><loc_85><loc_67></location>.</text>
<text><location><page_15><loc_85><loc_66><loc_85><loc_67></location>0</text>
<text><location><page_15><loc_85><loc_65><loc_85><loc_66></location>±</text>
<text><location><page_15><loc_85><loc_65><loc_85><loc_65></location>1</text>
<text><location><page_15><loc_85><loc_64><loc_85><loc_65></location>0</text>
<text><location><page_15><loc_85><loc_64><loc_85><loc_64></location>2</text>
<text><location><page_15><loc_85><loc_64><loc_85><loc_64></location>.</text>
<text><location><page_15><loc_85><loc_63><loc_85><loc_64></location>0</text>
<text><location><page_15><loc_85><loc_63><loc_85><loc_63></location>2</text>
<text><location><page_15><loc_85><loc_61><loc_85><loc_61></location>0</text>
<text><location><page_15><loc_85><loc_61><loc_85><loc_61></location>5</text>
<text><location><page_15><loc_85><loc_60><loc_85><loc_61></location>0</text>
<text><location><page_15><loc_85><loc_60><loc_85><loc_60></location>.</text>
<text><location><page_15><loc_85><loc_59><loc_85><loc_60></location>0</text>
<text><location><page_15><loc_85><loc_58><loc_85><loc_59></location>±</text>
<text><location><page_15><loc_85><loc_58><loc_85><loc_58></location>4</text>
<text><location><page_15><loc_85><loc_57><loc_85><loc_58></location>7</text>
<text><location><page_15><loc_85><loc_57><loc_85><loc_57></location>4</text>
<text><location><page_15><loc_85><loc_57><loc_85><loc_57></location>.</text>
<text><location><page_15><loc_85><loc_56><loc_85><loc_57></location>0</text>
<text><location><page_15><loc_85><loc_56><loc_85><loc_56></location>2</text>
<text><location><page_15><loc_85><loc_54><loc_85><loc_55></location>0</text>
<text><location><page_15><loc_85><loc_54><loc_85><loc_54></location>7</text>
<text><location><page_15><loc_85><loc_53><loc_85><loc_54></location>0</text>
<text><location><page_15><loc_85><loc_53><loc_85><loc_53></location>.</text>
<text><location><page_15><loc_85><loc_53><loc_85><loc_53></location>0</text>
<text><location><page_15><loc_85><loc_52><loc_85><loc_52></location>±</text>
<text><location><page_15><loc_85><loc_51><loc_85><loc_51></location>9</text>
<text><location><page_15><loc_85><loc_50><loc_85><loc_51></location>3</text>
<text><location><page_15><loc_85><loc_50><loc_85><loc_50></location>1</text>
<text><location><page_15><loc_85><loc_50><loc_85><loc_50></location>.</text>
<text><location><page_15><loc_85><loc_49><loc_85><loc_50></location>1</text>
<text><location><page_15><loc_85><loc_49><loc_85><loc_49></location>2</text>
<text><location><page_15><loc_85><loc_47><loc_85><loc_48></location>3</text>
<text><location><page_15><loc_85><loc_47><loc_85><loc_47></location>5</text>
<text><location><page_15><loc_85><loc_46><loc_85><loc_47></location>0</text>
<text><location><page_15><loc_85><loc_46><loc_85><loc_46></location>.</text>
<text><location><page_15><loc_85><loc_46><loc_85><loc_46></location>0</text>
<text><location><page_15><loc_85><loc_45><loc_85><loc_45></location>±</text>
<text><location><page_15><loc_85><loc_44><loc_85><loc_44></location>2</text>
<text><location><page_15><loc_85><loc_44><loc_85><loc_44></location>9</text>
<text><location><page_15><loc_85><loc_43><loc_85><loc_44></location>0</text>
<text><location><page_15><loc_85><loc_43><loc_85><loc_43></location>.</text>
<text><location><page_15><loc_85><loc_42><loc_85><loc_43></location>1</text>
<text><location><page_15><loc_85><loc_42><loc_85><loc_42></location>2</text>
<text><location><page_15><loc_85><loc_40><loc_85><loc_41></location>0</text>
<text><location><page_15><loc_85><loc_40><loc_85><loc_40></location>0</text>
<text><location><page_15><loc_85><loc_40><loc_85><loc_40></location>.</text>
<text><location><page_15><loc_85><loc_39><loc_85><loc_40></location>0</text>
<text><location><page_15><loc_85><loc_39><loc_85><loc_39></location>2</text>
<text><location><page_15><loc_85><loc_38><loc_85><loc_39></location>1</text>
<text><location><page_15><loc_85><loc_38><loc_85><loc_38></location>3</text>
<text><location><page_15><loc_85><loc_37><loc_85><loc_37></location>0</text>
<text><location><page_15><loc_85><loc_36><loc_85><loc_37></location>3</text>
<text><location><page_15><loc_85><loc_35><loc_85><loc_35></location>6</text>
<text><location><page_15><loc_85><loc_34><loc_85><loc_35></location>6</text>
<text><location><page_15><loc_85><loc_34><loc_85><loc_34></location>7</text>
<text><location><page_15><loc_85><loc_34><loc_85><loc_34></location>.</text>
<text><location><page_15><loc_85><loc_33><loc_85><loc_34></location>5</text>
<text><location><page_15><loc_85><loc_33><loc_85><loc_33></location>2</text>
<text><location><page_15><loc_85><loc_32><loc_85><loc_33></location>3</text>
<text><location><page_15><loc_85><loc_32><loc_85><loc_32></location>3</text>
<text><location><page_15><loc_85><loc_31><loc_85><loc_31></location>1</text>
<text><location><page_15><loc_85><loc_31><loc_85><loc_31></location>0</text>
<text><location><page_15><loc_85><loc_22><loc_85><loc_22></location>8</text>
<text><location><page_15><loc_85><loc_21><loc_85><loc_22></location>1</text>
<text><location><page_15><loc_85><loc_21><loc_85><loc_21></location>-</text>
<text><location><page_15><loc_85><loc_20><loc_85><loc_21></location>ZK</text>
<text><location><page_15><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_15><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_15><loc_85><loc_17><loc_85><loc_18></location>.</text>
<text><location><page_15><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_15><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_15><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_15><loc_85><loc_16><loc_85><loc_17></location>6</text>
<text><location><page_15><loc_85><loc_16><loc_85><loc_16></location>6</text>
<text><location><page_15><loc_85><loc_15><loc_85><loc_16></location>1</text>
<text><location><page_15><loc_86><loc_83><loc_87><loc_84></location>6</text>
<text><location><page_15><loc_86><loc_83><loc_87><loc_83></location>0</text>
<text><location><page_15><loc_86><loc_82><loc_87><loc_83></location>8</text>
<text><location><page_15><loc_86><loc_82><loc_87><loc_82></location>.</text>
<text><location><page_15><loc_86><loc_82><loc_87><loc_82></location>1</text>
<text><location><page_15><loc_86><loc_79><loc_87><loc_79></location>0</text>
<text><location><page_15><loc_86><loc_78><loc_87><loc_79></location>1</text>
<text><location><page_15><loc_86><loc_78><loc_87><loc_78></location>.</text>
<text><location><page_15><loc_86><loc_78><loc_87><loc_78></location>0</text>
<text><location><page_15><loc_86><loc_75><loc_87><loc_75></location>2</text>
<text><location><page_15><loc_86><loc_74><loc_87><loc_75></location>5</text>
<text><location><page_15><loc_86><loc_74><loc_87><loc_74></location>0</text>
<text><location><page_15><loc_86><loc_74><loc_87><loc_74></location>.</text>
<text><location><page_15><loc_86><loc_73><loc_87><loc_74></location>0</text>
<text><location><page_15><loc_86><loc_72><loc_87><loc_73></location>±</text>
<text><location><page_15><loc_86><loc_72><loc_87><loc_72></location>6</text>
<text><location><page_15><loc_86><loc_71><loc_87><loc_72></location>0</text>
<text><location><page_15><loc_86><loc_71><loc_87><loc_71></location>5</text>
<text><location><page_15><loc_86><loc_70><loc_87><loc_71></location>.</text>
<text><location><page_15><loc_86><loc_70><loc_87><loc_70></location>9</text>
<text><location><page_15><loc_86><loc_70><loc_87><loc_70></location>1</text>
<text><location><page_15><loc_86><loc_68><loc_87><loc_68></location>5</text>
<text><location><page_15><loc_86><loc_67><loc_87><loc_68></location>6</text>
<text><location><page_15><loc_86><loc_67><loc_87><loc_67></location>0</text>
<text><location><page_15><loc_86><loc_67><loc_87><loc_67></location>.</text>
<text><location><page_15><loc_86><loc_66><loc_87><loc_67></location>0</text>
<text><location><page_15><loc_86><loc_65><loc_87><loc_66></location>±</text>
<text><location><page_15><loc_86><loc_65><loc_87><loc_65></location>4</text>
<text><location><page_15><loc_86><loc_64><loc_87><loc_65></location>0</text>
<text><location><page_15><loc_86><loc_64><loc_87><loc_64></location>2</text>
<text><location><page_15><loc_86><loc_64><loc_87><loc_64></location>.</text>
<text><location><page_15><loc_86><loc_63><loc_87><loc_64></location>0</text>
<text><location><page_15><loc_86><loc_63><loc_87><loc_63></location>2</text>
<text><location><page_15><loc_86><loc_61><loc_87><loc_61></location>9</text>
<text><location><page_15><loc_86><loc_61><loc_87><loc_61></location>5</text>
<text><location><page_15><loc_86><loc_60><loc_87><loc_61></location>0</text>
<text><location><page_15><loc_86><loc_60><loc_87><loc_60></location>.</text>
<text><location><page_15><loc_86><loc_59><loc_87><loc_60></location>0</text>
<text><location><page_15><loc_86><loc_58><loc_87><loc_59></location>±</text>
<text><location><page_15><loc_86><loc_58><loc_87><loc_58></location>9</text>
<text><location><page_15><loc_86><loc_57><loc_87><loc_58></location>6</text>
<text><location><page_15><loc_86><loc_57><loc_87><loc_57></location>5</text>
<text><location><page_15><loc_86><loc_57><loc_87><loc_57></location>.</text>
<text><location><page_15><loc_86><loc_56><loc_87><loc_57></location>0</text>
<text><location><page_15><loc_86><loc_56><loc_87><loc_56></location>2</text>
<text><location><page_15><loc_86><loc_54><loc_87><loc_55></location>5</text>
<text><location><page_15><loc_86><loc_54><loc_87><loc_54></location>6</text>
<text><location><page_15><loc_86><loc_53><loc_87><loc_54></location>0</text>
<text><location><page_15><loc_86><loc_53><loc_87><loc_53></location>.</text>
<text><location><page_15><loc_86><loc_53><loc_87><loc_53></location>0</text>
<text><location><page_15><loc_86><loc_52><loc_87><loc_52></location>±</text>
<text><location><page_15><loc_86><loc_51><loc_87><loc_51></location>1</text>
<text><location><page_15><loc_86><loc_50><loc_87><loc_51></location>0</text>
<text><location><page_15><loc_86><loc_50><loc_87><loc_50></location>0</text>
<text><location><page_15><loc_86><loc_50><loc_87><loc_50></location>.</text>
<text><location><page_15><loc_86><loc_49><loc_87><loc_50></location>1</text>
<text><location><page_15><loc_86><loc_49><loc_87><loc_49></location>2</text>
<text><location><page_15><loc_86><loc_47><loc_87><loc_48></location>8</text>
<text><location><page_15><loc_86><loc_47><loc_87><loc_47></location>4</text>
<text><location><page_15><loc_86><loc_46><loc_87><loc_47></location>0</text>
<text><location><page_15><loc_86><loc_46><loc_87><loc_46></location>.</text>
<text><location><page_15><loc_86><loc_46><loc_87><loc_46></location>0</text>
<text><location><page_15><loc_86><loc_45><loc_87><loc_45></location>±</text>
<text><location><page_15><loc_86><loc_44><loc_87><loc_44></location>5</text>
<text><location><page_15><loc_86><loc_44><loc_87><loc_44></location>5</text>
<text><location><page_15><loc_86><loc_43><loc_87><loc_44></location>0</text>
<text><location><page_15><loc_86><loc_43><loc_87><loc_43></location>.</text>
<text><location><page_15><loc_86><loc_42><loc_87><loc_43></location>1</text>
<text><location><page_15><loc_86><loc_42><loc_87><loc_42></location>2</text>
<text><location><page_15><loc_86><loc_40><loc_87><loc_41></location>1</text>
<text><location><page_15><loc_86><loc_40><loc_87><loc_40></location>7</text>
<text><location><page_15><loc_86><loc_40><loc_87><loc_40></location>.</text>
<text><location><page_15><loc_86><loc_39><loc_87><loc_40></location>1</text>
<text><location><page_15><loc_86><loc_39><loc_87><loc_39></location>2</text>
<text><location><page_15><loc_86><loc_38><loc_87><loc_39></location>1</text>
<text><location><page_15><loc_86><loc_38><loc_87><loc_38></location>3</text>
<text><location><page_15><loc_86><loc_37><loc_87><loc_37></location>0</text>
<text><location><page_15><loc_86><loc_36><loc_87><loc_37></location>3</text>
<text><location><page_15><loc_86><loc_35><loc_87><loc_35></location>4</text>
<text><location><page_15><loc_86><loc_34><loc_87><loc_35></location>5</text>
<text><location><page_15><loc_86><loc_34><loc_87><loc_34></location>9</text>
<text><location><page_15><loc_86><loc_34><loc_87><loc_34></location>.</text>
<text><location><page_15><loc_86><loc_33><loc_87><loc_34></location>5</text>
<text><location><page_15><loc_86><loc_33><loc_87><loc_33></location>2</text>
<text><location><page_15><loc_86><loc_32><loc_87><loc_33></location>3</text>
<text><location><page_15><loc_86><loc_32><loc_87><loc_32></location>3</text>
<text><location><page_15><loc_86><loc_31><loc_87><loc_31></location>1</text>
<text><location><page_15><loc_86><loc_31><loc_87><loc_31></location>0</text>
<text><location><page_15><loc_86><loc_22><loc_87><loc_22></location>9</text>
<text><location><page_15><loc_86><loc_21><loc_87><loc_22></location>1</text>
<text><location><page_15><loc_86><loc_21><loc_87><loc_21></location>-</text>
<text><location><page_15><loc_86><loc_20><loc_87><loc_21></location>ZK</text>
<text><location><page_15><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_15><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_15><loc_86><loc_17><loc_87><loc_18></location>.</text>
<text><location><page_15><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_15><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_15><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_15><loc_86><loc_16><loc_87><loc_17></location>7</text>
<text><location><page_15><loc_86><loc_16><loc_87><loc_16></location>6</text>
<text><location><page_15><loc_86><loc_15><loc_87><loc_16></location>1</text>
<text><location><page_15><loc_87><loc_83><loc_88><loc_84></location>0</text>
<text><location><page_15><loc_87><loc_83><loc_88><loc_83></location>8</text>
<text><location><page_15><loc_87><loc_82><loc_88><loc_83></location>5</text>
<text><location><page_15><loc_87><loc_82><loc_88><loc_82></location>.</text>
<text><location><page_15><loc_87><loc_82><loc_88><loc_82></location>2</text>
<text><location><page_15><loc_87><loc_79><loc_88><loc_79></location>0</text>
<text><location><page_15><loc_87><loc_78><loc_88><loc_79></location>1</text>
<text><location><page_15><loc_87><loc_78><loc_88><loc_78></location>.</text>
<text><location><page_15><loc_87><loc_78><loc_88><loc_78></location>0</text>
<text><location><page_15><loc_87><loc_75><loc_88><loc_75></location>4</text>
<text><location><page_15><loc_87><loc_74><loc_88><loc_75></location>3</text>
<text><location><page_15><loc_87><loc_74><loc_88><loc_74></location>0</text>
<text><location><page_15><loc_87><loc_74><loc_88><loc_74></location>.</text>
<text><location><page_15><loc_87><loc_73><loc_88><loc_74></location>0</text>
<text><location><page_15><loc_87><loc_72><loc_88><loc_73></location>±</text>
<text><location><page_15><loc_87><loc_72><loc_88><loc_72></location>8</text>
<text><location><page_15><loc_87><loc_71><loc_88><loc_72></location>1</text>
<text><location><page_15><loc_87><loc_71><loc_88><loc_71></location>7</text>
<text><location><page_15><loc_87><loc_70><loc_88><loc_71></location>.</text>
<text><location><page_15><loc_87><loc_70><loc_88><loc_70></location>8</text>
<text><location><page_15><loc_87><loc_70><loc_88><loc_70></location>1</text>
<text><location><page_15><loc_87><loc_68><loc_88><loc_68></location>4</text>
<text><location><page_15><loc_87><loc_67><loc_88><loc_68></location>3</text>
<text><location><page_15><loc_87><loc_67><loc_88><loc_67></location>0</text>
<text><location><page_15><loc_87><loc_67><loc_88><loc_67></location>.</text>
<text><location><page_15><loc_87><loc_66><loc_88><loc_67></location>0</text>
<text><location><page_15><loc_87><loc_65><loc_88><loc_66></location>±</text>
<text><location><page_15><loc_87><loc_65><loc_88><loc_65></location>4</text>
<text><location><page_15><loc_87><loc_64><loc_88><loc_65></location>1</text>
<text><location><page_15><loc_87><loc_64><loc_88><loc_64></location>2</text>
<text><location><page_15><loc_87><loc_64><loc_88><loc_64></location>.</text>
<text><location><page_15><loc_87><loc_63><loc_88><loc_64></location>9</text>
<text><location><page_15><loc_87><loc_63><loc_88><loc_63></location>1</text>
<text><location><page_15><loc_87><loc_61><loc_88><loc_61></location>0</text>
<text><location><page_15><loc_87><loc_61><loc_88><loc_61></location>3</text>
<text><location><page_15><loc_87><loc_60><loc_88><loc_61></location>0</text>
<text><location><page_15><loc_87><loc_60><loc_88><loc_60></location>.</text>
<text><location><page_15><loc_87><loc_59><loc_88><loc_60></location>0</text>
<text><location><page_15><loc_87><loc_58><loc_88><loc_59></location>±</text>
<text><location><page_15><loc_87><loc_58><loc_88><loc_58></location>2</text>
<text><location><page_15><loc_87><loc_57><loc_88><loc_58></location>5</text>
<text><location><page_15><loc_87><loc_57><loc_88><loc_57></location>4</text>
<text><location><page_15><loc_87><loc_57><loc_88><loc_57></location>.</text>
<text><location><page_15><loc_87><loc_56><loc_88><loc_57></location>9</text>
<text><location><page_15><loc_87><loc_56><loc_88><loc_56></location>1</text>
<text><location><page_15><loc_87><loc_54><loc_88><loc_55></location>4</text>
<text><location><page_15><loc_87><loc_54><loc_88><loc_54></location>3</text>
<text><location><page_15><loc_87><loc_53><loc_88><loc_54></location>0</text>
<text><location><page_15><loc_87><loc_53><loc_88><loc_53></location>.</text>
<text><location><page_15><loc_87><loc_53><loc_88><loc_53></location>0</text>
<text><location><page_15><loc_87><loc_52><loc_88><loc_52></location>±</text>
<text><location><page_15><loc_87><loc_51><loc_88><loc_51></location>9</text>
<text><location><page_15><loc_87><loc_50><loc_88><loc_51></location>4</text>
<text><location><page_15><loc_87><loc_50><loc_88><loc_50></location>9</text>
<text><location><page_15><loc_87><loc_50><loc_88><loc_50></location>.</text>
<text><location><page_15><loc_87><loc_49><loc_88><loc_50></location>9</text>
<text><location><page_15><loc_87><loc_49><loc_88><loc_49></location>1</text>
<text><location><page_15><loc_87><loc_47><loc_88><loc_48></location>8</text>
<text><location><page_15><loc_87><loc_47><loc_88><loc_47></location>2</text>
<text><location><page_15><loc_87><loc_46><loc_88><loc_47></location>0</text>
<text><location><page_15><loc_87><loc_46><loc_88><loc_46></location>.</text>
<text><location><page_15><loc_87><loc_46><loc_88><loc_46></location>0</text>
<text><location><page_15><loc_87><loc_45><loc_88><loc_45></location>±</text>
<text><location><page_15><loc_87><loc_44><loc_88><loc_44></location>9</text>
<text><location><page_15><loc_87><loc_44><loc_88><loc_44></location>5</text>
<text><location><page_15><loc_87><loc_43><loc_88><loc_44></location>9</text>
<text><location><page_15><loc_87><loc_43><loc_88><loc_43></location>.</text>
<text><location><page_15><loc_87><loc_42><loc_88><loc_43></location>9</text>
<text><location><page_15><loc_87><loc_42><loc_88><loc_42></location>1</text>
<text><location><page_15><loc_87><loc_40><loc_88><loc_41></location>0</text>
<text><location><page_15><loc_87><loc_40><loc_88><loc_40></location>5</text>
<text><location><page_15><loc_87><loc_40><loc_88><loc_40></location>.</text>
<text><location><page_15><loc_87><loc_39><loc_88><loc_40></location>9</text>
<text><location><page_15><loc_87><loc_39><loc_88><loc_39></location>5</text>
<text><location><page_15><loc_87><loc_38><loc_88><loc_39></location>9</text>
<text><location><page_15><loc_87><loc_38><loc_88><loc_38></location>3</text>
<text><location><page_15><loc_87><loc_37><loc_88><loc_37></location>0</text>
<text><location><page_15><loc_87><loc_36><loc_88><loc_37></location>3</text>
<text><location><page_15><loc_87><loc_35><loc_88><loc_35></location>4</text>
<text><location><page_15><loc_87><loc_34><loc_88><loc_35></location>0</text>
<text><location><page_15><loc_87><loc_34><loc_88><loc_34></location>5</text>
<text><location><page_15><loc_87><loc_34><loc_88><loc_34></location>.</text>
<text><location><page_15><loc_87><loc_33><loc_88><loc_34></location>6</text>
<text><location><page_15><loc_87><loc_33><loc_88><loc_33></location>2</text>
<text><location><page_15><loc_87><loc_32><loc_88><loc_33></location>3</text>
<text><location><page_15><loc_87><loc_32><loc_88><loc_32></location>3</text>
<text><location><page_15><loc_87><loc_31><loc_88><loc_31></location>1</text>
<text><location><page_15><loc_87><loc_31><loc_88><loc_31></location>0</text>
<text><location><page_15><loc_87><loc_22><loc_88><loc_22></location>0</text>
<text><location><page_15><loc_87><loc_21><loc_88><loc_22></location>2</text>
<text><location><page_15><loc_87><loc_21><loc_88><loc_21></location>-</text>
<text><location><page_15><loc_87><loc_20><loc_88><loc_21></location>ZK</text>
<text><location><page_15><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_15><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_15><loc_87><loc_17><loc_88><loc_18></location>.</text>
<text><location><page_15><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_15><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_15><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_15><loc_87><loc_16><loc_88><loc_17></location>8</text>
<text><location><page_15><loc_87><loc_16><loc_88><loc_16></location>6</text>
<text><location><page_15><loc_87><loc_15><loc_88><loc_16></location>1</text>
<text><location><page_16><loc_9><loc_93><loc_10><loc_94></location>16</text>
<text><location><page_16><loc_50><loc_93><loc_52><loc_94></location>Ma</text>
<table>
<location><page_16><loc_15><loc_12><loc_84><loc_83></location>
</table>
<text><location><page_16><loc_13><loc_51><loc_14><loc_52></location>1</text>
<text><location><page_16><loc_13><loc_50><loc_14><loc_51></location>E</text>
<text><location><page_16><loc_13><loc_50><loc_14><loc_50></location>L</text>
<text><location><page_16><loc_13><loc_48><loc_14><loc_50></location>AB</text>
<text><location><page_16><loc_13><loc_47><loc_14><loc_48></location>T</text>
<text><location><page_16><loc_14><loc_52><loc_15><loc_53></location>)</text>
<text><location><page_16><loc_14><loc_52><loc_15><loc_52></location>.</text>
<text><location><page_16><loc_14><loc_52><loc_15><loc_52></location>d</text>
<text><location><page_16><loc_14><loc_51><loc_15><loc_52></location>e</text>
<text><location><page_16><loc_14><loc_50><loc_15><loc_51></location>u</text>
<text><location><page_16><loc_14><loc_50><loc_15><loc_50></location>n</text>
<text><location><page_16><loc_14><loc_49><loc_15><loc_50></location>i</text>
<text><location><page_16><loc_14><loc_49><loc_15><loc_49></location>t</text>
<text><location><page_16><loc_14><loc_48><loc_15><loc_49></location>n</text>
<text><location><page_16><loc_14><loc_48><loc_15><loc_48></location>o</text>
<text><location><page_16><loc_14><loc_47><loc_15><loc_48></location>C</text>
<text><location><page_16><loc_14><loc_46><loc_15><loc_47></location>(</text>
<text><location><page_16><loc_83><loc_83><loc_84><loc_83></location>4</text>
<text><location><page_16><loc_83><loc_82><loc_84><loc_83></location>6</text>
<text><location><page_16><loc_83><loc_82><loc_84><loc_82></location>0</text>
<text><location><page_16><loc_83><loc_82><loc_84><loc_82></location>.</text>
<text><location><page_16><loc_83><loc_81><loc_84><loc_82></location>2</text>
<text><location><page_16><loc_83><loc_78><loc_84><loc_79></location>0</text>
<text><location><page_16><loc_83><loc_78><loc_84><loc_78></location>1</text>
<text><location><page_16><loc_83><loc_78><loc_84><loc_78></location>.</text>
<text><location><page_16><loc_83><loc_77><loc_84><loc_78></location>0</text>
<text><location><page_16><loc_83><loc_74><loc_84><loc_75></location>3</text>
<text><location><page_16><loc_83><loc_74><loc_84><loc_74></location>6</text>
<text><location><page_16><loc_83><loc_74><loc_84><loc_74></location>0</text>
<text><location><page_16><loc_83><loc_73><loc_84><loc_74></location>.</text>
<text><location><page_16><loc_83><loc_73><loc_84><loc_73></location>0</text>
<text><location><page_16><loc_83><loc_72><loc_84><loc_73></location>±</text>
<text><location><page_16><loc_83><loc_71><loc_84><loc_72></location>6</text>
<text><location><page_16><loc_83><loc_71><loc_84><loc_71></location>6</text>
<text><location><page_16><loc_83><loc_70><loc_84><loc_71></location>4</text>
<text><location><page_16><loc_83><loc_70><loc_84><loc_70></location>.</text>
<text><location><page_16><loc_83><loc_70><loc_84><loc_70></location>9</text>
<text><location><page_16><loc_83><loc_69><loc_84><loc_70></location>1</text>
<text><location><page_16><loc_83><loc_67><loc_84><loc_68></location>1</text>
<text><location><page_16><loc_83><loc_67><loc_84><loc_67></location>4</text>
<text><location><page_16><loc_83><loc_67><loc_84><loc_67></location>0</text>
<text><location><page_16><loc_83><loc_66><loc_84><loc_67></location>.</text>
<text><location><page_16><loc_83><loc_66><loc_84><loc_66></location>0</text>
<text><location><page_16><loc_83><loc_65><loc_84><loc_66></location>±</text>
<text><location><page_16><loc_83><loc_64><loc_84><loc_65></location>6</text>
<text><location><page_16><loc_83><loc_64><loc_84><loc_64></location>0</text>
<text><location><page_16><loc_83><loc_63><loc_84><loc_64></location>5</text>
<text><location><page_16><loc_83><loc_63><loc_84><loc_63></location>.</text>
<text><location><page_16><loc_83><loc_63><loc_84><loc_63></location>9</text>
<text><location><page_16><loc_83><loc_62><loc_84><loc_63></location>1</text>
<text><location><page_16><loc_83><loc_61><loc_84><loc_61></location>8</text>
<text><location><page_16><loc_83><loc_60><loc_84><loc_61></location>2</text>
<text><location><page_16><loc_83><loc_60><loc_84><loc_60></location>0</text>
<text><location><page_16><loc_83><loc_59><loc_84><loc_60></location>.</text>
<text><location><page_16><loc_83><loc_59><loc_84><loc_59></location>0</text>
<text><location><page_16><loc_83><loc_58><loc_84><loc_59></location>±</text>
<text><location><page_16><loc_83><loc_57><loc_84><loc_58></location>7</text>
<text><location><page_16><loc_83><loc_57><loc_84><loc_57></location>2</text>
<text><location><page_16><loc_83><loc_56><loc_84><loc_57></location>5</text>
<text><location><page_16><loc_83><loc_56><loc_84><loc_56></location>.</text>
<text><location><page_16><loc_83><loc_56><loc_84><loc_56></location>9</text>
<text><location><page_16><loc_83><loc_55><loc_84><loc_56></location>1</text>
<text><location><page_16><loc_83><loc_54><loc_84><loc_54></location>3</text>
<text><location><page_16><loc_83><loc_53><loc_84><loc_54></location>2</text>
<text><location><page_16><loc_83><loc_53><loc_84><loc_53></location>0</text>
<text><location><page_16><loc_83><loc_53><loc_84><loc_53></location>.</text>
<text><location><page_16><loc_83><loc_52><loc_84><loc_53></location>0</text>
<text><location><page_16><loc_83><loc_51><loc_84><loc_52></location>±</text>
<text><location><page_16><loc_83><loc_50><loc_84><loc_51></location>3</text>
<text><location><page_16><loc_83><loc_50><loc_84><loc_50></location>3</text>
<text><location><page_16><loc_83><loc_50><loc_84><loc_50></location>8</text>
<text><location><page_16><loc_83><loc_49><loc_84><loc_50></location>.</text>
<text><location><page_16><loc_83><loc_49><loc_84><loc_49></location>9</text>
<text><location><page_16><loc_83><loc_48><loc_84><loc_49></location>1</text>
<text><location><page_16><loc_83><loc_47><loc_84><loc_47></location>0</text>
<text><location><page_16><loc_83><loc_46><loc_84><loc_47></location>2</text>
<text><location><page_16><loc_83><loc_46><loc_84><loc_46></location>0</text>
<text><location><page_16><loc_83><loc_46><loc_84><loc_46></location>.</text>
<text><location><page_16><loc_83><loc_45><loc_84><loc_46></location>0</text>
<text><location><page_16><loc_83><loc_44><loc_84><loc_45></location>±</text>
<text><location><page_16><loc_83><loc_44><loc_84><loc_44></location>0</text>
<text><location><page_16><loc_83><loc_43><loc_84><loc_44></location>3</text>
<text><location><page_16><loc_83><loc_43><loc_84><loc_43></location>6</text>
<text><location><page_16><loc_83><loc_42><loc_84><loc_43></location>.</text>
<text><location><page_16><loc_83><loc_42><loc_84><loc_42></location>9</text>
<text><location><page_16><loc_83><loc_42><loc_84><loc_42></location>1</text>
<text><location><page_16><loc_83><loc_40><loc_84><loc_40></location>5</text>
<text><location><page_16><loc_83><loc_39><loc_84><loc_40></location>6</text>
<text><location><page_16><loc_83><loc_39><loc_84><loc_39></location>.</text>
<text><location><page_16><loc_83><loc_39><loc_84><loc_39></location>1</text>
<text><location><page_16><loc_83><loc_38><loc_84><loc_39></location>4</text>
<text><location><page_16><loc_83><loc_38><loc_84><loc_38></location>3</text>
<text><location><page_16><loc_83><loc_37><loc_84><loc_38></location>3</text>
<text><location><page_16><loc_83><loc_37><loc_84><loc_37></location>0</text>
<text><location><page_16><loc_83><loc_36><loc_84><loc_37></location>3</text>
<text><location><page_16><loc_83><loc_34><loc_84><loc_35></location>6</text>
<text><location><page_16><loc_83><loc_34><loc_84><loc_34></location>5</text>
<text><location><page_16><loc_83><loc_34><loc_84><loc_34></location>5</text>
<text><location><page_16><loc_83><loc_33><loc_84><loc_34></location>.</text>
<text><location><page_16><loc_83><loc_33><loc_84><loc_33></location>3</text>
<text><location><page_16><loc_83><loc_32><loc_84><loc_33></location>0</text>
<text><location><page_16><loc_83><loc_32><loc_84><loc_32></location>4</text>
<text><location><page_16><loc_83><loc_31><loc_84><loc_32></location>3</text>
<text><location><page_16><loc_83><loc_31><loc_84><loc_31></location>1</text>
<text><location><page_16><loc_83><loc_30><loc_84><loc_31></location>0</text>
<text><location><page_16><loc_83><loc_22><loc_84><loc_22></location>8</text>
<text><location><page_16><loc_83><loc_21><loc_84><loc_22></location>7</text>
<text><location><page_16><loc_83><loc_21><loc_84><loc_21></location>-</text>
<text><location><page_16><loc_83><loc_20><loc_84><loc_21></location>ZK</text>
<text><location><page_16><loc_83><loc_18><loc_84><loc_19></location>.</text>
<text><location><page_16><loc_83><loc_18><loc_84><loc_18></location>.</text>
<text><location><page_16><loc_83><loc_18><loc_84><loc_18></location>.</text>
<text><location><page_16><loc_83><loc_18><loc_84><loc_18></location>.</text>
<text><location><page_16><loc_83><loc_17><loc_84><loc_18></location>.</text>
<text><location><page_16><loc_83><loc_17><loc_84><loc_17></location>.</text>
<text><location><page_16><loc_83><loc_17><loc_84><loc_17></location>1</text>
<text><location><page_16><loc_83><loc_16><loc_84><loc_17></location>2</text>
<text><location><page_16><loc_83><loc_16><loc_84><loc_16></location>2</text>
<text><location><page_16><loc_85><loc_83><loc_85><loc_83></location>2</text>
<text><location><page_16><loc_85><loc_82><loc_85><loc_83></location>2</text>
<text><location><page_16><loc_85><loc_82><loc_85><loc_82></location>3</text>
<text><location><page_16><loc_85><loc_82><loc_85><loc_82></location>.</text>
<text><location><page_16><loc_85><loc_81><loc_85><loc_82></location>2</text>
<text><location><page_16><loc_85><loc_78><loc_85><loc_79></location>0</text>
<text><location><page_16><loc_85><loc_78><loc_85><loc_78></location>1</text>
<text><location><page_16><loc_85><loc_78><loc_85><loc_78></location>.</text>
<text><location><page_16><loc_85><loc_77><loc_85><loc_78></location>0</text>
<text><location><page_16><loc_85><loc_74><loc_85><loc_75></location>1</text>
<text><location><page_16><loc_85><loc_74><loc_85><loc_74></location>3</text>
<text><location><page_16><loc_85><loc_74><loc_85><loc_74></location>0</text>
<text><location><page_16><loc_85><loc_73><loc_85><loc_74></location>.</text>
<text><location><page_16><loc_85><loc_73><loc_85><loc_73></location>0</text>
<text><location><page_16><loc_85><loc_72><loc_85><loc_73></location>±</text>
<text><location><page_16><loc_85><loc_71><loc_85><loc_72></location>3</text>
<text><location><page_16><loc_85><loc_71><loc_85><loc_71></location>8</text>
<text><location><page_16><loc_85><loc_70><loc_85><loc_71></location>2</text>
<text><location><page_16><loc_85><loc_70><loc_85><loc_70></location>.</text>
<text><location><page_16><loc_85><loc_70><loc_85><loc_70></location>9</text>
<text><location><page_16><loc_85><loc_69><loc_85><loc_70></location>1</text>
<text><location><page_16><loc_85><loc_67><loc_85><loc_68></location>4</text>
<text><location><page_16><loc_85><loc_67><loc_85><loc_67></location>3</text>
<text><location><page_16><loc_85><loc_67><loc_85><loc_67></location>0</text>
<text><location><page_16><loc_85><loc_66><loc_85><loc_67></location>.</text>
<text><location><page_16><loc_85><loc_66><loc_85><loc_66></location>0</text>
<text><location><page_16><loc_85><loc_65><loc_85><loc_66></location>±</text>
<text><location><page_16><loc_85><loc_64><loc_85><loc_65></location>5</text>
<text><location><page_16><loc_85><loc_64><loc_85><loc_64></location>7</text>
<text><location><page_16><loc_85><loc_63><loc_85><loc_64></location>7</text>
<text><location><page_16><loc_85><loc_63><loc_85><loc_63></location>.</text>
<text><location><page_16><loc_85><loc_63><loc_85><loc_63></location>9</text>
<text><location><page_16><loc_85><loc_62><loc_85><loc_63></location>1</text>
<text><location><page_16><loc_85><loc_61><loc_85><loc_61></location>9</text>
<text><location><page_16><loc_85><loc_60><loc_85><loc_61></location>2</text>
<text><location><page_16><loc_85><loc_60><loc_85><loc_60></location>0</text>
<text><location><page_16><loc_85><loc_59><loc_85><loc_60></location>.</text>
<text><location><page_16><loc_85><loc_59><loc_85><loc_59></location>0</text>
<text><location><page_16><loc_85><loc_58><loc_85><loc_59></location>±</text>
<text><location><page_16><loc_85><loc_57><loc_85><loc_58></location>3</text>
<text><location><page_16><loc_85><loc_57><loc_85><loc_57></location>2</text>
<text><location><page_16><loc_85><loc_56><loc_85><loc_57></location>0</text>
<text><location><page_16><loc_85><loc_56><loc_85><loc_56></location>.</text>
<text><location><page_16><loc_85><loc_56><loc_85><loc_56></location>0</text>
<text><location><page_16><loc_85><loc_55><loc_85><loc_56></location>2</text>
<text><location><page_16><loc_85><loc_54><loc_85><loc_54></location>7</text>
<text><location><page_16><loc_85><loc_53><loc_85><loc_54></location>2</text>
<text><location><page_16><loc_85><loc_53><loc_85><loc_53></location>0</text>
<text><location><page_16><loc_85><loc_53><loc_85><loc_53></location>.</text>
<text><location><page_16><loc_85><loc_52><loc_85><loc_53></location>0</text>
<text><location><page_16><loc_85><loc_51><loc_85><loc_52></location>±</text>
<text><location><page_16><loc_85><loc_50><loc_85><loc_51></location>5</text>
<text><location><page_16><loc_85><loc_50><loc_85><loc_50></location>4</text>
<text><location><page_16><loc_85><loc_50><loc_85><loc_50></location>4</text>
<text><location><page_16><loc_85><loc_49><loc_85><loc_50></location>.</text>
<text><location><page_16><loc_85><loc_49><loc_85><loc_49></location>0</text>
<text><location><page_16><loc_85><loc_48><loc_85><loc_49></location>2</text>
<text><location><page_16><loc_85><loc_47><loc_85><loc_47></location>2</text>
<text><location><page_16><loc_85><loc_46><loc_85><loc_47></location>2</text>
<text><location><page_16><loc_85><loc_46><loc_85><loc_46></location>0</text>
<text><location><page_16><loc_85><loc_46><loc_85><loc_46></location>.</text>
<text><location><page_16><loc_85><loc_45><loc_85><loc_46></location>0</text>
<text><location><page_16><loc_85><loc_44><loc_85><loc_45></location>±</text>
<text><location><page_16><loc_85><loc_44><loc_85><loc_44></location>2</text>
<text><location><page_16><loc_85><loc_43><loc_85><loc_44></location>9</text>
<text><location><page_16><loc_85><loc_43><loc_85><loc_43></location>0</text>
<text><location><page_16><loc_85><loc_42><loc_85><loc_43></location>.</text>
<text><location><page_16><loc_85><loc_42><loc_85><loc_42></location>0</text>
<text><location><page_16><loc_85><loc_42><loc_85><loc_42></location>2</text>
<text><location><page_16><loc_85><loc_40><loc_85><loc_40></location>3</text>
<text><location><page_16><loc_85><loc_39><loc_85><loc_40></location>6</text>
<text><location><page_16><loc_85><loc_39><loc_85><loc_39></location>.</text>
<text><location><page_16><loc_85><loc_39><loc_85><loc_39></location>1</text>
<text><location><page_16><loc_85><loc_38><loc_85><loc_39></location>2</text>
<text><location><page_16><loc_85><loc_38><loc_85><loc_38></location>7</text>
<text><location><page_16><loc_85><loc_37><loc_85><loc_38></location>2</text>
<text><location><page_16><loc_85><loc_37><loc_85><loc_37></location>0</text>
<text><location><page_16><loc_85><loc_36><loc_85><loc_37></location>3</text>
<text><location><page_16><loc_85><loc_34><loc_85><loc_35></location>1</text>
<text><location><page_16><loc_85><loc_34><loc_85><loc_34></location>5</text>
<text><location><page_16><loc_85><loc_34><loc_85><loc_34></location>6</text>
<text><location><page_16><loc_85><loc_33><loc_85><loc_34></location>.</text>
<text><location><page_16><loc_85><loc_33><loc_85><loc_33></location>4</text>
<text><location><page_16><loc_85><loc_32><loc_85><loc_33></location>0</text>
<text><location><page_16><loc_85><loc_32><loc_85><loc_32></location>4</text>
<text><location><page_16><loc_85><loc_31><loc_85><loc_32></location>3</text>
<text><location><page_16><loc_85><loc_31><loc_85><loc_31></location>1</text>
<text><location><page_16><loc_85><loc_30><loc_85><loc_31></location>0</text>
<text><location><page_16><loc_85><loc_22><loc_85><loc_22></location>9</text>
<text><location><page_16><loc_85><loc_21><loc_85><loc_22></location>7</text>
<text><location><page_16><loc_85><loc_21><loc_85><loc_21></location>-</text>
<text><location><page_16><loc_85><loc_20><loc_85><loc_21></location>ZK</text>
<text><location><page_16><loc_85><loc_18><loc_85><loc_19></location>.</text>
<text><location><page_16><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_16><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_16><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_16><loc_85><loc_17><loc_85><loc_18></location>.</text>
<text><location><page_16><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_16><loc_85><loc_17><loc_85><loc_17></location>2</text>
<text><location><page_16><loc_85><loc_16><loc_85><loc_17></location>2</text>
<text><location><page_16><loc_85><loc_16><loc_85><loc_16></location>2</text>
<text><location><page_16><loc_86><loc_83><loc_87><loc_83></location>2</text>
<text><location><page_16><loc_86><loc_82><loc_87><loc_83></location>2</text>
<text><location><page_16><loc_86><loc_82><loc_87><loc_82></location>3</text>
<text><location><page_16><loc_86><loc_82><loc_87><loc_82></location>.</text>
<text><location><page_16><loc_86><loc_81><loc_87><loc_82></location>2</text>
<text><location><page_16><loc_86><loc_78><loc_87><loc_79></location>0</text>
<text><location><page_16><loc_86><loc_78><loc_87><loc_78></location>1</text>
<text><location><page_16><loc_86><loc_78><loc_87><loc_78></location>.</text>
<text><location><page_16><loc_86><loc_77><loc_87><loc_78></location>0</text>
<text><location><page_16><loc_86><loc_74><loc_87><loc_75></location>8</text>
<text><location><page_16><loc_86><loc_74><loc_87><loc_74></location>3</text>
<text><location><page_16><loc_86><loc_74><loc_87><loc_74></location>0</text>
<text><location><page_16><loc_86><loc_73><loc_87><loc_74></location>.</text>
<text><location><page_16><loc_86><loc_73><loc_87><loc_73></location>0</text>
<text><location><page_16><loc_86><loc_72><loc_87><loc_73></location>±</text>
<text><location><page_16><loc_86><loc_71><loc_87><loc_72></location>5</text>
<text><location><page_16><loc_86><loc_71><loc_87><loc_71></location>0</text>
<text><location><page_16><loc_86><loc_70><loc_87><loc_71></location>5</text>
<text><location><page_16><loc_86><loc_70><loc_87><loc_70></location>.</text>
<text><location><page_16><loc_86><loc_70><loc_87><loc_70></location>9</text>
<text><location><page_16><loc_86><loc_69><loc_87><loc_70></location>1</text>
<text><location><page_16><loc_86><loc_67><loc_87><loc_68></location>3</text>
<text><location><page_16><loc_86><loc_67><loc_87><loc_67></location>3</text>
<text><location><page_16><loc_86><loc_67><loc_87><loc_67></location>0</text>
<text><location><page_16><loc_86><loc_66><loc_87><loc_67></location>.</text>
<text><location><page_16><loc_86><loc_66><loc_87><loc_66></location>0</text>
<text><location><page_16><loc_86><loc_65><loc_87><loc_66></location>±</text>
<text><location><page_16><loc_86><loc_64><loc_87><loc_65></location>7</text>
<text><location><page_16><loc_86><loc_64><loc_87><loc_64></location>3</text>
<text><location><page_16><loc_86><loc_63><loc_87><loc_64></location>8</text>
<text><location><page_16><loc_86><loc_63><loc_87><loc_63></location>.</text>
<text><location><page_16><loc_86><loc_63><loc_87><loc_63></location>9</text>
<text><location><page_16><loc_86><loc_62><loc_87><loc_63></location>1</text>
<text><location><page_16><loc_86><loc_61><loc_87><loc_61></location>4</text>
<text><location><page_16><loc_86><loc_60><loc_87><loc_61></location>3</text>
<text><location><page_16><loc_86><loc_60><loc_87><loc_60></location>0</text>
<text><location><page_16><loc_86><loc_59><loc_87><loc_60></location>.</text>
<text><location><page_16><loc_86><loc_59><loc_87><loc_59></location>0</text>
<text><location><page_16><loc_86><loc_58><loc_87><loc_59></location>±</text>
<text><location><page_16><loc_86><loc_57><loc_87><loc_58></location>7</text>
<text><location><page_16><loc_86><loc_57><loc_87><loc_57></location>5</text>
<text><location><page_16><loc_86><loc_56><loc_87><loc_57></location>2</text>
<text><location><page_16><loc_86><loc_56><loc_87><loc_56></location>.</text>
<text><location><page_16><loc_86><loc_56><loc_87><loc_56></location>0</text>
<text><location><page_16><loc_86><loc_55><loc_87><loc_56></location>2</text>
<text><location><page_16><loc_86><loc_54><loc_87><loc_54></location>2</text>
<text><location><page_16><loc_86><loc_53><loc_87><loc_54></location>3</text>
<text><location><page_16><loc_86><loc_53><loc_87><loc_53></location>0</text>
<text><location><page_16><loc_86><loc_53><loc_87><loc_53></location>.</text>
<text><location><page_16><loc_86><loc_52><loc_87><loc_53></location>0</text>
<text><location><page_16><loc_86><loc_51><loc_87><loc_52></location>±</text>
<text><location><page_16><loc_86><loc_50><loc_87><loc_51></location>3</text>
<text><location><page_16><loc_86><loc_50><loc_87><loc_50></location>5</text>
<text><location><page_16><loc_86><loc_50><loc_87><loc_50></location>7</text>
<text><location><page_16><loc_86><loc_49><loc_87><loc_50></location>.</text>
<text><location><page_16><loc_86><loc_49><loc_87><loc_49></location>0</text>
<text><location><page_16><loc_86><loc_48><loc_87><loc_49></location>2</text>
<text><location><page_16><loc_86><loc_47><loc_87><loc_47></location>4</text>
<text><location><page_16><loc_86><loc_46><loc_87><loc_47></location>3</text>
<text><location><page_16><loc_86><loc_46><loc_87><loc_46></location>0</text>
<text><location><page_16><loc_86><loc_46><loc_87><loc_46></location>.</text>
<text><location><page_16><loc_86><loc_45><loc_87><loc_46></location>0</text>
<text><location><page_16><loc_86><loc_44><loc_87><loc_45></location>±</text>
<text><location><page_16><loc_86><loc_44><loc_87><loc_44></location>1</text>
<text><location><page_16><loc_86><loc_43><loc_87><loc_44></location>3</text>
<text><location><page_16><loc_86><loc_43><loc_87><loc_43></location>7</text>
<text><location><page_16><loc_86><loc_42><loc_87><loc_43></location>.</text>
<text><location><page_16><loc_86><loc_42><loc_87><loc_42></location>0</text>
<text><location><page_16><loc_86><loc_42><loc_87><loc_42></location>2</text>
<text><location><page_16><loc_86><loc_40><loc_87><loc_40></location>2</text>
<text><location><page_16><loc_86><loc_39><loc_87><loc_40></location>2</text>
<text><location><page_16><loc_86><loc_39><loc_87><loc_39></location>.</text>
<text><location><page_16><loc_86><loc_39><loc_87><loc_39></location>0</text>
<text><location><page_16><loc_86><loc_38><loc_87><loc_39></location>2</text>
<text><location><page_16><loc_86><loc_38><loc_87><loc_38></location>8</text>
<text><location><page_16><loc_86><loc_37><loc_87><loc_38></location>2</text>
<text><location><page_16><loc_86><loc_37><loc_87><loc_37></location>0</text>
<text><location><page_16><loc_86><loc_36><loc_87><loc_37></location>3</text>
<text><location><page_16><loc_86><loc_34><loc_87><loc_35></location>4</text>
<text><location><page_16><loc_86><loc_34><loc_87><loc_34></location>7</text>
<text><location><page_16><loc_86><loc_34><loc_87><loc_34></location>9</text>
<text><location><page_16><loc_86><loc_33><loc_87><loc_34></location>.</text>
<text><location><page_16><loc_86><loc_33><loc_87><loc_33></location>4</text>
<text><location><page_16><loc_86><loc_32><loc_87><loc_33></location>0</text>
<text><location><page_16><loc_86><loc_32><loc_87><loc_32></location>4</text>
<text><location><page_16><loc_86><loc_31><loc_87><loc_32></location>3</text>
<text><location><page_16><loc_86><loc_31><loc_87><loc_31></location>1</text>
<text><location><page_16><loc_86><loc_30><loc_87><loc_31></location>0</text>
<text><location><page_16><loc_86><loc_22><loc_87><loc_22></location>0</text>
<text><location><page_16><loc_86><loc_21><loc_87><loc_22></location>8</text>
<text><location><page_16><loc_86><loc_21><loc_87><loc_21></location>-</text>
<text><location><page_16><loc_86><loc_20><loc_87><loc_21></location>ZK</text>
<text><location><page_16><loc_86><loc_18><loc_87><loc_19></location>.</text>
<text><location><page_16><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_16><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_16><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_16><loc_86><loc_17><loc_87><loc_18></location>.</text>
<text><location><page_16><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_16><loc_86><loc_17><loc_87><loc_17></location>3</text>
<text><location><page_16><loc_86><loc_16><loc_87><loc_17></location>2</text>
<text><location><page_16><loc_86><loc_16><loc_87><loc_16></location>2</text>
<text><location><page_16><loc_87><loc_83><loc_88><loc_83></location>2</text>
<text><location><page_16><loc_87><loc_82><loc_88><loc_83></location>2</text>
<text><location><page_16><loc_87><loc_82><loc_88><loc_82></location>3</text>
<text><location><page_16><loc_87><loc_82><loc_88><loc_82></location>.</text>
<text><location><page_16><loc_87><loc_81><loc_88><loc_82></location>2</text>
<text><location><page_16><loc_87><loc_78><loc_88><loc_79></location>0</text>
<text><location><page_16><loc_87><loc_78><loc_88><loc_78></location>1</text>
<text><location><page_16><loc_87><loc_78><loc_88><loc_78></location>.</text>
<text><location><page_16><loc_87><loc_77><loc_88><loc_78></location>0</text>
<text><location><page_16><loc_87><loc_74><loc_88><loc_75></location>2</text>
<text><location><page_16><loc_87><loc_74><loc_88><loc_74></location>2</text>
<text><location><page_16><loc_87><loc_74><loc_88><loc_74></location>0</text>
<text><location><page_16><loc_87><loc_73><loc_88><loc_74></location>.</text>
<text><location><page_16><loc_87><loc_73><loc_88><loc_73></location>0</text>
<text><location><page_16><loc_87><loc_72><loc_88><loc_73></location>±</text>
<text><location><page_16><loc_87><loc_71><loc_88><loc_72></location>4</text>
<text><location><page_16><loc_87><loc_71><loc_88><loc_71></location>6</text>
<text><location><page_16><loc_87><loc_70><loc_88><loc_71></location>8</text>
<text><location><page_16><loc_87><loc_70><loc_88><loc_70></location>.</text>
<text><location><page_16><loc_87><loc_70><loc_88><loc_70></location>8</text>
<text><location><page_16><loc_87><loc_69><loc_88><loc_70></location>1</text>
<text><location><page_16><loc_87><loc_67><loc_88><loc_68></location>3</text>
<text><location><page_16><loc_87><loc_67><loc_88><loc_67></location>2</text>
<text><location><page_16><loc_87><loc_67><loc_88><loc_67></location>0</text>
<text><location><page_16><loc_87><loc_66><loc_88><loc_67></location>.</text>
<text><location><page_16><loc_87><loc_66><loc_88><loc_66></location>0</text>
<text><location><page_16><loc_87><loc_65><loc_88><loc_66></location>±</text>
<text><location><page_16><loc_87><loc_64><loc_88><loc_65></location>9</text>
<text><location><page_16><loc_87><loc_64><loc_88><loc_64></location>7</text>
<text><location><page_16><loc_87><loc_63><loc_88><loc_64></location>1</text>
<text><location><page_16><loc_87><loc_63><loc_88><loc_63></location>.</text>
<text><location><page_16><loc_87><loc_63><loc_88><loc_63></location>9</text>
<text><location><page_16><loc_87><loc_62><loc_88><loc_63></location>1</text>
<text><location><page_16><loc_87><loc_61><loc_88><loc_61></location>2</text>
<text><location><page_16><loc_87><loc_60><loc_88><loc_61></location>2</text>
<text><location><page_16><loc_87><loc_60><loc_88><loc_60></location>0</text>
<text><location><page_16><loc_87><loc_59><loc_88><loc_60></location>.</text>
<text><location><page_16><loc_87><loc_59><loc_88><loc_59></location>0</text>
<text><location><page_16><loc_87><loc_58><loc_88><loc_59></location>±</text>
<text><location><page_16><loc_87><loc_57><loc_88><loc_58></location>3</text>
<text><location><page_16><loc_87><loc_57><loc_88><loc_57></location>0</text>
<text><location><page_16><loc_87><loc_56><loc_88><loc_57></location>5</text>
<text><location><page_16><loc_87><loc_56><loc_88><loc_56></location>.</text>
<text><location><page_16><loc_87><loc_56><loc_88><loc_56></location>9</text>
<text><location><page_16><loc_87><loc_55><loc_88><loc_56></location>1</text>
<text><location><page_16><loc_87><loc_54><loc_88><loc_54></location>0</text>
<text><location><page_16><loc_87><loc_53><loc_88><loc_54></location>2</text>
<text><location><page_16><loc_87><loc_53><loc_88><loc_53></location>0</text>
<text><location><page_16><loc_87><loc_53><loc_88><loc_53></location>.</text>
<text><location><page_16><loc_87><loc_52><loc_88><loc_53></location>0</text>
<text><location><page_16><loc_87><loc_51><loc_88><loc_52></location>±</text>
<text><location><page_16><loc_87><loc_50><loc_88><loc_51></location>7</text>
<text><location><page_16><loc_87><loc_50><loc_88><loc_50></location>3</text>
<text><location><page_16><loc_87><loc_50><loc_88><loc_50></location>8</text>
<text><location><page_16><loc_87><loc_49><loc_88><loc_50></location>.</text>
<text><location><page_16><loc_87><loc_49><loc_88><loc_49></location>9</text>
<text><location><page_16><loc_87><loc_48><loc_88><loc_49></location>1</text>
<text><location><page_16><loc_87><loc_47><loc_88><loc_47></location>3</text>
<text><location><page_16><loc_87><loc_46><loc_88><loc_47></location>1</text>
<text><location><page_16><loc_87><loc_46><loc_88><loc_46></location>0</text>
<text><location><page_16><loc_87><loc_46><loc_88><loc_46></location>.</text>
<text><location><page_16><loc_87><loc_45><loc_88><loc_46></location>0</text>
<text><location><page_16><loc_87><loc_44><loc_88><loc_45></location>±</text>
<text><location><page_16><loc_87><loc_44><loc_88><loc_44></location>1</text>
<text><location><page_16><loc_87><loc_43><loc_88><loc_44></location>9</text>
<text><location><page_16><loc_87><loc_43><loc_88><loc_43></location>4</text>
<text><location><page_16><loc_87><loc_42><loc_88><loc_43></location>.</text>
<text><location><page_16><loc_87><loc_42><loc_88><loc_42></location>9</text>
<text><location><page_16><loc_87><loc_42><loc_88><loc_42></location>1</text>
<text><location><page_16><loc_87><loc_40><loc_88><loc_40></location>8</text>
<text><location><page_16><loc_87><loc_39><loc_88><loc_40></location>3</text>
<text><location><page_16><loc_87><loc_39><loc_88><loc_39></location>.</text>
<text><location><page_16><loc_87><loc_39><loc_88><loc_39></location>4</text>
<text><location><page_16><loc_87><loc_38><loc_88><loc_39></location>0</text>
<text><location><page_16><loc_87><loc_38><loc_88><loc_38></location>8</text>
<text><location><page_16><loc_87><loc_37><loc_88><loc_38></location>2</text>
<text><location><page_16><loc_87><loc_37><loc_88><loc_37></location>0</text>
<text><location><page_16><loc_87><loc_36><loc_88><loc_37></location>3</text>
<text><location><page_16><loc_87><loc_34><loc_88><loc_35></location>6</text>
<text><location><page_16><loc_87><loc_34><loc_88><loc_34></location>3</text>
<text><location><page_16><loc_87><loc_34><loc_88><loc_34></location>7</text>
<text><location><page_16><loc_87><loc_33><loc_88><loc_34></location>.</text>
<text><location><page_16><loc_87><loc_33><loc_88><loc_33></location>6</text>
<text><location><page_16><loc_87><loc_32><loc_88><loc_33></location>0</text>
<text><location><page_16><loc_87><loc_32><loc_88><loc_32></location>4</text>
<text><location><page_16><loc_87><loc_31><loc_88><loc_32></location>3</text>
<text><location><page_16><loc_87><loc_31><loc_88><loc_31></location>1</text>
<text><location><page_16><loc_87><loc_30><loc_88><loc_31></location>0</text>
<text><location><page_16><loc_87><loc_22><loc_88><loc_22></location>1</text>
<text><location><page_16><loc_87><loc_21><loc_88><loc_22></location>8</text>
<text><location><page_16><loc_87><loc_21><loc_88><loc_21></location>-</text>
<text><location><page_16><loc_87><loc_20><loc_88><loc_21></location>ZK</text>
<text><location><page_16><loc_87><loc_18><loc_88><loc_19></location>.</text>
<text><location><page_16><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_16><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_16><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_16><loc_87><loc_17><loc_88><loc_18></location>.</text>
<text><location><page_16><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_16><loc_87><loc_17><loc_88><loc_17></location>4</text>
<text><location><page_16><loc_87><loc_16><loc_88><loc_17></location>2</text>
<text><location><page_16><loc_87><loc_16><loc_88><loc_16></location>2</text>
<text><location><page_17><loc_42><loc_93><loc_57><loc_94></location>Star clusters in M33</text>
<text><location><page_17><loc_90><loc_93><loc_92><loc_94></location>17</text>
<text><location><page_17><loc_48><loc_83><loc_48><loc_83></location>6</text>
<text><location><page_17><loc_48><loc_82><loc_48><loc_83></location>0</text>
<text><location><page_17><loc_48><loc_82><loc_48><loc_82></location>8</text>
<text><location><page_17><loc_48><loc_82><loc_48><loc_82></location>.</text>
<text><location><page_17><loc_48><loc_81><loc_48><loc_82></location>1</text>
<text><location><page_17><loc_48><loc_78><loc_48><loc_79></location>0</text>
<text><location><page_17><loc_48><loc_78><loc_48><loc_78></location>1</text>
<text><location><page_17><loc_48><loc_78><loc_48><loc_78></location>.</text>
<text><location><page_17><loc_48><loc_77><loc_48><loc_78></location>0</text>
<text><location><page_17><loc_48><loc_74><loc_48><loc_75></location>7</text>
<text><location><page_17><loc_48><loc_74><loc_48><loc_74></location>1</text>
<text><location><page_17><loc_48><loc_74><loc_48><loc_74></location>0</text>
<text><location><page_17><loc_48><loc_73><loc_48><loc_74></location>.</text>
<text><location><page_17><loc_48><loc_73><loc_48><loc_73></location>0</text>
<text><location><page_17><loc_48><loc_72><loc_48><loc_73></location>±</text>
<text><location><page_17><loc_48><loc_71><loc_48><loc_72></location>5</text>
<text><location><page_17><loc_48><loc_71><loc_48><loc_71></location>5</text>
<text><location><page_17><loc_48><loc_70><loc_48><loc_71></location>3</text>
<text><location><page_17><loc_48><loc_70><loc_48><loc_70></location>.</text>
<text><location><page_17><loc_48><loc_70><loc_48><loc_70></location>8</text>
<text><location><page_17><loc_48><loc_69><loc_48><loc_70></location>1</text>
<text><location><page_17><loc_48><loc_67><loc_48><loc_68></location>9</text>
<text><location><page_17><loc_48><loc_67><loc_48><loc_67></location>2</text>
<text><location><page_17><loc_48><loc_67><loc_48><loc_67></location>0</text>
<text><location><page_17><loc_48><loc_66><loc_48><loc_67></location>.</text>
<text><location><page_17><loc_48><loc_66><loc_48><loc_66></location>0</text>
<text><location><page_17><loc_48><loc_65><loc_48><loc_66></location>±</text>
<text><location><page_17><loc_48><loc_64><loc_48><loc_65></location>8</text>
<text><location><page_17><loc_48><loc_64><loc_48><loc_64></location>7</text>
<text><location><page_17><loc_48><loc_63><loc_48><loc_64></location>2</text>
<text><location><page_17><loc_48><loc_63><loc_48><loc_63></location>.</text>
<text><location><page_17><loc_48><loc_63><loc_48><loc_63></location>9</text>
<text><location><page_17><loc_48><loc_62><loc_48><loc_63></location>1</text>
<text><location><page_17><loc_48><loc_61><loc_48><loc_61></location>4</text>
<text><location><page_17><loc_48><loc_60><loc_48><loc_61></location>4</text>
<text><location><page_17><loc_48><loc_60><loc_48><loc_60></location>0</text>
<text><location><page_17><loc_48><loc_59><loc_48><loc_60></location>.</text>
<text><location><page_17><loc_48><loc_59><loc_48><loc_59></location>0</text>
<text><location><page_17><loc_45><loc_82><loc_46><loc_83></location>p</text>
<text><location><page_17><loc_46><loc_82><loc_47><loc_83></location>)</text>
<text><location><page_17><loc_46><loc_82><loc_47><loc_82></location>'</text>
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<text><location><page_17><loc_46><loc_81><loc_47><loc_82></location>(</text>
<text><location><page_17><loc_46><loc_79><loc_47><loc_79></location>)</text>
<text><location><page_17><loc_46><loc_78><loc_47><loc_79></location>g</text>
<text><location><page_17><loc_46><loc_78><loc_47><loc_78></location>a</text>
<text><location><page_17><loc_46><loc_77><loc_47><loc_78></location>m</text>
<text><location><page_17><loc_46><loc_77><loc_47><loc_77></location>(</text>
<text><location><page_17><loc_46><loc_73><loc_47><loc_73></location>)</text>
<text><location><page_17><loc_46><loc_72><loc_47><loc_73></location>g</text>
<text><location><page_17><loc_46><loc_72><loc_47><loc_72></location>a</text>
<text><location><page_17><loc_46><loc_71><loc_47><loc_72></location>m</text>
<text><location><page_17><loc_46><loc_71><loc_47><loc_71></location>(</text>
<text><location><page_17><loc_46><loc_66><loc_47><loc_66></location>)</text>
<text><location><page_17><loc_46><loc_65><loc_47><loc_66></location>g</text>
<text><location><page_17><loc_46><loc_65><loc_47><loc_65></location>a</text>
<text><location><page_17><loc_46><loc_64><loc_47><loc_65></location>m</text>
<text><location><page_17><loc_46><loc_64><loc_47><loc_64></location>(</text>
<text><location><page_17><loc_46><loc_59><loc_47><loc_59></location>)</text>
<text><location><page_17><loc_49><loc_83><loc_50><loc_83></location>4</text>
<text><location><page_17><loc_49><loc_82><loc_50><loc_83></location>5</text>
<text><location><page_17><loc_49><loc_82><loc_50><loc_82></location>3</text>
<text><location><page_17><loc_49><loc_82><loc_50><loc_82></location>.</text>
<text><location><page_17><loc_49><loc_81><loc_50><loc_82></location>3</text>
<text><location><page_17><loc_49><loc_78><loc_50><loc_79></location>0</text>
<text><location><page_17><loc_49><loc_78><loc_50><loc_78></location>1</text>
<text><location><page_17><loc_49><loc_78><loc_50><loc_78></location>.</text>
<text><location><page_17><loc_49><loc_77><loc_50><loc_78></location>0</text>
<text><location><page_17><loc_49><loc_74><loc_50><loc_75></location>6</text>
<text><location><page_17><loc_49><loc_74><loc_50><loc_74></location>4</text>
<text><location><page_17><loc_49><loc_74><loc_50><loc_74></location>0</text>
<text><location><page_17><loc_49><loc_73><loc_50><loc_74></location>.</text>
<text><location><page_17><loc_49><loc_73><loc_50><loc_73></location>0</text>
<text><location><page_17><loc_49><loc_72><loc_50><loc_73></location>±</text>
<text><location><page_17><loc_49><loc_71><loc_50><loc_72></location>5</text>
<text><location><page_17><loc_49><loc_71><loc_50><loc_71></location>7</text>
<text><location><page_17><loc_49><loc_70><loc_50><loc_71></location>6</text>
<text><location><page_17><loc_49><loc_70><loc_50><loc_70></location>.</text>
<text><location><page_17><loc_49><loc_70><loc_50><loc_70></location>8</text>
<text><location><page_17><loc_49><loc_69><loc_50><loc_70></location>1</text>
<text><location><page_17><loc_49><loc_67><loc_50><loc_68></location>6</text>
<text><location><page_17><loc_49><loc_67><loc_50><loc_67></location>3</text>
<text><location><page_17><loc_49><loc_67><loc_50><loc_67></location>0</text>
<text><location><page_17><loc_49><loc_66><loc_50><loc_67></location>.</text>
<text><location><page_17><loc_49><loc_66><loc_50><loc_66></location>0</text>
<text><location><page_17><loc_49><loc_65><loc_50><loc_66></location>±</text>
<text><location><page_17><loc_49><loc_64><loc_50><loc_65></location>4</text>
<text><location><page_17><loc_49><loc_64><loc_50><loc_64></location>0</text>
<text><location><page_17><loc_49><loc_63><loc_50><loc_64></location>1</text>
<text><location><page_17><loc_49><loc_63><loc_50><loc_63></location>.</text>
<text><location><page_17><loc_49><loc_63><loc_50><loc_63></location>9</text>
<text><location><page_17><loc_49><loc_62><loc_50><loc_63></location>1</text>
<text><location><page_17><loc_49><loc_61><loc_50><loc_61></location>4</text>
<text><location><page_17><loc_49><loc_60><loc_50><loc_61></location>3</text>
<text><location><page_17><loc_49><loc_60><loc_50><loc_60></location>0</text>
<text><location><page_17><loc_49><loc_59><loc_50><loc_60></location>.</text>
<text><location><page_17><loc_49><loc_59><loc_50><loc_59></location>0</text>
<text><location><page_17><loc_50><loc_83><loc_51><loc_83></location>0</text>
<text><location><page_17><loc_50><loc_82><loc_51><loc_83></location>8</text>
<text><location><page_17><loc_50><loc_82><loc_51><loc_82></location>5</text>
<text><location><page_17><loc_50><loc_82><loc_51><loc_82></location>.</text>
<text><location><page_17><loc_50><loc_81><loc_51><loc_82></location>2</text>
<text><location><page_17><loc_50><loc_78><loc_51><loc_79></location>0</text>
<text><location><page_17><loc_50><loc_78><loc_51><loc_78></location>1</text>
<text><location><page_17><loc_50><loc_78><loc_51><loc_78></location>.</text>
<text><location><page_17><loc_50><loc_77><loc_51><loc_78></location>0</text>
<text><location><page_17><loc_50><loc_74><loc_51><loc_75></location>9</text>
<text><location><page_17><loc_50><loc_74><loc_51><loc_74></location>3</text>
<text><location><page_17><loc_50><loc_74><loc_51><loc_74></location>0</text>
<text><location><page_17><loc_50><loc_73><loc_51><loc_74></location>.</text>
<text><location><page_17><loc_50><loc_73><loc_51><loc_73></location>0</text>
<text><location><page_17><loc_50><loc_72><loc_51><loc_73></location>±</text>
<text><location><page_17><loc_50><loc_71><loc_51><loc_72></location>9</text>
<text><location><page_17><loc_50><loc_71><loc_51><loc_71></location>8</text>
<text><location><page_17><loc_50><loc_70><loc_51><loc_71></location>5</text>
<text><location><page_17><loc_50><loc_70><loc_51><loc_70></location>.</text>
<text><location><page_17><loc_50><loc_70><loc_51><loc_70></location>9</text>
<text><location><page_17><loc_50><loc_69><loc_51><loc_70></location>1</text>
<text><location><page_17><loc_50><loc_67><loc_51><loc_68></location>0</text>
<text><location><page_17><loc_50><loc_67><loc_51><loc_67></location>3</text>
<text><location><page_17><loc_50><loc_67><loc_51><loc_67></location>0</text>
<text><location><page_17><loc_50><loc_66><loc_51><loc_67></location>.</text>
<text><location><page_17><loc_50><loc_66><loc_51><loc_66></location>0</text>
<text><location><page_17><loc_50><loc_65><loc_51><loc_66></location>±</text>
<text><location><page_17><loc_50><loc_64><loc_51><loc_65></location>3</text>
<text><location><page_17><loc_50><loc_64><loc_51><loc_64></location>0</text>
<text><location><page_17><loc_50><loc_63><loc_51><loc_64></location>7</text>
<text><location><page_17><loc_50><loc_63><loc_51><loc_63></location>.</text>
<text><location><page_17><loc_50><loc_63><loc_51><loc_63></location>9</text>
<text><location><page_17><loc_50><loc_62><loc_51><loc_63></location>1</text>
<text><location><page_17><loc_50><loc_61><loc_51><loc_61></location>8</text>
<text><location><page_17><loc_50><loc_60><loc_51><loc_61></location>2</text>
<text><location><page_17><loc_50><loc_60><loc_51><loc_60></location>0</text>
<text><location><page_17><loc_50><loc_59><loc_51><loc_60></location>.</text>
<text><location><page_17><loc_50><loc_59><loc_51><loc_59></location>0</text>
<text><location><page_17><loc_51><loc_83><loc_52><loc_83></location>6</text>
<text><location><page_17><loc_51><loc_82><loc_52><loc_83></location>9</text>
<text><location><page_17><loc_51><loc_82><loc_52><loc_82></location>0</text>
<text><location><page_17><loc_51><loc_82><loc_52><loc_82></location>.</text>
<text><location><page_17><loc_51><loc_81><loc_52><loc_82></location>3</text>
<text><location><page_17><loc_51><loc_78><loc_52><loc_79></location>0</text>
<text><location><page_17><loc_51><loc_78><loc_52><loc_78></location>1</text>
<text><location><page_17><loc_51><loc_78><loc_52><loc_78></location>.</text>
<text><location><page_17><loc_51><loc_77><loc_52><loc_78></location>0</text>
<text><location><page_17><loc_51><loc_74><loc_52><loc_75></location>3</text>
<text><location><page_17><loc_51><loc_74><loc_52><loc_74></location>4</text>
<text><location><page_17><loc_51><loc_74><loc_52><loc_74></location>0</text>
<text><location><page_17><loc_51><loc_73><loc_52><loc_74></location>.</text>
<text><location><page_17><loc_51><loc_73><loc_52><loc_73></location>0</text>
<text><location><page_17><loc_51><loc_72><loc_52><loc_73></location>±</text>
<text><location><page_17><loc_51><loc_71><loc_52><loc_72></location>6</text>
<text><location><page_17><loc_51><loc_71><loc_52><loc_71></location>5</text>
<text><location><page_17><loc_51><loc_70><loc_52><loc_71></location>3</text>
<text><location><page_17><loc_51><loc_70><loc_52><loc_70></location>.</text>
<text><location><page_17><loc_51><loc_70><loc_52><loc_70></location>9</text>
<text><location><page_17><loc_51><loc_69><loc_52><loc_70></location>1</text>
<text><location><page_17><loc_51><loc_67><loc_52><loc_68></location>3</text>
<text><location><page_17><loc_51><loc_67><loc_52><loc_67></location>3</text>
<text><location><page_17><loc_51><loc_67><loc_52><loc_67></location>0</text>
<text><location><page_17><loc_51><loc_66><loc_52><loc_67></location>.</text>
<text><location><page_17><loc_51><loc_66><loc_52><loc_66></location>0</text>
<text><location><page_17><loc_51><loc_65><loc_52><loc_66></location>±</text>
<text><location><page_17><loc_51><loc_64><loc_52><loc_65></location>1</text>
<text><location><page_17><loc_51><loc_64><loc_52><loc_64></location>4</text>
<text><location><page_17><loc_51><loc_63><loc_52><loc_64></location>3</text>
<text><location><page_17><loc_51><loc_63><loc_52><loc_63></location>.</text>
<text><location><page_17><loc_51><loc_63><loc_52><loc_63></location>9</text>
<text><location><page_17><loc_51><loc_62><loc_52><loc_63></location>1</text>
<text><location><page_17><loc_51><loc_61><loc_52><loc_61></location>3</text>
<text><location><page_17><loc_51><loc_60><loc_52><loc_61></location>2</text>
<text><location><page_17><loc_51><loc_60><loc_52><loc_60></location>0</text>
<text><location><page_17><loc_51><loc_59><loc_52><loc_60></location>.</text>
<text><location><page_17><loc_51><loc_59><loc_52><loc_59></location>0</text>
<paragraph><location><page_17><loc_46><loc_56><loc_52><loc_59></location>( m a g 0 3 6 ± 4 7 2 ± 9 0 7 ± 3 3 4 ±</paragraph>
<text><location><page_17><loc_48><loc_56><loc_48><loc_56></location>.</text>
<text><location><page_17><loc_48><loc_56><loc_48><loc_56></location>0</text>
<text><location><page_17><loc_48><loc_55><loc_48><loc_56></location>2</text>
<text><location><page_17><loc_49><loc_56><loc_50><loc_56></location>.</text>
<text><location><page_17><loc_49><loc_56><loc_50><loc_56></location>9</text>
<text><location><page_17><loc_49><loc_55><loc_50><loc_56></location>1</text>
<text><location><page_17><loc_50><loc_56><loc_51><loc_56></location>.</text>
<text><location><page_17><loc_50><loc_56><loc_51><loc_56></location>9</text>
<text><location><page_17><loc_50><loc_55><loc_51><loc_56></location>1</text>
<text><location><page_17><loc_51><loc_56><loc_52><loc_56></location>.</text>
<text><location><page_17><loc_51><loc_56><loc_52><loc_56></location>9</text>
<text><location><page_17><loc_51><loc_55><loc_52><loc_56></location>1</text>
<text><location><page_17><loc_53><loc_83><loc_53><loc_83></location>2</text>
<text><location><page_17><loc_53><loc_82><loc_53><loc_83></location>2</text>
<text><location><page_17><loc_53><loc_82><loc_53><loc_82></location>3</text>
<text><location><page_17><loc_53><loc_82><loc_53><loc_82></location>.</text>
<text><location><page_17><loc_53><loc_81><loc_53><loc_82></location>2</text>
<text><location><page_17><loc_53><loc_78><loc_53><loc_79></location>0</text>
<text><location><page_17><loc_53><loc_78><loc_53><loc_78></location>1</text>
<text><location><page_17><loc_53><loc_78><loc_53><loc_78></location>.</text>
<text><location><page_17><loc_53><loc_77><loc_53><loc_78></location>0</text>
<text><location><page_17><loc_53><loc_74><loc_53><loc_75></location>9</text>
<text><location><page_17><loc_53><loc_74><loc_53><loc_74></location>0</text>
<text><location><page_17><loc_53><loc_74><loc_53><loc_74></location>0</text>
<text><location><page_17><loc_53><loc_73><loc_53><loc_74></location>.</text>
<text><location><page_17><loc_53><loc_73><loc_53><loc_73></location>0</text>
<text><location><page_17><loc_53><loc_72><loc_53><loc_73></location>±</text>
<text><location><page_17><loc_53><loc_71><loc_53><loc_72></location>3</text>
<text><location><page_17><loc_53><loc_71><loc_53><loc_71></location>8</text>
<text><location><page_17><loc_53><loc_70><loc_53><loc_71></location>6</text>
<text><location><page_17><loc_53><loc_70><loc_53><loc_70></location>.</text>
<text><location><page_17><loc_53><loc_70><loc_53><loc_70></location>7</text>
<text><location><page_17><loc_53><loc_69><loc_53><loc_70></location>1</text>
<text><location><page_17><loc_53><loc_67><loc_53><loc_68></location>9</text>
<text><location><page_17><loc_53><loc_67><loc_53><loc_67></location>0</text>
<text><location><page_17><loc_53><loc_67><loc_53><loc_67></location>0</text>
<text><location><page_17><loc_53><loc_66><loc_53><loc_67></location>.</text>
<text><location><page_17><loc_53><loc_66><loc_53><loc_66></location>0</text>
<text><location><page_17><loc_53><loc_65><loc_53><loc_66></location>±</text>
<text><location><page_17><loc_53><loc_64><loc_53><loc_65></location>9</text>
<text><location><page_17><loc_53><loc_64><loc_53><loc_64></location>3</text>
<text><location><page_17><loc_53><loc_63><loc_53><loc_64></location>9</text>
<text><location><page_17><loc_53><loc_63><loc_53><loc_63></location>.</text>
<text><location><page_17><loc_53><loc_63><loc_53><loc_63></location>7</text>
<text><location><page_17><loc_53><loc_62><loc_53><loc_63></location>1</text>
<text><location><page_17><loc_53><loc_61><loc_53><loc_61></location>9</text>
<text><location><page_17><loc_53><loc_60><loc_53><loc_61></location>0</text>
<text><location><page_17><loc_53><loc_60><loc_53><loc_60></location>0</text>
<text><location><page_17><loc_53><loc_59><loc_53><loc_60></location>.</text>
<text><location><page_17><loc_53><loc_59><loc_53><loc_59></location>0</text>
<text><location><page_17><loc_53><loc_58><loc_53><loc_59></location>±</text>
<text><location><page_17><loc_53><loc_57><loc_53><loc_58></location>1</text>
<text><location><page_17><loc_53><loc_57><loc_53><loc_57></location>2</text>
<text><location><page_17><loc_53><loc_56><loc_53><loc_57></location>1</text>
<text><location><page_17><loc_53><loc_56><loc_53><loc_56></location>.</text>
<text><location><page_17><loc_53><loc_56><loc_53><loc_56></location>8</text>
<text><location><page_17><loc_53><loc_55><loc_53><loc_56></location>1</text>
<text><location><page_17><loc_54><loc_83><loc_55><loc_83></location>0</text>
<text><location><page_17><loc_54><loc_82><loc_55><loc_83></location>8</text>
<text><location><page_17><loc_54><loc_82><loc_55><loc_82></location>5</text>
<text><location><page_17><loc_54><loc_82><loc_55><loc_82></location>.</text>
<text><location><page_17><loc_54><loc_81><loc_55><loc_82></location>2</text>
<text><location><page_17><loc_54><loc_78><loc_55><loc_79></location>0</text>
<text><location><page_17><loc_54><loc_78><loc_55><loc_78></location>1</text>
<text><location><page_17><loc_54><loc_78><loc_55><loc_78></location>.</text>
<text><location><page_17><loc_54><loc_77><loc_55><loc_78></location>0</text>
<text><location><page_17><loc_54><loc_74><loc_55><loc_75></location>8</text>
<text><location><page_17><loc_54><loc_74><loc_55><loc_74></location>2</text>
<text><location><page_17><loc_54><loc_74><loc_55><loc_74></location>0</text>
<text><location><page_17><loc_54><loc_73><loc_55><loc_74></location>.</text>
<text><location><page_17><loc_54><loc_73><loc_55><loc_73></location>0</text>
<text><location><page_17><loc_54><loc_72><loc_54><loc_73></location>±</text>
<text><location><page_17><loc_54><loc_71><loc_55><loc_72></location>4</text>
<text><location><page_17><loc_54><loc_71><loc_55><loc_71></location>1</text>
<text><location><page_17><loc_54><loc_70><loc_55><loc_71></location>8</text>
<text><location><page_17><loc_54><loc_70><loc_55><loc_70></location>.</text>
<text><location><page_17><loc_54><loc_70><loc_55><loc_70></location>8</text>
<text><location><page_17><loc_54><loc_69><loc_55><loc_70></location>1</text>
<text><location><page_17><loc_54><loc_67><loc_55><loc_68></location>1</text>
<text><location><page_17><loc_54><loc_67><loc_55><loc_67></location>3</text>
<text><location><page_17><loc_54><loc_67><loc_55><loc_67></location>0</text>
<text><location><page_17><loc_54><loc_66><loc_55><loc_67></location>.</text>
<text><location><page_17><loc_54><loc_66><loc_55><loc_66></location>0</text>
<text><location><page_17><loc_54><loc_65><loc_54><loc_66></location>±</text>
<text><location><page_17><loc_54><loc_64><loc_55><loc_65></location>9</text>
<text><location><page_17><loc_54><loc_64><loc_55><loc_64></location>7</text>
<text><location><page_17><loc_54><loc_63><loc_55><loc_64></location>4</text>
<text><location><page_17><loc_54><loc_63><loc_55><loc_63></location>.</text>
<text><location><page_17><loc_54><loc_63><loc_55><loc_63></location>9</text>
<text><location><page_17><loc_54><loc_62><loc_55><loc_63></location>1</text>
<text><location><page_17><loc_54><loc_61><loc_55><loc_61></location>2</text>
<text><location><page_17><loc_54><loc_60><loc_55><loc_61></location>3</text>
<text><location><page_17><loc_54><loc_60><loc_55><loc_60></location>0</text>
<text><location><page_17><loc_54><loc_59><loc_55><loc_60></location>.</text>
<text><location><page_17><loc_54><loc_59><loc_55><loc_59></location>0</text>
<text><location><page_17><loc_54><loc_58><loc_54><loc_59></location>±</text>
<text><location><page_17><loc_54><loc_57><loc_55><loc_58></location>6</text>
<text><location><page_17><loc_54><loc_57><loc_55><loc_57></location>1</text>
<text><location><page_17><loc_54><loc_56><loc_55><loc_57></location>9</text>
<text><location><page_17><loc_54><loc_56><loc_55><loc_56></location>.</text>
<text><location><page_17><loc_54><loc_56><loc_55><loc_56></location>9</text>
<text><location><page_17><loc_54><loc_55><loc_55><loc_56></location>1</text>
<text><location><page_17><loc_55><loc_83><loc_56><loc_83></location>6</text>
<text><location><page_17><loc_55><loc_82><loc_56><loc_83></location>0</text>
<text><location><page_17><loc_55><loc_82><loc_56><loc_82></location>8</text>
<text><location><page_17><loc_55><loc_82><loc_56><loc_82></location>.</text>
<text><location><page_17><loc_55><loc_81><loc_56><loc_82></location>1</text>
<text><location><page_17><loc_55><loc_78><loc_56><loc_79></location>0</text>
<text><location><page_17><loc_55><loc_78><loc_56><loc_78></location>1</text>
<text><location><page_17><loc_55><loc_78><loc_56><loc_78></location>.</text>
<text><location><page_17><loc_55><loc_77><loc_56><loc_78></location>0</text>
<text><location><page_17><loc_55><loc_74><loc_56><loc_75></location>8</text>
<text><location><page_17><loc_55><loc_74><loc_56><loc_74></location>3</text>
<text><location><page_17><loc_55><loc_74><loc_56><loc_74></location>0</text>
<text><location><page_17><loc_55><loc_73><loc_56><loc_74></location>.</text>
<text><location><page_17><loc_55><loc_73><loc_56><loc_73></location>0</text>
<text><location><page_17><loc_55><loc_72><loc_56><loc_73></location>±</text>
<text><location><page_17><loc_55><loc_71><loc_56><loc_72></location>3</text>
<text><location><page_17><loc_55><loc_71><loc_56><loc_71></location>5</text>
<text><location><page_17><loc_55><loc_70><loc_56><loc_71></location>9</text>
<text><location><page_17><loc_55><loc_70><loc_56><loc_70></location>.</text>
<text><location><page_17><loc_55><loc_70><loc_56><loc_70></location>9</text>
<text><location><page_17><loc_55><loc_69><loc_56><loc_70></location>1</text>
<text><location><page_17><loc_55><loc_67><loc_56><loc_68></location>2</text>
<text><location><page_17><loc_55><loc_67><loc_56><loc_67></location>3</text>
<text><location><page_17><loc_55><loc_67><loc_56><loc_67></location>0</text>
<text><location><page_17><loc_55><loc_66><loc_56><loc_67></location>.</text>
<text><location><page_17><loc_55><loc_66><loc_56><loc_66></location>0</text>
<text><location><page_17><loc_55><loc_65><loc_56><loc_66></location>±</text>
<text><location><page_17><loc_55><loc_64><loc_56><loc_65></location>9</text>
<text><location><page_17><loc_55><loc_64><loc_56><loc_64></location>2</text>
<text><location><page_17><loc_55><loc_63><loc_56><loc_64></location>2</text>
<text><location><page_17><loc_55><loc_63><loc_56><loc_63></location>.</text>
<text><location><page_17><loc_55><loc_63><loc_56><loc_63></location>0</text>
<text><location><page_17><loc_55><loc_62><loc_56><loc_63></location>2</text>
<text><location><page_17><loc_55><loc_61><loc_56><loc_61></location>4</text>
<text><location><page_17><loc_55><loc_60><loc_56><loc_61></location>3</text>
<text><location><page_17><loc_55><loc_60><loc_56><loc_60></location>0</text>
<text><location><page_17><loc_55><loc_59><loc_56><loc_60></location>.</text>
<text><location><page_17><loc_55><loc_59><loc_56><loc_59></location>0</text>
<text><location><page_17><loc_55><loc_58><loc_56><loc_59></location>±</text>
<text><location><page_17><loc_55><loc_57><loc_56><loc_58></location>1</text>
<text><location><page_17><loc_55><loc_57><loc_56><loc_57></location>0</text>
<text><location><page_17><loc_55><loc_56><loc_56><loc_57></location>6</text>
<text><location><page_17><loc_55><loc_56><loc_56><loc_56></location>.</text>
<text><location><page_17><loc_55><loc_56><loc_56><loc_56></location>0</text>
<text><location><page_17><loc_55><loc_55><loc_56><loc_56></location>2</text>
<text><location><page_17><loc_56><loc_83><loc_57><loc_83></location>4</text>
<text><location><page_17><loc_56><loc_82><loc_57><loc_83></location>6</text>
<text><location><page_17><loc_56><loc_82><loc_57><loc_82></location>0</text>
<text><location><page_17><loc_56><loc_82><loc_57><loc_82></location>.</text>
<text><location><page_17><loc_56><loc_81><loc_57><loc_82></location>2</text>
<text><location><page_17><loc_56><loc_78><loc_57><loc_79></location>0</text>
<text><location><page_17><loc_56><loc_78><loc_57><loc_78></location>1</text>
<text><location><page_17><loc_56><loc_78><loc_57><loc_78></location>.</text>
<text><location><page_17><loc_56><loc_77><loc_57><loc_78></location>0</text>
<text><location><page_17><loc_56><loc_74><loc_57><loc_75></location>2</text>
<text><location><page_17><loc_56><loc_74><loc_57><loc_74></location>2</text>
<text><location><page_17><loc_56><loc_74><loc_57><loc_74></location>0</text>
<text><location><page_17><loc_56><loc_73><loc_57><loc_74></location>.</text>
<text><location><page_17><loc_56><loc_73><loc_57><loc_73></location>0</text>
<text><location><page_17><loc_56><loc_72><loc_57><loc_73></location>±</text>
<text><location><page_17><loc_56><loc_71><loc_57><loc_72></location>6</text>
<text><location><page_17><loc_56><loc_71><loc_57><loc_71></location>5</text>
<text><location><page_17><loc_56><loc_70><loc_57><loc_71></location>2</text>
<text><location><page_17><loc_56><loc_70><loc_57><loc_70></location>.</text>
<text><location><page_17><loc_56><loc_70><loc_57><loc_70></location>9</text>
<text><location><page_17><loc_56><loc_69><loc_57><loc_70></location>1</text>
<text><location><page_17><loc_56><loc_67><loc_57><loc_68></location>3</text>
<text><location><page_17><loc_56><loc_67><loc_57><loc_67></location>2</text>
<text><location><page_17><loc_56><loc_67><loc_57><loc_67></location>0</text>
<text><location><page_17><loc_56><loc_66><loc_57><loc_67></location>.</text>
<text><location><page_17><loc_56><loc_66><loc_57><loc_66></location>0</text>
<text><location><page_17><loc_56><loc_65><loc_57><loc_66></location>±</text>
<text><location><page_17><loc_56><loc_64><loc_57><loc_65></location>0</text>
<text><location><page_17><loc_56><loc_64><loc_57><loc_64></location>8</text>
<text><location><page_17><loc_56><loc_63><loc_57><loc_64></location>6</text>
<text><location><page_17><loc_56><loc_63><loc_57><loc_63></location>.</text>
<text><location><page_17><loc_56><loc_63><loc_57><loc_63></location>9</text>
<text><location><page_17><loc_56><loc_62><loc_57><loc_63></location>1</text>
<text><location><page_17><loc_56><loc_61><loc_57><loc_61></location>5</text>
<text><location><page_17><loc_56><loc_60><loc_57><loc_61></location>2</text>
<text><location><page_17><loc_56><loc_60><loc_57><loc_60></location>0</text>
<text><location><page_17><loc_56><loc_59><loc_57><loc_60></location>.</text>
<text><location><page_17><loc_56><loc_59><loc_57><loc_59></location>0</text>
<text><location><page_17><loc_56><loc_58><loc_57><loc_59></location>±</text>
<text><location><page_17><loc_56><loc_57><loc_57><loc_58></location>8</text>
<text><location><page_17><loc_56><loc_57><loc_57><loc_57></location>8</text>
<text><location><page_17><loc_56><loc_56><loc_57><loc_57></location>0</text>
<text><location><page_17><loc_56><loc_56><loc_57><loc_56></location>.</text>
<text><location><page_17><loc_56><loc_56><loc_57><loc_56></location>0</text>
<text><location><page_17><loc_56><loc_55><loc_57><loc_56></location>2</text>
<text><location><page_17><loc_57><loc_83><loc_58><loc_83></location>0</text>
<text><location><page_17><loc_57><loc_82><loc_58><loc_83></location>8</text>
<text><location><page_17><loc_57><loc_82><loc_58><loc_82></location>5</text>
<text><location><page_17><loc_57><loc_82><loc_58><loc_82></location>.</text>
<text><location><page_17><loc_57><loc_81><loc_58><loc_82></location>2</text>
<text><location><page_17><loc_57><loc_78><loc_58><loc_79></location>0</text>
<text><location><page_17><loc_57><loc_78><loc_58><loc_78></location>1</text>
<text><location><page_17><loc_57><loc_78><loc_58><loc_78></location>.</text>
<text><location><page_17><loc_57><loc_77><loc_58><loc_78></location>0</text>
<text><location><page_17><loc_57><loc_73><loc_58><loc_73></location>.</text>
<text><location><page_17><loc_57><loc_72><loc_58><loc_73></location>.</text>
<text><location><page_17><loc_57><loc_72><loc_58><loc_72></location>.</text>
<text><location><page_17><loc_57><loc_72><loc_58><loc_72></location>.</text>
<text><location><page_17><loc_57><loc_71><loc_58><loc_72></location>.</text>
<text><location><page_17><loc_57><loc_71><loc_58><loc_71></location>.</text>
<text><location><page_17><loc_57><loc_67><loc_58><loc_68></location>0</text>
<text><location><page_17><loc_57><loc_67><loc_58><loc_67></location>1</text>
<text><location><page_17><loc_57><loc_67><loc_58><loc_67></location>1</text>
<text><location><page_17><loc_57><loc_66><loc_58><loc_67></location>.</text>
<text><location><page_17><loc_57><loc_66><loc_58><loc_66></location>0</text>
<text><location><page_17><loc_57><loc_65><loc_58><loc_66></location>±</text>
<text><location><page_17><loc_57><loc_64><loc_58><loc_65></location>1</text>
<text><location><page_17><loc_57><loc_64><loc_58><loc_64></location>8</text>
<text><location><page_17><loc_57><loc_63><loc_58><loc_64></location>4</text>
<text><location><page_17><loc_57><loc_63><loc_58><loc_63></location>.</text>
<text><location><page_17><loc_57><loc_63><loc_58><loc_63></location>0</text>
<text><location><page_17><loc_57><loc_62><loc_58><loc_63></location>2</text>
<text><location><page_17><loc_57><loc_61><loc_58><loc_61></location>4</text>
<text><location><page_17><loc_57><loc_60><loc_58><loc_61></location>4</text>
<text><location><page_17><loc_57><loc_60><loc_58><loc_60></location>1</text>
<text><location><page_17><loc_57><loc_59><loc_58><loc_60></location>.</text>
<text><location><page_17><loc_57><loc_59><loc_58><loc_59></location>0</text>
<text><location><page_17><loc_57><loc_58><loc_58><loc_59></location>±</text>
<text><location><page_17><loc_57><loc_57><loc_58><loc_58></location>9</text>
<text><location><page_17><loc_57><loc_57><loc_58><loc_57></location>8</text>
<text><location><page_17><loc_57><loc_56><loc_58><loc_57></location>8</text>
<text><location><page_17><loc_57><loc_56><loc_58><loc_56></location>.</text>
<text><location><page_17><loc_57><loc_56><loc_58><loc_56></location>0</text>
<text><location><page_17><loc_57><loc_55><loc_58><loc_56></location>2</text>
<text><location><page_17><loc_59><loc_83><loc_59><loc_83></location>0</text>
<text><location><page_17><loc_59><loc_82><loc_59><loc_83></location>8</text>
<text><location><page_17><loc_59><loc_82><loc_59><loc_82></location>5</text>
<text><location><page_17><loc_59><loc_82><loc_59><loc_82></location>.</text>
<text><location><page_17><loc_59><loc_81><loc_59><loc_82></location>2</text>
<text><location><page_17><loc_59><loc_78><loc_59><loc_79></location>0</text>
<text><location><page_17><loc_59><loc_78><loc_59><loc_78></location>1</text>
<text><location><page_17><loc_59><loc_78><loc_59><loc_78></location>.</text>
<text><location><page_17><loc_59><loc_77><loc_59><loc_78></location>0</text>
<text><location><page_17><loc_59><loc_74><loc_59><loc_75></location>0</text>
<text><location><page_17><loc_59><loc_74><loc_59><loc_74></location>6</text>
<text><location><page_17><loc_59><loc_74><loc_59><loc_74></location>1</text>
<text><location><page_17><loc_59><loc_73><loc_59><loc_74></location>.</text>
<text><location><page_17><loc_59><loc_73><loc_59><loc_73></location>0</text>
<text><location><page_17><loc_59><loc_72><loc_59><loc_73></location>±</text>
<text><location><page_17><loc_59><loc_71><loc_59><loc_72></location>6</text>
<text><location><page_17><loc_59><loc_71><loc_59><loc_71></location>0</text>
<text><location><page_17><loc_59><loc_70><loc_59><loc_71></location>4</text>
<text><location><page_17><loc_59><loc_70><loc_59><loc_70></location>.</text>
<text><location><page_17><loc_59><loc_70><loc_59><loc_70></location>1</text>
<text><location><page_17><loc_59><loc_69><loc_59><loc_70></location>2</text>
<text><location><page_17><loc_59><loc_67><loc_59><loc_68></location>4</text>
<text><location><page_17><loc_59><loc_67><loc_59><loc_67></location>2</text>
<text><location><page_17><loc_59><loc_67><loc_59><loc_67></location>1</text>
<text><location><page_17><loc_59><loc_66><loc_59><loc_67></location>.</text>
<text><location><page_17><loc_59><loc_66><loc_59><loc_66></location>0</text>
<text><location><page_17><loc_59><loc_65><loc_59><loc_66></location>±</text>
<text><location><page_17><loc_59><loc_64><loc_59><loc_65></location>9</text>
<text><location><page_17><loc_59><loc_64><loc_59><loc_64></location>3</text>
<text><location><page_17><loc_59><loc_63><loc_59><loc_64></location>5</text>
<text><location><page_17><loc_59><loc_63><loc_59><loc_63></location>.</text>
<text><location><page_17><loc_59><loc_63><loc_59><loc_63></location>1</text>
<text><location><page_17><loc_59><loc_62><loc_59><loc_63></location>2</text>
<text><location><page_17><loc_59><loc_61><loc_59><loc_61></location>4</text>
<text><location><page_17><loc_59><loc_60><loc_59><loc_61></location>3</text>
<text><location><page_17><loc_59><loc_60><loc_59><loc_60></location>1</text>
<text><location><page_17><loc_59><loc_59><loc_59><loc_60></location>.</text>
<text><location><page_17><loc_59><loc_59><loc_59><loc_59></location>0</text>
<text><location><page_17><loc_59><loc_58><loc_59><loc_59></location>±</text>
<text><location><page_17><loc_59><loc_57><loc_59><loc_58></location>3</text>
<text><location><page_17><loc_59><loc_57><loc_59><loc_57></location>5</text>
<text><location><page_17><loc_59><loc_56><loc_59><loc_57></location>7</text>
<text><location><page_17><loc_59><loc_56><loc_59><loc_56></location>.</text>
<text><location><page_17><loc_59><loc_56><loc_59><loc_56></location>1</text>
<text><location><page_17><loc_59><loc_55><loc_59><loc_56></location>2</text>
<table>
<location><page_17><loc_15><loc_40><loc_84><loc_55></location>
</table>
<text><location><page_17><loc_48><loc_40><loc_48><loc_40></location>0</text>
<text><location><page_17><loc_48><loc_39><loc_48><loc_40></location>2</text>
<text><location><page_17><loc_48><loc_39><loc_48><loc_39></location>.</text>
<text><location><page_17><loc_48><loc_39><loc_48><loc_39></location>5</text>
<text><location><page_17><loc_48><loc_38><loc_48><loc_39></location>0</text>
<text><location><page_17><loc_48><loc_38><loc_48><loc_38></location>4</text>
<text><location><page_17><loc_48><loc_37><loc_48><loc_38></location>3</text>
<text><location><page_17><loc_48><loc_36><loc_48><loc_37></location>0</text>
<text><location><page_17><loc_48><loc_36><loc_48><loc_37></location>3</text>
<text><location><page_17><loc_48><loc_34><loc_48><loc_35></location>0</text>
<text><location><page_17><loc_48><loc_34><loc_48><loc_34></location>5</text>
<text><location><page_17><loc_48><loc_34><loc_48><loc_34></location>7</text>
<text><location><page_17><loc_48><loc_33><loc_48><loc_34></location>.</text>
<text><location><page_17><loc_48><loc_33><loc_48><loc_33></location>6</text>
<text><location><page_17><loc_48><loc_32><loc_48><loc_33></location>0</text>
<text><location><page_17><loc_48><loc_32><loc_48><loc_32></location>4</text>
<text><location><page_17><loc_48><loc_31><loc_48><loc_32></location>3</text>
<text><location><page_17><loc_48><loc_31><loc_48><loc_31></location>1</text>
<text><location><page_17><loc_48><loc_30><loc_48><loc_31></location>0</text>
<text><location><page_17><loc_48><loc_22><loc_48><loc_22></location>2</text>
<text><location><page_17><loc_48><loc_21><loc_48><loc_22></location>8</text>
<text><location><page_17><loc_48><loc_21><loc_48><loc_21></location>-</text>
<text><location><page_17><loc_48><loc_20><loc_48><loc_21></location>ZK</text>
<text><location><page_17><loc_48><loc_18><loc_48><loc_19></location>.</text>
<text><location><page_17><loc_48><loc_18><loc_48><loc_18></location>.</text>
<text><location><page_17><loc_48><loc_18><loc_48><loc_18></location>.</text>
<text><location><page_17><loc_48><loc_18><loc_48><loc_18></location>.</text>
<text><location><page_17><loc_48><loc_17><loc_48><loc_18></location>.</text>
<text><location><page_17><loc_48><loc_17><loc_48><loc_17></location>.</text>
<text><location><page_17><loc_48><loc_17><loc_48><loc_17></location>5</text>
<text><location><page_17><loc_48><loc_16><loc_48><loc_17></location>2</text>
<text><location><page_17><loc_48><loc_16><loc_48><loc_16></location>2</text>
<text><location><page_17><loc_49><loc_40><loc_50><loc_40></location>1</text>
<text><location><page_17><loc_49><loc_39><loc_50><loc_40></location>3</text>
<text><location><page_17><loc_49><loc_39><loc_50><loc_39></location>.</text>
<text><location><page_17><loc_49><loc_39><loc_50><loc_39></location>6</text>
<text><location><page_17><loc_49><loc_38><loc_50><loc_39></location>4</text>
<text><location><page_17><loc_49><loc_38><loc_50><loc_38></location>3</text>
<text><location><page_17><loc_49><loc_37><loc_50><loc_38></location>3</text>
<text><location><page_17><loc_49><loc_37><loc_50><loc_37></location>0</text>
<text><location><page_17><loc_49><loc_36><loc_50><loc_37></location>3</text>
<text><location><page_17><loc_49><loc_34><loc_50><loc_35></location>7</text>
<text><location><page_17><loc_49><loc_34><loc_50><loc_34></location>7</text>
<text><location><page_17><loc_49><loc_34><loc_50><loc_34></location>2</text>
<text><location><page_17><loc_49><loc_33><loc_50><loc_34></location>.</text>
<text><location><page_17><loc_49><loc_33><loc_50><loc_33></location>7</text>
<text><location><page_17><loc_49><loc_32><loc_50><loc_33></location>0</text>
<text><location><page_17><loc_49><loc_32><loc_50><loc_32></location>4</text>
<text><location><page_17><loc_49><loc_31><loc_50><loc_32></location>3</text>
<text><location><page_17><loc_49><loc_31><loc_50><loc_31></location>1</text>
<text><location><page_17><loc_49><loc_30><loc_50><loc_31></location>0</text>
<text><location><page_17><loc_49><loc_22><loc_50><loc_22></location>3</text>
<text><location><page_17><loc_49><loc_21><loc_50><loc_22></location>8</text>
<text><location><page_17><loc_49><loc_21><loc_50><loc_21></location>-</text>
<text><location><page_17><loc_49><loc_20><loc_50><loc_21></location>ZK</text>
<text><location><page_17><loc_49><loc_18><loc_50><loc_19></location>.</text>
<text><location><page_17><loc_49><loc_18><loc_50><loc_18></location>.</text>
<text><location><page_17><loc_49><loc_18><loc_50><loc_18></location>.</text>
<text><location><page_17><loc_49><loc_18><loc_50><loc_18></location>.</text>
<text><location><page_17><loc_49><loc_17><loc_50><loc_18></location>.</text>
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<text><location><page_17><loc_59><loc_30><loc_59><loc_31></location>0</text>
<text><location><page_17><loc_59><loc_22><loc_59><loc_22></location>1</text>
<text><location><page_17><loc_59><loc_21><loc_59><loc_22></location>9</text>
<text><location><page_17><loc_59><loc_21><loc_59><loc_21></location>-</text>
<text><location><page_17><loc_59><loc_20><loc_59><loc_21></location>ZK</text>
<text><location><page_17><loc_59><loc_18><loc_59><loc_19></location>.</text>
<text><location><page_17><loc_59><loc_18><loc_59><loc_18></location>.</text>
<text><location><page_17><loc_59><loc_18><loc_59><loc_18></location>.</text>
<text><location><page_17><loc_59><loc_18><loc_59><loc_18></location>.</text>
<text><location><page_17><loc_59><loc_17><loc_59><loc_18></location>.</text>
<text><location><page_17><loc_59><loc_17><loc_59><loc_17></location>.</text>
<text><location><page_17><loc_59><loc_17><loc_59><loc_17></location>4</text>
<text><location><page_17><loc_59><loc_16><loc_59><loc_17></location>3</text>
<text><location><page_17><loc_59><loc_16><loc_59><loc_16></location>2</text>
<text><location><page_17><loc_45><loc_82><loc_46><loc_82></location>a</text>
<text><location><page_17><loc_45><loc_81><loc_46><loc_82></location>r</text>
<text><location><page_17><loc_45><loc_80><loc_46><loc_80></location>)</text>
<text><location><page_17><loc_45><loc_79><loc_46><loc_79></location>V</text>
<text><location><page_17><loc_45><loc_78><loc_46><loc_79></location>-</text>
<text><location><page_17><loc_45><loc_77><loc_46><loc_78></location>B</text>
<text><location><page_17><loc_45><loc_77><loc_46><loc_77></location>(</text>
<text><location><page_17><loc_45><loc_76><loc_46><loc_77></location>E</text>
<text><location><page_17><loc_45><loc_72><loc_46><loc_72></location>C</text>
<text><location><page_17><loc_45><loc_71><loc_46><loc_72></location>I</text>
<text><location><page_17><loc_45><loc_65><loc_46><loc_66></location>C</text>
<text><location><page_17><loc_45><loc_64><loc_46><loc_65></location>R</text>
<text><location><page_17><loc_45><loc_58><loc_46><loc_58></location>V</text>
<text><location><page_17><loc_45><loc_39><loc_46><loc_39></location>.</text>
<text><location><page_17><loc_45><loc_39><loc_46><loc_39></location>l</text>
<text><location><page_17><loc_45><loc_38><loc_46><loc_39></location>c</text>
<text><location><page_17><loc_45><loc_38><loc_46><loc_38></location>e</text>
<text><location><page_17><loc_45><loc_37><loc_46><loc_38></location>D</text>
<text><location><page_17><loc_45><loc_33><loc_46><loc_33></location>.</text>
<text><location><page_17><loc_45><loc_32><loc_46><loc_33></location>A</text>
<text><location><page_17><loc_45><loc_32><loc_46><loc_32></location>.</text>
<text><location><page_17><loc_45><loc_32><loc_46><loc_32></location>R</text>
<text><location><page_17><loc_45><loc_28><loc_46><loc_29></location>D</text>
<text><location><page_17><loc_45><loc_28><loc_46><loc_28></location>I</text>
<text><location><page_17><loc_45><loc_26><loc_46><loc_27></location>D</text>
<text><location><page_17><loc_45><loc_26><loc_46><loc_26></location>I</text>
<text><location><page_17><loc_45><loc_24><loc_46><loc_24></location>D</text>
<text><location><page_17><loc_45><loc_24><loc_46><loc_24></location>I</text>
<text><location><page_17><loc_45><loc_21><loc_46><loc_22></location>D</text>
<text><location><page_17><loc_45><loc_21><loc_46><loc_21></location>I</text>
<text><location><page_17><loc_45><loc_17><loc_46><loc_18></location>D</text>
<text><location><page_17><loc_45><loc_17><loc_46><loc_17></location>I</text>
<text><location><page_17><loc_46><loc_40><loc_47><loc_40></location>)</text>
<text><location><page_17><loc_46><loc_39><loc_47><loc_40></location>0</text>
<text><location><page_17><loc_46><loc_39><loc_47><loc_39></location>.</text>
<text><location><page_17><loc_46><loc_38><loc_47><loc_39></location>0</text>
<text><location><page_17><loc_46><loc_38><loc_47><loc_39></location>0</text>
<text><location><page_17><loc_46><loc_38><loc_47><loc_38></location>0</text>
<text><location><page_17><loc_46><loc_37><loc_47><loc_38></location>2</text>
<text><location><page_17><loc_46><loc_37><loc_47><loc_37></location>J</text>
<text><location><page_17><loc_46><loc_36><loc_47><loc_37></location>(</text>
<text><location><page_17><loc_46><loc_34><loc_47><loc_34></location>)</text>
<text><location><page_17><loc_46><loc_33><loc_47><loc_34></location>0</text>
<text><location><page_17><loc_46><loc_33><loc_47><loc_33></location>.</text>
<text><location><page_17><loc_46><loc_33><loc_47><loc_33></location>0</text>
<text><location><page_17><loc_46><loc_32><loc_47><loc_33></location>0</text>
<text><location><page_17><loc_46><loc_32><loc_47><loc_32></location>0</text>
<text><location><page_17><loc_46><loc_31><loc_47><loc_32></location>2</text>
<text><location><page_17><loc_46><loc_31><loc_47><loc_31></location>J</text>
<text><location><page_17><loc_46><loc_31><loc_47><loc_31></location>(</text>
<text><location><page_18><loc_12><loc_89><loc_88><loc_90></location>Comparison between this Study and Previous studies of V Photometry for M33 Star Clusters Considered Here</text>
<table>
<location><page_18><loc_24><loc_76><loc_76><loc_89></location>
<caption>TABLE 2</caption>
</table>
<unordered_list>
<list_item><location><page_18><loc_8><loc_74><loc_74><loc_75></location>a The star cluster names following the naming convention of Park & Lee (2007) or San Roman et al. (2009).</list_item>
<list_item><location><page_18><loc_8><loc_72><loc_63><loc_73></location>b The star cluster names following the naming convention of Zloczewski & Kaluzny (2009).</list_item>
<list_item><location><page_18><loc_8><loc_71><loc_57><loc_72></location>c The photometry obtained by Park & Lee (2007) or by San Roman et al. (2009).</list_item>
<list_item><location><page_18><loc_8><loc_70><loc_45><loc_71></location>d The photometry obtained by Zloczewski & Kaluzny (2009).</list_item>
<list_item><location><page_18><loc_8><loc_69><loc_33><loc_70></location>e The photometry obtained in this paper.</list_item>
<list_item><location><page_18><loc_8><loc_67><loc_92><loc_69></location>f The magnitude difference between this study and Park & Lee (2007) or San Roman et al. (2009) (this study minus Park & Lee 2007 or San Roman et al. 2009).</list_item>
<list_item><location><page_18><loc_8><loc_66><loc_86><loc_67></location>g The magnitude difference between this study and Zloczewski & Kaluzny (2009) (this study minus Zloczewski & Kaluzny 2009).</list_item>
<list_item><location><page_18><loc_8><loc_64><loc_44><loc_66></location>h The aperture radius of photometry adopted in this paper.</list_item>
</unordered_list>
<text><location><page_19><loc_12><loc_51><loc_13><loc_52></location>3</text>
<text><location><page_19><loc_12><loc_50><loc_13><loc_51></location>E</text>
<text><location><page_19><loc_12><loc_50><loc_13><loc_50></location>L</text>
<text><location><page_19><loc_12><loc_48><loc_13><loc_50></location>AB</text>
<text><location><page_19><loc_12><loc_47><loc_13><loc_48></location>T</text>
<text><location><page_19><loc_14><loc_65><loc_15><loc_65></location>)</text>
<text><location><page_19><loc_14><loc_64><loc_15><loc_65></location>2</text>
<text><location><page_19><loc_14><loc_64><loc_15><loc_64></location>1</text>
<text><location><page_19><loc_14><loc_63><loc_15><loc_64></location>0</text>
<text><location><page_19><loc_14><loc_63><loc_15><loc_63></location>2</text>
<text><location><page_19><loc_14><loc_62><loc_15><loc_63></location>(</text>
<text><location><page_19><loc_14><loc_61><loc_15><loc_62></location>a</text>
<text><location><page_19><loc_14><loc_60><loc_15><loc_61></location>M</text>
<text><location><page_19><loc_14><loc_59><loc_15><loc_60></location>n</text>
<text><location><page_19><loc_14><loc_59><loc_15><loc_59></location>i</text>
<text><location><page_19><loc_14><loc_58><loc_15><loc_58></location>s</text>
<text><location><page_19><loc_14><loc_57><loc_15><loc_58></location>r</text>
<text><location><page_19><loc_14><loc_57><loc_15><loc_57></location>e</text>
<text><location><page_19><loc_14><loc_56><loc_15><loc_57></location>t</text>
<text><location><page_19><loc_14><loc_56><loc_15><loc_56></location>s</text>
<text><location><page_19><loc_14><loc_55><loc_15><loc_56></location>u</text>
<text><location><page_19><loc_14><loc_55><loc_15><loc_55></location>l</text>
<text><location><page_19><loc_14><loc_54><loc_15><loc_55></location>C</text>
<text><location><page_19><loc_14><loc_53><loc_15><loc_53></location>r</text>
<text><location><page_19><loc_14><loc_52><loc_15><loc_53></location>a</text>
<text><location><page_19><loc_14><loc_52><loc_15><loc_52></location>t</text>
<text><location><page_19><loc_14><loc_51><loc_15><loc_52></location>S</text>
<text><location><page_19><loc_14><loc_50><loc_15><loc_51></location>3</text>
<text><location><page_19><loc_14><loc_50><loc_15><loc_50></location>3</text>
<text><location><page_19><loc_14><loc_49><loc_15><loc_50></location>M</text>
<text><location><page_19><loc_14><loc_48><loc_15><loc_48></location>7</text>
<text><location><page_19><loc_14><loc_47><loc_15><loc_48></location>7</text>
<text><location><page_19><loc_14><loc_47><loc_15><loc_47></location>2</text>
<text><location><page_19><loc_14><loc_46><loc_15><loc_46></location>f</text>
<text><location><page_19><loc_14><loc_45><loc_15><loc_46></location>o</text>
<text><location><page_19><loc_14><loc_44><loc_15><loc_45></location>y</text>
<text><location><page_19><loc_14><loc_43><loc_15><loc_44></location>r</text>
<text><location><page_19><loc_14><loc_43><loc_15><loc_43></location>t</text>
<text><location><page_19><loc_14><loc_42><loc_15><loc_43></location>e</text>
<text><location><page_19><loc_14><loc_42><loc_15><loc_42></location>m</text>
<text><location><page_19><loc_14><loc_41><loc_15><loc_42></location>o</text>
<text><location><page_19><loc_14><loc_40><loc_15><loc_41></location>t</text>
<text><location><page_19><loc_14><loc_40><loc_15><loc_40></location>o</text>
<text><location><page_19><loc_14><loc_39><loc_15><loc_40></location>h</text>
<text><location><page_19><loc_14><loc_38><loc_15><loc_39></location>P</text>
<text><location><page_19><loc_14><loc_37><loc_15><loc_38></location>I</text>
<text><location><page_19><loc_14><loc_37><loc_15><loc_37></location>R</text>
<text><location><page_19><loc_14><loc_36><loc_15><loc_36></location>V</text>
<text><location><page_19><loc_14><loc_35><loc_15><loc_36></location>B</text>
<text><location><page_19><loc_14><loc_34><loc_15><loc_35></location>U</text>
<text><location><page_19><loc_42><loc_93><loc_57><loc_94></location>Star clusters in M33</text>
<text><location><page_19><loc_90><loc_93><loc_92><loc_94></location>19</text>
<table>
<location><page_19><loc_15><loc_11><loc_84><loc_84></location>
</table>
<text><location><page_19><loc_84><loc_83><loc_85><loc_83></location>0</text>
<text><location><page_19><loc_84><loc_82><loc_85><loc_83></location>7</text>
<text><location><page_19><loc_84><loc_82><loc_85><loc_82></location>8</text>
<text><location><page_19><loc_84><loc_82><loc_85><loc_82></location>.</text>
<text><location><page_19><loc_84><loc_81><loc_85><loc_82></location>3</text>
<text><location><page_19><loc_84><loc_79><loc_85><loc_79></location>0</text>
<text><location><page_19><loc_84><loc_78><loc_85><loc_79></location>1</text>
<text><location><page_19><loc_84><loc_78><loc_85><loc_78></location>.</text>
<text><location><page_19><loc_84><loc_77><loc_85><loc_78></location>0</text>
<text><location><page_19><loc_84><loc_75><loc_85><loc_75></location>0</text>
<text><location><page_19><loc_84><loc_74><loc_85><loc_75></location>1</text>
<text><location><page_19><loc_84><loc_74><loc_85><loc_74></location>0</text>
<text><location><page_19><loc_84><loc_73><loc_85><loc_74></location>.</text>
<text><location><page_19><loc_84><loc_73><loc_85><loc_73></location>0</text>
<text><location><page_19><loc_84><loc_72><loc_85><loc_73></location>±</text>
<text><location><page_19><loc_84><loc_71><loc_85><loc_72></location>6</text>
<text><location><page_19><loc_84><loc_71><loc_85><loc_71></location>0</text>
<text><location><page_19><loc_84><loc_70><loc_85><loc_71></location>2</text>
<text><location><page_19><loc_84><loc_70><loc_85><loc_70></location>.</text>
<text><location><page_19><loc_84><loc_70><loc_85><loc_70></location>7</text>
<text><location><page_19><loc_84><loc_69><loc_85><loc_70></location>1</text>
<text><location><page_19><loc_84><loc_68><loc_85><loc_68></location>2</text>
<text><location><page_19><loc_84><loc_67><loc_85><loc_68></location>1</text>
<text><location><page_19><loc_84><loc_67><loc_85><loc_67></location>0</text>
<text><location><page_19><loc_84><loc_67><loc_85><loc_67></location>.</text>
<text><location><page_19><loc_84><loc_66><loc_85><loc_67></location>0</text>
<text><location><page_19><loc_84><loc_65><loc_85><loc_66></location>±</text>
<text><location><page_19><loc_84><loc_64><loc_85><loc_65></location>4</text>
<text><location><page_19><loc_84><loc_64><loc_85><loc_64></location>4</text>
<text><location><page_19><loc_84><loc_64><loc_85><loc_64></location>6</text>
<text><location><page_19><loc_84><loc_63><loc_85><loc_64></location>.</text>
<text><location><page_19><loc_84><loc_63><loc_85><loc_63></location>7</text>
<text><location><page_19><loc_84><loc_62><loc_85><loc_63></location>1</text>
<text><location><page_19><loc_84><loc_61><loc_85><loc_61></location>4</text>
<text><location><page_19><loc_84><loc_60><loc_85><loc_61></location>1</text>
<text><location><page_19><loc_84><loc_60><loc_85><loc_60></location>0</text>
<text><location><page_19><loc_84><loc_60><loc_85><loc_60></location>.</text>
<text><location><page_19><loc_84><loc_59><loc_85><loc_60></location>0</text>
<text><location><page_19><loc_84><loc_58><loc_85><loc_59></location>±</text>
<text><location><page_19><loc_84><loc_58><loc_85><loc_58></location>6</text>
<text><location><page_19><loc_84><loc_57><loc_85><loc_58></location>3</text>
<text><location><page_19><loc_84><loc_57><loc_85><loc_57></location>0</text>
<text><location><page_19><loc_84><loc_56><loc_85><loc_57></location>.</text>
<text><location><page_19><loc_84><loc_56><loc_85><loc_56></location>8</text>
<text><location><page_19><loc_84><loc_56><loc_85><loc_56></location>1</text>
<text><location><page_19><loc_84><loc_54><loc_85><loc_54></location>2</text>
<text><location><page_19><loc_84><loc_53><loc_85><loc_54></location>2</text>
<text><location><page_19><loc_84><loc_53><loc_85><loc_53></location>0</text>
<text><location><page_19><loc_84><loc_53><loc_85><loc_53></location>.</text>
<text><location><page_19><loc_84><loc_52><loc_85><loc_53></location>0</text>
<text><location><page_19><loc_84><loc_51><loc_85><loc_52></location>±</text>
<text><location><page_19><loc_84><loc_51><loc_85><loc_51></location>1</text>
<text><location><page_19><loc_84><loc_50><loc_85><loc_51></location>4</text>
<text><location><page_19><loc_84><loc_50><loc_85><loc_50></location>7</text>
<text><location><page_19><loc_84><loc_50><loc_85><loc_50></location>.</text>
<text><location><page_19><loc_84><loc_49><loc_85><loc_50></location>8</text>
<text><location><page_19><loc_84><loc_49><loc_85><loc_49></location>1</text>
<text><location><page_19><loc_84><loc_47><loc_85><loc_47></location>6</text>
<text><location><page_19><loc_84><loc_47><loc_85><loc_47></location>2</text>
<text><location><page_19><loc_84><loc_46><loc_85><loc_47></location>0</text>
<text><location><page_19><loc_84><loc_46><loc_85><loc_46></location>.</text>
<text><location><page_19><loc_84><loc_45><loc_85><loc_46></location>0</text>
<text><location><page_19><loc_84><loc_44><loc_85><loc_45></location>±</text>
<text><location><page_19><loc_84><loc_44><loc_85><loc_44></location>8</text>
<text><location><page_19><loc_84><loc_43><loc_85><loc_44></location>8</text>
<text><location><page_19><loc_84><loc_43><loc_85><loc_43></location>9</text>
<text><location><page_19><loc_84><loc_43><loc_85><loc_43></location>.</text>
<text><location><page_19><loc_84><loc_42><loc_85><loc_43></location>8</text>
<text><location><page_19><loc_84><loc_42><loc_85><loc_42></location>1</text>
<text><location><page_19><loc_84><loc_40><loc_85><loc_41></location>5</text>
<text><location><page_19><loc_84><loc_40><loc_85><loc_40></location>5</text>
<text><location><page_19><loc_84><loc_39><loc_85><loc_40></location>.</text>
<text><location><page_19><loc_84><loc_39><loc_85><loc_39></location>1</text>
<text><location><page_19><loc_84><loc_39><loc_85><loc_39></location>2</text>
<text><location><page_19><loc_84><loc_38><loc_85><loc_38></location>2</text>
<text><location><page_19><loc_84><loc_37><loc_85><loc_38></location>2</text>
<text><location><page_19><loc_84><loc_37><loc_85><loc_37></location>0</text>
<text><location><page_19><loc_84><loc_36><loc_85><loc_37></location>3</text>
<text><location><page_19><loc_84><loc_35><loc_85><loc_35></location>8</text>
<text><location><page_19><loc_84><loc_34><loc_85><loc_35></location>9</text>
<text><location><page_19><loc_84><loc_34><loc_85><loc_34></location>6</text>
<text><location><page_19><loc_84><loc_33><loc_85><loc_34></location>.</text>
<text><location><page_19><loc_84><loc_33><loc_85><loc_33></location>0</text>
<text><location><page_19><loc_84><loc_33><loc_85><loc_33></location>3</text>
<text><location><page_19><loc_84><loc_32><loc_85><loc_32></location>3</text>
<text><location><page_19><loc_84><loc_31><loc_85><loc_32></location>3</text>
<text><location><page_19><loc_84><loc_31><loc_85><loc_31></location>1</text>
<text><location><page_19><loc_84><loc_30><loc_85><loc_31></location>0</text>
<text><location><page_19><loc_84><loc_25><loc_85><loc_26></location>9</text>
<text><location><page_19><loc_84><loc_25><loc_85><loc_25></location>1</text>
<text><location><page_19><loc_84><loc_25><loc_85><loc_25></location>1</text>
<text><location><page_19><loc_84><loc_24><loc_85><loc_25></location>L</text>
<text><location><page_19><loc_84><loc_23><loc_85><loc_24></location>P</text>
<text><location><page_19><loc_84><loc_22><loc_85><loc_22></location>2</text>
<text><location><page_19><loc_84><loc_21><loc_85><loc_22></location>0</text>
<text><location><page_19><loc_84><loc_21><loc_85><loc_21></location>1</text>
<text><location><page_19><loc_84><loc_20><loc_85><loc_21></location>M</text>
<text><location><page_19><loc_84><loc_20><loc_85><loc_20></location>S</text>
<text><location><page_19><loc_84><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_19><loc_84><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_19><loc_84><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_19><loc_84><loc_17><loc_85><loc_18></location>.</text>
<text><location><page_19><loc_84><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_19><loc_84><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_19><loc_84><loc_17><loc_85><loc_17></location>8</text>
<text><location><page_19><loc_84><loc_16><loc_85><loc_17></location>8</text>
<text><location><page_19><loc_84><loc_16><loc_85><loc_16></location>2</text>
<text><location><page_19><loc_85><loc_83><loc_86><loc_83></location>0</text>
<text><location><page_19><loc_85><loc_82><loc_86><loc_83></location>7</text>
<text><location><page_19><loc_85><loc_82><loc_86><loc_82></location>8</text>
<text><location><page_19><loc_85><loc_82><loc_86><loc_82></location>.</text>
<text><location><page_19><loc_85><loc_81><loc_86><loc_82></location>3</text>
<text><location><page_19><loc_85><loc_79><loc_86><loc_79></location>0</text>
<text><location><page_19><loc_85><loc_78><loc_86><loc_79></location>1</text>
<text><location><page_19><loc_85><loc_78><loc_86><loc_78></location>.</text>
<text><location><page_19><loc_85><loc_77><loc_86><loc_78></location>0</text>
<text><location><page_19><loc_85><loc_75><loc_86><loc_75></location>5</text>
<text><location><page_19><loc_85><loc_74><loc_86><loc_75></location>1</text>
<text><location><page_19><loc_85><loc_74><loc_86><loc_74></location>0</text>
<text><location><page_19><loc_85><loc_73><loc_86><loc_74></location>.</text>
<text><location><page_19><loc_85><loc_73><loc_86><loc_73></location>0</text>
<text><location><page_19><loc_85><loc_72><loc_86><loc_73></location>±</text>
<text><location><page_19><loc_85><loc_71><loc_86><loc_72></location>2</text>
<text><location><page_19><loc_85><loc_71><loc_86><loc_71></location>2</text>
<text><location><page_19><loc_85><loc_70><loc_86><loc_71></location>7</text>
<text><location><page_19><loc_85><loc_70><loc_86><loc_70></location>.</text>
<text><location><page_19><loc_85><loc_70><loc_86><loc_70></location>7</text>
<text><location><page_19><loc_85><loc_69><loc_86><loc_70></location>1</text>
<text><location><page_19><loc_85><loc_68><loc_86><loc_68></location>7</text>
<text><location><page_19><loc_85><loc_67><loc_86><loc_68></location>1</text>
<text><location><page_19><loc_85><loc_67><loc_86><loc_67></location>0</text>
<text><location><page_19><loc_85><loc_67><loc_86><loc_67></location>.</text>
<text><location><page_19><loc_85><loc_66><loc_86><loc_67></location>0</text>
<text><location><page_19><loc_85><loc_65><loc_86><loc_66></location>±</text>
<text><location><page_19><loc_85><loc_64><loc_86><loc_65></location>2</text>
<text><location><page_19><loc_85><loc_64><loc_86><loc_64></location>4</text>
<text><location><page_19><loc_85><loc_64><loc_86><loc_64></location>1</text>
<text><location><page_19><loc_85><loc_63><loc_86><loc_64></location>.</text>
<text><location><page_19><loc_85><loc_63><loc_86><loc_63></location>8</text>
<text><location><page_19><loc_85><loc_62><loc_86><loc_63></location>1</text>
<text><location><page_19><loc_85><loc_61><loc_86><loc_61></location>4</text>
<text><location><page_19><loc_85><loc_60><loc_86><loc_61></location>1</text>
<text><location><page_19><loc_85><loc_60><loc_86><loc_60></location>0</text>
<text><location><page_19><loc_85><loc_60><loc_86><loc_60></location>.</text>
<text><location><page_19><loc_85><loc_59><loc_86><loc_60></location>0</text>
<text><location><page_19><loc_85><loc_58><loc_86><loc_59></location>±</text>
<text><location><page_19><loc_85><loc_58><loc_86><loc_58></location>8</text>
<text><location><page_19><loc_85><loc_57><loc_86><loc_58></location>7</text>
<text><location><page_19><loc_85><loc_57><loc_86><loc_57></location>4</text>
<text><location><page_19><loc_85><loc_56><loc_86><loc_57></location>.</text>
<text><location><page_19><loc_85><loc_56><loc_86><loc_56></location>8</text>
<text><location><page_19><loc_85><loc_56><loc_86><loc_56></location>1</text>
<text><location><page_19><loc_85><loc_54><loc_86><loc_54></location>5</text>
<text><location><page_19><loc_85><loc_53><loc_86><loc_54></location>1</text>
<text><location><page_19><loc_85><loc_53><loc_86><loc_53></location>0</text>
<text><location><page_19><loc_85><loc_53><loc_86><loc_53></location>.</text>
<text><location><page_19><loc_85><loc_52><loc_86><loc_53></location>0</text>
<text><location><page_19><loc_85><loc_51><loc_86><loc_52></location>±</text>
<text><location><page_19><loc_85><loc_51><loc_86><loc_51></location>4</text>
<text><location><page_19><loc_85><loc_50><loc_86><loc_51></location>3</text>
<text><location><page_19><loc_85><loc_50><loc_86><loc_50></location>0</text>
<text><location><page_19><loc_85><loc_50><loc_86><loc_50></location>.</text>
<text><location><page_19><loc_85><loc_49><loc_86><loc_50></location>9</text>
<text><location><page_19><loc_85><loc_49><loc_86><loc_49></location>1</text>
<text><location><page_19><loc_85><loc_47><loc_86><loc_47></location>6</text>
<text><location><page_19><loc_85><loc_47><loc_86><loc_47></location>1</text>
<text><location><page_19><loc_85><loc_46><loc_86><loc_47></location>0</text>
<text><location><page_19><loc_85><loc_46><loc_86><loc_46></location>.</text>
<text><location><page_19><loc_85><loc_45><loc_86><loc_46></location>0</text>
<text><location><page_19><loc_85><loc_44><loc_86><loc_45></location>±</text>
<text><location><page_19><loc_85><loc_44><loc_86><loc_44></location>6</text>
<text><location><page_19><loc_85><loc_43><loc_86><loc_44></location>1</text>
<text><location><page_19><loc_85><loc_43><loc_86><loc_43></location>2</text>
<text><location><page_19><loc_85><loc_43><loc_86><loc_43></location>.</text>
<text><location><page_19><loc_85><loc_42><loc_86><loc_43></location>9</text>
<text><location><page_19><loc_85><loc_42><loc_86><loc_42></location>1</text>
<text><location><page_19><loc_85><loc_40><loc_86><loc_41></location>7</text>
<text><location><page_19><loc_85><loc_40><loc_86><loc_40></location>9</text>
<text><location><page_19><loc_85><loc_39><loc_86><loc_40></location>.</text>
<text><location><page_19><loc_85><loc_39><loc_86><loc_39></location>1</text>
<text><location><page_19><loc_85><loc_39><loc_86><loc_39></location>1</text>
<text><location><page_19><loc_85><loc_38><loc_86><loc_38></location>9</text>
<text><location><page_19><loc_85><loc_37><loc_86><loc_38></location>4</text>
<text><location><page_19><loc_85><loc_37><loc_86><loc_37></location>0</text>
<text><location><page_19><loc_85><loc_36><loc_86><loc_37></location>3</text>
<text><location><page_19><loc_85><loc_35><loc_86><loc_35></location>4</text>
<text><location><page_19><loc_85><loc_34><loc_86><loc_35></location>9</text>
<text><location><page_19><loc_85><loc_34><loc_86><loc_34></location>8</text>
<text><location><page_19><loc_85><loc_33><loc_86><loc_34></location>.</text>
<text><location><page_19><loc_85><loc_33><loc_86><loc_33></location>0</text>
<text><location><page_19><loc_85><loc_33><loc_86><loc_33></location>3</text>
<text><location><page_19><loc_85><loc_32><loc_86><loc_32></location>3</text>
<text><location><page_19><loc_85><loc_31><loc_86><loc_32></location>3</text>
<text><location><page_19><loc_85><loc_31><loc_86><loc_31></location>1</text>
<text><location><page_19><loc_85><loc_30><loc_86><loc_31></location>0</text>
<text><location><page_19><loc_85><loc_25><loc_86><loc_26></location>0</text>
<text><location><page_19><loc_85><loc_25><loc_86><loc_25></location>2</text>
<text><location><page_19><loc_85><loc_25><loc_86><loc_25></location>1</text>
<text><location><page_19><loc_85><loc_24><loc_86><loc_25></location>L</text>
<text><location><page_19><loc_85><loc_23><loc_86><loc_24></location>P</text>
<text><location><page_19><loc_85><loc_22><loc_86><loc_22></location>3</text>
<text><location><page_19><loc_85><loc_21><loc_86><loc_22></location>0</text>
<text><location><page_19><loc_85><loc_21><loc_86><loc_21></location>1</text>
<text><location><page_19><loc_85><loc_20><loc_86><loc_21></location>M</text>
<text><location><page_19><loc_85><loc_20><loc_86><loc_20></location>S</text>
<text><location><page_19><loc_85><loc_18><loc_86><loc_18></location>.</text>
<text><location><page_19><loc_85><loc_18><loc_86><loc_18></location>.</text>
<text><location><page_19><loc_85><loc_18><loc_86><loc_18></location>.</text>
<text><location><page_19><loc_85><loc_17><loc_86><loc_18></location>.</text>
<text><location><page_19><loc_85><loc_17><loc_86><loc_17></location>.</text>
<text><location><page_19><loc_85><loc_17><loc_86><loc_17></location>.</text>
<text><location><page_19><loc_85><loc_17><loc_86><loc_17></location>9</text>
<text><location><page_19><loc_85><loc_16><loc_86><loc_17></location>8</text>
<text><location><page_19><loc_85><loc_16><loc_86><loc_16></location>2</text>
<text><location><page_19><loc_86><loc_83><loc_87><loc_83></location>8</text>
<text><location><page_19><loc_86><loc_82><loc_87><loc_83></location>3</text>
<text><location><page_19><loc_86><loc_82><loc_87><loc_82></location>8</text>
<text><location><page_19><loc_86><loc_82><loc_87><loc_82></location>.</text>
<text><location><page_19><loc_86><loc_81><loc_87><loc_82></location>2</text>
<text><location><page_19><loc_86><loc_79><loc_87><loc_79></location>5</text>
<text><location><page_19><loc_86><loc_78><loc_87><loc_79></location>1</text>
<text><location><page_19><loc_86><loc_78><loc_87><loc_78></location>.</text>
<text><location><page_19><loc_86><loc_77><loc_87><loc_78></location>0</text>
<text><location><page_19><loc_86><loc_75><loc_87><loc_75></location>1</text>
<text><location><page_19><loc_86><loc_74><loc_87><loc_75></location>2</text>
<text><location><page_19><loc_86><loc_74><loc_87><loc_74></location>0</text>
<text><location><page_19><loc_86><loc_73><loc_87><loc_74></location>.</text>
<text><location><page_19><loc_86><loc_73><loc_87><loc_73></location>0</text>
<text><location><page_19><loc_86><loc_72><loc_87><loc_73></location>±</text>
<text><location><page_19><loc_86><loc_71><loc_87><loc_72></location>1</text>
<text><location><page_19><loc_86><loc_71><loc_87><loc_71></location>8</text>
<text><location><page_19><loc_86><loc_70><loc_87><loc_71></location>6</text>
<text><location><page_19><loc_86><loc_70><loc_87><loc_70></location>.</text>
<text><location><page_19><loc_86><loc_70><loc_87><loc_70></location>7</text>
<text><location><page_19><loc_86><loc_69><loc_87><loc_70></location>1</text>
<text><location><page_19><loc_86><loc_68><loc_87><loc_68></location>8</text>
<text><location><page_19><loc_86><loc_67><loc_87><loc_68></location>1</text>
<text><location><page_19><loc_86><loc_67><loc_87><loc_67></location>0</text>
<text><location><page_19><loc_86><loc_67><loc_87><loc_67></location>.</text>
<text><location><page_19><loc_86><loc_66><loc_87><loc_67></location>0</text>
<text><location><page_19><loc_86><loc_65><loc_87><loc_66></location>±</text>
<text><location><page_19><loc_86><loc_64><loc_87><loc_65></location>1</text>
<text><location><page_19><loc_86><loc_64><loc_87><loc_64></location>1</text>
<text><location><page_19><loc_86><loc_64><loc_87><loc_64></location>1</text>
<text><location><page_19><loc_86><loc_63><loc_87><loc_64></location>.</text>
<text><location><page_19><loc_86><loc_63><loc_87><loc_63></location>8</text>
<text><location><page_19><loc_86><loc_62><loc_87><loc_63></location>1</text>
<text><location><page_19><loc_86><loc_61><loc_87><loc_61></location>6</text>
<text><location><page_19><loc_86><loc_60><loc_87><loc_61></location>1</text>
<text><location><page_19><loc_86><loc_60><loc_87><loc_60></location>0</text>
<text><location><page_19><loc_86><loc_60><loc_87><loc_60></location>.</text>
<text><location><page_19><loc_86><loc_59><loc_87><loc_60></location>0</text>
<text><location><page_19><loc_86><loc_58><loc_87><loc_59></location>±</text>
<text><location><page_19><loc_86><loc_58><loc_87><loc_58></location>6</text>
<text><location><page_19><loc_86><loc_57><loc_87><loc_58></location>7</text>
<text><location><page_19><loc_86><loc_57><loc_87><loc_57></location>3</text>
<text><location><page_19><loc_86><loc_56><loc_87><loc_57></location>.</text>
<text><location><page_19><loc_86><loc_56><loc_87><loc_56></location>8</text>
<text><location><page_19><loc_86><loc_56><loc_87><loc_56></location>1</text>
<text><location><page_19><loc_86><loc_54><loc_87><loc_54></location>4</text>
<text><location><page_19><loc_86><loc_53><loc_87><loc_54></location>1</text>
<text><location><page_19><loc_86><loc_53><loc_87><loc_53></location>0</text>
<text><location><page_19><loc_86><loc_53><loc_87><loc_53></location>.</text>
<text><location><page_19><loc_86><loc_52><loc_87><loc_53></location>0</text>
<text><location><page_19><loc_86><loc_51><loc_87><loc_52></location>±</text>
<text><location><page_19><loc_86><loc_51><loc_87><loc_51></location>1</text>
<text><location><page_19><loc_86><loc_50><loc_87><loc_51></location>1</text>
<text><location><page_19><loc_86><loc_50><loc_87><loc_50></location>7</text>
<text><location><page_19><loc_86><loc_50><loc_87><loc_50></location>.</text>
<text><location><page_19><loc_86><loc_49><loc_87><loc_50></location>8</text>
<text><location><page_19><loc_86><loc_49><loc_87><loc_49></location>1</text>
<text><location><page_19><loc_86><loc_47><loc_87><loc_47></location>1</text>
<text><location><page_19><loc_86><loc_47><loc_87><loc_47></location>1</text>
<text><location><page_19><loc_86><loc_46><loc_87><loc_47></location>0</text>
<text><location><page_19><loc_86><loc_46><loc_87><loc_46></location>.</text>
<text><location><page_19><loc_86><loc_45><loc_87><loc_46></location>0</text>
<text><location><page_19><loc_86><loc_44><loc_87><loc_45></location>±</text>
<text><location><page_19><loc_86><loc_44><loc_87><loc_44></location>2</text>
<text><location><page_19><loc_86><loc_43><loc_87><loc_44></location>9</text>
<text><location><page_19><loc_86><loc_43><loc_87><loc_43></location>4</text>
<text><location><page_19><loc_86><loc_43><loc_87><loc_43></location>.</text>
<text><location><page_19><loc_86><loc_42><loc_87><loc_43></location>8</text>
<text><location><page_19><loc_86><loc_42><loc_87><loc_42></location>1</text>
<text><location><page_19><loc_86><loc_40><loc_87><loc_41></location>0</text>
<text><location><page_19><loc_86><loc_40><loc_87><loc_40></location>9</text>
<text><location><page_19><loc_86><loc_39><loc_87><loc_40></location>.</text>
<text><location><page_19><loc_86><loc_39><loc_87><loc_39></location>2</text>
<text><location><page_19><loc_86><loc_39><loc_87><loc_39></location>1</text>
<text><location><page_19><loc_86><loc_38><loc_87><loc_38></location>7</text>
<text><location><page_19><loc_86><loc_37><loc_87><loc_38></location>3</text>
<text><location><page_19><loc_86><loc_37><loc_87><loc_37></location>0</text>
<text><location><page_19><loc_86><loc_36><loc_87><loc_37></location>3</text>
<text><location><page_19><loc_86><loc_35><loc_87><loc_35></location>4</text>
<text><location><page_19><loc_86><loc_34><loc_87><loc_35></location>2</text>
<text><location><page_19><loc_86><loc_34><loc_87><loc_34></location>9</text>
<text><location><page_19><loc_86><loc_33><loc_87><loc_34></location>.</text>
<text><location><page_19><loc_86><loc_33><loc_87><loc_33></location>0</text>
<text><location><page_19><loc_86><loc_33><loc_87><loc_33></location>3</text>
<text><location><page_19><loc_86><loc_32><loc_87><loc_32></location>3</text>
<text><location><page_19><loc_86><loc_31><loc_87><loc_32></location>3</text>
<text><location><page_19><loc_86><loc_31><loc_87><loc_31></location>1</text>
<text><location><page_19><loc_86><loc_30><loc_87><loc_31></location>0</text>
<text><location><page_19><loc_86><loc_25><loc_87><loc_26></location>1</text>
<text><location><page_19><loc_86><loc_25><loc_87><loc_25></location>5</text>
<text><location><page_19><loc_86><loc_24><loc_87><loc_25></location>L</text>
<text><location><page_19><loc_86><loc_24><loc_87><loc_24></location>P</text>
<text><location><page_19><loc_86><loc_22><loc_87><loc_22></location>4</text>
<text><location><page_19><loc_86><loc_21><loc_87><loc_22></location>0</text>
<text><location><page_19><loc_86><loc_21><loc_87><loc_21></location>1</text>
<text><location><page_19><loc_86><loc_20><loc_87><loc_21></location>M</text>
<text><location><page_19><loc_86><loc_20><loc_87><loc_20></location>S</text>
<text><location><page_19><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_19><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_19><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_19><loc_86><loc_17><loc_87><loc_18></location>.</text>
<text><location><page_19><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_19><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_19><loc_86><loc_17><loc_87><loc_17></location>0</text>
<text><location><page_19><loc_86><loc_16><loc_87><loc_17></location>9</text>
<text><location><page_19><loc_86><loc_16><loc_87><loc_16></location>2</text>
<text><location><page_19><loc_88><loc_83><loc_89><loc_83></location>0</text>
<text><location><page_19><loc_88><loc_82><loc_89><loc_83></location>8</text>
<text><location><page_19><loc_88><loc_82><loc_89><loc_82></location>5</text>
<text><location><page_19><loc_88><loc_82><loc_89><loc_82></location>.</text>
<text><location><page_19><loc_88><loc_81><loc_89><loc_82></location>2</text>
<text><location><page_19><loc_88><loc_79><loc_89><loc_79></location>0</text>
<text><location><page_19><loc_88><loc_78><loc_89><loc_79></location>1</text>
<text><location><page_19><loc_88><loc_78><loc_89><loc_78></location>.</text>
<text><location><page_19><loc_88><loc_77><loc_89><loc_78></location>0</text>
<text><location><page_19><loc_88><loc_75><loc_89><loc_75></location>4</text>
<text><location><page_19><loc_88><loc_74><loc_89><loc_75></location>1</text>
<text><location><page_19><loc_88><loc_74><loc_89><loc_74></location>0</text>
<text><location><page_19><loc_88><loc_73><loc_89><loc_74></location>.</text>
<text><location><page_19><loc_88><loc_73><loc_89><loc_73></location>0</text>
<text><location><page_19><loc_88><loc_72><loc_88><loc_73></location>±</text>
<text><location><page_19><loc_88><loc_71><loc_89><loc_72></location>5</text>
<text><location><page_19><loc_88><loc_71><loc_89><loc_71></location>2</text>
<text><location><page_19><loc_88><loc_70><loc_89><loc_71></location>1</text>
<text><location><page_19><loc_88><loc_70><loc_89><loc_70></location>.</text>
<text><location><page_19><loc_88><loc_70><loc_89><loc_70></location>7</text>
<text><location><page_19><loc_88><loc_69><loc_89><loc_70></location>1</text>
<text><location><page_19><loc_88><loc_68><loc_89><loc_68></location>6</text>
<text><location><page_19><loc_88><loc_67><loc_89><loc_68></location>1</text>
<text><location><page_19><loc_88><loc_67><loc_89><loc_67></location>0</text>
<text><location><page_19><loc_88><loc_67><loc_89><loc_67></location>.</text>
<text><location><page_19><loc_88><loc_66><loc_89><loc_67></location>0</text>
<text><location><page_19><loc_88><loc_65><loc_88><loc_66></location>±</text>
<text><location><page_19><loc_88><loc_64><loc_89><loc_65></location>2</text>
<text><location><page_19><loc_88><loc_64><loc_89><loc_64></location>5</text>
<text><location><page_19><loc_88><loc_64><loc_89><loc_64></location>7</text>
<text><location><page_19><loc_88><loc_63><loc_89><loc_64></location>.</text>
<text><location><page_19><loc_88><loc_63><loc_89><loc_63></location>7</text>
<text><location><page_19><loc_88><loc_62><loc_89><loc_63></location>1</text>
<text><location><page_19><loc_88><loc_61><loc_89><loc_61></location>6</text>
<text><location><page_19><loc_88><loc_60><loc_89><loc_61></location>1</text>
<text><location><page_19><loc_88><loc_60><loc_89><loc_60></location>0</text>
<text><location><page_19><loc_88><loc_60><loc_89><loc_60></location>.</text>
<text><location><page_19><loc_88><loc_59><loc_89><loc_60></location>0</text>
<text><location><page_19><loc_88><loc_58><loc_88><loc_59></location>±</text>
<text><location><page_19><loc_88><loc_58><loc_89><loc_58></location>0</text>
<text><location><page_19><loc_88><loc_57><loc_89><loc_58></location>4</text>
<text><location><page_19><loc_88><loc_57><loc_89><loc_57></location>0</text>
<text><location><page_19><loc_88><loc_56><loc_89><loc_57></location>.</text>
<text><location><page_19><loc_88><loc_56><loc_89><loc_56></location>8</text>
<text><location><page_19><loc_88><loc_56><loc_89><loc_56></location>1</text>
<text><location><page_19><loc_88><loc_54><loc_89><loc_54></location>5</text>
<text><location><page_19><loc_88><loc_53><loc_89><loc_54></location>1</text>
<text><location><page_19><loc_88><loc_53><loc_89><loc_53></location>0</text>
<text><location><page_19><loc_88><loc_53><loc_89><loc_53></location>.</text>
<text><location><page_19><loc_88><loc_52><loc_89><loc_53></location>0</text>
<text><location><page_19><loc_88><loc_51><loc_88><loc_52></location>±</text>
<text><location><page_19><loc_88><loc_51><loc_89><loc_51></location>0</text>
<text><location><page_19><loc_88><loc_50><loc_89><loc_51></location>8</text>
<text><location><page_19><loc_88><loc_50><loc_89><loc_50></location>3</text>
<text><location><page_19><loc_88><loc_50><loc_89><loc_50></location>.</text>
<text><location><page_19><loc_88><loc_49><loc_89><loc_50></location>8</text>
<text><location><page_19><loc_88><loc_49><loc_89><loc_49></location>1</text>
<text><location><page_19><loc_88><loc_47><loc_89><loc_47></location>0</text>
<text><location><page_19><loc_88><loc_47><loc_89><loc_47></location>1</text>
<text><location><page_19><loc_88><loc_46><loc_89><loc_47></location>0</text>
<text><location><page_19><loc_88><loc_46><loc_89><loc_46></location>.</text>
<text><location><page_19><loc_88><loc_45><loc_89><loc_46></location>0</text>
<text><location><page_19><loc_88><loc_44><loc_88><loc_45></location>±</text>
<text><location><page_19><loc_88><loc_44><loc_89><loc_44></location>3</text>
<text><location><page_19><loc_88><loc_43><loc_89><loc_44></location>8</text>
<text><location><page_19><loc_88><loc_43><loc_89><loc_43></location>9</text>
<text><location><page_19><loc_88><loc_43><loc_89><loc_43></location>.</text>
<text><location><page_19><loc_88><loc_42><loc_89><loc_43></location>7</text>
<text><location><page_19><loc_88><loc_42><loc_89><loc_42></location>1</text>
<text><location><page_19><loc_88><loc_40><loc_89><loc_41></location>2</text>
<text><location><page_19><loc_88><loc_40><loc_89><loc_40></location>6</text>
<text><location><page_19><loc_88><loc_39><loc_89><loc_40></location>.</text>
<text><location><page_19><loc_88><loc_39><loc_89><loc_39></location>2</text>
<text><location><page_19><loc_88><loc_39><loc_89><loc_39></location>5</text>
<text><location><page_19><loc_88><loc_38><loc_89><loc_38></location>6</text>
<text><location><page_19><loc_88><loc_37><loc_89><loc_38></location>3</text>
<text><location><page_19><loc_88><loc_37><loc_89><loc_37></location>0</text>
<text><location><page_19><loc_88><loc_36><loc_89><loc_37></location>3</text>
<text><location><page_19><loc_88><loc_35><loc_89><loc_35></location>5</text>
<text><location><page_19><loc_88><loc_34><loc_89><loc_35></location>9</text>
<text><location><page_19><loc_88><loc_34><loc_89><loc_34></location>9</text>
<text><location><page_19><loc_88><loc_33><loc_89><loc_34></location>.</text>
<text><location><page_19><loc_88><loc_33><loc_89><loc_33></location>0</text>
<text><location><page_19><loc_88><loc_33><loc_89><loc_33></location>3</text>
<text><location><page_19><loc_88><loc_32><loc_89><loc_32></location>3</text>
<text><location><page_19><loc_88><loc_31><loc_89><loc_32></location>3</text>
<text><location><page_19><loc_88><loc_31><loc_89><loc_31></location>1</text>
<text><location><page_19><loc_88><loc_30><loc_89><loc_31></location>0</text>
<text><location><page_19><loc_88><loc_25><loc_89><loc_26></location>2</text>
<text><location><page_19><loc_88><loc_25><loc_89><loc_25></location>5</text>
<text><location><page_19><loc_88><loc_24><loc_89><loc_25></location>L</text>
<text><location><page_19><loc_88><loc_24><loc_89><loc_24></location>P</text>
<text><location><page_19><loc_88><loc_22><loc_89><loc_22></location>5</text>
<text><location><page_19><loc_88><loc_21><loc_89><loc_22></location>0</text>
<text><location><page_19><loc_88><loc_21><loc_89><loc_21></location>1</text>
<text><location><page_19><loc_88><loc_20><loc_89><loc_21></location>M</text>
<text><location><page_19><loc_88><loc_20><loc_89><loc_20></location>S</text>
<text><location><page_19><loc_88><loc_18><loc_89><loc_18></location>.</text>
<text><location><page_19><loc_88><loc_18><loc_89><loc_18></location>.</text>
<text><location><page_19><loc_88><loc_18><loc_89><loc_18></location>.</text>
<text><location><page_19><loc_88><loc_17><loc_89><loc_18></location>.</text>
<text><location><page_19><loc_88><loc_17><loc_89><loc_17></location>.</text>
<text><location><page_19><loc_88><loc_17><loc_89><loc_17></location>.</text>
<text><location><page_19><loc_88><loc_17><loc_89><loc_17></location>1</text>
<text><location><page_19><loc_88><loc_16><loc_89><loc_17></location>9</text>
<text><location><page_19><loc_88><loc_16><loc_89><loc_16></location>2</text>
<text><location><page_20><loc_9><loc_93><loc_10><loc_94></location>20</text>
<text><location><page_20><loc_50><loc_93><loc_52><loc_94></location>Ma</text>
<table>
<location><page_20><loc_15><loc_12><loc_84><loc_83></location>
</table>
<text><location><page_20><loc_13><loc_51><loc_14><loc_52></location>3</text>
<text><location><page_20><loc_13><loc_50><loc_14><loc_51></location>E</text>
<text><location><page_20><loc_13><loc_50><loc_14><loc_50></location>L</text>
<text><location><page_20><loc_13><loc_48><loc_14><loc_50></location>AB</text>
<text><location><page_20><loc_13><loc_47><loc_14><loc_48></location>T</text>
<text><location><page_20><loc_14><loc_52><loc_15><loc_53></location>)</text>
<text><location><page_20><loc_14><loc_52><loc_15><loc_52></location>.</text>
<text><location><page_20><loc_14><loc_52><loc_15><loc_52></location>d</text>
<text><location><page_20><loc_14><loc_51><loc_15><loc_52></location>e</text>
<text><location><page_20><loc_14><loc_50><loc_15><loc_51></location>u</text>
<text><location><page_20><loc_14><loc_50><loc_15><loc_50></location>n</text>
<text><location><page_20><loc_14><loc_49><loc_15><loc_50></location>i</text>
<text><location><page_20><loc_14><loc_49><loc_15><loc_49></location>t</text>
<text><location><page_20><loc_14><loc_48><loc_15><loc_49></location>n</text>
<text><location><page_20><loc_14><loc_48><loc_15><loc_48></location>o</text>
<text><location><page_20><loc_14><loc_47><loc_15><loc_48></location>C</text>
<text><location><page_20><loc_14><loc_46><loc_15><loc_47></location>(</text>
<text><location><page_20><loc_20><loc_83><loc_20><loc_84></location>0</text>
<text><location><page_20><loc_21><loc_83><loc_22><loc_84></location>4</text>
<text><location><page_20><loc_22><loc_83><loc_23><loc_84></location>4</text>
<text><location><page_20><loc_23><loc_83><loc_24><loc_84></location>2</text>
<text><location><page_20><loc_24><loc_83><loc_25><loc_84></location>2</text>
<text><location><page_20><loc_26><loc_83><loc_27><loc_84></location>6</text>
<text><location><page_20><loc_27><loc_83><loc_28><loc_84></location>8</text>
<text><location><page_20><loc_28><loc_83><loc_29><loc_84></location>2</text>
<text><location><page_20><loc_29><loc_83><loc_30><loc_84></location>0</text>
<text><location><page_20><loc_31><loc_83><loc_31><loc_84></location>0</text>
<text><location><page_20><loc_32><loc_83><loc_33><loc_84></location>6</text>
<text><location><page_20><loc_33><loc_83><loc_34><loc_84></location>8</text>
<text><location><page_20><loc_34><loc_83><loc_35><loc_84></location>4</text>
<text><location><page_20><loc_36><loc_83><loc_36><loc_84></location>0</text>
<text><location><page_20><loc_37><loc_83><loc_38><loc_84></location>6</text>
<text><location><page_20><loc_38><loc_83><loc_39><loc_84></location>0</text>
<text><location><page_20><loc_39><loc_83><loc_40><loc_84></location>6</text>
<text><location><page_20><loc_40><loc_83><loc_41><loc_84></location>8</text>
<text><location><page_20><loc_42><loc_83><loc_42><loc_84></location>2</text>
<text><location><page_20><loc_43><loc_83><loc_44><loc_84></location>8</text>
<text><location><page_20><loc_44><loc_83><loc_45><loc_84></location>4</text>
<text><location><page_20><loc_45><loc_83><loc_46><loc_84></location>0</text>
<text><location><page_20><loc_47><loc_83><loc_47><loc_84></location>8</text>
<text><location><page_20><loc_48><loc_83><loc_49><loc_84></location>4</text>
<text><location><page_20><loc_49><loc_83><loc_50><loc_84></location>0</text>
<text><location><page_20><loc_50><loc_83><loc_51><loc_84></location>0</text>
<text><location><page_20><loc_51><loc_83><loc_52><loc_84></location>8</text>
<text><location><page_20><loc_53><loc_83><loc_54><loc_84></location>2</text>
<text><location><page_20><loc_54><loc_83><loc_55><loc_84></location>2</text>
<text><location><page_20><loc_55><loc_83><loc_56><loc_84></location>6</text>
<text><location><page_20><loc_56><loc_83><loc_57><loc_84></location>6</text>
<text><location><page_20><loc_58><loc_83><loc_58><loc_84></location>2</text>
<text><location><page_20><loc_59><loc_83><loc_60><loc_84></location>4</text>
<text><location><page_20><loc_60><loc_83><loc_61><loc_84></location>0</text>
<text><location><page_20><loc_61><loc_83><loc_62><loc_84></location>2</text>
<text><location><page_20><loc_63><loc_83><loc_63><loc_84></location>6</text>
<text><location><page_20><loc_64><loc_83><loc_65><loc_84></location>6</text>
<text><location><page_20><loc_65><loc_83><loc_66><loc_84></location>2</text>
<text><location><page_20><loc_66><loc_83><loc_67><loc_84></location>2</text>
<text><location><page_20><loc_67><loc_83><loc_68><loc_84></location>6</text>
<text><location><page_20><loc_69><loc_83><loc_69><loc_84></location>4</text>
<text><location><page_20><loc_70><loc_83><loc_71><loc_84></location>4</text>
<text><location><page_20><loc_71><loc_83><loc_72><loc_84></location>0</text>
<text><location><page_20><loc_72><loc_83><loc_73><loc_84></location>0</text>
<text><location><page_20><loc_74><loc_83><loc_74><loc_84></location>2</text>
<text><location><page_20><loc_75><loc_83><loc_76><loc_84></location>2</text>
<text><location><page_20><loc_76><loc_83><loc_77><loc_84></location>0</text>
<text><location><page_20><loc_77><loc_83><loc_78><loc_84></location>4</text>
<text><location><page_20><loc_78><loc_83><loc_79><loc_84></location>4</text>
<text><location><page_20><loc_80><loc_83><loc_81><loc_84></location>6</text>
<text><location><page_20><loc_81><loc_83><loc_82><loc_84></location>0</text>
<text><location><page_20><loc_82><loc_83><loc_83><loc_84></location>0</text>
<text><location><page_20><loc_83><loc_83><loc_84><loc_84></location>8</text>
<text><location><page_20><loc_85><loc_83><loc_85><loc_84></location>0</text>
<text><location><page_20><loc_85><loc_83><loc_85><loc_83></location>8</text>
<text><location><page_20><loc_85><loc_82><loc_85><loc_83></location>5</text>
<text><location><page_20><loc_85><loc_82><loc_85><loc_82></location>.</text>
<text><location><page_20><loc_85><loc_82><loc_85><loc_82></location>2</text>
<text><location><page_20><loc_85><loc_79><loc_85><loc_79></location>0</text>
<text><location><page_20><loc_85><loc_78><loc_85><loc_79></location>2</text>
<text><location><page_20><loc_85><loc_78><loc_85><loc_78></location>.</text>
<text><location><page_20><loc_85><loc_78><loc_85><loc_78></location>0</text>
<text><location><page_20><loc_85><loc_75><loc_85><loc_75></location>2</text>
<text><location><page_20><loc_85><loc_74><loc_85><loc_75></location>1</text>
<text><location><page_20><loc_85><loc_74><loc_85><loc_74></location>0</text>
<text><location><page_20><loc_85><loc_74><loc_85><loc_74></location>.</text>
<text><location><page_20><loc_85><loc_73><loc_85><loc_74></location>0</text>
<text><location><page_20><loc_85><loc_72><loc_85><loc_73></location>±</text>
<text><location><page_20><loc_85><loc_72><loc_85><loc_72></location>7</text>
<text><location><page_20><loc_85><loc_71><loc_85><loc_72></location>7</text>
<text><location><page_20><loc_85><loc_71><loc_85><loc_71></location>6</text>
<text><location><page_20><loc_85><loc_70><loc_85><loc_71></location>.</text>
<text><location><page_20><loc_85><loc_70><loc_85><loc_70></location>7</text>
<text><location><page_20><loc_85><loc_70><loc_85><loc_70></location>1</text>
<text><location><page_20><loc_85><loc_68><loc_85><loc_68></location>6</text>
<text><location><page_20><loc_85><loc_67><loc_85><loc_68></location>1</text>
<text><location><page_20><loc_85><loc_67><loc_85><loc_67></location>0</text>
<text><location><page_20><loc_85><loc_67><loc_85><loc_67></location>.</text>
<text><location><page_20><loc_85><loc_66><loc_85><loc_67></location>0</text>
<text><location><page_20><loc_85><loc_65><loc_85><loc_66></location>±</text>
<text><location><page_20><loc_85><loc_65><loc_85><loc_65></location>5</text>
<text><location><page_20><loc_85><loc_64><loc_85><loc_65></location>7</text>
<text><location><page_20><loc_85><loc_64><loc_85><loc_64></location>2</text>
<text><location><page_20><loc_85><loc_64><loc_85><loc_64></location>.</text>
<text><location><page_20><loc_85><loc_63><loc_85><loc_64></location>8</text>
<text><location><page_20><loc_85><loc_63><loc_85><loc_63></location>1</text>
<text><location><page_20><loc_85><loc_61><loc_85><loc_61></location>7</text>
<text><location><page_20><loc_85><loc_61><loc_85><loc_61></location>1</text>
<text><location><page_20><loc_85><loc_60><loc_85><loc_61></location>0</text>
<text><location><page_20><loc_85><loc_60><loc_85><loc_60></location>.</text>
<text><location><page_20><loc_85><loc_59><loc_85><loc_60></location>0</text>
<text><location><page_20><loc_85><loc_59><loc_85><loc_59></location>±</text>
<text><location><page_20><loc_85><loc_58><loc_85><loc_58></location>9</text>
<text><location><page_20><loc_85><loc_57><loc_85><loc_58></location>5</text>
<text><location><page_20><loc_85><loc_57><loc_85><loc_57></location>7</text>
<text><location><page_20><loc_85><loc_57><loc_85><loc_57></location>.</text>
<text><location><page_20><loc_85><loc_56><loc_85><loc_57></location>8</text>
<text><location><page_20><loc_85><loc_56><loc_85><loc_56></location>1</text>
<text><location><page_20><loc_85><loc_54><loc_85><loc_55></location>8</text>
<text><location><page_20><loc_85><loc_54><loc_85><loc_54></location>2</text>
<text><location><page_20><loc_85><loc_53><loc_85><loc_54></location>0</text>
<text><location><page_20><loc_85><loc_53><loc_85><loc_53></location>.</text>
<text><location><page_20><loc_85><loc_53><loc_85><loc_53></location>0</text>
<text><location><page_20><loc_85><loc_52><loc_85><loc_52></location>±</text>
<text><location><page_20><loc_85><loc_51><loc_85><loc_51></location>8</text>
<text><location><page_20><loc_85><loc_50><loc_85><loc_51></location>1</text>
<text><location><page_20><loc_85><loc_50><loc_85><loc_50></location>6</text>
<text><location><page_20><loc_85><loc_50><loc_85><loc_50></location>.</text>
<text><location><page_20><loc_85><loc_49><loc_85><loc_50></location>9</text>
<text><location><page_20><loc_85><loc_49><loc_85><loc_49></location>1</text>
<text><location><page_20><loc_85><loc_47><loc_85><loc_48></location>5</text>
<text><location><page_20><loc_85><loc_47><loc_85><loc_47></location>2</text>
<text><location><page_20><loc_85><loc_46><loc_85><loc_47></location>0</text>
<text><location><page_20><loc_85><loc_46><loc_85><loc_46></location>.</text>
<text><location><page_20><loc_85><loc_46><loc_85><loc_46></location>0</text>
<text><location><page_20><loc_85><loc_45><loc_85><loc_45></location>±</text>
<text><location><page_20><loc_85><loc_44><loc_85><loc_44></location>8</text>
<text><location><page_20><loc_85><loc_44><loc_85><loc_44></location>0</text>
<text><location><page_20><loc_85><loc_43><loc_85><loc_44></location>5</text>
<text><location><page_20><loc_85><loc_43><loc_85><loc_43></location>.</text>
<text><location><page_20><loc_85><loc_42><loc_85><loc_43></location>9</text>
<text><location><page_20><loc_85><loc_42><loc_85><loc_42></location>1</text>
<text><location><page_20><loc_85><loc_40><loc_85><loc_41></location>2</text>
<text><location><page_20><loc_85><loc_40><loc_85><loc_40></location>3</text>
<text><location><page_20><loc_85><loc_40><loc_85><loc_40></location>.</text>
<text><location><page_20><loc_85><loc_39><loc_85><loc_40></location>6</text>
<text><location><page_20><loc_85><loc_39><loc_85><loc_39></location>3</text>
<text><location><page_20><loc_85><loc_38><loc_85><loc_39></location>6</text>
<text><location><page_20><loc_85><loc_38><loc_85><loc_38></location>4</text>
<text><location><page_20><loc_85><loc_37><loc_85><loc_37></location>0</text>
<text><location><page_20><loc_85><loc_37><loc_85><loc_37></location>3</text>
<text><location><page_20><loc_85><loc_35><loc_85><loc_35></location>1</text>
<text><location><page_20><loc_85><loc_34><loc_85><loc_35></location>6</text>
<text><location><page_20><loc_85><loc_34><loc_85><loc_34></location>9</text>
<text><location><page_20><loc_85><loc_34><loc_85><loc_34></location>.</text>
<text><location><page_20><loc_85><loc_33><loc_85><loc_34></location>6</text>
<text><location><page_20><loc_85><loc_33><loc_85><loc_33></location>4</text>
<text><location><page_20><loc_85><loc_32><loc_85><loc_33></location>3</text>
<text><location><page_20><loc_85><loc_32><loc_85><loc_32></location>3</text>
<text><location><page_20><loc_85><loc_31><loc_85><loc_31></location>1</text>
<text><location><page_20><loc_85><loc_31><loc_85><loc_31></location>0</text>
<text><location><page_20><loc_85><loc_25><loc_85><loc_26></location>0</text>
<text><location><page_20><loc_85><loc_25><loc_85><loc_25></location>5</text>
<text><location><page_20><loc_85><loc_24><loc_85><loc_25></location>1</text>
<text><location><page_20><loc_85><loc_24><loc_85><loc_24></location>L</text>
<text><location><page_20><loc_85><loc_23><loc_85><loc_24></location>P</text>
<text><location><page_20><loc_85><loc_22><loc_85><loc_22></location>4</text>
<text><location><page_20><loc_85><loc_21><loc_85><loc_22></location>8</text>
<text><location><page_20><loc_85><loc_21><loc_85><loc_21></location>1</text>
<text><location><page_20><loc_85><loc_20><loc_85><loc_21></location>M</text>
<text><location><page_20><loc_85><loc_20><loc_85><loc_20></location>S</text>
<text><location><page_20><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_20><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_20><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_20><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_20><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_20><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_20><loc_85><loc_16><loc_85><loc_17></location>5</text>
<text><location><page_20><loc_85><loc_16><loc_85><loc_16></location>4</text>
<text><location><page_20><loc_85><loc_15><loc_85><loc_16></location>3</text>
<text><location><page_20><loc_86><loc_83><loc_87><loc_84></location>0</text>
<text><location><page_20><loc_86><loc_83><loc_87><loc_83></location>8</text>
<text><location><page_20><loc_86><loc_82><loc_87><loc_83></location>5</text>
<text><location><page_20><loc_86><loc_82><loc_87><loc_82></location>.</text>
<text><location><page_20><loc_86><loc_82><loc_87><loc_82></location>2</text>
<text><location><page_20><loc_86><loc_79><loc_87><loc_79></location>0</text>
<text><location><page_20><loc_86><loc_78><loc_87><loc_79></location>1</text>
<text><location><page_20><loc_86><loc_78><loc_87><loc_78></location>.</text>
<text><location><page_20><loc_86><loc_78><loc_87><loc_78></location>0</text>
<text><location><page_20><loc_86><loc_75><loc_87><loc_75></location>5</text>
<text><location><page_20><loc_86><loc_74><loc_87><loc_75></location>1</text>
<text><location><page_20><loc_86><loc_74><loc_87><loc_74></location>0</text>
<text><location><page_20><loc_86><loc_74><loc_87><loc_74></location>.</text>
<text><location><page_20><loc_86><loc_73><loc_87><loc_74></location>0</text>
<text><location><page_20><loc_86><loc_72><loc_87><loc_73></location>±</text>
<text><location><page_20><loc_86><loc_72><loc_87><loc_72></location>1</text>
<text><location><page_20><loc_86><loc_71><loc_87><loc_72></location>4</text>
<text><location><page_20><loc_86><loc_71><loc_87><loc_71></location>7</text>
<text><location><page_20><loc_86><loc_70><loc_87><loc_71></location>.</text>
<text><location><page_20><loc_86><loc_70><loc_87><loc_70></location>7</text>
<text><location><page_20><loc_86><loc_70><loc_87><loc_70></location>1</text>
<text><location><page_20><loc_86><loc_68><loc_87><loc_68></location>8</text>
<text><location><page_20><loc_86><loc_67><loc_87><loc_68></location>1</text>
<text><location><page_20><loc_86><loc_67><loc_87><loc_67></location>0</text>
<text><location><page_20><loc_86><loc_67><loc_87><loc_67></location>.</text>
<text><location><page_20><loc_86><loc_66><loc_87><loc_67></location>0</text>
<text><location><page_20><loc_86><loc_65><loc_87><loc_66></location>±</text>
<text><location><page_20><loc_86><loc_65><loc_87><loc_65></location>6</text>
<text><location><page_20><loc_86><loc_64><loc_87><loc_65></location>3</text>
<text><location><page_20><loc_86><loc_64><loc_87><loc_64></location>2</text>
<text><location><page_20><loc_86><loc_64><loc_87><loc_64></location>.</text>
<text><location><page_20><loc_86><loc_63><loc_87><loc_64></location>8</text>
<text><location><page_20><loc_86><loc_63><loc_87><loc_63></location>1</text>
<text><location><page_20><loc_86><loc_61><loc_87><loc_61></location>8</text>
<text><location><page_20><loc_86><loc_61><loc_87><loc_61></location>1</text>
<text><location><page_20><loc_86><loc_60><loc_87><loc_61></location>0</text>
<text><location><page_20><loc_86><loc_60><loc_87><loc_60></location>.</text>
<text><location><page_20><loc_86><loc_59><loc_87><loc_60></location>0</text>
<text><location><page_20><loc_86><loc_59><loc_87><loc_59></location>±</text>
<text><location><page_20><loc_86><loc_58><loc_87><loc_58></location>5</text>
<text><location><page_20><loc_86><loc_57><loc_87><loc_58></location>2</text>
<text><location><page_20><loc_86><loc_57><loc_87><loc_57></location>6</text>
<text><location><page_20><loc_86><loc_57><loc_87><loc_57></location>.</text>
<text><location><page_20><loc_86><loc_56><loc_87><loc_57></location>8</text>
<text><location><page_20><loc_86><loc_56><loc_87><loc_56></location>1</text>
<text><location><page_20><loc_86><loc_54><loc_87><loc_55></location>0</text>
<text><location><page_20><loc_86><loc_54><loc_87><loc_54></location>2</text>
<text><location><page_20><loc_86><loc_53><loc_87><loc_54></location>0</text>
<text><location><page_20><loc_86><loc_53><loc_87><loc_53></location>.</text>
<text><location><page_20><loc_86><loc_53><loc_87><loc_53></location>0</text>
<text><location><page_20><loc_86><loc_52><loc_87><loc_52></location>±</text>
<text><location><page_20><loc_86><loc_51><loc_87><loc_51></location>6</text>
<text><location><page_20><loc_86><loc_50><loc_87><loc_51></location>3</text>
<text><location><page_20><loc_86><loc_50><loc_87><loc_50></location>3</text>
<text><location><page_20><loc_86><loc_50><loc_87><loc_50></location>.</text>
<text><location><page_20><loc_86><loc_49><loc_87><loc_50></location>9</text>
<text><location><page_20><loc_86><loc_49><loc_87><loc_49></location>1</text>
<text><location><page_20><loc_86><loc_47><loc_87><loc_48></location>0</text>
<text><location><page_20><loc_86><loc_47><loc_87><loc_47></location>2</text>
<text><location><page_20><loc_86><loc_46><loc_87><loc_47></location>0</text>
<text><location><page_20><loc_86><loc_46><loc_87><loc_46></location>.</text>
<text><location><page_20><loc_86><loc_46><loc_87><loc_46></location>0</text>
<text><location><page_20><loc_86><loc_45><loc_87><loc_45></location>±</text>
<text><location><page_20><loc_86><loc_44><loc_87><loc_44></location>8</text>
<text><location><page_20><loc_86><loc_44><loc_87><loc_44></location>7</text>
<text><location><page_20><loc_86><loc_43><loc_87><loc_44></location>4</text>
<text><location><page_20><loc_86><loc_43><loc_87><loc_43></location>.</text>
<text><location><page_20><loc_86><loc_42><loc_87><loc_43></location>9</text>
<text><location><page_20><loc_86><loc_42><loc_87><loc_42></location>1</text>
<text><location><page_20><loc_86><loc_40><loc_87><loc_41></location>2</text>
<text><location><page_20><loc_86><loc_40><loc_87><loc_40></location>7</text>
<text><location><page_20><loc_86><loc_40><loc_87><loc_40></location>.</text>
<text><location><page_20><loc_86><loc_39><loc_87><loc_40></location>8</text>
<text><location><page_20><loc_86><loc_39><loc_87><loc_39></location>3</text>
<text><location><page_20><loc_86><loc_38><loc_87><loc_39></location>5</text>
<text><location><page_20><loc_86><loc_38><loc_87><loc_38></location>4</text>
<text><location><page_20><loc_86><loc_37><loc_87><loc_37></location>0</text>
<text><location><page_20><loc_86><loc_37><loc_87><loc_37></location>3</text>
<text><location><page_20><loc_86><loc_35><loc_87><loc_35></location>6</text>
<text><location><page_20><loc_86><loc_34><loc_87><loc_35></location>5</text>
<text><location><page_20><loc_86><loc_34><loc_87><loc_34></location>4</text>
<text><location><page_20><loc_86><loc_34><loc_87><loc_34></location>.</text>
<text><location><page_20><loc_86><loc_33><loc_87><loc_34></location>8</text>
<text><location><page_20><loc_86><loc_33><loc_87><loc_33></location>4</text>
<text><location><page_20><loc_86><loc_32><loc_87><loc_33></location>3</text>
<text><location><page_20><loc_86><loc_32><loc_87><loc_32></location>3</text>
<text><location><page_20><loc_86><loc_31><loc_87><loc_31></location>1</text>
<text><location><page_20><loc_86><loc_31><loc_87><loc_31></location>0</text>
<text><location><page_20><loc_86><loc_25><loc_87><loc_26></location>1</text>
<text><location><page_20><loc_86><loc_25><loc_87><loc_25></location>5</text>
<text><location><page_20><loc_86><loc_24><loc_87><loc_25></location>1</text>
<text><location><page_20><loc_86><loc_24><loc_87><loc_24></location>L</text>
<text><location><page_20><loc_86><loc_23><loc_87><loc_24></location>P</text>
<text><location><page_20><loc_86><loc_22><loc_87><loc_22></location>6</text>
<text><location><page_20><loc_86><loc_21><loc_87><loc_22></location>8</text>
<text><location><page_20><loc_86><loc_21><loc_87><loc_21></location>1</text>
<text><location><page_20><loc_86><loc_20><loc_87><loc_21></location>M</text>
<text><location><page_20><loc_86><loc_20><loc_87><loc_20></location>S</text>
<text><location><page_20><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_20><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_20><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_20><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_20><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_20><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_20><loc_86><loc_16><loc_87><loc_17></location>6</text>
<text><location><page_20><loc_86><loc_16><loc_87><loc_16></location>4</text>
<text><location><page_20><loc_86><loc_15><loc_87><loc_16></location>3</text>
<text><location><page_20><loc_87><loc_83><loc_88><loc_84></location>8</text>
<text><location><page_20><loc_87><loc_83><loc_88><loc_83></location>4</text>
<text><location><page_20><loc_87><loc_82><loc_88><loc_83></location>5</text>
<text><location><page_20><loc_87><loc_82><loc_88><loc_82></location>.</text>
<text><location><page_20><loc_87><loc_82><loc_88><loc_82></location>1</text>
<text><location><page_20><loc_87><loc_79><loc_88><loc_79></location>0</text>
<text><location><page_20><loc_87><loc_78><loc_88><loc_79></location>1</text>
<text><location><page_20><loc_87><loc_78><loc_88><loc_78></location>.</text>
<text><location><page_20><loc_87><loc_78><loc_88><loc_78></location>0</text>
<text><location><page_20><loc_87><loc_75><loc_88><loc_75></location>5</text>
<text><location><page_20><loc_87><loc_74><loc_88><loc_75></location>3</text>
<text><location><page_20><loc_87><loc_74><loc_88><loc_74></location>0</text>
<text><location><page_20><loc_87><loc_74><loc_88><loc_74></location>.</text>
<text><location><page_20><loc_87><loc_73><loc_88><loc_74></location>0</text>
<text><location><page_20><loc_87><loc_72><loc_88><loc_73></location>±</text>
<text><location><page_20><loc_87><loc_72><loc_88><loc_72></location>2</text>
<text><location><page_20><loc_87><loc_71><loc_88><loc_72></location>3</text>
<text><location><page_20><loc_87><loc_71><loc_88><loc_71></location>3</text>
<text><location><page_20><loc_87><loc_70><loc_88><loc_71></location>.</text>
<text><location><page_20><loc_87><loc_70><loc_88><loc_70></location>9</text>
<text><location><page_20><loc_87><loc_70><loc_88><loc_70></location>1</text>
<text><location><page_20><loc_87><loc_68><loc_88><loc_68></location>9</text>
<text><location><page_20><loc_87><loc_67><loc_88><loc_68></location>3</text>
<text><location><page_20><loc_87><loc_67><loc_88><loc_67></location>0</text>
<text><location><page_20><loc_87><loc_67><loc_88><loc_67></location>.</text>
<text><location><page_20><loc_87><loc_66><loc_88><loc_67></location>0</text>
<text><location><page_20><loc_87><loc_65><loc_88><loc_66></location>±</text>
<text><location><page_20><loc_87><loc_65><loc_88><loc_65></location>6</text>
<text><location><page_20><loc_87><loc_64><loc_88><loc_65></location>6</text>
<text><location><page_20><loc_87><loc_64><loc_88><loc_64></location>9</text>
<text><location><page_20><loc_87><loc_64><loc_88><loc_64></location>.</text>
<text><location><page_20><loc_87><loc_63><loc_88><loc_64></location>9</text>
<text><location><page_20><loc_87><loc_63><loc_88><loc_63></location>1</text>
<text><location><page_20><loc_87><loc_61><loc_88><loc_61></location>2</text>
<text><location><page_20><loc_87><loc_61><loc_88><loc_61></location>3</text>
<text><location><page_20><loc_87><loc_60><loc_88><loc_61></location>0</text>
<text><location><page_20><loc_87><loc_60><loc_88><loc_60></location>.</text>
<text><location><page_20><loc_87><loc_59><loc_88><loc_60></location>0</text>
<text><location><page_20><loc_87><loc_59><loc_88><loc_59></location>±</text>
<text><location><page_20><loc_87><loc_58><loc_88><loc_58></location>1</text>
<text><location><page_20><loc_87><loc_57><loc_88><loc_58></location>6</text>
<text><location><page_20><loc_87><loc_57><loc_88><loc_57></location>2</text>
<text><location><page_20><loc_87><loc_57><loc_88><loc_57></location>.</text>
<text><location><page_20><loc_87><loc_56><loc_88><loc_57></location>0</text>
<text><location><page_20><loc_87><loc_56><loc_88><loc_56></location>2</text>
<text><location><page_20><loc_87><loc_54><loc_88><loc_55></location>1</text>
<text><location><page_20><loc_87><loc_54><loc_88><loc_54></location>3</text>
<text><location><page_20><loc_87><loc_53><loc_88><loc_54></location>0</text>
<text><location><page_20><loc_87><loc_53><loc_88><loc_53></location>.</text>
<text><location><page_20><loc_87><loc_53><loc_88><loc_53></location>0</text>
<text><location><page_20><loc_87><loc_52><loc_88><loc_52></location>±</text>
<text><location><page_20><loc_87><loc_51><loc_88><loc_51></location>7</text>
<text><location><page_20><loc_87><loc_50><loc_88><loc_51></location>8</text>
<text><location><page_20><loc_87><loc_50><loc_88><loc_50></location>6</text>
<text><location><page_20><loc_87><loc_50><loc_88><loc_50></location>.</text>
<text><location><page_20><loc_87><loc_49><loc_88><loc_50></location>0</text>
<text><location><page_20><loc_87><loc_49><loc_88><loc_49></location>2</text>
<text><location><page_20><loc_87><loc_47><loc_88><loc_48></location>8</text>
<text><location><page_20><loc_87><loc_47><loc_88><loc_47></location>2</text>
<text><location><page_20><loc_87><loc_46><loc_88><loc_47></location>0</text>
<text><location><page_20><loc_87><loc_46><loc_88><loc_46></location>.</text>
<text><location><page_20><loc_87><loc_46><loc_88><loc_46></location>0</text>
<text><location><page_20><loc_87><loc_45><loc_88><loc_45></location>±</text>
<text><location><page_20><loc_87><loc_44><loc_88><loc_44></location>6</text>
<text><location><page_20><loc_87><loc_44><loc_88><loc_44></location>3</text>
<text><location><page_20><loc_87><loc_43><loc_88><loc_44></location>6</text>
<text><location><page_20><loc_87><loc_43><loc_88><loc_43></location>.</text>
<text><location><page_20><loc_87><loc_42><loc_88><loc_43></location>0</text>
<text><location><page_20><loc_87><loc_42><loc_88><loc_42></location>2</text>
<text><location><page_20><loc_87><loc_40><loc_88><loc_41></location>2</text>
<text><location><page_20><loc_87><loc_40><loc_88><loc_40></location>6</text>
<text><location><page_20><loc_87><loc_40><loc_88><loc_40></location>.</text>
<text><location><page_20><loc_87><loc_39><loc_88><loc_40></location>2</text>
<text><location><page_20><loc_87><loc_39><loc_88><loc_39></location>4</text>
<text><location><page_20><loc_87><loc_38><loc_88><loc_39></location>7</text>
<text><location><page_20><loc_87><loc_38><loc_88><loc_38></location>4</text>
<text><location><page_20><loc_87><loc_37><loc_88><loc_37></location>0</text>
<text><location><page_20><loc_87><loc_37><loc_88><loc_37></location>3</text>
<text><location><page_20><loc_87><loc_35><loc_88><loc_35></location>9</text>
<text><location><page_20><loc_87><loc_34><loc_88><loc_35></location>3</text>
<text><location><page_20><loc_87><loc_34><loc_88><loc_34></location>6</text>
<text><location><page_20><loc_87><loc_34><loc_88><loc_34></location>.</text>
<text><location><page_20><loc_87><loc_33><loc_88><loc_34></location>8</text>
<text><location><page_20><loc_87><loc_33><loc_88><loc_33></location>4</text>
<text><location><page_20><loc_87><loc_32><loc_88><loc_33></location>3</text>
<text><location><page_20><loc_87><loc_32><loc_88><loc_32></location>3</text>
<text><location><page_20><loc_87><loc_31><loc_88><loc_31></location>1</text>
<text><location><page_20><loc_87><loc_31><loc_88><loc_31></location>0</text>
<text><location><page_20><loc_87><loc_25><loc_88><loc_26></location>2</text>
<text><location><page_20><loc_87><loc_25><loc_88><loc_25></location>5</text>
<text><location><page_20><loc_87><loc_24><loc_88><loc_25></location>1</text>
<text><location><page_20><loc_87><loc_24><loc_88><loc_24></location>L</text>
<text><location><page_20><loc_87><loc_23><loc_88><loc_24></location>P</text>
<text><location><page_20><loc_87><loc_22><loc_88><loc_22></location>7</text>
<text><location><page_20><loc_87><loc_21><loc_88><loc_22></location>8</text>
<text><location><page_20><loc_87><loc_21><loc_88><loc_21></location>1</text>
<text><location><page_20><loc_87><loc_20><loc_88><loc_21></location>M</text>
<text><location><page_20><loc_87><loc_20><loc_88><loc_20></location>S</text>
<text><location><page_20><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_20><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_20><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_20><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_20><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_20><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_20><loc_87><loc_16><loc_88><loc_17></location>7</text>
<text><location><page_20><loc_87><loc_16><loc_88><loc_16></location>4</text>
<text><location><page_20><loc_87><loc_15><loc_88><loc_16></location>3</text>
<text><location><page_21><loc_13><loc_51><loc_14><loc_52></location>3</text>
<text><location><page_21><loc_13><loc_50><loc_14><loc_51></location>E</text>
<text><location><page_21><loc_13><loc_50><loc_14><loc_50></location>L</text>
<text><location><page_21><loc_13><loc_48><loc_14><loc_50></location>AB</text>
<text><location><page_21><loc_13><loc_47><loc_14><loc_48></location>T</text>
<text><location><page_21><loc_14><loc_52><loc_15><loc_53></location>)</text>
<text><location><page_21><loc_14><loc_52><loc_15><loc_52></location>.</text>
<text><location><page_21><loc_14><loc_52><loc_15><loc_52></location>d</text>
<text><location><page_21><loc_14><loc_51><loc_15><loc_52></location>e</text>
<text><location><page_21><loc_14><loc_50><loc_15><loc_51></location>u</text>
<text><location><page_21><loc_14><loc_50><loc_15><loc_50></location>n</text>
<text><location><page_21><loc_14><loc_49><loc_15><loc_50></location>i</text>
<text><location><page_21><loc_14><loc_49><loc_15><loc_49></location>t</text>
<text><location><page_21><loc_14><loc_48><loc_15><loc_49></location>n</text>
<text><location><page_21><loc_14><loc_48><loc_15><loc_48></location>o</text>
<text><location><page_21><loc_14><loc_47><loc_15><loc_48></location>C</text>
<text><location><page_21><loc_14><loc_46><loc_15><loc_47></location>(</text>
<text><location><page_21><loc_20><loc_83><loc_20><loc_84></location>2</text>
<text><location><page_21><loc_21><loc_83><loc_22><loc_84></location>0</text>
<text><location><page_21><loc_22><loc_83><loc_23><loc_84></location>2</text>
<text><location><page_21><loc_23><loc_83><loc_24><loc_84></location>8</text>
<text><location><page_21><loc_24><loc_83><loc_25><loc_84></location>4</text>
<text><location><page_21><loc_26><loc_83><loc_27><loc_84></location>0</text>
<text><location><page_21><loc_27><loc_83><loc_28><loc_84></location>6</text>
<text><location><page_21><loc_28><loc_83><loc_29><loc_84></location>6</text>
<text><location><page_21><loc_29><loc_83><loc_30><loc_84></location>4</text>
<text><location><page_21><loc_31><loc_83><loc_31><loc_84></location>4</text>
<text><location><page_21><loc_32><loc_83><loc_33><loc_84></location>4</text>
<text><location><page_21><loc_33><loc_83><loc_34><loc_84></location>2</text>
<text><location><page_21><loc_34><loc_83><loc_35><loc_84></location>0</text>
<text><location><page_21><loc_36><loc_83><loc_36><loc_84></location>4</text>
<text><location><page_21><loc_37><loc_83><loc_38><loc_84></location>6</text>
<text><location><page_21><loc_38><loc_83><loc_39><loc_84></location>8</text>
<text><location><page_21><loc_39><loc_83><loc_40><loc_84></location>8</text>
<text><location><page_21><loc_40><loc_83><loc_41><loc_84></location>0</text>
<text><location><page_21><loc_42><loc_83><loc_42><loc_84></location>6</text>
<text><location><page_21><loc_43><loc_83><loc_44><loc_84></location>8</text>
<text><location><page_21><loc_44><loc_83><loc_45><loc_84></location>2</text>
<text><location><page_21><loc_45><loc_83><loc_46><loc_84></location>4</text>
<text><location><page_21><loc_47><loc_83><loc_47><loc_84></location>4</text>
<text><location><page_21><loc_48><loc_83><loc_49><loc_84></location>0</text>
<text><location><page_21><loc_49><loc_83><loc_50><loc_84></location>0</text>
<text><location><page_21><loc_50><loc_83><loc_51><loc_84></location>0</text>
<text><location><page_21><loc_51><loc_83><loc_52><loc_84></location>4</text>
<text><location><page_21><loc_53><loc_83><loc_54><loc_84></location>4</text>
<text><location><page_21><loc_54><loc_83><loc_55><loc_84></location>8</text>
<text><location><page_21><loc_55><loc_83><loc_56><loc_84></location>8</text>
<text><location><page_21><loc_56><loc_83><loc_57><loc_84></location>8</text>
<text><location><page_21><loc_58><loc_83><loc_58><loc_84></location>6</text>
<text><location><page_21><loc_59><loc_83><loc_60><loc_84></location>6</text>
<text><location><page_21><loc_60><loc_83><loc_61><loc_84></location>8</text>
<text><location><page_21><loc_61><loc_83><loc_62><loc_84></location>0</text>
<text><location><page_21><loc_63><loc_83><loc_63><loc_84></location>4</text>
<text><location><page_21><loc_64><loc_83><loc_65><loc_84></location>6</text>
<text><location><page_21><loc_65><loc_83><loc_66><loc_84></location>4</text>
<text><location><page_21><loc_66><loc_83><loc_67><loc_84></location>6</text>
<text><location><page_21><loc_67><loc_83><loc_68><loc_84></location>8</text>
<text><location><page_21><loc_69><loc_83><loc_69><loc_84></location>2</text>
<text><location><page_21><loc_70><loc_83><loc_71><loc_84></location>0</text>
<text><location><page_21><loc_71><loc_83><loc_72><loc_84></location>6</text>
<text><location><page_21><loc_72><loc_83><loc_73><loc_84></location>6</text>
<text><location><page_21><loc_74><loc_83><loc_74><loc_84></location>2</text>
<text><location><page_21><loc_75><loc_83><loc_76><loc_84></location>6</text>
<text><location><page_21><loc_76><loc_83><loc_77><loc_84></location>4</text>
<text><location><page_21><loc_77><loc_83><loc_78><loc_84></location>8</text>
<text><location><page_21><loc_78><loc_83><loc_79><loc_84></location>0</text>
<text><location><page_21><loc_80><loc_83><loc_81><loc_84></location>2</text>
<text><location><page_21><loc_81><loc_83><loc_82><loc_84></location>6</text>
<text><location><page_21><loc_82><loc_83><loc_83><loc_84></location>6</text>
<text><location><page_21><loc_83><loc_83><loc_84><loc_84></location>2</text>
<text><location><page_21><loc_42><loc_93><loc_57><loc_94></location>Star clusters in M33</text>
<text><location><page_21><loc_90><loc_93><loc_92><loc_94></location>21</text>
<table>
<location><page_21><loc_15><loc_12><loc_84><loc_83></location>
</table>
<text><location><page_21><loc_85><loc_83><loc_85><loc_84></location>6</text>
<text><location><page_21><loc_85><loc_83><loc_85><loc_83></location>0</text>
<text><location><page_21><loc_85><loc_82><loc_85><loc_83></location>8</text>
<text><location><page_21><loc_85><loc_82><loc_85><loc_82></location>.</text>
<text><location><page_21><loc_85><loc_82><loc_85><loc_82></location>1</text>
<text><location><page_21><loc_85><loc_79><loc_85><loc_79></location>5</text>
<text><location><page_21><loc_85><loc_78><loc_85><loc_79></location>1</text>
<text><location><page_21><loc_85><loc_78><loc_85><loc_78></location>.</text>
<text><location><page_21><loc_85><loc_78><loc_85><loc_78></location>0</text>
<text><location><page_21><loc_85><loc_75><loc_85><loc_75></location>2</text>
<text><location><page_21><loc_85><loc_74><loc_85><loc_75></location>4</text>
<text><location><page_21><loc_85><loc_74><loc_85><loc_74></location>0</text>
<text><location><page_21><loc_85><loc_74><loc_85><loc_74></location>.</text>
<text><location><page_21><loc_85><loc_73><loc_85><loc_74></location>0</text>
<text><location><page_21><loc_85><loc_72><loc_85><loc_73></location>±</text>
<text><location><page_21><loc_85><loc_72><loc_85><loc_72></location>8</text>
<text><location><page_21><loc_85><loc_71><loc_85><loc_72></location>1</text>
<text><location><page_21><loc_85><loc_71><loc_85><loc_71></location>7</text>
<text><location><page_21><loc_85><loc_70><loc_85><loc_71></location>.</text>
<text><location><page_21><loc_85><loc_70><loc_85><loc_70></location>9</text>
<text><location><page_21><loc_85><loc_70><loc_85><loc_70></location>1</text>
<text><location><page_21><loc_85><loc_68><loc_85><loc_68></location>0</text>
<text><location><page_21><loc_85><loc_67><loc_85><loc_68></location>4</text>
<text><location><page_21><loc_85><loc_67><loc_85><loc_67></location>0</text>
<text><location><page_21><loc_85><loc_67><loc_85><loc_67></location>.</text>
<text><location><page_21><loc_85><loc_66><loc_85><loc_67></location>0</text>
<text><location><page_21><loc_85><loc_65><loc_85><loc_66></location>±</text>
<text><location><page_21><loc_85><loc_65><loc_85><loc_65></location>7</text>
<text><location><page_21><loc_85><loc_64><loc_85><loc_65></location>1</text>
<text><location><page_21><loc_85><loc_64><loc_85><loc_64></location>0</text>
<text><location><page_21><loc_85><loc_64><loc_85><loc_64></location>.</text>
<text><location><page_21><loc_85><loc_63><loc_85><loc_64></location>0</text>
<text><location><page_21><loc_85><loc_63><loc_85><loc_63></location>2</text>
<text><location><page_21><loc_85><loc_61><loc_85><loc_61></location>3</text>
<text><location><page_21><loc_85><loc_61><loc_85><loc_61></location>3</text>
<text><location><page_21><loc_85><loc_60><loc_85><loc_61></location>0</text>
<text><location><page_21><loc_85><loc_60><loc_85><loc_60></location>.</text>
<text><location><page_21><loc_85><loc_59><loc_85><loc_60></location>0</text>
<text><location><page_21><loc_85><loc_59><loc_85><loc_59></location>±</text>
<text><location><page_21><loc_85><loc_58><loc_85><loc_58></location>8</text>
<text><location><page_21><loc_85><loc_57><loc_85><loc_58></location>7</text>
<text><location><page_21><loc_85><loc_57><loc_85><loc_57></location>1</text>
<text><location><page_21><loc_85><loc_57><loc_85><loc_57></location>.</text>
<text><location><page_21><loc_85><loc_56><loc_85><loc_57></location>0</text>
<text><location><page_21><loc_85><loc_56><loc_85><loc_56></location>2</text>
<text><location><page_21><loc_85><loc_54><loc_85><loc_55></location>5</text>
<text><location><page_21><loc_85><loc_54><loc_85><loc_54></location>3</text>
<text><location><page_21><loc_85><loc_53><loc_85><loc_54></location>0</text>
<text><location><page_21><loc_85><loc_53><loc_85><loc_53></location>.</text>
<text><location><page_21><loc_85><loc_53><loc_85><loc_53></location>0</text>
<text><location><page_21><loc_85><loc_52><loc_85><loc_52></location>±</text>
<text><location><page_21><loc_85><loc_51><loc_85><loc_51></location>0</text>
<text><location><page_21><loc_85><loc_50><loc_85><loc_51></location>6</text>
<text><location><page_21><loc_85><loc_50><loc_85><loc_50></location>6</text>
<text><location><page_21><loc_85><loc_50><loc_85><loc_50></location>.</text>
<text><location><page_21><loc_85><loc_49><loc_85><loc_50></location>0</text>
<text><location><page_21><loc_85><loc_49><loc_85><loc_49></location>2</text>
<text><location><page_21><loc_85><loc_47><loc_85><loc_48></location>6</text>
<text><location><page_21><loc_85><loc_47><loc_85><loc_47></location>2</text>
<text><location><page_21><loc_85><loc_46><loc_85><loc_47></location>0</text>
<text><location><page_21><loc_85><loc_46><loc_85><loc_46></location>.</text>
<text><location><page_21><loc_85><loc_46><loc_85><loc_46></location>0</text>
<text><location><page_21><loc_85><loc_45><loc_85><loc_45></location>±</text>
<text><location><page_21><loc_85><loc_44><loc_85><loc_44></location>8</text>
<text><location><page_21><loc_85><loc_44><loc_85><loc_44></location>0</text>
<text><location><page_21><loc_85><loc_43><loc_85><loc_44></location>4</text>
<text><location><page_21><loc_85><loc_43><loc_85><loc_43></location>.</text>
<text><location><page_21><loc_85><loc_42><loc_85><loc_43></location>0</text>
<text><location><page_21><loc_85><loc_42><loc_85><loc_42></location>2</text>
<text><location><page_21><loc_85><loc_40><loc_85><loc_41></location>6</text>
<text><location><page_21><loc_85><loc_40><loc_85><loc_40></location>3</text>
<text><location><page_21><loc_85><loc_40><loc_85><loc_40></location>.</text>
<text><location><page_21><loc_85><loc_39><loc_85><loc_40></location>8</text>
<text><location><page_21><loc_85><loc_39><loc_85><loc_39></location>3</text>
<text><location><page_21><loc_85><loc_38><loc_85><loc_39></location>7</text>
<text><location><page_21><loc_85><loc_38><loc_85><loc_38></location>4</text>
<text><location><page_21><loc_85><loc_37><loc_85><loc_37></location>0</text>
<text><location><page_21><loc_85><loc_37><loc_85><loc_37></location>3</text>
<text><location><page_21><loc_85><loc_35><loc_85><loc_35></location>0</text>
<text><location><page_21><loc_85><loc_34><loc_85><loc_35></location>4</text>
<text><location><page_21><loc_85><loc_34><loc_85><loc_34></location>6</text>
<text><location><page_21><loc_85><loc_34><loc_85><loc_34></location>.</text>
<text><location><page_21><loc_85><loc_33><loc_85><loc_34></location>9</text>
<text><location><page_21><loc_85><loc_33><loc_85><loc_33></location>5</text>
<text><location><page_21><loc_85><loc_32><loc_85><loc_33></location>3</text>
<text><location><page_21><loc_85><loc_32><loc_85><loc_32></location>3</text>
<text><location><page_21><loc_85><loc_31><loc_85><loc_31></location>1</text>
<text><location><page_21><loc_85><loc_31><loc_85><loc_31></location>0</text>
<text><location><page_21><loc_85><loc_25><loc_85><loc_26></location>1</text>
<text><location><page_21><loc_85><loc_25><loc_85><loc_25></location>8</text>
<text><location><page_21><loc_85><loc_24><loc_85><loc_25></location>1</text>
<text><location><page_21><loc_85><loc_24><loc_85><loc_24></location>L</text>
<text><location><page_21><loc_85><loc_23><loc_85><loc_24></location>P</text>
<text><location><page_21><loc_85><loc_22><loc_85><loc_22></location>6</text>
<text><location><page_21><loc_85><loc_21><loc_85><loc_22></location>5</text>
<text><location><page_21><loc_85><loc_21><loc_85><loc_21></location>2</text>
<text><location><page_21><loc_85><loc_20><loc_85><loc_21></location>M</text>
<text><location><page_21><loc_85><loc_20><loc_85><loc_20></location>S</text>
<text><location><page_21><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_21><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_21><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_21><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_21><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_21><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_21><loc_85><loc_16><loc_85><loc_17></location>1</text>
<text><location><page_21><loc_85><loc_16><loc_85><loc_16></location>0</text>
<text><location><page_21><loc_85><loc_15><loc_85><loc_16></location>4</text>
<text><location><page_21><loc_86><loc_83><loc_87><loc_84></location>0</text>
<text><location><page_21><loc_86><loc_83><loc_87><loc_83></location>8</text>
<text><location><page_21><loc_86><loc_82><loc_87><loc_83></location>5</text>
<text><location><page_21><loc_86><loc_82><loc_87><loc_82></location>.</text>
<text><location><page_21><loc_86><loc_82><loc_87><loc_82></location>2</text>
<text><location><page_21><loc_86><loc_79><loc_87><loc_79></location>0</text>
<text><location><page_21><loc_86><loc_78><loc_87><loc_79></location>1</text>
<text><location><page_21><loc_86><loc_78><loc_87><loc_78></location>.</text>
<text><location><page_21><loc_86><loc_78><loc_87><loc_78></location>0</text>
<text><location><page_21><loc_86><loc_75><loc_87><loc_75></location>6</text>
<text><location><page_21><loc_86><loc_74><loc_87><loc_75></location>1</text>
<text><location><page_21><loc_86><loc_74><loc_87><loc_74></location>0</text>
<text><location><page_21><loc_86><loc_74><loc_87><loc_74></location>.</text>
<text><location><page_21><loc_86><loc_73><loc_87><loc_74></location>0</text>
<text><location><page_21><loc_86><loc_72><loc_87><loc_73></location>±</text>
<text><location><page_21><loc_86><loc_72><loc_87><loc_72></location>9</text>
<text><location><page_21><loc_86><loc_71><loc_87><loc_72></location>7</text>
<text><location><page_21><loc_86><loc_71><loc_87><loc_71></location>3</text>
<text><location><page_21><loc_86><loc_70><loc_87><loc_71></location>.</text>
<text><location><page_21><loc_86><loc_70><loc_87><loc_70></location>7</text>
<text><location><page_21><loc_86><loc_70><loc_87><loc_70></location>1</text>
<text><location><page_21><loc_86><loc_68><loc_87><loc_68></location>0</text>
<text><location><page_21><loc_86><loc_67><loc_87><loc_68></location>1</text>
<text><location><page_21><loc_86><loc_67><loc_87><loc_67></location>0</text>
<text><location><page_21><loc_86><loc_67><loc_87><loc_67></location>.</text>
<text><location><page_21><loc_86><loc_66><loc_87><loc_67></location>0</text>
<text><location><page_21><loc_86><loc_65><loc_87><loc_66></location>±</text>
<text><location><page_21><loc_86><loc_65><loc_87><loc_65></location>8</text>
<text><location><page_21><loc_86><loc_64><loc_87><loc_65></location>3</text>
<text><location><page_21><loc_86><loc_64><loc_87><loc_64></location>3</text>
<text><location><page_21><loc_86><loc_64><loc_87><loc_64></location>.</text>
<text><location><page_21><loc_86><loc_63><loc_87><loc_64></location>7</text>
<text><location><page_21><loc_86><loc_63><loc_87><loc_63></location>1</text>
<text><location><page_21><loc_86><loc_61><loc_87><loc_61></location>7</text>
<text><location><page_21><loc_86><loc_61><loc_87><loc_61></location>0</text>
<text><location><page_21><loc_86><loc_60><loc_87><loc_61></location>0</text>
<text><location><page_21><loc_86><loc_60><loc_87><loc_60></location>.</text>
<text><location><page_21><loc_86><loc_59><loc_87><loc_60></location>0</text>
<text><location><page_21><loc_86><loc_59><loc_87><loc_59></location>±</text>
<text><location><page_21><loc_86><loc_58><loc_87><loc_58></location>2</text>
<text><location><page_21><loc_86><loc_57><loc_87><loc_58></location>6</text>
<text><location><page_21><loc_86><loc_57><loc_87><loc_57></location>3</text>
<text><location><page_21><loc_86><loc_57><loc_87><loc_57></location>.</text>
<text><location><page_21><loc_86><loc_56><loc_87><loc_57></location>7</text>
<text><location><page_21><loc_86><loc_56><loc_87><loc_56></location>1</text>
<text><location><page_21><loc_86><loc_54><loc_87><loc_55></location>7</text>
<text><location><page_21><loc_86><loc_54><loc_87><loc_54></location>0</text>
<text><location><page_21><loc_86><loc_53><loc_87><loc_54></location>0</text>
<text><location><page_21><loc_86><loc_53><loc_87><loc_53></location>.</text>
<text><location><page_21><loc_86><loc_53><loc_87><loc_53></location>0</text>
<text><location><page_21><loc_86><loc_52><loc_87><loc_52></location>±</text>
<text><location><page_21><loc_86><loc_51><loc_87><loc_51></location>1</text>
<text><location><page_21><loc_86><loc_50><loc_87><loc_51></location>5</text>
<text><location><page_21><loc_86><loc_50><loc_87><loc_50></location>5</text>
<text><location><page_21><loc_86><loc_50><loc_87><loc_50></location>.</text>
<text><location><page_21><loc_86><loc_49><loc_87><loc_50></location>7</text>
<text><location><page_21><loc_86><loc_49><loc_87><loc_49></location>1</text>
<text><location><page_21><loc_86><loc_47><loc_87><loc_48></location>3</text>
<text><location><page_21><loc_86><loc_47><loc_87><loc_47></location>0</text>
<text><location><page_21><loc_86><loc_46><loc_87><loc_47></location>0</text>
<text><location><page_21><loc_86><loc_46><loc_87><loc_46></location>.</text>
<text><location><page_21><loc_86><loc_46><loc_87><loc_46></location>0</text>
<text><location><page_21><loc_86><loc_45><loc_87><loc_45></location>±</text>
<text><location><page_21><loc_86><loc_44><loc_87><loc_44></location>3</text>
<text><location><page_21><loc_86><loc_44><loc_87><loc_44></location>6</text>
<text><location><page_21><loc_86><loc_43><loc_87><loc_44></location>7</text>
<text><location><page_21><loc_86><loc_43><loc_87><loc_43></location>.</text>
<text><location><page_21><loc_86><loc_42><loc_87><loc_43></location>6</text>
<text><location><page_21><loc_86><loc_42><loc_87><loc_42></location>1</text>
<text><location><page_21><loc_86><loc_40><loc_87><loc_41></location>5</text>
<text><location><page_21><loc_86><loc_40><loc_87><loc_40></location>3</text>
<text><location><page_21><loc_86><loc_40><loc_87><loc_40></location>.</text>
<text><location><page_21><loc_86><loc_39><loc_87><loc_40></location>4</text>
<text><location><page_21><loc_86><loc_39><loc_87><loc_39></location>2</text>
<text><location><page_21><loc_86><loc_38><loc_87><loc_39></location>1</text>
<text><location><page_21><loc_86><loc_38><loc_87><loc_38></location>4</text>
<text><location><page_21><loc_86><loc_37><loc_87><loc_37></location>0</text>
<text><location><page_21><loc_86><loc_37><loc_87><loc_37></location>3</text>
<text><location><page_21><loc_86><loc_35><loc_87><loc_35></location>4</text>
<text><location><page_21><loc_86><loc_34><loc_87><loc_35></location>3</text>
<text><location><page_21><loc_86><loc_34><loc_87><loc_34></location>7</text>
<text><location><page_21><loc_86><loc_34><loc_87><loc_34></location>.</text>
<text><location><page_21><loc_86><loc_33><loc_87><loc_34></location>9</text>
<text><location><page_21><loc_86><loc_33><loc_87><loc_33></location>5</text>
<text><location><page_21><loc_86><loc_32><loc_87><loc_33></location>3</text>
<text><location><page_21><loc_86><loc_32><loc_87><loc_32></location>3</text>
<text><location><page_21><loc_86><loc_31><loc_87><loc_31></location>1</text>
<text><location><page_21><loc_86><loc_31><loc_87><loc_31></location>0</text>
<text><location><page_21><loc_86><loc_25><loc_87><loc_26></location>2</text>
<text><location><page_21><loc_86><loc_25><loc_87><loc_25></location>8</text>
<text><location><page_21><loc_86><loc_24><loc_87><loc_25></location>1</text>
<text><location><page_21><loc_86><loc_24><loc_87><loc_24></location>L</text>
<text><location><page_21><loc_86><loc_23><loc_87><loc_24></location>P</text>
<text><location><page_21><loc_86><loc_22><loc_87><loc_22></location>7</text>
<text><location><page_21><loc_86><loc_21><loc_87><loc_22></location>5</text>
<text><location><page_21><loc_86><loc_21><loc_87><loc_21></location>2</text>
<text><location><page_21><loc_86><loc_20><loc_87><loc_21></location>M</text>
<text><location><page_21><loc_86><loc_20><loc_87><loc_20></location>S</text>
<text><location><page_21><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_21><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_21><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_21><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_21><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_21><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_21><loc_86><loc_16><loc_87><loc_17></location>2</text>
<text><location><page_21><loc_86><loc_16><loc_87><loc_16></location>0</text>
<text><location><page_21><loc_86><loc_15><loc_87><loc_16></location>4</text>
<text><location><page_21><loc_87><loc_83><loc_88><loc_84></location>0</text>
<text><location><page_21><loc_87><loc_83><loc_88><loc_83></location>8</text>
<text><location><page_21><loc_87><loc_82><loc_88><loc_83></location>5</text>
<text><location><page_21><loc_87><loc_82><loc_88><loc_82></location>.</text>
<text><location><page_21><loc_87><loc_82><loc_88><loc_82></location>2</text>
<text><location><page_21><loc_87><loc_79><loc_88><loc_79></location>5</text>
<text><location><page_21><loc_87><loc_78><loc_88><loc_79></location>1</text>
<text><location><page_21><loc_87><loc_78><loc_88><loc_78></location>.</text>
<text><location><page_21><loc_87><loc_78><loc_88><loc_78></location>0</text>
<text><location><page_21><loc_87><loc_75><loc_88><loc_75></location>4</text>
<text><location><page_21><loc_87><loc_74><loc_88><loc_75></location>6</text>
<text><location><page_21><loc_87><loc_74><loc_88><loc_74></location>0</text>
<text><location><page_21><loc_87><loc_74><loc_88><loc_74></location>.</text>
<text><location><page_21><loc_87><loc_73><loc_88><loc_74></location>0</text>
<text><location><page_21><loc_87><loc_72><loc_88><loc_73></location>±</text>
<text><location><page_21><loc_87><loc_72><loc_88><loc_72></location>1</text>
<text><location><page_21><loc_87><loc_71><loc_88><loc_72></location>6</text>
<text><location><page_21><loc_87><loc_71><loc_88><loc_71></location>9</text>
<text><location><page_21><loc_87><loc_70><loc_88><loc_71></location>.</text>
<text><location><page_21><loc_87><loc_70><loc_88><loc_70></location>7</text>
<text><location><page_21><loc_87><loc_70><loc_88><loc_70></location>1</text>
<text><location><page_21><loc_87><loc_68><loc_88><loc_68></location>6</text>
<text><location><page_21><loc_87><loc_67><loc_88><loc_68></location>6</text>
<text><location><page_21><loc_87><loc_67><loc_88><loc_67></location>0</text>
<text><location><page_21><loc_87><loc_67><loc_88><loc_67></location>.</text>
<text><location><page_21><loc_87><loc_66><loc_88><loc_67></location>0</text>
<text><location><page_21><loc_87><loc_65><loc_88><loc_66></location>±</text>
<text><location><page_21><loc_87><loc_65><loc_88><loc_65></location>4</text>
<text><location><page_21><loc_87><loc_64><loc_88><loc_65></location>6</text>
<text><location><page_21><loc_87><loc_64><loc_88><loc_64></location>5</text>
<text><location><page_21><loc_87><loc_64><loc_88><loc_64></location>.</text>
<text><location><page_21><loc_87><loc_63><loc_88><loc_64></location>8</text>
<text><location><page_21><loc_87><loc_63><loc_88><loc_63></location>1</text>
<text><location><page_21><loc_87><loc_61><loc_88><loc_61></location>3</text>
<text><location><page_21><loc_87><loc_61><loc_88><loc_61></location>7</text>
<text><location><page_21><loc_87><loc_60><loc_88><loc_61></location>0</text>
<text><location><page_21><loc_87><loc_60><loc_88><loc_60></location>.</text>
<text><location><page_21><loc_87><loc_59><loc_88><loc_60></location>0</text>
<text><location><page_21><loc_87><loc_59><loc_88><loc_59></location>±</text>
<text><location><page_21><loc_87><loc_58><loc_88><loc_58></location>1</text>
<text><location><page_21><loc_87><loc_57><loc_88><loc_58></location>8</text>
<text><location><page_21><loc_87><loc_57><loc_88><loc_57></location>0</text>
<text><location><page_21><loc_87><loc_57><loc_88><loc_57></location>.</text>
<text><location><page_21><loc_87><loc_56><loc_88><loc_57></location>9</text>
<text><location><page_21><loc_87><loc_56><loc_88><loc_56></location>1</text>
<text><location><page_21><loc_87><loc_54><loc_88><loc_55></location>7</text>
<text><location><page_21><loc_87><loc_54><loc_88><loc_54></location>8</text>
<text><location><page_21><loc_87><loc_53><loc_88><loc_54></location>0</text>
<text><location><page_21><loc_87><loc_53><loc_88><loc_53></location>.</text>
<text><location><page_21><loc_87><loc_53><loc_88><loc_53></location>0</text>
<text><location><page_21><loc_87><loc_52><loc_88><loc_52></location>±</text>
<text><location><page_21><loc_87><loc_51><loc_88><loc_51></location>7</text>
<text><location><page_21><loc_87><loc_50><loc_88><loc_51></location>0</text>
<text><location><page_21><loc_87><loc_50><loc_88><loc_50></location>8</text>
<text><location><page_21><loc_87><loc_50><loc_88><loc_50></location>.</text>
<text><location><page_21><loc_87><loc_49><loc_88><loc_50></location>9</text>
<text><location><page_21><loc_87><loc_49><loc_88><loc_49></location>1</text>
<text><location><page_21><loc_87><loc_47><loc_88><loc_48></location>0</text>
<text><location><page_21><loc_87><loc_47><loc_88><loc_47></location>7</text>
<text><location><page_21><loc_87><loc_46><loc_88><loc_47></location>0</text>
<text><location><page_21><loc_87><loc_46><loc_88><loc_46></location>.</text>
<text><location><page_21><loc_87><loc_46><loc_88><loc_46></location>0</text>
<text><location><page_21><loc_87><loc_45><loc_88><loc_45></location>±</text>
<text><location><page_21><loc_87><loc_44><loc_88><loc_44></location>5</text>
<text><location><page_21><loc_87><loc_44><loc_88><loc_44></location>5</text>
<text><location><page_21><loc_87><loc_43><loc_88><loc_44></location>3</text>
<text><location><page_21><loc_87><loc_43><loc_88><loc_43></location>.</text>
<text><location><page_21><loc_87><loc_42><loc_88><loc_43></location>9</text>
<text><location><page_21><loc_87><loc_42><loc_88><loc_42></location>1</text>
<text><location><page_21><loc_87><loc_40><loc_88><loc_41></location>1</text>
<text><location><page_21><loc_87><loc_40><loc_88><loc_40></location>4</text>
<text><location><page_21><loc_87><loc_40><loc_88><loc_40></location>.</text>
<text><location><page_21><loc_87><loc_39><loc_88><loc_40></location>5</text>
<text><location><page_21><loc_87><loc_39><loc_88><loc_39></location>4</text>
<text><location><page_21><loc_87><loc_38><loc_88><loc_39></location>9</text>
<text><location><page_21><loc_87><loc_38><loc_88><loc_38></location>3</text>
<text><location><page_21><loc_87><loc_37><loc_88><loc_37></location>0</text>
<text><location><page_21><loc_87><loc_37><loc_88><loc_37></location>3</text>
<text><location><page_21><loc_87><loc_35><loc_88><loc_35></location>5</text>
<text><location><page_21><loc_87><loc_34><loc_88><loc_35></location>1</text>
<text><location><page_21><loc_87><loc_34><loc_88><loc_34></location>8</text>
<text><location><page_21><loc_87><loc_34><loc_88><loc_34></location>.</text>
<text><location><page_21><loc_87><loc_33><loc_88><loc_34></location>9</text>
<text><location><page_21><loc_87><loc_33><loc_88><loc_33></location>5</text>
<text><location><page_21><loc_87><loc_32><loc_88><loc_33></location>3</text>
<text><location><page_21><loc_87><loc_32><loc_88><loc_32></location>3</text>
<text><location><page_21><loc_87><loc_31><loc_88><loc_31></location>1</text>
<text><location><page_21><loc_87><loc_31><loc_88><loc_31></location>0</text>
<text><location><page_21><loc_87><loc_25><loc_88><loc_25></location>4</text>
<text><location><page_21><loc_87><loc_25><loc_88><loc_25></location>8</text>
<text><location><page_21><loc_87><loc_24><loc_88><loc_25></location>L</text>
<text><location><page_21><loc_87><loc_24><loc_88><loc_24></location>P</text>
<text><location><page_21><loc_87><loc_22><loc_88><loc_22></location>8</text>
<text><location><page_21><loc_87><loc_21><loc_88><loc_22></location>5</text>
<text><location><page_21><loc_87><loc_21><loc_88><loc_21></location>2</text>
<text><location><page_21><loc_87><loc_20><loc_88><loc_21></location>M</text>
<text><location><page_21><loc_87><loc_20><loc_88><loc_20></location>S</text>
<text><location><page_21><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_21><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_21><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_21><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_21><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_21><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_21><loc_87><loc_16><loc_88><loc_17></location>3</text>
<text><location><page_21><loc_87><loc_16><loc_88><loc_16></location>0</text>
<text><location><page_21><loc_87><loc_15><loc_88><loc_16></location>4</text>
<text><location><page_22><loc_9><loc_93><loc_10><loc_94></location>22</text>
<text><location><page_22><loc_50><loc_93><loc_52><loc_94></location>Ma</text>
<table>
<location><page_22><loc_15><loc_12><loc_84><loc_83></location>
</table>
<text><location><page_22><loc_13><loc_51><loc_14><loc_52></location>3</text>
<text><location><page_22><loc_13><loc_50><loc_14><loc_51></location>E</text>
<text><location><page_22><loc_13><loc_50><loc_14><loc_50></location>L</text>
<text><location><page_22><loc_13><loc_48><loc_14><loc_50></location>AB</text>
<text><location><page_22><loc_13><loc_47><loc_14><loc_48></location>T</text>
<text><location><page_22><loc_14><loc_52><loc_15><loc_53></location>)</text>
<text><location><page_22><loc_14><loc_52><loc_15><loc_52></location>.</text>
<text><location><page_22><loc_14><loc_52><loc_15><loc_52></location>d</text>
<text><location><page_22><loc_14><loc_51><loc_15><loc_52></location>e</text>
<text><location><page_22><loc_14><loc_50><loc_15><loc_51></location>u</text>
<text><location><page_22><loc_14><loc_50><loc_15><loc_50></location>n</text>
<text><location><page_22><loc_14><loc_49><loc_15><loc_50></location>i</text>
<text><location><page_22><loc_14><loc_49><loc_15><loc_49></location>t</text>
<text><location><page_22><loc_14><loc_48><loc_15><loc_49></location>n</text>
<text><location><page_22><loc_14><loc_48><loc_15><loc_48></location>o</text>
<text><location><page_22><loc_14><loc_47><loc_15><loc_48></location>C</text>
<text><location><page_22><loc_14><loc_46><loc_15><loc_47></location>(</text>
<text><location><page_22><loc_20><loc_83><loc_20><loc_84></location>6</text>
<text><location><page_22><loc_21><loc_83><loc_22><loc_84></location>0</text>
<text><location><page_22><loc_22><loc_83><loc_23><loc_84></location>2</text>
<text><location><page_22><loc_23><loc_83><loc_24><loc_84></location>0</text>
<text><location><page_22><loc_24><loc_83><loc_25><loc_84></location>6</text>
<text><location><page_22><loc_26><loc_83><loc_27><loc_84></location>2</text>
<text><location><page_22><loc_27><loc_83><loc_28><loc_84></location>0</text>
<text><location><page_22><loc_28><loc_83><loc_29><loc_84></location>4</text>
<text><location><page_22><loc_29><loc_83><loc_30><loc_84></location>4</text>
<text><location><page_22><loc_31><loc_83><loc_31><loc_84></location>4</text>
<text><location><page_22><loc_32><loc_83><loc_33><loc_84></location>4</text>
<text><location><page_22><loc_33><loc_83><loc_34><loc_84></location>8</text>
<text><location><page_22><loc_34><loc_83><loc_35><loc_84></location>4</text>
<text><location><page_22><loc_36><loc_83><loc_36><loc_84></location>0</text>
<text><location><page_22><loc_37><loc_83><loc_38><loc_84></location>6</text>
<text><location><page_22><loc_38><loc_83><loc_39><loc_84></location>0</text>
<text><location><page_22><loc_39><loc_83><loc_40><loc_84></location>2</text>
<text><location><page_22><loc_40><loc_83><loc_41><loc_84></location>0</text>
<text><location><page_22><loc_42><loc_83><loc_42><loc_84></location>0</text>
<text><location><page_22><loc_43><loc_83><loc_44><loc_84></location>2</text>
<text><location><page_22><loc_44><loc_83><loc_45><loc_84></location>2</text>
<text><location><page_22><loc_45><loc_83><loc_46><loc_84></location>2</text>
<text><location><page_22><loc_47><loc_83><loc_47><loc_84></location>0</text>
<text><location><page_22><loc_48><loc_83><loc_49><loc_84></location>0</text>
<text><location><page_22><loc_49><loc_83><loc_50><loc_84></location>8</text>
<text><location><page_22><loc_50><loc_83><loc_51><loc_84></location>0</text>
<text><location><page_22><loc_51><loc_83><loc_52><loc_84></location>6</text>
<text><location><page_22><loc_53><loc_83><loc_54><loc_84></location>4</text>
<text><location><page_22><loc_54><loc_83><loc_55><loc_84></location>2</text>
<text><location><page_22><loc_55><loc_83><loc_56><loc_84></location>2</text>
<text><location><page_22><loc_56><loc_83><loc_57><loc_84></location>6</text>
<text><location><page_22><loc_58><loc_83><loc_58><loc_84></location>8</text>
<text><location><page_22><loc_59><loc_83><loc_60><loc_84></location>2</text>
<text><location><page_22><loc_60><loc_83><loc_61><loc_84></location>8</text>
<text><location><page_22><loc_61><loc_83><loc_62><loc_84></location>2</text>
<text><location><page_22><loc_63><loc_83><loc_63><loc_84></location>0</text>
<text><location><page_22><loc_64><loc_83><loc_65><loc_84></location>0</text>
<text><location><page_22><loc_65><loc_83><loc_66><loc_84></location>6</text>
<text><location><page_22><loc_66><loc_83><loc_67><loc_84></location>4</text>
<text><location><page_22><loc_67><loc_83><loc_68><loc_84></location>0</text>
<text><location><page_22><loc_69><loc_83><loc_69><loc_84></location>6</text>
<text><location><page_22><loc_70><loc_83><loc_71><loc_84></location>4</text>
<text><location><page_22><loc_71><loc_83><loc_72><loc_84></location>4</text>
<text><location><page_22><loc_72><loc_83><loc_73><loc_84></location>8</text>
<text><location><page_22><loc_74><loc_83><loc_74><loc_84></location>0</text>
<text><location><page_22><loc_75><loc_83><loc_76><loc_84></location>6</text>
<text><location><page_22><loc_76><loc_83><loc_77><loc_84></location>4</text>
<text><location><page_22><loc_77><loc_83><loc_78><loc_84></location>8</text>
<text><location><page_22><loc_78><loc_83><loc_79><loc_84></location>0</text>
<text><location><page_22><loc_80><loc_83><loc_81><loc_84></location>0</text>
<text><location><page_22><loc_81><loc_83><loc_82><loc_84></location>4</text>
<text><location><page_22><loc_82><loc_83><loc_83><loc_84></location>0</text>
<text><location><page_22><loc_83><loc_83><loc_84><loc_84></location>8</text>
<text><location><page_22><loc_85><loc_83><loc_85><loc_84></location>4</text>
<text><location><page_22><loc_85><loc_83><loc_85><loc_83></location>5</text>
<text><location><page_22><loc_85><loc_82><loc_85><loc_83></location>3</text>
<text><location><page_22><loc_85><loc_82><loc_85><loc_82></location>.</text>
<text><location><page_22><loc_85><loc_82><loc_85><loc_82></location>3</text>
<text><location><page_22><loc_85><loc_79><loc_85><loc_79></location>0</text>
<text><location><page_22><loc_85><loc_78><loc_85><loc_79></location>1</text>
<text><location><page_22><loc_85><loc_78><loc_85><loc_78></location>.</text>
<text><location><page_22><loc_85><loc_78><loc_85><loc_78></location>0</text>
<text><location><page_22><loc_85><loc_75><loc_85><loc_75></location>8</text>
<text><location><page_22><loc_85><loc_74><loc_85><loc_75></location>1</text>
<text><location><page_22><loc_85><loc_74><loc_85><loc_74></location>0</text>
<text><location><page_22><loc_85><loc_74><loc_85><loc_74></location>.</text>
<text><location><page_22><loc_85><loc_73><loc_85><loc_74></location>0</text>
<text><location><page_22><loc_85><loc_72><loc_85><loc_73></location>±</text>
<text><location><page_22><loc_85><loc_72><loc_85><loc_72></location>5</text>
<text><location><page_22><loc_85><loc_71><loc_85><loc_72></location>4</text>
<text><location><page_22><loc_85><loc_71><loc_85><loc_71></location>2</text>
<text><location><page_22><loc_85><loc_70><loc_85><loc_71></location>.</text>
<text><location><page_22><loc_85><loc_70><loc_85><loc_70></location>7</text>
<text><location><page_22><loc_85><loc_70><loc_85><loc_70></location>1</text>
<text><location><page_22><loc_85><loc_68><loc_85><loc_68></location>6</text>
<text><location><page_22><loc_85><loc_67><loc_85><loc_68></location>1</text>
<text><location><page_22><loc_85><loc_67><loc_85><loc_67></location>0</text>
<text><location><page_22><loc_85><loc_67><loc_85><loc_67></location>.</text>
<text><location><page_22><loc_85><loc_66><loc_85><loc_67></location>0</text>
<text><location><page_22><loc_85><loc_65><loc_85><loc_66></location>±</text>
<text><location><page_22><loc_85><loc_65><loc_85><loc_65></location>6</text>
<text><location><page_22><loc_85><loc_64><loc_85><loc_65></location>6</text>
<text><location><page_22><loc_85><loc_64><loc_85><loc_64></location>6</text>
<text><location><page_22><loc_85><loc_64><loc_85><loc_64></location>.</text>
<text><location><page_22><loc_85><loc_63><loc_85><loc_64></location>7</text>
<text><location><page_22><loc_85><loc_63><loc_85><loc_63></location>1</text>
<text><location><page_22><loc_85><loc_61><loc_85><loc_61></location>5</text>
<text><location><page_22><loc_85><loc_61><loc_85><loc_61></location>1</text>
<text><location><page_22><loc_85><loc_60><loc_85><loc_61></location>0</text>
<text><location><page_22><loc_85><loc_60><loc_85><loc_60></location>.</text>
<text><location><page_22><loc_85><loc_59><loc_85><loc_60></location>0</text>
<text><location><page_22><loc_85><loc_59><loc_85><loc_59></location>±</text>
<text><location><page_22><loc_85><loc_58><loc_85><loc_58></location>1</text>
<text><location><page_22><loc_85><loc_57><loc_85><loc_58></location>1</text>
<text><location><page_22><loc_85><loc_57><loc_85><loc_57></location>9</text>
<text><location><page_22><loc_85><loc_57><loc_85><loc_57></location>.</text>
<text><location><page_22><loc_85><loc_56><loc_85><loc_57></location>7</text>
<text><location><page_22><loc_85><loc_56><loc_85><loc_56></location>1</text>
<text><location><page_22><loc_85><loc_54><loc_85><loc_55></location>5</text>
<text><location><page_22><loc_85><loc_54><loc_85><loc_54></location>1</text>
<text><location><page_22><loc_85><loc_53><loc_85><loc_54></location>0</text>
<text><location><page_22><loc_85><loc_53><loc_85><loc_53></location>.</text>
<text><location><page_22><loc_85><loc_53><loc_85><loc_53></location>0</text>
<text><location><page_22><loc_85><loc_52><loc_85><loc_52></location>±</text>
<text><location><page_22><loc_85><loc_51><loc_85><loc_51></location>7</text>
<text><location><page_22><loc_85><loc_50><loc_85><loc_51></location>7</text>
<text><location><page_22><loc_85><loc_50><loc_85><loc_50></location>4</text>
<text><location><page_22><loc_85><loc_50><loc_85><loc_50></location>.</text>
<text><location><page_22><loc_85><loc_49><loc_85><loc_50></location>8</text>
<text><location><page_22><loc_85><loc_49><loc_85><loc_49></location>1</text>
<text><location><page_22><loc_85><loc_47><loc_85><loc_48></location>3</text>
<text><location><page_22><loc_85><loc_47><loc_85><loc_47></location>1</text>
<text><location><page_22><loc_85><loc_46><loc_85><loc_47></location>0</text>
<text><location><page_22><loc_85><loc_46><loc_85><loc_46></location>.</text>
<text><location><page_22><loc_85><loc_46><loc_85><loc_46></location>0</text>
<text><location><page_22><loc_85><loc_45><loc_85><loc_45></location>±</text>
<text><location><page_22><loc_85><loc_44><loc_85><loc_44></location>6</text>
<text><location><page_22><loc_85><loc_44><loc_85><loc_44></location>4</text>
<text><location><page_22><loc_85><loc_43><loc_85><loc_44></location>5</text>
<text><location><page_22><loc_85><loc_43><loc_85><loc_43></location>.</text>
<text><location><page_22><loc_85><loc_42><loc_85><loc_43></location>8</text>
<text><location><page_22><loc_85><loc_42><loc_85><loc_42></location>1</text>
<text><location><page_22><loc_85><loc_40><loc_85><loc_41></location>8</text>
<text><location><page_22><loc_85><loc_40><loc_85><loc_40></location>4</text>
<text><location><page_22><loc_85><loc_40><loc_85><loc_40></location>.</text>
<text><location><page_22><loc_85><loc_39><loc_85><loc_40></location>8</text>
<text><location><page_22><loc_85><loc_39><loc_85><loc_39></location>5</text>
<text><location><page_22><loc_85><loc_38><loc_85><loc_39></location>9</text>
<text><location><page_22><loc_85><loc_38><loc_85><loc_38></location>3</text>
<text><location><page_22><loc_85><loc_37><loc_85><loc_37></location>0</text>
<text><location><page_22><loc_85><loc_37><loc_85><loc_37></location>3</text>
<text><location><page_22><loc_85><loc_35><loc_85><loc_35></location>6</text>
<text><location><page_22><loc_85><loc_34><loc_85><loc_35></location>3</text>
<text><location><page_22><loc_85><loc_34><loc_85><loc_34></location>2</text>
<text><location><page_22><loc_85><loc_34><loc_85><loc_34></location>.</text>
<text><location><page_22><loc_85><loc_33><loc_85><loc_34></location>4</text>
<text><location><page_22><loc_85><loc_33><loc_85><loc_33></location>1</text>
<text><location><page_22><loc_85><loc_32><loc_85><loc_33></location>4</text>
<text><location><page_22><loc_85><loc_32><loc_85><loc_32></location>3</text>
<text><location><page_22><loc_85><loc_31><loc_85><loc_31></location>1</text>
<text><location><page_22><loc_85><loc_31><loc_85><loc_31></location>0</text>
<text><location><page_22><loc_85><loc_25><loc_85><loc_26></location>0</text>
<text><location><page_22><loc_85><loc_25><loc_85><loc_25></location>1</text>
<text><location><page_22><loc_85><loc_24><loc_85><loc_25></location>2</text>
<text><location><page_22><loc_85><loc_24><loc_85><loc_24></location>L</text>
<text><location><page_22><loc_85><loc_23><loc_85><loc_24></location>P</text>
<text><location><page_22><loc_85><loc_22><loc_85><loc_22></location>0</text>
<text><location><page_22><loc_85><loc_21><loc_85><loc_22></location>5</text>
<text><location><page_22><loc_85><loc_21><loc_85><loc_21></location>3</text>
<text><location><page_22><loc_85><loc_20><loc_85><loc_21></location>M</text>
<text><location><page_22><loc_85><loc_20><loc_85><loc_20></location>S</text>
<text><location><page_22><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_22><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_22><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_22><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_22><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_22><loc_85><loc_17><loc_85><loc_17></location>.</text>
<text><location><page_22><loc_85><loc_16><loc_85><loc_17></location>7</text>
<text><location><page_22><loc_85><loc_16><loc_85><loc_16></location>5</text>
<text><location><page_22><loc_85><loc_15><loc_85><loc_16></location>4</text>
<text><location><page_22><loc_86><loc_83><loc_87><loc_84></location>6</text>
<text><location><page_22><loc_86><loc_83><loc_87><loc_83></location>9</text>
<text><location><page_22><loc_86><loc_82><loc_87><loc_83></location>0</text>
<text><location><page_22><loc_86><loc_82><loc_87><loc_82></location>.</text>
<text><location><page_22><loc_86><loc_82><loc_87><loc_82></location>3</text>
<text><location><page_22><loc_86><loc_79><loc_87><loc_79></location>0</text>
<text><location><page_22><loc_86><loc_78><loc_87><loc_79></location>2</text>
<text><location><page_22><loc_86><loc_78><loc_87><loc_78></location>.</text>
<text><location><page_22><loc_86><loc_78><loc_87><loc_78></location>0</text>
<text><location><page_22><loc_86><loc_75><loc_87><loc_75></location>2</text>
<text><location><page_22><loc_86><loc_74><loc_87><loc_75></location>1</text>
<text><location><page_22><loc_86><loc_74><loc_87><loc_74></location>0</text>
<text><location><page_22><loc_86><loc_74><loc_87><loc_74></location>.</text>
<text><location><page_22><loc_86><loc_73><loc_87><loc_74></location>0</text>
<text><location><page_22><loc_86><loc_72><loc_87><loc_73></location>±</text>
<text><location><page_22><loc_86><loc_72><loc_87><loc_72></location>2</text>
<text><location><page_22><loc_86><loc_71><loc_87><loc_72></location>8</text>
<text><location><page_22><loc_86><loc_71><loc_87><loc_71></location>5</text>
<text><location><page_22><loc_86><loc_70><loc_87><loc_71></location>.</text>
<text><location><page_22><loc_86><loc_70><loc_87><loc_70></location>7</text>
<text><location><page_22><loc_86><loc_70><loc_87><loc_70></location>1</text>
<text><location><page_22><loc_86><loc_68><loc_87><loc_68></location>0</text>
<text><location><page_22><loc_86><loc_67><loc_87><loc_68></location>1</text>
<text><location><page_22><loc_86><loc_67><loc_87><loc_67></location>0</text>
<text><location><page_22><loc_86><loc_67><loc_87><loc_67></location>.</text>
<text><location><page_22><loc_86><loc_66><loc_87><loc_67></location>0</text>
<text><location><page_22><loc_86><loc_65><loc_87><loc_66></location>±</text>
<text><location><page_22><loc_86><loc_65><loc_87><loc_65></location>2</text>
<text><location><page_22><loc_86><loc_64><loc_87><loc_65></location>1</text>
<text><location><page_22><loc_86><loc_64><loc_87><loc_64></location>9</text>
<text><location><page_22><loc_86><loc_64><loc_87><loc_64></location>.</text>
<text><location><page_22><loc_86><loc_63><loc_87><loc_64></location>7</text>
<text><location><page_22><loc_86><loc_63><loc_87><loc_63></location>1</text>
<text><location><page_22><loc_86><loc_61><loc_87><loc_61></location>1</text>
<text><location><page_22><loc_86><loc_61><loc_87><loc_61></location>1</text>
<text><location><page_22><loc_86><loc_60><loc_87><loc_61></location>0</text>
<text><location><page_22><loc_86><loc_60><loc_87><loc_60></location>.</text>
<text><location><page_22><loc_86><loc_59><loc_87><loc_60></location>0</text>
<text><location><page_22><loc_86><loc_59><loc_87><loc_59></location>±</text>
<text><location><page_22><loc_86><loc_58><loc_87><loc_58></location>3</text>
<text><location><page_22><loc_86><loc_57><loc_87><loc_58></location>5</text>
<text><location><page_22><loc_86><loc_57><loc_87><loc_57></location>1</text>
<text><location><page_22><loc_86><loc_57><loc_87><loc_57></location>.</text>
<text><location><page_22><loc_86><loc_56><loc_87><loc_57></location>8</text>
<text><location><page_22><loc_86><loc_56><loc_87><loc_56></location>1</text>
<text><location><page_22><loc_86><loc_54><loc_87><loc_55></location>0</text>
<text><location><page_22><loc_86><loc_54><loc_87><loc_54></location>1</text>
<text><location><page_22><loc_86><loc_53><loc_87><loc_54></location>0</text>
<text><location><page_22><loc_86><loc_53><loc_87><loc_53></location>.</text>
<text><location><page_22><loc_86><loc_53><loc_87><loc_53></location>0</text>
<text><location><page_22><loc_86><loc_52><loc_87><loc_52></location>±</text>
<text><location><page_22><loc_86><loc_51><loc_87><loc_51></location>9</text>
<text><location><page_22><loc_86><loc_50><loc_87><loc_51></location>8</text>
<text><location><page_22><loc_86><loc_50><loc_87><loc_50></location>5</text>
<text><location><page_22><loc_86><loc_50><loc_87><loc_50></location>.</text>
<text><location><page_22><loc_86><loc_49><loc_87><loc_50></location>8</text>
<text><location><page_22><loc_86><loc_49><loc_87><loc_49></location>1</text>
<text><location><page_22><loc_86><loc_47><loc_87><loc_48></location>0</text>
<text><location><page_22><loc_86><loc_47><loc_87><loc_47></location>1</text>
<text><location><page_22><loc_86><loc_46><loc_87><loc_47></location>0</text>
<text><location><page_22><loc_86><loc_46><loc_87><loc_46></location>.</text>
<text><location><page_22><loc_86><loc_46><loc_87><loc_46></location>0</text>
<text><location><page_22><loc_86><loc_45><loc_87><loc_45></location>±</text>
<text><location><page_22><loc_86><loc_44><loc_87><loc_44></location>3</text>
<text><location><page_22><loc_86><loc_44><loc_87><loc_44></location>5</text>
<text><location><page_22><loc_86><loc_43><loc_87><loc_44></location>6</text>
<text><location><page_22><loc_86><loc_43><loc_87><loc_43></location>.</text>
<text><location><page_22><loc_86><loc_42><loc_87><loc_43></location>8</text>
<text><location><page_22><loc_86><loc_42><loc_87><loc_42></location>1</text>
<text><location><page_22><loc_86><loc_40><loc_87><loc_41></location>9</text>
<text><location><page_22><loc_86><loc_40><loc_87><loc_40></location>1</text>
<text><location><page_22><loc_86><loc_40><loc_87><loc_40></location>.</text>
<text><location><page_22><loc_86><loc_39><loc_87><loc_40></location>5</text>
<text><location><page_22><loc_86><loc_39><loc_87><loc_39></location>3</text>
<text><location><page_22><loc_86><loc_38><loc_87><loc_39></location>2</text>
<text><location><page_22><loc_86><loc_38><loc_87><loc_38></location>3</text>
<text><location><page_22><loc_86><loc_37><loc_87><loc_37></location>0</text>
<text><location><page_22><loc_86><loc_37><loc_87><loc_37></location>3</text>
<text><location><page_22><loc_86><loc_35><loc_87><loc_35></location>7</text>
<text><location><page_22><loc_86><loc_34><loc_87><loc_35></location>4</text>
<text><location><page_22><loc_86><loc_34><loc_87><loc_34></location>6</text>
<text><location><page_22><loc_86><loc_34><loc_87><loc_34></location>.</text>
<text><location><page_22><loc_86><loc_33><loc_87><loc_34></location>4</text>
<text><location><page_22><loc_86><loc_33><loc_87><loc_33></location>1</text>
<text><location><page_22><loc_86><loc_32><loc_87><loc_33></location>4</text>
<text><location><page_22><loc_86><loc_32><loc_87><loc_32></location>3</text>
<text><location><page_22><loc_86><loc_31><loc_87><loc_31></location>1</text>
<text><location><page_22><loc_86><loc_31><loc_87><loc_31></location>0</text>
<text><location><page_22><loc_86><loc_25><loc_87><loc_26></location>2</text>
<text><location><page_22><loc_86><loc_25><loc_87><loc_25></location>0</text>
<text><location><page_22><loc_86><loc_24><loc_87><loc_25></location>1</text>
<text><location><page_22><loc_86><loc_24><loc_87><loc_24></location>L</text>
<text><location><page_22><loc_86><loc_23><loc_87><loc_24></location>P</text>
<text><location><page_22><loc_86><loc_22><loc_87><loc_22></location>1</text>
<text><location><page_22><loc_86><loc_21><loc_87><loc_22></location>5</text>
<text><location><page_22><loc_86><loc_21><loc_87><loc_21></location>3</text>
<text><location><page_22><loc_86><loc_20><loc_87><loc_21></location>M</text>
<text><location><page_22><loc_86><loc_20><loc_87><loc_20></location>S</text>
<text><location><page_22><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_22><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_22><loc_86><loc_18><loc_87><loc_18></location>.</text>
<text><location><page_22><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_22><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_22><loc_86><loc_17><loc_87><loc_17></location>.</text>
<text><location><page_22><loc_86><loc_16><loc_87><loc_17></location>8</text>
<text><location><page_22><loc_86><loc_16><loc_87><loc_16></location>5</text>
<text><location><page_22><loc_86><loc_15><loc_87><loc_16></location>4</text>
<text><location><page_22><loc_87><loc_83><loc_88><loc_84></location>8</text>
<text><location><page_22><loc_87><loc_83><loc_88><loc_83></location>2</text>
<text><location><page_22><loc_87><loc_82><loc_88><loc_83></location>1</text>
<text><location><page_22><loc_87><loc_82><loc_88><loc_82></location>.</text>
<text><location><page_22><loc_87><loc_82><loc_88><loc_82></location>4</text>
<text><location><page_22><loc_87><loc_79><loc_88><loc_79></location>0</text>
<text><location><page_22><loc_87><loc_78><loc_88><loc_79></location>1</text>
<text><location><page_22><loc_87><loc_78><loc_88><loc_78></location>.</text>
<text><location><page_22><loc_87><loc_78><loc_88><loc_78></location>0</text>
<text><location><page_22><loc_87><loc_75><loc_88><loc_75></location>4</text>
<text><location><page_22><loc_87><loc_74><loc_88><loc_75></location>1</text>
<text><location><page_22><loc_87><loc_74><loc_88><loc_74></location>0</text>
<text><location><page_22><loc_87><loc_74><loc_88><loc_74></location>.</text>
<text><location><page_22><loc_87><loc_73><loc_88><loc_74></location>0</text>
<text><location><page_22><loc_87><loc_72><loc_88><loc_73></location>±</text>
<text><location><page_22><loc_87><loc_72><loc_88><loc_72></location>1</text>
<text><location><page_22><loc_87><loc_71><loc_88><loc_72></location>2</text>
<text><location><page_22><loc_87><loc_71><loc_88><loc_71></location>9</text>
<text><location><page_22><loc_87><loc_70><loc_88><loc_71></location>.</text>
<text><location><page_22><loc_87><loc_70><loc_88><loc_70></location>6</text>
<text><location><page_22><loc_87><loc_70><loc_88><loc_70></location>1</text>
<text><location><page_22><loc_87><loc_68><loc_88><loc_68></location>2</text>
<text><location><page_22><loc_87><loc_67><loc_88><loc_68></location>1</text>
<text><location><page_22><loc_87><loc_67><loc_88><loc_67></location>0</text>
<text><location><page_22><loc_87><loc_67><loc_88><loc_67></location>.</text>
<text><location><page_22><loc_87><loc_66><loc_88><loc_67></location>0</text>
<text><location><page_22><loc_87><loc_65><loc_88><loc_66></location>±</text>
<text><location><page_22><loc_87><loc_65><loc_88><loc_65></location>7</text>
<text><location><page_22><loc_87><loc_64><loc_88><loc_65></location>2</text>
<text><location><page_22><loc_87><loc_64><loc_88><loc_64></location>2</text>
<text><location><page_22><loc_87><loc_64><loc_88><loc_64></location>.</text>
<text><location><page_22><loc_87><loc_63><loc_88><loc_64></location>7</text>
<text><location><page_22><loc_87><loc_63><loc_88><loc_63></location>1</text>
<text><location><page_22><loc_87><loc_61><loc_88><loc_61></location>0</text>
<text><location><page_22><loc_87><loc_61><loc_88><loc_61></location>1</text>
<text><location><page_22><loc_87><loc_60><loc_88><loc_61></location>0</text>
<text><location><page_22><loc_87><loc_60><loc_88><loc_60></location>.</text>
<text><location><page_22><loc_87><loc_59><loc_88><loc_60></location>0</text>
<text><location><page_22><loc_87><loc_59><loc_88><loc_59></location>±</text>
<text><location><page_22><loc_87><loc_58><loc_88><loc_58></location>1</text>
<text><location><page_22><loc_87><loc_57><loc_88><loc_58></location>3</text>
<text><location><page_22><loc_87><loc_57><loc_88><loc_57></location>4</text>
<text><location><page_22><loc_87><loc_57><loc_88><loc_57></location>.</text>
<text><location><page_22><loc_87><loc_56><loc_88><loc_57></location>7</text>
<text><location><page_22><loc_87><loc_56><loc_88><loc_56></location>1</text>
<text><location><page_22><loc_87><loc_54><loc_88><loc_55></location>9</text>
<text><location><page_22><loc_87><loc_54><loc_88><loc_54></location>0</text>
<text><location><page_22><loc_87><loc_53><loc_88><loc_54></location>0</text>
<text><location><page_22><loc_87><loc_53><loc_88><loc_53></location>.</text>
<text><location><page_22><loc_87><loc_53><loc_88><loc_53></location>0</text>
<text><location><page_22><loc_87><loc_52><loc_88><loc_52></location>±</text>
<text><location><page_22><loc_87><loc_51><loc_88><loc_51></location>5</text>
<text><location><page_22><loc_87><loc_50><loc_88><loc_51></location>3</text>
<text><location><page_22><loc_87><loc_50><loc_88><loc_50></location>8</text>
<text><location><page_22><loc_87><loc_50><loc_88><loc_50></location>.</text>
<text><location><page_22><loc_87><loc_49><loc_88><loc_50></location>7</text>
<text><location><page_22><loc_87><loc_49><loc_88><loc_49></location>1</text>
<text><location><page_22><loc_87><loc_47><loc_88><loc_48></location>7</text>
<text><location><page_22><loc_87><loc_47><loc_88><loc_47></location>0</text>
<text><location><page_22><loc_87><loc_46><loc_88><loc_47></location>0</text>
<text><location><page_22><loc_87><loc_46><loc_88><loc_46></location>.</text>
<text><location><page_22><loc_87><loc_46><loc_88><loc_46></location>0</text>
<text><location><page_22><loc_87><loc_45><loc_88><loc_45></location>±</text>
<text><location><page_22><loc_87><loc_44><loc_88><loc_44></location>8</text>
<text><location><page_22><loc_87><loc_44><loc_88><loc_44></location>3</text>
<text><location><page_22><loc_87><loc_43><loc_88><loc_44></location>6</text>
<text><location><page_22><loc_87><loc_43><loc_88><loc_43></location>.</text>
<text><location><page_22><loc_87><loc_42><loc_88><loc_43></location>7</text>
<text><location><page_22><loc_87><loc_42><loc_88><loc_42></location>1</text>
<text><location><page_22><loc_87><loc_40><loc_88><loc_41></location>4</text>
<text><location><page_22><loc_87><loc_40><loc_88><loc_40></location>1</text>
<text><location><page_22><loc_87><loc_40><loc_88><loc_40></location>.</text>
<text><location><page_22><loc_87><loc_39><loc_88><loc_40></location>9</text>
<text><location><page_22><loc_87><loc_39><loc_88><loc_39></location>1</text>
<text><location><page_22><loc_87><loc_38><loc_88><loc_39></location>1</text>
<text><location><page_22><loc_87><loc_38><loc_88><loc_38></location>4</text>
<text><location><page_22><loc_87><loc_37><loc_88><loc_37></location>0</text>
<text><location><page_22><loc_87><loc_37><loc_88><loc_37></location>3</text>
<text><location><page_22><loc_87><loc_35><loc_88><loc_35></location>7</text>
<text><location><page_22><loc_87><loc_34><loc_88><loc_35></location>3</text>
<text><location><page_22><loc_87><loc_34><loc_88><loc_34></location>0</text>
<text><location><page_22><loc_87><loc_34><loc_88><loc_34></location>.</text>
<text><location><page_22><loc_87><loc_33><loc_88><loc_34></location>5</text>
<text><location><page_22><loc_87><loc_33><loc_88><loc_33></location>1</text>
<text><location><page_22><loc_87><loc_32><loc_88><loc_33></location>4</text>
<text><location><page_22><loc_87><loc_32><loc_88><loc_32></location>3</text>
<text><location><page_22><loc_87><loc_31><loc_88><loc_31></location>1</text>
<text><location><page_22><loc_87><loc_31><loc_88><loc_31></location>0</text>
<text><location><page_22><loc_87><loc_25><loc_88><loc_26></location>3</text>
<text><location><page_22><loc_87><loc_25><loc_88><loc_25></location>0</text>
<text><location><page_22><loc_87><loc_24><loc_88><loc_25></location>1</text>
<text><location><page_22><loc_87><loc_24><loc_88><loc_24></location>L</text>
<text><location><page_22><loc_87><loc_23><loc_88><loc_24></location>P</text>
<text><location><page_22><loc_87><loc_22><loc_88><loc_22></location>3</text>
<text><location><page_22><loc_87><loc_21><loc_88><loc_22></location>5</text>
<text><location><page_22><loc_87><loc_21><loc_88><loc_21></location>3</text>
<text><location><page_22><loc_87><loc_20><loc_88><loc_21></location>M</text>
<text><location><page_22><loc_87><loc_20><loc_88><loc_20></location>S</text>
<text><location><page_22><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_22><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_22><loc_87><loc_18><loc_88><loc_18></location>.</text>
<text><location><page_22><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_22><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_22><loc_87><loc_17><loc_88><loc_17></location>.</text>
<text><location><page_22><loc_87><loc_16><loc_88><loc_17></location>9</text>
<text><location><page_22><loc_87><loc_16><loc_88><loc_16></location>5</text>
<text><location><page_22><loc_87><loc_15><loc_88><loc_16></location>4</text>
<text><location><page_23><loc_15><loc_51><loc_17><loc_52></location>3</text>
<text><location><page_23><loc_15><loc_50><loc_17><loc_51></location>E</text>
<text><location><page_23><loc_15><loc_50><loc_17><loc_50></location>L</text>
<text><location><page_23><loc_15><loc_48><loc_17><loc_50></location>AB</text>
<text><location><page_23><loc_15><loc_47><loc_17><loc_48></location>T</text>
<text><location><page_23><loc_20><loc_82><loc_20><loc_82></location>p</text>
<text><location><page_23><loc_21><loc_82><loc_22><loc_82></location>)</text>
<text><location><page_23><loc_20><loc_82><loc_21><loc_82></location>'</text>
<text><location><page_23><loc_20><loc_82><loc_21><loc_82></location>'</text>
<text><location><page_23><loc_21><loc_81><loc_22><loc_82></location>(</text>
<text><location><page_23><loc_20><loc_82><loc_20><loc_82></location>a</text>
<text><location><page_23><loc_20><loc_81><loc_20><loc_82></location>r</text>
<text><location><page_23><loc_22><loc_82><loc_23><loc_83></location>2</text>
<text><location><page_23><loc_22><loc_82><loc_23><loc_82></location>1</text>
<text><location><page_23><loc_22><loc_82><loc_23><loc_82></location>6</text>
<text><location><page_23><loc_22><loc_81><loc_23><loc_82></location>.</text>
<text><location><page_23><loc_22><loc_81><loc_23><loc_81></location>3</text>
<text><location><page_23><loc_23><loc_82><loc_24><loc_83></location>6</text>
<text><location><page_23><loc_23><loc_82><loc_24><loc_82></location>9</text>
<text><location><page_23><loc_23><loc_82><loc_24><loc_82></location>0</text>
<text><location><page_23><loc_23><loc_81><loc_24><loc_82></location>.</text>
<text><location><page_23><loc_23><loc_81><loc_24><loc_81></location>3</text>
<text><location><page_23><loc_24><loc_82><loc_25><loc_83></location>8</text>
<text><location><page_23><loc_24><loc_82><loc_25><loc_82></location>3</text>
<text><location><page_23><loc_24><loc_82><loc_25><loc_82></location>8</text>
<text><location><page_23><loc_24><loc_81><loc_25><loc_82></location>.</text>
<text><location><page_23><loc_24><loc_81><loc_25><loc_81></location>2</text>
<text><location><page_23><loc_26><loc_82><loc_27><loc_83></location>8</text>
<text><location><page_23><loc_26><loc_82><loc_27><loc_82></location>3</text>
<text><location><page_23><loc_26><loc_82><loc_27><loc_82></location>8</text>
<text><location><page_23><loc_26><loc_81><loc_27><loc_82></location>.</text>
<text><location><page_23><loc_26><loc_81><loc_27><loc_81></location>2</text>
<text><location><page_23><loc_27><loc_82><loc_28><loc_83></location>0</text>
<text><location><page_23><loc_27><loc_82><loc_28><loc_82></location>8</text>
<text><location><page_23><loc_27><loc_82><loc_28><loc_82></location>5</text>
<text><location><page_23><loc_27><loc_81><loc_28><loc_82></location>.</text>
<text><location><page_23><loc_27><loc_81><loc_28><loc_81></location>2</text>
<text><location><page_23><loc_28><loc_82><loc_29><loc_83></location>8</text>
<text><location><page_23><loc_28><loc_82><loc_29><loc_82></location>4</text>
<text><location><page_23><loc_28><loc_82><loc_29><loc_82></location>5</text>
<text><location><page_23><loc_28><loc_81><loc_29><loc_82></location>.</text>
<text><location><page_23><loc_28><loc_81><loc_29><loc_81></location>1</text>
<text><location><page_23><loc_29><loc_82><loc_30><loc_83></location>6</text>
<text><location><page_23><loc_29><loc_82><loc_30><loc_82></location>9</text>
<text><location><page_23><loc_29><loc_82><loc_30><loc_82></location>0</text>
<text><location><page_23><loc_29><loc_81><loc_30><loc_82></location>.</text>
<text><location><page_23><loc_29><loc_81><loc_30><loc_81></location>3</text>
<text><location><page_23><loc_31><loc_82><loc_31><loc_83></location>8</text>
<text><location><page_23><loc_31><loc_82><loc_31><loc_82></location>3</text>
<text><location><page_23><loc_31><loc_82><loc_31><loc_82></location>8</text>
<text><location><page_23><loc_31><loc_81><loc_31><loc_82></location>.</text>
<text><location><page_23><loc_31><loc_81><loc_31><loc_81></location>2</text>
<text><location><page_23><loc_32><loc_82><loc_33><loc_83></location>0</text>
<text><location><page_23><loc_32><loc_82><loc_33><loc_82></location>8</text>
<text><location><page_23><loc_32><loc_82><loc_33><loc_82></location>5</text>
<text><location><page_23><loc_32><loc_81><loc_33><loc_82></location>.</text>
<text><location><page_23><loc_32><loc_81><loc_33><loc_81></location>2</text>
<text><location><page_23><loc_33><loc_82><loc_34><loc_83></location>0</text>
<text><location><page_23><loc_33><loc_82><loc_34><loc_82></location>8</text>
<text><location><page_23><loc_33><loc_82><loc_34><loc_82></location>5</text>
<text><location><page_23><loc_33><loc_81><loc_34><loc_82></location>.</text>
<text><location><page_23><loc_33><loc_81><loc_34><loc_81></location>2</text>
<text><location><page_23><loc_34><loc_82><loc_35><loc_83></location>0</text>
<text><location><page_23><loc_34><loc_82><loc_35><loc_82></location>8</text>
<text><location><page_23><loc_34><loc_82><loc_35><loc_82></location>5</text>
<text><location><page_23><loc_34><loc_81><loc_35><loc_82></location>.</text>
<text><location><page_23><loc_34><loc_81><loc_35><loc_81></location>2</text>
<text><location><page_23><loc_36><loc_82><loc_36><loc_83></location>6</text>
<text><location><page_23><loc_36><loc_82><loc_36><loc_82></location>9</text>
<text><location><page_23><loc_36><loc_82><loc_36><loc_82></location>0</text>
<text><location><page_23><loc_36><loc_81><loc_36><loc_82></location>.</text>
<text><location><page_23><loc_36><loc_81><loc_36><loc_81></location>3</text>
<text><location><page_23><loc_37><loc_82><loc_38><loc_83></location>0</text>
<text><location><page_23><loc_37><loc_82><loc_38><loc_82></location>8</text>
<text><location><page_23><loc_37><loc_82><loc_38><loc_82></location>5</text>
<text><location><page_23><loc_37><loc_81><loc_38><loc_82></location>.</text>
<text><location><page_23><loc_37><loc_81><loc_38><loc_81></location>2</text>
<text><location><page_23><loc_38><loc_82><loc_39><loc_83></location>6</text>
<text><location><page_23><loc_38><loc_82><loc_39><loc_82></location>9</text>
<text><location><page_23><loc_38><loc_82><loc_39><loc_82></location>0</text>
<text><location><page_23><loc_38><loc_81><loc_39><loc_82></location>.</text>
<text><location><page_23><loc_38><loc_81><loc_39><loc_81></location>3</text>
<text><location><page_23><loc_39><loc_82><loc_40><loc_83></location>4</text>
<text><location><page_23><loc_39><loc_82><loc_40><loc_82></location>5</text>
<text><location><page_23><loc_39><loc_82><loc_40><loc_82></location>3</text>
<text><location><page_23><loc_39><loc_81><loc_40><loc_82></location>.</text>
<text><location><page_23><loc_39><loc_81><loc_40><loc_81></location>3</text>
<text><location><page_23><loc_40><loc_82><loc_41><loc_83></location>4</text>
<text><location><page_23><loc_40><loc_82><loc_41><loc_82></location>5</text>
<text><location><page_23><loc_40><loc_82><loc_41><loc_82></location>3</text>
<text><location><page_23><loc_40><loc_81><loc_41><loc_82></location>.</text>
<text><location><page_23><loc_40><loc_81><loc_41><loc_81></location>3</text>
<text><location><page_23><loc_42><loc_93><loc_57><loc_94></location>Star clusters in M33</text>
<text><location><page_23><loc_90><loc_93><loc_92><loc_94></location>23</text>
<text><location><page_23><loc_42><loc_82><loc_42><loc_83></location>6</text>
<text><location><page_23><loc_42><loc_82><loc_42><loc_82></location>9</text>
<text><location><page_23><loc_42><loc_82><loc_42><loc_82></location>0</text>
<text><location><page_23><loc_42><loc_81><loc_42><loc_82></location>.</text>
<text><location><page_23><loc_42><loc_81><loc_42><loc_81></location>3</text>
<text><location><page_23><loc_43><loc_82><loc_44><loc_83></location>6</text>
<text><location><page_23><loc_43><loc_82><loc_44><loc_82></location>9</text>
<text><location><page_23><loc_43><loc_82><loc_44><loc_82></location>0</text>
<text><location><page_23><loc_43><loc_81><loc_44><loc_82></location>.</text>
<text><location><page_23><loc_43><loc_81><loc_44><loc_81></location>3</text>
<text><location><page_23><loc_44><loc_82><loc_45><loc_83></location>6</text>
<text><location><page_23><loc_44><loc_82><loc_45><loc_82></location>9</text>
<text><location><page_23><loc_44><loc_82><loc_45><loc_82></location>0</text>
<text><location><page_23><loc_44><loc_81><loc_45><loc_82></location>.</text>
<text><location><page_23><loc_44><loc_81><loc_45><loc_81></location>3</text>
<text><location><page_23><loc_45><loc_82><loc_46><loc_83></location>8</text>
<text><location><page_23><loc_45><loc_82><loc_46><loc_82></location>3</text>
<text><location><page_23><loc_45><loc_82><loc_46><loc_82></location>8</text>
<text><location><page_23><loc_45><loc_81><loc_46><loc_82></location>.</text>
<text><location><page_23><loc_45><loc_81><loc_46><loc_81></location>2</text>
<paragraph><location><page_23><loc_47><loc_82><loc_52><loc_83></location>3 8 8 0 9 6 9 6 5 4</paragraph>
<text><location><page_23><loc_47><loc_82><loc_47><loc_82></location>8</text>
<text><location><page_23><loc_47><loc_81><loc_47><loc_82></location>.</text>
<text><location><page_23><loc_47><loc_81><loc_47><loc_81></location>2</text>
<text><location><page_23><loc_48><loc_82><loc_49><loc_82></location>5</text>
<text><location><page_23><loc_48><loc_81><loc_49><loc_82></location>.</text>
<text><location><page_23><loc_48><loc_81><loc_49><loc_81></location>2</text>
<text><location><page_23><loc_49><loc_82><loc_50><loc_82></location>0</text>
<text><location><page_23><loc_49><loc_81><loc_50><loc_82></location>.</text>
<text><location><page_23><loc_49><loc_81><loc_50><loc_81></location>3</text>
<text><location><page_23><loc_50><loc_82><loc_51><loc_82></location>0</text>
<text><location><page_23><loc_50><loc_81><loc_51><loc_82></location>.</text>
<text><location><page_23><loc_50><loc_81><loc_51><loc_81></location>3</text>
<text><location><page_23><loc_51><loc_82><loc_52><loc_82></location>3</text>
<text><location><page_23><loc_51><loc_81><loc_52><loc_82></location>.</text>
<text><location><page_23><loc_51><loc_81><loc_52><loc_81></location>3</text>
<text><location><page_23><loc_53><loc_82><loc_54><loc_83></location>0</text>
<text><location><page_23><loc_53><loc_82><loc_54><loc_82></location>7</text>
<text><location><page_23><loc_53><loc_82><loc_54><loc_82></location>8</text>
<text><location><page_23><loc_53><loc_81><loc_54><loc_82></location>.</text>
<text><location><page_23><loc_53><loc_81><loc_54><loc_81></location>3</text>
<text><location><page_23><loc_54><loc_82><loc_55><loc_83></location>0</text>
<text><location><page_23><loc_54><loc_82><loc_55><loc_82></location>8</text>
<text><location><page_23><loc_54><loc_82><loc_55><loc_82></location>5</text>
<text><location><page_23><loc_54><loc_81><loc_55><loc_82></location>.</text>
<text><location><page_23><loc_54><loc_81><loc_55><loc_81></location>2</text>
<text><location><page_23><loc_55><loc_82><loc_56><loc_83></location>6</text>
<text><location><page_23><loc_55><loc_82><loc_56><loc_82></location>0</text>
<text><location><page_23><loc_55><loc_82><loc_56><loc_82></location>8</text>
<text><location><page_23><loc_55><loc_81><loc_56><loc_82></location>.</text>
<text><location><page_23><loc_55><loc_81><loc_56><loc_81></location>1</text>
<text><location><page_23><loc_56><loc_82><loc_57><loc_83></location>4</text>
<text><location><page_23><loc_56><loc_82><loc_57><loc_82></location>5</text>
<text><location><page_23><loc_56><loc_82><loc_57><loc_82></location>3</text>
<text><location><page_23><loc_56><loc_81><loc_57><loc_82></location>.</text>
<text><location><page_23><loc_56><loc_81><loc_57><loc_81></location>3</text>
<text><location><page_23><loc_58><loc_82><loc_58><loc_83></location>6</text>
<text><location><page_23><loc_58><loc_82><loc_58><loc_82></location>9</text>
<text><location><page_23><loc_58><loc_82><loc_58><loc_82></location>0</text>
<text><location><page_23><loc_58><loc_81><loc_58><loc_82></location>.</text>
<text><location><page_23><loc_58><loc_81><loc_58><loc_81></location>3</text>
<text><location><page_23><loc_59><loc_82><loc_60><loc_83></location>4</text>
<text><location><page_23><loc_59><loc_82><loc_60><loc_82></location>5</text>
<text><location><page_23><loc_59><loc_82><loc_60><loc_82></location>3</text>
<text><location><page_23><loc_59><loc_81><loc_60><loc_82></location>.</text>
<text><location><page_23><loc_59><loc_81><loc_60><loc_81></location>3</text>
<text><location><page_23><loc_60><loc_82><loc_61><loc_83></location>8</text>
<text><location><page_23><loc_60><loc_82><loc_61><loc_82></location>3</text>
<text><location><page_23><loc_60><loc_82><loc_61><loc_82></location>8</text>
<text><location><page_23><loc_60><loc_81><loc_61><loc_82></location>.</text>
<text><location><page_23><loc_60><loc_81><loc_61><loc_81></location>2</text>
<text><location><page_23><loc_61><loc_82><loc_62><loc_83></location>4</text>
<text><location><page_23><loc_61><loc_82><loc_62><loc_82></location>5</text>
<text><location><page_23><loc_61><loc_82><loc_62><loc_82></location>3</text>
<text><location><page_23><loc_61><loc_81><loc_62><loc_82></location>.</text>
<text><location><page_23><loc_61><loc_81><loc_62><loc_81></location>3</text>
<text><location><page_23><loc_63><loc_82><loc_63><loc_83></location>4</text>
<text><location><page_23><loc_63><loc_82><loc_63><loc_82></location>5</text>
<text><location><page_23><loc_63><loc_82><loc_63><loc_82></location>3</text>
<text><location><page_23><loc_63><loc_81><loc_63><loc_82></location>.</text>
<text><location><page_23><loc_63><loc_81><loc_63><loc_81></location>3</text>
<text><location><page_23><loc_64><loc_82><loc_65><loc_83></location>2</text>
<text><location><page_23><loc_64><loc_82><loc_65><loc_82></location>2</text>
<text><location><page_23><loc_64><loc_82><loc_65><loc_82></location>3</text>
<text><location><page_23><loc_64><loc_81><loc_65><loc_82></location>.</text>
<text><location><page_23><loc_64><loc_81><loc_65><loc_81></location>2</text>
<text><location><page_23><loc_65><loc_82><loc_66><loc_83></location>2</text>
<text><location><page_23><loc_65><loc_82><loc_66><loc_82></location>1</text>
<text><location><page_23><loc_65><loc_82><loc_66><loc_82></location>6</text>
<text><location><page_23><loc_65><loc_81><loc_66><loc_82></location>.</text>
<text><location><page_23><loc_65><loc_81><loc_66><loc_81></location>3</text>
<text><location><page_23><loc_66><loc_82><loc_67><loc_83></location>2</text>
<text><location><page_23><loc_66><loc_82><loc_67><loc_82></location>1</text>
<text><location><page_23><loc_66><loc_82><loc_67><loc_82></location>6</text>
<text><location><page_23><loc_66><loc_81><loc_67><loc_82></location>.</text>
<text><location><page_23><loc_66><loc_81><loc_67><loc_81></location>3</text>
<text><location><page_23><loc_67><loc_82><loc_68><loc_83></location>6</text>
<text><location><page_23><loc_67><loc_82><loc_68><loc_82></location>9</text>
<text><location><page_23><loc_67><loc_82><loc_68><loc_82></location>0</text>
<text><location><page_23><loc_67><loc_81><loc_68><loc_82></location>.</text>
<text><location><page_23><loc_67><loc_81><loc_68><loc_81></location>3</text>
<text><location><page_23><loc_69><loc_82><loc_69><loc_83></location>4</text>
<text><location><page_23><loc_69><loc_82><loc_69><loc_82></location>5</text>
<text><location><page_23><loc_69><loc_82><loc_69><loc_82></location>3</text>
<text><location><page_23><loc_69><loc_81><loc_69><loc_82></location>.</text>
<text><location><page_23><loc_69><loc_81><loc_69><loc_81></location>3</text>
<text><location><page_23><loc_70><loc_82><loc_71><loc_83></location>4</text>
<text><location><page_23><loc_70><loc_82><loc_71><loc_82></location>6</text>
<text><location><page_23><loc_70><loc_82><loc_71><loc_82></location>0</text>
<text><location><page_23><loc_70><loc_81><loc_71><loc_82></location>.</text>
<text><location><page_23><loc_70><loc_81><loc_71><loc_81></location>2</text>
<text><location><page_23><loc_71><loc_82><loc_72><loc_83></location>6</text>
<text><location><page_23><loc_71><loc_82><loc_72><loc_82></location>9</text>
<text><location><page_23><loc_71><loc_82><loc_72><loc_82></location>0</text>
<text><location><page_23><loc_71><loc_81><loc_72><loc_82></location>.</text>
<text><location><page_23><loc_71><loc_81><loc_72><loc_81></location>3</text>
<text><location><page_23><loc_72><loc_82><loc_73><loc_83></location>0</text>
<text><location><page_23><loc_72><loc_82><loc_73><loc_82></location>7</text>
<text><location><page_23><loc_72><loc_82><loc_73><loc_82></location>8</text>
<text><location><page_23><loc_72><loc_81><loc_73><loc_82></location>.</text>
<text><location><page_23><loc_72><loc_81><loc_73><loc_81></location>3</text>
<text><location><page_23><loc_74><loc_82><loc_74><loc_83></location>6</text>
<text><location><page_23><loc_74><loc_82><loc_74><loc_82></location>9</text>
<text><location><page_23><loc_74><loc_82><loc_74><loc_82></location>0</text>
<text><location><page_23><loc_74><loc_81><loc_74><loc_82></location>.</text>
<text><location><page_23><loc_74><loc_81><loc_74><loc_81></location>3</text>
<text><location><page_23><loc_75><loc_82><loc_76><loc_83></location>0</text>
<text><location><page_23><loc_75><loc_82><loc_76><loc_82></location>8</text>
<text><location><page_23><loc_75><loc_82><loc_76><loc_82></location>5</text>
<text><location><page_23><loc_75><loc_81><loc_76><loc_82></location>.</text>
<text><location><page_23><loc_75><loc_81><loc_76><loc_81></location>2</text>
<text><location><page_23><loc_76><loc_82><loc_77><loc_83></location>8</text>
<text><location><page_23><loc_76><loc_82><loc_77><loc_82></location>3</text>
<text><location><page_23><loc_76><loc_82><loc_77><loc_82></location>8</text>
<text><location><page_23><loc_76><loc_81><loc_77><loc_82></location>.</text>
<text><location><page_23><loc_76><loc_81><loc_77><loc_81></location>2</text>
<text><location><page_23><loc_77><loc_82><loc_78><loc_83></location>0</text>
<text><location><page_23><loc_77><loc_82><loc_78><loc_82></location>7</text>
<text><location><page_23><loc_77><loc_82><loc_78><loc_82></location>8</text>
<text><location><page_23><loc_77><loc_81><loc_78><loc_82></location>.</text>
<text><location><page_23><loc_77><loc_81><loc_78><loc_81></location>3</text>
<text><location><page_23><loc_78><loc_82><loc_79><loc_83></location>2</text>
<text><location><page_23><loc_78><loc_82><loc_79><loc_82></location>1</text>
<text><location><page_23><loc_78><loc_82><loc_79><loc_82></location>6</text>
<text><location><page_23><loc_78><loc_81><loc_79><loc_82></location>.</text>
<text><location><page_23><loc_78><loc_81><loc_79><loc_81></location>3</text>
<text><location><page_23><loc_80><loc_82><loc_81><loc_83></location>8</text>
<text><location><page_23><loc_80><loc_82><loc_81><loc_82></location>2</text>
<text><location><page_23><loc_80><loc_82><loc_81><loc_82></location>1</text>
<text><location><page_23><loc_80><loc_81><loc_81><loc_82></location>.</text>
<text><location><page_23><loc_80><loc_81><loc_81><loc_81></location>4</text>
<text><location><page_23><loc_81><loc_82><loc_82><loc_83></location>6</text>
<text><location><page_23><loc_81><loc_82><loc_82><loc_82></location>9</text>
<text><location><page_23><loc_81><loc_82><loc_82><loc_82></location>0</text>
<text><location><page_23><loc_81><loc_81><loc_82><loc_82></location>.</text>
<text><location><page_23><loc_81><loc_81><loc_82><loc_81></location>3</text>
<text><location><page_23><loc_82><loc_82><loc_83><loc_83></location>2</text>
<text><location><page_23><loc_82><loc_82><loc_83><loc_82></location>1</text>
<text><location><page_23><loc_82><loc_82><loc_83><loc_82></location>6</text>
<text><location><page_23><loc_82><loc_81><loc_83><loc_82></location>.</text>
<text><location><page_23><loc_82><loc_81><loc_83><loc_81></location>3</text>
<text><location><page_23><loc_83><loc_82><loc_84><loc_83></location>4</text>
<text><location><page_23><loc_83><loc_82><loc_84><loc_82></location>5</text>
<text><location><page_23><loc_83><loc_82><loc_84><loc_82></location>3</text>
<text><location><page_23><loc_83><loc_81><loc_84><loc_82></location>.</text>
<text><location><page_23><loc_83><loc_81><loc_84><loc_81></location>3</text>
<text><location><page_23><loc_83><loc_78><loc_84><loc_78></location>0</text>
<text><location><page_23><loc_83><loc_78><loc_84><loc_78></location>1</text>
<text><location><page_23><loc_83><loc_77><loc_84><loc_78></location>.</text>
<text><location><page_23><loc_83><loc_77><loc_84><loc_77></location>0</text>
<text><location><page_23><loc_83><loc_74><loc_84><loc_75></location>1</text>
<text><location><page_23><loc_83><loc_74><loc_84><loc_74></location>3</text>
<text><location><page_23><loc_83><loc_73><loc_84><loc_74></location>0</text>
<text><location><page_23><loc_83><loc_73><loc_84><loc_73></location>.</text>
<text><location><page_23><loc_83><loc_73><loc_84><loc_73></location>0</text>
<text><location><page_23><loc_83><loc_72><loc_84><loc_72></location>±</text>
<text><location><page_23><loc_83><loc_71><loc_84><loc_71></location>3</text>
<text><location><page_23><loc_83><loc_70><loc_84><loc_71></location>1</text>
<text><location><page_23><loc_83><loc_70><loc_84><loc_70></location>2</text>
<text><location><page_23><loc_83><loc_70><loc_84><loc_70></location>.</text>
<text><location><page_23><loc_83><loc_69><loc_84><loc_70></location>7</text>
<text><location><page_23><loc_83><loc_69><loc_84><loc_69></location>1</text>
<text><location><page_23><loc_83><loc_67><loc_84><loc_68></location>7</text>
<text><location><page_23><loc_83><loc_67><loc_84><loc_67></location>1</text>
<text><location><page_23><loc_83><loc_66><loc_84><loc_67></location>0</text>
<text><location><page_23><loc_83><loc_66><loc_84><loc_66></location>.</text>
<text><location><page_23><loc_83><loc_66><loc_84><loc_66></location>0</text>
<text><location><page_23><loc_83><loc_65><loc_84><loc_65></location>±</text>
<text><location><page_23><loc_83><loc_64><loc_84><loc_64></location>3</text>
<text><location><page_23><loc_83><loc_64><loc_84><loc_64></location>5</text>
<text><location><page_23><loc_83><loc_63><loc_84><loc_64></location>2</text>
<text><location><page_23><loc_83><loc_63><loc_84><loc_63></location>.</text>
<text><location><page_23><loc_83><loc_62><loc_84><loc_63></location>8</text>
<text><location><page_23><loc_83><loc_62><loc_84><loc_62></location>1</text>
<text><location><page_23><loc_83><loc_60><loc_84><loc_61></location>3</text>
<text><location><page_23><loc_83><loc_60><loc_84><loc_60></location>1</text>
<text><location><page_23><loc_83><loc_59><loc_84><loc_60></location>0</text>
<text><location><page_23><loc_83><loc_59><loc_84><loc_59></location>.</text>
<text><location><page_23><loc_83><loc_59><loc_84><loc_59></location>0</text>
<text><location><page_23><loc_83><loc_58><loc_84><loc_58></location>±</text>
<text><location><page_23><loc_83><loc_57><loc_84><loc_57></location>5</text>
<text><location><page_23><loc_83><loc_57><loc_84><loc_57></location>0</text>
<text><location><page_23><loc_83><loc_56><loc_84><loc_57></location>6</text>
<text><location><page_23><loc_83><loc_56><loc_84><loc_56></location>.</text>
<text><location><page_23><loc_83><loc_56><loc_84><loc_56></location>8</text>
<text><location><page_23><loc_83><loc_55><loc_84><loc_56></location>1</text>
<text><location><page_23><loc_83><loc_53><loc_84><loc_54></location>5</text>
<text><location><page_23><loc_83><loc_53><loc_84><loc_53></location>1</text>
<text><location><page_23><loc_83><loc_53><loc_84><loc_53></location>0</text>
<text><location><page_23><loc_83><loc_52><loc_84><loc_53></location>.</text>
<text><location><page_23><loc_83><loc_52><loc_84><loc_52></location>0</text>
<text><location><page_23><loc_83><loc_51><loc_84><loc_52></location>±</text>
<text><location><page_23><loc_83><loc_50><loc_84><loc_51></location>0</text>
<text><location><page_23><loc_83><loc_50><loc_84><loc_50></location>2</text>
<text><location><page_23><loc_83><loc_49><loc_84><loc_50></location>1</text>
<text><location><page_23><loc_83><loc_49><loc_84><loc_49></location>.</text>
<text><location><page_23><loc_83><loc_49><loc_84><loc_49></location>9</text>
<text><location><page_23><loc_83><loc_48><loc_84><loc_49></location>1</text>
<text><location><page_23><loc_83><loc_47><loc_84><loc_47></location>2</text>
<text><location><page_23><loc_83><loc_46><loc_84><loc_47></location>1</text>
<text><location><page_23><loc_83><loc_46><loc_84><loc_46></location>0</text>
<text><location><page_23><loc_83><loc_45><loc_84><loc_46></location>.</text>
<text><location><page_23><loc_83><loc_45><loc_84><loc_45></location>0</text>
<text><location><page_23><loc_83><loc_44><loc_84><loc_45></location>±</text>
<text><location><page_23><loc_83><loc_43><loc_84><loc_44></location>3</text>
<text><location><page_23><loc_83><loc_43><loc_84><loc_43></location>2</text>
<text><location><page_23><loc_83><loc_42><loc_84><loc_43></location>0</text>
<text><location><page_23><loc_83><loc_42><loc_84><loc_42></location>.</text>
<text><location><page_23><loc_83><loc_42><loc_84><loc_42></location>9</text>
<text><location><page_23><loc_83><loc_41><loc_84><loc_42></location>1</text>
<text><location><page_23><loc_83><loc_40><loc_84><loc_40></location>8</text>
<text><location><page_23><loc_83><loc_39><loc_84><loc_40></location>6</text>
<text><location><page_23><loc_83><loc_39><loc_84><loc_39></location>.</text>
<text><location><page_23><loc_83><loc_39><loc_84><loc_39></location>0</text>
<text><location><page_23><loc_83><loc_38><loc_84><loc_39></location>1</text>
<text><location><page_23><loc_83><loc_37><loc_84><loc_38></location>6</text>
<text><location><page_23><loc_83><loc_37><loc_84><loc_37></location>4</text>
<text><location><page_23><loc_83><loc_36><loc_84><loc_37></location>0</text>
<text><location><page_23><loc_83><loc_36><loc_84><loc_36></location>3</text>
<text><location><page_23><loc_83><loc_34><loc_84><loc_35></location>0</text>
<text><location><page_23><loc_83><loc_34><loc_84><loc_34></location>1</text>
<text><location><page_23><loc_83><loc_33><loc_84><loc_34></location>7</text>
<text><location><page_23><loc_83><loc_33><loc_84><loc_33></location>.</text>
<text><location><page_23><loc_83><loc_33><loc_84><loc_33></location>4</text>
<text><location><page_23><loc_83><loc_32><loc_84><loc_33></location>0</text>
<text><location><page_23><loc_83><loc_31><loc_84><loc_32></location>5</text>
<text><location><page_23><loc_83><loc_31><loc_84><loc_31></location>3</text>
<text><location><page_23><loc_83><loc_30><loc_84><loc_31></location>1</text>
<text><location><page_23><loc_83><loc_30><loc_84><loc_30></location>0</text>
<text><location><page_23><loc_83><loc_22><loc_84><loc_23></location>7</text>
<text><location><page_23><loc_83><loc_22><loc_84><loc_22></location>4</text>
<text><location><page_23><loc_83><loc_21><loc_84><loc_22></location>4</text>
<text><location><page_23><loc_83><loc_21><loc_84><loc_21></location>M</text>
<text><location><page_23><loc_83><loc_20><loc_84><loc_21></location>S</text>
<text><location><page_23><loc_83><loc_19><loc_84><loc_19></location>.</text>
<text><location><page_23><loc_83><loc_18><loc_84><loc_19></location>.</text>
<text><location><page_23><loc_83><loc_18><loc_84><loc_18></location>.</text>
<text><location><page_23><loc_83><loc_18><loc_84><loc_18></location>.</text>
<text><location><page_23><loc_83><loc_18><loc_84><loc_18></location>.</text>
<text><location><page_23><loc_83><loc_17><loc_84><loc_18></location>.</text>
<text><location><page_23><loc_83><loc_17><loc_84><loc_17></location>0</text>
<text><location><page_23><loc_83><loc_17><loc_84><loc_17></location>1</text>
<text><location><page_23><loc_83><loc_16><loc_84><loc_17></location>5</text>
<table>
<location><page_23><loc_16><loc_15><loc_83><loc_81></location>
</table>
<text><location><page_23><loc_85><loc_82><loc_85><loc_83></location>0</text>
<text><location><page_23><loc_85><loc_82><loc_85><loc_82></location>6</text>
<text><location><page_23><loc_85><loc_82><loc_85><loc_82></location>1</text>
<text><location><page_23><loc_85><loc_81><loc_85><loc_82></location>.</text>
<text><location><page_23><loc_85><loc_81><loc_85><loc_81></location>5</text>
<text><location><page_23><loc_85><loc_78><loc_85><loc_78></location>0</text>
<text><location><page_23><loc_85><loc_78><loc_85><loc_78></location>1</text>
<text><location><page_23><loc_85><loc_77><loc_85><loc_78></location>.</text>
<text><location><page_23><loc_85><loc_77><loc_85><loc_77></location>0</text>
<text><location><page_23><loc_85><loc_74><loc_85><loc_75></location>0</text>
<text><location><page_23><loc_85><loc_74><loc_85><loc_74></location>1</text>
<text><location><page_23><loc_85><loc_73><loc_85><loc_74></location>0</text>
<text><location><page_23><loc_85><loc_73><loc_85><loc_73></location>.</text>
<text><location><page_23><loc_85><loc_73><loc_85><loc_73></location>0</text>
<text><location><page_23><loc_85><loc_72><loc_85><loc_72></location>±</text>
<text><location><page_23><loc_85><loc_71><loc_85><loc_71></location>6</text>
<text><location><page_23><loc_85><loc_70><loc_85><loc_71></location>8</text>
<text><location><page_23><loc_85><loc_70><loc_85><loc_70></location>2</text>
<text><location><page_23><loc_85><loc_70><loc_85><loc_70></location>.</text>
<text><location><page_23><loc_85><loc_69><loc_85><loc_70></location>7</text>
<text><location><page_23><loc_85><loc_69><loc_85><loc_69></location>1</text>
<text><location><page_23><loc_85><loc_67><loc_85><loc_68></location>1</text>
<text><location><page_23><loc_85><loc_67><loc_85><loc_67></location>1</text>
<text><location><page_23><loc_85><loc_66><loc_85><loc_67></location>0</text>
<text><location><page_23><loc_85><loc_66><loc_85><loc_66></location>.</text>
<text><location><page_23><loc_85><loc_66><loc_85><loc_66></location>0</text>
<text><location><page_23><loc_85><loc_65><loc_85><loc_65></location>±</text>
<text><location><page_23><loc_85><loc_64><loc_85><loc_64></location>7</text>
<text><location><page_23><loc_85><loc_64><loc_85><loc_64></location>7</text>
<text><location><page_23><loc_85><loc_63><loc_85><loc_64></location>7</text>
<text><location><page_23><loc_85><loc_63><loc_85><loc_63></location>.</text>
<text><location><page_23><loc_85><loc_62><loc_85><loc_63></location>7</text>
<text><location><page_23><loc_85><loc_62><loc_85><loc_62></location>1</text>
<text><location><page_23><loc_85><loc_60><loc_85><loc_61></location>4</text>
<text><location><page_23><loc_85><loc_60><loc_85><loc_60></location>1</text>
<text><location><page_23><loc_85><loc_59><loc_85><loc_60></location>0</text>
<text><location><page_23><loc_85><loc_59><loc_85><loc_59></location>.</text>
<text><location><page_23><loc_85><loc_59><loc_85><loc_59></location>0</text>
<text><location><page_23><loc_85><loc_58><loc_85><loc_58></location>±</text>
<text><location><page_23><loc_85><loc_57><loc_85><loc_57></location>5</text>
<text><location><page_23><loc_85><loc_57><loc_85><loc_57></location>5</text>
<text><location><page_23><loc_85><loc_56><loc_85><loc_57></location>2</text>
<text><location><page_23><loc_85><loc_56><loc_85><loc_56></location>.</text>
<text><location><page_23><loc_85><loc_56><loc_85><loc_56></location>8</text>
<text><location><page_23><loc_85><loc_55><loc_85><loc_56></location>1</text>
<text><location><page_23><loc_85><loc_53><loc_85><loc_54></location>5</text>
<text><location><page_23><loc_85><loc_53><loc_85><loc_53></location>1</text>
<text><location><page_23><loc_85><loc_53><loc_85><loc_53></location>0</text>
<text><location><page_23><loc_85><loc_52><loc_85><loc_53></location>.</text>
<text><location><page_23><loc_85><loc_52><loc_85><loc_52></location>0</text>
<text><location><page_23><loc_85><loc_51><loc_85><loc_52></location>±</text>
<text><location><page_23><loc_85><loc_50><loc_85><loc_51></location>2</text>
<text><location><page_23><loc_85><loc_50><loc_85><loc_50></location>6</text>
<text><location><page_23><loc_85><loc_49><loc_85><loc_50></location>9</text>
<text><location><page_23><loc_85><loc_49><loc_85><loc_49></location>.</text>
<text><location><page_23><loc_85><loc_49><loc_85><loc_49></location>8</text>
<text><location><page_23><loc_85><loc_48><loc_85><loc_49></location>1</text>
<text><location><page_23><loc_85><loc_47><loc_85><loc_47></location>4</text>
<text><location><page_23><loc_85><loc_46><loc_85><loc_47></location>1</text>
<text><location><page_23><loc_85><loc_46><loc_85><loc_46></location>0</text>
<text><location><page_23><loc_85><loc_45><loc_85><loc_46></location>.</text>
<text><location><page_23><loc_85><loc_45><loc_85><loc_45></location>0</text>
<text><location><page_23><loc_85><loc_44><loc_85><loc_45></location>±</text>
<text><location><page_23><loc_85><loc_43><loc_85><loc_44></location>0</text>
<text><location><page_23><loc_85><loc_43><loc_85><loc_43></location>6</text>
<text><location><page_23><loc_85><loc_42><loc_85><loc_43></location>1</text>
<text><location><page_23><loc_85><loc_42><loc_85><loc_42></location>.</text>
<text><location><page_23><loc_85><loc_42><loc_85><loc_42></location>9</text>
<text><location><page_23><loc_85><loc_41><loc_85><loc_42></location>1</text>
<text><location><page_23><loc_85><loc_40><loc_85><loc_40></location>2</text>
<text><location><page_23><loc_85><loc_39><loc_85><loc_40></location>9</text>
<text><location><page_23><loc_85><loc_39><loc_85><loc_39></location>.</text>
<text><location><page_23><loc_85><loc_39><loc_85><loc_39></location>3</text>
<text><location><page_23><loc_85><loc_38><loc_85><loc_39></location>5</text>
<text><location><page_23><loc_85><loc_37><loc_85><loc_38></location>9</text>
<text><location><page_23><loc_85><loc_37><loc_85><loc_37></location>4</text>
<text><location><page_23><loc_85><loc_36><loc_85><loc_37></location>0</text>
<text><location><page_23><loc_85><loc_36><loc_85><loc_36></location>3</text>
<text><location><page_23><loc_85><loc_34><loc_85><loc_35></location>8</text>
<text><location><page_23><loc_85><loc_34><loc_85><loc_34></location>4</text>
<text><location><page_23><loc_85><loc_33><loc_85><loc_34></location>2</text>
<text><location><page_23><loc_85><loc_33><loc_85><loc_33></location>.</text>
<text><location><page_23><loc_85><loc_33><loc_85><loc_33></location>8</text>
<text><location><page_23><loc_85><loc_32><loc_85><loc_33></location>1</text>
<text><location><page_23><loc_85><loc_31><loc_85><loc_32></location>5</text>
<text><location><page_23><loc_85><loc_31><loc_85><loc_31></location>3</text>
<text><location><page_23><loc_85><loc_30><loc_85><loc_31></location>1</text>
<text><location><page_23><loc_85><loc_30><loc_85><loc_30></location>0</text>
<text><location><page_23><loc_85><loc_22><loc_85><loc_23></location>9</text>
<text><location><page_23><loc_85><loc_22><loc_85><loc_22></location>4</text>
<text><location><page_23><loc_85><loc_21><loc_85><loc_22></location>4</text>
<text><location><page_23><loc_85><loc_21><loc_85><loc_21></location>M</text>
<text><location><page_23><loc_85><loc_20><loc_85><loc_21></location>S</text>
<text><location><page_23><loc_85><loc_19><loc_85><loc_19></location>.</text>
<text><location><page_23><loc_85><loc_18><loc_85><loc_19></location>.</text>
<text><location><page_23><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_23><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_23><loc_85><loc_18><loc_85><loc_18></location>.</text>
<text><location><page_23><loc_85><loc_17><loc_85><loc_18></location>.</text>
<text><location><page_23><loc_85><loc_17><loc_85><loc_17></location>1</text>
<text><location><page_23><loc_85><loc_17><loc_85><loc_17></location>1</text>
<text><location><page_23><loc_85><loc_16><loc_85><loc_17></location>5</text>
</document>
[
{
"title": "ABSTRACT",
"content": "This is the second paper of our series. In this paper, we present UBVRI photometry for 234 star clusters in the field of M33. For most of these star clusters, there is photometry in only two bands in previous studies. The photometry of these star clusters is performed using archival images from the Local Group Galaxies Survey, which covers 0.8 deg 2 along the major axis of M33. Detailed comparisons show that, in general, our photometry is consistent with previous measurements, especially, our photometry is in good agreement with Zloczewski & Kaluzny. Combined with the star clusters' photometry in previous studies, we present some results: none of the M33 youngest clusters ( ∼ 10 7 yr) have masses approaching 10 5 M /circledot ; comparisons with models of simple stellar populations suggest a large range of ages of M33 star clusters, and some as old as the Galactic globular clusters. Subject headings: catalogs - galaxies: individual (M33) - galaxies: spiral - galaxies: star clusters: general",
"pages": [
1
]
},
{
"title": "NEW UBVRI PHOTOMETRY OF 234 M33 STAR CLUSTERS",
"content": "Jun Ma 1,2 AJ, in press",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Star clusters are an important tool for studying the star formation histories of galaxies. They represent, in distinct and luminous 'packets,' single-age and singleabundance points and encapsulate at least a partial history of the parent galaxy's evolution. M33 is a small Scd Local Group galaxy. It is located ∼ 809 ± 24 kpc from us (distance modulus ( m -M ) 0 = 24 . 54 ± 0 . 06; McConnachie et al. 2004, 2005). M33 is interesting and important because it represents an intermediate morphological type between the largest 'earlytype' spirals and the dwarf irregulars in the Local Group. So, it can provide an important link between the star cluster populations of earlier-type spirals (Milky Way and M31) and the numerous nearby later-type dwarf galaxies. In the pioneering work of M33 star clusters, Hiltner (1960) presented photometry for 23 M33 star cluster candidates and 23 M31 globular clusters in the UBV passbands using photographic plates taken with the Mt. Wilson 100-inch (2.5-m) telescope. And he found that, except for five of them, the star clusters in M33 are bluer and fainter than those in M31. At the same time, Kron & Mayall (1960) identified four M33 star clusters for which they gave PV photometry. Then, Melnick & D'Odorico (1978) detected 58 star cluster candidates in M33 based on a baked IIIa-J+GG385 plate covering a field of about 1 · in diameter, including B photometry of them. The most comprehensive catalog of nonstellar objects in M33 was compiled by Christian & Schommer (1982, 1988), who detected 250 nonstellar objects by visually examining a single photographic plate taken at the Ritchey-Chrestien focus of the 4-m telescope at Kitt Peak National Observatory. These authors obtained ground-based BVI photometry of 106 1 National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100012, China; [email protected] 2 Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China of these objects, which they believe to be star clusters. However, the star cluster candidates detected by these authors are limited to the outer part of M33. The first survey for M33 star clusters based on CCD imaging was performed by Mochejska et al. (1998), using the data collected in the DIRECT project (Kaluzny et al. 1998; Stanek et al. 1998). These authors detected 51 globular cluster candidates in M33, 32 of which were not previously cataloged. These globular cluster candidates covered the central region of M33. In addition, Mochejska et al. (1998) presented BVI photometry for these globular cluster candidates. Since the pioneering work of Chandar et al. (1999a), the era of detecting and studying M33 star clusters based on the images taken with Hubble Space Telescope ( HST ) has begun (Chandar et al. 1999a,b,c, 2001, 2002; Bedin et al. 2005; Park & Lee 2007; Sarajedini et al. 2007, 1998, 2000; Stonkut˙e et al. 2008; Park et al. 2009; Huxor et al. 2009; San Roman et al. 2009; Zloczewski & Kaluzny 2009). The HST resolution makes it easy to distinguish individual stars from star clusters at the distance of M33. So, M33 star clusters identified with HST images are much less likely to be contaminated by other extended sources, such as a background galaxy or an HII region (see Park & Lee 2007, for details). Ma et al. (2001, 2002a,b,c,d, 2004a,b) constructed spectral energy distributions in 13 intermediate filters of the Beijing-Arizona-Taiwan-Connecticut photometric system for known M33 star clusters and star cluster candidates, and estimated star cluster properties. In order to construct a single master catalog incorporating the entries in all of the individual catalogs including all known properties of each star cluster, Sarajedini & Mancone (2007) merged all of the abovementioned catalogs before 2007, for a summary of the properties of all of these catalogs. This catalog contains 451 star cluster candidates, of which 255 are confirmed star clusters based on the HST and high-resolution ground-based imaging. The positions of the star clusters in Sarajedini & Mancone (2007) were transformed to the J2000.0 epoch and refined using the Local Group Galaxies Survey (LGGS; Massey et al. 2006). Very recently, some authors used the images observed with the MegaCam camera on the 3.6-m Canada-France-Hawaii Telescope (CFHT/MegaCam) to detect star clusters in M33 (Zloczewski et al. 2008; San Roman et al. 2010). Sharina et al. (2010) presented the evolutionary parameters of 15 GCs in M33 based on the results of medium-resolution spectroscopy obtained at the Special Astrophysical Observatory 6-m telescope. Most recently, Cockcroft et al. (2011) searched for outer halo star clusters in M33 based on CFHT/MegaCam imaging as part of the Pan-Andromeda Archaeological Survey. Ma (2012) (Paper I) presented UBVRI photometry of 392 objects (277 star clusters and 115 star cluster candidates) in the field of M33, using the images of the LGGS (Massey et al. 2006). And he also provided properties of M33 star clusters such as their color-magnitude diagram and color-color diagram. In this paper, we perform aperture photometry of 234 M33 star clusters based on the M33 images of the LGGS. These sample star clusters are selected from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). This paper is organized as follows. Section 2 describes the sample star cluster selection and UBVRI photometry. In Section 3, we present an analysis of the star cluster properties. Lastly, our conclusions are presented in Section 4.",
"pages": [
1,
2
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},
{
"title": "2.1. Sample",
"content": "In Paper I, we presented an updated UBVRI photometric catalog containing 392 star clusters and star cluster candidates in the field of M33 which were selected from the most recent star cluster catalog of Sarajedini & Mancone (2007). And we also provided properties of M33 star clusters such as their colormagnitude diagram (CMD) and color-color diagram combined with the photometry of M33 star clusters from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). However, we found that most of M33 star clusters from San Roman et al. (2009) and Zloczewski & Kaluzny (2009) have photometry in only two bands V and I . In the color-color diagram of Paper I, there are only ∼ 300 M33 star clusters, since ∼ 200 star clusters have no B -V data. So, integrated magnitudes of these star clusters in B and V bands are emergently needed for studying the properties of M33 star clusters. In this paper, we will provide UBVRI photometry of M33 star clusters from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). Park & Lee (2007) found 104 star clusters in the HST /WFPC 2 archive images of 24 fields that were not included in previous studies, of which 32 star clusters are newly detected. Zloczewski et al. (2008) presented a catalog of 4780 extended sources in a 1 deg 2 region around M33 including 3554 new star cluster candidates using the MegaCam camera on the CFHT. Zloczewski & Kaluzny (2009) used deep Advanced Camera for Surveys Wide Field Channel (ACS/WFC) images of M33 to check the nature of extended objects detected by Zloczewski et al. (2008), and found that 24 star cluster candidates were confirmed to genuine compact star clusters. In addition, Zloczewski & Kaluzny (2009) detected 91 new star clusters based on these deep ASC/WFC images of M33, and provided integrated magnitudes and angular sizes for all these 115 star clusters. San Roman et al. (2009) presented integrated photometry and color-magnitude diagrams for 161 star clusters in M33 based on the ACS/WFC images, of which 115 were previously uncataloged. By cross-checking with the updated photometric catalog of M33 star cluster and candidate in Paper I, we found that, the photometry of 36 star clusters of Park & Lee (2007) was not presented in Paper I, of which the 32 star clusters were newly detected by Park & Lee (2007) and the remaining four were detected by previous studies. The three of the four star clusters were included in Sarajedini & Mancone (2007) and were classified as 'Stellar' (objects 69, 293 and 279 of Sarajedini & Mancone 2007 which being called star clusters 36, 195 and 197 in Park & Lee 2007, respectively), and the remaining one is star cluster 75 in Park & Lee (2007). The photometry of 118 star clusters of San Roman et al. (2009) was not presented in Paper I, of which 115 star clusters were newly detected by San Roman et al. (2009) based on the ACS/WFC images, and the remaining three star clusters were included in Sarajedini & Mancone (2007) which were classified as 'Galaxy' or 'Stellar' (objects 57, 62 and 69 of Sarajedini & Mancone 2007 which being called star clusters 27, 34 and 38 in San Roman et al. 2009). The photometry of all star clusters of Zloczewski & Kaluzny (2009) was not presented in Paper I, of which one star cluster was included in Sarajedini & Mancone (2007) and was classified as 'Galaxy' (object 57 of Sarajedini & Mancone 2007 which being called 33-3-021 in Zloczewski & Kaluzny 2009). So, in this paper, we will perform photometry for the M33 star clusters in Park & Lee (2007), Zloczewski & Kaluzny (2009) and San Roman et al. (2009) that were not presented in Paper I. Altogether, there are 269 star clusters combining the star clusters from Park & Lee (2007), Zloczewski & Kaluzny (2009) and San Roman et al. (2009). However, by cross-checking the coordinates of the star clusters of Park & Lee (2007), Zloczewski & Kaluzny (2009) and San Roman et al. (2009), and by checking the images of star clusters from the LGGS images, we found that, star clusters 7, 10, 14, and 18 of Park & Lee (2007) are the same objects with star clusters 33, 51, 59, and 64 of San Roman et al. (2009), respectively. In addition, there are 18 common star clusters between Zloczewski & Kaluzny (2009) and San Roman et al. (2009) (see Table 3 of San Roman et al. 2009). When we do photometry of the sample star clusters in this paper, we found that, there is nothing in the position of star cluster 195 of Park & Lee (2007) (i.e., no. 17 of Bedin et al. 2005), which was named object 293 in Sarajedini & Mancone (2007) and was classified as 'Stellar' by Sarajedini & Mancone (2007). We also found that, in the LGGS images of M33, (1) there are some bright objects near star cluster 12 of Park & Lee (2007); (2) there is a bright object near star clusters 23 and 32 of Park & Lee (2007), respectively; (3) there is a bright object very near star clusters 15, 114 and 141 of San Roman et al. (2009), respectively; (4) there are three bright objects near star cluster 143 of San Roman et al. (2009); (5) there is a very close object to star clusters ZK-21, ZK-22, ZK-28, ZK-66 and ZK-72 of Zloczewski & Kaluzny (2009), respectively. The photometry of these 13 star clusters cannot be determined accurately in this paper. So, this paper will present homogeneous UBVRI photometries for 234 star clusters in M33 using the images of the LGGS (see details about the LGGS in Paper I).",
"pages": [
2,
3
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},
{
"title": "2.2. Photometry",
"content": "We used the LGGS archival images of M33 in the UBVRI bands to do photometry (see details in Paper I). We performed aperture photometry of the 234 M33 star clusters found in the LGGS images in all of the UBVRI bands to provide a comprehensive and homogeneous photometric catalog for them. The photometry routine we used is iraf/daophot (Stetson 1987). The photometric process used in this paper is the same as in Paper I. We have checked the aperture of every sample star cluster considered here by visual examination to make sure that it was not too large (to avoid contamination from other sources). The aperture photometry of star clusters was transformed to the standard system using transformation (constant offsets neglecting color term) derived based on aperture photometry of stars whose UBVRI magnitudes were published by Massey et al. (2006), who calibrated their photometry with standard stars of Landolt (1992). Finally, except for star cluster 27 of San Roman et al. (2009) (i.e., SR27, which was named 33-3-021 in Zloczewski & Kaluzny 2009) and ZK-82 of Zloczewski & Kaluzny (2009) in the I band, and ZK-90 of Zloczewski & Kaluzny (2009) in the U and I bands, we obtained photometry for 234 star clusters in the individual UBVRI bands. SR27 falls in the gap of the LGGS image in the I band, and ZK-82 and ZK-90 in the I band fall in the bleeding CCD column of a saturated star, and ZK-90 in the U band does not lie in the LGGS image. Table 1 lists our new UBVRI magnitudes and the aperture radii used (we adopted 0.258 '' pixel -1 from the image header), with errors given by iraf/daophot . The star cluster names follow the naming convention of Sarajedini & Mancone (2007) (i.e., SM ××× ), Park & Lee (2007) (i.e., PL ××× ), San Roman et al. (2009) (i.e., SR ××× ), and Zloczewski & Kaluzny (2009). In addition, we also list the reddening values of the sample star clusters in Table 1 (see Section 3.1 for details). In Table 1, R C and I C mean that RI magnitudes are on Johnson-Kron-Cousins system. To examine the quality and reliability of our photometry, we compared the aperture magnitudes of the 234 star clusters obtained here with previous photometry of Park & Lee (2007), San Roman et al. (2009), and Zloczewski & Kaluzny (2009). There are eight star clusters, of which the magnitude scatters in the V band between this study and previous studies of Park & Lee (2007) and San Roman et al. (2009) are larger than 1.0 mag, i.e., our magnitudes are fainter than those obtained by Park & Lee (2007) and San Roman et al. (2009). We listed the comparison between this study and previous studies of V photometry for these eight star clusters in Table 2. We also plotted their images in Figure 2, in which the circles are photometric apertures adopted here. From this figure, we can see that nearly all these star clusters are close to one or more bright sources. If photometric apertures are larger than the values adopted here, the light from these bright sources will not be excluded. As we know that, in Park & Lee (2007), the BVI integrated aperture photometry of M33 star clusters, which is included in 50 ' × 80 ' field of M33 based on CCD images taken with the CFH12k mosaic camera at the CFHT, is derived with an aperture of r = 4 . 0 '' for V magnitude measurement and an aperture of r = 2 . 0 '' for the measurement of color. San Roman et al. (2009) derived integrated photometry and color-magnitude diagrams (CMDs) for 161 star clusters in M33 using the ACS/WFC images. These authors adopted an aperture radius of r = 2 . 2 '' for V magnitude measurements and r = 1 . 5 '' for the colors. For these eight star clusters, a large scatter in the V photometric measurement between this study and previous studies (Park & Lee 2007; San Roman et al. 2009) mainly results from different photometric aperture sizes adopted by different authors (see Paper I for details). Figures 3-5 show the comparison of our photometry of the star clusters with previous photometry of Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). PL197 is not included in the figure of ∆ V comparison of Figure 3 because of too large value of ∆ V to be drawn in the figure. In addition, in Figure 5 (and Figures 6, 8 and 9 below), we have transformed the ACS/WFC magnitudes in F475W, F606W and F814W bands to the Johnson-Cousins B , V and I magnitudes using the colordependent synthetic transformations given by Sirianni et al. (2005). From Figures 3-5, we can see that our measurements in the V band get systematically fainter than the photometric measurements in San Roman et al. (2009) for fainter sources ( V ≥ 19 mag). The ( V -I ) colors obtained here are in good agreement with those in Park & Lee (2007) and San Roman et al. (2009), however, the difference of ( B -V ) colors between San Roman et al. (2009) and this paper is large, which turned out to be 0 . 388 ± 0 . 040 with σ = 0 . 268. From Figure 5, we can see that both the ( B -V ) and ( V -I ) colors obtained here are in good agreement with those in Zloczewski & Kaluzny (2009), however, the V difference between this study and Zloczewski & Kaluzny (2009) turned out to be -0 . 103 ± 0 . 026 with σ = 0 . 262. By cross-identification, San Roman et al. (2009) provided 21 common star clusters in Zloczewski & Kaluzny (2009). We derived photometry for 18 of these 21 star clusters. We compared the photometry of these 18 star clusters with previous measurements in San Roman et al. (2009) and Zloczewski & Kaluzny (2009) for comparison. Figure 6 shows the comparison. From Figure 6, we can see that our measurements in V band get systematically fainter than the photometric measurements in San Roman et al. (2009) for fainter sources ( V ≥ 19 mag), however, this trend disappears between this study and Zloczewski & Kaluzny (2009). Both the ( B -V ) and ( V -I ) colors obtained here are in good agreement with those in San Roman et al. (2009) and Zloczewski & Kaluzny (2009). In Paper I, we has discussed the V difference between his study and previous studies in detail, and showed that the V difference resulted from different photometric apertures adopted in his study and previous studies. In Paper I, we showed that if the photometric apertures were adopted in our study to be the same as previous studies, the V difference disappeared.",
"pages": [
3,
4
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},
{
"title": "3. RESULTS",
"content": "In Paper I, we has presented some results for M33 star clusters including the CMD and color-color diagram. In addition, in Paper I, we pointed out that, before Zloczewski & Kaluzny (2009), none of M33 star clusters with V > 21 . 0 mag has been detected. And Zloczewski & Kaluzny (2009) emphasized that the faintest known globular cluster in the Milky Way has M V ∼ -1 mag comparing with M V ∼ -4 mag ( V ∼ 21 mag) observed for the faintest of the known M33 globular cluster candidates before Zloczewski & Kaluzny (2009). Zloczewski & Kaluzny (2009) provided integrated magnitudes for 115 M33 star clusters using the ACS/WFC images, of which nine have 21 . 0 mag < V < 22 . 0 mag corresponding to -4 mag < M V < -3 mag. Although the faintest star cluster of M33 detected by Zloczewski & Kaluzny (2009) is 2.0 mag brighter than the faintest Galactic globular cluster, it will provide something unique to the analysis of M33 star clusters when including them. In fact, Paper I included the photometry of the M33 star clusters in Zloczewski & Kaluzny (2009) when we provided the results for M33 star clusters, however, most star clusters in Zloczewski & Kaluzny (2009) have photometry in only two bands ( V and I ). There are only 19 sample star clusters of Zloczewski & Kaluzny (2009) in the color-color diagram provided in Paper I. In addition, most star clusters in San Roman et al. (2009) also have photometry in only two bands ( V and I ). So, it is necessary that we re-provide a CMD and color-color diagram of M33 including photometry obtained in this paper.",
"pages": [
4
]
},
{
"title": "3.1. Color-Magnitude Diagram",
"content": "The CMD can provide a qualitative modelindependent global indication of cluster-formation history that can be compared between galaxies because ( B -V ) 0 and ( V -I ) 0 are reasonably good age indicators, at least between young and old populations, with a secondary dependence on metallicity (Chandar et al. 1999b). CMDs of M33 star clusters have been previously discussed in the literature (Christian & Schommer 1982, 1988; Chandar et al. 1999b; Park & Lee 2007; Paper I). However, with a much larger star cluster sample in this paper, it is worth investigating them again. This paper includes 523 star clusters of M33, of which the photometry of 234 and 277 is derived in this paper and in Paper I, respectively; and the photometry of the remaining 12 star clusters is from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009), since we cannot accurately derive the photometry for these 12 star clusters (see Section 2.2 for details). The 277 star clusters from Paper I are confirmed by Sarajedini & Mancone (2007) (254 star clusters), Park & Lee (2007) (7 star clusters), and San Roman et al. (2009) (16 star clusters) based on the HST and high-resolution ground-based imaging. We point out that the photometry of M33 star clusters obtained in Paper I and this study is homogeneous photometric data in the same photometric system. For completeness of data and readers' references, we list the photometry of 277 star clusters of Paper I in Table 3 including the reddening values from Park & Lee (2007) and San Roman et al. (2009) in column 9 of Table 3 (Table 3 includes E ( B -V ) missed in Paper I.). In Table 3, R C and I C mean that RI magnitudes are on Johnson-Kron-Cousins system. For the reddening values of the star clusters, we used those from Park & Lee (2007) or San Roman et al. (2009). For the star clusters, Park & Lee (2007) and San Roman et al. (2009) both presented their reddening values, we adopted their mean values. For the star clusters, Park & Lee (2007) and San Roman et al. (2009) did not present their reddening values, we adopted a uniform value of E ( B -V ) = 0 . 1 typical of the published values for the line-of-sight reddenings to M33 that Sarajedini & Mancone (2007) adopted. Figure 7 shows the spatial distribution of these 523 star clusters. The large ellipse is the D 25 boundary of the M33 disk (de Vaucouleurs et al. 1991). Figure 8 displays the integrated M V -( B -V ) 0 and M V -( V -I ) 0 CMDs of the sample star clusters of M33. The absolute magnitudes of the star clusters were derived for the adopted distance modulus of ( m -M ) 0 = 24 . 64 obtained by Galleti et al. (2004). The interstellar extinction curve, A λ , is taken from Schlegel et al. (1998). Below each CMD in Figure 8 we plotted the star cluster distribution in color space. To the right of each CMD in Figure 8 we showed a histogram of the star clusters' absolute V magnitudes. Sarajedini & Mancone (2007), Park & Lee (2007), and Paper I showed that the M33 star clusters are roughly separated into blue and red groups with a color boundary of ( B -V ) 0 /similarequal 0 . 5 in the M V -( B -V ) 0 based on a small star cluster sample. However, this feature did not clearly appear in Figure 8 as previous studies (Sarajedini & Mancone 2007; Park & Lee 2007; Paper I). Figure 8 shows that the star cluster luminosity function peaks near M V ∼ -6 . 0 mag, and nearly half of star clusters lies between M V = -5 . 5 and M V = -7 . 0 mag. By adding models to the CMDs, we can obtain a more detailed history of star cluster formation. Three fading lines ( M V as a function of age) of Bruzual & Charlot (2003) for a metallicity of Z = 0 . 004 , Y = 0 . 24 which are thought to be appropriate for M33 star clusters (Chandar et al. 1999b), assuming a Salpeter initial mass function (IMF; Salpeter 1955) with lower and uppermass cut-offs of m L = 0 . 1 M /circledot and m U = 100 M /circledot , and using the Padova-1994 evolutionary tracks, are plotted on the CMDs of M33 star clusters for three different total initial masses: 10 5 , 10 4 , and 10 3 M /circledot . The majority of M33 star clusters fall between these three fading lines. From Figure 8, we note that none of the youngest clusters ( ∼ 10 7 yr) have masses approaching 10 5 M /circledot , which is consistent with the results of Chandar et al. (1999b) and Paper I. For ages older than 10 9 yr, some clusters with substantially higher masses are seen.",
"pages": [
5,
6
]
},
{
"title": "3.2. Color-Color Diagram",
"content": "Figure 9 shows the integrated ( B -V ) 0 versus ( V -I ) 0 color-color diagram for M33 star clusters. Galactic globular clusters from the online database of Harris (1996; 2010 update) are also plotted for comparison. We overplotted the theoretical evolutionary path for the single stellar population (SSP; Bruzual & Charlot 2003) for Z = 0 . 004 , Y = 0 . 24 that was appropriate for M33 (Chandar et al. 1999b). To identify different time periods, the different symbols correspond to 10 6 , 10 7 , 10 8 , 10 9 , and 10 10 yr. For comparison, the evolutionary path of the SSP for Z = 0 . 02 , Y = 0 . 28 is also overlaid. In general, the star clusters in M33 are located along the sequence that is consistent with the theoretical evolutionary path for Z = 0 . 004 , Y = 0 . 24, while some are on the redder or bluer side in the ( V -I ) 0 color. The wide color range of M33 star clusters implies a large range of ages, suggesting a prolonged epoch of formation. From Figure 9, we find that the photometry is shifted below the SSP lines, i.e., the sample star clusters are on the redder side in the ( B -V ) 0 color, when the star clusters have the ( V -I ) 0 color between -0 . 5 and 0 . 4. In the same time, from Figure 9, we also find that the photometry for most of the Galactic globular clusters is also below the SSP lines but with much smaller range. Large scatter observed for M33 star clusters possibly results from large errors of colors. By comparing with SSP models, we can see that there are a large range of ages of M33 star clusters, of which some star clusters are as old as the Galactic globular clusters.",
"pages": [
7
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},
{
"title": "4. SUMMARIES AND CONCLUSIONS",
"content": "In this paper, we present UBVRI photometric measurements for 234 star clusters in the field of M33. These sample star clusters of M33 are from Park & Lee (2007), San Roman et al. (2009) and Zloczewski & Kaluzny (2009). For most of these star clusters, there is photometry in only two bands ( V and I ) in previous studies. Photometry of these star clusters is performed using archival images from the LGGS (Massey et al. 2006). Detailed comparisons show that, in general, our photometry is consistent with previous measurements, especially, our photometry is in good agreement with that of Zloczewski & Kaluzny (2009). Combined with the star clusters' photometry in previous studies, we present some results: We would like to thank the anonymous referee for providing rapid and thoughtful report that helped improve the original manuscript greatly. This research was supported by the Chinese National Natural Science Founda- tion through grants 10873016 and 10633020, and by Na- tional Basic Research Program of China (973 Program) under grant 2007CB815403.",
"pages": [
7,
8
]
},
{
"title": "REFERENCES",
"content": "Bedin, L. R., Piotto, G., Baume, G., et al. 2005, A&A, 444, 831 Kron, G. E., & Mayall, N. U. 1960, AJ, 65, 581 Landolt, A. U. 1992, AJ, 104, 340 Stanek, K. Z., Kaluzny, J., Krockenberger, M., et al. 1998, AJ, 115, 1894 Stetson, P. B. 1987, PASP, 99, 191 Stonkut˙e, R., Vansevi˘cius, V., Arimoto, N., et al. 2008, AJ, 135, Zloczewski, K., & Kaluzny, J. 2009, Acta Astron., 59, 47 Zloczewski, K., Kaluzny, J., & Hartman, J. 2008, Acta Astron., 1482 58, 23 p ) ' ' ( a r 8 3 8 . 2 4 6 0 . 2 4 6 0 . 2 4 5 3 . 3 2 2 3 . 2 8 2 1 . 4 2 2 3 . 2 4 6 0 . 2 6 9 0 . 3 0 7 8 . 3 4 6 0 . 2 0 8 5 . 2 0 8 5 . 2 4 5 3 . 3 Star clusters in M33 13 3 . 3 0 . 2 5 . 2 5 . 2 5 . 2 0 . 3 0 . 3 5 . 2 5 . 2 0 . 2 3 . 2 5 . 2 3 . 3 0 . 2 8 . 2 5 . 2 5 . 2 0 . 1 2 . 1 0 . 2 2 . 1 8 . 1 2 2 3 . 2 0 8 5 . 2 6 0 8 . 1 6 9 0 . 3 4 6 0 . 2 0 9 2 . 1 0 8 5 . 2 6 9 0 . 3 0 8 5 . 2 0 8 5 . 2 2 2 3 . 2 8 3 8 . 2 0 8 5 . 2 6 9 0 . 3 2 2 3 . 2 0 8 5 . 2 0 7 8 . 3 2 1 6 . 3 6 9 0 . 3 2 1 . 0 6 3 0 . 0 ± 8 3 4 . 8 1 9 4 0 . 0 ± 2 9 1 . 9 1 4 6 0 . 0 ± 4 5 8 . 9 1 5 9 0 . 0 ± 6 7 6 . 0 2 5 6 0 . 0 ± 9 7 2 . 0 2 0 3 . 0 2 0 3 0 3 8 1 9 . 9 1 3 3 1 0 8 2 R S . . . . . . 5 5 6 9 0 . 3 5 0 . 0 3 1 0 . 0 ± 3 8 8 . 7 1 0 1 0 . 0 ± 5 7 1 . 8 1 9 0 0 . 0 ± 2 1 3 . 8 1 9 0 0 . 0 ± 8 5 5 . 8 1 7 0 0 . 0 ± 7 8 3 . 8 1 5 0 . 2 3 0 2 0 3 9 9 2 . 1 2 3 3 1 0 0 2 0 - 3 - 3 3 0 3 R S . . . . . . 6 5 14 Ma 5 3 . 6 9 0 . 2 2 3 . 8 3 8 . 8 3 8 . 4 4 6 . 8 3 8 . 2 2 3 . 4 6 0 . 8 3 8 . 8 4 5 . 0 8 5 . 8 4 5 . 4 6 0 . 8 3 8 . 0 8 5 . 6 9 0 . 6 9 0 . 6 0 8 . 4 6 0 . 0 8 5 . 8 4 5 . 2 2 3 . 8 5 . 2 3 . 2 3 . 3 8 . 0 7 8 . 0 8 5 . 0 8 5 . 0 9 2 . 6 0 8 . 8 4 5 . 0 8 5 . 4 6 0 . 2 2 3 . 6 9 0 . 4 5 3 . 6 9 0 . 4 4 6 . 6 9 0 . 0 8 5 . 4 5 3 . 4 5 3 . 0 8 5 . 2 1 6 . 0 8 5 . 2 2 3 . 8 3 8 . 0 8 5 . 0 8 5 . 6 0 8 . 2 1 6 . 4 6 0 . 1 E L AB T p ) ' ' ( a r 6 0 8 . 1 5 0 . 0 0 3 0 . 0 ± 4 3 2 . 8 1 6 1 0 . 0 ± 1 9 1 . 8 1 1 1 0 . 0 ± 9 8 0 . 8 1 9 0 0 . 0 ± 9 1 1 . 8 1 5 0 0 . 0 ± 8 9 1 . 7 1 1 9 . 5 3 6 3 0 3 3 8 6 . 4 4 3 3 1 0 1 1 1 R S . . . . . . 1 1 1 4 6 0 . 2 5 0 . 0 4 5 0 . 0 ± 1 9 7 . 8 1 2 4 0 . 0 ± 8 0 0 . 9 1 8 2 0 . 0 ± 6 7 9 . 8 1 5 2 0 . 0 ± 5 7 1 . 9 1 9 1 0 . 0 ± 9 2 5 . 8 1 9 1 . 9 3 4 3 0 3 0 8 8 . 4 4 3 3 1 0 2 1 1 R S . . . . . . 2 1 1 1 E L AB T ) . d e u n i t n o C ( 4 8 8 8 0 4 2 6 8 6 4 8 8 4 4 4 2 2 8 6 0 8 0 4 6 0 0 4 2 0 4 6 4 8 2 0 4 0 6 4 8 8 6 8 8 4 2 6 4 4 8 4 0 Star clusters in M33 15 6 0 8 . 1 0 1 . 0 2 5 0 . 0 ± 2 8 7 . 9 1 2 5 0 . 0 ± 1 0 2 . 0 2 0 5 0 . 0 ± 4 7 4 . 0 2 0 7 0 . 0 ± 9 3 1 . 1 2 3 5 0 . 0 ± 2 9 0 . 1 2 0 0 . 0 2 1 3 0 3 6 6 7 . 5 2 3 3 1 0 8 1 - ZK . . . . . . 6 6 1 6 0 8 . 1 0 1 . 0 2 5 0 . 0 ± 6 0 5 . 9 1 5 6 0 . 0 ± 4 0 2 . 0 2 9 5 0 . 0 ± 9 6 5 . 0 2 5 6 0 . 0 ± 1 0 0 . 1 2 8 4 0 . 0 ± 5 5 0 . 1 2 1 7 . 1 2 1 3 0 3 4 5 9 . 5 2 3 3 1 0 9 1 - ZK . . . . . . 7 6 1 0 8 5 . 2 0 1 . 0 4 3 0 . 0 ± 8 1 7 . 8 1 4 3 0 . 0 ± 4 1 2 . 9 1 0 3 0 . 0 ± 2 5 4 . 9 1 4 3 0 . 0 ± 9 4 9 . 9 1 8 2 0 . 0 ± 9 5 9 . 9 1 0 5 . 9 5 9 3 0 3 4 0 5 . 6 2 3 3 1 0 0 2 - ZK . . . . . . 8 6 1 16 Ma 1 E L AB T ) . d e u n i t n o C ( 4 6 0 . 2 0 1 . 0 3 6 0 . 0 ± 6 6 4 . 9 1 1 4 0 . 0 ± 6 0 5 . 9 1 8 2 0 . 0 ± 7 2 5 . 9 1 3 2 0 . 0 ± 3 3 8 . 9 1 0 2 0 . 0 ± 0 3 6 . 9 1 5 6 . 1 4 3 3 0 3 6 5 5 . 3 0 4 3 1 0 8 7 - ZK . . . . . . 1 2 2 2 2 3 . 2 0 1 . 0 1 3 0 . 0 ± 3 8 2 . 9 1 4 3 0 . 0 ± 5 7 7 . 9 1 9 2 0 . 0 ± 3 2 0 . 0 2 7 2 0 . 0 ± 5 4 4 . 0 2 2 2 0 . 0 ± 2 9 0 . 0 2 3 6 . 1 2 7 2 0 3 1 5 6 . 4 0 4 3 1 0 9 7 - ZK . . . . . . 2 2 2 2 2 3 . 2 0 1 . 0 8 3 0 . 0 ± 5 0 5 . 9 1 3 3 0 . 0 ± 7 3 8 . 9 1 4 3 0 . 0 ± 7 5 2 . 0 2 2 3 0 . 0 ± 3 5 7 . 0 2 4 3 0 . 0 ± 1 3 7 . 0 2 2 2 . 0 2 8 2 0 3 4 7 9 . 4 0 4 3 1 0 0 8 - ZK . . . . . . 3 2 2 2 2 3 . 2 0 1 . 0 2 2 0 . 0 ± 4 6 8 . 8 1 3 2 0 . 0 ± 9 7 1 . 9 1 2 2 0 . 0 ± 3 0 5 . 9 1 0 2 0 . 0 ± 7 3 8 . 9 1 3 1 0 . 0 ± 1 9 4 . 9 1 8 3 . 4 0 8 2 0 3 6 3 7 . 6 0 4 3 1 0 1 8 - ZK . . . . . . 4 2 2 Star clusters in M33 17 6 0 8 . 1 0 1 . 0 7 1 0 . 0 ± 5 5 3 . 8 1 9 2 0 . 0 ± 8 7 2 . 9 1 4 4 0 . 0 p ) ' ' ( ) g a m ( ) g a m ( ) g a m ( ) 4 5 3 . 3 0 1 . 0 6 4 0 . 0 ± 5 7 6 . 8 1 6 3 0 . 0 ± 4 0 1 . 9 1 4 3 0 . 0 0 8 5 . 2 0 1 . 0 9 3 0 . 0 ± 9 8 5 . 9 1 0 3 0 . 0 ± 3 0 7 . 9 1 8 2 0 . 0 6 9 0 . 3 0 1 . 0 3 4 0 . 0 ± 6 5 3 . 9 1 3 3 0 . 0 ± 1 4 3 . 9 1 3 2 0 . 0 . 0 2 . 9 1 . 9 1 . 9 1 2 2 3 . 2 0 1 . 0 9 0 0 . 0 ± 3 8 6 . 7 1 9 0 0 . 0 ± 9 3 9 . 7 1 9 0 0 . 0 ± 1 2 1 . 8 1 0 8 5 . 2 0 1 . 0 8 2 0 . 0 ± 4 1 8 . 8 1 1 3 0 . 0 ± 9 7 4 . 9 1 2 3 0 . 0 ± 6 1 9 . 9 1 6 0 8 . 1 0 1 . 0 8 3 0 . 0 ± 3 5 9 . 9 1 2 3 0 . 0 ± 9 2 2 . 0 2 4 3 0 . 0 ± 1 0 6 . 0 2 4 6 0 . 2 0 1 . 0 2 2 0 . 0 ± 6 5 2 . 9 1 3 2 0 . 0 ± 0 8 6 . 9 1 5 2 0 . 0 ± 8 8 0 . 0 2 0 8 5 . 2 0 1 . 0 . . . . . . 0 1 1 . 0 ± 1 8 4 . 0 2 4 4 1 . 0 ± 9 8 8 . 0 2 0 8 5 . 2 0 1 . 0 0 6 1 . 0 ± 6 0 4 . 1 2 4 2 1 . 0 ± 9 3 5 . 1 2 4 3 1 . 0 ± 3 5 7 . 1 2 0 2 . 5 0 4 3 0 3 0 5 7 . 6 0 4 3 1 0 2 8 - ZK . . . . . . 5 2 2 1 3 . 6 4 3 3 0 3 7 7 2 . 7 0 4 3 1 0 3 8 - ZK . . . . . . 6 2 2 0 0 . 5 0 5 2 0 3 1 9 6 . 9 0 4 3 1 0 4 8 - ZK . . . . . . 7 2 2 4 0 . 3 3 8 2 0 3 3 3 9 . 0 1 4 3 1 0 5 8 - ZK . . . . . . 8 2 2 5 2 . 6 4 8 2 0 3 3 3 9 . 2 1 4 3 1 0 6 8 - ZK . . . . . . 9 2 2 5 0 . 4 4 8 2 0 3 3 3 5 . 3 1 4 3 1 0 7 8 - ZK . . . . . . 0 3 2 0 9 . 8 0 7 2 0 3 9 7 7 . 7 1 4 3 1 0 8 8 - ZK . . . . . . 1 3 2 1 8 . 9 1 7 2 0 3 3 0 7 . 8 1 4 3 1 0 9 8 - ZK . . . . . . 2 3 2 5 4 . 1 2 4 1 1 3 3 6 2 . 2 0 5 3 1 0 0 9 - ZK . . . . . . 3 3 2 1 9 . 7 5 1 1 1 3 9 4 8 . 4 0 5 3 1 0 1 9 - ZK . . . . . . 4 3 2 a r ) V - B ( E C I C R V . l c e D . A . R D I D I D I D I D I ) 0 . 0 0 0 2 J ( ) 0 . 0 0 0 2 J ( Comparison between this Study and Previous studies of V Photometry for M33 Star Clusters Considered Here 3 E L AB T ) 2 1 0 2 ( a M n i s r e t s u l C r a t S 3 3 M 7 7 2 f o y r t e m o t o h P I R V B U Star clusters in M33 19 0 7 8 . 3 0 1 . 0 0 1 0 . 0 ± 6 0 2 . 7 1 2 1 0 . 0 ± 4 4 6 . 7 1 4 1 0 . 0 ± 6 3 0 . 8 1 2 2 0 . 0 ± 1 4 7 . 8 1 6 2 0 . 0 ± 8 8 9 . 8 1 5 5 . 1 2 2 2 0 3 8 9 6 . 0 3 3 3 1 0 9 1 1 L P 2 0 1 M S . . . . . . 8 8 2 0 7 8 . 3 0 1 . 0 5 1 0 . 0 ± 2 2 7 . 7 1 7 1 0 . 0 ± 2 4 1 . 8 1 4 1 0 . 0 ± 8 7 4 . 8 1 5 1 0 . 0 ± 4 3 0 . 9 1 6 1 0 . 0 ± 6 1 2 . 9 1 7 9 . 1 1 9 4 0 3 4 9 8 . 0 3 3 3 1 0 0 2 1 L P 3 0 1 M S . . . . . . 9 8 2 8 3 8 . 2 5 1 . 0 1 2 0 . 0 ± 1 8 6 . 7 1 8 1 0 . 0 ± 1 1 1 . 8 1 6 1 0 . 0 ± 6 7 3 . 8 1 4 1 0 . 0 ± 1 1 7 . 8 1 1 1 0 . 0 ± 2 9 4 . 8 1 0 9 . 2 1 7 3 0 3 4 2 9 . 0 3 3 3 1 0 1 5 L P 4 0 1 M S . . . . . . 0 9 2 0 8 5 . 2 0 1 . 0 4 1 0 . 0 ± 5 2 1 . 7 1 6 1 0 . 0 ± 2 5 7 . 7 1 6 1 0 . 0 ± 0 4 0 . 8 1 5 1 0 . 0 ± 0 8 3 . 8 1 0 1 0 . 0 ± 3 8 9 . 7 1 2 6 . 2 5 6 3 0 3 5 9 9 . 0 3 3 3 1 0 2 5 L P 5 0 1 M S . . . . . . 1 9 2 20 Ma 3 E L AB T ) . d e u n i t n o C ( 0 4 4 2 2 6 8 2 0 0 6 8 4 0 6 0 6 8 2 8 4 0 8 4 0 0 8 2 2 6 6 2 4 0 2 6 6 2 2 6 4 4 0 0 2 2 0 4 4 6 0 0 8 0 8 5 . 2 0 2 . 0 2 1 0 . 0 ± 7 7 6 . 7 1 6 1 0 . 0 ± 5 7 2 . 8 1 7 1 0 . 0 ± 9 5 7 . 8 1 8 2 0 . 0 ± 8 1 6 . 9 1 5 2 0 . 0 ± 8 0 5 . 9 1 2 3 . 6 3 6 4 0 3 1 6 9 . 6 4 3 3 1 0 0 5 1 L P 4 8 1 M S . . . . . . 5 4 3 0 8 5 . 2 0 1 . 0 5 1 0 . 0 ± 1 4 7 . 7 1 8 1 0 . 0 ± 6 3 2 . 8 1 8 1 0 . 0 ± 5 2 6 . 8 1 0 2 0 . 0 ± 6 3 3 . 9 1 0 2 0 . 0 ± 8 7 4 . 9 1 2 7 . 8 3 5 4 0 3 6 5 4 . 8 4 3 3 1 0 1 5 1 L P 6 8 1 M S . . . . . . 6 4 3 8 4 5 . 1 0 1 . 0 5 3 0 . 0 ± 2 3 3 . 9 1 9 3 0 . 0 ± 6 6 9 . 9 1 2 3 0 . 0 ± 1 6 2 . 0 2 1 3 0 . 0 ± 7 8 6 . 0 2 8 2 0 . 0 ± 6 3 6 . 0 2 2 6 . 2 4 7 4 0 3 9 3 6 . 8 4 3 3 1 0 2 5 1 L P 7 8 1 M S . . . . . . 7 4 3 3 E L AB T ) . d e u n i t n o C ( 2 0 2 8 4 0 6 6 4 4 4 2 0 4 6 8 8 0 6 8 2 4 4 0 0 0 4 4 8 8 8 6 6 8 0 4 6 4 6 8 2 0 6 6 2 6 4 8 0 2 6 6 2 Star clusters in M33 21 6 0 8 . 1 5 1 . 0 2 4 0 . 0 ± 8 1 7 . 9 1 0 4 0 . 0 ± 7 1 0 . 0 2 3 3 0 . 0 ± 8 7 1 . 0 2 5 3 0 . 0 ± 0 6 6 . 0 2 6 2 0 . 0 ± 8 0 4 . 0 2 6 3 . 8 3 7 4 0 3 0 4 6 . 9 5 3 3 1 0 1 8 1 L P 6 5 2 M S . . . . . . 1 0 4 0 8 5 . 2 0 1 . 0 6 1 0 . 0 ± 9 7 3 . 7 1 0 1 0 . 0 ± 8 3 3 . 7 1 7 0 0 . 0 ± 2 6 3 . 7 1 7 0 0 . 0 ± 1 5 5 . 7 1 3 0 0 . 0 ± 3 6 7 . 6 1 5 3 . 4 2 1 4 0 3 4 3 7 . 9 5 3 3 1 0 2 8 1 L P 7 5 2 M S . . . . . . 2 0 4 0 8 5 . 2 5 1 . 0 4 6 0 . 0 ± 1 6 9 . 7 1 6 6 0 . 0 ± 4 6 5 . 8 1 3 7 0 . 0 ± 1 8 0 . 9 1 7 8 0 . 0 ± 7 0 8 . 9 1 0 7 0 . 0 ± 5 5 3 . 9 1 1 4 . 5 4 9 3 0 3 5 1 8 . 9 5 3 3 1 0 4 8 L P 8 5 2 M S . . . . . . 3 0 4 22 Ma 3 E L AB T ) . d e u n i t n o C ( 6 0 2 0 6 2 0 4 4 4 4 8 4 0 6 0 2 0 0 2 2 2 0 0 8 0 6 4 2 2 6 8 2 8 2 0 0 6 4 0 6 4 4 8 0 6 4 8 0 0 4 0 8 4 5 3 . 3 0 1 . 0 8 1 0 . 0 ± 5 4 2 . 7 1 6 1 0 . 0 ± 6 6 6 . 7 1 5 1 0 . 0 ± 1 1 9 . 7 1 5 1 0 . 0 ± 7 7 4 . 8 1 3 1 0 . 0 ± 6 4 5 . 8 1 8 4 . 8 5 9 3 0 3 6 3 2 . 4 1 4 3 1 0 0 1 2 L P 0 5 3 M S . . . . . . 7 5 4 6 9 0 . 3 0 2 . 0 2 1 0 . 0 ± 2 8 5 . 7 1 0 1 0 . 0 ± 2 1 9 . 7 1 1 1 0 . 0 ± 3 5 1 . 8 1 0 1 0 . 0 ± 9 8 5 . 8 1 0 1 0 . 0 ± 3 5 6 . 8 1 9 1 . 5 3 2 3 0 3 7 4 6 . 4 1 4 3 1 0 2 0 1 L P 1 5 3 M S . . . . . . 8 5 4 8 2 1 . 4 0 1 . 0 4 1 0 . 0 ± 1 2 9 . 6 1 2 1 0 . 0 ± 7 2 2 . 7 1 0 1 0 . 0 ± 1 3 4 . 7 1 9 0 0 . 0 ± 5 3 8 . 7 1 7 0 0 . 0 ± 8 3 6 . 7 1 4 1 . 9 1 1 4 0 3 7 3 0 . 5 1 4 3 1 0 3 0 1 L P 3 5 3 M S . . . . . . 9 5 4 3 E L AB T p ) ' ' ( a r 2 1 6 . 3 6 9 0 . 3 8 3 8 . 2 8 3 8 . 2 0 8 5 . 2 8 4 5 . 1 6 9 0 . 3 8 3 8 . 2 0 8 5 . 2 0 8 5 . 2 0 8 5 . 2 6 9 0 . 3 0 8 5 . 2 6 9 0 . 3 4 5 3 . 3 4 5 3 . 3 Star clusters in M33 23 6 9 0 . 3 6 9 0 . 3 6 9 0 . 3 8 3 8 . 2 8 . 2 5 . 2 0 . 3 0 . 3 3 . 3 0 7 8 . 3 0 8 5 . 2 6 0 8 . 1 4 5 3 . 3 6 9 0 . 3 4 5 3 . 3 8 3 8 . 2 4 5 3 . 3 4 5 3 . 3 2 2 3 . 2 2 1 6 . 3 2 1 6 . 3 6 9 0 . 3 4 5 3 . 3 4 6 0 . 2 6 9 0 . 3 0 7 8 . 3 6 9 0 . 3 0 8 5 . 2 8 3 8 . 2 0 7 8 . 3 2 1 6 . 3 8 2 1 . 4 6 9 0 . 3 2 1 6 . 3 4 5 3 . 3 0 1 . 0 1 3 0 . 0 ± 3 1 2 . 7 1 7 1 0 . 0 ± 3 5 2 . 8 1 3 1 0 . 0 ± 5 0 6 . 8 1 5 1 0 . 0 ± 0 2 1 . 9 1 2 1 0 . 0 ± 3 2 0 . 9 1 8 6 . 0 1 6 4 0 3 0 1 7 . 4 0 5 3 1 0 7 4 4 M S . . . . . . 0 1 5 0 6 1 . 5 0 1 . 0 0 1 0 . 0 ± 6 8 2 . 7 1 1 1 0 . 0 ± 7 7 7 . 7 1 4 1 0 . 0 ± 5 5 2 . 8 1 5 1 0 . 0 ± 2 6 9 . 8 1 4 1 0 . 0 ± 0 6 1 . 9 1 2 9 . 3 5 9 4 0 3 8 4 2 . 8 1 5 3 1 0 9 4 4 M S . . . . . . 1 1 5",
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2013AJ....146...48C
https://arxiv.org/pdf/1306.3227.pdf
<document>
<section_header_level_1><location><page_1><loc_10><loc_81><loc_85><loc_85></location>KAT-7 Science Verification: Using H i Observations of NGC 3109 to Understand its Kinematics and Mass Distribution</section_header_level_1>
<text><location><page_1><loc_11><loc_73><loc_84><loc_78></location>C. Carignan 1 , B. S. Frank, K. M. Hess, D. M. Lucero and T. H. Randriamampandry Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa and</text>
<text><location><page_1><loc_22><loc_67><loc_73><loc_70></location>S. Goedhart and S. S. Passmoor SKA South Africa, The Park, Park Road, Pinelands, 7405, South Africa</text>
<text><location><page_1><loc_38><loc_65><loc_58><loc_66></location>[email protected]</text>
<section_header_level_1><location><page_1><loc_41><loc_58><loc_54><loc_60></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_13><loc_46><loc_82><loc_58></location>H i observations of the Magellanic-type spiral NGC 3109, obtained with the seven dish Karoo Array Telescope (KAT-7), are used to analyze its mass distribution. Our results are compared to what is obtained using VLA data. KAT-7 is the precursor of the SKA pathfinder MeerKAT, which is under construction. The short baselines and low system temperature of the telescope make it sensitive to large scale low surface brightness emission. The new observations with KAT7 allow the measurement of the rotation curve of NGC 3109 out to 32 ' , doubling the angular extent of existing measurements. A total H i mass of 4.6 × 10 8 M /circledot is derived, 40% more than what was detected by the VLA observations.</text>
<text><location><page_1><loc_13><loc_32><loc_82><loc_46></location>The observationally motivated pseudo-isothermal dark matter (DM) halo model can reproduce very well the observed rotation curve but the cosmologically motivated NFW DM model gives a much poorer fit to the data. While having a more accurate gas distribution has reduced the discrepancy between the observed RC and the MOdified Newtonian Dynamics (MOND) models, this is done at the expense of having to use unrealistic mass-to-light ratios for the stellar disk and/or very large values for the MOND universal constant a 0 . Different distances or H i contents cannot reconcile MOND with the observed kinematics, in view of the small errors on those two quantities. As for many slowly rotating gas-rich galaxies studied recently, the present result for NGC 3109 continues to pose a serious challenge to the MOND theory.</text>
<text><location><page_1><loc_13><loc_29><loc_82><loc_31></location>Subject headings: techniques: interferometric - galaxies: individual: NGC 3109 - galaxies: kinematics and dynamics - galaxies: haloes - cosmology: dark matter</text>
<section_header_level_1><location><page_1><loc_9><loc_26><loc_23><loc_27></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_9><loc_14><loc_45><loc_24></location>On 2012 May 25, South Africa was awarded the construction of the mid-frequency array of the Square Kilometer Array (SKA), while Australia will build the low-frequency array. The SKA will consist of an ensemble of 3000 ∼ 15 m dishes of which 80% will constitute the core portion in the Karoo desert while the remaining antennae will</text>
<text><location><page_1><loc_51><loc_11><loc_86><loc_27></location>extend all the way to the 8 African partner countries, namely Botswana, Ghana, Kenya, Madagascar, Mauritius, Mozambique, Namibia and Zambia. It is expected that the full SKA will be completed around 2025. A precursor array of 64 dishes, MeerKAT, is already under construction by South Africa and should be ready for science operation in 2016. In preparation for these two large projects, a pre-precursor array comprising 7 dishes, KAT-7, was completed in December 2010. While its main purpose is to test technical solu-</text>
<text><location><page_2><loc_9><loc_76><loc_45><loc_86></location>tions for MeerKAT and the SKA, scientific targets such as NGC 3109 were also observed during commissioning to test the H i spectral line mode. In this paper, we compare over 100 hours of observations taken with KAT-7 to previously obtained VLA data and perform a thorough analysis of the mass distribution of NGC 3109.</text>
<text><location><page_2><loc_9><loc_48><loc_49><loc_75></location>NGC3109is an SB(s)m galaxy (de Vaucouleurs et al. 1991) on the outskirts of the Local Group (van den Bergh 1994). It is even believed by certain authors to belong to the Local Group (e.g. Mateo 1998). While NGC 3109 looks like an Irregular galaxy on short exposures (Sandage 1961), it is clearly a spiral on longer exposures (Carignan 1985). Spiral arms are clearly visible, especially on the east side. This small spiral (scale length α -1 = 1.2 kpc) is a Low Surface Brightness (LSB) system with B (0) c = 23.17 (Carignan 1985). Its optical parameters are summarized in Table 1. One important parameter for mass modeling is the distance. Fortunately, because of its proximity, numerous Cepheids were observed in this Magellanic-type spiral, The most recent measurements are summarized in Table 2. For this study, we adopt a distance of 1.30 ± 0 . 02 Mpc (Soszy'nski et al. 2006).</text>
<text><location><page_2><loc_9><loc_21><loc_45><loc_48></location>NGC 3109 is of significant scientific interest for two main reasons. Firstly, Jobin & Carignan (1990) used observations with the hybrid VLA DnC configuration (synthesized beam of 36 '' × 27 '' and velocity resolution of 10.3 km s -1 ) to perform a dynamical study of this galaxy, comparing the rotation curve (RC) derived from a tilted-ring analysis (see Sec. 3.4.1) to models composed of a luminous disk (stars & gas) and of a dark isothermal (ISO) halo (see Sec. 4.1.1). Such a mass model provides an excellent fit to this nearly solid-body type RC. Combining the H i RC with higher resolution H α kinematical data, Blais-Ouellette, Amram & Carignan (2001) also obtained a very good ISO Dark Matter (DM) model but a much less accurate fit for the cosmologically motivated NFW (Navarro, Frenk & White 1997) DM model.</text>
<text><location><page_2><loc_9><loc_10><loc_45><loc_20></location>Recently, it was also shown that a MOdified Newtonian Dynamics (Milgrom 1983, 1988) model (MOND) could not reproduce the NGC 3109's RC (Randriamampandry 2013), at least with the data available. With our new data, it should be possible to compare DM (ISO and NFW) models to MOND (no dark matter) models and see</text>
<table>
<location><page_2><loc_50><loc_58><loc_91><loc_81></location>
<caption>Table 1: Optical parameters of NGC 3109 (DDO 236).</caption>
</table>
<table>
<location><page_2><loc_50><loc_33><loc_92><loc_42></location>
<caption>Table 2: Cepheids distance estimates for NGC 3109.</caption>
</table>
<text><location><page_2><loc_85><loc_32><loc_86><loc_34></location>±</text>
<text><location><page_2><loc_51><loc_23><loc_86><loc_29></location>if NGC 3109 really challenges the MOND theory. This is not the first time that NGC 3109 poses problems to MOND (see e.g. Sanders 1986; Begeman, Broeils & Sanders 1991).</text>
<text><location><page_2><loc_51><loc_10><loc_86><loc_22></location>Secondly, Barnes & de Blok (2001) used 21cm Multibeam data with the Parkes 64m dish (beam ∼ 15.5 ' and velocity resolution of 1.1 km s -1 ) to study the environment of NGC 3109. They provide a compelling argument that the warp in the H i disk of NGC 3109 could be due to a dynamical encounter with the Antlia dwarf. This is also suggested by the elongation of the optical isophotes</text>
<text><location><page_3><loc_9><loc_82><loc_45><loc_86></location>of NGC 3109 toward the south (Jobin & Carignan 1990) and those of Antlia in the direction of NGC 3109 (Penny et al. 2012).</text>
<text><location><page_3><loc_9><loc_59><loc_45><loc_81></location>However, recent derivation of various merger and/or interaction parameters (e.g. asymmetry, clumpiness) by Pimbblet & Couch (2012) are consistent with Antlia being an undisturbed dwarf elliptical. In fact, despite its dSph appearance, Antlia is better classified as a dSph/dIrr transition type (Grebel, Gallagher & Harbeck 2003) because of its high H i content. With high sensitivity and mainly better spatial resolution observations (KAT-7 vs HIPASS), it should be possible to map much better the traces of that interaction, if it exists. An encounter/interaction that has significantly altered NGC3109's kinematics would give less weight to the finding that MOND cannot reproduce the rotation curve.</text>
<text><location><page_3><loc_9><loc_44><loc_45><loc_58></location>The remainder of this paper is as follows. In Sec. 2, a description of the new radio interferometer KAT-7 is given. Sec. 3.1 describes in details the new H i data obtained with KAT-7, Sec. 3.2 those from the VLA-ANGST survey and Sec. 3.3 compares the different data sets. Sec. 3.4 derives the optimal RC that is used for the DM (ISO and NFW) and MOND models of Sec. 4. A discussion follows in Sec. 5 and a summary of the results and the final conclusions are given in Sec. 6.</text>
<section_header_level_1><location><page_3><loc_9><loc_41><loc_44><loc_42></location>2. A New Radio Interferometer: KAT-7</section_header_level_1>
<text><location><page_3><loc_9><loc_18><loc_45><loc_39></location>The seven-dish KAT-7 array, shown in Fig. 1, was built as an engineering testbed for the 64dish Karoo Array Telescope, known as MeerKAT, which is the South African pathfinder for the Square Kilometer Array (SKA). KAT-7 and MeerKAT are located close to the South African SKAcore site in the Northern Cape's Karoo desert region. KAT-7 is remotely controlled from Cape Town, some 800 km away from the site. Construction of the array started in early 2008 and was completed in December 2010, with 'first light' fringes obtained between two antennas in December 2009. The instrument is now in its science verification stage.</text>
<text><location><page_3><loc_9><loc_10><loc_45><loc_18></location>The array is extremely compact, with baselines ranging between 26 m to 185 m. The KAT-7 layout was determined using the optimization algorithm described in de Villiers (2007), which determined a layout with a Gaussian UV</text>
<figure>
<location><page_3><loc_50><loc_66><loc_86><loc_87></location>
<caption>Fig. 1.- Aerial view of the KAT-7 array in the Northern Cape's Karoo desert, South Africa.</caption>
</figure>
<text><location><page_3><loc_51><loc_35><loc_86><loc_59></location>distribution for a specified observation setting. The observation setting being optimized in this case was an 8 hour track (symmetric hour angle range), on a target at a -60 degree declination. The optimization objective was a Gaussian UV distribution at 1.4GHz, yielding a Gaussian synthesized beam with low sidelobes. Several randomly seeded layouts were generated and were evaluated for a set of observation options (time durations: snapshot, 4hr, 8hr, 12hr; declinations: 0, -30,-60, -90 degrees). The layout selected had the lowest sidelobes for the largest number of test observation settings considered. The antenna layout can be found at https://sites.google.com/a/ska.ac.za/public/kat7.</text>
<text><location><page_3><loc_51><loc_10><loc_86><loc_34></location>The KAT-7 dishes have a prime-focus alt-az design with a F/D of 0.38, optimized for single-pixel L-band feeds. The low noise amplifiers (LNAs) for the feeds are cryogenically cooled to 80 K using Stirling coolers. The key system specifications for KAT-7 are summarized in Table 3. The digital backend of the system is an FPGA (Field Programmed Gate Array)-based, flexible packetised correlator using the Reconfigurable Open Architecture Computing Hardware (ROACH: https://casper.berkeley.edu/wiki/ROACH), which is a flexible and scalable system enabling spectral line modes covering a wide range of resolutions. Table 4 gives the details of the recently commissioned correlator modes. Digital filters give a flat bandpass over the inner 75% of the band with a</text>
<text><location><page_4><loc_9><loc_85><loc_37><loc_86></location>rapid roll-off at the edges of the band.</text>
<table>
<location><page_4><loc_9><loc_57><loc_48><loc_80></location>
<caption>Table 3: KAT-7 specifications.Table 4: KAT-7 correlator modes.</caption>
</table>
<table>
<location><page_4><loc_9><loc_40><loc_49><loc_49></location>
</table>
<text><location><page_4><loc_9><loc_29><loc_45><loc_37></location>CASA ( Common Astronomy Software Applications ; McMullin et al. 2007) is the standard data reduction package being used for the reduction of the KAT-7 data and is anticipated to be used for MeerKAT.</text>
<section_header_level_1><location><page_4><loc_9><loc_26><loc_37><loc_28></location>3. H i Observations of NGC 3109</section_header_level_1>
<text><location><page_4><loc_9><loc_9><loc_45><loc_25></location>The KAT-7 H i observations of NGC 3109 provide a unique opportunity to simultaneously achieve H i spectral-line science verification and an original scientific result. They complement the high spatial resolution ( ∼ 10 '' ) but small field of view ( ∼ 30 ' ) of the VLA-ANGST data (Ott et al. 2012) and the high sensitivity ( ∼ 10 17 cm -2 ) but low spatial resolution ( ∼ 15 . 5 ' ) Multibeam data (Barnes & de Blok 2001). With its short baselines and low system temperature (T sys ∼ 26K), KAT-</text>
<text><location><page_4><loc_51><loc_82><loc_86><loc_86></location>7 is very sensitive to low surface brightness and large scale H i emission, characteristic of the signal expected from NGC 3109.</text>
<section_header_level_1><location><page_4><loc_51><loc_79><loc_77><loc_80></location>3.1. KAT-7 data on NGC 3109</section_header_level_1>
<text><location><page_4><loc_51><loc_62><loc_86><loc_78></location>In order to observe the H i in both NGC 3109 and Antlia, plus possible signs of interaction between the two, a mosaic of 3 fields was obtained to have good sensitivity over a region of 1 . 5 o (EW) × 3 o (NS). The data was collected over 13 observing sessions between 2012 November 20 and 2012 December 26 using the c16n7M4k spectral line mode (Table 4) for a median of 11 hours in each session and a total of 122 h 43 m 56 s , including calibration. This yielded a total time on source of ∼ 25 hours for each pointing.</text>
<text><location><page_4><loc_51><loc_39><loc_86><loc_61></location>The first three sessions were taken with 6 cold antennae, but the entire array was available for the remaining 10 observing sessions. The roughly 1 degree beam of KAT-7 is just large enough to image NGC 3109 in a single pointing. We used three pointings positioned in a straight line and extending slightly to the SE to mosaic the region between NGC 3109 and Antlia. The distance between pointings was chosen to give a uniform coverage between the phase centers. The c16n7M4k correlator mode gives velocity channels of 0.32 km s -1 over a flat bandpass of ∼ 1000 km s -1 , centered at 1417 MHz. The large bandwidth allows to collect H i data on background galaxies in the field.</text>
<text><location><page_4><loc_51><loc_23><loc_86><loc_38></location>The basic data reduction was done in CASA 3.4.0 and 4.0.0. More advanced analysis was done using either AIPS (Greisen 2003), MIRIAD (Sault, Teuben & Wright 1995) and/or GIPSY (van der Hulst et al. 1992). To start with, the data was flagged in an automated way to discard data for shadowing and flux calibrators below 20 degrees in elevation. The data was additionally examined as a function of frequency and baseline, and flagged by hand.</text>
<text><location><page_4><loc_51><loc_11><loc_86><loc_23></location>This testing of the HI spectral line mode led to the discovery of faint, very narrow, internally generated radio frequency interference (RFI) originating along the signal path, which has since been successfully eliminated in KAT-7 by the insertion of a low-pass filter. The RFI in our data is antenna dependent and only affects about 30 channels out of the central 3000 on three antennae. One of the</text>
<text><location><page_5><loc_9><loc_82><loc_45><loc_86></location>primary goals of the science verification phase is exactly to identify these type of problems and correct for them.</text>
<text><location><page_5><loc_9><loc_65><loc_45><loc_81></location>The standard interferometric data reduction strategy that has been employed for decades in AIPS and Miriad has been used. Each of the 13 observing sessions was reduced individually. Continuum subtraction was accomplished by selecting line free channels and using a first order fit. KAT7 does not use Doppler tracking, and CASA does not fully recognize frequency keywords, so special care was taken to produce image cubes with the proper velocity coordinates. This was a three steps process accomplished by:</text>
<unordered_list>
<list_item><location><page_5><loc_12><loc_60><loc_45><loc_64></location>· setting the MEAS FREQ REF and REF FREQUENCYkeywords in the SPECTRAL WINDOW table,</list_item>
<list_item><location><page_5><loc_12><loc_54><loc_45><loc_58></location>· specifying the reference frequency and setting the output frame to optical, barycentric in CVEL, and</list_item>
<list_item><location><page_5><loc_12><loc_50><loc_45><loc_53></location>· specifying the rest frequency again in the task CLEAN.</list_item>
</unordered_list>
<text><location><page_5><loc_9><loc_40><loc_45><loc_49></location>The calibration was applied and the three mosaic pointings were then SPLIT from the calibration sources. The data were averaged in time from 5 to 10 second integrations, and spectrally from 0.32 km s -1 to 1.28 km s -1 channels. All 13 data sets were then combined in CONCAT.</text>
<text><location><page_5><loc_9><loc_13><loc_45><loc_40></location>The data was imaged using the mosaic mode and the multi-scale clean option. Three cubes were produced by applying natural (na), uniform (un), and neutral (ro: robust=0) weighting (Table 5) to the uv data. The robust=0 cube was cleaned interactively using a mask to select regions of galaxy emission by hand in each channel. After each major clean cycle, the mask was expanded to include regions of fainter galaxy emission. After a final mask was created, the cube was reproduced using the final mask in a non-interactive clean down to the noise threshold. All cubes and images were produced using the same mask derived from the robust=0 weighted cube. This provided a compromise between surface brightness sensitivity to large-scale emission and a low noise threshold, while mitigating confusion from sidelobes and low-level artifacts due to instrument calibration.</text>
<text><location><page_5><loc_9><loc_10><loc_45><loc_12></location>In addition to NGC 3109, Antlia, ESO 499G037 and ESO 499-G038, an HI cloud which has</text>
<table>
<location><page_5><loc_50><loc_43><loc_91><loc_83></location>
<caption>Table 5: Parameters of the KAT-7 observations.</caption>
</table>
<text><location><page_5><loc_51><loc_15><loc_86><loc_39></location>no known optical counterpart was serendipitously discovered to the north of ESO 499-G038 at a similar velocity (Figure 2). The channels that contain this emission are remarkably clean and uniform in their noise characteristics. By contrast the channels which contain the brightest HI emission from NGC 3109 contain artifacts from sidelobes of the telescope's synthesized beam, which we have been unable to remove completely. The noise value in these channels is three times higher than elsewhere in the cube. For our analysis of NGC 3109, the cube produced with na weighting is used, except for the map showing the sum of all the channels (Figure 2) which used the ro weighting scheme. The parameters of the KAT-7 observations are summarized in Table 5.</text>
<text><location><page_5><loc_51><loc_10><loc_86><loc_15></location>Fig. 2 shows the total intensity map for all the channels of the data cube. The lowest contour is at 1.0 x 10 19 atoms cm -2 . Besides NGC</text>
<text><location><page_6><loc_9><loc_70><loc_45><loc_86></location>3109 to the north and Antlia to the south, the two background galaxies ESO 499-G037 (10:03:42 -27:01:40; V sys = 953 km s -1 ) and ESO 499-G038 (10:03:50 -26:36:46; V sys =871 km s -1 ) are clearly visible. More details about these two systems will be given in the Appendix. As mentioned earlier, the small cloud between ESO 499-G038 and NGC 3109 has no obvious optical counterpart. However, it is clearly associated with ESO 499-G038 and not NGC 3109, being at a velocity > 900 km s -1 .</text>
<figure>
<location><page_6><loc_9><loc_34><loc_45><loc_67></location>
<caption>Fig. 2.- Sum of the channel maps of the KAT-7 H i mosaic. The centers of the 3 fields are shown with red crosses. The contours are 0.1, 0.2, 0.3, 0.6, 1.0, 1.6, 3.2, 6.4, 12.8 × 10 20 atoms cm -2 , superposed on a DSS B image. NGC 3109 ( V sys = 404 km s -1 ) at the top and Antlia ( V sys = 360 km s -1 ) at the bottom are shown with white contours. The two background galaxies ESO 499-G037 ( V sys = 953 km s -1 ), ESO 499-G038 ( V sys = 871 km s -1 ) and its associated H i cloud ( V sys = 912 km s -1 ) are shown with blue contours. The synthesized beam is shown in the upper-right corner.</caption>
</figure>
<text><location><page_6><loc_11><loc_11><loc_45><loc_12></location>The natural weighted cube is the best place to</text>
<text><location><page_6><loc_51><loc_71><loc_86><loc_86></location>look for low-surface brightness emission between NGC 3109 and Antlia, but there is no obvious evidence of it there. In fact the elevated noise and strong sidelobes in the channels, which contain bright NGC 3109 data, prevent us from detecting lower surface brightness emission and limit what we can learn from smoothing the data. This work on NGC 3109 showed that better models of the KAT-7 primary beam are needed for calibration before we can go deeper.</text>
<text><location><page_6><loc_51><loc_56><loc_86><loc_71></location>Fig. 3 shows the result of the moment analysis of the NGC 3109 data. It can be seen that the H i extends over nearly 1 o , more than 4 times the optical diameter ( D 25 ). The nearly parallel isovelocity contours, typical of a solid-body type rotation curve, are clearly visible, as well as the warp of the H i disk in the outer parts. The velocity dispersion map shows very well the gradient of σ from 15 km s -1 in the center down to 5 km s -1 at the edge of the disk.</text>
<figure>
<location><page_6><loc_50><loc_30><loc_86><loc_53></location>
<caption>Fig. 3.- Moment maps of NGC 3109 from the KAT-7 na data cube. (top-left): total H i emission map with the synthesize beam in the bottomleft corner. The contours are 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25.6 × 10 20 atoms cm -2 , superposed on a DSS B image. (top-right): total H i emission map; (bottom-left): velocity field. The contours are 350, 370, 390, 410, 430, 450 km s -1 ; (bottomright): velocity dispersion.</caption>
</figure>
<text><location><page_6><loc_51><loc_9><loc_86><loc_13></location>Fig. 4 gives the integrated H i profile for NGC 3109. Profile widths of ∆V 50 = 118 ± 3 km s -1</text>
<text><location><page_7><loc_9><loc_62><loc_45><loc_86></location>and ∆V 20 = 136 ± 3 km s -1 are derived. Since the H i distribution is clearly lopsided, with more gas on the approaching (SW) than on the receding side, we adopt the midpoint velocity of 404 ± 2 km s -1 as more representative of the systemic velocity than the intensity-weighted mean velocity. This can be compared to 404 km s -1 , ∆V 50 = 123 km s -1 and ∆V 20 = 137 km s -1 in Jobin & Carignan (1990). An integrated flux of 1142 ± 110 Jy km s -1 is measured which corresponds at our adopted distance of 1.3 Mpc to a H i mass of M H i = 4 . 6 × 10 8 M /circledot for a H i mass-to-luminosity ratio M H i /L B of 1.0, showing the gas-rich nature of NGC 3109. With a HPBW of the primary beam of nearly one degree and the short baselines available, no flux should be missed by these observations.</text>
<figure>
<location><page_7><loc_10><loc_33><loc_44><loc_59></location>
<caption>Fig. 4.- Global H i line profile of NGC 3109 from the KAT-7 na data cube. The small dip ∼ 450 km s -1 is due to internally generated narrow band RFI.</caption>
</figure>
<text><location><page_7><loc_9><loc_10><loc_45><loc_23></location>Two methods of kinematical analysis will be used for the NGC 3109 data, namely an intensityweighted moment analysis and a Gauss-Hermite polynomial profile fit. With such high S/N data and low velocity gradient RC, not much difference is expected between the two types of analysis. As a result, the analysis yielding the smaller errors and the largest radius RC will be used for the mass model analysis in Sec. 4. The RCs are derived in</text>
<text><location><page_7><loc_51><loc_85><loc_56><loc_86></location>Sec. 3.4.</text>
<section_header_level_1><location><page_7><loc_51><loc_80><loc_86><loc_83></location>3.2. VLA-ANGST data on NGC 3109 and Antlia</section_header_level_1>
<text><location><page_7><loc_51><loc_59><loc_87><loc_79></location>NGC 3109 and Antlia were observed at the VLAas part of the VLA-ANGST survey (Ott et al. 2012). The galaxies were observed for ∼ 9 hours in BnA, ∼ 3 hours in CnB and ∼ 3 hours in DnC configurations giving access to scales from ∼ 6' to ∼ 15'. The hybrid configurations were used to get more circular beams for these two southern objects. The data were gridded with two different weighting functions: na weighting for maximum sensitivity and ro weighting for maximum spatial resolution (smaller synthesized beam). We use the ro weighted maps for NGC 3109 and the na weighted maps for Antlia. The parameters of the VLA observations are given in Table 6.</text>
<table>
<location><page_7><loc_50><loc_33><loc_94><loc_54></location>
<caption>Table 6: Parameters of the VLA-ANGST observations.</caption>
</table>
<text><location><page_7><loc_51><loc_11><loc_86><loc_32></location>Figure 5 shows the velocity field obtained with the ANGST data for NGC 3109. The nearly parallel contours are again clearly visible. From the H i emission map, we measure a total flux of 723 Jy km s -1 which, at our adopted distance, corresponds to a M H i = 2 . 9 × 10 8 M /circledot , which is nearly 40% less than the H i detected with KAT-7. Because the VLA is not sensitive to scales larger than 15 ' , the VLA-ANGST data will be missing some flux and their H i mass will be clearly underestimated for NGC 3109. In fact, the H i mass measured is exactly the same as that found by Jobin & Carignan (1990) with a VLA mosaic of two fields. So the problem with the VLA data is</text>
<text><location><page_8><loc_9><loc_83><loc_45><loc_86></location>not as much the smaller HPBW of the antennae but more the lack of short baselines.</text>
<figure>
<location><page_8><loc_9><loc_73><loc_45><loc_82></location>
<caption>Fig. 5.- Velocity field for the ro-weighted VLAANGST velocity field.</caption>
</figure>
<text><location><page_8><loc_9><loc_39><loc_45><loc_67></location>The VLA-ANGST data, with its high spatial resolution, is much better suited to study the H i distribution in Antlia, since KAT-7 has barely two beamwidths across the object. Figure 6 gives the total H i emission map for Antlia, where the lowest contour corresponds to 3 . 0 × 10 19 atoms cm -2 . A total flux of 3 . 7 ± 0 . 4 Jy km s -1 is found which, at an adopted distance of 1 . 31 ± 0 . 03 Mpc (Pimbblet & Couch 2012), corresponds to a M H i = 1 . 50 ± 0 . 15 × 10 6 M /circledot . This time, most of the flux should have been detected since Antlia is much smaller than NGC 3109. However, this total flux is twice as much as that of the HIPASS data where Barnes & de Blok (2001) found 1 . 7 ± 0 . 1 Jy km s -1 and still 40% more than the value of 2 . 7 ± 0 . 5 Jy km s -1 found by Fouqu'e et al. (1990). The reason for this large difference is not clear. But since we do not have access to the raw data, it is difficult for us to investigate further.</text>
<text><location><page_8><loc_9><loc_22><loc_45><loc_38></location>Figure 7 gives the integrated H i profile for Antlia. An integrated flux of 3 . 7 ± 0 . 30 Jy km s -1 is found, which is similar to the flux derived from the H i emission map. An intensity-weighted mean velocity of 360 ± 2 km s -1 is derived along with ∆V 50 = 23 ± 3 km s -1 and ∆V 20 = 33 ± 3 km s -1 . This can be compared to 362 ± 2 km s -1 and ∆V 20 = 30 ± 2 km s -1 for Barnes & de Blok (2001) and 361 ± 2 km s -1 ∆V 50 = 21 ± 4 km s -1 and a ∆V 20 = 33 ± 5 km s -1 for Fouqu'e et al. (1990).</text>
<section_header_level_1><location><page_8><loc_9><loc_17><loc_45><loc_20></location>3.3. Comparison of the different H i data sets</section_header_level_1>
<text><location><page_8><loc_9><loc_11><loc_45><loc_16></location>The limiting surface densities of the different interferometric studies are given in Table 7. As far as the VLA data are concerned, one should not be surprised that the Jobin & Carignan (1990) data</text>
<figure>
<location><page_8><loc_51><loc_63><loc_81><loc_86></location>
<caption>Fig. 6.- Total VLA-ANGST H i emission map of Antlia. The na-weighted data have been spatially smoothed to 45 '' (see the beam in the bottom right corner). The contours are at 0 . 3 , 0 . 45 , 0 . 9 , 1 . 5 , 2 . 1 & 2 . 7 × 10 20 atoms cm -2 . The contours are superposed on a DSS B image.</caption>
</figure>
<figure>
<location><page_8><loc_51><loc_30><loc_85><loc_50></location>
<caption>Fig. 7.- VLA-ANGST global H i profile of Antlia using the na-weighted data smoothed to 45 '' .</caption>
</figure>
<text><location><page_8><loc_51><loc_11><loc_86><loc_22></location>go deeper than the ANGST data since they are a mosaic of 2 fields with the same observing time in DnC configuration than the single field ANGST data. The 1.3 km s -1 resolution ANGST data is useful for comparisons with the Jobin & Carignan (1990) 10.3 km s -1 resolution data in the inner regions of NGC 3109. But mainly, that data provide</text>
<text><location><page_9><loc_9><loc_82><loc_45><loc_86></location>more information on the H i distribution of Antlia, for which the KAT-7 data is of too low spatial resolution.</text>
<paragraph><location><page_9><loc_9><loc_77><loc_45><loc_80></location>Table 7: Limiting H i surface densities of the different interferometer studies for NGC 3109.</paragraph>
<text><location><page_9><loc_33><loc_69><loc_35><loc_71></location>×</text>
<table>
<location><page_9><loc_9><loc_69><loc_48><loc_77></location>
<caption>Table 8: Different H i mass estimates for NGC 3109 ∗</caption>
</table>
<text><location><page_9><loc_9><loc_53><loc_47><loc_67></location>In view of the surface densities limits, we see that while both the KAT-7 and the Jobin & Carignan (1990) reach 1 . 0 × 10 19 cm -2 , the KAT-7 data covers a larger area since it is sensitive to large scales invisible to the VLA. As for the Barnes & de Blok (2001) data reaching the much lower surface densities of 2 . 0 × 10 17 cm -2 , they provide the largest detected size (85 ' x 55 ' ). However, this increase in size may be due partly to the large ∼ 15.5 ' HIPASS beam.</text>
<text><location><page_9><loc_9><loc_28><loc_45><loc_52></location>The H i mass estimates of both the single dish and the interferometric observations can be found in Table 8. The first thing to notice is the larger mass obtained by the single dish observations compared to the aperture synthesis ones, the only exception being the Whiteoak & Gardner (1977) data which come from a single pointing of the Parkes 64 m radio telescope. With a ∼ 15 ' beam, necessarily a lot of the flux extending over ∼ 1 o has been missed. For the others, the discrepancies can be explained by either the way the multi-pointing data have been combined or most likely that the correction for self-absorption that most of these authors have applied has been overestimated. No such correction has been applied to the synthesis data.</text>
<text><location><page_9><loc_9><loc_10><loc_45><loc_28></location>As for the synthesis data, we see that both sets of VLA data agree exactly. We would have expected some more flux from the deeper Jobin & Carignan (1990) data but since most of the flux is in the bright central components, the difference is probably just of the order of the errors. On the other hand, both the KAT-7 data and the HIPASS data agree very well which is surely indicative that, in both cases, no flux is missed. Because both those data sets see all the scales, they detect nearly 40% more flux than the VLA, which do not have the proper short spacings</text>
<text><location><page_9><loc_51><loc_83><loc_51><loc_84></location>.</text>
<table>
<location><page_9><loc_53><loc_63><loc_84><loc_83></location>
</table>
<text><location><page_9><loc_79><loc_62><loc_80><loc_64></location>±</text>
<text><location><page_9><loc_51><loc_53><loc_71><loc_54></location>to see scales larger than 15 ' .</text>
<section_header_level_1><location><page_9><loc_51><loc_50><loc_80><loc_51></location>3.4. Derivation of the optimal RC</section_header_level_1>
<text><location><page_9><loc_51><loc_42><loc_86><loc_49></location>The same method is used to derive the RC for both the VLA-ANGST and the KAT-7 data sets. For this study, we used the implementation of the tilted ring model in the GIPSY task ROTCUR (Begeman 1989).</text>
<section_header_level_1><location><page_9><loc_51><loc_39><loc_70><loc_40></location>3.4.1. Tilted Ring Models</section_header_level_1>
<text><location><page_9><loc_51><loc_23><loc_86><loc_38></location>A set of concentric rings is used to describe the motion of the gas in the galaxy. The gas is assumed to be in circular motion. Each ring is characterized by a set of 5 orientation parameters, namely: a rotation centre ( x c , y c ), a systemic velocity V sys , an inclination i , a Position Angle PA and by a rotation velocity V C . Naturally, the rotation centre ( x c , y c ) and the systemic velocity V sys should be the same for all the rings but i and PA will vary if the H i disk is warped.</text>
<text><location><page_9><loc_51><loc_19><loc_86><loc_22></location>The line of sight velocity at any ( x, y ) position in a ring with radius R is given by</text>
<formula><location><page_9><loc_57><loc_16><loc_86><loc_17></location>V ( x, y ) = V sys + V C sin ( i ) cos ( θ ) (1)</formula>
<text><location><page_9><loc_51><loc_11><loc_86><loc_15></location>where θ is the position angle with respect to the receding major axis measured in the plane of the galaxy. θ is related to the actual PA in the plane</text>
<text><location><page_10><loc_9><loc_85><loc_19><loc_86></location>of the sky by</text>
<formula><location><page_10><loc_10><loc_81><loc_44><loc_84></location>cos ( θ ) = -( x -x 0 ) sin ( PA ) + ( y -y 0 ) cos ( PA ) R</formula>
<formula><location><page_10><loc_10><loc_77><loc_45><loc_81></location>(2) sin ( θ ) = -( x -x 0 ) cos ( PA ) + ( y -y 0 ) cos ( PA ) Rcos ( i )</formula>
<text><location><page_10><loc_43><loc_75><loc_45><loc_77></location>(3)</text>
<text><location><page_10><loc_9><loc_62><loc_45><loc_75></location>A | cosθ | weighting function and an exclusion angle of ± 15 deg about the minor axis have been used to give maximum weight to the velocity points close to the major axis and minimize the influence of large deprojection errors close to the minor axis in view of the large inclination of the galaxy. The width of the rings has been matched to the synthesized beam size to make sure that the velocity points are independent.</text>
<text><location><page_10><loc_9><loc_54><loc_45><loc_61></location>The method consists at finding for each ring the best set of the 5 orientation parameters ( x c , y c ), V sys , i and PA which minimizes the dispersion of V C inside the ring. The following procedure is followed:</text>
<unordered_list>
<list_item><location><page_10><loc_12><loc_39><loc_45><loc_53></location>· The rotation center ( x c , y c ) and the systemic velocity V sys are determined first by keeping i and PA fixed (usually using the optical values). The rotation center and the systemic velocity have to be determined simultaneously since they are correlated. They are searched using only the central rings (e.g. R ≤ R 25 ) since there is usually no warp within the optical disk.</list_item>
<list_item><location><page_10><loc_12><loc_29><loc_45><loc_38></location>· Now, keeping ( x c , y c ) and V sys fixed, i and PA are looked for to map the warp of the H i disk, which usually starts just outside the optical. Here also, i and PA have to be determined simultaneously since they are also correlated.</list_item>
<list_item><location><page_10><loc_12><loc_20><loc_45><loc_28></location>· The previous two steps were done using the data of all the galaxy. Using the same fixed ( x c , y c ) and V sys , the previous step is repeated for the approaching and receding sides separately to see possible departures from axisymmetry.</list_item>
</unordered_list>
<text><location><page_10><loc_9><loc_14><loc_45><loc_18></location>The errors on V C will be the quadratic sum of the dispersion σ in each ring and half the difference between the approaching and the receding sides:</text>
<formula><location><page_10><loc_15><loc_9><loc_45><loc_12></location>∆ V = √ σ 2 ( V ) + ( | V app -V rec | 2 ) 2 (4)</formula>
<text><location><page_10><loc_51><loc_80><loc_86><loc_86></location>Since the mass models assume an axisymmetric system, we think that this way of calculating the errors is more representative of the true uncertainties, when comparing the RC to the model.</text>
<section_header_level_1><location><page_10><loc_51><loc_77><loc_69><loc_79></location>3.4.2. VLA-ANGST RC</section_header_level_1>
<text><location><page_10><loc_51><loc_51><loc_86><loc_76></location>For the derivation of the kinematics of NGC 3109, we use the ro-weighted VLA-ANGST data. We find that the rotation center is coincident with the optical center and derive a systemic velocity V sys = 402 km s -1 . By keeping those parameters fixed, we then fitted i and PA . The solutions for the whole galaxy and separately for the approaching and receding sides are shown in Fig. 8, along with a comparison with Jobin & Carignan (1990) in Fig. 9 . We see that the warp which starts around the Holmberg radius ( R HO ), is more important on the approaching (SW) side and that the RC from both VLA datasets agree very well, despite the difference in velocity resolutions (1.3 km s -1 vs 10.3 km s -1 ). Because Jobin & Carignan (1990) provide asymmetric drift corrections, their RC will be used for the mass models in Sec. 4.</text>
<figure>
<location><page_10><loc_53><loc_31><loc_83><loc_49></location>
<caption>Fig. 8.- Tilted-ring model using the ro VLAANGST data for both sides and independently for the approaching and the receding side.</caption>
</figure>
<section_header_level_1><location><page_10><loc_51><loc_20><loc_64><loc_21></location>3.4.3. KAT-7 RC</section_header_level_1>
<text><location><page_10><loc_51><loc_10><loc_86><loc_19></location>Fig. 10 shows the tilted-ting model for the intensity-weighted moment analysis of the KAT7 na-weighted data of NGC 3109. We find V sys = 405 ± 2 km s -1 , PA ∼ 96 o ± 4 and i ∼ 61 o ± 8. The rotation center is found to be ∼ 0.5 ' North from the optical center at 10 h 03 m 06.9 s -</text>
<figure>
<location><page_11><loc_12><loc_69><loc_41><loc_85></location>
<caption>Fig. 9.- Comparison of the VLA-ANGST and the Jobin & Carignan (1990) rotation curves.</caption>
</figure>
<text><location><page_11><loc_9><loc_45><loc_45><loc_61></location>26 o 08 ' 58 '' . This offset from the optical center is not significant and could be due to the larger synthesized beam of KAT-7. It can be seen that the agreement between the approaching and receding sides is much better than for the VLA-ANGST data. The increase in sensitivity allows us to extend the RC out to ∼ 32 ' ( ∼ 12 kpc). Despite the low spatial resolution, no real sign of beam smearing is seen when comparing this RC to the VLA data. This may not be surprising in view of the solid-body nature of the RC.</text>
<text><location><page_11><loc_9><loc_17><loc_45><loc_44></location>Fig. 11 shows the tilted-ting model for the Gauss-Hermite polynomials profile fitting analysis of the KAT-7 na-weighted data. The kinematical parameters found are very similar to those of the moment analysis with V sys = 406 km s -1 , PA ∼ 97 o and i ∼ 61 o and the same rotation center. The Gauss-Hermite polynomials are fitted to the spectra in each pixel, where the peak of the fitted profile rises above 5-sigma. As such, profiles from very faint emission at the edge of the galaxy are not strong enough to ensure a good fit. GaussHermite fits will therefore fail at large radii where the average signal-to-noise is lower than the cutoff. Lowering the cutoff produces too many bad velocity points. Therefore, since the RC using this technique is only defined out to 24 ' , the moment analysis RC is preferred for the mass models in Sec.4.</text>
<section_header_level_1><location><page_11><loc_9><loc_14><loc_35><loc_16></location>3.4.4. Asymmetric drift corrections</section_header_level_1>
<text><location><page_11><loc_9><loc_10><loc_45><loc_13></location>In the case of a galaxy like NGC 3109, where the velocity dispersion represents a substantial frac-</text>
<figure>
<location><page_11><loc_51><loc_61><loc_84><loc_86></location>
<caption>Fig. 10.- Tilted-ring model using the KAT-7 data derived from a moment analysis (intensity weighted) for both sides and independently for the approaching and the receding side and comparison with the RC of Jobin & Carignan (1990).</caption>
</figure>
<figure>
<location><page_11><loc_51><loc_24><loc_84><loc_50></location>
<caption>Fig. 11.- Tilted-ring model using the KAT7 data derived from a Gauss-Hermite polynomials analysis (profile fitting) for both sides and independently for the approaching and the receding side and comparison with the RC of Jobin & Carignan (1990).</caption>
</figure>
<text><location><page_12><loc_9><loc_77><loc_45><loc_86></location>tion of the rotational velocity ( σ/V max ≥ 15 -20%) and thus provides part of the gravitational support, a correction for asymmetric drift must be applied. Following the procedure used by Cˆot'e, Carignan & Freeman (2000), the corrected circular velocity is given by</text>
<formula><location><page_12><loc_16><loc_73><loc_45><loc_76></location>V 2 c = V 2 o -2 σ δσ δ ln R -σ 2 δ ln Σ δ ln R (5)</formula>
<text><location><page_12><loc_9><loc_65><loc_45><loc_73></location>where V c is the corrected velocity, V o is the observed one, σ is the velocity dispersion and Σ is the gas surface density. The asymmetric drift corrections are uncertain by about 25% (Lake & Skillman 1989).</text>
<section_header_level_1><location><page_12><loc_9><loc_32><loc_30><loc_33></location>4. Mass models analysis</section_header_level_1>
<text><location><page_12><loc_9><loc_10><loc_51><loc_31></location>Low mass Surface Density (LSD) galaxies are galaxies whose mass profiles are dominated by dark matter (DM) at all galactocentric radii. LSD properties were first identified in dwarf Irregular (dIrr) galaxies (such as the prototype dIrr DDO 154: Carignan & Freeman 1988; Carignan & Purton 1998) and later in late-type dwarf spirals (see e.g. NGC 5585: Cˆot'e, Carignan & Sancisi 1991). Despite the uncertainties on the exact M/L ratio of the luminous disk, LSD galaxies, such as NGC 3109, are clearly DM dominated at all radii. For that reason, they can be used to constrain important properties of dark matter haloes, such as the characteristic scale density</text>
<table>
<location><page_12><loc_51><loc_60><loc_92><loc_81></location>
<caption>Table 9: Radial variation of the surface densities Σ and of the velocity dispersion σ for the KAT-7 data of NGC 3109 from the moment analysis.Table 10: KAT-7 rotation curve of NGC 3109 from the moment analysis, corrected for asymmetric drift.</caption>
</table>
<table>
<location><page_12><loc_50><loc_37><loc_97><loc_53></location>
<caption>Table 9 shows the radial profiles for the surface densities and the velocity dispersion that were derived using the task IRING in AIPS. For the mass models, the H i surface densities will be multiplied by 4/3 to correct for Helium. The radial profiles will be used to correct for the asymmetric drift. Table 10 presents the corrected values: column (1) gives the radius in arcsec, column (2) the observed rotation velocities, column (3) the errors on those velocities, column (4) the ratio between the velocity dispersion and the circular velocity, column (5) gives the amplitude of the correction and column (6) the corrected velocities used for the mass models. As can be seen, when σ /V is greater than 20%, the corrections can be of the order of a few km s -1 which is nearly 10% for a slow rotator such as NGC 3109. Usually, when σ /V is less than 20%, the corrections are of 1 km s -1 or less and usually neglected because they are smaller than the errors.</caption>
</table>
<text><location><page_12><loc_51><loc_21><loc_86><loc_35></location>and radius, concentration, virial mass and the exact shape of the mass density profile. Ultimately, measuring the dark matter distribution of these galaxies is necessary if one wants to test the results obtained by numerical simulations of galaxy evolution in the framework of the Cold Dark Matter (CDM) paradigm (Navarro, Frenk & White 1997) or test alternative gravity theories such as MOND (Milgrom 1983).</text>
<text><location><page_12><loc_51><loc_10><loc_86><loc_21></location>The study of their mass distribution has generated in the last 15 years the so-called cusp-core controversy: are rotation curves of LSD galaxies better reproduced by a cuspy halo as seen in the ΛCDM numerical simulations or by a halo with a nearly constant central density core as seen in most high spatial resolution observations</text>
<text><location><page_13><loc_9><loc_80><loc_46><loc_86></location>(e.g. Blais-Ouellette, Amram & Carignan 2001; de Blok, McGaugh & Rubin 2001; Marchesini et al. 2002). A good review of this debate can be found in de Blok (2010).</text>
<text><location><page_13><loc_9><loc_62><loc_45><loc_80></location>Nowadays, galaxies are expected to form inside cuspy Cold Dark Matter halos. High resolution velocity fields have provided important observational constraints on the dark matter distribution in LSD galaxies. These two-dimensional data show clearly that dark matter-dominated galaxies tend to be more consistent with cored than cuspy halos, at odds with the theoretical expectations. So, a lot of efforts in the last few years has gone into identifying the physical processes that could have turned initially cuspy DM halos into cored ones (Governato et al. 2012;</text>
<text><location><page_13><loc_9><loc_50><loc_49><loc_62></location>Pontzen & Governato 2012; Kuzio de Naray & Spekkens 2011; Kuzio de Naray et al. 2010; Governato et al. 2010). For example, one recently suggested solution to this problem is to enforce strong supernovae outflows that move large amounts of lowangular-momentum gas from the central parts and that pull on the central dark matter concentration to create a core (Famaey & McGaugh 2013).</text>
<section_header_level_1><location><page_13><loc_9><loc_47><loc_31><loc_48></location>4.1. Dark Matter models</section_header_level_1>
<section_header_level_1><location><page_13><loc_9><loc_45><loc_44><loc_46></location>4.1.1. The pseudo-isothermal DM model (ISO)</section_header_level_1>
<text><location><page_13><loc_9><loc_39><loc_45><loc_44></location>The pseudo-isothermal DM halo is an observationally motivated model with a constant central density core. The density profile is given by:</text>
<formula><location><page_13><loc_19><loc_35><loc_45><loc_38></location>ρ ISO ( R ) = ρ 0 1 + ( R R c ) 2 (6)</formula>
<text><location><page_13><loc_9><loc_30><loc_45><loc_34></location>where ρ 0 is the central density and R c the core radius 1 . The corresponding rotation velocities are given by:</text>
<formula><location><page_13><loc_11><loc_22><loc_45><loc_27></location>V ISO ( R ) = √ 4 πGρ 0 R 2 C [1 -R R C arctan( R R C )] (7)</formula>
<text><location><page_13><loc_9><loc_16><loc_45><loc_22></location>We can describe the steepness of the inner slope of the mass density profile with a power law ρ ∼ r α . In the case of the ISO halo, where the inner density is an almost constant density core, α = 0.</text>
<section_header_level_1><location><page_13><loc_51><loc_83><loc_86><loc_86></location>4.1.2. The Navarro, Frenk and White DM model (NFW)</section_header_level_1>
<text><location><page_13><loc_51><loc_73><loc_86><loc_82></location>The NFW profile, also known as the 'universal density profile' (Navarro, Frenk & White 1997) is the commonly adopted dark matter halo profile in the context of the ΛCDM cosmology. It was derived from N-body simulations. The density profile is given by:</text>
<formula><location><page_13><loc_57><loc_69><loc_86><loc_73></location>ρ NFW ( R ) = ρ i R/R S (1 + R/R S ) 2 (8)</formula>
<text><location><page_13><loc_51><loc_62><loc_86><loc_68></location>where R S is the characteristic radius of the halo and ρ i is related to the density of the universe at the time of collapse of the dark matter halo.The corresponding rotation velocities are given by:</text>
<formula><location><page_13><loc_52><loc_56><loc_86><loc_61></location>V NFW ( R ) = V 200 √ ln (1 + cx ) -cx/ (1 + cx ) x [ ln (1 + c ) -c/ (1 + c )] (9)</formula>
<text><location><page_13><loc_51><loc_40><loc_86><loc_56></location>where x = R/R 200 . It is characterized by a concentration parameter c = R 200 /R S and a velocity V 200 . The radius R 200 is the radius where the density contrast with respect to the critical density of the universe exceeds 200, roughly the virial radius (Navarro, Frenk & White 1996). The characteristic velocity V 200 is the velocity at that radius. The NFW mass density profile is cuspy in the inner parts and can be represented by ρ ∼ r α , where α = -1.</text>
<section_header_level_1><location><page_13><loc_51><loc_38><loc_85><loc_39></location>4.2. ISO & NFW Models for NGC 3109</section_header_level_1>
<text><location><page_13><loc_51><loc_18><loc_86><loc_37></location>Because of the way the different velocity points are weighted in the mass model fitting algorithm, we will not combine the high spatial resolution VLA data (Jobin & Carignan 1990) with the low spatial resolution but high sensitivity KAT-7 data. Instead, we will run a set of models for each data set. The radial surface density profile of each data set will still be used, keeping in mind that the VLA data underestimate the H i content, which will not be the case for the KAT-7 data. The I band luminosity profile of Jobin & Carignan (1990) is preferred to IR (e.g. 2.6 µ m) profiles because it extends to much larger radii.</text>
<text><location><page_13><loc_51><loc_10><loc_86><loc_17></location>NGC 3109 presents an interesting test for the DM models. Because it has no bulge and a very shallow velocity gradient, it is an ideal system to address the cusp-core controversy. The DM models are shown in Fig. 12 for the Jobin & Carignan</text>
<text><location><page_14><loc_9><loc_68><loc_45><loc_86></location>(1990) data and in Fig. 13 for the KAT-7 data. The results are summarized in Table 11. It can be seen that the ISO models fit almost perfectly the observed RC with a reduced χ 2 of only 0.24 for the VLA data and 0.31 for the KAT-7 data. On the other hand, the NFW model has much less success with a reduced χ 2 =12.9 for the VLA data and 0.86 for the KAT-7 data. However, because of the low spatial resolution, the KAT-7 data do not probe the very inner parts where the discrepancy with the observations is expected to be the greatest.</text>
<figure>
<location><page_14><loc_10><loc_40><loc_42><loc_66></location>
<caption>Fig. 12.- DM ISO (top) & NFW (bottom) mass models for the observed VLA RC (blue points with errors) of NGC 3109 from Jobin & Carignan (1990). The red dash curve is for the H i disk, the dash-dot light blue curve is for the stellar disk, the purple dash curve is for the DM halo and the continuous green curve is the quadratic sum of the components. There is no disk component for the NFW model because the best-fit model yields M/L = 0</caption>
</figure>
<text><location><page_14><loc_9><loc_10><loc_45><loc_21></location>The NFW model completely fails in the inner 1 kpc, overestimating the first velocity point by a factor of two for the VLA data. However, the main problem with the NFW models is that the best fits to both the VLA and the KAT-7 data suggest a M/L of 0 for the stellar disk, which is unphysical. This is understandable since any stellar disk com-</text>
<figure>
<location><page_14><loc_52><loc_58><loc_83><loc_85></location>
<caption>Fig. 13.- DM ISO (top) & NFW (bottom) mass models for the observed KAT-7 RC (blue points with errors) of NGC 3109. The symbols are the same as in Fig. 12</caption>
</figure>
<table>
<location><page_14><loc_50><loc_19><loc_88><loc_45></location>
<caption>Table 11: Results for the DM mass models of NGC 3109.</caption>
</table>
<text><location><page_14><loc_51><loc_11><loc_86><loc_16></location>ponent would just increase the discrepancy in the inner parts. On the other hand, the best fit ISO model has (M/L) I =0.55-0.76 which is quite compatible with the value predicted by stellar popula-</text>
<text><location><page_15><loc_9><loc_80><loc_45><loc_86></location>tion models of 0.67 ± 0.04 (Bell & de Jong 2001) for the I band. Without any doubt, in the DM halo paradigm, those results confirm that NGC 3109 has a cored and not a cuspy halo.</text>
<section_header_level_1><location><page_15><loc_9><loc_77><loc_27><loc_79></location>4.3. MOND models</section_header_level_1>
<text><location><page_15><loc_9><loc_59><loc_45><loc_76></location>MOND was proposed by Milgrom (1983) as an alternative to dark matter. Milgrom postulated that at small accelerations the usual Newtonian dynamics break down and the law of gravity needs to be modified. MOND has been claimed to be able to explain the mass discrepancies in galaxies without dark matter (e.g. Begeman, Broeils & Sanders 1991; Sanders 1996; Bottema et al. 2002). Therefore, in the MOND formalism, only the contributions of the gas component and of the stellar component are required to explain the observed rotation curves.</text>
<text><location><page_15><loc_9><loc_49><loc_45><loc_58></location>The transition between the Newtonian and the MONDian regime is characterized by an acceleration threshold value called a 0 below which MOND should be used. So, in the MOND framework, the gravitational acceleration of a test particle is given by :</text>
<formula><location><page_15><loc_20><loc_48><loc_45><loc_49></location>µ ( x = g/a 0 ) g = g N (10)</formula>
<text><location><page_15><loc_9><loc_41><loc_45><loc_47></location>where g is the gravitational acceleration, a 0 is a new universal constant which should be the same for all galaxies, µ (x) is the MOND interpolating function and g N the Newtonian acceleration.</text>
<text><location><page_15><loc_9><loc_26><loc_45><loc_40></location>The standard and simple interpolating functions are mostly used in the literature. The standard µ -function is the original form of the interpolating function proposed by Milgrom (1983). However, Zhao & Famaey (2006) found that a simplified form of the interpolating function not only provides also good fits to the observed rotation curves but the derived mass-to-light ratios are more compatible with those obtained from stellar populations synthesis models.</text>
<text><location><page_15><loc_9><loc_21><loc_45><loc_24></location>4.3.1. MOND models using the 'standard' interpolation function</text>
<text><location><page_15><loc_11><loc_19><loc_45><loc_20></location>The standard interpolating function is given as</text>
<formula><location><page_15><loc_21><loc_15><loc_45><loc_18></location>µ ( x ) = x √ 1 + x 2 (11)</formula>
<text><location><page_15><loc_9><loc_10><loc_45><loc_14></location>For x /lessmuch 1 the system is in deep MOND regime with g = ( g N a 0 ) 1 / 2 and for x /greatermuch 1 the gravity is</text>
<text><location><page_15><loc_51><loc_85><loc_59><loc_86></location>Newtonian.</text>
<text><location><page_15><loc_53><loc_82><loc_79><loc_83></location>The MOND rotation curve becomes:</text>
<formula><location><page_15><loc_53><loc_74><loc_86><loc_79></location>V 2 rot = V 2 sum √ 2 √ 1 + √ 1 + (2 ra 0 /V 2 sum ) 2 (12)</formula>
<text><location><page_15><loc_53><loc_73><loc_57><loc_74></location>where</text>
<formula><location><page_15><loc_60><loc_71><loc_86><loc_73></location>V 2 sum = V 2 b + V 2 d + V 2 g (13)</formula>
<text><location><page_15><loc_51><loc_65><loc_86><loc_71></location>V b , V d , V g are the contributions from the bulge, the disk and the gas to the rotation curve. In the case of the Magellanic-type spiral NGC 3109, there is no bulge to consider.</text>
<text><location><page_15><loc_51><loc_60><loc_86><loc_63></location>4.3.2. MOND models using the 'simple' interpolation function</text>
<text><location><page_15><loc_53><loc_58><loc_85><loc_59></location>The simple interpolating function is given by</text>
<formula><location><page_15><loc_63><loc_54><loc_86><loc_57></location>µ ( x ) = x 1 + x (14)</formula>
<text><location><page_15><loc_51><loc_49><loc_86><loc_53></location>Using the same procedure as in previous section we can easily obtain the corresponding rotation velocities:</text>
<formula><location><page_15><loc_51><loc_44><loc_86><loc_48></location>V 2 rot = √ V 2 b + V 2 d + V 2 g ∗ √ a 0 ∗ r + V 2 b + V 2 d + V 2 g (15)</formula>
<section_header_level_1><location><page_15><loc_51><loc_41><loc_80><loc_43></location>4.4. MOND Models for NGC 3109</section_header_level_1>
<text><location><page_15><loc_51><loc_27><loc_86><loc_40></location>NGC 3109 presents an interesting test for MOND. As we have seen, it is close enough to have a very accurate distance determination using Cepheids and the largest portion of the luminous mass is in the form of gas and not stars, partly freeing us from the uncertainties due to the M/L value used for the disk. The internal accelerations are very low, therefore the galaxy is completely within the MOND regime (Lake 1989).</text>
<text><location><page_15><loc_51><loc_16><loc_86><loc_26></location>The MOND mass models for the VLA data are presented in Fig. 14 & Table 12 and in Fig. 15 & Table 13 for the KAT-7 data, for both the standard value of a 0 , namely 1.21 x 10 -8 cm sec -2 (Begeman, Broeils & Sanders 1991) and with a 0 left as a free parameter. The standard and the simple interpolation functions are also illustrated.</text>
<text><location><page_15><loc_51><loc_10><loc_86><loc_16></location>In the case of the VLA data, the fits are poor for all the cases: they overestimate the velocities in the inner parts and they underestimate them in the outer parts. The reduced χ 2 are much larger</text>
<figure>
<location><page_16><loc_11><loc_66><loc_42><loc_85></location>
<caption>Fig. 14.- MOND mass models with a 0 fixed (top) and a 0 free (bottom) and for the standard (left) and the simple (right) interpolation functions for NGC 3109 using the RC of Jobin & Carignan (1990). The red dash curve is for the H i disk, the dash-dot light blue curve is for the stellar disk, and the continuous green curve is the MOND model.</caption>
</figure>
<table>
<location><page_16><loc_9><loc_26><loc_45><loc_48></location>
<caption>Table 12: Results for the MOND models of NGC 3109 for the VLA data.</caption>
</table>
<text><location><page_16><loc_9><loc_18><loc_45><loc_23></location>than for the DM fits, varying from 5.5 to 12. However, since most of the luminous mass is in gas and since the VLA misses 40% of the flux, we should not expect good fits.</text>
<text><location><page_16><loc_9><loc_11><loc_45><loc_17></location>The MOND models have more significance for the KAT-7 data than for the VLA data, since we probe the gas on all scales. In this case we see that for the standard fixed value of a 0 = 1.21 x 10 -8</text>
<figure>
<location><page_16><loc_52><loc_66><loc_83><loc_85></location>
<caption>Fig. 15.- MOND mass models with a 0 fixed (top) and a 0 free (bottom) and for the standard (left) and the simple (right) interpolation functions for NGC 3109 using the RC from KAT-7 data. The symbols are the same as in Fig. 14</caption>
</figure>
<table>
<location><page_16><loc_51><loc_30><loc_86><loc_52></location>
<caption>Table 13: Results for the MOND models of NGC 3109 for the KAT-7 data.</caption>
</table>
<text><location><page_16><loc_51><loc_10><loc_86><loc_28></location>cm sec -2 , the results of the models are poor with reduced χ 2 of 3.0 to 3.4 and (M/L) B values 3 to 4 times larger than the value predicted by stellar population models. However, we see that if a 0 is free to vary, we get more reasonable fits with reduced χ 2 down to 1.30 and 1.37, still 4-5 times larger than for the DM ISO models. The main problems with those models are the very small (M/L) I values, 2 to 3 times smaller than the expected values and the large values of the constant a 0 which is greater than a factor of 2 compared to the standard value.</text>
<section_header_level_1><location><page_17><loc_9><loc_85><loc_21><loc_86></location>5. Discussion</section_header_level_1>
<text><location><page_17><loc_9><loc_61><loc_45><loc_83></location>We will now examine different questions that were raised by this study. The first one is the difference found between the kinematic inclination and the photometric values. This is an important point to understand since i scales the RC and is responsible for the velocity gradient of the rising part of the RC, which really constrains the mass models and set the M/L ratio of the luminous disk. Both tilted-ring models using the intensityweighted and the profile fitting techniques find the same inclination of i = 61 o . It is important to understand how this parameter is determined. Assuming an axisymmetric disk, the tilted-ring model tries to find the value that minimizes the dispersion of the velocities in the rings.</text>
<text><location><page_17><loc_9><loc_42><loc_45><loc_61></location>On the other hand, looking at Table 14, it can be seen that the inclination varies from 78.5 o in B to 73.5 o in I and 69.5 o in the 3.6 µ m. What is going on is quite clear. Each photometric band samples different stellar populations. The B-band samples the young blue Pop I stars which are confined to the thin disk, the I-band samples a mixture of young and old Pop I stars which are in a thicker disk while the 3.6 µ m is completely dominated by an old disk population in an even thicker disk. This explains that progression of the inclination from ∼ 80 o to ∼ 70 o .</text>
<text><location><page_17><loc_9><loc_20><loc_45><loc_42></location>It is instructive to look at the ellipse fits to the H i isophotes. As can be seen in Table 15, NGC 3109 is really composed of 2 disks: an inner one, corresponding to the optical disk, with i ∼ 76 o , which is the mean of the B and I inclinations and an outer disk with i ∼ 63 o which, within the errors, agree with the kinematical inclination. The double disk is quite apparent when looking at the H i isophotes in Fig. 2. Therefore, since the photometric inclination is most sensitive to the emission of the stellar populations being traced, it is quite clear that the kinematic inclination should be preferred. The photometric values should only be used as starting values in the tilted-ring modeling.</text>
<text><location><page_17><loc_9><loc_10><loc_46><loc_19></location>Another point worth discussing is beam-smearing. With such a large synthesized beam ∼ 4 ' , one would have expected beam smearing to be quite important. However when looking at Figures 10 and 11, this does not seem to be the case. As explained in Carignan (1985), beam smearing is</text>
<text><location><page_17><loc_80><loc_62><loc_82><loc_64></location>±</text>
<table>
<location><page_17><loc_50><loc_63><loc_90><loc_83></location>
<caption>Table 14: Optical orientation parameters of NGC 3109.</caption>
</table>
<text><location><page_17><loc_52><loc_56><loc_74><loc_57></location>References. - (1) Carignan (1985);</text>
<table>
<location><page_17><loc_50><loc_24><loc_92><loc_51></location>
<caption>Table 15: Fits to the H i isophotes.</caption>
</table>
<text><location><page_17><loc_51><loc_10><loc_86><loc_20></location>the result of the convolution of the Gaussian beam with the H i distribution and the velocity gradient across the beam. If the H i distribution is steep and/or the velocity gradient is large, the net effect will be to underestimate the observed velocity or conversely to overestimate the effective radius (the product of the convolution) that is observed. In</text>
<text><location><page_18><loc_9><loc_76><loc_45><loc_86></location>the case of NGC 3109, the H i distribution is fairly flat across the beam and the velocity gradient of that galaxy is very small. Those two properties render the beam smearing negligible. Should we be observing another galaxy with a step velocity gradient and/or a steep radial H i distribution, beam smearing would be important.</text>
<text><location><page_18><loc_9><loc_51><loc_45><loc_75></location>Let us now turn to the mass models. First, the results of the DM ISO models for both RCs confirm the previous results that it provides an almost perfect fit to the observed kinematics with the difference that the KAT-7 model has a more massive H i disk. As expected, this translates in a smaller stellar disk M/L value for the KAT-7 data. In both cases, the mass-to-light ratio found for the disk is compatible with population synthesis models. The NFW models again fail to reproduce the kinematics. In the inner kpc, the velocities are overestimated by a large factor, despite an unphysical M/L ratio of 0 for the stellar disk. In the DM halo paradigm, clearly NGC 3109 has a cored and not a cuspy halo, at least at the present epoch.</text>
<text><location><page_18><loc_9><loc_31><loc_45><loc_51></location>What about the MOND models ? Twenty-five years ago, Sanders (1986) pointed out that the MOND mass of NGC 3109 predicted using Milgrom's suggested value for a 0 was 5 x 10 8 M /circledot , thus larger than the H i mass using the larger distance estimates known at the time between 1.7 to 2.6 Mpc (Carignan 1985). This is not the case anymore with the smaller well determined distance of 1.3 Mpc, but still our determined H i mass with KAT-7 is less than 10% smaller than this MOND mass, which implies unphysically small M/L values for the stars in the case where the fits have been improved letting the constant a 0 free to vary.</text>
<text><location><page_18><loc_9><loc_10><loc_45><loc_31></location>When Begeman, Broeils & Sanders (1991) produced a MOND model using the Jobin & Carignan (1990) VLA data, they argued that they could not get a good fit because the VLA data was missing a substantial part of the flux and that the H i mass had to be multiplied by 1.67 to get a reasonable fit. However, since the KAT-7 data retrieve all the NGC 3109 flux, this cannot be used as an argument with the present data which convincingly show that MOND cannot reproduce the observed kinematics of NGC 3109 with physically acceptable parameter values. Unless some other explanation can be found, the KAT-7 data surely challenge the MOND theory.</text>
<text><location><page_18><loc_51><loc_65><loc_86><loc_86></location>What about the possible interaction between the Magellanic-type spiral NGC 3109 and the dIrr/dSph Antlia, suggested by the H i isophotes being slightly elongated ? The high surface brightness sensitivity of the KAT-7 observations allow us to trace the lopsidedness of NGC 3109 to larger radii, however there is no further obvious evidence of an interaction with Antlia, leaving the question open for further investigation. NGC 3109 has a systemic velocity of 404 km s -1 while Antlia has 360 km s -1 . Aparicio et al. (1997) calculated the physical separation between NGC 3109 and Antlia to be between 29 and 180 kpc, with a maximum separation of 37 kpc for the pair to be bound.</text>
<text><location><page_18><loc_51><loc_45><loc_86><loc_65></location>The situation for the Local Group dwarfs can guide us. Grcevich & Putman (2009) showed clearly that the majority of dwarf galaxies within 270 kpc of the Milky Way or Andromeda are undetected in H i ( < 10 4 M /circledot for the Milky Way dwarfs), while those further than 270 kpc are predominantly detected with masses 10 5 to 10 8 M /circledot (Antlia has an H i mass of ∼ 10 6 M /circledot ) meaning the nearby ones must have been stripped of their gas. While the halo of NGC 3109 is not as large as the Milky Way halo, if a close encounter had happened in the past, it is quite likely that Antlia would also have been stripped of its gas.</text>
<text><location><page_18><loc_51><loc_33><loc_86><loc_45></location>Nevertheless, some kind of interaction really seems to have taken place, as shown by the H i isophotes of the two galaxies pointing toward each other. However, in view of the large difference in masses between the two systems and the absence of any external traces of such an interaction, it is believed that the internal kinematics of NGC 3109 cannot have been severely altered.</text>
<text><location><page_18><loc_51><loc_10><loc_86><loc_32></location>Anyway, if such an interaction did take place, it would be more the rule than the exception. Massive galaxies usually have a significant population of gas-rich dwarf companions and interaction with these will show kinematic and morphological signatures in the extended HI disks (Mihos et al. 2012) such as warps, plumes, tidal tails, high-velocity clouds (e.g. Hibbard et al. 2001; Sancisi et al. 2008) or even stellar streams (Lewis et al. 2013). Galaxies are said to be embedded in the cosmic web, seen in the ΛCDM numerical simulations (Springel, Frenk &White 2006). Such signatures of interaction have been studied close to massive galaxies such as the interconnecting network in the M81/M82 system</text>
<text><location><page_19><loc_9><loc_71><loc_45><loc_86></location>(Yun, Ho & Lo 1994) or the tidal tail in the Leo triplet (Haynes, Giovanelli & Roberts 1979). More recently, Mihos et al. (2012) using the Green Bank Telescope (GBT) found a plume in the outer disk of M101 with a peak column density of 5 x 10 17 cm -2 and two new H i clouds close to that plume with masses of ∼ 10 7 M /circledot . While KAT-7 would not have detected such low column densities, it is interesting to look at our detection cloud mass limit.</text>
<text><location><page_19><loc_9><loc_65><loc_45><loc_71></location>To calculate a characteristic H i mass sensitivity, we assume that low-mass clouds would be unresolved in our beam and use the relation (Mihos et al. 2012):</text>
<formula><location><page_19><loc_11><loc_58><loc_45><loc_62></location>( σ M M /circledot ) = 2 . 36 × 10 5 ( D 2 Mpc )( σ s Jy )( ∆ V km s -1 ) (16)</formula>
<text><location><page_19><loc_9><loc_48><loc_45><loc_58></location>where D is the distance, σ s is the rms noise in one channel and ∆ V is the channel width. This means that our 3 σ cloud mass detection limit is around 5-6 x 10 3 M /circledot at the distance of NGC 3109. We should thus have easily detected similar clouds like the ones observed around M101, if they had been present.</text>
<section_header_level_1><location><page_19><loc_9><loc_45><loc_34><loc_46></location>6. Summary and conclusions</section_header_level_1>
<text><location><page_19><loc_9><loc_27><loc_45><loc_44></location>The first H i spectral line observations with the prototype radio telescope KAT-7 have been presented. The high sensitivity of KAT-7 to large scale, low column density emission comes not only from its compact configuration, but also from its very low T sys receivers. With ∼ 25 hours of observations per pointing, surface densities of 1.0 x 10 19 atoms cm -2 were reached, which could be improved when the telescope will be fully commissioned, since the theoretical noise was not reached with the present dataset.</text>
<text><location><page_19><loc_11><loc_25><loc_38><loc_27></location>The main results from this study are:</text>
<unordered_list>
<list_item><location><page_19><loc_12><loc_12><loc_45><loc_24></location>· A total H i mass of 4.6 x 10 8 M /circledot is measured for NGC 3109, using our adopted distance of 1.3 Mpc. This H i mass, which is ∼ 40% larger than the values calculated using VLA observations, is surely a better estimate of the total H i mass of NGC 3109 since KAT7 is sensitive to the large scales for which the VLA is not.</list_item>
<list_item><location><page_19><loc_12><loc_9><loc_45><loc_11></location>· The H i disk extends over a region of 58 ' (EW)</list_item>
</unordered_list>
<text><location><page_19><loc_55><loc_83><loc_86><loc_86></location>x 27 ' (NS) down to a limiting column density of 1.0 x 10 19 atoms cm -2 .</text>
<unordered_list>
<list_item><location><page_19><loc_53><loc_68><loc_86><loc_82></location>· The H i distribution is lopsided with more H i on the SW approaching side. Because of this, no intensity-weighted velocity is derived from the global profile but rather a mid-point velocity of 404 ± 2 km s -1 , believed to be more representative of the systemic velocity of NGC 3109. Profile widths of ∆V 50 = 118 ± 4 km s -1 and ∆V 20 = 133 ± 3 km s -1 are derived.</list_item>
<list_item><location><page_19><loc_53><loc_54><loc_86><loc_68></location>· VLA-ANGST data were used to derive the H i properties of the dSph/dIrr Antlia, since the spatial resolution of KAT-7 is too low to study this dwarf system. A total H i mass of 1.5 x 10 6 M /circledot is measured for our adopted distance of 1.31 Mpc. An intensity-weighted mean velocity of 360 ± 2 km s -1 is derived along with a ∆V 50 = 23 ± 3 km s -1 and a ∆V 20 = 33 ± 3 km s -1 .</list_item>
<list_item><location><page_19><loc_53><loc_37><loc_86><loc_53></location>· A tilted-ring model was obtained for the high velocity resolution VLA-ANGST data of NGC 3109. As on the H i total intensity map, it can be seen that the warp is more important on the approaching side. The RC found is nearly identical to the one derived by Jobin & Carignan (1990) which had a velocity resolution of ∼ 10 km s -1 . Because the latter study provides correction for asymmetric drift, it was preferred for the mass model analysis.</list_item>
<list_item><location><page_19><loc_53><loc_14><loc_86><loc_36></location>· Rotation curves from the KAT-7 data of NGC 3109 were derived from two different types of analysis: an intensity-weighted moment analysis and a Gauss-Hermite polynomial profile fitting. Both data sets give essentially the same result with V sys = 405 km s -1 and mean PA = 96 o and i = 61 o , with very little difference between the approaching and the receding side. The KAT-7 RCs agree very well with the VLA data in the inner parts while allowing to extend the rotation data by a factor of 2 out to 32 ' . Since the moment analysis data allow us to derive the RC further out, it was used for the mass models.</list_item>
<list_item><location><page_19><loc_53><loc_10><loc_86><loc_12></location>· The observationally motivated DM ISO model reproduces very well the observed</list_item>
</unordered_list>
<text><location><page_20><loc_13><loc_73><loc_45><loc_86></location>RCs of both the Jobin & Carignan (1990) and the KAT-7 data while a cosmologically motivated NFW model gives a much poorer fit, especially in the very inner parts. Because of the high spatial and velocity resolutions data available and the very small errors on those velocities, this cannot be attributed to poor data. NGC 3109 definitely has a cored and not a cuspy DM halo.</text>
<unordered_list>
<list_item><location><page_20><loc_12><loc_51><loc_45><loc_71></location>· While it is clear that having the proper gas distribution has reduced the discrepancies between the observed RC and the MOND models, the unreasonable (M/L) and large a 0 values obtained lead us to conclude that we cannot get acceptable MOND models for NGC3109. The distance being so well determined with very small errors from Cepheids observations and the H i mass so well constrained by the KAT-7 observations, uncertainties on these two values cannot explain why the MOND models fail to reproduce the observed kinematics with reasonable parameters.</list_item>
</unordered_list>
<text><location><page_20><loc_51><loc_74><loc_86><loc_86></location>testbed for MeerKAT and the SKA such that any scientific result that can be obtained is a bonus. While most of the extragalactic H i sources would be unresolved by the ∼ 4 ' synthesized beam, many projects such as this one on NGC 3109 can be done on nearby very extended objects such as Local Group galaxies or galaxies in nearby groups like Sculptor.</text>
<text><location><page_20><loc_51><loc_53><loc_86><loc_72></location>We thank all the team of SKA South Africa for allowing us to get scientific data during the commissioning phase of KAT-7 and are grateful to the ANGST team for making their reduced VLA data publicly available. CC's work is based upon research supported by the South African Research Chairs Initiative (SARChI) of the Department of Science and Technology (DST), the Square Kilometer Array South Africa (SKA SA) and the National Research Foundation (NRF). The research of BF, KH, DL & TR have been supported by SARChI, SKA SA and National Astrophysics and Space Science Programme (NASSP) bursaries.</text>
<unordered_list>
<list_item><location><page_20><loc_12><loc_41><loc_46><loc_49></location>· Besides some elongation of the outer isophotes, already seen in previous observations, no further evidence is found for past encounter and/or interaction between the Magellanictype spiral NGC 3109 and the dSph/dIrr Antlia.</list_item>
</unordered_list>
<text><location><page_20><loc_9><loc_21><loc_59><loc_39></location>Our findings for NGC 3109 are not an isolated case. Recently, S'anchez-Salcedo, Hidalgo-Gamez & Martinez-Garcia (2013) studied a sample of slowly rotating gasrich galaxies in the MOND framework. These are again galaxies in the full low acceleration MOND regime. They found at least five such systems (especially NGC 4861 and Holmberg II) that deviate strongly from the MOND predictions, unless their inclinations and distances differ strongly from the nominal values. In the case of NGC 3109, those two parameters are much more constrained which makes it harder to reconcile MOND with the ob-</text>
<text><location><page_20><loc_9><loc_20><loc_22><loc_21></location>served kinematics.</text>
<text><location><page_20><loc_9><loc_10><loc_45><loc_19></location>Those observations obtained with KAT-7 have shown that despite its relatively small collecting area (7 x 12 m antennae), this telescope really has a niche for detecting large scale low emission over the ∼ 1 o FWHM of its antennae. It should be kept in mind that this telescope was built primarily as a</text>
<section_header_level_1><location><page_21><loc_9><loc_85><loc_44><loc_86></location>A. Appendix: Other galaxies in the field</section_header_level_1>
<section_header_level_1><location><page_21><loc_9><loc_83><loc_38><loc_84></location>A.1. ESO 499-G037 (UGCA 196)</section_header_level_1>
<text><location><page_21><loc_9><loc_74><loc_86><loc_81></location>ESO 499-G037 is a SAB(s)d spiral (de Vaucouleurs et al. 1991). It has very bright H ii regions and star formation activity, as seen in the GALEX image (de Paz et al. 2007). Fig. 16 shows the H i intensity map, superposed on an optical image. We see that the H i disk has a diameter of ∼ 12.5 ' , nearly 4 times the optical size (de Vaucouleurs et al. 1991). Because of the low spatial resolution of the KAT-7 data, these observations do not allow to derive a proper RC.</text>
<text><location><page_21><loc_9><loc_63><loc_86><loc_74></location>Fig. 17 shows the global profile of ESO 499-G037. From it, a systemic velocity of 953 ± 3 km s -1 is found, similar to the HIPASS determination of 954 ± 5 km s -1 (Koribalski et al. 2004) and the value of 955 ± 1 km s -1 determined by Barnes & de Blok (2001). Velocity widths of ∆V 50 = 184 ± 4 km s -1 and ∆V 20 = 200 ± 4 km s -1 are derived. A total flux of 51.7 ± 5.2 Jy km s -1 is measured, which is ∼ 25% larger than the HIPASS flux of 40.2 ± 4.2 Jy km s -1 but consistent with the value of 49 ± 2 Jy km s -1 from Barnes & de Blok (2001), also using the Parkes multi-beam system, or the Green Bank value of 48.4 ± 2.4 Jy km s -1 (Springob et al. 2005).</text>
<section_header_level_1><location><page_21><loc_9><loc_60><loc_40><loc_62></location>A.2. ESO 499-G038 & the H i cloud</section_header_level_1>
<text><location><page_21><loc_9><loc_52><loc_86><loc_59></location>ESO 499-G038 is a late-type Sc galaxy with, as can be seen in Fig. 18, a very extended H i component and a likely associated H i cloud to the NW, as shown by the faintest contour at 2.5 x 10 18 cm -2 . While the velocity field shows clear rotation, it is not possible to say more about the kinematics with the present data. Our spatial resolution is sufficient, however, to nearly resolve the two components in the global H i profile shown in Fig. 19.</text>
<text><location><page_21><loc_9><loc_43><loc_86><loc_52></location>We measured a systemic velocity of 871 ± 4 km s -1 for ESO 499-G038 and 912 ± 5 km s -1 for the H i cloud. These are surely better estimates then the values of 885 ± 5 km s -1 (Koribalski et al. 2004) and 888 ± 3 km s -1 (Barnes & de Blok 2001) given for the systemic velocity of ESO 499-G038 from their unresolved multi-beam profiles. Fluxes of 9.4 ± 0.9 and 1.5 ± 0.2 Jy km s -1 are measured for the galaxy and the cloud. This can be compared to 9.5 ± 2 (Koribalski et al. 2004) and 11.4 ± 1 Jy km s -1 (Barnes & de Blok 2001) from the unresolved Parkes' spectra.</text>
<figure>
<location><page_22><loc_10><loc_55><loc_47><loc_80></location>
<caption>Fig. 16.- KAT-7 data on ESO 499-G037. The H i emission is superposed on a DSS B image The contours are 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4 × 10 20 atoms cm -2 .</caption>
</figure>
<figure>
<location><page_22><loc_10><loc_16><loc_44><loc_42></location>
<caption>Fig. 17.- Global H i profile for ESO 499-G037.</caption>
</figure>
<figure>
<location><page_23><loc_9><loc_55><loc_45><loc_82></location>
<caption>Fig. 18.- KAT-7 data on ESO 499-G038. The H i emission of the galaxy and the cloud to the NW are superposed on a DSS B image. The contours are 0.025, 0.1, 0.2, 0.4, 0.8, 1.6 × 10 20 atoms cm -2 .</caption>
</figure>
<figure>
<location><page_23><loc_12><loc_16><loc_83><loc_42></location>
<caption>Fig. 19.- Global H i profile for ESO 499-G038 ( ∼ 870 km s -1 ) and the cloud to the NW ( ∼ 910 km s -1 ).</caption>
</figure>
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</document>
[
{
"title": "ABSTRACT",
"content": "H i observations of the Magellanic-type spiral NGC 3109, obtained with the seven dish Karoo Array Telescope (KAT-7), are used to analyze its mass distribution. Our results are compared to what is obtained using VLA data. KAT-7 is the precursor of the SKA pathfinder MeerKAT, which is under construction. The short baselines and low system temperature of the telescope make it sensitive to large scale low surface brightness emission. The new observations with KAT7 allow the measurement of the rotation curve of NGC 3109 out to 32 ' , doubling the angular extent of existing measurements. A total H i mass of 4.6 × 10 8 M /circledot is derived, 40% more than what was detected by the VLA observations. The observationally motivated pseudo-isothermal dark matter (DM) halo model can reproduce very well the observed rotation curve but the cosmologically motivated NFW DM model gives a much poorer fit to the data. While having a more accurate gas distribution has reduced the discrepancy between the observed RC and the MOdified Newtonian Dynamics (MOND) models, this is done at the expense of having to use unrealistic mass-to-light ratios for the stellar disk and/or very large values for the MOND universal constant a 0 . Different distances or H i contents cannot reconcile MOND with the observed kinematics, in view of the small errors on those two quantities. As for many slowly rotating gas-rich galaxies studied recently, the present result for NGC 3109 continues to pose a serious challenge to the MOND theory. Subject headings: techniques: interferometric - galaxies: individual: NGC 3109 - galaxies: kinematics and dynamics - galaxies: haloes - cosmology: dark matter",
"pages": [
1
]
},
{
"title": "KAT-7 Science Verification: Using H i Observations of NGC 3109 to Understand its Kinematics and Mass Distribution",
"content": "C. Carignan 1 , B. S. Frank, K. M. Hess, D. M. Lucero and T. H. Randriamampandry Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa and S. Goedhart and S. S. Passmoor SKA South Africa, The Park, Park Road, Pinelands, 7405, South Africa [email protected]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "On 2012 May 25, South Africa was awarded the construction of the mid-frequency array of the Square Kilometer Array (SKA), while Australia will build the low-frequency array. The SKA will consist of an ensemble of 3000 ∼ 15 m dishes of which 80% will constitute the core portion in the Karoo desert while the remaining antennae will extend all the way to the 8 African partner countries, namely Botswana, Ghana, Kenya, Madagascar, Mauritius, Mozambique, Namibia and Zambia. It is expected that the full SKA will be completed around 2025. A precursor array of 64 dishes, MeerKAT, is already under construction by South Africa and should be ready for science operation in 2016. In preparation for these two large projects, a pre-precursor array comprising 7 dishes, KAT-7, was completed in December 2010. While its main purpose is to test technical solu- tions for MeerKAT and the SKA, scientific targets such as NGC 3109 were also observed during commissioning to test the H i spectral line mode. In this paper, we compare over 100 hours of observations taken with KAT-7 to previously obtained VLA data and perform a thorough analysis of the mass distribution of NGC 3109. NGC3109is an SB(s)m galaxy (de Vaucouleurs et al. 1991) on the outskirts of the Local Group (van den Bergh 1994). It is even believed by certain authors to belong to the Local Group (e.g. Mateo 1998). While NGC 3109 looks like an Irregular galaxy on short exposures (Sandage 1961), it is clearly a spiral on longer exposures (Carignan 1985). Spiral arms are clearly visible, especially on the east side. This small spiral (scale length α -1 = 1.2 kpc) is a Low Surface Brightness (LSB) system with B (0) c = 23.17 (Carignan 1985). Its optical parameters are summarized in Table 1. One important parameter for mass modeling is the distance. Fortunately, because of its proximity, numerous Cepheids were observed in this Magellanic-type spiral, The most recent measurements are summarized in Table 2. For this study, we adopt a distance of 1.30 ± 0 . 02 Mpc (Soszy'nski et al. 2006). NGC 3109 is of significant scientific interest for two main reasons. Firstly, Jobin & Carignan (1990) used observations with the hybrid VLA DnC configuration (synthesized beam of 36 '' × 27 '' and velocity resolution of 10.3 km s -1 ) to perform a dynamical study of this galaxy, comparing the rotation curve (RC) derived from a tilted-ring analysis (see Sec. 3.4.1) to models composed of a luminous disk (stars & gas) and of a dark isothermal (ISO) halo (see Sec. 4.1.1). Such a mass model provides an excellent fit to this nearly solid-body type RC. Combining the H i RC with higher resolution H α kinematical data, Blais-Ouellette, Amram & Carignan (2001) also obtained a very good ISO Dark Matter (DM) model but a much less accurate fit for the cosmologically motivated NFW (Navarro, Frenk & White 1997) DM model. Recently, it was also shown that a MOdified Newtonian Dynamics (Milgrom 1983, 1988) model (MOND) could not reproduce the NGC 3109's RC (Randriamampandry 2013), at least with the data available. With our new data, it should be possible to compare DM (ISO and NFW) models to MOND (no dark matter) models and see ± if NGC 3109 really challenges the MOND theory. This is not the first time that NGC 3109 poses problems to MOND (see e.g. Sanders 1986; Begeman, Broeils & Sanders 1991). Secondly, Barnes & de Blok (2001) used 21cm Multibeam data with the Parkes 64m dish (beam ∼ 15.5 ' and velocity resolution of 1.1 km s -1 ) to study the environment of NGC 3109. They provide a compelling argument that the warp in the H i disk of NGC 3109 could be due to a dynamical encounter with the Antlia dwarf. This is also suggested by the elongation of the optical isophotes of NGC 3109 toward the south (Jobin & Carignan 1990) and those of Antlia in the direction of NGC 3109 (Penny et al. 2012). However, recent derivation of various merger and/or interaction parameters (e.g. asymmetry, clumpiness) by Pimbblet & Couch (2012) are consistent with Antlia being an undisturbed dwarf elliptical. In fact, despite its dSph appearance, Antlia is better classified as a dSph/dIrr transition type (Grebel, Gallagher & Harbeck 2003) because of its high H i content. With high sensitivity and mainly better spatial resolution observations (KAT-7 vs HIPASS), it should be possible to map much better the traces of that interaction, if it exists. An encounter/interaction that has significantly altered NGC3109's kinematics would give less weight to the finding that MOND cannot reproduce the rotation curve. The remainder of this paper is as follows. In Sec. 2, a description of the new radio interferometer KAT-7 is given. Sec. 3.1 describes in details the new H i data obtained with KAT-7, Sec. 3.2 those from the VLA-ANGST survey and Sec. 3.3 compares the different data sets. Sec. 3.4 derives the optimal RC that is used for the DM (ISO and NFW) and MOND models of Sec. 4. A discussion follows in Sec. 5 and a summary of the results and the final conclusions are given in Sec. 6.",
"pages": [
1,
2,
3
]
},
{
"title": "2. A New Radio Interferometer: KAT-7",
"content": "The seven-dish KAT-7 array, shown in Fig. 1, was built as an engineering testbed for the 64dish Karoo Array Telescope, known as MeerKAT, which is the South African pathfinder for the Square Kilometer Array (SKA). KAT-7 and MeerKAT are located close to the South African SKAcore site in the Northern Cape's Karoo desert region. KAT-7 is remotely controlled from Cape Town, some 800 km away from the site. Construction of the array started in early 2008 and was completed in December 2010, with 'first light' fringes obtained between two antennas in December 2009. The instrument is now in its science verification stage. The array is extremely compact, with baselines ranging between 26 m to 185 m. The KAT-7 layout was determined using the optimization algorithm described in de Villiers (2007), which determined a layout with a Gaussian UV distribution for a specified observation setting. The observation setting being optimized in this case was an 8 hour track (symmetric hour angle range), on a target at a -60 degree declination. The optimization objective was a Gaussian UV distribution at 1.4GHz, yielding a Gaussian synthesized beam with low sidelobes. Several randomly seeded layouts were generated and were evaluated for a set of observation options (time durations: snapshot, 4hr, 8hr, 12hr; declinations: 0, -30,-60, -90 degrees). The layout selected had the lowest sidelobes for the largest number of test observation settings considered. The antenna layout can be found at https://sites.google.com/a/ska.ac.za/public/kat7. The KAT-7 dishes have a prime-focus alt-az design with a F/D of 0.38, optimized for single-pixel L-band feeds. The low noise amplifiers (LNAs) for the feeds are cryogenically cooled to 80 K using Stirling coolers. The key system specifications for KAT-7 are summarized in Table 3. The digital backend of the system is an FPGA (Field Programmed Gate Array)-based, flexible packetised correlator using the Reconfigurable Open Architecture Computing Hardware (ROACH: https://casper.berkeley.edu/wiki/ROACH), which is a flexible and scalable system enabling spectral line modes covering a wide range of resolutions. Table 4 gives the details of the recently commissioned correlator modes. Digital filters give a flat bandpass over the inner 75% of the band with a rapid roll-off at the edges of the band. CASA ( Common Astronomy Software Applications ; McMullin et al. 2007) is the standard data reduction package being used for the reduction of the KAT-7 data and is anticipated to be used for MeerKAT.",
"pages": [
3,
4
]
},
{
"title": "3. H i Observations of NGC 3109",
"content": "The KAT-7 H i observations of NGC 3109 provide a unique opportunity to simultaneously achieve H i spectral-line science verification and an original scientific result. They complement the high spatial resolution ( ∼ 10 '' ) but small field of view ( ∼ 30 ' ) of the VLA-ANGST data (Ott et al. 2012) and the high sensitivity ( ∼ 10 17 cm -2 ) but low spatial resolution ( ∼ 15 . 5 ' ) Multibeam data (Barnes & de Blok 2001). With its short baselines and low system temperature (T sys ∼ 26K), KAT- 7 is very sensitive to low surface brightness and large scale H i emission, characteristic of the signal expected from NGC 3109.",
"pages": [
4
]
},
{
"title": "3.1. KAT-7 data on NGC 3109",
"content": "In order to observe the H i in both NGC 3109 and Antlia, plus possible signs of interaction between the two, a mosaic of 3 fields was obtained to have good sensitivity over a region of 1 . 5 o (EW) × 3 o (NS). The data was collected over 13 observing sessions between 2012 November 20 and 2012 December 26 using the c16n7M4k spectral line mode (Table 4) for a median of 11 hours in each session and a total of 122 h 43 m 56 s , including calibration. This yielded a total time on source of ∼ 25 hours for each pointing. The first three sessions were taken with 6 cold antennae, but the entire array was available for the remaining 10 observing sessions. The roughly 1 degree beam of KAT-7 is just large enough to image NGC 3109 in a single pointing. We used three pointings positioned in a straight line and extending slightly to the SE to mosaic the region between NGC 3109 and Antlia. The distance between pointings was chosen to give a uniform coverage between the phase centers. The c16n7M4k correlator mode gives velocity channels of 0.32 km s -1 over a flat bandpass of ∼ 1000 km s -1 , centered at 1417 MHz. The large bandwidth allows to collect H i data on background galaxies in the field. The basic data reduction was done in CASA 3.4.0 and 4.0.0. More advanced analysis was done using either AIPS (Greisen 2003), MIRIAD (Sault, Teuben & Wright 1995) and/or GIPSY (van der Hulst et al. 1992). To start with, the data was flagged in an automated way to discard data for shadowing and flux calibrators below 20 degrees in elevation. The data was additionally examined as a function of frequency and baseline, and flagged by hand. This testing of the HI spectral line mode led to the discovery of faint, very narrow, internally generated radio frequency interference (RFI) originating along the signal path, which has since been successfully eliminated in KAT-7 by the insertion of a low-pass filter. The RFI in our data is antenna dependent and only affects about 30 channels out of the central 3000 on three antennae. One of the primary goals of the science verification phase is exactly to identify these type of problems and correct for them. The standard interferometric data reduction strategy that has been employed for decades in AIPS and Miriad has been used. Each of the 13 observing sessions was reduced individually. Continuum subtraction was accomplished by selecting line free channels and using a first order fit. KAT7 does not use Doppler tracking, and CASA does not fully recognize frequency keywords, so special care was taken to produce image cubes with the proper velocity coordinates. This was a three steps process accomplished by: The calibration was applied and the three mosaic pointings were then SPLIT from the calibration sources. The data were averaged in time from 5 to 10 second integrations, and spectrally from 0.32 km s -1 to 1.28 km s -1 channels. All 13 data sets were then combined in CONCAT. The data was imaged using the mosaic mode and the multi-scale clean option. Three cubes were produced by applying natural (na), uniform (un), and neutral (ro: robust=0) weighting (Table 5) to the uv data. The robust=0 cube was cleaned interactively using a mask to select regions of galaxy emission by hand in each channel. After each major clean cycle, the mask was expanded to include regions of fainter galaxy emission. After a final mask was created, the cube was reproduced using the final mask in a non-interactive clean down to the noise threshold. All cubes and images were produced using the same mask derived from the robust=0 weighted cube. This provided a compromise between surface brightness sensitivity to large-scale emission and a low noise threshold, while mitigating confusion from sidelobes and low-level artifacts due to instrument calibration. In addition to NGC 3109, Antlia, ESO 499G037 and ESO 499-G038, an HI cloud which has no known optical counterpart was serendipitously discovered to the north of ESO 499-G038 at a similar velocity (Figure 2). The channels that contain this emission are remarkably clean and uniform in their noise characteristics. By contrast the channels which contain the brightest HI emission from NGC 3109 contain artifacts from sidelobes of the telescope's synthesized beam, which we have been unable to remove completely. The noise value in these channels is three times higher than elsewhere in the cube. For our analysis of NGC 3109, the cube produced with na weighting is used, except for the map showing the sum of all the channels (Figure 2) which used the ro weighting scheme. The parameters of the KAT-7 observations are summarized in Table 5. Fig. 2 shows the total intensity map for all the channels of the data cube. The lowest contour is at 1.0 x 10 19 atoms cm -2 . Besides NGC 3109 to the north and Antlia to the south, the two background galaxies ESO 499-G037 (10:03:42 -27:01:40; V sys = 953 km s -1 ) and ESO 499-G038 (10:03:50 -26:36:46; V sys =871 km s -1 ) are clearly visible. More details about these two systems will be given in the Appendix. As mentioned earlier, the small cloud between ESO 499-G038 and NGC 3109 has no obvious optical counterpart. However, it is clearly associated with ESO 499-G038 and not NGC 3109, being at a velocity > 900 km s -1 . The natural weighted cube is the best place to look for low-surface brightness emission between NGC 3109 and Antlia, but there is no obvious evidence of it there. In fact the elevated noise and strong sidelobes in the channels, which contain bright NGC 3109 data, prevent us from detecting lower surface brightness emission and limit what we can learn from smoothing the data. This work on NGC 3109 showed that better models of the KAT-7 primary beam are needed for calibration before we can go deeper. Fig. 3 shows the result of the moment analysis of the NGC 3109 data. It can be seen that the H i extends over nearly 1 o , more than 4 times the optical diameter ( D 25 ). The nearly parallel isovelocity contours, typical of a solid-body type rotation curve, are clearly visible, as well as the warp of the H i disk in the outer parts. The velocity dispersion map shows very well the gradient of σ from 15 km s -1 in the center down to 5 km s -1 at the edge of the disk. Fig. 4 gives the integrated H i profile for NGC 3109. Profile widths of ∆V 50 = 118 ± 3 km s -1 and ∆V 20 = 136 ± 3 km s -1 are derived. Since the H i distribution is clearly lopsided, with more gas on the approaching (SW) than on the receding side, we adopt the midpoint velocity of 404 ± 2 km s -1 as more representative of the systemic velocity than the intensity-weighted mean velocity. This can be compared to 404 km s -1 , ∆V 50 = 123 km s -1 and ∆V 20 = 137 km s -1 in Jobin & Carignan (1990). An integrated flux of 1142 ± 110 Jy km s -1 is measured which corresponds at our adopted distance of 1.3 Mpc to a H i mass of M H i = 4 . 6 × 10 8 M /circledot for a H i mass-to-luminosity ratio M H i /L B of 1.0, showing the gas-rich nature of NGC 3109. With a HPBW of the primary beam of nearly one degree and the short baselines available, no flux should be missed by these observations. Two methods of kinematical analysis will be used for the NGC 3109 data, namely an intensityweighted moment analysis and a Gauss-Hermite polynomial profile fit. With such high S/N data and low velocity gradient RC, not much difference is expected between the two types of analysis. As a result, the analysis yielding the smaller errors and the largest radius RC will be used for the mass model analysis in Sec. 4. The RCs are derived in Sec. 3.4.",
"pages": [
4,
5,
6,
7
]
},
{
"title": "3.2. VLA-ANGST data on NGC 3109 and Antlia",
"content": "NGC 3109 and Antlia were observed at the VLAas part of the VLA-ANGST survey (Ott et al. 2012). The galaxies were observed for ∼ 9 hours in BnA, ∼ 3 hours in CnB and ∼ 3 hours in DnC configurations giving access to scales from ∼ 6' to ∼ 15'. The hybrid configurations were used to get more circular beams for these two southern objects. The data were gridded with two different weighting functions: na weighting for maximum sensitivity and ro weighting for maximum spatial resolution (smaller synthesized beam). We use the ro weighted maps for NGC 3109 and the na weighted maps for Antlia. The parameters of the VLA observations are given in Table 6. Figure 5 shows the velocity field obtained with the ANGST data for NGC 3109. The nearly parallel contours are again clearly visible. From the H i emission map, we measure a total flux of 723 Jy km s -1 which, at our adopted distance, corresponds to a M H i = 2 . 9 × 10 8 M /circledot , which is nearly 40% less than the H i detected with KAT-7. Because the VLA is not sensitive to scales larger than 15 ' , the VLA-ANGST data will be missing some flux and their H i mass will be clearly underestimated for NGC 3109. In fact, the H i mass measured is exactly the same as that found by Jobin & Carignan (1990) with a VLA mosaic of two fields. So the problem with the VLA data is not as much the smaller HPBW of the antennae but more the lack of short baselines. The VLA-ANGST data, with its high spatial resolution, is much better suited to study the H i distribution in Antlia, since KAT-7 has barely two beamwidths across the object. Figure 6 gives the total H i emission map for Antlia, where the lowest contour corresponds to 3 . 0 × 10 19 atoms cm -2 . A total flux of 3 . 7 ± 0 . 4 Jy km s -1 is found which, at an adopted distance of 1 . 31 ± 0 . 03 Mpc (Pimbblet & Couch 2012), corresponds to a M H i = 1 . 50 ± 0 . 15 × 10 6 M /circledot . This time, most of the flux should have been detected since Antlia is much smaller than NGC 3109. However, this total flux is twice as much as that of the HIPASS data where Barnes & de Blok (2001) found 1 . 7 ± 0 . 1 Jy km s -1 and still 40% more than the value of 2 . 7 ± 0 . 5 Jy km s -1 found by Fouqu'e et al. (1990). The reason for this large difference is not clear. But since we do not have access to the raw data, it is difficult for us to investigate further. Figure 7 gives the integrated H i profile for Antlia. An integrated flux of 3 . 7 ± 0 . 30 Jy km s -1 is found, which is similar to the flux derived from the H i emission map. An intensity-weighted mean velocity of 360 ± 2 km s -1 is derived along with ∆V 50 = 23 ± 3 km s -1 and ∆V 20 = 33 ± 3 km s -1 . This can be compared to 362 ± 2 km s -1 and ∆V 20 = 30 ± 2 km s -1 for Barnes & de Blok (2001) and 361 ± 2 km s -1 ∆V 50 = 21 ± 4 km s -1 and a ∆V 20 = 33 ± 5 km s -1 for Fouqu'e et al. (1990).",
"pages": [
7,
8
]
},
{
"title": "3.3. Comparison of the different H i data sets",
"content": "The limiting surface densities of the different interferometric studies are given in Table 7. As far as the VLA data are concerned, one should not be surprised that the Jobin & Carignan (1990) data go deeper than the ANGST data since they are a mosaic of 2 fields with the same observing time in DnC configuration than the single field ANGST data. The 1.3 km s -1 resolution ANGST data is useful for comparisons with the Jobin & Carignan (1990) 10.3 km s -1 resolution data in the inner regions of NGC 3109. But mainly, that data provide more information on the H i distribution of Antlia, for which the KAT-7 data is of too low spatial resolution. × In view of the surface densities limits, we see that while both the KAT-7 and the Jobin & Carignan (1990) reach 1 . 0 × 10 19 cm -2 , the KAT-7 data covers a larger area since it is sensitive to large scales invisible to the VLA. As for the Barnes & de Blok (2001) data reaching the much lower surface densities of 2 . 0 × 10 17 cm -2 , they provide the largest detected size (85 ' x 55 ' ). However, this increase in size may be due partly to the large ∼ 15.5 ' HIPASS beam. The H i mass estimates of both the single dish and the interferometric observations can be found in Table 8. The first thing to notice is the larger mass obtained by the single dish observations compared to the aperture synthesis ones, the only exception being the Whiteoak & Gardner (1977) data which come from a single pointing of the Parkes 64 m radio telescope. With a ∼ 15 ' beam, necessarily a lot of the flux extending over ∼ 1 o has been missed. For the others, the discrepancies can be explained by either the way the multi-pointing data have been combined or most likely that the correction for self-absorption that most of these authors have applied has been overestimated. No such correction has been applied to the synthesis data. As for the synthesis data, we see that both sets of VLA data agree exactly. We would have expected some more flux from the deeper Jobin & Carignan (1990) data but since most of the flux is in the bright central components, the difference is probably just of the order of the errors. On the other hand, both the KAT-7 data and the HIPASS data agree very well which is surely indicative that, in both cases, no flux is missed. Because both those data sets see all the scales, they detect nearly 40% more flux than the VLA, which do not have the proper short spacings . ± to see scales larger than 15 ' .",
"pages": [
8,
9
]
},
{
"title": "3.4. Derivation of the optimal RC",
"content": "The same method is used to derive the RC for both the VLA-ANGST and the KAT-7 data sets. For this study, we used the implementation of the tilted ring model in the GIPSY task ROTCUR (Begeman 1989).",
"pages": [
9
]
},
{
"title": "3.4.1. Tilted Ring Models",
"content": "A set of concentric rings is used to describe the motion of the gas in the galaxy. The gas is assumed to be in circular motion. Each ring is characterized by a set of 5 orientation parameters, namely: a rotation centre ( x c , y c ), a systemic velocity V sys , an inclination i , a Position Angle PA and by a rotation velocity V C . Naturally, the rotation centre ( x c , y c ) and the systemic velocity V sys should be the same for all the rings but i and PA will vary if the H i disk is warped. The line of sight velocity at any ( x, y ) position in a ring with radius R is given by where θ is the position angle with respect to the receding major axis measured in the plane of the galaxy. θ is related to the actual PA in the plane of the sky by (3) A | cosθ | weighting function and an exclusion angle of ± 15 deg about the minor axis have been used to give maximum weight to the velocity points close to the major axis and minimize the influence of large deprojection errors close to the minor axis in view of the large inclination of the galaxy. The width of the rings has been matched to the synthesized beam size to make sure that the velocity points are independent. The method consists at finding for each ring the best set of the 5 orientation parameters ( x c , y c ), V sys , i and PA which minimizes the dispersion of V C inside the ring. The following procedure is followed: The errors on V C will be the quadratic sum of the dispersion σ in each ring and half the difference between the approaching and the receding sides: Since the mass models assume an axisymmetric system, we think that this way of calculating the errors is more representative of the true uncertainties, when comparing the RC to the model.",
"pages": [
9,
10
]
},
{
"title": "3.4.2. VLA-ANGST RC",
"content": "For the derivation of the kinematics of NGC 3109, we use the ro-weighted VLA-ANGST data. We find that the rotation center is coincident with the optical center and derive a systemic velocity V sys = 402 km s -1 . By keeping those parameters fixed, we then fitted i and PA . The solutions for the whole galaxy and separately for the approaching and receding sides are shown in Fig. 8, along with a comparison with Jobin & Carignan (1990) in Fig. 9 . We see that the warp which starts around the Holmberg radius ( R HO ), is more important on the approaching (SW) side and that the RC from both VLA datasets agree very well, despite the difference in velocity resolutions (1.3 km s -1 vs 10.3 km s -1 ). Because Jobin & Carignan (1990) provide asymmetric drift corrections, their RC will be used for the mass models in Sec. 4.",
"pages": [
10
]
},
{
"title": "3.4.3. KAT-7 RC",
"content": "Fig. 10 shows the tilted-ting model for the intensity-weighted moment analysis of the KAT7 na-weighted data of NGC 3109. We find V sys = 405 ± 2 km s -1 , PA ∼ 96 o ± 4 and i ∼ 61 o ± 8. The rotation center is found to be ∼ 0.5 ' North from the optical center at 10 h 03 m 06.9 s - 26 o 08 ' 58 '' . This offset from the optical center is not significant and could be due to the larger synthesized beam of KAT-7. It can be seen that the agreement between the approaching and receding sides is much better than for the VLA-ANGST data. The increase in sensitivity allows us to extend the RC out to ∼ 32 ' ( ∼ 12 kpc). Despite the low spatial resolution, no real sign of beam smearing is seen when comparing this RC to the VLA data. This may not be surprising in view of the solid-body nature of the RC. Fig. 11 shows the tilted-ting model for the Gauss-Hermite polynomials profile fitting analysis of the KAT-7 na-weighted data. The kinematical parameters found are very similar to those of the moment analysis with V sys = 406 km s -1 , PA ∼ 97 o and i ∼ 61 o and the same rotation center. The Gauss-Hermite polynomials are fitted to the spectra in each pixel, where the peak of the fitted profile rises above 5-sigma. As such, profiles from very faint emission at the edge of the galaxy are not strong enough to ensure a good fit. GaussHermite fits will therefore fail at large radii where the average signal-to-noise is lower than the cutoff. Lowering the cutoff produces too many bad velocity points. Therefore, since the RC using this technique is only defined out to 24 ' , the moment analysis RC is preferred for the mass models in Sec.4.",
"pages": [
10,
11
]
},
{
"title": "3.4.4. Asymmetric drift corrections",
"content": "In the case of a galaxy like NGC 3109, where the velocity dispersion represents a substantial frac- tion of the rotational velocity ( σ/V max ≥ 15 -20%) and thus provides part of the gravitational support, a correction for asymmetric drift must be applied. Following the procedure used by Cˆot'e, Carignan & Freeman (2000), the corrected circular velocity is given by where V c is the corrected velocity, V o is the observed one, σ is the velocity dispersion and Σ is the gas surface density. The asymmetric drift corrections are uncertain by about 25% (Lake & Skillman 1989).",
"pages": [
11,
12
]
},
{
"title": "4. Mass models analysis",
"content": "Low mass Surface Density (LSD) galaxies are galaxies whose mass profiles are dominated by dark matter (DM) at all galactocentric radii. LSD properties were first identified in dwarf Irregular (dIrr) galaxies (such as the prototype dIrr DDO 154: Carignan & Freeman 1988; Carignan & Purton 1998) and later in late-type dwarf spirals (see e.g. NGC 5585: Cˆot'e, Carignan & Sancisi 1991). Despite the uncertainties on the exact M/L ratio of the luminous disk, LSD galaxies, such as NGC 3109, are clearly DM dominated at all radii. For that reason, they can be used to constrain important properties of dark matter haloes, such as the characteristic scale density and radius, concentration, virial mass and the exact shape of the mass density profile. Ultimately, measuring the dark matter distribution of these galaxies is necessary if one wants to test the results obtained by numerical simulations of galaxy evolution in the framework of the Cold Dark Matter (CDM) paradigm (Navarro, Frenk & White 1997) or test alternative gravity theories such as MOND (Milgrom 1983). The study of their mass distribution has generated in the last 15 years the so-called cusp-core controversy: are rotation curves of LSD galaxies better reproduced by a cuspy halo as seen in the ΛCDM numerical simulations or by a halo with a nearly constant central density core as seen in most high spatial resolution observations (e.g. Blais-Ouellette, Amram & Carignan 2001; de Blok, McGaugh & Rubin 2001; Marchesini et al. 2002). A good review of this debate can be found in de Blok (2010). Nowadays, galaxies are expected to form inside cuspy Cold Dark Matter halos. High resolution velocity fields have provided important observational constraints on the dark matter distribution in LSD galaxies. These two-dimensional data show clearly that dark matter-dominated galaxies tend to be more consistent with cored than cuspy halos, at odds with the theoretical expectations. So, a lot of efforts in the last few years has gone into identifying the physical processes that could have turned initially cuspy DM halos into cored ones (Governato et al. 2012; Pontzen & Governato 2012; Kuzio de Naray & Spekkens 2011; Kuzio de Naray et al. 2010; Governato et al. 2010). For example, one recently suggested solution to this problem is to enforce strong supernovae outflows that move large amounts of lowangular-momentum gas from the central parts and that pull on the central dark matter concentration to create a core (Famaey & McGaugh 2013).",
"pages": [
12,
13
]
},
{
"title": "4.1.1. The pseudo-isothermal DM model (ISO)",
"content": "The pseudo-isothermal DM halo is an observationally motivated model with a constant central density core. The density profile is given by: where ρ 0 is the central density and R c the core radius 1 . The corresponding rotation velocities are given by: We can describe the steepness of the inner slope of the mass density profile with a power law ρ ∼ r α . In the case of the ISO halo, where the inner density is an almost constant density core, α = 0.",
"pages": [
13
]
},
{
"title": "4.1.2. The Navarro, Frenk and White DM model (NFW)",
"content": "The NFW profile, also known as the 'universal density profile' (Navarro, Frenk & White 1997) is the commonly adopted dark matter halo profile in the context of the ΛCDM cosmology. It was derived from N-body simulations. The density profile is given by: where R S is the characteristic radius of the halo and ρ i is related to the density of the universe at the time of collapse of the dark matter halo.The corresponding rotation velocities are given by: where x = R/R 200 . It is characterized by a concentration parameter c = R 200 /R S and a velocity V 200 . The radius R 200 is the radius where the density contrast with respect to the critical density of the universe exceeds 200, roughly the virial radius (Navarro, Frenk & White 1996). The characteristic velocity V 200 is the velocity at that radius. The NFW mass density profile is cuspy in the inner parts and can be represented by ρ ∼ r α , where α = -1.",
"pages": [
13
]
},
{
"title": "4.2. ISO & NFW Models for NGC 3109",
"content": "Because of the way the different velocity points are weighted in the mass model fitting algorithm, we will not combine the high spatial resolution VLA data (Jobin & Carignan 1990) with the low spatial resolution but high sensitivity KAT-7 data. Instead, we will run a set of models for each data set. The radial surface density profile of each data set will still be used, keeping in mind that the VLA data underestimate the H i content, which will not be the case for the KAT-7 data. The I band luminosity profile of Jobin & Carignan (1990) is preferred to IR (e.g. 2.6 µ m) profiles because it extends to much larger radii. NGC 3109 presents an interesting test for the DM models. Because it has no bulge and a very shallow velocity gradient, it is an ideal system to address the cusp-core controversy. The DM models are shown in Fig. 12 for the Jobin & Carignan (1990) data and in Fig. 13 for the KAT-7 data. The results are summarized in Table 11. It can be seen that the ISO models fit almost perfectly the observed RC with a reduced χ 2 of only 0.24 for the VLA data and 0.31 for the KAT-7 data. On the other hand, the NFW model has much less success with a reduced χ 2 =12.9 for the VLA data and 0.86 for the KAT-7 data. However, because of the low spatial resolution, the KAT-7 data do not probe the very inner parts where the discrepancy with the observations is expected to be the greatest. The NFW model completely fails in the inner 1 kpc, overestimating the first velocity point by a factor of two for the VLA data. However, the main problem with the NFW models is that the best fits to both the VLA and the KAT-7 data suggest a M/L of 0 for the stellar disk, which is unphysical. This is understandable since any stellar disk com- ponent would just increase the discrepancy in the inner parts. On the other hand, the best fit ISO model has (M/L) I =0.55-0.76 which is quite compatible with the value predicted by stellar popula- tion models of 0.67 ± 0.04 (Bell & de Jong 2001) for the I band. Without any doubt, in the DM halo paradigm, those results confirm that NGC 3109 has a cored and not a cuspy halo.",
"pages": [
13,
14,
15
]
},
{
"title": "4.3. MOND models",
"content": "MOND was proposed by Milgrom (1983) as an alternative to dark matter. Milgrom postulated that at small accelerations the usual Newtonian dynamics break down and the law of gravity needs to be modified. MOND has been claimed to be able to explain the mass discrepancies in galaxies without dark matter (e.g. Begeman, Broeils & Sanders 1991; Sanders 1996; Bottema et al. 2002). Therefore, in the MOND formalism, only the contributions of the gas component and of the stellar component are required to explain the observed rotation curves. The transition between the Newtonian and the MONDian regime is characterized by an acceleration threshold value called a 0 below which MOND should be used. So, in the MOND framework, the gravitational acceleration of a test particle is given by : where g is the gravitational acceleration, a 0 is a new universal constant which should be the same for all galaxies, µ (x) is the MOND interpolating function and g N the Newtonian acceleration. The standard and simple interpolating functions are mostly used in the literature. The standard µ -function is the original form of the interpolating function proposed by Milgrom (1983). However, Zhao & Famaey (2006) found that a simplified form of the interpolating function not only provides also good fits to the observed rotation curves but the derived mass-to-light ratios are more compatible with those obtained from stellar populations synthesis models. 4.3.1. MOND models using the 'standard' interpolation function The standard interpolating function is given as For x /lessmuch 1 the system is in deep MOND regime with g = ( g N a 0 ) 1 / 2 and for x /greatermuch 1 the gravity is Newtonian. The MOND rotation curve becomes: where V b , V d , V g are the contributions from the bulge, the disk and the gas to the rotation curve. In the case of the Magellanic-type spiral NGC 3109, there is no bulge to consider. 4.3.2. MOND models using the 'simple' interpolation function The simple interpolating function is given by Using the same procedure as in previous section we can easily obtain the corresponding rotation velocities:",
"pages": [
15
]
},
{
"title": "4.4. MOND Models for NGC 3109",
"content": "NGC 3109 presents an interesting test for MOND. As we have seen, it is close enough to have a very accurate distance determination using Cepheids and the largest portion of the luminous mass is in the form of gas and not stars, partly freeing us from the uncertainties due to the M/L value used for the disk. The internal accelerations are very low, therefore the galaxy is completely within the MOND regime (Lake 1989). The MOND mass models for the VLA data are presented in Fig. 14 & Table 12 and in Fig. 15 & Table 13 for the KAT-7 data, for both the standard value of a 0 , namely 1.21 x 10 -8 cm sec -2 (Begeman, Broeils & Sanders 1991) and with a 0 left as a free parameter. The standard and the simple interpolation functions are also illustrated. In the case of the VLA data, the fits are poor for all the cases: they overestimate the velocities in the inner parts and they underestimate them in the outer parts. The reduced χ 2 are much larger than for the DM fits, varying from 5.5 to 12. However, since most of the luminous mass is in gas and since the VLA misses 40% of the flux, we should not expect good fits. The MOND models have more significance for the KAT-7 data than for the VLA data, since we probe the gas on all scales. In this case we see that for the standard fixed value of a 0 = 1.21 x 10 -8 cm sec -2 , the results of the models are poor with reduced χ 2 of 3.0 to 3.4 and (M/L) B values 3 to 4 times larger than the value predicted by stellar population models. However, we see that if a 0 is free to vary, we get more reasonable fits with reduced χ 2 down to 1.30 and 1.37, still 4-5 times larger than for the DM ISO models. The main problems with those models are the very small (M/L) I values, 2 to 3 times smaller than the expected values and the large values of the constant a 0 which is greater than a factor of 2 compared to the standard value.",
"pages": [
15,
16
]
},
{
"title": "5. Discussion",
"content": "We will now examine different questions that were raised by this study. The first one is the difference found between the kinematic inclination and the photometric values. This is an important point to understand since i scales the RC and is responsible for the velocity gradient of the rising part of the RC, which really constrains the mass models and set the M/L ratio of the luminous disk. Both tilted-ring models using the intensityweighted and the profile fitting techniques find the same inclination of i = 61 o . It is important to understand how this parameter is determined. Assuming an axisymmetric disk, the tilted-ring model tries to find the value that minimizes the dispersion of the velocities in the rings. On the other hand, looking at Table 14, it can be seen that the inclination varies from 78.5 o in B to 73.5 o in I and 69.5 o in the 3.6 µ m. What is going on is quite clear. Each photometric band samples different stellar populations. The B-band samples the young blue Pop I stars which are confined to the thin disk, the I-band samples a mixture of young and old Pop I stars which are in a thicker disk while the 3.6 µ m is completely dominated by an old disk population in an even thicker disk. This explains that progression of the inclination from ∼ 80 o to ∼ 70 o . It is instructive to look at the ellipse fits to the H i isophotes. As can be seen in Table 15, NGC 3109 is really composed of 2 disks: an inner one, corresponding to the optical disk, with i ∼ 76 o , which is the mean of the B and I inclinations and an outer disk with i ∼ 63 o which, within the errors, agree with the kinematical inclination. The double disk is quite apparent when looking at the H i isophotes in Fig. 2. Therefore, since the photometric inclination is most sensitive to the emission of the stellar populations being traced, it is quite clear that the kinematic inclination should be preferred. The photometric values should only be used as starting values in the tilted-ring modeling. Another point worth discussing is beam-smearing. With such a large synthesized beam ∼ 4 ' , one would have expected beam smearing to be quite important. However when looking at Figures 10 and 11, this does not seem to be the case. As explained in Carignan (1985), beam smearing is ± References. - (1) Carignan (1985); the result of the convolution of the Gaussian beam with the H i distribution and the velocity gradient across the beam. If the H i distribution is steep and/or the velocity gradient is large, the net effect will be to underestimate the observed velocity or conversely to overestimate the effective radius (the product of the convolution) that is observed. In the case of NGC 3109, the H i distribution is fairly flat across the beam and the velocity gradient of that galaxy is very small. Those two properties render the beam smearing negligible. Should we be observing another galaxy with a step velocity gradient and/or a steep radial H i distribution, beam smearing would be important. Let us now turn to the mass models. First, the results of the DM ISO models for both RCs confirm the previous results that it provides an almost perfect fit to the observed kinematics with the difference that the KAT-7 model has a more massive H i disk. As expected, this translates in a smaller stellar disk M/L value for the KAT-7 data. In both cases, the mass-to-light ratio found for the disk is compatible with population synthesis models. The NFW models again fail to reproduce the kinematics. In the inner kpc, the velocities are overestimated by a large factor, despite an unphysical M/L ratio of 0 for the stellar disk. In the DM halo paradigm, clearly NGC 3109 has a cored and not a cuspy halo, at least at the present epoch. What about the MOND models ? Twenty-five years ago, Sanders (1986) pointed out that the MOND mass of NGC 3109 predicted using Milgrom's suggested value for a 0 was 5 x 10 8 M /circledot , thus larger than the H i mass using the larger distance estimates known at the time between 1.7 to 2.6 Mpc (Carignan 1985). This is not the case anymore with the smaller well determined distance of 1.3 Mpc, but still our determined H i mass with KAT-7 is less than 10% smaller than this MOND mass, which implies unphysically small M/L values for the stars in the case where the fits have been improved letting the constant a 0 free to vary. When Begeman, Broeils & Sanders (1991) produced a MOND model using the Jobin & Carignan (1990) VLA data, they argued that they could not get a good fit because the VLA data was missing a substantial part of the flux and that the H i mass had to be multiplied by 1.67 to get a reasonable fit. However, since the KAT-7 data retrieve all the NGC 3109 flux, this cannot be used as an argument with the present data which convincingly show that MOND cannot reproduce the observed kinematics of NGC 3109 with physically acceptable parameter values. Unless some other explanation can be found, the KAT-7 data surely challenge the MOND theory. What about the possible interaction between the Magellanic-type spiral NGC 3109 and the dIrr/dSph Antlia, suggested by the H i isophotes being slightly elongated ? The high surface brightness sensitivity of the KAT-7 observations allow us to trace the lopsidedness of NGC 3109 to larger radii, however there is no further obvious evidence of an interaction with Antlia, leaving the question open for further investigation. NGC 3109 has a systemic velocity of 404 km s -1 while Antlia has 360 km s -1 . Aparicio et al. (1997) calculated the physical separation between NGC 3109 and Antlia to be between 29 and 180 kpc, with a maximum separation of 37 kpc for the pair to be bound. The situation for the Local Group dwarfs can guide us. Grcevich & Putman (2009) showed clearly that the majority of dwarf galaxies within 270 kpc of the Milky Way or Andromeda are undetected in H i ( < 10 4 M /circledot for the Milky Way dwarfs), while those further than 270 kpc are predominantly detected with masses 10 5 to 10 8 M /circledot (Antlia has an H i mass of ∼ 10 6 M /circledot ) meaning the nearby ones must have been stripped of their gas. While the halo of NGC 3109 is not as large as the Milky Way halo, if a close encounter had happened in the past, it is quite likely that Antlia would also have been stripped of its gas. Nevertheless, some kind of interaction really seems to have taken place, as shown by the H i isophotes of the two galaxies pointing toward each other. However, in view of the large difference in masses between the two systems and the absence of any external traces of such an interaction, it is believed that the internal kinematics of NGC 3109 cannot have been severely altered. Anyway, if such an interaction did take place, it would be more the rule than the exception. Massive galaxies usually have a significant population of gas-rich dwarf companions and interaction with these will show kinematic and morphological signatures in the extended HI disks (Mihos et al. 2012) such as warps, plumes, tidal tails, high-velocity clouds (e.g. Hibbard et al. 2001; Sancisi et al. 2008) or even stellar streams (Lewis et al. 2013). Galaxies are said to be embedded in the cosmic web, seen in the ΛCDM numerical simulations (Springel, Frenk &White 2006). Such signatures of interaction have been studied close to massive galaxies such as the interconnecting network in the M81/M82 system (Yun, Ho & Lo 1994) or the tidal tail in the Leo triplet (Haynes, Giovanelli & Roberts 1979). More recently, Mihos et al. (2012) using the Green Bank Telescope (GBT) found a plume in the outer disk of M101 with a peak column density of 5 x 10 17 cm -2 and two new H i clouds close to that plume with masses of ∼ 10 7 M /circledot . While KAT-7 would not have detected such low column densities, it is interesting to look at our detection cloud mass limit. To calculate a characteristic H i mass sensitivity, we assume that low-mass clouds would be unresolved in our beam and use the relation (Mihos et al. 2012): where D is the distance, σ s is the rms noise in one channel and ∆ V is the channel width. This means that our 3 σ cloud mass detection limit is around 5-6 x 10 3 M /circledot at the distance of NGC 3109. We should thus have easily detected similar clouds like the ones observed around M101, if they had been present.",
"pages": [
17,
18,
19
]
},
{
"title": "6. Summary and conclusions",
"content": "The first H i spectral line observations with the prototype radio telescope KAT-7 have been presented. The high sensitivity of KAT-7 to large scale, low column density emission comes not only from its compact configuration, but also from its very low T sys receivers. With ∼ 25 hours of observations per pointing, surface densities of 1.0 x 10 19 atoms cm -2 were reached, which could be improved when the telescope will be fully commissioned, since the theoretical noise was not reached with the present dataset. The main results from this study are: x 27 ' (NS) down to a limiting column density of 1.0 x 10 19 atoms cm -2 . RCs of both the Jobin & Carignan (1990) and the KAT-7 data while a cosmologically motivated NFW model gives a much poorer fit, especially in the very inner parts. Because of the high spatial and velocity resolutions data available and the very small errors on those velocities, this cannot be attributed to poor data. NGC 3109 definitely has a cored and not a cuspy DM halo. testbed for MeerKAT and the SKA such that any scientific result that can be obtained is a bonus. While most of the extragalactic H i sources would be unresolved by the ∼ 4 ' synthesized beam, many projects such as this one on NGC 3109 can be done on nearby very extended objects such as Local Group galaxies or galaxies in nearby groups like Sculptor. We thank all the team of SKA South Africa for allowing us to get scientific data during the commissioning phase of KAT-7 and are grateful to the ANGST team for making their reduced VLA data publicly available. CC's work is based upon research supported by the South African Research Chairs Initiative (SARChI) of the Department of Science and Technology (DST), the Square Kilometer Array South Africa (SKA SA) and the National Research Foundation (NRF). The research of BF, KH, DL & TR have been supported by SARChI, SKA SA and National Astrophysics and Space Science Programme (NASSP) bursaries. Our findings for NGC 3109 are not an isolated case. Recently, S'anchez-Salcedo, Hidalgo-Gamez & Martinez-Garcia (2013) studied a sample of slowly rotating gasrich galaxies in the MOND framework. These are again galaxies in the full low acceleration MOND regime. They found at least five such systems (especially NGC 4861 and Holmberg II) that deviate strongly from the MOND predictions, unless their inclinations and distances differ strongly from the nominal values. In the case of NGC 3109, those two parameters are much more constrained which makes it harder to reconcile MOND with the ob- served kinematics. Those observations obtained with KAT-7 have shown that despite its relatively small collecting area (7 x 12 m antennae), this telescope really has a niche for detecting large scale low emission over the ∼ 1 o FWHM of its antennae. It should be kept in mind that this telescope was built primarily as a",
"pages": [
19,
20
]
},
{
"title": "A.1. ESO 499-G037 (UGCA 196)",
"content": "ESO 499-G037 is a SAB(s)d spiral (de Vaucouleurs et al. 1991). It has very bright H ii regions and star formation activity, as seen in the GALEX image (de Paz et al. 2007). Fig. 16 shows the H i intensity map, superposed on an optical image. We see that the H i disk has a diameter of ∼ 12.5 ' , nearly 4 times the optical size (de Vaucouleurs et al. 1991). Because of the low spatial resolution of the KAT-7 data, these observations do not allow to derive a proper RC. Fig. 17 shows the global profile of ESO 499-G037. From it, a systemic velocity of 953 ± 3 km s -1 is found, similar to the HIPASS determination of 954 ± 5 km s -1 (Koribalski et al. 2004) and the value of 955 ± 1 km s -1 determined by Barnes & de Blok (2001). Velocity widths of ∆V 50 = 184 ± 4 km s -1 and ∆V 20 = 200 ± 4 km s -1 are derived. A total flux of 51.7 ± 5.2 Jy km s -1 is measured, which is ∼ 25% larger than the HIPASS flux of 40.2 ± 4.2 Jy km s -1 but consistent with the value of 49 ± 2 Jy km s -1 from Barnes & de Blok (2001), also using the Parkes multi-beam system, or the Green Bank value of 48.4 ± 2.4 Jy km s -1 (Springob et al. 2005).",
"pages": [
21
]
},
{
"title": "A.2. ESO 499-G038 & the H i cloud",
"content": "ESO 499-G038 is a late-type Sc galaxy with, as can be seen in Fig. 18, a very extended H i component and a likely associated H i cloud to the NW, as shown by the faintest contour at 2.5 x 10 18 cm -2 . While the velocity field shows clear rotation, it is not possible to say more about the kinematics with the present data. Our spatial resolution is sufficient, however, to nearly resolve the two components in the global H i profile shown in Fig. 19. We measured a systemic velocity of 871 ± 4 km s -1 for ESO 499-G038 and 912 ± 5 km s -1 for the H i cloud. These are surely better estimates then the values of 885 ± 5 km s -1 (Koribalski et al. 2004) and 888 ± 3 km s -1 (Barnes & de Blok 2001) given for the systemic velocity of ESO 499-G038 from their unresolved multi-beam profiles. Fluxes of 9.4 ± 0.9 and 1.5 ± 0.2 Jy km s -1 are measured for the galaxy and the cloud. This can be compared to 9.5 ± 2 (Koribalski et al. 2004) and 11.4 ± 1 Jy km s -1 (Barnes & de Blok 2001) from the unresolved Parkes' spectra.",
"pages": [
21
]
},
{
"title": "REFERENCES",
"content": "McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. 2007, Astronomical Data Analysis Software and Systems XVI, 376, 127 Mihos, J. C., Keating, K.M., Holley-Bockelmann, K., Pisano, D. J., & Kassim, N. E. 2012, ApJ, 761, 186 Milgrom, M. 1983, ApJ, 270, 365 Milgrom, M. 1988, ApJ, 333,689 Musella, I., Piotto, G., & Capaccioli, M. 1997, AJ, 114, 976 Navarro J. F., Frenk C. S., & White S. D. M. 1996, ApJ, 462, 563 Navarro J. F., Frenk C. S., & White S. D. M. 1997, ApJ, 490, 493 Ott, J. et al. 2012, AJ, 144, 123 Penny, S. J., Pimbblet, K. A., Conselice, C. J., Brown, M. J. I., Grtzbauch, R., & Floyd, D. J. E. 2012, ApJ, 758, 32 Pietrzy'nski, G. et al. 2006, ApJ, 648, 366 Pimbblet, K. A., & Couch, W. J. 2012, MNRAS, 419, 1153 Pontzen, A., & Governato, F. 2012, MNRAS, 421, 3464 Randriamampandry, T. H. 2013, Msc thesis, University of Cape Town S'anchez-Salcedo, F. J., Hidalgo-G'amez, A. M., & Mart'ınez-Garc'ıa, E. E. 2013, AJ, 145, 61 Sancisi, R., Fraternali, F., Oosterloo, T., & van der Hulst, T. 2008, A&AR, 15, 189 Sandage, A. 1961, The Hubble Atlas of Galaxies, (Washington: Carnegie Institution), p. 39 Sanders, R. H. 1986, MNRAS, 223, 539 Sanders, R. H. 1996, ApJ, 473, 117 Sault R. J., Teuben P. J., & Wright M. C. H. 1995. In Astronomical Data Analysis Software and Systems IV, ed. R. Shaw, H.E. Payne, J.J.E. Hayes, ASP Conference Series, 77, 433 Skillman, E. D., Bothun, G. D., Murray, M. A., & Warmels, R. H. 1987, A&A, 185, 61 Soszy'nski, I., Gieren, W., Pietrzy'nski, G., Bresolin, F., Kudritzki, R.-P., & Strom, J. 2006, ApJ, 648, 375 Springob, C. M., Haynes, M. P., Giovanelli, R., & Kent, B. R. 2005, ApJS, 160, 149 van Damme, K. J. 1966, Aust. J. Phys, 19, 687 van der Hulst, J. M., Terlouw, J. P., Begeman, K., Zwitser, W., & Roelfsema, P.R. 1992, in ASP Conf. Ser., Vol. 25, P. 131 van den Bergh, S. 1994, AJ, 107, 1328 Springel, V., Frenk, C. S., & White, S. D. M. 2006, Nature, 440, 1137 Whiteoak, J. B., & Gardner, F. F. 1977, Aust. J. Phys, 30, 187 Yun, M. S., Ho, P. T. P., & Lo, K. Y. 1994, Nature, 372, 530 Zhao, H. S., & Famaey, B. 2006, ApJ, 638, L9",
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}
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2013AJ....146...66W
https://arxiv.org/pdf/1307.0881.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_85><loc_86><loc_86></location>Optical and Near-Infrared Shocks in the L988 Cloud Complex</section_header_level_1>
<section_header_level_1><location><page_1><loc_44><loc_81><loc_56><loc_82></location>J. Walawender</section_header_level_1>
<text><location><page_1><loc_17><loc_78><loc_83><loc_79></location>Subaru Telescope, National Astronomical Observatory of Japan, Hilo, HI 96720</text>
<text><location><page_1><loc_43><loc_74><loc_57><loc_76></location>[email protected]</text>
<text><location><page_1><loc_45><loc_71><loc_55><loc_72></location>B. Reipurth</text>
<text><location><page_1><loc_20><loc_68><loc_80><loc_69></location>Institute for Astronomy, University of Hawaii at Manoa, Hilo, HI 96720</text>
<text><location><page_1><loc_48><loc_64><loc_52><loc_66></location>and</text>
<section_header_level_1><location><page_1><loc_47><loc_61><loc_53><loc_62></location>J. Bally</section_header_level_1>
<text><location><page_1><loc_12><loc_58><loc_88><loc_59></location>Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80309</text>
<section_header_level_1><location><page_1><loc_44><loc_53><loc_56><loc_55></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_39><loc_83><loc_50></location>We have searched the Lynds 988 dark cloud complex for optical (H α and [S ii ]) and near-IR (H 2 2.12 µ m) shocks from protostellar outflows. We find 20 new Herbig-Haro objects and 6 new H 2 shocks (MHO objects), 3 of which are cross detections. Using the morphology in the optical and near-IR, we connect several of these shocks into at least 5 distinct outflow systems and identify their source protostars from catalogs of infrared sources.</text>
<text><location><page_1><loc_17><loc_29><loc_83><loc_38></location>Two outflows in the cloud, from IRAS 21014+5001 and IRAS 21007+4951, are in excess of 1 pc in length. The IRAS 21007+4951 outflow has carved a large cavity in the cloud through which background stars can be seen. Also, we have found an optical shock which is the counterflow to the previously discovered 'northwest outflow' from LkH α 324SE.</text>
<text><location><page_1><loc_17><loc_22><loc_83><loc_26></location>Subject headings: ISM: Herbig-Haro objects - ISM: jets and outflows - ISM: individual (Lynds 988) - stars: formation</text>
<section_header_level_1><location><page_1><loc_42><loc_16><loc_58><loc_17></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_10><loc_88><loc_14></location>Star formation is a dynamic process whereby newborn stars interact with their parent cloud. High velocity outflows from accreting stars collide with parent molecular material</text>
<text><location><page_2><loc_12><loc_68><loc_88><loc_86></location>generating shocks (known as Herbig-Haro objects when detected optically), opening cavities (Quillen et al. 2005), and driving turbulence (Miesch & Bally 1994; Bally et al. 1999; Arce & Goodman 2002; Walawender et al. 2005). Shocks from outflows heat, dissociate, and ionize the gas. They also inject kinetic energy and momentum into the cloud which may affect the rate of gravitational collapse of cores within these clouds (Leorat et al. 1990, e.g). Outflows may play a fundamental role in the evolution of star forming molecular clouds, turbulence generation, and cloud destruction. In this paper, we have searched the Lynds 982, 984, and 988 dark cloud complex (L988 hereafter; see Fig. 1) for shocks from protostellar outflows using tracers in both optical (H α and [S ii ]) and near-IR (H 2 ) tracers.</text>
<text><location><page_2><loc_12><loc_56><loc_88><loc_67></location>L988 lies in Cygnus near the Cygnus OB7 association which is among the nearest of the Cygnus OB associations at roughly 740-800 pc. L988 is part of a larger cloud complex known as Kh 141 (Chavtasi 1960), or TGU 541 (Dobashi et al. 2005), and is sometimes called The Northern Coalsack. The two regions of highest extinction within the Kh 141 complex are L988 and L1003 (see Reipurth & Schneider 2008, Fig. 28), both of which are active regions of star formation.</text>
<text><location><page_2><loc_12><loc_43><loc_88><loc_54></location>Distance estimates for the L988 complex range between 500 and 780 pc. Chavarria (1981) estimated the distance at 700 pc based on photometry of several stars in the region. Later, Chavarria & de Lara (1981) estimated a distance of 780 pc. Shevchenko et al. (1991) found a distance of 550 pc based on extinction estimates. Alves et al. (1998) studied extinction toward the nearby L977 cloud and found a distance of 500 pc. For calculations in this paper, we assume an intermediate distance of 600 pc.</text>
<text><location><page_2><loc_12><loc_30><loc_88><loc_41></location>The first outflow study in the region was a millimeter CO line survey by Clark (1986) who found four molecular outflows around IRAS sources which he designated a , c , e , and f . Subsequently the flow surrounding IRAS 21007+4951 (Clark source a ) was imaged by Hodapp (1994) in the near-IR (K ' ) and by Staude & Elsasser (1993) in r. Staude & Elsasser (1993) found four HH objects which were not assigned catalog numbers. These HH objects correspond to our HH 1050 knots B, C, E, & F (see § 3).</text>
<text><location><page_2><loc_12><loc_23><loc_88><loc_28></location>Felli et al. (1992) searched for H 2 O masers around young stars and found a maser associated with Clark source a . Their search did not detect masers coincident with Clark sources e or f .</text>
<text><location><page_2><loc_12><loc_12><loc_88><loc_21></location>Herbig & Dahm (2006) examined the LkH α 324 region in L988 using broadband optical and near-IR imaging and optical spectroscopy and discovered a small cluster of YSOs surrounding LkH α 324. They found the age of the cluster surrounding LkH α 324 to be 0.6-1.7 Myr depending upon the evolutionary model used in the analysis. Herbig & Dahm (2006) also examined the LkH α 324SE star (IRAS 21014+5001, Clark source c ) in detail</text>
<figure>
<location><page_3><loc_12><loc_49><loc_88><loc_86></location>
<caption>Fig. 1.- H α image of the L988 cloud HH objects are marked with circles and candidate giant flow axis are marked with dashed lines. Boxes mark the areas shown in subsequent figures.</caption>
</figure>
<text><location><page_3><loc_12><loc_25><loc_88><loc_36></location>using Keck HIRES spectroscopy. They found features which they designate the 'northwest outflow' (later designated HH 899) which is composed of several condensations prominent in [S ii ] and [O ii ] lines. In a 7 '' long slit oriented at P.A. = 129/309 · , they found three [S ii ] condensations to the northwest at velocities of -160 to -185 km s -1 relative to the -18 km s -1 rest velocity of the star. No red-shifted counterparts to the 'northwest outflow' knots were detected.</text>
<text><location><page_3><loc_12><loc_20><loc_88><loc_23></location>Allen et al. (2008) examined the cluster surrounding Clark source e with the Spitzer Space Telescope and cataloged young stars in the region.</text>
<section_header_level_1><location><page_4><loc_42><loc_85><loc_58><loc_86></location>2. Observations</section_header_level_1>
<text><location><page_4><loc_12><loc_61><loc_88><loc_82></location>Near infrared data for this project were obtained on the nights of 2006 July 11-13 on the United Kingdom Infrared Telescope (UKIRT) using the Wide Field InfraRed Camera (WFCAM, Casali et al. 2001), which is comprised of four Rockwell Hawaii-II 2048 × 2048 pixel arrays separated by 94% of the size of an individual chip. The instantaneous field of view is 0.21 square degrees, however to obtain a contiguous field of view, four pointings of the telescope must be used to fill in the space between arrays. A four pointing 'tile' covers approximately 0.8 square degrees. In the J, H, and K filters, we obtained a total integration time of 6 minutes over the L988 tile. In the H 2 filter, we obtained 72 minutes of integration time. WFCAM data were pipeline processed by the Cambridge Astronomical Survey Unit (CASU). The 16 resulting image stacks were then mosaiced together using the Image Reduction and Analysis Facility 1 (IRAF) to form the full field of view of the tile.</text>
<text><location><page_4><loc_12><loc_50><loc_88><loc_59></location>Visible wavelength narrowband images were obtained on the night of 2006 May 28 on the Subaru Telescope using the Suprime-Cam instrument (Miyazaki et al. 2002). SuprimeCam is a wide field prime focus camera comprised of ten 2048 × 4096 pixel CCDs. The instantaneous field of view is approximately 34 ' × 27 ' . Images were taken in the H α and [S ii ] filters, each with a total exposure time of 50 minutes.</text>
<text><location><page_4><loc_12><loc_41><loc_88><loc_48></location>Subaru data were processed using IRAF's mscred package. Images were overscanned, trimmed, bias subtracted, and then flat fielded (using both dome and twilight flats) by the ccdproc task. Images were intensity matched using mscimatch and stacked using mscstack based on world coordinate system fits generated by msccmatch .</text>
<text><location><page_4><loc_12><loc_26><loc_88><loc_39></location>Visible wavelength SDSS i' images were obtained on the night of 2010 Aug 25 on the University of Hawaii 88 inch Telescope using the Wide Field Grism Spectrograph 2 (WFGS2; Uehara et al. 2004) instrument in imaging mode. WFGS2 uses the Tek2k CCD camera with 2048 × 2048 pixels. With the WFGS2 focal reducer, the field of view is approximately 11 arcminutes on a side. SDSS i' images were only obtained for the field centered on the IRAS 21007+4951 reflection nebula. A total of 35 minutes of integration time was obtained. Reductions, alignment, and stacking were performed using the ccdproc package in IRAF.</text>
<section_header_level_1><location><page_5><loc_45><loc_85><loc_55><loc_86></location>3. Results</section_header_level_1>
<text><location><page_5><loc_12><loc_71><loc_88><loc_82></location>The L988 cloud has several active protostellar outflows which are visible in our narrowband images. Some appear to be associated with cavities in the cloud which have been carved out by the action of the outflow. Fig. 1 shows the region of the cloud covered by our H α and [S ii ] images. Table 1 contains a list of all Herbig-Haro objects (HH objects; Reipurth 2000) and molecular hydrogen shocks (MHO objects; Davis et al. 2010) in our field. In the following paragraphs, we discuss individual shocks, organized into proposed outflow groups</text>
<text><location><page_5><loc_12><loc_58><loc_88><loc_70></location>HH 1061 & 1059: HH 1061 (Fig. 2) lies 0.4 ' south-southeast of LkH α 324SE (Clark source e , IRAS 21023+5002; see Table 2) and its associated reflection nebula and cluster of sources. The primary component is a thin H α bright filament, oriented northwest-southeast and roughly 10 '' long. There are additional faint filaments of emission (knots B, C, & D) stretching about 1.3 ' further to the southeast. The shock lies in a low extinction region which may be a cavity outflows have blown out of the cloud.</text>
<figure>
<location><page_5><loc_12><loc_34><loc_46><loc_56></location>
<caption>Fig. 2.- An H α image of the LkH α 324 region (IRAS 21023+5002; Clark source e ) region which includes the HH 1061 and 1059 shocks. LkH α 324 and LkH α 324SE are embedded in the reflection nebula and their positions are marked with white circles. The IRAS source is coincident with LkH α 324SE. Squares mark the positions of knots in the MHO 954 shock complex.</caption>
</figure>
<text><location><page_5><loc_12><loc_12><loc_88><loc_19></location>There are two compact knots (HH 1059A & B) in both the H α and [S ii ] images about 2 ' to the northwest of HH 1061 (Fig. 2). They lie along the line defined by the HH 1061 knots and lie across the cluster from HH 1061, thus they are likely counterflow components to HH 1061.</text>
<text><location><page_6><loc_12><loc_67><loc_88><loc_86></location>There are several young stars catalogued by Allen et al. (2008) in the LkH α 324 cluster, therefore it is not possible to determine with confidence which of the young stars may drive this outflow. However, using spectroscopy Herbig & Dahm (2006) detected a high velocity 'northwest outflow' (HH 899) within 3 '' of the LkH α 324SE star. That source lies close to the line defined by HH 1061 knots and HH 1059. The high velocity knots of Herbig & Dahm (2006) were detected in a spectrograph slit oriented at P.A. ∼ 129/309 · , the HH 1061/1059 flow lies at a position angle of ∼ 151/331 · . Given that the slit may not have been placed precisely along the outflow axis (which was unknown at the time of the observation), these values seem to be in reasonable agreement and it is likely that LkH α 324SE is the driving source and that HH 899 is part of a flow with HH 1061 & HH 1059.</text>
<text><location><page_6><loc_12><loc_58><loc_88><loc_65></location>The LkH α 324SE source has been detected in several infrared surveys (see Table 2). Those measured fluxes were used to fit the spectral energy distribution (SED) using the models of Robitaille et al. (2007) (see Fig. 16a). The SED shows evidence of strong disk and envelope components.</text>
<text><location><page_6><loc_12><loc_47><loc_88><loc_56></location>Clark (1986) found a bipolar outflow surrounding LkH α 324SE. The outflow is oriented roughly North-South with the blue-shifted lobe to the North, moving into the higher extinction region. It is unclear whether the CO outflow of Clark (1986) and HH 1061 & 1059 trace the same flow. While the Clark outflow appears to be oriented North-South (P.A. = 0/180 · ), the low resolution in Clark Figure 1 makes the association of the two unclear.</text>
<text><location><page_6><loc_12><loc_38><loc_88><loc_45></location>MHO 954: A bow shaped H 2 knot (MHO 954A) lies ∼ 1 ' due west of LkH α 324SE (see Fig. 2) along with a line of fainter knots (MHO 954B-E). Based on their position relative to the core of the cluster, it seems unlikely that these shocks are from the same outflow as HH 1061 and 1059.</text>
<text><location><page_6><loc_12><loc_27><loc_88><loc_36></location>HH 1057 & 1056: These are compact, H α bright shocks (Fig. 3) which lie in a dark portion of the cloud. There is no clear association with a known flow or source, however we note that the MHO 954 shock, HH 1057, and 1056 B lie along an axis which passes through the cluster of sources near LkH α 324SE and thus may be a single outflow emerging from one of the sources embedded in the reflection nebula.</text>
<text><location><page_6><loc_12><loc_14><loc_88><loc_25></location>HH 1062: These three knots lie in a low extinction region East of the cloud (Figs. 3 & 4). They surround a bright star visible in our narrowband H α and [S ii ] images which corresponds to an IRAS source (IRAS 21028+5001). This star was also detected by WISE (WISE J210428.01+501348.5) and it lies roughly on a line drawn between the shocks, but it is not clear if they are driven by it. Fluxes for the star are listed in Table 2 and the model SED is shown in Fig. 16b.</text>
<text><location><page_6><loc_16><loc_11><loc_88><loc_12></location>HH 1062 A lies 26 '' to the West of the source along PA ∼ 288 · while knots B and C</text>
<figure>
<location><page_7><loc_13><loc_64><loc_87><loc_86></location>
<caption>Fig. 3.- An H α image of the LkH α 324 region (IRAS 21023+5002; Clark source e ) region which includes the shock HH 1056-1059 & 1061-1062 shocks.</caption>
</figure>
<text><location><page_7><loc_12><loc_47><loc_88><loc_55></location>lie 52 '' and 59 '' to the East along PA ∼ 107 · and 116 · respectively. We also note that these shocks lie roughly along a line defined by the HH 1057 and 1056 shocks that passes through the reflection nebula. HH 1062 may be a shock in a larger flow and is perhaps not driven by the nearby IRAS 21028+5001.</text>
<figure>
<location><page_7><loc_12><loc_24><loc_46><loc_45></location>
<caption>Fig. 4.- An H α image of the HH 1062 shock system.</caption>
</figure>
<text><location><page_7><loc_12><loc_10><loc_88><loc_17></location>HH 1058: This is a faint, H α only shock (Figs. 3 & 5) which appears to be a jet emerging from an optically visible star along PA ∼ 125/305 · . The star was detected by both 2MASS and WISE (WISE J210339.46+501552.9) and those magnitudes are listed in Table 2. Using those fluxes, we fit the SED using the models of Robitaille et al. (2007) (see Fig. 16c). The</text>
<text><location><page_8><loc_12><loc_82><loc_88><loc_86></location>best fit models show that this is a low mass young star ( ∼ 0.25 M glyph[circledot] ) with a relatively low disk accretion rate ( ∼ 10 -11 M glyph[circledot] /yr).</text>
<figure>
<location><page_8><loc_12><loc_63><loc_46><loc_80></location>
<caption>Fig. 5.- An H α image of the HH 1058 and 1057 shocks.</caption>
</figure>
<text><location><page_8><loc_12><loc_49><loc_88><loc_56></location>HH 1053, 1049, 1046, 1060, & 1063: The HH 1053, 1049 (Fig. 6), & 1046 shocks (Fig. 7) appear to all be the western components of a single flow powered by IRAS 21014+5001 (aka Clark source c ), it is possible that HH 1049 or 1046 are from another source, but the alignment of these three shocks with IRAS 21014+5001 appears convincing.</text>
<text><location><page_8><loc_12><loc_40><loc_88><loc_47></location>The corresponding counterflow to the southeast emerges into a low extinction region of the cloud and is composed of the HH 1060 and 1063 shocks (Fig. 8). If this is all one flow which emerges from that source, then the length of the flow is 26.5 ' which corresponds to a length of 4.6 pc at an assumed distance of 600 pc.</text>
<text><location><page_8><loc_12><loc_25><loc_88><loc_38></location>Clark designated IRAS 21014+5001 as a molecular outflow source based upon finding a patch of blue-shifted gas West of the source (see Clark 1986 Fig. 1). This patch of blueshifted CO does not correspond to our HH 1053, 1049, 1046 outflow. The blue-shifted CO is centered South of the axis defined by our HH objects. Though the northernmost contour in Clark (1986, Fig. 1) comes close to our flow axis near HH 1049, the bulk of the blue-shifted CO is closer to our HH 1052 (see below). The IRAS 21014+5001 source was detected by WISE, the fluxes are listed in Table 2 and the model SED is shown in Fig. 16d.</text>
<text><location><page_8><loc_12><loc_10><loc_88><loc_24></location>MHO 955: There is a star visible in the J, H, & K images (and faintly in H α and [S ii ]) 1.2 ' east-southeast of IRAS 21014+5001 near the axis defined by the HH 1053, 1049, 1046, 1060, 1063 outflow which is coincident with a 0.2 ' long H 2 filament (MHO 955) pointing northeast from the star, at first glance it appears that it is emanating from the star. That star was determined to be a Class I protostar by Allen et al. (2008), however it lies along the axis of the HH 1053, 1049, 1046 flow from IRAS 21014+5001 and so may alternatively be a shock in the embedded counterflow which happens to be coincident with a star along our line of</text>
<figure>
<location><page_9><loc_13><loc_47><loc_87><loc_86></location>
<caption>Fig. 6.- An H α image of the HH 1053, 1049, & 1052 region. The large reflection nebula on the left side of the image surrounds IRAS 21014+5001 (Clark source c ; see Fig. 1 for the relationship).</caption>
</figure>
<text><location><page_9><loc_12><loc_34><loc_16><loc_36></location>sight.</text>
<text><location><page_9><loc_12><loc_25><loc_88><loc_33></location>HH 1044: This is a [S ii ] bright knot (Fig. 9) which lies at the northwest corner of the Subaru image. There appears to be a faint H α filament extending due North from it, but this may also be an illuminated cloud edge. IRAS 20595+5009 lies 2.5 ' north of the shock, outside of the field of view of our H α and [S ii ] images.</text>
<text><location><page_9><loc_12><loc_10><loc_88><loc_24></location>HH 1052: The A & B knots of this object (Figs. 6) are a pair of faint H α and [S ii ] filaments. The B component has an H 2 counterpart (MHO 956). There is a faint V-shaped reflection nebula visible in the H and K images 0.3 ' southeast of the knots. The reflection nebula opens toward both of the knots. At the apex of the reflection nebula is a candidate for the source star. While it is not detected in our J, H, or K S images, it is detected by WISE (WISE J210240.13+501236.5; Table 2). In addition, there is another candidate source star visible in our near-IR images which lies 19 '' to the southeast. It is coincident</text>
<figure>
<location><page_10><loc_12><loc_62><loc_46><loc_86></location>
<caption>Fig. 7.- A [S ii ] image of HH 1046 which lies at the north edge of our Subaru field.</caption>
</figure>
<figure>
<location><page_10><loc_13><loc_26><loc_87><loc_55></location>
<caption>Fig. 8.- An H α image of the HH 1060 & 1063 region.</caption>
</figure>
<text><location><page_10><loc_12><loc_15><loc_88><loc_19></location>with IRAS 21010+5000 and is detected in the WISE catalog (WISE J210242.41+501227.8; Table 2; Fig. 16e).</text>
<text><location><page_10><loc_12><loc_10><loc_88><loc_14></location>The blue-shifted CO which was discovered by Clark (1986) is coincident with the HH 1052 shock system. Clark associated this with IRAS 21014+5001, however we asso-</text>
<figure>
<location><page_11><loc_12><loc_61><loc_46><loc_86></location>
<caption>Fig. 9.- A [S ii ] image of the HH 1044 shock which lies near the extreme northwest edge of our Subaru field.</caption>
</figure>
<text><location><page_11><loc_12><loc_51><loc_56><loc_52></location>ciate that source with the HH 1053, 1049, 1046 flow.</text>
<text><location><page_11><loc_12><loc_46><loc_88><loc_49></location>HH 1047: This shock system appears to be a curved, C-shaped outflow. The C-shaped curve suggests that the source is moving to the southeast (Bally & Reipurth 2001).</text>
<text><location><page_11><loc_12><loc_25><loc_88><loc_44></location>In our near-IR images, several stars (many with corresponding WISE detections) lie on or near the arc of the flow and would be source candidates. Of these, three stand out as being directly along the arc of the flow (WISE J210214.15+501013.0, WISE J210218.93+501102.3, & WISE J210217.70+501046.5). The first of these is optically visible while the other two are visible only in our near-IR images. We examined the models of Robitaille et al. (2007) built based upon the WISE and 2MASS magnitudes of each of these and have selected the optically visible star (WISE J210214.15+501013.0) as the best candidate as it is the only one of the three with a significant envelope flux in the fitted SED. The fluxes for this star are listed in Table 2 and the result of the Robitaille et al. (2007) model fit can be seen in Fig. 16f.</text>
<text><location><page_11><loc_12><loc_10><loc_88><loc_23></location>It is also possible that this is merely a bow shock driven by a more distant source, however, the morphology is suggestive of a jet and even if this were a bow shock, the arc of the curve would indicate a forward facing bow shock coming from the northwest and there are no strong flows visible in our images in that direction. The star V1331 Cyg and its associated outflow (HH 389) lie along that axis a few arcminutes outside of the field of view of our SuPrimeCam images. The [S ii ] images of Mundt & Eisloffel (1998) show shocks to the north and south of V1331 Cyg. Their orientations relative to the source are inconsistent</text>
<figure>
<location><page_12><loc_12><loc_68><loc_46><loc_86></location>
<caption>Fig. 10.- A [S ii ] image of the HH 1047 outflow. The WISE source discussed in the text is labeled.</caption>
</figure>
<text><location><page_12><loc_12><loc_57><loc_51><loc_59></location>with HH 1047 being a component in that flow.</text>
<text><location><page_12><loc_12><loc_40><loc_88><loc_56></location>HH 1054: This is a compact cluster of [S ii ] dominant knots (Fig. 11) coincident with a short 7 '' V-shaped H 2 shock (MHO 957) which opens to the North. In that direction, there are two optical and near-IR stars about 1 arcminute away, both with reflection nebulosity. The first source (2MASS 21024889+5010351; Table 2) is seen in our visible light narrowband images as well and has a small reflection nebula surrounding it which (in our optical images) appears to open southward. This source has a brighter companion star 3.5 '' to the West (WISE J210248.45+501036.1). This star is a likely candidate for the outflow source as the orientation of the reflection nebula is aligned with the presumed flow direction.</text>
<text><location><page_12><loc_12><loc_27><loc_88><loc_39></location>Another candidate source star with a reflection nebula (WISE J210249.68+501041.9; Table 2) is visible in our near-IR images and lies about 1 arcminute North of the H 2 shock. Its reflection nebula, however, appears to open to the East. The source star does not appear in the 2MASS catalog. We were unable to determine reliable J, H, and K magnitudes for this star due to the presence of the reflection nebula, but it is clearly very red (invisible in J, faint in H, and bright in K).</text>
<text><location><page_12><loc_12><loc_20><loc_88><loc_26></location>HH 1051: The HH 1050 and 1051 outflow system is a complex arrangement of shocks and reflection nebulosity (Fig. 12). The reflection nebula appears to outline a two-lobed cavity surrounding Clark source a .</text>
<text><location><page_12><loc_12><loc_11><loc_88><loc_19></location>There are two stars embedded in the reflection nebula. The western star (WISE J210222.70+500308.3; Table 2; Fig. 16g) is not readily seen in the visible light images, but is detectable in the J images and is increasingly bright at the longer (H and K) wavelengths. The eastern star (WISE J210223.85+500306.8; Table 2; Fig. 16h) lies 15 '' East of</text>
<figure>
<location><page_13><loc_12><loc_67><loc_46><loc_86></location>
<caption>Fig. 11.- A [S ii ] image of the HH 1054 shock. The locations of 2MASS 21024889+5010351 (visible in the [S ii ] image) and WISE J210249.68+501041.9 (only visible in the near-IR) are marked.</caption>
</figure>
<text><location><page_13><loc_12><loc_53><loc_88><loc_56></location>the western star, is visible at all wavelengths, and is brighter than the western star at i', J, H, and K.</text>
<text><location><page_13><loc_12><loc_46><loc_88><loc_51></location>IRAS 21007+4951 lies in between the Eastern and Western stars, slightly closer to the Western star. Neither star lies within the error ellipse of the IRAS source (Fig. 13). It is possible that the IRAS source is a blend of the two WISE sources.</text>
<text><location><page_13><loc_12><loc_33><loc_88><loc_44></location>The eastern star appears to drive a faint, highly collimated [S ii ] jet (HH 1051 A & B; see Fig. 12) along position angle 60 · . To the northeast along the axis defined by the jet, there are two faint shocks (HH 1051 C & D) which lie 88 '' and 119 '' from the source respectively. These faint shocks are just visible in the [S ii ] images and have no corresponding signal in the H α or i ' images, nor are there faint stars at those locations in any of the near-IR images. The southwestern portion of the jet blends with the southern edge of the reflection nebula.</text>
<text><location><page_13><loc_12><loc_28><loc_88><loc_31></location>Further to the southwest are faint shocks (see Fig. 13) which may be part of this flow, however they overlap with the western lobe of the HH 1050 flow described below.</text>
<text><location><page_13><loc_12><loc_19><loc_88><loc_26></location>HH1050 & 1045: The western of the two stars in the region appears to drive a long outflow (HH 1050; see Fig. 13) in the East-West direction. This outflow is much more extended than the HH 1051 outflow and lies along a nearly East-West line (PA ∼ 90 · /270 · ). There is also a bright, compact H 2 , H α , and [S ii ] knot (HH 1050 F / MHO 958) 4 '' west of the western star.</text>
<text><location><page_13><loc_12><loc_10><loc_88><loc_17></location>Knots A-E of this shock system (Fig. 12) are the eastern component of the flow. The furthest is knot A which lies 1.6 ' east of the source. The B & C knots are bright in both H α and [S ii ] and both have H 2 counterparts (MHO 958). Knots D & E are fainter H α and [S ii ] knots with an H 2 knot (MHO 958) a few arcseconds southwest of E.</text>
<figure>
<location><page_14><loc_13><loc_40><loc_87><loc_86></location>
<caption>Fig. 12.- A [S ii ] image of the area around the HH 1048, 1050, and 1051 shock systems. The positions of the Eastern and Western stars described in the text are indicated with arrows and the circles mark the positions of HH objects.</caption>
</figure>
<text><location><page_14><loc_12><loc_22><loc_88><loc_27></location>HH 1050 knots F-P appear to comprise the western half of the outflow. The innermost shocks (knots F and G) appear to have the morphology of compact bow shocks emanating from the area at the center of the reflection nebula.</text>
<text><location><page_14><loc_12><loc_11><loc_88><loc_20></location>Knot J appears to be a shock outlining the edge of a dense cloud edge which is visible in the H α and H 2 images. The southern knots (J, K, N, O, and P) could be distant components of HH 1051, or the southern half of a less collimated component of HH 1050. Because there is faint, filamentary emission which appears to connect many of the shocks in this region, we favor the explanation that all of the knots (F-P) are part of the HH 1050 outflow, but</text>
<figure>
<location><page_15><loc_13><loc_49><loc_87><loc_86></location>
<caption>Fig. 13.- An H α image of the western half of the HH 1050 shock system. The positions of the Eastern and Western stars described in the text are indicated with arrows and the circles mark the positions of HH objects. The error ellipse for the position of IRAS 21007+4951 is indicated in white.</caption>
</figure>
<text><location><page_15><loc_12><loc_31><loc_88><loc_34></location>the possibility that at least some of these (especially the most southern knots J, K, and N) are associated with the HH 1051 flow cannot be excluded.</text>
<text><location><page_15><loc_12><loc_22><loc_88><loc_30></location>The pair of knots which make up HH 1045 comprise a ∼ 30 '' long filament of H α & [S ii ] emission which lies 8.1 ' West of the HH 1050 outflow source along the axis of the flow (see Fig. 14). This system appears to be a distant bow shock in that outflow. At an assumed distance of 600 pc, that makes the total length of the HH 1050 outflow 1.7 pc.</text>
<text><location><page_15><loc_12><loc_13><loc_88><loc_20></location>The reflection nebula surrounding the HH 1050 outflow source outlines a V-shaped cavity about 2 ' long with a wide ∼ 45 · opening angle (Fig. 13). The northern half of this cavity, past knots L, & K, emerges into a low extinction region in which background stars can be seen. The southern half of the cavity is a higher extinction region.</text>
<text><location><page_15><loc_16><loc_10><loc_88><loc_11></location>The Clark (1986) outflow map shows red- and blue-shifted lobes which correspond to</text>
<text><location><page_16><loc_12><loc_83><loc_88><loc_86></location>our HH 1050 outflow. The eastern half of the flow (knots A-E) correspond to red-shifted CO and the western half (knots F-P) correspond to blue-shifted CO.</text>
<figure>
<location><page_16><loc_12><loc_55><loc_46><loc_80></location>
<caption>Fig. 14.- A [S ii ] image of the HH 1045 shock, the western end of the giant IRAS 21007+4951 outflow.</caption>
</figure>
<text><location><page_16><loc_12><loc_39><loc_88><loc_46></location>HH 1048: Knot A of HH 1048 is a small, compact blob of emission just emerging from a star which lies at the apex of a C-shaped reflection nebula (Fig. 12) and which is coincident with WISE J210226.45+500203.4 (Table 2). Knot B of HH 1048 is an H α and [S ii ] filament which lies in the middle of that C-shaped reflection nebula.</text>
<text><location><page_16><loc_12><loc_26><loc_88><loc_37></location>HH 1048 knot C is a compact, H α only bow which lies near the eastern end of the reflection nebula, about 0.5 ' from the star. HH 1048 D is a compact, nearly starlike knot of H α and [S ii ] emission. HH 1048 knot E is another filament which lies roughly 1 ' east of the star and slightly north of the line defined by the knot B filament, it may trace the northern edge of the outflow cavity. The J, H, & K images also show one arc of the reflection nebula extending roughly 15 '' northeast of the source star.</text>
<text><location><page_16><loc_12><loc_17><loc_88><loc_24></location>The Clark (1986) outflow map shows a blob of blue-shifted CO which is connected to the blue-shifted lobe of his source a . While Clark did not discuss this as a separate outflow, it is perfectly coincident in position with our HH 1048 knots A & B and appears to match the outline of the associated reflection nebula in size.</text>
<text><location><page_16><loc_12><loc_10><loc_88><loc_15></location>HH 1055: This shock system is a cluster of faint, [S ii ] bright, low surface brightness shock filaments (Fig. 15) embedded in some patchy dust filaments along the eastern edge of the cloud. They lie near to the axis defined by the HH 1051 and 1050 outflows from the</text>
<text><location><page_17><loc_12><loc_83><loc_88><loc_86></location>IRAS 21007+4951 source, however a positive association with those outflows is not possible based on the present data.</text>
<figure>
<location><page_17><loc_12><loc_59><loc_46><loc_81></location>
<caption>Fig. 15.- A [S ii ] image of the HH 1055 shock, a possible eastern component of the giant IRAS 21007+4951 outflow.</caption>
</figure>
<section_header_level_1><location><page_17><loc_43><loc_46><loc_57><loc_48></location>4. Discussion</section_header_level_1>
<text><location><page_17><loc_12><loc_37><loc_88><loc_44></location>The L988 region contains significant outflow activity as revealed by our surveys for optical and near-IR shock tracers. The region contains nearly two dozen independent shock systems (20 Herbig-Haro objects and 3 MHO objects unaffiliated with HH objects), however we can only confidently identify the driving protostar for five outflows (LkH α 324SE,</text>
<text><location><page_17><loc_12><loc_35><loc_85><loc_36></location>IRAS 21014+5001, WISE J210214.15+501013.0, WISE J210222.70+500308.3, and WISE</text>
<text><location><page_17><loc_12><loc_22><loc_88><loc_33></location>Two outflows we have identified (from IRAS 21014+5001 and the IRAS 21007+4951 / WISE J210222.70+500308.3 / WISE 210223.85+500306.8 shock complex) each exceed 1 pc in length with the IRAS 21014+5001 flow being 4.6 pc long. Both of these large scale outflows originate from sources which are in the highest extinction regions of the cloud. We find several Herbig-Haro objects and one H 2 shock complex near the well studied cluster surrounding LkH α 324 (IRAS 21023+5002, Clark source e ).</text>
<text><location><page_17><loc_12><loc_13><loc_88><loc_20></location>While much of the outflow activity in the L988 cloud is widely distributed over a region ∼ 30 ' ( ∼ 4-7 pc) in diameter, a group of at least three sources which drive overlapping outflows is clustered around the IRAS 21007+4951 source and its associated reflection nebula, located in the center of the L988 cloud.</text>
<text><location><page_17><loc_16><loc_10><loc_88><loc_11></location>A notable feature of this study is that outflow activity is detected primarily at visible</text>
<figure>
<location><page_18><loc_23><loc_24><loc_77><loc_86></location>
<caption>Fig. 16.- Spectral energy distributions based on 2MASS, WISE, and IRAS catalog data fit with models by Robitaille et al. (2007).</caption>
</figure>
<text><location><page_18><loc_12><loc_10><loc_88><loc_16></location>wavelengths (H α and [S ii ]) while our near-IR images (H 2 ) show relatively little shock activity and most of what is detected in the near-IR is coincident with H α or [S ii ] shocks. This is likely due, at least in part, to the combination of the near-IR data being taken on a smaller</text>
<text><location><page_19><loc_12><loc_81><loc_88><loc_86></location>telescope (3.8 meter as opposed to 8.2 meter) and under much worse seeing conditions ( ∼ 1.5 '' FWHM for the H 2 images compared to 0.65-0.70 '' for the H α and [S ii ]). We suspect that further study of this region at near-IR wavelengths will reveal additional details.</text>
<text><location><page_19><loc_16><loc_76><loc_73><loc_77></location>We would like to thank an anonymous referee for helpful comments.</text>
<text><location><page_19><loc_16><loc_73><loc_83><loc_74></location>JW was supported by the NSF through grants AST-0507784 and AST-0407005.</text>
<text><location><page_19><loc_12><loc_66><loc_91><loc_71></location>JW and BR acknowledge support from the National Aeronautics and Space Administration through the NASA Astrobiology Institute under Cooperative Agreement No. NNA09DA77A issued through the Office of Space Science.</text>
<text><location><page_19><loc_12><loc_57><loc_88><loc_64></location>This work is based in part on data collected at the Subaru telescope, which is operated by the National Astronomical Observatory of Japan (NAOJ). We are grateful to Nobunari Kashikawa for permission to use his [SII] filter for the SuPrimeCam instrument on the Subaru Telescope.</text>
<text><location><page_19><loc_12><loc_50><loc_88><loc_55></location>This publication makes use of data obtained on the United Kingdom Infrared Telescope (UKIRT) which is operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the U.K.</text>
<text><location><page_19><loc_12><loc_41><loc_88><loc_48></location>This publication makes use of data products from the 2MASS, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.</text>
<text><location><page_19><loc_12><loc_32><loc_88><loc_39></location>This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.</text>
<text><location><page_19><loc_16><loc_29><loc_88><loc_30></location>This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France.</text>
<text><location><page_19><loc_16><loc_26><loc_69><loc_27></location>MHO catalogue is hosted by Liverpool John Moores University.</text>
<text><location><page_19><loc_12><loc_15><loc_88><loc_24></location>We also thank the University of Hawaii Time Allocation Committee for allocating the nights during which these observations were made. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this sacred mountain.</text>
<text><location><page_19><loc_12><loc_10><loc_88><loc_13></location>Facilities: Subaru (Suprime-Cam), UKIRT (WFCAM), UH 88 inch Telescope (Tek2k), WISE, 2MASS</text>
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<table>
<location><page_22><loc_22><loc_14><loc_78><loc_81></location>
<caption>Table 1. Positions of Shocks in the L988 region.</caption>
</table>
<table>
<location><page_23><loc_22><loc_15><loc_78><loc_81></location>
<caption>Table 1-Continued</caption>
</table>
<table>
<location><page_24><loc_22><loc_45><loc_78><loc_49></location>
<caption>Table 1-Continued</caption>
</table>
<section_header_level_1><location><page_25><loc_16><loc_26><loc_17><loc_53></location>T able 2. Photometry of Sources in L988.</section_header_level_1>
<text><location><page_25><loc_21><loc_81><loc_22><loc_83></location>IRAS</text>
<text><location><page_25><loc_21><loc_76><loc_22><loc_79></location>IRAS</text>
<text><location><page_25><loc_21><loc_72><loc_22><loc_75></location>IRAS</text>
<text><location><page_25><loc_21><loc_68><loc_22><loc_71></location>IRAS</text>
<text><location><page_25><loc_21><loc_63><loc_22><loc_66></location>WISE</text>
<text><location><page_25><loc_21><loc_59><loc_22><loc_61></location>WISE</text>
<text><location><page_25><loc_21><loc_54><loc_22><loc_57></location>WISE</text>
<text><location><page_25><loc_21><loc_51><loc_22><loc_52></location>SE</text>
<text><location><page_25><loc_21><loc_50><loc_22><loc_51></location>I</text>
<text><location><page_25><loc_21><loc_49><loc_22><loc_50></location>W</text>
<text><location><page_25><loc_21><loc_44><loc_22><loc_48></location>2MASS</text>
<text><location><page_25><loc_21><loc_39><loc_22><loc_43></location>2MASS</text>
<text><location><page_25><loc_21><loc_34><loc_22><loc_38></location>2MASS</text>
<text><location><page_25><loc_21><loc_24><loc_22><loc_28></location>Mission</text>
<text><location><page_25><loc_23><loc_83><loc_24><loc_84></location>m</text>
<text><location><page_25><loc_23><loc_82><loc_24><loc_83></location>µ</text>
<text><location><page_25><loc_23><loc_81><loc_24><loc_82></location>100</text>
<text><location><page_25><loc_23><loc_78><loc_24><loc_79></location>m</text>
<text><location><page_25><loc_23><loc_77><loc_24><loc_78></location>µ</text>
<text><location><page_25><loc_23><loc_76><loc_24><loc_77></location>60</text>
<text><location><page_25><loc_23><loc_74><loc_24><loc_75></location>m</text>
<text><location><page_25><loc_23><loc_73><loc_24><loc_74></location>µ</text>
<text><location><page_25><loc_23><loc_72><loc_24><loc_73></location>25</text>
<text><location><page_25><loc_23><loc_70><loc_24><loc_71></location>m</text>
<text><location><page_25><loc_23><loc_69><loc_24><loc_70></location>µ</text>
<text><location><page_25><loc_23><loc_68><loc_24><loc_69></location>12</text>
<text><location><page_25><loc_23><loc_65><loc_24><loc_66></location>m</text>
<text><location><page_25><loc_23><loc_64><loc_24><loc_65></location>µ</text>
<text><location><page_25><loc_23><loc_63><loc_24><loc_64></location>22</text>
<text><location><page_25><loc_23><loc_60><loc_24><loc_61></location>m</text>
<text><location><page_25><loc_23><loc_60><loc_24><loc_60></location>µ</text>
<text><location><page_25><loc_23><loc_59><loc_24><loc_60></location>12</text>
<text><location><page_25><loc_23><loc_56><loc_24><loc_57></location>m</text>
<text><location><page_25><loc_23><loc_55><loc_24><loc_56></location>µ</text>
<text><location><page_25><loc_23><loc_54><loc_24><loc_55></location>4.6</text>
<text><location><page_25><loc_23><loc_51><loc_24><loc_52></location>m</text>
<text><location><page_25><loc_23><loc_51><loc_24><loc_51></location>µ</text>
<text><location><page_25><loc_23><loc_49><loc_24><loc_51></location>3.4</text>
<text><location><page_25><loc_23><loc_45><loc_24><loc_46></location>K</text>
<text><location><page_25><loc_23><loc_40><loc_24><loc_41></location>H</text>
<text><location><page_25><loc_23><loc_36><loc_24><loc_36></location>J</text>
<text><location><page_25><loc_23><loc_25><loc_24><loc_27></location>Band</text>
<text><location><page_25><loc_24><loc_81><loc_26><loc_83></location>(Jy)</text>
<text><location><page_25><loc_24><loc_77><loc_26><loc_79></location>(Jy)</text>
<text><location><page_25><loc_24><loc_73><loc_26><loc_74></location>(Jy)</text>
<text><location><page_25><loc_24><loc_68><loc_26><loc_70></location>(Jy)</text>
<text><location><page_25><loc_24><loc_63><loc_26><loc_66></location>(mag)</text>
<text><location><page_25><loc_24><loc_59><loc_26><loc_61></location>(mag)</text>
<text><location><page_25><loc_24><loc_54><loc_26><loc_57></location>(mag)</text>
<text><location><page_25><loc_24><loc_49><loc_26><loc_52></location>(mag)</text>
<text><location><page_25><loc_24><loc_47><loc_26><loc_47></location>)</text>
<text><location><page_25><loc_24><loc_44><loc_26><loc_47></location>(mag</text>
<text><location><page_25><loc_24><loc_39><loc_26><loc_42></location>(mag)</text>
<text><location><page_25><loc_24><loc_34><loc_26><loc_37></location>(mag)</text>
<text><location><page_25><loc_24><loc_24><loc_26><loc_28></location>(Units)</text>
<text><location><page_25><loc_29><loc_81><loc_30><loc_83></location>199</text>
<text><location><page_25><loc_31><loc_82><loc_32><loc_83></location>44</text>
<text><location><page_25><loc_31><loc_81><loc_32><loc_82></location>±</text>
<text><location><page_25><loc_33><loc_82><loc_34><loc_83></location>199</text>
<text><location><page_25><loc_33><loc_81><loc_34><loc_82></location><</text>
<text><location><page_25><loc_39><loc_81><loc_41><loc_83></location>39.8</text>
<text><location><page_25><loc_41><loc_82><loc_42><loc_83></location>3.2</text>
<text><location><page_25><loc_41><loc_81><loc_42><loc_82></location>±</text>
<text><location><page_25><loc_46><loc_82><loc_47><loc_84></location>47.0</text>
<text><location><page_25><loc_46><loc_81><loc_47><loc_82></location><</text>
<text><location><page_25><loc_67><loc_81><loc_68><loc_83></location>31.6</text>
<text><location><page_25><loc_68><loc_82><loc_69><loc_83></location>2.5</text>
<text><location><page_25><loc_68><loc_81><loc_69><loc_82></location>±</text>
<text><location><page_25><loc_29><loc_34><loc_73><loc_79></location>10.56 8.27 6 . 4 6 3.94 2.20 0.33 -1.337 23.9 33.7 87 ± 0.02 ± 0.02 ± 0.02 ± 0.10 ± 0.09 ± 0.02 ± 0.008 ± 1.2 ± 1.0 ± 11 10.26 9.16 8 . 3 1 7.10 6.46 4.33 2.43 0.81 1.1 < 2.76 ± 0.02 ± 0.02 ± 0.02 ± 0.03 ± 0.02 ± 0.01 ± 0.01 ± 0.05 ± 0.08 · · · 12.76 11.89 11.45 11.07 10.61 8.78 7.1 · · · · · · · · · ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.04 ± 0.2 · · · · · · · · · 10.10 9.95 9 . 8 6 9.57 9.32 4.34 2.08 1.12 1.71 11.8 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.01 ± 0.02 ± 0.06 ± 0.10 ± 1.3 · · · · · · · · · 12.48 10.69 7.78 2.38 · · · · · · · · · · · · · · · · · · ± 0.03 ± 0.02 ± 0.03 ± 0.02 · · · · · · · · · < 16.98 14.42 12.17 11.39 9.11 6.09 2.53 < 0.36 0.81 < 11.8 · · · ± 0.05 ± 0.03 ± 0.02 ± 0.02 ± 0.02 ± 0.02 · · · ± 0.08 · · · 14.54 13.63 13.05 11.69 10.71 8.62 7.29 · · · · · · · · · ± 0.04 ± 0.04 ± 0.05 ± 0.04 ± 0.03 ± 0.04 ± 0.15 · · · · · · · · · 16.32 13.42 13.94 · · · · · · · · · · · · · · · · · · · · · ± 0.14 ± n ull ± 0.08 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13.55 11.06 8.44 4.38 · · · · · · · · · · · · · · · · · · ± 0.03 ± 0.02 ± 0.03 ± 0.03 · · · · · · · · · < 16.37 < 14.82 13.28 10.72 7.16 4.23 0.90 · · · · · · · · · · · · · · · ± 0.05 ± 0.03 ± 0.02 ± 0.02 ± 0.01 · · · · · · · · · 12.98 11.53 10.54 9 . 2 1 7.95 5.17 2.72 · · · · · · · · · ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 0.91 5.07 21.8 · · · · · · · · · · · · · · · · · · · · · ± 0.12 ± 0.35 ± 2.0 14.81 13.05 11.66 9.19 8.06 5.60 2.71 · · · · · · · · · ± 0.05 ± 0.03 ± 0.02 ± 0.006 ± 0.02 ± 0.014 ± 0.01 · · · · · · · · ·</text>
<text><location><page_25><loc_36><loc_33><loc_37><loc_33></location>c</text>
<text><location><page_25><loc_36><loc_23><loc_37><loc_33></location>J210339.46+501552.9</text>
<text><location><page_25><loc_36><loc_19><loc_37><loc_22></location>WISE</text>
<text><location><page_25><loc_49><loc_33><loc_50><loc_33></location>f</text>
<text><location><page_25><loc_50><loc_23><loc_51><loc_33></location>J210214.15+501013.0</text>
<text><location><page_25><loc_50><loc_19><loc_51><loc_22></location>WISE</text>
<text><location><page_25><loc_60><loc_33><loc_60><loc_33></location>g</text>
<text><location><page_25><loc_60><loc_23><loc_61><loc_33></location>J210222.70+500308.3</text>
<text><location><page_25><loc_60><loc_19><loc_61><loc_22></location>WISE</text>
<text><location><page_25><loc_63><loc_33><loc_64><loc_33></location>h</text>
<text><location><page_25><loc_63><loc_23><loc_64><loc_33></location>J210223.85+500306.8</text>
<text><location><page_25><loc_63><loc_19><loc_64><loc_22></location>WISE</text>
<text><location><page_25><loc_29><loc_19><loc_30><loc_26></location>LkH α 324SE a</text>
<text><location><page_25><loc_31><loc_19><loc_32><loc_20></location>-</text>
<text><location><page_25><loc_32><loc_19><loc_34><loc_29></location>IRAS 21028+5001 b</text>
<text><location><page_25><loc_34><loc_82><loc_35><loc_83></location>·</text>
<text><location><page_25><loc_34><loc_82><loc_35><loc_82></location>·</text>
<text><location><page_25><loc_34><loc_82><loc_35><loc_82></location>·</text>
<text><location><page_25><loc_34><loc_19><loc_35><loc_20></location>-</text>
<text><location><page_25><loc_36><loc_82><loc_37><loc_83></location>·</text>
<text><location><page_25><loc_36><loc_82><loc_37><loc_82></location>·</text>
<text><location><page_25><loc_36><loc_82><loc_37><loc_82></location>·</text>
<text><location><page_25><loc_38><loc_82><loc_39><loc_83></location>·</text>
<text><location><page_25><loc_38><loc_82><loc_39><loc_82></location>·</text>
<text><location><page_25><loc_38><loc_82><loc_39><loc_82></location>·</text>
<text><location><page_25><loc_38><loc_19><loc_39><loc_20></location>-</text>
<text><location><page_25><loc_39><loc_28><loc_40><loc_29></location>d</text>
<text><location><page_25><loc_39><loc_22><loc_41><loc_28></location>21014+5001</text>
<text><location><page_25><loc_39><loc_19><loc_41><loc_22></location>IRAS</text>
<text><location><page_25><loc_41><loc_19><loc_42><loc_20></location>-</text>
<text><location><page_25><loc_43><loc_82><loc_44><loc_83></location>·</text>
<text><location><page_25><loc_43><loc_82><loc_44><loc_82></location>·</text>
<text><location><page_25><loc_43><loc_82><loc_44><loc_82></location>·</text>
<text><location><page_25><loc_43><loc_23><loc_44><loc_33></location>J210240.13+501236.5</text>
<text><location><page_25><loc_43><loc_19><loc_44><loc_22></location>WISE</text>
<text><location><page_25><loc_44><loc_82><loc_46><loc_83></location>·</text>
<text><location><page_25><loc_44><loc_82><loc_46><loc_82></location>·</text>
<text><location><page_25><loc_44><loc_82><loc_46><loc_82></location>·</text>
<text><location><page_25><loc_44><loc_19><loc_46><loc_20></location>-</text>
<text><location><page_25><loc_46><loc_28><loc_47><loc_28></location>e</text>
<text><location><page_25><loc_46><loc_22><loc_47><loc_28></location>21010+5000</text>
<text><location><page_25><loc_46><loc_19><loc_47><loc_22></location>IRAS</text>
<text><location><page_25><loc_48><loc_82><loc_49><loc_83></location>·</text>
<text><location><page_25><loc_48><loc_82><loc_49><loc_82></location>·</text>
<text><location><page_25><loc_48><loc_82><loc_49><loc_82></location>·</text>
<text><location><page_25><loc_49><loc_82><loc_51><loc_83></location>·</text>
<text><location><page_25><loc_49><loc_82><loc_51><loc_82></location>·</text>
<text><location><page_25><loc_49><loc_82><loc_51><loc_82></location>·</text>
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<text><location><page_25><loc_51><loc_82><loc_52><loc_82></location>·</text>
<text><location><page_25><loc_48><loc_19><loc_49><loc_20></location>-</text>
<text><location><page_25><loc_51><loc_19><loc_52><loc_20></location>-</text>
<text><location><page_25><loc_53><loc_82><loc_54><loc_83></location>·</text>
<text><location><page_25><loc_53><loc_82><loc_54><loc_82></location>·</text>
<text><location><page_25><loc_53><loc_82><loc_54><loc_82></location>·</text>
<text><location><page_25><loc_53><loc_23><loc_54><loc_32></location>21024889+5010351</text>
<text><location><page_25><loc_53><loc_19><loc_54><loc_23></location>2MASS</text>
<text><location><page_25><loc_55><loc_82><loc_56><loc_83></location>·</text>
<text><location><page_25><loc_55><loc_82><loc_56><loc_82></location>·</text>
<text><location><page_25><loc_55><loc_82><loc_56><loc_82></location>·</text>
<text><location><page_25><loc_55><loc_19><loc_56><loc_20></location>-</text>
<text><location><page_25><loc_56><loc_82><loc_58><loc_83></location>·</text>
<text><location><page_25><loc_56><loc_82><loc_58><loc_82></location>·</text>
<text><location><page_25><loc_56><loc_82><loc_58><loc_82></location>·</text>
<text><location><page_25><loc_56><loc_23><loc_58><loc_33></location>J210249.68+501041.9</text>
<text><location><page_25><loc_56><loc_19><loc_58><loc_22></location>WISE</text>
<text><location><page_25><loc_58><loc_82><loc_59><loc_83></location>·</text>
<text><location><page_25><loc_58><loc_82><loc_59><loc_82></location>·</text>
<text><location><page_25><loc_58><loc_82><loc_59><loc_82></location>·</text>
<text><location><page_25><loc_58><loc_19><loc_59><loc_20></location>-</text>
<text><location><page_25><loc_60><loc_82><loc_61><loc_83></location>·</text>
<text><location><page_25><loc_60><loc_82><loc_61><loc_82></location>·</text>
<text><location><page_25><loc_60><loc_82><loc_61><loc_82></location>·</text>
<text><location><page_25><loc_61><loc_82><loc_63><loc_83></location>·</text>
<text><location><page_25><loc_61><loc_82><loc_63><loc_82></location>·</text>
<text><location><page_25><loc_61><loc_82><loc_63><loc_82></location>·</text>
<text><location><page_25><loc_61><loc_19><loc_63><loc_20></location>-</text>
<text><location><page_25><loc_63><loc_82><loc_64><loc_83></location>·</text>
<text><location><page_25><loc_63><loc_82><loc_64><loc_82></location>·</text>
<text><location><page_25><loc_63><loc_82><loc_64><loc_82></location>·</text>
<text><location><page_25><loc_65><loc_82><loc_66><loc_83></location>·</text>
<text><location><page_25><loc_65><loc_82><loc_66><loc_82></location>·</text>
<text><location><page_25><loc_65><loc_82><loc_66><loc_82></location>·</text>
<text><location><page_25><loc_65><loc_19><loc_66><loc_20></location>-</text>
<text><location><page_25><loc_66><loc_28><loc_67><loc_28></location>i</text>
<text><location><page_25><loc_67><loc_22><loc_68><loc_28></location>21007+4951</text>
<text><location><page_25><loc_67><loc_19><loc_68><loc_22></location>IRAS</text>
<text><location><page_25><loc_68><loc_19><loc_69><loc_20></location>-</text>
<text><location><page_25><loc_70><loc_82><loc_71><loc_83></location>·</text>
<text><location><page_25><loc_70><loc_82><loc_71><loc_82></location>·</text>
<text><location><page_25><loc_70><loc_82><loc_71><loc_82></location>·</text>
<text><location><page_25><loc_70><loc_19><loc_71><loc_33></location>WISE J210226.45+500203.4</text>
<text><location><page_25><loc_72><loc_82><loc_73><loc_83></location>·</text>
<text><location><page_25><loc_72><loc_82><loc_73><loc_82></location>·</text>
<text><location><page_25><loc_72><loc_82><loc_73><loc_82></location>·</text>
<text><location><page_25><loc_72><loc_19><loc_73><loc_20></location>-</text>
<section_header_level_1><location><page_25><loc_77><loc_20><loc_79><loc_56></location>a Clark source e , IRAS 2 1023+5002, WISE J2 10358.18+501439.9, see Fig. 16a</section_header_level_1>
<text><location><page_25><loc_80><loc_38><loc_81><loc_40></location>16b</text>
<text><location><page_25><loc_80><loc_36><loc_81><loc_38></location>Fig.</text>
<text><location><page_25><loc_80><loc_34><loc_81><loc_35></location>see</text>
<text><location><page_25><loc_80><loc_23><loc_81><loc_34></location>J210428.01+501348.5,</text>
<text><location><page_25><loc_80><loc_20><loc_81><loc_23></location>WISE</text>
<text><location><page_25><loc_80><loc_20><loc_81><loc_20></location>b</text>
<text><location><page_25><loc_82><loc_24><loc_84><loc_26></location>16c</text>
<text><location><page_25><loc_82><loc_22><loc_84><loc_24></location>Fig.</text>
<text><location><page_25><loc_82><loc_20><loc_84><loc_22></location>see</text>
<text><location><page_25><loc_82><loc_20><loc_83><loc_20></location>c</text>
<text><location><page_25><loc_85><loc_20><loc_86><loc_47></location>d Clark source c , WISE J210303.24+501312.4, see Fig. 16 d</text>
<text><location><page_26><loc_12><loc_20><loc_14><loc_40></location>e WISE J210242.41+501227.8, see Fig. 16e</text>
<text><location><page_26><loc_15><loc_20><loc_16><loc_33></location>f Clark source f , see Fig. 16f</text>
<text><location><page_26><loc_18><loc_31><loc_19><loc_33></location>16g</text>
<text><location><page_26><loc_18><loc_29><loc_19><loc_31></location>Fig.</text>
<text><location><page_26><loc_18><loc_27><loc_19><loc_28></location>see</text>
<text><location><page_26><loc_18><loc_24><loc_19><loc_27></location>Star,</text>
<text><location><page_26><loc_18><loc_22><loc_19><loc_24></location>stern</text>
<text><location><page_26><loc_18><loc_21><loc_19><loc_22></location>e</text>
<text><location><page_26><loc_18><loc_20><loc_19><loc_21></location>W</text>
<text><location><page_26><loc_17><loc_20><loc_18><loc_20></location>g</text>
<text><location><page_26><loc_20><loc_31><loc_21><loc_33></location>16h</text>
<text><location><page_26><loc_20><loc_29><loc_21><loc_30></location>Fig.</text>
<text><location><page_26><loc_20><loc_27><loc_21><loc_28></location>see</text>
<text><location><page_26><loc_20><loc_24><loc_21><loc_27></location>Star,</text>
<text><location><page_26><loc_20><loc_20><loc_21><loc_24></location>Eastern</text>
<text><location><page_26><loc_20><loc_20><loc_21><loc_20></location>h</text>
<text><location><page_26><loc_22><loc_20><loc_24><loc_78></location>i Clark sou rce a . This IRA S source ma y b e a blend of the t w o sources listed ab o v e it (WISE J210222.70+50030 8.3 & WISE</text>
<text><location><page_26><loc_24><loc_19><loc_26><loc_29></location>J210223.85+50030 6.8).</text>
</document>
[
{
"title": "ABSTRACT",
"content": "We have searched the Lynds 988 dark cloud complex for optical (H α and [S ii ]) and near-IR (H 2 2.12 µ m) shocks from protostellar outflows. We find 20 new Herbig-Haro objects and 6 new H 2 shocks (MHO objects), 3 of which are cross detections. Using the morphology in the optical and near-IR, we connect several of these shocks into at least 5 distinct outflow systems and identify their source protostars from catalogs of infrared sources. Two outflows in the cloud, from IRAS 21014+5001 and IRAS 21007+4951, are in excess of 1 pc in length. The IRAS 21007+4951 outflow has carved a large cavity in the cloud through which background stars can be seen. Also, we have found an optical shock which is the counterflow to the previously discovered 'northwest outflow' from LkH α 324SE. Subject headings: ISM: Herbig-Haro objects - ISM: jets and outflows - ISM: individual (Lynds 988) - stars: formation",
"pages": [
1
]
},
{
"title": "J. Walawender",
"content": "Subaru Telescope, National Astronomical Observatory of Japan, Hilo, HI 96720 [email protected] B. Reipurth Institute for Astronomy, University of Hawaii at Manoa, Hilo, HI 96720 and",
"pages": [
1
]
},
{
"title": "J. Bally",
"content": "Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80309",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Star formation is a dynamic process whereby newborn stars interact with their parent cloud. High velocity outflows from accreting stars collide with parent molecular material generating shocks (known as Herbig-Haro objects when detected optically), opening cavities (Quillen et al. 2005), and driving turbulence (Miesch & Bally 1994; Bally et al. 1999; Arce & Goodman 2002; Walawender et al. 2005). Shocks from outflows heat, dissociate, and ionize the gas. They also inject kinetic energy and momentum into the cloud which may affect the rate of gravitational collapse of cores within these clouds (Leorat et al. 1990, e.g). Outflows may play a fundamental role in the evolution of star forming molecular clouds, turbulence generation, and cloud destruction. In this paper, we have searched the Lynds 982, 984, and 988 dark cloud complex (L988 hereafter; see Fig. 1) for shocks from protostellar outflows using tracers in both optical (H α and [S ii ]) and near-IR (H 2 ) tracers. L988 lies in Cygnus near the Cygnus OB7 association which is among the nearest of the Cygnus OB associations at roughly 740-800 pc. L988 is part of a larger cloud complex known as Kh 141 (Chavtasi 1960), or TGU 541 (Dobashi et al. 2005), and is sometimes called The Northern Coalsack. The two regions of highest extinction within the Kh 141 complex are L988 and L1003 (see Reipurth & Schneider 2008, Fig. 28), both of which are active regions of star formation. Distance estimates for the L988 complex range between 500 and 780 pc. Chavarria (1981) estimated the distance at 700 pc based on photometry of several stars in the region. Later, Chavarria & de Lara (1981) estimated a distance of 780 pc. Shevchenko et al. (1991) found a distance of 550 pc based on extinction estimates. Alves et al. (1998) studied extinction toward the nearby L977 cloud and found a distance of 500 pc. For calculations in this paper, we assume an intermediate distance of 600 pc. The first outflow study in the region was a millimeter CO line survey by Clark (1986) who found four molecular outflows around IRAS sources which he designated a , c , e , and f . Subsequently the flow surrounding IRAS 21007+4951 (Clark source a ) was imaged by Hodapp (1994) in the near-IR (K ' ) and by Staude & Elsasser (1993) in r. Staude & Elsasser (1993) found four HH objects which were not assigned catalog numbers. These HH objects correspond to our HH 1050 knots B, C, E, & F (see § 3). Felli et al. (1992) searched for H 2 O masers around young stars and found a maser associated with Clark source a . Their search did not detect masers coincident with Clark sources e or f . Herbig & Dahm (2006) examined the LkH α 324 region in L988 using broadband optical and near-IR imaging and optical spectroscopy and discovered a small cluster of YSOs surrounding LkH α 324. They found the age of the cluster surrounding LkH α 324 to be 0.6-1.7 Myr depending upon the evolutionary model used in the analysis. Herbig & Dahm (2006) also examined the LkH α 324SE star (IRAS 21014+5001, Clark source c ) in detail using Keck HIRES spectroscopy. They found features which they designate the 'northwest outflow' (later designated HH 899) which is composed of several condensations prominent in [S ii ] and [O ii ] lines. In a 7 '' long slit oriented at P.A. = 129/309 · , they found three [S ii ] condensations to the northwest at velocities of -160 to -185 km s -1 relative to the -18 km s -1 rest velocity of the star. No red-shifted counterparts to the 'northwest outflow' knots were detected. Allen et al. (2008) examined the cluster surrounding Clark source e with the Spitzer Space Telescope and cataloged young stars in the region.",
"pages": [
1,
2,
3
]
},
{
"title": "2. Observations",
"content": "Near infrared data for this project were obtained on the nights of 2006 July 11-13 on the United Kingdom Infrared Telescope (UKIRT) using the Wide Field InfraRed Camera (WFCAM, Casali et al. 2001), which is comprised of four Rockwell Hawaii-II 2048 × 2048 pixel arrays separated by 94% of the size of an individual chip. The instantaneous field of view is 0.21 square degrees, however to obtain a contiguous field of view, four pointings of the telescope must be used to fill in the space between arrays. A four pointing 'tile' covers approximately 0.8 square degrees. In the J, H, and K filters, we obtained a total integration time of 6 minutes over the L988 tile. In the H 2 filter, we obtained 72 minutes of integration time. WFCAM data were pipeline processed by the Cambridge Astronomical Survey Unit (CASU). The 16 resulting image stacks were then mosaiced together using the Image Reduction and Analysis Facility 1 (IRAF) to form the full field of view of the tile. Visible wavelength narrowband images were obtained on the night of 2006 May 28 on the Subaru Telescope using the Suprime-Cam instrument (Miyazaki et al. 2002). SuprimeCam is a wide field prime focus camera comprised of ten 2048 × 4096 pixel CCDs. The instantaneous field of view is approximately 34 ' × 27 ' . Images were taken in the H α and [S ii ] filters, each with a total exposure time of 50 minutes. Subaru data were processed using IRAF's mscred package. Images were overscanned, trimmed, bias subtracted, and then flat fielded (using both dome and twilight flats) by the ccdproc task. Images were intensity matched using mscimatch and stacked using mscstack based on world coordinate system fits generated by msccmatch . Visible wavelength SDSS i' images were obtained on the night of 2010 Aug 25 on the University of Hawaii 88 inch Telescope using the Wide Field Grism Spectrograph 2 (WFGS2; Uehara et al. 2004) instrument in imaging mode. WFGS2 uses the Tek2k CCD camera with 2048 × 2048 pixels. With the WFGS2 focal reducer, the field of view is approximately 11 arcminutes on a side. SDSS i' images were only obtained for the field centered on the IRAS 21007+4951 reflection nebula. A total of 35 minutes of integration time was obtained. Reductions, alignment, and stacking were performed using the ccdproc package in IRAF.",
"pages": [
4
]
},
{
"title": "3. Results",
"content": "The L988 cloud has several active protostellar outflows which are visible in our narrowband images. Some appear to be associated with cavities in the cloud which have been carved out by the action of the outflow. Fig. 1 shows the region of the cloud covered by our H α and [S ii ] images. Table 1 contains a list of all Herbig-Haro objects (HH objects; Reipurth 2000) and molecular hydrogen shocks (MHO objects; Davis et al. 2010) in our field. In the following paragraphs, we discuss individual shocks, organized into proposed outflow groups HH 1061 & 1059: HH 1061 (Fig. 2) lies 0.4 ' south-southeast of LkH α 324SE (Clark source e , IRAS 21023+5002; see Table 2) and its associated reflection nebula and cluster of sources. The primary component is a thin H α bright filament, oriented northwest-southeast and roughly 10 '' long. There are additional faint filaments of emission (knots B, C, & D) stretching about 1.3 ' further to the southeast. The shock lies in a low extinction region which may be a cavity outflows have blown out of the cloud. There are two compact knots (HH 1059A & B) in both the H α and [S ii ] images about 2 ' to the northwest of HH 1061 (Fig. 2). They lie along the line defined by the HH 1061 knots and lie across the cluster from HH 1061, thus they are likely counterflow components to HH 1061. There are several young stars catalogued by Allen et al. (2008) in the LkH α 324 cluster, therefore it is not possible to determine with confidence which of the young stars may drive this outflow. However, using spectroscopy Herbig & Dahm (2006) detected a high velocity 'northwest outflow' (HH 899) within 3 '' of the LkH α 324SE star. That source lies close to the line defined by HH 1061 knots and HH 1059. The high velocity knots of Herbig & Dahm (2006) were detected in a spectrograph slit oriented at P.A. ∼ 129/309 · , the HH 1061/1059 flow lies at a position angle of ∼ 151/331 · . Given that the slit may not have been placed precisely along the outflow axis (which was unknown at the time of the observation), these values seem to be in reasonable agreement and it is likely that LkH α 324SE is the driving source and that HH 899 is part of a flow with HH 1061 & HH 1059. The LkH α 324SE source has been detected in several infrared surveys (see Table 2). Those measured fluxes were used to fit the spectral energy distribution (SED) using the models of Robitaille et al. (2007) (see Fig. 16a). The SED shows evidence of strong disk and envelope components. Clark (1986) found a bipolar outflow surrounding LkH α 324SE. The outflow is oriented roughly North-South with the blue-shifted lobe to the North, moving into the higher extinction region. It is unclear whether the CO outflow of Clark (1986) and HH 1061 & 1059 trace the same flow. While the Clark outflow appears to be oriented North-South (P.A. = 0/180 · ), the low resolution in Clark Figure 1 makes the association of the two unclear. MHO 954: A bow shaped H 2 knot (MHO 954A) lies ∼ 1 ' due west of LkH α 324SE (see Fig. 2) along with a line of fainter knots (MHO 954B-E). Based on their position relative to the core of the cluster, it seems unlikely that these shocks are from the same outflow as HH 1061 and 1059. HH 1057 & 1056: These are compact, H α bright shocks (Fig. 3) which lie in a dark portion of the cloud. There is no clear association with a known flow or source, however we note that the MHO 954 shock, HH 1057, and 1056 B lie along an axis which passes through the cluster of sources near LkH α 324SE and thus may be a single outflow emerging from one of the sources embedded in the reflection nebula. HH 1062: These three knots lie in a low extinction region East of the cloud (Figs. 3 & 4). They surround a bright star visible in our narrowband H α and [S ii ] images which corresponds to an IRAS source (IRAS 21028+5001). This star was also detected by WISE (WISE J210428.01+501348.5) and it lies roughly on a line drawn between the shocks, but it is not clear if they are driven by it. Fluxes for the star are listed in Table 2 and the model SED is shown in Fig. 16b. HH 1062 A lies 26 '' to the West of the source along PA ∼ 288 · while knots B and C lie 52 '' and 59 '' to the East along PA ∼ 107 · and 116 · respectively. We also note that these shocks lie roughly along a line defined by the HH 1057 and 1056 shocks that passes through the reflection nebula. HH 1062 may be a shock in a larger flow and is perhaps not driven by the nearby IRAS 21028+5001. HH 1058: This is a faint, H α only shock (Figs. 3 & 5) which appears to be a jet emerging from an optically visible star along PA ∼ 125/305 · . The star was detected by both 2MASS and WISE (WISE J210339.46+501552.9) and those magnitudes are listed in Table 2. Using those fluxes, we fit the SED using the models of Robitaille et al. (2007) (see Fig. 16c). The best fit models show that this is a low mass young star ( ∼ 0.25 M glyph[circledot] ) with a relatively low disk accretion rate ( ∼ 10 -11 M glyph[circledot] /yr). HH 1053, 1049, 1046, 1060, & 1063: The HH 1053, 1049 (Fig. 6), & 1046 shocks (Fig. 7) appear to all be the western components of a single flow powered by IRAS 21014+5001 (aka Clark source c ), it is possible that HH 1049 or 1046 are from another source, but the alignment of these three shocks with IRAS 21014+5001 appears convincing. The corresponding counterflow to the southeast emerges into a low extinction region of the cloud and is composed of the HH 1060 and 1063 shocks (Fig. 8). If this is all one flow which emerges from that source, then the length of the flow is 26.5 ' which corresponds to a length of 4.6 pc at an assumed distance of 600 pc. Clark designated IRAS 21014+5001 as a molecular outflow source based upon finding a patch of blue-shifted gas West of the source (see Clark 1986 Fig. 1). This patch of blueshifted CO does not correspond to our HH 1053, 1049, 1046 outflow. The blue-shifted CO is centered South of the axis defined by our HH objects. Though the northernmost contour in Clark (1986, Fig. 1) comes close to our flow axis near HH 1049, the bulk of the blue-shifted CO is closer to our HH 1052 (see below). The IRAS 21014+5001 source was detected by WISE, the fluxes are listed in Table 2 and the model SED is shown in Fig. 16d. MHO 955: There is a star visible in the J, H, & K images (and faintly in H α and [S ii ]) 1.2 ' east-southeast of IRAS 21014+5001 near the axis defined by the HH 1053, 1049, 1046, 1060, 1063 outflow which is coincident with a 0.2 ' long H 2 filament (MHO 955) pointing northeast from the star, at first glance it appears that it is emanating from the star. That star was determined to be a Class I protostar by Allen et al. (2008), however it lies along the axis of the HH 1053, 1049, 1046 flow from IRAS 21014+5001 and so may alternatively be a shock in the embedded counterflow which happens to be coincident with a star along our line of sight. HH 1044: This is a [S ii ] bright knot (Fig. 9) which lies at the northwest corner of the Subaru image. There appears to be a faint H α filament extending due North from it, but this may also be an illuminated cloud edge. IRAS 20595+5009 lies 2.5 ' north of the shock, outside of the field of view of our H α and [S ii ] images. HH 1052: The A & B knots of this object (Figs. 6) are a pair of faint H α and [S ii ] filaments. The B component has an H 2 counterpart (MHO 956). There is a faint V-shaped reflection nebula visible in the H and K images 0.3 ' southeast of the knots. The reflection nebula opens toward both of the knots. At the apex of the reflection nebula is a candidate for the source star. While it is not detected in our J, H, or K S images, it is detected by WISE (WISE J210240.13+501236.5; Table 2). In addition, there is another candidate source star visible in our near-IR images which lies 19 '' to the southeast. It is coincident with IRAS 21010+5000 and is detected in the WISE catalog (WISE J210242.41+501227.8; Table 2; Fig. 16e). The blue-shifted CO which was discovered by Clark (1986) is coincident with the HH 1052 shock system. Clark associated this with IRAS 21014+5001, however we asso- ciate that source with the HH 1053, 1049, 1046 flow. HH 1047: This shock system appears to be a curved, C-shaped outflow. The C-shaped curve suggests that the source is moving to the southeast (Bally & Reipurth 2001). In our near-IR images, several stars (many with corresponding WISE detections) lie on or near the arc of the flow and would be source candidates. Of these, three stand out as being directly along the arc of the flow (WISE J210214.15+501013.0, WISE J210218.93+501102.3, & WISE J210217.70+501046.5). The first of these is optically visible while the other two are visible only in our near-IR images. We examined the models of Robitaille et al. (2007) built based upon the WISE and 2MASS magnitudes of each of these and have selected the optically visible star (WISE J210214.15+501013.0) as the best candidate as it is the only one of the three with a significant envelope flux in the fitted SED. The fluxes for this star are listed in Table 2 and the result of the Robitaille et al. (2007) model fit can be seen in Fig. 16f. It is also possible that this is merely a bow shock driven by a more distant source, however, the morphology is suggestive of a jet and even if this were a bow shock, the arc of the curve would indicate a forward facing bow shock coming from the northwest and there are no strong flows visible in our images in that direction. The star V1331 Cyg and its associated outflow (HH 389) lie along that axis a few arcminutes outside of the field of view of our SuPrimeCam images. The [S ii ] images of Mundt & Eisloffel (1998) show shocks to the north and south of V1331 Cyg. Their orientations relative to the source are inconsistent with HH 1047 being a component in that flow. HH 1054: This is a compact cluster of [S ii ] dominant knots (Fig. 11) coincident with a short 7 '' V-shaped H 2 shock (MHO 957) which opens to the North. In that direction, there are two optical and near-IR stars about 1 arcminute away, both with reflection nebulosity. The first source (2MASS 21024889+5010351; Table 2) is seen in our visible light narrowband images as well and has a small reflection nebula surrounding it which (in our optical images) appears to open southward. This source has a brighter companion star 3.5 '' to the West (WISE J210248.45+501036.1). This star is a likely candidate for the outflow source as the orientation of the reflection nebula is aligned with the presumed flow direction. Another candidate source star with a reflection nebula (WISE J210249.68+501041.9; Table 2) is visible in our near-IR images and lies about 1 arcminute North of the H 2 shock. Its reflection nebula, however, appears to open to the East. The source star does not appear in the 2MASS catalog. We were unable to determine reliable J, H, and K magnitudes for this star due to the presence of the reflection nebula, but it is clearly very red (invisible in J, faint in H, and bright in K). HH 1051: The HH 1050 and 1051 outflow system is a complex arrangement of shocks and reflection nebulosity (Fig. 12). The reflection nebula appears to outline a two-lobed cavity surrounding Clark source a . There are two stars embedded in the reflection nebula. The western star (WISE J210222.70+500308.3; Table 2; Fig. 16g) is not readily seen in the visible light images, but is detectable in the J images and is increasingly bright at the longer (H and K) wavelengths. The eastern star (WISE J210223.85+500306.8; Table 2; Fig. 16h) lies 15 '' East of the western star, is visible at all wavelengths, and is brighter than the western star at i', J, H, and K. IRAS 21007+4951 lies in between the Eastern and Western stars, slightly closer to the Western star. Neither star lies within the error ellipse of the IRAS source (Fig. 13). It is possible that the IRAS source is a blend of the two WISE sources. The eastern star appears to drive a faint, highly collimated [S ii ] jet (HH 1051 A & B; see Fig. 12) along position angle 60 · . To the northeast along the axis defined by the jet, there are two faint shocks (HH 1051 C & D) which lie 88 '' and 119 '' from the source respectively. These faint shocks are just visible in the [S ii ] images and have no corresponding signal in the H α or i ' images, nor are there faint stars at those locations in any of the near-IR images. The southwestern portion of the jet blends with the southern edge of the reflection nebula. Further to the southwest are faint shocks (see Fig. 13) which may be part of this flow, however they overlap with the western lobe of the HH 1050 flow described below. HH1050 & 1045: The western of the two stars in the region appears to drive a long outflow (HH 1050; see Fig. 13) in the East-West direction. This outflow is much more extended than the HH 1051 outflow and lies along a nearly East-West line (PA ∼ 90 · /270 · ). There is also a bright, compact H 2 , H α , and [S ii ] knot (HH 1050 F / MHO 958) 4 '' west of the western star. Knots A-E of this shock system (Fig. 12) are the eastern component of the flow. The furthest is knot A which lies 1.6 ' east of the source. The B & C knots are bright in both H α and [S ii ] and both have H 2 counterparts (MHO 958). Knots D & E are fainter H α and [S ii ] knots with an H 2 knot (MHO 958) a few arcseconds southwest of E. HH 1050 knots F-P appear to comprise the western half of the outflow. The innermost shocks (knots F and G) appear to have the morphology of compact bow shocks emanating from the area at the center of the reflection nebula. Knot J appears to be a shock outlining the edge of a dense cloud edge which is visible in the H α and H 2 images. The southern knots (J, K, N, O, and P) could be distant components of HH 1051, or the southern half of a less collimated component of HH 1050. Because there is faint, filamentary emission which appears to connect many of the shocks in this region, we favor the explanation that all of the knots (F-P) are part of the HH 1050 outflow, but the possibility that at least some of these (especially the most southern knots J, K, and N) are associated with the HH 1051 flow cannot be excluded. The pair of knots which make up HH 1045 comprise a ∼ 30 '' long filament of H α & [S ii ] emission which lies 8.1 ' West of the HH 1050 outflow source along the axis of the flow (see Fig. 14). This system appears to be a distant bow shock in that outflow. At an assumed distance of 600 pc, that makes the total length of the HH 1050 outflow 1.7 pc. The reflection nebula surrounding the HH 1050 outflow source outlines a V-shaped cavity about 2 ' long with a wide ∼ 45 · opening angle (Fig. 13). The northern half of this cavity, past knots L, & K, emerges into a low extinction region in which background stars can be seen. The southern half of the cavity is a higher extinction region. The Clark (1986) outflow map shows red- and blue-shifted lobes which correspond to our HH 1050 outflow. The eastern half of the flow (knots A-E) correspond to red-shifted CO and the western half (knots F-P) correspond to blue-shifted CO. HH 1048: Knot A of HH 1048 is a small, compact blob of emission just emerging from a star which lies at the apex of a C-shaped reflection nebula (Fig. 12) and which is coincident with WISE J210226.45+500203.4 (Table 2). Knot B of HH 1048 is an H α and [S ii ] filament which lies in the middle of that C-shaped reflection nebula. HH 1048 knot C is a compact, H α only bow which lies near the eastern end of the reflection nebula, about 0.5 ' from the star. HH 1048 D is a compact, nearly starlike knot of H α and [S ii ] emission. HH 1048 knot E is another filament which lies roughly 1 ' east of the star and slightly north of the line defined by the knot B filament, it may trace the northern edge of the outflow cavity. The J, H, & K images also show one arc of the reflection nebula extending roughly 15 '' northeast of the source star. The Clark (1986) outflow map shows a blob of blue-shifted CO which is connected to the blue-shifted lobe of his source a . While Clark did not discuss this as a separate outflow, it is perfectly coincident in position with our HH 1048 knots A & B and appears to match the outline of the associated reflection nebula in size. HH 1055: This shock system is a cluster of faint, [S ii ] bright, low surface brightness shock filaments (Fig. 15) embedded in some patchy dust filaments along the eastern edge of the cloud. They lie near to the axis defined by the HH 1051 and 1050 outflows from the IRAS 21007+4951 source, however a positive association with those outflows is not possible based on the present data.",
"pages": [
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17
]
},
{
"title": "4. Discussion",
"content": "The L988 region contains significant outflow activity as revealed by our surveys for optical and near-IR shock tracers. The region contains nearly two dozen independent shock systems (20 Herbig-Haro objects and 3 MHO objects unaffiliated with HH objects), however we can only confidently identify the driving protostar for five outflows (LkH α 324SE, IRAS 21014+5001, WISE J210214.15+501013.0, WISE J210222.70+500308.3, and WISE Two outflows we have identified (from IRAS 21014+5001 and the IRAS 21007+4951 / WISE J210222.70+500308.3 / WISE 210223.85+500306.8 shock complex) each exceed 1 pc in length with the IRAS 21014+5001 flow being 4.6 pc long. Both of these large scale outflows originate from sources which are in the highest extinction regions of the cloud. We find several Herbig-Haro objects and one H 2 shock complex near the well studied cluster surrounding LkH α 324 (IRAS 21023+5002, Clark source e ). While much of the outflow activity in the L988 cloud is widely distributed over a region ∼ 30 ' ( ∼ 4-7 pc) in diameter, a group of at least three sources which drive overlapping outflows is clustered around the IRAS 21007+4951 source and its associated reflection nebula, located in the center of the L988 cloud. A notable feature of this study is that outflow activity is detected primarily at visible wavelengths (H α and [S ii ]) while our near-IR images (H 2 ) show relatively little shock activity and most of what is detected in the near-IR is coincident with H α or [S ii ] shocks. This is likely due, at least in part, to the combination of the near-IR data being taken on a smaller telescope (3.8 meter as opposed to 8.2 meter) and under much worse seeing conditions ( ∼ 1.5 '' FWHM for the H 2 images compared to 0.65-0.70 '' for the H α and [S ii ]). We suspect that further study of this region at near-IR wavelengths will reveal additional details. We would like to thank an anonymous referee for helpful comments. JW was supported by the NSF through grants AST-0507784 and AST-0407005. JW and BR acknowledge support from the National Aeronautics and Space Administration through the NASA Astrobiology Institute under Cooperative Agreement No. NNA09DA77A issued through the Office of Space Science. This work is based in part on data collected at the Subaru telescope, which is operated by the National Astronomical Observatory of Japan (NAOJ). We are grateful to Nobunari Kashikawa for permission to use his [SII] filter for the SuPrimeCam instrument on the Subaru Telescope. This publication makes use of data obtained on the United Kingdom Infrared Telescope (UKIRT) which is operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the U.K. This publication makes use of data products from the 2MASS, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. MHO catalogue is hosted by Liverpool John Moores University. We also thank the University of Hawaii Time Allocation Committee for allocating the nights during which these observations were made. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this sacred mountain. Facilities: Subaru (Suprime-Cam), UKIRT (WFCAM), UH 88 inch Telescope (Tek2k), WISE, 2MASS",
"pages": [
17,
18,
19
]
},
{
"title": "REFERENCES",
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"pages": [
20,
21
]
},
{
"title": "T able 2. Photometry of Sources in L988.",
"content": "IRAS IRAS IRAS IRAS WISE WISE WISE SE I W 2MASS 2MASS 2MASS Mission m µ 100 m µ 60 m µ 25 m µ 12 m µ 22 m µ 12 m µ 4.6 m µ 3.4 K H J Band (Jy) (Jy) (Jy) (Jy) (mag) (mag) (mag) (mag) ) (mag (mag) (mag) (Units) 199 44 ± 199 < 39.8 3.2 ± 47.0 < 31.6 2.5 ± 10.56 8.27 6 . 4 6 3.94 2.20 0.33 -1.337 23.9 33.7 87 ± 0.02 ± 0.02 ± 0.02 ± 0.10 ± 0.09 ± 0.02 ± 0.008 ± 1.2 ± 1.0 ± 11 10.26 9.16 8 . 3 1 7.10 6.46 4.33 2.43 0.81 1.1 < 2.76 ± 0.02 ± 0.02 ± 0.02 ± 0.03 ± 0.02 ± 0.01 ± 0.01 ± 0.05 ± 0.08 · · · 12.76 11.89 11.45 11.07 10.61 8.78 7.1 · · · · · · · · · ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.04 ± 0.2 · · · · · · · · · 10.10 9.95 9 . 8 6 9.57 9.32 4.34 2.08 1.12 1.71 11.8 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.01 ± 0.02 ± 0.06 ± 0.10 ± 1.3 · · · · · · · · · 12.48 10.69 7.78 2.38 · · · · · · · · · · · · · · · · · · ± 0.03 ± 0.02 ± 0.03 ± 0.02 · · · · · · · · · < 16.98 14.42 12.17 11.39 9.11 6.09 2.53 < 0.36 0.81 < 11.8 · · · ± 0.05 ± 0.03 ± 0.02 ± 0.02 ± 0.02 ± 0.02 · · · ± 0.08 · · · 14.54 13.63 13.05 11.69 10.71 8.62 7.29 · · · · · · · · · ± 0.04 ± 0.04 ± 0.05 ± 0.04 ± 0.03 ± 0.04 ± 0.15 · · · · · · · · · 16.32 13.42 13.94 · · · · · · · · · · · · · · · · · · · · · ± 0.14 ± n ull ± 0.08 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13.55 11.06 8.44 4.38 · · · · · · · · · · · · · · · · · · ± 0.03 ± 0.02 ± 0.03 ± 0.03 · · · · · · · · · < 16.37 < 14.82 13.28 10.72 7.16 4.23 0.90 · · · · · · · · · · · · · · · ± 0.05 ± 0.03 ± 0.02 ± 0.02 ± 0.01 · · · · · · · · · 12.98 11.53 10.54 9 . 2 1 7.95 5.17 2.72 · · · · · · · · · ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 ± 0.02 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 0.91 5.07 21.8 · · · · · · · · · · · · · · · · · · · · · ± 0.12 ± 0.35 ± 2.0 14.81 13.05 11.66 9.19 8.06 5.60 2.71 · · · · · · · · · ± 0.05 ± 0.03 ± 0.02 ± 0.006 ± 0.02 ± 0.014 ± 0.01 · · · · · · · · · c J210339.46+501552.9 WISE f J210214.15+501013.0 WISE g J210222.70+500308.3 WISE h J210223.85+500306.8 WISE LkH α 324SE a - IRAS 21028+5001 b · · · - · · · · · · - d 21014+5001 IRAS - · · · J210240.13+501236.5 WISE · · · - e 21010+5000 IRAS · · · · · · · · · - - · · · 21024889+5010351 2MASS · · · - · · · J210249.68+501041.9 WISE · · · - · · · · · · - · · · · · · - i 21007+4951 IRAS - · · · WISE J210226.45+500203.4 · · · -",
"pages": [
25
]
},
{
"title": "a Clark source e , IRAS 2 1023+5002, WISE J2 10358.18+501439.9, see Fig. 16a",
"content": "16b Fig. see J210428.01+501348.5, WISE b 16c Fig. see c d Clark source c , WISE J210303.24+501312.4, see Fig. 16 d e WISE J210242.41+501227.8, see Fig. 16e f Clark source f , see Fig. 16f 16g Fig. see Star, stern e W g 16h Fig. see Star, Eastern h i Clark sou rce a . This IRA S source ma y b e a blend of the t w o sources listed ab o v e it (WISE J210222.70+50030 8.3 & WISE J210223.85+50030 6.8).",
"pages": [
25,
26
]
}
]
2013AN....334...73D
https://arxiv.org/pdf/1303.1536.pdf
<document>
<text><location><page_1><loc_37><loc_81><loc_88><loc_86></location>Accepted for publication: Astronomische Nachrichten, (AN), 2013, 334, p. 73 ( Cambridge Workshop 17 on Cool Stars, Stellar Systems and the Sun )</text>
<section_header_level_1><location><page_1><loc_19><loc_75><loc_81><loc_79></location>New insights: the accretion process and variable wind from TW Hya 1</section_header_level_1>
<text><location><page_1><loc_44><loc_72><loc_56><loc_73></location>A. K. Dupree</text>
<text><location><page_1><loc_13><loc_67><loc_87><loc_70></location>Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 USA</text>
<text><location><page_1><loc_39><loc_64><loc_61><loc_65></location>[email protected]</text>
<section_header_level_1><location><page_1><loc_44><loc_60><loc_56><loc_61></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_24><loc_83><loc_58></location>For the first time in a classical T Tauri star, we are able to trace an accretion event signaled by an hour-long enhancement of X-rays from the accretion shock and revealed through substantial sequential changes in optical emission line profiles. Downflowing turbulent material appears in H α and H β emission. He D3 (5876 ˚ A) broadens, coupled with an increase in flux. Two hours after the X-ray accretion event, the optical veiling increases due to continuum emission from the hot splashdown region. The response of the stellar coronal emission to the heated photosphere follows about 2.4 hours later, giving direct evidence that the stellar corona is heated in part by accretion. Then, the stellar wind becomes re-established. A model that incorporates the dynamics of this sequential series of events includes: an accretion shock, a cooling downflow in a supersonically turbulent region, followed by photospheric and later, coronal heating. This model naturally explains the presence of broad optical and ultraviolet lines, and affects the mass accretion rates currently determined from emission line profiles. These results, coupled with the large heated coronal region revealed from X-ray diagnostics, suggest that current models are not adequate to explain the accretion process in young stars.</text>
<text><location><page_1><loc_17><loc_18><loc_83><loc_22></location>Subject headings: stars: individual (TW Hya) - stars: mass-loss - stars: variables: T Tauri stars - stars: winds, outflows - X-rays: stars</text>
<section_header_level_1><location><page_2><loc_42><loc_85><loc_58><loc_86></location>1. Introduction</section_header_level_1>
<text><location><page_2><loc_12><loc_67><loc_88><loc_82></location>TW Hya (CD -34 7151; HIP 53911) is arguably the closest accreting T Tauri star making it a choice object for detailed spectroscopic study. It is generally thought that cool material from the circumstellar disk surrounding the star is channeled by the stellar magnetic field and free-falls towards the star where a shock forms. The X-ray and optical spectra reported here probe this accretion process. Another major attribute of TW Hya is the fact that its surrounding circumstellar disk appears roughly face-on (Qi et al. 2004) so that the critical polar regions, where the accretion process occurs, can be observed directly without obscuration by the disk.</text>
<text><location><page_2><loc_12><loc_54><loc_88><loc_65></location>A major observational campaign was aimed towards TW Hya that involved dedicated X-ray spectroscopic observations amounting to 500 total ks with the CHANDRA spacecraft. These results are discussed in Brickhouse et al. (2010). Contemporaneous optical and infrared spectroscopy and photometry were carried out from 4 continents (Dupree et al. 2012). As a result, the process of accretion can be investigated, and for the first time, the source of the broad emission lines from the star can be reliably identified.</text>
<section_header_level_1><location><page_2><loc_35><loc_48><loc_65><loc_49></location>2. X-ray accretion signatures</section_header_level_1>
<text><location><page_2><loc_12><loc_26><loc_88><loc_45></location>The CHANDRA X-ray spectra contain many emission lines arising from high temperatures. Analysis of the line strengths reveals that three different components producing X-rays must be present in the TW Hya atmosphere: a high temperature ( ∼ 10 7 K) corona, a lower temperature (3 × 10 6 K) component arising from the accretion shock, and a large volume producing O VII , at slightly lower temperature (2.5 × 10 6 K) with density lower than the accretion shock itself (Brickhouse et al. 2010). The behavior of lines arising in the accretion shock, namely N VII , O VIII , Ne IX , Fe XVII , and Mg XI , can give a direct measure of the instantaneous strength of the accreting material. These lines are marked in the CHANDRA spectrum shown in Fig 1, and the variation of the strength of the sum of the accretion lines is shown in Fig. 2</text>
<text><location><page_2><loc_12><loc_19><loc_88><loc_24></location>The accretion line flux (Fig. 2) reveals an enhancement centered at JD 2454157.75 that represented the highest count rate in a 3 ks average of the long 500ks CHANDRA observation, and merits special study.</text>
<section_header_level_1><location><page_3><loc_34><loc_85><loc_66><loc_86></location>3. Simultaneous optical spectra</section_header_level_1>
<text><location><page_3><loc_12><loc_41><loc_88><loc_82></location>Many simultaneous high-resolution optical spectra were taken during the X-ray accretion enhancement, providing the opportunity to evaluate the effect of the increase in the accreting line flux on the optical emission lines. Echelle spectra were taken continuously over 3 nights with the MIKE spectrograph at the Magellan/CLAY telescope of Las Campanas Observatory. These spectra have a resolution ∼ 35,000 so that the line profiles are well-resolved. Fig. 3 shows the behavior of the total flux and the line profile asymmetries during the span of the X-ray measures shown in Fig. 2. The flux of H α does not exhibit any systematic change, which is not surprising since the line is surely optically thick. However, the asymmetry of the line does change quite abruptly following the X-ray accretion event. The asymmetry of a line profile indicates the mass flow in a differentially moving line-forming region (Hummer & Rybicki 1968). Of course, if a slab moves at constant velocity, the whole profile will shift by an amount corresponding to the constant velocity. But differential motion as found in a stellar wind or in downflowing material produces a change in the line asymmetry. If the short-wavelength side ('blue') of the line is stronger than the long-wavelength side ('red'), material is flowing away from the observer and vice versa . The abrupt increase in the value of the blue:red ratio for H α suggests an abrupt increase in down-flowing material that begins about 9 minutes after the increase in the X-ray accretion line flux. This increased inflow continues for about 1.5 hours. The H β emission line exhibits a similar increase in the ratio of blue to red emission, echoing the increased downflow of material exhibited by the H α line. In addition, an increase in the strength of the total H β emission occurs.</text>
<text><location><page_3><loc_12><loc_22><loc_88><loc_40></location>The D3 line of He I at 5876 ˚ A is also a valuable probe of the accretion process. It is known to have both a broad and narrow component of emission. The broad component is generally thought to signal accretion (Donati et al. 2011) in a similar way as the broad lines of the Balmer series. A sharp increase in the flux at the end of the X-ray accretion event results from an enhanced long wavelength wing of the line profile, and the increase in line flux beginning about 30 minutes later (see Fig. 4) is due to a 30% increase in the broad component of the line, whereas the narrow component is constant to within 15%. The sequential changes of the optical lines following the X-ray accretion strongly suggests that they form in the post-shock cooling zone.</text>
<text><location><page_3><loc_12><loc_11><loc_88><loc_20></location>The line widths themselves give additional support to this formation scenario. The Balmer lines have a FWHM of about ± 150 kms -1 , which is obviously in excess of a thermal width ( ∼ 21 kms -1 ) at a temperature of 10 4 K, and also in harmony with the measured widths of the Ne IX ( ± 165 kms -1 ) lines observed in the CHANDRA spectra (Brickhouse et al. 2010). Far ultraviolet line widths of C III and O VI , when corrected for wind absorption,</text>
<text><location><page_4><loc_12><loc_85><loc_66><loc_86></location>suggest similar line widths of ± 160 kms -1 (Dupree et al. 2005).</text>
<text><location><page_4><loc_12><loc_63><loc_88><loc_83></location>The veiling or 'weakening' of absorption lines in the optical spectrum arises from a continuum and perhaps a contribution from line emission (Petrov et al. 2011) produced by the accretion hot spot in the photosphere. The value of the veiling from the short wavelength region (4400-5000 ˚ A) of the MIKE spectra is shown in Fig 4 also. It too increases with a delay of 2 hours after the X-ray accretion event. Such a delay is consistent with a reasonable size of the photospheric 'hot spot'. Using a value of 35 km s -1 for the post shock downflow indicated by substantial absorption at that velocity in the H β profile suggests that material will traverse a distance comparable to the size of a hot spot covering ∼ 10% of a star with radius 0.8 R /circledot in 2.8 hours. The flux from the corona (represented by the first order CHANDRA spectrum) responds ∼ 2 hours later to an increase in veiling (Dupree et al. 2012).</text>
<section_header_level_1><location><page_4><loc_40><loc_57><loc_60><loc_59></location>4. The stellar wind</section_header_level_1>
<text><location><page_4><loc_12><loc_44><loc_88><loc_55></location>The Balmer profiles also reveal the wind structure and its variation. H α and H β profiles observed over 4 successive nights are shown in Fig. 5 and Fig. 6. The X-ray accretion event discussed earlier occurred during the first night when the H α profile is roughly symmetric. During the subsequent 3 nights, absorption appears and systematically increases on the negative velocity side of the line. The wind which appears very weak or perhaps absent on the first night, recovers and becomes more opaque during the following nights.</text>
<text><location><page_4><loc_12><loc_31><loc_88><loc_42></location>The symmetry of the broad H α profile on the first night demonstrates that the line is not formed in an accretion stream (which should appear only at positive velocities), but most likely in a turbulent region of the atmosphere with velocity centered on the TW Hya itself. H α has a higher opacity than H β and would be formed higher in the atmosphere ('at the edges') of a turbulent region than the H β transition. Thus it is not surprising that the inflow signature is stronger in the weaker H β line.</text>
<text><location><page_4><loc_12><loc_20><loc_88><loc_29></location>Because the wind also substantially modifies the emission line profiles, this suggests that the line width may not be a good indicator of the accretion rate as has been proposed (Natta et al. 2004). In fact, in our observations, the wind (and undoubtedly accretion contributes also) changes the width of the line at the 10% level which, if dependent only on accretion, corresponds to a factor of 5 in the mass accretion rate.</text>
<text><location><page_4><loc_12><loc_11><loc_88><loc_18></location>The near-infrared He I transition at λ 10830 has proved to be an excellent tracer of winds from T Tauri stars (Dupree et al. 2005). This transition arises from a metastable level of neutral helium and thus maintains a relatively high population which can absorb the strong infrared continuum from a cool star. The broad emission appears likely to arise also in the</text>
<text><location><page_5><loc_12><loc_72><loc_88><loc_86></location>post-shock cooling zone of TW Hya, and the extent of the absorption (to ∼ -300 kms -1 ) clearly documents the presence of a fast wind. The terminal velocity of the wind varies with time ( -260 kms -1 in 1992, Dupree et al. 2005; -330 kms -1 in 2002, Edwards et al. 2006; -300 kms -1 in 2007). Lines formed at even higher kinetic temperatures (O VI and C III ) also give evidence of similar high outflow velocities (Dupree et al. 2005) suggesting that this hot wind may be powered as a result of the accretion process which acts as a source of energy and momentum in the upper atmosphere (Matt et al. 2012; Cranmer 2009).</text>
<section_header_level_1><location><page_5><loc_42><loc_66><loc_58><loc_68></location>5. A new model</section_header_level_1>
<text><location><page_5><loc_12><loc_24><loc_88><loc_64></location>These observations reveal a distinct new view of the accretion process in classical T Tauri stars and suggest that the current models need revision. It has been common to attempt modeling of the emission features in the spectrum as arising from the accretion stream that is channeled by the magnetic field as it approaches free-fall velocity forming an accretion shock (Muzerolle et al. 2000; Kurosawa et al. 2011). The spectra shown here suggest that an accretion event (observed in X-rays) instigated a cascade of changes to the optical emission line profiles. The emission lines arise in the post-shock cooling volume, and the line widths from X-ray profiles (Brickhouse et al. 2010), far UV (Ardila et al. 2002), the optical and the near-IR helium line shown here are all commensurate and broad. Their breadth has been difficult to interpret in the framework of accreting streams (Ardila et al. 2002) or an accretion shock (Lamzin et al. 2007). A turbulent post-shock cooling zone offers the likely solution to the puzzle of the broad profiles, and is supported by the behavior of the optical lines. The emission measure of the post-shock cooling zone exceeds that of the accretion stream by a factor of 100 (Dupree et al. 2012). Another component of the postshock cooling process is the discovery from the O VII diagnostics in CHANDRA spectra (Brickhouse et al. 2010) of a large coronal region with 300 times the volume and 30 times the emission measure of the accretion shock. All of these observations call for a reassessment of current models of accretion in young stars. It appears that the accretion process can both heat the corona, cause turbulent broadening of the emission lines, and provide a means to power an accretion-driven stellar wind.</text>
<section_header_level_1><location><page_6><loc_43><loc_85><loc_58><loc_86></location>REFERENCES</section_header_level_1>
<text><location><page_6><loc_12><loc_79><loc_88><loc_83></location>Ardila, D. R., Basri, G., Walter, F. M., Valenti, J. A., Johns-Krull, C. M. 2002, ApJ, 566, 1100</text>
<text><location><page_6><loc_12><loc_74><loc_88><loc_77></location>Brickhouse, N. S., Cranmer, S. R., Dupree, A. K., Luna, G. J. M., Wolk, S. 2010, ApJ, 710, 1835</text>
<unordered_list>
<list_item><location><page_6><loc_12><loc_71><loc_42><loc_72></location>Cranmer, S. R. 2009, ApJ, 706, 824</list_item>
<list_item><location><page_6><loc_12><loc_67><loc_77><loc_69></location>Donati, J.-F., Gregory, S. G., Alencar, S. H. P., et al. 2011, MNRAS, 417, 472</list_item>
<list_item><location><page_6><loc_12><loc_64><loc_75><loc_66></location>Dupree, A. K., Brickhouse, N. S., Cranmer, S. R., et al. 2012, ApJ, 750, 73</list_item>
<list_item><location><page_6><loc_12><loc_61><loc_80><loc_62></location>Dupree, A. K., Brickhouse, N. S., Smith, G. H., Strader, J. 2005, ApJ, 625, L131</list_item>
</unordered_list>
<text><location><page_6><loc_12><loc_58><loc_72><loc_59></location>Edwards, S., Fischer, W., Hillenbrand, L., Kwan, J. 2006, ApJ, 646, 319</text>
<text><location><page_6><loc_12><loc_54><loc_57><loc_56></location>Hummer, D. G., Rybicki, G. B. 1968, ApJ, 153, L107</text>
<text><location><page_6><loc_12><loc_51><loc_74><loc_53></location>Kurosawa, R., Romanova, M. M., Harries, T. J. 2011, MNRAS, 416, 2623</text>
<text><location><page_6><loc_12><loc_46><loc_88><loc_49></location>Lamzin, S. A., Romanova, M. M., Kravtsova, A. S. 2007, in J. Bouvier, I. Appenzeller (eds.), Star-Disk Interaction in Young Stars , IAU Symp. 243 , p. 115</text>
<text><location><page_6><loc_12><loc_43><loc_74><loc_44></location>Matt, S. P., Pinz'on, G., Greene, T. P., Pudritz, R. E. 2012, ApJ, 745, 101</text>
<text><location><page_6><loc_12><loc_39><loc_87><loc_41></location>Muzerolle, J., Calvet, N., Brice˜no, C., Hartmann, L., Hillenbrand, L. 2000, ApJ, 535, L47</text>
<text><location><page_6><loc_12><loc_36><loc_88><loc_38></location>Natta, A., Testi, L., Muzerolle, J., Randich, S., Comer'on, F., Persi, P. 2004, A&A, 424, 603</text>
<text><location><page_6><loc_12><loc_31><loc_88><loc_34></location>Petrov, P. P., Gahm, G. F., Stempels, H. C., Walter, F. M., Artemenko, S. A. 2011, A&A, 535, A6</text>
<text><location><page_6><loc_12><loc_28><loc_55><loc_29></location>Qi, C., Ho, P., Wilner D., et al 2004, ApJ, 616, L11</text>
<figure>
<location><page_7><loc_25><loc_37><loc_76><loc_65></location>
<caption>Fig. 1.- Lines arising in the accretion shock (N VII , O VIII , Ne IX , Fe XVII , Mg XI ) marked in the MEG total spectrum (hatched areas).</caption>
</figure>
<figure>
<location><page_8><loc_11><loc_32><loc_79><loc_71></location>
<caption>Fig. 2.- Accretion lines (N VII , O VIII , Ne IX , Fe XVII , Mg XI ) binned over 1 ks (filled circles) or 3 ks and divided by 3 for display (solid line). The hatched region marks the accretion event and is carried forward in the following figures.</caption>
</figure>
<figure>
<location><page_9><loc_12><loc_22><loc_81><loc_82></location>
<caption>Fig. 3.- The behavior of the H α and H β line fluxes and profiles. The X-ray accretion event is marked by line hatching. The ratio 'blue:red' denotes the flux in 1 ˚ A bandpasss positioned -2 ˚ A ('blue') or +2 ˚ A ('red') from line center in continuum-normalized spectra.</caption>
</figure>
<figure>
<location><page_10><loc_12><loc_30><loc_81><loc_69></location>
<caption>Fig. 4.- The behavior of the He I 5876 ˚ A (D3) flux and the value of the average blue veiling derived from the MIKE spectra.</caption>
</figure>
<figure>
<location><page_11><loc_10><loc_32><loc_81><loc_72></location>
<caption>Fig. 5.- The H α profile over 4 successive nights. Note the systematic apparent onset and strengthening of the wind absorption on the negative velocity side of the profile. The Julian date of each spectrum is marked as JD -2454100. These profiles were taken from the red side spectra of MIKE.</caption>
</figure>
<figure>
<location><page_12><loc_11><loc_31><loc_85><loc_73></location>
<caption>Fig. 6.- The H β profile over 4 successive nights. Note the similarity to H α with the onset and strengthening of wind absorption. H β exhibits a clear infall signature with absorption at a velocity of ∼ +35 kms -1 . These profiles were taken from the blue side spectra of MIKE. The Julian date of each spectrum is marked as JD -2454100.</caption>
</figure>
<figure>
<location><page_13><loc_31><loc_44><loc_67><loc_75></location>
<caption>Fig. 7.- The wind-sensitive He I λ 10830 line taken with PHOENIX on Gemini-S on the same night (JD 2454160.7) and within an hour of the H α and H β spectra (Dupree et al. 2012). The near-IR helium absorption shows that the wind extends to ∼ -300 kms -1 , and the emission is weaker than found in previous years. In addition stronger downflow (extending to +300 kms -1 ) than found previously (Dupree et al. 2005) is indicated by absorption on the positive velocity side of the profile. At the same time, such high velocities are not visible in the Balmer series, although the wind clearly modifies these lines at lower velocities (0 to -200 kms -1 ). The H α profile is reduced for display in this figure by a factor of 4.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "For the first time in a classical T Tauri star, we are able to trace an accretion event signaled by an hour-long enhancement of X-rays from the accretion shock and revealed through substantial sequential changes in optical emission line profiles. Downflowing turbulent material appears in H α and H β emission. He D3 (5876 ˚ A) broadens, coupled with an increase in flux. Two hours after the X-ray accretion event, the optical veiling increases due to continuum emission from the hot splashdown region. The response of the stellar coronal emission to the heated photosphere follows about 2.4 hours later, giving direct evidence that the stellar corona is heated in part by accretion. Then, the stellar wind becomes re-established. A model that incorporates the dynamics of this sequential series of events includes: an accretion shock, a cooling downflow in a supersonically turbulent region, followed by photospheric and later, coronal heating. This model naturally explains the presence of broad optical and ultraviolet lines, and affects the mass accretion rates currently determined from emission line profiles. These results, coupled with the large heated coronal region revealed from X-ray diagnostics, suggest that current models are not adequate to explain the accretion process in young stars. Subject headings: stars: individual (TW Hya) - stars: mass-loss - stars: variables: T Tauri stars - stars: winds, outflows - X-rays: stars",
"pages": [
1
]
},
{
"title": "New insights: the accretion process and variable wind from TW Hya 1",
"content": "A. K. Dupree Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 USA [email protected]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "TW Hya (CD -34 7151; HIP 53911) is arguably the closest accreting T Tauri star making it a choice object for detailed spectroscopic study. It is generally thought that cool material from the circumstellar disk surrounding the star is channeled by the stellar magnetic field and free-falls towards the star where a shock forms. The X-ray and optical spectra reported here probe this accretion process. Another major attribute of TW Hya is the fact that its surrounding circumstellar disk appears roughly face-on (Qi et al. 2004) so that the critical polar regions, where the accretion process occurs, can be observed directly without obscuration by the disk. A major observational campaign was aimed towards TW Hya that involved dedicated X-ray spectroscopic observations amounting to 500 total ks with the CHANDRA spacecraft. These results are discussed in Brickhouse et al. (2010). Contemporaneous optical and infrared spectroscopy and photometry were carried out from 4 continents (Dupree et al. 2012). As a result, the process of accretion can be investigated, and for the first time, the source of the broad emission lines from the star can be reliably identified.",
"pages": [
2
]
},
{
"title": "2. X-ray accretion signatures",
"content": "The CHANDRA X-ray spectra contain many emission lines arising from high temperatures. Analysis of the line strengths reveals that three different components producing X-rays must be present in the TW Hya atmosphere: a high temperature ( ∼ 10 7 K) corona, a lower temperature (3 × 10 6 K) component arising from the accretion shock, and a large volume producing O VII , at slightly lower temperature (2.5 × 10 6 K) with density lower than the accretion shock itself (Brickhouse et al. 2010). The behavior of lines arising in the accretion shock, namely N VII , O VIII , Ne IX , Fe XVII , and Mg XI , can give a direct measure of the instantaneous strength of the accreting material. These lines are marked in the CHANDRA spectrum shown in Fig 1, and the variation of the strength of the sum of the accretion lines is shown in Fig. 2 The accretion line flux (Fig. 2) reveals an enhancement centered at JD 2454157.75 that represented the highest count rate in a 3 ks average of the long 500ks CHANDRA observation, and merits special study.",
"pages": [
2
]
},
{
"title": "3. Simultaneous optical spectra",
"content": "Many simultaneous high-resolution optical spectra were taken during the X-ray accretion enhancement, providing the opportunity to evaluate the effect of the increase in the accreting line flux on the optical emission lines. Echelle spectra were taken continuously over 3 nights with the MIKE spectrograph at the Magellan/CLAY telescope of Las Campanas Observatory. These spectra have a resolution ∼ 35,000 so that the line profiles are well-resolved. Fig. 3 shows the behavior of the total flux and the line profile asymmetries during the span of the X-ray measures shown in Fig. 2. The flux of H α does not exhibit any systematic change, which is not surprising since the line is surely optically thick. However, the asymmetry of the line does change quite abruptly following the X-ray accretion event. The asymmetry of a line profile indicates the mass flow in a differentially moving line-forming region (Hummer & Rybicki 1968). Of course, if a slab moves at constant velocity, the whole profile will shift by an amount corresponding to the constant velocity. But differential motion as found in a stellar wind or in downflowing material produces a change in the line asymmetry. If the short-wavelength side ('blue') of the line is stronger than the long-wavelength side ('red'), material is flowing away from the observer and vice versa . The abrupt increase in the value of the blue:red ratio for H α suggests an abrupt increase in down-flowing material that begins about 9 minutes after the increase in the X-ray accretion line flux. This increased inflow continues for about 1.5 hours. The H β emission line exhibits a similar increase in the ratio of blue to red emission, echoing the increased downflow of material exhibited by the H α line. In addition, an increase in the strength of the total H β emission occurs. The D3 line of He I at 5876 ˚ A is also a valuable probe of the accretion process. It is known to have both a broad and narrow component of emission. The broad component is generally thought to signal accretion (Donati et al. 2011) in a similar way as the broad lines of the Balmer series. A sharp increase in the flux at the end of the X-ray accretion event results from an enhanced long wavelength wing of the line profile, and the increase in line flux beginning about 30 minutes later (see Fig. 4) is due to a 30% increase in the broad component of the line, whereas the narrow component is constant to within 15%. The sequential changes of the optical lines following the X-ray accretion strongly suggests that they form in the post-shock cooling zone. The line widths themselves give additional support to this formation scenario. The Balmer lines have a FWHM of about ± 150 kms -1 , which is obviously in excess of a thermal width ( ∼ 21 kms -1 ) at a temperature of 10 4 K, and also in harmony with the measured widths of the Ne IX ( ± 165 kms -1 ) lines observed in the CHANDRA spectra (Brickhouse et al. 2010). Far ultraviolet line widths of C III and O VI , when corrected for wind absorption, suggest similar line widths of ± 160 kms -1 (Dupree et al. 2005). The veiling or 'weakening' of absorption lines in the optical spectrum arises from a continuum and perhaps a contribution from line emission (Petrov et al. 2011) produced by the accretion hot spot in the photosphere. The value of the veiling from the short wavelength region (4400-5000 ˚ A) of the MIKE spectra is shown in Fig 4 also. It too increases with a delay of 2 hours after the X-ray accretion event. Such a delay is consistent with a reasonable size of the photospheric 'hot spot'. Using a value of 35 km s -1 for the post shock downflow indicated by substantial absorption at that velocity in the H β profile suggests that material will traverse a distance comparable to the size of a hot spot covering ∼ 10% of a star with radius 0.8 R /circledot in 2.8 hours. The flux from the corona (represented by the first order CHANDRA spectrum) responds ∼ 2 hours later to an increase in veiling (Dupree et al. 2012).",
"pages": [
3,
4
]
},
{
"title": "4. The stellar wind",
"content": "The Balmer profiles also reveal the wind structure and its variation. H α and H β profiles observed over 4 successive nights are shown in Fig. 5 and Fig. 6. The X-ray accretion event discussed earlier occurred during the first night when the H α profile is roughly symmetric. During the subsequent 3 nights, absorption appears and systematically increases on the negative velocity side of the line. The wind which appears very weak or perhaps absent on the first night, recovers and becomes more opaque during the following nights. The symmetry of the broad H α profile on the first night demonstrates that the line is not formed in an accretion stream (which should appear only at positive velocities), but most likely in a turbulent region of the atmosphere with velocity centered on the TW Hya itself. H α has a higher opacity than H β and would be formed higher in the atmosphere ('at the edges') of a turbulent region than the H β transition. Thus it is not surprising that the inflow signature is stronger in the weaker H β line. Because the wind also substantially modifies the emission line profiles, this suggests that the line width may not be a good indicator of the accretion rate as has been proposed (Natta et al. 2004). In fact, in our observations, the wind (and undoubtedly accretion contributes also) changes the width of the line at the 10% level which, if dependent only on accretion, corresponds to a factor of 5 in the mass accretion rate. The near-infrared He I transition at λ 10830 has proved to be an excellent tracer of winds from T Tauri stars (Dupree et al. 2005). This transition arises from a metastable level of neutral helium and thus maintains a relatively high population which can absorb the strong infrared continuum from a cool star. The broad emission appears likely to arise also in the post-shock cooling zone of TW Hya, and the extent of the absorption (to ∼ -300 kms -1 ) clearly documents the presence of a fast wind. The terminal velocity of the wind varies with time ( -260 kms -1 in 1992, Dupree et al. 2005; -330 kms -1 in 2002, Edwards et al. 2006; -300 kms -1 in 2007). Lines formed at even higher kinetic temperatures (O VI and C III ) also give evidence of similar high outflow velocities (Dupree et al. 2005) suggesting that this hot wind may be powered as a result of the accretion process which acts as a source of energy and momentum in the upper atmosphere (Matt et al. 2012; Cranmer 2009).",
"pages": [
4,
5
]
},
{
"title": "5. A new model",
"content": "These observations reveal a distinct new view of the accretion process in classical T Tauri stars and suggest that the current models need revision. It has been common to attempt modeling of the emission features in the spectrum as arising from the accretion stream that is channeled by the magnetic field as it approaches free-fall velocity forming an accretion shock (Muzerolle et al. 2000; Kurosawa et al. 2011). The spectra shown here suggest that an accretion event (observed in X-rays) instigated a cascade of changes to the optical emission line profiles. The emission lines arise in the post-shock cooling volume, and the line widths from X-ray profiles (Brickhouse et al. 2010), far UV (Ardila et al. 2002), the optical and the near-IR helium line shown here are all commensurate and broad. Their breadth has been difficult to interpret in the framework of accreting streams (Ardila et al. 2002) or an accretion shock (Lamzin et al. 2007). A turbulent post-shock cooling zone offers the likely solution to the puzzle of the broad profiles, and is supported by the behavior of the optical lines. The emission measure of the post-shock cooling zone exceeds that of the accretion stream by a factor of 100 (Dupree et al. 2012). Another component of the postshock cooling process is the discovery from the O VII diagnostics in CHANDRA spectra (Brickhouse et al. 2010) of a large coronal region with 300 times the volume and 30 times the emission measure of the accretion shock. All of these observations call for a reassessment of current models of accretion in young stars. It appears that the accretion process can both heat the corona, cause turbulent broadening of the emission lines, and provide a means to power an accretion-driven stellar wind.",
"pages": [
5
]
},
{
"title": "REFERENCES",
"content": "Ardila, D. R., Basri, G., Walter, F. M., Valenti, J. A., Johns-Krull, C. M. 2002, ApJ, 566, 1100 Brickhouse, N. S., Cranmer, S. R., Dupree, A. K., Luna, G. J. M., Wolk, S. 2010, ApJ, 710, 1835 Edwards, S., Fischer, W., Hillenbrand, L., Kwan, J. 2006, ApJ, 646, 319 Hummer, D. G., Rybicki, G. B. 1968, ApJ, 153, L107 Kurosawa, R., Romanova, M. M., Harries, T. J. 2011, MNRAS, 416, 2623 Lamzin, S. A., Romanova, M. M., Kravtsova, A. S. 2007, in J. Bouvier, I. Appenzeller (eds.), Star-Disk Interaction in Young Stars , IAU Symp. 243 , p. 115 Matt, S. P., Pinz'on, G., Greene, T. P., Pudritz, R. E. 2012, ApJ, 745, 101 Muzerolle, J., Calvet, N., Brice˜no, C., Hartmann, L., Hillenbrand, L. 2000, ApJ, 535, L47 Natta, A., Testi, L., Muzerolle, J., Randich, S., Comer'on, F., Persi, P. 2004, A&A, 424, 603 Petrov, P. P., Gahm, G. F., Stempels, H. C., Walter, F. M., Artemenko, S. A. 2011, A&A, 535, A6 Qi, C., Ho, P., Wilner D., et al 2004, ApJ, 616, L11",
"pages": [
6
]
}
]
<document>
<section_header_level_1><location><page_1><loc_22><loc_80><loc_78><loc_84></location>CRPropa 2.0 - a Public Framework for Propagating High Energy Nuclei, Secondary Gamma Rays and Neutrinos</section_header_level_1>
<text><location><page_1><loc_25><loc_75><loc_75><loc_78></location>Karl-Heinz Kampert a , Jörg Kulbartz b , Luca Maccione c,d , Nils Nierstenhoefer a,b , Peter Schiffer b , Günter Sigl b , Arjen René van Vliet b</text>
<text><location><page_1><loc_23><loc_70><loc_77><loc_74></location>a University of Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany b II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany</text>
<section_header_level_1><location><page_1><loc_22><loc_59><loc_29><loc_60></location>Abstract</section_header_level_1>
<text><location><page_1><loc_22><loc_44><loc_78><loc_58></location>Version 2.0 of CRPropa 1 is public software to model the extra-galactic propagation of ultra-high energy nuclei of atomic number Z ≤ 26 through structured magnetic fields and ambient photon backgrounds taking into account all relevant particle interactions. CRPropa covers the energy range 6 × 10 16 < E/ eV < A × 10 22 where A is the nuclear mass number. CRPropa can also be used to track secondary γ -rays and neutrinos which allows the study of their link with the charged primary nuclei - the so called multi-messenger connection. After a general introduction we present several sample applications of current interest concerning the physics of extragalactic ultra-high energy radiation.</text>
<text><location><page_1><loc_22><loc_42><loc_74><loc_43></location>Keywords: Ultrahigh energy cosmic rays, Extragalactic magnetic fields.</text>
<section_header_level_1><location><page_1><loc_22><loc_37><loc_48><loc_38></location>1. Introduction and Motivation</section_header_level_1>
<text><location><page_1><loc_22><loc_23><loc_78><loc_36></location>Cosmic rays are ionized atomic nuclei reaching the Earth from outside the Solar System with energies that exceed 10 20 eV . Although ultra-high energy cosmic rays (UHECRs) were originally discovered in 1939, their sources and propagation mechanisms are still a subject of intense research. During the last decade significant progress has been made due to the advent of high quality and high statistics data from a new generation of large scale observatories. Observables of prime interest are the energy spectrum, mass composition and arrival direction of cosmic rays. A flux-suppression in the energy spectrum above E ∼ 5 · 10 19 eV has been observed by the HiRes and Pierre Auger Observatories</text>
<text><location><page_2><loc_22><loc_75><loc_78><loc_84></location>[1, 2] and possibly also by the Telescope Array [3] indicating either observation of the GZK-effect [4, 5] or the limiting energy of the sources. Moreover, data of the Pierre Auger Observatory indicate that the arrival directions of the highest energy cosmic rays are correlated with the depth of nearby Active Galactic Nuclei (AGN) or more generally with the nearby extra-galactic matter distribution [6].</text>
<text><location><page_2><loc_22><loc_63><loc_78><loc_75></location>Additionally, measurements of the position of the shower maximum and its fluctuations by the Pierre Auger Collaboration suggest a significant fraction of heavy primaries above 10 19 eV [7]. However, HiRes [8] and preliminary data of the Telescope Array [3]), suggest a proton dominance in the same energy range. Unfortunately, the limited number of observed events does not yet allow the extension of these measurements to the aforementioned cutoff energy. Independently of the mass composition, it is not uniquely settled yet if this flux depression is due to energy loss or maximum energy limitation of the sources.</text>
<text><location><page_2><loc_22><loc_60><loc_78><loc_63></location>Clearly, a better understanding of all of these features and of the effects of cosmic ray propagation through the local Universe is mandatory.</text>
<text><location><page_2><loc_22><loc_34><loc_78><loc_60></location>UHECRs do not propagate freely in the Inter Galactic Medium (IGM). During their propagation they suffer from catastrophic energy losses in reactions with the intergalactic background light and are deflected by poorly known magnetic fields. Thus, the effects of propagation alter the cosmic ray spectrum and composition injected by sources in the IGM and form the features detected by UHECR observatories. In order to establish the origin of UHECRs, it is of prime interest to quantitatively understand the imprint of the propagation and to disentangle it from the properties of the cosmic rays at their sources. In this respect, it is essential to compare the measured UHECR spectrum, composition and anisotropy with model predictions. This requires extensive simulations of the propagation of UHE nuclei and their secondaries within a given scenario. In particular, the observation that UHECRs may consist of a significant fraction of heavy nuclei challenges UHECR model predictions and propagation simulations. Indeed, compared to the case of ultra-high energy (UHE) nucleons, the propagation of nuclei leads to larger deflections in cosmic magnetic fields and additional particle interactions have to be taken into account, namely, photodisintegration and nuclear decay.</text>
<text><location><page_2><loc_22><loc_16><loc_78><loc_34></location>To provide the community with a versatile simulation tool we present in this paper a publicly available Monte Carlo code called CRPropa 2.0 which allows one to simulate the propagation of UHE nuclei in realistic one- (1D) and threedimensional (3D) scenarios taking into account all relevant particle interactions and magnetic deflections. To this end, we extended the former version 1.4 of CRPropa, which was restricted to nucleon primaries, to the propagation of UHE nuclei. CRPropa 1.4 provided an excellent basis for this effort as many of its features could be carried over to the case of UHE nuclei propagation. In the present paper, which accompanies the public release of CRPropa 2.0, the underlying physical and numerical frameworks of the implementation of nuclei propagation are introduced. For technical details the reader is referred to the documentation distributed along with this framework.</text>
<text><location><page_2><loc_24><loc_15><loc_78><loc_16></location>This paper is organized as follows: Section 2 starts with a short introduction</text>
<text><location><page_3><loc_22><loc_77><loc_78><loc_84></location>of the publicly available previous CRPropa 1.4. The extensions which were implemented for nuclei interactions in CRPropa 2.0 are the subject of section 3. Section 4 describes the general propagation algorithm and in section 5 example applications of nuclei propagation with CRPropa are presented. We present a short summary and an outlook in Section 6.</text>
<text><location><page_3><loc_22><loc_74><loc_78><loc_76></location>Unless stated otherwise, we use natural units glyph[planckover2pi1] = c = 1 throughout this paper.</text>
<section_header_level_1><location><page_3><loc_22><loc_70><loc_55><loc_71></location>2. Inherited features from CRPropa 1.4</section_header_level_1>
<text><location><page_3><loc_22><loc_39><loc_78><loc_68></location>The previous version 1.4 of CRPropa is a simulation tool aimed at studying the propagation of neutrons and protons in the intergalactic medium. It provides a one-dimensional (1D) and a three-dimensional (3D) mode. In 3D mode, magnetic field- and source distributions can be defined on a 3D grid. This allows one to perform simulations in realistic source scenarios with a highly structured magnetic field configuration as provided by, e.g., cosmological simulations. In 1D mode, magnetic fields can be specified as a function of the distance to the observer, but their effects are obviously restricted to energy losses of e + e -pairs due to synchrotron radiation within electromagnetic cascades. Furthermore, it is possible to specify the cosmological and the source evolution as well as the redshift scaling of the background light intensity in 1D simulations. All important interactions with the cosmic infrared (IRB) and microwave (CMB) background light are included, namely, production of electron-positron pairs, photopion production and neutron decay. Additionally, CRPropa allows for tracking and propagating secondary γ -rays, e + e -pairs and neutrinos. A module [9] is included that solves the one-dimensional transport equations for electromagnetic cascades that are initiated by electrons, positrons or photons taking into account single, double and triple pair production as well as up-scattering of low energy background photons by inverse Compton scattering. Synchrotron radiation along the line of sight can also be simulated.</text>
<text><location><page_3><loc_22><loc_31><loc_78><loc_38></location>Technically, CRPropa is a stand alone object-oriented C++ software package. It reads an input file which specifies technical parameters as well as details of the simulated 'Universe' such as source positions and magnetic fields. The CRPropa simulations for a given scenario generate output files of either detected events or full UHECR trajectories.</text>
<section_header_level_1><location><page_3><loc_22><loc_27><loc_61><loc_28></location>3. Modeling nuclei interactions in CRPropa 2.0</section_header_level_1>
<text><location><page_3><loc_22><loc_16><loc_78><loc_26></location>Similar to the case of protons, nuclei carry charge and suffer energy losses by electron-positron pair production in ambient photon fields. This can occur when photon energies boosted into the rest frame of the nucleus are of the order of glyph[epsilon1] ' ∼ 1 MeV . For photon energies at or above the nuclear binding energy glyph[epsilon1] ' glyph[greaterorsimilar] 8 -9 MeV , nucleons and light nuclei can be stripped off the nucleus (photodisintegration). Finally, at photon energies exceeding glyph[epsilon1] ' ∼ 145 MeV the quark structure of free or bound nucleons can be excited to produce mesons</text>
<text><location><page_4><loc_22><loc_80><loc_78><loc_84></location>(photopion production). In these reactions the nucleus can be disrupted and unstable elements be produced. Hence, nuclear decay has to be taken into account as well.</text>
<text><location><page_4><loc_22><loc_69><loc_78><loc_79></location>In CRPropa2.0 a nucleus with energy E and mass number A is considered a superposition of A nucleons with energy E/A . Thus, if one or several nucleons are stripped off, the initial energy E will be distributed among the outgoing nucleons and nuclei. The ultra-relativistic limit β → 1 (with β = v/c of the nucleus) is used in CRPropa such that all nuclear products are assigned the same velocity vector as the initial particle. This corresponds to a Lorentz factor Γ glyph[similarequal] 10 8 · ( E/ 10 17 eV ) · A -1 and a forward collimation within an angle glyph[similarequal] 1 / Γ .</text>
<section_header_level_1><location><page_4><loc_22><loc_66><loc_39><loc_67></location>3.1. Photodisintegration</section_header_level_1>
<text><location><page_4><loc_22><loc_57><loc_78><loc_65></location>Photodisintegration of nuclei has no analogy for free nucleons. Thus, implementing this new interaction process is mandatory to allow for propagation of nuclei within CRPropa. There are many competing photodisintegration processes of different cross sections which need to be accounted for along the path of the nucleus in the photon field. Thus, it is important to efficiently describe the specific photodisintegration pattern of each propagated nucleus in CRPropa.</text>
<text><location><page_4><loc_22><loc_46><loc_78><loc_56></location>The effects of the propagation of UHE nuclei have first been studied by Puget, Stecker and Bredekamp (PSB) [10]. The approach to model the photodisintegration process chosen in CRPropa 2.0 is similar to what was more recently discussed in Ref. [11]. Further details on the photodisintegration within CRPropa2.0 can be found in Ref. [12]. As target photon fields we shall consider the CMB and IRB, for which we adopt the more recent parametrization developed in [13].</text>
<section_header_level_1><location><page_4><loc_22><loc_43><loc_50><loc_44></location>3.1.1. The Photonuclear Cross Sections</section_header_level_1>
<text><location><page_4><loc_22><loc_26><loc_78><loc_43></location>We use the publicly available TALYS framework, version 1.0 [14] to compute photodisintegration cross sections. The nuclear models therein are reliable for mass numbers A ≥ 12 . 2 Thus, additional photodisintegration cross sections for light nuclei have to added in the modeling. In CRPropa 2.0 TALYS was applied to 287 isotopes up to iron ( Z = 26 ) 3 employing nuclear models and settings as suggested in Ref. [11]. The list of isotopes for which the cross sections were calculated was generated using data from Ref. [15]. It is assumed that excited nuclei will immediately return to their ground state. Hence, only nuclei in their ground states are considered when calculating the cross sections 4 . All cross sections were calculated for photon energies 1 keV ≤ glyph[epsilon1] ' ≤ 250 MeV in the rest frame of the nucleus and stored in 500 bins of energy. Knocked out neutrons ( n ),</text>
<text><location><page_5><loc_22><loc_77><loc_78><loc_84></location>protons ( p ), deuterium ( d ), tritium ( t ), helium-3 ( 3 He ) and helium-4 ( α ) nuclei and combinations thereof are considered by TALYS. The corresponding reaction channels are called exclusive channels . In the mass range of target nuclei where TALYS cannot be employed reliably, we use instead other prescriptions, as follows:</text>
<unordered_list>
<list_item><location><page_5><loc_24><loc_74><loc_57><loc_76></location>· 9 Be, 4 He, 3 He, t and d as given in Ref. [16].</list_item>
<list_item><location><page_5><loc_24><loc_66><loc_78><loc_73></location>· A parametrization of the total photonuclear cross section as function of the mass number A is used for 8 Li, 9 Li, 7 Be, 10 Be, 11 Be, 8 B, 10 B, 11 B, 9 C, 10 C, 11 C as described in [17]. In these cases the loss of one proton (neutron) is assumed if the neutron number N < Z ( N > Z ). For N = Z , the loss of one neutron or proton is modeled with equal probability.</list_item>
<list_item><location><page_5><loc_24><loc_62><loc_78><loc_65></location>· For 7 Li we use experimental data from Ref. [18, 19] and instead of using a parametrization we interpolate linearly between the measured data points.</list_item>
</unordered_list>
<text><location><page_5><loc_22><loc_59><loc_62><loc_60></location>In total 78449 exclusive channels are taken into account.</text>
<text><location><page_5><loc_22><loc_55><loc_78><loc_59></location>The TALYS output in general agrees reasonably well with available measured data and only in rare cases differs up to a factor of 2 for the integrated (total absorption) cross sections [11].</text>
<text><location><page_5><loc_22><loc_52><loc_78><loc_54></location>Alternatively, for comparison, the widely-used photodisintegration cross section estimates developed by Puget, Stecker and Bredekamp [10] can be used.</text>
<text><location><page_5><loc_22><loc_40><loc_78><loc_51></location>In the PSB case a reduced reaction network is implemented involving one nucleus for each atomic mass number A up to 56 Fe. Herein, the cross sections for one- and two-nucleon dissociation in the photon energy interval glyph[epsilon1] ' min ≤ glyph[epsilon1] ' ≤ 30 MeV are parametrized by a Gaussian approximation. Different from [10], the channel-dependent threshold energies glyph[epsilon1] ' min proposed in [20] are used. In the photon energy interval 30 ≤ glyph[epsilon1] ' ≤ 150 MeV the cross section is assumed to be constant. A comparison of results obtained with the TALYS and PSB cross sections is given in section 5.2.</text>
<section_header_level_1><location><page_5><loc_22><loc_37><loc_64><loc_38></location>3.1.2. Mean Free Path Calculations and Channel Thinning.</section_header_level_1>
<text><location><page_5><loc_22><loc_33><loc_78><loc_36></location>Once the photodisintegration cross section in the nucleus rest frame σ ( glyph[epsilon1] ' ) is given (cf. Sec. 3.1.1), the energy weighted average cross section</text>
<formula><location><page_5><loc_37><loc_29><loc_78><loc_32></location>¯ σ ( glyph[epsilon1] ' max ) = 2 ( glyph[epsilon1] ' max ) 2 ∫ glyph[epsilon1] ' max 0 glyph[epsilon1] ' σ ( glyph[epsilon1] ' ) dglyph[epsilon1] ' . (1)</formula>
<text><location><page_5><loc_22><loc_26><loc_51><loc_28></location>is tabulated as a function of glyph[epsilon1] ' max = 2Γ glyph[epsilon1] .</text>
<text><location><page_5><loc_22><loc_23><loc_78><loc_26></location>For a given ¯ σ ( glyph[epsilon1] ' max ) , for each isotope the mean free path λ (Γ) can be calculated as a function of the Lorentz factor according to Ref. [10],</text>
<formula><location><page_5><loc_35><loc_19><loc_78><loc_22></location>λ (Γ) -1 = ∫ glyph[epsilon1] max glyph[epsilon1] min n ( glyph[epsilon1], z ) ¯ σ ( glyph[epsilon1] ' max = 2Γ glyph[epsilon1] ) dglyph[epsilon1] , (2)</formula>
<text><location><page_5><loc_22><loc_15><loc_78><loc_17></location>where n ( glyph[epsilon1], z ) is the number density of the isotropic low energy photons per energy interval and volume. Variation due to cosmological redshift (cf. Sec. 3.5)</text>
<table>
<location><page_6><loc_36><loc_76><loc_64><loc_81></location>
<caption>Table 1: Values of the parameters used in Eq. (1) and (2) to create the mean free path tables for photodisintegration in CRPropa.</caption>
</table>
<text><location><page_6><loc_22><loc_67><loc_78><loc_72></location>is accounted for. For performance reasons, λ ( E ) is tabulated as a function of energy. The values of the integration limits glyph[epsilon1] min , glyph[epsilon1] max in Eq. (1) and (2) are listed in Tab. 1.</text>
<text><location><page_6><loc_22><loc_51><loc_78><loc_67></location>As the Monte Carlo rapidly slows down with increasing number of exclusive channels to be sampled, a thinning procedure was implemented: For each isotope, we include only the channels with the n largest interaction rates out of the N available exclusive channels, such that the sum ∑ n i λ -1 i /λ -1 tot > α in at least one energy bin. Here, α is the thinning factor and the λ -1 i are summed up in decreasing order. Furthermore, λ -1 tot = ∑ N i λ -1 i is calculated for each isotope. In this way a α = 90% channel-thinning reduces the number of photodisintegration channels to be tracked from 78449 to 6440. The thinning procedure leads to a systematic overestimation of the mean free path in the order of 1% for Lorentz factors of the UHECR below 10 10 . This deviation goes up to 10% for Lorentz factors above 10 12 (see Fig. 1).</text>
<section_header_level_1><location><page_6><loc_22><loc_48><loc_41><loc_49></location>3.2. Photopion Production</section_header_level_1>
<text><location><page_6><loc_22><loc_41><loc_78><loc_47></location>UHE nucleons can produce secondary mesons in interactions with low energy photon backgrounds. The most important reaction of this type is the production of pions in reactions of UHE protons with the CMB, which leads to the well known GZK cut-off [4, 5] at an energy of about E GZK = 5 · 10 19 eV.</text>
<text><location><page_6><loc_22><loc_24><loc_78><loc_41></location>Nuclei can also produce mesons, albeit with a higher threshold energy of E th ≈ A × E GZK . This is due to the fact that to good approximation the center of mass system (CMS) coincides with the rest frame of the nucleus. The threshold energy, therefore, does not depend on the total energy of the nucleus E , but on the Lorentz factor Γ ∝ E/A . Pion production is thus only relevant for extremely energetic nuclei. However, it is important to be included to properly account for production of secondary UHE photons and neutrinos, as well as for the propagation of secondary and primary protons and neutrons. Effectively this process leads to an energy scaling of the mean free path λ A,Z for photopion production of nuclei. The mean free path for pion production on the constituent protons λ p and neutrons λ n can thus we written as</text>
<formula><location><page_6><loc_33><loc_20><loc_78><loc_23></location>λ -1 A,Z ( E ) = Z λ -1 p ( E A ) + ( A -Z ) λ -1 n ( E A ) . (3)</formula>
<text><location><page_6><loc_22><loc_16><loc_78><loc_19></location>In CRPropa 2.0 we use Eq. (3) to reduce the mean free path for pion production by nuclei to the one for nucleons which in turn is modeled by the SOPHIA</text>
<figure>
<location><page_7><loc_22><loc_33><loc_78><loc_72></location>
<caption>Figure 1: The relative deviation of the total mean free path λ in photodisintegration reactions in the CMB and IRB for the thinned ( α = 90% ) and un-thinned case is given for all 287 isotopes (redshift z = 0 ).</caption>
</figure>
<text><location><page_8><loc_22><loc_68><loc_78><loc_84></location>package which was already used in CRPropa 1.3. This approximation is sufficient for our purposes because the pion mass m π ≈ 140 MeV is much larger than the binding energy per nucleon E b /A glyph[lessorsimilar] 8 MeV so that, above the threshold for pion production, the nuclear binding energy can be neglected and the nucleus be treated as a collection of free nucleons. Following this argument, we split the reaction into four parts, and calculate reactions of protons and neutrons on the CMB and on the IRB separately. The nucleus cross section σ A,Z for these four channels is then given by the cross sections of protons or neutrons times the number of the respective nucleons in the nucleus. The mean free path of the reaction was then obtained by folding this cross section with the respective photon background.</text>
<text><location><page_8><loc_22><loc_57><loc_78><loc_67></location>If a reaction takes place, we treat it as a reaction of a free nucleon. The interacting nucleon will suffer energy loss and be stripped off the nucleus. The disintegrated nucleon will then be propagated individually, while the produced meson will decay leading to secondary leptons, photons or neutrinos which are then propagated using the corresponding modules of CRPropa. Both the decay of the meson as well as the energy loss of the primary nucleon are calculated by using the SOPHIA package [21].</text>
<section_header_level_1><location><page_8><loc_22><loc_54><loc_36><loc_55></location>3.3. Pair production</section_header_level_1>
<text><location><page_8><loc_22><loc_40><loc_78><loc_54></location>Another interaction relevant for the propagation of UHE protons and nuclei is the creation of electron positron pairs in the low energy photon backgrounds. Both photomeson- and pair-production are less important in terms of energy loss of the primary nuclei which is dominated by photodisintegration (c.f. Fig. 3). Pair production is, however, the most important reaction for the creation of secondary photons in the TeV range. The mean free path for pair production is short, but the energy loss in each individual reaction is small. Thus, we treat pair production as a continuous energy loss which for interactions with the CMB can be parametrized by [10]</text>
<formula><location><page_8><loc_34><loc_36><loc_78><loc_39></location>-dE e + e -A,Z dt = 3 α em σ T h -3 Z 2 ( m e c 2 k B T ) f (Γ) . (4)</formula>
<text><location><page_8><loc_22><loc_24><loc_78><loc_35></location>Here, σ T is the Thomson cross section, m e and m p are the electron and proton rest masses, respectively, α em is the fine structure constant, T is the temperature of the CMB, and f (Γ) is a function which depends only on the Lorentz factor Γ and was parametrized by Blumenthal [22]. One can therefore express the energy loss length l A,Z = E ( dE e + e -A,Z /dt ) -1 for nuclei in terms of the energy loss length for protons l p = E ( dE e + e -1 , 1 /dt ) -1 , according to</text>
<formula><location><page_8><loc_43><loc_20><loc_78><loc_23></location>l A,Z (Γ) = Z 2 A l p (Γ) . (5)</formula>
<text><location><page_8><loc_22><loc_15><loc_78><loc_19></location>This scaling relation holds for arbitrary target photon backgrounds since the prefactor can be traced back to the scaling of the cross section and to the definition of the energy loss length. Eq. (5) is used in CRPropa 2.0 to generalize</text>
<text><location><page_9><loc_22><loc_80><loc_78><loc_84></location>the pair production loss rates from protons to nuclei, which in practice is obtained by integration over the corresponding secondary spectra as parametrized by [23].</text>
<text><location><page_9><loc_22><loc_66><loc_78><loc_80></location>The energy loss for e + e -pair production is calculated after each timestep ∆ t and is therefore taken into account at discrete positions and times. CRPropa can also propagate secondary electromagnetic cascades initiated by the e + e -pairs or by the γ -rays resulting from π 0 -decay. For the injected secondary spectra we use the parametrization given by Kelner and Aharonian [23]. It should be noted that, in particular, close to an observer a large time step can degrade the accuracy of the propagated spectra, due to the discrete injection of the electromagnetic cascade. We refer the reader to the CRPropa 2.0 manual for details.</text>
<section_header_level_1><location><page_9><loc_22><loc_63><loc_36><loc_64></location>3.4. Nuclear Decay</section_header_level_1>
<text><location><page_9><loc_22><loc_55><loc_78><loc_62></location>For the propagation of UHECRs, nuclear decay is relevant, if unstable particles are produced by photodisintegration or photopion production. On the one hand, nuclear decay can change both the nucleus type and its energy, while on the other hand it technically ensures that unstable nuclei decay back to stable nuclei whose photodisintegration cross sections are known.</text>
<text><location><page_9><loc_22><loc_51><loc_78><loc_55></location>In CRPropa, decays are modeled as a combination of α , β ± decays and dripping of single nucleons ( p, n ). The decay length of a nucleus is given by its life time τ and the Lorentz factor Γ to be</text>
<formula><location><page_9><loc_46><loc_48><loc_78><loc_49></location>λ decay = Γ τ. (6)</formula>
<text><location><page_9><loc_22><loc_39><loc_78><loc_46></location>In case of p, n dripping and α decay, the decay products are assumed to inherit the Lorentz factor Γ from the parent nucleus. This assumption is justified since the binding energy per nucleon is small compared to the masses of the decay products. The energy of all produced nuclei are, therefore, simply given by</text>
<formula><location><page_9><loc_44><loc_36><loc_78><loc_38></location>E A ' ,Z ' = Γ m A ' ,Z ' . (7)</formula>
<text><location><page_9><loc_22><loc_31><loc_78><loc_35></location>In case of β ± decay we also use Eq. (7) and the momenta of e ± and the neutrino are calculated from a three body decay (see e.g. [24]) and are then boosted to the simulation frame.</text>
<text><location><page_9><loc_22><loc_16><loc_78><loc_30></location>In CRPRopa the decay channels of the different nuclei as well as their decay constants at rest are stored in an internal database. It is based on the NuDat2 database [15] and contains 434 different nuclides with mass number A ≤ 56 and charge Z ≤ 26 . It should be noted that UHECRs, unlike the isotopes in the NuDat2 database, are fully ionized. This means that electron capture (EC) is not possible for UHECRs and the β + decays have to be calculated from the EC rates given in the NuDat2 database. Up to the squared matrix elements which are the same for EC and β + decay, the rates τ -1 EC and τ -1 β + for these two processes are just proportional to the available phase space of the final state products. If ∆ m ≡ m A,Z -m A ' ,Z ' is the mass difference of the fully ionized</text>
<table>
<location><page_10><loc_39><loc_56><loc_61><loc_75></location>
<caption>Table 2: All isotopes with τ β + differing from τ by more than 1% . Note that in the case of 36 Cl the very low branching ratio of 1 . 6% does not lead to a strong modification of the propagation properties. In addition, there are only 3 isotopes where τ β + is more than 10% larger than τ , 45 Ti , 48 Cr and 54 Mn , since 36 Cl and 40 K decay mostly by β -decay. Not included in the table are 10 isotopes which only decay via electron capture due to their low mass difference ∆ m<m e .</caption>
</table>
<text><location><page_10><loc_22><loc_39><loc_78><loc_52></location>nuclei and, since the nuclear recoil energy and the electron binding energy can be neglected, the kinetic energy of the final state leptons are given by the socalled Q-factors Q β + = ∆ m -m e and Q EC = E ν = ∆ m + m e = Q β + + 2 m e with E ν the neutrino energy. Therefore, τ -1 EC ∝ | ψ e (0) | 2 Q 2 EC /π with | ψ e (0) | 2 = ( Z/a 0 ) 3 the normalized density of the electron wave function at the nucleus and τ -1 β + ∝ (2 /π 3 ) ∫ ∆ m m e dE f ( E ) with f ( E ) = E √ E 2 -m 2 e (∆ m -E ) 2 the standard β + decay differential phase space density per total positron energy E (including rest mass) [24]. Thus we get</text>
<formula><location><page_10><loc_39><loc_34><loc_78><loc_38></location>τ EC τ β + = 2 π 2 ( a 0 Z ) 3 ∫ ∆ m m e f ( E ) dE (∆ m + m e ) 2 , (8)</formula>
<text><location><page_10><loc_22><loc_24><loc_78><loc_33></location>where everything has been expressed in terms of the bare nucleus mass difference ∆ m . For all channels involving β + decay (including compound channels), we compute τ β + from the lifetime of the dressed nucleus given in NuDat2 τ by multiplying with τ β + /τ = 1+ τ β + /τ EC . The resulting lifetimes τ β + of all isotopes in the database are shown in Fig. 2. In Tab. 2 we list the isotopes for which τ β + deviates most from τ .</text>
<text><location><page_10><loc_22><loc_21><loc_78><loc_24></location>In Fig. 3 the decay length is shown in comparison to other energy loss processes using the example of 47 Ca.</text>
<section_header_level_1><location><page_10><loc_22><loc_18><loc_54><loc_19></location>3.5. Photon fields and cosmological evolution</section_header_level_1>
<text><location><page_10><loc_22><loc_15><loc_78><loc_17></location>The implementation of photodisintegration and pion production in CRPropa2.0 is based on tabulated mean free path data calculated with the photon</text>
<figure>
<location><page_11><loc_23><loc_41><loc_78><loc_70></location>
<caption>Figure 2: Nuclear maps of the internal database. The life time is color-coded, where red corresponds to decay times less than 1 s corresponding to a decay length ≤ 0 . 1 Mpc at a Lorentz factor of Γ = 10 13 . Black denotes effectively stable nuclei with a lifetime larger than 4 · 10 10 s. This corresponds to a decay length larger than 1 /H 0 at Lorentz factors of Γ > 10 7 . Nuclei between these two extremes are shown in blue, where darker shades correspond to longer decay times.</caption>
</figure>
<text><location><page_12><loc_22><loc_72><loc_78><loc_84></location>density n ( glyph[epsilon1], z = 0) at a redshift z = 0 (Sec. 3.1.2). As the photon density n ( glyph[epsilon1], z ) evolves as a function of z , λ = λ [Γ , z ] is effectively altered, too. To model this change of λ as function of z , a scaling function s ( z ) is used. It approximately relates λ [Γ , z ] at redshift z with the available tabulated data of λ [Γ (1 + z ) , z = 0] at redshift z = 0 . For this scaling function s ( z ) , it is assumed that the normalized spectral shape of the photon field n ( glyph[epsilon1], z ) does not change as function of z in the comoving cosmological frame. In this approach the evolution of the photon number density n ( glyph[epsilon1], z ) can be absorbed by a separated evolution factor e ( z )</text>
<formula><location><page_12><loc_34><loc_68><loc_78><loc_71></location>n ( glyph[epsilon1], z ) = (1 + z ) 2 n ( glyph[epsilon1] 1 + z , 0 ) e ( z ) . (9)</formula>
<text><location><page_12><loc_22><loc_64><loc_78><loc_67></location>In the approximation of a redshift independent spectral shape of n ( glyph[epsilon1], z ) , the evolution factor is defined by</text>
<formula><location><page_12><loc_39><loc_59><loc_78><loc_63></location>e ( z ) = { 1 CMB ∫ ∞ glyph[epsilon1] i n ( glyph[epsilon1],z ) dglyph[epsilon1] ∫ ∞ glyph[epsilon1] i n ( glyph[epsilon1], 0) dglyph[epsilon1] IRB (10)</formula>
<text><location><page_12><loc_22><loc_56><loc_78><loc_58></location>Here, glyph[epsilon1] i is the intersection energy of the CMB and IRB photon number densities n CMB ( glyph[epsilon1] i , z ) = n IRB ( glyph[epsilon1] i , z ) in the comoving frame.</text>
<text><location><page_12><loc_22><loc_53><loc_78><loc_55></location>Substitution of Eq. (9) in Eq. (2) gives the scaling relation for the mean free path</text>
<formula><location><page_12><loc_32><loc_50><loc_78><loc_52></location>λ -1 [Γ , z ] = (1 + z ) 3 e ( z ) λ -1 [Γ (1 + z ) , z = 0] (11)</formula>
<text><location><page_12><loc_22><loc_40><loc_78><loc_49></location>from which one can find s ( z ) = (1 + z ) 3 e ( z ) . It should be noted that this result is valid under the assumption that the spectral shape of the IRB does not depend on redshift. This approximation does not exactly hold for the IRB, due to energy injection in the IGM from galaxy formation. Nevertheless this approximation provides a model for the redshift evolution of the IRB which is of importance for the production of secondary neutrinos [25].</text>
<section_header_level_1><location><page_12><loc_22><loc_37><loc_66><loc_38></location>4. Propagation Algorithm and Monte Carlo Approach</section_header_level_1>
<text><location><page_12><loc_22><loc_28><loc_78><loc_36></location>To handle the widely ranging reaction rates of UHE nuclei, a new propagation algorithm has been implemented in CRPropa 2.0. The main assumption is that the mean free paths λ are approximately constant during a time step. As λ = λ ( E ) is in general a function of the UHECR energy E , the numerical step size has to be small enough to ensure that no significant energy loss occurs.</text>
<text><location><page_12><loc_22><loc_24><loc_78><loc_28></location>The algorithm works as follows. Given the mean free path λ i for a given interaction channel of a given nucleus, where i runs over all N possible interaction and decay channels,</text>
<unordered_list>
<list_item><location><page_12><loc_24><loc_17><loc_78><loc_23></location>1. The inverse total mean free path λ -1 tot = ∑ N i =1 λ -1 i is calculated and a distance ∆ x 1 to the next reaction is selected according to an exponential distribution. This is realized by using a uniformly distributed random number 0 ≤ r ≤ 1 via</list_item>
</unordered_list>
<formula><location><page_12><loc_45><loc_15><loc_78><loc_16></location>∆ x 1 = -λ ln(1 -r ) . (12)</formula>
<figure>
<location><page_13><loc_24><loc_40><loc_75><loc_68></location>
<caption>Figure 3: Length scales for all interactions of 47 Ca as used by CRPropa. In the plot the dark blue (dash-dotted) line denotes the energy loss length of pair production. The red (dotted) and green (dashed) lines are the photodisintegration and pionproduction mean free paths respectively and the blue (dash-triple-dotted) line shows the decay length. The black (solid) line is the total mean free path of the catastrophic energy losses as used in the propagation algorithm. 47 Ca was chosen because the half life time of 4 . 5 days corresponds to a decay length comparable to the other interactions.</caption>
</figure>
<unordered_list>
<list_item><location><page_14><loc_24><loc_81><loc_78><loc_84></location>2. The fractional energy loss due to pair production (c.f. Sec. 3.3), is limited by imposing a maximum step size ∆ x 2 given by</list_item>
</unordered_list>
<formula><location><page_14><loc_41><loc_77><loc_78><loc_80></location>∫ x +∆ x 2 x dx dE e + e -A,Z dx ( E ) < δ E , (13)</formula>
<text><location><page_14><loc_26><loc_74><loc_64><loc_76></location>where δ is the maximal allowed fractional energy loss.</text>
<unordered_list>
<list_item><location><page_14><loc_24><loc_73><loc_56><loc_74></location>3. The particle is propagated over a distance</list_item>
</unordered_list>
<formula><location><page_14><loc_42><loc_70><loc_78><loc_72></location>∆ x = min(∆ x 1 , ∆ x 2 , ∆ x 3 ) , (14)</formula>
<text><location><page_14><loc_26><loc_63><loc_78><loc_69></location>where ∆ x 3 is an upper limit on the propagation step that can be provided by the user, with typical values of ∆ x 3 ∼ 1 -50 Mpc . This increases the accuracy of the calculation of pair production energy losses and the accuracy of the secondary pair production spectra.</text>
<unordered_list>
<list_item><location><page_14><loc_24><loc_59><loc_78><loc_63></location>4. If ∆ x 1 = ∆ x , the particle is propagated over the path length ∆ x 1 , where it performs an interaction. The choice of the specific interaction performed by the UHECR is taken by finding the smallest index i for which</list_item>
</unordered_list>
<formula><location><page_14><loc_47><loc_54><loc_78><loc_58></location>i ∑ a =1 λ tot λ a > w, (15)</formula>
<text><location><page_14><loc_26><loc_43><loc_78><loc_53></location>for a uniformly distributed random number 0 ≤ w ≤ 1 . Then the continuous energy losses are applied and the algorithm is restarted from the new position and the new particles produced in the interaction are added to the list of particles to be propagated, leading to a cascade of secondary nuclei (see Fig. 4). A comparison of the exclusive mean free path of the different channels λ a and the total mean free path for 47 Ca with the pair production loss length is shown in Fig. 3.</text>
<text><location><page_14><loc_26><loc_34><loc_78><loc_42></location>If instead ∆ x 1 > min(∆ x 2 , ∆ x 3 ) , then continuous energy losses are too large to allow for accurate propagation until the next interaction point or the user has requested that the maximum step size be smaller than the ∆ x 1 selected in step 1. In this case, the particle is propagated over the distance ∆ x after which continuous losses are applied and the algorithm is restarted without performing any interaction.</text>
<text><location><page_14><loc_22><loc_28><loc_78><loc_33></location>From the above description it is clear that if one of the interaction channels has a small mean free path λ i , the step size of the propagation will adjust itself automatically.</text>
<text><location><page_14><loc_22><loc_19><loc_78><loc_28></location>This approach is also applied to select an exclusive channel e.g. in case of photodisintegration: If photodisintegration is chosen to be the next reaction by the propagation algorithm, the exclusive channel is found by applying Eq. (15). In analogy, here λ tot = ( ∑ i λ -1 i ) -1 is the total mean free path for the isotope under consideration. The λ i are the mean free path values for the exclusive channels of the corresponding isotope.</text>
<text><location><page_14><loc_22><loc_15><loc_78><loc_19></location>If the user chooses to include secondary γ -rays and/or neutrinos, these neutral secondaries are propagated over a distance equal to the maximum propagation distance provided by the user minus the time of their production, such</text>
<figure>
<location><page_15><loc_22><loc_42><loc_76><loc_69></location>
<caption>Figure 4: 3D trajectory of an iron nucleus and its hadronic secondaries in the minimum of the photodisintegration mean free path ( E ∼ 1 . 2 × 10 21 eV) in a high magnetic field region of a structured magnetic field ( 10 -9 G < B < 10 -7 G ). The iron was injected at x = y = z = 2 Mpc along the negative x direction and enters the plotted volume on the top right. Color coded is the mass number of the secondary particles. Notice that after photodisintegration the heavy nucleus and its secondary particles have the same Lorentz factor Γ ∼ E/A and therefore secondary protons are stronger deflected than heavier nuclei due to their higher charge-tomass ratio.</caption>
</figure>
<text><location><page_16><loc_22><loc_74><loc_78><loc_84></location>that they reach an observer after the maximum propagation time independently of the chosen 1D or 3D environment. In addition it is possible to inject a mixed nuclei composition. Since simple arguments about astrophysical acceleration mechanisms indicate that these mixed compositions should be accelerated up to a given maximum rigidity R = E/Z in the sources, instead of a maximum energy, we included the option to inject up to a given maximum rigidity at the source.</text>
<text><location><page_16><loc_22><loc_62><loc_78><loc_73></location>The accuracy of the determination of the arrival direction and arrival time at the observer position is of course related to the actual implementation of detection and propagation in our algorithm. Besides the numerical error intrinsic to the detection algorithm, an additional error is introduced by the choice to take continuous losses into account only at the end of the time step and of course by the maximum propagation time, which can however be controlled by the user. This can be particularly relevant for bursted sources. We refer the interested reader to the manual for a deeper discussion on these issues.</text>
<section_header_level_1><location><page_16><loc_22><loc_58><loc_42><loc_59></location>5. Example Applications</section_header_level_1>
<text><location><page_16><loc_22><loc_45><loc_78><loc_56></location>In this section simulations are presented to demonstrate some features of CRPropa. All these simulations are restricted to a pure iron or a mixed galactic composition injected at the source. For the latter we adopt Ref. [26], similar to the approach of Ref. [27]. The injected power law dN/dE ∝ E -α is arbitrarily chosen to have a slope 5 of α = 2 . 2 . For the 3D simulations, a (75 Mpc) 3 simulation cube with periodic boundary conditions is defined and filled with the large scale structure extragalactic magnetic fields (LSS-EGMF) from the cosmological simulations given in Ref. [28].</text>
<section_header_level_1><location><page_16><loc_22><loc_42><loc_69><loc_43></location>5.1. Completeness of the Photodisintegration Cross Section Tables</section_header_level_1>
<text><location><page_16><loc_22><loc_22><loc_78><loc_41></location>To verify the completeness of the implemented photonuclear cross section tables presented in Sec. 3.1.1, i.e. to verify whether cross sections are available for all nuclei that occur during propagation, 1D simulations have been performed. To this purpose, 10 5 iron nuclei were injected with a dN/dE ∝ E -1 spectrum in the energy range 1 EeV ≤ E ≤ 56 × 10 3 EeV from a uniform source distribution extending up to a distance of 1 Gpc from the observer. In this simulation, all particles that were created and propagated within CRPropa were recorded in a two dimensional histogram (see Fig. 5) displaying the frequency of occurrence of isotopes in the simulation as a function of their mass and atomic number A,Z . In this figure, symbols are given to mark the isotopes for which cross sections are available in CRPropa and the type of the marker identifies the source of the cross section as listed in Sec. 3.1.1. At the upper right part of Fig. 5 some nuclei are created but do not have a photodisintegration cross section assigned. This</text>
<figure>
<location><page_17><loc_23><loc_39><loc_78><loc_67></location>
<caption>Figure 5: Isotopes and their frequency of occurrence during the propagation simulated by CRPropa for 10 5 injected iron nuclei rectilinearly propagated over a distance up to 1000 Mpc. Note that this does not reflect an observable abundance, which would also depend on the time of survival of the produced isotope.</caption>
</figure>
<figure>
<location><page_18><loc_23><loc_67><loc_47><loc_83></location>
<caption>Figure 6 depicts example 1D simulations comparing TALYS (Sec. 3.1.1) and PSB cross sections [10]. These simulations show the average mass number 〈 A 〉 of UHECRs as a function of the distance from the source for the two cross section models under consideration. Here two different cases, namely pure iron and pure silicon injection, with the same rigidity at injection R = 38 . 4 EeV (corresponding to injection energies of E = 1000 and 538 EeV respectively), are considered. Furthermore these two injection cases have been provided both for a scenario excluding secondary particles (a) and including secondary particles (b). In these simulations, pair production, pion production and redshift evolution have been disabled, photodisintegration is considered on the CMB only and the cosmic rays are tracked as long as their energy is above 0.1 EeV. In the PSB case, decay has been disabled in order to strictly follow the reduced reaction network of [10]. As the PSB tables do not provide photodisintegration cross sections</caption>
</figure>
<figure>
<location><page_18><loc_51><loc_67><loc_75><loc_83></location>
<caption>Figure 6: Average nuclear mass 〈 A 〉 as a function of the distance from the source, resulting from the CRPropa photodisintegration cross section tables (see Sec. 3.1.1) (solid markers) and the PSB cross section tables [10] (open markers). The 1D simulations assume emission of pure iron (black circles) and pure silicon (blue rectangles) with an injection rigidity of R = 38 . 4 EeV.</caption>
</figure>
<unordered_list>
<list_item><location><page_18><loc_22><loc_58><loc_76><loc_59></location>(a) Average mass number of the primary cosmic rays, disregarding all nuclei with A < 5 .</list_item>
<list_item><location><page_18><loc_22><loc_57><loc_62><loc_58></location>(b) Average mass number of all cosmic rays, including secondaries.</list_item>
</unordered_list>
<text><location><page_18><loc_22><loc_39><loc_78><loc_54></location>is not problematic since all of them are far off the valley of stability and can be expected to decay very quickly. A closer look at the remaining light nuclei suggests that five of them cannot be handled due to missing cross section data: 5 He, 5 Li, 9 B, 7 He and 6 Be. However, all these nuclei have a half-life time smaller than 10 -15 s and, hence, are too short-lived to undergo photodisintegration. Finally, due to mass and charge loss by pion production, 'nuclei' which consist only of neutrons or protons can be observed in figure 5. This is a purely technical artifact and those nuclei will immediately decay in CRPropa. Thus, this basic example simulation suggests that the compilation of photonuclear cross sections used in CRPropa 2.0 is complete for an application in UHECR astrophysics.</text>
<section_header_level_1><location><page_18><loc_22><loc_36><loc_75><loc_37></location>5.2. Comparison of the Photodisintegration Cross Section Tables with PSB</section_header_level_1>
<text><location><page_19><loc_22><loc_81><loc_78><loc_84></location>for 5 ≤ A ≤ 8 , particles that end up in this region are set to immediately photodisintegrate to A = 4 plus secondaries.</text>
<text><location><page_19><loc_22><loc_77><loc_78><loc_81></location>In scenario (a), in order to consider only the primary cosmic rays, all nuclei with A < 5 have been ignored. This case can be compared with, for instance, Fig. 5 of [11].</text>
<text><location><page_19><loc_22><loc_63><loc_78><loc_76></location>As noted in [11], the PSB agreement with experimental data is not as good as the one obtained with the Lorentzian parameterization of TALYS. Moreover, the PSB case employs a reduced reaction network involving only one nucleus for each atomic mass number A up to 56 Fe, whereas 287 nuclides with their photodisintegration cross sections have been implemented in CRPropa. Figure 6 shows the effect of these differences on the average mass of the primary particle. In particular it can be seen that CRPRopa employing TALYS (plus low-mass extensions) results on average in a faster photodisintegration rate than PSB does.</text>
<text><location><page_19><loc_22><loc_56><loc_78><loc_63></location>In scenario (b) all photodisintegrated particles are included. Due to the light secondary particles that are produced with each photodisintegration of the primary particle, the average mass number decreases faster in this scenario than in scenario (a). This shows the importance of taking secondary particles into account when predicting the average mass number.</text>
<text><location><page_19><loc_22><loc_45><loc_78><loc_55></location>A noticeable feature in this scenario is that, for CRPropa, after a certain propagation length the average mass number of injected silicon exceeds the average mass number of injected iron. This is due to the larger number of light secondaries disintegrated off the iron nucleus. This, in combination with the cross section dependence on the mass number, can cause a lower total average mass at a certain distance, even though the primary cosmic ray still has a higher mass on average.</text>
<text><location><page_19><loc_22><loc_33><loc_78><loc_45></location>Furthermore, in this scenario both iron and silicon injection show, at all distances, an average mass for the CRPropa tables larger or equal to the average mass for the PSB tables. This can be tracked to a difference in the type of secondaries that are created. In CRPropa photodisintegration can yield secondaries of mass number up to four ( n , p , d , t , 3 He and 4 He). In the PSB case all secondaries, with the exception of the reaction γ + 9 Be → 2 α + n , have a mass number of one, therefore decreasing the average mass number with respect to the CRPropa case.</text>
<section_header_level_1><location><page_19><loc_22><loc_30><loc_74><loc_31></location>5.3. 1D: Influence of Chemical Composition and Cosmological Evolution</section_header_level_1>
<text><location><page_19><loc_22><loc_16><loc_78><loc_29></location>The advantage of the 1D mode in CRPropa is that one can include the cosmological as well as the source evolution as function of the distance to the observer. We demonstrate this by using two simulations which only differ in the composition injected at the sources, namely pure iron injection or a galactic mixed composition [26, 27]. This allows one to investigate the influence of the poorly known initial composition. The parameters of these simulations are as follows: UHECRs are injected with an E -2 . 2 spectrum up to a rigidity of R = 384 . 6 EeV from a continuous source distribution with comoving injection rate scaling as (1 + z ) 4 up to z max = 2 . The cosmological evolution is characterized</text>
<figure>
<location><page_20><loc_23><loc_60><loc_47><loc_74></location>
<caption>(a) galactic composition</caption>
</figure>
<figure>
<location><page_20><loc_37><loc_40><loc_61><loc_56></location>
<caption>(b) pure ironFigure 7: Results of a 1D simulation with CRPropa 2.0 taking into account the cosmological expansion and a comoving source evolution scaling as (1 + z ) 4 up to z max = 2 . (Upper panels:) The simulated UHECR flux (black rectangles) has been normalized to the Pierre Auger spectrum (red dots) [29, 30]. The spectra of secondary γ -rays (blue triangles) and neutrinos (magenta triangles) have been normalized accordingly. The neutrino flux shown is the single-flavor flux, assuming a ratio of 1:1:1. This flux can be compared with the singleflavor neutrino limits (black lines) [31, 32, 33]. Green stars show the isotropic γ -ray flux measured by Fermi-LAT [34]. In the left upper panel a galactic mixed composition has been injected at the source while in the right upper panel a pure iron composition has been injected. (Lower panel:) Abundance of UHE nuclei above 1 EeV after propagation in case of a pure iron (blue open circles) and mixed galactic composition (black solid circles) injected. For comparison, the original galactic composition (light brown area) is also shown.</caption>
</figure>
<figure>
<location><page_20><loc_51><loc_60><loc_75><loc_74></location>
</figure>
<text><location><page_21><loc_22><loc_81><loc_78><loc_84></location>by a concordance Λ CDM Universe with a cosmological constant ( Ω m = 0 . 3 , Ω λ = 0 . 7 ) using a Hubble constant of H 0 = 72 km s -1 Mpc -1 .</text>
<text><location><page_21><loc_22><loc_68><loc_78><loc_81></location>The results are shown in Fig. 7. The simulated UHECR flux is normalized to the spectrum observed by the Pierre Auger Observatory at an energy of 10 19 EeV [29, 30] and the secondary γ -ray and neutrino fluxes are normalized accordingly. The reduction of the flux of observable secondary neutrinos and γ -rays for pure iron injection shown in Fig. 7(b) relative to Fig. 7(a) for a mixed injection composition is due to photodisintegration dominating with respect to photopion production for the heavier composition. The resulting simulated abundance of UHE nuclei for E > 1 EeV is shown in Fig 7(c). To compare with the propagated composition, the injected galactic composition is also shown.</text>
<text><location><page_21><loc_22><loc_62><loc_78><loc_67></location>Note that photons from nuclear de-excitation during a photodisintegration event are currently not taken into account in CRPropa. This might cause a moderate increase of the flux of photons at energies below ∼ 10 17 eV as discussed in e.g. [35, 36].</text>
<section_header_level_1><location><page_21><loc_22><loc_59><loc_77><loc_60></location>5.4. 3D: Continuous Source Distributions following the Large Scale Structure</section_header_level_1>
<text><location><page_21><loc_22><loc_36><loc_78><loc_58></location>A very attractive feature of CRPropa is the possibility to study the effect of the presence of a large scale structure extragalactic magnetic field (LSS-EGMF) on the UHECR spectrum, composition and anisotropy in 3D simulations. In the following example we study how a continuous source distribution following the LSS baryon density and deflections in the corresponding LSS-EGMF in the scenario of Ref. [28] can influence these quantities. To this end we inject a power law of dN/dE ∝ E -1 which we then reweigh to a power law of dN/dE ∝ E -2 . 2 , a well known trick to achieve sufficient statistics at high energy. As in the previous example, we consider a pure iron and a mixed galactic-like composition at injection and for comparison a pure proton composition has been added as well. Particles are injected up to a rigidity of R = 384 . 6 EeV and are tracked as long as their energy is above 1 EeV. The detection occurs on a sphere centered around the observer, called 'sphere around observer' in the code, with a radius of glyph[similarequal] 1 Mpc. The observer is placed in a magnetic environment that is similar to what is found in the vicinity of our Galaxy.</text>
<text><location><page_21><loc_22><loc_17><loc_78><loc_35></location>Fig. 8(a) shows that, in case of a pure iron injection, a bump in the UHECR spectrum is predicted at ∼ 15 EeV, which does not occur if a mixed galactic composition or pure proton composition is injected. Furthermore, the simulated spectra are not strongly affected by the presence of the LSS magnetic field or LSS source density. In contrast, the propagated composition of the pure iron injection case is affected by deflections, as shown in Fig. 8(b), since deflections increase the propagation path length, thereby enhancing interactions and reducing the average mass number 〈 A 〉 at detection. Finally, Fig. 8(c) illustrates that the pure iron case shows a smaller horizon for energies E glyph[greaterorsimilar] 1 EeV when compared to the case of an injected galactic or pure proton composition. This is mostly due to increased deflections and thus more interactions in case of primary iron nuclei.</text>
<figure>
<location><page_22><loc_22><loc_61><loc_47><loc_75></location>
<caption>(a) energy spectra</caption>
</figure>
<figure>
<location><page_22><loc_37><loc_43><loc_62><loc_57></location>
<caption>(b) mass spectra(c) source distance vs travel time</caption>
</figure>
<text><location><page_22><loc_22><loc_25><loc_78><loc_33></location>(a), (b) UHECR flux and average mass number 〈 A 〉 as function of energy. Apart from the three cases for injected composition discussed in the text, which are shown including deflections in the LSS-EGMF, a pure iron simulation without deflection is shown for comparison (dark blue triangles). In the case of the UHECR flux a simulation with pure proton injection without deflections and with a flat continuous source distribution (not following the LSS density) has been added for comparison as well (magenta stars). The flux is normalized to unity in the first bin to allow for a better comparison of the spectral shape.</text>
<text><location><page_22><loc_22><loc_23><loc_78><loc_25></location>(c) Distance of the UHECRs from their source as function of the propagation time for all cosmic rays above 1 EeV, including a scenario without deflections (dark blue line).</text>
<figure>
<location><page_22><loc_51><loc_61><loc_75><loc_75></location>
<caption>Figure 8: Example simulations of a continuous source distribution which follows the LSS density in the scenario of Ref. [28]. Magnetic deflections of the UHECRs in the corresponding LSS magnetic fields are taken into account in this 3D simulation. A pure iron composition (black rectangles), a galactic composition (red triangles) and a pure proton composition (light blue dots) have been injected at the source.</caption>
</figure>
<section_header_level_1><location><page_23><loc_22><loc_83><loc_70><loc_84></location>5.5. 3D: Simulating Observables at a given Distance from a Source</section_header_level_1>
<text><location><page_23><loc_22><loc_73><loc_78><loc_82></location>Apart from detecting particles on spheres around the observer, cf. Sec. 5.4, CRPropa also allows one to detect particles on spheres around sources. In this detection mode a simulated UHECR trajectory crossing a given sphere in a 3D simulation will be written to the output file. This allows one to study e.g. spectrum, composition and anisotropy of the UHECR flux from a given source as function of the distance, corresponding to the radii of the spheres.</text>
<text><location><page_23><loc_22><loc_57><loc_79><loc_73></location>As an example a galactic composition is injected from the center of a (75 Mpc) 3 simulation box filled with the magnetic field configuration as given in the scenario of Ref. [28]. Detection spheres with radii of 4, 8, 16 and 32 Mpc are placed around the source. The initial dN/dE ∝ E -1 spectrum up to a rigidity of R = 384 . 6 EeV is reweighted to a dN/dE ∝ E -2 . 2 spectrum. Only particles which have an energy larger than 55 EeV are taken into account. As shown in Fig. 9, the flux of cosmic rays at the highest energies is suppressed by particle interactions as the distance from the source increases. Furthermore, the cosmic ray distribution becomes more anisotropic with increasing distance from the source due to increasing deflections in the large scale magnetic field structure. This latter effect is exemplified in the sky maps shown in Fig. 9(b).</text>
<section_header_level_1><location><page_23><loc_22><loc_53><loc_43><loc_54></location>6. Summary and Outlook</section_header_level_1>
<text><location><page_23><loc_22><loc_25><loc_78><loc_51></location>In the present paper we have presented the new version of our UHECR propagation code CRPropa, a numerical tool to study the effect of extragalactic propagation on the spectrum, chemical composition and distribution of arrival directions of UHECRs on Earth. The main new feature introduced in this new version 2.0 is the propagation of UHE nuclei, taking also into account their interactions with the IGM, in particular photodisintegration, which is modeled according to the numerical framework TALYS. As photodisintegration introduced many more interaction channels than were present in the previous version of CRPropa, we needed to substantially improve the propagation algorithm both in efficiency and in accuracy. We also updated the default model for the extragalactic infrared light to a more recent one. CRPropa 2.0 can now be used to compute the main observable quantities related to UHECR propagation with the accuracy required by present data: particle spectra, mass composition and arrival direction on Earth, for highly customizable realizations of the IGM, including source distributions and magnetic fields. In addition, the spectra of secondary neutrinos and electromagnetic cascades can be computed down to MeV energies. One of the extensions planned for the future is to include a module to take into account the effect of galactic magnetic fields on deflections.</text>
<section_header_level_1><location><page_23><loc_22><loc_21><loc_40><loc_22></location>7. Acknowledgements</section_header_level_1>
<text><location><page_23><loc_22><loc_17><loc_78><loc_19></location>We warmly thank Ricard Tomàs and Mariam Tórtola for many interesting discussions and help with several parts of the code. This work was supported</text>
<text><location><page_24><loc_35><loc_77><loc_36><loc_79></location>9</text>
<text><location><page_24><loc_44><loc_62><loc_55><loc_63></location>(a) energy spectra</text>
<figure>
<location><page_24><loc_22><loc_30><loc_79><loc_60></location>
<caption>Figure 9: Spectrum and sky maps of UHECR above 55 EeV after propagating in a (75 Mpc) 3 simulation cube filled with an LSS-EGMF in the scenario of Ref. [28]. In this simulation detection spheres have been placed around the single source present in the simulated environment with the four radii 4, 8, 16, and 32 Mpc and the injection spectrum has been reweighted to a dN/dE ∝ E -2 . 2 source spectrum.</caption>
</figure>
<unordered_list>
<list_item><location><page_24><loc_22><loc_19><loc_78><loc_21></location>(b) Hammer-Aitoff projections of the arrival directions of the simulated UHECR trajectories as registered on the different detection spheres around the source.</list_item>
</unordered_list>
<text><location><page_25><loc_22><loc_74><loc_78><loc_84></location>by the Deutsche Forschungsgemeinschaft through the collaborative research centre SFB 676, by BMBF under grants 05A11GU1 and 05A11PX1, and by the 'Helmholtz Alliance for Astroparticle Phyics (HAP)' funded by the Initiative and Networking Fund of the Helmholtz Association. GS acknowledges support from the State of Hamburg, through the Collaborative Research program 'Connecting Particles with the Cosmos'. LM acknowledges support from the Alexander von Humboldt foundation.</text>
<section_header_level_1><location><page_25><loc_22><loc_70><loc_31><loc_71></location>References</section_header_level_1>
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<list_item><location><page_25><loc_23><loc_64><loc_78><loc_68></location>[1] The Pierre Auger Collaboration, Observation of the Suppression of the Flux of Cosmic Rays above 4 × 10 19 eV, Physical Review Letters 101 (2008) 061101.</list_item>
<list_item><location><page_25><loc_23><loc_60><loc_78><loc_63></location>[2] R. U. Abbasi, et al., First Observation of the GZK Cutoff in the HiRes Experiment, Phys. Rev. Lett. 100 (2008) 101101.</list_item>
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</unordered_list>
<table>
<location><page_26><loc_22><loc_15><loc_78><loc_84></location>
</table>
<table>
<location><page_27><loc_22><loc_37><loc_78><loc_84></location>
</table>
</document>
[
{
"title": "CRPropa 2.0 - a Public Framework for Propagating High Energy Nuclei, Secondary Gamma Rays and Neutrinos",
"content": "Karl-Heinz Kampert a , Jörg Kulbartz b , Luca Maccione c,d , Nils Nierstenhoefer a,b , Peter Schiffer b , Günter Sigl b , Arjen René van Vliet b a University of Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany b II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "Version 2.0 of CRPropa 1 is public software to model the extra-galactic propagation of ultra-high energy nuclei of atomic number Z ≤ 26 through structured magnetic fields and ambient photon backgrounds taking into account all relevant particle interactions. CRPropa covers the energy range 6 × 10 16 < E/ eV < A × 10 22 where A is the nuclear mass number. CRPropa can also be used to track secondary γ -rays and neutrinos which allows the study of their link with the charged primary nuclei - the so called multi-messenger connection. After a general introduction we present several sample applications of current interest concerning the physics of extragalactic ultra-high energy radiation. Keywords: Ultrahigh energy cosmic rays, Extragalactic magnetic fields.",
"pages": [
1
]
},
{
"title": "1. Introduction and Motivation",
"content": "Cosmic rays are ionized atomic nuclei reaching the Earth from outside the Solar System with energies that exceed 10 20 eV . Although ultra-high energy cosmic rays (UHECRs) were originally discovered in 1939, their sources and propagation mechanisms are still a subject of intense research. During the last decade significant progress has been made due to the advent of high quality and high statistics data from a new generation of large scale observatories. Observables of prime interest are the energy spectrum, mass composition and arrival direction of cosmic rays. A flux-suppression in the energy spectrum above E ∼ 5 · 10 19 eV has been observed by the HiRes and Pierre Auger Observatories [1, 2] and possibly also by the Telescope Array [3] indicating either observation of the GZK-effect [4, 5] or the limiting energy of the sources. Moreover, data of the Pierre Auger Observatory indicate that the arrival directions of the highest energy cosmic rays are correlated with the depth of nearby Active Galactic Nuclei (AGN) or more generally with the nearby extra-galactic matter distribution [6]. Additionally, measurements of the position of the shower maximum and its fluctuations by the Pierre Auger Collaboration suggest a significant fraction of heavy primaries above 10 19 eV [7]. However, HiRes [8] and preliminary data of the Telescope Array [3]), suggest a proton dominance in the same energy range. Unfortunately, the limited number of observed events does not yet allow the extension of these measurements to the aforementioned cutoff energy. Independently of the mass composition, it is not uniquely settled yet if this flux depression is due to energy loss or maximum energy limitation of the sources. Clearly, a better understanding of all of these features and of the effects of cosmic ray propagation through the local Universe is mandatory. UHECRs do not propagate freely in the Inter Galactic Medium (IGM). During their propagation they suffer from catastrophic energy losses in reactions with the intergalactic background light and are deflected by poorly known magnetic fields. Thus, the effects of propagation alter the cosmic ray spectrum and composition injected by sources in the IGM and form the features detected by UHECR observatories. In order to establish the origin of UHECRs, it is of prime interest to quantitatively understand the imprint of the propagation and to disentangle it from the properties of the cosmic rays at their sources. In this respect, it is essential to compare the measured UHECR spectrum, composition and anisotropy with model predictions. This requires extensive simulations of the propagation of UHE nuclei and their secondaries within a given scenario. In particular, the observation that UHECRs may consist of a significant fraction of heavy nuclei challenges UHECR model predictions and propagation simulations. Indeed, compared to the case of ultra-high energy (UHE) nucleons, the propagation of nuclei leads to larger deflections in cosmic magnetic fields and additional particle interactions have to be taken into account, namely, photodisintegration and nuclear decay. To provide the community with a versatile simulation tool we present in this paper a publicly available Monte Carlo code called CRPropa 2.0 which allows one to simulate the propagation of UHE nuclei in realistic one- (1D) and threedimensional (3D) scenarios taking into account all relevant particle interactions and magnetic deflections. To this end, we extended the former version 1.4 of CRPropa, which was restricted to nucleon primaries, to the propagation of UHE nuclei. CRPropa 1.4 provided an excellent basis for this effort as many of its features could be carried over to the case of UHE nuclei propagation. In the present paper, which accompanies the public release of CRPropa 2.0, the underlying physical and numerical frameworks of the implementation of nuclei propagation are introduced. For technical details the reader is referred to the documentation distributed along with this framework. This paper is organized as follows: Section 2 starts with a short introduction of the publicly available previous CRPropa 1.4. The extensions which were implemented for nuclei interactions in CRPropa 2.0 are the subject of section 3. Section 4 describes the general propagation algorithm and in section 5 example applications of nuclei propagation with CRPropa are presented. We present a short summary and an outlook in Section 6. Unless stated otherwise, we use natural units glyph[planckover2pi1] = c = 1 throughout this paper.",
"pages": [
1,
2,
3
]
},
{
"title": "2. Inherited features from CRPropa 1.4",
"content": "The previous version 1.4 of CRPropa is a simulation tool aimed at studying the propagation of neutrons and protons in the intergalactic medium. It provides a one-dimensional (1D) and a three-dimensional (3D) mode. In 3D mode, magnetic field- and source distributions can be defined on a 3D grid. This allows one to perform simulations in realistic source scenarios with a highly structured magnetic field configuration as provided by, e.g., cosmological simulations. In 1D mode, magnetic fields can be specified as a function of the distance to the observer, but their effects are obviously restricted to energy losses of e + e -pairs due to synchrotron radiation within electromagnetic cascades. Furthermore, it is possible to specify the cosmological and the source evolution as well as the redshift scaling of the background light intensity in 1D simulations. All important interactions with the cosmic infrared (IRB) and microwave (CMB) background light are included, namely, production of electron-positron pairs, photopion production and neutron decay. Additionally, CRPropa allows for tracking and propagating secondary γ -rays, e + e -pairs and neutrinos. A module [9] is included that solves the one-dimensional transport equations for electromagnetic cascades that are initiated by electrons, positrons or photons taking into account single, double and triple pair production as well as up-scattering of low energy background photons by inverse Compton scattering. Synchrotron radiation along the line of sight can also be simulated. Technically, CRPropa is a stand alone object-oriented C++ software package. It reads an input file which specifies technical parameters as well as details of the simulated 'Universe' such as source positions and magnetic fields. The CRPropa simulations for a given scenario generate output files of either detected events or full UHECR trajectories.",
"pages": [
3
]
},
{
"title": "3. Modeling nuclei interactions in CRPropa 2.0",
"content": "Similar to the case of protons, nuclei carry charge and suffer energy losses by electron-positron pair production in ambient photon fields. This can occur when photon energies boosted into the rest frame of the nucleus are of the order of glyph[epsilon1] ' ∼ 1 MeV . For photon energies at or above the nuclear binding energy glyph[epsilon1] ' glyph[greaterorsimilar] 8 -9 MeV , nucleons and light nuclei can be stripped off the nucleus (photodisintegration). Finally, at photon energies exceeding glyph[epsilon1] ' ∼ 145 MeV the quark structure of free or bound nucleons can be excited to produce mesons (photopion production). In these reactions the nucleus can be disrupted and unstable elements be produced. Hence, nuclear decay has to be taken into account as well. In CRPropa2.0 a nucleus with energy E and mass number A is considered a superposition of A nucleons with energy E/A . Thus, if one or several nucleons are stripped off, the initial energy E will be distributed among the outgoing nucleons and nuclei. The ultra-relativistic limit β → 1 (with β = v/c of the nucleus) is used in CRPropa such that all nuclear products are assigned the same velocity vector as the initial particle. This corresponds to a Lorentz factor Γ glyph[similarequal] 10 8 · ( E/ 10 17 eV ) · A -1 and a forward collimation within an angle glyph[similarequal] 1 / Γ .",
"pages": [
3,
4
]
},
{
"title": "3.1. Photodisintegration",
"content": "Photodisintegration of nuclei has no analogy for free nucleons. Thus, implementing this new interaction process is mandatory to allow for propagation of nuclei within CRPropa. There are many competing photodisintegration processes of different cross sections which need to be accounted for along the path of the nucleus in the photon field. Thus, it is important to efficiently describe the specific photodisintegration pattern of each propagated nucleus in CRPropa. The effects of the propagation of UHE nuclei have first been studied by Puget, Stecker and Bredekamp (PSB) [10]. The approach to model the photodisintegration process chosen in CRPropa 2.0 is similar to what was more recently discussed in Ref. [11]. Further details on the photodisintegration within CRPropa2.0 can be found in Ref. [12]. As target photon fields we shall consider the CMB and IRB, for which we adopt the more recent parametrization developed in [13].",
"pages": [
4
]
},
{
"title": "3.1.1. The Photonuclear Cross Sections",
"content": "We use the publicly available TALYS framework, version 1.0 [14] to compute photodisintegration cross sections. The nuclear models therein are reliable for mass numbers A ≥ 12 . 2 Thus, additional photodisintegration cross sections for light nuclei have to added in the modeling. In CRPropa 2.0 TALYS was applied to 287 isotopes up to iron ( Z = 26 ) 3 employing nuclear models and settings as suggested in Ref. [11]. The list of isotopes for which the cross sections were calculated was generated using data from Ref. [15]. It is assumed that excited nuclei will immediately return to their ground state. Hence, only nuclei in their ground states are considered when calculating the cross sections 4 . All cross sections were calculated for photon energies 1 keV ≤ glyph[epsilon1] ' ≤ 250 MeV in the rest frame of the nucleus and stored in 500 bins of energy. Knocked out neutrons ( n ), protons ( p ), deuterium ( d ), tritium ( t ), helium-3 ( 3 He ) and helium-4 ( α ) nuclei and combinations thereof are considered by TALYS. The corresponding reaction channels are called exclusive channels . In the mass range of target nuclei where TALYS cannot be employed reliably, we use instead other prescriptions, as follows: In total 78449 exclusive channels are taken into account. The TALYS output in general agrees reasonably well with available measured data and only in rare cases differs up to a factor of 2 for the integrated (total absorption) cross sections [11]. Alternatively, for comparison, the widely-used photodisintegration cross section estimates developed by Puget, Stecker and Bredekamp [10] can be used. In the PSB case a reduced reaction network is implemented involving one nucleus for each atomic mass number A up to 56 Fe. Herein, the cross sections for one- and two-nucleon dissociation in the photon energy interval glyph[epsilon1] ' min ≤ glyph[epsilon1] ' ≤ 30 MeV are parametrized by a Gaussian approximation. Different from [10], the channel-dependent threshold energies glyph[epsilon1] ' min proposed in [20] are used. In the photon energy interval 30 ≤ glyph[epsilon1] ' ≤ 150 MeV the cross section is assumed to be constant. A comparison of results obtained with the TALYS and PSB cross sections is given in section 5.2.",
"pages": [
4,
5
]
},
{
"title": "3.1.2. Mean Free Path Calculations and Channel Thinning.",
"content": "Once the photodisintegration cross section in the nucleus rest frame σ ( glyph[epsilon1] ' ) is given (cf. Sec. 3.1.1), the energy weighted average cross section is tabulated as a function of glyph[epsilon1] ' max = 2Γ glyph[epsilon1] . For a given ¯ σ ( glyph[epsilon1] ' max ) , for each isotope the mean free path λ (Γ) can be calculated as a function of the Lorentz factor according to Ref. [10], where n ( glyph[epsilon1], z ) is the number density of the isotropic low energy photons per energy interval and volume. Variation due to cosmological redshift (cf. Sec. 3.5) is accounted for. For performance reasons, λ ( E ) is tabulated as a function of energy. The values of the integration limits glyph[epsilon1] min , glyph[epsilon1] max in Eq. (1) and (2) are listed in Tab. 1. As the Monte Carlo rapidly slows down with increasing number of exclusive channels to be sampled, a thinning procedure was implemented: For each isotope, we include only the channels with the n largest interaction rates out of the N available exclusive channels, such that the sum ∑ n i λ -1 i /λ -1 tot > α in at least one energy bin. Here, α is the thinning factor and the λ -1 i are summed up in decreasing order. Furthermore, λ -1 tot = ∑ N i λ -1 i is calculated for each isotope. In this way a α = 90% channel-thinning reduces the number of photodisintegration channels to be tracked from 78449 to 6440. The thinning procedure leads to a systematic overestimation of the mean free path in the order of 1% for Lorentz factors of the UHECR below 10 10 . This deviation goes up to 10% for Lorentz factors above 10 12 (see Fig. 1).",
"pages": [
5,
6
]
},
{
"title": "3.2. Photopion Production",
"content": "UHE nucleons can produce secondary mesons in interactions with low energy photon backgrounds. The most important reaction of this type is the production of pions in reactions of UHE protons with the CMB, which leads to the well known GZK cut-off [4, 5] at an energy of about E GZK = 5 · 10 19 eV. Nuclei can also produce mesons, albeit with a higher threshold energy of E th ≈ A × E GZK . This is due to the fact that to good approximation the center of mass system (CMS) coincides with the rest frame of the nucleus. The threshold energy, therefore, does not depend on the total energy of the nucleus E , but on the Lorentz factor Γ ∝ E/A . Pion production is thus only relevant for extremely energetic nuclei. However, it is important to be included to properly account for production of secondary UHE photons and neutrinos, as well as for the propagation of secondary and primary protons and neutrons. Effectively this process leads to an energy scaling of the mean free path λ A,Z for photopion production of nuclei. The mean free path for pion production on the constituent protons λ p and neutrons λ n can thus we written as In CRPropa 2.0 we use Eq. (3) to reduce the mean free path for pion production by nuclei to the one for nucleons which in turn is modeled by the SOPHIA package which was already used in CRPropa 1.3. This approximation is sufficient for our purposes because the pion mass m π ≈ 140 MeV is much larger than the binding energy per nucleon E b /A glyph[lessorsimilar] 8 MeV so that, above the threshold for pion production, the nuclear binding energy can be neglected and the nucleus be treated as a collection of free nucleons. Following this argument, we split the reaction into four parts, and calculate reactions of protons and neutrons on the CMB and on the IRB separately. The nucleus cross section σ A,Z for these four channels is then given by the cross sections of protons or neutrons times the number of the respective nucleons in the nucleus. The mean free path of the reaction was then obtained by folding this cross section with the respective photon background. If a reaction takes place, we treat it as a reaction of a free nucleon. The interacting nucleon will suffer energy loss and be stripped off the nucleus. The disintegrated nucleon will then be propagated individually, while the produced meson will decay leading to secondary leptons, photons or neutrinos which are then propagated using the corresponding modules of CRPropa. Both the decay of the meson as well as the energy loss of the primary nucleon are calculated by using the SOPHIA package [21].",
"pages": [
6,
8
]
},
{
"title": "3.3. Pair production",
"content": "Another interaction relevant for the propagation of UHE protons and nuclei is the creation of electron positron pairs in the low energy photon backgrounds. Both photomeson- and pair-production are less important in terms of energy loss of the primary nuclei which is dominated by photodisintegration (c.f. Fig. 3). Pair production is, however, the most important reaction for the creation of secondary photons in the TeV range. The mean free path for pair production is short, but the energy loss in each individual reaction is small. Thus, we treat pair production as a continuous energy loss which for interactions with the CMB can be parametrized by [10] Here, σ T is the Thomson cross section, m e and m p are the electron and proton rest masses, respectively, α em is the fine structure constant, T is the temperature of the CMB, and f (Γ) is a function which depends only on the Lorentz factor Γ and was parametrized by Blumenthal [22]. One can therefore express the energy loss length l A,Z = E ( dE e + e -A,Z /dt ) -1 for nuclei in terms of the energy loss length for protons l p = E ( dE e + e -1 , 1 /dt ) -1 , according to This scaling relation holds for arbitrary target photon backgrounds since the prefactor can be traced back to the scaling of the cross section and to the definition of the energy loss length. Eq. (5) is used in CRPropa 2.0 to generalize the pair production loss rates from protons to nuclei, which in practice is obtained by integration over the corresponding secondary spectra as parametrized by [23]. The energy loss for e + e -pair production is calculated after each timestep ∆ t and is therefore taken into account at discrete positions and times. CRPropa can also propagate secondary electromagnetic cascades initiated by the e + e -pairs or by the γ -rays resulting from π 0 -decay. For the injected secondary spectra we use the parametrization given by Kelner and Aharonian [23]. It should be noted that, in particular, close to an observer a large time step can degrade the accuracy of the propagated spectra, due to the discrete injection of the electromagnetic cascade. We refer the reader to the CRPropa 2.0 manual for details.",
"pages": [
8,
9
]
},
{
"title": "3.4. Nuclear Decay",
"content": "For the propagation of UHECRs, nuclear decay is relevant, if unstable particles are produced by photodisintegration or photopion production. On the one hand, nuclear decay can change both the nucleus type and its energy, while on the other hand it technically ensures that unstable nuclei decay back to stable nuclei whose photodisintegration cross sections are known. In CRPropa, decays are modeled as a combination of α , β ± decays and dripping of single nucleons ( p, n ). The decay length of a nucleus is given by its life time τ and the Lorentz factor Γ to be In case of p, n dripping and α decay, the decay products are assumed to inherit the Lorentz factor Γ from the parent nucleus. This assumption is justified since the binding energy per nucleon is small compared to the masses of the decay products. The energy of all produced nuclei are, therefore, simply given by In case of β ± decay we also use Eq. (7) and the momenta of e ± and the neutrino are calculated from a three body decay (see e.g. [24]) and are then boosted to the simulation frame. In CRPRopa the decay channels of the different nuclei as well as their decay constants at rest are stored in an internal database. It is based on the NuDat2 database [15] and contains 434 different nuclides with mass number A ≤ 56 and charge Z ≤ 26 . It should be noted that UHECRs, unlike the isotopes in the NuDat2 database, are fully ionized. This means that electron capture (EC) is not possible for UHECRs and the β + decays have to be calculated from the EC rates given in the NuDat2 database. Up to the squared matrix elements which are the same for EC and β + decay, the rates τ -1 EC and τ -1 β + for these two processes are just proportional to the available phase space of the final state products. If ∆ m ≡ m A,Z -m A ' ,Z ' is the mass difference of the fully ionized nuclei and, since the nuclear recoil energy and the electron binding energy can be neglected, the kinetic energy of the final state leptons are given by the socalled Q-factors Q β + = ∆ m -m e and Q EC = E ν = ∆ m + m e = Q β + + 2 m e with E ν the neutrino energy. Therefore, τ -1 EC ∝ | ψ e (0) | 2 Q 2 EC /π with | ψ e (0) | 2 = ( Z/a 0 ) 3 the normalized density of the electron wave function at the nucleus and τ -1 β + ∝ (2 /π 3 ) ∫ ∆ m m e dE f ( E ) with f ( E ) = E √ E 2 -m 2 e (∆ m -E ) 2 the standard β + decay differential phase space density per total positron energy E (including rest mass) [24]. Thus we get where everything has been expressed in terms of the bare nucleus mass difference ∆ m . For all channels involving β + decay (including compound channels), we compute τ β + from the lifetime of the dressed nucleus given in NuDat2 τ by multiplying with τ β + /τ = 1+ τ β + /τ EC . The resulting lifetimes τ β + of all isotopes in the database are shown in Fig. 2. In Tab. 2 we list the isotopes for which τ β + deviates most from τ . In Fig. 3 the decay length is shown in comparison to other energy loss processes using the example of 47 Ca.",
"pages": [
9,
10
]
},
{
"title": "3.5. Photon fields and cosmological evolution",
"content": "The implementation of photodisintegration and pion production in CRPropa2.0 is based on tabulated mean free path data calculated with the photon density n ( glyph[epsilon1], z = 0) at a redshift z = 0 (Sec. 3.1.2). As the photon density n ( glyph[epsilon1], z ) evolves as a function of z , λ = λ [Γ , z ] is effectively altered, too. To model this change of λ as function of z , a scaling function s ( z ) is used. It approximately relates λ [Γ , z ] at redshift z with the available tabulated data of λ [Γ (1 + z ) , z = 0] at redshift z = 0 . For this scaling function s ( z ) , it is assumed that the normalized spectral shape of the photon field n ( glyph[epsilon1], z ) does not change as function of z in the comoving cosmological frame. In this approach the evolution of the photon number density n ( glyph[epsilon1], z ) can be absorbed by a separated evolution factor e ( z ) In the approximation of a redshift independent spectral shape of n ( glyph[epsilon1], z ) , the evolution factor is defined by Here, glyph[epsilon1] i is the intersection energy of the CMB and IRB photon number densities n CMB ( glyph[epsilon1] i , z ) = n IRB ( glyph[epsilon1] i , z ) in the comoving frame. Substitution of Eq. (9) in Eq. (2) gives the scaling relation for the mean free path from which one can find s ( z ) = (1 + z ) 3 e ( z ) . It should be noted that this result is valid under the assumption that the spectral shape of the IRB does not depend on redshift. This approximation does not exactly hold for the IRB, due to energy injection in the IGM from galaxy formation. Nevertheless this approximation provides a model for the redshift evolution of the IRB which is of importance for the production of secondary neutrinos [25].",
"pages": [
10,
12
]
},
{
"title": "4. Propagation Algorithm and Monte Carlo Approach",
"content": "To handle the widely ranging reaction rates of UHE nuclei, a new propagation algorithm has been implemented in CRPropa 2.0. The main assumption is that the mean free paths λ are approximately constant during a time step. As λ = λ ( E ) is in general a function of the UHECR energy E , the numerical step size has to be small enough to ensure that no significant energy loss occurs. The algorithm works as follows. Given the mean free path λ i for a given interaction channel of a given nucleus, where i runs over all N possible interaction and decay channels, where δ is the maximal allowed fractional energy loss. where ∆ x 3 is an upper limit on the propagation step that can be provided by the user, with typical values of ∆ x 3 ∼ 1 -50 Mpc . This increases the accuracy of the calculation of pair production energy losses and the accuracy of the secondary pair production spectra. for a uniformly distributed random number 0 ≤ w ≤ 1 . Then the continuous energy losses are applied and the algorithm is restarted from the new position and the new particles produced in the interaction are added to the list of particles to be propagated, leading to a cascade of secondary nuclei (see Fig. 4). A comparison of the exclusive mean free path of the different channels λ a and the total mean free path for 47 Ca with the pair production loss length is shown in Fig. 3. If instead ∆ x 1 > min(∆ x 2 , ∆ x 3 ) , then continuous energy losses are too large to allow for accurate propagation until the next interaction point or the user has requested that the maximum step size be smaller than the ∆ x 1 selected in step 1. In this case, the particle is propagated over the distance ∆ x after which continuous losses are applied and the algorithm is restarted without performing any interaction. From the above description it is clear that if one of the interaction channels has a small mean free path λ i , the step size of the propagation will adjust itself automatically. This approach is also applied to select an exclusive channel e.g. in case of photodisintegration: If photodisintegration is chosen to be the next reaction by the propagation algorithm, the exclusive channel is found by applying Eq. (15). In analogy, here λ tot = ( ∑ i λ -1 i ) -1 is the total mean free path for the isotope under consideration. The λ i are the mean free path values for the exclusive channels of the corresponding isotope. If the user chooses to include secondary γ -rays and/or neutrinos, these neutral secondaries are propagated over a distance equal to the maximum propagation distance provided by the user minus the time of their production, such that they reach an observer after the maximum propagation time independently of the chosen 1D or 3D environment. In addition it is possible to inject a mixed nuclei composition. Since simple arguments about astrophysical acceleration mechanisms indicate that these mixed compositions should be accelerated up to a given maximum rigidity R = E/Z in the sources, instead of a maximum energy, we included the option to inject up to a given maximum rigidity at the source. The accuracy of the determination of the arrival direction and arrival time at the observer position is of course related to the actual implementation of detection and propagation in our algorithm. Besides the numerical error intrinsic to the detection algorithm, an additional error is introduced by the choice to take continuous losses into account only at the end of the time step and of course by the maximum propagation time, which can however be controlled by the user. This can be particularly relevant for bursted sources. We refer the interested reader to the manual for a deeper discussion on these issues.",
"pages": [
12,
14,
16
]
},
{
"title": "5. Example Applications",
"content": "In this section simulations are presented to demonstrate some features of CRPropa. All these simulations are restricted to a pure iron or a mixed galactic composition injected at the source. For the latter we adopt Ref. [26], similar to the approach of Ref. [27]. The injected power law dN/dE ∝ E -α is arbitrarily chosen to have a slope 5 of α = 2 . 2 . For the 3D simulations, a (75 Mpc) 3 simulation cube with periodic boundary conditions is defined and filled with the large scale structure extragalactic magnetic fields (LSS-EGMF) from the cosmological simulations given in Ref. [28].",
"pages": [
16
]
},
{
"title": "5.1. Completeness of the Photodisintegration Cross Section Tables",
"content": "To verify the completeness of the implemented photonuclear cross section tables presented in Sec. 3.1.1, i.e. to verify whether cross sections are available for all nuclei that occur during propagation, 1D simulations have been performed. To this purpose, 10 5 iron nuclei were injected with a dN/dE ∝ E -1 spectrum in the energy range 1 EeV ≤ E ≤ 56 × 10 3 EeV from a uniform source distribution extending up to a distance of 1 Gpc from the observer. In this simulation, all particles that were created and propagated within CRPropa were recorded in a two dimensional histogram (see Fig. 5) displaying the frequency of occurrence of isotopes in the simulation as a function of their mass and atomic number A,Z . In this figure, symbols are given to mark the isotopes for which cross sections are available in CRPropa and the type of the marker identifies the source of the cross section as listed in Sec. 3.1.1. At the upper right part of Fig. 5 some nuclei are created but do not have a photodisintegration cross section assigned. This is not problematic since all of them are far off the valley of stability and can be expected to decay very quickly. A closer look at the remaining light nuclei suggests that five of them cannot be handled due to missing cross section data: 5 He, 5 Li, 9 B, 7 He and 6 Be. However, all these nuclei have a half-life time smaller than 10 -15 s and, hence, are too short-lived to undergo photodisintegration. Finally, due to mass and charge loss by pion production, 'nuclei' which consist only of neutrons or protons can be observed in figure 5. This is a purely technical artifact and those nuclei will immediately decay in CRPropa. Thus, this basic example simulation suggests that the compilation of photonuclear cross sections used in CRPropa 2.0 is complete for an application in UHECR astrophysics.",
"pages": [
16,
18
]
},
{
"title": "5.2. Comparison of the Photodisintegration Cross Section Tables with PSB",
"content": "for 5 ≤ A ≤ 8 , particles that end up in this region are set to immediately photodisintegrate to A = 4 plus secondaries. In scenario (a), in order to consider only the primary cosmic rays, all nuclei with A < 5 have been ignored. This case can be compared with, for instance, Fig. 5 of [11]. As noted in [11], the PSB agreement with experimental data is not as good as the one obtained with the Lorentzian parameterization of TALYS. Moreover, the PSB case employs a reduced reaction network involving only one nucleus for each atomic mass number A up to 56 Fe, whereas 287 nuclides with their photodisintegration cross sections have been implemented in CRPropa. Figure 6 shows the effect of these differences on the average mass of the primary particle. In particular it can be seen that CRPRopa employing TALYS (plus low-mass extensions) results on average in a faster photodisintegration rate than PSB does. In scenario (b) all photodisintegrated particles are included. Due to the light secondary particles that are produced with each photodisintegration of the primary particle, the average mass number decreases faster in this scenario than in scenario (a). This shows the importance of taking secondary particles into account when predicting the average mass number. A noticeable feature in this scenario is that, for CRPropa, after a certain propagation length the average mass number of injected silicon exceeds the average mass number of injected iron. This is due to the larger number of light secondaries disintegrated off the iron nucleus. This, in combination with the cross section dependence on the mass number, can cause a lower total average mass at a certain distance, even though the primary cosmic ray still has a higher mass on average. Furthermore, in this scenario both iron and silicon injection show, at all distances, an average mass for the CRPropa tables larger or equal to the average mass for the PSB tables. This can be tracked to a difference in the type of secondaries that are created. In CRPropa photodisintegration can yield secondaries of mass number up to four ( n , p , d , t , 3 He and 4 He). In the PSB case all secondaries, with the exception of the reaction γ + 9 Be → 2 α + n , have a mass number of one, therefore decreasing the average mass number with respect to the CRPropa case.",
"pages": [
19
]
},
{
"title": "5.3. 1D: Influence of Chemical Composition and Cosmological Evolution",
"content": "The advantage of the 1D mode in CRPropa is that one can include the cosmological as well as the source evolution as function of the distance to the observer. We demonstrate this by using two simulations which only differ in the composition injected at the sources, namely pure iron injection or a galactic mixed composition [26, 27]. This allows one to investigate the influence of the poorly known initial composition. The parameters of these simulations are as follows: UHECRs are injected with an E -2 . 2 spectrum up to a rigidity of R = 384 . 6 EeV from a continuous source distribution with comoving injection rate scaling as (1 + z ) 4 up to z max = 2 . The cosmological evolution is characterized by a concordance Λ CDM Universe with a cosmological constant ( Ω m = 0 . 3 , Ω λ = 0 . 7 ) using a Hubble constant of H 0 = 72 km s -1 Mpc -1 . The results are shown in Fig. 7. The simulated UHECR flux is normalized to the spectrum observed by the Pierre Auger Observatory at an energy of 10 19 EeV [29, 30] and the secondary γ -ray and neutrino fluxes are normalized accordingly. The reduction of the flux of observable secondary neutrinos and γ -rays for pure iron injection shown in Fig. 7(b) relative to Fig. 7(a) for a mixed injection composition is due to photodisintegration dominating with respect to photopion production for the heavier composition. The resulting simulated abundance of UHE nuclei for E > 1 EeV is shown in Fig 7(c). To compare with the propagated composition, the injected galactic composition is also shown. Note that photons from nuclear de-excitation during a photodisintegration event are currently not taken into account in CRPropa. This might cause a moderate increase of the flux of photons at energies below ∼ 10 17 eV as discussed in e.g. [35, 36].",
"pages": [
19,
21
]
},
{
"title": "5.4. 3D: Continuous Source Distributions following the Large Scale Structure",
"content": "A very attractive feature of CRPropa is the possibility to study the effect of the presence of a large scale structure extragalactic magnetic field (LSS-EGMF) on the UHECR spectrum, composition and anisotropy in 3D simulations. In the following example we study how a continuous source distribution following the LSS baryon density and deflections in the corresponding LSS-EGMF in the scenario of Ref. [28] can influence these quantities. To this end we inject a power law of dN/dE ∝ E -1 which we then reweigh to a power law of dN/dE ∝ E -2 . 2 , a well known trick to achieve sufficient statistics at high energy. As in the previous example, we consider a pure iron and a mixed galactic-like composition at injection and for comparison a pure proton composition has been added as well. Particles are injected up to a rigidity of R = 384 . 6 EeV and are tracked as long as their energy is above 1 EeV. The detection occurs on a sphere centered around the observer, called 'sphere around observer' in the code, with a radius of glyph[similarequal] 1 Mpc. The observer is placed in a magnetic environment that is similar to what is found in the vicinity of our Galaxy. Fig. 8(a) shows that, in case of a pure iron injection, a bump in the UHECR spectrum is predicted at ∼ 15 EeV, which does not occur if a mixed galactic composition or pure proton composition is injected. Furthermore, the simulated spectra are not strongly affected by the presence of the LSS magnetic field or LSS source density. In contrast, the propagated composition of the pure iron injection case is affected by deflections, as shown in Fig. 8(b), since deflections increase the propagation path length, thereby enhancing interactions and reducing the average mass number 〈 A 〉 at detection. Finally, Fig. 8(c) illustrates that the pure iron case shows a smaller horizon for energies E glyph[greaterorsimilar] 1 EeV when compared to the case of an injected galactic or pure proton composition. This is mostly due to increased deflections and thus more interactions in case of primary iron nuclei. (a), (b) UHECR flux and average mass number 〈 A 〉 as function of energy. Apart from the three cases for injected composition discussed in the text, which are shown including deflections in the LSS-EGMF, a pure iron simulation without deflection is shown for comparison (dark blue triangles). In the case of the UHECR flux a simulation with pure proton injection without deflections and with a flat continuous source distribution (not following the LSS density) has been added for comparison as well (magenta stars). The flux is normalized to unity in the first bin to allow for a better comparison of the spectral shape. (c) Distance of the UHECRs from their source as function of the propagation time for all cosmic rays above 1 EeV, including a scenario without deflections (dark blue line).",
"pages": [
21,
22
]
},
{
"title": "5.5. 3D: Simulating Observables at a given Distance from a Source",
"content": "Apart from detecting particles on spheres around the observer, cf. Sec. 5.4, CRPropa also allows one to detect particles on spheres around sources. In this detection mode a simulated UHECR trajectory crossing a given sphere in a 3D simulation will be written to the output file. This allows one to study e.g. spectrum, composition and anisotropy of the UHECR flux from a given source as function of the distance, corresponding to the radii of the spheres. As an example a galactic composition is injected from the center of a (75 Mpc) 3 simulation box filled with the magnetic field configuration as given in the scenario of Ref. [28]. Detection spheres with radii of 4, 8, 16 and 32 Mpc are placed around the source. The initial dN/dE ∝ E -1 spectrum up to a rigidity of R = 384 . 6 EeV is reweighted to a dN/dE ∝ E -2 . 2 spectrum. Only particles which have an energy larger than 55 EeV are taken into account. As shown in Fig. 9, the flux of cosmic rays at the highest energies is suppressed by particle interactions as the distance from the source increases. Furthermore, the cosmic ray distribution becomes more anisotropic with increasing distance from the source due to increasing deflections in the large scale magnetic field structure. This latter effect is exemplified in the sky maps shown in Fig. 9(b).",
"pages": [
23
]
},
{
"title": "6. Summary and Outlook",
"content": "In the present paper we have presented the new version of our UHECR propagation code CRPropa, a numerical tool to study the effect of extragalactic propagation on the spectrum, chemical composition and distribution of arrival directions of UHECRs on Earth. The main new feature introduced in this new version 2.0 is the propagation of UHE nuclei, taking also into account their interactions with the IGM, in particular photodisintegration, which is modeled according to the numerical framework TALYS. As photodisintegration introduced many more interaction channels than were present in the previous version of CRPropa, we needed to substantially improve the propagation algorithm both in efficiency and in accuracy. We also updated the default model for the extragalactic infrared light to a more recent one. CRPropa 2.0 can now be used to compute the main observable quantities related to UHECR propagation with the accuracy required by present data: particle spectra, mass composition and arrival direction on Earth, for highly customizable realizations of the IGM, including source distributions and magnetic fields. In addition, the spectra of secondary neutrinos and electromagnetic cascades can be computed down to MeV energies. One of the extensions planned for the future is to include a module to take into account the effect of galactic magnetic fields on deflections.",
"pages": [
23
]
},
{
"title": "7. Acknowledgements",
"content": "We warmly thank Ricard Tomàs and Mariam Tórtola for many interesting discussions and help with several parts of the code. This work was supported 9 (a) energy spectra by the Deutsche Forschungsgemeinschaft through the collaborative research centre SFB 676, by BMBF under grants 05A11GU1 and 05A11PX1, and by the 'Helmholtz Alliance for Astroparticle Phyics (HAP)' funded by the Initiative and Networking Fund of the Helmholtz Association. GS acknowledges support from the State of Hamburg, through the Collaborative Research program 'Connecting Particles with the Cosmos'. LM acknowledges support from the Alexander von Humboldt foundation.",
"pages": [
23,
24,
25
]
}
]
2013APh....49...28F
https://arxiv.org/pdf/1309.4908.pdf
<document>
<section_header_level_1><location><page_1><loc_19><loc_87><loc_81><loc_92></location>Fabrication and Response of High Concentration SIMPLE Superheated Droplet Detectors with Different Liquids</section_header_level_1>
<text><location><page_1><loc_23><loc_82><loc_78><loc_84></location>M. Felizardo 1,2 , T. Morlat 3 , J.G. Marques 4,2 , A.R. Ramos 4,2 , TA Girard 2,† ,</text>
<text><location><page_1><loc_24><loc_79><loc_76><loc_81></location>A. C. Fernandes 4,2 , A. Kling 4,2 , I. LÆzaro 2 , R.C. Martins 5 , J. Puibasset 6</text>
<text><location><page_1><loc_38><loc_76><loc_63><loc_77></location>( for the SIMPLE Collaboration )</text>
<text><location><page_1><loc_18><loc_62><loc_82><loc_72></location>1 Department of Physics, Universidade Nova de Lisboa, 2829-516 Monte da Caparica, Portugal 2 Centro de Física Nuclear, Universidade de Lisboa, 1649-003 Lisbon, Portugal 3 Ecole Normale Superieur de Montrouge, 1 Rue Aurice Arnoux, 92120 Montrouge, France 4 Instituto Tecnológico e Nuclear, IST, Universidade TØcnica de Lisboa, EN 10, 2686-953 SacavØm, Portugal 5 Instituto de Telecomunicaçıes, IST, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal 6 CRMD-CNRS and UniversitØ d'OrlØans, 1 bis Rue de la FØrollerie, 45071 OrlØans, France</text>
<text><location><page_1><loc_15><loc_55><loc_49><loc_56></location>Key words: dark matter; detectors; superheated liquids</text>
<section_header_level_1><location><page_1><loc_47><loc_49><loc_54><loc_50></location>Abstract</section_header_level_1>
<text><location><page_1><loc_15><loc_30><loc_85><loc_48></location>The combined measurement of dark matter interactions with different superheated liquids has recently been suggested as a cross-correlation technique in identifying WIMP candidates. We describe the fabrication of high concentration superheated droplet detectors based on the light nuclei liquids C3F8, C4F8, C4F10 and CCl2F2, and investigation of their irradiation response with respect to C2ClF5. The results are discussed in terms of the basic physics of superheated liquid response to particle interactions, as well as the necessary detector qualifications for application in dark matter search investigations. The possibility of heavier nuclei SDDs is explored using the light nuclei results as a basis, with CF3I provided as an example.</text>
<section_header_level_1><location><page_1><loc_15><loc_25><loc_31><loc_26></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_15><loc_10><loc_85><loc_21></location>The direct search for weakly interacting massive particle (WIMP) dark matter is generally based on one of five techniques: scintillators, semiconductors, cryogenic bolometers, noble liquids and superheated liquids. The last, in contrast to the others, relies on the stimulated transition of a metastable liquid to its gas phase by particle interaction: because the transition criteria are thermodynamic, the devices can be operated at temperatures and/or pressures at</text>
<text><location><page_2><loc_15><loc_88><loc_85><loc_92></location>which they are generally sensitive to only fast neutrons, α 's and other high linear energy transfer (LET) irradiations.</text>
<text><location><page_2><loc_15><loc_66><loc_85><loc_85></location>Only three WIMP search efforts employ the superheated liquid technique: PICASSO [1], COUPP [2] and SIMPLE [3], using C4F10, CF3I and C2ClF5 respectively. Of the three, COUPP is based on bubble chamber technology: only PICASSO and SIMPLE employ superheated droplet detectors (SDDs). Because of their fluorine content and fluorine's high proton spin sensitivity, as well as their otherwise light nuclei content relative to Ge, I, Xe, W and others, they have generally contributed most to the search for spin-dependent WIMP-proton interactions. COUPP, with CF3I, has also made a significant impact in the spin-independent sector.</text>
<text><location><page_2><loc_15><loc_49><loc_85><loc_63></location>A SDD consists of a uniform dispersion of micrometric-sized superheated liquid droplets homogeneously suspended in a hydrogenated, viscoelastic gel matrix. The phase transition generates a millimetric-sized gas bubble which can be recorded by either optical, acoustic or chemical means; both SDD experiments employ acoustic, while COUPP employs both acoustic and optical (the liquid is essentially transparent, whereas the gel matrix of the SDDs is at best translucent).</text>
<text><location><page_2><loc_15><loc_10><loc_85><loc_46></location>The significant difference between the two approaches is that SDDs are continuously sensitive for extended periods since the overall liquid droplet population is maintained in steady-state superheated conditions despite bubble nucleation of some droplets, whereas in the bubble chamber the bulk liquid is only sensitized between nucleation events, each of which precipitates the transition of the liquid volume hence requires recompression to re-establish the metastable state and leads to measurement deadtime. The advantage of the chamber approach is an ability to instrument large active target masses. SDDs have generally been confined to low concentration (< 1 wt% : liquid-to-colloid mass ratio) devices, for use in neutron [4-11], and heavy ion [12] detector applications, with impact in heavy ion and cosmic ray physics, exotic particle detection and imaging in cancer therapy [13,14]. For rare event applications such as a WIMP search, however, higher concentration detectors are required: the PICASSO devices are ~ 1 wt% concentrations. SIMPLE detectors in contrast are generally of 1-2 wt%; concentrations above 2 wt%, in which the droplets are sufficiently close in proximity, tend to self-destruct as a result of massive sympathetic bubble nucleation and induced fractures.</text>
<text><location><page_3><loc_15><loc_79><loc_85><loc_92></location>Recently, variation of the target liquids with different sensitivities to the possible scalar and axial vector components of a WIMP interaction has been suggested as a technique in identifying WIMP candidates [15], specifically in the case of COUPP in combined measurements using CF3I and C4F10. This measurement variation while maintaining equivalent sensitivities in the case of SDDs is not trivial, since device fabrication and operation depends on the individual thermodynamic characteristics of each liquid.</text>
<text><location><page_3><loc_15><loc_52><loc_85><loc_75></location>SIMPLE SDD fabrications generally proceed on the basis of density-matching the liquid with a 1.3 g/cm 3 food-based gel with low U/Th contamination: a significant difference in gel and liquid densities (as occurs with heavier nuclei liquids) results in inhomogeneous distributions of differential droplet sizes within the detector. Although this has been addressed by SIMPLE via viscosity-matching the gel [16,17], this approach is constrained by the SIMPLE gel melting at 35'C, limiting the temperature range of the device and hence restricting the liquids employed. The traditional addition of heavy salts such as CsCl to raise the gel density, as originally used by PICASSO with its polyacrylamide-based gels [18], is discouraged since this generally adds radioactive contaminants which must be later removed chemically with the highest efficiency possible.</text>
<text><location><page_3><loc_15><loc_15><loc_85><loc_48></location>Thus, the question of liquid variation in SDDs naturally raises the questions of whether or not such 'other' SDDs can in fact be fabricated, much less operated, and with what sensitivity. We here describe our fabrications and testing of small volume (150 ml), high concentration (1-2 wt%) SDD prototypes with C3F8, C4F8, C4F10, CCl2F2 and CF3I including for completeness a 'standard' C2ClF5 device of the SIMPLE dark matter search effort [3]. Section 2 provides an overview of the device fabrication, and describes the experimental testing of the products. The response of superheated liquids to irradiations in general, and liquid characteristics necessary to dark matter searches is discussed in Sec. 3, and applied to the fabricated SDD test results, with the salient aspects of particle discrimination as observed by SIMPLE identified in Sec. 4. Section 5 discusses the considerations necessary to the fabrication and implementation of heavier nuclei SDDs, to include the introduction of a figure of merit based on the light nuclei results by which an initial screening of possibilities can be made in the absence of a complete thermophysical description of the liquids: The fabrication and analysis of a CF3I is described as an example. Conclusions are formed in Sec. 6.</text>
<section_header_level_1><location><page_4><loc_15><loc_91><loc_36><loc_92></location>2. Light Nuclei Detectors</section_header_level_1>
<text><location><page_4><loc_15><loc_81><loc_85><loc_87></location>For light liquids, SDD construction generally consists of two parts: the gel, and the liquid droplet suspension. The variation of the liquid densities with temperature is shown in Fig. 1, and can be divided into three basic density groups:</text>
<unordered_list>
<list_item><location><page_4><loc_26><loc_76><loc_43><loc_78></location>(i) C2ClF5, C3F8 ,</list_item>
<list_item><location><page_4><loc_26><loc_74><loc_39><loc_75></location>(ii) CCl2F2 ,</list_item>
<list_item><location><page_4><loc_26><loc_71><loc_41><loc_73></location>(iii) C4F10, C4F8.</list_item>
</unordered_list>
<text><location><page_4><loc_15><loc_62><loc_85><loc_68></location>For those in groups (i) and (ii) with ρ ~ 1.3 g/cm 3 , small variations in the current C2ClF5 recipes are indicated; for the more dense liquids of group (iii), viscosity matching is necessary using an additive as discussed in detail in [16,17].</text>
<figure>
<location><page_4><loc_30><loc_36><loc_68><loc_58></location>
<caption>Fig. 1: variation of liquid densities with temperature [19].</caption>
</figure>
<section_header_level_1><location><page_4><loc_15><loc_28><loc_34><loc_29></location>2.1 Gel Fabrications</section_header_level_1>
<text><location><page_4><loc_15><loc_9><loc_85><loc_24></location>The basic SDD ingredients have been described previously [20]. In the density-matched, 'standard' case of C2ClF5, the gel composition is 1.71 wt% gelatin, 4.18 wt% polyvinylpyrrolidone (PVP), 15.48 wt% bi-distilled water and 78.16 wt% glycerin. The gelatin is selected on the basis of its organ origins to minimize the U/Th impurity content; the glycerin serves to enhance the viscosity and strength of the gel, and wet the container surfaces. The presence of the PVP (i) assists in fracture control by viscosity enhancement which decreases diffusion, (ii) improves the SDD homogeneity and reduces the droplet sizes via its</text>
<text><location><page_5><loc_15><loc_86><loc_85><loc_92></location>surfactant behavior, (iii) decreases the liquid solubility [21], (iv) inhibits clathrate hydrate formation, and (v) reduces the migration of α -emitters to droplet boundaries as a result of actinide complex ion polarity [22].</text>
<text><location><page_5><loc_15><loc_66><loc_85><loc_82></location>The basic process, minus several proprietary aspects, has been described in [20]. The ingredients are first formed: powdered gelatin (Sigma Aldrich G-1890 Type A), bi-distilled water and pre-eluted ion exchange resins for actinide removal are combined and left for 12-15 hrs at 45'C with slow agitation to homogenize the solution. Separately, PVP (Sigma Aldrich PVP-40T) and exchange resins are added to bi-distilled water, and stirred at ~65'C for 12-15 hrs. Resins and glycerin (Riedel-de-Haºn N' 33224) are combined separately, and left in medium stirring at ~50'C for 12-15 hrs.</text>
<text><location><page_5><loc_15><loc_52><loc_85><loc_63></location>The PVP solution is then slowly added to the gel solution ('concentrated gel'), and slowly agitated at 55-60'C for 2 hrs. The resins in all are next removed separately by filtering (Whatman 6725-5002A). The glycerin and concentrated gel are then combined at ~60'C, outgassed at ~ 70'C, and foam aspirated to eliminate trapped air bubbles. The solution is left at 48'C for 14 hrs with slow agitation to prevent bubble formation.</text>
<text><location><page_5><loc_15><loc_40><loc_85><loc_48></location>For the viscosity-matched protocol required for the C4F8 and C4F10, the gel composition is essentially the same as in the density-matched recipe, with a small agarose (Sigma Aldrich A0576) addition effected by combining it with glycerin at 90'C, then adding it to the concentrated gel mix prior its filtration.</text>
<text><location><page_5><loc_15><loc_32><loc_85><loc_36></location>Following resin purification, the gel yields measured U/Th contamination levels of < 8.7 mBq/kg 238 U, < 4.9 mBq/kg 235 U and < 6.9 mBq/kg 234 U.</text>
<section_header_level_1><location><page_5><loc_15><loc_27><loc_47><loc_29></location>2.2 Droplet Suspension Fabrications</section_header_level_1>
<text><location><page_5><loc_15><loc_18><loc_85><loc_24></location>The specific protocol for fabrication of a liquid droplet suspension depends on the thermodynamic properties of the liquid. The process with C2ClF5 is schematically shown in Fig. 2; the temperatures and pressures differ for each liquid.</text>
<text><location><page_5><loc_15><loc_10><loc_85><loc_14></location>Following transfer of the gel to the detector bottle, the bottle is first weighed and then removed to a container encased by a copper serpentine for cooling, positioned on a hotplate</text>
<text><location><page_6><loc_15><loc_81><loc_85><loc_92></location>within a hyperbaric chamber. Once stabilized at 35'C, the pressure is quickly raised to just above the vapor pressure (~11 bar) of the liquid with continued slow agitation. After thermalization, the agitation is stopped and the liquid injected into the gel through a flowline immersed in ice to simultaneously condense and distill it, and a 0.2 µm microsyringe filter (Gelman Acrodisc CR PTFE 4552T).</text>
<figure>
<location><page_6><loc_26><loc_53><loc_73><loc_79></location>
<caption>Fig. 2: variation of temperature and pressure following liquid injection in the fabrication of a C2ClF5 SDD.</caption>
</figure>
<text><location><page_6><loc_15><loc_18><loc_85><loc_44></location>Once injected, the pressure is quickly raised to 21 bar to prevent the liquid droplets from rising to the surface, and a rapid agitation simultaneously initiated to shear big droplets; simultaneously, the temperature is raised to 39'C to create a temperature gradient inside the matrix and to permit dispersion of the droplets. After 15 minutes, the temperature is reduced to 37'C for 30 min, then reduced to 35'C for 4 hrs with pressure and agitation unchanged, to fractionate the liquid into smaller droplets. Finally, the heating is stopped: the temperature decreases until the sol-gel transition is crossed, during which the agitation is maintained. Approximately 2 hrs later, the droplet suspension is quickly cooled to 15 o C with the serpentine, and left to set for 40 minutes with decreased agitation; the agitation is then stopped, and the pressure slowly reduced over 10 min to 11 bar, where it is maintained for ~ 15 hours with the temperature set to the selected measurement run temperature for the liquid.</text>
<text><location><page_6><loc_15><loc_11><loc_85><loc_15></location>Thereafter, the chamber pressure is slowly reduced to atmospheric, and the detector removed, weighed, and placed into either 'cool' storage or utilization: high temperature implies an</text>
<text><location><page_7><loc_15><loc_84><loc_85><loc_92></location>increased nucleation sensitivity, 'cold' (< 0'C) storage results in the formation of clathrate hydrates, which provoke spontaneous nucleation locally on the droplet surfaces in warming to room temperature, effectively destroying the device. Examples of the various completed fabrications are shown in Fig. 3.</text>
<figure>
<location><page_7><loc_16><loc_65><loc_84><loc_80></location>
<caption>Fig. 3: examples of the various detector fabrications.</caption>
</figure>
<text><location><page_7><loc_15><loc_44><loc_85><loc_60></location>The agitation process fractionates the liquid droplets, resulting in a homogeneously-dispersed droplet size distribution: longer fractionating times generally give smaller diameter distributions; shorter times, larger distributions. The protocol is specific to the liquid, both in terms of time and speed. This is illustrated in Fig. 4, which presents fits of measured frequency distributions of droplet sizes in 5 µ m intervals, obtained by optical microscopy from batch samples, for each of the SDDs with variations in their fractionating time and speed during their protocol development.</text>
<figure>
<location><page_7><loc_32><loc_21><loc_66><loc_42></location>
<caption>Fig. 4: various size distributions of fabricated detectors, resulting from variations in the fractionating time and speed, relative to a 'standard' C2ClF5 fabrication.</caption>
</figure>
<section_header_level_1><location><page_8><loc_15><loc_91><loc_35><loc_92></location>2.3 Irradiation Tests</section_header_level_1>
<text><location><page_8><loc_15><loc_81><loc_85><loc_87></location>The laboratory 'standard test' detector, a small version of the SIMPLE dark matter SDD fabricated with a scaled-down 'standard' recipe protocol described above, contained ~ 2.7 g of C2ClF5 suspended in a gel matrix within a 150 ml laboratory bottle (Schott Duran GL45).</text>
<text><location><page_8><loc_15><loc_66><loc_85><loc_78></location>Similar SDDs were fabricated using the above 'density-matched' protocol with CCl2F2 (2.5g), C3F8 (3.1g), and the 'viscosity-matched' protocol with C4F10 (2.6g) and C4F8 (2.8g). None of the device gels were resin-purified in order to profit from the α decay of the intrinsic U/Th impurities. The fractionating time of each was adjusted to provide approximately identical, normally-distributed droplet sizes of <r> = 30 µm.</text>
<text><location><page_8><loc_15><loc_42><loc_85><loc_63></location>Once formed, each SDD was instrumented with the same capping used in the search experiments, a hermetic construction containing feedthroughs for a pressure line and a high quality electret microphone cartridge (Panasonic MCE-200) with a frequency range of 0.02016 kHz (3 dB), SNR of 58 dB and a sensitivity of 7.9 mV/Pa at 1 kHz. The microphone, sheathed in a protective latex covering, was positioned inside the detector bottle within a 6 cm thick glycerin layer above the droplet emulsion, as shown in an empty device containment of Fig. 5: the microphone is seen below the cap, with the electronics cable interface vertical; the horizontal couple permits over-pressuring of the device up to 4 bar (the limit of the detector glass) , and is coupled to a pressure transducer (PTI-S-AG4-15-AQ) for readout.</text>
<figure>
<location><page_8><loc_38><loc_20><loc_62><loc_39></location>
<caption>Fig. 5: empty detector, showing the microphone interface (vertical)</caption>
</figure>
<paragraph><location><page_8><loc_38><loc_16><loc_63><loc_17></location>and pressure couple (horizontal).</paragraph>
<text><location><page_9><loc_15><loc_86><loc_85><loc_92></location>The microphone signal is remotely processed by a low noise, high-flexibility, digitallycontrolled microphone preamplifier (Texas Instruments PGA2500), which is coupled to the archiving PC via an I/O board (National Instruments PCI-6251).</text>
<text><location><page_9><loc_15><loc_62><loc_85><loc_82></location>Once fabricated, each detector was placed in the same temperature-controlled water bath situated inside an acoustic foam cage designed for environmental noise reduction, despite the capability of the microphone-based instrumentation to distinguish between the various noise events [23]. Measurements were performed in steps of 5'C over the temperature range of 5 35'C. The temperature was measured with a type K thermocouple (RS Amidata 219-4450): each change was stabilized over ~ 20 minutes. Data was acquired in Matlab files of ~ 10 MB each at a constant rate of 32 kSps for periods of 5 minutes each. Nucleation events were generally stimulated by low level α radiation from the gel/glass U/Th impurities in order to provide time-separated events.</text>
<figure>
<location><page_9><loc_22><loc_18><loc_48><loc_37></location>
<caption>Figure 6 shows a typical, particle-induced bubble nucleation signal event, generally described as a damped sinusoid with a typical duration of several milliseconds, and its frequency spectrum in a standard C2ClF5 SDD. The Fast Fourier Transform (FFT) is characterized by a primary peak at ~ 640 Hz, with some lower power harmonics at ~2 and ~4 kHz. Non-particle induced signals have been well characterized in terms of their time constants ( τ ), amplitudes ( A) and frequencies ( F) , and can be further discriminated from particle-induced events on the basis of their respective power density spectra which differ significantly from that of Fig. 6(b) [24].</caption>
</figure>
<figure>
<location><page_9><loc_52><loc_18><loc_79><loc_37></location>
<caption>Fig. 6: typical instrumentation pulse shape (a) and FFT (b) of a true particle-induced bubble nucleation event.</caption>
</figure>
<text><location><page_10><loc_15><loc_86><loc_85><loc_92></location>The results were subjected to a full, standard signal analyses [23]. The resulting acoustic background events were identified as normally-occurring gel fractures, trapped gas in the gel, and environmental noise intrinsic to SDD operation.</text>
<text><location><page_10><loc_15><loc_71><loc_85><loc_82></location>The noise levels were ~ 2 mV among all devices at all temperatures, except near 35'C where the level was ~ 4 mV since the detector gel was at a point of meltdown. A survey of the results at 1 bar is shown in Figs. 7(a)-(d); the 2 bar results will be discussed later. The error bars represent the standard deviation of the averages over the respective parameter measurement at each temperature: where not seen, they are smaller than the indicated data point.</text>
<figure>
<location><page_10><loc_17><loc_48><loc_48><loc_69></location>
</figure>
<figure>
<location><page_10><loc_52><loc_48><loc_83><loc_69></location>
</figure>
<text><location><page_10><loc_15><loc_45><loc_68><loc_47></location>(a) (b)</text>
<text><location><page_10><loc_15><loc_20><loc_69><loc_21></location>(c) (d)</text>
<figure>
<location><page_10><loc_16><loc_20><loc_48><loc_43></location>
</figure>
<figure>
<location><page_10><loc_51><loc_20><loc_83><loc_43></location>
<caption>Fig. 7: nucleation response for different refrigerants at 1 bar: (a) event rates normalized to detector mass, and signal (b) τ , (c) A , (d) F . The vertical line in each indicates the gel melt temperature (Tgel).</caption>
</figure>
<text><location><page_11><loc_15><loc_60><loc_85><loc_92></location>With the notable exception of the C3F8 event rates, the response of all liquids appears similar; with increasing temperature, the superheated liquids become more sensitive to incident radiation as a result of a reduced metastability barrier. Since the gel also becomes increasingly less stiff with temperature, an overall decreasing signal τ , increasing A and decreasing F might be expected. As seen in Figs. 7, all event rates tend to increase on approach to the gel melt temperature, as also the signal A . In contrast, the signal τ 's decrease, and F's fluctuate between 500-750 Hz. The results in all cases are consistent with the observed ranges observed with C2ClF5 for true bubble nucleations: τ within 5-40 ms, F within 0.45- 0.75 kHz [23]. The majority of signal A are > 125 mV: since neutrons in general produce nuclear recoil events with A < 100 mV [3], the results are consistent with the event triggering of the SDDs being principally from the α -emitting U/Th impurities of the detector gel and containment, as intended. Nonetheless, some events were recorded with A < 100 mV: 1 event with CC2F2 and 3 events with C4F10, to which we will return later.</text>
<text><location><page_11><loc_15><loc_45><loc_85><loc_56></location>The C3F8 device, in contrast to the other liquid SDDs, was a 2.1 wt% device, hence more susceptible to sympathetic nucleations occurring within the resolving time of the instrumentation. Also unlike the other devices, its gel above 30'C was in a state of decomposition: the glycerine layer surrounding the microphone was filled with foam, and identification of a particle-induced signal increasingly difficult.</text>
<section_header_level_1><location><page_11><loc_15><loc_41><loc_58><loc_42></location>3. Superheated Liquids and Irradiation Response</section_header_level_1>
<text><location><page_11><loc_15><loc_34><loc_85><loc_38></location>In order to more fully appreciate the above results, we discuss several aspects of both the superheated liquids and their response to irradiations.</text>
<section_header_level_1><location><page_11><loc_15><loc_30><loc_37><loc_32></location>3.1 Superheated liquids</section_header_level_1>
<text><location><page_11><loc_15><loc_9><loc_85><loc_28></location>The physics of the SDD operation, the same as with bubble chambers and described in detail in Ref. [24,25] and references therein, is based on the 'thermal spike' model of Seitz [26] which can be divided into several stages [27,28]. Initially, energy is deposited locally in a small volume of the liquid, producing a localized, high temperature region (the 'thermal spike'), the sudden expansion of which produces a shock wave in the surrounding liquid. In this stage, the temperature and pressure of the liquid within the shock enclosure exceed the critical temperature and pressures, Tc and pc respectively: there is no distinction between liquid and vapor, and no bubble. As the energy is transmitted from the thermalized region to</text>
<text><location><page_12><loc_15><loc_76><loc_85><loc_92></location>the surrounding medium through shock propagation and heat conduction, the temperature and pressure of the fluid within the shock enclosure decrease, the expansion process slows and the shock wave decays. As the temperature and pressure reach Tc and pc, a vapor-liquid interface is formed which generates a protobubble. If the deposited energy was sufficiently high, the vapor within the protobubble grows to a critical radius rc; if the energy was insufficient, cavity growth is impeded by interfacial and viscous forces and conduction heat loss, and the protobubble collapses.</text>
<text><location><page_12><loc_15><loc_71><loc_75><loc_73></location>To achieve rc, the deposited energy (E) must satisfy two thermodynamic criteria:</text>
<formula><location><page_12><loc_31><loc_64><loc_84><loc_68></location>E ≥ Ec p r 3 4 h r 3 4 ) T T ( r 4 3 c lv v 3 c 2 c ∆ π + ρ π + ∂ σ ∂ -σ π = (1)</formula>
<formula><location><page_12><loc_38><loc_59><loc_84><loc_63></location>dx dE ≥ c c r E Λ , (2)</formula>
<text><location><page_12><loc_15><loc_45><loc_86><loc_56></location>where rc = 2 σ / ∆ p, σ (T) is the droplet surface tension, ∆ p = pV - p is the liquid superheat, pV(T) is the vapor pressure of the liquid, p and T are the SDD operating pressure and temperature, hlv(T) is the liquid-vapor heat of vaporization, Λ rc is the effective ionic energy deposition length, and c c r E Λ is the critical LET. The first term represents the work required to</text>
<text><location><page_12><loc_15><loc_33><loc_85><loc_44></location>create the protobubble interface; the second, the energy required to evaporate the liquid during protobubble growth to rc. The third term describes the reversible work during protobubble expansion to rc against the liquid pressure. Generally, the second term is the largest, with the first ~ half. Not included in Eq. (1) are various irreversible processes which are generally small compared to the first three terms.</text>
<text><location><page_12><loc_15><loc_21><loc_85><loc_30></location>From Eq. (1), the Ec for bubble nucleation is strongly dependent on the hlv of the liquid, the variation of which is shown in Fig. 8 for the various liquids investigated, as obtained from hlv(T) = χ (1-T/Tc) n with χ and n for each liquid shown in Table I, and all temperatures in K. As seen, hlv decreases with temperature increase.</text>
<figure>
<location><page_13><loc_33><loc_71><loc_67><loc_92></location>
<caption>Fig. 8: variation of hlv with temperature for the various study liquids.</caption>
</figure>
<table>
<location><page_13><loc_14><loc_56><loc_80><loc_64></location>
<caption>Table I: χ , n for the study liquids, from Ref. [29].</caption>
</table>
<text><location><page_13><loc_15><loc_42><loc_85><loc_54></location>The liquid response is also seen to depend on the nucleation parameter ' Λ ' of the liquid in Eq. (2), in effect defining the energy density required for bubble nucleation. Its variation with temperature is shown in Fig. 9, using Λ = 4.3( ρ V/ ρ l) 1/3 which has been shown in agreement with experiment for C2ClF5 [22] and CCl2F2 [30]; although the ( ρ V/ ρ l) 1/3 is theoretically justified, its pre-factor is not in general and measurement is required.</text>
<figure>
<location><page_13><loc_31><loc_15><loc_69><loc_38></location>
<caption>Fig. 9: variation of the nucleation parameter with temperature for various liquids, calculated with Λ = 4.3( ρ V/ ρ l) 1/3 .</caption>
</figure>
<text><location><page_14><loc_15><loc_86><loc_85><loc_92></location>The critical LET in each case, of order 100 keV/ µ m, is sufficiently high that bubble nucleations can be triggered only by high LET irradiations - either ion recoils generated by neutron scatterings or by α 's.</text>
<text><location><page_14><loc_15><loc_57><loc_85><loc_82></location>The stopping power of the ions within the liquid is shown in Fig. 10(a) for the constituent nuclei of C2ClF5 and He from the U/Th contaminations of the SDD materials (which range in energy between 4.2 - 8.8 MeV) in C2ClF5 at 1.3 g/cm 3 . Figure 10(b) displays the α threshold energy (Ethr α ) of 5.5 MeV α 's in C2ClF5 at 1 and 2 bar, calculated with Eqs. (1) and (2) using thermodynamic parameters taken from Refs. [19,31], α stopping powers calculated with SRIM 2008 [32], and the experimentally determined Λ = 1.40 for C2ClF5 at 2 bar and 9'C [22,3]. The 'nose' of the α curves in Fig. 10(b) reflects the He Bragg peak in C2ClF5 seen in Fig. 10(a), with the SDD sensitivity at a given temperature lying between the lower and upper contours. From Fig. 10(b), at 9'C the α 'window' thresholds are clearly reduced at higher pressure; at 2.2 bar, the 'nose' lies to the right of the indicated 9'C line, and the α sensitivity vanishes.</text>
<figure>
<location><page_14><loc_16><loc_33><loc_50><loc_55></location>
<caption>Figure 11 shows the elastic Ethr nr contours for each of the C2ClF5 constituents with temperature variation, calculated as for Fig. 10(b) using SRIM and the experimental Λ = 1.40. The curves reflect the respective constituent recoil ion stopping powers of Fig. 10(a), which for Erecoil < 100 keV are well-below the respective Bragg peaks.</caption>
</figure>
<figure>
<location><page_14><loc_53><loc_33><loc_82><loc_55></location>
</figure>
<text><location><page_14><loc_43><loc_33><loc_63><loc_35></location>(b)</text>
<paragraph><location><page_14><loc_17><loc_28><loc_84><loc_33></location>Fig. 10: (a) stopping power of α 's and recoil ions in C2ClF5 ( ρ =1.3 g/cm 3 ) as a function of energy; (b) variation of Ethr α for C2ClF5 with temperature, at 1 (solid) and 2 (dashed) bar.</paragraph>
<figure>
<location><page_15><loc_32><loc_72><loc_67><loc_92></location>
<caption>Fig. 11: variation of liquid ion threshold recoil energy curves for</caption>
</figure>
<paragraph><location><page_15><loc_29><loc_66><loc_71><loc_67></location>C2ClF5 with temperature, at 1 (dashed) and 2 (solid) bar.</paragraph>
<text><location><page_15><loc_15><loc_58><loc_85><loc_63></location>The maximum ion recoil energy in a neutron elastic scattering on a nucleus of atomic mass A is given by Erecoil A = fAEn, where fA = ( ) 2 2 A 1 A 4 + and En is the incident neutron energy: for the</text>
<text><location><page_15><loc_15><loc_28><loc_85><loc_56></location>liquids of this study, fF = 0.19, fC = 0.27 so that a detector with a minimum nuclear recoil threshold energy Ethr nr = 8 keV implies a minimum response sensitivity to En = 42 and 30 keV for F and C recoils, respectively [45]. For the liquids with Cl, fCl = 0.10 and Ethr nr = 8 keV implies En = 80 keV; there are also two inelastic reactions with 35 Cl which may induce events through their recoiling ions: 35 Cl(n,p) 35 S and 35 Cl(n, α ) 32 P. In the first case the S ion has a maximum energy of 17 keV and can produce a nucleation for neutron energies ≤ 91 keV, whereas the P ion emerges with a minimum energy of 80 keV that can always provoke an event. However, as these reactions have cross sections smaller than those of elastic scattering on Cl by ~ 1-7 orders of magnitude, their contribution to the detector signal is generally small (with exceptions in thermal neutron beams at reactors). For C2ClF5 above 15'C, there is also the problem of events originating from high-dE / dx Auger electron cascades following interactions of environmental gamma rays with Cl atoms in the refrigerant.</text>
<text><location><page_15><loc_15><loc_14><loc_85><loc_25></location>The metastable barrier decreases with increasing temperature, which is by virtue of fA sequentially overcome by the recoiling constituent ions until a common threshold is reached at ~ 10'C (15'C) at 1 (2) bar. At 9'C and 2 bar, Ethr Cl,F = 8 keV while Ethr C ~ 80 keV. For fixed temperature operation, SDD pressure increase raises the Ethr nr curve and shifts it to higher temperatures.</text>
<text><location><page_16><loc_15><loc_64><loc_85><loc_92></location>As evident, the response sensitivity of each liquid is not the same at each temperature. This is a result of the variation in degree of superheating of the liquids, which varies significantly with T and p as seen in Table II. A 'universal' characterization of the response is obtained by replacing the temperature with the reduced superheat factor, S = (T - Tb)/(Tc * - Tb) with Tb the boiling temperature of the liquid at a given pressure and the critical temperature Tc * = 0.9Tc , with all temperatures in K, since the fluid phase of organic liquids ceases to exist at a temperature about 90% of the tabulated critical temperature Tc [33]. Equations (1) and (2), when satisfied simultaneously, provide the threshold energy (Ethr) for bubble nucleation, which when displayed as a function of S fall on a 'universal' curve for the nucleation onset of superheated liquid devices [25]. The range of S for each liquid is also shown in Table II. Numerous studies have shown the insensitivity of various liquid devices to γ 's, cosmics and minimum ionizing radiations for S < 0.72 [25,34].</text>
<table>
<location><page_16><loc_18><loc_44><loc_82><loc_57></location>
<caption>Table II: critical (Tc) and boiling temperature (Tb) at 1 and 2 bar for the different liquids (data from NIST [19]).</caption>
</table>
<section_header_level_1><location><page_16><loc_15><loc_38><loc_51><loc_39></location>3.2 The Irradiation Test Results Revisited</section_header_level_1>
<text><location><page_16><loc_15><loc_25><loc_85><loc_34></location>Given the above considerations, we now display the full experiment results with respect to S, beginning with the device responses in Fig. 12. Since the gel melting temperature (Tgel) is absolute hence appears at a different S for each liquid, these (denoted Sgel) are indicated for each device throughout.</text>
<figure>
<location><page_17><loc_18><loc_70><loc_49><loc_92></location>
</figure>
<figure>
<location><page_17><loc_51><loc_71><loc_82><loc_92></location>
<caption>Fig. 12: nucleation response for different refrigerants at (a) 1 and (b) 2 bar.</caption>
</figure>
<paragraph><location><page_17><loc_24><loc_65><loc_76><loc_66></location>The identified lines indicate the S for each liquid associated with Tgel.</paragraph>
<text><location><page_17><loc_15><loc_48><loc_85><loc_61></location>A higher reduced superheating implies a lower metastable energy barrier: the general response should be an asymmetric sigmoid, with the onset of minimum ionizing events occurring at S ~ 0.7. For S < 0.7, all event numbers should generally remain flat or increase with temperature depending on the degree of superheating, as observed herein; for S > 0.7, the liquids are increasingly sensitive to lower LET radiations which provide an additional contribution to the event rates.</text>
<text><location><page_17><loc_15><loc_21><loc_85><loc_44></location>In the case of C3F8, with an event response a factor ~ 10 larger than the other devices, the liquid above S = 0.8 is near its foam limit (S = 1) at which vapor phase transitions occur via thermal fluctuations, providing an explanation for the observed gel conditions (see Sec. 2.3). Moreover, its Ethr α is near 10 keV, an order of magnitude below that of the other liquids hence more susceptible to α 's otherwise reduced in energy by the gel to below thresholds of the other liquids. Apart from this, the geometric efficiency for α -induced nucleations increases for small droplet sizes as ε = 0.75f R α /r, where f is the active mass fraction, R α is the alpha particle range in the liquid, and r is the droplet radius [34]. Fig. 4, the C3F8 device exhibits the smallest size distribution of all, with <r> = 15 - 9 µ m; using the f's of the prototype fabrications, ε C3F8/ ε C2ClF5 ~ 3.5 consistent with Fig. 12.</text>
<text><location><page_17><loc_15><loc_11><loc_85><loc_17></location>In both regimes of S, the response is moderated by the effects of the gel becoming increasingly less stiff as its melting regime is entered [20]. The observed decrease of the C3F8 event response below Sgel is also in evidence for the other liquids, all of which are in states of</text>
<text><location><page_18><loc_15><loc_88><loc_85><loc_92></location>S < 0.7, and well below their respective foam limits, suggesting the gel relaxation to be principally responsible for the decrease.</text>
<text><location><page_18><loc_15><loc_78><loc_85><loc_85></location>The remainder of the results relate to the microphone-recorded signal characteristics which result from a bubble nucleation event, with the τ , F and A of the particle-induced signal events for each liquid as a function of S at each pressure shown in Figs. 13-15, respectively.</text>
<text><location><page_18><loc_32><loc_27><loc_70><loc_29></location>(a) (b)</text>
<figure>
<location><page_18><loc_16><loc_27><loc_48><loc_50></location>
<caption>Figures 13 display the signal decay constants: as anticipated, all are generally contained within 10-30 ms, with most showing an increase with temperature as a result of decreasing gel stiffness. With the exception of C3F8, all τ in Fig. 13(a) initially manifest considerable dispersion, condensing to 20-25 ms by 20'C ; C3F8 shows a slight decrease with approach to Sgel. In Fig. 13(b), the τ of C4F8 increases on approach to Sgel, then drops to 10 ms thereafter; for both C4F10 and CCl2F2, the τ fluctuates between 10-30 ms. In contrast, the C3F8 and C2ClF5 signal τ remain generally unchanged with temperature increase. Note that the τ of the 2 bar results are generally slightly increased relative to the 1 bar results, again as might be expected from a stiffer gel [20]. Also note, from Ref. [23], that τ 's for non-particle induced events are generally > 36 ms.</caption>
</figure>
<figure>
<location><page_18><loc_52><loc_27><loc_83><loc_50></location>
<caption>Fig . 13: signal τ for different refrigerants at (a) 1 and (b) 2 bar.</caption>
</figure>
<text><location><page_18><loc_15><loc_9><loc_86><loc_21></location>Since the frequency of an event is also defined by the elasticity of the medium, the signal F should tend to decrease with increasing temperature. This is not immediately discernible in Figs. 14. At 1 bar, F generally fluctuates until ~30'C (possibly the result of low statistics), with C2ClF5 showing an increase in approach to Sgel. At 2 bar, the F are slightly lower and more dispersed than those at 1 bar, with C3F8 also showing an increase towards Sgel. Note that</text>
<text><location><page_19><loc_15><loc_88><loc_85><loc_92></location>the recorded F differ significantly from those reported by PICASSO and COUPP, and that F of acoustic background events are generally < 100 Hz [23].</text>
<figure>
<location><page_19><loc_16><loc_61><loc_48><loc_84></location>
</figure>
<figure>
<location><page_19><loc_50><loc_61><loc_83><loc_84></location>
<caption>Fig. 14: signal F variations for different refrigerants at (a) 1 and (b) 2 bar.</caption>
</figure>
<text><location><page_19><loc_15><loc_51><loc_85><loc_55></location>The complete phase transition of a droplet results in a gas bubble harmonically oscillating about its equilibrium radius rb . The resonant frequency is given by Minnaert [39]:</text>
<formula><location><page_19><loc_43><loc_44><loc_84><loc_48></location>l 0 b r p 3 r 2 1 f ρ η π = , (3)</formula>
<text><location><page_19><loc_15><loc_32><loc_85><loc_40></location>where η is the polytropic coefficient of the gas, p0 is the ambient equilibrium pressure (effects of bubble movement caused by buoyancy forces, and spatial variation of the pressure during the growth process are neglected [40]). For typical parameters at 9'C and 2 bar, rb = 5 mm and η ~ 1.1 [41], fr = 700 s -1 consistent with the event records.</text>
<text><location><page_19><loc_15><loc_22><loc_85><loc_28></location>As seen in Figs. 15, all A generally increase with approach to Sgel, as expected with increased superheating, and are generally lower at 2 bar than those at 1 bar, as also expected with a stiffer gel.</text>
<figure>
<location><page_20><loc_17><loc_69><loc_48><loc_92></location>
</figure>
<figure>
<location><page_20><loc_51><loc_69><loc_83><loc_92></location>
<caption>Fig. 15: A variations for different refrigerants at (a) 1 and (b) 2 bar.</caption>
</figure>
<text><location><page_20><loc_15><loc_61><loc_85><loc_65></location>The emitted acoustic power (J) in a bubble nucleation is proportional to the acceleration of the bubble volume expansion [42] ,</text>
<formula><location><page_20><loc_37><loc_57><loc_84><loc_60></location>J ~ 2 l V c 4 & & π ρ , (4)</formula>
<text><location><page_20><loc_15><loc_50><loc_85><loc_54></location>where c is the speed of sound in the medium, V is the droplet volume and the dots denote differentiation with respect to time. The pressure P produced in a liquid bath without gel at a</text>
<formula><location><page_20><loc_15><loc_46><loc_76><loc_49></location>distance d from the source at time t is then J 4 c d 1 l π ρ which with V = 3 r 3 4 π reduces to</formula>
<formula><location><page_20><loc_38><loc_39><loc_84><loc_42></location>[ ] r r r r 2 d V d 4 ) t , d ( P 2 2 l & & & & & + ρ = π ρ = . (5)</formula>
<text><location><page_20><loc_15><loc_32><loc_85><loc_35></location>An idea of the pressure change is obtained from the solution to the Rayleigh-Plesset equation in the asymptotic limit [43]:</text>
<formula><location><page_20><loc_37><loc_27><loc_84><loc_31></location>2 / 1 l p 3 2 t ) t ( r ∆ ρ = ≡ t · v0(T) , (6)</formula>
<text><location><page_20><loc_15><loc_15><loc_85><loc_23></location>such that r & =v0 , r & & =0 and Eq. (5) becomes 3 0 l v d t 2 P ρ = . Figure 16 displays the calculated temperature variation of v0 for the liquids at 1 and 2 bar: note that all are continuously increasing, and similar to the experimental measurements in Fig. 15.</text>
<figure>
<location><page_21><loc_16><loc_72><loc_49><loc_92></location>
<caption>Fig. 16: variation of calculated v0 with temperature, for (a) 1 bar, and (b) 2 bar.</caption>
</figure>
<figure>
<location><page_21><loc_52><loc_70><loc_83><loc_91></location>
</figure>
<text><location><page_21><loc_15><loc_70><loc_36><loc_71></location>(a)</text>
<text><location><page_21><loc_15><loc_54><loc_85><loc_65></location>At 9'C and 2 bar, Fig. 16 gives v0 (C2ClF5) ~ 13 µm/µs. Transducers respond to P changes with sensitivities of µ V/ µ bar, with the sensitivity of the MCE-200 quoted at 7.9 mV/Pa at 1 kHz (-2dB) [44]: for C2ClF5, P ~ 6.2 x 10 2 µbar over the first 1 µ s at a distance of 10 cm, yielding signal A of ~ 1000 mV in reasonable agreement with those recorded experimentally for all liquids at all pressures.</text>
<section_header_level_1><location><page_21><loc_15><loc_49><loc_41><loc_50></location>3.3 Dark Matter Sensitivities</section_header_level_1>
<text><location><page_21><loc_15><loc_32><loc_85><loc_45></location>All direct dark matter search efforts are based on the detection of nuclear recoil events generated in WIMP-nucleus elastic scatterings. Neutrons also produce single recoil events via elastic scattering, generating a signal which is indistinguishable from that of WIMPs, and the response characterization of a detector to such recoils is generically obtained from neutron calibration measurements, either via weak neutron sources such as Am/Be or 252 Cf, or the use of accelerator or reactor facilities which provide monochromatic neutron beams.</text>
<text><location><page_21><loc_15><loc_15><loc_85><loc_29></location>The calculated variation in the minimum Ethr nr for both pressures for the various liquids of this study, using Λ = 4.3( ρ V/ ρ l) 1/3 , is shown in Fig. 17. Note the group separation which reflects the respective liquid densities: the higher density liquids must be operated at higher temperatures or lower pressures to achieve the same threshold as the lower density liquids; for example, C4F10 operated at 1 bar and ~ 42'C provides the same Ethr nr as C2ClF5 at 9'C or CCl2F2 at 29'C when operated at 2 bar.</text>
<figure>
<location><page_22><loc_29><loc_68><loc_71><loc_91></location>
<caption>Fig. 17: variation of Ethr nr for CCl2F2, C2ClF5, C4F10, C3F8 and C4F8 with temperature, at 1 (dashed) and 2 (solid) bar.</caption>
</figure>
<text><location><page_22><loc_15><loc_48><loc_85><loc_59></location>While C4F8 and C4F10 only provide recoil Ethr nr < 8 keV at temperatures > Tgel at either pressure, C3F8 permits a recoil Ethr nr ~ 2.4 keV at 15'C and 2 bar, and C2ClF5 a recoil Ethr nr ~ 5 keV at 12'C and 2 bar; operation at 12'C and 1 bar provides Ethr nr = 3 keV. Lower overpressuring of the SDDs generally provides lower Ethr nr , but operation at 2 bar is preferred as a radon suppression measure.</text>
<text><location><page_22><loc_15><loc_16><loc_85><loc_44></location>Apart from Ethr nr (T,P), the quality of any search effort depends on the detector's active mass, exposure and target sensitivity. The liquid solubility determines the amount of active target mass in the detector, as well as the fracture probability of the gel. Although fracturing occurs with or without bubble nucleation, since the liquid occupies any microscopic N2 gas pockets formed during the fractionating stage of the suspension fabrication, it is aggravated by nucleations arising from the ambient background radiations of the fabrication site. Table III displays the solubilities of the various liquids. As seen, the solubility of C4F8 is ~ half of C2ClF5, with C3F8 a factor 4 lower; C4F10 is the least soluble by a factor of ~ 10 relative to C2ClF5. Of all, CCl2F2 is the most soluble, hence may easily suffer from a reduced, timedependent active liquid concentration and lower triggering probability. These numbers however vary significantly between compilations, and must be measured for each liquid and suspension material prior use.</text>
<table>
<location><page_23><loc_14><loc_80><loc_66><loc_88></location>
<caption>Table III: liquid solubilities in water (in g/liter/bar) at 25'C, together with the active freon mass of each prototype detector in the reported measurements.</caption>
</table>
<text><location><page_23><loc_15><loc_54><loc_85><loc_75></location>Prior 2005, SIMPLE SDDs with C2ClF5 were usable for ~ 40 day as a result of signal avalanches resulting from fracture events [22], which the early fabrication chemistry did not address and the instrumentation was unable to discriminate. The lifetime has effectively increased to ~ 100 day, largely via instrumentation improvements which permit identification of fracture events, but also with improvements in the gel/detector fabrication to include the use of PVP and agarose, prohibition of storage below 0'C, and on-site detector fabrications in a quasi-clean room environment. Measurements conducted in 2006-2007 with a C2ClF5 SDD indicated an abrupt increase in the measured noise level only after 109 d of operation as a result of massive fracturing.</text>
<text><location><page_23><loc_15><loc_44><loc_85><loc_50></location>Apart from the liquid response, its dark matter search sensitivity depends on its constituent target A and spins. The WIMP-nucleus cross section σ A is to first order a sum of spinindependent (SI) and spin-dependent (SD) contributions, σ A = σ SI + σ SD, with</text>
<formula><location><page_23><loc_32><loc_38><loc_84><loc_41></location>( ) + + µ π = σ J 1 J S a S a G 32 2 n n p p 2 A 2 F SD , (7)</formula>
<formula><location><page_23><loc_32><loc_33><loc_84><loc_36></location>[ ] 2 n p 2 A 2 F SI N g Z g G 4 + µ π = σ , (8)</formula>
<text><location><page_23><loc_15><loc_11><loc_85><loc_29></location>with GF the Fermi constant, gp,n (ap,n) the SI (SD) WIMP couplings with the proton (neutron) respectively, µ A the WIMP-nuclide reduced mass, and J the total nuclear spin. With isospin conservation, gp = gn =1 and σ SI ~ A 2 : in comparison with the Xe-based experiments for example, the heavier target result is enhanced by a factor of (131/19) 2 = 48. Since fluorine possesses the largest <Sp> of all nuclides in common use (<Sp> = 0.475 [46]), superheated liquids have generally provided the most sensitive target for WIMP-proton SD studies, with less impact in the SI sector relative to their heavier counterparts owing to the A 2 enhancement of the WIMP-nucleus cross section.</text>
<text><location><page_24><loc_15><loc_76><loc_85><loc_92></location>As an example, consider C3F8 relative to the recent SIMPLE C2ClF5 result [3]: the effect of the larger fluorine component of C3F8 in the SD sector is shown in Fig. 18(a), assuming identical measurement results. As seen in Fig. 18(b) however, in the SI sector, the C3F8 impact is severely weakened, despite a molecular mass of 198 vs. the 154 of C2ClF5. A fictional 'C3ClF8' liquid yields a contour almost identical to C2ClF5, with the difference attributed to the Cl mass fraction of the molecule (0.17 for C3ClF8 vs. 0.24 for C2ClF5). Each exclusion calculation includes the C presence, suggesting its 'spectator' presence in the measurement.</text>
<figure>
<location><page_24><loc_17><loc_52><loc_46><loc_72></location>
</figure>
<figure>
<location><page_24><loc_49><loc_51><loc_82><loc_72></location>
<caption>Fig. 18: comparison of C3F8 sensitivities with C2ClF5 in both the spin-dependent (a) and spin-independent (b) sectors, for identical exposure and sensitivity.</caption>
</figure>
<text><location><page_24><loc_15><loc_26><loc_85><loc_44></location>Light nuclei liquids may still contribute to the SI sector because of the low recoil threshold energies possible with the technique, since the low Mw part of the exclusion contour tends to flatten with decreasing recoil Ethr [47] as seen in Fig. 19 for C4F10 with a 121 kgd exposure and no observed candidate events. Over an order of magnitude improvement in experimental sensitivity at low WIMP mass derives from a reduction in Ethr nr from 16 to 6 keV. This is also observed in Ref. [3], where SIMPLE at Ethr nr = 8 keV all but eliminates the CoGeNT result [48] at low Mw, while COUPP at Ethr nr = 15 keV - although more sensitive at higher Mw [2] -is unable to contribute.</text>
<figure>
<location><page_25><loc_34><loc_71><loc_65><loc_92></location>
<caption>Fig. 19: variation of the C4F10 exclusion contour in the SI sector with decrease in the measurement recoil Ethr nr as indicated for a 121 kgd exposure with no candidate events.</caption>
</figure>
<section_header_level_1><location><page_25><loc_15><loc_61><loc_37><loc_62></location>4. Particle Discrimination</section_header_level_1>
<text><location><page_25><loc_15><loc_38><loc_85><loc_57></location>Fundamentally, the ability of any detector to contribute to a dark matter search depends on its capability to discriminate between nuclear recoil and background α -induced signals, as demonstrated by all three superheated liquid programs on the basis of their respective signal A . In contrast to PICASSO and COUPP, in which the A obtain from integrations of the measured FFTs over a broad frequency range, the SIMPLE discrimination derives solely from the existence of a 30 mV gap between the recoil and α -induced event distributions of the primary harmonic of the FFTs, as seen in Fig. 20(a) [49]. This defines an empirical gap criterion of A α min > A nr max .</text>
<figure>
<location><page_25><loc_21><loc_13><loc_79><loc_34></location>
<caption>Fig. 20 : (a) initial neutron α discrimination as reported in Ref. [49];</caption>
</figure>
<text><location><page_25><loc_26><loc_9><loc_74><loc_10></location>(b) overlap of droplet size distribution with nuclear recoil events.</text>
<text><location><page_26><loc_15><loc_67><loc_85><loc_92></location>Although there is to date no complete understanding of this discrimination in any of the programs, the consensus is that its principle origin lies in the difference between the energy loss of the α and recoil interactions within the liquid, and inherent protobubble formation. In general, a recoil event is the result of a single neutron elastic scattering interaction anywhere in a droplet, in which the LET of the recoil ion exceeds the critical LET for bubble nucleation only within a micron of the scattering origin in the liquid as shown in Fig. 21(a): only O(1) protobubbles can be formed. The recoil event distribution mirrors the droplet size distribution, as indicated in Fig. 20(b) with the solid contour representing the normalized ln(r 6 ) distribution of Fig. 4 and a shift to match the means. From Eq. (4) with V= 3 4 π r 3 , and t0 a characteristic single protobubble nucleation time, A nr max ~ rmax 3 t0 -2 .</text>
<text><location><page_26><loc_15><loc_52><loc_85><loc_63></location>In contrast, the region of α LET > critical is generally distributed over several microns in the liquid, as seen in Fig. 21(b), so that an α event is capable of generating a number of protobubbles (npb); since each protobubble constitutes an evaporation center for the droplet, t α = t0 /npb and A α min ~ n 2 pb t0 -2 r 3 min -- n 2 pb constitutes an amplification factor for the α -generated amplitudes.</text>
<text><location><page_26><loc_15><loc_27><loc_85><loc_49></location>Thus the gap criterion reduces to n 2 pbr 3 min > r 3 max. Consider for example the energy loss of 5.5 MeV α 's in C2ClF5 at 9'C and 2 bar shown in Fig. 21(b): the critical LET (176 keV/ µ m) is only exceeded at penetration depths of 34-40 µ m, with an estimated npb ~ 12 per micron. Ignoring for the moment the PVP presence in the gel, the α 's originate from the droplet-gel interface [50], and droplets with r < 17 µ m cannot form a protobubble (providing an effective lower cutoff (rmin) to the observed A α spectrum [51,3]: with rmax = 60 µ m from Fig. 4, the gap criterion is satisfied, and particle discrimination may be anticipated. For E α = 8 MeV, the cutoff increases to rmin ~ 33 µ m since the Bragg peak is translated to larger penetration depths, and the criterion is easily satisfied.</text>
<figure>
<location><page_27><loc_17><loc_71><loc_48><loc_91></location>
</figure>
<figure>
<location><page_27><loc_51><loc_71><loc_83><loc_91></location>
<caption>Fig. 21: (a) LET of recoil F ions in C2ClF5 as a function of penetration depth; (b) comparison of the energy loss depth profiles for 5.5 and 8.0 MeV α 's in C2ClF5 and C4F10, at 2 bar and representative low Ethr temperatures.</caption>
</figure>
<text><location><page_27><loc_15><loc_43><loc_85><loc_60></location>The situation differs in the case of C4F10, since the critical LET at 2 bar and 50'C is only 103 keV/ µ m, which as seen in Fig. 21(b) is exceeded by 5.5 MeV α penetrations between 9-41 µ m. This suggests rmin ~ 5 µ m: with npb ~ 12 per micron, A α min < A nr max , and A α ' s should be mixed with A nr, as in fact observed in the measurements herein which yielded 3 events with A α < 100. While this is not the case for E α = 8.0 MeV (where rmin ~ 21 µ m), in order to achieve full exclusion of the U/Th contaminant α -contributions in a dark matter search, the C4F10 droplet size distribution would likely need to be reduced to <r> ~ 5 µ m.</text>
<text><location><page_27><loc_15><loc_33><loc_85><loc_39></location>The situation differs at 1 bar operation, where the critical LET for C2ClF5 and C4F10 are 123 keV/ µ m and 70 keV/ µ m, respectively. In this case, for C2ClF5 , rmin ~ 11 µ m and the gap criterion is unsatisfied, as also for C4F10 with rmin ~ 0.</text>
<text><location><page_27><loc_15><loc_11><loc_85><loc_29></location>We stress that the critical LET is dependent on Λ , which is not well-known in the case of C4F10 or most other liquids of this study, as well as the estimate of npb which varies for each liquid, and that the above illustration neglects entirely non-interface α origins (although the particle LETs in gel are insignificantly different from the liquids). The PICASSO-determined Λ = 3.8 for C4F10 at 1 bar and 24'C [52] is however higher than the 4.3( ρ V/ ρ l) 1/3 estimate of 1.13, and would lower the critical LET, worsening the situation. Although the PVP presence in the gel fabrication acts in part to suppress heavy ion migration to the droplet-gel interface, the efficiency is evidently < 100%. Further study is required to provide a complete description</text>
<text><location><page_28><loc_15><loc_88><loc_85><loc_92></location>of the gap formation, and the particle discrimination capacity of each SDD must therefore be determined both experimentally and individually.</text>
<section_header_level_1><location><page_28><loc_15><loc_84><loc_39><loc_85></location>5 . Heavier Nuclei Liquids</section_header_level_1>
<text><location><page_28><loc_15><loc_54><loc_85><loc_80></location>Given the above, one might immediately question whether SDDs using fluorine-based liquids with heavier A nuclei in detector fabrications are possible, towards maximizing a single experiment sensitivity in both SD and SI sectors. The question is not new, being in part responsible for the use of CF3I by COUPP. Because of its place in the periodic table, fluorine combines well with a variety of heavier halogens, offering a large number of possibilities which would provide the desired A 2 enhancement in the SI sector, to include I (IF, IF3, IF5, IF7), Xe (XeF2, XeF4, XeF6), Te (TeF5), Ta (TaF5), W (WF6), Re (ReF6) and a variety of fluorocarbons (CF3I, CBrF3, CBrClF2,…) - in most cases, with the heavier nuclei constituents possessing sufficient <Sp,n> [53-55] for significantly contributing in the SD sector as well; in the cases of Xe, Te, and W, the predominant contribution would be in <Sn>, simultaneously with the <Sp> of fluorine.</text>
<text><location><page_28><loc_15><loc_35><loc_85><loc_51></location>The immediate considerations to be addressed are: (1) fabrication feasibility of a quality SDD, and (2) dark matter search sensitivity. An immediate caveat, following from the light liquids, is that the higher the density, the generally higher are the recoil thresholds and solubilities (e.g. those of IF5 and IF7 , 0.8 g/liter and 0.5 g/liter respectively, are significantly higher than C2ClF5). A cursory overview of the possible candidates moreover indicates that none of the Xe compounds are liquids at temperatures usable with SIMPLE gels; XeF6 is liquid in the window of 49-76'C [56] and hydrolytic; UF6 reacts with water, and ClF5 is corrosive;</text>
<text><location><page_28><loc_15><loc_20><loc_85><loc_31></location>Generally, however, little is known regarding the liquid phase of such possibilities, in particular the thermophysical properties necessary to calculation of their respective Ec. Before embarking on an investigation of the properties, which would in most cases require dedicated measurements, it's useful to consider some screening of possible choices as regards their dark matter search suitability using the lessons obtained with the light nuclei liquids above.</text>
<section_header_level_1><location><page_29><loc_15><loc_91><loc_34><loc_92></location>5.1 Liquid Selection</section_header_level_1>
<text><location><page_29><loc_15><loc_76><loc_85><loc_87></location>As seen from Fig. 17 and the definition of S, a figure of merit for the recoil threshold energies can be defined by FM = T (S = 0.7), the temperature at which the liquid S = 0.7: the lower the FM, the lower the recoil threshold. We show in Table IV a small compendium of FMs for a number of heavy liquids possibilities, together with known thermophysical data and following the discussion of Sec. 3.3 - the heavy nuclei mass fractions (see Sec. 4).</text>
<table>
<location><page_29><loc_14><loc_35><loc_73><loc_71></location>
<caption>Table IV: FM's of various possible heavy target nuclei.</caption>
</table>
<text><location><page_29><loc_15><loc_19><loc_85><loc_32></location>Clearly, SF6, CBrF3, TeF6, CF3I, ClF5 and CBrClF2 (in descending order) provide the lowest threshold, whereas UF6, CF3I, PtF6, WF6 or ReF6, and CBrF3 provide the larger mass fractions, with intersections occurring for CBrF3 and CF3I. For SIMPLE gels however, SF6 and CBrF3 at 20°C are both S > 0.7 hence sensitive to complications from spontaneous nucleations and low LET irradiations; TeF6, with melting point -38.9'C and boiling at 37.6'C, is a liquid only in a 1'C window, hence not useful: only CF3I is S < 0.7.</text>
<text><location><page_29><loc_15><loc_9><loc_85><loc_15></location>We examine more closely the cases of CBrF3, CBrClF2 and CF3I for which complete thermophysical properties are known and Ec can be calculated. The corresponding recoil thresholds of each are shown in Fig. 22, calculated as in Fig. 17. As evident, the results</text>
<text><location><page_30><loc_15><loc_86><loc_85><loc_92></location>confirm the FMs of Table IV. With CBrF3, an Ethr nr ~ 1 keV can be achieved at 3'C and 2 bar (S ~ 0.57); CBrClF2 , an Ethr nr ~ 1 keV at 2 bar and 75'C (S ~ 0.7). In contrast, CF3I is only able to provide an Ethr nr ~ 10 keV at 25'C (near Tgel) and 2 bar (S ~ 0.32).</text>
<figure>
<location><page_30><loc_16><loc_63><loc_47><loc_82></location>
<caption>Fig. 22: recoil threshold curves for (a) CBrF3, (b) CBrClF2, and (c) CF3I with temperature.</caption>
</figure>
<figure>
<location><page_30><loc_51><loc_64><loc_83><loc_82></location>
</figure>
<text><location><page_30><loc_37><loc_61><loc_64><loc_62></location>(a) (b)</text>
<figure>
<location><page_30><loc_35><loc_40><loc_64><loc_59></location>
</figure>
<text><location><page_30><loc_37><loc_37><loc_53><loc_38></location>(c)</text>
<section_header_level_1><location><page_30><loc_15><loc_30><loc_39><loc_31></location>5.2 Detector Fabrications</section_header_level_1>
<text><location><page_30><loc_15><loc_27><loc_75><loc_28></location>The variation of the three liquid densities with temperature are shown in Fig. 23.</text>
<figure>
<location><page_31><loc_31><loc_71><loc_68><loc_91></location>
<caption>Fig. 23: temperature variation of densities of CBrF3, CBrClF2,</caption>
</figure>
<paragraph><location><page_31><loc_40><loc_66><loc_61><loc_67></location>and CF3I relative to C2ClF5.</paragraph>
<text><location><page_31><loc_15><loc_55><loc_85><loc_63></location>As evident from Fig. 23, the significantly higher-density heavy liquid SDD fabrications must generally proceed on the basis of a serious viscosity-matching of the liquid with the gel. An estimate of the minimum viscosity ( φ ) required to trap the droplets during the fabrication process is given by [64]</text>
<formula><location><page_31><loc_43><loc_48><loc_85><loc_51></location>D 9 gt r 2 g l 2 ρ -ρ = ϕ , (9)</formula>
<text><location><page_31><loc_15><loc_36><loc_85><loc_45></location>where r is the average droplet radius, D is the height of the gel, t is the time for a droplet to fall a distance D, and ρ l ( ρ g) is the liquid (gel) density. In the case of CF3I, for t = 1 hour (the time required for the setting of the gel during cooling), ρ l ( ρ g) = 2 x 10 3 kg/m 3 (1.3 x 10 3 kg/m 3 ), r = 35 x 10 -6 m, D = 5 x 10 -2 m, and φ = 0.13 kg/m/s.</text>
<text><location><page_31><loc_15><loc_9><loc_85><loc_33></location>The gel itself is formed as previously by combining powdered gelatin and bi-distilled water with slow agitation to homogenize the solution; separately, PVP is added to bi-distilled water, and agitated at 60'C. Pre-eluted ion-exchange resins for actinide removal are added to both, removed by filtering after blending in a detector bottle by agitation. The viscosity variations are effected with a 0.44 wt% agarose addition, effected by combining the additive (Sigma Aldrich A0576) with glycerin at 90'C to break the agarose chains, and its addition to the concentrated gel mix prior its filtration. Following outgassing and foam aspiration, the solution is left overnight at 42'C with slow agitation to prevent air bubble formation. The final gel matrix recipe, which produced a uniform and homogeneous distribution of droplets, had a measured φ = 0.17 kg/m/s, as well as an increased temperature at which the transition from</text>
<text><location><page_32><loc_15><loc_86><loc_85><loc_92></location>solution to gel (sol-gel transition) occurs. CBrF3 ( ρ ~ 1.5 g/cm 3 ) and CBrClF2 ( ρ ~ 1.8 g/cm 3 ) would also require the same fabrication technique, with the advantage of a somewhat smaller agarose addition.</text>
<text><location><page_32><loc_15><loc_71><loc_85><loc_82></location>SDD fabrication occurs via the same phase diagram of Fig. 2, adjusted for the pressure and temperature of the liquid. The detector bottle is removed to a hotplate within a hyperbaric chamber, and the pressure raised to just beyond the vapor pressure at 42'C. After thermalization, the agitation is stopped and the CF3I storage bottle opened to admit the liquid through the same condensing-distillation line with a 0.2 µm filter used previously.</text>
<text><location><page_32><loc_15><loc_37><loc_85><loc_68></location>Once the CF3I is injected, the pressure is quickly raised to 15 bar to prevent the droplets from rising to the surface, and a rapid agitation initiated to shear big droplets; simultaneously, the temperature was raised to 50'C to create a temperature gradient inside the matrix and permit dispersion of the droplets. After 20 minutes, the temperature is slightly reduced for 1 hr (with pressure and agitation unchanged). The CF3I, in liquid state, is divided into smaller droplets by the continued agitation. Finally, the heating is stopped: the temperature decreases until the sol-gel transition is crossed, during which the stirring is reduced and finally stopped. The droplet suspension is quickly cooled to 10'C and left to set for 40 minutes, then cooled to 5'C where it is maintained for ~ 15 hours. The pressure is then slowly reduced to atmospheric pressure, and the detector removed to cold storage: a fabrication example is shown in Fig. 24.. The process results in approximately uniform and homogeneous (40 ± 15 µm diameter) droplet distributions, as determined by optical microscopy. Longer fractionating times give narrower distributions of smaller diameters; shorter, broader distributions of larger diameters.</text>
<figure>
<location><page_32><loc_40><loc_14><loc_60><loc_34></location>
<caption>Fig. 24 : Completed CF3I detector prototype.</caption>
</figure>
<section_header_level_1><location><page_33><loc_15><loc_91><loc_39><loc_92></location>5,3 Solubility and Lifetime</section_header_level_1>
<text><location><page_33><loc_15><loc_79><loc_85><loc_87></location>As stated above, higher density liquids are generally characterized by higher solubilities, which determines the amount of active target mass in the detector, as well as the fracture probability of the gel. Table V indicates the solubilities of the three liquids, all of which are larger than that of CCl2F2 by a factor of 5-10.</text>
<table>
<location><page_33><loc_14><loc_63><loc_46><loc_73></location>
<caption>Table V: solubilities of CBrF3, CBrClF2 and CF3I.</caption>
</table>
<text><location><page_33><loc_15><loc_39><loc_85><loc_58></location>Unlike previous detectors made with C2ClF5, the CF3I prototypes began to significantly fracture within several hours of fabrication. The fracturing is inhibited by overpressuring the devices, but not eliminated. Tests with a SDD made by dissolving the liquid inside the gel produced cracks within 24 hrs, indicating the fracturing to occur because of a high solubility of CF3I gas inside the gel. Although this phenomenon occurs with or without bubble nucleation, because the CF3I gas inside the gel occupies any microscopic N2 gas pockets formed during the fractionating stage of the suspension fabrication, it is aggravated by nucleations arising from the ambient background radiations.</text>
<text><location><page_33><loc_15><loc_17><loc_85><loc_36></location>Despite the initial fracturing, the CF3I prototype remained active for almost a year after removal to an underground 'cool' storage at 16'C at 2 bar, with little growth of the fractures observed in the measurement [64]. Nevertheless, the problem of fracturing requires an improved understanding of the involved chemistry and development of new techniques, to include the possible use of gelifying agents not requiring water as a solvent or the use of ingredients to inhibit the diffusion of the dissolved gas, which in turn suggests a possible shift to organic gels if the radio-purity of the current gel fabrications can be maintained or improved.</text>
<section_header_level_1><location><page_34><loc_15><loc_91><loc_40><loc_92></location>5.4 Particle Discrimination</section_header_level_1>
<text><location><page_34><loc_15><loc_78><loc_85><loc_87></location>Similar tests made of the CF3I prototype [64] at 35'C and 1 bar with the instrumentation of the present light experiments under similar experimental conditions yielded signal events with F = 520-32 Hz, τ = 7.8-21 ms and A = 160-500 mV, consistent with the light nuclei SDD signals of α origin in Sec. 3.</text>
<text><location><page_34><loc_15><loc_54><loc_85><loc_75></location>Irradiations of the small volume device prototypes by 60 Co verified the device insensitivity to γ 's below Tgel , consistent with the general response of SDDs. Irradiations with a filtered neutron beam demonstrated sensitivity to reactor neutron irradiations via the induced recoils of fluorine, carbon and iodine. Fig. 25 displays the results of a 144 keV neutron irradiation of a device at 1 bar, with the rapid rate increase beginning ~ 40'C consistent with the iodine sensitivity onset observed in the temperature variation of the threshold incident neutron energies. The expected signal from fluorine and carbon at 20'C is masked by the iodine response to a broad, higher energy neutron component of the filtered beam, as identified in Ref. [45].</text>
<figure>
<location><page_34><loc_32><loc_32><loc_67><loc_51></location>
<caption>Fig. 25 : 144 keV filtered neutron beam irradiation of a CF3I prototype; the line represents an exponential fit to the data.</caption>
</figure>
<section_header_level_1><location><page_34><loc_15><loc_19><loc_39><loc_21></location>5.5 Particle Discrimination</section_header_level_1>
<text><location><page_34><loc_15><loc_10><loc_85><loc_16></location>With respect to the discussion of particle discrimination in Sec. 4, the critical LET = 76 keV/ µ m for CF3I at 50'C and 2 bar: as seen in Fig. 26, although the 5.5 MeV α Bragg peak is shifted to a larger depth, the protobubble production capability ranges 0-47 µ m: there is no</text>
<text><location><page_35><loc_15><loc_80><loc_85><loc_92></location>evident rmin in the droplet size, the gap criterion cannot be satisfied, and the resulting A will likely overlap -- as in fact observed in these measurements which yielded 4 events with A α < 100. For E α = 8.0 MeV, a rmin ~ 14 µ m exists, but remains unlikely to provide the gap. At 1 bar operation, the critical LET = 63 keV/ µ m, there is again no rmin and no simple discrimination seems possible.</text>
<figure>
<location><page_35><loc_29><loc_52><loc_71><loc_76></location>
<caption>Fig. 26: comparison of the energy loss depth profiles for 5.5 and 8.0 MeV α 's in CF3I and C2ClF5 at 2 bar and representative low Ethr temperatures.</caption>
</figure>
<text><location><page_35><loc_15><loc_32><loc_85><loc_43></location>Thus it would appear that in dark matter search applications, a SIMPLE CF3I device would be unable to provide a complete particle discrimination for the U/Th α 's without resorting to FFT integrations as employed by COUPP. Again however, as with C4F10 we stress that the critical LET is dependent on Λ which is also not well-known for these heavier liquids; for CF3I however, use of Λ = 4 as in Ref. [2] would lower the critical LET, exacerbating the situation.</text>
<section_header_level_1><location><page_35><loc_15><loc_28><loc_31><loc_30></location>6. Conclusions</section_header_level_1>
<text><location><page_35><loc_15><loc_9><loc_85><loc_25></location>SDDs with the light and heavy nuclei liquids in this study can be fabricated with the SIMPLE food-based gel, via either density- or viscosity-matching using appropriate protocols and gel chemistry to provide a homogeneous, reproducible, well-defined distribution of droplet sizes. The result is detectors with approximately the same response capability - although the operational temperatures and pressures to achieve a given Ethr nr are necessarily different, and constrained by the proximity of the SDD operating conditions to the melting point of the gel as well as the liquid solubility.</text>
<text><location><page_36><loc_15><loc_84><loc_85><loc_92></location>In contrast to PICASSO and COUPP, the characteristics of all particle-generated events of the various SDDs lie within the ranges previously defined for the C2ClF5 device with α -generated events, which we suspicion is attributable in part to the gel presence/nature -- but further study is required to confirm.</text>
<text><location><page_36><loc_15><loc_57><loc_85><loc_80></location>The signal response of the SDD in the case of particle-induced events is largely dependent on the droplet size distribution, which depends on the fractionating speed and time, and can be varied to yield differing distributions. For dark matter searches, discrimination between α and nuclear recoil events appears to depend on the relation between the droplet size distribution (which determines the recoil event spectrum), the background α Bragg peak in the liquid and its component ≥ critical LET, with the indication that neither C4F10 or CF3I in a SIMPLE configuration is able to provide a clear particle discrimination. Given however the lack of a complete understanding of the observed gap formation and liquid Λ , further research is required and the particle discrimination capacity of each SDD must at present be determined experimentally.</text>
<text><location><page_36><loc_15><loc_30><loc_85><loc_53></location>Thus said, the choice of SDD liquid remains fundamentally dependent on the required operating conditions to achieve both low Ethr nr and particle discrimination. Of the light nuclei liquids, PICASSO, using C4F10 operated at 50-60'C and 1 bar, obtains a Ethr nr ~ 1.7 keV for neutron-generated recoils, but without well-defined particle-discrimination. SIMPLE, using C2ClF5 with its food gel, runs at 9'C and 2 bar for a recoil Ethr nr = 8 keV, with an operating range generally limited to < 15'C because of the onset of Cl sensitivity to γ 's; for Ethr nr ≤ 8 keV, neither C4F8 or C4F10 seems usable in a SIMPLE device for WIMP search applications, given their Ethr nr at Tgel. Use of a different gel (as in early PICASSO) is possible, but the questions of increased backgrounds and particle discrimination would need to be addressed (possibly, using the PICASSO and COUPP analyses techniques).</text>
<text><location><page_36><loc_15><loc_10><loc_85><loc_27></location>The light nuclei devices described here, while suffering from the A 2 enhancement of the heavy liquids in the SI sector, are still capable of contributing to this sector if they can be operated at temperatures and pressures corresponding to Ethr nr ~ 2 keV, as in the recent case of PICASSO, owing to the flattening of the exclusion curves with decreasing Ethr nr . The liquid selection for SIMPLE devices is however constrained by its gel nature to C2ClF5, C3F8 and CBrF3 because - all else being equal - of their ability to achieve Ethr nr < 4 keV at temperatures < Tgel. Of these, C3F8 provides the lowest Ethr nr : a simultaneous measurement with separate SDDs of</text>
<text><location><page_37><loc_15><loc_88><loc_85><loc_92></location>C3F8 and CF3Br, operated at 15'C and 1 bar, could theoretically provide Ethr nr ~ 3 keV in both cases.</text>
<text><location><page_37><loc_15><loc_64><loc_85><loc_85></location>Numerous heavier target liquid possibilities exist which would provide, assuming SDD fabrication feasibility based on viscosity-matching or development of more temperatureresilient gels such as PICASSO's earlier polyacrylamide, an increased sensitivity in the SI sector as well as both sectors of the SD studies. Introduction of FM = T (S = 0.7) permits a pre-selection among the possibilities in terms of dark matter search suitability. Further investigations of their liquid phase parameters (as well as commercial availability, price and environmental impact) is however required before decisions can be taken in their regard, as also the development of new gels capable of supporting the thermodynamic conditions necessary to a low Ethr nr operation and particle discrimination.</text>
<section_header_level_1><location><page_37><loc_42><loc_59><loc_58><loc_60></location>Acknowledgements</section_header_level_1>
<text><location><page_37><loc_15><loc_43><loc_85><loc_56></location>We thank A.R. Costa for assistance in the production of the SDDs, and M. Silva for the construction of the hermetic device caps. The activity of M. Felizardo was supported by grant SFRH/BD/46545/2008 of the Portuguese Foundation for Science and Technology (FCT). The activity was supported in part by POCI grant FP/63407/2005 of FCT, co-financed by FEDER, by FCT POCTI grant FIS/55930/2004, and by FCT PTDC grants FIS/115733/2009 and FIS/121130/2010.</text>
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</document>
[
{
"title": "Fabrication and Response of High Concentration SIMPLE Superheated Droplet Detectors with Different Liquids",
"content": "M. Felizardo 1,2 , T. Morlat 3 , J.G. Marques 4,2 , A.R. Ramos 4,2 , TA Girard 2,† , A. C. Fernandes 4,2 , A. Kling 4,2 , I. LÆzaro 2 , R.C. Martins 5 , J. Puibasset 6 ( for the SIMPLE Collaboration ) 1 Department of Physics, Universidade Nova de Lisboa, 2829-516 Monte da Caparica, Portugal 2 Centro de Física Nuclear, Universidade de Lisboa, 1649-003 Lisbon, Portugal 3 Ecole Normale Superieur de Montrouge, 1 Rue Aurice Arnoux, 92120 Montrouge, France 4 Instituto Tecnológico e Nuclear, IST, Universidade TØcnica de Lisboa, EN 10, 2686-953 SacavØm, Portugal 5 Instituto de Telecomunicaçıes, IST, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal 6 CRMD-CNRS and UniversitØ d'OrlØans, 1 bis Rue de la FØrollerie, 45071 OrlØans, France Key words: dark matter; detectors; superheated liquids",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "The combined measurement of dark matter interactions with different superheated liquids has recently been suggested as a cross-correlation technique in identifying WIMP candidates. We describe the fabrication of high concentration superheated droplet detectors based on the light nuclei liquids C3F8, C4F8, C4F10 and CCl2F2, and investigation of their irradiation response with respect to C2ClF5. The results are discussed in terms of the basic physics of superheated liquid response to particle interactions, as well as the necessary detector qualifications for application in dark matter search investigations. The possibility of heavier nuclei SDDs is explored using the light nuclei results as a basis, with CF3I provided as an example.",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The direct search for weakly interacting massive particle (WIMP) dark matter is generally based on one of five techniques: scintillators, semiconductors, cryogenic bolometers, noble liquids and superheated liquids. The last, in contrast to the others, relies on the stimulated transition of a metastable liquid to its gas phase by particle interaction: because the transition criteria are thermodynamic, the devices can be operated at temperatures and/or pressures at which they are generally sensitive to only fast neutrons, α 's and other high linear energy transfer (LET) irradiations. Only three WIMP search efforts employ the superheated liquid technique: PICASSO [1], COUPP [2] and SIMPLE [3], using C4F10, CF3I and C2ClF5 respectively. Of the three, COUPP is based on bubble chamber technology: only PICASSO and SIMPLE employ superheated droplet detectors (SDDs). Because of their fluorine content and fluorine's high proton spin sensitivity, as well as their otherwise light nuclei content relative to Ge, I, Xe, W and others, they have generally contributed most to the search for spin-dependent WIMP-proton interactions. COUPP, with CF3I, has also made a significant impact in the spin-independent sector. A SDD consists of a uniform dispersion of micrometric-sized superheated liquid droplets homogeneously suspended in a hydrogenated, viscoelastic gel matrix. The phase transition generates a millimetric-sized gas bubble which can be recorded by either optical, acoustic or chemical means; both SDD experiments employ acoustic, while COUPP employs both acoustic and optical (the liquid is essentially transparent, whereas the gel matrix of the SDDs is at best translucent). The significant difference between the two approaches is that SDDs are continuously sensitive for extended periods since the overall liquid droplet population is maintained in steady-state superheated conditions despite bubble nucleation of some droplets, whereas in the bubble chamber the bulk liquid is only sensitized between nucleation events, each of which precipitates the transition of the liquid volume hence requires recompression to re-establish the metastable state and leads to measurement deadtime. The advantage of the chamber approach is an ability to instrument large active target masses. SDDs have generally been confined to low concentration (< 1 wt% : liquid-to-colloid mass ratio) devices, for use in neutron [4-11], and heavy ion [12] detector applications, with impact in heavy ion and cosmic ray physics, exotic particle detection and imaging in cancer therapy [13,14]. For rare event applications such as a WIMP search, however, higher concentration detectors are required: the PICASSO devices are ~ 1 wt% concentrations. SIMPLE detectors in contrast are generally of 1-2 wt%; concentrations above 2 wt%, in which the droplets are sufficiently close in proximity, tend to self-destruct as a result of massive sympathetic bubble nucleation and induced fractures. Recently, variation of the target liquids with different sensitivities to the possible scalar and axial vector components of a WIMP interaction has been suggested as a technique in identifying WIMP candidates [15], specifically in the case of COUPP in combined measurements using CF3I and C4F10. This measurement variation while maintaining equivalent sensitivities in the case of SDDs is not trivial, since device fabrication and operation depends on the individual thermodynamic characteristics of each liquid. SIMPLE SDD fabrications generally proceed on the basis of density-matching the liquid with a 1.3 g/cm 3 food-based gel with low U/Th contamination: a significant difference in gel and liquid densities (as occurs with heavier nuclei liquids) results in inhomogeneous distributions of differential droplet sizes within the detector. Although this has been addressed by SIMPLE via viscosity-matching the gel [16,17], this approach is constrained by the SIMPLE gel melting at 35'C, limiting the temperature range of the device and hence restricting the liquids employed. The traditional addition of heavy salts such as CsCl to raise the gel density, as originally used by PICASSO with its polyacrylamide-based gels [18], is discouraged since this generally adds radioactive contaminants which must be later removed chemically with the highest efficiency possible. Thus, the question of liquid variation in SDDs naturally raises the questions of whether or not such 'other' SDDs can in fact be fabricated, much less operated, and with what sensitivity. We here describe our fabrications and testing of small volume (150 ml), high concentration (1-2 wt%) SDD prototypes with C3F8, C4F8, C4F10, CCl2F2 and CF3I including for completeness a 'standard' C2ClF5 device of the SIMPLE dark matter search effort [3]. Section 2 provides an overview of the device fabrication, and describes the experimental testing of the products. The response of superheated liquids to irradiations in general, and liquid characteristics necessary to dark matter searches is discussed in Sec. 3, and applied to the fabricated SDD test results, with the salient aspects of particle discrimination as observed by SIMPLE identified in Sec. 4. Section 5 discusses the considerations necessary to the fabrication and implementation of heavier nuclei SDDs, to include the introduction of a figure of merit based on the light nuclei results by which an initial screening of possibilities can be made in the absence of a complete thermophysical description of the liquids: The fabrication and analysis of a CF3I is described as an example. Conclusions are formed in Sec. 6.",
"pages": [
1,
2,
3
]
},
{
"title": "2. Light Nuclei Detectors",
"content": "For light liquids, SDD construction generally consists of two parts: the gel, and the liquid droplet suspension. The variation of the liquid densities with temperature is shown in Fig. 1, and can be divided into three basic density groups: For those in groups (i) and (ii) with ρ ~ 1.3 g/cm 3 , small variations in the current C2ClF5 recipes are indicated; for the more dense liquids of group (iii), viscosity matching is necessary using an additive as discussed in detail in [16,17].",
"pages": [
4
]
},
{
"title": "2.1 Gel Fabrications",
"content": "The basic SDD ingredients have been described previously [20]. In the density-matched, 'standard' case of C2ClF5, the gel composition is 1.71 wt% gelatin, 4.18 wt% polyvinylpyrrolidone (PVP), 15.48 wt% bi-distilled water and 78.16 wt% glycerin. The gelatin is selected on the basis of its organ origins to minimize the U/Th impurity content; the glycerin serves to enhance the viscosity and strength of the gel, and wet the container surfaces. The presence of the PVP (i) assists in fracture control by viscosity enhancement which decreases diffusion, (ii) improves the SDD homogeneity and reduces the droplet sizes via its surfactant behavior, (iii) decreases the liquid solubility [21], (iv) inhibits clathrate hydrate formation, and (v) reduces the migration of α -emitters to droplet boundaries as a result of actinide complex ion polarity [22]. The basic process, minus several proprietary aspects, has been described in [20]. The ingredients are first formed: powdered gelatin (Sigma Aldrich G-1890 Type A), bi-distilled water and pre-eluted ion exchange resins for actinide removal are combined and left for 12-15 hrs at 45'C with slow agitation to homogenize the solution. Separately, PVP (Sigma Aldrich PVP-40T) and exchange resins are added to bi-distilled water, and stirred at ~65'C for 12-15 hrs. Resins and glycerin (Riedel-de-Haºn N' 33224) are combined separately, and left in medium stirring at ~50'C for 12-15 hrs. The PVP solution is then slowly added to the gel solution ('concentrated gel'), and slowly agitated at 55-60'C for 2 hrs. The resins in all are next removed separately by filtering (Whatman 6725-5002A). The glycerin and concentrated gel are then combined at ~60'C, outgassed at ~ 70'C, and foam aspirated to eliminate trapped air bubbles. The solution is left at 48'C for 14 hrs with slow agitation to prevent bubble formation. For the viscosity-matched protocol required for the C4F8 and C4F10, the gel composition is essentially the same as in the density-matched recipe, with a small agarose (Sigma Aldrich A0576) addition effected by combining it with glycerin at 90'C, then adding it to the concentrated gel mix prior its filtration. Following resin purification, the gel yields measured U/Th contamination levels of < 8.7 mBq/kg 238 U, < 4.9 mBq/kg 235 U and < 6.9 mBq/kg 234 U.",
"pages": [
4,
5
]
},
{
"title": "2.2 Droplet Suspension Fabrications",
"content": "The specific protocol for fabrication of a liquid droplet suspension depends on the thermodynamic properties of the liquid. The process with C2ClF5 is schematically shown in Fig. 2; the temperatures and pressures differ for each liquid. Following transfer of the gel to the detector bottle, the bottle is first weighed and then removed to a container encased by a copper serpentine for cooling, positioned on a hotplate within a hyperbaric chamber. Once stabilized at 35'C, the pressure is quickly raised to just above the vapor pressure (~11 bar) of the liquid with continued slow agitation. After thermalization, the agitation is stopped and the liquid injected into the gel through a flowline immersed in ice to simultaneously condense and distill it, and a 0.2 µm microsyringe filter (Gelman Acrodisc CR PTFE 4552T). Once injected, the pressure is quickly raised to 21 bar to prevent the liquid droplets from rising to the surface, and a rapid agitation simultaneously initiated to shear big droplets; simultaneously, the temperature is raised to 39'C to create a temperature gradient inside the matrix and to permit dispersion of the droplets. After 15 minutes, the temperature is reduced to 37'C for 30 min, then reduced to 35'C for 4 hrs with pressure and agitation unchanged, to fractionate the liquid into smaller droplets. Finally, the heating is stopped: the temperature decreases until the sol-gel transition is crossed, during which the agitation is maintained. Approximately 2 hrs later, the droplet suspension is quickly cooled to 15 o C with the serpentine, and left to set for 40 minutes with decreased agitation; the agitation is then stopped, and the pressure slowly reduced over 10 min to 11 bar, where it is maintained for ~ 15 hours with the temperature set to the selected measurement run temperature for the liquid. Thereafter, the chamber pressure is slowly reduced to atmospheric, and the detector removed, weighed, and placed into either 'cool' storage or utilization: high temperature implies an increased nucleation sensitivity, 'cold' (< 0'C) storage results in the formation of clathrate hydrates, which provoke spontaneous nucleation locally on the droplet surfaces in warming to room temperature, effectively destroying the device. Examples of the various completed fabrications are shown in Fig. 3. The agitation process fractionates the liquid droplets, resulting in a homogeneously-dispersed droplet size distribution: longer fractionating times generally give smaller diameter distributions; shorter times, larger distributions. The protocol is specific to the liquid, both in terms of time and speed. This is illustrated in Fig. 4, which presents fits of measured frequency distributions of droplet sizes in 5 µ m intervals, obtained by optical microscopy from batch samples, for each of the SDDs with variations in their fractionating time and speed during their protocol development.",
"pages": [
5,
6,
7
]
},
{
"title": "2.3 Irradiation Tests",
"content": "The laboratory 'standard test' detector, a small version of the SIMPLE dark matter SDD fabricated with a scaled-down 'standard' recipe protocol described above, contained ~ 2.7 g of C2ClF5 suspended in a gel matrix within a 150 ml laboratory bottle (Schott Duran GL45). Similar SDDs were fabricated using the above 'density-matched' protocol with CCl2F2 (2.5g), C3F8 (3.1g), and the 'viscosity-matched' protocol with C4F10 (2.6g) and C4F8 (2.8g). None of the device gels were resin-purified in order to profit from the α decay of the intrinsic U/Th impurities. The fractionating time of each was adjusted to provide approximately identical, normally-distributed droplet sizes of = 30 µm. = 30 µm. Once formed, each SDD was instrumented with the same capping used in the search experiments, a hermetic construction containing feedthroughs for a pressure line and a high quality electret microphone cartridge (Panasonic MCE-200) with a frequency range of 0.02016 kHz (3 dB), SNR of 58 dB and a sensitivity of 7.9 mV/Pa at 1 kHz. The microphone, sheathed in a protective latex covering, was positioned inside the detector bottle within a 6 cm thick glycerin layer above the droplet emulsion, as shown in an empty device containment of Fig. 5: the microphone is seen below the cap, with the electronics cable interface vertical; the horizontal couple permits over-pressuring of the device up to 4 bar (the limit of the detector glass) , and is coupled to a pressure transducer (PTI-S-AG4-15-AQ) for readout. The microphone signal is remotely processed by a low noise, high-flexibility, digitallycontrolled microphone preamplifier (Texas Instruments PGA2500), which is coupled to the archiving PC via an I/O board (National Instruments PCI-6251). Once fabricated, each detector was placed in the same temperature-controlled water bath situated inside an acoustic foam cage designed for environmental noise reduction, despite the capability of the microphone-based instrumentation to distinguish between the various noise events [23]. Measurements were performed in steps of 5'C over the temperature range of 5 35'C. The temperature was measured with a type K thermocouple (RS Amidata 219-4450): each change was stabilized over ~ 20 minutes. Data was acquired in Matlab files of ~ 10 MB each at a constant rate of 32 kSps for periods of 5 minutes each. Nucleation events were generally stimulated by low level α radiation from the gel/glass U/Th impurities in order to provide time-separated events. The results were subjected to a full, standard signal analyses [23]. The resulting acoustic background events were identified as normally-occurring gel fractures, trapped gas in the gel, and environmental noise intrinsic to SDD operation. The noise levels were ~ 2 mV among all devices at all temperatures, except near 35'C where the level was ~ 4 mV since the detector gel was at a point of meltdown. A survey of the results at 1 bar is shown in Figs. 7(a)-(d); the 2 bar results will be discussed later. The error bars represent the standard deviation of the averages over the respective parameter measurement at each temperature: where not seen, they are smaller than the indicated data point. (a) (b) (c) (d) With the notable exception of the C3F8 event rates, the response of all liquids appears similar; with increasing temperature, the superheated liquids become more sensitive to incident radiation as a result of a reduced metastability barrier. Since the gel also becomes increasingly less stiff with temperature, an overall decreasing signal τ , increasing A and decreasing F might be expected. As seen in Figs. 7, all event rates tend to increase on approach to the gel melt temperature, as also the signal A . In contrast, the signal τ 's decrease, and F's fluctuate between 500-750 Hz. The results in all cases are consistent with the observed ranges observed with C2ClF5 for true bubble nucleations: τ within 5-40 ms, F within 0.45- 0.75 kHz [23]. The majority of signal A are > 125 mV: since neutrons in general produce nuclear recoil events with A < 100 mV [3], the results are consistent with the event triggering of the SDDs being principally from the α -emitting U/Th impurities of the detector gel and containment, as intended. Nonetheless, some events were recorded with A < 100 mV: 1 event with CC2F2 and 3 events with C4F10, to which we will return later. The C3F8 device, in contrast to the other liquid SDDs, was a 2.1 wt% device, hence more susceptible to sympathetic nucleations occurring within the resolving time of the instrumentation. Also unlike the other devices, its gel above 30'C was in a state of decomposition: the glycerine layer surrounding the microphone was filled with foam, and identification of a particle-induced signal increasingly difficult.",
"pages": [
8,
9,
10,
11
]
},
{
"title": "3. Superheated Liquids and Irradiation Response",
"content": "In order to more fully appreciate the above results, we discuss several aspects of both the superheated liquids and their response to irradiations.",
"pages": [
11
]
},
{
"title": "3.1 Superheated liquids",
"content": "The physics of the SDD operation, the same as with bubble chambers and described in detail in Ref. [24,25] and references therein, is based on the 'thermal spike' model of Seitz [26] which can be divided into several stages [27,28]. Initially, energy is deposited locally in a small volume of the liquid, producing a localized, high temperature region (the 'thermal spike'), the sudden expansion of which produces a shock wave in the surrounding liquid. In this stage, the temperature and pressure of the liquid within the shock enclosure exceed the critical temperature and pressures, Tc and pc respectively: there is no distinction between liquid and vapor, and no bubble. As the energy is transmitted from the thermalized region to the surrounding medium through shock propagation and heat conduction, the temperature and pressure of the fluid within the shock enclosure decrease, the expansion process slows and the shock wave decays. As the temperature and pressure reach Tc and pc, a vapor-liquid interface is formed which generates a protobubble. If the deposited energy was sufficiently high, the vapor within the protobubble grows to a critical radius rc; if the energy was insufficient, cavity growth is impeded by interfacial and viscous forces and conduction heat loss, and the protobubble collapses. To achieve rc, the deposited energy (E) must satisfy two thermodynamic criteria: where rc = 2 σ / ∆ p, σ (T) is the droplet surface tension, ∆ p = pV - p is the liquid superheat, pV(T) is the vapor pressure of the liquid, p and T are the SDD operating pressure and temperature, hlv(T) is the liquid-vapor heat of vaporization, Λ rc is the effective ionic energy deposition length, and c c r E Λ is the critical LET. The first term represents the work required to create the protobubble interface; the second, the energy required to evaporate the liquid during protobubble growth to rc. The third term describes the reversible work during protobubble expansion to rc against the liquid pressure. Generally, the second term is the largest, with the first ~ half. Not included in Eq. (1) are various irreversible processes which are generally small compared to the first three terms. From Eq. (1), the Ec for bubble nucleation is strongly dependent on the hlv of the liquid, the variation of which is shown in Fig. 8 for the various liquids investigated, as obtained from hlv(T) = χ (1-T/Tc) n with χ and n for each liquid shown in Table I, and all temperatures in K. As seen, hlv decreases with temperature increase. The liquid response is also seen to depend on the nucleation parameter ' Λ ' of the liquid in Eq. (2), in effect defining the energy density required for bubble nucleation. Its variation with temperature is shown in Fig. 9, using Λ = 4.3( ρ V/ ρ l) 1/3 which has been shown in agreement with experiment for C2ClF5 [22] and CCl2F2 [30]; although the ( ρ V/ ρ l) 1/3 is theoretically justified, its pre-factor is not in general and measurement is required. The critical LET in each case, of order 100 keV/ µ m, is sufficiently high that bubble nucleations can be triggered only by high LET irradiations - either ion recoils generated by neutron scatterings or by α 's. The stopping power of the ions within the liquid is shown in Fig. 10(a) for the constituent nuclei of C2ClF5 and He from the U/Th contaminations of the SDD materials (which range in energy between 4.2 - 8.8 MeV) in C2ClF5 at 1.3 g/cm 3 . Figure 10(b) displays the α threshold energy (Ethr α ) of 5.5 MeV α 's in C2ClF5 at 1 and 2 bar, calculated with Eqs. (1) and (2) using thermodynamic parameters taken from Refs. [19,31], α stopping powers calculated with SRIM 2008 [32], and the experimentally determined Λ = 1.40 for C2ClF5 at 2 bar and 9'C [22,3]. The 'nose' of the α curves in Fig. 10(b) reflects the He Bragg peak in C2ClF5 seen in Fig. 10(a), with the SDD sensitivity at a given temperature lying between the lower and upper contours. From Fig. 10(b), at 9'C the α 'window' thresholds are clearly reduced at higher pressure; at 2.2 bar, the 'nose' lies to the right of the indicated 9'C line, and the α sensitivity vanishes. (b) The maximum ion recoil energy in a neutron elastic scattering on a nucleus of atomic mass A is given by Erecoil A = fAEn, where fA = ( ) 2 2 A 1 A 4 + and En is the incident neutron energy: for the liquids of this study, fF = 0.19, fC = 0.27 so that a detector with a minimum nuclear recoil threshold energy Ethr nr = 8 keV implies a minimum response sensitivity to En = 42 and 30 keV for F and C recoils, respectively [45]. For the liquids with Cl, fCl = 0.10 and Ethr nr = 8 keV implies En = 80 keV; there are also two inelastic reactions with 35 Cl which may induce events through their recoiling ions: 35 Cl(n,p) 35 S and 35 Cl(n, α ) 32 P. In the first case the S ion has a maximum energy of 17 keV and can produce a nucleation for neutron energies ≤ 91 keV, whereas the P ion emerges with a minimum energy of 80 keV that can always provoke an event. However, as these reactions have cross sections smaller than those of elastic scattering on Cl by ~ 1-7 orders of magnitude, their contribution to the detector signal is generally small (with exceptions in thermal neutron beams at reactors). For C2ClF5 above 15'C, there is also the problem of events originating from high-dE / dx Auger electron cascades following interactions of environmental gamma rays with Cl atoms in the refrigerant. The metastable barrier decreases with increasing temperature, which is by virtue of fA sequentially overcome by the recoiling constituent ions until a common threshold is reached at ~ 10'C (15'C) at 1 (2) bar. At 9'C and 2 bar, Ethr Cl,F = 8 keV while Ethr C ~ 80 keV. For fixed temperature operation, SDD pressure increase raises the Ethr nr curve and shifts it to higher temperatures. As evident, the response sensitivity of each liquid is not the same at each temperature. This is a result of the variation in degree of superheating of the liquids, which varies significantly with T and p as seen in Table II. A 'universal' characterization of the response is obtained by replacing the temperature with the reduced superheat factor, S = (T - Tb)/(Tc * - Tb) with Tb the boiling temperature of the liquid at a given pressure and the critical temperature Tc * = 0.9Tc , with all temperatures in K, since the fluid phase of organic liquids ceases to exist at a temperature about 90% of the tabulated critical temperature Tc [33]. Equations (1) and (2), when satisfied simultaneously, provide the threshold energy (Ethr) for bubble nucleation, which when displayed as a function of S fall on a 'universal' curve for the nucleation onset of superheated liquid devices [25]. The range of S for each liquid is also shown in Table II. Numerous studies have shown the insensitivity of various liquid devices to γ 's, cosmics and minimum ionizing radiations for S < 0.72 [25,34].",
"pages": [
11,
12,
13,
14,
15,
16
]
},
{
"title": "3.2 The Irradiation Test Results Revisited",
"content": "Given the above considerations, we now display the full experiment results with respect to S, beginning with the device responses in Fig. 12. Since the gel melting temperature (Tgel) is absolute hence appears at a different S for each liquid, these (denoted Sgel) are indicated for each device throughout. A higher reduced superheating implies a lower metastable energy barrier: the general response should be an asymmetric sigmoid, with the onset of minimum ionizing events occurring at S ~ 0.7. For S < 0.7, all event numbers should generally remain flat or increase with temperature depending on the degree of superheating, as observed herein; for S > 0.7, the liquids are increasingly sensitive to lower LET radiations which provide an additional contribution to the event rates. In the case of C3F8, with an event response a factor ~ 10 larger than the other devices, the liquid above S = 0.8 is near its foam limit (S = 1) at which vapor phase transitions occur via thermal fluctuations, providing an explanation for the observed gel conditions (see Sec. 2.3). Moreover, its Ethr α is near 10 keV, an order of magnitude below that of the other liquids hence more susceptible to α 's otherwise reduced in energy by the gel to below thresholds of the other liquids. Apart from this, the geometric efficiency for α -induced nucleations increases for small droplet sizes as ε = 0.75f R α /r, where f is the active mass fraction, R α is the alpha particle range in the liquid, and r is the droplet radius [34]. Fig. 4, the C3F8 device exhibits the smallest size distribution of all, with = 15 - 9 µ m; using the f's of the prototype fabrications, ε C3F8/ ε C2ClF5 ~ 3.5 consistent with Fig. 12. = 15 - 9 µ m; using the f's of the prototype fabrications, ε C3F8/ ε C2ClF5 ~ 3.5 consistent with Fig. 12. In both regimes of S, the response is moderated by the effects of the gel becoming increasingly less stiff as its melting regime is entered [20]. The observed decrease of the C3F8 event response below Sgel is also in evidence for the other liquids, all of which are in states of S < 0.7, and well below their respective foam limits, suggesting the gel relaxation to be principally responsible for the decrease. The remainder of the results relate to the microphone-recorded signal characteristics which result from a bubble nucleation event, with the τ , F and A of the particle-induced signal events for each liquid as a function of S at each pressure shown in Figs. 13-15, respectively. (a) (b) Since the frequency of an event is also defined by the elasticity of the medium, the signal F should tend to decrease with increasing temperature. This is not immediately discernible in Figs. 14. At 1 bar, F generally fluctuates until ~30'C (possibly the result of low statistics), with C2ClF5 showing an increase in approach to Sgel. At 2 bar, the F are slightly lower and more dispersed than those at 1 bar, with C3F8 also showing an increase towards Sgel. Note that the recorded F differ significantly from those reported by PICASSO and COUPP, and that F of acoustic background events are generally < 100 Hz [23]. The complete phase transition of a droplet results in a gas bubble harmonically oscillating about its equilibrium radius rb . The resonant frequency is given by Minnaert [39]: where η is the polytropic coefficient of the gas, p0 is the ambient equilibrium pressure (effects of bubble movement caused by buoyancy forces, and spatial variation of the pressure during the growth process are neglected [40]). For typical parameters at 9'C and 2 bar, rb = 5 mm and η ~ 1.1 [41], fr = 700 s -1 consistent with the event records. As seen in Figs. 15, all A generally increase with approach to Sgel, as expected with increased superheating, and are generally lower at 2 bar than those at 1 bar, as also expected with a stiffer gel. The emitted acoustic power (J) in a bubble nucleation is proportional to the acceleration of the bubble volume expansion [42] , where c is the speed of sound in the medium, V is the droplet volume and the dots denote differentiation with respect to time. The pressure P produced in a liquid bath without gel at a An idea of the pressure change is obtained from the solution to the Rayleigh-Plesset equation in the asymptotic limit [43]: such that r & =v0 , r & & =0 and Eq. (5) becomes 3 0 l v d t 2 P ρ = . Figure 16 displays the calculated temperature variation of v0 for the liquids at 1 and 2 bar: note that all are continuously increasing, and similar to the experimental measurements in Fig. 15. (a) At 9'C and 2 bar, Fig. 16 gives v0 (C2ClF5) ~ 13 µm/µs. Transducers respond to P changes with sensitivities of µ V/ µ bar, with the sensitivity of the MCE-200 quoted at 7.9 mV/Pa at 1 kHz (-2dB) [44]: for C2ClF5, P ~ 6.2 x 10 2 µbar over the first 1 µ s at a distance of 10 cm, yielding signal A of ~ 1000 mV in reasonable agreement with those recorded experimentally for all liquids at all pressures.",
"pages": [
16,
17,
18,
19,
20,
21
]
},
{
"title": "3.3 Dark Matter Sensitivities",
"content": "All direct dark matter search efforts are based on the detection of nuclear recoil events generated in WIMP-nucleus elastic scatterings. Neutrons also produce single recoil events via elastic scattering, generating a signal which is indistinguishable from that of WIMPs, and the response characterization of a detector to such recoils is generically obtained from neutron calibration measurements, either via weak neutron sources such as Am/Be or 252 Cf, or the use of accelerator or reactor facilities which provide monochromatic neutron beams. The calculated variation in the minimum Ethr nr for both pressures for the various liquids of this study, using Λ = 4.3( ρ V/ ρ l) 1/3 , is shown in Fig. 17. Note the group separation which reflects the respective liquid densities: the higher density liquids must be operated at higher temperatures or lower pressures to achieve the same threshold as the lower density liquids; for example, C4F10 operated at 1 bar and ~ 42'C provides the same Ethr nr as C2ClF5 at 9'C or CCl2F2 at 29'C when operated at 2 bar. While C4F8 and C4F10 only provide recoil Ethr nr < 8 keV at temperatures > Tgel at either pressure, C3F8 permits a recoil Ethr nr ~ 2.4 keV at 15'C and 2 bar, and C2ClF5 a recoil Ethr nr ~ 5 keV at 12'C and 2 bar; operation at 12'C and 1 bar provides Ethr nr = 3 keV. Lower overpressuring of the SDDs generally provides lower Ethr nr , but operation at 2 bar is preferred as a radon suppression measure. Apart from Ethr nr (T,P), the quality of any search effort depends on the detector's active mass, exposure and target sensitivity. The liquid solubility determines the amount of active target mass in the detector, as well as the fracture probability of the gel. Although fracturing occurs with or without bubble nucleation, since the liquid occupies any microscopic N2 gas pockets formed during the fractionating stage of the suspension fabrication, it is aggravated by nucleations arising from the ambient background radiations of the fabrication site. Table III displays the solubilities of the various liquids. As seen, the solubility of C4F8 is ~ half of C2ClF5, with C3F8 a factor 4 lower; C4F10 is the least soluble by a factor of ~ 10 relative to C2ClF5. Of all, CCl2F2 is the most soluble, hence may easily suffer from a reduced, timedependent active liquid concentration and lower triggering probability. These numbers however vary significantly between compilations, and must be measured for each liquid and suspension material prior use. Prior 2005, SIMPLE SDDs with C2ClF5 were usable for ~ 40 day as a result of signal avalanches resulting from fracture events [22], which the early fabrication chemistry did not address and the instrumentation was unable to discriminate. The lifetime has effectively increased to ~ 100 day, largely via instrumentation improvements which permit identification of fracture events, but also with improvements in the gel/detector fabrication to include the use of PVP and agarose, prohibition of storage below 0'C, and on-site detector fabrications in a quasi-clean room environment. Measurements conducted in 2006-2007 with a C2ClF5 SDD indicated an abrupt increase in the measured noise level only after 109 d of operation as a result of massive fracturing. Apart from the liquid response, its dark matter search sensitivity depends on its constituent target A and spins. The WIMP-nucleus cross section σ A is to first order a sum of spinindependent (SI) and spin-dependent (SD) contributions, σ A = σ SI + σ SD, with with GF the Fermi constant, gp,n (ap,n) the SI (SD) WIMP couplings with the proton (neutron) respectively, µ A the WIMP-nuclide reduced mass, and J the total nuclear spin. With isospin conservation, gp = gn =1 and σ SI ~ A 2 : in comparison with the Xe-based experiments for example, the heavier target result is enhanced by a factor of (131/19) 2 = 48. Since fluorine possesses the largest of all nuclides in common use ( = 0.475 [46]), superheated liquids have generally provided the most sensitive target for WIMP-proton SD studies, with less impact in the SI sector relative to their heavier counterparts owing to the A 2 enhancement of the WIMP-nucleus cross section. = 0.475 [46]), superheated liquids have generally provided the most sensitive target for WIMP-proton SD studies, with less impact in the SI sector relative to their heavier counterparts owing to the A 2 enhancement of the WIMP-nucleus cross section. As an example, consider C3F8 relative to the recent SIMPLE C2ClF5 result [3]: the effect of the larger fluorine component of C3F8 in the SD sector is shown in Fig. 18(a), assuming identical measurement results. As seen in Fig. 18(b) however, in the SI sector, the C3F8 impact is severely weakened, despite a molecular mass of 198 vs. the 154 of C2ClF5. A fictional 'C3ClF8' liquid yields a contour almost identical to C2ClF5, with the difference attributed to the Cl mass fraction of the molecule (0.17 for C3ClF8 vs. 0.24 for C2ClF5). Each exclusion calculation includes the C presence, suggesting its 'spectator' presence in the measurement. Light nuclei liquids may still contribute to the SI sector because of the low recoil threshold energies possible with the technique, since the low Mw part of the exclusion contour tends to flatten with decreasing recoil Ethr [47] as seen in Fig. 19 for C4F10 with a 121 kgd exposure and no observed candidate events. Over an order of magnitude improvement in experimental sensitivity at low WIMP mass derives from a reduction in Ethr nr from 16 to 6 keV. This is also observed in Ref. [3], where SIMPLE at Ethr nr = 8 keV all but eliminates the CoGeNT result [48] at low Mw, while COUPP at Ethr nr = 15 keV - although more sensitive at higher Mw [2] -is unable to contribute.",
"pages": [
21,
22,
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},
{
"title": "4. Particle Discrimination",
"content": "Fundamentally, the ability of any detector to contribute to a dark matter search depends on its capability to discriminate between nuclear recoil and background α -induced signals, as demonstrated by all three superheated liquid programs on the basis of their respective signal A . In contrast to PICASSO and COUPP, in which the A obtain from integrations of the measured FFTs over a broad frequency range, the SIMPLE discrimination derives solely from the existence of a 30 mV gap between the recoil and α -induced event distributions of the primary harmonic of the FFTs, as seen in Fig. 20(a) [49]. This defines an empirical gap criterion of A α min > A nr max . (b) overlap of droplet size distribution with nuclear recoil events. Although there is to date no complete understanding of this discrimination in any of the programs, the consensus is that its principle origin lies in the difference between the energy loss of the α and recoil interactions within the liquid, and inherent protobubble formation. In general, a recoil event is the result of a single neutron elastic scattering interaction anywhere in a droplet, in which the LET of the recoil ion exceeds the critical LET for bubble nucleation only within a micron of the scattering origin in the liquid as shown in Fig. 21(a): only O(1) protobubbles can be formed. The recoil event distribution mirrors the droplet size distribution, as indicated in Fig. 20(b) with the solid contour representing the normalized ln(r 6 ) distribution of Fig. 4 and a shift to match the means. From Eq. (4) with V= 3 4 π r 3 , and t0 a characteristic single protobubble nucleation time, A nr max ~ rmax 3 t0 -2 . In contrast, the region of α LET > critical is generally distributed over several microns in the liquid, as seen in Fig. 21(b), so that an α event is capable of generating a number of protobubbles (npb); since each protobubble constitutes an evaporation center for the droplet, t α = t0 /npb and A α min ~ n 2 pb t0 -2 r 3 min -- n 2 pb constitutes an amplification factor for the α -generated amplitudes. Thus the gap criterion reduces to n 2 pbr 3 min > r 3 max. Consider for example the energy loss of 5.5 MeV α 's in C2ClF5 at 9'C and 2 bar shown in Fig. 21(b): the critical LET (176 keV/ µ m) is only exceeded at penetration depths of 34-40 µ m, with an estimated npb ~ 12 per micron. Ignoring for the moment the PVP presence in the gel, the α 's originate from the droplet-gel interface [50], and droplets with r < 17 µ m cannot form a protobubble (providing an effective lower cutoff (rmin) to the observed A α spectrum [51,3]: with rmax = 60 µ m from Fig. 4, the gap criterion is satisfied, and particle discrimination may be anticipated. For E α = 8 MeV, the cutoff increases to rmin ~ 33 µ m since the Bragg peak is translated to larger penetration depths, and the criterion is easily satisfied. The situation differs in the case of C4F10, since the critical LET at 2 bar and 50'C is only 103 keV/ µ m, which as seen in Fig. 21(b) is exceeded by 5.5 MeV α penetrations between 9-41 µ m. This suggests rmin ~ 5 µ m: with npb ~ 12 per micron, A α min < A nr max , and A α ' s should be mixed with A nr, as in fact observed in the measurements herein which yielded 3 events with A α < 100. While this is not the case for E α = 8.0 MeV (where rmin ~ 21 µ m), in order to achieve full exclusion of the U/Th contaminant α -contributions in a dark matter search, the C4F10 droplet size distribution would likely need to be reduced to ~ 5 µ m. ~ 5 µ m. The situation differs at 1 bar operation, where the critical LET for C2ClF5 and C4F10 are 123 keV/ µ m and 70 keV/ µ m, respectively. In this case, for C2ClF5 , rmin ~ 11 µ m and the gap criterion is unsatisfied, as also for C4F10 with rmin ~ 0. We stress that the critical LET is dependent on Λ , which is not well-known in the case of C4F10 or most other liquids of this study, as well as the estimate of npb which varies for each liquid, and that the above illustration neglects entirely non-interface α origins (although the particle LETs in gel are insignificantly different from the liquids). The PICASSO-determined Λ = 3.8 for C4F10 at 1 bar and 24'C [52] is however higher than the 4.3( ρ V/ ρ l) 1/3 estimate of 1.13, and would lower the critical LET, worsening the situation. Although the PVP presence in the gel fabrication acts in part to suppress heavy ion migration to the droplet-gel interface, the efficiency is evidently < 100%. Further study is required to provide a complete description of the gap formation, and the particle discrimination capacity of each SDD must therefore be determined both experimentally and individually.",
"pages": [
25,
26,
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},
{
"title": "5 . Heavier Nuclei Liquids",
"content": "Given the above, one might immediately question whether SDDs using fluorine-based liquids with heavier A nuclei in detector fabrications are possible, towards maximizing a single experiment sensitivity in both SD and SI sectors. The question is not new, being in part responsible for the use of CF3I by COUPP. Because of its place in the periodic table, fluorine combines well with a variety of heavier halogens, offering a large number of possibilities which would provide the desired A 2 enhancement in the SI sector, to include I (IF, IF3, IF5, IF7), Xe (XeF2, XeF4, XeF6), Te (TeF5), Ta (TaF5), W (WF6), Re (ReF6) and a variety of fluorocarbons (CF3I, CBrF3, CBrClF2,…) - in most cases, with the heavier nuclei constituents possessing sufficient [53-55] for significantly contributing in the SD sector as well; in the cases of Xe, Te, and W, the predominant contribution would be in , simultaneously with the of fluorine. of fluorine. The immediate considerations to be addressed are: (1) fabrication feasibility of a quality SDD, and (2) dark matter search sensitivity. An immediate caveat, following from the light liquids, is that the higher the density, the generally higher are the recoil thresholds and solubilities (e.g. those of IF5 and IF7 , 0.8 g/liter and 0.5 g/liter respectively, are significantly higher than C2ClF5). A cursory overview of the possible candidates moreover indicates that none of the Xe compounds are liquids at temperatures usable with SIMPLE gels; XeF6 is liquid in the window of 49-76'C [56] and hydrolytic; UF6 reacts with water, and ClF5 is corrosive; Generally, however, little is known regarding the liquid phase of such possibilities, in particular the thermophysical properties necessary to calculation of their respective Ec. Before embarking on an investigation of the properties, which would in most cases require dedicated measurements, it's useful to consider some screening of possible choices as regards their dark matter search suitability using the lessons obtained with the light nuclei liquids above.",
"pages": [
28
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},
{
"title": "5.1 Liquid Selection",
"content": "As seen from Fig. 17 and the definition of S, a figure of merit for the recoil threshold energies can be defined by FM = T (S = 0.7), the temperature at which the liquid S = 0.7: the lower the FM, the lower the recoil threshold. We show in Table IV a small compendium of FMs for a number of heavy liquids possibilities, together with known thermophysical data and following the discussion of Sec. 3.3 - the heavy nuclei mass fractions (see Sec. 4). Clearly, SF6, CBrF3, TeF6, CF3I, ClF5 and CBrClF2 (in descending order) provide the lowest threshold, whereas UF6, CF3I, PtF6, WF6 or ReF6, and CBrF3 provide the larger mass fractions, with intersections occurring for CBrF3 and CF3I. For SIMPLE gels however, SF6 and CBrF3 at 20°C are both S > 0.7 hence sensitive to complications from spontaneous nucleations and low LET irradiations; TeF6, with melting point -38.9'C and boiling at 37.6'C, is a liquid only in a 1'C window, hence not useful: only CF3I is S < 0.7. We examine more closely the cases of CBrF3, CBrClF2 and CF3I for which complete thermophysical properties are known and Ec can be calculated. The corresponding recoil thresholds of each are shown in Fig. 22, calculated as in Fig. 17. As evident, the results confirm the FMs of Table IV. With CBrF3, an Ethr nr ~ 1 keV can be achieved at 3'C and 2 bar (S ~ 0.57); CBrClF2 , an Ethr nr ~ 1 keV at 2 bar and 75'C (S ~ 0.7). In contrast, CF3I is only able to provide an Ethr nr ~ 10 keV at 25'C (near Tgel) and 2 bar (S ~ 0.32). (a) (b) (c)",
"pages": [
29,
30
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},
{
"title": "5.2 Detector Fabrications",
"content": "The variation of the three liquid densities with temperature are shown in Fig. 23. As evident from Fig. 23, the significantly higher-density heavy liquid SDD fabrications must generally proceed on the basis of a serious viscosity-matching of the liquid with the gel. An estimate of the minimum viscosity ( φ ) required to trap the droplets during the fabrication process is given by [64] where r is the average droplet radius, D is the height of the gel, t is the time for a droplet to fall a distance D, and ρ l ( ρ g) is the liquid (gel) density. In the case of CF3I, for t = 1 hour (the time required for the setting of the gel during cooling), ρ l ( ρ g) = 2 x 10 3 kg/m 3 (1.3 x 10 3 kg/m 3 ), r = 35 x 10 -6 m, D = 5 x 10 -2 m, and φ = 0.13 kg/m/s. The gel itself is formed as previously by combining powdered gelatin and bi-distilled water with slow agitation to homogenize the solution; separately, PVP is added to bi-distilled water, and agitated at 60'C. Pre-eluted ion-exchange resins for actinide removal are added to both, removed by filtering after blending in a detector bottle by agitation. The viscosity variations are effected with a 0.44 wt% agarose addition, effected by combining the additive (Sigma Aldrich A0576) with glycerin at 90'C to break the agarose chains, and its addition to the concentrated gel mix prior its filtration. Following outgassing and foam aspiration, the solution is left overnight at 42'C with slow agitation to prevent air bubble formation. The final gel matrix recipe, which produced a uniform and homogeneous distribution of droplets, had a measured φ = 0.17 kg/m/s, as well as an increased temperature at which the transition from solution to gel (sol-gel transition) occurs. CBrF3 ( ρ ~ 1.5 g/cm 3 ) and CBrClF2 ( ρ ~ 1.8 g/cm 3 ) would also require the same fabrication technique, with the advantage of a somewhat smaller agarose addition. SDD fabrication occurs via the same phase diagram of Fig. 2, adjusted for the pressure and temperature of the liquid. The detector bottle is removed to a hotplate within a hyperbaric chamber, and the pressure raised to just beyond the vapor pressure at 42'C. After thermalization, the agitation is stopped and the CF3I storage bottle opened to admit the liquid through the same condensing-distillation line with a 0.2 µm filter used previously. Once the CF3I is injected, the pressure is quickly raised to 15 bar to prevent the droplets from rising to the surface, and a rapid agitation initiated to shear big droplets; simultaneously, the temperature was raised to 50'C to create a temperature gradient inside the matrix and permit dispersion of the droplets. After 20 minutes, the temperature is slightly reduced for 1 hr (with pressure and agitation unchanged). The CF3I, in liquid state, is divided into smaller droplets by the continued agitation. Finally, the heating is stopped: the temperature decreases until the sol-gel transition is crossed, during which the stirring is reduced and finally stopped. The droplet suspension is quickly cooled to 10'C and left to set for 40 minutes, then cooled to 5'C where it is maintained for ~ 15 hours. The pressure is then slowly reduced to atmospheric pressure, and the detector removed to cold storage: a fabrication example is shown in Fig. 24.. The process results in approximately uniform and homogeneous (40 ± 15 µm diameter) droplet distributions, as determined by optical microscopy. Longer fractionating times give narrower distributions of smaller diameters; shorter, broader distributions of larger diameters.",
"pages": [
30,
31,
32
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},
{
"title": "5,3 Solubility and Lifetime",
"content": "As stated above, higher density liquids are generally characterized by higher solubilities, which determines the amount of active target mass in the detector, as well as the fracture probability of the gel. Table V indicates the solubilities of the three liquids, all of which are larger than that of CCl2F2 by a factor of 5-10. Unlike previous detectors made with C2ClF5, the CF3I prototypes began to significantly fracture within several hours of fabrication. The fracturing is inhibited by overpressuring the devices, but not eliminated. Tests with a SDD made by dissolving the liquid inside the gel produced cracks within 24 hrs, indicating the fracturing to occur because of a high solubility of CF3I gas inside the gel. Although this phenomenon occurs with or without bubble nucleation, because the CF3I gas inside the gel occupies any microscopic N2 gas pockets formed during the fractionating stage of the suspension fabrication, it is aggravated by nucleations arising from the ambient background radiations. Despite the initial fracturing, the CF3I prototype remained active for almost a year after removal to an underground 'cool' storage at 16'C at 2 bar, with little growth of the fractures observed in the measurement [64]. Nevertheless, the problem of fracturing requires an improved understanding of the involved chemistry and development of new techniques, to include the possible use of gelifying agents not requiring water as a solvent or the use of ingredients to inhibit the diffusion of the dissolved gas, which in turn suggests a possible shift to organic gels if the radio-purity of the current gel fabrications can be maintained or improved.",
"pages": [
33
]
},
{
"title": "5.4 Particle Discrimination",
"content": "Similar tests made of the CF3I prototype [64] at 35'C and 1 bar with the instrumentation of the present light experiments under similar experimental conditions yielded signal events with F = 520-32 Hz, τ = 7.8-21 ms and A = 160-500 mV, consistent with the light nuclei SDD signals of α origin in Sec. 3. Irradiations of the small volume device prototypes by 60 Co verified the device insensitivity to γ 's below Tgel , consistent with the general response of SDDs. Irradiations with a filtered neutron beam demonstrated sensitivity to reactor neutron irradiations via the induced recoils of fluorine, carbon and iodine. Fig. 25 displays the results of a 144 keV neutron irradiation of a device at 1 bar, with the rapid rate increase beginning ~ 40'C consistent with the iodine sensitivity onset observed in the temperature variation of the threshold incident neutron energies. The expected signal from fluorine and carbon at 20'C is masked by the iodine response to a broad, higher energy neutron component of the filtered beam, as identified in Ref. [45].",
"pages": [
34
]
},
{
"title": "5.5 Particle Discrimination",
"content": "With respect to the discussion of particle discrimination in Sec. 4, the critical LET = 76 keV/ µ m for CF3I at 50'C and 2 bar: as seen in Fig. 26, although the 5.5 MeV α Bragg peak is shifted to a larger depth, the protobubble production capability ranges 0-47 µ m: there is no evident rmin in the droplet size, the gap criterion cannot be satisfied, and the resulting A will likely overlap -- as in fact observed in these measurements which yielded 4 events with A α < 100. For E α = 8.0 MeV, a rmin ~ 14 µ m exists, but remains unlikely to provide the gap. At 1 bar operation, the critical LET = 63 keV/ µ m, there is again no rmin and no simple discrimination seems possible. Thus it would appear that in dark matter search applications, a SIMPLE CF3I device would be unable to provide a complete particle discrimination for the U/Th α 's without resorting to FFT integrations as employed by COUPP. Again however, as with C4F10 we stress that the critical LET is dependent on Λ which is also not well-known for these heavier liquids; for CF3I however, use of Λ = 4 as in Ref. [2] would lower the critical LET, exacerbating the situation.",
"pages": [
34,
35
]
},
{
"title": "6. Conclusions",
"content": "SDDs with the light and heavy nuclei liquids in this study can be fabricated with the SIMPLE food-based gel, via either density- or viscosity-matching using appropriate protocols and gel chemistry to provide a homogeneous, reproducible, well-defined distribution of droplet sizes. The result is detectors with approximately the same response capability - although the operational temperatures and pressures to achieve a given Ethr nr are necessarily different, and constrained by the proximity of the SDD operating conditions to the melting point of the gel as well as the liquid solubility. In contrast to PICASSO and COUPP, the characteristics of all particle-generated events of the various SDDs lie within the ranges previously defined for the C2ClF5 device with α -generated events, which we suspicion is attributable in part to the gel presence/nature -- but further study is required to confirm. The signal response of the SDD in the case of particle-induced events is largely dependent on the droplet size distribution, which depends on the fractionating speed and time, and can be varied to yield differing distributions. For dark matter searches, discrimination between α and nuclear recoil events appears to depend on the relation between the droplet size distribution (which determines the recoil event spectrum), the background α Bragg peak in the liquid and its component ≥ critical LET, with the indication that neither C4F10 or CF3I in a SIMPLE configuration is able to provide a clear particle discrimination. Given however the lack of a complete understanding of the observed gap formation and liquid Λ , further research is required and the particle discrimination capacity of each SDD must at present be determined experimentally. Thus said, the choice of SDD liquid remains fundamentally dependent on the required operating conditions to achieve both low Ethr nr and particle discrimination. Of the light nuclei liquids, PICASSO, using C4F10 operated at 50-60'C and 1 bar, obtains a Ethr nr ~ 1.7 keV for neutron-generated recoils, but without well-defined particle-discrimination. SIMPLE, using C2ClF5 with its food gel, runs at 9'C and 2 bar for a recoil Ethr nr = 8 keV, with an operating range generally limited to < 15'C because of the onset of Cl sensitivity to γ 's; for Ethr nr ≤ 8 keV, neither C4F8 or C4F10 seems usable in a SIMPLE device for WIMP search applications, given their Ethr nr at Tgel. Use of a different gel (as in early PICASSO) is possible, but the questions of increased backgrounds and particle discrimination would need to be addressed (possibly, using the PICASSO and COUPP analyses techniques). The light nuclei devices described here, while suffering from the A 2 enhancement of the heavy liquids in the SI sector, are still capable of contributing to this sector if they can be operated at temperatures and pressures corresponding to Ethr nr ~ 2 keV, as in the recent case of PICASSO, owing to the flattening of the exclusion curves with decreasing Ethr nr . The liquid selection for SIMPLE devices is however constrained by its gel nature to C2ClF5, C3F8 and CBrF3 because - all else being equal - of their ability to achieve Ethr nr < 4 keV at temperatures < Tgel. Of these, C3F8 provides the lowest Ethr nr : a simultaneous measurement with separate SDDs of C3F8 and CF3Br, operated at 15'C and 1 bar, could theoretically provide Ethr nr ~ 3 keV in both cases. Numerous heavier target liquid possibilities exist which would provide, assuming SDD fabrication feasibility based on viscosity-matching or development of more temperatureresilient gels such as PICASSO's earlier polyacrylamide, an increased sensitivity in the SI sector as well as both sectors of the SD studies. Introduction of FM = T (S = 0.7) permits a pre-selection among the possibilities in terms of dark matter search suitability. Further investigations of their liquid phase parameters (as well as commercial availability, price and environmental impact) is however required before decisions can be taken in their regard, as also the development of new gels capable of supporting the thermodynamic conditions necessary to a low Ethr nr operation and particle discrimination.",
"pages": [
35,
36,
37
]
},
{
"title": "Acknowledgements",
"content": "We thank A.R. Costa for assistance in the production of the SDDs, and M. Silva for the construction of the hermetic device caps. The activity of M. Felizardo was supported by grant SFRH/BD/46545/2008 of the Portuguese Foundation for Science and Technology (FCT). The activity was supported in part by POCI grant FP/63407/2005 of FCT, co-financed by FEDER, by FCT POCTI grant FIS/55930/2004, and by FCT PTDC grants FIS/115733/2009 and FIS/121130/2010.",
"pages": [
37
]
}
]
2013ASPC..467..331D
https://arxiv.org/pdf/1209.3986.pdf
<document>
<section_header_level_1><location><page_1><loc_23><loc_78><loc_75><loc_81></location>Power spectrum of gravitational waves from unbound compact binaries</section_header_level_1>
<text><location><page_1><loc_23><loc_74><loc_64><loc_75></location>Lorenzo De Vittori 1 , Philippe Jetzer 1 and Antoine Klein 2</text>
<text><location><page_1><loc_23><loc_71><loc_71><loc_73></location>1 University of Zurich, Institute for Theoretical Physics, Switzerland</text>
<unordered_list>
<list_item><location><page_1><loc_23><loc_70><loc_72><loc_71></location>2 Montana State University, Departement of Physics, Bozeman, USA</list_item>
</unordered_list>
<text><location><page_1><loc_23><loc_54><loc_79><loc_68></location>Abstract. Unbound interacting compact binaries emit gravitational radiation in a wide frequency range. Since short burst-like signals are expected in future detectors, such as LISA or advanced LIGO, it is interesting to study their energy spectrum and the position of the frequency peak. Here we derive them for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation, following the work of Capozziello et al. In particular, we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. Within numerical approximation our formula is in agreement with the two known limiting cases: for the eccentricity ε = 1, the parabolic case, whose spectrum was computed by Berry and Gair, and the large ε limit with the formula given by Turner.</text>
<section_header_level_1><location><page_1><loc_18><loc_48><loc_38><loc_49></location>1. Theoretical framework</section_header_level_1>
<text><location><page_1><loc_18><loc_39><loc_79><loc_46></location>Since in the last years the Gravitational Waves (GWs) detection technology has improved very rapidly, and it is believed that the precision we reached should enable their detection, it is interesting to study the dynamics of typical systems and their emission of GWsand in particular their frequency spectrum, in order to know at which wave-length range we should expect gravitational radiation.</text>
<text><location><page_1><loc_18><loc_29><loc_79><loc_38></location>For the cases of binary systems or spinning black holes on circular and elliptical orbits the resulting energy spectra have already been well studied, e.g. Peters & Mathews (1963); Peters (1964). The energy spectrum for parabolic encounters has been computed either by direct integration along unbound orbits by Turner (1977) or more recently by taking the limit of the Peters and Mathews energy spectrum for eccentric Keplerian binaries, see Berry & Gair (2010).</text>
<text><location><page_1><loc_18><loc_19><loc_79><loc_29></location>The emission of GWs from a system of massive objects interacting on hyperbolic trajectories using the quadrupole approximation has been studied by Capozziello et al. (2008) and analytic expressions for the total energy output derived. However, the energy spectrum has been computed only for the large eccentricity ( ε /greatermuch 1) limit, see in Turner (1977). Here we present the work done in the last year, De Vittori et al. (2012). We derive the energy spectrum for hyperbolic encounters for all values ε ≥ 1 and we give an analytic expression for it in terms of Hankel functions.</text>
<text><location><page_1><loc_18><loc_14><loc_79><loc_17></location>GWs are solutions of the linearized field equations of General Relativity and the radiated power to leading order is given by Einstein's quadrupole formula, as follows</text>
<formula><location><page_1><loc_41><loc_10><loc_79><loc_13></location>P = G 45 c 5 〈 ... Dij ... Dij 〉 , (1)</formula>
<text><location><page_2><loc_18><loc_75><loc_79><loc_87></location>where we used as definition for the second moment tensors M i j : = 1 c 2 ∫ T 00 x i x j d 3 x , and for the quadrupole moment tensor D i j : = 3 M i j -δ i j M kk . The quantity M i j depends on the trajectories of the involved masses, and can easily be computed for all type of Keplerian trajectories. To compute the power spectrum, i.e. the amplitude of radiated power per unit frequency, requires a Fourier transform of equation (1), which is rather involved (for the elliptical case see e.g. Maggiore (2007)), and we will derive it below for hyperbolic encounters. The eccentricity ε of the hyperbola is</text>
<formula><location><page_2><loc_40><loc_71><loc_79><loc_75></location>ε : = √ 1 + 2 E L 2 /µ α 2 , (2)</formula>
<text><location><page_2><loc_18><loc_64><loc_79><loc_71></location>where E = 1 2 µ v 2 0 ( E is a conserved quantity for which we can take the energy at t = -∞ ), v 0 being the velocity of the incoming mass m 1 at infinity, the angular momentum L = µ bv 0 , the impact parameter b , the reduced mass µ : = m 1 m 2 m 1 + m 2 , the total mass m : = m 1 + m 2 , and the parameter α : = Gm µ .</text>
<text><location><page_2><loc_18><loc_61><loc_79><loc_64></location>Setting the angle of the incident body to ϕ = 0 at initial time t = -∞ , the radius of the trajectory as a function of the angle and as a function of time is given by</text>
<formula><location><page_2><loc_30><loc_56><loc_67><loc_60></location>r ( ϕ ) = a ( ε 2 -1) 1 + ε cos( ϕ -ϕ 0 ) , r ( ξ ) = a ( ε cosh ξ -1)</formula>
<text><location><page_2><loc_18><loc_50><loc_79><loc_57></location>with the time parametrized by ξ through the relation t ( ξ ) = √ µ a 3 α ( ε sinh ξ -ξ ), where ξ goes from -∞ to + ∞ . Expressing this in Cartesian coordinates in the orbital plane, we finally get the equations for hyperbolic trajectories</text>
<formula><location><page_2><loc_30><loc_46><loc_79><loc_50></location>x ( ξ ) = a ( ε -cosh ξ ) , y ( ξ ) = a √ ε 2 -1 sinh ξ . (3)</formula>
<section_header_level_1><location><page_2><loc_18><loc_43><loc_68><loc_45></location>2. Power spectrum of Gravitational waves from hyperbolic paths</section_header_level_1>
<section_header_level_1><location><page_2><loc_18><loc_40><loc_44><loc_42></location>2.1. Power emitted per unit angle</section_header_level_1>
<text><location><page_2><loc_18><loc_35><loc_79><loc_39></location>In Capozziello et al. (2008) the computation of the power emitted as a function of the angle, as well as the total energy emitted by the system has been already carried out. They turn out to be:</text>
<formula><location><page_2><loc_28><loc_30><loc_79><loc_34></location>P ( ϕ ) = -32 GL 6 µ 2 45 c 5 b 8 f ( ϕ, ϕ 0 ) , ∆ E = 32 G µ 2 v 5 0 bc 5 F ( ϕ 0 ) , (4)</formula>
<text><location><page_2><loc_18><loc_28><loc_54><loc_30></location>where for the factors f ( ϕ, ϕ 0 ) and F ( ϕ 0 ) one finds:</text>
<formula><location><page_2><loc_29><loc_24><loc_67><loc_28></location>f ( ϕ, ϕ 0 ) = sin( ϕ 0 -ϕ 2 ) 4 sin( ϕ 2 ) 4 tan( ϕ ) 2 sin( ϕ ) 6 · ( 150 + 72cos(2 ϕ 0 )</formula>
<text><location><page_2><loc_18><loc_10><loc_79><loc_13></location>This means that the total radiated energy of the system can be determined knowing the parameters b and v 0 , and of course the reduced mass µ .</text>
<formula><location><page_2><loc_28><loc_13><loc_69><loc_26></location>0 0 + + 66cos(2( ϕ 0 -ϕ )) -144 (cos(2 ϕ 0 -ϕ ) -cos( ϕ )) ) , F ( ϕ 0 ) = 1 720 tan 2 ϕ 0 sin 4 ϕ 0 × [2628 ϕ 0 + 2328 ϕ 0 cos 2 ϕ 0 + 144 ϕ 0 cos 4 ϕ 0 -1948sin 2 ϕ 0 -301sin 4 ϕ 0 ] .</formula>
<section_header_level_1><location><page_3><loc_18><loc_85><loc_34><loc_86></location>2.2. Power spectrum</section_header_level_1>
<text><location><page_3><loc_18><loc_73><loc_79><loc_83></location>We compute now P ( ω ), the Fourier transform of P ( t ), which describes the distribution of the amplitude of the power emitted in form of GWs depending on the frequency. In Landau & Lifshitz (1967) and Longair (2011) some hints are given when solving the analogous problem in electrodynamics. The crucial idea is to use Parseval's theorem on the integration of Fourier transforms, and then to express some quantities in terms of Hankel functions. This allows to get in an easier way the function P ( ω ), for which we use the expression given in eq. (1)</text>
<formula><location><page_3><loc_26><loc_63><loc_79><loc_72></location>∆ E = ∫ P ( t )d t = ∫ P ( ω )d ω = -G 45 c 5 ∫ < ... Dij ( t ) ... Dij ( t ) > d t = -G 45 c 5 ∫ ( | ̂ ... D 11 ( ω ) | 2 + | ̂ ... D 22 ( ω ) | 2 + 2 | ̂ ... D 12 ( ω ) | 2 + | ̂ ... D 33 ( ω ) | 2 ) d ω , (5)</formula>
<text><location><page_3><loc_18><loc_57><loc_79><loc_62></location>where ̂ ... Dij ( ω ) is the Fourier transform of ... Dij ( t ). It is easy to see that the last equation represents the total amount of energy dissipated in the encounter. Therefore, the integrand in the last line has to be equal to the power dissipated per unit frequency P ( ω ) :</text>
<formula><location><page_3><loc_25><loc_50><loc_79><loc_55></location>P ( ω ) = -G 45 c 5 ( | ̂ ... D 11 ( ω ) | 2 + | ̂ ... D 22 ( ω ) | 2 + 2 | ̂ ... D 12 ( ω ) | 2 + | ̂ ... D 33 ( ω ) | 2 ) . (6)</formula>
<text><location><page_3><loc_18><loc_43><loc_79><loc_50></location>As next, we need to compute the ̂ ... Dij ( ω ), take the square their norm and add them together, which yields the power spectrum. Computing the D i j explicitly - keeping in mind that we use the time parametrization t ( ξ ) = √ µ a 3 /α ( ε sinh ξ -ξ ) - we get:</text>
<formula><location><page_3><loc_18><loc_38><loc_78><loc_42></location>D 11 ( t ) ∼ ((3 -ε 2 ) cosh 2 ξ -8 ε cosh ξ ) , D 22 ( t ) ∼ (4 ε cosh ξ + (2 ε 2 -3) cosh 2 ξ ) , D 33 ( t ) ∼ (4 ε cosh ξ + ε 2 cosh 2 ξ ) , D 12 ( t ) ∼ (2 ε sinh ξ -sinh 2 ξ ) .</formula>
<text><location><page_3><loc_18><loc_26><loc_79><loc_37></location>The Fourier transform of the third derivatives of D i j ( t ) is given by ̂ ... Dij ( ω ) = i ω 3 ̂ D i j ( ω ), thus we have just to compute ̂ D i j ( ω ). We can closely follow the calculations performed in Landau & Lifshitz (1967), where the similar problem in electrodynamics of the emitted power spectrum for scattering charged particles on hyperbolic orbits is treated. In particular the following Fourier transforms are used (for their derivation see Appendix A in De Vittori et al. (2012)).</text>
<formula><location><page_3><loc_30><loc_21><loc_79><loc_25></location>̂ sinh ξ = -π ωε H (1) i ν ( i νε ) , ̂ cosh ξ = -π ω H (1) i ν ' ( i νε ) , (7)</formula>
<formula><location><page_3><loc_36><loc_16><loc_79><loc_19></location>H (1) ˜ α ' ( x ) = 1 2 ( H (1) ˜ α -1 ( x ) -H (1) ˜ α + 1 ( x )) , (8)</formula>
<text><location><page_3><loc_18><loc_9><loc_79><loc_14></location>where H (1) ˜ α ( x ) is the Hankel function of the first kind of order ˜ α , and where ν is defined as ν : = ω √ µ a 3 /α .</text>
<text><location><page_4><loc_18><loc_85><loc_43><loc_86></location>Taking the D i j ( t ) from above we get</text>
<formula><location><page_4><loc_28><loc_80><loc_68><loc_83></location>D 11 ( ω ) = a 2 m π [16 ε H (1) i ν ' ( i νε ) + ( ε 2 3) H (1) i ν ' ( i νε/ 2)]</formula>
<text><location><page_4><loc_18><loc_64><loc_79><loc_68></location>Inserting this result into eq. (6), and using the formula for the Fourier transform of the third derivative, we get the power spectrum of the gravitational wave emission for hyperbolic encounters</text>
<formula><location><page_4><loc_28><loc_68><loc_69><loc_82></location>̂ 4 ω -, ̂ D 22 ( ω ) = a 2 m π 4 ω [(3 -2 ε 2 ) H (1) i ν ' ( i νε/ 2) -8 ε H (1) i ν ' ( i νε )] , ̂ D 33 ( ω ) = a 2 m π 4 ω [8 ε H (1) i ν ' ( i νε ) + ε 2 H (1) i ν ' ( i νε/ 2)] , ̂ D 12 ( ω ) = 3 a 2 m π 4 ωε √ ε 2 -1 [ H (1) i ν ( i νε/ 2) -4 ε H (1) i ν ( i νε )] .</formula>
<formula><location><page_4><loc_37><loc_59><loc_79><loc_63></location>P ( ω ) = -Ga 4 m 2 π 2 720 c 5 ω 4 F ε ( ω ) , (9)</formula>
<text><location><page_4><loc_18><loc_56><loc_46><loc_58></location>where the function F ε ( ω ) turns out to be</text>
<formula><location><page_4><loc_18><loc_53><loc_79><loc_55></location>| [16 ε H (1) i ν ' ( i νε ) + ( ε 2 -3) H (1) i ν ' ( i νε/ 2)] | 2 + | [(3 -2 ε 2 ) H (1) i ν ' ( i νε/ 2) -8 ε H (1) i ν ' ( i νε )] | 2</formula>
<formula><location><page_4><loc_21><loc_50><loc_79><loc_53></location>+ | [8 ε H (1) i ν ' ( i νε ) + ε 2 H (1) i ν ' ( i νε/ 2)] | 2 + 9( ε 2 -1) ε 2 | [ H (1) i ν ( i νε/ 2) -4 ε H (1) i ν ( i νε )] | 2 .</formula>
<text><location><page_4><loc_18><loc_38><loc_79><loc_48></location>In Fig. 1 the function ω 4 F ε ( ω ) is plotted for some some values of ε : this is the frequency power spectrum of gravitational radiation emitted by an hyperbolic encounter. Unfortunately the expression for F ε ( ω ) is rather complicated and we could not find an analytical way to simplify it. We thus made some numerical tests to check its validity and clearly the integral of (9) has to be equal to ∆ E in (4), which was obtained by integrating over the power emitted per unit frequency, i.e. ∫ ∞ 0 P ( ω ) d ω = ∆ E .</text>
<text><location><page_4><loc_18><loc_33><loc_79><loc_39></location>We have checked the validity of this equality for di ff erent sets of values, comparable to those used in Capozziello et al. (2008), e.g. b = 1AU, v 0 = 200 km / s, and m 1 , 2 = 1 . 4 M /circledot , or similar. For all of these sets we got agreement within numerical accuracy.</text>
<text><location><page_4><loc_18><loc_24><loc_79><loc_33></location>More interesting is the case where the eccentricity approaches ε = 1. According to eq. (2) this is the case e.g. with the set of initial conditions b = 2 AU, v 0 = 6 . 4 km / s and m 1 , 2 = 1 . 4 M /circledot . Since this is a limit case for a parabolic trajectory, we can directly compare our result with the one studied by Berry & Gair (2010), and indeed they coincide, within numerical accuracy. For a discussion about the feasibility of an analytical comparison see Appendix B in De Vittori et al. (2012).</text>
<text><location><page_4><loc_18><loc_19><loc_79><loc_23></location>Finally, we turn to the large ε limit and compare our result with the one given in Turner (1977) and Wagoner & Will (1976). The expression for the total energy emitted during an hyperbolic interaction is written in Turner (1977) as:</text>
<formula><location><page_4><loc_18><loc_12><loc_79><loc_18></location>∆ E T = 8 15 G 7 / 2 c 5 m 1 / 2 m 2 1 m 2 2 r 7 / 2 min g ( ε ) , where for ε →∞ : g ( ε ) ∼ 37 π 8 √ ε + O ( ε -1 / 2 ) , (10)</formula>
<text><location><page_4><loc_18><loc_11><loc_61><loc_12></location>which also agrees with the result of Wagoner & Will (1976).</text>
<figure>
<location><page_5><loc_24><loc_61><loc_73><loc_86></location>
<caption>Figure 1. The frequency power spectrum of gravitational radiation emitted by an hyperbolic encounter. On the x -axis we have the angular frequency ω expressed in mHz units, whereas on the y -axis the amplitude of P ( ω ) is normalized to the maximum value of the ε ∼ 2 . 5 case. These are the expected emissions generated by a system of two supermassive black holes with m = 10 7 M /circledot , impact parameter b = 10 AU, and di ff erent relative velocities. With lower velocities the interactions are stronger and the eccentricity decreases. These spectra, in order from the highest to the lowest, represent systems with v 0 = 3 . 4 × 10 7 m / s ( ε ∼ 2 . 5), v 0 = 3 . 5 × 10 7 m / s ( ε ∼ 3), v 0 = 3 . 6 × 10 7 m / s ( ε ∼ 3 . 1), v 0 = 3 . 75 × 10 7 m / s ( ε ∼ 3 . 4), v 0 = 4 × 10 7 m / s ( ε ∼ 3 . 8), v 0 = 4 . 5 × 10 7 m / s ( ε ∼ 4 . 7), respectively. In particular the case with ε ∼ 3 (plotted with the dashed line) is discussed in the conclusions. As one can see, for higher eccentricities the peak frequency slowly decreases. This is only true for values of v 0 up to ∼ 6 × 10 7 m / s, whereas above it increases again. Moreover, decreasing the mass or increasing the impact parameter changes the eccentricity as well. We should be able to detect incoming waves in that range e.g. with eLISA, since the peak at ∼ 0 . 2 mHz fits in its observable band. For a more detailed discussion see Sec. 3 and e.g. LISA Collaboration (2012).</caption>
</figure>
<text><location><page_5><loc_18><loc_25><loc_79><loc_32></location>Comparing our total energy from the quadrupole approximation, eq. (4), with the expression for the energy ∆ E T (10) by Turner (1977) valid in the large ε limit, we see that they coincide for large eccentricities, having e.g. a 1% di ff erence after ε = 100, and a 5% di ff erence after ε = 20. For a more detailed discussion about these comparisons with previous results, see our full work De Vittori et al. (2012).</text>
<section_header_level_1><location><page_5><loc_18><loc_20><loc_30><loc_21></location>3. Conclusions</section_header_level_1>
<text><location><page_5><loc_18><loc_11><loc_79><loc_18></location>Short gravitational wave burst-like signals are expected in the data stream of detectors. Although these signals will likely be too short to allow us to measure the parameters of the emitting system accurately, the results presented in this paper could be used to get a rough estimate of these parameters, by observing the position of the peak, the amount of energy released and the timescale of the interaction.</text>
<text><location><page_6><loc_18><loc_74><loc_79><loc_86></location>Given the knowledge of the power spectrum we can easily see which kind of hyperbolic encounters could generate gravitational waves detectable e.g. with eLISA, advanced LIGO or advanced VIRGO. Measurements from unbound interactions with ground-based detectors could in principle be possible, though the energy emitted at e.g. ± 200 Hz is below the minimum threshold for advanced LIGO or advanced VIRGO, making detections unlikely but not impossible. The space-based interferometer instead is expected to cover frequencies ranging from 0 . 03 mHz up to 1 Hz, see e.g. LISA Collaboration (2012), where the interactions could release more energy.</text>
<text><location><page_6><loc_18><loc_51><loc_79><loc_74></location>An unbounded collision between two intermediate-mass black holes, let's say of 10 3 M /circledot each, with an encounter velocity of 2000 km / s at a distance of 1 AU, would generate, according to our eq. (9), a frequency spectrum with peak around 0 . 04 mHz, with 80% of the emission in the range between 0 . 01 and 0 . 07 mHz, i.e. in the lower range limit of eLISA. Another possible example of measurable impact would be an encounter between two supermassive black holes with mass, e.g., comparable to the expected mass of Sagittarius A*, the black hole believed to be at the center of our galaxy, i.e. ∼ 10 7 M /circledot . With a distance of some AU, and a high velocity (we want to exclude the bounded case) of tens of thousands km / s, such a collision would generate an energy spectrum with peak at ∼ 0 . 2 mHz with 80% between 0 . 03 and 0 . 37 mHz, thus in the observable range of eLISA. (Its energy spectrum is plotted with a dashed line in Fig. 1.) Estimates for the rate of such events have been considered e.g. in Capozziello & De Laurentis (2008). They consider e.g. typical compact stellar cluster around the Galactic Center, and expect an event rate of 10 -3 up to unity per year, depending on the radius of the object and the amount of such clusters in the near region.</text>
<text><location><page_6><loc_18><loc_46><loc_79><loc_50></location>Webelieve that with the energy spectrum found here one should be able to classify the di ff erent encounters depending on t di ff erent encounters depending on the detected shape, and therefore get a better insight into the map of our galaxy or the near universe.</text>
<text><location><page_6><loc_18><loc_36><loc_79><loc_44></location>Acknowledgments. We thank N. Straumann for useful discussions and for bringing to our attention the relevant treatment of the hyperbolic problem in electrodynamics in Landau & Lifschitz. We also thank L. Blanchet for his encouragement and for pointing out the possibility of treating the same problem in another way. Finally, we would also like to thank C. Berry for helping clarifying some details.</text>
<section_header_level_1><location><page_6><loc_18><loc_32><loc_25><loc_34></location>References</section_header_level_1>
<text><location><page_6><loc_18><loc_15><loc_79><loc_31></location>Berry, C., & Gair, J. 2010, Phys. Rev. D, 82, 10751 Capozziello, S., & De Laurentis, M. 2008, Astroparticle Physics, 30, 105 Capozziello, S., De Laurentis, M., De Paolis, F., Ingrosso, G., & Nucita, A. 2008, Mod.Phys.Lett.A 23:99-107 De Vittori, L., Jetzer, P., & Klein, A. 2012, Phys. Rev. D, 86, 044017 Landau, L., & Lifshitz, E. 1967, Theoretical Physics: Classical Theory of Fields LISA Collaboration 2012, arXiv:1201.3621v1 Longair, M. 2011, High Energy Astrophysics Maggiore, M. 2007, Gravitational Waves. Volume 1: Theory and Experiments Peters, P. 1964, Phys. Rev., 136, B1224 Peters, P., & Mathews, J. 1963, Phys. Rev., 131, 435 Turner, M. 1977, Astrophysical Journal, 216, 610-619</text>
<text><location><page_6><loc_18><loc_13><loc_58><loc_15></location>Wagoner, R., & Will, C. 1976, Astrophysical Journal, 210, 764</text>
</document>
[
{
"title": "Power spectrum of gravitational waves from unbound compact binaries",
"content": "Lorenzo De Vittori 1 , Philippe Jetzer 1 and Antoine Klein 2 1 University of Zurich, Institute for Theoretical Physics, Switzerland Abstract. Unbound interacting compact binaries emit gravitational radiation in a wide frequency range. Since short burst-like signals are expected in future detectors, such as LISA or advanced LIGO, it is interesting to study their energy spectrum and the position of the frequency peak. Here we derive them for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation, following the work of Capozziello et al. In particular, we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. Within numerical approximation our formula is in agreement with the two known limiting cases: for the eccentricity ε = 1, the parabolic case, whose spectrum was computed by Berry and Gair, and the large ε limit with the formula given by Turner.",
"pages": [
1
]
},
{
"title": "1. Theoretical framework",
"content": "Since in the last years the Gravitational Waves (GWs) detection technology has improved very rapidly, and it is believed that the precision we reached should enable their detection, it is interesting to study the dynamics of typical systems and their emission of GWsand in particular their frequency spectrum, in order to know at which wave-length range we should expect gravitational radiation. For the cases of binary systems or spinning black holes on circular and elliptical orbits the resulting energy spectra have already been well studied, e.g. Peters & Mathews (1963); Peters (1964). The energy spectrum for parabolic encounters has been computed either by direct integration along unbound orbits by Turner (1977) or more recently by taking the limit of the Peters and Mathews energy spectrum for eccentric Keplerian binaries, see Berry & Gair (2010). The emission of GWs from a system of massive objects interacting on hyperbolic trajectories using the quadrupole approximation has been studied by Capozziello et al. (2008) and analytic expressions for the total energy output derived. However, the energy spectrum has been computed only for the large eccentricity ( ε /greatermuch 1) limit, see in Turner (1977). Here we present the work done in the last year, De Vittori et al. (2012). We derive the energy spectrum for hyperbolic encounters for all values ε ≥ 1 and we give an analytic expression for it in terms of Hankel functions. GWs are solutions of the linearized field equations of General Relativity and the radiated power to leading order is given by Einstein's quadrupole formula, as follows where we used as definition for the second moment tensors M i j : = 1 c 2 ∫ T 00 x i x j d 3 x , and for the quadrupole moment tensor D i j : = 3 M i j -δ i j M kk . The quantity M i j depends on the trajectories of the involved masses, and can easily be computed for all type of Keplerian trajectories. To compute the power spectrum, i.e. the amplitude of radiated power per unit frequency, requires a Fourier transform of equation (1), which is rather involved (for the elliptical case see e.g. Maggiore (2007)), and we will derive it below for hyperbolic encounters. The eccentricity ε of the hyperbola is where E = 1 2 µ v 2 0 ( E is a conserved quantity for which we can take the energy at t = -∞ ), v 0 being the velocity of the incoming mass m 1 at infinity, the angular momentum L = µ bv 0 , the impact parameter b , the reduced mass µ : = m 1 m 2 m 1 + m 2 , the total mass m : = m 1 + m 2 , and the parameter α : = Gm µ . Setting the angle of the incident body to ϕ = 0 at initial time t = -∞ , the radius of the trajectory as a function of the angle and as a function of time is given by with the time parametrized by ξ through the relation t ( ξ ) = √ µ a 3 α ( ε sinh ξ -ξ ), where ξ goes from -∞ to + ∞ . Expressing this in Cartesian coordinates in the orbital plane, we finally get the equations for hyperbolic trajectories",
"pages": [
1,
2
]
},
{
"title": "2.1. Power emitted per unit angle",
"content": "In Capozziello et al. (2008) the computation of the power emitted as a function of the angle, as well as the total energy emitted by the system has been already carried out. They turn out to be: where for the factors f ( ϕ, ϕ 0 ) and F ( ϕ 0 ) one finds: This means that the total radiated energy of the system can be determined knowing the parameters b and v 0 , and of course the reduced mass µ .",
"pages": [
2
]
},
{
"title": "2.2. Power spectrum",
"content": "We compute now P ( ω ), the Fourier transform of P ( t ), which describes the distribution of the amplitude of the power emitted in form of GWs depending on the frequency. In Landau & Lifshitz (1967) and Longair (2011) some hints are given when solving the analogous problem in electrodynamics. The crucial idea is to use Parseval's theorem on the integration of Fourier transforms, and then to express some quantities in terms of Hankel functions. This allows to get in an easier way the function P ( ω ), for which we use the expression given in eq. (1) where ̂ ... Dij ( ω ) is the Fourier transform of ... Dij ( t ). It is easy to see that the last equation represents the total amount of energy dissipated in the encounter. Therefore, the integrand in the last line has to be equal to the power dissipated per unit frequency P ( ω ) : As next, we need to compute the ̂ ... Dij ( ω ), take the square their norm and add them together, which yields the power spectrum. Computing the D i j explicitly - keeping in mind that we use the time parametrization t ( ξ ) = √ µ a 3 /α ( ε sinh ξ -ξ ) - we get: The Fourier transform of the third derivatives of D i j ( t ) is given by ̂ ... Dij ( ω ) = i ω 3 ̂ D i j ( ω ), thus we have just to compute ̂ D i j ( ω ). We can closely follow the calculations performed in Landau & Lifshitz (1967), where the similar problem in electrodynamics of the emitted power spectrum for scattering charged particles on hyperbolic orbits is treated. In particular the following Fourier transforms are used (for their derivation see Appendix A in De Vittori et al. (2012)). where H (1) ˜ α ( x ) is the Hankel function of the first kind of order ˜ α , and where ν is defined as ν : = ω √ µ a 3 /α . Taking the D i j ( t ) from above we get Inserting this result into eq. (6), and using the formula for the Fourier transform of the third derivative, we get the power spectrum of the gravitational wave emission for hyperbolic encounters where the function F ε ( ω ) turns out to be In Fig. 1 the function ω 4 F ε ( ω ) is plotted for some some values of ε : this is the frequency power spectrum of gravitational radiation emitted by an hyperbolic encounter. Unfortunately the expression for F ε ( ω ) is rather complicated and we could not find an analytical way to simplify it. We thus made some numerical tests to check its validity and clearly the integral of (9) has to be equal to ∆ E in (4), which was obtained by integrating over the power emitted per unit frequency, i.e. ∫ ∞ 0 P ( ω ) d ω = ∆ E . We have checked the validity of this equality for di ff erent sets of values, comparable to those used in Capozziello et al. (2008), e.g. b = 1AU, v 0 = 200 km / s, and m 1 , 2 = 1 . 4 M /circledot , or similar. For all of these sets we got agreement within numerical accuracy. More interesting is the case where the eccentricity approaches ε = 1. According to eq. (2) this is the case e.g. with the set of initial conditions b = 2 AU, v 0 = 6 . 4 km / s and m 1 , 2 = 1 . 4 M /circledot . Since this is a limit case for a parabolic trajectory, we can directly compare our result with the one studied by Berry & Gair (2010), and indeed they coincide, within numerical accuracy. For a discussion about the feasibility of an analytical comparison see Appendix B in De Vittori et al. (2012). Finally, we turn to the large ε limit and compare our result with the one given in Turner (1977) and Wagoner & Will (1976). The expression for the total energy emitted during an hyperbolic interaction is written in Turner (1977) as: which also agrees with the result of Wagoner & Will (1976). Comparing our total energy from the quadrupole approximation, eq. (4), with the expression for the energy ∆ E T (10) by Turner (1977) valid in the large ε limit, we see that they coincide for large eccentricities, having e.g. a 1% di ff erence after ε = 100, and a 5% di ff erence after ε = 20. For a more detailed discussion about these comparisons with previous results, see our full work De Vittori et al. (2012).",
"pages": [
3,
4,
5
]
},
{
"title": "3. Conclusions",
"content": "Short gravitational wave burst-like signals are expected in the data stream of detectors. Although these signals will likely be too short to allow us to measure the parameters of the emitting system accurately, the results presented in this paper could be used to get a rough estimate of these parameters, by observing the position of the peak, the amount of energy released and the timescale of the interaction. Given the knowledge of the power spectrum we can easily see which kind of hyperbolic encounters could generate gravitational waves detectable e.g. with eLISA, advanced LIGO or advanced VIRGO. Measurements from unbound interactions with ground-based detectors could in principle be possible, though the energy emitted at e.g. ± 200 Hz is below the minimum threshold for advanced LIGO or advanced VIRGO, making detections unlikely but not impossible. The space-based interferometer instead is expected to cover frequencies ranging from 0 . 03 mHz up to 1 Hz, see e.g. LISA Collaboration (2012), where the interactions could release more energy. An unbounded collision between two intermediate-mass black holes, let's say of 10 3 M /circledot each, with an encounter velocity of 2000 km / s at a distance of 1 AU, would generate, according to our eq. (9), a frequency spectrum with peak around 0 . 04 mHz, with 80% of the emission in the range between 0 . 01 and 0 . 07 mHz, i.e. in the lower range limit of eLISA. Another possible example of measurable impact would be an encounter between two supermassive black holes with mass, e.g., comparable to the expected mass of Sagittarius A*, the black hole believed to be at the center of our galaxy, i.e. ∼ 10 7 M /circledot . With a distance of some AU, and a high velocity (we want to exclude the bounded case) of tens of thousands km / s, such a collision would generate an energy spectrum with peak at ∼ 0 . 2 mHz with 80% between 0 . 03 and 0 . 37 mHz, thus in the observable range of eLISA. (Its energy spectrum is plotted with a dashed line in Fig. 1.) Estimates for the rate of such events have been considered e.g. in Capozziello & De Laurentis (2008). They consider e.g. typical compact stellar cluster around the Galactic Center, and expect an event rate of 10 -3 up to unity per year, depending on the radius of the object and the amount of such clusters in the near region. Webelieve that with the energy spectrum found here one should be able to classify the di ff erent encounters depending on t di ff erent encounters depending on the detected shape, and therefore get a better insight into the map of our galaxy or the near universe. Acknowledgments. We thank N. Straumann for useful discussions and for bringing to our attention the relevant treatment of the hyperbolic problem in electrodynamics in Landau & Lifschitz. We also thank L. Blanchet for his encouragement and for pointing out the possibility of treating the same problem in another way. Finally, we would also like to thank C. Berry for helping clarifying some details.",
"pages": [
5,
6
]
},
{
"title": "References",
"content": "Berry, C., & Gair, J. 2010, Phys. Rev. D, 82, 10751 Capozziello, S., & De Laurentis, M. 2008, Astroparticle Physics, 30, 105 Capozziello, S., De Laurentis, M., De Paolis, F., Ingrosso, G., & Nucita, A. 2008, Mod.Phys.Lett.A 23:99-107 De Vittori, L., Jetzer, P., & Klein, A. 2012, Phys. Rev. D, 86, 044017 Landau, L., & Lifshitz, E. 1967, Theoretical Physics: Classical Theory of Fields LISA Collaboration 2012, arXiv:1201.3621v1 Longair, M. 2011, High Energy Astrophysics Maggiore, M. 2007, Gravitational Waves. Volume 1: Theory and Experiments Peters, P. 1964, Phys. Rev., 136, B1224 Peters, P., & Mathews, J. 1963, Phys. Rev., 131, 435 Turner, M. 1977, Astrophysical Journal, 216, 610-619 Wagoner, R., & Will, C. 1976, Astrophysical Journal, 210, 764",
"pages": [
6
]
}
]
2013ASPC..470..347K
https://arxiv.org/pdf/1206.1325.pdf
<document>
<section_header_level_1><location><page_1><loc_23><loc_80><loc_73><loc_83></location>Collateral Damage: the Implications of Utrecht Star Cluster Astrophysics for Galaxy Evolution</section_header_level_1>
<section_header_level_1><location><page_1><loc_23><loc_76><loc_40><loc_77></location>J. M. Diederik Kruijssen</section_header_level_1>
<text><location><page_1><loc_23><loc_72><loc_76><loc_75></location>Max-Planck Institut fur Astrophysik, Karl-Schwarzschild-Straße 1, 85748, Garching, Germany; [email protected]</text>
<text><location><page_1><loc_23><loc_55><loc_79><loc_70></location>Abstract. Until the early 2000s, the research portfolio of the Astronomical Institute in Utrecht (SIU) did not include galaxy evolution. Somewhat serendipitously, this changed with the advent of the star cluster group. In only a few years, a simple framework was developed to describe and quantify the properties of dynamically evolving star cluster populations. Since then, the 'Utrecht cluster disruption model' has shown that the galactic environment plays an important role in setting the evolution of stellar clusters. From this simple result, it follows that cluster populations bear some imprint of the characteristics and histories of their host galaxies, and that star clusters can be used to trace galaxy evolution - an aim for which the Utrecht star cluster models were never designed, but which they are well-capable of fulfilling. I review some of the work in this direction, with a strong emphasis on the contributions from the SIU.</text>
<text><location><page_1><loc_18><loc_42><loc_79><loc_53></location>In 1920, the famous Dutch poet Adriaan Roland Holst (1888-1976) published the wonderful story Deirdre en de zonen van Usnach , 1 based on an Irish-Celtic myth from the Ulster Cycle. It tells the tale of the lady Deirdre, who is so incredibly beautiful that every man who sees her loses his heart. While this enables her to do a lot of good, the story does not end well. In the finale, Deirdre goes west, to the seashore, where far beyond the horizon the paradise of Elysium lies. As she wanders into the sea and lets the waves take her, she leaves this world - but not without having changed it forever.</text>
<text><location><page_1><loc_18><loc_34><loc_79><loc_42></location>The closure of the Astronomical Institute Utrecht (SIU) prompted the conference of these proceedings, held at the Dutch west coast and aimed at celebrating the achievements of 370 years of astronomy in Utrecht. The occasion and location of the meeting drew a striking parallel with Deirdre's fate. Fortunately none of the participants followed her example and went for a swim - the North Sea is quite cold in early April.</text>
<section_header_level_1><location><page_1><loc_18><loc_30><loc_30><loc_32></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_18><loc_15><loc_79><loc_29></location>A stellar cluster evaporates due to successive encounters between its stars. The rate at which this process proceeds is not only set by internal dynamics, but also by the tidal field the cluster resides in. The stronger the tidal field is, the smaller the Jacobi radius beyond which stars are unbound, and hence the more easily stars can escape (e.g. Baumgardt 2001). If the orbital motion of a cluster causes it to experience timedependent tidal forces, a second environmental mechanism for cluster disruption comes into play. Varying tidal fields induce tidal heating, which increases the kinetic energy of the stars (Ostriker et al. 1972). Examples in nature of these 'tidal shocks' are pericentre passages or galaxy disc crossings of globular clusters (e.g. Gnedin & Ostriker 1997),</text>
<text><location><page_2><loc_18><loc_79><loc_79><loc_86></location>encounters with giant molecular clouds (Gieles et al. 2006), and spiral arm passages (Gieles et al. 2007). These examples illustrate that the disruption rate of stellar clusters is largely set by the galactic environment. In practice, the described cluster destruction processes are effectively mass-dependent, in that low-mass clusters are more rapidly disrupted than massive ones.</text>
<text><location><page_2><loc_18><loc_60><loc_79><loc_78></location>Due to the relation between the galactic environment and the dynamical evolution of stellar clusters, the properties of cluster populations vary among different galaxies. High-density galaxies with correspondingly high disruption rates (Lamers et al. 2005b; Kruijssen et al. 2011) generally contain very few old clusters (Boutloukos & Lamers 2003; Bastian et al. 2005; Gieles et al. 2005). Additionally, the mass-dependence of cluster disruption implies that disruptive environments contain fewer low-mass clusters (Larsen 2009; Gieles 2009). These trends are also present in a spatially resolved sense within single galaxies (Gieles et al. 2005; Kruijssen et al. 2011; Bastian et al. 2011, 2012), as well as over the course of galaxy histories, during which the galactic environment may have experienced substantial evolution (Kruijssen et al. 2012). When interpreted correctly, these relations imply that cluster populations provide clues to the evolutionary histories of their host galaxies.</text>
<section_header_level_1><location><page_2><loc_18><loc_55><loc_71><loc_57></location>2. The galactic environment and the Utrecht cluster disruption model</section_header_level_1>
<text><location><page_2><loc_18><loc_40><loc_79><loc_54></location>Lamers et al. (2005a) developed a simple analytic model to describe the age and mass distributions of evolving star cluster populations. In this model, the departure of both distributions from their initial forms (the cluster formation history and the initial cluster mass function, respectively) is caused by a non-zero disruption rate (or a finite disruption timescale) that is set by the galactic environment. For each galaxy individually, this rate has been assumed to be constant in space and time. The power of this single-parameter approach has been demonstrated by various successful applications to the cluster populations of nearby galaxies (Bastian et al. 2005; Gieles et al. 2005; Lamers & Gieles 2006; Gieles & Bastian 2008).</text>
<text><location><page_2><loc_18><loc_21><loc_79><loc_40></location>It was shown by Boutloukos & Lamers (2003) that the disruption rates of clusters vary between the Small Magellanic Cloud (SMC), the solar neighbourhood, M33, and M51. Lamers et al. (2005b) then found a correlation between the disruption rate and the ambient density within the host galaxy, approximately following the theoretically predicted relations by Portegies Zwart et al. (1998) and Baumgardt & Makino (2003). The one exception was the interacting galaxy M51, which turned out to have a disruption rate that is an order of magnitude higher than expected. We later showed in Kruijssen et al. (2012) that such an increase can be explained by considering the growth of the gas density during galaxy interactions, and the correspondingly enhanced disruption rate due to tidal shocks. Similarly, the single-parameter approach of a disruption rate that is constant in time and space does not successfully describe the cluster population of the interacting Antennae galaxies (Gieles & Bastian 2008).</text>
<text><location><page_2><loc_18><loc_11><loc_79><loc_21></location>While the above examples clearly show that the galactic environment influences cluster disruption and hence is an essential factor in setting the properties of the cluster population, it is also evident that the assumption of a single disruption rate throughout space and time only holds for a certain subset of (quiescent) galaxies. This assumption has recently been overcome in Kruijssen et al. (2011), where we expanded the Utrecht disruption model by including it in numerical simulations of galaxy evolution, in which the disruption rate is determined for each cluster individually, accounting for the steady</text>
<text><location><page_3><loc_18><loc_69><loc_79><loc_86></location>tidal field as well as for tidal shocks. The numerical models self-consistently follow the impact of the galactic environment on cluster disruption, and have been used to show that encounters with giant molecular clouds are the dominant disruption mechanism in disk galaxies (also see Gieles et al. 2006; Lamers & Gieles 2006). They have also been applied to predict how the cluster age distribution changes under different galactic conditions, providing some characteristic features that can be verified in observational work. For instance, we have shown that the mean disruption rate of a cluster population decreases with age (also see Elmegreen & Hunter 2010), due to the preferential survival of clusters in quiescent environments ('natural selection') and their migration away from their dense, natal environment. Observational evidence for such variations has been found by Bastian et al. (2011, 2012).</text>
<section_header_level_1><location><page_3><loc_18><loc_65><loc_61><loc_66></location>3. Star cluster populations as tracers of galaxy evolution</section_header_level_1>
<text><location><page_3><loc_18><loc_59><loc_79><loc_63></location>There are numerous ways in which the properties of the star cluster population may be used to derive the galaxy evolutionary history. In this section, we discuss some examples and provide an outlook for how this avenue can be expanded in future work.</text>
<text><location><page_3><loc_18><loc_43><loc_79><loc_58></location>The decrease of the disruption rate with age affects the slope of the cluster age distribution over the age range in which cluster migration and natural selection act on the cluster population. Both effects are most important in galaxies with a high density contrast between star-forming regions and their surroundings (Kruijssen et al. 2011). Because migration occurs on the global dynamical timescale of a system, it can be used to infer the duration of certain events in the history of the galaxy. For instance, it indicates the interaction timescale of an ongoing galaxy collision, or the dynamical timescale of an isolated galaxy. The latter tracer can be verified using an example. The dynamical timescale of the disc galaxy M83 is 1 / Ω ∼ 20 Myr, and there are indications of an evolving disruption rate over the same age range (Bastian et al. 2011, 2012).</text>
<text><location><page_3><loc_18><loc_26><loc_79><loc_43></location>Another illustration of how the galactic environment affects the cluster population was found in Kruijssen et al. (2012), where we performed numerical simulations of major mergers of disc galaxies, again including a model for the evolution of the cluster population. In galaxy mergers, tidal torques drive the gas towards the galaxy centres. As a result, the disruption of clusters by dense giant molecular clouds (Gieles et al. 2006) is prevalent, and counteracts a simultaneous increase of the cluster formation rate. The number of clusters in the merger remnant is therefore lower than in the progenitor disc galaxies. This can be quantified as a 'survival cluster fraction', which we have found to decrease with the starburst intensity (or increase with the gas depletion timescale). Number counts of stellar clusters in merger remnants could thus be used to infer the characteristics of the preceding galaxy interaction and starburst.</text>
<text><location><page_3><loc_18><loc_11><loc_79><loc_26></location>Extrapolating the approach of tracing galaxy-scale events using the surviving cluster population, old globular clusters are exemplary targets for similar analyses, because they may be used to infer the conditions of galaxy formation at high redshift. Although they have substantially higher characteristic masses than young clusters in nearby galaxies, it has been argued that globular clusters formed through the same physical mechanisms that we see locally (Elmegreen & Efremov 1997; Kruijssen & Cooper 2012). Their high average mass then implies that the vast majority of lower-mass globular clusters must have been disrupted due to dynamical evolution. However, the degree of disruption appears to be universal, which is hard to understand considering the widely varying galactic environments in which globular clusters currently reside.</text>
<section_header_level_1><location><page_4><loc_30><loc_88><loc_37><loc_90></location>Kruijssen</section_header_level_1>
<text><location><page_4><loc_18><loc_79><loc_79><loc_86></location>The efficient destruction of clusters in dense, star-forming environments might provide a solution. Globular clusters all formed in the dense, high-redshift universe, and if most of their disruption occurred early on, their present-day properties should be similar (Elmegreen 2010; Kruijssen et al. 2012). If true, this puts constraints on the high-redshift conditions under which globular clusters formed.</text>
<text><location><page_4><loc_18><loc_65><loc_79><loc_78></location>The origin of globular clusters is far from being a solved problem. The above scenario is a plausible solution, but it is generalised from physical systems that may not be adequate. It is thought that globular clusters did not form in major mergers, but instead have their roots in starburst dwarf galaxies, unstable high-redshift discs, and other highredshift, star-forming environments (see Kruijssen et al. 2012 and references therein). While it seems reasonable that these conditions were equally disruptive as the starbursts in our galaxy merger simulations, this requires explicit verification. Numerical simulations of galaxy formation with cosmologically motivated initial conditions (e.g. Prieto & Gnedin 2008) will be necessary to provide a definitive answer.</text>
<text><location><page_4><loc_18><loc_61><loc_79><loc_64></location>Acknowledgments. I am very grateful to the former SIU staff - Henny Lamers in particular - for their unlimited dedication to science and teaching.</text>
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[
{
"title": "J. M. Diederik Kruijssen",
"content": "Max-Planck Institut fur Astrophysik, Karl-Schwarzschild-Straße 1, 85748, Garching, Germany; [email protected] Abstract. Until the early 2000s, the research portfolio of the Astronomical Institute in Utrecht (SIU) did not include galaxy evolution. Somewhat serendipitously, this changed with the advent of the star cluster group. In only a few years, a simple framework was developed to describe and quantify the properties of dynamically evolving star cluster populations. Since then, the 'Utrecht cluster disruption model' has shown that the galactic environment plays an important role in setting the evolution of stellar clusters. From this simple result, it follows that cluster populations bear some imprint of the characteristics and histories of their host galaxies, and that star clusters can be used to trace galaxy evolution - an aim for which the Utrecht star cluster models were never designed, but which they are well-capable of fulfilling. I review some of the work in this direction, with a strong emphasis on the contributions from the SIU. In 1920, the famous Dutch poet Adriaan Roland Holst (1888-1976) published the wonderful story Deirdre en de zonen van Usnach , 1 based on an Irish-Celtic myth from the Ulster Cycle. It tells the tale of the lady Deirdre, who is so incredibly beautiful that every man who sees her loses his heart. While this enables her to do a lot of good, the story does not end well. In the finale, Deirdre goes west, to the seashore, where far beyond the horizon the paradise of Elysium lies. As she wanders into the sea and lets the waves take her, she leaves this world - but not without having changed it forever. The closure of the Astronomical Institute Utrecht (SIU) prompted the conference of these proceedings, held at the Dutch west coast and aimed at celebrating the achievements of 370 years of astronomy in Utrecht. The occasion and location of the meeting drew a striking parallel with Deirdre's fate. Fortunately none of the participants followed her example and went for a swim - the North Sea is quite cold in early April.",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "A stellar cluster evaporates due to successive encounters between its stars. The rate at which this process proceeds is not only set by internal dynamics, but also by the tidal field the cluster resides in. The stronger the tidal field is, the smaller the Jacobi radius beyond which stars are unbound, and hence the more easily stars can escape (e.g. Baumgardt 2001). If the orbital motion of a cluster causes it to experience timedependent tidal forces, a second environmental mechanism for cluster disruption comes into play. Varying tidal fields induce tidal heating, which increases the kinetic energy of the stars (Ostriker et al. 1972). Examples in nature of these 'tidal shocks' are pericentre passages or galaxy disc crossings of globular clusters (e.g. Gnedin & Ostriker 1997), encounters with giant molecular clouds (Gieles et al. 2006), and spiral arm passages (Gieles et al. 2007). These examples illustrate that the disruption rate of stellar clusters is largely set by the galactic environment. In practice, the described cluster destruction processes are effectively mass-dependent, in that low-mass clusters are more rapidly disrupted than massive ones. Due to the relation between the galactic environment and the dynamical evolution of stellar clusters, the properties of cluster populations vary among different galaxies. High-density galaxies with correspondingly high disruption rates (Lamers et al. 2005b; Kruijssen et al. 2011) generally contain very few old clusters (Boutloukos & Lamers 2003; Bastian et al. 2005; Gieles et al. 2005). Additionally, the mass-dependence of cluster disruption implies that disruptive environments contain fewer low-mass clusters (Larsen 2009; Gieles 2009). These trends are also present in a spatially resolved sense within single galaxies (Gieles et al. 2005; Kruijssen et al. 2011; Bastian et al. 2011, 2012), as well as over the course of galaxy histories, during which the galactic environment may have experienced substantial evolution (Kruijssen et al. 2012). When interpreted correctly, these relations imply that cluster populations provide clues to the evolutionary histories of their host galaxies.",
"pages": [
1,
2
]
},
{
"title": "2. The galactic environment and the Utrecht cluster disruption model",
"content": "Lamers et al. (2005a) developed a simple analytic model to describe the age and mass distributions of evolving star cluster populations. In this model, the departure of both distributions from their initial forms (the cluster formation history and the initial cluster mass function, respectively) is caused by a non-zero disruption rate (or a finite disruption timescale) that is set by the galactic environment. For each galaxy individually, this rate has been assumed to be constant in space and time. The power of this single-parameter approach has been demonstrated by various successful applications to the cluster populations of nearby galaxies (Bastian et al. 2005; Gieles et al. 2005; Lamers & Gieles 2006; Gieles & Bastian 2008). It was shown by Boutloukos & Lamers (2003) that the disruption rates of clusters vary between the Small Magellanic Cloud (SMC), the solar neighbourhood, M33, and M51. Lamers et al. (2005b) then found a correlation between the disruption rate and the ambient density within the host galaxy, approximately following the theoretically predicted relations by Portegies Zwart et al. (1998) and Baumgardt & Makino (2003). The one exception was the interacting galaxy M51, which turned out to have a disruption rate that is an order of magnitude higher than expected. We later showed in Kruijssen et al. (2012) that such an increase can be explained by considering the growth of the gas density during galaxy interactions, and the correspondingly enhanced disruption rate due to tidal shocks. Similarly, the single-parameter approach of a disruption rate that is constant in time and space does not successfully describe the cluster population of the interacting Antennae galaxies (Gieles & Bastian 2008). While the above examples clearly show that the galactic environment influences cluster disruption and hence is an essential factor in setting the properties of the cluster population, it is also evident that the assumption of a single disruption rate throughout space and time only holds for a certain subset of (quiescent) galaxies. This assumption has recently been overcome in Kruijssen et al. (2011), where we expanded the Utrecht disruption model by including it in numerical simulations of galaxy evolution, in which the disruption rate is determined for each cluster individually, accounting for the steady tidal field as well as for tidal shocks. The numerical models self-consistently follow the impact of the galactic environment on cluster disruption, and have been used to show that encounters with giant molecular clouds are the dominant disruption mechanism in disk galaxies (also see Gieles et al. 2006; Lamers & Gieles 2006). They have also been applied to predict how the cluster age distribution changes under different galactic conditions, providing some characteristic features that can be verified in observational work. For instance, we have shown that the mean disruption rate of a cluster population decreases with age (also see Elmegreen & Hunter 2010), due to the preferential survival of clusters in quiescent environments ('natural selection') and their migration away from their dense, natal environment. Observational evidence for such variations has been found by Bastian et al. (2011, 2012).",
"pages": [
2,
3
]
},
{
"title": "3. Star cluster populations as tracers of galaxy evolution",
"content": "There are numerous ways in which the properties of the star cluster population may be used to derive the galaxy evolutionary history. In this section, we discuss some examples and provide an outlook for how this avenue can be expanded in future work. The decrease of the disruption rate with age affects the slope of the cluster age distribution over the age range in which cluster migration and natural selection act on the cluster population. Both effects are most important in galaxies with a high density contrast between star-forming regions and their surroundings (Kruijssen et al. 2011). Because migration occurs on the global dynamical timescale of a system, it can be used to infer the duration of certain events in the history of the galaxy. For instance, it indicates the interaction timescale of an ongoing galaxy collision, or the dynamical timescale of an isolated galaxy. The latter tracer can be verified using an example. The dynamical timescale of the disc galaxy M83 is 1 / Ω ∼ 20 Myr, and there are indications of an evolving disruption rate over the same age range (Bastian et al. 2011, 2012). Another illustration of how the galactic environment affects the cluster population was found in Kruijssen et al. (2012), where we performed numerical simulations of major mergers of disc galaxies, again including a model for the evolution of the cluster population. In galaxy mergers, tidal torques drive the gas towards the galaxy centres. As a result, the disruption of clusters by dense giant molecular clouds (Gieles et al. 2006) is prevalent, and counteracts a simultaneous increase of the cluster formation rate. The number of clusters in the merger remnant is therefore lower than in the progenitor disc galaxies. This can be quantified as a 'survival cluster fraction', which we have found to decrease with the starburst intensity (or increase with the gas depletion timescale). Number counts of stellar clusters in merger remnants could thus be used to infer the characteristics of the preceding galaxy interaction and starburst. Extrapolating the approach of tracing galaxy-scale events using the surviving cluster population, old globular clusters are exemplary targets for similar analyses, because they may be used to infer the conditions of galaxy formation at high redshift. Although they have substantially higher characteristic masses than young clusters in nearby galaxies, it has been argued that globular clusters formed through the same physical mechanisms that we see locally (Elmegreen & Efremov 1997; Kruijssen & Cooper 2012). Their high average mass then implies that the vast majority of lower-mass globular clusters must have been disrupted due to dynamical evolution. However, the degree of disruption appears to be universal, which is hard to understand considering the widely varying galactic environments in which globular clusters currently reside.",
"pages": [
3
]
},
{
"title": "Kruijssen",
"content": "The efficient destruction of clusters in dense, star-forming environments might provide a solution. Globular clusters all formed in the dense, high-redshift universe, and if most of their disruption occurred early on, their present-day properties should be similar (Elmegreen 2010; Kruijssen et al. 2012). If true, this puts constraints on the high-redshift conditions under which globular clusters formed. The origin of globular clusters is far from being a solved problem. The above scenario is a plausible solution, but it is generalised from physical systems that may not be adequate. It is thought that globular clusters did not form in major mergers, but instead have their roots in starburst dwarf galaxies, unstable high-redshift discs, and other highredshift, star-forming environments (see Kruijssen et al. 2012 and references therein). While it seems reasonable that these conditions were equally disruptive as the starbursts in our galaxy merger simulations, this requires explicit verification. Numerical simulations of galaxy formation with cosmologically motivated initial conditions (e.g. Prieto & Gnedin 2008) will be necessary to provide a definitive answer. Acknowledgments. I am very grateful to the former SIU staff - Henny Lamers in particular - for their unlimited dedication to science and teaching.",
"pages": [
4
]
},
{
"title": "References",
"content": "Baumgardt H., 2001, MNRAS, 325, 1323 Boutloukos S. G., Lamers H. J. G. L. M., 2003, MNRAS, 338, 717 Elmegreen B. G., 2010, ApJ, 712, L184 Elmegreen B. G., Efremov Y. N., 1997, ApJ, 480, 235 Gnedin O. Y., Ostriker J. P., 1997, ApJ, 474, 223 Kruijssen J. M. D., Cooper A. P., 2012, MNRAS, 420, 340 Kruijssen J. M. D., Pelupessy F. I., Lamers H. J. G. L. M., Portegies Zwart S. F., Bastian N., Icke V., 2012, MNRAS, 421, 1927 Kruijssen J. M. D., Pelupessy F. I., Lamers H. J. G. L. M., Portegies Zwart S. F., Icke V., 2011, MNRAS, 414, 1339 Lamers H. J. G. L. M., Gieles M., 2006, A&A, 455, L17 Lamers H. J. G. L. M., Gieles M., Bastian N., Baumgardt H., Kharchenko N. V., Portegies Zwart S., 2005a, A&A, 441, 117 Lamers H. J. G. L. M., Gieles M., Portegies Zwart S. F., 2005b, A&A, 429, 173 Larsen S. S., 2009, A&A, 494, 539 Ostriker J. P., Spitzer L. J., Chevalier R. A., 1972, ApJ, 176, L51+ Portegies Zwart S. F., Hut P., Makino J., McMillan S. L. W., 1998, A&A, 337, 363 Prieto J. L., Gnedin O. Y., 2008, ApJ, 689, 919",
"pages": [
4
]
}
]
2013AcFut...7...67D
https://arxiv.org/pdf/1308.6766.pdf
<document>
<section_header_level_1><location><page_1><loc_17><loc_75><loc_83><loc_81></location>Atomic clocks: new prospects in metrology and geodesy</section_header_level_1>
<text><location><page_1><loc_35><loc_71><loc_67><loc_73></location>Pacˆome Delva ∗ , J'erˆome Lodewyck</text>
<text><location><page_1><loc_13><loc_67><loc_89><loc_68></location>LNE-SYRTE, Observatoire de Paris, CNRS, UPMC ; 61 avenue de l'Observatoire, 75014 Paris, France</text>
<text><location><page_1><loc_41><loc_64><loc_59><loc_65></location>September 2, 2013</text>
<section_header_level_1><location><page_1><loc_12><loc_58><loc_23><loc_60></location>Abstract</section_header_level_1>
<text><location><page_1><loc_12><loc_43><loc_49><loc_56></location>We present the latest developments in the field of atomic clocks and their applications in metrology and fundamental physics. In the light of recent advents in the accuracy of optical clocks, we present an introduction to the relativistic modelization of frequency transfer and a detailed review of chronometric geodesy.</text>
<section_header_level_1><location><page_1><loc_12><loc_37><loc_32><loc_39></location>1 Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_19><loc_49><loc_35></location>Atomic clocks went through tremendous evolutions and ameliorations since their invention in the middle of the twentieth century. The constant amelioration of their accuracy (figure 1) and stability permitted numerous applications in the field of metrology and fundamental physics. For a long time cold atom Caesium fountain clocks remained unchallenged in terms of accuracy and stability. However this is no longer</text>
<text><location><page_1><loc_14><loc_16><loc_15><loc_17></location>∗</text>
<text><location><page_1><loc_15><loc_16><loc_25><loc_17></location>Corresponding</text>
<text><location><page_1><loc_27><loc_16><loc_32><loc_17></location>author.</text>
<text><location><page_1><loc_38><loc_16><loc_49><loc_17></location>E-mail: Pa-</text>
<text><location><page_1><loc_12><loc_14><loc_28><loc_15></location>[email protected]</text>
<figure>
<location><page_1><loc_51><loc_35><loc_87><loc_52></location>
<caption>Figure 1: Accuracy records for microwave and optical clocks. From the first Cs clock by Essen and Parry in the 1950's, an order of magnitude is gained every ten years. The advent of optical frequency combs boosted the performances of optical clocks, and they recently overcome microwave clocks.</caption>
</figure>
<text><location><page_2><loc_12><loc_69><loc_49><loc_84></location>true with the recent development of optical clocks. This new generation of atomic clock opens new possibilities for applications, such as chronometric geodesy, and requires new developments, particularly in the field of frequency transfer. The LNE-SYRTE laboratory (CNRS/LNE/Paris Observatory/UPMC) is involved in many aspects of the development of atomic clocks and their applications.</text>
<text><location><page_2><loc_12><loc_47><loc_49><loc_68></location>In section 2 we present the latest developments in the field of atomic clocks: microwave clocks, optical clocks, their relation to international time-scales, means of comparisons and applications. Section 3 is an introduction to relativistic time transfer, the modelization of remote frequency comparisons, which lies at the heart of many applications of atomic clocks, such as the realization of international time-scales and chronometric geodesy. Finally, section 4 is a detailed review of the field of chronometric geodesy, an old idea which could become reality in the near future.</text>
<section_header_level_1><location><page_2><loc_12><loc_39><loc_34><loc_41></location>2 Atomic clocks</section_header_level_1>
<text><location><page_2><loc_12><loc_14><loc_49><loc_36></location>In 1967, the definition of the SI second was changed from astronomical references to atomic references by setting the frequency of an hyperfine transition in the Cs atom [39]. Since then, the accuracy of atomic clocks has improved by five orders of magnitude, enabling better and better time-keeping. More recently, a new generation of atomic clocks, based on atomic transitions in the optical domain are challenging the well established Cs standard and thus offer opportunities for new applications in fundamental physics and geodesy.</text>
<section_header_level_1><location><page_2><loc_51><loc_83><loc_74><loc_84></location>2.1 Microwave clocks</section_header_level_1>
<text><location><page_2><loc_51><loc_41><loc_88><loc_82></location>In a microwave atomic frequency standard, a microwave electro-magnetic radiation excites an hyperfine electronic transition in the ground state of an atomic species. Observing the fraction of excited atoms p after this interaction (or transition probability) gives an indicator of the difference between the frequency ν of the microwave radiation and the frequency ν 0 of the hyperfine atomic transition. This frequency difference ν -ν 0 (or error signal) is fed in a servo-loop that keeps the microwave radiation resonant with the atomic transition. According to Fourier's relation, the frequency resolution that can be achieved after such an interrogation procedure grows as the inverse of the interaction time T , and since consecutive interrogations are uncorrelated, the frequency resolution further improves as the square root of the total integration time τ . Quantitatively, the residual frequency fluctuation of the microwave radiation locked on the atomic resonance are (in dimension-less fractional units, that is to say divided by the microwave frequency):</text>
<formula><location><page_2><loc_60><loc_36><loc_88><loc_40></location>σ y ( τ ) = ξ ν 0 T √ N √ T c τ , (1)</formula>
<text><location><page_2><loc_51><loc_14><loc_88><loc_35></location>where T c is the cycle time (such that τ/T c is the number of clock interrogations), and N is the number of simultaneously (and independently) interrogated atoms. ξ is a numerical constant, close to unity, that depends on the physics of the interaction between the radiation and the atoms. This expression is the ultimate frequency (in)stability of an atomic clock, also called the Quantum Projection Noise (QPN) limit, referring to the quantum nature of the interaction between the radiation and the atoms. It is eventually reached if all</text>
<text><location><page_3><loc_12><loc_81><loc_49><loc_84></location>other sources of noise in the servo-loop are made negligible.</text>
<text><location><page_3><loc_12><loc_71><loc_49><loc_81></location>As seen from eq. (1), an efficient way to improve the clock stability is to increase the interaction time T . The first atomic clocks therefore comprised a long tube in which a thermal beam of Cs atoms is travelling while interacting with the microwave radiation.</text>
<text><location><page_3><loc_12><loc_50><loc_49><loc_71></location>The advance in the physics of cold atoms enabled to prepare atoms with a smaller velocity and consequently largely increase the interaction time, thus the frequency stability of atomic standards. In cold atoms clocks, the interrogation time is only limited by the time after which the atoms, exposed to gravity, escape the interrogation zone. In the atomic fountain clock (see fig. 2), a set of cold atoms are launched vertically in the interaction zone and are interrogated during their parabolic flight in the Earth gravitational field.</text>
<text><location><page_3><loc_12><loc_42><loc_49><loc_50></location>In micro-gravity, atoms are not subject to the Earth gravitational field and thus can be interrogated during a longer time window T . This will be the case for the Pharao space microwave clock [7].</text>
<text><location><page_3><loc_12><loc_28><loc_49><loc_41></location>The reproducibility of an atomic clock stems from the fact that all atoms of a given species are rigorously indistinguishable. For instance, two independent atomic clocks based on caesium will produce the same frequency (9,192,631,770 Hz exactly in the SI unit system), regardless of their manufacturer or their location in space-time.</text>
<text><location><page_3><loc_12><loc_14><loc_49><loc_28></location>However, in laboratory conditions, atoms are surrounded by an experimental environment that perturbs their electronic state and thus slightly modify their resonance frequency in a way that depends on experimental conditions. For instance, atoms will interact with DCor AC electro-magnetic perturbations, will be sensitive to collisions between them in a</text>
<text><location><page_3><loc_49><loc_11><loc_50><loc_12></location>3</text>
<figure>
<location><page_3><loc_51><loc_44><loc_87><loc_85></location>
<caption>Figure 2: Atomic fountain clock. About 10 6 cold atoms, at a temperature of 1 µ K are launched upwards by pushing laser beams. At the beginning and the end of their trajectory, they interact with a microwave radiation in a resonator and the hyperfine transition probability is measured by an optical detection. When scanning the microwave frequency, the transition probability follows a fringe (Ramsey) pattern much like a double slit interference pattern. During the clock operation, the microwave frequency is locked on the top of the central fringe. The frequency stability, defined by eq. (1), is a few 10 -14 after 1 s, and a statistical resolution down to 10 -16 is reached after a few days of continuous operation [12, 30].</caption>
</figure>
<text><location><page_4><loc_12><loc_64><loc_49><loc_84></location>way that depends on the atomic density or to the Doppler effect resulting from their residual motion. . . Such systematic effects, if not evaluated and correctd for, limit the universality of the atomic standard. Consequently, the accuracy of a clock quantifies the uncertainty on these systematic effects. Currently, the best microwave atomic fountain clocks have a relative accuracy of 2 × 10 -16 , which is presumably their ultimate performances given the many technical obstacles to further improve this accuracy.</text>
<section_header_level_1><location><page_4><loc_12><loc_60><loc_43><loc_61></location>2.2 SI second and time scales</section_header_level_1>
<text><location><page_4><loc_12><loc_14><loc_49><loc_59></location>About 250 clocks worldwide, connected by time and frequency transfer techniques (mainly through GNSS signals) realize a complete architecture that enable the creation of atomic time scales. For this, local time scales physically generated by metrology laboratories are a posteriori compared and common time-scales are decided upon. the International Bureau for Weights and Measures (BIPM) in S'evres (France) is responsible for establishing the International Atomic Time (TAI). First a free atomic time-scale is build, the EAL. However, this time-scale is freerunning and the participating clocks do not aim at realizing the SI second. The rate of EAL is measured by comparison with a few number of caesium atomic fountains which aim at realizing the SI second, and TAI is then derived from EAL by applying a rate correction, so that the scale unit of TAI is the SI second as realized on the rotating geoid [11]. It necessary to take into account the atomic fontain clocks frequency shift due to relativity (see section 3). Recently, a change of paradigm occured in the definition of TAI. According to UAI resolutions [36], TAI is a real-</text>
<text><location><page_4><loc_51><loc_68><loc_88><loc_84></location>ization of Terrestrial Time (TT), which is defined by applying a constant rate correction to Geocentric Coordinate Time (TCG). This definition has been adopted so that the reference surface of TAI is no longer the geoid, which is not a stable surface (see section 4). Finally, the Coordinated Universal Time (UTC) differs from TAI by an integer number of second in order to follow the irregularities of the Earth rotation.</text>
<text><location><page_4><loc_51><loc_61><loc_88><loc_67></location>The publication of such time-scales enables world-wide comparison of Cs fountain clocks [30, 31] and the realization of the SI second.</text>
<section_header_level_1><location><page_4><loc_51><loc_56><loc_71><loc_58></location>2.3 Optical clocks</section_header_level_1>
<text><location><page_4><loc_51><loc_14><loc_88><loc_55></location>A new generation of atomic clocks have appeared in the last 15 years. These clocks consist in locking an electromagnetic radiation in the optical domain ( ν = 300 to 800 THz) to a narrow electronic transition. As seen from eq. (1), increasing the frequency ν 0 of the clock frequency by several orders of magnitude drastically improves the ultimate clock stability, even though the number of interrogated atoms N is usually smaller in optical clocks. Increasing the clock frequency also improves the clock accuracy since most systematic effects (sensitivity to DC electromagnetic fields, cold collisions. . . ) are of the same order of magnitude in frequency units, and thus decrease in relative units. However, two notable exceptions remain, and both have triggered recent research in optical clocks. First, the sensitivity of the clock transition frequency on the ambient black-body radiation is mostly rejected in microwave clocks but not for optical transitions. Thus, the uncertainty on this effect usually only marginally improves when going to optical clocks (with</text>
<figure>
<location><page_5><loc_12><loc_45><loc_49><loc_80></location>
<caption>Figure 3: Sr optical lattice clock. The clock laser, prestabilized on an ultra-stable optical cavity, probes an optical transition of 10 4 atoms confined in an optical lattice. The excitation fraction (or transition probability) is detected by a fluorescence imaging and a numerical integrator acts on a frequency shifter (FS) to keep the laser on resonance with the atomic transition. The width of the resonance is Fourier-limited at 3 Hz, which, given the clock frequency ν 0 = 429 THz, yields a resonance quality factor Q = 1 . 4 × 10 14 , compared to 10 10 for microwave clocks.</caption>
</figure>
<text><location><page_5><loc_51><loc_69><loc_88><loc_84></location>the notable exception of a few atomic species such as Al + for which the sensitivity is accidentally small). Therefore, extra care has to be taken to control the temperature of the atoms environment. Second, the Doppler frequency shift δν due to the residual velocity v of the atoms scales as the clock frequency ν 0 , such that the relative frequency shift remains constant:</text>
<formula><location><page_5><loc_66><loc_65><loc_88><loc_69></location>δν ν 0 = v c (2)</formula>
<text><location><page_5><loc_51><loc_14><loc_88><loc_64></location>For this reason, the fountain architecture, for which the Doppler effect is one of the limitations, cannot be applicable to optical clocks, and the atoms have to be tightly confined in a trapping potential to cancel their velocity v . To achieve this goal, two different technologies have been developed. First, a single ion is trapped in a RF electric field. These ion optical clocks [34, 8, 16, 25] achieve record accuracies at 9 × 10 -18 . However, since only a single ion is trapped ( N = 1 , because of the electrostatic repulsion of ions), the stability of theses clocks is limited at the QPN level of 2 × 10 -15 at 1 s. Second, a more recent technology involves trapping of a few thousands neutral atoms in a powerful laser standing wave (or optical lattice) by the dipolar force. Due to its power, this trapping potential is highly perturbative, but for a given ' magic ' wavelength of the trapping light [38], the perturbation is equal for the two clock levels, hence cancelled for the clock transition frequency. These optical lattice clocks [38, 21, 29, 23, 26] have already reached an accuracy of 1 × 10 -16 and are rapidly catching up with ion clocks. Furthermore, the large number of interrogated atoms allowed the demonstration of unprecedented stabilities (a few 1 × 10 -16 at 1 s), heading toward their QPN below 1 × 10 -17 at 1 s.</text>
<section_header_level_1><location><page_6><loc_12><loc_81><loc_49><loc_84></location>2.4 Remote comparison of optical frequencies</section_header_level_1>
<text><location><page_6><loc_12><loc_49><loc_49><loc_79></location>The recent breakthrough of performances of optical clocks was permitted by the development of frequency combs [44], which realizes a 'ruler' in the frequency domain. These lasers enable the local comparison of different optical frequencies and comparisons between optical and microwave frequencies. However, although optical clocks now largely surpass microwave clocks, a complete architecture has to be established to enable remote comparison of optical frequencies, in order to validate the accuracy of optical clocks, build 'optical' time-scales, or enable applications of optical clocks such as geodesic measurements Indeed, the conventional remote frequency comparisons techniques, mainly through GPS links, cannot reach the level of stability and accuracy realized by optical clocks.</text>
<section_header_level_1><location><page_6><loc_12><loc_45><loc_21><loc_46></location>Fibre links</section_header_level_1>
<text><location><page_6><loc_12><loc_14><loc_49><loc_43></location>To overcome the limitations of remote clock comparisons using GNSS signals, comparison techniques using optical fibres are being developed. For this, a stable and accurate frequency signal produced by an optical clock is sent through a fibre optics that links metrology institutes, directly encoded in the phase of the optical carrier. Because of vibrations and temperature fluctuations, the fibre adds a significant phase noise to the signal. This added noise is measured by comparing the signal after a round trip in the fibre to the original signal, and subsequently cancelled. Such a signal can be transported through a dedicated fibre (dark fibre) when available [33], or, more practically along with the internet communication (dark channel) [24]. These compari-</text>
<text><location><page_6><loc_51><loc_57><loc_88><loc_84></location>son techniques are applicable at a continental scale ; such a network will presumably be in operation throughout Europe in the near future. In particular, the REFIMEVE+ project will provide a shared stable optical oscillator between a large number of laboratories in France, with a number of applications beside metrology. This network will be connected to international fibre links (NEAT-FT project 1 ) that will enable long distance comparisons between optical frequency standards located in various national metrology laboratories in Europe. The ITOC project 2 aims at collecting these comparisons result to demonstrate high accuracy frequency ratios measurements and geophysical applications.</text>
<section_header_level_1><location><page_6><loc_51><loc_53><loc_66><loc_54></location>Space-based links</section_header_level_1>
<text><location><page_6><loc_51><loc_33><loc_88><loc_52></location>When considering inter-continental time and frequency comparisons, only satellite link are conceivable. In this aspect, The two-way satellite time and frequency transfer (TWSTFT) involves a satellite that actively relays a frequency signal in a round-trip configuration. Also, the space mission Pharao-ACES [7] that involves an ensemble of clocks on board the International Space Station will comprise a number of ground receiver able to remotely compare optical clocks.</text>
<section_header_level_1><location><page_6><loc_51><loc_24><loc_88><loc_30></location>2.5 Towards a new definition of the SI second based on optical clocks</section_header_level_1>
<text><location><page_6><loc_51><loc_20><loc_88><loc_23></location>Unlike microwave clocks, for which Cs has been an unquestionable choice over half a cen-</text>
<text><location><page_7><loc_12><loc_59><loc_49><loc_84></location>tury, a large number of atomic species seem to be equally matched as a new frequency standard based on an optical transition. Ion clocks with Hg + , Al + , Yb + , Sr + , Ca + have been demonstrated, as well as optical lattice clocks with Sr, Yb and more prospectively Hg and Mg. As an illustration, four optical transitions have already been approved by the CIPM (International Committee for Weights and Measures) as secondary representation of the SI second. Therefore, although the SI second would already gain in precision with optical clock, a clear consensus has yet to emerge before the current microwave defined SI second can be replaced.</text>
<section_header_level_1><location><page_7><loc_12><loc_55><loc_48><loc_56></location>2.6 Applications of optical clocks</section_header_level_1>
<text><location><page_7><loc_12><loc_14><loc_49><loc_53></location>The level of accuracy reached by optical clocks opens a new range of applications, through the very precise frequency ratios measurements they enable. In fundamental physics, they enable the tracking of dimension-less fundamental constants such as the fine structure constant α , the electron to proton mass ratio µ = m e /m p , or the quantum chromodynamics mass scale m q / Λ QCD. Because each clock transition frequency have a different dependence on these constants, their variations imply drifts in clock frequency ratios that can be detected by repeated measurements. Currently, combined optical-tooptical and optical-to-microwave clock comparisons put an upper bound on the relative variation of fundamental constants in the 10 -17 /yr range [34, 13, 21, 22]. Other tests of fundamental physics are also possible with atomic clocks. The local position invariance can be tested by comparing frequency ratios in the course of the earth rotation around the earth [13, 21], and the gravitational red-shift</text>
<text><location><page_7><loc_51><loc_81><loc_88><loc_84></location>will be tested with clocks during the PharaoACES mission.</text>
<text><location><page_7><loc_51><loc_69><loc_88><loc_81></location>The TAI time scale is created from Cs standards, but recently, the Rb microwave transition started to contribute. In the near future, secondary representations of the SI second based on optical transitions could contribute to TAI, which would thus benefit from their much improved stability.</text>
<text><location><page_7><loc_51><loc_41><loc_88><loc_68></location>Clock frequencies, when compared to a coordinate time-scale, are sensitive to the gravitational potential of the Earth (see section 3). Therefore it is necessary to take into account their relative height difference when building atomic time-scales such as TAI. However, the most accurate optical clocks can resolve a height difference below 10 cm, which is a scale at which the global gravitational potential is unknown. Because of this, optical clock could become a tool to precisely measure this potential. They come as a decisive addition to relative and absolute gravimeters which are sensitive to the gravitational field, and to satellite based measurement which lack spatial resolution (see section 4).</text>
<section_header_level_1><location><page_7><loc_51><loc_32><loc_88><loc_36></location>3 Relativistic frequency transfer</section_header_level_1>
<text><location><page_7><loc_51><loc_14><loc_88><loc_29></location>In distant comparisons of frequency standards, we are face with the problem of curvature of space and relative motion of the clocks. These two effects change locally the flow of proper time with respect to a global coordinate time. In this section we describe how to compare distant clock frequencies by means of an electromagnetic signal, and how the comparison is affected by these effects.</text>
<section_header_level_1><location><page_8><loc_12><loc_81><loc_33><loc_84></location>3.1 The Einstein Principle</section_header_level_1>
<figure>
<location><page_8><loc_15><loc_60><loc_29><loc_74></location>
</figure>
<figure>
<location><page_8><loc_32><loc_60><loc_46><loc_74></location>
<caption>Figure 4: A photon of frequency ν A is emitted at point A toward point B, where the measured frequency is ν B . a) A and B are two points at rest in an accelerated frame, with acceleration glyph[vector]a in the same direction as the emitted photon. b) A and B are at rest in a non accelerated (locally inertial) frame in presence of a gravitational field such that glyph[vector]g = -glyph[vector]a .</caption>
</figure>
<text><location><page_8><loc_12><loc_14><loc_49><loc_43></location>Before we treat the general case, let's try to understand in simple terms what is the frequency shift effect. Indeed, it can be seen as a direct consequence of the Einstein Equivalence Principle (EEP), one of the pillars of modern physics [27, 41]. Let's consider a photon emitted at a point A in an accelerated reference system, toward a point B which lies in the direction of the acceleration (see fig.4). We assume that both point are separated by a distance h 0 , as measured in the accelerated frame. The photon time of flight is δt = h 0 /c , and the frame velocity during this time increases by δv = aδt = ah 0 /c , where a is the magnitude of the frame acceleration glyph[vector]a . The frequency at point B (reception) is then shifted because of Doppler effect, compared to the frequency at</text>
<text><location><page_8><loc_37><loc_83><loc_57><loc_84></location>Equivalence point A</text>
<section_header_level_1><location><page_8><loc_57><loc_83><loc_78><loc_84></location>(emission), by an amount:</section_header_level_1>
<formula><location><page_8><loc_59><loc_78><loc_88><loc_82></location>ν B ν A = 1 -δv c = 1 -ah 0 c 2 (3)</formula>
<text><location><page_8><loc_51><loc_69><loc_88><loc_77></location>Now, the EEP postulates that a gravitational field glyph[vector]g is locally equivalent to an acceleration field glyph[vector]a = -glyph[vector]g . We deduce that in a non accelerated (locally inertial) frame in presence of a gravitational field glyph[vector]g :</text>
<formula><location><page_8><loc_63><loc_64><loc_88><loc_68></location>ν B ν A = 1 -gh 0 c 2 (4)</formula>
<text><location><page_8><loc_51><loc_45><loc_88><loc_63></location>where g = | glyph[vector]g | , ν A is the photon frequency at emission (strong gravitational potential) and ν B is the photon frequency at reception (weak gravitational field). As ν B < ν A , it is usual to say that the frequency at the point of reception is 'red-shifted'. One can consider it in terms of conservation of energy. Intuitively, the photon that goes from A to B has to 'work' to be able to escape the gravitational field, then it looses energy and its frequency decreases by virtue of E = hν , with h the Planck constant.</text>
<figure>
<location><page_8><loc_51><loc_26><loc_88><loc_43></location>
<caption>Figure 5: Two clocks A and B are measuring proper time along their trajectory. One signal with phase S is emitted by A at proper time τ A , and another one with phase S + d S at time τ A + d τ A . They are received by clock B respectively at time τ B and τ + d τ B .</caption>
</figure>
<section_header_level_1><location><page_9><loc_12><loc_83><loc_31><loc_84></location>3.2 General case</section_header_level_1>
<text><location><page_9><loc_12><loc_65><loc_49><loc_81></location>The principle of frequency comparison is to measure the frequency of an electromagnetic signal with the help of the emitting clock, A , and then with the receiving clock, B . We obtain respectively two measurements ν A and ν B 3 . Let S ( x α ) be the phase of the electromagnetic signal emitted by clock A . It can be shown that light rays are contained in hypersurfaces of constant phase. The frequency measured by A/B is:</text>
<formula><location><page_9><loc_23><loc_60><loc_49><loc_63></location>ν A/B = 1 2 π d S d τ A/B (5)</formula>
<text><location><page_9><loc_12><loc_53><loc_49><loc_58></location>where τ A/B is the proper time along the worldline of clock A/B (see fig.5). We introduce the wave vector k A/B α = ( ∂ α S ) A/B to obtain:</text>
<formula><location><page_9><loc_22><loc_48><loc_49><loc_51></location>ν A/B = 1 2 π k A/B α u α A/B (6)</formula>
<text><location><page_9><loc_12><loc_41><loc_49><loc_46></location>where u α A/B = d x α A/B / d τ is the four-velocity of clock A/B . Finally, we obtain a fundamental relation for frequency transfer:</text>
<formula><location><page_9><loc_26><loc_36><loc_49><loc_40></location>ν A ν B = k A α u α A k B α u α B (7)</formula>
<text><location><page_9><loc_12><loc_28><loc_49><loc_34></location>This formula does not depend on a particular theory, and then can be used to perform tests of general relativity. Introducing v i = d x i / d t and ˆ k i = k i /k 0 , it is usually written as:</text>
<formula><location><page_9><loc_22><loc_21><loc_49><loc_26></location>ν A ν B = u 0 A u 0 B k A 0 k B 0 1 + ˆ k A i v i A c 1 + ˆ k B i v i B c (8)</formula>
<text><location><page_9><loc_51><loc_83><loc_74><loc_84></location>From eq. (5) we deduce that:</text>
<formula><location><page_9><loc_54><loc_78><loc_88><loc_81></location>ν A ν B = d τ B d τ A = ( d t d τ ) A d t B d t A ( d τ d t ) B (9)</formula>
<text><location><page_9><loc_51><loc_68><loc_88><loc_76></location>We suppose that space-time is stationary, ie. ∂ 0 g αβ = 0 . Then it can be shown that k 0 is constant along the light ray, meaning that k A 0 = k B 0 . We introduce the time transfer function:</text>
<formula><location><page_9><loc_60><loc_66><loc_88><loc_68></location>T ( x i A , x i B ) = t B -t A (10)</formula>
<text><location><page_9><loc_51><loc_62><loc_88><loc_65></location>Deriving the time transfer function with respect to t A one obtains:</text>
<formula><location><page_9><loc_62><loc_56><loc_88><loc_61></location>d t B d t A = 1 + ∂ T ∂x i A v i A 1 -∂ T ∂x i B v i B (11)</formula>
<text><location><page_9><loc_51><loc_52><loc_88><loc_55></location>Inserting eq. (11) in eq. (9), and comparing with eq. (8), we deduce:</text>
<formula><location><page_9><loc_58><loc_47><loc_88><loc_50></location>ˆ k A i = c ∂ T ∂x i A , ˆ k B i = -c ∂ T ∂x i B (12)</formula>
<text><location><page_9><loc_51><loc_43><loc_88><loc_46></location>General formula for non-stationary spacetimes can be found in [14, 20].</text>
<text><location><page_9><loc_51><loc_39><loc_88><loc_42></location>As an exemple, let's take the simple time transfer function:</text>
<formula><location><page_9><loc_55><loc_35><loc_88><loc_38></location>T ( x i A , x i B ) = R AB c + O ( 1 c 3 ) (13)</formula>
<text><location><page_9><loc_51><loc_30><loc_88><loc_33></location>where R AB = | R i AB | and R i AB = x i B -x i A . Then we obtain:</text>
<formula><location><page_9><loc_58><loc_24><loc_88><loc_29></location>d t B d t A = 1 + glyph[vector] N AB · glyph[vector]v A c + O ( 1 c 3 ) 1 + glyph[vector] N AB · glyph[vector]v B c + O ( 1 c 3 ) (14)</formula>
<text><location><page_9><loc_51><loc_14><loc_88><loc_23></location>where N i AB = R i AB /R AB . Up to the second order, this term does not depend on the gravitational field but on the relative motion of the two clocks. It is simply the first order Doppler effect.</text>
<text><location><page_10><loc_12><loc_78><loc_49><loc_84></location>The two other terms in eq. (9) depend on the relation between proper time and coordinate time. In a metric theory one has c 2 d τ = √ g αβ d x α d x β . We deduce that:</text>
<formula><location><page_10><loc_15><loc_70><loc_49><loc_76></location>u 0 A u 0 B = [ g 00 +2 g 0 i v i c + g ij v i v j c 2 ] 1 / 2 B [ g 00 +2 g 0 i v i c + g ij v i v j c 2 ] 1 / 2 A (15)</formula>
<section_header_level_1><location><page_10><loc_12><loc_64><loc_49><loc_68></location>3.3 Application to a static, spherically symmetric body</section_header_level_1>
<text><location><page_10><loc_12><loc_49><loc_49><loc_62></location>As an example, we apply this formalism for the case of a parametrized post-Minkowskian approximation of metric theories. This metric is a good approximation of the space-time metric around the Earth, for a class of theories which is larger than general relativity. Choosing spatial isotropic coordinates, we assume that the metric components can be written as:</text>
<formula><location><page_10><loc_15><loc_38><loc_49><loc_47></location>g 00 = -1 + 2( α +1) GM rc 2 + O ( 1 c 4 ) g 0 i = 0 (16) g ij = δ ij [ 1 + 2 γ GM rc 2 + O ( 1 c 4 )]</formula>
<text><location><page_10><loc_12><loc_31><loc_49><loc_36></location>where α and γ are two parameters of the theory (for general relativity α = 0 and γ = 1 ). Then:</text>
<formula><location><page_10><loc_13><loc_26><loc_49><loc_30></location>d τ d t = 1 -( α +1) GM rc 2 -v 2 2 c 2 + O ( 1 c 4 ) (17)</formula>
<text><location><page_10><loc_12><loc_19><loc_49><loc_24></location>where v = √ δ ij v i v j . The time transfer function of such a metric is given in eq. (108) of [20]. Then we calculate:</text>
<formula><location><page_10><loc_23><loc_14><loc_49><loc_18></location>d t B d t A = q A + O ( 1 c 5 ) q B + O ( 1 c 5 ) (18)</formula>
<text><location><page_10><loc_51><loc_83><loc_56><loc_84></location>where</text>
<formula><location><page_10><loc_52><loc_74><loc_88><loc_82></location>q A =1 -glyph[vector] N AB · glyph[vector]v A c -2( γ +1) GM c 3 × (19) R AB glyph[vector] N A · glyph[vector]v A +( r A + r B ) glyph[vector] N AB · glyph[vector]v A ( r A + r B ) 2 -R 2 AB</formula>
<formula><location><page_10><loc_52><loc_64><loc_88><loc_72></location>q B =1 -glyph[vector] N AB · glyph[vector]v B c -2( γ +1) GM c 3 × (20) R AB glyph[vector] N A · glyph[vector]v B -( r A + r B ) glyph[vector] N AB · glyph[vector]v B ( r A + r B ) 2 -R 2 AB</formula>
<text><location><page_10><loc_51><loc_56><loc_88><loc_63></location>Let assume that both clocks are at rest with respect to the chosen coordinate system, ie. glyph[vector]v A = glyph[vector] 0 = glyph[vector]v B and that r A = r 0 and r B = r 0 + δr , where δr glyph[lessmuch] r 0 . Then we find:</text>
<formula><location><page_10><loc_52><loc_52><loc_88><loc_55></location>ν A -ν B ν B = ( α +1) GM r 2 0 c 2 δr + O ( 1 c 4 ) (21)</formula>
<text><location><page_10><loc_51><loc_46><loc_88><loc_51></location>The same effect can be calculated with a different, not necessarily symmetric gravitational potential w ( t, x i ) . The results yields:</text>
<formula><location><page_10><loc_54><loc_41><loc_88><loc_44></location>ν A -ν B ν B = w A -w B c 2 + O ( 1 c 4 ) (22)</formula>
<text><location><page_10><loc_51><loc_18><loc_88><loc_40></location>This is the classic formula given in textbooks for the 'gravitational red-shift'. However one should bear in mind that this is valid for clocks at rest with respect to the coordinate system implicitly defined by the space-time metric (one uses usually the Geocentric Celestial Reference System), which is (almost) never the case. Moreover, the separation between a gravitational red-shift and a Doppler effect is specific to the approximation scheme used here. One can read the book by Synge [37] for a different interpretation in terms of relative velocity and Doppler effect only.</text>
<text><location><page_10><loc_51><loc_14><loc_88><loc_17></location>We note that the lowest order gravitational term in eq. (21) is a test of the Newtonian limit</text>
<text><location><page_11><loc_12><loc_68><loc_49><loc_84></location>of metric theories. Indeed, if one wants to recover the Newtonian law of gravitation for GM/rc 2 glyph[lessmuch] 1 and v glyph[lessmuch] 1 then it is necessary that α = 0 . Then this test is more fundamental than a test of general relativity, and can be interpreted as a test of Local Position Invariance (which is a part of the Einstein Equivalence Principle). See [41, 42] for more details on this interpretation, and a review of the experiments that tested the parameter α .</text>
<text><location><page_11><loc_12><loc_57><loc_49><loc_67></location>Amore realistic case of the space-time metric is treated in article [3], in the context of general relativity: all terms from the Earth gravitational potential are considered up to an accuracy of 5 . 10 -17 , specifically in prevision of the ACES mission [7].</text>
<section_header_level_1><location><page_11><loc_12><loc_52><loc_44><loc_53></location>4 Chronometric geodesy</section_header_level_1>
<text><location><page_11><loc_12><loc_35><loc_49><loc_50></location>Instead of using our knowledge of the Earth gravitational field to predict frequency shifts between distant clocks, one can revert the problem and ask if the measurement of frequency shifts between distant clocks can improve our knowledge of the gravitational field. To do simple orders of magnitude estimates it is good to have in mind some correspondences calculated thanks to eqs. (21) and (22):</text>
<formula><location><page_11><loc_19><loc_28><loc_49><loc_33></location>1 meter ↔ ∆ ν ν ∼ 10 -16 ↔ ∆ w ∼ 10 m 2 . s -2 (23)</formula>
<text><location><page_11><loc_12><loc_14><loc_49><loc_26></location>From this correspondence, we can already imagine two direct applications of clocks in geodesy: if we are capable to compare clocks to 10 -16 accuracy, we can determine height differences between clocks with one meter accuracy (levelling), or determine geopotential differences with 10 m 2 .s -2 accuracy.</text>
<section_header_level_1><location><page_11><loc_51><loc_81><loc_88><loc_84></location>4.1 A review of chronometric geodesy</section_header_level_1>
<text><location><page_11><loc_51><loc_42><loc_88><loc_79></location>The first article to explore seriously this possibility was written in 1983 by Martin Vermeer [40]. The article is named 'chronometric levelling'. The term 'chronometric' seems well suited for qualifying the method of using clocks to determine directly gravitational potential differences, as 'chronometry' is the science of the measurement of time. However the term 'levelling' seems too restrictive with respect to all the applications one could think of using the results of clock comparisons. Therefore we will use the term 'chronometric geodesy' to name the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, with the help of atomic clocks. It is sometimes named 'clock-based geodesy', or 'relativistic geodesy'. However this last designation is improper as relativistic geodesy aims at describing all possible techniques (including e.g. gravimetry and gradiometry) in a relativistic framework [18, 28, 35].</text>
<text><location><page_11><loc_51><loc_14><loc_88><loc_41></location>The natural arena of chronometric geodesy is the four-dimensional space-time. At the lowest order, there is proportionality between relative frequency shift measurements - corrected from the first order Doppler effect and (Newtonian) geopotential differences (see eq.(22)). To calculate this relation we have seen that we do not need the theory of general relativity, but only to postulate Local Position Invariance. Therefore, it is perfectly possible to use clock comparison measurements corrected from the first order Doppler effect as a direct measurement of geopotential differences in the framework of classical geodesy, if the measurement accuracy does not reach the magnitude of the higher order terms.</text>
<text><location><page_12><loc_12><loc_61><loc_49><loc_84></location>Comparisons between two clocks on the ground generally use a third clock in space. For the comparison between a clock on the ground and one in space, the terms of order c -3 in eqs. (19)-(20) reach a magnitude of ∼ 10 -15 and ∼ 3 × 10 -14 for respectively the ground and the space clock, if they are separated radially by 1000 km. Terms of order c -4 omitted in eqs. (21)-(22) can reach ∼ 5 × 10 -19 in relative frequency shift, which corresponds to a height difference of ∼ 5 mmand a geopotential difference of ∼ 5 × 10 -2 m 2 .s -2 . Clocks are far from reaching this accuracy today, but it cannot be excluded for the future.</text>
<text><location><page_12><loc_12><loc_18><loc_49><loc_60></location>In his article, Martin Vermeer explores the 'possibilities for technical realisation of a system for measuring potential differences over intercontinental distances' using clock comparisons [40]. The two main ingredients are of course accurate clocks and a mean to compare them. He considers hydrogen maser clocks. For the links he considers a 2-way satellite link over a geostationary satellite, or GPS receivers in interferometric mode. He has also to consider a mean to compare the proper frequencies of the different hydrogen maser clocks. However today this can be overcome by comparing Primary Frequency Standards (PFS), which have a well defined proper frequency based on a transition of Caesium 133, used for the definition of the second. However, this problem will rise again if one uses Secondary Frequency Standards which are not based on Caesium atoms. Then the proper frequency ratio between two different kinds of atomic clocks has to be determined locally. This is one of the purpose of the European project 'International timescales with optical clocks' 4 , where optical clocks based on dif-</text>
<text><location><page_12><loc_51><loc_74><loc_88><loc_84></location>ferent atoms will be compared one each other locally, and to the PFS. It is planned also to do a proof-of-principle experiment of chronometric geodesy, by comparing two optical clocks separated by a height difference of around 1 km using an optical fibre link.</text>
<text><location><page_12><loc_51><loc_31><loc_88><loc_74></location>In the foreseen applications of chronometric geodesy, Martin Vermeer mentions briefly intercontinental levelling, and the measurement of the true geoid (disentangled from geophysical sea surface effects) [40]. Few authors have seriously considered chronometric geodesy. Following Vermeer idea, Brumberg and Groten [5] demonstrated the possibility of using GPS observations to solve the problem of the determination of geoid heights, however leaving aside the practical feasibility of such a technique. Bondarescu et al. [4] discuss the value and future applicability of chronometric geodesy, including direct geoid mapping on continents and joint gravity-geopotential surveying to invert for subsurface density anomalies. They find that a geoid perturbation caused by a 1.5 km radius sphere with 20 per cent density anomaly buried at 2 km depth in the Earth's crust is already detectable by atomic clocks of achievable accuracy. Finally Chou et al. demonstrated the potentiality of the new generation of atomic clocks, based on optical transitions, to measure heights with a resolution of around 30 cm [9].</text>
<section_header_level_1><location><page_12><loc_51><loc_27><loc_81><loc_29></location>4.2 The chronometric geoid</section_header_level_1>
<text><location><page_12><loc_51><loc_23><loc_88><loc_26></location>Arne Bjerhammar in 1985 gives a precise definition of the 'relativistic geoid' [1, 2]:</text>
<text><location><page_12><loc_55><loc_14><loc_84><loc_21></location>'The relativistic geoid is the surface where precise clocks run with the same speed and the surface is nearest to mean sea level'</text>
<text><location><page_13><loc_12><loc_38><loc_49><loc_84></location>This is an operational definition. Soffel et al. [35] in 1988 translated this definition in the context of post-Newtonian theory. They also introduce a different operational definition of the relativistic geoid, based on gravimetric measurements: a surface orthogonal everywhere to the direction of the plumb-line and closest to mean sea level. He calls the two surfaces obtained with clocks and gravimetric measurements respectively the 'u-geoid' and the 'a-geoid'. He proves that these two surfaces coincide in the case of a stationary metric. In order to distinguish the operational definition of the geoid from its theoretical description, it is less ambiguous to give a name based on the particular technique to measure it. Relativistic geoid is too vague as Soffel et al. have defined two different ones. The names chosen by Soffel et al. are not particularly explicit, so instead of 'u-geoid' and 'a-geoid' one can call them chronometric and gravimetric geoid respectively. There can be no confusion with the geoid derived from satellite measurements, as this is a quasi-geoid that do not coincide with the geoid on the continents [15]. Other considerations on the chronometric geoid can be found in [18, 19, 28].</text>
<text><location><page_13><loc_12><loc_31><loc_49><loc_38></location>Let two clocks be at rest with respect to the chosen coordinate system ( v i = 0 ) in an arbitrary space-time. From formula (9), (11) and (15) we deduce that:</text>
<formula><location><page_13><loc_22><loc_26><loc_49><loc_30></location>ν A ν B = d τ B d τ A = [ g 00 ] 1 / 2 B [ g 00 ] 1 / 2 A (24)</formula>
<text><location><page_13><loc_12><loc_21><loc_49><loc_24></location>In this case the chronometric geoid is defined by the condition g 00 = cst.</text>
<text><location><page_13><loc_12><loc_14><loc_49><loc_21></location>Wenotice that the problem of defining a reference surface is closely related to the problem of realizing Terrestrial Time (TT). TT is defined with respect to Geocentric Coordinate</text>
<text><location><page_13><loc_51><loc_83><loc_80><loc_84></location>Time (TCG) by the relation [36, 32]:</text>
<formula><location><page_13><loc_62><loc_78><loc_88><loc_81></location>d TT d TCG = 1 -L G (25)</formula>
<text><location><page_13><loc_51><loc_43><loc_88><loc_77></location>where L G is a defining constant. This constant has been chosen so that TT coincides with the time given by a clock located on the classical geoid. It could be taken as a formal definition of the chronometric geoid [43]. If so, the chronometric geoid will differ in the future from the classical geoid: a level surface of the geopotential closest to the topographic mean sea level. Indeed, the value of the potential on the geoid, W 0 , depends on the global ocean level which changes with time [6]. With a value of d W 0 / d t ∼ 10 -3 m 2 .s -2 .y -1 , the difference in relative frequency between the classical and the chronometric geoid would be around 10 -18 after 100 years (the correspondence is made with the help of relations (23)). However, the rate of change of the global ocean level could change during the next decades. Predictions are highly model dependant [17].</text>
<section_header_level_1><location><page_13><loc_51><loc_38><loc_69><loc_40></location>5 Conclusion</section_header_level_1>
<text><location><page_13><loc_51><loc_14><loc_88><loc_36></location>We presented recent developments in the field of atomic clocks, as well as an introduction to relativistic frequency transfer and a detailed review of chronometric geodesy. If the control of systematic effects in optical clocks keep their promises, they could become very sensible to the gravitational field, which will ultimately degrade their stability at the surface of the Earth. One solution will be to send very stable and accurate clocks in space, which will become the reference against which the Earth clocks would be compared. Moreover, by sending at least four of these clocks in space,</text>
<text><location><page_14><loc_12><loc_80><loc_49><loc_84></location>it will be possible to realize a very stable and accurate four-dimensional reference system in space [10].</text>
<section_header_level_1><location><page_14><loc_12><loc_75><loc_26><loc_76></location>References</section_header_level_1>
<unordered_list>
<list_item><location><page_14><loc_13><loc_68><loc_49><loc_73></location>[1] A. Bjerhammar. On a relativistic geodesy. Bulletin Geodesique , 59:207220, 1985.</list_item>
<list_item><location><page_14><loc_13><loc_62><loc_49><loc_66></location>[2] A. Bjerhammar. Relativistic geodesy. Technical Report NON118 NGS36, NOAA Technical Report, 1986.</list_item>
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[
{
"title": "Atomic clocks: new prospects in metrology and geodesy",
"content": "Pacˆome Delva ∗ , J'erˆome Lodewyck LNE-SYRTE, Observatoire de Paris, CNRS, UPMC ; 61 avenue de l'Observatoire, 75014 Paris, France September 2, 2013",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "We present the latest developments in the field of atomic clocks and their applications in metrology and fundamental physics. In the light of recent advents in the accuracy of optical clocks, we present an introduction to the relativistic modelization of frequency transfer and a detailed review of chronometric geodesy.",
"pages": [
1
]
},
{
"title": "1 Introduction",
"content": "Atomic clocks went through tremendous evolutions and ameliorations since their invention in the middle of the twentieth century. The constant amelioration of their accuracy (figure 1) and stability permitted numerous applications in the field of metrology and fundamental physics. For a long time cold atom Caesium fountain clocks remained unchallenged in terms of accuracy and stability. However this is no longer ∗ Corresponding author. E-mail: Pa- [email protected] true with the recent development of optical clocks. This new generation of atomic clock opens new possibilities for applications, such as chronometric geodesy, and requires new developments, particularly in the field of frequency transfer. The LNE-SYRTE laboratory (CNRS/LNE/Paris Observatory/UPMC) is involved in many aspects of the development of atomic clocks and their applications. In section 2 we present the latest developments in the field of atomic clocks: microwave clocks, optical clocks, their relation to international time-scales, means of comparisons and applications. Section 3 is an introduction to relativistic time transfer, the modelization of remote frequency comparisons, which lies at the heart of many applications of atomic clocks, such as the realization of international time-scales and chronometric geodesy. Finally, section 4 is a detailed review of the field of chronometric geodesy, an old idea which could become reality in the near future.",
"pages": [
1,
2
]
},
{
"title": "2 Atomic clocks",
"content": "In 1967, the definition of the SI second was changed from astronomical references to atomic references by setting the frequency of an hyperfine transition in the Cs atom [39]. Since then, the accuracy of atomic clocks has improved by five orders of magnitude, enabling better and better time-keeping. More recently, a new generation of atomic clocks, based on atomic transitions in the optical domain are challenging the well established Cs standard and thus offer opportunities for new applications in fundamental physics and geodesy.",
"pages": [
2
]
},
{
"title": "2.1 Microwave clocks",
"content": "In a microwave atomic frequency standard, a microwave electro-magnetic radiation excites an hyperfine electronic transition in the ground state of an atomic species. Observing the fraction of excited atoms p after this interaction (or transition probability) gives an indicator of the difference between the frequency ν of the microwave radiation and the frequency ν 0 of the hyperfine atomic transition. This frequency difference ν -ν 0 (or error signal) is fed in a servo-loop that keeps the microwave radiation resonant with the atomic transition. According to Fourier's relation, the frequency resolution that can be achieved after such an interrogation procedure grows as the inverse of the interaction time T , and since consecutive interrogations are uncorrelated, the frequency resolution further improves as the square root of the total integration time τ . Quantitatively, the residual frequency fluctuation of the microwave radiation locked on the atomic resonance are (in dimension-less fractional units, that is to say divided by the microwave frequency): where T c is the cycle time (such that τ/T c is the number of clock interrogations), and N is the number of simultaneously (and independently) interrogated atoms. ξ is a numerical constant, close to unity, that depends on the physics of the interaction between the radiation and the atoms. This expression is the ultimate frequency (in)stability of an atomic clock, also called the Quantum Projection Noise (QPN) limit, referring to the quantum nature of the interaction between the radiation and the atoms. It is eventually reached if all other sources of noise in the servo-loop are made negligible. As seen from eq. (1), an efficient way to improve the clock stability is to increase the interaction time T . The first atomic clocks therefore comprised a long tube in which a thermal beam of Cs atoms is travelling while interacting with the microwave radiation. The advance in the physics of cold atoms enabled to prepare atoms with a smaller velocity and consequently largely increase the interaction time, thus the frequency stability of atomic standards. In cold atoms clocks, the interrogation time is only limited by the time after which the atoms, exposed to gravity, escape the interrogation zone. In the atomic fountain clock (see fig. 2), a set of cold atoms are launched vertically in the interaction zone and are interrogated during their parabolic flight in the Earth gravitational field. In micro-gravity, atoms are not subject to the Earth gravitational field and thus can be interrogated during a longer time window T . This will be the case for the Pharao space microwave clock [7]. The reproducibility of an atomic clock stems from the fact that all atoms of a given species are rigorously indistinguishable. For instance, two independent atomic clocks based on caesium will produce the same frequency (9,192,631,770 Hz exactly in the SI unit system), regardless of their manufacturer or their location in space-time. However, in laboratory conditions, atoms are surrounded by an experimental environment that perturbs their electronic state and thus slightly modify their resonance frequency in a way that depends on experimental conditions. For instance, atoms will interact with DCor AC electro-magnetic perturbations, will be sensitive to collisions between them in a 3 way that depends on the atomic density or to the Doppler effect resulting from their residual motion. . . Such systematic effects, if not evaluated and correctd for, limit the universality of the atomic standard. Consequently, the accuracy of a clock quantifies the uncertainty on these systematic effects. Currently, the best microwave atomic fountain clocks have a relative accuracy of 2 × 10 -16 , which is presumably their ultimate performances given the many technical obstacles to further improve this accuracy.",
"pages": [
2,
3,
4
]
},
{
"title": "2.2 SI second and time scales",
"content": "About 250 clocks worldwide, connected by time and frequency transfer techniques (mainly through GNSS signals) realize a complete architecture that enable the creation of atomic time scales. For this, local time scales physically generated by metrology laboratories are a posteriori compared and common time-scales are decided upon. the International Bureau for Weights and Measures (BIPM) in S'evres (France) is responsible for establishing the International Atomic Time (TAI). First a free atomic time-scale is build, the EAL. However, this time-scale is freerunning and the participating clocks do not aim at realizing the SI second. The rate of EAL is measured by comparison with a few number of caesium atomic fountains which aim at realizing the SI second, and TAI is then derived from EAL by applying a rate correction, so that the scale unit of TAI is the SI second as realized on the rotating geoid [11]. It necessary to take into account the atomic fontain clocks frequency shift due to relativity (see section 3). Recently, a change of paradigm occured in the definition of TAI. According to UAI resolutions [36], TAI is a real- ization of Terrestrial Time (TT), which is defined by applying a constant rate correction to Geocentric Coordinate Time (TCG). This definition has been adopted so that the reference surface of TAI is no longer the geoid, which is not a stable surface (see section 4). Finally, the Coordinated Universal Time (UTC) differs from TAI by an integer number of second in order to follow the irregularities of the Earth rotation. The publication of such time-scales enables world-wide comparison of Cs fountain clocks [30, 31] and the realization of the SI second.",
"pages": [
4
]
},
{
"title": "2.3 Optical clocks",
"content": "A new generation of atomic clocks have appeared in the last 15 years. These clocks consist in locking an electromagnetic radiation in the optical domain ( ν = 300 to 800 THz) to a narrow electronic transition. As seen from eq. (1), increasing the frequency ν 0 of the clock frequency by several orders of magnitude drastically improves the ultimate clock stability, even though the number of interrogated atoms N is usually smaller in optical clocks. Increasing the clock frequency also improves the clock accuracy since most systematic effects (sensitivity to DC electromagnetic fields, cold collisions. . . ) are of the same order of magnitude in frequency units, and thus decrease in relative units. However, two notable exceptions remain, and both have triggered recent research in optical clocks. First, the sensitivity of the clock transition frequency on the ambient black-body radiation is mostly rejected in microwave clocks but not for optical transitions. Thus, the uncertainty on this effect usually only marginally improves when going to optical clocks (with the notable exception of a few atomic species such as Al + for which the sensitivity is accidentally small). Therefore, extra care has to be taken to control the temperature of the atoms environment. Second, the Doppler frequency shift δν due to the residual velocity v of the atoms scales as the clock frequency ν 0 , such that the relative frequency shift remains constant: For this reason, the fountain architecture, for which the Doppler effect is one of the limitations, cannot be applicable to optical clocks, and the atoms have to be tightly confined in a trapping potential to cancel their velocity v . To achieve this goal, two different technologies have been developed. First, a single ion is trapped in a RF electric field. These ion optical clocks [34, 8, 16, 25] achieve record accuracies at 9 × 10 -18 . However, since only a single ion is trapped ( N = 1 , because of the electrostatic repulsion of ions), the stability of theses clocks is limited at the QPN level of 2 × 10 -15 at 1 s. Second, a more recent technology involves trapping of a few thousands neutral atoms in a powerful laser standing wave (or optical lattice) by the dipolar force. Due to its power, this trapping potential is highly perturbative, but for a given ' magic ' wavelength of the trapping light [38], the perturbation is equal for the two clock levels, hence cancelled for the clock transition frequency. These optical lattice clocks [38, 21, 29, 23, 26] have already reached an accuracy of 1 × 10 -16 and are rapidly catching up with ion clocks. Furthermore, the large number of interrogated atoms allowed the demonstration of unprecedented stabilities (a few 1 × 10 -16 at 1 s), heading toward their QPN below 1 × 10 -17 at 1 s.",
"pages": [
4,
5
]
},
{
"title": "2.4 Remote comparison of optical frequencies",
"content": "The recent breakthrough of performances of optical clocks was permitted by the development of frequency combs [44], which realizes a 'ruler' in the frequency domain. These lasers enable the local comparison of different optical frequencies and comparisons between optical and microwave frequencies. However, although optical clocks now largely surpass microwave clocks, a complete architecture has to be established to enable remote comparison of optical frequencies, in order to validate the accuracy of optical clocks, build 'optical' time-scales, or enable applications of optical clocks such as geodesic measurements Indeed, the conventional remote frequency comparisons techniques, mainly through GPS links, cannot reach the level of stability and accuracy realized by optical clocks.",
"pages": [
6
]
},
{
"title": "Fibre links",
"content": "To overcome the limitations of remote clock comparisons using GNSS signals, comparison techniques using optical fibres are being developed. For this, a stable and accurate frequency signal produced by an optical clock is sent through a fibre optics that links metrology institutes, directly encoded in the phase of the optical carrier. Because of vibrations and temperature fluctuations, the fibre adds a significant phase noise to the signal. This added noise is measured by comparing the signal after a round trip in the fibre to the original signal, and subsequently cancelled. Such a signal can be transported through a dedicated fibre (dark fibre) when available [33], or, more practically along with the internet communication (dark channel) [24]. These compari- son techniques are applicable at a continental scale ; such a network will presumably be in operation throughout Europe in the near future. In particular, the REFIMEVE+ project will provide a shared stable optical oscillator between a large number of laboratories in France, with a number of applications beside metrology. This network will be connected to international fibre links (NEAT-FT project 1 ) that will enable long distance comparisons between optical frequency standards located in various national metrology laboratories in Europe. The ITOC project 2 aims at collecting these comparisons result to demonstrate high accuracy frequency ratios measurements and geophysical applications.",
"pages": [
6
]
},
{
"title": "Space-based links",
"content": "When considering inter-continental time and frequency comparisons, only satellite link are conceivable. In this aspect, The two-way satellite time and frequency transfer (TWSTFT) involves a satellite that actively relays a frequency signal in a round-trip configuration. Also, the space mission Pharao-ACES [7] that involves an ensemble of clocks on board the International Space Station will comprise a number of ground receiver able to remotely compare optical clocks.",
"pages": [
6
]
},
{
"title": "2.5 Towards a new definition of the SI second based on optical clocks",
"content": "Unlike microwave clocks, for which Cs has been an unquestionable choice over half a cen- tury, a large number of atomic species seem to be equally matched as a new frequency standard based on an optical transition. Ion clocks with Hg + , Al + , Yb + , Sr + , Ca + have been demonstrated, as well as optical lattice clocks with Sr, Yb and more prospectively Hg and Mg. As an illustration, four optical transitions have already been approved by the CIPM (International Committee for Weights and Measures) as secondary representation of the SI second. Therefore, although the SI second would already gain in precision with optical clock, a clear consensus has yet to emerge before the current microwave defined SI second can be replaced.",
"pages": [
6,
7
]
},
{
"title": "2.6 Applications of optical clocks",
"content": "The level of accuracy reached by optical clocks opens a new range of applications, through the very precise frequency ratios measurements they enable. In fundamental physics, they enable the tracking of dimension-less fundamental constants such as the fine structure constant α , the electron to proton mass ratio µ = m e /m p , or the quantum chromodynamics mass scale m q / Λ QCD. Because each clock transition frequency have a different dependence on these constants, their variations imply drifts in clock frequency ratios that can be detected by repeated measurements. Currently, combined optical-tooptical and optical-to-microwave clock comparisons put an upper bound on the relative variation of fundamental constants in the 10 -17 /yr range [34, 13, 21, 22]. Other tests of fundamental physics are also possible with atomic clocks. The local position invariance can be tested by comparing frequency ratios in the course of the earth rotation around the earth [13, 21], and the gravitational red-shift will be tested with clocks during the PharaoACES mission. The TAI time scale is created from Cs standards, but recently, the Rb microwave transition started to contribute. In the near future, secondary representations of the SI second based on optical transitions could contribute to TAI, which would thus benefit from their much improved stability. Clock frequencies, when compared to a coordinate time-scale, are sensitive to the gravitational potential of the Earth (see section 3). Therefore it is necessary to take into account their relative height difference when building atomic time-scales such as TAI. However, the most accurate optical clocks can resolve a height difference below 10 cm, which is a scale at which the global gravitational potential is unknown. Because of this, optical clock could become a tool to precisely measure this potential. They come as a decisive addition to relative and absolute gravimeters which are sensitive to the gravitational field, and to satellite based measurement which lack spatial resolution (see section 4).",
"pages": [
7
]
},
{
"title": "3 Relativistic frequency transfer",
"content": "In distant comparisons of frequency standards, we are face with the problem of curvature of space and relative motion of the clocks. These two effects change locally the flow of proper time with respect to a global coordinate time. In this section we describe how to compare distant clock frequencies by means of an electromagnetic signal, and how the comparison is affected by these effects.",
"pages": [
7
]
},
{
"title": "3.1 The Einstein Principle",
"content": "Before we treat the general case, let's try to understand in simple terms what is the frequency shift effect. Indeed, it can be seen as a direct consequence of the Einstein Equivalence Principle (EEP), one of the pillars of modern physics [27, 41]. Let's consider a photon emitted at a point A in an accelerated reference system, toward a point B which lies in the direction of the acceleration (see fig.4). We assume that both point are separated by a distance h 0 , as measured in the accelerated frame. The photon time of flight is δt = h 0 /c , and the frame velocity during this time increases by δv = aδt = ah 0 /c , where a is the magnitude of the frame acceleration glyph[vector]a . The frequency at point B (reception) is then shifted because of Doppler effect, compared to the frequency at Equivalence point A",
"pages": [
8
]
},
{
"title": "(emission), by an amount:",
"content": "Now, the EEP postulates that a gravitational field glyph[vector]g is locally equivalent to an acceleration field glyph[vector]a = -glyph[vector]g . We deduce that in a non accelerated (locally inertial) frame in presence of a gravitational field glyph[vector]g : where g = | glyph[vector]g | , ν A is the photon frequency at emission (strong gravitational potential) and ν B is the photon frequency at reception (weak gravitational field). As ν B < ν A , it is usual to say that the frequency at the point of reception is 'red-shifted'. One can consider it in terms of conservation of energy. Intuitively, the photon that goes from A to B has to 'work' to be able to escape the gravitational field, then it looses energy and its frequency decreases by virtue of E = hν , with h the Planck constant.",
"pages": [
8
]
},
{
"title": "3.2 General case",
"content": "The principle of frequency comparison is to measure the frequency of an electromagnetic signal with the help of the emitting clock, A , and then with the receiving clock, B . We obtain respectively two measurements ν A and ν B 3 . Let S ( x α ) be the phase of the electromagnetic signal emitted by clock A . It can be shown that light rays are contained in hypersurfaces of constant phase. The frequency measured by A/B is: where τ A/B is the proper time along the worldline of clock A/B (see fig.5). We introduce the wave vector k A/B α = ( ∂ α S ) A/B to obtain: where u α A/B = d x α A/B / d τ is the four-velocity of clock A/B . Finally, we obtain a fundamental relation for frequency transfer: This formula does not depend on a particular theory, and then can be used to perform tests of general relativity. Introducing v i = d x i / d t and ˆ k i = k i /k 0 , it is usually written as: From eq. (5) we deduce that: We suppose that space-time is stationary, ie. ∂ 0 g αβ = 0 . Then it can be shown that k 0 is constant along the light ray, meaning that k A 0 = k B 0 . We introduce the time transfer function: Deriving the time transfer function with respect to t A one obtains: Inserting eq. (11) in eq. (9), and comparing with eq. (8), we deduce: General formula for non-stationary spacetimes can be found in [14, 20]. As an exemple, let's take the simple time transfer function: where R AB = | R i AB | and R i AB = x i B -x i A . Then we obtain: where N i AB = R i AB /R AB . Up to the second order, this term does not depend on the gravitational field but on the relative motion of the two clocks. It is simply the first order Doppler effect. The two other terms in eq. (9) depend on the relation between proper time and coordinate time. In a metric theory one has c 2 d τ = √ g αβ d x α d x β . We deduce that:",
"pages": [
9,
10
]
},
{
"title": "3.3 Application to a static, spherically symmetric body",
"content": "As an example, we apply this formalism for the case of a parametrized post-Minkowskian approximation of metric theories. This metric is a good approximation of the space-time metric around the Earth, for a class of theories which is larger than general relativity. Choosing spatial isotropic coordinates, we assume that the metric components can be written as: where α and γ are two parameters of the theory (for general relativity α = 0 and γ = 1 ). Then: where v = √ δ ij v i v j . The time transfer function of such a metric is given in eq. (108) of [20]. Then we calculate: where Let assume that both clocks are at rest with respect to the chosen coordinate system, ie. glyph[vector]v A = glyph[vector] 0 = glyph[vector]v B and that r A = r 0 and r B = r 0 + δr , where δr glyph[lessmuch] r 0 . Then we find: The same effect can be calculated with a different, not necessarily symmetric gravitational potential w ( t, x i ) . The results yields: This is the classic formula given in textbooks for the 'gravitational red-shift'. However one should bear in mind that this is valid for clocks at rest with respect to the coordinate system implicitly defined by the space-time metric (one uses usually the Geocentric Celestial Reference System), which is (almost) never the case. Moreover, the separation between a gravitational red-shift and a Doppler effect is specific to the approximation scheme used here. One can read the book by Synge [37] for a different interpretation in terms of relative velocity and Doppler effect only. We note that the lowest order gravitational term in eq. (21) is a test of the Newtonian limit of metric theories. Indeed, if one wants to recover the Newtonian law of gravitation for GM/rc 2 glyph[lessmuch] 1 and v glyph[lessmuch] 1 then it is necessary that α = 0 . Then this test is more fundamental than a test of general relativity, and can be interpreted as a test of Local Position Invariance (which is a part of the Einstein Equivalence Principle). See [41, 42] for more details on this interpretation, and a review of the experiments that tested the parameter α . Amore realistic case of the space-time metric is treated in article [3], in the context of general relativity: all terms from the Earth gravitational potential are considered up to an accuracy of 5 . 10 -17 , specifically in prevision of the ACES mission [7].",
"pages": [
10,
11
]
},
{
"title": "4 Chronometric geodesy",
"content": "Instead of using our knowledge of the Earth gravitational field to predict frequency shifts between distant clocks, one can revert the problem and ask if the measurement of frequency shifts between distant clocks can improve our knowledge of the gravitational field. To do simple orders of magnitude estimates it is good to have in mind some correspondences calculated thanks to eqs. (21) and (22): From this correspondence, we can already imagine two direct applications of clocks in geodesy: if we are capable to compare clocks to 10 -16 accuracy, we can determine height differences between clocks with one meter accuracy (levelling), or determine geopotential differences with 10 m 2 .s -2 accuracy.",
"pages": [
11
]
},
{
"title": "4.1 A review of chronometric geodesy",
"content": "The first article to explore seriously this possibility was written in 1983 by Martin Vermeer [40]. The article is named 'chronometric levelling'. The term 'chronometric' seems well suited for qualifying the method of using clocks to determine directly gravitational potential differences, as 'chronometry' is the science of the measurement of time. However the term 'levelling' seems too restrictive with respect to all the applications one could think of using the results of clock comparisons. Therefore we will use the term 'chronometric geodesy' to name the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, with the help of atomic clocks. It is sometimes named 'clock-based geodesy', or 'relativistic geodesy'. However this last designation is improper as relativistic geodesy aims at describing all possible techniques (including e.g. gravimetry and gradiometry) in a relativistic framework [18, 28, 35]. The natural arena of chronometric geodesy is the four-dimensional space-time. At the lowest order, there is proportionality between relative frequency shift measurements - corrected from the first order Doppler effect and (Newtonian) geopotential differences (see eq.(22)). To calculate this relation we have seen that we do not need the theory of general relativity, but only to postulate Local Position Invariance. Therefore, it is perfectly possible to use clock comparison measurements corrected from the first order Doppler effect as a direct measurement of geopotential differences in the framework of classical geodesy, if the measurement accuracy does not reach the magnitude of the higher order terms. Comparisons between two clocks on the ground generally use a third clock in space. For the comparison between a clock on the ground and one in space, the terms of order c -3 in eqs. (19)-(20) reach a magnitude of ∼ 10 -15 and ∼ 3 × 10 -14 for respectively the ground and the space clock, if they are separated radially by 1000 km. Terms of order c -4 omitted in eqs. (21)-(22) can reach ∼ 5 × 10 -19 in relative frequency shift, which corresponds to a height difference of ∼ 5 mmand a geopotential difference of ∼ 5 × 10 -2 m 2 .s -2 . Clocks are far from reaching this accuracy today, but it cannot be excluded for the future. In his article, Martin Vermeer explores the 'possibilities for technical realisation of a system for measuring potential differences over intercontinental distances' using clock comparisons [40]. The two main ingredients are of course accurate clocks and a mean to compare them. He considers hydrogen maser clocks. For the links he considers a 2-way satellite link over a geostationary satellite, or GPS receivers in interferometric mode. He has also to consider a mean to compare the proper frequencies of the different hydrogen maser clocks. However today this can be overcome by comparing Primary Frequency Standards (PFS), which have a well defined proper frequency based on a transition of Caesium 133, used for the definition of the second. However, this problem will rise again if one uses Secondary Frequency Standards which are not based on Caesium atoms. Then the proper frequency ratio between two different kinds of atomic clocks has to be determined locally. This is one of the purpose of the European project 'International timescales with optical clocks' 4 , where optical clocks based on dif- ferent atoms will be compared one each other locally, and to the PFS. It is planned also to do a proof-of-principle experiment of chronometric geodesy, by comparing two optical clocks separated by a height difference of around 1 km using an optical fibre link. In the foreseen applications of chronometric geodesy, Martin Vermeer mentions briefly intercontinental levelling, and the measurement of the true geoid (disentangled from geophysical sea surface effects) [40]. Few authors have seriously considered chronometric geodesy. Following Vermeer idea, Brumberg and Groten [5] demonstrated the possibility of using GPS observations to solve the problem of the determination of geoid heights, however leaving aside the practical feasibility of such a technique. Bondarescu et al. [4] discuss the value and future applicability of chronometric geodesy, including direct geoid mapping on continents and joint gravity-geopotential surveying to invert for subsurface density anomalies. They find that a geoid perturbation caused by a 1.5 km radius sphere with 20 per cent density anomaly buried at 2 km depth in the Earth's crust is already detectable by atomic clocks of achievable accuracy. Finally Chou et al. demonstrated the potentiality of the new generation of atomic clocks, based on optical transitions, to measure heights with a resolution of around 30 cm [9].",
"pages": [
11,
12
]
},
{
"title": "4.2 The chronometric geoid",
"content": "Arne Bjerhammar in 1985 gives a precise definition of the 'relativistic geoid' [1, 2]: 'The relativistic geoid is the surface where precise clocks run with the same speed and the surface is nearest to mean sea level' This is an operational definition. Soffel et al. [35] in 1988 translated this definition in the context of post-Newtonian theory. They also introduce a different operational definition of the relativistic geoid, based on gravimetric measurements: a surface orthogonal everywhere to the direction of the plumb-line and closest to mean sea level. He calls the two surfaces obtained with clocks and gravimetric measurements respectively the 'u-geoid' and the 'a-geoid'. He proves that these two surfaces coincide in the case of a stationary metric. In order to distinguish the operational definition of the geoid from its theoretical description, it is less ambiguous to give a name based on the particular technique to measure it. Relativistic geoid is too vague as Soffel et al. have defined two different ones. The names chosen by Soffel et al. are not particularly explicit, so instead of 'u-geoid' and 'a-geoid' one can call them chronometric and gravimetric geoid respectively. There can be no confusion with the geoid derived from satellite measurements, as this is a quasi-geoid that do not coincide with the geoid on the continents [15]. Other considerations on the chronometric geoid can be found in [18, 19, 28]. Let two clocks be at rest with respect to the chosen coordinate system ( v i = 0 ) in an arbitrary space-time. From formula (9), (11) and (15) we deduce that: In this case the chronometric geoid is defined by the condition g 00 = cst. Wenotice that the problem of defining a reference surface is closely related to the problem of realizing Terrestrial Time (TT). TT is defined with respect to Geocentric Coordinate Time (TCG) by the relation [36, 32]: where L G is a defining constant. This constant has been chosen so that TT coincides with the time given by a clock located on the classical geoid. It could be taken as a formal definition of the chronometric geoid [43]. If so, the chronometric geoid will differ in the future from the classical geoid: a level surface of the geopotential closest to the topographic mean sea level. Indeed, the value of the potential on the geoid, W 0 , depends on the global ocean level which changes with time [6]. With a value of d W 0 / d t ∼ 10 -3 m 2 .s -2 .y -1 , the difference in relative frequency between the classical and the chronometric geoid would be around 10 -18 after 100 years (the correspondence is made with the help of relations (23)). However, the rate of change of the global ocean level could change during the next decades. Predictions are highly model dependant [17].",
"pages": [
12,
13
]
},
{
"title": "5 Conclusion",
"content": "We presented recent developments in the field of atomic clocks, as well as an introduction to relativistic frequency transfer and a detailed review of chronometric geodesy. If the control of systematic effects in optical clocks keep their promises, they could become very sensible to the gravitational field, which will ultimately degrade their stability at the surface of the Earth. One solution will be to send very stable and accurate clocks in space, which will become the reference against which the Earth clocks would be compared. Moreover, by sending at least four of these clocks in space, it will be possible to realize a very stable and accurate four-dimensional reference system in space [10].",
"pages": [
13,
14
]
},
{
"title": "References",
"content": "approximation. In S. Boissier, P. de Laverny, N. Nardetto, R. Samadi, D. VallsGabaud, and H. Wozniak, editors, SF2A2012: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics , pages 145-148, December 2012. frequency reference in the deep ultraviolet with fractional uncertainty = 5 . 7 × 10 -15 . Phys. Rev. Lett. , 108:183004, May 2012.",
"pages": [
15,
16
]
}
]
2013AnGeo..31..639S
https://arxiv.org/pdf/1304.4841.pdf
<document>
<text><location><page_1><loc_8><loc_84><loc_41><loc_88></location>Manuscript prepared for Ann. Geophys. with version 5.0 of the L A T E X class copernicus.cls. Date: 2 October 2018</text>
<section_header_level_1><location><page_1><loc_8><loc_68><loc_87><loc_72></location>Non-adiabatic electron behaviour due to short-scale electric field structures at collisionless shock waves</section_header_level_1>
<text><location><page_1><loc_8><loc_65><loc_37><loc_66></location>V. See, R. F. Cameron, and S. J. Schwartz</text>
<text><location><page_1><loc_8><loc_63><loc_56><loc_64></location>Blackett Laboratory, Imperial College London, London, SW7 2AZ, UK</text>
<text><location><page_1><loc_8><loc_60><loc_44><loc_61></location>Correspondence to: V. See ([email protected])</text>
<text><location><page_1><loc_8><loc_34><loc_48><loc_57></location>Abstract. Under sufficiently high electric field gradients, electron behaviour within exactly perpendicular shocks is unstable to the so-called trajectory instability. We extend previous work paying special attention to shortiscale, high amplitude structures as observed within the electric field profile. Via test particle simulations, we show that such structures can cause the electron distribution to heat in a manner that violates conservation of the first adiabatic invariant. This is the case even if the overall shock width is larger than the upstream electron gyroradius. The spatial distance over which these structures occur therefore constitutes a new scale length relevant to the shock heating problem. Furthermore, we find that the spatial location of the short-scale structure is important in determining the total effect of non-adiabatic behaviour - a result that has not been previously noted.</text>
<text><location><page_1><loc_8><loc_31><loc_48><loc_33></location>Keywords. Space plasma physics (Shock waves; Numerical simulation studies)</text>
<section_header_level_1><location><page_1><loc_8><loc_26><loc_19><loc_27></location>1 Introduction</section_header_level_1>
<text><location><page_1><loc_8><loc_4><loc_48><loc_24></location>Collisionless shockwaves occur throughout the universe. While often cited as the production source for high energy cosmic rays, the heating mechanisms that act on the different sub-populations of particles are still not entirely understood. Numerous studies have been conducted into the electron heating problem, with the characteristic scale length of the shock emerging as an important parameter governing the evolution of the electron distribution (Balikhin et al., 1998; Lembege et al., 1999; Schwartz et al., 2011). Additionally, despite the amount of work conducted on shock scale lengths, there is still a lack of consensus regarding the relative scales over which the magnetic and electric fields in shocks actually vary.</text>
<text><location><page_1><loc_8><loc_1><loc_48><loc_4></location>Electrons are expected to behave adiabatically, conserving their magnetic moments µ m ≡ W ⊥ / B , as long as the shock</text>
<text><location><page_1><loc_52><loc_48><loc_92><loc_57></location>width is larger than the upstream electron gyroradius. This behaviour allows an electron to change the kinetic energy associated with its gyrovelocity perpendicular to the magnetic field smoothly as it crosses the shock. However, Cole (1976) showed that in the presence of an electric field with constant gradient,</text>
<formula><location><page_1><loc_52><loc_43><loc_92><loc_47></location>E = ( E 0 + ∂E x ∂x x ) ˆ x , (1)</formula>
<text><location><page_1><loc_52><loc_41><loc_88><loc_42></location>particles will gyrate at an effective frequency, given by</text>
<formula><location><page_1><loc_52><loc_36><loc_92><loc_39></location>Ω 2 eff =Ω 2 -q m ∂E x ∂x , (2)</formula>
<text><location><page_1><loc_52><loc_29><loc_92><loc_35></location>where Ω eff and Ω are the effective and normal gyrofrequencies, q is the charge on the particle and m is the particle mass. The effective gyrofrequency must then be used in calculating the gyroradii, i.e.</text>
<formula><location><page_1><loc_52><loc_24><loc_92><loc_27></location>r eff g = v Ω eff , (3)</formula>
<text><location><page_1><loc_52><loc_9><loc_92><loc_23></location>where r eff g is a new effective gyroradius and v is the gyrovelocity of the particle. The condition for adiabatic behaviour must be revised such that the shock width is much bigger than the effective gyroradius. Equation (2) shows that, for certain values of ∂E x / ∂x , the effective gyrofrequency can approach zero corresponding to an extremely large effective gyroradii. Non-adiabatic electron behaviour is therefore possible, even at shocks with scale lengths much larger than an upstream gyroradius.</text>
<text><location><page_1><loc_52><loc_1><loc_92><loc_9></location>The link between scale lengths and non-adiabatic heating was explored by Balikhin et al. (1993). The authors conducted a theoretical analysis of electron trajectories at exactly perpendicular shocks and identified the so-called trajectory instability. This instability causes two neighbouring electron</text>
<paragraph><location><page_2><loc_18><loc_87><loc_92><loc_88></location>V. See, R. F. Cameron & S. J. Schwartz: Electron behaviour due to short-scale structures at shock waves</paragraph>
<text><location><page_2><loc_8><loc_79><loc_48><loc_85></location>trajectories to diverge exponentially from each other in phase space, causing a breaking of magnetic moment conservation, wherever Ω 2 eff < 0 , i.e. as long as the following instability criterion is obeyed:</text>
<formula><location><page_2><loc_8><loc_74><loc_48><loc_77></location>-e m ∂E x ∂x -Ω 2 > 0 , (4)</formula>
<text><location><page_2><loc_8><loc_50><loc_48><loc_73></location>where e is magnitude of the electronic charge, m is the electron mass, Ω is the electron gyrofrequency and ∂E x / ∂x is the electric field gradient along the shock normal. The criterion requires that the electric field gradient be above some critical value or, equivalently for a given cross-shock potential, that the scale length of the electric field be below some critical value. This can be fulfilled even if the upstream gyroradius is smaller than the shock scale. The authors then showed via a series of test-particle simulations that the onset of the trajectory instability coincides with the onset of non-adiabatic heating. While Balikhin et al. (1993) draw a strong connection between the scale length of the shock and subsequent heating, they do not alter the scales of the electric and magnetic fields independently of each other, nor do they study the effect of displacing one with respect to the other.</text>
<text><location><page_2><loc_8><loc_39><loc_48><loc_50></location>This work was subsequently extended into the oblique regime by Balikhin et al. (1998). In this paper the authors also included terms that account for the changing magnetic field, which were previously neglected, and found that the divergence in phase space always occurs and that the rate of divergence is dependent on the gradients of both the magnetic and electric fields.</text>
<text><location><page_2><loc_8><loc_21><loc_48><loc_39></location>Further relevant work is done by Lembege et al. (2003). Two approaches were used to analyse the demagnetisation of the electrons at the shock front. In the first instance, nonstationary and nonuniformity effects were included in the form of a full-particle self-consistent simulation whilst in the second instance these effects have been removed. The authors found that the fraction of electrons which become demagnetised depends on the nonstationary behaviour found at shocks. However, it is difficult to attribute this result to any particular process or feature of the shock since it is impossible to systematically vary particular variables of interest in a full particle code.</text>
<text><location><page_2><loc_8><loc_9><loc_48><loc_21></location>It is clear that the relative scales over which the magnetic and electric fields vary have a large impact on the type of electron heating that occurs. Indeed, the relative field scales of shocks is a topic which we study within this paper. In their paper, Balikhin et al. (1998) outlined possible relationships between the fields, though it is a matter of contention which of them occurs in reality, since various observations and simulations support differing views.</text>
<text><location><page_2><loc_8><loc_1><loc_48><loc_9></location>It is common that both scales have the same order of magnitude in simulations and observations (Balikhin et al., 1993; Formisano and Torbert, 1982; Formisano, 1982; Balikhin et al., 2002; Leroy et al., 1982; Liewer et al., 1991; Scholer et al., 2003; Lembege and Dawson, 1989, 1987). Ba-</text>
<text><location><page_2><loc_52><loc_74><loc_92><loc_85></location>likhin and Gedalin (1994) suggest that the variation of electron heating with upstream electron thermal Mach number v flow / v thermal -e , reported by Schwartz et al. (1988), can be recovered in this simple configuration. On the other hand, Scudder et al. (1986) analysed a shock where the electrostatic potential varied over a scale larger than the magnetic field ramp.</text>
<text><location><page_2><loc_52><loc_58><loc_92><loc_74></location>However, Eselevich et al. (1971) reported on so-called isomagnetic jumps which were observed in laboratory plasma experiments whilst Heppner et al. (1978) reported the observations from ISEE-1 of large changes in the electric field over scales much shorter than the magnetic field ramp. More recently, Walker et al. (2004) and Bale and Mozer (2007) have shown the existence of short-scale, high-amplitude electric field structures or 'spikes' within the overall electric field profile with Bale and Mozer (2007) speculating that the spikes in the electric field profile may lead to incoherent heating of the electrons.</text>
<text><location><page_2><loc_52><loc_41><loc_92><loc_57></location>In this paper, we will show for the first time that this is indeed possible. Using test-particle simulations, we will find the effect of varying the electric field scale length independently of the magnetic scale length; which has not been done before. Additionally, we will vary the location of the electric field within the shock. We also investigate the consequences of an electric field spike within the shock. In doing so, we will demonstrate that these electric field spikes constitute a new scale length which is important to the shock heating problem, and that its location within the shock layer can dramatically change the amount of heating observed.</text>
<text><location><page_2><loc_52><loc_35><loc_92><loc_41></location>The rest of this paper will be structured as follows. Section 2 will cover the details behind the simulation, with the results and analysis following in section 3. Conclusions follow in section 4.</text>
<section_header_level_1><location><page_2><loc_52><loc_28><loc_65><loc_29></location>2 The Simulation</section_header_level_1>
<section_header_level_1><location><page_2><loc_52><loc_25><loc_65><loc_26></location>2.1 Field Profiles</section_header_level_1>
<text><location><page_2><loc_52><loc_1><loc_92><loc_22></location>A test-particle approach, where static electromagnetic fields are prescribed, is chosen for this investigation. The normalisation details can be found in Balikhin et al. (1993) and are briefly reproduced here. Time is normalised to the inverse gyrofrequency, Ω -1 ; coordinates are normalised to the electron inertial length, cω -1 pe ; velocity is normalised to the upstream Alfv'en speed, v A ; and magnetic fields are normalised in terms of the upstream magnetic field strength, B u . The field profiles used are based upon the profiles described by Balikhin et al. (1993). They are idealised versions of exactly perpendicular collisionless shocks. The field profiles are shown in Fig. 1 and are given by Eq. (5), (6) and (7). The shock is at rest in the simulation frame, with the upstreampointing normal in the -ˆ x direction.</text>
<section_header_level_1><location><page_3><loc_52><loc_84><loc_71><loc_85></location>2.2 Electron Distribution</section_header_level_1>
<text><location><page_3><loc_52><loc_75><loc_92><loc_82></location>For each simulation run, a Maxwellian distribution at a temperature of 10 eV consisting of 600 electrons is initialised far upstream from the shock. Since the shock is exactly perpendicular, the electrons only require two degrees of freedom in velocity space allowing us to set v z =0 .</text>
<text><location><page_3><loc_52><loc_70><loc_92><loc_74></location>For the purposes of this investigation, the temperature corresponding to the two perpendicular ( x , y ) degrees of freedom will be defined as follows:</text>
<formula><location><page_3><loc_52><loc_64><loc_92><loc_68></location>T = m 2 k B 〈 ( v -〈 v 〉 ) 2 〉 , (8)</formula>
<text><location><page_3><loc_52><loc_57><loc_92><loc_64></location>i.e. the temperature is proportional to the variance of the velocity vectors of all the electrons in the distribution. In practice, the parameter that will be of interest is the heating ratio, R H ; that is the ratio of the far downstream electron distribution temperature to the far upstream temperature.</text>
<section_header_level_1><location><page_3><loc_52><loc_53><loc_69><loc_54></location>3 Results and Analysis</section_header_level_1>
<text><location><page_3><loc_52><loc_43><loc_92><loc_52></location>To investigate short-scale electric field structures, it will be instructive to investigate, separately, the scale and location of the cross-shock electric field, E x . We will then move onto a final set of simulations in which the cross-shock electric field will vary over the same scale as the magnetic field with a spike embedded within it to better represent a real shock.</text>
<section_header_level_1><location><page_3><loc_52><loc_40><loc_75><loc_41></location>3.1 Electric Field Scale Length</section_header_level_1>
<text><location><page_3><loc_52><loc_27><loc_92><loc_39></location>For this experiment, we will vary D E whilst holding D B and the total cross-shock potential, e ∆ φ 0 , fixed. The starting shock parameters that will be considered are D E = D B =5 and e ∆ φ 0 =300eV . This scale length corresponds to a shock width, 2 D B , of 11.2 upstream gyroradii for a 10 eV electron. These conditions are adiabatic as shown in Fig. 4 of Balikhin et al. (1993) and will be the control case against which other simulations are compared.</text>
<text><location><page_3><loc_52><loc_8><loc_92><loc_26></location>Figure 2 shows that as D E is decreased, the heating remains roughly adiabatic for larger D E before increasing rapidly for scale lengths below D E ∼ 3 . At these smaller electric scale lengths, the heating is significantly nonadiabatic. By holding the cross-shock potential constant and decreasing D E , the electric field gradient becomes larger. This result should therefore not present much surprise since it is already known that the separation of the adiabatic and non-adiabatic regimes in perpendicular shocks depends on the electric field gradient as given by Eq. (4). According to this criterion, the threshold of the trajectory instability occurs at D E ∼ 3 . 1 for the parameters of our simulation.</text>
<section_header_level_1><location><page_3><loc_52><loc_6><loc_77><loc_7></location>3.2 Displacement of Electric Field</section_header_level_1>
<text><location><page_3><loc_52><loc_1><loc_92><loc_4></location>Having varied the width of the electric field profile, its position relative to the rest of the shock can be altered since</text>
<figure>
<location><page_3><loc_10><loc_63><loc_48><loc_83></location>
<caption>Fig. 1. Profiles for the electric, E x (red curve), and magnetic, B z (blue curve), fields in dimensionless units (see Eq. (5) - (7)). The shock width is set by the parameter D B , with the D B = D E =1 case illustrated in the figure. Note that the E x scale is negative.</caption>
</figure>
<formula><location><page_3><loc_8><loc_45><loc_48><loc_50></location>E x = -15∆ φ 0 16 D E ( ( x D E ) 2 -1 ) 2 (5)</formula>
<formula><location><page_3><loc_8><loc_43><loc_48><loc_44></location>E y = M A (6)</formula>
<formula><location><page_3><loc_8><loc_37><loc_48><loc_41></location>B z =2+ 1 8 ( 3 ( x D B ) 5 -10 ( x D B ) 3 +15 ( x D B ) ) (7)</formula>
<text><location><page_3><loc_8><loc_1><loc_48><loc_36></location>Here, ∆ φ 0 is the cross-shock potential and chosen to be 300 eV unless stated otherwise. E y is constant everywhere and calculated from the upstream bulk electron velocity and magnetic field strength, E y = V u B u . We use values of V u =400kms -1 and B u =5nT which are typical for earth's bow shock. When normalised, E y is equal to the Alfv'enic Mach number, M A , which we choose to be Mach 8. D E and D B are the half-electric and half-magnetic field widths normalised to the electron inertial length. Equation (5) only applies within the region of space -D E >x>D E . Everywhere outside this region, E x =0 . Similarly, Eq. (7) only applies within -D B >x>D B , taking the values B z =1 for x < -D B and B z =3 for x > D B . Adiabatic electron behaviour, conserving magnetic moment, would therefore correspond to a three-fold increase in the temperature of the electron distribution based on the jump in the magnetic field. We have chosen to use two scale lengths, D E and D B , rather than the single parameter, D = D E = D B , that Balikhin et al. (1993) use because it is important for this study that we are able to vary the two scale lengths independently. These particular forms were chosen by Balikhin et al. (1993) because they are smooth and well behaved at the shock edges and throughout the shock layer.</text>
<text><location><page_4><loc_78><loc_48><loc_79><loc_50></location>5</text>
<figure>
<location><page_4><loc_19><loc_47><loc_79><loc_81></location>
<caption>Fig. 2. Ratio of downstream to upstream electron temperature as a function of electric field scale length, D E . The magnetic field scale length is kept fixed at D B =5 . A sketch of the field profiles and their relative scale lengths is shown in the inset. For large D E , the heating stays adiabatic as the electric field scale decreases. Once the adiabaticity is broken at scale lengths shorter than roughly D E =3 , however, there is a negative correlation between the heating ratio and the electric scale length.</caption>
</figure>
<text><location><page_4><loc_51><loc_47><loc_52><loc_48></location>E</text>
<text><location><page_4><loc_8><loc_24><loc_48><loc_35></location>D E is smaller than D B . The inset of Fig. 3 shows the displacement of the electric field with respect to the magnetic field such that their centres of variation no longer coincide. For this set of simulations, we fix D E =0 . 5 . As before, D B =5 and e ∆ φ 0 =300eV . Figure 3 shows a clear trend of higher (lower) heating for displacements towards the upstream (downstream) side of the shock.</text>
<text><location><page_4><loc_8><loc_2><loc_48><loc_24></location>To understand why displacing the electric field would change the amount of heating, despite maintaining a constant electric field gradient, it is necessary to look at the drifts in the system. For the field geometries used, the electrons experience an E y ˆ y × B z ˆ z drift in the ˆ x direction, together with an E x ˆ x × B z ˆ z drift and a ∇| B | drift which are in the +ˆ y and -ˆ y directions, respectively. The E y ˆ y × B z ˆ z drift causes the electrons to drift through the shock and gain all the potential energy associated with the E x field, i.e. the cross-shock potential. This is fixed by the ∆ φ 0 parameter. The remaining two drifts cause the electrons to travel along the shock in opposite directions. The ∇| B | drift is directed such that the electrons gain kinetic energy from the motional electric field, E y . Conversely, the E x ˆ x × B z ˆ z drift is directed such that the electrons lose kinetic energy to this field. The lat-</text>
<text><location><page_4><loc_52><loc_29><loc_92><loc_35></location>ition to the fixed cross-shock potential, therefore determine the net kinetic energy gain of the electrons as they drift through the shock (Goodrich and Scudder, 1984).</text>
<text><location><page_4><loc_52><loc_1><loc_92><loc_29></location>It will be useful to compare two limiting cases in our explanation. The electrons will drift through most of the shock before encountering the electric field when it is displaced downstream. However, when the field is displaced upstream, the electrons will encounter it immediately and gain the entire cross-shock potential straight away. Since the ∇| B | drift speed is proportional to the kinetic energy of the electron, the magnitude of the ∇| B | drift will be larger in the second case as it has gained the energy from crossing the E x field earlier. Figure 4 shows the trajectories of three electrons which demonstrate this effect. The outer vertical lines represent the outer edges of the shock i.e. x = ± D B with the inner vertical lines representing the edges of the displaced electric field, i.e. x = δ E ± D E where δ E is the displacement of the electric field. All parameters are kept the same with the exception of the displacement of the electric field. The electron in panel (a) immediately picks up the cross-shock potential energy, e ∆ φ 0 . Initially the E x ˆ x × B z ˆ z drift dominates, resulting in</text>
<figure>
<location><page_5><loc_19><loc_47><loc_80><loc_81></location>
<caption>Fig. 3. Ratio of downstream to upstream electron temperature as a function of electric field displacement, δ E . The electric and magnetic field scale lengths are kept at D E =0 . 5 and D B =5 . A sketch of the field profiles and their relative scale lengths is shown in the inset. The displacement of the electric field spike given in terms of D B , i.e. δ E = -1 corresponds to the center of variations in the electric field coinciding with the upstream edge of the shock layer. The heating ratio is greater for displacements towards the upstream edge of the shock. Conversely, when the electric field is displaced towards the downstream end, the heating ratio is lower.</caption>
</figure>
<text><location><page_5><loc_8><loc_17><loc_48><loc_33></location>the loss of some of this energy. The ∇| B | drift then operates in the E x =0 region where, due to the enhanced perpendicular velocity, a large drift velocity results in a net -ˆ y drift. This corresponds to a large non-adiabatic energy increase. Panel (b) is similar but the ∇| B | drift is less effective since the electron spends less time in the postE x region, allowing less time for the ∇| B | drift to act. In panel (c), there is no space for the ∇| B | drift to act after the electrons have crossed the cross-shock potential. The E x ˆ x × B z ˆ z drift reduces the energy gained from e ∆ φ 0 the most compared to the other panels.</text>
<text><location><page_5><loc_8><loc_8><loc_48><loc_17></location>Outside the region in which E x is non-zero, the energy gains associated with the ∇| B | drift are roughly consistent, as expected, with adiabatic compression in the increasing magnetic field. Since this multiplies the existing particle energy, it gives the most energy to trajectories suffering early nonadiabatic processes as in panel (a).</text>
<text><location><page_5><loc_8><loc_2><loc_48><loc_7></location>To summarise, when the electric field is displaced downstream, the electrons drift through most of the shock adiabatically, losing energy as a result of the E x ˆ x × B z ˆ z drift, before encountering the non-adiabatic divergence in phase space as</text>
<text><location><page_5><loc_52><loc_23><loc_92><loc_33></location>discussed by Balikhin et al. (1993). When the electric field is displaced upstream, the electrons immediately experience the phase space divergence. As the electrons drift through the rest of the shock, they will undergo a further expansion in phase space due to the ∇| B | drift, the magnitude of which is larger when electric field is displaced upstream. This leads to a higher heating of the electron distribution.</text>
<text><location><page_5><loc_52><loc_9><loc_92><loc_23></location>We note that the trajectory instability is an essential ingredient in this non-adiabatic behaviour. While the displacement of the electric field toward the upstream enhances the instability by keeping the gyrofrquency, Ω , lower in Eq. (4), experiments with different values of constant Ω (not shown) are inconclusive. Thus, we prefer to discuss the non-adiabatic behaviour in terms of the various particle drifts. Other experiments (not shown) in which a field with a larger D E is displaced remain adiabatic.</text>
<section_header_level_1><location><page_5><loc_52><loc_6><loc_65><loc_7></location>3.3 Shock Spikes</section_header_level_1>
<text><location><page_5><loc_52><loc_1><loc_92><loc_4></location>Whilst it has been instructive to consider these simulations, observations show structures with a scale much smaller</text>
<text><location><page_6><loc_17><loc_75><loc_19><loc_76></location>y</text>
<figure>
<location><page_6><loc_18><loc_45><loc_80><loc_81></location>
<caption>Fig. 4. Three electron trajectories in the xy plane for different displacements of the electric field profile. In all three cases the magnetic field variations occur between the two outer vertical lines. The electric field variations are bound by the two left-most lines in panel (a), the centre two lines in panel (b), and the two right-most lines in panel (c). All other parameters are fixed. The drift directions are shown in panel (b). The panels show that when the electric field is displaced upstream, i.e. panel (a), the electron will drift in the negative ˆ y direction a lot more compared to when the displacement is downstream, i.e. panel (c)</caption>
</figure>
<text><location><page_6><loc_50><loc_44><loc_51><loc_46></location>x</text>
<text><location><page_6><loc_8><loc_7><loc_48><loc_30></location>than the total shock width embedded within a larger overall electric field profile (Walker et al., 2004). In one particular shock crossing, Walker et al. identified three large-amplitude, small-scale structures, the largest of which had a peak magnitude of around 45 mV / m , compared to an average motional electric field of around 14 mV / m . These were the largest amongst the field disturbances observed in the shock and occurred over the middle 50% of the shock transition. The authors estimate that the width of these structures to be around 1 -5 cω -1 pe , with the magnetic field ramp occurring over a scale ∼ 10 times this. It shall be the aim of the final set of simulations to encapsulate these features, if not the actual values themselves. Most importantly, for this particular shock crossing, Walker et al. report that the structures contribute 40% of the total cross-shock potential change.</text>
<text><location><page_6><loc_8><loc_3><loc_48><loc_7></location>The inset of Fig. 5 shows the field profile we used to model the electric field spikes. The electric field profile shown is constructed by adding together two profiles, both</text>
<text><location><page_6><loc_52><loc_3><loc_92><loc_30></location>described by Eq. (5) but with different D E values. The important features of the profile are D E = D B and D spike E /lessmuch D E . In keeping with the ratio of the scale lengths observed by Walker et al. (2004), D spike E is one tenth of D E . While Walker et al. (2004) reported that the overall electric field scale is slightly larger than that of the magnetic field ramp, the two scales have been kept equal here so as to allow for the independent investigation of the spikes alone. In any case, from the work of Balikhin et al. (1993), we would not expect that having D E >D B would cause the heating to be non-adiabatic, as this would make the electric field gradient smaller. For simplicity, only one electric field 'spike' has been modelled. Our base case will again be the adiabatic shock where D E = D B =5 and the total cross-shock potential is 300 eV . We choose 30 eV as the cross-spike potential with the rest of the shock accounting for the remaining 270 eV . We vary the position of the electric field spike to investigate its influence on the electron behaviour. Figure</text>
<figure>
<location><page_7><loc_18><loc_47><loc_80><loc_81></location>
<caption>Fig. 5. Ratio of downstream to upstream electron temperature as a function of electric field spike displacement, δ spike E . The electric and magnetic field scale lengths are kept fixed at D E = D B =5 and D spike E =0 . 5 . A sketch of the electric field profile is shown in the inset. The magnetic field has been omitted for clarity. The displacement of the electric field spike given in terms of D B i.e. a displacement of -1 would mean that the variations in the electric field are centered exactly at the upstream edge of the shock. The heating ratio is greater for displacement towards the upstream edge of the shock. Conversely, when the electric field spike is displaced towards the downstream end, the heating ratio is lower. For all displacements, the heating is non-adiabatic.</caption>
</figure>
<text><location><page_7><loc_8><loc_25><loc_48><loc_32></location>5 shows that for displacements towards the downstream side of the shock, the heating is non-adiabatic, but the amount of heating above the adiabatic case is small. For upstream displacements, there is a much higher non-adiabatic component to the heating.</text>
<text><location><page_7><loc_8><loc_3><loc_48><loc_24></location>The conclusions of the previous set of simulations can readily be applied here. By embedding a spike into the profile, there is now a region that satisfies the instability criterion in Eq. (4) when previously there was not, thus pushing the shock into the non-adiabatic regime. The same trend is noticed, with the heating ratio having high values for displacements towards the upstream end. However, the heating ratio is much smaller in comparison to the previous simulations; this should not be surprising given that the potential drop across the spike is much smaller. Just as before, the breaking of adiabaticity occurs earlier for displacements upstream, but the phase space expansion effect due to the ∇| B | drift is not as pronounced since the energy gains associated with the spike are smaller.</text>
<text><location><page_7><loc_52><loc_20><loc_92><loc_32></location>At 2 D E ∼ 1 cω -1 pe , the width of our spike is at the limit of the 1 -5 cω -1 pe widths reported by Walker et al. (2004). We conclude that in general, the presence of short-scale enhancements to the electric field can push an otherwise adiabatic shock into the non-adiabatic regime. The width of the electric field spikes therefore constitute a new scale length that is important in the study of electron heating at collisionless shocks.</text>
<text><location><page_7><loc_52><loc_2><loc_92><loc_20></location>We conducted a final simulation with three spikes at displacements of -0.5 D B , 0.0 D B and 0.5 D B embedded within an underlying electric field of width 2 D E =10 . Each spike, of width 2 D spike E =1 , contributed 30 eV to the cross-shock potential with the underlying profile contributing 210 eV for a total cross-shock potential of 300 eV . We find the heating ratio for this set-up to be R H =4 . 45 , which is not a surprising outcome based on our previous results. Figure 5 shows that the spikes at 0.0 D B and 0.5 D B have a minimal effect above adiabatic electron behaviour. The non-adiabatic behaviour found here is due predominantly to the upstreamdisplaced spike at -0 . 5 D B .</text>
<section_header_level_1><location><page_8><loc_8><loc_84><loc_19><loc_85></location>4 Conclusions</section_header_level_1>
<text><location><page_8><loc_8><loc_60><loc_48><loc_82></location>It has been the aim of this paper to look at the effect that the electric and magnetic field scales have on electron heating at collisionless shock waves with a focus on short-scale highamplitude structures in the electric field. Our work builds on the existing work of Balikhin et al. (1993) and is motivated by the observations of short-scale electric field structures observed by Walker et al. (2004) and Bale and Mozer (2007). Balikhin et al. (1993) showed that shorter scale lengths can lead to incoherent electron heating by satisfying an instability criterion with the short-scale electric field spike observations, providing a possible means of satisfying this criterion in reality. We have shown that the presence of small-scale structures can indeed push the heating of the electron distribution from the adiabatic into the non-adiabatic regime. Specifically, the main results of this report can be summarised as follows:</text>
<unordered_list>
<list_item><location><page_8><loc_8><loc_56><loc_48><loc_59></location>[1] Shorter-scale electric fields lead to non-adiabatic electron behaviour.</list_item>
<list_item><location><page_8><loc_8><loc_43><loc_48><loc_56></location>[2] The position of these electric fields has been shown, for the first time, to play an important role in determining the level of non-adiabaticity, with higher non-adiabatic behaviour observed for upstream displacements. This is due to the earlier energy gain of the electrons allowing for a large magnitude of subsequent ∇| B | drift. Equivalently, the magnetic moment of the electrons is increased more significantly for upstream displacements, allowing the electron to gain energy adiabatically in the subsequent magnetic field increase.</list_item>
<list_item><location><page_8><loc_8><loc_35><loc_48><loc_42></location>[3] This is true even when considering smaller-amplitude spikes embedded within a larger-scale electric field profile, provided that the magnitude of the electric field gradient is large enough. Such spikes have been observed (Walker et al., 2004; Bale and Mozer, 2007).</list_item>
<list_item><location><page_8><loc_8><loc_31><loc_48><loc_35></location>[4] The existence, scale and location within the shock of electric field spikes are therefore important new factors to consider in the context of electron heating.</list_item>
</unordered_list>
<text><location><page_8><loc_8><loc_12><loc_48><loc_30></location>The next step would be to extend our work into the oblique regime. The new scale length associated with the electric field spikes is relevant to the discussion of shock scale lengths and heating at oblique shocks by Balikhin et al. (1998). Other shock features of interest which could influence the electron dynamics include foot and overshoot regions, as well as the time dependence of the field profiles and higher-frequency fluctuations (Lembege and Savoini, 2002; Sundkvist et al., 2012). Finally, it would also be interesting to study the electrons within the shock layer, where the strong trajectory instability and short scales involved might be expected to break the gyrotropy of the distributions.</text>
<section_header_level_1><location><page_8><loc_8><loc_8><loc_16><loc_9></location>References</section_header_level_1>
<text><location><page_8><loc_8><loc_1><loc_48><loc_7></location>Bale, S. D. and Mozer, F. S.: Measurement of large parallel and perpendicular electric fields on electron spatial scales in the terrestrial bow shock, Physical Review Letters, 98, 205 001, pT: J; TC: 13; UT: WOS:000246624000031, 2007.</text>
<text><location><page_8><loc_52><loc_72><loc_92><loc_85></location>Balikhin, M., Gedalin, M., and Petrukovich, A.: New Mechanism for Electron Heating in Shocks, Physical Review Letters, 70, 1259-1262, pT: J; TC: 35; UT: WOS:A1993KN88700019, 1993. Balikhin, M., Krasnosel'skikh, V. V., Woolliscroft, L. J. C., and Gedalin, M.: A study of the dispersion of the electron distribution in the presence of E and B gradients: Application to electron heating at quasi-perpendicular shocks, Journal of Geophysical Research-Space Physics, 103, 2029-2040, pT: J; TC: 16; UT: WOS:000071845800014, 1998.</text>
<text><location><page_8><loc_52><loc_64><loc_92><loc_72></location>Balikhin, M. A., Nozdrachev, M., Dunlop, M., Krasnosel'skikh, V., Walker, S. N., Alleyne, H. S. K., Formisano, V., Andre, M., Balogh, A., Eriksson, A., and Yearby, K.: Observation of the terrestrial bow shock in quasi-electrostatic subshock regime, Journal of Geophysical Research-Space Physics, 107, 1155, pT: J; TC: 7; UT: WOS:000179009600036, 2002.</text>
<text><location><page_8><loc_52><loc_60><loc_92><loc_64></location>Cole, K. D.: Effects of crossed magnetic and (spatially dependent) electric fields on charged particle motion, Planetary and Space Science, 24, 515-518, 1976.</text>
<text><location><page_8><loc_52><loc_54><loc_92><loc_60></location>Eselevich, V. G., Eskov, A. G., Kurtmull, R. K., and Malyutin, A. I.: Isomagnetic Discontinuity in a Collisionless Shock Wave, Soviet Physics Jetp-Ussr, 33, 1120, pT: J; TC: 17; UT: WOS:A1971L306800013, 1971.</text>
<text><location><page_8><loc_52><loc_49><loc_92><loc_54></location>Formisano, V.: Measurement of the Potential Drop Across the Earths Collisionless Bow Shock, Geophysical Research Letters, 9, 1033-1036, pT: J; TC: 30; UT: WOS:A1982PH28800032, 1982.</text>
<text><location><page_8><loc_52><loc_43><loc_92><loc_48></location>Formisano, V. and Torbert, R.: Ion-Acoustic-Wave Forms Generated by Ion-Ion Streams at the Earths Bow Shock, Geophysical Research Letters, 9, 207-210, pT: J; TC: 16; UT: WOS:A1982NF68300010, 1982.</text>
<text><location><page_8><loc_52><loc_35><loc_92><loc_43></location>Goodrich, C. and Scudder, J.: The Adiabatic Energy Change of Plasma Electrons and the Frame Dependence of the Cross-Shock Potential at Collisionless Magnetosonic Shock-Waves, Journal of Geophysical Research-Space Physics, 89, 6654-6662, pT: J; NR: 25; TC: 127; J9: J GEOPHYS RES-SPACE; PG: 9; GA: TG541; UT: WOS:A1984TG54100007, 1984.</text>
<text><location><page_8><loc_52><loc_29><loc_92><loc_34></location>Heppner, J. P., Maynard, N. C., and Aggson, T. L.: Early Results from Isee-1 Electric-Field Measurements, Space Science Reviews, 22, 777-789, pT: J; TC: 22; UT: WOS:A1978GM11300006, 1978.</text>
<text><location><page_8><loc_52><loc_24><loc_92><loc_29></location>Lembege, B. and Dawson, J. M.: Self-Consistent Study of a Perpendicular Collisionless and Nonresistive Shock, Physics of Fluids, 30, 1767-1788, pT: J; TC: 62; UT: WOS:A1987H901600022, 1987.</text>
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<text><location><page_8><loc_52><loc_12><loc_92><loc_18></location>Lembege, B. and Savoini, P.: Formation of reflected electron bursts by the nonstationarity and nonuniformity of a collisionless shock front, Journal of Geophysical Research-Space Physics, 107, 1037, pT: J; TC: 16; UT: WOS:000178908300001, 2002.</text>
<text><location><page_8><loc_52><loc_3><loc_92><loc_12></location>Lembege, B., Walker, S., Savoini, P., Balikhin, M., and Krasnosel'skikh, V.: The spatial sizes of electric and magnetic field gradients in a simulated shock, Microscopic Processes in Space Plasmas and their Role in Macroscale Phenomena, 24, 109-112, pT: S; CT: Symposium D0 2 of COSPAR Scientific Commission D held at the 32nd COSPAR Scientific Assembly; CY: JUL 12-19, 1998; CL: NAGOYA, JAPAN; SP: Int Union Radio Sci,</text>
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<text><location><page_9><loc_8><loc_75><loc_48><loc_82></location>Lembege, B., Savoini, P., Balikhin, M., Walker, S., and Krasnoselskikh, V.: Demagnetization of transmitted electrons through a quasi-perpendicular collisionless shock, Journal of Geophysical Research-Space Physics, 108, 1256, pT: J; TC: 8; UT: WOS:000184593000002, 2003.</text>
<text><location><page_9><loc_8><loc_68><loc_48><loc_75></location>Leroy, M., Winske, D., Goodrich, C., Wu, C., and Papadopoulos, K.: The Structure of Perpendicular Bow Shocks, Journal of Geophysical Research-Space Physics, 87, 5081-5094, pT: J; NR: 40; TC: 323; J9: J GEOPHYS RES-SPACE; PG: 14; GA: NX692; UT: WOS:A1982NX69200005, 1982.</text>
<text><location><page_9><loc_8><loc_61><loc_48><loc_68></location>Liewer, P. C., Decyk, V. K., Dawson, J. M., and Lembege, B.: Numerical-Studies of Electron Dynamics in Oblique QuasiPerpendicular Collisionless Shock-Waves, Journal of Geophysical Research-Space Physics, 96, 9455-9465, pT: J; TC: 27; UT: WOS:A1991FV65100006, 1991.</text>
<text><location><page_9><loc_8><loc_54><loc_48><loc_61></location>Scholer, M., Shinohara, I., and Matsukiyo, S.: Quasi-perpendicular shocks: Length scale of the cross-shock potential, shock reformation, and implication for shock surfing, Journal of Geophysical Research-Space Physics, 108, 1014, pT: J; TC: 69; UT: WOS:000181563700004, 2003.</text>
<text><location><page_9><loc_8><loc_47><loc_48><loc_54></location>Schwartz, S. J., Thomsen, M. F., Bame, S. J., and Stansberry, J.: Electron Heating and the Potential Jump Across Fast Mode Shocks, Journal of Geophysical Research-Space Physics, 93, 12 923-12 931, pT: J; TC: 92; UT: WOS:A1988Q745000017, 1988.</text>
<text><location><page_9><loc_8><loc_40><loc_48><loc_47></location>Schwartz, S. J., Henley, E., Mitchell, J., and Krasnoselskikh, V.: Electron Temperature Gradient Scale at Collisionless Shocks, Physical Review Letters, 107, 215 002, pT: J; NR: 34; TC: 1; J9: PHYS REV LETT; PG: 4; GA: 849OJ; UT: WOS:000297134600011, 2011.</text>
<text><location><page_9><loc_8><loc_32><loc_48><loc_40></location>Scudder, J. D., Mangeney, A., Lacombe, C., Harvey, C. C., and Aggson, T. L.: The Resolved Layer of a Collisionless, High-Beta, Supercritical, Quasi-Perpendicular Shock-Wave .2. Dissipative Fluid Electrodynamics, Journal of Geophysical Research-Space Physics, 91, 1053-1073, pT: J; TC: 79; UT: WOS:A1986F001000009, 1986.</text>
<text><location><page_9><loc_8><loc_24><loc_48><loc_32></location>Sundkvist, D., Krasnoselskikh, V., Bale, S. D., Schwartz, S. J., Soucek, J., and Mozer, F.: Dispersive Nature of High Mach Number Collisionless Plasma Shocks: Poynting Flux of Oblique Whistler Waves, Physical Review Letters, 108, 025 002, pT: J; NR: 25; TC: 1; J9: PHYS REV LETT; PG: 4; GA: 874XM; UT: WOS:000298991400014, 2012.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Manuscript prepared for Ann. Geophys. with version 5.0 of the L A T E X class copernicus.cls. Date: 2 October 2018",
"pages": [
1
]
},
{
"title": "Non-adiabatic electron behaviour due to short-scale electric field structures at collisionless shock waves",
"content": "V. See, R. F. Cameron, and S. J. Schwartz Blackett Laboratory, Imperial College London, London, SW7 2AZ, UK Correspondence to: V. See ([email protected]) Abstract. Under sufficiently high electric field gradients, electron behaviour within exactly perpendicular shocks is unstable to the so-called trajectory instability. We extend previous work paying special attention to shortiscale, high amplitude structures as observed within the electric field profile. Via test particle simulations, we show that such structures can cause the electron distribution to heat in a manner that violates conservation of the first adiabatic invariant. This is the case even if the overall shock width is larger than the upstream electron gyroradius. The spatial distance over which these structures occur therefore constitutes a new scale length relevant to the shock heating problem. Furthermore, we find that the spatial location of the short-scale structure is important in determining the total effect of non-adiabatic behaviour - a result that has not been previously noted. Keywords. Space plasma physics (Shock waves; Numerical simulation studies)",
"pages": [
1
]
},
{
"title": "1 Introduction",
"content": "Collisionless shockwaves occur throughout the universe. While often cited as the production source for high energy cosmic rays, the heating mechanisms that act on the different sub-populations of particles are still not entirely understood. Numerous studies have been conducted into the electron heating problem, with the characteristic scale length of the shock emerging as an important parameter governing the evolution of the electron distribution (Balikhin et al., 1998; Lembege et al., 1999; Schwartz et al., 2011). Additionally, despite the amount of work conducted on shock scale lengths, there is still a lack of consensus regarding the relative scales over which the magnetic and electric fields in shocks actually vary. Electrons are expected to behave adiabatically, conserving their magnetic moments µ m ≡ W ⊥ / B , as long as the shock width is larger than the upstream electron gyroradius. This behaviour allows an electron to change the kinetic energy associated with its gyrovelocity perpendicular to the magnetic field smoothly as it crosses the shock. However, Cole (1976) showed that in the presence of an electric field with constant gradient, particles will gyrate at an effective frequency, given by where Ω eff and Ω are the effective and normal gyrofrequencies, q is the charge on the particle and m is the particle mass. The effective gyrofrequency must then be used in calculating the gyroradii, i.e. where r eff g is a new effective gyroradius and v is the gyrovelocity of the particle. The condition for adiabatic behaviour must be revised such that the shock width is much bigger than the effective gyroradius. Equation (2) shows that, for certain values of ∂E x / ∂x , the effective gyrofrequency can approach zero corresponding to an extremely large effective gyroradii. Non-adiabatic electron behaviour is therefore possible, even at shocks with scale lengths much larger than an upstream gyroradius. The link between scale lengths and non-adiabatic heating was explored by Balikhin et al. (1993). The authors conducted a theoretical analysis of electron trajectories at exactly perpendicular shocks and identified the so-called trajectory instability. This instability causes two neighbouring electron trajectories to diverge exponentially from each other in phase space, causing a breaking of magnetic moment conservation, wherever Ω 2 eff < 0 , i.e. as long as the following instability criterion is obeyed: where e is magnitude of the electronic charge, m is the electron mass, Ω is the electron gyrofrequency and ∂E x / ∂x is the electric field gradient along the shock normal. The criterion requires that the electric field gradient be above some critical value or, equivalently for a given cross-shock potential, that the scale length of the electric field be below some critical value. This can be fulfilled even if the upstream gyroradius is smaller than the shock scale. The authors then showed via a series of test-particle simulations that the onset of the trajectory instability coincides with the onset of non-adiabatic heating. While Balikhin et al. (1993) draw a strong connection between the scale length of the shock and subsequent heating, they do not alter the scales of the electric and magnetic fields independently of each other, nor do they study the effect of displacing one with respect to the other. This work was subsequently extended into the oblique regime by Balikhin et al. (1998). In this paper the authors also included terms that account for the changing magnetic field, which were previously neglected, and found that the divergence in phase space always occurs and that the rate of divergence is dependent on the gradients of both the magnetic and electric fields. Further relevant work is done by Lembege et al. (2003). Two approaches were used to analyse the demagnetisation of the electrons at the shock front. In the first instance, nonstationary and nonuniformity effects were included in the form of a full-particle self-consistent simulation whilst in the second instance these effects have been removed. The authors found that the fraction of electrons which become demagnetised depends on the nonstationary behaviour found at shocks. However, it is difficult to attribute this result to any particular process or feature of the shock since it is impossible to systematically vary particular variables of interest in a full particle code. It is clear that the relative scales over which the magnetic and electric fields vary have a large impact on the type of electron heating that occurs. Indeed, the relative field scales of shocks is a topic which we study within this paper. In their paper, Balikhin et al. (1998) outlined possible relationships between the fields, though it is a matter of contention which of them occurs in reality, since various observations and simulations support differing views. It is common that both scales have the same order of magnitude in simulations and observations (Balikhin et al., 1993; Formisano and Torbert, 1982; Formisano, 1982; Balikhin et al., 2002; Leroy et al., 1982; Liewer et al., 1991; Scholer et al., 2003; Lembege and Dawson, 1989, 1987). Ba- likhin and Gedalin (1994) suggest that the variation of electron heating with upstream electron thermal Mach number v flow / v thermal -e , reported by Schwartz et al. (1988), can be recovered in this simple configuration. On the other hand, Scudder et al. (1986) analysed a shock where the electrostatic potential varied over a scale larger than the magnetic field ramp. However, Eselevich et al. (1971) reported on so-called isomagnetic jumps which were observed in laboratory plasma experiments whilst Heppner et al. (1978) reported the observations from ISEE-1 of large changes in the electric field over scales much shorter than the magnetic field ramp. More recently, Walker et al. (2004) and Bale and Mozer (2007) have shown the existence of short-scale, high-amplitude electric field structures or 'spikes' within the overall electric field profile with Bale and Mozer (2007) speculating that the spikes in the electric field profile may lead to incoherent heating of the electrons. In this paper, we will show for the first time that this is indeed possible. Using test-particle simulations, we will find the effect of varying the electric field scale length independently of the magnetic scale length; which has not been done before. Additionally, we will vary the location of the electric field within the shock. We also investigate the consequences of an electric field spike within the shock. In doing so, we will demonstrate that these electric field spikes constitute a new scale length which is important to the shock heating problem, and that its location within the shock layer can dramatically change the amount of heating observed. The rest of this paper will be structured as follows. Section 2 will cover the details behind the simulation, with the results and analysis following in section 3. Conclusions follow in section 4.",
"pages": [
1,
2
]
},
{
"title": "2.1 Field Profiles",
"content": "A test-particle approach, where static electromagnetic fields are prescribed, is chosen for this investigation. The normalisation details can be found in Balikhin et al. (1993) and are briefly reproduced here. Time is normalised to the inverse gyrofrequency, Ω -1 ; coordinates are normalised to the electron inertial length, cω -1 pe ; velocity is normalised to the upstream Alfv'en speed, v A ; and magnetic fields are normalised in terms of the upstream magnetic field strength, B u . The field profiles used are based upon the profiles described by Balikhin et al. (1993). They are idealised versions of exactly perpendicular collisionless shocks. The field profiles are shown in Fig. 1 and are given by Eq. (5), (6) and (7). The shock is at rest in the simulation frame, with the upstreampointing normal in the -ˆ x direction.",
"pages": [
2
]
},
{
"title": "2.2 Electron Distribution",
"content": "For each simulation run, a Maxwellian distribution at a temperature of 10 eV consisting of 600 electrons is initialised far upstream from the shock. Since the shock is exactly perpendicular, the electrons only require two degrees of freedom in velocity space allowing us to set v z =0 . For the purposes of this investigation, the temperature corresponding to the two perpendicular ( x , y ) degrees of freedom will be defined as follows: i.e. the temperature is proportional to the variance of the velocity vectors of all the electrons in the distribution. In practice, the parameter that will be of interest is the heating ratio, R H ; that is the ratio of the far downstream electron distribution temperature to the far upstream temperature.",
"pages": [
3
]
},
{
"title": "3 Results and Analysis",
"content": "To investigate short-scale electric field structures, it will be instructive to investigate, separately, the scale and location of the cross-shock electric field, E x . We will then move onto a final set of simulations in which the cross-shock electric field will vary over the same scale as the magnetic field with a spike embedded within it to better represent a real shock.",
"pages": [
3
]
},
{
"title": "3.1 Electric Field Scale Length",
"content": "For this experiment, we will vary D E whilst holding D B and the total cross-shock potential, e ∆ φ 0 , fixed. The starting shock parameters that will be considered are D E = D B =5 and e ∆ φ 0 =300eV . This scale length corresponds to a shock width, 2 D B , of 11.2 upstream gyroradii for a 10 eV electron. These conditions are adiabatic as shown in Fig. 4 of Balikhin et al. (1993) and will be the control case against which other simulations are compared. Figure 2 shows that as D E is decreased, the heating remains roughly adiabatic for larger D E before increasing rapidly for scale lengths below D E ∼ 3 . At these smaller electric scale lengths, the heating is significantly nonadiabatic. By holding the cross-shock potential constant and decreasing D E , the electric field gradient becomes larger. This result should therefore not present much surprise since it is already known that the separation of the adiabatic and non-adiabatic regimes in perpendicular shocks depends on the electric field gradient as given by Eq. (4). According to this criterion, the threshold of the trajectory instability occurs at D E ∼ 3 . 1 for the parameters of our simulation.",
"pages": [
3
]
},
{
"title": "3.2 Displacement of Electric Field",
"content": "Having varied the width of the electric field profile, its position relative to the rest of the shock can be altered since Here, ∆ φ 0 is the cross-shock potential and chosen to be 300 eV unless stated otherwise. E y is constant everywhere and calculated from the upstream bulk electron velocity and magnetic field strength, E y = V u B u . We use values of V u =400kms -1 and B u =5nT which are typical for earth's bow shock. When normalised, E y is equal to the Alfv'enic Mach number, M A , which we choose to be Mach 8. D E and D B are the half-electric and half-magnetic field widths normalised to the electron inertial length. Equation (5) only applies within the region of space -D E >x>D E . Everywhere outside this region, E x =0 . Similarly, Eq. (7) only applies within -D B >x>D B , taking the values B z =1 for x < -D B and B z =3 for x > D B . Adiabatic electron behaviour, conserving magnetic moment, would therefore correspond to a three-fold increase in the temperature of the electron distribution based on the jump in the magnetic field. We have chosen to use two scale lengths, D E and D B , rather than the single parameter, D = D E = D B , that Balikhin et al. (1993) use because it is important for this study that we are able to vary the two scale lengths independently. These particular forms were chosen by Balikhin et al. (1993) because they are smooth and well behaved at the shock edges and throughout the shock layer. 5 E D E is smaller than D B . The inset of Fig. 3 shows the displacement of the electric field with respect to the magnetic field such that their centres of variation no longer coincide. For this set of simulations, we fix D E =0 . 5 . As before, D B =5 and e ∆ φ 0 =300eV . Figure 3 shows a clear trend of higher (lower) heating for displacements towards the upstream (downstream) side of the shock. To understand why displacing the electric field would change the amount of heating, despite maintaining a constant electric field gradient, it is necessary to look at the drifts in the system. For the field geometries used, the electrons experience an E y ˆ y × B z ˆ z drift in the ˆ x direction, together with an E x ˆ x × B z ˆ z drift and a ∇| B | drift which are in the +ˆ y and -ˆ y directions, respectively. The E y ˆ y × B z ˆ z drift causes the electrons to drift through the shock and gain all the potential energy associated with the E x field, i.e. the cross-shock potential. This is fixed by the ∆ φ 0 parameter. The remaining two drifts cause the electrons to travel along the shock in opposite directions. The ∇| B | drift is directed such that the electrons gain kinetic energy from the motional electric field, E y . Conversely, the E x ˆ x × B z ˆ z drift is directed such that the electrons lose kinetic energy to this field. The lat- ition to the fixed cross-shock potential, therefore determine the net kinetic energy gain of the electrons as they drift through the shock (Goodrich and Scudder, 1984). It will be useful to compare two limiting cases in our explanation. The electrons will drift through most of the shock before encountering the electric field when it is displaced downstream. However, when the field is displaced upstream, the electrons will encounter it immediately and gain the entire cross-shock potential straight away. Since the ∇| B | drift speed is proportional to the kinetic energy of the electron, the magnitude of the ∇| B | drift will be larger in the second case as it has gained the energy from crossing the E x field earlier. Figure 4 shows the trajectories of three electrons which demonstrate this effect. The outer vertical lines represent the outer edges of the shock i.e. x = ± D B with the inner vertical lines representing the edges of the displaced electric field, i.e. x = δ E ± D E where δ E is the displacement of the electric field. All parameters are kept the same with the exception of the displacement of the electric field. The electron in panel (a) immediately picks up the cross-shock potential energy, e ∆ φ 0 . Initially the E x ˆ x × B z ˆ z drift dominates, resulting in the loss of some of this energy. The ∇| B | drift then operates in the E x =0 region where, due to the enhanced perpendicular velocity, a large drift velocity results in a net -ˆ y drift. This corresponds to a large non-adiabatic energy increase. Panel (b) is similar but the ∇| B | drift is less effective since the electron spends less time in the postE x region, allowing less time for the ∇| B | drift to act. In panel (c), there is no space for the ∇| B | drift to act after the electrons have crossed the cross-shock potential. The E x ˆ x × B z ˆ z drift reduces the energy gained from e ∆ φ 0 the most compared to the other panels. Outside the region in which E x is non-zero, the energy gains associated with the ∇| B | drift are roughly consistent, as expected, with adiabatic compression in the increasing magnetic field. Since this multiplies the existing particle energy, it gives the most energy to trajectories suffering early nonadiabatic processes as in panel (a). To summarise, when the electric field is displaced downstream, the electrons drift through most of the shock adiabatically, losing energy as a result of the E x ˆ x × B z ˆ z drift, before encountering the non-adiabatic divergence in phase space as discussed by Balikhin et al. (1993). When the electric field is displaced upstream, the electrons immediately experience the phase space divergence. As the electrons drift through the rest of the shock, they will undergo a further expansion in phase space due to the ∇| B | drift, the magnitude of which is larger when electric field is displaced upstream. This leads to a higher heating of the electron distribution. We note that the trajectory instability is an essential ingredient in this non-adiabatic behaviour. While the displacement of the electric field toward the upstream enhances the instability by keeping the gyrofrquency, Ω , lower in Eq. (4), experiments with different values of constant Ω (not shown) are inconclusive. Thus, we prefer to discuss the non-adiabatic behaviour in terms of the various particle drifts. Other experiments (not shown) in which a field with a larger D E is displaced remain adiabatic.",
"pages": [
3,
4,
5
]
},
{
"title": "3.3 Shock Spikes",
"content": "Whilst it has been instructive to consider these simulations, observations show structures with a scale much smaller y x than the total shock width embedded within a larger overall electric field profile (Walker et al., 2004). In one particular shock crossing, Walker et al. identified three large-amplitude, small-scale structures, the largest of which had a peak magnitude of around 45 mV / m , compared to an average motional electric field of around 14 mV / m . These were the largest amongst the field disturbances observed in the shock and occurred over the middle 50% of the shock transition. The authors estimate that the width of these structures to be around 1 -5 cω -1 pe , with the magnetic field ramp occurring over a scale ∼ 10 times this. It shall be the aim of the final set of simulations to encapsulate these features, if not the actual values themselves. Most importantly, for this particular shock crossing, Walker et al. report that the structures contribute 40% of the total cross-shock potential change. The inset of Fig. 5 shows the field profile we used to model the electric field spikes. The electric field profile shown is constructed by adding together two profiles, both described by Eq. (5) but with different D E values. The important features of the profile are D E = D B and D spike E /lessmuch D E . In keeping with the ratio of the scale lengths observed by Walker et al. (2004), D spike E is one tenth of D E . While Walker et al. (2004) reported that the overall electric field scale is slightly larger than that of the magnetic field ramp, the two scales have been kept equal here so as to allow for the independent investigation of the spikes alone. In any case, from the work of Balikhin et al. (1993), we would not expect that having D E >D B would cause the heating to be non-adiabatic, as this would make the electric field gradient smaller. For simplicity, only one electric field 'spike' has been modelled. Our base case will again be the adiabatic shock where D E = D B =5 and the total cross-shock potential is 300 eV . We choose 30 eV as the cross-spike potential with the rest of the shock accounting for the remaining 270 eV . We vary the position of the electric field spike to investigate its influence on the electron behaviour. Figure 5 shows that for displacements towards the downstream side of the shock, the heating is non-adiabatic, but the amount of heating above the adiabatic case is small. For upstream displacements, there is a much higher non-adiabatic component to the heating. The conclusions of the previous set of simulations can readily be applied here. By embedding a spike into the profile, there is now a region that satisfies the instability criterion in Eq. (4) when previously there was not, thus pushing the shock into the non-adiabatic regime. The same trend is noticed, with the heating ratio having high values for displacements towards the upstream end. However, the heating ratio is much smaller in comparison to the previous simulations; this should not be surprising given that the potential drop across the spike is much smaller. Just as before, the breaking of adiabaticity occurs earlier for displacements upstream, but the phase space expansion effect due to the ∇| B | drift is not as pronounced since the energy gains associated with the spike are smaller. At 2 D E ∼ 1 cω -1 pe , the width of our spike is at the limit of the 1 -5 cω -1 pe widths reported by Walker et al. (2004). We conclude that in general, the presence of short-scale enhancements to the electric field can push an otherwise adiabatic shock into the non-adiabatic regime. The width of the electric field spikes therefore constitute a new scale length that is important in the study of electron heating at collisionless shocks. We conducted a final simulation with three spikes at displacements of -0.5 D B , 0.0 D B and 0.5 D B embedded within an underlying electric field of width 2 D E =10 . Each spike, of width 2 D spike E =1 , contributed 30 eV to the cross-shock potential with the underlying profile contributing 210 eV for a total cross-shock potential of 300 eV . We find the heating ratio for this set-up to be R H =4 . 45 , which is not a surprising outcome based on our previous results. Figure 5 shows that the spikes at 0.0 D B and 0.5 D B have a minimal effect above adiabatic electron behaviour. The non-adiabatic behaviour found here is due predominantly to the upstreamdisplaced spike at -0 . 5 D B .",
"pages": [
5,
6,
7
]
},
{
"title": "4 Conclusions",
"content": "It has been the aim of this paper to look at the effect that the electric and magnetic field scales have on electron heating at collisionless shock waves with a focus on short-scale highamplitude structures in the electric field. Our work builds on the existing work of Balikhin et al. (1993) and is motivated by the observations of short-scale electric field structures observed by Walker et al. (2004) and Bale and Mozer (2007). Balikhin et al. (1993) showed that shorter scale lengths can lead to incoherent electron heating by satisfying an instability criterion with the short-scale electric field spike observations, providing a possible means of satisfying this criterion in reality. We have shown that the presence of small-scale structures can indeed push the heating of the electron distribution from the adiabatic into the non-adiabatic regime. Specifically, the main results of this report can be summarised as follows: The next step would be to extend our work into the oblique regime. The new scale length associated with the electric field spikes is relevant to the discussion of shock scale lengths and heating at oblique shocks by Balikhin et al. (1998). Other shock features of interest which could influence the electron dynamics include foot and overshoot regions, as well as the time dependence of the field profiles and higher-frequency fluctuations (Lembege and Savoini, 2002; Sundkvist et al., 2012). Finally, it would also be interesting to study the electrons within the shock layer, where the strong trajectory instability and short scales involved might be expected to break the gyrotropy of the distributions.",
"pages": [
8
]
},
{
"title": "References",
"content": "Bale, S. D. and Mozer, F. S.: Measurement of large parallel and perpendicular electric fields on electron spatial scales in the terrestrial bow shock, Physical Review Letters, 98, 205 001, pT: J; TC: 13; UT: WOS:000246624000031, 2007. Balikhin, M., Gedalin, M., and Petrukovich, A.: New Mechanism for Electron Heating in Shocks, Physical Review Letters, 70, 1259-1262, pT: J; TC: 35; UT: WOS:A1993KN88700019, 1993. Balikhin, M., Krasnosel'skikh, V. V., Woolliscroft, L. J. C., and Gedalin, M.: A study of the dispersion of the electron distribution in the presence of E and B gradients: Application to electron heating at quasi-perpendicular shocks, Journal of Geophysical Research-Space Physics, 103, 2029-2040, pT: J; TC: 16; UT: WOS:000071845800014, 1998. Balikhin, M. A., Nozdrachev, M., Dunlop, M., Krasnosel'skikh, V., Walker, S. N., Alleyne, H. S. K., Formisano, V., Andre, M., Balogh, A., Eriksson, A., and Yearby, K.: Observation of the terrestrial bow shock in quasi-electrostatic subshock regime, Journal of Geophysical Research-Space Physics, 107, 1155, pT: J; TC: 7; UT: WOS:000179009600036, 2002. Cole, K. D.: Effects of crossed magnetic and (spatially dependent) electric fields on charged particle motion, Planetary and Space Science, 24, 515-518, 1976. Eselevich, V. G., Eskov, A. G., Kurtmull, R. K., and Malyutin, A. I.: Isomagnetic Discontinuity in a Collisionless Shock Wave, Soviet Physics Jetp-Ussr, 33, 1120, pT: J; TC: 17; UT: WOS:A1971L306800013, 1971. Formisano, V.: Measurement of the Potential Drop Across the Earths Collisionless Bow Shock, Geophysical Research Letters, 9, 1033-1036, pT: J; TC: 30; UT: WOS:A1982PH28800032, 1982. Formisano, V. and Torbert, R.: Ion-Acoustic-Wave Forms Generated by Ion-Ion Streams at the Earths Bow Shock, Geophysical Research Letters, 9, 207-210, pT: J; TC: 16; UT: WOS:A1982NF68300010, 1982. Goodrich, C. and Scudder, J.: The Adiabatic Energy Change of Plasma Electrons and the Frame Dependence of the Cross-Shock Potential at Collisionless Magnetosonic Shock-Waves, Journal of Geophysical Research-Space Physics, 89, 6654-6662, pT: J; NR: 25; TC: 127; J9: J GEOPHYS RES-SPACE; PG: 9; GA: TG541; UT: WOS:A1984TG54100007, 1984. Heppner, J. P., Maynard, N. C., and Aggson, T. L.: Early Results from Isee-1 Electric-Field Measurements, Space Science Reviews, 22, 777-789, pT: J; TC: 22; UT: WOS:A1978GM11300006, 1978. Lembege, B. and Dawson, J. M.: Self-Consistent Study of a Perpendicular Collisionless and Nonresistive Shock, Physics of Fluids, 30, 1767-1788, pT: J; TC: 62; UT: WOS:A1987H901600022, 1987. Lembege, B. and Savoini, P.: Formation of reflected electron bursts by the nonstationarity and nonuniformity of a collisionless shock front, Journal of Geophysical Research-Space Physics, 107, 1037, pT: J; TC: 16; UT: WOS:000178908300001, 2002. Lembege, B., Walker, S., Savoini, P., Balikhin, M., and Krasnosel'skikh, V.: The spatial sizes of electric and magnetic field gradients in a simulated shock, Microscopic Processes in Space Plasmas and their Role in Macroscale Phenomena, 24, 109-112, pT: S; CT: Symposium D0 2 of COSPAR Scientific Commission D held at the 32nd COSPAR Scientific Assembly; CY: JUL 12-19, 1998; CL: NAGOYA, JAPAN; SP: Int Union Radio Sci, Comm Space Res; NR: 14; TC: 7; J9: ADV SPACE RES; PG: 4; GA: BN87R; UT: WOS:000083308000020, 1999. Lembege, B., Savoini, P., Balikhin, M., Walker, S., and Krasnoselskikh, V.: Demagnetization of transmitted electrons through a quasi-perpendicular collisionless shock, Journal of Geophysical Research-Space Physics, 108, 1256, pT: J; TC: 8; UT: WOS:000184593000002, 2003. Leroy, M., Winske, D., Goodrich, C., Wu, C., and Papadopoulos, K.: The Structure of Perpendicular Bow Shocks, Journal of Geophysical Research-Space Physics, 87, 5081-5094, pT: J; NR: 40; TC: 323; J9: J GEOPHYS RES-SPACE; PG: 14; GA: NX692; UT: WOS:A1982NX69200005, 1982. Liewer, P. C., Decyk, V. K., Dawson, J. M., and Lembege, B.: Numerical-Studies of Electron Dynamics in Oblique QuasiPerpendicular Collisionless Shock-Waves, Journal of Geophysical Research-Space Physics, 96, 9455-9465, pT: J; TC: 27; UT: WOS:A1991FV65100006, 1991. Scholer, M., Shinohara, I., and Matsukiyo, S.: Quasi-perpendicular shocks: Length scale of the cross-shock potential, shock reformation, and implication for shock surfing, Journal of Geophysical Research-Space Physics, 108, 1014, pT: J; TC: 69; UT: WOS:000181563700004, 2003. Schwartz, S. J., Thomsen, M. F., Bame, S. J., and Stansberry, J.: Electron Heating and the Potential Jump Across Fast Mode Shocks, Journal of Geophysical Research-Space Physics, 93, 12 923-12 931, pT: J; TC: 92; UT: WOS:A1988Q745000017, 1988. Schwartz, S. J., Henley, E., Mitchell, J., and Krasnoselskikh, V.: Electron Temperature Gradient Scale at Collisionless Shocks, Physical Review Letters, 107, 215 002, pT: J; NR: 34; TC: 1; J9: PHYS REV LETT; PG: 4; GA: 849OJ; UT: WOS:000297134600011, 2011. Scudder, J. D., Mangeney, A., Lacombe, C., Harvey, C. C., and Aggson, T. L.: The Resolved Layer of a Collisionless, High-Beta, Supercritical, Quasi-Perpendicular Shock-Wave .2. Dissipative Fluid Electrodynamics, Journal of Geophysical Research-Space Physics, 91, 1053-1073, pT: J; TC: 79; UT: WOS:A1986F001000009, 1986. Sundkvist, D., Krasnoselskikh, V., Bale, S. D., Schwartz, S. J., Soucek, J., and Mozer, F.: Dispersive Nature of High Mach Number Collisionless Plasma Shocks: Poynting Flux of Oblique Whistler Waves, Physical Review Letters, 108, 025 002, pT: J; NR: 25; TC: 1; J9: PHYS REV LETT; PG: 4; GA: 874XM; UT: WOS:000298991400014, 2012. Walker, S. N., Alleyne, H. S. C. K., Balikhin, M. A., Andre, M., and Horbury, T. S.: Electric field scales at quasi-perpendicular shocks, Annales Geophysicae, 22, 2291-2300, pT: J; CT: Meeting on Spatio-Temporal Analysis and Multipoint Measurements in Space; CY: MAY 12-16, 2003; CL: Orleans, FRANCE; TC: 24; UT: WOS:000223620300002, 2004.",
"pages": [
8,
9
]
}
]
2013Ap&SS.343..435T
https://arxiv.org/pdf/1104.3401.pdf
<document>
<section_header_level_1><location><page_1><loc_33><loc_92><loc_68><loc_93></location>Stable Magnetic Universes Revisited</section_header_level_1>
<text><location><page_1><loc_30><loc_86><loc_70><loc_90></location>T. Tahamtan ∗ and M. Halilsoy † Department of Physics, Eastern Mediterranean University, G. Magusa, North Cyprus, Mersin 10 - Turkey.</text>
<text><location><page_1><loc_18><loc_74><loc_83><loc_85></location>A regular class of static, cylindrically symmetric pure magnetic field metrics is rederived in a different metric ansatz in all dimensions. Radial, time dependent perturbations show that for dimensions d > 3 such spacetimes are stable at both near r ≈ 0 and large radius r →∞ . In a different gauge these stability analysis and similar results were known beforehand. For d = 3, however, simultaneous stability requirement at both, near and far radial distances can not be reconciled for time - dependent perturbations. Restricted, numerical geodesics for neutral particles reveal a confinement around the center in the polar plane. Charged, time-like geodesics for d = 4 on the other hand are shown numerically to run toward infinity.</text>
<section_header_level_1><location><page_1><loc_42><loc_68><loc_59><loc_69></location>I. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_33><loc_58><loc_33><loc_60></location>/negationslash</text>
<text><location><page_1><loc_9><loc_50><loc_92><loc_66></location>In 4 -dimensional spacetimes the electric - magnetic duality symmetry of the Maxwell equations is an important property which can not be satisfied in other dimensions unless different form fields other than 2 -forms are introduced. For this reason a dyonic solution admits a meaningful interpretation only in d = 4. The Reissner - Nordestrom (RN) solution constitutes in this regard the best example which has both electric and magnetic solutions in a symmetric manner. In other dimensions ( d = 4 ) similar duality properties can, in principle, be defined as well but physical interpretation corresponding to electric and magnetic fields turn out to be rather abstract. For such reasons, in order to avoid complications due to the absence of a tangible duality, pure electric or pure magnetic solutions seemed to attract considerable attention. This amounts to only half of the Maxwell equations, the other half being trivially satisfied. From this token we wish to resort here to the pure magnetic solutions which yield a completely solvable class without much effort. From the physical side, occurrence of pure and very strong magnetic fields associated with astronomical objects such as magnetars motivate us to search for such solutions in general relativity.</text>
<text><location><page_1><loc_9><loc_39><loc_92><loc_50></location>It was Melvin, who first studied such cylindrically symmetric parallel magnetic lines of force remaining in equilibrium under their mutual gravitational attraction in d = 4[1]. Later on, generalized version of the Melvin's magnetic universe was also considered[2]. The Melvin universe is invariant under rotation and translation along the z i axis orthogonal to the polar plane ( r, ϕ ). Thorne popularized the Melvin universe further by showing its absolute stability against small radial perturbations[3]. Due to this stability property it can be presumed that astrophysical objects emitting strong beams of magnetic fields may everlast in an accelerating universe. Additionally, in d = 3 [4] and 5 dimensional [5] cases also pure magnetic field solutions were found and their energy content investigated [6]. Pure magnetic solutions in higher dimensions are also known to exist in string, Lovelock, Yang-Mills, Born-Infeld and other theories [7].</text>
<text><location><page_1><loc_9><loc_17><loc_92><loc_39></location>In this paper, we present in a particular cylindrically symmetric metric ansatz, a class of non-singular, source-free, static, pure magnetic solutions to Einstein-Maxwell (EM) equations in all dimensions. In a different metric ansatz these solutions were known previously [4, 8]. Our principal aim is to investigate the stability of such magnetic universes against time dependent small radial perturbations and explore the possible role of dimensionality of spacetime in such matters. It has been known for a long time that for d > 3 these kind of magnetic solutions are all stable [8] . We verify these results once more in a different metric (i.e. non canonical) ansatz with supplement of the d = 3 case.. We show that for d > 3 the metrics are stable against small perturbations at both near axis z i and at far distance away from z i . We observe also that when d = 3 these two regions behave differently. Namely, the metric can be made stable at r ≈ 0 or, at r →∞ , but not simultaneously, which we phrase as 'weakly' stable. The solutions justify once more the impossibility of cylindrical magnetic field lines implosion and therefore formation of such black holes. We investigate the time-like ( d ≥ 4,with fixed polar angle) and null ( d = 3 , 4 ) geodesics for neutral particles numerically. Only for d = 4 and 5 we were able to obtain exact integrals, albeit in non-invertible forms, of the geodesics equation. In each case a confinement of geodesics is observed to take place near the central region. Due to its physical importance we consider also the time-like geodesics of a charged particle. It turns out that such geodesics can not be confined and in their proper time they diverge to infinity.</text>
<text><location><page_2><loc_9><loc_43><loc_33><loc_45></location>From these relations we can write</text>
<text><location><page_2><loc_9><loc_31><loc_13><loc_33></location>where</text>
<formula><location><page_2><loc_16><loc_25><loc_92><loc_29></location>G 0 0 = 1 4 f 3 r [ 2 ff '' r ( k -( d -3)) + rf '2 ( -k 2 +( d -6) k -( d -8) ( d -3) 2 ) +2 ff '(2 k -( d -4)) ] (9)</formula>
<formula><location><page_2><loc_14><loc_18><loc_92><loc_22></location>G d -1 d -1 = 1 4 f 3 r [ -2 ff '' r ( d -2) -rf '2 ( ( d -2) ( d -7) 2 )] . (11)</formula>
<formula><location><page_2><loc_16><loc_22><loc_92><loc_25></location>G 1 1 = 1 4 f 3 r [ rf '2 ( ( d -2) k -( d -2) ( d -3) 2 ) -2 ff '( d -2) ] (10)</formula>
<text><location><page_2><loc_9><loc_16><loc_47><loc_18></location>From equation (6) we obtain the differential equation</text>
<formula><location><page_2><loc_39><loc_13><loc_92><loc_15></location>2 rf '' f +( k -2) rf ' 2 -2 ff '= 0 . (12)</formula>
<text><location><page_2><loc_9><loc_10><loc_28><loc_12></location>whose solution for d ≥ 4 is</text>
<text><location><page_2><loc_9><loc_89><loc_92><loc_93></location>Organization of the paper is as follows. In Section II we present our metric, field equations and solve them in d -dimensions. Perturbation analysis of our system follows in Section III. Geodesics motion is studied in Section IV. Our results are summarized in Conclusion which appears in Section V.</text>
<section_header_level_1><location><page_2><loc_19><loc_85><loc_81><loc_86></location>II. METRIC AND SOLUTIONS OF FIELD EQUATIONS IN d -DIMENSIONS</section_header_level_1>
<text><location><page_2><loc_10><loc_81><loc_69><loc_83></location>Our d -dimensional static, cylindrically symmetric line element ansatz is given by</text>
<formula><location><page_2><loc_24><loc_74><loc_92><loc_79></location>ds 2 = f ( r ) ( dt 2 -dr 2 -d -3 ∑ i =1 dz 2 i ) -r 2 b 2 0 f ( r ) k dϕ 2 , d ≥ 3 (1)</formula>
<text><location><page_2><loc_9><loc_72><loc_92><loc_75></location>in which f ( r ) is a function of r to be found and b 0 and k are constant parameters. Also the pure magnetic 2 -form field is chosen to be</text>
<formula><location><page_2><loc_45><loc_68><loc_92><loc_71></location>F = F rϕ dr ∧ dϕ, (2)</formula>
<text><location><page_2><loc_9><loc_67><loc_91><loc_68></location>where F rϕ is the only non-zero component of the electromagnetic field. The energy momentum tensor is defined by</text>
<formula><location><page_2><loc_39><loc_61><loc_92><loc_64></location>4 πT j i = -F ik F jk + 1 4 δ j i F mn F mn (3)</formula>
<text><location><page_2><loc_9><loc_59><loc_37><loc_61></location>which admits the non-zero components</text>
<formula><location><page_2><loc_28><loc_52><loc_92><loc_57></location>T j i = diag [ T 0 0 = T 2 2 = T 3 3 = · · · = -T 1 1 = -T d -1 d -1 ] = 1 8 π F rϕ F rϕ . (4)</formula>
<text><location><page_2><loc_9><loc_49><loc_92><loc_53></location>We note that our choice of indices { 0 , 1 , 2 , . . . , ( d -1) } denote { t, r, z 1 , · · · , z d -3 , ϕ } and the energy conditions satisfied by this energy-momentum tensor are discussed in the Appendix A. From the Einstein equations, T j i = G j i Eq. (4) implies that</text>
<formula><location><page_2><loc_37><loc_45><loc_92><loc_47></location>G 0 0 = G 2 2 = G 3 3 = · · · = -G 1 1 = -G d -1 d -1 . (5)</formula>
<formula><location><page_2><loc_45><loc_37><loc_92><loc_39></location>G 1 1 = G d -1 d -1 (6)</formula>
<formula><location><page_2><loc_45><loc_33><loc_92><loc_35></location>G 0 0 = -G d -1 d -1 (8)</formula>
<formula><location><page_2><loc_45><loc_35><loc_92><loc_37></location>G 1 1 = -G 0 0 (7)</formula>
<formula><location><page_2><loc_43><loc_8><loc_92><loc_10></location>f ( r ) = ( kr 2 + C 1 ) 2 k . (13)</formula>
<text><location><page_3><loc_9><loc_90><loc_92><loc_93></location>By putting this result into Eq. (7) for finding k we find out that for d ≥ 4, k is d -3 . On the other hand, for d = 3 the solution turns out to be</text>
<formula><location><page_3><loc_45><loc_88><loc_92><loc_90></location>f ( r ) = C 2 e cr 2 (14)</formula>
<text><location><page_3><loc_9><loc_85><loc_92><loc_88></location>for the integration constants C 2 and c . For convenience we make the choices C 1 = d -3 and C 2 = 1, so that the solution can be expressed by</text>
<formula><location><page_3><loc_23><loc_79><loc_92><loc_83></location>f ( r ) = { ( d -3) 2 d -3 ( r 2 +1) 2 d -3 d ≥ 4 e cr 2 d = 3 . (15)</formula>
<text><location><page_3><loc_9><loc_77><loc_40><loc_78></location>Accordingly, our line element takes the form</text>
<formula><location><page_3><loc_19><loc_70><loc_92><loc_75></location>ds 2 = ( d -3) 2 d -3 ( r 2 +1) 2 d -3 ( dt 2 -dr 2 -d -3 ∑ i =1 dz 2 i ) -r 2 b 2 0 ( d -3) 2 ( r 2 +1) 2 dϕ 2 , d ≥ 4 e cr 2 dt 2 -dr 2 -r 2 b 2 0 dϕ 2 , d = 3 . (16)</formula>
<text><location><page_3><loc_9><loc_66><loc_92><loc_72></location> ( ) We note that these solutions are not new, for they coincide with those of [8] (for d ≥ 4) and [4] for ( d = 3), respectively. It can easily be seen that for r → 0 it reduces to the following form</text>
<formula><location><page_3><loc_19><loc_60><loc_92><loc_65></location>ds 2 ≈ ( d -3) 2 d -3 ( dt 2 -dr 2 -d -3 ∑ i =1 dz 2 i ) -r 2 b 2 0 ( d -3) 2 dϕ 2 , d ≥ 4 ( dt 2 -dr 2 ) -r 2 b 2 0 dϕ 2 , d = 3 (17)</formula>
<text><location><page_3><loc_10><loc_53><loc_35><loc_55></location>From Maxwell's Eq. it fallows that</text>
<text><location><page_3><loc_9><loc_54><loc_92><loc_62></location> This represents a conical geometry signalling the existence of a cosmic string near r = 0. By choosing b 2 0 ( d -3) 2 = 1 for d ≥ 4 and b 0 = 1 for d = 3 , we have Minkowskian metrics as one approaches the axes z i . The solution (16) is a singularity free magnetic universe in d -dimensions in analogy with the Melvin space time.</text>
<formula><location><page_3><loc_26><loc_46><loc_92><loc_50></location>F rϕ = { B 0 ( d -3) 2 d -3 rb 0 (1+ r 2 ) 2 d -3 , d ≥ 4 B 0 rb 0 e -cr 2 , d = 3 (18)</formula>
<text><location><page_3><loc_32><loc_45><loc_33><loc_46></location>(</text>
<text><location><page_3><loc_33><loc_45><loc_34><loc_46></location>B</text>
<text><location><page_3><loc_34><loc_44><loc_35><loc_45></location>0</text>
<text><location><page_3><loc_35><loc_45><loc_55><loc_46></location>= an integration constant)</text>
<text><location><page_3><loc_9><loc_43><loc_58><loc_44></location>which implies that the magnetic field behaviors as a function of r are</text>
<formula><location><page_3><loc_32><loc_37><loc_68><loc_41></location>F rϕ ∼ { r (1+ r 2 ) 2 d ≥ 4 r d = 3 .</formula>
<text><location><page_3><loc_9><loc_34><loc_92><loc_37></location>The marked distinction between d = 3 and d ≥ 4 cases can already be seen from these behaviors. Accordingly the energy density reads</text>
<formula><location><page_3><loc_28><loc_27><loc_92><loc_32></location>T 0 0 = B 2 0 8 π ( d -3) 2 d -4 d -3 (1+ r 2 ) 2 d -4 d -3 d ≥ 4 B 2 0 8 π e -cr 2 d = 3 (19)</formula>
<text><location><page_3><loc_9><loc_25><loc_39><loc_29></location> while the Ricci scalar for the metric (16) is</text>
<formula><location><page_3><loc_37><loc_16><loc_92><loc_24></location>R = -4( d -4)( d -3) 1 -d d -3 (1+ r 2 ) 2( d -2) d -3 d ≥ 4 2 ce -cr 2 d = 3 . (20)</formula>
<text><location><page_3><loc_9><loc_16><loc_45><loc_20></location> Similarly, the Kretchmann scalar has the behavior</text>
<formula><location><page_3><loc_27><loc_11><loc_92><loc_15></location>K ∼ { 1 ( d -3) 4( d -2) d -3 (1+ r 2 ) 4( d -2) d -3 d ≥ 4 12 c 2 e -2 cr 2 d = 3 . (21)</formula>
<text><location><page_3><loc_9><loc_8><loc_84><loc_10></location>It is observed that regularity at r →∞ dictates us to make the choice c > 0 for the integration constant.</text>
<section_header_level_1><location><page_4><loc_36><loc_92><loc_64><loc_93></location>III. PERTURBATION ANALYSIS</section_header_level_1>
<text><location><page_4><loc_9><loc_84><loc_92><loc_88></location>In this section we perturb the metric and magnetic potential. Since the case d = 3 forms a special case we consider it separately. Similar analysis was carried out by Gibbons and Wiltshire [8] where they used the canonical metric ansatz. We shall show below that their results can also be obtained in a different metric ansatz.</text>
<formula><location><page_4><loc_43><loc_80><loc_58><loc_81></location>1. The case for d = 3</formula>
<text><location><page_4><loc_10><loc_77><loc_24><loc_78></location>Our line element is</text>
<text><location><page_4><loc_9><loc_69><loc_13><loc_70></location>where</text>
<formula><location><page_4><loc_37><loc_70><loc_92><loc_75></location>ds 2 = f ( r, t ) ( dt 2 -dr 2 ) -r 2 b 2 0 g ( r, t ) dϕ 2 (22)</formula>
<formula><location><page_4><loc_41><loc_65><loc_92><loc_68></location>f ( r, t ) = f 0 ( r ) + /epsilon1u ( r, t ) (23) g ( r, t ) = g 0 ( r ) + /epsilon1w ( r, t )</formula>
<text><location><page_4><loc_9><loc_62><loc_39><loc_63></location>and the magnetic potential is expressed by</text>
<text><location><page_4><loc_9><loc_56><loc_31><loc_57></location>The unperturbed functions are</text>
<formula><location><page_4><loc_41><loc_58><loc_92><loc_59></location>A ϕ ( r, t ) = A ϕ ( r ) + /epsilon1a ( r, t ) . (24)</formula>
<formula><location><page_4><loc_45><loc_51><loc_92><loc_53></location>f 0 ( r ) = e cr 2 (25)</formula>
<formula><location><page_4><loc_45><loc_50><loc_92><loc_51></location>g 0 ( r ) = 1 (26)</formula>
<formula><location><page_4><loc_44><loc_46><loc_92><loc_49></location>A ϕ ( r ) = B 0 b 0 r 2 2 (27)</formula>
<text><location><page_4><loc_9><loc_41><loc_92><loc_45></location>where u ( r, t ) , w ( r, t ) and a ( r, t ) are the perturbed functions. Since /epsilon1 is a small parameter we assume that /epsilon1 2 ≈ 0 in our analysis. We use Einstein's equations to find the perturbed functions. The differential equations satisfied by the perturbed functions are</text>
<formula><location><page_4><loc_11><loc_36><loc_92><loc_40></location>( cr 2 ∂w ( r, t ) ∂r -r ∂ 2 w ( r, t ) ∂t 2 ) e cr 2 + b 0 [ r ∂ 2 u ( r, t ) ∂r 2 -r ∂ 2 u ( r, t ) ∂t 2 -4 r 2 c ∂u ( r, t ) ∂r +4 r 3 c 2 u ( r, t ) -∂u ( r, t ) ∂r ] = 0 (28)</formula>
<formula><location><page_4><loc_36><loc_31><loc_92><loc_34></location>r ∂ 2 w ( r, t ) ∂r 2 +2 ∂w ( r, t ) ∂r -r ∂ 2 w ( r, t ) ∂t 2 = 0 (29)</formula>
<formula><location><page_4><loc_30><loc_26><loc_92><loc_29></location>-∂ 2 a ( r, t ) ∂t 2 + ∂ 2 a ( r, t ) ∂r 2 -1 r ∂a ( r, t ) ∂r + B 0 b 0 r 2 ∂w ( r, t ) ∂r = 0 . (30)</formula>
<text><location><page_4><loc_9><loc_24><loc_50><loc_25></location>This system of differential equations admits the solutions</text>
<formula><location><page_4><loc_15><loc_14><loc_92><loc_21></location>u ( r, t ) = e -αt + cr 2 ( 4 rB 0 b 0 [ B 1 I 1 ( αr ) + B 2 K 1 ( αr )] + (31) cre ( -αr -α ) { -(sinh αr +cosh αr )( E 1 + E 2 ) e 2 αr + e 2 α (sinh αr -cosh αr )( -E 1 + E 2 ) } + { ( crE 2 -αE 1 ) cosh αr +( crE 1 -αE 2 ) sinh αr } )</formula>
<formula><location><page_4><loc_36><loc_8><loc_92><loc_11></location>w ( r, t ) = e -αt ( E 1 sinh αr r + E 2 cosh αr r ) (32)</formula>
<formula><location><page_5><loc_15><loc_84><loc_92><loc_91></location>a ( r, t ) = re -αt ( B 1 I 1 ( αr ) + B 2 K 1 ( αr ) -(33) B 0 b 0 4 e -αr -α { (sinh αr +cosh αr )( E 1 + E 2 ) e 2 αr + e 2 α (sinh αr -cosh αr )( -E 1 + E 2 ) } ) ,</formula>
<text><location><page_5><loc_9><loc_80><loc_92><loc_85></location>where B 1 , B 2 , E 1 , E 2 and α are all integration constants while I 1 ( αr ) and K 1 ( αr ) are the modified Bessel functions of order one. At all times t , to a first order in /epsilon1 , the locally flat nature of the metric near r = 0 will not be altered [1]. This implies when r → 0</text>
<formula><location><page_5><loc_13><loc_73><loc_92><loc_78></location>u ( r, t ) = e -αt + cr 2 ( 4 rB 0 b 0 B 2 K 1 ( αr ) -crE 1 e -αr -α { (sinh αr +cosh αr ) e 2 rα + e 2 α (sinh αr -cosh αr ) } (34) + E 1 { cr sinh αr -α cosh αr } ) ,</formula>
<formula><location><page_5><loc_42><loc_68><loc_92><loc_71></location>w ( r, t ) = e -αt E 1 sinh αr r , (35)</formula>
<formula><location><page_5><loc_17><loc_61><loc_92><loc_66></location>a ( r, t ) = re -αt ( B 2 K 1 ( αr ) -b 0 B 0 4 E 1 e -αr -α { (sinh α +cosh α ) e 2 αr -e 2 α (sinh α -cosh α ) } ) . (36)</formula>
<text><location><page_5><loc_9><loc_54><loc_92><loc_62></location>It is seen that we can choose B 1 = 0 and E 2 = 0 to have finite limit when r → 0. However, for r → ∞ it can be checked that w ( r, t ) diverges and since g 0 ( r ) = 1 this implies that the ratio of w ( r,t ) g 0 ( r ) grows indefinitely. No other choice of constants suffice to eliminate this divergence. As a result the perturbation converges for r → 0 but diverges for r → ∞ in d = 3 case. Let us note that for the time - independent perturbation both, near and far - region perturbation terms become convergent.</text>
<section_header_level_1><location><page_5><loc_39><loc_50><loc_61><loc_51></location>2. The case for d = 5 and d > 5</section_header_level_1>
<text><location><page_5><loc_10><loc_46><loc_50><loc_47></location>Our perturbed line element now for d = 5 is of the form</text>
<formula><location><page_5><loc_33><loc_39><loc_92><loc_43></location>ds 2 = f ( r, t ) ( dt 2 -dr 2 -dx 2 -dy 2 ) -r 2 b 2 0 g ( r, t ) dϕ 2 (37)</formula>
<text><location><page_5><loc_9><loc_36><loc_92><loc_39></location>From Eq. (23) and (24) we introduce in analogy, the perturbed functions in which the unperturbed functions are given by</text>
<formula><location><page_5><loc_42><loc_32><loc_92><loc_34></location>f 0 ( r ) = 2( r 2 +1) (38)</formula>
<formula><location><page_5><loc_42><loc_31><loc_92><loc_32></location>g 0 ( r ) = 4( r 2 +1) 2 (39)</formula>
<formula><location><page_5><loc_41><loc_27><loc_92><loc_30></location>A ϕ ( r ) = -B 0 b 0 8 1 ( r 2 +1) (40)</formula>
<text><location><page_5><loc_9><loc_25><loc_92><loc_26></location>From the Einstein's equations we obtain to the first order in /epsilon1 the following differential equations for u ( r, t ) and w ( r, t )</text>
<formula><location><page_5><loc_38><loc_20><loc_92><loc_23></location>r ∂ 2 u ( r, t ) ∂r 2 -∂u ( r, t ) ∂r -ru ( r, t ) = 0 (41)</formula>
<formula><location><page_5><loc_38><loc_16><loc_92><loc_19></location>2( r 2 +1) ∂ 2 u ( r, t ) ∂t 2 -1 2 ∂ 2 w ( r, t ) ∂t 2 = 0 (42)</formula>
<text><location><page_5><loc_9><loc_14><loc_34><loc_16></location>Integration of these equations yield</text>
<formula><location><page_5><loc_34><loc_10><loc_92><loc_12></location>u ( r, t ) = e -αt [ r ( pI 1 ( αr ) + qK 1 ( αr ))] (43)</formula>
<formula><location><page_5><loc_33><loc_8><loc_92><loc_10></location>w ( r, t ) = 4 e -αt [ r ( pI 1 ( αr ) + qK 1 ( αr ))] ( r 2 +1) (44)</formula>
<text><location><page_6><loc_9><loc_87><loc_92><loc_93></location>for integration constants p, q and α , and I 1 ( αr ) and K 1 ( αr ) are the modified Bessel functions of order one. At all times t , to a first order in /epsilon1 , the locally flat nature of the metric near r = 0 remains intact. Also, for all times to a first order in /epsilon1 , the static metric for r → ∞ will not be altered. In this case we see that perturbed functions are finite at r = 0 , and when r →∞ they go to zero.</text>
<text><location><page_6><loc_9><loc_85><loc_92><loc_87></location>A similar analysis has been carried out for d = 6 , 7 , ... so that we found the general solution for the metric functions. In each case we have obtained the following relations between w ( r, t ) and u ( r, t )</text>
<formula><location><page_6><loc_40><loc_79><loc_92><loc_82></location>w ( r, t ) = ( d -3) g 0 ( r ) f 0 ( r ) u ( r, t ) (45)</formula>
<formula><location><page_6><loc_40><loc_76><loc_92><loc_79></location>f 0 ( r ) = ( d -3) 2 d -3 ( r 2 +1) 2 d -3 (46)</formula>
<formula><location><page_6><loc_41><loc_74><loc_92><loc_77></location>g 0 ( r ) = ( d -3) 2 ( r 2 +1) 2 . (47)</formula>
<text><location><page_6><loc_9><loc_72><loc_57><loc_74></location>Solutions for w ( r, t ) and u ( r, t ) are given in all dimensions as follow</text>
<formula><location><page_6><loc_29><loc_67><loc_92><loc_70></location>w ( r, t ) = ( d -3) 3 d -11 d -3 ( r 2 +1) 2 d -8 d -3 u ( r, t ) , (48)</formula>
<formula><location><page_6><loc_29><loc_65><loc_92><loc_68></location>u ( r, t ) = e -αt ( d -3) d -1 d -3 ( pI 1 ( αr ) + qK 1 ( αr )) r ( r 2 +1) d -5 d -3 , (49)</formula>
<text><location><page_6><loc_9><loc_59><loc_92><loc_63></location>in which p and q are constants. These are both finite at r → 0 and the ratio of them when r → ∞ go to zero. Now, from Maxwell's equations we attempt to find the perturbative solution for the magnetic potential. We take the potential in the form</text>
<formula><location><page_6><loc_41><loc_55><loc_60><loc_56></location>A ϕ ( r, t ) = A ϕ ( r ) + /epsilon1a ( r, t )</formula>
<text><location><page_6><loc_9><loc_53><loc_13><loc_54></location>where</text>
<formula><location><page_6><loc_40><loc_46><loc_92><loc_50></location>A ϕ ( r ) = -B 0 b 0 2( d -3) 2 1 ( r 2 +1) . (50)</formula>
<text><location><page_6><loc_10><loc_45><loc_48><loc_46></location>The differential equation satisfied by a ( r, t ) becomes</text>
<formula><location><page_6><loc_19><loc_37><loc_92><loc_42></location>-∂ 2 a ( r, t ) ∂t 2 + ∂ 2 a ( r, t ) ∂r 2 + ( 3 r 2 -1 ) r ( r 2 +1) ∂a ( r, t ) ∂r + b 0 B 0 r ( d -3) d -1 d -3 ( r 2 +1) 2 d dr [ u ( r, t ) ( r 2 +1) 2 d -3 ] = 0 (51)</formula>
<text><location><page_6><loc_9><loc_36><loc_15><loc_37></location>in which</text>
<formula><location><page_6><loc_29><loc_30><loc_92><loc_34></location>u ( r, t ) = e -αt ( d -3) d -1 d -3 ( pI 1 ( αr ) + qK 1 ( αr )) r ( r 2 +1) d -5 d -3 . (52)</formula>
<text><location><page_6><loc_10><loc_28><loc_86><loc_29></location>Upon substitution for u ( r, t ) we see that for all dimensions the equation satisfied by a ( r, t ) takes the form</text>
<formula><location><page_6><loc_16><loc_21><loc_92><loc_25></location>-∂ 2 a ( r, t ) ∂t 2 + ∂ 2 a ( r, t ) ∂r 2 + ( 3 r 2 -1 ) r ( r 2 +1) ∂a ( r, t ) ∂r + b 0 B 0 re -αt ( r 2 +1) 2 d dr [ r ( r 2 +1) ( pI 1 ( αr ) + qK 1 ( αr )) ] = 0 . (53)</formula>
<text><location><page_6><loc_9><loc_17><loc_92><loc_21></location>An exact solution for a ( r, t ) for all r is not at our disposal, therefore, we shall search for solutions near r = 0 and for r →∞ . The solution for the homogenous part is</text>
<formula><location><page_6><loc_35><loc_13><loc_92><loc_15></location>a H ( r, t ) = re -αt ( r 2 +1) ( C 1 I 1 ( αr ) + C 2 K 1 ( αr )) . (54)</formula>
<text><location><page_6><loc_9><loc_9><loc_92><loc_11></location>Since a particular solution is not available we proceed to study the answers for a limited case, when r is small (to order r )</text>
<formula><location><page_7><loc_36><loc_86><loc_92><loc_91></location>-∂ 2 a ( r, t ) ∂t 2 + ∂ 2 a ( r, t ) ∂r 2 -1 r ∂a ( r, t ) ∂r = 0 , (55) a ( r, t ) = e -αt r ( C 1 I 1 ( αr ) + C 2 K 1 ( αr )) .</formula>
<text><location><page_7><loc_9><loc_83><loc_54><loc_85></location>If we go to higher orders of r , (order r 3 for instance) we obtain</text>
<formula><location><page_7><loc_13><loc_77><loc_92><loc_81></location>-∂ 2 a ( r, t ) ∂t 2 + ∂ 2 a ( r, t ) ∂r 2 + [ 4 r -1 r ] ∂a ( r, t ) ∂r + b 0 B 0 r 2 { -pα ( -ln ( 1 2 α ) -ln r -γ ) + pα -2 q α } = 0 (56)</formula>
<text><location><page_7><loc_9><loc_75><loc_34><loc_76></location>whose solution can be expressed as</text>
<formula><location><page_7><loc_10><loc_69><loc_92><loc_73></location>a ( r, t ) = e -r 2 -αt { C 3 Whitta ker M ( -1 8 α 2 , 1 2 , 2 r 2 ) + C 4 Whitta ker M ( -1 8 α 2 , 1 2 , 2 r 2 ) } -B 0 b 0 e -αt α ( -8 + α 2 ) 2 (Ξ + Π) (57)</formula>
<text><location><page_7><loc_9><loc_67><loc_15><loc_68></location>in which</text>
<formula><location><page_7><loc_23><loc_60><loc_77><loc_66></location>Ξ = -α 2 r 2 q ( -8 + α 2 ) ln α -α 2 r 2 q ( -8 + α 2 ) ln r +[ q (ln 2 -γ ) -p ] α 4 r 2 , Π = ([ (8 γ -2 -8 ln 2) r 2 -2 ] q +8 r 2 p ) α 2 +16 q -16 r 2 q.</formula>
<text><location><page_7><loc_9><loc_57><loc_92><loc_61></location>Here p, q, C 3 , C 4 , α and γ are all constants and WhittakerM ( -1 8 α 2 , 1 2 , 2 r 2 ) stands for the Whittaker function[9]. For r → 0 the function a ( r, t ) is finite. Now, to see the case when r goes to infinity we solve the differential equation</text>
<formula><location><page_7><loc_34><loc_52><loc_92><loc_55></location>-∂ 2 a ( r, t ) ∂t 2 + ∂ 2 a ( r, t ) ∂r 2 = 0 , (to order 1 /r ) (58)</formula>
<text><location><page_7><loc_9><loc_50><loc_24><loc_51></location>whose solution reads</text>
<formula><location><page_7><loc_38><loc_43><loc_92><loc_47></location>a ( r, t ) = e -αt ( C 5 e αr + C 6 e -αr ) . (59)</formula>
<text><location><page_7><loc_9><loc_41><loc_92><loc_44></location>Here C 5 and C 6 are new integration constants. It can easily be checked that the ratio of this solution goes to zero for r →∞ if we choose C 5 = 0 .</text>
<section_header_level_1><location><page_7><loc_40><loc_38><loc_61><loc_39></location>IV. GEODESIC MOTION</section_header_level_1>
<text><location><page_7><loc_9><loc_31><loc_92><loc_35></location>In this section we shall investigate the time-like (for d ≥ 4) and null (for d = 3 , 4) geodesics by employing our line element given in Eq. (15). For d ≥ 4 we divide the line element by dτ ( τ is proper time) and for d = 3 by dλ ( λ is an affine parameter) so that the Lagrangian can be expressed in the form</text>
<formula><location><page_7><loc_15><loc_21><loc_92><loc_29></location>L = ( d -3) 2 d -3 ( r 2 +1) 2 d -3 [ ( dt dτ ) 2 -( dr dτ ) 2 -d -3 ∑ i =1 ( dz i dτ ) 2 ] -r 2 b 2 0 ( d -3) 2 ( r 2 +1) 2 ( dϕ dτ ) 2 , d ≥ 4 e cr 2 [ ( dt dλ ) 2 -( dr dλ ) 2 ] -r 2 b 2 0 ( dϕ dλ ) 2 , d = 3 . (60)</formula>
<text><location><page_7><loc_9><loc_19><loc_92><loc_22></location>For the equations of motion with constant azimuthal angle ( ϕ =constant for d ≥ 4) and null geodesics for d = 3 we obtain</text>
<formula><location><page_7><loc_37><loc_8><loc_92><loc_18></location> dt dτ = d 0 ( d -3) 2 d -3 ( r 2 +1) 2 d -3 dz i dτ = d i ( d -3) 2 d -3 ( r 2 +1) 2 d -3 d ≥ 4 dt dλ = H 0 e -cr 2 dϕ dλ = H 1 r 2 b 2 0 d = 3 (61)</formula>
<text><location><page_8><loc_9><loc_90><loc_92><loc_93></location>in which d 0 , d i , H 0 and H 1 are all constants of integration. From the metric condition we find dr dτ (for d ≥ 4, ϕ = constant) and dr dλ (for d = 3) as follow</text>
<formula><location><page_8><loc_17><loc_76><loc_92><loc_88></location> dr dτ = ± 1 ( d -3) 2 d -3 ( r 2 +1) 2 d -3 √ a 2 0 -( d -3) 2 d -3 ( r 2 +1) 2 d -3 a 2 0 = d 2 0 -d -3 ∑ i =1 d 2 i d ≥ 4 dr dλ = ± H 0 e -cr 2 √ 1 -H 2 2 r 2 e cr 2 H 2 = H 1 H 0 b 0 d = 3 (62)</formula>
<text><location><page_8><loc_9><loc_74><loc_92><loc_79></location> In effect, we obtain for d = 4 the relation between r and τ but for d = 3 we want to find the relation between r and ϕ.</text>
<formula><location><page_8><loc_17><loc_61><loc_92><loc_72></location> ± ( τ -τ 0 ) = ( d -3) 1 d -3 ∫ ( r 2 +1) 2 d -3 dr √ k 2 0 -( r 2 +1) 2 d -3 ( k 0 = a 0 ( d -3) 1 d -3 ) d ≥ 4 (63) ± ( ϕ -ϕ 0 ) = 1 H 0 ∫ e cr 2 dr r √ r 2 -H 2 2 e cr 2 d = 3 (64)</formula>
<text><location><page_8><loc_9><loc_60><loc_65><loc_61></location>in which, τ 0 and ϕ 0 are initial constants and we impose the restrictions so that</text>
<formula><location><page_8><loc_13><loc_54><loc_92><loc_57></location>{ ( r 2 +1) 2 d -3 < k 2 0 d ≥ 4 H 2 2 r 2 e cr 2 < 1 d = 3 . (65)</formula>
<text><location><page_8><loc_9><loc_51><loc_44><loc_53></location>For d = 4 and 5, we have exact integrals given by</text>
<text><location><page_8><loc_9><loc_40><loc_15><loc_42></location>in which</text>
<formula><location><page_8><loc_21><loc_40><loc_92><loc_49></location>τ -τ 0 = -1 3 r √ k 2 0 -( r 2 +1) 2 + √ 1+ r 2 ( k 0 +1) ( k 0 -1) √ 1 -r 2 ( k 0 -1) 3 √ k 2 0 -( r 2 +1) 2 √ k 0 -1 Ω d = 4 √ 2 [ -1 2 r √ k 2 0 -( r 2 +1) + 1 2 ( k 2 0 +1 ) arctan ( r √ k 2 0 -( r 2 +1) )] d = 5 (66)</formula>
<formula><location><page_8><loc_12><loc_35><loc_88><loc_40></location>Ω = ( k 2 0 -2 k 0 ) EllipticF ( r √ k 0 -1 , √ -1 + 2 ( k 0 +1) ) +(2 k 0 +2)EllipticF ( r √ k 0 -1 , √ -1 + 2 ( k 0 +1) ) .</formula>
<text><location><page_8><loc_9><loc_32><loc_92><loc_35></location>Fig.s 1a and 1b depict the behaviors of (63) (for d = 4) and (66) (for d = 5) , respectively. Now, we wish to consider the d = 4 null geodesics as well. The line element is</text>
<formula><location><page_8><loc_33><loc_25><loc_92><loc_30></location>ds 2 = ( r 2 +1) 2 ( dt 2 -dr 2 -dz 2 ) -r 2 b 2 0 ( r 2 +1) 2 dϕ 2 (67)</formula>
<text><location><page_8><loc_9><loc_24><loc_43><loc_25></location>Eq.s of motion imply for the affine parameter λ</text>
<formula><location><page_8><loc_30><loc_19><loc_92><loc_22></location>dt dλ = α 0 ( r 2 +1) 2 , dz dλ = β 0 ( r 2 +1) 2 , dϕ dλ = γ 0 ( r 2 +1) 2 r 2 (68)</formula>
<text><location><page_8><loc_9><loc_15><loc_92><loc_17></location>in which α 0 , β 0 and γ 0 are integration constants. We note that (67) and (68) correspond to Eq.s (1) and (6) of [3], respectively. From the null-metric condition ds 2 = 0 and upon shifting the independent variable to ϕ we obtain</text>
<formula><location><page_8><loc_37><loc_7><loc_92><loc_13></location>± ( ϕ -ϕ 0 ) = ∫ ( r 2 +1) 4 dr r √ λ 2 0 r 2 -b 2 0 ( r 2 +1) 4 , (69)</formula>
<text><location><page_9><loc_9><loc_90><loc_92><loc_93></location>where we have introduced the constant λ 0 as λ 2 0 = α 2 0 -β 2 0 γ 2 0 . Fig.s 2a and 2b are the plots corresponding to (64) and (69), respectively.</text>
<text><location><page_9><loc_9><loc_87><loc_92><loc_90></location>Finally, we study the 4-dimensional time-like geodesics of a charged particle with charge e whose Lagrangian is given by</text>
<formula><location><page_9><loc_18><loc_79><loc_92><loc_83></location>L = ( r 2 +1) 2 [ ( dt dτ ) 2 -( dr dτ ) 2 -( dz dτ ) 2 ] -r 2 b 2 0 ( r 2 +1) 2 ( dϕ dτ ) 2 -eB 0 b 0 2 1 ( r 2 +1) ( dϕ dτ ) . (70)</formula>
<text><location><page_9><loc_9><loc_77><loc_42><loc_78></location>The Euler-Lagrange equations of motion yield</text>
<formula><location><page_9><loc_20><loc_71><loc_92><loc_75></location>dt dτ = l 0 ( r 2 +1) 2 , dz dτ = µ 0 ( r 2 +1) 2 , dϕ dτ = 1 2 ( -σ 0 r 2 -σ 0 + b 0 a 1 ) ( r 2 +1) b 2 0 r 2 , a 1 = -eB 0 2 , (71)</formula>
<text><location><page_9><loc_9><loc_67><loc_92><loc_70></location>for the integration constants l 0 , µ 0 and σ 0 . Since we shall be interested only in the r ( τ ) behavior of the motion we derive the second order equation as follows</text>
<formula><location><page_9><loc_20><loc_54><loc_92><loc_65></location>-2( r 2 +1) 2 d 2 r dτ 2 + [ -8 r ( r 2 +1) + 4 r ( r 2 +1) 3 ( r 8 +4 r 6 +6 r 4 +4 r 2 +1 ) ]( dr dτ ) 2 (72) + 1 2 r 3 b 2 0 ( r 2 +1) 3 [ σ 2 0 r 10 +3 σ 2 0 r 8 + r 6 ( 2 σ 2 0 + b 2 0 a 2 1 ) -r 4 ( 2 σ 2 0 + b 2 0 [ -3 a 2 1 +2 µ 2 0 -2 l 2 0 ]) -r 2 ( 3 σ 2 0 -3 a 2 1 b 2 0 ) -σ 2 0 + a 2 1 b 2 0 ] = 0 .</formula>
<text><location><page_9><loc_9><loc_51><loc_92><loc_55></location>For a set of chosen constants and initial values we plot the behavior of r ( τ ) as depicted in Fig. 3. Our overall analysis shows that irrespective of the initial conditions r ( τ ) →∞ , with the increasing proper time.</text>
<section_header_level_1><location><page_9><loc_43><loc_48><loc_58><loc_49></location>V. CONCLUSION</section_header_level_1>
<text><location><page_9><loc_9><loc_31><loc_92><loc_46></location>We rederive the family of cylindrically symmetric magnetic universes in a particular metric ansatz which is conformally flat on each constant azimuthal angle. These are non-black hole solutions where unlike their spherical counterparts the gravity of magnetic fields is not strong enough to make black holes. The energy conditions (in the Appendix) of the magnetic field are satisfied only in particular dimensions. Being inspired by the stability properties of the original 4-dimensional Melvin's magnetic universe and those of Gibbons and Wiltshire we prove also the stability of present universes in a different gauge and in all dimensions including d = 3. Small radial perturbations of metric functions and the magnetic field (which automatically yields an electric field in accordance with the Maxwell equations) result in convergent expansions. Stability of the 3-dimensional case which was not considered in previous studies turns out to be weaker (i.e. convergence of perturbations are not satisfied simultaneously at r = 0 and at r →∞ ).</text>
<text><location><page_9><loc_9><loc_28><loc_92><loc_32></location>Geodesics show numerically that in running proper time uncharged particles are confined while null geodesics spiral around the center. Exact, particular geodesics in terms of the elementary functions are available in d = 5 , whereas in d = 4 we have elliptic functions.</text>
<text><location><page_9><loc_10><loc_26><loc_79><loc_27></location>Acknowledgment: We wish to thank S. Habib Mazharimousavi for much valuable discussions.</text>
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<list_item><location><page_9><loc_10><loc_19><loc_38><loc_20></location>[1] M. A. Melvin, Phys. Lett. 8, 65 (1964);</list_item>
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<text><location><page_9><loc_12><loc_18><loc_41><loc_19></location>M. A. Melvin, Phys. Rev. 139, B225 (1965).</text>
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<list_item><location><page_9><loc_10><loc_17><loc_53><loc_18></location>[2] D. Garfinkle and M. A. Melvin, Phys. Rev. D 50, 3859 (1994).</list_item>
<list_item><location><page_9><loc_10><loc_15><loc_41><loc_16></location>[3] K. S. Thorne, Phys. Rev.139, B 244 (1965);</list_item>
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<text><location><page_9><loc_12><loc_14><loc_40><loc_15></location>K. S. Thorne, Phys.Rev.138, B251 (1965).</text>
<text><location><page_9><loc_10><loc_13><loc_58><loc_14></location>[4] Mauricio Cataldo and Patricio Salgado, Phys. Rev. D 54, 2971 (1996);</text>
<text><location><page_9><loc_12><loc_11><loc_56><loc_12></location>E. W. Hirschmann and D. L. Welch, Phys .Rev. D 53, 5579 (1996).</text>
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<list_item><location><page_9><loc_10><loc_9><loc_63><loc_11></location>[5] Ajanta Das and A. Banerjee, Astrophysics and Space Science 268, 425 (1999); T. Dereli, A. Eris, A. Karasu, Nuovo.Cimento B 93, 102 (1989).</list_item>
<list_item><location><page_10><loc_10><loc_92><loc_43><loc_93></location>[6] S. S. Xulu, Int .J. Mod. Phys. A15 4849 (2000).</list_item>
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<list_item><location><page_10><loc_12><loc_88><loc_58><loc_89></location>S. H Mazharimousavi, and M. Halilsoy, Phys. Lett. B 665, 125 (2008);</list_item>
<list_item><location><page_10><loc_12><loc_87><loc_61><loc_88></location>G. W. Gibbons and C. A. R. Herdeiro, Class. Quant. Grav.18,1677 (2001);</list_item>
<list_item><location><page_10><loc_12><loc_85><loc_39><loc_86></location>A. Tseytlin, Phys. Lett. B 346, 55 (1995);</list_item>
<list_item><location><page_10><loc_12><loc_84><loc_65><loc_85></location>F. Dowker, J.Gauntlett, S. Giddings, G. Horowitz, Phys. Rev. D 50, 2662 (1994);</list_item>
<list_item><location><page_10><loc_12><loc_83><loc_65><loc_84></location>F. Dowker, J.Gauntlett, S. Giddings, G. Horowitz, Phys. Rev. D 52, 6929 (1995).</list_item>
<list_item><location><page_10><loc_10><loc_80><loc_92><loc_82></location>[8] G. W. Gibbons and D. L. Wiltshire, Nucl. Phys. B287, 717 (1987); (We thank Professor Gibbons for informing us about this reference.)</list_item>
<list_item><location><page_10><loc_10><loc_77><loc_92><loc_80></location>[9] G. B. Arfken and H. J. Weber, Mathematical Methods for Physics, Fifth edition, Chapter 13, page 858, printed in the USA (2001).</list_item>
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<section_header_level_1><location><page_10><loc_10><loc_72><loc_19><loc_73></location>Apendix A</section_header_level_1>
<section_header_level_1><location><page_10><loc_10><loc_71><loc_25><loc_72></location>Energy conditions</section_header_level_1>
<text><location><page_10><loc_9><loc_68><loc_92><loc_70></location>When a matter field couples to any system, energy conditions must be satisfied for physically acceptable solutions. We follow the steps as given in[10] .</text>
<text><location><page_10><loc_10><loc_66><loc_34><loc_67></location>Weak Energy Condition (WEC):</text>
<text><location><page_10><loc_10><loc_63><loc_26><loc_64></location>The WEC states that</text>
<formula><location><page_10><loc_46><loc_56><loc_92><loc_60></location>ρ ≥ 0 (A1) ρ + p i ≥ 0</formula>
<text><location><page_10><loc_10><loc_54><loc_63><loc_56></location>In which ρ is the energy density and p i are the principle pressure given by</text>
<formula><location><page_10><loc_39><loc_48><loc_92><loc_52></location>ρ = T 0 0 (A2) p i = -T i i , i = 1 , 2 , · · · , ( d -1)</formula>
<text><location><page_10><loc_10><loc_46><loc_41><loc_47></location>The WEC conditions are trivially satisfied.</text>
<text><location><page_10><loc_10><loc_44><loc_34><loc_46></location>Strong Energy Condition (SEC):</text>
<text><location><page_10><loc_10><loc_43><loc_29><loc_44></location>This condition states that</text>
<text><location><page_10><loc_10><loc_33><loc_27><loc_34></location>For d=3, it means that</text>
<formula><location><page_10><loc_41><loc_24><loc_92><loc_30></location>ρ + d -1 ∑ i =1 p i ≥ 0 ⇒ 3 T 0 0 ≥ 0 (A4) ρ + p i ≥ 0 ⇒ 2 T 0 0 ≥ 0</formula>
<text><location><page_10><loc_9><loc_19><loc_92><loc_24></location>which are satisfied. For 4 ≤ d ≤ 6 it is also satisfied because ρ + d -1 ∑ i =1 p i = -( d -6) T 0 0 . It can easily be seen also that for 7 ≤ d</text>
<formula><location><page_10><loc_41><loc_11><loc_92><loc_17></location>ρ + d -1 ∑ i =1 p i ≥ 0 ⇒-T 0 0 ≥ 0 (A5) ρ + p i ≥ 0 ⇒ T 0 0 ≥ 0</formula>
<text><location><page_10><loc_9><loc_9><loc_26><loc_10></location>i.e. the SEC is violated.</text>
<formula><location><page_10><loc_45><loc_35><loc_92><loc_40></location>ρ + d -1 ∑ i =1 p i ≥ 0 (A3) ρ + p i ≥ 0</formula>
<text><location><page_11><loc_10><loc_92><loc_37><loc_93></location>Dominant Energy Condition (DEC):</text>
<text><location><page_11><loc_10><loc_90><loc_74><loc_92></location>In accordance with DEC, the effective pressure should not be negative. This amounts to</text>
<formula><location><page_11><loc_37><loc_82><loc_92><loc_86></location>p eff = 1 d -1 d -1 ∑ i =1 T i i = ( d -5) d -1 T 0 0 ≥ 0 (A6)</formula>
<text><location><page_11><loc_10><loc_80><loc_41><loc_82></location>For having p eff ≥ o it is clear that d ≥ 5 .</text>
<section_header_level_1><location><page_11><loc_10><loc_78><loc_25><loc_79></location>Causality Condition:</section_header_level_1>
<text><location><page_11><loc_10><loc_76><loc_64><loc_78></location>In addition to the energy conditions one can impose the causality condition</text>
<formula><location><page_11><loc_46><loc_71><loc_92><loc_74></location>0 ≤ p eff ρ < 1 (A7)</formula>
<text><location><page_11><loc_10><loc_69><loc_23><loc_70></location>This implies that</text>
<text><location><page_11><loc_9><loc_60><loc_28><loc_62></location>which is satisfied for d ≥ 5 .</text>
<section_header_level_1><location><page_11><loc_10><loc_58><loc_23><loc_59></location>Figure captions</section_header_level_1>
<text><location><page_11><loc_9><loc_51><loc_92><loc_58></location>Fig. 1 : Radial distance behavior as a function of proper time for time-like, neutral particle geodesics. From Eq. (63) in the text, the behavior of r ( τ ) as the proper time τ runs from zero to infinity. The starting points are chosen such that r = 0 at τ = 0, in both d = 4 (Fig. 1a) and d = 5 (Fig. 1b)cases. The fact that r is confined is clearly seen from these plots. This particular property is already implied from Eq. (65). Let us note that in both cases for simplicity we choose (+) sign and τ 0 = 0. Further, we choose the constant k 0 = 2 .</text>
<text><location><page_11><loc_9><loc_43><loc_92><loc_51></location>Fig. 2 : Radial behavior as a function of the azimuthal angle ϕ for null geodesics in d = 3 (Fig 2a) and d = 4 dimensional (Fig. 2b) magnetic universes. The horizontal axis x (= r cos ϕ ) and vertical axis y (= r sin ϕ ) are plotted numerically in each case from the expressions given in Eq. (64) and Eq. (69) . For simplicity we choose the constants H 2 = 0 . 01, b 0 = 0 . 01 , H 0 = 1, c = 1 and λ 0 = 1 . Let us note that we have chosen the (+) sign in both (64) and (69) , which give outward orbits around the center. Obviously, the choice ( -) should yield inward orbits.</text>
<text><location><page_11><loc_9><loc_39><loc_92><loc_43></location>Fig. 3 : This is a numerical plot of the intricate second order differential equation (72) in d = 4. For technical reason we choose the constants a 1 , b 0 , l 0 , µ 0 and σ 0 all equal to one. Two different initial conditions are displayed (A and B) which reveal the pattern of increasing radial distance in proper time.</text>
<formula><location><page_11><loc_45><loc_62><loc_92><loc_66></location>0 ≤ ( d -5) d -1 < 1 (A8)</formula>
<text><location><page_12><loc_16><loc_44><loc_94><loc_45></location>This figure "4_with_charge_time_copy.jpg" is available in "jpg"GLYPH<10> format from:</text>
<text><location><page_12><loc_25><loc_39><loc_56><loc_40></location>http://arxiv.org/ps/1104.3401v2</text>
<text><location><page_13><loc_16><loc_44><loc_80><loc_45></location>This figure "null.3_copy.jpg" is available in "jpg"GLYPH<10> format from:</text>
<text><location><page_13><loc_25><loc_39><loc_56><loc_40></location>http://arxiv.org/ps/1104.3401v2</text>
<text><location><page_14><loc_16><loc_44><loc_80><loc_45></location>This figure "null.4_copy.jpg" is available in "jpg"GLYPH<10> format from:</text>
<text><location><page_14><loc_25><loc_39><loc_56><loc_40></location>http://arxiv.org/ps/1104.3401v2</text>
<text><location><page_15><loc_16><loc_44><loc_85><loc_45></location>This figure "time-like_4_copy.jpg" is available in "jpg"GLYPH<10> format from:</text>
<text><location><page_15><loc_25><loc_39><loc_56><loc_40></location>http://arxiv.org/ps/1104.3401v2</text>
<text><location><page_16><loc_16><loc_44><loc_85><loc_45></location>This figure "time-like_5_copy.jpg" is available in "jpg"GLYPH<10> format from:</text>
<text><location><page_16><loc_25><loc_39><loc_56><loc_40></location>http://arxiv.org/ps/1104.3401v2</text>
</document>
[
{
"title": "Stable Magnetic Universes Revisited",
"content": "T. Tahamtan ∗ and M. Halilsoy † Department of Physics, Eastern Mediterranean University, G. Magusa, North Cyprus, Mersin 10 - Turkey. A regular class of static, cylindrically symmetric pure magnetic field metrics is rederived in a different metric ansatz in all dimensions. Radial, time dependent perturbations show that for dimensions d > 3 such spacetimes are stable at both near r ≈ 0 and large radius r →∞ . In a different gauge these stability analysis and similar results were known beforehand. For d = 3, however, simultaneous stability requirement at both, near and far radial distances can not be reconciled for time - dependent perturbations. Restricted, numerical geodesics for neutral particles reveal a confinement around the center in the polar plane. Charged, time-like geodesics for d = 4 on the other hand are shown numerically to run toward infinity.",
"pages": [
1
]
},
{
"title": "I. INTRODUCTION",
"content": "/negationslash In 4 -dimensional spacetimes the electric - magnetic duality symmetry of the Maxwell equations is an important property which can not be satisfied in other dimensions unless different form fields other than 2 -forms are introduced. For this reason a dyonic solution admits a meaningful interpretation only in d = 4. The Reissner - Nordestrom (RN) solution constitutes in this regard the best example which has both electric and magnetic solutions in a symmetric manner. In other dimensions ( d = 4 ) similar duality properties can, in principle, be defined as well but physical interpretation corresponding to electric and magnetic fields turn out to be rather abstract. For such reasons, in order to avoid complications due to the absence of a tangible duality, pure electric or pure magnetic solutions seemed to attract considerable attention. This amounts to only half of the Maxwell equations, the other half being trivially satisfied. From this token we wish to resort here to the pure magnetic solutions which yield a completely solvable class without much effort. From the physical side, occurrence of pure and very strong magnetic fields associated with astronomical objects such as magnetars motivate us to search for such solutions in general relativity. It was Melvin, who first studied such cylindrically symmetric parallel magnetic lines of force remaining in equilibrium under their mutual gravitational attraction in d = 4[1]. Later on, generalized version of the Melvin's magnetic universe was also considered[2]. The Melvin universe is invariant under rotation and translation along the z i axis orthogonal to the polar plane ( r, ϕ ). Thorne popularized the Melvin universe further by showing its absolute stability against small radial perturbations[3]. Due to this stability property it can be presumed that astrophysical objects emitting strong beams of magnetic fields may everlast in an accelerating universe. Additionally, in d = 3 [4] and 5 dimensional [5] cases also pure magnetic field solutions were found and their energy content investigated [6]. Pure magnetic solutions in higher dimensions are also known to exist in string, Lovelock, Yang-Mills, Born-Infeld and other theories [7]. In this paper, we present in a particular cylindrically symmetric metric ansatz, a class of non-singular, source-free, static, pure magnetic solutions to Einstein-Maxwell (EM) equations in all dimensions. In a different metric ansatz these solutions were known previously [4, 8]. Our principal aim is to investigate the stability of such magnetic universes against time dependent small radial perturbations and explore the possible role of dimensionality of spacetime in such matters. It has been known for a long time that for d > 3 these kind of magnetic solutions are all stable [8] . We verify these results once more in a different metric (i.e. non canonical) ansatz with supplement of the d = 3 case.. We show that for d > 3 the metrics are stable against small perturbations at both near axis z i and at far distance away from z i . We observe also that when d = 3 these two regions behave differently. Namely, the metric can be made stable at r ≈ 0 or, at r →∞ , but not simultaneously, which we phrase as 'weakly' stable. The solutions justify once more the impossibility of cylindrical magnetic field lines implosion and therefore formation of such black holes. We investigate the time-like ( d ≥ 4,with fixed polar angle) and null ( d = 3 , 4 ) geodesics for neutral particles numerically. Only for d = 4 and 5 we were able to obtain exact integrals, albeit in non-invertible forms, of the geodesics equation. In each case a confinement of geodesics is observed to take place near the central region. Due to its physical importance we consider also the time-like geodesics of a charged particle. It turns out that such geodesics can not be confined and in their proper time they diverge to infinity. From these relations we can write where From equation (6) we obtain the differential equation whose solution for d ≥ 4 is Organization of the paper is as follows. In Section II we present our metric, field equations and solve them in d -dimensions. Perturbation analysis of our system follows in Section III. Geodesics motion is studied in Section IV. Our results are summarized in Conclusion which appears in Section V.",
"pages": [
1,
2
]
},
{
"title": "II. METRIC AND SOLUTIONS OF FIELD EQUATIONS IN d -DIMENSIONS",
"content": "Our d -dimensional static, cylindrically symmetric line element ansatz is given by in which f ( r ) is a function of r to be found and b 0 and k are constant parameters. Also the pure magnetic 2 -form field is chosen to be where F rϕ is the only non-zero component of the electromagnetic field. The energy momentum tensor is defined by which admits the non-zero components We note that our choice of indices { 0 , 1 , 2 , . . . , ( d -1) } denote { t, r, z 1 , · · · , z d -3 , ϕ } and the energy conditions satisfied by this energy-momentum tensor are discussed in the Appendix A. From the Einstein equations, T j i = G j i Eq. (4) implies that By putting this result into Eq. (7) for finding k we find out that for d ≥ 4, k is d -3 . On the other hand, for d = 3 the solution turns out to be for the integration constants C 2 and c . For convenience we make the choices C 1 = d -3 and C 2 = 1, so that the solution can be expressed by Accordingly, our line element takes the form ( ) We note that these solutions are not new, for they coincide with those of [8] (for d ≥ 4) and [4] for ( d = 3), respectively. It can easily be seen that for r → 0 it reduces to the following form From Maxwell's Eq. it fallows that This represents a conical geometry signalling the existence of a cosmic string near r = 0. By choosing b 2 0 ( d -3) 2 = 1 for d ≥ 4 and b 0 = 1 for d = 3 , we have Minkowskian metrics as one approaches the axes z i . The solution (16) is a singularity free magnetic universe in d -dimensions in analogy with the Melvin space time. ( B 0 = an integration constant) which implies that the magnetic field behaviors as a function of r are The marked distinction between d = 3 and d ≥ 4 cases can already be seen from these behaviors. Accordingly the energy density reads while the Ricci scalar for the metric (16) is Similarly, the Kretchmann scalar has the behavior It is observed that regularity at r →∞ dictates us to make the choice c > 0 for the integration constant.",
"pages": [
2,
3
]
},
{
"title": "III. PERTURBATION ANALYSIS",
"content": "In this section we perturb the metric and magnetic potential. Since the case d = 3 forms a special case we consider it separately. Similar analysis was carried out by Gibbons and Wiltshire [8] where they used the canonical metric ansatz. We shall show below that their results can also be obtained in a different metric ansatz. Our line element is where and the magnetic potential is expressed by The unperturbed functions are where u ( r, t ) , w ( r, t ) and a ( r, t ) are the perturbed functions. Since /epsilon1 is a small parameter we assume that /epsilon1 2 ≈ 0 in our analysis. We use Einstein's equations to find the perturbed functions. The differential equations satisfied by the perturbed functions are This system of differential equations admits the solutions where B 1 , B 2 , E 1 , E 2 and α are all integration constants while I 1 ( αr ) and K 1 ( αr ) are the modified Bessel functions of order one. At all times t , to a first order in /epsilon1 , the locally flat nature of the metric near r = 0 will not be altered [1]. This implies when r → 0 It is seen that we can choose B 1 = 0 and E 2 = 0 to have finite limit when r → 0. However, for r → ∞ it can be checked that w ( r, t ) diverges and since g 0 ( r ) = 1 this implies that the ratio of w ( r,t ) g 0 ( r ) grows indefinitely. No other choice of constants suffice to eliminate this divergence. As a result the perturbation converges for r → 0 but diverges for r → ∞ in d = 3 case. Let us note that for the time - independent perturbation both, near and far - region perturbation terms become convergent.",
"pages": [
4,
5
]
},
{
"title": "2. The case for d = 5 and d > 5",
"content": "Our perturbed line element now for d = 5 is of the form From Eq. (23) and (24) we introduce in analogy, the perturbed functions in which the unperturbed functions are given by From the Einstein's equations we obtain to the first order in /epsilon1 the following differential equations for u ( r, t ) and w ( r, t ) Integration of these equations yield for integration constants p, q and α , and I 1 ( αr ) and K 1 ( αr ) are the modified Bessel functions of order one. At all times t , to a first order in /epsilon1 , the locally flat nature of the metric near r = 0 remains intact. Also, for all times to a first order in /epsilon1 , the static metric for r → ∞ will not be altered. In this case we see that perturbed functions are finite at r = 0 , and when r →∞ they go to zero. A similar analysis has been carried out for d = 6 , 7 , ... so that we found the general solution for the metric functions. In each case we have obtained the following relations between w ( r, t ) and u ( r, t ) Solutions for w ( r, t ) and u ( r, t ) are given in all dimensions as follow in which p and q are constants. These are both finite at r → 0 and the ratio of them when r → ∞ go to zero. Now, from Maxwell's equations we attempt to find the perturbative solution for the magnetic potential. We take the potential in the form where The differential equation satisfied by a ( r, t ) becomes in which Upon substitution for u ( r, t ) we see that for all dimensions the equation satisfied by a ( r, t ) takes the form An exact solution for a ( r, t ) for all r is not at our disposal, therefore, we shall search for solutions near r = 0 and for r →∞ . The solution for the homogenous part is Since a particular solution is not available we proceed to study the answers for a limited case, when r is small (to order r ) If we go to higher orders of r , (order r 3 for instance) we obtain whose solution can be expressed as in which Here p, q, C 3 , C 4 , α and γ are all constants and WhittakerM ( -1 8 α 2 , 1 2 , 2 r 2 ) stands for the Whittaker function[9]. For r → 0 the function a ( r, t ) is finite. Now, to see the case when r goes to infinity we solve the differential equation whose solution reads Here C 5 and C 6 are new integration constants. It can easily be checked that the ratio of this solution goes to zero for r →∞ if we choose C 5 = 0 .",
"pages": [
5,
6,
7
]
},
{
"title": "IV. GEODESIC MOTION",
"content": "In this section we shall investigate the time-like (for d ≥ 4) and null (for d = 3 , 4) geodesics by employing our line element given in Eq. (15). For d ≥ 4 we divide the line element by dτ ( τ is proper time) and for d = 3 by dλ ( λ is an affine parameter) so that the Lagrangian can be expressed in the form For the equations of motion with constant azimuthal angle ( ϕ =constant for d ≥ 4) and null geodesics for d = 3 we obtain in which d 0 , d i , H 0 and H 1 are all constants of integration. From the metric condition we find dr dτ (for d ≥ 4, ϕ = constant) and dr dλ (for d = 3) as follow In effect, we obtain for d = 4 the relation between r and τ but for d = 3 we want to find the relation between r and ϕ. in which, τ 0 and ϕ 0 are initial constants and we impose the restrictions so that For d = 4 and 5, we have exact integrals given by in which Fig.s 1a and 1b depict the behaviors of (63) (for d = 4) and (66) (for d = 5) , respectively. Now, we wish to consider the d = 4 null geodesics as well. The line element is Eq.s of motion imply for the affine parameter λ in which α 0 , β 0 and γ 0 are integration constants. We note that (67) and (68) correspond to Eq.s (1) and (6) of [3], respectively. From the null-metric condition ds 2 = 0 and upon shifting the independent variable to ϕ we obtain where we have introduced the constant λ 0 as λ 2 0 = α 2 0 -β 2 0 γ 2 0 . Fig.s 2a and 2b are the plots corresponding to (64) and (69), respectively. Finally, we study the 4-dimensional time-like geodesics of a charged particle with charge e whose Lagrangian is given by The Euler-Lagrange equations of motion yield for the integration constants l 0 , µ 0 and σ 0 . Since we shall be interested only in the r ( τ ) behavior of the motion we derive the second order equation as follows For a set of chosen constants and initial values we plot the behavior of r ( τ ) as depicted in Fig. 3. Our overall analysis shows that irrespective of the initial conditions r ( τ ) →∞ , with the increasing proper time.",
"pages": [
7,
8,
9
]
},
{
"title": "V. CONCLUSION",
"content": "We rederive the family of cylindrically symmetric magnetic universes in a particular metric ansatz which is conformally flat on each constant azimuthal angle. These are non-black hole solutions where unlike their spherical counterparts the gravity of magnetic fields is not strong enough to make black holes. The energy conditions (in the Appendix) of the magnetic field are satisfied only in particular dimensions. Being inspired by the stability properties of the original 4-dimensional Melvin's magnetic universe and those of Gibbons and Wiltshire we prove also the stability of present universes in a different gauge and in all dimensions including d = 3. Small radial perturbations of metric functions and the magnetic field (which automatically yields an electric field in accordance with the Maxwell equations) result in convergent expansions. Stability of the 3-dimensional case which was not considered in previous studies turns out to be weaker (i.e. convergence of perturbations are not satisfied simultaneously at r = 0 and at r →∞ ). Geodesics show numerically that in running proper time uncharged particles are confined while null geodesics spiral around the center. Exact, particular geodesics in terms of the elementary functions are available in d = 5 , whereas in d = 4 we have elliptic functions. Acknowledgment: We wish to thank S. Habib Mazharimousavi for much valuable discussions. M. A. Melvin, Phys. Rev. 139, B225 (1965). K. S. Thorne, Phys.Rev.138, B251 (1965). [4] Mauricio Cataldo and Patricio Salgado, Phys. Rev. D 54, 2971 (1996); E. W. Hirschmann and D. L. Welch, Phys .Rev. D 53, 5579 (1996).",
"pages": [
9
]
},
{
"title": "Energy conditions",
"content": "When a matter field couples to any system, energy conditions must be satisfied for physically acceptable solutions. We follow the steps as given in[10] . Weak Energy Condition (WEC): The WEC states that In which ρ is the energy density and p i are the principle pressure given by The WEC conditions are trivially satisfied. Strong Energy Condition (SEC): This condition states that For d=3, it means that which are satisfied. For 4 ≤ d ≤ 6 it is also satisfied because ρ + d -1 ∑ i =1 p i = -( d -6) T 0 0 . It can easily be seen also that for 7 ≤ d i.e. the SEC is violated. Dominant Energy Condition (DEC): In accordance with DEC, the effective pressure should not be negative. This amounts to For having p eff ≥ o it is clear that d ≥ 5 .",
"pages": [
10,
11
]
},
{
"title": "Causality Condition:",
"content": "In addition to the energy conditions one can impose the causality condition This implies that which is satisfied for d ≥ 5 .",
"pages": [
11
]
},
{
"title": "Figure captions",
"content": "Fig. 1 : Radial distance behavior as a function of proper time for time-like, neutral particle geodesics. From Eq. (63) in the text, the behavior of r ( τ ) as the proper time τ runs from zero to infinity. The starting points are chosen such that r = 0 at τ = 0, in both d = 4 (Fig. 1a) and d = 5 (Fig. 1b)cases. The fact that r is confined is clearly seen from these plots. This particular property is already implied from Eq. (65). Let us note that in both cases for simplicity we choose (+) sign and τ 0 = 0. Further, we choose the constant k 0 = 2 . Fig. 2 : Radial behavior as a function of the azimuthal angle ϕ for null geodesics in d = 3 (Fig 2a) and d = 4 dimensional (Fig. 2b) magnetic universes. The horizontal axis x (= r cos ϕ ) and vertical axis y (= r sin ϕ ) are plotted numerically in each case from the expressions given in Eq. (64) and Eq. (69) . For simplicity we choose the constants H 2 = 0 . 01, b 0 = 0 . 01 , H 0 = 1, c = 1 and λ 0 = 1 . Let us note that we have chosen the (+) sign in both (64) and (69) , which give outward orbits around the center. Obviously, the choice ( -) should yield inward orbits. Fig. 3 : This is a numerical plot of the intricate second order differential equation (72) in d = 4. For technical reason we choose the constants a 1 , b 0 , l 0 , µ 0 and σ 0 all equal to one. Two different initial conditions are displayed (A and B) which reveal the pattern of increasing radial distance in proper time. This figure \"4_with_charge_time_copy.jpg\" is available in \"jpg\"GLYPH<10> format from: http://arxiv.org/ps/1104.3401v2 This figure \"null.3_copy.jpg\" is available in \"jpg\"GLYPH<10> format from: http://arxiv.org/ps/1104.3401v2 This figure \"null.4_copy.jpg\" is available in \"jpg\"GLYPH<10> format from: http://arxiv.org/ps/1104.3401v2 This figure \"time-like_4_copy.jpg\" is available in \"jpg\"GLYPH<10> format from: http://arxiv.org/ps/1104.3401v2 This figure \"time-like_5_copy.jpg\" is available in \"jpg\"GLYPH<10> format from: http://arxiv.org/ps/1104.3401v2",
"pages": [
11,
12,
13,
14,
15,
16
]
}
]
2013Ap&SS.346..443W
https://arxiv.org/pdf/1304.6867.pdf
<document>
<section_header_level_1><location><page_1><loc_16><loc_89><loc_84><loc_91></location>Stability of the classical type of relative equilibria of a rigid</section_header_level_1>
<section_header_level_1><location><page_1><loc_36><loc_85><loc_63><loc_87></location>body in the J 2 problem</section_header_level_1>
<text><location><page_1><loc_42><loc_81><loc_58><loc_83></location>Yue Wang * , Shijie Xu</text>
<text><location><page_1><loc_15><loc_77><loc_84><loc_80></location>Room B1024, New Main Building, Department of Guidance, Navigation and Control, School of Astronautics, Beijing University of Aeronautics and Astronautics, 100191, Beijing, China</text>
<section_header_level_1><location><page_1><loc_15><loc_72><loc_24><loc_74></location>Abstract</section_header_level_1>
<text><location><page_1><loc_15><loc_16><loc_85><loc_70></location>The motion of a point mass in the J 2 problem is generalized to that of a rigid body in a J 2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variational Lagrangian. With the stability conditions obtained, both the linear and nonlinear stability of the relative equilibria are investigated in details in a wide range of the parameters of the gravity field and the rigid body. We find that both the zonal</text>
<text><location><page_2><loc_15><loc_67><loc_85><loc_90></location>harmonic J 2 and the characteristic dimension of the rigid body have significant effects on the linear and nonlinear stability. Similar to the classical attitude stability in a central gravity field, the linear stability region is also consisted of two regions that are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. Our results are very useful for the studies on the motion of natural satellites in our solar system.</text>
<text><location><page_2><loc_15><loc_59><loc_85><loc_64></location>Keywords: J 2 problem; Rigid body; Non-canonical Hamiltonian structure; Relative equilibria; Linear stability; Nonlinear stability</text>
<section_header_level_1><location><page_2><loc_15><loc_53><loc_31><loc_55></location>1. Introduction</section_header_level_1>
<text><location><page_2><loc_15><loc_31><loc_85><loc_51></location>The J 2 problem, also called main problem of artificial satellite theory, in which the motion of a point mass in a gravity field truncated on the zonal harmonic J 2 is studied, is an important problem in the celestial mechanics and astrodynamics (Broucke 1994). The J 2 problem has its wide applications in the orbital dynamics and orbital design of spacecraft. This classical problem has been studied by many authors, such as Broucke (1994) and the literatures cited therein.</text>
<text><location><page_2><loc_15><loc_9><loc_85><loc_29></location>However, neither natural nor artificial celestial bodies are point masses or have spherical mass distributions. One of the generalizations of the point mass model is the rigid body model. Because of the non-spherical mass distribution, the orbital and rotational motions of the rigid body are coupled through the gravity field. The orbit-rotation coupling may cause qualitative effects on the motion, which are more significant when the ratio of the dimension of rigid body to the orbit radius is larger.</text>
<text><location><page_3><loc_15><loc_70><loc_85><loc_90></location>The orbit-rotation coupling and its qualitative effects have been discussed in several works on the motion of a rigid body or gyrostat in a central gravity field (Wang et al. 1991, 1992, 1995; Teixidó Román 2010). In Wang and Xu (in press), the orbit-rotation coupling of a rigid satellite around a spheroid planet was assessed. It was found that the significant orbit-rotation coupling should be considered for a spacecraft orbiting a small asteroid or an irregular natural satellite around a planet.</text>
<text><location><page_3><loc_15><loc_29><loc_85><loc_68></location>The effects of the orbit-rotation coupling have also been considered in many works on the Full Two Body Problem (F2BP), the problem of the rotational and orbital motions of two rigid bodies interacting through their mutual gravitational potential. A spherically-simplified model of F2BP, in which one body is assumed to be a homogeneous sphere, has been studied broadly, such as Kinoshita (1970), Barkin (1979), Aboelnaga and Barkin (1979), Beletskii and Ponomareva (1990), Scheeres (2004), Breiter et al. (2005), Balsas et al. (2008), Bellerose and Scheeres (2008) and Vereshchagin et al. (2010). There are also several works on the more general models of F2BP, in which both bodies are non-spherical, such as Maciejewski (1995), Scheeres (2002, 2009), Koon et al. (2004), Boué and Laskar (2009) and McMahon and Scheeres (in press).</text>
<text><location><page_3><loc_15><loc_11><loc_85><loc_27></location>When the dimension of the rigid body is very small in comparison with the orbital radius, the orbit-rotation coupling is not significant. In the case of an artificial Earth satellite, the point mass model of the J 2 problem works very well. However, when a spacecraft orbiting around an asteroid or an irregular natural satellite around a planet, such as Phobos, is considered, the mass distribution of the considered body is far</text>
<text><location><page_4><loc_15><loc_78><loc_85><loc_90></location>from a sphere and the dimension of the body is not small anymore in comparison with the orbital radius. In these cases, the orbit-rotation coupling causes significant effects and should be taken into account in the precise theories of the motion, as shown by Koon et al. (2004), Scheeres (2006), Wang and Xu (in press).</text>
<text><location><page_4><loc_15><loc_48><loc_85><loc_76></location>For the high-precision applications in the coupled orbital and rotational motions of a spacecraft orbiting a spheroid asteroid, or an irregular natural satellite around a dwarf planet or planet, we have generalized the J 2 problem to the motion of a rigid body in a J 2 gravity field in our previous paper (Wang and Xu 2013a). In that paper, the relative equilibria of the rigid body were determined from a global point of view in the framework of geometric mechanics. A classical type of relative equilibria, as well as a non-classical type of relative equilibria, was uncovered under the second-order gravitational potential.</text>
<text><location><page_4><loc_15><loc_18><loc_85><loc_46></location>Through the non-canonical Hamiltonian structure of the problem, geometric mechanics provides a systemic and effective method for determining the linear and nonlinear stability of the relative equilibria, as shown by Beck and Hall (1998). The linear and nonlinear stability of the classical type of relative equilibria already obtained in Wang and Xu (2013a) will be studied further in this paper in the framework of geometric mechanics. Through the stability properties of the relative equilibria, it is sufficient to understand the general dynamical properties of the system near the relative equilibria to a big extent.</text>
<text><location><page_4><loc_15><loc_11><loc_85><loc_16></location>Notice that the problem in McMahon and Scheeres (in press) is very similar to our problem. In their paper, the existence of stable equilibrium points, and the</text>
<text><location><page_5><loc_15><loc_78><loc_85><loc_90></location>linearized and nonlinear dynamics around equilibrium points in the planar F2BP with an oblate primary body were investigated. The differences with our problem are that in their problem the motion is restricted on the equatorial plane of the primary body and the mass center of the primary body is not fixed in the inertial space.</text>
<text><location><page_5><loc_15><loc_55><loc_85><loc_76></location>The equilibrium configuration exists generally among the natural celestial bodies in our solar system. It is well known that many natural satellites of big planets evolved tidally to the state of synchronous motion (Wisdom 1987). Notice that the gravity field of the big planets can be well approximated by a J 2 gravity field. The results on the stability of the relative equilibria in our problem are very useful for the studies on the motion of many natural satellites.</text>
<text><location><page_5><loc_15><loc_41><loc_85><loc_53></location>We also make comparisons with previous results on the stability of the relative equilibria of a rigid body in a central gravity field, such as Wang et al. (1991) and Teixidó Román (2010). The influence of the zonal harmonic J 2 on the stability of the relative equilibria is discussed in details.</text>
<section_header_level_1><location><page_5><loc_15><loc_37><loc_80><loc_39></location>2. Non-canonical Hamiltonian Structure and Relative Equilibria</section_header_level_1>
<figure>
<location><page_5><loc_34><loc_14><loc_66><loc_35></location>
<caption>Fig. 1. A small rigid body B in the J 2 gravity field of a massive axis-symmetrical body P</caption>
</figure>
<text><location><page_6><loc_15><loc_55><loc_85><loc_90></location>The problem we studied here is same as in Wang and Xu (2013a). As described in Fig. 1, we consider a small rigid body B in the gravity field of a massive axis-symmetrical body P . Assume that P is rotating uniformly around its axis of symmetry, and the mass center of P is stationary in the inertial space, i.e. P is in free motion without being affected by B . The gravity field of P is approximated through truncation on the second zonal harmonic J 2. The inertial reference frame is defined as S ={ e 1, e 2, e 3} with its origin O attached to the mass center of P . e 3 is along the axis of symmetry of P . The body-fixed reference frame is defined as Sb ={ i , j , k } with its origin C attached to the mass center of B . The frame Sb coincides with the principal axes reference frame of B .</text>
<text><location><page_6><loc_15><loc_33><loc_85><loc_53></location>In Wang and Xu (2013a), a Poisson reduction was applied on the original system by means of the symmetry of the problem. After the reduction process, the non-canonical Hamiltonian structure, i.e., Poisson tensor, Casimir functions and equations of motion, and a classical kind of relative equilibria of the problem were obtained. Here we only give the basic description of the problem and list the main results obtained by us there, see that paper for the details.</text>
<text><location><page_6><loc_15><loc_26><loc_85><loc_31></location>The attitude matrix of the rigid body B with respect to the inertial frame S is denoted by A ,</text>
<formula><location><page_6><loc_42><loc_22><loc_85><loc_24></location>[ , , ] (3) SO = ∈ A i j k , (1)</formula>
<text><location><page_6><loc_15><loc_11><loc_85><loc_20></location>where the vectors i , j and k are expressed in the frame S , and SO (3) is the 3-dimensional special orthogonal group. A is the coordinate transformation matrix from the frame Sb to the frame S . If [ , , ] x y z T W W W = W are components of a vector</text>
<text><location><page_7><loc_15><loc_89><loc_63><loc_90></location>in frame Sb , its components in frame S can be calculated by</text>
<formula><location><page_7><loc_46><loc_85><loc_85><loc_87></location>= w AW . (2)</formula>
<text><location><page_7><loc_15><loc_70><loc_85><loc_83></location>We define r as the radius vector of point C with respect to O in frame S . The radius vector of a mass element dm ( D ) of the body B with respect to C in frame Sb is denoted by D , then the radius vector of dm ( D ) with respect to O in frame S , denoted by x , is</text>
<formula><location><page_7><loc_46><loc_67><loc_85><loc_68></location>= + x r AD . (3)</formula>
<text><location><page_7><loc_18><loc_63><loc_71><loc_64></location>Therefore, the configuration space of the problem is the Lie group</text>
<formula><location><page_7><loc_46><loc_59><loc_85><loc_61></location>(3) Q SE = , (4)</formula>
<text><location><page_7><loc_15><loc_48><loc_84><loc_57></location>known as the Euclidean group of three space with elements ( , ) A r that is the semidirect product of SO (3) and 3 \ . The elements Ξ of the phase space, the cotangent bundle T Q ∗ , can be written in the following coordinates</text>
<formula><location><page_7><loc_43><loc_44><loc_85><loc_46></location>ˆ ( , ) = Ξ A, r; A Π p , (5)</formula>
<text><location><page_7><loc_15><loc_30><loc_85><loc_42></location>where Π is the angular momentum expressed in the body-fixed frame Sb and p is the linear momentum of the rigid body expressed in the inertial frame S (Wang and Xu 2012). The hat map 3 ^: (3) so → \ is the usual Lie algebra isomorphism, where (3) so is the Lie Algebras of Lie group SO (3).</text>
<text><location><page_7><loc_15><loc_22><loc_85><loc_28></location>The phase space T Q ∗ carries a natural symplectic structure (3) SE ω ω= , and the canonical bracket associated to ω can be written in coordinates Ξ as</text>
<formula><location><page_7><loc_24><loc_16><loc_85><loc_20></location>ˆ ˆ { , } ( ) , , T T T Q f g g f f g D f D g D g D f ∗ ∂ ∂ ∂ ∂ ⎛ ⎞ ⎛ ⎞ = -+ -⎜ ⎟ ⎜ ⎟ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ A A A Π A Π Ξ r p r p , (6)</formula>
<text><location><page_7><loc_15><loc_9><loc_84><loc_15></location>for any , ( ) f g C T Q ∞ ∗ ∈ , , ·· is the pairing between (3) T SO ∗ and (3) TSO , and D f B is a matrix whose elements are the partial derivates of the function f with</text>
<text><location><page_8><loc_15><loc_89><loc_74><loc_90></location>respect to the elements of matrix B respectively (Wang and Xu 2012).</text>
<text><location><page_8><loc_18><loc_85><loc_72><loc_87></location>The Hamiltonian of the problem : H T Q ∗ → \ is given as follows</text>
<formula><location><page_8><loc_38><loc_79><loc_85><loc_83></location>2 1 1 2 2 T T Q H V m τ -∗ = + + p Π I Π D , (7)</formula>
<text><location><page_8><loc_15><loc_72><loc_85><loc_78></location>where m is the mass of the rigid body, the matrix { } , , xx yy zz diag I I I = I is the tensor of inertia of the rigid body and : T Q T Q Q τ ∗ ∗ → is the canonical projection.</text>
<text><location><page_8><loc_15><loc_65><loc_84><loc_70></location>According to Wang and Xu (2013a), the gravitational potential : V Q → \ up to the second order is given in terms of moments of inertia as follows:</text>
<formula><location><page_8><loc_24><loc_60><loc_85><loc_63></location>( ) ( ) 2 (0) (2) 1 1 3 3 3 2 T GM m GM V V V tr m m R R ε ε ⎡ ⎤ = + = ---+ -· ⎢ ⎥ ⎣ ⎦ I R IR γ R , (8)</formula>
<text><location><page_8><loc_15><loc_46><loc_85><loc_59></location>where G is the Gravitational Constant, and M 1 is the mass of the body P . The parameter ε is defined as 2 2 E J a ε= , where aE is the mean equatorial radius of P . γ is the unit vector e 3 expressed in the frame Sb . T = R A r is the radius vector of the mass center of B expressed in frame Sb . Note that R = R and R = R R .</text>
<text><location><page_8><loc_15><loc_20><loc_85><loc_44></location>The J 2 gravity field is axis-symmetrical with axis of symmetry e 3. According to Wang and Xu (2012), the Hamiltonian of the system is 1 S -invariant, namely the system has symmetry, where 1 S is the one-sphere. Using this symmetry, we have carried out a reduction, induced a Hamiltonian on the quotient 1 / T Q S ∗ , and expressed the dynamics in terms of appropriate reduced variables in Wang and Xu (2012), where 1 / T Q S ∗ is the quotient of the phase space T Q ∗ with respect to the action of 1 S . The reduced variables in 1 / T Q S ∗ can be chosen as</text>
<formula><location><page_8><loc_39><loc_16><loc_85><loc_19></location>12 T T T T T ⎡ ⎤ = ∈ ⎣ ⎦ z Π , γ ,R ,P \ , (9)</formula>
<text><location><page_8><loc_15><loc_9><loc_85><loc_14></location>where T P = A p is the linear momentum of the body B expressed in the body-fixed frame Sb (Wang and Xu 2012). The projection from T Q ∗ to 1 / T Q S ∗ is given by</text>
<formula><location><page_9><loc_36><loc_88><loc_85><loc_91></location>( ) ˆ , T T T T T ⎡ ⎤ Ψ = ⎣ ⎦ A, r; A Π p Π , γ ,R ,P . (10)</formula>
<text><location><page_9><loc_15><loc_78><loc_85><loc_87></location>According to Marsden and Ratiu (1999), there is a unique non-canonical Hamiltonian structure on 1 / T Q S ∗ such that Ψ is a Poisson map. That is to say, there is a unique Poisson bracket 12 {, } ( ) · · z \ such that</text>
<formula><location><page_9><loc_35><loc_74><loc_85><loc_76></location>12 { , } ( ) { , } ( ) T Q f g f g ∗ Ψ = Ψ Ψ z Ξ \ D D D , (11)</formula>
<text><location><page_9><loc_15><loc_67><loc_85><loc_72></location>for any 12 , ( ) f g C ∞ ∈ \ , where {, } ( ) T Q ∗ · · Ξ is the natural canonical bracket of the system given by Eq. (6).</text>
<text><location><page_9><loc_15><loc_59><loc_84><loc_65></location>According to Wang and Xu (2012), the Poisson bracket 12 {, } ( ) · · z \ can be written in the following form</text>
<formula><location><page_9><loc_37><loc_55><loc_85><loc_58></location>( ) ( ) 12 { , } ( ) ( ) T f g f g = ∇ ∇ z z z B z \ , (12)</formula>
<text><location><page_9><loc_15><loc_52><loc_48><loc_53></location>with the Poisson tensor ( ) B z given by</text>
<formula><location><page_9><loc_40><loc_42><loc_85><loc_50></location>ˆ ˆ ˆ ˆ ˆ ( ) ˆ ˆ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ -⎣ ⎦ 0 0 0 0 0 E 0 E 0 Π γ R P γ B z R P , (13)</formula>
<text><location><page_9><loc_15><loc_24><loc_85><loc_40></location>where E is the identity matrix. This Poisson tensor has two independent Casimir functions. One is a geometric integral 1 1 1 ( ) 2 2 T C = ≡ z γγ , and the other one is ( ) 2 ˆ ( ) T C = + z γ Π RP , the third component of the angular momentum with respect to origin O expressed in the inertial frame S . 2 ( ) C z is the conservative quantity produced by the symmetry of the system, as stated by Noether's theorem.</text>
<text><location><page_9><loc_15><loc_16><loc_84><loc_22></location>The ten-dimensional invariant manifold or symplectic leaf of the system is defined in 12 \ by Casimir functions</text>
<formula><location><page_9><loc_26><loc_12><loc_85><loc_16></location>( ) ( ) { } 12 ˆ | 1, constant T T T T T T T Σ= ∈ = + = Π , γ ,R ,P γγ γ Π RP \ , (14)</formula>
<text><location><page_9><loc_15><loc_9><loc_85><loc_12></location>which is actually the reduced phase space ( ) 1 / T Q S ∗ of the symplectic reduction.</text>
<text><location><page_10><loc_15><loc_85><loc_84><loc_91></location>The restriction of the Poisson bracket 12 {, } ( ) · · z \ to Σ defines the symplectic structure on this symplectic leaf.</text>
<text><location><page_10><loc_18><loc_81><loc_81><loc_83></location>The equations of motion of the system can be written in the Hamiltonian form</text>
<formula><location><page_10><loc_37><loc_78><loc_85><loc_80></location>12 { , ( )} ( ) ( ) ( ) H H = = ∇ z z z z z B z z \ glyph<c=5,font=/DANIIO+MT-Extra> . (15)</formula>
<text><location><page_10><loc_15><loc_70><loc_85><loc_76></location>With the Hamiltonian ( ) H z given by Eq. (7), the explicit equations of motion are given by</text>
<formula><location><page_10><loc_33><loc_56><loc_85><loc_69></location>1 1 1 1 ( ) ( ) , , , ( ) . V V m V ----∂ ∂ = × + × + × ∂ ∂ = × = × + ∂ = × -∂ γ ,R γ , R Π Π I Π R γ R γ γ γ I Π P R R I Π γ ,R P P I Π R glyph<c=5,font=/DANIIO+MT-Extra> glyph<c=5,font=/DANIIO+MT-Extra> glyph<c=5,font=/DANIIO+MT-Extra> glyph<c=5,font=/DANIIO+MT-Extra> (16)</formula>
<text><location><page_10><loc_15><loc_28><loc_85><loc_55></location>Based on the equations of motion Eq. (16), we have obtained a classical kind of relative equilibria of the rigid body under the second-order gravitational potential in Wang and Xu (2013a). At this type of relative equilibria, the orbit of the mass center of the rigid body is a circle in the equatorial plane of body P with its center coinciding with origin O . The rigid body rotates uniformly around one of its principal axes that is parallel to 3 e in the inertial frame S in angular velocity that is equal to the orbital angular velocity e Ω . The radius vector e R and the linear momentum e P are parallel to another two principal axes of the rigid body.</text>
<text><location><page_10><loc_15><loc_17><loc_85><loc_26></location>When the radius vector e R is parallel to the principal axes of the rigid body i , j , k , the norm of the orbital angular velocity e Ω is given by the following three equations respectively:</text>
<formula><location><page_10><loc_32><loc_11><loc_85><loc_15></location>1/2 1 1 3 5 3 2 2 yy xx zz e e e I I GM GM I R R m m m ε ⎛ ⎞ ⎡ ⎤ Ω = + -+ + + ⎜ ⎟ ⎢ ⎥ ⎜ ⎟ ⎣ ⎦ ⎝ ⎠ , (17)</formula>
<formula><location><page_11><loc_33><loc_87><loc_85><loc_91></location>1/2 1 1 3 5 3 2 2 yy xx zz e e e I I GM GM I R R m m m ε ⎛ ⎞ ⎡ ⎤ Ω = + -+ + ⎜ ⎟ ⎢ ⎥ ⎜ ⎟ ⎣ ⎦ ⎝ ⎠ , (18)</formula>
<formula><location><page_11><loc_33><loc_81><loc_85><loc_85></location>1/2 1 1 3 5 3 2 2 yy xx zz e e e I I GM GM I R R m m m ε ⎛ ⎞ ⎡ ⎤ Ω = + + -+ ⎜ ⎟ ⎢ ⎥ ⎜ ⎟ ⎣ ⎦ ⎝ ⎠ . (19)</formula>
<text><location><page_11><loc_15><loc_78><loc_57><loc_79></location>The norm of the linear momentum e P is given by:</text>
<formula><location><page_11><loc_46><loc_74><loc_85><loc_76></location>e e e P mR = Ω . (20)</formula>
<text><location><page_11><loc_15><loc_63><loc_85><loc_72></location>With a given value of e R , there are 24 relative equilibria belonging to this classical type in total. Without of loss of generality, we will choose one of the relative equilibria as shown by Fig. 2 for stability conditions</text>
<formula><location><page_11><loc_31><loc_57><loc_85><loc_62></location>[ ] [ ] [ ] [ ] [ ] 0, 0, , 0, 0, 1 , 0 0 , 0 0 , 0 0 . T T T e e zz e e e T T e e e e e I R mR = Ω = = = Ω = Ω Π γ R P Ω (21)</formula>
<text><location><page_11><loc_15><loc_50><loc_85><loc_55></location>Other relative equilibria can be converted into this equilibrium by changing the arrangement of the axes of the reference frame Sb .</text>
<figure>
<location><page_11><loc_21><loc_38><loc_83><loc_48></location>
<caption>Fig. 2. One of the classical type of relative equilibria</caption>
</figure>
<section_header_level_1><location><page_11><loc_15><loc_31><loc_60><loc_33></location>3. Linear Stability of the Relative Equilibria</section_header_level_1>
<text><location><page_11><loc_15><loc_20><loc_85><loc_29></location>In this section, we will investigate the linear stability of the relative equilibria through the linear system matrix at the relative equilibria using the methods provided by the geometric mechanics (Beck and Hall 1998, Hall 2001).</text>
<section_header_level_1><location><page_11><loc_15><loc_17><loc_43><loc_18></location>3.1 Conditions of linear stability</section_header_level_1>
<text><location><page_11><loc_15><loc_9><loc_85><loc_15></location>The linear stability of the relative equilibrium e z depends on the eigenvalues of the linear system matrix of the system at the relative equilibrium. According to Beck</text>
<text><location><page_12><loc_15><loc_78><loc_85><loc_91></location>and Hall (1998), the linear system matrix ( ) e D z of the non-canonical Hamiltonian system at the relative equilibrium e z can be calculated through the multiplication of the Poisson tensor and the Hessian of the variational Lagrangian without performing linearization as follows:</text>
<formula><location><page_12><loc_41><loc_74><loc_85><loc_76></location>( ) ( ) ( ) 2 e e e F = ∇ D z B z z . (22)</formula>
<text><location><page_12><loc_15><loc_70><loc_58><loc_72></location>Here the variational Lagrangian ( ) F z is defined as</text>
<formula><location><page_12><loc_40><loc_66><loc_85><loc_69></location>( ) ( ) ( ) 2 1 i i i F H C μ = = -∑ z z z . (23)</formula>
<text><location><page_12><loc_15><loc_48><loc_85><loc_64></location>According to Beck and Hall (1998), the relative equilibrium of the rigid body in the problem corresponds to the stationary point of the Hamiltonian constrained by the Casimir functions. The stationary points can be determined by the first variation condition of the variational Lagrangian ( ) e F ∇ = 0 z . By using the formulations of the Hamiltonian and Casimir functions, the equilibrium conditions are obtained as:</text>
<formula><location><page_12><loc_32><loc_33><loc_85><loc_46></location>( ) ( ) 1 2 1 1 2 3 2 2 , 3 ˆ , ˆ , ˆ . e e e e e e e e e e e e e e e e GM m R V m μ ε μ μ μ μ --= · --+ = ∂ -+ = ∂ -+ = 0 0 0 0 I Π γ γ R R γ Π R P P γ R P γ R (24)</formula>
<text><location><page_12><loc_15><loc_22><loc_85><loc_31></location>As we expected, the relative equilibrium in Eq. (21) obtained based on the equations of motion is a solution of the equilibrium conditions Eq. (24), with the parameters 1 μ and 2 μ given by</text>
<formula><location><page_12><loc_38><loc_18><loc_85><loc_21></location>( ) 2 2 1 2 , e zz e e I mR μ μ =-Ω + =Ω . (25)</formula>
<text><location><page_12><loc_15><loc_11><loc_85><loc_16></location>By using the formulation of the second-order gravitational potential Eq. (8), the Hessian of the variational Lagrangian ( ) 2 F ∇ z is calculated as:</text>
<formula><location><page_13><loc_23><loc_77><loc_85><loc_91></location>( ) 1 2 3 3 2 1 2 3 3 1 3 3 2 2 5 2 2 2 2 2 2 2 2 3 3 3 ˆ ˆ ˆ ˆ 1 ˆ ˆ T T GM m V R F V V m μ ε μ μ μ μ μ μ μ μ -× × × × ⎡ ⎤ -⎢ ⎥ ⎛ ⎞ ⎢ ⎥ ∂ --+ -⎜ ⎟ ⎢ ⎥ ∂∂ ⎝ ⎠ ⎢ ⎥ ∇ = ⎢ ⎥ ∂ ∂ -⎢ ⎥ ∂∂ ∂ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ -⎣ ⎦ I 0 0 I I 0 0 I I RR P R γ R z P γ γ R R R γ . (26)</formula>
<text><location><page_13><loc_15><loc_70><loc_85><loc_76></location>The second-order partial derivates of the gravitational potential in Eq. (26) are obtained as follows:</text>
<formula><location><page_13><loc_31><loc_65><loc_85><loc_68></location>( ) ( ) 2 1 3 3 4 3 5 T T GM m V R ε × ∂ ⎡ ⎤ = · + -· ⎣ ⎦ ∂∂ I γ R γ R γ R RR γ R , (27)</formula>
<formula><location><page_13><loc_26><loc_49><loc_85><loc_63></location>( ) ( ) ( ) ( ) { } { } ( ) { } ( )( ) { } 2 1 3 3 2 3 2 1 3 3 5 1 5 1 5 3 3 5 1 5 7 2 3 15 . T T T T T T T T T GM m V R GM tr m R GM tr m m R GM m R ε ε ε ε × × ∂ = -∂ + ---· -+ ⎡ + ⎤ + + ⎣ ⎦ + ---· + I I RR R R IR I γ R RR I RR I γγ IRR RR I γ R γ R R γ (28)</formula>
<text><location><page_13><loc_15><loc_35><loc_85><loc_48></location>As described by Eqs. (17), (21) and (25), at the relative equilibrium e z , we have [ ] 0, 0, T e e zz I = Ω Π , [ ] 0, 0, 1 T e = γ , [ ] ,0,0 T e e R = R , [ ] 1, 0, 0 T e = R , [ ] 0, , 0 T e e e mR = Ω P , [ ] 0, 0, T e e = Ω Ω , ( ) 2 2 1 e zz e I mR μ =-Ω + and 2 e μ =Ω . Then the Hessian of the variational Lagrangian ( ) 2 e F ∇ z at the relative equilibrium e z can be obtained as:</text>
<formula><location><page_13><loc_21><loc_18><loc_85><loc_33></location>( ) 1 2 3 3 2 1 2 3 3 1 3 3 2 2 5 2 2 2 2 2 2 2 2 3 3 3 ˆ ˆ . ˆ ˆ 1 ˆ ˆ T T e e e e e e e e e e e e e GM m V R F V V m μ ε μ μ μ μ μ μ μ μ -× × × × ⎡ ⎤ -⎢ ⎥ ⎢ ⎥ ⎛ ⎞ ∂ --+ -⎢ ⎥ ⎜ ⎟ ∂∂ ⎝ ⎠ ⎢ ⎥ ⎢ ⎥ ∇ = ∂ ∂ ⎢ ⎥ -⎢ ⎥ ∂∂ ∂ ⎢ ⎥ ⎢ ⎥ -⎢ ⎥ ⎣ ⎦ I 0 0 I I 0 0 I I R R P R γ R z P γ γ R R R γ (29)</formula>
<text><location><page_13><loc_15><loc_11><loc_85><loc_16></location>The second-order partial derivates of the gravitational potential in Eq. (29) at the relative equilibrium e z are obtained through Eqs. (27)-(28) as follows:</text>
<formula><location><page_14><loc_41><loc_87><loc_85><loc_91></location>2 1 4 3 T e e e e GM m V R ε ∂ = ∂∂ γα γ R , (30)</formula>
<formula><location><page_14><loc_20><loc_81><loc_85><loc_86></location>( ) ( ) ( ) 2 1 1 3 3 2 3 5 3 3 15 5 5 2 3 = 3 2 2 5 T T xx e e e e T e e e e e xx I tr m m GM m GM V R R I tr m ε ε ε × × ⎧ ⎫ ⎡ --⎤ + ∂ ⎪⎣ ⎦ ⎪ -+ ⎨ ⎬ ∂ + - ⎡ --⎤ ⎪ ⎪ ⎣ ⎦ ⎩ ⎭ I I I αα γγ αα R I I , (31)</formula>
<text><location><page_14><loc_15><loc_78><loc_48><loc_80></location>where e α is defined as [ ] 1 0 0 T e = α .</text>
<text><location><page_14><loc_18><loc_74><loc_81><loc_76></location>The Poisson tensor ( ) e B z at the relative equilibrium e z can be obtained as:</text>
<formula><location><page_14><loc_34><loc_64><loc_85><loc_72></location>ˆ ˆ ˆ ˆ ˆ ( ) ˆ ˆ e zz e e e e e e e e e e e e e e I R mR R mR ⎡ ⎤ Ω Ω ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ Ω -⎣ ⎦ 0 0 0 0 0 E 0 E 0 γ γ α β γ B z α β , (32)</formula>
<text><location><page_14><loc_15><loc_61><loc_47><loc_63></location>where e β is defined as [ ] 0,1, 0 T e = β .</text>
<text><location><page_14><loc_18><loc_57><loc_39><loc_59></location>In Eqs. (29)-(32), we have</text>
<formula><location><page_14><loc_21><loc_50><loc_79><loc_56></location>0 0 0 ˆ 0 0 1 0 1 0 e ⎡ ⎤ ⎢ ⎥ = -⎢ ⎥ ⎢ ⎥ α , 0 0 1 ˆ 0 0 0 1 0 0 e ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ -β , 0 1 0 ˆ 1 0 0 0 0 0 e -⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ γ , 1 0 0 0 0 0 0 0 0 T e e ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ αα ,</formula>
<formula><location><page_14><loc_25><loc_42><loc_85><loc_54></location>⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (33) 0 0 0 0 0 0 0 0 1 T e e ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ γγ , 0 0 0 0 0 0 1 0 0 T e e ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ γα . (34)</formula>
<text><location><page_14><loc_15><loc_31><loc_85><loc_41></location>Then the linear system matrix ( ) e D z of the non-canonical Hamiltonian system can be calculated through Eqs. (22), (29) and (32). Through some rearrangement and simplification, the linear system matrix ( ) e D z can be written as follows:</text>
<formula><location><page_14><loc_18><loc_10><loc_86><loc_30></location>( ) ( ) 2 1 1 1 2 4 1 4 1 1 3 3 2 2 1 2 3 ˆ 5 ˆ 2 ˆ 3 ˆ ˆ ˆ 1 ˆ ˆ ˆ ˆ e e e xx e e zz e e e e e e e e e e e e e e e e e e e e e GM m GM mR I tr m I R R GM R R m V V mR ε ---× -= ⎡ ⎤ ⎧ ⎫ -Ω -⎡ --⎤ ⎢ ⎥ ⎨ ⎬ ⎣ ⎦ Ω ⎩ ⎭ ⎢ ⎥ ⎢ ⎥ -Ω ⎢ ⎥ + ⎢ ⎥ ⎢ ⎥ -Ω ⎢ ⎥ ⎢ ⎥ -Ω ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ∂ ∂ Ω ---Ω ⎢ ⎥ ∂∂ ∂ ⎣ ⎦ 0 0 0 0 0 I D z I α γ I γ α I γ I γ α I γ β I γ γ R R .(35)</formula>
<text><location><page_15><loc_15><loc_81><loc_85><loc_90></location>As stated above, the linear stability of the relative equilibrium e z depends on the eigenvalues of the linear system matrix of the system ( ) e D z . The characteristic polynomial of the linear system matrix ( ) e D z can be calculated by</text>
<formula><location><page_15><loc_40><loc_77><loc_85><loc_80></location>( ) 12 12 ( ) det e P s s × = ⎡ -⎤ ⎣ ⎦ I D z . (36)</formula>
<text><location><page_15><loc_15><loc_70><loc_84><loc_76></location>The eigenvalues of the linear system matrix ( ) e D z are roots of the characteristic equation of the linearized system, which is given by</text>
<formula><location><page_15><loc_41><loc_66><loc_85><loc_69></location>( ) 12 12 det 0 e s × ⎡ -⎤ = ⎣ ⎦ I D z . (37)</formula>
<text><location><page_15><loc_15><loc_59><loc_84><loc_64></location>Through Eqs. (35) and (37), with the help of Matlab and Maple , the characteristic equation can be obtained with the following form:</text>
<formula><location><page_15><loc_29><loc_55><loc_85><loc_57></location>2 2 4 2 6 4 2 2 0 4 2 0 ( )( ) 0 zz xx yy s m I s A s A mI I s B s B s B + + + + + = , (38)</formula>
<text><location><page_15><loc_15><loc_44><loc_85><loc_53></location>where the coefficients 2 A , 0 A , 4 B , 2 B and 0 B are functions of the parameters of the system: 1 GM , e Ω , e R , ε , m , xx I , yy I and zz I . The explicit formulations of the coefficients are given in the Appendix.</text>
<text><location><page_15><loc_15><loc_33><loc_85><loc_42></location>According to Beck and Hall (1998), the non-canonical Hamiltonian systems have special properties with regard to both the form of the characteristic polynomial and the eigenvalues of the linear system matrix ( ) e D z :</text>
<text><location><page_15><loc_15><loc_22><loc_84><loc_31></location>Property 1. There are only even terms in the characteristic polynomial of the linear system matrix, and the eigenvalues are symmetrical with respect to both the real and imaginary axes.</text>
<text><location><page_15><loc_15><loc_11><loc_85><loc_20></location>Property 2. A zero eigenvalue exists for each linearly independent Casimir function. Property 3. An additional pair of zero eigenvalues exists for each first integral, which is associated with a symmetry of the Hamiltonian by Noether's theorem.</text>
<text><location><page_16><loc_15><loc_63><loc_85><loc_90></location>Notice that in our problem, there are two linearly independent Casimir functions, and the two zero eigenvalues correspond to the two Casimir functions 1 ( ) C z and 2 ( ) C z . The remaining ten eigenvalues correspond to the motion constrained by the Casimir functions on the ten-dimensional invariant manifold Σ . We have carried out a Poisson reduction by means of the symmetry of the Hamiltonian, and expressed the dynamics on the reduced phase space. The additional pair of zero eigenvalues according to Property 3 has been eliminated by the reduction process. Therefore, our results in Eq. (38) are consistent with these three properties stated above.</text>
<text><location><page_16><loc_15><loc_29><loc_85><loc_61></location>According to the characteristic equation in Eq. (38), the ten-dimensional linear system on the invariant manifold Σ decouples into two entirely independent fourand six-dimensional subsystems under the second-order gravitational potential. It is worth our special attention that this is not the decoupling between the freedoms of the rotational motion and the orbital motion of the rigid body, since the orbit-rotation coupling is considered in our study. Actually, the four-dimensional subsystem and 2 s are the three freedoms of the orbital and rotational motions within the equatorial plane of the body P , and the other three freedoms, i.e. orbital and rotational motions outside the equatorial plane of the body P , constitute the six-dimensional subsystem.</text>
<text><location><page_16><loc_15><loc_11><loc_85><loc_27></location>The linear stability of the relative equilibria implies that there are no roots of the characteristic equation with positive real parts. According to Property 1 , the linear stability requires all the roots to be purely imaginary, that is 2 s is real and negative. Therefore, in this case of a conservative system, we can only get the necessary conditions of the stability through the linear stability of the relative equilibria.</text>
<text><location><page_17><loc_15><loc_85><loc_85><loc_90></location>According to the theory of the roots of the second and third degree polynomial equation, that the 2 s in Eq. (38) is real and negative is equivalent to</text>
<formula><location><page_17><loc_36><loc_79><loc_85><loc_83></location>2 0 2 2 0 2 2 4 0, 0, 0; zz zz A A A A m I m I ⎛ ⎞ -≥ > > ⎜ ⎟ ⎝ ⎠ (39)</formula>
<formula><location><page_17><loc_21><loc_73><loc_85><loc_78></location>3 2 2 3 0 4 2 4 4 2 2 2 2 1 1 1 2 0, 27 3 4 27 3 xx yy xx yy xx yy xx yy xx yy B B B B B B mI I mI I mI I m I I mI I ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ -+ + -+ ≤ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (40)</formula>
<text><location><page_17><loc_42><loc_70><loc_43><loc_72></location>B</text>
<text><location><page_17><loc_47><loc_70><loc_49><loc_72></location>B</text>
<text><location><page_17><loc_53><loc_70><loc_54><loc_72></location>B</text>
<text><location><page_17><loc_43><loc_70><loc_44><loc_71></location>4</text>
<text><location><page_17><loc_48><loc_70><loc_49><loc_71></location>2</text>
<text><location><page_17><loc_54><loc_70><loc_54><loc_71></location>0</text>
<text><location><page_17><loc_46><loc_70><loc_47><loc_72></location>0,</text>
<text><location><page_17><loc_51><loc_70><loc_52><loc_72></location>0,</text>
<text><location><page_17><loc_56><loc_70><loc_58><loc_72></location>0.</text>
<text><location><page_17><loc_44><loc_70><loc_45><loc_72></location>></text>
<text><location><page_17><loc_50><loc_70><loc_51><loc_72></location>></text>
<text><location><page_17><loc_55><loc_70><loc_56><loc_72></location>></text>
<text><location><page_17><loc_15><loc_59><loc_85><loc_68></location>We have given the conditions of linear stability of the relative equilibria in Eqs. (39) and (40). Given a set of the parameters of the system, we can determine whether the relative equilibria are linear stability by using the stability criterion given above.</text>
<section_header_level_1><location><page_17><loc_15><loc_55><loc_29><loc_57></location>3.2 Case studies</section_header_level_1>
<text><location><page_17><loc_15><loc_37><loc_85><loc_53></location>However, the expressions of coefficients 2 A , 0 A , 4 B , 2 B and 0 B in terms of the parameters of the system are tedious, since there are large amount of parameters in the system and the considered problem is a high-dimensional system. It is difficult to get general conditions of linear stability through Eqs. (39) and (40) in terms of the parameters of the system, i.e. 1 GM , e Ω , e R , ε , m , xx I , yy I and zz I .</text>
<text><location><page_17><loc_15><loc_22><loc_85><loc_35></location>We will consider an example planet P , which has the same mass and equatorial radius as the Earth, but has a different zonal harmonic J 2. That is 14 3 2 1 3.986005 10 m / s GM = × and 6 6.37814 10 m E a = × . Five different values of the zonal harmonic J 2 are considered</text>
<formula><location><page_17><loc_39><loc_18><loc_85><loc_20></location>2 0.5, 0.2, 0, 0.18, 0.2 J = --. (41)</formula>
<text><location><page_17><loc_15><loc_11><loc_84><loc_16></location>The orbital angular velocity e Ω is assumed to be equal to 3 1 1.163553 10 s --× with the orbital period equal to 1.5 hours.</text>
<text><location><page_18><loc_15><loc_81><loc_85><loc_90></location>With the parameters of the system given above, the stability criterion in Eqs. (39) and (40) can be determined by three mass distribution parameters of the rigid body: xx I m , x σ and y σ , where x σ and y σ are defined as</text>
<formula><location><page_18><loc_37><loc_75><loc_85><loc_80></location>zz yy x xx I I I σ -⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ , zz xx y yy I I I σ ⎛ ⎞ -= ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ . (42)</formula>
<text><location><page_18><loc_15><loc_65><loc_85><loc_74></location>The ratio xx I m describes the characteristic dimension of the rigid body; the ratios x σ and y σ describe the shape of the rigid body to the second order. Three different values of the parameter xx I m are considered as follows:</text>
<formula><location><page_18><loc_40><loc_60><loc_85><loc_63></location>3 7 11 5 10 , 5 10 , 5 10 xx I m = × × × , (43)</formula>
<text><location><page_18><loc_15><loc_54><loc_84><loc_59></location>which correspond to a rigid body with the characteristic dimension of order of 100m, 10km and 1000km respectively.</text>
<text><location><page_18><loc_15><loc_46><loc_84><loc_52></location>In the case of each value of xx I m , the parameters x σ and y σ are considered in the following range</text>
<formula><location><page_18><loc_41><loc_43><loc_85><loc_44></location>1 1, 1 1 x y σ σ - ≤ ≤ - ≤ ≤ , (44)</formula>
<text><location><page_18><loc_15><loc_39><loc_74><loc_40></location>which have covered all the possible mass distributions of the rigid body.</text>
<text><location><page_18><loc_15><loc_28><loc_85><loc_37></location>Given the mass distribution parameters of the rigid body, the orbital radius e R at the relative equilibrium can be calculated by Eq. (17). Then the stability criterion in Eqs. (39) and (40) can be calculated with all the parameters of the system known.</text>
<text><location><page_18><loc_15><loc_9><loc_85><loc_26></location>The linear stability criterion in Eqs. (39) and (40) is calculated for a rigid body within the range of the parameters Eqs. (43) and (44) in the cases of different values of the zonal harmonic J 2. The points, which correspond to the mass distribution parameters guaranteeing linear stability, are plotted on the y x σ σ -plane in the 15 cases of different values of xx I m and J 2 in Figs. (3)-(17) respectively.</text>
<text><location><page_19><loc_15><loc_59><loc_85><loc_90></location>In our problem, the gravitational potential in Eq. (8) is truncated on the second order. According to the conclusions in Wang and Xu (2013b), only the central component of the gravity field of the planet P is considered in the gravity gradient torque, with the zonal harmonic J 2 neglected. That is to say, the attitude motion of the rigid body in our problem, in the point view of the traditional attitude dynamics with the orbit-rotation coupling neglected, is actually the attitude dynamics on a circular orbit in a central gravity field. To make comparisons with the traditional attitude dynamics, we also plot the classical linear attitude stability region of a rigid body on a circular orbit in a central gravity field in Figs. (3)-(17), which is given by:</text>
<formula><location><page_19><loc_40><loc_51><loc_85><loc_58></location>0, 1 3 4 , 0. y x y x y x y x y σ σ σ σσ σσ σσ -> + + > > (45)</formula>
<text><location><page_19><loc_15><loc_33><loc_85><loc_50></location>The classical linear attitude stability region given by Eq. (45) is consisted of the Lagrange region I and the DeBra-Delp region II (Hughes 1986). The Lagrange region is the isosceles right triangle region in the first quadrant of the y x σ σ -plane below the straight line 0 y x σ σ -= , and DeBra-Delp region is a small region in the third quadrant below the straight line 0 y x σ σ -= .</text>
<text><location><page_19><loc_15><loc_15><loc_85><loc_31></location>Notice that at the relative equilibrium in our paper, the orientations of the principal axes of the rigid body are different from those at the equilibrium attitude in Hughes (1986), and then the definitions of the parameters y σ and x σ in our paper are different form those in Hughes (1986) to make sure that the linear attitude stability region is the same as in Hughes (1986).</text>
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<text><location><page_20><loc_60><loc_93><loc_62><loc_94></location>i</text>
<text><location><page_20><loc_60><loc_92><loc_62><loc_93></location>e</text>
<text><location><page_20><loc_60><loc_92><loc_62><loc_92></location>n</text>
<text><location><page_20><loc_60><loc_90><loc_62><loc_92></location>pla</text>
<text><location><page_20><loc_61><loc_89><loc_62><loc_89></location>x</text>
<text><location><page_20><loc_59><loc_88><loc_62><loc_89></location>σ</text>
<text><location><page_20><loc_59><loc_87><loc_62><loc_88></location>-</text>
<text><location><page_20><loc_61><loc_86><loc_62><loc_87></location>y</text>
<text><location><page_20><loc_59><loc_85><loc_62><loc_87></location>σ</text>
<text><location><page_20><loc_65><loc_88><loc_66><loc_89></location>11</text>
<text><location><page_20><loc_65><loc_88><loc_67><loc_88></location>0</text>
<text><location><page_20><loc_65><loc_87><loc_67><loc_88></location>1</text>
<text><location><page_20><loc_65><loc_86><loc_67><loc_87></location>×</text>
<text><location><page_20><loc_65><loc_85><loc_67><loc_86></location>5</text>
<figure>
<location><page_20><loc_8><loc_30><loc_95><loc_85></location>
<caption>Fig. 3.</caption>
</figure>
<text><location><page_20><loc_61><loc_29><loc_62><loc_30></location>x</text>
<text><location><page_20><loc_59><loc_28><loc_62><loc_30></location>σ</text>
<text><location><page_20><loc_59><loc_27><loc_62><loc_28></location>-</text>
<text><location><page_20><loc_61><loc_27><loc_62><loc_27></location>y</text>
<text><location><page_20><loc_59><loc_26><loc_62><loc_27></location>σ</text>
<text><location><page_20><loc_60><loc_23><loc_62><loc_25></location>on</text>
<text><location><page_20><loc_60><loc_22><loc_62><loc_23></location>on</text>
<text><location><page_20><loc_60><loc_22><loc_62><loc_22></location>i</text>
<text><location><page_20><loc_60><loc_19><loc_62><loc_22></location>y reg</text>
<text><location><page_20><loc_60><loc_19><loc_62><loc_19></location>it</text>
<text><location><page_20><loc_60><loc_18><loc_62><loc_19></location>il</text>
<text><location><page_20><loc_60><loc_17><loc_62><loc_18></location>ab</text>
<text><location><page_20><loc_60><loc_16><loc_62><loc_17></location>st</text>
<text><location><page_20><loc_60><loc_13><loc_62><loc_16></location>near</text>
<text><location><page_20><loc_60><loc_12><loc_62><loc_13></location>Li</text>
<text><location><page_20><loc_65><loc_28><loc_66><loc_28></location>3</text>
<text><location><page_20><loc_65><loc_27><loc_67><loc_28></location>0</text>
<text><location><page_20><loc_65><loc_27><loc_67><loc_27></location>1</text>
<text><location><page_20><loc_65><loc_26><loc_67><loc_27></location>×</text>
<text><location><page_20><loc_65><loc_25><loc_67><loc_26></location>5</text>
<text><location><page_20><loc_65><loc_24><loc_67><loc_25></location>=</text>
<text><location><page_20><loc_65><loc_23><loc_67><loc_24></location>m</text>
<text><location><page_20><loc_66><loc_21><loc_67><loc_22></location>xx</text>
<text><location><page_20><loc_65><loc_21><loc_67><loc_21></location>I</text>
<text><location><page_20><loc_65><loc_18><loc_67><loc_20></location>and</text>
<text><location><page_20><loc_65><loc_15><loc_67><loc_17></location>0.5</text>
<text><location><page_20><loc_65><loc_14><loc_67><loc_15></location>=</text>
<text><location><page_20><loc_66><loc_14><loc_67><loc_14></location>2</text>
<text><location><page_20><loc_65><loc_13><loc_67><loc_14></location>J</text>
<text><location><page_20><loc_65><loc_9><loc_67><loc_12></location>case of</text>
<text><location><page_21><loc_60><loc_94><loc_62><loc_94></location>n</text>
<text><location><page_21><loc_60><loc_93><loc_62><loc_94></location>i</text>
<text><location><page_21><loc_60><loc_92><loc_62><loc_93></location>e</text>
<text><location><page_21><loc_60><loc_92><loc_62><loc_92></location>n</text>
<text><location><page_21><loc_60><loc_90><loc_62><loc_92></location>pla</text>
<text><location><page_21><loc_61><loc_89><loc_62><loc_89></location>x</text>
<text><location><page_21><loc_59><loc_88><loc_62><loc_89></location>σ</text>
<text><location><page_21><loc_59><loc_87><loc_62><loc_88></location>-</text>
<text><location><page_21><loc_61><loc_86><loc_62><loc_87></location>y</text>
<text><location><page_21><loc_59><loc_85><loc_62><loc_87></location>σ</text>
<text><location><page_21><loc_65><loc_88><loc_66><loc_89></location>11</text>
<text><location><page_21><loc_65><loc_88><loc_67><loc_88></location>0</text>
<text><location><page_21><loc_65><loc_87><loc_67><loc_88></location>1</text>
<text><location><page_21><loc_65><loc_86><loc_67><loc_87></location>×</text>
<text><location><page_21><loc_65><loc_85><loc_67><loc_86></location>5</text>
<figure>
<location><page_21><loc_8><loc_30><loc_95><loc_85></location>
<caption>Fig. 6.</caption>
</figure>
<text><location><page_21><loc_61><loc_29><loc_62><loc_30></location>x</text>
<text><location><page_21><loc_59><loc_28><loc_62><loc_30></location>σ</text>
<text><location><page_21><loc_59><loc_27><loc_62><loc_28></location>-</text>
<text><location><page_21><loc_61><loc_27><loc_62><loc_27></location>y</text>
<text><location><page_21><loc_59><loc_26><loc_62><loc_27></location>σ</text>
<text><location><page_21><loc_60><loc_23><loc_62><loc_25></location>on</text>
<text><location><page_21><loc_60><loc_22><loc_62><loc_23></location>on</text>
<text><location><page_21><loc_60><loc_22><loc_62><loc_22></location>i</text>
<text><location><page_21><loc_60><loc_19><loc_62><loc_22></location>y reg</text>
<text><location><page_21><loc_60><loc_19><loc_62><loc_19></location>it</text>
<text><location><page_21><loc_60><loc_18><loc_62><loc_19></location>il</text>
<text><location><page_21><loc_60><loc_17><loc_62><loc_18></location>ab</text>
<text><location><page_21><loc_60><loc_16><loc_62><loc_17></location>st</text>
<text><location><page_21><loc_60><loc_13><loc_62><loc_16></location>near</text>
<text><location><page_21><loc_60><loc_12><loc_62><loc_13></location>Li</text>
<text><location><page_21><loc_65><loc_28><loc_66><loc_28></location>3</text>
<text><location><page_21><loc_65><loc_27><loc_67><loc_28></location>0</text>
<text><location><page_21><loc_65><loc_27><loc_67><loc_27></location>1</text>
<text><location><page_21><loc_65><loc_26><loc_67><loc_27></location>×</text>
<text><location><page_21><loc_65><loc_25><loc_67><loc_26></location>5</text>
<text><location><page_21><loc_65><loc_24><loc_67><loc_25></location>=</text>
<text><location><page_21><loc_65><loc_23><loc_67><loc_24></location>m</text>
<text><location><page_21><loc_66><loc_21><loc_67><loc_22></location>xx</text>
<text><location><page_21><loc_65><loc_21><loc_67><loc_21></location>I</text>
<text><location><page_21><loc_65><loc_18><loc_67><loc_20></location>and</text>
<text><location><page_21><loc_65><loc_15><loc_67><loc_17></location>0.2</text>
<text><location><page_21><loc_65><loc_14><loc_67><loc_15></location>=</text>
<text><location><page_21><loc_66><loc_14><loc_67><loc_14></location>2</text>
<text><location><page_21><loc_65><loc_13><loc_67><loc_14></location>J</text>
<text><location><page_21><loc_65><loc_9><loc_67><loc_12></location>case of</text>
<text><location><page_22><loc_60><loc_93><loc_62><loc_94></location>in</text>
<text><location><page_22><loc_60><loc_92><loc_62><loc_93></location>e</text>
<text><location><page_22><loc_60><loc_92><loc_62><loc_92></location>n</text>
<text><location><page_22><loc_60><loc_91><loc_62><loc_92></location>a</text>
<text><location><page_22><loc_60><loc_90><loc_62><loc_91></location>pl</text>
<text><location><page_22><loc_61><loc_89><loc_62><loc_89></location>x</text>
<text><location><page_22><loc_59><loc_88><loc_62><loc_89></location>σ</text>
<text><location><page_22><loc_59><loc_87><loc_62><loc_88></location>-</text>
<text><location><page_22><loc_61><loc_86><loc_62><loc_87></location>y</text>
<text><location><page_22><loc_59><loc_85><loc_62><loc_87></location>σ</text>
<text><location><page_22><loc_65><loc_87><loc_66><loc_88></location>11</text>
<text><location><page_22><loc_65><loc_87><loc_67><loc_87></location>0</text>
<text><location><page_22><loc_65><loc_86><loc_67><loc_87></location>1</text>
<text><location><page_22><loc_65><loc_85><loc_67><loc_86></location>×</text>
<figure>
<location><page_22><loc_8><loc_30><loc_95><loc_85></location>
<caption>Fig. 9.</caption>
</figure>
<text><location><page_22><loc_61><loc_29><loc_62><loc_30></location>x</text>
<text><location><page_22><loc_59><loc_28><loc_62><loc_30></location>σ</text>
<text><location><page_22><loc_59><loc_27><loc_62><loc_28></location>-</text>
<text><location><page_22><loc_61><loc_27><loc_62><loc_27></location>y</text>
<text><location><page_22><loc_59><loc_26><loc_62><loc_27></location>σ</text>
<text><location><page_22><loc_60><loc_23><loc_62><loc_25></location>on</text>
<text><location><page_22><loc_60><loc_22><loc_62><loc_23></location>on</text>
<text><location><page_22><loc_60><loc_22><loc_62><loc_22></location>i</text>
<text><location><page_22><loc_60><loc_19><loc_62><loc_22></location>y reg</text>
<text><location><page_22><loc_60><loc_19><loc_62><loc_19></location>it</text>
<text><location><page_22><loc_60><loc_18><loc_62><loc_19></location>il</text>
<text><location><page_22><loc_60><loc_17><loc_62><loc_18></location>ab</text>
<text><location><page_22><loc_60><loc_16><loc_62><loc_17></location>st</text>
<text><location><page_22><loc_60><loc_13><loc_62><loc_16></location>near</text>
<text><location><page_22><loc_60><loc_12><loc_62><loc_13></location>Li</text>
<text><location><page_22><loc_65><loc_27><loc_66><loc_27></location>3</text>
<text><location><page_22><loc_65><loc_26><loc_67><loc_27></location>0</text>
<text><location><page_22><loc_65><loc_26><loc_67><loc_26></location>1</text>
<text><location><page_22><loc_65><loc_25><loc_67><loc_26></location>×</text>
<text><location><page_22><loc_65><loc_24><loc_67><loc_25></location>5</text>
<text><location><page_22><loc_65><loc_23><loc_67><loc_24></location>=</text>
<text><location><page_22><loc_65><loc_22><loc_67><loc_23></location>m</text>
<text><location><page_22><loc_66><loc_21><loc_67><loc_21></location>xx</text>
<text><location><page_22><loc_65><loc_20><loc_67><loc_20></location>I</text>
<text><location><page_22><loc_65><loc_17><loc_67><loc_19></location>and</text>
<text><location><page_22><loc_65><loc_15><loc_67><loc_16></location>0</text>
<text><location><page_22><loc_65><loc_14><loc_67><loc_15></location>=</text>
<text><location><page_22><loc_66><loc_14><loc_67><loc_14></location>2</text>
<text><location><page_22><loc_65><loc_13><loc_67><loc_14></location>J</text>
<text><location><page_22><loc_65><loc_9><loc_67><loc_12></location>case of</text>
<text><location><page_23><loc_60><loc_94><loc_62><loc_94></location>n</text>
<text><location><page_23><loc_60><loc_93><loc_62><loc_94></location>i</text>
<text><location><page_23><loc_60><loc_92><loc_62><loc_93></location>e</text>
<text><location><page_23><loc_60><loc_92><loc_62><loc_92></location>n</text>
<text><location><page_23><loc_60><loc_90><loc_62><loc_92></location>pla</text>
<text><location><page_23><loc_61><loc_89><loc_62><loc_89></location>x</text>
<text><location><page_23><loc_59><loc_88><loc_62><loc_89></location>σ</text>
<text><location><page_23><loc_59><loc_87><loc_62><loc_88></location>-</text>
<text><location><page_23><loc_61><loc_86><loc_62><loc_87></location>y</text>
<text><location><page_23><loc_59><loc_85><loc_62><loc_87></location>σ</text>
<text><location><page_23><loc_65><loc_89><loc_66><loc_90></location>11</text>
<text><location><page_23><loc_65><loc_89><loc_67><loc_90></location>0</text>
<text><location><page_23><loc_65><loc_88><loc_67><loc_89></location>1</text>
<text><location><page_23><loc_65><loc_87><loc_67><loc_88></location>×</text>
<text><location><page_23><loc_65><loc_87><loc_67><loc_87></location>5</text>
<text><location><page_23><loc_65><loc_86><loc_67><loc_86></location>=</text>
<text><location><page_23><loc_65><loc_84><loc_67><loc_85></location>m</text>
<text><location><page_23><loc_65><loc_30><loc_67><loc_31></location>1</text>
<figure>
<location><page_23><loc_8><loc_30><loc_95><loc_85></location>
<caption>Fig. 12</caption>
</figure>
<text><location><page_23><loc_59><loc_30><loc_62><loc_31></location>σ</text>
<text><location><page_23><loc_59><loc_29><loc_62><loc_30></location>-</text>
<text><location><page_23><loc_61><loc_28><loc_62><loc_29></location>y</text>
<text><location><page_23><loc_59><loc_27><loc_62><loc_29></location>σ</text>
<text><location><page_23><loc_60><loc_25><loc_62><loc_27></location>on</text>
<text><location><page_23><loc_60><loc_24><loc_62><loc_25></location>n</text>
<text><location><page_23><loc_60><loc_23><loc_62><loc_24></location>gio</text>
<text><location><page_23><loc_60><loc_21><loc_62><loc_23></location>re</text>
<text><location><page_23><loc_60><loc_20><loc_62><loc_21></location>ity</text>
<text><location><page_23><loc_60><loc_19><loc_62><loc_20></location>il</text>
<text><location><page_23><loc_60><loc_18><loc_62><loc_19></location>b</text>
<text><location><page_23><loc_60><loc_16><loc_62><loc_18></location>ar sta</text>
<text><location><page_23><loc_60><loc_14><loc_62><loc_16></location>ne</text>
<text><location><page_23><loc_60><loc_13><loc_62><loc_14></location>Li</text>
<text><location><page_23><loc_60><loc_12><loc_62><loc_13></location>.</text>
<text><location><page_23><loc_65><loc_29><loc_67><loc_30></location>×</text>
<text><location><page_23><loc_65><loc_28><loc_67><loc_29></location>5</text>
<text><location><page_23><loc_65><loc_27><loc_67><loc_28></location>=</text>
<text><location><page_23><loc_65><loc_26><loc_67><loc_27></location>m</text>
<text><location><page_23><loc_66><loc_25><loc_67><loc_25></location>xx</text>
<text><location><page_23><loc_65><loc_24><loc_67><loc_25></location>I</text>
<text><location><page_23><loc_65><loc_21><loc_67><loc_23></location>and</text>
<text><location><page_23><loc_65><loc_20><loc_67><loc_20></location>8</text>
<text><location><page_23><loc_65><loc_19><loc_67><loc_20></location>1</text>
<text><location><page_23><loc_65><loc_18><loc_67><loc_19></location>0.</text>
<text><location><page_23><loc_65><loc_17><loc_67><loc_18></location>-</text>
<text><location><page_23><loc_65><loc_16><loc_67><loc_17></location>=</text>
<text><location><page_23><loc_66><loc_15><loc_67><loc_16></location>2</text>
<text><location><page_23><loc_65><loc_15><loc_67><loc_15></location>J</text>
<text><location><page_23><loc_65><loc_13><loc_67><loc_14></location>of</text>
<text><location><page_23><loc_65><loc_9><loc_67><loc_13></location>the case</text>
<text><location><page_24><loc_60><loc_94><loc_62><loc_94></location>n</text>
<text><location><page_24><loc_60><loc_93><loc_62><loc_94></location>i</text>
<text><location><page_24><loc_60><loc_92><loc_62><loc_93></location>e</text>
<text><location><page_24><loc_60><loc_92><loc_62><loc_92></location>n</text>
<text><location><page_24><loc_60><loc_90><loc_62><loc_92></location>pla</text>
<text><location><page_24><loc_61><loc_89><loc_62><loc_89></location>x</text>
<text><location><page_24><loc_59><loc_88><loc_62><loc_89></location>σ</text>
<text><location><page_24><loc_59><loc_87><loc_62><loc_88></location>-</text>
<text><location><page_24><loc_61><loc_86><loc_62><loc_87></location>y</text>
<text><location><page_24><loc_59><loc_85><loc_62><loc_87></location>σ</text>
<text><location><page_24><loc_65><loc_89><loc_66><loc_90></location>11</text>
<text><location><page_24><loc_65><loc_88><loc_67><loc_89></location>0</text>
<text><location><page_24><loc_65><loc_88><loc_67><loc_88></location>1</text>
<text><location><page_24><loc_65><loc_87><loc_67><loc_88></location>×</text>
<text><location><page_24><loc_65><loc_86><loc_67><loc_87></location>5</text>
<text><location><page_24><loc_65><loc_85><loc_67><loc_86></location>=</text>
<figure>
<location><page_24><loc_8><loc_30><loc_95><loc_85></location>
<caption>Fig. 15</caption>
</figure>
<text><location><page_24><loc_59><loc_30><loc_62><loc_31></location>σ</text>
<text><location><page_24><loc_59><loc_29><loc_62><loc_30></location>-</text>
<text><location><page_24><loc_61><loc_28><loc_62><loc_29></location>y</text>
<text><location><page_24><loc_59><loc_27><loc_62><loc_29></location>σ</text>
<text><location><page_24><loc_60><loc_25><loc_62><loc_27></location>on</text>
<text><location><page_24><loc_60><loc_24><loc_62><loc_25></location>n</text>
<text><location><page_24><loc_60><loc_23><loc_62><loc_24></location>gio</text>
<text><location><page_24><loc_60><loc_21><loc_62><loc_23></location>re</text>
<text><location><page_24><loc_60><loc_20><loc_62><loc_21></location>ity</text>
<text><location><page_24><loc_60><loc_19><loc_62><loc_20></location>il</text>
<text><location><page_24><loc_60><loc_18><loc_62><loc_19></location>b</text>
<text><location><page_24><loc_60><loc_16><loc_62><loc_18></location>ar sta</text>
<text><location><page_24><loc_60><loc_14><loc_62><loc_16></location>ne</text>
<text><location><page_24><loc_60><loc_13><loc_62><loc_14></location>Li</text>
<text><location><page_24><loc_60><loc_12><loc_62><loc_13></location>.</text>
<text><location><page_24><loc_65><loc_30><loc_67><loc_31></location>0</text>
<text><location><page_24><loc_65><loc_29><loc_67><loc_30></location>1</text>
<text><location><page_24><loc_65><loc_29><loc_67><loc_29></location>×</text>
<text><location><page_24><loc_65><loc_28><loc_67><loc_28></location>5</text>
<text><location><page_24><loc_65><loc_27><loc_67><loc_27></location>=</text>
<text><location><page_24><loc_65><loc_26><loc_67><loc_26></location>m</text>
<text><location><page_24><loc_66><loc_24><loc_67><loc_25></location>xx</text>
<text><location><page_24><loc_65><loc_24><loc_67><loc_24></location>I</text>
<text><location><page_24><loc_65><loc_21><loc_67><loc_23></location>and</text>
<text><location><page_24><loc_65><loc_19><loc_67><loc_20></location>2</text>
<text><location><page_24><loc_65><loc_18><loc_67><loc_19></location>0.</text>
<text><location><page_24><loc_65><loc_17><loc_67><loc_18></location>-</text>
<text><location><page_24><loc_65><loc_16><loc_67><loc_17></location>=</text>
<text><location><page_24><loc_66><loc_15><loc_67><loc_16></location>2</text>
<text><location><page_24><loc_65><loc_15><loc_67><loc_15></location>J</text>
<text><location><page_24><loc_65><loc_13><loc_67><loc_14></location>of</text>
<text><location><page_24><loc_65><loc_9><loc_67><loc_13></location>the case</text>
<section_header_level_1><location><page_25><loc_15><loc_89><loc_52><loc_90></location>3.3 Some discussions on the linear stability</section_header_level_1>
<text><location><page_25><loc_18><loc_85><loc_78><loc_87></location>From Figs. (3)-(17), we can easily achieve several conclusions as follows:</text>
<text><location><page_25><loc_15><loc_55><loc_85><loc_83></location>(a). Similar to the classical linear attitude stability region, which is consisted of the Lagrange region and the DeBra-Delp region, the linear stability region of the relative equilibrium of the rigid body in our problem is also consisted of two regions located in the first and third quadrant of the y x σ σ -plane respectively, which are the analogues of the Lagrange region and the DeBra-Delp region respectively. This is consistent with the conclusion by Teixidó Román (2010) that for a rigid body in a central gravity field there is a linear stability region in the third quadrant of the y x σ σ -plane, which is the analogue of the DeBra-Delp region.</text>
<text><location><page_25><loc_15><loc_41><loc_85><loc_53></location>However, when the planet P is very elongated with 2 0.2 J = -, for a small rigid body there is no linear stability region; only in the case of a very large rigid body with 11 5 10 xx I m = × , there is a linear stability region that is the analogue of the Lagrange region located in the first quadrant of the y x σ σ -plane.</text>
<unordered_list>
<list_item><location><page_25><loc_15><loc_18><loc_85><loc_39></location>(b). For a given value of the zonal harmonic J 2 (except 2 0.2 J = -), when the characteristic dimension of the rigid body is small, the characteristic dimension of the rigid body have no influence on the linear stability region, as shown by the linear stability region in the cases of 3 5 10 xx I m = × and 7 5 10 xx I m = × . In these cases, the linear stability region in the first quadrant of the y x σ σ -plane, the analogue of the Lagrange region, is actually the Lagrange region.</list_item>
</unordered_list>
<text><location><page_25><loc_15><loc_11><loc_85><loc_16></location>When the characteristic dimension of the rigid body is large enough, such as 11 5 10 xx I m = × , the linear stability region in the first quadrant of the y x σ σ -plane,</text>
<text><location><page_26><loc_15><loc_74><loc_85><loc_90></location>the analogue of the Lagrange region, is reduced by a triangle in the right part of the first quadrant of the y x σ σ -plane, as shown by Figs. (5), (8), (11) and (14). In the case of 2 0.18 J =-, also the linear stability region in the third quadrant of the y x σ σ -plane, the analogue of the DeBra-Delp region, is reduced by the large characteristic dimension of the rigid body, as shown by Fig. (14).</text>
<unordered_list>
<list_item><location><page_26><loc_15><loc_55><loc_85><loc_72></location>(c). For a given value of the characteristic dimension of the rigid body, as the zonal harmonic J 2 increases from -0.18 to 0.5, the linear stability region in the third quadrant of the y x σ σ -plane, the analogue of the DeBra-Delp region, expands in the direction of the boundary of the DeBra-Delp region, and cross the boundary of the DeBra-Delp region at 2 0 J = .</list_item>
</unordered_list>
<text><location><page_26><loc_15><loc_26><loc_85><loc_53></location>For a small value of the characteristic dimension of the rigid body, such as 3 5 10 xx I m = × and 7 5 10 xx I m = × , as the zonal harmonic J 2 increases from -0.18 to 0.5, the linear stability region in the first quadrant of the y x σ σ -plane, the analogue of the Lagrange region, keeps equal to the Lagrange region. Whereas for a large value of the characteristic dimension of the rigid body 11 5 10 xx I m = × , as the zonal harmonic J 2 increases from -0.18 to 0.5, the linear stability region in the first quadrant of the y x σ σ -plane, the analogue of the Lagrange region, shrinks by the influence of the zonal harmonic J 2.</text>
<section_header_level_1><location><page_26><loc_15><loc_22><loc_63><loc_24></location>4. Nonlinear Stability of the Relative Equilibria</section_header_level_1>
<text><location><page_26><loc_15><loc_11><loc_85><loc_20></location>In this section, we will investigate the nonlinear stability of the classical type of relative equilibria using the energy-Casimir method provided by the geometric mechanics adopted by Beck and Hall (1998), and Hall (2001).</text>
<section_header_level_1><location><page_27><loc_15><loc_89><loc_46><loc_90></location>4.1 Conditions of nonlinear stability</section_header_level_1>
<text><location><page_27><loc_15><loc_52><loc_85><loc_87></location>The energy-Casimir method, the generalization of Lagrange-Dirichlet criterion, is a powerful tool provided by the geometric mechanics for determining the nonlinear stability of the relative equilibria in a non-canonical Hamiltonian system (Marsden and Ratiu, 1999). According to the Lagrange-Dirichlet criterion in the canonical Hamiltonian system, the nonlinear stability of the equilibrium point is determined by the distributions of the eigenvalues of the Hessian matrix of the Hamiltonian. If all the eigenvalues of the Hessian matrix are positive or negative, that is the Hessian matrix of the Hamiltonian is positive- or negative-definite, then the equilibrium point is nonlinear stable. This follows from the conservation of energy and the fact that the level sets of the Hamiltonian near the equilibrium point are approximately ellipsoids.</text>
<text><location><page_27><loc_15><loc_11><loc_85><loc_50></location>However, the Hamiltonian system in our problem is non-canonical, and the phase flow of the system is constrained on the ten-dimensional invariant manifold or symplectic leaf Σ by Casimir functions. Therefore, rather than considering general perturbations in the whole phase space as in the Lagrange-Dirichlet criterion in the canonical Hamiltonian system, we need to restrict the consideration to perturbations on e T Σ z , the tangent space to the invariant manifold Σ at the relative equilibrium e z . e T Σ z is also the range space of Poisson tensor ( ) B z at the relative equilibrium e z , denoted by ( ) R ( ) e B z . This is the basic principle of the energy-Casimir method that the Hessian matrix needs to be considered restrictedly on the invariant manifold Σ of the system. This restriction is constituted through the projected Hessian matrix of the variational Lagrangian ( ) F z in Beck and Hall (1998).</text>
<text><location><page_28><loc_15><loc_55><loc_85><loc_90></location>According to the energy-Casimir method adopted by Beck and Hall (1998), the conditions of nonlinear stability of the relative equilibrium e z can be obtained through the distributions of the eigenvalues of the projected Hessian matrix of the variational Lagrangian ( ) F z . The projected Hessian matrix of the variational Lagrangian ( ) F z has the same number of zero eigenvalues as the linearly independent Casimir functions, which are associated with the nullspace [ ] N ( ) e B z , i.e. the complement space of e T Σ z . The remaining eigenvalues of the projected Hessian matrix are associated with the tangent space to the invariant manifold e T Σ z . If they are all positive, the relative equilibrium e z is a constrained minimum on the invariant manifold Σ and therefore it is nonlinear stable.</text>
<text><location><page_28><loc_16><loc_48><loc_85><loc_53></location>According to Beck and Hall (1998), the projected Hessian matrix is given by ( ) ( ) ( ) 2 e e e F ∇ P z z P z , where the projection operator is given by</text>
<formula><location><page_28><loc_33><loc_44><loc_85><loc_47></location>( ) ( ) 1 12 12 ( ) ( ) ( ) ( ) T T e e e e e -× = -I P z K z K z K z K z . (46)</formula>
<text><location><page_28><loc_18><loc_41><loc_83><loc_42></location>As described by Eqs. (17), (21) and (25), at the relative equilibrium e z , we have</text>
<formula><location><page_28><loc_36><loc_31><loc_85><loc_39></location>[ ] ˆ ( ) N ( ) ˆ ˆ e e e e e e e e e e e ⎡ ⎤ ⎢ ⎥ + ⎢ ⎥ = = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ 0 0 0 γ γ Π R P K z B z P γ γ R . (47)</formula>
<text><location><page_28><loc_15><loc_20><loc_85><loc_30></location>Using the Hessian of the variational Lagrangian ( ) 2 e F ∇ z given by Eq. (29) and the projection operator ( ) e P z , we can calculate the projected Hessian matrix ( ) ( ) ( ) 2 e e e F ∇ P z z P z .</text>
<text><location><page_28><loc_15><loc_9><loc_84><loc_18></location>As stated above, the nonlinear stability of the relative equilibrium e z depends on the eigenvalues of the projected Hessian matrix of the variational Lagrangian ( ) F z . The characteristic polynomial of the projected Hessian matrix ( ) ( ) ( ) 2 e e e F ∇ P z z P z</text>
<text><location><page_29><loc_15><loc_89><loc_32><loc_90></location>can be calculated by</text>
<formula><location><page_29><loc_34><loc_85><loc_85><loc_87></location>( ) ( ) ( ) 2 12 12 ( ) det e e e Q s s F × ⎡ ⎤ = -∇ ⎣ ⎦ I P z z P z . (48)</formula>
<text><location><page_29><loc_15><loc_78><loc_85><loc_83></location>The eigenvalues of the projected Hessian matrix are roots of the characteristic equation, which is given by</text>
<formula><location><page_29><loc_35><loc_74><loc_85><loc_76></location>( ) ( ) ( ) 2 12 12 det 0 e e e s F × ⎡ ⎤ -∇ = ⎣ ⎦ I P z z P z . (49)</formula>
<text><location><page_29><loc_15><loc_67><loc_85><loc_72></location>Through Eq. (49), with the help of Matlab and Maple , the characteristic equation can be obtained with the following form:</text>
<text><location><page_29><loc_15><loc_52><loc_85><loc_65></location>2 3 2 3 2 2 2 2 1 0 2 1 0 1 0 1 0 ( )( )( )( ) 0 s s C s C s C s D s Ds D s E s E s Fs F + + + + + + + + + + = , (50) where coefficients 2 C , 1 C , 0 C , 2 D , 1 D , 0 D , 1 E , 0 E , 1 F and 0 F are functions of the parameters of the system: 1 GM , e Ω , e R , ε , m , xx I , yy I and zz I . The explicit formulations of the coefficients are given in the Appendix.</text>
<text><location><page_29><loc_15><loc_29><loc_85><loc_50></location>In our problem there are two linearly independent Casimir functions, then as shown by Eq. (50), the projected Hessian matrix have two zero eigenvalues associated with the two-dimensional complement space of e T Σ z . The remaining ten eigenvalues are associated with the ten-dimensional tangent space e T Σ z to the invariant manifold, and if they are all positive, then the relative equilibrium e z is a constrained minimum on the invariant manifold Σ , therefore it is nonlinear stable.</text>
<text><location><page_29><loc_15><loc_15><loc_85><loc_27></location>Since the projected Hessian matrix is symmetrical, the eigenvalues are guaranteed to be real by the coefficients of the polynomials in Eq. (50) intrinsically. Therefore, in the conditions of nonlinear stability of the relative equilibria, it is only needed to guarantee that the roots of the polynomial equations in Eq. (50) are positive.</text>
<text><location><page_29><loc_18><loc_11><loc_85><loc_13></location>According to the theory of roots of the polynomial equation, that the remaining</text>
<text><location><page_30><loc_15><loc_89><loc_60><loc_90></location>ten eigenvalues in Eq. (50) are positive is equivalent to</text>
<formula><location><page_30><loc_42><loc_79><loc_85><loc_87></location>2 1 0 2 1 0 1 0 1 0 0, 0, 0, 0, 0, 0, 0, 0, 0, 0. C C C D D D E E F F < > < < > < < > < > (51)</formula>
<text><location><page_30><loc_15><loc_68><loc_84><loc_77></location>We have given the conditions of the nonlinear stability of the relative equilibria in Eq. (51). Given the parameters of the system, we can determine whether the relative equilibria are nonlinear stability using the stability criterion in Eq. (51).</text>
<section_header_level_1><location><page_30><loc_15><loc_65><loc_29><loc_66></location>4.2 Case studies</section_header_level_1>
<text><location><page_30><loc_15><loc_54><loc_85><loc_63></location>As in the studies of the linear stability, here we also give case studies using numerical method. The parameters of the problem considered here are same as in the linear stability studies.</text>
<text><location><page_30><loc_15><loc_31><loc_85><loc_51></location>We calculate the nonlinear stability criterion in Eqs. (51) for a rigid body within the range of the parameters given by Eqs. (43) and (44) in the cases of five different values of the zonal harmonic J 2 given by Eq. (41). The points, which correspond to the mass distribution parameters guaranteeing the nonlinear stability, are plotted on the y x σ σ -plane in the 15 cases of different values of xx I m and J 2 in Figs. (18)-(32) respectively.</text>
<text><location><page_30><loc_15><loc_13><loc_85><loc_29></location>To make comparisons with the traditional attitude dynamics, we have also given the classical nonlinear attitude stability region of a rigid body on a circular orbit in a central gravity field in the Figs. (18)-(32), which is the Lagrange region, the isosceles right triangle region in the first quadrant of the y x σ σ -plane below the straight line 0 y x σ σ -= .</text>
<text><location><page_31><loc_60><loc_94><loc_62><loc_95></location>e</text>
<text><location><page_31><loc_60><loc_93><loc_62><loc_94></location>an</text>
<text><location><page_31><loc_60><loc_93><loc_62><loc_93></location>l</text>
<text><location><page_31><loc_60><loc_91><loc_62><loc_93></location>p</text>
<text><location><page_31><loc_61><loc_91><loc_62><loc_91></location>x</text>
<text><location><page_31><loc_59><loc_90><loc_62><loc_91></location>σ</text>
<text><location><page_31><loc_59><loc_89><loc_62><loc_90></location>-</text>
<text><location><page_31><loc_61><loc_88><loc_62><loc_89></location>y</text>
<text><location><page_31><loc_59><loc_87><loc_62><loc_89></location>σ</text>
<text><location><page_31><loc_60><loc_86><loc_62><loc_87></location>n</text>
<text><location><page_31><loc_60><loc_85><loc_62><loc_86></location>o</text>
<text><location><page_31><loc_65><loc_89><loc_66><loc_90></location>11</text>
<text><location><page_31><loc_65><loc_89><loc_67><loc_89></location>0</text>
<text><location><page_31><loc_65><loc_88><loc_67><loc_89></location>1</text>
<text><location><page_31><loc_65><loc_87><loc_67><loc_88></location>×</text>
<text><location><page_31><loc_65><loc_86><loc_67><loc_87></location>5</text>
<text><location><page_31><loc_65><loc_85><loc_67><loc_86></location>=</text>
<figure>
<location><page_31><loc_8><loc_30><loc_96><loc_85></location>
<caption>Fig. 18</caption>
</figure>
<text><location><page_31><loc_61><loc_30><loc_62><loc_30></location>y</text>
<text><location><page_31><loc_59><loc_29><loc_62><loc_30></location>σ</text>
<text><location><page_31><loc_60><loc_27><loc_62><loc_28></location>n</text>
<text><location><page_31><loc_60><loc_26><loc_62><loc_27></location>o</text>
<text><location><page_31><loc_60><loc_25><loc_62><loc_26></location>on</text>
<text><location><page_31><loc_60><loc_23><loc_62><loc_25></location>regi</text>
<text><location><page_31><loc_60><loc_21><loc_62><loc_23></location>lity</text>
<text><location><page_31><loc_60><loc_21><loc_62><loc_21></location>i</text>
<text><location><page_31><loc_60><loc_20><loc_62><loc_21></location>b</text>
<text><location><page_31><loc_60><loc_18><loc_62><loc_20></location>r sta</text>
<text><location><page_31><loc_60><loc_17><loc_62><loc_18></location>a</text>
<text><location><page_31><loc_60><loc_16><loc_62><loc_17></location>ine</text>
<text><location><page_31><loc_60><loc_15><loc_62><loc_16></location>nl</text>
<text><location><page_31><loc_60><loc_13><loc_62><loc_15></location>No</text>
<text><location><page_31><loc_60><loc_12><loc_62><loc_13></location>.</text>
<text><location><page_31><loc_65><loc_30><loc_67><loc_31></location>1</text>
<text><location><page_31><loc_65><loc_29><loc_67><loc_30></location>×</text>
<text><location><page_31><loc_65><loc_28><loc_67><loc_29></location>5</text>
<text><location><page_31><loc_65><loc_27><loc_67><loc_28></location>=</text>
<text><location><page_31><loc_65><loc_26><loc_67><loc_27></location>m</text>
<text><location><page_31><loc_66><loc_25><loc_67><loc_25></location>xx</text>
<text><location><page_31><loc_65><loc_24><loc_67><loc_25></location>I</text>
<text><location><page_31><loc_65><loc_21><loc_67><loc_23></location>and</text>
<text><location><page_31><loc_65><loc_19><loc_67><loc_20></location>0.5</text>
<text><location><page_31><loc_65><loc_18><loc_67><loc_18></location>=</text>
<text><location><page_31><loc_66><loc_17><loc_67><loc_17></location>2</text>
<text><location><page_31><loc_65><loc_16><loc_67><loc_17></location>J</text>
<text><location><page_31><loc_65><loc_14><loc_67><loc_15></location>of</text>
<text><location><page_31><loc_65><loc_11><loc_67><loc_14></location>case</text>
<text><location><page_31><loc_65><loc_10><loc_67><loc_11></location>the</text>
<text><location><page_31><loc_65><loc_9><loc_67><loc_10></location>in</text>
<text><location><page_32><loc_60><loc_94><loc_62><loc_95></location>e</text>
<text><location><page_32><loc_60><loc_93><loc_62><loc_94></location>an</text>
<text><location><page_32><loc_60><loc_93><loc_62><loc_93></location>l</text>
<text><location><page_32><loc_60><loc_91><loc_62><loc_93></location>p</text>
<text><location><page_32><loc_61><loc_91><loc_62><loc_91></location>x</text>
<text><location><page_32><loc_59><loc_90><loc_62><loc_91></location>σ</text>
<text><location><page_32><loc_59><loc_89><loc_62><loc_90></location>-</text>
<text><location><page_32><loc_61><loc_88><loc_62><loc_89></location>y</text>
<text><location><page_32><loc_59><loc_87><loc_62><loc_89></location>σ</text>
<text><location><page_32><loc_60><loc_86><loc_62><loc_87></location>n</text>
<text><location><page_32><loc_60><loc_85><loc_62><loc_86></location>o</text>
<text><location><page_32><loc_65><loc_89><loc_66><loc_90></location>11</text>
<text><location><page_32><loc_65><loc_89><loc_67><loc_89></location>0</text>
<text><location><page_32><loc_65><loc_88><loc_67><loc_89></location>1</text>
<text><location><page_32><loc_65><loc_87><loc_67><loc_88></location>×</text>
<text><location><page_32><loc_65><loc_86><loc_67><loc_87></location>5</text>
<text><location><page_32><loc_65><loc_85><loc_67><loc_86></location>=</text>
<figure>
<location><page_32><loc_8><loc_30><loc_96><loc_85></location>
<caption>Fig. 21</caption>
</figure>
<text><location><page_32><loc_61><loc_30><loc_62><loc_30></location>y</text>
<text><location><page_32><loc_59><loc_29><loc_62><loc_30></location>σ</text>
<text><location><page_32><loc_60><loc_27><loc_62><loc_28></location>n</text>
<text><location><page_32><loc_60><loc_26><loc_62><loc_27></location>o</text>
<text><location><page_32><loc_60><loc_25><loc_62><loc_26></location>on</text>
<text><location><page_32><loc_60><loc_23><loc_62><loc_25></location>regi</text>
<text><location><page_32><loc_60><loc_21><loc_62><loc_23></location>lity</text>
<text><location><page_32><loc_60><loc_21><loc_62><loc_21></location>i</text>
<text><location><page_32><loc_60><loc_20><loc_62><loc_21></location>b</text>
<text><location><page_32><loc_60><loc_18><loc_62><loc_20></location>r sta</text>
<text><location><page_32><loc_60><loc_17><loc_62><loc_18></location>a</text>
<text><location><page_32><loc_60><loc_16><loc_62><loc_17></location>ine</text>
<text><location><page_32><loc_60><loc_15><loc_62><loc_16></location>nl</text>
<text><location><page_32><loc_60><loc_13><loc_62><loc_15></location>No</text>
<text><location><page_32><loc_60><loc_12><loc_62><loc_13></location>.</text>
<text><location><page_32><loc_65><loc_30><loc_67><loc_31></location>1</text>
<text><location><page_32><loc_65><loc_29><loc_67><loc_30></location>×</text>
<text><location><page_32><loc_65><loc_28><loc_67><loc_29></location>5</text>
<text><location><page_32><loc_65><loc_27><loc_67><loc_28></location>=</text>
<text><location><page_32><loc_65><loc_26><loc_67><loc_27></location>m</text>
<text><location><page_32><loc_66><loc_25><loc_67><loc_25></location>xx</text>
<text><location><page_32><loc_65><loc_24><loc_67><loc_25></location>I</text>
<text><location><page_32><loc_65><loc_21><loc_67><loc_23></location>and</text>
<text><location><page_32><loc_65><loc_19><loc_67><loc_20></location>0.2</text>
<text><location><page_32><loc_65><loc_18><loc_67><loc_18></location>=</text>
<text><location><page_32><loc_66><loc_17><loc_67><loc_17></location>2</text>
<text><location><page_32><loc_65><loc_16><loc_67><loc_17></location>J</text>
<text><location><page_32><loc_65><loc_14><loc_67><loc_15></location>of</text>
<text><location><page_32><loc_65><loc_11><loc_67><loc_14></location>case</text>
<text><location><page_32><loc_65><loc_10><loc_67><loc_11></location>the</text>
<text><location><page_32><loc_65><loc_9><loc_67><loc_10></location>in</text>
<text><location><page_33><loc_60><loc_94><loc_62><loc_95></location>e</text>
<text><location><page_33><loc_60><loc_93><loc_62><loc_94></location>an</text>
<text><location><page_33><loc_60><loc_93><loc_62><loc_93></location>l</text>
<text><location><page_33><loc_60><loc_91><loc_62><loc_93></location>p</text>
<text><location><page_33><loc_61><loc_91><loc_62><loc_91></location>x</text>
<text><location><page_33><loc_59><loc_90><loc_62><loc_91></location>σ</text>
<text><location><page_33><loc_59><loc_89><loc_62><loc_90></location>-</text>
<text><location><page_33><loc_61><loc_88><loc_62><loc_89></location>y</text>
<text><location><page_33><loc_59><loc_87><loc_62><loc_89></location>σ</text>
<text><location><page_33><loc_60><loc_86><loc_62><loc_87></location>n</text>
<text><location><page_33><loc_60><loc_85><loc_62><loc_86></location>o</text>
<text><location><page_33><loc_65><loc_88><loc_66><loc_89></location>11</text>
<text><location><page_33><loc_65><loc_88><loc_67><loc_88></location>0</text>
<text><location><page_33><loc_65><loc_87><loc_67><loc_88></location>1</text>
<text><location><page_33><loc_65><loc_86><loc_67><loc_87></location>×</text>
<text><location><page_33><loc_65><loc_85><loc_67><loc_86></location>5</text>
<figure>
<location><page_33><loc_8><loc_30><loc_96><loc_85></location>
<caption>Fig. 24</caption>
</figure>
<text><location><page_33><loc_61><loc_30><loc_62><loc_30></location>y</text>
<text><location><page_33><loc_59><loc_29><loc_62><loc_30></location>σ</text>
<text><location><page_33><loc_60><loc_27><loc_62><loc_28></location>n</text>
<text><location><page_33><loc_60><loc_26><loc_62><loc_27></location>o</text>
<text><location><page_33><loc_60><loc_25><loc_62><loc_26></location>on</text>
<text><location><page_33><loc_60><loc_23><loc_62><loc_25></location>regi</text>
<text><location><page_33><loc_60><loc_21><loc_62><loc_23></location>lity</text>
<text><location><page_33><loc_60><loc_21><loc_62><loc_21></location>i</text>
<text><location><page_33><loc_60><loc_20><loc_62><loc_21></location>b</text>
<text><location><page_33><loc_60><loc_18><loc_62><loc_20></location>r sta</text>
<text><location><page_33><loc_60><loc_17><loc_62><loc_18></location>a</text>
<text><location><page_33><loc_60><loc_16><loc_62><loc_17></location>ine</text>
<text><location><page_33><loc_60><loc_15><loc_62><loc_16></location>nl</text>
<text><location><page_33><loc_60><loc_13><loc_62><loc_15></location>No</text>
<text><location><page_33><loc_60><loc_12><loc_62><loc_13></location>.</text>
<text><location><page_33><loc_65><loc_30><loc_67><loc_30></location>0</text>
<text><location><page_33><loc_65><loc_29><loc_67><loc_30></location>1</text>
<text><location><page_33><loc_65><loc_28><loc_67><loc_29></location>×</text>
<text><location><page_33><loc_65><loc_27><loc_67><loc_28></location>5</text>
<text><location><page_33><loc_65><loc_26><loc_67><loc_27></location>=</text>
<text><location><page_33><loc_65><loc_25><loc_67><loc_26></location>m</text>
<text><location><page_33><loc_66><loc_24><loc_67><loc_24></location>xx</text>
<text><location><page_33><loc_65><loc_23><loc_67><loc_24></location>I</text>
<text><location><page_33><loc_65><loc_20><loc_67><loc_22></location>and</text>
<text><location><page_33><loc_65><loc_19><loc_67><loc_19></location>0</text>
<text><location><page_33><loc_65><loc_18><loc_67><loc_18></location>=</text>
<text><location><page_33><loc_66><loc_17><loc_67><loc_17></location>2</text>
<text><location><page_33><loc_65><loc_16><loc_67><loc_17></location>J</text>
<text><location><page_33><loc_65><loc_14><loc_67><loc_15></location>of</text>
<text><location><page_33><loc_65><loc_11><loc_67><loc_14></location>case</text>
<text><location><page_33><loc_65><loc_10><loc_67><loc_11></location>the</text>
<text><location><page_33><loc_65><loc_9><loc_67><loc_10></location>in</text>
<text><location><page_34><loc_60><loc_94><loc_62><loc_95></location>e</text>
<text><location><page_34><loc_60><loc_93><loc_62><loc_94></location>an</text>
<text><location><page_34><loc_60><loc_93><loc_62><loc_93></location>l</text>
<text><location><page_34><loc_60><loc_91><loc_62><loc_93></location>p</text>
<text><location><page_34><loc_61><loc_91><loc_62><loc_91></location>x</text>
<text><location><page_34><loc_59><loc_90><loc_62><loc_91></location>σ</text>
<text><location><page_34><loc_59><loc_89><loc_62><loc_90></location>-</text>
<text><location><page_34><loc_61><loc_88><loc_62><loc_89></location>y</text>
<text><location><page_34><loc_59><loc_87><loc_62><loc_89></location>σ</text>
<text><location><page_34><loc_60><loc_86><loc_62><loc_87></location>n</text>
<text><location><page_34><loc_60><loc_85><loc_62><loc_86></location>o</text>
<text><location><page_34><loc_65><loc_91><loc_66><loc_91></location>11</text>
<text><location><page_34><loc_65><loc_90><loc_67><loc_91></location>0</text>
<text><location><page_34><loc_65><loc_89><loc_67><loc_90></location>1</text>
<text><location><page_34><loc_65><loc_89><loc_67><loc_89></location>×</text>
<text><location><page_34><loc_65><loc_88><loc_67><loc_88></location>5</text>
<text><location><page_34><loc_65><loc_87><loc_67><loc_87></location>=</text>
<text><location><page_34><loc_65><loc_86><loc_67><loc_86></location>m</text>
<figure>
<location><page_34><loc_8><loc_30><loc_96><loc_85></location>
<caption>Fig. 27</caption>
</figure>
<text><location><page_34><loc_61><loc_30><loc_62><loc_30></location>y</text>
<text><location><page_34><loc_59><loc_29><loc_62><loc_30></location>σ</text>
<text><location><page_34><loc_60><loc_27><loc_62><loc_28></location>n</text>
<text><location><page_34><loc_60><loc_26><loc_62><loc_27></location>o</text>
<text><location><page_34><loc_60><loc_25><loc_62><loc_26></location>on</text>
<text><location><page_34><loc_60><loc_23><loc_62><loc_25></location>regi</text>
<text><location><page_34><loc_60><loc_21><loc_62><loc_23></location>lity</text>
<text><location><page_34><loc_60><loc_21><loc_62><loc_21></location>i</text>
<text><location><page_34><loc_60><loc_20><loc_62><loc_21></location>b</text>
<text><location><page_34><loc_60><loc_18><loc_62><loc_20></location>r sta</text>
<text><location><page_34><loc_60><loc_17><loc_62><loc_18></location>a</text>
<text><location><page_34><loc_60><loc_16><loc_62><loc_17></location>ine</text>
<text><location><page_34><loc_60><loc_15><loc_62><loc_16></location>nl</text>
<text><location><page_34><loc_60><loc_13><loc_62><loc_15></location>No</text>
<text><location><page_34><loc_60><loc_12><loc_62><loc_13></location>.</text>
<text><location><page_34><loc_65><loc_30><loc_67><loc_30></location>5</text>
<text><location><page_34><loc_65><loc_29><loc_67><loc_29></location>=</text>
<text><location><page_34><loc_65><loc_27><loc_67><loc_28></location>m</text>
<text><location><page_34><loc_66><loc_26><loc_67><loc_27></location>xx</text>
<text><location><page_34><loc_65><loc_25><loc_67><loc_26></location>I</text>
<text><location><page_34><loc_65><loc_22><loc_67><loc_24></location>and</text>
<text><location><page_34><loc_65><loc_21><loc_67><loc_22></location>8</text>
<text><location><page_34><loc_65><loc_19><loc_67><loc_21></location>0.1</text>
<text><location><page_34><loc_65><loc_19><loc_67><loc_19></location>-</text>
<text><location><page_34><loc_65><loc_18><loc_67><loc_18></location>=</text>
<text><location><page_34><loc_66><loc_17><loc_67><loc_17></location>2</text>
<text><location><page_34><loc_65><loc_16><loc_67><loc_17></location>J</text>
<text><location><page_34><loc_65><loc_14><loc_67><loc_15></location>of</text>
<text><location><page_34><loc_65><loc_11><loc_67><loc_14></location>case</text>
<text><location><page_34><loc_65><loc_10><loc_67><loc_11></location>the</text>
<text><location><page_34><loc_65><loc_9><loc_67><loc_10></location>in</text>
<text><location><page_35><loc_60><loc_94><loc_62><loc_95></location>e</text>
<text><location><page_35><loc_60><loc_93><loc_62><loc_94></location>an</text>
<text><location><page_35><loc_60><loc_93><loc_62><loc_93></location>l</text>
<text><location><page_35><loc_60><loc_91><loc_62><loc_93></location>p</text>
<text><location><page_35><loc_61><loc_91><loc_62><loc_91></location>x</text>
<text><location><page_35><loc_59><loc_90><loc_62><loc_91></location>σ</text>
<text><location><page_35><loc_59><loc_89><loc_62><loc_90></location>-</text>
<text><location><page_35><loc_61><loc_88><loc_62><loc_89></location>y</text>
<text><location><page_35><loc_59><loc_87><loc_62><loc_89></location>σ</text>
<text><location><page_35><loc_60><loc_86><loc_62><loc_87></location>n</text>
<text><location><page_35><loc_60><loc_85><loc_62><loc_86></location>o</text>
<text><location><page_35><loc_65><loc_90><loc_66><loc_91></location>11</text>
<text><location><page_35><loc_65><loc_89><loc_67><loc_90></location>0</text>
<text><location><page_35><loc_65><loc_89><loc_67><loc_89></location>1</text>
<text><location><page_35><loc_65><loc_88><loc_67><loc_89></location>×</text>
<text><location><page_35><loc_65><loc_87><loc_67><loc_88></location>5</text>
<text><location><page_35><loc_65><loc_86><loc_67><loc_87></location>=</text>
<text><location><page_35><loc_65><loc_85><loc_67><loc_86></location>m</text>
<text><location><page_35><loc_65><loc_30><loc_67><loc_31></location>×</text>
<text><location><page_35><loc_65><loc_29><loc_67><loc_30></location>5</text>
<text><location><page_35><loc_65><loc_28><loc_67><loc_29></location>=</text>
<text><location><page_35><loc_65><loc_27><loc_67><loc_28></location>m</text>
<text><location><page_35><loc_66><loc_25><loc_67><loc_26></location>xx</text>
<text><location><page_35><loc_65><loc_25><loc_67><loc_25></location>I</text>
<text><location><page_35><loc_65><loc_22><loc_67><loc_24></location>and</text>
<text><location><page_35><loc_65><loc_19><loc_67><loc_21></location>0.2</text>
<text><location><page_35><loc_65><loc_19><loc_67><loc_19></location>-</text>
<text><location><page_35><loc_65><loc_18><loc_67><loc_18></location>=</text>
<text><location><page_35><loc_66><loc_17><loc_67><loc_17></location>2</text>
<text><location><page_35><loc_65><loc_16><loc_67><loc_17></location>J</text>
<text><location><page_35><loc_65><loc_14><loc_67><loc_15></location>of</text>
<text><location><page_35><loc_65><loc_11><loc_67><loc_14></location>case</text>
<text><location><page_35><loc_65><loc_10><loc_67><loc_11></location>the</text>
<text><location><page_35><loc_65><loc_9><loc_67><loc_10></location>in</text>
<figure>
<location><page_35><loc_8><loc_30><loc_96><loc_85></location>
<caption>Fig. 30</caption>
</figure>
<text><location><page_35><loc_61><loc_30><loc_62><loc_30></location>y</text>
<text><location><page_35><loc_59><loc_29><loc_62><loc_30></location>σ</text>
<text><location><page_35><loc_60><loc_27><loc_62><loc_28></location>n</text>
<text><location><page_35><loc_60><loc_26><loc_62><loc_27></location>o</text>
<text><location><page_35><loc_60><loc_25><loc_62><loc_26></location>on</text>
<text><location><page_35><loc_60><loc_23><loc_62><loc_25></location>regi</text>
<text><location><page_35><loc_60><loc_21><loc_62><loc_23></location>lity</text>
<text><location><page_35><loc_60><loc_21><loc_62><loc_21></location>i</text>
<text><location><page_35><loc_60><loc_20><loc_62><loc_21></location>b</text>
<text><location><page_35><loc_60><loc_18><loc_62><loc_20></location>r sta</text>
<text><location><page_35><loc_60><loc_17><loc_62><loc_18></location>a</text>
<text><location><page_35><loc_60><loc_16><loc_62><loc_17></location>ine</text>
<text><location><page_35><loc_60><loc_15><loc_62><loc_16></location>nl</text>
<text><location><page_35><loc_60><loc_13><loc_62><loc_15></location>No</text>
<text><location><page_35><loc_60><loc_12><loc_62><loc_13></location>.</text>
<section_header_level_1><location><page_36><loc_15><loc_89><loc_55><loc_90></location>4.3 Some discussions on the nonlinear stability</section_header_level_1>
<text><location><page_36><loc_18><loc_85><loc_79><loc_87></location>From Figs. (18)-(32), we can easily achieve several conclusions as follows:</text>
<text><location><page_36><loc_15><loc_52><loc_85><loc_83></location>(a). In all the 15 cases of different values of xx I m and J 2, the nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. This is similar to the classical attitude stability problem of a rigid body in a central gravity field, in which the nonlinear attitude stability region is also the subset of the linear attitude stability region in the first quadrant, i.e., the Lagrange region. This is consistent with the stability theory of the Hamiltonian system that the linear stability is the necessary condition of the stability whereas the nonlinear stability is the sufficient condition of the stability, and the sufficient stability condition should be a subset of the necessary stability condition.</text>
<text><location><page_36><loc_15><loc_37><loc_85><loc_50></location>When the planet P is very elongated with 2 0.2 J = -, for a small rigid body there is no linear stability region and then there is no nonlinear stability region; only for a very large rigid body with 11 5 10 xx I m = × , there is a linear stability region, which is also a nonlinear stability region, located in the first quadrant of the y x σ σ -plane.</text>
<unordered_list>
<list_item><location><page_36><loc_15><loc_11><loc_85><loc_35></location>(b). For a given value of the zonal harmonic J 2 (except 2 0.2 J = -), when the characteristic dimension of the rigid body is small, the characteristic dimension of the rigid body have no influence on the nonlinear stability region, as shown by the nonlinear stability region in the cases of 3 5 10 xx I m = × and 7 5 10 xx I m = × . In these cases, the nonlinear stability region is actually the Lagrange region, which is consistent with conclusions by Wang et al. (1991) and Teixidó Román (2010) on the rigid body dynamics in a central gravity filed.</list_item>
</unordered_list>
<text><location><page_37><loc_15><loc_63><loc_85><loc_90></location>When the characteristic dimension of the rigid body is large enough, such as 11 5 10 xx I m = × , the nonlinear stability region, the Lagrange region, is reduced by a triangle in the right part of the first quadrant of the y x σ σ -plane, as shown by Figs. (5), (8), (11) and (14). As the zonal harmonic J 2 increases from -0.18 to 0.5, the reduction of the Lagrange region expands and the nonlinear stability region shrinks. Notice that even in a central gravity field with 2 0 J = , the nonlinear stability region is not the Lagrange region anymore. This result has not been obtained in previous works, such as Wang et al. (1991) and Teixidó Román (2010).</text>
<text><location><page_37><loc_15><loc_41><loc_85><loc_61></location>(c). For a small characteristic dimension of the rigid body, such as 3 5 10 xx I m = × and 7 5 10 xx I m = × , as the zonal harmonic J 2 increases from -0.18 to 0.5, the nonlinear stability region keeps equal to the Lagrange region. Whereas for a large value of the characteristic dimension of the rigid body 11 5 10 xx I m = × , as the zonal harmonic J 2 increases from -0.18 to 0.5, the nonlinear stability region shrinks by the influence of the zonal harmonic J 2.</text>
<section_header_level_1><location><page_37><loc_15><loc_37><loc_30><loc_39></location>5. Conclusions</section_header_level_1>
<text><location><page_37><loc_15><loc_18><loc_85><loc_35></location>For new high-precision applications in celestial mechanics and astrodynamics, we have generalized the classical J 2 problem to the motion of a rigid body in a J 2 gravity field. Based on our previous results on the relative equilibria, linear and nonlinear stability of the classical kind of relative equilibria of this generalized problem are investigated in the framework of geometric mechanics.</text>
<text><location><page_37><loc_15><loc_11><loc_85><loc_16></location>The conditions of linear stability of the relative equilibria are obtained based on the characteristic equation of the linear system matrix at the relative equilibria,</text>
<text><location><page_38><loc_15><loc_78><loc_85><loc_90></location>which is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the distribution of the eigenvalues of the projected Hessian matrix of the variational Lagrangian.</text>
<text><location><page_38><loc_15><loc_59><loc_85><loc_76></location>With the stability conditions, both the linear and nonlinear stability of the relative equilibria are investigated in a wide range of the parameters of the gravity field and the rigid body by using the numerical method. The stability region is plotted on the plane of the mass distribution parameters of the rigid body in the cases of different values of the zonal harmonic J 2 and the characteristic dimension of the rigid body.</text>
<text><location><page_38><loc_15><loc_41><loc_85><loc_57></location>Similar to the classical attitude stability in a central gravity field, the linear stability region is consisted of two regions located in the first and third quadrant of the y x σ σ -plane respectively, which are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant, the analogue of the Lagrange region.</text>
<text><location><page_38><loc_15><loc_11><loc_85><loc_38></location>Both the zonal harmonic J 2 and the characteristic dimension of the rigid body have significant influences on the linear and nonlinear stability. When the characteristic dimension of the rigid body is small, the analogue of the Lagrange region in the first quadrant of the y x σ σ -plane is actually the Lagrange region. When the characteristic dimension of the rigid body is large enough, the analogue of the Lagrange region is reduced by a triangle and this triangle expands as the zonal harmonic J 2 increases. For a given value of the characteristic dimension of the rigid body, as the zonal harmonic J 2 increases, the analogue of the DeBra-Delp region in</text>
<text><location><page_39><loc_15><loc_85><loc_85><loc_91></location>the third quadrant of the y x σ σ -plane expands in the direction of the boundary of the DeBra-Delp region, and cross the boundary of the DeBra-Delp region at 2 0 J = .</text>
<text><location><page_39><loc_15><loc_74><loc_85><loc_83></location>Our results on the stability of the relative equilibria are very useful for the studies on the motion of many natural satellites in our solar system, whose motion are close to the relative equilibria.</text>
<section_header_level_1><location><page_39><loc_15><loc_70><loc_84><loc_72></location>Appendix: Formulations of Coefficients in Characteristic Equations</section_header_level_1>
<text><location><page_39><loc_15><loc_64><loc_85><loc_69></location>The explicit formulations of the coefficients in the characteristic equations Eqs. (38) and (50) are given as follows:</text>
<formula><location><page_39><loc_19><loc_47><loc_84><loc_63></location>( ) 2 2 2 2 2 5 5 2 2 7 2 2 4 2 2 2 , ( 3 12 9 9 3 12 4 2 9 2 A.1) yy zz e xx zz e zz zz e e xx zz e e zz e e e yy e I I R mI mI R mI I R m m A R I I R m I m R R mI R m μ μ με μ μ με μ μ μ -+ + -+ ---Ω + Ω --= ( ) ( ) 2 5 2 10 2 7 2 4 2 2 2 5 2 2 2 2 2 0 9 12 2 2 3 3 * 3 2 6 8 6 12 6 6 12 6 1 2 , (A.2) yy xx e e e zz e e e e e e e zz e zz e yy e xx zz yy zz xx zz zz I I m R mR m I R m R R m R m R m I R mI R mI R mI mI I I I I I A μ μ μ με μ μ με μ μ μ με μ μ μ --+ -+ Ω --Ω ---Ω --+ --+ -=</formula>
<formula><location><page_39><loc_17><loc_38><loc_84><loc_47></location>( ) 2 2 5 2 2 4 2 5 2 2 5 2 7 2 2 5 2 5 2 2 2 2 2 4 5 3 2 12 2 3 4 2 2 9 9 2 12 1 2 , 9 (A.3) e yy xx yy xx e xx zz e yy xx e xx e e xx e yy xx e e xx e e yy e zz yy xx yy xx zz e e zz e xx e xx zz R I mI I I R mI I I I R m I R R m I R I mI R m B I R I m I I mI I I I R m I R mI R mI I μ μ μ μ με με μ μ μ ---+ Ω + ---Ω + Ω + Ω Ω + = ----</formula>
<text><location><page_39><loc_17><loc_15><loc_84><loc_37></location>( 5 2 3 2 2 7 2 5 2 8 2 5 2 2 10 4 2 2 2 5 2 2 5 2 2 2 7 2 2 5 2 2 2 7 8 27 2 5 3 1 2 6 19 27 11 2 3 2 2 yy e e zz yy e xx zz e e xx e e xx zz e e e e zz e e zz e xx yy e xx e xx zz e e zz e e zz yy e e yy e e I mR I I R I I m R I mR I I R m R I m R I R m I I mR I mI I mR I m R I I mR I m R B μ μ μ μ με με μ με μ μ μ -Ω + Ω + Ω -Ω + Ω -Ω + + Ω + + Ω + Ω -Ω -Ω = 2 2 10 4 2 10 4 3 2 3 2 2 2 2 2 8 4 2 3 2 2 3 2 3 2 3 2 2 8 4 2 5 2 2 5 2 3 2 2 9 36 9 2 6 9 9 21 2 3 3 24 e xx e yy e e e e zz xx xx e e zz yy e e zz yy e e zz e xx e zz e xx zz e e xx e zz yy e e e xx e yy e m R I I m R R I mI m I mR I I R I I mR I mR I I R I I mR I I I m R m R I I R I μ μ με μ ε μ με με μ με με -Ω + Ω + Ω -+ + Ω -Ω -Ω -Ω -Ω Ω -Ω -Ω -) 2 2 2 3 2 5 2 2 2 3 2 3 2 2 8 4 3 2 2 3 2 2 8 4 3 12 6 9 2 18 9 1 , (A.4 2 2 ) xx e yy e e zz e xx e yy e xx e e e zz yy e xx e yy e xx e yy xx e xx zz e yy e e zz I R I mR I I R I mR I I mR I I mR I I mI R I I I mR I μ μ μ μ με με με μ Ω -Ω -Ω + Ω + Ω + Ω + Ω + + Ω Ω</text>
<formula><location><page_40><loc_17><loc_81><loc_84><loc_91></location>( )( 2 3 2 2 5 2 3 2 3 2 8 3 2 2 5 2 2 2 2 2 2 2 7 2 5 2 3 2 2 3 2 2 0 9 11 3 21 9 27 14 9 36 6 2 3 2 12 3 9 e yy zz e zz e zz e e yy e zz e zz e xx e e zz e e zz e xx e yy xx e e e yy e e e xx e yy e xx e I I R I I mR I R I I R I R I mR I m m B R I I m mI R m m R I mR R I I R I m μ μ μ μ με με μ με με με μ μ μ μ μ Ω -Ω Ω -Ω + Ω -Ω -+ Ω -+ --Ω -Ω -Ω + Ω -= -) 2 2 3 2 2 5 2 2 10 4 9 3 , (A. ) 2 5 e xx e e e e e mR I m R m R ε με με + Ω + Ω + Ω</formula>
<formula><location><page_40><loc_31><loc_76><loc_85><loc_79></location>( ) 2 2 2 2 2 1 yy e e yy e zz y yy y I m R I m I C m I I m + Ω + =-Ω + , (A.6)</formula>
<formula><location><page_40><loc_28><loc_70><loc_85><loc_74></location>( ) 2 2 2 1 2 2 2 1 1 e zz yy e e e z yy z e yy I I m R C m mI I m I Ω + Ω + + Ω -= Ω , (A.7)</formula>
<formula><location><page_40><loc_42><loc_65><loc_85><loc_68></location>( ) 2 0 e yy yy zz I I C mI Ω -= , (A.8)</formula>
<formula><location><page_40><loc_20><loc_57><loc_84><loc_63></location>( ) 2 5 2 7 5 2 5 2 2 2 2 2 2 2 6 9 1 1 2 , (A ) 3 . 2 9 9 xx e e e xx e zz e e xx e xx xx xx zz x e xx x yy xx mI R R I I R mR I R m I m I I I D R I I I I μ εμ εμ μ μ μ -Ω + Ω + + + + -+ + =</formula>
<formula><location><page_40><loc_19><loc_40><loc_84><loc_55></location>( 2 5 2 8 2 3 2 5 3 2 10 4 3 2 2 2 2 5 2 10 2 2 1 2 8 2 5 5 5 2 1 2 27 11 2 3 2 9 2 9 9 3 2 36 3 6 12 xx zz e xx e zz e xx e yy e e zz xx e e e xx e e xx e zz yy xx e xx e e e xx yy e xx e e e xx e e xx m I I mR I I R I I R I I mR mR m R I R I I I mI m R I mR m I I m I R mR m D R R I I εμ μ μ μ εμ μ μ ε εμ εμ μ εμ μ + Ω -Ω + Ω + + -Ω + Ω + -Ω + Ω -+ Ω + -Ω = ) 2 2 2 2 8 2 3 3 2 7 2 3 2 2 2 2 2 3 3 2 9 2 3 12 2 12 6 9 9 , (A.10) xx e e zz yy e e xx e xx e e xx e zz e xx e zz e xx e zz m I R I I R R I m R I R I I R m I R I mR I I εμ μ μ μ μ εμ μ εμ + + Ω + -+ Ω Ω + + + Ω</formula>
<text><location><page_40><loc_19><loc_29><loc_84><loc_39></location>( 2 10 4 2 2 2 2 2 5 2 2 2 3 2 5 2 3 2 2 3 2 2 7 2 2 3 2 2 5 2 2 5 2 3 0 8 2 36 9 3 6 21 11 9 9 2 27 3 9 14 3 3 1 2 e e xx yy e e e e xx e zz e e zz e e zz e xx e e e zz y e y e e xx yy e xx e e e y xx y e m R m I m I R m R m R I I mR I R I mR I m R m I I R I I m mR I m R I R D R I εμ εμ μ εμ μ μ μ εμ μ εμ μ μ ε μ εμ μ Ω + --Ω -+ Ω -Ω -Ω + Ω -Ω -+ Ω -+ Ω + = Ω Ω ) 2 3 2 2 3 2 12 9 , (A.11) e zz e xx e e e zz I R I mR I μ εμ -Ω Ω</text>
<formula><location><page_40><loc_17><loc_20><loc_84><loc_28></location>( ) ( ) 2 2 2 2 5 2 2 7 2 7 2 2 7 2 1 5 2 2 2 2 3 2 4 2 2 2 1 1 , (A.12 6 2 12 6 3 6 12 2 6 6 ) 6 e zz e zz e zz e zz xx zz e e e zz yy e zz zz xx e e e z e zz z yy zz e z e e z z e z R m I R m E mR I I R I mR I I mI mR m R I I R I m mI I R m m R I I I m mR I m R m R I εμ μ μ μ μ μ μ μ μ εμ + --+ --Ω + --Ω + + Ω + = + + +</formula>
<formula><location><page_40><loc_18><loc_11><loc_84><loc_19></location>( ) ( ) 2 4 2 7 2 2 2 2 2 2 2 5 0 5 2 2 2 2 2 6 2 3 8 12 12 6 1 1 6 6 6 , (A.13) yy zz e e e e zz e xx zz xx yy e zz e e e e zz zz e e e zz I I m R m R R I m mR I I I I mR m E mR I R m R I I R m mR I μ μ μ μ μ μ εμ μ εμ --+ Ω -+ + --+ -Ω + --= Ω</formula>
<formula><location><page_41><loc_23><loc_87><loc_85><loc_90></location>( ) 5 2 2 2 1 5 3 12 9 2 3 2 1 2 zz xx yy e e e I m m I I m F m R m m R R μ μ μ εμ μ -+ ---= -, (A.14)</formula>
<formula><location><page_41><loc_24><loc_81><loc_85><loc_85></location>( ) 0 5 2 5 2 2 12 3 9 3 1 2 2 e e xx yy zz e e R m I m I I F mR mR μ μ ε μ μ μ - Ω -+ + + + = . (A.15)</formula>
<section_header_level_1><location><page_41><loc_15><loc_78><loc_35><loc_79></location>Acknowledgements</section_header_level_1>
<text><location><page_41><loc_15><loc_70><loc_84><loc_76></location>This work is supported by the Innovation Foundation of BUAA for PhD Graduates.</text>
<section_header_level_1><location><page_41><loc_15><loc_66><loc_27><loc_68></location>References</section_header_level_1>
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</document>
[
{
"title": "body in the J 2 problem",
"content": "Yue Wang * , Shijie Xu Room B1024, New Main Building, Department of Guidance, Navigation and Control, School of Astronautics, Beijing University of Aeronautics and Astronautics, 100191, Beijing, China",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "The motion of a point mass in the J 2 problem is generalized to that of a rigid body in a J 2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variational Lagrangian. With the stability conditions obtained, both the linear and nonlinear stability of the relative equilibria are investigated in details in a wide range of the parameters of the gravity field and the rigid body. We find that both the zonal harmonic J 2 and the characteristic dimension of the rigid body have significant effects on the linear and nonlinear stability. Similar to the classical attitude stability in a central gravity field, the linear stability region is also consisted of two regions that are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. Our results are very useful for the studies on the motion of natural satellites in our solar system. Keywords: J 2 problem; Rigid body; Non-canonical Hamiltonian structure; Relative equilibria; Linear stability; Nonlinear stability",
"pages": [
1,
2
]
},
{
"title": "1. Introduction",
"content": "The J 2 problem, also called main problem of artificial satellite theory, in which the motion of a point mass in a gravity field truncated on the zonal harmonic J 2 is studied, is an important problem in the celestial mechanics and astrodynamics (Broucke 1994). The J 2 problem has its wide applications in the orbital dynamics and orbital design of spacecraft. This classical problem has been studied by many authors, such as Broucke (1994) and the literatures cited therein. However, neither natural nor artificial celestial bodies are point masses or have spherical mass distributions. One of the generalizations of the point mass model is the rigid body model. Because of the non-spherical mass distribution, the orbital and rotational motions of the rigid body are coupled through the gravity field. The orbit-rotation coupling may cause qualitative effects on the motion, which are more significant when the ratio of the dimension of rigid body to the orbit radius is larger. The orbit-rotation coupling and its qualitative effects have been discussed in several works on the motion of a rigid body or gyrostat in a central gravity field (Wang et al. 1991, 1992, 1995; Teixidó Román 2010). In Wang and Xu (in press), the orbit-rotation coupling of a rigid satellite around a spheroid planet was assessed. It was found that the significant orbit-rotation coupling should be considered for a spacecraft orbiting a small asteroid or an irregular natural satellite around a planet. The effects of the orbit-rotation coupling have also been considered in many works on the Full Two Body Problem (F2BP), the problem of the rotational and orbital motions of two rigid bodies interacting through their mutual gravitational potential. A spherically-simplified model of F2BP, in which one body is assumed to be a homogeneous sphere, has been studied broadly, such as Kinoshita (1970), Barkin (1979), Aboelnaga and Barkin (1979), Beletskii and Ponomareva (1990), Scheeres (2004), Breiter et al. (2005), Balsas et al. (2008), Bellerose and Scheeres (2008) and Vereshchagin et al. (2010). There are also several works on the more general models of F2BP, in which both bodies are non-spherical, such as Maciejewski (1995), Scheeres (2002, 2009), Koon et al. (2004), Boué and Laskar (2009) and McMahon and Scheeres (in press). When the dimension of the rigid body is very small in comparison with the orbital radius, the orbit-rotation coupling is not significant. In the case of an artificial Earth satellite, the point mass model of the J 2 problem works very well. However, when a spacecraft orbiting around an asteroid or an irregular natural satellite around a planet, such as Phobos, is considered, the mass distribution of the considered body is far from a sphere and the dimension of the body is not small anymore in comparison with the orbital radius. In these cases, the orbit-rotation coupling causes significant effects and should be taken into account in the precise theories of the motion, as shown by Koon et al. (2004), Scheeres (2006), Wang and Xu (in press). For the high-precision applications in the coupled orbital and rotational motions of a spacecraft orbiting a spheroid asteroid, or an irregular natural satellite around a dwarf planet or planet, we have generalized the J 2 problem to the motion of a rigid body in a J 2 gravity field in our previous paper (Wang and Xu 2013a). In that paper, the relative equilibria of the rigid body were determined from a global point of view in the framework of geometric mechanics. A classical type of relative equilibria, as well as a non-classical type of relative equilibria, was uncovered under the second-order gravitational potential. Through the non-canonical Hamiltonian structure of the problem, geometric mechanics provides a systemic and effective method for determining the linear and nonlinear stability of the relative equilibria, as shown by Beck and Hall (1998). The linear and nonlinear stability of the classical type of relative equilibria already obtained in Wang and Xu (2013a) will be studied further in this paper in the framework of geometric mechanics. Through the stability properties of the relative equilibria, it is sufficient to understand the general dynamical properties of the system near the relative equilibria to a big extent. Notice that the problem in McMahon and Scheeres (in press) is very similar to our problem. In their paper, the existence of stable equilibrium points, and the linearized and nonlinear dynamics around equilibrium points in the planar F2BP with an oblate primary body were investigated. The differences with our problem are that in their problem the motion is restricted on the equatorial plane of the primary body and the mass center of the primary body is not fixed in the inertial space. The equilibrium configuration exists generally among the natural celestial bodies in our solar system. It is well known that many natural satellites of big planets evolved tidally to the state of synchronous motion (Wisdom 1987). Notice that the gravity field of the big planets can be well approximated by a J 2 gravity field. The results on the stability of the relative equilibria in our problem are very useful for the studies on the motion of many natural satellites. We also make comparisons with previous results on the stability of the relative equilibria of a rigid body in a central gravity field, such as Wang et al. (1991) and Teixidó Román (2010). The influence of the zonal harmonic J 2 on the stability of the relative equilibria is discussed in details.",
"pages": [
2,
3,
4,
5
]
},
{
"title": "2. Non-canonical Hamiltonian Structure and Relative Equilibria",
"content": "The problem we studied here is same as in Wang and Xu (2013a). As described in Fig. 1, we consider a small rigid body B in the gravity field of a massive axis-symmetrical body P . Assume that P is rotating uniformly around its axis of symmetry, and the mass center of P is stationary in the inertial space, i.e. P is in free motion without being affected by B . The gravity field of P is approximated through truncation on the second zonal harmonic J 2. The inertial reference frame is defined as S ={ e 1, e 2, e 3} with its origin O attached to the mass center of P . e 3 is along the axis of symmetry of P . The body-fixed reference frame is defined as Sb ={ i , j , k } with its origin C attached to the mass center of B . The frame Sb coincides with the principal axes reference frame of B . In Wang and Xu (2013a), a Poisson reduction was applied on the original system by means of the symmetry of the problem. After the reduction process, the non-canonical Hamiltonian structure, i.e., Poisson tensor, Casimir functions and equations of motion, and a classical kind of relative equilibria of the problem were obtained. Here we only give the basic description of the problem and list the main results obtained by us there, see that paper for the details. The attitude matrix of the rigid body B with respect to the inertial frame S is denoted by A , where the vectors i , j and k are expressed in the frame S , and SO (3) is the 3-dimensional special orthogonal group. A is the coordinate transformation matrix from the frame Sb to the frame S . If [ , , ] x y z T W W W = W are components of a vector in frame Sb , its components in frame S can be calculated by We define r as the radius vector of point C with respect to O in frame S . The radius vector of a mass element dm ( D ) of the body B with respect to C in frame Sb is denoted by D , then the radius vector of dm ( D ) with respect to O in frame S , denoted by x , is Therefore, the configuration space of the problem is the Lie group known as the Euclidean group of three space with elements ( , ) A r that is the semidirect product of SO (3) and 3 \\ . The elements Ξ of the phase space, the cotangent bundle T Q ∗ , can be written in the following coordinates where Π is the angular momentum expressed in the body-fixed frame Sb and p is the linear momentum of the rigid body expressed in the inertial frame S (Wang and Xu 2012). The hat map 3 ^: (3) so → \\ is the usual Lie algebra isomorphism, where (3) so is the Lie Algebras of Lie group SO (3). The phase space T Q ∗ carries a natural symplectic structure (3) SE ω ω= , and the canonical bracket associated to ω can be written in coordinates Ξ as for any , ( ) f g C T Q ∞ ∗ ∈ , , ·· is the pairing between (3) T SO ∗ and (3) TSO , and D f B is a matrix whose elements are the partial derivates of the function f with respect to the elements of matrix B respectively (Wang and Xu 2012). The Hamiltonian of the problem : H T Q ∗ → \\ is given as follows where m is the mass of the rigid body, the matrix { } , , xx yy zz diag I I I = I is the tensor of inertia of the rigid body and : T Q T Q Q τ ∗ ∗ → is the canonical projection. According to Wang and Xu (2013a), the gravitational potential : V Q → \\ up to the second order is given in terms of moments of inertia as follows: where G is the Gravitational Constant, and M 1 is the mass of the body P . The parameter ε is defined as 2 2 E J a ε= , where aE is the mean equatorial radius of P . γ is the unit vector e 3 expressed in the frame Sb . T = R A r is the radius vector of the mass center of B expressed in frame Sb . Note that R = R and R = R R . The J 2 gravity field is axis-symmetrical with axis of symmetry e 3. According to Wang and Xu (2012), the Hamiltonian of the system is 1 S -invariant, namely the system has symmetry, where 1 S is the one-sphere. Using this symmetry, we have carried out a reduction, induced a Hamiltonian on the quotient 1 / T Q S ∗ , and expressed the dynamics in terms of appropriate reduced variables in Wang and Xu (2012), where 1 / T Q S ∗ is the quotient of the phase space T Q ∗ with respect to the action of 1 S . The reduced variables in 1 / T Q S ∗ can be chosen as where T P = A p is the linear momentum of the body B expressed in the body-fixed frame Sb (Wang and Xu 2012). The projection from T Q ∗ to 1 / T Q S ∗ is given by According to Marsden and Ratiu (1999), there is a unique non-canonical Hamiltonian structure on 1 / T Q S ∗ such that Ψ is a Poisson map. That is to say, there is a unique Poisson bracket 12 {, } ( ) · · z \\ such that for any 12 , ( ) f g C ∞ ∈ \\ , where {, } ( ) T Q ∗ · · Ξ is the natural canonical bracket of the system given by Eq. (6). According to Wang and Xu (2012), the Poisson bracket 12 {, } ( ) · · z \\ can be written in the following form with the Poisson tensor ( ) B z given by where E is the identity matrix. This Poisson tensor has two independent Casimir functions. One is a geometric integral 1 1 1 ( ) 2 2 T C = ≡ z γγ , and the other one is ( ) 2 ˆ ( ) T C = + z γ Π RP , the third component of the angular momentum with respect to origin O expressed in the inertial frame S . 2 ( ) C z is the conservative quantity produced by the symmetry of the system, as stated by Noether's theorem. The ten-dimensional invariant manifold or symplectic leaf of the system is defined in 12 \\ by Casimir functions which is actually the reduced phase space ( ) 1 / T Q S ∗ of the symplectic reduction. The restriction of the Poisson bracket 12 {, } ( ) · · z \\ to Σ defines the symplectic structure on this symplectic leaf. The equations of motion of the system can be written in the Hamiltonian form With the Hamiltonian ( ) H z given by Eq. (7), the explicit equations of motion are given by Based on the equations of motion Eq. (16), we have obtained a classical kind of relative equilibria of the rigid body under the second-order gravitational potential in Wang and Xu (2013a). At this type of relative equilibria, the orbit of the mass center of the rigid body is a circle in the equatorial plane of body P with its center coinciding with origin O . The rigid body rotates uniformly around one of its principal axes that is parallel to 3 e in the inertial frame S in angular velocity that is equal to the orbital angular velocity e Ω . The radius vector e R and the linear momentum e P are parallel to another two principal axes of the rigid body. When the radius vector e R is parallel to the principal axes of the rigid body i , j , k , the norm of the orbital angular velocity e Ω is given by the following three equations respectively: The norm of the linear momentum e P is given by: With a given value of e R , there are 24 relative equilibria belonging to this classical type in total. Without of loss of generality, we will choose one of the relative equilibria as shown by Fig. 2 for stability conditions Other relative equilibria can be converted into this equilibrium by changing the arrangement of the axes of the reference frame Sb .",
"pages": [
6,
7,
8,
9,
10,
11
]
},
{
"title": "3. Linear Stability of the Relative Equilibria",
"content": "In this section, we will investigate the linear stability of the relative equilibria through the linear system matrix at the relative equilibria using the methods provided by the geometric mechanics (Beck and Hall 1998, Hall 2001).",
"pages": [
11
]
},
{
"title": "3.1 Conditions of linear stability",
"content": "The linear stability of the relative equilibrium e z depends on the eigenvalues of the linear system matrix of the system at the relative equilibrium. According to Beck and Hall (1998), the linear system matrix ( ) e D z of the non-canonical Hamiltonian system at the relative equilibrium e z can be calculated through the multiplication of the Poisson tensor and the Hessian of the variational Lagrangian without performing linearization as follows: Here the variational Lagrangian ( ) F z is defined as According to Beck and Hall (1998), the relative equilibrium of the rigid body in the problem corresponds to the stationary point of the Hamiltonian constrained by the Casimir functions. The stationary points can be determined by the first variation condition of the variational Lagrangian ( ) e F ∇ = 0 z . By using the formulations of the Hamiltonian and Casimir functions, the equilibrium conditions are obtained as: As we expected, the relative equilibrium in Eq. (21) obtained based on the equations of motion is a solution of the equilibrium conditions Eq. (24), with the parameters 1 μ and 2 μ given by By using the formulation of the second-order gravitational potential Eq. (8), the Hessian of the variational Lagrangian ( ) 2 F ∇ z is calculated as: The second-order partial derivates of the gravitational potential in Eq. (26) are obtained as follows: As described by Eqs. (17), (21) and (25), at the relative equilibrium e z , we have [ ] 0, 0, T e e zz I = Ω Π , [ ] 0, 0, 1 T e = γ , [ ] ,0,0 T e e R = R , [ ] 1, 0, 0 T e = R , [ ] 0, , 0 T e e e mR = Ω P , [ ] 0, 0, T e e = Ω Ω , ( ) 2 2 1 e zz e I mR μ =-Ω + and 2 e μ =Ω . Then the Hessian of the variational Lagrangian ( ) 2 e F ∇ z at the relative equilibrium e z can be obtained as: The second-order partial derivates of the gravitational potential in Eq. (29) at the relative equilibrium e z are obtained through Eqs. (27)-(28) as follows: where e α is defined as [ ] 1 0 0 T e = α . The Poisson tensor ( ) e B z at the relative equilibrium e z can be obtained as: where e β is defined as [ ] 0,1, 0 T e = β . In Eqs. (29)-(32), we have Then the linear system matrix ( ) e D z of the non-canonical Hamiltonian system can be calculated through Eqs. (22), (29) and (32). Through some rearrangement and simplification, the linear system matrix ( ) e D z can be written as follows: As stated above, the linear stability of the relative equilibrium e z depends on the eigenvalues of the linear system matrix of the system ( ) e D z . The characteristic polynomial of the linear system matrix ( ) e D z can be calculated by The eigenvalues of the linear system matrix ( ) e D z are roots of the characteristic equation of the linearized system, which is given by Through Eqs. (35) and (37), with the help of Matlab and Maple , the characteristic equation can be obtained with the following form: where the coefficients 2 A , 0 A , 4 B , 2 B and 0 B are functions of the parameters of the system: 1 GM , e Ω , e R , ε , m , xx I , yy I and zz I . The explicit formulations of the coefficients are given in the Appendix. According to Beck and Hall (1998), the non-canonical Hamiltonian systems have special properties with regard to both the form of the characteristic polynomial and the eigenvalues of the linear system matrix ( ) e D z : Property 1. There are only even terms in the characteristic polynomial of the linear system matrix, and the eigenvalues are symmetrical with respect to both the real and imaginary axes. Property 2. A zero eigenvalue exists for each linearly independent Casimir function. Property 3. An additional pair of zero eigenvalues exists for each first integral, which is associated with a symmetry of the Hamiltonian by Noether's theorem. Notice that in our problem, there are two linearly independent Casimir functions, and the two zero eigenvalues correspond to the two Casimir functions 1 ( ) C z and 2 ( ) C z . The remaining ten eigenvalues correspond to the motion constrained by the Casimir functions on the ten-dimensional invariant manifold Σ . We have carried out a Poisson reduction by means of the symmetry of the Hamiltonian, and expressed the dynamics on the reduced phase space. The additional pair of zero eigenvalues according to Property 3 has been eliminated by the reduction process. Therefore, our results in Eq. (38) are consistent with these three properties stated above. According to the characteristic equation in Eq. (38), the ten-dimensional linear system on the invariant manifold Σ decouples into two entirely independent fourand six-dimensional subsystems under the second-order gravitational potential. It is worth our special attention that this is not the decoupling between the freedoms of the rotational motion and the orbital motion of the rigid body, since the orbit-rotation coupling is considered in our study. Actually, the four-dimensional subsystem and 2 s are the three freedoms of the orbital and rotational motions within the equatorial plane of the body P , and the other three freedoms, i.e. orbital and rotational motions outside the equatorial plane of the body P , constitute the six-dimensional subsystem. The linear stability of the relative equilibria implies that there are no roots of the characteristic equation with positive real parts. According to Property 1 , the linear stability requires all the roots to be purely imaginary, that is 2 s is real and negative. Therefore, in this case of a conservative system, we can only get the necessary conditions of the stability through the linear stability of the relative equilibria. According to the theory of the roots of the second and third degree polynomial equation, that the 2 s in Eq. (38) is real and negative is equivalent to B B B 4 2 0 0, 0, 0. > > > We have given the conditions of linear stability of the relative equilibria in Eqs. (39) and (40). Given a set of the parameters of the system, we can determine whether the relative equilibria are linear stability by using the stability criterion given above.",
"pages": [
11,
12,
13,
14,
15,
16,
17
]
},
{
"title": "3.2 Case studies",
"content": "However, the expressions of coefficients 2 A , 0 A , 4 B , 2 B and 0 B in terms of the parameters of the system are tedious, since there are large amount of parameters in the system and the considered problem is a high-dimensional system. It is difficult to get general conditions of linear stability through Eqs. (39) and (40) in terms of the parameters of the system, i.e. 1 GM , e Ω , e R , ε , m , xx I , yy I and zz I . We will consider an example planet P , which has the same mass and equatorial radius as the Earth, but has a different zonal harmonic J 2. That is 14 3 2 1 3.986005 10 m / s GM = × and 6 6.37814 10 m E a = × . Five different values of the zonal harmonic J 2 are considered The orbital angular velocity e Ω is assumed to be equal to 3 1 1.163553 10 s --× with the orbital period equal to 1.5 hours. With the parameters of the system given above, the stability criterion in Eqs. (39) and (40) can be determined by three mass distribution parameters of the rigid body: xx I m , x σ and y σ , where x σ and y σ are defined as The ratio xx I m describes the characteristic dimension of the rigid body; the ratios x σ and y σ describe the shape of the rigid body to the second order. Three different values of the parameter xx I m are considered as follows: which correspond to a rigid body with the characteristic dimension of order of 100m, 10km and 1000km respectively. In the case of each value of xx I m , the parameters x σ and y σ are considered in the following range which have covered all the possible mass distributions of the rigid body. Given the mass distribution parameters of the rigid body, the orbital radius e R at the relative equilibrium can be calculated by Eq. (17). Then the stability criterion in Eqs. (39) and (40) can be calculated with all the parameters of the system known. The linear stability criterion in Eqs. (39) and (40) is calculated for a rigid body within the range of the parameters Eqs. (43) and (44) in the cases of different values of the zonal harmonic J 2. The points, which correspond to the mass distribution parameters guaranteeing linear stability, are plotted on the y x σ σ -plane in the 15 cases of different values of xx I m and J 2 in Figs. (3)-(17) respectively. In our problem, the gravitational potential in Eq. (8) is truncated on the second order. According to the conclusions in Wang and Xu (2013b), only the central component of the gravity field of the planet P is considered in the gravity gradient torque, with the zonal harmonic J 2 neglected. That is to say, the attitude motion of the rigid body in our problem, in the point view of the traditional attitude dynamics with the orbit-rotation coupling neglected, is actually the attitude dynamics on a circular orbit in a central gravity field. To make comparisons with the traditional attitude dynamics, we also plot the classical linear attitude stability region of a rigid body on a circular orbit in a central gravity field in Figs. (3)-(17), which is given by: The classical linear attitude stability region given by Eq. (45) is consisted of the Lagrange region I and the DeBra-Delp region II (Hughes 1986). The Lagrange region is the isosceles right triangle region in the first quadrant of the y x σ σ -plane below the straight line 0 y x σ σ -= , and DeBra-Delp region is a small region in the third quadrant below the straight line 0 y x σ σ -= . Notice that at the relative equilibrium in our paper, the orientations of the principal axes of the rigid body are different from those at the equilibrium attitude in Hughes (1986), and then the definitions of the parameters y σ and x σ in our paper are different form those in Hughes (1986) to make sure that the linear attitude stability region is the same as in Hughes (1986). n i e n pla x σ - y σ 11 0 1 × 5 x σ - y σ on on i y reg it il ab st near Li 3 0 1 × 5 = m xx I and 0.5 = 2 J case of n i e n pla x σ - y σ 11 0 1 × 5 x σ - y σ on on i y reg it il ab st near Li 3 0 1 × 5 = m xx I and 0.2 = 2 J case of in e n a pl x σ - y σ 11 0 1 × x σ - y σ on on i y reg it il ab st near Li 3 0 1 × 5 = m xx I and 0 = 2 J case of n i e n pla x σ - y σ 11 0 1 × 5 = m 1 σ - y σ on n gio re ity il b ar sta ne Li . × 5 = m xx I and 8 1 0. - = 2 J of the case n i e n pla x σ - y σ 11 0 1 × 5 = σ - y σ on n gio re ity il b ar sta ne Li . 0 1 × 5 = m xx I and 2 0. - = 2 J of the case",
"pages": [
17,
18,
19,
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21,
22,
23,
24
]
},
{
"title": "3.3 Some discussions on the linear stability",
"content": "From Figs. (3)-(17), we can easily achieve several conclusions as follows: (a). Similar to the classical linear attitude stability region, which is consisted of the Lagrange region and the DeBra-Delp region, the linear stability region of the relative equilibrium of the rigid body in our problem is also consisted of two regions located in the first and third quadrant of the y x σ σ -plane respectively, which are the analogues of the Lagrange region and the DeBra-Delp region respectively. This is consistent with the conclusion by Teixidó Román (2010) that for a rigid body in a central gravity field there is a linear stability region in the third quadrant of the y x σ σ -plane, which is the analogue of the DeBra-Delp region. However, when the planet P is very elongated with 2 0.2 J = -, for a small rigid body there is no linear stability region; only in the case of a very large rigid body with 11 5 10 xx I m = × , there is a linear stability region that is the analogue of the Lagrange region located in the first quadrant of the y x σ σ -plane. When the characteristic dimension of the rigid body is large enough, such as 11 5 10 xx I m = × , the linear stability region in the first quadrant of the y x σ σ -plane, the analogue of the Lagrange region, is reduced by a triangle in the right part of the first quadrant of the y x σ σ -plane, as shown by Figs. (5), (8), (11) and (14). In the case of 2 0.18 J =-, also the linear stability region in the third quadrant of the y x σ σ -plane, the analogue of the DeBra-Delp region, is reduced by the large characteristic dimension of the rigid body, as shown by Fig. (14). For a small value of the characteristic dimension of the rigid body, such as 3 5 10 xx I m = × and 7 5 10 xx I m = × , as the zonal harmonic J 2 increases from -0.18 to 0.5, the linear stability region in the first quadrant of the y x σ σ -plane, the analogue of the Lagrange region, keeps equal to the Lagrange region. Whereas for a large value of the characteristic dimension of the rigid body 11 5 10 xx I m = × , as the zonal harmonic J 2 increases from -0.18 to 0.5, the linear stability region in the first quadrant of the y x σ σ -plane, the analogue of the Lagrange region, shrinks by the influence of the zonal harmonic J 2.",
"pages": [
25,
26
]
},
{
"title": "4. Nonlinear Stability of the Relative Equilibria",
"content": "In this section, we will investigate the nonlinear stability of the classical type of relative equilibria using the energy-Casimir method provided by the geometric mechanics adopted by Beck and Hall (1998), and Hall (2001).",
"pages": [
26
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},
{
"title": "4.1 Conditions of nonlinear stability",
"content": "The energy-Casimir method, the generalization of Lagrange-Dirichlet criterion, is a powerful tool provided by the geometric mechanics for determining the nonlinear stability of the relative equilibria in a non-canonical Hamiltonian system (Marsden and Ratiu, 1999). According to the Lagrange-Dirichlet criterion in the canonical Hamiltonian system, the nonlinear stability of the equilibrium point is determined by the distributions of the eigenvalues of the Hessian matrix of the Hamiltonian. If all the eigenvalues of the Hessian matrix are positive or negative, that is the Hessian matrix of the Hamiltonian is positive- or negative-definite, then the equilibrium point is nonlinear stable. This follows from the conservation of energy and the fact that the level sets of the Hamiltonian near the equilibrium point are approximately ellipsoids. However, the Hamiltonian system in our problem is non-canonical, and the phase flow of the system is constrained on the ten-dimensional invariant manifold or symplectic leaf Σ by Casimir functions. Therefore, rather than considering general perturbations in the whole phase space as in the Lagrange-Dirichlet criterion in the canonical Hamiltonian system, we need to restrict the consideration to perturbations on e T Σ z , the tangent space to the invariant manifold Σ at the relative equilibrium e z . e T Σ z is also the range space of Poisson tensor ( ) B z at the relative equilibrium e z , denoted by ( ) R ( ) e B z . This is the basic principle of the energy-Casimir method that the Hessian matrix needs to be considered restrictedly on the invariant manifold Σ of the system. This restriction is constituted through the projected Hessian matrix of the variational Lagrangian ( ) F z in Beck and Hall (1998). According to the energy-Casimir method adopted by Beck and Hall (1998), the conditions of nonlinear stability of the relative equilibrium e z can be obtained through the distributions of the eigenvalues of the projected Hessian matrix of the variational Lagrangian ( ) F z . The projected Hessian matrix of the variational Lagrangian ( ) F z has the same number of zero eigenvalues as the linearly independent Casimir functions, which are associated with the nullspace [ ] N ( ) e B z , i.e. the complement space of e T Σ z . The remaining eigenvalues of the projected Hessian matrix are associated with the tangent space to the invariant manifold e T Σ z . If they are all positive, the relative equilibrium e z is a constrained minimum on the invariant manifold Σ and therefore it is nonlinear stable. According to Beck and Hall (1998), the projected Hessian matrix is given by ( ) ( ) ( ) 2 e e e F ∇ P z z P z , where the projection operator is given by As described by Eqs. (17), (21) and (25), at the relative equilibrium e z , we have Using the Hessian of the variational Lagrangian ( ) 2 e F ∇ z given by Eq. (29) and the projection operator ( ) e P z , we can calculate the projected Hessian matrix ( ) ( ) ( ) 2 e e e F ∇ P z z P z . As stated above, the nonlinear stability of the relative equilibrium e z depends on the eigenvalues of the projected Hessian matrix of the variational Lagrangian ( ) F z . The characteristic polynomial of the projected Hessian matrix ( ) ( ) ( ) 2 e e e F ∇ P z z P z can be calculated by The eigenvalues of the projected Hessian matrix are roots of the characteristic equation, which is given by Through Eq. (49), with the help of Matlab and Maple , the characteristic equation can be obtained with the following form: 2 3 2 3 2 2 2 2 1 0 2 1 0 1 0 1 0 ( )( )( )( ) 0 s s C s C s C s D s Ds D s E s E s Fs F + + + + + + + + + + = , (50) where coefficients 2 C , 1 C , 0 C , 2 D , 1 D , 0 D , 1 E , 0 E , 1 F and 0 F are functions of the parameters of the system: 1 GM , e Ω , e R , ε , m , xx I , yy I and zz I . The explicit formulations of the coefficients are given in the Appendix. In our problem there are two linearly independent Casimir functions, then as shown by Eq. (50), the projected Hessian matrix have two zero eigenvalues associated with the two-dimensional complement space of e T Σ z . The remaining ten eigenvalues are associated with the ten-dimensional tangent space e T Σ z to the invariant manifold, and if they are all positive, then the relative equilibrium e z is a constrained minimum on the invariant manifold Σ , therefore it is nonlinear stable. Since the projected Hessian matrix is symmetrical, the eigenvalues are guaranteed to be real by the coefficients of the polynomials in Eq. (50) intrinsically. Therefore, in the conditions of nonlinear stability of the relative equilibria, it is only needed to guarantee that the roots of the polynomial equations in Eq. (50) are positive. According to the theory of roots of the polynomial equation, that the remaining ten eigenvalues in Eq. (50) are positive is equivalent to We have given the conditions of the nonlinear stability of the relative equilibria in Eq. (51). Given the parameters of the system, we can determine whether the relative equilibria are nonlinear stability using the stability criterion in Eq. (51).",
"pages": [
27,
28,
29,
30
]
},
{
"title": "4.2 Case studies",
"content": "As in the studies of the linear stability, here we also give case studies using numerical method. The parameters of the problem considered here are same as in the linear stability studies. We calculate the nonlinear stability criterion in Eqs. (51) for a rigid body within the range of the parameters given by Eqs. (43) and (44) in the cases of five different values of the zonal harmonic J 2 given by Eq. (41). The points, which correspond to the mass distribution parameters guaranteeing the nonlinear stability, are plotted on the y x σ σ -plane in the 15 cases of different values of xx I m and J 2 in Figs. (18)-(32) respectively. To make comparisons with the traditional attitude dynamics, we have also given the classical nonlinear attitude stability region of a rigid body on a circular orbit in a central gravity field in the Figs. (18)-(32), which is the Lagrange region, the isosceles right triangle region in the first quadrant of the y x σ σ -plane below the straight line 0 y x σ σ -= . e an l p x σ - y σ n o 11 0 1 × 5 = y σ n o on regi lity i b r sta a ine nl No . 1 × 5 = m xx I and 0.5 = 2 J of case the in e an l p x σ - y σ n o 11 0 1 × 5 = y σ n o on regi lity i b r sta a ine nl No . 1 × 5 = m xx I and 0.2 = 2 J of case the in e an l p x σ - y σ n o 11 0 1 × 5 y σ n o on regi lity i b r sta a ine nl No . 0 1 × 5 = m xx I and 0 = 2 J of case the in e an l p x σ - y σ n o 11 0 1 × 5 = m y σ n o on regi lity i b r sta a ine nl No . 5 = m xx I and 8 0.1 - = 2 J of case the in e an l p x σ - y σ n o 11 0 1 × 5 = m × 5 = m xx I and 0.2 - = 2 J of case the in y σ n o on regi lity i b r sta a ine nl No .",
"pages": [
30,
31,
32,
33,
34,
35
]
},
{
"title": "4.3 Some discussions on the nonlinear stability",
"content": "From Figs. (18)-(32), we can easily achieve several conclusions as follows: (a). In all the 15 cases of different values of xx I m and J 2, the nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. This is similar to the classical attitude stability problem of a rigid body in a central gravity field, in which the nonlinear attitude stability region is also the subset of the linear attitude stability region in the first quadrant, i.e., the Lagrange region. This is consistent with the stability theory of the Hamiltonian system that the linear stability is the necessary condition of the stability whereas the nonlinear stability is the sufficient condition of the stability, and the sufficient stability condition should be a subset of the necessary stability condition. When the planet P is very elongated with 2 0.2 J = -, for a small rigid body there is no linear stability region and then there is no nonlinear stability region; only for a very large rigid body with 11 5 10 xx I m = × , there is a linear stability region, which is also a nonlinear stability region, located in the first quadrant of the y x σ σ -plane. When the characteristic dimension of the rigid body is large enough, such as 11 5 10 xx I m = × , the nonlinear stability region, the Lagrange region, is reduced by a triangle in the right part of the first quadrant of the y x σ σ -plane, as shown by Figs. (5), (8), (11) and (14). As the zonal harmonic J 2 increases from -0.18 to 0.5, the reduction of the Lagrange region expands and the nonlinear stability region shrinks. Notice that even in a central gravity field with 2 0 J = , the nonlinear stability region is not the Lagrange region anymore. This result has not been obtained in previous works, such as Wang et al. (1991) and Teixidó Román (2010). (c). For a small characteristic dimension of the rigid body, such as 3 5 10 xx I m = × and 7 5 10 xx I m = × , as the zonal harmonic J 2 increases from -0.18 to 0.5, the nonlinear stability region keeps equal to the Lagrange region. Whereas for a large value of the characteristic dimension of the rigid body 11 5 10 xx I m = × , as the zonal harmonic J 2 increases from -0.18 to 0.5, the nonlinear stability region shrinks by the influence of the zonal harmonic J 2.",
"pages": [
36,
37
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},
{
"title": "5. Conclusions",
"content": "For new high-precision applications in celestial mechanics and astrodynamics, we have generalized the classical J 2 problem to the motion of a rigid body in a J 2 gravity field. Based on our previous results on the relative equilibria, linear and nonlinear stability of the classical kind of relative equilibria of this generalized problem are investigated in the framework of geometric mechanics. The conditions of linear stability of the relative equilibria are obtained based on the characteristic equation of the linear system matrix at the relative equilibria, which is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the distribution of the eigenvalues of the projected Hessian matrix of the variational Lagrangian. With the stability conditions, both the linear and nonlinear stability of the relative equilibria are investigated in a wide range of the parameters of the gravity field and the rigid body by using the numerical method. The stability region is plotted on the plane of the mass distribution parameters of the rigid body in the cases of different values of the zonal harmonic J 2 and the characteristic dimension of the rigid body. Similar to the classical attitude stability in a central gravity field, the linear stability region is consisted of two regions located in the first and third quadrant of the y x σ σ -plane respectively, which are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant, the analogue of the Lagrange region. Both the zonal harmonic J 2 and the characteristic dimension of the rigid body have significant influences on the linear and nonlinear stability. When the characteristic dimension of the rigid body is small, the analogue of the Lagrange region in the first quadrant of the y x σ σ -plane is actually the Lagrange region. When the characteristic dimension of the rigid body is large enough, the analogue of the Lagrange region is reduced by a triangle and this triangle expands as the zonal harmonic J 2 increases. For a given value of the characteristic dimension of the rigid body, as the zonal harmonic J 2 increases, the analogue of the DeBra-Delp region in the third quadrant of the y x σ σ -plane expands in the direction of the boundary of the DeBra-Delp region, and cross the boundary of the DeBra-Delp region at 2 0 J = . Our results on the stability of the relative equilibria are very useful for the studies on the motion of many natural satellites in our solar system, whose motion are close to the relative equilibria.",
"pages": [
37,
38,
39
]
},
{
"title": "Appendix: Formulations of Coefficients in Characteristic Equations",
"content": "The explicit formulations of the coefficients in the characteristic equations Eqs. (38) and (50) are given as follows: ( 5 2 3 2 2 7 2 5 2 8 2 5 2 2 10 4 2 2 2 5 2 2 5 2 2 2 7 2 2 5 2 2 2 7 8 27 2 5 3 1 2 6 19 27 11 2 3 2 2 yy e e zz yy e xx zz e e xx e e xx zz e e e e zz e e zz e xx yy e xx e xx zz e e zz e e zz yy e e yy e e I mR I I R I I m R I mR I I R m R I m R I R m I I mR I mI I mR I m R I I mR I m R B μ μ μ μ με με μ με μ μ μ -Ω + Ω + Ω -Ω + Ω -Ω + + Ω + + Ω + Ω -Ω -Ω = 2 2 10 4 2 10 4 3 2 3 2 2 2 2 2 8 4 2 3 2 2 3 2 3 2 3 2 2 8 4 2 5 2 2 5 2 3 2 2 9 36 9 2 6 9 9 21 2 3 3 24 e xx e yy e e e e zz xx xx e e zz yy e e zz yy e e zz e xx e zz e xx zz e e xx e zz yy e e e xx e yy e m R I I m R R I mI m I mR I I R I I mR I mR I I R I I mR I I I m R m R I I R I μ μ με μ ε μ με με μ με με -Ω + Ω + Ω -+ + Ω -Ω -Ω -Ω -Ω Ω -Ω -Ω -) 2 2 2 3 2 5 2 2 2 3 2 3 2 2 8 4 3 2 2 3 2 2 8 4 3 12 6 9 2 18 9 1 , (A.4 2 2 ) xx e yy e e zz e xx e yy e xx e e e zz yy e xx e yy e xx e yy xx e xx zz e yy e e zz I R I mR I I R I mR I I mR I I mR I I mI R I I I mR I μ μ μ μ με με με μ Ω -Ω -Ω + Ω + Ω + Ω + Ω + + Ω Ω ( 2 10 4 2 2 2 2 2 5 2 2 2 3 2 5 2 3 2 2 3 2 2 7 2 2 3 2 2 5 2 2 5 2 3 0 8 2 36 9 3 6 21 11 9 9 2 27 3 9 14 3 3 1 2 e e xx yy e e e e xx e zz e e zz e e zz e xx e e e zz y e y e e xx yy e xx e e e y xx y e m R m I m I R m R m R I I mR I R I mR I m R m I I R I I m mR I m R I R D R I εμ εμ μ εμ μ μ μ εμ μ εμ μ μ ε μ εμ μ Ω + --Ω -+ Ω -Ω -Ω + Ω -Ω -+ Ω -+ Ω + = Ω Ω ) 2 3 2 2 3 2 12 9 , (A.11) e zz e xx e e e zz I R I mR I μ εμ -Ω Ω",
"pages": [
39,
40
]
},
{
"title": "Acknowledgements",
"content": "This work is supported by the Innovation Foundation of BUAA for PhD Graduates.",
"pages": [
41
]
},
{
"title": "References",
"content": "Aboelnaga, M.Z., Barkin, Y.V.: Stationary motion of a rigid body in the attraction field of a sphere. Astronom. Zh. 56 (3), 881-886 (1979) Balsas, M.C., Jiménez, E.S., Vera, J.A.: The motion of a gyrostat in a central gravitational field: phase portraits of an integrable case. J. Nonlinear Math. Phy. 15 (s3), 53-64 (2008) Barkin, Y.V.: Poincaré periodic solutions of the third kind in the problem of the translational-rotational motion of a rigid body in the gravitational field of a sphere. Astronom. Zh. 56 , 632-640 (1979) Beck, J.A., Hall, C.D.: Relative equilibria of a rigid satellite in a circular Keplerian orbit. J. Beletskii, V.V., Ponomareva, O.N.: A parametric analysis of relative equilibrium stability in a gravitational field. Kosm. Issled. 28 (5), 664-675 (1990) Bellerose, J., Scheeres, D.J.: Energy and stability in the full two body problem. Celest. Mech. Dyn. Astron. 100 , 63-91 (2008) Boué, G., Laskar, J.: Spin axis evolution of two interacting bodies. Icarus 201 , 750-767 (2009) Breiter, S., Melendo, B., Bartczak, P., Wytrzyszczak, I.: Synchronous motion in the Kinoshita problem. Applications to satellites and binary asteroids. Astron. Astrophys. 437 (2), 753-764 (2005) Broucke, R.A.: Numerical integration of periodic orbits in the main problem of artificial satellite theory. Celest. Mech. Dyn. Astron. 58 , 99-123 (1994) Hall, C.D.: Attitude dynamics of orbiting gyrostats, in: Pr ę tka-Ziomek, H., Wnuk, E., Seidelmann, P.K., Richardson, D. (Eds.), Dynamics of Natural and Artificial Celestial Bodies. Kluwer Academic Publishers, Dordrecht, pp. 177-186 (2001) Hughes, P.C.: Spacecraft Attitude Dynamics, John Wiley, New York, pp. 281-298 (1986) Kinoshita, H.: Stationary motions of an axisymmetric body around a spherical body and their stability. Publ. Astron. Soc. Jpn. 22 , 383-403 (1970) Koon, W.-S., Marsden, J.E., Ross, S.D., Lo, M., Scheeres, D.J.: Geometric mechanics and the dynamics of asteroid pairs. Ann. N. Y. Acad. Sci. 1017 , 11-38 (2004) Maciejewski, A.J.: Reduction, relative equilibria and potential in the two rigid bodies problem. Celest. Mech. Dyn. Astron. 63 , 1-28 (1995) Marsden, J.E., Ratiu, T.S.: Introduction to Mechanics and Symmetry, TAM Series 17, Springer Verlag, New York (1999) McMahon, J.W., Scheeres, D.J.: Dynamic limits on planar libration-orbit coupling around an oblate primary. Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-012-9469-0 (in press) Scheeres, D.J.: Stability in the full two-body problem. Celest. Mech. Dyn. Astron. 83 , 155-169 (2002) Scheeres, D.J.: Stability of relative equilibria in the full two-body problem. Ann. N. Y. Acad. Sci. 1017 , 81-94 (2004) Scheeres, D.J.: Spacecraft at small NEO. arXiv: physics/0608158v1 (2006) Scheeres, D.J.: Stability of the planar full 2-body problem. Celest. Mech. Dyn. Astron. 104 , 103-128 (2009) Teixidó Román, M.: Hamiltonian Methods in Stability and Bifurcations Problems for Artificial Satellite Dynamics. Master Thesis, Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, pp. 51-72 (2010) Vereshchagin, M., Maciejewski, A.J., Go ź dziewski, K.: Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body. Mon. Not. R. Astron. Soc. 403 , 848-858 (2010) Wang, Y., Xu, S.: Gravitational orbit-rotation coupling of a rigid satellite around a spheroid planet. J. Aerosp. Eng. doi: 10.1061/(ASCE)AS.1943-5525.0000222 (in press) Wang, Y., Xu, S.: Hamiltonian structures of dynamics of a gyrostat in a gravitational field. Nonlinear Dyn. 70 (1), 231-247 (2012) Wang, Y., Xu, S.: Symmetry, reduction and relative equilibria of a rigid body in the J 2 problem. Adv. Space Res. 51 (7), 1096-1109 (2013a) Wang, Y., Xu, S.: Gravity gradient torque of spacecraft orbiting asteroids. Aircr. Eng. Aerosp. Tec. 85 (1), 72-81 (2013b) Wang, L.-S., Krishnaprasad, P.S., Maddocks, J.H.: Hamiltonian dynamics of a rigid body in a central gravitational field. Celest. Mech. Dyn. Astron. 50 , 349-386 (1991) Wang, L.-S., Maddocks, J.H., Krishnaprasad, P.S.: Steady rigid-body motions in a central gravitational field. J. Astronaut. Sci. 40 (4), 449-478 (1992) Wang, L.-S., Lian, K.-Y., Chen, P.-T.: Steady motions of gyrostat satellites and their stability. IEEE T. Automat. Contr. 40 (10), 1732-1743 (1995) Wisdom, J.: Rotational dynamics of irregularly shaped natural satellites. Astron. J. 94 , 1350-1360 (1987)",
"pages": [
41,
42,
43,
44
]
}
]
2013ApJ...762....2M
https://arxiv.org/pdf/1211.2252.pdf
<document>
<section_header_level_1><location><page_1><loc_35><loc_79><loc_65><loc_81></location>Cygnus X-3's Little Friend</section_header_level_1>
<text><location><page_1><loc_35><loc_76><loc_65><loc_77></location>M. L. McCollough and R. K. Smith</text>
<text><location><page_1><loc_12><loc_73><loc_88><loc_74></location>Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA 02138, U.S.A.</text>
<section_header_level_1><location><page_1><loc_34><loc_69><loc_66><loc_71></location>[email protected]</section_header_level_1>
<text><location><page_1><loc_48><loc_66><loc_52><loc_67></location>and</text>
<text><location><page_1><loc_44><loc_62><loc_56><loc_64></location>L. A. Valencic</text>
<text><location><page_1><loc_21><loc_59><loc_79><loc_61></location>Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218</text>
<section_header_level_1><location><page_1><loc_44><loc_55><loc_56><loc_56></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_34><loc_83><loc_51></location>Using the unique X-ray imaging capabilities of the Chandra observatory, a 2006 observation of Cygnus X-3 has provided insight into a singular feature associated with this well-known microquasar. This extended emission, located ∼ 16 '' from Cygnus X-3, varies in flux and orbital phase (shifted by 0.56 in phase) with Cygnus X-3, acting like a celestial X-ray 'mirror'. The feature's spectrum, flux and time variations allow us to determine the location, size, density, and mass of the scatterer. We find that the scatterer is a Bok globule located along our line of sight, and discuss its relationship to Cygnus X-3. This is the first time such a feature has been identified with the Chandra X-ray Observatory.</text>
<text><location><page_1><loc_17><loc_28><loc_83><loc_31></location>Subject headings: X-rays: binaries - X-rays: individual(Cygnus X-3) - X-rays: ISM</text>
<section_header_level_1><location><page_1><loc_42><loc_22><loc_58><loc_23></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_10><loc_88><loc_19></location>At a distance of 9 kpc (Predehl et al. 2000), Cygnus X-3 is an unusual microquasar in which a Wolf-Rayet companion (van Kerkwijk et al. 1992) orbits a compact object with an orbital period of 4.8 hours. It is a strong radio source routinely producing radio flares of 1 to ∼ 20 Jy (Waltman et al. 1995). It has been shown to produce radio jets and the radio emission correlates with both the soft X-ray and hard X-ray emissions (Mioduszewski et al. 2001;</text>
<text><location><page_2><loc_12><loc_74><loc_88><loc_86></location>Miller-Jones et al. 2004; Szostek et al. 2008; McCollough et al. 1999). In 2000 Chandra observations found extended X-ray emission that is believed to be associated with Cygnus X-3 (Heindl et al. 2003). In this paper we analyze a 2006 Chandra observations of Cygnus X-3 and reexamine the previous Chandra observations discussed in Heindl et al. (2003). In particular we take a careful look at the timing and spectral properties of the extended feature and how they related to Cygnus X-3.</text>
<section_header_level_1><location><page_2><loc_35><loc_68><loc_65><loc_70></location>2. Observations and Analysis</section_header_level_1>
<text><location><page_2><loc_12><loc_59><loc_88><loc_66></location>Between 1999-2006 Cygnus X-3 was observed six times by Chandra using the ACISS/HETG with a Timed Event (TE) mode and covered a range of source activity (see Table 1). These observations provided grating spectra of Cygnus X-3 and on-axis zero order images which allow for spatial and spectral analysis of Cygnus X-3 and its surroundings.</text>
<text><location><page_2><loc_12><loc_42><loc_88><loc_57></location>The primary observation used for this analysis was a 50 ksec quenched state observation (OBSID: 6601 hereafter referred to as QS) obtained during a period of high X-ray activity. At the time of the observation the RXTE/ASM (2-12 keV) count rates were ∼ 25 -30 cts s -1 , Swift/BAT (15-50 keV) had an average count rate of ∼ 0 . 0 cts s -1 , and the Ryle radio telescope (15 GHz) showed radio fluxes of ∼ 1 mJy, all values typical of a Cygnus X-3 quenched state (Szostek et al. 2008; McCollough et al. 1999; Waltman et al. 1996). This observation has the longest duration of any of the observations and the feature has the greatest number of photons of any of the observations.</text>
<text><location><page_2><loc_12><loc_23><loc_88><loc_40></location>Since this analysis involves a region near a bright point source we also need to determine the impacts of pileup on the data. This can be determined by looking at the average number of counts per detection island (9 pixels region: see the Chandra POG (2011)) per observing frame. We do this by taking a series of annuli centered on Cygnus X-3 for the highest count rate observation (QS). Each annulus has a radial thickness of 2 ACIS pixels ( ∼ 1 '' ) with the readout streak regions excluded. We then sum the counts in each annulus and divide by the number of observation frames 1 and the of number detection islands (the area of the annulus in pixels divided by 9 pixels). In Figure 1 is a plot of counts/frame as a function of radial distance from Cygnus X-3, with the solid line represents the entire observation</text>
<text><location><page_3><loc_12><loc_78><loc_88><loc_86></location>and the dotted line the times of peak count rate. From Davis (2007) we have taken the counts/frame values for which one would expected pileup of 1% , 5%, and 10% and plotted them in Figure 1. We see that at radial distance of greater than ∼ 8 '' pileup should not be an issue and will not impact our analysis.</text>
<text><location><page_3><loc_12><loc_70><loc_88><loc_77></location>In our analysis of these observations, we used version 4.3 of the CIAO tools. The Chandra data retrieved from the archive were processed with ASCDS version 7.7.6 or higher. All event files were filter by their good times intervals and barycenter corrected using the CIAO tool axbary .</text>
<section_header_level_1><location><page_3><loc_30><loc_63><loc_70><loc_65></location>2.1. The Feature and its Characteristics</section_header_level_1>
<text><location><page_3><loc_12><loc_36><loc_88><loc_61></location>For each observation, we have extracted a zeroth-order image between 1 -8 keV binned at the nominal ACIS-S resolution ( ∼ 0 . 49 '' ). Figure 2 and 5 shows images for the QS observation. In each individual image, there is a bright, unresolved core with strong radial point-spread function (PSF) wings and a strong scattering halo (Predehl et al. 2000). In each observation the feature reported by Heindl et al. (2003) is present at the same location. An analysis of the QS observation shows the feature (RA : 20 h 32 m 27 . 1 s , DEC : +40 · 57 ' 33 . 8 '' ) lies at an angular distance of 15 . 6 '' from Cygnus X-3 at an angle of 68 . 5 · from the orientation of the observed radio jets of Cygnus X-3. The feature is extended and was fit using CIAO/SHERPA with a 2D-Gaussian with axes of 3 . 6 '' and 5 . 5 '' and a position angle of 78 . 7 · , measured counterclockwise with the top of the image being 0 · . If the feature and Cygnus X-3 are at the same distance, then their separation is 2 . 2 D 9 light-years (D 9 : distance in units of 9 kpc). This feature is present in all observations of Cygnus X-3 done throughout the Chandra mission (1999 to present).</text>
<section_header_level_1><location><page_3><loc_38><loc_29><loc_62><loc_31></location>2.2. Temporal Behavior</section_header_level_1>
<text><location><page_3><loc_12><loc_12><loc_88><loc_27></location>The feature is located amidst a high background region. This high background is due to the telescope PSF and a dust scattering halo. The majority of the photons in the background have energies above 2 keV and as such arise from scattering off micro-roughness in the telescope optics; see the discussion in Predehl et al. (2000). In order to examine the temporal variability of the feature we need to subtract the background flux from region of feature. To do this we used segments of annuli centered on Cygnus X-3 for the feature and background regions to extract the light curve for the feature and the background (see Figure 2). The annuli were chosen to maximize the number of counts for the feature as well as</text>
<text><location><page_4><loc_12><loc_80><loc_88><loc_86></location>have the feature and background regions sample the same radial region of the PSF/dust halo while avoiding the readout streaks. All data extraction was done with the CIAO tool dmextract .</text>
<section_header_level_1><location><page_4><loc_37><loc_74><loc_63><loc_76></location>2.2.1. Phase Folded Analysis</section_header_level_1>
<text><location><page_4><loc_12><loc_51><loc_88><loc_72></location>The phase-folded (1-8 keV) light curves of Cygnus X-3, the background region, and background subtracted feature region are shown in Figure 3. As might be expected the background which is mainly due to the scattered PSF emission demonstrates the same 4.79 hr orbital variation with the slow rise and rapid observed drop in Cygnus X-3. This is also reinforced in Figure 4 (top panel) which show no observed lag in the cross-correlation between Cygnus X-3 and the background. However, the feature surprisingly shows the same orbital modulation but with a phase shift of ∼ 0.6 . Phase-selected images reveal how this feature varies relative to Cygnus X-3 (see Figure 5), which can be seen more dramatically in the movie which accompanies this paper (see online version). This is also confirmed in the cross-correlation between Cygnus X-3 and the feature seen in Figure 4 (lower panel) which show a clear lag that peaks around 9460 seconds which corresponds to a phase lag of ∼ 0.55.</text>
<text><location><page_4><loc_12><loc_44><loc_88><loc_49></location>Fitting Phase Folded Light Curves: To address questions of a possible issues with background subtraction (over-subtraction) we took the light curve from feature annulus and fit it using the following model:</text>
<formula><location><page_4><loc_34><loc_38><loc_88><loc_40></location>C lf [i] = C bkgd [i] + a ∗ C bkgd [shift(i , j)] . (1)</formula>
<text><location><page_4><loc_12><loc_23><loc_88><loc_36></location>Where C lf [i] is the count rate for the feature's region in phase bin i, C bkgd [i] is the count rate from background region (scaled to the feature's region size) in phase bin i, and the last term a ∗ C bkgd [shift(i , j)] is the count rate of the background region scaled by a and shifted by j in phase. The fit parameters are a and j. We used the IDL routine MPFIT (Markwardt 2008) to fit the light curve. We did multiple fits of the light curve using a number of different phase binnings and found good fits for all binnings with consistent fit values (see Table 2). Our best fit a gave a = 0 . 29 ± 0 . 01 and phase shift(j) = 0 . 56 ± 0 . 02 (see Figure 6).</text>
<text><location><page_4><loc_12><loc_14><loc_88><loc_21></location>As a further test we replaced the second term in Equation 1 with a constant term which was used as a fit parameter. We found no acceptable fits for any of the binnings (see Table 2). This result is consistent with the feature varying with the same period as Cygnus X-3 but shifted in phase.</text>
<text><location><page_4><loc_16><loc_11><loc_88><loc_12></location>Phase Image: Finally, as another way to check to see if background subtraction could</text>
<text><location><page_5><loc_12><loc_68><loc_88><loc_86></location>be an issue for each Chandra detected event, a 'Cygnus X-3' phase value was determined from its arrival time. Photons falling into certain phase ranges were broken in separate 'phase' images. These images were assigned a certain color and combined to form a color coded phase image. The bands were: (red) 0.3-0.63 , (green) 0.63-0.96 , and (blue) 0.96-0.3 . The image is shown in Figure 7, note the blue color of the feature. This indicates that bulk of the photons are arriving in the 0.96-0.3 phase range. If the feature was constant we would expect it to be white (equal amounts of each color). It is also important to note that no background subtraction was done in this approach and hence there is no issue with the background subtraction creating a false time/phase variation of the feature.</text>
<section_header_level_1><location><page_5><loc_35><loc_62><loc_65><loc_64></location>2.2.2. Longer timescale Variability</section_header_level_1>
<text><location><page_5><loc_12><loc_49><loc_88><loc_60></location>To examine the temporal behavior of the feature on longer timescales we determined the flux 2 of Cygnus X-3 and the feature for each of the Chandra /ACIS observations (see Table 1). When Cygnus X-3's flux is plotted versus the flux from the feature there appears to be a correlation (see Figure 8) where the dashed line is a linear fit to the data. A Pearson's correlation test of the data yields a correlation coefficient of 0.98 indicating a linear correlation between the feature and Cygnus X-3.</text>
<section_header_level_1><location><page_5><loc_43><loc_42><loc_57><loc_44></location>2.3. Spectrum</section_header_level_1>
<text><location><page_5><loc_12><loc_31><loc_88><loc_40></location>The annuli used to extract the light curves (see Figure 2) were also used to extract spectra for the feature and background region. The final background-subtracted spectra of the feature contained from 78 to 3216 counts in the 1-8 keV band. Table 3 shows fits to the spectrum using simple absorbed power law and blackbody models all of which yield acceptable fits to the spectrum.</text>
<text><location><page_5><loc_12><loc_16><loc_89><loc_29></location>All of the Chandra /ACIS observations were HETG grating observations. The ± first order HEG spectra were combined and fit for each observation (see notes in Table 1). The continuum for Cygnus X-3 is complex and dependent on the state of activity (Hjalmarsdotter et al. 2008, 2009; Koljonen et al. 2010). In the X-ray (0.5-10 keV) the continuum can be modeled by partial covered disk blackbody during flaring/quenched states (Koljonen et al. 2010) and during the quiescence/transition states we found that continuum was best approximated by an absorbed power law. In all cases a large number of spectral features were added (see</text>
<text><location><page_6><loc_12><loc_85><loc_42><loc_86></location>Table 4) to improve the spectral fit.</text>
<text><location><page_6><loc_12><loc_73><loc_88><loc_83></location>We note that all of the spectra of the feature are more absorbed and very steep/soft, relative to the corresponding Cygnus X-3 spectra (see Table 3 & 4). As Cygnus X-3 transitions from a quiescent (hard state) to flaring/quenched state (soft state) its spectrum becomes softer. The spectrum of the feature is shown to follow suit and becomes steeper/softer as Cygnus X-3's spectrum does.</text>
<section_header_level_1><location><page_6><loc_38><loc_67><loc_62><loc_69></location>3. Nature of the Feature</section_header_level_1>
<text><location><page_6><loc_12><loc_54><loc_88><loc_65></location>To understand the feature's nature the following must be explained: (a) it is clearly extended; (b) its flux varies in phase with Cygnus X-3 with a phase shift of 0.56; (c) the flux from the feature shows a correlation with the flux from Cygnus X-3; (d) the phase-averaged flux of the feature is ∼ 10 -3 of Cygnus X-3's flux; (e) the time variation is 4.8 hrs but the separation between the feature and Cygnus X-3 is at least 2 . 2 D 9 light-years; and (f) its spectrum is heavily absorbed and lacks hard X-ray flux relative to Cygnus X-3.</text>
<text><location><page_6><loc_12><loc_35><loc_88><loc_52></location>Jet Emission: It is natural to try to associate this feature with the Cygnus X-3 jet emission. However, Cygnus X-3 was in a quenched state throughout the Chandra observation and for several days before and after, during which jet activity is strongly suppressed. Additionally, over a three year period prior to this observations Ryle/AMI-LA observed no radio flare exceeding 0.5 Jy (Pooley 2011). Furthermore, in earlier Chandra observations where there is jet activity, the feature is fainter. If the X-ray emission of the feature was due to the jet one would expect this to be synchrotron emission and one would not generally expect the spectrum to be so steep and heavily absorbed. Also the misalignment of the feature relative to the jets observed in the radio complicates this picture.</text>
<text><location><page_6><loc_12><loc_18><loc_88><loc_33></location>Jet Impact Area: Problems with this being a jet impact area have been noted by Heindl et al. (2003) (location relative to the radio jets, jet precession, and jet collimation). In addition the observed flux correlation between the feature and Cygnus X-3 provides problems given a likely separation of 2 . 2 D 9 light years. The strong phase modulation of the feature (varying the same as Cygnus X-3 by a factor of two), combined with a periodicity exactly matching that of Cygnus X-3, would be difficult to understand. One would expect the continuing impact of the jet would give rise to a brighter constant flux from the feature and drastically reduce the modulation which is observed.</text>
<text><location><page_6><loc_12><loc_11><loc_88><loc_16></location>Wind Interaction: The strongest arguments which were made by Heindl et al. (2003) for the feature's nature is that it is due to a wind/ISM interaction. The feature's distance, flux correlation and phase modulation with Cygnus X-3 make such a model difficult to</text>
<text><location><page_7><loc_12><loc_78><loc_88><loc_86></location>reconcile with the observations. In this interpretation the feature is created over timescales that are long ( ∼ 2000 years) compared to the observed orbital modulation. Also the direct change in the flux of the feature with Cygnus X-3 flux is difficult to reconcile with such a model.</text>
<section_header_level_1><location><page_7><loc_38><loc_72><loc_62><loc_74></location>3.1. Scattering Solution</section_header_level_1>
<text><location><page_7><loc_12><loc_55><loc_88><loc_70></location>A natural explanation for the feature's time variable behavior is that it is a result of scattering from a cloud (which acts as a kind of interstellar X-ray 'mirror') between Cygnus X-3 and the observer. This explanation would naturally lead to the observed phase difference between light curves as a difference in the path length of the scattered photons (Trumpler & Schonfelder 1973). This could also explain the flux correlation (see Figure 8) and overall flux difference ( ∼ 10 -3 ) since only a small fraction of the total flux will be scattered toward the observer. In figure 9 a diagram of the expected geometry for the scattering from a cloud is shown.</text>
<text><location><page_7><loc_12><loc_44><loc_88><loc_53></location>The spectrum of the feature can also be modeled as a scattered version of Cygnus X-3's spectrum. At these energies scattering will modify the spectrum by A ∗ E -2 (Smith et al. 2002), due to the reduced scattering efficiency at higher energies (Overbeck 1965). There will also be an additional reduction at low energies caused by absorption in the cloud (N cl ) and multiple scattering. We can then model the feature's spectrum as due to scattering as</text>
<formula><location><page_7><loc_35><loc_38><loc_88><loc_40></location>S lf = e -σ (E)N H (lf) ∗ A ∗ E -α ∗ S cont . (2)</formula>
<text><location><page_7><loc_12><loc_21><loc_88><loc_36></location>Where S lf is the scattering model for the feature, e -σ (E)N H (lf) is the additional absorption due to the cloud (modeled using phabs in XSPEC), A ∗ E -α represents the high energy attenuation due to scattering (modeled using plabs from XSPEC), and S cont is Cygnus X-3 continuum model determined from the grating data (see Table 4). The resulting fit parameters for the observations are shown in Table 5 and the fit to the QS observation's spectrum is shown in Figure 10. The resultant fluxes (1 -8 keV) for the feature and Cygnus X-3 are given in Tables 4 & 5. The flux ratio of the feature to Cygnus X-3 are all in the range of (4 -6) × 10 -4 .</text>
<text><location><page_7><loc_12><loc_14><loc_88><loc_19></location>This gives rise to a natural explanation of the observed spectral differences. The loss of the flux below 2 keV is the result of additional absorption in the cloud and the reduced flux at higher energy simply reflects the drop in scattering efficiency.</text>
<text><location><page_7><loc_16><loc_11><loc_88><loc_12></location>Distance to and Size of the Feature: Assuming that this feature is due to an individual</text>
<text><location><page_8><loc_12><loc_80><loc_88><loc_86></location>cloud the time delay is determined by the distance to the cloud (Trumpler & Schonfelder 1973; Predehl & Klose 1996; Predehl et al. 2000). The resulting time delay can be written as:</text>
<formula><location><page_8><loc_36><loc_74><loc_88><loc_78></location>∆t = Θ 2 2c Dx 1 -x = 1 . 15Θ 2 Dx 1 -x . (3)</formula>
<text><location><page_8><loc_12><loc_57><loc_88><loc_73></location>Where ∆t is the time delay (in seconds), D is the distance (in kpc) to the source, Θ is observed angular distance (in arcsec) from the source, x is the fractional distance of the scatter to the observer (see Figure 9), and c is the speed of light. From the observed phase observed phase offset, we know that time delay is given by ∆t = (0 . 56 + n)t cx3 where t cx3 = 17 . 25 ksec is the observed orbital period of Cygnus X-3, but we have an ambiguity in the total number orbital period offsets (n). Using ∆t = 0 . 56 ∗ t cx3 = 9 . 66 ksec , D = 9 kpc, and Θ = 15 . 6 '' , the resulting fractional distance is x = 0.79. This means that the cloud is close to Cygnus X-3 (within 1.9 kpc) and if n > 0, this distance could be less.</text>
<text><location><page_8><loc_12><loc_28><loc_88><loc_56></location>This degeneracy (n) can be removed using the fact that the feature is extended. From equation (3) we would expect that the delay scattered photons experience increases as a function of angle from Cygnus X-3. If we take the inner and outer edges of the feature to be 13 . 8 '' and 17 . 4 '' respectively then for x = 0.79 we would get a time delay of ∼ 1 . 2 hrs across the feature. For locations closer to Cygnus X-3 we would expect the delay across the feature to increase. To test this we have taken the extraction and background annuli (see Figure 2) and divided into an inner and outer set of annuli (11 . 2 '' to 15 . 6 '' and 15 . 6 '' to 20 . 0 '' respectively). In Figure 11 we show a cross correlation of the inner and outer light curves (for the QS observation with 5 minute time resolution) which shows a significant lag (at the 99 % confidence level) at 0 . 9 hrs. This would correspond to the n = 0 case. In Figure 12 are the phase folded light curves of the inner and outer region in which one can see that the light curve for the outer region is lagging the inner by ∼ 0 . 2 in phase. This corresponds to a lag of ∼ 1 hr. This puts the feature at a distance of 1.9 kpc from Cygnus X-3 making the observed dimensions of the feature 0.12 by 0.19 parsecs.</text>
<text><location><page_8><loc_12><loc_17><loc_88><loc_26></location>Density of the Cloud: From the spectral fit to the feature for the QS observations we have an absorbing column density of the feature of 5 . 0 +2 . 0 -1 . 7 × 10 22 cm -2 . This value is consistent with column density determined from spectral fits to the other observations (see Table 5). The column density of the feature can also be estimated from the flux ratio of the feature to Cygnus X-3 using the following relationship (see Appendix A for derivation)</text>
<formula><location><page_8><loc_19><loc_8><loc_57><loc_13></location>F lf F cx3 = N H (lf) [ π tan α 1 tan α 2 cos 2 ( θ s -θ ) (1 -x) 2 ]</formula>
<formula><location><page_9><loc_27><loc_81><loc_88><loc_86></location>× [ ∑ i=g , si N i d ∫ E 2 E 1 S(E)e -σ (E)N H (lf) ∫ a max a min a -3 . 5 ( d σ s (E , a , θ s ) dΩ ) dadE ] . (4)</formula>
<text><location><page_9><loc_12><loc_52><loc_88><loc_79></location>The flux ratio is equal to the product of three quantities. The first (N H (lf)) is the column density of the feature, the second is a solid angle term which relates to what fraction of Cygnus X-3's flux is intercepted by the feature, and final term is a scattering term which is a measure of the flux scattered by the dust in the cloud (this is solved for by numerical integration over the energy range and grain distribution). The last two terms are depend on x, the fractional distance between the observer and Cygnus X-3. Figure 13 shows a plot of the last two terms and their product as function of x. The solid line is for scattering due to silicates and the dotted line for scattering due to graphite. Equation 4 can be solved for the column density of the feature as a function of x as is shown in Figure 14. The parameters used to create these curves are given in Table 6. Also included are lines representing the column density from the spectral fit of QS with its uncertainties and a vertical line representing its location from the observed time delay. What we find is good agreement with the column density determined from the spectral fits and the column density (N lf = 3 . 6 × 10 22 cm -2 ) necessary to produce the observed flux ratio.</text>
<text><location><page_9><loc_12><loc_43><loc_88><loc_50></location>If we assume that path-length along the line-of-sight through the cloud is similar to the observed dimensions of the feature [(3 . 7 -5 . 9) × 10 17 cm] we can make an estimate of the density of the feature. Taking the column density to be 5 . 0 +2 . 0 -1 . 7 × 10 22 cm -2 we arrive at a density range of (0 . 6 -1 . 9) × 10 5 cm -3 making the feature a dense molecular cloud.</text>
<text><location><page_9><loc_12><loc_31><loc_88><loc_41></location>Mass of the Cloud: From the estimate of the density of the cloud and the size determined from the X-ray measurements we can make an estimate of the mass of the cloud. Using the simplifying assumption of a spherical cloud with a diameter of between 0 . 12 -0 . 19 pc with a density of 10 5 cm -3 we arrive, from X-ray observations alone, at an estimate of the mass of the cloud to be 2 -24 M /circledot .</text>
<text><location><page_9><loc_12><loc_25><loc_88><loc_30></location>From the cloud's size, density, and mass the feature has all of the characteristics of a Bok Globule (Bok & Reilly 1947; Clemens et al. 1991), but instead of seeing this as a dark obscuring feature in the optical we see it shining in scattered X-rays.</text>
<section_header_level_1><location><page_9><loc_35><loc_18><loc_65><loc_20></location>4. Relationship to Cygnus X-3</section_header_level_1>
<text><location><page_9><loc_12><loc_13><loc_88><loc_16></location>What is the relationship of this feature to Cygnus X-3? Three possibilities present themselves:</text>
<unordered_list>
<list_item><location><page_9><loc_16><loc_10><loc_88><loc_11></location>(1) Random Alignment : Cygnus X-3 and the feature both lie in the Galactic plane</list_item>
</unordered_list>
<text><location><page_10><loc_12><loc_72><loc_88><loc_86></location>(l ii = 79 . 845 · , b ii = 0 . 700 · ). The Cygnus X region that hosts Cygnus X-3 is rich in molecular clouds (Schneider et al. 2006). So this may be just a chance alignment. If so this gives us insight into the nature and structure of molecular clouds in the ISM. In this case we would be looking across three Galactic arms (with Cygnus X near the Local Spur, the feature in the Perseus arm at ∼ 5 kpc, and Cygnus X-3 in the Outer Arm at 7 -9 kpc). Bringing Cygnus X-3 closer, to 7 kpc, does not greatly change the distance estimate to the feature or the need for three star forming regions along the line of sight.</text>
<unordered_list>
<list_item><location><page_10><loc_12><loc_55><loc_88><loc_71></location>(2) Supergiant Bubble Shell : These structures have been observed in other galaxies (Kim et al. 1999). They have typical radii of 0.5-1.0 kpc and are driven by the radiation and outflows from OB associations, supernovae and their remnants, and XRBs. Molecular clouds have also been found to exist in these shells (Yamaguchi et al. 2001). Cygnus X-3 is a high-mass X-ray binary and likely still resides in such an OB association. This gives a natural explanation of the feature's location along our line-of-sight. Given the distance of the feature from Cygnus X-3 this would be a bubble comparable to the HI shell found in NGC 6822 (de Blok & Walter 2000).</list_item>
</unordered_list>
<text><location><page_10><loc_12><loc_38><loc_88><loc_54></location>(3) Microquasar Jet-Inflated Bubble : Within NGC 7793 a powerful microquasar is driving a 300 pc jet-inflated bubble (Pakull et al. 2010). Cygnus X-3 is a microquasar whose jets appear to be aimed along our line of sight (Mioduszewski et al. 2001; Miller-Jones et al. 2004). It is possible that rapid cooling near the working surface of the jet, in the shell of the cocoon, may allow a dense molecular cloud to form. This would explain the nature of the feature as well as its alignment with Cygnus X-3. Although it should be noted that there is research which suggest that the jet may not be close to the line of sight (Mart'ı, Paredes & Peracaula 2001), which would make this a less likely option.</text>
<text><location><page_10><loc_12><loc_23><loc_88><loc_37></location>Finally it should be noted that a combination of both (2) and (3) may be possible. The radiation and outflows from the OB association may create a large low density cavity in which the microquasar jet can more easily propagate. Evidence for large-scale cavities surrounding other microquasars has been noted (Hao & Zhang 2009). This could explain the large distance of the feature from Cygnus X-3 (1.9 kpc) and reduce the energetics necessary to produce it. The feature may be located at the place where jet interacts which the wall of the cavity.</text>
<section_header_level_1><location><page_10><loc_43><loc_17><loc_57><loc_19></location>5. Conclusion</section_header_level_1>
<text><location><page_10><loc_12><loc_12><loc_88><loc_15></location>This feature and its temporal relationship to Cygnus X-3 have unveiled the unique interaction between a microquasar and its environment. It has given us a tool to probe the</text>
<text><location><page_11><loc_12><loc_80><loc_88><loc_86></location>nature and structure of molecular clouds, providing information on their size and shape, possibly due to the microquasar interaction or the presence of ordered magnetic fields in the ISM. It has also given us our first X-ray view of a Bok Globule.</text>
<text><location><page_11><loc_12><loc_65><loc_88><loc_79></location>To date this is the first such feature found with Chandra . If the feature is indeed due to a microquasar interacting with its environment then we would expect there to be very few. This would be due to the limits of small angle scattering in the X-ray and the need for the lobes and associated molecular clouds to be aligned close to our line of sight. Depending on the nature of these sources the best candidates would be high mass X-ray binaries (because of their young age and hence likely relationship with an OB association and star forming regions) with a relatively short orbital periods.</text>
<section_header_level_1><location><page_11><loc_39><loc_59><loc_61><loc_61></location>6. Acknowledgments</section_header_level_1>
<text><location><page_11><loc_12><loc_46><loc_88><loc_57></location>MLM wishes to acknowledge support from NASA under grant/contract G06-7031X and NAS8-03060. MLM would also like to acknowledge the useful discussions with Ramesh Narayan concerning the scattering path through and interactions with interstellar clouds. We wish to thank the referee for the helpful comments and suggestions. This research has made use of data obtained from the Chandra Data Archive and software provided by the Chandra X-ray Center (CXC).</text>
<section_header_level_1><location><page_11><loc_15><loc_39><loc_85><loc_41></location>A. Derivation of Scattering Relations for Cygnus X-3's and the Feature</section_header_level_1>
<text><location><page_11><loc_12><loc_28><loc_88><loc_37></location>It is possible to derive some of the scatter's properties by comparison of the fluxes of Cygnus X-3 and the feature. This derivation is similar to that done for the scattering halo intensity of Smith & Dwek (1998). The geometry being used can be found in Figure 9. If we take the unabsorbed luminosity of Cygnus X-3 as a function of energy to be L cx3 (E) then the X-ray luminosity at the feature is given by</text>
<formula><location><page_11><loc_38><loc_21><loc_88><loc_25></location>L lf (E) = L cx3 (E)e -σ (E)N H (r s ) 4 π r s 2 . (A1)</formula>
<text><location><page_11><loc_12><loc_16><loc_88><loc_19></location>Where σ (E) is the X-ray absorption cross section, N H (r s ) is column density along the path (r s ) between Cygnus X-3 and the cloud.</text>
<text><location><page_11><loc_12><loc_11><loc_88><loc_14></location>The photons scattered into a solid angle dΩ by a single scatter for a source of luminosity L s (E) is given by</text>
<formula><location><page_12><loc_41><loc_81><loc_88><loc_85></location>P(E) = L s (E) d σ s dΩ dΩ . (A2)</formula>
<text><location><page_12><loc_12><loc_76><loc_88><loc_80></location>Where d σ s / dΩ is the differential scattering cross section (see Mathis & Lee (1991); Mauche & Gorenstein (1986)).</text>
<text><location><page_12><loc_12><loc_71><loc_88><loc_75></location>For a telescope with collecting area A ' we can chose dΩ such that A ' = r o 2 dΩ, where r o is the distance from the scatter to the observer.</text>
<text><location><page_12><loc_12><loc_66><loc_88><loc_70></location>The photon count rate that the observer will detect from scattering from a single dust particle as</text>
<formula><location><page_12><loc_15><loc_57><loc_88><loc_62></location>C s (E) = L s (E)e -σ (E)N H (r o ) ( d σ s dΩ ) A ' r o 2 = L cx3 (E)e -σ (E)[N H (r s )+N H (r o )] 4 π r s 2 ( d σ s dΩ ) A ' r o 2 . (A3)</formula>
<text><location><page_12><loc_16><loc_54><loc_78><loc_56></location>Where N H (r o ) is the column density between the scatter and the observer.</text>
<text><location><page_12><loc_12><loc_41><loc_88><loc_53></location>The feature has been fit with an elliptical Gaussian with semi-major and semi-minor axes of r 1 and r 2 respectively. For a distance of xD one can use the angular measurements of the semi-major and semi-minor axes, α 1 and α 2 respectively, to give the surface area of the feature as A lf = π r 1 r 2 = π x 2 D 2 tan α 1 tan α 2 . For a scattering region thickness of l s the scattering volume of the feature is given by V lf = A lf l s . For a dust grain number density of n g we can determine the total count rate and flux for the feature as</text>
<formula><location><page_12><loc_22><loc_34><loc_88><loc_39></location>F lf (a , E) = C tot (E) A ' = n g (a)L cx3 (E)e -σ (E)[N H (r s )+N H (r o )] 4 π r s 2 ( d σ s dΩ ) A lf l s r o 2 . (A4)</formula>
<text><location><page_12><loc_12><loc_28><loc_88><loc_33></location>In general n g will be a function of dust radius a. For our case we will consider n g to be uniform spatially at the location of the feature. Integrating over the dust size distribution gives the flux for the feature as</text>
<formula><location><page_12><loc_24><loc_20><loc_88><loc_25></location>F lf (E) = ∫ a max a min n g (a)L cx3 (E)e -σ (E)[N H (r s )+N H (r o )] 4 π r s 2 ( d σ s dΩ ) A lf l s r o 2 da . (A5)</formula>
<text><location><page_12><loc_12><loc_10><loc_88><loc_19></location>We can simplify the above equation by noting that the observed angle θ for the feature is very small and the overall angular dimensions ( α 1 and α 2 ) of the feature are small. In this case the path traveled by the scattered photon will be very close to the path traveled by the unscattered photon. Because of this the total hydrogen column density for both paths should be the same except for the additional column density of N H (lf) along the scattered</text>
<text><location><page_13><loc_12><loc_80><loc_88><loc_86></location>path due to the feature. If we take N H (cx3) to be the column density between the observer and Cygnus X-3 then the column density along the path of the scattered photon can be written as</text>
<formula><location><page_13><loc_34><loc_75><loc_88><loc_77></location>N H (r s ) + N H (r o ) = N H (cx3) + N H (lf) . (A6)</formula>
<text><location><page_13><loc_16><loc_72><loc_75><loc_73></location>F cx3 (E) the observed absorbed flux from Cygnus X-3 can be written as</text>
<formula><location><page_13><loc_37><loc_65><loc_88><loc_69></location>F cx3 (E) = L cx3 (E)e -σ (E)N H (cx3) 4 π D 2 . (A7)</formula>
<text><location><page_13><loc_16><loc_62><loc_66><loc_64></location>Finally from the scattering geometry (see Figure 9) we have</text>
<formula><location><page_13><loc_43><loc_56><loc_88><loc_60></location>1 r s = cos( θ s -θ ) D(1 -x) . (A8)</formula>
<text><location><page_13><loc_12><loc_49><loc_88><loc_55></location>Where x is the projected distance along path between the observer and Cygnus X-3. The measure angle of the feature ( θ ) and the scattering angle ( θ s ) are related to the projected distance x by θ = (1 -x) θ s . Using the above relations we arrive a the following substitution 3</text>
<formula><location><page_13><loc_25><loc_42><loc_88><loc_46></location>L cx3 (E)e -σ (E)[N H (r s )+N H (r o )] 4 π r s 2 ≈ F cx3 (E)e -σ (E)N H (lf) cos 2 ( θ s -θ ) (1 -x) 2 . (A9)</formula>
<text><location><page_13><loc_12><loc_35><loc_88><loc_41></location>If we integrate over energy bandpass and replace F cx3 (E) by F cx3 S(E) where F cx3 represents the measured flux from Cygnus X-3 and S(E) is its spectral form (normalized to one) we can write the flux relationship of the feature to Cygnus X-3 as</text>
<formula><location><page_13><loc_23><loc_23><loc_88><loc_32></location>F lf F cx3 = π tan α 1 tan α 2 l s cos 2 ( θ s -θ ) (1 -x ) 2 × ∫ E 2 E 1 S(E)e -σ (E)N H (lf) ∫ a max a min n g (a) ( d σ s (E , a , θ s ) dΩ ) dadE . (A10)</formula>
<text><location><page_13><loc_12><loc_18><loc_98><loc_21></location>Assuming a MRN grain size distribution (Mathis, Rumpl, & Nordsieck 1977; Weingartner & Draine 2001) then we have</text>
<formula><location><page_14><loc_40><loc_80><loc_88><loc_84></location>n g (a) = n h ∑ i=g , si N i d a -3 . 5 . (A11)</formula>
<text><location><page_14><loc_12><loc_71><loc_88><loc_79></location>Where n h is the hydrogen number density of the cloud, a is the radius of the grain and N i d is are the normalization in (grains / H atom) /µ m for graphite (g) and silicates (si). If we also note that n h l s is simple the column density of the cloud N H (lf). Substituting n g (a) in A10 gives us</text>
<formula><location><page_14><loc_18><loc_57><loc_88><loc_67></location>F lf F cx3 = N H (lf) [ π tan α 1 tan α 2 cos 2 ( θ s -θ ) (1 -x) 2 ] × [ ∑ i=g , si N i d ∫ E 2 E 1 S(E)e -σ (E)N H (lf) ∫ a max a min a -3 . 5 ( d σ s (E , a , θ s ) dΩ ) dadE ] . (A12)</formula>
<section_header_level_1><location><page_14><loc_43><loc_53><loc_58><loc_54></location>REFERENCES</section_header_level_1>
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<figure>
<location><page_17><loc_12><loc_34><loc_83><loc_75></location>
<caption>Fig. 1.- Plotted are the counts/frame for the QS observation as a function of radial distance from Cygnus X-3. The solid line is for the entire observation and the dotted line is for the times of the highest count rates (Cygnus X-3 phases 0.6-0.7). The counts/frame for various levels of expected pileup are given (Davis 2007). The long dashed vertical lines is the location of the feature and the shaded region give the feature's radial extent. Pileup should not be an issue for the observations used in this analysis.</caption>
</figure>
<figure>
<location><page_18><loc_24><loc_30><loc_74><loc_68></location>
<caption>Fig. 2.- Segments of annuli centered on Cygnus X-3 were used for the feature and background regions to extract the light curve and spectrum for the feature (blue) and the background (green). The inner edge of the annuli is 11 . 2 '' from Cygnus X-3 and the outer edge is 20 . 0 '' .</caption>
</figure>
<figure>
<location><page_19><loc_15><loc_34><loc_87><loc_73></location>
<caption>Fig. 3.- Phase folded 1-8 keV light curves of Cygnus X-3, the background, and the feature from the QS observation. Top: Phased fold light curve of Cygnus X-3. The data were taken from the ± first order HEG and MEG spectra. Middle: Phase folded light curve of the background region. Bottom: Phase folded light curve of the feature from QS (background subtracted). It can clearly be seen that the feature exhibits the same slow rise and rapid drop that one sees in Cygnus X-3 but with a phase lag of ∼ 0 . 6 .</caption>
</figure>
<figure>
<location><page_20><loc_11><loc_34><loc_88><loc_74></location>
<caption>Fig. 4.Cross correlation plots: The dashed vertical line corresponds to a lag of half of Cygnus X-3's period and the dot-dashed corresponds to a lag of Cygnus X-3's period. Top: The cross correlation between Cygnus X-3 ( grating data) and the background region (1-8 keV) using 600 second time samples. Note there is no lag between them. Bottom: The cross correlation between Cygnus X-3 ( grating data) and the feature (background subtracted) using 172 second time samples ( ∼ 0.01 of Cygnus X-3's period). Note the lag of 9460 seconds which corresponds to a phase shift of ∼ 0.55.</caption>
</figure>
<figure>
<location><page_21><loc_12><loc_48><loc_46><loc_82></location>
</figure>
<figure>
<location><page_21><loc_50><loc_48><loc_84><loc_82></location>
<caption>Fig. 5.- These phase selected images were created from the zero-order image Chandra grating observation (QS) using photons with energies between 1-8 kev. The count range and color scales are identical for both images. The bright readout streak caused by the ACIS CCD readout and the 'cratering' of the central source due to pileup are both instrumental effects. left: Phase range 0.96-0.3 image. The feature is prominent. right: Phase range 0.5-0.8 image. The feature is very weak. Online electronic edition: To better visualize the phase relationship between the feature and Cygnus X-3 a movie was created. For all of the events detected in QS a Cygnus X-3 orbital phase based on their arrival time was determined. The data was filtered to only include 1-8 keV energy photons. For the image a 256 by 256 pixels region centered on Cygnus X-3 was used. A set of images were created based on phase intervals, starting at 0.0 phase and with a duration of 0.20 of Cygnus X-3's phase. Each image was successively shifted by a 0.01 of Cygnus X-3's phase until images for the full Cygnus X-3 period were created and compiled to form the movie. The duration of the observation (50 ksec) corresponds to 2.96 orbits of Cygnus X-3, so phase coverage is relatively uniform. The duration of each image (0.2 phase) corresponds to an integration time of ∼ 10 4 seconds.</caption>
</figure>
<figure>
<location><page_22><loc_14><loc_33><loc_87><loc_72></location>
<caption>Fig. 6.- Fits to the phase folded 1-8 keV light curves of the feature with no background subtraction. Top: Phase folded light curve of Cygnus X-3 (50 phase bins) with a fit to the light curve (dotted line). Middle: Data minus model fit divided by the data error bars. With ± 1 σ error bars. Bottom: The model of the phase folded light curve of the feature from the fit.</caption>
</figure>
<figure>
<location><page_23><loc_12><loc_31><loc_57><loc_76></location>
<caption>Fig. 7.- A color coded phase image of Cygnus X-3 region. Note the blue color of the feature. This indicates that bulk of the photons are arriving in the 0.96-0.3 phase range. It is also important to note that no background subtraction was done and hence there is no issue with the background subtraction creating a false time/phase variation of the feature.</caption>
</figure>
<figure>
<location><page_24><loc_16><loc_29><loc_87><loc_73></location>
<caption>Fig. 8.- Plotted is the 1 -8 keV flux of Cygnus X-3 (determined from the grating data) versus the 1 -8 keV flux of the feature for each of the ACIS observations using the scattering model. The dashed line is a linear fit to the data.</caption>
</figure>
<figure>
<location><page_25><loc_11><loc_35><loc_76><loc_79></location>
<caption>Fig. 9.Scattering Diagram Definitions: Above is shown a diagram of how the scattering is taking place with various parameters labeled. X : Location of the X-ray source (Cygnus X-3). S : Location of the feature. O : Location of the observer. D : Distance from the observer to Cygnus X-3. x : Distance to the scatter along the path to Cygnus X-3. θ : Observed angle of the feature from Cygnus X-3. θ s : The scattering angle of the X-rays from Cygnus X-3 by the feature. r s : Distance from Cygnus X-3 to the feature. r o : Distance from the feature to the observer. h : Distance from the the feature to Cygnus X-3's line of sight to the observer.</caption>
</figure>
<figure>
<location><page_26><loc_11><loc_33><loc_79><loc_70></location>
<caption>Fig. 10.- The extracted spectrum of the feature, taken from QS, is shown above. Also given is the fit (in red) and residuals of a scattering model. A good agreement is found between the data and model.</caption>
</figure>
<figure>
<location><page_27><loc_12><loc_33><loc_84><loc_75></location>
<caption>Fig. 11.- A plot of the cross correlation between the inner (11 . 2 '' to 15 . 6 '' ) and outer (15 . 6 '' to 20 . 0 '' ) regions of the feature (both background subtracted). The time resolution was 5 minutes for the light curves. The dashed horizontal lines corresponds to a 99% confidence level. The dash, dot-dash, dots-dash, and large dash vertical lines correspond to lags one would observe across the feature for n = 0, 1, 2, and 3 respectively. Note the prominent peak at ∼ 1 hour corresponding to n = 0 lag.</caption>
</figure>
<figure>
<location><page_28><loc_13><loc_32><loc_80><loc_72></location>
<caption>Fig. 12.- A plot of the phase folded light curves of the inner (solid: blue online) and outer (dotted: red online) regions of the feature (both background subtracted). There is a noticeable lag in outer relative to the inner of ∼ 0 . 2 in phase which corresponds to ∼ 1 hr in time.</caption>
</figure>
<figure>
<location><page_29><loc_14><loc_35><loc_87><loc_73></location>
<caption>Fig. 13.- Plots of last two terms and their product of the flux ratio (see equation 4) as a function of x. Top: Plot of the solid angle term which is a measure of the flux the feature intercepts. Middle: Plot is of the scattering terms which takes into account what fraction of the X-ray flux is scattered to the observer. The solid lines is for silicates scatters and the dotted line is for graphite scatters. Bottom: This final plot is the product of the solid angle term with the sum of the two scattering terms.</caption>
</figure>
<figure>
<location><page_30><loc_13><loc_35><loc_80><loc_74></location>
<caption>Fig. 14.- A plot of the scattering column density necessary to produce the observed feature/Cygnus X-3 flux ratio (see equation 4) vs x. The vertical line (large dashes) is location for the feature determined from the time delay. The horizontal dashed lines represent the scattering column density determined from spectral fit and the shaded region between the dashed-dotted lines represent it uncertainties. We find good agreement between values found for the flux ratio and the spectra fit.</caption>
</figure>
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<text><location><page_31><loc_25><loc_27><loc_27><loc_28></location>7</text>
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<text><location><page_31><loc_29><loc_27><loc_31><loc_28></location>3</text>
<text><location><page_31><loc_29><loc_27><loc_31><loc_27></location>5</text>
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<text><location><page_31><loc_59><loc_41><loc_61><loc_42></location>x</text>
<text><location><page_31><loc_59><loc_34><loc_61><loc_35></location>a</text>
<text><location><page_31><loc_59><loc_33><loc_61><loc_34></location>in</text>
<text><location><page_31><loc_59><loc_32><loc_61><loc_32></location>e</text>
<text><location><page_31><loc_59><loc_31><loc_61><loc_32></location>n</text>
<text><location><page_31><loc_59><loc_31><loc_61><loc_31></location>o</text>
<text><location><page_31><loc_59><loc_30><loc_61><loc_31></location>d</text>
<text><location><page_31><loc_59><loc_29><loc_61><loc_29></location>e</text>
<text><location><page_31><loc_59><loc_28><loc_61><loc_29></location>r</text>
<text><location><page_31><loc_59><loc_28><loc_61><loc_28></location>e</text>
<text><location><page_31><loc_59><loc_27><loc_61><loc_28></location>w</text>
<text><location><page_31><loc_59><loc_26><loc_61><loc_27></location>6</text>
<text><location><page_31><loc_59><loc_25><loc_61><loc_26></location>2</text>
<text><location><page_31><loc_59><loc_25><loc_61><loc_25></location>4</text>
<text><location><page_31><loc_59><loc_23><loc_61><loc_24></location>d</text>
<text><location><page_31><loc_59><loc_23><loc_61><loc_23></location>n</text>
<text><location><page_31><loc_59><loc_22><loc_61><loc_23></location>a</text>
<text><location><page_31><loc_59><loc_21><loc_61><loc_22></location>5</text>
<text><location><page_31><loc_59><loc_20><loc_61><loc_21></location>2</text>
<text><location><page_31><loc_59><loc_20><loc_61><loc_20></location>4</text>
<text><location><page_31><loc_59><loc_19><loc_61><loc_19></location>s</text>
<text><location><page_31><loc_59><loc_18><loc_61><loc_19></location>id</text>
<text><location><page_31><loc_59><loc_17><loc_61><loc_18></location>s</text>
<text><location><page_31><loc_59><loc_17><loc_61><loc_17></location>b</text>
<text><location><page_31><loc_59><loc_16><loc_61><loc_17></location>O</text>
<text><location><page_31><loc_59><loc_15><loc_60><loc_16></location>c</text>
<text><location><page_31><loc_61><loc_61><loc_63><loc_62></location>v</text>
<text><location><page_31><loc_61><loc_61><loc_63><loc_61></location>r</text>
<text><location><page_31><loc_61><loc_60><loc_63><loc_61></location>e</text>
<text><location><page_31><loc_61><loc_59><loc_63><loc_60></location>s</text>
<text><location><page_31><loc_61><loc_59><loc_63><loc_59></location>b</text>
<text><location><page_31><loc_61><loc_58><loc_63><loc_59></location>o</text>
<text><location><page_31><loc_61><loc_50><loc_63><loc_51></location>a</text>
<text><location><page_31><loc_54><loc_82><loc_55><loc_82></location>e</text>
<text><location><page_31><loc_54><loc_81><loc_55><loc_82></location>h</text>
<text><location><page_31><loc_54><loc_81><loc_55><loc_81></location>t</text>
<text><location><page_31><loc_63><loc_22><loc_65><loc_22></location>.</text>
<text><location><page_31><loc_63><loc_21><loc_65><loc_22></location>d</text>
<text><location><page_31><loc_63><loc_21><loc_65><loc_21></location>e</text>
<text><location><page_31><loc_63><loc_20><loc_65><loc_21></location>s</text>
<text><location><page_31><loc_63><loc_19><loc_65><loc_20></location>u</text>
<text><location><page_31><loc_63><loc_18><loc_65><loc_19></location>e</text>
<text><location><page_31><loc_63><loc_18><loc_65><loc_18></location>r</text>
<text><location><page_31><loc_63><loc_17><loc_65><loc_18></location>e</text>
<text><location><page_31><loc_63><loc_16><loc_65><loc_17></location>w</text>
<text><location><page_31><loc_63><loc_16><loc_65><loc_16></location>)</text>
<text><location><page_31><loc_63><loc_15><loc_65><loc_16></location>c</text>
<text><location><page_31><loc_63><loc_14><loc_65><loc_15></location>e</text>
<text><location><page_31><loc_63><loc_14><loc_65><loc_14></location>s</text>
<table>
<location><page_32><loc_22><loc_41><loc_78><loc_66></location>
<caption>Table 2. Phase Folded Light Curve Fitting Parameters</caption>
</table>
<text><location><page_32><loc_22><loc_29><loc_78><loc_36></location>Note. - The Phase shifted model is the one give in Equation 1. The Constant model is the same as the Phase shifted model except that the shift term has been replaced with a constant which is used as a fit parameter.</text>
<table>
<location><page_33><loc_12><loc_37><loc_90><loc_65></location>
<caption>Table 3. Spectral Fit Parameters for the Feature</caption>
</table>
<table>
<location><page_34><loc_12><loc_62><loc_91><loc_81></location>
<caption>Table 4. Continuum Spectral Fit Parameters for Cygnus X-3</caption>
</table>
<text><location><page_34><loc_12><loc_52><loc_91><loc_58></location>Note. - The Chandra grating spectral are rich in spectral features (Paerels et al. 2000). To achieve acceptable fits we included a large number of spectral features (emission lines, absorption lines, edges, and radiative recombination continuum).</text>
<text><location><page_34><loc_14><loc_49><loc_42><loc_51></location>a Temperature of a disk blackbody.</text>
<text><location><page_34><loc_14><loc_46><loc_60><loc_48></location>b Measured flux in ergs sec -1 cm -2 in the 1-8 keV band.</text>
<table>
<location><page_34><loc_14><loc_20><loc_86><loc_36></location>
<caption>Table 5. Spectral Fit Parameters for Scattering Model for the Feature</caption>
</table>
<table>
<location><page_35><loc_18><loc_33><loc_82><loc_66></location>
<caption>Table 6. Scattering Flux Calculation Parameters</caption>
</table>
<text><location><page_35><loc_20><loc_29><loc_82><loc_30></location>a The dust grain parameters were taken from Weingartner & Draine (2001).</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Using the unique X-ray imaging capabilities of the Chandra observatory, a 2006 observation of Cygnus X-3 has provided insight into a singular feature associated with this well-known microquasar. This extended emission, located ∼ 16 '' from Cygnus X-3, varies in flux and orbital phase (shifted by 0.56 in phase) with Cygnus X-3, acting like a celestial X-ray 'mirror'. The feature's spectrum, flux and time variations allow us to determine the location, size, density, and mass of the scatterer. We find that the scatterer is a Bok globule located along our line of sight, and discuss its relationship to Cygnus X-3. This is the first time such a feature has been identified with the Chandra X-ray Observatory. Subject headings: X-rays: binaries - X-rays: individual(Cygnus X-3) - X-rays: ISM",
"pages": [
1
]
},
{
"title": "Cygnus X-3's Little Friend",
"content": "M. L. McCollough and R. K. Smith Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA 02138, U.S.A.",
"pages": [
1
]
},
{
"title": "[email protected]",
"content": "and L. A. Valencic Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "At a distance of 9 kpc (Predehl et al. 2000), Cygnus X-3 is an unusual microquasar in which a Wolf-Rayet companion (van Kerkwijk et al. 1992) orbits a compact object with an orbital period of 4.8 hours. It is a strong radio source routinely producing radio flares of 1 to ∼ 20 Jy (Waltman et al. 1995). It has been shown to produce radio jets and the radio emission correlates with both the soft X-ray and hard X-ray emissions (Mioduszewski et al. 2001; Miller-Jones et al. 2004; Szostek et al. 2008; McCollough et al. 1999). In 2000 Chandra observations found extended X-ray emission that is believed to be associated with Cygnus X-3 (Heindl et al. 2003). In this paper we analyze a 2006 Chandra observations of Cygnus X-3 and reexamine the previous Chandra observations discussed in Heindl et al. (2003). In particular we take a careful look at the timing and spectral properties of the extended feature and how they related to Cygnus X-3.",
"pages": [
1,
2
]
},
{
"title": "2. Observations and Analysis",
"content": "Between 1999-2006 Cygnus X-3 was observed six times by Chandra using the ACISS/HETG with a Timed Event (TE) mode and covered a range of source activity (see Table 1). These observations provided grating spectra of Cygnus X-3 and on-axis zero order images which allow for spatial and spectral analysis of Cygnus X-3 and its surroundings. The primary observation used for this analysis was a 50 ksec quenched state observation (OBSID: 6601 hereafter referred to as QS) obtained during a period of high X-ray activity. At the time of the observation the RXTE/ASM (2-12 keV) count rates were ∼ 25 -30 cts s -1 , Swift/BAT (15-50 keV) had an average count rate of ∼ 0 . 0 cts s -1 , and the Ryle radio telescope (15 GHz) showed radio fluxes of ∼ 1 mJy, all values typical of a Cygnus X-3 quenched state (Szostek et al. 2008; McCollough et al. 1999; Waltman et al. 1996). This observation has the longest duration of any of the observations and the feature has the greatest number of photons of any of the observations. Since this analysis involves a region near a bright point source we also need to determine the impacts of pileup on the data. This can be determined by looking at the average number of counts per detection island (9 pixels region: see the Chandra POG (2011)) per observing frame. We do this by taking a series of annuli centered on Cygnus X-3 for the highest count rate observation (QS). Each annulus has a radial thickness of 2 ACIS pixels ( ∼ 1 '' ) with the readout streak regions excluded. We then sum the counts in each annulus and divide by the number of observation frames 1 and the of number detection islands (the area of the annulus in pixels divided by 9 pixels). In Figure 1 is a plot of counts/frame as a function of radial distance from Cygnus X-3, with the solid line represents the entire observation and the dotted line the times of peak count rate. From Davis (2007) we have taken the counts/frame values for which one would expected pileup of 1% , 5%, and 10% and plotted them in Figure 1. We see that at radial distance of greater than ∼ 8 '' pileup should not be an issue and will not impact our analysis. In our analysis of these observations, we used version 4.3 of the CIAO tools. The Chandra data retrieved from the archive were processed with ASCDS version 7.7.6 or higher. All event files were filter by their good times intervals and barycenter corrected using the CIAO tool axbary .",
"pages": [
2,
3
]
},
{
"title": "2.1. The Feature and its Characteristics",
"content": "For each observation, we have extracted a zeroth-order image between 1 -8 keV binned at the nominal ACIS-S resolution ( ∼ 0 . 49 '' ). Figure 2 and 5 shows images for the QS observation. In each individual image, there is a bright, unresolved core with strong radial point-spread function (PSF) wings and a strong scattering halo (Predehl et al. 2000). In each observation the feature reported by Heindl et al. (2003) is present at the same location. An analysis of the QS observation shows the feature (RA : 20 h 32 m 27 . 1 s , DEC : +40 · 57 ' 33 . 8 '' ) lies at an angular distance of 15 . 6 '' from Cygnus X-3 at an angle of 68 . 5 · from the orientation of the observed radio jets of Cygnus X-3. The feature is extended and was fit using CIAO/SHERPA with a 2D-Gaussian with axes of 3 . 6 '' and 5 . 5 '' and a position angle of 78 . 7 · , measured counterclockwise with the top of the image being 0 · . If the feature and Cygnus X-3 are at the same distance, then their separation is 2 . 2 D 9 light-years (D 9 : distance in units of 9 kpc). This feature is present in all observations of Cygnus X-3 done throughout the Chandra mission (1999 to present).",
"pages": [
3
]
},
{
"title": "2.2. Temporal Behavior",
"content": "The feature is located amidst a high background region. This high background is due to the telescope PSF and a dust scattering halo. The majority of the photons in the background have energies above 2 keV and as such arise from scattering off micro-roughness in the telescope optics; see the discussion in Predehl et al. (2000). In order to examine the temporal variability of the feature we need to subtract the background flux from region of feature. To do this we used segments of annuli centered on Cygnus X-3 for the feature and background regions to extract the light curve for the feature and the background (see Figure 2). The annuli were chosen to maximize the number of counts for the feature as well as have the feature and background regions sample the same radial region of the PSF/dust halo while avoiding the readout streaks. All data extraction was done with the CIAO tool dmextract .",
"pages": [
3,
4
]
},
{
"title": "2.2.1. Phase Folded Analysis",
"content": "The phase-folded (1-8 keV) light curves of Cygnus X-3, the background region, and background subtracted feature region are shown in Figure 3. As might be expected the background which is mainly due to the scattered PSF emission demonstrates the same 4.79 hr orbital variation with the slow rise and rapid observed drop in Cygnus X-3. This is also reinforced in Figure 4 (top panel) which show no observed lag in the cross-correlation between Cygnus X-3 and the background. However, the feature surprisingly shows the same orbital modulation but with a phase shift of ∼ 0.6 . Phase-selected images reveal how this feature varies relative to Cygnus X-3 (see Figure 5), which can be seen more dramatically in the movie which accompanies this paper (see online version). This is also confirmed in the cross-correlation between Cygnus X-3 and the feature seen in Figure 4 (lower panel) which show a clear lag that peaks around 9460 seconds which corresponds to a phase lag of ∼ 0.55. Fitting Phase Folded Light Curves: To address questions of a possible issues with background subtraction (over-subtraction) we took the light curve from feature annulus and fit it using the following model: Where C lf [i] is the count rate for the feature's region in phase bin i, C bkgd [i] is the count rate from background region (scaled to the feature's region size) in phase bin i, and the last term a ∗ C bkgd [shift(i , j)] is the count rate of the background region scaled by a and shifted by j in phase. The fit parameters are a and j. We used the IDL routine MPFIT (Markwardt 2008) to fit the light curve. We did multiple fits of the light curve using a number of different phase binnings and found good fits for all binnings with consistent fit values (see Table 2). Our best fit a gave a = 0 . 29 ± 0 . 01 and phase shift(j) = 0 . 56 ± 0 . 02 (see Figure 6). As a further test we replaced the second term in Equation 1 with a constant term which was used as a fit parameter. We found no acceptable fits for any of the binnings (see Table 2). This result is consistent with the feature varying with the same period as Cygnus X-3 but shifted in phase. Phase Image: Finally, as another way to check to see if background subtraction could be an issue for each Chandra detected event, a 'Cygnus X-3' phase value was determined from its arrival time. Photons falling into certain phase ranges were broken in separate 'phase' images. These images were assigned a certain color and combined to form a color coded phase image. The bands were: (red) 0.3-0.63 , (green) 0.63-0.96 , and (blue) 0.96-0.3 . The image is shown in Figure 7, note the blue color of the feature. This indicates that bulk of the photons are arriving in the 0.96-0.3 phase range. If the feature was constant we would expect it to be white (equal amounts of each color). It is also important to note that no background subtraction was done in this approach and hence there is no issue with the background subtraction creating a false time/phase variation of the feature.",
"pages": [
4,
5
]
},
{
"title": "2.2.2. Longer timescale Variability",
"content": "To examine the temporal behavior of the feature on longer timescales we determined the flux 2 of Cygnus X-3 and the feature for each of the Chandra /ACIS observations (see Table 1). When Cygnus X-3's flux is plotted versus the flux from the feature there appears to be a correlation (see Figure 8) where the dashed line is a linear fit to the data. A Pearson's correlation test of the data yields a correlation coefficient of 0.98 indicating a linear correlation between the feature and Cygnus X-3.",
"pages": [
5
]
},
{
"title": "2.3. Spectrum",
"content": "The annuli used to extract the light curves (see Figure 2) were also used to extract spectra for the feature and background region. The final background-subtracted spectra of the feature contained from 78 to 3216 counts in the 1-8 keV band. Table 3 shows fits to the spectrum using simple absorbed power law and blackbody models all of which yield acceptable fits to the spectrum. All of the Chandra /ACIS observations were HETG grating observations. The ± first order HEG spectra were combined and fit for each observation (see notes in Table 1). The continuum for Cygnus X-3 is complex and dependent on the state of activity (Hjalmarsdotter et al. 2008, 2009; Koljonen et al. 2010). In the X-ray (0.5-10 keV) the continuum can be modeled by partial covered disk blackbody during flaring/quenched states (Koljonen et al. 2010) and during the quiescence/transition states we found that continuum was best approximated by an absorbed power law. In all cases a large number of spectral features were added (see Table 4) to improve the spectral fit. We note that all of the spectra of the feature are more absorbed and very steep/soft, relative to the corresponding Cygnus X-3 spectra (see Table 3 & 4). As Cygnus X-3 transitions from a quiescent (hard state) to flaring/quenched state (soft state) its spectrum becomes softer. The spectrum of the feature is shown to follow suit and becomes steeper/softer as Cygnus X-3's spectrum does.",
"pages": [
5,
6
]
},
{
"title": "3. Nature of the Feature",
"content": "To understand the feature's nature the following must be explained: (a) it is clearly extended; (b) its flux varies in phase with Cygnus X-3 with a phase shift of 0.56; (c) the flux from the feature shows a correlation with the flux from Cygnus X-3; (d) the phase-averaged flux of the feature is ∼ 10 -3 of Cygnus X-3's flux; (e) the time variation is 4.8 hrs but the separation between the feature and Cygnus X-3 is at least 2 . 2 D 9 light-years; and (f) its spectrum is heavily absorbed and lacks hard X-ray flux relative to Cygnus X-3. Jet Emission: It is natural to try to associate this feature with the Cygnus X-3 jet emission. However, Cygnus X-3 was in a quenched state throughout the Chandra observation and for several days before and after, during which jet activity is strongly suppressed. Additionally, over a three year period prior to this observations Ryle/AMI-LA observed no radio flare exceeding 0.5 Jy (Pooley 2011). Furthermore, in earlier Chandra observations where there is jet activity, the feature is fainter. If the X-ray emission of the feature was due to the jet one would expect this to be synchrotron emission and one would not generally expect the spectrum to be so steep and heavily absorbed. Also the misalignment of the feature relative to the jets observed in the radio complicates this picture. Jet Impact Area: Problems with this being a jet impact area have been noted by Heindl et al. (2003) (location relative to the radio jets, jet precession, and jet collimation). In addition the observed flux correlation between the feature and Cygnus X-3 provides problems given a likely separation of 2 . 2 D 9 light years. The strong phase modulation of the feature (varying the same as Cygnus X-3 by a factor of two), combined with a periodicity exactly matching that of Cygnus X-3, would be difficult to understand. One would expect the continuing impact of the jet would give rise to a brighter constant flux from the feature and drastically reduce the modulation which is observed. Wind Interaction: The strongest arguments which were made by Heindl et al. (2003) for the feature's nature is that it is due to a wind/ISM interaction. The feature's distance, flux correlation and phase modulation with Cygnus X-3 make such a model difficult to reconcile with the observations. In this interpretation the feature is created over timescales that are long ( ∼ 2000 years) compared to the observed orbital modulation. Also the direct change in the flux of the feature with Cygnus X-3 flux is difficult to reconcile with such a model.",
"pages": [
6,
7
]
},
{
"title": "3.1. Scattering Solution",
"content": "A natural explanation for the feature's time variable behavior is that it is a result of scattering from a cloud (which acts as a kind of interstellar X-ray 'mirror') between Cygnus X-3 and the observer. This explanation would naturally lead to the observed phase difference between light curves as a difference in the path length of the scattered photons (Trumpler & Schonfelder 1973). This could also explain the flux correlation (see Figure 8) and overall flux difference ( ∼ 10 -3 ) since only a small fraction of the total flux will be scattered toward the observer. In figure 9 a diagram of the expected geometry for the scattering from a cloud is shown. The spectrum of the feature can also be modeled as a scattered version of Cygnus X-3's spectrum. At these energies scattering will modify the spectrum by A ∗ E -2 (Smith et al. 2002), due to the reduced scattering efficiency at higher energies (Overbeck 1965). There will also be an additional reduction at low energies caused by absorption in the cloud (N cl ) and multiple scattering. We can then model the feature's spectrum as due to scattering as Where S lf is the scattering model for the feature, e -σ (E)N H (lf) is the additional absorption due to the cloud (modeled using phabs in XSPEC), A ∗ E -α represents the high energy attenuation due to scattering (modeled using plabs from XSPEC), and S cont is Cygnus X-3 continuum model determined from the grating data (see Table 4). The resulting fit parameters for the observations are shown in Table 5 and the fit to the QS observation's spectrum is shown in Figure 10. The resultant fluxes (1 -8 keV) for the feature and Cygnus X-3 are given in Tables 4 & 5. The flux ratio of the feature to Cygnus X-3 are all in the range of (4 -6) × 10 -4 . This gives rise to a natural explanation of the observed spectral differences. The loss of the flux below 2 keV is the result of additional absorption in the cloud and the reduced flux at higher energy simply reflects the drop in scattering efficiency. Distance to and Size of the Feature: Assuming that this feature is due to an individual cloud the time delay is determined by the distance to the cloud (Trumpler & Schonfelder 1973; Predehl & Klose 1996; Predehl et al. 2000). The resulting time delay can be written as: Where ∆t is the time delay (in seconds), D is the distance (in kpc) to the source, Θ is observed angular distance (in arcsec) from the source, x is the fractional distance of the scatter to the observer (see Figure 9), and c is the speed of light. From the observed phase observed phase offset, we know that time delay is given by ∆t = (0 . 56 + n)t cx3 where t cx3 = 17 . 25 ksec is the observed orbital period of Cygnus X-3, but we have an ambiguity in the total number orbital period offsets (n). Using ∆t = 0 . 56 ∗ t cx3 = 9 . 66 ksec , D = 9 kpc, and Θ = 15 . 6 '' , the resulting fractional distance is x = 0.79. This means that the cloud is close to Cygnus X-3 (within 1.9 kpc) and if n > 0, this distance could be less. This degeneracy (n) can be removed using the fact that the feature is extended. From equation (3) we would expect that the delay scattered photons experience increases as a function of angle from Cygnus X-3. If we take the inner and outer edges of the feature to be 13 . 8 '' and 17 . 4 '' respectively then for x = 0.79 we would get a time delay of ∼ 1 . 2 hrs across the feature. For locations closer to Cygnus X-3 we would expect the delay across the feature to increase. To test this we have taken the extraction and background annuli (see Figure 2) and divided into an inner and outer set of annuli (11 . 2 '' to 15 . 6 '' and 15 . 6 '' to 20 . 0 '' respectively). In Figure 11 we show a cross correlation of the inner and outer light curves (for the QS observation with 5 minute time resolution) which shows a significant lag (at the 99 % confidence level) at 0 . 9 hrs. This would correspond to the n = 0 case. In Figure 12 are the phase folded light curves of the inner and outer region in which one can see that the light curve for the outer region is lagging the inner by ∼ 0 . 2 in phase. This corresponds to a lag of ∼ 1 hr. This puts the feature at a distance of 1.9 kpc from Cygnus X-3 making the observed dimensions of the feature 0.12 by 0.19 parsecs. Density of the Cloud: From the spectral fit to the feature for the QS observations we have an absorbing column density of the feature of 5 . 0 +2 . 0 -1 . 7 × 10 22 cm -2 . This value is consistent with column density determined from spectral fits to the other observations (see Table 5). The column density of the feature can also be estimated from the flux ratio of the feature to Cygnus X-3 using the following relationship (see Appendix A for derivation) The flux ratio is equal to the product of three quantities. The first (N H (lf)) is the column density of the feature, the second is a solid angle term which relates to what fraction of Cygnus X-3's flux is intercepted by the feature, and final term is a scattering term which is a measure of the flux scattered by the dust in the cloud (this is solved for by numerical integration over the energy range and grain distribution). The last two terms are depend on x, the fractional distance between the observer and Cygnus X-3. Figure 13 shows a plot of the last two terms and their product as function of x. The solid line is for scattering due to silicates and the dotted line for scattering due to graphite. Equation 4 can be solved for the column density of the feature as a function of x as is shown in Figure 14. The parameters used to create these curves are given in Table 6. Also included are lines representing the column density from the spectral fit of QS with its uncertainties and a vertical line representing its location from the observed time delay. What we find is good agreement with the column density determined from the spectral fits and the column density (N lf = 3 . 6 × 10 22 cm -2 ) necessary to produce the observed flux ratio. If we assume that path-length along the line-of-sight through the cloud is similar to the observed dimensions of the feature [(3 . 7 -5 . 9) × 10 17 cm] we can make an estimate of the density of the feature. Taking the column density to be 5 . 0 +2 . 0 -1 . 7 × 10 22 cm -2 we arrive at a density range of (0 . 6 -1 . 9) × 10 5 cm -3 making the feature a dense molecular cloud. Mass of the Cloud: From the estimate of the density of the cloud and the size determined from the X-ray measurements we can make an estimate of the mass of the cloud. Using the simplifying assumption of a spherical cloud with a diameter of between 0 . 12 -0 . 19 pc with a density of 10 5 cm -3 we arrive, from X-ray observations alone, at an estimate of the mass of the cloud to be 2 -24 M /circledot . From the cloud's size, density, and mass the feature has all of the characteristics of a Bok Globule (Bok & Reilly 1947; Clemens et al. 1991), but instead of seeing this as a dark obscuring feature in the optical we see it shining in scattered X-rays.",
"pages": [
7,
8,
9
]
},
{
"title": "4. Relationship to Cygnus X-3",
"content": "What is the relationship of this feature to Cygnus X-3? Three possibilities present themselves: (l ii = 79 . 845 · , b ii = 0 . 700 · ). The Cygnus X region that hosts Cygnus X-3 is rich in molecular clouds (Schneider et al. 2006). So this may be just a chance alignment. If so this gives us insight into the nature and structure of molecular clouds in the ISM. In this case we would be looking across three Galactic arms (with Cygnus X near the Local Spur, the feature in the Perseus arm at ∼ 5 kpc, and Cygnus X-3 in the Outer Arm at 7 -9 kpc). Bringing Cygnus X-3 closer, to 7 kpc, does not greatly change the distance estimate to the feature or the need for three star forming regions along the line of sight. (3) Microquasar Jet-Inflated Bubble : Within NGC 7793 a powerful microquasar is driving a 300 pc jet-inflated bubble (Pakull et al. 2010). Cygnus X-3 is a microquasar whose jets appear to be aimed along our line of sight (Mioduszewski et al. 2001; Miller-Jones et al. 2004). It is possible that rapid cooling near the working surface of the jet, in the shell of the cocoon, may allow a dense molecular cloud to form. This would explain the nature of the feature as well as its alignment with Cygnus X-3. Although it should be noted that there is research which suggest that the jet may not be close to the line of sight (Mart'ı, Paredes & Peracaula 2001), which would make this a less likely option. Finally it should be noted that a combination of both (2) and (3) may be possible. The radiation and outflows from the OB association may create a large low density cavity in which the microquasar jet can more easily propagate. Evidence for large-scale cavities surrounding other microquasars has been noted (Hao & Zhang 2009). This could explain the large distance of the feature from Cygnus X-3 (1.9 kpc) and reduce the energetics necessary to produce it. The feature may be located at the place where jet interacts which the wall of the cavity.",
"pages": [
9,
10
]
},
{
"title": "5. Conclusion",
"content": "This feature and its temporal relationship to Cygnus X-3 have unveiled the unique interaction between a microquasar and its environment. It has given us a tool to probe the nature and structure of molecular clouds, providing information on their size and shape, possibly due to the microquasar interaction or the presence of ordered magnetic fields in the ISM. It has also given us our first X-ray view of a Bok Globule. To date this is the first such feature found with Chandra . If the feature is indeed due to a microquasar interacting with its environment then we would expect there to be very few. This would be due to the limits of small angle scattering in the X-ray and the need for the lobes and associated molecular clouds to be aligned close to our line of sight. Depending on the nature of these sources the best candidates would be high mass X-ray binaries (because of their young age and hence likely relationship with an OB association and star forming regions) with a relatively short orbital periods.",
"pages": [
10,
11
]
},
{
"title": "6. Acknowledgments",
"content": "MLM wishes to acknowledge support from NASA under grant/contract G06-7031X and NAS8-03060. MLM would also like to acknowledge the useful discussions with Ramesh Narayan concerning the scattering path through and interactions with interstellar clouds. We wish to thank the referee for the helpful comments and suggestions. This research has made use of data obtained from the Chandra Data Archive and software provided by the Chandra X-ray Center (CXC).",
"pages": [
11
]
},
{
"title": "A. Derivation of Scattering Relations for Cygnus X-3's and the Feature",
"content": "It is possible to derive some of the scatter's properties by comparison of the fluxes of Cygnus X-3 and the feature. This derivation is similar to that done for the scattering halo intensity of Smith & Dwek (1998). The geometry being used can be found in Figure 9. If we take the unabsorbed luminosity of Cygnus X-3 as a function of energy to be L cx3 (E) then the X-ray luminosity at the feature is given by Where σ (E) is the X-ray absorption cross section, N H (r s ) is column density along the path (r s ) between Cygnus X-3 and the cloud. The photons scattered into a solid angle dΩ by a single scatter for a source of luminosity L s (E) is given by Where d σ s / dΩ is the differential scattering cross section (see Mathis & Lee (1991); Mauche & Gorenstein (1986)). For a telescope with collecting area A ' we can chose dΩ such that A ' = r o 2 dΩ, where r o is the distance from the scatter to the observer. The photon count rate that the observer will detect from scattering from a single dust particle as Where N H (r o ) is the column density between the scatter and the observer. The feature has been fit with an elliptical Gaussian with semi-major and semi-minor axes of r 1 and r 2 respectively. For a distance of xD one can use the angular measurements of the semi-major and semi-minor axes, α 1 and α 2 respectively, to give the surface area of the feature as A lf = π r 1 r 2 = π x 2 D 2 tan α 1 tan α 2 . For a scattering region thickness of l s the scattering volume of the feature is given by V lf = A lf l s . For a dust grain number density of n g we can determine the total count rate and flux for the feature as In general n g will be a function of dust radius a. For our case we will consider n g to be uniform spatially at the location of the feature. Integrating over the dust size distribution gives the flux for the feature as We can simplify the above equation by noting that the observed angle θ for the feature is very small and the overall angular dimensions ( α 1 and α 2 ) of the feature are small. In this case the path traveled by the scattered photon will be very close to the path traveled by the unscattered photon. Because of this the total hydrogen column density for both paths should be the same except for the additional column density of N H (lf) along the scattered path due to the feature. If we take N H (cx3) to be the column density between the observer and Cygnus X-3 then the column density along the path of the scattered photon can be written as F cx3 (E) the observed absorbed flux from Cygnus X-3 can be written as Finally from the scattering geometry (see Figure 9) we have Where x is the projected distance along path between the observer and Cygnus X-3. The measure angle of the feature ( θ ) and the scattering angle ( θ s ) are related to the projected distance x by θ = (1 -x) θ s . Using the above relations we arrive a the following substitution 3 If we integrate over energy bandpass and replace F cx3 (E) by F cx3 S(E) where F cx3 represents the measured flux from Cygnus X-3 and S(E) is its spectral form (normalized to one) we can write the flux relationship of the feature to Cygnus X-3 as Assuming a MRN grain size distribution (Mathis, Rumpl, & Nordsieck 1977; Weingartner & Draine 2001) then we have Where n h is the hydrogen number density of the cloud, a is the radius of the grain and N i d is are the normalization in (grains / H atom) /µ m for graphite (g) and silicates (si). If we also note that n h l s is simple the column density of the cloud N H (lf). Substituting n g (a) in A10 gives us",
"pages": [
11,
12,
13,
14
]
},
{
"title": "REFERENCES",
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"pages": [
14,
15,
16,
31,
32,
34,
35
]
}
]
2013ApJ...762..132H
https://arxiv.org/pdf/1209.4602.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_81><loc_84><loc_85></location>Solar wave-field simulation for testing prospects of helioseismic measurements of deep meridional flows</section_header_level_1>
<text><location><page_1><loc_30><loc_76><loc_65><loc_77></location>T. Hartlep, J. Zhao, and A.G. Kosovichev</text>
<text><location><page_1><loc_16><loc_73><loc_80><loc_76></location>W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA, USA and</text>
<section_header_level_1><location><page_1><loc_42><loc_69><loc_54><loc_70></location>N.N. Mansour</section_header_level_1>
<text><location><page_1><loc_28><loc_67><loc_67><loc_68></location>NASA Ames Research Center, Moffett Field, CA, USA</text>
<section_header_level_1><location><page_1><loc_41><loc_60><loc_54><loc_61></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_13><loc_42><loc_82><loc_59></location>The meridional flow in the Sun is an axisymmetric flow that is generally poleward directed at the surface, and is presumed to be of fundamental importance in the generation and transport of magnetic fields. Its true shape and strength, however, is debated. We present a numerical simulation of helioseismic wave propagation in the whole solar interior in the presence of a prescribed, stationary, single-cell, deep meridional circulation serving as a test-bed for helioseismic measurement techniques. A deep-focusing time-distance helioseismology technique is applied to the artificial data showing that it can in fact be used to measure the effects of the meridional flow very deep in the solar convection zone. It is shown that the ray-approximation which is commonly used for interpretation of helioseismology measurements remains a reasonable approximation even for the very long distances between 12 · and 42 · corresponding to depths between 52 and 195 Mm considered here. From the measurement noise we extrapolate that on the order of a full solar cycle may be needed to probe the flow all the way to the base of the convection zone.</text>
<text><location><page_1><loc_13><loc_39><loc_74><loc_40></location>Subject headings: Methods: numerical, Sun: helioseismology, Sun: interior, Sun: oscillations</text>
<section_header_level_1><location><page_1><loc_9><loc_37><loc_35><loc_38></location>1. Motivation and Objectives</section_header_level_1>
<text><location><page_1><loc_9><loc_17><loc_45><loc_35></location>The meridional circulation is known as a poleward flow near the solar surface and is believed to be an important part of the dynamo process in the solar convection zone. Its true strength and shape in the deeper interior is presently unknown or at least highly debated. There are conflicting theories and observational evidences. On the one hand, theoretical works (e.g., Kitchatinov & Rudiger 2005) usually favor deep meridional flows. Due to mass conservation, the return flow then is relatively strong with flow velocities of the similar same order as the flow near the surface.</text>
<text><location><page_1><loc_9><loc_11><loc_45><loc_17></location>On the other hand, observational evidence points towards a shallow meridional flow. MitraKraev & Thompson (2007) measured p -mode frequency shifts from three months of SOHO/MDI</text>
<text><location><page_1><loc_51><loc_20><loc_86><loc_38></location>data and inferred a meridional flow that reverses at a depth of about 40 Mm. They also find evidence of a possible second reversal deeper below. Hathaway (2011) uses the advection of convection cells by the meridional circulation to measure the flow velocity at depth and finds a return flow starting at a depth of only 35 Mm. Other techniques, such as time-distance helioseismology have also been used to measure the meridional flow (e.g., Giles et al. 1998; Chou & Dai 2001; Zhao & Kosovichev 2004; Zhao et al. 2012) but primarily for small depths.</text>
<text><location><page_1><loc_51><loc_11><loc_86><loc_19></location>The goal of this work was to numerically simulate the propagation of helioseismic waves in the Sun in the presence of meridional and other large scale flows, and to use the artificial data from such simulations to evaluate the possibility of measuring small flows very deep in the Sun, in particular</text>
<text><location><page_2><loc_9><loc_56><loc_45><loc_86></location>using time-distance helioseismology. There have been previous works that addressed the measurability of deep meridional flows in the Sun such as Braun & Birch (2008). They concluded that as much observations as a full solar cycle may be needed to resolved flows near the base of the solar convection zone using the helioseismic holography technique. Various models of meridional flows have been proposed, and for this paper we have performed a numerical simulation of the solar acoustic wave field for a global-Sun model which included a meridional circulation with a deep return flow, and have performed time-distance helioseismology measurements for this model as if it were observational data. We compare the measurements with the predictions of the ray-path helioseismology theory and estimate the noise level due to the stochastic nature of solar oscillations, and the sensitivity of the helioseismology technique.</text>
<section_header_level_1><location><page_2><loc_9><loc_53><loc_31><loc_54></location>2. Numerical Simulation</section_header_level_1>
<section_header_level_1><location><page_2><loc_9><loc_51><loc_28><loc_52></location>2.1. Simulation Code</section_header_level_1>
<text><location><page_2><loc_9><loc_24><loc_45><loc_49></location>We have built a numerical code that solves the linearized propagation of helioseismic waves throughout the entire solar interior in the presence of a background structure and flow model (Hartlep & Mansour 2005). This code has been used in previous studies to simulate the effects of localized sound speed perturbations, e.g., for testing helioseismic far-side imaging by simulating the effects of model sunspots on the acoustic field (Hartlep et al. 2008; Ilonidis et al. 2009), for validating time - distance helioseismic measurements of tachocline perturbations (Zhao et al. 2009), and for studying the effects of localized subsurface perturbations (Hartlep et al. 2011). For the present case, the code has been extended to include the effects that mass flows have on the propagation of helioseismic waves.</text>
<text><location><page_2><loc_9><loc_13><loc_45><loc_23></location>The simulation code models solar acoustic oscillations in a spherical domain using the Euler equations linearized around a stationary background state characterized by the background density, ρ 0 , mass flows velocity, v 0 , sound speed, c 0 , and acceleration due to gravity, g 0 . The equations derived for the perturbations around the base state are</text>
<text><location><page_2><loc_51><loc_85><loc_54><loc_86></location>then:</text>
<formula><location><page_2><loc_52><loc_82><loc_86><loc_84></location>∂ t ρ ' = -∇· m ' + S , (1)</formula>
<formula><location><page_2><loc_51><loc_77><loc_86><loc_82></location>∂ t m ' = -∇ c 2 0 ρ ' + ρ ' g 0 + v 0 ( v 0 · ∇ ρ ' ) (2) + ρ ' ( v 0 · ∇ v 0 + v 0 ∇· v 0 ) -( v 0 · ∇ m ' + m ' · ∇ v 0 + m ' ∇· v 0 + v 0 ∇· m ' ) ,</formula>
<text><location><page_2><loc_51><loc_71><loc_86><loc_76></location>where ρ ' and m ' = ρ ' v 0 + ρ 0 v ' are the density and momentum perturbations associated with the waves, respectively.</text>
<text><location><page_2><loc_51><loc_51><loc_86><loc_71></location>Several simplifications where used in deriving these equations. In particular, perturbations of the gravitational potential have been neglected, and the adiabatic approximation has been used. The entropy gradient of the background model has been neglected in order to make the linearized equations convectively stable. Previous calculations have shown that this assumption does not significantly change the propagation properties of acoustic waves including their frequencies, except for the acoustic cut-off frequency, which is slightly reduced. Because of this simplification, no separate energy equation needs to be solved.</text>
<text><location><page_2><loc_51><loc_36><loc_86><loc_51></location>The equations are formulated in a non-rotating frame. Rotation can however be accounted for by prescribing an appropriate flow. This approach saves computing the usual Coriolis and centrifugal forces that appear in the equations written in a rotating frame. There is no additional timestepping or stability constraint on the numerical method because the rotation speed in the solar interior is always significantly smaller than the speed of sound.</text>
<text><location><page_2><loc_51><loc_22><loc_86><loc_35></location>In the Sun, vigorous turbulent flows near the photosphere are the primary sources of acoustic perturbations. This however is a non-linear process and is lost by linearizing the equations. A random function S has therefore been added to Eqn. 1 to mimic the excitation of these acoustic perturbations. S is random in time and horizontal space, and peaks at a depth of 150 km below the photosphere.</text>
<text><location><page_2><loc_51><loc_10><loc_86><loc_21></location>The equations are solved in spherical coordinates using a pseudo-spectral method. 2/3dealiasing is used. Scalar quantities such as pressure and density are expanded in spherical harmonic basis functions for their angular structure and B-splines (de Boor 1987; Loulou et al. 1997; Hartlep & Mansour 2004; Hartlep & Mansour 2005) for their radial dependence. Vector fields</text>
<text><location><page_3><loc_9><loc_62><loc_45><loc_86></location>such as the perturbation of the momentum are expanded in vector spherical harmonics and Bsplines. Vector spherical harmonics (Hansen 1935; Hill 1954) are analogous to spherical harmonic functions but for vector quantities. They were selected here because the coordinate singularities in spherical coordinates can be treated straightforwardly in these basis functions. Due to the nature of spherical harmonics, no special treatment is necessary for the poles, and only the center of the sphere needs special treatment. For the expanded variables to be finite at the center, we must enforce that the expansion coefficients follow specific asymptotic behaviors as r → 0. For details on how this is implemented using B-splines, the reader is referred to Hartlep et al. (2006).</text>
<text><location><page_3><loc_9><loc_42><loc_45><loc_62></location>B-splines of polynomial order 4 are used in our simulations. The spacing of the generating knot points is chosen to be proportional to the local speed of sound. This results in a high radial resolution near the solar surface, where the sound speed is low (less than 7 km/s), and a significantly lower resolution in the deep interior, where the sound speed surpasses 500 km/s. This provides a constant Courant-Friedrichs-Lewy (CFL) condition throughout the domain. A total of 350 B-splines are used to discretize the entire simulation domain reaching from the solar center to an outer radius of 700 Mm.</text>
<text><location><page_3><loc_9><loc_13><loc_45><loc_42></location>Effectively non-reflecting boundary conditions are used at the upper boundary by means of an absorbing buffer layer by adding terms -σρ ' and -σ m ' in the above equations. The equations are recast using an integrating factor exp σt , and advanced using a staggered leapfrog scheme in which ρ ' and m ' are offset by half of a time step. The purpose of the buffer layer is to damp waves passing thought the temperature minimum before they reach the numerical boundary. Such waves would ordinarily escape into the chromosphere, and we do not want them to artificially reflect back from the numerical boundary. The damping coefficient σ is non-negative, smooth and constant in time. It is zero in the interior and increases smoothly into the buffer layer. Similar damping is used in the deepest interior near the solar center. Waves of high spherical harmonic degree do not travel very deep. Their lower turning radius r t given by</text>
<formula><location><page_3><loc_19><loc_10><loc_45><loc_12></location>c 2 0 ( r t ) /r 2 t = ω 2 /l ( l +1) , (3)</formula>
<text><location><page_3><loc_51><loc_58><loc_86><loc_86></location>and decreases with increasing l . ω in the equation is the wave's temporal frequency. Therefore, as we go towards the center of the Sun, we only need to resolve waves of lesses and lesses spherical harmonic degrees. Carrying higher degrees than required would, in fact, unnecessarily limit the time step. In order to avoid this, we use damping coefficients that are l -dependent. Perturbations of spherical order l do not travel below their corresponding turning radius as given by Eqn. 3, and can be damped. However, we leave about 100 Mm of space below the turning radius before damping starts since the waves have finite extend. Such damping effectively removes highl perturbations in the deep interior without effecting the propagation of helioseismic waves. Modes below l = 40 are not damped at all because wave of such l can actually travel very close and even through the solar center.</text>
<text><location><page_3><loc_51><loc_30><loc_86><loc_57></location>Without flows in the background model, waves can, within the physics of this setup, only gain energy through the acoustic source term, and they can only loose energy through the top boundary. There is no feedback between waves and the sources. These simulations run stable and will eventually reach an energy equilibrium. In the the presence of mass flows in the base state, in particular with strong velocity gradients, it is conceivable that waves may gain momentum and energy from wave-flow instabilities, such as Kelvin-Helmholtz instability. Such growth would be proportional to the wave's own momentum. Our simulations have shown however that for solar-type flows such instabilities grow very slowly, and adding a small amount of viscous damping (not shown in the above equations) is enough to ensure long-term stability.</text>
<section_header_level_1><location><page_3><loc_51><loc_27><loc_82><loc_29></location>2.2. Flow Model and Simulation Run</section_header_level_1>
<text><location><page_3><loc_51><loc_10><loc_86><loc_26></location>For this study, we have simulated the propagation of helioseismic waves through a stationary model of the solar meridional circulation. The original flow model is the 'reference model' from Rempel (2006). A visualization of the model is shown in figure 1. This meridional flow is characterized by a single-cell circulation in each hemisphere with a deep return flow that starts at a depth of about 150 Mm below the surface. The model has a maximum poleward velocity near the surface of approximately 14 m/s and a maximum</text>
<figure>
<location><page_4><loc_11><loc_60><loc_42><loc_84></location>
<caption>Fig. 1.Visualization of the meridional flow model of Rempel (2006) used in the simulation. The arrows indicate the direction of the flow, and their size is proportional to the flow speed. The Sun's rotation axis is at the left edge of the panel with the north pole at the top. The flow in the southern hemisphere (not shown) is given by mirrorsymmetry about the equatorial plane.</caption>
</figure>
<text><location><page_4><loc_9><loc_11><loc_45><loc_47></location>return flow velocity of 3 m/s. Detecting such weak flows from helioseismic measurements is extremely challenging due to the inherent randomness of solar oscillations resulting in small signal-to-noise ratios (S/N). It is expected that very long observations on the order of many years are needed to measure the flow in the deepest parts of the convection zone (Braun & Birch 2008). Unfortunately, it is not practical to simulate such long time series giving current computer capabilities. The present simulation required approximately 1 day of computing time for every three hours of solar time using 264 cores on the Pleiades supercomputer at the National Aeronautics and Space Administration's (NASA) Advanced Supercomputing Division (NAS). However, the most measured quantities in helioseismology - in particular apparent travel-times, frequency shifts, etc depend linearly on the causing perturbations in the solar interior, i.e. sound speed variations or flows. This is a true as long as the perturbations are small, i.e. in the case of flows: as long as the flow velocities are small compared to the speed of sound. Therefore, we can improve the</text>
<text><location><page_4><loc_51><loc_59><loc_86><loc_86></location>S/N without changing the physics by uniformly increasing the amplitude of the background flow model in the simulation. Such a simulation run for a manageable time is in some sense equivalent to a simulation of the original model but run much longer - thanks to T.L. Duvall, Jr. (2011, private communication) for this suggestion. In this work, we have increased the meridional flow by a factor of approximately 36 such that the maximum flow velocity is 500 m/s. This speed is still significantly smaller than the sound speed anywhere in the solar interior, but provides a large increase in S/N. In fact, since the (uncorrelated) realization noise reduces approximately with the square root of the length of the time series, our simulation should have a S/N that is equivalent to a simulation of the original model but run for a period 36 2 times longer.</text>
<text><location><page_4><loc_51><loc_38><loc_86><loc_59></location>In the following, we list other parameters of the simulation in the study. The simulation resolves spherical harmonic degrees from 0 to 170. It is sufficient to capture only this range of small to moderate spherical harmonic degrees because we are only interested in large scale and deep flows. The time step was 1 second; results were saved with a cadence of 30 seconds; and the simulation produced a total of approximately 76 hours of data. The first 4 hours of data where discarded because they represent transient behavior as the simulation was started from a model without any waves in it. In the end, a total of 4,096 minutes of data have been produced and analyzed.</text>
<section_header_level_1><location><page_4><loc_51><loc_35><loc_73><loc_36></location>3. Measurement technique</section_header_level_1>
<text><location><page_4><loc_51><loc_13><loc_86><loc_33></location>In this study, we want to measure the effects that the meridional flow in the simulated Sun has on acoustic waves. When waves are advected by a flow, their travel time is reduced when they travel in the same direction as the flow and their travel time increases when they travel against the flow. The travel times are also effected by localized sound speed variations, however, the difference between the travel times of waves going in opposite directions along the same travel path is to first order not sensitive to local sound speed variations because both directions are effected the same way by such perturbations. The difference is only sensitive to the flow along the travel path.</text>
<text><location><page_4><loc_53><loc_11><loc_86><loc_12></location>In the following we describe the scheme we used</text>
<figure>
<location><page_5><loc_10><loc_66><loc_44><loc_86></location>
<caption>Fig. 2.Visualization of the deep focusing measurement scheme used in this study. Panel ( a ) shows examples of acoustic ray paths ( solid lines ) originating from and traveling to a range of annuli centered around a latitude of 30 · . Panel ( b ) shows a measurement annulus and its decomposition into sectors.</caption>
</figure>
<text><location><page_5><loc_9><loc_43><loc_45><loc_53></location>to measure the apparent acoustic travel-time differences between waves traveling northward and waves traveling southward, in the following referred to as N-S travel-time difference, as well as the travel-time difference between east- and westtraveling waves (E-W travel-time difference). This N-S difference is sensitive to the meridional flow.</text>
<text><location><page_5><loc_9><loc_20><loc_45><loc_42></location>From the simulation, we used a 4,096-minutelong time series of the radial component of the perturbation velocity at a fixed geometric height of 300 km above the photosphere. The simulation provides data on the full solar surface, however, we processed these data more similar to how one would process observations. First, the time series is split in 1,024-minute-long segments with 50% overlap. In each segment, we select 120 · × 120 · tiles centered at 0 · , 90 · , 180 · , and 270 · in longitude and -30 · , 0 · , and +30 · in latitude, and remap these into heliographic coordinates using Postel's projection with a pixel size of 0.6 · , the same resolution as SOHO /MDI mediuml data (Kosovichev et al. 1997).</text>
<text><location><page_5><loc_9><loc_11><loc_45><loc_19></location>The geometry of the measurement scheme is the following: On the surface, centered around each longitude and latitude, we select a series of onepixel-wide annuli ranging in diameter from 12 · to 42 · in 1.2 · increments. Examples of ray paths traveling from a point on an annulus to an oppos-</text>
<text><location><page_5><loc_51><loc_43><loc_86><loc_86></location>int is shown in Figure 2a. In each annulus, the instantaneous signal is averaged over 30 · -wide sectors in the north, south, east, and west direction (Fig. 2b). We then cross-correlate the sector-averaged signal with that from its opposing sector, i.e. the north sector with the south sector and the west sector with the east sector. Crosscorrelations for the same latitude within each tile are averaged together. The longitude-averaged cross-correlation functions for positive and negative time-lag are then fitted separately using Gabor wavelets (Kosovichev & Duvall 1997), and the resulting phase-travel times are subtracted from each other yielding the apparent travel-time difference between north- and south-going (N-S) waves and between east- and west-going (E-W) waves. A very small fraction of far outliers with travel-time differences larger than 2 minutes are misfittings, and are discarded. Measurement schemes of this type have previously been called deep-focusing schemes (e.g., Zhao et al. 2009) but should not be confused with other deep-focusing schemes such as Duvall (1995) which are constructed such that ray paths cross or 'focus' at a target location below the surface. Zhao et al. (2009) used a scheme very similar to the present one to measure deep sound speed perturbations. However, they employed 90 · -wide measurements sectors, i.e. quadrants, instead of the 30 · -wide sectors used here.</text>
<section_header_level_1><location><page_5><loc_51><loc_40><loc_60><loc_41></location>4. Results</section_header_level_1>
<section_header_level_1><location><page_5><loc_51><loc_37><loc_74><loc_38></location>4.1. Travel-time differences</section_header_level_1>
<text><location><page_5><loc_51><loc_18><loc_86><loc_36></location>N-S travel-time differences measured from the simulation data for a range of distances are presented in Figure 3. The travel distances of 12 · , 18 · , 24 · , 30 · , 36 · , and 42 · correspond to lower turning points of the ray paths of approximately 52, 78, 106, 134, 164, and 195 Mm below the photosphere, respectively. Since individual measurements are fairly noisy, it is advantageous to trade some spatial resolution for reduced noise. The results have therefore been averaged over a small range of travel distances ( ± 2 . 4 · ) as well as a range of latitudes ( ± 3 · ).</text>
<text><location><page_5><loc_51><loc_10><loc_86><loc_17></location>Figure 3 also shows the N-S travel-time differences expected from ray-approximation calculations for the prescribed flow. Assuming small perturbation, the ray paths are the same as in the case without flows, and the travel-time difference</text>
<figure>
<location><page_6><loc_10><loc_69><loc_33><loc_86></location>
</figure>
<figure>
<location><page_6><loc_36><loc_69><loc_59><loc_86></location>
</figure>
<figure>
<location><page_6><loc_61><loc_69><loc_84><loc_86></location>
</figure>
<figure>
<location><page_6><loc_10><loc_51><loc_33><loc_69></location>
</figure>
<figure>
<location><page_6><loc_36><loc_51><loc_59><loc_69></location>
</figure>
<figure>
<location><page_6><loc_62><loc_51><loc_84><loc_69></location>
<caption>Fig. 3.Travel-time differences between north-going and south-going waves for 6 different travel distances of 12, 18, 24, 30, 36, and 42 heliographic degrees. The panels show the values measured from 4,096 minutes of simulation data ( solid curves ) and corresponding ray-theory calculations ( dotted curves ). All values have been averaged over a range of ± 2 . 4 · in travel distance and smoothed over ± 3 · in latitude. Error bars in each panel show the size of the latitudinal average of the standard deviation, σ NS , a measure of the scatter between individual measurements, and the standard error of the mean, glyph[epsilon1] NS , as defined by Equations 6 and 7, respectively. Also, measures of the deviation of the measured travel-time diffrences from the their ray-approximation values are show by µ NS for the N-S travel-time differences plotted here, and for comparison the corresponding µ EW for the E-W travel-time differences from Figure 4.</caption>
</figure>
<text><location><page_6><loc_9><loc_29><loc_45><loc_37></location>can be computed by integrating along the ray path the flow component tangential to the ray. Specifically, in the first approximation the travel-time difference between waves going along a ray path and going along the same path in opposite direction is given by:</text>
<formula><location><page_6><loc_18><loc_24><loc_45><loc_27></location>∆ t = -2 ∫ raypath v 0 · T c 2 0 ds (4)</formula>
<text><location><page_6><loc_9><loc_18><loc_45><loc_23></location>where T is the unit vector tangential to the ray path (e.g., Kosovichev & Duvall 1997). The calculations in this study used ray paths computed from the ray-tracing code of Couvidat & Birch (2009).</text>
<text><location><page_6><loc_9><loc_10><loc_45><loc_17></location>We can see from Figure 3 that the results from the analysis of the simulated data are very close to the expected travel-time differences computed using ray theory. This is true especially for the four smaller travel distances. The signal-to-noise ratio</text>
<text><location><page_6><loc_51><loc_32><loc_86><loc_37></location>(S/N) is high here since the deviations from the ray-approximation calculations are rather small. For the two larger distances, however, the noise seems to be comparable with the signal.</text>
<section_header_level_1><location><page_6><loc_51><loc_29><loc_69><loc_30></location>4.2. Error estimation</section_header_level_1>
<text><location><page_6><loc_51><loc_10><loc_86><loc_28></location>When working with measurements, whether using actual observations or artificial data from numerical simulations, it is imperative to estimate the accuracy of the measurement results. This has been an important issue in helioseismology where the results are obtained using complicated data analysis procedures. Therefore, we present the error estimation in detail. Several error estimates are shown in Figure 3 and are explained in the following. Each data point in Figure 3 is the mean of a large number of individual measurements these are the travel-time differences from individ-</text>
<figure>
<location><page_7><loc_10><loc_69><loc_33><loc_86></location>
</figure>
<figure>
<location><page_7><loc_36><loc_69><loc_59><loc_86></location>
</figure>
<figure>
<location><page_7><loc_62><loc_69><loc_84><loc_86></location>
</figure>
<figure>
<location><page_7><loc_10><loc_51><loc_33><loc_69></location>
</figure>
<figure>
<location><page_7><loc_36><loc_51><loc_59><loc_69></location>
</figure>
<figure>
<location><page_7><loc_62><loc_51><loc_84><loc_69></location>
<caption>Fig. 4.Travel-time differences between east-going and west-going waves ( solid curves ) computed from the same data and for the same travel distances as in Figure 3. Values have also been averaged over a range of ± 2 . 4 · in travel distance and smoothed over ± 3 · in latitude. Since no flow in east-west direction was prescribed in the simulation, the travel time differences should be zero ( dotted curves ) if there was no measurement noise. Given error bars are analogous to those in Figure 3.</caption>
</figure>
<text><location><page_7><loc_9><loc_32><loc_45><loc_42></location>ual fittings of the cross-correlation function for the different measurement tiles, a range of distances, and a range of latitudes. From these, we can compute a statistical error estimate. Let us denote the individual measurements by y i with i ∈ [1 , N ], where N is the number of individual measurements averaged for each final data point, ¯ y . Here:</text>
<formula><location><page_7><loc_22><loc_26><loc_45><loc_30></location>¯ y = 1 N N ∑ i =1 y i . (5)</formula>
<text><location><page_7><loc_9><loc_22><loc_45><loc_25></location>The scatter in the individual measurements is given by the standard deviation, σ NS , defined as:</text>
<formula><location><page_7><loc_18><loc_17><loc_45><loc_21></location>σ NS = √ √ √ √ 1 N N ∑ i =1 ( y i -¯ y ) 2 . (6)</formula>
<text><location><page_7><loc_9><loc_10><loc_45><loc_15></location>σ NS is a measure of the deviation of an individual measurement from the mean ¯ y . However, we are not really interested in the error of an individual measurement but rather in the accuracy of the</text>
<text><location><page_7><loc_51><loc_41><loc_78><loc_42></location>mean ¯ y . Its error can be estimated by</text>
<formula><location><page_7><loc_64><loc_37><loc_86><loc_40></location>glyph[epsilon1] NS = σ NS √ N (7)</formula>
<text><location><page_7><loc_51><loc_19><loc_86><loc_35></location>if we can assume statistical independence of the individual measurements. This estimate, glyph[epsilon1] NS , is often called the standard error of the mean. As can be seen from Figure 3, glyph[epsilon1] NS is very small and is in fact significantly smaller than the difference between the measurements and the rayapproximation calculations. This indicates that there are either systematic differences between the measurements and the ray-approximation calculations or that statistical independence is a poor assumption.</text>
<text><location><page_7><loc_51><loc_10><loc_86><loc_19></location>An independent error estimation can be derived by looking at the deviation of the E-W travel-time differences from their expected values. It seems reasonable to assume that the error in both directions is of the same order. Results for the E-W travel-time difference are shown in Figure 4. Since</text>
<text><location><page_8><loc_9><loc_74><loc_45><loc_86></location>no azimuthal flow is prescribed in the simulation, E-W travel-time differences should strictly vanish for all latitudes without using any approximation, such as the ray approximation. However, due to the finite length of the measurement, non-zero values are found. The deviations can be used as an estimate of the error in both E-W and N-S traveltime differences. We define:</text>
<formula><location><page_8><loc_15><loc_69><loc_45><loc_73></location>µ EW = √ √ √ √ 1 M M ∑ j =1 [¯ y ( θ j ) -¯ y 0 ( θ j )] 2 (8)</formula>
<text><location><page_8><loc_9><loc_33><loc_45><loc_67></location>where ¯ y ( θ j ) is now the mean E-W travel-time difference as a function colatitude θ j , M is the number of different colatitudes, and ¯ y 0 ( θ j ) is the theoretically expected travel-time difference and is zero in this case. As is evident from Figures 3 and 4, µ EW seems to be a more appropriate estimate of the noise in both the N-S and E-W traveltime measurements than σ NS and σ EW . Also shown in these figures are values of the deviation of the N-S travel-time difference from their rayapproximation values, i.e. µ NS . It is computed like equation 8 except that ¯ y 0 is replaced by the N-S travel-time difference computed from the ray approximation. Values of µ NS and µ EW are similar indicating that the systematic error made by the ray approximation is probably small compared to the statistical variability of the measurements. It is somewhat surprising that µ EW is actually slightly larger than µ NS for the longest travel distances considered here. However, the scatter in the N-S and E-W travel-time measurements, i.e. σ NS and σ EW , are very much the same as seen in Figures 3 and 4.</text>
<section_header_level_1><location><page_8><loc_9><loc_30><loc_31><loc_31></location>4.3. Signal-to-noise ratio</section_header_level_1>
<text><location><page_8><loc_9><loc_10><loc_45><loc_29></location>Using the amplitude of the ray-approximation N-S travel-time difference and an estimates of the measurement noise in the form of the deviations µ NS , we can compute a signal-to-noise ratio (S/N) for our measurements. The results are shown in Figure 5 for a range of measurement lengths. As one would expect, S/N increases approximately as the square root of the measurement time. We can use this dependency to roughly estimate the duration of a time series one would need to measure, say, the flow near the bottom of the convection zone to a certain accuracy. For a heliographic distance of 42 · and 72 hours of measurement time</text>
<figure>
<location><page_8><loc_53><loc_57><loc_83><loc_83></location>
<caption>Fig. 5.S/N of the N-S travel-time difference measurements as a function of the length of the analyzed time series for different travel distances. S/N is here defined as the ratio between the maximum amplitude over latitudes of the ray-approximation N-S travel-time difference and the standard deviation, µ NS , of the measured travel-time differences from their ray-approximation values.</caption>
</figure>
<figure>
<location><page_8><loc_52><loc_22><loc_82><loc_40></location>
<caption>Fig. 6.Ratio between the amplitudes of the N-S traveltime differences from ray approximation computed for the return flow alone, ∆ t RF , and for the full meridional flow, ∆ t NS , as a function of travel distance. The peak contribution from the return flow in this case corresponds to about 0.9 seconds in travel-time difference.</caption>
</figure>
<text><location><page_9><loc_9><loc_56><loc_45><loc_86></location>(3 days) we have a S/N of approximately 1.25 according to Figure 5. However, remember that the flow velocities in the present simulation have been increased from their realistic values to 500 m/s at the surface to make the simulation and measurements feasible. For a more realistic meridional flow of, say, 20 m/s, the signal-to-noise ratio would be 25 times smaller. Assuming a S/N of 2 is desired, one would then need (25 × 2 / 1 . 25) 2 × 3 days or on the order of 10 years. MDI medium-l measurements are available for almost continuous 15 year, so this may be already possible. However, note that the signal for such long measurement distances still remains dominated by the strong poleward flow in the upper layers of the Sun. As shown in Figure 6, only a small portion of the signal - up to about 20% at its peak - is from the return flow which in the model considered here starts at a depth of approximately 146 Mm. So, a higher signal-to-noise ration may be desired.</text>
<section_header_level_1><location><page_9><loc_9><loc_53><loc_22><loc_54></location>5. Conclusions</section_header_level_1>
<text><location><page_9><loc_9><loc_10><loc_45><loc_52></location>We have simulated the propagation of acoustic waves in the full solar interior in the presence of a prescribed meridional flow with a deep return flow, and we performed time-distance helioseismology measurements to detect the effects of the meridional circulation on the acoustic travel-times difference between north- and south-going waves. The measurements were done for large travel distances between 12 and 42 heliographic degrees corresponding to lower turning points of the acoustic waves between 52 and 195 Mm below the photosphere, i.e. deep in the solar convection zone all the way to the tachocline. The flow velocity in the model was artificially increased by a significant factor to a value of 500 m/s in order to model the flow measurements using relatively short time series that can be calculated on currently available supercomputer systems. The results show that this approach works well without significantly changing the physics of wave propagation, as expected from theoretical grounds. The results also show that it is, in fact, possible to measure the effects of a meridional flow in the deeper solar convection zone by employing a deep-focusing timedistance helioseismology technique. Within the statistical variability (noise) of the measurements, the measured N-S travel-time differences agree well with the ray-approximation calculations. For</text>
<text><location><page_9><loc_51><loc_46><loc_86><loc_86></location>distances between 12 · and 30 · corresponding to lower turning depths between 52 and 136 Mm, the agreement is in fact excellent, and still good for 36 · (164 Mm depth). Noise starts to dominate for the very longest travel distance, however. We estimate that for realistic values of the meridional flow velocity ∼ 10 year time-series or longer may be needed for adequate S/N. Such data are currently available from the SOHO and SDO space observatories (since 1996), and ground-based GONG network (since 1996). It should be mentioned that the present simulation uses rather simple models for the excitation of acoustic waves as well as wave damping, and that therefore the noise properties of the Sun may not be very accurately represented in this numerical model. None-the-less does it seem clear than very long helioseismology observations are needed in order to detect small flows at the base of the convection zone. Still, S/N may be increased, for instance, by the use of phase-speed filters which we have not explored here, or by more spatial averaging. We also leave it for future work to develop and perform an inversion to infer actual flow velocities from the measured travel-time difference. It seems, however, that the current ray-approximation based traveltime inversion techniques are sufficiently accurate.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "The meridional flow in the Sun is an axisymmetric flow that is generally poleward directed at the surface, and is presumed to be of fundamental importance in the generation and transport of magnetic fields. Its true shape and strength, however, is debated. We present a numerical simulation of helioseismic wave propagation in the whole solar interior in the presence of a prescribed, stationary, single-cell, deep meridional circulation serving as a test-bed for helioseismic measurement techniques. A deep-focusing time-distance helioseismology technique is applied to the artificial data showing that it can in fact be used to measure the effects of the meridional flow very deep in the solar convection zone. It is shown that the ray-approximation which is commonly used for interpretation of helioseismology measurements remains a reasonable approximation even for the very long distances between 12 · and 42 · corresponding to depths between 52 and 195 Mm considered here. From the measurement noise we extrapolate that on the order of a full solar cycle may be needed to probe the flow all the way to the base of the convection zone. Subject headings: Methods: numerical, Sun: helioseismology, Sun: interior, Sun: oscillations",
"pages": [
1
]
},
{
"title": "Solar wave-field simulation for testing prospects of helioseismic measurements of deep meridional flows",
"content": "T. Hartlep, J. Zhao, and A.G. Kosovichev W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA, USA and",
"pages": [
1
]
},
{
"title": "N.N. Mansour",
"content": "NASA Ames Research Center, Moffett Field, CA, USA",
"pages": [
1
]
},
{
"title": "1. Motivation and Objectives",
"content": "The meridional circulation is known as a poleward flow near the solar surface and is believed to be an important part of the dynamo process in the solar convection zone. Its true strength and shape in the deeper interior is presently unknown or at least highly debated. There are conflicting theories and observational evidences. On the one hand, theoretical works (e.g., Kitchatinov & Rudiger 2005) usually favor deep meridional flows. Due to mass conservation, the return flow then is relatively strong with flow velocities of the similar same order as the flow near the surface. On the other hand, observational evidence points towards a shallow meridional flow. MitraKraev & Thompson (2007) measured p -mode frequency shifts from three months of SOHO/MDI data and inferred a meridional flow that reverses at a depth of about 40 Mm. They also find evidence of a possible second reversal deeper below. Hathaway (2011) uses the advection of convection cells by the meridional circulation to measure the flow velocity at depth and finds a return flow starting at a depth of only 35 Mm. Other techniques, such as time-distance helioseismology have also been used to measure the meridional flow (e.g., Giles et al. 1998; Chou & Dai 2001; Zhao & Kosovichev 2004; Zhao et al. 2012) but primarily for small depths. The goal of this work was to numerically simulate the propagation of helioseismic waves in the Sun in the presence of meridional and other large scale flows, and to use the artificial data from such simulations to evaluate the possibility of measuring small flows very deep in the Sun, in particular using time-distance helioseismology. There have been previous works that addressed the measurability of deep meridional flows in the Sun such as Braun & Birch (2008). They concluded that as much observations as a full solar cycle may be needed to resolved flows near the base of the solar convection zone using the helioseismic holography technique. Various models of meridional flows have been proposed, and for this paper we have performed a numerical simulation of the solar acoustic wave field for a global-Sun model which included a meridional circulation with a deep return flow, and have performed time-distance helioseismology measurements for this model as if it were observational data. We compare the measurements with the predictions of the ray-path helioseismology theory and estimate the noise level due to the stochastic nature of solar oscillations, and the sensitivity of the helioseismology technique.",
"pages": [
1,
2
]
},
{
"title": "2.1. Simulation Code",
"content": "We have built a numerical code that solves the linearized propagation of helioseismic waves throughout the entire solar interior in the presence of a background structure and flow model (Hartlep & Mansour 2005). This code has been used in previous studies to simulate the effects of localized sound speed perturbations, e.g., for testing helioseismic far-side imaging by simulating the effects of model sunspots on the acoustic field (Hartlep et al. 2008; Ilonidis et al. 2009), for validating time - distance helioseismic measurements of tachocline perturbations (Zhao et al. 2009), and for studying the effects of localized subsurface perturbations (Hartlep et al. 2011). For the present case, the code has been extended to include the effects that mass flows have on the propagation of helioseismic waves. The simulation code models solar acoustic oscillations in a spherical domain using the Euler equations linearized around a stationary background state characterized by the background density, ρ 0 , mass flows velocity, v 0 , sound speed, c 0 , and acceleration due to gravity, g 0 . The equations derived for the perturbations around the base state are then: where ρ ' and m ' = ρ ' v 0 + ρ 0 v ' are the density and momentum perturbations associated with the waves, respectively. Several simplifications where used in deriving these equations. In particular, perturbations of the gravitational potential have been neglected, and the adiabatic approximation has been used. The entropy gradient of the background model has been neglected in order to make the linearized equations convectively stable. Previous calculations have shown that this assumption does not significantly change the propagation properties of acoustic waves including their frequencies, except for the acoustic cut-off frequency, which is slightly reduced. Because of this simplification, no separate energy equation needs to be solved. The equations are formulated in a non-rotating frame. Rotation can however be accounted for by prescribing an appropriate flow. This approach saves computing the usual Coriolis and centrifugal forces that appear in the equations written in a rotating frame. There is no additional timestepping or stability constraint on the numerical method because the rotation speed in the solar interior is always significantly smaller than the speed of sound. In the Sun, vigorous turbulent flows near the photosphere are the primary sources of acoustic perturbations. This however is a non-linear process and is lost by linearizing the equations. A random function S has therefore been added to Eqn. 1 to mimic the excitation of these acoustic perturbations. S is random in time and horizontal space, and peaks at a depth of 150 km below the photosphere. The equations are solved in spherical coordinates using a pseudo-spectral method. 2/3dealiasing is used. Scalar quantities such as pressure and density are expanded in spherical harmonic basis functions for their angular structure and B-splines (de Boor 1987; Loulou et al. 1997; Hartlep & Mansour 2004; Hartlep & Mansour 2005) for their radial dependence. Vector fields such as the perturbation of the momentum are expanded in vector spherical harmonics and Bsplines. Vector spherical harmonics (Hansen 1935; Hill 1954) are analogous to spherical harmonic functions but for vector quantities. They were selected here because the coordinate singularities in spherical coordinates can be treated straightforwardly in these basis functions. Due to the nature of spherical harmonics, no special treatment is necessary for the poles, and only the center of the sphere needs special treatment. For the expanded variables to be finite at the center, we must enforce that the expansion coefficients follow specific asymptotic behaviors as r → 0. For details on how this is implemented using B-splines, the reader is referred to Hartlep et al. (2006). B-splines of polynomial order 4 are used in our simulations. The spacing of the generating knot points is chosen to be proportional to the local speed of sound. This results in a high radial resolution near the solar surface, where the sound speed is low (less than 7 km/s), and a significantly lower resolution in the deep interior, where the sound speed surpasses 500 km/s. This provides a constant Courant-Friedrichs-Lewy (CFL) condition throughout the domain. A total of 350 B-splines are used to discretize the entire simulation domain reaching from the solar center to an outer radius of 700 Mm. Effectively non-reflecting boundary conditions are used at the upper boundary by means of an absorbing buffer layer by adding terms -σρ ' and -σ m ' in the above equations. The equations are recast using an integrating factor exp σt , and advanced using a staggered leapfrog scheme in which ρ ' and m ' are offset by half of a time step. The purpose of the buffer layer is to damp waves passing thought the temperature minimum before they reach the numerical boundary. Such waves would ordinarily escape into the chromosphere, and we do not want them to artificially reflect back from the numerical boundary. The damping coefficient σ is non-negative, smooth and constant in time. It is zero in the interior and increases smoothly into the buffer layer. Similar damping is used in the deepest interior near the solar center. Waves of high spherical harmonic degree do not travel very deep. Their lower turning radius r t given by and decreases with increasing l . ω in the equation is the wave's temporal frequency. Therefore, as we go towards the center of the Sun, we only need to resolve waves of lesses and lesses spherical harmonic degrees. Carrying higher degrees than required would, in fact, unnecessarily limit the time step. In order to avoid this, we use damping coefficients that are l -dependent. Perturbations of spherical order l do not travel below their corresponding turning radius as given by Eqn. 3, and can be damped. However, we leave about 100 Mm of space below the turning radius before damping starts since the waves have finite extend. Such damping effectively removes highl perturbations in the deep interior without effecting the propagation of helioseismic waves. Modes below l = 40 are not damped at all because wave of such l can actually travel very close and even through the solar center. Without flows in the background model, waves can, within the physics of this setup, only gain energy through the acoustic source term, and they can only loose energy through the top boundary. There is no feedback between waves and the sources. These simulations run stable and will eventually reach an energy equilibrium. In the the presence of mass flows in the base state, in particular with strong velocity gradients, it is conceivable that waves may gain momentum and energy from wave-flow instabilities, such as Kelvin-Helmholtz instability. Such growth would be proportional to the wave's own momentum. Our simulations have shown however that for solar-type flows such instabilities grow very slowly, and adding a small amount of viscous damping (not shown in the above equations) is enough to ensure long-term stability.",
"pages": [
2,
3
]
},
{
"title": "2.2. Flow Model and Simulation Run",
"content": "For this study, we have simulated the propagation of helioseismic waves through a stationary model of the solar meridional circulation. The original flow model is the 'reference model' from Rempel (2006). A visualization of the model is shown in figure 1. This meridional flow is characterized by a single-cell circulation in each hemisphere with a deep return flow that starts at a depth of about 150 Mm below the surface. The model has a maximum poleward velocity near the surface of approximately 14 m/s and a maximum return flow velocity of 3 m/s. Detecting such weak flows from helioseismic measurements is extremely challenging due to the inherent randomness of solar oscillations resulting in small signal-to-noise ratios (S/N). It is expected that very long observations on the order of many years are needed to measure the flow in the deepest parts of the convection zone (Braun & Birch 2008). Unfortunately, it is not practical to simulate such long time series giving current computer capabilities. The present simulation required approximately 1 day of computing time for every three hours of solar time using 264 cores on the Pleiades supercomputer at the National Aeronautics and Space Administration's (NASA) Advanced Supercomputing Division (NAS). However, the most measured quantities in helioseismology - in particular apparent travel-times, frequency shifts, etc depend linearly on the causing perturbations in the solar interior, i.e. sound speed variations or flows. This is a true as long as the perturbations are small, i.e. in the case of flows: as long as the flow velocities are small compared to the speed of sound. Therefore, we can improve the S/N without changing the physics by uniformly increasing the amplitude of the background flow model in the simulation. Such a simulation run for a manageable time is in some sense equivalent to a simulation of the original model but run much longer - thanks to T.L. Duvall, Jr. (2011, private communication) for this suggestion. In this work, we have increased the meridional flow by a factor of approximately 36 such that the maximum flow velocity is 500 m/s. This speed is still significantly smaller than the sound speed anywhere in the solar interior, but provides a large increase in S/N. In fact, since the (uncorrelated) realization noise reduces approximately with the square root of the length of the time series, our simulation should have a S/N that is equivalent to a simulation of the original model but run for a period 36 2 times longer. In the following, we list other parameters of the simulation in the study. The simulation resolves spherical harmonic degrees from 0 to 170. It is sufficient to capture only this range of small to moderate spherical harmonic degrees because we are only interested in large scale and deep flows. The time step was 1 second; results were saved with a cadence of 30 seconds; and the simulation produced a total of approximately 76 hours of data. The first 4 hours of data where discarded because they represent transient behavior as the simulation was started from a model without any waves in it. In the end, a total of 4,096 minutes of data have been produced and analyzed.",
"pages": [
3,
4
]
},
{
"title": "3. Measurement technique",
"content": "In this study, we want to measure the effects that the meridional flow in the simulated Sun has on acoustic waves. When waves are advected by a flow, their travel time is reduced when they travel in the same direction as the flow and their travel time increases when they travel against the flow. The travel times are also effected by localized sound speed variations, however, the difference between the travel times of waves going in opposite directions along the same travel path is to first order not sensitive to local sound speed variations because both directions are effected the same way by such perturbations. The difference is only sensitive to the flow along the travel path. In the following we describe the scheme we used to measure the apparent acoustic travel-time differences between waves traveling northward and waves traveling southward, in the following referred to as N-S travel-time difference, as well as the travel-time difference between east- and westtraveling waves (E-W travel-time difference). This N-S difference is sensitive to the meridional flow. From the simulation, we used a 4,096-minutelong time series of the radial component of the perturbation velocity at a fixed geometric height of 300 km above the photosphere. The simulation provides data on the full solar surface, however, we processed these data more similar to how one would process observations. First, the time series is split in 1,024-minute-long segments with 50% overlap. In each segment, we select 120 · × 120 · tiles centered at 0 · , 90 · , 180 · , and 270 · in longitude and -30 · , 0 · , and +30 · in latitude, and remap these into heliographic coordinates using Postel's projection with a pixel size of 0.6 · , the same resolution as SOHO /MDI mediuml data (Kosovichev et al. 1997). The geometry of the measurement scheme is the following: On the surface, centered around each longitude and latitude, we select a series of onepixel-wide annuli ranging in diameter from 12 · to 42 · in 1.2 · increments. Examples of ray paths traveling from a point on an annulus to an oppos- int is shown in Figure 2a. In each annulus, the instantaneous signal is averaged over 30 · -wide sectors in the north, south, east, and west direction (Fig. 2b). We then cross-correlate the sector-averaged signal with that from its opposing sector, i.e. the north sector with the south sector and the west sector with the east sector. Crosscorrelations for the same latitude within each tile are averaged together. The longitude-averaged cross-correlation functions for positive and negative time-lag are then fitted separately using Gabor wavelets (Kosovichev & Duvall 1997), and the resulting phase-travel times are subtracted from each other yielding the apparent travel-time difference between north- and south-going (N-S) waves and between east- and west-going (E-W) waves. A very small fraction of far outliers with travel-time differences larger than 2 minutes are misfittings, and are discarded. Measurement schemes of this type have previously been called deep-focusing schemes (e.g., Zhao et al. 2009) but should not be confused with other deep-focusing schemes such as Duvall (1995) which are constructed such that ray paths cross or 'focus' at a target location below the surface. Zhao et al. (2009) used a scheme very similar to the present one to measure deep sound speed perturbations. However, they employed 90 · -wide measurements sectors, i.e. quadrants, instead of the 30 · -wide sectors used here.",
"pages": [
4,
5
]
},
{
"title": "4.1. Travel-time differences",
"content": "N-S travel-time differences measured from the simulation data for a range of distances are presented in Figure 3. The travel distances of 12 · , 18 · , 24 · , 30 · , 36 · , and 42 · correspond to lower turning points of the ray paths of approximately 52, 78, 106, 134, 164, and 195 Mm below the photosphere, respectively. Since individual measurements are fairly noisy, it is advantageous to trade some spatial resolution for reduced noise. The results have therefore been averaged over a small range of travel distances ( ± 2 . 4 · ) as well as a range of latitudes ( ± 3 · ). Figure 3 also shows the N-S travel-time differences expected from ray-approximation calculations for the prescribed flow. Assuming small perturbation, the ray paths are the same as in the case without flows, and the travel-time difference can be computed by integrating along the ray path the flow component tangential to the ray. Specifically, in the first approximation the travel-time difference between waves going along a ray path and going along the same path in opposite direction is given by: where T is the unit vector tangential to the ray path (e.g., Kosovichev & Duvall 1997). The calculations in this study used ray paths computed from the ray-tracing code of Couvidat & Birch (2009). We can see from Figure 3 that the results from the analysis of the simulated data are very close to the expected travel-time differences computed using ray theory. This is true especially for the four smaller travel distances. The signal-to-noise ratio (S/N) is high here since the deviations from the ray-approximation calculations are rather small. For the two larger distances, however, the noise seems to be comparable with the signal.",
"pages": [
5,
6
]
},
{
"title": "4.2. Error estimation",
"content": "When working with measurements, whether using actual observations or artificial data from numerical simulations, it is imperative to estimate the accuracy of the measurement results. This has been an important issue in helioseismology where the results are obtained using complicated data analysis procedures. Therefore, we present the error estimation in detail. Several error estimates are shown in Figure 3 and are explained in the following. Each data point in Figure 3 is the mean of a large number of individual measurements these are the travel-time differences from individ- ual fittings of the cross-correlation function for the different measurement tiles, a range of distances, and a range of latitudes. From these, we can compute a statistical error estimate. Let us denote the individual measurements by y i with i ∈ [1 , N ], where N is the number of individual measurements averaged for each final data point, ¯ y . Here: The scatter in the individual measurements is given by the standard deviation, σ NS , defined as: σ NS is a measure of the deviation of an individual measurement from the mean ¯ y . However, we are not really interested in the error of an individual measurement but rather in the accuracy of the mean ¯ y . Its error can be estimated by if we can assume statistical independence of the individual measurements. This estimate, glyph[epsilon1] NS , is often called the standard error of the mean. As can be seen from Figure 3, glyph[epsilon1] NS is very small and is in fact significantly smaller than the difference between the measurements and the rayapproximation calculations. This indicates that there are either systematic differences between the measurements and the ray-approximation calculations or that statistical independence is a poor assumption. An independent error estimation can be derived by looking at the deviation of the E-W travel-time differences from their expected values. It seems reasonable to assume that the error in both directions is of the same order. Results for the E-W travel-time difference are shown in Figure 4. Since no azimuthal flow is prescribed in the simulation, E-W travel-time differences should strictly vanish for all latitudes without using any approximation, such as the ray approximation. However, due to the finite length of the measurement, non-zero values are found. The deviations can be used as an estimate of the error in both E-W and N-S traveltime differences. We define: where ¯ y ( θ j ) is now the mean E-W travel-time difference as a function colatitude θ j , M is the number of different colatitudes, and ¯ y 0 ( θ j ) is the theoretically expected travel-time difference and is zero in this case. As is evident from Figures 3 and 4, µ EW seems to be a more appropriate estimate of the noise in both the N-S and E-W traveltime measurements than σ NS and σ EW . Also shown in these figures are values of the deviation of the N-S travel-time difference from their rayapproximation values, i.e. µ NS . It is computed like equation 8 except that ¯ y 0 is replaced by the N-S travel-time difference computed from the ray approximation. Values of µ NS and µ EW are similar indicating that the systematic error made by the ray approximation is probably small compared to the statistical variability of the measurements. It is somewhat surprising that µ EW is actually slightly larger than µ NS for the longest travel distances considered here. However, the scatter in the N-S and E-W travel-time measurements, i.e. σ NS and σ EW , are very much the same as seen in Figures 3 and 4.",
"pages": [
6,
7,
8
]
},
{
"title": "4.3. Signal-to-noise ratio",
"content": "Using the amplitude of the ray-approximation N-S travel-time difference and an estimates of the measurement noise in the form of the deviations µ NS , we can compute a signal-to-noise ratio (S/N) for our measurements. The results are shown in Figure 5 for a range of measurement lengths. As one would expect, S/N increases approximately as the square root of the measurement time. We can use this dependency to roughly estimate the duration of a time series one would need to measure, say, the flow near the bottom of the convection zone to a certain accuracy. For a heliographic distance of 42 · and 72 hours of measurement time (3 days) we have a S/N of approximately 1.25 according to Figure 5. However, remember that the flow velocities in the present simulation have been increased from their realistic values to 500 m/s at the surface to make the simulation and measurements feasible. For a more realistic meridional flow of, say, 20 m/s, the signal-to-noise ratio would be 25 times smaller. Assuming a S/N of 2 is desired, one would then need (25 × 2 / 1 . 25) 2 × 3 days or on the order of 10 years. MDI medium-l measurements are available for almost continuous 15 year, so this may be already possible. However, note that the signal for such long measurement distances still remains dominated by the strong poleward flow in the upper layers of the Sun. As shown in Figure 6, only a small portion of the signal - up to about 20% at its peak - is from the return flow which in the model considered here starts at a depth of approximately 146 Mm. So, a higher signal-to-noise ration may be desired.",
"pages": [
8,
9
]
},
{
"title": "5. Conclusions",
"content": "We have simulated the propagation of acoustic waves in the full solar interior in the presence of a prescribed meridional flow with a deep return flow, and we performed time-distance helioseismology measurements to detect the effects of the meridional circulation on the acoustic travel-times difference between north- and south-going waves. The measurements were done for large travel distances between 12 and 42 heliographic degrees corresponding to lower turning points of the acoustic waves between 52 and 195 Mm below the photosphere, i.e. deep in the solar convection zone all the way to the tachocline. The flow velocity in the model was artificially increased by a significant factor to a value of 500 m/s in order to model the flow measurements using relatively short time series that can be calculated on currently available supercomputer systems. The results show that this approach works well without significantly changing the physics of wave propagation, as expected from theoretical grounds. The results also show that it is, in fact, possible to measure the effects of a meridional flow in the deeper solar convection zone by employing a deep-focusing timedistance helioseismology technique. Within the statistical variability (noise) of the measurements, the measured N-S travel-time differences agree well with the ray-approximation calculations. For distances between 12 · and 30 · corresponding to lower turning depths between 52 and 136 Mm, the agreement is in fact excellent, and still good for 36 · (164 Mm depth). Noise starts to dominate for the very longest travel distance, however. We estimate that for realistic values of the meridional flow velocity ∼ 10 year time-series or longer may be needed for adequate S/N. Such data are currently available from the SOHO and SDO space observatories (since 1996), and ground-based GONG network (since 1996). It should be mentioned that the present simulation uses rather simple models for the excitation of acoustic waves as well as wave damping, and that therefore the noise properties of the Sun may not be very accurately represented in this numerical model. None-the-less does it seem clear than very long helioseismology observations are needed in order to detect small flows at the base of the convection zone. Still, S/N may be increased, for instance, by the use of phase-speed filters which we have not explored here, or by more spatial averaging. We also leave it for future work to develop and perform an inversion to infer actual flow velocities from the measured travel-time difference. It seems, however, that the current ray-approximation based traveltime inversion techniques are sufficiently accurate.",
"pages": [
9
]
},
{
"title": "REFERENCES",
"content": "Braun, D. C., & Birch, A. C. 2008, ApJ, 689, L161 Chou, D.-Y., & Dai, D.-C. 2001, ApJ, 559, L175 Couvidat, S., & Birch, A. C. 2009, Sol. Phys., 257, 217 de Boor, C. 1987, Applied Mathematical Sciences, Vol. 27, A Practical Guide to Splines (SpringerVerlag) Duvall, Jr., T. L. 1995, in Astronomical Society of the Pacific Conference Series, Vol. 76, GONG 1994. Helio- and Astro-Seismology from the Earth and Space, ed. R. K. Ulrich, E. J. Rhodes, Jr., & W. Dappen, 465 Giles, P. M., Duvall, Jr., T. L., & Scherrer, P. H. 1998, in ESA Special Publication, Vol. 418, Structure and Dynamics of the Interior of the Sun and Sun-like Stars, ed. S. Korzennik, 775 Hansen, W. W. 1935, Physical Review, 47, 139 Hartlep, T., Kosovichev, A. G., Zhao, J., & Mansour, N. N. 2011, Sol. Phys., 268, 321 Hartlep, T., & Mansour, N. N. 2004, Solar Convection Simulations using a B-Spline Method, Annual Research Briefs 2004, Center for Turbulence Research, NASA Ames/Stanford University Hartlep, T., & Mansour, N. N. 2005, Acoustic Wave Propagation in the Sun, Annual Research Briefs 2005, Center for Turbulence Research, NASA Ames/Stanford University Hartlep, T., Miesch, M. S., & Mansour, N. N. 2006, in Proceedings of the 2006 Summer Program, Center for Turbulence Research, NASA Ames/Stanford University Hartlep, T., Zhao, J., Mansour, N. N., & Kosovichev, A. G. 2008, Astrophys. J., 689, 1373 Hathaway, D. H. 2011, ArXiv e-prints Hill, E. L. 1954, Amer. J. Phys., 22, 211 Ilonidis, S., Zhao, J., & Hartlep, T. 2009, Solar Phys., 258, 181 Kitchatinov, L. L., & Rudiger, G. 2005, Astronomische Nachrichten, 326, 379 Kosovichev, A. G., & Duvall, Jr., T. L. 1997, in Astrophysics and Space Science Library, Vol. 225, SCORe'96 : Solar Convection and Oscillations and their Relationship, ed. F. P. Pijpers, J. Christensen-Dalsgaard, & C. S. Rosenthal, 241-260 Kosovichev, A. G., Schou, J., Scherrer, P. H., et al. 1997, Sol. Phys., 170, 43 Loulou, P., Moser, R. D., Mansour, N. N., & Cantwell, B. J. 1997, Direct numerical simulation of incompressible pipe flow using a BSpline Spectral Method, Technical Memorandum 110436, NASA Ames Research Center Mitra-Kraev, U., & Thompson, M. J. 2007, Astronomische Nachrichten, 328, 1009 Rempel, M. 2006, ApJ, 647, 662 Zhao, J., Hartlep, T., Kosovichev, A. G., & Mansour, N. N. 2009, Astrophys. J., 702, 1150 Zhao, J., & Kosovichev, A. G. 2004, ApJ, 603, 776 Zhao, J., Couvidat, S., Bogart, R. S., et al. 2012, Sol. Phys., 275, 375",
"pages": [
9,
10
]
}
]
2013ApJ...763...87A
https://arxiv.org/pdf/1212.1806.pdf
<document>
<text><location><page_1><loc_71><loc_85><loc_88><loc_86></location>A. Asai : 2012.11.15</text>
<section_header_level_1><location><page_1><loc_12><loc_77><loc_88><loc_81></location>Temporal and Spatial Analyses of Spectral Indices of Nonthermal Emissions Derived from Hard X-Rays and Microwaves</section_header_level_1>
<text><location><page_1><loc_15><loc_71><loc_85><loc_75></location>Ayumi Asai 1 , Junko Kiyohara 2 , Hiroyuki Takasaki 2 , 3 , Noriyuki Narukage 4 , Takaaki Yokoyama 5 , Satoshi Masuda 6 , Masumi Shimojo 7 , and Hiroshi Nakajima 7</text>
<text><location><page_1><loc_37><loc_68><loc_62><loc_69></location>[email protected]</text>
<section_header_level_1><location><page_1><loc_44><loc_63><loc_56><loc_64></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_36><loc_83><loc_60></location>We studied electron spectral indices of nonthermal emissions seen in hard X-rays (HXRs) and in microwaves. We analyzed 12 flares observed by the Hard X-ray Telescope aboard Yohkoh , Nobeyama Radio Polarimeters (NoRP), and the Nobeyama Radioheliograph (NoRH), and compared the spectral indices derived from total fluxes of hard X-rays and microwaves. Except for four events, which have very soft HXR spectra suffering from the thermal component, these flares show a gap ∆ δ between the electron spectral indices derived from hard X-rays δ X and those from microwaves δ µ (∆ δ = δ X -δ µ ) of about 1.6. Furthermore, from the start to the peak times of the HXR bursts, the time profiles of the HXR spectral index δ X evolve synchronously with those of the microwave spectral index δ µ , keeping the constant gap. We also examined the spatially resolved distribution of the microwave spectral index by using NoRH data. The microwave spectral</text>
<text><location><page_2><loc_17><loc_76><loc_83><loc_86></location>index δ µ tends to be larger, which means a softer spectrum, at HXR footpoint sources with stronger magnetic field than that at the loop tops. These results suggest that the electron spectra are bent at around several hundreds of keV, and become harder at the higher energy range that contributes the microwave gyrosynchrotron emission.</text>
<text><location><page_2><loc_17><loc_71><loc_83><loc_74></location>Subject headings: Sun: flares - Sun: corona - Sun: radio radiation - Sun: X-rays, gamma rays - acceleration of particles</text>
<section_header_level_1><location><page_2><loc_42><loc_65><loc_58><loc_66></location>1. Introduction</section_header_level_1>
<text><location><page_2><loc_12><loc_45><loc_88><loc_62></location>During the impulsive phase of solar flares, electrons are accelerated up to the energy of MeV, and are responsible for nonthermal emissions with power-law spectra observed in hard X-rays (HXRs) and in microwaves. In HXRs the bremsstrahlung emission from electrons with the energy of more than tens of keV is dominant (Brown 1971), while the gyrosynchrotron emission from more than several hundreds of keV electrons is dominant in microwaves (White & Kundu 1992; Bastian et al. 1998; Bastian 1999). HXR and microwave nonthermal emissions are very similar in the light curves (e.g., Kundu 1961; Kai 1986), and therefore, it has been generally accepted that they are produced by a common population of accelerated electrons.</text>
<text><location><page_2><loc_12><loc_10><loc_88><loc_43></location>The electron spectra derived from HXR emissions are, on the other hand, often different from those derived from microwave emissions. The electron spectral indices of the power-law distribution derived from HXRs δ X are, in many cases, larger than those derived from microwaves δ µ , that is δ X > δ µ (Kundu 1965; Silva et al. 1997, 2000). According to the study by Silva et al. (1997), the average gap between δ X and δ µ , ∆ δ (= δ X -δ µ ) is 0.5 - 2.0. This means that microwave spectra are harder than the HXR ones, and that acceleration and/or traveling mechanisms could be different for these wavelengths. For example, Melrose & Brown (1976) suggested the so-called trap-plus-precipitation model, in which the magnetic trap works more effectively for such higher energy electrons that emit microwaves than HXR emitting electrons with lower energy. Minoshima et al. (2008), on the other hand, showed in their numerical calculation that the gap ∆ δ is naturally generated even from the electron distribution with a single power-law spectrum, since microwave and HXR emissions are from different electrons (trapped and precipitating ones, respectively.) In the early phase of a flare, however, the magnetic trap is probably not so effective, and we can examine the features of the nonthermal electrons without having to deal with the trapping effect. Moreover, it is crucially important to analyze imaging data both in HXRs and in microwaves, since we can resolve spatially the precipitating (at footpoints) and trapped (at loop tops)</text>
<text><location><page_3><loc_12><loc_85><loc_31><loc_86></location>components with them.</text>
<text><location><page_3><loc_12><loc_61><loc_88><loc_83></location>In this paper, we report the results of the analyses on the electron spectral indices derived from HXRs and microwaves, and also discuss the temporal and spatial characteristics. We used the HXR data obtained with the Hard X-ray Telescope (HXT; Kosugi et al. 1991) aboard the Yohkoh satellite (Ogawara et al. 1991). The microwave data were taken with the Nobeyama Radio Polarimeters (NoRP; Torii et al. 1979; Shibasaki et al. 1979; Nakajima et al. 1985a), and the Nobeyama Radioheliograph (NoRH; Nakajima et al. 1994) at Nobeyama Solar Radio Observatory, National Astronomical Observatory of Japan. These data enable us to examine the nonthermal features of the accelerated electrons spatially, temporally, and spectroscopically both in HXRs and in microwaves. In § 2 and § 3 we summarize the observations and the method of the analyses, respectively, and we show the results of the statistical analyses in § 4. In § 5 we present discussions and our conclusions.</text>
<section_header_level_1><location><page_3><loc_42><loc_55><loc_58><loc_57></location>2. Observations</section_header_level_1>
<text><location><page_3><loc_12><loc_26><loc_88><loc_53></location>We used HXR data obtained with Yohkoh /HXT. By using the HXT data, we can synthesize the HXR images in four energy bands, namely the L band (14 - 23 keV), M1 band (23 - 33 keV), M2 band (33 - 53 keV), and H band (53 - 93 keV). The spatial and temporal resolutions of the HXT images are 5 '' and 0.5 s, respectively. To obtain the HXR photon spectral index γ ( I X ( /epsilon1 ) ∝ /epsilon1 -γ , where I X is the HXR intensity, and /epsilon1 is energy of the photon), we used the data in the two highest energy bands, i.e., the HXT M2 and H bands, because HXR emissions with energy less than 30 keV sometimes suffer from the contribution of the thermal emissions. Therefore, the HXR photon spectral index γ is roughly written as -log( I X (H) /I X (M2))(log( /epsilon1 H //epsilon1 M2 )) -1 , where /epsilon1 M2 and /epsilon1 H are the effective energies for the M2 and H bands. Though, as we will discuss later, some events showed the effects of the super-hot thermal components even in the M2 band. In this work we calculated the HXR photon spectral indices by using the programs hxt_powerlaw in the Solar SoftWare (SSW) package on IDL. We accumulated the HXT data for two seconds in the spectral analyses to reduce the photon noise.</text>
<text><location><page_3><loc_12><loc_11><loc_88><loc_24></location>We also used the HXR spectra derived from the Wide Band Spectrometer (WBS; Yoshimori et al. 1991). The Hard X-ray Spectrometer (HXS), one of the sensors installed on the WBS, is dedicated to taking HXR spectra over a wide energy range. WBS/HXS can obtain HXR spectra with higher spectral resolution than HXT, although it cannot obtain the spatial information. Therefore, the data of WBS/HXS and HXT are complementary for the imaging spectroscopy in HXRs. Sato et al. (2006) summarized all the events observed by WBS, and we used their database of the HXR spectra.</text>
<text><location><page_4><loc_12><loc_80><loc_88><loc_86></location>In microwaves the gyrosynchrotron emission is dominant during the impulsive phase of a flare. The spectrum in microwave range F ν is approximately fitted with the two power-law indices α tk and α tn by the function as follows:</text>
<formula><location><page_4><loc_13><loc_74><loc_88><loc_79></location>F ν = F ν,pk ( ν ν pk ) α tk { 1 -exp [ -( ν ν pk ) α tn -α tk ]} ≈ { F ν,pk ( ν/ν pk ) α tk for ν /lessmuch ν pk F ν,pk ( ν/ν pk ) α tn for ν /greatermuch ν pk (1)</formula>
<text><location><page_4><loc_12><loc_67><loc_88><loc_73></location>The optically thin part, therefore, follows the power law distribution with a negative spectral index α (= α tn ) as F ν ∝ ν α , where F ν is the flux density at frequency ν (e.g. Ramaty (1969); Dulk (1985)).</text>
<text><location><page_4><loc_12><loc_44><loc_88><loc_66></location>In this study we used the microwave data taken with NoRP, which measures the total fluxes at 1, 2, 3.75, 9.4, 17, 35, and 80 GHz, with a temporal resolution of 0.1 s. By fitting a NoRP spectrum with the equation (1), we can obtain the spectral index α P for the optically thin gyrosynchrotron. We did not use the NoRP 80 GHz data in this work due to the poor statistics. For some events, the NoRP 1 GHz data were also ruled out, because they clearly did not follow the gyrosynchrotron, but instead, the plasma emission. We accumulated the NoRP data for 5 s to reduce the noise level. The microwave fluxes of the NoRP data are determined with the error of less than 10 % of the signal for 1, 2, 4, 9.4 GHz, and 15 % for 17 and 35 GHz, which is mainly due to the observation conditions such as the calibration and the weather. The error to determine α P is also affected by the accuracy of fitting, and is finally estimated to be about ± 0.5.</text>
<text><location><page_4><loc_12><loc_27><loc_88><loc_43></location>NoRH also observes the sun at 17 and 34 GHz. The microwave 2-dimensional images are synthesized from the NoRH data, and the spatial resolutions (FWHMs of the synthesized beam) of about 14 '' for 17 GHz and 7 '' for 34 GHz. The time cadence of the data we used in this work is one second. We can derive the two-dimensional distribution (map) of the microwave spectral indices using the NoRH data ( α H ), by calculating log( F 34GHz /F 17GHz )(log(34GHz / 17GHz)) -1 for each position of images. If we assume that the turnover frequency is less than 17 GHz, the derive α H is for the optically thin gyrosynchrotron emission.</text>
<text><location><page_4><loc_12><loc_10><loc_88><loc_26></location>Here, we have to note the calibration of the NoRH 17 and 34 GHz data. NoRH calibrates phase and gain by using the sun itself (i.e. the solar disk) as a calibrator, thanks to the redundant antenna configuration. However, the fundamental (smallest) spacing of the antennas (= 1 . 5 m) corresponds to the maximum wavelength in the space of 20 ' (= 1200 '' ) at 34 GHz, which means that the whole solar disk is not resolved. The solar disk at 34 GHz is partially overlapped with other fake solar disk images, and therefore, the background (quiet) solar disk is possibly not well determined. To correct this, we adjusted the flux of the flare region taken by NoRH 34 GHz, which is subtracted by the preflare data, to the fitting results</text>
<text><location><page_5><loc_12><loc_62><loc_88><loc_86></location>derived from NoRP. NoRP calibrates those fluxes by using sky and absorber levels. In our cases the NoRH 34 GHz fluxes are usually smaller than the NoRP 35 GHz ones, and the ratio (NoRH 34 GHz)/(NoRP 35 GHz) is from 0.4 to 1.2. This calibration possibly reduces the derived spectral index α H about -1.0 at a maximum. We also corrected the NoRH 17 GHz flux of the flare region, by using the fitting result from NoRP. Although the correction ratio (NoRH 17 GHz)/(NoRP 17 GHz) ranges from 0.6 to 1.2, it is roughly comparable to 1 in most cases. This calibration causes the error on α H , mainly due to the measurement error of the radio flux by NoRP, and is about 0.4. The relative displacement between the images in 17 GHz and those in the 34 GHz due to the NoRH image syntheses also causes the error to estimate the spectral index α H . The NoRH image syntheses hold an uncertainty on the positioning of about 5 '' , and in this case, the error on α H is about ± 0.2 for bright emission sources.</text>
<section_header_level_1><location><page_5><loc_41><loc_56><loc_59><loc_58></location>3. Data Analyses</section_header_level_1>
<text><location><page_5><loc_12><loc_20><loc_88><loc_54></location>Strong (i.e., intense) and large events are preferable for our imaging spectroscopic analyses. Therefore, we sought solar flares observed by HXT, NoRH, and NoRP for the period from the start of the dual-frequency observation with NoRH (November 1995) to the end of the observation of Yohkoh (December 2001), and selected 12 flare events that meet the following criteria; (1) The flare is larger than M1.0 on the GOES scale. (2) The flare is an event listed in The Yohkoh HXT/SXT Flare Catalogue (Sato et al. 2003), and the maximum HXR intensity is so strong that the counts per second per subcollimator in the HXT M2 band are larger than 30. (3) The spatial size of the microwave emission source observed with NoRH at 17 GHz is large enough, and it is more than 4 times of the beam size. (4) The microwave images can be successfully synthesized from the NoRH data, in other words, the microwave emissions are not extremely strong 1 . (5) The optically thin parts of the gyrosynchrotron emission are well defined from the NoRP data, which means that the turn-over frequencies determined from the fitting do not reach 17 GHz or more. (6) The peak time of the event is between 00:00 UT to 06:00 UT, which corresponds to 09:00 and 15:00 JST (i.e. Japanese daytime), and the NoRH beam pattern is not so distorted. Table 1 lists all the 12 flares. Figure 1 also shows temporal and spatial features of each event. The selected events are widely distributed longitudinally and in the flare size.</text>
<section_header_level_1><location><page_6><loc_37><loc_85><loc_63><loc_86></location>3.1. HXR Spectral Indices</section_header_level_1>
<text><location><page_6><loc_12><loc_65><loc_88><loc_82></location>In the selected events we confirmed that the dominant HXR emissions are from footpoints of flare loops, and no loop top HXR sources are included, such as those reported by Masuda et al. (1994). This means that they are produced by bremsstrahlung caused by the interactions between the precipitating energetic electrons and the dense chromospheric plasma. Therefore, it is reasonable that we adopt the thick-target model (Brown 1971; Hudson et al. 1978; Sakao 1994) for the HXR emission sources. In this paper we determined the spectral indices γ from the total HXR intensities, assuming that the HXR emissions from the footpoint sources are so strong that we can approximately equate the total intensities to the emissions from the footpoint source.</text>
<text><location><page_6><loc_56><loc_54><loc_56><loc_55></location>/negationslash</text>
<text><location><page_6><loc_12><loc_46><loc_88><loc_63></location>The thick-target model suggests the relation between γ and the spectral index δ ' X of the number flux of the injected energetic electrons F N ( E ) (= dN ( E ) /dt ∝ E -δ ' X ), as δ ' X = γ +1 . 0. To estimate the spectral index δ X of the accelerated electron N ( E ), we further have to consider the traveling time of the electrons τ ( N ( E ) ≈ F N ( E ) τ ∝ E -δ X ), since energydependent τ moderates the spectral index and δ ' X = δ X . In this paper we adopted the typical timescale over which the precipitating electrons travel the effective length L in the flare loops with the velocity v , that is, τ = Lv -1 . The traveling time is proportional to v -1 , that is, τ ∝ E -0 . 5 . Then, the electron spectral index derived from the HXR emissions δ X follows the relation, δ X = γ +1 . 5.</text>
<text><location><page_6><loc_12><loc_33><loc_88><loc_44></location>The seventh column of Table 1 shows the derived spectral index δ X at a time when the HXR emission records the maximum in the HXT M2 band for each event as shown in the second column. The derived δ X ranges from 3.8 to 6.6. The error to estimate the spectral index γ is about ± 0.5, and the same is true for δ X , under the assumption of single powerlaw HXR spectra. The photon noise is the main factor of the error, and therefore, it is even reduced during strong HXR emissions (to about ± 0.2).</text>
<text><location><page_6><loc_12><loc_20><loc_88><loc_31></location>As shown in Figure 1, in most cases, the temporal variations of the spectral index, which are plotted with the cross mark (+), show the soft-hard-soft (SHS) behavior at the peak times of the HXR emissions. Therefore, δ X recorded in Table 1 is roughly the minimum value during the burst. As we describe below, for the 2000 January 12 (event b) and the 2000 March 3 (event f) flares, we chose other sub-peaks instead of the maximal intensities, because we could not well fit the microwave spectra.</text>
<text><location><page_6><loc_12><loc_11><loc_88><loc_18></location>In Figure 2 we show the HXR spectra derived from WBS/HXS. These are from the database of Sato et al. (2006). The times on the top are the integration time in UT, and they almost cover the HXR maxima. The solid lines are the power-law distribution of the HXR spectra derived from HXT, while the absolute values are arbitrary. For the 2000 March</text>
<text><location><page_7><loc_12><loc_78><loc_88><loc_86></location>3 (event f) and the 2001 March 30 (event k) flare, the integration times of WBS/HXS are out of the HXT peak times we took. We can confirm that the HXR spectral indices derived from HXT fit the HXR spectra of WBS/HXS within the margin of errors as small as ± 0.2 (Sato et al. 2006).</text>
<section_header_level_1><location><page_7><loc_34><loc_72><loc_66><loc_74></location>3.2. Microwave Spectral Indices</section_header_level_1>
<text><location><page_7><loc_12><loc_42><loc_88><loc_70></location>Next, we derived the spectral indices of the accelerated electrons δ µ from the microwave emissions taken with NoRP. For the optically thin gyrosynchrotron emission, α is related to the spectral index of the accelerated electrons δ µ . There have been several studies to derive the relation between δ µ and α , and we adopt the approximation derived by Dulk (1985) here, and δ µ = (1 . 22 -α ) / 0 . 9. In this paper, we distinguish the spectral index derived from NoRP δ µ P from that from NoRH δ µ H with the subscripts P and H . Figure 3 shows some examples of the NoRP spectra and the fitting result at the time of HXR maximal intensity (column 2). The eighth column of Table 1 also shows the spectral index derived from NoRP δ µ P at the time of the HXR maxim. As we mentioned above ( § 2), the error to determine α P is about ± 0.5, and therefore, that for δ µ P is about ± 0.6. We confirmed that the contribution from the free-free emission at the 35 GHz is negligible. The temporal variations of the δ µ P follow the gradual-hardening (GH) or soft-hard-harder (SHH) behaviors as shown in Figure 1. We added the gap between the spectral index derived from HXRs and that from microwaves ∆ δ = δ X -δ µ P in the ninth column. We will discuss ∆ δ in more detail later.</text>
<text><location><page_7><loc_12><loc_32><loc_88><loc_41></location>For the 2000 January 12 and 2000 March 3 flares (events b and f, respectively), the turnover frequencies are higher than 20 GHz at the HXT maxima, and we could not well fit the spectral indices α for the optically thin part of the gyrosynchrotron emission. Therefore, we chose other sub-peaks of the HXR light curves of these events for the spectral analysis. These peak times are shown with gray vertical lines in Figure 1.</text>
<text><location><page_7><loc_12><loc_12><loc_88><loc_30></location>From the NoRH data, we can derive the spatially resolved spectral indices α H (and therefore, δ µ H ). We can compare, for example, δ µ H at the footpoint sources with that of the loop-top ones. As we just mentioned, we confirmed that the turnover frequencies derived from NoRP are lower enough than 17 GHz except for the peak times of the events (b) and (f). For the two events, we again selected preceding sub-peaks for further spectral analyses. Therefore, the indices α H derived from only two frequencies (17 and 34 GHz) are mainly for the optically thin gyrosynchrotron, while we cannot rule out the possibility that they are locally enhanced to be close to or larger than 17 GHz. Figure 1 shows such two-dimensional distribution of the indexα H , which we call ' α -map' in the bottom right sub-figure.</text>
<section_header_level_1><location><page_8><loc_45><loc_85><loc_55><loc_86></location>4. Results</section_header_level_1>
<text><location><page_8><loc_12><loc_59><loc_88><loc_82></location>Table 1 lists the selected 12 events, with the peak time of the HXT M2 band (column 2), the delay of the peak times of microwave (NoRP 17 GHz) compared to those of HXR (HXT M2 band) in second (column 3), the spectral index derived from HXT δ X (column 7), that derived from NoRP δ µ P (column 8), and the gap ∆ δ (= δ X -δ µ P ) (column 9). In Figure 1 we present the time profiles of the HXR flux of HXT M2 band and the microwave flux at 17 GHz taken with NoRP (top left). The time profiles of the spectral indices δ X and δ µ P are also shown with the cross (+) and square ( /square ) signs, respectively, in the bottom left sub-figure. We also present the contour images in the microwave taken with NoRH at 17 GHz (top right) of the selected events. The contour levels of the microwave images are 20 %, 40 %, 60 %, 80 %, and 95% of the peak intensity. The microwave images are overlaid with the HXR contour images taken with HXT M2 band with the contour levels of 20 %, 40 %, 60 %, 80 %, and 95% of the peak intensities.</text>
<section_header_level_1><location><page_8><loc_30><loc_53><loc_70><loc_54></location>4.1. Peak Delay of Microwave Emissions</section_header_level_1>
<text><location><page_8><loc_12><loc_35><loc_88><loc_50></location>As the top left sub-figures of Figure 1 show, the microwave peaks almost always delay from the HXR peaks. The delay times for the events are listed in the third column of Table 1. These delays of microwave peaks to HXR ones have been often observed, and reported by various authors (e.g., Gudel et al. 1991). In the current case the delays are from 0 to 21 seconds, and the average is 7.3 seconds. These are comparable with the result by Nakajima et al. (1985b). Delays of microwave peaks to HXT ones are thought to be caused by magnetically trapping for microwave-emitting electrons, while HXR emissions are from the directly precipitated electrons to the chromosphere.</text>
<section_header_level_1><location><page_8><loc_34><loc_29><loc_66><loc_30></location>4.2. Gap of Spectral Indices ∆ δ</section_header_level_1>
<text><location><page_8><loc_12><loc_13><loc_88><loc_27></location>According to the results summarized in Figure 1 and Table 1, especially concerning the gap ∆ δ , we first categorize these events into two groups. As we mentioned above, the temporal variations of δ X clearly show the SHS behavior at the peaks, while those of δ µ P show hardening features (GH or SHH) as flares progress. In most cases, therefore, the listed gap ∆ δ is the smallest value near the HXR peaks. For all events, the gap ∆ δ is always positive, which means that the electron spectra derived from microwaves of this group are always harder than that from HXRs.</text>
<text><location><page_8><loc_16><loc_10><loc_88><loc_12></location>The first is the group with smaller gap (∆ δ < 2.2). This group shows the electron</text>
<text><location><page_9><loc_12><loc_64><loc_88><loc_86></location>spectral index derived from HXRs δ X of about 4.6 ± 0.8, while that derived from microwaves δ µ P is about 3.0 ± 0.8. The gap ∆ δ of about 1.6 is well consistent with the result by Silva et al. (2000). The eight events (from a to h) belong to this group. The other 4 events (from i to l), which belong to the second group, have much larger gaps ∆ δ of greater than 2.7. In particular, the electron spectral index derived from HXRs δ X is much larger than those of the first group, and is about 6.2 ± 0.5. We checked the HXT data for those events, and concluded that the HXR emissions suffered from the thermal components even in the M2 band. The HXR spectra derived from WBS/HXS (Fig. 2) are also very soft. Huang et al. (2006) studied one of them (the 1998 November 28 flare; event i), in more detail, and concluded that there is a vast super-hot thermal component in this flare, which softens the HXR spectrum. Henceforth, we discuss only the first group.</text>
<text><location><page_9><loc_12><loc_55><loc_88><loc_63></location>Even after we eliminate the second group, there remains the gap ∆ δ . Figure 4 shows the scatter plot with the horizontal axis of δ X and the vertical axis of δ µ P . The events are marked with the asterisks ( ∗ ). The solid line shows the points where δ X is equal to δ µ P . This also suggests that there is a certain gap between the spectral indices ∆ δ .</text>
<section_header_level_1><location><page_9><loc_33><loc_49><loc_67><loc_51></location>4.3. Microwave Emission Sources</section_header_level_1>
<text><location><page_9><loc_12><loc_30><loc_88><loc_47></location>As shown in Figure 1, the sites of the dominant microwave emissions are different for each event. According to the spatial displacement between the brightest position of the microwave emission sources and those of the HXR sources, and/or by using imaging observations in soft X-rays and in extreme ultraviolets, we categorized the microwave emission sources into two cases; footpoint source (group F; displacement is less than 5 '' ) and loop source (group L; displacement is larger than 5 '' ) as noted in the sixth column of Table 1. Here, we note that the brightest microwave emission source seen in the 2000 November 25 flare (event g) is confirmed to be a footpoint source (Takasaki et al. 2007), although it is displaced from the HXR source of about 40 '' . Therefore, we categorized this case as a footpoint event.</text>
<text><location><page_9><loc_12><loc_19><loc_88><loc_28></location>We confirmed that the dominant microwave emission sources appear at the tops or legs of flare loops for many cases (5 of 8 events). This is consistent with the result of Huang & Nakajima (2009) or Melnikov et al. (2002). We will discuss the difference between the temporal evolution of the spectral indices for group L and that for group F in the next subsection.</text>
<section_header_level_1><location><page_10><loc_28><loc_85><loc_72><loc_86></location>4.4. Temporal Evolution of Spectral Indices</section_header_level_1>
<text><location><page_10><loc_12><loc_73><loc_88><loc_82></location>We examine the temporal evolution of the spectral indices. The HXR spectral index δ X mostly shows the SHS behaviors at each short peak, while two of them (events f and g) show even GH features. The temporal evolution of the microwave spectral index δ µ P , on the other hand, seems different, according to the position of microwave emission sources (i.e. group L/F).</text>
<text><location><page_10><loc_12><loc_54><loc_88><loc_71></location>For group L (events a, b, c, d, and e), the time profiles of the spectral indices ( δ µ P and δ X ) show similar evolution from start to peak of the bursts, while the gap ∆ δ increases with time after the peaks. In other words, the electron spectral index derived from HXRs δ X increases after the peaks, showing the SHS features, while the electron spectral index from microwaves δ µ P becomes further smaller showing SHH or GH features. For group F (events f, g, and h), on the other hand, both the spectral indices ( δ µ P and δ X ) show similar evolution through the impulsive phase while maintaining a gap of about 1.6. However, event (h) is different from the other two events of group F. This event shows the SHS features both in the microwave index δ µ P and in the HXR index δ X , while the others show GH features.</text>
<text><location><page_10><loc_12><loc_41><loc_88><loc_52></location>From the point of the temporal evolution, we can, therefore, re-classify the eight events into the three groups: (L) microwave emission sources are located at loop tops/legs, and δ X and δ µ P show SHS and GH features, respectively (events a, b, c, d, and e), (F) microwave emission sources are from footpoints, and both δ X and δ µ P show GH features (events f and g), (F ∗ ) microwave emission source is again from footpoints, but both δ X and δ µ P show SHS features (event h).</text>
<text><location><page_10><loc_12><loc_10><loc_88><loc_39></location>Figure 5 is roughly a realignment of Figure 1, but much more focuses on the temporal evolution of the microwave spectral index δ µ P during the bursts for the groups (L; top) and (F; bottom). The vertical dotted lines correspond to the times when the microwave 17 GHz fluxes taken by NoRP exceeds 100 SFU (Solar Flux Unit). We determine this time as the start of the bursts. The vertical dashed lines correspond to the times when the 17 GHz fluxes become half of the peak values. We define this time as the end of the bursts. Although even after the end times the microwave indices δ µ P become smaller, the fluxes probably suffer from the thermal component in the microwave emissions, which should be avoided from the analysis. For the 2000 November 25 flare (event g), we defined the end time just after the peak HXR time, since the hardening seems saturated after 01:12 UT, and no further hardening is seen. The bottom panels again show the time profiles of the spectral index δ µ P with the square ( /square ) marks. The overlaid time profiles are the spectral index δ X (cross +). We subtracted 1.5 from the original value of the index to clearly show the temporal variation. The numbers noted in the figure show how much the microwave spectral indices δ µ P decrease during the two vertical dotted lines. We also summarized the hardening degree</text>
<text><location><page_11><loc_12><loc_78><loc_88><loc_86></location>in the tenth column of Table 1. As a result, the nonthermal spectra harden with the indices of 1.0 on the average. The hardening with the microwave spectral index of about 1 seems to be consistent with the discussion of the trapping time of relativistic electrons (Bai and Ramaty 1979; Petrosian 1985).</text>
<text><location><page_11><loc_12><loc_45><loc_88><loc_77></location>From the start to the peak of the HXR bursts, which corresponds to the time range from the dotted line to the thick gray line in Figure 5, both the time profiles of the microwave spectral index δ µ P and that of the HXR spectral index δ X decrease simultaneously, keeping a certain gap ∆ δ of about 1.5. The 2000 November 25 flare (event g) is a special case due to the very long duration and the smooth variation of the HXR and microwave emissions (Takasaki et al. 2007). This flare shows GH features even in the HXR spectral evolution, and is a typical 'type-C flare' (e.g. Hoyng et al. 1976), which have been discussed from the Hinotori era (Cliver et al. 1986; Kai 1986; Dennis 1985; Kosugi et al. 1988). These imply that the magnetic trap effectively works both on the microwave-emitting electrons and even on the HXR-emitting electrons. The HXR-emitting electrons are trapped in the magnetic loop at least once before they precipitate into the chromosphere. The dominant microwave emission source is located at the footpoint conjugated with the HXR source, which means that these microwave-emitting electrons escape from the magnetic trap. As Takasaki et al. (2007) reported, on the other hand, the microwave footpoint emission source disappears and the dominant emission source is from the loop top during the valley times. Therefore, the gaps ∆ δ increase during the valley times.</text>
<section_header_level_1><location><page_11><loc_30><loc_39><loc_70><loc_41></location>4.5. Spatial Features of Spectral Index δ µ</section_header_level_1>
<text><location><page_11><loc_12><loc_23><loc_88><loc_37></location>The difference between the microwave emission sources and the HXR emission sources implies that the microwave emissions mainly come from electrons trapped magnetically within the flare loop that connects the HXR footpoint sources. Spatially resolved analyses on the spectral indices are, therefore, required for these events, to explain the reason for the certain gap ∆ δ of about 1.6 confirmed in current study. By using the NoRH data, we examine the spatial distribution of the spectral indices derived from microwaves, and compare the value at the footpoint ( δ µ H (X)) with that at the loop top ( δ µ H ( µ )).</text>
<text><location><page_11><loc_12><loc_10><loc_88><loc_22></location>First, we derived the electron spectral index from NoRH microwave emission δ µ H at the brightest emission positions. The brightest regions are determined to be regions where the intensities at 17 GHz are larger than 80 % of the maximum intensities, and the derived spectral index is noted as δ µ H ( µ ). For many cases in our results, the dominant microwave emissions are from loop tops (or legs), and δ µ H ( µ ) show the values there. The twelfth column of Table 1 presents the list of δ µ H ( µ ). These items roughly correspond to those derived from</text>
<text><location><page_12><loc_12><loc_72><loc_88><loc_86></location>the total intensity δ µ P (column 8) with the displacement of about 0.5. The displacement is probably due to the spatial distribution of the spectral index. For the 2000 October 29 flare (event e), we failed to correctly derive the α -map, because of a large displacement between the position of the NoRH 17 GHz emission source and that at NoRH 34 GHz. The displacement is as large as 10 '' . Although the reason is unknown, it may be caused by other energy release processes that occurred in the preflare phase. We omitted this event from the further discussions.</text>
<text><location><page_12><loc_12><loc_39><loc_88><loc_71></location>Second, we determined the spectral index at the HXR footpoints, that is, δ µ H (X) from the NoRH α -map. If there are two HXR footpoint sources, we calculated them separately. For events (f) and (h), we could not, however, correctly derive the spectral index. This is because the HXR footpoint positions are too close to the loop top/leg microwave emission sources, and they are not spatially resolved. For events (a) and (b), one of the two footpoints is too close to the microwave emission source. We showed the spectral indices δ µ H (X) for these footpoint sources in parentheses in the eleventh column of Table 1. The number I/II is the same as that marked for the HXR footpoints in the Figure 1. Here we have to note that the error of δ µ H (X). The microwave emission from footpoints is weaker than that from loop tops/legs for most cases, and therefore, the error to estimate the spectral index δ µ H (X) could be larger than that for loop top one ( δ µ H ( µ )). We roughly expect the error to be about ± 0.7. Except for the 2000 April 8 flare (event c), we found the relation that the spectral indices for footpoint sources are larger, which corresponds to the softer spectra, than those at the loop tops/legs, that is, δ µ H (X) > δ µ H ( µ ). Especially, in events (d) and (g), δ µ H (X) is quite close to the δ X . We will discuss the spatial features of the spectral index δ µ and the relation with the magnetic field in the next section.</text>
<section_header_level_1><location><page_12><loc_35><loc_33><loc_65><loc_35></location>5. Discussion and Conclusions</section_header_level_1>
<text><location><page_12><loc_12><loc_11><loc_88><loc_31></location>We examined the electron spectral indices of nonthermal emissions seen in HXRs ( δ X ) and in microwaves ( δ µ ) for 12 flares observed by Yohkoh /HXT NoRP, and NoRH. Eight flares of the selected 12 events show gaps between the spectral indices, i.e. ∆ δ of about 1.6. The gaps are consistent with the result of Silva et al. (2000). The other four events show larger gaps ∆ δ > 2.7, since they suffer from softening of the HXR spectra (i.e. enlarging the HXR spectral index δ X ) due to the super-hot thermal component even in the HXT M2 band. In spite of the fact that we examined the spectral features for the impulsive phase to avoid the effect of magnetic trapping, there still remains a certain gap. On the other hand, from the start to the peak of the HXR bursts (that corresponds from the first vertical dotted line to the thick gray line in Figure 5), both the time profile of the microwave spectral index δ µ P</text>
<text><location><page_13><loc_12><loc_82><loc_88><loc_86></location>and that of the HXR spectral index δ X decrease simultaneously, keeping a certain gap ∆ δ of about 1.6.</text>
<text><location><page_13><loc_12><loc_57><loc_88><loc_81></location>We also investigated the positions of the emission sources by using the HXT and NoRH data. For five of the eight events, the brightest microwave emission sources are located on the loop tops (or legs; group L). On the other hand, for the other three events, they are different from the HXR emission sources, which are mainly from footpoints (group F/F ∗ )). This implies that the microwave emissions mainly come from electrons trapped magnetically within the flare loop that connects the HXR footpoint sources. The difference in the site of the emission sources possibly causes the gap of the spectral indices ∆ δ . The spatial distribution of the microwave spectral index derived from NoRH δ µ H should therefore be examined. Except for one event (event c), we confirmed that the microwave spectra for footpoint sources are softer than those at the loop tops/legs, that is, δ µ H (X) > δ µ H ( µ ). However, the spatial distribution of the microwave spectral index again cannot resolve the gap ∆ δ even at the sites of the HXR emission sources.</text>
<text><location><page_13><loc_12><loc_38><loc_88><loc_56></location>From these results, we concluded that the spectra of the accelerated electrons have a bent, and become harder above several hundreds of keV. This is also consistent with results of previous studies (Yoshimori et al. 1985; Dennis 1988; Matsumoto et al. 2005). Minoshima et al. (2008) numerically calculated the spectral indices of microwave and HXR emissions from the trapped and precipitating electrons, and showed that a softer HXR spectrum and a hard microwave spectrum can be generated. The difference of the spectral indices ∆ δ ∼ 1.5, is consistent with our result. However, we showed that the spatially resolved distribution of the microwave spectral index in our study cannot resolve the gap ∆ δ even at the footpoint sources. This means that there still remains a certain gap ∆ δ .</text>
<text><location><page_13><loc_12><loc_11><loc_88><loc_37></location>Here, we examine events (c) and (d) in more detail. Figure 6 shows the photospheric magnetograms for these events obtained by the Michelson Doppler Imager (MDI; Scherrer et al. 1995) aboard the Solar and Heliospheric Observatory ( SOHO ; Domingo et al. 1995). The levels of the contours are ± 400, ± 600, and ± 800 gauss with the red and blue lines for positive and negative magnetic polarities, respectively. We overlaid the microwave contour image of NoRH 17 GHz on each panel with light blue lines. The HXR contour image observed with HXT in the M2 band is also overlaid with green lines. The levels of these contours for both contour images are 40, 60, 80, and 95 % of the maximum intensities. From Figure 6, we clearly see weak magnetic field strength at HXR footpoints in event (c) of about 250 300 gauss, while there is quite a strong magnetic field in event (d) of about 900 - 1000 gauss. In event (d), therefore, we expect strong magnetic field for microwave footpoint position, and it could be several 100 gauss. The microwave gyrosynchrotron emission is strongly related to the magnetic field strength, and only high-energy electrons can contribute under</text>
<text><location><page_14><loc_12><loc_52><loc_88><loc_86></location>the condition of weak magnetic field strength. On the other hand, with strong magnetic field, weaker energy electrons can contribute the emission. As Bastian (1999) calculated, electrons with the energy of about 500 keV contribute at 500 gauss, while the energy must be higher than 1 MeV at 200 gauss to generate 17 GHz emission. This means that low energy electrons with the energy of about several 100 keV emit the gyrosynchrotron at the footpoints. The energy of several 100 keV is as low as that for electrons emitting HXR bremsstrahlung, which causes a very soft spectrum that has the same spectral index δ µ H (X) as δ X . The magnetic field strength at the loop top must be much smaller, and the microwave-emitting electrons have high enough energy of about several MeV, at which the harder spectral component appears. On the other hand, in event (c), the magnetic field strength is weak even at the HXR footpoint sources. This means that high-energy electrons are responsible for the microwave emission even at the footpoint, which corresponds to the observed harder spectral component. From these results, we concluded that the bent of the electron spectra seems to be at about several 100 keV, which is consistent with the previous suggestions (Yoshimori et al. 1985; Dennis 1988). In Figure 3, we cannot see the clear bent of the HXR spectra derived from WBS/HXS, and therefore, the bent of HXR spectra in the current case occurs at the energy higher than 300 keV.</text>
<text><location><page_14><loc_12><loc_34><loc_88><loc_49></location>We first would like to acknowledge an anonymous referee for her/his comments and suggestions. We would like to thank all the members of Nobeyama Solar Radio Observatory, NAOJ for their supports during the observation. We wish to thank Drs. S. Krucker and T. Minoshima for fruitful discussions and his helpful comments. This work was carried out by the joint research program of the Solar-Terrestrial Environment Laboratory, Nagoya University. The Yohkoh satellite is a Japanese national project, launched and operated by ISAS, and involving many domestic institutions, with multilateral international collaboration with the US and the UK.</text>
<text><location><page_14><loc_16><loc_31><loc_44><loc_32></location>Facilities: NoRH, NoRP, Yohkoh.</text>
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<text><location><page_17><loc_29><loc_87><loc_31><loc_87></location>3</text>
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<text><location><page_17><loc_31><loc_38><loc_33><loc_39></location>7</text>
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<text><location><page_17><loc_44><loc_80><loc_46><loc_81></location>.8</text>
<text><location><page_17><loc_44><loc_39><loc_46><loc_40></location>6</text>
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<text><location><page_17><loc_47><loc_80><loc_49><loc_81></location>.5</text>
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<text><location><page_17><loc_50><loc_37><loc_52><loc_38></location>E</text>
<text><location><page_17><loc_52><loc_39><loc_54><loc_40></location>1</text>
<text><location><page_17><loc_52><loc_38><loc_54><loc_39></location>6</text>
<text><location><page_17><loc_52><loc_37><loc_54><loc_38></location>W</text>
<text><location><page_17><loc_37><loc_31><loc_39><loc_31></location>1</text>
<text><location><page_17><loc_37><loc_27><loc_39><loc_28></location>8</text>
<text><location><page_17><loc_37><loc_26><loc_39><loc_27></location>:1</text>
<text><location><page_17><loc_37><loc_25><loc_39><loc_26></location>3</text>
<text><location><page_17><loc_37><loc_24><loc_39><loc_25></location>:1</text>
<text><location><page_17><loc_37><loc_23><loc_39><loc_24></location>4</text>
<text><location><page_17><loc_37><loc_23><loc_39><loc_23></location>0</text>
<text><location><page_17><loc_37><loc_20><loc_39><loc_20></location>6</text>
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<text><location><page_17><loc_44><loc_27><loc_46><loc_28></location>8</text>
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<text><location><page_17><loc_44><loc_25><loc_46><loc_26></location>1</text>
<text><location><page_17><loc_44><loc_24><loc_46><loc_25></location>:2</text>
<text><location><page_17><loc_44><loc_23><loc_46><loc_24></location>1</text>
<text><location><page_17><loc_44><loc_23><loc_46><loc_23></location>0</text>
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<text><location><page_17><loc_44><loc_15><loc_46><loc_16></location>0</text>
<text><location><page_17><loc_44><loc_14><loc_46><loc_15></location>0</text>
<text><location><page_17><loc_44><loc_13><loc_46><loc_14></location>0</text>
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<text><location><page_17><loc_50><loc_31><loc_52><loc_31></location>2</text>
<text><location><page_17><loc_50><loc_27><loc_52><loc_28></location>7</text>
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<text><location><page_17><loc_50><loc_25><loc_52><loc_26></location>0</text>
<text><location><page_17><loc_50><loc_24><loc_52><loc_25></location>:4</text>
<text><location><page_17><loc_50><loc_23><loc_52><loc_24></location>5</text>
<text><location><page_17><loc_50><loc_23><loc_52><loc_23></location>0</text>
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<text><location><page_17><loc_50><loc_16><loc_52><loc_17></location>N</text>
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<text><location><page_17><loc_34><loc_19><loc_36><loc_20></location>0</text>
<text><location><page_17><loc_34><loc_18><loc_36><loc_19></location>r</text>
<text><location><page_17><loc_34><loc_17><loc_36><loc_18></location>p</text>
<text><location><page_17><loc_34><loc_16><loc_36><loc_17></location>A</text>
<text><location><page_17><loc_34><loc_15><loc_36><loc_16></location>0</text>
<text><location><page_17><loc_34><loc_14><loc_36><loc_15></location>0</text>
<text><location><page_17><loc_34><loc_13><loc_36><loc_14></location>0</text>
<text><location><page_17><loc_34><loc_13><loc_36><loc_13></location>2</text>
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<text><location><page_17><loc_57><loc_39><loc_59><loc_39></location>1</text>
<text><location><page_17><loc_57><loc_38><loc_59><loc_39></location>0</text>
<text><location><page_17><loc_57><loc_37><loc_59><loc_38></location>E</text>
<text><location><page_17><loc_57><loc_31><loc_59><loc_32></location>0</text>
<text><location><page_17><loc_57><loc_27><loc_59><loc_28></location>6</text>
<text><location><page_17><loc_57><loc_26><loc_59><loc_27></location>:3</text>
<text><location><page_17><loc_57><loc_25><loc_59><loc_26></location>4</text>
<text><location><page_17><loc_57><loc_24><loc_59><loc_25></location>:3</text>
<text><location><page_17><loc_57><loc_23><loc_59><loc_24></location>4</text>
<text><location><page_17><loc_57><loc_23><loc_59><loc_23></location>0</text>
<text><location><page_17><loc_57><loc_19><loc_59><loc_20></location>5</text>
<text><location><page_17><loc_57><loc_19><loc_59><loc_19></location>2</text>
<text><location><page_17><loc_57><loc_17><loc_59><loc_18></location>p</text>
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<text><location><page_17><loc_57><loc_16><loc_59><loc_17></location>S</text>
<text><location><page_17><loc_57><loc_15><loc_59><loc_15></location>1</text>
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<text><location><page_17><loc_22><loc_16><loc_23><loc_17></location>a</text>
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<text><location><page_17><loc_22><loc_14><loc_23><loc_15></location>D</text>
<text><location><page_17><loc_26><loc_12><loc_28><loc_13></location>)</text>
<text><location><page_17><loc_26><loc_11><loc_28><loc_12></location>1</text>
<text><location><page_17><loc_26><loc_11><loc_28><loc_11></location>(</text>
<text><location><page_17><loc_39><loc_87><loc_41><loc_88></location>-</text>
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<text><location><page_17><loc_55><loc_39><loc_57><loc_40></location>8</text>
<text><location><page_17><loc_55><loc_38><loc_57><loc_39></location>1</text>
<text><location><page_17><loc_55><loc_37><loc_57><loc_38></location>W</text>
<text><location><page_17><loc_55><loc_31><loc_57><loc_32></location>3</text>
<text><location><page_17><loc_55><loc_27><loc_57><loc_28></location>5</text>
<text><location><page_17><loc_55><loc_26><loc_57><loc_27></location>:1</text>
<text><location><page_17><loc_55><loc_25><loc_57><loc_26></location>3</text>
<text><location><page_17><loc_55><loc_24><loc_57><loc_25></location>:1</text>
<text><location><page_17><loc_55><loc_23><loc_57><loc_24></location>5</text>
<text><location><page_17><loc_55><loc_23><loc_57><loc_23></location>0</text>
<text><location><page_17><loc_55><loc_20><loc_57><loc_21></location>0</text>
<text><location><page_17><loc_55><loc_19><loc_57><loc_20></location>3</text>
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<text><location><page_17><loc_55><loc_15><loc_57><loc_16></location>1</text>
<text><location><page_17><loc_55><loc_14><loc_57><loc_15></location>0</text>
<text><location><page_17><loc_55><loc_13><loc_57><loc_14></location>0</text>
<text><location><page_17><loc_55><loc_13><loc_57><loc_13></location>2</text>
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<text><location><page_17><loc_74><loc_28><loc_74><loc_28></location>µ</text>
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<text><location><page_17><loc_74><loc_26><loc_75><loc_26></location>X</text>
<text><location><page_17><loc_73><loc_25><loc_74><loc_26></location>δ</text>
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<text><location><page_17><loc_73><loc_23><loc_74><loc_24></location>δ</text>
<text><location><page_17><loc_73><loc_23><loc_74><loc_23></location>∆</text>
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<text><location><page_17><loc_73><loc_22><loc_74><loc_22></location>s</text>
<text><location><page_17><loc_73><loc_21><loc_74><loc_22></location>e</text>
<text><location><page_17><loc_73><loc_21><loc_74><loc_21></location>c</text>
<text><location><page_17><loc_73><loc_21><loc_74><loc_21></location>i</text>
<text><location><page_17><loc_73><loc_20><loc_74><loc_21></location>d</text>
<text><location><page_17><loc_73><loc_20><loc_74><loc_20></location>n</text>
<text><location><page_17><loc_73><loc_19><loc_74><loc_20></location>i</text>
<text><location><page_17><loc_73><loc_19><loc_74><loc_19></location>e</text>
<text><location><page_17><loc_73><loc_18><loc_74><loc_19></location>h</text>
<text><location><page_17><loc_73><loc_18><loc_74><loc_18></location>t</text>
<text><location><page_17><loc_73><loc_17><loc_74><loc_17></location>n</text>
<text><location><page_17><loc_73><loc_16><loc_74><loc_17></location>e</text>
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<text><location><page_17><loc_73><loc_15><loc_74><loc_16></location>w</text>
<text><location><page_17><loc_73><loc_15><loc_74><loc_15></location>t</text>
<text><location><page_17><loc_73><loc_15><loc_74><loc_15></location>e</text>
<text><location><page_17><loc_73><loc_14><loc_74><loc_15></location>b</text>
<text><location><page_17><loc_73><loc_13><loc_74><loc_14></location>p</text>
<text><location><page_17><loc_73><loc_13><loc_74><loc_13></location>a</text>
<text><location><page_17><loc_73><loc_12><loc_74><loc_13></location>G</text>
<text><location><page_17><loc_73><loc_11><loc_73><loc_12></location>d</text>
<text><location><page_17><loc_77><loc_36><loc_78><loc_36></location>.</text>
<text><location><page_17><loc_77><loc_36><loc_78><loc_36></location>6</text>
<text><location><page_17><loc_77><loc_35><loc_78><loc_35></location>e</text>
<text><location><page_17><loc_77><loc_35><loc_78><loc_35></location>r</text>
<text><location><page_17><loc_77><loc_34><loc_78><loc_35></location>u</text>
<text><location><page_17><loc_77><loc_34><loc_78><loc_34></location>g</text>
<text><location><page_17><loc_77><loc_33><loc_78><loc_34></location>i</text>
<text><location><page_17><loc_77><loc_33><loc_78><loc_33></location>F</text>
<text><location><page_17><loc_77><loc_32><loc_78><loc_32></location>d</text>
<text><location><page_17><loc_77><loc_31><loc_78><loc_32></location>n</text>
<text><location><page_17><loc_77><loc_31><loc_78><loc_31></location>a</text>
<text><location><page_17><loc_77><loc_30><loc_78><loc_31></location>t</text>
<text><location><page_17><loc_77><loc_30><loc_78><loc_30></location>x</text>
<text><location><page_17><loc_77><loc_29><loc_78><loc_30></location>e</text>
<text><location><page_17><loc_77><loc_29><loc_78><loc_29></location>t</text>
<text><location><page_17><loc_77><loc_28><loc_78><loc_29></location>,</text>
<text><location><page_17><loc_77><loc_28><loc_78><loc_28></location>e</text>
<text><location><page_17><loc_77><loc_28><loc_78><loc_28></location>e</text>
<text><location><page_17><loc_77><loc_27><loc_78><loc_28></location>S</text>
<text><location><page_17><loc_77><loc_26><loc_78><loc_27></location>.</text>
<text><location><page_17><loc_77><loc_26><loc_78><loc_26></location>s</text>
<text><location><page_17><loc_77><loc_26><loc_78><loc_26></location>t</text>
<text><location><page_17><loc_77><loc_25><loc_78><loc_26></location>s</text>
<text><location><page_17><loc_77><loc_25><loc_78><loc_25></location>r</text>
<text><location><page_17><loc_77><loc_24><loc_78><loc_25></location>u</text>
<text><location><page_17><loc_77><loc_24><loc_78><loc_24></location>b</text>
<text><location><page_17><loc_77><loc_23><loc_78><loc_24></location>e</text>
<text><location><page_17><loc_77><loc_23><loc_78><loc_23></location>h</text>
<text><location><page_17><loc_77><loc_22><loc_78><loc_23></location>t</text>
<text><location><page_17><loc_77><loc_22><loc_78><loc_22></location>g</text>
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<text><location><page_17><loc_77><loc_21><loc_78><loc_21></location>i</text>
<text><location><page_17><loc_77><loc_20><loc_78><loc_21></location>r</text>
<text><location><page_17><loc_77><loc_20><loc_78><loc_20></location>u</text>
<text><location><page_17><loc_77><loc_19><loc_78><loc_20></location>d</text>
<text><location><page_17><loc_77><loc_19><loc_78><loc_19></location>e</text>
<text><location><page_17><loc_77><loc_18><loc_78><loc_19></location>e</text>
<text><location><page_17><loc_77><loc_18><loc_78><loc_18></location>r</text>
<text><location><page_17><loc_77><loc_17><loc_78><loc_18></location>g</text>
<text><location><page_17><loc_77><loc_17><loc_78><loc_17></location>e</text>
<text><location><page_17><loc_77><loc_17><loc_78><loc_17></location>d</text>
<text><location><page_17><loc_77><loc_16><loc_78><loc_16></location>g</text>
<text><location><page_17><loc_77><loc_15><loc_78><loc_16></location>n</text>
<text><location><page_17><loc_77><loc_15><loc_78><loc_15></location>i</text>
<text><location><page_17><loc_77><loc_14><loc_78><loc_15></location>n</text>
<text><location><page_17><loc_77><loc_14><loc_78><loc_14></location>e</text>
<text><location><page_17><loc_77><loc_14><loc_78><loc_14></location>d</text>
<text><location><page_17><loc_77><loc_13><loc_78><loc_14></location>r</text>
<text><location><page_17><loc_77><loc_13><loc_78><loc_13></location>a</text>
<text><location><page_17><loc_77><loc_12><loc_78><loc_13></location>H</text>
<text><location><page_17><loc_76><loc_11><loc_77><loc_12></location>e</text>
<text><location><page_18><loc_19><loc_84><loc_21><loc_85></location>60</text>
<text><location><page_18><loc_19><loc_83><loc_21><loc_83></location>40</text>
<text><location><page_18><loc_19><loc_81><loc_21><loc_82></location>20</text>
<text><location><page_18><loc_19><loc_80><loc_21><loc_80></location>0</text>
<text><location><page_18><loc_19><loc_79><loc_21><loc_80></location>180</text>
<text><location><page_18><loc_19><loc_78><loc_21><loc_78></location>120</text>
<text><location><page_18><loc_19><loc_76><loc_21><loc_77></location>60</text>
<text><location><page_18><loc_19><loc_75><loc_21><loc_76></location>0</text>
<text><location><page_18><loc_19><loc_65><loc_21><loc_66></location>63</text>
<text><location><page_18><loc_19><loc_64><loc_21><loc_64></location>42</text>
<text><location><page_18><loc_19><loc_62><loc_21><loc_63></location>21</text>
<text><location><page_18><loc_19><loc_61><loc_21><loc_61></location>0</text>
<text><location><page_18><loc_19><loc_60><loc_21><loc_61></location>720</text>
<text><location><page_18><loc_19><loc_59><loc_21><loc_60></location>480</text>
<text><location><page_18><loc_19><loc_57><loc_21><loc_58></location>240</text>
<text><location><page_18><loc_19><loc_56><loc_21><loc_57></location>0</text>
<text><location><page_18><loc_19><loc_46><loc_21><loc_47></location>45</text>
<text><location><page_18><loc_19><loc_45><loc_21><loc_45></location>30</text>
<text><location><page_18><loc_19><loc_43><loc_21><loc_44></location>15</text>
<text><location><page_18><loc_19><loc_42><loc_21><loc_42></location>0</text>
<text><location><page_18><loc_19><loc_41><loc_21><loc_42></location>780</text>
<text><location><page_18><loc_19><loc_40><loc_21><loc_41></location>520</text>
<text><location><page_18><loc_19><loc_38><loc_21><loc_39></location>260</text>
<text><location><page_18><loc_19><loc_37><loc_21><loc_38></location>0</text>
<figure>
<location><page_18><loc_20><loc_29><loc_81><loc_85></location>
<caption>Fig. 1.- (Figure 1a) Time profiles and images for each selected event. The intensity (top) and spectral (bottom) time profiles are shown on the left-hand side of each sub-figure. The HXR and microwave light curves are taken by the HXT M2 band (33 - 53 keV) and the NoRP 17 GHz, respectively. The microwave and HXR spectral time profiles are plotted with the square ( /square ) and cross (+), respectively. The 17 GHz contour images obtained by NoRH and the HXR ones obtained with HXT (M2 band) are shown in the top right panel of each sub-figure by the black and gray lines, respectively. The contour levels of the microwave and HXR images are 20 %, 40 %, 60 %, 80 %, and 95% of the peak intensity.</caption>
</figure>
<text><location><page_19><loc_19><loc_77><loc_21><loc_78></location>120</text>
<text><location><page_19><loc_18><loc_72><loc_21><loc_73></location>2415</text>
<text><location><page_19><loc_18><loc_71><loc_21><loc_71></location>1610</text>
<text><location><page_19><loc_19><loc_69><loc_21><loc_70></location>805</text>
<text><location><page_19><loc_19><loc_58><loc_21><loc_59></location>330</text>
<text><location><page_19><loc_19><loc_57><loc_21><loc_57></location>220</text>
<text><location><page_19><loc_19><loc_55><loc_21><loc_56></location>110</text>
<text><location><page_19><loc_18><loc_53><loc_21><loc_54></location>1200</text>
<text><location><page_19><loc_19><loc_52><loc_21><loc_53></location>800</text>
<text><location><page_19><loc_19><loc_50><loc_21><loc_51></location>400</text>
<text><location><page_19><loc_19><loc_34><loc_21><loc_35></location>375</text>
<text><location><page_19><loc_19><loc_33><loc_21><loc_34></location>250</text>
<text><location><page_19><loc_19><loc_31><loc_21><loc_32></location>125</text>
<figure>
<location><page_19><loc_19><loc_21><loc_81><loc_78></location>
<caption>Fig. 2.- (Figure 1b) - continued.</caption>
</figure>
<figure>
<location><page_20><loc_12><loc_34><loc_89><loc_69></location>
<caption>Fig. 3.- (Figure 2) HXR spectra derived from WBS/HXS. The times on the top are the integration times in UT. The slopes of the power-law distributions derived from HXT are overlaid with the solid lines.</caption>
</figure>
<figure>
<location><page_21><loc_20><loc_29><loc_81><loc_73></location>
<caption>Fig. 4.- (Figure 3) The microwave spectra taken by NoRP for events (a), (c), (d), and (f). The solid lines are the fitting results.</caption>
</figure>
<figure>
<location><page_22><loc_18><loc_29><loc_81><loc_76></location>
<caption>Fig. 5.- (Figure 4) Scatter plot between the electron spectral index derived from microwaves δ µ (horizontal axis) and that from HXRs δ X (vertical axis). The solid line shows the points where δ X corresponds to δ µ (∆ δ = 0). Only the small gap events (∆ δ < 2 . 2, see text) are plotted.</caption>
</figure>
<figure>
<location><page_23><loc_12><loc_31><loc_88><loc_86></location>
<caption>Fig. 6.- (Figure 5) Hardening of microwave spectral index δ µ P for events (a), (b), (f), and (g). The vertical dotted lines correspond to the times when the microwave 17 GHz fluxes taken by NoRP exceed 100 SFU (Solar Flux Unit). The vertical dashed lines correspond to the times when the 17 GHz fluxes become half of the peak values, except for event (g), which show saturating the microwave spectral index. The bottom left panels show the time profiles of the spectral index δ µ P with the square ( /square ) marks. The overlaid time profiles are the spectral index δ X (cross; +). Note, we subtracted 1.5 from the original value of the index to clearly show the temporal variation. The numbers noted in the figure show how much the spectral indices δ µ P decrease during the two vertical dotted lines.</caption>
</figure>
<section_header_level_1><location><page_24><loc_25><loc_70><loc_39><loc_71></location>(c) 2000 Apr 08</section_header_level_1>
<section_header_level_1><location><page_24><loc_63><loc_70><loc_78><loc_71></location>(d) 2000 Sep 16</section_header_level_1>
<figure>
<location><page_24><loc_11><loc_37><loc_89><loc_70></location>
<caption>Fig. 7.- (Figure 6) Magnetic field strengths for events (c) and (d). The levels of the contours are 400, 600, and 800 gauss with the red and blue lines for positive and negative magnetic polarities, respectively. The microwave contour image of NoRH 17 GHz on each panel is overlaid with the light blue lines. The HXR contour image observed with HXT in the M2 band is also overlaid with the green lines. The levels of these contours for both images are 40, 60, 80, and 95 % of the maximum intensities.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "We studied electron spectral indices of nonthermal emissions seen in hard X-rays (HXRs) and in microwaves. We analyzed 12 flares observed by the Hard X-ray Telescope aboard Yohkoh , Nobeyama Radio Polarimeters (NoRP), and the Nobeyama Radioheliograph (NoRH), and compared the spectral indices derived from total fluxes of hard X-rays and microwaves. Except for four events, which have very soft HXR spectra suffering from the thermal component, these flares show a gap ∆ δ between the electron spectral indices derived from hard X-rays δ X and those from microwaves δ µ (∆ δ = δ X -δ µ ) of about 1.6. Furthermore, from the start to the peak times of the HXR bursts, the time profiles of the HXR spectral index δ X evolve synchronously with those of the microwave spectral index δ µ , keeping the constant gap. We also examined the spatially resolved distribution of the microwave spectral index by using NoRH data. The microwave spectral index δ µ tends to be larger, which means a softer spectrum, at HXR footpoint sources with stronger magnetic field than that at the loop tops. These results suggest that the electron spectra are bent at around several hundreds of keV, and become harder at the higher energy range that contributes the microwave gyrosynchrotron emission. Subject headings: Sun: flares - Sun: corona - Sun: radio radiation - Sun: X-rays, gamma rays - acceleration of particles",
"pages": [
1,
2
]
},
{
"title": "Temporal and Spatial Analyses of Spectral Indices of Nonthermal Emissions Derived from Hard X-Rays and Microwaves",
"content": "Ayumi Asai 1 , Junko Kiyohara 2 , Hiroyuki Takasaki 2 , 3 , Noriyuki Narukage 4 , Takaaki Yokoyama 5 , Satoshi Masuda 6 , Masumi Shimojo 7 , and Hiroshi Nakajima 7 [email protected]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "During the impulsive phase of solar flares, electrons are accelerated up to the energy of MeV, and are responsible for nonthermal emissions with power-law spectra observed in hard X-rays (HXRs) and in microwaves. In HXRs the bremsstrahlung emission from electrons with the energy of more than tens of keV is dominant (Brown 1971), while the gyrosynchrotron emission from more than several hundreds of keV electrons is dominant in microwaves (White & Kundu 1992; Bastian et al. 1998; Bastian 1999). HXR and microwave nonthermal emissions are very similar in the light curves (e.g., Kundu 1961; Kai 1986), and therefore, it has been generally accepted that they are produced by a common population of accelerated electrons. The electron spectra derived from HXR emissions are, on the other hand, often different from those derived from microwave emissions. The electron spectral indices of the power-law distribution derived from HXRs δ X are, in many cases, larger than those derived from microwaves δ µ , that is δ X > δ µ (Kundu 1965; Silva et al. 1997, 2000). According to the study by Silva et al. (1997), the average gap between δ X and δ µ , ∆ δ (= δ X -δ µ ) is 0.5 - 2.0. This means that microwave spectra are harder than the HXR ones, and that acceleration and/or traveling mechanisms could be different for these wavelengths. For example, Melrose & Brown (1976) suggested the so-called trap-plus-precipitation model, in which the magnetic trap works more effectively for such higher energy electrons that emit microwaves than HXR emitting electrons with lower energy. Minoshima et al. (2008), on the other hand, showed in their numerical calculation that the gap ∆ δ is naturally generated even from the electron distribution with a single power-law spectrum, since microwave and HXR emissions are from different electrons (trapped and precipitating ones, respectively.) In the early phase of a flare, however, the magnetic trap is probably not so effective, and we can examine the features of the nonthermal electrons without having to deal with the trapping effect. Moreover, it is crucially important to analyze imaging data both in HXRs and in microwaves, since we can resolve spatially the precipitating (at footpoints) and trapped (at loop tops) components with them. In this paper, we report the results of the analyses on the electron spectral indices derived from HXRs and microwaves, and also discuss the temporal and spatial characteristics. We used the HXR data obtained with the Hard X-ray Telescope (HXT; Kosugi et al. 1991) aboard the Yohkoh satellite (Ogawara et al. 1991). The microwave data were taken with the Nobeyama Radio Polarimeters (NoRP; Torii et al. 1979; Shibasaki et al. 1979; Nakajima et al. 1985a), and the Nobeyama Radioheliograph (NoRH; Nakajima et al. 1994) at Nobeyama Solar Radio Observatory, National Astronomical Observatory of Japan. These data enable us to examine the nonthermal features of the accelerated electrons spatially, temporally, and spectroscopically both in HXRs and in microwaves. In § 2 and § 3 we summarize the observations and the method of the analyses, respectively, and we show the results of the statistical analyses in § 4. In § 5 we present discussions and our conclusions.",
"pages": [
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},
{
"title": "2. Observations",
"content": "We used HXR data obtained with Yohkoh /HXT. By using the HXT data, we can synthesize the HXR images in four energy bands, namely the L band (14 - 23 keV), M1 band (23 - 33 keV), M2 band (33 - 53 keV), and H band (53 - 93 keV). The spatial and temporal resolutions of the HXT images are 5 '' and 0.5 s, respectively. To obtain the HXR photon spectral index γ ( I X ( /epsilon1 ) ∝ /epsilon1 -γ , where I X is the HXR intensity, and /epsilon1 is energy of the photon), we used the data in the two highest energy bands, i.e., the HXT M2 and H bands, because HXR emissions with energy less than 30 keV sometimes suffer from the contribution of the thermal emissions. Therefore, the HXR photon spectral index γ is roughly written as -log( I X (H) /I X (M2))(log( /epsilon1 H //epsilon1 M2 )) -1 , where /epsilon1 M2 and /epsilon1 H are the effective energies for the M2 and H bands. Though, as we will discuss later, some events showed the effects of the super-hot thermal components even in the M2 band. In this work we calculated the HXR photon spectral indices by using the programs hxt_powerlaw in the Solar SoftWare (SSW) package on IDL. We accumulated the HXT data for two seconds in the spectral analyses to reduce the photon noise. We also used the HXR spectra derived from the Wide Band Spectrometer (WBS; Yoshimori et al. 1991). The Hard X-ray Spectrometer (HXS), one of the sensors installed on the WBS, is dedicated to taking HXR spectra over a wide energy range. WBS/HXS can obtain HXR spectra with higher spectral resolution than HXT, although it cannot obtain the spatial information. Therefore, the data of WBS/HXS and HXT are complementary for the imaging spectroscopy in HXRs. Sato et al. (2006) summarized all the events observed by WBS, and we used their database of the HXR spectra. In microwaves the gyrosynchrotron emission is dominant during the impulsive phase of a flare. The spectrum in microwave range F ν is approximately fitted with the two power-law indices α tk and α tn by the function as follows: The optically thin part, therefore, follows the power law distribution with a negative spectral index α (= α tn ) as F ν ∝ ν α , where F ν is the flux density at frequency ν (e.g. Ramaty (1969); Dulk (1985)). In this study we used the microwave data taken with NoRP, which measures the total fluxes at 1, 2, 3.75, 9.4, 17, 35, and 80 GHz, with a temporal resolution of 0.1 s. By fitting a NoRP spectrum with the equation (1), we can obtain the spectral index α P for the optically thin gyrosynchrotron. We did not use the NoRP 80 GHz data in this work due to the poor statistics. For some events, the NoRP 1 GHz data were also ruled out, because they clearly did not follow the gyrosynchrotron, but instead, the plasma emission. We accumulated the NoRP data for 5 s to reduce the noise level. The microwave fluxes of the NoRP data are determined with the error of less than 10 % of the signal for 1, 2, 4, 9.4 GHz, and 15 % for 17 and 35 GHz, which is mainly due to the observation conditions such as the calibration and the weather. The error to determine α P is also affected by the accuracy of fitting, and is finally estimated to be about ± 0.5. NoRH also observes the sun at 17 and 34 GHz. The microwave 2-dimensional images are synthesized from the NoRH data, and the spatial resolutions (FWHMs of the synthesized beam) of about 14 '' for 17 GHz and 7 '' for 34 GHz. The time cadence of the data we used in this work is one second. We can derive the two-dimensional distribution (map) of the microwave spectral indices using the NoRH data ( α H ), by calculating log( F 34GHz /F 17GHz )(log(34GHz / 17GHz)) -1 for each position of images. If we assume that the turnover frequency is less than 17 GHz, the derive α H is for the optically thin gyrosynchrotron emission. Here, we have to note the calibration of the NoRH 17 and 34 GHz data. NoRH calibrates phase and gain by using the sun itself (i.e. the solar disk) as a calibrator, thanks to the redundant antenna configuration. However, the fundamental (smallest) spacing of the antennas (= 1 . 5 m) corresponds to the maximum wavelength in the space of 20 ' (= 1200 '' ) at 34 GHz, which means that the whole solar disk is not resolved. The solar disk at 34 GHz is partially overlapped with other fake solar disk images, and therefore, the background (quiet) solar disk is possibly not well determined. To correct this, we adjusted the flux of the flare region taken by NoRH 34 GHz, which is subtracted by the preflare data, to the fitting results derived from NoRP. NoRP calibrates those fluxes by using sky and absorber levels. In our cases the NoRH 34 GHz fluxes are usually smaller than the NoRP 35 GHz ones, and the ratio (NoRH 34 GHz)/(NoRP 35 GHz) is from 0.4 to 1.2. This calibration possibly reduces the derived spectral index α H about -1.0 at a maximum. We also corrected the NoRH 17 GHz flux of the flare region, by using the fitting result from NoRP. Although the correction ratio (NoRH 17 GHz)/(NoRP 17 GHz) ranges from 0.6 to 1.2, it is roughly comparable to 1 in most cases. This calibration causes the error on α H , mainly due to the measurement error of the radio flux by NoRP, and is about 0.4. The relative displacement between the images in 17 GHz and those in the 34 GHz due to the NoRH image syntheses also causes the error to estimate the spectral index α H . The NoRH image syntheses hold an uncertainty on the positioning of about 5 '' , and in this case, the error on α H is about ± 0.2 for bright emission sources.",
"pages": [
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},
{
"title": "3. Data Analyses",
"content": "Strong (i.e., intense) and large events are preferable for our imaging spectroscopic analyses. Therefore, we sought solar flares observed by HXT, NoRH, and NoRP for the period from the start of the dual-frequency observation with NoRH (November 1995) to the end of the observation of Yohkoh (December 2001), and selected 12 flare events that meet the following criteria; (1) The flare is larger than M1.0 on the GOES scale. (2) The flare is an event listed in The Yohkoh HXT/SXT Flare Catalogue (Sato et al. 2003), and the maximum HXR intensity is so strong that the counts per second per subcollimator in the HXT M2 band are larger than 30. (3) The spatial size of the microwave emission source observed with NoRH at 17 GHz is large enough, and it is more than 4 times of the beam size. (4) The microwave images can be successfully synthesized from the NoRH data, in other words, the microwave emissions are not extremely strong 1 . (5) The optically thin parts of the gyrosynchrotron emission are well defined from the NoRP data, which means that the turn-over frequencies determined from the fitting do not reach 17 GHz or more. (6) The peak time of the event is between 00:00 UT to 06:00 UT, which corresponds to 09:00 and 15:00 JST (i.e. Japanese daytime), and the NoRH beam pattern is not so distorted. Table 1 lists all the 12 flares. Figure 1 also shows temporal and spatial features of each event. The selected events are widely distributed longitudinally and in the flare size.",
"pages": [
5
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},
{
"title": "3.1. HXR Spectral Indices",
"content": "In the selected events we confirmed that the dominant HXR emissions are from footpoints of flare loops, and no loop top HXR sources are included, such as those reported by Masuda et al. (1994). This means that they are produced by bremsstrahlung caused by the interactions between the precipitating energetic electrons and the dense chromospheric plasma. Therefore, it is reasonable that we adopt the thick-target model (Brown 1971; Hudson et al. 1978; Sakao 1994) for the HXR emission sources. In this paper we determined the spectral indices γ from the total HXR intensities, assuming that the HXR emissions from the footpoint sources are so strong that we can approximately equate the total intensities to the emissions from the footpoint source. /negationslash The thick-target model suggests the relation between γ and the spectral index δ ' X of the number flux of the injected energetic electrons F N ( E ) (= dN ( E ) /dt ∝ E -δ ' X ), as δ ' X = γ +1 . 0. To estimate the spectral index δ X of the accelerated electron N ( E ), we further have to consider the traveling time of the electrons τ ( N ( E ) ≈ F N ( E ) τ ∝ E -δ X ), since energydependent τ moderates the spectral index and δ ' X = δ X . In this paper we adopted the typical timescale over which the precipitating electrons travel the effective length L in the flare loops with the velocity v , that is, τ = Lv -1 . The traveling time is proportional to v -1 , that is, τ ∝ E -0 . 5 . Then, the electron spectral index derived from the HXR emissions δ X follows the relation, δ X = γ +1 . 5. The seventh column of Table 1 shows the derived spectral index δ X at a time when the HXR emission records the maximum in the HXT M2 band for each event as shown in the second column. The derived δ X ranges from 3.8 to 6.6. The error to estimate the spectral index γ is about ± 0.5, and the same is true for δ X , under the assumption of single powerlaw HXR spectra. The photon noise is the main factor of the error, and therefore, it is even reduced during strong HXR emissions (to about ± 0.2). As shown in Figure 1, in most cases, the temporal variations of the spectral index, which are plotted with the cross mark (+), show the soft-hard-soft (SHS) behavior at the peak times of the HXR emissions. Therefore, δ X recorded in Table 1 is roughly the minimum value during the burst. As we describe below, for the 2000 January 12 (event b) and the 2000 March 3 (event f) flares, we chose other sub-peaks instead of the maximal intensities, because we could not well fit the microwave spectra. In Figure 2 we show the HXR spectra derived from WBS/HXS. These are from the database of Sato et al. (2006). The times on the top are the integration time in UT, and they almost cover the HXR maxima. The solid lines are the power-law distribution of the HXR spectra derived from HXT, while the absolute values are arbitrary. For the 2000 March 3 (event f) and the 2001 March 30 (event k) flare, the integration times of WBS/HXS are out of the HXT peak times we took. We can confirm that the HXR spectral indices derived from HXT fit the HXR spectra of WBS/HXS within the margin of errors as small as ± 0.2 (Sato et al. 2006).",
"pages": [
6,
7
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},
{
"title": "3.2. Microwave Spectral Indices",
"content": "Next, we derived the spectral indices of the accelerated electrons δ µ from the microwave emissions taken with NoRP. For the optically thin gyrosynchrotron emission, α is related to the spectral index of the accelerated electrons δ µ . There have been several studies to derive the relation between δ µ and α , and we adopt the approximation derived by Dulk (1985) here, and δ µ = (1 . 22 -α ) / 0 . 9. In this paper, we distinguish the spectral index derived from NoRP δ µ P from that from NoRH δ µ H with the subscripts P and H . Figure 3 shows some examples of the NoRP spectra and the fitting result at the time of HXR maximal intensity (column 2). The eighth column of Table 1 also shows the spectral index derived from NoRP δ µ P at the time of the HXR maxim. As we mentioned above ( § 2), the error to determine α P is about ± 0.5, and therefore, that for δ µ P is about ± 0.6. We confirmed that the contribution from the free-free emission at the 35 GHz is negligible. The temporal variations of the δ µ P follow the gradual-hardening (GH) or soft-hard-harder (SHH) behaviors as shown in Figure 1. We added the gap between the spectral index derived from HXRs and that from microwaves ∆ δ = δ X -δ µ P in the ninth column. We will discuss ∆ δ in more detail later. For the 2000 January 12 and 2000 March 3 flares (events b and f, respectively), the turnover frequencies are higher than 20 GHz at the HXT maxima, and we could not well fit the spectral indices α for the optically thin part of the gyrosynchrotron emission. Therefore, we chose other sub-peaks of the HXR light curves of these events for the spectral analysis. These peak times are shown with gray vertical lines in Figure 1. From the NoRH data, we can derive the spatially resolved spectral indices α H (and therefore, δ µ H ). We can compare, for example, δ µ H at the footpoint sources with that of the loop-top ones. As we just mentioned, we confirmed that the turnover frequencies derived from NoRP are lower enough than 17 GHz except for the peak times of the events (b) and (f). For the two events, we again selected preceding sub-peaks for further spectral analyses. Therefore, the indices α H derived from only two frequencies (17 and 34 GHz) are mainly for the optically thin gyrosynchrotron, while we cannot rule out the possibility that they are locally enhanced to be close to or larger than 17 GHz. Figure 1 shows such two-dimensional distribution of the indexα H , which we call ' α -map' in the bottom right sub-figure.",
"pages": [
7
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},
{
"title": "4. Results",
"content": "Table 1 lists the selected 12 events, with the peak time of the HXT M2 band (column 2), the delay of the peak times of microwave (NoRP 17 GHz) compared to those of HXR (HXT M2 band) in second (column 3), the spectral index derived from HXT δ X (column 7), that derived from NoRP δ µ P (column 8), and the gap ∆ δ (= δ X -δ µ P ) (column 9). In Figure 1 we present the time profiles of the HXR flux of HXT M2 band and the microwave flux at 17 GHz taken with NoRP (top left). The time profiles of the spectral indices δ X and δ µ P are also shown with the cross (+) and square ( /square ) signs, respectively, in the bottom left sub-figure. We also present the contour images in the microwave taken with NoRH at 17 GHz (top right) of the selected events. The contour levels of the microwave images are 20 %, 40 %, 60 %, 80 %, and 95% of the peak intensity. The microwave images are overlaid with the HXR contour images taken with HXT M2 band with the contour levels of 20 %, 40 %, 60 %, 80 %, and 95% of the peak intensities.",
"pages": [
8
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},
{
"title": "4.1. Peak Delay of Microwave Emissions",
"content": "As the top left sub-figures of Figure 1 show, the microwave peaks almost always delay from the HXR peaks. The delay times for the events are listed in the third column of Table 1. These delays of microwave peaks to HXR ones have been often observed, and reported by various authors (e.g., Gudel et al. 1991). In the current case the delays are from 0 to 21 seconds, and the average is 7.3 seconds. These are comparable with the result by Nakajima et al. (1985b). Delays of microwave peaks to HXT ones are thought to be caused by magnetically trapping for microwave-emitting electrons, while HXR emissions are from the directly precipitated electrons to the chromosphere.",
"pages": [
8
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},
{
"title": "4.2. Gap of Spectral Indices ∆ δ",
"content": "According to the results summarized in Figure 1 and Table 1, especially concerning the gap ∆ δ , we first categorize these events into two groups. As we mentioned above, the temporal variations of δ X clearly show the SHS behavior at the peaks, while those of δ µ P show hardening features (GH or SHH) as flares progress. In most cases, therefore, the listed gap ∆ δ is the smallest value near the HXR peaks. For all events, the gap ∆ δ is always positive, which means that the electron spectra derived from microwaves of this group are always harder than that from HXRs. The first is the group with smaller gap (∆ δ < 2.2). This group shows the electron spectral index derived from HXRs δ X of about 4.6 ± 0.8, while that derived from microwaves δ µ P is about 3.0 ± 0.8. The gap ∆ δ of about 1.6 is well consistent with the result by Silva et al. (2000). The eight events (from a to h) belong to this group. The other 4 events (from i to l), which belong to the second group, have much larger gaps ∆ δ of greater than 2.7. In particular, the electron spectral index derived from HXRs δ X is much larger than those of the first group, and is about 6.2 ± 0.5. We checked the HXT data for those events, and concluded that the HXR emissions suffered from the thermal components even in the M2 band. The HXR spectra derived from WBS/HXS (Fig. 2) are also very soft. Huang et al. (2006) studied one of them (the 1998 November 28 flare; event i), in more detail, and concluded that there is a vast super-hot thermal component in this flare, which softens the HXR spectrum. Henceforth, we discuss only the first group. Even after we eliminate the second group, there remains the gap ∆ δ . Figure 4 shows the scatter plot with the horizontal axis of δ X and the vertical axis of δ µ P . The events are marked with the asterisks ( ∗ ). The solid line shows the points where δ X is equal to δ µ P . This also suggests that there is a certain gap between the spectral indices ∆ δ .",
"pages": [
8,
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},
{
"title": "4.3. Microwave Emission Sources",
"content": "As shown in Figure 1, the sites of the dominant microwave emissions are different for each event. According to the spatial displacement between the brightest position of the microwave emission sources and those of the HXR sources, and/or by using imaging observations in soft X-rays and in extreme ultraviolets, we categorized the microwave emission sources into two cases; footpoint source (group F; displacement is less than 5 '' ) and loop source (group L; displacement is larger than 5 '' ) as noted in the sixth column of Table 1. Here, we note that the brightest microwave emission source seen in the 2000 November 25 flare (event g) is confirmed to be a footpoint source (Takasaki et al. 2007), although it is displaced from the HXR source of about 40 '' . Therefore, we categorized this case as a footpoint event. We confirmed that the dominant microwave emission sources appear at the tops or legs of flare loops for many cases (5 of 8 events). This is consistent with the result of Huang & Nakajima (2009) or Melnikov et al. (2002). We will discuss the difference between the temporal evolution of the spectral indices for group L and that for group F in the next subsection.",
"pages": [
9
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},
{
"title": "4.4. Temporal Evolution of Spectral Indices",
"content": "We examine the temporal evolution of the spectral indices. The HXR spectral index δ X mostly shows the SHS behaviors at each short peak, while two of them (events f and g) show even GH features. The temporal evolution of the microwave spectral index δ µ P , on the other hand, seems different, according to the position of microwave emission sources (i.e. group L/F). For group L (events a, b, c, d, and e), the time profiles of the spectral indices ( δ µ P and δ X ) show similar evolution from start to peak of the bursts, while the gap ∆ δ increases with time after the peaks. In other words, the electron spectral index derived from HXRs δ X increases after the peaks, showing the SHS features, while the electron spectral index from microwaves δ µ P becomes further smaller showing SHH or GH features. For group F (events f, g, and h), on the other hand, both the spectral indices ( δ µ P and δ X ) show similar evolution through the impulsive phase while maintaining a gap of about 1.6. However, event (h) is different from the other two events of group F. This event shows the SHS features both in the microwave index δ µ P and in the HXR index δ X , while the others show GH features. From the point of the temporal evolution, we can, therefore, re-classify the eight events into the three groups: (L) microwave emission sources are located at loop tops/legs, and δ X and δ µ P show SHS and GH features, respectively (events a, b, c, d, and e), (F) microwave emission sources are from footpoints, and both δ X and δ µ P show GH features (events f and g), (F ∗ ) microwave emission source is again from footpoints, but both δ X and δ µ P show SHS features (event h). Figure 5 is roughly a realignment of Figure 1, but much more focuses on the temporal evolution of the microwave spectral index δ µ P during the bursts for the groups (L; top) and (F; bottom). The vertical dotted lines correspond to the times when the microwave 17 GHz fluxes taken by NoRP exceeds 100 SFU (Solar Flux Unit). We determine this time as the start of the bursts. The vertical dashed lines correspond to the times when the 17 GHz fluxes become half of the peak values. We define this time as the end of the bursts. Although even after the end times the microwave indices δ µ P become smaller, the fluxes probably suffer from the thermal component in the microwave emissions, which should be avoided from the analysis. For the 2000 November 25 flare (event g), we defined the end time just after the peak HXR time, since the hardening seems saturated after 01:12 UT, and no further hardening is seen. The bottom panels again show the time profiles of the spectral index δ µ P with the square ( /square ) marks. The overlaid time profiles are the spectral index δ X (cross +). We subtracted 1.5 from the original value of the index to clearly show the temporal variation. The numbers noted in the figure show how much the microwave spectral indices δ µ P decrease during the two vertical dotted lines. We also summarized the hardening degree in the tenth column of Table 1. As a result, the nonthermal spectra harden with the indices of 1.0 on the average. The hardening with the microwave spectral index of about 1 seems to be consistent with the discussion of the trapping time of relativistic electrons (Bai and Ramaty 1979; Petrosian 1985). From the start to the peak of the HXR bursts, which corresponds to the time range from the dotted line to the thick gray line in Figure 5, both the time profiles of the microwave spectral index δ µ P and that of the HXR spectral index δ X decrease simultaneously, keeping a certain gap ∆ δ of about 1.5. The 2000 November 25 flare (event g) is a special case due to the very long duration and the smooth variation of the HXR and microwave emissions (Takasaki et al. 2007). This flare shows GH features even in the HXR spectral evolution, and is a typical 'type-C flare' (e.g. Hoyng et al. 1976), which have been discussed from the Hinotori era (Cliver et al. 1986; Kai 1986; Dennis 1985; Kosugi et al. 1988). These imply that the magnetic trap effectively works both on the microwave-emitting electrons and even on the HXR-emitting electrons. The HXR-emitting electrons are trapped in the magnetic loop at least once before they precipitate into the chromosphere. The dominant microwave emission source is located at the footpoint conjugated with the HXR source, which means that these microwave-emitting electrons escape from the magnetic trap. As Takasaki et al. (2007) reported, on the other hand, the microwave footpoint emission source disappears and the dominant emission source is from the loop top during the valley times. Therefore, the gaps ∆ δ increase during the valley times.",
"pages": [
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},
{
"title": "4.5. Spatial Features of Spectral Index δ µ",
"content": "The difference between the microwave emission sources and the HXR emission sources implies that the microwave emissions mainly come from electrons trapped magnetically within the flare loop that connects the HXR footpoint sources. Spatially resolved analyses on the spectral indices are, therefore, required for these events, to explain the reason for the certain gap ∆ δ of about 1.6 confirmed in current study. By using the NoRH data, we examine the spatial distribution of the spectral indices derived from microwaves, and compare the value at the footpoint ( δ µ H (X)) with that at the loop top ( δ µ H ( µ )). First, we derived the electron spectral index from NoRH microwave emission δ µ H at the brightest emission positions. The brightest regions are determined to be regions where the intensities at 17 GHz are larger than 80 % of the maximum intensities, and the derived spectral index is noted as δ µ H ( µ ). For many cases in our results, the dominant microwave emissions are from loop tops (or legs), and δ µ H ( µ ) show the values there. The twelfth column of Table 1 presents the list of δ µ H ( µ ). These items roughly correspond to those derived from the total intensity δ µ P (column 8) with the displacement of about 0.5. The displacement is probably due to the spatial distribution of the spectral index. For the 2000 October 29 flare (event e), we failed to correctly derive the α -map, because of a large displacement between the position of the NoRH 17 GHz emission source and that at NoRH 34 GHz. The displacement is as large as 10 '' . Although the reason is unknown, it may be caused by other energy release processes that occurred in the preflare phase. We omitted this event from the further discussions. Second, we determined the spectral index at the HXR footpoints, that is, δ µ H (X) from the NoRH α -map. If there are two HXR footpoint sources, we calculated them separately. For events (f) and (h), we could not, however, correctly derive the spectral index. This is because the HXR footpoint positions are too close to the loop top/leg microwave emission sources, and they are not spatially resolved. For events (a) and (b), one of the two footpoints is too close to the microwave emission source. We showed the spectral indices δ µ H (X) for these footpoint sources in parentheses in the eleventh column of Table 1. The number I/II is the same as that marked for the HXR footpoints in the Figure 1. Here we have to note that the error of δ µ H (X). The microwave emission from footpoints is weaker than that from loop tops/legs for most cases, and therefore, the error to estimate the spectral index δ µ H (X) could be larger than that for loop top one ( δ µ H ( µ )). We roughly expect the error to be about ± 0.7. Except for the 2000 April 8 flare (event c), we found the relation that the spectral indices for footpoint sources are larger, which corresponds to the softer spectra, than those at the loop tops/legs, that is, δ µ H (X) > δ µ H ( µ ). Especially, in events (d) and (g), δ µ H (X) is quite close to the δ X . We will discuss the spatial features of the spectral index δ µ and the relation with the magnetic field in the next section.",
"pages": [
11,
12
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},
{
"title": "5. Discussion and Conclusions",
"content": "We examined the electron spectral indices of nonthermal emissions seen in HXRs ( δ X ) and in microwaves ( δ µ ) for 12 flares observed by Yohkoh /HXT NoRP, and NoRH. Eight flares of the selected 12 events show gaps between the spectral indices, i.e. ∆ δ of about 1.6. The gaps are consistent with the result of Silva et al. (2000). The other four events show larger gaps ∆ δ > 2.7, since they suffer from softening of the HXR spectra (i.e. enlarging the HXR spectral index δ X ) due to the super-hot thermal component even in the HXT M2 band. In spite of the fact that we examined the spectral features for the impulsive phase to avoid the effect of magnetic trapping, there still remains a certain gap. On the other hand, from the start to the peak of the HXR bursts (that corresponds from the first vertical dotted line to the thick gray line in Figure 5), both the time profile of the microwave spectral index δ µ P and that of the HXR spectral index δ X decrease simultaneously, keeping a certain gap ∆ δ of about 1.6. We also investigated the positions of the emission sources by using the HXT and NoRH data. For five of the eight events, the brightest microwave emission sources are located on the loop tops (or legs; group L). On the other hand, for the other three events, they are different from the HXR emission sources, which are mainly from footpoints (group F/F ∗ )). This implies that the microwave emissions mainly come from electrons trapped magnetically within the flare loop that connects the HXR footpoint sources. The difference in the site of the emission sources possibly causes the gap of the spectral indices ∆ δ . The spatial distribution of the microwave spectral index derived from NoRH δ µ H should therefore be examined. Except for one event (event c), we confirmed that the microwave spectra for footpoint sources are softer than those at the loop tops/legs, that is, δ µ H (X) > δ µ H ( µ ). However, the spatial distribution of the microwave spectral index again cannot resolve the gap ∆ δ even at the sites of the HXR emission sources. From these results, we concluded that the spectra of the accelerated electrons have a bent, and become harder above several hundreds of keV. This is also consistent with results of previous studies (Yoshimori et al. 1985; Dennis 1988; Matsumoto et al. 2005). Minoshima et al. (2008) numerically calculated the spectral indices of microwave and HXR emissions from the trapped and precipitating electrons, and showed that a softer HXR spectrum and a hard microwave spectrum can be generated. The difference of the spectral indices ∆ δ ∼ 1.5, is consistent with our result. However, we showed that the spatially resolved distribution of the microwave spectral index in our study cannot resolve the gap ∆ δ even at the footpoint sources. This means that there still remains a certain gap ∆ δ . Here, we examine events (c) and (d) in more detail. Figure 6 shows the photospheric magnetograms for these events obtained by the Michelson Doppler Imager (MDI; Scherrer et al. 1995) aboard the Solar and Heliospheric Observatory ( SOHO ; Domingo et al. 1995). The levels of the contours are ± 400, ± 600, and ± 800 gauss with the red and blue lines for positive and negative magnetic polarities, respectively. We overlaid the microwave contour image of NoRH 17 GHz on each panel with light blue lines. The HXR contour image observed with HXT in the M2 band is also overlaid with green lines. The levels of these contours for both contour images are 40, 60, 80, and 95 % of the maximum intensities. From Figure 6, we clearly see weak magnetic field strength at HXR footpoints in event (c) of about 250 300 gauss, while there is quite a strong magnetic field in event (d) of about 900 - 1000 gauss. In event (d), therefore, we expect strong magnetic field for microwave footpoint position, and it could be several 100 gauss. The microwave gyrosynchrotron emission is strongly related to the magnetic field strength, and only high-energy electrons can contribute under the condition of weak magnetic field strength. On the other hand, with strong magnetic field, weaker energy electrons can contribute the emission. As Bastian (1999) calculated, electrons with the energy of about 500 keV contribute at 500 gauss, while the energy must be higher than 1 MeV at 200 gauss to generate 17 GHz emission. This means that low energy electrons with the energy of about several 100 keV emit the gyrosynchrotron at the footpoints. The energy of several 100 keV is as low as that for electrons emitting HXR bremsstrahlung, which causes a very soft spectrum that has the same spectral index δ µ H (X) as δ X . The magnetic field strength at the loop top must be much smaller, and the microwave-emitting electrons have high enough energy of about several MeV, at which the harder spectral component appears. On the other hand, in event (c), the magnetic field strength is weak even at the HXR footpoint sources. This means that high-energy electrons are responsible for the microwave emission even at the footpoint, which corresponds to the observed harder spectral component. From these results, we concluded that the bent of the electron spectra seems to be at about several 100 keV, which is consistent with the previous suggestions (Yoshimori et al. 1985; Dennis 1988). In Figure 3, we cannot see the clear bent of the HXR spectra derived from WBS/HXS, and therefore, the bent of HXR spectra in the current case occurs at the energy higher than 300 keV. We first would like to acknowledge an anonymous referee for her/his comments and suggestions. We would like to thank all the members of Nobeyama Solar Radio Observatory, NAOJ for their supports during the observation. We wish to thank Drs. S. Krucker and T. Minoshima for fruitful discussions and his helpful comments. This work was carried out by the joint research program of the Solar-Terrestrial Environment Laboratory, Nagoya University. The Yohkoh satellite is a Japanese national project, launched and operated by ISAS, and involving many domestic institutions, with multilateral international collaboration with the US and the UK. Facilities: NoRH, NoRP, Yohkoh.",
"pages": [
12,
13,
14
]
},
{
"title": "REFERENCES",
"content": "Bai, T. & Ramaty, R. 1979, ApJ, 227, 1072 Bastian, T. S., Benz, A. O., Gary, D. E. 1998, ARA&A, 36, 131 Bastian, T. S. 1999, in Proc. of the Nobeyama Symp. NRO No. 479, Ed. by T. Bastian, N. Gopalswamy, and K. Shibasaki (Nobeyama Radio Obs., Nagano, 1998), 211 Brown, J. C. 1971, Sol. Phys., 18, 489 806 Nakajima, H., Nishio, M., Enome, S., et al. 1994, Proc. IEEE, 82, 705 Ogawara, Y., Takano, T., Kato, T., Kosugi, T., Tsuneta, S., Watanabe, T., Kondo, I., and Uchida, U. 1991, Sol. Phys., 136, 10 Petrosian, V. 1985, ApJ, 299, 987 Ramaty, R. 1969, ApJ, 158, 753 Sakao, T. 1994, Ph.D. thesis, Univ. Tokyo Sato, J., Sawa, M., Yoshimura, K., Masuda, S., Kosugi, T. 2003, The Yohkoh HXT/SXT Flare Catalogue, (Montana State Univ., Montana; Inst. of Space and Astronautical Science, Sagamihara) Sato, J., Matsumoto, Y., Yoshimura, K., et al. 2006, Sol. Phys., 236, 351 Scherrer, P. H., et al. 1995, Sol. Phys., 162, 129 Shibasaki, K., Ishiguro, M., Enome, S. 1979, Proc. Res. Inst. Atmos., 26, 117 Silva, A. V. R., Gary, D. E., White, S. M., Lin, R. P., de Pater, I. 1997 Sol. Phys., 175, 157 Silva, A. V. R., Wang, H., Gary, D. E. 2000, ApJ, 545, 1116 Takasaki, H., Kiyohara, J., Asai, A., Nakajima, H., Yokoyama, T., Masuda, S., Sato, J., Kosugi, T. 2007, ApJ, 661, 1234 Torii, C., Tsukiji, Y., Kobayashi, S., Yoshimi, N., Tanaka, H., Enome, S. 1979, Proc. Res. Inst. Atmos., 26, 129 White, S. M., Kundu, M. R. 1992, Sol. Phys., 141, 347 Yoshimori, M., Watanabe, H., Nitta, N. 1985, J. Phys. Sol. Japan, 54, 4462 Yoshimori, M., Okudaira, K., Hirasima, Y. 1991, Sol. Phys., 136, 69 f o le ) µ ( H µ δ ) X n io ) 2 1 ( ) 1 ) .1 3 .2 2 .1 2 .8 2 2 i 1 i 1 i i 3 i i 5 0 W 0 7 W 5 7 E 8 2 E 4 3 E .9 2 ) .3 3 6 W .1 2 .8 6 4 E - 17 - .9 1 ) .5 2 4 W 1 4 E 1 6 W 1 8 :1 3 :1 4 0 6 1 p e S 0 0 0 2 ) d ( 1 8 :5 1 :2 1 0 5 2 v o N 0 0 0 2 ) g ( 2 7 :2 0 :4 5 0 8 2 v o N 8 9 9 1 i) ( 1 2 :2 9 :4 5 0 4 0 g u A 9 9 9 1 ) j ( t s t n e v e . T p o t p o e m F d n a c U n i d n d n a b 2 X H e h t o t 7 1 ( s e m i t k a e p e v a w o r c i m e h t f o y a l e D b T X H e h t n i x u fl R X H e h t f o e m i t k a e P a r u o s n o i s s i m e e v a w o r c i m e h t f o n o i t i s o P c 1 8 :3 3 :0 4 0 0 1 r a M 1 0 0 2 ) h ( - - 4 * 4 :0 2 :1 2 0 3 0 r a M 0 0 0 2 ) f ( 5 6 :0 7 :4 1 0 9 2 t c O 0 0 0 2 ) e ( 3 3 5 4 * 9 0 p e S 8 9 9 1 ) a ( 2 1 n a J 0 0 0 2 ) b ( 8 0 r p A 0 0 0 2 ) c ( 1 0 E 0 6 :3 4 :3 4 0 5 2 p e S 1 0 0 2 l) ( a t a D ) 1 ( - - 8 1 W 3 5 :1 3 :1 5 0 0 3 r a M 1 0 0 2 ) k ( - µ δ - X δ = δ ∆ , s e c i d n i e h t n e e w t e b p a G d . 6 e r u g i F d n a t x e t , e e S . s t s r u b e h t g n i r u d e e r g e d g n i n e d r a H e 60 40 20 0 180 120 60 0 63 42 21 0 720 480 240 0 45 30 15 0 780 520 260 0 120 2415 1610 805 330 220 110 1200 800 400 375 250 125",
"pages": [
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}
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2013ApJ...763...99P
https://arxiv.org/pdf/1212.1306.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_83><loc_89><loc_85></location>EQUILIBRIUM DISKS, MRI MODE EXCITATION, AND STEADY STATE TURBULENCE IN GLOBAL ACCRETION DISK SIMULATIONS.</section_header_level_1>
<text><location><page_1><loc_39><loc_81><loc_61><loc_82></location>E. R. Parkin & G. V. Bicknell</text>
<text><location><page_1><loc_21><loc_79><loc_79><loc_81></location>Research School of Astronomy and Astrophysics, The Australian National University, Australia Draft version September 17, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_76><loc_55><loc_77></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_56><loc_86><loc_76></location>Global three dimensional magnetohydrodynamic (MHD) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied. The local linear theory of the magnetorotational instability (MRI) is used as a predictor of the growth of magnetic field perturbations in the global simulations. The linear growth estimates and global simulations diverge when non-linear motions perhaps triggered by the onset of turbulence - upset the velocity perturbations used to excite the MRI. The saturated state is found to be independent of the initially excited MRI mode, showing that once the disk has expelled the initially net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of converged turbulence, such as the ratio of magnetic energies, are found to be in agreement with previous works. In particular, the globally averaged stress normalized to the gas pressure, < α P > = 0 . 034, with notably higher values achieved for simulations with higher azimuthal resolution. Supplementary tests are performed using different numerical algorithms and resolutions. Convergence with resolution during the initial linear MRI growth phase is found for 23 -35 cells per scaleheight (in the vertical direction).</text>
<text><location><page_1><loc_14><loc_54><loc_82><loc_55></location>Subject headings: accretion, accretion disks - magnetohydrodynamics - instabilities - turbulence</text>
<section_header_level_1><location><page_1><loc_22><loc_50><loc_35><loc_52></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_31><loc_48><loc_50></location>Accretion disks are ubiquitous in astrophysics and play an essential part in the formation of stars and galaxies. For accretion through a disk to be effective, angular momentum must be transported radially outwards, allowing material to move radially inwards. One means of achieving this is through viscous torques (Lynden-Bell & Pringle 1974), and considerable progress has been made using the phenomenological α -viscosity introduced by Shakura & Sunyaev (1973) which assumes that viscosity is provided by turbulent stresses which scale with the gas pressure. However, despite its successes, the α -viscosity model provides little physical insight into the mechanism(s) responsible for the turbulent stress.</text>
<text><location><page_1><loc_8><loc_7><loc_48><loc_31></location>Even prior to the work of Shakura & Sunyaev (1973), instabilities in magnetized rotating plasmas had been discovered by Velikhov (1959) and Chandrasekhar (1960). Yet, it was not until the seminal work of Balbus & Hawley (1991, 1998) that the so-called magnetorotational instability (MRI) received widespread attention as the agent responsible for the onset of accretion disk turbulence. Linear stability analysis has shown that the MRI will amplify a seed magnetic field indefinitely until confronted by the strong-field limit or the diffusion scale (Balbus & Hawley 1992; Terquem & Papaloizou 1996; Papaloizou & Terquem 1997). Non-linear stability analysis finds that growth of the magnetic field by the linear phase of the MRI is likely to be truncated by saturation resulting from secondary, or parasitic, instabilities (e.g. Goodman & Xu 1994; Pessah 2010). That saturation of the magnetic field occurs was clearly demonstrated by even the very first shearing box sim-</text>
<text><location><page_1><loc_52><loc_49><loc_92><loc_52></location>ulations (Brandenburg et al. 1995; Hawley et al. 1995; Stone et al. 1996).</text>
<text><location><page_1><loc_52><loc_5><loc_92><loc_49></location>Contemplating the next steps in magnetized disks studies is aided by summarising what we have already learned. For example, as mentioned above, it is clear that the magnetic field reaches saturation and that the resulting Maxwell stress dominates the angular momentum transport. In numerical simulations this necessitates high resolution to ensure that the fastest growing MRI modes are sufficiently well resolved (see, e.g., Sano et al. 2004; Fromang & Nelson 2006; Noble et al. 2010; Flock et al. 2011; Hawley et al. 2011). Related to this point is the importance of stratification, which introduces a characteristic length scale, removing the problem of non-convergence with simulation resolution encountered in unstratified simulations (Fromang & Papaloizou 2007; Lesur & Longaretti 2007; Simon et al. 2009; Guan et al. 2009; Davis et al. 2010; Sorathia et al. 2012). Stratification could also play a role in the dynamo process which sets the saturation stress (Brandenburg 2005; Vishniac 2009; Shi et al. 2010; Gressel 2010). However, the shearing box approximation used in a large number of numerical studies to-date has limitations (e.g. Regev & Umurhan 2008; Bodo et al. 2008, 2011), including the use of shearingperiodic boundary conditions in the radial direction, and/or periodic boundary conditions in the vertical direction. There boundary conditions artificially trap magnetic flux, assisting the maintenance of the turbulent dynamo and obscuring the dependence of the saturated state on resolution. This is supported by a comparison of periodic and open boundary conditions in global models by Fromang & Nelson (2006) where the former were found to assist the dynamo by preventing magnetic flux from being expelled from the domain. In this re-</text>
<text><location><page_2><loc_8><loc_86><loc_48><loc_90></location>gard global models have the advantage of removing the unphysical influence of the shearing box boundary conditions, albeit at a much larger computational expense.</text>
<text><location><page_2><loc_8><loc_70><loc_48><loc_86></location>Other motivations for global models are the results from stability analyses of non-axisymmetric disturbances in magnetized accretion disks, where the most robust MRI modes are localized and the most robust buoyant (Parker) modes are global (Terquem & Papaloizou 1996; Papaloizou & Terquem 1997). Therefore, large radial extents are required to accommodate the more global modes, and in this regard there is a limit to the radial periodicity adopted in most shearing box simulations. These factors point to the need for high resolution, global, stratified disk simulations to further unravel the complexities of magnetorotational turbulence.</text>
<text><location><page_2><loc_8><loc_36><loc_48><loc_70></location>Of the global simulation studies that have been performed a large number of the findings from local models have been maintained or have persisted; the ratio of the Maxwell and Reynolds stress is ∼ 3, and variations in toroidal magnetic field with time are suggestive of a dynamo cycle (Hawley 2000; Hawley & Krolik 2002; Fromang & Nelson 2006, 2009; Lyra et al. 2008; Sorathia et al. 2010, 2012; Flock et al. 2010, 2011, 2012; O'Neill et al. 2011; Hawley et al. 2011; Beckwith et al. 2011; Mignone et al. 2012; McKinney et al. 2012; Romanova et al. 2012). However, a large number of these simulations do not start from fully equilibrium initial conditions where the magnetic field is accounted for in the force balance and in the induction equation. Both local and global models started with poloidal fields which do not satisfy the induction equation show rapid disruption and re-arrangement of the disk (e.g. Miller & Stone 2000; Hawley 2000; Hawley et al. 2011). This introduces a transient phase where channel flows are fueled by rapid shearing of the poloidal field lines. As such, extended run times are required to ensure that transients have subsided. To our knowledge, no previous global simulations of the MRI in stratified disks have used a fully equilibrium initial disk (i.e. satisfying force balance and the induction equation).</text>
<text><location><page_2><loc_8><loc_18><loc_48><loc_35></location>We aim to explore the influence of magnetic fields on an accretion disk with global simulations. In this first paper we present equilibrium initial disk models with arbitrary radial density and temperature profiles. We then investigate the saturation (both locally and globally) of the growth of magnetic field perturbations. To this end we excite the MRI in global simulations using linear MRI calculations as a guide, and recover growth of magnetic field perturbations in agreement with estimates. In so doing we show that non-linear gas motions saturate the initial growth of the magnetic field and that at later times the turbulent state retains no knowledge of the initially excited MRI mode(s).</text>
<text><location><page_2><loc_8><loc_5><loc_48><loc_18></location>The plan of this paper is as follows: in § 2 we describe the equilibrium initial conditions and details of the numerical calculations and in § 3 we perform a linear perturbation analysis for the non-axisymmetric MRI. We present a suite of global magnetized disk simulations in § 4, which explore the effect of different MRI mode excitation and numerical algorithms. In § 5 we compare our results to previous work, and then close with conclusions in § 6.</text>
<section_header_level_1><location><page_2><loc_66><loc_89><loc_77><loc_90></location>2. THE MODEL</section_header_level_1>
<section_header_level_1><location><page_2><loc_65><loc_87><loc_79><loc_88></location>2.1. Simulation code</section_header_level_1>
<text><location><page_2><loc_52><loc_73><loc_92><loc_86></location>For our global disk simulations, we use a 3D spherical ( r, θ, φ ) coordinate system with a domain which closely encapsulates the initial disk (e.g. Fromang & Nelson 2006), and we solve the time-dependent equations of ideal MHD using the PLUTO code (Mignone et al. 2007). We note that throughout this work we describe our results in terms of both spherical ( r, θ, φ ) and/or cylindrical ( R,φ,z ) coordinates, with R = r sin θ and z = r cos θ . The relevant equations for mass, momentum, energy conservation, and magnetic field induction are:</text>
<formula><location><page_2><loc_70><loc_69><loc_92><loc_72></location>∂ρ ∂t + ∇· [ ρ v ] = 0 , (1)</formula>
<formula><location><page_2><loc_52><loc_66><loc_92><loc_69></location>∂ρ v ∂t + ∇· [ ρ vv -BB +( P + 1 2 | B | 2 ) I ] = -ρ ∇ Φ , (2)</formula>
<formula><location><page_2><loc_57><loc_63><loc_92><loc_66></location>∂E ∂t + ∇· [( E + P ) v -( v · B ) B ] = -ρ v · ∇ Φ -ρ Λ</formula>
<text><location><page_2><loc_90><loc_62><loc_92><loc_63></location>(3)</text>
<formula><location><page_2><loc_77><loc_58><loc_92><loc_61></location>∂ B ∂t = ∇× ( v × B ) . (4)</formula>
<text><location><page_2><loc_52><loc_49><loc_92><loc_58></location>Here E = ρ/epsilon1 + 1 2 ρ | v | 2 + 1 2 | B | 2 , is the total gas energy density, /epsilon1 is the internal energy per unit mass, v is the gas velocity, ρ is the mass density, and P is the pressure. We use the ideal gas equation of state, ρ/epsilon1 = P/ ( γ -1), where the adiabatic index γ = 5 / 3. The adopted scalings for density, velocity, temperature, and length are, respectively,</text>
<formula><location><page_2><loc_60><loc_40><loc_83><loc_48></location>ρ scale =1 . 67 × 10 -7 gm s -1 , v 0 = c, T scale = µmc 2 /k B = 6 . 5 × 10 12 K , l scale =1 . 48 × 10 13 cm ,</formula>
<text><location><page_2><loc_52><loc_36><loc_92><loc_40></location>where c is the speed of light, and the value of l scale corresponds to the gravitational radius of a 10 8 M /circledot black hole.</text>
<text><location><page_2><loc_52><loc_31><loc_92><loc_36></location>The gravitational potential, Φ of a central point mass (ignoring self-gravity of the disk), Φ is modelled using the pseudo-Newtonian potential introduced by Paczy'nsky & Wiita (1980):</text>
<formula><location><page_2><loc_68><loc_26><loc_92><loc_30></location>Φ = -1 r -2 . (5)</formula>
<text><location><page_2><loc_52><loc_12><loc_92><loc_27></location>Note that we take the gravitational radius (in scaled units), r g = 1. The Schwarzschild radius, r s = 2 for a spherical black hole and the innermost stable circular orbit (ISCO) lies at r = 6. The Λ term on the RHS of Eq (3) is an ad-hoc cooling term used to keep the scaleheight of the disk approximately constant throughout the simulations; without any explicit cooling in conjunction with an adiabatic equation of state, dissipation of magnetic and kinetic energy leads to an increase in gas pressure and, consequently, the disk scaleheight over time. The form of Λ is particularly simple,</text>
<formula><location><page_2><loc_62><loc_8><loc_92><loc_11></location>Λ = ρ ( γ -1) T ( R,z ) -T 0 ( R ) 2 πR/v φ (6)</formula>
<text><location><page_2><loc_52><loc_5><loc_92><loc_8></location>where T 0 ( R ) and T ( R,z ) are the position dependent initial and current temperature, respectively, v φ is the ro-</text>
<text><location><page_3><loc_8><loc_75><loc_48><loc_90></location>ational velocity, and R is the cylindrical radius. This cooling function drives the temperature distribution in the disk back towards the initial one over a timescale of an orbital period and is similar in its purpose to the cooling functions used by Shafee et al. (2008), Noble et al. (2010), and O'Neill et al. (2011). Note that we only apply cooling within | z | < 2 H , where H is the scaleheight of the disk, allowing heating via dissipation to occur freely in the corona. Our choice of an orbital period for the cooling timescale is somewhat arbitrary but is chosen as it represents a characteristic timescale for the disk.</text>
<text><location><page_3><loc_8><loc_54><loc_48><loc_75></location>The PLUTO code was configured to use the fivewave HLLD Riemann solver of Miyoshi & Kusano (2005), piece-wise parabolic reconstruction (PPM Colella & Woodward 1984), and second-order RungeKutta time-stepping. In order to maintain the ∇· B = 0 constraint for the magnetic field we use the upwind Constrained Transport (UCT) scheme of Gardiner & Stone (2008). Such a configuration has been shown to be effective in recovering the linear growth rates of the axisymmetric MRI by Flock et al. (2010). In § 4.4 we test a number of different numerical setups: order of reconstruction, slope limiters, and simulation resolution. However, in all of the other global simulations presented in § 4 we use reconstruction on characteristic variables (e.g. Rider et al. 2007). A Courant-Friedrichs-Lewy (CFL) value of 0.35 was used for all simulations.</text>
<text><location><page_3><loc_8><loc_5><loc_48><loc_54></location>The grid used for the global simulations is uniform in the r and φ directions and extends from r = 4 -34 and φ = 0 -π/ 2. In the θ direction we use a graded mesh which places slightly more than half of the cells within | z | ≤ 2 H of the disk mid-plane with a uniform ∆ θ , where H is the thermal disk scaleheight, and the remainder of the cells on a stretched mesh between 2 H < | z | < 5 H . For example, for simulation gblm 10 the 256 cells in the θ direction are distributed so that 140 cells are uniformly spaced between 2 H < | z | < 5 H . The respective grid resolutions and number of cells per scaleheight for the three global simulations are noted in Table 2. The grid cell aspect ratio at the mid-plane of the disk and at a radius of r = 18 . 5 (i.e. the disk midpoint) are r ∆ θ : ∆ r : r ∆ φ = 1 : 1 . 4 : 8 . 6 and 1 : 1 . 6 : 2 . 5 for models gblm 10 and gblm 10+, respectively. The r and θ boundary conditions depend on whether the cell adjacent to the boundary contains > 1% disk material - which we determine using a tracer variable. If this constraint is satisfied we use outflow boundary conditions on all hydrodynamic variables except v φ which is determined from a zero-shear boundary condition (i.e. d Ω /dr = 0) and the normal velocity, for which we enforce zero inflow. If the condition on disk material at the boundary is not satisfied we use outflow boundary conditions on hydrodynamic variables with the limit that the values must lie between the floor values and the initial conditions for the background atmosphere - we find this choice to be useful in setting up a steady background inflow during the early stages of the simulation before material initially in the disk evolves to fill the domain. For the magnetic field we use zero gradient boundary conditions on the tangential field components and allow the UCT algorithm to calculate the normal component so as to satisfy the divergence free constraint, with the exception that at the inner radial boundary we enforce a negative magnetic stress condition (e.g. Stone & Pringle 2001). A periodic</text>
<text><location><page_3><loc_52><loc_84><loc_92><loc_90></location>boundary condition is used in the φ direction. Finally, we use floor density and pressure values which scale linearly with radius and have values at the outer radial boundary of 10 -4 and 5 × 10 -9 , respectively.</text>
<section_header_level_1><location><page_3><loc_64><loc_82><loc_80><loc_83></location>2.2. Initial conditions</section_header_level_1>
<text><location><page_3><loc_52><loc_64><loc_92><loc_82></location>Motivated by the fact that magnetorotationally turbulent disks are dominated by toroidal field, we start from an analytic equilibrium disk with a purely toroidal magnetic field. The disk equilibrium is derived in axisymmetric cylindrical coordinates ( R,z ); further details can be found in Appendix A along with alternative disk solutions which may be of use in future work. In the following we briefly summarise the equations for the isothermal in height, T = T ( R ), constant ratio of gas-to-magnetic pressure, β = 2 P/ | B | 2 ≡ 2 P/B 2 φ , net magnetic flux disk adopted for the simulations presented in this paper. The choice of temperature and magnetic field lead to a density distribution, in scaled units,</text>
<formula><location><page_3><loc_53><loc_59><loc_92><loc_63></location>ρ ( R,z ) = ρ ( R, 0) exp ( -{ Φ( R,z ) -Φ( R, 0) } T ( R ) β 1 + β ) , (7)</formula>
<text><location><page_3><loc_52><loc_52><loc_92><loc_59></location>where the pressure, P = ρT . For the radial profiles ρ ( R, 0) and T ( R ) we use simple functions inspired by the Shakura & Sunyaev (1973) disk model, except with an additional truncation of the density profile at a specified outer radius:</text>
<formula><location><page_3><loc_59><loc_48><loc_92><loc_52></location>ρ ( R, 0)= ρ 0 f ( R,R 0 , R out ) ( R R 0 ) /epsilon1 , (8)</formula>
<formula><location><page_3><loc_61><loc_44><loc_92><loc_48></location>T ( R ) = T 0 ( R R 0 ) χ , (9)</formula>
<text><location><page_3><loc_52><loc_27><loc_92><loc_44></location>where ρ 0 sets the density scale, R 0 and R out are the radius of the inner and outer disk edge, respectively, f ( R,R 0 , R out ) is a tapering function and is described in Appendix A, and /epsilon1 and χ set the slope of the density and temperature profiles, respectively. In all of the global simulations R 0 = 7, R out = 30, ρ 0 = 10, T 0 = 4 . 5 × 10 -4 , /epsilon1 = -33 / 20, and χ = -9 / 10 (consistent with the radial scaling in the gas pressure and Thomson-scattering opacity dominated region from Shakura & Sunyaev 1973), producing disks with an aspect ratio, H/R = 0 . 05. The rotational velocity of the disk is close to Keplerian, with a minor modification due to the gas and magnetic pressure gradients,</text>
<formula><location><page_3><loc_54><loc_23><loc_92><loc_26></location>v 2 φ ( R,z ) = v 2 φ ( R, 0) + { Φ( R,z ) -Φ( R, 0) } R T dT dR , (10)</formula>
<text><location><page_3><loc_52><loc_21><loc_57><loc_22></location>where,</text>
<formula><location><page_3><loc_58><loc_13><loc_92><loc_20></location>v 2 φ ( R, 0) = R ∂ Φ( R, 0) ∂R + 2 T β + ( 1 + β β )( RT ρ ( R, 0) ∂ρ ( R, 0) ∂R + R dT dR ) . (11)</formula>
<text><location><page_3><loc_52><loc_8><loc_92><loc_13></location>One advantage using such an equilibrium disk is that one begins with a disk that is close to the expected scale height and density. An isothermal disk, for example, has a scale height that is proportional to R 3 / 2 .</text>
<text><location><page_3><loc_52><loc_5><loc_92><loc_8></location>Finally, the region outside of the disk is set to be an initially stationary, spherically symmetric, hydrostatic at-</text>
<text><location><page_4><loc_8><loc_89><loc_45><loc_90></location>mosphere with a temperature and density given by,</text>
<formula><location><page_4><loc_17><loc_85><loc_48><loc_88></location>T atm ( r ) = -Φ 2 , (12)</formula>
<formula><location><page_4><loc_17><loc_81><loc_48><loc_85></location>ρ atm ( r ) = ρ atm ( r ref ) ( Φ( r ) Φ( r ref ) ) , (13)</formula>
<text><location><page_4><loc_8><loc_74><loc_48><loc_81></location>where ρ atm = 4 × 10 -5 ρ 0 and r ref is a reference radius which we take to be R max , the radius of peak disk density (see Appendix A). The transition between the disk and background atmosphere occurs where their total pressures balance.</text>
<text><location><page_4><loc_8><loc_69><loc_48><loc_74></location>As an example, model gblm 10 corresponds to a disk with a peak density of 1 . 67 × 10 -7 gm s -1 and a peak temperature of 2 . 9 × 10 9 K.</text>
<section_header_level_1><location><page_4><loc_22><loc_68><loc_34><loc_69></location>2.3. Diagnostics</section_header_level_1>
<text><location><page_4><loc_8><loc_62><loc_48><loc_67></location>Turbulence is by its very nature chaotic. Therefore, averaged quantities are particularly useful diagnostics. In this section we describe how we calculate averages, and define the variables used to analyse the simulations.</text>
<text><location><page_4><loc_8><loc_58><loc_48><loc_62></location>To compute shell-averaged values (denoted by curly brackets) of a variable q at a radius r we average in the θ and φ directions via,</text>
<formula><location><page_4><loc_20><loc_51><loc_48><loc_57></location>{ q } = ∫ qr 2 sin θdθdφ ∫ r 2 sin θdθdφ . (14)</formula>
<text><location><page_4><loc_8><loc_50><loc_48><loc_53></location>Similarly, we calculate a horizontally averaged value (denoted by square brackets) as,</text>
<formula><location><page_4><loc_21><loc_46><loc_48><loc_49></location>[ q ] = ∫ qr sin θdrdφ r sin θdrdφ (15)</formula>
<text><location><page_4><loc_8><loc_41><loc_48><loc_48></location>∫ To attain a volume-averaged value (denoted by angled brackets) we integrate over the radial profile of shellaveraged values and normalize by the radial extent,</text>
<formula><location><page_4><loc_23><loc_37><loc_48><loc_41></location>< q > = ∫ { q } dr dr (16)</formula>
<text><location><page_4><loc_8><loc_18><loc_48><loc_39></location>∫ Time averages receive an overbar, such that a volume and time averaged quantity would read < q > . (Note that density-weighted averages are computed, but only for hydrodynamical variables.) For the analysis presented in § 4 we restrict the integration over r and θ to the range 10 < r < 30 and in π/ 2 -θ 2 H/R < θ < π/ 2 + θ 2 H/R , where θ 2 H/R = tan -1 (2 H/R ). We define this region as the 'disk body' and limit the integration over this region to allow comparison against recent global (e.g. Fromang & Nelson 2006; Beckwith et al. 2011; Sorathia et al. 2010; Flock et al. 2011, 2012; Hawley et al. 2011; Sorathia et al. 2012) and large local 1 simulations (e.g. Guan & Gammie 2011; Simon et al. 2012).</text>
<text><location><page_4><loc_8><loc_11><loc_48><loc_18></location>In order to keep a track of the fluctuations in the scaleheight of the disk during the simulation - which results from the interplay between adiabatic heating and our cooling function - a density-weighted average disk scaleheight is computed, where we take H/R = c s /v φ (where</text>
<text><location><page_4><loc_52><loc_86><loc_92><loc_90></location>c s is the sound speed), then perform a density-weighted shell-average followed by a radial averaging to acquire a volume averaged value, < H/R > .</text>
<text><location><page_4><loc_52><loc_77><loc_92><loc_86></location>For accretion to occur, angular momentum must be transported radially outwards by turbulent stresses, and a major focus of numerical simulations is quantifying the stress. To this end, we define the perturbed flow velocity as 2 δv i = v i -∫ v i r sin θdφ/ ∫ r sin θdφ with i = R , φ , and compute the R -φ component of the combined Reynolds and Maxwell stress,</text>
<formula><location><page_4><loc_63><loc_74><loc_92><loc_76></location>W Rφ = ρδv R δv φ -B R B φ , (17)</formula>
<text><location><page_4><loc_52><loc_72><loc_88><loc_73></location>which is normalized by the gas pressure to acquire,</text>
<formula><location><page_4><loc_66><loc_67><loc_92><loc_71></location>{ α P } = { W Rφ } { P } . (18)</formula>
<text><location><page_4><loc_52><loc_65><loc_92><loc_67></location>Furthermore, we calculate the R -φ component of the Maxwell stress normalized by the magnetic pressure,</text>
<formula><location><page_4><loc_64><loc_60><loc_92><loc_64></location>{ α M } = -2 { B R B φ } {| B | 2 } . (19)</formula>
<text><location><page_4><loc_52><loc_56><loc_92><loc_60></location>To examine the operation of dynamo activity in the disk we compute the toroidal magnetic flux, which is defined as,</text>
<formula><location><page_4><loc_61><loc_51><loc_92><loc_55></location>Ψ φ ( φ ) = ∫ ∫ B φ ( φ ) r sin θdrdθ. (20)</formula>
<text><location><page_4><loc_52><loc_43><loc_92><loc_51></location>The ability of the simulations to resolve the fastest growing MRI modes is quantified in the same fashion as Noble et al. (2010) and Hawley et al. (2011). The wavelength of the fastest growing MRI modes with respect to the grid resolution in the z and φ directions are, respectively,</text>
<formula><location><page_4><loc_59><loc_38><loc_92><loc_42></location>Q z = λ MRI -z ∆ z = √ 16 15 2 π | v Az | r sin θ v φ ∆ z , (21)</formula>
<text><location><page_4><loc_52><loc_36><loc_55><loc_38></location>and,</text>
<formula><location><page_4><loc_63><loc_33><loc_92><loc_36></location>Q φ = λ MRI -φ R ∆ φ = 2 π | v Aφ | ∆ φ , (22)</formula>
<text><location><page_4><loc_52><loc_22><loc_92><loc_32></location>where v Az and v A φ are the vertical and azimuthal Alfv'en speeds, respectively, ∆ θ and ∆ φ are the cell sizes in the θ and φ directions, respectively, and ∆ z = √ ( r sin θ ∆ θ ) 2 +(∆ r cos θ ) 2 is the corresponding cell size in the z direction. We define a single valued measure of resolvability as the fraction of cells in the disk body ( | z | < 2 H ) that have Q > 8 (e.g. Sorathia et al. 2012),</text>
<formula><location><page_4><loc_65><loc_19><loc_92><loc_22></location>N i = Σ C ( Q i > 8) Σ C (23)</formula>
<text><location><page_4><loc_52><loc_10><loc_92><loc_18></location>where i = z, φ and C represents a cell. The principal aim of calculating N z and N φ is to quantify how well resolved the turbulent state is in a simulation, and consequently whether global simulations are approaching the region of convergence found from shearing box simulations (Hawley et al. 2011).</text>
<table>
<location><page_5><loc_10><loc_78><loc_46><loc_87></location>
<caption>TABLE 1 Parameters used for the linear MRI growth calculations</caption>
</table>
<section_header_level_1><location><page_5><loc_21><loc_75><loc_36><loc_76></location>2.4. Fourier analysis</section_header_level_1>
<text><location><page_5><loc_8><loc_59><loc_48><loc_75></location>To allow a direct comparison between the growth of MRI modes estimated from a linear perturbation analysis ( § 3) and the results of global simulations ( § 4) we analyse the growth of magnetic field perturbations in Fourier space. The procedure we follow is to remap the disk body (which we define in § 2.3) to a cylindrical mesh with uniform cell spacing in all directions, and a sufficiently fine resolution to ensure that the smallest cells from the spherical simulation grid are sampled. We then perform a 3D Fourier Transform of the data on the cylindrical grid. A detailed description of the cylindrical Fourier transform can be found in Appendix B.</text>
<section_header_level_1><location><page_5><loc_20><loc_56><loc_36><loc_58></location>3. EXCITING THE MRI</section_header_level_1>
<text><location><page_5><loc_8><loc_43><loc_48><loc_56></location>Given that our global simulations commence with an equilibrium disk the MRI requires a seed perturbation to excite the growth of the magnetic field and development of turbulence. For this purpose we have chosen to excite a specific Fourier mode of the MRI using poloidal velocity perturbations. In the following we present perturbation calculations for the local, linear, non-axisymmetric MRI, the results of which are used in § 4 to elucidate the evolution of magnetic field perturbations in global numerical simulations.</text>
<section_header_level_1><location><page_5><loc_17><loc_40><loc_39><loc_41></location>3.1. Linear MRI growth models</section_header_level_1>
<text><location><page_5><loc_8><loc_5><loc_48><loc_39></location>Studies of the linear, non-axisymmetric MRI in weakly magnetized disks have been examined by a number of authors (Balbus & Hawley 1992; Terquem & Papaloizou 1996; Papaloizou & Terquem 1997). Balbus & Hawley (1992)'s local study showed that even if the seed magnetic field is purely toroidal then the instability is still present, albeit with growth rates roughly an order of magnitude lower than those found for initially poloidal fields (Balbus & Hawley 1991). This result was supported by growth timescales approaching an orbital period (for certain parameters) in more-global calculations by Terquem & Papaloizou (1996) where radial gradients were preserved. Furthermore, these authors found that in the k z /k R /lessmuch 1 limit - the primary domain of the MRI instabilities become increasingly localized with time. On the other hand, in the k R /k z /lessmuch 1 limit the Parker instability dominates. In fact, even in the presence of dissipation, MRI modes continue to become increasingly localized over time due to the time dependence of the radial wavenumber (Papaloizou & Terquem 1997). Common to these studies is the finding that the non-axisymmetric MRI acts as a mechanism for the transient amplification of seed magnetic/velocity field perturbations by many orders of magnitude over tens of orbits. One question is, how well does this immense field amplification carry through to global, fully non-linear simulations? To an-</text>
<text><location><page_5><loc_52><loc_83><loc_92><loc_90></location>swer this one needs an estimate of the linear growth. In this regard our analysis of the non-axisymmetric MRI in this paper is complementary to studies of the axisymmetric MRI in previous simulations (e.g. Hawley & Balbus 1991; Flock et al. 2010).</text>
<text><location><page_5><loc_52><loc_63><loc_92><loc_83></location>To construct our prediction for the global simulations we utilize the linear MRI model of Balbus & Hawley (1992). (The perturbation analysis used to quantify the linear MRI growth is performed in cylindrical coordinates ( R,φ,z ), whereas the global models presented in § 4 are performed in spherical coordinates ( r, θ, φ ).) In brief, Balbus & Hawley perform a linear stability analysis of a local patch of a disk using the shearing-sheet approximation (Goldreich & Lynden-Bell 1965) where the perturbations are assumed to have a spatial dependence exp[ i ( k R R + mφ + k z z )]. The equations for the evolution of the magnetic field perturbations form a pair of coupled second-order ordinary differential equations 3 . We let N be the Brunt-Vaisala frequency, which for the equilibrium disk described in § 2.2 is,</text>
<text><location><page_5><loc_52><loc_57><loc_81><loc_59></location>and define an independent time variable,</text>
<formula><location><page_5><loc_59><loc_58><loc_92><loc_63></location>N 2 = 2 5 1 T ( β 1 + β ) 2 ( z R ) 2 1 ( r -2) 4 , (24)</formula>
<formula><location><page_5><loc_59><loc_53><loc_92><loc_56></location>τ = k R ( t ) R = k R ( t = 0) R -m d Ω d ln R t, (25)</formula>
<formula><location><page_5><loc_58><loc_50><loc_92><loc_53></location>k 2 = k 2 R + m 2 R 2 + k 2 z . (26)</formula>
<text><location><page_5><loc_52><loc_44><loc_92><loc_50></location>Replacing the angular velocity with that due to a Paczynski-Wiita potential in the thin disk limit (i.e. H/R /lessmuch 1), Ω 2 = 1 /R 2 ( R -2), the equations describing linear perturbations are 4 ,</text>
<formula><location><page_5><loc_53><loc_31><loc_92><loc_43></location>d 2 δB z dτ 2 = 2 k z Rk 2 (3 R -2) ( 2 τ 2 m 2 ( R -2) -R -2 ) dδB R dτ -4 m 2 ( R -2 3 R -2 ) 2 δB z [ ( k · v A ) 2 Ω 2 + ( k 2 -k 2 z k 2 ) N 2 Ω 2 ] + 4 k z τ k 2 m 2 ( R -2 3 R -2 ) τ dδB z dτ , (27)</formula>
<formula><location><page_5><loc_54><loc_16><loc_92><loc_29></location>d 2 δB R dτ 2 = -4 m 2 ( 1 -k 2 R k 2 ) R -2 3 R -2 Rk z dδB z dτ + 2 R 2 k 2 R -2 3 R -2 [ 2 m 2 ( τ 2 -R 2 k 2 ) + R +2 R -2 ] τ dδB R dτ -4 m 2 ( R -2 3 R -2 ) 2 [ ( k · v A ) 2 Ω 2 δB R -k z Rk 2 N 2 Ω 2 τδB z ] (28)</formula>
<text><location><page_5><loc_52><loc_12><loc_92><loc_15></location>3 Note that there is a typographical error in equation (2.19) of Balbus & Hawley (1992) where the final term should read δB z N 2 ( k 2 z -k 2 ) /k 2 .</text>
<text><location><page_5><loc_52><loc_5><loc_92><loc_12></location>4 The angular velocity resulting from our disk model (cf Eqs (10) and (11)) actually includes a small offset to Keplerian rotation. However, we find that this makes little difference to the perturbation calculations, and the subsequent comparison against global simulations in § 4. Therefore, for the sake of simplicity, we adopt a purely Keplerian rotation profile for the local calculations.</text>
<text><location><page_6><loc_8><loc_87><loc_48><loc_90></location>where δB z and δB R are the vertical and radial magnetic field perturbations.</text>
<text><location><page_6><loc_8><loc_77><loc_48><loc_87></location>The time dependence of k R in Eq (25) is a consequence of the radial wavenumber being sheared. Therefore, within the framework of the Balbus & Hawley (1992) analysis the radial wavenumber can grow indefinitely so that radial disturbances can evolve to arbitrarily small spatial extent. Clearly, when we come to making a comparison against our global simulations, this will not be the case due to finite numerical resolution.</text>
<text><location><page_6><loc_8><loc_74><loc_48><loc_77></location>The magnetic field perturbations are related through the divergence-free constraint,</text>
<formula><location><page_6><loc_14><loc_71><loc_48><loc_74></location>k · δ B = k R δB R + m R δB φ + k z δB z = 0 . (29)</formula>
<text><location><page_6><loc_8><loc_66><loc_48><loc_70></location>The unperturbed magnetic field topology only enters through k · v A . For our initially purely toroidal magnetic field one finds,</text>
<formula><location><page_6><loc_18><loc_61><loc_48><loc_65></location>( k · v A Ω ) 2 = 2( R -2) m 2 T β , (30)</formula>
<text><location><page_6><loc_8><loc_58><loc_48><loc_61></location>To initiate the MRI we use the R and z components of the linearized induction equation,</text>
<formula><location><page_6><loc_21><loc_55><loc_48><loc_58></location>dδB R dt = i ( k · B ) δv R , (31)</formula>
<text><location><page_6><loc_8><loc_53><loc_11><loc_54></location>and,</text>
<formula><location><page_6><loc_21><loc_50><loc_48><loc_53></location>dδB z dt = i ( k · B ) δv z , (32)</formula>
<text><location><page_6><loc_8><loc_43><loc_48><loc_49></location>where δv R and δv z are the poloidal velocity perturbations (with the imaginary part of δv corresponding to the real part of dδB/dt ). For the perturbations in the z -components in both the linear MRI and global calculations we use a waveform,</text>
<formula><location><page_6><loc_17><loc_40><loc_48><loc_42></location>δv z = δv 0 cos( k R R + mφ + k z z ) , (33)</formula>
<text><location><page_6><loc_8><loc_36><loc_48><loc_40></location>which, on substitution into Eq (32), and with the conversion between real and imaginary parts accounted for by a phase shift in the trigonometric term, leads to,</text>
<formula><location><page_6><loc_11><loc_31><loc_48><loc_35></location>dδB z dt = δv 0 2 B φ v φ R -2 3 R -2 sin( k R R + mφ + k z z ) , (34)</formula>
<text><location><page_6><loc_8><loc_23><loc_48><loc_31></location>where δv 0 is the amplitude of the initial velocity perturbations. An equivalent treatment to Eq (34) is used for the perturbations in the R -components with the difference that we make use of the incompressibility condition, k · δ v = 0, and set,</text>
<formula><location><page_6><loc_16><loc_20><loc_48><loc_24></location>δv R = δv 0 k z k R cos( k R R + mφ + k z z ) , (35)</formula>
<text><location><page_6><loc_8><loc_17><loc_48><loc_20></location>The remaining parameters used in the calculations are summarised in Table 1.</text>
<text><location><page_6><loc_8><loc_5><loc_48><loc_17></location>Our first calculation, model linm 10, uses a β = 20 magnetic field and wavenumbers for the excited MRI mode of m = 10, k z = 5, and k R = 2 . 5. These wavenumbers are chosen to ensure sufficient resolution in the global simulations and we leave a more detailed discussion to § 4. The amplitude of the initial velocity perturbations, δv 0 , is set to 0 . 1 c s , where c s (= √ T ) is the sound speed. Since we intend to use these calculations as a guide for our global simulations, we use the equilibrium</text>
<figure>
<location><page_6><loc_54><loc_35><loc_89><loc_90></location>
<caption>Fig. 1.The evolution of magnetic field perturbations from linear MRI growth calculations showing successful magnetic field amplification. From top to bottom: δB R , δB z , and δB φ . The parameters used in these calculations are provided in Table 1.</caption>
</figure>
<text><location><page_6><loc_52><loc_5><loc_92><loc_27></location>disk model described in § 2.2 to choose the input density and temperature. Calculations are performed at a cylindrical radius, R = 20, and at the disk mid-plane where N 2 = 0 (see Eq (24)). From Eq (9) the disk temperature, T = 1 . 75 × 10 -4 , and the density, ρ = 0 . 46. The initial components of δ B are set to zero, so too is the initial azimuthal velocity perturbation, δv φ - the poloidal velocity perturbations seed the instability through the dδB/dt terms. To integrate Eqs (27) and (28) we use an adaptive stepsize, 4th-order, explicit Runge-Kutta method (Press et al. 1986). As Fig. 1 shows, the magnetic field perturbations grow extremely rapidly over the first few P orb 20 with noticeable oscillations, where P orb j is the radially dependent orbital period of the disk at cylindrical radius j. The upper panel of Fig. 2 shows the effective β for the MRI mode - the time required for</text>
<figure>
<location><page_7><loc_11><loc_53><loc_45><loc_90></location>
<caption>Fig. 2.(Top): The plasmaβ calculated from the linear MRI growth calculations - see Table 1 for the list of models and parameter values pertaining to each calculation. The vertical line indicates when model linm 10 reaches β = 1. (Bottom): The timedependent radial wavenumber. The red and blue lines corresponds to models linm 10 and linm 40, respectively. The horizontal lines indicate the k R values at the Nyquist limit for the global simulations gblm 10 and gblm 10-lllr (see Tables 3 and 2 and § 4).</caption>
</figure>
<text><location><page_7><loc_8><loc_8><loc_48><loc_41></location>the magnetic field to grow to β = 1 is only a few orbital periods for model linm 10. Evaluating the approximate growth rate, ω of the magnetic energy, β -1 (as the gas pressure remains constant) via β -1 = β -1 0 exp( ωt ), we find an average growth rate over the first six orbits, ω = 0 . 14 Ω. Applying the same approach to δB R we find ω = 0 . 09Ω. This is consistent with the findings of Terquem & Papaloizou (1996) but is roughly an order of magnitude larger than values of a few percent of the orbital frequency quoted in general for the development of the non-axisymmetric MRI by Balbus & Hawley (1992). Keeping all parameters fixed and then varying the initial magnetic field strength, one sees from models linm 10β 100 and linm 10β 300 the trend that the growth rate of δ B decreases with increasing initial β . In model linm 10β 300 s the size of the initial velocity perturbations is increased to δv 0 = 0 . 3 c s with the result that over the very first few orbits the growth of δB 's becomes very similar to that of a stronger initial field strength excited by smaller velocity perturbations. For a higher wavenumber perturbation the rate of initial growth increases, as evidenced by model linm 40 (see Figs. 1 and 2). Evaluating the approximate growth rate of the magnetic field energy and δB R for model linm 40 gives, ω = 0 . 68 Ω and 0 . 25Ω, respectively 5 . From these results one may predict</text>
<text><location><page_7><loc_54><loc_80><loc_56><loc_80></location>δ</text>
<figure>
<location><page_7><loc_54><loc_35><loc_89><loc_90></location>
<caption>Fig. 3.Evolution of δB R (upper), δB z (middle), and α m (lower) as a function of time in model linm 10 over a longer time duration than shown in Fig. 1.</caption>
</figure>
<text><location><page_7><loc_52><loc_23><loc_92><loc_28></location>that the development of δ B in simulations will depend on the initial field strength and/or the wavenumber of the excited mode(s). In § 4.3 we examine if this result holds true in global simulations.</text>
<text><location><page_7><loc_52><loc_8><loc_92><loc_23></location>Balbus & Hawley (1992) discuss the parameter ( k · v A ) 2 / Ω 2 and attribute to it an important role in the ability of the MRI to successfully amplify the seed field. They find that for ( k · v A ) 2 / Ω 2 ∼ > 2 . 9 the instability is stabilized and magnetic field oscillations are damped. For the models shown in Fig. 1, this parameter is much less than unity. From Eq (30) for ( k · v A ) 2 / Ω 2 one can see that to increase the value of this variable one can either decrease β - which increases the tension along field lines - or employ higher azimuthal wavenumbers, m . The latter has the side-effect of</text>
<text><location><page_8><loc_8><loc_71><loc_48><loc_90></location>increasing the growth rate of k R and causing tight wave crest wrapping, both of which lead to a more rapid stabilization of the radial disturbances. However, we find that irrespective of the value of ( k · v A ) 2 / Ω 2 , which is 0 . 03 for linm 10 (Table 1), the perturbation in the magnetic field ultimately decays. This is shown in Fig 3 (upper and middle panels) where the linm 10 calculation is plotted for a longer time duration. Despite continuing growth in δB z , there is decay in δB R , which is a consequence of the increase of k R ( t ) combined with the divergence-free constraint (Eq (29)). The ratio of the Maxwell stress to magnetic pressure ( α m ) predicted from the linear MRI growth calculations is shown in the lower panel of Fig. 3, where we define,</text>
<formula><location><page_8><loc_9><loc_65><loc_48><loc_69></location>α m = 2 δB R ( δB φ + B φ ) B 2 , B 2 = B 2 φ + δB 2 φ + δB 2 R + δB 2 z . (36)</formula>
<text><location><page_8><loc_8><loc_63><loc_44><loc_65></location>Clearly, considering that α m , or to be more exact</text>
<text><location><page_8><loc_8><loc_51><loc_48><loc_63></location>< α M > (its global analogue - see Eq (19)), is a commonly used diagnostic in numerical simulations (Hawley et al. 1995). Under the action of the linear MRI alone < α M > would never reach a steady value. This ultimate decay of linear MRI disturbances is consistent with Terquem & Papaloizou (1996)'s finding of transient instability growth in a number of numerical tests, in which k z > k R initially. Shear causes k R to grow but once k R > k z growth halts.</text>
<text><location><page_8><loc_8><loc_38><loc_48><loc_51></location>The ultimate decay of linear MRI modes has significance for global models because the maintenance of dynamo action requires all components of the field to be sufficiently strong. This highlights the need for an additional mechanism, other than the linear MRI growth, to replenish δB R (e.g. parasitic instabilities - Goodman & Xu 1994; Parker instability Tout & Pringle 1992, Vishniac 2009; dynamo action in the steady-state turbulence Brandenburg et al. 1995, Hawley et al. 1996).</text>
<text><location><page_8><loc_8><loc_5><loc_48><loc_38></location>The linear MRI growth calculations act as a check on our global simulations, principally to examine whether our setup recovers the growth rates of the linear MRI accurately. However, there is a limit to the time interval when we can confidently make a comparison between the linear growth models and global simulations. Firstly, the analysis of Balbus & Hawley (1992) adopts the Boussinesq approximation which becomes invalid when the azimuthal magnetic field becomes super-thermal. The upper panel of Fig. 2 shows that this limit is reached in approximately 2.3 orbits for linm 10 and 0.1 orbits for linm 40. Secondly, k R ( t ) can grow indefinitely in the linear growth models, yet this is not the case for our global simulations which are restricted by finite numerical resolution. Taking the Nyquist limit to be 2 grid cells, and considering, for example, the resolution of model gblm 10, the maximum resolvable radial wavenumber is k R -Nyquist = 86. This limit is reached after ∼ 16 . 5 and 2.3 orbits for models linm 10 and lin-40, respectively (lower panel of Fig. 2). Therefore, choosing to excite a higher wavenumber MRI mode limits the time interval where comparisons can be made against linear perturbation theory, and this is one reason why we choose to excite a lower wavenumber mode ( m = 10) in the global simulations.</text>
<text><location><page_8><loc_54><loc_81><loc_56><loc_82></location>></text>
<text><location><page_8><loc_54><loc_80><loc_56><loc_81></location>α</text>
<text><location><page_8><loc_54><loc_80><loc_56><loc_80></location><</text>
<figure>
<location><page_8><loc_55><loc_53><loc_89><loc_90></location>
<caption>Fig. 4.The evolution of < α P > (upper) and < α M > (lower) in the global models as a function of time in units of the orbital period at R = 30. See Table 3 for a list of the models and time averaged values.</caption>
</figure>
<section_header_level_1><location><page_8><loc_65><loc_45><loc_79><loc_46></location>4. GLOBAL MODELS</section_header_level_1>
<text><location><page_8><loc_52><loc_15><loc_92><loc_44></location>In this section we describe the results of global simulations using the initial conditions and simulation setup described in § 2. The global simulations are listed along with grid dimensions, number of cells per scaleheight, and approximate MRI growth rates in 2. Time and volume averaged variables quantifying the steady-state turbulence are given in Table 3. In models gblm 10 and gblm 10+ we excite a specific Fourier mode using a plane wave, which takes the form of Eq (33), as described in § 3. These models use the same wavenumbers as model linm 10 so as to allow a direct comparison of magnetic field growth. The third model, gbl-rand, uses random pressure and poloidal velocity perturbations to initially seed the disk disturbance. All of the global models start with a purely toroidal magnetic field with β = 20. Models gblm 10+ and gbl-rand are computed on grids with lower poloidal resolution (roughly 2/3 that of model gblm 10), but with a factor of three better azimuthal resolution. In the following section we present some properties of our model disks and demonstrate that higher φ resolution to be a crucial ingredient in producing a sustained, high valued turbulent stress, < α P > .</text>
<section_header_level_1><location><page_8><loc_65><loc_12><loc_79><loc_13></location>4.1. Model evolution</section_header_level_1>
<text><location><page_8><loc_52><loc_5><loc_92><loc_12></location>We begin with a description of the evolution of models gblm 10 and gblm 10+ (Tables 2 and 3). In this model we adopt an azimuthal wavenumber which varies with cylindrical radius, m = m ( R ). We give the azimuthal wavenumber a radial dependence of m ( R ) = m crit ( R ) / 6,</text>
<table>
<location><page_9><loc_15><loc_71><loc_85><loc_87></location>
<caption>TABLE 2 Global simulations and the corresponding linear growth rate.TABLE 3 Time averaged quantities from the global simulations..</caption>
</table>
<table>
<location><page_9><loc_14><loc_58><loc_85><loc_64></location>
</table>
<text><location><page_9><loc_10><loc_56><loc_48><loc_58></location>Note . -a Time interval over which averaging was performed,</text>
<figure>
<location><page_9><loc_12><loc_16><loc_45><loc_53></location>
<caption>Fig. 5.Resolvability of the MRI in the φ direction (upper) and z direction (lower) in models gblm 10, gblm 10+, and gbl-rand. For a definition of the resolvability see Eq (23) and § 2.3.</caption>
</figure>
<text><location><page_9><loc_8><loc_9><loc_48><loc_10></location>where the critical 6 azimuthal wavenumber for the linear,</text>
<text><location><page_9><loc_8><loc_5><loc_48><loc_8></location>6 Defined as the value of m for which disturbances grow most rapidly, which follows from equation (2.30) of Balbus & Hawley</text>
<figure>
<location><page_9><loc_55><loc_35><loc_89><loc_54></location>
<caption>Fig. 6.Density-weighted and volume averaged scaleheight of the disk, < H/R > as a function of time in models gblm 10 (solid line) and gblm 10+ (dashed line).</caption>
</figure>
<text><location><page_9><loc_52><loc_27><loc_69><loc_28></location>non-axisymmetric MRI,</text>
<formula><location><page_9><loc_65><loc_22><loc_92><loc_27></location>m crit = √ R R -2 √ β 2 T . (37)</formula>
<text><location><page_9><loc_52><loc_13><loc_92><loc_22></location>At R = 20 in model gblm 10, m crit = 60; adopting m = m crit / 6 ensures that the corresponding k z and k R are well resolved by the numerical grid. Balbus & Hawley (1992) noted that the fastest growing non-axisymmetric modes occur for k z = m 2 /R , and we also use this relation to calculate k z . Given that our grid resolution is coarser in r than it is in θ , we set k R = k z / 2.</text>
<text><location><page_9><loc_52><loc_8><loc_92><loc_13></location>The initial poloidal velocity perturbations seed the growth of magnetic field perturbations via the MRI and after roughly 1 -2 P orb 30 turbulent motions become ap-</text>
<text><location><page_9><loc_52><loc_5><loc_92><loc_7></location>(1992). The radial dependence of Eq (37) stems from the Paczy'nsky & Wiita (1980) potential (Eq (5)).</text>
<text><location><page_10><loc_8><loc_44><loc_48><loc_90></location>parent in the disk body. As the poloidal magnetic field becomes established throughout the disk the resulting Maxwell stresses disrupt the disk equilibrium. The evolution of models gblm 10 and gblm 10+ is largely similar during the first few orbits of the simulations. Examining the normalized stress, < α P > , shows that there is an initial transient phase which peaks after a simulation time of roughly 4 P orb 30 (Fig. 4). Following this, < α P > gradually decreases until a steady-state is reached after roughly 12 P orb 30 and the time-averaged stress for the remainder of the simulation, < α P > = 0 . 017 for gblm 10. The time-averaged ratio of the Maxwell stress to the magnetic energy, < α M > = 0 . 31, which is below the values of roughly 0.4 quoted by, for example, Hawley et al. (2011) for well resolved turbulence. To investigate the dependence of these values on the azimuthal resolution of the simulation we have also run model gblm 10+, which has 12.5 cells/ H in the φ direction (and a lower resolution in the poloidal direction - see Table 2). The higher φ resolution clearly influences the turbulent stresses in the simulation and for model gblm 10 we find < α M > = 0 . 41 and < α P > = 0 . 034, in agreement with high resolution shearing-box simulations. The resolvability of the fastest growing MRI modes (see Eq (23) and Fig. 5) also clearly show that a higher azimuthal resolution helps to maintain (or even strengthen) the poloidal magnetic field - models gblm 10 and gblm 10+ initially show similar values of N z but largely different values of N φ , and combined with the evidence mentioned above is evident that azimuthal resolution is very important for maintaining a healthy turbulent state (see also the discussion in Fromang & Nelson 2006; Flock et al. 2011; Hawley et al. 2011). In § 5 we compare further quantitative measures of the steady-state turbulence to previous works.</text>
<text><location><page_10><loc_8><loc_22><loc_48><loc_43></location>The poloidal magnetic field develops in flux tubes with small spatial scale, which dissipate magnetic energy via reconnection, heating the disk. In Fig. 6 we show the density-weighted and volume-averaged scaleheight of the disk, < H/R > as a function of time. In model gblm 10 the scaleheight of the disk increases initially until t ∼ 8 P orb 30 , after which it steadily declines. This shows that during the initial disk evolution, dissipation heats the disk more rapidly than the cooling function, Λ (see Eq (6)) can drive the temperature back to its initial value. In other words, the dissipative timescale is shorter than an orbital period. In contrast, for model gblm 10+, < H/R > remains roughly constant after the initial rise, which shows that the higher < α P > in this model (Fig. 4) is causing more heating, and a marginally thicker disk.</text>
<text><location><page_10><loc_8><loc_6><loc_48><loc_22></location>Fig. 7 shows a poloidal slice through the disk in model gblm 10+ at t = 14 P orb 30 . During the turbulent steady state the disk is characterised by a dense, cold, subthermally magnetized core close to the mid-plane and a tenuous, hot, trans-to-super thermal magnetic field at z ∼ > 2 H (the corona). Turbulent motions are clearly evident in the plot of β -1 in Fig. 7 with the dominant eddies appearing to have a larger size in the corona compared to the disk body. As noted by Fromang & Nelson (2006), such behaviour arises due to conservation of angular momentum in eddie motions - or wave action - as small scale eddies rise out of the dense disk mid-plane</text>
<figure>
<location><page_10><loc_53><loc_38><loc_92><loc_90></location>
<caption>Fig. 7.Slices in the poloidal plane from model gblm 10+ at t = 14 P orb 30 showing ρ (upper), T (middle), and β -1 (lower).</caption>
</figure>
<figure>
<location><page_10><loc_53><loc_11><loc_89><loc_30></location>
<caption>Fig. 8.Disk body, corona, and global volume averages of the plasmaβ for model gblm 10+.</caption>
</figure>
<figure>
<location><page_11><loc_12><loc_72><loc_45><loc_90></location>
<caption>Fig. 9.Comparison of | δB R ( m = 10 , k z = 5 , k R = 2 . 5) | from models linm 10 (local linear MRI) and models gblm 10, gblm 10+, and gbl-rand (fully non-linear global simulations).</caption>
</figure>
<text><location><page_11><loc_8><loc_35><loc_48><loc_66></location>into the less dense coronal region. Our intended purpose for the explicit cooling function, Λ (see § 2.1 for details) becomes more apparent from the temperature plot - we aim to take a step beyond the purely isothermal approximation and towards the observationally supported picture of a hot corona and cooler disk body. In Fig. 8 we show the volume-averaged plasmaβ . In the disk body, we find < β > = 17 and for the corona < β > = 6. The coronal value is higher than values of close to one found in previous isothermal (Miller & Stone 2000; Flock et al. 2011) and quasi-isothermal simulations (Fromang & Nelson 2006; Beckwith et al. 2011), which may be attributable to the lack of any explicit cooling in the corona in our simulations. However, although the gas in the corona is heated by dissipation, it does not continually heat up through the simulation, and in fact remains quasi-steady through the latter half of the simulation. This contrasts with adiabatic shearing-box simulations with imposed periodic boundary conditions, in which the gas does heat up (e.g. Stone et al. 1996; Sano et al. 2004) and demonstrates that when coronal gas is allowed to freely expand, adiabatic cooling can, to some extent, balance heating via turbulent dissipation.</text>
<section_header_level_1><location><page_11><loc_10><loc_32><loc_46><loc_33></location>4.2. Comparison with linear MRI growth estimates</section_header_level_1>
<text><location><page_11><loc_8><loc_8><loc_48><loc_32></location>In Fig. 9 we compare the evolution of | δB R | for the m = 10, k z = 5, k R = 2 . 5 mode (measured in Fourier space - see § 2.4) for model linm 10 (which describes linear MRI growth - see Tables 2 and 1) and models gblm 10 and gblm 10+ (global simulations which allow fully nonlinear evolution - see Table 3). Quantifying the initial growth by deriving approximate growth rates 7 , ω approx for the curves shown in Fig. 9 , we find that the linear MRI estimate is matched best by model gblm 10+, with gblm 10 (and gbl-rand) producing higher growth rates. The higher amplitude perturbation for model gblm 10 compared to gblm 10+ originates from the larger amplitude initial velocity perturbation of 0 . 1 c s (compared to 0 . 001 c s for gblm 10+ and gbl-rand - see Table 3). The agreement between the global simulations and linear growth estimate (model linm 10) begins to falter after roughly 2 P orb 20 and growth in | δB R | for the global simu-</text>
<figure>
<location><page_11><loc_56><loc_53><loc_89><loc_90></location>
<caption>Fig. 10.Plasmaβ from models linm 10 and gblm 10 (upper), and time evolution of some sample non-linear terms in model gblm 10 (lower).</caption>
</figure>
<text><location><page_11><loc_56><loc_64><loc_57><loc_64></location></text>
<text><location><page_11><loc_56><loc_63><loc_57><loc_63></location>v</text>
<text><location><page_11><loc_52><loc_31><loc_92><loc_47></location>lations levels off. From the linear MRI calculations shown in Fig. 2 one may anticipate that the growth in | δB | is halted by the magnetic pressure evolving to equipartition with the gas pressure - which is illustrated by the vertical dashed line in Fig. 9 - and would mean that one cannot rely on model linm 10 as a predictor for model gblm 10. However, Fig. 10 shows that β remains roughly constant in model gblm 10 over the first few orbits. What then causes the local MRI estimates and the global simulations to diverge? In the lower panel of Fig. 10 we plot the evolution of the following non-linear terms derived from the momentum equations,</text>
<formula><location><page_11><loc_79><loc_25><loc_80><loc_26></location>.</formula>
<formula><location><page_11><loc_64><loc_24><loc_79><loc_30></location>a = v r ∂v r ∂r , b = v θ r ∂v r ∂θ , c = v r ∂v θ ∂r , d = v θ r ∂v θ ∂θ</formula>
<text><location><page_11><loc_52><loc_5><loc_92><loc_24></location>Small spikes in these non-linear terms occur after ∼ 0 . 1 orbit. However, after 1-2 orbits considerably larger fluctuations become apparent, particularly in b which also appears to have the highest amplitude oscillations of the plotted terms thereafter. Considering that the linear MRI is seeded by velocity perturbations through the induction equation (Eqs (31) and (32)), the correlation in time between the non-linear velocity terms becoming active and the growth in | δB R | departing from the linear MRI growth predictions is highly suggestive of non-linear motions causing saturation in the growth of a specific MRI mode. Furthermore, the small amplitude kicks from these non-linear terms after 0.1 orbits may explain the early divergence between the β</text>
<figure>
<location><page_12><loc_9><loc_45><loc_47><loc_90></location>
<caption>Fig. 12.Same as Fig. 11 except for model gbl-rand.</caption>
</figure>
<figure>
<location><page_12><loc_53><loc_45><loc_90><loc_90></location>
<caption>Fig. 11.Logarithmic false-colour image showing the time evolution of | δB R ( k ) | in model gblm 10+. Values of δB R in the disk body were Fourier transformed and results are shown at specific values of m and k z , and the full range of k R . From top to bottom: m = 10 and k z = 5 (low wavenumber), m = 40 and k z = 80 (moderate wavenumber), and m = 120 and k z = 150 (high wavenumber).</caption>
</figure>
<text><location><page_12><loc_8><loc_17><loc_48><loc_32></location>values predicted from model linm 10 and those found from gblm 10. In this sense the non-linear motions provide saturation to the initial phase of local δ B growth. Whether the non-linear motions are attributable to secondary instabilities feeding off the linear MRI growth locally (e.g. Goodman & Xu 1994; Pessah et al. 2007; Pessah & Goodman 2009; Pessah 2010), or are due to the onset of turbulence (Latter et al. 2009) propagating radially outwards through the disk is unclear and would require an analysis of the non-linear growth of the nonaxisymmetric MRI, which we do not pursue here.</text>
<text><location><page_12><loc_8><loc_5><loc_48><loc_17></location>In summary, comparisons between linear growth calculations and global simulations highlights a number of potential saturation mechanisms. Such as, growth of magnetic field perturbations beyond the weak field limit, and/or growth of the radial wavenumber beyond the finite limit of the simulation resolution. However, for the simulations performed in this work, we find that saturation of growth in magnetic field perturbations correlates well with the onset of non-linear motions.</text>
<section_header_level_1><location><page_12><loc_63><loc_39><loc_80><loc_40></location>4.3. Trigger dependence</section_header_level_1>
<text><location><page_12><loc_52><loc_20><loc_92><loc_38></location>Amajor focus of magnetized accretion disk simulations is to study properties of the quasi-steady-state turbulence. A necessary test is whether the turbulent steady state depends on the MRI mode initially excited, and also whether prohibitive transient behaviour arises due to the choice of exciting a specific MRI mode. For this purpose we have computed model gbl-rand which uses the same initial disk as model gblm 10+ with the difference that the disk is perturbed with random perturbations in the both the poloidal velocity (amplitude δv 0 = 0 . 001 c s ) and gas pressure (10% amplitude) which excite a range of MRI modes. Simulation resolution and time-averaged measures of the turbulent state are listed in Tables 2 and 3, respectively.</text>
<text><location><page_12><loc_52><loc_5><loc_92><loc_20></location>The evolution of model gbl-rand is very similar to that of model gblm 10+; the initial perturbations excite the MRI and lead to growth of δB R . Both models show similar growth in the m = 10, k z , k R = 2 . 5 mode (Fig. 9) which one would expect given that this mode is excited with the same amplitude perturbation. After 3 P orb 20 ( /similarequal 0 . 5 P orb 30 ) values of δB R become almost identical between the models irrespective of the differing initial perturbations. We illustrate this in Figs. 11 and 12 in which we show the evolution of δB R in Fourier space for a range of k R values. The different panels in the figures corre-</text>
<text><location><page_13><loc_8><loc_79><loc_48><loc_90></location>nd to low, moderate, and high wavenumber values for m and k z (relative to the size of the disk and the Nyquist limit). As mentioned above, δB R values are very similar between the two models at t > 3 P orb 20 . Furthermore, even though we excite a specific low wavenumber mode in model gblm 10, a wide range of modes rapidly emerge. We attribute this behaviour to wave-wave coupling and the onset of a turbulent cascade.</text>
<text><location><page_13><loc_8><loc_55><loc_48><loc_79></location>Exciting larger wavenumbers should provide a larger initial MRI growth rate (see § 3), but how does this affect the evolution of magnetic field perturbations in the global simulations? In particular, does the wavenumber of the excited MRI mode affect the globally-averaged saturation stress? In model gbl-rand a white noise spectrum of perturbations has been excited. Therefore higher wavenumber modes can contribute to the initial growth phase in < α P > . There is an indication of this from Fig. 12) where the growth of | δB R | at a range of wavenumbers means that the Maxwell stress, and consequently < α P > will also grow across a range of wavenumbers. Fig. 4 shows that < α P > does grow faster for gbl-rand compared to gblm 10+ (which have identical grid resolution), supporting the notion that the growth in the globally averaged stress due to an ensemble of unstable modes is higher than for a single wavenumber mode.</text>
<text><location><page_13><loc_8><loc_27><loc_48><loc_55></location>All three models start with a toroidal magnetic field with a net flux, and during the early evolution of the disk, the combination of magnetic buoyancy and accretion expels magnetic flux from the disk body such that by the time the turbulent steady state is reached the net toroidal magnetic flux of the disk, Ψ φ is close to zero. Subsequently, Ψ φ oscillates about the zero-point with a period of roughly 5 orbits (upper panel of Fig. 13) consistent with previous global simulations and suggestive of a dynamo cycle (Fromang & Nelson 2006; O'Neill et al. 2011; Beckwith et al. 2011). All three models demonstrate this behaviour. However, minor differences in the toroidal magnetic flux, Ψ φ , are visible between models gblm 10+ and gbl-rand (Fig. 13). The different models are slightly out of phase, which is not surprising given the differences in the transient evolution at early simulation times (Fig. 4). Interestingly, model gbl-rand does not overshoot when expelling the initial net toroidal flux and thus settles into dynamo oscillations at a slightly earlier time, which may explain why the transient phase in < α P > takes a longer time to fade in this model.</text>
<text><location><page_13><loc_8><loc_19><loc_48><loc_27></location>In conclusion, once the disk reaches a turbulent steadystate the disk retains no knowledge of the MRI mode initially excited. This is supported by the almost identical time-averaged properties of the disk noted in Table 3 for models perturbed by a single low wavenumber mode or an ensemble of modes.</text>
<section_header_level_1><location><page_13><loc_13><loc_18><loc_43><loc_19></location>4.4. Algorithm and resolution dependence</section_header_level_1>
<text><location><page_13><loc_8><loc_5><loc_48><loc_17></location>In this section we examine the ability of different numerical algorithms to recover the growth of magnetic field perturbations resulting from the non-axisymmetric MRI. Comparisons between numerical simulations and analytical estimates for the axisymmetric MRI have been presented by Hawley & Balbus (1991) and Flock et al. (2010). Considering that MHD turbulence in accretion disks produces a predominantly toroidal field it is important to examine how well numerical algorithms</text>
<figure>
<location><page_13><loc_56><loc_72><loc_88><loc_90></location>
<caption>Fig. 13.Toroidal magnetic flux at φ = 0, Ψ φ ( φ = 0) as a function of time for models gblm 10, gblm 10+, and gbl-rand. See Eqs (20) for the definition of Ψ φ .</caption>
</figure>
<text><location><page_13><loc_52><loc_34><loc_92><loc_66></location>can recover the growth of δ B as a result of the nonaxisymmetric MRI. The setups used are listed in Table 2. The different combinations are intended to test different orders of reconstruction, parabolic limiters, and grid resolution 8 . Reconstruction refers to the order of accuracy used to interpolate cell interface values (which are then used in the Riemann solver to calculate fluxes of conserved variables). Parabolic limiters are used to preserve monotonicity and prevent extrema from being introduced by the reconstruction step. We examine the original limiter for PPM proposed by Colella & Woodward (1984), the extremum preserving limiters presented by Colella & Sekora (2008), and limiters based on reconstruction via characteristic variables (e.g. Rider et al. 2007). The aforementioned slope limiters are respectively denoted 'CW84', 'CS08', and 'Char' in Table 2. The last parameter we vary is the grid resolution, as this places a constraint on the maximum resolvable wavenumber, and for this purpose we compute models gblm 10hr, gblm 10, gblm 10-lr, gblm 10-llr, and gblm 10-lllr (which have decreasing resolution). Note that with the exception of models gblm 10+ and gbl-rand, all models have the same cell aspect ratio and the same ratio of cells in the disk body to cells in the corona as gblm 10.</text>
<text><location><page_13><loc_52><loc_27><loc_92><loc_34></location>As in § 4.2, we calculate approximate growth rates of the magnetic field perturbation, | δB R ( k ) | for the m = 10, k z = 5, k R = 2 . 5 mode via a Fourier analysis of the initial simulation evolution. The results are shown in Table 2, which we summarise as follows:</text>
<unordered_list>
<list_item><location><page_13><loc_54><loc_21><loc_92><loc_26></location>· The best agreement with the linear MRI growth rate comes from model gblm 10+, showing that azimuthal resolution is important for properly capturing MRI growth.</list_item>
<list_item><location><page_13><loc_54><loc_18><loc_92><loc_20></location>· Within errors the choice of limiter does not make a considerable difference to the resulting growth rate.</list_item>
<list_item><location><page_13><loc_54><loc_14><loc_92><loc_17></location>· Linear reconstruction produces a comparable growth rate to parabolic reconstruction.</list_item>
<list_item><location><page_13><loc_52><loc_5><loc_92><loc_13></location>8 Our aim is to examine the ability of different algorithms to capture waveforms. Balsara & Meyer (2010) found that Riemann solvers that do not resolve the Alfv'en wave are more likely to lead to turbulence dying out as a result of a higher level of numerical dissipation. Therefore, we have not endeavoured to test different Riemann solvers and we use the HLLD solver of Miyoshi & Kusano (2005) in all global simulations.</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_14><loc_11><loc_71><loc_48><loc_90></location>· There is a consistent trend that growth rates increase with increasing resolution (see models gblm 10-lllr, gblm 10-llr, gblm 10-lr, gblm 10, and gblm 10-hr). With 4 cells/ H in the φ direction the growth rates are converged (within errors) for roughly 23-35 cells/ H in the z direction. This is a slightly lower threshold than the ∼ > 40 cells/ H (in the vertical direction) found to achieve convergence in the time-averaged turbulent stress in stratified shearing-box simulations (Davis et al. 2010). Comparison with model gblm 10+ (which has 12.5 cells/ H in the φ direction) suggests that convergence in global disks may be achieved at lower resolutions when the cell aspect ratio is closer to unity.</list_item>
</unordered_list>
<section_header_level_1><location><page_14><loc_23><loc_69><loc_34><loc_70></location>5. DISCUSSION</section_header_level_1>
<text><location><page_14><loc_8><loc_55><loc_48><loc_69></location>With a growing number of studies using stratified shearing boxes with high resolution and/or a large spatial extent (Shi et al. 2010; Davis et al. 2010; Guan & Gammie 2011; Simon et al. 2011, 2012) and higher resolution global models (Fromang & Nelson 2006; Sorathia et al. 2010, 2012; Flock et al. 2011, 2012; Beckwith et al. 2011; Hawley et al. 2011; Mignone et al. 2012), quantifying the steady state turbulence and making direct comparisons between simulations provides a check of both consistency and convergence.</text>
<text><location><page_14><loc_8><loc_26><loc_48><loc_55></location>One of the most popular measures of the steady state is < α P > . In this regard, models gblm 10+ and gblrand produce values of ∼ 0 . 034 which is higher than recently reported by Beckwith et al. (2011) and, as noted by these authors, higher than previous global models and a number of high resolution shearing-box simulations (see Hawley et al. 2011, and references therein). We attribute the larger < α P > in our models to a higher azimuthal resolution than used by (Beckwith et al. 2011), but also note the possible indication that higher < α P > 's may be more readily achievable in global simulations. Our average < α M > ∼ 0 . 41 (for models gblm 10+ and gbl-rand) is in good agreement with the ∼ 0 . 36 -0 . 4 achieved by the highest resolution shearing-box simulations to-date (Davis et al. 2010; Simon et al. 2011, 2012). Considering that our models have a lower number of cells/ H than the aforementioned shearing-box models, there may also be an indication that convergence may be achieved at lower grid resolutions than in localized models, potentially due to averaging over a larger volume, and capturing lower wavenumber eddies.</text>
<text><location><page_14><loc_8><loc_13><loc_48><loc_26></location>Comparing models gblm 10 and gblm 10+, strong evidence points to the grid cell aspect ratio and, in particular, the resolution in the φ direction as an important parameter in achieving a high < α P > and < α M > (see the discussion in Fromang & Nelson 2006, Flock et al. 2011, Hawley et al. 2011 and Sorathia et al. 2012). A possible explanation for this is that the dynamo cycle - which helps to sustain the turbulent state and involves the MRI as a driving agent - can operate more effectively at higher frequencies when the cell aspect ratio is closer to unity.</text>
<text><location><page_14><loc_8><loc_5><loc_48><loc_13></location>Related to < α M > is the tilt angle, Θ tilt , where sin 2Θ tilt = < α M > (Guan et al. 2009; Beckwith et al. 2011). It has been argued by Sorathia et al. (2012) that this parameter provides a better measure of convergence than < α P > , at least in the case of unstratified turbulence for which the question of convergence</text>
<text><location><page_14><loc_52><loc_71><loc_92><loc_90></location>in the absence of explicit dissipation was raised by Fromang & Papaloizou (2007). We find Θ tilt ∼ 9 · for model gblm 10 which is consistent with previous findings for stratified global disks (Beckwith et al. 2011; Hawley et al. 2011; Flock et al. 2012). However, models gblm 10+ and gbl-rand have Θ tilt ∼ 12 · which is comparable to values of ∼ 11 · -13 · for shearing box simulations (both unstratified and stratified, e.g., Guan et al. 2009; Simon et al. 2012) and also for recent stratified global disks calculations performed with an orbital advection algorithm by Mignone et al. (2012). These results are encouraging as they show that global simulations are reaching sufficient grid resolution to reproduce shearingbox results.</text>
<text><location><page_14><loc_52><loc_56><loc_92><loc_71></location>The ratio of directional magnetic energy also provides insight into convergence and correspondence between simulations. We find, < B 2 R > / < B 2 φ > ∼ 0 . 13, < B 2 z > / < B 2 R > ∼ 0 . 30 and < B 2 z > / < B 2 φ > ∼ 0 . 036 for models gblm 10+ and gbl-rand. These values are higher than obtained by Hawley et al. (2011) for their global disk simulations, and in some cases only slightly lower than values found from high resolution shearingbox simulations (Shi et al. 2010; Davis et al. 2010; Simon et al. 2011; Guan & Gammie 2011; Simon et al. 2012).</text>
<text><location><page_14><loc_52><loc_44><loc_92><loc_56></location>Interestingly, model gblm 10 produces a sustained stress, albeit with a lower value than model gblm 10+, but with only 4 cells/ H in the φ -direction. Flock et al. (2011) found that at least 8 cells/ H were required to produce a sustained turbulent stress (see also Fromang & Nelson 2006). However, these authors used linear reconstruction, whereas we have used parabolic reconstruction which may permit a sustained stress at a slightly lower resolution.</text>
<text><location><page_14><loc_52><loc_33><loc_92><loc_44></location>Finally, we note that we do not see any prominent evidence of recurring transient phenomena due to linear growth revivals in the mean magnetic fields, as recently reported by Flock et al. (2012). This may be due to differences in the numerical setup between our models and those of Flock et al., or perhaps this phenomena occurs at later times that we have not reached with the simulation runtimes of our models.</text>
<section_header_level_1><location><page_14><loc_66><loc_31><loc_78><loc_32></location>6. CONCLUSIONS</section_header_level_1>
<text><location><page_14><loc_52><loc_19><loc_92><loc_31></location>We have performed global 3D MHD simulations of turbulent accretion disks which start from fully equilibrium MHD initial conditions. The local linear theory of the MRI is used as a predictor of the growth of magnetic field perturbations in the global simulations. Additional tests have also been performed to compare results obtained from global simulations using a number of different numerical algorithms and resolutions to the linear growth estimates. Our main findings are:</text>
<unordered_list>
<list_item><location><page_14><loc_53><loc_9><loc_92><loc_18></location>i) The growth of magnetic field perturbations in the global simulations shows good agreement with the linear MRI growth estimates during approximately the first orbit of the disk. Subsequently, the overwhelming influence of non-linear motions, which may be due either to the onset of turbulence or to secondary instabilities, saturates the local growth.</list_item>
<list_item><location><page_14><loc_53><loc_5><loc_92><loc_8></location>ii) The saturated state is found to be independent of the initially excited MRI mode, showing that once</list_item>
</unordered_list>
<text><location><page_15><loc_11><loc_80><loc_48><loc_90></location>the disk has expelled the initial net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of quasi-steady turbulence are found to be in agreement with previous work. In particular, the time averaged stress, < α P > ∼ 0 . 034.</text>
<unordered_list>
<list_item><location><page_15><loc_9><loc_68><loc_48><loc_80></location>iii) We find < B 2 R > / < B 2 φ > ∼ 0 . 13 for global stratified simulations with 12.5 cells/ H in the φ direction, which is in good agreement with value found from high resolution, stratified, shearing-box simulations. Higher φ resolution in the simulation (at least > 4 cells/ H ) is required to maintain stronger radial and vertical magnetic field, and consequently a larger < α P > .</list_item>
<list_item><location><page_15><loc_9><loc_64><loc_48><loc_67></location>iv) From the numerical algorithms that we tested, the choice of reconstruction order or limiter does not significantly alter the resulting linear MRI growth</list_item>
</unordered_list>
<text><location><page_15><loc_55><loc_79><loc_92><loc_90></location>rate. Convergence with resolution (for the linear MRI growth tests) is found for resolutions of roughly 23 -35 cells per scaleheight (in the vertical direction). However, above all, a higher azimuthal resolution contributes to a much better agreement with linear growth estimates, supporting the push for low cell aspect ratio (close to one) in global accretion disk simulations.</text>
<section_header_level_1><location><page_15><loc_62><loc_75><loc_81><loc_76></location>ACKNOWLEDGEMENTS</section_header_level_1>
<text><location><page_15><loc_52><loc_64><loc_92><loc_74></location>We thank the referee for a particularly useful report which helped to significantly improve the paper. This research was supported under the Australian Research Council's Discovery Projects funding scheme (project number DP1096417). E. R. P thanks the ARC for funding through this project. This work was supported by the NCI Facility at the ANU and by the iVEC facility at the Pawsey Centre, Perth, WA.</text>
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<section_header_level_1><location><page_16><loc_46><loc_87><loc_54><loc_88></location>APPENDIX</section_header_level_1>
<section_header_level_1><location><page_16><loc_37><loc_85><loc_63><loc_86></location>A. EQUILIBRIUM DISK SOLUTIONS</section_header_level_1>
<text><location><page_16><loc_8><loc_76><loc_92><loc_84></location>The initial conditions for our simulations are an equilibrium thin disk with a purely toriodal magnetic field. In the following we present some analytic solutions which are of use for numerical simulations of accretion disks and for disks in other environments, such as starburst galaxies (e.g. Cooper et al. 2008). These solutions incorporate more or less arbitrary radial profiles of density and temperature and a toroidal magnetic field. The latter involves either a constant ratio of gas-to-magnetic pressure, β , radially dependent β , constant B φ , and variants with net/zero toroidal magnetic flux.</text>
<text><location><page_16><loc_8><loc_74><loc_92><loc_76></location>In axisymmetric cylindrical coordinates ( R,φ,z ), in steady-state, and with v R = v z = B R = B z = 0, the induction equation is identically satisfied and we are left with the two momentum equations:</text>
<formula><location><page_16><loc_36><loc_70><loc_92><loc_73></location>∂P ∂R + ρ ∂ Φ ∂R -ρv 2 φ R + 1 2 R 2 ∂ ( R 2 B 2 φ ) ∂R =0 , (A1)</formula>
<formula><location><page_16><loc_46><loc_66><loc_92><loc_70></location>∂P ∂z + ρ ∂ Φ ∂z + 1 2 ∂B 2 φ ∂z =0 , (A2)</formula>
<text><location><page_16><loc_8><loc_65><loc_45><loc_66></location>where the pressure, P = ρT , with T in scaled units.</text>
<text><location><page_16><loc_8><loc_62><loc_92><loc_65></location>We derive a compatibility condition for the above equations by subtracting ∂/∂R of Eq (A2) from ∂/∂z of Eq (A1), to obtain,</text>
<formula><location><page_16><loc_21><loc_58><loc_92><loc_62></location>∂ ∂z ( v 2 φ R ) = ∂T ∂z 1 ρ ∂ρ ∂R -1 2 R 2 ρ 2 ∂ρ ∂z ∂ ( R 2 B 2 φ ) ∂R + 1 ρR ∂B 2 φ ∂z -∂T ∂R 1 ρ ∂ρ ∂z + 1 2 ρ 2 ∂ρ ∂R ∂B 2 φ ∂z (A3)</formula>
<text><location><page_16><loc_8><loc_50><loc_92><loc_57></location>To solve for the disk equilibrium we take the approach of using Eq (A2) to derive an equation for ρ ( R,z ), Eq (A3) to acquire v 2 φ ( R,z ), and Eq (A1) to obtain an expression for v 2 φ ( R, 0). The resulting equations require boundary conditions for the run of ρ and T at the disk midplane, which can be chosen arbitrarily. From here on we take the disk to be isothermal in height, T = T ( R ), and firstly consider a disk with a constant, β = 2 P/ | B | 2 ≡ 2 P/B 2 φ . Eq (A2) then becomes,</text>
<formula><location><page_16><loc_40><loc_46><loc_92><loc_50></location>1 ρ ∂ρ ∂z = -∂ Φ ∂z ( β 1 + β ) 1 T ( R ) (A4)</formula>
<text><location><page_16><loc_8><loc_45><loc_69><loc_46></location>which integrates to give an expression for the density in terms of its midplane value,</text>
<formula><location><page_16><loc_31><loc_41><loc_92><loc_44></location>ρ ( R,z ) = ρ ( R, 0) exp ( -{ Φ( R,z ) -Φ( R, 0) } T ( R ) β 1 + β ) . (A5)</formula>
<text><location><page_16><loc_8><loc_39><loc_67><loc_40></location>Turning to the rotational velocity, the compatibility relation (Eq (A3)) reduces to,</text>
<formula><location><page_16><loc_38><loc_34><loc_92><loc_38></location>∂ ∂z ( v 2 φ R ) = -( 1 + β β ) 1 ρ ∂ρ ∂z ∂T ∂R (A6)</formula>
<text><location><page_16><loc_8><loc_31><loc_92><loc_34></location>which upon integrating and using Eq (A4) leads to an expression for the azimuthal velocity in terms of its midplane value,</text>
<formula><location><page_16><loc_33><loc_28><loc_92><loc_31></location>v 2 φ ( R,z ) = v 2 φ ( R, 0) + { Φ( R,z ) -Φ( R, 0) } R T dT dR . (A7)</formula>
<text><location><page_16><loc_8><loc_25><loc_92><loc_28></location>The model is completed with a midplane rotational velocity, which is determined by substituting Eq (A5) into Eq (A1). This gives</text>
<formula><location><page_16><loc_25><loc_21><loc_92><loc_24></location>v 2 φ ( R, 0) = R ∂ Φ( R, 0) ∂R + 2 T β + ( 1 + β β )( RT ρ ( R, 0) ∂ρ ( R, 0) ∂R + R dT dR ) . (A8)</formula>
<text><location><page_16><loc_8><loc_18><loc_92><loc_20></location>The first term is the square of the Keplerian velocity; the remaining terms are proportional to the square of the sound speed so that Eq (A8) represents a minor departure from a Keplerian disk.</text>
<text><location><page_16><loc_8><loc_14><loc_92><loc_18></location>A possible variation to the aforementioned disk would be to make β radially dependent, i.e., β = β ( R ). For example, one may choose to make β ( R ) ∝ sin( kR ), where k is a radial wavenumber. In such a case Eq (A5) for ρ ( R,z ) is unchanged. However, the expression for the rotational velocity becomes,</text>
<formula><location><page_16><loc_26><loc_9><loc_92><loc_13></location>v 2 φ ( R,z ) = v 2 φ ( R, 0) + { Φ( R,z ) -Φ( R, 0) } ( R T dT dR -1 β (1 + β ) ∂β ∂R ) (A9)</formula>
<text><location><page_16><loc_8><loc_8><loc_38><loc_9></location>where, following substitution in Eq (A1),</text>
<formula><location><page_16><loc_22><loc_3><loc_92><loc_7></location>v 2 φ ( R, 0) = R ∂ Φ( R, 0) ∂R + 2 T β + ( 1 + β β )( RT ρ ( R, 0) ∂ρ ( R, 0) ∂R + R dT dR ) -RT β 2 ∂β ∂R . (A10)</formula>
<text><location><page_17><loc_8><loc_15><loc_13><loc_16></location>Hence,</text>
<text><location><page_17><loc_8><loc_12><loc_11><loc_13></location>and</text>
<text><location><page_17><loc_8><loc_87><loc_92><loc_90></location>Alternatively, one may desire a disk with a constant B φ ( R,z ) = B φ 0 , in which case the magnetic pressure does not influence the density profile, leading to,</text>
<formula><location><page_17><loc_33><loc_83><loc_92><loc_87></location>ρ ( R,z ) = ρ ( R, 0) exp ( -{ Φ( R,z ) -Φ( R, 0) } T ( R ) ) , (A11)</formula>
<text><location><page_17><loc_8><loc_82><loc_36><loc_83></location>and a corresponding velocity profile of,</text>
<formula><location><page_17><loc_24><loc_78><loc_92><loc_81></location>v 2 φ ( R,z ) = v 2 φ ( R, 0) + { Φ( R,z ) -Φ( R, 0) } R T dT dR + v 2 A φ ( R,z ) -v 2 A φ ( R, 0) , (A12)</formula>
<text><location><page_17><loc_8><loc_76><loc_12><loc_78></location>with,</text>
<formula><location><page_17><loc_26><loc_72><loc_92><loc_75></location>v 2 φ ( R, 0) = R ∂ Φ( R, 0) ∂R + v 2 A φ ( R, 0) + ( RT ρ ( R, 0) ∂ρ ( R, 0) ∂R + R dT dR ) , (A13)</formula>
<text><location><page_17><loc_8><loc_66><loc_92><loc_72></location>and where the Alfv'en speed, v A φ ( R,z ) = B φ 0 / √ ρ ( R,z ). As mentioned above, the radial profiles ρ ( R, 0) and T ( R ) required to complete the disk model may be chosen arbitrarily, subject to boundary constraints at the outer disk edge. As an example, we use simple functions inspired by the Shakura & Sunyaev (1973) disk model, modified by truncation of the density profile at a specified outer radius:</text>
<formula><location><page_17><loc_36><loc_62><loc_92><loc_66></location>ρ ( R, 0)= ρ 0 f ( R,R 0 , R out ) ( R R 0 ) /epsilon1 , (A14)</formula>
<formula><location><page_17><loc_31><loc_58><loc_92><loc_62></location>f ( R,R 0 , R out ) = ( √ R out R + √ R 0 R -√ R out R 0 R 2 -1 ) , (A15)</formula>
<formula><location><page_17><loc_37><loc_54><loc_92><loc_58></location>T ( R ) = T 0 ( R R 0 ) χ , (A16)</formula>
<text><location><page_17><loc_8><loc_47><loc_92><loc_54></location>where ρ 0 sets the density scale, R 0 and R out are the radius of the inner and outer disk edge, respectively, and /epsilon1 and χ set the slope of the density and temperature profiles, respectively. The tapering function, f ( R,R 0 , R out ) is used to truncate the disk at an inner and outer radius. In practice this function is normalized to give ρ ( R max , 0) = ρ 0 , where the radius of peak density, R max is given by the positive root of the quadratic resulting from taking ∂/∂R of Eq (A14), namely,</text>
<formula><location><page_17><loc_22><loc_43><loc_92><loc_47></location>√ R max = a 2 ( √ R out + √ R 0 ) + 1 2 √ a 2 ( √ R out + √ R 0 ) 2 -4(1 -/epsilon1 -1 ) √ R 0 R out (A17)</formula>
<text><location><page_17><loc_8><loc_34><loc_92><loc_44></location>where a = 1 -(2 /epsilon1 ) -1 . Once R max is known it is straightforward to renormalize the density profile. Finally, studies of turbulent dynamos in magnetized disks are often concerned with the net flux of the magnetic field (e.g. Brandenburg et al. 1995; Hawley et al. 1996; Fromang & Nelson 2006). For the initially purely toroidal field we have adopted in this paper the net flux of the disk is given by Ψ φ = ∫ ∫ B φ dRdz . Noting that in the above derivations we have used β to relate B 2 φ to P , meaning B φ = ± √ 2 ρT/β , i.e. we are free to choose the sign of B φ . Therefore, if a net flux field is required then one may set the sign of B φ the same everywhere, whereas if one desires a zero-net flux field then, for example, one may choose to make B φ anti-symmetric about the disk midplane.</text>
<section_header_level_1><location><page_17><loc_29><loc_31><loc_71><loc_32></location>B. FOURIER TRANSFORM IN CYLINDRICAL COORDINATES</section_header_level_1>
<text><location><page_17><loc_8><loc_28><loc_92><loc_30></location>We wish to evaluate the Fourier transform F ( k ) of a function f ( r ) = f ( R,φ,z ) expressed in terms of cylindrical polar coordinates ( R,φ,z ). The definition of the Fourier transform is</text>
<formula><location><page_17><loc_40><loc_23><loc_92><loc_27></location>F ( k ) = ∫ exp( i k · r ) f ( r ) d 3 x (B1)</formula>
<text><location><page_17><loc_8><loc_22><loc_73><loc_24></location>Cylindrical coordinates in real and Fourier space are expressed via the following equations:</text>
<formula><location><page_17><loc_38><loc_17><loc_92><loc_21></location>x = R cos φ k x = k R cos ψ y = R sin φ k y = k R sin ψ z = z k z = k z (B2)</formula>
<formula><location><page_17><loc_40><loc_13><loc_92><loc_15></location>k · r = k R R cos( φ -ψ ) + k z z (B3)</formula>
<formula><location><page_17><loc_29><loc_8><loc_92><loc_12></location>F ( k ) = ∫ V exp[ i ( k R R cos( φ -ψ ) + k z z )] f ( R,φ,z ) RdRdφdz (B4)</formula>
<text><location><page_17><loc_8><loc_7><loc_49><loc_8></location>where V is the computational region, usually of the form:</text>
<formula><location><page_17><loc_33><loc_4><loc_92><loc_6></location>R 0 < R < R 1 0 < φ < 2 π -z 0 < z < z 0 (B5)</formula>
<text><location><page_18><loc_10><loc_89><loc_68><loc_90></location>We begin by constructing a Fourier series in the periodic azimuthal coordinate φ :</text>
<formula><location><page_18><loc_38><loc_83><loc_92><loc_88></location>f ( R,φ,z ) = ∞ ∑ m = -∞ f m ( R,z ) e -imφ (B6)</formula>
<text><location><page_18><loc_8><loc_82><loc_40><loc_83></location>where the coefficients f m ( R,z ) are given by:</text>
<formula><location><page_18><loc_37><loc_77><loc_92><loc_81></location>f m ( R,z ) = 1 2 π ∫ 2 π 0 f ( R,φ,z ) e imφ dφ (B7)</formula>
<text><location><page_18><loc_8><loc_74><loc_92><loc_77></location>We now make the change of angular variable χ = φ -ψ ; the integration over χ is still over the interval [0 , 2 π ] since all of the angular functions within the integrand have period 2 π . The Fourier transform can now be expressed as:</text>
<formula><location><page_18><loc_21><loc_69><loc_92><loc_74></location>F ( k ) = ∞ ∑ m = -∞ e imψ ∫ R 1 R 0 [∫ z 0 -z 0 e ik z z f m ( R,z ) [∫ 2 π 0 e i ( -mχ + k R R cos χ ) dχ ] dz ] RdR (B8)</formula>
<text><location><page_18><loc_8><loc_68><loc_64><loc_69></location>The angular integral can be expressed in terms of Bessel functions ( J m ( k R R )):</text>
<formula><location><page_18><loc_35><loc_63><loc_92><loc_67></location>∫ 2 π 0 e i ( -mχ + k R R cos χ ) dχ = 2 π i m J m ( k R R ) (B9)</formula>
<text><location><page_18><loc_8><loc_62><loc_13><loc_63></location>Hence,</text>
<formula><location><page_18><loc_25><loc_57><loc_92><loc_62></location>F ( k ) = 2 π ∞ ∑ m = -∞ i m e imψ ∫ R 1 R 0 J m ( k R R ) [∫ z 0 -z 0 e ik z z f m ( R,z ) dz ] RdR (B10)</formula>
<text><location><page_18><loc_10><loc_56><loc_44><loc_57></location>Equation (B10) defines the following procedure:</text>
<unordered_list>
<list_item><location><page_18><loc_10><loc_52><loc_36><loc_53></location>1. Evaluate the angular coefficients:</list_item>
</unordered_list>
<formula><location><page_18><loc_37><loc_47><loc_92><loc_51></location>f m ( R,z ) = 1 2 π ∫ 2 π 0 f ( R,φ,z ) e imφ dφ (B11)</formula>
<unordered_list>
<list_item><location><page_18><loc_10><loc_46><loc_47><loc_47></location>2. Then perform the integration in the z direction:</list_item>
</unordered_list>
<formula><location><page_18><loc_38><loc_41><loc_92><loc_45></location>F m ( R,k z ) = ∫ z 0 -z 0 e ik z z f m ( R,z ) dz (B12)</formula>
<unordered_list>
<list_item><location><page_18><loc_10><loc_39><loc_65><loc_40></location>3. Finally, perform the (truncated) Hankel transform in the radial direction:</list_item>
</unordered_list>
<formula><location><page_18><loc_34><loc_34><loc_92><loc_38></location>ˆ F m ( k R , k z ) = ∫ R 1 R 0 RJ m ( k R R ) F m ( R,k z ) RdR (B13)</formula>
<unordered_list>
<list_item><location><page_18><loc_10><loc_32><loc_39><loc_34></location>4. The Fourier transform of f ( R,φ,z ) is</list_item>
</unordered_list>
<formula><location><page_18><loc_35><loc_27><loc_92><loc_31></location>F ( k R , ψ, k z ) = 2 π ∞ ∑ m = -∞ i m e imψ ˆ F m ( k R , k z ) (B14)</formula>
<text><location><page_18><loc_8><loc_21><loc_92><loc_26></location>Since the input data for f ( R,φ,z ) are on a grid, the azimuthal, vertical and radial wave numbers, m,k z and k R , are limited by the Nyquist limit. Let the number of intervals in each coordinate direction be ( n R , n φ , n z ) and the grid increments be (∆ R, ∆ φ, ∆ z ) = [( R 1 -R 0 ) /n R , 2 π/n φ , 2 z 0 /n z ]. The grid coordinates are R u , φ v , z w where:</text>
<formula><location><page_18><loc_35><loc_16><loc_92><loc_21></location>R u = R 0 + u ∆ R u = 0 , 1 , ..., n R -1 φ v = v ∆ φ v = 0 , 1 , ..., n φ -1 z w = -z 0 + w ∆ z w = 0 , 1 , ..., n z -1 (B15)</formula>
<text><location><page_18><loc_8><loc_13><loc_92><loc_16></location>The expressions for the azimuthal f m ( R,z ) and vertical F m ( R,k z ) parts of the Fourier transform can be approximated by discrete Fourier transforms as follows:</text>
<formula><location><page_18><loc_13><loc_3><loc_92><loc_12></location>f m ( R u , z w ) ≈ 1 n φ n φ -1 ∑ v =0 f ( R u , φ v , z w ) exp[2 πimv/n φ ] m = 0 , 1 , ..., n φ / 2 F m ( R u , k z ) ≈ 2 z 0 n z exp[ -ik z z 0 ] n z -1 ∑ w =0 f m ( R u , z w ) exp[2 πlw/n z ] l = 0 , 1 , ..., n z / 2 k z = π z 0 l (B16)</formula>
<text><location><page_19><loc_8><loc_89><loc_40><loc_90></location>The radial transform can be evaluated from</text>
<formula><location><page_19><loc_33><loc_84><loc_92><loc_88></location>ˆ F m ( k R , k z ) = k -2 R ∫ k R R 1 k R R 0 sJ m ( s ) F m ( s/k R , k z ) ds (B17)</formula>
<text><location><page_19><loc_10><loc_83><loc_87><loc_84></location>More accurate versions of equations (B16) may be evaluated using the approach given in Press et al. (1986).</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Global three dimensional magnetohydrodynamic (MHD) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied. The local linear theory of the magnetorotational instability (MRI) is used as a predictor of the growth of magnetic field perturbations in the global simulations. The linear growth estimates and global simulations diverge when non-linear motions perhaps triggered by the onset of turbulence - upset the velocity perturbations used to excite the MRI. The saturated state is found to be independent of the initially excited MRI mode, showing that once the disk has expelled the initially net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of converged turbulence, such as the ratio of magnetic energies, are found to be in agreement with previous works. In particular, the globally averaged stress normalized to the gas pressure, < α P > = 0 . 034, with notably higher values achieved for simulations with higher azimuthal resolution. Supplementary tests are performed using different numerical algorithms and resolutions. Convergence with resolution during the initial linear MRI growth phase is found for 23 -35 cells per scaleheight (in the vertical direction). Subject headings: accretion, accretion disks - magnetohydrodynamics - instabilities - turbulence",
"pages": [
1
]
},
{
"title": "EQUILIBRIUM DISKS, MRI MODE EXCITATION, AND STEADY STATE TURBULENCE IN GLOBAL ACCRETION DISK SIMULATIONS.",
"content": "E. R. Parkin & G. V. Bicknell Research School of Astronomy and Astrophysics, The Australian National University, Australia Draft version September 17, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Accretion disks are ubiquitous in astrophysics and play an essential part in the formation of stars and galaxies. For accretion through a disk to be effective, angular momentum must be transported radially outwards, allowing material to move radially inwards. One means of achieving this is through viscous torques (Lynden-Bell & Pringle 1974), and considerable progress has been made using the phenomenological α -viscosity introduced by Shakura & Sunyaev (1973) which assumes that viscosity is provided by turbulent stresses which scale with the gas pressure. However, despite its successes, the α -viscosity model provides little physical insight into the mechanism(s) responsible for the turbulent stress. Even prior to the work of Shakura & Sunyaev (1973), instabilities in magnetized rotating plasmas had been discovered by Velikhov (1959) and Chandrasekhar (1960). Yet, it was not until the seminal work of Balbus & Hawley (1991, 1998) that the so-called magnetorotational instability (MRI) received widespread attention as the agent responsible for the onset of accretion disk turbulence. Linear stability analysis has shown that the MRI will amplify a seed magnetic field indefinitely until confronted by the strong-field limit or the diffusion scale (Balbus & Hawley 1992; Terquem & Papaloizou 1996; Papaloizou & Terquem 1997). Non-linear stability analysis finds that growth of the magnetic field by the linear phase of the MRI is likely to be truncated by saturation resulting from secondary, or parasitic, instabilities (e.g. Goodman & Xu 1994; Pessah 2010). That saturation of the magnetic field occurs was clearly demonstrated by even the very first shearing box sim- ulations (Brandenburg et al. 1995; Hawley et al. 1995; Stone et al. 1996). Contemplating the next steps in magnetized disks studies is aided by summarising what we have already learned. For example, as mentioned above, it is clear that the magnetic field reaches saturation and that the resulting Maxwell stress dominates the angular momentum transport. In numerical simulations this necessitates high resolution to ensure that the fastest growing MRI modes are sufficiently well resolved (see, e.g., Sano et al. 2004; Fromang & Nelson 2006; Noble et al. 2010; Flock et al. 2011; Hawley et al. 2011). Related to this point is the importance of stratification, which introduces a characteristic length scale, removing the problem of non-convergence with simulation resolution encountered in unstratified simulations (Fromang & Papaloizou 2007; Lesur & Longaretti 2007; Simon et al. 2009; Guan et al. 2009; Davis et al. 2010; Sorathia et al. 2012). Stratification could also play a role in the dynamo process which sets the saturation stress (Brandenburg 2005; Vishniac 2009; Shi et al. 2010; Gressel 2010). However, the shearing box approximation used in a large number of numerical studies to-date has limitations (e.g. Regev & Umurhan 2008; Bodo et al. 2008, 2011), including the use of shearingperiodic boundary conditions in the radial direction, and/or periodic boundary conditions in the vertical direction. There boundary conditions artificially trap magnetic flux, assisting the maintenance of the turbulent dynamo and obscuring the dependence of the saturated state on resolution. This is supported by a comparison of periodic and open boundary conditions in global models by Fromang & Nelson (2006) where the former were found to assist the dynamo by preventing magnetic flux from being expelled from the domain. In this re- gard global models have the advantage of removing the unphysical influence of the shearing box boundary conditions, albeit at a much larger computational expense. Other motivations for global models are the results from stability analyses of non-axisymmetric disturbances in magnetized accretion disks, where the most robust MRI modes are localized and the most robust buoyant (Parker) modes are global (Terquem & Papaloizou 1996; Papaloizou & Terquem 1997). Therefore, large radial extents are required to accommodate the more global modes, and in this regard there is a limit to the radial periodicity adopted in most shearing box simulations. These factors point to the need for high resolution, global, stratified disk simulations to further unravel the complexities of magnetorotational turbulence. Of the global simulation studies that have been performed a large number of the findings from local models have been maintained or have persisted; the ratio of the Maxwell and Reynolds stress is ∼ 3, and variations in toroidal magnetic field with time are suggestive of a dynamo cycle (Hawley 2000; Hawley & Krolik 2002; Fromang & Nelson 2006, 2009; Lyra et al. 2008; Sorathia et al. 2010, 2012; Flock et al. 2010, 2011, 2012; O'Neill et al. 2011; Hawley et al. 2011; Beckwith et al. 2011; Mignone et al. 2012; McKinney et al. 2012; Romanova et al. 2012). However, a large number of these simulations do not start from fully equilibrium initial conditions where the magnetic field is accounted for in the force balance and in the induction equation. Both local and global models started with poloidal fields which do not satisfy the induction equation show rapid disruption and re-arrangement of the disk (e.g. Miller & Stone 2000; Hawley 2000; Hawley et al. 2011). This introduces a transient phase where channel flows are fueled by rapid shearing of the poloidal field lines. As such, extended run times are required to ensure that transients have subsided. To our knowledge, no previous global simulations of the MRI in stratified disks have used a fully equilibrium initial disk (i.e. satisfying force balance and the induction equation). We aim to explore the influence of magnetic fields on an accretion disk with global simulations. In this first paper we present equilibrium initial disk models with arbitrary radial density and temperature profiles. We then investigate the saturation (both locally and globally) of the growth of magnetic field perturbations. To this end we excite the MRI in global simulations using linear MRI calculations as a guide, and recover growth of magnetic field perturbations in agreement with estimates. In so doing we show that non-linear gas motions saturate the initial growth of the magnetic field and that at later times the turbulent state retains no knowledge of the initially excited MRI mode(s). The plan of this paper is as follows: in § 2 we describe the equilibrium initial conditions and details of the numerical calculations and in § 3 we perform a linear perturbation analysis for the non-axisymmetric MRI. We present a suite of global magnetized disk simulations in § 4, which explore the effect of different MRI mode excitation and numerical algorithms. In § 5 we compare our results to previous work, and then close with conclusions in § 6.",
"pages": [
1,
2
]
},
{
"title": "2.1. Simulation code",
"content": "For our global disk simulations, we use a 3D spherical ( r, θ, φ ) coordinate system with a domain which closely encapsulates the initial disk (e.g. Fromang & Nelson 2006), and we solve the time-dependent equations of ideal MHD using the PLUTO code (Mignone et al. 2007). We note that throughout this work we describe our results in terms of both spherical ( r, θ, φ ) and/or cylindrical ( R,φ,z ) coordinates, with R = r sin θ and z = r cos θ . The relevant equations for mass, momentum, energy conservation, and magnetic field induction are: (3) Here E = ρ/epsilon1 + 1 2 ρ | v | 2 + 1 2 | B | 2 , is the total gas energy density, /epsilon1 is the internal energy per unit mass, v is the gas velocity, ρ is the mass density, and P is the pressure. We use the ideal gas equation of state, ρ/epsilon1 = P/ ( γ -1), where the adiabatic index γ = 5 / 3. The adopted scalings for density, velocity, temperature, and length are, respectively, where c is the speed of light, and the value of l scale corresponds to the gravitational radius of a 10 8 M /circledot black hole. The gravitational potential, Φ of a central point mass (ignoring self-gravity of the disk), Φ is modelled using the pseudo-Newtonian potential introduced by Paczy'nsky & Wiita (1980): Note that we take the gravitational radius (in scaled units), r g = 1. The Schwarzschild radius, r s = 2 for a spherical black hole and the innermost stable circular orbit (ISCO) lies at r = 6. The Λ term on the RHS of Eq (3) is an ad-hoc cooling term used to keep the scaleheight of the disk approximately constant throughout the simulations; without any explicit cooling in conjunction with an adiabatic equation of state, dissipation of magnetic and kinetic energy leads to an increase in gas pressure and, consequently, the disk scaleheight over time. The form of Λ is particularly simple, where T 0 ( R ) and T ( R,z ) are the position dependent initial and current temperature, respectively, v φ is the ro- ational velocity, and R is the cylindrical radius. This cooling function drives the temperature distribution in the disk back towards the initial one over a timescale of an orbital period and is similar in its purpose to the cooling functions used by Shafee et al. (2008), Noble et al. (2010), and O'Neill et al. (2011). Note that we only apply cooling within | z | < 2 H , where H is the scaleheight of the disk, allowing heating via dissipation to occur freely in the corona. Our choice of an orbital period for the cooling timescale is somewhat arbitrary but is chosen as it represents a characteristic timescale for the disk. The PLUTO code was configured to use the fivewave HLLD Riemann solver of Miyoshi & Kusano (2005), piece-wise parabolic reconstruction (PPM Colella & Woodward 1984), and second-order RungeKutta time-stepping. In order to maintain the ∇· B = 0 constraint for the magnetic field we use the upwind Constrained Transport (UCT) scheme of Gardiner & Stone (2008). Such a configuration has been shown to be effective in recovering the linear growth rates of the axisymmetric MRI by Flock et al. (2010). In § 4.4 we test a number of different numerical setups: order of reconstruction, slope limiters, and simulation resolution. However, in all of the other global simulations presented in § 4 we use reconstruction on characteristic variables (e.g. Rider et al. 2007). A Courant-Friedrichs-Lewy (CFL) value of 0.35 was used for all simulations. The grid used for the global simulations is uniform in the r and φ directions and extends from r = 4 -34 and φ = 0 -π/ 2. In the θ direction we use a graded mesh which places slightly more than half of the cells within | z | ≤ 2 H of the disk mid-plane with a uniform ∆ θ , where H is the thermal disk scaleheight, and the remainder of the cells on a stretched mesh between 2 H < | z | < 5 H . For example, for simulation gblm 10 the 256 cells in the θ direction are distributed so that 140 cells are uniformly spaced between 2 H < | z | < 5 H . The respective grid resolutions and number of cells per scaleheight for the three global simulations are noted in Table 2. The grid cell aspect ratio at the mid-plane of the disk and at a radius of r = 18 . 5 (i.e. the disk midpoint) are r ∆ θ : ∆ r : r ∆ φ = 1 : 1 . 4 : 8 . 6 and 1 : 1 . 6 : 2 . 5 for models gblm 10 and gblm 10+, respectively. The r and θ boundary conditions depend on whether the cell adjacent to the boundary contains > 1% disk material - which we determine using a tracer variable. If this constraint is satisfied we use outflow boundary conditions on all hydrodynamic variables except v φ which is determined from a zero-shear boundary condition (i.e. d Ω /dr = 0) and the normal velocity, for which we enforce zero inflow. If the condition on disk material at the boundary is not satisfied we use outflow boundary conditions on hydrodynamic variables with the limit that the values must lie between the floor values and the initial conditions for the background atmosphere - we find this choice to be useful in setting up a steady background inflow during the early stages of the simulation before material initially in the disk evolves to fill the domain. For the magnetic field we use zero gradient boundary conditions on the tangential field components and allow the UCT algorithm to calculate the normal component so as to satisfy the divergence free constraint, with the exception that at the inner radial boundary we enforce a negative magnetic stress condition (e.g. Stone & Pringle 2001). A periodic boundary condition is used in the φ direction. Finally, we use floor density and pressure values which scale linearly with radius and have values at the outer radial boundary of 10 -4 and 5 × 10 -9 , respectively.",
"pages": [
2,
3
]
},
{
"title": "2.2. Initial conditions",
"content": "Motivated by the fact that magnetorotationally turbulent disks are dominated by toroidal field, we start from an analytic equilibrium disk with a purely toroidal magnetic field. The disk equilibrium is derived in axisymmetric cylindrical coordinates ( R,z ); further details can be found in Appendix A along with alternative disk solutions which may be of use in future work. In the following we briefly summarise the equations for the isothermal in height, T = T ( R ), constant ratio of gas-to-magnetic pressure, β = 2 P/ | B | 2 ≡ 2 P/B 2 φ , net magnetic flux disk adopted for the simulations presented in this paper. The choice of temperature and magnetic field lead to a density distribution, in scaled units, where the pressure, P = ρT . For the radial profiles ρ ( R, 0) and T ( R ) we use simple functions inspired by the Shakura & Sunyaev (1973) disk model, except with an additional truncation of the density profile at a specified outer radius: where ρ 0 sets the density scale, R 0 and R out are the radius of the inner and outer disk edge, respectively, f ( R,R 0 , R out ) is a tapering function and is described in Appendix A, and /epsilon1 and χ set the slope of the density and temperature profiles, respectively. In all of the global simulations R 0 = 7, R out = 30, ρ 0 = 10, T 0 = 4 . 5 × 10 -4 , /epsilon1 = -33 / 20, and χ = -9 / 10 (consistent with the radial scaling in the gas pressure and Thomson-scattering opacity dominated region from Shakura & Sunyaev 1973), producing disks with an aspect ratio, H/R = 0 . 05. The rotational velocity of the disk is close to Keplerian, with a minor modification due to the gas and magnetic pressure gradients, where, One advantage using such an equilibrium disk is that one begins with a disk that is close to the expected scale height and density. An isothermal disk, for example, has a scale height that is proportional to R 3 / 2 . Finally, the region outside of the disk is set to be an initially stationary, spherically symmetric, hydrostatic at- mosphere with a temperature and density given by, where ρ atm = 4 × 10 -5 ρ 0 and r ref is a reference radius which we take to be R max , the radius of peak disk density (see Appendix A). The transition between the disk and background atmosphere occurs where their total pressures balance. As an example, model gblm 10 corresponds to a disk with a peak density of 1 . 67 × 10 -7 gm s -1 and a peak temperature of 2 . 9 × 10 9 K.",
"pages": [
3,
4
]
},
{
"title": "2.3. Diagnostics",
"content": "Turbulence is by its very nature chaotic. Therefore, averaged quantities are particularly useful diagnostics. In this section we describe how we calculate averages, and define the variables used to analyse the simulations. To compute shell-averaged values (denoted by curly brackets) of a variable q at a radius r we average in the θ and φ directions via, Similarly, we calculate a horizontally averaged value (denoted by square brackets) as, ∫ To attain a volume-averaged value (denoted by angled brackets) we integrate over the radial profile of shellaveraged values and normalize by the radial extent, ∫ Time averages receive an overbar, such that a volume and time averaged quantity would read < q > . (Note that density-weighted averages are computed, but only for hydrodynamical variables.) For the analysis presented in § 4 we restrict the integration over r and θ to the range 10 < r < 30 and in π/ 2 -θ 2 H/R < θ < π/ 2 + θ 2 H/R , where θ 2 H/R = tan -1 (2 H/R ). We define this region as the 'disk body' and limit the integration over this region to allow comparison against recent global (e.g. Fromang & Nelson 2006; Beckwith et al. 2011; Sorathia et al. 2010; Flock et al. 2011, 2012; Hawley et al. 2011; Sorathia et al. 2012) and large local 1 simulations (e.g. Guan & Gammie 2011; Simon et al. 2012). In order to keep a track of the fluctuations in the scaleheight of the disk during the simulation - which results from the interplay between adiabatic heating and our cooling function - a density-weighted average disk scaleheight is computed, where we take H/R = c s /v φ (where c s is the sound speed), then perform a density-weighted shell-average followed by a radial averaging to acquire a volume averaged value, < H/R > . For accretion to occur, angular momentum must be transported radially outwards by turbulent stresses, and a major focus of numerical simulations is quantifying the stress. To this end, we define the perturbed flow velocity as 2 δv i = v i -∫ v i r sin θdφ/ ∫ r sin θdφ with i = R , φ , and compute the R -φ component of the combined Reynolds and Maxwell stress, which is normalized by the gas pressure to acquire, Furthermore, we calculate the R -φ component of the Maxwell stress normalized by the magnetic pressure, To examine the operation of dynamo activity in the disk we compute the toroidal magnetic flux, which is defined as, The ability of the simulations to resolve the fastest growing MRI modes is quantified in the same fashion as Noble et al. (2010) and Hawley et al. (2011). The wavelength of the fastest growing MRI modes with respect to the grid resolution in the z and φ directions are, respectively, and, where v Az and v A φ are the vertical and azimuthal Alfv'en speeds, respectively, ∆ θ and ∆ φ are the cell sizes in the θ and φ directions, respectively, and ∆ z = √ ( r sin θ ∆ θ ) 2 +(∆ r cos θ ) 2 is the corresponding cell size in the z direction. We define a single valued measure of resolvability as the fraction of cells in the disk body ( | z | < 2 H ) that have Q > 8 (e.g. Sorathia et al. 2012), where i = z, φ and C represents a cell. The principal aim of calculating N z and N φ is to quantify how well resolved the turbulent state is in a simulation, and consequently whether global simulations are approaching the region of convergence found from shearing box simulations (Hawley et al. 2011).",
"pages": [
4
]
},
{
"title": "2.4. Fourier analysis",
"content": "To allow a direct comparison between the growth of MRI modes estimated from a linear perturbation analysis ( § 3) and the results of global simulations ( § 4) we analyse the growth of magnetic field perturbations in Fourier space. The procedure we follow is to remap the disk body (which we define in § 2.3) to a cylindrical mesh with uniform cell spacing in all directions, and a sufficiently fine resolution to ensure that the smallest cells from the spherical simulation grid are sampled. We then perform a 3D Fourier Transform of the data on the cylindrical grid. A detailed description of the cylindrical Fourier transform can be found in Appendix B.",
"pages": [
5
]
},
{
"title": "3. EXCITING THE MRI",
"content": "Given that our global simulations commence with an equilibrium disk the MRI requires a seed perturbation to excite the growth of the magnetic field and development of turbulence. For this purpose we have chosen to excite a specific Fourier mode of the MRI using poloidal velocity perturbations. In the following we present perturbation calculations for the local, linear, non-axisymmetric MRI, the results of which are used in § 4 to elucidate the evolution of magnetic field perturbations in global numerical simulations.",
"pages": [
5
]
},
{
"title": "3.1. Linear MRI growth models",
"content": "Studies of the linear, non-axisymmetric MRI in weakly magnetized disks have been examined by a number of authors (Balbus & Hawley 1992; Terquem & Papaloizou 1996; Papaloizou & Terquem 1997). Balbus & Hawley (1992)'s local study showed that even if the seed magnetic field is purely toroidal then the instability is still present, albeit with growth rates roughly an order of magnitude lower than those found for initially poloidal fields (Balbus & Hawley 1991). This result was supported by growth timescales approaching an orbital period (for certain parameters) in more-global calculations by Terquem & Papaloizou (1996) where radial gradients were preserved. Furthermore, these authors found that in the k z /k R /lessmuch 1 limit - the primary domain of the MRI instabilities become increasingly localized with time. On the other hand, in the k R /k z /lessmuch 1 limit the Parker instability dominates. In fact, even in the presence of dissipation, MRI modes continue to become increasingly localized over time due to the time dependence of the radial wavenumber (Papaloizou & Terquem 1997). Common to these studies is the finding that the non-axisymmetric MRI acts as a mechanism for the transient amplification of seed magnetic/velocity field perturbations by many orders of magnitude over tens of orbits. One question is, how well does this immense field amplification carry through to global, fully non-linear simulations? To an- swer this one needs an estimate of the linear growth. In this regard our analysis of the non-axisymmetric MRI in this paper is complementary to studies of the axisymmetric MRI in previous simulations (e.g. Hawley & Balbus 1991; Flock et al. 2010). To construct our prediction for the global simulations we utilize the linear MRI model of Balbus & Hawley (1992). (The perturbation analysis used to quantify the linear MRI growth is performed in cylindrical coordinates ( R,φ,z ), whereas the global models presented in § 4 are performed in spherical coordinates ( r, θ, φ ).) In brief, Balbus & Hawley perform a linear stability analysis of a local patch of a disk using the shearing-sheet approximation (Goldreich & Lynden-Bell 1965) where the perturbations are assumed to have a spatial dependence exp[ i ( k R R + mφ + k z z )]. The equations for the evolution of the magnetic field perturbations form a pair of coupled second-order ordinary differential equations 3 . We let N be the Brunt-Vaisala frequency, which for the equilibrium disk described in § 2.2 is, and define an independent time variable, Replacing the angular velocity with that due to a Paczynski-Wiita potential in the thin disk limit (i.e. H/R /lessmuch 1), Ω 2 = 1 /R 2 ( R -2), the equations describing linear perturbations are 4 , 3 Note that there is a typographical error in equation (2.19) of Balbus & Hawley (1992) where the final term should read δB z N 2 ( k 2 z -k 2 ) /k 2 . 4 The angular velocity resulting from our disk model (cf Eqs (10) and (11)) actually includes a small offset to Keplerian rotation. However, we find that this makes little difference to the perturbation calculations, and the subsequent comparison against global simulations in § 4. Therefore, for the sake of simplicity, we adopt a purely Keplerian rotation profile for the local calculations. where δB z and δB R are the vertical and radial magnetic field perturbations. The time dependence of k R in Eq (25) is a consequence of the radial wavenumber being sheared. Therefore, within the framework of the Balbus & Hawley (1992) analysis the radial wavenumber can grow indefinitely so that radial disturbances can evolve to arbitrarily small spatial extent. Clearly, when we come to making a comparison against our global simulations, this will not be the case due to finite numerical resolution. The magnetic field perturbations are related through the divergence-free constraint, The unperturbed magnetic field topology only enters through k · v A . For our initially purely toroidal magnetic field one finds, To initiate the MRI we use the R and z components of the linearized induction equation, and, where δv R and δv z are the poloidal velocity perturbations (with the imaginary part of δv corresponding to the real part of dδB/dt ). For the perturbations in the z -components in both the linear MRI and global calculations we use a waveform, which, on substitution into Eq (32), and with the conversion between real and imaginary parts accounted for by a phase shift in the trigonometric term, leads to, where δv 0 is the amplitude of the initial velocity perturbations. An equivalent treatment to Eq (34) is used for the perturbations in the R -components with the difference that we make use of the incompressibility condition, k · δ v = 0, and set, The remaining parameters used in the calculations are summarised in Table 1. Our first calculation, model linm 10, uses a β = 20 magnetic field and wavenumbers for the excited MRI mode of m = 10, k z = 5, and k R = 2 . 5. These wavenumbers are chosen to ensure sufficient resolution in the global simulations and we leave a more detailed discussion to § 4. The amplitude of the initial velocity perturbations, δv 0 , is set to 0 . 1 c s , where c s (= √ T ) is the sound speed. Since we intend to use these calculations as a guide for our global simulations, we use the equilibrium disk model described in § 2.2 to choose the input density and temperature. Calculations are performed at a cylindrical radius, R = 20, and at the disk mid-plane where N 2 = 0 (see Eq (24)). From Eq (9) the disk temperature, T = 1 . 75 × 10 -4 , and the density, ρ = 0 . 46. The initial components of δ B are set to zero, so too is the initial azimuthal velocity perturbation, δv φ - the poloidal velocity perturbations seed the instability through the dδB/dt terms. To integrate Eqs (27) and (28) we use an adaptive stepsize, 4th-order, explicit Runge-Kutta method (Press et al. 1986). As Fig. 1 shows, the magnetic field perturbations grow extremely rapidly over the first few P orb 20 with noticeable oscillations, where P orb j is the radially dependent orbital period of the disk at cylindrical radius j. The upper panel of Fig. 2 shows the effective β for the MRI mode - the time required for the magnetic field to grow to β = 1 is only a few orbital periods for model linm 10. Evaluating the approximate growth rate, ω of the magnetic energy, β -1 (as the gas pressure remains constant) via β -1 = β -1 0 exp( ωt ), we find an average growth rate over the first six orbits, ω = 0 . 14 Ω. Applying the same approach to δB R we find ω = 0 . 09Ω. This is consistent with the findings of Terquem & Papaloizou (1996) but is roughly an order of magnitude larger than values of a few percent of the orbital frequency quoted in general for the development of the non-axisymmetric MRI by Balbus & Hawley (1992). Keeping all parameters fixed and then varying the initial magnetic field strength, one sees from models linm 10β 100 and linm 10β 300 the trend that the growth rate of δ B decreases with increasing initial β . In model linm 10β 300 s the size of the initial velocity perturbations is increased to δv 0 = 0 . 3 c s with the result that over the very first few orbits the growth of δB 's becomes very similar to that of a stronger initial field strength excited by smaller velocity perturbations. For a higher wavenumber perturbation the rate of initial growth increases, as evidenced by model linm 40 (see Figs. 1 and 2). Evaluating the approximate growth rate of the magnetic field energy and δB R for model linm 40 gives, ω = 0 . 68 Ω and 0 . 25Ω, respectively 5 . From these results one may predict δ that the development of δ B in simulations will depend on the initial field strength and/or the wavenumber of the excited mode(s). In § 4.3 we examine if this result holds true in global simulations. Balbus & Hawley (1992) discuss the parameter ( k · v A ) 2 / Ω 2 and attribute to it an important role in the ability of the MRI to successfully amplify the seed field. They find that for ( k · v A ) 2 / Ω 2 ∼ > 2 . 9 the instability is stabilized and magnetic field oscillations are damped. For the models shown in Fig. 1, this parameter is much less than unity. From Eq (30) for ( k · v A ) 2 / Ω 2 one can see that to increase the value of this variable one can either decrease β - which increases the tension along field lines - or employ higher azimuthal wavenumbers, m . The latter has the side-effect of increasing the growth rate of k R and causing tight wave crest wrapping, both of which lead to a more rapid stabilization of the radial disturbances. However, we find that irrespective of the value of ( k · v A ) 2 / Ω 2 , which is 0 . 03 for linm 10 (Table 1), the perturbation in the magnetic field ultimately decays. This is shown in Fig 3 (upper and middle panels) where the linm 10 calculation is plotted for a longer time duration. Despite continuing growth in δB z , there is decay in δB R , which is a consequence of the increase of k R ( t ) combined with the divergence-free constraint (Eq (29)). The ratio of the Maxwell stress to magnetic pressure ( α m ) predicted from the linear MRI growth calculations is shown in the lower panel of Fig. 3, where we define, Clearly, considering that α m , or to be more exact < α M > (its global analogue - see Eq (19)), is a commonly used diagnostic in numerical simulations (Hawley et al. 1995). Under the action of the linear MRI alone < α M > would never reach a steady value. This ultimate decay of linear MRI disturbances is consistent with Terquem & Papaloizou (1996)'s finding of transient instability growth in a number of numerical tests, in which k z > k R initially. Shear causes k R to grow but once k R > k z growth halts. The ultimate decay of linear MRI modes has significance for global models because the maintenance of dynamo action requires all components of the field to be sufficiently strong. This highlights the need for an additional mechanism, other than the linear MRI growth, to replenish δB R (e.g. parasitic instabilities - Goodman & Xu 1994; Parker instability Tout & Pringle 1992, Vishniac 2009; dynamo action in the steady-state turbulence Brandenburg et al. 1995, Hawley et al. 1996). The linear MRI growth calculations act as a check on our global simulations, principally to examine whether our setup recovers the growth rates of the linear MRI accurately. However, there is a limit to the time interval when we can confidently make a comparison between the linear growth models and global simulations. Firstly, the analysis of Balbus & Hawley (1992) adopts the Boussinesq approximation which becomes invalid when the azimuthal magnetic field becomes super-thermal. The upper panel of Fig. 2 shows that this limit is reached in approximately 2.3 orbits for linm 10 and 0.1 orbits for linm 40. Secondly, k R ( t ) can grow indefinitely in the linear growth models, yet this is not the case for our global simulations which are restricted by finite numerical resolution. Taking the Nyquist limit to be 2 grid cells, and considering, for example, the resolution of model gblm 10, the maximum resolvable radial wavenumber is k R -Nyquist = 86. This limit is reached after ∼ 16 . 5 and 2.3 orbits for models linm 10 and lin-40, respectively (lower panel of Fig. 2). Therefore, choosing to excite a higher wavenumber MRI mode limits the time interval where comparisons can be made against linear perturbation theory, and this is one reason why we choose to excite a lower wavenumber mode ( m = 10) in the global simulations. > α <",
"pages": [
5,
6,
7,
8
]
},
{
"title": "4. GLOBAL MODELS",
"content": "In this section we describe the results of global simulations using the initial conditions and simulation setup described in § 2. The global simulations are listed along with grid dimensions, number of cells per scaleheight, and approximate MRI growth rates in 2. Time and volume averaged variables quantifying the steady-state turbulence are given in Table 3. In models gblm 10 and gblm 10+ we excite a specific Fourier mode using a plane wave, which takes the form of Eq (33), as described in § 3. These models use the same wavenumbers as model linm 10 so as to allow a direct comparison of magnetic field growth. The third model, gbl-rand, uses random pressure and poloidal velocity perturbations to initially seed the disk disturbance. All of the global models start with a purely toroidal magnetic field with β = 20. Models gblm 10+ and gbl-rand are computed on grids with lower poloidal resolution (roughly 2/3 that of model gblm 10), but with a factor of three better azimuthal resolution. In the following section we present some properties of our model disks and demonstrate that higher φ resolution to be a crucial ingredient in producing a sustained, high valued turbulent stress, < α P > .",
"pages": [
8
]
},
{
"title": "4.1. Model evolution",
"content": "We begin with a description of the evolution of models gblm 10 and gblm 10+ (Tables 2 and 3). In this model we adopt an azimuthal wavenumber which varies with cylindrical radius, m = m ( R ). We give the azimuthal wavenumber a radial dependence of m ( R ) = m crit ( R ) / 6, Note . -a Time interval over which averaging was performed, where the critical 6 azimuthal wavenumber for the linear, 6 Defined as the value of m for which disturbances grow most rapidly, which follows from equation (2.30) of Balbus & Hawley non-axisymmetric MRI, At R = 20 in model gblm 10, m crit = 60; adopting m = m crit / 6 ensures that the corresponding k z and k R are well resolved by the numerical grid. Balbus & Hawley (1992) noted that the fastest growing non-axisymmetric modes occur for k z = m 2 /R , and we also use this relation to calculate k z . Given that our grid resolution is coarser in r than it is in θ , we set k R = k z / 2. The initial poloidal velocity perturbations seed the growth of magnetic field perturbations via the MRI and after roughly 1 -2 P orb 30 turbulent motions become ap- (1992). The radial dependence of Eq (37) stems from the Paczy'nsky & Wiita (1980) potential (Eq (5)). parent in the disk body. As the poloidal magnetic field becomes established throughout the disk the resulting Maxwell stresses disrupt the disk equilibrium. The evolution of models gblm 10 and gblm 10+ is largely similar during the first few orbits of the simulations. Examining the normalized stress, < α P > , shows that there is an initial transient phase which peaks after a simulation time of roughly 4 P orb 30 (Fig. 4). Following this, < α P > gradually decreases until a steady-state is reached after roughly 12 P orb 30 and the time-averaged stress for the remainder of the simulation, < α P > = 0 . 017 for gblm 10. The time-averaged ratio of the Maxwell stress to the magnetic energy, < α M > = 0 . 31, which is below the values of roughly 0.4 quoted by, for example, Hawley et al. (2011) for well resolved turbulence. To investigate the dependence of these values on the azimuthal resolution of the simulation we have also run model gblm 10+, which has 12.5 cells/ H in the φ direction (and a lower resolution in the poloidal direction - see Table 2). The higher φ resolution clearly influences the turbulent stresses in the simulation and for model gblm 10 we find < α M > = 0 . 41 and < α P > = 0 . 034, in agreement with high resolution shearing-box simulations. The resolvability of the fastest growing MRI modes (see Eq (23) and Fig. 5) also clearly show that a higher azimuthal resolution helps to maintain (or even strengthen) the poloidal magnetic field - models gblm 10 and gblm 10+ initially show similar values of N z but largely different values of N φ , and combined with the evidence mentioned above is evident that azimuthal resolution is very important for maintaining a healthy turbulent state (see also the discussion in Fromang & Nelson 2006; Flock et al. 2011; Hawley et al. 2011). In § 5 we compare further quantitative measures of the steady-state turbulence to previous works. The poloidal magnetic field develops in flux tubes with small spatial scale, which dissipate magnetic energy via reconnection, heating the disk. In Fig. 6 we show the density-weighted and volume-averaged scaleheight of the disk, < H/R > as a function of time. In model gblm 10 the scaleheight of the disk increases initially until t ∼ 8 P orb 30 , after which it steadily declines. This shows that during the initial disk evolution, dissipation heats the disk more rapidly than the cooling function, Λ (see Eq (6)) can drive the temperature back to its initial value. In other words, the dissipative timescale is shorter than an orbital period. In contrast, for model gblm 10+, < H/R > remains roughly constant after the initial rise, which shows that the higher < α P > in this model (Fig. 4) is causing more heating, and a marginally thicker disk. Fig. 7 shows a poloidal slice through the disk in model gblm 10+ at t = 14 P orb 30 . During the turbulent steady state the disk is characterised by a dense, cold, subthermally magnetized core close to the mid-plane and a tenuous, hot, trans-to-super thermal magnetic field at z ∼ > 2 H (the corona). Turbulent motions are clearly evident in the plot of β -1 in Fig. 7 with the dominant eddies appearing to have a larger size in the corona compared to the disk body. As noted by Fromang & Nelson (2006), such behaviour arises due to conservation of angular momentum in eddie motions - or wave action - as small scale eddies rise out of the dense disk mid-plane into the less dense coronal region. Our intended purpose for the explicit cooling function, Λ (see § 2.1 for details) becomes more apparent from the temperature plot - we aim to take a step beyond the purely isothermal approximation and towards the observationally supported picture of a hot corona and cooler disk body. In Fig. 8 we show the volume-averaged plasmaβ . In the disk body, we find < β > = 17 and for the corona < β > = 6. The coronal value is higher than values of close to one found in previous isothermal (Miller & Stone 2000; Flock et al. 2011) and quasi-isothermal simulations (Fromang & Nelson 2006; Beckwith et al. 2011), which may be attributable to the lack of any explicit cooling in the corona in our simulations. However, although the gas in the corona is heated by dissipation, it does not continually heat up through the simulation, and in fact remains quasi-steady through the latter half of the simulation. This contrasts with adiabatic shearing-box simulations with imposed periodic boundary conditions, in which the gas does heat up (e.g. Stone et al. 1996; Sano et al. 2004) and demonstrates that when coronal gas is allowed to freely expand, adiabatic cooling can, to some extent, balance heating via turbulent dissipation.",
"pages": [
8,
9,
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]
},
{
"title": "4.2. Comparison with linear MRI growth estimates",
"content": "In Fig. 9 we compare the evolution of | δB R | for the m = 10, k z = 5, k R = 2 . 5 mode (measured in Fourier space - see § 2.4) for model linm 10 (which describes linear MRI growth - see Tables 2 and 1) and models gblm 10 and gblm 10+ (global simulations which allow fully nonlinear evolution - see Table 3). Quantifying the initial growth by deriving approximate growth rates 7 , ω approx for the curves shown in Fig. 9 , we find that the linear MRI estimate is matched best by model gblm 10+, with gblm 10 (and gbl-rand) producing higher growth rates. The higher amplitude perturbation for model gblm 10 compared to gblm 10+ originates from the larger amplitude initial velocity perturbation of 0 . 1 c s (compared to 0 . 001 c s for gblm 10+ and gbl-rand - see Table 3). The agreement between the global simulations and linear growth estimate (model linm 10) begins to falter after roughly 2 P orb 20 and growth in | δB R | for the global simu- v lations levels off. From the linear MRI calculations shown in Fig. 2 one may anticipate that the growth in | δB | is halted by the magnetic pressure evolving to equipartition with the gas pressure - which is illustrated by the vertical dashed line in Fig. 9 - and would mean that one cannot rely on model linm 10 as a predictor for model gblm 10. However, Fig. 10 shows that β remains roughly constant in model gblm 10 over the first few orbits. What then causes the local MRI estimates and the global simulations to diverge? In the lower panel of Fig. 10 we plot the evolution of the following non-linear terms derived from the momentum equations, Small spikes in these non-linear terms occur after ∼ 0 . 1 orbit. However, after 1-2 orbits considerably larger fluctuations become apparent, particularly in b which also appears to have the highest amplitude oscillations of the plotted terms thereafter. Considering that the linear MRI is seeded by velocity perturbations through the induction equation (Eqs (31) and (32)), the correlation in time between the non-linear velocity terms becoming active and the growth in | δB R | departing from the linear MRI growth predictions is highly suggestive of non-linear motions causing saturation in the growth of a specific MRI mode. Furthermore, the small amplitude kicks from these non-linear terms after 0.1 orbits may explain the early divergence between the β values predicted from model linm 10 and those found from gblm 10. In this sense the non-linear motions provide saturation to the initial phase of local δ B growth. Whether the non-linear motions are attributable to secondary instabilities feeding off the linear MRI growth locally (e.g. Goodman & Xu 1994; Pessah et al. 2007; Pessah & Goodman 2009; Pessah 2010), or are due to the onset of turbulence (Latter et al. 2009) propagating radially outwards through the disk is unclear and would require an analysis of the non-linear growth of the nonaxisymmetric MRI, which we do not pursue here. In summary, comparisons between linear growth calculations and global simulations highlights a number of potential saturation mechanisms. Such as, growth of magnetic field perturbations beyond the weak field limit, and/or growth of the radial wavenumber beyond the finite limit of the simulation resolution. However, for the simulations performed in this work, we find that saturation of growth in magnetic field perturbations correlates well with the onset of non-linear motions.",
"pages": [
11,
12
]
},
{
"title": "4.3. Trigger dependence",
"content": "Amajor focus of magnetized accretion disk simulations is to study properties of the quasi-steady-state turbulence. A necessary test is whether the turbulent steady state depends on the MRI mode initially excited, and also whether prohibitive transient behaviour arises due to the choice of exciting a specific MRI mode. For this purpose we have computed model gbl-rand which uses the same initial disk as model gblm 10+ with the difference that the disk is perturbed with random perturbations in the both the poloidal velocity (amplitude δv 0 = 0 . 001 c s ) and gas pressure (10% amplitude) which excite a range of MRI modes. Simulation resolution and time-averaged measures of the turbulent state are listed in Tables 2 and 3, respectively. The evolution of model gbl-rand is very similar to that of model gblm 10+; the initial perturbations excite the MRI and lead to growth of δB R . Both models show similar growth in the m = 10, k z , k R = 2 . 5 mode (Fig. 9) which one would expect given that this mode is excited with the same amplitude perturbation. After 3 P orb 20 ( /similarequal 0 . 5 P orb 30 ) values of δB R become almost identical between the models irrespective of the differing initial perturbations. We illustrate this in Figs. 11 and 12 in which we show the evolution of δB R in Fourier space for a range of k R values. The different panels in the figures corre- nd to low, moderate, and high wavenumber values for m and k z (relative to the size of the disk and the Nyquist limit). As mentioned above, δB R values are very similar between the two models at t > 3 P orb 20 . Furthermore, even though we excite a specific low wavenumber mode in model gblm 10, a wide range of modes rapidly emerge. We attribute this behaviour to wave-wave coupling and the onset of a turbulent cascade. Exciting larger wavenumbers should provide a larger initial MRI growth rate (see § 3), but how does this affect the evolution of magnetic field perturbations in the global simulations? In particular, does the wavenumber of the excited MRI mode affect the globally-averaged saturation stress? In model gbl-rand a white noise spectrum of perturbations has been excited. Therefore higher wavenumber modes can contribute to the initial growth phase in < α P > . There is an indication of this from Fig. 12) where the growth of | δB R | at a range of wavenumbers means that the Maxwell stress, and consequently < α P > will also grow across a range of wavenumbers. Fig. 4 shows that < α P > does grow faster for gbl-rand compared to gblm 10+ (which have identical grid resolution), supporting the notion that the growth in the globally averaged stress due to an ensemble of unstable modes is higher than for a single wavenumber mode. All three models start with a toroidal magnetic field with a net flux, and during the early evolution of the disk, the combination of magnetic buoyancy and accretion expels magnetic flux from the disk body such that by the time the turbulent steady state is reached the net toroidal magnetic flux of the disk, Ψ φ is close to zero. Subsequently, Ψ φ oscillates about the zero-point with a period of roughly 5 orbits (upper panel of Fig. 13) consistent with previous global simulations and suggestive of a dynamo cycle (Fromang & Nelson 2006; O'Neill et al. 2011; Beckwith et al. 2011). All three models demonstrate this behaviour. However, minor differences in the toroidal magnetic flux, Ψ φ , are visible between models gblm 10+ and gbl-rand (Fig. 13). The different models are slightly out of phase, which is not surprising given the differences in the transient evolution at early simulation times (Fig. 4). Interestingly, model gbl-rand does not overshoot when expelling the initial net toroidal flux and thus settles into dynamo oscillations at a slightly earlier time, which may explain why the transient phase in < α P > takes a longer time to fade in this model. In conclusion, once the disk reaches a turbulent steadystate the disk retains no knowledge of the MRI mode initially excited. This is supported by the almost identical time-averaged properties of the disk noted in Table 3 for models perturbed by a single low wavenumber mode or an ensemble of modes.",
"pages": [
12,
13
]
},
{
"title": "4.4. Algorithm and resolution dependence",
"content": "In this section we examine the ability of different numerical algorithms to recover the growth of magnetic field perturbations resulting from the non-axisymmetric MRI. Comparisons between numerical simulations and analytical estimates for the axisymmetric MRI have been presented by Hawley & Balbus (1991) and Flock et al. (2010). Considering that MHD turbulence in accretion disks produces a predominantly toroidal field it is important to examine how well numerical algorithms can recover the growth of δ B as a result of the nonaxisymmetric MRI. The setups used are listed in Table 2. The different combinations are intended to test different orders of reconstruction, parabolic limiters, and grid resolution 8 . Reconstruction refers to the order of accuracy used to interpolate cell interface values (which are then used in the Riemann solver to calculate fluxes of conserved variables). Parabolic limiters are used to preserve monotonicity and prevent extrema from being introduced by the reconstruction step. We examine the original limiter for PPM proposed by Colella & Woodward (1984), the extremum preserving limiters presented by Colella & Sekora (2008), and limiters based on reconstruction via characteristic variables (e.g. Rider et al. 2007). The aforementioned slope limiters are respectively denoted 'CW84', 'CS08', and 'Char' in Table 2. The last parameter we vary is the grid resolution, as this places a constraint on the maximum resolvable wavenumber, and for this purpose we compute models gblm 10hr, gblm 10, gblm 10-lr, gblm 10-llr, and gblm 10-lllr (which have decreasing resolution). Note that with the exception of models gblm 10+ and gbl-rand, all models have the same cell aspect ratio and the same ratio of cells in the disk body to cells in the corona as gblm 10. As in § 4.2, we calculate approximate growth rates of the magnetic field perturbation, | δB R ( k ) | for the m = 10, k z = 5, k R = 2 . 5 mode via a Fourier analysis of the initial simulation evolution. The results are shown in Table 2, which we summarise as follows:",
"pages": [
13
]
},
{
"title": "5. DISCUSSION",
"content": "With a growing number of studies using stratified shearing boxes with high resolution and/or a large spatial extent (Shi et al. 2010; Davis et al. 2010; Guan & Gammie 2011; Simon et al. 2011, 2012) and higher resolution global models (Fromang & Nelson 2006; Sorathia et al. 2010, 2012; Flock et al. 2011, 2012; Beckwith et al. 2011; Hawley et al. 2011; Mignone et al. 2012), quantifying the steady state turbulence and making direct comparisons between simulations provides a check of both consistency and convergence. One of the most popular measures of the steady state is < α P > . In this regard, models gblm 10+ and gblrand produce values of ∼ 0 . 034 which is higher than recently reported by Beckwith et al. (2011) and, as noted by these authors, higher than previous global models and a number of high resolution shearing-box simulations (see Hawley et al. 2011, and references therein). We attribute the larger < α P > in our models to a higher azimuthal resolution than used by (Beckwith et al. 2011), but also note the possible indication that higher < α P > 's may be more readily achievable in global simulations. Our average < α M > ∼ 0 . 41 (for models gblm 10+ and gbl-rand) is in good agreement with the ∼ 0 . 36 -0 . 4 achieved by the highest resolution shearing-box simulations to-date (Davis et al. 2010; Simon et al. 2011, 2012). Considering that our models have a lower number of cells/ H than the aforementioned shearing-box models, there may also be an indication that convergence may be achieved at lower grid resolutions than in localized models, potentially due to averaging over a larger volume, and capturing lower wavenumber eddies. Comparing models gblm 10 and gblm 10+, strong evidence points to the grid cell aspect ratio and, in particular, the resolution in the φ direction as an important parameter in achieving a high < α P > and < α M > (see the discussion in Fromang & Nelson 2006, Flock et al. 2011, Hawley et al. 2011 and Sorathia et al. 2012). A possible explanation for this is that the dynamo cycle - which helps to sustain the turbulent state and involves the MRI as a driving agent - can operate more effectively at higher frequencies when the cell aspect ratio is closer to unity. Related to < α M > is the tilt angle, Θ tilt , where sin 2Θ tilt = < α M > (Guan et al. 2009; Beckwith et al. 2011). It has been argued by Sorathia et al. (2012) that this parameter provides a better measure of convergence than < α P > , at least in the case of unstratified turbulence for which the question of convergence in the absence of explicit dissipation was raised by Fromang & Papaloizou (2007). We find Θ tilt ∼ 9 · for model gblm 10 which is consistent with previous findings for stratified global disks (Beckwith et al. 2011; Hawley et al. 2011; Flock et al. 2012). However, models gblm 10+ and gbl-rand have Θ tilt ∼ 12 · which is comparable to values of ∼ 11 · -13 · for shearing box simulations (both unstratified and stratified, e.g., Guan et al. 2009; Simon et al. 2012) and also for recent stratified global disks calculations performed with an orbital advection algorithm by Mignone et al. (2012). These results are encouraging as they show that global simulations are reaching sufficient grid resolution to reproduce shearingbox results. The ratio of directional magnetic energy also provides insight into convergence and correspondence between simulations. We find, < B 2 R > / < B 2 φ > ∼ 0 . 13, < B 2 z > / < B 2 R > ∼ 0 . 30 and < B 2 z > / < B 2 φ > ∼ 0 . 036 for models gblm 10+ and gbl-rand. These values are higher than obtained by Hawley et al. (2011) for their global disk simulations, and in some cases only slightly lower than values found from high resolution shearingbox simulations (Shi et al. 2010; Davis et al. 2010; Simon et al. 2011; Guan & Gammie 2011; Simon et al. 2012). Interestingly, model gblm 10 produces a sustained stress, albeit with a lower value than model gblm 10+, but with only 4 cells/ H in the φ -direction. Flock et al. (2011) found that at least 8 cells/ H were required to produce a sustained turbulent stress (see also Fromang & Nelson 2006). However, these authors used linear reconstruction, whereas we have used parabolic reconstruction which may permit a sustained stress at a slightly lower resolution. Finally, we note that we do not see any prominent evidence of recurring transient phenomena due to linear growth revivals in the mean magnetic fields, as recently reported by Flock et al. (2012). This may be due to differences in the numerical setup between our models and those of Flock et al., or perhaps this phenomena occurs at later times that we have not reached with the simulation runtimes of our models.",
"pages": [
14
]
},
{
"title": "6. CONCLUSIONS",
"content": "We have performed global 3D MHD simulations of turbulent accretion disks which start from fully equilibrium MHD initial conditions. The local linear theory of the MRI is used as a predictor of the growth of magnetic field perturbations in the global simulations. Additional tests have also been performed to compare results obtained from global simulations using a number of different numerical algorithms and resolutions to the linear growth estimates. Our main findings are: the disk has expelled the initial net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of quasi-steady turbulence are found to be in agreement with previous work. In particular, the time averaged stress, < α P > ∼ 0 . 034. rate. Convergence with resolution (for the linear MRI growth tests) is found for resolutions of roughly 23 -35 cells per scaleheight (in the vertical direction). However, above all, a higher azimuthal resolution contributes to a much better agreement with linear growth estimates, supporting the push for low cell aspect ratio (close to one) in global accretion disk simulations.",
"pages": [
14,
15
]
},
{
"title": "ACKNOWLEDGEMENTS",
"content": "We thank the referee for a particularly useful report which helped to significantly improve the paper. This research was supported under the Australian Research Council's Discovery Projects funding scheme (project number DP1096417). E. R. P thanks the ARC for funding through this project. This work was supported by the NCI Facility at the ANU and by the iVEC facility at the Pawsey Centre, Perth, WA. REFERENCES Pessah, M. E., & Goodman, J. 2009, ApJ, 698, L72 Velikhov, E. P. 1959, J. Expl. Theoret. Phys., 36, 1398",
"pages": [
15
]
},
{
"title": "A. EQUILIBRIUM DISK SOLUTIONS",
"content": "The initial conditions for our simulations are an equilibrium thin disk with a purely toriodal magnetic field. In the following we present some analytic solutions which are of use for numerical simulations of accretion disks and for disks in other environments, such as starburst galaxies (e.g. Cooper et al. 2008). These solutions incorporate more or less arbitrary radial profiles of density and temperature and a toroidal magnetic field. The latter involves either a constant ratio of gas-to-magnetic pressure, β , radially dependent β , constant B φ , and variants with net/zero toroidal magnetic flux. In axisymmetric cylindrical coordinates ( R,φ,z ), in steady-state, and with v R = v z = B R = B z = 0, the induction equation is identically satisfied and we are left with the two momentum equations: where the pressure, P = ρT , with T in scaled units. We derive a compatibility condition for the above equations by subtracting ∂/∂R of Eq (A2) from ∂/∂z of Eq (A1), to obtain, To solve for the disk equilibrium we take the approach of using Eq (A2) to derive an equation for ρ ( R,z ), Eq (A3) to acquire v 2 φ ( R,z ), and Eq (A1) to obtain an expression for v 2 φ ( R, 0). The resulting equations require boundary conditions for the run of ρ and T at the disk midplane, which can be chosen arbitrarily. From here on we take the disk to be isothermal in height, T = T ( R ), and firstly consider a disk with a constant, β = 2 P/ | B | 2 ≡ 2 P/B 2 φ . Eq (A2) then becomes, which integrates to give an expression for the density in terms of its midplane value, Turning to the rotational velocity, the compatibility relation (Eq (A3)) reduces to, which upon integrating and using Eq (A4) leads to an expression for the azimuthal velocity in terms of its midplane value, The model is completed with a midplane rotational velocity, which is determined by substituting Eq (A5) into Eq (A1). This gives The first term is the square of the Keplerian velocity; the remaining terms are proportional to the square of the sound speed so that Eq (A8) represents a minor departure from a Keplerian disk. A possible variation to the aforementioned disk would be to make β radially dependent, i.e., β = β ( R ). For example, one may choose to make β ( R ) ∝ sin( kR ), where k is a radial wavenumber. In such a case Eq (A5) for ρ ( R,z ) is unchanged. However, the expression for the rotational velocity becomes, where, following substitution in Eq (A1), Hence, and Alternatively, one may desire a disk with a constant B φ ( R,z ) = B φ 0 , in which case the magnetic pressure does not influence the density profile, leading to, and a corresponding velocity profile of, with, and where the Alfv'en speed, v A φ ( R,z ) = B φ 0 / √ ρ ( R,z ). As mentioned above, the radial profiles ρ ( R, 0) and T ( R ) required to complete the disk model may be chosen arbitrarily, subject to boundary constraints at the outer disk edge. As an example, we use simple functions inspired by the Shakura & Sunyaev (1973) disk model, modified by truncation of the density profile at a specified outer radius: where ρ 0 sets the density scale, R 0 and R out are the radius of the inner and outer disk edge, respectively, and /epsilon1 and χ set the slope of the density and temperature profiles, respectively. The tapering function, f ( R,R 0 , R out ) is used to truncate the disk at an inner and outer radius. In practice this function is normalized to give ρ ( R max , 0) = ρ 0 , where the radius of peak density, R max is given by the positive root of the quadratic resulting from taking ∂/∂R of Eq (A14), namely, where a = 1 -(2 /epsilon1 ) -1 . Once R max is known it is straightforward to renormalize the density profile. Finally, studies of turbulent dynamos in magnetized disks are often concerned with the net flux of the magnetic field (e.g. Brandenburg et al. 1995; Hawley et al. 1996; Fromang & Nelson 2006). For the initially purely toroidal field we have adopted in this paper the net flux of the disk is given by Ψ φ = ∫ ∫ B φ dRdz . Noting that in the above derivations we have used β to relate B 2 φ to P , meaning B φ = ± √ 2 ρT/β , i.e. we are free to choose the sign of B φ . Therefore, if a net flux field is required then one may set the sign of B φ the same everywhere, whereas if one desires a zero-net flux field then, for example, one may choose to make B φ anti-symmetric about the disk midplane.",
"pages": [
16,
17
]
},
{
"title": "B. FOURIER TRANSFORM IN CYLINDRICAL COORDINATES",
"content": "We wish to evaluate the Fourier transform F ( k ) of a function f ( r ) = f ( R,φ,z ) expressed in terms of cylindrical polar coordinates ( R,φ,z ). The definition of the Fourier transform is Cylindrical coordinates in real and Fourier space are expressed via the following equations: where V is the computational region, usually of the form: We begin by constructing a Fourier series in the periodic azimuthal coordinate φ : where the coefficients f m ( R,z ) are given by: We now make the change of angular variable χ = φ -ψ ; the integration over χ is still over the interval [0 , 2 π ] since all of the angular functions within the integrand have period 2 π . The Fourier transform can now be expressed as: The angular integral can be expressed in terms of Bessel functions ( J m ( k R R )): Hence, Equation (B10) defines the following procedure: Since the input data for f ( R,φ,z ) are on a grid, the azimuthal, vertical and radial wave numbers, m,k z and k R , are limited by the Nyquist limit. Let the number of intervals in each coordinate direction be ( n R , n φ , n z ) and the grid increments be (∆ R, ∆ φ, ∆ z ) = [( R 1 -R 0 ) /n R , 2 π/n φ , 2 z 0 /n z ]. The grid coordinates are R u , φ v , z w where: The expressions for the azimuthal f m ( R,z ) and vertical F m ( R,k z ) parts of the Fourier transform can be approximated by discrete Fourier transforms as follows: The radial transform can be evaluated from More accurate versions of equations (B16) may be evaluated using the approach given in Press et al. (1986).",
"pages": [
17,
18,
19
]
}
]
2013ApJ...763L...5D
https://arxiv.org/pdf/1210.4830.pdf
<document>
<section_header_level_1><location><page_1><loc_13><loc_82><loc_87><loc_86></location>The power-law spectra of energetic particles during multi-island magnetic reconnection</section_header_level_1>
<text><location><page_1><loc_34><loc_78><loc_66><loc_80></location>J. F. Drake 1 , M. Swisdak 1 , R. Fermo 2</text>
<section_header_level_1><location><page_1><loc_44><loc_74><loc_56><loc_75></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_37><loc_83><loc_71></location>Power-law distributions are a near universal feature of energetic particle spectra in the heliosphere. Anomalous Cosmic Rays (ACRs), super-Alfv'enic ions in the solar wind and the hardest energetic electron spectra in flares all have energy fluxes with power-laws that depend on energy E approximately as E -1 . 5 . We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocityspace anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of pressure anisotropy on the merging dynamics. By including pitch-angle scattering we obtain an equation for the omnidirectional particle distribution f ( v, t ) that is solved in closed form to reveal v -5 (corresponding to an energy flux varying as E -1 . 5 ) as a near-universal solution as long as the characteristic acceleration time is short compared with the characteristic loss time. In such a state the total energy in the energetic particles reaches parity with the remaining magnetic free energy. More generally, the resulting transport equation can serve as the basis for calculating the distribution of energetic particles resulting from reconnection in large-scale inhomogeneous systems.</text>
<text><location><page_1><loc_17><loc_31><loc_83><loc_34></location>Subject headings: acceleration of particles - magnetic reconnection - Sun: corona - Sun: flares</text>
<section_header_level_1><location><page_1><loc_39><loc_25><loc_61><loc_26></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_12><loc_17><loc_96><loc_23></location>Accelerated particles with power-law spectra are a nearly universal feature of heliospheric plasmas and also characterize the cosmic ray spectrum. Anomalous Cosmic Rays (ACRs) (Stone et al. 2008; Decker et al. 2010), super-Alfv'enic ions in the solar wind (Fisk & Gloeckler</text>
<text><location><page_2><loc_12><loc_78><loc_88><loc_86></location>2006) and the hardest energetic electron spectra in flares (Holman et al. 2003) all have energy fluxes with power-laws that depend on energy E approximately as E -1 . 5 . An important question is whether there is a common acceleration mechanism in these very disparate environments.</text>
<text><location><page_2><loc_12><loc_43><loc_88><loc_77></location>A range of acceleration mechanisms have been proposed to explain the spectra of energetic electrons (up to several MeV ) and ions (up to several GeV ) in impulsive flares, including the reconnection process itself and reconnection-driven turbulence (Miller et al. 1997; Dmitruk et al. 2004; Liu et al. 2006; Zharkova et al. 2011). Significant challenges have been to explain the large numbers of accelerated electrons and the surprising efficiency of the conversion of magnetic energy to the energetic particles (Lin & Hudson 1971; Emslie et al. 2005; Krucker et al. 2010). The single x-line model of reconnection in flares, in which electrons are accelerated by parallel electric fields, can not explain the large number of accelerated electrons (Miller et al. 1997). On the other hand both observations (Sheeley et al. 2004; Savage et al. 2012) and modeling (Kliem 1994; Shibata & Tanuma 2001; Drake et al. 2006b,a; Onofri et al. 2006; Oka et al. 2010; Huang et al. 2011; Daughton et al. 2011; Fermo et al. 2012) suggest that reconnection in flares involves the dynamics of large numbers of x-lines and magnetic islands or flux ropes. In magnetohydrodynamic (MHD) simulations of multi-island reconnection test particles rapidly gain more energy than is available in the driving magnetic field (Onofri et al. 2006). Thus, developing a model of particle acceleration in a multi-island reconnecting environment with feedback on the driving fields is the key to understanding flare-produced energetic particle spectra.</text>
<text><location><page_2><loc_12><loc_16><loc_88><loc_42></location>The seed population of ACRs are interstellar pickup particles since their composition matches that of interstellar neutrals (Cummings & Stone 1996, 2007). However, the conventional idea that they are accelerated at the termination shock (TS)(Pesses et al. 1981) was called into question when the Voyagers crossed the TS and found that the intensity of the ACR spectrum did not peak there (Stone et al. 2005, 2008). A possible alternate source is magnetic reconnection of the sectored heliosheath (Lazarian & Opher 2009; Drake et al. 2010). Simulations of reconnection in the sectored field region revealed that the dominant heating mechanism was Fermi reflection in contracting and merging islands (Drake et al. 2010; Kowal et al. 2011; Schoeffler et al. 2011). Because contraction increases the energy parallel to the local magnetic field and reduces the perpendicular energy, the heating mechanism drives the system to the firehose stability boundary α = 1 -( β ‖ -β ⊥ ) / 2 = 0 where reconnection is throttled because the magnetic tension drive is absent (Drake et al. 2006b, 2010; Opher et al. 2011; Schoeffler et al. 2011).</text>
<text><location><page_2><loc_12><loc_11><loc_88><loc_15></location>While multi-island simulations have revealed that Fermi reflection in contracting islands controls energy gain and drives the system to the marginal firehose condition, a rigorous</text>
<text><location><page_3><loc_12><loc_70><loc_88><loc_86></location>model for particle acceleration in such a multi-island system has not yet been developed. The Parker equation does not describe particle acceleration in nearly incompressible systems (Parker 1965) and extensions do not account for the geometry of reconnection and island merging (Earl et al. 1988). In the present manuscript we explore particle acceleration in a bath of merging magnetic islands with a particle distribution function f ( v ‖ , v ⊥ ) that accounts for the velocity space anisotropy along ( v ‖ ) and across ( v ⊥ ) the local magnetic field and includes a phenomenological pitch-angle scattering operator. Thus, the pressure anisotropy can be directly evaluated and the feedback on island merging calculated.</text>
<section_header_level_1><location><page_3><loc_29><loc_64><loc_71><loc_66></location>2. Particle dynamics during island merger</section_header_level_1>
<text><location><page_3><loc_12><loc_35><loc_88><loc_62></location>We develop a probabilistic model of particle acceleration in a bath of merging 2-D magnetic islands with a distribution of magnetic flux ψ and area A given by g ( ψ, A ) (Fermo et al. 2010). The development of structure in 3-D may ultimately be important and should be addressed but observations (Phan et al. 2006) and simulations (Hesse et al. 2001) suggest that at the largest scales reconnection is nearly 2-D and this limit is therefore a reasonable starting point. We first calculate the particle energy gain during the merging of two circular islands of radii r 1 and r 2 with r j = √ A j /π as shown in the schematic in Fig. 1. Merging leads to a single island of area A f = A 1 + A 2 and with magnetic flux ψ f given by the larger of ψ 1 and ψ 2 (Fermo et al. 2010). The reduction of energy by the factor ( ψ 2 1 + ψ 2 2 ) /ψ 2 f results from the shortening of the field lines as merging proceeds. Thus, energy release takes place not at the merging site, but as reconnected field lines contract after merger. As long as the kinetic-scale, boundary layer where reconnection occurs is small compared with the island radii, the dominant energy exchange with particles takes place on the closed, reconnected field lines that release magnetic energy as they contract.</text>
<text><location><page_3><loc_12><loc_11><loc_88><loc_33></location>We take advantage of two adiabatic invariants, the magnetic moment µ = mv 2 ⊥ /B and the parallel action ∮ v ‖ d/lscript , which are constants if the gyration time of particles around the local magnetic field and their circulation time around islands are short compared with the merging time. The former describes the reduction in v ⊥ as B decreases and the latter the increase in v ‖ as /lscript decreases. The parallel action invariant is valid for velocities that exceed the local Alfv'en speed, which implies that a seed heating mechanism is needed for low β systems such as the solar corona (Drake et al. 2009a; Knizhnik et al. 2011) but not in high β systems such as the sectored heliosheath. To calculate ˙ /lscript , we first calculate the merging velocity ˙ r sep of two islands with differing radii and magnetic fields, ˙ r sep = ˙ r 1 + ˙ r 2 = -˙ ψ ( B 1 + B 2 ) / ( B 1 B 2 ), since merging magnetic islands reconnect their magnetic flux at the same rate. The reconnection rate is given by Cassak & Shay (2007), ˙ ψ = 2 V 12 B 1 B 2 / ( B 1 + B 2 ), with</text>
<text><location><page_4><loc_12><loc_74><loc_88><loc_86></location>V 12 = /epsilon1 r √ α 12 B 1 B 2 / 4 πρ , where /epsilon1 r ∼ 0 . 1 is the normalized rate of reconnection and α 12 = 1 -4 π ( p ‖ -p ⊥ ) / ( B 1 B 2 ). Thus, ˙ r sep = -2 V 12 and V 12 is the island merging velocity. The rate of line shortening can now be calculated from the total merging time ( r 1 + r 2 ) / (2 V 12 ) and the difference between the intial field line length as merging starts and the final length using area conservation, ˙ /lscript = -2 πh 12 V 12 with h 12 = 2( r 1 + r 2 -√ r 2 1 + r 2 2 ) / ( r 1 + r 2 ). Parallel action conservation then yields an equation for v ‖ ,</text>
<formula><location><page_4><loc_43><loc_70><loc_88><loc_73></location>dv ‖ dt = v ‖ h 12 V 12 r 1 + r 2 . (1)</formula>
<text><location><page_4><loc_12><loc_63><loc_88><loc_69></location>To obtain the corresponding equation for ˙ v ⊥ , we use the conservation of magnetic flux and area as a flux tube contracts so that B//lscript is constant. Therefore, from µ conservation v 2 ⊥ //lscript is also constant and</text>
<formula><location><page_4><loc_42><loc_60><loc_88><loc_63></location>dv 2 ⊥ dt = -v 2 ⊥ h 12 V 12 r 1 + r 2 . (2)</formula>
<text><location><page_4><loc_12><loc_56><loc_88><loc_59></location>Thus, the perpendicular energy goes down during island merger as the parallel energy increases.</text>
<section_header_level_1><location><page_4><loc_17><loc_50><loc_83><loc_51></location>3. A kinetic equation for particle acceleration during island merger</section_header_level_1>
<text><location><page_4><loc_12><loc_34><loc_88><loc_47></location>From the energy gain of particles in merging islands we can formulate a model of particle acceleration in a very long current layer of length L . Particles are injected into the bath of interacting islands in the current layer from upstream as each individual island grows due to reconnection of the upstream field. They then undergo acceleration in the merging islands until they are convectively lost. The rate of injection of particles is given by the upstream distribution function f up ( v ) times the integrated rate of area increase of all of the magnetic islands ˙ A T (Fermo et al. 2010),</text>
<formula><location><page_4><loc_34><loc_29><loc_88><loc_33></location>˙ A T = 2 π/epsilon1 r c Aup ∫ ∞ 0 ∫ ∞ 0 dAdψrg ( ψ, A ) , (3)</formula>
<text><location><page_4><loc_12><loc_20><loc_88><loc_28></location>with the island radius given by r = √ A/π . The probability of two islands of radii r 1 and r 2 merging is given by their overlap probability 4 r 1 r 2 /L 2 . Using the conservation of phase space volume and summing over all merging islands in the layer, we obtain a differential equation for f ( v ‖ , v ⊥ ),</text>
<formula><location><page_4><loc_20><loc_14><loc_88><loc_19></location>∂f ∂t + R ( ∂ ∂v ‖ v ‖ -1 2 v ⊥ ∂ ∂v ⊥ v 2 ⊥ ) f -ν ∂ ∂ζ ( 1 -ζ 2 ) ∂ ∂ζ f + c Aup L f = ˙ A T f up , (4)</formula>
<text><location><page_4><loc_12><loc_13><loc_17><loc_14></location>where</text>
<formula><location><page_4><loc_37><loc_9><loc_88><loc_13></location>R = ∫ ∫ d 1 d 2 g 1 g 2 4 r 1 r 2 h 12 V 12 L 2 ( r 1 + r 2 ) . (5)</formula>
<text><location><page_5><loc_12><loc_66><loc_90><loc_86></location>with di = dA i dψ i . In earlier simulations of multi-island reconnection strong pressure anisotropy with p ‖ > p ⊥ within the core of merging islands was limited by anisotropy instabilities (Drake et al. 2010; Schoeffler et al. 2011) so we have included a phenomenological pitchangle scattering operator of strength ν that acts on the angle ζ = v ‖ /v to reduce anisotropy. Importantly, the drive R is independent of the particle velocity. It depends on the pressure anisotropy through the merging velocity V 12 . The integral over islands includes only interactions for which V 12 is real ( α 12 > 0). To estimate the scaling of R we note that N T = ∫ dig i is the total number of islands in the layer, so for densely packed islands we can define a characteristic island radius r N = L/ 2 N T . Thus, R ∼ /epsilon1 r c A /r N . Of course, R can be much smaller if α 12 in the expression for V 12 approaches zero.</text>
<text><location><page_5><loc_12><loc_40><loc_88><loc_65></location>If f were isotropic and therefore only a function of v , the energy drive operator in Eq. (4) would vanish when averaged over the angle ζ . In this limit there is zero net energy gain, consistent with Parker's equation in the incompressible limit (Parker 1965). Equation (4) is an equi-dimensional equation and therefore has no characteristic velocity scale. Solutions therefore take the form of power-laws. An important property of such an equation is that the fluid moments of a given order completely decouple from those of differing order and their solutions can therefore be readily obtained from Eq. (4) in closed form. Specifically an equation for p ‖ and p ⊥ can be obtained so that α 12 in the energy drive R can be evaluated explicitly. Thus, the feedback of energetic particles on the dynamics of reconnection can be computed. In the case of no source, sink or scattering, for example, Eq. (4) yields ∂p ‖ /∂t = 2 Rp ‖ and ∂p ⊥ /∂t = -Rp ⊥ so that p ‖ and p ⊥ increase and decrease in time, respectively, but the total energetic particle pressure p increases, ∂p/∂t = (2 R/ 3)( p ‖ -p ⊥ ).</text>
<text><location><page_5><loc_12><loc_18><loc_88><loc_40></location>Instead of directly evaluating the full moments of Eq. (4), we simplify the equation by ordering the magnitudes of the rates R , ν and c A /L . Since the scattering represented by ν arises from the pressure anisotropy driven by contraction, we argue that ν ∼ R . On the other hand as the spectrum begins to saturate at firehose marginal stability R is reduced and ν increases. We therefore take ν /greatermuch R ∼ /epsilon1 r c A /r N /greatermuch c A /L , where the latter follows because L /greatermuch r N . The large ν assumption allows us to solve Eq. (4) by expanding f in a series of Legendre polynomials f = ∑ j P j ( ζ ) f j ( v ) where P j is the j th order Legendre polynomial. By the symmetry in v ‖ , f 1 is zero. The equation for f 2 follows from balancing the reconnection drive acting on f 0 with the scattering operator acting on f 2 P 2 ( ζ ), f 2 ( v ) = -( Rv/ 6 ν ) ∂f 0 ( v ) /∂v . By averaging Eq. (4) over ζ , the scattering term vanishes and the energy drive term acting on f 2 P 2 ( ζ ) yields an equation for f 0 ( v ),</text>
<formula><location><page_5><loc_32><loc_14><loc_88><loc_17></location>∂f 0 ∂t -R 2 30 ν 1 v 2 ∂ ∂v v 4 ∂ ∂v f 0 + c Aup L f 0 = ˙ A T f up . (6)</formula>
<text><location><page_5><loc_12><loc_10><loc_88><loc_13></location>This equation is again of equi-dimensional form and has power-law solutions whose individual moments can be calculated. Evaluating the density in steady state, for example, by</text>
<text><location><page_6><loc_12><loc_78><loc_88><loc_86></location>integrating over velocity, the drive term vanishes and the total number of particles undergoing acceleration n T is given by n T = A T n up , where A T = ˙ A T L/c Aup is the integrated area of all of the islands in the layer. The firehose parameter needs to be self-consistently evaluated and for this we need</text>
<formula><location><page_6><loc_26><loc_73><loc_88><loc_78></location>p ‖ -p ⊥ = 1 A T ∫ 1 -1 dζ ∫ ∞ 0 dv 2 πv 2 m ( v 2 ‖ -1 2 v 2 ⊥ ) f 2 ( v ) P 2 ( ζ ) . (7)</formula>
<text><location><page_6><loc_12><loc_70><loc_75><loc_72></location>Using the expression for f 2 and noting that v 2 ‖ -v 2 ⊥ / 2 = v 2 P 2 ( ζ ), we obtain</text>
<formula><location><page_6><loc_31><loc_65><loc_88><loc_69></location>p ‖ -p ⊥ = R 6 A T ν ∫ ∞ 0 dv 4 πmv 4 f 0 ( v ) = R 2 ν p 0 , (8)</formula>
<text><location><page_6><loc_12><loc_62><loc_56><loc_64></location>where p 0 is the isotropic pressure calculated from f 0 ,</text>
<formula><location><page_6><loc_41><loc_57><loc_88><loc_62></location>p 0 = p up 1 -R 2 L/ 3 c Aup ν . (9)</formula>
<text><location><page_6><loc_12><loc_55><loc_39><loc_57></location>The firehose parameter becomes</text>
<formula><location><page_6><loc_37><loc_49><loc_88><loc_54></location>α /similarequal 1 -4 πp up ¯ B 2 R/ 2 ν 1 -R 2 L/ 3 c Aup ν , (10)</formula>
<text><location><page_6><loc_12><loc_18><loc_88><loc_49></location>where ¯ B is the average island magnetic field strength based on the sum in Eq. (5). A key feature of Eq. (10) is its singular behavior when δ = R 2 L/ 3 c Aup ν = 1. This singularity can be understood from the power-law solutions to f 0 , which describe its behavior at energies greater than that of the source f up . Taking f 0 ∝ v -γ , from Eq. (6) we obtain γ ( γ -3) = 10 /δ so that when δ = 1, γ = 5. The second solution, γ = -2, corresponds to divergent behavior and must be rejected. The singularity in Eq. (10) therefore arises when f 0 ∝ v -5 and corresponds to a divergence of the pressure integral. Thus, it is clear that the requirement that the pressure be bounded requires that γ > 5 or δ < 1. In deriving Eq. (6) for f 0 we have assumed large scattering so that ν /greatermuch R . On the other hand, since island contraction drives the anisotropy, we argued previously that ν ∼ /epsilon1 r c A /r N . Thus, δ ∼ /epsilon1 r L/r N /greatermuch 1. Namely, the acceleration rate should always exceed the system convective loss rate since L is much larger than the characteristic island size. The resulting divergence of the pressure can only be avoided if the reconnection drive R ∝ √ α is reduced by its approach to firehose marginal stability, which forces R /lessmuch ν . Unless p up is very large, the only way that the firehose condition in Eq. (10) can be reached is if δ /similarequal 1 or γ /similarequal 5 and f 0 ∝ v -5 .</text>
<text><location><page_6><loc_12><loc_13><loc_88><loc_18></location>The total energy content W 0 = 3 p 0 / 2 of this high energy tail can be directly calculated from the pressure in Eq. (9) using α /similarequal 0 and δ /similarequal 1,</text>
<formula><location><page_6><loc_41><loc_9><loc_88><loc_13></location>W 0 = ¯ B 2 4 π √ 3 νL/c Aup . (11)</formula>
<text><location><page_7><loc_12><loc_76><loc_88><loc_86></location>Thus, depending on the level of scattering, the total energy density of the energetic particles is of the order of, or somewhat greater than, the remaining magnetic energy. In a system with low initial β equipartition between energetic particles and magnetic field is energetically accessible. In a system with high initial β equipartition can only be reached if the system is open such that energetic particles can access additional sources of magnetic free energy.</text>
<section_header_level_1><location><page_7><loc_43><loc_70><loc_57><loc_72></location>4. Discussion</section_header_level_1>
<text><location><page_7><loc_12><loc_51><loc_88><loc_68></location>We have derived a general equation (Eq. (4)) for particle acceleration in a bath of merging magnetic islands in a large 1-D current layer. We demonstrated that the E -1 . 5 spectrum is a nearly universal feature of a multi-island reconnecting system for all values of initial β as long as the nominal acceleration time of energetic particles is shorter than their loss rate. This is the correct limit as long as the characteristic magnetic island radius is much smaller than the system scale size L . We argue therefore that the widely observed E -1 . 5 spectrum in the heliosphere is a natural consequence of multi-island reconnection. The total energy content of this E -1 . 5 spectrum reaches parity with the remaining magnetic field energy in the system.</text>
<text><location><page_7><loc_12><loc_32><loc_88><loc_49></location>Equation (4) can be readily generalized to a 2-D system by replacing the factors 2 r i /L by 4 r 2 i /L 2 in the drive term R . The estimate for the scaling of R is unchanged. The model loss term c Aup f/L should also be replaced by the convective loss rate u · ∇ f with u the convective velocity of the system. The arguments leading to the f ∝ v -5 also apply to the 2-D equations. In a system in which the driver R is spatially non-uniform the 2-D version of Eq. (4) could then be numerically solved for the spatial distribution of energetic particles from reconnection. The impact of the finite structure of magnetic islands that might develop in the third direction remains an important open issue (Onofri et al. 2006; Schreier et al. 2010; Daughton et al. 2011).</text>
<text><location><page_7><loc_12><loc_19><loc_88><loc_30></location>There have now been several published simulations of particle acceleration and associated spectra in 2-D multi-current layer systems (Drake et al. 2010; Drake & Swisdak 2012). We can compare the spectra predicted from our equation with the results of those simulations. Since the simulations were doubly periodic, there was no convective loss. Further, the pressure anisotropy was strong so we consider the non-scattering limit of Eq. (4) in which the source and loss terms are discarded. The exact solution for f is given by</text>
<formula><location><page_7><loc_35><loc_15><loc_88><loc_17></location>f ( v 2 ‖ , v 2 ⊥ , t ) = f ( v 2 ‖ e -2 G ( t ) , v 2 ⊥ e G ( t ) , 0) , (12)</formula>
<text><location><page_7><loc_12><loc_10><loc_88><loc_14></location>where G ( t ) = ∫ t 0 dτR ( τ ). This is consistent with exponential growth of the effective parallel temperature and an exponential decrease in the perpendicular temperature. The omnidirec-</text>
<text><location><page_8><loc_12><loc_42><loc_88><loc_86></location>al distribution function can be computed numerically for any specified initial distribution function for comparison with simulation data. The comparison is made with a system with sixteen initial current layers in a 409 . 6 d i × 204 . 8 d i domain, where d i = c/ω pi is the ion inertial length (Drake et al. 2010). In Fig. 2 we show the magnetic field strength at late time ( t = 100Ω -1 ci ) in the simulation after islands on adjacent current layers have overlapped. The typical island radius r N at this time is around 15 d i . The characteristic acceleration rate R ∼ /epsilon1 r c A /r N ∼ 0 . 007Ω -1 ci , where Ω ci is the ion cyclotron frequency. Reconnection remains strong for a total time of around 100Ω -1 ci when the pressure anisotropy shuts off reconnection. Thus, the integrated acceleration rate is G ∼ 0 . 7. The comparison between the model and the simulation data is shown in Fig. 3. The particle energy spectrum from the simulation is shown in the initial state and at t = 200Ω -1 ci in the solid lines. Note that the initial state is not a simple Maxwellian because of the shift in the ion velocity distribution that is required in the current layers. The fit of the initial spectrum with a single Maxwellian, shown in the dot-dashed line in Fig. 3 therefore matches the low energy portion of the spectrum very well but underestimates the number of particles at high energy. The late time energy spectrum from the solution given in Eq. (12), after integration over the angle ζ is given by the dashed line in Fig. 3. The best fit corresponds to G = 0 . 82 rather than the estimate of 0 . 7. The model reproduces the overall late-time energy spectrum very well but modestly overestimates the number of particles in the high energy tail. This is probably because the ions in the initial spectrum have thermal speeds that are sub-Alfv'enic so the Fermi acceleration of the low energy ions is delayed until they gain sufficient energy in reconnection exhausts (Drake et al. 2009b).</text>
<text><location><page_8><loc_12><loc_17><loc_88><loc_41></location>Observations in the quiet solar wind have revealed that the super-Alfv'enic ions display an f ( v ) ∝ v -5 distribution (Fisk & Gloeckler 2006). It has been suggested that solar wind turbulence would be dissipated in reconnection current layers (Servidio et al. 2009) and therefore that reconnection is an important dissipation mechanism in the turbulent solar wind. Solar wind observations also reveal that the pressure anisotropy bumps against the firehose threshold in some regions and that there are enhanced magnetic fluctuations at these locations (Bale et al. 2009). There are therefore mechanisms in solar wind turbulence driving anisotropy and the anisotropy is limited by enhanced scattering. Finally, the direct observations of reconnection events in the solar wind reveal heating but no localized regions of energetic particles (Gosling et al. 2005). This is consistent with our picture that the energetic particle spectrum is not produced at a single x-line but requires that the ions interact with many reconnection sites.</text>
<text><location><page_8><loc_12><loc_9><loc_88><loc_16></location>The spectrum of energetic electrons in impulsive flares are not measured in situ and must be inferred from chromospheric x-ray emission. Nevertheless, the energetic particle fluxes do occasionally reveal spectra as hard as E -1 . 5 , which corresponds to f ∝ v -5 (Holman et al.</text>
<text><location><page_9><loc_12><loc_74><loc_88><loc_86></location>2003). In recent over-the-limb observations of flares in which the reconnection region high in the corona can be directly diagnosed, it was found that all of the electrons in the acceleration region became part of the energetic component, indicating that all electrons in the region of energy release underwent acceleration (Krucker et al. 2010), which is consistent with our model. The β of these electrons was of order unity, which is also consistent with our predictions.</text>
<text><location><page_9><loc_12><loc_55><loc_88><loc_73></location>Whether the sectored heliosheath magnetic field has reconnected remains an open issue because the Voyager magnetometers are at the limits of their resolutions at the magnetic field strengths in the heliosheath (Burlaga et al. 2006). Large drops in the energetic electron and ACR population as Voyager 2 exited from the sectored zone are consistent with reconnection as the ACR driver (Opher et al. 2011). The spectral index of the ACR particle flux measured at Voyager 1 is slightly above 1 . 5 (Stone et al. 2008; Decker et al. 2010). Further, the integrated energy density of the measured ACR spectrum between 1 and 100 MeV and is comparable to that of the magnetic field, which has a magnitude of around 0 . 15 nT . This is again consistent with the predictions of our model.</text>
<text><location><page_9><loc_12><loc_40><loc_88><loc_54></location>The equations presented here were derived in the non-relativistic limit. However, the ideas can be easily extended to the case where the particles are relativistic but where reconnection itself is non-relativistic. We express the distribution of particles in terms of the particle momentum p . For the pressure integral to remain bounded γ > 4 for power-law distributions with f 0 ( p ) ∝ p -γ . The resulting particle flux per unit energy interval Γ is given by Γ ∝ p 2 f ( p ) ∝ p 2 -γ . Thus, the spectrum of the flux in the strongly relativistic limit should scale as p -2 .</text>
<text><location><page_9><loc_12><loc_34><loc_88><loc_37></location>This work has been supported by NSF Grant AGS1202330 and NASA grants APL975268 and NNX08AV87G.</text>
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<table>
<location><page_11><loc_12><loc_12><loc_89><loc_86></location>
</table>
<text><location><page_11><loc_15><loc_10><loc_59><loc_11></location>This preprint was prepared with the AAS L A T E X macros v5.2.</text>
<figure>
<location><page_12><loc_12><loc_13><loc_59><loc_87></location>
<caption>Fig. 1.- Schematic of the merger of two islands of differing radii and magnetic field strength.</caption>
</figure>
<figure>
<location><page_13><loc_12><loc_61><loc_59><loc_78></location>
<caption>Fig. 2.- The distribution of magnetic strength at late time from a multi-current layer simulation (Drake et al. 2010).</caption>
</figure>
<figure>
<location><page_13><loc_13><loc_23><loc_57><loc_41></location>
<caption>Fig. 3.- The spectra of ions from the simulation of Fig. 2 (solid lines) at t = 0 , 200Ω -1 ci and from the model (dashed and dot-dashed lines).</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "Power-law distributions are a near universal feature of energetic particle spectra in the heliosphere. Anomalous Cosmic Rays (ACRs), super-Alfv'enic ions in the solar wind and the hardest energetic electron spectra in flares all have energy fluxes with power-laws that depend on energy E approximately as E -1 . 5 . We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocityspace anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of pressure anisotropy on the merging dynamics. By including pitch-angle scattering we obtain an equation for the omnidirectional particle distribution f ( v, t ) that is solved in closed form to reveal v -5 (corresponding to an energy flux varying as E -1 . 5 ) as a near-universal solution as long as the characteristic acceleration time is short compared with the characteristic loss time. In such a state the total energy in the energetic particles reaches parity with the remaining magnetic free energy. More generally, the resulting transport equation can serve as the basis for calculating the distribution of energetic particles resulting from reconnection in large-scale inhomogeneous systems. Subject headings: acceleration of particles - magnetic reconnection - Sun: corona - Sun: flares",
"pages": [
1
]
},
{
"title": "The power-law spectra of energetic particles during multi-island magnetic reconnection",
"content": "J. F. Drake 1 , M. Swisdak 1 , R. Fermo 2",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Accelerated particles with power-law spectra are a nearly universal feature of heliospheric plasmas and also characterize the cosmic ray spectrum. Anomalous Cosmic Rays (ACRs) (Stone et al. 2008; Decker et al. 2010), super-Alfv'enic ions in the solar wind (Fisk & Gloeckler 2006) and the hardest energetic electron spectra in flares (Holman et al. 2003) all have energy fluxes with power-laws that depend on energy E approximately as E -1 . 5 . An important question is whether there is a common acceleration mechanism in these very disparate environments. A range of acceleration mechanisms have been proposed to explain the spectra of energetic electrons (up to several MeV ) and ions (up to several GeV ) in impulsive flares, including the reconnection process itself and reconnection-driven turbulence (Miller et al. 1997; Dmitruk et al. 2004; Liu et al. 2006; Zharkova et al. 2011). Significant challenges have been to explain the large numbers of accelerated electrons and the surprising efficiency of the conversion of magnetic energy to the energetic particles (Lin & Hudson 1971; Emslie et al. 2005; Krucker et al. 2010). The single x-line model of reconnection in flares, in which electrons are accelerated by parallel electric fields, can not explain the large number of accelerated electrons (Miller et al. 1997). On the other hand both observations (Sheeley et al. 2004; Savage et al. 2012) and modeling (Kliem 1994; Shibata & Tanuma 2001; Drake et al. 2006b,a; Onofri et al. 2006; Oka et al. 2010; Huang et al. 2011; Daughton et al. 2011; Fermo et al. 2012) suggest that reconnection in flares involves the dynamics of large numbers of x-lines and magnetic islands or flux ropes. In magnetohydrodynamic (MHD) simulations of multi-island reconnection test particles rapidly gain more energy than is available in the driving magnetic field (Onofri et al. 2006). Thus, developing a model of particle acceleration in a multi-island reconnecting environment with feedback on the driving fields is the key to understanding flare-produced energetic particle spectra. The seed population of ACRs are interstellar pickup particles since their composition matches that of interstellar neutrals (Cummings & Stone 1996, 2007). However, the conventional idea that they are accelerated at the termination shock (TS)(Pesses et al. 1981) was called into question when the Voyagers crossed the TS and found that the intensity of the ACR spectrum did not peak there (Stone et al. 2005, 2008). A possible alternate source is magnetic reconnection of the sectored heliosheath (Lazarian & Opher 2009; Drake et al. 2010). Simulations of reconnection in the sectored field region revealed that the dominant heating mechanism was Fermi reflection in contracting and merging islands (Drake et al. 2010; Kowal et al. 2011; Schoeffler et al. 2011). Because contraction increases the energy parallel to the local magnetic field and reduces the perpendicular energy, the heating mechanism drives the system to the firehose stability boundary α = 1 -( β ‖ -β ⊥ ) / 2 = 0 where reconnection is throttled because the magnetic tension drive is absent (Drake et al. 2006b, 2010; Opher et al. 2011; Schoeffler et al. 2011). While multi-island simulations have revealed that Fermi reflection in contracting islands controls energy gain and drives the system to the marginal firehose condition, a rigorous model for particle acceleration in such a multi-island system has not yet been developed. The Parker equation does not describe particle acceleration in nearly incompressible systems (Parker 1965) and extensions do not account for the geometry of reconnection and island merging (Earl et al. 1988). In the present manuscript we explore particle acceleration in a bath of merging magnetic islands with a particle distribution function f ( v ‖ , v ⊥ ) that accounts for the velocity space anisotropy along ( v ‖ ) and across ( v ⊥ ) the local magnetic field and includes a phenomenological pitch-angle scattering operator. Thus, the pressure anisotropy can be directly evaluated and the feedback on island merging calculated.",
"pages": [
1,
2,
3
]
},
{
"title": "2. Particle dynamics during island merger",
"content": "We develop a probabilistic model of particle acceleration in a bath of merging 2-D magnetic islands with a distribution of magnetic flux ψ and area A given by g ( ψ, A ) (Fermo et al. 2010). The development of structure in 3-D may ultimately be important and should be addressed but observations (Phan et al. 2006) and simulations (Hesse et al. 2001) suggest that at the largest scales reconnection is nearly 2-D and this limit is therefore a reasonable starting point. We first calculate the particle energy gain during the merging of two circular islands of radii r 1 and r 2 with r j = √ A j /π as shown in the schematic in Fig. 1. Merging leads to a single island of area A f = A 1 + A 2 and with magnetic flux ψ f given by the larger of ψ 1 and ψ 2 (Fermo et al. 2010). The reduction of energy by the factor ( ψ 2 1 + ψ 2 2 ) /ψ 2 f results from the shortening of the field lines as merging proceeds. Thus, energy release takes place not at the merging site, but as reconnected field lines contract after merger. As long as the kinetic-scale, boundary layer where reconnection occurs is small compared with the island radii, the dominant energy exchange with particles takes place on the closed, reconnected field lines that release magnetic energy as they contract. We take advantage of two adiabatic invariants, the magnetic moment µ = mv 2 ⊥ /B and the parallel action ∮ v ‖ d/lscript , which are constants if the gyration time of particles around the local magnetic field and their circulation time around islands are short compared with the merging time. The former describes the reduction in v ⊥ as B decreases and the latter the increase in v ‖ as /lscript decreases. The parallel action invariant is valid for velocities that exceed the local Alfv'en speed, which implies that a seed heating mechanism is needed for low β systems such as the solar corona (Drake et al. 2009a; Knizhnik et al. 2011) but not in high β systems such as the sectored heliosheath. To calculate ˙ /lscript , we first calculate the merging velocity ˙ r sep of two islands with differing radii and magnetic fields, ˙ r sep = ˙ r 1 + ˙ r 2 = -˙ ψ ( B 1 + B 2 ) / ( B 1 B 2 ), since merging magnetic islands reconnect their magnetic flux at the same rate. The reconnection rate is given by Cassak & Shay (2007), ˙ ψ = 2 V 12 B 1 B 2 / ( B 1 + B 2 ), with V 12 = /epsilon1 r √ α 12 B 1 B 2 / 4 πρ , where /epsilon1 r ∼ 0 . 1 is the normalized rate of reconnection and α 12 = 1 -4 π ( p ‖ -p ⊥ ) / ( B 1 B 2 ). Thus, ˙ r sep = -2 V 12 and V 12 is the island merging velocity. The rate of line shortening can now be calculated from the total merging time ( r 1 + r 2 ) / (2 V 12 ) and the difference between the intial field line length as merging starts and the final length using area conservation, ˙ /lscript = -2 πh 12 V 12 with h 12 = 2( r 1 + r 2 -√ r 2 1 + r 2 2 ) / ( r 1 + r 2 ). Parallel action conservation then yields an equation for v ‖ , To obtain the corresponding equation for ˙ v ⊥ , we use the conservation of magnetic flux and area as a flux tube contracts so that B//lscript is constant. Therefore, from µ conservation v 2 ⊥ //lscript is also constant and Thus, the perpendicular energy goes down during island merger as the parallel energy increases.",
"pages": [
3,
4
]
},
{
"title": "3. A kinetic equation for particle acceleration during island merger",
"content": "From the energy gain of particles in merging islands we can formulate a model of particle acceleration in a very long current layer of length L . Particles are injected into the bath of interacting islands in the current layer from upstream as each individual island grows due to reconnection of the upstream field. They then undergo acceleration in the merging islands until they are convectively lost. The rate of injection of particles is given by the upstream distribution function f up ( v ) times the integrated rate of area increase of all of the magnetic islands ˙ A T (Fermo et al. 2010), with the island radius given by r = √ A/π . The probability of two islands of radii r 1 and r 2 merging is given by their overlap probability 4 r 1 r 2 /L 2 . Using the conservation of phase space volume and summing over all merging islands in the layer, we obtain a differential equation for f ( v ‖ , v ⊥ ), where with di = dA i dψ i . In earlier simulations of multi-island reconnection strong pressure anisotropy with p ‖ > p ⊥ within the core of merging islands was limited by anisotropy instabilities (Drake et al. 2010; Schoeffler et al. 2011) so we have included a phenomenological pitchangle scattering operator of strength ν that acts on the angle ζ = v ‖ /v to reduce anisotropy. Importantly, the drive R is independent of the particle velocity. It depends on the pressure anisotropy through the merging velocity V 12 . The integral over islands includes only interactions for which V 12 is real ( α 12 > 0). To estimate the scaling of R we note that N T = ∫ dig i is the total number of islands in the layer, so for densely packed islands we can define a characteristic island radius r N = L/ 2 N T . Thus, R ∼ /epsilon1 r c A /r N . Of course, R can be much smaller if α 12 in the expression for V 12 approaches zero. If f were isotropic and therefore only a function of v , the energy drive operator in Eq. (4) would vanish when averaged over the angle ζ . In this limit there is zero net energy gain, consistent with Parker's equation in the incompressible limit (Parker 1965). Equation (4) is an equi-dimensional equation and therefore has no characteristic velocity scale. Solutions therefore take the form of power-laws. An important property of such an equation is that the fluid moments of a given order completely decouple from those of differing order and their solutions can therefore be readily obtained from Eq. (4) in closed form. Specifically an equation for p ‖ and p ⊥ can be obtained so that α 12 in the energy drive R can be evaluated explicitly. Thus, the feedback of energetic particles on the dynamics of reconnection can be computed. In the case of no source, sink or scattering, for example, Eq. (4) yields ∂p ‖ /∂t = 2 Rp ‖ and ∂p ⊥ /∂t = -Rp ⊥ so that p ‖ and p ⊥ increase and decrease in time, respectively, but the total energetic particle pressure p increases, ∂p/∂t = (2 R/ 3)( p ‖ -p ⊥ ). Instead of directly evaluating the full moments of Eq. (4), we simplify the equation by ordering the magnitudes of the rates R , ν and c A /L . Since the scattering represented by ν arises from the pressure anisotropy driven by contraction, we argue that ν ∼ R . On the other hand as the spectrum begins to saturate at firehose marginal stability R is reduced and ν increases. We therefore take ν /greatermuch R ∼ /epsilon1 r c A /r N /greatermuch c A /L , where the latter follows because L /greatermuch r N . The large ν assumption allows us to solve Eq. (4) by expanding f in a series of Legendre polynomials f = ∑ j P j ( ζ ) f j ( v ) where P j is the j th order Legendre polynomial. By the symmetry in v ‖ , f 1 is zero. The equation for f 2 follows from balancing the reconnection drive acting on f 0 with the scattering operator acting on f 2 P 2 ( ζ ), f 2 ( v ) = -( Rv/ 6 ν ) ∂f 0 ( v ) /∂v . By averaging Eq. (4) over ζ , the scattering term vanishes and the energy drive term acting on f 2 P 2 ( ζ ) yields an equation for f 0 ( v ), This equation is again of equi-dimensional form and has power-law solutions whose individual moments can be calculated. Evaluating the density in steady state, for example, by integrating over velocity, the drive term vanishes and the total number of particles undergoing acceleration n T is given by n T = A T n up , where A T = ˙ A T L/c Aup is the integrated area of all of the islands in the layer. The firehose parameter needs to be self-consistently evaluated and for this we need Using the expression for f 2 and noting that v 2 ‖ -v 2 ⊥ / 2 = v 2 P 2 ( ζ ), we obtain where p 0 is the isotropic pressure calculated from f 0 , The firehose parameter becomes where ¯ B is the average island magnetic field strength based on the sum in Eq. (5). A key feature of Eq. (10) is its singular behavior when δ = R 2 L/ 3 c Aup ν = 1. This singularity can be understood from the power-law solutions to f 0 , which describe its behavior at energies greater than that of the source f up . Taking f 0 ∝ v -γ , from Eq. (6) we obtain γ ( γ -3) = 10 /δ so that when δ = 1, γ = 5. The second solution, γ = -2, corresponds to divergent behavior and must be rejected. The singularity in Eq. (10) therefore arises when f 0 ∝ v -5 and corresponds to a divergence of the pressure integral. Thus, it is clear that the requirement that the pressure be bounded requires that γ > 5 or δ < 1. In deriving Eq. (6) for f 0 we have assumed large scattering so that ν /greatermuch R . On the other hand, since island contraction drives the anisotropy, we argued previously that ν ∼ /epsilon1 r c A /r N . Thus, δ ∼ /epsilon1 r L/r N /greatermuch 1. Namely, the acceleration rate should always exceed the system convective loss rate since L is much larger than the characteristic island size. The resulting divergence of the pressure can only be avoided if the reconnection drive R ∝ √ α is reduced by its approach to firehose marginal stability, which forces R /lessmuch ν . Unless p up is very large, the only way that the firehose condition in Eq. (10) can be reached is if δ /similarequal 1 or γ /similarequal 5 and f 0 ∝ v -5 . The total energy content W 0 = 3 p 0 / 2 of this high energy tail can be directly calculated from the pressure in Eq. (9) using α /similarequal 0 and δ /similarequal 1, Thus, depending on the level of scattering, the total energy density of the energetic particles is of the order of, or somewhat greater than, the remaining magnetic energy. In a system with low initial β equipartition between energetic particles and magnetic field is energetically accessible. In a system with high initial β equipartition can only be reached if the system is open such that energetic particles can access additional sources of magnetic free energy.",
"pages": [
4,
5,
6,
7
]
},
{
"title": "4. Discussion",
"content": "We have derived a general equation (Eq. (4)) for particle acceleration in a bath of merging magnetic islands in a large 1-D current layer. We demonstrated that the E -1 . 5 spectrum is a nearly universal feature of a multi-island reconnecting system for all values of initial β as long as the nominal acceleration time of energetic particles is shorter than their loss rate. This is the correct limit as long as the characteristic magnetic island radius is much smaller than the system scale size L . We argue therefore that the widely observed E -1 . 5 spectrum in the heliosphere is a natural consequence of multi-island reconnection. The total energy content of this E -1 . 5 spectrum reaches parity with the remaining magnetic field energy in the system. Equation (4) can be readily generalized to a 2-D system by replacing the factors 2 r i /L by 4 r 2 i /L 2 in the drive term R . The estimate for the scaling of R is unchanged. The model loss term c Aup f/L should also be replaced by the convective loss rate u · ∇ f with u the convective velocity of the system. The arguments leading to the f ∝ v -5 also apply to the 2-D equations. In a system in which the driver R is spatially non-uniform the 2-D version of Eq. (4) could then be numerically solved for the spatial distribution of energetic particles from reconnection. The impact of the finite structure of magnetic islands that might develop in the third direction remains an important open issue (Onofri et al. 2006; Schreier et al. 2010; Daughton et al. 2011). There have now been several published simulations of particle acceleration and associated spectra in 2-D multi-current layer systems (Drake et al. 2010; Drake & Swisdak 2012). We can compare the spectra predicted from our equation with the results of those simulations. Since the simulations were doubly periodic, there was no convective loss. Further, the pressure anisotropy was strong so we consider the non-scattering limit of Eq. (4) in which the source and loss terms are discarded. The exact solution for f is given by where G ( t ) = ∫ t 0 dτR ( τ ). This is consistent with exponential growth of the effective parallel temperature and an exponential decrease in the perpendicular temperature. The omnidirec- al distribution function can be computed numerically for any specified initial distribution function for comparison with simulation data. The comparison is made with a system with sixteen initial current layers in a 409 . 6 d i × 204 . 8 d i domain, where d i = c/ω pi is the ion inertial length (Drake et al. 2010). In Fig. 2 we show the magnetic field strength at late time ( t = 100Ω -1 ci ) in the simulation after islands on adjacent current layers have overlapped. The typical island radius r N at this time is around 15 d i . The characteristic acceleration rate R ∼ /epsilon1 r c A /r N ∼ 0 . 007Ω -1 ci , where Ω ci is the ion cyclotron frequency. Reconnection remains strong for a total time of around 100Ω -1 ci when the pressure anisotropy shuts off reconnection. Thus, the integrated acceleration rate is G ∼ 0 . 7. The comparison between the model and the simulation data is shown in Fig. 3. The particle energy spectrum from the simulation is shown in the initial state and at t = 200Ω -1 ci in the solid lines. Note that the initial state is not a simple Maxwellian because of the shift in the ion velocity distribution that is required in the current layers. The fit of the initial spectrum with a single Maxwellian, shown in the dot-dashed line in Fig. 3 therefore matches the low energy portion of the spectrum very well but underestimates the number of particles at high energy. The late time energy spectrum from the solution given in Eq. (12), after integration over the angle ζ is given by the dashed line in Fig. 3. The best fit corresponds to G = 0 . 82 rather than the estimate of 0 . 7. The model reproduces the overall late-time energy spectrum very well but modestly overestimates the number of particles in the high energy tail. This is probably because the ions in the initial spectrum have thermal speeds that are sub-Alfv'enic so the Fermi acceleration of the low energy ions is delayed until they gain sufficient energy in reconnection exhausts (Drake et al. 2009b). Observations in the quiet solar wind have revealed that the super-Alfv'enic ions display an f ( v ) ∝ v -5 distribution (Fisk & Gloeckler 2006). It has been suggested that solar wind turbulence would be dissipated in reconnection current layers (Servidio et al. 2009) and therefore that reconnection is an important dissipation mechanism in the turbulent solar wind. Solar wind observations also reveal that the pressure anisotropy bumps against the firehose threshold in some regions and that there are enhanced magnetic fluctuations at these locations (Bale et al. 2009). There are therefore mechanisms in solar wind turbulence driving anisotropy and the anisotropy is limited by enhanced scattering. Finally, the direct observations of reconnection events in the solar wind reveal heating but no localized regions of energetic particles (Gosling et al. 2005). This is consistent with our picture that the energetic particle spectrum is not produced at a single x-line but requires that the ions interact with many reconnection sites. The spectrum of energetic electrons in impulsive flares are not measured in situ and must be inferred from chromospheric x-ray emission. Nevertheless, the energetic particle fluxes do occasionally reveal spectra as hard as E -1 . 5 , which corresponds to f ∝ v -5 (Holman et al. 2003). In recent over-the-limb observations of flares in which the reconnection region high in the corona can be directly diagnosed, it was found that all of the electrons in the acceleration region became part of the energetic component, indicating that all electrons in the region of energy release underwent acceleration (Krucker et al. 2010), which is consistent with our model. The β of these electrons was of order unity, which is also consistent with our predictions. Whether the sectored heliosheath magnetic field has reconnected remains an open issue because the Voyager magnetometers are at the limits of their resolutions at the magnetic field strengths in the heliosheath (Burlaga et al. 2006). Large drops in the energetic electron and ACR population as Voyager 2 exited from the sectored zone are consistent with reconnection as the ACR driver (Opher et al. 2011). The spectral index of the ACR particle flux measured at Voyager 1 is slightly above 1 . 5 (Stone et al. 2008; Decker et al. 2010). Further, the integrated energy density of the measured ACR spectrum between 1 and 100 MeV and is comparable to that of the magnetic field, which has a magnitude of around 0 . 15 nT . This is again consistent with the predictions of our model. The equations presented here were derived in the non-relativistic limit. However, the ideas can be easily extended to the case where the particles are relativistic but where reconnection itself is non-relativistic. We express the distribution of particles in terms of the particle momentum p . For the pressure integral to remain bounded γ > 4 for power-law distributions with f 0 ( p ) ∝ p -γ . The resulting particle flux per unit energy interval Γ is given by Γ ∝ p 2 f ( p ) ∝ p 2 -γ . Thus, the spectrum of the flux in the strongly relativistic limit should scale as p -2 . This work has been supported by NSF Grant AGS1202330 and NASA grants APL975268 and NNX08AV87G.",
"pages": [
7,
8,
9
]
},
{
"title": "REFERENCES",
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"pages": [
9,
10,
11
]
}
]
2013ApJ...764...48K
https://arxiv.org/pdf/1209.2482.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_83><loc_86><loc_85></location>TESTING MODELS OF INTRINSIC BRIGHTNESS VARIATIONS IN TYPE IA SUPERNOVAE, AND THEIR IMPACT ON MEASURING COSMOLOGICAL PARAMETERS</section_header_level_1>
<text><location><page_1><loc_11><loc_78><loc_88><loc_82></location>Richard Kessler, 1,2 Julien Guy, 3 John Marriner, 4 Marc Betoule, 3 Jon Brinkmann, 5 David Cinabro, 6 Patrick El-Hage, 3 Joshua A. Frieman, 1,2,4 Saurabh Jha, 7 Jennifer Mosher, 8 and Donald P. Schneider 9,10 accepted by ApJ</text>
<section_header_level_1><location><page_1><loc_45><loc_76><loc_55><loc_77></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_45><loc_86><loc_75></location>For spectroscopically confirmed Type Ia supernovae we evaluate models of intrinsic brightness variations with detailed data/Monte Carlo comparisons of the dispersion in the following quantities: Hubble-diagram scatter, color difference ( B -V -c ) between the true B -V color and the fitted color ( c ) from the salt-ii light curve model, and photometric redshift residual. The data sample includes 251 ugriz light curves from the three-season Sloan Digital Sky Survey-II and 191 griz light curves from the Supernova Legacy Survey 3 year data release. We find that the simplest model of a wavelengthindependent (coherent) scatter is not adequate, and that to describe the data the intrinsic-scatter model must have wavelength-dependent variations resulting in a ∼ 0 . 02 mag scatter in B -V -c . Relatively weak constraints are obtained on the nature of intrinsic scatter because a variety of different models can reasonably describe this photometric data sample. We use Monte Carlo simulations to examine the standard approach of adding a coherent-scatter term in quadrature to the distance-modulus uncertainty in order to bring the reduced χ 2 to unity when fitting a Hubble diagram. If the light curve fits include model uncertainties with the correct wavelength dependence of the scatter, we find that this approach is valid and that the bias on the dark energy equation of state parameter w is much smaller ( ∼ 0 . 001) than current systematic uncertainties. However, incorrect model uncertainties can lead to a significant bias on the distance moduli, with up to ∼ 0 . 05 mag redshift-dependent variation. This bias is roughly reduced in half after applying a Malmquist bias correction. For the recent SNLS3 cosmology results we estimate that this effect introduces an additional systematic uncertainty on w of ∼ 0 . 02, well below the total uncertainty. This uncertainty depends on the choice of viable scatter models and the choice of supernova (SN) samples, and thus this small w -uncertainty is not guaranteed in future cosmology results. For example, the w -uncertainty for SDSS+SNLS (dropping the nearby SNe) increases to ∼ 0 . 04.</text>
<text><location><page_1><loc_14><loc_43><loc_34><loc_44></location>Subject headings: supernova</text>
<section_header_level_1><location><page_1><loc_21><loc_39><loc_36><loc_40></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_31><loc_48><loc_38></location>For more than a decade Type Ia supernovae (SN Ia) have been used as standardizable candles to measure luminosity distances. These distances, along with the associated redshifts, have been used to measure properties of dark energy (Riess et al. 1998; Perlmutter et al. 1999; Riess et al. 2004; Astier et al.</text>
<text><location><page_1><loc_10><loc_28><loc_25><loc_29></location>[email protected]</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_25><loc_48><loc_28></location>1 Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA</list_item>
<list_item><location><page_1><loc_10><loc_23><loc_48><loc_25></location>2 Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue Chicago, IL 60637, USA</list_item>
<list_item><location><page_1><loc_10><loc_20><loc_48><loc_23></location>3 Laboratoire de Physique Nucl'eaire et des Hautes Energies, UPMC Univ. Paris 6, UPD Univ. Paris 7, CNRS IN2P3, 4 place Jussieu F-75005, Paris, France</list_item>
<list_item><location><page_1><loc_10><loc_18><loc_48><loc_20></location>4 Center for Particle Astrophysics, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510, USA</list_item>
<list_item><location><page_1><loc_10><loc_16><loc_48><loc_18></location>5 Apache Point Observatory, P.O. Box 59, Sunspot, NM 88349, USA</list_item>
<list_item><location><page_1><loc_10><loc_14><loc_48><loc_16></location>6 Department of Physics, Wayne State University, Detroit, MI 48202, USA</list_item>
<list_item><location><page_1><loc_10><loc_12><loc_48><loc_14></location>7 Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854, USA</list_item>
<list_item><location><page_1><loc_10><loc_10><loc_48><loc_12></location>8 Department of Physics and Astronomy, University of Pennsylvania, 203 South 33rd Street, Philadelphia, PA 19104, USA</list_item>
<list_item><location><page_1><loc_10><loc_7><loc_48><loc_10></location>9 Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA</list_item>
<list_item><location><page_1><loc_10><loc_5><loc_48><loc_8></location>10 Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA</list_item>
</unordered_list>
<text><location><page_1><loc_52><loc_22><loc_92><loc_40></location>2006; Wood-Vasey et al. 2007; Freedman et al. 2009; Kessler et al. 2009a; Conley et al. 2011). The uncorrected variation in the SN Ia peak brightness is ∼ 1 mag, and this variation is reduced to ∼ 0 . 1 mag after empirical corrections based on the measured stretch (Phillips 1993) and color (Riess et al. 1996; Tripp 1997). This 0.1 mag intrinsic scatter increases the scatter in the Hubble diagram well beyond what is expected from the distance modulus uncertainties, and the resulting cosmology fits have reduced chi-squared ( χ 2 r ≡ χ 2 /N dof ) significantly larger than unity. To obtain χ 2 r = 1, all SNIa-cosmology analyses to date have introduced an ad hoc intrinsicscatter term ( σ int ∼ 0 . 1 mag) that is added in quadrature to the measured distance modulus uncertainties.</text>
<text><location><page_1><loc_52><loc_6><loc_92><loc_22></location>This procedure of adding a constant ad hoc scatter term would be correct if the unknown source of intrinsic variation is independent of redshift, and if it is fully coherent such that the variation is the same for all wavelengths and passbands. Kessler et al. (2010, hereafter K10) found evidence contradicting a coherent variation in a study comparing the photoz precision between data and Monte Carlo simulations (MC). Using the coherent-scatter model in the MC underestimated the fitted photoz precision observed in the data, while simulating a model using color variations gave better agreement. Guy et al. (2010, hereafter G10) examined</text>
<text><location><page_2><loc_8><loc_75><loc_48><loc_90></location>residuals from the salt-ii training and showed that the variation about the best-fit spectral model is wavelength dependent; this wavelength-dependent uncertainty is included in the light curve fitting model. Marriner et al. (2011, hereafter M11) presented a more formal treatment of σ int based on an intrinsic scatter covariance matrix that depends on a coherent term, a stretch term, and a color term. 11 They compared Sloan Digital Sky Survey-II (SDSS-II) SN Ia data and simulations within this framework and suggest that the coherent and color terms are significant, while the stretch term is negligible.</text>
<text><location><page_2><loc_8><loc_49><loc_48><loc_75></location>The importance of understanding the nature of intrinsic scatter is tied to understanding systematic uncertainties in cosmology analyses using SNe Ia. If this scatter is truly random, as suggested by explosion models showing brightness variation with viewing angle (Kasen et al. 2009, hereafter KRW09), then there is no intrinsic bias and the uncertainty will decrease with increasing sample size. Even in this optimistic scenario a wavelengthdependent scatter results in a redshift-dependent dispersion because with broadband filters different rest-frame wavelengths are probed as a function of redshift. This variation must be properly accounted for, except in the hypothetically ideal scenario of measuring high-quality spectra to determine synthetic magnitudes with the same rest-frame passbands at all redshifts. If this scatter depends on more subtle physics related to the explosion mechanism and the host-galaxy environment, there could be additional redshift-dependent effects not yet detected with current data samples, but that become apparent in future surveys with much larger samples.</text>
<text><location><page_2><loc_8><loc_19><loc_48><loc_49></location>Significant effort to reduce this scatter has been attempted using near infrared (NIR) photometry and spectroscopic features. Mandel et al. (2011) report that optical+NIR photometry result in a Hubble scatter that is ∼ 30% smaller compared to using only optical data. A decade of effort on spectroscopic correlations can be summarized with results from three groups. Blondin et al. (2011) examined spectra from the CfA Supernova Program and used spectral features to reduce the Hubble scatter by at most 10%, albeit with only 2 σ significance. From the Berkeley SNIa Program, Silverman et al. (2012) examined 108 high quality SNe Ia with a spectrum taken within 5 days of maximum brightness and found similar results. The best Hubble scatter reduction was obtained by Bailey et al. (2009) using very high quality spectra from the Supernova Factory (Aldering et al. 2002). Using spectra within 2.5 days of peak brightness, they scanned every possible flux-ratio in ∼ 40 ˚ A bins and found a minimum Hubble scatter using the ratio F (642 nm) /F (443 nm); the resulting scatter is about 25% lower compared to the traditional photometric analysis with the salt-ii light curve model.</text>
<text><location><page_2><loc_8><loc_9><loc_48><loc_19></location>To realize significant reductions ( ∼ 30%) in the Hubble scatter requires optical photometry combined with either rest-frame NIR photometry or very high quality spectra near the epoch of peak brightness. Both of these supplemental data samples are difficult to obtain at low redshift, and it is not yet clear what resources could be allocated to obtain large data samples for higher redshift SNe that are needed to construct a cosmologically inter-</text>
<text><location><page_2><loc_52><loc_79><loc_92><loc_90></location>ting Hubble diagram. Given the unlikely prospects for significantly reducing the Hubble scatter, we take a different approach here and explore models to describe the scatter in more detail. Such models of intrinsic scatter can be used to evaluate and constrain systematic uncertainties from assuming an incorrect model, and possibly lead to a better understanding of the underlying wavelength dependence of SN brightness variations.</text>
<text><location><page_2><loc_52><loc_49><loc_92><loc_79></location>In this work we demonstrate a method for evaluating models of intrinsic scatter by computing three scatterdependent dispersion variables and making the following data/MC comparisons: (1) the traditional Hubblediagram residual; (2) B -V -c , where B -V is the true rest-frame color and c is the fitted color parameter from the salt-ii model; and (3) the photoz residual. In the hypothetical limit of observing SNe Ia with infinite photon statistics and no intrinsic scatter, the distribution for each variable would be a Diracδ function. Simulations that include fluctuations from photon statistics, but no intrinsic-scatter model, underestimate the measured dispersion in these variables. A viable model of intrinsic scatter must predict the dispersion for each variable and for multiple data sets. These three variables do not constitute an exhaustive list of photometric observables; for example one could examine other rest-frame colors ( U -B , V -R ), correlations among colors, and the dependence of the scatter on redshift, stretch, and color. With our current statistics and signal to noise we limit this initial study to the three variables described above, but larger and higher-quality SN samples from current and future surveys should enable a more thorough study.</text>
<text><location><page_2><loc_52><loc_40><loc_92><loc_49></location>Three classes of wavelength-dependent intrinsic-scatter models are investigated. First we try purely phenomenological functions of rest-frame wavelength with parameters tuned to match observations. The second class is based on measurements from data. The third class uses theoretical explosion models (KRW09) to perturb the salt-ii spectral model.</text>
<text><location><page_2><loc_52><loc_28><loc_92><loc_39></location>This work is part of the SDSS+SNLS joint analysis, and the data sets used here include 251 spectroscopically confirmed SNe Ia from the 3 year SDSS-II sample (Frieman et al. 2008), and another 191 spectroscopically confirmed SNe Ia from the Supernova Legacy Survey (SNLS3; Conley et al. 2011). All simulations and light curve fitting are done with the publicly available SNANA package 12 (Kessler et al. 2009b, version v10 07 ) and the salt-ii light curve model (G10).</text>
<text><location><page_2><loc_52><loc_17><loc_92><loc_28></location>The outline of the paper is as follows. The data samples are described in Section 2 and the simulation and intrinsic-scatter models are described in Section 3. The determination of each dispersion variable is in Section 4, and the resulting data/MC comparisons are in Section 5 along with some systematics tests. Finally, in Section 6 we investigate the potential Hubble diagram bias from using an incorrect model of intrinsic scatter.</text>
<section_header_level_1><location><page_2><loc_55><loc_15><loc_89><loc_16></location>2. THE SDSS-II AND SNLS DATA SAMPLES</section_header_level_1>
<text><location><page_2><loc_52><loc_8><loc_92><loc_14></location>We use two SN Ia data samples that are well calibrated with ∼ 1% photometric precision, and that span complementary redshift ranges. The lower redshift SNe ( z < 0 . 4) are from the full three-season SDSS-II sample (Frieman et al. 2008), and the higher redshift SNe</text>
<text><location><page_3><loc_8><loc_86><loc_48><loc_90></location>( z < 1) are from the publicly available 3 year SNLS3 sample (Conley et al. 2011). Below we give a brief description of these samples.</text>
<text><location><page_3><loc_8><loc_57><loc_48><loc_86></location>The SDSS-II Supernova Survey used the SDSS camera (Gunn et al. 1998) on the SDSS 2.5 m telescope (Gunn et al. 2006; York et al. 2000) at the Apache Point Observatory to search for SNe in the Fall seasons (September 1 through November 30) of 2005-2007. This survey scanned a region (designated stripe 82) centered on the celestial equator in the Southern Galactic hemisphere that is 2.5 · wide and runs between right ascensions of 20 h and 4 h , covering a total area of 300 deg 2 with a typical cadence of every four nights per region. Images were obtained in five broad passbands, ugriz (Fukugita et al. 1996), with 55 s exposures and processed through the PHOTO photometric pipeline (Lupton et al. 2001). Within 24 hr of collecting the data, the images were searched for SN candidates that were selected for spectroscopic observations in a program involving about a dozen telescopes. The SDSS-II Supernova Survey discovered and spectroscopically confirmed a total of ∼ 500 Type Ia SNe. Details of the SDSS-II SN Survey are given in Frieman et al. (2008) and Sako et al. (2008), and the procedures for spectroscopic identification and redshift determinations are described in Zheng et al. (2008).</text>
<text><location><page_3><loc_8><loc_34><loc_48><loc_57></location>The SN photometry for SDSS-II is based on Scene Model Photometry (SMP) described in Holtzman et al. (2008). The basic approach of SMP is to simultaneously model the ensemble of survey images covering an SN location as a time-varying point source (the SN) and sky background plus time-independent galaxy background and nearby calibration stars, all convolved with a time-varying point-spread function (PSF). The fitted parameters are SN position, SN flux for each epoch and passband, and the host-galaxy intensity distribution in each passband. The galaxy model for each passband is a 20 × 20 grid (with a grid scale set by the CCD pixel scale, 0 . 4 '' × 0 . 4 '' ) in sky coordinates, and each of the 400 × 5 = 2000 galaxy intensities is an independent fit parameter. As there is no pixel re-sampling or image convolution, the procedure yields correct statistical error estimates.</text>
<text><location><page_3><loc_8><loc_17><loc_48><loc_34></location>The SNLS was a 5 year survey covering four 1 deg 2 fields using the MegaCam imager on the 3.6 m CanadaFrance-Hawaii Telescope (CFHT). Images were taken in four bands similar to those used by the SDSS: g M , r M , i M , z M , where the subscript M denotes the MegaCam system. The SNLS exposures were ∼ 1 hr in order to discover SNe at redshifts up to z ∼ 1. The SNLS images were processed in a fashion similar to the SDSS-II so that spectroscopic observations could be used to confirm the identities and determine the redshifts of the SN candidates. Additional information about the SNLS can be found in Astier et al. (2006) and references within.</text>
<text><location><page_3><loc_8><loc_5><loc_48><loc_17></location>The SNLS3 SN photometry is based on a simultaneous fit of the SN flux and position, a residual sky background per image, and a galaxy intensity map. Images are resampled to the same reference pixel grid prior to the fit. The SN+galaxy image model is PSF-matched to the resampled images. Only sky noise is included in the photometric uncertainties (host galaxy and source noise are negligible for most SNe). Because resampling introduces pixel correlations, the uncertainties ignoring correlations</text>
<text><location><page_3><loc_52><loc_87><loc_92><loc_90></location>are scaled such that the reduced χ 2 is one when assuming a constant SN flux per night.</text>
<text><location><page_3><loc_52><loc_83><loc_92><loc_87></location>To ensure good quality fits to the light curves, the following selection criteria are applied to both the SDSS-II and SNLS3 data samples,</text>
<unordered_list>
<list_item><location><page_3><loc_54><loc_80><loc_92><loc_82></location>· At least one epoch before the epoch of peak brightness in the B band (defined as T rest = 0)</list_item>
<list_item><location><page_3><loc_54><loc_76><loc_85><loc_79></location>· At least one epoch with T rest > 10 days.</list_item>
<list_item><location><page_3><loc_54><loc_74><loc_92><loc_76></location>· At least three filters with an observation that has a signal-to-noise ratio (S/N) above 8</list_item>
<list_item><location><page_3><loc_54><loc_67><loc_92><loc_72></location>· At least five observations in the fitted epoch range -12 < T rest < +25 days. The maximum T rest is set by the range for one of the models (KRW09) of intrinsic brightness variation.</list_item>
<list_item><location><page_3><loc_54><loc_63><loc_92><loc_66></location>· Color excess from Milky Way Galactic extinction (Schlegel et al. 1998) is E ( B -V ) < 0 . 2.</list_item>
<list_item><location><page_3><loc_54><loc_54><loc_92><loc_62></location>· After fitting each light curve to the salt-ii model (Section 4.1), we require the SNIa fit probability to be P fit > 0 . 02, where P fit is computed from the fitχ 2 and the number of degrees of freedom. After all other requirements, this cut removes 14 (3) events from the SDSS-II (SNLS3) samples.</list_item>
</unordered_list>
<text><location><page_3><loc_52><loc_51><loc_92><loc_53></location>The sample statistics after these requirements are given in Section 4.5.</text>
<section_header_level_1><location><page_3><loc_65><loc_48><loc_79><loc_49></location>3. SIMULATIONS</section_header_level_1>
<text><location><page_3><loc_52><loc_34><loc_92><loc_48></location>We use the SNANA MC code (Kessler et al. 2009b) to generate realistic SN Ia light curves that are analyzed in exactly the same manner as the data. The MC is used to make detailed comparisons with the data using different models of intrinsic SN Ia brightness variations. All simulations are based on a standard ΛCDM cosmology with w = -1, Ω M = 0 . 3, Ω Λ = 0 . 7. Details of the simulation are described in Kessler et al. (2009b) and in Section 6 of Kessler et al. (2009a, hereafter K09); here we give a brief overview.</text>
<text><location><page_3><loc_52><loc_22><loc_92><loc_34></location>Simulations are generated using the salt-ii model (G10) that is based on a time sequence of rest-frame spectra. The spectral model is explained in more detail in Section 4 within the context of light curve fitting. Observer-frame magnitudes are computed by redshifting the rest-frame spectrum for each epoch, reddening the spectra from Galactic extinction (Schlegel et al. 1998) using R V = 3 . 1, and summing the flux in the appropriate filter-response curves.</text>
<text><location><page_3><loc_52><loc_8><loc_92><loc_22></location>To account for non-photometric conditions and varying time intervals between observations due to bad weather, actual observing conditions are used for both the SDSSII and SNLS surveys. For each simulated observation, the noise is determined from the measured PSF, 13 Poisson noise from the source, and sky background. Noise from the host-galaxy background is included for the SDSS-II simulations where it has a small effect at low redshifts. Host-galaxy noise for the higher redshift SNLS sample is negligible, and thus not simulated. Additional details of the simulation of noise are given in Section 3.1.</text>
<text><location><page_4><loc_8><loc_86><loc_48><loc_90></location>The simulated flux in CCD counts is based on a mag-toflux zeropoint, and a random fluctuation drawn from the noise estimate.</text>
<text><location><page_4><loc_8><loc_82><loc_48><loc_86></location>The parent distributions of the salt-ii stretch ( x 1 ) and color ( c ) are well described by an asymmetric Gaussian that is a function of three parameters,</text>
<formula><location><page_4><loc_19><loc_79><loc_48><loc_81></location>e [ -( x 1 -¯ x 1 ) 2 / 2 σ 2 -] x 1 < ¯ x 1 (1)</formula>
<formula><location><page_4><loc_19><loc_77><loc_48><loc_79></location>e [ -( x 1 -¯ x 1 ) 2 / 2 σ 2 + ] x 1 > ¯ x 1 (2)</formula>
<text><location><page_4><loc_8><loc_43><loc_48><loc_76></location>and a similar function with x 1 → c . The parameters for each distribution are shown in Table 1. After accounting for Malmquist bias, we find that the higher-redshift SNLS3 sample is slightly brighter and bluer compared to the SDSS-II sample. This difference is expected from previous results showing that younger star-former galaxies host brighter/bluer SNe Ia than older passive galaxies (Sullivan et al. 2006; Lampeitl et al. 2010; Smith et al. 2012). The younger star-forming galaxies are more abundant at higher redshifts, thus qualitatively explaining the brightness difference between the two surveys. While the redshift-dependent variation in the stretch population is well established, the variation in the color population has been reported only in Smith et al. (2012) where they show that the SN Ia color population is the same for passive and moderately star-forming galaxies, but different in highly star-forming galaxies. Previous studies comparing passive and all star-forming galaxies found no color variation, and should not be considered inconsistent with the results of Smith et al. (2012). We show in the systematics analysis (Section 5.1) that the simulated intrinsic scatter is rather insensitive to the parameters describing the parent populations in Table 1, and therefore it does not matter if these parameters are the same or slightly different for each survey.</text>
<table>
<location><page_4><loc_11><loc_28><loc_46><loc_36></location>
<caption>TABLE 1 Asymmetric Gaussian Parameters to Describe the Parent Distribution of x 1 and c .</caption>
</table>
<text><location><page_4><loc_23><loc_28><loc_24><loc_29></location>-</text>
<text><location><page_4><loc_38><loc_28><loc_39><loc_29></location>-</text>
<text><location><page_4><loc_8><loc_8><loc_48><loc_25></location>The simulation includes a detailed treatment of the search efficiency, including spectroscopic selection effects. For the SDSS-II, the search-pipeline efficiency has been measured separately for each g, r, i filter using fake SNe inserted into the images (Dilday et al. 2008). The spectroscopic selection efficiency ( /epsilon1 spec ) has been estimated from matching data/MC distributions for redshift and for the fitted observer-frame magnitudes at the epoch of peak brightness. /epsilon1 spec is adequately described as a function of peak r -band magnitude and the peak color g -r . These efficiency functions are available in tabular form. 14 For the SNLS3, /epsilon1 spec has been evaluated as a function of peak i M -band magnitude ( M i ) in Figure 9 of</text>
<text><location><page_4><loc_52><loc_87><loc_92><loc_90></location>Perrett et al. (2010). For the SNANA simulation we parameterize this function as</text>
<formula><location><page_4><loc_53><loc_84><loc_92><loc_87></location>/epsilon1 SNLS3 spec = { 0 . 5 + 1 π tan -1 [ 24 . 3 -M i 0 . 2 ]} × C /epsilon1 ( M i ) (3)</formula>
<text><location><page_4><loc_52><loc_77><loc_92><loc_83></location>where C /epsilon1 ( M i ) = 1 for M i < 23 and C /epsilon1 ( M i ) = exp[(23 -M i ) / 0 . 63] for M i > 23. The function in parentheses is a first-order estimate and C /epsilon1 ( M i ) is a correction obtained from a fit to the data/MC ratio as a function of M i .</text>
<text><location><page_4><loc_52><loc_71><loc_92><loc_77></location>For this analysis we generate MC samples with sizes corresponding to six times the data statistics. The quality of the simulation for each sample is illustrated with several data/MC comparisons in Figures 1 and 2; the overall agreement is good.</text>
<section_header_level_1><location><page_4><loc_58><loc_67><loc_86><loc_68></location>Data/MC Comparisons for SDSS</section_header_level_1>
<figure>
<location><page_4><loc_55><loc_36><loc_91><loc_68></location>
<caption>Fig. 1.Comparison of distributions for SDSS-II data (dots) and MC (histogram), where each MC distribution is scaled to have the same sample size as the data. The distributions are redshift, number of degrees of freedom in the salt-ii light curve fit, maximum rest-frame time difference (gap) between observations, maximum S/N, fitted salt-ii color ( c ) and stretch parameter ( x 1 ). The bottom two panels show the mean fitted salt-ii color ( c ) and shape parameter ( x 1 ) vs. redshift.</caption>
</figure>
<section_header_level_1><location><page_4><loc_63><loc_21><loc_81><loc_23></location>3.1. Simulation of Noise</section_header_level_1>
<text><location><page_4><loc_52><loc_9><loc_92><loc_21></location>Since the three scatter-dependent variables (Hubble scatter, B -V -c photoz precision) are sensitive to the flux uncertainties, it is important to accurately simulate these uncertainties. The simulation strategy is to first calculate the uncertainties from a model based on measurements of the sky level and PSF. To accurately check the model, the true uncertainty for each observation in the data 15 is compared to the calculated model uncertainty. Discrepancies between the true and calculated</text>
<figure>
<location><page_5><loc_11><loc_57><loc_47><loc_90></location>
<caption>Fig. 2.Same as Figure 1, except for the SNLS3 sample.</caption>
</figure>
<text><location><page_5><loc_8><loc_49><loc_48><loc_53></location>uncertainties are corrected by fitting for ad-hoc parameters. The simulated uncertainty model in photoelectrons ( σ SIM ) is given by</text>
<formula><location><page_5><loc_12><loc_45><loc_48><loc_48></location>σ 2 SIM = F +( A · b ) + ( qF ) 2 +( σ 0 · 10 0 . 4 · ZPT pe ) 2 + σ 2 HOST (4)</formula>
<text><location><page_5><loc_8><loc_29><loc_48><loc_44></location>where F is the flux, A = [2 π ∫ PSF 2 ( r, θ ) rdr ] -1 is the noise-equivalent area, b is the effective sky level including dark current and readout noise, and q and σ 0 are fitted ad-hoc parameters. ZPT pe is defined such that the number of CCD photoelectrons for a point source of magnitude m is given by 10 -0 . 4( m -ZPT pe ) ; thus the σ 0 term is independent of the PSF, sky level and host-galaxy. The quantity σ HOST is simulated for the SDSS-II sample using a library of galaxies that have a spectroscopic redshift and a well measured profile consistent with either exponential or de Vaucouleurs.</text>
<text><location><page_5><loc_8><loc_6><loc_48><loc_29></location>To check the uncertainty calculation, σ SIM is computed for each epoch in the data and compared to the measured uncertainty σ DATA . The left panels in Figure 3 show that the first two terms, F + Ab , are not adequate to reproduce the observations. The right panels in Figure 3 show that the fitted σ 0 term results in good agreement over a wide range of PSF values. A separate σ 0 value is evaluated for each filter and for each sample (Table 2). The quadratic term q is sensitive to large flux values with S / N ∼ 10 2 . The value of q is obtained from minimizing χ 2 = ∑ s [( σ SIM /σ DATA ) s -1] 2 , where the sum ( s ) is over log 10 (S / N) bins; q /similarequal 0 . 01 for the SDSS bands, and q ∼ 0 . 001 for the SNLS bands. For SNLS, it is difficult to interpret this low value of q because uncertainties on the SN flux (Poisson noise and flat-fielding noise) only arise via the normalization of errors based on the intra-night flux scatter.</text>
<text><location><page_5><loc_10><loc_4><loc_48><loc_6></location>Finally, note that the terms F + ( A · b ) + σ 2 HOST are</text>
<text><location><page_5><loc_52><loc_81><loc_92><loc_90></location>determined from observations and first principles, while q and σ 0 are empirically determined parameters. The q term corresponds to a zeropoint uncertainty. The σ 0 term is not understood, although this term works surprisingly well for both the SDSS-II and SNLS3 surveys even though the respective photometry codes are independent.</text>
<figure>
<location><page_5><loc_54><loc_51><loc_91><loc_78></location>
<caption>Fig. 3.Left panels show the r -band flux-uncertainty distribution for the data (black dots) and for the calculation (histogram), σ SIM = √ F + Ab with σ 0 = 0 and q = 0. Each descending plot is for a different PSF range (FWHM, arcsec) as indicated on the plot. Right panels show the σ SIM calculation including the best-fit σ 0 value labeled on the plot and shown by the arrow. The flux unit shown is that used for light curve fits (not photoelectrons).</caption>
</figure>
<table>
<location><page_5><loc_63><loc_25><loc_81><loc_34></location>
<caption>TABLE 2 Fitted σ 0 values for SDSS-II and SNLS3.</caption>
</table>
<section_header_level_1><location><page_5><loc_62><loc_17><loc_82><loc_19></location>3.2. Intrinsic-scatter Models</section_header_level_1>
<text><location><page_5><loc_52><loc_5><loc_92><loc_17></location>The intrinsic scatter models are summarized in Table 3. These models are defined as wavelength-dependent perturbations to the salt-ii spectral model, and these perturbations average to zero so that the underlying saltii model is not changed. All models are independent of redshift, and only the explosion models from KRW09 depend on epoch. We begin with the phenomenological functions (see 'FUN' prefix) with parameters arbitrarily chosen to increase the scatter. The coherent model</text>
<text><location><page_6><loc_8><loc_67><loc_48><loc_90></location>(FUN-COH) assigns a single magnitude shift for all wavelengths; for each SN this shift is given by a Gaussianrandom number with σ COH = 0 . 13 mag. The other two FUN functions are designed to probe a wider variety of wavelength-dependent scatter with a coherence length of a few hundred ˚ A. First a sequence of nodes is defined at 1000 ˚ A intervals in the rest frame. An independent Gaussian random scatter is selected at each node with σ node = σ 5500 exp[ -( λ node -5500) / 3000] so that there is more scatter at bluer wavelengths. The variation is the same at all epochs. A continuous function of wavelength is constructed by connecting the node values with sine functions so that the derivative is zero at each node. FUN-COLOR is defined with σ 5500 = 0 . 06 and is shown in Figure 4 for a few simulated SN. FUN-MIX is defined with σ 5500 = 0 . 045 along with a coherent term σ COH = 0 . 09 mag.</text>
<figure>
<location><page_6><loc_10><loc_55><loc_46><loc_66></location>
<caption>Fig. 4.Illustration of FUN-COLOR for four simulated SNe. Black lines show the λ rest -dependent variation. Solid dots show the Gaussian-random variations at the nodes, and dashed lines show ± 1 σ vs. λ rest .</caption>
</figure>
<text><location><page_6><loc_20><loc_42><loc_46><loc_44></location>refers to rest-frame wavelength.</text>
<table>
<location><page_6><loc_9><loc_12><loc_46><loc_41></location>
<caption>TABLE 3 Summary of Intrinsic-scatter Models. λ rest</caption>
</table>
<text><location><page_6><loc_9><loc_9><loc_39><loc_10></location>a 'iso' = isotropic and 'dc' = detonation criteria.</text>
<text><location><page_6><loc_10><loc_5><loc_48><loc_6></location>The next two models (G10 and C11) are based on mea-</text>
<text><location><page_6><loc_52><loc_59><loc_92><loc_90></location>surements from data combined with assumptions needed to create a model that is a continuous function of wavelength. The G10 error model was obtained as part of the salt-ii training process in which they minimized the likelihood of light curve amplitude residuals using a parametric function of central rest-frame wavelength, assuming uncorrelated residuals in different passbands. The resulting wavelength-dependent function (Figure 8 of G10) has approximate values of 0.07, 0.03, 0.02, 0.03, 0.06 mag at the U, B, V, R, I central wavelengths, respectively. This function is not intended to represent a wavelength dependent scatter, but rather it is a model of independent broadband scatter as a function of central wavelength. To translate this broadband model into a wavelength model, independent random scatter values ( σ node ) are selected every 800 ˚ A, and these node values are connected with the same sine-interpolation that is used for the phenomenological 'FUN' functions. Since this procedure reduces the resulting broadband scatter, σ node is multiplied by 1+( λ rest -2157) / 9259 so that the simulated UBVRI broadband scatter matches the G10 function. In addition to a wavelength-dependent function, the G10 model includes a coherent term, σ COH = 0 . 09 mag.</text>
<text><location><page_6><loc_52><loc_15><loc_92><loc_59></location>The model of Chotard (2011); Chotard et al. (2011, hereafter C11) is based on a covariance scatter matrix among the UBVRI filter passbands, and is derived from an analysis of spectral correlations using high quality spectra from the Supernova Factory (Aldering et al. 2002). The broadband covariance model is translated into a wavelength-dependent model as follows. First, the model is extrapolated to wavelengths below the U band (3600 ˚ A) by defining an ad-hoc U ' filter with central wavelength ¯ λ obs = 2500 ˚ A. The G10 scatter value of σ node = 0 . 59 mag is used for U ' , and we model three different assumptions for the reduced correlation between U ' and U : ρ U ' ,U = 0 (incoherent,C11 0), ρ U ' ,U = +1 (C11 1), and ρ U ' ,U = -1 (C11 2). For each simulated SN, six random magnitude shifts are selected according to the C11 correlation matrix in upper half of Table 4; these shifts are assigned to the central U ' UBVRI wavelengths. A continuous function of wavelength is obtained by interpolating these six points with a sine function, similar to the FUN-COLOR interpolation in Figure 4. Finally, the scatter function is multiplied by 1.3 to compensate for the fact that the wavelength interpolation reduces the broadband covariances. The correlation matrix realized by the simulation is shown in bottom half of Table 4 for the C11 1 model. The realized correlation matrix is slightly different than the input model because the input model is described by broadband covariances, while the simulated model depends on wavelength. In principle a more finely tuned spectral model in the simulation would result in the exact C11 covariances, but we believe that the simple and approximate model used here is adequate, especially in light of the large and unknown uncertainties on the covariances.</text>
<text><location><page_6><loc_52><loc_6><loc_92><loc_15></location>The final class of brightness variations is based on 2D explosion models with random ignition points (KRW09), followed by radiative transfer calculations using the SEDONA program (Kasen et al. 2006). Isotropic models are obtained from ignition points that are randomly placed throughout the white dwarf (WD), while asymmetric models are obtained from ignition points within</text>
<text><location><page_7><loc_8><loc_63><loc_48><loc_90></location>a cone whose apex is at the center of the WD. Both the isotropic and asymmetric models result in explosion asymmetries and a viewing angle dependence that contributes significantly to the intrinsic scatter. The widthluminosity relation is related to the number of ignition points ( N ignit ) because N ignit affects the amount of preexpansion before detonation, and hence the amount of 56 Ni produced in the explosion. In a recent study by Blondin et al. (2011, hereafter B11), detailed comparisons between data and the KRW09 models were made. They conclude that the KRW09 models with the best spectroscopic agreement also have the best photometric agreement, and they identified a subset of eight models with the best agreement to data. Here we use these same eight models; they are shown in Table 3 along with a few parameters describing the number of ignition points and the detonation criteria. All of these models have an isotropic distribution of ignition points, and B11 note that radial fluctuations in isotropic models can lead to significant viewing angle asymmetries.</text>
<text><location><page_7><loc_8><loc_54><loc_48><loc_63></location>We initially used these KRW09 models in the SNANA simulation to generate light curves corresponding to the SDSS-II and SNLS3. While the data/MC comparisons are visually impressive, the simulated light curves are not adequate for this study because the salt-ii light curve fits are in general rather poor. This trend of poor light curve fits was also noted in B11.</text>
<text><location><page_7><loc_8><loc_46><loc_48><loc_54></location>Instead of attempting an absolute prediction with the KRW09 models, we have instead used these models as a perturbation on the salt-ii model. In short, the salt-ii model describes the stretch and color relations, while the KRW09 models are used to describe the intrinsic scatter. The spectral flux ( F ) is given by</text>
<formula><location><page_7><loc_15><loc_42><loc_48><loc_45></location>F = F SALT2 × F KRW09 (random cos φ ) F KRW09 (cos φ = 0) (5)</formula>
<text><location><page_7><loc_8><loc_40><loc_48><loc_41></location>where φ is the viewing angle. The corresponding mag-</text>
<table>
<location><page_7><loc_10><loc_10><loc_46><loc_33></location>
<caption>TABLE 4 Reduced Correlation Matrix from the C11 1 Model a and Realized from the Simulation</caption>
</table>
<text><location><page_7><loc_8><loc_5><loc_48><loc_8></location>b Diag = √ COV ii with i = U ' , U, B, V, R, I are from the PhD thesis and differ slightly from those given in Chotard et al. (2011).</text>
<text><location><page_7><loc_52><loc_87><loc_92><loc_90></location>shifts are illustrated in Figure 5 as a function of wavelength for a two extreme viewing angles.</text>
<text><location><page_7><loc_65><loc_83><loc_66><loc_84></location>φ</text>
<text><location><page_7><loc_81><loc_83><loc_81><loc_84></location>φ</text>
<text><location><page_7><loc_82><loc_83><loc_83><loc_84></location>-</text>
<figure>
<location><page_7><loc_54><loc_60><loc_90><loc_84></location>
<caption>Fig. 5.Magnitude shift applied to the salt-ii spectral model vs. wavelength for the KRW09 models. The solid and dashed curves reflect different viewing angles as indicated in the legend above the plots. The label on each panel indicates the specific explosion model as defined in Table 3.</caption>
</figure>
<section_header_level_1><location><page_7><loc_67><loc_50><loc_77><loc_52></location>4. ANALYSIS</section_header_level_1>
<text><location><page_7><loc_52><loc_45><loc_92><loc_50></location>Here we describe the determination of the three scatter-dependent quantities used to evaluate models of intrinsic brightness variations. All analyses are based on light curve fits using the salt-ii model.</text>
<section_header_level_1><location><page_7><loc_62><loc_42><loc_83><loc_44></location>4.1. Review of salt-ii Model</section_header_level_1>
<text><location><page_7><loc_52><loc_39><loc_92><loc_42></location>The salt-ii SN Ia model flux is a function of wavelength ( λ ) and time ( t ) in the rest-frame,</text>
<formula><location><page_7><loc_53><loc_36><loc_92><loc_38></location>F ( t, λ ) = x 0 [ M 0 ( t, λ ) + x 1 M 1 ( t, λ )] × exp[ c · CL( λ )] (6)</formula>
<text><location><page_7><loc_52><loc_23><loc_92><loc_36></location>where the spectral sequences ( M 0 and M 1 ) and color law (CL( λ )) are derived from the training in G10. Synthetic photometry in the observer frame is obtained by redshifting Eq. 6 and multiplying by the filter response and Galactic transmission. The overall scale ( x 0 ), stretch ( x 1 ), color ( c ) and time of peak brightness ( t 0 ) are determined for each SN in a light curve fit that minimizes a χ 2 based on the difference between the data and synthetic photometry. Eq. 6 is valid for 2000 < λ < 9200 ˚ A, and the model is valid for observer-frame filters that satisfy</text>
<formula><location><page_7><loc_61><loc_21><loc_92><loc_22></location>2800 < ¯ λ obs / (1 + z ) < 7000 ˚ A , (7)</formula>
<text><location><page_7><loc_52><loc_18><loc_87><loc_20></location>where ¯ λ obs is the central wavelength of the filter.</text>
<text><location><page_7><loc_52><loc_12><loc_92><loc_18></location>An effective B -band magnitude is defined to be m B = -2 . 5 log 10 ( x 0 ) + 10 . 635; this is the observed magnitude through an idealized filter that corresponds to the B band in the rest-frame of the SN. The fitted distance modulus is given by</text>
<formula><location><page_7><loc_62><loc_9><loc_92><loc_11></location>µ fit = m B -M + αx 1 -βc (8)</formula>
<text><location><page_7><loc_52><loc_5><loc_92><loc_9></location>where α , β and M are determined from a global fit to all of the SNe using the ' SALT2mu ' program described in M11 and below in Section 6.</text>
<section_header_level_1><location><page_8><loc_22><loc_89><loc_35><loc_90></location>4.2. Hubble Scatter</section_header_level_1>
<text><location><page_8><loc_8><loc_79><loc_48><loc_88></location>The well known Hubble scatter is defined as the dispersion on ∆ µ , the difference between the fitted (measured) distance modulus and the distance modulus calculated from the best-fit cosmological parameters. To simplify the analysis here we do not fit for the α and β parameters, nor do we fit for the best-fit cosmological parameters. Instead we compute the dispersion of</text>
<formula><location><page_8><loc_15><loc_76><loc_48><loc_78></location>∆ µ ≡ µ fit (Eq . 8) -µ calc ( z, Ω M , Ω Λ , w ) (9)</formula>
<text><location><page_8><loc_8><loc_66><loc_48><loc_76></location>where α = 0 . 11, β = 3 . 2, M = -19 . 36 ( H 0 = 70 km s -1 Mpc -1 ), and µ calc is the calculated distance modulus assuming a ΛCDM cosmology with w = -1, Ω M = 0 . 3, Ω Λ = 0 . 7. Although the fitted α and β may have given slightly different ∆ µ values, the resulting bias is more than an order of magnitude smaller than the dispersion, and hence the impact of this approximation is negligible.</text>
<section_header_level_1><location><page_8><loc_21><loc_64><loc_36><loc_65></location>4.3. Color Precision</section_header_level_1>
<text><location><page_8><loc_8><loc_54><loc_48><loc_63></location>The color precision test compares the fitted salt-ii color ( c ) to the true B -V rest-frame color at the epoch of peak brightness. Since the fitted color is really a color excess, c = E ( B -V ), and the color also depends slightly on the stretch, the true B -V color does not exactly correspond to c . A numerical examination of the model shows that with no intrinsic scatter,</text>
<formula><location><page_8><loc_10><loc_51><loc_48><loc_53></location>B -V = c ' = (1 . 016 × c ) + ( x 1 / 1250) + 0 . 0232 (10)</formula>
<text><location><page_8><loc_8><loc_34><loc_48><loc_51></location>and therefore we examine the dispersion on B -V -c ' . The dispersion on c -c ' is ∼ 0 . 001, more than an order of magnitude smaller than the dispersion on B -V -c ' , and thus this correction has little effect. The evaluation of c ' is from simply plugging the fitted c and x 1 values into Eq. 10. The naive rest-frame magnitudes M /star B and M /star V are obtained from Eq. 6 using the best-fit parameters ( c , x 0 , x 1 ) and using the B and V filter-transmission functions. However, these naive magnitudes are not necessarily the true values if there are intrinsic color variations. To obtain a better approximation for the magnitudes we fit only the two nearest observer-frame bands that bracket the B or V band in wavelength.</text>
<text><location><page_8><loc_8><loc_18><loc_48><loc_34></location>The details of the fitting procedure are as follows. First a normal fit is done using all filters to determine the fit parameters ( t 0 , c , x 0 , x 1 ). For each rest-frame band one additional fit is performed using only the two nearest observer-frame bands and holding t 0 and x 1 fixed from the normal fit. The floated color ( c ) and distance ( x 0 ) parameters provide the flexibility to fit both observerframe bands regardless of how much intrinsic color variation exists. The two-band fit parameters are c B , x B 0 for the B band, and c V , x V 0 for the V band. After finishing both two-band fits the B -V color is computed as</text>
<formula><location><page_8><loc_15><loc_14><loc_48><loc_19></location>B -V = M /star ( T B , t 0 , x 1 = 0 , c B , x B 0 ) -M /star ( T V , t 0 , x 1 = 0 , c V , x V 0 ) (11)</formula>
<text><location><page_8><loc_8><loc_9><loc_48><loc_14></location>where M /star is the magnitude computed from Eq. 6 using filter-transmission functions T B,V , and with x 1 = 0 so that all B -V colors correspond to an SN Ia with the same stretch.</text>
<text><location><page_8><loc_8><loc_5><loc_48><loc_9></location>This fitting procedure was tested on an SNLS3 simulation in which the maximum S/N was artificially set to 1000 for every SN regardless of redshift. The rms on</text>
<text><location><page_8><loc_52><loc_87><loc_92><loc_90></location>B -V -c ' is 0.002 mag, an order of magnitude smaller than the observed dispersion.</text>
<section_header_level_1><location><page_8><loc_64><loc_85><loc_80><loc_86></location>4.4. Photoz Precision</section_header_level_1>
<text><location><page_8><loc_52><loc_71><loc_92><loc_84></location>The photoz precision is based on the difference between the SN redshift determined from broad band photometry and the more precise spectroscopic redshift. The basic photoz method is to extend the usual methods of fitting light curves to include the redshift as a fifth fit parameter. Particular attention is needed to estimate initial parameter values near those corresponding to the global minimumχ 2 , and to iteratively determine which filters satisfy Eq. 7. Details of the photoz fitting process are given in K10.</text>
<text><location><page_8><loc_52><loc_48><loc_92><loc_71></location>There are two modifications in our photoz fitting procedure compared to K10. The first change is that we use the known spectroscopic redshift as the initial estimate in order to reduce catastrophic outliers. The fitting task has thus been changed to find a local photoz minimum near the true redshift instead of searching the entire redshift range for a global minimum. The second change is related to estimating the initial parameter x 0 for each color value along the coarse-grid search in color. In K10, x 0 at each grid point was calculated using the current color, photoz and a reference cosmology. Here we analytically minimize for x 0 , making the fitted photoz less sensitive to the absolute brightness. To check that the fitted photoz depends only on the SN colors we have applied this method to simulations with no intrinsic scatter and with the coherent scatter model (see COH entry in Table 3); the photoz precision is the same in both cases.</text>
<section_header_level_1><location><page_8><loc_63><loc_45><loc_81><loc_47></location>4.5. Statistics Summary</section_header_level_1>
<text><location><page_8><loc_52><loc_40><loc_92><loc_45></location>After applying the selection requirements in Section 2, along with the light curve fitting requirements for each dispersion variable, the number of SNe Ia for each sample and for each dispersion variable is shown in Table 5</text>
<text><location><page_8><loc_52><loc_29><loc_92><loc_39></location>The smaller photoz samples arise from a light curve fitting requirement. For each successive fit iteration, observer-frame filters are added or dropped based on which filters satisfy the salt-ii wavelength range in Eq. 7 with z = photoz . If any filter fails this wavelength requirement after the last fit iteration, the SN is rejected; this requirement avoids fitting to wavelength regions in which the salt-ii model may be poorly defined.</text>
<text><location><page_8><loc_52><loc_24><loc_92><loc_29></location>The smaller SNLS3 sample for the B -V -c ' analysis is due to SNe Ia at z > 0 . 7; for these objects the observerframe i and z bands no longer bound the rest-frame V band.</text>
<table>
<location><page_8><loc_56><loc_12><loc_88><loc_17></location>
<caption>TABLE 5 Number of SNe Ia After Selection Requirements.</caption>
</table>
<section_header_level_1><location><page_9><loc_17><loc_89><loc_40><loc_90></location>4.6. Quantifying the Dispersions</section_header_level_1>
<text><location><page_9><loc_8><loc_86><loc_48><loc_88></location>The data and MC dispersions are measured from the following variables,</text>
<formula><location><page_9><loc_18><loc_79><loc_48><loc_85></location>∆ µ ≡ ( µ fit -µ calc ) / (1 + z ) ∆ c ≡ ( B -V -c ' ) / (1 + z ) ∆ z ≡ ( Z phot -Z spec ) / (1 + z ) (12)</formula>
<text><location><page_9><loc_8><loc_64><loc_48><loc_79></location>where the (1 + z ) -1 factor is included to reduce the redshift-dependent variation from measurement uncertainties. These three quantities are shown in Figure 6 for the data and MC, and for both the SDSS-II and SNLS3 samples. The MC includes only Poisson noise (no intrinsic variation), and hence the data-MC difference in the width illustrates the size of the intrinsic component that is needed. The ∆ µ comparison shows the most obvious discrepancy. The ∆ z and ∆ c discrepancies are more subtle, indicating that the effect of color variations is smaller than the coherent variation.</text>
<figure>
<location><page_9><loc_9><loc_33><loc_48><loc_62></location>
<caption>Fig. 6.Comparison of ∆ µ , ∆ c and ∆ z distributions for data (dots) and MC (histogram). The upper plots are for the SDSS-II and lower plots are for SNLS3. The MC includes Poisson noise but no intrinsic brightness variation, and each MC distribution is scaled to have the same sample size as the data.</caption>
</figure>
<text><location><page_9><loc_8><loc_20><loc_48><loc_25></location>To quantify the dispersions we compute the median, M ∆ ≡ median | ∆ x | , where x = µ, z, c indicates the variable type. In particular, we compute the MC/data ratio of medians,</text>
<formula><location><page_9><loc_19><loc_17><loc_48><loc_19></location>R MC / Data = M MC ∆ /M Data ∆ . (13)</formula>
<text><location><page_9><loc_8><loc_13><loc_48><loc_17></location>With the correct model of brightness variations we expect R MC / Data = 1 for all three variables and for both surveys.</text>
<text><location><page_9><loc_8><loc_5><loc_48><loc_13></location>The uncertainty on the median is calculated as follows. For N SNe, the statistical uncertainty on N/ 2 is σ ( N/ 2) = √ N/ 2. The median uncertainty ( σ M ) is defined such that N -σ ( N/ 2) values of | ∆ x | lie below M -σ -M and N + σ ( N/ 2) values lie below M + σ + M . For a rapidly falling</text>
<text><location><page_9><loc_52><loc_86><loc_92><loc_90></location>distribution we typically find that σ + M > σ -M . Here we define a symmetric uncertainty, σ M ≡ ( σ -M + σ + M ) / 2.</text>
<text><location><page_9><loc_52><loc_76><loc_92><loc_87></location>As a numerical crosscheck we analyze SDSS-II simulations in which the exposure time is adjusted for each SN so that the maximum S/N is 10 4 . The resulting dispersions, defined simply as a Gaussian fitted σ , are 0 . 0003, 0 . 002, and 0 . 001 mag for the three variables (Eq. 12), respectively; these dispersions are more than an order of magnitude smaller than the dispersions observed in the data.</text>
<section_header_level_1><location><page_9><loc_67><loc_74><loc_77><loc_75></location>5. RESULTS</section_header_level_1>
<text><location><page_9><loc_52><loc_44><loc_92><loc_73></location>The MC/data ratio of medians, R MC / Data (Eq. 13), is shown in Figure 7 for all of the models in Table 3, and for both surveys. With no model of intrinsic scatter, R MC / Data is well below unity in all cases. Adding a coherent scatter (FUN-COH) predicts the Hubble dispersion (∆ µ ), but has no impact on the color and photoz dispersion. The FUN-COLOR model almost predicts the Hubble dispersion, but may overestimate the color precision. FUN-MIX has been artificially tuned to predict the dispersion in all quantities, although the photoz dispersion may still be underestimated. The G10, C11 0 and C11 1 models provide decent predictions, with a slight underestimate in the photoz dispersion. The C11 2 model underestimates the Hubble dispersion. Recall that the G10 model includes only positive correlations, mainly from the coherent term σ COH = 0 . 09, while the C11 model includes both positive and negative correlations. This G10 versus C11 comparison illustrates that there can be significant degeneracies among models of intrinsic brightness variations. The KRW09 models give a poorer description of the dispersion because the Hubble dispersion is always underestimated.</text>
<section_header_level_1><location><page_9><loc_64><loc_41><loc_80><loc_43></location>5.1. Systematics Tests</section_header_level_1>
<text><location><page_9><loc_52><loc_33><loc_92><loc_41></location>Here we describe some systematics tests to demonstrate the robustness of the results in Figure 7. We use the FUN-COH scatter model as the reference simulation for these tests which are summarized in Figure 8. For each test a change is applied to the simulation and then analyzed in exactly the same manner.</text>
<text><location><page_9><loc_52><loc_24><loc_92><loc_33></location>The first test is based on the precision in the flux uncertainties in the data. For pre-explosion epochs in which the true SN flux is known to be zero, examining the S/N distribution shows that the uncertainties are accurate to within 5%. The test labeled σ SIM × 1 . 05 corresponds to a simulation with 5% larger uncertainties on all of the fluxes.</text>
<text><location><page_9><loc_52><loc_18><loc_92><loc_24></location>The next set of tests is based on a 0.02 mag zeropoint change in each filter ( δ ZPT griz ). Note that this change is two times larger than the uncertainty reported by each survey team.</text>
<text><location><page_9><loc_52><loc_13><loc_92><loc_18></location>Uncertainties on the Galactic extinction are examined by first increasing the estimated 16% scatter to 24% ( × 1 . 5 MW-Gal), and then increasing the reddening parameter by 10%, to R V = 3 . 4.</text>
<text><location><page_9><loc_52><loc_10><loc_92><loc_13></location>The next test is based on changing β from 3.2 to 2.5, a 5 σ change from G10.</text>
<text><location><page_9><loc_52><loc_5><loc_92><loc_10></location>The next two tests are based on changing the population parameters for x 1 and c (Table 1). The simulated x 1 population is shifted toward faster-declining light curves by setting σ + = 0 . 5 and σ -= 1 . 8 (compare to nomi-</text>
<figure>
<location><page_10><loc_9><loc_24><loc_90><loc_74></location>
<caption>Fig. 7.R MC / Data for ∆ µ,z,c as indicated in the legend panel. Solid-filled symbols are for the SDSS-II and open symbols are for SNLS3. The intrinsic variation model for the simulation is indicated at the top of each panel.</caption>
</figure>
<figure>
<location><page_11><loc_11><loc_36><loc_44><loc_90></location>
<caption>Fig. 8.R MC / Data for ∆ µ,z,c as indicated in the legend panel from Figure 7. The first panel is for the FUN-COH scatter model using the nominal simulation. The systematic test indicated above each panel is applied to the simulation using the same FUN-COH scatter model. The horizontal dashed lines are the same in each panel, and are intended to guide the eye.</caption>
</figure>
<text><location><page_11><loc_8><loc_20><loc_48><loc_27></location>nal parameters in Table 1). The simulated color population is shifted toward the red by setting σ + = 0 . 18 and σ -= 0 . 05. For these systematic tests, the resulting data/MC comparisons for stretch and color are shown in Figure 9; the data and MC are clearly discrepant.</text>
<text><location><page_11><loc_8><loc_13><loc_48><loc_20></location>For all of these systematic tests, R MC / Data remains significantly below unity for the B -V -c ' and photoz variables. We also note that the independent SDSS-II and SNLS3 results are consistent, showing consistency over different redshift ranges.</text>
<section_header_level_1><location><page_11><loc_9><loc_10><loc_48><loc_12></location>6. IMPACT OF INTRINSIC SCATTER MODEL ON THE HUBBLE DIAGRAM</section_header_level_1>
<text><location><page_11><loc_8><loc_5><loc_48><loc_9></location>Here we investigate the potential Hubble diagram bias from using an incorrect model of intrinsic scatter. We use four intrinsic scatter models that give reasonable</text>
<figure>
<location><page_11><loc_53><loc_68><loc_91><loc_90></location>
<caption>Fig. 9.Comparison of fitted stretch ( x 1 ) and color ( c ) distributions for data (dots) and modified MC (histogram), where each MC distribution is scaled to have the same statistics as the data. The simulated populations have been modified for systematic tests explained in the text.</caption>
</figure>
<text><location><page_11><loc_52><loc_53><loc_92><loc_59></location>data/MC agreement in Figure 7: FUN-MIX, G10, C11 0 and C11 1. Recall that data/MC agreement in these dispersion variables means that the intrinsic scatter model cannot be ruled out, but the agreement does not ensure that the underlying model is correct.</text>
<text><location><page_11><loc_52><loc_35><loc_92><loc_52></location>The Hubble bias is determined from the difference between an ideal analysis using the correct intrinsic scatter matrix (Section 6.1), and a conventional analysis that adds a wavelength-independent scatter to bring the reduced χ 2 to unity (Section 6.2). The ideal analysis is based on simulations with the correct model of intrinsic scatter, and thus does not reflect a realistic analysis that could be applied to data. The conventional analysis, however, reflects a realistic analysis that has often been applied to data. In Section 6.3 the Hubble bias is translated into a bias on the dark energy equation of state parameter w , and in Section 6.4 the biases are reevaluated with Malmquist bias corrections.</text>
<section_header_level_1><location><page_11><loc_56><loc_33><loc_88><loc_34></location>6.1. Determining the Intrinsic-scatter Matrix</section_header_level_1>
<text><location><page_11><loc_52><loc_25><loc_92><loc_32></location>To evaluate the effect of intrinsic scatter in the analysis of cosmological parameters, we first need to briefly summarize the concept of an intrinsic scatter matrix introduced in Section 2 of M11. Cosmology fitters in general minimize the function</text>
<formula><location><page_11><loc_61><loc_22><loc_92><loc_25></location>χ 2 = ∑ i ∆ µ i / ( σ stat ,i 2 + σ int ,i 2 ) (14)</formula>
<text><location><page_11><loc_52><loc_9><loc_92><loc_21></location>where ∆ µ i is the difference between the fitted and calculated distance modulus (Eq. 9) for the ith SN, σ stat ,i is the statistical (fitted) error on ∆ µ i , and σ int ,i is an ad hoc parameter defined so that χ 2 /N dof = 1. Since σ stat ,i is computed from a statistical correlation matrix between the salt-ii fit parameters ( m B , x 1 , c ), M11 proposed an analogous 'intrinsic-scatter covariance matrix' (denoted Σ) to compute σ int . Dropping the SN index i , the ad-hoc error term is</text>
<formula><location><page_11><loc_60><loc_4><loc_92><loc_8></location>σ 2 int =Σ 00 + α 2 Σ 11 + β 2 Σ cc +2 α Σ 01 -2 β Σ 0 c -2 αβ Σ 1 c , (15)</formula>
<text><location><page_12><loc_8><loc_70><loc_48><loc_90></location>where the subscript correspondence is 0 , 1 , c → m B , x 1 , c , √ Σ 00 ≡ σ int m B , √ Σ 11 ≡ σ int x 1 , and √ Σ cc ≡ σ int c . All SNIacosmology analyses to date have used the simplifying assumption that σ int = σ int m B = √ Σ 00 , and ignored the other Σ terms in Eq. 15. We refer to this method as the ' m B -only' method, while the Σ-fit method refers to using additional terms in Eq. 15. The m B -only method is valid if the intrinsic scatter is independent of wavelength, or if σ stat ,i from the light curve fit includes the wavelength dependence of the scatter. The FUN-COH panel in in Figure 7 clearly shows that the intrinsic scatter cannot be constant (i.e., wavelength independent). M11 noted that using the m B -only method can lead to biased values of α and β . Here we go a step further and examine biases in simulated Hubble diagrams.</text>
<text><location><page_12><loc_8><loc_45><loc_48><loc_70></location>Since we do not have reliable methods for determining Σ from the data, we determine Σ from an artificial analysis using a simulation with the correct model of intrinsic scatter but without Poisson fluctuations from the calculated measurement uncertainties (Eq. 4); therefore the only source of scatter is from intrinsic variations. Although Poisson fluctuations are not applied, the uncertainties are included in the light curve fitχ 2 calculations so that the correct filter-dependent weights are used. For example, the SDSS u band has relatively poor S/N compared to the other bands and therefore this passband has less weight in determining Σ. We refer to these simulations as 'intrinsic-only' to distinguish them from the 'nominal' simulations that include Poisson fluctuations. This intrinsic-only simulation is illustrated in Figure 10 for the special case with no intrinsic scatter; the simulated fluxes lie exactly on the best-fit salt-ii model and they have the correct uncertainties corresponding to real observations.</text>
<text><location><page_12><loc_8><loc_29><loc_48><loc_45></location>To better compare the resulting bias to the uncertainty reported in Sullivan et al. (2011), the simulations have been adjusted to better match the data sample used in this SNLS3 analysis. First, the SDSS-II sample size is reduced by a factor of three to correspond to the firstseason sample used in the SNLS3 analysis. The next change is that the S/N requirement in the three passbands (see end of Section 2) is relaxed from 8 to 5. Finally, we have included a simulated nearby ( z < 0 . 1) sample as explained in the Appendix. To measure biases with good precision, the MC sample sizes correspond to 20 times the data statistics.</text>
<text><location><page_12><loc_8><loc_14><loc_48><loc_29></location>After performing salt-ii light curve fits on the simulated intrinsic-only sample, we define ∆ SIM m B ≡ m B (fit) -m B (true) and ∆ SIM c ≡ c (fit) -c (true), where 'true' indicates the true value from the simulation and 'fit' indicates the result from a light curve fit. The true values are defined by the underlying salt-ii model before the intrinsic smearing model is applied. The covariance terms with the stretch parameter x 1 are negligible because the intrinsic scatter models are epoch-independent and thus do not change the light curve shape; the x 1 -terms in Σ are therefore ignored.</text>
<text><location><page_12><loc_10><loc_12><loc_45><loc_14></location>The 2 × 2 intrinsic scatter matrix is defined to be</text>
<formula><location><page_12><loc_19><loc_4><loc_48><loc_11></location>√ Σ 00 = σ int m B = rms | ∆ SIM m B | √ Σ cc = σ int c = rms | ∆ SIM c | Σ 0 c = 〈 ∆ SIM m B ∆ SIM c 〉 , (16)</formula>
<text><location><page_12><loc_52><loc_72><loc_92><loc_90></location>where 〈〉 indicates the mean value of the enclosed quantity. Another caveat is that Σ depends on the redshift and on which filters are included in the light curve fit. This dependence is linked to the salt-ii color parameter ( c ) that is evaluated by extrapolating a color law to the central wavelengths of the B and V passbands. To address this caveat, Σ is evaluated as a function of redshift and sample as shown in Figure 11. A second-order polynomial function of redshift is adequate to describe the components of Σ. For the FUN-MIX and G10 models, σ int m B and βσ int c give a comparable contribution ( ∼ 0 . 1) to σ int . For the C11 models, σ int m B ∼ 0 . 03 is much smaller than the contribution from βσ int c .</text>
<section_header_level_1><location><page_12><loc_56><loc_70><loc_89><loc_71></location>6.2. Fitting for α , β , and the Distance Moduli</section_header_level_1>
<text><location><page_12><loc_52><loc_33><loc_92><loc_69></location>Using the fitted salt-ii parameters and uncertainties from the nominal MC, we use the SALT2mu program (M11) to minimize Eq. 14. This minimization gives the best-fit values of α and β , along with an independent offset ( M z ) in each 0.1-wide redshift bin (Eq. 8). The separate offsets are used to eliminate the µ -dependence on cosmological parameters. These fitted parameters are used to compute a distance modulus for each SN, and the resulting redshift+distance pairs form a Hubble diagram that can be fit for cosmological parameters. To properly evaluate the fit χ 2 using the scatter matrix Σ, the light curve fits have been done with the salt-ii model uncertainties set to zero (hence reducing σ stat ,i ) because they are now included in the SALT2mu fit as part of the σ int calculation. This modification only affects the SALT2mu χ 2 and has a negligible impact on the fitted parameters. The m B -only fit is based on the traditional method of tuning σ int m B such that χ 2 /N dof = 1, while setting all of the other covariance terms to zero. The light curve fits include the salt-ii model errors, and hence the intrinsic uncertainties corresponding to the G10 model are included. We note that there is an improved statistical treatment in March et al. (2011), using a Bayesian hierarchical model. While they obtain an uncertainty on σ int m B , their scatter model is fundamentally the same as our m B -only model because they do not include additional covariance terms.</text>
<text><location><page_12><loc_52><loc_20><loc_92><loc_33></location>The SALT2mu fit results for both intrinsic scatter methods ( m B -only and Σ) are shown in Table 6. For both methods the fitted values of α agree well with the simulated input, α SIM = 0 . 11. For the FUN-MIX and G10 scatter models, the fitted values of β agree well with the simulated input ( β SIM = 3 . 2) for both methods. For the C11 models, however, the situation is quite different. The m B -only fitted β values are too low by 0.3-0.6, and the significance of this bias ranges from 6 to 15 standard deviations. The Σ-fit β values are consistent with β SIM .</text>
<figure>
<location><page_12><loc_55><loc_9><loc_90><loc_18></location>
<caption>Fig. 10.Simulated SDSS-II light curve (solid dots) with no Poisson noise and no intrinsic scatter. Each curve is the best-fit salt-ii model.</caption>
</figure>
<text><location><page_13><loc_9><loc_73><loc_91><loc_74></location>α and β Fit Results from Simulations with Different Intrinsic-scatter Models, and w -bias Results from Cosmology Fits</text>
<table>
<location><page_13><loc_18><loc_26><loc_80><loc_71></location>
<caption>TABLE 6 a</caption>
</table>
<unordered_list>
<list_item><location><page_13><loc_9><loc_23><loc_40><loc_24></location>a Bias uncertainties are MC statistical uncertainties.</list_item>
<list_item><location><page_13><loc_9><loc_22><loc_24><loc_23></location>b Simulated α SIM = 0 . 11.</list_item>
<list_item><location><page_13><loc_9><loc_21><loc_24><loc_22></location>c Simulated β SIM = 3 . 20.</list_item>
<list_item><location><page_13><loc_9><loc_20><loc_73><loc_21></location>d For m B -only method, correction is from simulation using fitted β value and G10 intrinsic scatter model.</list_item>
</unordered_list>
<text><location><page_14><loc_8><loc_79><loc_48><loc_90></location>The reduced χ 2 values are close to unity for the m B -only method because of the explicit σ int m B tuning. However, there is no such tuning for the Σ-fit method and the reduced χ 2 are within about 10%-20% of unity. In summary, using the correct intrinsic scatter matrix Σ in the SALT2mu fit results in unbiased β values, and χ 2 /N dof /similarequal 1. Using the simplistic m B -only method results in a significant bias on β for the C11 models.</text>
<text><location><page_14><loc_8><loc_71><loc_48><loc_79></location>Since the Σ-fit method results in unbiased β values we define the µ -bias to be ∆ µ = µ mB -only -µ Σ : µ Σ is the distance modulus from the Σ-fit method and µ mB -only is the distance from the m B -only method. Figure 12 displays ∆ µ versus redshift for each scatter model. For the FUN-MIX and G10 scatter models, the maximum</text>
<text><location><page_14><loc_9><loc_64><loc_11><loc_65></location>σ</text>
<text><location><page_14><loc_9><loc_51><loc_11><loc_51></location>σ</text>
<text><location><page_14><loc_9><loc_37><loc_11><loc_38></location>σ</text>
<text><location><page_14><loc_9><loc_23><loc_11><loc_24></location>σ</text>
<figure>
<location><page_14><loc_9><loc_16><loc_47><loc_69></location>
<caption>Fig. 11.Elements of intrinsic scatter matrix (Σ ) for the simulated models indicated above each set of plots. The panels show the following parameters vs. redshift: σ m B = √ Σ 00 (left), 3 σ c = 3 √ Σ cc (middle), and ρ m B ,c = Σ 0 c / ( σ m B σ c ) (right). The 'int' superscripts have been dropped for clarity. Note that σ m B and 3 σ c are in roughly the same units as the scatter in the distance modulus residual. The simulated SNLS3 (SDSS-II) samples are indicated by solid (open) circles. Each solid curves represents a second-order polynomial function of redshift used to describe Σ.</caption>
</figure>
<text><location><page_14><loc_52><loc_70><loc_92><loc_90></location>∆ µ variation is only ∼ 0 . 01 mag over the redshift range of each survey. For the C11 models ∆ µ varies by several hundredths over the redshift range of each survey. This µ -bias is caused by the bias in β combined with Malmquist bias that results in bluer SN with increasing redshift. Figure 13 shows the mean fitted color value versus redshift, and the corresponding µ -bias is ∆ µ /similarequal ∆ β × 〈 c fit 〉 where ∆ β is the bias in β and 〈 c fit 〉 is the mean salt-ii color. The redshift dependence on ∆ µ is therefore directly proportional to the redshift dependence of 〈 c fit 〉 . Figure 13 also shows the mean fitted stretch parameter ( x 1 ) versus redshift. However, since the corresponding bias on α is less than 0 . 01, the resulting µ -bias is less than 0 . 01 × 0 . 3 ∼ 0 . 003, and is thus much smaller than the bias from the color term.</text>
<text><location><page_14><loc_52><loc_44><loc_92><loc_70></location>To summarize, these bias tests show that the G10 model is internally consistent and that the wavelength dependence of the intrinsic scatter can be described with both methods. In the first method the scatter is described by the uncertainties in the salt-ii light curve fitting model, and the m B -only scatter matrix is used in the SALT2mu stage. In the second Σ-fit method the light curve fitting model uncertainties are set to zero and the full intrinsic scatter matrix is used in the SALT2mu fitting stage. The difference in results between these two methods, as applied to simulations based on the G10 model, is negligible. However, if the simulated scatter model includes large anti-correlations such as those suggested by C11, then these two methods are not consistent and the traditional m B -only method results in a significant redshift-dependent bias in the distance moduli (Figure 12). More specifically, the bias is a result of incorrectly using the salt-ii (i.e., G10) uncertainties in the light curve fits of the samples generated with the C11 model.</text>
<text><location><page_14><loc_52><loc_36><loc_54><loc_36></location>µ</text>
<text><location><page_14><loc_52><loc_35><loc_54><loc_35></location>-</text>
<text><location><page_14><loc_52><loc_31><loc_54><loc_31></location>µ</text>
<text><location><page_14><loc_52><loc_22><loc_54><loc_23></location>µ</text>
<text><location><page_14><loc_52><loc_21><loc_54><loc_22></location>-</text>
<text><location><page_14><loc_52><loc_17><loc_54><loc_18></location>µ</text>
<figure>
<location><page_14><loc_52><loc_12><loc_91><loc_40></location>
<caption>Fig. 12.Average difference between the distance modulus from the m B -only fit and that from the Σ-fit, vs. redshift. The simulated (true) scatter model is indicated in each panel. The simulated samples are nearby (solid triangles), SDSS-II (open circles), and SNLS3 (solid circles).</caption>
</figure>
<text><location><page_15><loc_29><loc_89><loc_30><loc_89></location>></text>
<text><location><page_15><loc_29><loc_88><loc_30><loc_89></location>fit</text>
<text><location><page_15><loc_29><loc_87><loc_30><loc_88></location>x</text>
<figure>
<location><page_15><loc_10><loc_77><loc_30><loc_90></location>
<caption>Figure 14 shows the µ -bias versus redshift with the Malmquist correction applied. Overall the redshiftdependent bias is smaller than for the uncorrected distances in Figure 12, but the bias is still significant for the C11 models. The bias is zero for the G10 model because the fitted light curve model (G10) corresponds to the correct model of intrinsic scatter. The Malmquistcorrected w -bias results are shown in the last column of Table 6. Compared to the bias from the uncorrected Hubble diagrams, the w -bias is typically smaller when the Malmquist correction is applied.</caption>
</figure>
<figure>
<location><page_15><loc_30><loc_77><loc_47><loc_90></location>
</figure>
<text><location><page_15><loc_29><loc_87><loc_30><loc_87></location><</text>
<paragraph><location><page_15><loc_8><loc_68><loc_48><loc_76></location>Fig. 13.Mean fitted salt-ii color vs. redshift for the nearby (solid triangles), SDSS-II (open blue circles) and SNLS3 (solid red circles) simulation. Right panel shows mean fitted salt-ii stretch parameters ( x 1 ) vs. redshift. Although this simulation uses the G10 intrinsic scatter model, there is little difference for the other scatter models. Also note that the analogous plots in the bottom panels of Figures 1 and 2 show a larger variation because of the more strict selection requirement of three passbands with S/N > 8.</paragraph>
<section_header_level_1><location><page_15><loc_19><loc_63><loc_38><loc_64></location>6.3. Estimating the w -bias</section_header_level_1>
<text><location><page_15><loc_8><loc_47><loc_48><loc_62></location>To estimate the bias on the dark energy parameter w , we fit the simulated Hubble diagram in a manner similar to that described in Section 8 of K09. The effect of Malmquist corrections is discussed later in Section 6.4. The w -bias is defined to be the difference between w obtained from the m B -only method and the Σ-fit method. Priors are included from measurements of baryon acoustic oscillations from the SDSS Luminous Red Galaxy sample (Eisenstein et al. 2005) and from the cosmic microwave background temperature anisotropy measured from the Wilkinson Microwave Anistropy Probe (Komatsu et al. 2009).</text>
<text><location><page_15><loc_8><loc_29><loc_48><loc_46></location>Since the simulated SN sample consists of 20 times the data statistics, the uncertainties on the priors have been reduced by a factor of √ 20. We checked this procedure by splitting the simulated sample into 20 independent sub-samples and fitting each sub-sample with the nominal priors; the average of the 20 fitted w -values is in good agreement with that from using the full simulation and priors with reduced uncertainties. The β -bias and Malmquist-uncorrected w -bias values are defined as the difference between the m B -only and Σ-fit methods, and they are shown in Table 6. The uncertainty on the w -bias is given by rms / √ 20, where rms is the dispersion among the 20 independent w -bias measurements.</text>
<text><location><page_15><loc_8><loc_5><loc_48><loc_29></location>For the FUN-MIX and G10 models the w -bias is small ( < 0 . 02) for all sample combinations. This small bias is expected since the fitted β and distance moduli show a very small bias. For the C11 models, the w -bias is larger. Fitting the SDSS-II or SNLS3 sample alone, the w -bias is ∼ 0 . 07 for the C11 0 model and ∼ 0 . 12 for the C11 1 model. Combining the SDSS-II + SNLS3 samples, the w -bias is reduced by a factor of ∼ 2 for each of the C11 models. Including the nearby sample (nearby+SDSSII+SNLS3) the w -bias is further reduced: 0 . 01 and 0 . 02 for the C11 0 and C11 1 models, respectively. The reduction in w -bias as more samples are combined is a result of the fortuitous circumstance that the mean saltii color for each sample is very close: -0 . 005, -0 . 015, and -0 . 005 for the nearby, SDSS-II, and SNLS3, respectively. To illustrate this point we have redone the analysis using a simulated nearby sample that has no Malmquist bias and a mean salt-ii color that is 0.06 mag</text>
<text><location><page_15><loc_52><loc_87><loc_92><loc_90></location>redder than the data; the resulting w -bias on the combined nearby+SDSS-II+SNLS3 sample increases to 0.05.</text>
<section_header_level_1><location><page_15><loc_55><loc_85><loc_90><loc_86></location>6.4. Monte Carlo Correction for Malmquist Bias</section_header_level_1>
<text><location><page_15><loc_52><loc_71><loc_92><loc_84></location>In Section 6.3 the w -bias is determined without accounting for differences in the Malmquist bias correction. While the true Malmquist bias should not depend on the analysis method ( m B -only versus Σ-method), here we show that the evaluated Malmquist bias, using the fitted value of β , does indeed depend on the analysis method. In addition, using the evaluated Malmquist bias reduces the µ -bias shown in Figure 12. In the discussion below, 'MqSIM' refers to the simulation used to evaluate the Malmquist bias correction.</text>
<text><location><page_15><loc_52><loc_52><loc_92><loc_71></location>For the Σ-fit method the MqSIM uses the correct model of intrinsic scatter and the correct α and β parameters. In principle the intrinsic-scatter matrix would have to be translated into a wavelength-dependent scatter model for the simulation, but we have not preformed this step. For the m B -only method the MqSIM for each sample uses the G10 model and the fitted (biased) value of β fit from Table 6. This procedure is used because it closely reflects the procedure in previous analyses. The distance-modulus corrections are from a second-order polynomial fit to µ fit -µ true versus redshift: µ true is the true distance modulus in the MqSIM, and µ fit is the distance computed from the SALT2-fitted parameters (color and stretch) and the simulated values of α and β .</text>
<text><location><page_15><loc_52><loc_28><loc_92><loc_38></location>While using an incorrect model of intrinsic scatter can lead to a significant bias in the Hubble diagram, this bias is somewhat reduced by simply applying a simulated Malmquist bias correction using the fitted value of β in the simulation. The bias reduction depends on the intrinsic scatter model, and we cannot rule out increased sensitivity on other systematic effects.</text>
<section_header_level_1><location><page_15><loc_65><loc_26><loc_79><loc_27></location>7. CONCLUSIONS</section_header_level_1>
<text><location><page_15><loc_52><loc_10><loc_92><loc_25></location>We have used high quality SDSS-II and SNLS3 data and simulations to show that SN Ia intrinsic brightness variations include wavelength dependent variations resulting in a color dispersion of ∼ 0 . 02 mag. A broad range of simulated intrinsic-scatter models (Table 3) is roughly consistent with the following photometric observables: Hubble scatter, dispersion in B -V -c ' , and photoz residuals. These models include the G10 model that is dominated by a coherent term and has only positive wavelength correlations, and the C11 model that has a small coherent term and large anti-correlations.</text>
<text><location><page_15><loc_52><loc_5><loc_92><loc_10></location>We have used these intrinsic scatter models in highstatistics simulations to test the standard procedure of adding a constant distance-modulus uncertainty ( σ int ) to the measured uncertainties so that χ 2 /N dof = 1 for</text>
<figure>
<location><page_16><loc_11><loc_64><loc_45><loc_89></location>
<caption>Fig. 14.Same as Figure 12, but after applying Malmquist bias correction.</caption>
</figure>
<text><location><page_16><loc_8><loc_27><loc_48><loc_58></location>cosmology fits to the SN Ia Hubble-diagram. The constant σ int assumption is valid if the light curve fits include model uncertainties with the correct wavelength dependence of the scatter. If these model uncertainties are not correct, such as using the salt-ii uncertainties to fit a simulated sample with large anti-correlations in the scatter (C11 model), then significant biases can appear in the Hubble diagram. For the specific simulation tests reported here the distance-modulus bias varies by up to 0.05 mag over the redshift range of the each survey, although this bias is roughly halved after applying Malmquist bias corrections. For the combined nearby+SDSS-II+SNLS3 simulated sample, which corresponds closely to the 472 SNe Ia analyzed in Sullivan et al. (2011), the w -bias is only ∼ 0 . 02, in part because the mean color for each sample is very nearly the same. While this w -bias is well below the total systematic uncertainty reported in Sullivan et al. (2011) ( δw syst = 0 . 06), there is no assurance that future analyses on larger data sets will benefit from the fortuitous cancellations. For example, replacing the biased nearby sample with an unbiased sample increases the w -bias to 0 . 05, comparable to the current systematic uncertainty.</text>
<text><location><page_16><loc_8><loc_18><loc_48><loc_27></location>We have also shown that applying a simulated Malmquist bias correction, based on the fitted (biased) β value, may reduce the bias from using an incorrect model of intrinsic scatter. However, we urge caution in relying on this apparent 'free lunch' because we have not fully explored if this naive correction increases the sensitivity to other systematic effects.</text>
<text><location><page_16><loc_8><loc_9><loc_48><loc_18></location>It is important not to interpret our results as proof that such biases exist in current SNIa-cosmology results; we have shown, for example, that this intrinsic scatter bias is negligible if the G10 model is correct. However, until the intrinsic scatter correlations can be better constrained, our results suggest that an additional systematic uncertainty should be included.</text>
<text><location><page_16><loc_52><loc_78><loc_92><loc_90></location>Although the intrinsic-scatter models considered here depend only on wavelength (except for the KRW09 models), the true behavior could include a dependence on epoch, color, stretch, and redshift. The impact of the scatter models on the salt-ii training is under investigation and will be published later. To obtain more robust systematic constraints on cosmological parameters, we encourage additional studies to measure or constrain the nature of intrinsic scatter.</text>
<text><location><page_16><loc_52><loc_71><loc_92><loc_78></location>J.F. and R.K. are grateful for the support of National Science Foundation grant 1009457, a grant from 'France and Chicago Collaborating in the Sciences' (FACCTS), and support from the Kavli Institute for Cosmological Physics at the University of Chicago.</text>
<text><location><page_16><loc_52><loc_48><loc_92><loc_71></location>The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPA), the MaxPlanck-Institute for Astrophysics (MPiA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.</text>
<text><location><page_16><loc_52><loc_9><loc_92><loc_47></location>This work is based in part on observations made at the following telescopes. The Hobby-Eberly Telescope (HET) is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximillians-Universitat Munchen, and Georg-August-Universitat Gottingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. The Marcario LowResolution Spectrograph is named for Mike Marcario of High Lonesome Optics, who fabricated several optical elements for the instrument but died before its completion; it is a joint project of the Hobby-Eberly Telescope partnership and the Instituto de Astronom'ıa de la Universidad Nacional Aut'onoma de M'exico. The Apache Point Observatory 3.5 m telescope is owned and operated by the Astrophysical Research Consortium. We thank the observatory director, Suzanne Hawley, and site manager, Bruce Gillespie, for their support of this project. The Subaru Telescope is operated by the National Astronomical Observatory of Japan. The William Herschel Telescope is operated by the Isaac Newton Group on the island of La Palma in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. The W.M. Keck Observatory is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.</text>
<section_header_level_1><location><page_17><loc_46><loc_89><loc_55><loc_90></location>APPENDIX</section_header_level_1>
<section_header_level_1><location><page_17><loc_32><loc_87><loc_69><loc_88></location>SIMULATION OF NEARBY SN IA SAMPLE</section_header_level_1>
<text><location><page_17><loc_8><loc_78><loc_92><loc_86></location>Here we describe the simulation of the nearby ( z < 0 . 1) SN Ia sample corresponding to the 123 nearby SNe Ia used in Conley et al. (2011). While the nearby SN data are from several surveys and filter sets, we simplify the simulation by considering only the CFA3-Keplercam light curves (Hicken et al. 2009) using the UBVr filters. The i band is dropped because it is outside the valid wavelength range of the salt-ii model. Since the CFA3-Keplercam simulation is a proxy for the entire nearby SN sample, we simulate the correct nearby-SN statistics corresponding to about half that of the SNLS3 sample.</text>
<text><location><page_17><loc_8><loc_63><loc_92><loc_78></location>Since we do not have the observing conditions (mainly PSF and sky noise) needed for the SNANA simulation, we adopt a different strategy. The basic idea is to use each observed SN to define an observational sequence. The observed redshift and time of peak brightness are used along with the cadence. A random salt-ii stretch and color are chosen for each SN, and the simulated S/N for each epoch is essentially scaled from the observed S/N. More technically, we artificially fixed the PSF to be 0 . 8 '' and then for each epoch compute the sky noise needed to simulate the observed uncertainty; this strategy allows generating nearby SNe in exactly the same manner as for the SDSS-II and SNLS3. With little knowledge of the spectroscopic selection criteria we cannot simulate the selection bias from first principles. We therefore modified the population parameters in Table 1 so that the simulated color and stretch distributions match those of the nearby sample. For the generated color distribution the peak-probability value depends on redshift, -0 . 02 -z/ 2, and the Gaussian width parameters are σ -= 0 . 06 and σ + = 0 . 10. For the generated stretch distribution, the peak-probability value is reduced to 0.2.</text>
<text><location><page_17><loc_8><loc_58><loc_92><loc_63></location>The intrinsic-scatter matrix is determined for the nearby sample with the same procedure used on the SDSS-II and SNLS3 simulations, and using SALT2mu we have checked that the fitted β values are in good agreement with the simulated input, β SIM = 3 . 2. We have also examined the analogous data/MC comparisons in Figures 1 and 2, and find equally good agreement.</text>
<section_header_level_1><location><page_17><loc_45><loc_56><loc_55><loc_57></location>REFERENCES</section_header_level_1>
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</document>
[
{
"title": "ABSTRACT",
"content": "For spectroscopically confirmed Type Ia supernovae we evaluate models of intrinsic brightness variations with detailed data/Monte Carlo comparisons of the dispersion in the following quantities: Hubble-diagram scatter, color difference ( B -V -c ) between the true B -V color and the fitted color ( c ) from the salt-ii light curve model, and photometric redshift residual. The data sample includes 251 ugriz light curves from the three-season Sloan Digital Sky Survey-II and 191 griz light curves from the Supernova Legacy Survey 3 year data release. We find that the simplest model of a wavelengthindependent (coherent) scatter is not adequate, and that to describe the data the intrinsic-scatter model must have wavelength-dependent variations resulting in a ∼ 0 . 02 mag scatter in B -V -c . Relatively weak constraints are obtained on the nature of intrinsic scatter because a variety of different models can reasonably describe this photometric data sample. We use Monte Carlo simulations to examine the standard approach of adding a coherent-scatter term in quadrature to the distance-modulus uncertainty in order to bring the reduced χ 2 to unity when fitting a Hubble diagram. If the light curve fits include model uncertainties with the correct wavelength dependence of the scatter, we find that this approach is valid and that the bias on the dark energy equation of state parameter w is much smaller ( ∼ 0 . 001) than current systematic uncertainties. However, incorrect model uncertainties can lead to a significant bias on the distance moduli, with up to ∼ 0 . 05 mag redshift-dependent variation. This bias is roughly reduced in half after applying a Malmquist bias correction. For the recent SNLS3 cosmology results we estimate that this effect introduces an additional systematic uncertainty on w of ∼ 0 . 02, well below the total uncertainty. This uncertainty depends on the choice of viable scatter models and the choice of supernova (SN) samples, and thus this small w -uncertainty is not guaranteed in future cosmology results. For example, the w -uncertainty for SDSS+SNLS (dropping the nearby SNe) increases to ∼ 0 . 04. Subject headings: supernova",
"pages": [
1
]
},
{
"title": "TESTING MODELS OF INTRINSIC BRIGHTNESS VARIATIONS IN TYPE IA SUPERNOVAE, AND THEIR IMPACT ON MEASURING COSMOLOGICAL PARAMETERS",
"content": "Richard Kessler, 1,2 Julien Guy, 3 John Marriner, 4 Marc Betoule, 3 Jon Brinkmann, 5 David Cinabro, 6 Patrick El-Hage, 3 Joshua A. Frieman, 1,2,4 Saurabh Jha, 7 Jennifer Mosher, 8 and Donald P. Schneider 9,10 accepted by ApJ",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "For more than a decade Type Ia supernovae (SN Ia) have been used as standardizable candles to measure luminosity distances. These distances, along with the associated redshifts, have been used to measure properties of dark energy (Riess et al. 1998; Perlmutter et al. 1999; Riess et al. 2004; Astier et al. [email protected] 2006; Wood-Vasey et al. 2007; Freedman et al. 2009; Kessler et al. 2009a; Conley et al. 2011). The uncorrected variation in the SN Ia peak brightness is ∼ 1 mag, and this variation is reduced to ∼ 0 . 1 mag after empirical corrections based on the measured stretch (Phillips 1993) and color (Riess et al. 1996; Tripp 1997). This 0.1 mag intrinsic scatter increases the scatter in the Hubble diagram well beyond what is expected from the distance modulus uncertainties, and the resulting cosmology fits have reduced chi-squared ( χ 2 r ≡ χ 2 /N dof ) significantly larger than unity. To obtain χ 2 r = 1, all SNIa-cosmology analyses to date have introduced an ad hoc intrinsicscatter term ( σ int ∼ 0 . 1 mag) that is added in quadrature to the measured distance modulus uncertainties. This procedure of adding a constant ad hoc scatter term would be correct if the unknown source of intrinsic variation is independent of redshift, and if it is fully coherent such that the variation is the same for all wavelengths and passbands. Kessler et al. (2010, hereafter K10) found evidence contradicting a coherent variation in a study comparing the photoz precision between data and Monte Carlo simulations (MC). Using the coherent-scatter model in the MC underestimated the fitted photoz precision observed in the data, while simulating a model using color variations gave better agreement. Guy et al. (2010, hereafter G10) examined residuals from the salt-ii training and showed that the variation about the best-fit spectral model is wavelength dependent; this wavelength-dependent uncertainty is included in the light curve fitting model. Marriner et al. (2011, hereafter M11) presented a more formal treatment of σ int based on an intrinsic scatter covariance matrix that depends on a coherent term, a stretch term, and a color term. 11 They compared Sloan Digital Sky Survey-II (SDSS-II) SN Ia data and simulations within this framework and suggest that the coherent and color terms are significant, while the stretch term is negligible. The importance of understanding the nature of intrinsic scatter is tied to understanding systematic uncertainties in cosmology analyses using SNe Ia. If this scatter is truly random, as suggested by explosion models showing brightness variation with viewing angle (Kasen et al. 2009, hereafter KRW09), then there is no intrinsic bias and the uncertainty will decrease with increasing sample size. Even in this optimistic scenario a wavelengthdependent scatter results in a redshift-dependent dispersion because with broadband filters different rest-frame wavelengths are probed as a function of redshift. This variation must be properly accounted for, except in the hypothetically ideal scenario of measuring high-quality spectra to determine synthetic magnitudes with the same rest-frame passbands at all redshifts. If this scatter depends on more subtle physics related to the explosion mechanism and the host-galaxy environment, there could be additional redshift-dependent effects not yet detected with current data samples, but that become apparent in future surveys with much larger samples. Significant effort to reduce this scatter has been attempted using near infrared (NIR) photometry and spectroscopic features. Mandel et al. (2011) report that optical+NIR photometry result in a Hubble scatter that is ∼ 30% smaller compared to using only optical data. A decade of effort on spectroscopic correlations can be summarized with results from three groups. Blondin et al. (2011) examined spectra from the CfA Supernova Program and used spectral features to reduce the Hubble scatter by at most 10%, albeit with only 2 σ significance. From the Berkeley SNIa Program, Silverman et al. (2012) examined 108 high quality SNe Ia with a spectrum taken within 5 days of maximum brightness and found similar results. The best Hubble scatter reduction was obtained by Bailey et al. (2009) using very high quality spectra from the Supernova Factory (Aldering et al. 2002). Using spectra within 2.5 days of peak brightness, they scanned every possible flux-ratio in ∼ 40 ˚ A bins and found a minimum Hubble scatter using the ratio F (642 nm) /F (443 nm); the resulting scatter is about 25% lower compared to the traditional photometric analysis with the salt-ii light curve model. To realize significant reductions ( ∼ 30%) in the Hubble scatter requires optical photometry combined with either rest-frame NIR photometry or very high quality spectra near the epoch of peak brightness. Both of these supplemental data samples are difficult to obtain at low redshift, and it is not yet clear what resources could be allocated to obtain large data samples for higher redshift SNe that are needed to construct a cosmologically inter- ting Hubble diagram. Given the unlikely prospects for significantly reducing the Hubble scatter, we take a different approach here and explore models to describe the scatter in more detail. Such models of intrinsic scatter can be used to evaluate and constrain systematic uncertainties from assuming an incorrect model, and possibly lead to a better understanding of the underlying wavelength dependence of SN brightness variations. In this work we demonstrate a method for evaluating models of intrinsic scatter by computing three scatterdependent dispersion variables and making the following data/MC comparisons: (1) the traditional Hubblediagram residual; (2) B -V -c , where B -V is the true rest-frame color and c is the fitted color parameter from the salt-ii model; and (3) the photoz residual. In the hypothetical limit of observing SNe Ia with infinite photon statistics and no intrinsic scatter, the distribution for each variable would be a Diracδ function. Simulations that include fluctuations from photon statistics, but no intrinsic-scatter model, underestimate the measured dispersion in these variables. A viable model of intrinsic scatter must predict the dispersion for each variable and for multiple data sets. These three variables do not constitute an exhaustive list of photometric observables; for example one could examine other rest-frame colors ( U -B , V -R ), correlations among colors, and the dependence of the scatter on redshift, stretch, and color. With our current statistics and signal to noise we limit this initial study to the three variables described above, but larger and higher-quality SN samples from current and future surveys should enable a more thorough study. Three classes of wavelength-dependent intrinsic-scatter models are investigated. First we try purely phenomenological functions of rest-frame wavelength with parameters tuned to match observations. The second class is based on measurements from data. The third class uses theoretical explosion models (KRW09) to perturb the salt-ii spectral model. This work is part of the SDSS+SNLS joint analysis, and the data sets used here include 251 spectroscopically confirmed SNe Ia from the 3 year SDSS-II sample (Frieman et al. 2008), and another 191 spectroscopically confirmed SNe Ia from the Supernova Legacy Survey (SNLS3; Conley et al. 2011). All simulations and light curve fitting are done with the publicly available SNANA package 12 (Kessler et al. 2009b, version v10 07 ) and the salt-ii light curve model (G10). The outline of the paper is as follows. The data samples are described in Section 2 and the simulation and intrinsic-scatter models are described in Section 3. The determination of each dispersion variable is in Section 4, and the resulting data/MC comparisons are in Section 5 along with some systematics tests. Finally, in Section 6 we investigate the potential Hubble diagram bias from using an incorrect model of intrinsic scatter.",
"pages": [
1,
2
]
},
{
"title": "2. THE SDSS-II AND SNLS DATA SAMPLES",
"content": "We use two SN Ia data samples that are well calibrated with ∼ 1% photometric precision, and that span complementary redshift ranges. The lower redshift SNe ( z < 0 . 4) are from the full three-season SDSS-II sample (Frieman et al. 2008), and the higher redshift SNe ( z < 1) are from the publicly available 3 year SNLS3 sample (Conley et al. 2011). Below we give a brief description of these samples. The SDSS-II Supernova Survey used the SDSS camera (Gunn et al. 1998) on the SDSS 2.5 m telescope (Gunn et al. 2006; York et al. 2000) at the Apache Point Observatory to search for SNe in the Fall seasons (September 1 through November 30) of 2005-2007. This survey scanned a region (designated stripe 82) centered on the celestial equator in the Southern Galactic hemisphere that is 2.5 · wide and runs between right ascensions of 20 h and 4 h , covering a total area of 300 deg 2 with a typical cadence of every four nights per region. Images were obtained in five broad passbands, ugriz (Fukugita et al. 1996), with 55 s exposures and processed through the PHOTO photometric pipeline (Lupton et al. 2001). Within 24 hr of collecting the data, the images were searched for SN candidates that were selected for spectroscopic observations in a program involving about a dozen telescopes. The SDSS-II Supernova Survey discovered and spectroscopically confirmed a total of ∼ 500 Type Ia SNe. Details of the SDSS-II SN Survey are given in Frieman et al. (2008) and Sako et al. (2008), and the procedures for spectroscopic identification and redshift determinations are described in Zheng et al. (2008). The SN photometry for SDSS-II is based on Scene Model Photometry (SMP) described in Holtzman et al. (2008). The basic approach of SMP is to simultaneously model the ensemble of survey images covering an SN location as a time-varying point source (the SN) and sky background plus time-independent galaxy background and nearby calibration stars, all convolved with a time-varying point-spread function (PSF). The fitted parameters are SN position, SN flux for each epoch and passband, and the host-galaxy intensity distribution in each passband. The galaxy model for each passband is a 20 × 20 grid (with a grid scale set by the CCD pixel scale, 0 . 4 '' × 0 . 4 '' ) in sky coordinates, and each of the 400 × 5 = 2000 galaxy intensities is an independent fit parameter. As there is no pixel re-sampling or image convolution, the procedure yields correct statistical error estimates. The SNLS was a 5 year survey covering four 1 deg 2 fields using the MegaCam imager on the 3.6 m CanadaFrance-Hawaii Telescope (CFHT). Images were taken in four bands similar to those used by the SDSS: g M , r M , i M , z M , where the subscript M denotes the MegaCam system. The SNLS exposures were ∼ 1 hr in order to discover SNe at redshifts up to z ∼ 1. The SNLS images were processed in a fashion similar to the SDSS-II so that spectroscopic observations could be used to confirm the identities and determine the redshifts of the SN candidates. Additional information about the SNLS can be found in Astier et al. (2006) and references within. The SNLS3 SN photometry is based on a simultaneous fit of the SN flux and position, a residual sky background per image, and a galaxy intensity map. Images are resampled to the same reference pixel grid prior to the fit. The SN+galaxy image model is PSF-matched to the resampled images. Only sky noise is included in the photometric uncertainties (host galaxy and source noise are negligible for most SNe). Because resampling introduces pixel correlations, the uncertainties ignoring correlations are scaled such that the reduced χ 2 is one when assuming a constant SN flux per night. To ensure good quality fits to the light curves, the following selection criteria are applied to both the SDSS-II and SNLS3 data samples, The sample statistics after these requirements are given in Section 4.5.",
"pages": [
2,
3
]
},
{
"title": "3. SIMULATIONS",
"content": "We use the SNANA MC code (Kessler et al. 2009b) to generate realistic SN Ia light curves that are analyzed in exactly the same manner as the data. The MC is used to make detailed comparisons with the data using different models of intrinsic SN Ia brightness variations. All simulations are based on a standard ΛCDM cosmology with w = -1, Ω M = 0 . 3, Ω Λ = 0 . 7. Details of the simulation are described in Kessler et al. (2009b) and in Section 6 of Kessler et al. (2009a, hereafter K09); here we give a brief overview. Simulations are generated using the salt-ii model (G10) that is based on a time sequence of rest-frame spectra. The spectral model is explained in more detail in Section 4 within the context of light curve fitting. Observer-frame magnitudes are computed by redshifting the rest-frame spectrum for each epoch, reddening the spectra from Galactic extinction (Schlegel et al. 1998) using R V = 3 . 1, and summing the flux in the appropriate filter-response curves. To account for non-photometric conditions and varying time intervals between observations due to bad weather, actual observing conditions are used for both the SDSSII and SNLS surveys. For each simulated observation, the noise is determined from the measured PSF, 13 Poisson noise from the source, and sky background. Noise from the host-galaxy background is included for the SDSS-II simulations where it has a small effect at low redshifts. Host-galaxy noise for the higher redshift SNLS sample is negligible, and thus not simulated. Additional details of the simulation of noise are given in Section 3.1. The simulated flux in CCD counts is based on a mag-toflux zeropoint, and a random fluctuation drawn from the noise estimate. The parent distributions of the salt-ii stretch ( x 1 ) and color ( c ) are well described by an asymmetric Gaussian that is a function of three parameters, and a similar function with x 1 → c . The parameters for each distribution are shown in Table 1. After accounting for Malmquist bias, we find that the higher-redshift SNLS3 sample is slightly brighter and bluer compared to the SDSS-II sample. This difference is expected from previous results showing that younger star-former galaxies host brighter/bluer SNe Ia than older passive galaxies (Sullivan et al. 2006; Lampeitl et al. 2010; Smith et al. 2012). The younger star-forming galaxies are more abundant at higher redshifts, thus qualitatively explaining the brightness difference between the two surveys. While the redshift-dependent variation in the stretch population is well established, the variation in the color population has been reported only in Smith et al. (2012) where they show that the SN Ia color population is the same for passive and moderately star-forming galaxies, but different in highly star-forming galaxies. Previous studies comparing passive and all star-forming galaxies found no color variation, and should not be considered inconsistent with the results of Smith et al. (2012). We show in the systematics analysis (Section 5.1) that the simulated intrinsic scatter is rather insensitive to the parameters describing the parent populations in Table 1, and therefore it does not matter if these parameters are the same or slightly different for each survey. - - The simulation includes a detailed treatment of the search efficiency, including spectroscopic selection effects. For the SDSS-II, the search-pipeline efficiency has been measured separately for each g, r, i filter using fake SNe inserted into the images (Dilday et al. 2008). The spectroscopic selection efficiency ( /epsilon1 spec ) has been estimated from matching data/MC distributions for redshift and for the fitted observer-frame magnitudes at the epoch of peak brightness. /epsilon1 spec is adequately described as a function of peak r -band magnitude and the peak color g -r . These efficiency functions are available in tabular form. 14 For the SNLS3, /epsilon1 spec has been evaluated as a function of peak i M -band magnitude ( M i ) in Figure 9 of Perrett et al. (2010). For the SNANA simulation we parameterize this function as where C /epsilon1 ( M i ) = 1 for M i < 23 and C /epsilon1 ( M i ) = exp[(23 -M i ) / 0 . 63] for M i > 23. The function in parentheses is a first-order estimate and C /epsilon1 ( M i ) is a correction obtained from a fit to the data/MC ratio as a function of M i . For this analysis we generate MC samples with sizes corresponding to six times the data statistics. The quality of the simulation for each sample is illustrated with several data/MC comparisons in Figures 1 and 2; the overall agreement is good.",
"pages": [
3,
4
]
},
{
"title": "3.1. Simulation of Noise",
"content": "Since the three scatter-dependent variables (Hubble scatter, B -V -c photoz precision) are sensitive to the flux uncertainties, it is important to accurately simulate these uncertainties. The simulation strategy is to first calculate the uncertainties from a model based on measurements of the sky level and PSF. To accurately check the model, the true uncertainty for each observation in the data 15 is compared to the calculated model uncertainty. Discrepancies between the true and calculated uncertainties are corrected by fitting for ad-hoc parameters. The simulated uncertainty model in photoelectrons ( σ SIM ) is given by where F is the flux, A = [2 π ∫ PSF 2 ( r, θ ) rdr ] -1 is the noise-equivalent area, b is the effective sky level including dark current and readout noise, and q and σ 0 are fitted ad-hoc parameters. ZPT pe is defined such that the number of CCD photoelectrons for a point source of magnitude m is given by 10 -0 . 4( m -ZPT pe ) ; thus the σ 0 term is independent of the PSF, sky level and host-galaxy. The quantity σ HOST is simulated for the SDSS-II sample using a library of galaxies that have a spectroscopic redshift and a well measured profile consistent with either exponential or de Vaucouleurs. To check the uncertainty calculation, σ SIM is computed for each epoch in the data and compared to the measured uncertainty σ DATA . The left panels in Figure 3 show that the first two terms, F + Ab , are not adequate to reproduce the observations. The right panels in Figure 3 show that the fitted σ 0 term results in good agreement over a wide range of PSF values. A separate σ 0 value is evaluated for each filter and for each sample (Table 2). The quadratic term q is sensitive to large flux values with S / N ∼ 10 2 . The value of q is obtained from minimizing χ 2 = ∑ s [( σ SIM /σ DATA ) s -1] 2 , where the sum ( s ) is over log 10 (S / N) bins; q /similarequal 0 . 01 for the SDSS bands, and q ∼ 0 . 001 for the SNLS bands. For SNLS, it is difficult to interpret this low value of q because uncertainties on the SN flux (Poisson noise and flat-fielding noise) only arise via the normalization of errors based on the intra-night flux scatter. Finally, note that the terms F + ( A · b ) + σ 2 HOST are determined from observations and first principles, while q and σ 0 are empirically determined parameters. The q term corresponds to a zeropoint uncertainty. The σ 0 term is not understood, although this term works surprisingly well for both the SDSS-II and SNLS3 surveys even though the respective photometry codes are independent.",
"pages": [
4,
5
]
},
{
"title": "3.2. Intrinsic-scatter Models",
"content": "The intrinsic scatter models are summarized in Table 3. These models are defined as wavelength-dependent perturbations to the salt-ii spectral model, and these perturbations average to zero so that the underlying saltii model is not changed. All models are independent of redshift, and only the explosion models from KRW09 depend on epoch. We begin with the phenomenological functions (see 'FUN' prefix) with parameters arbitrarily chosen to increase the scatter. The coherent model (FUN-COH) assigns a single magnitude shift for all wavelengths; for each SN this shift is given by a Gaussianrandom number with σ COH = 0 . 13 mag. The other two FUN functions are designed to probe a wider variety of wavelength-dependent scatter with a coherence length of a few hundred ˚ A. First a sequence of nodes is defined at 1000 ˚ A intervals in the rest frame. An independent Gaussian random scatter is selected at each node with σ node = σ 5500 exp[ -( λ node -5500) / 3000] so that there is more scatter at bluer wavelengths. The variation is the same at all epochs. A continuous function of wavelength is constructed by connecting the node values with sine functions so that the derivative is zero at each node. FUN-COLOR is defined with σ 5500 = 0 . 06 and is shown in Figure 4 for a few simulated SN. FUN-MIX is defined with σ 5500 = 0 . 045 along with a coherent term σ COH = 0 . 09 mag. refers to rest-frame wavelength. a 'iso' = isotropic and 'dc' = detonation criteria. The next two models (G10 and C11) are based on mea- surements from data combined with assumptions needed to create a model that is a continuous function of wavelength. The G10 error model was obtained as part of the salt-ii training process in which they minimized the likelihood of light curve amplitude residuals using a parametric function of central rest-frame wavelength, assuming uncorrelated residuals in different passbands. The resulting wavelength-dependent function (Figure 8 of G10) has approximate values of 0.07, 0.03, 0.02, 0.03, 0.06 mag at the U, B, V, R, I central wavelengths, respectively. This function is not intended to represent a wavelength dependent scatter, but rather it is a model of independent broadband scatter as a function of central wavelength. To translate this broadband model into a wavelength model, independent random scatter values ( σ node ) are selected every 800 ˚ A, and these node values are connected with the same sine-interpolation that is used for the phenomenological 'FUN' functions. Since this procedure reduces the resulting broadband scatter, σ node is multiplied by 1+( λ rest -2157) / 9259 so that the simulated UBVRI broadband scatter matches the G10 function. In addition to a wavelength-dependent function, the G10 model includes a coherent term, σ COH = 0 . 09 mag. The model of Chotard (2011); Chotard et al. (2011, hereafter C11) is based on a covariance scatter matrix among the UBVRI filter passbands, and is derived from an analysis of spectral correlations using high quality spectra from the Supernova Factory (Aldering et al. 2002). The broadband covariance model is translated into a wavelength-dependent model as follows. First, the model is extrapolated to wavelengths below the U band (3600 ˚ A) by defining an ad-hoc U ' filter with central wavelength ¯ λ obs = 2500 ˚ A. The G10 scatter value of σ node = 0 . 59 mag is used for U ' , and we model three different assumptions for the reduced correlation between U ' and U : ρ U ' ,U = 0 (incoherent,C11 0), ρ U ' ,U = +1 (C11 1), and ρ U ' ,U = -1 (C11 2). For each simulated SN, six random magnitude shifts are selected according to the C11 correlation matrix in upper half of Table 4; these shifts are assigned to the central U ' UBVRI wavelengths. A continuous function of wavelength is obtained by interpolating these six points with a sine function, similar to the FUN-COLOR interpolation in Figure 4. Finally, the scatter function is multiplied by 1.3 to compensate for the fact that the wavelength interpolation reduces the broadband covariances. The correlation matrix realized by the simulation is shown in bottom half of Table 4 for the C11 1 model. The realized correlation matrix is slightly different than the input model because the input model is described by broadband covariances, while the simulated model depends on wavelength. In principle a more finely tuned spectral model in the simulation would result in the exact C11 covariances, but we believe that the simple and approximate model used here is adequate, especially in light of the large and unknown uncertainties on the covariances. The final class of brightness variations is based on 2D explosion models with random ignition points (KRW09), followed by radiative transfer calculations using the SEDONA program (Kasen et al. 2006). Isotropic models are obtained from ignition points that are randomly placed throughout the white dwarf (WD), while asymmetric models are obtained from ignition points within a cone whose apex is at the center of the WD. Both the isotropic and asymmetric models result in explosion asymmetries and a viewing angle dependence that contributes significantly to the intrinsic scatter. The widthluminosity relation is related to the number of ignition points ( N ignit ) because N ignit affects the amount of preexpansion before detonation, and hence the amount of 56 Ni produced in the explosion. In a recent study by Blondin et al. (2011, hereafter B11), detailed comparisons between data and the KRW09 models were made. They conclude that the KRW09 models with the best spectroscopic agreement also have the best photometric agreement, and they identified a subset of eight models with the best agreement to data. Here we use these same eight models; they are shown in Table 3 along with a few parameters describing the number of ignition points and the detonation criteria. All of these models have an isotropic distribution of ignition points, and B11 note that radial fluctuations in isotropic models can lead to significant viewing angle asymmetries. We initially used these KRW09 models in the SNANA simulation to generate light curves corresponding to the SDSS-II and SNLS3. While the data/MC comparisons are visually impressive, the simulated light curves are not adequate for this study because the salt-ii light curve fits are in general rather poor. This trend of poor light curve fits was also noted in B11. Instead of attempting an absolute prediction with the KRW09 models, we have instead used these models as a perturbation on the salt-ii model. In short, the salt-ii model describes the stretch and color relations, while the KRW09 models are used to describe the intrinsic scatter. The spectral flux ( F ) is given by where φ is the viewing angle. The corresponding mag- b Diag = √ COV ii with i = U ' , U, B, V, R, I are from the PhD thesis and differ slightly from those given in Chotard et al. (2011). shifts are illustrated in Figure 5 as a function of wavelength for a two extreme viewing angles. φ φ -",
"pages": [
5,
6,
7
]
},
{
"title": "4. ANALYSIS",
"content": "Here we describe the determination of the three scatter-dependent quantities used to evaluate models of intrinsic brightness variations. All analyses are based on light curve fits using the salt-ii model.",
"pages": [
7
]
},
{
"title": "4.1. Review of salt-ii Model",
"content": "The salt-ii SN Ia model flux is a function of wavelength ( λ ) and time ( t ) in the rest-frame, where the spectral sequences ( M 0 and M 1 ) and color law (CL( λ )) are derived from the training in G10. Synthetic photometry in the observer frame is obtained by redshifting Eq. 6 and multiplying by the filter response and Galactic transmission. The overall scale ( x 0 ), stretch ( x 1 ), color ( c ) and time of peak brightness ( t 0 ) are determined for each SN in a light curve fit that minimizes a χ 2 based on the difference between the data and synthetic photometry. Eq. 6 is valid for 2000 < λ < 9200 ˚ A, and the model is valid for observer-frame filters that satisfy where ¯ λ obs is the central wavelength of the filter. An effective B -band magnitude is defined to be m B = -2 . 5 log 10 ( x 0 ) + 10 . 635; this is the observed magnitude through an idealized filter that corresponds to the B band in the rest-frame of the SN. The fitted distance modulus is given by where α , β and M are determined from a global fit to all of the SNe using the ' SALT2mu ' program described in M11 and below in Section 6.",
"pages": [
7
]
},
{
"title": "4.2. Hubble Scatter",
"content": "The well known Hubble scatter is defined as the dispersion on ∆ µ , the difference between the fitted (measured) distance modulus and the distance modulus calculated from the best-fit cosmological parameters. To simplify the analysis here we do not fit for the α and β parameters, nor do we fit for the best-fit cosmological parameters. Instead we compute the dispersion of where α = 0 . 11, β = 3 . 2, M = -19 . 36 ( H 0 = 70 km s -1 Mpc -1 ), and µ calc is the calculated distance modulus assuming a ΛCDM cosmology with w = -1, Ω M = 0 . 3, Ω Λ = 0 . 7. Although the fitted α and β may have given slightly different ∆ µ values, the resulting bias is more than an order of magnitude smaller than the dispersion, and hence the impact of this approximation is negligible.",
"pages": [
8
]
},
{
"title": "4.3. Color Precision",
"content": "The color precision test compares the fitted salt-ii color ( c ) to the true B -V rest-frame color at the epoch of peak brightness. Since the fitted color is really a color excess, c = E ( B -V ), and the color also depends slightly on the stretch, the true B -V color does not exactly correspond to c . A numerical examination of the model shows that with no intrinsic scatter, and therefore we examine the dispersion on B -V -c ' . The dispersion on c -c ' is ∼ 0 . 001, more than an order of magnitude smaller than the dispersion on B -V -c ' , and thus this correction has little effect. The evaluation of c ' is from simply plugging the fitted c and x 1 values into Eq. 10. The naive rest-frame magnitudes M /star B and M /star V are obtained from Eq. 6 using the best-fit parameters ( c , x 0 , x 1 ) and using the B and V filter-transmission functions. However, these naive magnitudes are not necessarily the true values if there are intrinsic color variations. To obtain a better approximation for the magnitudes we fit only the two nearest observer-frame bands that bracket the B or V band in wavelength. The details of the fitting procedure are as follows. First a normal fit is done using all filters to determine the fit parameters ( t 0 , c , x 0 , x 1 ). For each rest-frame band one additional fit is performed using only the two nearest observer-frame bands and holding t 0 and x 1 fixed from the normal fit. The floated color ( c ) and distance ( x 0 ) parameters provide the flexibility to fit both observerframe bands regardless of how much intrinsic color variation exists. The two-band fit parameters are c B , x B 0 for the B band, and c V , x V 0 for the V band. After finishing both two-band fits the B -V color is computed as where M /star is the magnitude computed from Eq. 6 using filter-transmission functions T B,V , and with x 1 = 0 so that all B -V colors correspond to an SN Ia with the same stretch. This fitting procedure was tested on an SNLS3 simulation in which the maximum S/N was artificially set to 1000 for every SN regardless of redshift. The rms on B -V -c ' is 0.002 mag, an order of magnitude smaller than the observed dispersion.",
"pages": [
8
]
},
{
"title": "4.4. Photoz Precision",
"content": "The photoz precision is based on the difference between the SN redshift determined from broad band photometry and the more precise spectroscopic redshift. The basic photoz method is to extend the usual methods of fitting light curves to include the redshift as a fifth fit parameter. Particular attention is needed to estimate initial parameter values near those corresponding to the global minimumχ 2 , and to iteratively determine which filters satisfy Eq. 7. Details of the photoz fitting process are given in K10. There are two modifications in our photoz fitting procedure compared to K10. The first change is that we use the known spectroscopic redshift as the initial estimate in order to reduce catastrophic outliers. The fitting task has thus been changed to find a local photoz minimum near the true redshift instead of searching the entire redshift range for a global minimum. The second change is related to estimating the initial parameter x 0 for each color value along the coarse-grid search in color. In K10, x 0 at each grid point was calculated using the current color, photoz and a reference cosmology. Here we analytically minimize for x 0 , making the fitted photoz less sensitive to the absolute brightness. To check that the fitted photoz depends only on the SN colors we have applied this method to simulations with no intrinsic scatter and with the coherent scatter model (see COH entry in Table 3); the photoz precision is the same in both cases.",
"pages": [
8
]
},
{
"title": "4.5. Statistics Summary",
"content": "After applying the selection requirements in Section 2, along with the light curve fitting requirements for each dispersion variable, the number of SNe Ia for each sample and for each dispersion variable is shown in Table 5 The smaller photoz samples arise from a light curve fitting requirement. For each successive fit iteration, observer-frame filters are added or dropped based on which filters satisfy the salt-ii wavelength range in Eq. 7 with z = photoz . If any filter fails this wavelength requirement after the last fit iteration, the SN is rejected; this requirement avoids fitting to wavelength regions in which the salt-ii model may be poorly defined. The smaller SNLS3 sample for the B -V -c ' analysis is due to SNe Ia at z > 0 . 7; for these objects the observerframe i and z bands no longer bound the rest-frame V band.",
"pages": [
8
]
},
{
"title": "4.6. Quantifying the Dispersions",
"content": "The data and MC dispersions are measured from the following variables, where the (1 + z ) -1 factor is included to reduce the redshift-dependent variation from measurement uncertainties. These three quantities are shown in Figure 6 for the data and MC, and for both the SDSS-II and SNLS3 samples. The MC includes only Poisson noise (no intrinsic variation), and hence the data-MC difference in the width illustrates the size of the intrinsic component that is needed. The ∆ µ comparison shows the most obvious discrepancy. The ∆ z and ∆ c discrepancies are more subtle, indicating that the effect of color variations is smaller than the coherent variation. To quantify the dispersions we compute the median, M ∆ ≡ median | ∆ x | , where x = µ, z, c indicates the variable type. In particular, we compute the MC/data ratio of medians, With the correct model of brightness variations we expect R MC / Data = 1 for all three variables and for both surveys. The uncertainty on the median is calculated as follows. For N SNe, the statistical uncertainty on N/ 2 is σ ( N/ 2) = √ N/ 2. The median uncertainty ( σ M ) is defined such that N -σ ( N/ 2) values of | ∆ x | lie below M -σ -M and N + σ ( N/ 2) values lie below M + σ + M . For a rapidly falling distribution we typically find that σ + M > σ -M . Here we define a symmetric uncertainty, σ M ≡ ( σ -M + σ + M ) / 2. As a numerical crosscheck we analyze SDSS-II simulations in which the exposure time is adjusted for each SN so that the maximum S/N is 10 4 . The resulting dispersions, defined simply as a Gaussian fitted σ , are 0 . 0003, 0 . 002, and 0 . 001 mag for the three variables (Eq. 12), respectively; these dispersions are more than an order of magnitude smaller than the dispersions observed in the data.",
"pages": [
9
]
},
{
"title": "5. RESULTS",
"content": "The MC/data ratio of medians, R MC / Data (Eq. 13), is shown in Figure 7 for all of the models in Table 3, and for both surveys. With no model of intrinsic scatter, R MC / Data is well below unity in all cases. Adding a coherent scatter (FUN-COH) predicts the Hubble dispersion (∆ µ ), but has no impact on the color and photoz dispersion. The FUN-COLOR model almost predicts the Hubble dispersion, but may overestimate the color precision. FUN-MIX has been artificially tuned to predict the dispersion in all quantities, although the photoz dispersion may still be underestimated. The G10, C11 0 and C11 1 models provide decent predictions, with a slight underestimate in the photoz dispersion. The C11 2 model underestimates the Hubble dispersion. Recall that the G10 model includes only positive correlations, mainly from the coherent term σ COH = 0 . 09, while the C11 model includes both positive and negative correlations. This G10 versus C11 comparison illustrates that there can be significant degeneracies among models of intrinsic brightness variations. The KRW09 models give a poorer description of the dispersion because the Hubble dispersion is always underestimated.",
"pages": [
9
]
},
{
"title": "5.1. Systematics Tests",
"content": "Here we describe some systematics tests to demonstrate the robustness of the results in Figure 7. We use the FUN-COH scatter model as the reference simulation for these tests which are summarized in Figure 8. For each test a change is applied to the simulation and then analyzed in exactly the same manner. The first test is based on the precision in the flux uncertainties in the data. For pre-explosion epochs in which the true SN flux is known to be zero, examining the S/N distribution shows that the uncertainties are accurate to within 5%. The test labeled σ SIM × 1 . 05 corresponds to a simulation with 5% larger uncertainties on all of the fluxes. The next set of tests is based on a 0.02 mag zeropoint change in each filter ( δ ZPT griz ). Note that this change is two times larger than the uncertainty reported by each survey team. Uncertainties on the Galactic extinction are examined by first increasing the estimated 16% scatter to 24% ( × 1 . 5 MW-Gal), and then increasing the reddening parameter by 10%, to R V = 3 . 4. The next test is based on changing β from 3.2 to 2.5, a 5 σ change from G10. The next two tests are based on changing the population parameters for x 1 and c (Table 1). The simulated x 1 population is shifted toward faster-declining light curves by setting σ + = 0 . 5 and σ -= 1 . 8 (compare to nomi- nal parameters in Table 1). The simulated color population is shifted toward the red by setting σ + = 0 . 18 and σ -= 0 . 05. For these systematic tests, the resulting data/MC comparisons for stretch and color are shown in Figure 9; the data and MC are clearly discrepant. For all of these systematic tests, R MC / Data remains significantly below unity for the B -V -c ' and photoz variables. We also note that the independent SDSS-II and SNLS3 results are consistent, showing consistency over different redshift ranges.",
"pages": [
9,
11
]
},
{
"title": "6. IMPACT OF INTRINSIC SCATTER MODEL ON THE HUBBLE DIAGRAM",
"content": "Here we investigate the potential Hubble diagram bias from using an incorrect model of intrinsic scatter. We use four intrinsic scatter models that give reasonable data/MC agreement in Figure 7: FUN-MIX, G10, C11 0 and C11 1. Recall that data/MC agreement in these dispersion variables means that the intrinsic scatter model cannot be ruled out, but the agreement does not ensure that the underlying model is correct. The Hubble bias is determined from the difference between an ideal analysis using the correct intrinsic scatter matrix (Section 6.1), and a conventional analysis that adds a wavelength-independent scatter to bring the reduced χ 2 to unity (Section 6.2). The ideal analysis is based on simulations with the correct model of intrinsic scatter, and thus does not reflect a realistic analysis that could be applied to data. The conventional analysis, however, reflects a realistic analysis that has often been applied to data. In Section 6.3 the Hubble bias is translated into a bias on the dark energy equation of state parameter w , and in Section 6.4 the biases are reevaluated with Malmquist bias corrections.",
"pages": [
11
]
},
{
"title": "6.1. Determining the Intrinsic-scatter Matrix",
"content": "To evaluate the effect of intrinsic scatter in the analysis of cosmological parameters, we first need to briefly summarize the concept of an intrinsic scatter matrix introduced in Section 2 of M11. Cosmology fitters in general minimize the function where ∆ µ i is the difference between the fitted and calculated distance modulus (Eq. 9) for the ith SN, σ stat ,i is the statistical (fitted) error on ∆ µ i , and σ int ,i is an ad hoc parameter defined so that χ 2 /N dof = 1. Since σ stat ,i is computed from a statistical correlation matrix between the salt-ii fit parameters ( m B , x 1 , c ), M11 proposed an analogous 'intrinsic-scatter covariance matrix' (denoted Σ) to compute σ int . Dropping the SN index i , the ad-hoc error term is where the subscript correspondence is 0 , 1 , c → m B , x 1 , c , √ Σ 00 ≡ σ int m B , √ Σ 11 ≡ σ int x 1 , and √ Σ cc ≡ σ int c . All SNIacosmology analyses to date have used the simplifying assumption that σ int = σ int m B = √ Σ 00 , and ignored the other Σ terms in Eq. 15. We refer to this method as the ' m B -only' method, while the Σ-fit method refers to using additional terms in Eq. 15. The m B -only method is valid if the intrinsic scatter is independent of wavelength, or if σ stat ,i from the light curve fit includes the wavelength dependence of the scatter. The FUN-COH panel in in Figure 7 clearly shows that the intrinsic scatter cannot be constant (i.e., wavelength independent). M11 noted that using the m B -only method can lead to biased values of α and β . Here we go a step further and examine biases in simulated Hubble diagrams. Since we do not have reliable methods for determining Σ from the data, we determine Σ from an artificial analysis using a simulation with the correct model of intrinsic scatter but without Poisson fluctuations from the calculated measurement uncertainties (Eq. 4); therefore the only source of scatter is from intrinsic variations. Although Poisson fluctuations are not applied, the uncertainties are included in the light curve fitχ 2 calculations so that the correct filter-dependent weights are used. For example, the SDSS u band has relatively poor S/N compared to the other bands and therefore this passband has less weight in determining Σ. We refer to these simulations as 'intrinsic-only' to distinguish them from the 'nominal' simulations that include Poisson fluctuations. This intrinsic-only simulation is illustrated in Figure 10 for the special case with no intrinsic scatter; the simulated fluxes lie exactly on the best-fit salt-ii model and they have the correct uncertainties corresponding to real observations. To better compare the resulting bias to the uncertainty reported in Sullivan et al. (2011), the simulations have been adjusted to better match the data sample used in this SNLS3 analysis. First, the SDSS-II sample size is reduced by a factor of three to correspond to the firstseason sample used in the SNLS3 analysis. The next change is that the S/N requirement in the three passbands (see end of Section 2) is relaxed from 8 to 5. Finally, we have included a simulated nearby ( z < 0 . 1) sample as explained in the Appendix. To measure biases with good precision, the MC sample sizes correspond to 20 times the data statistics. After performing salt-ii light curve fits on the simulated intrinsic-only sample, we define ∆ SIM m B ≡ m B (fit) -m B (true) and ∆ SIM c ≡ c (fit) -c (true), where 'true' indicates the true value from the simulation and 'fit' indicates the result from a light curve fit. The true values are defined by the underlying salt-ii model before the intrinsic smearing model is applied. The covariance terms with the stretch parameter x 1 are negligible because the intrinsic scatter models are epoch-independent and thus do not change the light curve shape; the x 1 -terms in Σ are therefore ignored. The 2 × 2 intrinsic scatter matrix is defined to be where 〈〉 indicates the mean value of the enclosed quantity. Another caveat is that Σ depends on the redshift and on which filters are included in the light curve fit. This dependence is linked to the salt-ii color parameter ( c ) that is evaluated by extrapolating a color law to the central wavelengths of the B and V passbands. To address this caveat, Σ is evaluated as a function of redshift and sample as shown in Figure 11. A second-order polynomial function of redshift is adequate to describe the components of Σ. For the FUN-MIX and G10 models, σ int m B and βσ int c give a comparable contribution ( ∼ 0 . 1) to σ int . For the C11 models, σ int m B ∼ 0 . 03 is much smaller than the contribution from βσ int c .",
"pages": [
11,
12
]
},
{
"title": "6.2. Fitting for α , β , and the Distance Moduli",
"content": "Using the fitted salt-ii parameters and uncertainties from the nominal MC, we use the SALT2mu program (M11) to minimize Eq. 14. This minimization gives the best-fit values of α and β , along with an independent offset ( M z ) in each 0.1-wide redshift bin (Eq. 8). The separate offsets are used to eliminate the µ -dependence on cosmological parameters. These fitted parameters are used to compute a distance modulus for each SN, and the resulting redshift+distance pairs form a Hubble diagram that can be fit for cosmological parameters. To properly evaluate the fit χ 2 using the scatter matrix Σ, the light curve fits have been done with the salt-ii model uncertainties set to zero (hence reducing σ stat ,i ) because they are now included in the SALT2mu fit as part of the σ int calculation. This modification only affects the SALT2mu χ 2 and has a negligible impact on the fitted parameters. The m B -only fit is based on the traditional method of tuning σ int m B such that χ 2 /N dof = 1, while setting all of the other covariance terms to zero. The light curve fits include the salt-ii model errors, and hence the intrinsic uncertainties corresponding to the G10 model are included. We note that there is an improved statistical treatment in March et al. (2011), using a Bayesian hierarchical model. While they obtain an uncertainty on σ int m B , their scatter model is fundamentally the same as our m B -only model because they do not include additional covariance terms. The SALT2mu fit results for both intrinsic scatter methods ( m B -only and Σ) are shown in Table 6. For both methods the fitted values of α agree well with the simulated input, α SIM = 0 . 11. For the FUN-MIX and G10 scatter models, the fitted values of β agree well with the simulated input ( β SIM = 3 . 2) for both methods. For the C11 models, however, the situation is quite different. The m B -only fitted β values are too low by 0.3-0.6, and the significance of this bias ranges from 6 to 15 standard deviations. The Σ-fit β values are consistent with β SIM . α and β Fit Results from Simulations with Different Intrinsic-scatter Models, and w -bias Results from Cosmology Fits The reduced χ 2 values are close to unity for the m B -only method because of the explicit σ int m B tuning. However, there is no such tuning for the Σ-fit method and the reduced χ 2 are within about 10%-20% of unity. In summary, using the correct intrinsic scatter matrix Σ in the SALT2mu fit results in unbiased β values, and χ 2 /N dof /similarequal 1. Using the simplistic m B -only method results in a significant bias on β for the C11 models. Since the Σ-fit method results in unbiased β values we define the µ -bias to be ∆ µ = µ mB -only -µ Σ : µ Σ is the distance modulus from the Σ-fit method and µ mB -only is the distance from the m B -only method. Figure 12 displays ∆ µ versus redshift for each scatter model. For the FUN-MIX and G10 scatter models, the maximum σ σ σ σ ∆ µ variation is only ∼ 0 . 01 mag over the redshift range of each survey. For the C11 models ∆ µ varies by several hundredths over the redshift range of each survey. This µ -bias is caused by the bias in β combined with Malmquist bias that results in bluer SN with increasing redshift. Figure 13 shows the mean fitted color value versus redshift, and the corresponding µ -bias is ∆ µ /similarequal ∆ β × 〈 c fit 〉 where ∆ β is the bias in β and 〈 c fit 〉 is the mean salt-ii color. The redshift dependence on ∆ µ is therefore directly proportional to the redshift dependence of 〈 c fit 〉 . Figure 13 also shows the mean fitted stretch parameter ( x 1 ) versus redshift. However, since the corresponding bias on α is less than 0 . 01, the resulting µ -bias is less than 0 . 01 × 0 . 3 ∼ 0 . 003, and is thus much smaller than the bias from the color term. To summarize, these bias tests show that the G10 model is internally consistent and that the wavelength dependence of the intrinsic scatter can be described with both methods. In the first method the scatter is described by the uncertainties in the salt-ii light curve fitting model, and the m B -only scatter matrix is used in the SALT2mu stage. In the second Σ-fit method the light curve fitting model uncertainties are set to zero and the full intrinsic scatter matrix is used in the SALT2mu fitting stage. The difference in results between these two methods, as applied to simulations based on the G10 model, is negligible. However, if the simulated scatter model includes large anti-correlations such as those suggested by C11, then these two methods are not consistent and the traditional m B -only method results in a significant redshift-dependent bias in the distance moduli (Figure 12). More specifically, the bias is a result of incorrectly using the salt-ii (i.e., G10) uncertainties in the light curve fits of the samples generated with the C11 model. µ - µ µ - µ > fit x <",
"pages": [
12,
13,
14,
15
]
},
{
"title": "6.3. Estimating the w -bias",
"content": "To estimate the bias on the dark energy parameter w , we fit the simulated Hubble diagram in a manner similar to that described in Section 8 of K09. The effect of Malmquist corrections is discussed later in Section 6.4. The w -bias is defined to be the difference between w obtained from the m B -only method and the Σ-fit method. Priors are included from measurements of baryon acoustic oscillations from the SDSS Luminous Red Galaxy sample (Eisenstein et al. 2005) and from the cosmic microwave background temperature anisotropy measured from the Wilkinson Microwave Anistropy Probe (Komatsu et al. 2009). Since the simulated SN sample consists of 20 times the data statistics, the uncertainties on the priors have been reduced by a factor of √ 20. We checked this procedure by splitting the simulated sample into 20 independent sub-samples and fitting each sub-sample with the nominal priors; the average of the 20 fitted w -values is in good agreement with that from using the full simulation and priors with reduced uncertainties. The β -bias and Malmquist-uncorrected w -bias values are defined as the difference between the m B -only and Σ-fit methods, and they are shown in Table 6. The uncertainty on the w -bias is given by rms / √ 20, where rms is the dispersion among the 20 independent w -bias measurements. For the FUN-MIX and G10 models the w -bias is small ( < 0 . 02) for all sample combinations. This small bias is expected since the fitted β and distance moduli show a very small bias. For the C11 models, the w -bias is larger. Fitting the SDSS-II or SNLS3 sample alone, the w -bias is ∼ 0 . 07 for the C11 0 model and ∼ 0 . 12 for the C11 1 model. Combining the SDSS-II + SNLS3 samples, the w -bias is reduced by a factor of ∼ 2 for each of the C11 models. Including the nearby sample (nearby+SDSSII+SNLS3) the w -bias is further reduced: 0 . 01 and 0 . 02 for the C11 0 and C11 1 models, respectively. The reduction in w -bias as more samples are combined is a result of the fortuitous circumstance that the mean saltii color for each sample is very close: -0 . 005, -0 . 015, and -0 . 005 for the nearby, SDSS-II, and SNLS3, respectively. To illustrate this point we have redone the analysis using a simulated nearby sample that has no Malmquist bias and a mean salt-ii color that is 0.06 mag redder than the data; the resulting w -bias on the combined nearby+SDSS-II+SNLS3 sample increases to 0.05.",
"pages": [
15
]
},
{
"title": "6.4. Monte Carlo Correction for Malmquist Bias",
"content": "In Section 6.3 the w -bias is determined without accounting for differences in the Malmquist bias correction. While the true Malmquist bias should not depend on the analysis method ( m B -only versus Σ-method), here we show that the evaluated Malmquist bias, using the fitted value of β , does indeed depend on the analysis method. In addition, using the evaluated Malmquist bias reduces the µ -bias shown in Figure 12. In the discussion below, 'MqSIM' refers to the simulation used to evaluate the Malmquist bias correction. For the Σ-fit method the MqSIM uses the correct model of intrinsic scatter and the correct α and β parameters. In principle the intrinsic-scatter matrix would have to be translated into a wavelength-dependent scatter model for the simulation, but we have not preformed this step. For the m B -only method the MqSIM for each sample uses the G10 model and the fitted (biased) value of β fit from Table 6. This procedure is used because it closely reflects the procedure in previous analyses. The distance-modulus corrections are from a second-order polynomial fit to µ fit -µ true versus redshift: µ true is the true distance modulus in the MqSIM, and µ fit is the distance computed from the SALT2-fitted parameters (color and stretch) and the simulated values of α and β . While using an incorrect model of intrinsic scatter can lead to a significant bias in the Hubble diagram, this bias is somewhat reduced by simply applying a simulated Malmquist bias correction using the fitted value of β in the simulation. The bias reduction depends on the intrinsic scatter model, and we cannot rule out increased sensitivity on other systematic effects.",
"pages": [
15
]
},
{
"title": "7. CONCLUSIONS",
"content": "We have used high quality SDSS-II and SNLS3 data and simulations to show that SN Ia intrinsic brightness variations include wavelength dependent variations resulting in a color dispersion of ∼ 0 . 02 mag. A broad range of simulated intrinsic-scatter models (Table 3) is roughly consistent with the following photometric observables: Hubble scatter, dispersion in B -V -c ' , and photoz residuals. These models include the G10 model that is dominated by a coherent term and has only positive wavelength correlations, and the C11 model that has a small coherent term and large anti-correlations. We have used these intrinsic scatter models in highstatistics simulations to test the standard procedure of adding a constant distance-modulus uncertainty ( σ int ) to the measured uncertainties so that χ 2 /N dof = 1 for cosmology fits to the SN Ia Hubble-diagram. The constant σ int assumption is valid if the light curve fits include model uncertainties with the correct wavelength dependence of the scatter. If these model uncertainties are not correct, such as using the salt-ii uncertainties to fit a simulated sample with large anti-correlations in the scatter (C11 model), then significant biases can appear in the Hubble diagram. For the specific simulation tests reported here the distance-modulus bias varies by up to 0.05 mag over the redshift range of the each survey, although this bias is roughly halved after applying Malmquist bias corrections. For the combined nearby+SDSS-II+SNLS3 simulated sample, which corresponds closely to the 472 SNe Ia analyzed in Sullivan et al. (2011), the w -bias is only ∼ 0 . 02, in part because the mean color for each sample is very nearly the same. While this w -bias is well below the total systematic uncertainty reported in Sullivan et al. (2011) ( δw syst = 0 . 06), there is no assurance that future analyses on larger data sets will benefit from the fortuitous cancellations. For example, replacing the biased nearby sample with an unbiased sample increases the w -bias to 0 . 05, comparable to the current systematic uncertainty. We have also shown that applying a simulated Malmquist bias correction, based on the fitted (biased) β value, may reduce the bias from using an incorrect model of intrinsic scatter. However, we urge caution in relying on this apparent 'free lunch' because we have not fully explored if this naive correction increases the sensitivity to other systematic effects. It is important not to interpret our results as proof that such biases exist in current SNIa-cosmology results; we have shown, for example, that this intrinsic scatter bias is negligible if the G10 model is correct. However, until the intrinsic scatter correlations can be better constrained, our results suggest that an additional systematic uncertainty should be included. Although the intrinsic-scatter models considered here depend only on wavelength (except for the KRW09 models), the true behavior could include a dependence on epoch, color, stretch, and redshift. The impact of the scatter models on the salt-ii training is under investigation and will be published later. To obtain more robust systematic constraints on cosmological parameters, we encourage additional studies to measure or constrain the nature of intrinsic scatter. J.F. and R.K. are grateful for the support of National Science Foundation grant 1009457, a grant from 'France and Chicago Collaborating in the Sciences' (FACCTS), and support from the Kavli Institute for Cosmological Physics at the University of Chicago. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPA), the MaxPlanck-Institute for Astrophysics (MPiA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. This work is based in part on observations made at the following telescopes. The Hobby-Eberly Telescope (HET) is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximillians-Universitat Munchen, and Georg-August-Universitat Gottingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. The Marcario LowResolution Spectrograph is named for Mike Marcario of High Lonesome Optics, who fabricated several optical elements for the instrument but died before its completion; it is a joint project of the Hobby-Eberly Telescope partnership and the Instituto de Astronom'ıa de la Universidad Nacional Aut'onoma de M'exico. The Apache Point Observatory 3.5 m telescope is owned and operated by the Astrophysical Research Consortium. We thank the observatory director, Suzanne Hawley, and site manager, Bruce Gillespie, for their support of this project. The Subaru Telescope is operated by the National Astronomical Observatory of Japan. The William Herschel Telescope is operated by the Isaac Newton Group on the island of La Palma in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. The W.M. Keck Observatory is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.",
"pages": [
15,
16
]
},
{
"title": "SIMULATION OF NEARBY SN IA SAMPLE",
"content": "Here we describe the simulation of the nearby ( z < 0 . 1) SN Ia sample corresponding to the 123 nearby SNe Ia used in Conley et al. (2011). While the nearby SN data are from several surveys and filter sets, we simplify the simulation by considering only the CFA3-Keplercam light curves (Hicken et al. 2009) using the UBVr filters. The i band is dropped because it is outside the valid wavelength range of the salt-ii model. Since the CFA3-Keplercam simulation is a proxy for the entire nearby SN sample, we simulate the correct nearby-SN statistics corresponding to about half that of the SNLS3 sample. Since we do not have the observing conditions (mainly PSF and sky noise) needed for the SNANA simulation, we adopt a different strategy. The basic idea is to use each observed SN to define an observational sequence. The observed redshift and time of peak brightness are used along with the cadence. A random salt-ii stretch and color are chosen for each SN, and the simulated S/N for each epoch is essentially scaled from the observed S/N. More technically, we artificially fixed the PSF to be 0 . 8 '' and then for each epoch compute the sky noise needed to simulate the observed uncertainty; this strategy allows generating nearby SNe in exactly the same manner as for the SDSS-II and SNLS3. With little knowledge of the spectroscopic selection criteria we cannot simulate the selection bias from first principles. We therefore modified the population parameters in Table 1 so that the simulated color and stretch distributions match those of the nearby sample. For the generated color distribution the peak-probability value depends on redshift, -0 . 02 -z/ 2, and the Gaussian width parameters are σ -= 0 . 06 and σ + = 0 . 10. For the generated stretch distribution, the peak-probability value is reduced to 0.2. The intrinsic-scatter matrix is determined for the nearby sample with the same procedure used on the SDSS-II and SNLS3 simulations, and using SALT2mu we have checked that the fitted β values are in good agreement with the simulated input, β SIM = 3 . 2. We have also examined the analogous data/MC comparisons in Figures 1 and 2, and find equally good agreement.",
"pages": [
17
]
},
{
"title": "REFERENCES",
"content": "Aldering, G. et al. 2002, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 4836, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, ed. J. A. Tyson & S. Wolff, 61-72 Astier, P. et al. 2006, A&A, 447, 31 Bailey, S. et al. 2009, A&A, 500, L17 Blondin, S., Mandel, K. S., & Kirshner, R. P. 2011, A&A, 526, A81 Blondin, S. et al. 2011, MNRAS, 417, 1280 Chotard, N. 2011, PhD thesis, University Claude Bernard Lyon, 1, Lyon, France Chotard, N. et al. 2011, A&A, 529, L4 Conley, A. et al. 2011, ApJS, 192, 1 Dilday, B. et al. 2008, ApJ, 682, 262 Eisenstein, D. et al. 2005, ApJ, 633, 560 Freedman, W. et al. 2009, ApJ, 704, 1036 Frieman, J. A. et al. 2008, AJ, 135, 338 Fukugita, M. et al. 1996, AJ, 111, 1748 Gunn, J. E. et al. 1998, AJ, 116, 3040 -. 2006, AJ, 131, 2332 Guy, J. et al. 2010, A&A, 523, A7 Hicken, M. et al. 2009, ApJ, 700, 331 Holtzman, J. et al. 2008, AJ, 136, 2306 Kasen, D., Ropke, F. K., & Woosley, S. E. 2009, Nature, 460, 869 Kasen, D., Thomas, R. C., & Nugent, P. 2006, ApJ, 651, 366 Kessler, R. et al. 2009a, ApJS, 185, 32 -. 2009b, PASP, 121, 1028 Kessler, R. et al. 2010, ApJ, 717, 40 Komatsu, E. et al. 2009, ApJS, 180, 330 Lampeitl, H. et al. 2010, ApJ, 722, 566 Lupton, R. et al. 2001, in ASP Conf. Ser. 238: Astronomical Data Analysis Software and Systems X, ed. F. R. Harnden, Jr., F. A. Primini, & H. E. Payne, 269-+ Mandel, K. S., Narayan, G., & Kirshner, R. P. 2011, ApJ, 731, 120 March, M. C. et al. 2011, MNRAS, 418, 2308 Marriner, J. et al. 2011, ApJ, 740, 72 Perlmutter, S. et al. 1999, ApJ, 517, 565 Perrett, K. et al. 2010, AJ, 140, 518 Phillips, M. M. 1993, ApJ, 413, 105 Riess, A. et al. 1998, AJ, 116, 1009 Riess, A. G., Press, W. H., & Kirshner, R. P. 1996, ApJ, 473, 88 Riess, A. G. et al. 2004, ApJ, 607, 665 Sako, M. et al. 2008, AJ, 135, 348 Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525 Silverman, J. M. et al. 2012, MNRAS, 425, 1889 Smith, M. et al. 2012, ApJ, 755, 61 Sullivan, M. et al. 2006, ApJ, 648, 868 Sullivan, M. et al. 2011, ApJ, 737, 102 Tripp, R. 1997, A&A, 325, 871 Wood-Vasey, W. M. et al. 2007, ApJ, 666, 694 York, D. G. et al. 2000, AJ, 120, 1579 Zheng, C. et al. 2008, AJ, 135, 1766",
"pages": [
17
]
}
]
2013ApJ...764..123S
https://arxiv.org/pdf/1211.1120.pdf
<document>
<section_header_level_1><location><page_1><loc_9><loc_86><loc_91><loc_87></location>MERIDIONAL TILT OF THE STELLAR VELOCITY ELLIPSOID DURING BAR BUCKLING INSTABILITY</section_header_level_1>
<text><location><page_1><loc_30><loc_84><loc_70><loc_85></location>Kanak Saha 1 , Daniel Pfenniger 2 , & Ronald E. Taam 3 , 4</text>
<text><location><page_1><loc_20><loc_83><loc_81><loc_84></location>1 Max-Planck-Institut fr Extraterrestrische Physik, Giessenbachstraße, D-85748 Garching, Germany,</text>
<text><location><page_1><loc_27><loc_82><loc_74><loc_83></location>2 Geneva Observatory, University of Geneva, CH-1290 Sauverny, Switzerland,</text>
<text><location><page_1><loc_26><loc_81><loc_74><loc_82></location>3 Institute of Astronomy and Astrophysics, Academia Sinica-TIARA, Taiwan,</text>
<text><location><page_1><loc_22><loc_80><loc_78><loc_81></location>4 Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA</text>
<text><location><page_1><loc_42><loc_78><loc_58><loc_79></location>e-mail: [email protected]</text>
<text><location><page_1><loc_42><loc_77><loc_58><loc_78></location>Draft version July 20, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_75><loc_55><loc_76></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_62><loc_86><loc_74></location>The structure and evolution of the stellar velocity ellipsoid plays an important role in shaping galaxies undergoing bar driven secular evolution and the eventual formation of a boxy/peanut bulge such as present in the Milky Way. Using collisionless N-body simulations, we show that during the formation of such a boxy/peanut bulge, the meridional shear stress of stars, which can be measured by the meridional tilt of the velocity ellipsoid, reaches a characteristic peak in its time evolution. It is shown that the onset of a bar buckling instability is closely connected to the maximum meridional tilt of the stellar velocity ellipsoid. Our findings bring new insight to this complex gravitational instability of the bar which complements the buckling instability studies based on orbital models. We briefly discuss the observed diagnostics of the stellar velocity ellipsoid during such a phenomenon.</text>
<text><location><page_1><loc_14><loc_59><loc_86><loc_62></location>Subject headings: galaxies: bulges - galaxies:kinematics and dynamics - galaxies: structure galaxies:evolution - Galaxy: disk, galaxies:halos, stellar dynamics</text>
<section_header_level_1><location><page_1><loc_22><loc_56><loc_35><loc_57></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_7><loc_48><loc_55></location>Understanding the structure and dynamics of a galaxy crucially depends on the knowledge of the three dimensional stellar distribution function (DF), which is not a direct observable. The first few moments of the DF, e.g., density, mean velocity and the velocity dispersion tensor together can provide important clues regarding the dynamical state of the galaxy and the gravitational instabilities it might have undergone (van der Kruit 1999). Of particular interest is the buckling instability of a stellar bar in a disk galaxy and the subsequent formation of a boxy/peanut bulge (Combes et al. 1990; Pfenniger & Friedli 1991; Raha et al. 1991; Pfenniger 1993; Athanassoula 2005). A bar buckles under its own self-gravity when it becomes sufficiently strong, thereby bringing substantial changes in the velocity distribution of stars and the galactic potential. One possible way to quantify such a change is to study the structure and evolution of the stellar velocity ellipsoid during the buckling instability and to provide potential diagnostic observables. In particular, how is the tilt of the velocity ellipsoid related to the boxy/peanut bulge such as presented in the Milky Way (Dwek et al. 1995). This requires, however, an unambiguous identification of the buckling event that a galaxy might be experiencing. However, the onset of buckling instability is not clearly understood because it is difficult to follow the orbits of stars subject to a rapidly changing gravitational potential during the buckling. During this transient phase the dynamics is strongly collective and an orbit decomposition can only be a partial description of the process. Nevertheless, numerous simulation studies marked this event by a decrease in the bar strength or in the ratio of vertical-toradial velocity dispersion ( σ z /σ r ) (Combes et al. 1990; Martinez-Valpuesta et al. 2006), providing a gross understanding of this event. Simulations show that often such demarcation is blurred and a more precise indica-</text>
<text><location><page_1><loc_52><loc_50><loc_92><loc_57></location>r of this event would be useful and complementary to the already existing ideas. It is worth re-investigating the buckling instability and the relation it might have with the orientation of the stellar velocity ellipsoid, in particular with the tilt angle.</text>
<text><location><page_1><loc_52><loc_19><loc_92><loc_50></location>The shape and orientation of the stellar velocity ellipsoid are tightly connected to the symmetry of the underlying galaxy potential (Lindblad 1930; Lynden-Bell 1962; Amendt & Cuddeford 1991). In a stationary, axisymmetric disk galaxy the stellar velocity ellipsoid in the galactic midplane is perfectly aligned with the galactocentric coordinate axes, in other words, all the offdiagonal elements of the velocity dispersion tensor are zero (Binney & Tremaine 1987). Thus, measuring the off-diagonal components of the dispersion tensor in observation may provide one with an inference about the presence of non-axisymmetric features in a galaxy. Away from the galactic midplane, the tilt of the velocity elliposid might depend on the mass distribution of the galactic disc as well as the flattening of the dark matter halo. In the context of the Milky Way, the analysis of the RAVE survey data release 2 (Zwitter et al 2008) shows that the velocity ellipsoid is tilted towards the Galactic Plane (Siebert et al. 2008) and has been nicely demonstrated in a recent paper by Pasetto et al. (2012). However, the measured tilt angles can not put a strong constraint on the disc parameters and halo flattening due to large proper motion errors and small sample size in the RAVE DR2 (Siebert et al. 2008).</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_19></location>On the other hand, non-axisymmetric structures such as bars, spiral arms in disk galaxies might play an important role in accounting for the observed orientation of the stellar velocity ellipsoid. Numerical study by Vorobyov & Theis (2008) shows that the vertex deviation of the velocity ellipsoid is globally correlated to the amplitude of the spiral arms. Using Hipparcos data and dynamical modeling, Dehnen (2000) has shown how</text>
<text><location><page_2><loc_8><loc_80><loc_48><loc_92></location>the Galactic Bar (Blitz & Spergel 1991; Binney et al. 1991; Dwek et al. 1995) could have influenced the velocity distribution in the solar neighborhood. The observed low-velocity streams in the solar neighborhood are also thought to have arisen due to the Galactic Bar (Minchev et al. 2010). It would be useful to understand how the presence of a bar or spiral arms which are highly time dependent would change the orientation of the velocity ellipsoid.</text>
<text><location><page_2><loc_8><loc_61><loc_48><loc_80></location>We use N-body simulations to follow the evolution of the stellar velocity ellipsoid in a galaxy which undergoes bar instability and forms a boxy bulge during the secular evolution in a self-consistent way. The buckling of the bar causes the morphological evolution of the disk, converting its central parts into a boxy/peanut bulge. In order to gain further insight into the physics of bar buckling (Merrifleld 1996; Martinez-Valpuesta & Shlosman 2004), we investigate the role of anisotropic stellar pressure and show that there is a characteristic signature in the way the stellar velocity ellipsoid evolves. The primary goal of this paper is to understand the buckling event of a bar which forms the boxy/peanut bulge and its relation with the tilt of the stellar velocity ellipsoid.</text>
<text><location><page_2><loc_8><loc_48><loc_48><loc_61></location>The paper is organized as follows. In the next section, we outline the general concept of the stellar velocity ellipsoid and the relevant quantities that we measure from our simulation. Section 3 briefly describes the galaxy models used for the present study and simulation. The disk evolution and boxy bulge formation is described in section 4. The shear stress and its relation to bar buckling is shown in section 5. We discuss the tilt angle of the velocity ellipsoid in section 5.1. Finally, section 6 presents the discussion and conclusions from this work.</text>
<section_header_level_1><location><page_2><loc_16><loc_46><loc_41><loc_47></location>2. STELLAR VELOCITY ELLIPSOID</section_header_level_1>
<text><location><page_2><loc_8><loc_40><loc_48><loc_45></location>The components of the velocity dispersion tensor at a radial location r in the stellar disk are computed from the velocity components of a group of stars using the following formula (Binney & Tremaine 1987):</text>
<formula><location><page_2><loc_20><loc_37><loc_48><loc_39></location>σ 2 ij = 〈 v i v j 〉 - 〈 v i 〉〈 v j 〉 , (1)</formula>
<text><location><page_2><loc_8><loc_29><loc_48><loc_36></location>where v i and v j denote the velocities of a group of stars. i, j = r, ϕ, z in a cylindrical coordinate system. Angular bracket denotes the averaging over a group of stars. Given the velocity dispersion tensor, the stress tensor of the stellar fluid can be written as</text>
<formula><location><page_2><loc_23><loc_27><loc_48><loc_29></location>τ = -ρ ( r ) σ 2 , (2)</formula>
<text><location><page_2><loc_8><loc_20><loc_48><loc_26></location>where ρ ( r ) is the local volume density of stars at a position r . It is convenient to think of the entire stress tensor as a sum of two different kinds of forces acting on a small differential imaginary surface ( dS ) between two adjacent volumes of stars, i.e.,</text>
<formula><location><page_2><loc_24><loc_18><loc_48><loc_19></location>τ = τ n + τ s , (3)</formula>
<text><location><page_2><loc_44><loc_12><loc_44><loc_14></location>/negationslash</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_17></location>where τ n,i = -ρ ( r ) σ 2 ii is called the normal stress acting along the normal to dS and σ 2 ii are the diagonal components of the above matrix. τ s,ij = -ρ ( r ) σ 2 ij , i = j is called the shear stress, acting along a direction perpendicular to the normal to dS , i.e., in the plane dS . In general, the shape of the velocity ellipsoid is determined by the normal stress, and the shear stress is responsible for</text>
<figure>
<location><page_2><loc_52><loc_57><loc_89><loc_92></location>
<caption>Fig. 1.Initial circular velocity curves for the model RCG051A and RHG057. In both panels, red dashed line denotes the disk, blue dotted line the bulge and green dash-dot line the dark halo. Solid black line denotes the total circular velocity curve. The inner regions of RCG051A are disk dominated, while that of RHG057 are dark matter dominated.</caption>
</figure>
<paragraph><location><page_2><loc_69><loc_47><loc_75><loc_48></location>TABLE 1</paragraph>
<table>
<location><page_2><loc_52><loc_36><loc_90><loc_42></location>
<caption>Initial disk, halo and bulge parameters. Q is the Toomre stability parameter at 2 . 5 R d ; M h and M b are the masses of halo and bulge.</caption>
</table>
<text><location><page_2><loc_52><loc_26><loc_92><loc_34></location>the orientation or deformation of the ellipsoid w.r.t. the galactocentric axes (ˆ e r , ˆ e ϕ , ˆ e z ). The orientation of the velocity ellipsoid can be computed using the off-diagonal components of the velocity dispersion tensor. The meridional tilt of the velocity ellipsoid can be computed using the following relation:</text>
<formula><location><page_2><loc_61><loc_22><loc_92><loc_25></location>Θ tilt = 1 2 arctan [ 2 σ 2 rz σ 2 rr -σ 2 zz ] . (4)</formula>
<text><location><page_2><loc_52><loc_15><loc_92><loc_21></location>Weevaluate the shape of the velocity ellipsoid and the tilt angle in the inner region of the disk where the dynamics of stars is dominated by a bar and study their evolution as the bar enters into the non-linear regime where an analytic understanding is difficult.</text>
<section_header_level_1><location><page_2><loc_62><loc_13><loc_82><loc_14></location>3. INITIAL GALAXY MODELS</section_header_level_1>
<text><location><page_2><loc_52><loc_7><loc_92><loc_12></location>In order to study the evolution of the stellar velocity ellipsoid subject to a non-axisymmetric bar potential, we perform a large number of simulations of isolated galaxies built using the method of Kuijken & Dubinski (1995).</text>
<text><location><page_3><loc_8><loc_72><loc_48><loc_92></location>Of these, we present here 3 fiducial models (named as RCG051A, RHG057 and RHG097) of disk galaxies with varying dark matter distribution and Toomre stability parameter (Q). The initial disk has an exponentially declining surface density with a scale length R d and mass M d . The live dark matter halo and bulge are modelled with a lowered Evans and King DF respectively. For further details on model construction, the reader is referred to Saha et al. (2010, 2012). We scale the models such that R d = 4 kpc and the disk masses are given in Table 1. Orbital time scales T orb (at 2 . 5 R d ) and other initial parameters are given in Table 1. In Fig. 1, we show the circular velocity curves for RCG051A and RHG057. Circular velocity curve for RHG097 can be found in Fig. 2 of Saha et al. (2010).</text>
<text><location><page_3><loc_8><loc_57><loc_48><loc_72></location>The simulations were performed using the Gadget code (Springel et al. 2001) which uses a variant of the leapfrog method for the time integration. The gravitational forces between the particles are calculated using the BarnesHut tree algorithm with a tolerance parameter θ tol = 0 . 7. The integration time step used was ∼ 0 . 82Myr for RCG051A, 0 . 65Myr for RHG097 and 1 . 5Myr for RHG057. Two of these models were evolved for about 6 -7 Gyr, and RHG057 was evolved for about 12Gyr to understand the long term evolution, bar growth and the asymptotic properties of the stellar velocity ellipsoid.</text>
<text><location><page_3><loc_8><loc_41><loc_48><loc_57></location>Each of these models were constructed using a total of 2 . 2 million particles, out of which disk and halo have 1 . 05 million each and 0 . 1 million particles are assigned to the bulge. The softening lengths for disk, bulge and halo particles were chosen so that the maximum force on each particle is nearly the same (McMillan & Dehnen 2007). In the model RHG097, the softening lengths used for the disk, bulge and halo were 12 , 25 and 33 pc respectively. For RCG051A, they were 12, 10 and 31pc and for RHG057, 12, 17 and 57pc respectively. The total energy is conserved well within 0.2% till the end of the simulation.</text>
<section_header_level_1><location><page_3><loc_12><loc_39><loc_45><loc_40></location>4. DISK EVOLUTION THROUGH BAR GROWTH</section_header_level_1>
<text><location><page_3><loc_8><loc_21><loc_48><loc_39></location>Bar driven secular evolution is an important internal process through which galaxies change their morphology and kinematics. The rapidity of such a process depends on various factors of which bar strength plays a significant role. A bar forms out of the disk instability and grows via nonlinear processes as the disk stars exchange energy and angular momentum with the surrounding dark matter halo and a preexisting classical bulge (Saha et al. 2012) through gravitational interaction. The evolution of an initially axisymmetric stellar disk and growth of a bar is depicted in Fig. 2, Fig. 3 and Fig. 4 which present the surface density maps of all the stars including that of a preexisting classical bulge.</text>
<text><location><page_3><loc_8><loc_7><loc_48><loc_21></location>In Fig. 5, we present the time evolution of the bar amplitude measured by the m = 2 Fourier component of the surface density of disk stars alone for the three fiducial models mentioned above. The growth rates of bars are significantly different in these models which also differ in the relative fraction of dark matter within the disk region. In model RHG057, the dark matter dominates the disk right from the center of the galaxy, see Fig. 1. According to the classification of Saha et al. (2010), model RHG057 forms a type-II bar and models RCG051A and RHG097 form a type-I bar. Typically, type-I bars are</text>
<figure>
<location><page_3><loc_52><loc_62><loc_88><loc_92></location>
<caption>Fig. 2.Face-on surface density maps of all the stars belonging to the disk and a preexisting classical bulge in the galaxy model RCG051A. Top left panel shows surface density at T = 0, top right at 2 . 0, bottom left at 3 . 4, and bottom right at 5 . 5 Gyrs.</caption>
</figure>
<figure>
<location><page_3><loc_52><loc_25><loc_89><loc_56></location>
<caption>Fig. 3.Same as in Fig. 2 but for RHG097. Top left panel shows surface density at T = 0, top right at 2 . 0, bottom left at 3 . 4, and bottom right at 5 . 5 Gyrs.</caption>
</figure>
<text><location><page_3><loc_52><loc_7><loc_92><loc_20></location>strong and go through the well known vertical buckling instability (Combes et al. 1990; Pfenniger & Friedli 1991; Raha et al. 1991; Martinez-Valpuesta et al. 2006; Debattista et al. 2006) leading to the formation of a boxy/peanut (hereafter b/p) bulge as depicted in Fig. 11 and Fig. 12. Whereas type-II bars which are weak and grow on secular evolution time scale, normally do not go through any appreciable buckling instability. We evolved the model RHG057 for a Hubble time and the disk showed no signature of buckling instability, although</text>
<figure>
<location><page_4><loc_8><loc_62><loc_45><loc_92></location>
<caption>Fig. 6.Vertical resonances in the stellar disks of two galaxy models mentioned in the figure. Green dashed lines represent the angular frequencies (Ω) at t = 2 . 2 Gyr (for upper panel) and t = 3 . 6 Gyr (lower panel). In the upper panel, Ω -ν/ 2 profiles (red solid and blue dash-dot lines) are drawn at t = 2 . 2 and 4 . 8 Gyr and the corresponding bar pattern speeds at those times are denoted by the dashed and solid black lines. In the lower panel, they are at t = 3 . 6 and 7 . 0 Gyr and the corresponding bar pattern speeds are denoted by horizontal black lines. The unit of frequencies for RHG097 and RHG057 are 44 . 65 and 19 . 0 kms -1 kpc -1 .</caption>
</figure>
<figure>
<location><page_4><loc_52><loc_54><loc_89><loc_92></location>
<caption>Fig. 4.Same as in Fig. 2 but for RHG057. Top left panel shows surface density at T = 0, top right at 2 . 0, bottom left at 3 . 5, and bottom right at 7 Gyrs.</caption>
</figure>
<figure>
<location><page_4><loc_8><loc_34><loc_48><loc_57></location>
<caption>Fig. 5.Time evolution of normalized bar amplitude for model RCG051A (green), RHG097 (red) and RHG057 (blue).</caption>
</figure>
<text><location><page_4><loc_8><loc_7><loc_48><loc_31></location>it has grown a moderate size bar by that time. As a result, the disk in this model did not form a b/p bulge by that time. A thorough understanding of the buckling instability would perhaps require a tool combining the orbital analysis and collective effect of the stars in the disk and their role at the 2 : 1 vertical inner Lindblad resonance (ILR). In order to pinpoint the location of the ILR, corotation resonances (CR), we first compute the disk frequencies (Ω, κ , ν ) by a direct sum of the first and second derivatives of the N -body potential obtained from the reflection symmetrized particle distribution with respect to the z = 0 plane and the R = 0 rotation axis. We carry out this exercise for each snapshot and compare Ω and Ω -ν/ 2 with the pattern speed of the bar. Fig. 6 shows the locations of the vertical ILRs and CRs at two different epochs for the two models RHG097 and RHG057. In the case of RHG097, the locations of vertical ILRs before ( t = 2 . 2 Gyr) and after ( t = 4 . 8 Gyr) the</text>
<text><location><page_4><loc_52><loc_24><loc_92><loc_43></location>buckling instability are still within the bar region indicating that the orbits lie close to the 2 : 1 vertical oscillations before and after the peanut formation. A detailed orbital analysis by Pfenniger & Friedli (1991) shows that the 2 : 1 vertical resonance is essentially responsible for the formation of b/p bulge, but the collective behaviour of stars in the vicinity of such resonances remains obscured. For example, it is not understood what is the role of shear stress or the anisotropic stellar pressure in such a process which eventually leads to the formation of b/p bulges. Below we elaborate on the possible relation between the buckling instability and the structure and evolution of the stellar velocity ellipsoid, in particular the shear stress due to the disk stars.</text>
<section_header_level_1><location><page_4><loc_55><loc_22><loc_89><loc_23></location>5. SHEAR STRESS AND BUCKLING INSTABILITY</section_header_level_1>
<text><location><page_4><loc_52><loc_7><loc_92><loc_21></location>As the bar becomes stronger it enters into the regime of the buckling instability. This instability is highly nonlinear in the sense that the bending oscillation amplitude is not proportional to self-gravity. In the case of a bending instability, we would expect a proportionality between the bending oscillation and the imposed load (here, self-gravity). In the linear regime, a stellar disk is stable against the low order (e.g., m = 0 , 1) bending perturbation and the self-gravity of the perturbation acts like a stabilizing agent as shown by several authors, e.g., Toomre (1966), Araki (1985),</text>
<figure>
<location><page_5><loc_8><loc_70><loc_48><loc_92></location>
</figure>
<figure>
<location><page_5><loc_52><loc_69><loc_91><loc_92></location>
<caption>Fig. 7.Time evolution of A 1 ,z denoting the vertical asymmetry in the bar region. Green line denotes model RCG051A, red line for RHG097 and blue for RHG057.</caption>
</figure>
<text><location><page_5><loc_8><loc_35><loc_48><loc_65></location>Merritt & Sellwood (1994), Sellwood (1996), Saha & Jog (2006). It is the pressure forces which destabilizes a stellar disk in response to a bending perturbation. From the works of Toomre (1966), Araki (1985) and Fridman & Poliachenko (1984), we learnt that a stellar slab of finite thickness would go bending unstable if σ z /σ r < 0 . 3. However, the critical value of σ z /σ r , at which a self-consistent rotating stellar bar would go bending unstable is unclear. Actually, it is doubtful that a criterion based only on a local quantity such as σ z /σ r would apply in a bar, as the 2 / 1 vertical resonance is a crucial factor which reflects a non-local feature of the system: its orbital behavior. Indeed and contrary to collisional fluids, collisionless fluids may develop long range correlations which are not captured by a purely local description. The distinction between kinematic based and spatial mass distribution based instabilities in collisionless system has been presented by Pfenniger (1996, 1998). A fire-hose instability belongs to instabilities depending on a strong gradient in the velocity part of the DF, while a bar buckling instability belongs to instabilities mainly related to the presence of a strong resonance, which is determined by the spatial mass distribution.</text>
<text><location><page_5><loc_8><loc_29><loc_48><loc_35></location>In this section, we investigate the role played by the shear stress, in particular, the meridional component ( τ s,rz ) which exerts a torque in the vertical direction on an imaginary cube of the stellar fluid.</text>
<text><location><page_5><loc_8><loc_7><loc_48><loc_29></location>First, we quantify the buckling amplitude ( A 1 z ) by computing the m = 1 Fourier component in the r -z plane of the disk with the major axis of the bar aligned to the disk major axis and identify the buckling phase by studying the time evolution of A 1 z . During the the buckling phase A 1 z reaches a peak value and sometimes goes through a second buckling (Martinez-Valpuesta et al. 2006). In Fig. 7, we present the time evolution of A 1 z for the three models. A 1 z for RCG051A shows a strong peak at T ∼ 2Gyr usually considered as the first buckling of the bar. It is interesting to note that the bar in this model suffers subsequent buckling of smaller amplitudes. The onset of the buckling instability can be indicated by different physical parameters, e.g., a drop in A 2 or σ z /σ r as mentioned above. For the model RCG051A, both Fig. 5 and Fig. 8 indicate that at around 2 Gyr, there is a drop in A 2 and σ z /σ r respectively as found in</text>
<figure>
<location><page_5><loc_52><loc_42><loc_91><loc_64></location>
<caption>Fig. 8.Time evolution of the flattening of the velocity ellipsoid in galaxy models RCG051A(green solid line), RHG097 (red dashed line) and RHG057 (blue dotted line).Fig. 9.Time evolution of the meridional shear stress normalized by the initial normal stress along the radial direction in RCG051A(green), RHG097 (red) and RHG057 (blue).</caption>
</figure>
<figure>
<location><page_5><loc_52><loc_13><loc_91><loc_36></location>
<caption>Fig. 10.Radial variation of the disk midplane in the bar region for the model RHG097. The profiles are drawn at T = 0 (dashdot-dot line), 3.4 (solid black line), 4.0 (red dashed line), 4.4 (green dash-dot line) and 5.5 (blue dotted line) Gyrs.</caption>
</figure>
<figure>
<location><page_6><loc_9><loc_59><loc_45><loc_92></location>
</figure>
<figure>
<location><page_6><loc_52><loc_59><loc_89><loc_92></location>
<caption>Fig. 11.Edge-on projection of the surface density maps of the stellar disk in model RCG051A. Time shown in the panels is in Gyr. Buckling instability is evident from the vertical asymmetry of the density contours at t = 2 Gyrs.</caption>
</figure>
<text><location><page_6><loc_8><loc_51><loc_20><loc_52></location>previous studies.</text>
<text><location><page_6><loc_8><loc_33><loc_48><loc_51></location>In Fig. 9, we show the time evolution of the meridional shear stress normalized by the initial normal stress defined in Eq. 3. It demonstrates clearly that the meridional stress develop slowly as the bar evolves and reaches its first peak value as the bar enters the buckling phase at about 2 Gyr following closely the time evolution of A 1 z in RCG051A. We establish, here, a new indicator of the bar buckling instability that correlates well with other indicators mentioned above in a galaxy with a cold stellar disk undergoing a rapid phase of bar growth (here, RCG051A). Let us now examine the other two models where the bar growth rate is rather slow in comparison to RCG051A.</text>
<text><location><page_6><loc_8><loc_19><loc_48><loc_33></location>In model RHG097, the peak in A 1 z (see Fig. 7) coincides with that in the meridional stress shown in Fig. 9 at around 3 . 4Gyr. However, the drop in σ z /σ r occurs noticeably earlier at around 1 . 5Gyr, when no buckling event was found from the time evolution of A 1 z as well as from the visual inspection of the surface density maps in edge-on projection (see Fig. 12). It is evident that a drop in σ z /σ r is not an unambiguous indicator of the buckling event of strong bars, whereas the meridional stress is promising in indicating the onset of buckling instability.</text>
<text><location><page_6><loc_8><loc_7><loc_48><loc_19></location>On the other hand, for a dark matter dominated radially hot stellar disk as in model RHG057, the bar grows on a much slower rate (see Fig. 5) and shows no peak in A 1 z (see Fig. 7). Also Fig. 8 shows no appreciable drop in σ z /σ r except at around 6 Gyr where a smooth decrease in σ z /σ r is apparent. The meridional stress remains nearly flat and close to zero for this galaxy model which has been evolved for about 12 Gyr during which no buckling event was detected.</text>
<figure>
<location><page_6><loc_52><loc_21><loc_89><loc_55></location>
<caption>Fig. 12.Same as in Fig. 11 but for model RHG097. Buckling instability occurs at t = 3 . 4 Gyrs.Fig. 13.Same as in Fig. 11 but for model RHG057. No vertical asymmetry in the density contours detected within t /similarequal 12 Gyrs.</caption>
</figure>
<text><location><page_6><loc_52><loc_10><loc_92><loc_17></location>As the bar evolves through the buckling phase, the disk midplane also responds and exhibits a characteristic buckling mode. We compute the location of the disk midplane using the following formula to follow the buckling:</text>
<formula><location><page_6><loc_65><loc_4><loc_92><loc_9></location>〈 z 〉 = ∫ zρ ( r, z ) dz ∫ ρ ( r, z ) dz , (5)</formula>
<text><location><page_7><loc_8><loc_85><loc_48><loc_92></location>where ρ ( r, z ) is the volume density distribution of stars. Since the meridional shear stress for the model RHG097 was comparatively high, the disk midplane was expected to show noticeable bending. We discuss here only the case of RHG097 and mention briefly the other models.</text>
<text><location><page_7><loc_8><loc_69><loc_48><loc_85></location>Initially, the disk midplane remains flat at z = 0 as shown in Fig. 10 for the model RHG097. At t = 3 . 4 Gyrs, the midplane reaches its peak value 〈 z 〉 ∼ 130 pc. Subsequently, the z -amplitude decreases to nearly zero at around 5 . 5 Gyrs restoring the symmetry along the vertical direction. The buckling modes of the bar in this model have characteristic nodes at R ∼ 0 . 6 R d and ∼ 1 . 8 R d (see Fig. 10). Comparing with Fig. 6, we find that the location of the second node is close to the corotation of the bar. The time evolution of the z -amplitude indicates that the buckling instability is a sudden event in the galaxy evolution.</text>
<text><location><page_7><loc_8><loc_65><loc_48><loc_69></location>The model RCG051A also showed similar behaviour in the z -amplitude. But the z -amplitude in model RHG057 remained close to zero at all times.</text>
<section_header_level_1><location><page_7><loc_13><loc_63><loc_43><loc_64></location>5.1. Meridional tilt of the velocity ellipsoid</section_header_level_1>
<text><location><page_7><loc_8><loc_24><loc_48><loc_63></location>In this section, we discuss the orientation of the stellar velocity ellipsoid in the meridional plane ( R -z plane) of the galactic disk. Since the buckling instability creates an asymmetry in the vertical density distribution and assuming it preserves reflection symmetry with respect to the galactic centre, we consider only one half of the meridional plane for the computation of the stellar velocity ellipsoid. When the bar has formed, we rotate it so that its major axis is perpendicular to the line-ofsight; in other words, the tilt is calculated in the meridional plane containing the bar major axis. In edge-on projection, the meridional plane would closely resemble the surface density maps shown, for example, in Fig. 12. In order to understand the spatio-temporal variation of the stellar velocity ellipsoid in a model galaxy, we further subdivide the entire meridional plane into several small cells each of which contain sufficient number of particles for reasonable estimate of the velocity dispersion and the meridional tilt. The cell sizes are fixed at ∆ R = 0 . 4 R d in radius and ∆ z = 0 . 2 R d . The number of particles in each of these cells vary over time as they are subject to mixing and migration driven by the combined effect of an evolving bar and spiral structures in the disk (Minchev & Famaey 2010). To give an idea of the number of particles used, the cell at R = 1 . 8 -2 . 4 R d and z = 0 . 3 -0 . 5 R d contains about 20 , 000 particles and the innermost cells have about 100000 particles at t = 4 . 8 Gyr for the model RHG097 (for reference see Fig. 14).</text>
<text><location><page_7><loc_8><loc_7><loc_48><loc_24></location>Fig. 14 depicts the spatio-temporal variation of the velocity ellipsoid in the meridional plane of the galaxy model RHG097. Initially, the velocity ellipsoid in the disk are all aligned with the galactocentric coordinate axes and the same holds true for a period of about 3 Gyr when the bar has fully developed in the disk, see Fig. 3. At 3 . 4 Gyr, the bar undergoes a sudden buckling instability and the meridional tilt of the velocity ellipsoid reaches a peak value as can be seen from the corresponding panel in Fig. 14. Note that the maximum of the tilt occurs at the first node of the buckled bar (see Fig. 10) which roughly coincides with the edge of the peanut shape in this model (see Fig. 12). In general, higher values of tilt</text>
<text><location><page_7><loc_52><loc_73><loc_92><loc_92></location>angle can be found in the b/p region away from the minor axis of the galaxy during the buckling phase. It is interesting to notice the spontaneous symmetry breaking in the shape distribution of the velocity ellipsoid in the meridional plane about the midplane of the galaxy just after the peak of the buckling phase. Such asymmetry continues to persist for about 1 -1 . 5 Gyr since the onset of buckling instability, during which the density distribution is also asymmetric about the midplane (see, Fig. 12). After the peak of the buckling phase, the tilt angle of the velocity ellipsoid gradually decreases to a low value during the subsequent evolution of the galaxy, restoring symmetry both in the shape distribution of the velocity ellipsoid and the mass density about the midplane.</text>
<text><location><page_7><loc_52><loc_49><loc_92><loc_73></location>Note that, the velocity ellipsoid near the minor axis of the galaxy remains nearly aligned with the galactocentric coordinate axes before the onset of buckling instability and at later times. Although not shown explicitly here, the meridional tilt angle of the velocity ellipsoid along the minor axis of the galaxy remains zero at all times during the galaxy evolution. The meridional tilt of the velocity ellipsoid outside the b/p region is nearly unaffected by the buckling instability. As shown clearly in Fig. 14 (see panel at t = 2 . 4 Gyr), the meridional tilt angle is nearly zero for galaxies which host a bar that did not go through a buckling instability. From Fig. 14, it is clear that the size of the velocity ellipsoid near the minor axis nearly doubles at times when buckling instability is at its maximum and their sizes continue to increase. Since the semi-major axis of the velocity ellisoid actually measures the radial velocity dispersion, it shows clear indication of heating in the whole b/p region of the galaxy model.</text>
<text><location><page_7><loc_52><loc_11><loc_92><loc_49></location>Fig. 15 shows the time evolution of the average meridional tilt angle (Θ tilt ) of the velocity ellipsoid computed in the b/p region for all the models. In both models RHG097 and RCG051A, the meridional tilt angle rises to a peak value during the buckling instability phase. On the other hand, the tilt angle scatters around zero for the model RHG057 at all times. From the time evolution, a large value of the tilt angle is a characteristic signature of the buckling phase that these model galaxies might have undergone. In other words, findings of a large value of the tilt angle in the b/p region of a galaxy would indicate that it might be in the buckling phase or near the vicinity of the buckling instability. The subsequent evolution of the buckling instability in model RHG097 is particularly interesting because of the gradual decrement of the tilt angle. It takes about 1 Gyr for the meridional tilt angle to fall by half its peak value and can be considered as the half-life of the buckling phase ( T tilt , 1 / 2 ) the galaxy has experienced. We find that T tilt , 1 / 2 ∼ 3 × T orb , where T orb is the orbital time at the disk half-mass radius (for this model), which is quite short compared to the galaxy's lifetime. This might be the reason for the difficulty in observing galaxies in the buckling phase. However, T tilt , 1 / 2 may depend on various parameters of the galaxy models and a thorough search of the parameter space is required to find an optimal galaxy model which would show large values of tilt angle over long periods of time. The dependence of T tilt , 1 / 2 on the dark halo and bulge properties will be considered in a future paper.</text>
<figure>
<location><page_8><loc_8><loc_6><loc_91><loc_89></location>
<caption>Fig. 14.2D map of the stellar velocity ellipsoid in the meridional ( R -z ) plane of the disk in model RHG097. Time units are in Gyrs. Color bar represents the amplitude of the radial velocity dispersion ( σ r ). The actual value of σ r is obtained by multiplying the color indices by 893 kms -1 . The major and minor axes of the velocity ellipsoid are determined by σ r and σ z and they are denoted as inscribed crosses. A rough estimate of the tilt angle for each ellipsoid can be gleaned from Fig. 15.</caption>
</figure>
<figure>
<location><page_9><loc_8><loc_71><loc_45><loc_92></location>
<caption>Fig. 15.Time evolution of the meridional tilt angle of the stellar velocity ellipsoid in the boxy bulge region in three modelsRCG051A (green), RHG097 (red) and RHG057 (blue).</caption>
</figure>
<text><location><page_9><loc_8><loc_20><loc_48><loc_67></location>The calculation of the stellar velocity ellipsoid assumes that the moment integrals of the DF exist and returns a finite value. However, the validity of such an assumption is questionable, especially when the stellar system is undergoing an unstable phase e.g., buckling instability in the present case. The resonant parts of the phase space during such an instability can develop bi-modal and/or particle distribution with long tail for which the very notion of first or second moment of the DF is mathematically no longer meaningful. Bimodal velocity distribution has been observed for late-type stars in the solar neighborhood by Hipparcos and numerical models of disk response to a bar is shown to have reproduced many such features in the local velocity distribution (Dehnen 2000; Fux 2001; Minchev et al. 2010). In Fig. 16, we show the normalized histograms for radial ( v r ) and vertical ( v z ) velocities in the model RHG097 during and after the buckling instability nearly disappeared. We picked up three different regions in the meridional plane and histograms, in the two regions ( R = 0 . 6 , z = 0 . and R = 0 . 6 , z = 0 . 2) where the meridional tilt was maximum, are fairly well represented by a single Gaussian DF with different variances. In the region close to the minor axis of the galaxy i.e., R = 0 . 2 , z = 0 . 2, the radial velocity histograms needed two Gaussian DFs: one with cold component with dispersion ∼ 30 kms -1 and one with a hot component with a dispersion ∼ 102 kms -1 . A close inspection of Fig. 14 indicates that the stars are heated strongly in that region as it is clear from the size of the ellipsoids. At the time of buckling, the size of the ellipsoid nearly doubles indicating an increase in the velocity dispersion by a factor of two. In any case, in all the regions examined, we have a unimodal DF to represent the stars in the meridional plane and they show well behaved first and second moments.</text>
<section_header_level_1><location><page_9><loc_16><loc_18><loc_41><loc_19></location>6. DISCUSSION AND CONCLUSIONS</section_header_level_1>
<text><location><page_9><loc_8><loc_7><loc_48><loc_17></location>The buckling instability is one of the routes through which an initially axisymmetric stellar disk would form a boxy/peanut bulge such as present in our own Galaxy. In order to understand the formation of such a boxy/peanut morphology, it is important to have further insight on the buckling instability. How and when would a bar go buckling unstable? How many buckling events has a present day galaxy experienced? How does it depend on the</text>
<figure>
<location><page_9><loc_53><loc_40><loc_94><loc_91></location>
<caption>Fig. 16.Velocity histograms of stars at 3 different regions (as indicated in the panels) in the meridional plane of the galaxy model RHG097. Blue lines indicate vertical velocity and red and broader ones indicate radial. Only the radial velocity histograms are fitted with Gaussians, just for illustration.</caption>
</figure>
<text><location><page_9><loc_53><loc_64><loc_54><loc_68></location>dN/(NdV)</text>
<text><location><page_9><loc_52><loc_16><loc_92><loc_32></location>dark matter fraction in galaxies? There are several issues needed to be addressed in order to grasp this phenomenon. The current paper addresses one such issue on the onset of a buckling event in a disk galaxy. It is shown that there is a connection between the onset of the buckling instability and the shear stress of stars. We see that the shear stress reaches its peak value during the buckling phase and then decreases gradually. The development of a shear stress in the stars is a result of collective process in the disk. If these stars are also trapped in the vertical ILRs, this would eventually lead to the buckling instability (Pfenniger & Friedli 1991; Quillen 2002).</text>
<text><location><page_9><loc_52><loc_7><loc_92><loc_16></location>From our study, it is clear that a bar that grows very slowly, on a several Gyr time scale, does neither develop any appreciable shear stress nor go through any buckling instability. On the other hand, bars that grow very rapidly such as in RCG051A, develop both, shear stress and buckling instability. In no cases that we have studied does a shear stress develop in the bar and not go</text>
<text><location><page_10><loc_8><loc_83><loc_48><loc_92></location>through the buckling instability. One emerging scenario is that the development of shear stress is related to the rate at which a bar grows i.e., the rate at which a bar strength grows through transport of angular momentum outward. In galaxy models with higher values of Toomre Q , the growth of bar strength is rather slow leading to weak bar and insignificant amount of shear stress.</text>
<text><location><page_10><loc_8><loc_60><loc_48><loc_82></location>Several important kinematical changes occur in the galaxy during and after the episode of the buckling instability. From the Fig. 14, it is clear that the stars are heated in the b/p region, especially close to the minor axis of the galaxy, by a factor of ∼ 2 during the buckling instability. This was shown previously by Saha et al. (2010) for model RHG097 and others. Another interesting aspect is the kinematical changes in the vertical structure of the galaxy. Note, the stellar disk is isothermal initially (see the first panel at t = 1 . 1 Gyr in Fig. 14). In the after-episode of the buckling phase, there is a clear distinction in the velocity dispersion above and below the disk midplane indicating spontaneous breaking of isothermal structure in the b/p region. Such nonisothermal vertical structure in the b/p region is persistent long after the buckling phase. We will address this issue in more detail in a future paper.</text>
<text><location><page_10><loc_8><loc_55><loc_48><loc_60></location>Our main conclusions from this work are as follows: 1. We show that the meridional tilt of the stellar velocity ellipsoid is a better indicator compared to a drop in the bar amplitude or σ z /σ r for the onset of the buck-</text>
<text><location><page_10><loc_52><loc_84><loc_92><loc_92></location>ng instability of a stellar bar in a disk galaxy. During the buckling event, the tilt angle reaches a peak value followed by a gradual decrease. Outside the buckling episode, the tilt angle is nearly zero. The meridional shear stress of stars and the onset of the buckling instability of a stellar bar is closely connected.</text>
<unordered_list>
<list_item><location><page_10><loc_52><loc_77><loc_92><loc_84></location>2. A large value of the tilt angle of the stellar velocity ellipsoid in the b/p region indicates the occurrence of a buckling event in the galaxy. The meridional tilt angle of the velocity ellipsoid remains close to zero if the bar does not experience the buckling phase.</list_item>
<list_item><location><page_10><loc_52><loc_72><loc_92><loc_77></location>3. Disk galaxies that are radially hot and highly dominated by the dark matter halo might not have gone through a buckling instability. Buckling instability appears to depend on the growth rate of bar strength.</list_item>
<list_item><location><page_10><loc_52><loc_67><loc_92><loc_72></location>4. Buckling instability changes the vertical structure and kinematics in the boxy/peanut region of the galaxy, in particular it changes vertical structure from isothermal to non-isothermal in one of our models.</list_item>
</unordered_list>
<section_header_level_1><location><page_10><loc_64><loc_65><loc_80><loc_66></location>ACKNOWLEDGEMENT</section_header_level_1>
<text><location><page_10><loc_52><loc_53><loc_92><loc_65></location>The simulations presented in this paper were carried out on the computer cluster system of ASIAA. This work was supported, in part, by the Theoretical Institute for Advanced Research in Astrophysics operated under the ASIAA. K.S. acknowledges support from the Alexander von Humboldt Foundation. D.P. acknowledges support from the Swiss National Science Foundation. The authors thank the anonymous referee for insightful comments on the manuscript.</text>
<section_header_level_1><location><page_10><loc_45><loc_51><loc_55><loc_52></location>REFERENCES</section_header_level_1>
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</document>
[
{
"title": "ABSTRACT",
"content": "The structure and evolution of the stellar velocity ellipsoid plays an important role in shaping galaxies undergoing bar driven secular evolution and the eventual formation of a boxy/peanut bulge such as present in the Milky Way. Using collisionless N-body simulations, we show that during the formation of such a boxy/peanut bulge, the meridional shear stress of stars, which can be measured by the meridional tilt of the velocity ellipsoid, reaches a characteristic peak in its time evolution. It is shown that the onset of a bar buckling instability is closely connected to the maximum meridional tilt of the stellar velocity ellipsoid. Our findings bring new insight to this complex gravitational instability of the bar which complements the buckling instability studies based on orbital models. We briefly discuss the observed diagnostics of the stellar velocity ellipsoid during such a phenomenon. Subject headings: galaxies: bulges - galaxies:kinematics and dynamics - galaxies: structure galaxies:evolution - Galaxy: disk, galaxies:halos, stellar dynamics",
"pages": [
1
]
},
{
"title": "MERIDIONAL TILT OF THE STELLAR VELOCITY ELLIPSOID DURING BAR BUCKLING INSTABILITY",
"content": "Kanak Saha 1 , Daniel Pfenniger 2 , & Ronald E. Taam 3 , 4 1 Max-Planck-Institut fr Extraterrestrische Physik, Giessenbachstraße, D-85748 Garching, Germany, 2 Geneva Observatory, University of Geneva, CH-1290 Sauverny, Switzerland, 3 Institute of Astronomy and Astrophysics, Academia Sinica-TIARA, Taiwan, 4 Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA e-mail: [email protected] Draft version July 20, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Understanding the structure and dynamics of a galaxy crucially depends on the knowledge of the three dimensional stellar distribution function (DF), which is not a direct observable. The first few moments of the DF, e.g., density, mean velocity and the velocity dispersion tensor together can provide important clues regarding the dynamical state of the galaxy and the gravitational instabilities it might have undergone (van der Kruit 1999). Of particular interest is the buckling instability of a stellar bar in a disk galaxy and the subsequent formation of a boxy/peanut bulge (Combes et al. 1990; Pfenniger & Friedli 1991; Raha et al. 1991; Pfenniger 1993; Athanassoula 2005). A bar buckles under its own self-gravity when it becomes sufficiently strong, thereby bringing substantial changes in the velocity distribution of stars and the galactic potential. One possible way to quantify such a change is to study the structure and evolution of the stellar velocity ellipsoid during the buckling instability and to provide potential diagnostic observables. In particular, how is the tilt of the velocity ellipsoid related to the boxy/peanut bulge such as presented in the Milky Way (Dwek et al. 1995). This requires, however, an unambiguous identification of the buckling event that a galaxy might be experiencing. However, the onset of buckling instability is not clearly understood because it is difficult to follow the orbits of stars subject to a rapidly changing gravitational potential during the buckling. During this transient phase the dynamics is strongly collective and an orbit decomposition can only be a partial description of the process. Nevertheless, numerous simulation studies marked this event by a decrease in the bar strength or in the ratio of vertical-toradial velocity dispersion ( σ z /σ r ) (Combes et al. 1990; Martinez-Valpuesta et al. 2006), providing a gross understanding of this event. Simulations show that often such demarcation is blurred and a more precise indica- r of this event would be useful and complementary to the already existing ideas. It is worth re-investigating the buckling instability and the relation it might have with the orientation of the stellar velocity ellipsoid, in particular with the tilt angle. The shape and orientation of the stellar velocity ellipsoid are tightly connected to the symmetry of the underlying galaxy potential (Lindblad 1930; Lynden-Bell 1962; Amendt & Cuddeford 1991). In a stationary, axisymmetric disk galaxy the stellar velocity ellipsoid in the galactic midplane is perfectly aligned with the galactocentric coordinate axes, in other words, all the offdiagonal elements of the velocity dispersion tensor are zero (Binney & Tremaine 1987). Thus, measuring the off-diagonal components of the dispersion tensor in observation may provide one with an inference about the presence of non-axisymmetric features in a galaxy. Away from the galactic midplane, the tilt of the velocity elliposid might depend on the mass distribution of the galactic disc as well as the flattening of the dark matter halo. In the context of the Milky Way, the analysis of the RAVE survey data release 2 (Zwitter et al 2008) shows that the velocity ellipsoid is tilted towards the Galactic Plane (Siebert et al. 2008) and has been nicely demonstrated in a recent paper by Pasetto et al. (2012). However, the measured tilt angles can not put a strong constraint on the disc parameters and halo flattening due to large proper motion errors and small sample size in the RAVE DR2 (Siebert et al. 2008). On the other hand, non-axisymmetric structures such as bars, spiral arms in disk galaxies might play an important role in accounting for the observed orientation of the stellar velocity ellipsoid. Numerical study by Vorobyov & Theis (2008) shows that the vertex deviation of the velocity ellipsoid is globally correlated to the amplitude of the spiral arms. Using Hipparcos data and dynamical modeling, Dehnen (2000) has shown how the Galactic Bar (Blitz & Spergel 1991; Binney et al. 1991; Dwek et al. 1995) could have influenced the velocity distribution in the solar neighborhood. The observed low-velocity streams in the solar neighborhood are also thought to have arisen due to the Galactic Bar (Minchev et al. 2010). It would be useful to understand how the presence of a bar or spiral arms which are highly time dependent would change the orientation of the velocity ellipsoid. We use N-body simulations to follow the evolution of the stellar velocity ellipsoid in a galaxy which undergoes bar instability and forms a boxy bulge during the secular evolution in a self-consistent way. The buckling of the bar causes the morphological evolution of the disk, converting its central parts into a boxy/peanut bulge. In order to gain further insight into the physics of bar buckling (Merrifleld 1996; Martinez-Valpuesta & Shlosman 2004), we investigate the role of anisotropic stellar pressure and show that there is a characteristic signature in the way the stellar velocity ellipsoid evolves. The primary goal of this paper is to understand the buckling event of a bar which forms the boxy/peanut bulge and its relation with the tilt of the stellar velocity ellipsoid. The paper is organized as follows. In the next section, we outline the general concept of the stellar velocity ellipsoid and the relevant quantities that we measure from our simulation. Section 3 briefly describes the galaxy models used for the present study and simulation. The disk evolution and boxy bulge formation is described in section 4. The shear stress and its relation to bar buckling is shown in section 5. We discuss the tilt angle of the velocity ellipsoid in section 5.1. Finally, section 6 presents the discussion and conclusions from this work.",
"pages": [
1,
2
]
},
{
"title": "2. STELLAR VELOCITY ELLIPSOID",
"content": "The components of the velocity dispersion tensor at a radial location r in the stellar disk are computed from the velocity components of a group of stars using the following formula (Binney & Tremaine 1987): where v i and v j denote the velocities of a group of stars. i, j = r, ϕ, z in a cylindrical coordinate system. Angular bracket denotes the averaging over a group of stars. Given the velocity dispersion tensor, the stress tensor of the stellar fluid can be written as where ρ ( r ) is the local volume density of stars at a position r . It is convenient to think of the entire stress tensor as a sum of two different kinds of forces acting on a small differential imaginary surface ( dS ) between two adjacent volumes of stars, i.e., /negationslash where τ n,i = -ρ ( r ) σ 2 ii is called the normal stress acting along the normal to dS and σ 2 ii are the diagonal components of the above matrix. τ s,ij = -ρ ( r ) σ 2 ij , i = j is called the shear stress, acting along a direction perpendicular to the normal to dS , i.e., in the plane dS . In general, the shape of the velocity ellipsoid is determined by the normal stress, and the shear stress is responsible for the orientation or deformation of the ellipsoid w.r.t. the galactocentric axes (ˆ e r , ˆ e ϕ , ˆ e z ). The orientation of the velocity ellipsoid can be computed using the off-diagonal components of the velocity dispersion tensor. The meridional tilt of the velocity ellipsoid can be computed using the following relation: Weevaluate the shape of the velocity ellipsoid and the tilt angle in the inner region of the disk where the dynamics of stars is dominated by a bar and study their evolution as the bar enters into the non-linear regime where an analytic understanding is difficult.",
"pages": [
2
]
},
{
"title": "3. INITIAL GALAXY MODELS",
"content": "In order to study the evolution of the stellar velocity ellipsoid subject to a non-axisymmetric bar potential, we perform a large number of simulations of isolated galaxies built using the method of Kuijken & Dubinski (1995). Of these, we present here 3 fiducial models (named as RCG051A, RHG057 and RHG097) of disk galaxies with varying dark matter distribution and Toomre stability parameter (Q). The initial disk has an exponentially declining surface density with a scale length R d and mass M d . The live dark matter halo and bulge are modelled with a lowered Evans and King DF respectively. For further details on model construction, the reader is referred to Saha et al. (2010, 2012). We scale the models such that R d = 4 kpc and the disk masses are given in Table 1. Orbital time scales T orb (at 2 . 5 R d ) and other initial parameters are given in Table 1. In Fig. 1, we show the circular velocity curves for RCG051A and RHG057. Circular velocity curve for RHG097 can be found in Fig. 2 of Saha et al. (2010). The simulations were performed using the Gadget code (Springel et al. 2001) which uses a variant of the leapfrog method for the time integration. The gravitational forces between the particles are calculated using the BarnesHut tree algorithm with a tolerance parameter θ tol = 0 . 7. The integration time step used was ∼ 0 . 82Myr for RCG051A, 0 . 65Myr for RHG097 and 1 . 5Myr for RHG057. Two of these models were evolved for about 6 -7 Gyr, and RHG057 was evolved for about 12Gyr to understand the long term evolution, bar growth and the asymptotic properties of the stellar velocity ellipsoid. Each of these models were constructed using a total of 2 . 2 million particles, out of which disk and halo have 1 . 05 million each and 0 . 1 million particles are assigned to the bulge. The softening lengths for disk, bulge and halo particles were chosen so that the maximum force on each particle is nearly the same (McMillan & Dehnen 2007). In the model RHG097, the softening lengths used for the disk, bulge and halo were 12 , 25 and 33 pc respectively. For RCG051A, they were 12, 10 and 31pc and for RHG057, 12, 17 and 57pc respectively. The total energy is conserved well within 0.2% till the end of the simulation.",
"pages": [
2,
3
]
},
{
"title": "4. DISK EVOLUTION THROUGH BAR GROWTH",
"content": "Bar driven secular evolution is an important internal process through which galaxies change their morphology and kinematics. The rapidity of such a process depends on various factors of which bar strength plays a significant role. A bar forms out of the disk instability and grows via nonlinear processes as the disk stars exchange energy and angular momentum with the surrounding dark matter halo and a preexisting classical bulge (Saha et al. 2012) through gravitational interaction. The evolution of an initially axisymmetric stellar disk and growth of a bar is depicted in Fig. 2, Fig. 3 and Fig. 4 which present the surface density maps of all the stars including that of a preexisting classical bulge. In Fig. 5, we present the time evolution of the bar amplitude measured by the m = 2 Fourier component of the surface density of disk stars alone for the three fiducial models mentioned above. The growth rates of bars are significantly different in these models which also differ in the relative fraction of dark matter within the disk region. In model RHG057, the dark matter dominates the disk right from the center of the galaxy, see Fig. 1. According to the classification of Saha et al. (2010), model RHG057 forms a type-II bar and models RCG051A and RHG097 form a type-I bar. Typically, type-I bars are strong and go through the well known vertical buckling instability (Combes et al. 1990; Pfenniger & Friedli 1991; Raha et al. 1991; Martinez-Valpuesta et al. 2006; Debattista et al. 2006) leading to the formation of a boxy/peanut (hereafter b/p) bulge as depicted in Fig. 11 and Fig. 12. Whereas type-II bars which are weak and grow on secular evolution time scale, normally do not go through any appreciable buckling instability. We evolved the model RHG057 for a Hubble time and the disk showed no signature of buckling instability, although it has grown a moderate size bar by that time. As a result, the disk in this model did not form a b/p bulge by that time. A thorough understanding of the buckling instability would perhaps require a tool combining the orbital analysis and collective effect of the stars in the disk and their role at the 2 : 1 vertical inner Lindblad resonance (ILR). In order to pinpoint the location of the ILR, corotation resonances (CR), we first compute the disk frequencies (Ω, κ , ν ) by a direct sum of the first and second derivatives of the N -body potential obtained from the reflection symmetrized particle distribution with respect to the z = 0 plane and the R = 0 rotation axis. We carry out this exercise for each snapshot and compare Ω and Ω -ν/ 2 with the pattern speed of the bar. Fig. 6 shows the locations of the vertical ILRs and CRs at two different epochs for the two models RHG097 and RHG057. In the case of RHG097, the locations of vertical ILRs before ( t = 2 . 2 Gyr) and after ( t = 4 . 8 Gyr) the buckling instability are still within the bar region indicating that the orbits lie close to the 2 : 1 vertical oscillations before and after the peanut formation. A detailed orbital analysis by Pfenniger & Friedli (1991) shows that the 2 : 1 vertical resonance is essentially responsible for the formation of b/p bulge, but the collective behaviour of stars in the vicinity of such resonances remains obscured. For example, it is not understood what is the role of shear stress or the anisotropic stellar pressure in such a process which eventually leads to the formation of b/p bulges. Below we elaborate on the possible relation between the buckling instability and the structure and evolution of the stellar velocity ellipsoid, in particular the shear stress due to the disk stars.",
"pages": [
3,
4
]
},
{
"title": "5. SHEAR STRESS AND BUCKLING INSTABILITY",
"content": "As the bar becomes stronger it enters into the regime of the buckling instability. This instability is highly nonlinear in the sense that the bending oscillation amplitude is not proportional to self-gravity. In the case of a bending instability, we would expect a proportionality between the bending oscillation and the imposed load (here, self-gravity). In the linear regime, a stellar disk is stable against the low order (e.g., m = 0 , 1) bending perturbation and the self-gravity of the perturbation acts like a stabilizing agent as shown by several authors, e.g., Toomre (1966), Araki (1985), Merritt & Sellwood (1994), Sellwood (1996), Saha & Jog (2006). It is the pressure forces which destabilizes a stellar disk in response to a bending perturbation. From the works of Toomre (1966), Araki (1985) and Fridman & Poliachenko (1984), we learnt that a stellar slab of finite thickness would go bending unstable if σ z /σ r < 0 . 3. However, the critical value of σ z /σ r , at which a self-consistent rotating stellar bar would go bending unstable is unclear. Actually, it is doubtful that a criterion based only on a local quantity such as σ z /σ r would apply in a bar, as the 2 / 1 vertical resonance is a crucial factor which reflects a non-local feature of the system: its orbital behavior. Indeed and contrary to collisional fluids, collisionless fluids may develop long range correlations which are not captured by a purely local description. The distinction between kinematic based and spatial mass distribution based instabilities in collisionless system has been presented by Pfenniger (1996, 1998). A fire-hose instability belongs to instabilities depending on a strong gradient in the velocity part of the DF, while a bar buckling instability belongs to instabilities mainly related to the presence of a strong resonance, which is determined by the spatial mass distribution. In this section, we investigate the role played by the shear stress, in particular, the meridional component ( τ s,rz ) which exerts a torque in the vertical direction on an imaginary cube of the stellar fluid. First, we quantify the buckling amplitude ( A 1 z ) by computing the m = 1 Fourier component in the r -z plane of the disk with the major axis of the bar aligned to the disk major axis and identify the buckling phase by studying the time evolution of A 1 z . During the the buckling phase A 1 z reaches a peak value and sometimes goes through a second buckling (Martinez-Valpuesta et al. 2006). In Fig. 7, we present the time evolution of A 1 z for the three models. A 1 z for RCG051A shows a strong peak at T ∼ 2Gyr usually considered as the first buckling of the bar. It is interesting to note that the bar in this model suffers subsequent buckling of smaller amplitudes. The onset of the buckling instability can be indicated by different physical parameters, e.g., a drop in A 2 or σ z /σ r as mentioned above. For the model RCG051A, both Fig. 5 and Fig. 8 indicate that at around 2 Gyr, there is a drop in A 2 and σ z /σ r respectively as found in previous studies. In Fig. 9, we show the time evolution of the meridional shear stress normalized by the initial normal stress defined in Eq. 3. It demonstrates clearly that the meridional stress develop slowly as the bar evolves and reaches its first peak value as the bar enters the buckling phase at about 2 Gyr following closely the time evolution of A 1 z in RCG051A. We establish, here, a new indicator of the bar buckling instability that correlates well with other indicators mentioned above in a galaxy with a cold stellar disk undergoing a rapid phase of bar growth (here, RCG051A). Let us now examine the other two models where the bar growth rate is rather slow in comparison to RCG051A. In model RHG097, the peak in A 1 z (see Fig. 7) coincides with that in the meridional stress shown in Fig. 9 at around 3 . 4Gyr. However, the drop in σ z /σ r occurs noticeably earlier at around 1 . 5Gyr, when no buckling event was found from the time evolution of A 1 z as well as from the visual inspection of the surface density maps in edge-on projection (see Fig. 12). It is evident that a drop in σ z /σ r is not an unambiguous indicator of the buckling event of strong bars, whereas the meridional stress is promising in indicating the onset of buckling instability. On the other hand, for a dark matter dominated radially hot stellar disk as in model RHG057, the bar grows on a much slower rate (see Fig. 5) and shows no peak in A 1 z (see Fig. 7). Also Fig. 8 shows no appreciable drop in σ z /σ r except at around 6 Gyr where a smooth decrease in σ z /σ r is apparent. The meridional stress remains nearly flat and close to zero for this galaxy model which has been evolved for about 12 Gyr during which no buckling event was detected. As the bar evolves through the buckling phase, the disk midplane also responds and exhibits a characteristic buckling mode. We compute the location of the disk midplane using the following formula to follow the buckling: where ρ ( r, z ) is the volume density distribution of stars. Since the meridional shear stress for the model RHG097 was comparatively high, the disk midplane was expected to show noticeable bending. We discuss here only the case of RHG097 and mention briefly the other models. Initially, the disk midplane remains flat at z = 0 as shown in Fig. 10 for the model RHG097. At t = 3 . 4 Gyrs, the midplane reaches its peak value 〈 z 〉 ∼ 130 pc. Subsequently, the z -amplitude decreases to nearly zero at around 5 . 5 Gyrs restoring the symmetry along the vertical direction. The buckling modes of the bar in this model have characteristic nodes at R ∼ 0 . 6 R d and ∼ 1 . 8 R d (see Fig. 10). Comparing with Fig. 6, we find that the location of the second node is close to the corotation of the bar. The time evolution of the z -amplitude indicates that the buckling instability is a sudden event in the galaxy evolution. The model RCG051A also showed similar behaviour in the z -amplitude. But the z -amplitude in model RHG057 remained close to zero at all times.",
"pages": [
4,
5,
6,
7
]
},
{
"title": "5.1. Meridional tilt of the velocity ellipsoid",
"content": "In this section, we discuss the orientation of the stellar velocity ellipsoid in the meridional plane ( R -z plane) of the galactic disk. Since the buckling instability creates an asymmetry in the vertical density distribution and assuming it preserves reflection symmetry with respect to the galactic centre, we consider only one half of the meridional plane for the computation of the stellar velocity ellipsoid. When the bar has formed, we rotate it so that its major axis is perpendicular to the line-ofsight; in other words, the tilt is calculated in the meridional plane containing the bar major axis. In edge-on projection, the meridional plane would closely resemble the surface density maps shown, for example, in Fig. 12. In order to understand the spatio-temporal variation of the stellar velocity ellipsoid in a model galaxy, we further subdivide the entire meridional plane into several small cells each of which contain sufficient number of particles for reasonable estimate of the velocity dispersion and the meridional tilt. The cell sizes are fixed at ∆ R = 0 . 4 R d in radius and ∆ z = 0 . 2 R d . The number of particles in each of these cells vary over time as they are subject to mixing and migration driven by the combined effect of an evolving bar and spiral structures in the disk (Minchev & Famaey 2010). To give an idea of the number of particles used, the cell at R = 1 . 8 -2 . 4 R d and z = 0 . 3 -0 . 5 R d contains about 20 , 000 particles and the innermost cells have about 100000 particles at t = 4 . 8 Gyr for the model RHG097 (for reference see Fig. 14). Fig. 14 depicts the spatio-temporal variation of the velocity ellipsoid in the meridional plane of the galaxy model RHG097. Initially, the velocity ellipsoid in the disk are all aligned with the galactocentric coordinate axes and the same holds true for a period of about 3 Gyr when the bar has fully developed in the disk, see Fig. 3. At 3 . 4 Gyr, the bar undergoes a sudden buckling instability and the meridional tilt of the velocity ellipsoid reaches a peak value as can be seen from the corresponding panel in Fig. 14. Note that the maximum of the tilt occurs at the first node of the buckled bar (see Fig. 10) which roughly coincides with the edge of the peanut shape in this model (see Fig. 12). In general, higher values of tilt angle can be found in the b/p region away from the minor axis of the galaxy during the buckling phase. It is interesting to notice the spontaneous symmetry breaking in the shape distribution of the velocity ellipsoid in the meridional plane about the midplane of the galaxy just after the peak of the buckling phase. Such asymmetry continues to persist for about 1 -1 . 5 Gyr since the onset of buckling instability, during which the density distribution is also asymmetric about the midplane (see, Fig. 12). After the peak of the buckling phase, the tilt angle of the velocity ellipsoid gradually decreases to a low value during the subsequent evolution of the galaxy, restoring symmetry both in the shape distribution of the velocity ellipsoid and the mass density about the midplane. Note that, the velocity ellipsoid near the minor axis of the galaxy remains nearly aligned with the galactocentric coordinate axes before the onset of buckling instability and at later times. Although not shown explicitly here, the meridional tilt angle of the velocity ellipsoid along the minor axis of the galaxy remains zero at all times during the galaxy evolution. The meridional tilt of the velocity ellipsoid outside the b/p region is nearly unaffected by the buckling instability. As shown clearly in Fig. 14 (see panel at t = 2 . 4 Gyr), the meridional tilt angle is nearly zero for galaxies which host a bar that did not go through a buckling instability. From Fig. 14, it is clear that the size of the velocity ellipsoid near the minor axis nearly doubles at times when buckling instability is at its maximum and their sizes continue to increase. Since the semi-major axis of the velocity ellisoid actually measures the radial velocity dispersion, it shows clear indication of heating in the whole b/p region of the galaxy model. Fig. 15 shows the time evolution of the average meridional tilt angle (Θ tilt ) of the velocity ellipsoid computed in the b/p region for all the models. In both models RHG097 and RCG051A, the meridional tilt angle rises to a peak value during the buckling instability phase. On the other hand, the tilt angle scatters around zero for the model RHG057 at all times. From the time evolution, a large value of the tilt angle is a characteristic signature of the buckling phase that these model galaxies might have undergone. In other words, findings of a large value of the tilt angle in the b/p region of a galaxy would indicate that it might be in the buckling phase or near the vicinity of the buckling instability. The subsequent evolution of the buckling instability in model RHG097 is particularly interesting because of the gradual decrement of the tilt angle. It takes about 1 Gyr for the meridional tilt angle to fall by half its peak value and can be considered as the half-life of the buckling phase ( T tilt , 1 / 2 ) the galaxy has experienced. We find that T tilt , 1 / 2 ∼ 3 × T orb , where T orb is the orbital time at the disk half-mass radius (for this model), which is quite short compared to the galaxy's lifetime. This might be the reason for the difficulty in observing galaxies in the buckling phase. However, T tilt , 1 / 2 may depend on various parameters of the galaxy models and a thorough search of the parameter space is required to find an optimal galaxy model which would show large values of tilt angle over long periods of time. The dependence of T tilt , 1 / 2 on the dark halo and bulge properties will be considered in a future paper. The calculation of the stellar velocity ellipsoid assumes that the moment integrals of the DF exist and returns a finite value. However, the validity of such an assumption is questionable, especially when the stellar system is undergoing an unstable phase e.g., buckling instability in the present case. The resonant parts of the phase space during such an instability can develop bi-modal and/or particle distribution with long tail for which the very notion of first or second moment of the DF is mathematically no longer meaningful. Bimodal velocity distribution has been observed for late-type stars in the solar neighborhood by Hipparcos and numerical models of disk response to a bar is shown to have reproduced many such features in the local velocity distribution (Dehnen 2000; Fux 2001; Minchev et al. 2010). In Fig. 16, we show the normalized histograms for radial ( v r ) and vertical ( v z ) velocities in the model RHG097 during and after the buckling instability nearly disappeared. We picked up three different regions in the meridional plane and histograms, in the two regions ( R = 0 . 6 , z = 0 . and R = 0 . 6 , z = 0 . 2) where the meridional tilt was maximum, are fairly well represented by a single Gaussian DF with different variances. In the region close to the minor axis of the galaxy i.e., R = 0 . 2 , z = 0 . 2, the radial velocity histograms needed two Gaussian DFs: one with cold component with dispersion ∼ 30 kms -1 and one with a hot component with a dispersion ∼ 102 kms -1 . A close inspection of Fig. 14 indicates that the stars are heated strongly in that region as it is clear from the size of the ellipsoids. At the time of buckling, the size of the ellipsoid nearly doubles indicating an increase in the velocity dispersion by a factor of two. In any case, in all the regions examined, we have a unimodal DF to represent the stars in the meridional plane and they show well behaved first and second moments.",
"pages": [
7,
9
]
},
{
"title": "6. DISCUSSION AND CONCLUSIONS",
"content": "The buckling instability is one of the routes through which an initially axisymmetric stellar disk would form a boxy/peanut bulge such as present in our own Galaxy. In order to understand the formation of such a boxy/peanut morphology, it is important to have further insight on the buckling instability. How and when would a bar go buckling unstable? How many buckling events has a present day galaxy experienced? How does it depend on the dN/(NdV) dark matter fraction in galaxies? There are several issues needed to be addressed in order to grasp this phenomenon. The current paper addresses one such issue on the onset of a buckling event in a disk galaxy. It is shown that there is a connection between the onset of the buckling instability and the shear stress of stars. We see that the shear stress reaches its peak value during the buckling phase and then decreases gradually. The development of a shear stress in the stars is a result of collective process in the disk. If these stars are also trapped in the vertical ILRs, this would eventually lead to the buckling instability (Pfenniger & Friedli 1991; Quillen 2002). From our study, it is clear that a bar that grows very slowly, on a several Gyr time scale, does neither develop any appreciable shear stress nor go through any buckling instability. On the other hand, bars that grow very rapidly such as in RCG051A, develop both, shear stress and buckling instability. In no cases that we have studied does a shear stress develop in the bar and not go through the buckling instability. One emerging scenario is that the development of shear stress is related to the rate at which a bar grows i.e., the rate at which a bar strength grows through transport of angular momentum outward. In galaxy models with higher values of Toomre Q , the growth of bar strength is rather slow leading to weak bar and insignificant amount of shear stress. Several important kinematical changes occur in the galaxy during and after the episode of the buckling instability. From the Fig. 14, it is clear that the stars are heated in the b/p region, especially close to the minor axis of the galaxy, by a factor of ∼ 2 during the buckling instability. This was shown previously by Saha et al. (2010) for model RHG097 and others. Another interesting aspect is the kinematical changes in the vertical structure of the galaxy. Note, the stellar disk is isothermal initially (see the first panel at t = 1 . 1 Gyr in Fig. 14). In the after-episode of the buckling phase, there is a clear distinction in the velocity dispersion above and below the disk midplane indicating spontaneous breaking of isothermal structure in the b/p region. Such nonisothermal vertical structure in the b/p region is persistent long after the buckling phase. We will address this issue in more detail in a future paper. Our main conclusions from this work are as follows: 1. We show that the meridional tilt of the stellar velocity ellipsoid is a better indicator compared to a drop in the bar amplitude or σ z /σ r for the onset of the buck- ng instability of a stellar bar in a disk galaxy. During the buckling event, the tilt angle reaches a peak value followed by a gradual decrease. Outside the buckling episode, the tilt angle is nearly zero. The meridional shear stress of stars and the onset of the buckling instability of a stellar bar is closely connected.",
"pages": [
9,
10
]
},
{
"title": "ACKNOWLEDGEMENT",
"content": "The simulations presented in this paper were carried out on the computer cluster system of ASIAA. This work was supported, in part, by the Theoretical Institute for Advanced Research in Astrophysics operated under the ASIAA. K.S. acknowledges support from the Alexander von Humboldt Foundation. D.P. acknowledges support from the Swiss National Science Foundation. The authors thank the anonymous referee for insightful comments on the manuscript.",
"pages": [
10
]
},
{
"title": "REFERENCES",
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"pages": [
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}
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2013ApJ...765..142M
https://arxiv.org/pdf/1301.5072.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_86><loc_88><loc_87></location>THE MICROARCSECOND STRUCTURE OF AN AGN JET VIA INTERSTELLAR SCINTILLATION</section_header_level_1>
<text><location><page_1><loc_26><loc_82><loc_74><loc_85></location>J.-P. Macquart 1 , L.E.H. Godfrey, H.E. Bignall, J.A. Hodgson 2 ICRAR/Curtin University, Bentley, WA 6845, Australia Draft version March 4, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_79><loc_55><loc_80></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_63><loc_86><loc_79></location>We describe a new tool for studying the structure and physical characteristics of ultracompact AGN jets and their surroundings with µ as precision. This tool is based on the frequency dependence of the light curves observed for intra-day variable radio sources, where the variability is caused by interstellar scintillation. We apply this method to PKS 1257-326 to resolve the core-shift as a function of frequency on scales well below ∼ 12 µ as. We find that the frequency dependence of the position of the scintillating component is r ∝ ν -0 . 1 ± 0 . 24 (99% confidence interval) and the frequency dependence of the size of the scintillating component is d ∝ ν -0 . 64 ± 0 . 006 . Together, these results imply that the jet opening angle increases with distance along the jet: d ∝ r n d with n d > 1 . 8. We show that the flaring of the jet, and flat frequency dependence of the core position is broadly consistent with a model in which the jet is hydrostatically confined and traversing a steep pressure gradient in the confining medium with p ∝ r -n p and n p /greaterorsimilar 7. Such steep pressure gradients have previously been suggested based on VLBI studies of the frequency dependent core shifts in AGN.</text>
<text><location><page_1><loc_14><loc_59><loc_86><loc_62></location>Subject headings: galaxies: jets - techniques: high angular resolution - quasars: individual (PKS1257 -326) - scattering</text>
<section_header_level_1><location><page_1><loc_22><loc_56><loc_35><loc_57></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_40><loc_48><loc_55></location>The brightest, most compact feature of an AGN jet, the 'core', is identified with the part of the jet at which the optical depth ( τ ν ) is of order unity (Blandford & Konigl 1979), and is often referred to as the τ ν = 1 surface, or photosphere. Due to positional variation of the opacity in the jet and/or surrounding medium, the position of the τ ν = 1 surface is frequency dependent, and therefore, so too is the absolute position of the core (eg. Konigl 1981; Lobanov 1998; Kovalev et al. 2008; Sokolovsky et al. 2011). The frequency dependent position of the core is referred to simply as the core shift.</text>
<text><location><page_1><loc_8><loc_26><loc_48><loc_39></location>The core shift effect provides an observational tool with which to investigate the structure and physical conditions in parsec-scale AGN jets. Moreover, modelling the effect may provide information about the confinement mechanism and pressure gradients in the external medium. The core shift effect is also relevant to the quest for high precision absolute astrometry for the International Celestial Reference Frame, as it can introduce a significant offset in positions determined using group delay measurements (Porcas 2009).</text>
<text><location><page_1><loc_8><loc_13><loc_48><loc_26></location>The magnitude of the core shift between 2.3 and 8.4 GHz is typically of order a few hundred µ as or less (O'Sullivan & Gabuzda 2009; Sokolovsky et al. 2011; Pushkarev et al. 2012), and therefore detecting this effect requires very high accuracy registration of images at two or more frequencies. Despite the technical challenges, the core-shift effect obtained from VLBI imaging has been reported for an ever-increasing number of radio galaxies (Marcaide & Shapiro 1984; Lobanov 1998; Kovalev et al. 2008; O'Sullivan & Gabuzda 2009;</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_9><loc_48><loc_12></location>1 ARC Centre of Excellence for All-Sky Astrophysics (CAASTRO)</list_item>
</unordered_list>
<text><location><page_1><loc_52><loc_51><loc_92><loc_57></location>Sokolovsky et al. 2011; Pushkarev et al. 2012). More recently, Kudryavtseva et al. (2011) have employed an indirect method to measure the core shift effect based on frequency-dependent time lags of flares observed using single-dish data spanning several years.</text>
<text><location><page_1><loc_52><loc_17><loc_92><loc_51></location>The frequency dependence of core position is typically assumed to follow a power-law of the form r ∝ ν -1 /k r . In many sources for which core shifts can be measured with VLBI imaging, the absolute core position varies approximately with the inverse of the frequency (i. e. k r = 1) (O'Sullivan & Gabuzda 2009; Sokolovsky et al. 2011). This situation is consistent with the standard model of a conical jet in which the plasma is in a state of equipartition between particle and magnetic energy densities (Blandford & Konigl 1979). However, values of k r much greater than unity are observed in some sources, which may be due to free-free absorption in the immediate vicinity of the jet, or due to rapid changes in pressure in the external medium if hydrostatic confinement is important (Lobanov 1998). Lobanov (1998) has shown that while k r ∼ 1 at large distances downstream from the black hole, the value of k r increases towards the jet base. Kudryavtseva et al. (2011) have shown that the value of k r is time-dependent, and correlated with flux density. Finally, the pc-scale jet of M87 is observed to deviate from a conical geometry near to the core (Asada & Nakamura 2012). Further investigation into the frequency dependence of core position is therefore warranted, and highly relevant to the study of ultracompact AGN jets.</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_17></location>Here we present a potentially powerful new method for the study of ultracompact jets in AGN, which enables simultaneous measurement of the core shift effect and jet geometry to very high precision. This new technique uses auto- and cross-correlation analysis of multi-frequency light curves of a rapidly scintillating AGN to measure the frequency dependence of the position and size of the</text>
<text><location><page_2><loc_8><loc_91><loc_25><loc_92></location>scintillating component.</text>
<text><location><page_2><loc_8><loc_80><loc_48><loc_90></location>In section 2 we present the observations and data analysis. In Section 3 we discuss the mathematical formulation of the auto- and cross-correlation analysis, and derive the frequency dependent source position and size for PKS 1257-326. In Section 4 we discuss the implications of our findings, and model the jet in terms of a hydrostatically confined jet traversing a steep pressure gradient. Finally, in Section 5 we present our conclusions.</text>
<section_header_level_1><location><page_2><loc_13><loc_78><loc_44><loc_79></location>2. OBSERVATIONS AND DATA CALIBRATION</section_header_level_1>
<text><location><page_2><loc_8><loc_53><loc_48><loc_77></location>PKS1257 -326 was observed at the ATCA for ten hours on 15 January 2011, with two 2 GHz bands, centred on frequencies of 5.5 and 9.0 GHz. The output data included all four polarisation products and 2048 spectral channels each 1 MHz wide in each of the two bands. Flagging and calibration of the data were performed using the Miriad software package. The ATCA primary calibrator PKS1934 -638 was used to correct the overall flux density scale and the spectral slope. In order to solve for the bandpass and to correct gain amplitudes as a function of time and pointing for each antenna, the secondary calibrator PKS1255 -316, only 1 · from PKS1257 -326, was observed for 1 minute approximately every 20 minutes, interleaved with observations of the target source. Phase self-calibration assuming a point source model was performed with a short (10 s) solution interval. After initial calibration the data were split into 128 MHz sub-bands for further analysis.</text>
<text><location><page_2><loc_8><loc_15><loc_48><loc_53></location>At least 98% of the total flux density of PKS 1257 -326 is unresolved with the ATCA, and there is no significant confusion in the field at frequencies above 4 GHz. Therefore, to obtain the light curves of the source variations we averaged the real part of the calibrated visibilities over all baselines and frequency points within each 128 MHz band. The relative stability of the calibration as a function of time and frequency within each 2 GHz band is estimated to be ∼ 1% or better, based on the PKS 1255 -316 data. The bandpass is observed to be stable over the duration of our observations in the 5 GHz band, but there are small frequency- and elevation-dependent gain variations across the higher frequency band, which were corrected with a time-dependent bandpass solution derived from PKS1255 -316. Although the frequency dependence of the primary calibrator PKS1934 -638 is well known, archival data on the secondary calibrator PKS1255 -316 shows it to be variable by up to ∼ 50% on timescales of months to years. Hence there is a small uncertainty in the spectral slope correction for the 9GHz band, due to the variations with time and pointing, and the fact that the spectrum of PKS 1255-316 is not known a priori. In any case, the average spectrum of PKS1257 -326 is relatively smooth across the entire range of frequencies, suggesting that the calibration is accurate. Moreover any residual constant offsets in the flux density scale which may be present between different frequencies have no effect on the cross-correlation analysis presented in this paper.</text>
<text><location><page_2><loc_8><loc_11><loc_48><loc_14></location>Figure 1 shows the large, rapid intra-hour variations exhibited by PKS1257 -326.</text>
<section_header_level_1><location><page_2><loc_15><loc_9><loc_41><loc_10></location>3. DERIVATION OF JET STRUCTURE</section_header_level_1>
<text><location><page_2><loc_22><loc_8><loc_35><loc_9></location>3.1. Interpretation</text>
<text><location><page_2><loc_52><loc_79><loc_92><loc_92></location>The rapid fluctuations observed in the centimetre wavelength flux density of the intra-hour variable quasar PKS1257 -326 are due to interstellar scintillation (Bignall et al. 2003, 2006). This is established from the measurement of a time delay in the arrival time of the variations between telescopes separated by several thousand kilometers. The timescale of the variations also undergoes an annual modulation due to relative motion of the Earth about the Sun, which in turn moves relative to the interstellar medium responsible for the variations.</text>
<text><location><page_2><loc_52><loc_63><loc_92><loc_78></location>Inspection of Figure 1 reveals that there is a time offset in the arrival time of the intensity variations between different frequencies, with the variations at high frequency leading those at lower frequencies. This behaviour is consistent with observations in previous epochs. Bignall et al. (2003) reported that variations at 4.8 and 8.6 GHz are closely correlated, and there is a systematic time delay between the variations at these two frequencies. The magnitude of the time delay was observed to follow an annual cycle which is not identical to the annual cycle in variability timescale but, it was argued, can be explained on the basis of it, as we discuss below.</text>
<text><location><page_2><loc_52><loc_36><loc_92><loc_63></location>PKS 1257-326 was monitored with the ATCA at 4.8 and 8.6 GHz at 19 epochs between 2001 February and 2002 April. Typical observations were over a 12 hour period, and 6 epochs covered 2 × 12 hours in 48 hour sessions as part of a multi-source monitoring program. The minimum duration of each light curve is ∼ 10 times the length of the characteristic timescale. In every one of these epochs, the time delay between 4.8 and 8.6 GHz has the same sign, with 8.6 GHz variations always leading. Moreover, a clear annual cycle is observed in the two-frequency time delay, with the longest delays being observed from late July to mid-August. Such an annual cycle is expected for a core-shift which remains stable over the course of the year, and the observed annual cycle is well modelled by such a shift on a scale of order 10 µ as (Bignall et al. 2003), although the precise magnitude and direction of the core shift could not be uniquely determined. These data provide strong evidence that the core shift effect dominates over any refractive effects or 'jitter' in the ISS pattern.</text>
<text><location><page_2><loc_52><loc_12><loc_92><loc_36></location>We argue that the temporal offset in the present data arises as a direct consequence of an angular offset between two compact components within the scintillating source. The effect may be understood as follows. When an angular separation, θ , is present between two components, this results in a spatial displacement of their respective scintillation patterns across the plane of an observer by an amount D θ , whe re D is distance between the observer and the scattering material (Little & Hewish 1966). Since the scintillation patterns are in motion across this plane with some velocity v , the result is a separation in the arrival time of the scintillations associated with each component. In the present case, a displacement in the lightcurves between closely-spaced frequencies arises because there is an angular offset in the image centroids between the respective frequencies. For any pair of frequencies, the time delay is, in terms of the centroid offset θ (see Appendix A),</text>
<formula><location><page_2><loc_56><loc_5><loc_92><loc_9></location>∆ t = -D θ · v +( R 2 -1)( D θ × ˆ S )( v × ˆ S ) v 2 +( R 2 -1)( v × ˆ S ) 2 , (1)</formula>
<figure>
<location><page_3><loc_15><loc_51><loc_86><loc_92></location>
<caption>Fig. 1.PKS1257 -326 flux density measurements as a function of time, plotted with 1-minute averaging, showing each 128 MHz band in a different colour. Frequency increases from top to bottom. The heavy black points show the average of each 2 GHz wide-band dataset, corresponding to the centre frequencies of 5.5 and 9 GHz.</caption>
</figure>
<text><location><page_3><loc_8><loc_33><loc_48><loc_46></location>where R is the anisotropy ratio of the scintillation pattern and ˆ S = (cos β, sin β ) is the direction of its major axis, which we measure with respect to the RA axis. The scintillation parameters have been derived from annual cycle and two-station time-delay measurements, and are given in Table 1. It is evident that this delay is modulated both by the annual cycle in the magnitude of v and by changes in the angle of the velocity vector with respect to θ ; this latter effect causes the annual cycle experienced by ∆ t to differ from the annual cycle in scintillation velocity.</text>
<text><location><page_3><loc_8><loc_8><loc_48><loc_33></location>Phase gradients in the ISM may, in principle, also cause temporal offsets of lightcurves as a function of frequency in a scintillating source. However, the offset observed here is difficult to attribute to such an extrinsic cause for several reasons: (i) the sense and magnitude of the delay is constant throughout the dataset; upon dividing the dataset in two halves (in time) and deriving time offsets based on these two halves separately, we find the same offsets to within the margin of error of the estimates. (ii) The delay is observed over a timescale of 10 hours, whereas refractive phase gradients in the ISM in the regime of weak scintillation for a Kolmogorov spectrum of phase inhomogeneities would occur on the timescale associated with the scintillations, and the time offset should converge to zero as the average is performed over an increasing number of scintles. Any small jitter in the offset between individual scintles appears to be dominated by the systematic offset. (iii) An annual cycle in the time offset is reported by Bignall et al. (2003), in-</text>
<text><location><page_3><loc_52><loc_44><loc_92><loc_46></location>dicating that the offset persists on a timescale of greater than a year.</text>
<section_header_level_1><location><page_3><loc_61><loc_41><loc_82><loc_42></location>3.2. Time delay measurement</section_header_level_1>
<text><location><page_3><loc_52><loc_37><loc_92><loc_41></location>To determine the relative time delay between each pair of lightcurves, I ( t, ν 1 ) and I ( t, ν 2 ), we computed the cross-correlation function,</text>
<formula><location><page_3><loc_52><loc_30><loc_96><loc_36></location>C (∆ t ; ν 1 , ν 2 ) = 〈 [ I ( t ' , ν 1 ) -¯ I ( t, ν 1 )][ I ( t ' +∆ t, ν 2 ) -¯ I ( t, ν 2 )] 〉 √ var[ I ( t, ν 1 )]var[ I ( t, ν 2 )] . (2)</formula>
<text><location><page_3><loc_52><loc_26><loc_92><loc_30></location>A peak in the cross correlation at positive delay, ∆ t , indicates that the fluctuations at frequency ν 2 precede those at ν 1 . We fitted a gaussian of the form,</text>
<formula><location><page_3><loc_62><loc_21><loc_92><loc_25></location>C ( t ) = A exp [ -( t -t 0 ) 2 B 2 ] , (3)</formula>
<text><location><page_3><loc_52><loc_7><loc_92><loc_21></location>to the inner part of the cross-correlation function, C (∆ t ; ν 1 , ν 1 ) (equivalent to the auto-correlation function), to obtain an estimate of the time delay between each frequency-lightcurve pair and its associated error. An example cross-correlation function and its associated fit is shown in Fig. 2. Typical errors in the estimated delay are 50 s. The derived delays as a function of ν 1 and ν 2 are shown in Fig. 3. The estimated 50 s uncertainties in the delay between each frequency pair are derived from least-squares fitting of a gaussian to the peak of the delay, thus the errors are directly related to the width of</text>
<text><location><page_4><loc_32><loc_89><loc_69><loc_90></location>The parameters of the scintillations in PKS 1257 326.</text>
<table>
<location><page_4><loc_30><loc_80><loc_70><loc_88></location>
<caption>TABLE 1 -</caption>
</table>
<text><location><page_4><loc_30><loc_71><loc_70><loc_79></location>a Parameters are derived on the basis of the annual cycle in the variability timescale (Bignall et al. 2003) and measurements of the time delay observed between two stations (Bignall et al. 2006, henceforth B06). An alternate fit to the scintillation data provided by Walker, de Bruyn & Bignall (2009) (henceforth W09) is also listed. The scintillation velocity quoted here is the addition of Earth's relative to the Sun velocity on the observation date and the velocity of the scattering medium relative to the Sun.</text>
<text><location><page_4><loc_8><loc_34><loc_48><loc_70></location>the peak in the cross-correlation functions 3 . These uncertainties are in turn derived from the least squares fit to the cross-correlation function; the errors in the individual points in the cross-correlation function are dominated, at low time lags, by Poisson errors associated with the number of independent measurements of the cross-correlation measureable from the lightcurve. This error is indicated by the scatter between points in the CCF. Fitting to the CCF yields a typical formal error of ≈ 20 s. However the high degree of cross correlation between the lightcurves in our observations means that the error in the time delay estimate for any given frequency pair is not completely independent from the time delay estimate of any other frequency pair. It is necessary to take the cross-correlation into account because it becomes an important factor when assessing the significance of the fit to the frequency dependence of the time delay using a least-squares approach (see below), which is the primary reason to estimate the error in the time lag. Failure to take into account this interdependence in time lag estimates would lead to an overestimate of the significance of the fit to the frequency dependence of the time shift. It was found empirically, from examination of the reduced chi-squared in the fit procedure that this cross-correlation is taken into account in the error analysis with errors that are 2 . 5 times larger than the formal error.</text>
<text><location><page_4><loc_8><loc_21><loc_48><loc_34></location>In most models of jet structure the angular offset between the jet base and the centroid of the emission at a frequency ν is fitted to a power law, ∆ θ = Aν -ζ , where A and ζ are constants to be determined. Since the time delay is linearly proportional to | θ | , we fitted a function of the form ∆ t ( ν 1 , ν 2 ) = K ( ν -ζ 1 -ν -ζ 2 ) to the delays. The best-fitting parameters are ζ = 0 . 10 and K = (1 . 6 ± 0 . 5) × 10 4 s MHz ζ , with the 99% confidence interval of ζ extending over the range [ -0 . 14 , 0 . 34]; the best-fitting surface is plotted over the data in Fig. 3 4 .</text>
<text><location><page_4><loc_8><loc_9><loc_48><loc_19></location>3 This error is significantly smaller than the time delay errors that might be estimated on the basis of the data presented in Bignall et al. (2003). As is evident from Fig. 2 in Bignall et al. (2003), the data in most of those epochs contain considerably few scintles from which to estimate the time lag. Thus one would expect the errors to be larger relative to the 2011 data. The dataset obtained on 4 Jan 2001 contains a comparable number of scintles, but here the temporal sampling of the lightcurve was too sparse to estimate a time delay.</text>
<text><location><page_4><loc_8><loc_7><loc_48><loc_9></location>4 The 99% confidence limits are calculated, in the conventional way, from the change in the sum of the squares of the residuals</text>
<text><location><page_4><loc_52><loc_64><loc_92><loc_70></location>The best-fitting exponent indicates a core-shift dependence on frequency that is much shallower than the value ζ = 1 typically found in other quasars on the basis of VLBI measurements (e.g. O'Sullivan & Gabuzda 2009; Sokolovsky et al. 2011).</text>
<text><location><page_4><loc_52><loc_54><loc_92><loc_64></location>We also measure the timescale of the scintillations, which is derived from the parameter B in eq. (3) (and with ν 1 = ν 2 ). Figure 4 shows that the timescale is wellfit by a relation scaling as ν -0 . 642 ± 0 . 006 ; a fit using a broken power law reveals the both the 4-5 and 8-9 GHz timescales follow the same scaling with frequency within the (small) margin of error.</text>
<text><location><page_4><loc_52><loc_45><loc_92><loc_54></location>In the regime in which the angular size of the source, θ src , exceeds the angular size of the Fresnel scale at the distance of the scattering screen, θ F = √ c/ 2 πνD , the scintillation timescale is linearly proportional to the size of the scintillating component. In the opposite regime, θ src < θ F , the scintillation timescale is determined by Dθ F /v = r F /v , which scales as ν -0 . 5 .</text>
<text><location><page_4><loc_52><loc_18><loc_92><loc_45></location>We wish to determine whether the timescale of the scintillations measures θ F or θ src . The expected Fresnel crossing timescale is 1 . 0 × 10 3 ( D/ 10 pc) 1 / 2 ( ν/ 5 GHz) -1 / 2 ( v/ 54 kms -1 ) -1 s. The observed scintillation timescale at 5.0 GHz is 1 . 4 × 10 3 s, so if the source is unresolved there must be an error in the nominal scintillation parameters; if the scintillation velocity is held at its nominal value one must have D > 19 pc, or if the screen distance is held at its nominal value one must have v < 40 kms -1 . The latter option is viable for the scintillation velocity derived by Walker, de Bruyn & Bignall (2009), so we conclude that it is plausible that the source is unresolved by the scintillations. However, the fact that the scaling of scintillation timescale is significantly different from ν -0 . 5 suggests that the source is at least partially resolved in any case. The smooth trend evident in both timescale and scintillating amplitude with frequency suggests that the source remains resolved over the entire frequency range 5-10 GHz.</text>
<text><location><page_4><loc_52><loc_15><loc_92><loc_18></location>Although tangential to the objectives of this paper, we can, in addition, estimate the amplitude of the scintil-</text>
<text><location><page_4><loc_52><loc_7><loc_92><loc_13></location>of the fit. Now, in practice, since the lightcurves are correlated between frequencies, the time lag estimate between adjacent frequency pairs are strictly not independent, and this influences the chi-squared estimate. However, this effect is treated by accounting for the cross-correlation in the estimates of the time delays for each frequency pair.</text>
<figure>
<location><page_5><loc_11><loc_75><loc_45><loc_92></location>
<caption>Fig. 2.The cross correlation between the lightcurves at 8040 and 4540 MHz, and the associated best-fit gaussian. The peak of the gaussian represents the location of the time-delay. The positive offset of the peak indicates that the variations at 8040 MHz lead those at lower frequency.</caption>
</figure>
<text><location><page_5><loc_8><loc_62><loc_48><loc_68></location>lating component of the source. For an extended source of size θ src in the regime of weak scintillation caused by a Kolmogorov spectrum of turbulent fluctuations, the observed rms, 〈 δI 2 〉 1 / 2 can be expressed in the form (Narayan 1992),</text>
<formula><location><page_5><loc_13><loc_56><loc_48><loc_61></location>〈 δI 2 〉 1 / 2 〈 I 〉 ≈ ( r diff r F ) 5 / 6 { ( θ F θ src ) 7 / 6 θ src > θ F 1 θ src < θ F , (4)</formula>
<text><location><page_5><loc_8><loc_37><loc_48><loc_56></location>where 〈 I 〉 is the flux density of the scintillating component of the source and r diff ∝ ν 6 / 5 is the diffractive scale, which is determined by the properties of the interstellar turbulence (see Narayan 1992). In the regime of intermediate scattering one has r diff ≈ r F , with equality at the transition frequency, which likely occurs in the range 37GHz based upon the modelling of Walker (1998). One then solves for 〈 I 〉 using the measurements of 〈 δI 2 〉 1 / 2 . Assuming that the source size exceeds the Fresnel angular scale, one determines θ src /θ F from the ratio t scint /t F . We performed a fit using the measured values of 〈 δI 2 〉 and t scint , and subject to the assumption that r diff = r F at 4 GHz, to derive a rough estimate of the flux density of the scintillating component:</text>
<formula><location><page_5><loc_18><loc_32><loc_48><loc_36></location>S scint = 19 ( ν 5 GHz ) 0 . 5 mJy . (5)</formula>
<text><location><page_5><loc_8><loc_23><loc_48><loc_32></location>We caution that the spectral index of the component derived here is only approximate because the expression for the modulation index in eq.(4) is only approximate at frequencies where r diff ≈ r F . A more sophisticated estimate would employ a more complicated approximation to the modulation index near the transition frequency and take into account the anisotropy of the scintillations.</text>
<section_header_level_1><location><page_5><loc_20><loc_21><loc_37><loc_22></location>3.3. Overall source scale</section_header_level_1>
<text><location><page_5><loc_8><loc_15><loc_48><loc_20></location>Although the frequency scaling of the core position and size are the primary results of our analysis, it is possible to roughly relate these measurements back to physical scales within the source.</text>
<text><location><page_5><loc_8><loc_6><loc_48><loc_15></location>The Schwarzschild radius of the black hole at the centre of PKS1257 -326 is R S = 2 . 95 × 10 12 M 9 m, where M 9 = 10 9 M /circledot is the BH mass, which is estimated from measurements of the broad line emission width to be 10 8 . 8 M /circledot (D'Elia, Padovani & Landt, 2003). At the redshift of PKS1257 -326, z = 1 . 256, 1 µ as subtends</text>
<figure>
<location><page_5><loc_53><loc_67><loc_92><loc_92></location>
<caption>Fig. 3.The time delay associated with each pair of lightcurves measured at frequencies ν 1 and ν 2 . The red surface corresponds to the best-fitting model of the form ∆ t = A ( ν -ζ 1 -ν -ζ 2 ) (see text for details).</caption>
</figure>
<figure>
<location><page_5><loc_55><loc_43><loc_89><loc_60></location>
<caption>Fig. 4.The timescale of the scintillations as a function of frequency. The line represents the best-fitting model of the form τ = Kν -β (see text for details). Note that the intrinsic scatter between adjacent points is smaller than the error bars: this is because the lightcurves are highly correlated leading to a smaller scatter than is reflective of the errors.</caption>
</figure>
<text><location><page_5><loc_52><loc_26><loc_92><loc_35></location>8 . 5 × 10 -3 pc, equivalent to 89 /M 9 Schwarzschild radii 5 . The time delay is related to angular structure in the source using eq. (1) and the scintillation parameters in Table 1. This also depends on the angle, ξ , that θ makes with the right ascension axis, which is unknown. For a time offset ∆ t , the expected amplitude of the angular offset is given by</text>
<formula><location><page_5><loc_56><loc_21><loc_92><loc_25></location>| θ | =∆ t { (27 . 7 cos ξ +38 . 8 sin ξ ) -1 µ as , B06 , (43 . 9 cos ξ +61 . 8 sin ξ ) -1 µ as , W09 , (6)</formula>
<text><location><page_5><loc_52><loc_11><loc_92><loc_21></location>where the two solutions denote the scintillation parameters found by Bignall et al. (2006) (B06) and Walker et al. (2009) (W09). For instance, the angular separation implied by the 520s delay observed between the lowest (4540MHz) and highest (9960MHz) frequency bands of our observations is 19 µ as (12 µ as) for the scintillation parameters of B06 (W09) if ξ = 0 (i.e. if the angular separation is aligned parallel to the right ascension axis).</text>
<text><location><page_6><loc_8><loc_89><loc_48><loc_92></location>This translates to a physical scale of 0.16 pc (0.10 pc) at the source.</text>
<text><location><page_6><loc_8><loc_80><loc_48><loc_89></location>However, these estimates are subject to uncertainties in both the screen distance and the orientation of the separation ξ . For instance, doubling D above its nominal value of 10 pc would result in estimates of | θ | lower by a factor of two. They thus serve only as a guide to the order of magnitude of scales which are probed by these measurements.</text>
<text><location><page_6><loc_8><loc_75><loc_48><loc_80></location>In the same vein, we also estimate the angular scale of the source from the variability timescale, using eq. (A10) in Appendix A to find the characteristic angular scale of the scintillation pattern,</text>
<formula><location><page_6><loc_8><loc_69><loc_50><loc_74></location>θ src ( ν ) = [ 28 64 ] ( ν 9 . 96 GHz ) -0 . 64 ( D 10 pc ) -1 µ as [ B 06 W 09 ] . (7)</formula>
<text><location><page_6><loc_8><loc_65><loc_48><loc_70></location>The minor axis of the scintillation pattern has a size θ src / √ R while the major axis has a characteristic size of θ src √ R .</text>
<section_header_level_1><location><page_6><loc_23><loc_63><loc_34><loc_64></location>4. DISCUSSION</section_header_level_1>
<section_header_level_1><location><page_6><loc_17><loc_61><loc_39><loc_62></location>4.1. Observational Constraints</section_header_level_1>
<text><location><page_6><loc_8><loc_39><loc_48><loc_61></location>The foregoing analysis indicates that the centroid of the scintillating component has a frequency dependence of the form: r core ∝ ν -0 . 1 ± 0 . 24 . In the terminology of Konigl (1981) and Lobanov (1998), r core ∝ ν -1 /k r , we have k r > 3. We proceed under the assumption that the source is resolved, as suggested by the frequency dependence of the scintillation time-scale (Section 3.2). In that case, the jet diameter has a frequency dependence of the form: d ∝ ν -0 . 64 ± 0 . 006 . Taken together, these results imply d ∝ r n d core with n d > 1 . 8. The scenario implied by our analysis is illustrated in Figure 5. This is in contrast to the frequency dependence of the core position in VLBI studies: typically r core ∝ ν -1 , consistent with expectations for a conical jet in which the particle and magnetic energy densities are in equipartition (Sokolovsky et al. 2011).</text>
<figure>
<location><page_6><loc_15><loc_23><loc_42><loc_36></location>
<caption>Fig. 5.A cartoon illustrating the constraints implied by our analysis.</caption>
</figure>
<section_header_level_1><location><page_6><loc_12><loc_14><loc_44><loc_17></location>4.2. Interpretation in terms of hydrostatic jet confinement in a steep pressure gradient</section_header_level_1>
<text><location><page_6><loc_8><loc_7><loc_48><loc_13></location>Lobanov (1998) suggested that the changes in jet opacity observed for a sample of sources appear consistent with a self-absorbed jet propagating through a region with a steep pressure gradient of the form p ∝ r -6 . Here we consider such a model to explain the inferred</text>
<text><location><page_6><loc_52><loc_81><loc_92><loc_92></location>frequency dependence of the core size and position in PKS 1257-326. Specifically, we consider whether such a model can simultaneously account for the increase in opening angle along the jet ( d ∝ r n d core with n d > 1 . 8), and the flat frequency dependence of core position ( r core ∝ ν -1 /k r , with k r > 3). The relevant model equations, for a pressure profile p ∝ r -n p , are (see Appendix B)</text>
<text><location><page_6><loc_52><loc_55><loc_92><loc_72></location>Here m B is a parameter determined by the magnetic field geometry as discussed in Appendix B, and α is the optically thin spectral index which directly relates to the electron energy distribution N ( γ ) ∝ γ -(2 α +1) , as opposed to α core , which is the optically thick spectral index of the self-absorbed core. We assume α = 0 . 5, m B = 1 (i. e. a predominantly toroidal magnetic field configuration) and take n p = 7 . 2 so that n d = 1 . 8. In that case, the jet Lorentz factor goes as Γ / Γ 0 = ( r/r 0 ) 1 . 8 , so that for reasonable values of the jet viewing angle (5 · < φ < 40 · ) and initial Lorentz factor (2 /lessorsimilar Γ 0 /lessorsimilar 10), we have -0 . 5 /lessorsimilar n δ /lessorsimilar 0 . 5, which implies:</text>
<formula><location><page_6><loc_53><loc_71><loc_90><loc_82></location>n d = n p 4 k r = ( n p / 4)[(1 . 5 + α )(2 + m B ) -1] -(1 . 5 + α ) n δ 2 . 5 + α α core = 5 2 -1 2 k r [ n p ( 1 + m B 4 ) + n δ ]</formula>
<formula><location><page_6><loc_66><loc_52><loc_92><loc_55></location>2 . 7 /lessorsimilar k r /lessorsimilar 3 . 3 , (8) 0 . 7 /lessorsimilar α core /lessorsimilar 1 . 2 .</formula>
<text><location><page_6><loc_52><loc_32><loc_92><loc_51></location>There is excellent agreement between the predicted and observed frequency dependence of core position and radial dependence of core size. The agreement between the predicted and observed core spectral index is poorer, but this is perhaps unsurprising since, as remarked above, observational determination of the core spectral index is marred by uncertainties in the model used to derive it. We therefore suggest that this simple model of hydrostatic confinement is broadly consistent with the data, provided n p /greaterorsimilar 7 . 2. The required pressure gradient in the external medium ( n p /greaterorsimilar 7 . 2) appears very steep, however, such pressure gradients have previously been suggested in studies of core shifts in AGN (Lobanov 1998).</text>
<text><location><page_6><loc_52><loc_22><loc_92><loc_32></location>Finally, we note that the frequency dependence of core position may also be influenced by free-free absorption in the immediate environment of the jet (e. g. Lobanov 1998). However, we find no evidence for a significant rotation measure, and such an interpretation cannot account for the flaring jet geometry, so that an additional mechanism, such as entrainment, would also be required to explain these results.</text>
<section_header_level_1><location><page_6><loc_66><loc_19><loc_78><loc_20></location>5. CONCLUSIONS</section_header_level_1>
<text><location><page_6><loc_52><loc_9><loc_92><loc_19></location>We have developed a new technique to probe the structure of AGN jets on micro-arcsecond scales, by using interstellar scintillation to simultaneously determine the shift in the position of the AGN core as a function of frequency, and the frequency scaling of the core size, to high precision. This approach is amenable to sources which harbour compact ( /lessorsimilar 100 µ as) features.</text>
<text><location><page_6><loc_52><loc_7><loc_92><loc_9></location>This method was applied to broadband observations of PKS1257-326 with the Australia Telescope Compact</text>
<text><location><page_7><loc_8><loc_53><loc_48><loc_92></location>Array. The scaling of the core-shift is found to be remarkably shallow with frequency; the best fit to the position of the scintillating component in the source scales as r ∝ ν -0 . 10 , with the 99% confidence interval of the index extending over the range [ -0 . 34 , 0 . 14]. This constrasts with previous VLBI studies which typically - though not exclusively - find r ∝ ν -1 . The scaling of the jet size is also determined, based on the scaling of the scintillation timescale with frequency. This shows that the jet size scales formally as d ∝ ν -0 . 64 ± 0 . 006 . It is possible to determine the scaling of the core shift and jet diameter to high precision because they do not depend critically on complete knowledge of the properties of the scattering medium responsible for the scintillations. Determination of the absolute physical scale of the core shift does, however, require knowledge of the scintillation parameters, and we can only determine these quantities approximately. The observed 520 s time offset between the scintillations at the the lowest (4540 MHz) and highest (9960MHz) frequency bands of our observations implies an angular separation of /greaterorsimilar 12 µ as, for an assumed scattering screen distance of 10 pc. This translates to a physical scale of ∼ 0 . 10pc at the source. This physical scale probed is an order of magnitude smaller than typical core shifts obtained with VLBI measurements. We further note that this technique easily detects the core-shift between frequency pairs separated by only ∼ 300 MHz, thus providing sub-microarcsecond resolution of the jet structure.</text>
<text><location><page_7><loc_8><loc_43><loc_48><loc_53></location>A major conclusion arising from our analysis is that that the often assumed frequency scaling of core position, r core ∝ ν -1 (e. g. Pushkarev et al. 2012), may not be applicable to all sources, in line with similar findings of Lobanov (1998) and Kudryavtseva et al. (2011). Further, our results hint at a physical difference between persistent intra-day variable (IDV) sources, and the broader population of AGN.</text>
<text><location><page_7><loc_8><loc_33><loc_48><loc_43></location>To place these results in a physical context, we have explored a simple model based on a hydrostatically confined jet traversing a pressure gradient. The pressure profile implied by this model is steep: p ∝ r -n p ; n p /greaterorsimilar 7. Such steep pressure gradients have previously been suggested in VLBI studies of the frequency dependent core shifts in AGN (Lobanov 1998).</text>
<text><location><page_7><loc_10><loc_32><loc_48><loc_33></location>The discrepancy between the frequency scaling of</text>
<text><location><page_7><loc_52><loc_76><loc_92><loc_92></location>core position observed in PKS 1257-326, and the typical r core ∝ ν -1 scaling observed in sources studied with VLBI may arise because different types of source lend themselves to different types of analysis. Only the largest core shifts can be detected with VLBI imaging. In an analysis of 277 objects by Kovalev et al. (2008), only 10% gave reliable core shift measurements. The sources used in the detailed, multi-frequency VLBI study of the core shift effect by Sokolovsky et al. (2011) were selected based on their known large core shift, in addition to their bright optically thin jet features that were required to enable accurate registration of the images.</text>
<text><location><page_7><loc_52><loc_47><loc_92><loc_76></location>More specifically, we suggest that the peculiar nature of the core-shift frequency dependence in PKS 1257-326 is related to a number of other remarkable source properties. The implied brightness temperature of the scintillating component in PKS1257-326 is high, > 10 12 K (Bignall et al. 2006), and the source has exhibited such bright emission at least as long as IDV has been observed, since 1995. The persistence of this IDV over more than 15 years is relatively rare amongst IDV sources. During the 4-epoch, one year duration MASIV survey, Lovell et al. (2008) found that sources which consistently exhibited IDV over all four epochs accounted for only 20% of all IDV sources observed. Moreover, the stability of the annual cycle in the source variability timescale (Bignall et al. 2003, 2006) suggests that the size of the source is remarkably stable on a timescale of years. Physically, this implies that the ultracompact jet in this source is both remarkably bright and stable. It is tempting to speculate, therefore, that the hydrostatic confinement provided by the strong pressure gradient suggested by our simple model is responsible for the observed stability of the jet.</text>
<text><location><page_7><loc_52><loc_31><loc_92><loc_45></location>The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. The observations presented here were made by JAH as part of the CSIRO Astronomy & Space Science (CASS) Vacation Scholarship Program. JAH thanks Dominic Schnitzeler for assistance with the observing setup. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020.</text>
<text><location><page_7><loc_53><loc_30><loc_67><loc_31></location>Facilities: ATCA ()</text>
<section_header_level_1><location><page_7><loc_46><loc_27><loc_54><loc_28></location>APPENDIX</section_header_level_1>
<section_header_level_1><location><page_7><loc_14><loc_26><loc_86><loc_27></location>DERIVING SOURCE STRUCTURE FROM THE TIME DELAY BETWEEN SCINTILLATION LIGHTCURVES</section_header_level_1>
<text><location><page_7><loc_8><loc_21><loc_92><loc_25></location>Here we relate the time delay observed between the scintillations at two frequencies to the angular displacement θ between the centroids of the source emission at the two frequencies. The time delay depends not only on the velocity, but also on the axial ratio, R , and orientation of the interstellar scintillation pattern.</text>
<text><location><page_7><loc_8><loc_18><loc_92><loc_21></location>For intensity fluctuations ∆ I ( r , t ) measured at two locations r ' and r ' + r on the observer's plane at time t , the intensity correlation function is defined as,</text>
<formula><location><page_7><loc_36><loc_14><loc_92><loc_18></location>ρ ( r , t ) = 〈 ∆ I ( r ' , t ' )∆ I ( r ' + r , t ' + t ) 〉 〈 ∆ I 2 〉 . (A1)</formula>
<text><location><page_7><loc_8><loc_10><loc_92><loc_14></location>We follow the treatment of Coles & Kaufman (1978), in which the simplest approximation is that the contours of equal spatial correlation comprise a family of similar ellipses, and the model for the spatial correlation function takes the form</text>
<formula><location><page_7><loc_42><loc_5><loc_92><loc_9></location>ρ ( r , 0) = f ( | C r | 2 σ 2 ) , (A2)</formula>
<text><location><page_8><loc_8><loc_89><loc_92><loc_92></location>where f is a monotonically decreasing function of | C r | 2 . If the scintles are elliptical with axial ratio R and x axis is inclined at an angle β with respect to the major axis, then C takes the form</text>
<formula><location><page_8><loc_40><loc_84><loc_92><loc_89></location>C = [ cos β/ √ R sin β/ √ R -√ R sin β √ R cos β ] . (A3)</formula>
<text><location><page_8><loc_8><loc_81><loc_92><loc_84></location>The scintillation pattern is assumed frozen onto a screen that moves past the observer at velocity v , so there is a direction relation between the spatial and temporal dependence of the autcorrelation,</text>
<formula><location><page_8><loc_40><loc_77><loc_92><loc_80></location>ρ ( r , t ) = f ( | C ( r -v t ) | 2 σ 2 ) . (A4)</formula>
<text><location><page_8><loc_8><loc_74><loc_92><loc_76></location>Surfaces of constant correlation correspond to curves of constant | C ( r -v t ) | 2 . The maximum of ρ ( r , t ) occurs at a time lag ∆ t given by</text>
<formula><location><page_8><loc_46><loc_70><loc_92><loc_73></location>∆ t = a · r (A5)</formula>
<text><location><page_8><loc_8><loc_69><loc_12><loc_70></location>where</text>
<formula><location><page_8><loc_44><loc_64><loc_92><loc_68></location>a = ( C T C ) · v | C · v | 2 . (A6)</formula>
<text><location><page_8><loc_8><loc_62><loc_81><loc_64></location>Equations (A2) -(A6) are derived in Coles & Kaufman (1978), and are shown here for completeness.</text>
<text><location><page_8><loc_8><loc_59><loc_92><loc_63></location>Now suppose a source possesses similar structure at two frequencies ν 1 and ν 2 , but that they are displaced by an angle θ . Then the scintilation fluctuations at ν 1 , ∆ I 1 ( r , t ), are identical to those at ν 2 , ∆ I 2 ( r , t ), except that they are displaced by a linear scale D θ (see, e.g. Little & Hewish 1966):</text>
<formula><location><page_8><loc_43><loc_56><loc_92><loc_58></location>I 2 ( r ) = I 1 ( r -D θ ) , (A7)</formula>
<text><location><page_8><loc_8><loc_54><loc_78><loc_55></location>where D is the scattering screen distance. The cross-correlation between I 1 and I 2 takes the form</text>
<formula><location><page_8><loc_19><loc_49><loc_81><loc_53></location>〈 ∆ I 1 ( r ' , t ' )∆ I 2 ( r ' + r , t ' + t ) 〉 〈 ∆ I 1 ∆ I 2 〉 = 〈 ∆ I 1 ( r ' , t ' )∆ I 1 ( r ' + r -D θ , t ' + t ) 〉 〈 ∆ I 1 ∆ I 2 〉 ≡ ρ I 1 I 2 ( r -D θ , t ) .</formula>
<text><location><page_8><loc_89><loc_48><loc_92><loc_50></location>(A8)</text>
<text><location><page_8><loc_8><loc_41><loc_92><loc_47></location>Once again, we assume that ρ I 1 I 2 is a montonically decreasing function of r that takes the form given by equation (A2). Now, if the scintillations are measured at identical locations, we are interested in the maximum of ρ I 1 I 2 ( -D θ , t ). In this case the time delay measured between I 1 and I 2 is the same as that given by eq. (A5) above, with r replaced by -D θ , namely,</text>
<formula><location><page_8><loc_31><loc_37><loc_92><loc_41></location>∆ t = -D a · θ = -D θ · v +( R 2 -1)( D θ × ˆ S )( v × ˆ S ) v 2 +( R 2 -1)( v × ˆ S ) 2 . (A9)</formula>
<text><location><page_8><loc_8><loc_32><loc_92><loc_37></location>where ˆ S = (cos β, sin β ) is the direction along which the scintles are oriented. The cross product of a vector with ˆ S is the component of that vector that points orthogonal to the elongation axis. For instance, r × ˆ S is the component of r orthogonal to the long axis of the scintillation pattern.</text>
<text><location><page_8><loc_8><loc_29><loc_92><loc_32></location>Finally, we note that the timescale of the scintillations can also be derived from the foregoing formalism, and is given by,</text>
<formula><location><page_8><loc_38><loc_23><loc_92><loc_29></location>t scint = σ √ R √ v 2 +( R 2 -1)( v × ˆ S ) 2 , (A10)</formula>
<text><location><page_8><loc_8><loc_22><loc_67><loc_23></location>where σ , defined by eq. (A2), is the overall scale factor of the scintillation pattern.</text>
<section_header_level_1><location><page_8><loc_29><loc_20><loc_72><loc_21></location>CORE SHIFT IN THE PRESENCE OF A PRESSURE GRADIENT</section_header_level_1>
<text><location><page_8><loc_8><loc_11><loc_92><loc_19></location>As discussed by Lobanov (1998), the frequency dependence of core position may be influenced by the pressure gradients in the external medium if hydrostatic confinement is important. Lobanov (1998) plotted the frequency dependence of core position as a function of the power-law index of the pressure profile, but neglected the effect of the changing Doppler factor along the jet. Accordingly, we present a derivation of the properties of the core (diameter, distance along the jet, and spectral index) for a simple model of a hydrostatically confined jet in the presence of a power-law pressure profile, accounting for the effect of a radially dependent Doppler factor.</text>
<text><location><page_8><loc_8><loc_6><loc_92><loc_11></location>Let L be the path length through the source, d the diameter of the jet perpendicular to the jet axis, D A the angular size distance, φ the jet viewing angle, and α ' ν ' the absorption coefficient in the source co-moving frame, at the rest frequency ν ' = 1+ z δ ν . Assuming the jet opening angle is small compared to the jet viewing angle (that is, we</text>
<text><location><page_9><loc_37><loc_78><loc_37><loc_79></location>'</text>
<text><location><page_9><loc_37><loc_77><loc_37><loc_78></location>ν</text>
<text><location><page_9><loc_36><loc_78><loc_37><loc_79></location>α</text>
<text><location><page_9><loc_38><loc_78><loc_38><loc_78></location>'</text>
<text><location><page_9><loc_39><loc_78><loc_40><loc_79></location>=</text>
<text><location><page_9><loc_40><loc_78><loc_41><loc_79></location>C</text>
<text><location><page_9><loc_42><loc_78><loc_42><loc_79></location>(</text>
<text><location><page_9><loc_42><loc_78><loc_43><loc_79></location>α</text>
<text><location><page_9><loc_43><loc_78><loc_44><loc_79></location>)</text>
<text><location><page_9><loc_44><loc_78><loc_45><loc_79></location>k</text>
<text><location><page_9><loc_45><loc_78><loc_45><loc_78></location>e</text>
<text><location><page_9><loc_45><loc_78><loc_47><loc_79></location>B</text>
<text><location><page_9><loc_8><loc_91><loc_63><loc_92></location>approximate the jet as a cylinder), we can approximate the optical depth as,</text>
<formula><location><page_9><loc_40><loc_83><loc_92><loc_90></location>τ ν = Lα ν ≈ d sin φ α ν = d sin φ (1 + z ) δ α ' ν ' , (B1)</formula>
<text><location><page_9><loc_8><loc_81><loc_82><loc_82></location>since να ν is a relativistic invariant. For a power law electron distribution, the absorption coefficient is,</text>
<text><location><page_9><loc_51><loc_76><loc_52><loc_80></location>(</text>
<text><location><page_9><loc_52><loc_79><loc_54><loc_80></location>1 +</text>
<text><location><page_9><loc_55><loc_79><loc_56><loc_80></location>z</text>
<text><location><page_9><loc_53><loc_77><loc_54><loc_78></location>δ</text>
<text><location><page_9><loc_56><loc_78><loc_57><loc_79></location>ν</text>
<text><location><page_9><loc_57><loc_76><loc_58><loc_80></location>)</text>
<text><location><page_9><loc_64><loc_78><loc_64><loc_79></location>,</text>
<text><location><page_9><loc_8><loc_75><loc_75><loc_76></location>where C ( α ) is a constant which depends only on the optically thin spectral index α . So now,</text>
<formula><location><page_9><loc_32><loc_69><loc_92><loc_74></location>τ ν = d sin φ C ( α ) k e B α +1 . 5 ( 1 + z δ ) -( α +1 . 5) ν -( α +2 . 5) . (B2)</formula>
<text><location><page_9><loc_8><loc_68><loc_72><loc_69></location>Hence, at the τ ν = 1 surface, which we identify with the scintillating component, or core:</text>
<formula><location><page_9><loc_33><loc_63><loc_92><loc_67></location>( ν ν 0 ) ( α +2 . 5) = d ( r ) d ( r 0 ) k e ( r ) k e ( r 0 ) [ δ ( r ) B ( r ) δ ( r 0 ) B ( r 0 ) ] 1 . 5+ α , (B3)</formula>
<text><location><page_9><loc_8><loc_61><loc_59><loc_63></location>where r 0 is the position of the τ ν = 1 surface, or core, at frequency ν 0 .</text>
<text><location><page_9><loc_8><loc_53><loc_92><loc_61></location>Hydrostatic confinement implies that the pressure inside the jet adjusts to the pressure of the surrounding medium. In that case, the diameter of the jet, d ( r ), is determined entirely by the pressure gradient of the external medium, and the lateral expansion of the jet dictates the run of magnetic field, particle density, and Lorentz factor along the jet. Consider a jet with ultra-relativistic equation of state, and relativistic particle energy distribution of the form N ( γ ) = K e γ -a between some minimum and maximum Lorentz factor, γ min and γ max , confined by an ambient medium with pressure p ext ∝ r -n p . In that case, conservation equations imply that the following relations hold:</text>
<formula><location><page_9><loc_44><loc_38><loc_92><loc_53></location>d ( r ) ∝ r n p / 4 (B4) Γ( r ) ∝ r n p / 4 B || ∝ r -n p / 2 B ⊥ ∝ r -n p / 4 n ∝ r -3 n p / 4 γ min ∝ r -n p / 4 k e ∝ r -np ( α +1 . 5) 2</formula>
<text><location><page_9><loc_8><loc_37><loc_59><loc_38></location>Following Konigl (1981) and Lobanov (1998), let us define k r such that</text>
<formula><location><page_9><loc_45><loc_34><loc_92><loc_36></location>r core ∝ ν -1 /k r . (B5)</formula>
<text><location><page_9><loc_8><loc_32><loc_21><loc_34></location>and m B such that</text>
<formula><location><page_9><loc_45><loc_30><loc_92><loc_32></location>B ∝ r -m B np 4 . (B6)</formula>
<text><location><page_9><loc_8><loc_25><loc_92><loc_30></location>In that case, m B = 1 corresponds to a predominantly toroidal (perpendicular) magnetic field, while m B = 2 corresponds to a predominantly poloidal (parallel) magnetic field. Approximating the radial dependence in Doppler factor as a power law of the form δ ∝ r n δ , Equations B3 and B4 give</text>
<formula><location><page_9><loc_32><loc_22><loc_92><loc_25></location>k r = ( n p / 4)[(1 . 5 + α )(2 + m B ) -1] -(1 . 5 + α ) n δ 2 . 5 + α . (B7)</formula>
<text><location><page_9><loc_8><loc_18><loc_92><loc_21></location>Note that n δ may be positive or negative depending on the initial Lorentz factor, Γ( r 0 ), and jet viewing angle φ , and therefore the effect of the Doppler factor may be to steepen or flatten the relationship between r and ν .</text>
<text><location><page_9><loc_8><loc_16><loc_92><loc_18></location>For a self-absorbed synchrotron source, the flux density at the peak frequency (which we associate with the flux density at the observed frequency) is,</text>
<formula><location><page_9><loc_41><loc_12><loc_92><loc_15></location>S m ∝ ν 5 / 2 m θ 2 d B -1 / 2 δ 1 / 2 . (B8)</formula>
<text><location><page_9><loc_8><loc_9><loc_92><loc_12></location>This expression, when combined with the functions d(r), B(r), δ (r) and r( ν ), allows a prediction of the core spectral index (see Konigl 1981, equation 12). Here we define the spectral index of the core, α core , such that S ν ∝ ν α core , and</text>
<formula><location><page_9><loc_36><loc_5><loc_92><loc_9></location>α core = 5 2 -1 2 k r [ n p ( 1 + m B 4 ) + n δ ] . (B9)</formula>
<text><location><page_9><loc_58><loc_79><loc_59><loc_80></location>-</text>
<text><location><page_9><loc_59><loc_79><loc_59><loc_80></location>(</text>
<text><location><page_9><loc_59><loc_79><loc_60><loc_80></location>α</text>
<text><location><page_9><loc_60><loc_79><loc_62><loc_80></location>+2</text>
<text><location><page_9><loc_62><loc_79><loc_62><loc_80></location>.</text>
<text><location><page_9><loc_62><loc_79><loc_64><loc_80></location>5)</text>
<text><location><page_9><loc_47><loc_78><loc_48><loc_79></location>α</text>
<text><location><page_9><loc_48><loc_78><loc_49><loc_79></location>+1</text>
<text><location><page_9><loc_49><loc_78><loc_50><loc_79></location>.</text>
<text><location><page_9><loc_50><loc_78><loc_50><loc_79></location>5</text>
<unordered_list>
<list_item><location><page_10><loc_8><loc_73><loc_48><loc_90></location>Asada, K., & Nakamura, M. 2012, ApJ, 745, L28 Bignall, H.E., Jauncey, D.L., Lovell, J.E.J., Kedziora-Chudczer, L., Macquart, J.-P., Tingay, S.J., Rayner, D.P. & Clay, R.W. 2003, ApJ, 585, 653 Bignall, H.E., Macquart, J.-P., Jauncey, D.L., Lovell, J.E.J., Tzioumis, A.K. & Kedziora-Chudczer, L. 2006, ApJ, 652, 1050 Blandford, R. D., & Konigl, A. 1979, ApJ, 232, 34 D'Elia, V., Padovani, P. & Landt, H. 2003, MNRAS, 339, 1081 Georganopoulos, M., & Marscher, A. P. 1996, Energy Transport in Radio Galaxies and Quasars, 100, 67 Konigl, A. 1981, ApJ, 243, 700 Kovalev, Y. Y., Lobanov, A. P., Pushkarev, A. B., & Zensus, J. A. 2008, A&A, 483, 759 Kudryavtseva, N. A., Gabuzda, D. C., Aller, M. F., & Aller, H. D. 2011, MNRAS, 415, 1631</list_item>
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<text><location><page_10><loc_52><loc_74><loc_91><loc_90></location>Lobanov, A. P. 1998, A&A, 330, 79 Lovell, J.E.J., Rickett, B.J., Macquart, J.-P., Jauncey, D.L., Bignall, H.E., Kedziora-Chudczer, L., Ojha, R., Pursimo, T., Dutka, M., Senkbeil, C. & Shabala, S. 2008, ApJ, 689, 108 Marcaide, J. M., & Shapiro, I. I. 1984, ApJ, 276, 56 Narayan, R. 1992, Phil. Soc. R. Soc. Lond. A, 341, 151 O'Sullivan, S. P., & Gabuzda, D. C. 2009, MNRAS, 400, 26 Porcas, R. W. 2009, A&A, 505, L1 Pushkarev, A. B., Hovatta, T., Kovalev, Y. Y., et al. 2012, arXiv:1207.5457 Sokolovsky, K. V., Kovalev, Y. Y., Pushkarev, A. B., & Lobanov, A. P. 2011, A&A, 532, A38 Walker, M.A., de Bruyn, A.G. & Bignall, H.E. 2009, MNRAS, 397, 447</text>
</document>
[
{
"title": "ABSTRACT",
"content": "We describe a new tool for studying the structure and physical characteristics of ultracompact AGN jets and their surroundings with µ as precision. This tool is based on the frequency dependence of the light curves observed for intra-day variable radio sources, where the variability is caused by interstellar scintillation. We apply this method to PKS 1257-326 to resolve the core-shift as a function of frequency on scales well below ∼ 12 µ as. We find that the frequency dependence of the position of the scintillating component is r ∝ ν -0 . 1 ± 0 . 24 (99% confidence interval) and the frequency dependence of the size of the scintillating component is d ∝ ν -0 . 64 ± 0 . 006 . Together, these results imply that the jet opening angle increases with distance along the jet: d ∝ r n d with n d > 1 . 8. We show that the flaring of the jet, and flat frequency dependence of the core position is broadly consistent with a model in which the jet is hydrostatically confined and traversing a steep pressure gradient in the confining medium with p ∝ r -n p and n p /greaterorsimilar 7. Such steep pressure gradients have previously been suggested based on VLBI studies of the frequency dependent core shifts in AGN. Subject headings: galaxies: jets - techniques: high angular resolution - quasars: individual (PKS1257 -326) - scattering",
"pages": [
1
]
},
{
"title": "THE MICROARCSECOND STRUCTURE OF AN AGN JET VIA INTERSTELLAR SCINTILLATION",
"content": "J.-P. Macquart 1 , L.E.H. Godfrey, H.E. Bignall, J.A. Hodgson 2 ICRAR/Curtin University, Bentley, WA 6845, Australia Draft version March 4, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "The brightest, most compact feature of an AGN jet, the 'core', is identified with the part of the jet at which the optical depth ( τ ν ) is of order unity (Blandford & Konigl 1979), and is often referred to as the τ ν = 1 surface, or photosphere. Due to positional variation of the opacity in the jet and/or surrounding medium, the position of the τ ν = 1 surface is frequency dependent, and therefore, so too is the absolute position of the core (eg. Konigl 1981; Lobanov 1998; Kovalev et al. 2008; Sokolovsky et al. 2011). The frequency dependent position of the core is referred to simply as the core shift. The core shift effect provides an observational tool with which to investigate the structure and physical conditions in parsec-scale AGN jets. Moreover, modelling the effect may provide information about the confinement mechanism and pressure gradients in the external medium. The core shift effect is also relevant to the quest for high precision absolute astrometry for the International Celestial Reference Frame, as it can introduce a significant offset in positions determined using group delay measurements (Porcas 2009). The magnitude of the core shift between 2.3 and 8.4 GHz is typically of order a few hundred µ as or less (O'Sullivan & Gabuzda 2009; Sokolovsky et al. 2011; Pushkarev et al. 2012), and therefore detecting this effect requires very high accuracy registration of images at two or more frequencies. Despite the technical challenges, the core-shift effect obtained from VLBI imaging has been reported for an ever-increasing number of radio galaxies (Marcaide & Shapiro 1984; Lobanov 1998; Kovalev et al. 2008; O'Sullivan & Gabuzda 2009; Sokolovsky et al. 2011; Pushkarev et al. 2012). More recently, Kudryavtseva et al. (2011) have employed an indirect method to measure the core shift effect based on frequency-dependent time lags of flares observed using single-dish data spanning several years. The frequency dependence of core position is typically assumed to follow a power-law of the form r ∝ ν -1 /k r . In many sources for which core shifts can be measured with VLBI imaging, the absolute core position varies approximately with the inverse of the frequency (i. e. k r = 1) (O'Sullivan & Gabuzda 2009; Sokolovsky et al. 2011). This situation is consistent with the standard model of a conical jet in which the plasma is in a state of equipartition between particle and magnetic energy densities (Blandford & Konigl 1979). However, values of k r much greater than unity are observed in some sources, which may be due to free-free absorption in the immediate vicinity of the jet, or due to rapid changes in pressure in the external medium if hydrostatic confinement is important (Lobanov 1998). Lobanov (1998) has shown that while k r ∼ 1 at large distances downstream from the black hole, the value of k r increases towards the jet base. Kudryavtseva et al. (2011) have shown that the value of k r is time-dependent, and correlated with flux density. Finally, the pc-scale jet of M87 is observed to deviate from a conical geometry near to the core (Asada & Nakamura 2012). Further investigation into the frequency dependence of core position is therefore warranted, and highly relevant to the study of ultracompact AGN jets. Here we present a potentially powerful new method for the study of ultracompact jets in AGN, which enables simultaneous measurement of the core shift effect and jet geometry to very high precision. This new technique uses auto- and cross-correlation analysis of multi-frequency light curves of a rapidly scintillating AGN to measure the frequency dependence of the position and size of the scintillating component. In section 2 we present the observations and data analysis. In Section 3 we discuss the mathematical formulation of the auto- and cross-correlation analysis, and derive the frequency dependent source position and size for PKS 1257-326. In Section 4 we discuss the implications of our findings, and model the jet in terms of a hydrostatically confined jet traversing a steep pressure gradient. Finally, in Section 5 we present our conclusions.",
"pages": [
1,
2
]
},
{
"title": "2. OBSERVATIONS AND DATA CALIBRATION",
"content": "PKS1257 -326 was observed at the ATCA for ten hours on 15 January 2011, with two 2 GHz bands, centred on frequencies of 5.5 and 9.0 GHz. The output data included all four polarisation products and 2048 spectral channels each 1 MHz wide in each of the two bands. Flagging and calibration of the data were performed using the Miriad software package. The ATCA primary calibrator PKS1934 -638 was used to correct the overall flux density scale and the spectral slope. In order to solve for the bandpass and to correct gain amplitudes as a function of time and pointing for each antenna, the secondary calibrator PKS1255 -316, only 1 · from PKS1257 -326, was observed for 1 minute approximately every 20 minutes, interleaved with observations of the target source. Phase self-calibration assuming a point source model was performed with a short (10 s) solution interval. After initial calibration the data were split into 128 MHz sub-bands for further analysis. At least 98% of the total flux density of PKS 1257 -326 is unresolved with the ATCA, and there is no significant confusion in the field at frequencies above 4 GHz. Therefore, to obtain the light curves of the source variations we averaged the real part of the calibrated visibilities over all baselines and frequency points within each 128 MHz band. The relative stability of the calibration as a function of time and frequency within each 2 GHz band is estimated to be ∼ 1% or better, based on the PKS 1255 -316 data. The bandpass is observed to be stable over the duration of our observations in the 5 GHz band, but there are small frequency- and elevation-dependent gain variations across the higher frequency band, which were corrected with a time-dependent bandpass solution derived from PKS1255 -316. Although the frequency dependence of the primary calibrator PKS1934 -638 is well known, archival data on the secondary calibrator PKS1255 -316 shows it to be variable by up to ∼ 50% on timescales of months to years. Hence there is a small uncertainty in the spectral slope correction for the 9GHz band, due to the variations with time and pointing, and the fact that the spectrum of PKS 1255-316 is not known a priori. In any case, the average spectrum of PKS1257 -326 is relatively smooth across the entire range of frequencies, suggesting that the calibration is accurate. Moreover any residual constant offsets in the flux density scale which may be present between different frequencies have no effect on the cross-correlation analysis presented in this paper. Figure 1 shows the large, rapid intra-hour variations exhibited by PKS1257 -326.",
"pages": [
2
]
},
{
"title": "3. DERIVATION OF JET STRUCTURE",
"content": "3.1. Interpretation The rapid fluctuations observed in the centimetre wavelength flux density of the intra-hour variable quasar PKS1257 -326 are due to interstellar scintillation (Bignall et al. 2003, 2006). This is established from the measurement of a time delay in the arrival time of the variations between telescopes separated by several thousand kilometers. The timescale of the variations also undergoes an annual modulation due to relative motion of the Earth about the Sun, which in turn moves relative to the interstellar medium responsible for the variations. Inspection of Figure 1 reveals that there is a time offset in the arrival time of the intensity variations between different frequencies, with the variations at high frequency leading those at lower frequencies. This behaviour is consistent with observations in previous epochs. Bignall et al. (2003) reported that variations at 4.8 and 8.6 GHz are closely correlated, and there is a systematic time delay between the variations at these two frequencies. The magnitude of the time delay was observed to follow an annual cycle which is not identical to the annual cycle in variability timescale but, it was argued, can be explained on the basis of it, as we discuss below. PKS 1257-326 was monitored with the ATCA at 4.8 and 8.6 GHz at 19 epochs between 2001 February and 2002 April. Typical observations were over a 12 hour period, and 6 epochs covered 2 × 12 hours in 48 hour sessions as part of a multi-source monitoring program. The minimum duration of each light curve is ∼ 10 times the length of the characteristic timescale. In every one of these epochs, the time delay between 4.8 and 8.6 GHz has the same sign, with 8.6 GHz variations always leading. Moreover, a clear annual cycle is observed in the two-frequency time delay, with the longest delays being observed from late July to mid-August. Such an annual cycle is expected for a core-shift which remains stable over the course of the year, and the observed annual cycle is well modelled by such a shift on a scale of order 10 µ as (Bignall et al. 2003), although the precise magnitude and direction of the core shift could not be uniquely determined. These data provide strong evidence that the core shift effect dominates over any refractive effects or 'jitter' in the ISS pattern. We argue that the temporal offset in the present data arises as a direct consequence of an angular offset between two compact components within the scintillating source. The effect may be understood as follows. When an angular separation, θ , is present between two components, this results in a spatial displacement of their respective scintillation patterns across the plane of an observer by an amount D θ , whe re D is distance between the observer and the scattering material (Little & Hewish 1966). Since the scintillation patterns are in motion across this plane with some velocity v , the result is a separation in the arrival time of the scintillations associated with each component. In the present case, a displacement in the lightcurves between closely-spaced frequencies arises because there is an angular offset in the image centroids between the respective frequencies. For any pair of frequencies, the time delay is, in terms of the centroid offset θ (see Appendix A), where R is the anisotropy ratio of the scintillation pattern and ˆ S = (cos β, sin β ) is the direction of its major axis, which we measure with respect to the RA axis. The scintillation parameters have been derived from annual cycle and two-station time-delay measurements, and are given in Table 1. It is evident that this delay is modulated both by the annual cycle in the magnitude of v and by changes in the angle of the velocity vector with respect to θ ; this latter effect causes the annual cycle experienced by ∆ t to differ from the annual cycle in scintillation velocity. Phase gradients in the ISM may, in principle, also cause temporal offsets of lightcurves as a function of frequency in a scintillating source. However, the offset observed here is difficult to attribute to such an extrinsic cause for several reasons: (i) the sense and magnitude of the delay is constant throughout the dataset; upon dividing the dataset in two halves (in time) and deriving time offsets based on these two halves separately, we find the same offsets to within the margin of error of the estimates. (ii) The delay is observed over a timescale of 10 hours, whereas refractive phase gradients in the ISM in the regime of weak scintillation for a Kolmogorov spectrum of phase inhomogeneities would occur on the timescale associated with the scintillations, and the time offset should converge to zero as the average is performed over an increasing number of scintles. Any small jitter in the offset between individual scintles appears to be dominated by the systematic offset. (iii) An annual cycle in the time offset is reported by Bignall et al. (2003), in- dicating that the offset persists on a timescale of greater than a year.",
"pages": [
2,
3
]
},
{
"title": "3.2. Time delay measurement",
"content": "To determine the relative time delay between each pair of lightcurves, I ( t, ν 1 ) and I ( t, ν 2 ), we computed the cross-correlation function, A peak in the cross correlation at positive delay, ∆ t , indicates that the fluctuations at frequency ν 2 precede those at ν 1 . We fitted a gaussian of the form, to the inner part of the cross-correlation function, C (∆ t ; ν 1 , ν 1 ) (equivalent to the auto-correlation function), to obtain an estimate of the time delay between each frequency-lightcurve pair and its associated error. An example cross-correlation function and its associated fit is shown in Fig. 2. Typical errors in the estimated delay are 50 s. The derived delays as a function of ν 1 and ν 2 are shown in Fig. 3. The estimated 50 s uncertainties in the delay between each frequency pair are derived from least-squares fitting of a gaussian to the peak of the delay, thus the errors are directly related to the width of The parameters of the scintillations in PKS 1257 326. a Parameters are derived on the basis of the annual cycle in the variability timescale (Bignall et al. 2003) and measurements of the time delay observed between two stations (Bignall et al. 2006, henceforth B06). An alternate fit to the scintillation data provided by Walker, de Bruyn & Bignall (2009) (henceforth W09) is also listed. The scintillation velocity quoted here is the addition of Earth's relative to the Sun velocity on the observation date and the velocity of the scattering medium relative to the Sun. the peak in the cross-correlation functions 3 . These uncertainties are in turn derived from the least squares fit to the cross-correlation function; the errors in the individual points in the cross-correlation function are dominated, at low time lags, by Poisson errors associated with the number of independent measurements of the cross-correlation measureable from the lightcurve. This error is indicated by the scatter between points in the CCF. Fitting to the CCF yields a typical formal error of ≈ 20 s. However the high degree of cross correlation between the lightcurves in our observations means that the error in the time delay estimate for any given frequency pair is not completely independent from the time delay estimate of any other frequency pair. It is necessary to take the cross-correlation into account because it becomes an important factor when assessing the significance of the fit to the frequency dependence of the time delay using a least-squares approach (see below), which is the primary reason to estimate the error in the time lag. Failure to take into account this interdependence in time lag estimates would lead to an overestimate of the significance of the fit to the frequency dependence of the time shift. It was found empirically, from examination of the reduced chi-squared in the fit procedure that this cross-correlation is taken into account in the error analysis with errors that are 2 . 5 times larger than the formal error. In most models of jet structure the angular offset between the jet base and the centroid of the emission at a frequency ν is fitted to a power law, ∆ θ = Aν -ζ , where A and ζ are constants to be determined. Since the time delay is linearly proportional to | θ | , we fitted a function of the form ∆ t ( ν 1 , ν 2 ) = K ( ν -ζ 1 -ν -ζ 2 ) to the delays. The best-fitting parameters are ζ = 0 . 10 and K = (1 . 6 ± 0 . 5) × 10 4 s MHz ζ , with the 99% confidence interval of ζ extending over the range [ -0 . 14 , 0 . 34]; the best-fitting surface is plotted over the data in Fig. 3 4 . 3 This error is significantly smaller than the time delay errors that might be estimated on the basis of the data presented in Bignall et al. (2003). As is evident from Fig. 2 in Bignall et al. (2003), the data in most of those epochs contain considerably few scintles from which to estimate the time lag. Thus one would expect the errors to be larger relative to the 2011 data. The dataset obtained on 4 Jan 2001 contains a comparable number of scintles, but here the temporal sampling of the lightcurve was too sparse to estimate a time delay. 4 The 99% confidence limits are calculated, in the conventional way, from the change in the sum of the squares of the residuals The best-fitting exponent indicates a core-shift dependence on frequency that is much shallower than the value ζ = 1 typically found in other quasars on the basis of VLBI measurements (e.g. O'Sullivan & Gabuzda 2009; Sokolovsky et al. 2011). We also measure the timescale of the scintillations, which is derived from the parameter B in eq. (3) (and with ν 1 = ν 2 ). Figure 4 shows that the timescale is wellfit by a relation scaling as ν -0 . 642 ± 0 . 006 ; a fit using a broken power law reveals the both the 4-5 and 8-9 GHz timescales follow the same scaling with frequency within the (small) margin of error. In the regime in which the angular size of the source, θ src , exceeds the angular size of the Fresnel scale at the distance of the scattering screen, θ F = √ c/ 2 πνD , the scintillation timescale is linearly proportional to the size of the scintillating component. In the opposite regime, θ src < θ F , the scintillation timescale is determined by Dθ F /v = r F /v , which scales as ν -0 . 5 . We wish to determine whether the timescale of the scintillations measures θ F or θ src . The expected Fresnel crossing timescale is 1 . 0 × 10 3 ( D/ 10 pc) 1 / 2 ( ν/ 5 GHz) -1 / 2 ( v/ 54 kms -1 ) -1 s. The observed scintillation timescale at 5.0 GHz is 1 . 4 × 10 3 s, so if the source is unresolved there must be an error in the nominal scintillation parameters; if the scintillation velocity is held at its nominal value one must have D > 19 pc, or if the screen distance is held at its nominal value one must have v < 40 kms -1 . The latter option is viable for the scintillation velocity derived by Walker, de Bruyn & Bignall (2009), so we conclude that it is plausible that the source is unresolved by the scintillations. However, the fact that the scaling of scintillation timescale is significantly different from ν -0 . 5 suggests that the source is at least partially resolved in any case. The smooth trend evident in both timescale and scintillating amplitude with frequency suggests that the source remains resolved over the entire frequency range 5-10 GHz. Although tangential to the objectives of this paper, we can, in addition, estimate the amplitude of the scintil- of the fit. Now, in practice, since the lightcurves are correlated between frequencies, the time lag estimate between adjacent frequency pairs are strictly not independent, and this influences the chi-squared estimate. However, this effect is treated by accounting for the cross-correlation in the estimates of the time delays for each frequency pair. lating component of the source. For an extended source of size θ src in the regime of weak scintillation caused by a Kolmogorov spectrum of turbulent fluctuations, the observed rms, 〈 δI 2 〉 1 / 2 can be expressed in the form (Narayan 1992), where 〈 I 〉 is the flux density of the scintillating component of the source and r diff ∝ ν 6 / 5 is the diffractive scale, which is determined by the properties of the interstellar turbulence (see Narayan 1992). In the regime of intermediate scattering one has r diff ≈ r F , with equality at the transition frequency, which likely occurs in the range 37GHz based upon the modelling of Walker (1998). One then solves for 〈 I 〉 using the measurements of 〈 δI 2 〉 1 / 2 . Assuming that the source size exceeds the Fresnel angular scale, one determines θ src /θ F from the ratio t scint /t F . We performed a fit using the measured values of 〈 δI 2 〉 and t scint , and subject to the assumption that r diff = r F at 4 GHz, to derive a rough estimate of the flux density of the scintillating component: We caution that the spectral index of the component derived here is only approximate because the expression for the modulation index in eq.(4) is only approximate at frequencies where r diff ≈ r F . A more sophisticated estimate would employ a more complicated approximation to the modulation index near the transition frequency and take into account the anisotropy of the scintillations.",
"pages": [
3,
4,
5
]
},
{
"title": "3.3. Overall source scale",
"content": "Although the frequency scaling of the core position and size are the primary results of our analysis, it is possible to roughly relate these measurements back to physical scales within the source. The Schwarzschild radius of the black hole at the centre of PKS1257 -326 is R S = 2 . 95 × 10 12 M 9 m, where M 9 = 10 9 M /circledot is the BH mass, which is estimated from measurements of the broad line emission width to be 10 8 . 8 M /circledot (D'Elia, Padovani & Landt, 2003). At the redshift of PKS1257 -326, z = 1 . 256, 1 µ as subtends 8 . 5 × 10 -3 pc, equivalent to 89 /M 9 Schwarzschild radii 5 . The time delay is related to angular structure in the source using eq. (1) and the scintillation parameters in Table 1. This also depends on the angle, ξ , that θ makes with the right ascension axis, which is unknown. For a time offset ∆ t , the expected amplitude of the angular offset is given by where the two solutions denote the scintillation parameters found by Bignall et al. (2006) (B06) and Walker et al. (2009) (W09). For instance, the angular separation implied by the 520s delay observed between the lowest (4540MHz) and highest (9960MHz) frequency bands of our observations is 19 µ as (12 µ as) for the scintillation parameters of B06 (W09) if ξ = 0 (i.e. if the angular separation is aligned parallel to the right ascension axis). This translates to a physical scale of 0.16 pc (0.10 pc) at the source. However, these estimates are subject to uncertainties in both the screen distance and the orientation of the separation ξ . For instance, doubling D above its nominal value of 10 pc would result in estimates of | θ | lower by a factor of two. They thus serve only as a guide to the order of magnitude of scales which are probed by these measurements. In the same vein, we also estimate the angular scale of the source from the variability timescale, using eq. (A10) in Appendix A to find the characteristic angular scale of the scintillation pattern, The minor axis of the scintillation pattern has a size θ src / √ R while the major axis has a characteristic size of θ src √ R .",
"pages": [
5,
6
]
},
{
"title": "4.1. Observational Constraints",
"content": "The foregoing analysis indicates that the centroid of the scintillating component has a frequency dependence of the form: r core ∝ ν -0 . 1 ± 0 . 24 . In the terminology of Konigl (1981) and Lobanov (1998), r core ∝ ν -1 /k r , we have k r > 3. We proceed under the assumption that the source is resolved, as suggested by the frequency dependence of the scintillation time-scale (Section 3.2). In that case, the jet diameter has a frequency dependence of the form: d ∝ ν -0 . 64 ± 0 . 006 . Taken together, these results imply d ∝ r n d core with n d > 1 . 8. The scenario implied by our analysis is illustrated in Figure 5. This is in contrast to the frequency dependence of the core position in VLBI studies: typically r core ∝ ν -1 , consistent with expectations for a conical jet in which the particle and magnetic energy densities are in equipartition (Sokolovsky et al. 2011).",
"pages": [
6
]
},
{
"title": "4.2. Interpretation in terms of hydrostatic jet confinement in a steep pressure gradient",
"content": "Lobanov (1998) suggested that the changes in jet opacity observed for a sample of sources appear consistent with a self-absorbed jet propagating through a region with a steep pressure gradient of the form p ∝ r -6 . Here we consider such a model to explain the inferred frequency dependence of the core size and position in PKS 1257-326. Specifically, we consider whether such a model can simultaneously account for the increase in opening angle along the jet ( d ∝ r n d core with n d > 1 . 8), and the flat frequency dependence of core position ( r core ∝ ν -1 /k r , with k r > 3). The relevant model equations, for a pressure profile p ∝ r -n p , are (see Appendix B) Here m B is a parameter determined by the magnetic field geometry as discussed in Appendix B, and α is the optically thin spectral index which directly relates to the electron energy distribution N ( γ ) ∝ γ -(2 α +1) , as opposed to α core , which is the optically thick spectral index of the self-absorbed core. We assume α = 0 . 5, m B = 1 (i. e. a predominantly toroidal magnetic field configuration) and take n p = 7 . 2 so that n d = 1 . 8. In that case, the jet Lorentz factor goes as Γ / Γ 0 = ( r/r 0 ) 1 . 8 , so that for reasonable values of the jet viewing angle (5 · < φ < 40 · ) and initial Lorentz factor (2 /lessorsimilar Γ 0 /lessorsimilar 10), we have -0 . 5 /lessorsimilar n δ /lessorsimilar 0 . 5, which implies: There is excellent agreement between the predicted and observed frequency dependence of core position and radial dependence of core size. The agreement between the predicted and observed core spectral index is poorer, but this is perhaps unsurprising since, as remarked above, observational determination of the core spectral index is marred by uncertainties in the model used to derive it. We therefore suggest that this simple model of hydrostatic confinement is broadly consistent with the data, provided n p /greaterorsimilar 7 . 2. The required pressure gradient in the external medium ( n p /greaterorsimilar 7 . 2) appears very steep, however, such pressure gradients have previously been suggested in studies of core shifts in AGN (Lobanov 1998). Finally, we note that the frequency dependence of core position may also be influenced by free-free absorption in the immediate environment of the jet (e. g. Lobanov 1998). However, we find no evidence for a significant rotation measure, and such an interpretation cannot account for the flaring jet geometry, so that an additional mechanism, such as entrainment, would also be required to explain these results.",
"pages": [
6
]
},
{
"title": "5. CONCLUSIONS",
"content": "We have developed a new technique to probe the structure of AGN jets on micro-arcsecond scales, by using interstellar scintillation to simultaneously determine the shift in the position of the AGN core as a function of frequency, and the frequency scaling of the core size, to high precision. This approach is amenable to sources which harbour compact ( /lessorsimilar 100 µ as) features. This method was applied to broadband observations of PKS1257-326 with the Australia Telescope Compact Array. The scaling of the core-shift is found to be remarkably shallow with frequency; the best fit to the position of the scintillating component in the source scales as r ∝ ν -0 . 10 , with the 99% confidence interval of the index extending over the range [ -0 . 34 , 0 . 14]. This constrasts with previous VLBI studies which typically - though not exclusively - find r ∝ ν -1 . The scaling of the jet size is also determined, based on the scaling of the scintillation timescale with frequency. This shows that the jet size scales formally as d ∝ ν -0 . 64 ± 0 . 006 . It is possible to determine the scaling of the core shift and jet diameter to high precision because they do not depend critically on complete knowledge of the properties of the scattering medium responsible for the scintillations. Determination of the absolute physical scale of the core shift does, however, require knowledge of the scintillation parameters, and we can only determine these quantities approximately. The observed 520 s time offset between the scintillations at the the lowest (4540 MHz) and highest (9960MHz) frequency bands of our observations implies an angular separation of /greaterorsimilar 12 µ as, for an assumed scattering screen distance of 10 pc. This translates to a physical scale of ∼ 0 . 10pc at the source. This physical scale probed is an order of magnitude smaller than typical core shifts obtained with VLBI measurements. We further note that this technique easily detects the core-shift between frequency pairs separated by only ∼ 300 MHz, thus providing sub-microarcsecond resolution of the jet structure. A major conclusion arising from our analysis is that that the often assumed frequency scaling of core position, r core ∝ ν -1 (e. g. Pushkarev et al. 2012), may not be applicable to all sources, in line with similar findings of Lobanov (1998) and Kudryavtseva et al. (2011). Further, our results hint at a physical difference between persistent intra-day variable (IDV) sources, and the broader population of AGN. To place these results in a physical context, we have explored a simple model based on a hydrostatically confined jet traversing a pressure gradient. The pressure profile implied by this model is steep: p ∝ r -n p ; n p /greaterorsimilar 7. Such steep pressure gradients have previously been suggested in VLBI studies of the frequency dependent core shifts in AGN (Lobanov 1998). The discrepancy between the frequency scaling of core position observed in PKS 1257-326, and the typical r core ∝ ν -1 scaling observed in sources studied with VLBI may arise because different types of source lend themselves to different types of analysis. Only the largest core shifts can be detected with VLBI imaging. In an analysis of 277 objects by Kovalev et al. (2008), only 10% gave reliable core shift measurements. The sources used in the detailed, multi-frequency VLBI study of the core shift effect by Sokolovsky et al. (2011) were selected based on their known large core shift, in addition to their bright optically thin jet features that were required to enable accurate registration of the images. More specifically, we suggest that the peculiar nature of the core-shift frequency dependence in PKS 1257-326 is related to a number of other remarkable source properties. The implied brightness temperature of the scintillating component in PKS1257-326 is high, > 10 12 K (Bignall et al. 2006), and the source has exhibited such bright emission at least as long as IDV has been observed, since 1995. The persistence of this IDV over more than 15 years is relatively rare amongst IDV sources. During the 4-epoch, one year duration MASIV survey, Lovell et al. (2008) found that sources which consistently exhibited IDV over all four epochs accounted for only 20% of all IDV sources observed. Moreover, the stability of the annual cycle in the source variability timescale (Bignall et al. 2003, 2006) suggests that the size of the source is remarkably stable on a timescale of years. Physically, this implies that the ultracompact jet in this source is both remarkably bright and stable. It is tempting to speculate, therefore, that the hydrostatic confinement provided by the strong pressure gradient suggested by our simple model is responsible for the observed stability of the jet. The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. The observations presented here were made by JAH as part of the CSIRO Astronomy & Space Science (CASS) Vacation Scholarship Program. JAH thanks Dominic Schnitzeler for assistance with the observing setup. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. Facilities: ATCA ()",
"pages": [
6,
7
]
},
{
"title": "DERIVING SOURCE STRUCTURE FROM THE TIME DELAY BETWEEN SCINTILLATION LIGHTCURVES",
"content": "Here we relate the time delay observed between the scintillations at two frequencies to the angular displacement θ between the centroids of the source emission at the two frequencies. The time delay depends not only on the velocity, but also on the axial ratio, R , and orientation of the interstellar scintillation pattern. For intensity fluctuations ∆ I ( r , t ) measured at two locations r ' and r ' + r on the observer's plane at time t , the intensity correlation function is defined as, We follow the treatment of Coles & Kaufman (1978), in which the simplest approximation is that the contours of equal spatial correlation comprise a family of similar ellipses, and the model for the spatial correlation function takes the form where f is a monotonically decreasing function of | C r | 2 . If the scintles are elliptical with axial ratio R and x axis is inclined at an angle β with respect to the major axis, then C takes the form The scintillation pattern is assumed frozen onto a screen that moves past the observer at velocity v , so there is a direction relation between the spatial and temporal dependence of the autcorrelation, Surfaces of constant correlation correspond to curves of constant | C ( r -v t ) | 2 . The maximum of ρ ( r , t ) occurs at a time lag ∆ t given by where Equations (A2) -(A6) are derived in Coles & Kaufman (1978), and are shown here for completeness. Now suppose a source possesses similar structure at two frequencies ν 1 and ν 2 , but that they are displaced by an angle θ . Then the scintilation fluctuations at ν 1 , ∆ I 1 ( r , t ), are identical to those at ν 2 , ∆ I 2 ( r , t ), except that they are displaced by a linear scale D θ (see, e.g. Little & Hewish 1966): where D is the scattering screen distance. The cross-correlation between I 1 and I 2 takes the form (A8) Once again, we assume that ρ I 1 I 2 is a montonically decreasing function of r that takes the form given by equation (A2). Now, if the scintillations are measured at identical locations, we are interested in the maximum of ρ I 1 I 2 ( -D θ , t ). In this case the time delay measured between I 1 and I 2 is the same as that given by eq. (A5) above, with r replaced by -D θ , namely, where ˆ S = (cos β, sin β ) is the direction along which the scintles are oriented. The cross product of a vector with ˆ S is the component of that vector that points orthogonal to the elongation axis. For instance, r × ˆ S is the component of r orthogonal to the long axis of the scintillation pattern. Finally, we note that the timescale of the scintillations can also be derived from the foregoing formalism, and is given by, where σ , defined by eq. (A2), is the overall scale factor of the scintillation pattern.",
"pages": [
7,
8
]
},
{
"title": "CORE SHIFT IN THE PRESENCE OF A PRESSURE GRADIENT",
"content": "As discussed by Lobanov (1998), the frequency dependence of core position may be influenced by the pressure gradients in the external medium if hydrostatic confinement is important. Lobanov (1998) plotted the frequency dependence of core position as a function of the power-law index of the pressure profile, but neglected the effect of the changing Doppler factor along the jet. Accordingly, we present a derivation of the properties of the core (diameter, distance along the jet, and spectral index) for a simple model of a hydrostatically confined jet in the presence of a power-law pressure profile, accounting for the effect of a radially dependent Doppler factor. Let L be the path length through the source, d the diameter of the jet perpendicular to the jet axis, D A the angular size distance, φ the jet viewing angle, and α ' ν ' the absorption coefficient in the source co-moving frame, at the rest frequency ν ' = 1+ z δ ν . Assuming the jet opening angle is small compared to the jet viewing angle (that is, we ' ν α ' = C ( α ) k e B approximate the jet as a cylinder), we can approximate the optical depth as, since να ν is a relativistic invariant. For a power law electron distribution, the absorption coefficient is, ( 1 + z δ ν ) , where C ( α ) is a constant which depends only on the optically thin spectral index α . So now, Hence, at the τ ν = 1 surface, which we identify with the scintillating component, or core: where r 0 is the position of the τ ν = 1 surface, or core, at frequency ν 0 . Hydrostatic confinement implies that the pressure inside the jet adjusts to the pressure of the surrounding medium. In that case, the diameter of the jet, d ( r ), is determined entirely by the pressure gradient of the external medium, and the lateral expansion of the jet dictates the run of magnetic field, particle density, and Lorentz factor along the jet. Consider a jet with ultra-relativistic equation of state, and relativistic particle energy distribution of the form N ( γ ) = K e γ -a between some minimum and maximum Lorentz factor, γ min and γ max , confined by an ambient medium with pressure p ext ∝ r -n p . In that case, conservation equations imply that the following relations hold: Following Konigl (1981) and Lobanov (1998), let us define k r such that and m B such that In that case, m B = 1 corresponds to a predominantly toroidal (perpendicular) magnetic field, while m B = 2 corresponds to a predominantly poloidal (parallel) magnetic field. Approximating the radial dependence in Doppler factor as a power law of the form δ ∝ r n δ , Equations B3 and B4 give Note that n δ may be positive or negative depending on the initial Lorentz factor, Γ( r 0 ), and jet viewing angle φ , and therefore the effect of the Doppler factor may be to steepen or flatten the relationship between r and ν . For a self-absorbed synchrotron source, the flux density at the peak frequency (which we associate with the flux density at the observed frequency) is, This expression, when combined with the functions d(r), B(r), δ (r) and r( ν ), allows a prediction of the core spectral index (see Konigl 1981, equation 12). Here we define the spectral index of the core, α core , such that S ν ∝ ν α core , and - ( α +2 . 5) α +1 . 5 Lobanov, A. P. 1998, A&A, 330, 79 Lovell, J.E.J., Rickett, B.J., Macquart, J.-P., Jauncey, D.L., Bignall, H.E., Kedziora-Chudczer, L., Ojha, R., Pursimo, T., Dutka, M., Senkbeil, C. & Shabala, S. 2008, ApJ, 689, 108 Marcaide, J. M., & Shapiro, I. I. 1984, ApJ, 276, 56 Narayan, R. 1992, Phil. Soc. R. Soc. Lond. A, 341, 151 O'Sullivan, S. P., & Gabuzda, D. C. 2009, MNRAS, 400, 26 Porcas, R. W. 2009, A&A, 505, L1 Pushkarev, A. B., Hovatta, T., Kovalev, Y. Y., et al. 2012, arXiv:1207.5457 Sokolovsky, K. V., Kovalev, Y. Y., Pushkarev, A. B., & Lobanov, A. P. 2011, A&A, 532, A38 Walker, M.A., de Bruyn, A.G. & Bignall, H.E. 2009, MNRAS, 397, 447",
"pages": [
8,
9,
10
]
}
]
2013ApJ...765L...8R
https://arxiv.org/pdf/1212.1465.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_86><loc_86><loc_87></location>PLANET FORMATION IN SMALL SEPARATION BINARIES: NOT SO EXCITED AFTER ALL</section_header_level_1>
<text><location><page_1><loc_42><loc_84><loc_57><loc_85></location>Roman R. Rafikov 1</text>
<text><location><page_1><loc_42><loc_83><loc_58><loc_84></location>Draft version June 2, 2021</text>
<section_header_level_1><location><page_1><loc_45><loc_80><loc_55><loc_81></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_63><loc_86><loc_80></location>Existence of planets is binaries with relatively small separations (around 20 AU), such as α Centauri or γ Cephei poses severe challenges to standard planet formation theories. The problem lies in the vigorous secular excitation of planetesimal eccentricities at separations of several AU, where some of the planets are found, by the massive, eccentric stellar companions. High relative velocities of planetesimals preclude their growth in mutual collisions for a wide range of sizes, from below 1 km up to several hundred km, resulting in fragmentation barrier to planet formation. Here we show that rapid apsidal precession of planetesimal orbits, caused by the gravity of the circumstellar protoplanetary disk, acts to strongly reduce eccentricity excitation, lowering planetesimal velocities by an order of magnitude or even more at 1 AU. By examining the details of planetesimal dynamics we demonstrate that this effect eliminates fragmentation barrier for in-situ growth of planetesimals as small as /lessorsimilar 10 km even at separations as wide as 2.6 AU (semi-major axis of the giant planet in HD 196885), provided that the circumstellar protoplanetary disk is relatively massive, ∼ 0 . 1 M /circledot .</text>
<text><location><page_1><loc_14><loc_60><loc_86><loc_63></location>Subject headings: planets and satellites: formation - protoplanetary disks - planetary systems binaries: close</text>
<section_header_level_1><location><page_1><loc_22><loc_57><loc_34><loc_58></location>1. introduction.</section_header_level_1>
<text><location><page_1><loc_8><loc_33><loc_48><loc_56></location>About 20% of planets detected via stellar radial velocity variations reside in binaries (Desidera & Barbieri 2007). The majority of these systems are wide separation binaries, with semi-major axis a b /greaterorsimilar 30 AU. At the same time, four relatively small separation binaries with a b ≈ 20 AU (HD 196885, γ Cephei, Gl 86 and HD 41004; Chauvin et al. 2011) are also known to harbor giant planets with projected masses M pl sin i ≈ (1 . 6 -4) M J . In these systems the mass of the secondary star (we call 'secondary' the binary component other than the star orbited by the planet, which we denote as 'primary') M s is found to be close to 0 . 4 M /circledot and binary eccentricity e b is close to 0 . 4. Also, Dumusque et al. (2012) have recently announced an Earth-mass companion to α Centauri B, a member of the binary (or, possibly, a triple) with a b = 17 . 6 AU, e b = 0 . 52, and M s = 1 . 1 M /circledot . In this system planet orbits the star at ≈ 0 . 04 AU separation.</text>
<text><location><page_1><loc_8><loc_9><loc_48><loc_33></location>The uniqueness of these systems lies in the fact that forming planets in them is known to provide extreme challenge to planet formation theories (Zhou et al. 2012). With the exception of α Cen and Gl 86, planets in these binaries reside in rather wide orbits, with planetary semimajor axes a pl ≈ 1 . 6 -2 . 6 AU. In-situ formation of these gas giants is expected to proceed through continuous agglomeration of planetesimals at these locations, starting from very small objects (easily /lessorsimilar 1 km). However, gravitational perturbations from the eccentric stellar companion inevitably result in rapid secular evolution (Heppenheimer 1978), driving planetesimal eccentricities far above the level at which bodies can avoid destruction in mutual collisions (Th'ebault et al. 2008). This problem, which is often called collisional or fragmentation barrier , is especially severe for small planetesimals, 1 -10 2 km in size, for which the ratio of binding to kinetic energy is small. It is also more pronounced far from the primary,</text>
<unordered_list>
<list_item><location><page_1><loc_8><loc_6><loc_48><loc_8></location>1 Department of Astrophysical Sciences, Princeton University, Ivy Lane, Princeton, NJ 08540; [email protected]</list_item>
</unordered_list>
<text><location><page_1><loc_52><loc_56><loc_92><loc_58></location>where the secular forcing by the companion is strongest and planetesimal eccentricities are high.</text>
<text><location><page_1><loc_52><loc_42><loc_92><loc_55></location>Marzari & Scholl (2000) suggested that a combination of secular forcing by the companion and gas drag acting on small (1 -10 km) planetesimals leads to apsidal alignment of their orbits, resulting in smaller relative velocities, and allowing colliding objects to grow. However, Th'ebault et al. (2006, 2008) demonstrated that the planetesimal size-dependence of apsidal alignment acts to break orbital phasing between objects of different sizes, resulting in high velocity collisions between them and reinforcing collisional barrier.</text>
<text><location><page_1><loc_52><loc_23><loc_92><loc_42></location>Interestingly, most studies of planetesimal growth in small separation binaries have included the effect of the protoplanetary disk on planetesimal dynamics only via associated gas drag (Th'ebault et al. 2004, 2006, 2008, 2009; Paardekooper et al. 2008; Paardekooper & Leinhardt 2010), without accounting for the gravitational effect of the disk. Batygin et al. (2011) have considered disk gravity in the context of planet formation and evolution in systems with highly misaligned, distant (10 2 -10 3 AU) stellar companions, affected by the Lidov-Kozai effect (Lidov 1961; Kozai 1962). However, this effect is probably irrelevant for planetesimal dynamics in small separation (tens of AU) binaries, which are likely coplanar with circumstellar disks.</text>
<text><location><page_1><loc_52><loc_11><loc_92><loc_23></location>In this Letter we show that apsidal precession of planetesimal orbits induced by disk gravity dominates secular evolution of planetesimals at separations of several AU. As a result, relative velocities at which bodies collide are reduced, sometimes by more than an order of magnitude. In massive disks this effect presents a natural solution of the fragmentation barrier issue for the in-situ formation of the giant planets in small separation binaries, such as γ Cephei.</text>
<section_header_level_1><location><page_1><loc_64><loc_8><loc_80><loc_9></location>2. secular evolution.</section_header_level_1>
<text><location><page_1><loc_52><loc_5><loc_92><loc_8></location>We consider planetesimal motion as Keplerian motion around the primary perturbed by the gravity of the</text>
<text><location><page_2><loc_8><loc_82><loc_48><loc_92></location>companion, that moves on larger, eccentric orbit, and the disk. Mass of the primary is M p , and we define µ ≡ M s / ( M p + M s ). We assume eccentricity of the stellar binary e b to be small and planetesimal orbit to be coplanar with the binary. Planetesimals are immersed in a massive, axisymmetric gaseous disk, characterized by surface density Σ( r ) specified in § 22.1.</text>
<text><location><page_2><loc_8><loc_74><loc_48><loc_82></location>Assuming e /lessmuch 1 the secular (averaged over the planetesimal and binary orbital motion) disturbing function for a planetesimal with semimajor axis a and eccentricity vector e = ( k, h ) = ( e cos /pi1, e sin /pi1 ) (with apsidal angle /pi1 counted from the binary apsidal line, which is assumed fixed 2 ) is (Murray & Dermott 1999)</text>
<text><location><page_2><loc_8><loc_68><loc_12><loc_69></location>where</text>
<formula><location><page_2><loc_13><loc_69><loc_48><loc_73></location>R = na 2 × [ 1 2 ( A + ˙ /pi1 d ) ( h 2 + k 2 ) -Bk ] , (1)</formula>
<formula><location><page_2><loc_18><loc_63><loc_48><loc_67></location>A = 3 4 µ n 2 b n ( 1 + 3 2 e 2 b ) , (2)</formula>
<formula><location><page_2><loc_18><loc_60><loc_48><loc_63></location>B = 15 16 e b µ n 2 b n a a b ( 1 + 5 2 e 2 b ) , (3)</formula>
<text><location><page_2><loc_8><loc_58><loc_11><loc_59></location>and</text>
<formula><location><page_2><loc_16><loc_52><loc_48><loc_57></location>˙ /pi1 d = -1 2 n ( 2 r ∂U d ∂r + ∂ 2 U d ∂r 2 ) ∣ ∣ r = a (4)</formula>
<text><location><page_2><loc_8><loc_43><loc_48><loc_55></location>∣ is the precession frequency of planetesimal orbit due to the disk potential U d . Here n b = [ G ( M p + M s ) /a 3 b ] 1 / 2 and n = ( GM p /a 3 ) 1 / 2 are the mean motions of the binary and planetesimal, respectively. The contribution to R proportional to ˙ /pi1 d arises from expansion of the disk potential along the eccentric planetesimal orbit and averaging over its mean longitude.</text>
<text><location><page_2><loc_8><loc_38><loc_48><loc_43></location>Evolution equations for h and k are written using dh/dt = ( na 2 ) -1 ∂R/∂k , dk/dt = -( na 2 ) -1 ∂R/∂h as</text>
<formula><location><page_2><loc_13><loc_36><loc_48><loc_39></location>dh dt = ( A + ˙ /pi1 d ) k -B, dk dt = -( A + ˙ /pi1 d ) h. (5)</formula>
<text><location><page_2><loc_8><loc_32><loc_48><loc_35></location>These equations agree with the work of Marzari & Scholl (2000) as long as ˙ /pi1 d = 0.</text>
<text><location><page_2><loc_8><loc_30><loc_48><loc_32></location>We write down the solution for e ( t ) = e free ( t ) + e forced ( t ), where</text>
<formula><location><page_2><loc_13><loc_25><loc_48><loc_29></location>{ k free ( t ) h free ( t ) } = e free { cos [( A + ˙ /pi1 d ) t + /pi1 0 ] sin [( A + ˙ /pi1 d ) t + /pi1 0 ] } , (6)</formula>
<text><location><page_2><loc_8><loc_23><loc_24><loc_25></location>/pi1 0 is a constant, and</text>
<formula><location><page_2><loc_11><loc_18><loc_48><loc_22></location>{ k forced ( t ) h forced ( t ) } = e forced { 1 0 } , e forced = B A + ˙ /pi1 d . (7)</formula>
<text><location><page_2><loc_8><loc_13><loc_48><loc_18></location>Thus, free eccentricity vector e free rotates at a rate A + ˙ /pi1 d around the endpoint of the fixed forced eccentricity vector e forced . Note that setting ˙ /pi1 d = 0 we reproduce the solution obtained by Heppenheimer (1978).</text>
<text><location><page_2><loc_8><loc_9><loc_48><loc_13></location>Planetesimals starting on circular orbits have e free = e forced so that their eccentricity oscillates with amplitude 2 e forced and period 2 π/ ( A + ˙ /pi1 d ).</text>
<section_header_level_1><location><page_2><loc_66><loc_91><loc_78><loc_92></location>2.1. Disk model.</section_header_level_1>
<text><location><page_2><loc_52><loc_83><loc_92><loc_90></location>We model the disk as a constant ˙ M disk extending out to the outer truncation radius r t . Numerical simulations of accretion disks in binaries suggest that r t ∼ (0 . 2 -0 . 4) a b (Zhou et al. 2012), depending on e b and µ . In our study we will commonly take r t = 0 . 25 a b .</text>
<text><location><page_2><loc_52><loc_76><loc_92><loc_83></location>Constant ˙ M assumption is a necessary simplification, which ignores the details of the disk structure at r ∼ r t . Assuming viscosity ν in the disk to be well described by the radius-independent effective α -parameter (Shakura & Sunyaev 1973), one can write</text>
<formula><location><page_2><loc_64><loc_72><loc_92><loc_75></location>Σ( r ) = ˙ M 3 πν = Ω ˙ M 3 παc 2 s . (8)</formula>
<text><location><page_2><loc_52><loc_68><loc_92><loc_71></location>From this it is obvious that if the disk temperature scales as T ∝ r -q then the surface density behaves as</text>
<formula><location><page_2><loc_61><loc_63><loc_92><loc_67></location>Σ( r ) = Σ 0 ( r 0 r ) p , p = 3 2 -q, (9)</formula>
<text><location><page_2><loc_52><loc_62><loc_87><loc_64></location>where r 0 is some fiducial radius and Σ 0 = Σ( r 0 ).</text>
<text><location><page_2><loc_52><loc_50><loc_92><loc_62></location>Models of protoplanetary disks typically find q to be close to 1 / 2, so that p ≈ 1. In particular, the passive disk model of Chiang & Goldreich (1997) has q = 3 / 7, so that p -1 = 1 / 14. Outer parts of a disk in a binary are additionally heated by the radiation of the companion and tidal dissipation, so that q may be lower than 3 / 7 even for a passive disk. For simplicity, in our calculations we will assume p = 1, which corresponds to a classical Mestel disk (Mestel 1963) if r t →∞ .</text>
<text><location><page_2><loc_52><loc_46><loc_92><loc_50></location>Assuming that the disk has power law profile (9) with p = 1 all the way to r t we can express its surface density via the total disk mass M d enclosed within r t as</text>
<formula><location><page_2><loc_54><loc_42><loc_92><loc_45></location>Σ( r ) ≈ M d 2 πr t r -1 ≈ 2800 g cm -2 M d 10 -2 M /circledot r -1 t, 5 r -1 1 , (10)</formula>
<text><location><page_2><loc_52><loc_36><loc_92><loc_41></location>where r t, 5 ≡ r t / (5AU), and r 1 ≡ r/ (1AU). Interestingly, gas surface density at 1 AU in such a disk with M d = 0 . 01 M /circledot is not very different from that in a Minimum Mass Solar Nebula (MMSN; Hayashi 1981).</text>
<section_header_level_1><location><page_2><loc_61><loc_33><loc_83><loc_34></location>2.2. Precession due to the disk.</section_header_level_1>
<text><location><page_2><loc_52><loc_28><loc_92><loc_32></location>Adisk with the density profile (9) with p = 1 extending to infinity is known to have constant circular velocity (Mestel 1963)</text>
<formula><location><page_2><loc_59><loc_23><loc_92><loc_27></location>v c = ( r ∂U d ∂r ) 1 / 2 = (2 πG Σ 0 r 0 ) 1 / 2 . (11)</formula>
<text><location><page_2><loc_52><loc_13><loc_92><loc_23></location>Expressing ∂U d /∂r from this relation and plugging it in equation (4) we find ˙ /pi1 d = -πG Σ( r ) / ( nr ), where from now on we use r instead of a . Even though the circumprimary disk in our problem is truncated at r t this expression should still be able to give us a reasonable estimate of the precession rate ˙ /pi1 d due to the disk potential for r /lessorsimilar r t . Using equation (10) we find</text>
<formula><location><page_2><loc_61><loc_9><loc_92><loc_12></location>˙ /pi1 d ≈ -GM d nr t r -2 = -n M d M p r r t . (12)</formula>
<text><location><page_2><loc_52><loc_5><loc_92><loc_8></location>Note that ˙ /pi1 d varies rather weakly with r , as r -1 / 2 , which is consistent with Batygin et al. (2011).</text>
<section_header_level_1><location><page_3><loc_17><loc_91><loc_40><loc_92></location>2.3. Planetesimal eccentricities.</section_header_level_1>
<text><location><page_3><loc_8><loc_87><loc_48><loc_90></location>To assess the role of disk-driven precession on secular evolution of planetesimals we evaluate</text>
<formula><location><page_3><loc_14><loc_84><loc_48><loc_87></location>| ˙ /pi1 d | A ≈ 4 3 M d M s a 3 b r t r 2 ≈ 20 M d /M s 10 -2 a 3 b, 20 r t, 5 r -2 1 , (13)</formula>
<text><location><page_3><loc_8><loc_76><loc_48><loc_83></location>where a b, 20 ≡ a b / (20AU). In making this estimate we neglected the term quadratic in e b in equation (2). It is obvious that dynamics of planetesimals at several AU is strongly affected by the disk-driven precession. Indeed, | ˙ /pi1 d | exceeds A for</text>
<formula><location><page_3><loc_15><loc_72><loc_48><loc_76></location>r /lessorsimilar r cr ≈ 4 . 6AU ( M d /M s 10 -2 a 3 b, 20 r t, 5 ) 1 / 2 , (14)</formula>
<text><location><page_3><loc_8><loc_63><loc_48><loc_71></location>i.e. over essentially the whole assumed extent of the disk even for the disk mass as small as ∼ 10 -2 M /circledot . Thus, if we are interested in planet formation at 2 -3 AU we can neglect planetesimal precession due to the secondary compared to the disk-driven precession, i.e. neglect A compared to ˙ /pi1 d in equation (7) and other formulae.</text>
<text><location><page_3><loc_8><loc_60><loc_48><loc_63></location>Equation (7) then predicts that the amplitude of eccentricity oscillations is</text>
<formula><location><page_3><loc_15><loc_56><loc_48><loc_60></location>e disk ( r ) = 2 B | ˙ /pi1 d | ≈ 15 8 e b M s M d r 3 r t a 4 b (15)</formula>
<formula><location><page_3><loc_20><loc_53><loc_48><loc_56></location>≈ 3 × 10 -3 e b 0 . 5 0 . 01 M d /M s r t, 5 a 4 b, 20 r 3 1 , (16)</formula>
<text><location><page_3><loc_8><loc_50><loc_48><loc_53></location>where we again neglected e 2 b term in equation (3). This is to be compared with</text>
<formula><location><page_3><loc_13><loc_46><loc_48><loc_49></location>e n / disk ( r ) = 5 2 r a b e b ≈ 6 . 3 × 10 -2 e b 0 . 5 r 1 a b, 20 , (17)</formula>
<text><location><page_3><loc_8><loc_38><loc_48><loc_46></location>which one finds neglecting disk-driven precession, i.e. dropping ˙ /pi1 d in equation (7). It is obvious that neglecting disk-driven precession leads to an overestimate of the planetesimal eccentricity at ∼ AU separations by more than an order of magnitude. This has important consequences for planetesimal growth as we discuss further.</text>
<section_header_level_1><location><page_3><loc_23><loc_36><loc_34><loc_37></location>2.4. Gas drag.</section_header_level_1>
<text><location><page_3><loc_8><loc_21><loc_48><loc_35></location>Equation (15) accounts for the presence of the disk only through the precession caused by its gravity. However, for small planetesimals the effect of gas drag is also important. Assuming quadratic drag force in the form F ≈ -v v ρ g / ( ρd ) (here d and ρ are the object's radius and bulk density, ρ g ≈ Σ /h is the gas density and h is the disk scale height) we account for its effect on planetesimal dynamics by adding terms -D { h, k } ( h 2 + k 2 ) 1 / 2 to the first and second equations (5), respectively (Marzari & Scholl 2000). Here</text>
<formula><location><page_3><loc_21><loc_17><loc_48><loc_20></location>D = n ρ g r ρd = n Σ ρd r h . (18)</formula>
<text><location><page_3><loc_8><loc_9><loc_48><loc_17></location>For small planetesimal sizes (to be specified later by equation (20)), in the gas drag-dominated regime, the drag force balances eccentricity excitation due to the secondary, i.e. the B term in the first equation (5). This results in the following estimate for the gas drag-mediated planetesimal eccentricity:</text>
<formula><location><page_3><loc_12><loc_4><loc_48><loc_8></location>e gas ≈ ( B D ) 1 / 2 = ( e b M s M p h r ρd Σ ) 1 / 2 ( r a b ) 2 . (19)</formula>
<text><location><page_3><loc_52><loc_87><loc_92><loc_92></location>This expression agrees with Paardekooper et al. (2008) and predicts that e gas ∝ d 1 / 2 . As a result, for small bodies one finds e gas < e disk .</text>
<text><location><page_3><loc_52><loc_82><loc_92><loc_87></location>The transition between the drag-dominated behavior (19) and the drag-free eccentricity scaling (15) occurs at the planetesimal size d gas where these two equations yield the same eccentricity:</text>
<formula><location><page_3><loc_58><loc_78><loc_92><loc_81></location>d gas ≈ 4 n B r h Σ ρ e 2 forced = 15 8 π e b r h M s M d M p r t r ρa 4 b (20)</formula>
<formula><location><page_3><loc_61><loc_75><loc_92><loc_78></location>≈ 1 km e b 0 . 5 r/h 30 0 . 01 M d /M s M p, 1 r t, 5 r 1 ρ 3 a 4 b, 20 , (21)</formula>
<text><location><page_3><loc_52><loc_71><loc_92><loc_74></location>where ρ 3 ≡ ρ/ (3 g cm -3 ), M p, 1 ≡ M p /M /circledot and we have used equation (10).</text>
<text><location><page_3><loc_52><loc_57><loc_92><loc_71></location>Planetesimal eccentricity behaves according to formula (19) for d /lessorsimilar d gas , and switches to drag-free regime (15) for d /greaterorsimilar d gas , see Figure 1. The dependence of d gas on gas disk density and mass d gas ∝ M -1 d - is somewhat counter-intuitive, since higher gas density results in stronger drag, making it more important for larger bodies. However, the gas-free planetesimal eccentricity (15) is itself a function of M d and decreases faster with increasing M d than does e gas , explaining the nontrivial d gas ( M d ) dependence.</text>
<section_header_level_1><location><page_3><loc_58><loc_55><loc_86><loc_56></location>3. implications for planet formation.</section_header_level_1>
<text><location><page_3><loc_52><loc_43><loc_92><loc_55></location>Planetesimals grow in mutual collisions as long as their encounter velocity v coll (measured at infinity) is such that collisions do not result in the net loss of mass. The conditions for this depend, in particular, on planetesimal size and on whether planetesimals are strength- or gravity-dominated. Using results of Leinhardt & Stewart (2012) for collisions of equal mass (the most disruptive) strengthless bodies we roughly estimate the condition for planetesimal growth to be</text>
<formula><location><page_3><loc_67><loc_41><loc_92><loc_42></location>v coll /lessorsimilar 2 v esc , (22)</formula>
<text><location><page_3><loc_52><loc_37><loc_92><loc_40></location>where the escape speed from the surface of an object of radius d and bulk density ρ is</text>
<formula><location><page_3><loc_57><loc_33><loc_92><loc_37></location>v esc = ( 8 π 3 Gρ ) 1 / 2 d ≈ 1 . 3 m s -1 ρ 1 / 2 3 d 1 (23)</formula>
<text><location><page_3><loc_52><loc_26><loc_92><loc_33></location>(here d 1 ≡ d/ (1km)). It becomes harder to break planetesimals when they are small enough for their internal strength to dominate over the gravitational energy, which is expected to happen for d /lessorsimilar d s ∼ 10 km (Holsapple 1994).</text>
<text><location><page_3><loc_52><loc_22><loc_92><loc_26></location>Planetesimal collisions occur at velocity of order v coll ( r ) ≈ e disk v K , where v K = nr is the Keplerian speed. Using expression (15) we find</text>
<formula><location><page_3><loc_56><loc_17><loc_92><loc_21></location>v coll ( r ) ≈ 90 m s -1 e b 0 . 5 0 . 01 M d /M s M 1 / 2 p, 1 r t, 5 a 4 b, 20 r 5 / 2 1 . (24)</formula>
<text><location><page_3><loc_52><loc_13><loc_92><loc_17></location>Plugging equations (23) and (24) into the condition (22) we find that erosion in equal-mass planetesimal collisions is avoided for bodies with d /greaterorsimilar d coll , where</text>
<formula><location><page_3><loc_55><loc_8><loc_92><loc_12></location>d coll ≈ 35 km e b 0 . 5 0 . 01 M d /M s ( M p, 1 ρ 3 ) 1 / 2 r t, 5 a 4 b, 20 r 5 / 2 1 . (25)</formula>
<text><location><page_3><loc_52><loc_5><loc_92><loc_8></location>Thus, for the fiducial binary parameters adopted here and for M d ∼ 10 -2 M /circledot only planetesimals larger than</text>
<text><location><page_4><loc_8><loc_87><loc_48><loc_92></location>≈ 35 km would be able to grow at 1 AU. At 2 AU the semi-major axis of γ Cephei Ab - only bodies larger than 200 km in radius would be able to survive in equalmass collisions.</text>
<text><location><page_4><loc_8><loc_80><loc_48><loc_86></location>However, in the absence of a disk the problem is much worse: evaluating collisional velocity as v coll = e n / disk v K using equation (17) and applying condition (22) one finds than in the absence of disk-induced precession only planetesimals larger than</text>
<formula><location><page_4><loc_13><loc_75><loc_48><loc_79></location>d n / disk coll ≈ 700 km e b 0 . 5 ( M p, 1 ρ 3 ) 1 / 2 a -1 b, 20 r 1 / 2 1 (26)</formula>
<text><location><page_4><loc_8><loc_67><loc_48><loc_74></location>are able to survive in equal-mass collisions. Clearly, collisional barrier appears far more severe if one disregards the effects of the disk on the secular evolution of planetesimals. We compare the behavior of d gas , d coll , and d n / disk coll as a function of r in Figure 1.</text>
<text><location><page_4><loc_8><loc_55><loc_48><loc_67></location>We also point out that d coll is very sensitive to the binary semi-major axis a b , unlike d n / disk coll , see equations (25) and (26): increasing a b from 20 AU to 30 AU reduces d coll by a factor of 5. The size of the region where disk-driven precession dominates secular evolution also expands rapidly with increasing a b , see equation (14). To summarize, properly accounting for the disk gravity considerably alleviates the collisional barrier in binaries, certainly for r /lessorsimilar 1 AU.</text>
<section_header_level_1><location><page_4><loc_8><loc_52><loc_48><loc_53></location>4. planetesimal accretion is possible in massive disks</section_header_level_1>
<text><location><page_4><loc_8><loc_48><loc_48><loc_52></location>We now propose a solution to the problem of planetesimal accumulation in binaries, raised in § 1. We argue that if</text>
<unordered_list>
<list_item><location><page_4><loc_11><loc_45><loc_34><loc_47></location>· disk is massive , M d ∼ 0 . 1 M /circledot ,</list_item>
<list_item><location><page_4><loc_11><loc_41><loc_48><loc_44></location>· planetesimals are strength-dominated below ∼ 10 km,</list_item>
</unordered_list>
<text><location><page_4><loc_8><loc_36><loc_48><loc_40></location>then the fragmentation barrier can be overcome even at separations of ≈ 2 AU, where planets in several binaries are found.</text>
<text><location><page_4><loc_8><loc_17><loc_48><loc_36></location>Equation (25) shows that higher M d results in smaller planetesimal size d coll , below which strengthless objects are destroyed or eroded in equal-mass collisions. Smaller planetesimals are (1) more resistive to collisional erosion because of their internal strength and (2) stronger affected by gas drag. When the latter dominates, planetesimal velocities are reduced and collisions are less destructive. However, increasing M d reduces not only d coll but also d gas in such a way that d coll /d gas stays constant. At 1 AU this ratio is about 30 so that independent of M d there is still a significant 'danger zone' between the planetesimal size d gas below which gas drag lowers v coll helping accretion and the radius d coll above which colliding strengthless bodies can grow, see Figure 1.</text>
<text><location><page_4><loc_8><loc_9><loc_48><loc_17></location>On the other hand, equation (26) predicts that d coll /lessorsimilar d s at r = 2 AU for M d /M s = 0 . 2, if internal strength dominates over the gravitational binding energy of the body with d s = 10 km making it harder to erode or destroy. This is a resolution of the collisional barrier problem in binaries that we favor in this work.</text>
<text><location><page_4><loc_8><loc_5><loc_48><loc_9></location>To avoid fragmentation barrier we thus require that d coll < d s . Using equation (25) we can rephrase this condition in the form of a lower limit on the disk mass</text>
<figure>
<location><page_4><loc_52><loc_62><loc_90><loc_91></location>
<caption>Fig. 1.Characteristic planetesimal sizes vs. radius for two disk masses M d : (a) 0 . 01 M /circledot and (b) 0 . 1 M /circledot . We display d coll ( solid , eq. [25]), d gas ( dot-dashed , eq. [20]), d n / disk coll ( short-dashed , eq. [26]), and planetesimal radius d s = 10 km below which we consider objects as strength-dominated ( long-dashed ). The two latter sizes do not depend on M d . Calculations are done for e b = 0 . 4, M s = 0 . 4 M /circledot , a b = 20 AU, M p = M /circledot (typical for small separation binaries, Chauvin et al. 2011), r t = 5 AU, and r/h = 30. Planetesimals in the shaded region ('danger zone') get destroyed in equal-mass collisions according to criterion (22) precluding planetary growth at corresponding separations. Accretion-friendly zone is to the left of the vertical dotted line in each plot; it is wider for higher M d and extends to ≈ 2 . 5 AU for M d = 0 . 1 M /circledot .</caption>
</figure>
<text><location><page_4><loc_52><loc_42><loc_83><loc_43></location>at a given separation a pl from the primary:</text>
<formula><location><page_4><loc_56><loc_37><loc_92><loc_41></location>M d M s /greaterorsimilar 0 . 035 e b 0 . 5 ( M p, 1 ρ 3 ) 1 / 2 r t /a b 0 . 25 a 5 / 2 pl a -3 b, 20 . (27)</formula>
<text><location><page_4><loc_52><loc_30><loc_92><loc_37></location>In Figure 2 we illustrate this constraint as a function of the binary semi-major axis, for different values of a pl . It is clear that in very small separation binaries with a b = 10 AU growing planets even at 1 AU requires a massive disk, M p ≈ 0 . 2 M s .</text>
<text><location><page_4><loc_52><loc_21><loc_92><loc_30></location>External companions in giant planet-hosting binaries typically have mass M s ≈ 0 . 4 M /circledot (Chauvin et al. 2011), meaning that our scenario of planet formation at 2 AU needs M d ≈ 0 . 1 M /circledot . Such disk mass may seem high but it is also the case that planet-hosting binary systems with a b ≈ 20 AU that we consider here contain more mass in total than the descendants of the typical T Tauri stars.</text>
<text><location><page_4><loc_52><loc_15><loc_92><loc_20></location>One might worry that such massive disks would be prone to gravitational instability (GI). With the density profile (10) we estimate the Toomre Q ≡ nc s / ( πG Σ) ( c s is the sound speed) as</text>
<formula><location><page_4><loc_56><loc_11><loc_92><loc_14></location>Q ≈ 2 M p M d h r r t r ≈ 3 ( 0 . 1 M d /M p )( 30 r/h ) r t, 5 r 1 . (28)</formula>
<text><location><page_4><loc_52><loc_5><loc_92><loc_10></location>Thus, even for M d = 0 . 1 M p ≈ 0 . 1 M /circledot the disk is at most marginally unstable to GI at 2 AU. However, even if it were unstable, the surface density and optical depth at this distance would be so high that the cooling time</text>
<figure>
<location><page_5><loc_8><loc_61><loc_46><loc_91></location>
<caption>Fig. 2.Plot of a b -M d /M s phase space illustrating conditions under which planets can form in binaries, assuming d s = 10 km. Different curves show the relation (27) for different values of the planetary semi-major axis a pl , interior to which planet formation is possible: a pl = 1 AU ( solid ), a pl = 2 AU ( dotted ), a pl = 3 AU ( dashed ). Calculation assumes e b = 0 . 4, fixed r t /a b = 0 . 25, a b = 20 AU, and M p = M /circledot . At a given a pl fragmentation barrier is avoided and planet formation proceeds smoothly through the planetesimal stage to the right (and above) of the corresponding line.</caption>
</figure>
<text><location><page_5><loc_8><loc_40><loc_48><loc_47></location>would far exceed the local dynamical time, making planet formation by direct disk fragmentation impossible (Gammie 2001; Rafikov 2005). Instead, the disk would slowly evolve under the action of gravitoturbulence (Rafikov 2009).</text>
<text><location><page_5><loc_8><loc_24><loc_48><loc_40></location>On the other hand, high M d simplifies planet formation in other ways. In particular, planets in these systems are quite massive (Chauvin et al. 2011) and larger M d provides mass reservoir for their assembly. Higher surface density of the protoplanetary disk also means larger isolation mass (Lissauer 1993) possibly making it high enough at 2 AU to trigger core accretion without the need to go through the long-lasting stage of giant impacts (Chambers 2004). Higher Σ likely implies larger dead zone (Gammie 1996) in the disk, providing quiet conditions for planetesimal formation and growth, and resulting in smaller viscosity, which, possibly, means longer</text>
<text><location><page_5><loc_52><loc_89><loc_92><loc_92></location>disk lifetime. The timescale on which planets form also goes down as M d increases.</text>
<text><location><page_5><loc_52><loc_78><loc_92><loc_89></location>Another potential solution to the collisional barrier problem in binaries is the direct formation of large planetesimals by e.g. streaming and/or gravitational instabilities (Johansen et al. 2007; Th'ebault 2011). Large M d and small d coll are helpful for this mechanism as well since to overcome fragmentation barrier in a massive disk such instabilities would only need to produce bodies with sizes of tens of km, rather than ∼ 10 3 km dwarf planets.</text>
<section_header_level_1><location><page_5><loc_67><loc_75><loc_77><loc_76></location>5. discussion.</section_header_level_1>
<text><location><page_5><loc_52><loc_51><loc_92><loc_74></location>We now mention several additional factors that may strengthen or weaken our conclusions. First, our collisional growth condition (22) may be too stringent. Previously, using a more refined fragmentation criterion Th'ebault (2011) found that in HD 196885 ( M p = 1 . 3 M /circledot , a b = 21 AU , e b = 0 . 42) planetesimal growth is possible even in the absence of disk-driven precession at 2 . 6 AU as long as the planetesimal size exceeds 250 km. However, according to our formula (26) with the same assumptions (same system parameters and ˙ /pi1 d = 0), growth is possible only for d /greaterorsimilar 10 3 km. Thus, our fragmentation criterion likely overestimates planetesimal size above which objects grow efficiently, and, in fact, it might be easier to overcome the fragmentation barrier with the more realistic growth condition than our simple criterion (22). At a given distance this would lower the value of M d needed to overcome fragmentation barrier.</text>
<text><location><page_5><loc_52><loc_40><loc_92><loc_51></location>Second, even if planetesimals are collisionally weak their growth may still proceed mainly via unequal-mass collisions (which more frequently result in mergers) if the number of relatively massive objects is small (Th'ebault 2011). Outward migration of planets by scattering of planetesimals has also been invoked (Payne et al. 2009) to explain planets on AU-scale orbits in small separation binaries.</text>
<text><location><page_5><loc_52><loc_29><loc_92><loc_40></location>On the other hand, there are also factors complicating planetesimal growth. In particular, eccentricity of the gaseous disk induced by the companion may affect planetary growth at small sizes ( d /lessorsimilar d gas ). Also, gas drag-induced inspiral of planetesimals may deplete the disk of some solids. The relative importance of these factors for planet formation in binaries will be assessed in the future.</text>
<text><location><page_5><loc_52><loc_24><loc_92><loc_26></location>This work was supported by NSF via grant AST0908269.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Existence of planets is binaries with relatively small separations (around 20 AU), such as α Centauri or γ Cephei poses severe challenges to standard planet formation theories. The problem lies in the vigorous secular excitation of planetesimal eccentricities at separations of several AU, where some of the planets are found, by the massive, eccentric stellar companions. High relative velocities of planetesimals preclude their growth in mutual collisions for a wide range of sizes, from below 1 km up to several hundred km, resulting in fragmentation barrier to planet formation. Here we show that rapid apsidal precession of planetesimal orbits, caused by the gravity of the circumstellar protoplanetary disk, acts to strongly reduce eccentricity excitation, lowering planetesimal velocities by an order of magnitude or even more at 1 AU. By examining the details of planetesimal dynamics we demonstrate that this effect eliminates fragmentation barrier for in-situ growth of planetesimals as small as /lessorsimilar 10 km even at separations as wide as 2.6 AU (semi-major axis of the giant planet in HD 196885), provided that the circumstellar protoplanetary disk is relatively massive, ∼ 0 . 1 M /circledot . Subject headings: planets and satellites: formation - protoplanetary disks - planetary systems binaries: close",
"pages": [
1
]
},
{
"title": "PLANET FORMATION IN SMALL SEPARATION BINARIES: NOT SO EXCITED AFTER ALL",
"content": "Roman R. Rafikov 1 Draft version June 2, 2021",
"pages": [
1
]
},
{
"title": "1. introduction.",
"content": "About 20% of planets detected via stellar radial velocity variations reside in binaries (Desidera & Barbieri 2007). The majority of these systems are wide separation binaries, with semi-major axis a b /greaterorsimilar 30 AU. At the same time, four relatively small separation binaries with a b ≈ 20 AU (HD 196885, γ Cephei, Gl 86 and HD 41004; Chauvin et al. 2011) are also known to harbor giant planets with projected masses M pl sin i ≈ (1 . 6 -4) M J . In these systems the mass of the secondary star (we call 'secondary' the binary component other than the star orbited by the planet, which we denote as 'primary') M s is found to be close to 0 . 4 M /circledot and binary eccentricity e b is close to 0 . 4. Also, Dumusque et al. (2012) have recently announced an Earth-mass companion to α Centauri B, a member of the binary (or, possibly, a triple) with a b = 17 . 6 AU, e b = 0 . 52, and M s = 1 . 1 M /circledot . In this system planet orbits the star at ≈ 0 . 04 AU separation. The uniqueness of these systems lies in the fact that forming planets in them is known to provide extreme challenge to planet formation theories (Zhou et al. 2012). With the exception of α Cen and Gl 86, planets in these binaries reside in rather wide orbits, with planetary semimajor axes a pl ≈ 1 . 6 -2 . 6 AU. In-situ formation of these gas giants is expected to proceed through continuous agglomeration of planetesimals at these locations, starting from very small objects (easily /lessorsimilar 1 km). However, gravitational perturbations from the eccentric stellar companion inevitably result in rapid secular evolution (Heppenheimer 1978), driving planetesimal eccentricities far above the level at which bodies can avoid destruction in mutual collisions (Th'ebault et al. 2008). This problem, which is often called collisional or fragmentation barrier , is especially severe for small planetesimals, 1 -10 2 km in size, for which the ratio of binding to kinetic energy is small. It is also more pronounced far from the primary, where the secular forcing by the companion is strongest and planetesimal eccentricities are high. Marzari & Scholl (2000) suggested that a combination of secular forcing by the companion and gas drag acting on small (1 -10 km) planetesimals leads to apsidal alignment of their orbits, resulting in smaller relative velocities, and allowing colliding objects to grow. However, Th'ebault et al. (2006, 2008) demonstrated that the planetesimal size-dependence of apsidal alignment acts to break orbital phasing between objects of different sizes, resulting in high velocity collisions between them and reinforcing collisional barrier. Interestingly, most studies of planetesimal growth in small separation binaries have included the effect of the protoplanetary disk on planetesimal dynamics only via associated gas drag (Th'ebault et al. 2004, 2006, 2008, 2009; Paardekooper et al. 2008; Paardekooper & Leinhardt 2010), without accounting for the gravitational effect of the disk. Batygin et al. (2011) have considered disk gravity in the context of planet formation and evolution in systems with highly misaligned, distant (10 2 -10 3 AU) stellar companions, affected by the Lidov-Kozai effect (Lidov 1961; Kozai 1962). However, this effect is probably irrelevant for planetesimal dynamics in small separation (tens of AU) binaries, which are likely coplanar with circumstellar disks. In this Letter we show that apsidal precession of planetesimal orbits induced by disk gravity dominates secular evolution of planetesimals at separations of several AU. As a result, relative velocities at which bodies collide are reduced, sometimes by more than an order of magnitude. In massive disks this effect presents a natural solution of the fragmentation barrier issue for the in-situ formation of the giant planets in small separation binaries, such as γ Cephei.",
"pages": [
1
]
},
{
"title": "2. secular evolution.",
"content": "We consider planetesimal motion as Keplerian motion around the primary perturbed by the gravity of the companion, that moves on larger, eccentric orbit, and the disk. Mass of the primary is M p , and we define µ ≡ M s / ( M p + M s ). We assume eccentricity of the stellar binary e b to be small and planetesimal orbit to be coplanar with the binary. Planetesimals are immersed in a massive, axisymmetric gaseous disk, characterized by surface density Σ( r ) specified in § 22.1. Assuming e /lessmuch 1 the secular (averaged over the planetesimal and binary orbital motion) disturbing function for a planetesimal with semimajor axis a and eccentricity vector e = ( k, h ) = ( e cos /pi1, e sin /pi1 ) (with apsidal angle /pi1 counted from the binary apsidal line, which is assumed fixed 2 ) is (Murray & Dermott 1999) where and ∣ is the precession frequency of planetesimal orbit due to the disk potential U d . Here n b = [ G ( M p + M s ) /a 3 b ] 1 / 2 and n = ( GM p /a 3 ) 1 / 2 are the mean motions of the binary and planetesimal, respectively. The contribution to R proportional to ˙ /pi1 d arises from expansion of the disk potential along the eccentric planetesimal orbit and averaging over its mean longitude. Evolution equations for h and k are written using dh/dt = ( na 2 ) -1 ∂R/∂k , dk/dt = -( na 2 ) -1 ∂R/∂h as These equations agree with the work of Marzari & Scholl (2000) as long as ˙ /pi1 d = 0. We write down the solution for e ( t ) = e free ( t ) + e forced ( t ), where /pi1 0 is a constant, and Thus, free eccentricity vector e free rotates at a rate A + ˙ /pi1 d around the endpoint of the fixed forced eccentricity vector e forced . Note that setting ˙ /pi1 d = 0 we reproduce the solution obtained by Heppenheimer (1978). Planetesimals starting on circular orbits have e free = e forced so that their eccentricity oscillates with amplitude 2 e forced and period 2 π/ ( A + ˙ /pi1 d ).",
"pages": [
1,
2
]
},
{
"title": "2.1. Disk model.",
"content": "We model the disk as a constant ˙ M disk extending out to the outer truncation radius r t . Numerical simulations of accretion disks in binaries suggest that r t ∼ (0 . 2 -0 . 4) a b (Zhou et al. 2012), depending on e b and µ . In our study we will commonly take r t = 0 . 25 a b . Constant ˙ M assumption is a necessary simplification, which ignores the details of the disk structure at r ∼ r t . Assuming viscosity ν in the disk to be well described by the radius-independent effective α -parameter (Shakura & Sunyaev 1973), one can write From this it is obvious that if the disk temperature scales as T ∝ r -q then the surface density behaves as where r 0 is some fiducial radius and Σ 0 = Σ( r 0 ). Models of protoplanetary disks typically find q to be close to 1 / 2, so that p ≈ 1. In particular, the passive disk model of Chiang & Goldreich (1997) has q = 3 / 7, so that p -1 = 1 / 14. Outer parts of a disk in a binary are additionally heated by the radiation of the companion and tidal dissipation, so that q may be lower than 3 / 7 even for a passive disk. For simplicity, in our calculations we will assume p = 1, which corresponds to a classical Mestel disk (Mestel 1963) if r t →∞ . Assuming that the disk has power law profile (9) with p = 1 all the way to r t we can express its surface density via the total disk mass M d enclosed within r t as where r t, 5 ≡ r t / (5AU), and r 1 ≡ r/ (1AU). Interestingly, gas surface density at 1 AU in such a disk with M d = 0 . 01 M /circledot is not very different from that in a Minimum Mass Solar Nebula (MMSN; Hayashi 1981).",
"pages": [
2
]
},
{
"title": "2.2. Precession due to the disk.",
"content": "Adisk with the density profile (9) with p = 1 extending to infinity is known to have constant circular velocity (Mestel 1963) Expressing ∂U d /∂r from this relation and plugging it in equation (4) we find ˙ /pi1 d = -πG Σ( r ) / ( nr ), where from now on we use r instead of a . Even though the circumprimary disk in our problem is truncated at r t this expression should still be able to give us a reasonable estimate of the precession rate ˙ /pi1 d due to the disk potential for r /lessorsimilar r t . Using equation (10) we find Note that ˙ /pi1 d varies rather weakly with r , as r -1 / 2 , which is consistent with Batygin et al. (2011).",
"pages": [
2
]
},
{
"title": "2.3. Planetesimal eccentricities.",
"content": "To assess the role of disk-driven precession on secular evolution of planetesimals we evaluate where a b, 20 ≡ a b / (20AU). In making this estimate we neglected the term quadratic in e b in equation (2). It is obvious that dynamics of planetesimals at several AU is strongly affected by the disk-driven precession. Indeed, | ˙ /pi1 d | exceeds A for i.e. over essentially the whole assumed extent of the disk even for the disk mass as small as ∼ 10 -2 M /circledot . Thus, if we are interested in planet formation at 2 -3 AU we can neglect planetesimal precession due to the secondary compared to the disk-driven precession, i.e. neglect A compared to ˙ /pi1 d in equation (7) and other formulae. Equation (7) then predicts that the amplitude of eccentricity oscillations is where we again neglected e 2 b term in equation (3). This is to be compared with which one finds neglecting disk-driven precession, i.e. dropping ˙ /pi1 d in equation (7). It is obvious that neglecting disk-driven precession leads to an overestimate of the planetesimal eccentricity at ∼ AU separations by more than an order of magnitude. This has important consequences for planetesimal growth as we discuss further.",
"pages": [
3
]
},
{
"title": "2.4. Gas drag.",
"content": "Equation (15) accounts for the presence of the disk only through the precession caused by its gravity. However, for small planetesimals the effect of gas drag is also important. Assuming quadratic drag force in the form F ≈ -v v ρ g / ( ρd ) (here d and ρ are the object's radius and bulk density, ρ g ≈ Σ /h is the gas density and h is the disk scale height) we account for its effect on planetesimal dynamics by adding terms -D { h, k } ( h 2 + k 2 ) 1 / 2 to the first and second equations (5), respectively (Marzari & Scholl 2000). Here For small planetesimal sizes (to be specified later by equation (20)), in the gas drag-dominated regime, the drag force balances eccentricity excitation due to the secondary, i.e. the B term in the first equation (5). This results in the following estimate for the gas drag-mediated planetesimal eccentricity: This expression agrees with Paardekooper et al. (2008) and predicts that e gas ∝ d 1 / 2 . As a result, for small bodies one finds e gas < e disk . The transition between the drag-dominated behavior (19) and the drag-free eccentricity scaling (15) occurs at the planetesimal size d gas where these two equations yield the same eccentricity: where ρ 3 ≡ ρ/ (3 g cm -3 ), M p, 1 ≡ M p /M /circledot and we have used equation (10). Planetesimal eccentricity behaves according to formula (19) for d /lessorsimilar d gas , and switches to drag-free regime (15) for d /greaterorsimilar d gas , see Figure 1. The dependence of d gas on gas disk density and mass d gas ∝ M -1 d - is somewhat counter-intuitive, since higher gas density results in stronger drag, making it more important for larger bodies. However, the gas-free planetesimal eccentricity (15) is itself a function of M d and decreases faster with increasing M d than does e gas , explaining the nontrivial d gas ( M d ) dependence.",
"pages": [
3
]
},
{
"title": "3. implications for planet formation.",
"content": "Planetesimals grow in mutual collisions as long as their encounter velocity v coll (measured at infinity) is such that collisions do not result in the net loss of mass. The conditions for this depend, in particular, on planetesimal size and on whether planetesimals are strength- or gravity-dominated. Using results of Leinhardt & Stewart (2012) for collisions of equal mass (the most disruptive) strengthless bodies we roughly estimate the condition for planetesimal growth to be where the escape speed from the surface of an object of radius d and bulk density ρ is (here d 1 ≡ d/ (1km)). It becomes harder to break planetesimals when they are small enough for their internal strength to dominate over the gravitational energy, which is expected to happen for d /lessorsimilar d s ∼ 10 km (Holsapple 1994). Planetesimal collisions occur at velocity of order v coll ( r ) ≈ e disk v K , where v K = nr is the Keplerian speed. Using expression (15) we find Plugging equations (23) and (24) into the condition (22) we find that erosion in equal-mass planetesimal collisions is avoided for bodies with d /greaterorsimilar d coll , where Thus, for the fiducial binary parameters adopted here and for M d ∼ 10 -2 M /circledot only planetesimals larger than ≈ 35 km would be able to grow at 1 AU. At 2 AU the semi-major axis of γ Cephei Ab - only bodies larger than 200 km in radius would be able to survive in equalmass collisions. However, in the absence of a disk the problem is much worse: evaluating collisional velocity as v coll = e n / disk v K using equation (17) and applying condition (22) one finds than in the absence of disk-induced precession only planetesimals larger than are able to survive in equal-mass collisions. Clearly, collisional barrier appears far more severe if one disregards the effects of the disk on the secular evolution of planetesimals. We compare the behavior of d gas , d coll , and d n / disk coll as a function of r in Figure 1. We also point out that d coll is very sensitive to the binary semi-major axis a b , unlike d n / disk coll , see equations (25) and (26): increasing a b from 20 AU to 30 AU reduces d coll by a factor of 5. The size of the region where disk-driven precession dominates secular evolution also expands rapidly with increasing a b , see equation (14). To summarize, properly accounting for the disk gravity considerably alleviates the collisional barrier in binaries, certainly for r /lessorsimilar 1 AU.",
"pages": [
3,
4
]
},
{
"title": "4. planetesimal accretion is possible in massive disks",
"content": "We now propose a solution to the problem of planetesimal accumulation in binaries, raised in § 1. We argue that if then the fragmentation barrier can be overcome even at separations of ≈ 2 AU, where planets in several binaries are found. Equation (25) shows that higher M d results in smaller planetesimal size d coll , below which strengthless objects are destroyed or eroded in equal-mass collisions. Smaller planetesimals are (1) more resistive to collisional erosion because of their internal strength and (2) stronger affected by gas drag. When the latter dominates, planetesimal velocities are reduced and collisions are less destructive. However, increasing M d reduces not only d coll but also d gas in such a way that d coll /d gas stays constant. At 1 AU this ratio is about 30 so that independent of M d there is still a significant 'danger zone' between the planetesimal size d gas below which gas drag lowers v coll helping accretion and the radius d coll above which colliding strengthless bodies can grow, see Figure 1. On the other hand, equation (26) predicts that d coll /lessorsimilar d s at r = 2 AU for M d /M s = 0 . 2, if internal strength dominates over the gravitational binding energy of the body with d s = 10 km making it harder to erode or destroy. This is a resolution of the collisional barrier problem in binaries that we favor in this work. To avoid fragmentation barrier we thus require that d coll < d s . Using equation (25) we can rephrase this condition in the form of a lower limit on the disk mass at a given separation a pl from the primary: In Figure 2 we illustrate this constraint as a function of the binary semi-major axis, for different values of a pl . It is clear that in very small separation binaries with a b = 10 AU growing planets even at 1 AU requires a massive disk, M p ≈ 0 . 2 M s . External companions in giant planet-hosting binaries typically have mass M s ≈ 0 . 4 M /circledot (Chauvin et al. 2011), meaning that our scenario of planet formation at 2 AU needs M d ≈ 0 . 1 M /circledot . Such disk mass may seem high but it is also the case that planet-hosting binary systems with a b ≈ 20 AU that we consider here contain more mass in total than the descendants of the typical T Tauri stars. One might worry that such massive disks would be prone to gravitational instability (GI). With the density profile (10) we estimate the Toomre Q ≡ nc s / ( πG Σ) ( c s is the sound speed) as Thus, even for M d = 0 . 1 M p ≈ 0 . 1 M /circledot the disk is at most marginally unstable to GI at 2 AU. However, even if it were unstable, the surface density and optical depth at this distance would be so high that the cooling time would far exceed the local dynamical time, making planet formation by direct disk fragmentation impossible (Gammie 2001; Rafikov 2005). Instead, the disk would slowly evolve under the action of gravitoturbulence (Rafikov 2009). On the other hand, high M d simplifies planet formation in other ways. In particular, planets in these systems are quite massive (Chauvin et al. 2011) and larger M d provides mass reservoir for their assembly. Higher surface density of the protoplanetary disk also means larger isolation mass (Lissauer 1993) possibly making it high enough at 2 AU to trigger core accretion without the need to go through the long-lasting stage of giant impacts (Chambers 2004). Higher Σ likely implies larger dead zone (Gammie 1996) in the disk, providing quiet conditions for planetesimal formation and growth, and resulting in smaller viscosity, which, possibly, means longer disk lifetime. The timescale on which planets form also goes down as M d increases. Another potential solution to the collisional barrier problem in binaries is the direct formation of large planetesimals by e.g. streaming and/or gravitational instabilities (Johansen et al. 2007; Th'ebault 2011). Large M d and small d coll are helpful for this mechanism as well since to overcome fragmentation barrier in a massive disk such instabilities would only need to produce bodies with sizes of tens of km, rather than ∼ 10 3 km dwarf planets.",
"pages": [
4,
5
]
},
{
"title": "5. discussion.",
"content": "We now mention several additional factors that may strengthen or weaken our conclusions. First, our collisional growth condition (22) may be too stringent. Previously, using a more refined fragmentation criterion Th'ebault (2011) found that in HD 196885 ( M p = 1 . 3 M /circledot , a b = 21 AU , e b = 0 . 42) planetesimal growth is possible even in the absence of disk-driven precession at 2 . 6 AU as long as the planetesimal size exceeds 250 km. However, according to our formula (26) with the same assumptions (same system parameters and ˙ /pi1 d = 0), growth is possible only for d /greaterorsimilar 10 3 km. Thus, our fragmentation criterion likely overestimates planetesimal size above which objects grow efficiently, and, in fact, it might be easier to overcome the fragmentation barrier with the more realistic growth condition than our simple criterion (22). At a given distance this would lower the value of M d needed to overcome fragmentation barrier. Second, even if planetesimals are collisionally weak their growth may still proceed mainly via unequal-mass collisions (which more frequently result in mergers) if the number of relatively massive objects is small (Th'ebault 2011). Outward migration of planets by scattering of planetesimals has also been invoked (Payne et al. 2009) to explain planets on AU-scale orbits in small separation binaries. On the other hand, there are also factors complicating planetesimal growth. In particular, eccentricity of the gaseous disk induced by the companion may affect planetary growth at small sizes ( d /lessorsimilar d gas ). Also, gas drag-induced inspiral of planetesimals may deplete the disk of some solids. The relative importance of these factors for planet formation in binaries will be assessed in the future. This work was supported by NSF via grant AST0908269.",
"pages": [
5
]
},
{
"title": "REFERENCES",
"content": "Batygin, K., Morbidelli, A., & Tsiganis, K. 2011, A&A, 533, id. A7 Chambers, J. E. 2004, Earth Planet. Sci. Lett., 223, 241 Chauvin, G., Beust, H., Lagrange, A.-M., & Eggenberger, A. 2011, A&A, 528, id.A8 Chiang, E. I. & Goldreich, P. 1997, ApJ, 490, 368 Desidera, S. & Barbieri, M. 2007, A&A, 462, 345 Dumusque, X., Pepe, F., Lovis, C., et al. 2012, Nature, 491, 207 Gammie, C. F. 1996, ApJ, 457, 355 Gammie, C. F. 2001, ApJ, 553, 174 Hayashi, C. 1981, Prog. Theor. Phys. Suppl., 70, 35 Heppenheimer, T. A. 1978, A&A, 65, 421 Holsapple, K. A. 1994, Planet. Space Sci., 42, 1067 Johansen, A., Oishi, J. S., Mac Low, M.-M., Klahr, H., Henning, T., & Youdin, A. 2007, Nature, 448, 1022 Kozai, Y. 1962, ApJ, 67, 591 Lissauer, J. J. 1993, ARA&A, 31, 129 Payne, M. J., Wyatt, M. C., & Th'ebault, P. 2009, MNRAS, 400, 1936 Rafikov, R. R. 2005, ApJ, 621, L69 Rafikov, R. R. 2009, ApJ, 704, 281 Th'ebault, P. 2011, Cel. Mech. Dyn. Astr., 111, 29 Th'ebault, P., Marzari, F., Scholl, H., Turrini, D., & Barbieri, M. 2004, A&A, 427, 1097 Th'ebault, P., Marzari, F., & Scholl, H. 2006, Icarus, 183, 19 Th'ebault, P., Marzari, F., & Scholl, H. 2008, MNRAS, 388, 1528 Th'ebault, P., Marzari, F., & Scholl, H. 2009, MNRAS, 393, L21 Zhou, J.-L., Xie, J.-W., Liu, H.-G., Zhang, H., & Sun, Y.-S. 2012, RA&A, 12, 1081",
"pages": [
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}
]
2013ApJ...766....8A
https://arxiv.org/pdf/1302.1403.pdf
<document>
<section_header_level_1><location><page_1><loc_26><loc_85><loc_75><loc_87></location>PROTOPLANETARY DISK STRUCTURE WITH GRAIN EVOLUTION: THE ANDES MODEL</section_header_level_1>
<text><location><page_1><loc_9><loc_81><loc_91><loc_84></location>V. AKIMKIN 1 , S. ZHUKOVSKA 2 , D. WIEBE 1 , D. SEMENOV 2 , YA. PAVLYUCHENKOV 1 , A. VASYUNIN 3 , T. BIRNSTIEL 4 , TH. HENNING 2 1 Institute of Astronomy of the RAS, Pyatnitskaya str. 48, Moscow, Russia</text>
<text><location><page_1><loc_28><loc_80><loc_73><loc_81></location>2 Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany</text>
<text><location><page_1><loc_34><loc_79><loc_67><loc_80></location>3 Department of Chemistry, the University of Virginia, USA and</text>
<text><location><page_1><loc_12><loc_77><loc_89><loc_79></location>4 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA Excellence Cluster Universe, Technische Universität München, Boltzmannstr. 2, 85748 Garching, Germany</text>
<text><location><page_1><loc_38><loc_76><loc_62><loc_76></location>Accepted for publication in ApJ, Feb 1, 2013</text>
<section_header_level_1><location><page_1><loc_46><loc_73><loc_54><loc_74></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_53><loc_86><loc_72></location>We present a self-consistent model of a protoplanetary disk: 'ANDES' ('AccretioN disk with Dust Evolution and Sedimentation'). ANDES is based on a flexible and extendable modular structure that includes 1) a 1+1D frequency-dependent continuum radiative transfer module, 2) a module to calculate the chemical evolution using an extended gas-grain network with UV/X-ray-driven processes surface reactions, 3) a module to calculate the gas thermal energy balance, and 4) a 1+1D module that simulates dust grain evolution. For the first time, grain evolution and time-dependent molecular chemistry are included in a protoplanetary disk model. We find that grain growth and sedimentation of large grains to the disk midplane lead to a dust-depleted atmosphere. Consequently, dust and gas temperatures become higher in the inner disk ( R /lessorsimilar 50 AU) and lower in the outer disk ( R /greaterorsimilar 50 AU), in comparison with the disk model with pristine dust. The response of disk chemical structure to the dust growth and sedimentation is twofold. First, due to higher transparency a partly UV-shielded molecular layer is shifted closer to the dense midplane. Second, the presence of big grains in the disk midplane delays the freeze-out of volatile gas-phase species such as CO there, while in adjacent upper layers the depletion is still effective. Molecular concentrations and thus column densities of many species are enhanced in the disk model with dust evolution, e.g., CO2, NH2CN, HNO, H2O, HCOOH, HCN, CO. We also show that time-dependent chemistry is important for a proper description of gas thermal balance.</text>
<text><location><page_1><loc_22><loc_51><loc_86><loc_52></location>accretion, accretion disks - circumstellar matter - stars: formation - stars: pre-main-sequence,</text>
<text><location><page_1><loc_14><loc_50><loc_31><loc_52></location>Keywords: astrochemistry</text>
<section_header_level_1><location><page_1><loc_21><loc_46><loc_35><loc_47></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_26><loc_49><loc_45></location>The planet formation and, in particular, the origin of the Solar System are among the most fascinating astrophysical problems that are far from being fully understood. The quickly growing number of detected exoplanets hints to ubiquitous planet formation in our Galaxy. Space-born facilities (e.g., Hubble, Spitzer, Herschel ) as well as ground-based observatories (e.g., VLT, Keck, Subaru, PdBI, IRAM 30-m, SMA, early ALMA) provide unique information on the appearance, structure, chemical composition, and evolution of nearby protoplanetary disks (e.g., Dutrey et al. 1997; Fukagawa et al. 2004; Andrews & Williams 2005; Hernández et al. 2007; Natta et al. 2007; Semenov et al. 2010; Sturm et al. 2010; Muto et al. 2012). Relatively compact sizes of ∼ 100 -1000 AU and low masses of ∼ 0 . 01 M /circledot make disks a challenging target for observational studies.</text>
<text><location><page_1><loc_8><loc_10><loc_48><loc_25></location>Another obstacle to investigate the formation of planets is an enormous range of physical conditions encountered in a protoplanetary disk and a wide variety of interrelated processes (e.g., Williams & Cieza 2011). The combined action of these processes defines the appearance of the disk in scattered light, dust continuum, and atomic and molecular lines. Modeling of continuum and line radiation implies knowing stellar spectrum, dust density, dust temperature, and size distribution as well as gas density, gas temperature, and molecular content throughout the disk, and in full 3D. If all this information is available, a multi-dimensional radiation transfer (RT) model can be used to build a synthetic disk map at any wavelength</text>
<text><location><page_1><loc_52><loc_33><loc_92><loc_47></location>(e.g., Whitney & Hartmann 1992; Men'shchikov & Henning 1997; Wolf et al. 1999; Dullemond et al. 2002). Due to computational difficulties to follow global disk evolution in 3DMHD, particularly, coupled with chemical kinetics models, and the lack of necessary constraints related to the magnetic field structure, turbulence, grain size distribution, etc., a disk model needs to be simplified. One can steadily approach the warranted level of physical complexity by adding new components to the model (e.g., going from 1D to 2D geometry or from gray to non-gray radiative transfer) and comparing with observations at each development step.</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_33></location>Anumberof disk models has been developed over time (see review in Dullemond et al. 2007b). These models have been based on an RT-based disk structure (either 1D, 1+1D/2D, or 3D), molecular abundances, and dust and gas thermal balance. Disk models with detailed vertical structure and thermal balance regulated solely by dust heating and cooling, and, in some cases, accretion heating, have been developed by, e.g., Bell et al. (1997); Chiang & Goldreich (1997); Men'shchikov & Henning (1997); Dullemond & Dominik (2004); Hueso & Guillot (2005). It has been typically assumed in such studies that the dust is well mixed with the gas, and its properties do not differ from properties of the ISM dust. One of the most widely used models of this kind has been developed by D'Alessio et al. (1998, 1999). It has been extensively used in many subsequent studies as a template of the disk density and temperature distribution (e.g., Chiang et al. 2001; Semenov et al. 2004; Furlan et al. 2006). Other similar models, utilizing more accurate frequencydependent RT algorithms or other improvements (e.g., a</text>
<text><location><page_2><loc_8><loc_87><loc_48><loc_92></location>full 2D geometry, evolving disk structure, more realistic dust opacities) have been presented by Malbet et al. (2001); Dullemond (2002); Nomura (2002); Gorti et al. (2009), to name a few.</text>
<text><location><page_2><loc_8><loc_52><loc_48><loc_86></location>An important development of the protoplanetary disk models was to account for the energy balance of dust and gas separately in dilute disk regions. There the rate of gasdust collisions drops so low that the gas becomes thermally decoupled from the dust (e.g., Jonkheid et al. 2004; Kamp & Dullemond 2004; Gorti & Hollenbach 2008). The most recent and most advanced addition to this family, the 'ProDiMo' model, is presented by Woitke et al. (2009) and updated in Thi et al. (2011) and Aresu et al. (2011). This model is based on iterative calculations of a 1+1D vertical hydrostatic disk structure, 2D frequency-dependent dust continuum RT, gas-grain and FUV-photochemistry to calculate abundances of molecular coolants, and an escape probability method to model non-LTE heating and cooling of the gas. It is derived from thermo-chemical models of Kamp & Bertoldi (2000), Kamp & van Zadelhoff (2001), and Kamp & Dullemond (2004). Since 2011 it includes X-ray-driven chemistry and heating via H2 ionization and Coulomb heating (Aresu et al. 2011). Uniform dust abundances and power-law size distributions are typically assumed (Aresu et al. 2012), with opacities for a dust mixture calculated by Effective Medium Theory (Bruggeman 1935). Abundances of molecules are calculated assuming chemical equilibrium and element conservation, which may not be a valid approach to disk chemical evolution (e.g., Barshay & Lewis 1976; Ilgner et al. 2004; Semenov & Wiebe 2011).</text>
<text><location><page_2><loc_8><loc_14><loc_49><loc_52></location>Recent observations at IR and mm-/cm-wavelengths have shown that many disks around young stars of ages /greaterorsimilar 1 Myr have already a deficit of of small grains in the inner regions, r /lessorsimilar 10 -50 AU and the presence of large, pebble-sized dust grains in the midplanes compared to the pristine ISM dust (e.g., Williams & Cieza 2011; Williams 2012). From the analysis of SEDs at millimeter and centimeter wavelengths, grain sizes of at least 1 cm have been inferred for many disks (e.g., Rodmann et al. 2006; Lommen et al. 2009, 2010; Ricci et al. 2010; Melis et al. 2011; Pérez et al. 2012). Guilloteau et al. (2011) have used high-resolution interferometric PdBI observations to discern dust emissivity slopes at millimeter wavelengths in a sample of young stars. Their analysis has shown that in the Taurus-Auriga star-forming region some disks show very low dust emissivity indices in the inner regions, characteristic of grains with sizes of /greaterorsimilar 1 mm, and slopes that are indicative of smaller grains toward the disk edges. In addition, Spitzer IR spectroscopy of silicate bands at 10 and 20 µ mhas revealed efficient crystallization and growth of the sub-micron-sized ISM grains in warm disk atmospheres in many young systems, regardless of their ages, accretion rates, and disk masses (e.g., Kessler-Silacci et al. 2006; Furlan et al. 2009; Juhász et al. 2010; McClure et al. 2010; Oliveira et al. 2011; Sicilia-Aguilar et al. 2011). The dust settling associated with grain growth reduces disk scale heights and flaring angles, and thus leads to less intense mid-IR disk emission than expected from conventional hydrostatic models with uniform dust, in accordance with observations of most T Tauri stars (Williams & Cieza 2011).</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_13></location>As dust is a very important ingredient of the disk physics, evolution of its properties should also be considered in disk models. Usually both the grain growth and sedimentation are accounted for in disk models in a parameterized way, by assuming an increased upper limit of grain size a max and arti-</text>
<text><location><page_2><loc_52><loc_81><loc_92><loc_92></location>ficially changing the dust density and the slope of dust size distribution in various disk regions. For example, expanding on their earlier works, D'Alessio et al. (2001) have studied the influence of dust evolution on the disk structure and its spectral energy distribution (SED). Grain growth has been simulated as an increase of a max up to 10 cm and change of the dust size distribution slope p from -3 . 5 to -2 . 5. In these models dust has been assumed to be well-mixed with the gas.</text>
<text><location><page_2><loc_52><loc_65><loc_92><loc_81></location>To study the effect of dust settling, D'Alessio et al. (2006) have included two dust populations in the model, with different spatial distributions. D'Alessio et al. (2006) shown that the evolved dust model better reproduces observed millimeter fluxes and spectral slopes. A similar approach to study the effect of dust settling on the disk thermal and chemical structure has been taken by Jonkheid et al. (2004) and Fogel et al. (2011). Settling has been simulated using variable dust/gas mass ratio. A variable a max value has been used by Aikawa & Nomura (2006) to investigate changes in disk density, gas and dust temperature, and molecular abundances due to dust growth.</text>
<text><location><page_2><loc_52><loc_52><loc_92><loc_65></location>More accurate methods to model dust growth are mainly based on solving the coagulation (Smoluchowski) equation. Here the main attribute of the model is whether the dust evolution is computed for a fixed disk structure or the dust evolution and disk structure are mutually consistent. The first approach is used, e.g., in Nomura & Nakagawa (2006); Schräpler & Henning (2004); Tanaka et al. (2005); Ciesla (2007), who used parameterized disk structure. The second approach has been used by Schmitt et al. (1997); Tanaka et al. (2005); Nomura et al. (2007); Tannirkulam et al. (2007).</text>
<text><location><page_2><loc_52><loc_29><loc_92><loc_52></location>An efficient scheme to tackle the modeling of dust coagulation, fragmentation, sedimentation, turbulent stirring around a 'snow line' in a protoplanetary disk has been proposed by Brauer et al. (2008). They have found that major factors affecting grain evolution are trapping of dust particles in gas pressure maxima and the presence of a turbulently quiescent 'dead zone' in disk inner midplane. Birnstiel et al. (2010) have updated this model by considering time-dependent viscous evolution of a gas disk. They have found that dust properties, gas pressure gradients, and the strength of turbulence are more important factors for dust evolution than the initial conditions and the early formation phase of the protoplanetary disk. Birnstiel et al. (2011) have shown that, upon evolution, grain size distribution reaches a quasi-steady state, which however, does not follow the standard MRN-like power-law size distribution and is sensitive to the gas surface density, amount of turbulence, and disk thermal structure.</text>
<text><location><page_2><loc_52><loc_15><loc_92><loc_29></location>The next step in protoplanetary disk modeling was made by Vasyunin et al. (2011), where detailed dust evolution was considered along with comprehensive set of gas-phase and surface chemical reactions. However, to calculate disk thermal structure, they take into account only two heating sources, namely, viscous dissipation and dust grain irradiation by the central star. It was shown that column densities of some molecules (like C2H, HC2 n + 1N ( n = 0-3), H2O and C2H2/HCN abundance ratio) can be used as observational tracers of early stages of the grain evolution in protoplanetary disks.</text>
<text><location><page_2><loc_52><loc_7><loc_92><loc_15></location>In this paper, for the first time, we consider the influence of dust evolution on the disk structure by combining the detailed computation of the radiation field with the dust growth, fragmentation, and sedimentation model. When computing the disk density and temperature we take into account the full grain size distribution as a function of location in the disk.</text>
<text><location><page_3><loc_8><loc_71><loc_48><loc_92></location>Gas temperature and dust temperature are computed separately, with taking into account the disk chemical structure. These two factors represent a major improvement in comparison with Vasyunin et al. (2011)'s model. Also, a new detailed RT treatment is implemented with high frequency resolution from ultraviolet to far infrared. The organization of the paper is the following. In Section 2 the disk model 'ANDES' (AccretioN Disk with Dust Evolution and Sedimentation) is described. In Section 3 we present a physical structure for a typical protoplanetary disk computed both for both pristine dust and for evolved dust. Also, the chemical structure is described in this section, and specific features of the disk chemical compositions are presented for various dust models. Discussion and conclusions follow. Details of gas energy balance processes and benchmarking results are presented in Appendix A and B.</text>
<section_header_level_1><location><page_3><loc_16><loc_67><loc_40><loc_68></location>2. DISK PHYSICAL STRUCTURE</section_header_level_1>
<text><location><page_3><loc_8><loc_16><loc_49><loc_66></location>Amultitude of processes (gas dynamics, dust evolution, energy transport processes, chemistry, etc.) makes modeling of protoplanetary disks a challenge. With the current level of computing resources a global 3D radiative MHD simulation, including gas and dust evolution and chemical kinetics, remains a topic for the future (but see, e.g., Flock et al. (2012) for such models). Nevertheless a sufficient understanding of protoplanetary disk physics may be achieved by detailed modeling of primary processes that govern its structure and observational characteristics, and simplified modeling of secondary processes. This makes the problem tractable. For Class II objects (Lada 1987; Evans et al. 2009) it is usually assumed that a disk structure is in a steady-state regime over a time span of ∼ 1 Myr. This is supported by observations of disk kinematics via molecular lines and disk surface densities via (sub-)millimeter dust emissivity. The line profiles are indicative of Keplerian motion in most of the disks (Koerner et al. 1993; Guilloteau & Dutrey 1998; Piétu et al. 2007). The estimates of the disk masses and density distributions show that self-gravity is negligible for Class II objects (Isella et al. 2009). The assumption that these disks evolve on a diffusion timescale and not on a hydrodynamicalone allows setting aside hydrodynamicalsimulations and reducing a 3D problem to a 1+1D problem. The azimuthal dimension is eliminated due to the axial symmetry of an unperturbed disk. The other two dimensions are usually split into the radial structure that is determined by diffusive evolution, and the vertical structure that is derived from the hydrostatic equilibrium equation (D'Alessio et al. 1998; Dullemond et al. 2002). The 1+1D description is suitable for dust continuum radiation transfer. For disk regions outward of a few AU a radial optical depth for a location close to the midplane is higher than the vertical optical depth, so that the dust temperature is mostly determined by vertical diffusion of radiation. A gain in computation time that is acquired by a 1D radiation transfer, compared to a 2D RT, allows better frequency resolution, which is important for dust temperature calculations (Dullemond et al. 2002) and for modeling photochemistry.</text>
<text><location><page_3><loc_8><loc_7><loc_48><loc_16></location>In this paper we adopt a 1+1D approach to calculate disk density and temperature. As the disk consist of two main ingredients (dust and gas), the overall problem is reduced to calculating four physical quantities: dust and gas temperatures ( T d , T g), and dust and gas densities ( ρ d , ρ g). This allows to split the disk model into four blocks, calculating the corresponding quantities at each disk radius R :</text>
<unordered_list>
<list_item><location><page_3><loc_54><loc_83><loc_92><loc_92></location>I. Dust temperature . Dust temperature and radiation field J ν are found by solving the radiation transfer problem in vertical direction. The following quantities are considered as input: the dust density, its optical properties (absorption and scattering coefficients κ ν , σ ν ), external irradiation and all necessary parameters describing non-radiative dust heating functions.</list_item>
<list_item><location><page_3><loc_54><loc_71><loc_92><loc_81></location>II. Gas temperature . To determine the gas temperature, we solve the local energy balance equation, accounting for various heating and cooling processes. Since gas heating and cooling rates depend on abundances of main heating/cooling species and their level populations, it is necessary to include chemical reactions and simplified line radiation transport in the gas temperature calculation.</list_item>
<list_item><location><page_3><loc_53><loc_58><loc_92><loc_69></location>III. Dust density . The dust evolution is an essential part of our disk model. The surface density of dust is assumed to be equal to 1% of the total gas density, whereas its detailed vertical structure and size distribution are determined from the dust growth and sedimentation physics. We consider coagulation and fragmentation of dust grains and their redistribution due to turbulent stirring and gravitational settling to the midplane. We also consider disk structure with for comparison.</list_item>
<list_item><location><page_3><loc_53><loc_49><loc_92><loc_56></location>IV. Gas density . We assume that the gas vertical structure is defined by the local hydrostatic equilibrium . In this case the gas density ρ g can be found if its temperature T g, mean molecular weight µ , and surface density Σ g are known. The surface density is assumed to be given by the predefined function Σ g ( R ).</list_item>
</unordered_list>
<text><location><page_3><loc_52><loc_21><loc_92><loc_47></location>As all these quantities are not independent, we iterate between the modules until convergence is reached. The overall computational flowchart for ANDES is shown in Figure 1. Assuming the surface density profile, we calculate dust evolution for 2 Myr starting from the MRN initial distribution. The resultant dust structure is then used to derive radiation field and gas disk structure using radiation transfer, energy balance and hydrostatic structure modules. As a fiducial dust model we also consider pristine grains with the following parameters: 0.1 µ min size, astronomical silicate, dust to gas ratio 0.01 at every location in the disk. The list of basic assumptions is: (i) a disk is quasi-static, axially symmetric and treated in 1+1D approach; (ii) the gas surface density is assumed to be specified, and the dust surface density is 0.01 of the gas surface density; (iii) gas vertical structure is determined from the hydrostatic equilibrium, while dust vertical structure is a consequence of turbulent stirring and grain settling. Also, calculating the chemical evolution we keep the dust properties fixed both for pristine and evolved dust cases. Below we describe each part of the model in detail.</text>
<section_header_level_1><location><page_3><loc_65><loc_18><loc_80><loc_19></location>2.1. Radiative transfer</section_header_level_1>
<text><location><page_3><loc_52><loc_7><loc_92><loc_17></location>The radiation in a protoplanetary disk plays a two-fold role. First, it is a main energy carrier that redistributes energy coming from the stellar irradiation and viscous dissipation, and thus defines the overall disk structure. Second, it determines rates of photoreactions and thus shapes the disk chemical structure and observational appearance. These two aspects pose different requirements to the radiation transfer model. The radiation field as a contributor to the disk energy balance</text>
<figure>
<location><page_4><loc_9><loc_74><loc_47><loc_89></location>
<caption>Figure 1. Overall computational scheme for ANDES.</caption>
</figure>
<text><location><page_4><loc_8><loc_55><loc_48><loc_64></location>should be known in a wide range of wavelengths, from FUV (radiation from the accretion region and non-thermal radiation from the central star) to visual (thermal stellar radiation) to the infrared and submillimeter wavelengths (thermal disk radiation). This requirement makes multi-dimensional RT approaches with high spectral resolution too slow for iterative disk modeling.</text>
<text><location><page_4><loc_8><loc_40><loc_48><loc_55></location>On the other hand, in a narrow range of UV wavelengths (from 912 Å to, say, 4000 Å) such a good spectral resolution is important for accurate calculation of the photochemical rates, as the dependence of photoreaction cross-sections on λ is complicated. Protoplanetary disks usually have high optical depths at λ /lessorsimilar 100 µ m(e.g., Beckwith & Sargent 1991), which calls for using suitable methods to solve the radiation transfer (RT) problem for optically thick media. As our primary focus is on the chemical modeling in disks with evolved dust, we developed such a method with a particularly good wavelength resolution in the UV part of the spectrum.</text>
<section_header_level_1><location><page_4><loc_22><loc_37><loc_35><loc_39></location>2.1.1. Main equations</section_header_level_1>
<text><location><page_4><loc_8><loc_32><loc_48><loc_37></location>It is easy to show that in the cases of SchwarzschildSchuster and Eddington approximations the RT equation for a plane-parallel 1D medium can be written using the mean intensity J ν :</text>
<formula><location><page_4><loc_15><loc_28><loc_48><loc_31></location>q χ ν ( z ) ∂ ∂ z [ 1 χ ν ( z ) ∂ J ν ( z ) ∂ z ] = J ν ( z ) -S ν ( z ) , (1)</formula>
<text><location><page_4><loc_8><loc_23><loc_48><loc_27></location>where χ ν [ cm -1 ] is the extinction coefficient, S ν is the source function, and q = 1 / 4 and q = 1 / 3 for the SchwarzschildSchuster and the Eddington approximation, respectively.</text>
<text><location><page_4><loc_8><loc_19><loc_48><loc_22></location>If we consider only dust continuum absorption, thermal emission, and coherent isotropic scattering, the source function is</text>
<formula><location><page_4><loc_16><loc_16><loc_48><loc_19></location>S ν ( z ) = κ ν ( z ) B ν ( T d ( z )) + σ ν ( z ) J ν ( z ) κ ν ( z ) + σ ν ( z ) . (2)</formula>
<text><location><page_4><loc_8><loc_11><loc_48><loc_15></location>Here κ ν [cm -1 ] is the absorption coefficient, σ ν [cm -1 ] is the scattering coefficient ( χ ν = κ ν + σ ν ) and B ν is the Planck function.</text>
<text><location><page_4><loc_8><loc_7><loc_48><loc_11></location>In the 1+1D approach the anisotropic scattering by dust grains can also be taken into account. It is important for UV photons interacting with small dust grains, whereas at</text>
<text><location><page_4><loc_52><loc_77><loc_92><loc_92></location>IR wavelengths scattering can be considered negligible compared to absorption/emission. The p parameter describing anisotropy of scattering ( p > 1 / 2 and p < 1 / 2 denote forward and backward scattering, respectively) can be introduced in our RT model in such a way that dust extinction efficiency σ is substituted by the combination 2(1 -p ) σ . In the limit of predominantly forward scattering grains, the role of UV dust heating in deep disk layers renders less significant than in the case of the isotropic scattering used in our study. That is, our current approach tends to slightly overestimate the role of scattering and thus overall dust heating in disk upper layers.</text>
<text><location><page_4><loc_52><loc_75><loc_92><loc_77></location>Equations (1)-(2) are closed with the energy balance equation</text>
<formula><location><page_4><loc_53><loc_69><loc_92><loc_73></location>4 π ∞ ∫ 0 κ ν ( z ) B ν ( T d( z )) d ν = 4 π ∞ ∫ 0 κ ν ( z ) J ν ( z ) d ν + Γ nr( z ) . (3)</formula>
<text><location><page_4><loc_52><loc_63><loc_92><loc_67></location>Here Γ nr( z ) [ erg cm -3 s -1 ] accounts for non-radiative heating/cooling mechanisms (gas-grain interaction, see Equation (A14)).</text>
<text><location><page_4><loc_52><loc_44><loc_92><loc_63></location>Equations (1)-(3) represent the complete system for J ν ( z ) and T d( z ). We solve this system with the analogue of the Feautrier method (Mihalas 1978). Specifically, we introduce a wavelength and coordinate grid where J ν ( z ) is defined, and linearize the Planck function, B ν , with respect to T d. Equation (1) is approximated by a set of finite difference equations for each z -grid point, while Equation (3) is represented by a finite sum. As a result, we get a system of linear equations for J ν i ( zk ) that can be written using a hypermatrix formalism. This hypermatrix system is solved with the tridiagonal Thomas algorithm (Press et al. 1992). After the new values of J ν i ( zk ) and T d( zk ) are obtained we refine linearization for the Planck function, update the system, and repeat iterations until convergence is achieved.</text>
<text><location><page_4><loc_52><loc_17><loc_92><loc_44></location>The stellar and diffuse interstellar radiation fields can be treated as boundary conditions to the above system of equations. We use an approach developed by Dullemond et al. (2002) and consider stellar and interstellar fields as nonradiative additional source terms in Equation (3). This approach takes into account the shielding of the star by the inner parts of the disk. For that one needs to know the fraction of stellar radiation intercepted by the disk at each radius. We compute the corresponding grazing angle as an angle between dust density isoline at ρ d = 5 · 10 -24 gcm -3 and the direction toward the star. For the stellar spectrum, we use a 4000 K blackbody for λ > 4000Å. For shorter wavelengths, we use the interstellar radiation field (Draine 1978; Draine & Bertoldi 1996) with an extension to longer wavelength (van Dishoeck & Black 1982), where we have scaled the intensity so that it is continuous at the transition wavelength of 4000 Å . Such a normalization leads to typical values of stellar UV intensity at disk atmosphere being equal to ∼ 500 'Draine units' (Röllig et al. 2007) at a radius of 100AU.</text>
<section_header_level_1><location><page_4><loc_59><loc_13><loc_85><loc_14></location>2.1.2. Dust opacities and size distributions</section_header_level_1>
<text><location><page_4><loc_52><loc_7><loc_92><loc_12></location>As a result of dust evolution modeling we get dust size distribution functions f ( a , R , z )[cm -4 ] being the fraction of grains with sizes within ( a , a + da ) interval. To compute dust opacities one should know efficiency factors for dust absorption</text>
<text><location><page_5><loc_8><loc_90><loc_24><loc_92></location>Q abs and scattering Q sca:</text>
<formula><location><page_5><loc_19><loc_85><loc_48><loc_90></location>κ ν = amax ∫ amin π a 2 Q abs( a , ν ) f ( a ) da . (4)</formula>
<formula><location><page_5><loc_19><loc_80><loc_48><loc_84></location>σ ν = amax ∫ amin π a 2 Q sca( a , ν ) f ( a ) da . (5)</formula>
<text><location><page_5><loc_8><loc_75><loc_48><loc_79></location>Q abs and Q sca are computed from the Mie theory for astrosilicate grains (Laor & Draine 1993), but any other opacity model can be easily adapted.</text>
<section_header_level_1><location><page_5><loc_20><loc_72><loc_37><loc_74></location>2.2. Gas thermal balance</section_header_level_1>
<text><location><page_5><loc_8><loc_69><loc_48><loc_72></location>The kinetic gas temperature T g is obtained by solving the thermal balance equation:</text>
<formula><location><page_5><loc_14><loc_65><loc_48><loc_68></location>∑ k Γ k ( T g , T d , ρ i ) -∑ k Λ k ( T g , T d , ρ i , n sp j ) = 0 , (6)</formula>
<text><location><page_5><loc_8><loc_54><loc_48><loc_65></location>where Γ and Λ are gas heating and cooling rates in ergs -1 cm -3 . They depend on absolute abundances of main heating/cooling species ρ i and their level populations n sp j , which in turn depend on the gas temperature. Therefore, the problem is solved iteratively at each grid point, starting from the disk atmosphere boundary toward the midplane for any given radius, by means of the Brent method (Press et al. 1992).</text>
<text><location><page_5><loc_8><loc_33><loc_48><loc_54></location>Stellar FUV radiation is the main gas heating source in protoplanetary disks, leading to a PDR-like structure of the upper disk regions. There, gas is mainly heated via the photoelectric (PE) effect on dust grains and PAHs. In addition, collisional de-excitation of H2 pumped by FUV photons, photodissociation of H2, and carbon photoionization are important heating sources in specific disk regions. Gas heating by exothermic chemical reactions plays only a minor role, with the largest contribution coming from H2 recombination on grains. In the optically thick, dense disk interiors, the dominant heating sources are the cosmic ray ionization of H and H2, and viscous heating due to dissipation of accretion energy. Gas mainly cools via non-LTE atomic and molecular line emission, collisions with grains, and, at high temperatures, by emitting Ly α and metastable line emission. The details of heating and cooling processes can be found in Appendix A.</text>
<section_header_level_1><location><page_5><loc_23><loc_30><loc_33><loc_31></location>2.3. Chemistry</section_header_level_1>
<text><location><page_5><loc_8><loc_10><loc_48><loc_29></location>An important ingredient of the thermal balance calculations is chemistry. While often a fast, simplified equilibrium approach is adopted, time-dependent chemical modeling may be more appropriate for calculations of abundances of major molecular coolants. We adopted the same gas-grain chemical model as in Vasyunin et al. (2011). The reactions and reaction rates are based on the RATE'06 chemical ratefile (Woodall et al. 2007). For all photochemical reaction rates, we use the local mean intensity (as a function of ν ) computed with the RT model. To compute photoreaction rates, the dissociation and ionization cross-sections from van Dishoeck et al. (2006) and the AMOP database 1 are utilized. If cross-sections are not available for a certain reaction, we retain the standard χ 0 exp( -γ A V) formalism, with a γ value taken from RATE'06 ratefile, χ 0 estimated at the upper disk boundary, and A V</text>
<text><location><page_5><loc_52><loc_80><loc_92><loc_92></location>computed as ln( χ/χ 0). The same values are used to estimate photodesorption rates. Thus, the calculation of photoprocesses takes into account the detailed shape of the incident UV spectrum of the central star and its penetration through the disk. Self-shielding for H2 dissociation is computed using the Draine & Bertoldi (1996) formalism, with the modified A V values used to account for dust attenuation. The selfand mutual shielding for CO photodissociation are computed using recent tabular data of Visser et al. (2009).</text>
<text><location><page_5><loc_52><loc_63><loc_92><loc_80></location>The unattenuated cosmic ray (CR) ionization rate is assumed to be 1 . 3 × 10 -17 s -1 . The surface reactions are taken from Garrod & Herbst (2006) and assumed to proceed without hydrogen tunneling via potential wells of the surface sites and reaction barriers. Thus only thermal hopping is a source of surface species mobility. A diffusion-to-desorption energy ratio of 0.77 is adopted for all species (Ruffle & Herbst 2000). Under these conditions, stochastic effects in grain surface chemistry are negligible, and classical rate equations may be safely used (Vasyunin et al. 2009; Garrod et al. 2009). As the initial abundances, we utilize a set of 'low metals' neutral abundances from Lee et al. (1998), where most of refractory elements are assumed to be locked in dust grains.</text>
<text><location><page_5><loc_52><loc_47><loc_92><loc_62></location>As the density and temperature distributions, computed here, are similar to those used in Vasyunin et al. (2011), we decided to use the same vertical distributions of X-ray ionization rates regarding them as reference values. In the chemical module they are simply added up to CR ionization rates. For the purpose of chemical evolution, we assume that dust is represented by grains with a single size which is computed from the local grain size distribution as described in Vasyunin et al. (2011). With this chemical model, a disk chemical structure is computed using dust properties and physical conditions from the previous iteration. We assume that the grain properties do not change over the computational time span of 2 Myr.</text>
<section_header_level_1><location><page_5><loc_63><loc_44><loc_82><loc_45></location>2.4. Vertical gas distribution</section_header_level_1>
<text><location><page_5><loc_52><loc_38><loc_92><loc_44></location>Given that the gas temperature T g( R , z ) and the mean molecular weight µ ( R , z ) are known, the vertical gas density distribution can be found by integrating the hydrostatic equilibrium equation:</text>
<formula><location><page_5><loc_62><loc_33><loc_92><loc_38></location>∂ P ( R , z ) ∂ z = -ρ ( R , z ) GM /star z ( R 2 + z 2 ) 3 / 2 , (7)</formula>
<text><location><page_5><loc_52><loc_33><loc_83><loc_34></location>coupled to the equation of state of the ideal gas:</text>
<formula><location><page_5><loc_63><loc_29><loc_92><loc_32></location>P ( R , z ) = kT g( R , z ) m p µ ( R , z ) ρ ( R , z ) , (8)</formula>
<text><location><page_5><loc_52><loc_26><loc_92><loc_28></location>In this study we assume that the radial profile of the surface density is given by the known function Σ ( R ).</text>
<section_header_level_1><location><page_5><loc_66><loc_23><loc_78><loc_25></location>2.5. Dust evolution</section_header_level_1>
<text><location><page_5><loc_52><loc_18><loc_92><loc_23></location>The evolution of the dust size distribution is calculated using the model presented in Birnstiel et al. (2010). In this work, we consider neither the viscous evolution of the gas disk nor the radial evolution of the dust surface density.</text>
<text><location><page_5><loc_52><loc_7><loc_92><loc_17></location>The grain evolution begins with grains sticking at low collision velocities. Disruptive collisions at higher impact velocities cause erosion or fragmentation, which poses an obstacle towards further grain growth and replenishes the population of small grains. Typical threshold collision velocities for the onset of fragmentation are found to be about 1 m s -1 for silicate dust grains (Blum & Wurm 2008). Icy particles are expected to fragment at higher velocities due to the increased</text>
<text><location><page_6><loc_8><loc_84><loc_48><loc_92></location>surface binding energies (Wada et al. 2008; Gundlach et al. 2011). We therefore use a threshold velocity for fragmenting collisions of 10 and 30 m s -1 in our dust models. Grain collisions are driven by relative velocities due to Brownian motion, turbulent motion (Ormel & Cuzzi 2007), radial and azimuthal drift as well as vertical turbulent settling.</text>
<text><location><page_6><loc_8><loc_64><loc_48><loc_84></location>In order to make the calculation of the dust evolution feasible, we consider a radially constant, vertically integrated dustto-gas ratio and an azimuthally symmetric disk. The vertical settling of dust is taken into account by using a vertically integrated kernel (see Brauer et al. 2008; Birnstiel et al. 2010). The integration implicitly assumes that the vertical distribution of each dust species follows a Gaussian distribution with a size-dependent scale height. This is a good approximation for the regions close to the disk midplane where coagulation is most effective. However, for modeling of the chemical evolution the detailed vertical distribution of each dust species needs to be known. We therefore use a vertical mixing/settling equilibrium distribution (Dullemond & Dominik 2004), taking a vertical structure of the previously calculated dust surface densities.</text>
<section_header_level_1><location><page_6><loc_24><loc_61><loc_33><loc_62></location>3. RESULTS</section_header_level_1>
<section_header_level_1><location><page_6><loc_10><loc_58><loc_47><loc_61></location>3.1. Disk physical structure for evolved and pristine dust cases</section_header_level_1>
<text><location><page_6><loc_8><loc_31><loc_48><loc_57></location>As an initial approximation, we adopt a disk from Vasyunin et al. (2011) with mass M disk = 0 . 055 M /circledot and gas surface density profile Σ ( R ) close to a power-law with index p = -0 . 85 and Σ (1AU) = 34 g/cm 2 . The dust surface density is equal to 1% of the gas surface density. We assume the following parameters for a central star: a mass M /star = 0 . 7 M /circledot , a radius R /star = 2 . 64 R /circledot and an effective temperature T /star = 4000 K. This system closely resembles the DM Tau disk. As UV-excess we use the standard interstellar diffuse radiation field (Draine 1978) and its extension to longer wavelengths (van Dishoeck & Black 1982) as described in Section 2.1.1 ('JD' case from Akimkin et al. (2011)). To show the influence of dust evolution on the disk thermal and density structure we present results for two cases: the pristine dust with uniform distribution and grain size of 0 . 1 µ m (Model A) and the dust distribution and sizes as obtained with the dust evolution model after 2 Myr of evolution (Model Ev). The maximum grain size, attained in the midplane in Model Ev, varies from 4 · 10 -3 cm at 550 AU to 0.02 cm at 10 AU. The minimum grain size is always 3 · 10 -7 cm.</text>
<text><location><page_6><loc_8><loc_10><loc_48><loc_31></location>In Figure 2 the dust temperature distribution is shown for the both cases. The disk model with evolved dust is hotter by about 70 K in the inner disk atmosphere ( R < 200 AU) and by ∼ 10 -20 K in the outer atmosphere ( R > 200 AU) compared to the disk model with the pristine dust, whereas the dust midplane temperatures are quite similar in the both cases. Higher dust temperatures at the disk surface in the evolved dust model are explained by a steeper slope of dust opacities in the mid-IR, where such dust predominantly emits. Since both disk models have similar dust midplane temperatures and due to transparency of the bulk disk matter to the far-IR/millimeter emission, the emergent disk spectral energy distributions (SED) are similar. The difference in emergent spectra between Model A and Model Ev becomes apparent mostly at mid-IR wavelengths, where dust continuum emission from the inner disk parts peaks.</text>
<text><location><page_6><loc_8><loc_7><loc_48><loc_9></location>Gas temperature distributions in the disk models with the evolved and the pristine dust are shown in Figure 3 and can</text>
<figure>
<location><page_6><loc_56><loc_73><loc_90><loc_87></location>
</figure>
<figure>
<location><page_6><loc_56><loc_50><loc_90><loc_65></location>
<caption>Figure 2. Dust thermal structure for the disk model with the evolved (left panel) and pristine well-mixed (right panel) dust.</caption>
</figure>
<text><location><page_6><loc_52><loc_27><loc_92><loc_43></location>be compared with the dust temperatures in Figure 2. The extent of the gas-dust thermal coupling zone (where T d = T g) in Model Ev is slightly smaller than in Model A, primarily due to sedimentation. As the midplane dust temperatures for the two models do not significantly differ, the gas temperatures also inherit this behavior. On the other hand, the gas temperature distributions above the coupling zone are quite different. In the both cases, the inner disk atmosphere is heated up to several thousand Kelvin by photoelectric heating, but it is /greaterorsimilar 1000 K cooler in Model Ev. This is due to the reduced abundance of grains in the Model Ev, where the main contribution to the photoelectric heating comes from PAHs.</text>
<text><location><page_6><loc_52><loc_8><loc_92><loc_27></location>In contrast, in Model A grains dominate photoelectric heating. Their intense heating in the upper atmosphere has to be balanced by Ly α cooling, while in Model Ev remaining grains in the inner disk and the [O I] line cooling at larger distances ( /greaterorsimilar 40 AU) can balance the photoelectric heating from PAHs. Radial extent of hot tenuous atmosphere is drastically different for the two disk models: it exceeds 100 AU in Model A, whereas in Model Ev gas is cooler than 1 000 K even at R =60 AU. Absence of grains in the disk atmosphere in Model Ev leads to an increase of the gas temperatures by about factor of 2 at z / R between ≈ 0 . 3 and 0.6 at R ≈ 100 -300 AU. Somewhat smaller increase of the gas temperatures in the upper layers is also present in more distant regions of the disk. Rates of main heating and cooling processes are shown in Figure 4.</text>
<text><location><page_6><loc_53><loc_7><loc_92><loc_8></location>Dust density distributions for Models Ev and A are com-</text>
<figure>
<location><page_7><loc_12><loc_73><loc_46><loc_87></location>
</figure>
<figure>
<location><page_7><loc_12><loc_50><loc_46><loc_65></location>
<caption>Figure 3. Gas thermal structure for the disk model with the evolved (left panel) and pristine well-mixed (right panel) dust.</caption>
</figure>
<text><location><page_7><loc_8><loc_27><loc_48><loc_42></location>pared in Figure 5. The dust densities differ by several orders of magnitude, mainly due to sedimentation. This process also leads to dramatic changes in the dust-to-gas ratio. While in Model A this value is constant and equal to 10 -2 , in Model Ev we encounter the whole range of values, from 10 -1 to 10 -8 (see Figure 6). However, dust-to-gas ratios below 10 -4 lead to unstable solutions and poor convergence of the code, therefore in the calculations we assume that the minimal value of dust-to-gas ratio is 10 -4 . In Figure 7 the dust cross-section per hydrogen atom is presented for Model Ev. In case of Model A this value is equal to 5 . 9 · 10 -22 cm 2 /H everywhere in the disk.</text>
<section_header_level_1><location><page_7><loc_21><loc_25><loc_36><loc_26></location>3.2. Chemical structure</section_header_level_1>
<text><location><page_7><loc_8><loc_7><loc_48><loc_24></location>One of the main goals of our study is to probe potential changes in the disk chemical structure that may arise due to various processes related to the dust evolution. In the section we present a detailed comparison of molecular abundances in the disk models with pristine and evolved dust for radii of 10 AU, 100 AU, and 550 AU. These are the same radii that have been analyzed by Vasyunin et al. (2011). We consider only those species that have mean abundances exceeding 10 -12 at least in one of the two considered models. The mean abundance is computed as a ratio of the species column density to the column density of hydrogen nuclei. Remember that in all three cases we ignore and do not show the vertical structure at the height where the mass density of dust grains</text>
<text><location><page_7><loc_52><loc_85><loc_92><loc_92></location>drops below the adopted limit of 5 · 10 -24 g cm -3 in the evolved model, and the medium can be considered as purely gaseous. In the case of the well-mixed dust disk model, this value corresponds to the hydrogen number density of 2 · 10 2 cm -3 , and is even lower for the dust evolving disk model.</text>
<text><location><page_7><loc_52><loc_77><loc_92><loc_85></location>The key disk properties at the selected radii are shown in Figure 8. Up to a certain height the gas density is almost the same in both models. Above this height the vertical density profile flattens in Model Ev, because gas temperature either stops increasing or decreases with z , and density stays nearly constant to keep the disk hydrostatically stable.</text>
<text><location><page_7><loc_52><loc_63><loc_92><loc_77></location>The main reason for that is the disk transparency. The dashdotted lines in Figure 8 (b, d, f) show the water photodissociation rates that are used here as a descriptive characteristics of the radiation field strength. Obviously, in Model Ev the UV radiation penetrates deeper into the disk. Dust is warmer in this model than in Model A almost everywhere in the disk. In Model Ev gas is also significantly hotter that in the model with pristine dust in the more illuminated region that extends approximately from 1.5 AU to 3 AU at R = 10 AU, from 30 AU to 50 AU at R = 100 AU, and from 100 AU to 600 AU at R = 550 AU.</text>
<text><location><page_7><loc_52><loc_45><loc_92><loc_62></location>We characterize the dust evolution using the total dust surface area per unit volume that is shown in Figure 8 (b, d, f) (solid lines). It is smaller in the evolved model as both grain growth and sedimentation reduce the total surface of dust grains. While in the midplane this reduction is mostly caused by the growth of dust grains and is quite moderate, from an order of magnitude at 10 AU to less than a factor of 2 at 550 AU, in the upper disk, where sedimentation is important, the total dust surface area in Model A is greater by orders of magnitude than in Model Ev. However, this difference may not necessarily be important for chemistry as it is mostly confined to the illuminated disk regions where dust mantles are evaporated anyway by the UV photons.</text>
<section_header_level_1><location><page_7><loc_67><loc_43><loc_77><loc_45></location>3.2.1. Outer disk</section_header_level_1>
<text><location><page_7><loc_52><loc_32><loc_92><loc_43></location>We start the description of the disk chemical structure from the outer disk, where only minor changes in the disk physical parameters are caused by the grain evolution. Because of ineffective grain growth the total grain surface area per unit volume is nearly the same in both models, except for the outermost disk atmosphere (Figure 8, f). Second, the dust temperature is quite low in the disk midplane, so surface reactions with heavy reactants should be mostly suppressed there.</text>
<text><location><page_7><loc_52><loc_15><loc_92><loc_32></location>After 2 Myr of evolution we end up with 91 gas-phase species and 81 surface species that have mean abundances greater than 10 -12 either in Model A or in Model Ev. In most cases grain evolution increases column densities for gasphase components. Among the 91 gas-phase species only 13 have column densities that are smaller in Model Ev than in Model A. The reason is quite straightforward. As grains grow and settle down toward the midplane, the so-called warm molecular layer moves down as well, to a denser disk region. Even if relative abundances do not change significantly in the process, column densities grow due to higher volume densities. Vertical abundance distributions for some species are shown in Figure 9.</text>
<text><location><page_7><loc_52><loc_7><loc_92><loc_15></location>In the upper row of Figure 9 we present vertical abundance profiles for H2, H + 3 , and CO. The key difference between Model A and Model Ev is that in the former the warm molecular layer is located below the H2 dissociation boundary, while in the latter a portion of the molecular layer is located above this boundary, where free H atoms are abundant. This mutual</text>
<figure>
<location><page_8><loc_12><loc_53><loc_89><loc_91></location>
<caption>Figure 4. Main gas heating and cooling processes at selected radii. To avoid confusion, the legend is split into two parts. Same line styles apply on all plots. To illustrate the thermal coupling zone extent the cooling and heating functions are not plotted in regions with T d ∼ = T g.</caption>
</figure>
<figure>
<location><page_8><loc_13><loc_28><loc_46><loc_43></location>
<caption>Figure 6. Dust-to-gas ratio for Model Ev.</caption>
</figure>
<figure>
<location><page_8><loc_56><loc_28><loc_89><loc_43></location>
<caption>Figure 5. Distribution of the dust density in Model Ev (left panel) and Model A (right panel).</caption>
</figure>
<text><location><page_8><loc_8><loc_7><loc_48><loc_19></location>disposition is not impossible as the molecular layer and the H2 photodissociation front are not directly related to each other. Grain absorption of the FUV photons responsible for the H2 dissociation is less significant in the model with evolved dust, and the H2 dissociation front is located deeper in Model Ev. However, the overall transparency of evolved dust in the entire UV range is smaller than for FUV photons only. Because of that the molecular layer that is controlled by desorption from dust grains and dissociation of trace molecules is located</text>
<text><location><page_8><loc_52><loc_16><loc_92><loc_20></location>somewhat higher. This specific result, of course, depends on the adopted description of dust opacities and photoreaction rates.</text>
<text><location><page_8><loc_52><loc_7><loc_92><loc_16></location>Simple atomic and diatomic components dominate the list of the gas-phase species, whose column densities are enhanced in Model Ev. The largest column density increase at 550 AU is found for SiO2 (Figure 9, d), N2O, and water (Figure 9, e). In all cases it is related to higher abundance of a molecule in the molecular layer. Note that almost all physical characteristics of the medium are nearly the same in</text>
<figure>
<location><page_9><loc_12><loc_75><loc_46><loc_89></location>
<caption>Figure 7. Dust cross-section per hydrogen atom for Model Ev. The correspondent value for Model A is 5 . 9 · 10 -22 cm 2 /H.</caption>
</figure>
<text><location><page_9><loc_8><loc_60><loc_48><loc_66></location>the molecular layers of the two disk models, except for the gas density and the X-ray ionization rate. Higher density in the molecular layer of Model Ev accelerates two-body processes and shifts equilibrium abundances of many molecules to higher values.</text>
<text><location><page_9><loc_8><loc_33><loc_48><loc_60></location>The relative location of the molecular layer and the HH2 boundary, mentioned above, also plays a role in defining molecular column densities, especially, for species that are produced in reactions with atomic hydrogen, like water. In Model Ev a significant portion of the molecular layer is located above this transition, where abundant H atoms are available. This speeds up the gas-phase water synthesis in H + OH reaction as well as surface synthesis of water molecules that are immediately released into the gas-phase due to photodesorption. This explains a huge water spike located at height of about 300 AU. In Model A water is mostly produced in surface reactions that are less effective because of low H gasphase abundance and lower rate of the UV photodesorption. Also, water molecules are more rapidly destroyed in reactions with ions such as HCO + that are abundant in the molecular layer due to higher X-ray ionization rate. The sharp drop-off in water abundance in both models coincides with the carbon ionization front. Above the front, the main destruction routes for water molecules are the reaction with C + and photodissociation.</text>
<text><location><page_9><loc_8><loc_14><loc_48><loc_33></location>The situation is somewhat different for complex hydrocarbons, in particular, for long carbon chains. Their abundances in Model A are significantly enhanced in the molecular layer in comparison with Model Ev. This is again related to a more elevated position of the molecular layer in Model A. Because of that, it is less protected not only from the UV irradiation but from X-rays as well. Accordingly, ionized helium is more abundant in the molecular layer of Model A than in the molecular layer of Model Ev. Abundant C-bearing molecules, like CO, are destroyed by He + more efficiently in Model A in the disk upper region. Then, C + is consumed to produce simple CH + n species that stick to grains and produce long carbon chains by surface processes. The dust temperature of the order of 30 K is high enough to drive desorption of these molecules into the gas-phase.</text>
<text><location><page_9><loc_8><loc_7><loc_48><loc_13></location>This effect should not be overestimated. Even though the total column densities of carbon chains are greater in Model A than in Model Ev, their absolute values are low, with the mean abundance exceeding 10 -12 only for C2H, C4, C4H, C5, C5H, and C6H. The effect is most pronounced for C5H</text>
<text><location><page_9><loc_52><loc_83><loc_92><loc_92></location>(Figure 9, f), with the ratio of column densities in Model A and Model Ev of 15. For the observed C2H molecule the higher relative abundance in Model A (related to more effective He + chemistry) is nearly compensated by the higher absolute abundance in Model Ev (related to deeper location of the molecular layer), so its column densities are nearly the same in both models.</text>
<text><location><page_9><loc_52><loc_65><loc_92><loc_82></location>The behavior of surface species is different in the two disk models. While column densities of gas-phase species are increased by grain evolution, column densities of many surface species decrease. There are 81 abundant surface species at 550 AU, and only 30 of them have greater column densities in Model Ev. Also the difference of column densities of surface species is quite modest in the two models. Only for ten of 81 species column densities differ by more than a factor of 3. Dominant surface carbon compounds (in terms of column densities) in both models are carbon monoxide and methane. Because of low dust temperature, s-CO2 production is suppressed, and this molecule in neither model reaches the high abundance seen at smaller radii (see below).</text>
<text><location><page_9><loc_52><loc_57><loc_92><loc_65></location>Surface species that have greater column densities in Model Ev are mostly silicon and phosphorus compounds, which are not involved in surface chemistry (relevant reactions are not included in our chemical network). Their abundances are enhanced in the 'main' molecular layer as are abundances of their gas-phase counterparts (Figure 9, g).</text>
<text><location><page_9><loc_52><loc_43><loc_92><loc_57></location>Abundances of some surface carbon chains are enhanced in Model A by about an order of magnitude due to more intense X-ray ionization than in Model Ev (see above). Also, species like s-C2O (Figure 9, h) and s-C2N involved in surface chemistry have greater column densities in Model A because their midplane abundances are higher in this model due to greater available surface area for their synthesis. Carbon chains not involved in surface chemistry in our chemical model, like sC4N (Figure 9, i), mirror evolution of their gas-phase counterparts and have higher abundances in the upper carbon chain layer described above.</text>
<section_header_level_1><location><page_9><loc_65><loc_41><loc_79><loc_42></location>3.2.2. Intermediate disk</section_header_level_1>
<text><location><page_9><loc_52><loc_23><loc_92><loc_40></location>As we move closer to the star, at distances of about 50100 AU, the fingerprint of dust evolution becomes more pronounced. While the mass density of dust is greater in the midplane of Model Ev due to sedimentation, the total surface area is still 2.5 times less than in Model A. In the upper disk the difference in the surface area reaches a factor of 70. It is interesting to note that the uppermost disk atmosphere is actually colder in Model Ev than in Model A, despite being more transparent (Figure 8, c). This is because dust is not only the main source of opacity but also an important heating agent (due to photo-effect). As dust is depleted in the upper disk, the equilibrium temperature shifts to lower values, dictated by the PAH heating.</text>
<text><location><page_9><loc_52><loc_14><loc_92><loc_23></location>At R = 100 AU, among 78 gas-phase species, having mean abundances higher than 10 -12 at least in one of the two models, most species (72) have higher column densities in Model Ev, as at R = 550 AU, but the list of these species is somewhat different. Some examples of vertical abundance profiles for gas-phase species at R = 100 AU are shown in the top and middle row of Figure 10.</text>
<text><location><page_9><loc_52><loc_7><loc_92><loc_13></location>The main features of the chemical structure are the same as at 550 AU. In Model Ev the molecular layer, as marked by the CO distribution (Figure 10, c), is located above the H2 photodissociation front (Figure 10, a). In Model A the situation is the opposite. Also, in Model A ions, like H + 3 (Figure 10, b) are</text>
<figure>
<location><page_10><loc_24><loc_32><loc_78><loc_87></location>
<caption>Figure 8. Vertical distributions of selected disk parameters at three radii selected for a chemical analysis as indicated in titles. In all plots red lines correspond to a model with pristine dust, while blue lines correspond to a model with evolved dust. Shown in the left column are gas densities (dashed lines), dust temperatures (dotted lines), and gas temperatures (solid lines). Plots in the right column show dust surface area per unit volume (solid lines) and water photodissociation rates (dot-dashed lines).</caption>
</figure>
<text><location><page_10><loc_77><loc_39><loc_78><loc_39></location>2</text>
<text><location><page_10><loc_8><loc_19><loc_48><loc_21></location>somewhat more abundant in the molecular layer which further decreases abundances of neutral unsaturated molecules.</text>
<text><location><page_10><loc_8><loc_7><loc_48><loc_18></location>The largest difference between the two models is again observed for SiO2 that has a column density 3 . 6 · 10 8 cm -2 in Model A and 1 . 8 · 10 12 cm -2 in Model Ev. Grain evolution causes water column density to increase from 7 . 1 · 10 13 cm -2 to 5 . 2 · 10 16 cm -2 . This is again related to the different arrangement of the molecular layer and H-H2 transition in Model A and Model Ev (Figure 10, a). The upper boundary of the water layer is defined by the location of the C ionization</text>
<text><location><page_10><loc_52><loc_20><loc_56><loc_21></location>front.</text>
<text><location><page_10><loc_52><loc_11><loc_92><loc_20></location>Many complex gas-phase hydrocarbons, like formaldehyde (Figure 10, d) and cyanoacetylene (Figure 10, e), are also affected. Among more or less abundant molecules the only exception to this rule is methane (Figure 10, f), with column density being about 3 times larger in Model A than in Model Ev. This difference is related to the surface chemistry as we will explain below.</text>
<text><location><page_10><loc_52><loc_8><loc_92><loc_10></location>The chemical evolution of surface species is complicated as it is affected by at least two competing factors related to</text>
<section_header_level_1><location><page_11><loc_68><loc_93><loc_82><loc_94></location>THE ANDES MODEL</section_header_level_1>
<figure>
<location><page_11><loc_16><loc_39><loc_84><loc_94></location>
<caption>Figure 9. Vertical abundance distributions of selected species at R = 550 AU.</caption>
</figure>
<text><location><page_11><loc_8><loc_28><loc_48><loc_35></location>grain growth. Less grain surface is available to the mantle formation in Model Ev, but because of higher grain temperature surface species are more mobile than in Model A, which intensifies the surface recombination. The interplay between these processes causes various responses of surface species to the grain evolution.</text>
<text><location><page_11><loc_8><loc_8><loc_48><loc_27></location>Thirty five of 72 abundant mantle components have higher column densities in Model Ev. Only for 24 species the ratio of column densities in the two models exceeds a factor of 3. Higher abundances in Model Ev are mostly typical for complex surface molecules with large desorption energies that have accreted from the gas phase and are not involved in surface chemistry. These species mirror the behavior of their gas-phase counterparts. Two striking examples of greater column densities in Model A are presented by s-CO and s-CH4 (Figure 10, g and h). Surface methane is underabundant by about 3 orders of magnitude in Model Ev, while surface CO is underabundant by more than 4 orders of magnitude in this model. As surface species are mostly concentrated in the midplane, to explain this difference we need to consider chemistry in this disk region.</text>
<text><location><page_11><loc_52><loc_20><loc_92><loc_35></location>Surface methane chemistry is quite limited in the adopted network. Methane is synthesized in a sequence of hydrogen addition reactions, while the only effective route of its removal from the mantle is desorption. So, its abundance is regulated by the balance between hydrogen addition and desorption. As the desorption energy of methane is not very large (1300K), desorption wins in this competition, and the steadystate s-CH4 abundance in Model Ev shifts toward lower values. This does not work for other saturated molecules (like water and ammonia), as they have much higher desorption energies, so their midplane abundances in both models are just (nearly) equal to the abundances of the corresponding atoms.</text>
<text><location><page_11><loc_52><loc_8><loc_92><loc_19></location>Carbon monoxide is different from methane in the sense that it is not a 'dead end' of some surface chemistry route, but rather an intermediary on the route to s-CO2 formation and synthesis of complex organic molecules like CH3OH. The reaction between s-OH and s-CO, leading to s-CO2, has a 80 K barrier. This implies very strong dependence on the dust temperature at critical T d < 20 -40 K. Because of this dependence, s-CO2 formation is much more efficient in Model Ev. While s-CO2 is the most abundant carbon compound in the</text>
<figure>
<location><page_12><loc_16><loc_39><loc_84><loc_93></location>
<caption>Figure 10. Vertical abundance distributions of selected species at R = 100 AU.</caption>
</figure>
<text><location><page_12><loc_8><loc_22><loc_48><loc_35></location>disk midplane in both models, in Model A its abundance is about two times lower than in Model Ev (Figure 10, i). Thus, in Model A, carbon atoms that are not bound in s-CO2 are available for other surface processes and are almost equally distributed between surface methane, surface CO, and some other species, with s-CH4 having almost the same abundance as s-CO2. In Model Ev, s-CO2 synthesis proceeds faster, and this component becomes not only the dominant C carrier, but also the dominant oxygen carrier, leaving almost no place for either surface or gas-phase CO.</text>
<text><location><page_12><loc_8><loc_8><loc_48><loc_22></location>The described trends are mostly preserved at R = 50 AU. At this radius, dust evolution also causes column densities of abundant gas-phase species to increase (mostly due to enhanced photodesorption). Water, carbon dioxide, formaldehyde, and cyanoacetylene are among species mostly affected. Gas-phase methane column density is nearly the same in both models. Surface methane and CO ice are underabundant in Model Ev at R = 50 AU, but to a less degree than at R = 100 AU. Dust temperatures in Model A and in Model Ev are nearly equal at this radius, so that in both cases surface s-CO2 synthesis is very effective, decreasing s-CO and s-CH4</text>
<text><location><page_12><loc_52><loc_32><loc_92><loc_35></location>abundances and leveling differences between the two models. Abundances at 50 AU will be further discussed in the last subsection of Section 3.</text>
<section_header_level_1><location><page_12><loc_67><loc_29><loc_77><loc_30></location>3.2.3. Inner disk</section_header_level_1>
<text><location><page_12><loc_52><loc_7><loc_92><loc_28></location>At R = 10 AU we have 75 abundant gas-phase molecules, and 62 of them share the common trend to be more abundant in the model with evolved dust. However, the magnitude of the difference in column densities as well as its origin are related to other factors. The molecular layers both in Model A and in Model Ev are located above the H-H2 transition (Figure 11, a). In both cases abundant H atoms are available both for surface and gas-phase reactions. Despite the fact, water column density in Model Ev exceeds that in Model A by more than 4 orders of magnitude (Figure 11, g). This difference is much greater than at other radii where we related it to the difference in atomic hydrogen abundance. At these warm temperatures of 50 -200 K (see Figure 8, a), the formation of water is dominated by neutral-neutral reaction of O with H2 (with the barrier of 1660 K), followed by the neutralneutral reaction of OH with H2 (with the barrier of 3163 K),</text>
<section_header_level_1><location><page_13><loc_68><loc_93><loc_82><loc_94></location>THE ANDES MODEL</section_header_level_1>
<figure>
<location><page_13><loc_16><loc_39><loc_84><loc_94></location>
<caption>Figure 11. Vertical abundance distributions of selected species at R = 10 AU.</caption>
</figure>
<text><location><page_13><loc_8><loc_34><loc_40><loc_36></location>see Woodall et al. (2007) and Najita et al. (2011).</text>
<text><location><page_13><loc_8><loc_8><loc_48><loc_34></location>As H abundances in the molecular layers are nearly the same in both models, we need to find another explanation for the raise in water abundance in Model Ev. It is obviously related to the difference in physical parameters in the two molecular layers. Again, the molecular layer in Model Ev is shifted toward the midplane and, thus, resides in a denser disk region. Because of higher density in the molecular layer of Model Ev, surface water synthesis is more effective there, increasing its gas-phase abundance as well. Higher X-ray ionization rate in the molecular layer of Model A leads to higher ion abundances. In particular, it greatly enhances abundance of H + that is one of the major water destroyers. Another difference is the UV radiation spectrum that favors carbon ionization in Model A. In the adopted photoionization model, carbon atoms are ionized by the UV radiation with wavelengths shorter than 1100 Å. This radiation is absorbed less efficien tly in Model A, and because of that the C/C + transition zone is further vertically expanded, so that the water layer falls in the region where C + abundance is still significant (Figure 11, d). This also leads to rapid water destruction.</text>
<text><location><page_13><loc_52><loc_15><loc_92><loc_36></location>Different water abundances cause even greater differences in column densities of SO and SO2. In the case of SO2 the difference exceeds 9 orders of magnitude (Figure 11, e). Significant growth of SO and SO2 abundances can be traced to the greater abundance of O2 in Model Ev. An SO2 molecule is produced from SO, SO is produced in reaction S + OH, atomic sulfur is the product of SO + dissociative recombination, and SO + is produced in the reaction between S + and O2. Abundance of molecular oxygen in Model Ev is greater by almost 4 orders of magnitude than in Model A (Figure 11, h), which is also related to different H + abundances, as the H + + O2 reaction is one of the major O2 destruction pathways. Thus, we conclude that at R = 10 AU chemical differences between Model Ev and Model A arise because grain evolution shifts the molecular layer in the region of the disk that is more protected from X-rays and FUV radiation.</text>
<text><location><page_13><loc_52><loc_8><loc_92><loc_14></location>Among species, that have their column densities decreased by grain growth, are HCN (Figure 11, f) and HNC. They are mostly concentrated in the midplane, and their midplane abundances in Model A exceed those in Model Ev by an order of magnitude. Analysis of chemical processes indicates</text>
<text><location><page_14><loc_8><loc_80><loc_48><loc_92></location>that this difference is related to surface processes, that is, higher gas-phase HCN abundance in Model A simply reflects more effective surface synthesis of the molecule because the available surface area is greater in this model (Figure 11, i). Then, HCN desorbs into the gas-phase and gets protonated by reactions with HCO + or H + 3 . Dissociative recombination of HCNH + produces either HCN or HNC, so the overabundance of HCN in Model A is partially transferred into the overabundance of HNC.</text>
<text><location><page_14><loc_8><loc_71><loc_48><loc_80></location>As for surface species, at this radius there are 64 abundant surface components, mainly heavy molecules. Nearly half of them are more abundant in Model Ev, but the increase in column densities is not significant for most molecules. Two extreme examples of greater column densities in Model A are represented by s-HCN and s-HNC, for the reasons described above.</text>
<section_header_level_1><location><page_14><loc_14><loc_68><loc_42><loc_69></location>3.3. Model with more efficient dust growth</section_header_level_1>
<text><location><page_14><loc_8><loc_59><loc_48><loc_67></location>To check the sensitivity of our results to some details of the adopted grain physics, we considered additional models for dust evolution. In this subsection we present a detailed description of Model Evx with a threshold velocity for fragmenting collisions increased from 10 to 30 m s -1 , which leads to more significant grain growth in the dense regions.</text>
<text><location><page_14><loc_8><loc_42><loc_48><loc_59></location>Models A, Ev, and Evx can be viewed as successive stages of the grain evolution process. So, in Model Evx we may expect to see a continuation of the same trends as were noted above for Model Ev. In Figure 12 we show the main disk structural properties at R = 50 AU in the three models. Obviously, more advanced grain evolution causes the disk to become more transparent. As a result, hot atmosphere becomes more extended, and dust becomes warmer, with the midplane grain temperature raising from 28 K in Model A to 33 K in Model Evx. As we will see below, this relatively small difference has a noticeable effect on the disk chemical structure. Dust surface, available for chemical reactions, is an order of magnitude smaller in Model Evx than in Model A.</text>
<text><location><page_14><loc_8><loc_24><loc_48><loc_41></location>Vertical profiles of some species for Models A, Ev, and Evx are shown in Figure 13. As in previous cases, we start from H2 (Figure 13, a) and notice that the H2 photodissociation front sinks even deeper, so that hydrogen is almost fully atomic above ∼ 6 AU. Due to warmer dust, gas-phase abundances of some molecules with low desorption energy are increased in the midplane of Model Evx (like in Model Ev at R = 10 AU). One can see the progressive growth of CO midplane abundance from Model A to Model Evx in Figure 13 (c). Similar to CO, gaseous N2 appears in the disk midplane in Model Evx. Protonation of such abundant molecules lowers the H + 3 abundance in the Evx model midplane (Figure 13, b), which affects abundances of some other ions, like H3O + .</text>
<text><location><page_14><loc_8><loc_15><loc_48><loc_24></location>A typical example of the molecular abundance evolution is shown in Figure 13 (d). A peak of water abundance shifts toward the midplane and grows higher. Due to increasing overall gas density and more intense photodesorption, gasphase water column density increases up to 4 . 7 · 10 17 cm -2 in Model Evx. The upper boundary of water layer is defined by the C + ionization front (Figure 13, e).</text>
<text><location><page_14><loc_8><loc_7><loc_48><loc_15></location>A significant growth is observed for N2H + column density. It increases from 4 . 8 · 10 9 cm -2 to 1 . 5 · 10 10 cm -2 in Model Ev and 5 . 1 · 10 11 cm -2 in Model Evx (vertical abundance profile is shown in Figure 13 (g)). This is related to increased thermal desorption of the N2 ice and lower abundances of surface species that are mostly synthesized on grains, like methane</text>
<text><location><page_14><loc_52><loc_81><loc_92><loc_92></location>(Figure 13, f) or ammonia (Figure 13, h). In the latter case, some nitrogen atoms in the midplane are free to be incorporated into N2 molecules (Figure 13, i) and further into N2H + molecules. Species, significantly affected by the advanced grain growth, also include other gas-phase molecules, related to surface chemistry. Column densities are increased by more than an order of magnitude in Model Evx relative to Model Ev for H2O2, CH4, CO2, and some others.</text>
<text><location><page_14><loc_52><loc_69><loc_92><loc_81></location>We have also considered the effects of dust radial mixing. The radial mixing is modeled as diffusion, using the Schmidt number from Youdin & Lithwick (2007), i.e. D dust = D gas / (1 + St 2 ). The dust diffusivity is taken to be the dust viscosity ( D gas = ν gas) which is the Shakura & Sunyaev (1973) viscosity for the given alpha value. We found that radial mixing does not change the disk physical and chemical structure significantly and leads to the gas/dust temperature increase by several K at intermediate radii.</text>
<section_header_level_1><location><page_14><loc_66><loc_67><loc_78><loc_68></location>4. DISCUSSION</section_header_level_1>
<section_header_level_1><location><page_14><loc_58><loc_65><loc_86><loc_66></location>4.1. Comparison to Vasyunin et al. (2011)</section_header_level_1>
<text><location><page_14><loc_52><loc_42><loc_92><loc_64></location>While many aspects of the presented model are derived from the model used by Vasyunin et al. (2011), the new treatment of the disk structure results in parameters that are too different to allow a direct comparison of the 'old' and 'new' results. While density profiles are nearly the same in both studies, there are two key differences in the disk dust temperature and in the disk radiation field (Figure 14). First, the improved radiation transfer model makes dust in the 'new' disk midplane significantly warmer than dust in the 'old' disk midplane, at least, in the remote parts of the disk ( R > 100 AU). Second, because of scattering the 'new' disk is less transparent to dissociating far-UV radiation than the 'old' one. These two differences are related to the radiation transfer treatment , so we may expect that basic inferences of Vasyunin et al. (2011) on the disk chemical structure should be retained in the new results, if they are mostly related to the dust evolution .</text>
<text><location><page_14><loc_52><loc_33><loc_92><loc_42></location>This is indeed the case, with a few exceptions. First, the general conclusion of Vasyunin et al. (2011) that dust evolution increases gas-phase column densities of most species is entirely confirmed in the present study. Second, almost all species, designated as sensitive to grain evolution in Vasyunin et al. (2011), like CO, CO2, H2O, C2H, retain this status in the present study 2 .</text>
<text><location><page_14><loc_52><loc_12><loc_92><loc_33></location>In Table 1 we show column densities for species listed in Table 2 from Vasyunin et al. (2011), along with the newly calculated column densities. Few remarks are needed. Some species, like methanol, cyanopolyynes or formic acid, are significantly less abundant in the new model. This is due to generally less effective surface chemistry in a warmer disk midplane, where depletion of CO and other similar volatile ices is less severe and where a desorption rate of hydrogen atoms from dust surfaces is higher. The chances for them to be observed are, thus, slim (within the framework of our modeling approach). For some species from this list the 'sensitivity region' (the region where the two models differ most) shifts or extends to other radii (typically, from ten to hundred AU). These are HCNH + (derived mainly from HCN), NH3, and OH. Surface hydrogenation also plays an important role in the synthesis of these species.</text>
<figure>
<location><page_15><loc_26><loc_75><loc_75><loc_92></location>
<caption>Figure 12. Main disk structural properties at R = 50 AU. In all cases red lines correspond to Model A, blue lines correspond to Model Ev, and green lines correspond to Model Evx. In the left panel gas temperature (solid lines) and dust surface area per unit volume (dashed lines) are shown. Plotted in the right panel are dust temperature (solid lines) and gas number density (dashed lines).</caption>
</figure>
<figure>
<location><page_15><loc_21><loc_22><loc_80><loc_69></location>
<caption>Figure 13. Vertical abundance distributions of selected species at R = 50 AU. Blue dashed line corresponds to the Model Evx.</caption>
</figure>
<text><location><page_15><loc_8><loc_7><loc_48><loc_19></location>Column densities of three species, H2CS, HC5N, and HCO + , while still enhanced by the dust growth, differ by less than an order of magnitude in the new calculation, so they do not conform to our sensitivity criterion. Thioformaldehyde that has been mentioned in Vasyunin et al. (2011) as a molecule most sensitive to dust growth and HCO + are now significantly more abundant in the midplane of Model A due to higher dust temperature and less severe depletion of their parental species, CO and (H)CS. This shortens the break be-</text>
<text><location><page_15><loc_52><loc_18><loc_80><loc_19></location>tween the pristine and evolved dust models.</text>
<text><location><page_15><loc_52><loc_7><loc_92><loc_18></location>Abundance of CH3CH3 is also significantly enhanced in the midplane at R = 10 AU, relative to results of Vasyunin et al. (2011), and is nearly the same both in Model A and in Model Ev. As our model has a warmer inner midplane, surface radicals out of which CH3CH3 is formed become more mobile and reactive. A molecular layer no more dominates in its column density, so the molecule loses its sensitivity to the dust growth in the inner disk. In the outer disk the situation</text>
<figure>
<location><page_16><loc_17><loc_62><loc_84><loc_92></location>
<caption>Figure 14. Top row: disk structure in the present study and in Vasyunin et al. (2011), their Model GS. As in Figure 8, dashed lines show the gas density, and dotted lines show dust temperature. Note that dust and gas temperature are equal in Model GS. Bottom row: water dissociation rates at the selected radii in the present study and in Vasyunin et al. (2011). Different colors correspond to the same models as in the top row.</caption>
</figure>
<text><location><page_16><loc_8><loc_48><loc_48><loc_56></location>is more complicated. There, CH3CH3 is still sensitive to dust growth, but the sign of the sensitivity is different. While in Vasyunin et al. (2011) its column density was greater in the model with pristine dust, now CH3CH3 shares the common behavior and is enhanced in the molecular layer of Model Ev due to higher density there.</text>
<text><location><page_16><loc_8><loc_32><loc_48><loc_48></location>Another molecule that shows the 'reversed' sensitivity is HCN. As we mentioned above, its abundance in the midplane is higher in Model A because of more effective surface synthesis. It also exceeds HCN column density in Model A5 from Vasyunin et al. (2011) due to somewhat higher dust temperature, that also intensifies HCN ice production (as surface production of CN is faster in the warmer ANDES model). At larger radii, HCN behavior is similar in both studies. These findings demonstrate the importance of the correct treatment of the radiation transport and also imply that the stellar and interstellar radiation fields need to be discretized as good as possible.</text>
<text><location><page_16><loc_8><loc_14><loc_48><loc_32></location>Table 1 contains only a few representative species. To have a broader perspective, we perform a general comparison relating the column density ratios in the models with pristine and evolved dust computed in Vasyunin et al. (2011) and in the present study, for all species at 10, 100, and 550 AU. Results of comparison for R = 100 AU are shown in Figure 15. Only gas-phase species with mean abundances greater than 10 -10 are shown. Most species are concentrated around a red line that corresponds to equal old and new ratios. This indicates that most column densities respond similarly to dust growth both in Vasyunin et al. (2011) and in the present study. Also, most species reside in the upper right quadrant, showing that in both studies dust evolution, as a rule, increases molecular column densities.</text>
<text><location><page_16><loc_8><loc_7><loc_48><loc_14></location>Carbon dioxide is most sensitive to dust growth and is, thus, located in the upper right corner. This is not surprising as its production mostly occurs on grain surfaces via slightly endothermic reactions of CO and OH. A quite high water sensitivity was obtained in Vasyunin et al. (2011), and now it be-</text>
<figure>
<location><page_16><loc_52><loc_25><loc_94><loc_57></location>
<caption>Figure 15. Relation between molecular dust growth sensitivity in the present study and in Vasyunin et al. (2011). Plotted are ratios of column densities at R = 100 AU in the models with evolved and pristine dust. The red line corresponds to equal sensitivity. Species in upper right and lower left quadrants show the same kind of sensitivity in both studies. Species within green lines have their column densities decreased by the dust growth in the previous study, while in the present study dust evolution increases their column densities. A black square indicates difference in column densities less than an order of magnitude, which we interpret as an absence of strong sensitivity.</caption>
</figure>
<text><location><page_16><loc_52><loc_7><loc_92><loc_12></location>comes even higher. Similar to water and carbon dioxide, HNO was very sensitive to dust growth in our old computation because its main production route is surface synthesis. In the new computation this route is less effective due to warmer</text>
<paragraph><location><page_17><loc_48><loc_90><loc_52><loc_91></location>Table 1</paragraph>
<table>
<location><page_17><loc_12><loc_58><loc_87><loc_87></location>
<caption>Species sensitive to grain evolution. Observed column densities are compiled from Piétu et al. (2007), Dutrey et al. (2007), Chapillon et al. (2012), Bergin et al. (2010), and Henning et al. (2010).</caption>
</table>
<text><location><page_17><loc_8><loc_47><loc_48><loc_56></location>dust, so HNO is mostly produced in the gas phase. This makes it less susceptible to changes in dust properties. It must be kept in mind that warmer dust has dual effect on surface chemistry. On one hand, a larger temperature implies more rapid hopping and larger reaction rates. On the other hand, more volatile reactants evaporate faster from warmer grains, thus, quenching the formation of some species.</text>
<text><location><page_17><loc_8><loc_25><loc_48><loc_47></location>An opposite example is represented by formaldehyde. This species was barely sensitive to dust growth in the old computation, with column density being slightly smaller in the model with evolved dust. In the present study, H2CO column density is significantly greater in the model with evolved dust. This behavior is related to details of the UV penetration. In the old models, where only the UV absorption has been taken into account, the UV field intensity falls off quite slowly as we go deeper into the disk. Because of that abundance maxima in the molecular layer for molecules that are mostly susceptible to photodesorption and photodissociation are extended and shallow. Thus, their column densities are less sensitive to dust evolution. Detailed treatment of the radiation transfer in the new model predicts a sharper transition from the illuminated atmosphere to the dark interior. The molecular layer becomes significantly narrower and is, thus, much more sensitive to the extent of dust growth and sedimentation.</text>
<text><location><page_17><loc_8><loc_10><loc_48><loc_24></location>The overall conclusion from the presented comparison is the following. We confirm that dust evolution changes column densities of many molecules (see Table 1 and Figure 15). Most species that have been listed as especially sensitive to dust evolution in Vasyunin et al. (2011) retain this status in the present study. However, column densities of some species turn out to depend on the details of the radiation transfer treatment, and this dependence will become even stronger when we will proceed from column densities to line intensities. ANDES makes all the necessary preparatory work for that, providing us with both abundances and gas temperatures.</text>
<text><location><page_17><loc_8><loc_7><loc_48><loc_10></location>However, there is another aspect, apart from the radiation transfer, that may affect our conclusions. This aspect is re-</text>
<text><location><page_17><loc_52><loc_52><loc_92><loc_56></location>lated to possible evolutionary changes. As in ANDES we use time-dependent chemistry, we can provisionally estimate its importance.</text>
<section_header_level_1><location><page_17><loc_56><loc_50><loc_88><loc_52></location>4.2. Disk structure with time-dependent chemistry</section_header_level_1>
<text><location><page_17><loc_52><loc_32><loc_92><loc_50></location>In order to demonstrate the effect of time-dependent chemistry on the disk chemical structure we perform model calculations with abundances of major molecular coolants at 10 4 , 10 5 , and 2 × 10 6 years. We assume that the disk chemically evolves from mostly neutral atomic gas, with molecular hydrogen and a low fraction of atomic hydrogen (10 -3 to the total number of hydrogen nuclei). We do not consider the time evolution of dust grain distribution in order to focus on effects of chemical evolution, and utilize vertical dust distribution after 2 Myr. Results are presented in Figure 16, showing the relative abundances of H2, H, CO, C, and C + as a function of height at the distinct epochs for disk radii of 10, 100 and 550 AU.</text>
<text><location><page_17><loc_52><loc_18><loc_92><loc_32></location>As can be clearly seen, the location of the H2/H transition shifts toward the midplane with time for all the considered radii due to slow photodissociation of molecular hydrogen, self-shielded from the strong FUV stellar radiation. H2 cannot be quickly re-formed in this region in Model Ev due to overall lack of grains, providing catalytic surface for H + H reaction. Consequently, between 10 4 and 210 6 years, at radii of 10, 100, and 550 AU, the PDR zone shifts from 1.6 to ≈ 1 . 4 AU, from 31 to 22 AU, and from 425 till 290 AU, respectively. This effect is more pronounced in the outer disk, where densities and density gradient are lower.</text>
<text><location><page_17><loc_52><loc_7><loc_92><loc_17></location>An interesting feature of the chemical structure in Model Ev is the presence of a 'dip' in H2 vertical distribution at the final time moment at all radii. This region with depression in H2 concentration is caused by its slow X-ray/UV destruction, which cannot be compensated by the H2 surface production on a few remaining grains. However, just above this depression region dust-to-gas ratio locally increases, and so does the available surface for hydrogen recombination (per</text>
<text><location><page_18><loc_8><loc_88><loc_48><loc_92></location>unit gas volume). The reason for the elevated dust-to-gas ratio is a gas redistribution from the top of the coupling region to greater heights due to extra heating.</text>
<text><location><page_18><loc_8><loc_62><loc_48><loc_88></location>In contrast, the evolution of ionized carbon reaches a chemical steady-state rapidly everywhere in the disk thanks to its fast ion-molecule chemistry pathways, so the C + concentration is not time-sensitive (after 10 4 years), see Figure 16. The chemical evolution of C + is governed by a simple and limited gas-phase reaction network in the disk atmosphere, where it is an important coolant with a relative abundance of ≈ 10 -4 (see, e.g. Semenov et al. 2004; Semenov & Wiebe 2011). Neutral atomic carbon shows little time evolution, if any, in the disk regions adjacent to the midplane at radii smaller than ∼ 100 AU. Due to relatively large densities in disk equatorial regions, neutral carbon is rapidly converted to CO and hydrocarbons. This is not true for lower-density outer disk regions, at R /greaterorsimilar 500 AU and z / R ∼ 0 . 3 -0 . 6, where the C abundance changes substantially with time. Since initially all elemental carbon is in the atomic form, in the outer disk, less dense and more transparent to the interstellar FUV radiation, conversion of C into CO and hydrocarbonstakes more than 10 4 years (see Figure 16, bottom row).</text>
<text><location><page_18><loc_8><loc_37><loc_48><loc_62></location>The gas-phase CO abundances follow the pattern of H2/H and C and do not reach a steady-state within 2 Myr everywhere in the disk model with evolved dust. The grain growth increases the CO freeze-out timescale to /greaterorsimilar 1 Myr in the inner and intermediate radii (Figure 16, top and middle rows). In the midplane, where gas-phase CO abundance is low, this molecule is present as CO ice. The final distribution of the CO abundance at R /lessorsimilar 100 AU shows an interesting feature: due to severe grain growth CO freeze-out is inefficient in the midplane, but still effective at disk heights of z / R ≈ 0 . 2 AU. At even larger heights the CO molecular layer starts, so CO emission lines are excited both in the very cold and warm regions. Since 12 CO, 13 CO and C 18 O isotopologue lines, having vastly different opacities, allow probing these two temperature zones, this should be visible with modern radiointerferometers. Intriguingly, evidence for the presence of very cold CO gas was found by Dartois et al. (2003), and, later, for other molecules like HCO + , CCH, CN, and HCN (see discussion in Semenov & Wiebe 2011).</text>
<text><location><page_18><loc_8><loc_16><loc_48><loc_37></location>Enhanced amounts of H2 at 10 4 years in disk regions with high FUV radiation intensities lead to additional heating by the UV-excited H2. Since the H2/H boundary is moving down, the gas thermal structure of the disk responds accordingly and also shows strong variations of T g in a narrow disk layer, in particular, at R > 100 AU (see Figure 17). While the gas temperature varies from 250 K to ≈ 200 K (25%) at R = 10 AU, at the outer disk region, R = 550 AU, the gas temperature difference at various times is about 250 K (from 320 K to ≈ 75 K, or a factor of 4), compare top and bottom panels of Figure 17. Naturally, it should also have a strong impact on chemical composition and appearance of the disk molecular layer, from which most of line emission emerges. More importantly, it demonstrates the importance of using the time-dependent chemistry for calculating abundances of key gaseous coolant instead of the commonly applied steady-state approach.</text>
<section_header_level_1><location><page_18><loc_22><loc_13><loc_35><loc_14></location>5. CONCLUSIONS</section_header_level_1>
<text><location><page_18><loc_8><loc_7><loc_48><loc_12></location>A multi-dimensional self-consistent model of protoplanetary disks 'ANDES' is introduced and described. The purpose of ANDES is to provide researchers with a state-of-the-art, most up-to-date detailed thermo-chemical model of a proto-</text>
<text><location><page_18><loc_52><loc_85><loc_92><loc_92></location>planetary disk that can be used to analyze high-quality IR and (sub-)millimeter observations of individual nearby disks. For the first time grain evolution and large-scale time-dependent molecular chemistry are included in modeling of physical structure of protoplanetary disks.</text>
<text><location><page_18><loc_52><loc_73><loc_92><loc_85></location>The iterative ANDES code is based on a flexible modular structure that includes 1) a 1+1D continuum radiative transfer module to calculate dust temperature, 2) a module to calculate gas-grain chemical evolution, 3) a 1+1D module to calculate detailed gas energy balance, and 4) a 1+1D module that calculates dust grain evolution. The disk structure is computed iteratively, assuming fixed dust density structure after the first iteration. Typically it takes ∼ 10 iterations to reach convergence at 1% level of accuracy.</text>
<text><location><page_18><loc_52><loc_59><loc_92><loc_73></location>The continuum radiative transfer module is based on the two-stream Feautrier method with a high-resolution frequency grid. We consider dust continuum absorption, thermal emission, and coherent isotropic scattering. The dust evolution is modeled by accounting for coagulation, fragmentation, and gravitational sedimentation towards the disk midplane balanced by turbulent upward stirring. The chemical model is based on a gas-grain realization of the RATE'06 network, and includes surface reactions and X-ray/UV processes. All modules have been thoroughly benchmarked with previous studies, with overall good agreement and performance.</text>
<text><location><page_18><loc_52><loc_44><loc_92><loc_58></location>We study the impact of dust evolution on dust temperature, gas temperature, and chemical composition by comparing results of the disk models with evolved and pristine dust. We compute gas thermal structure corresponding to chemical abundances evolving from the initial abundances for 10 4 , 10 5 , and 2 · 10 6 years. We show that time-dependent chemistry is important for a proper description of gas thermal balance. The strongest impact on the gas temperature (up to 100 K) occurs in the outer, low-density region beyond 100 AU. This is mainly due to the shift of H2/H PDR transition deeper into the disk with time.</text>
<text><location><page_18><loc_52><loc_28><loc_92><loc_44></location>In accordance with previous studies, it is found that the gas becomes hotter than the dust in elevated disk regions reaching 1000-10000 K in the inner atmosphere. However, the main heating source is different for the two dust models. In the disk with pristine dust it is photoelectric heating by grains. In the atmosphere of disk with evolved dust grains are strongly depleted, therefore photoelectric heating by PAHs becomes a dominant heating process. Thus a realistic, observationallybased estimates of absolute PAH abundances and sizes are required to calculate accurately gas temperature in the inner, ∼ 1 -50 AU disk atmosphere accessible with Spitzer, Herschel, and ALMA.</text>
<text><location><page_18><loc_52><loc_8><loc_92><loc_28></location>The response of disk chemical structure to the dust growth and sedimentation is twofold. First, due to higher transparency a partly UV-shielded molecular layer is shifted closer to the dense midplane. Second, the presence of big grains in the disk midplane delays the freeze-out of volatile gas-phase species such as CO there, while in adjacent upper layers the depletion is still effective. Even though the dust evolution shifts the molecular layer of the water vapor closer toward the cooler, midplane disk region, it increases its overall concentration. This aggravates the disagreement between the water vapor column densities predicted by modern astrochemical models, which are higher than those observed with Herschel in the disks around TW Hya (Hogerheijde et al. 2011) and DM Tau (Bergin et al. 2010) by factors of at least several (see also discussion in Semenov & Wiebe (2011)). Overall,</text>
<figure>
<location><page_19><loc_10><loc_71><loc_46><loc_92></location>
</figure>
<figure>
<location><page_19><loc_49><loc_71><loc_85><loc_91></location>
</figure>
<text><location><page_19><loc_28><loc_69><loc_32><loc_70></location>R=100 AU</text>
<figure>
<location><page_19><loc_10><loc_50><loc_46><loc_69></location>
</figure>
<text><location><page_19><loc_28><loc_48><loc_32><loc_49></location>R=550 AU</text>
<figure>
<location><page_19><loc_10><loc_29><loc_47><loc_48></location>
</figure>
<text><location><page_19><loc_67><loc_69><loc_72><loc_70></location>R=100 AU</text>
<figure>
<location><page_19><loc_49><loc_50><loc_85><loc_69></location>
</figure>
<text><location><page_19><loc_67><loc_48><loc_72><loc_49></location>R=550 AU</text>
<figure>
<location><page_19><loc_49><loc_29><loc_86><loc_48></location>
<caption>Figure 16. The left panels show H2 /H transition at selected radii calculated for different epochs: 10 4 , 10 5 , and 2 · 10 6 yrs for the disk with evolved dust. The right panels show the CO/C/C + transition.</caption>
</figure>
<text><location><page_19><loc_8><loc_21><loc_48><loc_24></location>molecular concentrations and thus column densities of many species are enhanced in the disk model with dust evolution, e.g., CO2, NH2CN, HNO, H2O, HCOOH, HCN, CO.</text>
<section_header_level_1><location><page_19><loc_19><loc_18><loc_37><loc_19></location>ACKNOWLEDGEMENTS</section_header_level_1>
<text><location><page_19><loc_8><loc_7><loc_48><loc_17></location>This research made use of NASA's Astrophysics Data System. This work is supported by the RFBR grants 1002-00612, 12-02-31248, Federal Targeted Program 'Scientific resources of Innovation-Driven Russia' for 2009-2013 and NSh-3602.2012.2. SZ is supported by the Deutsche Forschungsgemeinschaft through SPP 1573: 'Physics of the Interstellar Medium". DS acknowledges support by the Deutsche Forschungsgemeinschaft through SPP 1385: 'The</text>
<text><location><page_19><loc_52><loc_14><loc_92><loc_24></location>first ten million years of the solar system - a planetary materials approach' (SE 1962/1-1 and 1-2). A. V. acknowledges the support of the National Science Foundation (US) for the astrochemistry program at the University of Virginia. We thank Kees Dullemond, Andras Zsom, Ewine F. van Dishoeck and Simon Bruderer for valuable discussions. We highly appreciate comments and suggestions of an anonymous referee, that helped us a lot to improve the quality of the paper.</text>
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<location><page_20><loc_10><loc_27><loc_47><loc_46></location>
<caption>Figure 17. Gas temperature profiles at selected radii (10, 100, 550 AU from top to bottom) calculated with chemical abundances at different epochs: 10 4 , 10 5 , and 2 · 10 6 yrs.</caption>
</figure>
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<text><location><page_21><loc_53><loc_28><loc_62><loc_29></location>A&A, 466, 1197</text>
<text><location><page_21><loc_52><loc_27><loc_79><loc_28></location>Youdin, A. N. & Lithwick, Y. 2007, Icarus, 192, 588</text>
<text><location><page_22><loc_8><loc_86><loc_92><loc_92></location>where k UV abs is the dust absorption coefficient at UV wavelengths, χ is the strength of the UV radiation field in units of the Draine FUV interstellar field (Draine 1978), and /epsilon1 dust is the photoelectric efficiency determined by the grain charge parameter x = √ T g χ/ n e (here n e is the electron number density). For /epsilon1 we adopt expressions from Kamp & van Zadelhoff (2001). The relative strength of the FUV, χ , is defined as</text>
<formula><location><page_22><loc_43><loc_81><loc_92><loc_86></location>χ = ∫ 110nm 91 . 2nm λ u λ d λ ∫ 110nm 91 . 2nm λ u Draine λ d λ . (A2)</formula>
<text><location><page_22><loc_8><loc_79><loc_92><loc_81></location>The average dust opacity at UV wavelengths is determined by integration of frequency-dependent dust absorption cross-sections in the UV frequency range</text>
<formula><location><page_22><loc_38><loc_75><loc_92><loc_78></location>k UV abs = 1 ∆ ν ∫ ∫ f ( a ) π a 2 Q abs( a ) dad ν, (A3)</formula>
<text><location><page_22><loc_8><loc_73><loc_40><loc_75></location>where f ( a ) is given by the dust evolution model.</text>
<text><location><page_22><loc_8><loc_66><loc_92><loc_72></location>PHOTOELECTRIC HEATING BY PAHS Polycyclic aromatic hydrocarbons (PAHs) possess large cross-sections for UV photon absorption and therefore can efficiently heat gas by photoelectric emission, even if their abundance is low. Heating by PAHs can be particularly important for disks with evolved dust, since PAHs are better mixed with gas than macroscopic dust particles, and thus remain in the disk atmosphere while bigger grains settle towards the midplane (Dullemond et al. 2007a). Bakes & Tielens (1994) derived a simple analytical expression for their PE heating rate:</text>
<formula><location><page_22><loc_41><loc_63><loc_92><loc_65></location>Γ PAH PE = 10 -24 f PAH n H /epsilon1 PAH χ, (A4)</formula>
<text><location><page_22><loc_8><loc_50><loc_92><loc_63></location>where n H is the hydrogen nuclei number density, and /epsilon1 PAH = 0 . 0487 / (1 + 4 × 10 -3 x 0 . 73 ). The parameter f PAH is the depletion factor of the PAH abundance relative to the diffuse ISM value, which is estimated to be ∼ 10 -20% of the total carbon budget (Draine & Li 2007). The details of the evolution of PAHs in protoplanetary disks are far from being fully understood, though it is clear that high-energy stellar radiation may play an enormous role in their destruction and chemical transformation (Acke et al. 2010; Siebenmorgen & Krügel 2010; Siebenmorgen & Heymann 2012). Therefore, we do not consider PAHs in the simulations of dust evolution and treat f PAH as a free parameter of the model. In the present paper we assume f PAH = 0 . 1 based on estimates from observations of PAH spectra in disks surrounding young T Tauri and Herbig Ae stars (Keller et al. 2008; Kamp 2011). A detailed study of the effects of PAHs heating on the structure of protoplanetary disks with evolved dust is beyond the scope of the present paper.</text>
<text><location><page_22><loc_8><loc_47><loc_92><loc_49></location>COSMIC RAY HEATING Cosmic ray (CR) particles deposit energy mainly through ionization of H2 and H at the rate (Bakes & Tielens 1994):</text>
<formula><location><page_22><loc_34><loc_43><loc_92><loc_47></location>Γ CR = ζ CR ( 5 . 5 × 10 -12 n (H) + 2 . 5 × 10 -11 n (H2) ) , (A5)</formula>
<text><location><page_22><loc_8><loc_43><loc_72><loc_44></location>where ζ CR s -1 is the attenuated CR ionization rate and n (X) denotes concentration of a species X.</text>
<text><location><page_22><loc_8><loc_35><loc_92><loc_41></location>HEATING BY SURFACE H 2 FORMATION Formation of one H2 molecule on the grain surface liberates 4.48 eV of energy, but the exact partitioning of this energy into H2 vibration, rotation, translation and accommodation by a grain lattice remains uncertain. It is commonly assumed that this energy is equally redistributed between rotational, vibrational and translational movements. We assume that formation of one hydrogen molecule returns only 1.5 eV (2 . 4 × 10 -12 erg) to the gas (Black & Dalgarno 1976). Then, the corresponding heating rate is</text>
<formula><location><page_22><loc_40><loc_33><loc_92><loc_35></location>Γ H2form = 2 . 4 × 10 -12 R H2form n H , (A6)</formula>
<text><location><page_22><loc_8><loc_29><loc_92><loc_32></location>where R H2form is the H2 formation rate in s -1 . The further details of calculation of chemical reactions rates are described in Sect. 2.3.</text>
<text><location><page_22><loc_8><loc_24><loc_92><loc_29></location>PHOTODISSOCIATION OF H 2 We take into account only spontaneous radiative dissociation of H2 : H2 + h ν → H2 ∗ → H + H + h ν . Assuming that the average kinetic energy of dissociation products is 0.45 eV (Stephens & Dalgarno 1973), the corresponding heating rate is</text>
<formula><location><page_22><loc_39><loc_23><loc_92><loc_24></location>Γ H2dis = 6 . 4 × 10 -13 R H2 phdis n (H2) , (A7)</formula>
<text><location><page_22><loc_8><loc_19><loc_92><loc_22></location>where R H2 phdis is the photodissociation rate of H2 . To calculate this rate, we take into account self-shielding of H2 molecules as given by Eq.(37) from Draine & Bertoldi (1996).</text>
<text><location><page_22><loc_8><loc_13><loc_92><loc_18></location>COLLISIONAL DE-EXCITATION OF H 2 In dense PDR regions collisional de-excitation of FUV-pumped H ∗ 2 is the second most important heating mechanism (Sternberg & Dalgarno 1995). Here we adopt a simple two-level approximation of H2vibrational heating and cooling from Röllig et al. (2006), which nevertheless well reproduces the net heating rate computed by Sternberg & Dalgarno (1995) with 15 vibrational levels. The net vibrational heating is given by the following expression:</text>
<formula><location><page_22><loc_45><loc_10><loc_92><loc_12></location>Γ net = Γ H ∗ 2 -Λ H2 , (A8)</formula>
<text><location><page_22><loc_8><loc_7><loc_92><loc_10></location>where Γ H ∗ 2 is the vibrational heating rate by collisional de-excitation and Λ H2 is the vibrational cooling rate. For details of the calculation of the heating and cooling rates we refer to the Appendix C in Röllig et al. (2006).</text>
<text><location><page_23><loc_8><loc_89><loc_92><loc_92></location>C photoionization - Ionization of atomic carbon releases electrons with kinetic energies of ∼ 1 eV (Black 1987). The corresponding heating rate can be approximated as:</text>
<formula><location><page_23><loc_41><loc_87><loc_92><loc_89></location>Γ C = 1 . 6 × 10 -12 R Cph n (C) , (A9)</formula>
<text><location><page_23><loc_8><loc_85><loc_43><loc_86></location>where R Cph is the photoionization rate of the C atoms.</text>
<text><location><page_23><loc_9><loc_82><loc_57><loc_83></location>Viscous heating - The viscous heating rate is given by (Frank et al. 1992):</text>
<formula><location><page_23><loc_44><loc_78><loc_92><loc_81></location>Γ vis = 9 4 ρν kin Ω 2 kep , (A10)</formula>
<text><location><page_23><loc_8><loc_75><loc_92><loc_78></location>where the kinematic viscosity of the gas is parameterized as ν kin = α cT H g (Shakura & Sunyaev 1973), cT is the isothermal sound speed, Hg is the gas pressure scale height, and Ω kep is the Keplerian velocity.</text>
<section_header_level_1><location><page_23><loc_41><loc_73><loc_60><loc_74></location>A.2. Main cooling processes</section_header_level_1>
<text><location><page_23><loc_8><loc_65><loc_92><loc_72></location>NLTE LINE COOLING The net line cooling rate for a given species is determined by the total amount of upwards and downwards radiative transitions. Level populations for each coolant are calculated from statistical equilibrium equations. Unlike FUV, the local FIR intensity that enters these equations depends on the temperature and level populations over the large part of the disk. This requires iterations over all vertical grid points simultaneously. To simplify a calculation, we adopt an escape probability approach using the expression (B9) in Tielens & Hollenbach (1985).</text>
<text><location><page_23><loc_8><loc_59><loc_92><loc_66></location>We perform the full non-LTE calculations, considering the major coolants for a typical PDR: fine structure lines of C, O, C + and rotational lines for the CO molecule. The data for energy levels, collision, emission and absorption coefficients for computation of the NLTE line cooling are taken from the LAMDA database (Schöier et al. 2005). The data include collision rate coefficients for collisions of H2 , H, e -, He, and H + with O and C atoms, as well as collisions of H2 , H, and e -with C + , and H2 with CO. For minor coolants we use approximate formulas presented below.</text>
<text><location><page_23><loc_8><loc_54><loc_92><loc_58></location>HIGH-TEMPERATURE COOLANTS The cooling by emission from metastable levels of neutral and ionic species becomes important at temperatures exceeding several thousand Kelvin. We calculate the cooling rate from 1 D -3 P emission by O I (630 nm) according to Sternberg & Dalgarno (1989):</text>
<formula><location><page_23><loc_35><loc_51><loc_92><loc_53></location>Λ OI630 = 1 . 8 × 10 -24 n (O) n e exp( -22800 / T g) , (A11)</formula>
<text><location><page_23><loc_8><loc_49><loc_38><loc_50></location>where n O is the neutral oxygen concentration.</text>
<text><location><page_23><loc_8><loc_46><loc_92><loc_49></location>The cooling by electron impact excitation of metastable levels of ionic species (e.g., Fe + , Fe ++ , Si + ) is calculated by approximate formula from Dalgarno & McCray (1972):</text>
<formula><location><page_23><loc_40><loc_45><loc_92><loc_46></location>Λ ion( T ) = AiT -1 / 2 g exp( -Ti / T g) , (A12)</formula>
<text><location><page_23><loc_8><loc_42><loc_61><loc_44></location>where parameters Ai and Ti for each ion are given in Dalgarno & McCray (1972).</text>
<text><location><page_23><loc_8><loc_40><loc_92><loc_42></location>Another important cooling process at high temperatures is Ly α emission. We adopt the cooling rate by Ly α emission from Spitzer (1978):</text>
<formula><location><page_23><loc_36><loc_38><loc_92><loc_40></location>Λ Ly α = 7 . 3 × 10 -19 n e n (H)exp( -118400 / T g) . (A13)</formula>
<text><location><page_23><loc_8><loc_33><loc_92><loc_37></location>H 2 O LINE EMISSION Rotational line emission of the H2O molecule can contribute to cooling in dense disk regions. We include line cooling rates of H2O due to the excitation by H2 , using analytical fits from Neufeld & Kaufman (1993) for T > 100 K and from Neufeld et al. (1995) for 10 K < T < 100 K.</text>
<text><location><page_23><loc_8><loc_27><loc_92><loc_32></location>THERMAL ACCOMMODATION Thermal accommodation is the energy exchange by inelastic collisions between dust and gas. In disk models with standard ISM-like dust it is a dominant cooling process, with the exception of the upper, tenuous atmosphere and outer radii ( R > 400 AU) (e.g., Woitke et al. 2009). We utilize the corresponding cooling rate from Burke & Hollenbach (1983):</text>
<formula><location><page_23><loc_36><loc_23><loc_92><loc_27></location>Λ d -g = 4 × 10 -12 π 〈 a 2 〉 ndn H α T √ T g( T g -T d) , (A14)</formula>
<text><location><page_23><loc_8><loc_23><loc_76><loc_24></location>where the thermal accommodation coefficient α T is set to 0.3 ( a typical value for silicates and carbon).</text>
<section_header_level_1><location><page_23><loc_20><loc_20><loc_81><loc_22></location>B. RADIATIVE TRANSFER AND GAS THERMAL BALANCE BENCHMARKING</section_header_level_1>
<text><location><page_23><loc_10><loc_18><loc_90><loc_20></location>The RT module of the ANDES code was checked for the following cases which allow an analytic or semi-analytic solution:</text>
<unordered_list>
<list_item><location><page_23><loc_11><loc_12><loc_92><loc_17></location>· Optically thin case, zero non-radiative heating source (A14), arbitrary incident radiation. In this case the mean intensity in the media is equal to the incident one and temperature may be derived from (3) and it is the same for every position in media. Tests show an equality of temperatures which are derived by our RT code and by independent numerical solution of the energy balance equation (3).</list_item>
<list_item><location><page_23><loc_11><loc_7><loc_92><loc_11></location>· Arbitrary media (optically thick, non-gray opacities) with the non-diluted Planck incident radiation. In this case the media becomes isothermal with temperature of radiation. Test show an equality of temperatures and radiation field derived from analytical and numerical solutions.</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_24><loc_11><loc_87><loc_92><loc_92></location>· Optically thick media with gray opacities, arbitrary incident radiation and non-radiative dust heating function which is proportional to dust density and has no other z -dependence. In this case the system of Equations (1)-(3) narrow down to the second order linear ODE and may be solved analytically. A comparison of the analytical and numerical solutions is presented in Figure 18. The mean intensity parabolic profile is shown in the inset graph as well.</list_item>
</unordered_list>
<figure>
<location><page_24><loc_33><loc_65><loc_67><loc_84></location>
<caption>Figure 18. Computed and analytical temperatures and mean intensities for a test case.</caption>
</figure>
<figure>
<location><page_24><loc_14><loc_37><loc_52><loc_58></location>
<caption>Figure 19. Left panel. Comparison of H2, H, H + density profiles calculated by our code (solid red line) with post-benchmark results from Röllig et al. (2007) (code markings are the same as in Figure 20) for benchmark model V4 ( n = 10 5 . 5 cm -3 , χ = 10 5 ). Right panel. The same for C, C + , CO density profiles.</caption>
</figure>
<text><location><page_24><loc_35><loc_36><loc_36><loc_37></location>v</text>
<text><location><page_24><loc_53><loc_57><loc_55><loc_58></location>1e-02</text>
<text><location><page_24><loc_53><loc_56><loc_55><loc_57></location>1e-04</text>
<text><location><page_24><loc_53><loc_55><loc_55><loc_55></location>1e-06</text>
<text><location><page_24><loc_53><loc_54><loc_55><loc_54></location>1e-08</text>
<text><location><page_24><loc_53><loc_52><loc_55><loc_53></location>1e-10</text>
<text><location><page_24><loc_53><loc_51><loc_55><loc_51></location>1e-02</text>
<text><location><page_24><loc_53><loc_49><loc_55><loc_50></location>1e-04</text>
<text><location><page_24><loc_53><loc_48><loc_55><loc_49></location>1e-06</text>
<text><location><page_24><loc_53><loc_47><loc_55><loc_48></location>1e-08</text>
<text><location><page_24><loc_53><loc_46><loc_55><loc_47></location>1e-10</text>
<text><location><page_24><loc_53><loc_44><loc_55><loc_45></location>1e-02</text>
<text><location><page_24><loc_53><loc_43><loc_55><loc_44></location>1e-04</text>
<text><location><page_24><loc_53><loc_42><loc_55><loc_42></location>1e-06</text>
<text><location><page_24><loc_53><loc_41><loc_55><loc_41></location>1e-08</text>
<text><location><page_24><loc_53><loc_39><loc_55><loc_40></location>1e-10</text>
<text><location><page_24><loc_55><loc_38><loc_57><loc_38></location>0.001</text>
<text><location><page_24><loc_62><loc_38><loc_64><loc_38></location>0.01</text>
<text><location><page_24><loc_70><loc_38><loc_71><loc_38></location>0.1</text>
<text><location><page_24><loc_78><loc_38><loc_78><loc_38></location>1</text>
<text><location><page_24><loc_85><loc_38><loc_86><loc_38></location>10</text>
<text><location><page_24><loc_71><loc_37><loc_72><loc_37></location>A</text>
<text><location><page_24><loc_72><loc_36><loc_72><loc_37></location>V</text>
<text><location><page_24><loc_8><loc_25><loc_92><loc_32></location>The surface of the disk is a photodissociation region (PDR) controlled by UV radiation from a star and interstellar radiation field. Therefore, we perform benchmarking of the thermal balance in our code as proposed in the PDR code comparison study (Röllig et al. 2007). For benchmarking purposes we use a reduced chemical network restricted to the most abundant elements (H, He, O, C, e -) and 31 species(Table 4 in Röllig et al. 2007). The reaction rates are taken from the UMIST99 database with some corrections from A. Sternberg. H2 dissociation rate is 5 × 10 -18 χ/ 10s -1 . Cosmic ray H ionization rate is ζ = 5 × 10 -17 s -1 . For more details of benchmark test we refer to Röllig et al. (2007).</text>
<text><location><page_24><loc_8><loc_15><loc_92><loc_24></location>All benchmark models assume plane-parallel, semi-infinite geometry of clouds of total constant hydrogen density of 10 3 and 10 5 . 5 cm -3 . The values of the standard far UV field were taken as χ = 10 and 10 5 times the Draine (1978) field. There are two sets of benchmark models: four with fixed dust and gas temperatures of 30 and 50 K, respectively, and the other set of four models with the gas temperature resulting from thermal balance. The first set of models with fixed temperature aims at testing main ingredients of the thermal balance: solutions of chemistry and statistical equilibrium equations for level populations of main coolants, while the second set examines solution of thermal balance. Here we present results of benchmark tests for both kinds of models with density n tot H = 10 5 . 5 cm -3 and far UV field strength χ = 10 5 (models F4 and V4 in Röllig et al. (2007)).</text>
<text><location><page_24><loc_8><loc_12><loc_92><loc_15></location>The left panel of Figure 19 shows comparison of our calculations with post-benchmark results for the H/H2 transition zone typical for PDR environment. Right panel of Figure 19 shows the C + /CO/C transition zone.</text>
<text><location><page_24><loc_8><loc_7><loc_92><loc_12></location>Main heating and cooling rates included in benchmarking are shown in the left panel of Figure 20. Gas-grain cooling and [OI] 63 µ mline are the dominant cooling processes for AV < 0 . 5. CO lines dominate cooling at high attenuated regions. Our line cooling rates show remarkable agreement with data from Röllig et al. (2007) for dominant cooling processes: [CII] 158 µ m, [OI] 63, 145 µ m, [CI] 370, 610 µ mlines. Comparison of our model results for gas temperature in the slab with other PDR codes is</text>
<text><location><page_24><loc_51><loc_55><loc_52><loc_56></location>H</text>
<text><location><page_24><loc_51><loc_54><loc_52><loc_55></location>el</text>
<text><location><page_24><loc_51><loc_49><loc_52><loc_49></location>H</text>
<text><location><page_24><loc_51><loc_48><loc_52><loc_48></location>el</text>
<text><location><page_24><loc_51><loc_42><loc_52><loc_43></location>H</text>
<text><location><page_24><loc_51><loc_41><loc_52><loc_42></location>el</text>
<text><location><page_24><loc_59><loc_56><loc_61><loc_57></location>CO</text>
<text><location><page_24><loc_59><loc_50><loc_60><loc_51></location>C</text>
<text><location><page_24><loc_60><loc_41><loc_60><loc_42></location>+</text>
<text><location><page_24><loc_59><loc_41><loc_60><loc_42></location>C</text>
<figure>
<location><page_25><loc_9><loc_70><loc_48><loc_91></location>
</figure>
<figure>
<location><page_25><loc_51><loc_70><loc_86><loc_91></location>
<caption>Figure 20. Left panel. Comparison of gas temperature calculated by our code (red solid curve) with post-benchmark results from different PDR codes from Röllig et al. (2007). Thick magenta dashed line marks average gas temperature from the benchmarking data. Right panel. Main heating and cooling processes included in our code for the benchmark model V4.</caption>
</figure>
<text><location><page_25><loc_8><loc_61><loc_92><loc_64></location>shown in Figure 20. At small AV the gas temperature is much higher than the dust temperature due to photoelectric heating and agrees well with other PDR codes.</text>
</document>
[
{
"title": "ABSTRACT",
"content": "We present a self-consistent model of a protoplanetary disk: 'ANDES' ('AccretioN disk with Dust Evolution and Sedimentation'). ANDES is based on a flexible and extendable modular structure that includes 1) a 1+1D frequency-dependent continuum radiative transfer module, 2) a module to calculate the chemical evolution using an extended gas-grain network with UV/X-ray-driven processes surface reactions, 3) a module to calculate the gas thermal energy balance, and 4) a 1+1D module that simulates dust grain evolution. For the first time, grain evolution and time-dependent molecular chemistry are included in a protoplanetary disk model. We find that grain growth and sedimentation of large grains to the disk midplane lead to a dust-depleted atmosphere. Consequently, dust and gas temperatures become higher in the inner disk ( R /lessorsimilar 50 AU) and lower in the outer disk ( R /greaterorsimilar 50 AU), in comparison with the disk model with pristine dust. The response of disk chemical structure to the dust growth and sedimentation is twofold. First, due to higher transparency a partly UV-shielded molecular layer is shifted closer to the dense midplane. Second, the presence of big grains in the disk midplane delays the freeze-out of volatile gas-phase species such as CO there, while in adjacent upper layers the depletion is still effective. Molecular concentrations and thus column densities of many species are enhanced in the disk model with dust evolution, e.g., CO2, NH2CN, HNO, H2O, HCOOH, HCN, CO. We also show that time-dependent chemistry is important for a proper description of gas thermal balance. accretion, accretion disks - circumstellar matter - stars: formation - stars: pre-main-sequence, Keywords: astrochemistry",
"pages": [
1
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},
{
"title": "PROTOPLANETARY DISK STRUCTURE WITH GRAIN EVOLUTION: THE ANDES MODEL",
"content": "V. AKIMKIN 1 , S. ZHUKOVSKA 2 , D. WIEBE 1 , D. SEMENOV 2 , YA. PAVLYUCHENKOV 1 , A. VASYUNIN 3 , T. BIRNSTIEL 4 , TH. HENNING 2 1 Institute of Astronomy of the RAS, Pyatnitskaya str. 48, Moscow, Russia 2 Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany 3 Department of Chemistry, the University of Virginia, USA and 4 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA Excellence Cluster Universe, Technische Universität München, Boltzmannstr. 2, 85748 Garching, Germany Accepted for publication in ApJ, Feb 1, 2013",
"pages": [
1
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},
{
"title": "1. INTRODUCTION",
"content": "The planet formation and, in particular, the origin of the Solar System are among the most fascinating astrophysical problems that are far from being fully understood. The quickly growing number of detected exoplanets hints to ubiquitous planet formation in our Galaxy. Space-born facilities (e.g., Hubble, Spitzer, Herschel ) as well as ground-based observatories (e.g., VLT, Keck, Subaru, PdBI, IRAM 30-m, SMA, early ALMA) provide unique information on the appearance, structure, chemical composition, and evolution of nearby protoplanetary disks (e.g., Dutrey et al. 1997; Fukagawa et al. 2004; Andrews & Williams 2005; Hernández et al. 2007; Natta et al. 2007; Semenov et al. 2010; Sturm et al. 2010; Muto et al. 2012). Relatively compact sizes of ∼ 100 -1000 AU and low masses of ∼ 0 . 01 M /circledot make disks a challenging target for observational studies. Another obstacle to investigate the formation of planets is an enormous range of physical conditions encountered in a protoplanetary disk and a wide variety of interrelated processes (e.g., Williams & Cieza 2011). The combined action of these processes defines the appearance of the disk in scattered light, dust continuum, and atomic and molecular lines. Modeling of continuum and line radiation implies knowing stellar spectrum, dust density, dust temperature, and size distribution as well as gas density, gas temperature, and molecular content throughout the disk, and in full 3D. If all this information is available, a multi-dimensional radiation transfer (RT) model can be used to build a synthetic disk map at any wavelength (e.g., Whitney & Hartmann 1992; Men'shchikov & Henning 1997; Wolf et al. 1999; Dullemond et al. 2002). Due to computational difficulties to follow global disk evolution in 3DMHD, particularly, coupled with chemical kinetics models, and the lack of necessary constraints related to the magnetic field structure, turbulence, grain size distribution, etc., a disk model needs to be simplified. One can steadily approach the warranted level of physical complexity by adding new components to the model (e.g., going from 1D to 2D geometry or from gray to non-gray radiative transfer) and comparing with observations at each development step. Anumberof disk models has been developed over time (see review in Dullemond et al. 2007b). These models have been based on an RT-based disk structure (either 1D, 1+1D/2D, or 3D), molecular abundances, and dust and gas thermal balance. Disk models with detailed vertical structure and thermal balance regulated solely by dust heating and cooling, and, in some cases, accretion heating, have been developed by, e.g., Bell et al. (1997); Chiang & Goldreich (1997); Men'shchikov & Henning (1997); Dullemond & Dominik (2004); Hueso & Guillot (2005). It has been typically assumed in such studies that the dust is well mixed with the gas, and its properties do not differ from properties of the ISM dust. One of the most widely used models of this kind has been developed by D'Alessio et al. (1998, 1999). It has been extensively used in many subsequent studies as a template of the disk density and temperature distribution (e.g., Chiang et al. 2001; Semenov et al. 2004; Furlan et al. 2006). Other similar models, utilizing more accurate frequencydependent RT algorithms or other improvements (e.g., a full 2D geometry, evolving disk structure, more realistic dust opacities) have been presented by Malbet et al. (2001); Dullemond (2002); Nomura (2002); Gorti et al. (2009), to name a few. An important development of the protoplanetary disk models was to account for the energy balance of dust and gas separately in dilute disk regions. There the rate of gasdust collisions drops so low that the gas becomes thermally decoupled from the dust (e.g., Jonkheid et al. 2004; Kamp & Dullemond 2004; Gorti & Hollenbach 2008). The most recent and most advanced addition to this family, the 'ProDiMo' model, is presented by Woitke et al. (2009) and updated in Thi et al. (2011) and Aresu et al. (2011). This model is based on iterative calculations of a 1+1D vertical hydrostatic disk structure, 2D frequency-dependent dust continuum RT, gas-grain and FUV-photochemistry to calculate abundances of molecular coolants, and an escape probability method to model non-LTE heating and cooling of the gas. It is derived from thermo-chemical models of Kamp & Bertoldi (2000), Kamp & van Zadelhoff (2001), and Kamp & Dullemond (2004). Since 2011 it includes X-ray-driven chemistry and heating via H2 ionization and Coulomb heating (Aresu et al. 2011). Uniform dust abundances and power-law size distributions are typically assumed (Aresu et al. 2012), with opacities for a dust mixture calculated by Effective Medium Theory (Bruggeman 1935). Abundances of molecules are calculated assuming chemical equilibrium and element conservation, which may not be a valid approach to disk chemical evolution (e.g., Barshay & Lewis 1976; Ilgner et al. 2004; Semenov & Wiebe 2011). Recent observations at IR and mm-/cm-wavelengths have shown that many disks around young stars of ages /greaterorsimilar 1 Myr have already a deficit of of small grains in the inner regions, r /lessorsimilar 10 -50 AU and the presence of large, pebble-sized dust grains in the midplanes compared to the pristine ISM dust (e.g., Williams & Cieza 2011; Williams 2012). From the analysis of SEDs at millimeter and centimeter wavelengths, grain sizes of at least 1 cm have been inferred for many disks (e.g., Rodmann et al. 2006; Lommen et al. 2009, 2010; Ricci et al. 2010; Melis et al. 2011; Pérez et al. 2012). Guilloteau et al. (2011) have used high-resolution interferometric PdBI observations to discern dust emissivity slopes at millimeter wavelengths in a sample of young stars. Their analysis has shown that in the Taurus-Auriga star-forming region some disks show very low dust emissivity indices in the inner regions, characteristic of grains with sizes of /greaterorsimilar 1 mm, and slopes that are indicative of smaller grains toward the disk edges. In addition, Spitzer IR spectroscopy of silicate bands at 10 and 20 µ mhas revealed efficient crystallization and growth of the sub-micron-sized ISM grains in warm disk atmospheres in many young systems, regardless of their ages, accretion rates, and disk masses (e.g., Kessler-Silacci et al. 2006; Furlan et al. 2009; Juhász et al. 2010; McClure et al. 2010; Oliveira et al. 2011; Sicilia-Aguilar et al. 2011). The dust settling associated with grain growth reduces disk scale heights and flaring angles, and thus leads to less intense mid-IR disk emission than expected from conventional hydrostatic models with uniform dust, in accordance with observations of most T Tauri stars (Williams & Cieza 2011). As dust is a very important ingredient of the disk physics, evolution of its properties should also be considered in disk models. Usually both the grain growth and sedimentation are accounted for in disk models in a parameterized way, by assuming an increased upper limit of grain size a max and arti- ficially changing the dust density and the slope of dust size distribution in various disk regions. For example, expanding on their earlier works, D'Alessio et al. (2001) have studied the influence of dust evolution on the disk structure and its spectral energy distribution (SED). Grain growth has been simulated as an increase of a max up to 10 cm and change of the dust size distribution slope p from -3 . 5 to -2 . 5. In these models dust has been assumed to be well-mixed with the gas. To study the effect of dust settling, D'Alessio et al. (2006) have included two dust populations in the model, with different spatial distributions. D'Alessio et al. (2006) shown that the evolved dust model better reproduces observed millimeter fluxes and spectral slopes. A similar approach to study the effect of dust settling on the disk thermal and chemical structure has been taken by Jonkheid et al. (2004) and Fogel et al. (2011). Settling has been simulated using variable dust/gas mass ratio. A variable a max value has been used by Aikawa & Nomura (2006) to investigate changes in disk density, gas and dust temperature, and molecular abundances due to dust growth. More accurate methods to model dust growth are mainly based on solving the coagulation (Smoluchowski) equation. Here the main attribute of the model is whether the dust evolution is computed for a fixed disk structure or the dust evolution and disk structure are mutually consistent. The first approach is used, e.g., in Nomura & Nakagawa (2006); Schräpler & Henning (2004); Tanaka et al. (2005); Ciesla (2007), who used parameterized disk structure. The second approach has been used by Schmitt et al. (1997); Tanaka et al. (2005); Nomura et al. (2007); Tannirkulam et al. (2007). An efficient scheme to tackle the modeling of dust coagulation, fragmentation, sedimentation, turbulent stirring around a 'snow line' in a protoplanetary disk has been proposed by Brauer et al. (2008). They have found that major factors affecting grain evolution are trapping of dust particles in gas pressure maxima and the presence of a turbulently quiescent 'dead zone' in disk inner midplane. Birnstiel et al. (2010) have updated this model by considering time-dependent viscous evolution of a gas disk. They have found that dust properties, gas pressure gradients, and the strength of turbulence are more important factors for dust evolution than the initial conditions and the early formation phase of the protoplanetary disk. Birnstiel et al. (2011) have shown that, upon evolution, grain size distribution reaches a quasi-steady state, which however, does not follow the standard MRN-like power-law size distribution and is sensitive to the gas surface density, amount of turbulence, and disk thermal structure. The next step in protoplanetary disk modeling was made by Vasyunin et al. (2011), where detailed dust evolution was considered along with comprehensive set of gas-phase and surface chemical reactions. However, to calculate disk thermal structure, they take into account only two heating sources, namely, viscous dissipation and dust grain irradiation by the central star. It was shown that column densities of some molecules (like C2H, HC2 n + 1N ( n = 0-3), H2O and C2H2/HCN abundance ratio) can be used as observational tracers of early stages of the grain evolution in protoplanetary disks. In this paper, for the first time, we consider the influence of dust evolution on the disk structure by combining the detailed computation of the radiation field with the dust growth, fragmentation, and sedimentation model. When computing the disk density and temperature we take into account the full grain size distribution as a function of location in the disk. Gas temperature and dust temperature are computed separately, with taking into account the disk chemical structure. These two factors represent a major improvement in comparison with Vasyunin et al. (2011)'s model. Also, a new detailed RT treatment is implemented with high frequency resolution from ultraviolet to far infrared. The organization of the paper is the following. In Section 2 the disk model 'ANDES' (AccretioN Disk with Dust Evolution and Sedimentation) is described. In Section 3 we present a physical structure for a typical protoplanetary disk computed both for both pristine dust and for evolved dust. Also, the chemical structure is described in this section, and specific features of the disk chemical compositions are presented for various dust models. Discussion and conclusions follow. Details of gas energy balance processes and benchmarking results are presented in Appendix A and B.",
"pages": [
1,
2,
3
]
},
{
"title": "2. DISK PHYSICAL STRUCTURE",
"content": "Amultitude of processes (gas dynamics, dust evolution, energy transport processes, chemistry, etc.) makes modeling of protoplanetary disks a challenge. With the current level of computing resources a global 3D radiative MHD simulation, including gas and dust evolution and chemical kinetics, remains a topic for the future (but see, e.g., Flock et al. (2012) for such models). Nevertheless a sufficient understanding of protoplanetary disk physics may be achieved by detailed modeling of primary processes that govern its structure and observational characteristics, and simplified modeling of secondary processes. This makes the problem tractable. For Class II objects (Lada 1987; Evans et al. 2009) it is usually assumed that a disk structure is in a steady-state regime over a time span of ∼ 1 Myr. This is supported by observations of disk kinematics via molecular lines and disk surface densities via (sub-)millimeter dust emissivity. The line profiles are indicative of Keplerian motion in most of the disks (Koerner et al. 1993; Guilloteau & Dutrey 1998; Piétu et al. 2007). The estimates of the disk masses and density distributions show that self-gravity is negligible for Class II objects (Isella et al. 2009). The assumption that these disks evolve on a diffusion timescale and not on a hydrodynamicalone allows setting aside hydrodynamicalsimulations and reducing a 3D problem to a 1+1D problem. The azimuthal dimension is eliminated due to the axial symmetry of an unperturbed disk. The other two dimensions are usually split into the radial structure that is determined by diffusive evolution, and the vertical structure that is derived from the hydrostatic equilibrium equation (D'Alessio et al. 1998; Dullemond et al. 2002). The 1+1D description is suitable for dust continuum radiation transfer. For disk regions outward of a few AU a radial optical depth for a location close to the midplane is higher than the vertical optical depth, so that the dust temperature is mostly determined by vertical diffusion of radiation. A gain in computation time that is acquired by a 1D radiation transfer, compared to a 2D RT, allows better frequency resolution, which is important for dust temperature calculations (Dullemond et al. 2002) and for modeling photochemistry. In this paper we adopt a 1+1D approach to calculate disk density and temperature. As the disk consist of two main ingredients (dust and gas), the overall problem is reduced to calculating four physical quantities: dust and gas temperatures ( T d , T g), and dust and gas densities ( ρ d , ρ g). This allows to split the disk model into four blocks, calculating the corresponding quantities at each disk radius R : As all these quantities are not independent, we iterate between the modules until convergence is reached. The overall computational flowchart for ANDES is shown in Figure 1. Assuming the surface density profile, we calculate dust evolution for 2 Myr starting from the MRN initial distribution. The resultant dust structure is then used to derive radiation field and gas disk structure using radiation transfer, energy balance and hydrostatic structure modules. As a fiducial dust model we also consider pristine grains with the following parameters: 0.1 µ min size, astronomical silicate, dust to gas ratio 0.01 at every location in the disk. The list of basic assumptions is: (i) a disk is quasi-static, axially symmetric and treated in 1+1D approach; (ii) the gas surface density is assumed to be specified, and the dust surface density is 0.01 of the gas surface density; (iii) gas vertical structure is determined from the hydrostatic equilibrium, while dust vertical structure is a consequence of turbulent stirring and grain settling. Also, calculating the chemical evolution we keep the dust properties fixed both for pristine and evolved dust cases. Below we describe each part of the model in detail.",
"pages": [
3
]
},
{
"title": "2.1. Radiative transfer",
"content": "The radiation in a protoplanetary disk plays a two-fold role. First, it is a main energy carrier that redistributes energy coming from the stellar irradiation and viscous dissipation, and thus defines the overall disk structure. Second, it determines rates of photoreactions and thus shapes the disk chemical structure and observational appearance. These two aspects pose different requirements to the radiation transfer model. The radiation field as a contributor to the disk energy balance should be known in a wide range of wavelengths, from FUV (radiation from the accretion region and non-thermal radiation from the central star) to visual (thermal stellar radiation) to the infrared and submillimeter wavelengths (thermal disk radiation). This requirement makes multi-dimensional RT approaches with high spectral resolution too slow for iterative disk modeling. On the other hand, in a narrow range of UV wavelengths (from 912 Å to, say, 4000 Å) such a good spectral resolution is important for accurate calculation of the photochemical rates, as the dependence of photoreaction cross-sections on λ is complicated. Protoplanetary disks usually have high optical depths at λ /lessorsimilar 100 µ m(e.g., Beckwith & Sargent 1991), which calls for using suitable methods to solve the radiation transfer (RT) problem for optically thick media. As our primary focus is on the chemical modeling in disks with evolved dust, we developed such a method with a particularly good wavelength resolution in the UV part of the spectrum.",
"pages": [
3,
4
]
},
{
"title": "2.1.1. Main equations",
"content": "It is easy to show that in the cases of SchwarzschildSchuster and Eddington approximations the RT equation for a plane-parallel 1D medium can be written using the mean intensity J ν : where χ ν [ cm -1 ] is the extinction coefficient, S ν is the source function, and q = 1 / 4 and q = 1 / 3 for the SchwarzschildSchuster and the Eddington approximation, respectively. If we consider only dust continuum absorption, thermal emission, and coherent isotropic scattering, the source function is Here κ ν [cm -1 ] is the absorption coefficient, σ ν [cm -1 ] is the scattering coefficient ( χ ν = κ ν + σ ν ) and B ν is the Planck function. In the 1+1D approach the anisotropic scattering by dust grains can also be taken into account. It is important for UV photons interacting with small dust grains, whereas at IR wavelengths scattering can be considered negligible compared to absorption/emission. The p parameter describing anisotropy of scattering ( p > 1 / 2 and p < 1 / 2 denote forward and backward scattering, respectively) can be introduced in our RT model in such a way that dust extinction efficiency σ is substituted by the combination 2(1 -p ) σ . In the limit of predominantly forward scattering grains, the role of UV dust heating in deep disk layers renders less significant than in the case of the isotropic scattering used in our study. That is, our current approach tends to slightly overestimate the role of scattering and thus overall dust heating in disk upper layers. Equations (1)-(2) are closed with the energy balance equation Here Γ nr( z ) [ erg cm -3 s -1 ] accounts for non-radiative heating/cooling mechanisms (gas-grain interaction, see Equation (A14)). Equations (1)-(3) represent the complete system for J ν ( z ) and T d( z ). We solve this system with the analogue of the Feautrier method (Mihalas 1978). Specifically, we introduce a wavelength and coordinate grid where J ν ( z ) is defined, and linearize the Planck function, B ν , with respect to T d. Equation (1) is approximated by a set of finite difference equations for each z -grid point, while Equation (3) is represented by a finite sum. As a result, we get a system of linear equations for J ν i ( zk ) that can be written using a hypermatrix formalism. This hypermatrix system is solved with the tridiagonal Thomas algorithm (Press et al. 1992). After the new values of J ν i ( zk ) and T d( zk ) are obtained we refine linearization for the Planck function, update the system, and repeat iterations until convergence is achieved. The stellar and diffuse interstellar radiation fields can be treated as boundary conditions to the above system of equations. We use an approach developed by Dullemond et al. (2002) and consider stellar and interstellar fields as nonradiative additional source terms in Equation (3). This approach takes into account the shielding of the star by the inner parts of the disk. For that one needs to know the fraction of stellar radiation intercepted by the disk at each radius. We compute the corresponding grazing angle as an angle between dust density isoline at ρ d = 5 · 10 -24 gcm -3 and the direction toward the star. For the stellar spectrum, we use a 4000 K blackbody for λ > 4000Å. For shorter wavelengths, we use the interstellar radiation field (Draine 1978; Draine & Bertoldi 1996) with an extension to longer wavelength (van Dishoeck & Black 1982), where we have scaled the intensity so that it is continuous at the transition wavelength of 4000 Å . Such a normalization leads to typical values of stellar UV intensity at disk atmosphere being equal to ∼ 500 'Draine units' (Röllig et al. 2007) at a radius of 100AU.",
"pages": [
4
]
},
{
"title": "2.1.2. Dust opacities and size distributions",
"content": "As a result of dust evolution modeling we get dust size distribution functions f ( a , R , z )[cm -4 ] being the fraction of grains with sizes within ( a , a + da ) interval. To compute dust opacities one should know efficiency factors for dust absorption Q abs and scattering Q sca: Q abs and Q sca are computed from the Mie theory for astrosilicate grains (Laor & Draine 1993), but any other opacity model can be easily adapted.",
"pages": [
4,
5
]
},
{
"title": "2.2. Gas thermal balance",
"content": "The kinetic gas temperature T g is obtained by solving the thermal balance equation: where Γ and Λ are gas heating and cooling rates in ergs -1 cm -3 . They depend on absolute abundances of main heating/cooling species ρ i and their level populations n sp j , which in turn depend on the gas temperature. Therefore, the problem is solved iteratively at each grid point, starting from the disk atmosphere boundary toward the midplane for any given radius, by means of the Brent method (Press et al. 1992). Stellar FUV radiation is the main gas heating source in protoplanetary disks, leading to a PDR-like structure of the upper disk regions. There, gas is mainly heated via the photoelectric (PE) effect on dust grains and PAHs. In addition, collisional de-excitation of H2 pumped by FUV photons, photodissociation of H2, and carbon photoionization are important heating sources in specific disk regions. Gas heating by exothermic chemical reactions plays only a minor role, with the largest contribution coming from H2 recombination on grains. In the optically thick, dense disk interiors, the dominant heating sources are the cosmic ray ionization of H and H2, and viscous heating due to dissipation of accretion energy. Gas mainly cools via non-LTE atomic and molecular line emission, collisions with grains, and, at high temperatures, by emitting Ly α and metastable line emission. The details of heating and cooling processes can be found in Appendix A.",
"pages": [
5
]
},
{
"title": "2.3. Chemistry",
"content": "An important ingredient of the thermal balance calculations is chemistry. While often a fast, simplified equilibrium approach is adopted, time-dependent chemical modeling may be more appropriate for calculations of abundances of major molecular coolants. We adopted the same gas-grain chemical model as in Vasyunin et al. (2011). The reactions and reaction rates are based on the RATE'06 chemical ratefile (Woodall et al. 2007). For all photochemical reaction rates, we use the local mean intensity (as a function of ν ) computed with the RT model. To compute photoreaction rates, the dissociation and ionization cross-sections from van Dishoeck et al. (2006) and the AMOP database 1 are utilized. If cross-sections are not available for a certain reaction, we retain the standard χ 0 exp( -γ A V) formalism, with a γ value taken from RATE'06 ratefile, χ 0 estimated at the upper disk boundary, and A V computed as ln( χ/χ 0). The same values are used to estimate photodesorption rates. Thus, the calculation of photoprocesses takes into account the detailed shape of the incident UV spectrum of the central star and its penetration through the disk. Self-shielding for H2 dissociation is computed using the Draine & Bertoldi (1996) formalism, with the modified A V values used to account for dust attenuation. The selfand mutual shielding for CO photodissociation are computed using recent tabular data of Visser et al. (2009). The unattenuated cosmic ray (CR) ionization rate is assumed to be 1 . 3 × 10 -17 s -1 . The surface reactions are taken from Garrod & Herbst (2006) and assumed to proceed without hydrogen tunneling via potential wells of the surface sites and reaction barriers. Thus only thermal hopping is a source of surface species mobility. A diffusion-to-desorption energy ratio of 0.77 is adopted for all species (Ruffle & Herbst 2000). Under these conditions, stochastic effects in grain surface chemistry are negligible, and classical rate equations may be safely used (Vasyunin et al. 2009; Garrod et al. 2009). As the initial abundances, we utilize a set of 'low metals' neutral abundances from Lee et al. (1998), where most of refractory elements are assumed to be locked in dust grains. As the density and temperature distributions, computed here, are similar to those used in Vasyunin et al. (2011), we decided to use the same vertical distributions of X-ray ionization rates regarding them as reference values. In the chemical module they are simply added up to CR ionization rates. For the purpose of chemical evolution, we assume that dust is represented by grains with a single size which is computed from the local grain size distribution as described in Vasyunin et al. (2011). With this chemical model, a disk chemical structure is computed using dust properties and physical conditions from the previous iteration. We assume that the grain properties do not change over the computational time span of 2 Myr.",
"pages": [
5
]
},
{
"title": "2.4. Vertical gas distribution",
"content": "Given that the gas temperature T g( R , z ) and the mean molecular weight µ ( R , z ) are known, the vertical gas density distribution can be found by integrating the hydrostatic equilibrium equation: coupled to the equation of state of the ideal gas: In this study we assume that the radial profile of the surface density is given by the known function Σ ( R ).",
"pages": [
5
]
},
{
"title": "2.5. Dust evolution",
"content": "The evolution of the dust size distribution is calculated using the model presented in Birnstiel et al. (2010). In this work, we consider neither the viscous evolution of the gas disk nor the radial evolution of the dust surface density. The grain evolution begins with grains sticking at low collision velocities. Disruptive collisions at higher impact velocities cause erosion or fragmentation, which poses an obstacle towards further grain growth and replenishes the population of small grains. Typical threshold collision velocities for the onset of fragmentation are found to be about 1 m s -1 for silicate dust grains (Blum & Wurm 2008). Icy particles are expected to fragment at higher velocities due to the increased surface binding energies (Wada et al. 2008; Gundlach et al. 2011). We therefore use a threshold velocity for fragmenting collisions of 10 and 30 m s -1 in our dust models. Grain collisions are driven by relative velocities due to Brownian motion, turbulent motion (Ormel & Cuzzi 2007), radial and azimuthal drift as well as vertical turbulent settling. In order to make the calculation of the dust evolution feasible, we consider a radially constant, vertically integrated dustto-gas ratio and an azimuthally symmetric disk. The vertical settling of dust is taken into account by using a vertically integrated kernel (see Brauer et al. 2008; Birnstiel et al. 2010). The integration implicitly assumes that the vertical distribution of each dust species follows a Gaussian distribution with a size-dependent scale height. This is a good approximation for the regions close to the disk midplane where coagulation is most effective. However, for modeling of the chemical evolution the detailed vertical distribution of each dust species needs to be known. We therefore use a vertical mixing/settling equilibrium distribution (Dullemond & Dominik 2004), taking a vertical structure of the previously calculated dust surface densities.",
"pages": [
5,
6
]
},
{
"title": "3.1. Disk physical structure for evolved and pristine dust cases",
"content": "As an initial approximation, we adopt a disk from Vasyunin et al. (2011) with mass M disk = 0 . 055 M /circledot and gas surface density profile Σ ( R ) close to a power-law with index p = -0 . 85 and Σ (1AU) = 34 g/cm 2 . The dust surface density is equal to 1% of the gas surface density. We assume the following parameters for a central star: a mass M /star = 0 . 7 M /circledot , a radius R /star = 2 . 64 R /circledot and an effective temperature T /star = 4000 K. This system closely resembles the DM Tau disk. As UV-excess we use the standard interstellar diffuse radiation field (Draine 1978) and its extension to longer wavelengths (van Dishoeck & Black 1982) as described in Section 2.1.1 ('JD' case from Akimkin et al. (2011)). To show the influence of dust evolution on the disk thermal and density structure we present results for two cases: the pristine dust with uniform distribution and grain size of 0 . 1 µ m (Model A) and the dust distribution and sizes as obtained with the dust evolution model after 2 Myr of evolution (Model Ev). The maximum grain size, attained in the midplane in Model Ev, varies from 4 · 10 -3 cm at 550 AU to 0.02 cm at 10 AU. The minimum grain size is always 3 · 10 -7 cm. In Figure 2 the dust temperature distribution is shown for the both cases. The disk model with evolved dust is hotter by about 70 K in the inner disk atmosphere ( R < 200 AU) and by ∼ 10 -20 K in the outer atmosphere ( R > 200 AU) compared to the disk model with the pristine dust, whereas the dust midplane temperatures are quite similar in the both cases. Higher dust temperatures at the disk surface in the evolved dust model are explained by a steeper slope of dust opacities in the mid-IR, where such dust predominantly emits. Since both disk models have similar dust midplane temperatures and due to transparency of the bulk disk matter to the far-IR/millimeter emission, the emergent disk spectral energy distributions (SED) are similar. The difference in emergent spectra between Model A and Model Ev becomes apparent mostly at mid-IR wavelengths, where dust continuum emission from the inner disk parts peaks. Gas temperature distributions in the disk models with the evolved and the pristine dust are shown in Figure 3 and can be compared with the dust temperatures in Figure 2. The extent of the gas-dust thermal coupling zone (where T d = T g) in Model Ev is slightly smaller than in Model A, primarily due to sedimentation. As the midplane dust temperatures for the two models do not significantly differ, the gas temperatures also inherit this behavior. On the other hand, the gas temperature distributions above the coupling zone are quite different. In the both cases, the inner disk atmosphere is heated up to several thousand Kelvin by photoelectric heating, but it is /greaterorsimilar 1000 K cooler in Model Ev. This is due to the reduced abundance of grains in the Model Ev, where the main contribution to the photoelectric heating comes from PAHs. In contrast, in Model A grains dominate photoelectric heating. Their intense heating in the upper atmosphere has to be balanced by Ly α cooling, while in Model Ev remaining grains in the inner disk and the [O I] line cooling at larger distances ( /greaterorsimilar 40 AU) can balance the photoelectric heating from PAHs. Radial extent of hot tenuous atmosphere is drastically different for the two disk models: it exceeds 100 AU in Model A, whereas in Model Ev gas is cooler than 1 000 K even at R =60 AU. Absence of grains in the disk atmosphere in Model Ev leads to an increase of the gas temperatures by about factor of 2 at z / R between ≈ 0 . 3 and 0.6 at R ≈ 100 -300 AU. Somewhat smaller increase of the gas temperatures in the upper layers is also present in more distant regions of the disk. Rates of main heating and cooling processes are shown in Figure 4. Dust density distributions for Models Ev and A are com- pared in Figure 5. The dust densities differ by several orders of magnitude, mainly due to sedimentation. This process also leads to dramatic changes in the dust-to-gas ratio. While in Model A this value is constant and equal to 10 -2 , in Model Ev we encounter the whole range of values, from 10 -1 to 10 -8 (see Figure 6). However, dust-to-gas ratios below 10 -4 lead to unstable solutions and poor convergence of the code, therefore in the calculations we assume that the minimal value of dust-to-gas ratio is 10 -4 . In Figure 7 the dust cross-section per hydrogen atom is presented for Model Ev. In case of Model A this value is equal to 5 . 9 · 10 -22 cm 2 /H everywhere in the disk.",
"pages": [
6,
7
]
},
{
"title": "3.2. Chemical structure",
"content": "One of the main goals of our study is to probe potential changes in the disk chemical structure that may arise due to various processes related to the dust evolution. In the section we present a detailed comparison of molecular abundances in the disk models with pristine and evolved dust for radii of 10 AU, 100 AU, and 550 AU. These are the same radii that have been analyzed by Vasyunin et al. (2011). We consider only those species that have mean abundances exceeding 10 -12 at least in one of the two considered models. The mean abundance is computed as a ratio of the species column density to the column density of hydrogen nuclei. Remember that in all three cases we ignore and do not show the vertical structure at the height where the mass density of dust grains drops below the adopted limit of 5 · 10 -24 g cm -3 in the evolved model, and the medium can be considered as purely gaseous. In the case of the well-mixed dust disk model, this value corresponds to the hydrogen number density of 2 · 10 2 cm -3 , and is even lower for the dust evolving disk model. The key disk properties at the selected radii are shown in Figure 8. Up to a certain height the gas density is almost the same in both models. Above this height the vertical density profile flattens in Model Ev, because gas temperature either stops increasing or decreases with z , and density stays nearly constant to keep the disk hydrostatically stable. The main reason for that is the disk transparency. The dashdotted lines in Figure 8 (b, d, f) show the water photodissociation rates that are used here as a descriptive characteristics of the radiation field strength. Obviously, in Model Ev the UV radiation penetrates deeper into the disk. Dust is warmer in this model than in Model A almost everywhere in the disk. In Model Ev gas is also significantly hotter that in the model with pristine dust in the more illuminated region that extends approximately from 1.5 AU to 3 AU at R = 10 AU, from 30 AU to 50 AU at R = 100 AU, and from 100 AU to 600 AU at R = 550 AU. We characterize the dust evolution using the total dust surface area per unit volume that is shown in Figure 8 (b, d, f) (solid lines). It is smaller in the evolved model as both grain growth and sedimentation reduce the total surface of dust grains. While in the midplane this reduction is mostly caused by the growth of dust grains and is quite moderate, from an order of magnitude at 10 AU to less than a factor of 2 at 550 AU, in the upper disk, where sedimentation is important, the total dust surface area in Model A is greater by orders of magnitude than in Model Ev. However, this difference may not necessarily be important for chemistry as it is mostly confined to the illuminated disk regions where dust mantles are evaporated anyway by the UV photons.",
"pages": [
7
]
},
{
"title": "3.2.1. Outer disk",
"content": "We start the description of the disk chemical structure from the outer disk, where only minor changes in the disk physical parameters are caused by the grain evolution. Because of ineffective grain growth the total grain surface area per unit volume is nearly the same in both models, except for the outermost disk atmosphere (Figure 8, f). Second, the dust temperature is quite low in the disk midplane, so surface reactions with heavy reactants should be mostly suppressed there. After 2 Myr of evolution we end up with 91 gas-phase species and 81 surface species that have mean abundances greater than 10 -12 either in Model A or in Model Ev. In most cases grain evolution increases column densities for gasphase components. Among the 91 gas-phase species only 13 have column densities that are smaller in Model Ev than in Model A. The reason is quite straightforward. As grains grow and settle down toward the midplane, the so-called warm molecular layer moves down as well, to a denser disk region. Even if relative abundances do not change significantly in the process, column densities grow due to higher volume densities. Vertical abundance distributions for some species are shown in Figure 9. In the upper row of Figure 9 we present vertical abundance profiles for H2, H + 3 , and CO. The key difference between Model A and Model Ev is that in the former the warm molecular layer is located below the H2 dissociation boundary, while in the latter a portion of the molecular layer is located above this boundary, where free H atoms are abundant. This mutual disposition is not impossible as the molecular layer and the H2 photodissociation front are not directly related to each other. Grain absorption of the FUV photons responsible for the H2 dissociation is less significant in the model with evolved dust, and the H2 dissociation front is located deeper in Model Ev. However, the overall transparency of evolved dust in the entire UV range is smaller than for FUV photons only. Because of that the molecular layer that is controlled by desorption from dust grains and dissociation of trace molecules is located somewhat higher. This specific result, of course, depends on the adopted description of dust opacities and photoreaction rates. Simple atomic and diatomic components dominate the list of the gas-phase species, whose column densities are enhanced in Model Ev. The largest column density increase at 550 AU is found for SiO2 (Figure 9, d), N2O, and water (Figure 9, e). In all cases it is related to higher abundance of a molecule in the molecular layer. Note that almost all physical characteristics of the medium are nearly the same in the molecular layers of the two disk models, except for the gas density and the X-ray ionization rate. Higher density in the molecular layer of Model Ev accelerates two-body processes and shifts equilibrium abundances of many molecules to higher values. The relative location of the molecular layer and the HH2 boundary, mentioned above, also plays a role in defining molecular column densities, especially, for species that are produced in reactions with atomic hydrogen, like water. In Model Ev a significant portion of the molecular layer is located above this transition, where abundant H atoms are available. This speeds up the gas-phase water synthesis in H + OH reaction as well as surface synthesis of water molecules that are immediately released into the gas-phase due to photodesorption. This explains a huge water spike located at height of about 300 AU. In Model A water is mostly produced in surface reactions that are less effective because of low H gasphase abundance and lower rate of the UV photodesorption. Also, water molecules are more rapidly destroyed in reactions with ions such as HCO + that are abundant in the molecular layer due to higher X-ray ionization rate. The sharp drop-off in water abundance in both models coincides with the carbon ionization front. Above the front, the main destruction routes for water molecules are the reaction with C + and photodissociation. The situation is somewhat different for complex hydrocarbons, in particular, for long carbon chains. Their abundances in Model A are significantly enhanced in the molecular layer in comparison with Model Ev. This is again related to a more elevated position of the molecular layer in Model A. Because of that, it is less protected not only from the UV irradiation but from X-rays as well. Accordingly, ionized helium is more abundant in the molecular layer of Model A than in the molecular layer of Model Ev. Abundant C-bearing molecules, like CO, are destroyed by He + more efficiently in Model A in the disk upper region. Then, C + is consumed to produce simple CH + n species that stick to grains and produce long carbon chains by surface processes. The dust temperature of the order of 30 K is high enough to drive desorption of these molecules into the gas-phase. This effect should not be overestimated. Even though the total column densities of carbon chains are greater in Model A than in Model Ev, their absolute values are low, with the mean abundance exceeding 10 -12 only for C2H, C4, C4H, C5, C5H, and C6H. The effect is most pronounced for C5H (Figure 9, f), with the ratio of column densities in Model A and Model Ev of 15. For the observed C2H molecule the higher relative abundance in Model A (related to more effective He + chemistry) is nearly compensated by the higher absolute abundance in Model Ev (related to deeper location of the molecular layer), so its column densities are nearly the same in both models. The behavior of surface species is different in the two disk models. While column densities of gas-phase species are increased by grain evolution, column densities of many surface species decrease. There are 81 abundant surface species at 550 AU, and only 30 of them have greater column densities in Model Ev. Also the difference of column densities of surface species is quite modest in the two models. Only for ten of 81 species column densities differ by more than a factor of 3. Dominant surface carbon compounds (in terms of column densities) in both models are carbon monoxide and methane. Because of low dust temperature, s-CO2 production is suppressed, and this molecule in neither model reaches the high abundance seen at smaller radii (see below). Surface species that have greater column densities in Model Ev are mostly silicon and phosphorus compounds, which are not involved in surface chemistry (relevant reactions are not included in our chemical network). Their abundances are enhanced in the 'main' molecular layer as are abundances of their gas-phase counterparts (Figure 9, g). Abundances of some surface carbon chains are enhanced in Model A by about an order of magnitude due to more intense X-ray ionization than in Model Ev (see above). Also, species like s-C2O (Figure 9, h) and s-C2N involved in surface chemistry have greater column densities in Model A because their midplane abundances are higher in this model due to greater available surface area for their synthesis. Carbon chains not involved in surface chemistry in our chemical model, like sC4N (Figure 9, i), mirror evolution of their gas-phase counterparts and have higher abundances in the upper carbon chain layer described above.",
"pages": [
7,
8,
9
]
},
{
"title": "3.2.2. Intermediate disk",
"content": "As we move closer to the star, at distances of about 50100 AU, the fingerprint of dust evolution becomes more pronounced. While the mass density of dust is greater in the midplane of Model Ev due to sedimentation, the total surface area is still 2.5 times less than in Model A. In the upper disk the difference in the surface area reaches a factor of 70. It is interesting to note that the uppermost disk atmosphere is actually colder in Model Ev than in Model A, despite being more transparent (Figure 8, c). This is because dust is not only the main source of opacity but also an important heating agent (due to photo-effect). As dust is depleted in the upper disk, the equilibrium temperature shifts to lower values, dictated by the PAH heating. At R = 100 AU, among 78 gas-phase species, having mean abundances higher than 10 -12 at least in one of the two models, most species (72) have higher column densities in Model Ev, as at R = 550 AU, but the list of these species is somewhat different. Some examples of vertical abundance profiles for gas-phase species at R = 100 AU are shown in the top and middle row of Figure 10. The main features of the chemical structure are the same as at 550 AU. In Model Ev the molecular layer, as marked by the CO distribution (Figure 10, c), is located above the H2 photodissociation front (Figure 10, a). In Model A the situation is the opposite. Also, in Model A ions, like H + 3 (Figure 10, b) are 2 somewhat more abundant in the molecular layer which further decreases abundances of neutral unsaturated molecules. The largest difference between the two models is again observed for SiO2 that has a column density 3 . 6 · 10 8 cm -2 in Model A and 1 . 8 · 10 12 cm -2 in Model Ev. Grain evolution causes water column density to increase from 7 . 1 · 10 13 cm -2 to 5 . 2 · 10 16 cm -2 . This is again related to the different arrangement of the molecular layer and H-H2 transition in Model A and Model Ev (Figure 10, a). The upper boundary of the water layer is defined by the location of the C ionization front. Many complex gas-phase hydrocarbons, like formaldehyde (Figure 10, d) and cyanoacetylene (Figure 10, e), are also affected. Among more or less abundant molecules the only exception to this rule is methane (Figure 10, f), with column density being about 3 times larger in Model A than in Model Ev. This difference is related to the surface chemistry as we will explain below. The chemical evolution of surface species is complicated as it is affected by at least two competing factors related to",
"pages": [
9,
10
]
},
{
"title": "THE ANDES MODEL",
"content": "see Woodall et al. (2007) and Najita et al. (2011). As H abundances in the molecular layers are nearly the same in both models, we need to find another explanation for the raise in water abundance in Model Ev. It is obviously related to the difference in physical parameters in the two molecular layers. Again, the molecular layer in Model Ev is shifted toward the midplane and, thus, resides in a denser disk region. Because of higher density in the molecular layer of Model Ev, surface water synthesis is more effective there, increasing its gas-phase abundance as well. Higher X-ray ionization rate in the molecular layer of Model A leads to higher ion abundances. In particular, it greatly enhances abundance of H + that is one of the major water destroyers. Another difference is the UV radiation spectrum that favors carbon ionization in Model A. In the adopted photoionization model, carbon atoms are ionized by the UV radiation with wavelengths shorter than 1100 Å. This radiation is absorbed less efficien tly in Model A, and because of that the C/C + transition zone is further vertically expanded, so that the water layer falls in the region where C + abundance is still significant (Figure 11, d). This also leads to rapid water destruction. Different water abundances cause even greater differences in column densities of SO and SO2. In the case of SO2 the difference exceeds 9 orders of magnitude (Figure 11, e). Significant growth of SO and SO2 abundances can be traced to the greater abundance of O2 in Model Ev. An SO2 molecule is produced from SO, SO is produced in reaction S + OH, atomic sulfur is the product of SO + dissociative recombination, and SO + is produced in the reaction between S + and O2. Abundance of molecular oxygen in Model Ev is greater by almost 4 orders of magnitude than in Model A (Figure 11, h), which is also related to different H + abundances, as the H + + O2 reaction is one of the major O2 destruction pathways. Thus, we conclude that at R = 10 AU chemical differences between Model Ev and Model A arise because grain evolution shifts the molecular layer in the region of the disk that is more protected from X-rays and FUV radiation. Among species, that have their column densities decreased by grain growth, are HCN (Figure 11, f) and HNC. They are mostly concentrated in the midplane, and their midplane abundances in Model A exceed those in Model Ev by an order of magnitude. Analysis of chemical processes indicates that this difference is related to surface processes, that is, higher gas-phase HCN abundance in Model A simply reflects more effective surface synthesis of the molecule because the available surface area is greater in this model (Figure 11, i). Then, HCN desorbs into the gas-phase and gets protonated by reactions with HCO + or H + 3 . Dissociative recombination of HCNH + produces either HCN or HNC, so the overabundance of HCN in Model A is partially transferred into the overabundance of HNC. As for surface species, at this radius there are 64 abundant surface components, mainly heavy molecules. Nearly half of them are more abundant in Model Ev, but the increase in column densities is not significant for most molecules. Two extreme examples of greater column densities in Model A are represented by s-HCN and s-HNC, for the reasons described above.",
"pages": [
13,
14
]
},
{
"title": "3.2.3. Inner disk",
"content": "At R = 10 AU we have 75 abundant gas-phase molecules, and 62 of them share the common trend to be more abundant in the model with evolved dust. However, the magnitude of the difference in column densities as well as its origin are related to other factors. The molecular layers both in Model A and in Model Ev are located above the H-H2 transition (Figure 11, a). In both cases abundant H atoms are available both for surface and gas-phase reactions. Despite the fact, water column density in Model Ev exceeds that in Model A by more than 4 orders of magnitude (Figure 11, g). This difference is much greater than at other radii where we related it to the difference in atomic hydrogen abundance. At these warm temperatures of 50 -200 K (see Figure 8, a), the formation of water is dominated by neutral-neutral reaction of O with H2 (with the barrier of 1660 K), followed by the neutralneutral reaction of OH with H2 (with the barrier of 3163 K),",
"pages": [
12
]
},
{
"title": "3.3. Model with more efficient dust growth",
"content": "To check the sensitivity of our results to some details of the adopted grain physics, we considered additional models for dust evolution. In this subsection we present a detailed description of Model Evx with a threshold velocity for fragmenting collisions increased from 10 to 30 m s -1 , which leads to more significant grain growth in the dense regions. Models A, Ev, and Evx can be viewed as successive stages of the grain evolution process. So, in Model Evx we may expect to see a continuation of the same trends as were noted above for Model Ev. In Figure 12 we show the main disk structural properties at R = 50 AU in the three models. Obviously, more advanced grain evolution causes the disk to become more transparent. As a result, hot atmosphere becomes more extended, and dust becomes warmer, with the midplane grain temperature raising from 28 K in Model A to 33 K in Model Evx. As we will see below, this relatively small difference has a noticeable effect on the disk chemical structure. Dust surface, available for chemical reactions, is an order of magnitude smaller in Model Evx than in Model A. Vertical profiles of some species for Models A, Ev, and Evx are shown in Figure 13. As in previous cases, we start from H2 (Figure 13, a) and notice that the H2 photodissociation front sinks even deeper, so that hydrogen is almost fully atomic above ∼ 6 AU. Due to warmer dust, gas-phase abundances of some molecules with low desorption energy are increased in the midplane of Model Evx (like in Model Ev at R = 10 AU). One can see the progressive growth of CO midplane abundance from Model A to Model Evx in Figure 13 (c). Similar to CO, gaseous N2 appears in the disk midplane in Model Evx. Protonation of such abundant molecules lowers the H + 3 abundance in the Evx model midplane (Figure 13, b), which affects abundances of some other ions, like H3O + . A typical example of the molecular abundance evolution is shown in Figure 13 (d). A peak of water abundance shifts toward the midplane and grows higher. Due to increasing overall gas density and more intense photodesorption, gasphase water column density increases up to 4 . 7 · 10 17 cm -2 in Model Evx. The upper boundary of water layer is defined by the C + ionization front (Figure 13, e). A significant growth is observed for N2H + column density. It increases from 4 . 8 · 10 9 cm -2 to 1 . 5 · 10 10 cm -2 in Model Ev and 5 . 1 · 10 11 cm -2 in Model Evx (vertical abundance profile is shown in Figure 13 (g)). This is related to increased thermal desorption of the N2 ice and lower abundances of surface species that are mostly synthesized on grains, like methane (Figure 13, f) or ammonia (Figure 13, h). In the latter case, some nitrogen atoms in the midplane are free to be incorporated into N2 molecules (Figure 13, i) and further into N2H + molecules. Species, significantly affected by the advanced grain growth, also include other gas-phase molecules, related to surface chemistry. Column densities are increased by more than an order of magnitude in Model Evx relative to Model Ev for H2O2, CH4, CO2, and some others. We have also considered the effects of dust radial mixing. The radial mixing is modeled as diffusion, using the Schmidt number from Youdin & Lithwick (2007), i.e. D dust = D gas / (1 + St 2 ). The dust diffusivity is taken to be the dust viscosity ( D gas = ν gas) which is the Shakura & Sunyaev (1973) viscosity for the given alpha value. We found that radial mixing does not change the disk physical and chemical structure significantly and leads to the gas/dust temperature increase by several K at intermediate radii.",
"pages": [
14
]
},
{
"title": "4.1. Comparison to Vasyunin et al. (2011)",
"content": "While many aspects of the presented model are derived from the model used by Vasyunin et al. (2011), the new treatment of the disk structure results in parameters that are too different to allow a direct comparison of the 'old' and 'new' results. While density profiles are nearly the same in both studies, there are two key differences in the disk dust temperature and in the disk radiation field (Figure 14). First, the improved radiation transfer model makes dust in the 'new' disk midplane significantly warmer than dust in the 'old' disk midplane, at least, in the remote parts of the disk ( R > 100 AU). Second, because of scattering the 'new' disk is less transparent to dissociating far-UV radiation than the 'old' one. These two differences are related to the radiation transfer treatment , so we may expect that basic inferences of Vasyunin et al. (2011) on the disk chemical structure should be retained in the new results, if they are mostly related to the dust evolution . This is indeed the case, with a few exceptions. First, the general conclusion of Vasyunin et al. (2011) that dust evolution increases gas-phase column densities of most species is entirely confirmed in the present study. Second, almost all species, designated as sensitive to grain evolution in Vasyunin et al. (2011), like CO, CO2, H2O, C2H, retain this status in the present study 2 . In Table 1 we show column densities for species listed in Table 2 from Vasyunin et al. (2011), along with the newly calculated column densities. Few remarks are needed. Some species, like methanol, cyanopolyynes or formic acid, are significantly less abundant in the new model. This is due to generally less effective surface chemistry in a warmer disk midplane, where depletion of CO and other similar volatile ices is less severe and where a desorption rate of hydrogen atoms from dust surfaces is higher. The chances for them to be observed are, thus, slim (within the framework of our modeling approach). For some species from this list the 'sensitivity region' (the region where the two models differ most) shifts or extends to other radii (typically, from ten to hundred AU). These are HCNH + (derived mainly from HCN), NH3, and OH. Surface hydrogenation also plays an important role in the synthesis of these species. Column densities of three species, H2CS, HC5N, and HCO + , while still enhanced by the dust growth, differ by less than an order of magnitude in the new calculation, so they do not conform to our sensitivity criterion. Thioformaldehyde that has been mentioned in Vasyunin et al. (2011) as a molecule most sensitive to dust growth and HCO + are now significantly more abundant in the midplane of Model A due to higher dust temperature and less severe depletion of their parental species, CO and (H)CS. This shortens the break be- tween the pristine and evolved dust models. Abundance of CH3CH3 is also significantly enhanced in the midplane at R = 10 AU, relative to results of Vasyunin et al. (2011), and is nearly the same both in Model A and in Model Ev. As our model has a warmer inner midplane, surface radicals out of which CH3CH3 is formed become more mobile and reactive. A molecular layer no more dominates in its column density, so the molecule loses its sensitivity to the dust growth in the inner disk. In the outer disk the situation is more complicated. There, CH3CH3 is still sensitive to dust growth, but the sign of the sensitivity is different. While in Vasyunin et al. (2011) its column density was greater in the model with pristine dust, now CH3CH3 shares the common behavior and is enhanced in the molecular layer of Model Ev due to higher density there. Another molecule that shows the 'reversed' sensitivity is HCN. As we mentioned above, its abundance in the midplane is higher in Model A because of more effective surface synthesis. It also exceeds HCN column density in Model A5 from Vasyunin et al. (2011) due to somewhat higher dust temperature, that also intensifies HCN ice production (as surface production of CN is faster in the warmer ANDES model). At larger radii, HCN behavior is similar in both studies. These findings demonstrate the importance of the correct treatment of the radiation transport and also imply that the stellar and interstellar radiation fields need to be discretized as good as possible. Table 1 contains only a few representative species. To have a broader perspective, we perform a general comparison relating the column density ratios in the models with pristine and evolved dust computed in Vasyunin et al. (2011) and in the present study, for all species at 10, 100, and 550 AU. Results of comparison for R = 100 AU are shown in Figure 15. Only gas-phase species with mean abundances greater than 10 -10 are shown. Most species are concentrated around a red line that corresponds to equal old and new ratios. This indicates that most column densities respond similarly to dust growth both in Vasyunin et al. (2011) and in the present study. Also, most species reside in the upper right quadrant, showing that in both studies dust evolution, as a rule, increases molecular column densities. Carbon dioxide is most sensitive to dust growth and is, thus, located in the upper right corner. This is not surprising as its production mostly occurs on grain surfaces via slightly endothermic reactions of CO and OH. A quite high water sensitivity was obtained in Vasyunin et al. (2011), and now it be- comes even higher. Similar to water and carbon dioxide, HNO was very sensitive to dust growth in our old computation because its main production route is surface synthesis. In the new computation this route is less effective due to warmer dust, so HNO is mostly produced in the gas phase. This makes it less susceptible to changes in dust properties. It must be kept in mind that warmer dust has dual effect on surface chemistry. On one hand, a larger temperature implies more rapid hopping and larger reaction rates. On the other hand, more volatile reactants evaporate faster from warmer grains, thus, quenching the formation of some species. An opposite example is represented by formaldehyde. This species was barely sensitive to dust growth in the old computation, with column density being slightly smaller in the model with evolved dust. In the present study, H2CO column density is significantly greater in the model with evolved dust. This behavior is related to details of the UV penetration. In the old models, where only the UV absorption has been taken into account, the UV field intensity falls off quite slowly as we go deeper into the disk. Because of that abundance maxima in the molecular layer for molecules that are mostly susceptible to photodesorption and photodissociation are extended and shallow. Thus, their column densities are less sensitive to dust evolution. Detailed treatment of the radiation transfer in the new model predicts a sharper transition from the illuminated atmosphere to the dark interior. The molecular layer becomes significantly narrower and is, thus, much more sensitive to the extent of dust growth and sedimentation. The overall conclusion from the presented comparison is the following. We confirm that dust evolution changes column densities of many molecules (see Table 1 and Figure 15). Most species that have been listed as especially sensitive to dust evolution in Vasyunin et al. (2011) retain this status in the present study. However, column densities of some species turn out to depend on the details of the radiation transfer treatment, and this dependence will become even stronger when we will proceed from column densities to line intensities. ANDES makes all the necessary preparatory work for that, providing us with both abundances and gas temperatures. However, there is another aspect, apart from the radiation transfer, that may affect our conclusions. This aspect is re- lated to possible evolutionary changes. As in ANDES we use time-dependent chemistry, we can provisionally estimate its importance.",
"pages": [
14,
15,
16,
17
]
},
{
"title": "4.2. Disk structure with time-dependent chemistry",
"content": "In order to demonstrate the effect of time-dependent chemistry on the disk chemical structure we perform model calculations with abundances of major molecular coolants at 10 4 , 10 5 , and 2 × 10 6 years. We assume that the disk chemically evolves from mostly neutral atomic gas, with molecular hydrogen and a low fraction of atomic hydrogen (10 -3 to the total number of hydrogen nuclei). We do not consider the time evolution of dust grain distribution in order to focus on effects of chemical evolution, and utilize vertical dust distribution after 2 Myr. Results are presented in Figure 16, showing the relative abundances of H2, H, CO, C, and C + as a function of height at the distinct epochs for disk radii of 10, 100 and 550 AU. As can be clearly seen, the location of the H2/H transition shifts toward the midplane with time for all the considered radii due to slow photodissociation of molecular hydrogen, self-shielded from the strong FUV stellar radiation. H2 cannot be quickly re-formed in this region in Model Ev due to overall lack of grains, providing catalytic surface for H + H reaction. Consequently, between 10 4 and 210 6 years, at radii of 10, 100, and 550 AU, the PDR zone shifts from 1.6 to ≈ 1 . 4 AU, from 31 to 22 AU, and from 425 till 290 AU, respectively. This effect is more pronounced in the outer disk, where densities and density gradient are lower. An interesting feature of the chemical structure in Model Ev is the presence of a 'dip' in H2 vertical distribution at the final time moment at all radii. This region with depression in H2 concentration is caused by its slow X-ray/UV destruction, which cannot be compensated by the H2 surface production on a few remaining grains. However, just above this depression region dust-to-gas ratio locally increases, and so does the available surface for hydrogen recombination (per unit gas volume). The reason for the elevated dust-to-gas ratio is a gas redistribution from the top of the coupling region to greater heights due to extra heating. In contrast, the evolution of ionized carbon reaches a chemical steady-state rapidly everywhere in the disk thanks to its fast ion-molecule chemistry pathways, so the C + concentration is not time-sensitive (after 10 4 years), see Figure 16. The chemical evolution of C + is governed by a simple and limited gas-phase reaction network in the disk atmosphere, where it is an important coolant with a relative abundance of ≈ 10 -4 (see, e.g. Semenov et al. 2004; Semenov & Wiebe 2011). Neutral atomic carbon shows little time evolution, if any, in the disk regions adjacent to the midplane at radii smaller than ∼ 100 AU. Due to relatively large densities in disk equatorial regions, neutral carbon is rapidly converted to CO and hydrocarbons. This is not true for lower-density outer disk regions, at R /greaterorsimilar 500 AU and z / R ∼ 0 . 3 -0 . 6, where the C abundance changes substantially with time. Since initially all elemental carbon is in the atomic form, in the outer disk, less dense and more transparent to the interstellar FUV radiation, conversion of C into CO and hydrocarbonstakes more than 10 4 years (see Figure 16, bottom row). The gas-phase CO abundances follow the pattern of H2/H and C and do not reach a steady-state within 2 Myr everywhere in the disk model with evolved dust. The grain growth increases the CO freeze-out timescale to /greaterorsimilar 1 Myr in the inner and intermediate radii (Figure 16, top and middle rows). In the midplane, where gas-phase CO abundance is low, this molecule is present as CO ice. The final distribution of the CO abundance at R /lessorsimilar 100 AU shows an interesting feature: due to severe grain growth CO freeze-out is inefficient in the midplane, but still effective at disk heights of z / R ≈ 0 . 2 AU. At even larger heights the CO molecular layer starts, so CO emission lines are excited both in the very cold and warm regions. Since 12 CO, 13 CO and C 18 O isotopologue lines, having vastly different opacities, allow probing these two temperature zones, this should be visible with modern radiointerferometers. Intriguingly, evidence for the presence of very cold CO gas was found by Dartois et al. (2003), and, later, for other molecules like HCO + , CCH, CN, and HCN (see discussion in Semenov & Wiebe 2011). Enhanced amounts of H2 at 10 4 years in disk regions with high FUV radiation intensities lead to additional heating by the UV-excited H2. Since the H2/H boundary is moving down, the gas thermal structure of the disk responds accordingly and also shows strong variations of T g in a narrow disk layer, in particular, at R > 100 AU (see Figure 17). While the gas temperature varies from 250 K to ≈ 200 K (25%) at R = 10 AU, at the outer disk region, R = 550 AU, the gas temperature difference at various times is about 250 K (from 320 K to ≈ 75 K, or a factor of 4), compare top and bottom panels of Figure 17. Naturally, it should also have a strong impact on chemical composition and appearance of the disk molecular layer, from which most of line emission emerges. More importantly, it demonstrates the importance of using the time-dependent chemistry for calculating abundances of key gaseous coolant instead of the commonly applied steady-state approach.",
"pages": [
17,
18
]
},
{
"title": "5. CONCLUSIONS",
"content": "A multi-dimensional self-consistent model of protoplanetary disks 'ANDES' is introduced and described. The purpose of ANDES is to provide researchers with a state-of-the-art, most up-to-date detailed thermo-chemical model of a proto- planetary disk that can be used to analyze high-quality IR and (sub-)millimeter observations of individual nearby disks. For the first time grain evolution and large-scale time-dependent molecular chemistry are included in modeling of physical structure of protoplanetary disks. The iterative ANDES code is based on a flexible modular structure that includes 1) a 1+1D continuum radiative transfer module to calculate dust temperature, 2) a module to calculate gas-grain chemical evolution, 3) a 1+1D module to calculate detailed gas energy balance, and 4) a 1+1D module that calculates dust grain evolution. The disk structure is computed iteratively, assuming fixed dust density structure after the first iteration. Typically it takes ∼ 10 iterations to reach convergence at 1% level of accuracy. The continuum radiative transfer module is based on the two-stream Feautrier method with a high-resolution frequency grid. We consider dust continuum absorption, thermal emission, and coherent isotropic scattering. The dust evolution is modeled by accounting for coagulation, fragmentation, and gravitational sedimentation towards the disk midplane balanced by turbulent upward stirring. The chemical model is based on a gas-grain realization of the RATE'06 network, and includes surface reactions and X-ray/UV processes. All modules have been thoroughly benchmarked with previous studies, with overall good agreement and performance. We study the impact of dust evolution on dust temperature, gas temperature, and chemical composition by comparing results of the disk models with evolved and pristine dust. We compute gas thermal structure corresponding to chemical abundances evolving from the initial abundances for 10 4 , 10 5 , and 2 · 10 6 years. We show that time-dependent chemistry is important for a proper description of gas thermal balance. The strongest impact on the gas temperature (up to 100 K) occurs in the outer, low-density region beyond 100 AU. This is mainly due to the shift of H2/H PDR transition deeper into the disk with time. In accordance with previous studies, it is found that the gas becomes hotter than the dust in elevated disk regions reaching 1000-10000 K in the inner atmosphere. However, the main heating source is different for the two dust models. In the disk with pristine dust it is photoelectric heating by grains. In the atmosphere of disk with evolved dust grains are strongly depleted, therefore photoelectric heating by PAHs becomes a dominant heating process. Thus a realistic, observationallybased estimates of absolute PAH abundances and sizes are required to calculate accurately gas temperature in the inner, ∼ 1 -50 AU disk atmosphere accessible with Spitzer, Herschel, and ALMA. The response of disk chemical structure to the dust growth and sedimentation is twofold. First, due to higher transparency a partly UV-shielded molecular layer is shifted closer to the dense midplane. Second, the presence of big grains in the disk midplane delays the freeze-out of volatile gas-phase species such as CO there, while in adjacent upper layers the depletion is still effective. Even though the dust evolution shifts the molecular layer of the water vapor closer toward the cooler, midplane disk region, it increases its overall concentration. This aggravates the disagreement between the water vapor column densities predicted by modern astrochemical models, which are higher than those observed with Herschel in the disks around TW Hya (Hogerheijde et al. 2011) and DM Tau (Bergin et al. 2010) by factors of at least several (see also discussion in Semenov & Wiebe (2011)). Overall, R=100 AU R=550 AU R=100 AU R=550 AU molecular concentrations and thus column densities of many species are enhanced in the disk model with dust evolution, e.g., CO2, NH2CN, HNO, H2O, HCOOH, HCN, CO.",
"pages": [
18,
19
]
},
{
"title": "ACKNOWLEDGEMENTS",
"content": "This research made use of NASA's Astrophysics Data System. This work is supported by the RFBR grants 1002-00612, 12-02-31248, Federal Targeted Program 'Scientific resources of Innovation-Driven Russia' for 2009-2013 and NSh-3602.2012.2. SZ is supported by the Deutsche Forschungsgemeinschaft through SPP 1573: 'Physics of the Interstellar Medium\". DS acknowledges support by the Deutsche Forschungsgemeinschaft through SPP 1385: 'The first ten million years of the solar system - a planetary materials approach' (SE 1962/1-1 and 1-2). A. V. acknowledges the support of the National Science Foundation (US) for the astrochemistry program at the University of Virginia. We thank Kees Dullemond, Andras Zsom, Ewine F. van Dishoeck and Simon Bruderer for valuable discussions. We highly appreciate comments and suggestions of an anonymous referee, that helped us a lot to improve the quality of the paper.",
"pages": [
19
]
},
{
"title": "REFERENCES",
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Tielens, 271-283 Koerner, D. W., Sargent, A. I., & Beckwith, S. V. W. 1993, Icarus, 106, 2 Lada, C. J. 1987, in IAU Symposium, Vol. 115, Star Forming Regions, ed. M. Peimbert & J. Jugaku, 1-17 Malbet, F., Lachaume, R., & Monin, J.-L. 2001, A&A, 379, 515 Men'shchikov, A. B. & Henning, T. 1997, A&A, 318, 879 Mihalas, D. 1978, Stellar atmospheres /2nd edition/, ed. Hevelius, J. Muto, T., Grady, C. A., Hashimoto, J., Fukagawa, M., Hornbeck, J. B., Sitko, M., Russell, R., Werren, C., Curé, M., Currie, T., Ohashi, N., Okamoto, Y., Momose, M., Honda, M., Inutsuka, S., Takeuchi, T., Dong, R., Abe, L., Brandner, W., Brandt, T., Carson, J., Egner, S., Feldt, M., Fukue, T., Goto, M., Guyon, O., Hayano, Y., Hayashi, M., Hayashi, S., Henning, T., Hodapp, K. W., Ishii, M., Iye, M., Janson, M., Kandori, R., Knapp, G. R., Kudo, T., Kusakabe, N., Kuzuhara, M., Matsuo, T., Mayama, S., McElwain, M. 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"pages": [
20,
21
]
},
{
"title": "A. MAIN GAS HEATING AND COOLING PROCESSES",
"content": "A.1. Main heating processes PHOTOELECTRICHEATING BY GRAINS We follow Kamp & van Zadelhoff (2001) and calculate the photoelectric heating rate by silicate grains as Röllig, M., Abel, N., Bell, T., Bensch, F., Black, J., Ferland, G., Jonkheid, B., Kamp, I., Kaufman, M., Bourlot, J. L., Petit, F. L., Meijerink, R., Morata, O., Ossenkopf, V., Roueff, E., Shaw, G., Spaans, M., Sternberg, A., Stutzki, J., Thi, W., Dishoeck, E. V., Hoof, P. V., Viti, S., & Wolfire, M. 2007, A&A, 467, 187 Isotopic Evolution of the Solar Nebula and Protoplanetary Disks, ed. Apai, D. A. & Lauretta, D. S., 97-127 Shakura, N. I. & Sunyaev, R. A. 1973, A&A, 24, 337 Tanaka, H., Himeno, Y., & Ida, S. 2005, ApJ, 625, 414 Tannirkulam, A., Harries, T. J., & Monnier, J. D. 2007, ApJ, 661, 374 Thi, W.-F., Woitke, P., & Kamp, I. 2011, MNRAS, 412, 711 Tielens, A. G. G. M. & Hollenbach, D. 1985, ApJ, 291, 722 van Dishoeck, E. F. & Black, J. H. 1982, ApJ, 258, 533 Woodall, J., Agúndez, M., Markwick-Kemper, A. J., & Millar,T. J. 2007, A&A, 466, 1197 Youdin, A. N. & Lithwick, Y. 2007, Icarus, 192, 588 where k UV abs is the dust absorption coefficient at UV wavelengths, χ is the strength of the UV radiation field in units of the Draine FUV interstellar field (Draine 1978), and /epsilon1 dust is the photoelectric efficiency determined by the grain charge parameter x = √ T g χ/ n e (here n e is the electron number density). For /epsilon1 we adopt expressions from Kamp & van Zadelhoff (2001). The relative strength of the FUV, χ , is defined as The average dust opacity at UV wavelengths is determined by integration of frequency-dependent dust absorption cross-sections in the UV frequency range where f ( a ) is given by the dust evolution model. PHOTOELECTRIC HEATING BY PAHS Polycyclic aromatic hydrocarbons (PAHs) possess large cross-sections for UV photon absorption and therefore can efficiently heat gas by photoelectric emission, even if their abundance is low. Heating by PAHs can be particularly important for disks with evolved dust, since PAHs are better mixed with gas than macroscopic dust particles, and thus remain in the disk atmosphere while bigger grains settle towards the midplane (Dullemond et al. 2007a). Bakes & Tielens (1994) derived a simple analytical expression for their PE heating rate: where n H is the hydrogen nuclei number density, and /epsilon1 PAH = 0 . 0487 / (1 + 4 × 10 -3 x 0 . 73 ). The parameter f PAH is the depletion factor of the PAH abundance relative to the diffuse ISM value, which is estimated to be ∼ 10 -20% of the total carbon budget (Draine & Li 2007). The details of the evolution of PAHs in protoplanetary disks are far from being fully understood, though it is clear that high-energy stellar radiation may play an enormous role in their destruction and chemical transformation (Acke et al. 2010; Siebenmorgen & Krügel 2010; Siebenmorgen & Heymann 2012). Therefore, we do not consider PAHs in the simulations of dust evolution and treat f PAH as a free parameter of the model. In the present paper we assume f PAH = 0 . 1 based on estimates from observations of PAH spectra in disks surrounding young T Tauri and Herbig Ae stars (Keller et al. 2008; Kamp 2011). A detailed study of the effects of PAHs heating on the structure of protoplanetary disks with evolved dust is beyond the scope of the present paper. COSMIC RAY HEATING Cosmic ray (CR) particles deposit energy mainly through ionization of H2 and H at the rate (Bakes & Tielens 1994): where ζ CR s -1 is the attenuated CR ionization rate and n (X) denotes concentration of a species X. HEATING BY SURFACE H 2 FORMATION Formation of one H2 molecule on the grain surface liberates 4.48 eV of energy, but the exact partitioning of this energy into H2 vibration, rotation, translation and accommodation by a grain lattice remains uncertain. It is commonly assumed that this energy is equally redistributed between rotational, vibrational and translational movements. We assume that formation of one hydrogen molecule returns only 1.5 eV (2 . 4 × 10 -12 erg) to the gas (Black & Dalgarno 1976). Then, the corresponding heating rate is where R H2form is the H2 formation rate in s -1 . The further details of calculation of chemical reactions rates are described in Sect. 2.3. PHOTODISSOCIATION OF H 2 We take into account only spontaneous radiative dissociation of H2 : H2 + h ν → H2 ∗ → H + H + h ν . Assuming that the average kinetic energy of dissociation products is 0.45 eV (Stephens & Dalgarno 1973), the corresponding heating rate is where R H2 phdis is the photodissociation rate of H2 . To calculate this rate, we take into account self-shielding of H2 molecules as given by Eq.(37) from Draine & Bertoldi (1996). COLLISIONAL DE-EXCITATION OF H 2 In dense PDR regions collisional de-excitation of FUV-pumped H ∗ 2 is the second most important heating mechanism (Sternberg & Dalgarno 1995). Here we adopt a simple two-level approximation of H2vibrational heating and cooling from Röllig et al. (2006), which nevertheless well reproduces the net heating rate computed by Sternberg & Dalgarno (1995) with 15 vibrational levels. The net vibrational heating is given by the following expression: where Γ H ∗ 2 is the vibrational heating rate by collisional de-excitation and Λ H2 is the vibrational cooling rate. For details of the calculation of the heating and cooling rates we refer to the Appendix C in Röllig et al. (2006). C photoionization - Ionization of atomic carbon releases electrons with kinetic energies of ∼ 1 eV (Black 1987). The corresponding heating rate can be approximated as: where R Cph is the photoionization rate of the C atoms. Viscous heating - The viscous heating rate is given by (Frank et al. 1992): where the kinematic viscosity of the gas is parameterized as ν kin = α cT H g (Shakura & Sunyaev 1973), cT is the isothermal sound speed, Hg is the gas pressure scale height, and Ω kep is the Keplerian velocity.",
"pages": [
21,
22,
23
]
},
{
"title": "A.2. Main cooling processes",
"content": "NLTE LINE COOLING The net line cooling rate for a given species is determined by the total amount of upwards and downwards radiative transitions. Level populations for each coolant are calculated from statistical equilibrium equations. Unlike FUV, the local FIR intensity that enters these equations depends on the temperature and level populations over the large part of the disk. This requires iterations over all vertical grid points simultaneously. To simplify a calculation, we adopt an escape probability approach using the expression (B9) in Tielens & Hollenbach (1985). We perform the full non-LTE calculations, considering the major coolants for a typical PDR: fine structure lines of C, O, C + and rotational lines for the CO molecule. The data for energy levels, collision, emission and absorption coefficients for computation of the NLTE line cooling are taken from the LAMDA database (Schöier et al. 2005). The data include collision rate coefficients for collisions of H2 , H, e -, He, and H + with O and C atoms, as well as collisions of H2 , H, and e -with C + , and H2 with CO. For minor coolants we use approximate formulas presented below. HIGH-TEMPERATURE COOLANTS The cooling by emission from metastable levels of neutral and ionic species becomes important at temperatures exceeding several thousand Kelvin. We calculate the cooling rate from 1 D -3 P emission by O I (630 nm) according to Sternberg & Dalgarno (1989): where n O is the neutral oxygen concentration. The cooling by electron impact excitation of metastable levels of ionic species (e.g., Fe + , Fe ++ , Si + ) is calculated by approximate formula from Dalgarno & McCray (1972): where parameters Ai and Ti for each ion are given in Dalgarno & McCray (1972). Another important cooling process at high temperatures is Ly α emission. We adopt the cooling rate by Ly α emission from Spitzer (1978): H 2 O LINE EMISSION Rotational line emission of the H2O molecule can contribute to cooling in dense disk regions. We include line cooling rates of H2O due to the excitation by H2 , using analytical fits from Neufeld & Kaufman (1993) for T > 100 K and from Neufeld et al. (1995) for 10 K < T < 100 K. THERMAL ACCOMMODATION Thermal accommodation is the energy exchange by inelastic collisions between dust and gas. In disk models with standard ISM-like dust it is a dominant cooling process, with the exception of the upper, tenuous atmosphere and outer radii ( R > 400 AU) (e.g., Woitke et al. 2009). We utilize the corresponding cooling rate from Burke & Hollenbach (1983): where the thermal accommodation coefficient α T is set to 0.3 ( a typical value for silicates and carbon).",
"pages": [
23
]
},
{
"title": "B. RADIATIVE TRANSFER AND GAS THERMAL BALANCE BENCHMARKING",
"content": "The RT module of the ANDES code was checked for the following cases which allow an analytic or semi-analytic solution: v 1e-02 1e-04 1e-06 1e-08 1e-10 1e-02 1e-04 1e-06 1e-08 1e-10 1e-02 1e-04 1e-06 1e-08 1e-10 0.001 0.01 0.1 1 10 A V The surface of the disk is a photodissociation region (PDR) controlled by UV radiation from a star and interstellar radiation field. Therefore, we perform benchmarking of the thermal balance in our code as proposed in the PDR code comparison study (Röllig et al. 2007). For benchmarking purposes we use a reduced chemical network restricted to the most abundant elements (H, He, O, C, e -) and 31 species(Table 4 in Röllig et al. 2007). The reaction rates are taken from the UMIST99 database with some corrections from A. Sternberg. H2 dissociation rate is 5 × 10 -18 χ/ 10s -1 . Cosmic ray H ionization rate is ζ = 5 × 10 -17 s -1 . For more details of benchmark test we refer to Röllig et al. (2007). All benchmark models assume plane-parallel, semi-infinite geometry of clouds of total constant hydrogen density of 10 3 and 10 5 . 5 cm -3 . The values of the standard far UV field were taken as χ = 10 and 10 5 times the Draine (1978) field. There are two sets of benchmark models: four with fixed dust and gas temperatures of 30 and 50 K, respectively, and the other set of four models with the gas temperature resulting from thermal balance. The first set of models with fixed temperature aims at testing main ingredients of the thermal balance: solutions of chemistry and statistical equilibrium equations for level populations of main coolants, while the second set examines solution of thermal balance. Here we present results of benchmark tests for both kinds of models with density n tot H = 10 5 . 5 cm -3 and far UV field strength χ = 10 5 (models F4 and V4 in Röllig et al. (2007)). The left panel of Figure 19 shows comparison of our calculations with post-benchmark results for the H/H2 transition zone typical for PDR environment. Right panel of Figure 19 shows the C + /CO/C transition zone. Main heating and cooling rates included in benchmarking are shown in the left panel of Figure 20. Gas-grain cooling and [OI] 63 µ mline are the dominant cooling processes for AV < 0 . 5. CO lines dominate cooling at high attenuated regions. Our line cooling rates show remarkable agreement with data from Röllig et al. (2007) for dominant cooling processes: [CII] 158 µ m, [OI] 63, 145 µ m, [CI] 370, 610 µ mlines. Comparison of our model results for gas temperature in the slab with other PDR codes is H el H el H el CO C + C shown in Figure 20. At small AV the gas temperature is much higher than the dust temperature due to photoelectric heating and agrees well with other PDR codes.",
"pages": [
23,
24,
25
]
}
]
2013ApJ...766...41S
https://arxiv.org/pdf/1205.6774.pdf
<document>
<section_header_level_1><location><page_1><loc_10><loc_81><loc_85><loc_85></location>Identifying the Location in the Host Galaxy of the Short GRB111117A with the Chandra Sub-arcsecond Position</section_header_level_1>
<text><location><page_1><loc_9><loc_67><loc_86><loc_78></location>T. Sakamoto 1 , 2 , 3 , 4 , E. Troja 1 , 3 , 5 , 6 , K. Aoki 7 , S. Guiriec 5 , M. Im 8 , G. Leloudas 9 , 18 , D. Malesani 9 , A. Melandri 10 , A. de Ugarte Postigo 9 , 13 , Y. Urata 11 , D. Xu 12 , P. D'Avanzo 10 , J. Gorosabel 13 , Y. Jeon 8 , R. S'anchez-Ram'ırez 13 , M. I. Andersen 9 , 19 , J. Bai 21 , 22 , S. D. Barthelmy 3 , M. S. Briggs 25 , S. Foley 26 , A. S. Fruchter 15 , J. P. U. Fynbo 9 , N. Gehrels 3 , K. Huang 14 , M. Jang 8 , N. Kawai 16 , H. Korhonen 19 , 24 , J. Mao 21 , 22 , 23 , J. P. Norris 17 , R. D. Preece 25 , J. L. Racusin 3 , C. C. Thone 13 , K. Vida 20 X. Zhao 21 , 22</text>
<section_header_level_1><location><page_1><loc_41><loc_60><loc_54><loc_62></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_13><loc_46><loc_82><loc_60></location>We present our successful Chandra program designed to identify, with sub-arcsecond accuracy, the X-ray afterglow of the short GRB 111117A, which was discovered by Swift and Fermi . Thanks to our rapid target of opportunity request, Chandra clearly detected the X-ray afterglow, though no optical afterglow was found in deep optical observations. The host galaxy was clearly detected in the optical and near-infrared band, with the best photometric redshift of z = 1 . 31 +0 . 46 -0 . 23 (90% confidence), making it one of the highest known short GRB redshifts. Furthermore, we see an offset of 1 . 0 ± 0 . 2 arcseconds, which corresponds to 8 . 4 ± 1 . 7 kpc, between the host and the afterglow position. We discuss the importance of using Chandra for obtaining sub-arcsecond X-ray localizations of short GRB afterglows to study GRB environments.</text>
<text><location><page_1><loc_13><loc_44><loc_38><loc_45></location>Subject headings: gamma rays: bursts</text>
<unordered_list>
<list_item><location><page_1><loc_9><loc_26><loc_45><loc_31></location>4 Department of Physics and Mathematics, College of Science and Engineering, Aoyama Gakuin University, 510-1 Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa 2525258, Japan</list_item>
</unordered_list>
<text><location><page_1><loc_9><loc_24><loc_45><loc_26></location>5 NASA Postdoctoral Program Fellow, Goddard Space Flight Center, Greenbelt, MD 20771</text>
<text><location><page_1><loc_9><loc_15><loc_45><loc_18></location>8 Center for the Exploration of the Origin of the Universe (CEOU), Department of Physics and Astronomy, Seoul National University, Seoul, 151-747, Korea</text>
<text><location><page_1><loc_9><loc_11><loc_45><loc_14></location>9 Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen Ø, Denmark</text>
<section_header_level_1><location><page_2><loc_9><loc_85><loc_23><loc_86></location>1. Introduction</section_header_level_1>
<text><location><page_2><loc_9><loc_38><loc_45><loc_83></location>Gamma-ray bursts (GRBs) are traditionally divided in two classes based on their duration and spectral hardness: the long duration/soft spectrum GRBs, and the short duration/hard spectrum GRBs (Kouveliotou et al. 1993). The two classes of bursts further differ in their spectral lags, the measurement of the delay in the arrival time of the low-energy photons with respect to the higher energy ones: long bursts tend to have large positive lags, while short bursts exhibit negligible or negative lags (Norris & Bonnell 2006). The long standing paradigm is that these two phenomenological classes of GRBs originate from different progenitor systems. A preponderance of evidence now links long GRBs with the death of massive stars (Woosley & Bloom 2006, and references therein), yet the origin of short GRBs remains largely unknown. The common notion that short bursts originate from coalescing compact binaries, either neutron star-neutron star (NSNS) or neutron star-black hole (NS-BH) mergers (e.g., Eichler et al. 1989; Paczynski 1991; Narayan et al. 1992; Rosswog 2005; Rezzolla et al. 2011), makes them the most promising tool to aid in the direct detection of gravitational waves (GWs) by forthcoming facilities such as AdvancedLIGO, Advanced-VIRGO or LCGT (KAGRA) (e.g., Nissanke et al. 2010). It is therefore of primary importance to convincingly corroborate the merger scenario with a robust observational basis.</text>
<text><location><page_2><loc_9><loc_31><loc_45><loc_38></location>Significant progress in understanding the origin of short GRBs has been achieved only recently. This advance was enabled by the detection of their afterglows in 2005 thanks to the rapid position notice and response by HETE-2 (Ricker et al. 2003)</text>
<text><location><page_2><loc_51><loc_73><loc_86><loc_86></location>and Swift (Gehrels et al. 2004). The very first localizations of short GRBs immediately provided us with fundamental clues about their nature. They demonstrated that short GRBs are cosmological events with an isotropic equivalent energy scale of 10 49 -10 52 erg, that they occur in different environments than long GRBs, and are not associated with bright Type Ic supernovae (Bloom et al. 2006; Prochaska et al. 2006; Covino et al. 2006).</text>
<text><location><page_2><loc_51><loc_41><loc_86><loc_72></location>Since 2005 the sample of well-localized short GRBs has significantly grown, allowing for a deeper insight into the nature of their progenitors. The observed redshift distribution, ranging 0 . 11 /lessorsimilar z /lessorsimilar 1, hints at a progenitor system with a broad range of lifetimes (Berger et al. 2007). Another critical test of the progenitor models is the observed offset distribution of short bursts (Troja et al. 2008; Fong et al. 2010; Church et al. 2011). The median physical projected offset between the host center and the short GRB position is ∼ 5 kpc (Fong et al. 2010), which is about five times larger than that of long GRBs (Bloom et al. 2002), and shows a broader dispersion. This is in agreement with the merger scenario, as several models NS-NS/NS-BH systems are expected to receive significant kick velocities at birth (Bloom et al. 1999; Fryer et al. 1999; Belczynski et al. 2006), or to dynamically form in globular clusters in the outskirts of their galaxies (Grindlay et al. 2006).</text>
<text><location><page_2><loc_51><loc_19><loc_86><loc_40></location>Despite the major progress of the last few years, the study of short GRBs and their progenitors has still been suffering from their less secure afterglow positions and redshifts. Unlike long GRBs, none of the redshifts of short GRBs 1 has been directly measured through afterglow spectroscopy, and only in the case of GRB 060121, a photometric redshift was derived from the afterglow spectral energy distribution (de Ugarte Postigo et al. 2006; Levan et al. 2006). This is because the optical afterglows are significantly fainter than those of long GRBs (Nysewander et al. 2009; Kann et al. 2011). The redshifts of short GRBs are instead measured from spectroscopic observa-</text>
<text><location><page_3><loc_9><loc_71><loc_45><loc_86></location>tions of the 'associated' host galaxy. The likelihood of a spurious association is small when a sub-arcsec position is available. However, if an afterglow is only detected by the Swift X-Ray Telescope (XRT; Burrows et al. 2005), the probability of a chance alignment is higher due to the larger uncertainty in the localization (2-5 '' ). Unfortunately, the latter scenario represents the majority of cases ( ∼ 65% of the Swift short bursts sample).</text>
<text><location><page_3><loc_9><loc_36><loc_45><loc_71></location>A further bias is introduced by the fact that sub-arcsecond positions are mainly derived from optical afterglow detections, which are subject both to absorption along the line of sight and density effects. In fact, in the standard fireball model, the optical brightness depends sensitively on the density of the circumburst environment (Kumar & Panaitescu 2000). This effect disfavors the accurate localization of short GRBs occurring in the lower-density galaxy halo or even outside their own galaxy, in the intergalactic medium. Such populations of large-offest short GRBs has already been suggested by Bloom et al. (2007) and Troja et al. (2008). However being localized mainly by XRT, their association with the putative host galaxy remains uncertain. Increasing the sample of large-offset short bursts with subarcsecond localization is crucial to discriminate whether their progenitors were ejected from their birth site, favoring models which predict NS binaries with large kick velocities and ∼ Gyr lifetimes, or they were formed from dynamical interactions in globular clusters (Salvaterra et al. 2010).</text>
<text><location><page_3><loc_9><loc_10><loc_45><loc_36></location>In this context, rapid Chandra observations of short GRB afterglows represent the critical observational gateway to overcome the current observational limits. Since 65% of Swift short GRBs are detected in X-rays, and only 25% of them are detected in the optical band, X-ray observations have a higher probability of detecting the afterglows of short GRBs. The superb angular resolution of Chandra allows for a sub-arcsecond localization, comparable to optical localizations, thus enabling the secure host identification and the precise measurement of the GRB projected offset. Furthermore, because the X-ray afterglow is less subject to absorption and density effects, Chandra localizations allow us to build a sample of well-localized short GRBs with limited bias, complementing the information derived from the sample of optically</text>
<text><location><page_3><loc_51><loc_79><loc_86><loc_86></location>localized short GRBs. This is the key to distinguish between the different possible short GRB populations (Sakamoto & Gehrels 2009), which could arise from a different progenitor and/or environment.</text>
<text><location><page_3><loc_51><loc_39><loc_86><loc_78></location>In this paper, we report the first results of our Chandra program which led to the accurate localization of GRB 111117A detected by Swift and Fermi . GRB 111117A is the 2nd short burst 2 in which the Chandra position is crucial for the host identification. Our results were leveraged with an intense ground-based follow-up campaign. No optical/infrared counterpart was found, therefore our Chandra localization uniquely provides the only accurate sub-arcsecond position. The paper is organized as follows: we introduce GRB 111117A in § 2. In section § 3, we describe the analysis softwares and methods used in this paper. We report the prompt emission properties in § 4, the X-ray afterglow properties in § 5.1, the deep optical afterglow limits in § 5.2, and the host galaxy properties in § 6. We discuss and summarize our results in § 7. The quoted errors are at the 90% confidence level for prompt emission and X-ray afterglow data, and at the 68% confidence level for optical and near infrared data unless stated otherwise. The reported optical and near infrared magnitudes are in the Vega system unless stated otherwise. Throughout the paper, we use the cosmological parameters, Ω m = 0.27, Ω Λ = 0.73 and H 0 = 71 km s -1 Mpc -1 .</text>
<section_header_level_1><location><page_3><loc_51><loc_36><loc_65><loc_38></location>2. GRB111117A</section_header_level_1>
<text><location><page_3><loc_51><loc_13><loc_88><loc_35></location>On 2011 November 17 at 12:13:41.921 UT, the Swift Burst Alert Telescope (BAT; Barthelmy et al. 2005a) triggered and localized the short GRB 111117A (Mangano et al. 2011). The Fermi Gamma-ray Burst Monitor (GBM; Meegan et al. 2009) also triggered on the burst (Foley et al. 2011). The BAT location derived from the ground analysis was (R.A., Dec.) (J2000) = (00 h 50 m 49.4 s , +23 · 00 ' 36 '' ) with a 90% error radius of 1.8 ' . The Swift XRT started its observation 76.8 s after the trigger. A fading X-ray source was found at the location of (R.A., Dec.) (J2000) = (00 h 50 m 46.22 s , +23 · 00 ' 39.2 '' ) with a 90% error radius of 2.1 '' (Melandri et al. 2011a). The Swift UVOptical Telescope (UVOT; Roming et al. 2005)</text>
<text><location><page_4><loc_9><loc_82><loc_45><loc_86></location>began the observations of the field 137 s after the trigger, and no optical afterglow was detected (Oates et al. 2011).</text>
<text><location><page_4><loc_9><loc_51><loc_45><loc_81></location>The earliest ground observations of the field were performed by the Gao-Mei-Gu telescope (GMG) at 1.96 hr after the BAT trigger, and no afterglow was detected within the XRT error circle with an exposure time of 600 s in the R band (Zhao et al. 2011). The Nordic Optical Telescope (NOT) observed the field at 8.9 hr after the burst, and found an optical source inside the XRT error circle (Andersen et al. 2011), which was later confirmed to have a possible extended morphology by the Magellan/Baade telescope (Fong et al. 2011), the Gemini-South telescope (Cucchiara et al. 2011), the GROND telescope (Schmidl et al. 2011), and the Telescopio Nazionale Galileo (TNG; Melandri et al. 2011b). The Gran Telescopio CANARIAS (GTC), the Subaru telescope, the United Kingdom Infrared Telescope (UKIRT) and the Canada-FranceHawai Telescope (CFHT) also collected images of the field.</text>
<text><location><page_4><loc_9><loc_39><loc_45><loc_51></location>Based on no clear detection of an optical afterglow of the short GRB 111117A, we triggered our Chandra Target of Opportunity (ToO) observation 6 hr after the trigger (Sakamoto et al. 2011b), and the observation started 3 days later. The Xray afterglow was clearly detected in 20 ks, obtaining a sub-arcsecond position of the afterglow in X-rays (Sakamoto et al. 2011c).</text>
<section_header_level_1><location><page_4><loc_9><loc_36><loc_24><loc_37></location>3. Data Analysis</section_header_level_1>
<text><location><page_4><loc_9><loc_15><loc_45><loc_35></location>HEAsoft version 6.11 and the Swift CALDB (version 20090130) were used for the Swift BAT data analysis. The XRT data products were obtained from the automated results available from the UK Swift Science Data Center (Evans et al. 2007, 2009). CIAO 4.3 and CALDB 4.4.6 were used for the Chandra data analysis. The Fermi Gamma-ray Burst Monitor (GBM) data were prepared using the RMFIT software package, 3 with data from three Sodium Iodide (NaI) scintillation detectors (detector ID 6, 7 and 9) and two Bismuth Germanate (BGO) scintillation detectors (detector ID 0 and 1).</text>
<text><location><page_4><loc_11><loc_13><loc_45><loc_15></location>A standard data reduction of optical and near</text>
<text><location><page_4><loc_51><loc_56><loc_86><loc_86></location>infrared images was performed using the IRAF 4 software package. SExtractor 5 (Bertin & Arnouts 1996), SkyCat Gaia 6 and IRAF were used to extract sources and perform the photometry. To accomplish consistent photometry for images collected by various telescopes, we selected 10 common stars in the field and performed relative photometry. When some of the stars were saturated (especially for a large aperture telescope such as GTC), a subset of these 10 reference stars were used. The USNO B-1 R2 magnitude or the SDSS magnitudes were used as the reference magnitude for the stars. For the near infrared images of UKIRT and CFHT, we use the reference stars in the 2MASS catalog. The Galactic extinction has been corrected using E ( B -V ) = 0 . 03 mag toward the direction to this burst (Schlegel et al. 1998). The log of optical and near infrared observations presented in this paper are summarized in Table 1.</text>
<section_header_level_1><location><page_4><loc_51><loc_53><loc_68><loc_54></location>4. Prompt Emission</section_header_level_1>
<text><location><page_4><loc_51><loc_16><loc_86><loc_52></location>The light curve of the prompt emission is composed of two episodes: the first episode shows multiple overlapping pulses with a total duration of 0.3 s, and the second episode is composed of two pulses with a duration of 0.1 s (Figure 1). The duration is T 90 = 464 ± 54 ms (1 σ error; 15-350 keV) measured using the BAT background-subtracted light curve using the mask modulation (e.g., maskweighted light curve). This T 90 duration is significantly shorter than 2 s, which is the standard classification of short GRBs form BATSE (Kouveliotou et al. 1993). Furthermore, this duration is shorter than 0.7 s, which is claimed to be the dividing line between long and short GRBs for the Swift sample (Bromberg et al. 2012). The hard-to-soft spectral evolution is seen in both the first and the second episode of GRB 111117A (see the hardness ratio plot at the bottom panel of Figure 1). There is no indication of extended emission (Norris et al. 2011) down to a flux level of ∼ 2 × 10 -10 erg cm -2 s -1 , assuming a power-law spectrum with a photon index of α = -2 ( N ( E ) ∝ E α ) in the 14-200 keV band by examining the BAT sky image from 60 s (after the spacecraft slew set-</text>
<text><location><page_5><loc_9><loc_71><loc_45><loc_86></location>950 s after the BAT trigger time (hereafter t 0 , BAT ). The spectral lag between the 100-350 keV and the 25-50 keV band is 0 . 6 ± 2 . 4 ms, which is consistent with zero, using the BAT raw light curves (non mask-weighted light curves) by subtracting a constant background measured around the burst. In the fluence ratio versus T 90 plane, GRB111117A is located in the same region where most of the BAT short GRBs are located (Figure 2), further confirming its short GRB nature.</text>
<text><location><page_5><loc_9><loc_16><loc_45><loc_71></location>The time-integrated spectral properties are investigated by performing a joint spectral analysis with BAT and GBM data. The spectrum is extracted from t 0 , BAT + 0.024 s to t 0 , BAT + 0.520 s using batbinevt for the BAT data and using the RMFIT software package for the GBM data in the same time interval. The BAT energy response file is generated by batdrmgen . The GBMenergy response files were retrieved from the HEASARC Fermi archive for trigger bn111117510. We use the xspec spectral fitting package to do the joint fit. The energy ranges of 15-150 keV, 8-900 keV and 0.2-45 MeV are used for the BAT, the GBM-NaI and the GBM-BGO instruments, respectively. The model includes a inter-calibration multiplicative factor to take into account the calibration uncertainty among the different instruments. The best fit spectral parameters are summarized in Table 2. We find that a power-law multiplied by an exponential cutoff (CPL) 7 provides the best representative model of the data. The best fit parameters in this model are the power-law photon index α CPL = -0 . 28 +0 . 31 -0 . 26 and E peak = 420 +170 -110 keV ( χ 2 /d.o.f. = 627/661). The 90% confidence interval of the inter-calibration factor of the GBM detectors is between 0.50 and 0.78 which is an acceptable range taking into account the current spectral calibration uncertainty between the BAT and the GBM. A simple powerlaw model yields a significantly worse fit to the data ( χ 2 /d.o.f. = 729/662). Furthermore, the significant difference in the power-law photon index the BAT data ( -0 . 52 +0 . 24 -0 . 22 ) and the GBM data ( -1 . 44 +0 . 06 -0 . 08 ) alone disfavors a simple power-law model as the representative model. There is no significant improvement in χ 2 using a Band func-</text>
<text><location><page_5><loc_51><loc_56><loc_86><loc_86></location>(Band et al. 1993) fit ( χ 2 /d.o.f. = 627/660) over a CPL fit. The preferential fit to a CPL model and the systematically harder photon index compared to long GRBs are general characteristics of a time-integrated spectrum of short GRBs (e.g., Ghirlanda et al. 2009; Ohno et al. 2008). The fluence in the 8-1000 keV band calculated using the best fit time-integrated spectral parameters based on a CPL fit above is 7 . 3 +2 . 6 -2 . 1 × 10 -7 erg cm -2 . Due to poor statistics in extracting a spectrum from a very short time window, the peak flux was calculated by scaling the BAT maskweighted countrate into a flux by folding the BAT energy response and assuming the best fit timeintegrated spectral parameters in a CPL model. The peak energy flux at the 8-1000 keV band in the 50 ms window starting from t 0 , BAT + 0.450 s is (3 . 8 ± 1 . 2) × 10 -6 erg cm -2 s -1 . The timeresolved spectroscopy is difficult to perform due to the limited statistics in the data.</text>
<text><location><page_5><loc_51><loc_32><loc_86><loc_56></location>We search for pre-burst emission by analyzing the BAT survey data (detector plane histogram; DPH). Approximately 4.5 hr before the burst trigger, GRB 111117A was in the field of view of BAT (26.1 · from the boresight direction) for ∼ 1 ks during the observation of the blazar PKS 0235+16 (observation ID 00030880085). We use batsurvey script to process the DPH data. The extracted rates at the location of GRB 111117A are corrected to the on-axis rate by applying an off-axis correction based on observations of the Crab. We find no significant emission during this observation at the location of GRB 111117A. The 3 sigma upper limit assuming a power-law spectrum with a photon index of α = -2 is 1 . 4 × 10 -9 erg cm -2 s -1 at the 14-200 keV band in 300 s exposure.</text>
<section_header_level_1><location><page_5><loc_51><loc_29><loc_62><loc_30></location>5. Afterglow</section_header_level_1>
<section_header_level_1><location><page_5><loc_51><loc_26><loc_61><loc_27></location>5.1. X-rays</section_header_level_1>
<text><location><page_5><loc_51><loc_10><loc_86><loc_25></location>The Swift XRT X-ray afterglow light curve can be fit to a simple power-law decay (Figure 4). The spectrum collected in the photon counting (PC) mode is well described by an absorbed power-law model. The best fit spectral parameters are a photon index of -2 . 19 +0 . 36 -0 . 38 and an excess N H of 1 . 8 +1 . 1 -1 . 0 × 10 21 cm -2 ( z = 0) assuming the galactic N H at the burst direction of 3 . 7 × 10 20 cm -2 (Kalberla et al. 2005). Both the measured photon index and N H for GRB111117A</text>
<text><location><page_6><loc_9><loc_83><loc_45><loc_86></location>are consistent with those of other Swift short GRBs (Kopaˇc et al. 2012; Fong et al. 2012).</text>
<text><location><page_6><loc_9><loc_24><loc_45><loc_83></location>The Chandra observation started at 12:39:25 UT, and ended at 18:39:10 UT on 2011 November 20 with a total exposure of 19.8 ks. The ACIS instrument had five CCD chips (S3, S4, S5, I2 and I3) enabled, with the S3 chip as the aiming point for the source. The data were collected in the FAINT mode. The X-ray afterglow is clearly detected in the Chandra observation with 3.9 σ significance by wavdetect (source net counts of 8) within the XRT error circle. To refine the astrometry of the Chandra data, we apply the same analysis method described in Feng & Kaaret (2008). We extract the Chandra image (0.35 - 8 keV) that overlaps with the GTC image (4 . 4 ' × 8 . 7 ' ). The astrometry of the GTC image is calibrated against the SDSS catalog, and its standard deviation is ∼ 0.3 '' . We run wavdetect with options of scales='1.0 2.0 4.0 8.0 16.0' and sigthresh = 4 × 10 -6 to the extracted Chandra image. There are four sources which have a good match between the images. We then use the geomap task in the IRAF IMMATCH package to find the best coordinate transformation between the Chandra and the GTC image by fitting those four sources. Finally, we apply geoxytrans task (IRAF IMMATCH package) for the originally detected Chandra position using the coordinate transformation calculated by geomap to find the astrometrically corrected Chandra afterglow position. The refined afterglow position is shifted by δ R.A. = -0 . 221 '' and δ Dec. = -0 . 020 '' from the position originally derived by wavdetect . The best Chandra X-ray afterglow position is (R.A., Dec.) (J2000) = (00 h 50 m 46.264 s , +23 · 00 ' 39.98 '' ) with 1 σ statistical uncertainty of 0.09 '' in right ascension and 0.16 '' in declination. When we include the systematic uncertainty of 0.3 '' , 1 σ error radius of the Chandra position is 0.35 '' . The Chandra position is well within the XRT 90% error circle (see Figure 3).</text>
<text><location><page_6><loc_9><loc_16><loc_45><loc_24></location>The combined Swift XRT and Chandra X-ray afterglow light curve is well fit by a simple powerlaw with index of -1 . 25 +0 . 09 -0 . 12 . As shown in Figure 4, the X-ray afterglow of GRB 111117A belongs to a dim population of the Swift short GRBs.</text>
<section_header_level_1><location><page_6><loc_9><loc_14><loc_20><loc_15></location>5.2. Optical</section_header_level_1>
<text><location><page_6><loc_9><loc_10><loc_45><loc_12></location>We investigate the possible optical afterglow emission by using the image subtraction technique</text>
<text><location><page_6><loc_51><loc_58><loc_86><loc_86></location>between the early and the late time epoch observations by TNG and GTC. We use the ISIS software package (Alard & Lupton 1998) to perform the image subtraction. The early and the late epoch observations of TNG and GTC were obtained at t 0 , BAT + 7.23 hr and t 0 , BAT + 7.89 hr, and t 0 , BAT + 11.4 days and t 0 , BAT + 14.4 days, respectively. We find no significant emission at the Chandra Xray afterglow location in the subtracted images in both the TNG and the GTC observations (Figure 5), with 3 sigma upper limits of R > 24.1 mag for TNG and r > 24.9 (AB) mag for GTC. The TNG limiting magnitudes of the first and second epochs are R > 24 . 7 mag and R > 25 . 4 mag, respectively. For GTC, the limiting magnitude of the first and second epoch are r > 25 . 8 (AB) mag and r > 26 . 1 (AB) mag, respectively. Those limits are some of the deepest optical limits on short GRBs ever obtained (see upper panel of Figure 6).</text>
<section_header_level_1><location><page_6><loc_51><loc_55><loc_64><loc_56></location>6. Host Galaxy</section_header_level_1>
<text><location><page_6><loc_51><loc_20><loc_86><loc_53></location>The host galaxy of GRB 111117A has been detected in the near infrared and optical bands. There is only one near-infrared/optical source located near the Chandra X-ray afterglow position. Although the weak nature of the source makes it difficult to investigate whether the source is extended or not, the optical flux of the source is constant between 7 hr and 14 days after the burst at a level of ∼ 1.1 µ Jy (bottom panel of Figure 6). Using the formula provided by Bloom et al. (2002), the probability of finding an unrelated galaxy of the R magnitude of ∼ 23.3 with the distance of 1.0 '' is 0.8%. We also investigate the chance probabilities of the three nearby objects. The probabilities of those objects are between 24% and 42% which are significantly larger than that of the host candidate. Although the chance probability of the host candidate is non-negligible, the chance of a misidentification of the host galaxy is reasonably small. Therefore, we conclude that the source detected in the K , J , z , i , r , g , and R bands is the host galaxy of GRB 111117A (Figure 7).</text>
<text><location><page_6><loc_51><loc_11><loc_86><loc_20></location>To estimate the redshift of the host galaxy, we perform a spectral energy density (SED) fit with the stellar population model of Maraston (2005). We use the single stellar populations (SSP) models with a Salpeter initial mass function (Salpeter 1955), solar metallicity which ranges from 0.005</text>
<text><location><page_7><loc_9><loc_11><loc_45><loc_86></location>Z /circledot to 3.5 Z /circledot (0.005, 0.02, 0.5, 1.0, 2.0 and 3.5 Z /circledot ), and a red or blue horizontal branch morphology. A total number of 269 SED templates ranging in stellar age from 10 Myr to 15 Gyr was applied. The Bayesian Photometric Redshift software (BPZ; Ben'ıtez 2000) is used to fit the data in g , r , and i bands (GTC), z band (GMG), J band (CFHT) and K band (UKIRT) with those SED templates. We find that the best fit SED template corresponds to a solar metallicity, a red horizontal branch morphology and the luminosity weighted mean stellar age of 0.1 Gyr with a redshift of 1.36 +0 . 45 -1 . 18 . Our best fit SED template of SSP model with a solar metallicity and a red horizontal branch matches well with other short GRB hosts studied by Leibler & Berger (2010). As seen in Figure 8 (top), there is a less significant low redshift solution ( z < 0 . 25). We find that this low redshift solution is coming from the template with the young stellar age of ∼ 10 Myr. As we will discuss in § 7, it is unlikely that the host galaxy has the stellar age of ∼ 10 Myr. Therefore, to constrain the redshift better, we focus on 41 SED templates with solar metallicity and a red horizontal branch morphology with stellar age from 20 Myr to 15 Gyr. The signal-to-noise is low, and there are no clear absorption or emission line features in the spectrum. The continuum is consistent with the best fit SED template. The bottom panel of Figure 8 shows the posterior probability distribution of the estimated redshift for this SED fit. No low redshift solution is evident in the probability distribution. We find the best estimated redshift to be 1.31 (90% confidence interval 1 . 08 < z ph < 1 . 77). The likelihood that the redshift is correct is 80% (reduced χ 2 of the fit is 0.65 with 2 d.o.f.). The best fit SED template is the case with the luminosity weighted mean stellar age of 0.1 Gyr and a mass of ∼ 1 × 10 9 M /circledot . Figure 9 shows the best fit SED with the photometric data, and the GTC spectrum with an exposure time of 4 × 1800 s. GTC spectroscopy was performed with the R1000B grism, which has a central wavelength of 5510 ˚ A and covers the spectral range between 3700 and 7000 ˚ Awith a resolution of ∼ 1000 at 5500 ˚ A. To investigate the likelihood of the host being a star-forming galaxy, we also examine the SED templates with an exponentially decaying star formation rate (Maraston 2010), with an e -folding time of 0.1, 1 and 10 Gyr (stellar age</text>
<text><location><page_7><loc_51><loc_35><loc_86><loc_86></location>ranges from 10 Myr to 15 Gyr). Although our J band data point shows a relatively poor agreement with the best fit template with an e -folding time of 0.1 Gyr and the luminosity weighted mean stellar age of 0.3 Gyr, the fit is still acceptable (reduced χ 2 = 0.91 with 2 d.o.f.). The best fit redshift in this case is 1.18 +0 . 61 -0 . 21 . The fit becomes worse if the e -folding time gets larger. Therefore, our current data also support of an ∼ 0 . 1 Gyr post-starburst galaxy (see bottom panel of Figure 9). We also fitted the optical-NIR SED using MAGPHYS package (de Cunha et al. 2008) to check the validity of the fitting result. The MAGPHYS fit includes an extinction parameter as a part of the fit, but performs the fitting at a given redshift. An exponentially decaying star formation rate is assumed. The redshifts were increased by a step of 0.05 from 0.8 to 1.5. We confirm that the returned χ 2 is the smallest in the range of the z ph from the BPZ, and a moderate extinction of A V = 0 . 2 -0 . 5 mag is found. The best fit solutions give the exponential time scale of about 1.5 Gyr, with the luminosity weighted mean stellar age (in r -band) of a few hundred Myr, and a stellar mass of a few times 10 9 M /circledot . These output values are consistent with the solutions derived with the photometric redshift. In summary, based on various SED template fits, we can conclude the following about the host galaxy: the redshift of the host is ∼ 1.3 regardless of the SED model and the host is either a star-forming galaxy of the luminosity weighted mean stellar age of 0.1 Gyr and a mass of ∼ 1 × 10 9 M /circledot or a poststarburst galaxy. Further deep J or Y band data are crucial to pin down the host properties.</text>
<text><location><page_7><loc_51><loc_11><loc_86><loc_34></location>A significant offset between the center of the host galaxy and the X-ray afterglow has been found for GRB111117A. The center position of the host galaxy has been examined by running SExtractor on the second epoch of the GTC r image, our highest quality optical image. The best location of the host center is (R.A., Dec.) (J2000) = (00 h 50 m 46.258 s , +23 · 00 ' 40.97 '' ). The position moves by less than half a pixel ( < 0 . 13 '' ) by changing the detection threshold of SExtractor from 1.5 to 3.0 sigma. Therefore, the projected offset between the center of the host galaxy and the X-ray afterglow is 1.0 '' ( δ R.A. = 0 . 083 '' and δ Dec. = -0 . 990 '' ; see Figure 7). Taking into account the statistical error in the X-ray afterglow position of 0 . 18 '' and the statistical error of the</text>
<text><location><page_8><loc_9><loc_80><loc_45><loc_86></location>host center location of 0 . 13 '' , we estimate the offset with its error to be 1 . 0 ± 0 . 2 arcseconds, which corresponding to a distance of 8 . 4 ± 1 . 7 kpc at a redshift of z = 1 . 31.</text>
<section_header_level_1><location><page_8><loc_9><loc_77><loc_21><loc_78></location>7. Discussion</section_header_level_1>
<text><location><page_8><loc_9><loc_41><loc_45><loc_76></location>Our photometric redshift of 1 . 31 +0 . 46 -0 . 23 (90% confidence) for the host galaxy of GRB 111117A is realistic for the following reasons. First, by plotting the observed r AB magnitude ( r AB ) of the host galaxies of short GRBs as a function of redshift (Berger 2009), we find that the relatively faint magnitude of the host galaxy, r AB = 24 . 20 ± 0 . 07, is located at the redshift range of > 0.5 (Figure 10). Second, we find that the less significant low redshift solution ( z < 0 . 25) in the photometric redshift estimation (Figure 8) is coming from the templates with the unrealistic young stellar ages of ∼ 10 Myr. At z = 0 . 25, if the galaxy is star forming, there would be a chance of seeing emissions of [OII], Hβ and [OIII] in the optical spectrum, yet, we see none of those lines in the GTC spectrum. Furthermore, ∼ 10 Myr is in general too young for a whole galaxy, as opposed to a specific star forming region. Therefore the low redshift solution for the photometric redshift is unlikely to be the case of GRB111117A. Therefore, hereafter, we will discuss the rest-frame properties of GRB 111117A using our best photometric redshift of 1.31.</text>
<text><location><page_8><loc_9><loc_14><loc_45><loc_41></location>Assuming the redshift of 1.31, the isotropic equivalent γ -ray energy ( E γ, iso ) which is integrated from 1 keV to 10 MeV in the rest frame is 3 . 4 +5 . 7 -1 . 5 × 10 51 erg. The peak energy at the rest-frame ( E src peak ) is 945 +455 -310 keV. The 90% errors in E γ, iso and E src peak are taking into account not only a statistical error but also an uncertainty in the estimated redshift. As shown in Figure 11, the E γ, iso of GRB111117A is located at the high end of the E γ, iso distribution of short GRBs and at the low end of the E γ, iso distribution of long GRBs. Relatively low E γ, iso and high E src peak compared to those of long GRBs make GRB 111117A inconsistent with the E src peak -E γ, iso (Amati) relation (Amati et al. 2002). This characteristic is consistent with being a short GRB because most of the short GRBs are well known outliers of the Amati relation (Amati 2006; Nava et al. 2012).</text>
<text><location><page_8><loc_11><loc_12><loc_48><loc_13></location>The optical-to-X-ray spectral index (Jakobsson et al.</text>
<text><location><page_8><loc_51><loc_85><loc_55><loc_86></location>2004),</text>
<section_header_level_1><location><page_8><loc_52><loc_82><loc_85><loc_84></location>β OX ( ≡ log { f ν ( R ) /f ν (3 keV) } / log( ν 3 keV /ν R )) ,</section_header_level_1>
<text><location><page_8><loc_51><loc_37><loc_86><loc_81></location>is estimated to be /lessorsimilar 0.78 using the same definition on the X-ray flux density at 3 keV measured at 11 hrs after the burst, and the optical afterglow limit based on the GTC r band. This upper limit of β OX is within the allowed range of the standard afterglow model between 0.5 to 1.25. Furthermore, according to Margutti et al. (2012b), the optical and the radio afterglow limit is consistent with the external shock model (Granot & Sari 2002) for a small number density ( n /lessorsimilar 0.01-0.2 cm -3 ). However, there is a possibility that a significant amount of the optical afterglow flux was extinguished by the host galaxy. When we fit the Xray afterglow spectrum to a power-law model with the intrinsic absorption at z = 1 . 31, the intrinsic N H is estimated to be 7 . 2 +0 . 7 -0 . 5 × 10 21 cm -2 . Assuming a host extinction law similar to the Milky Way, A V is 4.1 mag (Predehl & Schmitt 1995). Therefore, a significant amount of extinction in the optical flux is expected from the X-ray column density measurement. On the other hand, it is still not clear whether it is possible to have such high extinction at the outskirts of the host where the X-ray afterglow is indicated. Moreover, the amount of extinction which we derived from the SED fit of the host is A V = 0 . 2 -0 . 5 mag (see § 6). At this stage, the origin of the large column density seen in the X-ray afterglow of GRB 111117A is still remains puzzling.</text>
<text><location><page_8><loc_51><loc_12><loc_86><loc_37></location>The projected offset between the afterglow location and the host galaxy center is 8 . 4 ± 1 . 7 kpc using the estimated redshift of 1.31. Although this offset is larger than the median projected offset of ∼ 5 kpc for previously studied short GRBs (Fong et al. 2010), it is within the offset distribution of short GRBs. Using the projected offset of r = 8 . 4 kpc and the stellar age of τ = 0 . 1 Gyr, the minimum kick velocity, v = r/τ , is estimated to be ≈ 80 km s -1 . The estimated kick velocity is similar to or possibly larger than the inferred kick velocity of GRB 060502B (Bloom et al. 2007). Using the typical age of 110 Gyr in the early-type short GRB hosts such as GRB 050509B, GRB 070809 and GRB 090515 (Bloom et al. 2006; Berger 2010), the minimum kick velocity is estimated to be ≈ 1-8 km s -1 .</text>
<text><location><page_8><loc_53><loc_10><loc_86><loc_11></location>In this paper, we have reported the prompt</text>
<text><location><page_9><loc_9><loc_44><loc_45><loc_86></location>emission, the afterglow and the host galaxy properties of short GRB 111117A. The prompt emission observed by the Swift BAT and the Fermi GBM showed 1) a short duration, 2) no extended emission, 3) no measurable spectral lag and 4) a hard spectrum. All those properties can securely classify this burst as a short GRB. Although the optical afterglow has not been detected by our deep observations by TNG and GTC, our rapid Chandra ToO observation provides a sub-arcsec position of the afterglow in X-rays. This Chandra position is crucial to identify the host galaxy and also to measure the significant offset of 1.0 '' between the host center and the afterglow location. Our deep near infrared to optical photometry data of GMG, TNG, NOT, GTC, UKIRT and CFHT enable us to estimate the redshift of the host to 1.31. The observation of GRB 111117A suggests that X-rays are more promising than optical to locate short GRBs with sub-arcsecond accuracy. Combining the sub-arcsecond afterglow position in the X-ray and the deep optical images from the ground telescopes, we successfully investigate the host properties of GRB 111117A even without an optical afterglow. Rapid Chandra ToO observations of short GRBs are still key to increasing the golden sample of short GRBs with redshifts to pin down their nature.</text>
<text><location><page_9><loc_9><loc_10><loc_45><loc_42></location>We would like to thank the anonymous referee for comments and suggestions that materially improved the paper. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. This work is based on the observations using the United Kingdom Infrared Telescope, which is operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the U.K. with a partial support by Swift mission (e.g., Swift Cycle 7 GI grant NNX12AE75G) and the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof'ısica de Canarias, in the island of La Palma. The Dark Cosmology Centre is funded by the Danish National Research Fundation. Partly based on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los</text>
<text><location><page_9><loc_51><loc_58><loc_86><loc_86></location>Muchachos of the Instituto de Astrof'ısica de Canarias. This work was supported by Chandra Cycle 13 grant GO2-13084X. The research activity of AdUP, CCT, RSR and JG is supported by Spanish research projects AYA2011-24780/ESP, AYA200914000-C03-01/ESP and AYA2010-21887-C04-01. GL is supported by the Swedish Research Council through grant No. 623-2011-7117. KV is grateful to the Hungarian Science Research Program (OTKA) for support under the grant K-81421. This work is supported by the 'Lendulet' Young Researchers' Program of the Hungarian Academy of Sciences. HK acknowledges the support from the European Commission under the Marie Curie IEF Programme in FP7. MI and YJ were supported by the he Creative Research Initiative program, No. 2010-0000712, of the National Research Foundation of Korea (NRFK) funded by the Korea government (MEST).</text>
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<figure>
<location><page_12><loc_51><loc_36><loc_85><loc_70></location>
<caption>Fig. 1.- The background subtracted 5 ms light curves of Swift BAT (15-25 keV, 25-50 keV, 50100 keV and 100-350 keV) and Fermi GBM(8-200 keV and 200-400 keV). The bottom panel shows the hardness ratio between the 100-350 keV and the 25-50 keV of the BAT data.</caption>
</figure>
<table>
<location><page_13><loc_13><loc_57><loc_82><loc_75></location>
<caption>Table 1 Log of optical and near-infrared observations of GRB111117A. The magnitudes are corrected for Galactic extinction.</caption>
</table>
<table>
<location><page_13><loc_16><loc_17><loc_79><loc_32></location>
<caption>Table 2 Time-integrated spectral parameters of GRB 111117A.</caption>
</table>
<figure>
<location><page_14><loc_8><loc_60><loc_46><loc_82></location>
<caption>Fig. 2.- Fluence ratios between the 50-100 keV and the 25-50 keV band versus T 90 are shown for GRB111117A (red) and the Swift BAT GRBs. The values of the Swift BAT GRBs are extracted from Sakamoto et al. (2011a).</caption>
</figure>
<figure>
<location><page_14><loc_14><loc_21><loc_40><loc_42></location>
<caption>Fig. 3.- GTC r image (17 '' × 17 '' ) with the XRT 90% error circle in blue and the Chandra 1 sigma error circle, which includes the statistical and the systematic error, in red.</caption>
</figure>
<figure>
<location><page_14><loc_48><loc_51><loc_88><loc_74></location>
<caption>Fig. 4.- Comparison of X-ray afterglow light curves of long-lived and short-lived short GRBs observed by Swift XRT and GRB111117A (red). The Chandra data point of GRB111117A is shown in red filled circle. The long-lived short GRBs include in this figure are GRB050724, GRB051221A, GRB051227, GRB060313, GRB061006, GRB061201, GRB061210, GRB070714B, GRB070724A, GRB070809, GRB071227, GRB080123, GRB080426, GRB090426, GRB090510, GRB090607, GRB090621B and GRB091109B. The shortlived short GRBs include in this figure are GRB050509B, GRB050813, GRB051210, GRB060502B, GRB060801, GRB061217, GRB070429B, GRB080503, GRB080702A, GRB080905A, GRB080919, GRB081024A and GRB081226A.</caption>
</figure>
<figure>
<location><page_15><loc_8><loc_66><loc_46><loc_85></location>
<caption>Fig. 5.- Deep optical TNG (R; 1.4 ' × 1.2 ' ) and GTC (r; 1.1 ' × 1.0 ' ) images of two epochs. The right panel shows the subtracted image of the first and second epoch. No significant residuals are seen in both TNG and GTC subtracted images at the host location (red circle).</caption>
</figure>
<figure>
<location><page_15><loc_8><loc_29><loc_46><loc_51></location>
<caption>Fig. 6.- Top: optical fluxes of the first optical detection (black circle) or an upper limit (filled triangle) of short GRBs (Berger 2010) is shown as a function of the trigger time. The TNG and GTC upper limits of the optical afterglow of GRB 111117A are shown in green and blue filled triangle. Bottom: optical light curves of GRB111117A in R and r band are shown. The plot includes R band measurement from GMG, TNG and NOT, and also the r band measurement from GTC.</caption>
</figure>
<figure>
<location><page_15><loc_51><loc_49><loc_85><loc_63></location>
<caption>Fig. 7.- Multi-color images at the field of GRB111117A. From left to right, and top to bottom, the images are TNG R , NOT R , GTC g , GTC r , GTC i , GMG z , CFHT J and UKIRT K . The host galaxy is marked in a green circle. The X-ray afterglow position determined by Chandra is marked as a red cross. The image scale is 17 '' × 17 '' . All the images are smoothed by the Gaussian function with 3 pixel radius.</caption>
</figure>
<figure>
<location><page_16><loc_11><loc_57><loc_42><loc_74></location>
<caption>Fig. 9.- Top: The SED fit to the photometric data ( g , r , i , z , J and K ) using the templates of the single stellar populations model (Maraston 2005). The GTC spectrum is shown in gray. Bottom: The best fit SED template of the ∼ 0.1 Gyr post-starburst galaxy is overlaid in magenta.</caption>
</figure>
<figure>
<location><page_16><loc_10><loc_36><loc_43><loc_54></location>
<caption>Fig. 8.- Top: Posterior probability distribution of the photometric redshift by the SED fit of the host. All 269 SED templates are used. Bottom: Posterior probability distribution of the photometric redshift of the host by 41 SED templates of a solar metallicity and a red horizontal branch morphology with stellar age from 20 Myr to 15 Gyr.</caption>
</figure>
<figure>
<location><page_16><loc_50><loc_54><loc_86><loc_75></location>
</figure>
<text><location><page_16><loc_65><loc_52><loc_74><loc_52></location>Restframe wavelength (Å)</text>
<text><location><page_16><loc_50><loc_43><loc_51><loc_44></location>(Jy)</text>
<text><location><page_16><loc_50><loc_43><loc_51><loc_43></location>y</text>
<text><location><page_16><loc_50><loc_43><loc_51><loc_43></location>t</text>
<text><location><page_16><loc_50><loc_42><loc_51><loc_43></location>si</text>
<text><location><page_16><loc_50><loc_42><loc_51><loc_42></location>n</text>
<text><location><page_16><loc_50><loc_42><loc_51><loc_42></location>e</text>
<text><location><page_16><loc_50><loc_41><loc_51><loc_42></location>d</text>
<text><location><page_16><loc_50><loc_41><loc_51><loc_41></location>x</text>
<text><location><page_16><loc_50><loc_40><loc_51><loc_41></location>u</text>
<text><location><page_16><loc_50><loc_40><loc_51><loc_40></location>l</text>
<text><location><page_16><loc_50><loc_40><loc_51><loc_40></location>F</text>
<text><location><page_16><loc_53><loc_49><loc_54><loc_49></location>-6</text>
<text><location><page_16><loc_52><loc_48><loc_53><loc_49></location>3x10</text>
<text><location><page_16><loc_53><loc_45><loc_54><loc_45></location>-6</text>
<text><location><page_16><loc_52><loc_45><loc_53><loc_45></location>2x10</text>
<text><location><page_16><loc_53><loc_39><loc_54><loc_39></location>-6</text>
<text><location><page_16><loc_52><loc_39><loc_53><loc_39></location>1x10</text>
<text><location><page_16><loc_53><loc_37><loc_54><loc_37></location>-7</text>
<text><location><page_16><loc_52><loc_37><loc_53><loc_37></location>8x10</text>
<text><location><page_16><loc_53><loc_35><loc_54><loc_35></location>-7</text>
<text><location><page_16><loc_52><loc_34><loc_53><loc_35></location>6x10</text>
<text><location><page_16><loc_53><loc_32><loc_55><loc_33></location>4000</text>
<text><location><page_16><loc_57><loc_32><loc_58><loc_33></location>5000</text>
<text><location><page_16><loc_60><loc_32><loc_62><loc_33></location>6000</text>
<text><location><page_16><loc_63><loc_32><loc_64><loc_33></location>7000</text>
<text><location><page_16><loc_65><loc_32><loc_67><loc_33></location>8000</text>
<text><location><page_16><loc_67><loc_32><loc_71><loc_33></location>9000 10000</text>
<text><location><page_16><loc_76><loc_32><loc_78><loc_33></location>15000</text>
<text><location><page_16><loc_85><loc_32><loc_87><loc_33></location>25000</text>
<text><location><page_16><loc_65><loc_32><loc_74><loc_32></location>Observed wavelength (Å)</text>
<text><location><page_16><loc_56><loc_51><loc_57><loc_52></location>2000</text>
<text><location><page_16><loc_63><loc_51><loc_64><loc_52></location>3000</text>
<text><location><page_16><loc_68><loc_51><loc_69><loc_52></location>4000</text>
<text><location><page_16><loc_72><loc_51><loc_73><loc_52></location>5000</text>
<text><location><page_16><loc_75><loc_51><loc_76><loc_52></location>6000</text>
<text><location><page_16><loc_77><loc_51><loc_79><loc_52></location>7000</text>
<text><location><page_16><loc_80><loc_51><loc_81><loc_52></location>8000</text>
<text><location><page_16><loc_82><loc_51><loc_85><loc_52></location>9000 10000</text>
<figure>
<location><page_17><loc_6><loc_62><loc_48><loc_85></location>
<caption>Fig. 10.- Magnitude of the short GRB hosts as a function of redshift. The right panel shows the magnitude of the hosts without a confirmed redshift. GRB111117A (z=1.31) is shown as a red star.</caption>
</figure>
<figure>
<location><page_17><loc_8><loc_27><loc_46><loc_49></location>
<caption>Fig. 11.- Comparison of E iso between short (upper panel) and long (lower panel) GRBs. The short GRB E iso values are from Berger (2010) (short GRBs with detected afterglows and coincident host galaxies), and the long GRB E iso values are from Nava et al. (2012) (only Swift long GRBs). GRB111117A (3 . 4 × 10 51 erg) is located at the high end of E iso distribution of short GRBs.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "We present our successful Chandra program designed to identify, with sub-arcsecond accuracy, the X-ray afterglow of the short GRB 111117A, which was discovered by Swift and Fermi . Thanks to our rapid target of opportunity request, Chandra clearly detected the X-ray afterglow, though no optical afterglow was found in deep optical observations. The host galaxy was clearly detected in the optical and near-infrared band, with the best photometric redshift of z = 1 . 31 +0 . 46 -0 . 23 (90% confidence), making it one of the highest known short GRB redshifts. Furthermore, we see an offset of 1 . 0 ± 0 . 2 arcseconds, which corresponds to 8 . 4 ± 1 . 7 kpc, between the host and the afterglow position. We discuss the importance of using Chandra for obtaining sub-arcsecond X-ray localizations of short GRB afterglows to study GRB environments. Subject headings: gamma rays: bursts 5 NASA Postdoctoral Program Fellow, Goddard Space Flight Center, Greenbelt, MD 20771 8 Center for the Exploration of the Origin of the Universe (CEOU), Department of Physics and Astronomy, Seoul National University, Seoul, 151-747, Korea 9 Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen Ø, Denmark",
"pages": [
1
]
},
{
"title": "Identifying the Location in the Host Galaxy of the Short GRB111117A with the Chandra Sub-arcsecond Position",
"content": "T. Sakamoto 1 , 2 , 3 , 4 , E. Troja 1 , 3 , 5 , 6 , K. Aoki 7 , S. Guiriec 5 , M. Im 8 , G. Leloudas 9 , 18 , D. Malesani 9 , A. Melandri 10 , A. de Ugarte Postigo 9 , 13 , Y. Urata 11 , D. Xu 12 , P. D'Avanzo 10 , J. Gorosabel 13 , Y. Jeon 8 , R. S'anchez-Ram'ırez 13 , M. I. Andersen 9 , 19 , J. Bai 21 , 22 , S. D. Barthelmy 3 , M. S. Briggs 25 , S. Foley 26 , A. S. Fruchter 15 , J. P. U. Fynbo 9 , N. Gehrels 3 , K. Huang 14 , M. Jang 8 , N. Kawai 16 , H. Korhonen 19 , 24 , J. Mao 21 , 22 , 23 , J. P. Norris 17 , R. D. Preece 25 , J. L. Racusin 3 , C. C. Thone 13 , K. Vida 20 X. Zhao 21 , 22",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Gamma-ray bursts (GRBs) are traditionally divided in two classes based on their duration and spectral hardness: the long duration/soft spectrum GRBs, and the short duration/hard spectrum GRBs (Kouveliotou et al. 1993). The two classes of bursts further differ in their spectral lags, the measurement of the delay in the arrival time of the low-energy photons with respect to the higher energy ones: long bursts tend to have large positive lags, while short bursts exhibit negligible or negative lags (Norris & Bonnell 2006). The long standing paradigm is that these two phenomenological classes of GRBs originate from different progenitor systems. A preponderance of evidence now links long GRBs with the death of massive stars (Woosley & Bloom 2006, and references therein), yet the origin of short GRBs remains largely unknown. The common notion that short bursts originate from coalescing compact binaries, either neutron star-neutron star (NSNS) or neutron star-black hole (NS-BH) mergers (e.g., Eichler et al. 1989; Paczynski 1991; Narayan et al. 1992; Rosswog 2005; Rezzolla et al. 2011), makes them the most promising tool to aid in the direct detection of gravitational waves (GWs) by forthcoming facilities such as AdvancedLIGO, Advanced-VIRGO or LCGT (KAGRA) (e.g., Nissanke et al. 2010). It is therefore of primary importance to convincingly corroborate the merger scenario with a robust observational basis. Significant progress in understanding the origin of short GRBs has been achieved only recently. This advance was enabled by the detection of their afterglows in 2005 thanks to the rapid position notice and response by HETE-2 (Ricker et al. 2003) and Swift (Gehrels et al. 2004). The very first localizations of short GRBs immediately provided us with fundamental clues about their nature. They demonstrated that short GRBs are cosmological events with an isotropic equivalent energy scale of 10 49 -10 52 erg, that they occur in different environments than long GRBs, and are not associated with bright Type Ic supernovae (Bloom et al. 2006; Prochaska et al. 2006; Covino et al. 2006). Since 2005 the sample of well-localized short GRBs has significantly grown, allowing for a deeper insight into the nature of their progenitors. The observed redshift distribution, ranging 0 . 11 /lessorsimilar z /lessorsimilar 1, hints at a progenitor system with a broad range of lifetimes (Berger et al. 2007). Another critical test of the progenitor models is the observed offset distribution of short bursts (Troja et al. 2008; Fong et al. 2010; Church et al. 2011). The median physical projected offset between the host center and the short GRB position is ∼ 5 kpc (Fong et al. 2010), which is about five times larger than that of long GRBs (Bloom et al. 2002), and shows a broader dispersion. This is in agreement with the merger scenario, as several models NS-NS/NS-BH systems are expected to receive significant kick velocities at birth (Bloom et al. 1999; Fryer et al. 1999; Belczynski et al. 2006), or to dynamically form in globular clusters in the outskirts of their galaxies (Grindlay et al. 2006). Despite the major progress of the last few years, the study of short GRBs and their progenitors has still been suffering from their less secure afterglow positions and redshifts. Unlike long GRBs, none of the redshifts of short GRBs 1 has been directly measured through afterglow spectroscopy, and only in the case of GRB 060121, a photometric redshift was derived from the afterglow spectral energy distribution (de Ugarte Postigo et al. 2006; Levan et al. 2006). This is because the optical afterglows are significantly fainter than those of long GRBs (Nysewander et al. 2009; Kann et al. 2011). The redshifts of short GRBs are instead measured from spectroscopic observa- tions of the 'associated' host galaxy. The likelihood of a spurious association is small when a sub-arcsec position is available. However, if an afterglow is only detected by the Swift X-Ray Telescope (XRT; Burrows et al. 2005), the probability of a chance alignment is higher due to the larger uncertainty in the localization (2-5 '' ). Unfortunately, the latter scenario represents the majority of cases ( ∼ 65% of the Swift short bursts sample). A further bias is introduced by the fact that sub-arcsecond positions are mainly derived from optical afterglow detections, which are subject both to absorption along the line of sight and density effects. In fact, in the standard fireball model, the optical brightness depends sensitively on the density of the circumburst environment (Kumar & Panaitescu 2000). This effect disfavors the accurate localization of short GRBs occurring in the lower-density galaxy halo or even outside their own galaxy, in the intergalactic medium. Such populations of large-offest short GRBs has already been suggested by Bloom et al. (2007) and Troja et al. (2008). However being localized mainly by XRT, their association with the putative host galaxy remains uncertain. Increasing the sample of large-offset short bursts with subarcsecond localization is crucial to discriminate whether their progenitors were ejected from their birth site, favoring models which predict NS binaries with large kick velocities and ∼ Gyr lifetimes, or they were formed from dynamical interactions in globular clusters (Salvaterra et al. 2010). In this context, rapid Chandra observations of short GRB afterglows represent the critical observational gateway to overcome the current observational limits. Since 65% of Swift short GRBs are detected in X-rays, and only 25% of them are detected in the optical band, X-ray observations have a higher probability of detecting the afterglows of short GRBs. The superb angular resolution of Chandra allows for a sub-arcsecond localization, comparable to optical localizations, thus enabling the secure host identification and the precise measurement of the GRB projected offset. Furthermore, because the X-ray afterglow is less subject to absorption and density effects, Chandra localizations allow us to build a sample of well-localized short GRBs with limited bias, complementing the information derived from the sample of optically localized short GRBs. This is the key to distinguish between the different possible short GRB populations (Sakamoto & Gehrels 2009), which could arise from a different progenitor and/or environment. In this paper, we report the first results of our Chandra program which led to the accurate localization of GRB 111117A detected by Swift and Fermi . GRB 111117A is the 2nd short burst 2 in which the Chandra position is crucial for the host identification. Our results were leveraged with an intense ground-based follow-up campaign. No optical/infrared counterpart was found, therefore our Chandra localization uniquely provides the only accurate sub-arcsecond position. The paper is organized as follows: we introduce GRB 111117A in § 2. In section § 3, we describe the analysis softwares and methods used in this paper. We report the prompt emission properties in § 4, the X-ray afterglow properties in § 5.1, the deep optical afterglow limits in § 5.2, and the host galaxy properties in § 6. We discuss and summarize our results in § 7. The quoted errors are at the 90% confidence level for prompt emission and X-ray afterglow data, and at the 68% confidence level for optical and near infrared data unless stated otherwise. The reported optical and near infrared magnitudes are in the Vega system unless stated otherwise. Throughout the paper, we use the cosmological parameters, Ω m = 0.27, Ω Λ = 0.73 and H 0 = 71 km s -1 Mpc -1 .",
"pages": [
2,
3
]
},
{
"title": "2. GRB111117A",
"content": "On 2011 November 17 at 12:13:41.921 UT, the Swift Burst Alert Telescope (BAT; Barthelmy et al. 2005a) triggered and localized the short GRB 111117A (Mangano et al. 2011). The Fermi Gamma-ray Burst Monitor (GBM; Meegan et al. 2009) also triggered on the burst (Foley et al. 2011). The BAT location derived from the ground analysis was (R.A., Dec.) (J2000) = (00 h 50 m 49.4 s , +23 · 00 ' 36 '' ) with a 90% error radius of 1.8 ' . The Swift XRT started its observation 76.8 s after the trigger. A fading X-ray source was found at the location of (R.A., Dec.) (J2000) = (00 h 50 m 46.22 s , +23 · 00 ' 39.2 '' ) with a 90% error radius of 2.1 '' (Melandri et al. 2011a). The Swift UVOptical Telescope (UVOT; Roming et al. 2005) began the observations of the field 137 s after the trigger, and no optical afterglow was detected (Oates et al. 2011). The earliest ground observations of the field were performed by the Gao-Mei-Gu telescope (GMG) at 1.96 hr after the BAT trigger, and no afterglow was detected within the XRT error circle with an exposure time of 600 s in the R band (Zhao et al. 2011). The Nordic Optical Telescope (NOT) observed the field at 8.9 hr after the burst, and found an optical source inside the XRT error circle (Andersen et al. 2011), which was later confirmed to have a possible extended morphology by the Magellan/Baade telescope (Fong et al. 2011), the Gemini-South telescope (Cucchiara et al. 2011), the GROND telescope (Schmidl et al. 2011), and the Telescopio Nazionale Galileo (TNG; Melandri et al. 2011b). The Gran Telescopio CANARIAS (GTC), the Subaru telescope, the United Kingdom Infrared Telescope (UKIRT) and the Canada-FranceHawai Telescope (CFHT) also collected images of the field. Based on no clear detection of an optical afterglow of the short GRB 111117A, we triggered our Chandra Target of Opportunity (ToO) observation 6 hr after the trigger (Sakamoto et al. 2011b), and the observation started 3 days later. The Xray afterglow was clearly detected in 20 ks, obtaining a sub-arcsecond position of the afterglow in X-rays (Sakamoto et al. 2011c).",
"pages": [
3,
4
]
},
{
"title": "3. Data Analysis",
"content": "HEAsoft version 6.11 and the Swift CALDB (version 20090130) were used for the Swift BAT data analysis. The XRT data products were obtained from the automated results available from the UK Swift Science Data Center (Evans et al. 2007, 2009). CIAO 4.3 and CALDB 4.4.6 were used for the Chandra data analysis. The Fermi Gamma-ray Burst Monitor (GBM) data were prepared using the RMFIT software package, 3 with data from three Sodium Iodide (NaI) scintillation detectors (detector ID 6, 7 and 9) and two Bismuth Germanate (BGO) scintillation detectors (detector ID 0 and 1). A standard data reduction of optical and near infrared images was performed using the IRAF 4 software package. SExtractor 5 (Bertin & Arnouts 1996), SkyCat Gaia 6 and IRAF were used to extract sources and perform the photometry. To accomplish consistent photometry for images collected by various telescopes, we selected 10 common stars in the field and performed relative photometry. When some of the stars were saturated (especially for a large aperture telescope such as GTC), a subset of these 10 reference stars were used. The USNO B-1 R2 magnitude or the SDSS magnitudes were used as the reference magnitude for the stars. For the near infrared images of UKIRT and CFHT, we use the reference stars in the 2MASS catalog. The Galactic extinction has been corrected using E ( B -V ) = 0 . 03 mag toward the direction to this burst (Schlegel et al. 1998). The log of optical and near infrared observations presented in this paper are summarized in Table 1.",
"pages": [
4
]
},
{
"title": "4. Prompt Emission",
"content": "The light curve of the prompt emission is composed of two episodes: the first episode shows multiple overlapping pulses with a total duration of 0.3 s, and the second episode is composed of two pulses with a duration of 0.1 s (Figure 1). The duration is T 90 = 464 ± 54 ms (1 σ error; 15-350 keV) measured using the BAT background-subtracted light curve using the mask modulation (e.g., maskweighted light curve). This T 90 duration is significantly shorter than 2 s, which is the standard classification of short GRBs form BATSE (Kouveliotou et al. 1993). Furthermore, this duration is shorter than 0.7 s, which is claimed to be the dividing line between long and short GRBs for the Swift sample (Bromberg et al. 2012). The hard-to-soft spectral evolution is seen in both the first and the second episode of GRB 111117A (see the hardness ratio plot at the bottom panel of Figure 1). There is no indication of extended emission (Norris et al. 2011) down to a flux level of ∼ 2 × 10 -10 erg cm -2 s -1 , assuming a power-law spectrum with a photon index of α = -2 ( N ( E ) ∝ E α ) in the 14-200 keV band by examining the BAT sky image from 60 s (after the spacecraft slew set- 950 s after the BAT trigger time (hereafter t 0 , BAT ). The spectral lag between the 100-350 keV and the 25-50 keV band is 0 . 6 ± 2 . 4 ms, which is consistent with zero, using the BAT raw light curves (non mask-weighted light curves) by subtracting a constant background measured around the burst. In the fluence ratio versus T 90 plane, GRB111117A is located in the same region where most of the BAT short GRBs are located (Figure 2), further confirming its short GRB nature. The time-integrated spectral properties are investigated by performing a joint spectral analysis with BAT and GBM data. The spectrum is extracted from t 0 , BAT + 0.024 s to t 0 , BAT + 0.520 s using batbinevt for the BAT data and using the RMFIT software package for the GBM data in the same time interval. The BAT energy response file is generated by batdrmgen . The GBMenergy response files were retrieved from the HEASARC Fermi archive for trigger bn111117510. We use the xspec spectral fitting package to do the joint fit. The energy ranges of 15-150 keV, 8-900 keV and 0.2-45 MeV are used for the BAT, the GBM-NaI and the GBM-BGO instruments, respectively. The model includes a inter-calibration multiplicative factor to take into account the calibration uncertainty among the different instruments. The best fit spectral parameters are summarized in Table 2. We find that a power-law multiplied by an exponential cutoff (CPL) 7 provides the best representative model of the data. The best fit parameters in this model are the power-law photon index α CPL = -0 . 28 +0 . 31 -0 . 26 and E peak = 420 +170 -110 keV ( χ 2 /d.o.f. = 627/661). The 90% confidence interval of the inter-calibration factor of the GBM detectors is between 0.50 and 0.78 which is an acceptable range taking into account the current spectral calibration uncertainty between the BAT and the GBM. A simple powerlaw model yields a significantly worse fit to the data ( χ 2 /d.o.f. = 729/662). Furthermore, the significant difference in the power-law photon index the BAT data ( -0 . 52 +0 . 24 -0 . 22 ) and the GBM data ( -1 . 44 +0 . 06 -0 . 08 ) alone disfavors a simple power-law model as the representative model. There is no significant improvement in χ 2 using a Band func- (Band et al. 1993) fit ( χ 2 /d.o.f. = 627/660) over a CPL fit. The preferential fit to a CPL model and the systematically harder photon index compared to long GRBs are general characteristics of a time-integrated spectrum of short GRBs (e.g., Ghirlanda et al. 2009; Ohno et al. 2008). The fluence in the 8-1000 keV band calculated using the best fit time-integrated spectral parameters based on a CPL fit above is 7 . 3 +2 . 6 -2 . 1 × 10 -7 erg cm -2 . Due to poor statistics in extracting a spectrum from a very short time window, the peak flux was calculated by scaling the BAT maskweighted countrate into a flux by folding the BAT energy response and assuming the best fit timeintegrated spectral parameters in a CPL model. The peak energy flux at the 8-1000 keV band in the 50 ms window starting from t 0 , BAT + 0.450 s is (3 . 8 ± 1 . 2) × 10 -6 erg cm -2 s -1 . The timeresolved spectroscopy is difficult to perform due to the limited statistics in the data. We search for pre-burst emission by analyzing the BAT survey data (detector plane histogram; DPH). Approximately 4.5 hr before the burst trigger, GRB 111117A was in the field of view of BAT (26.1 · from the boresight direction) for ∼ 1 ks during the observation of the blazar PKS 0235+16 (observation ID 00030880085). We use batsurvey script to process the DPH data. The extracted rates at the location of GRB 111117A are corrected to the on-axis rate by applying an off-axis correction based on observations of the Crab. We find no significant emission during this observation at the location of GRB 111117A. The 3 sigma upper limit assuming a power-law spectrum with a photon index of α = -2 is 1 . 4 × 10 -9 erg cm -2 s -1 at the 14-200 keV band in 300 s exposure.",
"pages": [
4,
5
]
},
{
"title": "5.1. X-rays",
"content": "The Swift XRT X-ray afterglow light curve can be fit to a simple power-law decay (Figure 4). The spectrum collected in the photon counting (PC) mode is well described by an absorbed power-law model. The best fit spectral parameters are a photon index of -2 . 19 +0 . 36 -0 . 38 and an excess N H of 1 . 8 +1 . 1 -1 . 0 × 10 21 cm -2 ( z = 0) assuming the galactic N H at the burst direction of 3 . 7 × 10 20 cm -2 (Kalberla et al. 2005). Both the measured photon index and N H for GRB111117A are consistent with those of other Swift short GRBs (Kopaˇc et al. 2012; Fong et al. 2012). The Chandra observation started at 12:39:25 UT, and ended at 18:39:10 UT on 2011 November 20 with a total exposure of 19.8 ks. The ACIS instrument had five CCD chips (S3, S4, S5, I2 and I3) enabled, with the S3 chip as the aiming point for the source. The data were collected in the FAINT mode. The X-ray afterglow is clearly detected in the Chandra observation with 3.9 σ significance by wavdetect (source net counts of 8) within the XRT error circle. To refine the astrometry of the Chandra data, we apply the same analysis method described in Feng & Kaaret (2008). We extract the Chandra image (0.35 - 8 keV) that overlaps with the GTC image (4 . 4 ' × 8 . 7 ' ). The astrometry of the GTC image is calibrated against the SDSS catalog, and its standard deviation is ∼ 0.3 '' . We run wavdetect with options of scales='1.0 2.0 4.0 8.0 16.0' and sigthresh = 4 × 10 -6 to the extracted Chandra image. There are four sources which have a good match between the images. We then use the geomap task in the IRAF IMMATCH package to find the best coordinate transformation between the Chandra and the GTC image by fitting those four sources. Finally, we apply geoxytrans task (IRAF IMMATCH package) for the originally detected Chandra position using the coordinate transformation calculated by geomap to find the astrometrically corrected Chandra afterglow position. The refined afterglow position is shifted by δ R.A. = -0 . 221 '' and δ Dec. = -0 . 020 '' from the position originally derived by wavdetect . The best Chandra X-ray afterglow position is (R.A., Dec.) (J2000) = (00 h 50 m 46.264 s , +23 · 00 ' 39.98 '' ) with 1 σ statistical uncertainty of 0.09 '' in right ascension and 0.16 '' in declination. When we include the systematic uncertainty of 0.3 '' , 1 σ error radius of the Chandra position is 0.35 '' . The Chandra position is well within the XRT 90% error circle (see Figure 3). The combined Swift XRT and Chandra X-ray afterglow light curve is well fit by a simple powerlaw with index of -1 . 25 +0 . 09 -0 . 12 . As shown in Figure 4, the X-ray afterglow of GRB 111117A belongs to a dim population of the Swift short GRBs.",
"pages": [
5,
6
]
},
{
"title": "5.2. Optical",
"content": "We investigate the possible optical afterglow emission by using the image subtraction technique between the early and the late time epoch observations by TNG and GTC. We use the ISIS software package (Alard & Lupton 1998) to perform the image subtraction. The early and the late epoch observations of TNG and GTC were obtained at t 0 , BAT + 7.23 hr and t 0 , BAT + 7.89 hr, and t 0 , BAT + 11.4 days and t 0 , BAT + 14.4 days, respectively. We find no significant emission at the Chandra Xray afterglow location in the subtracted images in both the TNG and the GTC observations (Figure 5), with 3 sigma upper limits of R > 24.1 mag for TNG and r > 24.9 (AB) mag for GTC. The TNG limiting magnitudes of the first and second epochs are R > 24 . 7 mag and R > 25 . 4 mag, respectively. For GTC, the limiting magnitude of the first and second epoch are r > 25 . 8 (AB) mag and r > 26 . 1 (AB) mag, respectively. Those limits are some of the deepest optical limits on short GRBs ever obtained (see upper panel of Figure 6).",
"pages": [
6
]
},
{
"title": "6. Host Galaxy",
"content": "The host galaxy of GRB 111117A has been detected in the near infrared and optical bands. There is only one near-infrared/optical source located near the Chandra X-ray afterglow position. Although the weak nature of the source makes it difficult to investigate whether the source is extended or not, the optical flux of the source is constant between 7 hr and 14 days after the burst at a level of ∼ 1.1 µ Jy (bottom panel of Figure 6). Using the formula provided by Bloom et al. (2002), the probability of finding an unrelated galaxy of the R magnitude of ∼ 23.3 with the distance of 1.0 '' is 0.8%. We also investigate the chance probabilities of the three nearby objects. The probabilities of those objects are between 24% and 42% which are significantly larger than that of the host candidate. Although the chance probability of the host candidate is non-negligible, the chance of a misidentification of the host galaxy is reasonably small. Therefore, we conclude that the source detected in the K , J , z , i , r , g , and R bands is the host galaxy of GRB 111117A (Figure 7). To estimate the redshift of the host galaxy, we perform a spectral energy density (SED) fit with the stellar population model of Maraston (2005). We use the single stellar populations (SSP) models with a Salpeter initial mass function (Salpeter 1955), solar metallicity which ranges from 0.005 Z /circledot to 3.5 Z /circledot (0.005, 0.02, 0.5, 1.0, 2.0 and 3.5 Z /circledot ), and a red or blue horizontal branch morphology. A total number of 269 SED templates ranging in stellar age from 10 Myr to 15 Gyr was applied. The Bayesian Photometric Redshift software (BPZ; Ben'ıtez 2000) is used to fit the data in g , r , and i bands (GTC), z band (GMG), J band (CFHT) and K band (UKIRT) with those SED templates. We find that the best fit SED template corresponds to a solar metallicity, a red horizontal branch morphology and the luminosity weighted mean stellar age of 0.1 Gyr with a redshift of 1.36 +0 . 45 -1 . 18 . Our best fit SED template of SSP model with a solar metallicity and a red horizontal branch matches well with other short GRB hosts studied by Leibler & Berger (2010). As seen in Figure 8 (top), there is a less significant low redshift solution ( z < 0 . 25). We find that this low redshift solution is coming from the template with the young stellar age of ∼ 10 Myr. As we will discuss in § 7, it is unlikely that the host galaxy has the stellar age of ∼ 10 Myr. Therefore, to constrain the redshift better, we focus on 41 SED templates with solar metallicity and a red horizontal branch morphology with stellar age from 20 Myr to 15 Gyr. The signal-to-noise is low, and there are no clear absorption or emission line features in the spectrum. The continuum is consistent with the best fit SED template. The bottom panel of Figure 8 shows the posterior probability distribution of the estimated redshift for this SED fit. No low redshift solution is evident in the probability distribution. We find the best estimated redshift to be 1.31 (90% confidence interval 1 . 08 < z ph < 1 . 77). The likelihood that the redshift is correct is 80% (reduced χ 2 of the fit is 0.65 with 2 d.o.f.). The best fit SED template is the case with the luminosity weighted mean stellar age of 0.1 Gyr and a mass of ∼ 1 × 10 9 M /circledot . Figure 9 shows the best fit SED with the photometric data, and the GTC spectrum with an exposure time of 4 × 1800 s. GTC spectroscopy was performed with the R1000B grism, which has a central wavelength of 5510 ˚ A and covers the spectral range between 3700 and 7000 ˚ Awith a resolution of ∼ 1000 at 5500 ˚ A. To investigate the likelihood of the host being a star-forming galaxy, we also examine the SED templates with an exponentially decaying star formation rate (Maraston 2010), with an e -folding time of 0.1, 1 and 10 Gyr (stellar age ranges from 10 Myr to 15 Gyr). Although our J band data point shows a relatively poor agreement with the best fit template with an e -folding time of 0.1 Gyr and the luminosity weighted mean stellar age of 0.3 Gyr, the fit is still acceptable (reduced χ 2 = 0.91 with 2 d.o.f.). The best fit redshift in this case is 1.18 +0 . 61 -0 . 21 . The fit becomes worse if the e -folding time gets larger. Therefore, our current data also support of an ∼ 0 . 1 Gyr post-starburst galaxy (see bottom panel of Figure 9). We also fitted the optical-NIR SED using MAGPHYS package (de Cunha et al. 2008) to check the validity of the fitting result. The MAGPHYS fit includes an extinction parameter as a part of the fit, but performs the fitting at a given redshift. An exponentially decaying star formation rate is assumed. The redshifts were increased by a step of 0.05 from 0.8 to 1.5. We confirm that the returned χ 2 is the smallest in the range of the z ph from the BPZ, and a moderate extinction of A V = 0 . 2 -0 . 5 mag is found. The best fit solutions give the exponential time scale of about 1.5 Gyr, with the luminosity weighted mean stellar age (in r -band) of a few hundred Myr, and a stellar mass of a few times 10 9 M /circledot . These output values are consistent with the solutions derived with the photometric redshift. In summary, based on various SED template fits, we can conclude the following about the host galaxy: the redshift of the host is ∼ 1.3 regardless of the SED model and the host is either a star-forming galaxy of the luminosity weighted mean stellar age of 0.1 Gyr and a mass of ∼ 1 × 10 9 M /circledot or a poststarburst galaxy. Further deep J or Y band data are crucial to pin down the host properties. A significant offset between the center of the host galaxy and the X-ray afterglow has been found for GRB111117A. The center position of the host galaxy has been examined by running SExtractor on the second epoch of the GTC r image, our highest quality optical image. The best location of the host center is (R.A., Dec.) (J2000) = (00 h 50 m 46.258 s , +23 · 00 ' 40.97 '' ). The position moves by less than half a pixel ( < 0 . 13 '' ) by changing the detection threshold of SExtractor from 1.5 to 3.0 sigma. Therefore, the projected offset between the center of the host galaxy and the X-ray afterglow is 1.0 '' ( δ R.A. = 0 . 083 '' and δ Dec. = -0 . 990 '' ; see Figure 7). Taking into account the statistical error in the X-ray afterglow position of 0 . 18 '' and the statistical error of the host center location of 0 . 13 '' , we estimate the offset with its error to be 1 . 0 ± 0 . 2 arcseconds, which corresponding to a distance of 8 . 4 ± 1 . 7 kpc at a redshift of z = 1 . 31.",
"pages": [
6,
7,
8
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},
{
"title": "7. Discussion",
"content": "Our photometric redshift of 1 . 31 +0 . 46 -0 . 23 (90% confidence) for the host galaxy of GRB 111117A is realistic for the following reasons. First, by plotting the observed r AB magnitude ( r AB ) of the host galaxies of short GRBs as a function of redshift (Berger 2009), we find that the relatively faint magnitude of the host galaxy, r AB = 24 . 20 ± 0 . 07, is located at the redshift range of > 0.5 (Figure 10). Second, we find that the less significant low redshift solution ( z < 0 . 25) in the photometric redshift estimation (Figure 8) is coming from the templates with the unrealistic young stellar ages of ∼ 10 Myr. At z = 0 . 25, if the galaxy is star forming, there would be a chance of seeing emissions of [OII], Hβ and [OIII] in the optical spectrum, yet, we see none of those lines in the GTC spectrum. Furthermore, ∼ 10 Myr is in general too young for a whole galaxy, as opposed to a specific star forming region. Therefore the low redshift solution for the photometric redshift is unlikely to be the case of GRB111117A. Therefore, hereafter, we will discuss the rest-frame properties of GRB 111117A using our best photometric redshift of 1.31. Assuming the redshift of 1.31, the isotropic equivalent γ -ray energy ( E γ, iso ) which is integrated from 1 keV to 10 MeV in the rest frame is 3 . 4 +5 . 7 -1 . 5 × 10 51 erg. The peak energy at the rest-frame ( E src peak ) is 945 +455 -310 keV. The 90% errors in E γ, iso and E src peak are taking into account not only a statistical error but also an uncertainty in the estimated redshift. As shown in Figure 11, the E γ, iso of GRB111117A is located at the high end of the E γ, iso distribution of short GRBs and at the low end of the E γ, iso distribution of long GRBs. Relatively low E γ, iso and high E src peak compared to those of long GRBs make GRB 111117A inconsistent with the E src peak -E γ, iso (Amati) relation (Amati et al. 2002). This characteristic is consistent with being a short GRB because most of the short GRBs are well known outliers of the Amati relation (Amati 2006; Nava et al. 2012). The optical-to-X-ray spectral index (Jakobsson et al. 2004),",
"pages": [
8
]
},
{
"title": "β OX ( ≡ log { f ν ( R ) /f ν (3 keV) } / log( ν 3 keV /ν R )) ,",
"content": "is estimated to be /lessorsimilar 0.78 using the same definition on the X-ray flux density at 3 keV measured at 11 hrs after the burst, and the optical afterglow limit based on the GTC r band. This upper limit of β OX is within the allowed range of the standard afterglow model between 0.5 to 1.25. Furthermore, according to Margutti et al. (2012b), the optical and the radio afterglow limit is consistent with the external shock model (Granot & Sari 2002) for a small number density ( n /lessorsimilar 0.01-0.2 cm -3 ). However, there is a possibility that a significant amount of the optical afterglow flux was extinguished by the host galaxy. When we fit the Xray afterglow spectrum to a power-law model with the intrinsic absorption at z = 1 . 31, the intrinsic N H is estimated to be 7 . 2 +0 . 7 -0 . 5 × 10 21 cm -2 . Assuming a host extinction law similar to the Milky Way, A V is 4.1 mag (Predehl & Schmitt 1995). Therefore, a significant amount of extinction in the optical flux is expected from the X-ray column density measurement. On the other hand, it is still not clear whether it is possible to have such high extinction at the outskirts of the host where the X-ray afterglow is indicated. Moreover, the amount of extinction which we derived from the SED fit of the host is A V = 0 . 2 -0 . 5 mag (see § 6). At this stage, the origin of the large column density seen in the X-ray afterglow of GRB 111117A is still remains puzzling. The projected offset between the afterglow location and the host galaxy center is 8 . 4 ± 1 . 7 kpc using the estimated redshift of 1.31. Although this offset is larger than the median projected offset of ∼ 5 kpc for previously studied short GRBs (Fong et al. 2010), it is within the offset distribution of short GRBs. Using the projected offset of r = 8 . 4 kpc and the stellar age of τ = 0 . 1 Gyr, the minimum kick velocity, v = r/τ , is estimated to be ≈ 80 km s -1 . The estimated kick velocity is similar to or possibly larger than the inferred kick velocity of GRB 060502B (Bloom et al. 2007). Using the typical age of 110 Gyr in the early-type short GRB hosts such as GRB 050509B, GRB 070809 and GRB 090515 (Bloom et al. 2006; Berger 2010), the minimum kick velocity is estimated to be ≈ 1-8 km s -1 . In this paper, we have reported the prompt emission, the afterglow and the host galaxy properties of short GRB 111117A. The prompt emission observed by the Swift BAT and the Fermi GBM showed 1) a short duration, 2) no extended emission, 3) no measurable spectral lag and 4) a hard spectrum. All those properties can securely classify this burst as a short GRB. Although the optical afterglow has not been detected by our deep observations by TNG and GTC, our rapid Chandra ToO observation provides a sub-arcsec position of the afterglow in X-rays. This Chandra position is crucial to identify the host galaxy and also to measure the significant offset of 1.0 '' between the host center and the afterglow location. Our deep near infrared to optical photometry data of GMG, TNG, NOT, GTC, UKIRT and CFHT enable us to estimate the redshift of the host to 1.31. The observation of GRB 111117A suggests that X-rays are more promising than optical to locate short GRBs with sub-arcsecond accuracy. Combining the sub-arcsecond afterglow position in the X-ray and the deep optical images from the ground telescopes, we successfully investigate the host properties of GRB 111117A even without an optical afterglow. Rapid Chandra ToO observations of short GRBs are still key to increasing the golden sample of short GRBs with redshifts to pin down their nature. We would like to thank the anonymous referee for comments and suggestions that materially improved the paper. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. This work is based on the observations using the United Kingdom Infrared Telescope, which is operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the U.K. with a partial support by Swift mission (e.g., Swift Cycle 7 GI grant NNX12AE75G) and the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof'ısica de Canarias, in the island of La Palma. The Dark Cosmology Centre is funded by the Danish National Research Fundation. Partly based on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof'ısica de Canarias. This work was supported by Chandra Cycle 13 grant GO2-13084X. The research activity of AdUP, CCT, RSR and JG is supported by Spanish research projects AYA2011-24780/ESP, AYA200914000-C03-01/ESP and AYA2010-21887-C04-01. GL is supported by the Swedish Research Council through grant No. 623-2011-7117. KV is grateful to the Hungarian Science Research Program (OTKA) for support under the grant K-81421. This work is supported by the 'Lendulet' Young Researchers' Program of the Hungarian Academy of Sciences. HK acknowledges the support from the European Commission under the Marie Curie IEF Programme in FP7. MI and YJ were supported by the he Creative Research Initiative program, No. 2010-0000712, of the National Research Foundation of Korea (NRFK) funded by the Korea government (MEST).",
"pages": [
8,
9
]
},
{
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2013ApJ...766..114S
https://arxiv.org/pdf/1302.3018.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_86><loc_88><loc_87></location>DECIPHERING THE IONIZED GAS CONTENT IN THE MASSIVE STAR FORMING COMPLEX G75.78 + 0.34</section_header_level_1>
<text><location><page_1><loc_9><loc_83><loc_91><loc_85></location>Á lvaro S' anchez -M onge 1,2,3 , S tan K urtz 3 , A ina P alau 4 , R obert E stalella 2 , D ebra S hepherd 5 , S usana L izano 3 , J os ' e F ranco 6 , G uido G aray 7 1 Osservatorio Astrofisico di Arcetri, INAF, Largo E. Fermi 5, I-50125 Firenze, Italy; [email protected]</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_78><loc_91><loc_83></location>2 Dpt d'Astronomia i Meteorologia (IEEC-UB), Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès, 1, E-08028 Barcelona, Spain 3 Centro de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, Apdo. Postal 3-72, 58090, Morelia,Michoacán, Mexico 4 Institut de Ciències de l'Espai (CSIC-IEEC), Campus UAB - Facultat de Ciències, Torre C5p 2, E-08193 Bellaterra, Catalunya, Spain 5 NRAO, P.O. Box O, Socorro, NM 87801-0387, USA</list_item>
<list_item><location><page_1><loc_17><loc_76><loc_84><loc_78></location>6 Instituto de Astronomía, Universidad Nacional Autónoma deMéxico, Apdo. Postal 70-264, 04510 México, D.F., Mexico and 7 Departamento de Astronomía, Universidad de Chile, Camino el Observatorio 1515, Las Condes, Santiago, Chile</list_item>
</unordered_list>
<text><location><page_1><loc_43><loc_74><loc_58><loc_75></location>Draft version August 1, 2021</text>
<section_header_level_1><location><page_1><loc_46><loc_72><loc_54><loc_73></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_51><loc_86><loc_71></location>We present sub-arcsecond observations toward the massive star forming region G75.78 + 0.34. We used the Very Large Array to study the centimeter continuum and H2O and CH3OH maser emission, and the Owens Valley Radio Observatory and Submillimeter Array to study the millimeter continuum and recombination lines (H40 α and H30 α ). We found radio continuum emission at all wavelengths, coming from three components: (1) a cometary ultracompact (UC) H II region with an electron density ∼ 3 . 7 × 10 4 cm -3 , excited by a B0 type star, and with no associated dust emission; (2) an almost unresolved UCH II region (EAST), located ∼ 6 '' to the east of the cometary UCH II region, with an electron density ∼ 1 . 3 × 10 5 cm -3 , and associated with a compact dust clump detected at millimeter and mid-infrared wavelengths; and (3) a compact source (CORE), located ∼ 2 '' to the southwest of the cometary arc, with a flux density increasing with frequency, and embedded in a dust condensation of 30 M /circledot . The CORE source is resolved into two compact and unresolved sources which can be well-fit by two homogeneous hypercompact H II regions each one photo-ionized by a B0.5 ZAMS star, or by free-free radiation from shock-ionized gas resulting from the interaction of a jet / outflow system with the surrounding environment. The spatial distribution and kinematics of water masers close to the CORE-N and S sources, together with excess emission at 4.5 µ mand the detected dust emission, suggest that the CORE source is a massive protostar driving a jet / outflow.</text>
<text><location><page_1><loc_14><loc_49><loc_86><loc_51></location>Subject headings: stars: formation - ISM: individual objects (G75.78 + 0.34) - ISM: HII regions - ISM: dust - radio continuum: ISM</text>
<section_header_level_1><location><page_1><loc_21><loc_45><loc_35><loc_46></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_30><loc_48><loc_44></location>Massive stars are key to understanding many physical phenomena in the Galaxy, however their first stages of formation are still poorly understood. One of the main reasons is that massive stars evolve more quickly to the main-sequence than low mass stars, and they radiate large amounts of ultraviolet (UV) photons and drive strong winds while they are still deeply embedded and accreting matter (e. g., Beuther & Shepherd 2005; Keto 2007). The interaction of the UV radiation and winds with the surrounding environment, resulting in bright radio continuum sources, must be well understood to comprehend the formation of high-mass stars.</text>
<text><location><page_1><loc_8><loc_7><loc_49><loc_30></location>Thermal (free-free) radio emission at centimeter wavelengths in regions of massive star formation can have distinct origins: i) H II regions photoionized by embedded massive stars, with homogeneous density distributions (e. g., Mezger & Henderson 1967) or with density gradients (e. g., Olnon 1975; Panagia & Felli 1975; Franco et al. 2000); ii) clumps of gas or circumstellar disks externally ionized by luminous early-type stars (e. g., Garay 1987; O'Dell & Wong 1996; Zapata et al. 2004); iii) shock waves arising either in dense interstellar gas (e. g., Ghavamian & Hartigan 1998; Araya et al. 2009) or from the collision of thermal radio jets from young stellar objects (YSOs) with their surroundings (e. g., Anglada 1996; Eislo ff el et al. 2000; Rodríguez et al. 2005); iv) ionized accretion flows where the material becomes ionized while accreting onto the massive protostar (e. g., Keto 2002, 2003, 2007); v) photoevaporated disks where the radiation of the newly-formed star ionizes and evaporates the</text>
<text><location><page_1><loc_52><loc_21><loc_92><loc_46></location>surrounding disk (e. g., Hollenbach et al. 1994; Lugo et al. 2004; Ávalos & Lizano 2012); vi) equatorial winds with the emission produced by small-scale ionized stellar winds (e. g., Hoare 2006). All these mechanisms produce radio continuum sources with spectral indices, α ( S ν ∝ ν α ), between -0 . 1 and + 2 (i.e., thermal emission; see Rodríguez et al. 1989). In addition, several works have found negative spectral indices (typical of non-thermal emission) associated with massive YSOs (e. g., Rodríguez et al. 1989; Zapata et al. 2006). These non-thermal sources can be young stars with active magnetospheres producing gyro-synchrotron emission (e. g., Feigelson & Montmerle 1999); synchrotron emission from fast shocks in disks or jets (e. g., Reid et al. 1995; Shepherd & Kurtz 1999; Shchekinov & Sobolev 2004); or extremely embedded YSOs where the UV photons from the massive protostars are heavily absorbed by large amounts of dust, with mass column densities /greaterorsimilar 10 3 g cm -2 (Rodríguez et al. 1993). A similar description of these mechanisms producing centimeter continuum emission can be found in Rodríguez et al. (2012).</text>
<text><location><page_1><loc_52><loc_13><loc_92><loc_21></location>It is possible - and indeed, probable - that several of these emission mechanisms, either thermal or non-thermal, occur within massive star formation regions, either simultaneously or at di ff erent evolutionary epochs. Any complete model of high-mass star formation must address the presence of these multiple modes of radio continuum emission.</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_13></location>The ON-2 star forming complex contains several early-type (O and B) stars within a massive ( /greaterorsimilar 10 4 M /circledot , Matthews et al. 1986; Dent et al. 1988) molecular cloud that spans ∼ 10 ' on the sky. Seen in CO, the cloud has two distinct condensa-</text>
<text><location><page_2><loc_34><loc_90><loc_66><loc_91></location>M G75.78 0.34</text>
<table>
<location><page_2><loc_16><loc_71><loc_84><loc_89></location>
<caption>TABLE 1 ain continuum observational parameters of +</caption>
</table>
<table>
<location><page_2><loc_14><loc_55><loc_86><loc_65></location>
<caption>TABLE 2 M ain observational parameters of the VLA and OVRO spectral line observations</caption>
</table>
<text><location><page_2><loc_8><loc_43><loc_48><loc_52></location>tions, with a roughly north-south orientation (Matthews et al. 1986). Multiple ionized regions within the southern condensation were identified by Matthews et al. (1973, 1977). They reported an extended H II region G75.77 + 0.34, and also the ultracompact (UC) H II region G75.78 + 0.34 (hereafter G75); the latter is associated with strong OH maser emission first reported by Elldér et al. (1969).</text>
<text><location><page_2><loc_8><loc_17><loc_48><loc_42></location>ON-2 lies toward Cygnus-X, and hence it has been problematic to assign a reliable distance. Early estimates ranged from 0.9 to 5.5 kpc with the nearer distance coming from extinction or luminosity arguments and the farther distance coming from Galactic rotation models and radio recombination line velocities. A helpful summary is presented by Campbell et al. (1982). More recent works, focusing on the UC H II region rather than the molecular cloud, tend to adopt a kinematic distance of 5.6 kpc (e. g., Wood & Churchwell 1989; Hanson et al. 2002). More recently, Ando et al. (2011) observed the water masers associated with the G75 UC H II region as part of the VERA (VLBI Exploration of Radio Astrometry) project. They measured the trigonometric parallax and report a heliocentric distance of 3.83 ± 0.13 kpc. We consider this distance measurement to be the most reliable and we adopt 3.83 kpc for our analysis. This distance places G75 close to other star forming regions (G75.76 + 0.35 and AFGL2591; Rygl et al. 2012), and close to the solar circle (Ando et al. 2011; Nagayama et al. 2012).</text>
<text><location><page_2><loc_8><loc_8><loc_48><loc_17></location>At centimeter wavelengths, G75 is dominated by a cometary UCH II region reported by Wood & Churchwell (1989). Hofner & Churchwell (1996) detected a cluster of water masers located about 2 '' (10 4 AU) southwest of the UCH II region, coincident with a compact radio continuum source (Carral et al. 1997) with a spectral index of + 1 . 5 ± 0 . 4 from 6 cm through 3 mm. Franco et al. (2000) modeled this</text>
<text><location><page_2><loc_52><loc_31><loc_93><loc_52></location>compact continuum source as a hypercompact (HC) H II region with ne ∝ r -4 . They note that this very steep density gradient is probably unrealistic, and mentioned several possible causes, including a contribution from warm dust to the flux density at 0.7 cm. Additionally, emission from a myriad of molecular line transitions has been reported in singledish surveys (e. g., Shirley et al. 2003, Roberts & Millar 2007, Klaassen & Wilson 2007, Bisschop et al. 2007). Higher angular resolution observations of di ff erent dense gas tracers show that most of the molecular emission comes from the compact radio continuum source associated with the cluster of water masers (Codella et al. 2010; Sánchez-Monge 2011). Finally, up to four distinct outflows have been identified in the ON-2 cloud core (Shepherd et al. 1997). All this makes G75 an excellent target to study the nature of the centimeter continuum sources in a massive star forming region.</text>
<text><location><page_2><loc_52><loc_23><loc_92><loc_30></location>In this paper, we present high angular resolution centimeter continuum observations together with 22 GHz H2O and 44 GHz CH3OH maser observations toward G75. We complement this data with millimeter continuum and radio recombination line observations, with the goal of deciphering the nature of the centimeter continuum sources.</text>
<section_header_level_1><location><page_2><loc_65><loc_21><loc_79><loc_22></location>2. OBSERVATIONS</section_header_level_1>
<section_header_level_1><location><page_2><loc_59><loc_19><loc_85><loc_20></location>2.1. VLA radio continuum observations</section_header_level_1>
<text><location><page_2><loc_52><loc_12><loc_92><loc_18></location>G75.78 + 0.34 was observed with the Very Large Array (VLA 1 ) at 6.0, 3.6, 2.0, 1.3, and 0.7 cm from January 1996 to April 2001, using the array in the CnB, B, and A configurations. In Table 1 we summarize these observations. The data reduction followed standard procedures for calibration of</text>
<text><location><page_2><loc_52><loc_7><loc_92><loc_10></location>1 The Very Large Array (VLA) is operated by the National Radio Astronomy Observatory (NRAO), a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.</text>
<text><location><page_3><loc_8><loc_72><loc_48><loc_92></location>high frequency data, using the NRAO package AIPS. Initial images were produced with a robust parameter (Briggs 1995) of 1 (see Table 1 for synthesized beams and rms noise levels of these images). These data can be grouped into two categories based on angular resolution: those with θ beam ≥ 1 . '' 0, and those with θ beam ∼ 0 . '' 2. The continuum images at 1.3 cm and 0.7 cm, from projects AK490 and AK500, were crosscalibrated with the strongest H2O and CH3OH maser components, respectively, which were observed simultaneously with the continuum emission (see Section 2.2 and Table 2). After comparing the initial maps for consistency, we combined the uv -data at the same frequencies to obtain final images with better uv -coverage and sensitivity. The resulting synthesized beams and rms noise levels of the combined images are given in Table 3.</text>
<text><location><page_3><loc_8><loc_65><loc_48><loc_72></location>At 6 cm, the H II region G75.77 + 0.34, approximately 1 ' to the southwest (e.g., Ri ff el & Lüdke 2010), produced nonimageable artifacts. The shortest baselines ( < 5 k λ ) were excluded, producing essentially no change in the measured flux density but significantly improving the quality of the map.</text>
<section_header_level_1><location><page_3><loc_13><loc_63><loc_44><loc_64></location>2.2. VLA H 2 O and CH 3 OH maser observations</section_header_level_1>
<text><location><page_3><loc_8><loc_55><loc_48><loc_62></location>The water maser line at 22.23508 GHz (616 -523 transition) was observed with the VLA in the A configuration (project AK490) simultaneously with the 1.3 cm continuum emission. Two di ff erent correlator configurations were used, providing spectral resolutions of 0.3 and 1.3 km s -1 ; with velocity coverages of 21 and 83 km s -1 , respectively.</text>
<text><location><page_3><loc_8><loc_48><loc_48><loc_54></location>The class I methanol maser line at 44.06941 GHz (70 -61 A + transition) was observed with the VLA in the B configuration (project AK500) simultaneously with the 0.7 cm continuum emission. Details of the spectrometer configuration are given in Table 2.</text>
<text><location><page_3><loc_8><loc_37><loc_48><loc_48></location>The H2O and CH3OH maser data were calibrated following the AIPS guidelines for calibration of high frequency data. Self-calibration was performed on the strongest maser component, and the solutions were applied to the spectral line and continuum data. The images were constructed using uniform and natural weighting to measure the maser positions at the highest angular resolution and to estimate the intensity of the di ff erent maser components, respectively.</text>
<section_header_level_1><location><page_3><loc_20><loc_35><loc_37><loc_36></location>2.3. OVRO observations</section_header_level_1>
<text><location><page_3><loc_8><loc_21><loc_48><loc_34></location>The Owens Valley Radio Observatory (OVRO 2 ) observations at 3 and 1 mm were made in the L (Low) and H (High) resolution configurations during September, October and December 1997. In March 1998, additional 3 mm observations were made in the uH (ultra-High) resolution configuration. All the observations were made in the double sideband mode, simultaneously observing at 3 and 1 mm. The continuum was observed in two 1 GHz channels, centered at 95.78 GHz and 98.78 GHz for 3 mm and 228.85 GHz and 231.85 GHz for 1 mm.</text>
<text><location><page_3><loc_8><loc_11><loc_48><loc_21></location>In addition, spectral line modules covered the H40 α (99.02296 GHz) and H30 α (231.90094 GHz) radio recombination lines (RRLs). Each spectral line setup consisted of 62 Hanning smoothed channels of 2 MHz each, providing resolutions of 6.1 and 2.6 km s -1 at 3 mm and 1 mm, respectively. The assumed LSR velocity for both lines was -8 km s -1 . Bandpass calibration was performed by observing the quasar 3C454.3. Amplitude and phase calibration were</text>
<figure>
<location><page_3><loc_53><loc_49><loc_91><loc_92></location>
<caption>F ig . 1.- G75.78 + 0.34 star-forming region. (a) : VLA 6.0 cm continuum image. Levels are -3, 3, 6, 10, 15, 25, 35, 45, and 55 times 490 µ Jy beam -1 . Ten-point red stars indicate CH3OH masers, and three-point yellow stars indicate H2O masers. The dashed box shows the region zoomed in the bottom panel. (b) : VLA 3.6 cm continuum image. Levels are -4, 4, 8, 12, 20, 30, and 40 times 50 µ Jy beam -1 . Synthesized beams of the continuum images are shown in the bottom-left corner; spatial scales are indicated in the top-right corner of each panel.</caption>
</figure>
<text><location><page_3><loc_52><loc_24><loc_92><loc_35></location>achieved by monitoring BL Lac during the di ff erent observing tracks. The absolute flux density scale was determined from Uranus, with an estimated uncertainty of 20% at 3 mm and 30% at 1 mm. The data were reduced using a combination of routines from the OVRO reduction package MMA, from MIRIAD, and from AIPS. Imaging was performed with the task IMAGR of AIPS. In Tables 1 and 2 we list details of the continuum and radio recombination line observations.</text>
<section_header_level_1><location><page_3><loc_64><loc_22><loc_80><loc_23></location>2.4. SMA observations</section_header_level_1>
<text><location><page_3><loc_52><loc_12><loc_92><loc_21></location>G75.78 + 0.34 was observed with the Submillimeter Array (SMA 3 ) in the 1.3 mm (230 GHz) band using the compact configuration on 2010 June 10. A total bandwidth of 2 × 4 GHz was used, covering the frequency ranges 218.2222.2 GHz and 230.2-234.3 GHz, with a spectral resolution of ∼ 1 km s -1 . System temperatures ranged between 150 and 250 K. The zenith opacities at 225 GHz were around 0.10</text>
<text><location><page_3><loc_52><loc_7><loc_92><loc_10></location>3 The SMA is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics, and is funded by the Smithsonian Institution and the Academia Sinica.</text>
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</figure>
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</figure>
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<caption>F ig . 2.- Close-up continuum images of the UCHII, EAST and CORE sources. In each panel we show the VLA image at the wavelength indicated in the top-right corners. Left column : UCHII source. For all panels, levels are -4, 4, 8, 12, 20, 30, and 40 times the rms noise level of the map: 485, 61, 138, 67, and 159 µ Jy beam -1 , for 6.0, 3.6, 2.0, 1.3, and 0.7 cm maps, respectively. Center column : EAST source. For all panels, levels are -4, 4, 8, 12, 16, 20, 25, and 30 times the rms noise level of the map: 61, 138, 67, and 159 µ Jy beam -1 , for 3.6, 2.0, 1.3, and 0.7 cm maps, respectively. Right column : CORE (N and S) source. For all panels, levels are -3, 3, 6, 12, 18, 24, and 30 times the rms noise level of the map: 61, 144, 67, and 186 µ Jy beam -1 , for 3.6, 2.0, 1.3, and 0.7 cm maps, respectively. See Table 3 for details of the synthesized beams, and the flux densities and sizes of the sources. Blue crosses in all panels indicate the position of the four continuum sources: UCHII, EAST, CORE-N and CORE-S (see Table 3). The scale in arcseconds is shown in the 2.0 cm panels. At the adopted distance of 3.8 kpc, 2 '' corresponds to 7600 AU while 0 . 5 '' is 1900 AU.</caption>
</figure>
<text><location><page_4><loc_8><loc_8><loc_48><loc_18></location>and 0.15 during the 3-hour track. The FWHM of the primary beam at 1.3 mm was ∼ 56 '' . Bandpass calibration was performed by observing the quasar 3C454.3. Amplitude and phase calibrations were made by monitoring 2025 + 337 and 2015 + 371, with an rms phase of ∼ 40 · . The absolute flux density scale was determined from Callisto with an estimated uncertainty around 15%. Data were calibrated and imaged with the MIRIAD software package. The continuum was con-</text>
<text><location><page_4><loc_52><loc_8><loc_92><loc_18></location>n the ( u,v ) domain from the line-free channels. Imaging was performed using natural weighting, resulting in a synthesized beam of 6 . '' 4 × 2 . '' 7 with a P.A. = -76 · , and 1 σ rms of 8.4 mJy beam -1 for the continuum. The two 4 GHz passbands include several molecular transitions, including CO, CH3CN, and CH3CCH. These molecular line data will be presented in a forthcoming paper together with VLA ammonia observations (Sánchez-Monge et al., in prep.).</text>
<table>
<location><page_5><loc_18><loc_31><loc_82><loc_88></location>
<caption>TABLE 3 M ultiwavelength results for the YSO s in the star -forming region G75.78 + 0.34</caption>
</table>
<section_header_level_1><location><page_5><loc_24><loc_20><loc_33><loc_21></location>3. RESULTS</section_header_level_1>
<section_header_level_1><location><page_5><loc_17><loc_18><loc_40><loc_19></location>3.1. Centimeter continuum emission</section_header_level_1>
<text><location><page_5><loc_8><loc_7><loc_48><loc_18></location>We detected centimeter radio continuum emission at all wavelengths. In Figure 1 we show a global overview of the G75 region at 6.0 cm (panel a) and 3.6 cm (panel b). As seen in the figure, the centimeter continuum emission is dominated by three components that we name UCHII, EAST and CORE. In Figure 2 we show a close-up of these three sources for the combined maps at each frequency, and in Table 3 we list their flux densities and sizes, together with the beams, and</text>
<text><location><page_5><loc_52><loc_20><loc_79><loc_21></location>rms noise levels of the combined images.</text>
<text><location><page_5><loc_52><loc_8><loc_92><loc_20></location>The strongest source (UCHII; G75.7826 + 0.3429) is a cometary UCH II region with an integrated flux density of ∼ 35 mJy and an angular diameter of ∼ 1 '' ( ∼ 0.02 pc at a distance of 3.8 kpc; previously imaged by Wood & Churchwell 1989 and Carral et al. 1997). Located ∼ 6 '' to the east, we identify a compact source (EAST; G75.7830 + 0.3416), with a flux density of ∼ 4 mJy and an angular diameter of ∼ 0 . '' 2 ( ∼ 760 AU at a distance of 3.8 kpc). This source appears at the ∼ 5 σ level in the 7 mm maps of Carral et al. (1997).</text>
<figure>
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<caption>F ig . 3.- OVRO and SMA millimeter continuum maps. Levels are -4, 4, 8, 12, 20, 30, and 40 times the rms noise level of the map: 0.6, 4, and 8.4 mJy beam -1 , for OVRO 3.1 mm, OVRO 1.3 mm, and SMA 1.3 mm maps, respectively. See Table 3 and Section 3.2 for details of the flux and beam of each image. Blue crosses show the position of the radiocontinuum sources, as in Figure 2.</caption>
</figure>
<figure>
<location><page_6><loc_18><loc_47><loc_82><loc_67></location>
<caption>F ig . 4.- H2O maser distribution in G75. Black contours: VLA 1.3 cm continuum image as in Figure 2 - middle column. Color circles show the position of the 35 water maser spots (see Table 4). Di ff erent colors are used to indicate the maser LSR velocities, according to the color scale (in km s -1 ) on the right hand side of the plot.</caption>
</figure>
<text><location><page_6><loc_8><loc_25><loc_48><loc_40></location>Finally, at the head of the cometary arc we find a compact source (CORE; G75.7821 + 0.3418) slightly elongated in the northeast-southwest direction, with a flux density of a few mJy and increasing with frequency. This source is coincident with the 7 mm continuum source reported by Carral et al. (1997) and with the clump of H2O masers (Hofner & Churchwell 1996). Our higher angular resolution observations ( ≤ 0 . '' 3) allow us to resolve the CORE source into two distinct (marginally resolved) condensations: COREN (G75.7821 + 0.3428) and CORE-S (G75.7820 + 0.3429; see Figure 2).</text>
<section_header_level_1><location><page_6><loc_17><loc_23><loc_40><loc_24></location>3.2. Millimeter continuum emission</section_header_level_1>
<text><location><page_6><loc_8><loc_7><loc_48><loc_23></location>In Figure 3 we show the OVRO and SMA millimeter continuum images of the G75 region. At 3.1 mm we detect emission from all three sources, with the emission from the UCHII and CORE sources barely resolved. At 1.3 mm we only detect emission associated with the CORE source, probably due to a lack of sensitivity that precludes the detection of faint emission from the EAST and UCHII sources. The angular resolution of our millimeter continuum images (10-15 times poorer than the angular resolution at centimeter wavelengths) does not allow us to resolve the components CORE-N and CORES. In Table 3 we list the flux densities and sizes, and the beams and rms noise levels of the OVRO observations. For the SMA</text>
<text><location><page_6><loc_52><loc_20><loc_92><loc_40></location>1.3 mm source, we fit a two-dimensional Gaussian obtaining a primary beam corrected flux density of 0 . 60 ± 0 . 17 Jy with a deconvolved size of (4 × 2 ± 1) '' at a P.A. = (75 ± 10) · . The SMA 1.3 mm source, although centered on the CORE position, encompasses the UCHII source and shows an extension to the EAST source. In addition, the flux density measured in the SMA image is almost twice the flux density measured in the OVRO image, suggesting that there is some faint, extended emission not detected in the OVRO map. We refrain from combining the OVRO and SMA 1.3 mm continuum images because of the poorer uv -coverage and sensitivity of the latter. Higher sensitivity maps are needed to confirm the 1 mm continuum emission associated with the UCHII and EAST sources, and higher angular resolution is needed to identify the millimeter emission of CORE-N and S sources.</text>
<text><location><page_6><loc_52><loc_8><loc_92><loc_20></location>At 3.5 mm Ri ff el & Lüdke (2010) measured a flux density of 119 mJy with a synthesized beam of 18 '' , while Shepherd et al. (1997) measured 75 mJy with a resolution of 5 '' , both observations made with the BIMA telescope. Our measurement ( ∼ 75 mJy, including all the flux at 3.1 mm) is in good agreement with that of Shepherd et al. but somewhat lower than that of Ri ff el & Lüdke. This di ff erence may arise because the latter work (with 18 '' resolution) was more sensitive to weak, extended emission.</text>
<table>
<location><page_7><loc_8><loc_27><loc_49><loc_88></location>
<caption>TABLE 4 22 GH z water and 44 GH z methanol masers in G75.78 + 0.34</caption>
</table>
<section_header_level_1><location><page_7><loc_16><loc_18><loc_41><loc_19></location>3.3. H 2 O and CH 3 OH maser emission</section_header_level_1>
<text><location><page_7><loc_8><loc_7><loc_48><loc_17></location>Hofner & Churchwell (1996) reported a cluster of water masers located 2 '' southwest from the UCH II region, at the same position as the CORE source (as reported by Carral et al. 1997). Our H2O maser observations at 22.235 GHz have a double aim: to cross-calibrate the radio continuum data at 1.3 cm, and to observe the masers with higher angular resolution ( ∼ 0 . '' 1 versus ∼ 0 . '' 4 of previous observations). Two different spectral resolutions ( ∼ 0.3 and ∼ 1.3 km s -1 ) were used</text>
<text><location><page_7><loc_52><loc_60><loc_92><loc_92></location>to observe the H2O maser emission, allowing us to look for maser components in a velocity range of ( -40 , + 40) km s -1 . In Figure 4 we show the di ff erent H2O maser positions (colored circles) overlaid on the 1.3 cm continuum image. We detected a total of 35 spots with velocities ranging from -36 to + 14 km s -1 . In Table 4 we list the position, intensity, velocity, and integrated intensity of each H2O maser component, indicating in the last column at which spectral resolution the component was detected. The water masers appear to form an arc at a distance of ∼ 2 '' from the head of the cometary UCH II region (cf. Figure 1), with only a few of them directly associated with the CORE-S continuum source. We note that there are no instrumental o ff sets to be considered between the 1.3 cm continuum and the H2O maser images, since the observations were simultaneous. This arc distribution of the maser spots was also reported by Ando et al. (2011) with VERA observations at 10 mas scales. In Figure 4 we use di ff erent colors as an indicator of the velocity of the maser component. No clear velocity gradients are found in the H2O maser emission, although most of them appear slightly redshifted with respect to the cloud velocity, v LSR ≈ 0 km s -1 (Olmi & Cesaroni 1999; Codella et al. 2010). In Section 5.2 we discuss the possible association between water masers and the continuum emission.</text>
<text><location><page_7><loc_52><loc_27><loc_93><loc_60></location>Regarding the class I methanol masers at 44.069 GHz, we detect four general locations of emission (with a total of 8 di ff erent components; see Figure 1 panel a). In Table 4 we list the position, intensity, velocity, and integrated intensity for all the methanol maser components. None of the 44 GHz CH3OH spots appear to be directly associated with any of the radio continuum sources, but rather are located at a distance of 10 '' -20 '' (0.2-0.4 pc for a distance of 3.8 kpc) to the northeast of the three main YSOs. As in other star-forming regions (e. g., Kurtz et al. 2004), class I methanol masers rarely coincide with other signposts of star formation (e. g., H II regions, OH masers, class II methanol masers). Theoretical models of methanol masers suggest that the class I masers arise in an environment where collisional processes dominate (Cragg et al. 1992; Pratap et al. 2008). The G75 star-forming region contains up to four di ff erent molecular outflows (Shepherd et al. 1997), suggesting that the 44 GHz CH3OH masers could be pumped by collisions resulting from the molecular outflows. In particular, some of the methanol masers we detect are close to or within the red lobe of a molecular outflow seen in the CO (2-1) and 13 CO(2-1) lines (Sánchez-Monge 2011; see also Figure 7). Furthermore, the velocities of these maser components are red-shifted (see Table 4) which would be expected if they are excited by collisions in the red-shifted lobe of the molecular outflow.</text>
<section_header_level_1><location><page_7><loc_59><loc_24><loc_85><loc_25></location>3.4. Radio recombination line emission</section_header_level_1>
<text><location><page_7><loc_52><loc_7><loc_92><loc_23></location>We used the OVRO interferometer to observe the radio recombination lines at 3 mm (H40 α ) and 1 mm (H30 α ) towards G75, to determine the contribution of the ionized gas component at millimeter wavelengths. However, we did not clearly detect either of these lines. The spectra are dominated by continuum emission coming from either dust or ionized gas (see Section 4). Our 1 σ rms noise levels for the line (continuumfree emission) are 10 and 15 mJy beam -1 for the H40 α and H30 α , respectively. Although we did not detect the radio recombination lines, the upper limits can be used to constrain the emission from ionized gas in the millimeter range (see Section 5.2 for more details).</text>
<figure>
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<caption>F ig . 5.- Spectral energy distributions for UCHII (top) and EAST (bottom) sources. Circles and upper limits correspond to the observational data from Table 3. Red dashed lines: linear fit ( S ν ∝ ν α ) to the centimeter data (from 6 up to 0.7 cm; see Table 5).</caption>
</figure>
<section_header_level_1><location><page_8><loc_15><loc_39><loc_41><loc_41></location>4. FLUX DENSITY DISTRIBUTIONS</section_header_level_1>
<text><location><page_8><loc_8><loc_20><loc_48><loc_39></location>In Figures 5 and 6 we show the flux density distributions (FDDs) of the radio continuum sources found towards G75. The UCHII source has a flat distribution, with a spectral index ( α ; S ν ∝ ν α ) of -0 . 19 ± 0 . 06, typical of optically thin free-free emission. This FDD is well-fit by an optically thin H II region with an electron density of 3 . 7 × 10 4 cm -3 , a diameter of ∼ 0.019 pc ( ∼ 3800 AU; consistent with the observed deconvolved size), and ionized by a B0 type star. In Table 5 we list the main physical parameters of the cometary UCH II region. The emission detected at 3.1 mm and the upper limit at 1.3 mm are consistent with the millimeter continuum emission coming from ionized gas, suggesting that almost no dust emission is associated with the cometary UCH II region, in agreement with Ri ff el & Lüdke (2010).</text>
<text><location><page_8><loc_8><loc_7><loc_48><loc_20></location>The eastern continuum source (EAST), barely resolved (cf. Figure 2 and Table 3), has a flat spectral index ( α = -0 . 16 ± 0 . 12). Its FDD (see Figure 5) can be fit, at centimeter wavelengths, by an optically thin H II region with diameter ∼ 0.004 pc (900 AU; consistent with the deconvolved size listed in Table 3) and an electron density of 1 . 3 × 10 5 cm -3 , requiring the equivalent of at least one B0.5 star to provide the ionizing photon flux. Its physical parameters are listed in Table 5. At 3.1 mm there is an excess of continuum emission with respect to the optically thin H II region assumption,</text>
<figure>
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<caption>F ig . 6.- Flux density distributions for CORE (top), CORE-N (middle) and CORE-S (bottom) sources. Circles and upper limits correspond to the data from Table 3. Red dashed lines: linear fit ( S ν ∝ ν α ) to the centimeter data (from 6 to 0.7 cm; see Table 5). Blue dotted lines: homogeneous H II region with an electron density specified in the panel. Green dotted lines: modified black body law for the dust envelope with a dust emissivity index of β = 1, a source radius of 3 '' , a dust temperature of 50 K, a dust mass of 30 M /circledot , and a dust mass opacity coe ffi cient of 0.9 cm 2 g -1 at 1.3 mm (Ossenkopf & Henning 1994).</caption>
</figure>
<text><location><page_8><loc_52><loc_7><loc_92><loc_15></location>probably coming from a dust envelope of ∼ 15-36 M /circledot (see last column in Table 5). We refrain from fitting a dust envelope to the millimeter points of the FDD, because we have only an upper limit at 1.3 mm. Instead, we estimate an upper limit for the dust emissivity index β < 1 . 4, from the 3 mm detection and the 1 mm upper limit.</text>
<paragraph><location><page_9><loc_26><loc_89><loc_72><loc_91></location>TABLE 5 hysical parameters of the regions and dust properties for the sources in +</paragraph>
<table>
<location><page_9><loc_17><loc_74><loc_83><loc_88></location>
<caption>P H II G75.78 0.34</caption>
</table>
<formula><location><page_9><loc_30><loc_68><loc_92><loc_70></location>S ν = B ν ( T e) (1 -e -τ f f ( ν ) ) Ω source = 2 h ν 3 c 2 1 e h ν/ kT e -1 (1 -e -τ f f ( ν ) ) Ω source , (1)</formula>
<text><location><page_9><loc_12><loc_61><loc_92><loc_67></location>where S ν is the flux density at frequency ν , B ν ( T e) is the Planck function corresponding to the electronic temperature T e assumed to be 10 4 K, Ω source is the source solid angle, and τ f f ( ν ) is the optical depth defined by τ f f ( ν ) ≈ 0 . 08235 [ EM cm -6 pc ] [ T e K ] -1 . 35 [ ν GHz ] -2 . 1 (Altenho ff et al. 1960). The free parameters in the fit are the emission measure and the size of the source. The spectral type is determined from Panagia (1973) using the number of ionized photons, ˙ N i.</text>
<unordered_list>
<list_item><location><page_9><loc_11><loc_52><loc_92><loc_57></location>c Dust and gas mass estimated from the millimeter emission (after subtracting the contribution of the ionized gas). For the UCH II source, all the millimeter continuum emission is thermal ionized gas emission. For the EAST source we assumed a dust emissivity index of 1.5, a dust mass opacity coe ffi cient of 0.9 cm 2 g -1 at 1.3 mm (Ossenkopf & Henning 1994), and a dust temperature of 50 and 20 K, respectively. For CORE, CORE-N and CORE-S sources we provide the mass estimated assuming a dust emissivity index of 1, a dust mass opacity coe ffi cient of 0.9 cm 2 g -1 at 1.3 mm, and a dust temperature of 50 K. The upper limits are due to the low angular resolution at millimeter wavelengths that does not allow to resolve the CORE-N and CORE-S sources.</list_item>
</unordered_list>
<text><location><page_9><loc_8><loc_30><loc_48><loc_50></location>Finally, we construct the FDD for the CORE source, first including all the emission and then for CORE-N and CORES separately (Figure 6). At centimeter wavelengths, the emission is partially optically thick, with a spectral index of + 1 . 1 ± 0 . 2 for the total emission of the CORE. The major difference between the FDDs of CORE, CORE-N and CORE-S is the flux density at 7 mm. However, in all cases the centimeter emission can be well-fit by an H II region with an electron density of ∼ 10 6 cm -3 and a size < 0 . 001 pc ( < 200 AU; see Table 5). An H II region with these properties has a spectral turnover in the centimeter regime. At millimeter wavelengths, where we spatially resolve the contributions of CORE-N and CORE-S, the emission is dominated by hot dust; we estimate an envelope mass of 30 M /circledot and a temperature of 50 K (see Table 5).</text>
<section_header_level_1><location><page_9><loc_12><loc_27><loc_45><loc_29></location>5. NATURE OF THE IONIZED GAS EMISSION</section_header_level_1>
<text><location><page_9><loc_8><loc_19><loc_48><loc_27></location>We report the detection of four distinct radio continuum sources toward the high-mass star forming region G75: UCHII, EAST, CORE-N and CORE-S (the latter two correspond to the CORE source for angular resolutions coarse than 0 . '' 3). In this section we discuss the nature of these four sources.</text>
<section_header_level_1><location><page_9><loc_11><loc_17><loc_46><loc_18></location>5.1. UCHII and EAST: two ultracompact H II regions</section_header_level_1>
<text><location><page_9><loc_8><loc_7><loc_48><loc_16></location>The UCHII and EAST sources can be well-characterized as homogeneous H II regions with sizes (3800 AU and 900 AU) and electron densities (3 . 7 × 10 4 cm -3 and 1 . 3 × 10 5 cm -3 ) characteristic of small ultracompact H II regions (e. g., Kurtz 2005). They are probably ionized by B0 and B0.5 ZAMS stars, respectively, and are optically thin at centimeter wavelengths (i. e., spectral index of -0 . 1; see Table 5). Despite</text>
<text><location><page_9><loc_52><loc_15><loc_92><loc_50></location>these similarities, the two sources are distinctly di ff erent in their infrared emission. In particular, there is substantial IR dust emission associated with the EAST source but not with the UCHII source. In Figure 7 we show infrared and submillimeter images of the G75 star-forming complex. Infrared emission between 2.2 and 8.0 µ m is clearly associated with the EAST source, while no infrared emission at these wavelengths is associated with the cometary UCHII source (cf. close-up views in Figure 7). The absence of infrared emission from the UCHII source is unusual; ultracompact H II regions typically present substantial IR emission (Hoare et al. 2007). A possible explanation is that the UCH II region may be partially obscured by a cloud of gas and dust that absorbs the near- and mid-infrared emission. In fact, such a cloud is seen in emission at submillimeter wavelengths (cf. emission at 450 and 850 µ min Figure 7; Di Francesco et al. 2008), and in absorption at infrared wavelengths (cf. obscured region in the infrared maps in Figure 7), and its peak falls very close to the UCHII source. In addition, if the EAST source were located closer to the border of the dust cloud (seen in the 450 µ m and 850 µ m images), its IR emission would be less obscured than that of the UCHII source, resulting in the di ff erent infrared properties of the two sources. The non-detection of UCHII at 1.3 mm (see Fig. 3) does not contradict this scenario; as we noted in Sect. 3.2, the non-dection is probably due to inadequate sensitivity.</text>
<section_header_level_1><location><page_9><loc_55><loc_13><loc_89><loc_14></location>5.2. CORE: hypercompact H II regions or shocks?</section_header_level_1>
<text><location><page_9><loc_52><loc_7><loc_92><loc_12></location>Regarding the emission from the CORE (N and S) source, we examine several models to explain the origin of the ionized gas emission. Franco et al. (2000) modeled the CORE source as an H II region with a density distribution n e ∝ r -4 , mo-</text>
<figure>
<location><page_10><loc_10><loc_38><loc_90><loc_93></location>
<caption>F ig . 7.- Submillimeter (JCMT) and infrared ( Spitzer and UKIDSS) images of G75. Top-left : 450 µ m JCMT continuum image (white contours, levels start at 10% increasing in steps of 10% of the peak intensity 99.6 Jy) overlaid on the 5.8 µ m IRAC-Spitzer image. Top-right : 850 µ m JCMT continuum image (white contours, levels start at 10% increasing in steps of 10% of the peak intensity 10.3 Jy), overlaid on the 4.5 µ m IRAC-Spitzer image. The white box shows the region zoomed in the bottom panels. The large infrared and submillimeter source toward the southwest of the images corresponds to the H II region G75.77 + 0.34. A dark region is seen toward the northeast in the infrared images, coincident with the strong submillimeter emission, and associated with the G75 star forming complex. The strongest sources in the region, including the large H II region G75.77 + 0.33, appear saturated (black pixels) in the Spitzer images. Bottom : Close-up view of the region studied with interferometers showing the 5.8 µ m, 4.5 µ m, and 2.2 µ m images. The white contours in the lower left panel show the 450 µ mJCMTcontinuum emission as in the top panel. The solid / dashed white contours in the bottom middle panel show the blue / red-shifted CO (2-1) emission (Sánchez-Monge 2011; the contours are 10, 30, 70, 120 and 150Jy beam -1 km s -1 ) tracing the molecular outflow with a direction similar to the elongation seen at 4.5 µ m. The white / black stars mark the positions of the radio continuum sources: UCHII, EAST and CORE-N and CORE-S (see Table 3). No infrared emission is associated with the UCHII source, while strong emission is coincident with the EAST source (see main text for discussion). In all panels, the units of the color scales are 10 3 MJy sr -1 .</caption>
</figure>
<text><location><page_10><loc_8><loc_8><loc_48><loc_21></location>vated by optically thick centimeter continuum emission at frequencies up to ∼ 100 GHz. Our new, higher resolution observations suggest that the emission becomes optically thin at frequencies ∼ 30 GHz. Figure 6 suggests that a homogeneous density distribution can account for the emission from the N and S sources. Furthermore, the RRL upper limits are also consistent with optically thin emission. Assuming optically thin emission for line and continuum, and 3 σ upper limits for H30 α and H40 α (i. e., 30 and 45 mJy beam -1 , respectively), we can calculate the expected continuum emission from ion-iz</text>
<text><location><page_10><loc_52><loc_20><loc_77><loc_21></location>with (Rohlfs & Wilson 2004)</text>
<formula><location><page_10><loc_57><loc_16><loc_92><loc_19></location>[ S L S C ] = 6940 [ ∆ v km s -1 ] -1 [ T e K ] -1 . 15 [ ν GHz ] 1 . 1 , (2)</formula>
<text><location><page_10><loc_52><loc_7><loc_92><loc_15></location>where S L is the line flux density, S C is the continuum flux density, ∆ v is the width of the radio recombination line (assumed to be 30 km s -1 ; Kurtz 2005), T e is the electron temperature assumed to be 10 4 K, and ν is the frequency of the line. We find that the continuum flux density of ionized gas at 3 and 1 mm should be < 30 and < 18 mJy, respectively. These</text>
<text><location><page_11><loc_8><loc_83><loc_48><loc_92></location>values are in agreement with the homogeneous H II region fits given in Section 4, for which the expected flux densities at 3 and 1 mm are ∼ 3 mJy (i. e., /lessmuch 18 mJy). Thus, we conclude that the ionized gas emission becomes optically thin for frequencies > 30 GHz. This new result, compared to Franco et al. (2000), arises because we resolve the CORE source into two components.</text>
<text><location><page_11><loc_8><loc_63><loc_48><loc_82></location>From the FDD analysis (see Section 4), both sources (CORE-N and S) appear to be hypercompact H II regions ionized by B0.5 ZAMS stars, and separated by a distance of 0 . '' 36 (1400 AU at a distance of 3.8 kpc). This scenario suggests a wide, massive binary system (Sana & Evans 2011). We searched the literature for similar systems, with two close massive radio continuum sources, and found several examples: in G31.41 + 0.31 there is a system of two centimeter continuum sources separated by 0 . '' 19 (1500 AU at 7.9 kpc; Araya et al. 2008); in G10.47 + 0.03 there are two similar sources separated by 0 . '' 53 (5700 AU at 10.8 kpc; Cesaroni et al. 2010); and in DR21(OH) a similar system is separated by 0 . '' 45 (900 AU at 2 kpc; Araya et al. 2009). Thus, it seems that it is not unusual to detect double radio continuum sources, separated by ∼ 2000 AU, in massive star-forming regions.</text>
<text><location><page_11><loc_8><loc_51><loc_48><loc_62></location>It should be noted that the radio continuum emission from some of the previously listed binary systems is not always interpreted as arising from photo-ionized H II regions. Araya et al. (2009) propose that the radio continuum emission in DR(21)OH is free-free radiation originating in interstellar shocks, following the theoretical development of Ghavamian & Hartigan (1998). In this scenario, the free-free emission arises from shock-ionized, rather than photo-ionized, gas, being comparable to the Herbig-Haro objects seen in the optical.</text>
<text><location><page_11><loc_8><loc_14><loc_49><loc_51></location>We note that the infrared emission at 4.5 µ m (see Figure 7) shows an elongated structure 'emanating' from the position of the CORE source. The fluxes of this structure in the four IRAC / Spitzer bands are 4 mJy at 3.6 µ m, 52 mJy at 4.5 µ m, 96 mJy at 5.8 µ m, and 115 mJy at 8.0 µ m, and thus it fulfills the criteria 4 defined by Chambers et al. (2009) to be classified as a 'green fuzzy' (see also Cyganowski et al. 2008). The excess 4.5 µ m emission can be produced by shocks associated with outflows, scattered continuum in outflow cavities, obscuration a ff ecting the emission at 3.6 µ m, or fluorescence H2 emission (e. g., Noriega-Crespo et al. 2004; Smith et al. 2006; Qiu et al. 2008; De Buizer & Vacca 2010; Takami et al. 2010; Varricatt 2011; Simpson et al. 2012; Lee et al. 2012; Takami et al. 2012), and only spectroscopic studies in the mid-infrared can clearly determine the origin of the 4.5 µ m excess. However, in G75, the northeast-southwest direction of the 4.5 µ m elongated structure is consistent with the direction of the molecular outflow likely associated with the CORE source (see the solid / dashed contours in the bottom middle panel of Figure 7, Sánchez-Monge 2011) which is also consistent with the direction of the outflow reported by Ri ff el & Lüdke (2010) at larger scales, thus favoring the interpretation of the 4.5 µ m emission arising from shocks. In addition, the spatial distribution of water masers (Figure 4) is also indicative of shocks and jets, as found in other star forming regions (e. g., IRAS 20126 + 4104: Hofner et al. 2007). A milliarcsecond kinematical study of water masers in G75.78 + 0.34 (see Figure 3 in Ando et al. 2011) is consistent with a shock inter-</text>
<text><location><page_11><loc_52><loc_80><loc_92><loc_92></location>r the centimeter continuum emission. The group of masers associated with CORE-S have velocities mainly in the southwest direction (similar to the elongated structure seen at 4.5 µ m), while the two groups of maser spots located to the northwest and southeast of CORE-S show a velocity field suggesting expansion. Together with the arc morphology of all the maser spots this is suggestive of a bow-shock, implying that at least the CORE-S emission might arise from shocks.</text>
<text><location><page_11><loc_52><loc_52><loc_92><loc_80></location>A stellar jet / outflow with a mass-loss rate larger than 4 10 -6 M /circledot yr -1 and a terminal velocity of order several hundred km s -1 , shocking the ambient medium, would have sufficient energy to ionize, heat, and move the gas of both the CORE-N and CORE-S sources (see Appendix A). Although the cooling time (and hence recombination) of the high density gas is very short (Franco et al. 1994), the jet / outflow would continuously re-ionize the material. In this case, the exciting source would be located between the two radio continuum sources, with its own H II region quenched by the high density medium. I.e., a jet / outflow with such a high mass-loss rate would be neutral because the ionization front would be trapped very close to the star. The possibility of a neutral jet / outflow shocking the ambient gas cannot presently be ruled out because our observations are sensitive to ionized gas. This scenario can be tested with future centimeter continuum observations with the JVLA, to determine if CORE-S (and the water maser spots) have been displaced with respect to the other continuum sources. Assuming a jet velocity of order several hundred km s -1 , relative motions could be detected within the next five years.</text>
<text><location><page_11><loc_52><loc_29><loc_92><loc_52></location>As noted in Section 1, other mechanisms might also cause the centimeter emission from CORE-N and S. However,we consider most of these to be unlikely candidates. Equatorial winds (Hoare 2006) or thermal radio jets (Anglada 1996) typically predict constant spectral indices of + 0 . 6 and a relation between the source size and the frequency. Our observations indicate spectral indices ∼ + 1; the uncertainties in the deconvolved source sizes are too large to determine a sizefrequency dependence. A photoevaporated disk model has been proposed to explain the continuum emission of doublepeaked sources with an hour-glass morphology (Lugo et al. 2004). Although the CORE N and S peaks might be fit as a photoevaporated disk, recent studies indicate that the peaks from photoevaporated disks should change their separation with frequency, moving closer at higher frequencies (Tafoya et al. 2004). The peak positions of N and S do not change between 3.6 and 0.7 cm to a precision of ∼ 0 . '' 02.</text>
<text><location><page_11><loc_52><loc_20><loc_92><loc_29></location>Summarizing, the centimeter continuum emission from CORE N and S can be well fitted by homogeneous H II regions, each one photo-ionized by a B0.5 ZAMS star. Alternatively, free-free radiation from shock-ionized gas resulting from the interaction of a jet / outflow system with the surrounding environment appears to be a viable scenario as well. Other possible mechanisms are deemed unlikely.</text>
<section_header_level_1><location><page_11><loc_65><loc_18><loc_78><loc_19></location>6. CONCLUSIONS</section_header_level_1>
<text><location><page_11><loc_52><loc_7><loc_92><loc_17></location>We have carried out subarcsecond angular resolution observations with the VLA in the centimeter continuum and in H2O and CH3OH maser emission toward the massive star forming complex G75.78 + 0.34. We have complemented these observations with OVRO and SMA millimeter continuum and radio recombination line observations, and submillimeter / infrared data from on-line databases. Our conclusions can be summarized as follows:</text>
<unordered_list>
<list_item><location><page_12><loc_10><loc_84><loc_48><loc_92></location>1. Our radio continuum data reveal centimeter continuum emission at all wavelengths, with the emission coming from four distinct compact sources: UCHII, EAST, CORE-N and CORE-S. The two last sources appear unresolved (CORE source) when observed with angular resolutions /greaterorsimilar 0 . '' 3.</list_item>
<list_item><location><page_12><loc_10><loc_60><loc_48><loc_83></location>2. The strongest source, UCHII, is a cometary UCH II region with a size of 0.02 pc (3800 AU), an electron density of 3 . 7 × 10 4 cm -3 and is ionized by the equivalent of a B0 ZAMS star. The EAST source, located ∼ 6 '' to the east of UCHII, is also an UCH II region with an electron density of 1 . 3 × 10 5 cm -3 , ionized by a B0.5 equivalent ZAMS star, but with a smaller (barely resolved) size of 0.004 pc (900 AU). The millimeter continuum emission associated with these two UCH II regions has di ff erent origins: for the UCHII source it probably traces the ionized gas, while for the EAST source there is a millimeter excess, suggesting that this source is still embedded in a compact dust clump also detectable at mid-infrared wavelengths, with a mass of 15-36 M /circledot . We suggest that the non-detection of thermal dust emission in the UCHII source results from foreground extinction, not from an absence of warm dust.</list_item>
<list_item><location><page_12><loc_10><loc_43><loc_48><loc_59></location>3. The CORE-N and S sources are located 2 '' to the southwest of the cometary arc of the UCHII source, and are associated with water maser and dense molecular gas emission. The two sources are very close to one another (0 . '' 36, 1400 AU) and have similar properties: flux density increasing with frequency, and unresolved emission. The free-free continuum emission may be produced by two hypercompact H II regions ionized by B0.5 ZAMS stars or by the collision between a jet / outflow and the surrounding environment. A dust clump of ∼ 30 M /circledot associated with the CORE source is detected at millimeter wavelengths.</list_item>
<list_item><location><page_12><loc_10><loc_37><loc_48><loc_42></location>4. We have also reported high angular resolution observations of H2O and class I CH3OH maser emission. The class I methanol maser spots are found far from any of the radio continuum sources, and are probably excited</list_item>
</unordered_list>
<text><location><page_12><loc_56><loc_77><loc_92><loc_92></location>by collisional processes due to the presence of multiple molecular outflows. The water maser spots appear close to the CORE-N and S sources, with only a few of them spatially coincident with the S source. The spatial distribution of the water masers and the kinematics observed at milliarcsecond angular resolution, suggest that they could originate in a shock between a jet / outflow and the local surroundings. In addition, extended 4.5 µ m emission likely tracing shocked gas could be associated with a jet driven by the CORE source.</text>
<text><location><page_12><loc_52><loc_64><loc_92><loc_76></location>In summary, we have characterized the radio-continuum emission toward the massive star forming complex G75.78 + 0.34, revealing the presence of four sources: two ultracompact H II regions (named UCHII and EAST) ionized by B0-B0.5 ZAMS stars, one with an extended and cometary shape and the other being barely resolved; and two compact sources (named CORE-N and CORE-S) associated with at least one massive protostar embedded in a dense and massive envelope and with hints of driving an outflow.</text>
<text><location><page_12><loc_52><loc_38><loc_92><loc_61></location>The authors are grateful to the anonymous referee for valuable comments. Á.S.-M., A.P. and R.E. are partially supported by the Spanish MICINN grants AYA 2008-06189-C03 and AYA 201130228-C03 (co-funded with FEDER funds). Á.S.-M. and S.L. ac knowledges support by PAPIIT-UNAM IN100412 and CONACyT 146521. S.K. acknowledges support from DGAPA, UNAM, project IN101310. A.P. is supported by a JAE-Doc CSIC fellowship cofunded with the European Social Fund under the program 'Junta para la Ampliación de Estudios', by the Spanish MICINN grant AYA2011-30228-C03-02 (co-funded with FEDER funds) and by the AGAUR grant 2009SGR1172 (Catalonia). G.G. acknowledges support from CONICYT project PFB-06. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center / California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.</text>
<section_header_level_1><location><page_12><loc_46><loc_34><loc_54><loc_35></location>APPENDIX</section_header_level_1>
<section_header_level_1><location><page_12><loc_43><loc_32><loc_57><loc_33></location>ENERGY BUDGET</section_header_level_1>
<text><location><page_12><loc_8><loc_27><loc_92><loc_31></location>Consider a star that ejects into a cloud a bipolar jet / outflow with a mass-loss rate ˙ M j and a jet velocity v j. The jet will collide with the ambient material in two opposite directions and will produce two shocked ionized regions. The luminosity of the jet, L j, is given by</text>
<formula><location><page_12><loc_29><loc_23><loc_92><loc_26></location>L j = 1 2 ˙ M j v 2 j = 7 . 9 × 10 35 [ ˙ M j 10 -5 M /circledot yr -1 ] [ v j 500 km s -1 ] 2 erg s -1 . (A1)</formula>
<text><location><page_12><loc_8><loc_18><loc_92><loc_22></location>The shocked ionized gas is post shock ambient gas pushed and heated by the stellar bipolar jet. For simplicity, we will assume both shocked ionized regions have the same physical characteristics. Then, the minimum luminosity required to keep the post shock gas ionized is</text>
<formula><location><page_12><loc_36><loc_14><loc_92><loc_18></location>L i = E 0 ˙ N i = 2 . 2 × 10 35 [ ˙ N i 10 46 s -1 ] erg s -1 , (A2)</formula>
<text><location><page_12><loc_8><loc_10><loc_92><loc_13></location>where E 0 = 13 . 6 eV is the ionization energy of the hydrogen atom and ˙ N i is the rate of ionizing photons inferred from the radio continuum emission of the ionized region. Furthermore, the energy lost by radiation from each region is</text>
<formula><location><page_12><loc_30><loc_6><loc_92><loc_9></location>L rad ∼ Λ ( T ) V i = 4 . 2 × 10 34 [ n e 10 6 cm -3 ] 2 [ r i 100 AU ] 3 erg s -1 , (A3)</formula>
<text><location><page_13><loc_8><loc_88><loc_92><loc_92></location>where we assume a cooling rate per unit volume Λ (10 4 K) / ( n e n p) ∼ 3 × 10 -24 erg cm 3 s -1 (Osterbrock 1989), a volume of each region with radius r i, V i = 4 π r 3 i / 3, and assume that the electron density is equal to the proton density, n e = n p. Also, we estimate the kinetic luminosity of each ionized region averaged over its lifetime as</text>
<formula><location><page_13><loc_23><loc_83><loc_92><loc_87></location>L K ∼ M i v 2 i 2 τ cross = 1 . 5 × 10 34 [ n e 10 6 cm -3 ] [ r i 100 AU ] 3 [ v i 200 km s -1 ] 2 [ τ cross 10 yr ] -1 erg s -1 , (A4)</formula>
<text><location><page_13><loc_8><loc_80><loc_92><loc_83></location>where the mass of ionized gas is M i = m H n p V i, the velocity is v i, and τ cross is the crossing time that can be estimated from τ cross = l /v i, where l is the distance from the ionized region to the star emitting the jet.</text>
<text><location><page_13><loc_8><loc_67><loc_92><loc_80></location>We consider now the particular case of the CORE-N and CORE-S sources. From Table 5 we take n i ∼ 10 6 cm -3 , r i ∼ 100 AU, and ˙ N i ∼ 4 × 10 45 s -1 . We assume that each core is the ionized working surface (WS) of the jet moving into the cloud. For strong shocks, the speed of each WS is given by ram pressure balance as v i = βv j / (1 + β ), where β = √ ρ j /ρ a is the square root of the ratio of the jet and ambient densities (e. g., Raga et al. 1990). For large jet mass-loss rates, close to the emitting source, we assume β ∼ 1. Then, for a jet velocity v j ∼ 500 km s -1 (of the order of the escape speed of a 10 M /circledot star assumed to be the source of the jet) the shocked ionized gas moves with a speed, v i ∼ v j / 2 ∼ 250 km s -1 . Because the two continuum sources are separated by ∼ 1700 AU, we assume a distance to the jet source in between CORE-N and CORE-S, l ∼ 850 AU. Then, the resulting crossing time for both ionized regions is τ cross ∼ 16 . 2 yr. Introducing these values in Eq. A2, A3, and A4, we obtain for each shocked ionized region L i ≈ 8 . 8 × 10 34 erg s -1 , L rad ≈ 4 . 2 × 10 34 erg s -1 , and L K ≈ 1 . 5 × 10 34 erg s -1 .</text>
<text><location><page_13><loc_8><loc_63><loc_92><loc_67></location>Finally, one can now estimate the minimum mass-loss rate and velocity of a jet necessary to ionized, heat, and move the CORE-N and CORE-S sources. The energy budget has to fulfill the relation L j > 2( L i + L rad + L K). From Eq. A1, the minimum mass-loss rate of the bipolar jet / outflow that heats and moves the ionized the regions would be ˙ M j > 3 . 7 × 10 -6 M /circledot yr -1 .</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "We present sub-arcsecond observations toward the massive star forming region G75.78 + 0.34. We used the Very Large Array to study the centimeter continuum and H2O and CH3OH maser emission, and the Owens Valley Radio Observatory and Submillimeter Array to study the millimeter continuum and recombination lines (H40 α and H30 α ). We found radio continuum emission at all wavelengths, coming from three components: (1) a cometary ultracompact (UC) H II region with an electron density ∼ 3 . 7 × 10 4 cm -3 , excited by a B0 type star, and with no associated dust emission; (2) an almost unresolved UCH II region (EAST), located ∼ 6 '' to the east of the cometary UCH II region, with an electron density ∼ 1 . 3 × 10 5 cm -3 , and associated with a compact dust clump detected at millimeter and mid-infrared wavelengths; and (3) a compact source (CORE), located ∼ 2 '' to the southwest of the cometary arc, with a flux density increasing with frequency, and embedded in a dust condensation of 30 M /circledot . The CORE source is resolved into two compact and unresolved sources which can be well-fit by two homogeneous hypercompact H II regions each one photo-ionized by a B0.5 ZAMS star, or by free-free radiation from shock-ionized gas resulting from the interaction of a jet / outflow system with the surrounding environment. The spatial distribution and kinematics of water masers close to the CORE-N and S sources, together with excess emission at 4.5 µ mand the detected dust emission, suggest that the CORE source is a massive protostar driving a jet / outflow. Subject headings: stars: formation - ISM: individual objects (G75.78 + 0.34) - ISM: HII regions - ISM: dust - radio continuum: ISM",
"pages": [
1
]
},
{
"title": "DECIPHERING THE IONIZED GAS CONTENT IN THE MASSIVE STAR FORMING COMPLEX G75.78 + 0.34",
"content": "Á lvaro S' anchez -M onge 1,2,3 , S tan K urtz 3 , A ina P alau 4 , R obert E stalella 2 , D ebra S hepherd 5 , S usana L izano 3 , J os ' e F ranco 6 , G uido G aray 7 1 Osservatorio Astrofisico di Arcetri, INAF, Largo E. Fermi 5, I-50125 Firenze, Italy; [email protected] Draft version August 1, 2021",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Massive stars are key to understanding many physical phenomena in the Galaxy, however their first stages of formation are still poorly understood. One of the main reasons is that massive stars evolve more quickly to the main-sequence than low mass stars, and they radiate large amounts of ultraviolet (UV) photons and drive strong winds while they are still deeply embedded and accreting matter (e. g., Beuther & Shepherd 2005; Keto 2007). The interaction of the UV radiation and winds with the surrounding environment, resulting in bright radio continuum sources, must be well understood to comprehend the formation of high-mass stars. Thermal (free-free) radio emission at centimeter wavelengths in regions of massive star formation can have distinct origins: i) H II regions photoionized by embedded massive stars, with homogeneous density distributions (e. g., Mezger & Henderson 1967) or with density gradients (e. g., Olnon 1975; Panagia & Felli 1975; Franco et al. 2000); ii) clumps of gas or circumstellar disks externally ionized by luminous early-type stars (e. g., Garay 1987; O'Dell & Wong 1996; Zapata et al. 2004); iii) shock waves arising either in dense interstellar gas (e. g., Ghavamian & Hartigan 1998; Araya et al. 2009) or from the collision of thermal radio jets from young stellar objects (YSOs) with their surroundings (e. g., Anglada 1996; Eislo ff el et al. 2000; Rodríguez et al. 2005); iv) ionized accretion flows where the material becomes ionized while accreting onto the massive protostar (e. g., Keto 2002, 2003, 2007); v) photoevaporated disks where the radiation of the newly-formed star ionizes and evaporates the surrounding disk (e. g., Hollenbach et al. 1994; Lugo et al. 2004; Ávalos & Lizano 2012); vi) equatorial winds with the emission produced by small-scale ionized stellar winds (e. g., Hoare 2006). All these mechanisms produce radio continuum sources with spectral indices, α ( S ν ∝ ν α ), between -0 . 1 and + 2 (i.e., thermal emission; see Rodríguez et al. 1989). In addition, several works have found negative spectral indices (typical of non-thermal emission) associated with massive YSOs (e. g., Rodríguez et al. 1989; Zapata et al. 2006). These non-thermal sources can be young stars with active magnetospheres producing gyro-synchrotron emission (e. g., Feigelson & Montmerle 1999); synchrotron emission from fast shocks in disks or jets (e. g., Reid et al. 1995; Shepherd & Kurtz 1999; Shchekinov & Sobolev 2004); or extremely embedded YSOs where the UV photons from the massive protostars are heavily absorbed by large amounts of dust, with mass column densities /greaterorsimilar 10 3 g cm -2 (Rodríguez et al. 1993). A similar description of these mechanisms producing centimeter continuum emission can be found in Rodríguez et al. (2012). It is possible - and indeed, probable - that several of these emission mechanisms, either thermal or non-thermal, occur within massive star formation regions, either simultaneously or at di ff erent evolutionary epochs. Any complete model of high-mass star formation must address the presence of these multiple modes of radio continuum emission. The ON-2 star forming complex contains several early-type (O and B) stars within a massive ( /greaterorsimilar 10 4 M /circledot , Matthews et al. 1986; Dent et al. 1988) molecular cloud that spans ∼ 10 ' on the sky. Seen in CO, the cloud has two distinct condensa- M G75.78 0.34 tions, with a roughly north-south orientation (Matthews et al. 1986). Multiple ionized regions within the southern condensation were identified by Matthews et al. (1973, 1977). They reported an extended H II region G75.77 + 0.34, and also the ultracompact (UC) H II region G75.78 + 0.34 (hereafter G75); the latter is associated with strong OH maser emission first reported by Elldér et al. (1969). ON-2 lies toward Cygnus-X, and hence it has been problematic to assign a reliable distance. Early estimates ranged from 0.9 to 5.5 kpc with the nearer distance coming from extinction or luminosity arguments and the farther distance coming from Galactic rotation models and radio recombination line velocities. A helpful summary is presented by Campbell et al. (1982). More recent works, focusing on the UC H II region rather than the molecular cloud, tend to adopt a kinematic distance of 5.6 kpc (e. g., Wood & Churchwell 1989; Hanson et al. 2002). More recently, Ando et al. (2011) observed the water masers associated with the G75 UC H II region as part of the VERA (VLBI Exploration of Radio Astrometry) project. They measured the trigonometric parallax and report a heliocentric distance of 3.83 ± 0.13 kpc. We consider this distance measurement to be the most reliable and we adopt 3.83 kpc for our analysis. This distance places G75 close to other star forming regions (G75.76 + 0.35 and AFGL2591; Rygl et al. 2012), and close to the solar circle (Ando et al. 2011; Nagayama et al. 2012). At centimeter wavelengths, G75 is dominated by a cometary UCH II region reported by Wood & Churchwell (1989). Hofner & Churchwell (1996) detected a cluster of water masers located about 2 '' (10 4 AU) southwest of the UCH II region, coincident with a compact radio continuum source (Carral et al. 1997) with a spectral index of + 1 . 5 ± 0 . 4 from 6 cm through 3 mm. Franco et al. (2000) modeled this compact continuum source as a hypercompact (HC) H II region with ne ∝ r -4 . They note that this very steep density gradient is probably unrealistic, and mentioned several possible causes, including a contribution from warm dust to the flux density at 0.7 cm. Additionally, emission from a myriad of molecular line transitions has been reported in singledish surveys (e. g., Shirley et al. 2003, Roberts & Millar 2007, Klaassen & Wilson 2007, Bisschop et al. 2007). Higher angular resolution observations of di ff erent dense gas tracers show that most of the molecular emission comes from the compact radio continuum source associated with the cluster of water masers (Codella et al. 2010; Sánchez-Monge 2011). Finally, up to four distinct outflows have been identified in the ON-2 cloud core (Shepherd et al. 1997). All this makes G75 an excellent target to study the nature of the centimeter continuum sources in a massive star forming region. In this paper, we present high angular resolution centimeter continuum observations together with 22 GHz H2O and 44 GHz CH3OH maser observations toward G75. We complement this data with millimeter continuum and radio recombination line observations, with the goal of deciphering the nature of the centimeter continuum sources.",
"pages": [
1,
2
]
},
{
"title": "2.1. VLA radio continuum observations",
"content": "G75.78 + 0.34 was observed with the Very Large Array (VLA 1 ) at 6.0, 3.6, 2.0, 1.3, and 0.7 cm from January 1996 to April 2001, using the array in the CnB, B, and A configurations. In Table 1 we summarize these observations. The data reduction followed standard procedures for calibration of 1 The Very Large Array (VLA) is operated by the National Radio Astronomy Observatory (NRAO), a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. high frequency data, using the NRAO package AIPS. Initial images were produced with a robust parameter (Briggs 1995) of 1 (see Table 1 for synthesized beams and rms noise levels of these images). These data can be grouped into two categories based on angular resolution: those with θ beam ≥ 1 . '' 0, and those with θ beam ∼ 0 . '' 2. The continuum images at 1.3 cm and 0.7 cm, from projects AK490 and AK500, were crosscalibrated with the strongest H2O and CH3OH maser components, respectively, which were observed simultaneously with the continuum emission (see Section 2.2 and Table 2). After comparing the initial maps for consistency, we combined the uv -data at the same frequencies to obtain final images with better uv -coverage and sensitivity. The resulting synthesized beams and rms noise levels of the combined images are given in Table 3. At 6 cm, the H II region G75.77 + 0.34, approximately 1 ' to the southwest (e.g., Ri ff el & Lüdke 2010), produced nonimageable artifacts. The shortest baselines ( < 5 k λ ) were excluded, producing essentially no change in the measured flux density but significantly improving the quality of the map.",
"pages": [
2,
3
]
},
{
"title": "2.2. VLA H 2 O and CH 3 OH maser observations",
"content": "The water maser line at 22.23508 GHz (616 -523 transition) was observed with the VLA in the A configuration (project AK490) simultaneously with the 1.3 cm continuum emission. Two di ff erent correlator configurations were used, providing spectral resolutions of 0.3 and 1.3 km s -1 ; with velocity coverages of 21 and 83 km s -1 , respectively. The class I methanol maser line at 44.06941 GHz (70 -61 A + transition) was observed with the VLA in the B configuration (project AK500) simultaneously with the 0.7 cm continuum emission. Details of the spectrometer configuration are given in Table 2. The H2O and CH3OH maser data were calibrated following the AIPS guidelines for calibration of high frequency data. Self-calibration was performed on the strongest maser component, and the solutions were applied to the spectral line and continuum data. The images were constructed using uniform and natural weighting to measure the maser positions at the highest angular resolution and to estimate the intensity of the di ff erent maser components, respectively.",
"pages": [
3
]
},
{
"title": "2.3. OVRO observations",
"content": "The Owens Valley Radio Observatory (OVRO 2 ) observations at 3 and 1 mm were made in the L (Low) and H (High) resolution configurations during September, October and December 1997. In March 1998, additional 3 mm observations were made in the uH (ultra-High) resolution configuration. All the observations were made in the double sideband mode, simultaneously observing at 3 and 1 mm. The continuum was observed in two 1 GHz channels, centered at 95.78 GHz and 98.78 GHz for 3 mm and 228.85 GHz and 231.85 GHz for 1 mm. In addition, spectral line modules covered the H40 α (99.02296 GHz) and H30 α (231.90094 GHz) radio recombination lines (RRLs). Each spectral line setup consisted of 62 Hanning smoothed channels of 2 MHz each, providing resolutions of 6.1 and 2.6 km s -1 at 3 mm and 1 mm, respectively. The assumed LSR velocity for both lines was -8 km s -1 . Bandpass calibration was performed by observing the quasar 3C454.3. Amplitude and phase calibration were achieved by monitoring BL Lac during the di ff erent observing tracks. The absolute flux density scale was determined from Uranus, with an estimated uncertainty of 20% at 3 mm and 30% at 1 mm. The data were reduced using a combination of routines from the OVRO reduction package MMA, from MIRIAD, and from AIPS. Imaging was performed with the task IMAGR of AIPS. In Tables 1 and 2 we list details of the continuum and radio recombination line observations.",
"pages": [
3
]
},
{
"title": "2.4. SMA observations",
"content": "G75.78 + 0.34 was observed with the Submillimeter Array (SMA 3 ) in the 1.3 mm (230 GHz) band using the compact configuration on 2010 June 10. A total bandwidth of 2 × 4 GHz was used, covering the frequency ranges 218.2222.2 GHz and 230.2-234.3 GHz, with a spectral resolution of ∼ 1 km s -1 . System temperatures ranged between 150 and 250 K. The zenith opacities at 225 GHz were around 0.10 3 The SMA is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics, and is funded by the Smithsonian Institution and the Academia Sinica. and 0.15 during the 3-hour track. The FWHM of the primary beam at 1.3 mm was ∼ 56 '' . Bandpass calibration was performed by observing the quasar 3C454.3. Amplitude and phase calibrations were made by monitoring 2025 + 337 and 2015 + 371, with an rms phase of ∼ 40 · . The absolute flux density scale was determined from Callisto with an estimated uncertainty around 15%. Data were calibrated and imaged with the MIRIAD software package. The continuum was con- n the ( u,v ) domain from the line-free channels. Imaging was performed using natural weighting, resulting in a synthesized beam of 6 . '' 4 × 2 . '' 7 with a P.A. = -76 · , and 1 σ rms of 8.4 mJy beam -1 for the continuum. The two 4 GHz passbands include several molecular transitions, including CO, CH3CN, and CH3CCH. These molecular line data will be presented in a forthcoming paper together with VLA ammonia observations (Sánchez-Monge et al., in prep.).",
"pages": [
3,
4
]
},
{
"title": "3.1. Centimeter continuum emission",
"content": "We detected centimeter radio continuum emission at all wavelengths. In Figure 1 we show a global overview of the G75 region at 6.0 cm (panel a) and 3.6 cm (panel b). As seen in the figure, the centimeter continuum emission is dominated by three components that we name UCHII, EAST and CORE. In Figure 2 we show a close-up of these three sources for the combined maps at each frequency, and in Table 3 we list their flux densities and sizes, together with the beams, and rms noise levels of the combined images. The strongest source (UCHII; G75.7826 + 0.3429) is a cometary UCH II region with an integrated flux density of ∼ 35 mJy and an angular diameter of ∼ 1 '' ( ∼ 0.02 pc at a distance of 3.8 kpc; previously imaged by Wood & Churchwell 1989 and Carral et al. 1997). Located ∼ 6 '' to the east, we identify a compact source (EAST; G75.7830 + 0.3416), with a flux density of ∼ 4 mJy and an angular diameter of ∼ 0 . '' 2 ( ∼ 760 AU at a distance of 3.8 kpc). This source appears at the ∼ 5 σ level in the 7 mm maps of Carral et al. (1997). Finally, at the head of the cometary arc we find a compact source (CORE; G75.7821 + 0.3418) slightly elongated in the northeast-southwest direction, with a flux density of a few mJy and increasing with frequency. This source is coincident with the 7 mm continuum source reported by Carral et al. (1997) and with the clump of H2O masers (Hofner & Churchwell 1996). Our higher angular resolution observations ( ≤ 0 . '' 3) allow us to resolve the CORE source into two distinct (marginally resolved) condensations: COREN (G75.7821 + 0.3428) and CORE-S (G75.7820 + 0.3429; see Figure 2).",
"pages": [
5,
6
]
},
{
"title": "3.2. Millimeter continuum emission",
"content": "In Figure 3 we show the OVRO and SMA millimeter continuum images of the G75 region. At 3.1 mm we detect emission from all three sources, with the emission from the UCHII and CORE sources barely resolved. At 1.3 mm we only detect emission associated with the CORE source, probably due to a lack of sensitivity that precludes the detection of faint emission from the EAST and UCHII sources. The angular resolution of our millimeter continuum images (10-15 times poorer than the angular resolution at centimeter wavelengths) does not allow us to resolve the components CORE-N and CORES. In Table 3 we list the flux densities and sizes, and the beams and rms noise levels of the OVRO observations. For the SMA 1.3 mm source, we fit a two-dimensional Gaussian obtaining a primary beam corrected flux density of 0 . 60 ± 0 . 17 Jy with a deconvolved size of (4 × 2 ± 1) '' at a P.A. = (75 ± 10) · . The SMA 1.3 mm source, although centered on the CORE position, encompasses the UCHII source and shows an extension to the EAST source. In addition, the flux density measured in the SMA image is almost twice the flux density measured in the OVRO image, suggesting that there is some faint, extended emission not detected in the OVRO map. We refrain from combining the OVRO and SMA 1.3 mm continuum images because of the poorer uv -coverage and sensitivity of the latter. Higher sensitivity maps are needed to confirm the 1 mm continuum emission associated with the UCHII and EAST sources, and higher angular resolution is needed to identify the millimeter emission of CORE-N and S sources. At 3.5 mm Ri ff el & Lüdke (2010) measured a flux density of 119 mJy with a synthesized beam of 18 '' , while Shepherd et al. (1997) measured 75 mJy with a resolution of 5 '' , both observations made with the BIMA telescope. Our measurement ( ∼ 75 mJy, including all the flux at 3.1 mm) is in good agreement with that of Shepherd et al. but somewhat lower than that of Ri ff el & Lüdke. This di ff erence may arise because the latter work (with 18 '' resolution) was more sensitive to weak, extended emission.",
"pages": [
6
]
},
{
"title": "3.3. H 2 O and CH 3 OH maser emission",
"content": "Hofner & Churchwell (1996) reported a cluster of water masers located 2 '' southwest from the UCH II region, at the same position as the CORE source (as reported by Carral et al. 1997). Our H2O maser observations at 22.235 GHz have a double aim: to cross-calibrate the radio continuum data at 1.3 cm, and to observe the masers with higher angular resolution ( ∼ 0 . '' 1 versus ∼ 0 . '' 4 of previous observations). Two different spectral resolutions ( ∼ 0.3 and ∼ 1.3 km s -1 ) were used to observe the H2O maser emission, allowing us to look for maser components in a velocity range of ( -40 , + 40) km s -1 . In Figure 4 we show the di ff erent H2O maser positions (colored circles) overlaid on the 1.3 cm continuum image. We detected a total of 35 spots with velocities ranging from -36 to + 14 km s -1 . In Table 4 we list the position, intensity, velocity, and integrated intensity of each H2O maser component, indicating in the last column at which spectral resolution the component was detected. The water masers appear to form an arc at a distance of ∼ 2 '' from the head of the cometary UCH II region (cf. Figure 1), with only a few of them directly associated with the CORE-S continuum source. We note that there are no instrumental o ff sets to be considered between the 1.3 cm continuum and the H2O maser images, since the observations were simultaneous. This arc distribution of the maser spots was also reported by Ando et al. (2011) with VERA observations at 10 mas scales. In Figure 4 we use di ff erent colors as an indicator of the velocity of the maser component. No clear velocity gradients are found in the H2O maser emission, although most of them appear slightly redshifted with respect to the cloud velocity, v LSR ≈ 0 km s -1 (Olmi & Cesaroni 1999; Codella et al. 2010). In Section 5.2 we discuss the possible association between water masers and the continuum emission. Regarding the class I methanol masers at 44.069 GHz, we detect four general locations of emission (with a total of 8 di ff erent components; see Figure 1 panel a). In Table 4 we list the position, intensity, velocity, and integrated intensity for all the methanol maser components. None of the 44 GHz CH3OH spots appear to be directly associated with any of the radio continuum sources, but rather are located at a distance of 10 '' -20 '' (0.2-0.4 pc for a distance of 3.8 kpc) to the northeast of the three main YSOs. As in other star-forming regions (e. g., Kurtz et al. 2004), class I methanol masers rarely coincide with other signposts of star formation (e. g., H II regions, OH masers, class II methanol masers). Theoretical models of methanol masers suggest that the class I masers arise in an environment where collisional processes dominate (Cragg et al. 1992; Pratap et al. 2008). The G75 star-forming region contains up to four di ff erent molecular outflows (Shepherd et al. 1997), suggesting that the 44 GHz CH3OH masers could be pumped by collisions resulting from the molecular outflows. In particular, some of the methanol masers we detect are close to or within the red lobe of a molecular outflow seen in the CO (2-1) and 13 CO(2-1) lines (Sánchez-Monge 2011; see also Figure 7). Furthermore, the velocities of these maser components are red-shifted (see Table 4) which would be expected if they are excited by collisions in the red-shifted lobe of the molecular outflow.",
"pages": [
7
]
},
{
"title": "3.4. Radio recombination line emission",
"content": "We used the OVRO interferometer to observe the radio recombination lines at 3 mm (H40 α ) and 1 mm (H30 α ) towards G75, to determine the contribution of the ionized gas component at millimeter wavelengths. However, we did not clearly detect either of these lines. The spectra are dominated by continuum emission coming from either dust or ionized gas (see Section 4). Our 1 σ rms noise levels for the line (continuumfree emission) are 10 and 15 mJy beam -1 for the H40 α and H30 α , respectively. Although we did not detect the radio recombination lines, the upper limits can be used to constrain the emission from ionized gas in the millimeter range (see Section 5.2 for more details).",
"pages": [
7
]
},
{
"title": "4. FLUX DENSITY DISTRIBUTIONS",
"content": "In Figures 5 and 6 we show the flux density distributions (FDDs) of the radio continuum sources found towards G75. The UCHII source has a flat distribution, with a spectral index ( α ; S ν ∝ ν α ) of -0 . 19 ± 0 . 06, typical of optically thin free-free emission. This FDD is well-fit by an optically thin H II region with an electron density of 3 . 7 × 10 4 cm -3 , a diameter of ∼ 0.019 pc ( ∼ 3800 AU; consistent with the observed deconvolved size), and ionized by a B0 type star. In Table 5 we list the main physical parameters of the cometary UCH II region. The emission detected at 3.1 mm and the upper limit at 1.3 mm are consistent with the millimeter continuum emission coming from ionized gas, suggesting that almost no dust emission is associated with the cometary UCH II region, in agreement with Ri ff el & Lüdke (2010). The eastern continuum source (EAST), barely resolved (cf. Figure 2 and Table 3), has a flat spectral index ( α = -0 . 16 ± 0 . 12). Its FDD (see Figure 5) can be fit, at centimeter wavelengths, by an optically thin H II region with diameter ∼ 0.004 pc (900 AU; consistent with the deconvolved size listed in Table 3) and an electron density of 1 . 3 × 10 5 cm -3 , requiring the equivalent of at least one B0.5 star to provide the ionizing photon flux. Its physical parameters are listed in Table 5. At 3.1 mm there is an excess of continuum emission with respect to the optically thin H II region assumption, probably coming from a dust envelope of ∼ 15-36 M /circledot (see last column in Table 5). We refrain from fitting a dust envelope to the millimeter points of the FDD, because we have only an upper limit at 1.3 mm. Instead, we estimate an upper limit for the dust emissivity index β < 1 . 4, from the 3 mm detection and the 1 mm upper limit. where S ν is the flux density at frequency ν , B ν ( T e) is the Planck function corresponding to the electronic temperature T e assumed to be 10 4 K, Ω source is the source solid angle, and τ f f ( ν ) is the optical depth defined by τ f f ( ν ) ≈ 0 . 08235 [ EM cm -6 pc ] [ T e K ] -1 . 35 [ ν GHz ] -2 . 1 (Altenho ff et al. 1960). The free parameters in the fit are the emission measure and the size of the source. The spectral type is determined from Panagia (1973) using the number of ionized photons, ˙ N i. Finally, we construct the FDD for the CORE source, first including all the emission and then for CORE-N and CORES separately (Figure 6). At centimeter wavelengths, the emission is partially optically thick, with a spectral index of + 1 . 1 ± 0 . 2 for the total emission of the CORE. The major difference between the FDDs of CORE, CORE-N and CORE-S is the flux density at 7 mm. However, in all cases the centimeter emission can be well-fit by an H II region with an electron density of ∼ 10 6 cm -3 and a size < 0 . 001 pc ( < 200 AU; see Table 5). An H II region with these properties has a spectral turnover in the centimeter regime. At millimeter wavelengths, where we spatially resolve the contributions of CORE-N and CORE-S, the emission is dominated by hot dust; we estimate an envelope mass of 30 M /circledot and a temperature of 50 K (see Table 5).",
"pages": [
8,
9
]
},
{
"title": "5. NATURE OF THE IONIZED GAS EMISSION",
"content": "We report the detection of four distinct radio continuum sources toward the high-mass star forming region G75: UCHII, EAST, CORE-N and CORE-S (the latter two correspond to the CORE source for angular resolutions coarse than 0 . '' 3). In this section we discuss the nature of these four sources.",
"pages": [
9
]
},
{
"title": "5.1. UCHII and EAST: two ultracompact H II regions",
"content": "The UCHII and EAST sources can be well-characterized as homogeneous H II regions with sizes (3800 AU and 900 AU) and electron densities (3 . 7 × 10 4 cm -3 and 1 . 3 × 10 5 cm -3 ) characteristic of small ultracompact H II regions (e. g., Kurtz 2005). They are probably ionized by B0 and B0.5 ZAMS stars, respectively, and are optically thin at centimeter wavelengths (i. e., spectral index of -0 . 1; see Table 5). Despite these similarities, the two sources are distinctly di ff erent in their infrared emission. In particular, there is substantial IR dust emission associated with the EAST source but not with the UCHII source. In Figure 7 we show infrared and submillimeter images of the G75 star-forming complex. Infrared emission between 2.2 and 8.0 µ m is clearly associated with the EAST source, while no infrared emission at these wavelengths is associated with the cometary UCHII source (cf. close-up views in Figure 7). The absence of infrared emission from the UCHII source is unusual; ultracompact H II regions typically present substantial IR emission (Hoare et al. 2007). A possible explanation is that the UCH II region may be partially obscured by a cloud of gas and dust that absorbs the near- and mid-infrared emission. In fact, such a cloud is seen in emission at submillimeter wavelengths (cf. emission at 450 and 850 µ min Figure 7; Di Francesco et al. 2008), and in absorption at infrared wavelengths (cf. obscured region in the infrared maps in Figure 7), and its peak falls very close to the UCHII source. In addition, if the EAST source were located closer to the border of the dust cloud (seen in the 450 µ m and 850 µ m images), its IR emission would be less obscured than that of the UCHII source, resulting in the di ff erent infrared properties of the two sources. The non-detection of UCHII at 1.3 mm (see Fig. 3) does not contradict this scenario; as we noted in Sect. 3.2, the non-dection is probably due to inadequate sensitivity.",
"pages": [
9
]
},
{
"title": "5.2. CORE: hypercompact H II regions or shocks?",
"content": "Regarding the emission from the CORE (N and S) source, we examine several models to explain the origin of the ionized gas emission. Franco et al. (2000) modeled the CORE source as an H II region with a density distribution n e ∝ r -4 , mo- vated by optically thick centimeter continuum emission at frequencies up to ∼ 100 GHz. Our new, higher resolution observations suggest that the emission becomes optically thin at frequencies ∼ 30 GHz. Figure 6 suggests that a homogeneous density distribution can account for the emission from the N and S sources. Furthermore, the RRL upper limits are also consistent with optically thin emission. Assuming optically thin emission for line and continuum, and 3 σ upper limits for H30 α and H40 α (i. e., 30 and 45 mJy beam -1 , respectively), we can calculate the expected continuum emission from ion-iz with (Rohlfs & Wilson 2004) where S L is the line flux density, S C is the continuum flux density, ∆ v is the width of the radio recombination line (assumed to be 30 km s -1 ; Kurtz 2005), T e is the electron temperature assumed to be 10 4 K, and ν is the frequency of the line. We find that the continuum flux density of ionized gas at 3 and 1 mm should be < 30 and < 18 mJy, respectively. These values are in agreement with the homogeneous H II region fits given in Section 4, for which the expected flux densities at 3 and 1 mm are ∼ 3 mJy (i. e., /lessmuch 18 mJy). Thus, we conclude that the ionized gas emission becomes optically thin for frequencies > 30 GHz. This new result, compared to Franco et al. (2000), arises because we resolve the CORE source into two components. From the FDD analysis (see Section 4), both sources (CORE-N and S) appear to be hypercompact H II regions ionized by B0.5 ZAMS stars, and separated by a distance of 0 . '' 36 (1400 AU at a distance of 3.8 kpc). This scenario suggests a wide, massive binary system (Sana & Evans 2011). We searched the literature for similar systems, with two close massive radio continuum sources, and found several examples: in G31.41 + 0.31 there is a system of two centimeter continuum sources separated by 0 . '' 19 (1500 AU at 7.9 kpc; Araya et al. 2008); in G10.47 + 0.03 there are two similar sources separated by 0 . '' 53 (5700 AU at 10.8 kpc; Cesaroni et al. 2010); and in DR21(OH) a similar system is separated by 0 . '' 45 (900 AU at 2 kpc; Araya et al. 2009). Thus, it seems that it is not unusual to detect double radio continuum sources, separated by ∼ 2000 AU, in massive star-forming regions. It should be noted that the radio continuum emission from some of the previously listed binary systems is not always interpreted as arising from photo-ionized H II regions. Araya et al. (2009) propose that the radio continuum emission in DR(21)OH is free-free radiation originating in interstellar shocks, following the theoretical development of Ghavamian & Hartigan (1998). In this scenario, the free-free emission arises from shock-ionized, rather than photo-ionized, gas, being comparable to the Herbig-Haro objects seen in the optical. We note that the infrared emission at 4.5 µ m (see Figure 7) shows an elongated structure 'emanating' from the position of the CORE source. The fluxes of this structure in the four IRAC / Spitzer bands are 4 mJy at 3.6 µ m, 52 mJy at 4.5 µ m, 96 mJy at 5.8 µ m, and 115 mJy at 8.0 µ m, and thus it fulfills the criteria 4 defined by Chambers et al. (2009) to be classified as a 'green fuzzy' (see also Cyganowski et al. 2008). The excess 4.5 µ m emission can be produced by shocks associated with outflows, scattered continuum in outflow cavities, obscuration a ff ecting the emission at 3.6 µ m, or fluorescence H2 emission (e. g., Noriega-Crespo et al. 2004; Smith et al. 2006; Qiu et al. 2008; De Buizer & Vacca 2010; Takami et al. 2010; Varricatt 2011; Simpson et al. 2012; Lee et al. 2012; Takami et al. 2012), and only spectroscopic studies in the mid-infrared can clearly determine the origin of the 4.5 µ m excess. However, in G75, the northeast-southwest direction of the 4.5 µ m elongated structure is consistent with the direction of the molecular outflow likely associated with the CORE source (see the solid / dashed contours in the bottom middle panel of Figure 7, Sánchez-Monge 2011) which is also consistent with the direction of the outflow reported by Ri ff el & Lüdke (2010) at larger scales, thus favoring the interpretation of the 4.5 µ m emission arising from shocks. In addition, the spatial distribution of water masers (Figure 4) is also indicative of shocks and jets, as found in other star forming regions (e. g., IRAS 20126 + 4104: Hofner et al. 2007). A milliarcsecond kinematical study of water masers in G75.78 + 0.34 (see Figure 3 in Ando et al. 2011) is consistent with a shock inter- r the centimeter continuum emission. The group of masers associated with CORE-S have velocities mainly in the southwest direction (similar to the elongated structure seen at 4.5 µ m), while the two groups of maser spots located to the northwest and southeast of CORE-S show a velocity field suggesting expansion. Together with the arc morphology of all the maser spots this is suggestive of a bow-shock, implying that at least the CORE-S emission might arise from shocks. A stellar jet / outflow with a mass-loss rate larger than 4 10 -6 M /circledot yr -1 and a terminal velocity of order several hundred km s -1 , shocking the ambient medium, would have sufficient energy to ionize, heat, and move the gas of both the CORE-N and CORE-S sources (see Appendix A). Although the cooling time (and hence recombination) of the high density gas is very short (Franco et al. 1994), the jet / outflow would continuously re-ionize the material. In this case, the exciting source would be located between the two radio continuum sources, with its own H II region quenched by the high density medium. I.e., a jet / outflow with such a high mass-loss rate would be neutral because the ionization front would be trapped very close to the star. The possibility of a neutral jet / outflow shocking the ambient gas cannot presently be ruled out because our observations are sensitive to ionized gas. This scenario can be tested with future centimeter continuum observations with the JVLA, to determine if CORE-S (and the water maser spots) have been displaced with respect to the other continuum sources. Assuming a jet velocity of order several hundred km s -1 , relative motions could be detected within the next five years. As noted in Section 1, other mechanisms might also cause the centimeter emission from CORE-N and S. However,we consider most of these to be unlikely candidates. Equatorial winds (Hoare 2006) or thermal radio jets (Anglada 1996) typically predict constant spectral indices of + 0 . 6 and a relation between the source size and the frequency. Our observations indicate spectral indices ∼ + 1; the uncertainties in the deconvolved source sizes are too large to determine a sizefrequency dependence. A photoevaporated disk model has been proposed to explain the continuum emission of doublepeaked sources with an hour-glass morphology (Lugo et al. 2004). Although the CORE N and S peaks might be fit as a photoevaporated disk, recent studies indicate that the peaks from photoevaporated disks should change their separation with frequency, moving closer at higher frequencies (Tafoya et al. 2004). The peak positions of N and S do not change between 3.6 and 0.7 cm to a precision of ∼ 0 . '' 02. Summarizing, the centimeter continuum emission from CORE N and S can be well fitted by homogeneous H II regions, each one photo-ionized by a B0.5 ZAMS star. Alternatively, free-free radiation from shock-ionized gas resulting from the interaction of a jet / outflow system with the surrounding environment appears to be a viable scenario as well. Other possible mechanisms are deemed unlikely.",
"pages": [
9,
10,
11
]
},
{
"title": "6. CONCLUSIONS",
"content": "We have carried out subarcsecond angular resolution observations with the VLA in the centimeter continuum and in H2O and CH3OH maser emission toward the massive star forming complex G75.78 + 0.34. We have complemented these observations with OVRO and SMA millimeter continuum and radio recombination line observations, and submillimeter / infrared data from on-line databases. Our conclusions can be summarized as follows: by collisional processes due to the presence of multiple molecular outflows. The water maser spots appear close to the CORE-N and S sources, with only a few of them spatially coincident with the S source. The spatial distribution of the water masers and the kinematics observed at milliarcsecond angular resolution, suggest that they could originate in a shock between a jet / outflow and the local surroundings. In addition, extended 4.5 µ m emission likely tracing shocked gas could be associated with a jet driven by the CORE source. In summary, we have characterized the radio-continuum emission toward the massive star forming complex G75.78 + 0.34, revealing the presence of four sources: two ultracompact H II regions (named UCHII and EAST) ionized by B0-B0.5 ZAMS stars, one with an extended and cometary shape and the other being barely resolved; and two compact sources (named CORE-N and CORE-S) associated with at least one massive protostar embedded in a dense and massive envelope and with hints of driving an outflow. The authors are grateful to the anonymous referee for valuable comments. Á.S.-M., A.P. and R.E. are partially supported by the Spanish MICINN grants AYA 2008-06189-C03 and AYA 201130228-C03 (co-funded with FEDER funds). Á.S.-M. and S.L. ac knowledges support by PAPIIT-UNAM IN100412 and CONACyT 146521. S.K. acknowledges support from DGAPA, UNAM, project IN101310. A.P. is supported by a JAE-Doc CSIC fellowship cofunded with the European Social Fund under the program 'Junta para la Ampliación de Estudios', by the Spanish MICINN grant AYA2011-30228-C03-02 (co-funded with FEDER funds) and by the AGAUR grant 2009SGR1172 (Catalonia). G.G. acknowledges support from CONICYT project PFB-06. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center / California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.",
"pages": [
11,
12
]
},
{
"title": "ENERGY BUDGET",
"content": "Consider a star that ejects into a cloud a bipolar jet / outflow with a mass-loss rate ˙ M j and a jet velocity v j. The jet will collide with the ambient material in two opposite directions and will produce two shocked ionized regions. The luminosity of the jet, L j, is given by The shocked ionized gas is post shock ambient gas pushed and heated by the stellar bipolar jet. For simplicity, we will assume both shocked ionized regions have the same physical characteristics. Then, the minimum luminosity required to keep the post shock gas ionized is where E 0 = 13 . 6 eV is the ionization energy of the hydrogen atom and ˙ N i is the rate of ionizing photons inferred from the radio continuum emission of the ionized region. Furthermore, the energy lost by radiation from each region is where we assume a cooling rate per unit volume Λ (10 4 K) / ( n e n p) ∼ 3 × 10 -24 erg cm 3 s -1 (Osterbrock 1989), a volume of each region with radius r i, V i = 4 π r 3 i / 3, and assume that the electron density is equal to the proton density, n e = n p. Also, we estimate the kinetic luminosity of each ionized region averaged over its lifetime as where the mass of ionized gas is M i = m H n p V i, the velocity is v i, and τ cross is the crossing time that can be estimated from τ cross = l /v i, where l is the distance from the ionized region to the star emitting the jet. We consider now the particular case of the CORE-N and CORE-S sources. From Table 5 we take n i ∼ 10 6 cm -3 , r i ∼ 100 AU, and ˙ N i ∼ 4 × 10 45 s -1 . We assume that each core is the ionized working surface (WS) of the jet moving into the cloud. For strong shocks, the speed of each WS is given by ram pressure balance as v i = βv j / (1 + β ), where β = √ ρ j /ρ a is the square root of the ratio of the jet and ambient densities (e. g., Raga et al. 1990). For large jet mass-loss rates, close to the emitting source, we assume β ∼ 1. Then, for a jet velocity v j ∼ 500 km s -1 (of the order of the escape speed of a 10 M /circledot star assumed to be the source of the jet) the shocked ionized gas moves with a speed, v i ∼ v j / 2 ∼ 250 km s -1 . Because the two continuum sources are separated by ∼ 1700 AU, we assume a distance to the jet source in between CORE-N and CORE-S, l ∼ 850 AU. Then, the resulting crossing time for both ionized regions is τ cross ∼ 16 . 2 yr. Introducing these values in Eq. A2, A3, and A4, we obtain for each shocked ionized region L i ≈ 8 . 8 × 10 34 erg s -1 , L rad ≈ 4 . 2 × 10 34 erg s -1 , and L K ≈ 1 . 5 × 10 34 erg s -1 . Finally, one can now estimate the minimum mass-loss rate and velocity of a jet necessary to ionized, heat, and move the CORE-N and CORE-S sources. The energy budget has to fulfill the relation L j > 2( L i + L rad + L K). From Eq. A1, the minimum mass-loss rate of the bipolar jet / outflow that heats and moves the ionized the regions would be ˙ M j > 3 . 7 × 10 -6 M /circledot yr -1 .",
"pages": [
12,
13
]
},
{
"title": "REFERENCES",
"content": "Altenho ff , W., Mezger, P. G., Wendker, H., & Westerhout, G. 1960, Vero ff . Univ. Sternwarte Bonn, 59, 48 Elldér, J., Rönnäng, B., & Winnberg, A. 1969, Nature, 222, 67 Feigelson, E. D., & Montmerle, T. 1999, ARA&A, 37, 363 Lee, H.-T., Takami, M., Duan, H.-Y., et al. 2012, ApJS, 200, 2 Lugo, J., Lizano, S., & Garay, G. 2004, ApJ, 614, 807 Marti, J., Rodriguez, L. F., & Reipurth, B. 1993, ApJ, 416, 208 Matthews, H. E., Goss, W. M., Winnberg, A., & Habing, H. J. 1973, A&A, 29, 309 Nagayama, T., & VERA project members 2012, IAU Symposium Cosmic John Simon Guggenheim Memorial Foundation, University of Minnesota, et al. Mill Valley, CA, University Science Books, 1989, 422 p. Panagia, N., & Felli, M. 1975, A&A, 39, 1 Panagia, N. 1973, AJ, 78, 929 Raga, A. C., Binette, L., Cantó, J., & Calvet, N. 1990, ApJ, 364, 601",
"pages": [
13
]
}
]
2013ApJ...768...82N
https://arxiv.org/pdf/1303.2338.pdf
<document>
<text><location><page_1><loc_10><loc_85><loc_10><loc_85></location>1</text>
<text><location><page_1><loc_10><loc_82><loc_10><loc_83></location>2</text>
<text><location><page_1><loc_9><loc_51><loc_10><loc_51></location>10</text>
<section_header_level_1><location><page_1><loc_12><loc_82><loc_88><loc_86></location>Suppression of Dielectronic Recombination Due to Finite Density Effects</section_header_level_1>
<text><location><page_1><loc_32><loc_77><loc_68><loc_79></location>D. Nikoli´c 1 , T. W. Gorczyca, K. T. Korista</text>
<text><location><page_1><loc_10><loc_78><loc_10><loc_78></location>3</text>
<text><location><page_1><loc_28><loc_74><loc_72><loc_76></location>Western Michigan University, Kalamazoo, MI, USA</text>
<text><location><page_1><loc_10><loc_75><loc_10><loc_75></location>4</text>
<text><location><page_1><loc_44><loc_70><loc_56><loc_72></location>G. J. Ferland</text>
<text><location><page_1><loc_10><loc_71><loc_10><loc_71></location>5</text>
<text><location><page_1><loc_31><loc_67><loc_69><loc_69></location>University of Kentucky, Lexington, KY, USA</text>
<text><location><page_1><loc_10><loc_68><loc_10><loc_68></location>6</text>
<text><location><page_1><loc_48><loc_63><loc_52><loc_64></location>and</text>
<text><location><page_1><loc_10><loc_63><loc_10><loc_64></location>7</text>
<text><location><page_1><loc_44><loc_59><loc_56><loc_60></location>N. R. Badnell</text>
<text><location><page_1><loc_10><loc_59><loc_10><loc_59></location>8</text>
<text><location><page_1><loc_33><loc_56><loc_67><loc_57></location>University of Strathclyde, Glasgow, UK</text>
<text><location><page_1><loc_10><loc_56><loc_10><loc_56></location>9</text>
<text><location><page_1><loc_20><loc_51><loc_27><loc_52></location>Received</text>
<text><location><page_1><loc_48><loc_51><loc_49><loc_52></location>;</text>
<text><location><page_1><loc_52><loc_51><loc_59><loc_52></location>accepted</text>
<text><location><page_2><loc_9><loc_85><loc_10><loc_85></location>11</text>
<text><location><page_2><loc_9><loc_79><loc_10><loc_80></location>12</text>
<text><location><page_2><loc_9><loc_22><loc_10><loc_22></location>13</text>
<section_header_level_1><location><page_2><loc_44><loc_85><loc_56><loc_86></location>ABSTRACT</section_header_level_1>
<text><location><page_2><loc_17><loc_26><loc_83><loc_80></location>We have developed a general model for determining density-dependent effective dielectronic recombination (DR) rate coefficients in order to explore finitedensity effects on the ionization balance of plasmas. Our model consists of multiplying by a suppression factor those highly-accurate total zero-density DR rate coefficients which have been produced from state-of-the-art theoretical calculations and which have been benchmarked by experiment. The suppression factor is based-upon earlier detailed collision-radiative calculations which were made for a wide range of ions at various densities and temperatures, but used a simplified treatment of DR. A general suppression formula is then developed as a function of isoelectronic sequence, charge, density, and temperature. These densitydependent effective DR rate coefficients are then used in the plasma simulation code Cloudy to compute ionization balance curves for both collisionally ionized and photoionized plasmas at very low ( n e = 1 cm -3 ) and finite ( n e = 10 10 cm -3 ) densities. We find that the denser case is significantly more ionized due to suppression of DR, warranting further studies of density effects on DR by detailed collisional-radiative calculations which utilize state-of-the-art partial DR rate coefficients. This is expected to impact the predictions of the ionization balance in denser cosmic gases such as those found in nova and supernova shells, accretion disks, and the broad emission line regions in active galactic nuclei.</text>
<text><location><page_3><loc_9><loc_85><loc_10><loc_85></location>14</text>
<section_header_level_1><location><page_3><loc_42><loc_85><loc_58><loc_86></location>1. Introduction</section_header_level_1>
<text><location><page_3><loc_9><loc_68><loc_87><loc_81></location>Astronomical emission or absorption sources have an enormous range of densities. 15 Two examples include the intergalactic medium, with n e ∼ 10 -4 cm -3 , and the broad 16 emission-line regions of Active Galactic Nuclei, with n e ∼ 10 10 cm -3 . The gas producing 17 the spectrum is not in thermodynamic equilibrium (Osterbrock & Ferland 2006), so 18 microphysical processes determine the physical conditions. 19</text>
<text><location><page_3><loc_9><loc_41><loc_88><loc_66></location>The two common cases encountered for ionization are photoionization and collisional 20 (e.g., electron-impact) ionization. In both cases, ions are recombined by dielectronic 21 and radiative recombination, with dielectronic recombination (DR) usually the dominant 22 process for elements heavier than helium. Databases give ionization and recombination 23 rates that are the sum of several contributing processes. Examples include Voronov (1997) 24 for electron impact ionization, Verner & Yakovlev (1995) for photoionization, and the 25 DR project (Badnell et al. 2003) for dielectronic recombination and Badnell (2006a) for 26 radiative recombination; it is these latter data 1 which will be of primary interest to us in 27 the present study. 28</text>
<text><location><page_3><loc_9><loc_17><loc_88><loc_39></location>The collisional ionization and recombination rate coefficients used in astrophysics are 29 frequently assumed to depend on temperature but to have no density dependence. The 30 rigorous treatment of density dependent ionization and recombination rate coefficients is 31 via collisional-radiative modeling. This was introduced by Bates et al. (1962) for radiative 32 recombination only and extended to treat the much more complex case of dielectronic 33 recombination by Burgess & Summers (1969). Summers applied their techniques to 34 determine density dependent ionization and recombination rate coefficients, and the 35 consequential ionization balance for collisional plasmas, for H-like thru Ar-like ions. 36</text>
<unordered_list>
<list_item><location><page_4><loc_9><loc_85><loc_87><loc_86></location>Graphical results were presented for the elements C, O and Ne (Summers 1972) and then 37</list_item>
<list_item><location><page_4><loc_9><loc_82><loc_86><loc_83></location>N, Mg and Si (Summers 1974). Reduced temperatures and densities were used so as to 38</list_item>
<list_item><location><page_4><loc_9><loc_79><loc_88><loc_80></location>enable easy interpolation for other elements. Tables of such recombination rate coefficients 39</list_item>
<list_item><location><page_4><loc_9><loc_76><loc_87><loc_77></location>were made available only via a Laboratory Report - Summers (1974 & 1979) - due to 40</list_item>
<list_item><location><page_4><loc_9><loc_73><loc_88><loc_74></location>their voluminous nature at that point in history. The 'difficulty' in utilizing this pioneering 41</list_item>
<list_item><location><page_4><loc_9><loc_70><loc_85><loc_71></location>data led to some modelers attempting to develop simplified approaches. For example, 42</list_item>
<list_item><location><page_4><loc_9><loc_67><loc_87><loc_69></location>Jordan (1969) used an approach which was based on truncating the zero-density DR sum 43</list_item>
<list_item><location><page_4><loc_9><loc_64><loc_86><loc_66></location>over Rydberg states using a simple density dependent cut-off which itself was based on 44</list_item>
<list_item><location><page_4><loc_9><loc_61><loc_87><loc_63></location>early collisional-radiative calculations by Burgess & Summers (1969); a suppression factor 45</list_item>
<list_item><location><page_4><loc_9><loc_58><loc_86><loc_60></location>was formed from its ratio to the zero-density value and then used more generally. Also, 46</list_item>
<list_item><location><page_4><loc_9><loc_55><loc_88><loc_57></location>Davidson (1975) simplified the collisional-radiative approach of Burgess & Summers (1969) 47</list_item>
<list_item><location><page_4><loc_9><loc_52><loc_86><loc_54></location>and, using hydrogenic atomic data, determined suppression factors for Li-like C IV and 48</list_item>
<list_item><location><page_4><loc_9><loc_49><loc_88><loc_51></location>O VI . New calculations for C IV were made by Badnell et al. (1993) utilizing more advanced 49</list_item>
<list_item><location><page_4><loc_9><loc_47><loc_88><loc_48></location>(generalized) collisional-radiative modeling (Summers & Hooper 1983) and much improved 50</list_item>
<list_item><location><page_4><loc_9><loc_44><loc_88><loc_45></location>atomic data at collisional plasma temperatures (see the references in Badnell et al. (1993)). 51</list_item>
<list_item><location><page_4><loc_9><loc_40><loc_10><loc_41></location>52</list_item>
<list_item><location><page_4><loc_9><loc_37><loc_10><loc_38></location>53</list_item>
<list_item><location><page_4><loc_12><loc_37><loc_86><loc_41></location>All of the above works were for electron collisional plasmas and used rather basic DR data (excluding Badnell et al. (1993)) as epitomized in the Burgess (1965) General</list_item>
<list_item><location><page_4><loc_9><loc_34><loc_85><loc_35></location>Formula, viz. a common dipole transition for dielectronic capture, autoionization, and 54</list_item>
<list_item><location><page_4><loc_9><loc_31><loc_87><loc_33></location>radiative stabilization. The purpose of the present paper is to explore density suppression 55</list_item>
<list_item><location><page_4><loc_9><loc_28><loc_87><loc_30></location>of DR in photoionized plasmas, and within collisional plasmas, using state-of-the art DR 56</list_item>
<list_item><location><page_4><loc_9><loc_25><loc_87><loc_27></location>data which takes account of a myriad of pathways not feasible in the early works above, 57</list_item>
<list_item><location><page_4><loc_9><loc_22><loc_86><loc_24></location>but which has been shown to be necessary by comparison with experiment. We wish to 58</list_item>
<list_item><location><page_4><loc_9><loc_19><loc_86><loc_21></location>gain a broad overview utilizing the large test-suite maintained by the plasma simulation 59</list_item>
<list_item><location><page_4><loc_9><loc_16><loc_88><loc_18></location>code Cloudy. We utilize an approach to DR suppression which is motivated initially by the 60</list_item>
<list_item><location><page_4><loc_9><loc_13><loc_87><loc_15></location>detailed collisional-radiative results given in Badnell et al. (1993) for C IV at T = 10 5 K, 61</list_item>
<list_item><location><page_4><loc_9><loc_11><loc_88><loc_12></location>along with known scalings to all temperatures, charges, and densities. Using these results as 62</list_item>
</unordered_list>
<text><location><page_5><loc_9><loc_76><loc_88><loc_86></location>a guideline, a more general suppression formula is then determined by fitting to suppression 63 results from extensive detailed collisional-radiative calculations (Summers 1974 & 1979) for 64 a wide range of ions at several densities and (high) temperatures. Additional modifications 65 are then introduced to account for low temperature DR. 66</text>
<text><location><page_5><loc_9><loc_60><loc_88><loc_73></location>The outline of the rest of the paper is as follows: in the next section we describe the 67 DR suppression model we use; we then apply this suppression to the zero-density DR data, 68 and use the resultant density-dependent DR data in Cloudy to determine the ionization 69 distribution produced under photoionized and collisional ionization equilibrium at low and 70 moderate densities. 71</text>
<text><location><page_5><loc_9><loc_53><loc_10><loc_54></location>72</text>
<section_header_level_1><location><page_5><loc_29><loc_53><loc_71><loc_54></location>2. Generalized Density Suppression Model</section_header_level_1>
<text><location><page_5><loc_9><loc_25><loc_88><loc_50></location>We use the following approach, detailed more fully in the subsections below. First, 73 the high-temperature collisional-radiative modeling results of Badnell et al. (1993) for DR 74 suppression in C IV are parameterized by a pseudo-Voigt profile to study the qualitative 75 behavior of suppression as a function of density and temperature. Next, this formulation 76 is then used as a guideline for developing a more comprehensive suppression formula which 77 is obtained by fitting to collisional radiative data for various isoelectronic sequences, ionic 78 charges, densities, and temperatures (Summers 1974 & 1979). Lastly, the suppression 79 formulation is extended to low-temperatures according to the nature of the sequence-specific 80 DR. 81</text>
<text><location><page_5><loc_9><loc_18><loc_10><loc_19></location>82</text>
<section_header_level_1><location><page_5><loc_25><loc_18><loc_75><loc_19></location>2.1. High-Temperature Suppression for Li-like C IV</section_header_level_1>
<text><location><page_5><loc_9><loc_11><loc_88><loc_15></location>We begin by considering DR of Li-like C IV , for which the density dependent total DR 83 rate coefficient, and therefore the suppression factor, has been computed rigorously within 84</text>
<text><location><page_6><loc_9><loc_85><loc_64><loc_86></location>a collisional-radiative modeling approach (Badnell et al. 1993). 85</text>
<unordered_list>
<list_item><location><page_6><loc_9><loc_78><loc_88><loc_82></location>In the electron collisional ionization case, because of the consequential high temperature 86 of peak abundance, dielectronic recombination occurs mainly through energetically high87</list_item>
<list_item><location><page_6><loc_9><loc_75><loc_88><loc_76></location>lying autoionizing states (via dipole core-excitations) for which radiative stabilization is by 88</list_item>
<list_item><location><page_6><loc_9><loc_72><loc_66><loc_73></location>the core electron into final states just below the ionization limit: 89</list_item>
</unordered_list>
<formula><location><page_6><loc_32><loc_66><loc_88><loc_69></location>e -+1 s 2 2 s → 1 s 2 2 pnl → 1 s 2 2 snl + hν . (1)</formula>
<text><location><page_6><loc_9><loc_57><loc_88><loc_65></location>In the zero-density limit, the intermediate 1 s 2 2 snl states can only decay further via radiative 90 cascading until the 1 s 2 2 s 2 final recombined ground state is reached, thereby completing the 91 DR process: 92</text>
<formula><location><page_6><loc_24><loc_52><loc_88><loc_55></location>1 s 2 2 snl -→ 1 s 2 2 sn ' l ' + hν 1 → ... → 1 s 2 2 s 2 + hν 1 + hν 2 + ... (2)</formula>
<text><location><page_6><loc_9><loc_46><loc_88><loc_50></location>For finite electron densities n e , on the other hand, there is also the possibility for reionization 93 via electron impact, either directly or stepwise, 94</text>
<formula><location><page_6><loc_25><loc_40><loc_88><loc_43></location>e -+1 s 2 2 snl -→ 1 s 2 2 sn ' l ' + e -→ ... → 1 s 2 2 s + e -+ e -, (3)</formula>
<text><location><page_6><loc_9><loc_28><loc_88><loc_38></location>and the probability of the latter pathway is proportional to the electron density n e . Because 95 of this alternative reionization pathway at finite densities, the effective DR rate coefficient 96 α eff DR ( n e , T ) is thus suppressed from the zero-density value α DR ( T ) by a density-dependent 97 suppression factor S ( n e , T ): 98</text>
<formula><location><page_6><loc_36><loc_23><loc_88><loc_26></location>α eff DR ( n e , T ) ≡ S ( n e , T ) α DR ( T ) . (4)</formula>
<text><location><page_6><loc_9><loc_10><loc_88><loc_20></location>From the earlier detailed studies of Davidson (1975) and Badnell et al. (1993), the 99 suppression factor is found to remain unity, corresponding to zero suppression, at lower 100 densities until a certain activation density n e , a is reached, beyond which this factor decreases 101 exponentially from unity with increasing density. We have found that this suppression 102</text>
<text><location><page_7><loc_9><loc_76><loc_88><loc_86></location>factor, as a function of the dimensionless log density parameter x = log 10 n e , can be modeled 103 quite effectively by a pseudo-Voigt profile (Wertheim et al. 1974) - a weighted mixture µ 104 of Lorentzian and Gaussian profiles of widths w for densities above the activation density 105 x a = log 10 n e , a : 106</text>
<formula><location><page_7><loc_25><loc_67><loc_88><loc_75></location>S ( x ; x a ) = 1 x ≤ x a µ [ 1 1+( x -x a w ) 2 ] +(1 -µ ) [ e -( x -x a w/ √ ln 2 ) 2 ] x ≥ x a . (5)</formula>
<text><location><page_7><loc_9><loc_58><loc_86><loc_71></location> Fitting this expression to the suppression factor of Badnell et al. (1993) for C IV (which 107 was computed at T = 10 5 K) yielded the values µ = 0 . 372, w = 4 . 969, and x a = 0 . 608, 108 and this parameterization formula is found to be accurate to within 5% for all densities 109 considered (see Fig. 1). 110</text>
<text><location><page_7><loc_9><loc_51><loc_10><loc_52></location>111</text>
<section_header_level_1><location><page_7><loc_22><loc_51><loc_78><loc_52></location>2.2. Generalized High-Temperature Suppression Formula</section_header_level_1>
<text><location><page_7><loc_9><loc_20><loc_88><loc_48></location>Given the suppression formula for Li-like C IV , corresponding to ionic charge q 0 = 3 112 and temperature T 0 = 10 5 K, we wish to generalize this expression to other Li-like ions of 113 charge q and (high) T according to the following qualitative guidelines. It is well known that 114 density effects scale as q 7 - see Bates et al. (1962) and Burgess & Summers (1969). The 115 activation density is attained when the reionization rate in Eq. 3, which depends linearly on 116 the density, becomes comparable to the radiative stabilization rate in Eq. 2. The radiative 117 rate is independent of density and temperature, but scales with charge as A r ∼ q 4 , whereas 118 the electron-impact ionization rate depends on all three, viz. n e α eII ∼ n e q -3 T -1 / 2 . An 119 initial suggestion is that the activation density is attained when these two are approximately 120 equal, i.e., 121</text>
<formula><location><page_7><loc_40><loc_15><loc_88><loc_18></location>n e , a q -3 T -1 / 2 ∼ q 4 , (6)</formula>
<text><location><page_7><loc_9><loc_10><loc_88><loc_14></location>indicating that the activation density should scale as n e , a ∼ q 7 T 1 / 2 , if the above qualitative 122 discussion holds. The log activation density for all q and T might therefore be expected to 123</text>
<figure>
<location><page_8><loc_12><loc_40><loc_88><loc_79></location>
<caption>Fig. 1.- Pseudo-Voigt fit of the suppression factor for C IV , as given in Eq. 5 with a scaled activation density as given by Eq. 7, shown for two different temperatures. The red solid curve shows that the parameterization for T = 1 × 10 5 K, corresponding to an activation density of x a = 0 . 608 (with µ = 0 . 372 and w = 4 . 969), is in close agreement with the actual data of Badnell et al. (1993) (open circles). The blue dashed curve is the parameterization for T = 1 . 5 × 10 4 K, using instead an activation density of x a = 0 . 196 (and the same µ and w ), and giving satisfactory agreement with the data of Davidson (1975) (solid circles).</caption>
</figure>
<text><location><page_8><loc_65><loc_40><loc_65><loc_40></location>/s49 /s48</text>
<text><location><page_8><loc_68><loc_40><loc_68><loc_40></location>/s101</text>
<text><location><page_9><loc_9><loc_85><loc_36><loc_86></location>obey the scaling relationship 124</text>
<formula><location><page_9><loc_29><loc_78><loc_88><loc_83></location>x a ( q, T ) = x a ( q 0 , T 0 ) + log 10 [ ( q q 0 ) 7 ( T T 0 ) 1 / 2 ] , (7)</formula>
<text><location><page_9><loc_9><loc_60><loc_88><loc_77></location>where x a ( q 0 , T 0 ) = 0 . 608, q 0 = 3, and T 0 = 10 5 K are the (log) activation density, the charge, 125 and the temperature for the C IV case treated by Badnell et al. (1993). We note that this 126 expression, when applied to Li-like O VI , gives an increase in the activation density by a 127 factor of (5 / 3) 7 = 35 . 7, in agreement with the approximate factor of 40 found by Davidson 128 (1975). Furthermore, when scaled in temperature, the formula gives fairly good agreement 129 with the suppression results of Davidson (1975) for C IV at T = 1 . 5 × 10 4 K (see Fig. 1). 130</text>
<text><location><page_9><loc_9><loc_54><loc_10><loc_54></location>131</text>
<section_header_level_1><location><page_9><loc_31><loc_54><loc_69><loc_55></location>2.2.1. Fit to the Collisional Radiative Data</section_header_level_1>
<text><location><page_9><loc_9><loc_20><loc_88><loc_51></location>The preceding treatment reasonably extends the C IV suppression factor at 10 5 K 132 to other high temperatures and to other Li-like ions. However, we need suppression 133 factors applicable to all ionization stages of all elements up to at least Zn for a general 134 implementation within Cloudy. Unfortunately, detailed collisional-radiative modeling data 135 with state-of-the-art DR data is still rather limited. However, extensive tables of effective 136 recombination rate coefficients have been computed by Summers (1974 & 1979) for a wide 137 variety of isoelectronic sequences, charge-states, temperatures, and densities. The treatment 138 of DR there is somewhat simplified, but we only require the ratio of finite- to zero-density 139 rate coefficients to determine the suppression factor. We then combine this ratio with our 140 state-of-the-art zero density DR rate coefficients again for use within Cloudy. This ratio is 141 much less sensitive to the specific treatment of DR. 142</text>
<text><location><page_9><loc_9><loc_10><loc_88><loc_17></location>The rather simplistic scaling formula in Eq. 7 was found to be inadequate when 143 applied to the extensive tabulation of suppression factors found in Summers (1974 & 1979). 144 Instead, in order to fit the data accurately, a more generalized formula was arrived at, 145</text>
<text><location><page_10><loc_9><loc_85><loc_80><loc_86></location>where a pseudo-Gaussian, corresponding to µ = 0 in Eq. 5, was more appropriate, 146</text>
<formula><location><page_10><loc_30><loc_77><loc_88><loc_83></location>S N ( x ; q, T ) = 1 x ≤ x a ( q, T, N ) e -( x -xa ( q,T,N ) w/ √ ln 2 ) 2 x ≥ x a ( q, T, N ) . (8)</formula>
<text><location><page_10><loc_9><loc_74><loc_83><loc_79></location> Furthermore, the activation density was found to be best represented by the function 147</text>
<formula><location><page_10><loc_25><loc_68><loc_88><loc_73></location>x a ( q, T, N ) = x 0 a + log 10 [ ( q q 0 ( q, N ) ) 7 ( T T 0 ( q, N ) ) 1 / 2 ] , (9)</formula>
<text><location><page_10><loc_9><loc_54><loc_88><loc_67></location>where the variables q 0 ( q, N ) and T 0 ( q, N ) are taken to be functions of the charge q and 148 the isoelectronic sequence, labeled by N . A fit of the suppression factors of Summers 149 (1974 & 1979) for all ions yielded a global (log) activation density x 0 a = 10 . 1821 and more 150 complicated expressions for the zero-point temperature T 0 and charge q 0 . These were found 151 to depend on both the ionic charge q and the isoelectronic sequence N viz. 152</text>
<formula><location><page_10><loc_37><loc_49><loc_88><loc_51></location>T 0 ( q, N ) = 5 × 10 4 [ q 0 ( q, N )] 2 (10)</formula>
<text><location><page_10><loc_9><loc_45><loc_15><loc_47></location>and 153</text>
<text><location><page_10><loc_9><loc_37><loc_17><loc_38></location>where 154</text>
<formula><location><page_10><loc_31><loc_31><loc_88><loc_35></location>A ( N ) = 12 + 10 N 1 + 10 N 1 -2 N 2 N 1 -N 2 ( N -N 1 ) (12)</formula>
<text><location><page_10><loc_9><loc_26><loc_88><loc_30></location>depends on the isoelectronic sequence in the periodic table according to the specification of 155 the parameters 156</text>
<formula><location><page_10><loc_22><loc_14><loc_88><loc_24></location>( N 1 , N 2 ) = (3 , 10) N ∈ 2 nd row (37 , 54) N ∈ 5 th row (11 , 18) N ∈ 3 rd row (55 , 86) N ∈ 6 th row (19 , 36) N ∈ 4 th row (87 , 118) N ∈ 7 th row . (13)</formula>
<text><location><page_10><loc_9><loc_9><loc_88><loc_14></location>However, even this rather complicated parameterization was inadequate for the lower 157 isoelectronic sequences N ≤ 5, and for these we explicitly list the optimal values for A ( N ) 158</text>
<formula><location><page_10><loc_34><loc_38><loc_88><loc_44></location>q 0 ( q, N ) = (1 -√ 2 / 3 q ) A ( N ) / √ q , (11)</formula>
<text><location><page_11><loc_9><loc_76><loc_88><loc_86></location>in Table 1. Furthermore, at electron temperatures and/or ionic charges for which the 159 q -scaled temperature θ ≡ T/q 2 was very low ( θ ≤ 2 . 5 × 10 4 K), a further modification to the 160 coefficients A ( N ) for N ≤ 5 is necessary in that the values in Table 1 should be multiplied 161 by a factor of two. 162</text>
<text><location><page_11><loc_9><loc_34><loc_88><loc_73></location>The above final formulation, which consists of the use of Eq. 8, with µ = 0, w = 5 . 64548, 163 and a rather complicated activation density given by Eqs. 9, 10, 11, 12, and 13, with 164 x 0 a = 10 . 1821, has been found to model the entire database of ions, temperatures, and 165 densities considered in the Summers (1974 & 1979) data fairly well. To illustrate the 166 general level of agreement over a large range of ions and environments, we compare our 167 parameterized model formulation to the actual suppression data from that report (Summers 168 1974 & 1979) for a few selected cases in Fig. 2. In order to quantify more fully the extent of 169 agreement, we focus on the case of iron ions, for which we study density effects on ionization 170 balance determination in the next section. A comparison is shown in Fig. 3 between our 171 predicted suppression factors and the data from the Summers (1974 & 1979) report. It is 172 seen that our model fits that data to within 21% for all densities, temperatures, and ionic 173 stages reported (Summers 1974 & 1979). More broadly, we have applied a similar 2 -σ 174 analysis to all ions in that report, at all temperatures and densities, and find the same 175 agreement (20-26% confidence level). 176</text>
<text><location><page_11><loc_9><loc_13><loc_88><loc_32></location>Lastly, it is of interest to investigate how our final suppression factor in Eq. 8 compares 177 to our original, motivating, formulation of Eq. 8 for C IV , shown in Fig. 4. There is 178 generally good qualitative agreement. However, it is seen that the original formulation, 179 based on the Badnell et al. (1993) results, shows a somewhat stronger suppression effect 180 up to x ≈ 11. This is likely due to the more accurate treatment of the partial DR data of 181 Badnell et al. (1993) entering the collisional-radiative modeling, although some difference 182 due to the collisional-radiative modeling itself may also be present. This indicates that even 183</text>
<figure>
<location><page_12><loc_13><loc_21><loc_90><loc_85></location>
<caption>Fig. 2.A comparison between the present parameterized suppression factor and the collisional radiative results of Summers (1974 & 1979) for a sample of ions and temperatures, as a function of density.</caption>
</figure>
<figure>
<location><page_13><loc_24><loc_28><loc_77><loc_86></location>
<caption>Fig. 3.- Agreement between the suppression curve of Eq. 9 and the Summers (1974 & 1979) data for all iron ions Fe q + , q = 9 -19. The upper panel shows the detailed level of agreement of the two end cases, Fe 9+ and Fe 19+ . The lower panel shows the 2 -σ (95.4%) confidence level as a function of charge state; this means that 95.4% of all density data points in the Summers (1974 & 1979) data, for the given charge and temperature, are within that percentage of the prediction from Eq. 8. The symbols denote different values of the scaled temperature θ = T/q 2 .</caption>
</figure>
<figure>
<location><page_14><loc_12><loc_38><loc_88><loc_78></location>
<caption>Fig. 4.- A comparison between the final suppression factor of Eq. 8 (solid line), corresponding to a pseudo-Gaussian profile with activation density x a = 0 . 8314 ( q 0 = 40 . 284) and width w = 5 . 64548, the Summers (1974 & 1979) data points (solid diamonds), and the original formulation of Eq. 5 (dashed line), corresponding to a pseudo-Voigt profile with activation density x a = 0 . 608, width w = 4 . 696, and mixture coefficient µ = 0 . 372. The temperature T = 1 × 10 5 K is the same as in Fig. 1.</caption>
</figure>
<text><location><page_14><loc_66><loc_38><loc_67><loc_38></location>/s49 /s48</text>
<text><location><page_14><loc_69><loc_38><loc_69><loc_38></location>/s101</text>
<text><location><page_15><loc_9><loc_73><loc_88><loc_86></location>collisional plasmas require collisional-radiative modeling with state-of-the-art DR data. 184 The stronger suppression tails-off at x /greaterorsimilar 11 as three-body recombination starts to become 185 relevant and which, at even higher densities (not shown), causes the suppression factor to 186 rise (since it is a ratio of effective recombination rate coefficients, i.e. includes three-body 187 recombination.) 188</text>
<text><location><page_15><loc_9><loc_66><loc_10><loc_67></location>189</text>
<section_header_level_1><location><page_15><loc_26><loc_66><loc_74><loc_67></location>2.3. Suppression Formula at Low Temperatures.</section_header_level_1>
<text><location><page_15><loc_16><loc_61><loc_86><loc_63></location>The preceding formulation was based on the suppression factor found by Summers</text>
<text><location><page_15><loc_9><loc_35><loc_88><loc_62></location>190 (1974 & 1979) for electron collisionally ionized plasmas, i.e., at higher temperatures, where 191 DR is dominated by highn resonances attached to a dipole-allowed core excited state. 192 In photoionization equilibrium, however, the temperature at which a given ion forms is 193 substantially smaller than that found in the electron collisional case. Due to the lower 194 kinetic temperatures, DR occurs mainly through energetically low-lying autoionizing states, 195 often via non-dipole core-excitations for which radiative stabilization is by the (outer) 196 Rydberg electron. These states are not, in general, as susceptible to density suppression as 197 their highn counterparts, and so it may be necessary to modify the preceding suppression 198 formulation. 199</text>
<text><location><page_15><loc_9><loc_12><loc_88><loc_33></location>We first consider sequences with partially-occupied p -subshells in the ground state, 200 which includes the B-like 2 p ( 2 P 1 / 2 , 3 / 2 ), C-like 2 p 2 ( 3 P 0 , 1 , 2 ), O-like 2 p 4 ( 3 P 0 , 1 , 2 ), F-like 201 2 p 5 ( 2 P 3 / 2 , 1 / 2 ), Al-like 3 p ( 2 P 1 / 2 , 3 / 2 ), Si-like 3 p 2 ( 3 P 0 , 1 , 2 ), S-like 3 p 4 ( 3 P 0 , 1 , 2 ), and Cl-like 202 3 p 5 ( 2 P 3 / 2 , 1 / 2 ) systems. For these sequences, there is fine-structure splitting in the ground 203 state and a correspondingly small excitation energy, /epsilon1 N , giving dielectronic capture into high 204 principal quantum numbers (because of the Rydberg relation q 2 /n 2 ≤ /epsilon1 N ). Stabilization 205 is via n → n ' transitions and the recombined final state is built upon an excited parent. 206</text>
<unordered_list>
<list_item><location><page_15><loc_9><loc_11><loc_87><loc_12></location>Ultimately, it is the strength of collisional coupling of this final state with the continuum 207</list_item>
</unordered_list>
<text><location><page_16><loc_9><loc_60><loc_87><loc_86></location>which determines whether recombination or ionization prevails. As the density increases, 208 collisional LTE extends further down the energy spectrum. It is difficult to give a general 209 statement about the position of such final states relative to the ionization limit. So, 210 we assume a worst case scenario, i.e., that such states are subject to suppression, and 211 we use the preceding suppression formula. If density effects are found to be small in 212 photoionized plasmas then this is likely sufficient. If they appear to be significant then 213 a more detailed treatment based on collisional-radiative modeling will be needed. Thus, 214 for these systems, we retain the same suppression formula developed above, that is, 215 S N ( x, q, T ) = S ( x, x a ( q, T )) for N = { 5 , 6 , 8 , 9 , 13 , 14 , 16 , 17 } , and for all q and T . 216</text>
<text><location><page_16><loc_9><loc_37><loc_88><loc_59></location>For the hydrogenic and the closed-shell He-like and Ne-like cases, on the other hand, 217 the excitations proceed via an increase in core principal quantum number - 1 s → 2 s or 218 { 2 s, 2 p } → { 3 s, 3 p, 3 d } - giving the dominant dielectronic capture into the lown < 10 219 resonances. Even following core radiative stabilization, these low-lying states are impervious 220 to collisional reionization for the range of densities x ≤ 10, and thus we set S N ( x, q, T ) = 1 . 0 221 for N = { 1 , 2 , 10 } . However, at densities x > 10, the Summers (1974 & 1979) data for these 222 three isoelectronic sequence show suppression factors that are fit well by the usual Eq. 8, so 223 we do not modify S N ( x, q, T ) for these cases. 224</text>
<text><location><page_16><loc_9><loc_11><loc_88><loc_34></location>Lastly, we consider the intermediate isoelectronic sequences for which excitation 225 arises from neither a fine-structure splitting of the ground state nor a change in principal 226 quantum number of the core. These include the Li-like 2 s → 2 p , Be-like 2 s 2 → 2 s 2 p , 227 N-like 2 s 2 2 p 3 ( 4 S ) → 2 s 2 p 4 ( 4 P ), Na-like 3 s → 3 p , Mg-like 3 s 2 → 3 s 3 p , and P-like 228 3 s 2 3 p 3 ( 4 S ) → 3 s 3 p 4 ( 4 P ) cases up through the third row sequences. Any large low229 temperature DR contribution arising from near threshold resonances is to low-lying states, 230 for which suppression is negligible, i.e. the high-temperature suppression factor must be 231 switched-off ( S N → 1) at lowT . 232</text>
<text><location><page_17><loc_9><loc_49><loc_88><loc_86></location>To illustrate the general demarcation between lowT and highT DR, we first consider 233 DR of C IV , an overview of which is depicted in Fig. 5. The DR cross section, shown in the 234 inset, is dominated by two features. The first is the n → ∞ accumulation of resonances 235 at the /epsilon1 = 8 eV series limit - those which can be treated in the usual highT fashion 236 (Burgess 1965; Burgess & Summers 1969) and are therefore susceptible to suppression 237 according to our formulation above. However, there is a second strong contribution from 238 the lowest accessible resonances just above the threshold electron energy, which, according 239 to the Rydberg consideration 3 2 /n 2 ≈ /epsilon1 3 = 0 . 6 Ryd, occur here for n = 4. More generally, 240 these low-lying states are typical of the low-lying DR spectrum (Nussbaumer & Storey 241 1984) 2 . The 1 s 2 2 p 4 l resonances decay predominantly to the 1 s 2 2 s 2 p , 1 s 2 2 p 2 and 1 s 2 2 s 4 l 242 states. These states lie well below the ionization limit and so are not susceptible to 243 further reionization. Since there should be no density suppression then, we seek a modified 244 suppression factor which tends toward unity (i.e., no suppression) at lower temperatures. 245</text>
<text><location><page_17><loc_9><loc_39><loc_88><loc_47></location>In order to make a smooth transition from the highT suppression factor S ( x ; q, T ) 246 given in Eq. 8, which is appropriate for the highT peak region kT ≈ kT max = 2 /epsilon1 N / 3, to the 247 lowT region, where S N → 1, we use the modified factor 248</text>
<formula><location><page_17><loc_28><loc_33><loc_88><loc_38></location>S N ( x ; q, T ) = 1 -[1 -S ( x ; q, T )] exp ( -/epsilon1 N ( q ) 10 kT ) , (14)</formula>
<text><location><page_17><loc_9><loc_22><loc_88><loc_32></location>where /epsilon1 N ( q ) = 8 eV for the particular case of C IV ( N = 3 and q = 3). As seen in Fig. 5, the 249 density-dependent effective DR rate coefficient, α eff DR ( n e , T ), indeed satisfies the requirement 250 that the highT peak is suppressed according to the formulation of Badnell et al. (1993) 251 whereas suppression is totally turned off for the lowerT peak. 252</text>
<text><location><page_17><loc_9><loc_19><loc_10><loc_19></location>253</text>
<text><location><page_17><loc_16><loc_18><loc_88><loc_20></location>We have investigated the application of Eq. 14 for all ions that exhibit these same lowT</text>
<figure>
<location><page_18><loc_12><loc_36><loc_88><loc_82></location>
<caption>Fig. 5.- DR of C IV . The inset shows the (zero-density) DR cross section convoluted with a 0.1 eV FWHM Gaussian. The spectrum is dominated by two features: the n = 4 DR resonance manifold below 1.0 eV and the n →∞ Rydberg resonances accumulating at the 2 s → 2 p series limit /epsilon1 3 ( q 0 ) ≈ 8 eV. The main figure shows the effective DR rate coefficient for several densities. Our modified suppression formulation for x > 0, using Eqs. 8 and 14, ensures that the highT peak, corresponding to the n →∞ Rydberg series of resonances, is suppressed but the lowT peak, corresponding to the n = 4 resonances, is not suppressed.</caption>
</figure>
<text><location><page_19><loc_9><loc_73><loc_88><loc_86></location>resonances features, namely, all isoelectronic sequences N = { 3 , 4 , 7 , 11 , 12 , 15 } , and we have 254 found that the correct transitioning from suppression at the highT -peak to no suppression 255 at lowT is indeed satisfied, provided, of course, that the appropriate dipole-allowed 256 excitation energy /epsilon1 N ( q ) is employed. For efficient representation, the excitation energies 257 along each isoelectronic sequence are parameterized by the expression 258</text>
<formula><location><page_19><loc_39><loc_66><loc_88><loc_71></location>/epsilon1 N ( q ) = 5 ∑ j =0 p N,j ( q 10 ) j . (15)</formula>
<text><location><page_19><loc_9><loc_61><loc_86><loc_65></location>These parameters, which are determined by fitting the above expression to the available 259 NIST excitation energies (Ralchenko et al. 2011), are listed in Table 2. 260</text>
<text><location><page_19><loc_9><loc_33><loc_88><loc_58></location>We note that all isoelectronic sequences and ionization stages are now included in 261 this prescription - our final comprehensive model for treating DR suppression, albeit 262 in a simplified fashion. For those ions with fine-structure splitting in the ground state, 263 we have /epsilon1 N ( q ) ≈ 0, so that S N ( x ; q, T ) = S ( x ; q, T ). (We apply this generally also for 264 Ar-like sequences and above ( N ≥ 18), based-on the density of states - see, for example, 265 Badnell (2006b).) For the closed-shell cases, on the other hand, we have /epsilon1 N ( q ) →∞ . Thus, 266 S N ( x ; q, T ) = 1 for hydrogenic and closed-shell systems, i.e., there is no suppression (for 267 x ≤ 10). Lastly, for the intermediate cases, the suppression factor is gradually increased 268 toward unity at lower temperatures and begins to admit lown DR resonances. 269</text>
<text><location><page_19><loc_9><loc_27><loc_10><loc_27></location>270</text>
<section_header_level_1><location><page_19><loc_45><loc_26><loc_55><loc_28></location>3. Results</section_header_level_1>
<text><location><page_19><loc_9><loc_16><loc_87><loc_23></location>The suppression factors derived here have been applied to the state-of-the-art total 271 DR rate coefficients taken from the most recent DR database. 3 These modified data have 272 been incorporated into version C13 of the plasma simulation code Cloudy, most recently 273</text>
<table>
<location><page_20><loc_30><loc_59><loc_70><loc_81></location>
<caption>Table 1. Modified A ( N ) coefficients from Eq. (12).</caption>
</table>
<table>
<location><page_20><loc_16><loc_14><loc_84><loc_41></location>
<caption>Table 2. Fitting coefficients for the excitation energies /epsilon1 N ( q ) = ∑ 5 j =0 p N,j ( q 10 ) j , in eV. Numbers in square brackets denote powers of 10.</caption>
</table>
<text><location><page_21><loc_9><loc_82><loc_86><loc_86></location>described by Ferland et al. (2013). Cloudy can do simulations of both photoionized and 274 collisionally ionized cases, and we show the effects of collisional suppression on both. 275</text>
<text><location><page_21><loc_9><loc_63><loc_88><loc_79></location>Figure 6 shows the ionization distribution of iron for the collisional ionization case. 276 Figure 7 shows a similar calculation for photoionization equilibrium. Both show two 277 hydrogen densities, 1 cm -3 , where collisional suppression of DR should be negligible, and 278 10 10 cm -3 , where collisional suppression should greatly affect the rates for lower charges 279 and temperatures. The upper panel shows the ionization fractions themselves, for these two 280 densities, while the lower panel shows the ratio of the high to low density abundances. 281</text>
<text><location><page_21><loc_9><loc_50><loc_86><loc_61></location>Cloudy's assumptions in computing collisional ionization equilibrium, as shown in 282 Figure 6, have been described by Lykins et al. (2012). It is determined by the balance 283 between collisional ionization from the ground state and recombination by radiative, 284 dielectronic, and three body recombination to all levels of the recombined species. 285</text>
<text><location><page_21><loc_9><loc_41><loc_88><loc_48></location>The photoionization case shown in Figure 7 depicts the Active Galactic Nucleus 286 spectral energy distribution (SED), described by Mathews & Ferland (1987), as a function 287 of the ionization parameter 288</text>
<formula><location><page_21><loc_44><loc_35><loc_88><loc_39></location>U ≡ Φ H n H c , (16)</formula>
<text><location><page_21><loc_9><loc_20><loc_88><loc_33></location>where Φ H is the hydrogen-ionizing photon flux, n H is the density of hydrogen, and c is the 289 speed of light. There is only an indirect relationship between the gas kinetic temperature 290 and the ionization of the gas in this case. Here, the level of ionization is determined by a 291 balance between photoionization by the energetic continuum and the total recombination 292 rate. 293</text>
<text><location><page_21><loc_9><loc_10><loc_87><loc_18></location>The lower panels of Figs. 6 and 7 show that the amount that the ionization increases 294 due to DR suppression can be large - the ratio can easily exceed 1 dex. Clearly, these 295 results demonstrate that density effects on the ionization balance need to be considered 296</text>
<figure>
<location><page_22><loc_12><loc_34><loc_88><loc_78></location>
<caption>Fig. 6.- Upper panel: collisional ionization fractional abundance vs. electron temperature for all ionization stages of Fe. The solid curves correspond to a density of 1 cm -3 and the dashed curves correspond to a density of 10 10 cm -3 . From left to right, the curves range from Fe I to Fe XXVII . Lower panel: ratio of the calculated fractional abundances for the two densities.</caption>
</figure>
<figure>
<location><page_23><loc_12><loc_34><loc_88><loc_78></location>
<caption>Fig. 7.- Upper panel: photoionization fractional abundance vs. the ionization parameter U for all ionization stages of Fe. The solid curves correspond to a density of 1 cm -3 and the dashed curves correspond to a density of 10 10 cm -3 . From left to right, the curves range from Fe I to Fe XXVII . Lower panel: ratio of the calculated fractional abundances for the two densities.</caption>
</figure>
<text><location><page_24><loc_9><loc_85><loc_10><loc_85></location>297</text>
<text><location><page_24><loc_9><loc_78><loc_10><loc_78></location>298</text>
<section_header_level_1><location><page_24><loc_43><loc_77><loc_57><loc_79></location>4. Conclusion</section_header_level_1>
<text><location><page_24><loc_9><loc_38><loc_88><loc_74></location>We have investigated the effects of finite densities on the effective DR rate coefficients 299 by developing a suppression factor model, which was motivated by the early work of 300 Badnell et al. (1993) for C IV and extended to all other ions using physically-motivated 301 scaling considerations, and more precise fitting of collisional-radiative data (Summers 302 1974 & 1979). Accurate zero-density DR rate coefficients were then multiplied by this 303 suppression factor and introduced into Cloudy to study the finite-density effects on 304 computed ionization balances of both collisionally ionized and photoionized plasmas. It 305 is found that the difference in ionization balance between the near-zero and finite-density 306 cases is substantial, and thus there is sufficient justification for further studies of collisional 307 suppression from generalized collisional-radiative calculations. This is expected to impact 308 the predictions of the ionization balance in denser cosmic gases such as those found in nova 309 and supernova shells, accretion disks, and the broad emission line regions in active galactic 310 nuclei. 311</text>
<text><location><page_24><loc_9><loc_11><loc_88><loc_35></location>The present results are intended to be preliminary, and to demonstrate the importance 312 of density effects on dielectronic recombination in astrophysical plasmas. Given the 313 approximations adopted, we suggest that their incorporation into models (e.g., via Cloudy) 314 be used with a little caution. For example, one might run models with and without the 315 effects of suppression at finite density, especially in modeling higher density plasmas (e.g., 316 the broad emission line region in quasars). Nevertheless, it is nearly half a century since 317 Burgess & Summers (1969) demonstrated significant density effects on DR, and it is time 318 that some representation exists within astrophysical modeling codes to assess its impact on 319 the much more rigorous demands made by modern day modeling, especially given its routine 320</text>
<text><location><page_24><loc_12><loc_85><loc_24><loc_86></location>more precisely.</text>
<text><location><page_25><loc_9><loc_79><loc_87><loc_86></location>incorporation by magnetic fusion plasma modeling codes. In the longer term, we intend 321 to present results based on detailed collisional-radiative calculations using state-of-the-art 322 state-specific DR rate coefficients. 323</text>
<text><location><page_25><loc_9><loc_72><loc_10><loc_72></location>324</text>
<section_header_level_1><location><page_25><loc_39><loc_72><loc_61><loc_73></location>5. Acknowledgments</section_header_level_1>
<text><location><page_25><loc_9><loc_55><loc_88><loc_68></location>DN, TWG, and KTK acknowledge support by NASA (NNX11AF32G). GJF 325 acknowledges support by NSF (1108928; and 1109061), NASA (10-ATP10-0053, 10326 ADAP10-0073, and NNX12AH73G), and STScI (HST-AR-12125.01, GO-12560, and 327 HST-GO-12309). UK undergraduates Mitchell Martin and Terry Yun assisted in coding the 328 DR routines used here. NRB acknowledges support by STFC (ST/J000892/1). 329</text>
<section_header_level_1><location><page_26><loc_43><loc_85><loc_58><loc_86></location>REFERENCES</section_header_level_1>
<table>
<location><page_26><loc_8><loc_10><loc_88><loc_84></location>
</table>
<unordered_list>
<list_item><location><page_27><loc_9><loc_85><loc_10><loc_85></location>350</list_item>
<list_item><location><page_27><loc_9><loc_81><loc_10><loc_81></location>351</list_item>
<list_item><location><page_27><loc_9><loc_74><loc_10><loc_77></location>352 353</list_item>
<list_item><location><page_27><loc_9><loc_69><loc_10><loc_70></location>354</list_item>
<list_item><location><page_27><loc_9><loc_65><loc_10><loc_66></location>355</list_item>
<list_item><location><page_27><loc_9><loc_61><loc_10><loc_62></location>356</list_item>
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</unordered_list>
<code><location><page_27><loc_12><loc_57><loc_85><loc_86></location>Summers, H. P. 1972, MNRAS, 158, 255 Summers, H. P. 1974, MNRAS, 169, 633 Summers, H. P. 1974 & 1979, Appleton Laboratory Internal Memorandum IM367 & re-issued with improvements as AL-R-5 Summers, H. P. & Hooper, M. B. 1983, Plasma Physics, 25, 1311 Verner, D. A. & Yakovlev, D. G. 1995, A&AS, 109, 125 Voronov, G. S. 1997, Atomic Data and Nuclear Data Tables, 65, 1 Wertheim, G. K., Butler, M. A., West, K. W., & Buchanan, D. N. E. 1974, Rev. Sci.</code>
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<list_item><location><page_27><loc_18><loc_54><loc_33><loc_55></location>Instrum., 45, 1369</list_item>
</unordered_list>
</document>
[
{
"title": "ABSTRACT",
"content": "We have developed a general model for determining density-dependent effective dielectronic recombination (DR) rate coefficients in order to explore finitedensity effects on the ionization balance of plasmas. Our model consists of multiplying by a suppression factor those highly-accurate total zero-density DR rate coefficients which have been produced from state-of-the-art theoretical calculations and which have been benchmarked by experiment. The suppression factor is based-upon earlier detailed collision-radiative calculations which were made for a wide range of ions at various densities and temperatures, but used a simplified treatment of DR. A general suppression formula is then developed as a function of isoelectronic sequence, charge, density, and temperature. These densitydependent effective DR rate coefficients are then used in the plasma simulation code Cloudy to compute ionization balance curves for both collisionally ionized and photoionized plasmas at very low ( n e = 1 cm -3 ) and finite ( n e = 10 10 cm -3 ) densities. We find that the denser case is significantly more ionized due to suppression of DR, warranting further studies of density effects on DR by detailed collisional-radiative calculations which utilize state-of-the-art partial DR rate coefficients. This is expected to impact the predictions of the ionization balance in denser cosmic gases such as those found in nova and supernova shells, accretion disks, and the broad emission line regions in active galactic nuclei. 14",
"pages": [
2,
3
]
},
{
"title": "Suppression of Dielectronic Recombination Due to Finite Density Effects",
"content": "D. Nikoli´c 1 , T. W. Gorczyca, K. T. Korista 3 Western Michigan University, Kalamazoo, MI, USA 4 G. J. Ferland 5 University of Kentucky, Lexington, KY, USA 6 and 7 N. R. Badnell 8 University of Strathclyde, Glasgow, UK 9 Received ; accepted 11 12 13",
"pages": [
1,
2
]
},
{
"title": "1. Introduction",
"content": "Astronomical emission or absorption sources have an enormous range of densities. 15 Two examples include the intergalactic medium, with n e ∼ 10 -4 cm -3 , and the broad 16 emission-line regions of Active Galactic Nuclei, with n e ∼ 10 10 cm -3 . The gas producing 17 the spectrum is not in thermodynamic equilibrium (Osterbrock & Ferland 2006), so 18 microphysical processes determine the physical conditions. 19 The two common cases encountered for ionization are photoionization and collisional 20 (e.g., electron-impact) ionization. In both cases, ions are recombined by dielectronic 21 and radiative recombination, with dielectronic recombination (DR) usually the dominant 22 process for elements heavier than helium. Databases give ionization and recombination 23 rates that are the sum of several contributing processes. Examples include Voronov (1997) 24 for electron impact ionization, Verner & Yakovlev (1995) for photoionization, and the 25 DR project (Badnell et al. 2003) for dielectronic recombination and Badnell (2006a) for 26 radiative recombination; it is these latter data 1 which will be of primary interest to us in 27 the present study. 28 The collisional ionization and recombination rate coefficients used in astrophysics are 29 frequently assumed to depend on temperature but to have no density dependence. The 30 rigorous treatment of density dependent ionization and recombination rate coefficients is 31 via collisional-radiative modeling. This was introduced by Bates et al. (1962) for radiative 32 recombination only and extended to treat the much more complex case of dielectronic 33 recombination by Burgess & Summers (1969). Summers applied their techniques to 34 determine density dependent ionization and recombination rate coefficients, and the 35 consequential ionization balance for collisional plasmas, for H-like thru Ar-like ions. 36 a guideline, a more general suppression formula is then determined by fitting to suppression 63 results from extensive detailed collisional-radiative calculations (Summers 1974 & 1979) for 64 a wide range of ions at several densities and (high) temperatures. Additional modifications 65 are then introduced to account for low temperature DR. 66 The outline of the rest of the paper is as follows: in the next section we describe the 67 DR suppression model we use; we then apply this suppression to the zero-density DR data, 68 and use the resultant density-dependent DR data in Cloudy to determine the ionization 69 distribution produced under photoionized and collisional ionization equilibrium at low and 70 moderate densities. 71 72",
"pages": [
3,
5
]
},
{
"title": "2. Generalized Density Suppression Model",
"content": "We use the following approach, detailed more fully in the subsections below. First, 73 the high-temperature collisional-radiative modeling results of Badnell et al. (1993) for DR 74 suppression in C IV are parameterized by a pseudo-Voigt profile to study the qualitative 75 behavior of suppression as a function of density and temperature. Next, this formulation 76 is then used as a guideline for developing a more comprehensive suppression formula which 77 is obtained by fitting to collisional radiative data for various isoelectronic sequences, ionic 78 charges, densities, and temperatures (Summers 1974 & 1979). Lastly, the suppression 79 formulation is extended to low-temperatures according to the nature of the sequence-specific 80 DR. 81 82",
"pages": [
5
]
},
{
"title": "2.1. High-Temperature Suppression for Li-like C IV",
"content": "We begin by considering DR of Li-like C IV , for which the density dependent total DR 83 rate coefficient, and therefore the suppression factor, has been computed rigorously within 84 a collisional-radiative modeling approach (Badnell et al. 1993). 85 In the zero-density limit, the intermediate 1 s 2 2 snl states can only decay further via radiative 90 cascading until the 1 s 2 2 s 2 final recombined ground state is reached, thereby completing the 91 DR process: 92 For finite electron densities n e , on the other hand, there is also the possibility for reionization 93 via electron impact, either directly or stepwise, 94 and the probability of the latter pathway is proportional to the electron density n e . Because 95 of this alternative reionization pathway at finite densities, the effective DR rate coefficient 96 α eff DR ( n e , T ) is thus suppressed from the zero-density value α DR ( T ) by a density-dependent 97 suppression factor S ( n e , T ): 98 From the earlier detailed studies of Davidson (1975) and Badnell et al. (1993), the 99 suppression factor is found to remain unity, corresponding to zero suppression, at lower 100 densities until a certain activation density n e , a is reached, beyond which this factor decreases 101 exponentially from unity with increasing density. We have found that this suppression 102 factor, as a function of the dimensionless log density parameter x = log 10 n e , can be modeled 103 quite effectively by a pseudo-Voigt profile (Wertheim et al. 1974) - a weighted mixture µ 104 of Lorentzian and Gaussian profiles of widths w for densities above the activation density 105 x a = log 10 n e , a : 106 Fitting this expression to the suppression factor of Badnell et al. (1993) for C IV (which 107 was computed at T = 10 5 K) yielded the values µ = 0 . 372, w = 4 . 969, and x a = 0 . 608, 108 and this parameterization formula is found to be accurate to within 5% for all densities 109 considered (see Fig. 1). 110 111",
"pages": [
5,
6,
7
]
},
{
"title": "2.2. Generalized High-Temperature Suppression Formula",
"content": "Given the suppression formula for Li-like C IV , corresponding to ionic charge q 0 = 3 112 and temperature T 0 = 10 5 K, we wish to generalize this expression to other Li-like ions of 113 charge q and (high) T according to the following qualitative guidelines. It is well known that 114 density effects scale as q 7 - see Bates et al. (1962) and Burgess & Summers (1969). The 115 activation density is attained when the reionization rate in Eq. 3, which depends linearly on 116 the density, becomes comparable to the radiative stabilization rate in Eq. 2. The radiative 117 rate is independent of density and temperature, but scales with charge as A r ∼ q 4 , whereas 118 the electron-impact ionization rate depends on all three, viz. n e α eII ∼ n e q -3 T -1 / 2 . An 119 initial suggestion is that the activation density is attained when these two are approximately 120 equal, i.e., 121 indicating that the activation density should scale as n e , a ∼ q 7 T 1 / 2 , if the above qualitative 122 discussion holds. The log activation density for all q and T might therefore be expected to 123 /s49 /s48 /s101 obey the scaling relationship 124 where x a ( q 0 , T 0 ) = 0 . 608, q 0 = 3, and T 0 = 10 5 K are the (log) activation density, the charge, 125 and the temperature for the C IV case treated by Badnell et al. (1993). We note that this 126 expression, when applied to Li-like O VI , gives an increase in the activation density by a 127 factor of (5 / 3) 7 = 35 . 7, in agreement with the approximate factor of 40 found by Davidson 128 (1975). Furthermore, when scaled in temperature, the formula gives fairly good agreement 129 with the suppression results of Davidson (1975) for C IV at T = 1 . 5 × 10 4 K (see Fig. 1). 130 131",
"pages": [
7,
8,
9
]
},
{
"title": "2.2.1. Fit to the Collisional Radiative Data",
"content": "The preceding treatment reasonably extends the C IV suppression factor at 10 5 K 132 to other high temperatures and to other Li-like ions. However, we need suppression 133 factors applicable to all ionization stages of all elements up to at least Zn for a general 134 implementation within Cloudy. Unfortunately, detailed collisional-radiative modeling data 135 with state-of-the-art DR data is still rather limited. However, extensive tables of effective 136 recombination rate coefficients have been computed by Summers (1974 & 1979) for a wide 137 variety of isoelectronic sequences, charge-states, temperatures, and densities. The treatment 138 of DR there is somewhat simplified, but we only require the ratio of finite- to zero-density 139 rate coefficients to determine the suppression factor. We then combine this ratio with our 140 state-of-the-art zero density DR rate coefficients again for use within Cloudy. This ratio is 141 much less sensitive to the specific treatment of DR. 142 The rather simplistic scaling formula in Eq. 7 was found to be inadequate when 143 applied to the extensive tabulation of suppression factors found in Summers (1974 & 1979). 144 Instead, in order to fit the data accurately, a more generalized formula was arrived at, 145 where a pseudo-Gaussian, corresponding to µ = 0 in Eq. 5, was more appropriate, 146 Furthermore, the activation density was found to be best represented by the function 147 where the variables q 0 ( q, N ) and T 0 ( q, N ) are taken to be functions of the charge q and 148 the isoelectronic sequence, labeled by N . A fit of the suppression factors of Summers 149 (1974 & 1979) for all ions yielded a global (log) activation density x 0 a = 10 . 1821 and more 150 complicated expressions for the zero-point temperature T 0 and charge q 0 . These were found 151 to depend on both the ionic charge q and the isoelectronic sequence N viz. 152 and 153 where 154 depends on the isoelectronic sequence in the periodic table according to the specification of 155 the parameters 156 However, even this rather complicated parameterization was inadequate for the lower 157 isoelectronic sequences N ≤ 5, and for these we explicitly list the optimal values for A ( N ) 158 in Table 1. Furthermore, at electron temperatures and/or ionic charges for which the 159 q -scaled temperature θ ≡ T/q 2 was very low ( θ ≤ 2 . 5 × 10 4 K), a further modification to the 160 coefficients A ( N ) for N ≤ 5 is necessary in that the values in Table 1 should be multiplied 161 by a factor of two. 162 The above final formulation, which consists of the use of Eq. 8, with µ = 0, w = 5 . 64548, 163 and a rather complicated activation density given by Eqs. 9, 10, 11, 12, and 13, with 164 x 0 a = 10 . 1821, has been found to model the entire database of ions, temperatures, and 165 densities considered in the Summers (1974 & 1979) data fairly well. To illustrate the 166 general level of agreement over a large range of ions and environments, we compare our 167 parameterized model formulation to the actual suppression data from that report (Summers 168 1974 & 1979) for a few selected cases in Fig. 2. In order to quantify more fully the extent of 169 agreement, we focus on the case of iron ions, for which we study density effects on ionization 170 balance determination in the next section. A comparison is shown in Fig. 3 between our 171 predicted suppression factors and the data from the Summers (1974 & 1979) report. It is 172 seen that our model fits that data to within 21% for all densities, temperatures, and ionic 173 stages reported (Summers 1974 & 1979). More broadly, we have applied a similar 2 -σ 174 analysis to all ions in that report, at all temperatures and densities, and find the same 175 agreement (20-26% confidence level). 176 Lastly, it is of interest to investigate how our final suppression factor in Eq. 8 compares 177 to our original, motivating, formulation of Eq. 8 for C IV , shown in Fig. 4. There is 178 generally good qualitative agreement. However, it is seen that the original formulation, 179 based on the Badnell et al. (1993) results, shows a somewhat stronger suppression effect 180 up to x ≈ 11. This is likely due to the more accurate treatment of the partial DR data of 181 Badnell et al. (1993) entering the collisional-radiative modeling, although some difference 182 due to the collisional-radiative modeling itself may also be present. This indicates that even 183 /s49 /s48 /s101 collisional plasmas require collisional-radiative modeling with state-of-the-art DR data. 184 The stronger suppression tails-off at x /greaterorsimilar 11 as three-body recombination starts to become 185 relevant and which, at even higher densities (not shown), causes the suppression factor to 186 rise (since it is a ratio of effective recombination rate coefficients, i.e. includes three-body 187 recombination.) 188 189",
"pages": [
9,
10,
11,
14,
15
]
},
{
"title": "2.3. Suppression Formula at Low Temperatures.",
"content": "The preceding formulation was based on the suppression factor found by Summers 190 (1974 & 1979) for electron collisionally ionized plasmas, i.e., at higher temperatures, where 191 DR is dominated by highn resonances attached to a dipole-allowed core excited state. 192 In photoionization equilibrium, however, the temperature at which a given ion forms is 193 substantially smaller than that found in the electron collisional case. Due to the lower 194 kinetic temperatures, DR occurs mainly through energetically low-lying autoionizing states, 195 often via non-dipole core-excitations for which radiative stabilization is by the (outer) 196 Rydberg electron. These states are not, in general, as susceptible to density suppression as 197 their highn counterparts, and so it may be necessary to modify the preceding suppression 198 formulation. 199 We first consider sequences with partially-occupied p -subshells in the ground state, 200 which includes the B-like 2 p ( 2 P 1 / 2 , 3 / 2 ), C-like 2 p 2 ( 3 P 0 , 1 , 2 ), O-like 2 p 4 ( 3 P 0 , 1 , 2 ), F-like 201 2 p 5 ( 2 P 3 / 2 , 1 / 2 ), Al-like 3 p ( 2 P 1 / 2 , 3 / 2 ), Si-like 3 p 2 ( 3 P 0 , 1 , 2 ), S-like 3 p 4 ( 3 P 0 , 1 , 2 ), and Cl-like 202 3 p 5 ( 2 P 3 / 2 , 1 / 2 ) systems. For these sequences, there is fine-structure splitting in the ground 203 state and a correspondingly small excitation energy, /epsilon1 N , giving dielectronic capture into high 204 principal quantum numbers (because of the Rydberg relation q 2 /n 2 ≤ /epsilon1 N ). Stabilization 205 is via n → n ' transitions and the recombined final state is built upon an excited parent. 206 which determines whether recombination or ionization prevails. As the density increases, 208 collisional LTE extends further down the energy spectrum. It is difficult to give a general 209 statement about the position of such final states relative to the ionization limit. So, 210 we assume a worst case scenario, i.e., that such states are subject to suppression, and 211 we use the preceding suppression formula. If density effects are found to be small in 212 photoionized plasmas then this is likely sufficient. If they appear to be significant then 213 a more detailed treatment based on collisional-radiative modeling will be needed. Thus, 214 for these systems, we retain the same suppression formula developed above, that is, 215 S N ( x, q, T ) = S ( x, x a ( q, T )) for N = { 5 , 6 , 8 , 9 , 13 , 14 , 16 , 17 } , and for all q and T . 216 For the hydrogenic and the closed-shell He-like and Ne-like cases, on the other hand, 217 the excitations proceed via an increase in core principal quantum number - 1 s → 2 s or 218 { 2 s, 2 p } → { 3 s, 3 p, 3 d } - giving the dominant dielectronic capture into the lown < 10 219 resonances. Even following core radiative stabilization, these low-lying states are impervious 220 to collisional reionization for the range of densities x ≤ 10, and thus we set S N ( x, q, T ) = 1 . 0 221 for N = { 1 , 2 , 10 } . However, at densities x > 10, the Summers (1974 & 1979) data for these 222 three isoelectronic sequence show suppression factors that are fit well by the usual Eq. 8, so 223 we do not modify S N ( x, q, T ) for these cases. 224 Lastly, we consider the intermediate isoelectronic sequences for which excitation 225 arises from neither a fine-structure splitting of the ground state nor a change in principal 226 quantum number of the core. These include the Li-like 2 s → 2 p , Be-like 2 s 2 → 2 s 2 p , 227 N-like 2 s 2 2 p 3 ( 4 S ) → 2 s 2 p 4 ( 4 P ), Na-like 3 s → 3 p , Mg-like 3 s 2 → 3 s 3 p , and P-like 228 3 s 2 3 p 3 ( 4 S ) → 3 s 3 p 4 ( 4 P ) cases up through the third row sequences. Any large low229 temperature DR contribution arising from near threshold resonances is to low-lying states, 230 for which suppression is negligible, i.e. the high-temperature suppression factor must be 231 switched-off ( S N → 1) at lowT . 232 To illustrate the general demarcation between lowT and highT DR, we first consider 233 DR of C IV , an overview of which is depicted in Fig. 5. The DR cross section, shown in the 234 inset, is dominated by two features. The first is the n → ∞ accumulation of resonances 235 at the /epsilon1 = 8 eV series limit - those which can be treated in the usual highT fashion 236 (Burgess 1965; Burgess & Summers 1969) and are therefore susceptible to suppression 237 according to our formulation above. However, there is a second strong contribution from 238 the lowest accessible resonances just above the threshold electron energy, which, according 239 to the Rydberg consideration 3 2 /n 2 ≈ /epsilon1 3 = 0 . 6 Ryd, occur here for n = 4. More generally, 240 these low-lying states are typical of the low-lying DR spectrum (Nussbaumer & Storey 241 1984) 2 . The 1 s 2 2 p 4 l resonances decay predominantly to the 1 s 2 2 s 2 p , 1 s 2 2 p 2 and 1 s 2 2 s 4 l 242 states. These states lie well below the ionization limit and so are not susceptible to 243 further reionization. Since there should be no density suppression then, we seek a modified 244 suppression factor which tends toward unity (i.e., no suppression) at lower temperatures. 245 In order to make a smooth transition from the highT suppression factor S ( x ; q, T ) 246 given in Eq. 8, which is appropriate for the highT peak region kT ≈ kT max = 2 /epsilon1 N / 3, to the 247 lowT region, where S N → 1, we use the modified factor 248 where /epsilon1 N ( q ) = 8 eV for the particular case of C IV ( N = 3 and q = 3). As seen in Fig. 5, the 249 density-dependent effective DR rate coefficient, α eff DR ( n e , T ), indeed satisfies the requirement 250 that the highT peak is suppressed according to the formulation of Badnell et al. (1993) 251 whereas suppression is totally turned off for the lowerT peak. 252 253 We have investigated the application of Eq. 14 for all ions that exhibit these same lowT resonances features, namely, all isoelectronic sequences N = { 3 , 4 , 7 , 11 , 12 , 15 } , and we have 254 found that the correct transitioning from suppression at the highT -peak to no suppression 255 at lowT is indeed satisfied, provided, of course, that the appropriate dipole-allowed 256 excitation energy /epsilon1 N ( q ) is employed. For efficient representation, the excitation energies 257 along each isoelectronic sequence are parameterized by the expression 258 These parameters, which are determined by fitting the above expression to the available 259 NIST excitation energies (Ralchenko et al. 2011), are listed in Table 2. 260 We note that all isoelectronic sequences and ionization stages are now included in 261 this prescription - our final comprehensive model for treating DR suppression, albeit 262 in a simplified fashion. For those ions with fine-structure splitting in the ground state, 263 we have /epsilon1 N ( q ) ≈ 0, so that S N ( x ; q, T ) = S ( x ; q, T ). (We apply this generally also for 264 Ar-like sequences and above ( N ≥ 18), based-on the density of states - see, for example, 265 Badnell (2006b).) For the closed-shell cases, on the other hand, we have /epsilon1 N ( q ) →∞ . Thus, 266 S N ( x ; q, T ) = 1 for hydrogenic and closed-shell systems, i.e., there is no suppression (for 267 x ≤ 10). Lastly, for the intermediate cases, the suppression factor is gradually increased 268 toward unity at lower temperatures and begins to admit lown DR resonances. 269 270",
"pages": [
15,
16,
17,
19
]
},
{
"title": "3. Results",
"content": "The suppression factors derived here have been applied to the state-of-the-art total 271 DR rate coefficients taken from the most recent DR database. 3 These modified data have 272 been incorporated into version C13 of the plasma simulation code Cloudy, most recently 273 described by Ferland et al. (2013). Cloudy can do simulations of both photoionized and 274 collisionally ionized cases, and we show the effects of collisional suppression on both. 275 Figure 6 shows the ionization distribution of iron for the collisional ionization case. 276 Figure 7 shows a similar calculation for photoionization equilibrium. Both show two 277 hydrogen densities, 1 cm -3 , where collisional suppression of DR should be negligible, and 278 10 10 cm -3 , where collisional suppression should greatly affect the rates for lower charges 279 and temperatures. The upper panel shows the ionization fractions themselves, for these two 280 densities, while the lower panel shows the ratio of the high to low density abundances. 281 Cloudy's assumptions in computing collisional ionization equilibrium, as shown in 282 Figure 6, have been described by Lykins et al. (2012). It is determined by the balance 283 between collisional ionization from the ground state and recombination by radiative, 284 dielectronic, and three body recombination to all levels of the recombined species. 285 The photoionization case shown in Figure 7 depicts the Active Galactic Nucleus 286 spectral energy distribution (SED), described by Mathews & Ferland (1987), as a function 287 of the ionization parameter 288 where Φ H is the hydrogen-ionizing photon flux, n H is the density of hydrogen, and c is the 289 speed of light. There is only an indirect relationship between the gas kinetic temperature 290 and the ionization of the gas in this case. Here, the level of ionization is determined by a 291 balance between photoionization by the energetic continuum and the total recombination 292 rate. 293 The lower panels of Figs. 6 and 7 show that the amount that the ionization increases 294 due to DR suppression can be large - the ratio can easily exceed 1 dex. Clearly, these 295 results demonstrate that density effects on the ionization balance need to be considered 296 297 298",
"pages": [
19,
21,
24
]
},
{
"title": "4. Conclusion",
"content": "We have investigated the effects of finite densities on the effective DR rate coefficients 299 by developing a suppression factor model, which was motivated by the early work of 300 Badnell et al. (1993) for C IV and extended to all other ions using physically-motivated 301 scaling considerations, and more precise fitting of collisional-radiative data (Summers 302 1974 & 1979). Accurate zero-density DR rate coefficients were then multiplied by this 303 suppression factor and introduced into Cloudy to study the finite-density effects on 304 computed ionization balances of both collisionally ionized and photoionized plasmas. It 305 is found that the difference in ionization balance between the near-zero and finite-density 306 cases is substantial, and thus there is sufficient justification for further studies of collisional 307 suppression from generalized collisional-radiative calculations. This is expected to impact 308 the predictions of the ionization balance in denser cosmic gases such as those found in nova 309 and supernova shells, accretion disks, and the broad emission line regions in active galactic 310 nuclei. 311 The present results are intended to be preliminary, and to demonstrate the importance 312 of density effects on dielectronic recombination in astrophysical plasmas. Given the 313 approximations adopted, we suggest that their incorporation into models (e.g., via Cloudy) 314 be used with a little caution. For example, one might run models with and without the 315 effects of suppression at finite density, especially in modeling higher density plasmas (e.g., 316 the broad emission line region in quasars). Nevertheless, it is nearly half a century since 317 Burgess & Summers (1969) demonstrated significant density effects on DR, and it is time 318 that some representation exists within astrophysical modeling codes to assess its impact on 319 the much more rigorous demands made by modern day modeling, especially given its routine 320 more precisely. incorporation by magnetic fusion plasma modeling codes. In the longer term, we intend 321 to present results based on detailed collisional-radiative calculations using state-of-the-art 322 state-specific DR rate coefficients. 323 324",
"pages": [
24,
25
]
},
{
"title": "5. Acknowledgments",
"content": "DN, TWG, and KTK acknowledge support by NASA (NNX11AF32G). GJF 325 acknowledges support by NSF (1108928; and 1109061), NASA (10-ATP10-0053, 10326 ADAP10-0073, and NNX12AH73G), and STScI (HST-AR-12125.01, GO-12560, and 327 HST-GO-12309). UK undergraduates Mitchell Martin and Terry Yun assisted in coding the 328 DR routines used here. NRB acknowledges support by STFC (ST/J000892/1). 329",
"pages": [
25
]
}
]
2013ApJ...768..114W
https://arxiv.org/pdf/1303.5181.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_83><loc_87><loc_84></location>MODELING THE FREQUENCY-DEPENDENCE OF RADIO BEAMS FOR CONE-DOMINANT PULSARS</section_header_level_1>
<text><location><page_1><loc_40><loc_80><loc_61><loc_82></location>P. F. WANG, J. L. HAN, C. WANG</text>
<text><location><page_1><loc_18><loc_78><loc_83><loc_80></location>National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100012, China. Email: pfwang, hjl, [email protected]</text>
<text><location><page_1><loc_43><loc_77><loc_58><loc_78></location>Draft version June 20, 2018</text>
<section_header_level_1><location><page_1><loc_46><loc_75><loc_55><loc_76></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_56><loc_87><loc_74></location>Beam radii for cone-dominant pulsars follow a power-law relation with frequency, ϑ = ( ν/ν 0) k + ϑ 0, which has not yet well explained in previous works. We study this frequency dependence of beam radius (FDB) for cone-dominant pulsars by using the curvature radiation mechanism. Considering various density and energy distributions of particles in the pulsar open field line region, we numerically simulate the emission intensity distribution across emission height and rotation phase, and get integrated profiles at different frequencies and obtain the FDB curves. For the density model of a conal-like distribution, the simulated profiles always shrink to one component at high frequencies. In the density model with two separated density patches, the profiles always have two distinct components, and the power-law indices k are found to be in the range from -0 . 1 to -2 . 5, consistent with observational results. Energy distributions of streaming particles have significant influence on the frequency-dependence behavior. Radial energy decay of particles are necessary to get proper ϑ 0 in models. We conclude that by using the curvature radiation mechanism, the observed frequency dependence of beam radius for the cone-dominant pulsars can only be explained by the emission model of particles in two density patches with a Gaussian energy distribution and a radial energy loss.</text>
<text><location><page_1><loc_14><loc_54><loc_79><loc_56></location>Subject headings: pulsars: general - star: magnetic fields - relativistic particles - curvature radiation</text>
<section_header_level_1><location><page_1><loc_22><loc_52><loc_34><loc_53></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_43><loc_49><loc_51></location>A pulsar profile is explained as being the line-of-sight cuts through the emission beam when a pulsar rotates. For conedominant pulsars, profiles widen at low frequencies. The variation of pulsar profile width or component separation, W , against the observation frequency, ν , can be described by a power-law function (Thorsett 1991)</text>
<formula><location><page_1><loc_23><loc_41><loc_49><loc_42></location>W = a ν k + W 0 . (1)</formula>
<text><location><page_1><loc_8><loc_32><loc_49><loc_40></location>Here, W 0 is a width constant. With a dipole field geometry for pulsar emission region, the emission of lower frequencies is believed to be generated at larger heights for the wider open angles of the emission cone. This is well known as the radiusto-frequency mapping (Ruderman & Sutherland 1975; Cordes 1978; Phillips 1992).</text>
<text><location><page_1><loc_8><loc_16><loc_49><loc_31></location>Observed profile width can be expressed by, for example, the peak separation between the outermost components, Wpp (i.e. the peak-peak separation), the pulse width at the 10% of the highest intensity peak, W 10, and the pulse width at the 50% of the peak, W 50. In order to understand the frequency dependence of pulsar profiles in a much wider frequency range, Xilouris et al. (1996) observed a number of nearby bright pulsars up to 32 GHz and measured their W 50. Combining with previous measurements at lower frequencies, they fitted the pulse widths by W 50 = a ν k + W 0, and got -0 . 29 > k > -0 . 94 for a sample of pulsars.</text>
<text><location><page_1><loc_8><loc_14><loc_49><loc_16></location>The radius of the pulsar emission beam, ϑ , is related to the profile width, W , by (Gil 1981),</text>
<formula><location><page_1><loc_13><loc_10><loc_49><loc_13></location>ϑ = 2arcsin[sin 2 W 4 sin α sin( α + β ) + sin 2 β 2 ] 1 / 2 . (2)</formula>
<text><location><page_1><loc_8><loc_0><loc_49><loc_10></location>Here, α is the inclination angle of the magnetic axis related to the rotation axis, β is the impact angle of the line of sight to the magnetic axis. For many pulsars with good polarization measurements, the values of α and β have been determined (Lyne & Manchester 1988; Rankin 1990; Everett & Weisberg 2001). For a given pulsar, the beam radius, ϑ , and the profile width, W , are quasi-linearly related for various frequencies.</text>
<text><location><page_1><loc_56><loc_47><loc_90><loc_50></location>GEOMETRY PARAMETERS AND FITTED k AND ϑ 0 FOR 7 CONE-DOMINANT PULSARS WITH CLEAR FREQUENCY DEPENDENCE (MITRA & RANKIN 2002).</text>
<table>
<location><page_1><loc_52><loc_38><loc_94><loc_46></location>
<caption>TABLE 1</caption>
</table>
<text><location><page_1><loc_53><loc_26><loc_94><loc_34></location>Therefore, the variation of pulse-width with frequency should be physically related to the frequency dependence of pulsar beam radius. Mitra & Rankin (2002) collected observed pulse widths for 7 cone-dominant pulsars and calculated their beam radii at various frequencies. They found that the radius of the outer-cone beam of 7 pulsars follows</text>
<formula><location><page_1><loc_67><loc_24><loc_94><loc_26></location>ϑ = ( ν/ν 0) k + ϑ 0 , (3)</formula>
<text><location><page_1><loc_53><loc_12><loc_94><loc_23></location>here ϑ 0 is the beam radius at the infinite-frequency, and the ν 0 is the characteristic frequency. The values of the power-law index k are in the range of -0 . 3 to -1 . 2. The values of β are smaller than those of ϑ 0, as shown in Table 1. We noticed that for a given pulsar the k value obtained from pulse widths is almost the same as that fitted from the beam radii. Mitra & Rankin (2002) noticed that the beam radii of inner-cone do not show the frequency dependence.</text>
<text><location><page_1><loc_53><loc_5><loc_94><loc_12></location>The frequency dependence of beam radii or profile widths can be easily explained by the open field-lines of the emission region in a dipole field geometry of neutron stars, as long as the radius-frequency-mapping holds (Ruderman & Sutherland 1975). Different emission mechanisms can lead to different</text>
<text><location><page_1><loc_53><loc_0><loc_100><loc_5></location>power-law indices k . The electron bremsstrahlung model (Vitarmo & Jau 1973) predicts k ∼ -0 . 45. The vacuum inner gap model (Ruderman & Sut 1975) can give k ∼ -1 / 3. The curvature plasma model (Beskin et al.</text>
<figure>
<location><page_2><loc_9><loc_65><loc_47><loc_87></location>
<caption>FIG. 1.- Geometry and parameters defined for an emitting beam. Ω indicates the rotation axis in z direction, µ represents the magnetic axis, which is inclined by an angle of α with respect to Ω . The LOF is tangential to the light cylinder, which has a polar angle θ from the magnetic axis µ . The radiation beam has a radius of ϑ at a height of r .</caption>
</figure>
<text><location><page_2><loc_8><loc_50><loc_49><loc_56></location>either k ∼ -0 . 14 or k ∼ -0 . 29. The emission from the cyclotron instability (Machabeli & Usov 1989) gives k ∼ -0 . 17. These theoretical values can not cover the wide range of the observed k .</text>
<text><location><page_2><loc_8><loc_34><loc_49><loc_50></location>In this paper, we try to explain the frequency dependence of the radio beam observed for cone-dominant pulsars using the curvature radiation mechanism. If the edge of pulsar beam is generated by particles flowing along the last open field-lines (LOF), we can calculate the radio beams, and investigate their dependence on pulsar parameters, period P , inclination angle α , impact angle β and the Lorentz factor of particles γ . Using some generalized energy and density distributions of particles in the magnetosphere, we numerically calculate the radio emission beams and fit their frequency dependence. We also investigate the influence on the pulsar beam by the radial decrease of particle energy and the particle energy distribution.</text>
<section_header_level_1><location><page_2><loc_8><loc_30><loc_48><loc_32></location>2. CURVATURE RADIATION BEAM FOR PARTICLES WITH A GIVEN γ IN A DIPOLE FIELD</section_header_level_1>
<text><location><page_2><loc_8><loc_16><loc_49><loc_29></location>In general, pulsar radio emission is assumed to be generated by curvature radiation of secondary particles streaming along the last open field-lines. In the radio emission region, magnetic fields can be described as a static dipole (e.g. Gangadhara 2004), because the multipolar field components of a neutron star vanish there and the sweeping effect due to rotation is also negligible according to Dyks & Harding (2004). Therefore, in this paper, we will use the dipole field to study the frequency dependence of beam radius (FDB).</text>
<text><location><page_2><loc_8><loc_1><loc_49><loc_16></location>The size and geometry of a dipole magnetic field is determined by pulsar period P , inclination angle α and impact angle β . In the polar coordinate system with the polar axis along the magnetic axis direction (Fig. 1), a dipole field-line can be described by r = re sin 2 θ , here θ is the polar angle from the magnetic axis, r is the distance from the dipole origin, re is the fieldline constant, which is the distance from the origin to the point of the field-line intersection with the magnetic equatorial plane of θ = 90 · . For an inclined dipole, the LOF are contained in the light cylinder (see Fig. 1). The radius of the light-cylinder, R lc = cP / 2 π , gives the limit of the field line constants re for the</text>
<figure>
<location><page_2><loc_56><loc_66><loc_90><loc_88></location>
<caption>FIG. 2.- Frequency dependence of the beam radius (FDB curve) calculated from the curvature radiation from particles of a single γ for an inclined dipole of α = 60 · . Beam radii in the magnetic azimuth of φ = 0 · and φ = 90 · are frequency dependent, though the beam size of φ = 0 · is smaller than that of φ = 90 · at any frequency. This behavior is shown in the top panel for 300 MHz, 1.0 GHz and 2.0 GHz emission. The solid lines are calculated using two terms in Eq. (7), and the dashed lines are only for its first term. Here period P = 1 s and γ = 400 are taken for calculations.</caption>
</figure>
<text><location><page_2><loc_53><loc_34><loc_94><loc_54></location>LOF, which is different for pulsars with different periods. The angular diameter of the polar cap defined by the feet of LOF on the neutron star surface is related to the pulsar period, P , by 2 θ pc = 1 . 6 · P -1 / 2 . The opening angle of the beam from the tangents of the LOF near the surface is about 1 . 2 · P -1 / 2 , which defines the minimum geometrical beam angle. Observations show ϑ 0 > 1 . 2 · P -1 / 2 . The emission beam determined by the LOF is not circular but compressed in the meridional direction in the plane of rotation and magnetic axes (Biggs 1990). We define the magnetic azimuthal angle, φ , starting from the connection between the magnetic axis and the rotation axis (to the top being the north) as being φ = 0 · (see Fig. 2). The beam radius in the direction of φ = 0 · is smaller than that in the direction of φ = 90 · (to the east).</text>
<text><location><page_2><loc_53><loc_24><loc_94><loc_34></location>In the curvature radiation mechanism, the emission frequency is not only related to the field geometry but also to the Lorentz factor γ of particles. The simplest case we consider here is that particles have the same Lorentz factor γ , and that the radio beam is defined by the tangents of the LOF. When a relativistic particle streams along a field-line, it can produce curvature radiation with a characteristic frequency of</text>
<formula><location><page_2><loc_70><loc_21><loc_94><loc_24></location>ν = 3 γ 3 c 4 πρ . (4)</formula>
<text><location><page_2><loc_53><loc_17><loc_94><loc_21></location>Here, γ is the Lorentz factor of particles in the range 10 2 -10 4 , ρ is the curvature radius of the particle trajectory. In any fieldline, the curvature radius can be expressed by (Gangadhara 2004)</text>
<formula><location><page_2><loc_64><loc_13><loc_94><loc_16></location>ρ = re sin θ (5 + 3cos2 θ ) 3 / 2 3 √ 2(3 + 2cos2 θ ) . (5)</formula>
<text><location><page_2><loc_53><loc_10><loc_94><loc_13></location>Note that θ varies with r . The angle between the tangent of a field-line of θ and the magnetic axis is</text>
<formula><location><page_2><loc_64><loc_7><loc_94><loc_10></location>ϑ = arccos( 1 + 3cos2 θ √ 10 + 6cos2 θ ) . (6)</formula>
<text><location><page_2><loc_53><loc_3><loc_94><loc_7></location>Combining Eq. (5) and Eq. (6), one can find the relation between ϑ and ρ for any field-line of re . Because the radiation frequency ν is related to ρ by Eq. (4), we get</text>
<formula><location><page_2><loc_63><loc_0><loc_94><loc_3></location>ϑ = 15 . 4 · ( γ 3 c ) + 0 . 43 · ( γ 3 c ) 3 . (7)</formula>
<figure>
<location><page_3><loc_9><loc_68><loc_48><loc_88></location>
<caption>FIG. 3.- Beam radii at a series of frequencies calculated from the curvature radiation of particles with a single γ . Default model parameters are P = 0 . 5 s, α = 60 · , β = 0 · and γ = 400. Various curves have been calculated for different parameters, α , β , P and γ in four panels. Note that the two curves for α = 60 · and α = 30 · in the upper left panel are completely overlapped.</caption>
</figure>
<text><location><page_3><loc_8><loc_43><loc_49><loc_59></location>One can use Eq. (15) from Gangadhara (2004) to get the fieldline constants re for each LOF. Obviously, as indicated in Eq. (7), the beam radius is related to the radiation frequency. At a higher frequency of ν /greatermuch γ 3 c / re , the second term can be neglected, and the beam radius ϑ is related to the frequency ν by roughly a power-law with the index of k = -1. At a low frequency of ν ≤ γ 3 c / re , the frequency dependence becomes slightly steeper due to the contribution from the second term. Note that the beam radii in all magnetic azimuthal directions are frequency dependent. Clearly, the first term of Eq. (7) is a good approximation of the frequency dependence of pulsar beam, which has a power-law index k = -1.</text>
<text><location><page_3><loc_8><loc_14><loc_49><loc_42></location>We calculated the beam radii at different frequencies for various model parameters, as shown in Fig. 3. All curves show the frequency dependence of radiation beam with a power-law index of approximately -1, which is different from observational values in the range of -0 . 3 > k > -1 . 2 (Mitra & Rankin 2002). We found that there is no influence on the frequency dependence of beam size by the magnetic inclination α , because α only leads to the compression of beam in the meridional direction, and has almost no influence on the radius of φ = 90 · . Different impacts of line of sight with different β values lead to different cuts of the beam from β = 0 · to β = ϑ . The lower limit of ϑ is determined by the angular size of the polar cap (3/2 θ pc) or the β value. Pulsars with a small period P have a small R lc and hence a small re and a small curvature radius [Eq. (5)], which corresponds to a larger radiation frequency [Eq. (4)], as shown in Fig. 3. Note also that in the pulsar emission region curvature radiation of particles with a single γ cannot produce radio emission over a wide frequency range from hundreds MHz to ten GHz. Particles with larger γ produce curvature radiation at much higher frequency, which shifts the FDB curves to higher frequency ranges.</text>
<text><location><page_3><loc_8><loc_1><loc_49><loc_13></location>The calculations shown in Fig.2 and 3 were made with assumptions that pulsar beams are bounded by the LOF. However, Ruderman & Sutherland (1975) suggested that beam edge should be bounded by the critical field-lines, which are orthogonal to (instead of tangent to) the light cylinder at the intersection points. The critical field-lines are located between the magnetic axis and the LOF. Here, the parameter η is used to describe the location of field-lines, with η = 0 for the magnetic axis, η = 1 for the LOF. To generate the curvature emission beam of the</text>
<text><location><page_3><loc_53><loc_82><loc_94><loc_87></location>same open angle, the emission height from the critical field lines (0 < η < 0 . 74, depending on α ) is larger than that from the LOF as shown in Fig. 3, and the curvature radius is also larger, so that the emission has a smaller frequency of,</text>
<formula><location><page_3><loc_65><loc_78><loc_94><loc_81></location>ν = ν lof × η 2 = 3 γ 3 c 4 πρ η 2 , (8)</formula>
<text><location><page_3><loc_53><loc_69><loc_94><loc_77></location>with ν lof the corresponding emission frequency for the LOF. We carried out a set of calculations, and found that the curvature radiation for the critical field lines has almost the same frequency dependence of emission beam as that for the LOF, and k and ϑ 0 values are consistent within 5%, though ν 0 is smaller due to larger curvature radii of field lines.</text>
<section_header_level_1><location><page_3><loc_53><loc_65><loc_93><loc_68></location>3. CURVATURE RADIATION BEAM FROM PARTICLES WITH VARIOUS ENERGY AND DENSITY DISTRIBUTIONS</section_header_level_1>
<text><location><page_3><loc_53><loc_51><loc_94><loc_64></location>Particles in pulsar magnetosphere should have an energy distribution, which radiate in a range of frequencies at a range of heights for a given LOF. Furthermore, particles flow out along a set of open field-lines, rather than just the LOF. The pulsar radio emission from a given height and a given rotation phase is contributed from particles not only in the field lines which are tangential towards the observer, but also in the nearby field lines in the bunch within the 1 /γ emission cone. The emission is coherent radiation from a bunch of particles (Buschauer & Benford 1976).</text>
<text><location><page_3><loc_53><loc_45><loc_94><loc_51></location>According to simulation results of Medin & Lai (2010), we assume in this section that secondary particles for curvature radiation at radio bands follow a Gaussian energy distribution with a peak at γ m of several hundreds:</text>
<formula><location><page_3><loc_65><loc_41><loc_94><loc_45></location>n e( γ ) ∼ exp[ -( γ -γ m ) 2 2 σ 2 γ ] . (9)</formula>
<text><location><page_3><loc_53><loc_37><loc_94><loc_41></location>Here, the standard deviation σ γ is of several tens. Considering the continuity of the particles flowing along the field-line tube, we got the number density of particles at r as</text>
<formula><location><page_3><loc_67><loc_34><loc_94><loc_36></location>n e( r ) = n e0( r / R /star ) -3 . (10)</formula>
<text><location><page_3><loc_53><loc_31><loc_94><loc_34></location>Here, n e0 represents the number density at the bottom of a magnetic field tube near the surface of a neutron star.</text>
<text><location><page_3><loc_53><loc_28><loc_94><loc_31></location>The power of curvature radiation at a frequency ν from one particle is given by,</text>
<formula><location><page_3><loc_68><loc_25><loc_94><loc_28></location>P e = 2 q 2 γ 4 3 c ( c ρ ) 2 . (11)</formula>
<text><location><page_3><loc_53><loc_20><loc_94><loc_24></location>Nb particles in a field bunch in the region with a dimension size of less than half emission wavelength produce the total emission power of approximately N 2 b P e.</text>
<text><location><page_3><loc_53><loc_10><loc_94><loc_20></location>Because the curvature radius varies everywhere in the dipole field, according to Eq. (4) and (11), the observed emission at frequency ν and rotation phase ϕ should come from the tangents of a set of open field-lines with the same magnetic azimuth φ , where the curvature radius ρ of a field-line and particle energy γ are nicely combined to produce emission. The observed total power therefore should be the sum of them,</text>
<formula><location><page_3><loc_61><loc_7><loc_94><loc_10></location>I ( ν,ϕ ) = ∫ r max r min n e( r , γ ) N 2 b P e( r , φ, γ ) dr . (12)</formula>
<text><location><page_3><loc_53><loc_1><loc_94><loc_6></location>Note that the magnetic azimuth φ is a monotonic function of the rotation phase ϕ , as given by Eq. (11) in Gangadhara (2004) which is equivalent to the well-known S -curve for polarization angle.</text>
<figure>
<location><page_4><loc_17><loc_70><loc_39><loc_87></location>
<caption>FIG. 4.- Illustration for the uniform density distribution of particles in pulsar magnetosphere. Here, n e = n e0( r / R /star ) -3 .</caption>
</figure>
<figure>
<location><page_4><loc_9><loc_47><loc_27><loc_66></location>
</figure>
<figure>
<location><page_4><loc_29><loc_47><loc_48><loc_65></location>
<caption>FIG. 5.(a): Upper panel: Emission intensities at a given frequency (here ν = 200 MHz) for various rotation phases ϕ and emission heights, radiated by a group of particles which have a Gaussian energy distribution and an uniform number distribution in magnetic polar angles as shown in Fig. 4. Lower panel: The accumulated emission profile (also at ν = 200 MHz). The model parameters used are P = 1s, α = 45 · and β = 3 · , and γ m = 350 and σ γ = 30. (b): Same as left panels (a) , but the abberation and retardation effects have been considered.</caption>
</figure>
<section_header_level_1><location><page_4><loc_9><loc_32><loc_47><loc_35></location>3.1. Emission beam from particles uniformly distributed in magnetic polar angles</section_header_level_1>
<text><location><page_4><loc_8><loc_28><loc_49><loc_31></location>As the first try, we assume that particles follow a Gaussian energy distribution and are uniformly distributed in the open field-lines for all magnetic polar angles, as shown in Fig. 4.</text>
<text><location><page_4><loc_8><loc_10><loc_49><loc_27></location>We can calculate the emission from each open field-line at every tangent for each frequency. At a given emission height, the central open field-lines have larger curvature radii than the outer open field-lines. Particles with a given Lorentz factor in the central field lines would produce a lower frequency emission [see Eq. (4)] than they do in the outer field lines. For a group of particles with a Gaussian energy distribution, only these particles with larger Lorentz factors in the central field lines can produce the emission at the same frequency as particles of lower Lorentz factors in the outer field lines, but their emission intensity is reduced by a factor of 1 /γ 2 . Note that magnetic fields have smaller curvature radii at lower height. All these factors produce the bifurcation feature shown in Fig.5.</text>
<text><location><page_4><loc_8><loc_1><loc_49><loc_9></location>We limited our calculations for the region of r max < 0 . 1 R lc, because the emission intensity from higher regions is negligible (see Fig. 5) due to the relatively small particle density and large curvature radius. For P = 1 s, R lc /similarequal 47771 km /similarequal 4777 R ∗ , if we take R ∗ =10 km. We consider the phase shift (Gangadhara 2005) of the emission from any height of every field-line, and</text>
<figure>
<location><page_4><loc_62><loc_70><loc_83><loc_88></location>
<caption>FIG. 6.- Illustration for the conal density distribution of particles in pulsar magnetosphere. The density follows Eq. (14).</caption>
</figure>
<text><location><page_4><loc_53><loc_55><loc_94><loc_63></location>integrate their emission for profiles at every observation frequency (lower panels in Fig. 5). We found that aberration and retardation effects can change the projection position of emission in the sky plane, which cause the profile to be enhanced by about 20% at the phase of ϕ = -10 · and weakened by about 22%at the phase of ϕ =10 · for the model calculations in Fig. 5.</text>
<text><location><page_4><loc_53><loc_51><loc_94><loc_55></location>Weconcludethat curvature radiation from particles uniformly distributed in magnetic polar angles cannot produce double conal profiles.</text>
<section_header_level_1><location><page_4><loc_55><loc_47><loc_91><loc_50></location>3.2. Emission beam from particles in the conal density distribution</section_header_level_1>
<text><location><page_4><loc_53><loc_34><loc_99><loc_46></location>Small curvature radii of the magnetic field lines near the edge of the pulsar polar cap make curvature radiation more efficiently being generated, which then causes the sparkings more probably located around the edge of polar cap (Ruderman & Sutherland 1975; Qiao et al. 2001). It is therefore possible that accelerated particles are more likely distributed in a conal area, instead of an uniform distribution. Noticed that charged particles flow out along a fixed line tube, we define the density distribution in a conal area on the polar cap as</text>
<formula><location><page_4><loc_64><loc_30><loc_94><loc_34></location>n e0( η ) = n e0exp[ -( η -η m ) 2 2 σ 2 η ] , (13)</formula>
<text><location><page_4><loc_53><loc_26><loc_94><loc_30></location>here η m denotes the peak position of the cone, and the standard derivation σ η describes the cone width. At any radius r and any magnetic polar angle η the density is</text>
<formula><location><page_4><loc_65><loc_24><loc_94><loc_26></location>n e( r , η ) = n e0( η )( r / R /star ) -3 , (14)</formula>
<text><location><page_4><loc_53><loc_21><loc_94><loc_23></location>which does not vary with magnetic azimuthal angle φ . The illustration for the conal density distribution is given in Fig. 6.</text>
<text><location><page_4><loc_53><loc_1><loc_94><loc_20></location>Similar to the uniform model in Sect.3.1, we calculated the curvature radiation of particles in such a density cone from each field line at every tangent at each frequency, to composite the emission beam between 100 MHz to 30 GHz. Fig. 7 shows the distribution of emission intensities for various heights and rotation phases as well as integrated profiles at two example frequencies, 200 MHz and 800 MHz. There are two components in the integrated profile at 200 MHz, though the emission for central rotation phases coming from the region of several tens of R /star is relatively strong compared to those from higher regions. The aberration and retardation effects, which shift highaltitude emission to early rotation phases, can cause the leading profile component to be wider and weaker than the trailing one at 200 MHz, as demonstrated by Dyks et al. (2010). At</text>
<text><location><page_5><loc_14><loc_69><loc_22><loc_70></location>(a) 200 MHz</text>
<figure>
<location><page_5><loc_29><loc_69><loc_48><loc_88></location>
<caption>FIG. 7.- Same as Fig. 5 for emission intensity distributions and the accumulated profiles (a): at 200 MHz and (b): at 800 MHz for a conal density model. The particle energy and density distribution parameters are γ m = 350, σ γ = 30, η m = 0 . 75 and σ η = 0 . 08, with P = 1s, α = 45 · and β = 5 · .</caption>
</figure>
<figure>
<location><page_5><loc_19><loc_40><loc_38><loc_63></location>
<caption>FIG. 8.- Integrated profiles at a series of frequencies calculated from curvature radiation of particles with a conal density distribution. The model parameters are the same as those in Fig. 7. The profiles are aligned to the absolute zero rotation phase when the sight line is in the meridional plane defined by the rotation and magnetic axes.</caption>
</figure>
<text><location><page_5><loc_8><loc_23><loc_49><loc_31></location>r = 10 ∼ 20 R /star , rather than a few hundred of R /star for 200 MHz emission, where the sight line cuts only the beam edge and the emission from higher regions is too weak, so that only one component appears in the integrated profile. The profile evolves from two components at low frequencies to one component at frequencies of above 400 MHz (see Fig. 8).</text>
<text><location><page_5><loc_8><loc_8><loc_49><loc_23></location>We measured the profile width at 10% of the peak intensity, and calculate the corresponding beam radius ϑ using Eq. (2). The FDB curves are plotted in Fig. 9 for various initial conditions. These curves are fitted using Eq. (3), and results are listed in Table 2. The profile width is close to zero when β = ϑ . We have to fix ϑ 0 to be the same as the impact angle β during the fitting, because the emission at very high frequencies comes from the lowest emission point on the LOF. As seen in Fig. 9 and Table. 2, the FDB curves are closely related to emission geometry ( α , β ), particle energy ( γ , σ γ ) and conal density distributions ( η m ).</text>
<text><location><page_5><loc_8><loc_1><loc_49><loc_8></location>We noticed that the FDB curves in all panels of Fig. 9 are converged to a similarly flattened FDB curve at high frequencies, except for various β in panel b . As leaned from Fig. 7, the emission at high frequency comes from a very small height, so that the emission beam is rather narrow due to the geometrical</text>
<figure>
<location><page_5><loc_55><loc_64><loc_91><loc_88></location>
<caption>FIG. 9.- Various FDB curves calculated from particles with a Gaussian energy distribution and a conal density distribution above the polar cap with different model parameters of α , β , γ m , σ γ , η m and σ η . The default parameters are the same as those in Fig. 7.</caption>
</figure>
<text><location><page_5><loc_54><loc_52><loc_91><loc_55></location>FITTED PARAMETERS FOR VARIOUS FDB CURVES IN FIG. 9 FROM VARIOUS CONAL DENSITY MODELS WITH DIFFERENT PARAMETERS OF α , β , γ m , σ γ , η m AND σ η</text>
<table>
<location><page_5><loc_53><loc_32><loc_93><loc_51></location>
<caption>TABLE 2</caption>
</table>
<text><location><page_5><loc_53><loc_19><loc_94><loc_28></location>effect. The density distribution ( η m , σ η ) and energy distribution ( γ , σ γ ) of particles as well as the magnetic inclination ( α ) do not have any obvious effect on the beam at high frequencies, as shown by the similarly converged flat FDB curves in all panels in Fig. 9. As expected, a sight line with a small impact angle β can look into the much deeper magnetosphere and detect a much smaller beam at high frequencies (panel b in Fig. 9).</text>
<text><location><page_5><loc_53><loc_0><loc_94><loc_18></location>The FDB curves in Fig. 9 are influenced by α , γ , σ γ and η m more obviously at the lower frequency end. For a larger magnetic inclination angle α , the polar cap as well as pulsar beam will be more compressed in the meridian dimension (Fig. 2). When other model parameters are fixed, for a dipole field geometry with a larger α , the fixed η m means that the bunch of field lines closer to the magnetic axis are used to calculate the emission beam, which have large curvature radii and emission frequencies are systematically smaller. The characteristic frequency ν 0 of the FDB curves is therefore also smaller (see Table 2). Particles with a larger γ m produce emission of a given frequency at higher altitudes with larger curvature radii, which produce a wider beams (panel c in Fig. 9) with a large char-</text>
<figure>
<location><page_6><loc_8><loc_76><loc_47><loc_90></location>
<caption>FIG. 10.- Distributions of k and ν 0 from 6375 combinations of various model parameter values of the conal density model.</caption>
</figure>
<figure>
<location><page_6><loc_10><loc_50><loc_27><loc_72></location>
</figure>
<figure>
<location><page_6><loc_29><loc_50><loc_46><loc_72></location>
<caption>FIG. 11.- Profile evolution with frequency for two extreme k values: Panel (a) for an extreme steep frequency dependence of k = -2 . 64 with model parameters of α = 45 · , β = 9 · , γ m = 300, σ γ = 10, η m = 0 . 9 and σ η = 0 . 05; and Panel (b) for an extreme flat frequency dependence of k = -0 . 32 with model parameters of α = 65 · , β = 1 · , γ m = 200, σ γ = 50, η m = 0 . 3 and σ η = 0 . 25.</caption>
</figure>
<text><location><page_6><loc_8><loc_24><loc_49><loc_41></location>frequency ν 0 (Table 2). If the energy distribution of particles is rather wide, e.g. for a model with a larger σ γ , the emission region at a given frequency is very extended along field lines. However the dominant emission always comes from a lower emission height, and the integrated profile and hence the beam is much less sensitive to frequencies (panel d in Fig. 9). The particle distribution ( η m ) is directly related to the field lines where the emission is produced. It is easy to understand that particle distributed with a small η m tends to emit with a smaller beam at any frequencies (panel e in Fig. 9). We noticed that the particle distribution width σ η does not have obvious influence on the FDB curves ( panel f in Fig. 9).</text>
<text><location><page_6><loc_8><loc_0><loc_49><loc_24></location>To further investigate the frequency dependence of pulsar beam radius on model parameters in a wide range of values, we have calculated the emission intensity distribution and integrated profiles (as shown in Fig. 7 and Fig. 8) for 6375 combinations of different parameter values: α = (5 · , 25 · , 45 · , 65 · , 85 · ), β = (1 · , 3 · , 5 · , 7 · , 9 · ), γ m = (200, 250, 300, 250, 400), σ γ = (10, 30, 50), η m = (0 . 3, 0 . 5, 0 . 7, 0 . 9) and σ η = (0 . 05, 0 . 1, 0 . 15, 0 . 2, 0 . 25). Pulsar period is fixed to be P = 1s. The frequency dependence of beam radii are fitted with Eq. (3) to get k and ν 0. We got the distributions of k and ν 0 from these combinations as shown in Fig. 10. We found that values of k are in the range of -0 . 2 to -2 . 7, consistent with observed values. However, profile components always merge to one component above ∼ 300 MHz , which is very different from observational facts of cone-dominant pulsars (Mitra & Rankin 2002). We show in Fig. 11 the profile evolutions for two extremes of k values: k = -2 . 64 and k = -0 . 32. For the case of k = -0 . 32, the</text>
<figure>
<location><page_6><loc_63><loc_70><loc_84><loc_87></location>
<caption>FIG. 12.- Illustration for the particle distribution in two density patches. The density follows Eq. (15).</caption>
</figure>
<figure>
<location><page_6><loc_54><loc_47><loc_72><loc_65></location>
</figure>
<figure>
<location><page_6><loc_74><loc_47><loc_93><loc_65></location>
<caption>FIG. 13.- Same as Fig. 5 for emission intensity distributions and the accumulated profiles (a): at 400 MHz and (b): at 1 . 6 GHz for a model of two density patches. The particle energy and density distribution parameters are γ m = 350, σ γ = 30, η m = 0 . 75, σ η = 0 . 08, φ m = 45 · and σ φ = 12 . 5 · , with P = 1s, α = 45 · and β = 3 · .</caption>
</figure>
<text><location><page_6><loc_53><loc_28><loc_94><loc_38></location>two profile components merge even at a very low frequency below 100 MHz . The merging happens when γ m < 250 or σ γ > 30 or η m < 0 . 5 or σ η > 0 . 15. We noticed that when γ m > 350, for models of curvature radiation from particles in the conal density distribution, the emission below about 100 MHz comes from the region of several thousands of R /star , which leads profiles as wide as about 200 · .</text>
<text><location><page_6><loc_53><loc_21><loc_94><loc_28></location>In summary, though curvature radiation models of particles in a conal density distribution can produce a proper range of k , the merging of profile components above few hundreds MHz is the main reason to reject the models for cone-dominated profiles.</text>
<section_header_level_1><location><page_6><loc_54><loc_19><loc_92><loc_20></location>3.3. Emission beam from particles of two density patches</section_header_level_1>
<text><location><page_6><loc_53><loc_3><loc_94><loc_18></location>In the inner gap model (Ruderman & Sutherland 1975), the sparkings do not continually happen above the polar cap and are not concentrating in a ring area to produce the conal density distribution discussed above. The most probably case is that the sparkings occur separately above the polar cap, which produce the subbeams of the observed conal beam (Rankin 1983) or the patchy beam (Lyne & Manchester 1988; Han & Manchester 2001). In the following we work on the models of curvature radiation of particles in two density patches which could be reasonably produced by two sparkings in the inner gap of a rotating neutron star.</text>
<text><location><page_6><loc_54><loc_1><loc_94><loc_3></location>The density distribution of two patches can be defined on the</text>
<section_header_level_1><location><page_7><loc_48><loc_82><loc_52><loc_84></location>AND σ φ</section_header_level_1>
<table>
<location><page_7><loc_21><loc_57><loc_80><loc_82></location>
<caption>TABLE 3 PARAMETERS FITTED TO THE FDB CURVES IN FIG. 15 FOR MODELS OF TWO DENSITY PATCHES WITH VARIOUS α , β , γ m , σ γ , η m , σ η , φ m</caption>
</table>
<figure>
<location><page_7><loc_19><loc_31><loc_38><loc_53></location>
<caption>FIG. 14.- Same as Fig. 8 except for the model of two density patches. The model parameters are the same as those in Fig. 13.</caption>
</figure>
<text><location><page_7><loc_8><loc_19><loc_49><loc_25></location>For simplicity, we model two density patches (see Fig. 12) which are symmetrically located about the meridional plane and peaked at ( η m , φ m ) and ( η m , -φ m ), respectively, with Gaussian widths of σ η and σ φ in the magnetic polar and azimuthal directions, i.e.</text>
<formula><location><page_7><loc_10><loc_14><loc_49><loc_19></location>n e( r , η, φ ) = ne 0( r / R /star ) -3 exp[ -( η -η m ) 2 2 σ 2 η ]exp[ -( φ ± φ m ) 2 2 σ 2 φ ] . (15)</formula>
<text><location><page_7><loc_8><loc_1><loc_49><loc_14></location>The distribution of the emission intensity across height and the rotation phase and the evolution of integrated profiles with frequency for the curvature radiation model from particles of two density patches are shown in Fig. 13 and 14, respectively. Our model calculations show that: 1) the leading component is always slightly wider and weaker than the trailing one; 2) emission at a lower frequency comes from relatively higher and wider region (10 -50 R /star for 400 MHz compared to 8 -20 R /star for 1 . 6 GHz); 3) the low-frequency profiles become wider and are</text>
<figure>
<location><page_7><loc_54><loc_22><loc_92><loc_53></location>
<caption>FIG. 15.- Same as Fig. 9 but for the model for two density patches. The model parameters are the same as those in Fig. 13.</caption>
</figure>
<text><location><page_7><loc_53><loc_13><loc_94><loc_16></location>always remain resolved even at very high frequencies, because two density patches keep separated even down to the star surface.</text>
<text><location><page_7><loc_53><loc_0><loc_94><loc_12></location>From simulated profiles at a set of frequencies, we calculated the beam radius and checked the frequency dependence of pulsar beam. We also checked if FDB curves are related to emission geometry ( α , β ), particle energy distribution ( γ , σ γ ) and patch geometry ( η m , σ η , φ m and σ φ ). The curves are shown in Fig. 15 and fitted parameters are listed in Table 3. The influence of these parameters on the FDB curves are more or less similar to those found from the conal density models. We noticed that φ has the similar effect on the FDB curves as η , both of</text>
<text><location><page_8><loc_8><loc_83><loc_49><loc_87></location>which determine the separation of the two patches. Particles in two patches with a larger σ φ can produce the emission beams with a steeper FDB curve.</text>
<figure>
<location><page_8><loc_9><loc_70><loc_47><loc_82></location>
<caption>FIG. 16.- Distributions of k and ν 0 from 29070 combinations of various model parameter values of the two density patch model.</caption>
</figure>
<text><location><page_8><loc_14><loc_41><loc_16><loc_42></location>(a)</text>
<text><location><page_8><loc_16><loc_41><loc_17><loc_42></location>k</text>
<text><location><page_8><loc_17><loc_41><loc_18><loc_42></location>=</text>
<figure>
<location><page_8><loc_29><loc_41><loc_47><loc_64></location>
<caption>FIG. 17.- Profile evolutions with frequency in the two density patch model for two extreme values of k , Panel (a) for k = -2 . 02 and Panel (b) for k = -0 . 09. Model parameters for panel (a) are α = 45 · , β = 5 · , γ m = 400, σ γ = 10, η m = 0 . 9, σ η = 0 . 1, φ m = 65 · and σ φ = 15 · , and for panel (b) are α = 45 · , β = 1 · , γ m = 200, σ γ = 90, η m = 0 . 3, σ η = 0 . 05, φ m = 45 · and σ φ = 5 · .</caption>
</figure>
<text><location><page_8><loc_18><loc_41><loc_19><loc_43></location>-</text>
<text><location><page_8><loc_19><loc_41><loc_20><loc_42></location>2</text>
<text><location><page_8><loc_20><loc_41><loc_20><loc_42></location>.</text>
<text><location><page_8><loc_20><loc_41><loc_22><loc_42></location>02</text>
<text><location><page_8><loc_8><loc_14><loc_49><loc_33></location>To investigate the possible range of k and ν 0 in the two density patch model, we have calculated the integrated profiles and fitted the FDB curves for 29070 sets of models with different combinations of model parameters of α = (5 · , 45 · , 85 · ), β = (1 · , 5 · , 9 · ), γ m = (200, 300, 400), σ γ = (10, 50, 90), η m = (0 . 1, 0 . 3, 0 . 5, 0 . 7, 0 . 9), σ η = (0 . 05, 0 . 1, 0 . 15, 0 . 2, 0 . 25), φ m = (25 · , 45 · , 65 · , 85 · ) and σ φ = (5 · , 15 · , 25 · , 35 · , 45 · ). The distributions of the power-law indices k and the characteristic frequency ν 0 are shown in Fig. 16. We noticed that k values are in the range between -0 . 1 and -2 . 5. Two components are always resolved, except for the extreme case shown in Fig. 17(a) in which emission is radiated by particles with a narrower energy distribution ( σ γ = 10) and peaking at a larger energy ( γ m = 400) at very high η m = 0 . 9 and φ m = 65.</text>
<text><location><page_8><loc_8><loc_2><loc_49><loc_14></location>In above beam calculations, we used the profile width W 10 at 10% of pulse peak. If the separations Wpp of two components are used to calculated the beam radii, the beam sizes are obviously smaller than those calculated from the 50% and 10% widths (Fig. 18). We compared in Fig. 19 the k and ν 0 values calculated from ϑ 10 (written as k 10 and ν 0 , 10) with the k and ν 0 values from ϑ pp (written as kpp and ν 0 , pp ), and found that they are correlated and scatter at small ν 0 or large k values (due to error-bar as expected).</text>
<text><location><page_8><loc_9><loc_0><loc_49><loc_1></location>In summary, the curvature radiation from particles in two</text>
<figure>
<location><page_8><loc_60><loc_75><loc_86><loc_88></location>
<caption>FIG. 18.- Beam radii ( ϑ 10) calculated from the 10% profile widths ( W 10) at a series of frequencies are compared with beam radii ( ϑ 50) calculated from the 50% profile widths ( W 50) and beam radii ( ϑ pp ) calculated from component separations ( Wpp ). Parameters for this example model are γ m = 200, σ γ = 50, η m = 0 . 7, σ η = 0 . 2, φ m = 65 · and σ φ = 15 · , with P = 1 s , α = 45 · and β = 5 · .</caption>
</figure>
<figure>
<location><page_8><loc_54><loc_51><loc_73><loc_67></location>
</figure>
<figure>
<location><page_8><loc_74><loc_51><loc_93><loc_67></location>
<caption>FIG. 19.- Comparison of k and ν 0 values calculated from ϑ 10 and ϑ pp</caption>
</figure>
<text><location><page_8><loc_53><loc_43><loc_94><loc_47></location>density patches can not only give a proper range of k values, but also keeps the two components resolved in general even at very high frequencies.</text>
<section_header_level_1><location><page_8><loc_67><loc_40><loc_79><loc_41></location>4. DISCUSSIONS</section_header_level_1>
<text><location><page_8><loc_53><loc_29><loc_94><loc_39></location>In the previous section, we conclude that the FDB curves with two resolved components can be preferably explained by curvature radiations of particles in two density patches. Here we discuss influences on the FDB curves by the radial decay of particle energy and by other possible energy distribution of particles, and discuss the possible FDB curve flattening at low frequencies. Finally we will look at the real FDB data and make a model.</text>
<section_header_level_1><location><page_8><loc_53><loc_24><loc_93><loc_27></location>4.1. Radial decay of particle energy and the lowest emission height</section_header_level_1>
<text><location><page_8><loc_53><loc_17><loc_94><loc_24></location>As shown in Fig. 9 and 15, the values of beam radii at the infinite-frequency, ϑ 0, calculated from models are always very close to those of β , no matter what model parameters are in putted. However, both on observational ground (Table. 1) and theoretical expectations, ϑ 0 is larger than β .</text>
<text><location><page_8><loc_53><loc_6><loc_94><loc_17></location>In simulations above we assume that particles in the magnetosphere have a Gaussian energy distribution with a peak Lorentz factor γ m and a spread width σ γ along the whole trajectory. In reality, the particle energy distribution may be much more complicated due to the Compton loss (Zhang et al. 1997) or other processes. It is reasonable to believe that particle energy decreases when they flow out along the field lines in the inner magnetosphere.</text>
<text><location><page_8><loc_53><loc_0><loc_94><loc_6></location>In the vacuum-gap model (Ruderman & Sutherland 1975), electron-positron pairs are produced by the avalanche process in the pulsar polar cap. The maximum Lorentz factor of the primary particles after accelerating across the gap is γ max =</text>
<figure>
<location><page_9><loc_15><loc_56><loc_41><loc_88></location>
<caption>FIG. 20.- FDB curves for the curvature radiation model by particles in two density patches with an energy distribution of Eq. (9) and Eq. (16). The default model parameters are the same as those in Fig 13 (e.g. β = 3 · ) but also with γ m 0 = 10 6 , q = 0 . 3 and γ s = 350.</caption>
</figure>
<text><location><page_9><loc_8><loc_32><loc_49><loc_49></location>1 . 2 × 10 7 B /star 12 h 2 4 / P 1s, with B /star 12 = B /star / 10 12 G the surface magnetic field, h 4 = h / 10 4 cm the gap height and P 1s = P / 1s. Pair cascade occurs within a few stellar radii near the surface, which generates the secondary particles with much lower Lorentz factors of a few hundred. Detailed numerical simulations on the pair cascade process were carried out by Medin & Lai (2010), in which they found that for various initial parameters (such as surface magnetic field, period and primary energy), the pair cascade process maybe finishes at a height of several star-radius, from less than 2 R /star to more than 10 R /star . Here we naively assume a toy model to describe the rapid decay of particle energy during the pair cascade process, which reads</text>
<formula><location><page_9><loc_19><loc_28><loc_49><loc_32></location>γ m = γ m 0 exp( -q r -R /star R /star ) + γ s , (16)</formula>
<text><location><page_9><loc_8><loc_10><loc_49><loc_28></location>here γ m is the peak Lorentz factor of the Gaussian distribution we used above, γ m 0 and γ s are the corresponding values of the primary particles and the final secondary particles before and after the pair cascade, respectively. The factor q (less than 1) determines how fast the energy decreases with height for the cascade. This energy model has been used by Qiao et al. (2001) and Zhang et al. (2007) to simulate the inverse-Compton scattering emission, where they ignored the energy term γ s . To use the above energy model in our simulation for the model for two density patches, one should substitute γ m of Eq. (16) into the Gaussian energy distribution Eq. (9). Note that the number of the particles n e0 in Eq. (15) should also be replaced by n e0 γ s /γ m to keep the conservation of total energy.</text>
<text><location><page_9><loc_8><loc_0><loc_49><loc_10></location>Example FDB curves from the curvature radiation model by particles in two density patches with an energy distribution described by Eq. (9) and Eq. (16) are demonstrated in Fig. 20, and the fitted parameters are listed in Table. 4. We found that a larger primary Lorentz factor γ m 0 or a smaller q lead to larger beam radius ϑ 0 at very high frequencies. A larger γ s leads to a steeper FDB curve.</text>
<table>
<location><page_9><loc_56><loc_72><loc_90><loc_83></location>
<caption>TABLE 4 FITTED PARAMETERS OF FDB CURVES IN FIG. 20</caption>
</table>
<figure>
<location><page_9><loc_54><loc_58><loc_93><loc_70></location>
<caption>FIG. 21.- Characteristic Lorentz factor γ c at lowest radio emission height well related to γ m 0 and q . Symbols ∗ come from simulation data as in Table 4 and lines are the fitting.</caption>
</figure>
<text><location><page_9><loc_53><loc_43><loc_94><loc_51></location>In these model the values of ϑ 0 are always larger than those of β , which means that there exists the lowest radio emission height r low = R lc sin 2 (2 ϑ 0 / 3), which is > R lc sin 2 (2 β/ 3). For a small value of ϑ 0, the corresponding beam radii at the infinite frequency can be written as ϑ 0 /similarequal 3 / 2 √ r low / R lc. Now, what is the value of r low?</text>
<text><location><page_9><loc_53><loc_39><loc_94><loc_43></location>According to Eq. (16), at the lowest radio emission height r low, there exists a characteristic Lorentz factor γ c . We noticed that r low and γ c are related with γ m 0 and q by:</text>
<formula><location><page_9><loc_67><loc_35><loc_94><loc_38></location>r low R /star = 1 -1 q ln γ c γ m 0 . (17)</formula>
<text><location><page_9><loc_53><loc_30><loc_94><loc_35></location>From simulations similarly as presented Table 4, we can get a set of r low from ϑ 0 for various γ m 0 and q , and then we got γ c using Eq. (17). We find that γ c are also very well related to γ m 0 and q , as shown in Fig. 21, by</text>
<formula><location><page_9><loc_65><loc_28><loc_94><loc_30></location>γ c = 55 . 0 γ 0 . 4 m 0 exp( -2 q ) . (18)</formula>
<text><location><page_9><loc_53><loc_26><loc_75><loc_27></location>Substituting into Eq. (17), we find</text>
<formula><location><page_9><loc_63><loc_23><loc_94><loc_26></location>r low = R /star (3 + 1 . 38log γ m 0 -4 q ) . (19)</formula>
<section_header_level_1><location><page_9><loc_59><loc_21><loc_87><loc_22></location>4.2. On the energy distribution of particles</section_header_level_1>
<text><location><page_9><loc_53><loc_6><loc_94><loc_20></location>At any height, the secondary particles in the magnetosphere for the curvature radio emission were assumed to have an energy distribution in the Gaussian function. It is possible that the particles follow other energy distribution functions. For example, according to Arons (1981), the multi-component plasma in pulsar magnetosphere contains secondary pairs, a high-energy plasma 'tail', and some primary particles. The joint energy distribution of secondary particles and high-energy 'tail' can be described by a power-law with two cutoffs at its two ends, which reads as,</text>
<formula><location><page_9><loc_63><loc_3><loc_94><loc_6></location>n e( γ ) ∼ γ s , γ s , min <γ < γ s , max , (20)</formula>
<text><location><page_9><loc_53><loc_1><loc_94><loc_4></location>where s is the power-law index. The curvature radiation from particles in two density patches with such an energy distribu-</text>
<figure>
<location><page_10><loc_19><loc_66><loc_37><loc_88></location>
<caption>FIG. 22.- Same as Fig. 14 but a power-law energy distribution with index s = -2. Other model parameters are γ s , min = 150 and γ s , max = 2000, γ m = 350, σ γ = 30, η m = 0 . 75, σ η = 0 . 08, φ m = 45 · and σ φ = 12 . 5 · , with P = 1s, α = 45 · and β = 3 · .</caption>
</figure>
<figure>
<location><page_10><loc_15><loc_47><loc_41><loc_60></location>
<caption>FIG. 23.- Example of Low frequency flattening the FDB curve. The model parameters are γ m = 400, σ γ = 10, η m = 0 . 7, σ η = 0 . 1, φ m = 45 · and σ φ = 5 · with P = 1 s , α = 45 · and β = 5 · .</caption>
</figure>
<text><location><page_10><loc_8><loc_32><loc_49><loc_40></location>with a similar shape and a constant pulse width between 80 MHz and 40 GHz, as shown in Fig. 22. We can not find the profile differences for a range of s values, e.g. a difference less than 2% for the pulse width values between s = -2 and s = -3. We also found that the values of γ s , min and γ s , max determine the frequency range for the constant profile width.</text>
<section_header_level_1><location><page_10><loc_10><loc_30><loc_47><loc_31></location>4.3. Possible low frequency flattening of the FDB curves</section_header_level_1>
<text><location><page_10><loc_8><loc_22><loc_49><loc_29></location>During the model calculations, we noticed that the FDB curves tend to be flattening at low frequencies. For some input parameters of the two density patch model, the effect is very obvious (Fig. 23), especially when Lorentz factors are large ( γ m > 400) and/or the energy distribution is broad ( σ γ > 80).</text>
<text><location><page_10><loc_8><loc_3><loc_49><loc_22></location>This is understandable. Because of the dipole bending of magnetic field lines, as pulsar rotates, a fixed sight-line cut across the two density patches (see Fig. 12) with a clear lower limit and upper limit of height and a clear left and right limit of the rotation phase. Very low frequency emissions tend to come from the high regions of two patches in such a limited volume. In that high regions near the upper bound, the lower frequency emission comes from particles of the lower energy, but the pulse-width or beam-width of the emission from two patches is determined by the geometry. This happens to very low-frequency, depending on the γ m . The low-frequency flattening of FDB curves are often seen in the models when patches are small (small σ φ ), or energy of particles are very high and/or the energy distribution is broad (large γ m and σ γ ).</text>
<section_header_level_1><location><page_10><loc_15><loc_1><loc_41><loc_2></location>4.4. Observed FDB curve and a model</section_header_level_1>
<figure>
<location><page_10><loc_58><loc_48><loc_89><loc_88></location>
<caption>FIG. 24.Upper panel: An example of real data and model-fitting. The observed data of PSR B2020+28 are taken from Mitra & Rankin (2002). The solid line is the best model calculated from the curvature radiation of particles in two density patches with parameters γ m 0 = 10 6 , γ s = 225, σ γ = 15, q = 0 . 25, η m = 0 . 75, σ η = 0 . 08, φ m = 45 · and σ φ = 12 . 5 · . The geometrical parameters α and β and the period of this pulsar can be found from Table 1. Lower panel: The χ 2 distribution for a pair of the most influential parameters, γ s and q , for the fitting. The best values are γ s = 225 and q = 0 . 25.</caption>
</figure>
<text><location><page_10><loc_53><loc_17><loc_94><loc_36></location>We have worked on a huge number of models for the radio emission intensity distribution across the height and rotation phase and integrated profiles. We now look at data of a real cone-dominant pulsar, PSR B2020+28, and make a model. The data are taken from (Mitra & Rankin 2002). To keep the two profile components separated even at very high frequencies, we have to choose a model of the curvature radiations of particles in two density patches and consider the energy distribution of particles as described by Eq. (9) and Eq. (16). As shown in Figure 24, the model can fit data nicely with a local minimum of χ 2 = 10 . 24 in the parameter space of γ s and q . The model is obtained with sparsely separated parameter grids, which may be improved by a global fitting for 8 parameters but that is very computational expensive.</text>
<section_header_level_1><location><page_10><loc_63><loc_14><loc_83><loc_15></location>5. SUMMARY AND OUTLOOK</section_header_level_1>
<text><location><page_10><loc_53><loc_9><loc_94><loc_13></location>We studied the frequency dependence of beam radius for cone-dominant pulsars by using the curvature radiation mechanism.</text>
<text><location><page_10><loc_53><loc_1><loc_94><loc_9></location>For the simplest case in which pulsar radio emission is generated by curvature radiation of relativistic particles with a single γ and streaming along fixed open field-lines, we obtain the analytic formula in Eq. (7) for the frequency dependence. It has the power-law index k = -1, and ϑ 0 = 0, both are different from observations.</text>
<text><location><page_11><loc_8><loc_76><loc_49><loc_87></location>Considering various density distribution and energy distribution of particles, we numerically calculated the intensity of curvature radiation from all the possible emission heights in the open field line region, and get integrated mean pulse profiles from which the FDB curves are derived. We found that the power-law index k and ϑ 0 are strongly influenced by the density distribution and energy distribution of particles in the open field-line region.</text>
<text><location><page_11><loc_8><loc_71><loc_49><loc_76></location>When particles are uniformly distributed in whole open field lines, the curvature radiation can produce only one profile component, which can not explain the two resolved components of cone-dominant pulsars.</text>
<text><location><page_11><loc_8><loc_64><loc_50><loc_70></location>Whenparticles are distributed in a conal area, the low-frequency emission comes from very high regions so that profile is very wide. Profiles at high frequencies cannot have two separated components, because emission comes from low heights where the sight line always continually cuts the edge of density cone.</text>
<text><location><page_11><loc_8><loc_51><loc_49><loc_63></location>To keep two profile components separated or resolved, the particles must come from two density patches. Model calculations from a huge amount of parameter combinations show that the k values of the FDB curves are in the range of -0 . 1 to -2 . 5, in agreement with the observations. Because of the limited upper boundary of the density patches cut by a given sight line, the FDB curves tends to be flattened at low frequencies, especially for models with a large Lorentz factor and/or broad particle energy distribution.</text>
<text><location><page_11><loc_8><loc_41><loc_49><loc_51></location>The geometry of density distribution of particles and the energy distribution of particles in the model certainly affect the FDB curves. For a Gaussian energy distribution, high energy particles with large γ m will produce a wide beam at low frequency. Particles in a narrow energy distribution with a small σ γ produce a steep FDB curve. The radial decay of particle energy is important to get a reasonable ϑ 0 in models.</text>
<text><location><page_11><loc_8><loc_14><loc_49><loc_41></location>Through model calculations of pulsar beam and profile evolution by using the curvature radiation mechanism, we have clarified some important issues on particle density and energy distributions. However, in our simulations, we considered only the simple case that particles are emitting radio waves with the characteristic frequency for curvature radiation determined by the Lorentz factor. The real curvature emission of any particles has an energy spectrum, which is a power-law with an index 1 / 3 at the low frequency limit (much less than the characteristic frequency) and becomes exponential at high frequencies. This may significantly affect the emission regions and modify the FDB curves, which we should investigate in future. Another important fact is that the real pulsar radio emission is believed to be highly coherent, while in this paper we simply treat the coherence by assuming that the emission comes from point-like huge charge. Moreover, other emission mechanisms may also work in pulsar magnetosphere, such as inverse Compton scattering, plasma oscillation, cyclotron instability and Coulomb bremsstrahlung emission, etc, which are not considered in this paper and may lead to their own FDB curves.</text>
<text><location><page_11><loc_8><loc_7><loc_49><loc_12></location>The authors thank Professor Chou Chih Kang for helpful discussions and the referee for constructive comments. This work has been supported by the National Natural Science Foundation of China (11003023 and 10833003).</text>
<text><location><page_11><loc_53><loc_59><loc_94><loc_87></location>Arons, J. 1981, in ESA Special Publication, Vol. 161, ESA Special Publication, ed. T. D. Guyenne & G. Lévy, 273 Beskin, V. S., Gurevich, A. V., & Istomin, Y. N. 1988, Ap&SS, 146, 205 Biggs, J. D. 1990, MNRAS, 245, 514 Buschauer, R. & Benford, G. 1976, MNRAS, 177, 109 Cordes, J. M. 1978, ApJ, 222, 1006 Dyks, J. & Harding, A. K. 2004, ApJ, 614, 869 Dyks, J., Wright, G. A. E., & Demorest, P. 2010, MNRAS, 405, 509 Everett, J. E. & Weisberg, J. M. 2001, ApJ, 553, 341 Gangadhara, R. T. 2004, ApJ, 609, 335 Gangadhara, R. T. 2005, ApJ, 628, 923 Gil, J. 1981, Acta Phys. Pol., B12, 1081 Han, J. L. & Manchester, R. N. 2001, MNRAS, 320, L35 Lyne, A. G. & Manchester, R. N. 1988, MNRAS, 234, 477 Machabeli, G. Z. & Usov, V. V. 1989, Sov. Astron. Lett., 15, 393 Manchester, R. N. 1995, J. Astrophys. Astr., 16, 107 Medin, Z. & Lai, D. 2010, MNRAS, 406, 1379 Mitra, D. & Rankin, J. M. 2002, ApJ, 577, 322 Phillips, J. A. 1992, ApJ, 385, 282 Qiao, G. J., Liu, J. F., Zhang, B., & Han, J. L. 2001, A&A, 377, 964 Rankin, J. M. 1983, ApJ, 274, 333 Rankin, J. M. 1990, ApJ, 352, 247 Ruderman, M. A. & Sutherland, P. G. 1975, ApJ, 196, 51 Thorsett, S. E. 1991, ApJ, 377, 263 Vitarmo, J. & Jauho, P. 1973, ApJ, 182, 935 Xilouris, K. M., Kramer, M., Jessner, A., Wielebinski, R., & Timofeev, M. 1996, A&A, 309, 481 Zhang, B., Qiao, G. J., & Han, J. L. 1997, ApJ, 491, 891</text>
<unordered_list>
<list_item><location><page_11><loc_53><loc_57><loc_94><loc_59></location>Zhang, H., Qiao, G. J., Han, J. L., Lee, K. J., & Wang, H. G. 2007, A&A, 465, 525</list_item>
</document>
[
{
"title": "ABSTRACT",
"content": "Beam radii for cone-dominant pulsars follow a power-law relation with frequency, ϑ = ( ν/ν 0) k + ϑ 0, which has not yet well explained in previous works. We study this frequency dependence of beam radius (FDB) for cone-dominant pulsars by using the curvature radiation mechanism. Considering various density and energy distributions of particles in the pulsar open field line region, we numerically simulate the emission intensity distribution across emission height and rotation phase, and get integrated profiles at different frequencies and obtain the FDB curves. For the density model of a conal-like distribution, the simulated profiles always shrink to one component at high frequencies. In the density model with two separated density patches, the profiles always have two distinct components, and the power-law indices k are found to be in the range from -0 . 1 to -2 . 5, consistent with observational results. Energy distributions of streaming particles have significant influence on the frequency-dependence behavior. Radial energy decay of particles are necessary to get proper ϑ 0 in models. We conclude that by using the curvature radiation mechanism, the observed frequency dependence of beam radius for the cone-dominant pulsars can only be explained by the emission model of particles in two density patches with a Gaussian energy distribution and a radial energy loss. Subject headings: pulsars: general - star: magnetic fields - relativistic particles - curvature radiation",
"pages": [
1
]
},
{
"title": "MODELING THE FREQUENCY-DEPENDENCE OF RADIO BEAMS FOR CONE-DOMINANT PULSARS",
"content": "P. F. WANG, J. L. HAN, C. WANG National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100012, China. Email: pfwang, hjl, [email protected] Draft version June 20, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "A pulsar profile is explained as being the line-of-sight cuts through the emission beam when a pulsar rotates. For conedominant pulsars, profiles widen at low frequencies. The variation of pulsar profile width or component separation, W , against the observation frequency, ν , can be described by a power-law function (Thorsett 1991) Here, W 0 is a width constant. With a dipole field geometry for pulsar emission region, the emission of lower frequencies is believed to be generated at larger heights for the wider open angles of the emission cone. This is well known as the radiusto-frequency mapping (Ruderman & Sutherland 1975; Cordes 1978; Phillips 1992). Observed profile width can be expressed by, for example, the peak separation between the outermost components, Wpp (i.e. the peak-peak separation), the pulse width at the 10% of the highest intensity peak, W 10, and the pulse width at the 50% of the peak, W 50. In order to understand the frequency dependence of pulsar profiles in a much wider frequency range, Xilouris et al. (1996) observed a number of nearby bright pulsars up to 32 GHz and measured their W 50. Combining with previous measurements at lower frequencies, they fitted the pulse widths by W 50 = a ν k + W 0, and got -0 . 29 > k > -0 . 94 for a sample of pulsars. The radius of the pulsar emission beam, ϑ , is related to the profile width, W , by (Gil 1981), Here, α is the inclination angle of the magnetic axis related to the rotation axis, β is the impact angle of the line of sight to the magnetic axis. For many pulsars with good polarization measurements, the values of α and β have been determined (Lyne & Manchester 1988; Rankin 1990; Everett & Weisberg 2001). For a given pulsar, the beam radius, ϑ , and the profile width, W , are quasi-linearly related for various frequencies. GEOMETRY PARAMETERS AND FITTED k AND ϑ 0 FOR 7 CONE-DOMINANT PULSARS WITH CLEAR FREQUENCY DEPENDENCE (MITRA & RANKIN 2002). Therefore, the variation of pulse-width with frequency should be physically related to the frequency dependence of pulsar beam radius. Mitra & Rankin (2002) collected observed pulse widths for 7 cone-dominant pulsars and calculated their beam radii at various frequencies. They found that the radius of the outer-cone beam of 7 pulsars follows here ϑ 0 is the beam radius at the infinite-frequency, and the ν 0 is the characteristic frequency. The values of the power-law index k are in the range of -0 . 3 to -1 . 2. The values of β are smaller than those of ϑ 0, as shown in Table 1. We noticed that for a given pulsar the k value obtained from pulse widths is almost the same as that fitted from the beam radii. Mitra & Rankin (2002) noticed that the beam radii of inner-cone do not show the frequency dependence. The frequency dependence of beam radii or profile widths can be easily explained by the open field-lines of the emission region in a dipole field geometry of neutron stars, as long as the radius-frequency-mapping holds (Ruderman & Sutherland 1975). Different emission mechanisms can lead to different power-law indices k . The electron bremsstrahlung model (Vitarmo & Jau 1973) predicts k ∼ -0 . 45. The vacuum inner gap model (Ruderman & Sut 1975) can give k ∼ -1 / 3. The curvature plasma model (Beskin et al. either k ∼ -0 . 14 or k ∼ -0 . 29. The emission from the cyclotron instability (Machabeli & Usov 1989) gives k ∼ -0 . 17. These theoretical values can not cover the wide range of the observed k . In this paper, we try to explain the frequency dependence of the radio beam observed for cone-dominant pulsars using the curvature radiation mechanism. If the edge of pulsar beam is generated by particles flowing along the last open field-lines (LOF), we can calculate the radio beams, and investigate their dependence on pulsar parameters, period P , inclination angle α , impact angle β and the Lorentz factor of particles γ . Using some generalized energy and density distributions of particles in the magnetosphere, we numerically calculate the radio emission beams and fit their frequency dependence. We also investigate the influence on the pulsar beam by the radial decrease of particle energy and the particle energy distribution.",
"pages": [
1,
2
]
},
{
"title": "2. CURVATURE RADIATION BEAM FOR PARTICLES WITH A GIVEN γ IN A DIPOLE FIELD",
"content": "In general, pulsar radio emission is assumed to be generated by curvature radiation of secondary particles streaming along the last open field-lines. In the radio emission region, magnetic fields can be described as a static dipole (e.g. Gangadhara 2004), because the multipolar field components of a neutron star vanish there and the sweeping effect due to rotation is also negligible according to Dyks & Harding (2004). Therefore, in this paper, we will use the dipole field to study the frequency dependence of beam radius (FDB). The size and geometry of a dipole magnetic field is determined by pulsar period P , inclination angle α and impact angle β . In the polar coordinate system with the polar axis along the magnetic axis direction (Fig. 1), a dipole field-line can be described by r = re sin 2 θ , here θ is the polar angle from the magnetic axis, r is the distance from the dipole origin, re is the fieldline constant, which is the distance from the origin to the point of the field-line intersection with the magnetic equatorial plane of θ = 90 · . For an inclined dipole, the LOF are contained in the light cylinder (see Fig. 1). The radius of the light-cylinder, R lc = cP / 2 π , gives the limit of the field line constants re for the LOF, which is different for pulsars with different periods. The angular diameter of the polar cap defined by the feet of LOF on the neutron star surface is related to the pulsar period, P , by 2 θ pc = 1 . 6 · P -1 / 2 . The opening angle of the beam from the tangents of the LOF near the surface is about 1 . 2 · P -1 / 2 , which defines the minimum geometrical beam angle. Observations show ϑ 0 > 1 . 2 · P -1 / 2 . The emission beam determined by the LOF is not circular but compressed in the meridional direction in the plane of rotation and magnetic axes (Biggs 1990). We define the magnetic azimuthal angle, φ , starting from the connection between the magnetic axis and the rotation axis (to the top being the north) as being φ = 0 · (see Fig. 2). The beam radius in the direction of φ = 0 · is smaller than that in the direction of φ = 90 · (to the east). In the curvature radiation mechanism, the emission frequency is not only related to the field geometry but also to the Lorentz factor γ of particles. The simplest case we consider here is that particles have the same Lorentz factor γ , and that the radio beam is defined by the tangents of the LOF. When a relativistic particle streams along a field-line, it can produce curvature radiation with a characteristic frequency of Here, γ is the Lorentz factor of particles in the range 10 2 -10 4 , ρ is the curvature radius of the particle trajectory. In any fieldline, the curvature radius can be expressed by (Gangadhara 2004) Note that θ varies with r . The angle between the tangent of a field-line of θ and the magnetic axis is Combining Eq. (5) and Eq. (6), one can find the relation between ϑ and ρ for any field-line of re . Because the radiation frequency ν is related to ρ by Eq. (4), we get One can use Eq. (15) from Gangadhara (2004) to get the fieldline constants re for each LOF. Obviously, as indicated in Eq. (7), the beam radius is related to the radiation frequency. At a higher frequency of ν /greatermuch γ 3 c / re , the second term can be neglected, and the beam radius ϑ is related to the frequency ν by roughly a power-law with the index of k = -1. At a low frequency of ν ≤ γ 3 c / re , the frequency dependence becomes slightly steeper due to the contribution from the second term. Note that the beam radii in all magnetic azimuthal directions are frequency dependent. Clearly, the first term of Eq. (7) is a good approximation of the frequency dependence of pulsar beam, which has a power-law index k = -1. We calculated the beam radii at different frequencies for various model parameters, as shown in Fig. 3. All curves show the frequency dependence of radiation beam with a power-law index of approximately -1, which is different from observational values in the range of -0 . 3 > k > -1 . 2 (Mitra & Rankin 2002). We found that there is no influence on the frequency dependence of beam size by the magnetic inclination α , because α only leads to the compression of beam in the meridional direction, and has almost no influence on the radius of φ = 90 · . Different impacts of line of sight with different β values lead to different cuts of the beam from β = 0 · to β = ϑ . The lower limit of ϑ is determined by the angular size of the polar cap (3/2 θ pc) or the β value. Pulsars with a small period P have a small R lc and hence a small re and a small curvature radius [Eq. (5)], which corresponds to a larger radiation frequency [Eq. (4)], as shown in Fig. 3. Note also that in the pulsar emission region curvature radiation of particles with a single γ cannot produce radio emission over a wide frequency range from hundreds MHz to ten GHz. Particles with larger γ produce curvature radiation at much higher frequency, which shifts the FDB curves to higher frequency ranges. The calculations shown in Fig.2 and 3 were made with assumptions that pulsar beams are bounded by the LOF. However, Ruderman & Sutherland (1975) suggested that beam edge should be bounded by the critical field-lines, which are orthogonal to (instead of tangent to) the light cylinder at the intersection points. The critical field-lines are located between the magnetic axis and the LOF. Here, the parameter η is used to describe the location of field-lines, with η = 0 for the magnetic axis, η = 1 for the LOF. To generate the curvature emission beam of the same open angle, the emission height from the critical field lines (0 < η < 0 . 74, depending on α ) is larger than that from the LOF as shown in Fig. 3, and the curvature radius is also larger, so that the emission has a smaller frequency of, with ν lof the corresponding emission frequency for the LOF. We carried out a set of calculations, and found that the curvature radiation for the critical field lines has almost the same frequency dependence of emission beam as that for the LOF, and k and ϑ 0 values are consistent within 5%, though ν 0 is smaller due to larger curvature radii of field lines.",
"pages": [
2,
3
]
},
{
"title": "3. CURVATURE RADIATION BEAM FROM PARTICLES WITH VARIOUS ENERGY AND DENSITY DISTRIBUTIONS",
"content": "Particles in pulsar magnetosphere should have an energy distribution, which radiate in a range of frequencies at a range of heights for a given LOF. Furthermore, particles flow out along a set of open field-lines, rather than just the LOF. The pulsar radio emission from a given height and a given rotation phase is contributed from particles not only in the field lines which are tangential towards the observer, but also in the nearby field lines in the bunch within the 1 /γ emission cone. The emission is coherent radiation from a bunch of particles (Buschauer & Benford 1976). According to simulation results of Medin & Lai (2010), we assume in this section that secondary particles for curvature radiation at radio bands follow a Gaussian energy distribution with a peak at γ m of several hundreds: Here, the standard deviation σ γ is of several tens. Considering the continuity of the particles flowing along the field-line tube, we got the number density of particles at r as Here, n e0 represents the number density at the bottom of a magnetic field tube near the surface of a neutron star. The power of curvature radiation at a frequency ν from one particle is given by, Nb particles in a field bunch in the region with a dimension size of less than half emission wavelength produce the total emission power of approximately N 2 b P e. Because the curvature radius varies everywhere in the dipole field, according to Eq. (4) and (11), the observed emission at frequency ν and rotation phase ϕ should come from the tangents of a set of open field-lines with the same magnetic azimuth φ , where the curvature radius ρ of a field-line and particle energy γ are nicely combined to produce emission. The observed total power therefore should be the sum of them, Note that the magnetic azimuth φ is a monotonic function of the rotation phase ϕ , as given by Eq. (11) in Gangadhara (2004) which is equivalent to the well-known S -curve for polarization angle.",
"pages": [
3
]
},
{
"title": "3.1. Emission beam from particles uniformly distributed in magnetic polar angles",
"content": "As the first try, we assume that particles follow a Gaussian energy distribution and are uniformly distributed in the open field-lines for all magnetic polar angles, as shown in Fig. 4. We can calculate the emission from each open field-line at every tangent for each frequency. At a given emission height, the central open field-lines have larger curvature radii than the outer open field-lines. Particles with a given Lorentz factor in the central field lines would produce a lower frequency emission [see Eq. (4)] than they do in the outer field lines. For a group of particles with a Gaussian energy distribution, only these particles with larger Lorentz factors in the central field lines can produce the emission at the same frequency as particles of lower Lorentz factors in the outer field lines, but their emission intensity is reduced by a factor of 1 /γ 2 . Note that magnetic fields have smaller curvature radii at lower height. All these factors produce the bifurcation feature shown in Fig.5. We limited our calculations for the region of r max < 0 . 1 R lc, because the emission intensity from higher regions is negligible (see Fig. 5) due to the relatively small particle density and large curvature radius. For P = 1 s, R lc /similarequal 47771 km /similarequal 4777 R ∗ , if we take R ∗ =10 km. We consider the phase shift (Gangadhara 2005) of the emission from any height of every field-line, and integrate their emission for profiles at every observation frequency (lower panels in Fig. 5). We found that aberration and retardation effects can change the projection position of emission in the sky plane, which cause the profile to be enhanced by about 20% at the phase of ϕ = -10 · and weakened by about 22%at the phase of ϕ =10 · for the model calculations in Fig. 5. Weconcludethat curvature radiation from particles uniformly distributed in magnetic polar angles cannot produce double conal profiles.",
"pages": [
4
]
},
{
"title": "3.2. Emission beam from particles in the conal density distribution",
"content": "Small curvature radii of the magnetic field lines near the edge of the pulsar polar cap make curvature radiation more efficiently being generated, which then causes the sparkings more probably located around the edge of polar cap (Ruderman & Sutherland 1975; Qiao et al. 2001). It is therefore possible that accelerated particles are more likely distributed in a conal area, instead of an uniform distribution. Noticed that charged particles flow out along a fixed line tube, we define the density distribution in a conal area on the polar cap as here η m denotes the peak position of the cone, and the standard derivation σ η describes the cone width. At any radius r and any magnetic polar angle η the density is which does not vary with magnetic azimuthal angle φ . The illustration for the conal density distribution is given in Fig. 6. Similar to the uniform model in Sect.3.1, we calculated the curvature radiation of particles in such a density cone from each field line at every tangent at each frequency, to composite the emission beam between 100 MHz to 30 GHz. Fig. 7 shows the distribution of emission intensities for various heights and rotation phases as well as integrated profiles at two example frequencies, 200 MHz and 800 MHz. There are two components in the integrated profile at 200 MHz, though the emission for central rotation phases coming from the region of several tens of R /star is relatively strong compared to those from higher regions. The aberration and retardation effects, which shift highaltitude emission to early rotation phases, can cause the leading profile component to be wider and weaker than the trailing one at 200 MHz, as demonstrated by Dyks et al. (2010). At (a) 200 MHz r = 10 ∼ 20 R /star , rather than a few hundred of R /star for 200 MHz emission, where the sight line cuts only the beam edge and the emission from higher regions is too weak, so that only one component appears in the integrated profile. The profile evolves from two components at low frequencies to one component at frequencies of above 400 MHz (see Fig. 8). We measured the profile width at 10% of the peak intensity, and calculate the corresponding beam radius ϑ using Eq. (2). The FDB curves are plotted in Fig. 9 for various initial conditions. These curves are fitted using Eq. (3), and results are listed in Table 2. The profile width is close to zero when β = ϑ . We have to fix ϑ 0 to be the same as the impact angle β during the fitting, because the emission at very high frequencies comes from the lowest emission point on the LOF. As seen in Fig. 9 and Table. 2, the FDB curves are closely related to emission geometry ( α , β ), particle energy ( γ , σ γ ) and conal density distributions ( η m ). We noticed that the FDB curves in all panels of Fig. 9 are converged to a similarly flattened FDB curve at high frequencies, except for various β in panel b . As leaned from Fig. 7, the emission at high frequency comes from a very small height, so that the emission beam is rather narrow due to the geometrical FITTED PARAMETERS FOR VARIOUS FDB CURVES IN FIG. 9 FROM VARIOUS CONAL DENSITY MODELS WITH DIFFERENT PARAMETERS OF α , β , γ m , σ γ , η m AND σ η effect. The density distribution ( η m , σ η ) and energy distribution ( γ , σ γ ) of particles as well as the magnetic inclination ( α ) do not have any obvious effect on the beam at high frequencies, as shown by the similarly converged flat FDB curves in all panels in Fig. 9. As expected, a sight line with a small impact angle β can look into the much deeper magnetosphere and detect a much smaller beam at high frequencies (panel b in Fig. 9). The FDB curves in Fig. 9 are influenced by α , γ , σ γ and η m more obviously at the lower frequency end. For a larger magnetic inclination angle α , the polar cap as well as pulsar beam will be more compressed in the meridian dimension (Fig. 2). When other model parameters are fixed, for a dipole field geometry with a larger α , the fixed η m means that the bunch of field lines closer to the magnetic axis are used to calculate the emission beam, which have large curvature radii and emission frequencies are systematically smaller. The characteristic frequency ν 0 of the FDB curves is therefore also smaller (see Table 2). Particles with a larger γ m produce emission of a given frequency at higher altitudes with larger curvature radii, which produce a wider beams (panel c in Fig. 9) with a large char- frequency ν 0 (Table 2). If the energy distribution of particles is rather wide, e.g. for a model with a larger σ γ , the emission region at a given frequency is very extended along field lines. However the dominant emission always comes from a lower emission height, and the integrated profile and hence the beam is much less sensitive to frequencies (panel d in Fig. 9). The particle distribution ( η m ) is directly related to the field lines where the emission is produced. It is easy to understand that particle distributed with a small η m tends to emit with a smaller beam at any frequencies (panel e in Fig. 9). We noticed that the particle distribution width σ η does not have obvious influence on the FDB curves ( panel f in Fig. 9). To further investigate the frequency dependence of pulsar beam radius on model parameters in a wide range of values, we have calculated the emission intensity distribution and integrated profiles (as shown in Fig. 7 and Fig. 8) for 6375 combinations of different parameter values: α = (5 · , 25 · , 45 · , 65 · , 85 · ), β = (1 · , 3 · , 5 · , 7 · , 9 · ), γ m = (200, 250, 300, 250, 400), σ γ = (10, 30, 50), η m = (0 . 3, 0 . 5, 0 . 7, 0 . 9) and σ η = (0 . 05, 0 . 1, 0 . 15, 0 . 2, 0 . 25). Pulsar period is fixed to be P = 1s. The frequency dependence of beam radii are fitted with Eq. (3) to get k and ν 0. We got the distributions of k and ν 0 from these combinations as shown in Fig. 10. We found that values of k are in the range of -0 . 2 to -2 . 7, consistent with observed values. However, profile components always merge to one component above ∼ 300 MHz , which is very different from observational facts of cone-dominant pulsars (Mitra & Rankin 2002). We show in Fig. 11 the profile evolutions for two extremes of k values: k = -2 . 64 and k = -0 . 32. For the case of k = -0 . 32, the two profile components merge even at a very low frequency below 100 MHz . The merging happens when γ m < 250 or σ γ > 30 or η m < 0 . 5 or σ η > 0 . 15. We noticed that when γ m > 350, for models of curvature radiation from particles in the conal density distribution, the emission below about 100 MHz comes from the region of several thousands of R /star , which leads profiles as wide as about 200 · . In summary, though curvature radiation models of particles in a conal density distribution can produce a proper range of k , the merging of profile components above few hundreds MHz is the main reason to reject the models for cone-dominated profiles.",
"pages": [
4,
5,
6
]
},
{
"title": "3.3. Emission beam from particles of two density patches",
"content": "In the inner gap model (Ruderman & Sutherland 1975), the sparkings do not continually happen above the polar cap and are not concentrating in a ring area to produce the conal density distribution discussed above. The most probably case is that the sparkings occur separately above the polar cap, which produce the subbeams of the observed conal beam (Rankin 1983) or the patchy beam (Lyne & Manchester 1988; Han & Manchester 2001). In the following we work on the models of curvature radiation of particles in two density patches which could be reasonably produced by two sparkings in the inner gap of a rotating neutron star. The density distribution of two patches can be defined on the",
"pages": [
6
]
},
{
"title": "AND σ φ",
"content": "For simplicity, we model two density patches (see Fig. 12) which are symmetrically located about the meridional plane and peaked at ( η m , φ m ) and ( η m , -φ m ), respectively, with Gaussian widths of σ η and σ φ in the magnetic polar and azimuthal directions, i.e. The distribution of the emission intensity across height and the rotation phase and the evolution of integrated profiles with frequency for the curvature radiation model from particles of two density patches are shown in Fig. 13 and 14, respectively. Our model calculations show that: 1) the leading component is always slightly wider and weaker than the trailing one; 2) emission at a lower frequency comes from relatively higher and wider region (10 -50 R /star for 400 MHz compared to 8 -20 R /star for 1 . 6 GHz); 3) the low-frequency profiles become wider and are always remain resolved even at very high frequencies, because two density patches keep separated even down to the star surface. From simulated profiles at a set of frequencies, we calculated the beam radius and checked the frequency dependence of pulsar beam. We also checked if FDB curves are related to emission geometry ( α , β ), particle energy distribution ( γ , σ γ ) and patch geometry ( η m , σ η , φ m and σ φ ). The curves are shown in Fig. 15 and fitted parameters are listed in Table 3. The influence of these parameters on the FDB curves are more or less similar to those found from the conal density models. We noticed that φ has the similar effect on the FDB curves as η , both of which determine the separation of the two patches. Particles in two patches with a larger σ φ can produce the emission beams with a steeper FDB curve. (a) k = - 2 . 02 To investigate the possible range of k and ν 0 in the two density patch model, we have calculated the integrated profiles and fitted the FDB curves for 29070 sets of models with different combinations of model parameters of α = (5 · , 45 · , 85 · ), β = (1 · , 5 · , 9 · ), γ m = (200, 300, 400), σ γ = (10, 50, 90), η m = (0 . 1, 0 . 3, 0 . 5, 0 . 7, 0 . 9), σ η = (0 . 05, 0 . 1, 0 . 15, 0 . 2, 0 . 25), φ m = (25 · , 45 · , 65 · , 85 · ) and σ φ = (5 · , 15 · , 25 · , 35 · , 45 · ). The distributions of the power-law indices k and the characteristic frequency ν 0 are shown in Fig. 16. We noticed that k values are in the range between -0 . 1 and -2 . 5. Two components are always resolved, except for the extreme case shown in Fig. 17(a) in which emission is radiated by particles with a narrower energy distribution ( σ γ = 10) and peaking at a larger energy ( γ m = 400) at very high η m = 0 . 9 and φ m = 65. In above beam calculations, we used the profile width W 10 at 10% of pulse peak. If the separations Wpp of two components are used to calculated the beam radii, the beam sizes are obviously smaller than those calculated from the 50% and 10% widths (Fig. 18). We compared in Fig. 19 the k and ν 0 values calculated from ϑ 10 (written as k 10 and ν 0 , 10) with the k and ν 0 values from ϑ pp (written as kpp and ν 0 , pp ), and found that they are correlated and scatter at small ν 0 or large k values (due to error-bar as expected). In summary, the curvature radiation from particles in two density patches can not only give a proper range of k values, but also keeps the two components resolved in general even at very high frequencies.",
"pages": [
7,
8
]
},
{
"title": "4. DISCUSSIONS",
"content": "In the previous section, we conclude that the FDB curves with two resolved components can be preferably explained by curvature radiations of particles in two density patches. Here we discuss influences on the FDB curves by the radial decay of particle energy and by other possible energy distribution of particles, and discuss the possible FDB curve flattening at low frequencies. Finally we will look at the real FDB data and make a model.",
"pages": [
8
]
},
{
"title": "4.1. Radial decay of particle energy and the lowest emission height",
"content": "As shown in Fig. 9 and 15, the values of beam radii at the infinite-frequency, ϑ 0, calculated from models are always very close to those of β , no matter what model parameters are in putted. However, both on observational ground (Table. 1) and theoretical expectations, ϑ 0 is larger than β . In simulations above we assume that particles in the magnetosphere have a Gaussian energy distribution with a peak Lorentz factor γ m and a spread width σ γ along the whole trajectory. In reality, the particle energy distribution may be much more complicated due to the Compton loss (Zhang et al. 1997) or other processes. It is reasonable to believe that particle energy decreases when they flow out along the field lines in the inner magnetosphere. In the vacuum-gap model (Ruderman & Sutherland 1975), electron-positron pairs are produced by the avalanche process in the pulsar polar cap. The maximum Lorentz factor of the primary particles after accelerating across the gap is γ max = 1 . 2 × 10 7 B /star 12 h 2 4 / P 1s, with B /star 12 = B /star / 10 12 G the surface magnetic field, h 4 = h / 10 4 cm the gap height and P 1s = P / 1s. Pair cascade occurs within a few stellar radii near the surface, which generates the secondary particles with much lower Lorentz factors of a few hundred. Detailed numerical simulations on the pair cascade process were carried out by Medin & Lai (2010), in which they found that for various initial parameters (such as surface magnetic field, period and primary energy), the pair cascade process maybe finishes at a height of several star-radius, from less than 2 R /star to more than 10 R /star . Here we naively assume a toy model to describe the rapid decay of particle energy during the pair cascade process, which reads here γ m is the peak Lorentz factor of the Gaussian distribution we used above, γ m 0 and γ s are the corresponding values of the primary particles and the final secondary particles before and after the pair cascade, respectively. The factor q (less than 1) determines how fast the energy decreases with height for the cascade. This energy model has been used by Qiao et al. (2001) and Zhang et al. (2007) to simulate the inverse-Compton scattering emission, where they ignored the energy term γ s . To use the above energy model in our simulation for the model for two density patches, one should substitute γ m of Eq. (16) into the Gaussian energy distribution Eq. (9). Note that the number of the particles n e0 in Eq. (15) should also be replaced by n e0 γ s /γ m to keep the conservation of total energy. Example FDB curves from the curvature radiation model by particles in two density patches with an energy distribution described by Eq. (9) and Eq. (16) are demonstrated in Fig. 20, and the fitted parameters are listed in Table. 4. We found that a larger primary Lorentz factor γ m 0 or a smaller q lead to larger beam radius ϑ 0 at very high frequencies. A larger γ s leads to a steeper FDB curve. In these model the values of ϑ 0 are always larger than those of β , which means that there exists the lowest radio emission height r low = R lc sin 2 (2 ϑ 0 / 3), which is > R lc sin 2 (2 β/ 3). For a small value of ϑ 0, the corresponding beam radii at the infinite frequency can be written as ϑ 0 /similarequal 3 / 2 √ r low / R lc. Now, what is the value of r low? According to Eq. (16), at the lowest radio emission height r low, there exists a characteristic Lorentz factor γ c . We noticed that r low and γ c are related with γ m 0 and q by: From simulations similarly as presented Table 4, we can get a set of r low from ϑ 0 for various γ m 0 and q , and then we got γ c using Eq. (17). We find that γ c are also very well related to γ m 0 and q , as shown in Fig. 21, by Substituting into Eq. (17), we find",
"pages": [
8,
9
]
},
{
"title": "4.2. On the energy distribution of particles",
"content": "At any height, the secondary particles in the magnetosphere for the curvature radio emission were assumed to have an energy distribution in the Gaussian function. It is possible that the particles follow other energy distribution functions. For example, according to Arons (1981), the multi-component plasma in pulsar magnetosphere contains secondary pairs, a high-energy plasma 'tail', and some primary particles. The joint energy distribution of secondary particles and high-energy 'tail' can be described by a power-law with two cutoffs at its two ends, which reads as, where s is the power-law index. The curvature radiation from particles in two density patches with such an energy distribu- with a similar shape and a constant pulse width between 80 MHz and 40 GHz, as shown in Fig. 22. We can not find the profile differences for a range of s values, e.g. a difference less than 2% for the pulse width values between s = -2 and s = -3. We also found that the values of γ s , min and γ s , max determine the frequency range for the constant profile width.",
"pages": [
9,
10
]
},
{
"title": "4.3. Possible low frequency flattening of the FDB curves",
"content": "During the model calculations, we noticed that the FDB curves tend to be flattening at low frequencies. For some input parameters of the two density patch model, the effect is very obvious (Fig. 23), especially when Lorentz factors are large ( γ m > 400) and/or the energy distribution is broad ( σ γ > 80). This is understandable. Because of the dipole bending of magnetic field lines, as pulsar rotates, a fixed sight-line cut across the two density patches (see Fig. 12) with a clear lower limit and upper limit of height and a clear left and right limit of the rotation phase. Very low frequency emissions tend to come from the high regions of two patches in such a limited volume. In that high regions near the upper bound, the lower frequency emission comes from particles of the lower energy, but the pulse-width or beam-width of the emission from two patches is determined by the geometry. This happens to very low-frequency, depending on the γ m . The low-frequency flattening of FDB curves are often seen in the models when patches are small (small σ φ ), or energy of particles are very high and/or the energy distribution is broad (large γ m and σ γ ).",
"pages": [
10
]
},
{
"title": "4.4. Observed FDB curve and a model",
"content": "We have worked on a huge number of models for the radio emission intensity distribution across the height and rotation phase and integrated profiles. We now look at data of a real cone-dominant pulsar, PSR B2020+28, and make a model. The data are taken from (Mitra & Rankin 2002). To keep the two profile components separated even at very high frequencies, we have to choose a model of the curvature radiations of particles in two density patches and consider the energy distribution of particles as described by Eq. (9) and Eq. (16). As shown in Figure 24, the model can fit data nicely with a local minimum of χ 2 = 10 . 24 in the parameter space of γ s and q . The model is obtained with sparsely separated parameter grids, which may be improved by a global fitting for 8 parameters but that is very computational expensive.",
"pages": [
10
]
},
{
"title": "5. SUMMARY AND OUTLOOK",
"content": "We studied the frequency dependence of beam radius for cone-dominant pulsars by using the curvature radiation mechanism. For the simplest case in which pulsar radio emission is generated by curvature radiation of relativistic particles with a single γ and streaming along fixed open field-lines, we obtain the analytic formula in Eq. (7) for the frequency dependence. It has the power-law index k = -1, and ϑ 0 = 0, both are different from observations. Considering various density distribution and energy distribution of particles, we numerically calculated the intensity of curvature radiation from all the possible emission heights in the open field line region, and get integrated mean pulse profiles from which the FDB curves are derived. We found that the power-law index k and ϑ 0 are strongly influenced by the density distribution and energy distribution of particles in the open field-line region. When particles are uniformly distributed in whole open field lines, the curvature radiation can produce only one profile component, which can not explain the two resolved components of cone-dominant pulsars. Whenparticles are distributed in a conal area, the low-frequency emission comes from very high regions so that profile is very wide. Profiles at high frequencies cannot have two separated components, because emission comes from low heights where the sight line always continually cuts the edge of density cone. To keep two profile components separated or resolved, the particles must come from two density patches. Model calculations from a huge amount of parameter combinations show that the k values of the FDB curves are in the range of -0 . 1 to -2 . 5, in agreement with the observations. Because of the limited upper boundary of the density patches cut by a given sight line, the FDB curves tends to be flattened at low frequencies, especially for models with a large Lorentz factor and/or broad particle energy distribution. The geometry of density distribution of particles and the energy distribution of particles in the model certainly affect the FDB curves. For a Gaussian energy distribution, high energy particles with large γ m will produce a wide beam at low frequency. Particles in a narrow energy distribution with a small σ γ produce a steep FDB curve. The radial decay of particle energy is important to get a reasonable ϑ 0 in models. Through model calculations of pulsar beam and profile evolution by using the curvature radiation mechanism, we have clarified some important issues on particle density and energy distributions. However, in our simulations, we considered only the simple case that particles are emitting radio waves with the characteristic frequency for curvature radiation determined by the Lorentz factor. The real curvature emission of any particles has an energy spectrum, which is a power-law with an index 1 / 3 at the low frequency limit (much less than the characteristic frequency) and becomes exponential at high frequencies. This may significantly affect the emission regions and modify the FDB curves, which we should investigate in future. Another important fact is that the real pulsar radio emission is believed to be highly coherent, while in this paper we simply treat the coherence by assuming that the emission comes from point-like huge charge. Moreover, other emission mechanisms may also work in pulsar magnetosphere, such as inverse Compton scattering, plasma oscillation, cyclotron instability and Coulomb bremsstrahlung emission, etc, which are not considered in this paper and may lead to their own FDB curves. The authors thank Professor Chou Chih Kang for helpful discussions and the referee for constructive comments. This work has been supported by the National Natural Science Foundation of China (11003023 and 10833003). Arons, J. 1981, in ESA Special Publication, Vol. 161, ESA Special Publication, ed. T. D. Guyenne & G. Lévy, 273 Beskin, V. S., Gurevich, A. V., & Istomin, Y. N. 1988, Ap&SS, 146, 205 Biggs, J. D. 1990, MNRAS, 245, 514 Buschauer, R. & Benford, G. 1976, MNRAS, 177, 109 Cordes, J. M. 1978, ApJ, 222, 1006 Dyks, J. & Harding, A. K. 2004, ApJ, 614, 869 Dyks, J., Wright, G. A. E., & Demorest, P. 2010, MNRAS, 405, 509 Everett, J. E. & Weisberg, J. M. 2001, ApJ, 553, 341 Gangadhara, R. T. 2004, ApJ, 609, 335 Gangadhara, R. T. 2005, ApJ, 628, 923 Gil, J. 1981, Acta Phys. Pol., B12, 1081 Han, J. L. & Manchester, R. N. 2001, MNRAS, 320, L35 Lyne, A. G. & Manchester, R. N. 1988, MNRAS, 234, 477 Machabeli, G. Z. & Usov, V. V. 1989, Sov. Astron. Lett., 15, 393 Manchester, R. N. 1995, J. Astrophys. Astr., 16, 107 Medin, Z. & Lai, D. 2010, MNRAS, 406, 1379 Mitra, D. & Rankin, J. M. 2002, ApJ, 577, 322 Phillips, J. A. 1992, ApJ, 385, 282 Qiao, G. J., Liu, J. F., Zhang, B., & Han, J. L. 2001, A&A, 377, 964 Rankin, J. M. 1983, ApJ, 274, 333 Rankin, J. M. 1990, ApJ, 352, 247 Ruderman, M. A. & Sutherland, P. G. 1975, ApJ, 196, 51 Thorsett, S. E. 1991, ApJ, 377, 263 Vitarmo, J. & Jauho, P. 1973, ApJ, 182, 935 Xilouris, K. M., Kramer, M., Jessner, A., Wielebinski, R., & Timofeev, M. 1996, A&A, 309, 481 Zhang, B., Qiao, G. J., & Han, J. L. 1997, ApJ, 491, 891",
"pages": [
10,
11
]
}
]
2013ApJ...768..181V
https://arxiv.org/pdf/1302.4308.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_82><loc_88><loc_86></location>Interacting Galactic Neutral Hydrogen Filaments and Associated High-Frequency Continuum Emission</section_header_level_1>
<text><location><page_1><loc_42><loc_78><loc_58><loc_80></location>Gerrit L. Verschuur</text>
<text><location><page_1><loc_22><loc_75><loc_78><loc_77></location>Physics Department, University of Memphis, Memphis, TN 38152</text>
<text><location><page_1><loc_41><loc_72><loc_59><loc_73></location>[email protected]</text>
<section_header_level_1><location><page_1><loc_44><loc_67><loc_56><loc_69></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_29><loc_83><loc_64></location>Galactic HI emission profiles in an area where several large-scale filaments at velocities ranging from -46 km s -1 to 0 km s -1 overlap were decomposed into Gaussian components. Eighteen families of components defined by similarities of center velocity and line width were identified and related to small-scale structure in the high-frequency continuum emission observed by the WMAP spacecraft, as evidenced in the Internal Linear Combination ( ILC ) map of Hinshaw et al. (2007). When the center velocities of the Gaussian families, which summarize the properties of all the HI along the lines-of-sight in a given area, are used to focus on HI channel maps the phenomenon of close associations between HI and ILC peaks reported in previous papers is dramatically highlighted. Of particular interest, each of two pairs of HI peaks straddles a continuum peak. The previously hypothesized model for producing the continuum radiation (Verschuur, 2010) involving free-free emission from electrons is re-examined in the light of the new data. By choosing reasonable values for the parameters required to evaluate the model, the distance for associated HI -ILC features is of order 30 to 100 pc. No associated H α radiation is expected because the electrons involved exist throughout the Milky Way. The mechanism for clumping and separation of neutrals and electrons needs to be explored.</text>
<text><location><page_1><loc_17><loc_24><loc_63><loc_26></location>Subject headings: ISM:atoms - ISM:clouds - cosmology</text>
<section_header_level_1><location><page_1><loc_42><loc_18><loc_58><loc_19></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_11><loc_88><loc_16></location>In three previous reports (Verschuur, 2007a: Paper 1; 2007b; 2010: Paper 2) 108 close associations between foreground galactic neutral hydrogen (HI) features and small-scale structures found in the Wilkinson Microwave Anisotropy Probe ( WMAP ) Internal Linear</text>
<text><location><page_2><loc_12><loc_71><loc_88><loc_86></location>Combination ( ILC ) map of Hinshaw et al. (2007) were listed. The latter structures are purported to have a cosmic origin while the former are features within the disk of the Milky Way relatively close to the Sun. In Paper 2 it was argued that a possible mechanism for generating the necessary high frequency continuum radiation is free-free emission from electrons produced by localized ionization of hydrogen. However, no associated H α radiation is found and hence the model appears to fail. In this paper the mechanism is re-considered in the light of what is revealed of the HI properties through the Gaussian analysis of emission profiles.</text>
<text><location><page_2><loc_12><loc_52><loc_88><loc_69></location>Since the onset of work on the associations between HI features and peaks in the ILC data, the manner in which the HI data have been considered has evolved. In Paper 1, associations were found by comparing ILC data with structure found in HI area maps produced at 10 km s -1 intervals, each covering an effective velocity range of 11.3 km s -1 . In Paper 2 HI data were displayed in velocity maps made with a 3.3 km s -1 effective bandwidth plotted every 2 km s -1 in velocity. These revealed the presence of the HI -ILC associations more clearly. The present study shows that when maps of the column density of HI Gaussian component families are compared to ILC features, the relationship becomes even more revealing.</text>
<text><location><page_2><loc_12><loc_37><loc_88><loc_50></location>In § 2 some of the HI data used in this study are displayed and in § 3 the Gaussian analysis is described. In § 4 the results of sorting Gaussian components into families are presented and their morphological relationship to the high-frequency continuum emission structure is shown in § 5. The apparent failure of the previously suggested model for producing the highfrequency continuum radiation is considered in § 6. The discussion section in § 7 shows that the model does work when it is recognized that the necessary electrons already exist in the interstellar medium. Conclusions are offered in § 8</text>
<section_header_level_1><location><page_2><loc_43><loc_30><loc_57><loc_32></location>2. The Data</section_header_level_1>
<text><location><page_2><loc_12><loc_23><loc_88><loc_28></location>The HI spectral line data used in this paper were drawn from the Leiden-ArgentinaBonn (LAB) All-Sky HI Survey (Kalberla et al. 2005) performed with a 0. · 6 beam width and a 1.3 km s -1 velocity resolution.</text>
<text><location><page_2><loc_12><loc_12><loc_88><loc_21></location>To describe the context of the work to follow, Figure 1 displays five HI contour maps of brightness temperature in a 3.3 km s -1 bandwidth as a function of galactic coordinates, longitude (GLON or l ) and latitude (GLAT or b ), for an area bordered by l = 70 · & 110 · and b = 50 · & 70 · . Such maps were produced and examined at 2 km s -1 intervals from +14 km s -1 to -70 and then every 4 km s -1 to -160 km s -1 with respect to the local standard</text>
<text><location><page_3><loc_12><loc_83><loc_88><loc_86></location>of rest. Contour levels are shown in the captions. The velocities of these displayed examples were chosen to illustrate several key points in the analysis to follow.</text>
<text><location><page_3><loc_12><loc_66><loc_88><loc_81></location>Fig. 1a shows the HI brightness centered at a velocity of -46 km s -1 . A curving filamentary feature can be followed from ( l,b ) = (100 · , 70 · ) to ( l,b ) = (78 · , 50 · ). It will be referred to as Filament Alpha. A weak extension from ( l,b ) = (85 · , 57 · ) to ( l,b ) = (71 · , 50 · ) suggests that filaments may be overlapping in the area around ( l,b ) = (87 · , 59 · ). In the data of Hartmann & Burton (1997: page 131) Filament Alpha can be followed well beyond the bounds of Fig. 1a. Fig. 1b shows the HI morphology at -36 km s -1 . The HI distribution in the center is dominated by two peaks to be called South Pair. They appear to lie on Filament Alpha. However, other structure suggests that the picture may be more complex.</text>
<text><location><page_3><loc_12><loc_51><loc_88><loc_64></location>Fig. 1c shows HI brightness at -30 km s -1 . A part of a twisted S -shaped filament, named Gamma, runs across the center of the area terminating in a bright feature at ( l,b ) = (103 · , 61 · ) before turning south. The elongated peak at ( l,b ) = (89 · , 56 · ) appears to be an extension to this velocity of the southern component of South Pair. Fig. 1d shows the HI brightness at -13 km s -1 and a pair of peaks at ( l,b ) = (91 · , 62 · ) lies on Filament Delta that stretches to the lower-right corner of the area. These two peaks will be referred to as North Pair and they are located where Filament Delta crosses Filament Gamma.</text>
<text><location><page_3><loc_12><loc_44><loc_88><loc_49></location>Fig. 1e shows the HI brightness at +1 km s -1 . The bright HI feature at ( l,b ) = (87 · , 60 · ) lies on a complex filamentary feature labeled Beta and is located where Filament Beta overlaps Alpha; that is, between the two components of South Pair seen in Fig. 1b.</text>
<text><location><page_3><loc_12><loc_27><loc_88><loc_42></location>Fig. 1f shows the positive amplitude ILC peaks and the two areas labeled 1 & 2 marked by dashed lines are the boundaries within which Gaussian fitting was carried out. The firstyear ILC data used here is the same set used in Papers 1 & 2 drawn from Hinshaw et al. (2007), effective beam width 1 · , mapped as contours from +0.02 mK in steps of 0.03 mK. A visual comparison of the ILC data with this sample of HI maps shows associations between the two types of features. A concentration of low-velocity HI in the region of enhanced ILC emission seen around ( l,b ) = (80 · , 57 · ) is obvious. To avoid the complexity manifest in that region, the present study was limited to the Areas 1 & 2.</text>
<text><location><page_3><loc_12><loc_12><loc_88><loc_25></location>Fig. 2 shows channel maps for these two areas at the velocities indicated in the caption with the same ILC contours shown in Fig 1f overlain. The velocities were chosen based on the average velocities of individual Gaussian component families to be discussed below. Fig. 2a shows low-level HI features that precisely skirt the boundary of extended ILC structure. Fig. 2b shows the HI features labeled South Pair straddling an ILC peak and Fig. 2e shows North Pair. What is striking is that without exception the small-scale HI peaks are associated with and closely offset from equally small-scale ILC features. This offset between</text>
<text><location><page_4><loc_12><loc_69><loc_88><loc_86></location>the two types of radiation is what was reported in Papers 1 & 2. However, only one of the associations reported in Paper 1, Source 16 at ( l,b ) = (101. · 8, 59. · 5), is seen here. Its HI signature is evident in Figs. 2e & f. In Paper 1 the center velocity of S16 was listed as -5 km s -1 , but that analysis used area maps made every 10 km s -1 covering a band width of 11.3 km s -1 . Fig. 2f shows its peak to be at -9 km s -1 and illustrates that more is learned about HI -ILC associations when these narrower channel maps are used. While Paper 1 only revealed one pair of associations in this area, because it only considered the brightest ILC peaks, the maps in Fig. 2 reveal at least nine more closely spaced associations with no cases of direct overlap, which is true for most of the 108 pairs listed in Papers 1 & 2..</text>
<text><location><page_4><loc_12><loc_46><loc_88><loc_67></location>At this point the analysis could end because Fig. 2 clearly confirms what was found in other sections of sky as outlined in Papers 1 & 2. In general small-scale structure in the high-frequency background continuum radiation maps observed by WMAP as revealed in the ILC data is associated with, but slightly offset from, structure in galactic HI emission.. However, noting associations reveals nothing substantive about the physical properties of the HI being observed; for example, what are the volume densities and temperatures of the HI and what process could give rise to the associated high-frequency continuum emission? As the next step in this process, the efficacy of using Gaussian analysis to understand the HI properties was explored to determine if this clarifies the underlying physics that might, in turn, help understand the nature of the emission process giving rise to the high-frequency continuum radiation.</text>
<section_header_level_1><location><page_4><loc_39><loc_39><loc_61><loc_41></location>3. Gaussian Analysis</section_header_level_1>
<text><location><page_4><loc_12><loc_18><loc_88><loc_37></location>The HI area maps discussed so far reveal only the amplitude of the HI emission at a given velocity; they reveal little about the physics or dynamics of the structures that are present. HI emission profiles usually consist of multiple Gaussian components produced by concentrations of HI along the line-of-sight or by motion or temperature variations within coherent sub-features within a given volume of space. Each Gaussian is characterized by a peak brightness temperature, T B (max), a center velocity, v c , and a line width, W , the full width at half maximum brightness. The area maps in Figs. 1 & 2 represent the total of the brightness temperatures at any given velocity that is produced by overlapping components. The goal of the present study translates to untangling the Gaussian structure to identify the properties of the overlapping components.</text>
<text><location><page_4><loc_12><loc_11><loc_88><loc_16></location>The hypothesis that the HI component line shape is Gaussian rests on the assumption that motions within any mass of HI will show a random velocity distribution that can be described by a Gaussian function. However, Gaussian analysis of HI profiles is difficult</text>
<text><location><page_5><loc_12><loc_63><loc_88><loc_86></location>because a given solution may not be unique and that means that relatively few researchers have ventured into the realm of such analyses. The challenge has been discussed by Verschuur (2004), Verschuur & Peratt (1999), and Verschuur & Schmelz (2010). The algorithm used in the present Gaussian decomposition of LAB profiles was described by Verschuur (2004). A crucial difference between this approach and the totally automated analysis used by, for example, Haud (2000) and subsequently by Haud & Kalberla (2007), is that in the present study each profile and the associated Gaussian fit is examined visually to assure that the results are consistent. The problem is that the Gauss fitting algorithm is set to minimize residuals and false minima can be found for a set of Gaussian components that bear no relationship to the profiles in their immediate vicinity. While other researchers may have attempted to design their algorithms to take in account neighboring solutions, in our experience that is not necessarily sufficient, as will illustrated with examples to follow.</text>
<text><location><page_5><loc_12><loc_52><loc_88><loc_61></location>Gaussian decomposition of HI profiles in the present study was performed for Areas 1 & 2 (Fig. 1f) using profiles every 1 · in l and 0. · 5 in b . At the latitude of these areas (60 · ) this created a uniform sampling grid of 588 profiles separated in real angle of 0. · 5 in both coordinates. The Gaussian decompositions allowed the fitting of up to 9 components although very few profiles actually required that many.</text>
<text><location><page_5><loc_12><loc_12><loc_88><loc_50></location>During the analysis it became clear that Gaussian decomposition is subject not only to the presence of noise but is especially vulnerable to non-noise-like low-level (interference?) features found even in the baseline areas of the LAB profiles where no HI is present. In some profiles these showed a negative amplitude. When they occured at a velocity at the edge of a profile, the properties of the component fit that included the relevant velocity range could be dragged to apparent line widths that were either higher or lower than those found for similar components in neighboring profiles. This problem could only be identified by visually examining the Gaussian fits. Obviously there is no way to detect the presence of such non-noise-like deviations within the velocity range of the HI emission itself, which contributes to noise in the values of the derived component parameters. Visual examination of each Gauss fit compared to neighboring profiles allows the distortion produced by these non-noise structures near the profile edges to be recognized and the algorithm was then run with a different initial setting to produce a results consistent with neighboring profiles. In several profiles small interference spikes in only one channel were present and in two profiles single-channel negative spikes that could be confused with narrow absorption lines occurred at velocities that also contributed to producing spurious Gaussian parameters. These obvious cases were dealt with by canceling the problem spike in a given channel. It is highly doubtful that an automatic Gaussian analysis could deal with these problems unless it used advanced AI techniques.</text>
<text><location><page_6><loc_12><loc_73><loc_88><loc_86></location>To initiate the search for the best-fit Gaussians for any given profile, the results for an adjacent solution were used. When the results of a given initialization were clearly inconsistent with the trends observed in surrounding profiles, the profile was re-initialized using another of the adjacent Gauss fits. Note that while the process of fitting Gaussian components to individual profiles is inherently noisy, the data for an ensemble of fits do produce coherent patterns in column density maps that allow families of components to be recognized and mapped.</text>
<text><location><page_6><loc_12><loc_52><loc_88><loc_71></location>A pervasive, underlying broad line width component is the signature of every profile, both at LV and IV. Its width is predominantly about 33 km s -1 . However, after the initial analysis and sorting of families of Gaussian and making maps of the HI column densities in Area 2, a systematic error was recognized that was readily rectified. The data showed that the broad components often manifested line widths of order 24 km s -1 in addition to the 33 km s -1 regime. When maps of the narrow line width components were made it was found that the dominant one, called LV1, to be discussed below, was absent in the those directions where 24 km s -1 wide components were found. Thus the initially produced area map of the HI column density for LV1 had holes in the directions where the Gauss fitting routine had found a solution involving a broad component of order 24 km s -1 wide.</text>
<text><location><page_6><loc_12><loc_26><loc_88><loc_50></location>The profiles in those direction were therefore reconsidered and it was found that a significantly better fit could be obtained by initializing the algorithm using the nearest solutions in which the 33 km s -1 lines was present. Thus the 24 km s -1 components turned out to be the result of a self-perpetuating fit that produced false minima. The relevant profiles were rerun and subsequent mapping of component LV1, using the better Gauss fits, did not show any holes. In fact LV1 is found to be pervasive, as are the underlying broad components of order 33 km s -1 wide, see tables below for details. This unfortunate state of affairs and its rectification is highlighted because automated Gaussian fitting programs are subject to the problem of false minima in residual phase space and future attempts to duplicate the present study should pay close attention to the result for given profiles to make sure no such systematic effects creep in. Fortunately, such effects stamp their presence of otherwise ordered column density maps, which allows their presence to be recognized.</text>
<text><location><page_6><loc_12><loc_11><loc_88><loc_25></location>Figure 3 illustrates several examples of Gaussian fitting to a variety of profiles at the positions indicated. Fig. 3a shows a profile defined by a single, underlying broad component with line width W = 36.2 km s -1 at v c = -8.9 km s -1 . The profile just 1 · away in longitude shown in Fig. 3b reveals the presence of a second underlying broad component at intermediate velocity (IV) v c = -30.0 km s -1 with W = 35.1 km s -1 while the other is at low velocity (LV) centered at v c = +0.7 km s -1 with W = 33.9 km s -1 . The separation on the sky of these two profiles is 0. · 5 in true angle and serves to illustrate the tremendous amount</text>
<text><location><page_7><loc_12><loc_79><loc_88><loc_86></location>of structure found in the HI distribution. Fig. 3c shows two broad underlying components whose presence is easy to discern because they manifest so clearly in the wings of the overall profile. The broad IV component has W = 35.1 km s -1 while the LV broad component has W = 34.8 km s -1 .</text>
<text><location><page_7><loc_12><loc_58><loc_88><loc_77></location>The profile displayed in Fig. 3d is notable because of the presence of a narrow component at the center of the profile, only 3.4 km s -1 wide. The underlying broad components for this profile are 37.5 km s -1 wide at IV and 37.2 km s -1 wide at LV. In adjacent profiles the amplitude of the HI emission between velocities of -80 and -30 km s -1 produced an almost straight line slope and solutions were only obtained by painstakingly using the surrounding profiles to find a fit consistent with the trends in the data around those positions. It seems very unlikely that an automated program would find solutions to such a profile. Fig. 3e shows an extremely bright and narrow center component 3.0 km s -1 wide at -17.2 km s -1 , which is part of component family LV13, see below. The associated broad components are 27.8 km s -1 wide at -47.8 km s -1 and 36.8 km s -1 wide at -5.0 km s -1 .</text>
<text><location><page_7><loc_12><loc_47><loc_88><loc_56></location>Fig. 3f shows a profile where the peak brightness temperature at IV and LV are maxima for the entire mapped area. The underlying broad components have W = 30.6 km s -1 at IV and W = 32.0 km s -1 at LV. The fact that both peaks reach maxima here is an indication that the structures at IV and LV are directly related, as will be discussed in the context of examining all the data, below.</text>
<section_header_level_1><location><page_7><loc_28><loc_40><loc_72><loc_42></location>4. Sorting Gaussians into parameter families</section_header_level_1>
<text><location><page_7><loc_12><loc_21><loc_88><loc_38></location>Gaussian analysis of 288 profiles yielded 3,706 Gaussian components that were sorted into 18 distinct families most of which were recognized in both Areas 1 &2. The sorting of Gaussians into families was usually straightforward because of clear continuity in center velocity and/or line width that could be followed across many adjacent profiles. When the data were gathered into families and plotted as area maps, the presence of components that had not been assigned to the correct family was quickly apparent. They could then be assigned to the appropriate family and the resulting maps show a high degree of order as will be displayed below. Only six components could not be fit into any of the families and may be regarded as noise in the data.</text>
<text><location><page_7><loc_12><loc_12><loc_88><loc_19></location>Table 1 summarizes the key properties of component families for the Area 1 and Table 2 applies to Area 2. Col. 1 gives the name of the family, Col. 2 lists the number of Gaussians used to define the family, Col. 3 lists the average center velocity, v c , for the family and Col. 4 its average line width (full-width, half-maximum), W , both with one standard deviation</text>
<text><location><page_8><loc_12><loc_71><loc_88><loc_86></location>errors. Col. 5 lists the peak column density found for a given family. Table 3 summarizes all the family data. Col. 1 is again the family name, Col. 2 is the total HI column density summed over all the members of that family in both Areas and Col. 3 is the fraction of the total column density for a given family. The average column density of the family is given in Col. 4 and the peak value in Col.5, which corresponds to the value in either Table 1 or 2. Of these component families three (Broad LV, Broad IV and LV1) were found in all directions, although for some of the Broad IV features the amplitudes are so low as to be comparable to the peak-to-peak noise in the data.</text>
<text><location><page_8><loc_12><loc_31><loc_88><loc_69></location>For all the broad components listed in Tables 1 & 2, which includes 1176 cases, W = 33.1 ± 1.1 km s -1 . A simple test was performed to show that this large line width is not an artifact of the observing beam width encompassing velocity gradients within the beam to produce the higher line width values. HI profiles obtained by Verschuur (2013) toward a high-velocity HI feature known as A0 using the Green Bank Telescope (9. ' 1 beam width) were Gaussian analyzed and the results compared with a similar decomposition of profiles from the LAB survey toward the same feature. Both sets of data revealed an underlying broad component about 22 km s -1 wide with no hint of a 33 km s -1 wide component. Thus, in general, it is not simply an artifact of lower angular resolution that generates the 33 km s -1 wide components. It is notable that the present study did not reveal any convincing evidence for components that could be associated with a so-called WNM, of Warm Neutral Medium, at 8,000 K, which would produce line width of order 20 km s -1 . However, the data in Table 2 show that for two component families labeled IV-HV and HV the average line widths are in the 20 km s -1 regime. That is a property of anomalous velocity HI, not the gas at lower velocities. [In an unrelated and as yet unpublished study of the Gaussian component structure of high-velocity clouds by the author, the LAB data show that a component of order 22 km s -1 wide is common and also that another component about 34 km s -1 wide is present in many cases. In some directions, the HI emission profile can be fit by only one Gaussian, which is then found to be either about 22 or 34 km s -1 wide.]</text>
<text><location><page_8><loc_12><loc_10><loc_88><loc_30></location>When compared to Gaussian line width data obtained from totally unrelated studies the numerical value for the broad component line width is striking. Verschuur & Schmelz (2010) gathered together line width data in their Table 2 pertaining to an underlying broad linewidth background component reported in 9 published papers by various researchers as well as their own data that together produced W = 33.7 ± 2.4 km s -1 . This is essentially identical to the value of 33.1 ± 1.1 km s -1 in the present study. [The possible role of a mysterious plasma phenomenon known as the Critical Ionization Velocity effect in affecting the line widths of the broad components is discussed by Verschuur (2007b) and Verschuur & Schmelz (2010) and references therein. Further consideration of that poorly understood phenomenon is beyond the scope of the present study.] Several other families listed in Tables 1 & 2 include</text>
<text><location><page_9><loc_12><loc_75><loc_88><loc_86></location>1139 components with a weighted average line width of 14.6 ± 1.2 km s -1 . Again, this value is significant when compared to the results summarized by Verschuur & Schmelz (2010) in their Table 3 of 13.9 ± 0.9 km s -1 . For completeness, 10 entries in Tables 1 & 2 have W values between 4.1 & 8.1 km s -1 involving 923 components for a weighted average line width of 5.7 ± 0.6 km s -1 . The remaining 339 components have average line widths between 8.7 & 10.7 km s -1 to produce a weighted average line width of 9.6 ± 1.3 km s -1 .</text>
<section_header_level_1><location><page_9><loc_16><loc_68><loc_84><loc_70></location>5. The relationship between the HI component families and ILC peaks</section_header_level_1>
<text><location><page_9><loc_12><loc_61><loc_88><loc_66></location>The HI column density maps for the families of components are next plotted and compared with ILC data. What will become apparent is that a great deal more remains to be revealed about the crucial HI structure in future higher resolution studies.</text>
<text><location><page_9><loc_12><loc_34><loc_88><loc_59></location>Figures 4a -c show the morphology of the families of HI components at intermediate velocities from -48 to -35 km s -1 that encompass the emission from South Pair at the right-hand side. The ILC peak at l,b = (88. · 5, 58. · 5) bridges the space between the major peaks in the HI defining South Pair. A fourth IV component at -55 km s -1 seen in Fig. 4d is associated with ILC peaks at the top-left of the area. It is striking that South Pair is clearly defined by HI components with three distinct line widths, see Table 1. The Gaussian analysis does not reveal the greater extent of Filament Alpha in these HI column density maps since column density is given by the product of line width and amplitude. An intrinsically narrower yet bright feature may not stand out against a background of somewhat wider components, even if it is a member of the same family. The presence of three distinct component families with different line widths at the location of the northern half of South Pair may be indicative of the contributions from three distinctly different filaments whose existence can be inferred by close examination of Fig. 1.</text>
<text><location><page_9><loc_12><loc_11><loc_88><loc_32></location>Figure 5 shows area maps of the HI column densities for the families with v c between -26 & -19 km s -1 , LV11, 12, 13 & 14, compared to the ILC contours. Fig. 5a shows the patchy morphology of LV11 and its brightest peak appears to be associated with North Pair and another ILC peak at the left-hand edge of the map around l = 100 · is found in the region of more complex ILC structure. The members of the LV11 family were identified by similarities in line width. Fig. 5b shows the morphology of LV12 that is clearly related to the presence of the ILC peaks. Its average line width is similar to LV11 but its center velocities are very different, Table 1. Fig. 5c shows LV13 & 14 combined since their morphologies smoothly blend although their velocities show a considerable change from Area 1 to Area 2, see tables. Again, HI column density peaks are clearly associated with ILC peaks. When combined in Fig. 5d these four HI component families are located where several filaments</text>
<text><location><page_10><loc_12><loc_71><loc_88><loc_86></location>intersect or overlap, see Figs. 1c, d &e and the overall feature in Fig. 5d thus manifests variations along its length of center velocities and line widths. Together these patterns imply that a great deal of complexity is hidden from view because of the poor angular resolution of the available data. This is borne out by the HI profiles in the region of North Pair. They are extremely complex, see, for example, Fig. 3d, which makes the task of confidently identifying families of line widths in this area very difficult. What remains true, however, is that the HI column density maps reinforce the notion that HI and ILC structures are related, as is so clearly evident in Fig. 2.</text>
<text><location><page_10><loc_12><loc_56><loc_88><loc_69></location>Fig. 6 shows the morphology of the low velocity components. Fig. 6a plots the ILC contours on a map of component family LV1 that is found throughout the area and is therefore a pervasive background or 'field' component. Its morphology is not obviously related to the presence of ILC structure. Fig. 6b shows the morphology of LV2, which is part of Filament Beta (Fig. 1e) and this segment of filamentary structure is clearly related to the presence of the ILC peak where it appears to terminate at ( l,b = 88 · , 58 · ) but examination of Fig. 1e suggests it then curves back and away to the west from that terminus.</text>
<text><location><page_10><loc_12><loc_34><loc_88><loc_54></location>The high-frequency continuum radiation creating the ILC peak in South Pair originates in a volume of space where the two filaments, Alpha and Beta overlap. Also, very striking, is the fact that where the HI peak in IV-A ( v c = -38.6 km s -1 ) overlaps LV3 ( v c = -0 . 4 km s -1 ) at l,b = (87. · 0, 59. · 5) the HI brightness of both the IV and LV component is by far the greatest for the area mapped. The relevant profile is shown in Fig. 3f. This is strong circumstantial evidence that HI at very different velocities is somehow interacting and hence at the same distance. This phenomenon that HI at very different velocities is directly associated was also found in several areas described Paper 1. Fig. 6c shows the morphology of LV3 and its properties are so similar to LV2 that they could well be combined, yet they appear to represent two distinct families in one filamentary feature.</text>
<text><location><page_10><loc_12><loc_23><loc_88><loc_33></location>The other three frames in Fig. 6 show the HI column density maps for the remaining LV component families and the fact that the majority of the structures, albeit patchy, seem to be associated with immediately adjacent ILC features suggests that there is more to be learned from higher-resolution HI mapping. The HI associated with S16 discussed above can be seen in Figs. 6d & e and in this display is less dramatic than found in Figs. 2e & f.</text>
<text><location><page_10><loc_12><loc_10><loc_88><loc_22></location>For completeness, Fig. 7 gathers together the column density maps for the remaining component families. Fig. 7a shows the HI morphology for the LV broad line-width component and Fig. 7b is the same for the IV broad line-width family. There is some indication for diagonal features but these area maps are not readily related to the ILC structures. An exception is the bright patch just to the south of the North Pair ILC feature in Fig. 7a. It contributes to the pattern seen in Fig. 2b, center frame. Examination of the HI profile in</text>
<text><location><page_11><loc_12><loc_83><loc_88><loc_86></location>this direction again shows it to be extremely complex, similar to the profile in Fig. 3d, and the complexity can only be untangled using higher resolution HI data.</text>
<text><location><page_11><loc_12><loc_66><loc_88><loc_81></location>The final two frames in Fig. 7 refer to component families that were not a carefully mapped because their brightness temperatures are very low, barely above peak-to-peak noise in some cases. The case of Component IV-HV ( v c = -78 km s -1 ) is shown in Fig. 7c. In some directions its spectrum is well separated from the bulk of the HI emission in velocity while in other directions it overlaps the wings of the HI emission from the bulk of the IV gas. Yet, its peak column density lies toward the North Pair ILC peak. Finally, Fig 7d shows the column density map for weak high-velocity HI, called Component HV ( v c = -109 km s -1 ), which favors other peaks in the ILC map.</text>
<section_header_level_1><location><page_11><loc_30><loc_59><loc_70><loc_61></location>5.1. What the Gaussian mapping reveals</section_header_level_1>
<text><location><page_11><loc_12><loc_30><loc_88><loc_57></location>Overall, the goal of mapping Gaussian components with a view to clarifying the relationship between HI and ILC peaks has done little to reveal a more edifying picture. Instead the picture has become more complex. On the one hand there is strong evidence that HI at very different velocities appears to be involved where ILC peaks are located, and on the other hand those interactions are complex and somehow give rise to the small-scale structure in the high-frequency continuum radiation found in the ILC map. The patterns seen in the HI area maps displayed in Fig. 2 are also found in the Component maps, Figs. 4 -7, so the area maps at specific velocities determined by Gaussian family average velocities may be the most effective way to identify close associations between HI and small-scale ILC structure. This reduces the task from having to sort through 60 to 100 HI channel maps to find associations to considering only a dozen or so data sets determined by the identification of Gaussian families. Bear in mind that the HI column density maps of the ensemble of component families contain between them information about ALL the HI found over the total line-of-sight through any given area.</text>
<section_header_level_1><location><page_11><loc_29><loc_23><loc_71><loc_25></location>5.2. A note on the statistics of associations</section_header_level_1>
<text><location><page_11><loc_12><loc_12><loc_88><loc_21></location>In Paper 1 an attempt was made to show that the association between HI and slightly offset ILC features was significant. In Paper 2 it was shown that there is no evidence for widespread direct positional associations, which was never claimed in any case. Yet the question remained as to whether the near positional associations discussed here and in Papers 1 & 2 are significant or due to chance.</text>
<text><location><page_12><loc_12><loc_69><loc_88><loc_86></location>Interstellar HI structure is seen all over the sky and so is the structure revealed by ILC data. However, for any given area of sky as many as 100 HI area maps at velocities separated by 2 km s -1 need to be studied and the likelihood of chance associations becomes large. At the same time, the data discussed above and in Papers 1 & 2 show that no two examples of associations are identical. Providing convincing statistical arguments that a given association between an HI feature and one found in the ILC data is significant may be impossible. There is no a priori standard for defining an association that can be tested for statistically. Instead we must rely on looking at the actual data that show the associations clearly.</text>
<text><location><page_12><loc_12><loc_50><loc_88><loc_67></location>Seen from another perspective, the entire sky is filled with small-scale structure found in the high-frequency continuum emission observed by WMAP as revealed in the ILC map, which was produced after possible sources of intervening radiation had been removed, Hinshaw at al. (2007). But interstellar HI structure also covers the entire sky and that was not taken into account in the production of the ILC map. There would have been no a priori reason for doing so. While random coincidences in position between ILC and HI peaks are to be expected, this is not what is found. In general, apparently associated ILC and HI features are offset from one another by a small amount, on average 0. · 8, as stated in Paper 2, and estimated to be closer to 1 · for the patterns seen in Fig. 2.</text>
<section_header_level_1><location><page_12><loc_27><loc_43><loc_73><loc_45></location>6. The apparent failure of the previous model</section_header_level_1>
<text><location><page_12><loc_12><loc_28><loc_88><loc_41></location>The area maps presented in Fig. 2 reveal the presence of several sets of associated HI -ILC features. In Paper 2 it was suggested that the continuum radiation is produced by free-free emission from electrons interacting with electrons and that the excess electrons are produced by the ionization of hydrogen atoms where HI features interact. It was also noted that for the emission mechanism to account for the data, the continuum sources would have to be unresolved in the WMAP survey in order for the presence of the phenomenon to have been missed in the original ILC analysis of the WMAP data.</text>
<text><location><page_12><loc_12><loc_11><loc_88><loc_26></location>For the present data an order-of-magnitude calculation can be performed. For example for North Pair using the HI column density of the associated peak of 67 × 10 18 cm -2 (Fig. 5d), it is possible to calculate (using the formula derived in Paper 2, see Eqtn. 1, below) the degree of ionization required to produce the observed ILC peak of 0.08 mK. For a distance of 100 pc, an electron excitation temperature of 8,000 K, a source width of 0. · 2, and a depth along the line of sight equal to that width, the fractional ionization required is 0.45. The electron density that is implied is 28.3 cm -3 and the corresponding emission measure (given that the path length is known for a given distance) should produce H α emission at</text>
<text><location><page_13><loc_12><loc_69><loc_88><loc_86></location>a level of 125 R in the 1 · beam of the WHAM survey of Haffner et al. (2003). However, examination of the WHAM data reveals no such structure. The maximum emission measure over the relevant area of sky is 0.7 R, barely above a 0.5 R background level. Therefore, the hypothesis that the continuum peaks in the ILC data are due to free-free emission from electrons produced through localized ionization of the HI in the galactic disk, as suggested in Paper 2, fails. No combination of parameters (distance, angular size, aspect ratio, and excitation temperature) can account for both the observed continuum emission level and the lack of H α signal. But what, then, is the source for the high-frequency continuum radiation if the associations seen in Fig. 2 are real?</text>
<section_header_level_1><location><page_13><loc_43><loc_62><loc_57><loc_64></location>7. Discussion</section_header_level_1>
<text><location><page_13><loc_12><loc_27><loc_88><loc_60></location>The original goal of this project was to determine the properties of two pairs of HI features in directions where filaments cross and at which locations peaks in the ILC data were found. As a result of mapping families of Gaussian components in the area, the HI distribution was found to be more complex than the impression garnered from examining up to 100 area maps of brightness temperature at specific velocities at 2 km s -1 , for example. In instead the average velocities of the Gaussian families are used to focus attention on specific HI channel maps the relationship between HI structure and ILC structure emerges in dramatic detail, see Fig. 2. In fact, Fig. 2 & Figs. 4 -7 confirm the claims made in Papers 1 & 2 that close associations between small-scale HI and ILC features are real. However it is not immediately clear how the high-frequency continuum emission is generated in local interstellar space, local because the HI data discussed here is at high galactic latitudes of 60 · and the velocities imply a galactic origin. As this discussion proceeds it will become increasingly obvious that we are venturing into uncharted territory. The most fundamental issue that has yet to be resolved is at what angular scale both the HI and the ILC structures can be claimed to be resolved. Given that uncertainty it will be shown below that it is nevertheless possible to obtain an apparently good fit to the data using the model proposed in Paper 2.</text>
<text><location><page_13><loc_12><loc_12><loc_88><loc_25></location>A solution requires that several questions be answered. First, given that the free-free emission from electrons appears to work quite well as outlined in Paper 2, other than the absence of associated H α radiation, what might be the source of electrons so as to avoid the H α dilemma? A second question concerns what mechanism is operating to cause the HI and the electrons to cluster? Also, why would the neutrals and electrons cluster in slightly offset directions? Lastly, if a source of electrons can be identified and a mechanism for clustering suggested, is it still possible to account for production of the high-frequency continuum</text>
<text><location><page_14><loc_12><loc_85><loc_63><loc_86></location>radiation through invoking free-free emission from electrons?</text>
<section_header_level_1><location><page_14><loc_38><loc_78><loc_62><loc_80></location>7.1. Source of electrons</section_header_level_1>
<text><location><page_14><loc_12><loc_49><loc_88><loc_76></location>It is well known that free electrons exist everywhere in interstellar space as inferred from pulsar dispersion measures and radio source rotation measures. Average electron densities along path lengths of hundreds to thousands of pc are estimated to be in the range 0.03 to 0.3 cm -3 (see, for example, Wood & Linsky, 1997; Allen, Snow & Jenkins, 1990; Lyne, Manchester & Taylor, 1985). Unfortunately, essentially nothing is known about the clumping of these electrons along a given line-of-sight. In contrast, the clumping of the HI is its most basic characteristic, producing morphologies such as seen in Fig. 1. Using the data in Table 3 the average HI column density for the 588 lines-of-sight included in the study is 123 × 10 18 cm -2 . Assuming a typical path length of 100 pc the average HI volume density is 0.41 cm -3 . An average electron density of 10% of the HI, that is 0.04 cm -3 , lies in the range interstellar electron density from pulsar dispersion measure data. This offers a first-order approach to determining whether a reasonable set of parameters can be found that can be used with the electron Brehmstrahlung model to account for the observed amplitudes of the high-frequency continuum signals found in the ILC data.</text>
<section_header_level_1><location><page_14><loc_35><loc_42><loc_65><loc_44></location>7.2. Application of the theory</section_header_level_1>
<text><location><page_14><loc_12><loc_35><loc_88><loc_40></location>From Eqtn. 12 in Paper 2, the brightness temperature T B ( ν ) of the high-frequency continuum radiation at a frequency ν produced by free-free emission from (cold) electrons with an excitation temperature, T e , is given by:</text>
<formula><location><page_14><loc_20><loc_32><loc_88><loc_33></location>T B ( ν ) = 1 . 86 × 10 17 ν -2 T -0 . 5 e ln (4 . 7 × 10 10 T e /ν ) f 2 N 2 H ( θ o A L ) -1 K , (1)</formula>
<text><location><page_14><loc_12><loc_23><loc_88><loc_30></location>where N H is the observed HI column density in units of 10 18 cm -2 and the electron density is expressed as a fractional degree of ionization, f . The angular width of the electron enhancements (or cloud) on the sky is θ o and A is the Aspect Ratio, the depth of feature relative to its width. L is the distance in pc.</text>
<text><location><page_14><loc_12><loc_10><loc_88><loc_21></location>In order to evaluate Eqtn. 1, several assumptions have to be made and then, based on what is found, the direction of future research may be indicated. The electron excitation temperature is set to 100 K, the typical kinetic temperature of interstellar neutral hydrogen, bearing in mind that the data show little evidence for a Warm Neutral Medium at 8,000 K, as noted in § 4. The reasons for the Gaussian family line width much greater than expected for this temperature have been alluded to in § 4 and deserves a detailed discussion</text>
<text><location><page_15><loc_12><loc_69><loc_88><loc_86></location>beyond the bounds of the present study. [Such a discussion would in any case conclude that electrons exist in abundance that are not created by localized ionization of neutral hydrogen.] An angular width of the small-scale ILC features has to be assumed since the structures considered above are usually about 1 · across, which is the resolution of the ILC map. Thus it is fair to assume that the sources of high-frequency continuum radiation are unresolved on this scale. (Others with access to high resolution observations of the highfrequency continuum radiation should look into this issue; e.g., those who use the Planck spacecraft data.) In order to explore whether Eqtn. 1 works, the model amplitudes are calculated for the two ends of the WMAP band, 23 & 94 GHz, and then averaged.</text>
<text><location><page_15><loc_12><loc_37><loc_88><loc_67></location>Eqtn. 1 is applied to the two cases of close associations between HI and ILC peaks, North Pair and South Pair, and it is used to determine the distance at which it can account for the observed ILC positive amplitudes as a function of the required degree of ionization of the associated HI column density (as a first-order approach to the data). The results are shown in Fig. 9. For example, if the angular scale of the unresolved ILC peak in South Pair is 0. · 1 then the solid line in Fig. 9 so labeled indicates that for a range of electron densities equal to 0.10 to 0.17 times the associated HI peaks the distance of the source required to produce the observed ILC amplitude of 0.12 mK would be between about 30 and 100 pc. The calculation used the peak HI column density for IV-A as the guide to the column density of the associated electron cloud. It remains to be determined just what value should be used given that there are several distinct HI families of line widths involved in this direction, see Fig. 4. But to first-order the model does match the data. The difference between this calculation and the one reported in § 6 is that the electron temperature is not 8,000 K as would be expected from localized ionization of HI but closer to 100 K consistent with the temperature of the cold hydrogen atoms.</text>
<text><location><page_15><loc_12><loc_24><loc_88><loc_36></location>The fact that the curves in Fig. 9 for North Pair and South Pair appear to encompass a region of phase space that is reasonable as regards the required electron column densities and distances, for the 100 K regime, indicates that the possibility that the ILC structures are indeed located in the galactic disk relatively close to the Sun should be seriously considered. But what mechanism would simultaneously act to clump the neutrals and the electrons and have them physically separated yet close associated in space.</text>
<section_header_level_1><location><page_15><loc_16><loc_18><loc_84><loc_20></location>7.3. On the clumping and separation of electrons with respect to HI</section_header_level_1>
<text><location><page_15><loc_12><loc_11><loc_88><loc_16></location>Fig. 1 shows clear evidence for the presence of several large-scale filaments of HI in the area under consideration and Fig. 2 shows that HI and ILC features over the target area for this study are connected and offset from one another. These are observational facts that</text>
<text><location><page_16><loc_12><loc_81><loc_88><loc_86></location>have to be recognized. There appear to be several ways in which electrons and neutrals could become spatially separated in interstellar space, although none has been formally studied for such an environment. The options are only briefly mentioned here.</text>
<text><location><page_16><loc_12><loc_62><loc_88><loc_79></location>In a completely different astrophysical situation, namely the solar environment, many papers have deal with a phenomenon called the First Ionization Potential (FIP) Effect. It is used to account for the spatial separation either in layers in the solar atmosphere, or along flux tubes, of various atomic species. The FIP Effect is invoked to account for solar abundance variations that are otherwise difficult to comprehend. A number of references that indicate how the FIP Effect may be important include Raymond (1999), Laming (2009) and Schmelz et al. (2012). Another way of considering this is to recognize that the offset between the HI and ILC peaks is one of e/H abundance variations in interstellar space, either along a given filament or between adjacent volumes of space.</text>
<text><location><page_16><loc_12><loc_47><loc_88><loc_60></location>A little known instability occurring within flux tubes is described by Marklund (1979) who suggested that if an electric field is present in a plasma permeated by a magnetic field and has a component perpendicular to the field, the E x B force will cause electrons and ions, but not neutral particles, to migrate to the axis of a flux tube. As Peratt & Verschuur (2010) note, because of different ionization potentials of various atomic species and cooling within the filaments, ionic species will then separate within a flux tube. This mechanism, akin to the FIP effect, also has the seeds for separating the HI from the electrons.</text>
<text><location><page_16><loc_12><loc_11><loc_88><loc_45></location>Another possibility for separating electrons and neutrals may involve interacting magnetically controlled filaments. Fig. 1 shows two HI features, South Pair, which straddle a high-frequency continuum source, as displayed in Fig. 4a. In that same direction the data indicate that a number of filaments of HI intersect, see Fig.1. This raises the interesting possibility that magnetic reconnection may play a role in creating pockets of HI that are pulled away from a central X-neutral point where magnetic fields, likely to be present in the filaments, are reconnecting. The continuum radiation revealed in the ILC data is then being produced at the X-neutral point. Unfortunately the necessary theory to help account for the data invoking magnetic reconnection does not yet appear to exist. Priest & Forbes (2000) note that concerning the question of what actually happens to the particles at the X-point as regards energies and spectra, and how magnetic energy is converted to heat, kinetic energy and particle energy is largely unknown. They state that 'These apparently simple questions have not yet been answered fully [and] the answers are likely to be highly complex.' In this context they list at least 12 possible types of reconnection that may play a role. While their work also focused on events in the solar corona, future consideration of what may be occurring in interstellar space could clarify why so many associations exist between HI structures and high-frequency continuum peaks in the ILC data.</text>
<text><location><page_17><loc_12><loc_71><loc_88><loc_86></location>These tentative suggestions should not cause us to avoid what the data show, that galactic HI peaks (clouds?) and ILC peaks are associated and slightly offset from one another, perhaps even along the axes of one or more of the filaments that pervade a volume of interstellar space. The fact that even a simplistic consideration of the magnitudes of the parameters required to evaluate Eqtn. 1, Fig. 9, leads to reasonable values of the distance and electron densities is surely sufficient evidence that the issue is deserving of further study, given the importance attached to the conventional explanation of the ILC structure being at cosmological distances.</text>
<section_header_level_1><location><page_17><loc_42><loc_64><loc_58><loc_66></location>8. Conclusions</section_header_level_1>
<text><location><page_17><loc_12><loc_31><loc_88><loc_62></location>Galactic HI profiles in an area bounded by longitudes 85 · & 110 · and latitudes 55 · and 65 · were decomposed into Gaussians. The area was divided into two sections separated at l=85.5 and the analysis proceeded many months apart without cross-talk between them. In all, 588 profiles at 0. · 5 spacing netted 3,706 Gaussian components. These were sorted into 18 families, each defined by similarity of center velocity and line width. When the average velocities of the derived Gaussian families are used to focus attention on specific HI channel maps, associations between HI peaks and structure in the Internal Linear Combination ( ILC ) map of Hinshaw et al. (2007), based on the WMAP survey data, are dramatically revealed. These associations are confirmed by comparing the morphology of the column densities of the Gaussian families and the ILC structures. The step of first identifying Gaussian families in a given area of sky and using their center velocities as a guide, makes the task of finding associations with the ILC peaks manageable because only a fraction of the up to 100 channel maps that could be created for any area then need to be studied. In addition, given that the Gaussian families summarize the properties of all the HI along the line-of-sight in the area, statistical arguments about whether or not the associations are due to chance becomes less relevant.</text>
<text><location><page_17><loc_12><loc_20><loc_88><loc_29></location>The relationships between some of the families of HI Gaussian components show that despite their velocity differences they are physically related to one another and hence at the same distance. This phenomenon was also reported in Paper 1. This would never have been discovered if it were not for attention drawn to the properties of the HI because of the associations with small-scale ILC structure.</text>
<text><location><page_17><loc_12><loc_11><loc_88><loc_18></location>The Gaussian mapping reveals details in the HI morphology of several components at widely different velocities, from 0 km s -1 to -109 km s -1 . In an area labeled North Pair, two HI features straddle an ILC source that is located at the point of overlap of two filaments at velocities of order -30 and -13 km s -1 . Similarly, in an area named South Pair, two</text>
<text><location><page_18><loc_12><loc_79><loc_88><loc_86></location>HI peaks straddle an ILC peak and here the HI consists of three families of components at intermediate velocities around -36 km s -1 with average line widths of 14.7, 7.0 & 4.6 km s -1 found where HI filaments at distinctly different velocities, around 0 km s -1 & -38 km s -1 overlap.</text>
<text><location><page_18><loc_12><loc_58><loc_88><loc_77></location>The previously hypothesized mechanism for producing the high-frequency continuum radiation from interacting HI features in interstellar space involving free-free emission from electrons (Verschuur, 2010) is re-examined in the light of the new data. It is found to account for the existence of the small-scale ILC peaks if the sources are located from 30 to 100 pc from the Sun. The pervasive presence of interstellar electrons is revealed in observations of pulsar dispersion measures and to fit the model the of necessity cold electrons have to be clumped on scales that are similar to those seen in the HI distribution with densities from 10 to 25% of the immediately adjacent HI peaks. Associated H α radiation at the location of the ILC peaks is not expected because the source of electrons does not require the localized ionization of HI as was hypothesized in Paper 2.</text>
<text><location><page_18><loc_12><loc_43><loc_88><loc_56></location>In order to determine unequivocally whether or not the claimed associations are real, higher resolution observations are required. For example, Planck data should be compared with high-resolution HI observations obtained with suitably large radio telescopes, provided attention is focussed on high-latitude regions where the confusion created by having too much HI in the beam is minimized. In the meantime caution should be exercised in drawing far-reaching cosmological conclusions from the ILC data that may be compromised by the presence of intervening galactic sources of high-frequency continuum radiation.</text>
<text><location><page_18><loc_12><loc_34><loc_88><loc_41></location>Dr. Joan Schmelz is thanked for patiently hearing me out while I struggled to make sense of what is reported here. I also am grateful for discussions with Gary Hinshaw, Adolf Witt, John Raymond, Mahboubeh Asgari-Targhi, and Michael Cervetti for a useful discussion on statistics</text>
<section_header_level_1><location><page_18><loc_43><loc_27><loc_57><loc_29></location>REFERENCES</section_header_level_1>
<text><location><page_18><loc_12><loc_24><loc_64><loc_25></location>Allen, M.M., Snow, T.P., & Jenkins, E.B., 1990, ApJ, 355, 130</text>
<text><location><page_18><loc_12><loc_19><loc_88><loc_22></location>Haffner, L.M., Reynolds, R.J., Tufte, S.L., Madsen, G.J., Jaehnig, K.P., Percival, J.W. 2003, ApJS, 149, 405</text>
<text><location><page_18><loc_12><loc_15><loc_37><loc_17></location>Haud, U. 2000, A&A, 364, 83</text>
<text><location><page_18><loc_12><loc_12><loc_56><loc_14></location>Haud, U., & Kalberla, P.M.W. 2007, A&A, 466, 555</text>
<text><location><page_19><loc_12><loc_30><loc_88><loc_86></location>Hartmann, D., & Burton, W. B. 1997, Atlas of Galactic Neutral Hydrogen (Cambridge: Cambridge University Press) Hinshaw, G. et al. 2007, ApJS, 170, 288 Kalberla, P.M.W., Burton, W.B., Hartmann, D., Arnal, E.M., Bajaja, E., Morras, R., & Poppel, W.G.L. 2005, A&A, 440, 775 Laming, J.m. 2009, ApJ, 695, 954 Lyne, A.G., Manchester, R.N., & Taylor, J.H. 1985, MNRAS, 213, 613 Peratt, A.L., & Verschuur, G.L. 2000, IEEE Trans. Plasma Sci., 38, 2122 Priest, E., & Forbes,T. 2000, Magnetic Reconnection (Cambridge: Cambridge University Press) Raymond, J.C. 1999, Sp.Sci. Rev., 87, 55 Schmelz, J.T., Reames, D.V., von Steiger, R. & Basu, S. 2012, ApJ, 755,33 Verschuur, G.L. 2004, AJ, 127, 394 Verschuur, G.L. 2007a, ApJ, 671, 447 ( Paper 1) Verschuur, G.L. 2007b, IEEE Trans. Plasma Sci., 35, 759 Verschuur, G.L. 2010, ApJ, 711, 1208 (Paper 2) Verschuur, G.L. 2013, ApJ, submitted Verschuur, G.L., & Peratt, A.L. 1999, AJ, 118, 1252 Verschuur, G.L., & Schmelz, J.T. 2010, AJ, 139, 2410</text>
<text><location><page_19><loc_12><loc_26><loc_52><loc_28></location>Wood, B.E., & Linksy, J.L. 1997, ApJ, 474, L39</text>
<table>
<location><page_20><loc_17><loc_25><loc_83><loc_70></location>
<caption>Table 1. Area 1 Component Families</caption>
</table>
<table>
<location><page_21><loc_17><loc_24><loc_83><loc_71></location>
<caption>Table 2. Area 2 Component Families</caption>
</table>
<table>
<location><page_22><loc_23><loc_23><loc_77><loc_72></location>
<caption>Table 3. Properties of Gaussian Families</caption>
</table>
<figure>
<location><page_23><loc_32><loc_35><loc_68><loc_76></location>
<caption>Fig. 1a-b.- Contour maps of the HI brightness in a 3.3 km s -1 band centered at the following velocities. (a) At -46 km s -1 , contours 0.5:[email protected], 1.7:7.7@1 K.km s -1 . The bright filamentary feature that curves from the upper left to the lower center is referred to as Filament Alpha and it shows weak parallel strand below b =57 · . (b) At -36 km s -1 , contours 1:[email protected], 7:20@3, 26:40@6 K.km s -1 . The central pair of features is referred to as South Pair, see text.</caption>
</figure>
<figure>
<location><page_24><loc_32><loc_32><loc_68><loc_75></location>
<caption>Fig. 1c-d.- (c) At -30 km s -1 , contours 1:4@1, 7:28@3 K.km s -1 The curved feature at the center is referred to as Filament Gamma in the text. (d) At -13 km s -1 , contours 1:5@1, 7:17@2 K.km s -1 . The diagonal feature is referred to as Filament Delta in the text. It encompasses a pair of peaks around l,b = (92 · , 62 · ) called North Pair, see text.</caption>
</figure>
<figure>
<location><page_25><loc_31><loc_32><loc_68><loc_74></location>
<caption>Fig. 1e-f.- (e) At +1 km s -1 in upper frame, contours 4:7@1, 10:22@3, 26:42@4 K.km s -1 . The diagonal feature is referred to as Filament Beta in the text. (f) The ILC amplitudes for the area displayed as contours 0.02:[email protected] mK. The two areas over which Gaussian analysis was performed are indicated by the dashed lines and the numerals 1 & 2, see below.</caption>
</figure>
<text><location><page_25><loc_50><loc_31><loc_53><loc_32></location>GLON</text>
<figure>
<location><page_26><loc_23><loc_41><loc_77><loc_79></location>
<caption>Fig. 2a-d.- Images of the HI brightness in a 3.3 km s -1 band at velocities pertinent to the derived Gaussian families with the ILC contours overlain. The HI brightnesses are indicated in the legends and the ILC contours are the same as for Fig. 1c. (a) HI at -48 km s -1 . (b) HI at -38 km s -1 . South Pair is seen here. (c) HI at -28 km s -1 . (d) HI at -20 km s -1 .</caption>
</figure>
<figure>
<location><page_27><loc_23><loc_41><loc_77><loc_79></location>
<caption>Fig. 2e-h.- (e) HI at -12 km s -1 . North Pair is at the upper right and the signature of S16, see text, is at l,b = (100 · , 58 · ). (f) HI at -9 km s -1 . The southern half of North Pair is barely visible but S16 is dominant, see text. (g) HI at 0 km s -1 . (h) HI at +8 km s -1 .</caption>
</figure>
<figure>
<location><page_28><loc_24><loc_39><loc_75><loc_79></location>
<caption>Fig. 3.- Examples of Gauss decompositions discussed in the text for profiles in the directions indicated.</caption>
</figure>
<figure>
<location><page_29><loc_23><loc_42><loc_77><loc_79></location>
<caption>Fig. 4.- The HI column density distributions for families of Gaussian components at intermediate velocities with the WMAP contours overlain, same contour levels as in Fig. 1c. (a) IV-A. (b) IV-B. (c) IV-C. (d) IV-D. See text.</caption>
</figure>
<figure>
<location><page_30><loc_23><loc_40><loc_77><loc_79></location>
<caption>Fig. 5.- The HI column density distributions for three families of Gaussian components at velocities between those included in figs. 5 & 6, again with the WMAP contours overlain, same contour levels as in Fig. 1c. (a) LV11. (b) LV12. (c) LV13 & 14 combined. (d) Sum of LV11, 12, 13 & 14. See text.</caption>
</figure>
<figure>
<location><page_31><loc_26><loc_30><loc_74><loc_80></location>
<caption>Fig. 6.- The HI column density distributions for six families of Gaussian components at low velocities with the WMAP contours overlain, same contour levels as in Fig. 1c. (a) LV1, a pervasive component seen in all directions over the area. (b) LV2. (c) LV3. (d) LV4. (e) LV5. (f) LV6. See text.</caption>
</figure>
<figure>
<location><page_32><loc_26><loc_45><loc_74><loc_80></location>
<caption>Fig. 7.- The HI column density distributions for four remaining families of Gaussian components with the WMAP contours overlain, same contour levels as in Fig. 1c. (a) The low-velocity broad line width components, which are pervasive over the area. (b) Similar to a) but for intermediate velocity broad line width components that are also pervasive. (c) A limited number of components making up a family called IV-HV. (d) High-velocity components HV. See text.</caption>
</figure>
<figure>
<location><page_33><loc_32><loc_49><loc_68><loc_76></location>
<caption>Fig. 8.- The distance required to match the ILC amplitude for two cases indicated as a function of the electron column density expressed as a fraction of the associated HI peak. The curves represent the values derived for different assumed angular widths of unresolved features. The dashed line square is the suggested regime where the model calculations, § 7.2, give reasonable distances for reasonable values of the parameters required to evaluate Eqtn. 1, see text.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "Galactic HI emission profiles in an area where several large-scale filaments at velocities ranging from -46 km s -1 to 0 km s -1 overlap were decomposed into Gaussian components. Eighteen families of components defined by similarities of center velocity and line width were identified and related to small-scale structure in the high-frequency continuum emission observed by the WMAP spacecraft, as evidenced in the Internal Linear Combination ( ILC ) map of Hinshaw et al. (2007). When the center velocities of the Gaussian families, which summarize the properties of all the HI along the lines-of-sight in a given area, are used to focus on HI channel maps the phenomenon of close associations between HI and ILC peaks reported in previous papers is dramatically highlighted. Of particular interest, each of two pairs of HI peaks straddles a continuum peak. The previously hypothesized model for producing the continuum radiation (Verschuur, 2010) involving free-free emission from electrons is re-examined in the light of the new data. By choosing reasonable values for the parameters required to evaluate the model, the distance for associated HI -ILC features is of order 30 to 100 pc. No associated H α radiation is expected because the electrons involved exist throughout the Milky Way. The mechanism for clumping and separation of neutrals and electrons needs to be explored. Subject headings: ISM:atoms - ISM:clouds - cosmology",
"pages": [
1
]
},
{
"title": "Interacting Galactic Neutral Hydrogen Filaments and Associated High-Frequency Continuum Emission",
"content": "Gerrit L. Verschuur Physics Department, University of Memphis, Memphis, TN 38152 [email protected]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "In three previous reports (Verschuur, 2007a: Paper 1; 2007b; 2010: Paper 2) 108 close associations between foreground galactic neutral hydrogen (HI) features and small-scale structures found in the Wilkinson Microwave Anisotropy Probe ( WMAP ) Internal Linear Combination ( ILC ) map of Hinshaw et al. (2007) were listed. The latter structures are purported to have a cosmic origin while the former are features within the disk of the Milky Way relatively close to the Sun. In Paper 2 it was argued that a possible mechanism for generating the necessary high frequency continuum radiation is free-free emission from electrons produced by localized ionization of hydrogen. However, no associated H α radiation is found and hence the model appears to fail. In this paper the mechanism is re-considered in the light of what is revealed of the HI properties through the Gaussian analysis of emission profiles. Since the onset of work on the associations between HI features and peaks in the ILC data, the manner in which the HI data have been considered has evolved. In Paper 1, associations were found by comparing ILC data with structure found in HI area maps produced at 10 km s -1 intervals, each covering an effective velocity range of 11.3 km s -1 . In Paper 2 HI data were displayed in velocity maps made with a 3.3 km s -1 effective bandwidth plotted every 2 km s -1 in velocity. These revealed the presence of the HI -ILC associations more clearly. The present study shows that when maps of the column density of HI Gaussian component families are compared to ILC features, the relationship becomes even more revealing. In § 2 some of the HI data used in this study are displayed and in § 3 the Gaussian analysis is described. In § 4 the results of sorting Gaussian components into families are presented and their morphological relationship to the high-frequency continuum emission structure is shown in § 5. The apparent failure of the previously suggested model for producing the highfrequency continuum radiation is considered in § 6. The discussion section in § 7 shows that the model does work when it is recognized that the necessary electrons already exist in the interstellar medium. Conclusions are offered in § 8",
"pages": [
1,
2
]
},
{
"title": "2. The Data",
"content": "The HI spectral line data used in this paper were drawn from the Leiden-ArgentinaBonn (LAB) All-Sky HI Survey (Kalberla et al. 2005) performed with a 0. · 6 beam width and a 1.3 km s -1 velocity resolution. To describe the context of the work to follow, Figure 1 displays five HI contour maps of brightness temperature in a 3.3 km s -1 bandwidth as a function of galactic coordinates, longitude (GLON or l ) and latitude (GLAT or b ), for an area bordered by l = 70 · & 110 · and b = 50 · & 70 · . Such maps were produced and examined at 2 km s -1 intervals from +14 km s -1 to -70 and then every 4 km s -1 to -160 km s -1 with respect to the local standard of rest. Contour levels are shown in the captions. The velocities of these displayed examples were chosen to illustrate several key points in the analysis to follow. Fig. 1a shows the HI brightness centered at a velocity of -46 km s -1 . A curving filamentary feature can be followed from ( l,b ) = (100 · , 70 · ) to ( l,b ) = (78 · , 50 · ). It will be referred to as Filament Alpha. A weak extension from ( l,b ) = (85 · , 57 · ) to ( l,b ) = (71 · , 50 · ) suggests that filaments may be overlapping in the area around ( l,b ) = (87 · , 59 · ). In the data of Hartmann & Burton (1997: page 131) Filament Alpha can be followed well beyond the bounds of Fig. 1a. Fig. 1b shows the HI morphology at -36 km s -1 . The HI distribution in the center is dominated by two peaks to be called South Pair. They appear to lie on Filament Alpha. However, other structure suggests that the picture may be more complex. Fig. 1c shows HI brightness at -30 km s -1 . A part of a twisted S -shaped filament, named Gamma, runs across the center of the area terminating in a bright feature at ( l,b ) = (103 · , 61 · ) before turning south. The elongated peak at ( l,b ) = (89 · , 56 · ) appears to be an extension to this velocity of the southern component of South Pair. Fig. 1d shows the HI brightness at -13 km s -1 and a pair of peaks at ( l,b ) = (91 · , 62 · ) lies on Filament Delta that stretches to the lower-right corner of the area. These two peaks will be referred to as North Pair and they are located where Filament Delta crosses Filament Gamma. Fig. 1e shows the HI brightness at +1 km s -1 . The bright HI feature at ( l,b ) = (87 · , 60 · ) lies on a complex filamentary feature labeled Beta and is located where Filament Beta overlaps Alpha; that is, between the two components of South Pair seen in Fig. 1b. Fig. 1f shows the positive amplitude ILC peaks and the two areas labeled 1 & 2 marked by dashed lines are the boundaries within which Gaussian fitting was carried out. The firstyear ILC data used here is the same set used in Papers 1 & 2 drawn from Hinshaw et al. (2007), effective beam width 1 · , mapped as contours from +0.02 mK in steps of 0.03 mK. A visual comparison of the ILC data with this sample of HI maps shows associations between the two types of features. A concentration of low-velocity HI in the region of enhanced ILC emission seen around ( l,b ) = (80 · , 57 · ) is obvious. To avoid the complexity manifest in that region, the present study was limited to the Areas 1 & 2. Fig. 2 shows channel maps for these two areas at the velocities indicated in the caption with the same ILC contours shown in Fig 1f overlain. The velocities were chosen based on the average velocities of individual Gaussian component families to be discussed below. Fig. 2a shows low-level HI features that precisely skirt the boundary of extended ILC structure. Fig. 2b shows the HI features labeled South Pair straddling an ILC peak and Fig. 2e shows North Pair. What is striking is that without exception the small-scale HI peaks are associated with and closely offset from equally small-scale ILC features. This offset between the two types of radiation is what was reported in Papers 1 & 2. However, only one of the associations reported in Paper 1, Source 16 at ( l,b ) = (101. · 8, 59. · 5), is seen here. Its HI signature is evident in Figs. 2e & f. In Paper 1 the center velocity of S16 was listed as -5 km s -1 , but that analysis used area maps made every 10 km s -1 covering a band width of 11.3 km s -1 . Fig. 2f shows its peak to be at -9 km s -1 and illustrates that more is learned about HI -ILC associations when these narrower channel maps are used. While Paper 1 only revealed one pair of associations in this area, because it only considered the brightest ILC peaks, the maps in Fig. 2 reveal at least nine more closely spaced associations with no cases of direct overlap, which is true for most of the 108 pairs listed in Papers 1 & 2.. At this point the analysis could end because Fig. 2 clearly confirms what was found in other sections of sky as outlined in Papers 1 & 2. In general small-scale structure in the high-frequency background continuum radiation maps observed by WMAP as revealed in the ILC data is associated with, but slightly offset from, structure in galactic HI emission.. However, noting associations reveals nothing substantive about the physical properties of the HI being observed; for example, what are the volume densities and temperatures of the HI and what process could give rise to the associated high-frequency continuum emission? As the next step in this process, the efficacy of using Gaussian analysis to understand the HI properties was explored to determine if this clarifies the underlying physics that might, in turn, help understand the nature of the emission process giving rise to the high-frequency continuum radiation.",
"pages": [
2,
3,
4
]
},
{
"title": "3. Gaussian Analysis",
"content": "The HI area maps discussed so far reveal only the amplitude of the HI emission at a given velocity; they reveal little about the physics or dynamics of the structures that are present. HI emission profiles usually consist of multiple Gaussian components produced by concentrations of HI along the line-of-sight or by motion or temperature variations within coherent sub-features within a given volume of space. Each Gaussian is characterized by a peak brightness temperature, T B (max), a center velocity, v c , and a line width, W , the full width at half maximum brightness. The area maps in Figs. 1 & 2 represent the total of the brightness temperatures at any given velocity that is produced by overlapping components. The goal of the present study translates to untangling the Gaussian structure to identify the properties of the overlapping components. The hypothesis that the HI component line shape is Gaussian rests on the assumption that motions within any mass of HI will show a random velocity distribution that can be described by a Gaussian function. However, Gaussian analysis of HI profiles is difficult because a given solution may not be unique and that means that relatively few researchers have ventured into the realm of such analyses. The challenge has been discussed by Verschuur (2004), Verschuur & Peratt (1999), and Verschuur & Schmelz (2010). The algorithm used in the present Gaussian decomposition of LAB profiles was described by Verschuur (2004). A crucial difference between this approach and the totally automated analysis used by, for example, Haud (2000) and subsequently by Haud & Kalberla (2007), is that in the present study each profile and the associated Gaussian fit is examined visually to assure that the results are consistent. The problem is that the Gauss fitting algorithm is set to minimize residuals and false minima can be found for a set of Gaussian components that bear no relationship to the profiles in their immediate vicinity. While other researchers may have attempted to design their algorithms to take in account neighboring solutions, in our experience that is not necessarily sufficient, as will illustrated with examples to follow. Gaussian decomposition of HI profiles in the present study was performed for Areas 1 & 2 (Fig. 1f) using profiles every 1 · in l and 0. · 5 in b . At the latitude of these areas (60 · ) this created a uniform sampling grid of 588 profiles separated in real angle of 0. · 5 in both coordinates. The Gaussian decompositions allowed the fitting of up to 9 components although very few profiles actually required that many. During the analysis it became clear that Gaussian decomposition is subject not only to the presence of noise but is especially vulnerable to non-noise-like low-level (interference?) features found even in the baseline areas of the LAB profiles where no HI is present. In some profiles these showed a negative amplitude. When they occured at a velocity at the edge of a profile, the properties of the component fit that included the relevant velocity range could be dragged to apparent line widths that were either higher or lower than those found for similar components in neighboring profiles. This problem could only be identified by visually examining the Gaussian fits. Obviously there is no way to detect the presence of such non-noise-like deviations within the velocity range of the HI emission itself, which contributes to noise in the values of the derived component parameters. Visual examination of each Gauss fit compared to neighboring profiles allows the distortion produced by these non-noise structures near the profile edges to be recognized and the algorithm was then run with a different initial setting to produce a results consistent with neighboring profiles. In several profiles small interference spikes in only one channel were present and in two profiles single-channel negative spikes that could be confused with narrow absorption lines occurred at velocities that also contributed to producing spurious Gaussian parameters. These obvious cases were dealt with by canceling the problem spike in a given channel. It is highly doubtful that an automatic Gaussian analysis could deal with these problems unless it used advanced AI techniques. To initiate the search for the best-fit Gaussians for any given profile, the results for an adjacent solution were used. When the results of a given initialization were clearly inconsistent with the trends observed in surrounding profiles, the profile was re-initialized using another of the adjacent Gauss fits. Note that while the process of fitting Gaussian components to individual profiles is inherently noisy, the data for an ensemble of fits do produce coherent patterns in column density maps that allow families of components to be recognized and mapped. A pervasive, underlying broad line width component is the signature of every profile, both at LV and IV. Its width is predominantly about 33 km s -1 . However, after the initial analysis and sorting of families of Gaussian and making maps of the HI column densities in Area 2, a systematic error was recognized that was readily rectified. The data showed that the broad components often manifested line widths of order 24 km s -1 in addition to the 33 km s -1 regime. When maps of the narrow line width components were made it was found that the dominant one, called LV1, to be discussed below, was absent in the those directions where 24 km s -1 wide components were found. Thus the initially produced area map of the HI column density for LV1 had holes in the directions where the Gauss fitting routine had found a solution involving a broad component of order 24 km s -1 wide. The profiles in those direction were therefore reconsidered and it was found that a significantly better fit could be obtained by initializing the algorithm using the nearest solutions in which the 33 km s -1 lines was present. Thus the 24 km s -1 components turned out to be the result of a self-perpetuating fit that produced false minima. The relevant profiles were rerun and subsequent mapping of component LV1, using the better Gauss fits, did not show any holes. In fact LV1 is found to be pervasive, as are the underlying broad components of order 33 km s -1 wide, see tables below for details. This unfortunate state of affairs and its rectification is highlighted because automated Gaussian fitting programs are subject to the problem of false minima in residual phase space and future attempts to duplicate the present study should pay close attention to the result for given profiles to make sure no such systematic effects creep in. Fortunately, such effects stamp their presence of otherwise ordered column density maps, which allows their presence to be recognized. Figure 3 illustrates several examples of Gaussian fitting to a variety of profiles at the positions indicated. Fig. 3a shows a profile defined by a single, underlying broad component with line width W = 36.2 km s -1 at v c = -8.9 km s -1 . The profile just 1 · away in longitude shown in Fig. 3b reveals the presence of a second underlying broad component at intermediate velocity (IV) v c = -30.0 km s -1 with W = 35.1 km s -1 while the other is at low velocity (LV) centered at v c = +0.7 km s -1 with W = 33.9 km s -1 . The separation on the sky of these two profiles is 0. · 5 in true angle and serves to illustrate the tremendous amount of structure found in the HI distribution. Fig. 3c shows two broad underlying components whose presence is easy to discern because they manifest so clearly in the wings of the overall profile. The broad IV component has W = 35.1 km s -1 while the LV broad component has W = 34.8 km s -1 . The profile displayed in Fig. 3d is notable because of the presence of a narrow component at the center of the profile, only 3.4 km s -1 wide. The underlying broad components for this profile are 37.5 km s -1 wide at IV and 37.2 km s -1 wide at LV. In adjacent profiles the amplitude of the HI emission between velocities of -80 and -30 km s -1 produced an almost straight line slope and solutions were only obtained by painstakingly using the surrounding profiles to find a fit consistent with the trends in the data around those positions. It seems very unlikely that an automated program would find solutions to such a profile. Fig. 3e shows an extremely bright and narrow center component 3.0 km s -1 wide at -17.2 km s -1 , which is part of component family LV13, see below. The associated broad components are 27.8 km s -1 wide at -47.8 km s -1 and 36.8 km s -1 wide at -5.0 km s -1 . Fig. 3f shows a profile where the peak brightness temperature at IV and LV are maxima for the entire mapped area. The underlying broad components have W = 30.6 km s -1 at IV and W = 32.0 km s -1 at LV. The fact that both peaks reach maxima here is an indication that the structures at IV and LV are directly related, as will be discussed in the context of examining all the data, below.",
"pages": [
4,
5,
6,
7
]
},
{
"title": "4. Sorting Gaussians into parameter families",
"content": "Gaussian analysis of 288 profiles yielded 3,706 Gaussian components that were sorted into 18 distinct families most of which were recognized in both Areas 1 &2. The sorting of Gaussians into families was usually straightforward because of clear continuity in center velocity and/or line width that could be followed across many adjacent profiles. When the data were gathered into families and plotted as area maps, the presence of components that had not been assigned to the correct family was quickly apparent. They could then be assigned to the appropriate family and the resulting maps show a high degree of order as will be displayed below. Only six components could not be fit into any of the families and may be regarded as noise in the data. Table 1 summarizes the key properties of component families for the Area 1 and Table 2 applies to Area 2. Col. 1 gives the name of the family, Col. 2 lists the number of Gaussians used to define the family, Col. 3 lists the average center velocity, v c , for the family and Col. 4 its average line width (full-width, half-maximum), W , both with one standard deviation errors. Col. 5 lists the peak column density found for a given family. Table 3 summarizes all the family data. Col. 1 is again the family name, Col. 2 is the total HI column density summed over all the members of that family in both Areas and Col. 3 is the fraction of the total column density for a given family. The average column density of the family is given in Col. 4 and the peak value in Col.5, which corresponds to the value in either Table 1 or 2. Of these component families three (Broad LV, Broad IV and LV1) were found in all directions, although for some of the Broad IV features the amplitudes are so low as to be comparable to the peak-to-peak noise in the data. For all the broad components listed in Tables 1 & 2, which includes 1176 cases, W = 33.1 ± 1.1 km s -1 . A simple test was performed to show that this large line width is not an artifact of the observing beam width encompassing velocity gradients within the beam to produce the higher line width values. HI profiles obtained by Verschuur (2013) toward a high-velocity HI feature known as A0 using the Green Bank Telescope (9. ' 1 beam width) were Gaussian analyzed and the results compared with a similar decomposition of profiles from the LAB survey toward the same feature. Both sets of data revealed an underlying broad component about 22 km s -1 wide with no hint of a 33 km s -1 wide component. Thus, in general, it is not simply an artifact of lower angular resolution that generates the 33 km s -1 wide components. It is notable that the present study did not reveal any convincing evidence for components that could be associated with a so-called WNM, of Warm Neutral Medium, at 8,000 K, which would produce line width of order 20 km s -1 . However, the data in Table 2 show that for two component families labeled IV-HV and HV the average line widths are in the 20 km s -1 regime. That is a property of anomalous velocity HI, not the gas at lower velocities. [In an unrelated and as yet unpublished study of the Gaussian component structure of high-velocity clouds by the author, the LAB data show that a component of order 22 km s -1 wide is common and also that another component about 34 km s -1 wide is present in many cases. In some directions, the HI emission profile can be fit by only one Gaussian, which is then found to be either about 22 or 34 km s -1 wide.] When compared to Gaussian line width data obtained from totally unrelated studies the numerical value for the broad component line width is striking. Verschuur & Schmelz (2010) gathered together line width data in their Table 2 pertaining to an underlying broad linewidth background component reported in 9 published papers by various researchers as well as their own data that together produced W = 33.7 ± 2.4 km s -1 . This is essentially identical to the value of 33.1 ± 1.1 km s -1 in the present study. [The possible role of a mysterious plasma phenomenon known as the Critical Ionization Velocity effect in affecting the line widths of the broad components is discussed by Verschuur (2007b) and Verschuur & Schmelz (2010) and references therein. Further consideration of that poorly understood phenomenon is beyond the scope of the present study.] Several other families listed in Tables 1 & 2 include 1139 components with a weighted average line width of 14.6 ± 1.2 km s -1 . Again, this value is significant when compared to the results summarized by Verschuur & Schmelz (2010) in their Table 3 of 13.9 ± 0.9 km s -1 . For completeness, 10 entries in Tables 1 & 2 have W values between 4.1 & 8.1 km s -1 involving 923 components for a weighted average line width of 5.7 ± 0.6 km s -1 . The remaining 339 components have average line widths between 8.7 & 10.7 km s -1 to produce a weighted average line width of 9.6 ± 1.3 km s -1 .",
"pages": [
7,
8,
9
]
},
{
"title": "5. The relationship between the HI component families and ILC peaks",
"content": "The HI column density maps for the families of components are next plotted and compared with ILC data. What will become apparent is that a great deal more remains to be revealed about the crucial HI structure in future higher resolution studies. Figures 4a -c show the morphology of the families of HI components at intermediate velocities from -48 to -35 km s -1 that encompass the emission from South Pair at the right-hand side. The ILC peak at l,b = (88. · 5, 58. · 5) bridges the space between the major peaks in the HI defining South Pair. A fourth IV component at -55 km s -1 seen in Fig. 4d is associated with ILC peaks at the top-left of the area. It is striking that South Pair is clearly defined by HI components with three distinct line widths, see Table 1. The Gaussian analysis does not reveal the greater extent of Filament Alpha in these HI column density maps since column density is given by the product of line width and amplitude. An intrinsically narrower yet bright feature may not stand out against a background of somewhat wider components, even if it is a member of the same family. The presence of three distinct component families with different line widths at the location of the northern half of South Pair may be indicative of the contributions from three distinctly different filaments whose existence can be inferred by close examination of Fig. 1. Figure 5 shows area maps of the HI column densities for the families with v c between -26 & -19 km s -1 , LV11, 12, 13 & 14, compared to the ILC contours. Fig. 5a shows the patchy morphology of LV11 and its brightest peak appears to be associated with North Pair and another ILC peak at the left-hand edge of the map around l = 100 · is found in the region of more complex ILC structure. The members of the LV11 family were identified by similarities in line width. Fig. 5b shows the morphology of LV12 that is clearly related to the presence of the ILC peaks. Its average line width is similar to LV11 but its center velocities are very different, Table 1. Fig. 5c shows LV13 & 14 combined since their morphologies smoothly blend although their velocities show a considerable change from Area 1 to Area 2, see tables. Again, HI column density peaks are clearly associated with ILC peaks. When combined in Fig. 5d these four HI component families are located where several filaments intersect or overlap, see Figs. 1c, d &e and the overall feature in Fig. 5d thus manifests variations along its length of center velocities and line widths. Together these patterns imply that a great deal of complexity is hidden from view because of the poor angular resolution of the available data. This is borne out by the HI profiles in the region of North Pair. They are extremely complex, see, for example, Fig. 3d, which makes the task of confidently identifying families of line widths in this area very difficult. What remains true, however, is that the HI column density maps reinforce the notion that HI and ILC structures are related, as is so clearly evident in Fig. 2. Fig. 6 shows the morphology of the low velocity components. Fig. 6a plots the ILC contours on a map of component family LV1 that is found throughout the area and is therefore a pervasive background or 'field' component. Its morphology is not obviously related to the presence of ILC structure. Fig. 6b shows the morphology of LV2, which is part of Filament Beta (Fig. 1e) and this segment of filamentary structure is clearly related to the presence of the ILC peak where it appears to terminate at ( l,b = 88 · , 58 · ) but examination of Fig. 1e suggests it then curves back and away to the west from that terminus. The high-frequency continuum radiation creating the ILC peak in South Pair originates in a volume of space where the two filaments, Alpha and Beta overlap. Also, very striking, is the fact that where the HI peak in IV-A ( v c = -38.6 km s -1 ) overlaps LV3 ( v c = -0 . 4 km s -1 ) at l,b = (87. · 0, 59. · 5) the HI brightness of both the IV and LV component is by far the greatest for the area mapped. The relevant profile is shown in Fig. 3f. This is strong circumstantial evidence that HI at very different velocities is somehow interacting and hence at the same distance. This phenomenon that HI at very different velocities is directly associated was also found in several areas described Paper 1. Fig. 6c shows the morphology of LV3 and its properties are so similar to LV2 that they could well be combined, yet they appear to represent two distinct families in one filamentary feature. The other three frames in Fig. 6 show the HI column density maps for the remaining LV component families and the fact that the majority of the structures, albeit patchy, seem to be associated with immediately adjacent ILC features suggests that there is more to be learned from higher-resolution HI mapping. The HI associated with S16 discussed above can be seen in Figs. 6d & e and in this display is less dramatic than found in Figs. 2e & f. For completeness, Fig. 7 gathers together the column density maps for the remaining component families. Fig. 7a shows the HI morphology for the LV broad line-width component and Fig. 7b is the same for the IV broad line-width family. There is some indication for diagonal features but these area maps are not readily related to the ILC structures. An exception is the bright patch just to the south of the North Pair ILC feature in Fig. 7a. It contributes to the pattern seen in Fig. 2b, center frame. Examination of the HI profile in this direction again shows it to be extremely complex, similar to the profile in Fig. 3d, and the complexity can only be untangled using higher resolution HI data. The final two frames in Fig. 7 refer to component families that were not a carefully mapped because their brightness temperatures are very low, barely above peak-to-peak noise in some cases. The case of Component IV-HV ( v c = -78 km s -1 ) is shown in Fig. 7c. In some directions its spectrum is well separated from the bulk of the HI emission in velocity while in other directions it overlaps the wings of the HI emission from the bulk of the IV gas. Yet, its peak column density lies toward the North Pair ILC peak. Finally, Fig 7d shows the column density map for weak high-velocity HI, called Component HV ( v c = -109 km s -1 ), which favors other peaks in the ILC map.",
"pages": [
9,
10,
11
]
},
{
"title": "5.1. What the Gaussian mapping reveals",
"content": "Overall, the goal of mapping Gaussian components with a view to clarifying the relationship between HI and ILC peaks has done little to reveal a more edifying picture. Instead the picture has become more complex. On the one hand there is strong evidence that HI at very different velocities appears to be involved where ILC peaks are located, and on the other hand those interactions are complex and somehow give rise to the small-scale structure in the high-frequency continuum radiation found in the ILC map. The patterns seen in the HI area maps displayed in Fig. 2 are also found in the Component maps, Figs. 4 -7, so the area maps at specific velocities determined by Gaussian family average velocities may be the most effective way to identify close associations between HI and small-scale ILC structure. This reduces the task from having to sort through 60 to 100 HI channel maps to find associations to considering only a dozen or so data sets determined by the identification of Gaussian families. Bear in mind that the HI column density maps of the ensemble of component families contain between them information about ALL the HI found over the total line-of-sight through any given area.",
"pages": [
11
]
},
{
"title": "5.2. A note on the statistics of associations",
"content": "In Paper 1 an attempt was made to show that the association between HI and slightly offset ILC features was significant. In Paper 2 it was shown that there is no evidence for widespread direct positional associations, which was never claimed in any case. Yet the question remained as to whether the near positional associations discussed here and in Papers 1 & 2 are significant or due to chance. Interstellar HI structure is seen all over the sky and so is the structure revealed by ILC data. However, for any given area of sky as many as 100 HI area maps at velocities separated by 2 km s -1 need to be studied and the likelihood of chance associations becomes large. At the same time, the data discussed above and in Papers 1 & 2 show that no two examples of associations are identical. Providing convincing statistical arguments that a given association between an HI feature and one found in the ILC data is significant may be impossible. There is no a priori standard for defining an association that can be tested for statistically. Instead we must rely on looking at the actual data that show the associations clearly. Seen from another perspective, the entire sky is filled with small-scale structure found in the high-frequency continuum emission observed by WMAP as revealed in the ILC map, which was produced after possible sources of intervening radiation had been removed, Hinshaw at al. (2007). But interstellar HI structure also covers the entire sky and that was not taken into account in the production of the ILC map. There would have been no a priori reason for doing so. While random coincidences in position between ILC and HI peaks are to be expected, this is not what is found. In general, apparently associated ILC and HI features are offset from one another by a small amount, on average 0. · 8, as stated in Paper 2, and estimated to be closer to 1 · for the patterns seen in Fig. 2.",
"pages": [
11,
12
]
},
{
"title": "6. The apparent failure of the previous model",
"content": "The area maps presented in Fig. 2 reveal the presence of several sets of associated HI -ILC features. In Paper 2 it was suggested that the continuum radiation is produced by free-free emission from electrons interacting with electrons and that the excess electrons are produced by the ionization of hydrogen atoms where HI features interact. It was also noted that for the emission mechanism to account for the data, the continuum sources would have to be unresolved in the WMAP survey in order for the presence of the phenomenon to have been missed in the original ILC analysis of the WMAP data. For the present data an order-of-magnitude calculation can be performed. For example for North Pair using the HI column density of the associated peak of 67 × 10 18 cm -2 (Fig. 5d), it is possible to calculate (using the formula derived in Paper 2, see Eqtn. 1, below) the degree of ionization required to produce the observed ILC peak of 0.08 mK. For a distance of 100 pc, an electron excitation temperature of 8,000 K, a source width of 0. · 2, and a depth along the line of sight equal to that width, the fractional ionization required is 0.45. The electron density that is implied is 28.3 cm -3 and the corresponding emission measure (given that the path length is known for a given distance) should produce H α emission at a level of 125 R in the 1 · beam of the WHAM survey of Haffner et al. (2003). However, examination of the WHAM data reveals no such structure. The maximum emission measure over the relevant area of sky is 0.7 R, barely above a 0.5 R background level. Therefore, the hypothesis that the continuum peaks in the ILC data are due to free-free emission from electrons produced through localized ionization of the HI in the galactic disk, as suggested in Paper 2, fails. No combination of parameters (distance, angular size, aspect ratio, and excitation temperature) can account for both the observed continuum emission level and the lack of H α signal. But what, then, is the source for the high-frequency continuum radiation if the associations seen in Fig. 2 are real?",
"pages": [
12,
13
]
},
{
"title": "7. Discussion",
"content": "The original goal of this project was to determine the properties of two pairs of HI features in directions where filaments cross and at which locations peaks in the ILC data were found. As a result of mapping families of Gaussian components in the area, the HI distribution was found to be more complex than the impression garnered from examining up to 100 area maps of brightness temperature at specific velocities at 2 km s -1 , for example. In instead the average velocities of the Gaussian families are used to focus attention on specific HI channel maps the relationship between HI structure and ILC structure emerges in dramatic detail, see Fig. 2. In fact, Fig. 2 & Figs. 4 -7 confirm the claims made in Papers 1 & 2 that close associations between small-scale HI and ILC features are real. However it is not immediately clear how the high-frequency continuum emission is generated in local interstellar space, local because the HI data discussed here is at high galactic latitudes of 60 · and the velocities imply a galactic origin. As this discussion proceeds it will become increasingly obvious that we are venturing into uncharted territory. The most fundamental issue that has yet to be resolved is at what angular scale both the HI and the ILC structures can be claimed to be resolved. Given that uncertainty it will be shown below that it is nevertheless possible to obtain an apparently good fit to the data using the model proposed in Paper 2. A solution requires that several questions be answered. First, given that the free-free emission from electrons appears to work quite well as outlined in Paper 2, other than the absence of associated H α radiation, what might be the source of electrons so as to avoid the H α dilemma? A second question concerns what mechanism is operating to cause the HI and the electrons to cluster? Also, why would the neutrals and electrons cluster in slightly offset directions? Lastly, if a source of electrons can be identified and a mechanism for clustering suggested, is it still possible to account for production of the high-frequency continuum radiation through invoking free-free emission from electrons?",
"pages": [
13,
14
]
},
{
"title": "7.1. Source of electrons",
"content": "It is well known that free electrons exist everywhere in interstellar space as inferred from pulsar dispersion measures and radio source rotation measures. Average electron densities along path lengths of hundreds to thousands of pc are estimated to be in the range 0.03 to 0.3 cm -3 (see, for example, Wood & Linsky, 1997; Allen, Snow & Jenkins, 1990; Lyne, Manchester & Taylor, 1985). Unfortunately, essentially nothing is known about the clumping of these electrons along a given line-of-sight. In contrast, the clumping of the HI is its most basic characteristic, producing morphologies such as seen in Fig. 1. Using the data in Table 3 the average HI column density for the 588 lines-of-sight included in the study is 123 × 10 18 cm -2 . Assuming a typical path length of 100 pc the average HI volume density is 0.41 cm -3 . An average electron density of 10% of the HI, that is 0.04 cm -3 , lies in the range interstellar electron density from pulsar dispersion measure data. This offers a first-order approach to determining whether a reasonable set of parameters can be found that can be used with the electron Brehmstrahlung model to account for the observed amplitudes of the high-frequency continuum signals found in the ILC data.",
"pages": [
14
]
},
{
"title": "7.2. Application of the theory",
"content": "From Eqtn. 12 in Paper 2, the brightness temperature T B ( ν ) of the high-frequency continuum radiation at a frequency ν produced by free-free emission from (cold) electrons with an excitation temperature, T e , is given by: where N H is the observed HI column density in units of 10 18 cm -2 and the electron density is expressed as a fractional degree of ionization, f . The angular width of the electron enhancements (or cloud) on the sky is θ o and A is the Aspect Ratio, the depth of feature relative to its width. L is the distance in pc. In order to evaluate Eqtn. 1, several assumptions have to be made and then, based on what is found, the direction of future research may be indicated. The electron excitation temperature is set to 100 K, the typical kinetic temperature of interstellar neutral hydrogen, bearing in mind that the data show little evidence for a Warm Neutral Medium at 8,000 K, as noted in § 4. The reasons for the Gaussian family line width much greater than expected for this temperature have been alluded to in § 4 and deserves a detailed discussion beyond the bounds of the present study. [Such a discussion would in any case conclude that electrons exist in abundance that are not created by localized ionization of neutral hydrogen.] An angular width of the small-scale ILC features has to be assumed since the structures considered above are usually about 1 · across, which is the resolution of the ILC map. Thus it is fair to assume that the sources of high-frequency continuum radiation are unresolved on this scale. (Others with access to high resolution observations of the highfrequency continuum radiation should look into this issue; e.g., those who use the Planck spacecraft data.) In order to explore whether Eqtn. 1 works, the model amplitudes are calculated for the two ends of the WMAP band, 23 & 94 GHz, and then averaged. Eqtn. 1 is applied to the two cases of close associations between HI and ILC peaks, North Pair and South Pair, and it is used to determine the distance at which it can account for the observed ILC positive amplitudes as a function of the required degree of ionization of the associated HI column density (as a first-order approach to the data). The results are shown in Fig. 9. For example, if the angular scale of the unresolved ILC peak in South Pair is 0. · 1 then the solid line in Fig. 9 so labeled indicates that for a range of electron densities equal to 0.10 to 0.17 times the associated HI peaks the distance of the source required to produce the observed ILC amplitude of 0.12 mK would be between about 30 and 100 pc. The calculation used the peak HI column density for IV-A as the guide to the column density of the associated electron cloud. It remains to be determined just what value should be used given that there are several distinct HI families of line widths involved in this direction, see Fig. 4. But to first-order the model does match the data. The difference between this calculation and the one reported in § 6 is that the electron temperature is not 8,000 K as would be expected from localized ionization of HI but closer to 100 K consistent with the temperature of the cold hydrogen atoms. The fact that the curves in Fig. 9 for North Pair and South Pair appear to encompass a region of phase space that is reasonable as regards the required electron column densities and distances, for the 100 K regime, indicates that the possibility that the ILC structures are indeed located in the galactic disk relatively close to the Sun should be seriously considered. But what mechanism would simultaneously act to clump the neutrals and the electrons and have them physically separated yet close associated in space.",
"pages": [
14,
15
]
},
{
"title": "7.3. On the clumping and separation of electrons with respect to HI",
"content": "Fig. 1 shows clear evidence for the presence of several large-scale filaments of HI in the area under consideration and Fig. 2 shows that HI and ILC features over the target area for this study are connected and offset from one another. These are observational facts that have to be recognized. There appear to be several ways in which electrons and neutrals could become spatially separated in interstellar space, although none has been formally studied for such an environment. The options are only briefly mentioned here. In a completely different astrophysical situation, namely the solar environment, many papers have deal with a phenomenon called the First Ionization Potential (FIP) Effect. It is used to account for the spatial separation either in layers in the solar atmosphere, or along flux tubes, of various atomic species. The FIP Effect is invoked to account for solar abundance variations that are otherwise difficult to comprehend. A number of references that indicate how the FIP Effect may be important include Raymond (1999), Laming (2009) and Schmelz et al. (2012). Another way of considering this is to recognize that the offset between the HI and ILC peaks is one of e/H abundance variations in interstellar space, either along a given filament or between adjacent volumes of space. A little known instability occurring within flux tubes is described by Marklund (1979) who suggested that if an electric field is present in a plasma permeated by a magnetic field and has a component perpendicular to the field, the E x B force will cause electrons and ions, but not neutral particles, to migrate to the axis of a flux tube. As Peratt & Verschuur (2010) note, because of different ionization potentials of various atomic species and cooling within the filaments, ionic species will then separate within a flux tube. This mechanism, akin to the FIP effect, also has the seeds for separating the HI from the electrons. Another possibility for separating electrons and neutrals may involve interacting magnetically controlled filaments. Fig. 1 shows two HI features, South Pair, which straddle a high-frequency continuum source, as displayed in Fig. 4a. In that same direction the data indicate that a number of filaments of HI intersect, see Fig.1. This raises the interesting possibility that magnetic reconnection may play a role in creating pockets of HI that are pulled away from a central X-neutral point where magnetic fields, likely to be present in the filaments, are reconnecting. The continuum radiation revealed in the ILC data is then being produced at the X-neutral point. Unfortunately the necessary theory to help account for the data invoking magnetic reconnection does not yet appear to exist. Priest & Forbes (2000) note that concerning the question of what actually happens to the particles at the X-point as regards energies and spectra, and how magnetic energy is converted to heat, kinetic energy and particle energy is largely unknown. They state that 'These apparently simple questions have not yet been answered fully [and] the answers are likely to be highly complex.' In this context they list at least 12 possible types of reconnection that may play a role. While their work also focused on events in the solar corona, future consideration of what may be occurring in interstellar space could clarify why so many associations exist between HI structures and high-frequency continuum peaks in the ILC data. These tentative suggestions should not cause us to avoid what the data show, that galactic HI peaks (clouds?) and ILC peaks are associated and slightly offset from one another, perhaps even along the axes of one or more of the filaments that pervade a volume of interstellar space. The fact that even a simplistic consideration of the magnitudes of the parameters required to evaluate Eqtn. 1, Fig. 9, leads to reasonable values of the distance and electron densities is surely sufficient evidence that the issue is deserving of further study, given the importance attached to the conventional explanation of the ILC structure being at cosmological distances.",
"pages": [
15,
16,
17
]
},
{
"title": "8. Conclusions",
"content": "Galactic HI profiles in an area bounded by longitudes 85 · & 110 · and latitudes 55 · and 65 · were decomposed into Gaussians. The area was divided into two sections separated at l=85.5 and the analysis proceeded many months apart without cross-talk between them. In all, 588 profiles at 0. · 5 spacing netted 3,706 Gaussian components. These were sorted into 18 families, each defined by similarity of center velocity and line width. When the average velocities of the derived Gaussian families are used to focus attention on specific HI channel maps, associations between HI peaks and structure in the Internal Linear Combination ( ILC ) map of Hinshaw et al. (2007), based on the WMAP survey data, are dramatically revealed. These associations are confirmed by comparing the morphology of the column densities of the Gaussian families and the ILC structures. The step of first identifying Gaussian families in a given area of sky and using their center velocities as a guide, makes the task of finding associations with the ILC peaks manageable because only a fraction of the up to 100 channel maps that could be created for any area then need to be studied. In addition, given that the Gaussian families summarize the properties of all the HI along the line-of-sight in the area, statistical arguments about whether or not the associations are due to chance becomes less relevant. The relationships between some of the families of HI Gaussian components show that despite their velocity differences they are physically related to one another and hence at the same distance. This phenomenon was also reported in Paper 1. This would never have been discovered if it were not for attention drawn to the properties of the HI because of the associations with small-scale ILC structure. The Gaussian mapping reveals details in the HI morphology of several components at widely different velocities, from 0 km s -1 to -109 km s -1 . In an area labeled North Pair, two HI features straddle an ILC source that is located at the point of overlap of two filaments at velocities of order -30 and -13 km s -1 . Similarly, in an area named South Pair, two HI peaks straddle an ILC peak and here the HI consists of three families of components at intermediate velocities around -36 km s -1 with average line widths of 14.7, 7.0 & 4.6 km s -1 found where HI filaments at distinctly different velocities, around 0 km s -1 & -38 km s -1 overlap. The previously hypothesized mechanism for producing the high-frequency continuum radiation from interacting HI features in interstellar space involving free-free emission from electrons (Verschuur, 2010) is re-examined in the light of the new data. It is found to account for the existence of the small-scale ILC peaks if the sources are located from 30 to 100 pc from the Sun. The pervasive presence of interstellar electrons is revealed in observations of pulsar dispersion measures and to fit the model the of necessity cold electrons have to be clumped on scales that are similar to those seen in the HI distribution with densities from 10 to 25% of the immediately adjacent HI peaks. Associated H α radiation at the location of the ILC peaks is not expected because the source of electrons does not require the localized ionization of HI as was hypothesized in Paper 2. In order to determine unequivocally whether or not the claimed associations are real, higher resolution observations are required. For example, Planck data should be compared with high-resolution HI observations obtained with suitably large radio telescopes, provided attention is focussed on high-latitude regions where the confusion created by having too much HI in the beam is minimized. In the meantime caution should be exercised in drawing far-reaching cosmological conclusions from the ILC data that may be compromised by the presence of intervening galactic sources of high-frequency continuum radiation. Dr. Joan Schmelz is thanked for patiently hearing me out while I struggled to make sense of what is reported here. I also am grateful for discussions with Gary Hinshaw, Adolf Witt, John Raymond, Mahboubeh Asgari-Targhi, and Michael Cervetti for a useful discussion on statistics",
"pages": [
17,
18
]
},
{
"title": "REFERENCES",
"content": "Allen, M.M., Snow, T.P., & Jenkins, E.B., 1990, ApJ, 355, 130 Haffner, L.M., Reynolds, R.J., Tufte, S.L., Madsen, G.J., Jaehnig, K.P., Percival, J.W. 2003, ApJS, 149, 405 Haud, U. 2000, A&A, 364, 83 Haud, U., & Kalberla, P.M.W. 2007, A&A, 466, 555 Hartmann, D., & Burton, W. B. 1997, Atlas of Galactic Neutral Hydrogen (Cambridge: Cambridge University Press) Hinshaw, G. et al. 2007, ApJS, 170, 288 Kalberla, P.M.W., Burton, W.B., Hartmann, D., Arnal, E.M., Bajaja, E., Morras, R., & Poppel, W.G.L. 2005, A&A, 440, 775 Laming, J.m. 2009, ApJ, 695, 954 Lyne, A.G., Manchester, R.N., & Taylor, J.H. 1985, MNRAS, 213, 613 Peratt, A.L., & Verschuur, G.L. 2000, IEEE Trans. Plasma Sci., 38, 2122 Priest, E., & Forbes,T. 2000, Magnetic Reconnection (Cambridge: Cambridge University Press) Raymond, J.C. 1999, Sp.Sci. Rev., 87, 55 Schmelz, J.T., Reames, D.V., von Steiger, R. & Basu, S. 2012, ApJ, 755,33 Verschuur, G.L. 2004, AJ, 127, 394 Verschuur, G.L. 2007a, ApJ, 671, 447 ( Paper 1) Verschuur, G.L. 2007b, IEEE Trans. Plasma Sci., 35, 759 Verschuur, G.L. 2010, ApJ, 711, 1208 (Paper 2) Verschuur, G.L. 2013, ApJ, submitted Verschuur, G.L., & Peratt, A.L. 1999, AJ, 118, 1252 Verschuur, G.L., & Schmelz, J.T. 2010, AJ, 139, 2410 Wood, B.E., & Linksy, J.L. 1997, ApJ, 474, L39 GLON",
"pages": [
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2013ApJ...769...11Y
https://arxiv.org/pdf/1303.4742.pdf
<document>
<section_header_level_1><location><page_1><loc_24><loc_85><loc_76><loc_87></location>LINE EMISSION FROM RADIATION-PRESSURIZED HII REGIONS I: INTERNAL STRUCTURE AND LINE RATIOS</section_header_level_1>
<text><location><page_1><loc_10><loc_82><loc_90><loc_84></location>Sherry C. C. Yeh 1 , Silvia Verdolini 2 , Mark R. Krumholz 3 , Christopher D. Matzner 1 , Alexander G. G. M. Tielens 2</text>
<text><location><page_1><loc_35><loc_80><loc_65><loc_81></location>Accepted for publication in ApJ, March 12, 2013</text>
<section_header_level_1><location><page_1><loc_45><loc_78><loc_55><loc_79></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_56><loc_86><loc_77></location>The emission line ratios [ O III ] λ 5007/H β and [ N II ] λ 6584/H α have been adopted as an empirical way to distinguish between the fundamentally different mechanisms of ionization in emission-line galaxies. However, detailed interpretation of these diagnostics requires calculations of the internal structure of the emitting H II regions, and these calculations depend on the assumptions one makes about the relative importance of radiation pressure and stellar winds. In this paper we construct a grid of quasi-static H II region models to explore how choices about these parameters alter H II regions' emission line ratios. We find that, when radiation pressure is included in our models, H II regions reach a saturation point beyond which further increases in the luminosity of the driving stars does not produce any further increase in effective ionization parameter, and thus does not yield any further alteration in an H II region's line ratio. We also show that, if stellar winds are assumed to be strong, the maximum possible ionization parameter is quite low. As a result of this effect, it is inconsistent to simultaneously assume that H II regions are wind-blown bubbles and that they have high ionization parameters; some popular H II region models suffer from this inconsistency. Our work in this paper provides a foundation for a companion paper in which we embed the model grids we compute here within a population synthesis code that enables us to compute the integrated line emission from galactic populations of H II regions.</text>
<text><location><page_1><loc_14><loc_53><loc_86><loc_55></location>Subject headings: galaxies: high-redshift - galaxies: ISM - HII regions - ISM: bubbles - ISM: lines and bands</text>
<section_header_level_1><location><page_1><loc_22><loc_49><loc_35><loc_50></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_30><loc_48><loc_49></location>The line ratios [ O III ] λ 5007/H β and [ N II ] λ 6584/H α , first proposed for use in galaxy classification by Baldwin et al. (1981) (hereafter BPT), are commonly used to diagnose the origins of emission lines from galaxies, and in particular to discriminate between galaxies whose emission is powered by star formation-driven H II regions and from those powered by active galactic nuclei (AGNs). These emission line pairs are particularly useful because (1) they are bright and thus relatively easy to measure, (2) blending between the lines can be corrected with reasonable accuracy, so long as the spectra are taken with sufficient resolution, and (3) the wavelengths in each line pair are quite similar, so the line ratio is relatively insensitive to dust-reddening (Veilleux & Osterbrock 1987).</text>
<text><location><page_1><loc_8><loc_16><loc_48><loc_30></location>The power of these line ratios as diagnostics comes from their sensitivity to the spectral shape of the radiation field driving the ionization, which can be understood from a simple physical picture. To first order, the intensities of the H α and H β lines simply measure the total photoionization rate, and thus normalize out the ionizing luminosity. On the other hand, the [ O III ] and [ N II ] intensities are sensitive not only to the total ionizing luminosity, but also to the shape of the ionizing spectrum and to the ionization parameter U , which measures the ratio of photons to baryons in the ionized</text>
<text><location><page_1><loc_10><loc_14><loc_23><loc_14></location>[email protected]</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_11><loc_48><loc_14></location>1 Department of Astronomy & Astrophysics, University of Toronto, 50 St. George St., Toronto, ON M5S 3H4, Canada</list_item>
</unordered_list>
<text><location><page_1><loc_10><loc_7><loc_48><loc_9></location>3 Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064</text>
<text><location><page_1><loc_52><loc_19><loc_92><loc_51></location>gas. When the ionizing flux arises from hot stars, the ionizing spectrum is dominated by low-energy photons that have short mean-free paths through neutral gas. Thus the H II region consists of a fully ionized zone with a sharp boundary. Within this region, as U increases, more of the ionized gas volume becomes filled with high ionization-potential species such as O ++ , and less with low-ionization potential species such as N + . As a result, H II regions ionized by hot stars tend to fall along a sequence that runs from high [ O III ]/H β , low [ N II ]/H α to low [ O III ]/H β , high [ N II ]/H α . On the other hand, if the ionizing spectrum follows a power-law, as expected for AGN, then a significant amount of the ionization is produced by X-ray photons capable of ionizing higher ionization potential species like O ++ . Moreover, these photons have large mean-free paths, giving rise to a large zone of partial ionization rather than a smaller region of full ionization as in the stellar case. In this configuration, [ O III ]/H β and [ N II ]/H α both increase with U , and either one or the other tends to be larger than in the stellar case, leading to a sequence that runs from intermediate to high [ O III ]/H β and [ N II ]/H α and is well-separated from the locus occupied by H II regions dominated by stellar sources.</text>
<text><location><page_1><loc_52><loc_7><loc_92><loc_19></location>This simple picture is roughly consistent with local observations: star-forming galaxies in the Sloan Digital Sky Survey (SDSS; median redshift z = 0 . 1) obey a tight correlation between the [ O III ]/H β and [ N II ]/H α ratios in the BPT diagram (Brinchmann et al. 2004; Tremonti et al. 2004). However, higher redshift starforming galaxies are offset from this sequence to higher values of [ O III ]/H β , without joining the locus of points occupied by AGN in the SDSS sample (Shapley et al.</text>
<text><location><page_2><loc_8><loc_85><loc_48><loc_92></location>2005; Erb et al. 2006, 2010; Brinchmann et al. 2008; Liu et al. 2008). As our work is motivated by a desire to better understand the physical information encoded in the BPT diagram, we pause to consider how this shift in the BPT locus might arise.</text>
<text><location><page_2><loc_8><loc_69><loc_48><loc_85></location>The difference in line luminosity ratios could be intrinsic to the galaxies' H II regions. As we have said, the ionization parameter is a major controlling factor which positions regions along the star-forming locus. Line emission from these regions will be also affected by the metallicity and dust content of the interstellar gas; by the density of that gas (through the critical densities of the lines); by the ionizing spectra of the stars (which reflect stellar masses, metallicities and rotation rates). In addition, stellar winds can alter the boundary conditions for ionized zones, a point discussed by Yeh & Matzner (2012, hereafter YM12) and to which we return below.</text>
<text><location><page_2><loc_8><loc_53><loc_48><loc_69></location>Alternatively, the shift in the BPT diagram could arise from outside the H II regions if their light is mixed with line emission from shocks or an unresolved AGN (e.g., Liu et al. 2008). Indeed, Wright et al. (2010) use integral field spectroscopy to demonstrate that a weak AGN is responsible for the shift in a single galaxy at z = 1 . 6, and Trump et al. (2011) stack HST grism data of many galaxies to show that this phenomenon is reasonably common. Taken together, these studies raise the possibility that H II regions at z ≈ 2 lie along the same BPT locus as those nearby, and the shift is an optical illusion caused by active nuclei.</text>
<text><location><page_2><loc_8><loc_35><loc_48><loc_53></location>However, the distribution of high-redshift galaxies in the BPT diagram is also shifted in the direction of high U . Because radiation pressure rises, relative to gas pressure, in proportion to U , this implies that the radiation force typically is more important in high-redshift galaxies. This radiation-force-dominated condition is also more prevalent among starburst galaxies in the local Universe, as YM12 argue on the basis of mid-infrared line emission. This possibility has also received significant support from recent resolved observations of H II regions, which provide direct evidence that radiation pressure is significant for the most luminous examples ( Lopez et al. 2011, but also see Pellegrini et al. 2011 and Silich & Tenorio-Tagle 2013).</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_35></location>The detailed role of radiation pressure in altering the line ratios of starlight-ionized H II regions has received relatively little attention, although the phenomenon has been explored in the context of AGN narrow-line regions (Binette et al. 1997; Dopita et al. 2002). Early models ignored radiation pressure entirely (e.g. Dopita et al. 2000, hereafter D00). Although more recent models include radiation pressure (e.g. Dopita et al. 2005, 2006a,b; Groves et al. 2008; Levesque et al. 2010), it is either explicitly or implicitly assumed that the geometries and internal structures of H II regions are dominated by stellar wind bubbles rather than radiation pressure. As we discuss below, the assumption that stellar wind pressure exceeds radiation pressure is often physically inconsistent with the range of ionization parameters being probed. Moreover, resolved observations of the brightest nearby H II regions indicate the hot gas produced by shocked stellar winds for the most part does not remain confined within H II regions, and instead leaks out into the lowdensity ISM (Townsley et al. 2003; Harper-Clark & Murray 2009). As a result, the pressure of shocked stellar</text>
<text><location><page_2><loc_52><loc_89><loc_92><loc_92></location>wind gas is often smaller rather than larger than radiation pressure (Lopez et al. 2011; YM12) 4 .</text>
<text><location><page_2><loc_52><loc_64><loc_92><loc_89></location>In this paper we explore how radiation pressure influences the line emission of H II regions. To do so, we compute a sequence of hydrostatic H II region models under a variety of physical assumptions about the relative importance of radiation pressure and stellar wind pressure ( § 2), and we explore how varying the physical assumptions alters the loci occupied by the model H II regions in the BPT diagram ( § 3). We then compare our models to those published by other authors ( § 4) and draw conclusions ( § 5). In a companion paper (Verdolini et al. 2012, hereafter Paper II), we use the grid of H II region models presented in this paper to construct a population synthesis model capable of predicting the line ratios of starforming galaxies containing many different H II regions. We use these models to compare to observations of starforming galaxies. Although this study cannot replace a full investigation of the factors affecting the H II region locus within the BPT diagram, it is the first to explore the roles of radiation and wind pressure.</text>
<section_header_level_1><location><page_2><loc_61><loc_62><loc_83><loc_63></location>2. PHOTOIONIZATION MODELS</section_header_level_1>
<section_header_level_1><location><page_2><loc_58><loc_60><loc_86><loc_61></location>2.1. Input Parameters and Calculations</section_header_level_1>
<text><location><page_2><loc_52><loc_36><loc_92><loc_59></location>To study the influence of radiation pressure on H II regions, we construct a grid of static, single H II regions, with a wide range of sizes, ionizing luminosities, and wind strengths. Our procedure is as follows. We first use the stellar population synthesis code Starburst99 (Leitherer et al. 1999) to generate spectra from coeval star clusters. We assume that all of the clusters are massive enough to fully sample the stellar initial mass function, which we take to have exponents -1.3 and -2.3 between stellar mass boundaries 0.1, 0.5, and 120 M glyph[circledot] . We employed the Geneva standard evolutionary tracks (Charbonnel et al. 1996; Schaerer et al. 1993a,b; Schaller et al. 1992) with solar metallicity, and Lejeune-Schmutz stellar atmospheres (Lejeune et al. 1997, 1998; Schmutz 1998), which incorporate plane-parallel atmospheres and stars with strong winds. We record the Starburst99 output spectra for cluster ages of 0 to 11 Myr at 0.5 Myr intervals.</text>
<text><location><page_2><loc_52><loc_17><loc_92><loc_35></location>We then use the photoionization code Cloudy 08.00, last described by Ferland et al. (1998), to compute the structure of static, spherical H II regions driven by point sources whose spectra are taken from the Starburst99 calculations. In addition to the spectrum of the driving source, Cloudy requires a number of other input parameters. The first of these is the total luminosity of the ionizing source, for which we run a series of models with L = 10 33 -10 46 erg s -1 in 1 dex steps. The second is the number density of hydrogen nuclei at the innermost zone of the H II region, which we set to values from n H , in = 10 -1 -10 5 in steps of 1 dex. The third is the distance of the innermost zone from the point source, which we vary from R in = 10 -2 ˜ r ch -10 2 ˜ r ch in steps of 0.2 dex.</text>
<unordered_list>
<list_item><location><page_2><loc_52><loc_7><loc_92><loc_16></location>4 Note that Pellegrini et al. (2011) assume a smaller filling factor for the X-ray emitting gas, and so assign it a much higher pressure than Lopez et al. (2011). For the same luminosity, small, higher-pressure bubbles have a greater dynamical effect on their immediate surroundings. But these bubbles are less important for the entire region than large, lower-pressure ones. This is a consequence of the virial theorem, which ties dynamics to the net energy budget.</list_item>
</unordered_list>
<table>
<location><page_3><loc_12><loc_60><loc_89><loc_88></location>
<caption>Table 1 Comparison of Model Parameters</caption>
</table>
<text><location><page_3><loc_8><loc_54><loc_29><loc_55></location>Here the characteristic radius</text>
<formula><location><page_3><loc_20><loc_51><loc_48><loc_54></location>˜ r ch = αL 2 12 π (2 . 2 k B Tc ) 2 S (1)</formula>
<text><location><page_3><loc_8><loc_22><loc_48><loc_50></location>is the radius of a uniform-density, dust-free Stromgren sphere for which the gas pressure is equal to the unattenuated radiation pressure at its edge (Krumholz & Matzner 2009; YM12); in this equation, α is the recombination rate coefficient, T is the gas temperature, and L and S are the bolometric luminosity and the output of ionizing photons per unit time, respectively, from the point source. In all the calculations presented here we adopt the same fiducial parameters as YM12: T = 8000 K, α = 3 . 0 × 10 -13 cm 3 s -1 . Finally, we adopt Cloudy's default ISM dust grain abundance and size distributions at solar metallicity, but in order to allow more meaningful comparison between our results and those of D00, we adjust the gas-phase element abundances in our calculation to match theirs. These choices mean that the dust discriminant parameter (Draine 2011) takes the same value, γ = 7 . 4, as in YM12: so, dust opacity is significant within radiation pressure-dominated ionized zones. We summarize all the parameters we use in our calculations in Table 1. The Table also describes the parameter choices used in D00 and Levesque et al. (2010, hereafter L10).</text>
<text><location><page_3><loc_8><loc_10><loc_48><loc_22></location>For each set of input parameters, we use Cloudy to calculate the structure of the resulting H II region, halting at the point where the gas temperature drops to 100 K in order to ensure that the ionization front is fully enclosed. We perform each calculation twice, once with radiation pressure turned off, and once with radiation pressure turned on and allowed to exceed gas pressure (in contrast to Cloudy's default setting, which does not allow radiation pressure to be greater than gas pressure.)</text>
<section_header_level_1><location><page_3><loc_12><loc_8><loc_44><loc_9></location>2.2. Model Outputs and Physical Parameters</section_header_level_1>
<text><location><page_3><loc_52><loc_40><loc_92><loc_55></location>The output of our calculations is two fourdimensional grids of models defined by the parameters ( t, n H , in , L, R in ), where t is the age of the stellar population used to generate the ionizing spectrum. One grid contains models with radiation pressure turned on, which we refer to as the RP models, and the other contains models with radiation pressure disabled, which we refer to as gas pressure, or GP, models. For each run in both model grids, we compute several optical emission line luminosities integrated over the ionized gas, including the lines used to construct the BPT diagram: H α , H β , [ O III ] λ 5007, and [ N II ] λ 6584.</text>
<text><location><page_3><loc_52><loc_33><loc_92><loc_39></location>In order to understand the physical meaning of the results, it is helpful to characterize each model by two dimensionless numbers that can be computed from the Cloudy output. Following YM12, we define the radiation pressure parameter</text>
<formula><location><page_3><loc_68><loc_29><loc_92><loc_32></location>Ψ ≡ R IF ˜ r ch , (2)</formula>
<text><location><page_3><loc_52><loc_21><loc_92><loc_29></location>where R IF is the radius of the ionization front (IF). A value of Ψ < 1 indicates that the entire IF falls within ˜ r ch , and thus that radiation pressure is more important than gas pressure in determining its structure. Again following YM12, we define a separate stellar wind parameter</text>
<formula><location><page_3><loc_64><loc_18><loc_92><loc_21></location>Ω ≡ P in V in P IF V IF -P in V in , (3)</formula>
<text><location><page_3><loc_52><loc_7><loc_92><loc_17></location>where P IF and P in are the gas pressures at the edge of the ionization front and the innermost zone, respectively, and V IF = (4 / 3) πR 3 IF and V in = (4 / 3) πR 3 in are the volumes contained within the IF and the inner edge of the H II region, respectively. The inner edge of the photoionized region is the outer edge of the bubble of hot gas inflated by the stars' winds. Thus Ω reflects the contribution of a pressurized wind bubble to the total energy budget</text>
<figure>
<location><page_4><loc_11><loc_71><loc_45><loc_92></location>
<caption>Figure 1. An example of how our models fill the parameter space of Ψ and Ω. In the Figure, each plot symbol shows the values of Ψ and Ω computed for a particular calculation in our model grid at t = 0, n H , in = 10 cm -3 , with radiation pressure on. Colors indicate lines of constant L , running from 10 33 -10 46 erg s -1 as indicated in the legend. The sequence of points along a given model corresponds to varying R in from 10 -2 ˜ r ch -10 2 ˜ r ch , with Ω increasing with R in . Note that Ψ is a function of density as well as ionizing source luminosity. Radiation pressure can be significant in a high density region with relatively lower ionizing luminosity. Note that our full H II region model grids are incorporated into the dynamical models in Paper II.</caption>
</figure>
<text><location><page_4><loc_8><loc_52><loc_48><loc_56></location>of the H II region. In a region strongly pressurized by stellar winds Ω glyph[greatermuch] 1, while in a region with negligible wind pressure Ω glyph[lessmuch] 1.</text>
<text><location><page_4><loc_8><loc_31><loc_48><loc_52></location>For each Cloudy model, we compute the quantities Ψ and Ω, and thus we may think of our models as describing a parameter space ( t, n H , in , Ψ , Ω), as illustrated by Figure 1. This parameter space describes H II regions for which both radiation and wind pressure run from strong to negligible. To study the effects of winds, we reduce this fourdimensional parameter space to a three-dimensional one by selecting two representative values of Ω: we designate models with log Ω = 2 as strong wind (SW) models, and those with log Ω = -1 . 5 as weak wind (WW) models. Since our models never produce log Ω = -1 . 5 or 2 exactly, we construct these models by interpolation. At each age t , density n H , in , and luminosity L , we find the two models whose values of Ω bracket our target one, and we compute line luminosities at the target value of Ω by interpolating between the two bracketing models.</text>
<text><location><page_4><loc_8><loc_23><loc_48><loc_31></location>Through this procedure, we obtain a set of four reduced model grids, which we refer to as RPWW (radiation pressure turned on, log Ω = -1 . 5), RPSW (radiation pressure turned on, log Ω = 2), GPWW (radiation pressure turned off, log Ω = -1 . 5), and GPSW (radiation pressure turned off, log Ω = 2).</text>
<text><location><page_4><loc_8><loc_7><loc_48><loc_23></location>It is important to bear in mind that our RP models are physically self-consistent, whereas the GP models are deliberately not. Thus, RPWW models make a transition from classical spherical Stromgren spheres to radiationconfined shells, along the sequence described by Draine (2011), as Ψ decreases through unity. RPSW models are always thin shells: both radiation and wind pressure play a role in confining them, but, as we explain below, wind pressure always dominates. GPSW models are also thin shells, but due to the neglect of radiation pressure they sample a range of ionization parameters inaccessible to real regions. Finally, GPWW models are always filled</text>
<text><location><page_4><loc_52><loc_87><loc_92><loc_92></location>Stromgren spheres, even when the radiation force should confine them. They can also sample unphysically high values of U . Our GP models have strictly uniform gas pressure, as they include no other forces.</text>
<text><location><page_4><loc_52><loc_72><loc_92><loc_86></location>Each of these model grids gives the line luminosities of H II regions as a function of the three remaining parameters, ( t, n H , in , Ψ), or equivalently ( t, n H , L ). We summarize the properties of the models in Table 2. We will make use of the four full model grids in Paper II, but for the remainder of this paper we concentrate on the particular case t = 0, n H , in = 10 cm -3 , in order to understand how the choice of input physics alters the structure of H II regions. We choose these parameters in particular because they match the ones used by a number of previous authors, thus facilitating easy comparison.</text>
<section_header_level_1><location><page_4><loc_68><loc_69><loc_76><loc_70></location>3. RESULTS</section_header_level_1>
<section_header_level_1><location><page_4><loc_64><loc_67><loc_80><loc_69></location>3.1. One-Zone Models</section_header_level_1>
<text><location><page_4><loc_52><loc_50><loc_92><loc_67></location>For a given spectral shape, each ionized parcel with uniform density and temperature can be characterized by only two parameters: the density n H and the ionization parameter U = n γ,i /n H , where n γ,i is the number density of ionizing photons. Therefore there is a unique mapping between U and initial densities on the BPT diagram. The one-zone models also represent simple analogs of H II regions, for one can decompose an H II region into zones in which U , n H , and ionizing spectrum are nearly constant. Thus the one-zone models represent thin, uniformly ionized regions which are very much like the ionized layer of a wind bubble. As such, they resemble best the SW models to be discussed in § 3.2.2.</text>
<text><location><page_4><loc_52><loc_35><loc_92><loc_49></location>We run an additional set of Cloudy 'one-zone' calculations in which we only compute the properties of line emission from the first, innermost zone. In this zone we can specify the value of U by choosing the the density n H and the bolometric luminosity L (and thus the ionizing photon luminosity S ). We run models with n H = 10 -1 -10 6 cm -3 in 1 dex steps, and U = 10 -4 -10 0 . 6 in 0.2 dex steps, all using an input spectrum corresponding to our t = 0 Starburst99 model, and using the same abundances and other parameters as the rest of our models.</text>
<text><location><page_4><loc_52><loc_12><loc_92><loc_35></location>In Figure 2, we show the constant U and constant n H contours marked with black solids lines and blue dashed lines, respectively, on the BPT diagram computed with the one-zone models. The ionization parameter U and ionizing luminosity S increase from lower right to upper left, and increasing the density shifts models up and to the right, until the density exceeds ∼ 10 4 -10 5 cm -3 . Beyond this point, the models shift down and to the left, because the density exceeded the critical densities of the [ N II ] and [ O III ] emission lines, which are 6 . 6 × 10 4 cm -3 and 6 . 8 × 10 5 cm -3 , respectively (Osterbrock & Ferland 2006). In Paper II, we will return to the discussion of line ratios, U , and critical densities on the BPT diagram, and further discuss most extreme H II regions exceeding the upper limit of line ratios set by Kewley et al. (2001), which is based on the mapping between line ratios and U but ignored the effect of densities.</text>
<text><location><page_4><loc_52><loc_7><loc_92><loc_12></location>We note that the BPT locations of macroscopic H II regions will differ from those of individual gas parcels, because of spatial variations in the physical quantities. In all cases U drops and the ionizing spectrum changes</text>
<table>
<location><page_5><loc_27><loc_81><loc_74><loc_88></location>
<caption>Table 2 Model Properties</caption>
</table>
<figure>
<location><page_5><loc_11><loc_59><loc_45><loc_80></location>
<caption>Figure 3. Electron density versus radius for sample H II regions. Top panel: RPWW (blue solid line) and GPWW (black dashed line) regions. Bottom panel: RPSW (blue solid line) and GPSW (black dashed line) regions. The age of the ionizing star cluster in these regions is 0 Myr and the density at the inner boundary is 10 cm -3 . The luminosity in all models is 10 43 erg s -1 . We select the value of R in from our grid that gives log Ω closest to -1 . 5 and 2; exact values of Ω for the four cases shown are as indicated in the legend. See Section 2.2 for details. Again we note that high luminosity is required here to reach radiation pressure-dominated state because the density is low.</caption>
</figure>
<figure>
<location><page_5><loc_55><loc_59><loc_89><loc_80></location>
</figure>
<text><location><page_5><loc_27><loc_59><loc_29><loc_60></location>log1o</text>
<paragraph><location><page_5><loc_8><loc_50><loc_48><loc_58></location>Figure 2. Models in the BPT diagram. Black lines show onezone models with constant U , while blue dashed lines show onezone models of constant n H ; both are calculated for an ionizing spectrum corresponding to a zero-age stellar population and Solar metallicity. We also show models RPWW, RPSW, GPWW, and GPSW (orange and green lines, as indicated by the legend) with n H , in = 10 cm -3 , calculated with the same ionizing spectrum and metallicity.</paragraph>
<text><location><page_5><loc_8><loc_34><loc_48><loc_49></location>as one approaches the ionization front, because of selective absorption by neutral H atoms, and in some cases by dust grains. When radiation pressure is strong (and is included) and winds are weak, the gas density increases significantly across the layer. We therefore anticipate that full H II region models should differ from the onezone calculation, even though the innermost zones are accounted by it. Moreover the macroscopic physical parameters, the assumed geometry, and the inclusion or neglect of radiation pressure should affect the BPT loci. We explore these dependencies in the subsequent sections.</text>
<section_header_level_1><location><page_5><loc_22><loc_32><loc_34><loc_33></location>3.2. Full Models</section_header_level_1>
<text><location><page_5><loc_8><loc_17><loc_48><loc_31></location>We now turn to our four full (radially resolved) H II region models, RPWW, GPWW, RPSW, and GPSW. In Figure 2, we overlay these models with t = 0 and n H , in = 10 cm -3 on the one-zone calculations. Other choices of density give qualitatively similar results, as long as the density is well below the critical densities of the [ O III ] and [ N II ] lines. As with the one-zone models, the full models form a sequence of values defined by Ψ or U , which we control by varying L : high-Ψ, lowU , lowL models are found at the bottom right and low-Ψ, highU , highL ones at the top left of each sequence.</text>
<section_header_level_1><location><page_5><loc_20><loc_14><loc_37><loc_15></location>3.2.1. Weak Wind Models</section_header_level_1>
<text><location><page_5><loc_8><loc_7><loc_48><loc_13></location>When stellar wind pressure is negligible (log Ω = -1 . 5), H II regions at the low L end of the sequence are very similar to each other. This is because L determines the balance between radiation pressure and gas pressure; a high luminosity produces a large ˜ r ch (Equation 1) and</text>
<text><location><page_5><loc_52><loc_39><loc_92><loc_45></location>thus a small value of Ψ (Equation 2). Thus when L is low radiation pressure forces are negligible, and the results do not change much depending on whether we include them or not. The density within both H II regions is roughly constant at n H = n H , in = 10 cm -3 .</text>
<text><location><page_5><loc_52><loc_14><loc_92><loc_39></location>At the high L , on the other hand, RPWW and GPWW differ substantially. In model GPWW, as L increases, we find that [ O III ]/H β increases and [ N II ]/H α decreases without limit. In contrast, in model RPWW these line ratios saturate at a finite value. If one were to infer ionization parameters from these line ratios based on one-zone models, one would say that U saturates at a finite value in model RPWW, while in model GPWW it can increase without limit as L does. We can understand the difference in behavior by examining the density structures of RPWW and GPWW regions, of which we show an example in Figure 3. At high L , RPWW model H II regions are strongly dominated by radiation pressure. Under force balance, radiation pressure confines ionized gas into a much thinner layer and leads to a steep increase in density towards the IF. Much of the line emission comes from this dense layer, within which U is much lower than it is closer to the central source. YM12 discuss this effect in detail.</text>
<text><location><page_5><loc_52><loc_7><loc_92><loc_13></location>This effect does not operate in the GPWW models, where we have artificially disabled radiation pressure. As a result, these H II regions remain at nearly constant density regardless of the source luminosity. This allows U to increase without limit, and in turn allows the [ O III ]/H β</text>
<text><location><page_6><loc_8><loc_89><loc_48><loc_92></location>and [ N II ]/H α line ratios to continue changing even at large L .</text>
<text><location><page_6><loc_8><loc_71><loc_48><loc_89></location>Finally, it is interesting to note that, despite the uniform pressure in the GPWW models, the actual values of the line ratios are still significantly offset from the corresponding one-zone models of the same density, n H = 10 cm -3 . At small L the shape of the sequence is similar but the models are displaced to slightly higher [ N II ]/H α and [ O III ]/H β , while at large L the deviation is larger and the shape of the sequence is different as well. This difference occurs because, even though the pressure is uniform in the GPWW models, other quantities are not. In particular, the spectrum of the ionizing radiation field varies with radius, due to selective absorption of lowerenergy photons by neutral H atoms and of higher-energy photons by dust within the ionized layer.</text>
<section_header_level_1><location><page_6><loc_19><loc_69><loc_37><loc_70></location>3.2.2. Strong Wind Models</section_header_level_1>
<text><location><page_6><loc_8><loc_60><loc_48><loc_68></location>In the RPSW and GPSW models (log Ω = 2), strong stellar wind pressure produces large 'voids' of diffuse, high temperature stellar wind gas at the centers of the model H II regions. As a result, the ionized gas is confined to a thin shell between the wind bubble and the IF.</text>
<text><location><page_6><loc_8><loc_28><loc_48><loc_60></location>The location of the RPSW model in the BPT diagram is strikingly far from the locations of other models. Like the RPWW models, the RPSW models saturate at finite values of [ N II ]/H α and [ O III ]/H β , regardless of how high the luminosity becomes. However, unlike in case RPWW, the saturation values are extraordinarily far down the sequence of one-zone models: [ N II ]/H α > 10 -0 . 5 and [ O III ]/H β < 10 0 , corresponding to a one-zone value of U < 10 -3 . 3 . We can understand this effect by considering the relative importance of radiation and wind pressure in controlling the internal structures of H II regions. A value of log Ω = 2 requires that P IF V IF /P in V in = 1 . 01. Physically, this amounts to saying that the energy of the wind bubble constitutes 99% of the internal energy of the entire H II region. We note that V IF is strictly greater than V in . Similarly, P IF is strictly greater than P in , since the radiation force necessarily falls to zero at the IF, and thus pressure balance requires that gas pressure at the IF exceed that at the edge of the wind bubble. Thus models with log Ω = 2 necessarily have both V IF ≈ V in and P IF ≈ P in . This corresponds to the H II region being a thin shell of nearly constant gas pressure. Figure 3 shows an example of this uniform density.</text>
<text><location><page_6><loc_8><loc_7><loc_48><loc_28></location>The RPSW configuration clearly cannot have radiation pressure as a significant force. If the radiation pressure force were significant, then we could not have P IF ≈ P in , since the pressure at the IF would be pure gas pressure, and this would have to balance the gas plus radiation pressure at the inner edge. The conclusion of this analysis is that it is not possible to construct a physically consistent model in which wind pressure and radiation pressure are both strong in the dimensionless sense. Indeed, our model grids reflect this fact in that there are no models with radiation pressure turned on that are simultaneously dominated by wind (Ω glyph[greatermuch] 1) and dominated by radiation pressure (Ψ glyph[lessmuch] 1). This physical effect manifests in the BPT diagram as a saturation in the range of line ratios that the RPSW models are able to reach. As discussed above, the location of an H II region driven by</text>
<text><location><page_6><loc_52><loc_77><loc_92><loc_92></location>a stellar source in the BPT diagram is effectively controlled by U , the photon to baryon ratio. However, U may also be thought of as a measure of the importance of radiation pressure, since increasing the photon number density relative to the baryon density also increases the radiation pressure relative to gas pressure. The fact that RPSW models cannot reach small values of Ψ also means that they cannot reach large values of U , and thus cannot reach the line ratios associated with large U . YM12 used this point to derive upper limits on the wind energy budget within individual H II regions and entire galaxies.</text>
<text><location><page_6><loc_52><loc_59><loc_92><loc_77></location>In contrast, radiation pressure is completely neglected in GPSW models. As there are no other forces to balance gas pressure gradients, these models have P IF = P in independent of the luminosity, and thus a value of log Ω = 2 simply implies that the shell is very thin: R IF = 1 . 003 R in . In these models one can achieve arbitrarily high U by raising the luminosity and increasing R in to keep up with R IF . Figure 3 shows an example of such a model. Thus the GPSW models are not restricted in the range of U they can represent. However, the comparison with the RPSW models shows that GPSW models at high U are unphysical, because radiation force would have compressed the gas and limited U in a real region.</text>
<text><location><page_6><loc_52><loc_44><loc_92><loc_58></location>The comparison between RPSW, GPSW, and onezone models shown in Figure 2 also reflects these effects. Both RPSW and GPSW models are wind-dominated and therefore have nearly uniform densities, and thus can be reasonably-well represented by one-zone models, leaving aside the issues of radiation field hardening and nonuniform temperature discussed in Section 3.2.1. Thus both RPSW and GPSW models follow the one-zone sequence reasonably closely. They differ only in the range of U values within that sequence that they are able to sample.</text>
<section_header_level_1><location><page_6><loc_58><loc_42><loc_85><loc_43></location>4. COMPARISON TO PREVIOUS WORK</section_header_level_1>
<text><location><page_6><loc_52><loc_28><loc_92><loc_41></location>It is interesting to revisit earlier published models for H II region line ratios in the context of our exploration of how these line ratios respond to changes in the included physics. We have chosen our model parameters in Starburst99 and Cloudy to be as close as possible to those used by D00 in order to facilitate this comparison. In Figure 4, we compare our four model results with the results computed by D00 and L10, at the same age of ionizing star cluster (0 Myr) and same density n H , in = 10 cm -3 .</text>
<text><location><page_6><loc_52><loc_7><loc_92><loc_28></location>The D00 model, which did not include radiation pressure and adopted plane-parallel ionized gas slabs at a fixed density, is essentially a wind-dominated model. This is because a plane-parallel slab can be thought of as a thin shell of material at roughly fixed distance from the ionizing source, and the only way to create a thin shell of constant gas pressure is to confine it with hot gas. Therefore our closest model to the D00 model is GPSW, and indeed we find that our GPSW results agree with the D00 model fairly well. Differences in line ratios between D00 and GPSW are around 0.1 to 0.2 dex. Our model sequence extends somewhat further, but this is simply a result of our having used a slightly larger range of input luminosities. The agreement between the models confirms that our Cloudy calculations, with input parameters set very close to the D00 settings, can reasonably</text>
<figure>
<location><page_7><loc_11><loc_71><loc_45><loc_92></location>
<caption>Figure 4. A comparison of model results on the BPT diagram. All results shown are for n H , in = 10 cm -3 and a spectrum corresponding to a zero-age stellar population. The D00 model (marked as Kewley01 in the legend) is shown in dark blue, the L10 model result is in light blue, and our model results are shown in orange and green lines.</caption>
</figure>
<text><location><page_7><loc_8><loc_52><loc_48><loc_63></location>well reproduce the earlier results. However, we note the comparison shows that the D00 models are not physically realistic at high luminosity, because one cannot neglect radiation pressure in very bright H II regions. Radiation pressure limits the physical range of U , particularly for wind-confined slabs, and models without radiation pressure such as those of D00 do not properly capture this effect.</text>
<text><location><page_7><loc_8><loc_23><loc_48><loc_52></location>The models from L10 are similar to those of D00 in that they are based on plane-parallel ionized gas slabs, but the L10 models include radiation pressure. Therefore when U is low, the regions must be confined by wind pressure (like our RPSW). On the other hand, when U is high, the L10 models should be confined by radiation pressure (like our RPWW). However, Figure 4 shows that overall L10's models closely track our GPSW curve (maximum separation < 0 . 1 dex). In light of our results, we can see that the L10 models, while not physically inconsistent, do represent a rather odd cut through parameter space. There are two structural parameters describing H II regions, and the L10 models sample a one-dimensional path through this two-dimensional space. Along this path the ratio of wind pressure to radiation pressure varies systematically from large values (Ω glyph[greatermuch] 1, Ψ glyph[greatermuch] 1) at low ionization parameter to small values (Ω glyph[lessmuch] 1, Ψ glyph[lessmuch] 1) at high ionization parameter. There is no obvious physical reason such a systematic variation in wind to radiation pressure strength should occur, particularly since the ratio of stellar wind momentum flux to luminosity is roughly the same for all O stars (Repolust et al. 2004).</text>
<section_header_level_1><location><page_7><loc_22><loc_21><loc_34><loc_22></location>5. CONCLUSIONS</section_header_level_1>
<text><location><page_7><loc_8><loc_7><loc_48><loc_20></location>We have computed a grid of quasi-static H II region models using Starburst 99 and Cloudy that covers a large range of density, luminosity, and stellar population age. In order to understand how radiation pressure and stellar winds alter H II regions' internal structures and observable line emission, we run two sets of models, one with radiation pressure enabled and one with it disabled, and we vary the radius at which the inner, wind-dominated bubble ends and the photoionized region begins. In the manner, we construct four sets of model H II regions:</text>
<text><location><page_7><loc_52><loc_83><loc_92><loc_92></location>(1) ones with radiation pressure and weak stellar winds (RPWW), (2) wind bubbles that also include radiation pressure (RPSW), (3) Stromgren spheres where radiation pressure is ignored and winds are weak (GPWW), and (4) wind-dominated bubbles where radiation pressure is disabled (GPSW). We then explore how each set of H II regions populates the BPT diagram.</text>
<text><location><page_7><loc_52><loc_63><loc_92><loc_82></location>Our models reveal a number of interesting effects. All models form a sequence that runs from the lower right corner of the BPT diagram (high [ N II ]/H α , low [ O III ]/H β ) to the upper left corner (low [ N II ]/H α , high [ O III ]/H β ), with the position of an H II region along the sequence dictated by its luminosity, or equivalently its effective ionization parameter U . However, the range of U explored by the models is limited when radiation pressure is included. Because strong radiation pressure, which would produce high U , also causes gas to pile into a dense shell, the characteristic value of U within the shell is limited at a finite value. (See YM12 for more detail.) As a consequence, models which neglect radiation pressure can reflect an arbitrarily high value of U , which real regions cannot.</text>
<text><location><page_7><loc_52><loc_35><loc_92><loc_62></location>The interaction of winds with radiation pressure further enhances this effect. We show that a stellar winddominated region cannot also have strong radiation pressure while remaining in hydrostatic balance, and as a result the range of U is severely limited. This means that wind-dominated H II regions can never occupy the upper-left portion of the BPT diagram, and, conversely, those H II regions that are observed to lie in this region must either have negligible wind pressure, be far from pressure balance, or be kept in pressure balance by forces other than gas and radiation pressure (e.g. strong magnetic pressure; YM12). The most realistic option, and the one favored by direct observations of nearby H II regions (Harper-Clark & Murray 2009; Lopez et al. 2011) as well as mid-infrarared line ratios (YM12) is the first one: wind pressure is not dynamically significant, at least for bright H II regions. Further, the fact that the high-redshift galaxy population has characteristically high ionization parameters implies that radiation pressure is significant within these galaxies' ionized zones, in an ionization-weighted sense.</text>
<text><location><page_7><loc_52><loc_16><loc_92><loc_35></location>We have compared our results to the earlier models of Dopita et al. (2000, D00) and Levesque et al. (2010, L10). In these models the H II region is assumed to be a wind-dominated thin ionized shell, which corresponds to our GPSW model. We find that this model agrees well with the results of D00 and L10. However, we show that these models are inconsistent at the high luminosity end. The D00 models neglect radiation pressure for H II regions where it is non-negligible. The L10 models include radiation pressure, but we show that the assumed plane-parallel slab geometry is physically realistic only if the strength of the ratio of stellar wind pressure to radiation pressure varies systematically with H II region properties in a physically unexpected manner.</text>
<text><location><page_7><loc_52><loc_7><loc_92><loc_16></location>While these calculations provide insight into how the physics driving H II regions' structures translates into observable properties such as line ratios, a full model for where galaxies fall in the BPT diagram requires attention to H II regions' dynamical expansion as well as their internal structure. This problem is the subject of Paper II.</text>
<text><location><page_8><loc_8><loc_77><loc_48><loc_92></location>This project was initiated during the 2010 International Summer Institute for Modeling in Astrophysics (ISIMA) summer program, whose support is gratefully acknowledged. SCCY and CDM would like to acknowledge an NSERC Discovery grant and conversations with Stephen Ro and Shelley Wright. MRK acknowledges support from an Alfred P. Sloan Fellowship, from the National Science Foundation through grant CAREER0955300, from NASA through Astrophysics Theory and Fundamental Physics grant NNX09AK31G, and a Chandra Telescope Grant.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "The emission line ratios [ O III ] λ 5007/H β and [ N II ] λ 6584/H α have been adopted as an empirical way to distinguish between the fundamentally different mechanisms of ionization in emission-line galaxies. However, detailed interpretation of these diagnostics requires calculations of the internal structure of the emitting H II regions, and these calculations depend on the assumptions one makes about the relative importance of radiation pressure and stellar winds. In this paper we construct a grid of quasi-static H II region models to explore how choices about these parameters alter H II regions' emission line ratios. We find that, when radiation pressure is included in our models, H II regions reach a saturation point beyond which further increases in the luminosity of the driving stars does not produce any further increase in effective ionization parameter, and thus does not yield any further alteration in an H II region's line ratio. We also show that, if stellar winds are assumed to be strong, the maximum possible ionization parameter is quite low. As a result of this effect, it is inconsistent to simultaneously assume that H II regions are wind-blown bubbles and that they have high ionization parameters; some popular H II region models suffer from this inconsistency. Our work in this paper provides a foundation for a companion paper in which we embed the model grids we compute here within a population synthesis code that enables us to compute the integrated line emission from galactic populations of H II regions. Subject headings: galaxies: high-redshift - galaxies: ISM - HII regions - ISM: bubbles - ISM: lines and bands",
"pages": [
1
]
},
{
"title": "LINE EMISSION FROM RADIATION-PRESSURIZED HII REGIONS I: INTERNAL STRUCTURE AND LINE RATIOS",
"content": "Sherry C. C. Yeh 1 , Silvia Verdolini 2 , Mark R. Krumholz 3 , Christopher D. Matzner 1 , Alexander G. G. M. Tielens 2 Accepted for publication in ApJ, March 12, 2013",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "The line ratios [ O III ] λ 5007/H β and [ N II ] λ 6584/H α , first proposed for use in galaxy classification by Baldwin et al. (1981) (hereafter BPT), are commonly used to diagnose the origins of emission lines from galaxies, and in particular to discriminate between galaxies whose emission is powered by star formation-driven H II regions and from those powered by active galactic nuclei (AGNs). These emission line pairs are particularly useful because (1) they are bright and thus relatively easy to measure, (2) blending between the lines can be corrected with reasonable accuracy, so long as the spectra are taken with sufficient resolution, and (3) the wavelengths in each line pair are quite similar, so the line ratio is relatively insensitive to dust-reddening (Veilleux & Osterbrock 1987). The power of these line ratios as diagnostics comes from their sensitivity to the spectral shape of the radiation field driving the ionization, which can be understood from a simple physical picture. To first order, the intensities of the H α and H β lines simply measure the total photoionization rate, and thus normalize out the ionizing luminosity. On the other hand, the [ O III ] and [ N II ] intensities are sensitive not only to the total ionizing luminosity, but also to the shape of the ionizing spectrum and to the ionization parameter U , which measures the ratio of photons to baryons in the ionized [email protected] 3 Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 gas. When the ionizing flux arises from hot stars, the ionizing spectrum is dominated by low-energy photons that have short mean-free paths through neutral gas. Thus the H II region consists of a fully ionized zone with a sharp boundary. Within this region, as U increases, more of the ionized gas volume becomes filled with high ionization-potential species such as O ++ , and less with low-ionization potential species such as N + . As a result, H II regions ionized by hot stars tend to fall along a sequence that runs from high [ O III ]/H β , low [ N II ]/H α to low [ O III ]/H β , high [ N II ]/H α . On the other hand, if the ionizing spectrum follows a power-law, as expected for AGN, then a significant amount of the ionization is produced by X-ray photons capable of ionizing higher ionization potential species like O ++ . Moreover, these photons have large mean-free paths, giving rise to a large zone of partial ionization rather than a smaller region of full ionization as in the stellar case. In this configuration, [ O III ]/H β and [ N II ]/H α both increase with U , and either one or the other tends to be larger than in the stellar case, leading to a sequence that runs from intermediate to high [ O III ]/H β and [ N II ]/H α and is well-separated from the locus occupied by H II regions dominated by stellar sources. This simple picture is roughly consistent with local observations: star-forming galaxies in the Sloan Digital Sky Survey (SDSS; median redshift z = 0 . 1) obey a tight correlation between the [ O III ]/H β and [ N II ]/H α ratios in the BPT diagram (Brinchmann et al. 2004; Tremonti et al. 2004). However, higher redshift starforming galaxies are offset from this sequence to higher values of [ O III ]/H β , without joining the locus of points occupied by AGN in the SDSS sample (Shapley et al. 2005; Erb et al. 2006, 2010; Brinchmann et al. 2008; Liu et al. 2008). As our work is motivated by a desire to better understand the physical information encoded in the BPT diagram, we pause to consider how this shift in the BPT locus might arise. The difference in line luminosity ratios could be intrinsic to the galaxies' H II regions. As we have said, the ionization parameter is a major controlling factor which positions regions along the star-forming locus. Line emission from these regions will be also affected by the metallicity and dust content of the interstellar gas; by the density of that gas (through the critical densities of the lines); by the ionizing spectra of the stars (which reflect stellar masses, metallicities and rotation rates). In addition, stellar winds can alter the boundary conditions for ionized zones, a point discussed by Yeh & Matzner (2012, hereafter YM12) and to which we return below. Alternatively, the shift in the BPT diagram could arise from outside the H II regions if their light is mixed with line emission from shocks or an unresolved AGN (e.g., Liu et al. 2008). Indeed, Wright et al. (2010) use integral field spectroscopy to demonstrate that a weak AGN is responsible for the shift in a single galaxy at z = 1 . 6, and Trump et al. (2011) stack HST grism data of many galaxies to show that this phenomenon is reasonably common. Taken together, these studies raise the possibility that H II regions at z ≈ 2 lie along the same BPT locus as those nearby, and the shift is an optical illusion caused by active nuclei. However, the distribution of high-redshift galaxies in the BPT diagram is also shifted in the direction of high U . Because radiation pressure rises, relative to gas pressure, in proportion to U , this implies that the radiation force typically is more important in high-redshift galaxies. This radiation-force-dominated condition is also more prevalent among starburst galaxies in the local Universe, as YM12 argue on the basis of mid-infrared line emission. This possibility has also received significant support from recent resolved observations of H II regions, which provide direct evidence that radiation pressure is significant for the most luminous examples ( Lopez et al. 2011, but also see Pellegrini et al. 2011 and Silich & Tenorio-Tagle 2013). The detailed role of radiation pressure in altering the line ratios of starlight-ionized H II regions has received relatively little attention, although the phenomenon has been explored in the context of AGN narrow-line regions (Binette et al. 1997; Dopita et al. 2002). Early models ignored radiation pressure entirely (e.g. Dopita et al. 2000, hereafter D00). Although more recent models include radiation pressure (e.g. Dopita et al. 2005, 2006a,b; Groves et al. 2008; Levesque et al. 2010), it is either explicitly or implicitly assumed that the geometries and internal structures of H II regions are dominated by stellar wind bubbles rather than radiation pressure. As we discuss below, the assumption that stellar wind pressure exceeds radiation pressure is often physically inconsistent with the range of ionization parameters being probed. Moreover, resolved observations of the brightest nearby H II regions indicate the hot gas produced by shocked stellar winds for the most part does not remain confined within H II regions, and instead leaks out into the lowdensity ISM (Townsley et al. 2003; Harper-Clark & Murray 2009). As a result, the pressure of shocked stellar wind gas is often smaller rather than larger than radiation pressure (Lopez et al. 2011; YM12) 4 . In this paper we explore how radiation pressure influences the line emission of H II regions. To do so, we compute a sequence of hydrostatic H II region models under a variety of physical assumptions about the relative importance of radiation pressure and stellar wind pressure ( § 2), and we explore how varying the physical assumptions alters the loci occupied by the model H II regions in the BPT diagram ( § 3). We then compare our models to those published by other authors ( § 4) and draw conclusions ( § 5). In a companion paper (Verdolini et al. 2012, hereafter Paper II), we use the grid of H II region models presented in this paper to construct a population synthesis model capable of predicting the line ratios of starforming galaxies containing many different H II regions. We use these models to compare to observations of starforming galaxies. Although this study cannot replace a full investigation of the factors affecting the H II region locus within the BPT diagram, it is the first to explore the roles of radiation and wind pressure.",
"pages": [
1,
2
]
},
{
"title": "2.1. Input Parameters and Calculations",
"content": "To study the influence of radiation pressure on H II regions, we construct a grid of static, single H II regions, with a wide range of sizes, ionizing luminosities, and wind strengths. Our procedure is as follows. We first use the stellar population synthesis code Starburst99 (Leitherer et al. 1999) to generate spectra from coeval star clusters. We assume that all of the clusters are massive enough to fully sample the stellar initial mass function, which we take to have exponents -1.3 and -2.3 between stellar mass boundaries 0.1, 0.5, and 120 M glyph[circledot] . We employed the Geneva standard evolutionary tracks (Charbonnel et al. 1996; Schaerer et al. 1993a,b; Schaller et al. 1992) with solar metallicity, and Lejeune-Schmutz stellar atmospheres (Lejeune et al. 1997, 1998; Schmutz 1998), which incorporate plane-parallel atmospheres and stars with strong winds. We record the Starburst99 output spectra for cluster ages of 0 to 11 Myr at 0.5 Myr intervals. We then use the photoionization code Cloudy 08.00, last described by Ferland et al. (1998), to compute the structure of static, spherical H II regions driven by point sources whose spectra are taken from the Starburst99 calculations. In addition to the spectrum of the driving source, Cloudy requires a number of other input parameters. The first of these is the total luminosity of the ionizing source, for which we run a series of models with L = 10 33 -10 46 erg s -1 in 1 dex steps. The second is the number density of hydrogen nuclei at the innermost zone of the H II region, which we set to values from n H , in = 10 -1 -10 5 in steps of 1 dex. The third is the distance of the innermost zone from the point source, which we vary from R in = 10 -2 ˜ r ch -10 2 ˜ r ch in steps of 0.2 dex. Here the characteristic radius is the radius of a uniform-density, dust-free Stromgren sphere for which the gas pressure is equal to the unattenuated radiation pressure at its edge (Krumholz & Matzner 2009; YM12); in this equation, α is the recombination rate coefficient, T is the gas temperature, and L and S are the bolometric luminosity and the output of ionizing photons per unit time, respectively, from the point source. In all the calculations presented here we adopt the same fiducial parameters as YM12: T = 8000 K, α = 3 . 0 × 10 -13 cm 3 s -1 . Finally, we adopt Cloudy's default ISM dust grain abundance and size distributions at solar metallicity, but in order to allow more meaningful comparison between our results and those of D00, we adjust the gas-phase element abundances in our calculation to match theirs. These choices mean that the dust discriminant parameter (Draine 2011) takes the same value, γ = 7 . 4, as in YM12: so, dust opacity is significant within radiation pressure-dominated ionized zones. We summarize all the parameters we use in our calculations in Table 1. The Table also describes the parameter choices used in D00 and Levesque et al. (2010, hereafter L10). For each set of input parameters, we use Cloudy to calculate the structure of the resulting H II region, halting at the point where the gas temperature drops to 100 K in order to ensure that the ionization front is fully enclosed. We perform each calculation twice, once with radiation pressure turned off, and once with radiation pressure turned on and allowed to exceed gas pressure (in contrast to Cloudy's default setting, which does not allow radiation pressure to be greater than gas pressure.)",
"pages": [
2,
3
]
},
{
"title": "2.2. Model Outputs and Physical Parameters",
"content": "The output of our calculations is two fourdimensional grids of models defined by the parameters ( t, n H , in , L, R in ), where t is the age of the stellar population used to generate the ionizing spectrum. One grid contains models with radiation pressure turned on, which we refer to as the RP models, and the other contains models with radiation pressure disabled, which we refer to as gas pressure, or GP, models. For each run in both model grids, we compute several optical emission line luminosities integrated over the ionized gas, including the lines used to construct the BPT diagram: H α , H β , [ O III ] λ 5007, and [ N II ] λ 6584. In order to understand the physical meaning of the results, it is helpful to characterize each model by two dimensionless numbers that can be computed from the Cloudy output. Following YM12, we define the radiation pressure parameter where R IF is the radius of the ionization front (IF). A value of Ψ < 1 indicates that the entire IF falls within ˜ r ch , and thus that radiation pressure is more important than gas pressure in determining its structure. Again following YM12, we define a separate stellar wind parameter where P IF and P in are the gas pressures at the edge of the ionization front and the innermost zone, respectively, and V IF = (4 / 3) πR 3 IF and V in = (4 / 3) πR 3 in are the volumes contained within the IF and the inner edge of the H II region, respectively. The inner edge of the photoionized region is the outer edge of the bubble of hot gas inflated by the stars' winds. Thus Ω reflects the contribution of a pressurized wind bubble to the total energy budget of the H II region. In a region strongly pressurized by stellar winds Ω glyph[greatermuch] 1, while in a region with negligible wind pressure Ω glyph[lessmuch] 1. For each Cloudy model, we compute the quantities Ψ and Ω, and thus we may think of our models as describing a parameter space ( t, n H , in , Ψ , Ω), as illustrated by Figure 1. This parameter space describes H II regions for which both radiation and wind pressure run from strong to negligible. To study the effects of winds, we reduce this fourdimensional parameter space to a three-dimensional one by selecting two representative values of Ω: we designate models with log Ω = 2 as strong wind (SW) models, and those with log Ω = -1 . 5 as weak wind (WW) models. Since our models never produce log Ω = -1 . 5 or 2 exactly, we construct these models by interpolation. At each age t , density n H , in , and luminosity L , we find the two models whose values of Ω bracket our target one, and we compute line luminosities at the target value of Ω by interpolating between the two bracketing models. Through this procedure, we obtain a set of four reduced model grids, which we refer to as RPWW (radiation pressure turned on, log Ω = -1 . 5), RPSW (radiation pressure turned on, log Ω = 2), GPWW (radiation pressure turned off, log Ω = -1 . 5), and GPSW (radiation pressure turned off, log Ω = 2). It is important to bear in mind that our RP models are physically self-consistent, whereas the GP models are deliberately not. Thus, RPWW models make a transition from classical spherical Stromgren spheres to radiationconfined shells, along the sequence described by Draine (2011), as Ψ decreases through unity. RPSW models are always thin shells: both radiation and wind pressure play a role in confining them, but, as we explain below, wind pressure always dominates. GPSW models are also thin shells, but due to the neglect of radiation pressure they sample a range of ionization parameters inaccessible to real regions. Finally, GPWW models are always filled Stromgren spheres, even when the radiation force should confine them. They can also sample unphysically high values of U . Our GP models have strictly uniform gas pressure, as they include no other forces. Each of these model grids gives the line luminosities of H II regions as a function of the three remaining parameters, ( t, n H , in , Ψ), or equivalently ( t, n H , L ). We summarize the properties of the models in Table 2. We will make use of the four full model grids in Paper II, but for the remainder of this paper we concentrate on the particular case t = 0, n H , in = 10 cm -3 , in order to understand how the choice of input physics alters the structure of H II regions. We choose these parameters in particular because they match the ones used by a number of previous authors, thus facilitating easy comparison.",
"pages": [
3,
4
]
},
{
"title": "3.1. One-Zone Models",
"content": "For a given spectral shape, each ionized parcel with uniform density and temperature can be characterized by only two parameters: the density n H and the ionization parameter U = n γ,i /n H , where n γ,i is the number density of ionizing photons. Therefore there is a unique mapping between U and initial densities on the BPT diagram. The one-zone models also represent simple analogs of H II regions, for one can decompose an H II region into zones in which U , n H , and ionizing spectrum are nearly constant. Thus the one-zone models represent thin, uniformly ionized regions which are very much like the ionized layer of a wind bubble. As such, they resemble best the SW models to be discussed in § 3.2.2. We run an additional set of Cloudy 'one-zone' calculations in which we only compute the properties of line emission from the first, innermost zone. In this zone we can specify the value of U by choosing the the density n H and the bolometric luminosity L (and thus the ionizing photon luminosity S ). We run models with n H = 10 -1 -10 6 cm -3 in 1 dex steps, and U = 10 -4 -10 0 . 6 in 0.2 dex steps, all using an input spectrum corresponding to our t = 0 Starburst99 model, and using the same abundances and other parameters as the rest of our models. In Figure 2, we show the constant U and constant n H contours marked with black solids lines and blue dashed lines, respectively, on the BPT diagram computed with the one-zone models. The ionization parameter U and ionizing luminosity S increase from lower right to upper left, and increasing the density shifts models up and to the right, until the density exceeds ∼ 10 4 -10 5 cm -3 . Beyond this point, the models shift down and to the left, because the density exceeded the critical densities of the [ N II ] and [ O III ] emission lines, which are 6 . 6 × 10 4 cm -3 and 6 . 8 × 10 5 cm -3 , respectively (Osterbrock & Ferland 2006). In Paper II, we will return to the discussion of line ratios, U , and critical densities on the BPT diagram, and further discuss most extreme H II regions exceeding the upper limit of line ratios set by Kewley et al. (2001), which is based on the mapping between line ratios and U but ignored the effect of densities. We note that the BPT locations of macroscopic H II regions will differ from those of individual gas parcels, because of spatial variations in the physical quantities. In all cases U drops and the ionizing spectrum changes log1o as one approaches the ionization front, because of selective absorption by neutral H atoms, and in some cases by dust grains. When radiation pressure is strong (and is included) and winds are weak, the gas density increases significantly across the layer. We therefore anticipate that full H II region models should differ from the onezone calculation, even though the innermost zones are accounted by it. Moreover the macroscopic physical parameters, the assumed geometry, and the inclusion or neglect of radiation pressure should affect the BPT loci. We explore these dependencies in the subsequent sections.",
"pages": [
4,
5
]
},
{
"title": "3.2. Full Models",
"content": "We now turn to our four full (radially resolved) H II region models, RPWW, GPWW, RPSW, and GPSW. In Figure 2, we overlay these models with t = 0 and n H , in = 10 cm -3 on the one-zone calculations. Other choices of density give qualitatively similar results, as long as the density is well below the critical densities of the [ O III ] and [ N II ] lines. As with the one-zone models, the full models form a sequence of values defined by Ψ or U , which we control by varying L : high-Ψ, lowU , lowL models are found at the bottom right and low-Ψ, highU , highL ones at the top left of each sequence.",
"pages": [
5
]
},
{
"title": "3.2.1. Weak Wind Models",
"content": "When stellar wind pressure is negligible (log Ω = -1 . 5), H II regions at the low L end of the sequence are very similar to each other. This is because L determines the balance between radiation pressure and gas pressure; a high luminosity produces a large ˜ r ch (Equation 1) and thus a small value of Ψ (Equation 2). Thus when L is low radiation pressure forces are negligible, and the results do not change much depending on whether we include them or not. The density within both H II regions is roughly constant at n H = n H , in = 10 cm -3 . At the high L , on the other hand, RPWW and GPWW differ substantially. In model GPWW, as L increases, we find that [ O III ]/H β increases and [ N II ]/H α decreases without limit. In contrast, in model RPWW these line ratios saturate at a finite value. If one were to infer ionization parameters from these line ratios based on one-zone models, one would say that U saturates at a finite value in model RPWW, while in model GPWW it can increase without limit as L does. We can understand the difference in behavior by examining the density structures of RPWW and GPWW regions, of which we show an example in Figure 3. At high L , RPWW model H II regions are strongly dominated by radiation pressure. Under force balance, radiation pressure confines ionized gas into a much thinner layer and leads to a steep increase in density towards the IF. Much of the line emission comes from this dense layer, within which U is much lower than it is closer to the central source. YM12 discuss this effect in detail. This effect does not operate in the GPWW models, where we have artificially disabled radiation pressure. As a result, these H II regions remain at nearly constant density regardless of the source luminosity. This allows U to increase without limit, and in turn allows the [ O III ]/H β and [ N II ]/H α line ratios to continue changing even at large L . Finally, it is interesting to note that, despite the uniform pressure in the GPWW models, the actual values of the line ratios are still significantly offset from the corresponding one-zone models of the same density, n H = 10 cm -3 . At small L the shape of the sequence is similar but the models are displaced to slightly higher [ N II ]/H α and [ O III ]/H β , while at large L the deviation is larger and the shape of the sequence is different as well. This difference occurs because, even though the pressure is uniform in the GPWW models, other quantities are not. In particular, the spectrum of the ionizing radiation field varies with radius, due to selective absorption of lowerenergy photons by neutral H atoms and of higher-energy photons by dust within the ionized layer.",
"pages": [
5,
6
]
},
{
"title": "3.2.2. Strong Wind Models",
"content": "In the RPSW and GPSW models (log Ω = 2), strong stellar wind pressure produces large 'voids' of diffuse, high temperature stellar wind gas at the centers of the model H II regions. As a result, the ionized gas is confined to a thin shell between the wind bubble and the IF. The location of the RPSW model in the BPT diagram is strikingly far from the locations of other models. Like the RPWW models, the RPSW models saturate at finite values of [ N II ]/H α and [ O III ]/H β , regardless of how high the luminosity becomes. However, unlike in case RPWW, the saturation values are extraordinarily far down the sequence of one-zone models: [ N II ]/H α > 10 -0 . 5 and [ O III ]/H β < 10 0 , corresponding to a one-zone value of U < 10 -3 . 3 . We can understand this effect by considering the relative importance of radiation and wind pressure in controlling the internal structures of H II regions. A value of log Ω = 2 requires that P IF V IF /P in V in = 1 . 01. Physically, this amounts to saying that the energy of the wind bubble constitutes 99% of the internal energy of the entire H II region. We note that V IF is strictly greater than V in . Similarly, P IF is strictly greater than P in , since the radiation force necessarily falls to zero at the IF, and thus pressure balance requires that gas pressure at the IF exceed that at the edge of the wind bubble. Thus models with log Ω = 2 necessarily have both V IF ≈ V in and P IF ≈ P in . This corresponds to the H II region being a thin shell of nearly constant gas pressure. Figure 3 shows an example of this uniform density. The RPSW configuration clearly cannot have radiation pressure as a significant force. If the radiation pressure force were significant, then we could not have P IF ≈ P in , since the pressure at the IF would be pure gas pressure, and this would have to balance the gas plus radiation pressure at the inner edge. The conclusion of this analysis is that it is not possible to construct a physically consistent model in which wind pressure and radiation pressure are both strong in the dimensionless sense. Indeed, our model grids reflect this fact in that there are no models with radiation pressure turned on that are simultaneously dominated by wind (Ω glyph[greatermuch] 1) and dominated by radiation pressure (Ψ glyph[lessmuch] 1). This physical effect manifests in the BPT diagram as a saturation in the range of line ratios that the RPSW models are able to reach. As discussed above, the location of an H II region driven by a stellar source in the BPT diagram is effectively controlled by U , the photon to baryon ratio. However, U may also be thought of as a measure of the importance of radiation pressure, since increasing the photon number density relative to the baryon density also increases the radiation pressure relative to gas pressure. The fact that RPSW models cannot reach small values of Ψ also means that they cannot reach large values of U , and thus cannot reach the line ratios associated with large U . YM12 used this point to derive upper limits on the wind energy budget within individual H II regions and entire galaxies. In contrast, radiation pressure is completely neglected in GPSW models. As there are no other forces to balance gas pressure gradients, these models have P IF = P in independent of the luminosity, and thus a value of log Ω = 2 simply implies that the shell is very thin: R IF = 1 . 003 R in . In these models one can achieve arbitrarily high U by raising the luminosity and increasing R in to keep up with R IF . Figure 3 shows an example of such a model. Thus the GPSW models are not restricted in the range of U they can represent. However, the comparison with the RPSW models shows that GPSW models at high U are unphysical, because radiation force would have compressed the gas and limited U in a real region. The comparison between RPSW, GPSW, and onezone models shown in Figure 2 also reflects these effects. Both RPSW and GPSW models are wind-dominated and therefore have nearly uniform densities, and thus can be reasonably-well represented by one-zone models, leaving aside the issues of radiation field hardening and nonuniform temperature discussed in Section 3.2.1. Thus both RPSW and GPSW models follow the one-zone sequence reasonably closely. They differ only in the range of U values within that sequence that they are able to sample.",
"pages": [
6
]
},
{
"title": "4. COMPARISON TO PREVIOUS WORK",
"content": "It is interesting to revisit earlier published models for H II region line ratios in the context of our exploration of how these line ratios respond to changes in the included physics. We have chosen our model parameters in Starburst99 and Cloudy to be as close as possible to those used by D00 in order to facilitate this comparison. In Figure 4, we compare our four model results with the results computed by D00 and L10, at the same age of ionizing star cluster (0 Myr) and same density n H , in = 10 cm -3 . The D00 model, which did not include radiation pressure and adopted plane-parallel ionized gas slabs at a fixed density, is essentially a wind-dominated model. This is because a plane-parallel slab can be thought of as a thin shell of material at roughly fixed distance from the ionizing source, and the only way to create a thin shell of constant gas pressure is to confine it with hot gas. Therefore our closest model to the D00 model is GPSW, and indeed we find that our GPSW results agree with the D00 model fairly well. Differences in line ratios between D00 and GPSW are around 0.1 to 0.2 dex. Our model sequence extends somewhat further, but this is simply a result of our having used a slightly larger range of input luminosities. The agreement between the models confirms that our Cloudy calculations, with input parameters set very close to the D00 settings, can reasonably well reproduce the earlier results. However, we note the comparison shows that the D00 models are not physically realistic at high luminosity, because one cannot neglect radiation pressure in very bright H II regions. Radiation pressure limits the physical range of U , particularly for wind-confined slabs, and models without radiation pressure such as those of D00 do not properly capture this effect. The models from L10 are similar to those of D00 in that they are based on plane-parallel ionized gas slabs, but the L10 models include radiation pressure. Therefore when U is low, the regions must be confined by wind pressure (like our RPSW). On the other hand, when U is high, the L10 models should be confined by radiation pressure (like our RPWW). However, Figure 4 shows that overall L10's models closely track our GPSW curve (maximum separation < 0 . 1 dex). In light of our results, we can see that the L10 models, while not physically inconsistent, do represent a rather odd cut through parameter space. There are two structural parameters describing H II regions, and the L10 models sample a one-dimensional path through this two-dimensional space. Along this path the ratio of wind pressure to radiation pressure varies systematically from large values (Ω glyph[greatermuch] 1, Ψ glyph[greatermuch] 1) at low ionization parameter to small values (Ω glyph[lessmuch] 1, Ψ glyph[lessmuch] 1) at high ionization parameter. There is no obvious physical reason such a systematic variation in wind to radiation pressure strength should occur, particularly since the ratio of stellar wind momentum flux to luminosity is roughly the same for all O stars (Repolust et al. 2004).",
"pages": [
6,
7
]
},
{
"title": "5. CONCLUSIONS",
"content": "We have computed a grid of quasi-static H II region models using Starburst 99 and Cloudy that covers a large range of density, luminosity, and stellar population age. In order to understand how radiation pressure and stellar winds alter H II regions' internal structures and observable line emission, we run two sets of models, one with radiation pressure enabled and one with it disabled, and we vary the radius at which the inner, wind-dominated bubble ends and the photoionized region begins. In the manner, we construct four sets of model H II regions: (1) ones with radiation pressure and weak stellar winds (RPWW), (2) wind bubbles that also include radiation pressure (RPSW), (3) Stromgren spheres where radiation pressure is ignored and winds are weak (GPWW), and (4) wind-dominated bubbles where radiation pressure is disabled (GPSW). We then explore how each set of H II regions populates the BPT diagram. Our models reveal a number of interesting effects. All models form a sequence that runs from the lower right corner of the BPT diagram (high [ N II ]/H α , low [ O III ]/H β ) to the upper left corner (low [ N II ]/H α , high [ O III ]/H β ), with the position of an H II region along the sequence dictated by its luminosity, or equivalently its effective ionization parameter U . However, the range of U explored by the models is limited when radiation pressure is included. Because strong radiation pressure, which would produce high U , also causes gas to pile into a dense shell, the characteristic value of U within the shell is limited at a finite value. (See YM12 for more detail.) As a consequence, models which neglect radiation pressure can reflect an arbitrarily high value of U , which real regions cannot. The interaction of winds with radiation pressure further enhances this effect. We show that a stellar winddominated region cannot also have strong radiation pressure while remaining in hydrostatic balance, and as a result the range of U is severely limited. This means that wind-dominated H II regions can never occupy the upper-left portion of the BPT diagram, and, conversely, those H II regions that are observed to lie in this region must either have negligible wind pressure, be far from pressure balance, or be kept in pressure balance by forces other than gas and radiation pressure (e.g. strong magnetic pressure; YM12). The most realistic option, and the one favored by direct observations of nearby H II regions (Harper-Clark & Murray 2009; Lopez et al. 2011) as well as mid-infrarared line ratios (YM12) is the first one: wind pressure is not dynamically significant, at least for bright H II regions. Further, the fact that the high-redshift galaxy population has characteristically high ionization parameters implies that radiation pressure is significant within these galaxies' ionized zones, in an ionization-weighted sense. We have compared our results to the earlier models of Dopita et al. (2000, D00) and Levesque et al. (2010, L10). In these models the H II region is assumed to be a wind-dominated thin ionized shell, which corresponds to our GPSW model. We find that this model agrees well with the results of D00 and L10. However, we show that these models are inconsistent at the high luminosity end. The D00 models neglect radiation pressure for H II regions where it is non-negligible. The L10 models include radiation pressure, but we show that the assumed plane-parallel slab geometry is physically realistic only if the strength of the ratio of stellar wind pressure to radiation pressure varies systematically with H II region properties in a physically unexpected manner. While these calculations provide insight into how the physics driving H II regions' structures translates into observable properties such as line ratios, a full model for where galaxies fall in the BPT diagram requires attention to H II regions' dynamical expansion as well as their internal structure. This problem is the subject of Paper II. This project was initiated during the 2010 International Summer Institute for Modeling in Astrophysics (ISIMA) summer program, whose support is gratefully acknowledged. SCCY and CDM would like to acknowledge an NSERC Discovery grant and conversations with Stephen Ro and Shelley Wright. MRK acknowledges support from an Alfred P. Sloan Fellowship, from the National Science Foundation through grant CAREER0955300, from NASA through Astrophysics Theory and Fundamental Physics grant NNX09AK31G, and a Chandra Telescope Grant.",
"pages": [
7,
8
]
},
{
"title": "REFERENCES",
"content": "Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5 Binette, L., Wilson, A. S., Raga, A., & Storchi-Bergmann, T. 1997, A&A, 327, 909 D. R., & Reddy, N. A. 2010, ApJ, 719, 1168 Krumholz, M. R. & Matzner, C. D. 2009, ApJ, 703, 1352 Leitherer, C., Schaerer, D., Goldader, J. D., Gonz'alez Delgado,",
"pages": [
8
]
}
]
2013ApJ...769..102P
https://arxiv.org/pdf/1211.6112.pdf
<document>
<section_header_level_1><location><page_1><loc_9><loc_85><loc_91><loc_87></location>HIGH CONTRAST IMAGING WITH AN ARBITRARY APERTURE: ACTIVE CORRECTION OF APERTURE DISCONTINUITIES</section_header_level_1>
<text><location><page_1><loc_37><loc_81><loc_62><loc_84></location>Laurent Pueyo 1 , Colin Norman 1 ApJ Accepted 11-26-2012</text>
<section_header_level_1><location><page_1><loc_45><loc_79><loc_55><loc_80></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_49><loc_86><loc_78></location>We present a new method to achieve high-contrast images using segmented and/or on-axis telescopes. Our approach relies on using two sequential Deformable Mirrors to compensate for the large amplitude excursions in the telescope aperture due to secondary support structures and/or segment gaps. In this configuration the parameter landscape of Deformable Mirror Surfaces that yield high contrast Point Spread Functions is not linear, and non-linear methods are needed to find the true minimum in the optimization topology. We solve the highly non-linear Monge-Ampere equation that is the fundamental equation describing the physics of phase induced amplitude modulation. We determine the optimum configuration for our two sequential Deformable Mirror system and show that high-throughput and high contrast solutions can be achieved using realistic surface deformations that are accessible using existing technologies. We name this process Active Compensation of Aperture Discontinuities (ACAD). We show that for geometries similar to JWST, ACAD can attain at least 10 -7 in contrast and an order of magnitude higher for both the future Extremely Large Telescopes and on-axis architectures reminiscent of HST. We show that the converging non-linear mappings resulting from our Deformable Mirror shapes actually damp near-field diffraction artifacts in the vicinity of the discontinuities. Thus ACAD actually lowers the chromatic ringing due to diffraction by segment gaps and strut's while not amplifying the diffraction at the aperture edges beyond the Fresnel regime. This outer Fresnel ringing can be mitigated by properly designing the optical system. Consequently, ACAD is a true broadband solution to the problem of high-contrast imaging with segmented and/or on-axis apertures. We finally show that once the non-linear solution is found, fine tuning with linear methods used in wavefront control can be applied to further contrast by another order of magnitude. Generally speaking, the ACAD technique can be used to significantly improve a broad class of telescope designs for a variety of problems.</text>
<text><location><page_1><loc_14><loc_47><loc_73><loc_49></location>Subject headings: planetary systems - techniques: coronagraphy, wavefront control</text>
<section_header_level_1><location><page_1><loc_22><loc_44><loc_35><loc_45></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_11><loc_48><loc_43></location>Exo-planetary systems that are directly imaged using existing facilities (Marois et al. 2008; Kalas et al. 2008; Lagrange et al. 2010) give a unique laboratory to constrain planetary formation at wide separations (Rafikov 2005; Dodson-Robinson et al. 2009; Kratter et al. 2010; Johnson et al. 2010), to study the planetary luminosity distribution at critical young ages (Spiegel & Burrows 2012; Fortney et al. 2008) and the atmospheric properties of low surface gravity objects (Barman et al. 2011b,a; Marley et al. 2010; Madhusudhan et al. 2011). Upcoming surveys, conducted with instruments specifically designed for high-contrast (Dohlen et al. 2006; Graham et al. 2007; Hinkley et al. 2011), will unravel the bulk of this population of self-luminous jovian planets and provide an unprecedented understanding of their formation history. Such instruments will reach the contrast required to achieve their scientific goals by combining Extreme Adaptive Optics systems (Ex-AO, Poyneer & V'eran (2005)), optimized coronagraphs (Soummer et al. 2011; Guyon 2003; Rouan et al. 2000) and nanometer class wavefront calibration (Sauvage et al. 2007; Wallace et al. 2009; Pueyo et al. 2010). In the future, highcontrast instruments on Extremely Large Telescopes will focus on probing planetary formation in distant star</text>
<text><location><page_1><loc_10><loc_9><loc_24><loc_10></location>email: [email protected]</text>
<text><location><page_1><loc_10><loc_7><loc_48><loc_9></location>1 Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA</text>
<text><location><page_1><loc_52><loc_34><loc_92><loc_45></location>forming regions (Macintosh et al. 2006), characterizing both the spectra of cooler gas giants (V'erinaud et al. 2010) and the reflected light of planets in the habitable zone of low mass stars. The formidable contrast necessary to investigate the presence of biomarkers at the surface of earth analogs ( > 10 10 ) cannot be achieved from the ground beneath atmospheric turbulence and will require dedicated space-based instruments (Guyon 2005).</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_34></location>The coronagraphs that will equip upcoming Ex-AO instruments on 8 meter class telescopes have been designed for contrasts of at most ∼ 10 -7 . Secondary support structures (or spiders: 4 struts each 1 cm wide, ∼ 0 . 3% of the total pupil diameter in the case of Gemini South) have a small impact on starlight extinction at such levels of contrasts. In this case, coronagraphs have thus been optimized on circularly symmetric apertures, which only take into account the central obscuration (Soummer et al. 2011). However, high-contrast instrumentation on future observatories will not benefit from such gentle circumstances. ELTs will have to support a substantially heavier secondary than 8 meter class observatories do, and over larger lengths: as a consequence the relative area covered by the secondary support will increase by a factor of 10 (30 cm wide spiders, occupying ∼ 3% of the pupil diameter in the case of TMT). This will degrade the contrast of coronagraphs only designed for circularly obscured geometries by a factor ∼ 100, when the actual envisioned contrast for an ELT exo-planet imager can be as</text>
<text><location><page_2><loc_8><loc_39><loc_48><loc_92></location>low as ∼ 10 -8 (Macintosh et al. 2006). While the tradeoffs associated with minimization of spider width in the space-based case have yet to be explored, secondary support structures will certainly hamper the contrast depth of coronagraphic instruments of such observatories at levels that are well above the 10 10 contrast requirement. As a consequence, telescope architectures currently envisioned for direct characterization of exo-earths consist of monolithic, off-axis, and thus un-obscured, telescopes (Guyon et al. 2008; Trauger et al. 2010). Coronagraphs for such architectures take advantage of the pupil symmetry to reach a theoretical contrast of ten orders of magnitude (Guyon et al. 2005; Vanderbei et al. 2003a,b; Kasdin et al. 2005; Mawet et al. 2010; Kuchner & Traub 2002; Soummer et al. 2003). However, using obscured on-axis and/or segmented apertures take full advantage of the limited real estate associated with a given launch vehicle and can allow larger apertures that increase the scientific return of space-based direct imaging survey. Recent solutions can mitigate the presence of secondary support structures in on-axis apertures. However these concepts present practical limitations: APLCs on arbitrary apertures (Soummer et al. 2009) and Shaped Pupils (Carlotti et al. 2011) suffer from throughput loss for very high contrast designs, and PIAAMCM (Guyon et al. 2010a) rely on a phase mask technology whose chromatic properties have not yet been fully characterized. Moreover segmentation will further complicate the structure of the telescope's pupil: both the amplitude discontinuities created by the segments gaps and the phase discontinuities resulting from imperfect phasing will thus further degrade coronagraphic contrast. Devising a practical solution for broadband coronagraphy on asymmetric, unfriendly apertures is an outstanding problem in high contrast instrumentation. The purpose of the present paper is to introduce a family of practical solutions to this problem. As their ultimate performances depend strongly on the pupil structure we limit the scope of this paper to a few characteristic examples. Full optimization for specific telescope geometries can be conducted as needed.</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_39></location>The method proposed here takes advantage of stateof-the art Deformable Mirrors in modern high-contrast instruments to address the problem of pupil amplitude discontinuities for on-axis and/or segmented telescopes. Indeed, coronagraphs are not sufficient to reach the high contrast required to image faint exo-planets: wavefront control is needed to remove the light scattered by small imperfections on the optical surfaces (Brown & Burrows 1990). Over the past eight years, significant progress has been made in this area, both in the development of new algorithms (Bord'e & Traub 2006; Give'on et al. 2007) and in the experimental demonstration of high-contrast imaging with a variety of coronagraphs (Give'on et al. 2007; Trauger & Traub 2007; Guyon et al. 2010b; Belikov et al. 2011). These experiments rely on a system with a single Deformable Mirror which is controlled based on diagnostics downstream of the coronagraph, either at the science camera or as close as possible to the end detector (Wallace et al. 2009; Pueyo et al. 2010). Such configurations are well suited to correct phase wavefront errors arising from surface roughness but have limitations in the presence of pure amplitude errors (reflectivity), or phase-induced amplitude errors, which result from the propagation of surface errors in optics that are not con-</text>
<text><location><page_2><loc_52><loc_53><loc_92><loc_92></location>ugate to the telescope pupil (Shaklan & Green 2006; Pueyo & Kasdin 2007). Indeed a single DM can only mimic half of the spatial frequency content of amplitude errors and compensate for them only on one half of the image plane (thus limiting the scientific field of view) over a moderate bandwidth. In theory, architectures with two sequential Deformable Mirrors, can circumvent this problem and create a symmetric broadband high contrast PSF (Shaklan & Green 2006; Pueyo & Kasdin 2007). The first demonstration of symmetric dark hole was reported in Pueyo et al. (2009) and has since been generalized to broadband by Groff et al. (2011). In such experiments the coronagraph has been designed over a full circular aperture, the DM control strategy is based on a linearization of the relationship between surface deformations and electrical field at the science camera, and the modeling tools underlying the control loop consist of classic Fourier and fresnel propagators. This is illustrated on the left panel of Fig. 1. As a consequence, a wavefront control system composed of two sequential Deformable Mirrors is currently the baseline architecture of currently envisioned coronagraphic space-based instruments (Shaklan et al. 2006; Krist et al. 2011) and ELT planet imagers (Macintosh et al. 2006). One can thus naturally be motivated to investigate if such wavefront control systems can be used to cancel the light diffracted by secondary supports and segments in large telescopes, since such structures are amplitude errors, albeit large amplitude errors.</text>
<text><location><page_2><loc_52><loc_7><loc_92><loc_53></location>The purpose of our study is to demonstrate that indeed a two Deformable Mirror (DM for the remainder of this paper) wavefront control system can mitigate the impact of the pupil asymmetries, such as spiders and segments, on contrast and thus enable high contrast on unfriendly apertures. In § . 2 we first present a new approach to coronagraph design in the presence of a central obscuration, but in the absence of spiders or segments. We show that for coronagraphs with a pupil apodization and an opaque focal plane stop, contrasts of 10 -10 can be reached for any central obscuration diameter, provided that the Inner Working Angle is large enough. Naturally the secondary support structures, and in the segmented cases, segment gaps, will degrade this contrast. As our goal is to use two DMs as an amplitude modulation device, we first briefly review in § . 3 the physics of such a modulation. In § . 4 we introduce a solution to this problem: we show how to compute DM surfaces that mitigate spiders and segment gaps. Current algorithms used for amplitude control operate under the assumption that amplitude errors are small, and thus they cannot be readily applied to the problem of compensating aperture discontinuities, which have inherently large reflectivity non-uniformities. Fig. 1 illustrates how the present manuscript introduces a control strategy for the DMs that is radically different from previously published amplitude modulators in the high-contrast imaging literature. Our technique, which we name Active Compensation of Aperture Discontinuities (hereafter ACAD), finds the adequate DM shapes in the true non-linear large amplitude error regime. In this case the DMs' surfaces are calculated as the solution of a non-linear partial differential equation, called the Monge-Ampere Equation. We describe our methodology to solve this equation in § . 4 and illustrate each step using an obscured and seg-</text>
<text><location><page_3><loc_8><loc_35><loc_48><loc_92></location>ed geometry similar to JWST. As ACAD DM surfaces are prescribed in the ray-optics approximation this is a fundamentally broadband technique provided that chromatic diffractive artifacts, edge ringing in particular, do not significantly impact the contrast. This is what we discuss in § . 5. We find that when remapping small discontinuities with Deformable Mirrors, the spectral bandwidth is only limited by wavelength-dependent edge-diffraction ringing in the Fresnel approximation (as discussed in Pueyo & Kasdin (2007) for instance). Highcontrast instruments where this ringing is mitigated have already been designed; while future work in high precision optical modeling is necessary to fully quantify the true chromatic performances of ACAD, we do not expect these effects to be a major limitation to broadband operations. In § . 6 we present the application of our method to various observatory architectures. Note that the contrast levels stated in § . 6 represent a non-optimal estimate of ACAD performances with on-axis and/or segmented apertures. Our calculations are carried out in the absence of atmospheric turbulence, quasi-static wavefront errors or coronagraphic manufacturing defects. We discuss these limitations in § . 7, with a specific emphasis on quasi-static phase errors in a segmented telescope. We show that when the aperture discontinuities are thin enough field distortion is negligible for spatial frequencies within the field of view defined by the DMs controllable spatial frequencies. We then discuss issues associated with phase discontinuities when applying ACAD to a segmented telescope. We show that they can be corrected by superposing single DM classical wavefront control solutions to the ACAD shape of the second DM. We finally argue, that should high precision diffractive models be developed, then the solutions presented herein can be used as the starting point of dual DMs iterative algorithms relying on an image-plane based metric and thus lead to higher contrast than reported herein. Most of the future exo-planet imagers, either on ELTs or on future space missions, are envisioned to control their wavefront in real time with two sequential DMs. The method presented in this manuscript thus renders high contrast coronagraphy possible on any observatory geometry without adding any new hardware.</text>
<section_header_level_1><location><page_3><loc_9><loc_32><loc_48><loc_33></location>2. CORONAGRAPHY WITH A CENTRAL OBSCURATION</section_header_level_1>
<section_header_level_1><location><page_3><loc_9><loc_29><loc_47><loc_31></location>2.1. Optimizing pupil apodization in the presence of a central obscuration</section_header_level_1>
<text><location><page_3><loc_8><loc_7><loc_48><loc_28></location>Because the pupil obscuration in an on-axis telescope is large it will be very difficult to mitigate its impact with DMs with a limited stroke. Indeed, the main hindrance to high-contrast coronagraphy in on-axis telescope is the presence of the central obscuration: it often shadows much more than 10% of the aperture width while secondary supports and segments gaps cover ∼ 1%. We thus first focus of azimuthally symmetric coronagraphic designs in the presence of a central obscuration. This problem (without the support structures) has been addressed in previous publications either using circularly symmetric pupil apodization (Soummer et al. 2011) or a series of phase masks (Mawet et al. 2011). Both solutions however are subject to limitations. The singularity at the center of the Optical Vector Vortex Coronagraph might be difficult to manufacture and a circular opaque</text>
<figure>
<location><page_3><loc_56><loc_40><loc_89><loc_92></location>
<caption>Figure 1. Top, blue: Envisioned architecture of future exo-earth imaging missions: a monolithic un-obscured telescope feeds a coronagraph designed on a circular aperture. The wavefront errors are corrected using two sequential Deformable Mirrors (DMs) that are controlled using a quasi-linear feedback loop based on image plane diagnostics. The propagation between optical surfaces, between the DMs in particular is assumed to occur in the Fresnel regime. Bottom, orange: ACAD solution: the coronagraph is designed for a circular geometry around the central obscuration. The two sequential DMs are controlled in the non-linear regime based on a pupil plane cost function. The propagation between the DMs is modeled using ray optics, and a we conduct a quantitative onedimensional analysis of the diffraction artifacts.</caption>
</figure>
<text><location><page_3><loc_52><loc_10><loc_92><loc_23></location>spot thus lies in the central portion of the phase mask ( < λ/D ) which results in a degradation of the ideal contrast of such a coronagraph (Krist et al. 2011). The solutions in Soummer et al. (2011) result from an optimization seeking to maximize the off-axis throughput for a given focal plane stop diameter: the final contrast is absent from the optimization metric and is only a byproduct of the chosen geometry. Higher contrasts are then obtained by increasing the size of the focal plane mask, and thus result in a loss in IWA.</text>
<text><location><page_4><loc_8><loc_73><loc_48><loc_92></location>Here we revisit the solution proposed by Soummer et al. (2011) in a slightly different framework. We recognize that, in the presence of wavefront errors, high contrast can only be achieved in an area of the field of view that is bounded by the spatial frequency corresponding to the DM's actuator spacing. We thus consider the design of an Apodized Pupil Lyot Coronagraph which only aims at generating high contrast between the Inner Working Angle (IWA) and Outer Working Angle (OWA). In order to do so, we rewrite coronagraphs described by Soummer et al. (2003) as an operator C which relates the entrance pupil P ( r ) to the electrical field in the final image plane. We first call ˆ P ( ξ ) the Hankel transform of the entrance pupil:</text>
<formula><location><page_4><loc_18><loc_68><loc_48><loc_71></location>ˆ P ( ξ ) = ∫ D/ 2 D S / 2 P ( r ) J 0 ( rξ ) rdr (1)</formula>
<text><location><page_4><loc_8><loc_51><loc_48><loc_67></location>where D is the pupil diameter, D S the diameter of the secondary and ξ the coordinate at the science detector expressed in units of angular resolution ( λ 0 /D ). λ 0 is the design wavelength of the coronagraph chosen to translate the actual physical size of the focal plane mask in units of angular resolution (often at the center of the bandwidth of interest). λ is then the wavelength at which the coronagraph is operating (e.g. the physical size of the focal plane mask remains constant as the width of the diffraction pattern changes with wavelength). For the purpose of the monochromatic designs presented herein λ = λ 0 . Then the operator is given by:</text>
<formula><location><page_4><loc_11><loc_46><loc_48><loc_49></location>C [ P ( r )] ( ξ ) = ˆ P ( ξ ) -λ 2 λ 2 0 ∫ D/ 2 D S / 2 ˆ P ( η ) K ( ξ, η ) ηdη (2)</formula>
<text><location><page_4><loc_8><loc_42><loc_48><loc_44></location>where K ( ξ, η ) is the convolution kernel that captures the effect of the focal plane stop of diameter M stop :</text>
<formula><location><page_4><loc_15><loc_37><loc_48><loc_40></location>K ( ξ, η ) = ∫ M stop / 2 0 J 0 ( uη ) J 0 ( uξ ) udu (3)</formula>
<text><location><page_4><loc_8><loc_28><loc_48><loc_35></location>An analytical closed form for this kernel can be calculated using Lommel functions. Note that this Eq. 2 assumes that the Lyot stop is not undersized. Since we are interested in high contrast regions that only span radially all the way up to a finite OWA, we seek pupil apodization of the form:</text>
<formula><location><page_4><loc_19><loc_22><loc_48><loc_26></location>P ( r ) = N modes ∑ k =0 p k J Q ( r α Q k ) (4)</formula>
<text><location><page_4><loc_8><loc_7><loc_48><loc_21></location>where J Q ( r ) denotes the Bessel function of the first kind of order Q and α Q k the k th zero of this Bessel function. In order to devise optimal apodizations overobscured pupils, Q , can be chosen to be large enough so that J Q ( r ) glyph[lessmuch] 1 for r < D S / 2 (in practice we choose Q = 10). The α Q k corresponds to the spatial scale of oscillations in the coronagraph entrance pupil, and such a basis set yields high contrast regions all the way to OWA glyph[similarequal] N modes λ 0 /D . Since the operator in Eq. 2 is linear, finding the optimal p k can be written as the fol-</text>
<text><location><page_4><loc_52><loc_91><loc_78><loc_92></location>ing linear programming problem:</text>
<formula><location><page_4><loc_54><loc_86><loc_92><loc_89></location>max { p k } [ min r ( P ( r )) ] Under the constraints: (5a)</formula>
<formula><location><page_4><loc_54><loc_84><loc_92><loc_86></location>|C [( P ( r ))] ( ξ ) | < 10 -√ C for IWA < ξ < OWA (5b)</formula>
<formula><location><page_4><loc_54><loc_81><loc_92><loc_83></location>max r ( P ( r )) = 1 (5c)</formula>
<formula><location><page_4><loc_54><loc_78><loc_92><loc_81></location>| d dr [ P ( r )] | < b. (5d)</formula>
<text><location><page_4><loc_52><loc_75><loc_92><loc_77></location>Our choice of cost function and constraints has been directed by the following rationale:</text>
<unordered_list>
<list_item><location><page_4><loc_53><loc_66><loc_92><loc_74></location>5.a We maximize the smallest value on the apodization function in an attempt to maximize throughput. The actual throughput is a quadratic function of the p k . Maximizing it requires the solution of a non-linear optimization problem (as described in Vanderbei et al. (2003b))</list_item>
<list_item><location><page_4><loc_53><loc_62><loc_92><loc_65></location>5.b The contrast constraint is enforced between the IWA and the OWA ( < N modes ).</list_item>
<list_item><location><page_4><loc_53><loc_57><loc_92><loc_61></location>5.c The maximum of the apodization function is set to one (otherwise the p k will be chosen to be sufficiently small so that the contrast constraint is met).</list_item>
<list_item><location><page_4><loc_53><loc_47><loc_92><loc_56></location>5.d The absolute value of the derivative across the pupil cannot be larger than a limit, denoted as b here. As the natural solutions of such problem are very oscillatory (or 'bang bang', Vanderbei et al. (2003b,a)), a smoothness constraint has to be enforced (see Vanderbei et al. (2007) for a similar case).</list_item>
</unordered_list>
<text><location><page_4><loc_52><loc_38><loc_92><loc_46></location>Note that the linear transfer function in Eq. 2 can also be derived for other coronagraphs, with grayscale and phase image- plane masks, or for the case of under-sized Lyot stops. As general coronagraphic design in obscured circular geometries is not our main purpose, we limit the scope of the paper to coronagraphs represented by Eq. 2.</text>
<section_header_level_1><location><page_4><loc_61><loc_35><loc_83><loc_36></location>2.3. Results of the optimization</section_header_level_1>
<text><location><page_4><loc_52><loc_7><loc_92><loc_35></location>Typical results of the monochromatic optimization in Eqs. 5d, with λ = λ 0 , are shown in Fig. 2 for central obscurations of 10, 20 and 30%. In the first two cases the size of the focal plane stop is equal to 3 λ/D , the IWA is 4 λ/D and the OWA is 30 λ/D . As the size of the central obscuration increases the resulting optimal apodization becomes more oscillatory and the contrast constraint has to be loosened in order for the linear programming optimizer to converge to a smoother solution. Alternatively increasing the size of the focal plane stop yield smooth apodizers with high contrast, at cost in angular resolutions (bottom panel with a central obscuration of 30%, a focal plane mask of radius 4 λ/D , an IWA of 5 λ/D and an OWA of 30 λ/D ). These trade-offs were described in Soummer et al. (2011), however our linear programming approach to the design of pupil apodizations now imposes the final contrast instead of having it be a by product of fixed central obscuration and focal plane stop. These apodizations can either be generated using grayscale screen (at a cost in throughput and angular resolution) or a series of two aspherical PIAA</text>
<figure>
<location><page_5><loc_9><loc_21><loc_91><loc_90></location>
</figure>
<text><location><page_5><loc_64><loc_85><loc_65><loc_91></location>/Slash1</text>
<paragraph><location><page_5><loc_8><loc_10><loc_92><loc_24></location>0.0 0.2 0.4 0.6 0.8 1.0 r /Slash1 D 0 10 /Minus 14 Λ /Slash1 Figure 2. Optimal design Apodized Pupil Lyot Coronagraphs on circularly obscured apertures. With fixed obscuration ratio, size of opaque focal plane mask, IWA and OWA, our linear programming approach yields solutions with theoretical contrast below 10 10 . All PSFs shown on this figure are monochromatic for λ = λ 0 . When all other quantities remain equal and the central obscuration ratio increases (from 10% in the top panel to 20% in the middle panel), then the solution becomes more oscillatory (e.g less feasible) and the contrast constraint has to be relaxed. Eventually the optimizer does not find a solution and the size of the opaque focal plane mask (and thus the IWA) has to be increased (central obscuration of 30% in the bottom panel). On the right hand side, we present our results in two configurations: when the apodization is achieved using at grayscale screen (APLC), 'on-sky' λ/D bottom x-axis, and when the apodization is achieved via two pupil remapping mirrors (PIAAC), 'on-sky' λ/D top x-axis. We adopt this presentation to show that ACAD is 'coronagraph independent' and that it can be applied to coronagraphs with high throughput and small IWA.</paragraph>
<text><location><page_6><loc_8><loc_72><loc_48><loc_92></location>mirrors (for better throughput and angular resolution). In order not to lose generality, we present our results on Fig. 2 considering the two types of practical implementations (classical apodization and PIAA apodization). In the case of a grayscale amplitude screen the angular resolution units are as defined in Eq. 2 and the throughput is smaller than unity. In the case of PIAA apodisation the throughput is unity and the angular resolution units have been magnified by the field independent centroid based angular magnification defined in Pueyo et al. (2011). We adopt this presentation for the remainder of the paper where one dimensional PSFs will be presented with 'APLC angular resolution units' in the bottom horizontal axis and'PIAAC angular resolution units' in the top horizontal axis.</text>
<text><location><page_6><loc_8><loc_27><loc_48><loc_72></location>Note that this linear programming approach only optimizes the contrast for a given wavelength. However, since the solutions presented in Fig. 2 feature contrasts below 10 10 , we choose not to focus on coronagraph chromatic optimizations. Instead, in order to account for the chromatic behavior of the coronagraph, the monochromatic simulations in § . 6 are carried out under the conservative assumption that the physical size of the focal plane stop is somewhat smaller than optimal (or that the operating wavelength of the coronagraph is slightly off, λ = 1 . 2 λ 0 ). As a consequence the raw contrast of the coronagraphs presented in § . 6 is ∼ 10 -9 . Note that this choice is not representative of all possible Apodized Pupil Coronagraph chromatic configurations. It is merely a shortcut we use to cover the variety of cases presented in § . 6. In § . 7.2 we present a set of broadband simulations that include wavefront errors and the true coronagraphic chromaticity for a specific configuration and show that bandwidth is more likely to be limited by the spectral bandwidth of the wavefront control system than by the coronagraph. However, future studies aimed at defining the true contrast limits of a given telescope geometry will have to rely on solutions of the linear problem in Eqs. 5d which has been augmented to accommodate for broadband observations. In theory, the method presented here can also be applied to asymmetric pupils. However, the optimization quickly becomes computationally intensive as the dimensionality of the linear programming increases (in particular when the smoothness constraint and the bounds on the apodization have to be enforced at all points of a two dimensional array). This problem can be somewhat mitigated when seeking for binary apodizations, as shown in Carlotti et al. (2011), at a cost in throughput and angular resolution.</text>
<section_header_level_1><location><page_6><loc_13><loc_24><loc_43><loc_25></location>3. PHYSICS OF AMPLITUDE MODULATION</section_header_level_1>
<section_header_level_1><location><page_6><loc_20><loc_22><loc_36><loc_23></location>3.1. General equations</section_header_level_1>
<text><location><page_6><loc_8><loc_7><loc_48><loc_21></location>We have shown in § . 2 that by considering the design of pupil apodized coronagraphs in the presence of a circular central obscuration as a linear optimization problem, high contrast can be reached provided that the focal plane mask is large enough. In practice, the secondary support structures and the other asymmetric discontinuities in the telescope aperture (such as segment gaps) will prevent such levels of starlight suppression. We demonstrate that well controlled DMs can circumvent the obstacle of spiders and segment gaps. In this section, we first set-up our notations and review the physics of phase</text>
<text><location><page_6><loc_52><loc_72><loc_92><loc_92></location>to amplitude modulation. We consider the system represented on Fig. 3 where two sequential DMs are located between the telescope aperture and the entrance pupil of the coronagraph. In this configuration, the telescope aperture and the pupil apodizer are not in conjugate planes. This will have an impact on the chromaticity of the system and is discussed in § . 5. Without loss of generality we work under the 'folded' assumption illustrated on Fig. 5 where the DMs are not tilted with respect to the optical axis and can be considered as lenses of index of refraction -1 (as discussed in Vanderbei & Traub (2005) . In the scalar approximation the relationship between the incoming field, E DM 1 ( x, y ), and the outgoing field, E DM 2 ( x 2 , y 2 ), is given by the diffractive Huygens Integral:</text>
<formula><location><page_6><loc_52><loc_68><loc_91><loc_71></location>E DM 2 ( x 2 , y 2 ) = 1 iλZ ∫ A E DM 1 ( x, y ) e i 2 π λ Q ( x,y,x 2 ,y 2 ) dxdy</formula>
<text><location><page_6><loc_90><loc_67><loc_92><loc_68></location>(6)</text>
<text><location><page_6><loc_52><loc_63><loc_92><loc_67></location>where A corresponds to the telescope aperture and Q ( x, y, x 2 , y 2 ) stands for the optical path length between any two points at DM1 and DM2:</text>
<formula><location><page_6><loc_53><loc_60><loc_92><loc_62></location>Q ( x, y, x 2 , y 2 ) = h 1 ( x, y )+ S ( x, y, x 2 , y 2 ) -h 2 ( x 2 , y 2 ) (7)</formula>
<text><location><page_6><loc_52><loc_57><loc_92><loc_60></location>S ( x, y, x 2 , y 2 ) is the free space propagation between the DMs:</text>
<formula><location><page_6><loc_53><loc_52><loc_92><loc_55></location>√ ( x -x 2 ) 2 +( y -y 2 ) 2 +( Z + h 1 ( x, y ) -h 2 ( x 2 , y 2 )) 2 (8)</formula>
<text><location><page_6><loc_52><loc_40><loc_92><loc_52></location>where Z is the distance between between the two DMs, h 1 and h 2 are the shapes of DM1 and DM2 respectively (as shown on Fig. 5) and λ is the wavelength. We recognize that two sequential DMs act as a pupil remapping unit similar to PIAA coronagraph (Guyon 2003) whose ray optics equations were first derived by Traub & Vanderbei (2003). We briefly state the notation used to describe such an optical system as introduced in Pueyo et al. (2011):</text>
<unordered_list>
<list_item><location><page_6><loc_54><loc_35><loc_92><loc_39></location>· For a given location at DM2, ( x 2 , y 2 ), the location at DM1 of the incident ray according to ray optics is given by:</list_item>
</unordered_list>
<formula><location><page_6><loc_64><loc_33><loc_92><loc_34></location>x 1 ( x 2 , y 2 ) = f 1 ( x 2 , y 2 ) (9a)</formula>
<formula><location><page_6><loc_64><loc_31><loc_92><loc_32></location>y 1 ( x 2 , y 2 ) = g 1 ( x 2 , y 2 ) . (9b)</formula>
<unordered_list>
<list_item><location><page_6><loc_54><loc_26><loc_92><loc_29></location>· Conversely, for a given location at DM1, ( x 1 , y 1 ), the location at DM2 of the outgoing ray according to geometric optics is given by:</list_item>
</unordered_list>
<formula><location><page_6><loc_64><loc_23><loc_92><loc_25></location>x 2 ( x 1 , y 1 ) = f 2 ( x 1 , y 1 ) (10a)</formula>
<formula><location><page_6><loc_64><loc_21><loc_92><loc_23></location>y 2 ( x 1 , y 1 ) = g 2 ( x 1 , y 1 ) . (10b)</formula>
<unordered_list>
<list_item><location><page_6><loc_54><loc_16><loc_92><loc_20></location>· Fermat's principle dictates the following relationships between the remapping functions and the shape of DM1:</list_item>
</unordered_list>
<formula><location><page_6><loc_62><loc_10><loc_92><loc_13></location>∂h 1 ∂x ∣ ∣ ∣ ( x 1 ,y 1 ) = x 1 -f 2 ( x 1 , y 1 ) Z (11a)</formula>
<formula><location><page_6><loc_62><loc_7><loc_92><loc_10></location>∂h 1 ∂y ∣ ∣ ∣ ( x 1 ,y 1 ) = y 1 -g 2 ( x 1 , y 1 ) Z . (11b)</formula>
<unordered_list>
<list_item><location><page_7><loc_11><loc_88><loc_48><loc_92></location>· Conversely, if we choose the surface of DM2 to ensure that the outgoing on-axis wavefront is flat, we then find:</list_item>
</unordered_list>
<formula><location><page_7><loc_18><loc_82><loc_48><loc_85></location>∂h 2 ∂x ∣ ∣ ∣ ( x 2 ,y 2 ) = x 2 -f 1 ( x 2 , y 2 ) Z (12a)</formula>
<section_header_level_1><location><page_7><loc_55><loc_91><loc_89><loc_92></location>3.2. Fresnel approximation and Talbot Imaging</section_header_level_1>
<text><location><page_7><loc_52><loc_82><loc_92><loc_90></location>In Pueyo et al. (2011) we showed that one could approximate the propagation integral in Eq. 6 by taking in a second order Taylor expansion of Q ( x, y, x 2 , y 2 ) around the rays that trace ( f 1 ( x 2 , y 2 ) , g 1 ( x 2 , y 2 )) to ( x 2 , y 2 ). In this case the relationship between the fields at DM1 and DM2 is:</text>
<formula><location><page_7><loc_18><loc_79><loc_48><loc_82></location>∂h 2 ∂y ∣ ∣ ∣ ( x 2 ,y 2 ) = y 2 -g 1 ( x 2 , y 2 ) Z . (12b)</formula>
<formula><location><page_7><loc_15><loc_72><loc_92><loc_76></location>E DM 2 ( x 2 , y 2 ) = e 2 iπ λ Z iλZ { ∫ A E DM 1 ( x, y ) e iπ λZ [ ∂f 2 ∂x ( x -x 1 ) 2 +2 ∂g 2 ∂x ( x -x 1 )( y -y 1 )+ ∂g 2 ∂y ( y -y 1 ) 2 ] dxdy }∣ ∣ ∣ ∣ ∣ ( x 1 ,y 1 ) (13)</formula>
<text><location><page_7><loc_8><loc_66><loc_92><loc_71></location>When the mirror's deformations are very small compared to both the wavelength and D 2 /Z , the net effect of the wavefront disturbance created by DM1 can be captured in E DM 1 ( x, y ) and the surface of DM2 can be factored out of Eq. 6. In this case x 1 = x 2 , y 1 = y 2 , ∂f 2 ∂x ∣ ∣ x 1 ,y 1 = 1, ∂f 2 ∂y ∣ ∣ x 1 ,y 1 = 0, ∂g 2 ∂y ∣ ∣ x 1 ,y 1 = 1. Then, Eq. 13 reduces to:</text>
<formula><location><page_7><loc_22><loc_62><loc_92><loc_66></location>E DM 2 ( x 2 , y 2 ) = e 2 iπ λ ( Z -h 2 ( x 2 ,y 2 )) iλZ ∫ Aperture e 2 iπ λ ( h 1 ( x,y )) e iπ λZ ( ( x -x 2 ) 2 +( y -y 2 ) 2 ) dxdy (14)</formula>
<text><location><page_7><loc_8><loc_54><loc_48><loc_58></location>which is the Fresnel approximation. If moreover h 1 ( x, y ) = λglyph[epsilon1] cos( 2 π D ( mx + ny )), h 2 ( x, y ) = -h 1 ( x, y ), with glyph[epsilon1] glyph[lessmuch] 1, then the outgoing field is to first order:</text>
<formula><location><page_7><loc_9><loc_49><loc_48><loc_53></location>E DM 2 ( x 2 , y 2 ) ∝ πλZ ( m 2 + n 2 ) D 2 λglyph[epsilon1] cos( 2 π D ( mx 2 + ny 2 )) . (15)</formula>
<text><location><page_7><loc_8><loc_31><loc_48><loc_49></location>This phase-to-amplitude coupling is a well known optical phenomenon called Talbot imaging and was introduced to the context of high contrast imaging by Shaklan & Green (2006). In the small deformation regime, the phase on DM1 becomes an amplitude at DM2 according to the coupling in Eq. 15. When two sequential DMs are controlled to cancel small amplitude errors, as in Pueyo et al. (2009), they operate in this regime. Note, however, that the coupling factor scales with wavelength (the resulting amplitude modulation is wavelength independent, but the coupling scales as λ ): this formalism is thus not applicable to our case, for which we are seeking to correct large amplitude errors (secondary support structures and</text>
<text><location><page_7><loc_52><loc_38><loc_92><loc_58></location>segments) with the DMs. In practice, when using Eq. 15 in the wavefront control scheme outlined in Pueyo et al. (2009) to correct aperture discontinuities, this weak coupling results in large mirror shapes that lie beyond the range of the linear assumption made by the DM control algorithm. For this reason, methods outlined on the left panel of Fig. 1 to correct for aperture discontinuities do not converge to high contrast. Because phase to amplitude conversion is fundamentally a very non-linear phenomena, these descending gradient methods (Bord'e & Traub 2006; Give'on et al. 2007; Pueyo et al. 2009) are not suitable to find DM shapes that mitigate apertures discontinuities. We circumvent these numerical limitations by calculating DMs shapes that are based on the full non-linear problem, right panel of Fig. 1.</text>
<section_header_level_1><location><page_7><loc_59><loc_36><loc_84><loc_37></location>3.3. The SR-Fresnel approximation</section_header_level_1>
<text><location><page_7><loc_52><loc_31><loc_92><loc_35></location>In the general case, starting from Eq. 13 and following the derivation described in § . 5, the field at DM2 can be written as follows:</text>
<formula><location><page_7><loc_17><loc_25><loc_92><loc_29></location>E DM 2 ( x 2 , y 2 ) = { √ | det[ J ] | ∫ FP ̂ E DM 1 ( ξ, η ) e i 2 π ( ξf 1 + ηg 1 ) e -i πλZ det[ J ] ( ∂g 1 ∂y ξ 2 + ∂f 1 ∂x η 2 ) dξdη }∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (16)</formula>
<text><location><page_7><loc_8><loc_14><loc_48><loc_22></location>where ̂ E DM 1 ( ξ, η ) is the Fourier transform of the telescope aperture, FP and stands for the Fourier plane. We call this integral the Stretched-Remapped Fresnel approximation (SR-Fresnel). Moreover det[ J ( x 2 , y 2 )] is the determinant of the Jacobian of the change of variables that maps ( x 2 , y 2 ) to ( x 1 , y 1 ):</text>
<formula><location><page_7><loc_10><loc_6><loc_48><loc_10></location>det [ J ( x 2 , y 2 )] = { ∂f 1 ∂x ∂g 1 ∂y -( ∂g 1 ∂x ) 2 } ∣ ∣ ∣ ∣ ( x 2 ,y 2 ) . (17)</formula>
<text><location><page_7><loc_52><loc_19><loc_92><loc_22></location>In the ray optics approximation, λ ∼ 0, the non linear transfer function between the two DMs becomes:</text>
<formula><location><page_7><loc_55><loc_15><loc_92><loc_19></location>E DM 2 ( x 2 , y 2 ) = { √ | det[ J ] | E DM 1 ( f 1 , g 1 ) } ∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (18)</formula>
<formula><location><page_7><loc_53><loc_12><loc_92><loc_15></location>[ E DM 2 ( x 2 , y 2 )] 2 = { det[ J ] [ E DM 1 ( f 1 , g 1 )] 2 } ∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (19)</formula>
<text><location><page_7><loc_52><loc_7><loc_92><loc_11></location>The square form (e.g Eq. 19) of this transfer function can also be derived based on conservation of energy principles and is a generalization to arbitrary geometries of the</text>
<figure>
<location><page_8><loc_17><loc_55><loc_85><loc_91></location>
<caption>Figure 3. Schematic of the optical system considered: the telescope apertures is followed by two sequential Defromable Mirrors (DMs) in non-conjugate planes whose purpose is to remap the pupil discontinuities. The beam then enters a coronagraph to suppress the bulk of the starlight: in this figure we show an Apodized Lyot Pupil Coronagraph (APLC). This is the coronagraphic architecture we consider for the remainder of the paper but we stress that the method presented herein is applicable to any coronagraph.</caption>
</figure>
<text><location><page_8><loc_8><loc_7><loc_48><loc_47></location>equation driving the design of PIAA coronagraphs (Vanderbei & Traub 2005). A full diffractive optimization of the DM surfaces requires use of the complete transfer function shown in Eq. 16. However, there do not exist yet tractable numerical method to evaluate Eq. 16 efficiently enough in order for this model to be included in an optimization algorithm. Moreover even solving the ray optics problem is extremely complicated: it requires to find the mapping function ( f 1 , g 1 ) which solves the non-linear partial differential equation in Eq. 19. Substituting for( f 1 , g 1 ) and using Eqs. 12b yields a second order non-linear partial differential equation in h 2 . This is the problem that we set ourselves to tackle in the next section, and is the cornerstone of our Adpative Compensation of Aperture Discontinuities. As a check, one can verify that in the small deformation regime (e.g. if h 1 ( x, y ) = λglyph[epsilon1] cos( 2 π D ( mx + ny )) and h 2 ( x, y ) = -h 1 ( x, y )) Eq. 19 yields the same phase-to-amplitude coupling as in Talbot imaging (Pueyo 2008). Eq. 19 is a well know optimal transport problem (Monge 1781), which has already been identified as underlying optical illumination optimizations (Glimm & Oliker 2002). While the existence and uniqueness of solutions in arbitrary dimensions have been extensively discussed in the mathematical literature (see Dacorogna & Moser (1990) for a review), there was no practical numerical solution published up until recently. In particular, to our knowledge, not even a dimensional solution for which the DM surfaces can be described using a realistic basis-set has been published yet. We now introduce a method that calculates solu-</text>
<text><location><page_8><loc_52><loc_44><loc_92><loc_47></location>ons to Eq. 19 which can be represented by feasible DM shapes.</text>
<section_header_level_1><location><page_8><loc_54><loc_41><loc_89><loc_43></location>4. CALCULATION OF THE DEFORMABLE MIRROR SHAPES</section_header_level_1>
<section_header_level_1><location><page_8><loc_61><loc_39><loc_82><loc_40></location>4.1. Statement of the problem</section_header_level_1>
<text><location><page_8><loc_52><loc_7><loc_92><loc_39></location>Ideally, we seek DM shapes that fully cancel all the discontinuities at the surface of the primary mirror and yield a uniform amplitude distribution, as shown in the top panel of Fig. 4. A solutions for a particular geometry with four secondary support has been derived by Lozi et al. (2009). It relies on reducing the dimensionality of the problem to the direction orthogonal to the spiders. It is implemented using a transmissive correcting plate that is a four-faced prism arranged such that the vertices coincides with the location of the spiders. The curvature discontinuities at the location of the spiders are responsible for the local remapping that removes the spiders in the coronagraph pupil. However such a solution cannot be readily generalized to the case of more complex apertures, where the secondary support structures might vary in width, or in the presence of segment gaps. Moreover it is transmissive and thus highly chromatic. Here we focus on a different class of solutions and seek to answer a different question. How well can we mitigate the effect of pupil discontinuities using DMs with smooth surfaces, a limited number of actuators (e.g a limited maximal curvature), and a limited stroke? Under these constraints directly solving Eq. 19 (e.g. solving the forward problem illustrated in the top panel of Fig. 4)</text>
<section_header_level_1><location><page_9><loc_14><loc_89><loc_43><loc_92></location>The forward problem</section_header_level_1>
<figure>
<location><page_9><loc_9><loc_80><loc_49><loc_89></location>
</figure>
<section_header_level_1><location><page_9><loc_8><loc_76><loc_49><loc_79></location>The tapered reverse problem</section_header_level_1>
<figure>
<location><page_9><loc_8><loc_67><loc_49><loc_76></location>
<caption>Figure 4. Top : In the ideal case the two DMs would fully remap all the discontinuities in the telescope's aperture to feed a fully uniform beam to the coronagraph. However this would require discontinuities in the mirror's curvatures which cannot be achieved in practice. Moreover solving the Monge-Ampere Equation in this direction is a difficult exercise as the right hand side of Eq. 19 presents an implicit dependence on the solution h 2 . Bottom : We circumvent this problem by solving the reverse problem, where the the input beam is now uniform and the implicit dependence drops out. Moreover we taper the edges of the discontinuities by convolving the target field A ( x 1 , y 1 ) by a gaussian of full width at half maximum ω ( ω = 50 cycles per aperture in this figure).</caption>
</figure>
<text><location><page_9><loc_8><loc_40><loc_48><loc_50></location>is not tractable as both factors on the left hand side of Eq. 19 depend on h 2 . More specifically, the implicit dependence of E DM 1 ( f 1 ( x 2 , y 2 ) , g 1 ( x 2 , y 2 )) on h 2 can only be addressed using finite elements solvers, whose solutions might not be realistically representable using a DM. However this can be circumvented using the reversibility of light and solving the reverse problem, where the two mirrors have been swapped. Indeed, since</text>
<formula><location><page_9><loc_18><loc_37><loc_48><loc_39></location>x 2 = f 2 ( f 1 ( x 2 , y 2 ) , g 1 ( x 2 , y 2 )) (20)</formula>
<formula><location><page_9><loc_18><loc_36><loc_48><loc_37></location>y 2 = g 2 ( f 1 ( x 2 , y 2 ) , g 1 ( x 2 , y 2 )) (21)</formula>
<text><location><page_9><loc_8><loc_32><loc_48><loc_35></location>then we have the following relationship between the determinants of the forward and reverse remappings:</text>
<formula><location><page_9><loc_8><loc_26><loc_52><loc_31></location>1 = { ∂f 2 ∂x ∂g 2 ∂y -( ∂g 2 ∂x ) 2 } ∣ ∣ ∣ ∣ ( x 1 ,y 1 ) { ∂f 1 ∂x ∂g 1 ∂y ( ∂g 1 ∂x ) 2 } ∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (22)</formula>
<text><location><page_9><loc_52><loc_87><loc_92><loc_92></location>Moreover we are only interested in compensating asymmetric structures located between the secondary and the edge of the primary. We thus only seek to find ( f 2 , g 2 ) such that:</text>
<formula><location><page_9><loc_56><loc_81><loc_92><loc_86></location>E DM 1 ( x 1 , y 1 ) = A ( x 1 , y 1 ) = ( [ P ( x, y ) -(1 -P O ( x, y ))] ∗ e -x 2 + y 2 ω 2 ) ∣ ∣ ∣ ( x 1 ,y 1 ) (25)</formula>
<text><location><page_9><loc_52><loc_45><loc_92><loc_80></location>where P O ( x 1 , y 1 ) is the obscured pupil, without segments or secondary supports. Finally, we focus on solutions with a high contrast only up to a finite OWA. We artificially taper the discontinuities by convolving the control term in the Monge Ampere Equation, [ P ( x, y ) -(1 -P O ( x, y ))], with a gaussian of width ω . Note that this tapering is only applied when calculating the DM shapes via solving the reverse problem. When the resulting solutions are propagated through Eq. 19 we use the true telescope pupil for E DM 1 ( x 1 , y 1 ). The parameter ω has a significant impact on the final postcoronagraphic contrast. Indeed we are here working with a merit function that is based on a pupil-plane residual, while ideally our cost function should be based on imageplane intensity. By convolving the control term in the reverse Monge Ampere Equation, we low pass filter the discontinuities. This is equivalent to giving a stronger weight to low-to-mid spatial frequencies of interest in the context of exo-planets imaging . For each case presented in § . 6 we calculate our DM shapes over a grid of values of ω which correspond to low pass filters with cutoff frequencies ranging from ∼ OWAto ∼ 2 OWA and we keep the shapes which yield the best contrast. This somewhat ad-hoc approach can certainly be optimized for higher contrasts. However such an optimization is beyond the scope of the present manuscript.</text>
<text><location><page_9><loc_52><loc_41><loc_92><loc_45></location>The problem we are seeking to solve is illustrated in the second panel of Fig. 4. In this configuration the full second order Monge Ampere Equation can be written as:</text>
<formula><location><page_9><loc_53><loc_37><loc_92><loc_40></location>(1+ Z ∂ 2 h 1 ∂x 2 )(1+ Z ∂ 2 h 1 ∂y 2 ) -( Z ∂ 2 h 1 ∂x∂y ) 2 = A ( x, y ) 2 (26)</formula>
<text><location><page_9><loc_52><loc_31><loc_92><loc_36></location>where we have dropped the ( x 1 , y 1 ) dependence for clarity. Since we are interested in surface deformations which can realistically be created using a DM, we seek for a Fourier representation of the DMs surface:</text>
<text><location><page_9><loc_8><loc_22><loc_48><loc_26></location>We thus focus on the inverse problem, bottom panel of Fig. 4, that consists of first finding the surface of h 1 as the solution of:</text>
<formula><location><page_9><loc_10><loc_16><loc_48><loc_22></location>{ [ E DM 2 ( f 2 , g 2 )] 2 [ ∂f 2 ∂x ∂g 2 ∂y -( ∂g 2 ∂x ) 2 ]} ∣ ∣ ∣ ∣ ( x 1 ,y 1 ) =[ E DM 1 ( x 1 , y 1 )] 2 (23)</formula>
<text><location><page_9><loc_8><loc_12><loc_48><loc_15></location>Since our goal is to obtain a pupil as uniform a possible we seek a field at DM2 as uniform as possible:</text>
<formula><location><page_9><loc_16><loc_6><loc_48><loc_11></location>E DM 2 ( f 2 ( x 1 , y 1 ) , g 2 ( x 1 , y 1 )) = √ ∫ A E DM 1 ( x, y ) 2 dxdy = Constant . (24)</formula>
<formula><location><page_9><loc_58><loc_22><loc_92><loc_30></location>h 1 ( x, y ) = D 2 Z H 1 ( X,Y ) = D 2 Z N/ 2 ∑ n = -N/ 2 N/ 2 ∑ m = -N/ 2 a m,n e i 2 π D ( mX + nX ) (27)</formula>
<text><location><page_9><loc_52><loc_15><loc_92><loc_21></location>with a -m, -n = a glyph[star] -m, -n , where N is the limited number of actuators across the DM. Note that we have normalized the dimensions in the pupil plane X = x/D , Y = y/D . The normalized second order Monge Ampere Equation is then:</text>
<formula><location><page_9><loc_53><loc_10><loc_92><loc_14></location>(1 + ∂ 2 H 1 ∂X 2 )(1 + ∂ 2 H 1 ∂Y 2 ) -( ∂ 2 H 1 ∂X∂Y ) 2 = A ( X,Y ) 2 (28)</formula>
<text><location><page_9><loc_52><loc_7><loc_92><loc_9></location>For each configuration in this paper we first solve Eq. 28 and then transform the normalized solution in physical</text>
<section_header_level_1><location><page_10><loc_9><loc_90><loc_43><loc_92></location>Forward coordinate system</section_header_level_1>
<text><location><page_10><loc_52><loc_89><loc_92><loc_92></location>units, which depends on the DMs diameter D and their separation Z .</text>
<figure>
<location><page_10><loc_9><loc_78><loc_48><loc_89></location>
</figure>
<section_header_level_1><location><page_10><loc_9><loc_75><loc_43><loc_77></location>Reverse coordinate system</section_header_level_1>
<figure>
<location><page_10><loc_9><loc_61><loc_48><loc_74></location>
<caption>Figure 5. Forward and reverse coordinate systems, with their respective forward and reverse coordinate transforms, in the case of the folded system studied in this paper. Note that this figure shows normalized units. As explained in the body of the text the correspondence between normalized and real units scales as follow: ( x i , y i ) = ( DX i , DY i ), ( f i , g i ) = ( DF i , DG i ), H i = D 2 Z h i , where i = 1 , 2, D is the aperture diameter and Z the separation between DMs. We solve Monge Ampere Equation in normalized coordinates and then apply the scalings in order to find the true DM shapes.</caption>
</figure>
<section_header_level_1><location><page_10><loc_54><loc_85><loc_90><loc_87></location>4.2. Solving the Monge-Ampere equation to find H 1</section_header_level_1>
<text><location><page_10><loc_52><loc_68><loc_92><loc_85></location>Over the past few years a number of numerical algorithms aimed at solving Eq. 28 have emerged in the literature (Loeper & Rapetti 2005; Benamou et al. 2010). Here we summarize our implementation of two of them: an explicit Newton method (Loeper & Rapetti 2005), and a semi-implicit method (Froese & Oberman 2012). We do not delve into the proof of convergence of each method, they can be found in Loeper & Rapetti (2005); Benamou et al. (2010); Froese & Oberman (2012). Note that Zheligovsky et al. (2010) discussed both approaches in a cosmological context and devised Fourier based solutions. Here we are interested in a two dimensional problem and we outline below the essence of each algorithm.</text>
<section_header_level_1><location><page_10><loc_61><loc_64><loc_83><loc_65></location>4.2.1. Explicit Newton algorithm</section_header_level_1>
<text><location><page_10><loc_52><loc_59><loc_92><loc_63></location>This method was first introduced by Loeper & Rapetti (2005) and relies on the fact that Eq. 28 can be re-written as</text>
<formula><location><page_10><loc_52><loc_53><loc_92><loc_58></location>det [( 1 + ∂ 2 H 1 ∂X 2 ∂ 2 H 1 ∂X∂Y ∂ 2 H 1 ∂X∂Y 1 + ∂ 2 H 1 ∂Y 2 )] = det[ Id + H ( H 1 ( X,Y ))] (29)</formula>
<text><location><page_10><loc_52><loc_49><loc_92><loc_53></location>where H ( · ) is the two dimensional Hessian of a scalar field and Id the identity matrix. If one writes H 1 = u + v with || v || glyph[lessmuch] || u || then:</text>
<formula><location><page_10><loc_24><loc_45><loc_92><loc_46></location>det[ Id + H ( u + δv )] = det[ Id + H ( u )] + δ Tr [ ( Id + H ( u )) † T H ( v ) ] + o ( δ 2 ) (30)</formula>
<text><location><page_10><loc_8><loc_42><loc_68><loc_43></location>where ( · ) † T denotes the transpose of the comatrix. Eq. 28 can thus be linearized as:</text>
<formula><location><page_10><loc_17><loc_38><loc_92><loc_41></location>(1 + ∂ 2 u ∂Y 2 ) ∂ 2 v ∂X 2 +(1 + ∂ 2 u ∂X 2 ) ∂ 2 v ∂Y 2 -2 ∂ 2 u ∂X∂Y ∂ 2 v ∂X∂Y = ( A ( X,Y ) 2 -det[ H ( X 2 + Y 2 2 + u )] ) (31)</formula>
<text><location><page_10><loc_8><loc_36><loc_92><loc_37></location>The explicit Newton algorithm relies on Eq. 31 and can then be summarized as carrying out the following iterations:</text>
<unordered_list>
<list_item><location><page_10><loc_11><loc_34><loc_30><loc_35></location>· Choose a first guess H 0 1 .</list_item>
<list_item><location><page_10><loc_11><loc_31><loc_89><loc_33></location>· At each iteration k we seek for a solution of the form H k +1 1 = H k 1 + V k , where V k is the DM shape update.</list_item>
<list_item><location><page_10><loc_11><loc_29><loc_33><loc_31></location>· In order to find V k we write:</list_item>
</unordered_list>
<formula><location><page_10><loc_25><loc_26><loc_92><loc_29></location>L E ( H k 1 , V k ) = (1 + ∂ 2 H k 1 ∂Y 2 ) ∂ 2 V k ∂X 2 +(1 + ∂ 2 H k 1 ∂X 2 ) ∂ 2 V k ∂Y 2 -2 ∂ 2 H k 1 ∂X∂Y ∂ 2 V k ∂X∂Y (32)</formula>
<formula><location><page_10><loc_27><loc_23><loc_92><loc_26></location>R E ( H k 1 ) = 1 τ ( A 2 -det[ Id + H ( H k 1 )] ) (33)</formula>
<formula><location><page_10><loc_42><loc_20><loc_92><loc_21></location>L E ( H k 1 , V k ) = R E ( H k 1 ) . (34)</formula>
<text><location><page_10><loc_12><loc_16><loc_92><loc_19></location>Eq. 38 is a linear partial differential equation in V k . Since we are interested in a solution which can be expanded in a Fourier series we write V k as:</text>
<formula><location><page_10><loc_33><loc_12><loc_92><loc_16></location>V k 1 ( X,Y ) = N/ 2 ∑ n = -N/ 2 N/ 2 ∑ m = -N/ 2 v k m,n e i 2 π D ( mX + nX ) . (35)</formula>
<text><location><page_10><loc_12><loc_7><loc_92><loc_11></location>Both the right hand side and the left hand side of Eq. 38 can be written as a Fourier series, with a spatial frequency content between -N and N cycles per aperture. Equating each Fourier coefficient in these two series yields the following linear system of (2 N +1) 2 equations with ( N +1) 2 unknowns.</text>
<text><location><page_10><loc_12><loc_21><loc_19><loc_22></location>and solve</text>
<formula><location><page_11><loc_20><loc_89><loc_92><loc_92></location>For all m 0 , n 0 ∈ [ -N,N ]: ∫ DM e i 2 π ( m 0 X + n 0 Y ) [ L E ( H k 1 , V k ) -R E ( H k 1 ) ] dX dY = 0 (36)</formula>
<text><location><page_11><loc_12><loc_86><loc_92><loc_88></location>When searching for V k as a Fourier series over the square geometry chosen here, this inverse problem is always well posed.</text>
<unordered_list>
<list_item><location><page_11><loc_11><loc_83><loc_41><loc_85></location>· Update the solution H k +1 1 = H k 1 + V k +1 1</list_item>
</unordered_list>
<text><location><page_11><loc_8><loc_63><loc_48><loc_79></location>The convergence of this algorithm relies on the introduction of a damping constant τ > 1. Loeper & Rapetti (2005) showed that as long as X 2 + Y 2 2 + H k 1 remains convex, which is always true for ACAD with reasonably small aperture discontinuities, there exists a τ large enough so that this algorithm converge towards a solution of Eq. 28. However since this algorithm is gradient based, it is not guaranteed that it converges to the global minimum of the underlying non-linear problem. In order to avoid having this solver stall in a local minimum we follow the methodology outlined by Froese & Oberman (2012) and first carry out a series of implicit iterations</text>
<text><location><page_11><loc_52><loc_77><loc_92><loc_79></location>to get within a reasonable neighborhood of the global minimum.</text>
<section_header_level_1><location><page_11><loc_64><loc_73><loc_80><loc_74></location>4.2.2. Implicit algorithm</section_header_level_1>
<text><location><page_11><loc_52><loc_68><loc_92><loc_72></location>This algorithm, along with its convergence proof, is thoroughly explained in Froese & Oberman (2012) . It relies on rewriting Eq. 28 as:</text>
<formula><location><page_11><loc_52><loc_63><loc_92><loc_67></location>∂ 2 H 1 ∂X 2 + ∂ 2 H 1 ∂Y 2 = √ det[ Id + H ( H 1 ( X,Y ))] 2 +2 A ( X,Y ) 2 (37)</formula>
<text><location><page_11><loc_10><loc_59><loc_59><loc_60></location>The implicit method consists of carrying out the following iterations:</text>
<unordered_list>
<list_item><location><page_11><loc_11><loc_57><loc_29><loc_58></location>· Choose a first guess H 0 1</list_item>
<list_item><location><page_11><loc_11><loc_54><loc_35><loc_56></location>· In order to find H k +1 we write:</list_item>
</unordered_list>
<text><location><page_11><loc_12><loc_47><loc_19><loc_48></location>and solve</text>
<formula><location><page_11><loc_32><loc_45><loc_92><loc_54></location>L I ( H k 1 , V k ) = ∂ 2 H k +1 1 ∂X 2 + ∂ 2 H k +1 1 ∂Y 2 R E ( H k 1 ) = √ det[ Id + H ( H 1 ( X,Y ))] 2 +2 A ( X,Y ) 2 L I ( H k +1 1 ) = R I ( H k 1 ) . (38)</formula>
<text><location><page_11><loc_12><loc_42><loc_92><loc_44></location>This problem is a linear system of ( N +1) 2 equations with ( N +1) 2 unknowns and can be solved using projections on a Fourier Basis:</text>
<formula><location><page_11><loc_20><loc_38><loc_92><loc_41></location>For all m 0 , n 0 ∈ [ -N,N ]: ∫ DM e i 2 π ( m 0 X + n 0 Y ) [ L I ( H k 1 , V k ) -R I ( H k 1 ) ] dX dY = 0 (39)</formula>
<text><location><page_11><loc_12><loc_36><loc_83><loc_37></location>Note that the term under the square root in R I ( H k 1 ) is guaranteed to be positive at each iteration.</text>
<unordered_list>
<list_item><location><page_11><loc_11><loc_34><loc_22><loc_35></location>· Iterate over k</list_item>
</unordered_list>
<text><location><page_11><loc_8><loc_7><loc_48><loc_30></location>The inverse problem in Eq. 39 is always well posed, for any basis set or pupil geometry, while the explicit Newton method runs into convergence issues when not using a Fourier basis over a square. When seeking to use a basis set that is more adapted to the geometry of the spiders and segments or when using a trial influence function basis for the DM, the implicit method is the most promising method. In this paper we have limited our scope to solving the reverse problem in the bottom panel of Fig. 4, and used a Fourier representation for the DM, we are able to use both methods. In order to make sure that the algorithm converges towards the true solution of Eq. 28 we first run a few tens of iterations of the implicit method and, once it has converged, we seek for a more accurate solutions using the Newton algorithm. Typical results are shown in Fig. 6 where most of the residual error resides in the high spatial frequency content (e.g.</text>
<text><location><page_11><loc_52><loc_15><loc_92><loc_30></location>above N cycles per aperture). Our solutions are limited by the non- optimality of the Fourier basis to describe the mostly radial and azimuthal structures present in telescopes's apertures. Moreover the DM shape is the result of the minimization of a least squares residual in the virtual end-plane of the reverse problem, with little regard to the spatial frequency content of the solution in the final image plane of the coronagraph. While this method yields significant contrast improvements, as reported in § . 6, we discuss in § . 7 how it can be refined for higher contrast.</text>
<section_header_level_1><location><page_11><loc_58><loc_13><loc_86><loc_14></location>4.3. Deformation of the Second Mirror</section_header_level_1>
<text><location><page_11><loc_52><loc_7><loc_92><loc_12></location>Once the surface of DM1 has been calculated as a solution of Eq. 19, we compute the surface of DM2 based on Eqs. 12b, which stem from enforcing flatness of the outgoing on-axis wavefront. We seek a Fourier represen-</text>
<figure>
<location><page_12><loc_9><loc_75><loc_30><loc_92></location>
</figure>
<figure>
<location><page_12><loc_33><loc_74><loc_58><loc_91></location>
</figure>
<figure>
<location><page_12><loc_62><loc_74><loc_93><loc_92></location>
<caption>Figure 6. Virtual field at M1 when solving the reverse problem. A ( X 1 , Y 1 ) is the desired apodization (top), A n ( X 1 , Y 1 ) is the apodization obtained after solving the Monge Ampere Equation (center). The bottom panel shows the difference between the two quantities: the bulk of the energy in the residual is located in high spatial frequencies that cannot be controlled by the DMs.</caption>
</figure>
<text><location><page_12><loc_52><loc_62><loc_73><loc_63></location>tation for the surface of DM2:</text>
<figure>
<location><page_12><loc_9><loc_34><loc_50><loc_62></location>
<caption>Figure 7. Boundary conditions seen in the horizontal remapped space. Should the boundary conditions have strictly been enforced by our solver then F 2 ( -1 2 , Y ) = -1 2 , F 2 ( 1 2 , Y ) = 1 2 , F 2 ( X, -1 2 ) = X , F 2 ( X, 1 2 ) = X . The remapping function obtained with our solutions are very close to these theoretical boundary conditions and the residuals can easily be mitigated by sacrificing the edge rows and columns of actuators on each DM.</caption>
</figure>
<formula><location><page_12><loc_59><loc_54><loc_92><loc_62></location>h 2 ( x, y ) = D 2 Z H 2 ( X,Y ) = D 2 Z N/ 2 ∑ n = -N/ 2 N/ 2 ∑ m = -N/ 2 b m,n e i 2 π D ( mX + nX ) (40)</formula>
<text><location><page_12><loc_52><loc_49><loc_92><loc_53></location>Plugging the solution found in the previous step for h 1 into Eqs. 11b yields a closed form for the normalized remapping functions, ( F 2 , G 2 ):</text>
<formula><location><page_12><loc_52><loc_44><loc_94><loc_48></location>F 2 ( X 1 , Y 1 ) = X 1 -N/ 2 ∑ n = -N/ 2 N/ 2 ∑ m = -N/ 2 i 2 πm a m,n e i 2 π ( mX 1 + nY 1</formula>
<formula><location><page_12><loc_52><loc_39><loc_93><loc_43></location>G 2 ( X 1 , Y 1 ) = Y 1 -N/ 2 ∑ n = -N/ 2 N/ 2 ∑ m = -N/ 2 i 2 πn a m,n e i 2 π ( mX 1 + nY 1</formula>
<formula><location><page_12><loc_93><loc_41><loc_94><loc_47></location>) )</formula>
<text><location><page_12><loc_52><loc_36><loc_92><loc_38></location>Then the normalized version of Eqs. 12b can be rewritten as:</text>
<formula><location><page_12><loc_52><loc_31><loc_94><loc_35></location>L x ( X 1 , Y 1 ) = N/ 2 ∑ m = -N/ 2 i 2 πm b m,n e i 2 π ( mF 2 ( X 1 ,Y 1 )+ nF 2 ( X 1 ,Y 1 ))</formula>
<formula><location><page_12><loc_52><loc_27><loc_94><loc_30></location>R x ( X 1 , Y 1 ) = X 1 -F 2 ( X 1 , Y 1 ) L x = R x (41)</formula>
<formula><location><page_12><loc_52><loc_22><loc_93><loc_26></location>L y ( X 1 , Y 1 ) = N/ 2 ∑ m = -N/ 2 i 2 πn b m,n e i 2 π ( mF 2 ( X 1 ,Y 1 )+ nF 2 ( X 1 ,Y 1 ))</formula>
<formula><location><page_12><loc_52><loc_19><loc_94><loc_22></location>R y ( X 1 , Y 1 ) = Y 1 -G 2 ( X 1 , Y 1 ) L y = R y (42)</formula>
<text><location><page_12><loc_52><loc_17><loc_89><loc_18></location>We then multiply each side of Eq. 41 and Eq. 42 by:</text>
<text><location><page_12><loc_52><loc_11><loc_92><loc_16></location>e i 2 π ( m 0 F 2 ( X 1 ,Y 1 )+ n 0 F 2 ( X 1 ,Y 1 )) det [ Id + H ( H k 1 ( X 1 , Y 1 ) )] where ( m 0 , n 0 ) corresponds to a given DM spatial frequency.</text>
<text><location><page_13><loc_8><loc_91><loc_53><loc_92></location>system of 2 ∗ ( N +1) 2 equations with ( N +1) 2 real unknowns:</text>
<formula><location><page_13><loc_19><loc_86><loc_81><loc_88></location>2 πi m 0 b m 0 ,n 0 = ∫ R x ( X,Y ) det[ Id + H ( H k 1 ( X,Y ))] e i 2 π ( m 0 F 2 ( X,Y )+ n 0 F 2 ( X,Y )) dXdY</formula>
<formula><location><page_13><loc_20><loc_83><loc_34><loc_90></location>For all ( m 0 , n 0 ): DM For all ( m 0 , n 0 ):</formula>
<formula><location><page_13><loc_19><loc_80><loc_81><loc_83></location>i 2 πi n 0 b m 0 ,n 0 = ∫ DM R x ( X,Y ) det[ Id + H ( H k 1 ( X,Y ))] e i 2 π ( m 0 F 2 ( X,Y )+ n 0 F 2 ( X,Y )) dXdY</formula>
<text><location><page_13><loc_8><loc_78><loc_79><loc_79></location>We then find H 2 , the normalized surface of DM2, by solving this system in the least squares sense.</text>
<figure>
<location><page_13><loc_9><loc_41><loc_49><loc_75></location>
<caption>Figure 8. Boundary conditions seen in the vertical remapped space. Should the boundary conditions have strictly been enforced by our solver then G 2 ( -1 2 , Y ) = Y , G 2 ( 1 2 , Y ) = Y , G 2 ( X, -1 2 ) = -1 2 , G 2 ( X, 1 2 ) = 1 2 . The remapping function obtained with our solutions are very close to these theoretical boundary conditions and the residuals can easily be mitigated by sacrificing the edge rows and columns of actuators on each DM.</caption>
</figure>
<text><location><page_13><loc_8><loc_22><loc_48><loc_30></location>Once the Monge Ampere Equation has been solved, the calculation of the surface of the second mirror is a much easier problem. Indeed, by virtue of the conservation of the on-axis optical path length, finding the surface of DM2 only consists of solving a linear system (see Traub & Vanderbei (2003)).</text>
<section_header_level_1><location><page_13><loc_63><loc_74><loc_81><loc_75></location>4.4. Boundary Conditions</section_header_level_1>
<text><location><page_13><loc_52><loc_68><loc_92><loc_73></location>The method described above does not enforce any boundary conditions associated with Eq. 28. One practical set of boundary conditions consists of forcing the edges of each DM to map to each other:</text>
<formula><location><page_13><loc_66><loc_64><loc_92><loc_67></location>F i ( ± 1 2 , Y ) = ± 1 2 (43)</formula>
<formula><location><page_13><loc_66><loc_61><loc_92><loc_64></location>F i ( X, ± 1 2 ) = X (44)</formula>
<formula><location><page_13><loc_66><loc_58><loc_92><loc_61></location>G i ( ± 1 2 , Y ) = Y (45)</formula>
<formula><location><page_13><loc_66><loc_55><loc_92><loc_58></location>G i ( X, ± 1 2 ) = ± 1 2 (46)</formula>
<text><location><page_13><loc_52><loc_34><loc_92><loc_54></location>with i = 1 , 2. These correspond to a set of Neumann boundary conditions in H 1 ( X,Y ) and H 2 ( X,Y ). These boundary conditions can be enforced by augmenting the dimensionality of the linear systems on Eq. 36 and Eq. 39, however doing so increases the residual least squares errors and thus hampers the contrast of the final solution. Moreover Fig. 7 and Fig. 8 show that, because of the one to one remapping near the DM edges in the control term of the reverse problem, the boundary conditions are almost met in practice. For the remainder of this paper we thus do not include boundary conditions when calculating the DM shapes, when solving for H 1 ( X,Y ) in Eq. 28 since, in the worse case, only the edge rows and columns of the DMs actuator will have to be sacrificed in order for the edges to truly map to each other.</text>
<section_header_level_1><location><page_13><loc_63><loc_31><loc_80><loc_32></location>4.5. Remapped aperture</section_header_level_1>
<text><location><page_13><loc_52><loc_22><loc_92><loc_30></location>For a given pupil geometry we have calculated ( H 1 , H 2 ). We then convert the DM surfaces to real units, ( h 1 , h 2 ), by multiplication with D 2 /Z . We evaluate the remapping functions using Eqs. 11b and 12b and obtain the field at the entrance of the coronagraph in the ray optic approximation</text>
<formula><location><page_13><loc_24><loc_16><loc_92><loc_19></location>E DM 2 ( x 2 , y 2 ) = { √ det [ J ] E DM 1 ( f 1 , g 1 ) e i 2 π λ ( S ( f 1 ,g 1 )+ h 1 ( f 1 ,g 1 ) -h 2 ) } ∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (47)</formula>
<text><location><page_13><loc_8><loc_7><loc_48><loc_12></location>where the exponential factor corresponds to the Optical Path Length through the two DMs. Even if the surface of the DMs has been calculated using only a finite set of Fourier modes, we check that the optical</text>
<text><location><page_13><loc_52><loc_11><loc_70><loc_12></location>path length is conserved.</text>
<text><location><page_13><loc_52><loc_7><loc_92><loc_10></location>Fig. 9 shows that since the curvature of the DMs is limited by the number of modes N , our solution does</text>
<text><location><page_14><loc_52><loc_83><loc_92><loc_92></location>and discussed in § . 6. Eq. 47 assumes that the propagation between the two DMs occurs according to the laws of ray optics. In the next section we derive the actual diffractive field at DM2, e.g Eq. 16, and show that in the pupil remapping regime of ACAD, edge ringing due to the free space propagation is actually smaller than in the Fresnel regime.</text>
<section_header_level_1><location><page_14><loc_62><loc_80><loc_82><loc_81></location>5. CHROMATIC PROPERTIES</section_header_level_1>
<section_header_level_1><location><page_14><loc_55><loc_78><loc_89><loc_80></location>5.1. Analytical expression of the diffracted field</section_header_level_1>
<text><location><page_14><loc_52><loc_41><loc_92><loc_78></location>ACADis based on ray optics. It is an inherently broadband technique, and provided that the coronagraph is optimized for broadband performance ACAD will provide high contrast over large spectral windows. However, when taking into account the edge diffraction effects that are captured by the quadratic integral in Eq. 16, the true propagated field at DM2 becomes wavelength dependent. More specifically, when λ is not zero then the oscillatory integral superposes on the ray optics field a series of high spatial frequency oscillations. In theory, it would be best to use this as the full transfer function to include chromatic effects in the computation of the DMs shapes. However, as discussed in S. 4, solving the non-linear Monge-Ampere Equation is already a delicate exercise, and we thus have limited the scope of this paper to ray optics solutions. Nonetheless, once the DMs' shapes have been determined using ray optics, one should check whether or not the oscillations due to edge diffraction will hamper the contrast. This approach is reminiscent of the design of PIAA systems where the mirror shapes are calculated first using geometric optics and are then propagated through the diffractive integral in order to check a posteriori whether or not the chromatic diffractive artifacts are below the design contrast (Pluzhnik et al. 2005). In this section we detail the derivation of Eq. 16 that is the diffractive integral for the two DMs remapping system and use this formulation to discuss the diffractive properties of ACAD.</text>
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</figure>
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<caption>Figure 9. Beam amplitude before and after the DMs in the case of a geometry similar to JWST. We chose to solve the reverse problem over a square using a Fourier basis-set and not stricly enforcing boundary conditions. This results in small distortions of the edges of the actual aperture in the vicinity of segments gaps and secondary supports. We address this problem by slightly oversizing the secondary obscuration and undersizing the aperture edge in the coronagraph.</caption>
</figure>
<text><location><page_14><loc_8><loc_41><loc_48><loc_67></location>not fully map out the discontinuities induced by the secondary supports and the segments. However, they are significantly thinner and one can expect that their impact on contrast will be attenuated by orders of magnitude. In order to quantify the final coronagraphic contrasts of our solution we then propagate it through an APLC coronagraph designed using the method in § . 2. In the case of a hexagon based primary (such as JWST), we use a coronographic apodizer with a slightly oversized secondary obscuration and undersize outer edge in order to circularize the pupil. Note that this choice is mainly driven by the type of coronagraph we chose in § . 2 to illustrate our technique. Since the DM control strategy presented in this section is independent of the coronagraph, it can be generalized to any of the starlight suppression systems which have been discussed in the literature. For succinctness we present our results using coronagraph solely based on using pupil apodization (either in an APLC or in a PIAAC configuration). Results for a JWST geometry are shown on Fig. 11 and Fig. 12</text>
<text><location><page_14><loc_10><loc_37><loc_92><loc_38></location>We start with the expression of the second order diffractive field at DM2 as derived in Pueyo et al. (2011), Eq. 13 .</text>
<formula><location><page_14><loc_16><loc_32><loc_84><loc_35></location>E DM 2 ( x 2 , y 2 ) = 1 iλZ { ∫ E DM 1 ( x, y ) e iπ λZ [ ∂f 2 ∂x ( x -x 1 ) 2 +2 ∂g 2 ∂x ( x -x 1 )( y -y 1 )+ ∂g 2 ∂y ( y -y 1 ) 2 ] dxdy } ∣ ∣ ∣ ( x 1 ,y 1 )</formula>
<text><location><page_14><loc_8><loc_29><loc_46><loc_30></location>We write E DM 1 ( x, y ) as its inverse Fourier transform</text>
<formula><location><page_14><loc_34><loc_25><loc_92><loc_27></location>E DM 1 ( x, y ) = ∫ ̂ E DM 1 ( ξ, η ) e i 2 π ( xξ + yη ) dξdη (48)</formula>
<text><location><page_14><loc_10><loc_22><loc_87><loc_23></location>and insert this expression in Eq. 13. Completing the squares in the quadratic exponential factor then yields:</text>
<formula><location><page_14><loc_12><loc_17><loc_92><loc_21></location>E DM 2 ( x 2 , y 2 ) = 1 iλZ {∫ ̂ E DM 1 ( ξ, η ) I 1 ( f 1 , g 1 ) e i 2 π [ f 1 ξ + g 1 η ] e -iπλZ ( ∂f 2 ∂y | ( f 1 ,g 1 ) ξ 2 + ∂g 2 ∂x | ( f 1 ,g 1 ) η 2 ) dξdη }∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (49)</formula>
<text><location><page_14><loc_8><loc_15><loc_11><loc_16></location>with</text>
<formula><location><page_14><loc_19><loc_10><loc_92><loc_14></location>I 1 ( y 1 , x 1 ) = ∫ e iπ λZ [ ∂f 2 ∂x ( x -x 1 -ξλZ ∂f 2 ∂x ) 2 +2 ∂g 2 ∂x ( x -x 1 )( y -y 1 )+ ∂g 2 ∂y ( y -y 1 -ηλZ ∂g 2 ∂x ) 2 ] dxdy ∣ ∣ ∣ ∣ ( x 1 ,y 1 ) . (50)</formula>
<text><location><page_14><loc_10><loc_7><loc_92><loc_8></location>The integral over space, I 1 ( y 1 , x 1 ), is the integral of a complex gaussian and can be evaluated analytically. This</text>
<section_header_level_1><location><page_14><loc_11><loc_90><loc_42><loc_92></location>Before DMs After DMs</section_header_level_1>
<text><location><page_15><loc_8><loc_91><loc_13><loc_92></location>yields:</text>
<formula><location><page_15><loc_14><loc_84><loc_92><loc_90></location>E DM 2 ( x 2 , y 2 ) = 1 √ | ∂f 2 ∂x ∂g 2 ∂y -( ∂g 2 ∂x ) 2 | ∫ ̂ E DM 1 ( ξ, η ) e i 2 π [ x 1 ξ + y 1 η ] e -iπλZ ( ∂f 2 ∂y ξ 2 + ∂g 2 ∂x η 2 ) dξdη ∣ ∣ ∣ ∣ ( x 1 ,y 1 ) . (51)</formula>
<text><location><page_15><loc_8><loc_78><loc_92><loc_82></location>We thus have expressed E DM 2 ( x 2 , y 2 ) as a function of ( x 1 , y 1 ) = ( f 1 ( x 2 , y 2 ) , g 1 ( x 2 , y 2 )). This expression can be further simplified: using Eqs. 20 to 22 one can derive ∂f 2 ∂x | ( x 1 ,y 1 ) = 1 det[ J ( x 2 ,y 2 )] ∂g 1 ∂y | ( x 2 ,y 2 ) and ∂g 2 ∂y | ( x 1 ,y 1 ) = 1 det[ J ( x 2 ,y 2 )] ∂f 1 ∂x | ( x 2 ,y 2 ) . Which finishes to prove Eq. 16:</text>
<formula><location><page_15><loc_17><loc_74><loc_92><loc_77></location>E DM 2 ( x 2 , y 2 ) = { √ | det[ J ] | ∫ FP ̂ E DM 1 ( ξ, η ) e i 2 π ( ξf 1 + ηg 1 ) e -i πλZ det[ J ] ( ∂g 1 ∂y ξ 2 + ∂f 1 ∂x η 2 ) dξdη }∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (52)</formula>
<text><location><page_15><loc_8><loc_72><loc_76><loc_73></location>This expression is very similar to a modified Fresnel propagation and can be rewritten as such:</text>
<formula><location><page_15><loc_19><loc_68><loc_92><loc_71></location>E DM 2 ( x 2 , y 2 ) = {∫ A E DM 1 ( x, y ) e -i πdet [ J ] λZ ( ( ∂g 1 ∂y ) -1 ( x -f 1 ) 2 +( ∂f 1 ∂x ) -2 ( y -g 1 ) 2 ) dxdy }∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (53)</formula>
<text><location><page_15><loc_8><loc_61><loc_92><loc_67></location>Because of this similarity we call this integral the Stretched- Remapped Fresnel approximation (SR-Fresnel). Indeed in this approximation the propagation distance is stretched by ( ∂g 1 ∂y det [ J ] , ∂f 1 ∂x det [ J ] ) and the integral is centered around the remapped pupil ( f 1 , g 1 ).</text>
<section_header_level_1><location><page_15><loc_23><loc_57><loc_34><loc_58></location>5.2. Discussion</section_header_level_1>
<text><location><page_15><loc_8><loc_54><loc_48><loc_57></location>The integral form provides physical insight about the behavior of the chromatic edge oscillations. If we write</text>
<formula><location><page_15><loc_21><loc_50><loc_48><loc_53></location>Γ x = det [ J ] ∂g 1 ∂y ∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (54)</formula>
<formula><location><page_15><loc_21><loc_46><loc_48><loc_49></location>Γ y = det [ J ] ∂f 1 ∂x ∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (55)</formula>
<text><location><page_15><loc_8><loc_44><loc_40><loc_45></location>we can identify a several diffractive regimes:</text>
<unordered_list>
<list_item><location><page_15><loc_10><loc_36><loc_48><loc_43></location>1. when Γ x = Γ y = 1 the E DM 2 ( x 2 , y 2 ) reduces to a simple Fresnel propagation. Edge ringing can them be mitigated using classical techniques such as preapodization, or re-imaging into a conjugate plane using oversized relay optics.</list_item>
<list_item><location><page_15><loc_10><loc_31><loc_48><loc_35></location>2. when Γ x , Γ y < 1 then it is as if the effective propagation length through the remapping unit was increased . This magnifies the edge chromatic ringing.</list_item>
<list_item><location><page_15><loc_10><loc_26><loc_48><loc_30></location>3. when Γ x , Γ y > 1 then it is as if the effective propagation length through the remapping unit was decreased . This damps the edge chromatic ringing.</list_item>
<list_item><location><page_15><loc_10><loc_16><loc_48><loc_25></location>4. when Γ x > 1 and Γ y < 1, e.g. at a saddle point in the DM surface, then it is as if the effective propagation length through the remapping unit was decreased in one direction and increased in the other. The edge chromatic ringing can either be damped or magnified depending on the relative magnitude of Γ x and Γ y .</list_item>
</unordered_list>
<text><location><page_15><loc_8><loc_7><loc_48><loc_15></location>In the case of a PIAA coronagraphs, the mirror shapes are such that Γ x , Γ y > 1 at the center of the pupil and Γ x , Γ y glyph[lessmuch] 1 at the edges of the pupil, where the discontinuities occur. As a consequence the edge oscillations are largely magnified when compared to Fresnel oscillations (see right panel of Fig. 10), and apodizing screens</text>
<text><location><page_15><loc_52><loc_13><loc_92><loc_59></location>are necessary in order to reduce the local curvature of the mirror's shape (as also discussed in Pluzhnik et al. (2005); Pueyo et al. (2011)). In the case of ACAD, where the x-axis is chosen to be perpendicular to the discontinuity, the surface curvature is such that Γ x > 1, Γ y ∼ 1 at the discontinuities inside the pupil and Γ x > 1, Γ y ∼ 1 elsewhere. This yields damped chromatic oscillations at the remapped discontinuities and Fresnel oscillations at the edges of the pupil (see right panel of Fig. 10). Note that Fig. 10 was generated using a one dimensional toy model that assumes Eq. 16 is separable, e.g Γ y = 1, as described in Pueyo et al. (2011). In practice at the saddle points of the optical surfaces, near the junction of two spiders for instance, γ x > 1, Γ y < ∼ 1 and thus our separable model does not guarantee than in the true 2D case chromatic edge oscillations might not be locally amplified. However even near the saddle points ACAD provides a strong converging remapping in the direction perpendicular to the discontinuity and very little diverging re-mapping in the other direction. As a consequence Γ x glyph[greatermuch] 1 and Γ y is smaller than but close to one. We thus predict that even at these locations chromatic ringing will not be amplified. Even if ACAD based on pupil remapping, its diffraction properties are qualitatively very different from PIAA coronagraphs since edge ringing is not amplified beyond the Fresnel regime at the pupil edges, and is attenuated near the discontinuities. We conclude that in most cases ACAD operates in a regime where edge chromatic oscillations are not larger than classical Fresnel oscillations, and sometimes actually smaller. As a consequence the chromaticity of this ringing can be mitigated using standard techniques developed in the Fresnel regime and we do not expect this phenomenon to be a major obstacle to ACAD broadband operations.</text>
<text><location><page_15><loc_53><loc_10><loc_91><loc_13></location>5.3. Diffraction artifacts in ACAD are no worse than Fresnel ringing</text>
<text><location><page_15><loc_52><loc_7><loc_92><loc_9></location>We have established that the diffractive chromatic oscillations introduced by the fact that DM1 and DM2 are</text>
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<caption>Figure 10. Left: Comparison of edge diffraction between PIAA and Fresnel propagation. Because the discontinuities in the pupil occur at the location where Γ x < 1, a PIAA amplifies the chromatic ringing when compared to a more classical propagation. Right: Comparison of edge diffraction between ACAD and Fresnel propagation. Because the discontinuities in the pupil occur at the location where Γ x > 1, a ACAD damps the chromatic ringing when compared to a more classical propagation. These simulations were carried out for a one dimensional aperture. In this case the Monge Ampere Equation can be solved using finite elements and the calculation of the diffractive effects reduces to the evaluation of various Fresnel special functions at varying wavelength. The full two-dimensional problem is not separable and requires the development of novel numerical tools.</caption>
</figure>
<text><location><page_16><loc_33><loc_48><loc_34><loc_53></location>/Slash1</text>
<text><location><page_16><loc_73><loc_48><loc_74><loc_53></location>/Slash1</text>
<text><location><page_16><loc_8><loc_30><loc_48><loc_41></location>not located in conjugate planes is no worse than classical Fresnel ringing from the aperture edges and can be mitigated using well-know techniques which have been developed for this regime. While a quantitive tradeoff study of how to design a high contrast instrument which minimizes such oscillations regime is beyond the scope of this paper, we briefly remind their qualitative essence to the reader:</text>
<unordered_list>
<list_item><location><page_16><loc_11><loc_21><loc_48><loc_29></location>· The edges of the discontinuities in the telescope aperture can be smoothed via pupil apodization before DM1. This solution is not particularly appealing as it requires the introduction of a transmissive, and thus dispersive, component in the optical train.</list_item>
<list_item><location><page_16><loc_11><loc_7><loc_48><loc_20></location>· The distance between the two DMs can be reduced. Indeed the DMs deformations presented herein, for 3 cm DMs separated by 1 m, are all ≤ 1 µ m while current technologies allow for deformations of several microns. As the edge ringing scales as Z/D 2 chromatic oscillations will be reduced by decreasing Z . Since the DM surfaces scale as D 2 /Z reducing Z will increase the DM deformations but have little impact on the feasibility of our solution as current DM technologies can reach 4 µ m strokes.</list_item>
<list_item><location><page_16><loc_54><loc_28><loc_92><loc_41></location>· The coronagrahic apodizer can be placed in a plane that is conjugate to the DM1. This can be achieved by re-imaging DM2 through a system of oversized optics (the over-sizing factor increases steeply when the pupil diameter decreases). By definition there are no Fresnel edge oscillations in such a plane. Alternatively a coronagraph without a pupil apodization (amplitude or phase mask in the image plane) can be used, and in this configuration it is only sufficient for the optics to be oversized.</list_item>
</unordered_list>
<text><location><page_16><loc_52><loc_7><loc_92><loc_27></location>Note that these three solutions are not mutually exclusive and that only a full diffractive analysis, which uses robust numerical propagators that have been developed based on Eq. 16, can quantitatively address the tradeoffs discussed above. The development of such propagators is our next priority. In Pueyo et al. (2011) we laid out the theoretical foundations of such a numerical tool in the case of circularly symmetric pupil remapping and this solution has been since then practically implemented, as reported by Krist et al. (2010). Generalizing this method to a tractable propagator in the case of arbitrary remapping is a yet unsolved computational problem. In the meantime we emphasize that while the spectral bandwidth of coronagraphs whose incoming amplitude has been corrected using ACAD will certainly be</text>
<section_header_level_1><location><page_17><loc_13><loc_89><loc_36><loc_91></location>Coronagraph pupil with flat DMs</section_header_level_1>
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<caption>Figure 11. Results obtained when applying our approach to a geometry similar to JWST . We used two 3 cm DMs of 64 actuators separated by 1 m. Their maximal surface deformation is 1 . 1 µ m, well within the stroke limit of current DM technologies. The residual light in the corrected PSF follows the secondary support structures and can potentially be further cancelled by controlling the DMs using an image plane based cost function, see Fig. 23 .</caption>
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<caption>PSF flat DMs</caption>
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<text><location><page_17><loc_45><loc_67><loc_46><loc_68></location>0</text>
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<section_header_level_1><location><page_17><loc_52><loc_89><loc_79><loc_91></location>Coronagraph pupil with actuated DMs</section_header_level_1>
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<caption>PSF with actuated DMs</caption>
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<text><location><page_17><loc_81><loc_37><loc_91><loc_38></location>Log[Contrast]</text>
<text><location><page_17><loc_87><loc_36><loc_89><loc_37></location>4.</text>
<text><location><page_17><loc_87><loc_32><loc_90><loc_33></location>4.6</text>
<text><location><page_17><loc_87><loc_23><loc_90><loc_24></location>5.8</text>
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<location><page_18><loc_8><loc_71><loc_49><loc_92></location>
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<text><location><page_18><loc_24><loc_91><loc_24><loc_92></location>Λ</text>
<text><location><page_18><loc_24><loc_89><loc_25><loc_93></location>/Slash1</text>
<paragraph><location><page_18><loc_8><loc_59><loc_48><loc_73></location>/Slash1 Figure 12. Case of JWST: Radial average obtained when applying ACAD. We used two 3 cm DMs of 64 actuators separated by 1 m. Their maximal surface deformation is 1 . 1 µ m, well within the stroke limit of current DM technologies. ACAD yields a gain in contrast of two orders of magnitude, and provides contrasts levels similar to upcoming Ex-AO instruments, which are designed on much friendlier apertures geometries. Since ACAD removes the bulk of the light diffracted by the asymmetric aperture discontinuities, the final contrast can be improved by controlling the DMs using and image plane based cost function, see Fig. 23 .</paragraph>
<text><location><page_18><loc_8><loc_46><loc_48><loc_57></location>limited by edge diffraction effects, but these effects are no worse than Fresnel ringing and can thus be mitigated using optical designs which are now routinely used in high contrast instruments (see V'erinaud et al. (2010) for such discussions). For the remainder of this paper we thus assume the diffractive artifacts have been adequately mitigated and we compute our results assuming a geometric propagation between DM1 and DM2.</text>
<section_header_level_1><location><page_18><loc_24><loc_44><loc_32><loc_45></location>6. RESULTS</section_header_level_1>
<section_header_level_1><location><page_18><loc_14><loc_41><loc_42><loc_44></location>6.1. Application to future observatories 6.1.1. JWST</section_header_level_1>
<text><location><page_18><loc_8><loc_7><loc_48><loc_40></location>We have illustrated each step of the calculation of the DM shapes in § . 4 using a geometry similar of JWST. This configuration is somewhat a conservative illustration of an on-axis segmented telescope as it features thick secondary supports and a 'small' number of segments whose gaps diffract light in regions of the image plane close to the optical axis (the first diffraction order of a six hexagons structure is located at ∼ 3 λ/D ). In order to assess the performances of ACAD on such an observatory architecture we chose to use a coronagraph designed around a slightly oversized secondary obscuration of diameter 0 . 25 D , with a focal plane mask of diameter 8 λ/D , an IWA of 5 λ/D and an OWA of 30 λ/D . The field at the entrance of the coronagraph after remapping by the DMs is shown on the top right panel of Fig. 11. The DMsurfaces, calculated assuming 64 actuators across the pupil ( N = 64 in the Fourier expansion) and DMs of diameter 3 cm separated by Z = 1 m, are shown on the middle panel of Fig. 11. They are well within the stroke limit of current DM technologies. The surfaces were calculated by solving the reverse problem over an even grid of 10 cutoff low-pass spatial frequencies ranging between 30 and 70 cycles per apertures for the tapering kernel ω . The value yielding the best contrast was chosen. Note that the optimal cutoff frequency depends on the spa-</text>
<text><location><page_18><loc_52><loc_71><loc_92><loc_92></location>le of the discontinuities, and that higher contrasts could be obtained by choosing a set of two convolution kernels for the reverse problem and finding the optimal solution using a finer grid. However, the results in the bottom row of Fig. 11 are extremely promising. Fig. 12 shows a contrast improvement of a factor of 100 when compared to the raw coronagraphic PSF, which is quite remarkable for an algorithm which is not based on an image-plane metric. These results illustrate that even with a very unfriendly aperture similar to JWST one can obtain contrasts as high as envisioned for upcoming Ex-AO instruments, which have been designed for much friendlier apertures. While we certainly do not advocate to use such a technique on JWST, this demonstrates that ACAD is a powerful tool for coronagraphy with on-axis segmented apertures.</text>
<section_header_level_1><location><page_18><loc_61><loc_69><loc_83><loc_70></location>6.1.2. Extremely Large Telescopes</section_header_level_1>
<text><location><page_18><loc_52><loc_7><loc_92><loc_68></location>We now discuss the case of Extremely Large Telescopes and provide an illustration using the example of the Thirty Meter Telescope. We considered the aperture geometry shown on the top left panel of Fig. 13. It consists of a pupil 37 segments across in the longest direction and a secondary of diameter ∼ 0 . 12 D which is held by three main thick struts and six thin cables. As seen on the bottom left panel of Fig. 13 the impact of segment gaps is minor as they diffract light beyond the OWA of the coronagraph. When using a coronagraph with a larger OWA the segment gaps will have to be taken into account, and will have to be mitigated using DMs with a larger number of actuators. In order to obtain first order estimates of the performances of ACAD on the aperture geometry shown on the top left panel of Fig. 13, we chose to use a coronagraph designed around a slightly oversized secondary obscuration of diameter 0 . 15 D , with a focal plane mask of 6 λ/D diameter, an IWA of 4 λ/D and an OWA of 30 λ/D . The field at the entrance of the coronagraph after remapping by the DMs is shown on the top right panel of Fig. 13. The DM surfaces, calculated assuming 64 actuators across the pupil ( N = 64 in the Fourier expansion) and DMs of diameter 3 cm separated by Z = 1 m, are shown on the middle panel of Fig. 13. They are well within the stroke limit of current DM technologies. The surfaces were calculated by solving the reverse problem over an even grid of 10 cutoff low-pass spatial frequencies ranging between 30 and 70 cycles per apertures for the tapering kernel ω . The value yielding the best contrast was chosen. The final PSF is shown on the bottom right panel of Fig. 13 and features a high contrast dark hole with residual diffracted light at the location of the spiders' diffraction structures. The impact on coronagraphic contrast of secondary supports was thoroughly studied by Martinez et al. (2008). They concluded that under a 90% Strehl ratio, the contrast in most types of coronagraphs is driven by the secondary support structures to levels ranging from 10 -4 to 10 -5 . This, in turn, leads to a final contrast after postprocessing (called Differential Imaging) of ∼ 10 -7 -10 -8 . Fig. 14 shows that using ACAD on an ELT pupil yields contrasts before any post-processing which are comparable to the ones obtained by Martinez et al. (2008) after Differential Imaging. This demonstrates that should two sequential DMs be integrated into a future planet finding instrument, setting their surface deformation according</text>
<paragraph><location><page_19><loc_21><loc_89><loc_29><loc_91></location>TMT Pupil</paragraph>
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<caption>Surface of DMI</caption>
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<caption>Surface of DM2</caption>
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<caption>Figure 13. Results obtained when applying our approach to a TMT geometry. We used two 3 cm DMs of 64 actuators separated by 1 m. Their maximal surface deformation is 0 . 9 µ m, well within the stroke limit of current DM technologies. The final contrast is below 10 7 , in a regime favorable for direct imaging of exo-planets with ELTs.</caption>
</figure>
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<text><location><page_19><loc_40><loc_36><loc_50><loc_38></location>Log[Contrast]</text>
<text><location><page_19><loc_47><loc_22><loc_49><loc_24></location>6.1</text>
<text><location><page_19><loc_87><loc_22><loc_89><loc_24></location>6.1</text>
<text><location><page_19><loc_47><loc_18><loc_49><loc_19></location>6.8</text>
<text><location><page_19><loc_87><loc_18><loc_89><loc_19></location>6.8</text>
<text><location><page_19><loc_87><loc_14><loc_89><loc_15></location>=7.5</text>
<paragraph><location><page_19><loc_57><loc_36><loc_73><loc_38></location>PSF with actuated DMs</paragraph>
<text><location><page_19><loc_81><loc_36><loc_91><loc_38></location>Log[Contrast]</text>
<text><location><page_19><loc_87><loc_31><loc_89><loc_32></location>4.7</text>
<section_header_level_1><location><page_19><loc_54><loc_89><loc_76><loc_91></location>Coronagraph pupil with flat DMs</section_header_level_1>
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<location><page_19><loc_51><loc_67><loc_88><loc_90></location>
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<location><page_20><loc_8><loc_71><loc_49><loc_92></location>
<caption>Figure 14. Case of TMT: radial average obtained when applying ACAD. We used two 3 cm DMs of 64 actuators separated by 1 m. Their maximal surface deformation is 0 . 9 µ m, well within the stroke limit of current DM technologies. The final contrast is below 10 7 , in a regime favorable for direct imaging of exo-planets with ELTs. Since ACAD removes the bulk of the light diffracted by the asymmetric aperture discontinuities, the final contrast can be enhanced by controlling the DMs using and image plane based metric.</caption>
</figure>
<text><location><page_20><loc_24><loc_89><loc_25><loc_93></location>/Slash1</text>
<text><location><page_20><loc_24><loc_68><loc_25><loc_73></location>/Slash1</text>
<text><location><page_20><loc_8><loc_51><loc_48><loc_59></location>to the methodology presenting above would allow this instrument to perform its scientific program at a very high contrast. Moreover the surface of the DMs could be adjusted to mitigate for the effect of missing segments at the surface of the primary (when for instance the telescope is operating while some segments are being serviced).</text>
<section_header_level_1><location><page_20><loc_20><loc_48><loc_36><loc_49></location>6.2. Hypothetical cases</section_header_level_1>
<section_header_level_1><location><page_20><loc_10><loc_45><loc_46><loc_48></location>6.2.1. Constant area covered by the secondary support structures</section_header_level_1>
<text><location><page_20><loc_8><loc_12><loc_48><loc_45></location>In the case of ELTs with large number of small segments (when compared to the aperture size), gaps diffract light far from the optical axis (see Fig. 13 for an example). The secondary support structures are then the major source of unfriendly coronagraphic diffracted light. Under the assumption that thick structures are necessary to support the heavy secondary over the very large ELT pupils, one can use the aperture area covered by the spiders as a proxy of the secondary lift constraint. We have thus explored a series of geometries for which the number of spiders increases as they get thinner while the overall area covered by the secondary support structures remains constant. In the examples shown from Fig. 15 to Fig. 18, the area covered by the secondary support structures is 1 . 5 times greater than in the TMT geometry discussed above. In all cases we used a coronagraph with a central obscuration of 0 . 15 D , with a focal plane mask of 6 λ/D diameter, and IWA of 4 λ/D and an OWA of 30 λ/D . The surfaces were calculated by solving the reverse problem over an even grid of 10 cutoff low-pass spatial frequencies ranging between 30 and 70 cycles per apertures for the tapering kernel. The value yielding the best contrast was chosen. This exercise leads to several conclusions pertaining to the performances of ACAD with various potential ELT geometries.</text>
<section_header_level_1><location><page_20><loc_10><loc_10><loc_48><loc_11></location>Clocking of the spiders with respect to the DM</section_header_level_1>
<text><location><page_20><loc_10><loc_7><loc_48><loc_8></location>The top two panels of Fig. 15 illustrate the importance</text>
<text><location><page_20><loc_52><loc_80><loc_92><loc_92></location>of the clocking of the spiders with respect to the DMs actuator grid (or the Fourier grid in our case). When the secondary support structures are clocked by 45 · with respect to the DM actuators they are much more attenuated by ACAD, thus yielding higher contrast. This is an artifact of the Fourier basis set chosen and would be mitigated by using DMs whose actuator placement presents circular and azimuthal symmetries (Watanabe et al. 2008).</text>
<section_header_level_1><location><page_20><loc_52><loc_77><loc_92><loc_79></location>Annulus in the PSF with a large number of spiders</section_header_level_1>
<text><location><page_20><loc_52><loc_61><loc_92><loc_76></location>When the number of secondary support struts becomes very large ( > 20), an interesting phenomena occurs in the raw PSF: the spiders diffract light outside an annulus of radius N Spiders /π/D , just as spiderweb masks do in the case of shaped pupil coronagraphs (Vanderbei et al. 2003b). The 'bump' located beyond that spatial frequency is more difficult to attenuate using the DMs (see Fig. 15 for an illustration). ACAD creates small ripples at the edges of the remapped discontinuities and when too many discontinuities are in the vicinity of each other, then these ripples interfere constructively and hamper the starlight extinction level yielded by ACAD.</text>
<section_header_level_1><location><page_20><loc_52><loc_58><loc_92><loc_60></location>A lot of thin spiders is more favorable than a few thick spiders</section_header_level_1>
<text><location><page_20><loc_52><loc_8><loc_92><loc_57></location>In general decreasing the width of the spiders while increasing their number is beneficial to the contrast obtained after ACAD as illustrated on the radial averages on Fig. 16 and Fig. 18. When one increases the number of spiders while decreasing their width in a classical coronagraph, the peak intensity of the diffraction pattern of one spider decreases as the squared width of the spider. The radially averaged contrast improvement without ACAD is then somewhat lesser than the square of the spider thinning factor as it is mitigated by the increasing number of spiders. When using ACAD the spiders are seen by the coronagraph as much thinner than they actually are (by a factor τ ) and thus the peak intensity of their diffraction pattern is lower by a factor of τ 2 . Our numerical experiments show that τ increases when the spider width decreases. As consequence, the overall contrast gain after ACAD when decreasing the width of the spiders while increasing their number is greater than in the case of a classical coronagraph. When designing ELT secondary support structures and planning to correct for them using ACAD, increasing the number of spiders to 8 or even 12 has a beneficial impact on contrast as it enables each discontinuity to become thinner and thus to be corrected to higher contrast using the DMs. The PSFs of apertures with more than 12 spiders present diffraction structures which are poorly suited for correction with square DMs. While the contrast resulting from applying ACAD to such apertures is still a decreasing function of the number of spiders, Fig. 18 shows that the net contrast gain brought by the DM based remapping is smaller than in the more gentle cases of 12 spiders. The study presented on Fig. 15 to Fig. 18 remains to be fully optimized for each potential design of an ELT planet finding instrument (in particular using a finer grid of cutoff spatial frequencies). It however demonstrates the flexibility of ACAD for various aperture geometries and provides a first order rule of thumb to design telescope apertures</text>
<section_header_level_1><location><page_21><loc_18><loc_90><loc_30><loc_92></location>Flat DMs</section_header_level_1>
<figure>
<location><page_21><loc_9><loc_65><loc_38><loc_87></location>
</figure>
<figure>
<location><page_21><loc_9><loc_38><loc_38><loc_60></location>
<caption>12 spiders, 0.4 % of D wide</caption>
</figure>
<figure>
<location><page_21><loc_9><loc_12><loc_39><loc_35></location>
</figure>
<section_header_level_1><location><page_21><loc_56><loc_90><loc_76><loc_92></location>Actuated DMs</section_header_level_1>
<figure>
<location><page_21><loc_40><loc_64><loc_49><loc_88></location>
</figure>
<figure>
<location><page_21><loc_82><loc_64><loc_91><loc_88></location>
</figure>
<figure>
<location><page_21><loc_40><loc_38><loc_49><loc_62></location>
</figure>
<figure>
<location><page_21><loc_40><loc_12><loc_49><loc_36></location>
</figure>
<figure>
<location><page_21><loc_82><loc_38><loc_91><loc_62></location>
<caption>Log[Contrast] 3.5</caption>
</figure>
<text><location><page_21><loc_88><loc_30><loc_90><loc_31></location>4.4</text>
<text><location><page_21><loc_88><loc_25><loc_90><loc_26></location>5.3</text>
<text><location><page_21><loc_88><loc_21><loc_90><loc_22></location>6.2</text>
<text><location><page_21><loc_56><loc_87><loc_57><loc_88></location>4</text>
<figure>
<location><page_21><loc_51><loc_64><loc_81><loc_87></location>
<caption>8 spiders, 0.6 % of D wide</caption>
</figure>
<figure>
<location><page_21><loc_51><loc_38><loc_81><loc_61></location>
</figure>
<figure>
<location><page_21><loc_51><loc_12><loc_81><loc_35></location>
<caption>Figure 15. PSFs resulting from ACAD when varying the number and thickness of secondary support structures while maintaining their covered surface constant. The surface area covered in this example is 50% greater than in the TMT example shown on Fig. 13. As the spiders get thinner their impact on raw contrast becomes smaller and the starlight suppression after DM correction becomes bigger. For a relatively small number of spiders ( < 12) the contrast improvement on each single structure is the dominant phenomenon, regardless of the number of spiders. ELTs designed with a moderate to large number of thin secondary support structure (6 to 12) present aperture discontinuities which are easy to correct with ACAD.</caption>
</figure>
<figure>
<location><page_22><loc_8><loc_25><loc_49><loc_92></location>
<caption>Figure 16. Radial PSF profiles resulting from ACAD when varying the number and thickness of secondary support structures while maintaining their covered surface constant. The surface area covered in this example is 50% greater than in the TMT example shown on Fig. 13. As the spiders get thinner their impact on raw contrast becomes lesser and the starlight suppression after DM correction becomes greater. In the 12 spiders example, at large separations, the average contrast is an order of magnitude higher than reported on Fig. 14.</caption>
</figure>
<text><location><page_22><loc_24><loc_89><loc_25><loc_93></location>/Slash1</text>
<text><location><page_22><loc_25><loc_91><loc_36><loc_92></location>D in case of a PIAAC</text>
<text><location><page_22><loc_25><loc_25><loc_36><loc_26></location>D in case of an APLC</text>
<text><location><page_22><loc_24><loc_23><loc_25><loc_27></location>/Slash1</text>
<text><location><page_22><loc_8><loc_7><loc_48><loc_12></location>which are friendly to direct imaging of exo-planets: 'A lot of thin spiders is more favorable than a few thick spiders'. In practice the number of spiders will be limited by effects not treated in our analysis such as the me-</text>
<text><location><page_22><loc_52><loc_81><loc_92><loc_92></location>chanical rigidity, requirements on the perfection of their periodic spacing and glancing reflections from the sides of multiple spiders. We thus advocate that, should future ELTs be built with high contrast exo-planetary science as a main scientific driver, then such effect ought to be thoroughly analyzed as a large numbers of thin spiders is more favorable from a contrast standpoint when using ACAD to mitigate for pupil amplitude asymmetries.</text>
<section_header_level_1><location><page_22><loc_60><loc_78><loc_84><loc_79></location>6.2.2. Monolithic on-axis apertures.</section_header_level_1>
<text><location><page_22><loc_52><loc_63><loc_92><loc_77></location>When discussing the case of JWST we stressed the complexity associated with the optimization of ACAD in the presence of aperture discontinuities of varying width. Carrying out such an exercise would be extremely valuable to study the feasibility of the direct imaging of exoearth with an on-axis segmented future flagship observatory such as ATLAST (Postman et al. 2010). However, such an effort is computationally heavy and thus beyond the scope of the present paper, which focuses on introducing the ACAD methodology and illustrating using key basic examples.</text>
<text><location><page_22><loc_52><loc_7><loc_92><loc_63></location>So far, none of the examples in this manuscript demonstrate that ACAD can yield corrections all the way down to the theoretical contrast floor that is set by the coronagraph design. When seeking to image exo-earths from space, future missions will need to reach this limit. In order to explore this regime, we conducted a detailed study of an hypothetical on-axis monolithic telescope with four secondary support struts. To establish the true contrast limits we varied the thickness of the spiders and for each geometries. The surfaces were calculated by solving the reverse problem over an even grid of 70 cutoff low-pass spatial frequencies ranging between 30 and 70 cycles per apertures for the tapering kernel. The value yielding the best contrast was chosen. In all cases we used a coronagraph with a central obscuration of 0 . 15 D , with a focal plane mask of 6 λ/D diameter, and IWA of 4 λ/D , and an OWA of 30 λ/D . Note that when using coronagraphs relying on pupil apodization these results can be readily generalized to larger circular secondary obscurations, at a loss in IWA (as shown on Fig. 2). Moreover we clocked the telescope aperture by 45 · with respect to the grid of Fourier modes. We found that, indeed, the theoretical contrast floor set by the coronagraph design is met for thin spiders (0 . 02 D ) and it is very close to be met for spiders only half the thickness of the the ones currently equipping the Hubble Space Telecope (0 . 05 D ), see Fig. 19 and Fig. 20. Even in the case of thick struts (0 . 1 D ) we find contrasts an order of magnitude higher than in the similar configuration on the top panel of Fig. 16, due to our thorough optimization of the cutoff frequency of the tapering kernel and careful clocking of the aperture with respect to the actuators. On-axis telescopes are thus a viable option to image earth-analogs from space: their secondary support structures can be corrected down to contrast levels comparable to the target contrast of recent missions concept studies (Guyon et al. 2008; Trauger et al. 2010). Since the baseline wavefront control architecture for future space coronagraphs relies on two sequential DMs, ACAD does not add any extra complexity to such missions and merely consists of controlling the DMs in order to optimally compensate for the effects of asymmetric aperture discontinuities.</text>
<text><location><page_22><loc_23><loc_91><loc_24><loc_92></location>Λ</text>
<section_header_level_1><location><page_23><loc_18><loc_90><loc_31><loc_92></location>Flat DMs</section_header_level_1>
<text><location><page_23><loc_13><loc_87><loc_35><loc_89></location>16 spiders, 0.39 of D wide</text>
<figure>
<location><page_23><loc_9><loc_64><loc_39><loc_87></location>
</figure>
<figure>
<location><page_23><loc_51><loc_64><loc_81><loc_87></location>
<caption>24 spiders, 0.2 % of D wide</caption>
</figure>
<figure>
<location><page_23><loc_9><loc_38><loc_39><loc_61></location>
</figure>
<figure>
<location><page_23><loc_51><loc_38><loc_81><loc_61></location>
</figure>
<figure>
<location><page_23><loc_9><loc_12><loc_38><loc_36></location>
</figure>
<figure>
<location><page_23><loc_40><loc_12><loc_49><loc_36></location>
</figure>
<figure>
<location><page_23><loc_82><loc_12><loc_91><loc_36></location>
<caption>24 spiders, 0.2 % of D wide</caption>
</figure>
<figure>
<location><page_23><loc_51><loc_12><loc_81><loc_35></location>
<caption>Figure 17. PSFs resulting from ACAD when varying the number and thickness of secondary support structures while maintaining their covered surface constant. The surface area covered in this example is 50% greater than in the TMT example shown on Fig. 13. When the number of spiders increases, they produce a sharp circular diffraction feature at N Spiders /π λ/D . If this number is greater than the size of the focal plane mask this structure appears in the high contrast zone and is very difficult to correct with ACAD. The brightness of this structure is mitigated by the fact that the spiders are very thin.</caption>
</figure>
<section_header_level_1><location><page_23><loc_56><loc_90><loc_76><loc_92></location>Actuated DMs</section_header_level_1>
<figure>
<location><page_23><loc_40><loc_64><loc_49><loc_88></location>
</figure>
<figure>
<location><page_23><loc_40><loc_38><loc_49><loc_62></location>
</figure>
<text><location><page_23><loc_55><loc_87><loc_77><loc_89></location>16 spiders, 0.39 of D wide</text>
<figure>
<location><page_23><loc_82><loc_64><loc_91><loc_88></location>
<caption>Log[Contrast] 3.5</caption>
</figure>
<text><location><page_23><loc_88><loc_56><loc_90><loc_57></location>4.4</text>
<text><location><page_23><loc_88><loc_51><loc_90><loc_52></location>5.3</text>
<text><location><page_23><loc_88><loc_47><loc_90><loc_48></location>6.2</text>
<text><location><page_24><loc_8><loc_80><loc_9><loc_83></location>Contrast</text>
<figure>
<location><page_24><loc_8><loc_27><loc_49><loc_92></location>
<caption>Figure 18. Radial PSF profiles resulting from ACAD when varying the number and thickness of secondary support structures while maintaining their covered surface constant. The surface area covered in this example is 50% greater than in the TMT example shown on Fig. 13. With a large number of spiders the bright ring in the PSF structure located at N Spiders /π λ/D is difficult to correct with ACAD. However since the spiders becomes thinner its net effect on contrast after ACAD remains small.</caption>
</figure>
<text><location><page_24><loc_24><loc_89><loc_24><loc_93></location>/Slash1</text>
<text><location><page_24><loc_24><loc_26><loc_24><loc_27></location>Λ</text>
<text><location><page_24><loc_25><loc_26><loc_36><loc_27></location>D in case of an APLC</text>
<text><location><page_24><loc_24><loc_24><loc_25><loc_28></location>/Slash1</text>
<section_header_level_1><location><page_24><loc_15><loc_13><loc_41><loc_14></location>7. DISCUSSION AND FUTURE WORK</section_header_level_1>
<section_header_level_1><location><page_24><loc_17><loc_11><loc_39><loc_13></location>7.1. Field dependent distortion</section_header_level_1>
<text><location><page_24><loc_8><loc_7><loc_48><loc_11></location>Because ACAD relies on deforming the DMs surfaces in an aspherical fashion, off-axis wavefronts seen through the two DMs apparatus will be distorted, just as in a</text>
<text><location><page_24><loc_52><loc_73><loc_92><loc_92></location>PIAA coronagraph (Martinache et al. 2006). However the asphericity of the surfaces in the case of ACAD operating on reasonably thin discontinuities, is much smaller than in a PIAA remapping unit. Fig. 21 shows the impact on off-axis PSFs of such a distortion in the worsecase scenario of a geometry similar to JWST. We demonstrate that most of the flux remains in the central disk of radius λ/D for all sources in the field of view of the coronagraphs considered here (all the way to 30 cycles per capture). We conclude that, because of the small deformations of the DMs, PSF distortion will not be a major hindrance in exo-planet imaging instruments whose DMs are controlled in order to mitigate for discontinuities in the aperture.</text>
<text><location><page_24><loc_53><loc_63><loc_91><loc_65></location>7.2. Impact of wavefront discontinuities in segmented telescopes.</text>
<text><location><page_24><loc_53><loc_60><loc_91><loc_62></location>7.2.1. General equations in the presence of incident phase errors and discontinuities</text>
<text><location><page_24><loc_52><loc_8><loc_92><loc_57></location>So far we have treated primary mirrors' segmentation as a pure amplitude effect. In reality the contrast floor in segmented telescopes will be driven by both phase and amplitude discontinuities: here we explore the impact of phase errors and discontinuities occurring before two DMs whose surfaces have been set using ACAD. There are two main phenomena to be considered. The first is the conversion of the incident wavefront phase before DM1: 2 π λ ∆ h 1 into amplitude at the second mirror. The second is the projection of this wavefront phase into a remapped phase errors at DM2: 2 π λ ∆ h 1 ( f 1 ( x 1 , y 2 ) , g 1 ( x 1 , y 2 )). Since the remapping unit is designed using deformable mirrors, both DM1 and DM2 a complete correction could be attained in principle. However, the deformable mirrors are continuous while ∆ h 1 presented discontinuities. Thus, complete corrections for segmented mirrors might not be achieved in practice. Below we discuss the following two main points. (1) Even if the phase wavefront error ∆ h 1 has discontinuities, the phase errors within in segment still drive the phase to amplitude conversion and thus the propagated amplitude at DM2. In that case treatments of these phenomenons that have already been discussed in the literature for monolithic apertures are still valid for small enough phase errors Eqs. 56-56 and smooth enough remapping functions. For ACAD remapping this smoothness constraint is naturally enforced by the limited number of actuators across the DM surface. In this case phase to amplitude conversion between can in principle be corrected using DM1. (2) Remapped phase discontinuities can be corrected for a finite number of spatial frequencies using a continuous phase sheet deformable mirror. We illustrate this partial correction over a 20% bandwidth using numerical simulations of a post-ACAD half dark hole created by superposing a small perturbation, computed using a linear wavefront control algorithm, to the ACAD DM2 surface.</text>
<section_header_level_1><location><page_25><loc_19><loc_89><loc_31><loc_92></location>Flat DMs</section_header_level_1>
<section_header_level_1><location><page_25><loc_57><loc_90><loc_77><loc_92></location>Actuated DMs</section_header_level_1>
<text><location><page_25><loc_14><loc_87><loc_15><loc_88></location>4</text>
<figure>
<location><page_25><loc_9><loc_64><loc_38><loc_87></location>
<caption>4 spiders, 0.5 % of D wide</caption>
</figure>
<figure>
<location><page_25><loc_9><loc_38><loc_38><loc_60></location>
<caption>4 spiders, 1 % of D wide</caption>
</figure>
<figure>
<location><page_25><loc_9><loc_12><loc_38><loc_34></location>
</figure>
<figure>
<location><page_25><loc_40><loc_64><loc_49><loc_88></location>
</figure>
<figure>
<location><page_25><loc_40><loc_38><loc_49><loc_62></location>
<caption>Log[Contrast] 3.4</caption>
</figure>
<figure>
<location><page_25><loc_41><loc_11><loc_49><loc_35></location>
</figure>
<figure>
<location><page_25><loc_82><loc_64><loc_91><loc_88></location>
</figure>
<figure>
<location><page_25><loc_82><loc_38><loc_91><loc_62></location>
<caption>Log[Contrast] 3.4</caption>
</figure>
<text><location><page_25><loc_88><loc_29><loc_90><loc_30></location>4.5</text>
<text><location><page_25><loc_88><loc_20><loc_90><loc_21></location>6.7</text>
<text><location><page_25><loc_88><loc_16><loc_90><loc_17></location>7.8</text>
<text><location><page_25><loc_88><loc_11><loc_90><loc_12></location>8.9</text>
<text><location><page_25><loc_56><loc_87><loc_58><loc_89></location>4</text>
<figure>
<location><page_25><loc_51><loc_64><loc_81><loc_87></location>
<caption>4 spiders, 0.5 % of D wide</caption>
</figure>
<figure>
<location><page_25><loc_51><loc_38><loc_81><loc_60></location>
<caption>4 spiders, 1 % of D wide</caption>
</figure>
<figure>
<location><page_25><loc_51><loc_11><loc_81><loc_34></location>
<caption>Figure 19. PSFs resulting from ACAD when varying the number and thickness of secondary support structures. As the spiders get thinner their impact on raw contrast becomes lesser and the starlight suppression after DM correction becomes greater. In this case ω was optimized on a very fine grid and the aperture we clocked in a favorable direction with respect to the Fourier basis.</caption>
</figure>
<figure>
<location><page_26><loc_8><loc_26><loc_49><loc_92></location>
<caption>Figure 20. PFSs resulting from ACAD when varying the number and thickness of secondary support structures. As the spiders get thinner their impact on raw contrast becomes lesser and the starlight suppression after DM correction becomes greater. In this case ω was optimized on a very fine grid and the aperture we clocked in a favorable direction with respect to the Fourier basis. Even for spiders as thick as 0 . 5% of the telescope aperture the designed contrast of the coronagraph is retrieved.</caption>
</figure>
<text><location><page_26><loc_24><loc_89><loc_25><loc_93></location>/Slash1</text>
<text><location><page_26><loc_24><loc_26><loc_24><loc_27></location>Λ</text>
<text><location><page_26><loc_25><loc_26><loc_36><loc_27></location>D in case of an APLC</text>
<text><location><page_26><loc_52><loc_82><loc_92><loc_92></location>If the incoming wavefront is written as ∆ h 1 and the solution of the Monge Ampere Equation for DM1 as h 0 1 then one can conduct the analysis in Eq. 6 to 12b using ˜ h 1 = h 0 1 + ∆ h 1 . Under the assumption that surface of DM2is set as ˜ h 2 in order to conserve Optical Path Length then one can re-write the remapping as ( ˜ f 1 , ˜ g 1 ) defined by:</text>
<formula><location><page_26><loc_58><loc_73><loc_92><loc_80></location>∂ ˜ h 1 ∂x ∣ ∣ ∣ ( ˜ f 1 ( x 2 ,y 2 ) , ˜ g 1 ( x 2 ,y 2 )) = ˜ f 1 ( x 2 , y 2 ) -x 2 Z ∂ ˜ h 1 ∂y ∣ ∣ ∣ ( ˜ f 1 ( x 2 ,y 2 ) , ˜ g 1 ( x 2 ,y 2 )) = ˜ g 1 ( x 2 , y 2 ) -y 2 Z . (56)</formula>
<text><location><page_26><loc_63><loc_46><loc_63><loc_50></location>/Slash1</text>
<text><location><page_26><loc_70><loc_46><loc_70><loc_50></location>/LBracket1</text>
<text><location><page_26><loc_71><loc_46><loc_72><loc_50></location>/RBracket1</text>
<text><location><page_26><loc_84><loc_46><loc_85><loc_50></location>/Slash1</text>
<text><location><page_26><loc_91><loc_46><loc_91><loc_50></location>/LBracket1</text>
<text><location><page_26><loc_92><loc_46><loc_93><loc_50></location>/RBracket1</text>
<figure>
<location><page_26><loc_52><loc_24><loc_93><loc_49></location>
<caption>Figure 21. Off-axis PSF after ACAD in the case of a geometry similar to JWST. The aspheric surface of the DMs introduce a slight field-dependent distortion. However the core of the PSF is still concentrated within the central airy disk and the DMs only have an effect on the PSF tail. Field distortion does not thus hamper the detectability of faint off-axis sources.</caption>
</figure>
<text><location><page_26><loc_10><loc_12><loc_92><loc_13></location>Moreover if edge ringing has been properly mitigated then the ray optics solution is valid and the field at DM2 can</text>
<text><location><page_26><loc_24><loc_23><loc_25><loc_28></location>/Slash1</text>
<formula><location><page_27><loc_12><loc_62><loc_20><loc_63></location>∂y ∂y</formula>
<text><location><page_27><loc_8><loc_91><loc_18><loc_92></location>be written as:</text>
<formula><location><page_27><loc_16><loc_86><loc_92><loc_90></location>E DM 2 ( x 2 , y 2 ) = E DM 1 (1 + ∂ 2 ˜ h 1 ∂x 2 )(1 + ∂ 2 ˜ h 1 ∂y 2 ) -( ∂ 2 ˜ h 1 ∂x∂x ) 2 ∣ ∣ ∣ ∣ ( ˜ f 1 , ˜ g 1 ) e i 2 π λ ( S ( ˜ f 1 , ˜ g 1 )+ ˜ h 1 ( ˜ f 1 , ˜ g 1 ) -˜ h 2 ) ∣ ∣ ∣ ∣ ( x 2 ,y 2 ) (57)</formula>
<section_header_level_1><location><page_27><loc_14><loc_80><loc_43><loc_81></location>7.2.2. Impact on the amplitude after ACAD</section_header_level_1>
<text><location><page_27><loc_8><loc_75><loc_48><loc_80></location>We first consider the amplitude profile in Eq. 57: it is composed of two factors the remapped telescope aperture, E DM 1 ( ˜ f 1 , ˜ g 1 ), and the determinant of Id + H [ ˜ h 1 ].</text>
<text><location><page_27><loc_41><loc_70><loc_41><loc_72></location>glyph[negationslash]</text>
<text><location><page_27><loc_8><loc_69><loc_48><loc_76></location>The first condition necessary for the incoming wavefront not to perturb the ACAD solution is: ∆ h 1 is such that the remapping is not modified at the pupil locations where the telescope aperture is not zero E DM 1 = 0. This results into the conditions</text>
<text><location><page_27><loc_43><loc_66><loc_43><loc_67></location>glyph[negationslash]</text>
<formula><location><page_27><loc_11><loc_63><loc_46><loc_68></location>∂ ∆ h 1 ∂x glyph[lessmuch] ∂ ∆ h 0 1 ∂x for ( x, y )such that E DM 1 ( x, y ) = 0 ∂ ∆ h 1 glyph[lessmuch] ∂ ∆ h 0 1 for ( x, y )such that E DM 1 ( x, y ) = 0</formula>
<text><location><page_27><loc_43><loc_63><loc_43><loc_64></location>glyph[negationslash]</text>
<text><location><page_27><loc_8><loc_56><loc_48><loc_61></location>At the locations where E DM 1 = 0 there is no light illuminating the discontinuous wavefront and thus the large local slopes at these location have no impact on the remapping functions ( f 1 , g 1 ). These conditions are</text>
<text><location><page_27><loc_52><loc_66><loc_92><loc_82></location>not true in segmented telescopes that are not properly phased, for which the tip-tilt error over each segment can reach several waves. However under the assumption that the primary has been properly phased (for instance the residual rms wavefront after phasing is expect to be ∼ 1 / 10 th of a wave, similar to values expected for JWST NIRCAM) then these conditions are true within the boundaries of each segment. Moreover, while the local wavefront slopes at the segment's discontinuities do not respect this condition the incident amplitude at these points is E DM 1 ( x, y ) = 0 and they thus do not perturb the ACAD remapping solution.</text>
<text><location><page_27><loc_52><loc_57><loc_92><loc_66></location>The second necessary condition resides in the fact that the determinant of Id + H ( ˜ h 1 ) is not equal to det [ Id + H ( h 0 1 )] at the pupil locations where the telescope aperture is not zero ought not have a severe impact on contrast. One can use the linearization in Loeper & Rapetti (2005) to show that:</text>
<formula><location><page_27><loc_22><loc_49><loc_92><loc_53></location>1 det [ Id + H ( ˜ h 1 )] = 1 det [ Id + H ( h 0 1 )](1 + (1+ h 0 1 xx )∆ h 1 yy +(1+ h 0 1 yy )∆ h 1 xx -2 ∗ h 0 1 xy ∆ h 1 xy det [ Id + H ( h 0 1 )] ) (58)</formula>
<formula><location><page_27><loc_22><loc_45><loc_92><loc_49></location>1 det [ Id + H ( ˜ h 1 )] = 1 det [ Id + H ( h 0 1 )](1 + ∆ A (∆ h 1 )) (59)</formula>
<text><location><page_27><loc_8><loc_7><loc_48><loc_42></location>The perturbation term ∆ A (∆ h 1 ) corresponds to the full non-linear expression of the phase to amplitude conversion of wavefront errors that occurs in pupil remapping units. In Pueyo et al. (2011) we derived a similar expression in the linear case, when ∆ h 1 glyph[lessmuch] λ and showed that in the pupil regions where the the beam is converging this phase to amplitude conversion was enhanced when compared to the case of a Fresnel propagation. In a recent study Krist et al. (2011) presented simulations predicting that this effect was quite severe in PIAA coronagraphs and can limit the broadband contrast after wavefront control unless DMs where placed before the remapping unit. In principle ACAD will not suffer from this limitation as the first aspherical surface of the remapping unit is actually a Deformable Mirror that can actually compensate for ∆ h 1 , before any phase to amplitude wavefront modulation occurs. Devising a wavefront controller that relies on DM1 requires moreover a computationally efficient model to propagate arbitrary wavefronts thought ACAD. Such a tool was developed in Krist et al. (2010) assuming azimuthally symmetric geometries. Since devising such a tool in ACAD's case, in the asymmetric case, represents a substantial effort well beyond the problem of prescribing ACAD DM shapes, we chose not to include such simulations in the present manuscript. Since we are using Deformable Mirrors with</text>
<text><location><page_27><loc_52><loc_12><loc_92><loc_42></location>a limited number of actuators, ACAD remapping is in general less severe than in the case of PIAA. We thus expect the results regarding the wavefront correction before the remapping unit reported in Krist et al. (2011) to hold. This is provided that the DM actuators can adequately capture the high spatial frequency content of ∆ h 1 to create a dark hole in the coronagraphic PSF. We tackle this particular aspect next when discussing the case of phase errors, in the absence of wavefront phase to amplitude conversion. Once again note that while the local wavefront curvatures are very large at the segment's discontinuities, the incident amplitude at these points is E DM 1 ( x, y ) = 0 and they thus they do not have an impact on the ACAD phase to amplitude modulation. In practice if the DM is not exactly located at a location conjugate to the telescope pupil the actual wavefront discontinuities will be slightly illuminated and might perturb the remapping functions and the phase to amplitude conversion. While this might tighten requirements regarding the positioning of DM1 in the direction of the optical axis we do not expect this effect to be a major obstacle to successful ACAD implementations.</text>
<section_header_level_1><location><page_27><loc_59><loc_10><loc_85><loc_11></location>7.2.3. Impact on the phase after ACAD</section_header_level_1>
<text><location><page_27><loc_52><loc_7><loc_92><loc_10></location>In practice, when ∆ h 1 presents discontinuities, the surface of DM2 cannot be set to the deformation ˜ h 2 that</text>
<text><location><page_28><loc_14><loc_78><loc_34><loc_79></location>Wavefront at the coronagraph entrance</text>
<figure>
<location><page_28><loc_9><loc_55><loc_39><loc_78></location>
<caption>Figure 22. Broadband wavefront correction (20% bandwidth around 700 nm) with a single DM in segmented telescope with discontinuous surface errors. Top Left: wavefront before the coronagraph. Top Right: broadband aberrated PSF with DM at rest. Bottom Left: DM surface resulting from the wavefront control algorithm. Bottom Right: broadband corrected PSF. Note that the wavefront control algorithm seeks to compensate for the diffractive artifacts associated with the secondary support structures: it attenuates them on the right side of the PSF while it strengthens them on the left side of the PSF. As a result the DM surface becomes too large at the pupil spider's location and the quasi-linear wavefront control algorithm eventually diverges.</caption>
</figure>
<figure>
<location><page_28><loc_50><loc_54><loc_80><loc_78></location>
<caption>Deformation of DM2 Ahz</caption>
</figure>
<figure>
<location><page_28><loc_9><loc_29><loc_39><loc_52></location>
</figure>
<figure>
<location><page_28><loc_50><loc_29><loc_80><loc_52></location>
</figure>
<figure>
<location><page_28><loc_43><loc_54><loc_48><loc_79></location>
</figure>
<text><location><page_28><loc_43><loc_52><loc_45><loc_53></location>nm</text>
<text><location><page_28><loc_45><loc_51><loc_47><loc_52></location>190.1</text>
<text><location><page_28><loc_88><loc_51><loc_89><loc_52></location>1.9</text>
<text><location><page_28><loc_45><loc_47><loc_47><loc_48></location>118.3</text>
<text><location><page_28><loc_87><loc_47><loc_89><loc_48></location>3.2</text>
<text><location><page_28><loc_45><loc_42><loc_47><loc_43></location>46.6</text>
<text><location><page_28><loc_45><loc_33><loc_47><loc_34></location>96.8</text>
<text><location><page_28><loc_45><loc_28><loc_48><loc_29></location>168.6</text>
<text><location><page_28><loc_88><loc_38><loc_89><loc_38></location>5.8</text>
<paragraph><location><page_28><loc_51><loc_52><loc_79><loc_53></location>Non ACAD PSF with DM2 correcting for wavefront error</paragraph>
<text><location><page_28><loc_88><loc_68><loc_89><loc_68></location>4.5</text>
<text><location><page_28><loc_87><loc_63><loc_89><loc_64></location>5.8</text>
<text><location><page_28><loc_84><loc_52><loc_89><loc_53></location>Contrast</text>
<text><location><page_29><loc_8><loc_80><loc_48><loc_92></location>conserves Optical Path Length, since we work under the assumption that the DMs has a continuous phase-sheet. While this has no impact on the discussion above regarding the amplitude of E DM 2 , since DM1 is solely responsible for this part, it ought to be taken into account when discussing the phase at DM2. Under the assumption that ∆ h 1 does not perturb the nominal ACAD remapping function then one can show that the phase at DM2 is:</text>
<formula><location><page_29><loc_11><loc_74><loc_48><loc_79></location>arg [ E DM 2 ( x 2 , y 2 )] = = 2 π λ (∆ h 1 ( f 0 1 ( x 2 , y 2 ) , g 0 1 ( x 2 , y 2 )) + ∆ h 2 ( x 2 , y 2 ))(60)</formula>
<text><location><page_29><loc_8><loc_52><loc_48><loc_73></location>where ∆ h 2 ( x 2 , y 2 ) is a small continuous surface deformation superposed to the ACAD shape of DM2 and ∆ h 1 ( f 0 1 ( x 2 , y 2 ) , g 0 1 ( x 2 , y 2 )) is the telescope OPD seen through the DM based remapping unit. This second term presents phase discontinuities whose spatial scale has been contracted by ACAD. When these discontinuities are very small then their high spatial frequency content does not disrupt the ability of DM2 to correct for low to mid-spatial frequency wavefront errors wavefront errors. However as the discontinuities become larger their high spatial frequency content can fold into the region of the PSF that the DMs seek to cancel. These 'frequency folding' speckles are highly chromatic (Give'on et al. 2006) and can have a severe impact on the spectral bandwidth of a coronagraph whose wavefront is corrected using a continuous DM.</text>
<text><location><page_29><loc_8><loc_7><loc_48><loc_52></location>In order to assess the impact of this phenomenon, we conducted a series of simulations based on single DM wavefront control algorithm that seeks to create a dark hole in one half of the image plane at in as in Bord'e & Traub (2006). We use the example of a geometry similar to JWST and work under the assumption that the discontinuous wavefront incident to the coronagraph has the same spatial frequency content as a JWST NIRCAM Optical Path Difference that has been adjusted to 70 nm rms in order to mimic a visible Strehl similar to the near-infrared Strehl of JWST. The non-linear wavefront and sensing and control problem associated with phasing a primary mirror to such level of precision is undoubtedly a colossal endeavor and is well beyond the scope of this paper. In this section we work under the assumption that the primary mirror either has been phased to such a level, that the wavefront discontinuities are no larger than 200 nm peak to valley or that the wavefront has been otherwise corrected down to this specification using a segmented Deformable Mirror that is conjugate with the primary mirror. Moreover we assume (1) that the residual post-phasing wavefront map has been characterized and can be used in order to build the linear model underlying the wavefront controller (2) the focal plane wavefront estimator (carried using DM diversity as in Bord'e & Traub (2006) for instance) is capable to yield an exact estimate of the complex electrical field at the science camera. Underlying this last assumption is the overly optimistic premise that wavefront will remain unchanged over the course of each high-contrast exposure. While this is not a realistic assumption one could envision the introduction of specific wavefront sensing schemes, with architectures similar to the one currently considered for low order wavefront sensors on monolithic</text>
<text><location><page_29><loc_52><loc_8><loc_92><loc_92></location>apertures (Guyon et al. 2009; Wallace et al. 2011), or using a separate metrology system. The results presented here are thus limited to configurations for which segment phasing will be dynamically compensated using specific sensing and control beyond the scope of this paper. As this section merely seeks to address the controllability of wavefront errors in segmented telescopes we chose to conduct our simulations with a perfect estimator. Finally we use the stroke minimization wavefront control algorithm presented in Pueyo et al. (2009) to ensure convergence for as many iteration as possible. We first tested the case of a segmented telescope in the absence of ACAD, using a azimuthally symmetric coronagraph and a single DM. We sough to create a Dark Hole between 5 and 28 λ 0 /D under a 20% bandwidth with λ 0 = 700 nm. Fig 22 shows the results of such a simulation. The DM can indeed correct for the discontinuities over a broadband in one half of the image plane. However the wavefront control algorithm seeks to compensate for the diffractive artifacts associated with the secondary support structures: it attenuates them on the right side of the PSF while it strengthens them on the left side of the PSF. As a result the DM surface becomes too large at the pupil spider's location and the quasi-linear wavefront control algorithm eventually diverges for contrasts ∼ 10 6 . We then proceeded to simulate the same configuration in the presence of two DMs whose surface at rest was calculated using ACAD. Since there does not exist a model yet to propagate arbitrary wavefronts through ACAD (the models in Krist et al. (2011) only operate under the assumption of an azimuthally symmetric remapping) we can only use the second DM for wavefront control. We work under the assumption that the incident wavefront does not perturb the nominal ACAD remapping (which is true in the case of the surface map we chose for our example) and that the arguments in Krist et al. (2010) hold so that phase to amplitude conversion in ACAD can be compensated by actuating DM1. Frequency folding will then be the phenomenon responsible for the true contrast limit. In this section we are interested in exploring how this impacts the controllability of wavefront discontinuities using continuous phase-sheet DMs. We used a azimuthally symmetric coronagraph and superposed our wavefront control solution to DM2. We sough to create a Dark Hole between 5 and 28 λ 0 /D under a 20% bandwidth with λ 0 = 700 nm. Fig 22 shows the results of such a simulation. When the incident wavefront is small enough it is indeed possible to superpose a 'classical linear wavefront control' solution to the non-linear ACAD DM shapes in order to carve PSF dark holes. The wavefront control algorithm now yields a DM surface that does not feature prominent deformations at the location of the spiders. Most of the DM stroke is located at the edge of the segments, at location of the wavefront discontinuities and seek to correct the frequency folding terms associated with such discontinuities. At these locations the DM surface eventually becomes too large and the linear wavefront control algorithm diverges. However this divergence occurs at contrast levels much higher than when the ACAD solution is not applied to the DMs. These simulations show that indeed discontinuous phases can be corrected using the second DM of a ACAD whose surfaces have preliminary been set to</text>
<figure>
<location><page_30><loc_9><loc_68><loc_39><loc_91></location>
<caption>Deformation of DM2 Ahz</caption>
</figure>
<figure>
<location><page_30><loc_9><loc_42><loc_39><loc_65></location>
</figure>
<figure>
<location><page_30><loc_51><loc_67><loc_81><loc_91></location>
<caption>ACAD PSF with DM2 correcting for wavefront error</caption>
</figure>
<figure>
<location><page_30><loc_51><loc_42><loc_81><loc_65></location>
<caption>Figure 23. Broadband wavefront correction (20% bandwidth around 700 nm) in a segmented telescope whose pupil has been re-arranged using ACAD. The surface of the first DM is set according to the ACAD equations. The surface of the second DM is the sum of the ACAD solution and a small perturbation calculated using a quasi-linear wavefront control algorithm . Top Left: wavefront before the coronagraph. Note that the ACAD remapping has compressed the wavefront errors near the struts and the segment gaps. Top Right: broadband aberrated PSF with DMs set to the ACAD solution. Bottom Left: perturbation of DM2's surface resulting from the wavefront control algorithm. Bottom Right: broadband corrected PSF. The wavefront control algorithm now yields a DM surface that does not feature prominent deformations at the location of the spiders. Most of the DM stroke is located at the edge of the segments, at location of the wavefront discontinuities. There, the DM surface eventually becomes too large and the quasi-linear wavefront control algorithm diverges. However this occurs higher contrasts than in the absence of ACAD.</caption>
</figure>
<text><location><page_30><loc_8><loc_28><loc_43><loc_29></location>mitigate the effects of spiders and segment gaps.</text>
<section_header_level_1><location><page_30><loc_18><loc_25><loc_38><loc_26></location>7.3. Ultimate contrast limits</section_header_level_1>
<text><location><page_30><loc_8><loc_7><loc_48><loc_24></location>Assuming that edge ringing has been properly mitigated, so that the ray optics approximation underlying the calculation of the DMs shapes is valid, one can wonder about the ultimate contrast limitations of the results presented in this manuscript. Increasing the number of actuators would have dramatic effects on contrast if the actuator count would be such that N > D/d where d is the scale of the aperture discontinuities. Unfortunately current DM technologies are currently far from such a requirement and the solutions presented here are in the regime where N glyph[lessmuch] D/d . In this regime N only has a marginal influence on contrast when compared to the impact of the cutoff frequency of the tapering kernel.</text>
<text><location><page_30><loc_52><loc_27><loc_92><loc_29></location>In the regime described here varying the actuator count only changes the size of the corrected region.</text>
<text><location><page_30><loc_52><loc_8><loc_92><loc_26></location>The residual PSF artifacts in Figs. 11 to 20 follow the direction of the initial diffraction pattern associated with secondary support structures and segments. When addressing the problem of aperture discontinuities by solving the Monge-Ampere Equation, ACAD calculates the DM shapes based on a pupil plane metric and thus mostly focuses on attenuating these structures with little regard to the final contrast. It is actually quite remarkable that such a pupil-only approach yields levels of starlight extinction of two to three orders of magnitude. A more appropriate metric would be the final intensity distribution in the post-coronagraphic image plane. However, as discussed in § . 3 classical wavefront control algorithms based on a linearization of the DMs</text>
<figure>
<location><page_31><loc_8><loc_71><loc_49><loc_92></location>
<caption>Figure 24. Radial average in the half dark plane of the PSFs on Fig 22 and Fig. 23. In the presence of wavefront discontinuities corrected using a continuous membrane DM, ACAD still yields, over a 20% bandwidth around 700 nm, PSF with a contrast 100 larger than in a classical segmented telescope. Moreover this figure illustrates that since it is based on a true image plane metric, the wavefront control algorithm can be used ( within the limits of its linear regime) to improve upon the ACAD DM shapes derived solving the Monge Ampere Equation.</caption>
</figure>
<text><location><page_31><loc_8><loc_25><loc_48><loc_57></location>deformations around local equilibrium shapes (such as the ones presented in Bord'e & Traub (2006); Give'on et al. (2007) in the one DM case or Pueyo et al. (2009) for one or two DMs) cannot be used to compensate the full aperture discontinuities. This is illustrated in Fig 22, where the DM surface in the vicinity of spiders becomes too large after a certain number of iterations, which leads the iterative algorithm to diverge. When attempting to circumvent this problem by recomputing the linearization at each iteration, we managed to somewhat stabilize the problem for a few iterations and reached marginal contrast improvements, but the overall algorithm remained unstable unless a prohibitively small step size was used. This is the problem which motivated our effort to calculate the DM shapes as the full non-linear solution of the Monge-Ampere Equation. While doing so yields significant contrast improvements in both the case of JWST like geometries, TMT and on axis-monolithic apertures similar, this approach does not give a proper weight to the spatial frequencies of interest for high contrast imaging. We mitigated this effect by giving a strong weight to the spatial frequencies of interest (in the Dark Hole) when solving the Monge Ampere Equation.</text>
<text><location><page_31><loc_8><loc_7><loc_48><loc_24></location>The next natural step is thus to use non-linear solutions presented herein to correct for the bulk of the aperture discontinuities and to serve as a starting point for classical linearized waveform control algorithms, as illustrated on Fig. 25. Fig. 24 indeed illustrates that when superposing an image plane based wavefront controller to the Monge Ampere ACAD solution, the contrast can be improved beyond the floor shown on Fig. 12. However one DM solutions, are of limited interest as they only operate efficiently over a finite bandwidth and over half of the image plane. ACAD yields a true broadband solution, and consequently it would be preferable to use the two DMs in the quasi-linear regime to quan-</text>
<figure>
<location><page_31><loc_52><loc_61><loc_92><loc_92></location>
<caption>Figure 25. Future work towards higher contrasts with ACAD. The blue and orange colors respectively represent the current state of the art in wavefront control and the work described in the present manuscript, as in Fig. 1. In brown are listed the potential avenues to further the contrasts presented herein: 1) combining ACAD with coronagraphs designed on segmented and/or on-axis apertures, 2) using diffractive models to close a quasi-linear focal plane based loop using a metric whose starting point corresponds to the DM shapes calculated in the non-linear regime.</caption>
</figure>
<text><location><page_31><loc_52><loc_32><loc_92><loc_48></location>tify the true contrast limits of ACAD . In such a scheme the DM surfaces are first evaluated as the solution of the Monge-Ampere Equation and then adjusted using the image plane based wavefront control algorithm presented in Pueyo et al. (2009). However such an exercise requires efficient and robust numerical algorithms to evaluate Eq. 16. Such tool only exist so far in the case of azimuthally symmetric remapping units (Krist et al. 2010). Developing such numerical tools is thus of primary interest to both quantifying the chromaticity and the true contrast limits achievable with on-axis and/or segmented telescopes.</text>
<section_header_level_1><location><page_31><loc_66><loc_30><loc_78><loc_31></location>8. CONCLUSION</section_header_level_1>
<text><location><page_31><loc_52><loc_7><loc_92><loc_29></location>We have introduced a technique that takes advantage of the presence of Deformable Mirrors in modern highcontrast coronagraph to compensate for amplitude discontinuities in on-axis and/or segmented telescopes. Our calculations predict that this high throughput class of solutions operates under broadband illumination even in the presence of reasonably small wavefront errors and discontinuities. Our approach relies on controlling two sequential Deformable Mirrors in a non-linear regime yet unexplored in the field of high-contrast imaging. Indeed the mirror's shapes are calculated as the solution of the twodimensional pupil remapping problem, which can be expressed as a non-linear partial differential equation called Monge Ampere Equation. We called this technique Active Compensation of Aperture Discontinuities. While we illustrated the efficiency of ACAD using Apodized Pupil Lyot and Phase Induced Amplitude Coronagraph,</text>
<text><location><page_32><loc_8><loc_61><loc_48><loc_92></location>it is is applicable to all types of coronagraphs and thus enables one to translate the past decade of investigation in coronagraphy with unobscured monolithic apertures to a much wider class of telescope architectures. Because ACAD consists of a simple remapping of the telescope pupil, it is a true broadband solution. Provided that the coronagraph chosen operates under a broadband illumination, ACAD allows high contrast observations over a large spectral bandwidth as pupil remapping is an achromatic phenomenon. We showed that wavelength edge diffraction artifacts, which are the source of spectral bandwidth limits in PIAA coronagraphs (also based on pupil remapping), are no larger than classical Fresnel ringing. We thus argued that they will only marginally impact the spectral bandwidth of a coronagraph whose input beam has been corrected with ACAD. The mirror deformations we find can be achieved, both in curvature and in stroke, with technologies currently used in Ex-AO ground based instruments and in various testbeds aimed at demonstrating high-contrast for space based applications. Implementing ACAD on a given on-axis and/or segmented thus does not require substantial technology development of critical components.</text>
<text><location><page_32><loc_8><loc_39><loc_48><loc_61></location>For geometries analogous to JWST we have demonstrated that ACAD can achieve at least contrast ∼ 10 -7 , provided that dynamic high precision segment phasing can be achieved. For TMT and ELT, ACAD can achieve at least contrasts ∼ 10 -8 . For on-axis monolithic observatories the design contrast of the coronagraph can be reached with ACAD when the secondary support structures are 5 times thinner than on HST. When they are just as thick as HST contrasts as high as 10 8 can be reached. These numbers are, however, conservative: an optimal solution can be obtained by fine tuning the control term in the Monge Ampere Equation to the characteristic scale of each discontinuity. As our goal was to introduce this technique to the astronomical community and emphasize its broad appeal to a wide class of architectures (JWST,ATLAST,HST,TMT,E-ELT) we left this observatory specific exercise for future work.</text>
<text><location><page_32><loc_8><loc_7><loc_48><loc_39></location>The true contrast limitation of ACAD resides in the fact that the Deformable Mirrors are controlled using a pre-coronagraph pupil based metric. However, as illustrated in Fig. 25, the solution provided by ACAD can be used as the starting point for classical linearized waveform control algorithms based in image plane diagnostics. In such a control strategy, the surfaces are first evaluated as the solution of the Monge- Ampere Equation and then adjusted using the quasi-linear method presented in Pueyo et al. (2009). This control strategy requires efficient and robust numerical algorithms to evaluate the full diffractive propagation in the remapped Fresnel regime. All the contrasts reported here are achieved without aberrations and we showed that in practice, quasi-linear DM controls based on images at the science camera will have to be superposed to the ACAD solutions. Finally, as ACAD is broadly applicable to all types of coronagraphs, the remapped pupil can be used as the entry point to relax the design of coronagraphs that do operate on segmented apertures such as discussed in Carlotti et al. (2011); Guyon et al. (2010a), also illustrated in Fig. 25. ACAD is thus a promising tool for future high contrast imaging instruments on a wide range of observatories as it will allow astronomers to devise high through-</text>
<text><location><page_32><loc_52><loc_81><loc_92><loc_92></location>put broadband solutions for a variety of coronagraphs. It only relies on hardware (Deformable Mirrors) that have been extensively tested over the past ten years. Finally since ACAD can operate with all type of coronagraphs and it renders the last decade of research on high-contrast imaging technologies with off-axis unobscured apertures applicable to much broader range of telescope architectures.</text>
<text><location><page_32><loc_52><loc_58><loc_92><loc_79></location>The authors thank Dr Bruce Macintosh who steered our attention towards this problem and provided invaluable guidance in the early stages of this manuscript. The authors also thank the anonymous referee for insightful comments which greatly improved this manuscript, Dr Remi Soummer, Dr Marshall Perrin, Prof. N. Jeremy Kasdin and Prof. Robert Vanderbei for very helpful discussions and Matt Sheckells for his help coding the linear wavefront control algorithms. This material is partially based upon work supported by the National Aeronautics and Space Administration under Grant NNX12AG05G issued through the Astrophysics Research and Analysis (APRA) program . This work was performed in part under contract with the California Institute of Technology funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "We present a new method to achieve high-contrast images using segmented and/or on-axis telescopes. Our approach relies on using two sequential Deformable Mirrors to compensate for the large amplitude excursions in the telescope aperture due to secondary support structures and/or segment gaps. In this configuration the parameter landscape of Deformable Mirror Surfaces that yield high contrast Point Spread Functions is not linear, and non-linear methods are needed to find the true minimum in the optimization topology. We solve the highly non-linear Monge-Ampere equation that is the fundamental equation describing the physics of phase induced amplitude modulation. We determine the optimum configuration for our two sequential Deformable Mirror system and show that high-throughput and high contrast solutions can be achieved using realistic surface deformations that are accessible using existing technologies. We name this process Active Compensation of Aperture Discontinuities (ACAD). We show that for geometries similar to JWST, ACAD can attain at least 10 -7 in contrast and an order of magnitude higher for both the future Extremely Large Telescopes and on-axis architectures reminiscent of HST. We show that the converging non-linear mappings resulting from our Deformable Mirror shapes actually damp near-field diffraction artifacts in the vicinity of the discontinuities. Thus ACAD actually lowers the chromatic ringing due to diffraction by segment gaps and strut's while not amplifying the diffraction at the aperture edges beyond the Fresnel regime. This outer Fresnel ringing can be mitigated by properly designing the optical system. Consequently, ACAD is a true broadband solution to the problem of high-contrast imaging with segmented and/or on-axis apertures. We finally show that once the non-linear solution is found, fine tuning with linear methods used in wavefront control can be applied to further contrast by another order of magnitude. Generally speaking, the ACAD technique can be used to significantly improve a broad class of telescope designs for a variety of problems. Subject headings: planetary systems - techniques: coronagraphy, wavefront control",
"pages": [
1
]
},
{
"title": "HIGH CONTRAST IMAGING WITH AN ARBITRARY APERTURE: ACTIVE CORRECTION OF APERTURE DISCONTINUITIES",
"content": "Laurent Pueyo 1 , Colin Norman 1 ApJ Accepted 11-26-2012",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Exo-planetary systems that are directly imaged using existing facilities (Marois et al. 2008; Kalas et al. 2008; Lagrange et al. 2010) give a unique laboratory to constrain planetary formation at wide separations (Rafikov 2005; Dodson-Robinson et al. 2009; Kratter et al. 2010; Johnson et al. 2010), to study the planetary luminosity distribution at critical young ages (Spiegel & Burrows 2012; Fortney et al. 2008) and the atmospheric properties of low surface gravity objects (Barman et al. 2011b,a; Marley et al. 2010; Madhusudhan et al. 2011). Upcoming surveys, conducted with instruments specifically designed for high-contrast (Dohlen et al. 2006; Graham et al. 2007; Hinkley et al. 2011), will unravel the bulk of this population of self-luminous jovian planets and provide an unprecedented understanding of their formation history. Such instruments will reach the contrast required to achieve their scientific goals by combining Extreme Adaptive Optics systems (Ex-AO, Poyneer & V'eran (2005)), optimized coronagraphs (Soummer et al. 2011; Guyon 2003; Rouan et al. 2000) and nanometer class wavefront calibration (Sauvage et al. 2007; Wallace et al. 2009; Pueyo et al. 2010). In the future, highcontrast instruments on Extremely Large Telescopes will focus on probing planetary formation in distant star email: [email protected] 1 Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA forming regions (Macintosh et al. 2006), characterizing both the spectra of cooler gas giants (V'erinaud et al. 2010) and the reflected light of planets in the habitable zone of low mass stars. The formidable contrast necessary to investigate the presence of biomarkers at the surface of earth analogs ( > 10 10 ) cannot be achieved from the ground beneath atmospheric turbulence and will require dedicated space-based instruments (Guyon 2005). The coronagraphs that will equip upcoming Ex-AO instruments on 8 meter class telescopes have been designed for contrasts of at most ∼ 10 -7 . Secondary support structures (or spiders: 4 struts each 1 cm wide, ∼ 0 . 3% of the total pupil diameter in the case of Gemini South) have a small impact on starlight extinction at such levels of contrasts. In this case, coronagraphs have thus been optimized on circularly symmetric apertures, which only take into account the central obscuration (Soummer et al. 2011). However, high-contrast instrumentation on future observatories will not benefit from such gentle circumstances. ELTs will have to support a substantially heavier secondary than 8 meter class observatories do, and over larger lengths: as a consequence the relative area covered by the secondary support will increase by a factor of 10 (30 cm wide spiders, occupying ∼ 3% of the pupil diameter in the case of TMT). This will degrade the contrast of coronagraphs only designed for circularly obscured geometries by a factor ∼ 100, when the actual envisioned contrast for an ELT exo-planet imager can be as low as ∼ 10 -8 (Macintosh et al. 2006). While the tradeoffs associated with minimization of spider width in the space-based case have yet to be explored, secondary support structures will certainly hamper the contrast depth of coronagraphic instruments of such observatories at levels that are well above the 10 10 contrast requirement. As a consequence, telescope architectures currently envisioned for direct characterization of exo-earths consist of monolithic, off-axis, and thus un-obscured, telescopes (Guyon et al. 2008; Trauger et al. 2010). Coronagraphs for such architectures take advantage of the pupil symmetry to reach a theoretical contrast of ten orders of magnitude (Guyon et al. 2005; Vanderbei et al. 2003a,b; Kasdin et al. 2005; Mawet et al. 2010; Kuchner & Traub 2002; Soummer et al. 2003). However, using obscured on-axis and/or segmented apertures take full advantage of the limited real estate associated with a given launch vehicle and can allow larger apertures that increase the scientific return of space-based direct imaging survey. Recent solutions can mitigate the presence of secondary support structures in on-axis apertures. However these concepts present practical limitations: APLCs on arbitrary apertures (Soummer et al. 2009) and Shaped Pupils (Carlotti et al. 2011) suffer from throughput loss for very high contrast designs, and PIAAMCM (Guyon et al. 2010a) rely on a phase mask technology whose chromatic properties have not yet been fully characterized. Moreover segmentation will further complicate the structure of the telescope's pupil: both the amplitude discontinuities created by the segments gaps and the phase discontinuities resulting from imperfect phasing will thus further degrade coronagraphic contrast. Devising a practical solution for broadband coronagraphy on asymmetric, unfriendly apertures is an outstanding problem in high contrast instrumentation. The purpose of the present paper is to introduce a family of practical solutions to this problem. As their ultimate performances depend strongly on the pupil structure we limit the scope of this paper to a few characteristic examples. Full optimization for specific telescope geometries can be conducted as needed. The method proposed here takes advantage of stateof-the art Deformable Mirrors in modern high-contrast instruments to address the problem of pupil amplitude discontinuities for on-axis and/or segmented telescopes. Indeed, coronagraphs are not sufficient to reach the high contrast required to image faint exo-planets: wavefront control is needed to remove the light scattered by small imperfections on the optical surfaces (Brown & Burrows 1990). Over the past eight years, significant progress has been made in this area, both in the development of new algorithms (Bord'e & Traub 2006; Give'on et al. 2007) and in the experimental demonstration of high-contrast imaging with a variety of coronagraphs (Give'on et al. 2007; Trauger & Traub 2007; Guyon et al. 2010b; Belikov et al. 2011). These experiments rely on a system with a single Deformable Mirror which is controlled based on diagnostics downstream of the coronagraph, either at the science camera or as close as possible to the end detector (Wallace et al. 2009; Pueyo et al. 2010). Such configurations are well suited to correct phase wavefront errors arising from surface roughness but have limitations in the presence of pure amplitude errors (reflectivity), or phase-induced amplitude errors, which result from the propagation of surface errors in optics that are not con- ugate to the telescope pupil (Shaklan & Green 2006; Pueyo & Kasdin 2007). Indeed a single DM can only mimic half of the spatial frequency content of amplitude errors and compensate for them only on one half of the image plane (thus limiting the scientific field of view) over a moderate bandwidth. In theory, architectures with two sequential Deformable Mirrors, can circumvent this problem and create a symmetric broadband high contrast PSF (Shaklan & Green 2006; Pueyo & Kasdin 2007). The first demonstration of symmetric dark hole was reported in Pueyo et al. (2009) and has since been generalized to broadband by Groff et al. (2011). In such experiments the coronagraph has been designed over a full circular aperture, the DM control strategy is based on a linearization of the relationship between surface deformations and electrical field at the science camera, and the modeling tools underlying the control loop consist of classic Fourier and fresnel propagators. This is illustrated on the left panel of Fig. 1. As a consequence, a wavefront control system composed of two sequential Deformable Mirrors is currently the baseline architecture of currently envisioned coronagraphic space-based instruments (Shaklan et al. 2006; Krist et al. 2011) and ELT planet imagers (Macintosh et al. 2006). One can thus naturally be motivated to investigate if such wavefront control systems can be used to cancel the light diffracted by secondary supports and segments in large telescopes, since such structures are amplitude errors, albeit large amplitude errors. The purpose of our study is to demonstrate that indeed a two Deformable Mirror (DM for the remainder of this paper) wavefront control system can mitigate the impact of the pupil asymmetries, such as spiders and segments, on contrast and thus enable high contrast on unfriendly apertures. In § . 2 we first present a new approach to coronagraph design in the presence of a central obscuration, but in the absence of spiders or segments. We show that for coronagraphs with a pupil apodization and an opaque focal plane stop, contrasts of 10 -10 can be reached for any central obscuration diameter, provided that the Inner Working Angle is large enough. Naturally the secondary support structures, and in the segmented cases, segment gaps, will degrade this contrast. As our goal is to use two DMs as an amplitude modulation device, we first briefly review in § . 3 the physics of such a modulation. In § . 4 we introduce a solution to this problem: we show how to compute DM surfaces that mitigate spiders and segment gaps. Current algorithms used for amplitude control operate under the assumption that amplitude errors are small, and thus they cannot be readily applied to the problem of compensating aperture discontinuities, which have inherently large reflectivity non-uniformities. Fig. 1 illustrates how the present manuscript introduces a control strategy for the DMs that is radically different from previously published amplitude modulators in the high-contrast imaging literature. Our technique, which we name Active Compensation of Aperture Discontinuities (hereafter ACAD), finds the adequate DM shapes in the true non-linear large amplitude error regime. In this case the DMs' surfaces are calculated as the solution of a non-linear partial differential equation, called the Monge-Ampere Equation. We describe our methodology to solve this equation in § . 4 and illustrate each step using an obscured and seg- ed geometry similar to JWST. As ACAD DM surfaces are prescribed in the ray-optics approximation this is a fundamentally broadband technique provided that chromatic diffractive artifacts, edge ringing in particular, do not significantly impact the contrast. This is what we discuss in § . 5. We find that when remapping small discontinuities with Deformable Mirrors, the spectral bandwidth is only limited by wavelength-dependent edge-diffraction ringing in the Fresnel approximation (as discussed in Pueyo & Kasdin (2007) for instance). Highcontrast instruments where this ringing is mitigated have already been designed; while future work in high precision optical modeling is necessary to fully quantify the true chromatic performances of ACAD, we do not expect these effects to be a major limitation to broadband operations. In § . 6 we present the application of our method to various observatory architectures. Note that the contrast levels stated in § . 6 represent a non-optimal estimate of ACAD performances with on-axis and/or segmented apertures. Our calculations are carried out in the absence of atmospheric turbulence, quasi-static wavefront errors or coronagraphic manufacturing defects. We discuss these limitations in § . 7, with a specific emphasis on quasi-static phase errors in a segmented telescope. We show that when the aperture discontinuities are thin enough field distortion is negligible for spatial frequencies within the field of view defined by the DMs controllable spatial frequencies. We then discuss issues associated with phase discontinuities when applying ACAD to a segmented telescope. We show that they can be corrected by superposing single DM classical wavefront control solutions to the ACAD shape of the second DM. We finally argue, that should high precision diffractive models be developed, then the solutions presented herein can be used as the starting point of dual DMs iterative algorithms relying on an image-plane based metric and thus lead to higher contrast than reported herein. Most of the future exo-planet imagers, either on ELTs or on future space missions, are envisioned to control their wavefront in real time with two sequential DMs. The method presented in this manuscript thus renders high contrast coronagraphy possible on any observatory geometry without adding any new hardware.",
"pages": [
1,
2,
3
]
},
{
"title": "2.1. Optimizing pupil apodization in the presence of a central obscuration",
"content": "Because the pupil obscuration in an on-axis telescope is large it will be very difficult to mitigate its impact with DMs with a limited stroke. Indeed, the main hindrance to high-contrast coronagraphy in on-axis telescope is the presence of the central obscuration: it often shadows much more than 10% of the aperture width while secondary supports and segments gaps cover ∼ 1%. We thus first focus of azimuthally symmetric coronagraphic designs in the presence of a central obscuration. This problem (without the support structures) has been addressed in previous publications either using circularly symmetric pupil apodization (Soummer et al. 2011) or a series of phase masks (Mawet et al. 2011). Both solutions however are subject to limitations. The singularity at the center of the Optical Vector Vortex Coronagraph might be difficult to manufacture and a circular opaque spot thus lies in the central portion of the phase mask ( < λ/D ) which results in a degradation of the ideal contrast of such a coronagraph (Krist et al. 2011). The solutions in Soummer et al. (2011) result from an optimization seeking to maximize the off-axis throughput for a given focal plane stop diameter: the final contrast is absent from the optimization metric and is only a byproduct of the chosen geometry. Higher contrasts are then obtained by increasing the size of the focal plane mask, and thus result in a loss in IWA. Here we revisit the solution proposed by Soummer et al. (2011) in a slightly different framework. We recognize that, in the presence of wavefront errors, high contrast can only be achieved in an area of the field of view that is bounded by the spatial frequency corresponding to the DM's actuator spacing. We thus consider the design of an Apodized Pupil Lyot Coronagraph which only aims at generating high contrast between the Inner Working Angle (IWA) and Outer Working Angle (OWA). In order to do so, we rewrite coronagraphs described by Soummer et al. (2003) as an operator C which relates the entrance pupil P ( r ) to the electrical field in the final image plane. We first call ˆ P ( ξ ) the Hankel transform of the entrance pupil: where D is the pupil diameter, D S the diameter of the secondary and ξ the coordinate at the science detector expressed in units of angular resolution ( λ 0 /D ). λ 0 is the design wavelength of the coronagraph chosen to translate the actual physical size of the focal plane mask in units of angular resolution (often at the center of the bandwidth of interest). λ is then the wavelength at which the coronagraph is operating (e.g. the physical size of the focal plane mask remains constant as the width of the diffraction pattern changes with wavelength). For the purpose of the monochromatic designs presented herein λ = λ 0 . Then the operator is given by: where K ( ξ, η ) is the convolution kernel that captures the effect of the focal plane stop of diameter M stop : An analytical closed form for this kernel can be calculated using Lommel functions. Note that this Eq. 2 assumes that the Lyot stop is not undersized. Since we are interested in high contrast regions that only span radially all the way up to a finite OWA, we seek pupil apodization of the form: where J Q ( r ) denotes the Bessel function of the first kind of order Q and α Q k the k th zero of this Bessel function. In order to devise optimal apodizations overobscured pupils, Q , can be chosen to be large enough so that J Q ( r ) glyph[lessmuch] 1 for r < D S / 2 (in practice we choose Q = 10). The α Q k corresponds to the spatial scale of oscillations in the coronagraph entrance pupil, and such a basis set yields high contrast regions all the way to OWA glyph[similarequal] N modes λ 0 /D . Since the operator in Eq. 2 is linear, finding the optimal p k can be written as the fol- ing linear programming problem: Our choice of cost function and constraints has been directed by the following rationale: Note that the linear transfer function in Eq. 2 can also be derived for other coronagraphs, with grayscale and phase image- plane masks, or for the case of under-sized Lyot stops. As general coronagraphic design in obscured circular geometries is not our main purpose, we limit the scope of the paper to coronagraphs represented by Eq. 2.",
"pages": [
3,
4
]
},
{
"title": "2.3. Results of the optimization",
"content": "Typical results of the monochromatic optimization in Eqs. 5d, with λ = λ 0 , are shown in Fig. 2 for central obscurations of 10, 20 and 30%. In the first two cases the size of the focal plane stop is equal to 3 λ/D , the IWA is 4 λ/D and the OWA is 30 λ/D . As the size of the central obscuration increases the resulting optimal apodization becomes more oscillatory and the contrast constraint has to be loosened in order for the linear programming optimizer to converge to a smoother solution. Alternatively increasing the size of the focal plane stop yield smooth apodizers with high contrast, at cost in angular resolutions (bottom panel with a central obscuration of 30%, a focal plane mask of radius 4 λ/D , an IWA of 5 λ/D and an OWA of 30 λ/D ). These trade-offs were described in Soummer et al. (2011), however our linear programming approach to the design of pupil apodizations now imposes the final contrast instead of having it be a by product of fixed central obscuration and focal plane stop. These apodizations can either be generated using grayscale screen (at a cost in throughput and angular resolution) or a series of two aspherical PIAA /Slash1 mirrors (for better throughput and angular resolution). In order not to lose generality, we present our results on Fig. 2 considering the two types of practical implementations (classical apodization and PIAA apodization). In the case of a grayscale amplitude screen the angular resolution units are as defined in Eq. 2 and the throughput is smaller than unity. In the case of PIAA apodisation the throughput is unity and the angular resolution units have been magnified by the field independent centroid based angular magnification defined in Pueyo et al. (2011). We adopt this presentation for the remainder of the paper where one dimensional PSFs will be presented with 'APLC angular resolution units' in the bottom horizontal axis and'PIAAC angular resolution units' in the top horizontal axis. Note that this linear programming approach only optimizes the contrast for a given wavelength. However, since the solutions presented in Fig. 2 feature contrasts below 10 10 , we choose not to focus on coronagraph chromatic optimizations. Instead, in order to account for the chromatic behavior of the coronagraph, the monochromatic simulations in § . 6 are carried out under the conservative assumption that the physical size of the focal plane stop is somewhat smaller than optimal (or that the operating wavelength of the coronagraph is slightly off, λ = 1 . 2 λ 0 ). As a consequence the raw contrast of the coronagraphs presented in § . 6 is ∼ 10 -9 . Note that this choice is not representative of all possible Apodized Pupil Coronagraph chromatic configurations. It is merely a shortcut we use to cover the variety of cases presented in § . 6. In § . 7.2 we present a set of broadband simulations that include wavefront errors and the true coronagraphic chromaticity for a specific configuration and show that bandwidth is more likely to be limited by the spectral bandwidth of the wavefront control system than by the coronagraph. However, future studies aimed at defining the true contrast limits of a given telescope geometry will have to rely on solutions of the linear problem in Eqs. 5d which has been augmented to accommodate for broadband observations. In theory, the method presented here can also be applied to asymmetric pupils. However, the optimization quickly becomes computationally intensive as the dimensionality of the linear programming increases (in particular when the smoothness constraint and the bounds on the apodization have to be enforced at all points of a two dimensional array). This problem can be somewhat mitigated when seeking for binary apodizations, as shown in Carlotti et al. (2011), at a cost in throughput and angular resolution.",
"pages": [
4,
5,
6
]
},
{
"title": "3.1. General equations",
"content": "We have shown in § . 2 that by considering the design of pupil apodized coronagraphs in the presence of a circular central obscuration as a linear optimization problem, high contrast can be reached provided that the focal plane mask is large enough. In practice, the secondary support structures and the other asymmetric discontinuities in the telescope aperture (such as segment gaps) will prevent such levels of starlight suppression. We demonstrate that well controlled DMs can circumvent the obstacle of spiders and segment gaps. In this section, we first set-up our notations and review the physics of phase to amplitude modulation. We consider the system represented on Fig. 3 where two sequential DMs are located between the telescope aperture and the entrance pupil of the coronagraph. In this configuration, the telescope aperture and the pupil apodizer are not in conjugate planes. This will have an impact on the chromaticity of the system and is discussed in § . 5. Without loss of generality we work under the 'folded' assumption illustrated on Fig. 5 where the DMs are not tilted with respect to the optical axis and can be considered as lenses of index of refraction -1 (as discussed in Vanderbei & Traub (2005) . In the scalar approximation the relationship between the incoming field, E DM 1 ( x, y ), and the outgoing field, E DM 2 ( x 2 , y 2 ), is given by the diffractive Huygens Integral: (6) where A corresponds to the telescope aperture and Q ( x, y, x 2 , y 2 ) stands for the optical path length between any two points at DM1 and DM2: S ( x, y, x 2 , y 2 ) is the free space propagation between the DMs: where Z is the distance between between the two DMs, h 1 and h 2 are the shapes of DM1 and DM2 respectively (as shown on Fig. 5) and λ is the wavelength. We recognize that two sequential DMs act as a pupil remapping unit similar to PIAA coronagraph (Guyon 2003) whose ray optics equations were first derived by Traub & Vanderbei (2003). We briefly state the notation used to describe such an optical system as introduced in Pueyo et al. (2011):",
"pages": [
6
]
},
{
"title": "3.2. Fresnel approximation and Talbot Imaging",
"content": "In Pueyo et al. (2011) we showed that one could approximate the propagation integral in Eq. 6 by taking in a second order Taylor expansion of Q ( x, y, x 2 , y 2 ) around the rays that trace ( f 1 ( x 2 , y 2 ) , g 1 ( x 2 , y 2 )) to ( x 2 , y 2 ). In this case the relationship between the fields at DM1 and DM2 is: When the mirror's deformations are very small compared to both the wavelength and D 2 /Z , the net effect of the wavefront disturbance created by DM1 can be captured in E DM 1 ( x, y ) and the surface of DM2 can be factored out of Eq. 6. In this case x 1 = x 2 , y 1 = y 2 , ∂f 2 ∂x ∣ ∣ x 1 ,y 1 = 1, ∂f 2 ∂y ∣ ∣ x 1 ,y 1 = 0, ∂g 2 ∂y ∣ ∣ x 1 ,y 1 = 1. Then, Eq. 13 reduces to: which is the Fresnel approximation. If moreover h 1 ( x, y ) = λglyph[epsilon1] cos( 2 π D ( mx + ny )), h 2 ( x, y ) = -h 1 ( x, y ), with glyph[epsilon1] glyph[lessmuch] 1, then the outgoing field is to first order: This phase-to-amplitude coupling is a well known optical phenomenon called Talbot imaging and was introduced to the context of high contrast imaging by Shaklan & Green (2006). In the small deformation regime, the phase on DM1 becomes an amplitude at DM2 according to the coupling in Eq. 15. When two sequential DMs are controlled to cancel small amplitude errors, as in Pueyo et al. (2009), they operate in this regime. Note, however, that the coupling factor scales with wavelength (the resulting amplitude modulation is wavelength independent, but the coupling scales as λ ): this formalism is thus not applicable to our case, for which we are seeking to correct large amplitude errors (secondary support structures and segments) with the DMs. In practice, when using Eq. 15 in the wavefront control scheme outlined in Pueyo et al. (2009) to correct aperture discontinuities, this weak coupling results in large mirror shapes that lie beyond the range of the linear assumption made by the DM control algorithm. For this reason, methods outlined on the left panel of Fig. 1 to correct for aperture discontinuities do not converge to high contrast. Because phase to amplitude conversion is fundamentally a very non-linear phenomena, these descending gradient methods (Bord'e & Traub 2006; Give'on et al. 2007; Pueyo et al. 2009) are not suitable to find DM shapes that mitigate apertures discontinuities. We circumvent these numerical limitations by calculating DMs shapes that are based on the full non-linear problem, right panel of Fig. 1.",
"pages": [
7
]
},
{
"title": "3.3. The SR-Fresnel approximation",
"content": "In the general case, starting from Eq. 13 and following the derivation described in § . 5, the field at DM2 can be written as follows: where ̂ E DM 1 ( ξ, η ) is the Fourier transform of the telescope aperture, FP and stands for the Fourier plane. We call this integral the Stretched-Remapped Fresnel approximation (SR-Fresnel). Moreover det[ J ( x 2 , y 2 )] is the determinant of the Jacobian of the change of variables that maps ( x 2 , y 2 ) to ( x 1 , y 1 ): In the ray optics approximation, λ ∼ 0, the non linear transfer function between the two DMs becomes: The square form (e.g Eq. 19) of this transfer function can also be derived based on conservation of energy principles and is a generalization to arbitrary geometries of the equation driving the design of PIAA coronagraphs (Vanderbei & Traub 2005). A full diffractive optimization of the DM surfaces requires use of the complete transfer function shown in Eq. 16. However, there do not exist yet tractable numerical method to evaluate Eq. 16 efficiently enough in order for this model to be included in an optimization algorithm. Moreover even solving the ray optics problem is extremely complicated: it requires to find the mapping function ( f 1 , g 1 ) which solves the non-linear partial differential equation in Eq. 19. Substituting for( f 1 , g 1 ) and using Eqs. 12b yields a second order non-linear partial differential equation in h 2 . This is the problem that we set ourselves to tackle in the next section, and is the cornerstone of our Adpative Compensation of Aperture Discontinuities. As a check, one can verify that in the small deformation regime (e.g. if h 1 ( x, y ) = λglyph[epsilon1] cos( 2 π D ( mx + ny )) and h 2 ( x, y ) = -h 1 ( x, y )) Eq. 19 yields the same phase-to-amplitude coupling as in Talbot imaging (Pueyo 2008). Eq. 19 is a well know optimal transport problem (Monge 1781), which has already been identified as underlying optical illumination optimizations (Glimm & Oliker 2002). While the existence and uniqueness of solutions in arbitrary dimensions have been extensively discussed in the mathematical literature (see Dacorogna & Moser (1990) for a review), there was no practical numerical solution published up until recently. In particular, to our knowledge, not even a dimensional solution for which the DM surfaces can be described using a realistic basis-set has been published yet. We now introduce a method that calculates solu- ons to Eq. 19 which can be represented by feasible DM shapes.",
"pages": [
7,
8
]
},
{
"title": "4.1. Statement of the problem",
"content": "Ideally, we seek DM shapes that fully cancel all the discontinuities at the surface of the primary mirror and yield a uniform amplitude distribution, as shown in the top panel of Fig. 4. A solutions for a particular geometry with four secondary support has been derived by Lozi et al. (2009). It relies on reducing the dimensionality of the problem to the direction orthogonal to the spiders. It is implemented using a transmissive correcting plate that is a four-faced prism arranged such that the vertices coincides with the location of the spiders. The curvature discontinuities at the location of the spiders are responsible for the local remapping that removes the spiders in the coronagraph pupil. However such a solution cannot be readily generalized to the case of more complex apertures, where the secondary support structures might vary in width, or in the presence of segment gaps. Moreover it is transmissive and thus highly chromatic. Here we focus on a different class of solutions and seek to answer a different question. How well can we mitigate the effect of pupil discontinuities using DMs with smooth surfaces, a limited number of actuators (e.g a limited maximal curvature), and a limited stroke? Under these constraints directly solving Eq. 19 (e.g. solving the forward problem illustrated in the top panel of Fig. 4)",
"pages": [
8
]
},
{
"title": "The tapered reverse problem",
"content": "is not tractable as both factors on the left hand side of Eq. 19 depend on h 2 . More specifically, the implicit dependence of E DM 1 ( f 1 ( x 2 , y 2 ) , g 1 ( x 2 , y 2 )) on h 2 can only be addressed using finite elements solvers, whose solutions might not be realistically representable using a DM. However this can be circumvented using the reversibility of light and solving the reverse problem, where the two mirrors have been swapped. Indeed, since then we have the following relationship between the determinants of the forward and reverse remappings: Moreover we are only interested in compensating asymmetric structures located between the secondary and the edge of the primary. We thus only seek to find ( f 2 , g 2 ) such that: where P O ( x 1 , y 1 ) is the obscured pupil, without segments or secondary supports. Finally, we focus on solutions with a high contrast only up to a finite OWA. We artificially taper the discontinuities by convolving the control term in the Monge Ampere Equation, [ P ( x, y ) -(1 -P O ( x, y ))], with a gaussian of width ω . Note that this tapering is only applied when calculating the DM shapes via solving the reverse problem. When the resulting solutions are propagated through Eq. 19 we use the true telescope pupil for E DM 1 ( x 1 , y 1 ). The parameter ω has a significant impact on the final postcoronagraphic contrast. Indeed we are here working with a merit function that is based on a pupil-plane residual, while ideally our cost function should be based on imageplane intensity. By convolving the control term in the reverse Monge Ampere Equation, we low pass filter the discontinuities. This is equivalent to giving a stronger weight to low-to-mid spatial frequencies of interest in the context of exo-planets imaging . For each case presented in § . 6 we calculate our DM shapes over a grid of values of ω which correspond to low pass filters with cutoff frequencies ranging from ∼ OWAto ∼ 2 OWA and we keep the shapes which yield the best contrast. This somewhat ad-hoc approach can certainly be optimized for higher contrasts. However such an optimization is beyond the scope of the present manuscript. The problem we are seeking to solve is illustrated in the second panel of Fig. 4. In this configuration the full second order Monge Ampere Equation can be written as: where we have dropped the ( x 1 , y 1 ) dependence for clarity. Since we are interested in surface deformations which can realistically be created using a DM, we seek for a Fourier representation of the DMs surface: We thus focus on the inverse problem, bottom panel of Fig. 4, that consists of first finding the surface of h 1 as the solution of: Since our goal is to obtain a pupil as uniform a possible we seek a field at DM2 as uniform as possible: with a -m, -n = a glyph[star] -m, -n , where N is the limited number of actuators across the DM. Note that we have normalized the dimensions in the pupil plane X = x/D , Y = y/D . The normalized second order Monge Ampere Equation is then: For each configuration in this paper we first solve Eq. 28 and then transform the normalized solution in physical",
"pages": [
9
]
},
{
"title": "Forward coordinate system",
"content": "units, which depends on the DMs diameter D and their separation Z .",
"pages": [
10
]
},
{
"title": "4.2. Solving the Monge-Ampere equation to find H 1",
"content": "Over the past few years a number of numerical algorithms aimed at solving Eq. 28 have emerged in the literature (Loeper & Rapetti 2005; Benamou et al. 2010). Here we summarize our implementation of two of them: an explicit Newton method (Loeper & Rapetti 2005), and a semi-implicit method (Froese & Oberman 2012). We do not delve into the proof of convergence of each method, they can be found in Loeper & Rapetti (2005); Benamou et al. (2010); Froese & Oberman (2012). Note that Zheligovsky et al. (2010) discussed both approaches in a cosmological context and devised Fourier based solutions. Here we are interested in a two dimensional problem and we outline below the essence of each algorithm.",
"pages": [
10
]
},
{
"title": "4.2.1. Explicit Newton algorithm",
"content": "This method was first introduced by Loeper & Rapetti (2005) and relies on the fact that Eq. 28 can be re-written as where H ( · ) is the two dimensional Hessian of a scalar field and Id the identity matrix. If one writes H 1 = u + v with || v || glyph[lessmuch] || u || then: where ( · ) † T denotes the transpose of the comatrix. Eq. 28 can thus be linearized as: The explicit Newton algorithm relies on Eq. 31 and can then be summarized as carrying out the following iterations: Eq. 38 is a linear partial differential equation in V k . Since we are interested in a solution which can be expanded in a Fourier series we write V k as: Both the right hand side and the left hand side of Eq. 38 can be written as a Fourier series, with a spatial frequency content between -N and N cycles per aperture. Equating each Fourier coefficient in these two series yields the following linear system of (2 N +1) 2 equations with ( N +1) 2 unknowns. and solve When searching for V k as a Fourier series over the square geometry chosen here, this inverse problem is always well posed. The convergence of this algorithm relies on the introduction of a damping constant τ > 1. Loeper & Rapetti (2005) showed that as long as X 2 + Y 2 2 + H k 1 remains convex, which is always true for ACAD with reasonably small aperture discontinuities, there exists a τ large enough so that this algorithm converge towards a solution of Eq. 28. However since this algorithm is gradient based, it is not guaranteed that it converges to the global minimum of the underlying non-linear problem. In order to avoid having this solver stall in a local minimum we follow the methodology outlined by Froese & Oberman (2012) and first carry out a series of implicit iterations to get within a reasonable neighborhood of the global minimum.",
"pages": [
10,
11
]
},
{
"title": "4.2.2. Implicit algorithm",
"content": "This algorithm, along with its convergence proof, is thoroughly explained in Froese & Oberman (2012) . It relies on rewriting Eq. 28 as: The implicit method consists of carrying out the following iterations: and solve This problem is a linear system of ( N +1) 2 equations with ( N +1) 2 unknowns and can be solved using projections on a Fourier Basis: Note that the term under the square root in R I ( H k 1 ) is guaranteed to be positive at each iteration. The inverse problem in Eq. 39 is always well posed, for any basis set or pupil geometry, while the explicit Newton method runs into convergence issues when not using a Fourier basis over a square. When seeking to use a basis set that is more adapted to the geometry of the spiders and segments or when using a trial influence function basis for the DM, the implicit method is the most promising method. In this paper we have limited our scope to solving the reverse problem in the bottom panel of Fig. 4, and used a Fourier representation for the DM, we are able to use both methods. In order to make sure that the algorithm converges towards the true solution of Eq. 28 we first run a few tens of iterations of the implicit method and, once it has converged, we seek for a more accurate solutions using the Newton algorithm. Typical results are shown in Fig. 6 where most of the residual error resides in the high spatial frequency content (e.g. above N cycles per aperture). Our solutions are limited by the non- optimality of the Fourier basis to describe the mostly radial and azimuthal structures present in telescopes's apertures. Moreover the DM shape is the result of the minimization of a least squares residual in the virtual end-plane of the reverse problem, with little regard to the spatial frequency content of the solution in the final image plane of the coronagraph. While this method yields significant contrast improvements, as reported in § . 6, we discuss in § . 7 how it can be refined for higher contrast.",
"pages": [
11
]
},
{
"title": "4.3. Deformation of the Second Mirror",
"content": "Once the surface of DM1 has been calculated as a solution of Eq. 19, we compute the surface of DM2 based on Eqs. 12b, which stem from enforcing flatness of the outgoing on-axis wavefront. We seek a Fourier represen- tation for the surface of DM2: Plugging the solution found in the previous step for h 1 into Eqs. 11b yields a closed form for the normalized remapping functions, ( F 2 , G 2 ): Then the normalized version of Eqs. 12b can be rewritten as: We then multiply each side of Eq. 41 and Eq. 42 by: e i 2 π ( m 0 F 2 ( X 1 ,Y 1 )+ n 0 F 2 ( X 1 ,Y 1 )) det [ Id + H ( H k 1 ( X 1 , Y 1 ) )] where ( m 0 , n 0 ) corresponds to a given DM spatial frequency. system of 2 ∗ ( N +1) 2 equations with ( N +1) 2 real unknowns: We then find H 2 , the normalized surface of DM2, by solving this system in the least squares sense. Once the Monge Ampere Equation has been solved, the calculation of the surface of the second mirror is a much easier problem. Indeed, by virtue of the conservation of the on-axis optical path length, finding the surface of DM2 only consists of solving a linear system (see Traub & Vanderbei (2003)).",
"pages": [
11,
12,
13
]
},
{
"title": "4.4. Boundary Conditions",
"content": "The method described above does not enforce any boundary conditions associated with Eq. 28. One practical set of boundary conditions consists of forcing the edges of each DM to map to each other: with i = 1 , 2. These correspond to a set of Neumann boundary conditions in H 1 ( X,Y ) and H 2 ( X,Y ). These boundary conditions can be enforced by augmenting the dimensionality of the linear systems on Eq. 36 and Eq. 39, however doing so increases the residual least squares errors and thus hampers the contrast of the final solution. Moreover Fig. 7 and Fig. 8 show that, because of the one to one remapping near the DM edges in the control term of the reverse problem, the boundary conditions are almost met in practice. For the remainder of this paper we thus do not include boundary conditions when calculating the DM shapes, when solving for H 1 ( X,Y ) in Eq. 28 since, in the worse case, only the edge rows and columns of the DMs actuator will have to be sacrificed in order for the edges to truly map to each other.",
"pages": [
13
]
},
{
"title": "4.5. Remapped aperture",
"content": "For a given pupil geometry we have calculated ( H 1 , H 2 ). We then convert the DM surfaces to real units, ( h 1 , h 2 ), by multiplication with D 2 /Z . We evaluate the remapping functions using Eqs. 11b and 12b and obtain the field at the entrance of the coronagraph in the ray optic approximation where the exponential factor corresponds to the Optical Path Length through the two DMs. Even if the surface of the DMs has been calculated using only a finite set of Fourier modes, we check that the optical path length is conserved. Fig. 9 shows that since the curvature of the DMs is limited by the number of modes N , our solution does and discussed in § . 6. Eq. 47 assumes that the propagation between the two DMs occurs according to the laws of ray optics. In the next section we derive the actual diffractive field at DM2, e.g Eq. 16, and show that in the pupil remapping regime of ACAD, edge ringing due to the free space propagation is actually smaller than in the Fresnel regime.",
"pages": [
13,
14
]
},
{
"title": "5.1. Analytical expression of the diffracted field",
"content": "ACADis based on ray optics. It is an inherently broadband technique, and provided that the coronagraph is optimized for broadband performance ACAD will provide high contrast over large spectral windows. However, when taking into account the edge diffraction effects that are captured by the quadratic integral in Eq. 16, the true propagated field at DM2 becomes wavelength dependent. More specifically, when λ is not zero then the oscillatory integral superposes on the ray optics field a series of high spatial frequency oscillations. In theory, it would be best to use this as the full transfer function to include chromatic effects in the computation of the DMs shapes. However, as discussed in S. 4, solving the non-linear Monge-Ampere Equation is already a delicate exercise, and we thus have limited the scope of this paper to ray optics solutions. Nonetheless, once the DMs' shapes have been determined using ray optics, one should check whether or not the oscillations due to edge diffraction will hamper the contrast. This approach is reminiscent of the design of PIAA systems where the mirror shapes are calculated first using geometric optics and are then propagated through the diffractive integral in order to check a posteriori whether or not the chromatic diffractive artifacts are below the design contrast (Pluzhnik et al. 2005). In this section we detail the derivation of Eq. 16 that is the diffractive integral for the two DMs remapping system and use this formulation to discuss the diffractive properties of ACAD. not fully map out the discontinuities induced by the secondary supports and the segments. However, they are significantly thinner and one can expect that their impact on contrast will be attenuated by orders of magnitude. In order to quantify the final coronagraphic contrasts of our solution we then propagate it through an APLC coronagraph designed using the method in § . 2. In the case of a hexagon based primary (such as JWST), we use a coronographic apodizer with a slightly oversized secondary obscuration and undersize outer edge in order to circularize the pupil. Note that this choice is mainly driven by the type of coronagraph we chose in § . 2 to illustrate our technique. Since the DM control strategy presented in this section is independent of the coronagraph, it can be generalized to any of the starlight suppression systems which have been discussed in the literature. For succinctness we present our results using coronagraph solely based on using pupil apodization (either in an APLC or in a PIAAC configuration). Results for a JWST geometry are shown on Fig. 11 and Fig. 12 We start with the expression of the second order diffractive field at DM2 as derived in Pueyo et al. (2011), Eq. 13 . We write E DM 1 ( x, y ) as its inverse Fourier transform and insert this expression in Eq. 13. Completing the squares in the quadratic exponential factor then yields: with The integral over space, I 1 ( y 1 , x 1 ), is the integral of a complex gaussian and can be evaluated analytically. This",
"pages": [
14
]
},
{
"title": "Before DMs After DMs",
"content": "yields: We thus have expressed E DM 2 ( x 2 , y 2 ) as a function of ( x 1 , y 1 ) = ( f 1 ( x 2 , y 2 ) , g 1 ( x 2 , y 2 )). This expression can be further simplified: using Eqs. 20 to 22 one can derive ∂f 2 ∂x | ( x 1 ,y 1 ) = 1 det[ J ( x 2 ,y 2 )] ∂g 1 ∂y | ( x 2 ,y 2 ) and ∂g 2 ∂y | ( x 1 ,y 1 ) = 1 det[ J ( x 2 ,y 2 )] ∂f 1 ∂x | ( x 2 ,y 2 ) . Which finishes to prove Eq. 16: This expression is very similar to a modified Fresnel propagation and can be rewritten as such: Because of this similarity we call this integral the Stretched- Remapped Fresnel approximation (SR-Fresnel). Indeed in this approximation the propagation distance is stretched by ( ∂g 1 ∂y det [ J ] , ∂f 1 ∂x det [ J ] ) and the integral is centered around the remapped pupil ( f 1 , g 1 ).",
"pages": [
15
]
},
{
"title": "5.2. Discussion",
"content": "The integral form provides physical insight about the behavior of the chromatic edge oscillations. If we write we can identify a several diffractive regimes: In the case of a PIAA coronagraphs, the mirror shapes are such that Γ x , Γ y > 1 at the center of the pupil and Γ x , Γ y glyph[lessmuch] 1 at the edges of the pupil, where the discontinuities occur. As a consequence the edge oscillations are largely magnified when compared to Fresnel oscillations (see right panel of Fig. 10), and apodizing screens are necessary in order to reduce the local curvature of the mirror's shape (as also discussed in Pluzhnik et al. (2005); Pueyo et al. (2011)). In the case of ACAD, where the x-axis is chosen to be perpendicular to the discontinuity, the surface curvature is such that Γ x > 1, Γ y ∼ 1 at the discontinuities inside the pupil and Γ x > 1, Γ y ∼ 1 elsewhere. This yields damped chromatic oscillations at the remapped discontinuities and Fresnel oscillations at the edges of the pupil (see right panel of Fig. 10). Note that Fig. 10 was generated using a one dimensional toy model that assumes Eq. 16 is separable, e.g Γ y = 1, as described in Pueyo et al. (2011). In practice at the saddle points of the optical surfaces, near the junction of two spiders for instance, γ x > 1, Γ y < ∼ 1 and thus our separable model does not guarantee than in the true 2D case chromatic edge oscillations might not be locally amplified. However even near the saddle points ACAD provides a strong converging remapping in the direction perpendicular to the discontinuity and very little diverging re-mapping in the other direction. As a consequence Γ x glyph[greatermuch] 1 and Γ y is smaller than but close to one. We thus predict that even at these locations chromatic ringing will not be amplified. Even if ACAD based on pupil remapping, its diffraction properties are qualitatively very different from PIAA coronagraphs since edge ringing is not amplified beyond the Fresnel regime at the pupil edges, and is attenuated near the discontinuities. We conclude that in most cases ACAD operates in a regime where edge chromatic oscillations are not larger than classical Fresnel oscillations, and sometimes actually smaller. As a consequence the chromaticity of this ringing can be mitigated using standard techniques developed in the Fresnel regime and we do not expect this phenomenon to be a major obstacle to ACAD broadband operations. 5.3. Diffraction artifacts in ACAD are no worse than Fresnel ringing We have established that the diffractive chromatic oscillations introduced by the fact that DM1 and DM2 are /Slash1 /Slash1 not located in conjugate planes is no worse than classical Fresnel ringing from the aperture edges and can be mitigated using well-know techniques which have been developed for this regime. While a quantitive tradeoff study of how to design a high contrast instrument which minimizes such oscillations regime is beyond the scope of this paper, we briefly remind their qualitative essence to the reader: Note that these three solutions are not mutually exclusive and that only a full diffractive analysis, which uses robust numerical propagators that have been developed based on Eq. 16, can quantitatively address the tradeoffs discussed above. The development of such propagators is our next priority. In Pueyo et al. (2011) we laid out the theoretical foundations of such a numerical tool in the case of circularly symmetric pupil remapping and this solution has been since then practically implemented, as reported by Krist et al. (2010). Generalizing this method to a tractable propagator in the case of arbitrary remapping is a yet unsolved computational problem. In the meantime we emphasize that while the spectral bandwidth of coronagraphs whose incoming amplitude has been corrected using ACAD will certainly be",
"pages": [
15,
16
]
},
{
"title": "Coronagraph pupil with flat DMs",
"content": "/Slash1 /Slash1 to the methodology presenting above would allow this instrument to perform its scientific program at a very high contrast. Moreover the surface of the DMs could be adjusted to mitigate for the effect of missing segments at the surface of the primary (when for instance the telescope is operating while some segments are being serviced).",
"pages": [
20
]
},
{
"title": "Coronagraph pupil with actuated DMs",
"content": "Log[Contrast] 4. 4.6 5.8 Λ /Slash1 limited by edge diffraction effects, but these effects are no worse than Fresnel ringing and can thus be mitigated using optical designs which are now routinely used in high contrast instruments (see V'erinaud et al. (2010) for such discussions). For the remainder of this paper we thus assume the diffractive artifacts have been adequately mitigated and we compute our results assuming a geometric propagation between DM1 and DM2.",
"pages": [
17,
18
]
},
{
"title": "6.1. Application to future observatories 6.1.1. JWST",
"content": "We have illustrated each step of the calculation of the DM shapes in § . 4 using a geometry similar of JWST. This configuration is somewhat a conservative illustration of an on-axis segmented telescope as it features thick secondary supports and a 'small' number of segments whose gaps diffract light in regions of the image plane close to the optical axis (the first diffraction order of a six hexagons structure is located at ∼ 3 λ/D ). In order to assess the performances of ACAD on such an observatory architecture we chose to use a coronagraph designed around a slightly oversized secondary obscuration of diameter 0 . 25 D , with a focal plane mask of diameter 8 λ/D , an IWA of 5 λ/D and an OWA of 30 λ/D . The field at the entrance of the coronagraph after remapping by the DMs is shown on the top right panel of Fig. 11. The DMsurfaces, calculated assuming 64 actuators across the pupil ( N = 64 in the Fourier expansion) and DMs of diameter 3 cm separated by Z = 1 m, are shown on the middle panel of Fig. 11. They are well within the stroke limit of current DM technologies. The surfaces were calculated by solving the reverse problem over an even grid of 10 cutoff low-pass spatial frequencies ranging between 30 and 70 cycles per apertures for the tapering kernel ω . The value yielding the best contrast was chosen. Note that the optimal cutoff frequency depends on the spa- le of the discontinuities, and that higher contrasts could be obtained by choosing a set of two convolution kernels for the reverse problem and finding the optimal solution using a finer grid. However, the results in the bottom row of Fig. 11 are extremely promising. Fig. 12 shows a contrast improvement of a factor of 100 when compared to the raw coronagraphic PSF, which is quite remarkable for an algorithm which is not based on an image-plane metric. These results illustrate that even with a very unfriendly aperture similar to JWST one can obtain contrasts as high as envisioned for upcoming Ex-AO instruments, which have been designed for much friendlier apertures. While we certainly do not advocate to use such a technique on JWST, this demonstrates that ACAD is a powerful tool for coronagraphy with on-axis segmented apertures.",
"pages": [
18
]
},
{
"title": "6.1.2. Extremely Large Telescopes",
"content": "We now discuss the case of Extremely Large Telescopes and provide an illustration using the example of the Thirty Meter Telescope. We considered the aperture geometry shown on the top left panel of Fig. 13. It consists of a pupil 37 segments across in the longest direction and a secondary of diameter ∼ 0 . 12 D which is held by three main thick struts and six thin cables. As seen on the bottom left panel of Fig. 13 the impact of segment gaps is minor as they diffract light beyond the OWA of the coronagraph. When using a coronagraph with a larger OWA the segment gaps will have to be taken into account, and will have to be mitigated using DMs with a larger number of actuators. In order to obtain first order estimates of the performances of ACAD on the aperture geometry shown on the top left panel of Fig. 13, we chose to use a coronagraph designed around a slightly oversized secondary obscuration of diameter 0 . 15 D , with a focal plane mask of 6 λ/D diameter, an IWA of 4 λ/D and an OWA of 30 λ/D . The field at the entrance of the coronagraph after remapping by the DMs is shown on the top right panel of Fig. 13. The DM surfaces, calculated assuming 64 actuators across the pupil ( N = 64 in the Fourier expansion) and DMs of diameter 3 cm separated by Z = 1 m, are shown on the middle panel of Fig. 13. They are well within the stroke limit of current DM technologies. The surfaces were calculated by solving the reverse problem over an even grid of 10 cutoff low-pass spatial frequencies ranging between 30 and 70 cycles per apertures for the tapering kernel ω . The value yielding the best contrast was chosen. The final PSF is shown on the bottom right panel of Fig. 13 and features a high contrast dark hole with residual diffracted light at the location of the spiders' diffraction structures. The impact on coronagraphic contrast of secondary supports was thoroughly studied by Martinez et al. (2008). They concluded that under a 90% Strehl ratio, the contrast in most types of coronagraphs is driven by the secondary support structures to levels ranging from 10 -4 to 10 -5 . This, in turn, leads to a final contrast after postprocessing (called Differential Imaging) of ∼ 10 -7 -10 -8 . Fig. 14 shows that using ACAD on an ELT pupil yields contrasts before any post-processing which are comparable to the ones obtained by Martinez et al. (2008) after Differential Imaging. This demonstrates that should two sequential DMs be integrated into a future planet finding instrument, setting their surface deformation according Log[Contrast] 6.1 6.1 6.8 6.8 =7.5 Log[Contrast] 4.7",
"pages": [
18,
19
]
},
{
"title": "6.2.1. Constant area covered by the secondary support structures",
"content": "In the case of ELTs with large number of small segments (when compared to the aperture size), gaps diffract light far from the optical axis (see Fig. 13 for an example). The secondary support structures are then the major source of unfriendly coronagraphic diffracted light. Under the assumption that thick structures are necessary to support the heavy secondary over the very large ELT pupils, one can use the aperture area covered by the spiders as a proxy of the secondary lift constraint. We have thus explored a series of geometries for which the number of spiders increases as they get thinner while the overall area covered by the secondary support structures remains constant. In the examples shown from Fig. 15 to Fig. 18, the area covered by the secondary support structures is 1 . 5 times greater than in the TMT geometry discussed above. In all cases we used a coronagraph with a central obscuration of 0 . 15 D , with a focal plane mask of 6 λ/D diameter, and IWA of 4 λ/D and an OWA of 30 λ/D . The surfaces were calculated by solving the reverse problem over an even grid of 10 cutoff low-pass spatial frequencies ranging between 30 and 70 cycles per apertures for the tapering kernel. The value yielding the best contrast was chosen. This exercise leads to several conclusions pertaining to the performances of ACAD with various potential ELT geometries.",
"pages": [
20
]
},
{
"title": "Clocking of the spiders with respect to the DM",
"content": "The top two panels of Fig. 15 illustrate the importance of the clocking of the spiders with respect to the DMs actuator grid (or the Fourier grid in our case). When the secondary support structures are clocked by 45 · with respect to the DM actuators they are much more attenuated by ACAD, thus yielding higher contrast. This is an artifact of the Fourier basis set chosen and would be mitigated by using DMs whose actuator placement presents circular and azimuthal symmetries (Watanabe et al. 2008).",
"pages": [
20
]
},
{
"title": "Annulus in the PSF with a large number of spiders",
"content": "When the number of secondary support struts becomes very large ( > 20), an interesting phenomena occurs in the raw PSF: the spiders diffract light outside an annulus of radius N Spiders /π/D , just as spiderweb masks do in the case of shaped pupil coronagraphs (Vanderbei et al. 2003b). The 'bump' located beyond that spatial frequency is more difficult to attenuate using the DMs (see Fig. 15 for an illustration). ACAD creates small ripples at the edges of the remapped discontinuities and when too many discontinuities are in the vicinity of each other, then these ripples interfere constructively and hamper the starlight extinction level yielded by ACAD.",
"pages": [
20
]
},
{
"title": "A lot of thin spiders is more favorable than a few thick spiders",
"content": "In general decreasing the width of the spiders while increasing their number is beneficial to the contrast obtained after ACAD as illustrated on the radial averages on Fig. 16 and Fig. 18. When one increases the number of spiders while decreasing their width in a classical coronagraph, the peak intensity of the diffraction pattern of one spider decreases as the squared width of the spider. The radially averaged contrast improvement without ACAD is then somewhat lesser than the square of the spider thinning factor as it is mitigated by the increasing number of spiders. When using ACAD the spiders are seen by the coronagraph as much thinner than they actually are (by a factor τ ) and thus the peak intensity of their diffraction pattern is lower by a factor of τ 2 . Our numerical experiments show that τ increases when the spider width decreases. As consequence, the overall contrast gain after ACAD when decreasing the width of the spiders while increasing their number is greater than in the case of a classical coronagraph. When designing ELT secondary support structures and planning to correct for them using ACAD, increasing the number of spiders to 8 or even 12 has a beneficial impact on contrast as it enables each discontinuity to become thinner and thus to be corrected to higher contrast using the DMs. The PSFs of apertures with more than 12 spiders present diffraction structures which are poorly suited for correction with square DMs. While the contrast resulting from applying ACAD to such apertures is still a decreasing function of the number of spiders, Fig. 18 shows that the net contrast gain brought by the DM based remapping is smaller than in the more gentle cases of 12 spiders. The study presented on Fig. 15 to Fig. 18 remains to be fully optimized for each potential design of an ELT planet finding instrument (in particular using a finer grid of cutoff spatial frequencies). It however demonstrates the flexibility of ACAD for various aperture geometries and provides a first order rule of thumb to design telescope apertures",
"pages": [
20
]
},
{
"title": "Actuated DMs",
"content": "4 4.5 6.7 7.8 8.9 4 /Slash1 Λ D in case of an APLC If the incoming wavefront is written as ∆ h 1 and the solution of the Monge Ampere Equation for DM1 as h 0 1 then one can conduct the analysis in Eq. 6 to 12b using ˜ h 1 = h 0 1 + ∆ h 1 . Under the assumption that surface of DM2is set as ˜ h 2 in order to conserve Optical Path Length then one can re-write the remapping as ( ˜ f 1 , ˜ g 1 ) defined by: /Slash1 /LBracket1 /RBracket1 /Slash1 /LBracket1 /RBracket1 Moreover if edge ringing has been properly mitigated then the ray optics solution is valid and the field at DM2 can /Slash1 be written as:",
"pages": [
25,
26,
27
]
},
{
"title": "6.2.2. Monolithic on-axis apertures.",
"content": "When discussing the case of JWST we stressed the complexity associated with the optimization of ACAD in the presence of aperture discontinuities of varying width. Carrying out such an exercise would be extremely valuable to study the feasibility of the direct imaging of exoearth with an on-axis segmented future flagship observatory such as ATLAST (Postman et al. 2010). However, such an effort is computationally heavy and thus beyond the scope of the present paper, which focuses on introducing the ACAD methodology and illustrating using key basic examples. So far, none of the examples in this manuscript demonstrate that ACAD can yield corrections all the way down to the theoretical contrast floor that is set by the coronagraph design. When seeking to image exo-earths from space, future missions will need to reach this limit. In order to explore this regime, we conducted a detailed study of an hypothetical on-axis monolithic telescope with four secondary support struts. To establish the true contrast limits we varied the thickness of the spiders and for each geometries. The surfaces were calculated by solving the reverse problem over an even grid of 70 cutoff low-pass spatial frequencies ranging between 30 and 70 cycles per apertures for the tapering kernel. The value yielding the best contrast was chosen. In all cases we used a coronagraph with a central obscuration of 0 . 15 D , with a focal plane mask of 6 λ/D diameter, and IWA of 4 λ/D , and an OWA of 30 λ/D . Note that when using coronagraphs relying on pupil apodization these results can be readily generalized to larger circular secondary obscurations, at a loss in IWA (as shown on Fig. 2). Moreover we clocked the telescope aperture by 45 · with respect to the grid of Fourier modes. We found that, indeed, the theoretical contrast floor set by the coronagraph design is met for thin spiders (0 . 02 D ) and it is very close to be met for spiders only half the thickness of the the ones currently equipping the Hubble Space Telecope (0 . 05 D ), see Fig. 19 and Fig. 20. Even in the case of thick struts (0 . 1 D ) we find contrasts an order of magnitude higher than in the similar configuration on the top panel of Fig. 16, due to our thorough optimization of the cutoff frequency of the tapering kernel and careful clocking of the aperture with respect to the actuators. On-axis telescopes are thus a viable option to image earth-analogs from space: their secondary support structures can be corrected down to contrast levels comparable to the target contrast of recent missions concept studies (Guyon et al. 2008; Trauger et al. 2010). Since the baseline wavefront control architecture for future space coronagraphs relies on two sequential DMs, ACAD does not add any extra complexity to such missions and merely consists of controlling the DMs in order to optimally compensate for the effects of asymmetric aperture discontinuities. Λ",
"pages": [
22
]
},
{
"title": "Flat DMs",
"content": "16 spiders, 0.39 of D wide",
"pages": [
23
]
},
{
"title": "7.1. Field dependent distortion",
"content": "Because ACAD relies on deforming the DMs surfaces in an aspherical fashion, off-axis wavefronts seen through the two DMs apparatus will be distorted, just as in a PIAA coronagraph (Martinache et al. 2006). However the asphericity of the surfaces in the case of ACAD operating on reasonably thin discontinuities, is much smaller than in a PIAA remapping unit. Fig. 21 shows the impact on off-axis PSFs of such a distortion in the worsecase scenario of a geometry similar to JWST. We demonstrate that most of the flux remains in the central disk of radius λ/D for all sources in the field of view of the coronagraphs considered here (all the way to 30 cycles per capture). We conclude that, because of the small deformations of the DMs, PSF distortion will not be a major hindrance in exo-planet imaging instruments whose DMs are controlled in order to mitigate for discontinuities in the aperture. 7.2. Impact of wavefront discontinuities in segmented telescopes. 7.2.1. General equations in the presence of incident phase errors and discontinuities So far we have treated primary mirrors' segmentation as a pure amplitude effect. In reality the contrast floor in segmented telescopes will be driven by both phase and amplitude discontinuities: here we explore the impact of phase errors and discontinuities occurring before two DMs whose surfaces have been set using ACAD. There are two main phenomena to be considered. The first is the conversion of the incident wavefront phase before DM1: 2 π λ ∆ h 1 into amplitude at the second mirror. The second is the projection of this wavefront phase into a remapped phase errors at DM2: 2 π λ ∆ h 1 ( f 1 ( x 1 , y 2 ) , g 1 ( x 1 , y 2 )). Since the remapping unit is designed using deformable mirrors, both DM1 and DM2 a complete correction could be attained in principle. However, the deformable mirrors are continuous while ∆ h 1 presented discontinuities. Thus, complete corrections for segmented mirrors might not be achieved in practice. Below we discuss the following two main points. (1) Even if the phase wavefront error ∆ h 1 has discontinuities, the phase errors within in segment still drive the phase to amplitude conversion and thus the propagated amplitude at DM2. In that case treatments of these phenomenons that have already been discussed in the literature for monolithic apertures are still valid for small enough phase errors Eqs. 56-56 and smooth enough remapping functions. For ACAD remapping this smoothness constraint is naturally enforced by the limited number of actuators across the DM surface. In this case phase to amplitude conversion between can in principle be corrected using DM1. (2) Remapped phase discontinuities can be corrected for a finite number of spatial frequencies using a continuous phase sheet deformable mirror. We illustrate this partial correction over a 20% bandwidth using numerical simulations of a post-ACAD half dark hole created by superposing a small perturbation, computed using a linear wavefront control algorithm, to the ACAD DM2 surface.",
"pages": [
24
]
},
{
"title": "7.2.2. Impact on the amplitude after ACAD",
"content": "We first consider the amplitude profile in Eq. 57: it is composed of two factors the remapped telescope aperture, E DM 1 ( ˜ f 1 , ˜ g 1 ), and the determinant of Id + H [ ˜ h 1 ]. glyph[negationslash] The first condition necessary for the incoming wavefront not to perturb the ACAD solution is: ∆ h 1 is such that the remapping is not modified at the pupil locations where the telescope aperture is not zero E DM 1 = 0. This results into the conditions glyph[negationslash] glyph[negationslash] At the locations where E DM 1 = 0 there is no light illuminating the discontinuous wavefront and thus the large local slopes at these location have no impact on the remapping functions ( f 1 , g 1 ). These conditions are not true in segmented telescopes that are not properly phased, for which the tip-tilt error over each segment can reach several waves. However under the assumption that the primary has been properly phased (for instance the residual rms wavefront after phasing is expect to be ∼ 1 / 10 th of a wave, similar to values expected for JWST NIRCAM) then these conditions are true within the boundaries of each segment. Moreover, while the local wavefront slopes at the segment's discontinuities do not respect this condition the incident amplitude at these points is E DM 1 ( x, y ) = 0 and they thus do not perturb the ACAD remapping solution. The second necessary condition resides in the fact that the determinant of Id + H ( ˜ h 1 ) is not equal to det [ Id + H ( h 0 1 )] at the pupil locations where the telescope aperture is not zero ought not have a severe impact on contrast. One can use the linearization in Loeper & Rapetti (2005) to show that: The perturbation term ∆ A (∆ h 1 ) corresponds to the full non-linear expression of the phase to amplitude conversion of wavefront errors that occurs in pupil remapping units. In Pueyo et al. (2011) we derived a similar expression in the linear case, when ∆ h 1 glyph[lessmuch] λ and showed that in the pupil regions where the the beam is converging this phase to amplitude conversion was enhanced when compared to the case of a Fresnel propagation. In a recent study Krist et al. (2011) presented simulations predicting that this effect was quite severe in PIAA coronagraphs and can limit the broadband contrast after wavefront control unless DMs where placed before the remapping unit. In principle ACAD will not suffer from this limitation as the first aspherical surface of the remapping unit is actually a Deformable Mirror that can actually compensate for ∆ h 1 , before any phase to amplitude wavefront modulation occurs. Devising a wavefront controller that relies on DM1 requires moreover a computationally efficient model to propagate arbitrary wavefronts thought ACAD. Such a tool was developed in Krist et al. (2010) assuming azimuthally symmetric geometries. Since devising such a tool in ACAD's case, in the asymmetric case, represents a substantial effort well beyond the problem of prescribing ACAD DM shapes, we chose not to include such simulations in the present manuscript. Since we are using Deformable Mirrors with a limited number of actuators, ACAD remapping is in general less severe than in the case of PIAA. We thus expect the results regarding the wavefront correction before the remapping unit reported in Krist et al. (2011) to hold. This is provided that the DM actuators can adequately capture the high spatial frequency content of ∆ h 1 to create a dark hole in the coronagraphic PSF. We tackle this particular aspect next when discussing the case of phase errors, in the absence of wavefront phase to amplitude conversion. Once again note that while the local wavefront curvatures are very large at the segment's discontinuities, the incident amplitude at these points is E DM 1 ( x, y ) = 0 and they thus they do not have an impact on the ACAD phase to amplitude modulation. In practice if the DM is not exactly located at a location conjugate to the telescope pupil the actual wavefront discontinuities will be slightly illuminated and might perturb the remapping functions and the phase to amplitude conversion. While this might tighten requirements regarding the positioning of DM1 in the direction of the optical axis we do not expect this effect to be a major obstacle to successful ACAD implementations.",
"pages": [
27
]
},
{
"title": "7.2.3. Impact on the phase after ACAD",
"content": "In practice, when ∆ h 1 presents discontinuities, the surface of DM2 cannot be set to the deformation ˜ h 2 that Wavefront at the coronagraph entrance nm 190.1 1.9 118.3 3.2 46.6 96.8 168.6 5.8 4.5 5.8 Contrast conserves Optical Path Length, since we work under the assumption that the DMs has a continuous phase-sheet. While this has no impact on the discussion above regarding the amplitude of E DM 2 , since DM1 is solely responsible for this part, it ought to be taken into account when discussing the phase at DM2. Under the assumption that ∆ h 1 does not perturb the nominal ACAD remapping function then one can show that the phase at DM2 is: where ∆ h 2 ( x 2 , y 2 ) is a small continuous surface deformation superposed to the ACAD shape of DM2 and ∆ h 1 ( f 0 1 ( x 2 , y 2 ) , g 0 1 ( x 2 , y 2 )) is the telescope OPD seen through the DM based remapping unit. This second term presents phase discontinuities whose spatial scale has been contracted by ACAD. When these discontinuities are very small then their high spatial frequency content does not disrupt the ability of DM2 to correct for low to mid-spatial frequency wavefront errors wavefront errors. However as the discontinuities become larger their high spatial frequency content can fold into the region of the PSF that the DMs seek to cancel. These 'frequency folding' speckles are highly chromatic (Give'on et al. 2006) and can have a severe impact on the spectral bandwidth of a coronagraph whose wavefront is corrected using a continuous DM. In order to assess the impact of this phenomenon, we conducted a series of simulations based on single DM wavefront control algorithm that seeks to create a dark hole in one half of the image plane at in as in Bord'e & Traub (2006). We use the example of a geometry similar to JWST and work under the assumption that the discontinuous wavefront incident to the coronagraph has the same spatial frequency content as a JWST NIRCAM Optical Path Difference that has been adjusted to 70 nm rms in order to mimic a visible Strehl similar to the near-infrared Strehl of JWST. The non-linear wavefront and sensing and control problem associated with phasing a primary mirror to such level of precision is undoubtedly a colossal endeavor and is well beyond the scope of this paper. In this section we work under the assumption that the primary mirror either has been phased to such a level, that the wavefront discontinuities are no larger than 200 nm peak to valley or that the wavefront has been otherwise corrected down to this specification using a segmented Deformable Mirror that is conjugate with the primary mirror. Moreover we assume (1) that the residual post-phasing wavefront map has been characterized and can be used in order to build the linear model underlying the wavefront controller (2) the focal plane wavefront estimator (carried using DM diversity as in Bord'e & Traub (2006) for instance) is capable to yield an exact estimate of the complex electrical field at the science camera. Underlying this last assumption is the overly optimistic premise that wavefront will remain unchanged over the course of each high-contrast exposure. While this is not a realistic assumption one could envision the introduction of specific wavefront sensing schemes, with architectures similar to the one currently considered for low order wavefront sensors on monolithic apertures (Guyon et al. 2009; Wallace et al. 2011), or using a separate metrology system. The results presented here are thus limited to configurations for which segment phasing will be dynamically compensated using specific sensing and control beyond the scope of this paper. As this section merely seeks to address the controllability of wavefront errors in segmented telescopes we chose to conduct our simulations with a perfect estimator. Finally we use the stroke minimization wavefront control algorithm presented in Pueyo et al. (2009) to ensure convergence for as many iteration as possible. We first tested the case of a segmented telescope in the absence of ACAD, using a azimuthally symmetric coronagraph and a single DM. We sough to create a Dark Hole between 5 and 28 λ 0 /D under a 20% bandwidth with λ 0 = 700 nm. Fig 22 shows the results of such a simulation. The DM can indeed correct for the discontinuities over a broadband in one half of the image plane. However the wavefront control algorithm seeks to compensate for the diffractive artifacts associated with the secondary support structures: it attenuates them on the right side of the PSF while it strengthens them on the left side of the PSF. As a result the DM surface becomes too large at the pupil spider's location and the quasi-linear wavefront control algorithm eventually diverges for contrasts ∼ 10 6 . We then proceeded to simulate the same configuration in the presence of two DMs whose surface at rest was calculated using ACAD. Since there does not exist a model yet to propagate arbitrary wavefronts through ACAD (the models in Krist et al. (2011) only operate under the assumption of an azimuthally symmetric remapping) we can only use the second DM for wavefront control. We work under the assumption that the incident wavefront does not perturb the nominal ACAD remapping (which is true in the case of the surface map we chose for our example) and that the arguments in Krist et al. (2010) hold so that phase to amplitude conversion in ACAD can be compensated by actuating DM1. Frequency folding will then be the phenomenon responsible for the true contrast limit. In this section we are interested in exploring how this impacts the controllability of wavefront discontinuities using continuous phase-sheet DMs. We used a azimuthally symmetric coronagraph and superposed our wavefront control solution to DM2. We sough to create a Dark Hole between 5 and 28 λ 0 /D under a 20% bandwidth with λ 0 = 700 nm. Fig 22 shows the results of such a simulation. When the incident wavefront is small enough it is indeed possible to superpose a 'classical linear wavefront control' solution to the non-linear ACAD DM shapes in order to carve PSF dark holes. The wavefront control algorithm now yields a DM surface that does not feature prominent deformations at the location of the spiders. Most of the DM stroke is located at the edge of the segments, at location of the wavefront discontinuities and seek to correct the frequency folding terms associated with such discontinuities. At these locations the DM surface eventually becomes too large and the linear wavefront control algorithm diverges. However this divergence occurs at contrast levels much higher than when the ACAD solution is not applied to the DMs. These simulations show that indeed discontinuous phases can be corrected using the second DM of a ACAD whose surfaces have preliminary been set to mitigate the effects of spiders and segment gaps.",
"pages": [
27,
28,
29,
30
]
},
{
"title": "7.3. Ultimate contrast limits",
"content": "Assuming that edge ringing has been properly mitigated, so that the ray optics approximation underlying the calculation of the DMs shapes is valid, one can wonder about the ultimate contrast limitations of the results presented in this manuscript. Increasing the number of actuators would have dramatic effects on contrast if the actuator count would be such that N > D/d where d is the scale of the aperture discontinuities. Unfortunately current DM technologies are currently far from such a requirement and the solutions presented here are in the regime where N glyph[lessmuch] D/d . In this regime N only has a marginal influence on contrast when compared to the impact of the cutoff frequency of the tapering kernel. In the regime described here varying the actuator count only changes the size of the corrected region. The residual PSF artifacts in Figs. 11 to 20 follow the direction of the initial diffraction pattern associated with secondary support structures and segments. When addressing the problem of aperture discontinuities by solving the Monge-Ampere Equation, ACAD calculates the DM shapes based on a pupil plane metric and thus mostly focuses on attenuating these structures with little regard to the final contrast. It is actually quite remarkable that such a pupil-only approach yields levels of starlight extinction of two to three orders of magnitude. A more appropriate metric would be the final intensity distribution in the post-coronagraphic image plane. However, as discussed in § . 3 classical wavefront control algorithms based on a linearization of the DMs deformations around local equilibrium shapes (such as the ones presented in Bord'e & Traub (2006); Give'on et al. (2007) in the one DM case or Pueyo et al. (2009) for one or two DMs) cannot be used to compensate the full aperture discontinuities. This is illustrated in Fig 22, where the DM surface in the vicinity of spiders becomes too large after a certain number of iterations, which leads the iterative algorithm to diverge. When attempting to circumvent this problem by recomputing the linearization at each iteration, we managed to somewhat stabilize the problem for a few iterations and reached marginal contrast improvements, but the overall algorithm remained unstable unless a prohibitively small step size was used. This is the problem which motivated our effort to calculate the DM shapes as the full non-linear solution of the Monge-Ampere Equation. While doing so yields significant contrast improvements in both the case of JWST like geometries, TMT and on axis-monolithic apertures similar, this approach does not give a proper weight to the spatial frequencies of interest for high contrast imaging. We mitigated this effect by giving a strong weight to the spatial frequencies of interest (in the Dark Hole) when solving the Monge Ampere Equation. The next natural step is thus to use non-linear solutions presented herein to correct for the bulk of the aperture discontinuities and to serve as a starting point for classical linearized waveform control algorithms, as illustrated on Fig. 25. Fig. 24 indeed illustrates that when superposing an image plane based wavefront controller to the Monge Ampere ACAD solution, the contrast can be improved beyond the floor shown on Fig. 12. However one DM solutions, are of limited interest as they only operate efficiently over a finite bandwidth and over half of the image plane. ACAD yields a true broadband solution, and consequently it would be preferable to use the two DMs in the quasi-linear regime to quan- tify the true contrast limits of ACAD . In such a scheme the DM surfaces are first evaluated as the solution of the Monge-Ampere Equation and then adjusted using the image plane based wavefront control algorithm presented in Pueyo et al. (2009). However such an exercise requires efficient and robust numerical algorithms to evaluate Eq. 16. Such tool only exist so far in the case of azimuthally symmetric remapping units (Krist et al. 2010). Developing such numerical tools is thus of primary interest to both quantifying the chromaticity and the true contrast limits achievable with on-axis and/or segmented telescopes.",
"pages": [
30,
31
]
},
{
"title": "8. CONCLUSION",
"content": "We have introduced a technique that takes advantage of the presence of Deformable Mirrors in modern highcontrast coronagraph to compensate for amplitude discontinuities in on-axis and/or segmented telescopes. Our calculations predict that this high throughput class of solutions operates under broadband illumination even in the presence of reasonably small wavefront errors and discontinuities. Our approach relies on controlling two sequential Deformable Mirrors in a non-linear regime yet unexplored in the field of high-contrast imaging. Indeed the mirror's shapes are calculated as the solution of the twodimensional pupil remapping problem, which can be expressed as a non-linear partial differential equation called Monge Ampere Equation. We called this technique Active Compensation of Aperture Discontinuities. While we illustrated the efficiency of ACAD using Apodized Pupil Lyot and Phase Induced Amplitude Coronagraph, it is is applicable to all types of coronagraphs and thus enables one to translate the past decade of investigation in coronagraphy with unobscured monolithic apertures to a much wider class of telescope architectures. Because ACAD consists of a simple remapping of the telescope pupil, it is a true broadband solution. Provided that the coronagraph chosen operates under a broadband illumination, ACAD allows high contrast observations over a large spectral bandwidth as pupil remapping is an achromatic phenomenon. We showed that wavelength edge diffraction artifacts, which are the source of spectral bandwidth limits in PIAA coronagraphs (also based on pupil remapping), are no larger than classical Fresnel ringing. We thus argued that they will only marginally impact the spectral bandwidth of a coronagraph whose input beam has been corrected with ACAD. The mirror deformations we find can be achieved, both in curvature and in stroke, with technologies currently used in Ex-AO ground based instruments and in various testbeds aimed at demonstrating high-contrast for space based applications. Implementing ACAD on a given on-axis and/or segmented thus does not require substantial technology development of critical components. For geometries analogous to JWST we have demonstrated that ACAD can achieve at least contrast ∼ 10 -7 , provided that dynamic high precision segment phasing can be achieved. For TMT and ELT, ACAD can achieve at least contrasts ∼ 10 -8 . For on-axis monolithic observatories the design contrast of the coronagraph can be reached with ACAD when the secondary support structures are 5 times thinner than on HST. When they are just as thick as HST contrasts as high as 10 8 can be reached. These numbers are, however, conservative: an optimal solution can be obtained by fine tuning the control term in the Monge Ampere Equation to the characteristic scale of each discontinuity. As our goal was to introduce this technique to the astronomical community and emphasize its broad appeal to a wide class of architectures (JWST,ATLAST,HST,TMT,E-ELT) we left this observatory specific exercise for future work. The true contrast limitation of ACAD resides in the fact that the Deformable Mirrors are controlled using a pre-coronagraph pupil based metric. However, as illustrated in Fig. 25, the solution provided by ACAD can be used as the starting point for classical linearized waveform control algorithms based in image plane diagnostics. In such a control strategy, the surfaces are first evaluated as the solution of the Monge- Ampere Equation and then adjusted using the quasi-linear method presented in Pueyo et al. (2009). This control strategy requires efficient and robust numerical algorithms to evaluate the full diffractive propagation in the remapped Fresnel regime. All the contrasts reported here are achieved without aberrations and we showed that in practice, quasi-linear DM controls based on images at the science camera will have to be superposed to the ACAD solutions. Finally, as ACAD is broadly applicable to all types of coronagraphs, the remapped pupil can be used as the entry point to relax the design of coronagraphs that do operate on segmented apertures such as discussed in Carlotti et al. (2011); Guyon et al. (2010a), also illustrated in Fig. 25. ACAD is thus a promising tool for future high contrast imaging instruments on a wide range of observatories as it will allow astronomers to devise high through- put broadband solutions for a variety of coronagraphs. It only relies on hardware (Deformable Mirrors) that have been extensively tested over the past ten years. Finally since ACAD can operate with all type of coronagraphs and it renders the last decade of research on high-contrast imaging technologies with off-axis unobscured apertures applicable to much broader range of telescope architectures. The authors thank Dr Bruce Macintosh who steered our attention towards this problem and provided invaluable guidance in the early stages of this manuscript. The authors also thank the anonymous referee for insightful comments which greatly improved this manuscript, Dr Remi Soummer, Dr Marshall Perrin, Prof. N. Jeremy Kasdin and Prof. Robert Vanderbei for very helpful discussions and Matt Sheckells for his help coding the linear wavefront control algorithms. This material is partially based upon work supported by the National Aeronautics and Space Administration under Grant NNX12AG05G issued through the Astrophysics Research and Analysis (APRA) program . This work was performed in part under contract with the California Institute of Technology funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute.",
"pages": [
31,
32
]
},
{
"title": "REFERENCES",
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2013ApJ...770...49O
https://arxiv.org/pdf/1304.7007.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_84><loc_88><loc_86></location>MODELING THE ATOMIC-TO-MOLECULAR TRANSITION AND CHEMICAL DISTRIBUTIONS OF TURBULENT STAR-FORMING CLOUDS</section_header_level_1>
<text><location><page_1><loc_42><loc_82><loc_57><loc_83></location>Stella S. R. Offner</text>
<text><location><page_1><loc_57><loc_83><loc_58><loc_83></location>∗</text>
<text><location><page_1><loc_30><loc_81><loc_70><loc_82></location>Department of Astronomy, Yale University, New Haven, CT 06511</text>
<section_header_level_1><location><page_1><loc_43><loc_78><loc_57><loc_78></location>Thomas G. Bisbas</section_header_level_1>
<text><location><page_1><loc_20><loc_76><loc_81><loc_77></location>Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6B</text>
<section_header_level_1><location><page_1><loc_46><loc_73><loc_54><loc_73></location>Serena Viti</section_header_level_1>
<text><location><page_1><loc_20><loc_71><loc_81><loc_72></location>Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6B</text>
<section_header_level_1><location><page_1><loc_44><loc_68><loc_56><loc_69></location>Thomas A. Bell</section_header_level_1>
<text><location><page_1><loc_24><loc_65><loc_78><loc_68></location>Centro de Astrobiolog'ıa (CSIC-INTA), Carretera de Ajalvir, km 4, 28850 Madrid, Spain Draft version March 7, 2022</text>
<section_header_level_1><location><page_1><loc_45><loc_63><loc_55><loc_64></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_42><loc_86><loc_62></location>We use 3d-pdr , a three-dimensional astrochemistry code for modeling photodissociation regions (PDRs), to post-process hydrodynamic simulations of turbulent, star-forming clouds. We focus on the transition from atomic to molecular gas, with specific attention to the formation and distribution of H, C + , C, H 2 and CO. First, we demonstrate that the details of the cloud chemistry and our conclusions are insensitive to the simulation spatial resolution, to the resolution at the cloud edge, and to the ray angular resolution. We then investigate the effect of geometry and simulation parameters on chemical abundances and find weak dependence on cloud morphology as dictated by gravity and turbulent Mach number. For a uniform external radiation field, we find similar distributions to those derived using a one-dimensional PDR code. However, we demonstrate that a three-dimensional treatment is necessary for a spatially varying external field, and we caution against using one-dimensional treatments for non-symmetric problems. We compare our results with the work of Glover et al. (2010), who selfconsistently followed the time evolution of molecule formation in hydrodynamic simulations using a reduced chemical network. In general, we find good agreement with this in situ approach for C and CO abundances. However, the temperature and H 2 abundances are discrepant in the boundary regions (Av ≤ 5), which is due to the different number of rays used by the two approaches.</text>
<text><location><page_1><loc_14><loc_41><loc_26><loc_42></location>Subject headings:</text>
<text><location><page_1><loc_27><loc_39><loc_86><loc_42></location>astrochemistry, hydrodynamics, molecular processes, turbulence, stars: formation, ISM:molecules</text>
<section_header_level_1><location><page_1><loc_22><loc_36><loc_35><loc_37></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_8><loc_48><loc_35></location>In the local universe, stars appear to form exclusively in cold, dense clouds of predominately molecular gas (McKee & Ostriker 2007). Understanding the evolution of these molecular clouds (MCs) and the formation of stars within them is a fundamental problem in astrophysics that is hampered by distance, projection effects, and the high optical depth in these regions. Probing the mass and velocity distributions of the gas is further complicated by the fact that the most abundant molecule, H 2 , lacks a dipole moment. The next most abundant molecule, CO, which is commonly used to probe the cold molecular gas distribution in lieu of H 2 , has a typical average abundance of about one per 10 4 H 2 molecules in the Milky Way. In addition, the relationship between CO abundance and total gas mass is a complicated one that depends upon metallicity, the three-dimensional radiation field, the abundances of other molecules, and dust chemistry (Bell et al. 2006; Glover & Mac Low 2011; Shetty et al. 2011). Accurately modeling the formation of H 2 and the relative abundances of homologous molecules</text>
<text><location><page_1><loc_52><loc_33><loc_92><loc_37></location>such as CO requires following complex chemical reaction networks that encompass hundreds of species and thousands of reactions.</text>
<text><location><page_1><loc_52><loc_9><loc_92><loc_33></location>Traditionally, the computational expense of evolving large chemical networks limited astrochemical investigations to simple one-dimensional hydrodynamic models (e.g., Bergin et al. 2004) or to post-processing (e.g., Levrier et al. 2012). However, in recent years 'reduced' chemical networks have been adopted to investigate chemistry concurrently with three-dimensional hydrodynamics (Nelson & Langer 1997, 1999; Pavlovski et al. 2002, 2006; Glover & Mac Low 2007a,b; Glover et al. 2010). Such methods have the advantage of being able to follow the temperature evolution of the gas due to UV heating and atomic and molecular cooling, which in principle influences the gas dynamics since shock jump conditions depend upon the local temperature. Nonetheless, the expense of following the molecular evolution in situ necessitates various simplifications, including neglect of dust physics and coarse treatment of the radiation field.</text>
<text><location><page_1><loc_52><loc_5><loc_92><loc_8></location>Thus far, turbulent cloud calculations including simplified chemistry have also focused on larger cloud complexes and generally neglected the self-gravity of the</text>
<text><location><page_2><loc_8><loc_75><loc_48><loc_91></location>gas (see Glover & Clark 2012 as an exception including gravity). Neglecting gravity obviates the need for considerable additional resolution which would otherwise be required to resolve collapsing gas (Truelove et al. 1997). In addition, without forming embedded sources to provide additional radiation (e.g., Offner et al. 2009; Krumholz et al. 2007), heating depends only on the external cloud environment, leading to simpler radiative conditions. The gas temperature range induced by a standard external interstellar radiation field is generally limited ( glyph[lessorsimilar] 100K) and deviates from 10 K mainly at low Av.</text>
<text><location><page_2><loc_8><loc_56><loc_48><loc_75></location>Despite such simplifications, the astrochemistry under investigation is rich and not well understood. For example, cloud boundary regions are especially interesting because this is where gas transitions from being ionized and atomic to predominantly molecular. These low-Av transitions areas are by definition PDRs, where FUV photons dominate the energy balance and gas chemistry. PDRs are ubiquitous in the interstellar medium and are the source of most of the infrared radiation in galaxies. The recent development of 3d-pdr (Bisbas et al. 2012, hereafter B12), which is the first dedicated PDR code able to treat arbitrary three-dimensional density distribution, now allows the accurate study of these regions in more complex structures.</text>
<text><location><page_2><loc_8><loc_34><loc_48><loc_56></location>We dedicate this paper to three main goals. First, we compare 3D and 1D treatments of a complex PDR region in order to evaluate the impact of dimensionality on chemical results. Thus, we extend the work of B12, who demonstrated the importance of higher dimensional treatment in accurately modeling simple 3D problems, to consider complex, turbulent gas distributions. Second, we use self-gravitating, hydrodynamic simulations of molecular clouds with different Mach numbers to evaluate the importance of underlying physical parameters on chemical abundances and distributions. Finally, we explore the differences between two astrochemistry approaches by considering results obtained via postprocessing using 3d-pdr and results obtained from a chemical network calculation preformed 'in situ' (e.g., Glover et al. 2010).</text>
<text><location><page_2><loc_8><loc_21><loc_48><loc_34></location>The paper is organized as follows. In section 2 we describe the 3d-pdr methodology and our hydrodynamic numerical simulations. In section 3 we validate our choice of spatial resolution by presenting convergence studies of grid-sampling in the cloud interior and at the cloud boundaries. We present our results in section 4, including a comparison to Glover et al. (2010) and discussions of chemical dependence on domain dimensionality, external radiation field, and cloud physical parameters. Section 5 contains a discussion of future work and conclusions.</text>
<section_header_level_1><location><page_2><loc_24><loc_18><loc_33><loc_19></location>2. METHODS</section_header_level_1>
<section_header_level_1><location><page_2><loc_17><loc_16><loc_39><loc_17></location>2.1. Hydrodynamic Simulations</section_header_level_1>
<text><location><page_2><loc_8><loc_4><loc_48><loc_15></location>In this paper, we analyze snapshots of four different hydrodynamic simulations of turbulent molecular clouds. The simulation parameters are summarized in Table 1. Three of the simulations (Rm4, Rm6 and Rm9) are performed with the orion adaptive mesh refinement (AMR) code (Truelove et al. 1998; Klein 1999). Since these simulations have not been previously published, we describe our method in detail below.</text>
<text><location><page_2><loc_52><loc_87><loc_92><loc_91></location>orion employs a conservative second order Godunov scheme to solve the equations of compressible gas dynamics:</text>
<formula><location><page_2><loc_64><loc_84><loc_92><loc_87></location>∂ρ ∂t + ∇· ( ρ v ) = 0 , (1)</formula>
<formula><location><page_2><loc_62><loc_81><loc_92><loc_83></location>∂ρ v ∂t + ∇· ( ρ vv ) = -∇ P -ρ ∇ φ, (2)</formula>
<formula><location><page_2><loc_59><loc_78><loc_92><loc_80></location>∂ρe ∂t + ∇· [( ρe + P ) v ] = ρ v ∇ φ, (3)</formula>
<text><location><page_2><loc_52><loc_72><loc_92><loc_77></location>where ρ , P , v are the gas density, pressure, and velocity, respectively. Here, e is the total energy e = 1 2 ρ v 2 + P γ -1 , where γ is the ratio of specific heats. orion solves the Poisson equation for the gravitational potential, φ :</text>
<formula><location><page_2><loc_59><loc_67><loc_92><loc_71></location>∇ 2 φ = 4 πG [ ρ + ∑ n m n δ ( x -x n ) ] , (4)</formula>
<text><location><page_2><loc_52><loc_64><loc_92><loc_66></location>where m n and x n are the mass and position of the n th star, respectively.</text>
<text><location><page_2><loc_52><loc_61><loc_92><loc_63></location>We close these equations with an isothermal equations of state:</text>
<formula><location><page_2><loc_67><loc_58><loc_92><loc_61></location>P = ρ k B T µ p m H , (5)</formula>
<text><location><page_2><loc_52><loc_28><loc_92><loc_57></location>where k B is the Boltzmann constant, µ p = 2 . 33 is the mean mass per particle, m H is the hydrogen mass, and T = 10 K is the isothermal gas temperature. Authors sometimes adopt a barotropic equation of state (e.g., Offner et al. 2008), which sets a characteristic density above which the gas becomes optically thick and ceases to be isothermal. However, the density at which this occurs, ρ c ∼ 10 -14 g cm -3 , as calculated using full radiative transfer (Masunaga et al. 1998), exceeds the maximum density at our maximum AMR resolution ( ∼ 5 × 10 -16 g cm -3 ). Consequently, the isothermal approximation is appropriate here. Alternatively, we might solve for the radiation field using a flux-limited diffusion (FLD) approach and thus take into account heating from forming stars (Offner et al. 2009). This would be more numerically expensive but more physically accurate in the dense star-forming gas. However, without some prescription for protostellar outflows the stellar heating in the calculation would be an over-estimate (Hansen et al. 2012), and moreover, an FLD approach would not supply more accurate information about the temperatures of the lowextinction gas as 3d-pdr does.</text>
<text><location><page_2><loc_52><loc_25><loc_92><loc_28></location>We insert finer AMR grids when the local density violates the Truelove criterion (Truelove et al. 1997):</text>
<formula><location><page_2><loc_63><loc_21><loc_92><loc_24></location>ρ < ρ J = J 2 πk B T Gµ p m H ∆ x 2 l , (6)</formula>
<text><location><page_2><loc_52><loc_13><loc_92><loc_20></location>where ∆ x l is the cell size on level l and we adopt a Jeans number of J = 0 . 125. A sink particle is inserted when the gas exceeds the Jeans density for J = 0 . 25 on the maximum level (Krumholz et al. 2004). In this paper, we do not analyze the sink particle distribution and properties; these are the subject of Kirk et al. (in preparation).</text>
<text><location><page_2><loc_52><loc_4><loc_92><loc_12></location>We initialize the simulations with uniform density and then perturb the gas for three crossing times using a random velocity field (e.g., Mac Low 1999). This field has a flat power spectrum for wavenumbers k = 1 .. 2, which corresponds to physical scales of L..L/ 2. We re-normalize the perturbations to maintain a constant</text>
<figure>
<location><page_3><loc_17><loc_38><loc_84><loc_91></location>
<caption>Fig. 1.Total gas column density for orion snapshots Rm6 1.0 (top left), Rm9 1.0 (top right), Rm6 0.0 (bottom left), Rm4 1.0 (bottom right). The snapshot times are 1 t ff , 1 t ff , 0 t ff , and 1 t ff , respectively.</caption>
</figure>
<text><location><page_3><loc_8><loc_25><loc_48><loc_33></location>cloud velocity dispersion. In the fiducial simulation, Rm6, the Mach number is chosen to satisfy the observed linewidth-size relation (McKee & Ostriker 2007). Following the driving initialization, the simulations achieve a well-mixed turbulent state and we turn on gravity, allowing collapse to proceed for a global free-fall time.</text>
<text><location><page_3><loc_8><loc_14><loc_48><loc_25></location>The orion simulations all have a 256 3 base grid and four levels of AMR refinement. As summarized in Table 1, these three calculation have a total gas mass of 600 M glyph[circledot] , domain size of 2 pc (∆ x 4 = 100 AU), and turbulent 3D Mach numbers of 4.2, 6.6 and 8.9. For comparison, we also analyze Rm6 without gravity, i.e., at t = 0 t ff , and at half a free-fall time. Figure 1 shows the integrated column density at one free-fall time for these runs.</text>
<text><location><page_3><loc_8><loc_6><loc_48><loc_14></location>We include the third simulation, n300, in order to directly compare our PDR methodology to that of Glover et al. (2010), henceforth G10. The n300 simulation was performed by S. Glover with a modified version of ZEUSMP , which tracks the abundances of 32 chemical species. The n300 calculation uses a fixed 256 3 grid. Turbulence</text>
<text><location><page_3><loc_52><loc_26><loc_92><loc_33></location>is generated using random velocity perturbations in a manner similar to that used for the orion simulations. It does not include self-gravity but does solve the equations of ideal magneto-hydrodynamics and begins with an initially uniform magnetic field of 6 µ G.</text>
<text><location><page_3><loc_52><loc_10><loc_92><loc_26></location>Figure 2 shows the mass-weighted and volumeweighted density distributions and corresponding chemical regimes for each of the orion snapshots. The density distribution functions exhibit a characteristic lognormal shape as expected for supersonic turbulent gas (e.g., Padoan et al. 1997; Kritsuk et al. 2007). As self-gravity becomes important, the density distribution grows a high-density tail (Mac Low & Klessen 2004). The cells at the peak of the density distribution fall into the PDR regime for the simulation parameters we adopt. The vertical lines in the histogram indicate the division between ionized, PDR and molecular gas.</text>
<section_header_level_1><location><page_3><loc_67><loc_8><loc_76><loc_9></location>2.2. 3d-pdr</section_header_level_1>
<text><location><page_3><loc_52><loc_4><loc_92><loc_7></location>3d-pdr (Bisbas et al. 2012) is a three-dimensional time-dependent astrochemistry code for treating pho-</text>
<figure>
<location><page_4><loc_17><loc_68><loc_48><loc_90></location>
</figure>
<figure>
<location><page_4><loc_52><loc_68><loc_84><loc_90></location>
<caption>Fig. 2.Density distributions for runs Rm9 1.0 12 (black, solid), Rm6 1.0 12 (red, dot), Rm4 1.0 12 (purple, dash), Rm6 0.5 12 (blue, dot-dash), and Rm6 0.0 12 (green, dot-dot-dash). The gas state is characterized as ionized (left), PDR (middle) or molecular (right), where vertical lines indicate the state boundaries.</caption>
</figure>
<text><location><page_4><loc_8><loc_42><loc_48><loc_62></location>todissociation regions (PDRs) of arbitrary density distribution. The code is able to solve self-consistently the chemistry and the thermal balance within any threedimensional cloud. It uses an escape probability approximation (or Large Velocity Gradient - Sobolev 1960; Castor 1970; de Jong et al. 1975) to compute the cooling functions. To do this, 3d-pdr uses a ray tracing scheme in which the directions of the rays are controlled by the healpix algorithm (G'orski et al. 2005). This ray tracing scheme creates a discrete set of evaluation points by projecting the elements of the cloud along each ray. It can thus evaluate the column densities, the attenuation of the far ultraviolet radiation into the PDR, and the propagation of the FIR/submm line emission out of the PDR.</text>
<text><location><page_4><loc_8><loc_6><loc_48><loc_42></location>As a further development of the fully bench-marked one-dimensional ucl pdr code (Bell et al. 2006), 3dpdr adopts the same chemical model features. For the simulations presented in this paper, we use a chemical network which is a subset of the UMIST data base of reaction rates (Woodall et al. 2007). This 'reduced' network consists of 320 reactions and 33 species (including electrons). However, 3d-pdr also includes heating due to photoionization and photodissociation reactions in addition to the standard gas-phase chemistry. Self-shielding of H 2 and CO against photodissociation is accounted for. Comprehensive treatment of various gas heating mechanisms (i.e., photoelectric heating from dust grains and PAHs, collisional de-excitation of vibrationally excited H 2 following FUV pumping, photoionization of neutral carbon, cosmic ray heating) and emission from major cooling lines ([CII], [CI], [OI], CO) are calculated at each element. 3d-pdr also includes turbulent heating, which is proportional to v 3 TURB /L , where v TURB is the turbulent velocity and L is the integral scale. Here, we adopt constant values of L = 5 pc and v TURB = 1kms -1 . In practice, L should be set to the simulation domain size and v TURB to the 1D turbulent Mach number times the mean sound speed, however we find that the turbulent heating is small compared to photoelectric, cosmic-ray and chemical heating, which are the other main sources of heating. (See the Appendix for a discussion of the</text>
<text><location><page_4><loc_52><loc_38><loc_92><loc_62></location>relative heating rates.) The thermal balance is solved self-consistently with the chemistry to determine the gas temperature. Unless otherwise specified, we adopt total Carbon and Oxygen abundances of x C = 10 -4 and x O = 3 . 16 × 10 -4 . Further details can be found in B12. For the purposes of this paper we consider as PDR any H-nucleus density within the region 200 ≤ n H ≤ 10 4 cm -3 . Below n H = 200cm -3 we consider it ionized, whereas above n H = 10 4 cm -3 we consider it fully molecular, with constant gas temperature and abundances that are independent of the external radiation field. The lower density limit is somewhat arbitrary since the H to H 2 transition can occur down to lower densities depending on the temperature. We impose this cutoff on the PDR calculations since we assume that gas at lower densities represents the HII component of the medium, which can only be reliably modeled using a photoionization code (e.g., MOCASSIN Ercolano et al. (2003, 2005, 2008).</text>
<text><location><page_4><loc_52><loc_26><loc_92><loc_38></location>In this paper, once the gas is fully molecular we do not solve for its properties with 3d-pdr . Instead, we adopt the limiting values of the temperature and abundances for a uniform density of n H = 10 5 cm -3 , which correspond to 10 K and n CO /n H = 10 -4 , wherein no atomic Carbon remains. This is a reasonable approximation for these densities since this gas, by definition, is well shielded from the external radiation and is almost entirely molecular.</text>
<text><location><page_4><loc_52><loc_6><loc_92><loc_26></location>The cosmic ray ionization rate per H 2 molecule is taken to be ζ = 5 × 10 -17 s -1 . The dust temperature is constant and set to T dust = 20K. We use N glyph[lscript] = 12 rays of healpix refinement (level glyph[lscript] = 0) and we use θ crit = 0 . 5( glyph[similarequal] π/ 6) rad for the search angle criterion. We neglect the contribution of the diffusive component of the FUV field by invoking the on-the-spot approximation (Osterbrock 1974). We consider we have obtained thermal balance either when the heating and cooling rates differ by σ err ≤ 0 . 5%, or when the difference in temperature between two consecutive iterations is T diff ≤ 0 . 01 K. Finally, we typically evolve the 3d-pdr simulation to final times from 5 . 7 -100 Myr at which point the chemistry is in equilibrium (e.g., Bayet et al. 2009). Table 2 summarizes all the runs we perform with 3d-pdr .</text>
<table>
<location><page_5><loc_8><loc_77><loc_47><loc_87></location>
<caption>TABLE 1 Simulation Properties</caption>
</table>
<text><location><page_5><loc_8><loc_73><loc_47><loc_76></location>a Simulation output ID, box length, total initial gas mass, Mach number, and fraction of a global free-fall time with gravity, respectively.</text>
<text><location><page_5><loc_9><loc_72><loc_47><loc_73></location>b The wavenumber range of the random velocity perturbations.</text>
<text><location><page_5><loc_8><loc_62><loc_48><loc_71></location>Although Rm4, Rm6 and Rm9 each have 4 levels of grid refinement with a minimum cell size of 100 AU, we consider only the 256 3 base-grid data when postprocessing. The refined cloud regions, by construction, contain high-density gas that is glyph[greaterorsimilar] 10 4 cm -3 . At these densities, 3d-pdr considers the gas to be fully molecular and adopts a constant gas temperature and abundances.</text>
<section_header_level_1><location><page_5><loc_10><loc_59><loc_46><loc_60></location>2.3. 'One-Way' Hydrodynamic-Chemical Coupling</section_header_level_1>
<text><location><page_5><loc_8><loc_13><loc_48><loc_58></location>Our method can be considered a 'one-way' code coupling, because 3d-pdr uses the density output of the hydrodynamic calculations to compute the chemical distribution. A benefit of this approach is that it is computationally efficient, and large networks of reactions may be considered that would otherwise be too time consuming to compute in combination with the hydrodynamics. In addition, the affects of different radiative conditions and metallicity may be studied using the same hydrodynamical simulation. The deficit to this approach is that the corresponding temperatures computed by 3d-pdr do not affect the subsequent hydrodynamic evolution. In a one-way coupling, consistency between the hydrodynamic quantities and chemistry is only achieved if the a priori simulated values are chosen to reflect the anticipated post-processed values. Because 3d-pdr computes a wide distribution of temperatures, it is not possible to achieve consistency by adopting a single, constant temperature. For example, for Rm6 1.0 12 3d-pdr determines a mass-weighted temperature of ∼ 22 K, which is a factor of two above the fiducial 10 K simulation temperature. However, because we adopt 10 K for the simulation, by construction the densest regions, i.e., the star-forming gas ( n glyph[greaterorsimilar] a few 10 3 ), their dynamics will be in fairly good agreement with the computed 3d-pdr temperatures. It is also worth noting that for a simulation with a 1D rms velocity of 0.7 km s -1 , gas temperatures would need to reach ∼ 140 K in order to obtain dynamic parity with the turbulent gas pressure (assuming a stellar external radiation field). Since the 3d-pdr computed gas temperatures are generally much less than 140 K, the hydrodynamics would remain governed by turbulence and so only a small difference would be expected if the 3d-pdr temperatures were fed back into the simulation.</text>
<text><location><page_5><loc_8><loc_4><loc_48><loc_12></location>In the simulation we also adopt a fixed value for the mean mass per particle, µ p , which implicitly assumes that the gas is entirely molecular. We will show later that the hydrogen is almost all in molecular form throughout the domain with the exception of a few cells at the domain edge. Since molecular hydrogen dominates the</text>
<text><location><page_5><loc_52><loc_87><loc_92><loc_91></location>mass budget of the gas by several orders of magnitude this particle mass approximation is a good one for the simulations used in this study.</text>
<text><location><page_5><loc_52><loc_59><loc_92><loc_87></location>A second discrepancy between the dynamics and the chemistry occurs because 3d-pdr assumes that the radiation field impinges on the gas at the box boundaries, while the hydrodynamics assume periodic boundary conditions, i.e., there is no edge. This incongruity is also part of the G10 approach, which adopts periodicity for the gas but not the radiation field. For any boundary convention, high-density gas will have high-extinction nearly independently of location with respect to the boundary. Since turbulent clouds are naturally porous and the dense gas has a low-volume filling fraction, we can expect that radiation would penetrate many lower density regions for some sight-line to the 'edge.' Practically, the effect of the incident radiation field is to define a new effective boundary for the molecular gas, which reflects the filamentary and inhomogenous shape of the gas. Authors that seek to model an entire cloud rather than a periodic piece must instead wrestle with the arguably equally difficult problem of how the cloud connects to the larger-scale ISM, which is related to the issue of molecular cloud formation (e.g., Banerjee et al. 2009; Van Loo et al. 2013).</text>
<section_header_level_1><location><page_5><loc_63><loc_56><loc_81><loc_57></location>3. METHOD VALIDATION</section_header_level_1>
<section_header_level_1><location><page_5><loc_65><loc_54><loc_79><loc_55></location>3.1. Grid Sampling</section_header_level_1>
<text><location><page_5><loc_52><loc_40><loc_92><loc_54></location>We first verify that our results are converged and independent of the 3d-pdr grid resolution by comparing the calculated abundances for the same simulation input (Rm6 1.0) sampled with three different resolutions. These are the runs Rm6 1.0 12, Rm6 1.0 25 and Rm6 1.0 50 listed in Table 2. This is a useful exercise because 3d-pdr post-processing requires non-negligible time even when run in parallel. Throughout this paper, we analyze a coarser resolution than is actually achieved by the hydrodynamic simulations.</text>
<text><location><page_5><loc_52><loc_31><loc_92><loc_40></location>Table 3 gives the mean abundance and standard deviation over all grid points for each of the three sampling resolutions. We find that differences in the mean abundances are generally only a few percent and are, without exception, much smaller than the standard deviation of the distributions. The mean gas temperature is also fairly insensitive to increasing resolution.</text>
<text><location><page_5><loc_52><loc_13><loc_92><loc_31></location>Figure 3 shows the fractional abundances for a single random sight-line through the cloud. Increasing the sampling resolution of 3d-pdr has little effect on the calculated cloud chemistry and the abundances of H, H 2 and CO. Different sight-lines exhibit similar good convergence. The small differences between resolutions imply that the results should also be similar for simulation data with higher base grid resolutions. This comparison suggests that in the future it will be possible to follow the time-dependent chemical evolution coarsely but accurately with 3d-pdr . However, for stronger UV fields, the resolution could be more important since the C + /C/CO transition will occur further from the boundary.</text>
<section_header_level_1><location><page_5><loc_62><loc_10><loc_82><loc_11></location>3.2. Boundary Convergence</section_header_level_1>
<text><location><page_5><loc_52><loc_4><loc_92><loc_10></location>Some authors have suggested that the details of the interior cloud chemistry depend on the resolution of the atomic-to-molecular transition. To investigate this issue, we compare molecular abundances in the cloud interior</text>
<table>
<location><page_6><loc_12><loc_68><loc_88><loc_87></location>
<caption>TABLE 2 3d-pdr Run Parameters</caption>
</table>
<text><location><page_6><loc_13><loc_66><loc_47><loc_67></location>a Input sampling of the simulation data used by 3d-pdr .</text>
<unordered_list>
<list_item><location><page_6><loc_13><loc_65><loc_47><loc_66></location>b Magnitude of the UV field in Draines at the box edge.</list_item>
<list_item><location><page_6><loc_12><loc_63><loc_87><loc_65></location>c The direction of the field at the boundaries. The field is either a uniform field that is plane-parallel to the box faces, isotropic, or a combination of the two.</list_item>
<list_item><location><page_6><loc_13><loc_62><loc_23><loc_63></location>d Number of rays.</list_item>
<list_item><location><page_6><loc_13><loc_61><loc_46><loc_62></location>e Range of 3d-pdr densities assumed in the calculation.</list_item>
</unordered_list>
<text><location><page_6><loc_13><loc_59><loc_69><loc_61></location>f Run uses the same C and O abundances as G10 ( x C = 1 . 41 × 10 -4 and x O = 3 . 16 × 10 -4 ).</text>
<table>
<location><page_6><loc_16><loc_48><loc_84><loc_53></location>
<caption>TABLE 3 Mean fractional values at various resolutions</caption>
</table>
<text><location><page_6><loc_16><loc_45><loc_84><loc_47></location>a Simulation output ID and mass-weighted mean abundances. The standard deviation for each is given in parentheses.</text>
<figure>
<location><page_6><loc_10><loc_19><loc_48><loc_43></location>
<caption>Fig. 3.Mean fractional H, H 2 and CO abundances for a line of sight through the cloud center at three different resolutions. The resolutions differ by factors of two in the number of grid points.</caption>
</figure>
<text><location><page_6><loc_8><loc_4><loc_48><loc_12></location>for two cloud edge resolutions. Figure 4 shows the same sight-line computed with a fixed linear spacing and with logarithmically spaced points concentrated at the boundary. All grid points are assumed to be part of the PDR and are treated with the PDR code. We find that the abundances in the cloud interior are virtually identical</text>
<text><location><page_6><loc_52><loc_32><loc_92><loc_44></location>despite the very different boundary resolutions. In fact, the values computed with coarse resolution vary somewhat only within one or two coarse cells directly adjacent to the boundary. This demonstrates that the chemistry in the cloud interior is not sensitive to the edge resolution for the densities and FUV field strengths considered here and provides further evidence that our lower resolution 3d-pdr calculations are chemically converged for the bulk of the cloud.</text>
<section_header_level_1><location><page_6><loc_64><loc_29><loc_80><loc_30></location>3.3. Ray Convergence</section_header_level_1>
<text><location><page_6><loc_52><loc_4><loc_92><loc_29></location>In order to assess the sensitivity of our results to the number of rays, N glyph[lscript] , we compare 3d-pdr calculations with 12 ( l = 0) and 48 ( l = 1) rays. In principle, higher ray resolution will be more accurate for asymmetric and fractal geometries. Figure 5 shows the fractional abundances for a line of sight through the cloud center. Generally, we find good agreement for the two resolutions. The H 2 and C abundances are almost identical, while some differences of up to an order of magnitude are apparent for some H and CO points. For H 2 and CO, the resolution does affect the molecular transition at the boundary, where the abundance is lower at higher ray resolution. We can understand this by considering the simpler 6ray case for a cell on the domain boundary. Assuming that no radiation impinges on the cell from the opposite cloud edge, this cell should see 2 π sr of the UV field and be completely unshielded. However, for 6 perpendicular rays, only the ray perpendicular to the boundary will see</text>
<figure>
<location><page_7><loc_10><loc_64><loc_48><loc_90></location>
<caption>Fig. 4.Mean fractional H, H 2 , C, and CO abundances for a line of sight through the cloud center for constant resolution (crosses with a solid line) and for logarithmic spacing at the cloud edge (diamonds with a dotted line). The right axis indicates the gas number density (gray). A uniform 1 Draine radiation field is imposed on the cloud from the left ( L = 0 pc).</caption>
</figure>
<figure>
<location><page_7><loc_10><loc_28><loc_50><loc_54></location>
<caption>Fig. 5.Mean fractional H (solid), H 2 (dot-dashed), C (dashed), and CO (dottted) abundances for a line of sight through the cloud center for Rm6 1.0 12 NC (crosses) with the fiducial ray resolution ( N glyph[lscript] = 12) and for Rm6 1.0 12 48 (diamonds), which has N glyph[lscript] = 48. Here we plot only the abundances for 50 ≤ n ≤ 10 4 cm -3 , which are the 3d-pdr density limits of Rm6 1.0 12 48.</caption>
</figure>
<text><location><page_7><loc_8><loc_7><loc_48><loc_19></location>the UV field, which results in an angular attenuation of 4 π/ 6 = 2 π/ 3 sr. Depending on the field strength, this may be sufficient to shield the boundary cell from the UV field. As more rays are added the angular dependence of the field at the boundary becomes better resolved, reducing the amount of extinction. In Figure 5, we see this issue only affects a few cells adjacent to the domain edge and does not appear to directly impact the subsequent internal cloud chemistry.</text>
<section_header_level_1><location><page_7><loc_54><loc_89><loc_90><loc_91></location>4.1. Code Comparison: Post-processing vs. In situ Calculation</section_header_level_1>
<text><location><page_7><loc_52><loc_62><loc_92><loc_88></location>In this section we compare our results using 3d-pdr to the coupled chemical and dynamical method described in G10. There are a few key differences between the two approaches. 3d-pdr follows 320 reactions of 33 species (including electrons) while G10 follows 218 reactions of 32 species. We note that these 218 reactions are not an exact subset of the 320 followed by 3d-pdr since they include more reactions with negative ions. G10 adopts the older reaction rates of UMIST99 (Le Teuff et al. 2000) instead of UMIST07 (Woodall et al. 2007). G10 employs a 'six-ray' approach (Nelson & Langer 1997, 1999; Glover & Mac Low 2007b) to calculate the local attenuated radiation field whereas 3d-pdr uses N glyph[lscript] = 12 × 4 glyph[lscript] rays (in this paper we use 12 rays, i.e. glyph[lscript] =0). Both methods include heating due to the photoelectric effect, H 2 photodissociation, UV pumping of H 2 , H 2 formation on dust grains, and cosmic ray ionization. However, 3d-pdr also includes photo-ionization of neutral Carbon and turbulent heating.</text>
<text><location><page_7><loc_52><loc_46><loc_92><loc_62></location>Both methods neglect the impact of the gas velocity distribution on the chemistry. In practice, the details of the velocity field affect the H 2 shielding, since the H 2 photodissociation rate from any given Lyman-Werner line is related to the escape probability for that line (see Glover & Mac Low (2007a) and discussion therein). G10 and previous papers instead adopt a six-ray approximation to estimate the shielding, which includes no velocity information. 3d-pdr relates the line optical depth to an effective linewidth, which is proportional to the root mean square of the thermal sound speed and turbulent gas velocity.</text>
<text><location><page_7><loc_52><loc_32><loc_92><loc_46></location>In modeling cooling, both methods include emission by C, C + and O fine structure lines, gas-grain collisional cooling, cooling by rotational lines of CO, and H 2 collisional dissociation, but 3d-pdr neglects H 2 and H 2 O rovibrational and OH rotational lines, which are included in the one-dimensional code ucl pdr (Bayet et al. 2010), as well as H collisional ionization and Compton cooling. However, these lines do not produce significant cooling under the conditions considered here, and so neglecting them is a good approximation.</text>
<text><location><page_7><loc_52><loc_24><loc_92><loc_32></location>To perform a precise comparison of the two methods we apply 3d-pdr directly to the density field of n300. We adopt identical C and O abundances ( x C = 1 . 41 × 10 -4 and x O = 3 . 16 × 10 -4 in all forms relative to hydrogen), evolve to the same final time of 5.7 Myr, and apply the same stellar FUV field at the boundary.</text>
<text><location><page_7><loc_52><loc_19><loc_92><loc_24></location>Figure 6 shows the H, H 2 , C, and CO abundances binned as a function of effective extinction for the two methods. We define the effective extinction following G10:</text>
<formula><location><page_7><loc_59><loc_13><loc_92><loc_17></location>A v , eff = -1 . 0 2 . 5 ln ( 1 N glyph[lscript] N glyph[lscript] ∑ i =1 e -2 . 5 A v [ i ] ) , (7)</formula>
<text><location><page_7><loc_52><loc_4><loc_92><loc_11></location>where A v , eff is a weighting over the extinctions of all N glyph[lscript] = 12 rays. For comparison, we include the abundances for a different simulated density field in order to assess the sensitivity to the underlying density distribution. In Figures 6 and 7 we consider only densities 200</text>
<text><location><page_8><loc_8><loc_90><loc_25><loc_91></location>cm -3 ≤ n ≤ 10 4 cm -3 . 1</text>
<text><location><page_8><loc_8><loc_74><loc_48><loc_90></location>We find that the G10 and 3d-pdr results differ the most at low extinction ( A v , eff < 0 . 3). These cells are near the simulation boundaries, where the impinging radiation field dissociates the H 2 . Surprisingly, this transition is largely absent in the G10 method, which also appears to over-estimate the fraction of atomic hydrogen throughout the PDR. At higher extinction, the G10 and 3d-pdr methods show reasonable confluence between the distributions of C and CO. The similarity between the n300 and Rm6 1.0 12 distributions illustrates that the PDR is not overly sensitive to the underlying density distribution.</text>
<text><location><page_8><loc_8><loc_61><loc_48><loc_73></location>We note that the abundance distributions of Rm6 0.0 12, which we evolve to 100 Myr, and those of Rm6 0.0 12b, which we conclude at 5.7 Myr, are very similar. This suggests that these species achieve chemical equilibrium by 5.7 Myr (see also Bayet et al. 2009). The formation time of molecular hydrogen for gas with n = 10 3 cm -3 is t form glyph[similarequal] 10 9 n -1 yr glyph[similarequal] 1 Myr (Hollenbach et al. 1971). CO forms rapidly provided A v glyph[greaterorsimilar] 0 . 7 (Bergin et al. 2004)</text>
<text><location><page_8><loc_8><loc_51><loc_48><loc_61></location>Figure 7 illustrates the gas temperature distributions in the three cases. G10 reaches a slightly lower temperature at low Av, but otherwise the calculations are within a standard deviation. The temperature histograms, which show the relative number of cells at different temperatures, are somewhat different. All simulations exhibit a peak in the temperature distribution at ∼ 30 -50 K.</text>
<text><location><page_8><loc_8><loc_19><loc_48><loc_50></location>Despite the general congruence of mean properties, Figure 8 demonstrates that individual cells may have very different fractional abundances. H 2 abundance has the best point-by-point agreement since it is nearly constant throughout the domain. The exception occurs at the cloud boundaries, where the G10 method does not appear to model the PDR regime as well as 3d-pdr . The discrepancy is likely due to the lower ray resolution of G10, which causes the H 2 fraction to be over-estimated (see discussion in section 3.3). G10 mention ray resolution as a possible deficit of their 6-ray approach. The H abundance shows fairly good correspondence between the two methods but does differ by an order of magnitude at some points. The higher H fractional abundance at high-Av shown for n300 G10 may be due to turbulent mixing, which we do not include in our approach. However, since n300 does not include gravity, which would reduce turbulent turnover at high-densities, this H fractional abundance may also be an over-estimate (S. Glover private communication). The C and CO abundances produced by the two methods are also generally similar with the most difference occurring in the range -5 pc < x < 0 pc, which corresponds to gas densities n < 10 2 cm -3 .</text>
<text><location><page_8><loc_8><loc_11><loc_48><loc_19></location>Since the input densities, grid resolution, and atomic abundances are identical, all discrepancies must be due to differences in methodology and chemical assumptions. Although the magnitude of the abundance variation appears quite large, such differences are consistent with those typically found between PDR codes (Rollig et al.</text>
<text><location><page_8><loc_8><loc_5><loc_48><loc_10></location>1 We find that Figures 6 and 7 appear very similar assuming a lower cutoff of n ≥ 50 cm -3 (e.g., Rm6 1.0 12 48 and Rm6 1.0 12 NC). The main result of including lower densities in the PDR calculation is that the low-Av gas becomes increasingly (and inaccurately) warm.</text>
<section_header_level_1><location><page_8><loc_54><loc_88><loc_90><loc_89></location>4.2. Dependence on Dimensionality: 1D versus 3D</section_header_level_1>
<text><location><page_8><loc_52><loc_72><loc_92><loc_87></location>Figure 9 shows the extinction distribution as a function of the local gas number density. As shown by G10 (e.g., their Figure 14), gas extinction and density are only very weakly correlated. Overall, extinction is more strongly correlated with position within the cloud than with density. Figure 9 exhibits two populations of points: those in the interior and those spatially within < 1% the boundary, which have distinctly lower extinction and stand out in the regime 3 . 5 < log n < 4. These boundary cells appear to be missing from the results of G10. We discuss them further in section 4.3.</text>
<text><location><page_8><loc_52><loc_61><loc_92><loc_72></location>Figure 10 illustrates how the H 2 , C + , C, and CO fractional abundances depend upon extinction, UV field, and location within the cloud. Both H 2 and CO, which are the most sensitive to the extinction, appear to behave differently at the cloud edge and in the interior. Some of the discontinuity in the distribution is likely artificial since better edge resolution, as shown in Figure 3, would join the two populations more smoothly.</text>
<text><location><page_8><loc_52><loc_51><loc_92><loc_61></location>The left column plots verify that the the local extinction and UV field magnitude are completely correlated (i.e., the extinction indicated by the color-scale varies completely linearly with the magnitude of the UV field). Relative to extinction, proximity to the cloud edge has a weaker influence since the abundances depend upon the column density along each ray, which varies as the density distribution.</text>
<text><location><page_8><loc_52><loc_41><loc_92><loc_50></location>Figure 11 illustrates how abundances correlate with the gas temperature. Temperature varies smoothly with both UV and A v , eff . For C, a discrete region of boundary cells becomes apparent, which was previously degenerate with the cells near but not abutting the boundary. These boundary cells show up as a slight offset in temperature for A v , eff < -0 . 5.</text>
<text><location><page_8><loc_52><loc_13><loc_92><loc_41></location>The shape of the abundance-UV field distributions depends on the range of underlying densities in the PDR. Figure 12 shows the abundance distributions over plotted with lines showing the abundances computed for simple 1D models. The 1D models assume constant density along the line-of-sight and an incident 1 Draine UV field at one end. These curves illustrate that the range in abundance for any given UV field simply depends on the range in local gas density for a given UV field. Since we define the PDR region as those points with densities n = 200 cm -3 to 10 4 cm -3 the curves with these densities correlate well with the data of the 3D simulations. Thus, while turbulence dictates the distribution of densities and hence the fraction of cells within a given density range, the abundance distribution is set by chemistry and the details of the species response to the local UV field. In summary, although the determination of the extinction at a particular point within the volume is a three-dimensional problem, we find that once the local UV field is computed, the resulting abundances are nearly identical to those derived from a 1D model.</text>
<section_header_level_1><location><page_8><loc_57><loc_10><loc_86><loc_11></location>4.3. Dependence on Physical Parameters</section_header_level_1>
<text><location><page_8><loc_52><loc_4><loc_92><loc_10></location>In this section we investigate the sensitivity of the chemistry to the bulk simulation properties. In a selfconsistent treatment of molecule formation, the distribution of shock properties (e.g. the post-shock densities</text>
<figure>
<location><page_9><loc_17><loc_42><loc_49><loc_65></location>
<caption>Fig. 6.Mean fractional H, H 2 , C, and CO abundances as a function of log extinction, where the error bars indicate the standard deviation in each bin. The triangles show the results of the n300 simulation as performed by S. Glover. The diamonds indicate the results for 3d-pdr assuming the same n300 density distribution evolved to the same time (5.7 Myr) using the same x C and x O abundances. The squares indicate the results for Rm6 1.0 12b, which has a different underlying density distribution. In all cases, only gas with 200 cm -3 ≥ n ≤ 10 4 cm -3 is included in the averages.</caption>
</figure>
<figure>
<location><page_9><loc_17><loc_9><loc_49><loc_32></location>
</figure>
<figure>
<location><page_9><loc_52><loc_9><loc_84><loc_32></location>
<caption>Fig. 7.Mass-weighted temperature distribution versus extinction (left) and temperature distributions (right) for the same runs shown in Figure 6.</caption>
</figure>
<figure>
<location><page_10><loc_11><loc_69><loc_50><loc_89></location>
<caption>Fig. 8.Fractional abundances computed for a line-of-sight through the cloud center of simulation n300 for the G10 method (narrow lines) and 3d-pdr (thick lines). The gas number density (right axis) is indicated by a gray, solid line. For comparison, no cutoff is applied to the 3d-pdr calculation.</caption>
</figure>
<figure>
<location><page_10><loc_10><loc_36><loc_48><loc_59></location>
<caption>Fig. 9.Log extinction versus number density for Rm6 1.0 12. The colorbar indicates the minimum distance to a cloud boundary in pc.</caption>
</figure>
<text><location><page_10><loc_8><loc_11><loc_48><loc_30></location>and temperatures) could imprint an observable signature in the measured abundances. For example, molecules such as CH 2 , HCO + and OH are directly sensitive to turbulent density fluctuations Kumar & Fisher (2013) and would likely vary as a function of simulation Mach number. In contrast, the abundance of H 2 and CO predominantly depends on the amount of shielding from the UV radiation field (Bergin et al. 2004). A parcel of gas embedded within a completely smooth ( A v > 0 . 7) cloud will be well-shielded from the UV field, whereas a parcel of gas in a highly fractal cloud will have a high probability of having a sight-line with low extinction. Consequently, we can expect that the morphological distribution of the gas will have some effect on these abundances.</text>
<text><location><page_10><loc_8><loc_4><loc_48><loc_11></location>Figure 13 shows the mass-weighted abundances for simulations with two different Mach numbers at various evolutionary times. All orion simulations have the same mean density such that apparent differences are directly due to variations in the gas morphology.</text>
<text><location><page_10><loc_52><loc_78><loc_92><loc_91></location>Due to the relatively high simulation mean-density, we find that the H 2 abundance is fairly insensitive to changes in the density distribution caused by gravity. Glover & Mac Low (2007a) found that the H 2 fraction increased with gravitational collapse for a smooth density distribution. However, in their case the initial mean densities were much lower than the initial density of our runs. Thus, in our simulations the gas is predominantly molecular at all times since most gas parcels are well-shielded with or without gravity.</text>
<text><location><page_10><loc_52><loc_59><loc_92><loc_78></location>We find that C and C + abundances vary by less than 20%. The CO abundance demonstrates the largest variation and declines by more than a factor of two as the gas becomes self-gravitating. Much of this effect is due to a non-negligible fraction of the mass becoming concentrated in small, dense and well-shielded volumes that have fixed, maximal 10 -4 abundance, which decreases the extinction in the remainder of the volume (see Figure 2). Differences of ∼ 30% in 3D Mach number have a relatively small impact (less than a factor of 2) on the total mean abundance but CO does show some sensitivity with abundance increasing with Mach number. H 2 and C + fractions decrease slightly with increasing Mach number.</text>
<text><location><page_10><loc_52><loc_40><loc_92><loc_58></location>For reference, Figure 13 includes the mean abundances of n300. In order to compare the PDR results we only consider n300 gas with densities exceeding 200 cm -3 . 2 In this case, the abundance differences are dominated by the different mean extinctions. n300 has ¯ Av ∼ 0 . 04 while Rm6 has ¯ Av ∼ 0 . 02, which results in slightly lower mean C and CO abundances. The n300 mean H 2 abundance is lower than for those computed for Rm6; however, Figure 4 in G10 exhibits a higher H 2 abundance ( ∼ 0 . 98) for a simulation with the same mean density but lower magnetic field. This suggests that there is a morphological component to the H 2 abundance difference that is related to the magnetic field strength (S. Glover private communication).</text>
<text><location><page_10><loc_52><loc_28><loc_92><loc_39></location>Figure 14 illustrates the CO distribution as a function of gas temperature. As gravity influences the gas distribution, the number of cells with high CO abundance and cold temperature (10 ≤ T ≤ 20) increases. This is related to the volume filling factor of the dense gas, which decreases as gas becomes more concentrated in dense, collapsing regions. The shape of the temperatureabundance distribution is otherwise roughly constant with Mach number and time.</text>
<text><location><page_10><loc_52><loc_19><loc_92><loc_27></location>In all panels, points near the edge of the simulation box comprise a distinct swath of high-temperature/lowabundance points. We color points within 2% of the edge red to highlight this dichotomy. This region directly corresponds to the lowA v , mostly atomic region at the boundary.</text>
<section_header_level_1><location><page_10><loc_56><loc_16><loc_88><loc_17></location>4.4. Dependence on External Radiation Field</section_header_level_1>
<text><location><page_10><loc_52><loc_9><loc_92><loc_16></location>In order to investigate how abundance depends on the external radiation field, we consider two 3d-pdr calculations with external fields each with a magnitude of 1 Draine but with different vectors. Run Rm6 1.0 12i has an external isotropic radiation field, while Run</text>
<figure>
<location><page_11><loc_22><loc_10><loc_79><loc_89></location>
<caption>Fig. 10.Left: Rm6 1.0 12 fractional abundances as a function of log UV radiation field where the colorbar indicates the extinction. Right: Rm6 1.0 12 fractional abundances as a function of log extinction (right), where the colorbar indicates the minimum distance in pc to the cloud boundary.</caption>
</figure>
<figure>
<location><page_12><loc_22><loc_9><loc_79><loc_89></location>
<caption>Fig. 11.Same as Figure 10 but with color indicating the gas temperature.</caption>
</figure>
<figure>
<location><page_13><loc_20><loc_67><loc_50><loc_88></location>
</figure>
<figure>
<location><page_13><loc_53><loc_67><loc_81><loc_88></location>
</figure>
<figure>
<location><page_13><loc_21><loc_42><loc_49><loc_64></location>
</figure>
<figure>
<location><page_13><loc_53><loc_42><loc_81><loc_64></location>
<caption>Fig. 12.Log abundance versus log UV field for run Rm6 1.0 12, where the color scale indicates the log of the mean density for a given abundance and local field. The gray solid lines show the values from 1D runs with constant density and incident 1 Draine UV field. The lines increase in density for line thickness going from thin to thick with values of 200, 500,10 3 , 2 × 10 3 , 5 × 10 3 , 10 4 cm -3 .</caption>
</figure>
<figure>
<location><page_13><loc_17><loc_9><loc_48><loc_34></location>
</figure>
<figure>
<location><page_13><loc_54><loc_9><loc_84><loc_34></location>
<caption>Fig. 13.Mean H, H 2 , C + , C, CO abundances for Rm6 0.0 12, Rm6 0.5 12, Rm6 1.0 12 (red), Rm9 1.0 12 (purple), Rm4 1.0 12 (green) and n300 using the G10 method (blue). On the right abundances have been normalized to the values of Rm6 1.0 12.</caption>
</figure>
<figure>
<location><page_14><loc_16><loc_26><loc_78><loc_72></location>
<caption>Fig. 14.CO abundance as a function of gas temperature for different times and Mach numbers. The cells that are within 2% of the box boundary are colored red.</caption>
</figure>
<figure>
<location><page_15><loc_11><loc_67><loc_46><loc_91></location>
<caption>Fig. 15.Schematic of the incident radiation field used in the 3d-pdr runs. The cube represents the entire computational domain. The thin solid lines represent the boundaries of the 12ray healpix structure as they are emanated from a point placed in the center of the computational domain. The direction of the isotropic radiation field is opposite to the direction of each healpix ray as shown in the figure. The additional dashed lines on the left represent the direction of the plane-parallel radiation field added in run Rm6 1.0 12ui.</caption>
</figure>
<text><location><page_15><loc_8><loc_49><loc_48><loc_56></location>Rm6 1.0 12ui has an external field that is a superposition of a half Draine isotropic field and a half Draine uniform field (i.e., a field that is plane parallel to the simulation boundary at all faces). Figure 15 illustrates the incident radiation field geometry for the two cases.</text>
<text><location><page_15><loc_8><loc_19><loc_48><loc_49></location>Figure 16 illustrates that by simply changing the field incidence the internal point-by-point UV distribution is very different. The figure includes only points with a net field greater than 0.5 Draines; these points are ones which feel both the isotropic and plane-parallel components of the incident field and thus display the maximum difference. Figure 17 shows the effect of the field differences on the H, H 2 , C, and CO fractional abundances. Since CO abundance depends mainly on the local UV field and these distributions are distinct, it is unsurprising that individual abundances change by as much as 50% for different field configurations. Likewise, C and H are strongly affected by the field distribution. Figure 17 shows that the mixed field simulation has fewer high UV points and more lower UV points, which is consistent with the elevated C and CO abundances displayed in Figure 17. Since the molecular hydrogen abundance is nearly constant within the cloud, the field configuration at the boundary has little effect. The higher density gas ( n > 10 3 cm -3 ), which is well self-shielded by definition, is also largely insensitive to field changes of this magnitude.</text>
<text><location><page_15><loc_8><loc_10><loc_48><loc_19></location>In summary, even a modest change in the UV field incidence reinforces the conclusion that three-dimensional PDR treatment is preferable to a one-dimensional treatment for complex or non-symmetric problems. We expect differences to be more significant for larger external field variations and for the inclusion of internal UV sources, i.e., protostars.</text>
<section_header_level_1><location><page_15><loc_22><loc_8><loc_34><loc_9></location>5. CONCLUSIONS</section_header_level_1>
<text><location><page_15><loc_8><loc_4><loc_48><loc_7></location>We use 3d-pdr in combination with hydrodynamic molecular cloud simulations to explore the importance</text>
<figure>
<location><page_15><loc_53><loc_65><loc_93><loc_90></location>
<caption>Fig. 16.Distribution of UV field for the Rm6 1.0 12i run which has an isotropic-only external 1 Draine field (blue, dotted) and the Rm6 1.0 12ui run which has a 0.5 Draine isotropic and 0.5 Draine uniform external field (solid, purple). Only the points that have a net field greater than 0.5 Draines are plotted. The two 3d-pdr runs use the same input density distribution.</caption>
</figure>
<text><location><page_15><loc_52><loc_52><loc_92><loc_56></location>of dimensionality in PDR chemistry, to consider complex gas morphologies and to compare with prior results using an in situ astrochemistry treatment.</text>
<text><location><page_15><loc_52><loc_45><loc_92><loc_52></location>First, we demonstrate that our results are robust as a function of grid sampling and edge resolution. In fact, we find that the interior cloud abundances are remarkably insensitive to the resolution of the atomic to molecular transition at the cloud boundary.</text>
<text><location><page_15><loc_52><loc_27><loc_92><loc_45></location>We obtain reasonable agreement between the G10 in situ and 3d-pdr approaches for the C and CO abundance distributions. This is because molecules such as CO and H 2 are not particularly sensitive to the dynamical history of the gas but instead depend predominantly on the local radiation field. The two approaches differ the most for H and H 2 abundances near the cloud boundary and for cells that have low-extinction. For example, in G10 hydrogen is either entirely molecular or fully dissociated. This discrepancy appears to result from differences in the methodologies rather than chemical details, and we assert that the treatment of 3d-pdr should be more accurate in transition regions.</text>
<text><location><page_15><loc_52><loc_18><loc_92><loc_27></location>We demonstrate that morphological differences due to cloud Mach number and evolutionary time can produce significant differences in the abundance distributions. While this may be difficult to observe directly since point by point abundances are difficult to infer, it may indirectly impact the properties of the observed molecular emission lines emerging from the cloud.</text>
<text><location><page_15><loc_52><loc_11><loc_92><loc_18></location>Finally, we find that a relatively modest change in the external UV radiation field produces large changes in the chemical abundances. This supports the finding by B12 that three-dimensional treatment is crucial for complex and non-symmetric problems.</text>
<text><location><page_15><loc_52><loc_4><loc_92><loc_11></location>In paper II, we plan to implement several improvements to our method. First, we will relax our simple abundance approximations at densities > 10 4 cm -3 and instead couple 3d-pdr to a one-zone gas-grain chemical network code. This will allow us to include molec-</text>
<figure>
<location><page_16><loc_16><loc_43><loc_86><loc_90></location>
<caption>Fig. 17.-</caption>
</figure>
<text><location><page_16><loc_16><loc_41><loc_46><loc_42></location>Normalized relative differences between the H, H</text>
<text><location><page_16><loc_46><loc_41><loc_46><loc_41></location>2</text>
<text><location><page_16><loc_47><loc_41><loc_92><loc_42></location>, C and CO abundances for Rm6 1.0 12i and Rm6 1.0 12ui (the same runs</text>
<text><location><page_16><loc_8><loc_28><loc_48><loc_41></location>as in Figure 16). ular freezeout onto dust grains, gas-grain thermal coupling, and a more extensive chemical network. Second, we will investigate the effect of embedded UV sources on the chemical distribution. The orion simulations that we analyze here contain detailed information about the masses and accretion rates of embedded protostars that we have neglected in this study. In addition to these changes, work is ongoing to couple 3d-pdr to the photoionization and radiative transfer code MOCASSIN .</text>
<text><location><page_16><loc_52><loc_28><loc_92><loc_40></location>sions and thank the referee, Robert Fisher, for suggestions that significantly improved the paper. The authors acknowledge support from NSF grant AST0901055 (S.S.R.O), NASA grant HF-51311.01 (S.S.R.O), STFC grant ST/J001511/1 (T.G.B), and a JAE-DOC research contract (T.A.B.). T.A.B also thanks the Spanish MINECO for funding support through grants AYA200907304 and CSD200900038. The orion simulations were performed on the Trestles XSEDE cluster.</text>
<text><location><page_16><loc_10><loc_24><loc_48><loc_26></location>The authors thank Simon Glover for helpful discus-</text>
<section_header_level_1><location><page_16><loc_46><loc_22><loc_54><loc_23></location>APPENDIX</section_header_level_1>
<section_header_level_1><location><page_16><loc_43><loc_20><loc_58><loc_21></location>HEATING RATES</section_header_level_1>
<text><location><page_16><loc_8><loc_4><loc_92><loc_19></location>There are four main contributions to the local heating at each domain point. First, there is photoelectric heating, which is produced by UV photon interactions with dust grains and PAHs, and which dominates near the cloud surface. Second, there is cosmic-ray ionization heating, which is set by the standard cosmic-ray density and becomes dominant deeper into the cloud. Third, there is chemical heating as the result of various exothermic reactions. Finally, there is turbulent heating, which is due to energy dissipation through shocks and depends on the turbulent outer scale (e.g., cloud size) and turbulent Mach number. Figure A1 shows the distribution of heating rates for each of these contributions. Photoelectric heating dominates in most cases, and the turbulent heating generally provides the smallest contribution. If the turbulent heating is proportional to v 3 TURB /L , then for the 2pc simulations here it should range from v 3 TURB /L = 1 . 5 × 10 -5 -1 . 4 × 10 -4 cm 2 s -3 , which brackets the constant value, 6 . 5 × 10 -5 cm 2 s -3 , we adopt in our calculations. We direct the reader to Pan & Padoan (2009) and Kumar & Fisher (2013) for additional discussion and modeling of heating due to turbulent dissipation, intermittency, and shear flows.</text>
<figure>
<location><page_17><loc_24><loc_48><loc_77><loc_90></location>
<caption>Fig. A1.Distribution of heating rates in Rm6 1.0 12 as a function of effective extinction for the total photoelectric (blue, top contours), cosmic-ray (green, top-middle contours), chemical (black, bottom-middle contours) and turbulent heating (red, bottom contours) in each cell. The contours correspond to the number of cells, n , with a given extinction and heating rate: n =100 (inner contour), n = 30 (middle contour), and n = 10 (outer contour).</caption>
</figure>
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</document>
[
{
"title": "ABSTRACT",
"content": "We use 3d-pdr , a three-dimensional astrochemistry code for modeling photodissociation regions (PDRs), to post-process hydrodynamic simulations of turbulent, star-forming clouds. We focus on the transition from atomic to molecular gas, with specific attention to the formation and distribution of H, C + , C, H 2 and CO. First, we demonstrate that the details of the cloud chemistry and our conclusions are insensitive to the simulation spatial resolution, to the resolution at the cloud edge, and to the ray angular resolution. We then investigate the effect of geometry and simulation parameters on chemical abundances and find weak dependence on cloud morphology as dictated by gravity and turbulent Mach number. For a uniform external radiation field, we find similar distributions to those derived using a one-dimensional PDR code. However, we demonstrate that a three-dimensional treatment is necessary for a spatially varying external field, and we caution against using one-dimensional treatments for non-symmetric problems. We compare our results with the work of Glover et al. (2010), who selfconsistently followed the time evolution of molecule formation in hydrodynamic simulations using a reduced chemical network. In general, we find good agreement with this in situ approach for C and CO abundances. However, the temperature and H 2 abundances are discrepant in the boundary regions (Av ≤ 5), which is due to the different number of rays used by the two approaches. Subject headings: astrochemistry, hydrodynamics, molecular processes, turbulence, stars: formation, ISM:molecules",
"pages": [
1
]
},
{
"title": "MODELING THE ATOMIC-TO-MOLECULAR TRANSITION AND CHEMICAL DISTRIBUTIONS OF TURBULENT STAR-FORMING CLOUDS",
"content": "Stella S. R. Offner ∗ Department of Astronomy, Yale University, New Haven, CT 06511",
"pages": [
1
]
},
{
"title": "Thomas G. Bisbas",
"content": "Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6B",
"pages": [
1
]
},
{
"title": "Serena Viti",
"content": "Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6B",
"pages": [
1
]
},
{
"title": "Thomas A. Bell",
"content": "Centro de Astrobiolog'ıa (CSIC-INTA), Carretera de Ajalvir, km 4, 28850 Madrid, Spain Draft version March 7, 2022",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "In the local universe, stars appear to form exclusively in cold, dense clouds of predominately molecular gas (McKee & Ostriker 2007). Understanding the evolution of these molecular clouds (MCs) and the formation of stars within them is a fundamental problem in astrophysics that is hampered by distance, projection effects, and the high optical depth in these regions. Probing the mass and velocity distributions of the gas is further complicated by the fact that the most abundant molecule, H 2 , lacks a dipole moment. The next most abundant molecule, CO, which is commonly used to probe the cold molecular gas distribution in lieu of H 2 , has a typical average abundance of about one per 10 4 H 2 molecules in the Milky Way. In addition, the relationship between CO abundance and total gas mass is a complicated one that depends upon metallicity, the three-dimensional radiation field, the abundances of other molecules, and dust chemistry (Bell et al. 2006; Glover & Mac Low 2011; Shetty et al. 2011). Accurately modeling the formation of H 2 and the relative abundances of homologous molecules such as CO requires following complex chemical reaction networks that encompass hundreds of species and thousands of reactions. Traditionally, the computational expense of evolving large chemical networks limited astrochemical investigations to simple one-dimensional hydrodynamic models (e.g., Bergin et al. 2004) or to post-processing (e.g., Levrier et al. 2012). However, in recent years 'reduced' chemical networks have been adopted to investigate chemistry concurrently with three-dimensional hydrodynamics (Nelson & Langer 1997, 1999; Pavlovski et al. 2002, 2006; Glover & Mac Low 2007a,b; Glover et al. 2010). Such methods have the advantage of being able to follow the temperature evolution of the gas due to UV heating and atomic and molecular cooling, which in principle influences the gas dynamics since shock jump conditions depend upon the local temperature. Nonetheless, the expense of following the molecular evolution in situ necessitates various simplifications, including neglect of dust physics and coarse treatment of the radiation field. Thus far, turbulent cloud calculations including simplified chemistry have also focused on larger cloud complexes and generally neglected the self-gravity of the gas (see Glover & Clark 2012 as an exception including gravity). Neglecting gravity obviates the need for considerable additional resolution which would otherwise be required to resolve collapsing gas (Truelove et al. 1997). In addition, without forming embedded sources to provide additional radiation (e.g., Offner et al. 2009; Krumholz et al. 2007), heating depends only on the external cloud environment, leading to simpler radiative conditions. The gas temperature range induced by a standard external interstellar radiation field is generally limited ( glyph[lessorsimilar] 100K) and deviates from 10 K mainly at low Av. Despite such simplifications, the astrochemistry under investigation is rich and not well understood. For example, cloud boundary regions are especially interesting because this is where gas transitions from being ionized and atomic to predominantly molecular. These low-Av transitions areas are by definition PDRs, where FUV photons dominate the energy balance and gas chemistry. PDRs are ubiquitous in the interstellar medium and are the source of most of the infrared radiation in galaxies. The recent development of 3d-pdr (Bisbas et al. 2012, hereafter B12), which is the first dedicated PDR code able to treat arbitrary three-dimensional density distribution, now allows the accurate study of these regions in more complex structures. We dedicate this paper to three main goals. First, we compare 3D and 1D treatments of a complex PDR region in order to evaluate the impact of dimensionality on chemical results. Thus, we extend the work of B12, who demonstrated the importance of higher dimensional treatment in accurately modeling simple 3D problems, to consider complex, turbulent gas distributions. Second, we use self-gravitating, hydrodynamic simulations of molecular clouds with different Mach numbers to evaluate the importance of underlying physical parameters on chemical abundances and distributions. Finally, we explore the differences between two astrochemistry approaches by considering results obtained via postprocessing using 3d-pdr and results obtained from a chemical network calculation preformed 'in situ' (e.g., Glover et al. 2010). The paper is organized as follows. In section 2 we describe the 3d-pdr methodology and our hydrodynamic numerical simulations. In section 3 we validate our choice of spatial resolution by presenting convergence studies of grid-sampling in the cloud interior and at the cloud boundaries. We present our results in section 4, including a comparison to Glover et al. (2010) and discussions of chemical dependence on domain dimensionality, external radiation field, and cloud physical parameters. Section 5 contains a discussion of future work and conclusions.",
"pages": [
1,
2
]
},
{
"title": "2.1. Hydrodynamic Simulations",
"content": "In this paper, we analyze snapshots of four different hydrodynamic simulations of turbulent molecular clouds. The simulation parameters are summarized in Table 1. Three of the simulations (Rm4, Rm6 and Rm9) are performed with the orion adaptive mesh refinement (AMR) code (Truelove et al. 1998; Klein 1999). Since these simulations have not been previously published, we describe our method in detail below. orion employs a conservative second order Godunov scheme to solve the equations of compressible gas dynamics: where ρ , P , v are the gas density, pressure, and velocity, respectively. Here, e is the total energy e = 1 2 ρ v 2 + P γ -1 , where γ is the ratio of specific heats. orion solves the Poisson equation for the gravitational potential, φ : where m n and x n are the mass and position of the n th star, respectively. We close these equations with an isothermal equations of state: where k B is the Boltzmann constant, µ p = 2 . 33 is the mean mass per particle, m H is the hydrogen mass, and T = 10 K is the isothermal gas temperature. Authors sometimes adopt a barotropic equation of state (e.g., Offner et al. 2008), which sets a characteristic density above which the gas becomes optically thick and ceases to be isothermal. However, the density at which this occurs, ρ c ∼ 10 -14 g cm -3 , as calculated using full radiative transfer (Masunaga et al. 1998), exceeds the maximum density at our maximum AMR resolution ( ∼ 5 × 10 -16 g cm -3 ). Consequently, the isothermal approximation is appropriate here. Alternatively, we might solve for the radiation field using a flux-limited diffusion (FLD) approach and thus take into account heating from forming stars (Offner et al. 2009). This would be more numerically expensive but more physically accurate in the dense star-forming gas. However, without some prescription for protostellar outflows the stellar heating in the calculation would be an over-estimate (Hansen et al. 2012), and moreover, an FLD approach would not supply more accurate information about the temperatures of the lowextinction gas as 3d-pdr does. We insert finer AMR grids when the local density violates the Truelove criterion (Truelove et al. 1997): where ∆ x l is the cell size on level l and we adopt a Jeans number of J = 0 . 125. A sink particle is inserted when the gas exceeds the Jeans density for J = 0 . 25 on the maximum level (Krumholz et al. 2004). In this paper, we do not analyze the sink particle distribution and properties; these are the subject of Kirk et al. (in preparation). We initialize the simulations with uniform density and then perturb the gas for three crossing times using a random velocity field (e.g., Mac Low 1999). This field has a flat power spectrum for wavenumbers k = 1 .. 2, which corresponds to physical scales of L..L/ 2. We re-normalize the perturbations to maintain a constant cloud velocity dispersion. In the fiducial simulation, Rm6, the Mach number is chosen to satisfy the observed linewidth-size relation (McKee & Ostriker 2007). Following the driving initialization, the simulations achieve a well-mixed turbulent state and we turn on gravity, allowing collapse to proceed for a global free-fall time. The orion simulations all have a 256 3 base grid and four levels of AMR refinement. As summarized in Table 1, these three calculation have a total gas mass of 600 M glyph[circledot] , domain size of 2 pc (∆ x 4 = 100 AU), and turbulent 3D Mach numbers of 4.2, 6.6 and 8.9. For comparison, we also analyze Rm6 without gravity, i.e., at t = 0 t ff , and at half a free-fall time. Figure 1 shows the integrated column density at one free-fall time for these runs. We include the third simulation, n300, in order to directly compare our PDR methodology to that of Glover et al. (2010), henceforth G10. The n300 simulation was performed by S. Glover with a modified version of ZEUSMP , which tracks the abundances of 32 chemical species. The n300 calculation uses a fixed 256 3 grid. Turbulence is generated using random velocity perturbations in a manner similar to that used for the orion simulations. It does not include self-gravity but does solve the equations of ideal magneto-hydrodynamics and begins with an initially uniform magnetic field of 6 µ G. Figure 2 shows the mass-weighted and volumeweighted density distributions and corresponding chemical regimes for each of the orion snapshots. The density distribution functions exhibit a characteristic lognormal shape as expected for supersonic turbulent gas (e.g., Padoan et al. 1997; Kritsuk et al. 2007). As self-gravity becomes important, the density distribution grows a high-density tail (Mac Low & Klessen 2004). The cells at the peak of the density distribution fall into the PDR regime for the simulation parameters we adopt. The vertical lines in the histogram indicate the division between ionized, PDR and molecular gas.",
"pages": [
2,
3
]
},
{
"title": "2.2. 3d-pdr",
"content": "3d-pdr (Bisbas et al. 2012) is a three-dimensional time-dependent astrochemistry code for treating pho- todissociation regions (PDRs) of arbitrary density distribution. The code is able to solve self-consistently the chemistry and the thermal balance within any threedimensional cloud. It uses an escape probability approximation (or Large Velocity Gradient - Sobolev 1960; Castor 1970; de Jong et al. 1975) to compute the cooling functions. To do this, 3d-pdr uses a ray tracing scheme in which the directions of the rays are controlled by the healpix algorithm (G'orski et al. 2005). This ray tracing scheme creates a discrete set of evaluation points by projecting the elements of the cloud along each ray. It can thus evaluate the column densities, the attenuation of the far ultraviolet radiation into the PDR, and the propagation of the FIR/submm line emission out of the PDR. As a further development of the fully bench-marked one-dimensional ucl pdr code (Bell et al. 2006), 3dpdr adopts the same chemical model features. For the simulations presented in this paper, we use a chemical network which is a subset of the UMIST data base of reaction rates (Woodall et al. 2007). This 'reduced' network consists of 320 reactions and 33 species (including electrons). However, 3d-pdr also includes heating due to photoionization and photodissociation reactions in addition to the standard gas-phase chemistry. Self-shielding of H 2 and CO against photodissociation is accounted for. Comprehensive treatment of various gas heating mechanisms (i.e., photoelectric heating from dust grains and PAHs, collisional de-excitation of vibrationally excited H 2 following FUV pumping, photoionization of neutral carbon, cosmic ray heating) and emission from major cooling lines ([CII], [CI], [OI], CO) are calculated at each element. 3d-pdr also includes turbulent heating, which is proportional to v 3 TURB /L , where v TURB is the turbulent velocity and L is the integral scale. Here, we adopt constant values of L = 5 pc and v TURB = 1kms -1 . In practice, L should be set to the simulation domain size and v TURB to the 1D turbulent Mach number times the mean sound speed, however we find that the turbulent heating is small compared to photoelectric, cosmic-ray and chemical heating, which are the other main sources of heating. (See the Appendix for a discussion of the relative heating rates.) The thermal balance is solved self-consistently with the chemistry to determine the gas temperature. Unless otherwise specified, we adopt total Carbon and Oxygen abundances of x C = 10 -4 and x O = 3 . 16 × 10 -4 . Further details can be found in B12. For the purposes of this paper we consider as PDR any H-nucleus density within the region 200 ≤ n H ≤ 10 4 cm -3 . Below n H = 200cm -3 we consider it ionized, whereas above n H = 10 4 cm -3 we consider it fully molecular, with constant gas temperature and abundances that are independent of the external radiation field. The lower density limit is somewhat arbitrary since the H to H 2 transition can occur down to lower densities depending on the temperature. We impose this cutoff on the PDR calculations since we assume that gas at lower densities represents the HII component of the medium, which can only be reliably modeled using a photoionization code (e.g., MOCASSIN Ercolano et al. (2003, 2005, 2008). In this paper, once the gas is fully molecular we do not solve for its properties with 3d-pdr . Instead, we adopt the limiting values of the temperature and abundances for a uniform density of n H = 10 5 cm -3 , which correspond to 10 K and n CO /n H = 10 -4 , wherein no atomic Carbon remains. This is a reasonable approximation for these densities since this gas, by definition, is well shielded from the external radiation and is almost entirely molecular. The cosmic ray ionization rate per H 2 molecule is taken to be ζ = 5 × 10 -17 s -1 . The dust temperature is constant and set to T dust = 20K. We use N glyph[lscript] = 12 rays of healpix refinement (level glyph[lscript] = 0) and we use θ crit = 0 . 5( glyph[similarequal] π/ 6) rad for the search angle criterion. We neglect the contribution of the diffusive component of the FUV field by invoking the on-the-spot approximation (Osterbrock 1974). We consider we have obtained thermal balance either when the heating and cooling rates differ by σ err ≤ 0 . 5%, or when the difference in temperature between two consecutive iterations is T diff ≤ 0 . 01 K. Finally, we typically evolve the 3d-pdr simulation to final times from 5 . 7 -100 Myr at which point the chemistry is in equilibrium (e.g., Bayet et al. 2009). Table 2 summarizes all the runs we perform with 3d-pdr . a Simulation output ID, box length, total initial gas mass, Mach number, and fraction of a global free-fall time with gravity, respectively. b The wavenumber range of the random velocity perturbations. Although Rm4, Rm6 and Rm9 each have 4 levels of grid refinement with a minimum cell size of 100 AU, we consider only the 256 3 base-grid data when postprocessing. The refined cloud regions, by construction, contain high-density gas that is glyph[greaterorsimilar] 10 4 cm -3 . At these densities, 3d-pdr considers the gas to be fully molecular and adopts a constant gas temperature and abundances.",
"pages": [
3,
4,
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]
},
{
"title": "2.3. 'One-Way' Hydrodynamic-Chemical Coupling",
"content": "Our method can be considered a 'one-way' code coupling, because 3d-pdr uses the density output of the hydrodynamic calculations to compute the chemical distribution. A benefit of this approach is that it is computationally efficient, and large networks of reactions may be considered that would otherwise be too time consuming to compute in combination with the hydrodynamics. In addition, the affects of different radiative conditions and metallicity may be studied using the same hydrodynamical simulation. The deficit to this approach is that the corresponding temperatures computed by 3d-pdr do not affect the subsequent hydrodynamic evolution. In a one-way coupling, consistency between the hydrodynamic quantities and chemistry is only achieved if the a priori simulated values are chosen to reflect the anticipated post-processed values. Because 3d-pdr computes a wide distribution of temperatures, it is not possible to achieve consistency by adopting a single, constant temperature. For example, for Rm6 1.0 12 3d-pdr determines a mass-weighted temperature of ∼ 22 K, which is a factor of two above the fiducial 10 K simulation temperature. However, because we adopt 10 K for the simulation, by construction the densest regions, i.e., the star-forming gas ( n glyph[greaterorsimilar] a few 10 3 ), their dynamics will be in fairly good agreement with the computed 3d-pdr temperatures. It is also worth noting that for a simulation with a 1D rms velocity of 0.7 km s -1 , gas temperatures would need to reach ∼ 140 K in order to obtain dynamic parity with the turbulent gas pressure (assuming a stellar external radiation field). Since the 3d-pdr computed gas temperatures are generally much less than 140 K, the hydrodynamics would remain governed by turbulence and so only a small difference would be expected if the 3d-pdr temperatures were fed back into the simulation. In the simulation we also adopt a fixed value for the mean mass per particle, µ p , which implicitly assumes that the gas is entirely molecular. We will show later that the hydrogen is almost all in molecular form throughout the domain with the exception of a few cells at the domain edge. Since molecular hydrogen dominates the mass budget of the gas by several orders of magnitude this particle mass approximation is a good one for the simulations used in this study. A second discrepancy between the dynamics and the chemistry occurs because 3d-pdr assumes that the radiation field impinges on the gas at the box boundaries, while the hydrodynamics assume periodic boundary conditions, i.e., there is no edge. This incongruity is also part of the G10 approach, which adopts periodicity for the gas but not the radiation field. For any boundary convention, high-density gas will have high-extinction nearly independently of location with respect to the boundary. Since turbulent clouds are naturally porous and the dense gas has a low-volume filling fraction, we can expect that radiation would penetrate many lower density regions for some sight-line to the 'edge.' Practically, the effect of the incident radiation field is to define a new effective boundary for the molecular gas, which reflects the filamentary and inhomogenous shape of the gas. Authors that seek to model an entire cloud rather than a periodic piece must instead wrestle with the arguably equally difficult problem of how the cloud connects to the larger-scale ISM, which is related to the issue of molecular cloud formation (e.g., Banerjee et al. 2009; Van Loo et al. 2013).",
"pages": [
5
]
},
{
"title": "3.1. Grid Sampling",
"content": "We first verify that our results are converged and independent of the 3d-pdr grid resolution by comparing the calculated abundances for the same simulation input (Rm6 1.0) sampled with three different resolutions. These are the runs Rm6 1.0 12, Rm6 1.0 25 and Rm6 1.0 50 listed in Table 2. This is a useful exercise because 3d-pdr post-processing requires non-negligible time even when run in parallel. Throughout this paper, we analyze a coarser resolution than is actually achieved by the hydrodynamic simulations. Table 3 gives the mean abundance and standard deviation over all grid points for each of the three sampling resolutions. We find that differences in the mean abundances are generally only a few percent and are, without exception, much smaller than the standard deviation of the distributions. The mean gas temperature is also fairly insensitive to increasing resolution. Figure 3 shows the fractional abundances for a single random sight-line through the cloud. Increasing the sampling resolution of 3d-pdr has little effect on the calculated cloud chemistry and the abundances of H, H 2 and CO. Different sight-lines exhibit similar good convergence. The small differences between resolutions imply that the results should also be similar for simulation data with higher base grid resolutions. This comparison suggests that in the future it will be possible to follow the time-dependent chemical evolution coarsely but accurately with 3d-pdr . However, for stronger UV fields, the resolution could be more important since the C + /C/CO transition will occur further from the boundary.",
"pages": [
5
]
},
{
"title": "3.2. Boundary Convergence",
"content": "Some authors have suggested that the details of the interior cloud chemistry depend on the resolution of the atomic-to-molecular transition. To investigate this issue, we compare molecular abundances in the cloud interior a Input sampling of the simulation data used by 3d-pdr . f Run uses the same C and O abundances as G10 ( x C = 1 . 41 × 10 -4 and x O = 3 . 16 × 10 -4 ). a Simulation output ID and mass-weighted mean abundances. The standard deviation for each is given in parentheses. for two cloud edge resolutions. Figure 4 shows the same sight-line computed with a fixed linear spacing and with logarithmically spaced points concentrated at the boundary. All grid points are assumed to be part of the PDR and are treated with the PDR code. We find that the abundances in the cloud interior are virtually identical despite the very different boundary resolutions. In fact, the values computed with coarse resolution vary somewhat only within one or two coarse cells directly adjacent to the boundary. This demonstrates that the chemistry in the cloud interior is not sensitive to the edge resolution for the densities and FUV field strengths considered here and provides further evidence that our lower resolution 3d-pdr calculations are chemically converged for the bulk of the cloud.",
"pages": [
5,
6
]
},
{
"title": "3.3. Ray Convergence",
"content": "In order to assess the sensitivity of our results to the number of rays, N glyph[lscript] , we compare 3d-pdr calculations with 12 ( l = 0) and 48 ( l = 1) rays. In principle, higher ray resolution will be more accurate for asymmetric and fractal geometries. Figure 5 shows the fractional abundances for a line of sight through the cloud center. Generally, we find good agreement for the two resolutions. The H 2 and C abundances are almost identical, while some differences of up to an order of magnitude are apparent for some H and CO points. For H 2 and CO, the resolution does affect the molecular transition at the boundary, where the abundance is lower at higher ray resolution. We can understand this by considering the simpler 6ray case for a cell on the domain boundary. Assuming that no radiation impinges on the cell from the opposite cloud edge, this cell should see 2 π sr of the UV field and be completely unshielded. However, for 6 perpendicular rays, only the ray perpendicular to the boundary will see the UV field, which results in an angular attenuation of 4 π/ 6 = 2 π/ 3 sr. Depending on the field strength, this may be sufficient to shield the boundary cell from the UV field. As more rays are added the angular dependence of the field at the boundary becomes better resolved, reducing the amount of extinction. In Figure 5, we see this issue only affects a few cells adjacent to the domain edge and does not appear to directly impact the subsequent internal cloud chemistry.",
"pages": [
6,
7
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},
{
"title": "4.1. Code Comparison: Post-processing vs. In situ Calculation",
"content": "In this section we compare our results using 3d-pdr to the coupled chemical and dynamical method described in G10. There are a few key differences between the two approaches. 3d-pdr follows 320 reactions of 33 species (including electrons) while G10 follows 218 reactions of 32 species. We note that these 218 reactions are not an exact subset of the 320 followed by 3d-pdr since they include more reactions with negative ions. G10 adopts the older reaction rates of UMIST99 (Le Teuff et al. 2000) instead of UMIST07 (Woodall et al. 2007). G10 employs a 'six-ray' approach (Nelson & Langer 1997, 1999; Glover & Mac Low 2007b) to calculate the local attenuated radiation field whereas 3d-pdr uses N glyph[lscript] = 12 × 4 glyph[lscript] rays (in this paper we use 12 rays, i.e. glyph[lscript] =0). Both methods include heating due to the photoelectric effect, H 2 photodissociation, UV pumping of H 2 , H 2 formation on dust grains, and cosmic ray ionization. However, 3d-pdr also includes photo-ionization of neutral Carbon and turbulent heating. Both methods neglect the impact of the gas velocity distribution on the chemistry. In practice, the details of the velocity field affect the H 2 shielding, since the H 2 photodissociation rate from any given Lyman-Werner line is related to the escape probability for that line (see Glover & Mac Low (2007a) and discussion therein). G10 and previous papers instead adopt a six-ray approximation to estimate the shielding, which includes no velocity information. 3d-pdr relates the line optical depth to an effective linewidth, which is proportional to the root mean square of the thermal sound speed and turbulent gas velocity. In modeling cooling, both methods include emission by C, C + and O fine structure lines, gas-grain collisional cooling, cooling by rotational lines of CO, and H 2 collisional dissociation, but 3d-pdr neglects H 2 and H 2 O rovibrational and OH rotational lines, which are included in the one-dimensional code ucl pdr (Bayet et al. 2010), as well as H collisional ionization and Compton cooling. However, these lines do not produce significant cooling under the conditions considered here, and so neglecting them is a good approximation. To perform a precise comparison of the two methods we apply 3d-pdr directly to the density field of n300. We adopt identical C and O abundances ( x C = 1 . 41 × 10 -4 and x O = 3 . 16 × 10 -4 in all forms relative to hydrogen), evolve to the same final time of 5.7 Myr, and apply the same stellar FUV field at the boundary. Figure 6 shows the H, H 2 , C, and CO abundances binned as a function of effective extinction for the two methods. We define the effective extinction following G10: where A v , eff is a weighting over the extinctions of all N glyph[lscript] = 12 rays. For comparison, we include the abundances for a different simulated density field in order to assess the sensitivity to the underlying density distribution. In Figures 6 and 7 we consider only densities 200 cm -3 ≤ n ≤ 10 4 cm -3 . 1 We find that the G10 and 3d-pdr results differ the most at low extinction ( A v , eff < 0 . 3). These cells are near the simulation boundaries, where the impinging radiation field dissociates the H 2 . Surprisingly, this transition is largely absent in the G10 method, which also appears to over-estimate the fraction of atomic hydrogen throughout the PDR. At higher extinction, the G10 and 3d-pdr methods show reasonable confluence between the distributions of C and CO. The similarity between the n300 and Rm6 1.0 12 distributions illustrates that the PDR is not overly sensitive to the underlying density distribution. We note that the abundance distributions of Rm6 0.0 12, which we evolve to 100 Myr, and those of Rm6 0.0 12b, which we conclude at 5.7 Myr, are very similar. This suggests that these species achieve chemical equilibrium by 5.7 Myr (see also Bayet et al. 2009). The formation time of molecular hydrogen for gas with n = 10 3 cm -3 is t form glyph[similarequal] 10 9 n -1 yr glyph[similarequal] 1 Myr (Hollenbach et al. 1971). CO forms rapidly provided A v glyph[greaterorsimilar] 0 . 7 (Bergin et al. 2004) Figure 7 illustrates the gas temperature distributions in the three cases. G10 reaches a slightly lower temperature at low Av, but otherwise the calculations are within a standard deviation. The temperature histograms, which show the relative number of cells at different temperatures, are somewhat different. All simulations exhibit a peak in the temperature distribution at ∼ 30 -50 K. Despite the general congruence of mean properties, Figure 8 demonstrates that individual cells may have very different fractional abundances. H 2 abundance has the best point-by-point agreement since it is nearly constant throughout the domain. The exception occurs at the cloud boundaries, where the G10 method does not appear to model the PDR regime as well as 3d-pdr . The discrepancy is likely due to the lower ray resolution of G10, which causes the H 2 fraction to be over-estimated (see discussion in section 3.3). G10 mention ray resolution as a possible deficit of their 6-ray approach. The H abundance shows fairly good correspondence between the two methods but does differ by an order of magnitude at some points. The higher H fractional abundance at high-Av shown for n300 G10 may be due to turbulent mixing, which we do not include in our approach. However, since n300 does not include gravity, which would reduce turbulent turnover at high-densities, this H fractional abundance may also be an over-estimate (S. Glover private communication). The C and CO abundances produced by the two methods are also generally similar with the most difference occurring in the range -5 pc < x < 0 pc, which corresponds to gas densities n < 10 2 cm -3 . Since the input densities, grid resolution, and atomic abundances are identical, all discrepancies must be due to differences in methodology and chemical assumptions. Although the magnitude of the abundance variation appears quite large, such differences are consistent with those typically found between PDR codes (Rollig et al. 1 We find that Figures 6 and 7 appear very similar assuming a lower cutoff of n ≥ 50 cm -3 (e.g., Rm6 1.0 12 48 and Rm6 1.0 12 NC). The main result of including lower densities in the PDR calculation is that the low-Av gas becomes increasingly (and inaccurately) warm.",
"pages": [
7,
8
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},
{
"title": "4.2. Dependence on Dimensionality: 1D versus 3D",
"content": "Figure 9 shows the extinction distribution as a function of the local gas number density. As shown by G10 (e.g., their Figure 14), gas extinction and density are only very weakly correlated. Overall, extinction is more strongly correlated with position within the cloud than with density. Figure 9 exhibits two populations of points: those in the interior and those spatially within < 1% the boundary, which have distinctly lower extinction and stand out in the regime 3 . 5 < log n < 4. These boundary cells appear to be missing from the results of G10. We discuss them further in section 4.3. Figure 10 illustrates how the H 2 , C + , C, and CO fractional abundances depend upon extinction, UV field, and location within the cloud. Both H 2 and CO, which are the most sensitive to the extinction, appear to behave differently at the cloud edge and in the interior. Some of the discontinuity in the distribution is likely artificial since better edge resolution, as shown in Figure 3, would join the two populations more smoothly. The left column plots verify that the the local extinction and UV field magnitude are completely correlated (i.e., the extinction indicated by the color-scale varies completely linearly with the magnitude of the UV field). Relative to extinction, proximity to the cloud edge has a weaker influence since the abundances depend upon the column density along each ray, which varies as the density distribution. Figure 11 illustrates how abundances correlate with the gas temperature. Temperature varies smoothly with both UV and A v , eff . For C, a discrete region of boundary cells becomes apparent, which was previously degenerate with the cells near but not abutting the boundary. These boundary cells show up as a slight offset in temperature for A v , eff < -0 . 5. The shape of the abundance-UV field distributions depends on the range of underlying densities in the PDR. Figure 12 shows the abundance distributions over plotted with lines showing the abundances computed for simple 1D models. The 1D models assume constant density along the line-of-sight and an incident 1 Draine UV field at one end. These curves illustrate that the range in abundance for any given UV field simply depends on the range in local gas density for a given UV field. Since we define the PDR region as those points with densities n = 200 cm -3 to 10 4 cm -3 the curves with these densities correlate well with the data of the 3D simulations. Thus, while turbulence dictates the distribution of densities and hence the fraction of cells within a given density range, the abundance distribution is set by chemistry and the details of the species response to the local UV field. In summary, although the determination of the extinction at a particular point within the volume is a three-dimensional problem, we find that once the local UV field is computed, the resulting abundances are nearly identical to those derived from a 1D model.",
"pages": [
8
]
},
{
"title": "4.3. Dependence on Physical Parameters",
"content": "In this section we investigate the sensitivity of the chemistry to the bulk simulation properties. In a selfconsistent treatment of molecule formation, the distribution of shock properties (e.g. the post-shock densities and temperatures) could imprint an observable signature in the measured abundances. For example, molecules such as CH 2 , HCO + and OH are directly sensitive to turbulent density fluctuations Kumar & Fisher (2013) and would likely vary as a function of simulation Mach number. In contrast, the abundance of H 2 and CO predominantly depends on the amount of shielding from the UV radiation field (Bergin et al. 2004). A parcel of gas embedded within a completely smooth ( A v > 0 . 7) cloud will be well-shielded from the UV field, whereas a parcel of gas in a highly fractal cloud will have a high probability of having a sight-line with low extinction. Consequently, we can expect that the morphological distribution of the gas will have some effect on these abundances. Figure 13 shows the mass-weighted abundances for simulations with two different Mach numbers at various evolutionary times. All orion simulations have the same mean density such that apparent differences are directly due to variations in the gas morphology. Due to the relatively high simulation mean-density, we find that the H 2 abundance is fairly insensitive to changes in the density distribution caused by gravity. Glover & Mac Low (2007a) found that the H 2 fraction increased with gravitational collapse for a smooth density distribution. However, in their case the initial mean densities were much lower than the initial density of our runs. Thus, in our simulations the gas is predominantly molecular at all times since most gas parcels are well-shielded with or without gravity. We find that C and C + abundances vary by less than 20%. The CO abundance demonstrates the largest variation and declines by more than a factor of two as the gas becomes self-gravitating. Much of this effect is due to a non-negligible fraction of the mass becoming concentrated in small, dense and well-shielded volumes that have fixed, maximal 10 -4 abundance, which decreases the extinction in the remainder of the volume (see Figure 2). Differences of ∼ 30% in 3D Mach number have a relatively small impact (less than a factor of 2) on the total mean abundance but CO does show some sensitivity with abundance increasing with Mach number. H 2 and C + fractions decrease slightly with increasing Mach number. For reference, Figure 13 includes the mean abundances of n300. In order to compare the PDR results we only consider n300 gas with densities exceeding 200 cm -3 . 2 In this case, the abundance differences are dominated by the different mean extinctions. n300 has ¯ Av ∼ 0 . 04 while Rm6 has ¯ Av ∼ 0 . 02, which results in slightly lower mean C and CO abundances. The n300 mean H 2 abundance is lower than for those computed for Rm6; however, Figure 4 in G10 exhibits a higher H 2 abundance ( ∼ 0 . 98) for a simulation with the same mean density but lower magnetic field. This suggests that there is a morphological component to the H 2 abundance difference that is related to the magnetic field strength (S. Glover private communication). Figure 14 illustrates the CO distribution as a function of gas temperature. As gravity influences the gas distribution, the number of cells with high CO abundance and cold temperature (10 ≤ T ≤ 20) increases. This is related to the volume filling factor of the dense gas, which decreases as gas becomes more concentrated in dense, collapsing regions. The shape of the temperatureabundance distribution is otherwise roughly constant with Mach number and time. In all panels, points near the edge of the simulation box comprise a distinct swath of high-temperature/lowabundance points. We color points within 2% of the edge red to highlight this dichotomy. This region directly corresponds to the lowA v , mostly atomic region at the boundary.",
"pages": [
8,
10
]
},
{
"title": "4.4. Dependence on External Radiation Field",
"content": "In order to investigate how abundance depends on the external radiation field, we consider two 3d-pdr calculations with external fields each with a magnitude of 1 Draine but with different vectors. Run Rm6 1.0 12i has an external isotropic radiation field, while Run Rm6 1.0 12ui has an external field that is a superposition of a half Draine isotropic field and a half Draine uniform field (i.e., a field that is plane parallel to the simulation boundary at all faces). Figure 15 illustrates the incident radiation field geometry for the two cases. Figure 16 illustrates that by simply changing the field incidence the internal point-by-point UV distribution is very different. The figure includes only points with a net field greater than 0.5 Draines; these points are ones which feel both the isotropic and plane-parallel components of the incident field and thus display the maximum difference. Figure 17 shows the effect of the field differences on the H, H 2 , C, and CO fractional abundances. Since CO abundance depends mainly on the local UV field and these distributions are distinct, it is unsurprising that individual abundances change by as much as 50% for different field configurations. Likewise, C and H are strongly affected by the field distribution. Figure 17 shows that the mixed field simulation has fewer high UV points and more lower UV points, which is consistent with the elevated C and CO abundances displayed in Figure 17. Since the molecular hydrogen abundance is nearly constant within the cloud, the field configuration at the boundary has little effect. The higher density gas ( n > 10 3 cm -3 ), which is well self-shielded by definition, is also largely insensitive to field changes of this magnitude. In summary, even a modest change in the UV field incidence reinforces the conclusion that three-dimensional PDR treatment is preferable to a one-dimensional treatment for complex or non-symmetric problems. We expect differences to be more significant for larger external field variations and for the inclusion of internal UV sources, i.e., protostars.",
"pages": [
10,
15
]
},
{
"title": "5. CONCLUSIONS",
"content": "We use 3d-pdr in combination with hydrodynamic molecular cloud simulations to explore the importance of dimensionality in PDR chemistry, to consider complex gas morphologies and to compare with prior results using an in situ astrochemistry treatment. First, we demonstrate that our results are robust as a function of grid sampling and edge resolution. In fact, we find that the interior cloud abundances are remarkably insensitive to the resolution of the atomic to molecular transition at the cloud boundary. We obtain reasonable agreement between the G10 in situ and 3d-pdr approaches for the C and CO abundance distributions. This is because molecules such as CO and H 2 are not particularly sensitive to the dynamical history of the gas but instead depend predominantly on the local radiation field. The two approaches differ the most for H and H 2 abundances near the cloud boundary and for cells that have low-extinction. For example, in G10 hydrogen is either entirely molecular or fully dissociated. This discrepancy appears to result from differences in the methodologies rather than chemical details, and we assert that the treatment of 3d-pdr should be more accurate in transition regions. We demonstrate that morphological differences due to cloud Mach number and evolutionary time can produce significant differences in the abundance distributions. While this may be difficult to observe directly since point by point abundances are difficult to infer, it may indirectly impact the properties of the observed molecular emission lines emerging from the cloud. Finally, we find that a relatively modest change in the external UV radiation field produces large changes in the chemical abundances. This supports the finding by B12 that three-dimensional treatment is crucial for complex and non-symmetric problems. In paper II, we plan to implement several improvements to our method. First, we will relax our simple abundance approximations at densities > 10 4 cm -3 and instead couple 3d-pdr to a one-zone gas-grain chemical network code. This will allow us to include molec- Normalized relative differences between the H, H 2 , C and CO abundances for Rm6 1.0 12i and Rm6 1.0 12ui (the same runs as in Figure 16). ular freezeout onto dust grains, gas-grain thermal coupling, and a more extensive chemical network. Second, we will investigate the effect of embedded UV sources on the chemical distribution. The orion simulations that we analyze here contain detailed information about the masses and accretion rates of embedded protostars that we have neglected in this study. In addition to these changes, work is ongoing to couple 3d-pdr to the photoionization and radiative transfer code MOCASSIN . sions and thank the referee, Robert Fisher, for suggestions that significantly improved the paper. The authors acknowledge support from NSF grant AST0901055 (S.S.R.O), NASA grant HF-51311.01 (S.S.R.O), STFC grant ST/J001511/1 (T.G.B), and a JAE-DOC research contract (T.A.B.). T.A.B also thanks the Spanish MINECO for funding support through grants AYA200907304 and CSD200900038. The orion simulations were performed on the Trestles XSEDE cluster. The authors thank Simon Glover for helpful discus-",
"pages": [
15,
16
]
},
{
"title": "HEATING RATES",
"content": "There are four main contributions to the local heating at each domain point. First, there is photoelectric heating, which is produced by UV photon interactions with dust grains and PAHs, and which dominates near the cloud surface. Second, there is cosmic-ray ionization heating, which is set by the standard cosmic-ray density and becomes dominant deeper into the cloud. Third, there is chemical heating as the result of various exothermic reactions. Finally, there is turbulent heating, which is due to energy dissipation through shocks and depends on the turbulent outer scale (e.g., cloud size) and turbulent Mach number. Figure A1 shows the distribution of heating rates for each of these contributions. Photoelectric heating dominates in most cases, and the turbulent heating generally provides the smallest contribution. If the turbulent heating is proportional to v 3 TURB /L , then for the 2pc simulations here it should range from v 3 TURB /L = 1 . 5 × 10 -5 -1 . 4 × 10 -4 cm 2 s -3 , which brackets the constant value, 6 . 5 × 10 -5 cm 2 s -3 , we adopt in our calculations. We direct the reader to Pan & Padoan (2009) and Kumar & Fisher (2013) for additional discussion and modeling of heating due to turbulent dissipation, intermittency, and shear flows.",
"pages": [
16
]
},
{
"title": "REFERENCES",
"content": "Banerjee, R., V'azquez-Semadeni, E., Hennebelle, P., & Klessen, R. S. 2009, MNRAS, 398, 1082 Bayet, E., Hartquist, T. W., Viti, S., Williams, D. A., & Bell, T. A. 2010, A&A, 521, A16 Bayet, E., Viti, S., Williams, D. A., Rawlings, J. M. C., & Bell, T. 2009, ApJ, 696, 1466 Bell, T. A., Roueff, E., Viti, S., & Williams, D. A. 2006, MNRAS, 371, 1865 Bergin, E. A., Hartmann, L. W., Raymond, J. C., & BallesterosParedes, J. 2004, ApJ, 612, 921 Bisbas, T. G., Bell, T. A., Viti, S., Yates, J., & Barlow, M. J. 2012, MNRAS, 427, 2100 de Jong, T., Dalgarno, A., & Chu, S.-I. 1975, ApJ, 199, 69 Ercolano, B., Barlow, M. J., Storey, P. J., & Liu, X.-W. 2003, MNRAS, 340, 1136 -. 2007b, ApJ, 659, 1317 G'orski, K. M., Hivon, E., Banday, A. J., et al. 2005, ApJ, 622, 759 Hansen, C. E., Klein, R. I., McKee, C. F., & Fisher, R. T. 2012, ApJ, 747, 22 Hollenbach, D. J., Werner, M. W., & Salpeter, E. E. 1971, ApJ, 163, 165 Klein, R. I. 1999, JCoAM, 109, 123 Krumholz, M. R., Klein, R. I., & McKee, C. F. 2007, ApJ, 656, 959 Krumholz, M. R., McKee, C. F., & Klein, R. I. 2004, ApJ, 611, 399 Kumar, A. & Fisher, R. T. 2013, MNRAS, 431, 455 Le Teuff, Y. H., Millar, T. J., & Markwick, A. J. 2000, A&AS, 146, 157 Levrier, F., Le Petit, F., Hennebelle, P., et al. 2012, A&A, 544, A22 Mac Low, M.-M. 1999, ApJ, 524, 169 Nelson, R. P. & Langer, W. D. 1997, ApJ, 482, 796 -. 1999, ApJ, 524, 923 Offner, S. S. R., Klein, R. I., & McKee, C. F. 2008, ApJ, 681, 375 Offner, S. S. R., Klein, R. I., McKee, C. F., & Krumholz, M. R. 2009, ApJ, 703, 131 Osterbrock, D. E. 1974, Research supported by the Research Corp., Wisconsin Alumni Research Foundation, John Simon Guggenheim Memorial Foundation, Institute for Advanced Studies, and National Science Foundation. San Francisco, W. H. Freeman and Co., 1974. 263 p. Padoan, P., Nordlund, A., & Jones, B. J. T. 1997, MNRAS, 288, 145 Pan, L. & Padoan, P. 2009, ApJ, 692, 594",
"pages": [
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}
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2013ApJ...770L..32G
https://arxiv.org/pdf/1305.4150.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_85><loc_89><loc_87></location>DYNAMICAL EVIDENCE FOR A MAGNETOCENTRIFUGAL WIND FROM A 20 M /circledot BINARY YOUNG STELLAR OBJECT</section_header_level_1>
<text><location><page_1><loc_16><loc_81><loc_83><loc_84></location>L. J. Greenhill, 1 C. Goddi, 2 C. J. Chandler, 3 L. D. Matthews, 4 and E. M. L. Humphreys 2 Draft version June 5, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_79><loc_55><loc_80></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_64><loc_86><loc_78></location>In Orion BN/KL, proper motions of λ 7 mm vibrationally-excited SiO masers trace rotation of a nearly edge-on disk and a bipolar wide-angle outflow 10-100AU from radio Source I, a binary young stellar object (YSO) of ∼ 20M /circledot . Here we map ground-state λ 7 mm SiO emission with the Very Large Array and track proper motions over 9 years. The innermost and strongest emission lies in two extended arcs bracketing Source I. The proper motions trace a northeast-southwest bipolar outflow 100-1000AU from Source I with a median 3D motion of ∼ 18 km s -1 . An overlying distribution of λ 1 . 3cm H 2 O masers betrays similar flow characteristics. Gas dynamics and emission morphology traced by the masers suggest the presence of a magnetocentrifugal disk-wind. Reinforcing evidence lies in the colinearity of the flow, apparent rotation across the flow parallel to the disk rotation, and recollimation that narrows the flow opening angle ∼ 120AU downstream. The arcs of ground-state SiO emission may mark the transition point to a shocked super-Alfv'enic outflow.</text>
<text><location><page_1><loc_14><loc_61><loc_86><loc_63></location>Subject headings: ISM: individual objects (Orion BN/KL) - ISM: jets and outflows - ISM: Kinematics and dynamics - ISM: molecules - masers - stars: formation</text>
<section_header_level_1><location><page_1><loc_22><loc_57><loc_35><loc_58></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_45><loc_48><loc_57></location>The balance of gravitational, radiative, and magnetic forces driving high-mass star formation is poorly understood, in part because it has not been possible in general to resolve regions where outflows are launched and collimated. Complicating study, high-mass young stellar objects (YSOs) are deeply embedded during the accretion phase, evolve rapidly, and tend to form in distant crowded regions for which observations may be confusion-limited.</text>
<text><location><page_1><loc_8><loc_26><loc_48><loc_45></location>The nearest high-mass YSO, radio Source I in Orion BN/KL (418 ± 6pc; Kim et al. 2008) offers unique opportunities for investigation. It is deeply embedded (Greenhill et al. 2004a) in a crowded region (Gezari et al. 1998; Shuping et al. 2004). However, it is surrounded by a compact ionized disk with R ∼ 40 AU resolved in the radio continuum (Goddi et al. 2011a), interpreted as either a hypercompact-HII region at T ∼ 8000 K emitting p/e Bremsstrahlung around a ∼ 10 M /circledot YSO or a massive disk at T < 4500 K emitting via H -opacity and heated by ∼ 10 5 L /circledot (Reid et al. 2007; Plambeck et al. 2013). Goddi et al. (2011a) have estimated a robust dynamical mass of ∼ 20M /circledot in an equal-mass binary, favoring p/e Bremsstrahlung.</text>
<text><location><page_1><loc_8><loc_17><loc_48><loc_26></location>Gas dynamical study is enabled by an unusually large number of maser transitions of SiO and H 2 O excited by the YSO (e.g., Goddi et al. 2009; Greenhill et al. 1998). Specifically, the position-velocity structure of vibrationally-excited SiO masers at projected radii of 10100AU, resolved with very long baseline interferometry, outlines the limbs of a nearly edge-on, ∼ 14AU thick ob-</text>
<text><location><page_1><loc_52><loc_52><loc_92><loc_58></location>uring disk and a bipolar wide-angle outflow oriented northeast-southwest (Greenhill et al. 2004b; Kim et al. 2008; Matthews et al. 2010). Maser proper motions clearly trace rotation and expansion in a disk/outflow (Matthews et al. 2010).</text>
<text><location><page_1><loc_52><loc_41><loc_92><loc_52></location>Here, we analyze angular distributions and time evolution for ground-state λ 7 mm SiO and λ 1 cm H 2 O maser emission around Source I. The masers sample outflow on scales up to 1000 AU, reinforcing the disk-outflow model, and provide among the best dynamical evidence thus far of a magnetocentrifugal disk-wind (Blandford & Payne 1982; Konigl & Pudritz 2000) associated with a highmass YSO.</text>
<section_header_level_1><location><page_1><loc_65><loc_39><loc_78><loc_40></location>2. OBSERVATIONS</section_header_level_1>
<text><location><page_1><loc_52><loc_33><loc_92><loc_38></location>We observed SiO and H 2 O maser emission toward Source I with the Very Large Array (VLA) of the National Radio Astronomy Observatory 5 at multiple epochs over 9 years (Table 1).</text>
<text><location><page_1><loc_52><loc_21><loc_92><loc_33></location>SiOWe correlated two simultaneous, singlepolarization basebands per epoch, one tuned to the v =0 transition ( ν rest = 43423 . 79MHz) and the other to the much stronger v =1 transition ( ν rest = 43122 . 08MHz). 3C286 or 3C48 were used as absolute flux calibrators; 0530+135 or 3C84 were used as bandpass calibrators. A 6.25 MHz bandwidth covered V lsr = -13.7 to 29.4 km s -1 toward Source I, with 97.656kHz (0.65 km s -1 ) channel spacing.</text>
<text><location><page_1><loc_52><loc_12><loc_92><loc_21></location>We selected a strong v =1 Doppler component as a reference to self-calibrate antenna gain and tropospheric fluctuations on 10 s time-scales. Scans of J0541-056 enabled calibration of slowly-varying phase offsets between the signal paths for the two observing bands every 1530 m , which enabled us to transfer the antenna and tropospheric calibration to the band containing the (weaker)</text>
<text><location><page_1><loc_52><loc_7><loc_92><loc_10></location>5 The NRAO is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.</text>
<table>
<location><page_2><loc_8><loc_75><loc_48><loc_88></location>
<caption>Table 1 Summary of Observations</caption>
</table>
<text><location><page_2><loc_8><loc_73><loc_48><loc_75></location>(a) A: 35 km maximum baseline; A+: 73 km maximum baseline via addition of the Pie-Town antenna.</text>
<figure>
<location><page_2><loc_11><loc_47><loc_46><loc_71></location>
<caption>Figure 1. Nested tracers of gas surrounding Source I as observed at λ 7 mm. Velocity-integrated emission from the v =0 J = 1 → 0 transition of SiO (this work; epoch 2002.25) is shown in grayscale (26 Jy bm -1 kms -1 peak) with overlaid logarithmic contours (2 N ). Compact contours at the center depict λ 7 mm continuum emission (Goddi et al. 2011a). Black 'fuzz' extending beyond these contours depicts the distribution SiO v =1,2 maser emission as imaged with the VLBA (Matthews et al. 2010). The bulk of this emission lies in densely-sampled loci ('arms') within ∼ 50 AU of Source I, but isolated clumps (outlined in boxes for clarity) are found out to ∼ 80 AU. Dashed lines extend the four SiO v =1,2 arms to highlight that the v =0 emission subtends the same opening angle as structures on smaller scales.</caption>
</figure>
<text><location><page_2><loc_8><loc_30><loc_32><loc_31></location>v =0 line (see Goddi et al. 2009).</text>
<text><location><page_2><loc_8><loc_22><loc_48><loc_30></location>We imaged a region within ± 5 '' of Source I. Because v =0 emission contains both extended and compact maser components ( T peak b ∼ 4 × 10 6 K), we used uniform ( u,v ) weighting to isolate compact knots and estimate proper motions. For other purposes, we used ROBUST=0 weighting in AIPS (Table 1).</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_22></location>We tracked proper motions for 457 maser spots for between 2 and 4 epochs. To estimate proper motions, we searched for maser spots stronger than 5 σ within each channel-map and fit each with a two-dimensional elliptical Gaussian to obtain position, flux-density, and angular size. Images of v =0 emission are noise-limited, and relative position errors are given by 0 . 5 θ SNR , where θ is beamwidth and SNR is the peak intensity divided by the RMS noise in each velocity channel. Uncertainties for moderately bright emission were a few mas. Crossreferencing of maser spots among different epochs could</text>
<text><location><page_2><loc_52><loc_80><loc_92><loc_92></location>be done by eye because the structure of the emission in each channel persisted with shifts of < 1 beamwidth. Proper motions were calculated using an error-weighted linear least-squares fit to the fitted positions. To correct for motion of the reference v =1 component, we computed proper motions relative to the strong v =0 feature at +2.7 km s -1 and then subtracted the mean motion of all those measured (6 . 11 ± 0 . 02 km s -1 in right-ascension, 23 . 26 ± 0 . 04 km s -1 in declination).</text>
<text><location><page_2><loc_52><loc_73><loc_92><loc_80></location>We inferred absolute astrometry by measuring separation from BN, in frequency-averaged images. This agreed with that obtained using fast-switching to J0541-0541. The estimated absolute position uncertainty is ∼ 3mas, (based on this comparison).</text>
<text><location><page_2><loc_52><loc_48><loc_92><loc_73></location>H 2 OWe correlated pairs of overlapping basebands, stepped to cover V lsr = -138 to 137 km s -1 ( ν rest = 22235 . 08MHz). We report here on mapping features in the so-called H 2 O Shell (Genzel et al. 1981) associated with Source I. Each baseband was 1.56 MHz and channel spacing was 0.16 km s -1 after Hanning-smoothing. 3C286 and J0530+135 were observed as absolute-flux and bandpass calibrators, respectively. One band within each pair was tuned to include the line emission peak near -4.5 km s -1 . Ringing affected the strongest emission between -4.02 and -5.18 km s -1 . We flagged these data and used the emission at -3.86 km s -1 (1700Jy) to obtain self-calibration solutions every 10 s that were applied to both 1.56MHz bands. Scans of J0541-056 every 45 m enabled calibration of instrumental phase offsets between bands. We detected emission from -10 . 0 to 16.4 km s -1 , complete to ∼ 1 Jy in each channel, except between 8.5 and 11.3 km s -1 where the completeness limit was restricted to 2-8 Jy due to dynamic range.</text>
<text><location><page_2><loc_52><loc_41><loc_92><loc_48></location>Absolute astrometry was derived from interleaved scans of water maser emission and J0605-085, calibrated using J0541-0541, all observed in dual-polarization continuum mode with 25MHz bandwidth. The estimated absolute position uncertainty is 2 mas.</text>
<section_header_level_1><location><page_2><loc_68><loc_39><loc_76><loc_40></location>3. RESULTS</section_header_level_1>
<text><location><page_2><loc_52><loc_26><loc_92><loc_39></location>The most intense v =0 SiO maser emission occupies two arcs bracketing Source I, each at a projected radius of ∼ 100AU. This is just outside the maximum radius at which isolated v =1 masers are observed (Figure1). The arcs subtend about the same opening-angle as the nearly radial arms at smaller radii, along which v =1,2 maser features are seen to move systematically outward (Matthews et al. 2010). The northeast arc also overlies in part a 3.78 µ m/4.67 µ m color temperature minimum (Sitarski et al. 2013).</text>
<text><location><page_2><loc_52><loc_7><loc_92><loc_25></location>The angular structure of the v =0 emission is suggestive of outflow in the sky-plane, and its velocity structure confirms it (Figure 2). We tracked proper motions of 59 maser spots for four epochs, 169 for three epochs, and 219 for two epochs (457 total). The median proper motion for maser spots tracked for at least 3 epochs was 18 km s -1 . The corresponding range of 3D velocities in the local frame (V LSR =5 km s -1 ) was 4-36 km s -1 . Overlap in the ranges of radial velocity for the two lobes suggests a close to edge-on geometry (Figure 2, upperleft panel). Interpretation as an outflow is strengthened by H 2 O maser emission overlying each lobe of v =0 SiO emission (Figure 2). The H 2 O emission displays a similar range of line-of-sight velocity (-10.0 to 16.4 km s -1 ).</text>
<figure>
<location><page_3><loc_18><loc_23><loc_83><loc_84></location>
<caption>Figure 2. Tracers of outflow at radii of 10-1000 AU from Source I. ( bottom ) Overlay of SiO v =0 ( circles ) and H 2 O masers ( squares ); the latter appear more concentrated toward Source I ( /circledot ) ( middle ) Proper motions for SiO v =0 emission clumps, 1999 to 2009. Proper motions of SiO v=0 emission centroids tracked over 3 or 4 epochs (heavy arrows) and for 2 epochs (light arrows). The horizontal black arrow indicates motion of 30 km s -1 . On both halves of the lower panel, colors indicate V lsr in km s -1 ( color bar ); the systemic velocity is 5 km s -1 . ( upper left ) Distributions of line-of-sight velocities of SiO masers in the northeast and southwest lobes; their similarity indicates a flow-axis close to the sky-plane. ( upper middle ) Histogram of proper motions of SiO spots measured over at least three epochs ( shaded ) or two epochs ( unshaded ). ( upper right ) Distributions of total space velocity for SiO maser spots in the northeast and southwest lobes.</caption>
</figure>
<text><location><page_4><loc_8><loc_87><loc_48><loc_92></location>A 20 km s -1 expansion in the angular extent of the H 2 O distribution over ∼ 8years (Greenhill et al. 1998) and ∼ 18years (Figure 4, lower-left panel) is consistent with the median SiO maser proper motion.</text>
<text><location><page_4><loc_8><loc_68><loc_48><loc_86></location>The flow orientation can be estimated from the emission locus as well as the sky position and proper motions of maser spots. We obtain a common mean position angle (PA) of 56 · by reflecting the southwest lobe about a northwest-southeast line at PA 142 · , which minimizes the standard deviation of the overlapping distributions (29 · ). Using the most reliable proper motions (derived from ≥ 3 epochs), the mean motion lies at a PA= 55 ± 34 · (northeast) and -128 ± 43 · (southwest). Reflecting the southwest lobe, we obtain a mean outflow PA= 55 · and a minimum standard deviation of 34 · for a reflection axis of 142 · . Hence, we take 56 ± 1 · as the PA of the outflow, measured independently from emission locus and proper motions.</text>
<text><location><page_4><loc_8><loc_60><loc_48><loc_68></location>Although the flow inside ∼ 100AU appears to follow a fixed opening-angle, the outflow further downstream appears to become more narrowly collimated. Indeed, the inner quartile range of maser motion position angles at projected radii 0. '' 1-0. '' 3 from Source I is 80 · , broader than the range of 47 · beyond 0. '' 3 (120AU).</text>
<text><location><page_4><loc_8><loc_48><loc_48><loc_60></location>From our measurements, we estimate the outflow massloss rate ˙ M = 5 × 10 -6 V 18 R 2 200 n 6 Ω / 4 π M /circledot yr -1 , where V 18 is the average maser velocity in units of 18 km s -1 , R 200 is the average distance of SiO masers in units of 200 AU, n 6 is the volume density in units of 10 6 cm -3 , and Ω is the solid angle for a conical flow. The main uncertainty in the formula above is the density required for excitation of ground-state SiO masers, known within an order of magnitude (10 6 ± 1 cm -3 ; Goddi et al. 2009).</text>
<text><location><page_4><loc_8><loc_28><loc_48><loc_48></location>There is no indication of acceleration/deceleration with radius in the flow. But interestingly, in each lobe there is a discernible velocity offset across the minor axis, manifested in the line-of-sight velocities of both SiO and H 2 O masers (e.g., Figure 3, upper panel). Toward the southeast-facing edge, there is a greater preponderance of blueshifted emission; redshifted emission lies preferentially toward the northwest. The velocity data exhibit a non-Gaussian scatter, so to quantify the trend, we estimate the trimean LSR velocity (the weighted average of median and quartiles) as a function of distance along the minor axis for emission 0. '' 1-0. '' 4 from Source I: a 5 km s -1 shift for v=0 SiO and a 10 km s -1 shift for H 2 O maser emission. We interpret this velocity offset as a signature of rotation parallel to the minor axis of the flow.</text>
<text><location><page_4><loc_8><loc_9><loc_48><loc_28></location>Ground state SiO J = 1 -0 maser emission and proper motions displayed in Figures 1-3 trace only the inner portions of the bipolar outflow traced by J = 2 -1 emission and mapped with CARMA at 0. '' 5 resolution (Plambeck et al. 2009), or the J = 5 -4 emission mapped with ALMA at 1. '' 5 resolution (Zapata et al. 2012; Niederhofer et al. 2012). These transitions show basically the same 'butterfly' morphology at projected radii /lessorsimilar 500AU and excellent agreement in the outflow PA (56 · ). While complex brightness and velocity-field morphologies are evident well away from Source I, this may be a consequence of external heating (Niederhofer et al. 2012), e.g., by the Hot-Core and compact mid-infrared sources (Figure 4).</text>
<figure>
<location><page_4><loc_57><loc_14><loc_88><loc_92></location>
<caption>Figure 3. Expanded view of the outflow. ( top ) SiO v =0 and H 2 O masers ( open circles and squares , respectively), velocity-integrated SiO v =1 masers ( red contours ), and Source I λ 7 mm continuum ( black contours ), as mapped with the VLA. ( middle ) Expanded view of SiO v =0 maser proper motions in the northeast lobe of Source I. ( bottom ) Expanded view of the southwest lobe.</caption>
</figure>
<figure>
<location><page_5><loc_15><loc_49><loc_76><loc_92></location>
<caption>Figure 4. Source I outflow, dense Hot-Core gas, and proximate mid-infrared sources. The outflow is shown in velocity-integrated emission of λ 3 mm J = 2 → 1 emission covering -5 to 5 km s -1 , observed with a beamwidth of 0. '' 5 ( red contours ; Plambeck et al. 2009). Contours are 3.5, 1.9, 0.55, 0.30, 0.16, 0.086, 0.046, 0.025 Jy bm -1 averaged over 10 km s -1 . Only the lower right panel includes the lowest two levels. Dense gas is shown via an NH 3 column-density map with 0. '' 8 beamwidth ( greyscale ; Goddi et al. 2011b). The lower-right panel substitutes a mid-infrared image obtained with Keck (Greenhill et al. 2004a). Crosses mark the positions of three YSOs: sources I, SMA1, and n (left to right, as in Goddi et al. 2011b). ( Upper-left ) Proper motions of outflowing SiO v =0 masers ( arrows ). ( Upper-right ) Superposition of H 2 O masers observed in 1983 ( × ) - Greenhill et al. (1998), and 2001 ( · ) - this work, demonstrating expansion of the locus. ( Lower-left ) Superposition of SiO v =0 (+) and H 2 O masers in 2001 ( · ). ( Lower-right ) Overlay of the SiO outflow with mid-infrared sources over a larger field-of-view.</caption>
</figure>
<section_header_level_1><location><page_5><loc_14><loc_36><loc_43><loc_37></location>4.1. Outflow 100-1000 AU from Source I</section_header_level_1>
<text><location><page_5><loc_8><loc_14><loc_48><loc_36></location>The X-shaped morphology traced by vibrationallyexcited SiO maser emission within 100AU of Source I is interpreted as the edges of a bipolar outflow orthogonal to an edge-on rotating disk (Matthews et al. 2010). Our new mapping of the ground-state SiO and H 2 O maser emission confirms and extends to 1000AU the disk-outflow model. Three lines of evidence support this scenario: (i) the most intense v =0 SiO maser emission occupies two arcs that bracket Source I at a radius of ∼ 100AU and subtend an angle corresponding to the opening-angle of the vibrationally-excited SiO masers; (ii) the PA of the outflow at radii > 100 AU is the same as that of the disk and flow axes at small radii; (iii) the line-of-sight velocities of v = 0 SiO masers indicate an outflow close to the sky-plane, consistent with the nearly edge-on disk.</text>
<text><location><page_5><loc_8><loc_10><loc_48><loc_14></location>Three striking features in the outflow are evident from our measurements: colinearity, recollimation, and rotation.</text>
<text><location><page_5><loc_8><loc_8><loc_48><loc_10></location>Colinearity of northeast and southwest flows ( § 3) is notable because (i) Source I lies at the edge of the</text>
<text><location><page_5><loc_52><loc_13><loc_92><loc_37></location>dense gas associated with the Orion Hot-Core (Figure 4; Goddi et al. 2011b), (ii) the outflow motion is comparable to the stellar motion, (iii) SiO maser dynamics inside 1000AU are indicative of a ∼ 500yr crossing time for the outflow, and (iv) the crossing time for Source I from the center of dynamical interaction with BN is also ∼ 500yr (Goddi et al. 2011a), indicating that the onset of flow is contemporaneous with the interaction with BN. For a hypothetical hydrodynamic flow, the absence of curvature as a result of the YSO motion requires the momentum flux to exceed that of the ambient medium into which Source I is moving. Since ground-state SiO maser emission requires densities of 10 6 -10 7 cm -3 (e.g., Goddi et al. 2009), the density of ambient material would have to be /lessmuch 10 6 cm -3 . However, ambient gas densities in the vicinity of the Hot-Core are at least this (e.g., Goddi et al. 2011b), thus requiring greater flow energy density than from hydrodynamics alone.</text>
<text><location><page_5><loc_52><loc_7><loc_92><loc_13></location>Outflow (re)collimation is indicated by a narrower distribution of SiO proper motion position angles far from the YSO, as well as greater preponderance of line-of-sight velocities close to systemic ( § 3; Figures 2, 3). Mechanical collimation from the ambient medium is rendered prob-</text>
<text><location><page_6><loc_8><loc_81><loc_48><loc_92></location>ematic by the similarity of the leading and trailing edges of the flow despite the anticipated ambient density gradient toward the Hot-Core. In principle, maser excitation effects could bias the inferred morphology of the flow if these favor emission close to the outflow axis, but this would not explain comparable leading and trailing edge gradients in the intensity of thermal SiO emission (e.g., Figure 4, top).</text>
<text><location><page_6><loc_8><loc_73><loc_48><loc_81></location>Finally, there is a discernible rotation signature about the major axis of the flow in each lobe, consistent with the rotation observed at radii of tens of AU in the vibrationally-excited SiO masers (Matthews et al. 2010). Our data are suggestive of these dynamics being communicated from scales of O(10) AU to at least O(100)AU.</text>
<section_header_level_1><location><page_6><loc_9><loc_71><loc_47><loc_72></location>4.2. Magnetocentrifugal Wind from a high-mass YSO</section_header_level_1>
<text><location><page_6><loc_8><loc_57><loc_48><loc_71></location>The possibility of a magnetohydrodynamic disk-wind is raised by the evidence of a rotating wide-angle outflow launched from a compact disk, that is recollimated downstream, and that proceeds undeflected through a dense medium. Rotation is anticipated for a magnetized outflow with the field anchored to a rotating disk. Magnetic field lines threading the flow would raise its energy density, while a toroidal field and corresponding hoop stress generated by rotation could efficiently narrow collimation with distance.</text>
<text><location><page_6><loc_8><loc_39><loc_48><loc_57></location>Matthews et al. (2010) conservatively interpreted the maser data in the context of Keplerian motion and the dominant action of gravity, inferring a dynamical mass of ∼ 8M /circledot . However, early indirect evidence of nongravitational effects were noted (e.g., curved maser trajectories), possibly due to magnetic fields, by which rotation would appear Keplerian though the YSO mass would be underestimated. The latter is consistent with the difference between YSO masses inferred by Matthews et al. (2010) and Goddi et al. (2011a) under the assumption that BN and Source I are in recoil (cf. Chatterjee & Tan 2012). This early evidence, along with the morphology and dynamics of outflow on scales out to 1000AU, strengthens the case for a magnetic flow.</text>
<text><location><page_6><loc_8><loc_23><loc_48><loc_39></location>Using axisymmetric MHD numerical simulations, Vaidya & Goddi (2013) have explored the plausibility of an MHD origin of the wide-angle flow probed by vibrationally-excited SiO masers inside 100AU from Source I, and proposed that the SiO masers may be excited as an MHD driven wind interacts with the ambient molecular medium in form of shocks. Seifried et al. (2012) studied earlier conditions, applying MHD theory from the collapse of magnetized cloud cores to disk formation and outflow launching, and demonstrated magnetocentrifugal launching of massive outflows, similar to the case of low-mass outflows.</text>
<text><location><page_6><loc_8><loc_11><loc_48><loc_23></location>Why do intense ground-state SiO and H 2 O maser emission arise suddenly at 100 AU? Why are SiO and H 2 O masers apparently intermixed when the densities required for emission differ by (conservatively) an order of magnitude? For a YSO luminosity of 2 × 10 4 L /circledot (i.e., a binary with two 10 M /circledot stars), the sublimation radius is /lessmuch 100AU, and since maser emission requires a high gasphase abundance, its appearance so far out in the flow is significant.</text>
<text><location><page_6><loc_8><loc_7><loc_48><loc_11></location>We propose that the arcs of maser emission at ∼ 100AU radius indicate the onset of strong shocks in dusty outflowing material. Hydromagnetic C-type shocks as</text>
<text><location><page_6><loc_52><loc_71><loc_92><loc_92></location>slow as 10-20kms -1 (comparable to the flow speed) are capable of sputtering grains (Schilke et al. 1997; Van Loo et al. 2013, and references therein), a process that would raise the gas-phase abundance of SiO and H 2 O. Formation of two continuous shock structures subtending broad ranges of polar angle and narrow ranges in radius indicates a systematic change in physical conditions. Transition to a super-Alfv'enic flow and consequent shock formation may trigger the observed (re)appearance of maser emission in the outflow at ∼ 100AU. Decline in Alfv'en velocity below the outflow velocity would require the magnetic field to decline at least linearly with radius if density falls quadratically. This is not implausible. An observational consequence is that the inner edge of the maser emission locus would not appear to expand with time.</text>
<text><location><page_6><loc_52><loc_57><loc_92><loc_71></location>The presence of maser emission well downstream, suggests persistent high gas-phase abundance, as well as energy that can drive maser pumping. Flow speeds in excess of the sound and Alfv'en speeds would drive shocks and impart pump energy over a wide range of radii, assuming that cooling timescales are much shorter than dynamical time scales. In this region, observed fading of the velocity gradient indicative of rotation around the flow axis is consistent with decoupling of the neutral gas from the field as expected from MHD disk-wind models.</text>
<section_header_level_1><location><page_6><loc_66><loc_55><loc_78><loc_56></location>5. CONCLUSIONS</section_header_level_1>
<text><location><page_6><loc_52><loc_36><loc_92><loc_55></location>Data for SiO and H 2 O masers provide an unusually detailed view of the launch and collimation of an outflow from the surface of a compact disk surrounding Source I in BN/KL. Position and velocity resolved gas dynamics at projected radii of 10 AU to 1000 AU suggest the presence of a magnetocentrifugal disk-wind driven by a massive YSO. This is notable in view of continuing ambiguity concerning the role of magnetic fields in high-mass star formation. While the outflow structure up to 1000 AU in this high-mass YSO is remarkable in terms of symmetry, colinearity, collimation, and rotation, larger scales reveal the effects of the interaction of the massive outflow with the typically complex environment of a massive star forming region.</text>
<section_header_level_1><location><page_6><loc_67><loc_34><loc_77><loc_35></location>REFERENCES</section_header_level_1>
<text><location><page_6><loc_52><loc_7><loc_92><loc_32></location>Blandford, R. D. & Payne, D. G. 1982, MNRAS, 199, 883 Chatterjee, S., & Tan, J. C. 2012, ApJ, 754, 152 Genzel, R., Reid, M. J., Moran, J. M., & Downes, D. 1981, ApJ, 244, 884 Gezari, D. Y., Backman, D. E., & Werner, M. W. 1998, ApJ, 509, 283 Goddi, C., Greenhill, L. J., Chandler, C. J., Humphreys, E. M. L., Matthews, L. D., & Gray, M. D. 2009, ApJ, 698, 1165 Goddi, C., Humphreys, E. M. L., Greenhill, L. J., Chandler, C. J., Matthews, L. D. 2011a, ApJ, 728, 15 Goddi, C., Greenhill, L. J., Humphreys, E. M. L., Chandler, C. J., & Matthews, L. D. 2011b, ApJ, 739, L13 Greenhill, L. J., Gwinn, C. R., Schwartz, C., Moran, J. M., & Diamond, P. J. 1998, Nature, 396, 650 Greenhill, L. J., Gezari, D. Y., Danchi, W. C., Najita, J., Monnier, J. D., & Tuthill, P. G. 2004a, ApJ, 605, L57 Greenhill, L. J., Reid, M. J., Chandler, C. J., Diamond, P. J., & Elitzur, M. 2004b, Star Formation at High Angular Resolution, 221, 155 Kim, M. K., et al. 2008, PASJ, 60, 991 Konigl, A. & Pudritz, R. E. 2000, Protostars and Planets IV, ed. V. Mannings, A. P. Boss, & S. S. Russell (Tucson, AZ: Univ. Arizona Press), 759</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "In Orion BN/KL, proper motions of λ 7 mm vibrationally-excited SiO masers trace rotation of a nearly edge-on disk and a bipolar wide-angle outflow 10-100AU from radio Source I, a binary young stellar object (YSO) of ∼ 20M /circledot . Here we map ground-state λ 7 mm SiO emission with the Very Large Array and track proper motions over 9 years. The innermost and strongest emission lies in two extended arcs bracketing Source I. The proper motions trace a northeast-southwest bipolar outflow 100-1000AU from Source I with a median 3D motion of ∼ 18 km s -1 . An overlying distribution of λ 1 . 3cm H 2 O masers betrays similar flow characteristics. Gas dynamics and emission morphology traced by the masers suggest the presence of a magnetocentrifugal disk-wind. Reinforcing evidence lies in the colinearity of the flow, apparent rotation across the flow parallel to the disk rotation, and recollimation that narrows the flow opening angle ∼ 120AU downstream. The arcs of ground-state SiO emission may mark the transition point to a shocked super-Alfv'enic outflow. Subject headings: ISM: individual objects (Orion BN/KL) - ISM: jets and outflows - ISM: Kinematics and dynamics - ISM: molecules - masers - stars: formation",
"pages": [
1
]
},
{
"title": "DYNAMICAL EVIDENCE FOR A MAGNETOCENTRIFUGAL WIND FROM A 20 M /circledot BINARY YOUNG STELLAR OBJECT",
"content": "L. J. Greenhill, 1 C. Goddi, 2 C. J. Chandler, 3 L. D. Matthews, 4 and E. M. L. Humphreys 2 Draft version June 5, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "The balance of gravitational, radiative, and magnetic forces driving high-mass star formation is poorly understood, in part because it has not been possible in general to resolve regions where outflows are launched and collimated. Complicating study, high-mass young stellar objects (YSOs) are deeply embedded during the accretion phase, evolve rapidly, and tend to form in distant crowded regions for which observations may be confusion-limited. The nearest high-mass YSO, radio Source I in Orion BN/KL (418 ± 6pc; Kim et al. 2008) offers unique opportunities for investigation. It is deeply embedded (Greenhill et al. 2004a) in a crowded region (Gezari et al. 1998; Shuping et al. 2004). However, it is surrounded by a compact ionized disk with R ∼ 40 AU resolved in the radio continuum (Goddi et al. 2011a), interpreted as either a hypercompact-HII region at T ∼ 8000 K emitting p/e Bremsstrahlung around a ∼ 10 M /circledot YSO or a massive disk at T < 4500 K emitting via H -opacity and heated by ∼ 10 5 L /circledot (Reid et al. 2007; Plambeck et al. 2013). Goddi et al. (2011a) have estimated a robust dynamical mass of ∼ 20M /circledot in an equal-mass binary, favoring p/e Bremsstrahlung. Gas dynamical study is enabled by an unusually large number of maser transitions of SiO and H 2 O excited by the YSO (e.g., Goddi et al. 2009; Greenhill et al. 1998). Specifically, the position-velocity structure of vibrationally-excited SiO masers at projected radii of 10100AU, resolved with very long baseline interferometry, outlines the limbs of a nearly edge-on, ∼ 14AU thick ob- uring disk and a bipolar wide-angle outflow oriented northeast-southwest (Greenhill et al. 2004b; Kim et al. 2008; Matthews et al. 2010). Maser proper motions clearly trace rotation and expansion in a disk/outflow (Matthews et al. 2010). Here, we analyze angular distributions and time evolution for ground-state λ 7 mm SiO and λ 1 cm H 2 O maser emission around Source I. The masers sample outflow on scales up to 1000 AU, reinforcing the disk-outflow model, and provide among the best dynamical evidence thus far of a magnetocentrifugal disk-wind (Blandford & Payne 1982; Konigl & Pudritz 2000) associated with a highmass YSO.",
"pages": [
1
]
},
{
"title": "2. OBSERVATIONS",
"content": "We observed SiO and H 2 O maser emission toward Source I with the Very Large Array (VLA) of the National Radio Astronomy Observatory 5 at multiple epochs over 9 years (Table 1). SiOWe correlated two simultaneous, singlepolarization basebands per epoch, one tuned to the v =0 transition ( ν rest = 43423 . 79MHz) and the other to the much stronger v =1 transition ( ν rest = 43122 . 08MHz). 3C286 or 3C48 were used as absolute flux calibrators; 0530+135 or 3C84 were used as bandpass calibrators. A 6.25 MHz bandwidth covered V lsr = -13.7 to 29.4 km s -1 toward Source I, with 97.656kHz (0.65 km s -1 ) channel spacing. We selected a strong v =1 Doppler component as a reference to self-calibrate antenna gain and tropospheric fluctuations on 10 s time-scales. Scans of J0541-056 enabled calibration of slowly-varying phase offsets between the signal paths for the two observing bands every 1530 m , which enabled us to transfer the antenna and tropospheric calibration to the band containing the (weaker) 5 The NRAO is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. (a) A: 35 km maximum baseline; A+: 73 km maximum baseline via addition of the Pie-Town antenna. v =0 line (see Goddi et al. 2009). We imaged a region within ± 5 '' of Source I. Because v =0 emission contains both extended and compact maser components ( T peak b ∼ 4 × 10 6 K), we used uniform ( u,v ) weighting to isolate compact knots and estimate proper motions. For other purposes, we used ROBUST=0 weighting in AIPS (Table 1). We tracked proper motions for 457 maser spots for between 2 and 4 epochs. To estimate proper motions, we searched for maser spots stronger than 5 σ within each channel-map and fit each with a two-dimensional elliptical Gaussian to obtain position, flux-density, and angular size. Images of v =0 emission are noise-limited, and relative position errors are given by 0 . 5 θ SNR , where θ is beamwidth and SNR is the peak intensity divided by the RMS noise in each velocity channel. Uncertainties for moderately bright emission were a few mas. Crossreferencing of maser spots among different epochs could be done by eye because the structure of the emission in each channel persisted with shifts of < 1 beamwidth. Proper motions were calculated using an error-weighted linear least-squares fit to the fitted positions. To correct for motion of the reference v =1 component, we computed proper motions relative to the strong v =0 feature at +2.7 km s -1 and then subtracted the mean motion of all those measured (6 . 11 ± 0 . 02 km s -1 in right-ascension, 23 . 26 ± 0 . 04 km s -1 in declination). We inferred absolute astrometry by measuring separation from BN, in frequency-averaged images. This agreed with that obtained using fast-switching to J0541-0541. The estimated absolute position uncertainty is ∼ 3mas, (based on this comparison). H 2 OWe correlated pairs of overlapping basebands, stepped to cover V lsr = -138 to 137 km s -1 ( ν rest = 22235 . 08MHz). We report here on mapping features in the so-called H 2 O Shell (Genzel et al. 1981) associated with Source I. Each baseband was 1.56 MHz and channel spacing was 0.16 km s -1 after Hanning-smoothing. 3C286 and J0530+135 were observed as absolute-flux and bandpass calibrators, respectively. One band within each pair was tuned to include the line emission peak near -4.5 km s -1 . Ringing affected the strongest emission between -4.02 and -5.18 km s -1 . We flagged these data and used the emission at -3.86 km s -1 (1700Jy) to obtain self-calibration solutions every 10 s that were applied to both 1.56MHz bands. Scans of J0541-056 every 45 m enabled calibration of instrumental phase offsets between bands. We detected emission from -10 . 0 to 16.4 km s -1 , complete to ∼ 1 Jy in each channel, except between 8.5 and 11.3 km s -1 where the completeness limit was restricted to 2-8 Jy due to dynamic range. Absolute astrometry was derived from interleaved scans of water maser emission and J0605-085, calibrated using J0541-0541, all observed in dual-polarization continuum mode with 25MHz bandwidth. The estimated absolute position uncertainty is 2 mas.",
"pages": [
1,
2
]
},
{
"title": "3. RESULTS",
"content": "The most intense v =0 SiO maser emission occupies two arcs bracketing Source I, each at a projected radius of ∼ 100AU. This is just outside the maximum radius at which isolated v =1 masers are observed (Figure1). The arcs subtend about the same opening-angle as the nearly radial arms at smaller radii, along which v =1,2 maser features are seen to move systematically outward (Matthews et al. 2010). The northeast arc also overlies in part a 3.78 µ m/4.67 µ m color temperature minimum (Sitarski et al. 2013). The angular structure of the v =0 emission is suggestive of outflow in the sky-plane, and its velocity structure confirms it (Figure 2). We tracked proper motions of 59 maser spots for four epochs, 169 for three epochs, and 219 for two epochs (457 total). The median proper motion for maser spots tracked for at least 3 epochs was 18 km s -1 . The corresponding range of 3D velocities in the local frame (V LSR =5 km s -1 ) was 4-36 km s -1 . Overlap in the ranges of radial velocity for the two lobes suggests a close to edge-on geometry (Figure 2, upperleft panel). Interpretation as an outflow is strengthened by H 2 O maser emission overlying each lobe of v =0 SiO emission (Figure 2). The H 2 O emission displays a similar range of line-of-sight velocity (-10.0 to 16.4 km s -1 ). A 20 km s -1 expansion in the angular extent of the H 2 O distribution over ∼ 8years (Greenhill et al. 1998) and ∼ 18years (Figure 4, lower-left panel) is consistent with the median SiO maser proper motion. The flow orientation can be estimated from the emission locus as well as the sky position and proper motions of maser spots. We obtain a common mean position angle (PA) of 56 · by reflecting the southwest lobe about a northwest-southeast line at PA 142 · , which minimizes the standard deviation of the overlapping distributions (29 · ). Using the most reliable proper motions (derived from ≥ 3 epochs), the mean motion lies at a PA= 55 ± 34 · (northeast) and -128 ± 43 · (southwest). Reflecting the southwest lobe, we obtain a mean outflow PA= 55 · and a minimum standard deviation of 34 · for a reflection axis of 142 · . Hence, we take 56 ± 1 · as the PA of the outflow, measured independently from emission locus and proper motions. Although the flow inside ∼ 100AU appears to follow a fixed opening-angle, the outflow further downstream appears to become more narrowly collimated. Indeed, the inner quartile range of maser motion position angles at projected radii 0. '' 1-0. '' 3 from Source I is 80 · , broader than the range of 47 · beyond 0. '' 3 (120AU). From our measurements, we estimate the outflow massloss rate ˙ M = 5 × 10 -6 V 18 R 2 200 n 6 Ω / 4 π M /circledot yr -1 , where V 18 is the average maser velocity in units of 18 km s -1 , R 200 is the average distance of SiO masers in units of 200 AU, n 6 is the volume density in units of 10 6 cm -3 , and Ω is the solid angle for a conical flow. The main uncertainty in the formula above is the density required for excitation of ground-state SiO masers, known within an order of magnitude (10 6 ± 1 cm -3 ; Goddi et al. 2009). There is no indication of acceleration/deceleration with radius in the flow. But interestingly, in each lobe there is a discernible velocity offset across the minor axis, manifested in the line-of-sight velocities of both SiO and H 2 O masers (e.g., Figure 3, upper panel). Toward the southeast-facing edge, there is a greater preponderance of blueshifted emission; redshifted emission lies preferentially toward the northwest. The velocity data exhibit a non-Gaussian scatter, so to quantify the trend, we estimate the trimean LSR velocity (the weighted average of median and quartiles) as a function of distance along the minor axis for emission 0. '' 1-0. '' 4 from Source I: a 5 km s -1 shift for v=0 SiO and a 10 km s -1 shift for H 2 O maser emission. We interpret this velocity offset as a signature of rotation parallel to the minor axis of the flow. Ground state SiO J = 1 -0 maser emission and proper motions displayed in Figures 1-3 trace only the inner portions of the bipolar outflow traced by J = 2 -1 emission and mapped with CARMA at 0. '' 5 resolution (Plambeck et al. 2009), or the J = 5 -4 emission mapped with ALMA at 1. '' 5 resolution (Zapata et al. 2012; Niederhofer et al. 2012). These transitions show basically the same 'butterfly' morphology at projected radii /lessorsimilar 500AU and excellent agreement in the outflow PA (56 · ). While complex brightness and velocity-field morphologies are evident well away from Source I, this may be a consequence of external heating (Niederhofer et al. 2012), e.g., by the Hot-Core and compact mid-infrared sources (Figure 4).",
"pages": [
2,
4
]
},
{
"title": "4.1. Outflow 100-1000 AU from Source I",
"content": "The X-shaped morphology traced by vibrationallyexcited SiO maser emission within 100AU of Source I is interpreted as the edges of a bipolar outflow orthogonal to an edge-on rotating disk (Matthews et al. 2010). Our new mapping of the ground-state SiO and H 2 O maser emission confirms and extends to 1000AU the disk-outflow model. Three lines of evidence support this scenario: (i) the most intense v =0 SiO maser emission occupies two arcs that bracket Source I at a radius of ∼ 100AU and subtend an angle corresponding to the opening-angle of the vibrationally-excited SiO masers; (ii) the PA of the outflow at radii > 100 AU is the same as that of the disk and flow axes at small radii; (iii) the line-of-sight velocities of v = 0 SiO masers indicate an outflow close to the sky-plane, consistent with the nearly edge-on disk. Three striking features in the outflow are evident from our measurements: colinearity, recollimation, and rotation. Colinearity of northeast and southwest flows ( § 3) is notable because (i) Source I lies at the edge of the dense gas associated with the Orion Hot-Core (Figure 4; Goddi et al. 2011b), (ii) the outflow motion is comparable to the stellar motion, (iii) SiO maser dynamics inside 1000AU are indicative of a ∼ 500yr crossing time for the outflow, and (iv) the crossing time for Source I from the center of dynamical interaction with BN is also ∼ 500yr (Goddi et al. 2011a), indicating that the onset of flow is contemporaneous with the interaction with BN. For a hypothetical hydrodynamic flow, the absence of curvature as a result of the YSO motion requires the momentum flux to exceed that of the ambient medium into which Source I is moving. Since ground-state SiO maser emission requires densities of 10 6 -10 7 cm -3 (e.g., Goddi et al. 2009), the density of ambient material would have to be /lessmuch 10 6 cm -3 . However, ambient gas densities in the vicinity of the Hot-Core are at least this (e.g., Goddi et al. 2011b), thus requiring greater flow energy density than from hydrodynamics alone. Outflow (re)collimation is indicated by a narrower distribution of SiO proper motion position angles far from the YSO, as well as greater preponderance of line-of-sight velocities close to systemic ( § 3; Figures 2, 3). Mechanical collimation from the ambient medium is rendered prob- ematic by the similarity of the leading and trailing edges of the flow despite the anticipated ambient density gradient toward the Hot-Core. In principle, maser excitation effects could bias the inferred morphology of the flow if these favor emission close to the outflow axis, but this would not explain comparable leading and trailing edge gradients in the intensity of thermal SiO emission (e.g., Figure 4, top). Finally, there is a discernible rotation signature about the major axis of the flow in each lobe, consistent with the rotation observed at radii of tens of AU in the vibrationally-excited SiO masers (Matthews et al. 2010). Our data are suggestive of these dynamics being communicated from scales of O(10) AU to at least O(100)AU.",
"pages": [
5,
6
]
},
{
"title": "4.2. Magnetocentrifugal Wind from a high-mass YSO",
"content": "The possibility of a magnetohydrodynamic disk-wind is raised by the evidence of a rotating wide-angle outflow launched from a compact disk, that is recollimated downstream, and that proceeds undeflected through a dense medium. Rotation is anticipated for a magnetized outflow with the field anchored to a rotating disk. Magnetic field lines threading the flow would raise its energy density, while a toroidal field and corresponding hoop stress generated by rotation could efficiently narrow collimation with distance. Matthews et al. (2010) conservatively interpreted the maser data in the context of Keplerian motion and the dominant action of gravity, inferring a dynamical mass of ∼ 8M /circledot . However, early indirect evidence of nongravitational effects were noted (e.g., curved maser trajectories), possibly due to magnetic fields, by which rotation would appear Keplerian though the YSO mass would be underestimated. The latter is consistent with the difference between YSO masses inferred by Matthews et al. (2010) and Goddi et al. (2011a) under the assumption that BN and Source I are in recoil (cf. Chatterjee & Tan 2012). This early evidence, along with the morphology and dynamics of outflow on scales out to 1000AU, strengthens the case for a magnetic flow. Using axisymmetric MHD numerical simulations, Vaidya & Goddi (2013) have explored the plausibility of an MHD origin of the wide-angle flow probed by vibrationally-excited SiO masers inside 100AU from Source I, and proposed that the SiO masers may be excited as an MHD driven wind interacts with the ambient molecular medium in form of shocks. Seifried et al. (2012) studied earlier conditions, applying MHD theory from the collapse of magnetized cloud cores to disk formation and outflow launching, and demonstrated magnetocentrifugal launching of massive outflows, similar to the case of low-mass outflows. Why do intense ground-state SiO and H 2 O maser emission arise suddenly at 100 AU? Why are SiO and H 2 O masers apparently intermixed when the densities required for emission differ by (conservatively) an order of magnitude? For a YSO luminosity of 2 × 10 4 L /circledot (i.e., a binary with two 10 M /circledot stars), the sublimation radius is /lessmuch 100AU, and since maser emission requires a high gasphase abundance, its appearance so far out in the flow is significant. We propose that the arcs of maser emission at ∼ 100AU radius indicate the onset of strong shocks in dusty outflowing material. Hydromagnetic C-type shocks as slow as 10-20kms -1 (comparable to the flow speed) are capable of sputtering grains (Schilke et al. 1997; Van Loo et al. 2013, and references therein), a process that would raise the gas-phase abundance of SiO and H 2 O. Formation of two continuous shock structures subtending broad ranges of polar angle and narrow ranges in radius indicates a systematic change in physical conditions. Transition to a super-Alfv'enic flow and consequent shock formation may trigger the observed (re)appearance of maser emission in the outflow at ∼ 100AU. Decline in Alfv'en velocity below the outflow velocity would require the magnetic field to decline at least linearly with radius if density falls quadratically. This is not implausible. An observational consequence is that the inner edge of the maser emission locus would not appear to expand with time. The presence of maser emission well downstream, suggests persistent high gas-phase abundance, as well as energy that can drive maser pumping. Flow speeds in excess of the sound and Alfv'en speeds would drive shocks and impart pump energy over a wide range of radii, assuming that cooling timescales are much shorter than dynamical time scales. In this region, observed fading of the velocity gradient indicative of rotation around the flow axis is consistent with decoupling of the neutral gas from the field as expected from MHD disk-wind models.",
"pages": [
6
]
},
{
"title": "5. CONCLUSIONS",
"content": "Data for SiO and H 2 O masers provide an unusually detailed view of the launch and collimation of an outflow from the surface of a compact disk surrounding Source I in BN/KL. Position and velocity resolved gas dynamics at projected radii of 10 AU to 1000 AU suggest the presence of a magnetocentrifugal disk-wind driven by a massive YSO. This is notable in view of continuing ambiguity concerning the role of magnetic fields in high-mass star formation. While the outflow structure up to 1000 AU in this high-mass YSO is remarkable in terms of symmetry, colinearity, collimation, and rotation, larger scales reveal the effects of the interaction of the massive outflow with the typically complex environment of a massive star forming region.",
"pages": [
6
]
},
{
"title": "REFERENCES",
"content": "Blandford, R. D. & Payne, D. G. 1982, MNRAS, 199, 883 Chatterjee, S., & Tan, J. C. 2012, ApJ, 754, 152 Genzel, R., Reid, M. J., Moran, J. M., & Downes, D. 1981, ApJ, 244, 884 Gezari, D. Y., Backman, D. E., & Werner, M. W. 1998, ApJ, 509, 283 Goddi, C., Greenhill, L. J., Chandler, C. J., Humphreys, E. M. L., Matthews, L. D., & Gray, M. D. 2009, ApJ, 698, 1165 Goddi, C., Humphreys, E. M. L., Greenhill, L. J., Chandler, C. J., Matthews, L. D. 2011a, ApJ, 728, 15 Goddi, C., Greenhill, L. J., Humphreys, E. M. L., Chandler, C. J., & Matthews, L. D. 2011b, ApJ, 739, L13 Greenhill, L. J., Gwinn, C. R., Schwartz, C., Moran, J. M., & Diamond, P. J. 1998, Nature, 396, 650 Greenhill, L. J., Gezari, D. Y., Danchi, W. C., Najita, J., Monnier, J. D., & Tuthill, P. G. 2004a, ApJ, 605, L57 Greenhill, L. J., Reid, M. J., Chandler, C. J., Diamond, P. J., & Elitzur, M. 2004b, Star Formation at High Angular Resolution, 221, 155 Kim, M. K., et al. 2008, PASJ, 60, 991 Konigl, A. & Pudritz, R. E. 2000, Protostars and Planets IV, ed. V. Mannings, A. P. Boss, & S. S. Russell (Tucson, AZ: Univ. Arizona Press), 759 R. S. 2012, MNRAS, 422, 347 Shuping, R. Y., Morris, M., & Bally, J. 2004, AJ, 128, 363 Sitarski, B. N., Morris, M. R., Lu, J. R., Duchˆene, G., Stolte, A., Becklin, E. E., Ghez, A., Zinnecker, H. 2013, ApJ, in press Vaidya, B., & Goddi, C. 2013, MNRAS, 429, L50 Van Loo, S., Ashmore, I., Caselli, P., Falle, S. A. E. G., & Hartquist, T. W. 2013, MNRAS, 428, 381",
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}
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2013ApJ...771...10M
https://arxiv.org/pdf/1304.5853.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_85><loc_86><loc_86></location>Direct Imaging in the Habitable Zone and the Problem of Orbital Motion</section_header_level_1>
<text><location><page_1><loc_32><loc_82><loc_68><loc_83></location>Jared R. Males, Andrew J. Skemer, Laird M. Close</text>
<text><location><page_1><loc_27><loc_79><loc_73><loc_81></location>Steward Observatory, University of Arizona, Tucson, AZ 85721</text>
<text><location><page_1><loc_41><loc_77><loc_60><loc_78></location>[email protected]</text>
<section_header_level_1><location><page_1><loc_45><loc_73><loc_55><loc_74></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_16><loc_46><loc_84><loc_71></location>High contrast imaging searches for exoplanets have been conducted on 2.4-10 m telescopes, typically at H band (1.6 µ m) and used exposure times of ∼ 1hr to search for planets with semimajor axes of /greaterorsimilar 10 AU. We are beginning to plan for surveys using extreme-AO systems on the next generation of 30-meter class telescopes, where we hope to begin probing the habitable zones (HZs) of nearby stars. Here we highlight a heretofore ignorable problem in direct imaging: planets orbit their stars. Under the parameters of current surveys, orbital motion is negligible over the duration of a typical observation. However, this motion is not negligible when using large diameter telescopes to observe at relatively close stellar distances (1-10pc), over the long exposure times (10-20 hrs) necessary for direct detection of older planets in the HZ. We show that this motion will limit our achievable signal-to-noise ratio and degrade observational completeness. Even on current 8m class telescopes, orbital motion will need to be accounted for in an attempt to detect HZ planets around the nearest sun-like stars α Cen A&B, a binary system now known to harbor at least one planet. Here we derive some basic tools for analyzing this problem, and ultimately show that the prospects are good for de-orbiting a series of shorter exposures to correct for orbital motion.</text>
<section_header_level_1><location><page_1><loc_43><loc_41><loc_57><loc_42></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_30><loc_88><loc_39></location>Orbital motion has been used in one fashion or another to detect planets around stars other than our Sun in large numbers. The radial velocity (RV) technique monitors the Doppler shift of a stellar spectrum as the star itself orbits the planet-star center of mass, thus allowing us to infer the presence of a planet. Similarly, the astrometry technique monitors the motion of the star on the sky and likewise infers the presence of a planet. The transit technique monitors the reduction in brightness of the star as the orbiting planet temporarily crosses the line of sight between the telescope and the star.</text>
<text><location><page_1><loc_12><loc_16><loc_88><loc_28></location>Unlike these indirect techniques, direct imaging detects light from the planet itself and spatially resolves it from the light of the star (Traub & Oppenheimer 2011). The extreme difference in brightness between star and planet at small projected separations has generally limited direct imaging efforts to wide separations where orbital motion is ignorable. The next generation of large telescopes will move us into a new regime of direct imaging, moving closer to the star. We will even be able to begin probing the liquid water habitable zone (HZ). Here we point out that at these tight separations orbital motion will no longer be negligible in direct imaging. As we will show the motion of planets in the HZ (and closer), during the required integration times, will be large enough to limit our sensitivity unless we take action to correct it.</text>
<text><location><page_1><loc_12><loc_10><loc_88><loc_14></location>In Section 2 we present our motivation for this study and briefly review some of the related prior work. In Section 3 we develop the basic tools needed to analyze this problem, including the expected speed of orbital motion in the focal plane and the effect it has on signal-to-noise ratio ( SNR ). In Section 4 we</text>
<text><location><page_2><loc_12><loc_77><loc_88><loc_86></location>analyze the impact orbital motion will have on a search of α Cen A by the Giant Magellan Telescope (GMT) working at 10 µ m, and propose a method to mitigate this impact by de-orbiting a sequence of observations. Then in Section 5 we treat the more favorable case of a cued search, where we have prior information from an RV detection. To do so we analyze the case of the potentially habitable planet Gl 581d being observed by the planned European Extremely Large Telescope (E-ELT). Finally, in Section 6, we present our conclusions and prospects for future work.</text>
<section_header_level_1><location><page_2><loc_36><loc_71><loc_64><loc_73></location>2. Motivation and Related Work</section_header_level_1>
<text><location><page_2><loc_12><loc_65><loc_88><loc_70></location>Moving the hunt for exoplanets into the HZ of nearby stars marks a departure from prior efforts. Here we briefly discuss the definition of the HZ, review direct imaging results to date, discuss the differences between them and and future efforts, and finally review some closely related prior work.</text>
<section_header_level_1><location><page_2><loc_38><loc_60><loc_62><loc_61></location>2.1. Nearby Habitable Zones</section_header_level_1>
<text><location><page_2><loc_12><loc_50><loc_88><loc_58></location>The HZ is generally agreed to be the region around a star where a planet can have liquid water on its surface. This is far from simply related to the blackbody equilibrium temperature, as it depends on atmospheric composition and the action of the greenhouse effect (Kasting et al. 1993; Kopparapu et al. 2013), among other factors. For our purposes it is enough to assume that the HZ is generally located at about one AU from a star, scaled by the star's luminosity</text>
<formula><location><page_2><loc_42><loc_45><loc_88><loc_49></location>a HZ ≈ √ L ∗ /L /circledot AU . (1)</formula>
<text><location><page_2><loc_12><loc_35><loc_88><loc_45></location>Traub (2012) provided three widths for the HZ based on various considerations, and then used the first 136 days of data from the Kepler mission to estimate that the fraction of sun-like stars (spectral types FGK) with an earth-like planet in the HZ is η ⊕ ≈ 0 . 34. More generally, this analysis indicates that η planet ≈ 1 . 2, implying that every sun-like star is likely to have a planet in its HZ, and some will have more than one . While this exciting result is based on a very large extrapolation from the earliest Kepler results, it is currently one of our best estimates of planet frequency in the HZ.</text>
<text><location><page_2><loc_12><loc_28><loc_88><loc_34></location>This topic was recently brought to the fore with the announcement of α Cen Bb by Dumusque et al. (2012). Discovered using the RV technique, α Cen Bb is an m sin i = 1 . 13 M ⊕ planet orbiting a K1 star at 0.04 AU. While certainly not in the HZ, this discovery has exciting implications for the presence of planets in the HZ of the nearest two sun-like stars.</text>
<text><location><page_2><loc_12><loc_20><loc_88><loc_27></location>The above arguments hint that planets will be common in the HZ of sun-like stars. We are about to enter a new era of exoplanet direct imaging. With the next generation of giant telescopes and high-performance spaced-based coronagraphs we will be searching for planets in this scientifically important region around nearby stars.</text>
<section_header_level_1><location><page_2><loc_40><loc_15><loc_60><loc_16></location>2.2. A Different Regime</section_header_level_1>
<text><location><page_2><loc_12><loc_10><loc_88><loc_13></location>The typical search for exoplanets with direct imaging has used 2.4m (Hubble Space Telescope, HST) to 10m (Keck) telescopes. These surveys have mostly concentrated on young giant planets, which are expected</text>
<text><location><page_3><loc_12><loc_73><loc_88><loc_86></location>to be self-luminous as they dissipate heat from their formation. This allows them to be detected at wider separations from their host stars, where reflected starlight would be too faint. This has also caused planet searches to typically work at H band ( ∼ 1 . 6 µ m), with exposure times of ∼ 1 hr. Examples conforming to these stereotypes include Lowrance et al. (2005) using HST/NICMOS; the Gemini Deep Planet Search (Lafreni'ere et al. 2007); the Simultaneous Differential Imaging survey using the Very Large Telescope and MMT(Biller et al. 2007); the Lyot Project at the Advanced Electro-Optical System telescope (Leconte et al. 2010); the International Deep Planet Survey (Vigan et al. 2012); and the Near Infrared Coronagraphic Imager at Gemini South (Liu et al. 2010).</text>
<text><location><page_3><loc_12><loc_62><loc_88><loc_72></location>These searches have had some success. Examples include the 4 planets orbiting the A5V star HR 8799 (Marois et al. 2008b, 2010), with projected separations of 68, 38, 24, and ∼ 15 AU. These correspond to orbital periods of ∼ 460, ∼ 190, ∼ 100, and ∼ 50 years, respectively. The A5V star β Pic also has a planet (Lagrange et al. 2010) orbiting at ∼ 8 . 5 AU with a period of ∼ 20 years (Chauvin et al. 2012). Another A star, Fomalhaut, has a candidate planet on an 872 year (115 AU) orbit (Kalas et al. 2008). At these wide separations it takes months, or even years, to notice orbital motion.</text>
<text><location><page_3><loc_12><loc_55><loc_88><loc_61></location>In the much closer HZ, however, orbital periods will be on the order of one year. We show in some detail that this is fast enough to yield projected motions of significant fractions of the point spread function (PSF) full width at half maximum (FWHM) over the course of an integration. The resulting smeared out image of the planet will have a lower SNR , making our observations less sensitive.</text>
<section_header_level_1><location><page_3><loc_38><loc_50><loc_62><loc_51></location>2.3. Long Integration Times</section_header_level_1>
<text><location><page_3><loc_12><loc_37><loc_88><loc_48></location>In addition to HZ planets having higher orbital speeds than the current generation of imaged exoplanets, integration times required to detect them will be much longer. Direct imaging surveys to date have mostly worked in the infrared while attempting to detect young planets still cooling after formation. The coming campaigns to image planets in the HZ of nearby stars will focus on older planets, which will be less luminous in the near infrared. In the HZ, starlight reflected from the planet will be more important. The result is integration times required to detect such planets will be tens of hours, rather than the ∼ 1 hour characteristic of current campaigns.</text>
<text><location><page_3><loc_12><loc_21><loc_88><loc_36></location>Consider the Exoplanet Imaging Camera and Spectrograph (EPICS), an instrument proposed for the E-ELT. Kasper et al. (2010) predicted that EPICS will be able to image the RV detected planet Gl 581d, which has a semi-major axis of 0.22 AU with a period of ∼ 67 days (Forveille et al. 2011; Vogt et al. 2012). This orbit places it on the outer edge of the HZ of its M2.5V star (von Braun et al. 2011). EPICS will be able to detect Gl 581d, at a planet/star contrast of 2 . 5 × 10 -8 , in 20 hrs with SNR = 5 (Kasper et al. 2010). Since this is a ground based instrument, a 20 hour integration will be broken up over at least 2 nights. Plausible observing scenarios could extend this to several nights, taking into account such things as the need for sky rotation. As we will show, the planet will move several FWHM on the EPICS detector during a multi-day observation.</text>
<text><location><page_3><loc_12><loc_12><loc_88><loc_20></location>More generally, Cavarroc et al. (2006) showed that when realistic non-common path wavefront errors are taken into account, the integration times required to achieve the 10 -9 to 10 -10 contrast necessary to detect an earth-like planet around a sun-like star approach 100 hours on the ground, even on a 100m telescope with extreme-AO and a perfect coronagraph. One of several concerns about the feasibility of a 100 hour observation from the ground is that such a long observation will be broken up over many nights.</text>
<text><location><page_4><loc_12><loc_82><loc_88><loc_86></location>With net exposure times of 20 to 100 hrs, and total elapsed times for ground based observations of several to tens of days, HZ planets will move significantly over the course of a detection attempt. The focus of this investigation is the impact of the orbital motion of a potentially detectable planet on sensitivity.</text>
<section_header_level_1><location><page_4><loc_42><loc_76><loc_58><loc_78></location>2.4. Related Work</section_header_level_1>
<text><location><page_4><loc_12><loc_57><loc_88><loc_75></location>Though it has not yet been a significant issue in direct imaging of exoplanets, orbital motion has been considered in several closely related contexts. Here we briefly review a select portion of the literature. A very similar problem has been addressed in the context of searching for objects in our solar system, such as Kuiper Belt objects (KBOs), which can have proper motions on the order of 1' to 6' per hour (Chiang & Brown 1999). Blinking images to look for moving objects by eye is a well established technique. A more computationally intensive form of blinking images proceeds by shifting-and-adding a series of short exposures along trial paths, usually assumed to be linear. This 'digital tracking' makes it possible to detect KBOs too faint to appear in a single exposure. This has been done both from the ground (Chiang & Brown 1999; Yamamoto et al. 2008) and from space with HST (Bernstein et al. 2004). More recently Parker & Kavelaars (2010) have taken into account nonlinear motion and optimized selection of the search space, especially important given the large data sets that facilities such as the Large Synoptic Survey Telescope will produce.</text>
<text><location><page_4><loc_12><loc_39><loc_88><loc_55></location>Orbital motion is an important consideration when planning coronagraphic surveys of the HZs of nearby stars. Brown (2005) treats the problem of completeness extensively. Large parts of the HZ will be within the inner working angle of the Terrestrial Planet Finder-Coronagraph (TPF-C) and so undetectable during a single observation. Also discussed in Brown (2005) is photometric completeness - that is how long the TPF-C must integrate on a given star to detect an earth-like planet in the HZ. Other work on this topic includes Brown & Soummer (2010) and Brown (2004). These analyses consider orbital motion only between observations, not during a single observation as we do here. In general, the scenarios considered for these studies involved space-based high-performance coronagraphs on medium to large telescopes. In such cases exposure times were short enough and continuous so that orbital motion should be negligible during a single observation.</text>
<text><location><page_4><loc_12><loc_27><loc_88><loc_38></location>The work most similar to our analysis here is the detection of Sirius B at 10 µ m by Skemer & Close (2011), in fact, it was part of our motivation for the present study. Skemer & Close (2011) used the well known orbit of the white dwarf companion to Sirius to de-orbit 4 years worth of images. Before accounting for orbital motion, Sirius B appeared as only a low SNR streak, but after shifting based on its orbit it appears as a higher SNR point source from which photometry can be extracted. Similar to this method, we will analyze the prospects for de-orbiting sequences of images, only we consider the case with no prior information at all, and with orbital elements with significant uncertainties.</text>
<section_header_level_1><location><page_4><loc_38><loc_22><loc_62><loc_23></location>3. Quantifying The Problem</section_header_level_1>
<text><location><page_4><loc_12><loc_15><loc_88><loc_20></location>In this section we will quantify the effects of orbital motion on an attempt to detect an exoplanet. Our first step will be to determine how fast planets move when projected on the focal plane of a telescope. Then we'll illustrate the impact this motion will have on the SNR and the statistical sensitivity of an observation.</text>
<section_header_level_1><location><page_5><loc_41><loc_85><loc_59><loc_86></location>3.1. Basic Equations</section_header_level_1>
<text><location><page_5><loc_12><loc_80><loc_88><loc_83></location>We begin by considering a focal plane detector working at a wavelength λ in µ m. The FWHM of the PSF for a telescope of diameter D in m, neglecting the central obscuration, is</text>
<formula><location><page_5><loc_40><loc_76><loc_88><loc_79></location>FWHM = 0 . 2063 λ D arcsec . (2)</formula>
<text><location><page_5><loc_12><loc_72><loc_88><loc_75></location>If we are observing a planet in a face-on circular (FOC) orbit with a semi-major axis of a in AU at distance d in pc, its angular separation will be a/d arcsec. At the focal plane the projected separation will then be</text>
<formula><location><page_5><loc_41><loc_68><loc_88><loc_71></location>ρ = 4 . 847 aD λd in FWHM . (3)</formula>
<text><location><page_5><loc_12><loc_64><loc_88><loc_67></location>We note that it will occasionally be convenient to specify ρ in AU instead of FWHM. When it is not clear from the context we will use the notation ρ au to denote this.</text>
<text><location><page_5><loc_12><loc_58><loc_88><loc_63></location>The orbital period is P = 365 . 25 √ a 3 /M ∗ days around a star of mass M ∗ in M /circledot . In one period, the planet will move a distance equal to the circumference of its orbit, 2 πρ , so the speed of the motion in a FOC orbit will be ∗</text>
<formula><location><page_5><loc_22><loc_53><loc_88><loc_57></location>v FOC = 0 . 0834 ( D 1m )( 1 µ m λ )( 1pc d ) √ ( M ∗ 1 M /circledot )( 1AU a ) in FWHM day -1 . (4)</formula>
<text><location><page_5><loc_15><loc_50><loc_62><loc_52></location>In the general case, the equations of motion in the focal plane are</text>
<formula><location><page_5><loc_22><loc_33><loc_88><loc_49></location>˙ x = v FOC √ 1 1 -e 2 [ e sin( f ) (cos(Ω) cos( ω + f ) -sin(Ω) sin( ω + f ) cos( i )) -(1 + e cos( f )) (cos(Ω) sin( ω + f ) + sin(Ω) cos( ω + f ) cos( i )) ] ˙ y = v FOC √ 1 1 -e 2 [ e sin ( f ) (sin (Ω) cos( ω + f ) + cos(Ω) sin( ω + f ) cos( i )) (5) -(1 + e cos( f )) (sin(Ω) sin( ω + f ) -cos(Ω) cos( ω + f ) cos( i )) ] v om = √ ˙ x 2 + ˙ y 2</formula>
<text><location><page_5><loc_12><loc_29><loc_88><loc_33></location>where Ω is the longitude of the ascending node, ω is the argument of pericenter, i is the inclination, and the true anomaly f depends on a , e , and the time of pericenter passage τ through Kepler's equation (Murray & Correia 2010).</text>
<text><location><page_5><loc_12><loc_20><loc_88><loc_27></location>In Figure 1 we show the variation in projected orbital speed for both circular orbits at several inclinations, and face-on eccentric orbits ( i = 0), for a planet orbiting a 1 M /circledot star at 1 AU. In the plots we normalized speed to 1, and provide v FOC for several interesting cases. These various scenarios produce projected orbital speeds of appreciable fractions of a FWHM per day. We will later show that, especially for ground based imaging, this causes a significant degradation in our sensitivity.</text>
<text><location><page_5><loc_12><loc_15><loc_88><loc_19></location>Our main focus here is on planets in the HZ. Our simple definition of the HZ results in a HZ ∝ √ L ∗ . Now, on the main sequence mass and luminosity approximately follow scaling laws of the form L ∗ ∝ M b ∗ ,</text>
<text><location><page_6><loc_26><loc_51><loc_27><loc_52></location>)</text>
<text><location><page_6><loc_26><loc_50><loc_27><loc_51></location>FOC</text>
<text><location><page_6><loc_26><loc_33><loc_27><loc_50></location>Normalized Projected Speed (v</text>
<text><location><page_6><loc_28><loc_49><loc_30><loc_50></location>2.0</text>
<text><location><page_6><loc_28><loc_44><loc_30><loc_45></location>1.5</text>
<text><location><page_6><loc_28><loc_39><loc_30><loc_40></location>1.0</text>
<text><location><page_6><loc_28><loc_35><loc_30><loc_35></location>0.5</text>
<text><location><page_6><loc_28><loc_30><loc_30><loc_31></location>0.0</text>
<text><location><page_6><loc_30><loc_29><loc_31><loc_30></location>0</text>
<text><location><page_6><loc_42><loc_29><loc_43><loc_30></location>50</text>
<text><location><page_6><loc_54><loc_29><loc_56><loc_30></location>100</text>
<text><location><page_6><loc_66><loc_29><loc_68><loc_30></location>150</text>
<text><location><page_6><loc_44><loc_28><loc_61><loc_29></location>True Anomaly (degrees)</text>
<figure>
<location><page_6><loc_26><loc_57><loc_75><loc_84></location>
<caption>Fig. 1.- Magnitude of projected orbital speed, normalized to 1 FWHM day -1 , for 1 AU orbits around a 1 M /circledot star. In (a) we show the orbital speeds for circular orbits at various inclinations, and in (b) we show the speeds for face-on orbits at various eccentricities. We give scaling factors in (a) for MagAO/VisAO (Close et al. 2012), GPI (Macintosh et al. 2012), SPHERE/ZIMPOL (Roelfsema et al. 2010), GMT (Johns et al. 2012), and E-ELT/EPICS (Kasper et al. 2010). These scalings can be applied to the y-axis of either plot for various scenarios. These cases can also be scaled for different semi-major axes, telescopes, wavelengths, star masses and distances, by v FOC ∝ D λd √ M ∗ a . See the text for the general equations of motion for arbitrarily oriented eccentric orbits.</caption>
</figure>
<text><location><page_6><loc_28><loc_54><loc_30><loc_55></location>2.5</text>
<text><location><page_6><loc_39><loc_52><loc_43><loc_53></location>e=0.7</text>
<text><location><page_6><loc_37><loc_49><loc_41><loc_50></location>e=0.6</text>
<text><location><page_6><loc_35><loc_45><loc_38><loc_46></location>e=0.4</text>
<text><location><page_6><loc_33><loc_41><loc_36><loc_42></location>e=0.1</text>
<text><location><page_6><loc_31><loc_39><loc_33><loc_40></location>e=0</text>
<text><location><page_6><loc_33><loc_31><loc_54><loc_32></location>i=0 (face-on) for each curve</text>
<text><location><page_6><loc_71><loc_52><loc_73><loc_53></location>(b)</text>
<text><location><page_7><loc_12><loc_80><loc_88><loc_86></location>where b > 2 except for very massive stars. So according to Equation (4) we expect v FOC in the HZ to increase as M ∗ decreases, i.e. M stars will have faster HZ planets than G stars. For example, a planet in the HZ of α Cen B ( M ∗ = 0 . 9 M /circledot , L ∗ = 0 . 5 L /circledot ) will be moving roughly 20% faster than a planet in the HZ of α Cen A ( M ∗ = 1 . 1 M /circledot , L ∗ = 1 . 5 L /circledot ) (stellar parameters from Bruntt et al. (2010)).</text>
<text><location><page_7><loc_12><loc_67><loc_88><loc_79></location>To provide a more concrete example we return to the 20 hour observation of Gl 581d by the EELT/EPICS proposed by Kasper et al. (2010). Using a wavelength of 0 . 75 µm with Equation (4) we find v FOC = 0 . 82 FWHM per day, or a total of 0.68 FWHM for a continuous 20 hour observation. Since this is a ground based observation the actual amount of motion to consider is ∼ 1 . 15 FWHM over the ∼ 1 . 4 days minimum it would take to integrate for 20 hours. Were this a face-on orbit, an eccentricity of 0.25 (Forveille et al. 2011) would increase the maximum orbital speed to as much as 1.05 FWHM per day, or 1.47 FWHM minimum for a 20 hour ground based observation.</text>
<section_header_level_1><location><page_7><loc_34><loc_62><loc_66><loc_63></location>3.2. Impact on Signal-to-Noise Ratio</section_header_level_1>
<text><location><page_7><loc_12><loc_44><loc_88><loc_60></location>So what does the orbital motion calculated above do to our observations? To find out we consider a simple model of aperture photometry. Let us assume that we are conducting aperture photometry with a fixed radius r ap , that the PSF is Gaussian, and that we are limited by Poisson noise from a photon flux N per unit area. With these assumptions, the optimum r ap is 0.7 FWHM, but taking into account centroiding uncertainty r ap ≈ 1 FWHM is typical. We will approximate orbital motion at speed v om by substituting x → x -v om t -x 0 . Orbits are of course not linear, but this will be approximately valid over short periods of time. The parameter x 0 allows us to optimize the placement of the aperture to obtain the maximum signal, i.e. centering the aperture in the planet's smeared out flux. Note that with the exception of this centering parameter, this model appears quite naive in that we are not adapting the aperture radius and are pretending that we won't notice a smeared out streak in our images.</text>
<text><location><page_7><loc_15><loc_42><loc_59><loc_43></location>Now the SNR in the fixed-size aperture after time ∆ t will be</text>
<formula><location><page_7><loc_25><loc_33><loc_88><loc_41></location>SNR fix = ∫ r ap 0 ∫ 2 π 0 ∫ ∆ t 0 I 0 e ( -4 ln 2(( r cos θ -v om t -x 0 ) 2 + r 2 sin 2 θ ) ) dtdθrdr. √ Nπr 2 ap ∆ t int (6)</formula>
<formula><location><page_7><loc_43><loc_27><loc_88><loc_31></location>SNR o = 0 . 6 I 0 √ ∆ t √ N . (7)</formula>
<text><location><page_7><loc_12><loc_30><loc_88><loc_33></location>where I 0 is the peak value of the PSF. In the case of no orbital motion v om = 0 and aperture r ap = 1 FWHM, so we have</text>
<text><location><page_7><loc_12><loc_22><loc_88><loc_27></location>As a simple alternative to a fixed size aperture, we also consider allowing our photometric aperture to expand along with the motion of the planet. This aperture will collect the same signal as in SNR o , but the noise increases with the area as 2 r ap v om ∆ t , so we have</text>
<formula><location><page_7><loc_38><loc_15><loc_88><loc_21></location>SNR exp = 0 . 6 I 0 √ ∆ t √ N (1 + (2 /π ) v om ∆ t ) . (8)</formula>
<text><location><page_7><loc_12><loc_11><loc_88><loc_17></location>A convenient scaling is to multiply top and bottom by √ v om and work in normalized SNR units of I o / √ Nv om . This puts time in terms of FWHM of motion, /epsilon1 = v om ∆ t , and allows comparisons without specifying v om .</text>
<figure>
<location><page_8><loc_25><loc_27><loc_75><loc_83></location>
<caption>Fig. 2.- Top panel: SNR of a Gaussian PSF with and without orbital motion, in normalized units with time given as FWHM of motion. With no orbital motion SNR o ∝ √ t . Equation (6) was used to calculate the SNR with orbital motion. After ∼ 2 FWHM of movement, a maximum is reached and the observation can only be degraded by integrating further. Note that the fixed-aperture orbital motion case eventually goes down as SNR ∝ 1 / √ t . For comparison we also show the results with an aperture expanding with the moving planet, which eventually reaches a limit of 0.75. In the bottom panel we show the fractional reduction in SNR due to orbital motion for the fixed radius photometric aperture.</caption>
</figure>
<text><location><page_9><loc_12><loc_80><loc_88><loc_86></location>In Figure 2 we plot the normalized SNR vs. time (measured in terms of FWHM of motion) with and without orbital motion and for both the fixed and expanding aperture cases. For the fixed aperture, after ∼ 2 FWHM of orbital motion a maximum of 0.69 is reached, and from there noise is added faster than signal. This means that further integration only degrades the observation.</text>
<text><location><page_9><loc_12><loc_76><loc_88><loc_79></location>The expanding aperture SNR exp exceeds the maximum of SNR fix after about 8 FWHM of motion, and</text>
<formula><location><page_9><loc_36><loc_68><loc_88><loc_74></location>lim x →∞ 0 . 6 √ x √ 1 + (2 /π ) x = 0 . 6 √ π 2 ≈ 0 . 75 . (9)</formula>
<text><location><page_9><loc_12><loc_61><loc_88><loc_69></location>So if we integrate 4 times longer, adjusting the aperture size would allow us to gather a little more SNR , but only to a point. Given this large increase in telescope time for a relatively small improvement in SNR (only ∼ 9% even if we integrate forever), and its better performance for smaller amounts of motion, the fixed-radius aperture will be our baseline for further analysis - keeping in mind that in some cases it may not be the true optimum.</text>
<text><location><page_9><loc_12><loc_50><loc_88><loc_59></location>The peak in SNR fix (equation 6) sets the maximum nominal integration time before orbital motion will prevent us from achieving the science goal. That is ∆ t max = ( SNR max / 0 . 6) 2 . If the observation of a stationary planet would require an integration time longer than ∆ t max , then we can't achieve the desired SNR on an orbiting planet . This also sets the maximum orbital motion /epsilon1 max = v om ∆ t max . From Figure 2 we find that /epsilon1 max = 1 . 3 FWHM. If more than 1.3 FWHM of motion occurs during an observation, we will not achieve the required SNR .</text>
<text><location><page_9><loc_12><loc_42><loc_88><loc_49></location>We also show the fractional reduction in SNR in Figure 2. Almost no degradation occurs until after ∼ 0 . 2 FWHM of motion has occurred. SNR is reduced by ∼ 1% after 0.5 FWHM of motion, ∼ 5% after 1.0 FWHM, and by ∼ 19% after 2.0 FWHM of motion. We must now decide how much SNR loss we can accept in our observation.</text>
<text><location><page_9><loc_12><loc_32><loc_88><loc_41></location>The above analysis assumes a continuous integration. On a ground-based telescope one must consider that the maximum continuous integration time is /lessorsimilar 12 hours, and in practice will likely be much shorter when performing high contrast AO corrected imaging. For instance, an exposure of 20 hours might have to be broken up over 4 or 5 or more nights, when considering the vagaries of seeing (required AO performance), airmass (either through transmission or r 0 requirements), rotation rate (for ADI), and weather. We can adapt the calculations for a ground based integration as follows</text>
<formula><location><page_9><loc_20><loc_22><loc_88><loc_31></location>SNR gnd = ∫ r ap 0 ∫ 2 π 0 j = M ∑ j =1 ∫ t j +∆ t j t j I 0 e ( -4 ln 2(( r cos θ -v om t -x 0 ) 2 + r 2 sin 2 θ ) ) dt dθrdr. √ Nπr 2 ap ∆ t int (10)</formula>
<text><location><page_9><loc_12><loc_15><loc_88><loc_22></location>In this expression we have broken the observation up into M integration sets which start at times t j and have lengths ∆ t j . The total integration time is ∆ t int = j = M ∑ j =1 ∆ t j and the total elapsed time of the observation is ∆ t tot = t M +∆ t M -t 1 .</text>
<text><location><page_9><loc_12><loc_10><loc_88><loc_14></location>We plot the results for a few ground-based scenarios in Figure 3. As one can see, observations of planets with orbital motion will be significantly degraded from the ground. This problem, which has been negligible in the high contrast planet searches to date, only becomes worse as we consider larger telescopes</text>
<figure>
<location><page_10><loc_25><loc_38><loc_75><loc_65></location>
<caption>Fig. 3.- Here we show the impact of orbital motion when combined with finite nightly integration times. The SNR of a Gaussian PSF with and without orbital motion is plotted in arbitrary units vs ∆ t int . The orbital speed v om is given in FWHM day -1 .</caption>
</figure>
<text><location><page_11><loc_12><loc_82><loc_88><loc_86></location>and improvements in AO technology which allow searches at shorter wavelengths. We next analyze how this reduction in SNR will affect our ability to detect exoplanets by increasing the rate at which spurious detections occur.</text>
<section_header_level_1><location><page_11><loc_34><loc_76><loc_66><loc_78></location>3.3. Impact on Statistical Sensitivity</section_header_level_1>
<text><location><page_11><loc_12><loc_68><loc_88><loc_75></location>Now we turn to the problem of detecting a planet of a given brightness. A planet is considered detected if its flux is above some threshold SNR t , which is chosen for statistical significance. The goal in choosing this threshold is to detect faint planets while minimizing the number of false alarms. For the purposes of this analysis we assume Gaussian statistics, in which case the false alarm probability ( P FA ) per trial is</text>
<formula><location><page_11><loc_42><loc_63><loc_88><loc_67></location>P FA = 1 2 erfc ( SNR √ 2 ) (11)</formula>
<text><location><page_11><loc_12><loc_60><loc_88><loc_63></location>Typically, planet hunters use a threshold of SNR = 5, which gives P FA = 2 . 9 × 10 -7 . The number of false alarms per star, the false alarm rate ( FAR ), is then</text>
<formula><location><page_11><loc_42><loc_57><loc_88><loc_59></location>FAR = P FA × N trials . (12)</formula>
<text><location><page_11><loc_12><loc_43><loc_88><loc_56></location>where N trials is the number of statistical trials per star. Following Marois et al. (2008a), for a stationary planet N trials is just the number of photometric apertures in the image. A typical Nyquist sampled detector of size 1024x1024 pixels has N trials ∼ 8 × 10 4 . Thus, an SNR = 5 threshold will result in FAR ∼ 0 . 02 about 1 false alarm for every 50 observations. In the speckle limited case with non-Gaussian statistics, FAR will be worse than this for the same SNR (Marois et al. 2008a). In any case, the FAR is the statistic which determines the efficiency of a search for exoplanets with direct imaging. A high FAR will cause us to waste telescope time following up spurious detections, while raising the SNR threshold to counter this limits the number of real planets we will detect.</text>
<text><location><page_11><loc_12><loc_36><loc_88><loc_42></location>The reduction of SNR caused by orbital motion confronts us with three options. Option I is to maintain the detection threshold constant and accept the loss of sensitivity. Option II is to lower the detection threshold to maintain sensitivity, accepting the increase in FAR. Option III is to correct for orbital motion, which as we will show also causes an increase in FAR.</text>
<section_header_level_1><location><page_11><loc_39><loc_31><loc_61><loc_32></location>3.3.1. Option I: Do Nothing</section_header_level_1>
<text><location><page_11><loc_12><loc_23><loc_88><loc_29></location>The default option is to do nothing, keeping our detection threshold set as if orbital motion is not significant. The drawback to this is that we will detect fewer planets. To quantify this we use the concept of completeness, that is the fraction of planets of a given brightness we detect. For Gaussian statistics and detection threshold SNR t = 5, the search completeness is given by</text>
<formula><location><page_11><loc_38><loc_18><loc_88><loc_22></location>C ( /epsilon1 ) = 1 -1 2 erfc ( SNR ( /epsilon1 ) -5 √ 2 ) . (13)</formula>
<text><location><page_11><loc_12><loc_9><loc_88><loc_18></location>where /epsilon1 = v om ∆ t is the amount of motion. In Figure 4 (top) we show the impact of orbital motion on search completeness. Maintaining the detection threshold lowers completeness. How much depends on the completeness level, with brighter planets being less affected. For planets bright enough to yield 95% completeness with no motion, significant reduction in the number of detections begins after ∼ 1 FWHM of motion. For 99.7% completeness the impact becomes significant after ∼ 1 . 5 FWHM.</text>
<text><location><page_12><loc_26><loc_66><loc_28><loc_74></location>Completeness</text>
<text><location><page_12><loc_28><loc_81><loc_31><loc_82></location>1.0</text>
<text><location><page_12><loc_28><loc_76><loc_31><loc_77></location>0.8</text>
<text><location><page_12><loc_28><loc_72><loc_31><loc_73></location>0.6</text>
<text><location><page_12><loc_28><loc_67><loc_31><loc_68></location>0.4</text>
<text><location><page_12><loc_28><loc_62><loc_31><loc_63></location>0.2</text>
<text><location><page_12><loc_28><loc_58><loc_31><loc_59></location>0.0</text>
<text><location><page_12><loc_31><loc_57><loc_32><loc_58></location>0</text>
<text><location><page_12><loc_34><loc_70><loc_35><loc_71></location>5</text>
<text><location><page_12><loc_35><loc_70><loc_36><loc_71></location>σ</text>
<text><location><page_12><loc_32><loc_59><loc_52><loc_60></location>Option I - Lower Completeness</text>
<text><location><page_12><loc_40><loc_57><loc_40><loc_58></location>1</text>
<text><location><page_12><loc_48><loc_57><loc_49><loc_58></location>2</text>
<text><location><page_12><loc_57><loc_57><loc_57><loc_58></location>3</text>
<text><location><page_12><loc_65><loc_57><loc_66><loc_58></location>4</text>
<text><location><page_12><loc_74><loc_57><loc_74><loc_58></location>5</text>
<text><location><page_12><loc_43><loc_55><loc_56><loc_57></location>Orbital Motion</text>
<text><location><page_12><loc_56><loc_55><loc_57><loc_57></location>ε</text>
<text><location><page_12><loc_57><loc_55><loc_63><loc_57></location>(FWHM)</text>
<figure>
<location><page_12><loc_26><loc_26><loc_75><loc_53></location>
<caption>Fig. 4.- Top panel: completeness as a function of orbital motion if we maintain our detection threshold at 5 σ . Planet brightness is expressed as the SNR at which we would be 50%(5 σ ), 68%(5 . 47 σ ), 95%(6 . 65 σ ), and 99.7% (7 . 75 σ ) complete with no orbital motion. Bottom panel: the increase in false alarm probability ( P FA ) if we lower the detection threshold to maintain 50% completeness for an orbiting planet that would have a brightness of 5 σ were it stationary. After ∼ 1 FWHM of motion P FA increases exponentially until ∼ 4 FWHM where it becomes asymptotic to 0.5.</caption>
</figure>
<text><location><page_12><loc_37><loc_72><loc_41><loc_74></location>5.47</text>
<text><location><page_12><loc_40><loc_72><loc_41><loc_73></location>σ</text>
<text><location><page_12><loc_43><loc_77><loc_46><loc_79></location>6.65</text>
<text><location><page_12><loc_45><loc_77><loc_47><loc_78></location>σ</text>
<text><location><page_12><loc_47><loc_79><loc_50><loc_81></location>7.75</text>
<text><location><page_12><loc_49><loc_78><loc_51><loc_80></location>σ</text>
<section_header_level_1><location><page_13><loc_37><loc_85><loc_63><loc_86></location>3.3.2. Option II: Lower Threshold</section_header_level_1>
<text><location><page_13><loc_12><loc_70><loc_88><loc_83></location>Once orbital motion is recognized to be significant, a simple countermeasure would be to lower the detection SNR threshold in order to maintain completeness. The drawback to this option is that we have more false alarms, which must then be followed up using more telescope time. This results in a less efficient search. In Figure 4 (bottom) we show P FA as a function of orbital motion, and denote the detection threshold we must use to maintain 50% completeness for a planet bright enough to give SNR = 5 were it stationary. Note that P FA begins to increase exponentially after ∼ 1 FWHM of motion. After ∼ 4 FWHM P FA begins approaching 0.5 asymptotically. Once /epsilon1 ≈ 2 FWHM the number of false alarms per 1024x1024 image approaches 1.</text>
<section_header_level_1><location><page_13><loc_40><loc_65><loc_60><loc_66></location>3.3.3. Option III: De-orbit</section_header_level_1>
<text><location><page_13><loc_12><loc_49><loc_88><loc_63></location>Option III is to correct for orbital motion, hoping to maintain sensitivity while limiting the increase in P FA . The essence of any such technique will be calculating the position of the planet during the observation, and de-orbiting in some way, say shift-and-add (SAA) on a sequence of images. The drawback of this approach is that it will produce more false alarms per observed star due to the increased number of trials, similar to lowering the detection threshold. If the orbit were precisely known, we could proceed with almost no impact on FAR . However, in the presence of uncertainties in orbital parameters or in a completely blind search we will have to consider many trial orbits. For now we can perform a 'back-of-the-envelope' estimate of the number of possible orbits to understand how much FAR will increase. To do so, we begin by placing bounds on the problem.</text>
<text><location><page_13><loc_12><loc_41><loc_88><loc_48></location>We can first establish where on the detector we must consider orbital motion. At any separation r from the star, the slowest un-bound orbit will have the escape velocity. Since we know that physical separation is greater than or equal to projected separation, r ≥ ρ , and that maximum projected speed will occur for inclination i = 0, we know that</text>
<formula><location><page_13><loc_42><loc_39><loc_88><loc_42></location>v esc = √ 2 v FOC ( a → ρ ) (14)</formula>
<text><location><page_13><loc_12><loc_34><loc_88><loc_38></location>sets the upper limit on the projected focal plane speed of an object in a bound orbit. We can also set an upper limit on the amount of motion /epsilon1 max we can tolerate over the duration ∆ t tot of the observation based on the SNR degradation it would cause. So we only need consider orbital motion when</text>
<formula><location><page_13><loc_41><loc_31><loc_88><loc_33></location>√ 2 v FOC ( ρ )∆ t tot > /epsilon1 max . (15)</formula>
<text><location><page_13><loc_12><loc_28><loc_88><loc_29></location>From here we determine the upper limit on projected separation from the star for considering this problem:</text>
<formula><location><page_13><loc_37><loc_23><loc_88><loc_27></location>ρ max = 0 . 0136 M ∗ ( D λd ∆ t tot /epsilon1 max ) 2 AU. (16)</formula>
<text><location><page_13><loc_12><loc_21><loc_79><loc_22></location>By the same logic, for any point closer than ρ max the maximum possible change in position is</text>
<formula><location><page_13><loc_36><loc_17><loc_88><loc_21></location>∆ ρ max ≈ √ 2 v FOC ( ρ )∆ t tot in FWHM . (17)</formula>
<text><location><page_13><loc_12><loc_14><loc_88><loc_17></location>Then we must evaluate possible orbits ending anywhere in an area of π (∆ ρ max ) 2 FWHM 2 around an initial position.</text>
<text><location><page_13><loc_12><loc_10><loc_88><loc_13></location>These two limits set the statistical sensitivity of an attempt to de-orbit an observation. The number of different orbits, N orb , will be determined by the area of the detector where orbital motion is non-negligible,</text>
<text><location><page_14><loc_12><loc_85><loc_62><loc_86></location>and the size of the region around each point that we consider. That is</text>
<formula><location><page_14><loc_41><loc_80><loc_88><loc_84></location>N orb ∝ ∫ ρ max 0 ∆ ρ 2 max ρdρ. (18)</formula>
<text><location><page_14><loc_12><loc_78><loc_13><loc_80></location>so</text>
<formula><location><page_14><loc_39><loc_75><loc_88><loc_79></location>N orb ∝ ( M ∗ /epsilon1 ) 2 ( D λd ) 4 ∆ t 4 tot . (19)</formula>
<text><location><page_14><loc_12><loc_66><loc_88><loc_74></location>In general N trials ∝ N orb , so FAR ∝ P FA × N orb . Larger D , shorter λ , closer d , and smaller acceptable orbital motion /epsilon1 will then all increase FAR † . Perhaps the most important feature of this result is that N orb ∝ ∆ t 4 tot -increasing integration time rapidly increases the FAR of a blind search . Note that this is still less severe than the exponential increase in P FA found for merely lowering the threshold. In the next section we will test these relationships after fully applying orbital mechanics, and see that they hold.</text>
<section_header_level_1><location><page_14><loc_27><loc_61><loc_73><loc_62></location>4. Blind Search: Recovering SNR after Orbital Motion</section_header_level_1>
<text><location><page_14><loc_12><loc_49><loc_88><loc_59></location>In this section we consider in detail a blind search, i.e. an observation of a star for which we have no prior knowledge of exoplanet orbits. We showed above that the problem is well constrained. Here we derive several ways to further limit the number of trial orbits we must consider. After that, we describe an algorithm for determining the orbital elements that must be considered and then discuss the results. Finally, we use this algorithm to de-orbit a sequence of simulated images and analyze the impact of correlations between trial orbits on FAR .</text>
<text><location><page_14><loc_12><loc_38><loc_88><loc_48></location>To provide numerical illustrations throughout this section we consider the problem of a 20 hour observation of α Cen A using the GMT at 10 µ m. This scenario is loosely based on performance predictions made for the proposed TIGER instrument, a mid-IR diffraction limited imager for the GMT (Hinz et al. 2012). The details of these predictions are not important for our purposes, so we will only assert that this is a plausible case. There are other examples in the literature with similar integration times, such as the EPICS prediction we discussed earlier.</text>
<text><location><page_14><loc_12><loc_24><loc_88><loc_37></location>We assume that this 20 hr observation is broken up into five ∆ t = 4 hr exposures, spread over 7 nights or ∆ t tot = 6 . 2 elapsed days from start to finish. The choice of ∆ t is essentially arbitrary, but we have good reasons to expect it to be shorter than an entire night. An important consideration is the planned use of ADI, and the attendant need to obtain sufficient field rotation in a short enough time to provide good PSF calibration while avoiding self-subtraction (Marois et al. 2006). The effect of airmass on seeing through r 0 ∝ cos( z ) 3 / 5 , where z is the zenith angle, and hence on AO system performance, could also cause us to observe as near transit as possible. Efficiency will be affected by chopping and nodding, necessary for background subtraction at 10 µ m. This will limit the net exposure time obtainable in one night..</text>
<text><location><page_14><loc_12><loc_15><loc_88><loc_23></location>Few ground-based astronomers would object to an assertion that we loose 2 nights out of 7 to weather. We could be observing in queue mode, such that these observations are only attempted when seeing is at least some minimal value, or precipitable water vapor is low. One can even imagine the opposite case at 10 µ m, such that nights of the very best seeing are devoted to shorter wavelength programs. While this scenario may be somewhat contrived, we feel that it is both plausible and realistic. We now proceed to</text>
<text><location><page_15><loc_12><loc_83><loc_88><loc_86></location>describe a technique that would mitigate the effects of orbital motion for our GMT example and should be applicable to other long exposure cases.</text>
<section_header_level_1><location><page_15><loc_39><loc_78><loc_61><loc_79></location>4.1. Limiting Trial Orbits</section_header_level_1>
<text><location><page_15><loc_12><loc_72><loc_88><loc_76></location>Here we derive limits on the semi-major axis and eccentricity of trial orbits to consider. These limits are based only on the amount of orbital motion tolerable for the science case, and do not represent physical limits on possible orbits around the star.</text>
<text><location><page_15><loc_12><loc_67><loc_88><loc_70></location>It is always true that r ≥ ρ . This implies that, for any orbit, the separation of apocenter must obey r a ≥ ρ . This allows us to set a lower bound on a , a min , given a choice of e through</text>
<formula><location><page_15><loc_44><loc_64><loc_88><loc_66></location>ρ au ≤ a min (1 + e ) (20)</formula>
<text><location><page_15><loc_12><loc_62><loc_20><loc_64></location>which gives</text>
<formula><location><page_15><loc_41><loc_59><loc_88><loc_62></location>a min = 0 . 2063 λdρ D (1 + e ) . (21)</formula>
<text><location><page_15><loc_12><loc_53><loc_88><loc_58></location>The fastest speed in a bound planet's orbit will occur at pericenter, and using the maximum tolerable motion /epsilon1 max during our observation of total elapsed time ∆ t tot we can set an upper bound on a by noting that</text>
<text><location><page_15><loc_12><loc_49><loc_22><loc_50></location>which leads to</text>
<formula><location><page_15><loc_38><loc_49><loc_88><loc_53></location>v FOC ( a max ) √ 1 + e 1 -e ∆ t tot ≤ /epsilon1 max (22)</formula>
<formula><location><page_15><loc_35><loc_45><loc_88><loc_49></location>a max = ( 0 . 0834 D λd ) 2 1 + e 1 -e M ∗ ( ∆ t tot /epsilon1 max ) 2 . (23)</formula>
<text><location><page_15><loc_12><loc_38><loc_88><loc_44></location>Using the GMT example: for e = 0 . 0, a max = 3 . 9 AU; and for e = 0 . 5, a max = 11 . 8 AU. Using Equation 16 we have a projected separation limit of ρ max = 7 . 7 AU, so it is possible for these definitions to produce a max < a min for certain choices of e at a given ρ . This condition tells us that at such a value of e no orbits can move fast enough to warrant consideration. Thus we can set a lower limit on e at projected separation ρ</text>
<text><location><page_15><loc_12><loc_32><loc_40><loc_33></location>where we have simplified by pulling out</text>
<formula><location><page_15><loc_40><loc_32><loc_88><loc_37></location>e min = 1 2 √ ξ 2 +8 ξ -1 -ξ 2 (24)</formula>
<formula><location><page_15><loc_40><loc_27><loc_88><loc_31></location>ξ = 29 . 66 ρ M ∗ ( /epsilon1 ∆ t ) 2 ( λd D ) 3 . (25)</formula>
<text><location><page_15><loc_12><loc_21><loc_88><loc_26></location>In practice, we might consider eccentricity ranges with e max less than 1, thus improving our sensitivity. Inputs to our choice of e max could include some prior distribution of eccentricities, or dynamical stability considerations in binary star systems and systems with known outer companions.</text>
<section_header_level_1><location><page_15><loc_37><loc_16><loc_64><loc_17></location>4.2. Choosing Orbital Elements</section_header_level_1>
<text><location><page_15><loc_12><loc_10><loc_88><loc_14></location>Now we describe an algorithm for sampling the possible trial orbits over a set of M sequential images. For now, we assume no prior knowledge of orbital parameters. We will employ a simple grid search through the parameter space bounded as described above.</text>
<unordered_list>
<list_item><location><page_16><loc_14><loc_85><loc_62><loc_86></location>1. Determine the region around the star to consider using Eq. (16).</list_item>
<list_item><location><page_16><loc_14><loc_76><loc_88><loc_83></location>2. Identify regions of interest. In the best cases the orbital motion will be small enough that we will be able stack the images and search the result for regions with higher SNR (e.g. SNR > 4) and limit further analysis to those areas. In the worst cases orbital motion will be large enough that we will need to blindly apply this algorithm at each pixel within the bounding region identified in the previous step. In the present GMTα Cen example we are in the former case.</list_item>
<list_item><location><page_16><loc_14><loc_73><loc_64><loc_74></location>3. For each region, choose a size, perhaps based on v esc (as in Eq. 17).</list_item>
<list_item><location><page_16><loc_14><loc_68><loc_88><loc_72></location>4. Chose a starting point ( x 1 , y 1 ), with ρ 1 = √ x 2 1 + y 2 1 . If we are proceeding pixel by pixel, then ( x 1 , y 1 ) describes the current pixel.</list_item>
<list_item><location><page_16><loc_14><loc_65><loc_72><loc_67></location>5. Choose e ∈ e min ( ρ 1 ) . . . e max using Equation (24) and assumptions about e max .</list_item>
<list_item><location><page_16><loc_14><loc_62><loc_62><loc_64></location>6. Choose a ∈ a min ( ρ 1 , e ) . . . a max ( e ) using Equations (21) and (23).</list_item>
<list_item><location><page_16><loc_14><loc_57><loc_88><loc_62></location>7. Choose time of pericenter τ ∈ t 1 -P ( M ∗ , a ) . . . t 1 where P is the orbital period and t 1 is the time of the first image. Now calculate the true anomaly f ( t 1 ; a, e, τ, P ) using Kepler 's equation and physical separation using:</list_item>
</unordered_list>
<formula><location><page_16><loc_46><loc_54><loc_88><loc_57></location>r = a (1 -e ) 1 + e cos( f ) (26)</formula>
<text><location><page_16><loc_19><loc_49><loc_19><loc_51></location>/negationslash</text>
<unordered_list>
<list_item><location><page_16><loc_14><loc_48><loc_36><loc_51></location>8. if e = 0: Choose ω ∈ 0 . . . 2 π if e = 0: set ω = 0.</list_item>
<list_item><location><page_16><loc_14><loc_46><loc_28><loc_47></location>9. if sin( ω + f ) > 0:</list_item>
<list_item><location><page_16><loc_17><loc_43><loc_43><loc_44></location>(a) Given e , a , τ , f , and ω , calculate</list_item>
</unordered_list>
<formula><location><page_16><loc_44><loc_38><loc_88><loc_42></location>cos i = ± √ ρ 2 r 2 -cos 2 ( ω + f ) sin( ω + f ) (27)</formula>
<formula><location><page_16><loc_39><loc_33><loc_88><loc_36></location>sin Ω = y cos( ω + f ) -x sin( ω + f ) cos i r (cos 2 ( ω + f ) + sin 2 ( ω + f ) cos 2 i ) (28)</formula>
<formula><location><page_16><loc_39><loc_29><loc_88><loc_32></location>cos Ω = y sin( ω + f ) cos i + x cos( ω + f ) r (cos 2 ( ω + f ) + sin 2 ( ω + f ) cos 2 i ) (29)</formula>
<text><location><page_16><loc_19><loc_27><loc_59><loc_28></location>where Ω should be determined in the correct quadrant.</text>
<unordered_list>
<list_item><location><page_16><loc_16><loc_20><loc_88><loc_26></location>(b) We now have a complete set of elements, and so can SAA the sequence of images based on these orbits (one for each i ). Doing so requires calculating the true anomaly f j at the time of each image, and then calculating the projected orbital position of the prospective companion in each image.</list_item>
<list_item><location><page_16><loc_13><loc_16><loc_88><loc_19></location>10. if sin( ω + f ) = 0, we do not have a unique solution for inclination. This is the special case where the planet is passing through the plane of the sky.</list_item>
<list_item><location><page_17><loc_17><loc_85><loc_38><loc_86></location>(a) for ω + f = 0 calculate Ω:</list_item>
</unordered_list>
<text><location><page_17><loc_19><loc_77><loc_40><loc_79></location>or for ω + f = π calculate Ω:</text>
<text><location><page_17><loc_19><loc_70><loc_47><loc_71></location>determining Ω in the correct quadrant.</text>
<text><location><page_17><loc_13><loc_59><loc_88><loc_62></location>11. Repeat the above steps until the parameters ω , τ , a , and e are sufficiently sampled for each starting point.</text>
<section_header_level_1><location><page_17><loc_26><loc_54><loc_74><loc_55></location>4.3. De-orbiting: Unique Sequences of Whole-Pixel Shifts</section_header_level_1>
<text><location><page_17><loc_12><loc_44><loc_88><loc_52></location>The algorithm just described will produce a large number of trial orbits, many of which will be very similar. The information content of our image is set by the resolution of the telescope, so we can take advantage of this similarity to greatly reduce the number of statistical trials. This is done by grouping similar orbits into sequences of whole-pixel shift sequences, where the pixels are at least as small as FWHM / 2. As we will see, we typically will want to oversample, to say FWHM / 3, to ensure adequate SNR recovery.</text>
<text><location><page_17><loc_12><loc_35><loc_88><loc_43></location>We calculate the pixel-shift sequence for each orbit by determining which pixel the trial planet (or rather, the center of its PSF) lands on at each time step. Many orbits end up producing the same sequences of pixel-shifts, and we will keep only the unique ones for use in de-orbiting the observation. In Figure 5 we illustrate the outcome of the pixel-shift algorithm, showing two unique sequences and a few of the orbits that produced them.</text>
<text><location><page_17><loc_12><loc_25><loc_88><loc_34></location>To test the above algorithm and the pixel-shift technique, we used our GMT α Cen A example and determined the trial orbits for various separations and ∆ t s. We set /epsilon1 max = 0 . 5 based on our earlier analysis of SNR . The results are summarized in Figure 6. The problem is generally well constrained in that we only have a finite search space for any initial point. The data used to construct Figure 6 are provided in Table 1. Comparing N orb to N shifts , note the large reduction in the number of trials ( ∼ 10 8 to ∼ 10 2 ) due to combining similar orbits.</text>
<section_header_level_1><location><page_17><loc_42><loc_19><loc_58><loc_21></location>4.4. N orb Scalings</section_header_level_1>
<text><location><page_17><loc_12><loc_10><loc_88><loc_18></location>In Figure 7 we plot the area of the detector which contains the possible trial orbits at ρ 1 = 1 . 0 AU vs. the total elapsed time ∆ t tot . We conclude from this plot that the area around a given starting point is proportional to ∆ t 2 tot . Also in Figure 7 we plot area vs separation from the star, and conclude that area is proportional to 1 /ρ 1 . Taken together these results give confidence that the N orb ∝ ∆ t 4 tot scaling derived earlier holds when we fully apply orbital mechanics rather than the escape velocity approximation.</text>
<formula><location><page_17><loc_51><loc_82><loc_88><loc_85></location>sin Ω = y r (30)</formula>
<formula><location><page_17><loc_50><loc_79><loc_88><loc_82></location>cos Ω = x r (31)</formula>
<formula><location><page_17><loc_50><loc_75><loc_88><loc_78></location>sin Ω = -y r (32)</formula>
<formula><location><page_17><loc_50><loc_71><loc_88><loc_74></location>cos Ω = -x r (33)</formula>
<figure>
<location><page_18><loc_14><loc_34><loc_67><loc_72></location>
<caption>Fig. 5.- Two sequences of whole pixel-shifts, one in red and one in blue. We also show a few of the many orbits that produce these shift sequences. Once these shifts are determined, a set of 5 images can be de-orbited by shifting the images by the indicated sequence 5-4-3-2-1, that is the pixel containing the orbit in image 2 is is shifted and added to the pixel containing the orbit in image 1, and likewise for images 3, 4, and 5. Of course, the entire image is shifted, not just single pixels.</caption>
</figure>
<figure>
<location><page_19><loc_25><loc_38><loc_76><loc_77></location>
<caption>Fig. 6.- Example trial orbits for the GMT, working at 10 µ m, observing α Cen A. Plotted are the end points of orbits calculated using the algorithm given in Section 4.2 for the given initial projected planet separations ρ 1 and elapsed observation times ∆ t tot . The red points show the effect of changing initial separation for a constant elapsed time. At 1 AU initial separation the colors correspond to different elapsed times as indicated in the legend. We further analyze these relationships in Table 1 and Figure 7. The results of the algorithm appear more complicated than the simple escape-velocity circle analysis in Section 3.3.3. The end-point clouds are not circularly symmetric about the starting point, and have some azimuthal structure. For instance there is a triangle extending azimuthally corresponding to face-on highe orbits, and there are gaps along the radius from the star corresponding to i very near 90 o . These structures are consequences of the chosen grid resolution.</caption>
</figure>
<table>
<location><page_20><loc_29><loc_42><loc_71><loc_61></location>
<caption>Table 1: Results of applying the algorithm detailed in Section 4.2 for various separations and elapsed observation times. See also Figure 7. Note the dramatic reduction in the number of trials ( N orb vs. N shifts ) after combining similar orbits into whole-pixel shift sequences.</caption>
</table>
<text><location><page_20><loc_59><loc_42><loc_60><loc_44></location>×</text>
<text><location><page_21><loc_12><loc_70><loc_88><loc_86></location>Things are a bit more complicated when we consider the scaling of the number of while-pixel shift sequences. We conducted two sets of trials at ρ 1 = 1 . 0 AU. In the first, the number of observations and their relative spacing was held constant regardless of ∆ t tot . In the second set, the number of observations scaled with ∆ t tot . As shown in Figure 7, when the number of observations is constant, the number of shifts scales as ∆ t 2 tot , but when the number of observations grows with ∆ t tot the number of shifts scales as roughly ∆ t 3 . 6 tot . Figure 7d shows that the number of shifts scales as 1 /ρ 1 . Taken together, we see that for a constant number of observations the pixel-shift technique will follow the N orb ∝ ∆ t 4 tot scaling. However, if the number of observations also scales with ∆ t tot , then our results imply that N orb ∝ ∆ t 5 . 6 tot . The value of the exponent likely depends on the details of the observation sequence, but this has important implications for observation planning.</text>
<section_header_level_1><location><page_21><loc_41><loc_65><loc_59><loc_66></location>4.5. Recovering SNR</section_header_level_1>
<text><location><page_21><loc_12><loc_47><loc_88><loc_63></location>We next consider whether de-orbiting by whole-pixels adequately recovers SNR . To test this we 'orbited' a Gaussian PSF on face-on orbits with various eccentricities, starting from pericenter. We then calculated shifts for detector samplings of 2, 3, and 4 pixels/FWHM, and then de-orbited by these shifts. The results are summarized in Table 2. On a critically sampled detector we only recover a 5 σ planet to ∼ 4 . 9 σ , a 2% loss of SNR . At 3 pixels/FWHM we do much better, recovering SNR to 4.97 for low eccentricities, and 4.95 for higher eccentricities. Performance for 4 pixels/FHWM sampling is similar. A 2% loss of SNR nearly doubles P FA , so it appears that we should oversample to at least 3 pixels/FWHM, either optically or by re-sampling images during data reduction. In our analysis we have assumed that the limiting noise source is background photons (PSF halo or sky), so we ignore the increased readout noise expected from oversampling.</text>
<section_header_level_1><location><page_21><loc_30><loc_41><loc_70><loc_43></location>4.6. Correlations And The True Impact On P FA</section_header_level_1>
<text><location><page_21><loc_12><loc_29><loc_88><loc_40></location>As we have noted several times, the main impact of orbital motion is to reduce SNR , which in turn reduces our statistical sensitivity. If we attempt to de-orbit an observation in order to recover SNR , we do so at the cost of a large increase in the number of trials. Worst case, this results in a proportional increase in FAR since nominally FAR = P FA × N orb . However, we expect significant correlation between trials of neighboring orbits and whole-pixel shifts. To investigate this, we performed a series of monte carlo experiments. A sequence of images with Gaussian noise was generated, and first stacked without shifting, hereafter called the naive-add. The same sequence was then shifted by each possible whole-pixel shift,</text>
<table>
<location><page_21><loc_21><loc_13><loc_79><loc_22></location>
<caption>Table 2. SNR recovered after de-orbiting with whole-pixel shifts for various samplings.</caption>
</table>
<figure>
<location><page_22><loc_13><loc_36><loc_83><loc_73></location>
<caption>Fig. 7.- Scaling of the number of orbits and the number of resulting whole-pixel shifts with observation elapsed time and with distance from the star. These results demonstrate that the number of trial orbits N orb ∝ ∆ t 4 tot scaling that we derived using the escape velocity holds when we rigorously apply orbital mechanics. Note though that the situation is more complicated with the number of shifts - if the number of observations increases with elapsed time then the number of shifts grows faster than ∆ t 2 tot , implying that N orb will increase faster than ∆ t 4 tot . These scalings lead to one of our main, if seemingly obvious, conclusions: one must limit the elapsed time of an observation as much as possible when orbital motion is significant.</caption>
</figure>
<text><location><page_23><loc_12><loc_83><loc_88><loc_86></location>assuming a 1AU initial separation around α Cen A. This experiment was conducted for observations with total elapsed times ∆ t tot of 4.2, 6.2, 8.2, and 10.2 days, with samplings of 2, 3, and 4 pixels/FWHM.</text>
<text><location><page_23><loc_12><loc_72><loc_88><loc_82></location>We performed several tests on each sequence. The first was a simple threshold test on the naive-add, with the threshold set for the worst case orbital motion given by Equation 10 with v om = v esc . We performed simple aperture photometry, with a r ap = 1 FHWM. As expected the resultant P FA 1 is as predicted by Equation 11. The next test was to apply a 5 σ threshold after de-orbiting by whole-pixel shifts and adding. If all shifts were completely uncorrelated, then we would expect FAR = (2 . 9 × 10 -7 ) × N shifts , but as we predicted, shifts are correlated and P FA 2 is lower than this.</text>
<text><location><page_23><loc_12><loc_65><loc_88><loc_71></location>The final test performed was to apply both thresholds in sequence, such that a detection is made only if the naive-add results in SNR greater than the threshold for worst case orbital motion, and the de-orbited SAA results in SNR > 5. This P FA 3 is lower than either P FA 1 or P FA 2 , but still higher than if no orbital motion occurred.</text>
<text><location><page_23><loc_12><loc_54><loc_88><loc_64></location>The results of each trial are present in Table 3. Applying both threshold tests results in significant improvement over the naive-add in terms of FAR . Another interesting result is that sampling has only a minor impact on P FA 3 . This makes some sense as we expect the correlation of neighboring shifts to be set by the FWHM, not the sampling. So even though the accuracy of SNR recovery is improved, and quite a few more shifts are required, these shifts remain correlated across the same spatial scale resulting in little change in the overall FAR .</text>
<section_header_level_1><location><page_23><loc_30><loc_49><loc_70><loc_50></location>4.7. Impact on Completeness of the Double Test</section_header_level_1>
<text><location><page_23><loc_12><loc_38><loc_88><loc_47></location>There is still an impact on completeness, however, because we are now conducting two trials instead of one. This lowers the true positive probability ( P TP ). Consider a 5 σ planet on the worst case fastest possible orbit, for the 10.2 day elapsed time case. The threshold for the naive add is 2.625. We have a 50% probability of detecting this planet after the naive add. If it is detected on the first test, there is then some probability P TP < 1 of detecting at SNR ≥ 5 after de-orbiting. Worst case, this will be 50%, resulting in a net P TP of 25%. In reality, it will be better than this as the two trials will be strongly correlated.</text>
<text><location><page_23><loc_12><loc_25><loc_88><loc_36></location>Even if this worst case of 25% were realized this is still significant improvement over Option I. A 2 . 6 σ signal would only be detected 10% of the time with a 5 σ threshold. Given the reduction in P FA from 4 . 3 × 10 -3 to 2 . 2 × 10 -5 , likewise an improvement over Option II at 2 . 6 σ , it is clear that de-orbiting by whole-pixel shifts does improve our ability to detect an orbiting planet . The situation will be even better for slower planets, and most of the area searched will not be subject to the worst case orbital speed. We leave a complete analysis of the impact on search completeness for future work. One can also imagine adjusting the thresholds to optimize completeness at the expense of worse P FA .</text>
<section_header_level_1><location><page_23><loc_35><loc_20><loc_65><loc_21></location>4.8. Tractability of a Blind Search</section_header_level_1>
<text><location><page_23><loc_12><loc_10><loc_88><loc_18></location>We end this section by concluding that a blind search when orbital motion is significant is tractable. Orbital motion will make such a search less sensitive, both in terms of number of false alarms and in terms of completeness, but Keplerian mechanics gives us enough tools to bound the problem. As we have shown deorbiting a sequence of observations can recover SNR to its nominal value, and we can do so while controlling the impact on statistical sensitivity. For the ∆ t tot = 6 . 2 day observation, P FA 3 was roughly a factor of 10</text>
<table>
<location><page_24><loc_21><loc_39><loc_79><loc_74></location>
<caption>Table 3. False alarm probabilities after de-orbiting Gaussian noise images.</caption>
</table>
<text><location><page_25><loc_12><loc_76><loc_88><loc_86></location>higher than if no orbital motion occurred. This increase only occurs over a bounded region around the star, so the net effect on FAR will be contained. Using this factor of 10 as the mean value over the 7.7 AU = 69.1 FWHM radius region around α Cen A where orbital motion is significant, the FAR in this area will have gone from ∼ 1 / 1000 to ∼ 1 / 100 in our GMT/10 µ m example. The key, though, appears to be to limit the elapsed time of the observation as the number of trials increases - decreasing sensitivity - proportionally to at least ∆ t 4 tot in a blind search.</text>
<text><location><page_25><loc_12><loc_69><loc_88><loc_75></location>The main caveat at this point in our analysis is that we have drawn the conclusion of tractability using Gaussian statistics. It is well known that speckle noise, which will often be the limiting noise source for high contrast imaging in the HZ, is not Gaussian and results in much higher P FA for a given SNR (Marois et al. 2008a). Future work on this problem will need to take this into account.</text>
<text><location><page_25><loc_12><loc_65><loc_88><loc_68></location>Next we consider a more strongly bounded scenario, where we have significant prior information about the orbit of the planet from radial velocity surveys.</text>
<section_header_level_1><location><page_25><loc_36><loc_60><loc_64><loc_61></location>5. Cued Search: Using RV Priors</section_header_level_1>
<text><location><page_25><loc_12><loc_45><loc_88><loc_58></location>The situation is greatly improved if we have prior information, such as orbit parameters from RV or astrometry. Here we consider the case of Gliese 581d, and the previously discussed future observation of this planet by EPICS at the E-ELT (Kasper et al. 2010). There is some controversy surrounding the solution to the RV signal, and whether planet d even exists (Forveille et al. 2011; Vogt et al. 2012; Baluev 2012). We show results for both the floating eccentricity Keplerian fits of Forveille et al. (2011)[hereafter F11], and the all circular interacting model of Vogt et al. (2012)[hereafter V12]. Doing so allows us to illustrate the impact of eccentricity on the analysis, and prevents us having to take a stand in a currently raging debate. The parameters used herein are listed in Table 4.</text>
<text><location><page_25><loc_12><loc_38><loc_88><loc_44></location>Instead of a grid search, we use a monte carlo (MC) method. The RV technique provides the parameters a , e , ω and t 0 or their equivalents. We can take the results of fitting orbits to the RV signal, and the associated uncertainties, as prior distributions which we sample to form trial orbits. We will assume that all uncertainties are uncorrelated and are from Gaussian distributions.</text>
<text><location><page_25><loc_12><loc_30><loc_88><loc_36></location>We assume that the 20 hr integration is broken up over 6.2 nights based on the same logic discussed in Section 4. Kasper et al. (2010) actually assumed 20 × 1 hr observations based on the amount of rotation needed, but did not consider the effects of orbital motion over 20 days of a 67 day period (M. Kasper, personal communication (2012)).</text>
<table>
<location><page_25><loc_21><loc_22><loc_79><loc_28></location>
<caption>Table 4: Orbital parameters for Gl 581d used in this analysis. We derived the values reported here from other parameters where necessary. Only the uncertainty in t 0 impacts our analysis. In both models the orbital period is 66 . 6 days.</caption>
</table>
<text><location><page_25><loc_43><loc_22><loc_45><loc_24></location>±</text>
<text><location><page_25><loc_54><loc_22><loc_55><loc_24></location>±</text>
<text><location><page_25><loc_64><loc_22><loc_65><loc_24></location>±</text>
<text><location><page_25><loc_72><loc_22><loc_74><loc_24></location>±</text>
<section_header_level_1><location><page_26><loc_43><loc_85><loc_57><loc_86></location>5.1. Constraints</section_header_level_1>
<text><location><page_26><loc_12><loc_80><loc_88><loc_83></location>In order to minimize the number of trial orbits to consider, we can apply various constraints taking advantage of the information we have from the RV detection.</text>
<text><location><page_26><loc_12><loc_72><loc_88><loc_78></location>In the case of a multi-planet system dynamical analysis can place constraints on the inclination based on system stability. For Gl 581, Mayor et al. (2009) found the system was stable for i > 30. We can also make use of the geometric prior for inclination, where we expect P i = sin( i ) in a population of randomly oriented systems.</text>
<text><location><page_26><loc_12><loc_68><loc_88><loc_70></location>Since this is a reflected light observation, the orbital phase and its impact on the brightness of the planet must be considered. The planet's reflected flux is given by</text>
<formula><location><page_26><loc_39><loc_63><loc_88><loc_67></location>F p ( α ) = F ∗ ( R p r ) 2 A g ( λ )Φ( α ) (34)</formula>
<text><location><page_26><loc_12><loc_59><loc_88><loc_62></location>where F ∗ is the stellar flux, R p is the planet's radius, r its separation, A g ( λ ) is the wavelength dependent geometric albedo, and Φ is the phase function at phase angle α . The phase angle is given by</text>
<formula><location><page_26><loc_41><loc_57><loc_88><loc_58></location>cos( α ) = sin( f + ω ) sin( i ) . (35)</formula>
<text><location><page_26><loc_12><loc_53><loc_88><loc_56></location>In general, determining the quantity A g ( λ )Φ( α ) requires atmospheric modeling (Cahoy et al. 2010). For now, we assume that Φ follows the Lambert phase function</text>
<formula><location><page_26><loc_38><loc_49><loc_88><loc_52></location>Φ( α ) = 1 π [sin( α ) + ( π -α ) cos( α )] (36)</formula>
<text><location><page_26><loc_12><loc_44><loc_88><loc_48></location>We assume that the prediction of Kasper et al. (2010) was made for the planet at quadrature, α = π/ 2, where Φ = 0 . 318 . We then require that the mean value of Φ during the observation be greater than this value - that is the planet is as bright or brighter than it is at quadrature.</text>
<section_header_level_1><location><page_26><loc_41><loc_39><loc_59><loc_40></location>5.2. Initial Detection</section_header_level_1>
<text><location><page_26><loc_12><loc_29><loc_88><loc_37></location>An important consideration in an RV-cued observation will be when to begin. As a first approximation, we assume that maximizing planet-star separation will maximize our sensitivity. This may not be true when working in reflected light due to the phase and separation dependent brightness of the planet in this regime. Proceeding with the approximation for now, we expect to plan this observation to be as close to apocenter as possible. In this case we will begin integrating 3.1 days before t 0 + P/ 2.</text>
<text><location><page_26><loc_12><loc_10><loc_88><loc_28></location>To understand the area where we will be searching for Gl 581d, we first conducted an MC experiment to calculate the possible positions of the planet at t = t 0 + P/ 2 -3 . 1 days. To do so, we drew random values of a , e , w , and t 0 from Gaussian distributions with the parameters of Table 4. We drew a random value of i from the sin( i ) distribution, and rejected any value of i ≤ 30 based on the dynamical prior. Finally Ω was drawn from a uniform distribution in 0 . . . 2 π . This process was repeated 10 9 times, and the frequency at which starting points occur in the area around the star was recorded. The results are shown in Figure 8 for the V12 circular model and for the F11 eccentric model. The Figure shows the area which must be searched to obtain various completeness. For instance, if we desire 95% completeness in the V12 model, we must consider an area of 71 apertures. Since this SNR = 5 detection is broken up into 5 distinct integrations, our first attempt will have SNR = 2 . 24, giving a FAR = 0 . 89 for the first 4 hr integration. In other words, we should expect a false alarm in addition to a real detection.</text>
<figure>
<location><page_27><loc_29><loc_23><loc_78><loc_84></location>
<caption>Fig. 8.- Possible starting points for Gl 581d, observed near apocenter. Top: using the parameters of Forveille et al. (2011)'s eccentric model. Bottom: assuming the parameters of Vogt et al. (2012)'s circular interacting model. The color shading is in units of probability per aperture (each aperture has area π FWHM 2 ). The legend indicates the color which encloses the given completeness intervals, and the enclosed area in apertures, which can be directly related to the false alarm rate as discussed in the text.</caption>
</figure>
<section_header_level_1><location><page_28><loc_36><loc_85><loc_64><loc_86></location>5.3. Calculating Orbits and Shifts</section_header_level_1>
<text><location><page_28><loc_12><loc_78><loc_88><loc_83></location>Now we assume that we have an initial detection at SNR ∼ 2 . 24 within the highest probability regions ‡ . In order to follow-up this detection over subsequent nights, we must determine the possible locations of the planet, constrained by the RV-derived orbital elements.</text>
<text><location><page_28><loc_12><loc_59><loc_88><loc_77></location>We proceed by choosing a , e , ω , and t 0 from Gaussian distributions as above. Now as long as r > ρ we will have a unique solution for i and Ω given the randomly chosen parameters (see the blind search algorithm above). We take into account dynamical stability by rejecting any orbit which has i ≤ 30. The orbit determined in this fashion was then projected 6.2 days into the future and the frequency of these final points was recorded. We show the result for the V11 model in Figure 9, top panel. Using the RV determined parameters and their uncertainties allows us to determine the probability density of orbit endpoints, and determine how much of the search space we must consider for a given completeness. The whole-pixel shifts were also calculated using a sampling of FWHM/3, and are shown in the legend. We also applied the blind search algorithm to this observation from the same starting point, and show the results for comparison in the bottom panel of Figure 9. As expected the RV priors significantly reduce the search space - we have 942 trial shift-sequences to consider instead of 12000.</text>
<text><location><page_28><loc_12><loc_47><loc_88><loc_58></location>Another important consideration here is that our initial 2 . 24 σ detection will have a large position uncertainty, which we estimate by σ ρ 0 = FWHM/SNR . We added a random draw for the starting position, and repeated the MC experiment for F11 and also conducted a run for the V12 parameters. The results are shown in Figure 10. The number of shift sequences is much higher due to the uncertainty in the starting position caused by our low SNR initial detection, but we expect correlations to come to the rescue as in our α Cen example. To compare to Figure 9 keep in mind that the blind search would have to be applied to all 5500 pixels in the search space indicated by Figure 8.</text>
<text><location><page_28><loc_12><loc_36><loc_88><loc_46></location>As in the GMT/ α Cen example, we leave for future work a complete analysis of sensitivity and completeness. The large number of trial shifts calculated when we include uncertainty in the starting position motivates us to suggest that we will ultimately turn this analysis over to a much more robust optimization strategy, such as a Markov Chain Monte Carlo (MCMC) routine. Once an area of the image was identified with a high post-shift SNR , a MCMC analysis could determine the very best orbit and assign robust measures of significance to the result.</text>
<text><location><page_28><loc_12><loc_30><loc_88><loc_35></location>We also note that these results likely overestimate the number of trial orbits since we have assumed uncorrelated errors. In reality the RV best fit parameters are likely strongly correlated, which should act to reduce the number of orbits to consider.</text>
<section_header_level_1><location><page_28><loc_43><loc_25><loc_57><loc_26></location>6. Conclusions</section_header_level_1>
<text><location><page_28><loc_12><loc_16><loc_88><loc_23></location>In the coming campaigns to directly image planets in the HZs of nearby stars, orbital motion will be large enough to degrade our sensitivity. This effect has been ignorable in direct imaging campaigns to date, which have typically looked for wide separation planets. We have analyzed this issue in some detail, and shown that applying basic Keplerian orbital mechanics allows us to bound the problem sufficiently that we believe direct imaging in the HZ to be a tractable problem. Our main conclusions are:</text>
<figure>
<location><page_29><loc_31><loc_58><loc_76><loc_85></location>
</figure>
<figure>
<location><page_29><loc_31><loc_28><loc_70><loc_56></location>
<caption>Fig. 9.- Trial orbits for Gl 581d, observed near maximum elongation. In the top panel we use the parameters of Forveille et al. (2011)'s eccentric model. The bottom panel shows the results for a blind search from the same starting point. The red cross shows the starting point, and the star is located at the origin. The top panel color shading is in units of probability per aperture (each aperture has area π FWHM 2 ). The legend indicates the color which encloses the given completeness intervals, the enclosed area in apertures, and the number of unique whole-pixel shift sequences which must be tried in order to de-orbit the observation. The number of shift sequences is directly related to the false alarm rate, and hence the sensitivity. For comparison, the blind search algorithm produced ∼ 12000 shifts. RV cueing greatly improves our sensitivity in the presence of orbital motion.</caption>
</figure>
<figure>
<location><page_30><loc_30><loc_57><loc_76><loc_85></location>
</figure>
<figure>
<location><page_30><loc_30><loc_27><loc_76><loc_55></location>
<caption>Fig. 10.- Trial orbits for Gl 581d, observed near maximum elongation, assuming the parameters of (top) Forveille et al. (2011)'s Keplerian eccentric model and (bottom) Vogt et al. (2012)'s circular interacting model. In this simulation we allowed the initial position to vary with standard deviation σ x,y = FWHM/SNR . The red cross shows the starting point, and the star is located at the origin. The color shading is in units of probability per aperture (each aperture has area π FWHM 2 ). The legend indicates the color which encloses the given completeness intervals, the enclosed area in apertures, and the number of unique whole-pixel shift sequences which must be tried in order to de-orbit the observation. The number of shift sequences is directly related to the false alarm rate, and hence the sensitivity.</caption>
</figure>
<unordered_list>
<list_item><location><page_31><loc_15><loc_85><loc_88><loc_86></location>(1) When projected onto the focal plane, a planet in a face-on circular orbit moves with speed given by</list_item>
</unordered_list>
<formula><location><page_31><loc_34><loc_79><loc_88><loc_83></location>v FOC = 0 . 0834 ( D λd ) √ M ∗ a FWHM day -1 . (37)</formula>
<text><location><page_31><loc_12><loc_73><loc_88><loc_77></location>In the HZ of nearby stars, especially when considering giant telescopes, speeds are high enough that planets will move significant fractions of a PSF FWHM during a single observation. This smears out the planet's flux resulting in a lower SNR .</text>
<unordered_list>
<list_item><location><page_31><loc_12><loc_65><loc_88><loc_72></location>(2) In background limited photometry, an SNR maximum is reached after about ∼ 2 FWHM of motion has occurred on the focal plane. From there, integrating longer offers no improvement with a fixed-size aperture. Adapting the aperture could mitigate this to some extent, but at the cost of significantly longer exposure times.</list_item>
<list_item><location><page_31><loc_12><loc_58><loc_88><loc_64></location>(3) When SNR is reduced by orbital motion, we have three options. Option I is to do nothing, and accept the loss of completeness due to planets appearing fainter. Option II is to adjust our detection threshold at the cost of more false alarm detections. Option III is to de-orbit an observation, recovering SNR to its nominal value, but also at the cost of more false alarms.</list_item>
<list_item><location><page_31><loc_12><loc_51><loc_88><loc_57></location>(4) For exposure times of 10s of hours, we expect an observation to extend over several days under realistic assumptions about ground based observing. If we naively attempt to de-orbit such an observation, the false alarm rate per star will increase by at least FAR ∝ ∆ t 4 tot , where ∆ t tot is the total elapsed time of the observation.</list_item>
<list_item><location><page_31><loc_12><loc_43><loc_88><loc_49></location>(5) De-orbiting a sequence of shorter exposures is possible, and tractable. Taking advantage of strong correlations between trial orbits, we will realize increases in the FAR on the order of a factor of 10 in the region around a star where orbital motion matters. Since this will be a small, bounded region, this increase in FAR appears to be acceptable.</list_item>
<list_item><location><page_31><loc_12><loc_36><loc_88><loc_42></location>(6) Cueing from another detection method, such as RV, provides significant benefit. It allows us to initiate our search at the optimum time, and significantly reduces the size of the search space. Having prior distributions for some of the orbital elements will allow us to efficiently determine where and how to search to optimize completeness.</list_item>
</unordered_list>
<text><location><page_31><loc_12><loc_30><loc_88><loc_34></location>We thank the anonymous referee for insightful and constructive comments. We thank Jessica Orwig for reviewing this manuscript. JRM is grateful for the generous support of the Phoenix ARCS foundation. LMC and JRM acknowledge support from the NSF AAG.</text>
<section_header_level_1><location><page_31><loc_44><loc_25><loc_56><loc_26></location>REFERENCES</section_header_level_1>
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<text><location><page_31><loc_12><loc_15><loc_41><loc_16></location>Biller, B. A., et al. 2007, ApJS, 173, 143</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "High contrast imaging searches for exoplanets have been conducted on 2.4-10 m telescopes, typically at H band (1.6 µ m) and used exposure times of ∼ 1hr to search for planets with semimajor axes of /greaterorsimilar 10 AU. We are beginning to plan for surveys using extreme-AO systems on the next generation of 30-meter class telescopes, where we hope to begin probing the habitable zones (HZs) of nearby stars. Here we highlight a heretofore ignorable problem in direct imaging: planets orbit their stars. Under the parameters of current surveys, orbital motion is negligible over the duration of a typical observation. However, this motion is not negligible when using large diameter telescopes to observe at relatively close stellar distances (1-10pc), over the long exposure times (10-20 hrs) necessary for direct detection of older planets in the HZ. We show that this motion will limit our achievable signal-to-noise ratio and degrade observational completeness. Even on current 8m class telescopes, orbital motion will need to be accounted for in an attempt to detect HZ planets around the nearest sun-like stars α Cen A&B, a binary system now known to harbor at least one planet. Here we derive some basic tools for analyzing this problem, and ultimately show that the prospects are good for de-orbiting a series of shorter exposures to correct for orbital motion.",
"pages": [
1
]
},
{
"title": "Direct Imaging in the Habitable Zone and the Problem of Orbital Motion",
"content": "Jared R. Males, Andrew J. Skemer, Laird M. Close Steward Observatory, University of Arizona, Tucson, AZ 85721 [email protected]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Orbital motion has been used in one fashion or another to detect planets around stars other than our Sun in large numbers. The radial velocity (RV) technique monitors the Doppler shift of a stellar spectrum as the star itself orbits the planet-star center of mass, thus allowing us to infer the presence of a planet. Similarly, the astrometry technique monitors the motion of the star on the sky and likewise infers the presence of a planet. The transit technique monitors the reduction in brightness of the star as the orbiting planet temporarily crosses the line of sight between the telescope and the star. Unlike these indirect techniques, direct imaging detects light from the planet itself and spatially resolves it from the light of the star (Traub & Oppenheimer 2011). The extreme difference in brightness between star and planet at small projected separations has generally limited direct imaging efforts to wide separations where orbital motion is ignorable. The next generation of large telescopes will move us into a new regime of direct imaging, moving closer to the star. We will even be able to begin probing the liquid water habitable zone (HZ). Here we point out that at these tight separations orbital motion will no longer be negligible in direct imaging. As we will show the motion of planets in the HZ (and closer), during the required integration times, will be large enough to limit our sensitivity unless we take action to correct it. In Section 2 we present our motivation for this study and briefly review some of the related prior work. In Section 3 we develop the basic tools needed to analyze this problem, including the expected speed of orbital motion in the focal plane and the effect it has on signal-to-noise ratio ( SNR ). In Section 4 we analyze the impact orbital motion will have on a search of α Cen A by the Giant Magellan Telescope (GMT) working at 10 µ m, and propose a method to mitigate this impact by de-orbiting a sequence of observations. Then in Section 5 we treat the more favorable case of a cued search, where we have prior information from an RV detection. To do so we analyze the case of the potentially habitable planet Gl 581d being observed by the planned European Extremely Large Telescope (E-ELT). Finally, in Section 6, we present our conclusions and prospects for future work.",
"pages": [
1,
2
]
},
{
"title": "2. Motivation and Related Work",
"content": "Moving the hunt for exoplanets into the HZ of nearby stars marks a departure from prior efforts. Here we briefly discuss the definition of the HZ, review direct imaging results to date, discuss the differences between them and and future efforts, and finally review some closely related prior work.",
"pages": [
2
]
},
{
"title": "2.1. Nearby Habitable Zones",
"content": "The HZ is generally agreed to be the region around a star where a planet can have liquid water on its surface. This is far from simply related to the blackbody equilibrium temperature, as it depends on atmospheric composition and the action of the greenhouse effect (Kasting et al. 1993; Kopparapu et al. 2013), among other factors. For our purposes it is enough to assume that the HZ is generally located at about one AU from a star, scaled by the star's luminosity Traub (2012) provided three widths for the HZ based on various considerations, and then used the first 136 days of data from the Kepler mission to estimate that the fraction of sun-like stars (spectral types FGK) with an earth-like planet in the HZ is η ⊕ ≈ 0 . 34. More generally, this analysis indicates that η planet ≈ 1 . 2, implying that every sun-like star is likely to have a planet in its HZ, and some will have more than one . While this exciting result is based on a very large extrapolation from the earliest Kepler results, it is currently one of our best estimates of planet frequency in the HZ. This topic was recently brought to the fore with the announcement of α Cen Bb by Dumusque et al. (2012). Discovered using the RV technique, α Cen Bb is an m sin i = 1 . 13 M ⊕ planet orbiting a K1 star at 0.04 AU. While certainly not in the HZ, this discovery has exciting implications for the presence of planets in the HZ of the nearest two sun-like stars. The above arguments hint that planets will be common in the HZ of sun-like stars. We are about to enter a new era of exoplanet direct imaging. With the next generation of giant telescopes and high-performance spaced-based coronagraphs we will be searching for planets in this scientifically important region around nearby stars.",
"pages": [
2
]
},
{
"title": "2.2. A Different Regime",
"content": "The typical search for exoplanets with direct imaging has used 2.4m (Hubble Space Telescope, HST) to 10m (Keck) telescopes. These surveys have mostly concentrated on young giant planets, which are expected to be self-luminous as they dissipate heat from their formation. This allows them to be detected at wider separations from their host stars, where reflected starlight would be too faint. This has also caused planet searches to typically work at H band ( ∼ 1 . 6 µ m), with exposure times of ∼ 1 hr. Examples conforming to these stereotypes include Lowrance et al. (2005) using HST/NICMOS; the Gemini Deep Planet Search (Lafreni'ere et al. 2007); the Simultaneous Differential Imaging survey using the Very Large Telescope and MMT(Biller et al. 2007); the Lyot Project at the Advanced Electro-Optical System telescope (Leconte et al. 2010); the International Deep Planet Survey (Vigan et al. 2012); and the Near Infrared Coronagraphic Imager at Gemini South (Liu et al. 2010). These searches have had some success. Examples include the 4 planets orbiting the A5V star HR 8799 (Marois et al. 2008b, 2010), with projected separations of 68, 38, 24, and ∼ 15 AU. These correspond to orbital periods of ∼ 460, ∼ 190, ∼ 100, and ∼ 50 years, respectively. The A5V star β Pic also has a planet (Lagrange et al. 2010) orbiting at ∼ 8 . 5 AU with a period of ∼ 20 years (Chauvin et al. 2012). Another A star, Fomalhaut, has a candidate planet on an 872 year (115 AU) orbit (Kalas et al. 2008). At these wide separations it takes months, or even years, to notice orbital motion. In the much closer HZ, however, orbital periods will be on the order of one year. We show in some detail that this is fast enough to yield projected motions of significant fractions of the point spread function (PSF) full width at half maximum (FWHM) over the course of an integration. The resulting smeared out image of the planet will have a lower SNR , making our observations less sensitive.",
"pages": [
2,
3
]
},
{
"title": "2.3. Long Integration Times",
"content": "In addition to HZ planets having higher orbital speeds than the current generation of imaged exoplanets, integration times required to detect them will be much longer. Direct imaging surveys to date have mostly worked in the infrared while attempting to detect young planets still cooling after formation. The coming campaigns to image planets in the HZ of nearby stars will focus on older planets, which will be less luminous in the near infrared. In the HZ, starlight reflected from the planet will be more important. The result is integration times required to detect such planets will be tens of hours, rather than the ∼ 1 hour characteristic of current campaigns. Consider the Exoplanet Imaging Camera and Spectrograph (EPICS), an instrument proposed for the E-ELT. Kasper et al. (2010) predicted that EPICS will be able to image the RV detected planet Gl 581d, which has a semi-major axis of 0.22 AU with a period of ∼ 67 days (Forveille et al. 2011; Vogt et al. 2012). This orbit places it on the outer edge of the HZ of its M2.5V star (von Braun et al. 2011). EPICS will be able to detect Gl 581d, at a planet/star contrast of 2 . 5 × 10 -8 , in 20 hrs with SNR = 5 (Kasper et al. 2010). Since this is a ground based instrument, a 20 hour integration will be broken up over at least 2 nights. Plausible observing scenarios could extend this to several nights, taking into account such things as the need for sky rotation. As we will show, the planet will move several FWHM on the EPICS detector during a multi-day observation. More generally, Cavarroc et al. (2006) showed that when realistic non-common path wavefront errors are taken into account, the integration times required to achieve the 10 -9 to 10 -10 contrast necessary to detect an earth-like planet around a sun-like star approach 100 hours on the ground, even on a 100m telescope with extreme-AO and a perfect coronagraph. One of several concerns about the feasibility of a 100 hour observation from the ground is that such a long observation will be broken up over many nights. With net exposure times of 20 to 100 hrs, and total elapsed times for ground based observations of several to tens of days, HZ planets will move significantly over the course of a detection attempt. The focus of this investigation is the impact of the orbital motion of a potentially detectable planet on sensitivity.",
"pages": [
3,
4
]
},
{
"title": "2.4. Related Work",
"content": "Though it has not yet been a significant issue in direct imaging of exoplanets, orbital motion has been considered in several closely related contexts. Here we briefly review a select portion of the literature. A very similar problem has been addressed in the context of searching for objects in our solar system, such as Kuiper Belt objects (KBOs), which can have proper motions on the order of 1' to 6' per hour (Chiang & Brown 1999). Blinking images to look for moving objects by eye is a well established technique. A more computationally intensive form of blinking images proceeds by shifting-and-adding a series of short exposures along trial paths, usually assumed to be linear. This 'digital tracking' makes it possible to detect KBOs too faint to appear in a single exposure. This has been done both from the ground (Chiang & Brown 1999; Yamamoto et al. 2008) and from space with HST (Bernstein et al. 2004). More recently Parker & Kavelaars (2010) have taken into account nonlinear motion and optimized selection of the search space, especially important given the large data sets that facilities such as the Large Synoptic Survey Telescope will produce. Orbital motion is an important consideration when planning coronagraphic surveys of the HZs of nearby stars. Brown (2005) treats the problem of completeness extensively. Large parts of the HZ will be within the inner working angle of the Terrestrial Planet Finder-Coronagraph (TPF-C) and so undetectable during a single observation. Also discussed in Brown (2005) is photometric completeness - that is how long the TPF-C must integrate on a given star to detect an earth-like planet in the HZ. Other work on this topic includes Brown & Soummer (2010) and Brown (2004). These analyses consider orbital motion only between observations, not during a single observation as we do here. In general, the scenarios considered for these studies involved space-based high-performance coronagraphs on medium to large telescopes. In such cases exposure times were short enough and continuous so that orbital motion should be negligible during a single observation. The work most similar to our analysis here is the detection of Sirius B at 10 µ m by Skemer & Close (2011), in fact, it was part of our motivation for the present study. Skemer & Close (2011) used the well known orbit of the white dwarf companion to Sirius to de-orbit 4 years worth of images. Before accounting for orbital motion, Sirius B appeared as only a low SNR streak, but after shifting based on its orbit it appears as a higher SNR point source from which photometry can be extracted. Similar to this method, we will analyze the prospects for de-orbiting sequences of images, only we consider the case with no prior information at all, and with orbital elements with significant uncertainties.",
"pages": [
4
]
},
{
"title": "3. Quantifying The Problem",
"content": "In this section we will quantify the effects of orbital motion on an attempt to detect an exoplanet. Our first step will be to determine how fast planets move when projected on the focal plane of a telescope. Then we'll illustrate the impact this motion will have on the SNR and the statistical sensitivity of an observation.",
"pages": [
4
]
},
{
"title": "3.1. Basic Equations",
"content": "We begin by considering a focal plane detector working at a wavelength λ in µ m. The FWHM of the PSF for a telescope of diameter D in m, neglecting the central obscuration, is If we are observing a planet in a face-on circular (FOC) orbit with a semi-major axis of a in AU at distance d in pc, its angular separation will be a/d arcsec. At the focal plane the projected separation will then be We note that it will occasionally be convenient to specify ρ in AU instead of FWHM. When it is not clear from the context we will use the notation ρ au to denote this. The orbital period is P = 365 . 25 √ a 3 /M ∗ days around a star of mass M ∗ in M /circledot . In one period, the planet will move a distance equal to the circumference of its orbit, 2 πρ , so the speed of the motion in a FOC orbit will be ∗ In the general case, the equations of motion in the focal plane are where Ω is the longitude of the ascending node, ω is the argument of pericenter, i is the inclination, and the true anomaly f depends on a , e , and the time of pericenter passage τ through Kepler's equation (Murray & Correia 2010). In Figure 1 we show the variation in projected orbital speed for both circular orbits at several inclinations, and face-on eccentric orbits ( i = 0), for a planet orbiting a 1 M /circledot star at 1 AU. In the plots we normalized speed to 1, and provide v FOC for several interesting cases. These various scenarios produce projected orbital speeds of appreciable fractions of a FWHM per day. We will later show that, especially for ground based imaging, this causes a significant degradation in our sensitivity. Our main focus here is on planets in the HZ. Our simple definition of the HZ results in a HZ ∝ √ L ∗ . Now, on the main sequence mass and luminosity approximately follow scaling laws of the form L ∗ ∝ M b ∗ , ) FOC Normalized Projected Speed (v 2.0 1.5 1.0 0.5 0.0 0 50 100 150 True Anomaly (degrees) 2.5 e=0.7 e=0.6 e=0.4 e=0.1 e=0 i=0 (face-on) for each curve (b) where b > 2 except for very massive stars. So according to Equation (4) we expect v FOC in the HZ to increase as M ∗ decreases, i.e. M stars will have faster HZ planets than G stars. For example, a planet in the HZ of α Cen B ( M ∗ = 0 . 9 M /circledot , L ∗ = 0 . 5 L /circledot ) will be moving roughly 20% faster than a planet in the HZ of α Cen A ( M ∗ = 1 . 1 M /circledot , L ∗ = 1 . 5 L /circledot ) (stellar parameters from Bruntt et al. (2010)). To provide a more concrete example we return to the 20 hour observation of Gl 581d by the EELT/EPICS proposed by Kasper et al. (2010). Using a wavelength of 0 . 75 µm with Equation (4) we find v FOC = 0 . 82 FWHM per day, or a total of 0.68 FWHM for a continuous 20 hour observation. Since this is a ground based observation the actual amount of motion to consider is ∼ 1 . 15 FWHM over the ∼ 1 . 4 days minimum it would take to integrate for 20 hours. Were this a face-on orbit, an eccentricity of 0.25 (Forveille et al. 2011) would increase the maximum orbital speed to as much as 1.05 FWHM per day, or 1.47 FWHM minimum for a 20 hour ground based observation.",
"pages": [
5,
6,
7
]
},
{
"title": "3.2. Impact on Signal-to-Noise Ratio",
"content": "So what does the orbital motion calculated above do to our observations? To find out we consider a simple model of aperture photometry. Let us assume that we are conducting aperture photometry with a fixed radius r ap , that the PSF is Gaussian, and that we are limited by Poisson noise from a photon flux N per unit area. With these assumptions, the optimum r ap is 0.7 FWHM, but taking into account centroiding uncertainty r ap ≈ 1 FWHM is typical. We will approximate orbital motion at speed v om by substituting x → x -v om t -x 0 . Orbits are of course not linear, but this will be approximately valid over short periods of time. The parameter x 0 allows us to optimize the placement of the aperture to obtain the maximum signal, i.e. centering the aperture in the planet's smeared out flux. Note that with the exception of this centering parameter, this model appears quite naive in that we are not adapting the aperture radius and are pretending that we won't notice a smeared out streak in our images. Now the SNR in the fixed-size aperture after time ∆ t will be where I 0 is the peak value of the PSF. In the case of no orbital motion v om = 0 and aperture r ap = 1 FWHM, so we have As a simple alternative to a fixed size aperture, we also consider allowing our photometric aperture to expand along with the motion of the planet. This aperture will collect the same signal as in SNR o , but the noise increases with the area as 2 r ap v om ∆ t , so we have A convenient scaling is to multiply top and bottom by √ v om and work in normalized SNR units of I o / √ Nv om . This puts time in terms of FWHM of motion, /epsilon1 = v om ∆ t , and allows comparisons without specifying v om . In Figure 2 we plot the normalized SNR vs. time (measured in terms of FWHM of motion) with and without orbital motion and for both the fixed and expanding aperture cases. For the fixed aperture, after ∼ 2 FWHM of orbital motion a maximum of 0.69 is reached, and from there noise is added faster than signal. This means that further integration only degrades the observation. The expanding aperture SNR exp exceeds the maximum of SNR fix after about 8 FWHM of motion, and So if we integrate 4 times longer, adjusting the aperture size would allow us to gather a little more SNR , but only to a point. Given this large increase in telescope time for a relatively small improvement in SNR (only ∼ 9% even if we integrate forever), and its better performance for smaller amounts of motion, the fixed-radius aperture will be our baseline for further analysis - keeping in mind that in some cases it may not be the true optimum. The peak in SNR fix (equation 6) sets the maximum nominal integration time before orbital motion will prevent us from achieving the science goal. That is ∆ t max = ( SNR max / 0 . 6) 2 . If the observation of a stationary planet would require an integration time longer than ∆ t max , then we can't achieve the desired SNR on an orbiting planet . This also sets the maximum orbital motion /epsilon1 max = v om ∆ t max . From Figure 2 we find that /epsilon1 max = 1 . 3 FWHM. If more than 1.3 FWHM of motion occurs during an observation, we will not achieve the required SNR . We also show the fractional reduction in SNR in Figure 2. Almost no degradation occurs until after ∼ 0 . 2 FWHM of motion has occurred. SNR is reduced by ∼ 1% after 0.5 FWHM of motion, ∼ 5% after 1.0 FWHM, and by ∼ 19% after 2.0 FWHM of motion. We must now decide how much SNR loss we can accept in our observation. The above analysis assumes a continuous integration. On a ground-based telescope one must consider that the maximum continuous integration time is /lessorsimilar 12 hours, and in practice will likely be much shorter when performing high contrast AO corrected imaging. For instance, an exposure of 20 hours might have to be broken up over 4 or 5 or more nights, when considering the vagaries of seeing (required AO performance), airmass (either through transmission or r 0 requirements), rotation rate (for ADI), and weather. We can adapt the calculations for a ground based integration as follows In this expression we have broken the observation up into M integration sets which start at times t j and have lengths ∆ t j . The total integration time is ∆ t int = j = M ∑ j =1 ∆ t j and the total elapsed time of the observation is ∆ t tot = t M +∆ t M -t 1 . We plot the results for a few ground-based scenarios in Figure 3. As one can see, observations of planets with orbital motion will be significantly degraded from the ground. This problem, which has been negligible in the high contrast planet searches to date, only becomes worse as we consider larger telescopes and improvements in AO technology which allow searches at shorter wavelengths. We next analyze how this reduction in SNR will affect our ability to detect exoplanets by increasing the rate at which spurious detections occur.",
"pages": [
7,
9,
11
]
},
{
"title": "3.3. Impact on Statistical Sensitivity",
"content": "Now we turn to the problem of detecting a planet of a given brightness. A planet is considered detected if its flux is above some threshold SNR t , which is chosen for statistical significance. The goal in choosing this threshold is to detect faint planets while minimizing the number of false alarms. For the purposes of this analysis we assume Gaussian statistics, in which case the false alarm probability ( P FA ) per trial is Typically, planet hunters use a threshold of SNR = 5, which gives P FA = 2 . 9 × 10 -7 . The number of false alarms per star, the false alarm rate ( FAR ), is then where N trials is the number of statistical trials per star. Following Marois et al. (2008a), for a stationary planet N trials is just the number of photometric apertures in the image. A typical Nyquist sampled detector of size 1024x1024 pixels has N trials ∼ 8 × 10 4 . Thus, an SNR = 5 threshold will result in FAR ∼ 0 . 02 about 1 false alarm for every 50 observations. In the speckle limited case with non-Gaussian statistics, FAR will be worse than this for the same SNR (Marois et al. 2008a). In any case, the FAR is the statistic which determines the efficiency of a search for exoplanets with direct imaging. A high FAR will cause us to waste telescope time following up spurious detections, while raising the SNR threshold to counter this limits the number of real planets we will detect. The reduction of SNR caused by orbital motion confronts us with three options. Option I is to maintain the detection threshold constant and accept the loss of sensitivity. Option II is to lower the detection threshold to maintain sensitivity, accepting the increase in FAR. Option III is to correct for orbital motion, which as we will show also causes an increase in FAR.",
"pages": [
11
]
},
{
"title": "3.3.1. Option I: Do Nothing",
"content": "The default option is to do nothing, keeping our detection threshold set as if orbital motion is not significant. The drawback to this is that we will detect fewer planets. To quantify this we use the concept of completeness, that is the fraction of planets of a given brightness we detect. For Gaussian statistics and detection threshold SNR t = 5, the search completeness is given by where /epsilon1 = v om ∆ t is the amount of motion. In Figure 4 (top) we show the impact of orbital motion on search completeness. Maintaining the detection threshold lowers completeness. How much depends on the completeness level, with brighter planets being less affected. For planets bright enough to yield 95% completeness with no motion, significant reduction in the number of detections begins after ∼ 1 FWHM of motion. For 99.7% completeness the impact becomes significant after ∼ 1 . 5 FWHM. Completeness 1.0 0.8 0.6 0.4 0.2 0.0 0 5 σ Option I - Lower Completeness 1 2 3 4 5 Orbital Motion ε (FWHM) 5.47 σ 6.65 σ 7.75 σ",
"pages": [
11,
12
]
},
{
"title": "3.3.2. Option II: Lower Threshold",
"content": "Once orbital motion is recognized to be significant, a simple countermeasure would be to lower the detection SNR threshold in order to maintain completeness. The drawback to this option is that we have more false alarms, which must then be followed up using more telescope time. This results in a less efficient search. In Figure 4 (bottom) we show P FA as a function of orbital motion, and denote the detection threshold we must use to maintain 50% completeness for a planet bright enough to give SNR = 5 were it stationary. Note that P FA begins to increase exponentially after ∼ 1 FWHM of motion. After ∼ 4 FWHM P FA begins approaching 0.5 asymptotically. Once /epsilon1 ≈ 2 FWHM the number of false alarms per 1024x1024 image approaches 1.",
"pages": [
13
]
},
{
"title": "3.3.3. Option III: De-orbit",
"content": "Option III is to correct for orbital motion, hoping to maintain sensitivity while limiting the increase in P FA . The essence of any such technique will be calculating the position of the planet during the observation, and de-orbiting in some way, say shift-and-add (SAA) on a sequence of images. The drawback of this approach is that it will produce more false alarms per observed star due to the increased number of trials, similar to lowering the detection threshold. If the orbit were precisely known, we could proceed with almost no impact on FAR . However, in the presence of uncertainties in orbital parameters or in a completely blind search we will have to consider many trial orbits. For now we can perform a 'back-of-the-envelope' estimate of the number of possible orbits to understand how much FAR will increase. To do so, we begin by placing bounds on the problem. We can first establish where on the detector we must consider orbital motion. At any separation r from the star, the slowest un-bound orbit will have the escape velocity. Since we know that physical separation is greater than or equal to projected separation, r ≥ ρ , and that maximum projected speed will occur for inclination i = 0, we know that sets the upper limit on the projected focal plane speed of an object in a bound orbit. We can also set an upper limit on the amount of motion /epsilon1 max we can tolerate over the duration ∆ t tot of the observation based on the SNR degradation it would cause. So we only need consider orbital motion when From here we determine the upper limit on projected separation from the star for considering this problem: By the same logic, for any point closer than ρ max the maximum possible change in position is Then we must evaluate possible orbits ending anywhere in an area of π (∆ ρ max ) 2 FWHM 2 around an initial position. These two limits set the statistical sensitivity of an attempt to de-orbit an observation. The number of different orbits, N orb , will be determined by the area of the detector where orbital motion is non-negligible, and the size of the region around each point that we consider. That is so In general N trials ∝ N orb , so FAR ∝ P FA × N orb . Larger D , shorter λ , closer d , and smaller acceptable orbital motion /epsilon1 will then all increase FAR † . Perhaps the most important feature of this result is that N orb ∝ ∆ t 4 tot -increasing integration time rapidly increases the FAR of a blind search . Note that this is still less severe than the exponential increase in P FA found for merely lowering the threshold. In the next section we will test these relationships after fully applying orbital mechanics, and see that they hold.",
"pages": [
13,
14
]
},
{
"title": "4. Blind Search: Recovering SNR after Orbital Motion",
"content": "In this section we consider in detail a blind search, i.e. an observation of a star for which we have no prior knowledge of exoplanet orbits. We showed above that the problem is well constrained. Here we derive several ways to further limit the number of trial orbits we must consider. After that, we describe an algorithm for determining the orbital elements that must be considered and then discuss the results. Finally, we use this algorithm to de-orbit a sequence of simulated images and analyze the impact of correlations between trial orbits on FAR . To provide numerical illustrations throughout this section we consider the problem of a 20 hour observation of α Cen A using the GMT at 10 µ m. This scenario is loosely based on performance predictions made for the proposed TIGER instrument, a mid-IR diffraction limited imager for the GMT (Hinz et al. 2012). The details of these predictions are not important for our purposes, so we will only assert that this is a plausible case. There are other examples in the literature with similar integration times, such as the EPICS prediction we discussed earlier. We assume that this 20 hr observation is broken up into five ∆ t = 4 hr exposures, spread over 7 nights or ∆ t tot = 6 . 2 elapsed days from start to finish. The choice of ∆ t is essentially arbitrary, but we have good reasons to expect it to be shorter than an entire night. An important consideration is the planned use of ADI, and the attendant need to obtain sufficient field rotation in a short enough time to provide good PSF calibration while avoiding self-subtraction (Marois et al. 2006). The effect of airmass on seeing through r 0 ∝ cos( z ) 3 / 5 , where z is the zenith angle, and hence on AO system performance, could also cause us to observe as near transit as possible. Efficiency will be affected by chopping and nodding, necessary for background subtraction at 10 µ m. This will limit the net exposure time obtainable in one night.. Few ground-based astronomers would object to an assertion that we loose 2 nights out of 7 to weather. We could be observing in queue mode, such that these observations are only attempted when seeing is at least some minimal value, or precipitable water vapor is low. One can even imagine the opposite case at 10 µ m, such that nights of the very best seeing are devoted to shorter wavelength programs. While this scenario may be somewhat contrived, we feel that it is both plausible and realistic. We now proceed to describe a technique that would mitigate the effects of orbital motion for our GMT example and should be applicable to other long exposure cases.",
"pages": [
14,
15
]
},
{
"title": "4.1. Limiting Trial Orbits",
"content": "Here we derive limits on the semi-major axis and eccentricity of trial orbits to consider. These limits are based only on the amount of orbital motion tolerable for the science case, and do not represent physical limits on possible orbits around the star. It is always true that r ≥ ρ . This implies that, for any orbit, the separation of apocenter must obey r a ≥ ρ . This allows us to set a lower bound on a , a min , given a choice of e through which gives The fastest speed in a bound planet's orbit will occur at pericenter, and using the maximum tolerable motion /epsilon1 max during our observation of total elapsed time ∆ t tot we can set an upper bound on a by noting that which leads to Using the GMT example: for e = 0 . 0, a max = 3 . 9 AU; and for e = 0 . 5, a max = 11 . 8 AU. Using Equation 16 we have a projected separation limit of ρ max = 7 . 7 AU, so it is possible for these definitions to produce a max < a min for certain choices of e at a given ρ . This condition tells us that at such a value of e no orbits can move fast enough to warrant consideration. Thus we can set a lower limit on e at projected separation ρ where we have simplified by pulling out In practice, we might consider eccentricity ranges with e max less than 1, thus improving our sensitivity. Inputs to our choice of e max could include some prior distribution of eccentricities, or dynamical stability considerations in binary star systems and systems with known outer companions.",
"pages": [
15
]
},
{
"title": "4.2. Choosing Orbital Elements",
"content": "Now we describe an algorithm for sampling the possible trial orbits over a set of M sequential images. For now, we assume no prior knowledge of orbital parameters. We will employ a simple grid search through the parameter space bounded as described above. /negationslash where Ω should be determined in the correct quadrant. or for ω + f = π calculate Ω: determining Ω in the correct quadrant. 11. Repeat the above steps until the parameters ω , τ , a , and e are sufficiently sampled for each starting point.",
"pages": [
15,
16,
17
]
},
{
"title": "4.3. De-orbiting: Unique Sequences of Whole-Pixel Shifts",
"content": "The algorithm just described will produce a large number of trial orbits, many of which will be very similar. The information content of our image is set by the resolution of the telescope, so we can take advantage of this similarity to greatly reduce the number of statistical trials. This is done by grouping similar orbits into sequences of whole-pixel shift sequences, where the pixels are at least as small as FWHM / 2. As we will see, we typically will want to oversample, to say FWHM / 3, to ensure adequate SNR recovery. We calculate the pixel-shift sequence for each orbit by determining which pixel the trial planet (or rather, the center of its PSF) lands on at each time step. Many orbits end up producing the same sequences of pixel-shifts, and we will keep only the unique ones for use in de-orbiting the observation. In Figure 5 we illustrate the outcome of the pixel-shift algorithm, showing two unique sequences and a few of the orbits that produced them. To test the above algorithm and the pixel-shift technique, we used our GMT α Cen A example and determined the trial orbits for various separations and ∆ t s. We set /epsilon1 max = 0 . 5 based on our earlier analysis of SNR . The results are summarized in Figure 6. The problem is generally well constrained in that we only have a finite search space for any initial point. The data used to construct Figure 6 are provided in Table 1. Comparing N orb to N shifts , note the large reduction in the number of trials ( ∼ 10 8 to ∼ 10 2 ) due to combining similar orbits.",
"pages": [
17
]
},
{
"title": "4.4. N orb Scalings",
"content": "In Figure 7 we plot the area of the detector which contains the possible trial orbits at ρ 1 = 1 . 0 AU vs. the total elapsed time ∆ t tot . We conclude from this plot that the area around a given starting point is proportional to ∆ t 2 tot . Also in Figure 7 we plot area vs separation from the star, and conclude that area is proportional to 1 /ρ 1 . Taken together these results give confidence that the N orb ∝ ∆ t 4 tot scaling derived earlier holds when we fully apply orbital mechanics rather than the escape velocity approximation. × Things are a bit more complicated when we consider the scaling of the number of while-pixel shift sequences. We conducted two sets of trials at ρ 1 = 1 . 0 AU. In the first, the number of observations and their relative spacing was held constant regardless of ∆ t tot . In the second set, the number of observations scaled with ∆ t tot . As shown in Figure 7, when the number of observations is constant, the number of shifts scales as ∆ t 2 tot , but when the number of observations grows with ∆ t tot the number of shifts scales as roughly ∆ t 3 . 6 tot . Figure 7d shows that the number of shifts scales as 1 /ρ 1 . Taken together, we see that for a constant number of observations the pixel-shift technique will follow the N orb ∝ ∆ t 4 tot scaling. However, if the number of observations also scales with ∆ t tot , then our results imply that N orb ∝ ∆ t 5 . 6 tot . The value of the exponent likely depends on the details of the observation sequence, but this has important implications for observation planning.",
"pages": [
17,
20,
21
]
},
{
"title": "4.5. Recovering SNR",
"content": "We next consider whether de-orbiting by whole-pixels adequately recovers SNR . To test this we 'orbited' a Gaussian PSF on face-on orbits with various eccentricities, starting from pericenter. We then calculated shifts for detector samplings of 2, 3, and 4 pixels/FWHM, and then de-orbited by these shifts. The results are summarized in Table 2. On a critically sampled detector we only recover a 5 σ planet to ∼ 4 . 9 σ , a 2% loss of SNR . At 3 pixels/FWHM we do much better, recovering SNR to 4.97 for low eccentricities, and 4.95 for higher eccentricities. Performance for 4 pixels/FHWM sampling is similar. A 2% loss of SNR nearly doubles P FA , so it appears that we should oversample to at least 3 pixels/FWHM, either optically or by re-sampling images during data reduction. In our analysis we have assumed that the limiting noise source is background photons (PSF halo or sky), so we ignore the increased readout noise expected from oversampling.",
"pages": [
21
]
},
{
"title": "4.6. Correlations And The True Impact On P FA",
"content": "As we have noted several times, the main impact of orbital motion is to reduce SNR , which in turn reduces our statistical sensitivity. If we attempt to de-orbit an observation in order to recover SNR , we do so at the cost of a large increase in the number of trials. Worst case, this results in a proportional increase in FAR since nominally FAR = P FA × N orb . However, we expect significant correlation between trials of neighboring orbits and whole-pixel shifts. To investigate this, we performed a series of monte carlo experiments. A sequence of images with Gaussian noise was generated, and first stacked without shifting, hereafter called the naive-add. The same sequence was then shifted by each possible whole-pixel shift, assuming a 1AU initial separation around α Cen A. This experiment was conducted for observations with total elapsed times ∆ t tot of 4.2, 6.2, 8.2, and 10.2 days, with samplings of 2, 3, and 4 pixels/FWHM. We performed several tests on each sequence. The first was a simple threshold test on the naive-add, with the threshold set for the worst case orbital motion given by Equation 10 with v om = v esc . We performed simple aperture photometry, with a r ap = 1 FHWM. As expected the resultant P FA 1 is as predicted by Equation 11. The next test was to apply a 5 σ threshold after de-orbiting by whole-pixel shifts and adding. If all shifts were completely uncorrelated, then we would expect FAR = (2 . 9 × 10 -7 ) × N shifts , but as we predicted, shifts are correlated and P FA 2 is lower than this. The final test performed was to apply both thresholds in sequence, such that a detection is made only if the naive-add results in SNR greater than the threshold for worst case orbital motion, and the de-orbited SAA results in SNR > 5. This P FA 3 is lower than either P FA 1 or P FA 2 , but still higher than if no orbital motion occurred. The results of each trial are present in Table 3. Applying both threshold tests results in significant improvement over the naive-add in terms of FAR . Another interesting result is that sampling has only a minor impact on P FA 3 . This makes some sense as we expect the correlation of neighboring shifts to be set by the FWHM, not the sampling. So even though the accuracy of SNR recovery is improved, and quite a few more shifts are required, these shifts remain correlated across the same spatial scale resulting in little change in the overall FAR .",
"pages": [
21,
23
]
},
{
"title": "4.7. Impact on Completeness of the Double Test",
"content": "There is still an impact on completeness, however, because we are now conducting two trials instead of one. This lowers the true positive probability ( P TP ). Consider a 5 σ planet on the worst case fastest possible orbit, for the 10.2 day elapsed time case. The threshold for the naive add is 2.625. We have a 50% probability of detecting this planet after the naive add. If it is detected on the first test, there is then some probability P TP < 1 of detecting at SNR ≥ 5 after de-orbiting. Worst case, this will be 50%, resulting in a net P TP of 25%. In reality, it will be better than this as the two trials will be strongly correlated. Even if this worst case of 25% were realized this is still significant improvement over Option I. A 2 . 6 σ signal would only be detected 10% of the time with a 5 σ threshold. Given the reduction in P FA from 4 . 3 × 10 -3 to 2 . 2 × 10 -5 , likewise an improvement over Option II at 2 . 6 σ , it is clear that de-orbiting by whole-pixel shifts does improve our ability to detect an orbiting planet . The situation will be even better for slower planets, and most of the area searched will not be subject to the worst case orbital speed. We leave a complete analysis of the impact on search completeness for future work. One can also imagine adjusting the thresholds to optimize completeness at the expense of worse P FA .",
"pages": [
23
]
},
{
"title": "4.8. Tractability of a Blind Search",
"content": "We end this section by concluding that a blind search when orbital motion is significant is tractable. Orbital motion will make such a search less sensitive, both in terms of number of false alarms and in terms of completeness, but Keplerian mechanics gives us enough tools to bound the problem. As we have shown deorbiting a sequence of observations can recover SNR to its nominal value, and we can do so while controlling the impact on statistical sensitivity. For the ∆ t tot = 6 . 2 day observation, P FA 3 was roughly a factor of 10 higher than if no orbital motion occurred. This increase only occurs over a bounded region around the star, so the net effect on FAR will be contained. Using this factor of 10 as the mean value over the 7.7 AU = 69.1 FWHM radius region around α Cen A where orbital motion is significant, the FAR in this area will have gone from ∼ 1 / 1000 to ∼ 1 / 100 in our GMT/10 µ m example. The key, though, appears to be to limit the elapsed time of the observation as the number of trials increases - decreasing sensitivity - proportionally to at least ∆ t 4 tot in a blind search. The main caveat at this point in our analysis is that we have drawn the conclusion of tractability using Gaussian statistics. It is well known that speckle noise, which will often be the limiting noise source for high contrast imaging in the HZ, is not Gaussian and results in much higher P FA for a given SNR (Marois et al. 2008a). Future work on this problem will need to take this into account. Next we consider a more strongly bounded scenario, where we have significant prior information about the orbit of the planet from radial velocity surveys.",
"pages": [
23,
25
]
},
{
"title": "5. Cued Search: Using RV Priors",
"content": "The situation is greatly improved if we have prior information, such as orbit parameters from RV or astrometry. Here we consider the case of Gliese 581d, and the previously discussed future observation of this planet by EPICS at the E-ELT (Kasper et al. 2010). There is some controversy surrounding the solution to the RV signal, and whether planet d even exists (Forveille et al. 2011; Vogt et al. 2012; Baluev 2012). We show results for both the floating eccentricity Keplerian fits of Forveille et al. (2011)[hereafter F11], and the all circular interacting model of Vogt et al. (2012)[hereafter V12]. Doing so allows us to illustrate the impact of eccentricity on the analysis, and prevents us having to take a stand in a currently raging debate. The parameters used herein are listed in Table 4. Instead of a grid search, we use a monte carlo (MC) method. The RV technique provides the parameters a , e , ω and t 0 or their equivalents. We can take the results of fitting orbits to the RV signal, and the associated uncertainties, as prior distributions which we sample to form trial orbits. We will assume that all uncertainties are uncorrelated and are from Gaussian distributions. We assume that the 20 hr integration is broken up over 6.2 nights based on the same logic discussed in Section 4. Kasper et al. (2010) actually assumed 20 × 1 hr observations based on the amount of rotation needed, but did not consider the effects of orbital motion over 20 days of a 67 day period (M. Kasper, personal communication (2012)). ± ± ± ±",
"pages": [
25
]
},
{
"title": "5.1. Constraints",
"content": "In order to minimize the number of trial orbits to consider, we can apply various constraints taking advantage of the information we have from the RV detection. In the case of a multi-planet system dynamical analysis can place constraints on the inclination based on system stability. For Gl 581, Mayor et al. (2009) found the system was stable for i > 30. We can also make use of the geometric prior for inclination, where we expect P i = sin( i ) in a population of randomly oriented systems. Since this is a reflected light observation, the orbital phase and its impact on the brightness of the planet must be considered. The planet's reflected flux is given by where F ∗ is the stellar flux, R p is the planet's radius, r its separation, A g ( λ ) is the wavelength dependent geometric albedo, and Φ is the phase function at phase angle α . The phase angle is given by In general, determining the quantity A g ( λ )Φ( α ) requires atmospheric modeling (Cahoy et al. 2010). For now, we assume that Φ follows the Lambert phase function We assume that the prediction of Kasper et al. (2010) was made for the planet at quadrature, α = π/ 2, where Φ = 0 . 318 . We then require that the mean value of Φ during the observation be greater than this value - that is the planet is as bright or brighter than it is at quadrature.",
"pages": [
26
]
},
{
"title": "5.2. Initial Detection",
"content": "An important consideration in an RV-cued observation will be when to begin. As a first approximation, we assume that maximizing planet-star separation will maximize our sensitivity. This may not be true when working in reflected light due to the phase and separation dependent brightness of the planet in this regime. Proceeding with the approximation for now, we expect to plan this observation to be as close to apocenter as possible. In this case we will begin integrating 3.1 days before t 0 + P/ 2. To understand the area where we will be searching for Gl 581d, we first conducted an MC experiment to calculate the possible positions of the planet at t = t 0 + P/ 2 -3 . 1 days. To do so, we drew random values of a , e , w , and t 0 from Gaussian distributions with the parameters of Table 4. We drew a random value of i from the sin( i ) distribution, and rejected any value of i ≤ 30 based on the dynamical prior. Finally Ω was drawn from a uniform distribution in 0 . . . 2 π . This process was repeated 10 9 times, and the frequency at which starting points occur in the area around the star was recorded. The results are shown in Figure 8 for the V12 circular model and for the F11 eccentric model. The Figure shows the area which must be searched to obtain various completeness. For instance, if we desire 95% completeness in the V12 model, we must consider an area of 71 apertures. Since this SNR = 5 detection is broken up into 5 distinct integrations, our first attempt will have SNR = 2 . 24, giving a FAR = 0 . 89 for the first 4 hr integration. In other words, we should expect a false alarm in addition to a real detection.",
"pages": [
26
]
},
{
"title": "5.3. Calculating Orbits and Shifts",
"content": "Now we assume that we have an initial detection at SNR ∼ 2 . 24 within the highest probability regions ‡ . In order to follow-up this detection over subsequent nights, we must determine the possible locations of the planet, constrained by the RV-derived orbital elements. We proceed by choosing a , e , ω , and t 0 from Gaussian distributions as above. Now as long as r > ρ we will have a unique solution for i and Ω given the randomly chosen parameters (see the blind search algorithm above). We take into account dynamical stability by rejecting any orbit which has i ≤ 30. The orbit determined in this fashion was then projected 6.2 days into the future and the frequency of these final points was recorded. We show the result for the V11 model in Figure 9, top panel. Using the RV determined parameters and their uncertainties allows us to determine the probability density of orbit endpoints, and determine how much of the search space we must consider for a given completeness. The whole-pixel shifts were also calculated using a sampling of FWHM/3, and are shown in the legend. We also applied the blind search algorithm to this observation from the same starting point, and show the results for comparison in the bottom panel of Figure 9. As expected the RV priors significantly reduce the search space - we have 942 trial shift-sequences to consider instead of 12000. Another important consideration here is that our initial 2 . 24 σ detection will have a large position uncertainty, which we estimate by σ ρ 0 = FWHM/SNR . We added a random draw for the starting position, and repeated the MC experiment for F11 and also conducted a run for the V12 parameters. The results are shown in Figure 10. The number of shift sequences is much higher due to the uncertainty in the starting position caused by our low SNR initial detection, but we expect correlations to come to the rescue as in our α Cen example. To compare to Figure 9 keep in mind that the blind search would have to be applied to all 5500 pixels in the search space indicated by Figure 8. As in the GMT/ α Cen example, we leave for future work a complete analysis of sensitivity and completeness. The large number of trial shifts calculated when we include uncertainty in the starting position motivates us to suggest that we will ultimately turn this analysis over to a much more robust optimization strategy, such as a Markov Chain Monte Carlo (MCMC) routine. Once an area of the image was identified with a high post-shift SNR , a MCMC analysis could determine the very best orbit and assign robust measures of significance to the result. We also note that these results likely overestimate the number of trial orbits since we have assumed uncorrelated errors. In reality the RV best fit parameters are likely strongly correlated, which should act to reduce the number of orbits to consider.",
"pages": [
28
]
},
{
"title": "6. Conclusions",
"content": "In the coming campaigns to directly image planets in the HZs of nearby stars, orbital motion will be large enough to degrade our sensitivity. This effect has been ignorable in direct imaging campaigns to date, which have typically looked for wide separation planets. We have analyzed this issue in some detail, and shown that applying basic Keplerian orbital mechanics allows us to bound the problem sufficiently that we believe direct imaging in the HZ to be a tractable problem. Our main conclusions are: In the HZ of nearby stars, especially when considering giant telescopes, speeds are high enough that planets will move significant fractions of a PSF FWHM during a single observation. This smears out the planet's flux resulting in a lower SNR . We thank the anonymous referee for insightful and constructive comments. We thank Jessica Orwig for reviewing this manuscript. JRM is grateful for the generous support of the Phoenix ARCS foundation. LMC and JRM acknowledge support from the NSF AAG.",
"pages": [
28,
31
]
},
{
"title": "REFERENCES",
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"pages": [
31,
32,
33
]
}
]
2013ApJ...773...99R
https://arxiv.org/pdf/1303.1554.pdf
<document>
<section_header_level_1><location><page_1><loc_29><loc_86><loc_72><loc_87></location>HOT ELECTROMAGNETIC OUTFLOWS II: JET BREAKOUT</section_header_level_1>
<section_header_level_1><location><page_1><loc_44><loc_84><loc_56><loc_85></location>MATTHEW RUSSO</section_header_level_1>
<text><location><page_1><loc_25><loc_83><loc_76><loc_84></location>Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada.</text>
<section_header_level_1><location><page_1><loc_42><loc_80><loc_58><loc_81></location>CHRISTOPHER THOMPSON</section_header_level_1>
<text><location><page_1><loc_25><loc_77><loc_76><loc_79></location>Canadian Institute for Theoretical Astrophysics, 60 St. George St., Toronto, ON M5S 3H8, Canada. Submitted to The Astrophysical Journal</text>
<section_header_level_1><location><page_1><loc_46><loc_74><loc_54><loc_76></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_54><loc_86><loc_74></location>We consider the interaction between radiation, matter and a magnetic field in a compact, relativistic jet. The entrained matter accelerates outward as the jet breaks out of a star or other confining medium. In some circumstances, such as gamma-ray bursts (GRBs), the magnetization of the jet is greatly reduced by an advected radiation field while the jet is optically thick to scattering. Where magnetic flux surfaces diverge rapidly, a strong outward Lorentz force develops and radiation and matter begin to decouple. The increase in magnetization is coupled to a rapid growth in Lorentz factor. We take two approaches to this problem. The first examines the flow outside the fast magnetosonic critical surface, and calculates the flow speed and the angular distribution of the radiation field over a range of scattering depths. The second considers the flow structure on both sides of the critical surface in the optically thin regime, using a relaxation method. In both approaches, we find how the terminal Lorentz factor, and radial profile of the outflow, depend on the radiation intensity and optical depth at breakout. The effect of bulk Compton scattering on the radiation spectrum is calculated by a Monte Carlo method, while neglecting the effects of internal dissipation. The peak of the scattered spectrum sits near the seed peak if radiation pressure dominates the acceleration, but is pushed to a higher frequency if the Lorentz force dominates, and especially if the seed photon cone is broadened by interaction with a slower component of the outflow.</text>
<text><location><page_1><loc_14><loc_53><loc_74><loc_54></location>Subject headings: MHD-plasmas - radiative transfer - scattering - gamma rays: stars</text>
<section_header_level_1><location><page_1><loc_44><loc_49><loc_56><loc_50></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_41><loc_92><loc_48></location>Gamma-ray bursts involve collimated, relativistic outflows, as deduced from their rapid variability, extreme apparent energies (which can exceed the binding energy of a neutron star: Kulkarni et al. 1999; Amati et al. 2002), and the expected presence of non-relativistic material surrounding the engine. The jet is heated as it works through this denser material, which may represent a stellar envelope (Woosley 1993; Paczynski 1998), or neutron-rich debris from a binary neutron star merger (e.g. Dessart et al. 2009). As a result, a nearly blackbody radiation field may carry a significant fraction of the energy flux near the point of breakout.</text>
<text><location><page_1><loc_8><loc_27><loc_92><loc_41></location>We focus here on strongly magnetized jets that are driven outward by a combination of the Lorentz force, and the force of radiation scattering off ionized matter. The acceleration of such a 'hot electromagnetic outflow' (Thompson 1994; Meszaros & Rees 1997; Drenkhahn & Spruit 2002; Thompson 2006; Giannios & Spruit 2007; Zhang & Yan 2011), in which radiation pressure dominates matter pressure, has been treated quantitatively in Russo & Thompson (2012) (Paper I) in the approximation that the poloidal magnetic field lines threading the outflow are radial and monopolar. The radiation field is self-collimating outside the scattering photosphere, but may continue to interact with slower material that it entrained by the jet. In Paper I, the outflow was followed both inside and outside the fast magnetosonic critical point. The radiation force is especially important outside the fast point: even where the kinetic energy flux of the entrained charged particles is small compared with the magnetic Poynting flux, they provide an efficient couple between magnetic field and radiation. The relative influence of the two stresses on the asymptotic Lorentz factor depends on the radiation compactness. Generally, the importance of radiation pressure is enhanced by bulk relativistic motion at the photosphere.</text>
<text><location><page_1><loc_8><loc_19><loc_92><loc_27></location>In this paper we generalize the calculation of Paper I to include non-spherical effects. A magnetized outflow experiences a strong Lorentz force where poloidal flux surfaces in the jet diverge from each other faster than in a monopolar geometry (Camenzind 1987; Li et al. 1992b; Begelman & Li 1994; Vlahakis & Königl 2003a,b; Beskin & Nokhrina 2006; Tchekhovskoy et al. 2009). In particular, a magnetized jet accelerates rapidly when it breaks out of the confining material (Tchekhovskoy et al. 2010). The simulations in that paper demonstrated the effect for a cold magnetohydrodynamic (MHD) outflow, but did not include the effects of radiation pressure and drag.</text>
<text><location><page_1><loc_8><loc_12><loc_92><loc_19></location>The magnetization of a hot electromagnetic outflow remains modest inside its scattering photosphere, where the radiation is tied to the matter, and the radiation enthalpy contributes to the inertia. Our first task in this paper is, therefore, to examine how the radiation field begins to decouple from the matter when the jet material breaks out. We define a bulk frame in which the radiation force vanishes, by taking angular moments of the radiation field, and then track the proportions of the energy flux carried by matter, radiation, and magnetic field, at both large and small optical depths.</text>
<text><location><page_1><loc_8><loc_8><loc_92><loc_12></location>Given the flow profile so obtained, the radiation spectrum is calculated by a Monte Carlo method. Here we focus on the effects of bulk Compton scattering, which provide a direct probe of the outflow dynamics. We neglect the effects of internal dissipation by various process such as MHD wave damping, magnetic reconnection, or shocks.</text>
<text><location><page_1><loc_10><loc_7><loc_92><loc_8></location>The second principal goal of this paper is to obtain the longitudinal motion along a magnetic flux surface, taking into account</text>
<text><location><page_2><loc_8><loc_85><loc_92><loc_92></location>both the radiation force and the singularity in the flow equations which appears at the fast point. Our focus here is on the zone near and outside the transparency surface; previous efforts to calculate the effect of pressure gradient forces on relativistic outflows (e.g. Vlahakis & Königl 2003b) have focused on the optically thin regime. We argued in Paper I that the effect of a magnetic pressure gradient driven by internal reconnection (Drenkhahn & Spruit 2002) has been overestimated, because it neglects the addition to the outflow inertia from particle heating and a strong non-radial magnetic field.</text>
<text><location><page_2><loc_8><loc_77><loc_92><loc_85></location>Coupled wind equations for the matter Lorentz factor and angular momentum are derived in an arbitrary poloidal field geometry, restricted to the case of small angles near the rotational axis, but allowing for arbitrary relative flaring of the flux surfaces. The fast point generally sits close to the breakout surface of the jet. Our main simplification of the problem is to impose a particular shape for the poloidal flux surfaces, and not to solve self-consistently for the cross-field force balance. Two constraints are applied to the imposed magnetic field profile: that the rate of flaring is causal, and that the transverse component of the radiation force is at most a perturbation to the transverse Lorentz force.</text>
<text><location><page_2><loc_8><loc_64><loc_92><loc_77></location>The plan of this paper is as follows. Section 2 reviews the acceleration of a relativistic MHD outflow driven by the differential flaring of magnetic flux surfaces, and considers the radiation transfer equation in the limit of small angles. Equations are derived for the acceleration of a steady MHD outflow outside its fast point, in combination with the radial evolution of the magnetization, radiation energy flux, scattering depth, and the frame in which the radiation force vanishes. These equations are solved in particular cases relevant to GRB jets. Section 3 presents a simple model of a spreading thin jet outside its photosphere, and derives the corresponding steady flow equations for arbitrary radiation force and magnetization. The effect of radiation pressure on the fast point is considered analytically, and numerical solutions for the flow both inside and outside the fast point are presented. Section 4 describes Monte Carlo calculations of the emerging radiation spectrum in both the causal jet model of Section 2, and the optically thin model of Section 3. Section 5 summarizes our results. The Appendix presents a derivation of the radiation force in a thin, transparent jet.</text>
<section_header_level_1><location><page_2><loc_24><loc_62><loc_77><loc_63></location>2. FLARING, HOT MAGNETIZED JET: TRANSITION TO LOW OPTICAL DEPTH (MODEL I).</section_header_level_1>
<text><location><page_2><loc_8><loc_57><loc_92><loc_61></location>We consider a stationary, axisymmetric outflow of perfectly conducting material that is tied to a very strong magnetic field. The outflow is also a strong source of radiation, which scatters off the advected light particles (electrons as well as positrons). Matter pressure gradients are neglected in comparison with inertial and Lorentz forces as well as the radiation force.</text>
<text><location><page_2><loc_8><loc_54><loc_92><loc_57></location>We start by considering the exchange of energy between different components of the outflow. Deviations from radial motion are assumed to be small compared with the angular width of the photon beam: that is, the interaction between matter and radiation</text>
<figure>
<location><page_2><loc_19><loc_22><loc_81><loc_44></location>
<caption>FIG. 1.- Geometry and approximate scale of the flow solutions for jet model I.</caption>
</figure>
<text><location><page_2><loc_8><loc_7><loc_92><loc_12></location>is calculated assuming radial matter motion, but allowance is made for strong radial Lorentz forces driven by a small amount of magnetic field line flaring. The beam angular width is set, more or less, by the Lorentz factor of the outflow at its transparency surface. Here allowance is made for a finite optical depth of the magnetofluid. By taking angular moments of the radiation field, we track the difference between the Lorentz factor of the matter, and of the frame in which the radiation force vanishes, as the</text>
<text><location><page_3><loc_8><loc_88><loc_92><loc_92></location>matter is accelerated by a strong Lorentz force. This approach is suited to a single-component magnetofluid, but also allows for the presence of a second, slower component that scatters the radiation field into a broader cone, and plausibly is present in GRBs (Paper I).</text>
<text><location><page_3><loc_8><loc_73><loc_92><loc_88></location>Given the complications introduced by a finite optical depth, we now consider only supermagnetosonic outflows. In a second approach (Section 3), we account for non-radial matter motion and follow the flow across the fast critical surface, but restrict the calculation to low optical depth. The geometry of the model is shown in Figure 6. After being launched by the central engine (with angular frequency Ω ) the flow enters the jet zone along the rotation axis. We ignore the details of the acceleration while the jet is still very optically thick, and laterally confined. Our calculation begins a short distance inside breakout (at radius r ∗ ), by which point the flow is assumed to be supermagnetosonic. Outside breakout, transverse pressure support effectively vanishes and field lines begin to diverge differentially. The outward Lorentz force increases dramatically over a narrow range of radius, until a loss of causal contact across the jet forces the flow lines to straighten out, and the acceleration is cut off. Although the scattering photosphere could, in principal, sit anywhere in the outflow, breakout is associated with a large drop in optical depth. In our calculations, the photosphere therefore usually sits just outside breakout. Low optical depth at breakout does produce an interesting imprint of bulk Compton scattering on the emergent spectrum (Section 4).</text>
<section_header_level_1><location><page_3><loc_30><loc_71><loc_70><loc_72></location>2.1. Exchange of Energy between Radiation and Magnetofluid</section_header_level_1>
<text><location><page_3><loc_8><loc_65><loc_92><loc_70></location>We consider the flow along a poloidal magnetic field line θ f ( r ), starting at a large enough radius that the streamline sits well outside the light cylinder of the central engine. Deviations from radial motion are neglected, except in so far that they influence the radial Lorentz force. Then the outflow has a fixed total luminosity per sterad, including contributions from matter, magnetic field, and radiation,</text>
<formula><location><page_3><loc_40><loc_62><loc_92><loc_65></location>dL d Ω = dLk d Ω + dLP d Ω + dL γ d Ω = const . (1)</formula>
<text><location><page_3><loc_8><loc_60><loc_11><loc_61></location>Here</text>
<formula><location><page_3><loc_40><loc_57><loc_92><loc_60></location>1 r 2 dLk d Ω = Γ c 2 · Γ ρ vp = Γ c 2 r 2 d ˙ M d Ω (2)</formula>
<text><location><page_3><loc_8><loc_54><loc_92><loc_56></location>is the kinetic energy flux of material of proper density ρ , poloidal (radial) speed vp , and Lorentz factor Γ . The poloidal Poynting flux is expressed in terms of the electric and magnetic vectors E , B by</text>
<formula><location><page_3><loc_43><loc_50><loc_92><loc_53></location>1 r 2 dLP d Ω = ˆ Bp · E × B 4 π c . (3)</formula>
<text><location><page_3><loc_8><loc_45><loc_92><loc_49></location>Substituting E = -v × B / c into the induction equation gives ∂ B /∂ t = ∇ × ( v × B ), where v is the fluid velocity. The steady solution to this equation involves the pattern angular velocity Ω f of the magnetic field, which is constant along a poloidal flux surface. It relates the toroidal components of B and v via</text>
<formula><location><page_3><loc_42><loc_41><loc_92><loc_45></location>B φ = v φ -Ω f r sin θ f vp Bp . (4)</formula>
<text><location><page_3><loc_8><loc_39><loc_28><loc_40></location>Substituting this into (3) gives</text>
<formula><location><page_3><loc_41><loc_36><loc_92><loc_39></location>1 r 2 dLP d Ω = -Ω f r sin θ f BpB φ 4 π . (5)</formula>
<text><location><page_3><loc_8><loc_33><loc_92><loc_35></location>Far outside the light cylinder, the outflow rotates slowly and the magnetic field is predominantly toroidal: v φ /lessmuch vp /similarequal c and | B φ | /greatermuch | Bp | . Hence</text>
<formula><location><page_3><loc_41><loc_29><loc_92><loc_32></location>1 r 2 dLP d Ω /similarequal ( Ω f r sin θ f ) 2 B 2 p 4 π c . (6)</formula>
<text><location><page_3><loc_8><loc_26><loc_92><loc_29></location>It is useful to normalize all components of the energy flux to the poloidal mass flux, which is conserved along a poloidal flux surface in a steady MHD wind, d ˙ M / d Φ p = Γ ρ vp / Bp = const. Assuming further that Γ /greatermuch 1, the magnetization becomes</text>
<formula><location><page_3><loc_36><loc_20><loc_92><loc_26></location>σ = dLP / d Ω ( d ˙ M / d Ω ) c 2 /similarequal ( Ω f r sin θ f ) 2 Bp 4 π c 3 Bp Γ ρ vp ∣ ∣ ∣ ∗ , (7)</formula>
<text><location><page_3><loc_8><loc_17><loc_92><loc_23></location>∣ The radius r ∗ and the label ∗ denote a position in the jet where the confining medium changes rapidly, e.g. the jet moves beyond the photosphere of a Wolf-Rayet star. (We will distinguish this from an inner boundary ri for the jet integration, which typically is set just interior to the breakout radius.) Taking r ∗ /greatermuch c / Ω f ,</text>
<text><location><page_3><loc_44><loc_14><loc_45><loc_16></location>σ</text>
<text><location><page_3><loc_44><loc_13><loc_45><loc_13></location>∗</text>
<text><location><page_3><loc_43><loc_13><loc_44><loc_14></location>σ</text>
<text><location><page_3><loc_47><loc_14><loc_48><loc_16></location>(</text>
<text><location><page_3><loc_48><loc_14><loc_48><loc_16></location>r</text>
<text><location><page_3><loc_49><loc_14><loc_51><loc_16></location>sin</text>
<text><location><page_3><loc_51><loc_14><loc_51><loc_16></location>θ</text>
<text><location><page_3><loc_47><loc_13><loc_48><loc_14></location>(</text>
<text><location><page_3><loc_48><loc_13><loc_48><loc_14></location>r</text>
<text><location><page_3><loc_49><loc_13><loc_50><loc_14></location>sin</text>
<text><location><page_3><loc_51><loc_13><loc_51><loc_14></location>θ</text>
<text><location><page_3><loc_52><loc_14><loc_52><loc_15></location>f</text>
<text><location><page_3><loc_52><loc_13><loc_52><loc_13></location>f</text>
<text><location><page_3><loc_52><loc_14><loc_53><loc_16></location>)</text>
<text><location><page_3><loc_52><loc_13><loc_53><loc_14></location>)</text>
<text><location><page_3><loc_53><loc_15><loc_53><loc_16></location>2</text>
<text><location><page_3><loc_53><loc_13><loc_53><loc_14></location>2</text>
<text><location><page_3><loc_53><loc_13><loc_53><loc_13></location>∗</text>
<text><location><page_3><loc_54><loc_14><loc_56><loc_16></location>Bp</text>
<text><location><page_3><loc_55><loc_13><loc_56><loc_13></location>∗</text>
<text><location><page_3><loc_54><loc_13><loc_55><loc_14></location>Bp</text>
<text><location><page_3><loc_8><loc_9><loc_92><loc_12></location>(Note that our definition of σ differs by a factor Γ from the one used by Tchekhovskoy et al. 2009 in a similar derivation.) Defining the normalized photon luminosity by</text>
<formula><location><page_3><loc_44><loc_6><loc_92><loc_9></location>R = dL γ / d Ω ( d ˙ M / d Ω ) c 2 , (9)</formula>
<text><location><page_3><loc_46><loc_14><loc_47><loc_15></location>=</text>
<text><location><page_3><loc_56><loc_14><loc_57><loc_15></location>.</text>
<text><location><page_3><loc_90><loc_14><loc_92><loc_15></location>(8)</text>
<text><location><page_4><loc_8><loc_91><loc_43><loc_92></location>the equation of energy conservation (1) can be written</text>
<formula><location><page_4><loc_41><loc_88><loc_92><loc_90></location>Γ -Γ ∗ = -( σ -σ ∗ + R -R ∗ ) . (10)</formula>
<text><location><page_4><loc_8><loc_86><loc_80><loc_87></location>Note that R is related to the photon compactness and the scattering depth measured outward from radius r by</text>
<formula><location><page_4><loc_39><loc_82><loc_92><loc_85></location>χ ≡ σ T r ¯ mc 3 dL γ d Ω ∼ (2 -6) Γ 2 τ es R , (11)</formula>
<text><location><page_4><loc_8><loc_79><loc_92><loc_82></location>where σ T is the Thomson cross section and ¯ m is the material inertia per scattering charge. The coefficient here depends on the acceleration of the outflow, as can be seen from the expression for the optical depth of a (radially moving) photon</text>
<formula><location><page_4><loc_31><loc_74><loc_92><loc_79></location>τ es( r ) = α es( r ) ∫ ∞ r [ 1 -β ( r ' ) ] r 2 dr ' β ( r ' ) r ' 2 ; β ( r ) ≡ v c /similarequal vr c (12)</formula>
<text><location><page_4><loc_8><loc_72><loc_92><loc_74></location>[see equation (26) for notation]. The coefficient is ∼ 2 when the Lorentz factor is constant and reaches ∼ 6 for a linear growth, Γ ∝ r .</text>
<figure>
<location><page_4><loc_30><loc_39><loc_70><loc_69></location>
<caption>FIG. 2.- Radiation compactness at breakout for different ratios of Poynting to radiation flux: 1 (red), 100 (blue). Rescaled scattering optical depth τ es ∗ Γ 2 ∗ = 10 , 10 2 , 10 3 is plotted as solid, long-dashed and short-dashed respectively. The compactness drops below these curves beyond the breakout point. Strong radiative driving increases the Lorentz factor above the photospheric value Γ ( r τ ) if χ ∗ /greaterorsimilar Γ ( r τ ) 3 .</caption>
</figure>
<section_header_level_1><location><page_4><loc_20><loc_29><loc_80><loc_30></location>2.2. Importance of Radiative Driving in Outflows with a Relativistically Moving Photosphere</section_header_level_1>
<text><location><page_4><loc_8><loc_19><loc_92><loc_28></location>Jets of a high magnetization can encounter a scattering photosphere not too far outside breakout from a confining medium such as a Wolf-Rayet envelope or or neutron-rich debris cloud. Let us take a fiducial luminosity 4 π dL γ / d Ω = 10 51 L 51 erg s -1 and a deconfinement radius r ∗ = 10 10 r ∗ , 10 cm. The corresponding compactness (11) is χ ∗ = 1 × 10 8 L 51 r -1 ∗ , 10 ( mp / ¯ m ). Since the Lorentz factor increases rapidly after breakout due to MHD stresses, we fix r and then consider the condition for a photosphere to emerge at a radius r τ /greaterorsimilar r ∗ . This corresponds to Γ 2 ( r τ ) R ( r τ ) ∼ 10 7 ( mp / ¯ m ). For example, if the jet is hot and strongly magnetized, R∼ σ ∼ 10 5 , and pairs have largely annihilated within the bulk of the jet material, then the photosphere emerges at Γ ( r τ ) ∼ 10. The radiation field is capable of driving a light baryonic outflow to a terminal Lorentz factor (see Section 2 of Paper I),</text>
<formula><location><page_4><loc_43><loc_16><loc_92><loc_18></location>Γ ∞ ∼ [ Γ ( r τ ) χ ( r τ )] 1 / 4 . (13)</formula>
<text><location><page_4><loc_8><loc_13><loc_92><loc_15></location>Moderately relativistic motion at the photosphere enhances Γ ∞ and, as we now motivate, a larger radiation compactness. When the Lorentz force is taken into account self-consistently, Γ ∞ can be greater or smaller than (13), as we detail in this paper.</text>
<text><location><page_4><loc_8><loc_10><loc_92><loc_12></location>An upper limit on the photon compactness is derived by demanding that the fluid be optically thin at breakout, τ es( r ∗ ) ≤ 1. Then the photosphere sits at r τ < r ∗ , and the compactness (11) at breakout is</text>
<formula><location><page_4><loc_37><loc_6><loc_92><loc_9></location>χ ∗ = r τ r ∗ χ ( r τ ) /similarequal 6 r τ r ∗ Γ 2 ( r τ ) dL γ ∗ / d Ω ( d ˙ M / d Ω ) c 2 . (14)</formula>
<text><location><page_5><loc_8><loc_90><loc_75><loc_92></location>Hence Γ ∞ ∝ Γ ( r τ ) 3 / 4 in a jet of a fixed R . The radiation flux at breakout is below the Poynting flux if</text>
<formula><location><page_5><loc_44><loc_87><loc_92><loc_90></location>χ ∗ /lessorsimilar 6 r τ r ∗ Γ 2 ( r τ ) σ ∗ . (15)</formula>
<text><location><page_5><loc_8><loc_84><loc_92><loc_86></location>In Figure 2 we relate the compactness, magnetization and optical depth at breakout for different ratios of Poynting to radiation flux.</text>
<text><location><page_5><loc_8><loc_80><loc_92><loc_84></location>The aforementioned hot jet moving at Γ ( r τ ) ∼ 10 at its photosphere, with a magnetization σ ∼ R ∼ 10 5 , can be pushed by radiation pressure up to a terminal Lorentz factor Γ ∞ ∼ (1 × 10 9 ) 0 . 25 ∼ 200. More relativistic material accelerated by the Lorentz force will, alternatively, feel a retarding force from the radiation field.</text>
<section_header_level_1><location><page_5><loc_34><loc_77><loc_66><loc_78></location>2.3. Cold MHD Flow without Radiation Pressure</section_header_level_1>
<text><location><page_5><loc_8><loc_71><loc_92><loc_77></location>To begin, we review the case where photons are absent, and assume a thin jet in which the magnetic field lines have poloidal angle θ f /lessmuch 1. Only a small differential bending of the field lines is needed to push a cold magnetofluid to large Γ : their polar angle must deviate from conical geometry by δθ f /θ f ∼ Γ /σ . A basic constraint on the rate of bending is obtained if the transverse component of the Lorentz force in the matter rest frame is limited to</text>
<text><location><page_5><loc_8><loc_65><loc_75><loc_66></location>The prime ' denotes the rest frame, in which r / Γ is a characteristic causal distance, and β ≡ v / c . Then</text>
<formula><location><page_5><loc_38><loc_64><loc_92><loc_71></location>1 c ∣ ∣ ∣ ∣ J ' × B ' -β · ( J ' × B ' ) β β 2 ∣ ∣ ∣ ∣ /lessorsimilar B ' 2 φ 4 π r / Γ . (16)</formula>
<formula><location><page_5><loc_45><loc_61><loc_92><loc_64></location>r d ( δθ f ) dr /lessorsimilar 1 Γ , (17)</formula>
<text><location><page_5><loc_8><loc_58><loc_92><loc_61></location>so that typically δθ f ∼ 1 / Γ . This is seen in the dynamic cold MHD calculations of Tchekhovskoy et al. (2009), where strong Lorentz forces are generated in a narrow fan near the jet edge.</text>
<text><location><page_5><loc_8><loc_55><loc_92><loc_58></location>Conservation of magnetic flux implies that Bpr 2 θ f d θ f = const. Hence, writing θ f = θ f ( r ∗ ) + δθ f ≡ θ f ∗ + δθ f , equation (8) becomes</text>
<formula><location><page_5><loc_42><loc_52><loc_92><loc_56></location>σ = σ ∗ [ 1 -d ( δθ f /θ f ∗ ) d ln θ f ∗ ] . (18)</formula>
<text><location><page_5><loc_8><loc_50><loc_55><loc_52></location>The change in the ratio of Poynting and mass fluxes can then be written</text>
<formula><location><page_5><loc_40><loc_46><loc_92><loc_50></location>1 σ ∗ d σ dr = -θ f ∗ d d θ f ∗ ( K Γ θ f ∗ r ) . (19)</formula>
<text><location><page_5><loc_8><loc_44><loc_86><loc_46></location>The envelope function K ( θ f ) ∼ 1 away from the jet axis, and vanishes on the axis given the assumption of axisymmetry.</text>
<section_header_level_1><location><page_5><loc_43><loc_42><loc_57><loc_43></location>2.4. Radiation Force</section_header_level_1>
<text><location><page_5><loc_8><loc_39><loc_92><loc_41></location>Given the relativistic motion of the matter, the radiation field can be assumed to interact with it via Thomson scattering. In a frame where the matter moves with velocity β c , and a photon has wave vector k = k ˆ k , a scattering charge feels a force</text>
<formula><location><page_5><loc_34><loc_34><loc_92><loc_39></location>F rad = σ T I c ∫ ( 1 -β · ˆ k )[ ˆ k -β Γ 2 ( 1 -β · ˆ k )] d Ω . (20)</formula>
<formula><location><page_5><loc_35><loc_27><loc_92><loc_31></location>Fn ≡ 2 π ∫ d µ (1 -µ ) n I ( µ ) ≡ 2 π ∫ ( ∆ µ ) n I ( ∆ µ ) , (21)</formula>
<text><location><page_5><loc_8><loc_30><loc_84><loc_35></location>Here I ( µ ) = ∫ d ν I ν is the spectral intensity integrated over frequency, and µ is the direction cosine µ = cos( θ ) = ˆ k · ˆ r . It is useful to define angular moments of I ,</text>
<text><location><page_5><loc_8><loc_23><loc_92><loc_27></location>so that for a narrow beam, ∆ µ /similarequal 1 2 θ 2 /lessmuch 1, the radiation energy flux is approximately equal to F 0 = R Γ ρ c 3 . We may define a frame moving at Lorentz factor Γ eq (speed β eq) in which the radiation field is nearly isotropic and the radiation force vanishes. Defining the bulk frame radiation energy density by u ' , one has</text>
<formula><location><page_5><loc_36><loc_18><loc_92><loc_22></location>I ( ∆ µ ) /similarequal cu ' / 4 π [ Γ eq(1 -β eq µ )] 4 = I (0) (1 + 2 Γ 2 eq ∆ µ ) 4 . (22)</formula>
<text><location><page_5><loc_8><loc_16><loc_38><loc_18></location>Substituting this into (21) yields the relations</text>
<formula><location><page_5><loc_40><loc_13><loc_92><loc_16></location>F 1 = 1 4 Γ 2 eq F 0; F 2 = 1 Γ 2 eq F 1 . (23)</formula>
<text><location><page_5><loc_8><loc_10><loc_39><loc_12></location>Expanding the radiation force (20) in ∆ µ gives</text>
<formula><location><page_5><loc_34><loc_5><loc_92><loc_10></location>F rad r = σ T 4 Γ 2 c [ F 0 -4 Γ 4 F 2 ] = σ T F 0 4 Γ 2 c [ 1 -( Γ Γ eq ) 4 ] . (24)</formula>
<text><location><page_6><loc_8><loc_86><loc_92><loc_92></location>The main approximation here is that each field line experiences a small differential bending, so that the bending angle is small compared with (2 ∆ µ ) 1 / 2 . This is consistent with rapid acceleration by the Lorentz force near the jet edge (Tchekhovskoy et al. 2010), e.g. δθ f ∼ θ j -θ f /lessmuch θ f . In the context of GRBs, we can also assume that the flow has propagated far outside the light cylinder, so that β φ /lessmuch 1 and the toroidal radiation force can be neglected.</text>
<section_header_level_1><location><page_6><loc_26><loc_84><loc_74><loc_85></location>2.5. Transfer of a Narrow Photon Beam Near a Relativistic Photosphere</section_header_level_1>
<text><location><page_6><loc_8><loc_81><loc_92><loc_83></location>We work with the transfer equation in the inertial frame into which the outflow is expanding; a prime denotes the matter rest frame. The radiation transfer equation is written (e.g. Mihalas 1978)</text>
<formula><location><page_6><loc_44><loc_77><loc_92><loc_80></location>dI ν ds = α es( S ν -I ν ) , (25)</formula>
<text><location><page_6><loc_8><loc_75><loc_12><loc_76></location>where</text>
<text><location><page_6><loc_8><loc_70><loc_30><loc_71></location>is the grey scattering opacity, and</text>
<formula><location><page_6><loc_25><loc_64><loc_92><loc_70></location>S ν = 1 [ Γ (1 -βµ )] 3 S ' ν = 1 2[ Γ (1 -βµ )] 3 ∫ d µ ' I ' ν = 1 2 Γ (1 -βµ )] 3 ∫ d ˜ µ (1 -β ˜ µ ) I ˜ ν (27)</formula>
<text><location><page_6><loc_8><loc_59><loc_92><loc_66></location>is the source function in the isotropic scattering approximation. The Doppler relation between unscattered and scattered photon frequencies is ˜ ν (1 -β ˜ µ ) = ν (1 -βµ ), and I ' ν = [ Γ (1 -βµ )] 3 I ν ; d Ω ' = 2 π d µ ' = 2 π d µ [ Γ (1 -βµ )] 2 (28)</text>
<text><location><page_6><loc_8><loc_57><loc_49><loc_58></location>are the usual transformations. Integrating over frequency gives</text>
<text><location><page_6><loc_8><loc_51><loc_74><loc_53></location>Setting ∆ µ → 0, the path length is ds = dr /µ /similarequal dr , and one has d ∆ µ/ dr /similarequal -2 ∆ µ/ r . Making use of</text>
<formula><location><page_6><loc_33><loc_47><loc_92><loc_51></location>d dr Fn = -2( n + 1) r 1 2 ∫ d µ ( ∆ µ ) n I + 1 2 ∫ d µ ( ∆ µ ) n dI dr , (30)</formula>
<formula><location><page_6><loc_28><loc_51><loc_92><loc_57></location>dI ds = α es( S -I ); S = ∫ S ν d ν = 1 2 Γ 2 (1 -βµ ) 4 ∫ I ( ˜ µ )(1 -β ˜ µ ) 2 d ˜ µ. (29)</formula>
<formula><location><page_6><loc_26><loc_40><loc_92><loc_46></location>1 r 2 d dr ( r 2 F 0 ) = -α es ∗ 4 Γ 2 ( r / r ∗ ) 2 ( 1 -4 Γ 4 F 2 F 0 ) F 0 = -α es ∗ 4 Γ 2 ( r / r ∗ ) 2 ( 1 -Γ 4 Γ 4 eq ) F 0 , (31)</formula>
<formula><location><page_6><loc_37><loc_35><loc_92><loc_40></location>1 r 4 d dr ( r 4 F 1 ) = α es ∗ 8 Γ 4 ( r / r ∗ ) 2 ( 1 -Γ 4 Γ 4 eq ) F 0 , (32)</formula>
<text><location><page_6><loc_8><loc_46><loc_12><loc_47></location>gives</text>
<text><location><page_6><loc_8><loc_40><loc_11><loc_41></location>and</text>
<text><location><page_6><loc_8><loc_32><loc_92><loc_35></location>where we have set β → 1 in the coefficient. These two equations, in combination with (23), allow us to evolve Γ eq near the scattering photosphere.</text>
<text><location><page_6><loc_8><loc_30><loc_92><loc_32></location>The radial evolution of Γ and R is obtained by differentiating (10), substituting (19) and (31), and expressing the radiation energy flux in terms of R ,</text>
<formula><location><page_6><loc_28><loc_25><loc_92><loc_30></location>r d Γ dr = σ ∗ d d θ f ( K Γ ) -r d R dr ; d R dr = -α es ∗ 4 Γ 2 ( r / r ∗ ) 2 ( 1 -Γ 4 Γ 4 eq ) R . (33)</formula>
<section_header_level_1><location><page_6><loc_43><loc_23><loc_58><loc_24></location>2.6. Numerical Results</section_header_level_1>
<text><location><page_6><loc_8><loc_12><loc_92><loc_22></location>Profiles are obtained for Γ ( x ), Γ eq( x ), R ( x ) and θ f ( x ) by integrating in the radial dimension. We have made the substitutions d / d θ f → δθ -1 gradient and K = θ f ∗ /θ j in (33). This choice forces the field-line bending to zero near the center of the jet. The gradient angle δθ gradient is of the order of θ j , but may be smaller near the edge of the jet as it emerges from a confining medium. For example, the strong acceleration seen near the jet edge in the simulations of Tchekhovskoy et al. (2010) is consistent with δθ gradient ∼ γ -1 ∼ 0 . 1 θ j ; it would presumably be reduced if the jet did not have a sharp edge. In our fiducial model we consider a field line anchored at θ f ∗ = 0 . 1, and take the jet opening half-angle to be θ j = 0 . 2. To illustrate the effect of jet breakout on the flow parameters, we begin the integration just inside the breakout radius, ri = 0 . 8 r ∗ .</text>
<text><location><page_6><loc_8><loc_7><loc_92><loc_12></location>In our first set of integrations, the scattering optical depth is chosen to be large at the breakout radius. At this point, the radiation is still tied to the matter, Γ eq( r ∗ ) = Γ ( r ∗ ), but the rapid MHD acceleration experienced by the flaring jet quickly forces a transition to low τ es. The optical depth for a photon propagating radially from r = r ∗ is given by equation (12), and is thus unknown a priori . To impose a particular value of τ es( r ∗ ), we first choose an approximate value of α es ∗ , evolve the equations of motion</text>
<formula><location><page_6><loc_32><loc_72><loc_92><loc_75></location>α es = Γ (1 -βµ ) α ' es = Γ ρσ ¯ m (1 -βµ ) ≡ α es ∗ β ( r / r ∗ ) 2 (1 -βµ ) (26)</formula>
<figure>
<location><page_7><loc_16><loc_67><loc_47><loc_91></location>
</figure>
<figure>
<location><page_7><loc_55><loc_67><loc_86><loc_91></location>
<caption>FIG. 3.- Profiles of Lorentz factor Γ (blue), magnetization σ (green), and radiation energy flux R (red), in a flaring MHD outflow ( σ ∗ = 10 3 ) with radiative driving. The radiation force vanishes in a frame moving with Lorentz factor Γ eq (dotted blue). Scattering depth integrated from radius r to infinity (black curve) drops rapidly from τ es ∗ = 10 as the flow accelerates. The gradient scale δθ gradient sets the relative degree of flaring between neighboring field lines. Left panel: R i = 1, right panel: R i = 1000. Other parameters: ri = 0 . 8 r ∗ , Γ i = Γ eq , i = 10.</caption>
</figure>
<figure>
<location><page_7><loc_16><loc_35><loc_47><loc_59></location>
</figure>
<figure>
<location><page_7><loc_55><loc_35><loc_86><loc_59></location>
</figure>
<figure>
<location><page_7><loc_16><loc_10><loc_47><loc_34></location>
<caption>FIG. 4.- Same as Figure 3, but for τ es ∗ = 1 (top plots) and τ es ∗ = 0 . 1 (bottom plots).</caption>
</figure>
<figure>
<location><page_7><loc_55><loc_10><loc_86><loc_34></location>
</figure>
<figure>
<location><page_8><loc_17><loc_46><loc_46><loc_68></location>
<caption>FIG. 5.- Same as Figures 3, 4, except δθ gradient = θ j / 2 = 0 . 1 and θ f ∗ = 0 . 15. Optical depth at breakout: τ es ∗ = 10 in top plots and τ es ∗ = 0 . 1 in bottom plots.</caption>
</figure>
<text><location><page_8><loc_8><loc_35><loc_92><loc_40></location>and then iterate. The Lorentz force term in d Γ / dr is only valid outside the fast magnetosonic critical point, and so we take Γ ( ri ) /greaterorsimilar Γ c /similarequal σ 1 / 3 ∗ . Radial integrations are done using a 5th-order Runge-Kutta algorithm with adaptive step size (see Sections 7.3, 7.5 of Kiusalaas 2010).</text>
<text><location><page_8><loc_8><loc_26><loc_92><loc_35></location>Results are plotted in Figure 3 for an outflow with magnetization σ i = σ ∗ = 1000, and both low and high radiation fluxes ( R i = 1 , 1000) at the inner boundary. The action of the Lorentz force is concentrated at a small radius where the flaring is most severe, causing an increase in Γ that is initially much faster than linear. When the radiation energy flux is weak compared with the magnetic Poynting flux, the outflow experiences strong but logarithmic acceleration after breakout with Γ ∝ ln 1 / 2 x , a direct consequence of causally limited flaring, δθ f ∼ 1 / Γ [equation (33)]. While the optical depth is large, the photon field is advected with the plasma, remaining nearly isotropic in the comoving frame. Once the optical depth falls below unity the photon field decouples and is free to self-collimate, so that Γ eq ∝ x .</text>
<text><location><page_8><loc_8><loc_23><loc_92><loc_26></location>High radiation fluxes ( R∼ σ ) force the flow back to the shallower profile Γ /similarequal Γ eq, even while the magnetic flaring grows stronger (1 / Γ is larger). The acceleration zone is therefore widened in the radial direction compared with the radiation-free jet.</text>
<text><location><page_8><loc_8><loc_20><loc_92><loc_23></location>Quite generally, we find that the terminal Lorentz factor is insensitive to the initial radiation energy flux. The growth in radiation energy flux outside the photosphere is therefore largely compensated by a further reduction in outflow magnetization.</text>
<text><location><page_8><loc_8><loc_14><loc_92><loc_20></location>We also consider a low scattering depth at the breakout radius. In this case the matter is only weakly coupled to the radiation field, and the Lorentz factor is forced well above Γ eq a small distance outside the breakout radius (Figure 4). As in the case of higher optical depths, high radiation fluxes limit the growth of Γ and force it toward Γ eq. But the mismatch between Γ and Γ eq remains unless R /greaterorsimilar σ . Energy is transferred from the magnetic field to the photons, resulting in a significantly modified spectrum (Section 4).</text>
<text><location><page_8><loc_8><loc_11><loc_92><loc_14></location>Faster jet flaring, corresponding to a jet edge with δθ gradient = 0 . 5 θ j , produces faster acceleration and terminal Lorentz factors closer to σ ∗ , but otherwise qualitatively similar behavior (Figure 5).</text>
<text><location><page_8><loc_8><loc_7><loc_92><loc_11></location>A novel effect becomes clear when the compactness is large: the magnetization can show a significant reduction, dropping significantly below R and even Γ , and therefore resulting in a weakly magnetized outflow. This is caused by the strong radiation drag at small radius, which restricts the growth of Γ which allows for stronger jet flaring.</text>
<section_header_level_1><location><page_9><loc_32><loc_91><loc_68><loc_92></location>3. FLARING, HOT MAGNETIZED JET: TRANSPARENT FLOW</section_header_level_1>
<text><location><page_9><loc_35><loc_90><loc_65><loc_90></location>ACROSS THE FAST CRITICAL SURFACE (MODEL II)</text>
<text><location><page_9><loc_8><loc_80><loc_92><loc_89></location>The dynamics of the outflow can be calculated more precisely in the optically thin regime, where the radiation field is prescribed at an emitting surface (radius rs ) and passively collimates outside that surface. This allows us to study the critical point structure of the flow, at the price of neglecting the effects of multiple scattering. In the spherical case, the emission surface could, if one wanted, be identified with the physical surface of a star. But the model of a passively collimating photon field can also be applied to outflows that are already relativistic at the photosphere, including those with a jet geometry. In this section, we solve the wind equations for a steady, flaring jet which is optically thin but sub-magnetosonic at breakout. In contrast to the model presented in Section 2, here we prescribe the flaring profile in advance.</text>
<figure>
<location><page_9><loc_20><loc_49><loc_81><loc_71></location>
<caption>FIG. 6.- Geometry and approximate scale of the flow solutions for jet model II.</caption>
</figure>
<text><location><page_9><loc_8><loc_32><loc_92><loc_37></location>The flow geometry is shown in Figure 6. The photon source radius sits in the confined portion of the jet, inside the breakout radius r ∗ . After breakout, the optically thin flow is accelerated though the magnetosonic surface, whose location and shape are calculated self consistently (analytic approximations to the position of the critical surface can be found in Section 3.5). We follow the flow along a field line θ f ( r ), situated well outside the light cylinder, from just outside the source radius.</text>
<text><location><page_9><loc_8><loc_24><loc_92><loc_32></location>Our solution to the flow below the breakout point formally is in the optically thin regime. Because the jet has already typically attained relativistic motion before breaking out, we can view the photon emission as arising from a virtual surface located below the physical photosphere, at a radius rs , eff ∼ r τ / Γ ( r τ ). At a high radiation intensity, the matter is locked into the bulk frame defined by the photon field, Γ /similarequal Γ eq ∼ ( r -rs ) / ( θ jrs ), around breakout. This means that the flow profile closely mimics an optically thick, radiation-dominated flow inside breakout, and we expect that our flow solutions should adequately represent the dynamics of a jet which encounters a photosphere at a radius r ∗ ∼ r τ > rs .</text>
<text><location><page_9><loc_8><loc_19><loc_92><loc_24></location>Our procedure is first to choose the poloidal field geometry and radiation profile, and then evolve the energy and angular momentum along the poloidal flux surfaces. A simple description of the photon field is possible when the jet geometry is locally spherical - that is, when the streamlines are conical inside breakout. This constrains the non-radial Lorentz force to vanish at r < r ∗ , which in the small-angle limit can be written as</text>
<formula><location><page_9><loc_34><loc_15><loc_92><loc_18></location>1 c ( J × B ) θ /similarequal -B φ 4 π r θ d ( B φ θ ) d θ = 0 ⇒ B φ ∝ θ -1 . (34)</formula>
<text><location><page_9><loc_8><loc_12><loc_92><loc_15></location>A jet with such a line current profile will de-collimate at r > r ∗ , as the external pressure is removed. This decollimation leads to rapid outward acceleration of the cold matter entrained in the jet, even in the absence of radiative forcing.</text>
<text><location><page_9><loc_8><loc_7><loc_92><loc_12></location>Other jet profiles are easily constructed and may be more natural: in the cold MHD jet calculation of Tchekhovskoy et al. (2010), the confining surface has a parabolic structure inside breakout, transitioning to a conical geometry outside. Nonetheless, the radial Lorentz factor profiles that we obtain are (in the absence of radiation) very similar to those of Tchekhovskoy et al. (2010), and only depend on the magnitude of the differential flaring between magnetic flux surfaces.</text>
<text><location><page_10><loc_8><loc_84><loc_92><loc_92></location>We focus on the local dynamics within magnetic flux surfaces, taking into account the effect of radiation pressure. This longitudinal dynamics is sensitive to the relative flaring rates of neighboring flux surfaces, but not to the global profile of Poynting flux transverse to the jet axis. Although the transverse force balance is not explicitly taken into account, we do check that i) the degree of magnetic flaring is consistent with causal stresses; and ii) that the transverse component of the radiation force is weak compared with the transverse Lorentz force (so that the radiation flow is not strong enough to comb out the field lines into a conical geometry: see Appendix D).</text>
<section_header_level_1><location><page_10><loc_44><loc_82><loc_56><loc_83></location>3.1. Jet Properties</section_header_level_1>
<text><location><page_10><loc_8><loc_74><loc_92><loc_82></location>To construct an optically thin radiation field, we consider the simplest case of uniform intensity I = ∫ I ν d ν at the emission radius rs , as we did in Paper I, but now restrict the sampling of the radiation field to polar angles θ < θ j . The emission patch covers a small angular disk of area π ( θ jrs ) 2 (Figure 6), and the luminosity per sterad is dL γ ∗ / d Ω ∼ πθ 2 j I . This allows an analytic calculation of the radiation force acting on a particle of arbitrary Lorentz factor and direction, which is presented in Appendix A. This result generalizes the simpler angular moment formalism used in Section 2 and presented in equation (24).</text>
<text><location><page_10><loc_8><loc_69><loc_92><loc_74></location>We showed in Paper I that if we normalize the photon intensity and the angular width of the photon beam by fixing i) the radiation force and ii) the relativistic frame Γ eq in which this force vanishes, then other quantities, such as the mean power radiated by an electron in its bulk frame, are nearly identical to those obtained from a radiation field that is isotropic at a relativistically moving photosphere.</text>
<text><location><page_10><loc_8><loc_64><loc_92><loc_69></location>The radiation streams freely outward at r > rs , and its cone contracts with increasing radius. The size and orientation of this cone now vary with distance from the jet axis (in contrast with the case of a spherical emission surface; Paper I). There is generally a misalignment of the direction of peak radiation intensity with respect to both the radial direction, and the local flow direction. The alignment is strongest at a small but finite distance from the rotation axis, and produces a peak in the radiation force there. 1</text>
<text><location><page_10><loc_10><loc_62><loc_71><loc_63></location>We normalize distances to rs , but measure the photon compactness (11) at the breakout radius,</text>
<formula><location><page_10><loc_35><loc_58><loc_92><loc_61></location>x ≡ r rs ; ω ≡ Ω f rs c χ ∗ ≡ σ T r ∗ πθ 2 j I ¯ mc 3 ( x ∗ -1) 2 . (35)</formula>
<text><location><page_10><loc_8><loc_54><loc_92><loc_57></location>In a GRB outflow, the photosphere generally lies outside the light cylinder of the rotating engine, so we take ω = Ω f rs / c > 1 in our calculations. In this context, the magnetization can be most simply defined as 2</text>
<formula><location><page_10><loc_40><loc_50><loc_92><loc_54></location>σ ≡ B 2 r Ω 2 f ( r θ f ) 2 4 π Γ ρ vrc 3 ( θ f /lessmuch 1) . (36)</formula>
<text><location><page_10><loc_8><loc_48><loc_71><loc_50></location>Neglecting the radiation field, the energy and angular momentum per unit rest mass are given by</text>
<formula><location><page_10><loc_30><loc_44><loc_92><loc_48></location>µ c 2 = ( Γ -Ω f BrB φ 4 π Γ ρ vr ) c 2 ; L rsc = ( Γ v φ -BrB φ 4 π Γ ρ vr ) r θ f , (37)</formula>
<text><location><page_10><loc_8><loc_43><loc_78><loc_44></location>and in a steady MHD outflow are conserved along field lines. They can be written in a dimensionless form,</text>
<formula><location><page_10><loc_27><loc_39><loc_92><loc_42></location>µ = Γ -σ ω x θ f B φ Br /similarequal Γ + σ ; L = Γ x θ f β φ -σ ω 2 x θ f B φ Br ≡ L m + L P . (38)</formula>
<section_header_level_1><location><page_10><loc_39><loc_37><loc_61><loc_38></location>3.2. Poloidal Field Configuration</section_header_level_1>
<text><location><page_10><loc_8><loc_31><loc_92><loc_36></location>To incorporate a strong radial Lorentz force into the outflow, we choose the poloidal flux surfaces by fixing the function θ f ( x , θ f ∗ ), where θ f ∗ is the polar angle at the breakout radius. The Lorentz force is large and positive if neighboring flux surfaces diverge from each other more rapidly than in a monopolar geometry. The effect of this differential expansion appears in the wind equations via the function</text>
<formula><location><page_10><loc_31><loc_27><loc_92><loc_31></location>A ( x , θ f ∗ ) ≡ d ln θ f d ln θ f ∗ ; Br = Br ∗ x 2 ∗ Ax 2 ( θ f ∗ θ f ) 2 ; σ = σ ∗ A . (39)</formula>
<text><location><page_10><loc_8><loc_24><loc_92><loc_27></location>We focus on the dynamics along a single flux surface, and so do not have to consider the angular dependence of Br ∗ = Br ( r ∗ ). The critical point structure of the longitudinal flow is insensitive to angular gradients in the flow magnetization.</text>
<text><location><page_10><loc_10><loc_23><loc_78><loc_24></location>The flaring profile used in our calculations is described in Section 3.4, followed by the numerical results.</text>
<section_header_level_1><location><page_10><loc_39><loc_20><loc_61><loc_22></location>3.3. Longitudinal Wind Equations</section_header_level_1>
<text><location><page_10><loc_8><loc_17><loc_92><loc_20></location>We now consider the longitudinal evolution of the outflow variables along a magnetic flux surface. A radiation force (20) is added to the Euler equation, which becomes</text>
<formula><location><page_10><loc_32><loc_14><loc_92><loc_17></location>ρ Γ v · ∇ ( Γ v ) = 1 4 π [( ∇ · E ) E + ( ∇ × B ) × B ] + Γ ρ ¯ m F rad . (40)</formula>
<text><location><page_11><loc_8><loc_89><loc_92><loc_92></location>Taking the dot product of equation (40) with the unit poloidal field vector ˆ B p, defining the longitudinal derivative ∂ l = ˆ Bp · ∇ , and taking the small-angle limit, we have</text>
<text><location><page_11><loc_8><loc_82><loc_32><loc_84></location>The φ -component of equation (40) is</text>
<formula><location><page_11><loc_34><loc_83><loc_92><loc_88></location>∂ l Γ c 2 -v φ r θ f ∂ l L m = -B φ 4 π Γ ρ r θ f ∂ l ( r θ f B φ ) + F rad p ¯ m (41)</formula>
<formula><location><page_11><loc_37><loc_77><loc_92><loc_82></location>vp ∂ l L m = Bp 4 π Γ ρ ∂ l ( r θ f B φ ) + ( r θ f ) F rad φ ¯ m . (42)</formula>
<text><location><page_11><loc_8><loc_72><loc_92><loc_78></location>Here L m is the specific matter angular momentum [equation (38)], and we have made use of the fact that the poloidal flow velocity v p is aligned with B p . The Coulomb force only contributes to the transverse force balance and does not appear in equations (41) or (42). Both of these features are easily derived by noting that the toroidal electric field vanishes in a steady, axisymmetric MHD wind ( E · B = 0), which implies that v p × B p = 0 and E p · B p = 0.</text>
<text><location><page_11><loc_8><loc_70><loc_92><loc_72></location>In Appendix A we calculate the radiation force (20) in a thin jet, and express the poloidal and toroidal components in terms of dimensionless functions Rj , Pj ,</text>
<formula><location><page_11><loc_32><loc_65><loc_92><loc_69></location>F rad p = χ ∗ ¯ mc 2 rs Rj ( r , Γ , β φ ); F rad φ = χ ∗ ¯ mc 2 rs Pj ( r , Γ , β φ ) . (43)</formula>
<text><location><page_11><loc_8><loc_61><loc_92><loc_64></location>Rotation of the photon field at the emission surface tends to reduce the azimuthal drag. It can be incorporated by modifying the β φ -dependence of equations (43), as is discussed in Appendix B, but is generally negligible when the outflow lies far outside the light cylinder ( ω /greatermuch 1).</text>
<text><location><page_11><loc_10><loc_59><loc_70><loc_61></location>A good approximation to the poloidal force can be obtained on field lines ( x ω ) -1 /lessmuch θ f /lessmuch θ j ,</text>
<formula><location><page_11><loc_42><loc_54><loc_92><loc_59></location>Rj /similarequal x ∗ 4 x 2 Γ 2 ( 1 -θ 4 j Γ 4 3 x 4 ) , (44)</formula>
<text><location><page_11><loc_8><loc_50><loc_92><loc_53></location>in agreement with equation (24). The result for a spherical emission surface (Paper I) differs only in the absence of the factor θ 4 j . The vanishing of the radiation force occurs at a significantly higher Lorentz factor when the photon beam is collimated,</text>
<formula><location><page_11><loc_46><loc_46><loc_92><loc_49></location>Γ eq /similarequal x -1 θ j (45)</formula>
<text><location><page_11><loc_8><loc_44><loc_48><loc_45></location>up to a numerical factor of order unity as shown in Figure 15.</text>
<text><location><page_11><loc_8><loc_36><loc_92><loc_44></location>The deviation of the field lines from a purely radial direction is measured by ∆ θ B = B θ / Br , which we take to be small, so that Bp = (1 + ∆ θ 2 B ) 1 / 2 Br /similarequal Br , vp /similarequal vr . As is detailed in Appendix C, the derivatives along field lines on the right hand side of equations (41) and (42) can be written in the small-angle approximation. Ignoring the cross-field force balance then allows us to express (41), (42) as two ordinary differential equations, which can be re-written in terms of d Γ / dl and d L m / dl . The various terms on the right-hand side of these equations can be separated into purely magnetocentrifugal pieces (which do not depend on the radiation force), the direct radiation force, and a cross term:</text>
<formula><location><page_11><loc_31><loc_31><loc_92><loc_35></location>d Γ dl = Γ ' σ + Γ ' σχ + Γ ' χ µ eff ; d L m dl = ( L ' m ) σ + ( L ' m ) σχ + ( L ' m ) χ µ eff (46)</formula>
<text><location><page_11><loc_8><loc_29><loc_12><loc_30></location>where</text>
<text><location><page_11><loc_8><loc_19><loc_12><loc_20></location>where</text>
<formula><location><page_11><loc_25><loc_25><loc_92><loc_30></location>Γ ' σ + Γ ' σχ + Γ ' χ ≡ -σ x θ f ωβ r Ψ -σχ ∗ ( x θ f ω ) 2 β r Γ ( Rj + B φ Br Pj ) Λ + χ ∗ ( Rj + β φ β r Pj ) (47)</formula>
<formula><location><page_11><loc_19><loc_20><loc_92><loc_25></location>( L ' m ) σ + ( L ' m ) σχ + ( L ' m ) χ ≡ -σ x θ f ω 2 β r Ψ -σχ ∗ x θ f ω 2 β r Γ ( β φ Λ + 1 β r Γ 2 B φ Br )( Rj + B φ Br Pj ) + χ ∗ x θ f β r Pj (48)</formula>
<formula><location><page_11><loc_30><loc_15><loc_92><loc_19></location>Λ ≡ 1 + β φ β r B φ Br ; Ψ ≡ ( 1 + ∆ θ B θ f ) (1 + Λ ) β φ x + B φ Br β r A dA dl (49)</formula>
<text><location><page_11><loc_8><loc_13><loc_11><loc_14></location>and</text>
<text><location><page_11><loc_8><loc_7><loc_23><loc_8></location>is the effective inertia.</text>
<formula><location><page_11><loc_29><loc_8><loc_92><loc_14></location>µ eff ≡ 1 -σ ( β r Γ ) 3 ( 1 + β 2 φ Γ 2 ) -σ ( x θ f ω ) 2 β r Γ ( 1 + β 2 φ β 2 r ) + 2 σβ φ x ωθ f β 3 r Γ (50)</formula>
<section_header_level_1><location><page_12><loc_42><loc_91><loc_59><loc_92></location>3.4. Poloidal Field Profile</section_header_level_1>
<text><location><page_12><loc_8><loc_85><loc_92><loc_90></location>We now prescribe the poloidal field profile outside the breakout surface, which, in a steady jet, also determines the poloidal streamlines. The profile inside r ∗ is assumed to be straight and conical, θ f ∗ = θ f , s . A strong Lorentz force is obtained outside r ∗ if the net change θ f , ∞ -θ f ∗ in polar angle is itself a growing function of θ f ∗ . A simple choice, that is asymptotically conical at a large radius, is</text>
<text><location><page_12><loc_8><loc_79><loc_77><loc_81></location>This connects smoothly with the inner cone if α > 1. The net change in polar angle is determined by 3 δθ ,</text>
<formula><location><page_12><loc_37><loc_81><loc_92><loc_85></location>θ f ( x ) θ f ∗ = 1 + θ f ∗ δθ ( 1 -x ∗ x ) α ( x > x ∗ ) . (51)</formula>
<formula><location><page_12><loc_42><loc_75><loc_92><loc_79></location>θ f , ∞ -θ f ∗ = ( θ f ∗ δθ ) θ f ∗ . (52)</formula>
<text><location><page_12><loc_8><loc_74><loc_54><loc_75></location>The local change in the field line direction, relative to the total bend, is</text>
<formula><location><page_12><loc_41><loc_70><loc_92><loc_73></location>∆ θ B θ f -θ f ∗ = B θ / Br θ f -θ f ∗ = 2 α x ∗ x -x ∗ . (53)</formula>
<text><location><page_12><loc_8><loc_66><loc_92><loc_69></location>The flux spreading factor works out to A = 2 -θ f ∗ /θ f for any field-line profile of the form (51). In the absence of radiation, the Lorentz factor can be obtained by imposing energy conservation. It depends on the flaring profile of the jet via</text>
<formula><location><page_12><loc_31><loc_59><loc_92><loc_66></location>Γ /similarequal Γ ∗ + σ ∗ -σ = Γ ∗ + σ ∗ ( 1 -A -1 ) = Γ ∗ + σ ∗ θ f /θ f ∗ -1 2 θ f /θ f ∗ -1 ; Γ ∞ /similarequal Γ ∗ + σ ∗ θ f ∗ /δθ 1 + 2 θ f ∗ /δθ . (54)</formula>
<text><location><page_12><loc_8><loc_55><loc_92><loc_58></location>The acceleration tends to be more concentrated in radius for smaller values of the parameter α ; in what follows α = 2. In Figure 7 we show sample field lines given by (51) with strong flaring ( δθ = 0 . 3) for several values of θ f ∗ .</text>
<figure>
<location><page_12><loc_34><loc_28><loc_66><loc_53></location>
<caption>FIG. 7.- Sample field line profiles of the type (51) with strong flaring ( δθ = 0 . 3) and breakout radius x ∗ = r ∗ / rs = 3 (dashed line). The emission radius bounds the inner grey zone.</caption>
</figure>
<section_header_level_1><location><page_12><loc_36><loc_20><loc_64><loc_21></location>3.5. Position of Fast Magnetosonic Surface</section_header_level_1>
<text><location><page_12><loc_8><loc_12><loc_92><loc_19></location>When the flow speed surpasses the fast magnetosonic speed, radial magnetic disturbances are swept downstream and cannot interact with the part of the jet interior to the fast critical surface. The inertia of the electromagnetic field also becomes insignificant in the radial force balance, so that radiation pressure is relatively more important. We first consider how the position xc = rc / rs of the critical surface is modified by field-line flaring, and then consider the effects of radiation. The critical surface sits at infinite radius only if the poloidal magnetic field is constrained to be radial and radiation is absent (Goldreich & Julian 1970).</text>
<text><location><page_12><loc_8><loc_10><loc_92><loc_12></location>The critical surface is obtained by setting µ eff = 0 in equations (46). Retaining χ ∗ = 0, and assuming σ /greatermuch 1, this corresponds to Γ /similarequal σ 1 / 3 [a vanishing coefficient of d Γ / dl in equation (C4)], and Ψ = 0. When δθ f = O ( θ j ), the magnetofluid rapidly accelerates</text>
<text><location><page_13><loc_8><loc_91><loc_49><loc_92></location>outside radius r ∗ , and so we can expand A /similarequal 1 near this radius:</text>
<formula><location><page_13><loc_31><loc_85><loc_92><loc_90></location>dA d ln l /similarequal α θ f ∗ δθ ( 1 -x ∗ x ) α -1 x ∗ x ; Ψ /similarequal 1 x 2 θ f ω -( x θ f ω ) dA dl . (55)</formula>
<text><location><page_13><loc_8><loc_84><loc_50><loc_86></location>Here we have approximated β φ /similarequal 1 / x θ f ω /lessmuch 1. Then, for α = 2,</text>
<formula><location><page_13><loc_43><loc_80><loc_92><loc_83></location>xc x ∗ /similarequal 1 + δθ/θ f ∗ 2( x ∗ θ f ∗ ω ) 2 . (56)</formula>
<text><location><page_13><loc_8><loc_76><loc_92><loc_79></location>In the absence of magnetic-field flaring, the radiation stress forces the fast surface in from infinity (Paper I). Taking instead δθ = ∞ but allowing for finite χ ∗ , the fast surface corresponds to Γ /similarequal σ 1 / 3 and Γ ' σ /similarequal Γ ' χ . Then</text>
<formula><location><page_13><loc_42><loc_72><loc_92><loc_75></location>xc x ∗ /similarequal 4 σ 5 / 3 χ ∗ ( x ∗ -1) 2 ω 2 θ 2 f ∗ . (57)</formula>
<text><location><page_13><loc_8><loc_68><loc_92><loc_71></location>This differs from the spherical case (Paper I) mainly by the factor 1 /θ 2 f ∗ . At a very high compactness, the flow is tied to the collimating radiation field, and thus the critical surface is pulled in to where Γ eq( x , θ f ) /similarequal Γ c /similarequal σ 1 / 3 .</text>
<figure>
<location><page_13><loc_12><loc_36><loc_89><loc_65></location>
<caption>FIG. 8.- Magnetosonic surface inside a flaring jet at low radiation compactness (dotted blue, χ → 0) and high compactness [dotted red, χ / σ /lessmuch 1 but still satisfying the bound given in equation (D3)]. Left panels: Radius xc = rc / rs of the magnetosonic point as a function of field line footprint angle, for weak flaring (top) and strong flaring (bottom). Right panel: Two dimensional depiction of the magnetosonic surface (weak flaring).</caption>
</figure>
<text><location><page_13><loc_8><loc_23><loc_92><loc_30></location>The fast surface is shown as a function of angle in Figure 8, for a breakout radius x ∗ = 3. At low radiation compactness, this surface typically lies just outside breakout, xc /greaterorsimilar x ∗ , in agreement with equation (56). As the compactness is increased, the critical surface can either move inward or outward, depending on the location where Γ eq = σ 1 / 3 . The critical surface is typically pulled inward near the rotation axis if the magnetic field is weakly flared, and also at larger polar angles if x ∗ /greatermuch θ j σ 1 / 3 . Then its position follows equation (57) until reaching the high-compactness limit at</text>
<formula><location><page_13><loc_44><loc_19><loc_92><loc_22></location>χ ∗ /similarequal 4 σ 4 / 3 x ∗ ω 2 θ 2 f ∗ θ j . (58)</formula>
<text><location><page_13><loc_8><loc_17><loc_73><loc_18></location>If alternatively the breakout radius is small, then the critical surface is pushed out by radiation drag,</text>
<formula><location><page_13><loc_41><loc_12><loc_92><loc_16></location>xc x ∗ /similarequal ( χ ∗ 24 σ 1 / 3 δθ θ f ∗ θ 4 j x 4 ∗ ) 1 / 7 , (59)</formula>
<text><location><page_13><loc_8><loc_10><loc_33><loc_11></location>reaching its high-compactness limit at</text>
<formula><location><page_13><loc_42><loc_5><loc_92><loc_10></location>χ ∗ /similarequal 24 θ f ∗ δθ ( θ j xj ) 3 σ 8 / 3 . (60)</formula>
<text><location><page_14><loc_8><loc_86><loc_92><loc_92></location>The deviation of xc toward large radius that is seen close to the rotation axis is due to a combination of effects: a reduction in the outward Lorentz force due to the weaker field-line flaring; and a mis-match between the radiation and matter flows driven by strong rotation. The first effect dominates at low χ ∗ . The change in critical radius at high χ ∗ can be estimated using equation (A17) for Γ eq near the axis:</text>
<formula><location><page_14><loc_40><loc_83><loc_92><loc_86></location>xc /similarequal σ 1 / 3 ωθ f , ( θ f /lessmuch ω -1 θ -1 j ) . (61)</formula>
<section_header_level_1><location><page_14><loc_43><loc_80><loc_58><loc_81></location>3.6. Numerical Results</section_header_level_1>
<text><location><page_14><loc_8><loc_74><loc_92><loc_79></location>We now examine the solutions to the wind equations (46)-(50) that we have derived for a geometrically and optically thin jet. The singularity at the fast magnetosonic critical point, and the stiffness of the equations associated with large values of σ and χ , means that simple integration techniques such as Runge-Kutta are inadequate. To determine the position of the critical point and the flow solution inside it, we use the relaxation method described in Paper I (see also London & Flannery 1982).</text>
<figure>
<location><page_14><loc_13><loc_15><loc_88><loc_72></location>
<caption>FIG. 9.- Acceleration in a thin, strongly magnetized jet ( σ ∗ = 1000, ω = 100, θ j = 0 . 2), along a field line anchored at θ f ∗ = 0 . 1. The radiation compactness at the breakout radius x ∗ = r ∗ / rs = 3 is varied: χ ∗ = 1 , 10 3 , 10 5 , corresponding to the top to bottom curves on the left side. Left panel: δθ = 10 (weak flaring); right panel: δθ = 1; bottom panel: δθ = 0 . 3 (strong flaring). (The distance along the field line l differs little from the radial coordinate since the degree of flaring is small).</caption>
</figure>
<text><location><page_15><loc_8><loc_84><loc_92><loc_92></location>The inner boundary radius ri of the integration is chosen somewhat differently than in Paper I: we set it to twice the photon emission radius ( xi = 2) because we only evaluate the radiation force where photons propagate at small angles with respect to the jet axis (requiring that xi -1 /greatermuch θ j ). The solutions for Γ and L m obtained by an integration inside the critical point are required to be smooth near xi ; avoiding sharp gradients restricts the boundary values at xi to a narrow range. We also make a first guess for the critical point radius xc . The regularity of the solution at xc then allows us to determine the flow variables at the critical point from the equations</text>
<text><location><page_15><loc_8><loc_75><loc_92><loc_80></location>An approximate solution is chosen which connects the inner boundary values to the critical point. 4 This solution, along with the position of the critical point, is then relaxed to within a desired tolerance using a Newton-Raphson method, all the while satisfying the regularity condition (62). As a last step, the flow outside the critical point is obtained by shooting outward using a fifth-order Runge-Kutta algorithm.</text>
<formula><location><page_15><loc_39><loc_79><loc_92><loc_84></location>( Γ ' σ + Γ ' σχ + Γ ' χ ) xc = 0 = µ eff( xc ) . (62)</formula>
<text><location><page_15><loc_8><loc_67><loc_92><loc_75></location>Solutions are obtained for a range of photon compactness and a high magnetization ( σ ∗ = 1000). The part of the jet studied sits well outside the light cylinder, ω = 100 in equation (35). Choosing the flaring profile (51), we follow the flow along a field line with initial footprint θ f ∗ = 0 . 1, in a jet of half-opening angle θ j = 0 . 2 and a breakout radius x ∗ = 3 = 1 . 5 xi . The magnitude of the jet flaring is adjusted by choosing the parameter δθ , with values 10 , 1 , 0 . 3 corresponding to a net angular shift θ f , ∞ /θ f ∗ -1 = 0 . 1 θ f ∗ , θ f ∗ , 3 . 3 θ f ∗ between breakout and infinity. The maximal flaring chosen ( δθ = 0 . 3) still satisfies equation (17), and so the divergence of neighboring magnetic field lines is consistent with causal stresses.</text>
<text><location><page_15><loc_8><loc_61><loc_92><loc_67></location>The results are show in Figure 9. At low radiation compactness, they resemble those obtained by Tchekhovskoy et al. (2010) for a cold MHD jet. A slow, nearly linear, increase in Γ within the star is followed by rapid (but logarithmic) growth beyond the breakout point, where the field lines begin to diverge. As χ ∗ increases above ∼ σ , photon drag begins to dominate the weak Lorentz force inside the breakout radius, and Γ tends to Γ eq /similarequal x /θ j [equation (45)]. After breaking out, the fluid is quickly</text>
<text><location><page_15><loc_8><loc_58><loc_92><loc_61></location>accelerated through the fast point. A strong radiation field forces the position of the critical point to a radius where Γ eq /similarequal σ 1 / 3 ∗ (in this case, the displacement is outward). We do not search for solutions with the fast point inside the star, corresponding to x ∗ /greaterorsimilar 3.</text>
<figure>
<location><page_15><loc_30><loc_24><loc_69><loc_54></location>
<caption>FIG. 10.- Asymptotic Lorentz factor of flaring magnetized jet ( σ ∗ = 1000, ω = 100, θ j = 0 . 2), as a function of compactness χ ∗ at the breakout radius. Curves correspond to a field line anchored at θ f ∗ = 0 . 1 and represent varying degrees of flaring (weak: δθ = 10; intermediate: δθ = 1; strong: δθ = 0 . 3). Dashed black line: asymptotic Lorentz factor 0 . 8( χ ∗ x ∗ / 4 θ j ) 1 / 4 of an unmagnetized, radial, monopolar outflow.</caption>
</figure>
<text><location><page_15><loc_8><loc_12><loc_92><loc_17></location>The influence of the radiation field can be clearly seen in the dependence of asymptotic Lorentz factor Γ ∞ on χ ∗ (Figure 10). When flaring is strong ( δθ /lessorsimilar 1), the matter is pushed rapidly to Γ > Γ eq and it feels a net drag outside the magnetosonic point. The asymptotic Lorentz factor is reduced from (54). At very high χ ∗ , the radiation drag is able to suppress the acceleration and, therefore, the asymptotic Lorentz factor.</text>
<text><location><page_15><loc_10><loc_10><loc_92><loc_11></location>The minimal compactness needed to significantly affect the post-breakout flow can be estimated by equating the leading terms</text>
<text><location><page_16><loc_8><loc_91><loc_74><loc_92></location>in (47) at x = 3 x ∗ / 2, the point where the relative flaring of poloidal field lines is maximal. This gives</text>
<formula><location><page_16><loc_45><loc_87><loc_92><loc_90></location>χ ∗ /greaterorsimilar σ 5 / 3 ∗ θ f ∗ δθ . (63)</formula>
<text><location><page_16><loc_8><loc_82><loc_92><loc_86></location>In this case, the sign of the effect of radiation pressure outside the critical point still depends on the degree of magnetic field line flaring. If flaring is weaker ( δθ /greaterorsimilar 1) then the details of the flow profile near breakout differ from the unmagnetized flow, but Γ ∞ is still well approximated by an unmagnetized, radiatively driven flow:</text>
<formula><location><page_16><loc_35><loc_80><loc_92><loc_81></location>Γ ∞ /similarequal 0 . 8( χ ∗ x ∗ /θ j ) 1 / 4 ( σ = 0 , δθ →∞ ) . (64)</formula>
<text><location><page_16><loc_8><loc_74><loc_92><loc_79></location>Our solutions, in the part of parameter space that we have explored, satisfy two basic constraints. First, the outflow is optically thin at (or near) breakout if the compactness sits below the bound (15). Second, the component of the radiation force transverse to the poloidal flux surfaces must remain small compared with the transverse Lorentz force that is implied by the chosen flaring profile. The corresponding upper bound (D3) on the compactness is derived in Appendix D.</text>
<section_header_level_1><location><page_16><loc_38><loc_71><loc_62><loc_72></location>4. SPECTRUM OF SCATTERED PHOTONS</section_header_level_1>
<text><location><page_16><loc_8><loc_67><loc_92><loc_71></location>We now consider the self-consistent spectrum of photons that scatter off a hot electromagnetic outflow near its photosphere. Our focus is solely on the signature of the differential flow of matter and photons - that is, we neglect any internal processes that would heat particles or induce small-scale deviations from a uniform flow.</text>
<text><location><page_16><loc_8><loc_60><loc_92><loc_67></location>We first consider the jet model of Section 2, in which the optical depth is finite but the flow is considered only outside its fast magnetosonic surface. Then we turn to the optically thin jet model of Sections 3 and 3.6, in which the entire flow is solved inside and outside the critical surface, but the region interior to the photosphere is ignored. As in Paper I, we neglect any internal dissipation in the outflow, which can contribute to the high-energy tail of the spectrum (Thompson 1994; Giannios 2006; Beloborodov 2010).</text>
<section_header_level_1><location><page_16><loc_26><loc_58><loc_74><loc_59></location>4.1. Spectrum in Jet Model I (Super-magnetosonic): Monte Carlo Method</section_header_level_1>
<text><location><page_16><loc_8><loc_50><loc_92><loc_57></location>Here we follow the photon field self-consistently across the jet photosphere, which is assumed to sit outside the fast magnetosonic point (Figure 1). The exchange of energy between photons and magnetic field was calculated in Section 2 in parallel with the flaring rate of the poloidal field lines outside a fixed breakout radius. The radiation force on the matter, and the evolution of the equilibrium Lorentz factor Γ eq of the radiation field, defined in equations (23) and (24), are both calculated by taking angular moments (21) of the intensity.</text>
<text><location><page_16><loc_8><loc_43><loc_92><loc_50></location>To calculate the emergent spectrum, we i) take the flow velocity profile as a given background, and then ii) inject photons from the inner radius ri = 0 . 8 r ∗ with an isotropic distribution in a frame moving with Lorentz factor Γ eq , i . Photon parameters in the rest frame of the 'star' at r > ri are obtained by a simple Lorentz boost. Defining a radial direction cosine by µ = ˆ k · ˆ r , one has µ = ( µ ' + β ) / (1 + βµ ' ), ω = Γ (1 + βµ ' ) ω ' , where the prime labels the matter rest frame. Deviations from radial flow are assumed small compared with the width of the photon beam.</text>
<text><location><page_16><loc_8><loc_40><loc_92><loc_43></location>Electron scatterings are handled in the Thomson approximation (the outflow moves relativistically in the case of a GRB), by drawing a random number 1 -e -∆ τ es . The position of the next scatter point is calculated by integrating</text>
<formula><location><page_16><loc_32><loc_36><loc_92><loc_40></location>∆ τ es[ r 1 , r 2 , µ ( r 1)] = α es ∗ r ∗ ∫ r 2 r 1 [1 -µ ( r ) β ( r )] r ∗ dr µ ( r ) β ( r ) r 2 (65)</formula>
<text><location><page_16><loc_8><loc_32><loc_92><loc_36></location>along the photon ray. Note that the outflow solution of Section 2 has been iterated so that the coefficient α es ∗ corresponds to a prescribed value of the radial optical depth τ es( r ∗ , ∞ , 1) at the breakout radius. Other initial flow parameters are defined at ri . The direction cosine evolves from a scattering radius r to r 2 > r according to</text>
<formula><location><page_16><loc_36><loc_26><loc_92><loc_31></location>1 -µ ( r 2) 2 = ( r r 2 ) 2 [ 1 -µ ( r ) 2 ] ( r 2 > r ) . (66)</formula>
<text><location><page_16><loc_8><loc_20><loc_92><loc_26></location>The frequency distribution of the outgoing photons is first obtained with a monochromatic photon source, I ν = I 0 ν 0 δ ( ν -ν 0). This output spectrum is then convolved a source spectrum that is either a pure blackbody, or a function 5 that mimics the lowfrequency slope of a GRB, F ν = const × e -h ν / kT 0 . For both types of seed spectrum, the temperature T 0 is normalized by requiring F ν to peak at the fixed reference frequency ν 0.</text>
<text><location><page_16><loc_8><loc_25><loc_55><loc_27></location>The photon escapes if ∆ τ es exceeds the total optical depth along the ray.</text>
<text><location><page_16><loc_8><loc_17><loc_92><loc_20></location>Scatterings are taken to be elastic in the bulk frame, where the matter is assumed cold, so that the outgoing and ingoing frequencies satisfy the usual Doppler relation,</text>
<formula><location><page_16><loc_40><loc_13><loc_92><loc_17></location>ν em ν = 1 -βµ 1 -βµ em = 1 + βµ ' em 1 + βµ ' . (67)</formula>
<text><location><page_16><loc_8><loc_9><loc_92><loc_13></location>After transforming µ to the local bulk frame, we pick scattering angles θ ' s , φ ' s with respect to the flow direction. The direction cosine of the outgoing photon is determined via µ ' em = µ ' cos θ ' s + (1 -µ ' 2 ) 1 / 2 sin θ ' s cos φ ' s , followed by a boost to the stellar frame.</text>
<text><location><page_17><loc_8><loc_89><loc_92><loc_92></location>The peak of the seed photon distribution is stretched to higher frequencies when the outflow Lorentz factor Γ /greaterorsimilar Γ eq [equation (45)]. A scattered photon has a frequency in the range ν min <ν < ν max, where</text>
<formula><location><page_17><loc_35><loc_84><loc_92><loc_89></location>ν max = 1 -βµ min 1 -β ν 0 /similarequal ( 1 + Γ 2 x 2 ) ν 0 ( x , Γ /greatermuch 1) (68)</formula>
<text><location><page_17><loc_8><loc_82><loc_34><loc_84></location>and ν min = [(1 -β ) / (1 + β )] ν 0 ∼ ν 0 / 4 Γ 2 .</text>
<section_header_level_1><location><page_17><loc_38><loc_80><loc_62><loc_81></location>4.2. Spectrum in Jet Model I: Results</section_header_level_1>
<text><location><page_17><loc_8><loc_72><loc_92><loc_79></location>Figure 11 shows spectra for the case where matter and radiation field are initially locked together at Γ i = Γ eq , i = 10. The curves correspond to a variety of optical depths, as well as low and high initial photon fluxes, R i = 1 , 10 3 . The peak of the spectrum is somewhat broadened compared with a pure blackbody, and the segment shortward in frequency of the peak has a flattened spectrum, although not as flat as is seen in GRBs. A similar effect was seen in Paper I in the case of hot electromagnetic outflows accelerating along a radial, monopolar monopolar magnetic field. The spectrum below the peak is flattened even more if the</text>
<figure>
<location><page_17><loc_13><loc_15><loc_88><loc_70></location>
<caption>FIG. 11.- Spectra of photons emerging from a relativistic jet with a radial profile calculated by the method of Section 2, for various values of the optical depth at breakout τ es ∗ = 0 . 1 , 1 , 10 [equation (12)]. Black curves correspond to a monochromatic seed, green curves to a blackbody seed, red curves to a GRB-like seed spectrum, F ν = const × e -h ν / kT 0 [the lower-frequency half of the Band (1993) function extended to all frequencies]. Normalized photon energy flux at the inner radius ri = 0 . 8 r ∗ : R i = 1 (left), R i = 10 3 (right). Initial Lorentz factor Γ i = 10. Bulk frame of the radiation field Γ eq , i = 10, except for the dashed curves which correspond to Γ eq , i = Γ i / 2 = 5, τ es ∗ = 0 . 1.</caption>
</figure>
<text><location><page_18><loc_8><loc_88><loc_92><loc_92></location>radiation field emerging at the jet photosphere is broader than the matter Lorentz cone: the dashed curve in the R i = 1 panels is the result for Γ eq , i = Γ i / 2 = 5 and a low optical depth ( τ es ∗ = 0 . 1) at the breakout radius . As expected from the above argument, the peak of the spectrum is stretched upward in frequency above the peak of the seed spectrum.</text>
<section_header_level_1><location><page_18><loc_33><loc_85><loc_67><loc_86></location>4.3. Spectrum in Jet Model II (Trans-magnetosonic)</section_header_level_1>
<text><location><page_18><loc_8><loc_76><loc_92><loc_85></location>The output spectrum is calculated by a similar method to that described in Section 4.1. The background flow is prescribed, in this case by the solutions obtained in Section 3.6, and the flow is approximated as radial. Since we are not, now, following the outflow across its photosphere, and the entire simulation volume is assumed optically thin, we take a similar input photon distribution as was used to calculate the flow acceleration: the intensity is constant, I = I 0 for θ < θ j = 0 . 2 radian. The jet breakout radius is taken to be x ∗ = 3, as in Figure 9, and the radial optical depth ∆ τ res( xi = 2 , ∞ , µ = 1) = 1. Results are shown in Figures 12-13 for three different degrees of magnetic field flaring: strong [corresponding to δθ = 0 . 3 in equation (51)], intermediate ( δθ = 1), and weak ( δθ = 10). The high-energy extension of the spectrum becomes broader as the radiation compactness is</text>
<figure>
<location><page_18><loc_15><loc_49><loc_47><loc_73></location>
</figure>
<figure>
<location><page_18><loc_54><loc_49><loc_86><loc_73></location>
<caption>FIG. 12.- Photon spectrum emerging from a highly magnetized jet with radial profile given in Figure 9, corresponding to strong magnetic flaring [ δθ = 0 . 3 in equation (51)]. The radiation compactness χ ∗ = 1 , 10 3 , 10 5 at the breakout radius x ∗ = 3. (The spectra extend to higher frequency at a lower compactness.) The optical depth to radially moving photons is unity at the inner boundary x = 2. Black lines: monochromatic seed spectrum. Left Panel: black-body photon source (green lines). Right Panel: GRB-like seed spectrum, F ν = const × e -h ν / kT 0 . Dotted curves: source spectrum.</caption>
</figure>
<text><location><page_18><loc_8><loc_38><loc_92><loc_41></location>reduced: stronger radiation drag limits the increase in Γ above Γ eq. In the case of a monochromatic input spectrum, one notices the appearance of a few distinct orders of Compton scattering. The bumps in the spectrum are smoothed out when convolved with a blackbody source.</text>
<section_header_level_1><location><page_18><loc_46><loc_35><loc_54><loc_36></location>5. SUMMARY</section_header_level_1>
<text><location><page_18><loc_8><loc_28><loc_92><loc_35></location>We have examined the effect of intense radiation pressure on a cold, magnetized outflow with a jet geometry. The poloidal magnetic field lines are allowed to deviate from spherical symmetry, e.g. due to breakout from a confining medium. The outflow experiences a strong outward Lorentz force as a result, so that the magnetofluid and radiation field have a tendency to flow differentially outside the transparency surface. We have considered the combined dynamics of the magnetofluid and radiation, and as well as the modification to the radiation spectrum by multiple scattering.</text>
<text><location><page_18><loc_8><loc_21><loc_92><loc_28></location>We first considered the transition zone straddling the scattering photosphere. While the jet is still optically thick, its magnetization is suppressed by the inertia of the advected radiation. Outside the breakout point, the jet experiences a strong outward Lorentz force, which forces a rapid reduction in optical depth. This approach assumes that the fast critical surface lies deep in the jet, but calculates the radial flaring of the field lines self-consistently with a simple causal prescription, and calculates the interaction between the radiation and matter for arbitrary scattering depth.</text>
<text><location><page_18><loc_8><loc_15><loc_92><loc_21></location>If the jet is still optically thick at breakout, then the emergent spectrum is modestly broadened and hardened below the peak. On the other hand, breakout outside the transparency surface results in a photon beam that is significantly broader than the Lorentz cone of the accelerating jet, and therefore results in a more extended high-energy component to the spectrum. A stronger radiation field suppresses the accelerating effect of jet flaring and brings the spectrum closer to the original thermal input. Broadening of the photon beam could also be due to scattering by a shell of slower material entrained at the jet head (Thompson 2006).</text>
<text><location><page_18><loc_8><loc_7><loc_92><loc_15></location>Our second approach to the problem focuses on the zone outside the jet photosphere, but allows for large enough magnetization that the flow passes through the fast critical surface just outside the breakout radius. We then solve for the flow profile along magnetic flux surfaces, both inside and outside the critical point. In doing this, we choose a realistic angular distribution for the radiation field but prescribe a flaring profile for the poloidal field lines. The cross-field force balance is not solved selfconsistently, but we check that in all cases the transverse component of the radiation force is small compared with the transverse Lorentz force that is implied by the chosen field profiles.</text>
<figure>
<location><page_19><loc_15><loc_41><loc_86><loc_91></location>
<caption>FIG. 13.- Same as 12, but with δθ = 1 = 5 θ j (top), and δθ = 10 = 50 θ j (bottom).</caption>
</figure>
<text><location><page_19><loc_8><loc_23><loc_92><loc_30></location>As regards the longitudinal motion along magnetic flux surfaces, we define the critical compactness χ of the radiation field above which the matter and radiation are locked, and the Lorentz force is subdominant. For small jet flaring, the radiation force leads to an increase in terminal Lorentz factor at high values of χ , but can somewhat suppress the acceleration if the flaring is strong. The extent of the high-energy component of the spectrum is shown to depend in an interesting way on the degree of flaring and the position of the photosphere relative to the breakout radius.</text>
<text><location><page_19><loc_8><loc_7><loc_92><loc_23></location>Issues not addressed in this paper include the effects of multiple scattering at the magnetosonic critical surface, an ambient radiation field generated far outside the engine (e.g. Li et al. 1992a; Beskin et al. 2004), or the feedback of an intense radiation flow on the poloidal structure of the magnetic field. An effect specific to gamma-ray bursts involves the sidescattering of gammarays outside the forward shock, combined with the radiative acceleration of the pair-enriched material up to a Lorentz factor comparable to that of the relativistic ejecta (Thompson & Madau 2000; Beloborodov 2002). This delays the deceleration of the ejecta, and makes the medium ahead of the shock optically thick to scattering (Thompson 2006). Photons side-scattered through large angles would continue to interact with jet material at a smaller radius, creating pairs downstream of the forward shock, delaying the decoupling of the photons from the jet fluid, and generating a high-energy tail to the photon spectrum by bulk Comptonization. This means that the outermost shell of jet material (of a thickness ∼ θ 2 j r ∗ ) may avoid strong outward acceleration during jet breakout. However, jet material flowing at much greater distances back of the jet head sees weaker Compton drag and rates of pair creation during breakout. The slow forward shell becomes geometrically thin as it is pushed outward and, eventually, subject to a corrugation instability (Thompson 2006).</text>
<text><location><page_20><loc_10><loc_91><loc_39><loc_92></location>We thank the NSERC of Canada for support.</text>
<section_header_level_1><location><page_20><loc_47><loc_87><loc_53><loc_88></location>APPENDIX</section_header_level_1>
<section_header_level_1><location><page_20><loc_35><loc_85><loc_66><loc_86></location>GEOMETRYOF SCATTERING IN A NARROW JET</section_header_level_1>
<text><location><page_20><loc_8><loc_76><loc_92><loc_84></location>We now calculate the radiation force on plasma moving on a general trajectory within a thin jet of opening angle θ j /lessmuch 1, following the setup of Section 3.1. Our goal is to obtain an analytic expression for this force, which is possible by assuming a uniform intensity I = ∫ I ν d ν at the 'emission' surface (radius rs ), and taking this surface to be locally spherical. When considering the interaction with matter, this intensity distribution gives similar results to a radiation field that is locally isotropic in the relativistic frame of the emitting medium. (See the discussion in Section 3.1 and Section 3.3 of Paper I.) The result generalizes the simpler angular moment formalism used in Section 2 and presented in equation (24).</text>
<text><location><page_20><loc_8><loc_71><loc_92><loc_76></location>Photons are emitted from coordinates { θ γ , φ γ } within a patch of angular radius θ γ ≤ θ j , and scatter in the jet the position { x = r / rs > 1, θ f , φ f = 0}. The presence of an absorbing surface at the edge of the jet would change the radiation force at angles θ f > θ j . Given the uncertain nature of the medium outside the jet, we restrict the calculation of the force to angles < θ j . The photon trajectory is tilted with respect to the radial line passing through the scattering point, by an angle (Figure 14)</text>
<formula><location><page_20><loc_46><loc_67><loc_92><loc_70></location>θ γ , r = ( θ γ , r ) s x -1 . (A1)</formula>
<text><location><page_20><loc_8><loc_65><loc_11><loc_66></location>Here</text>
<text><location><page_20><loc_8><loc_60><loc_92><loc_63></location>is the corresponding angle measured on the 'emission' surface, and we have assumed that x -1 /greatermuch θ j in making the expansion in x . The intensity at the point of scattering can then be expressed as</text>
<formula><location><page_20><loc_38><loc_61><loc_92><loc_66></location>( θ γ , r ) s = ( θ 2 f + θ 2 γ -2 θ f θ γ cos φ γ ) 1 / 2 (A2)</formula>
<formula><location><page_20><loc_29><loc_55><loc_92><loc_60></location>I = ∫ d ν I ν = I 0 for θ γ , r < √ θ 2 f + θ 2 j -2 θ f θ j cos φ γ ( rs r -rs ) . (A3)</formula>
<figure>
<location><page_20><loc_33><loc_12><loc_67><loc_53></location>
<caption>FIG. 14.- Geometry of photon emission and scattering in a thin jet. The emission surface is a circular patch of radius θ j rs . We take the photon intensity to be independent of angle and uniform on this surface. Coordinates { θ γ , φ γ } label the point of emission, and θ γ , r is the angle cos -1 ( ˆ k · ˆ r ) at the point of scattering on a field line of polar angle { θ f , φ f = 0 } .</caption>
</figure>
<text><location><page_21><loc_8><loc_51><loc_11><loc_53></location>with</text>
<text><location><page_21><loc_10><loc_91><loc_50><loc_92></location>The unit wave vector in the local ( ˆ r , ˆ θ, ˆ φ ) coordinate system is</text>
<text><location><page_21><loc_8><loc_85><loc_27><loc_86></location>with the poloidal component</text>
<formula><location><page_21><loc_31><loc_85><loc_92><loc_91></location>ˆ k = ( kr , k θ , k φ ) = ( 1 -1 2 θ 2 γ , r , θ f -θ γ cos φ γ x -1 , -θ γ sin φ γ x -1 ) (A4)</formula>
<formula><location><page_21><loc_19><loc_78><loc_92><loc_84></location>kp = β r β p kr + β θ β p k θ = kr + ∆ θ Bk θ √ 1 + ∆ θ 2 B /similarequal 1 -1 2 ( θ f x -1 -∆ θ B ) 2 -θ 2 γ 2( x -1) 2 + θ γ x -1 ( θ f x -1 -∆ θ B ) cos φ γ (A5)</formula>
<text><location><page_21><loc_8><loc_77><loc_92><loc_79></location>where ∆ θ B = B θ / Br is the angle that a bending field line makes with the local radial vector. To evaluate the lab-frame radiation force (20) we relate the solid angle of incoming photons to the emission coordinates via</text>
<formula><location><page_21><loc_43><loc_73><loc_92><loc_76></location>d Ω = θ γ ( x -1) 2 d θ γ d φ γ . (A6)</formula>
<text><location><page_21><loc_8><loc_71><loc_67><loc_72></location>The poloidal and toroidal radiation force is then evaluated as follows. We begin by writing</text>
<formula><location><page_21><loc_40><loc_68><loc_92><loc_70></location>1 -β · ˆ k = A + B cos φ γ + C sin φ γ (A7)</formula>
<text><location><page_21><loc_8><loc_66><loc_41><loc_68></location>and express the components of the wave vector as</text>
<formula><location><page_21><loc_37><loc_64><loc_92><loc_66></location>ˆ β p , φ · ˆ k = Dp , φ + Ep , φ cos φ γ + Fp , φ sin φ γ . (A8)</formula>
<text><location><page_21><loc_8><loc_62><loc_52><loc_63></location>Integrating first over φ γ and then θ γ at the 'emission' surface gives</text>
<formula><location><page_21><loc_22><loc_56><loc_92><loc_62></location>F rad p , φ = σ T I c ( x -1) 2 ∫ θ j 0 d θ γ θ γ [ 2 π ADp , φ + π BEp , φ + π CFp , φ -β p , φ Γ 2 ( 2 π A 2 + π B 2 + π C 2 )] (A9)</formula>
<formula><location><page_21><loc_34><loc_53><loc_92><loc_57></location>= ¯ mc 2 rs χ ∗ ( x ∗ -1) 2 x ∗ ( x -1) 2 [ 1 2 Gp , φ + 1 4 θ 2 j Hp , φ + 1 6 θ 4 j Kp , φ ] (A10)</formula>
<formula><location><page_21><loc_28><loc_47><loc_92><loc_52></location>Gp /similarequal 2 ( 1 -β p )[ 1 -β p Γ 2 ( 1 -β p )] -1 2 β p ( 1 + β 2 p Γ 2 ) ( θ f x -1 -∆ θ B ) 4 (A11)</formula>
<formula><location><page_21><loc_36><loc_43><loc_92><loc_48></location>Hp /similarequal -β 3 p Γ 2 ( x -1) 2 [ 2 ( θ f x -1 -∆ θ B ) 2 + β 2 φ β 2 p ] (A12)</formula>
<formula><location><page_21><loc_41><loc_38><loc_92><loc_43></location>Kp = -β p 2( x -1) 4 ( 1 + β 2 p Γ 2 ) . (A13)</formula>
<formula><location><page_21><loc_28><loc_29><loc_92><loc_35></location>H φ = -β φ ( x -1) 2 [ 1 + Γ 2 ( 2 β p (1 -β p ) + β 2 φ ) + 2 β 2 p Γ 2 ( θ f x -1 -∆ θ B ) 2 ] (A15)</formula>
<formula><location><page_21><loc_24><loc_34><loc_92><loc_40></location>G φ = -2 β φ Γ 2 [ ( 1 -β p ) 2 + β p ( 1 -β p ) ( θ f x -1 -∆ θ B ) 2 + 1 4 β 2 p ( θ f x -1 -∆ θ B ) 4 ] (A14)</formula>
<formula><location><page_21><loc_45><loc_26><loc_92><loc_30></location>K φ = -β φ β 2 p Γ 2 2( x -1) 4 (A16)</formula>
<text><location><page_21><loc_8><loc_17><loc_92><loc_26></location>where Gp and Hp are accurate to first order in Γ -2 and ( θ/ x ) 2 . The equilibrium Lorentz factor of the photon field, the frame in which F rad vanishes, is found by solving Γ ' χ = 0 in (47). The results are shown in Figure 15 for the poloidal field line profile described in Sec. 3.2. At a radius x -1 /greatermuch θ j one finds Γ eq /similarequal x /θ j , with a coefficient of order unity that depends on the footprint angle and flaring profile. A thin jet defines a relativistic frame at relatively small distances from the 'emission' surface, as compared with a spherically symmetric outflow (for which Γ eq /similarequal 3 1 / 4 x ). Photons arriving at a scattering point from large angles provide relatively strong drag.</text>
<text><location><page_21><loc_8><loc_14><loc_92><loc_17></location>The jet fluid maintains rapid rotation around the light cylinder, θ f ∼ 1 / x ω , where the fluid flow is less aligned with the radiation field and Γ eq is reduced. Estimating β φ /similarequal 1 / x ωθ f (just outside the light cylinder), one finds</text>
<formula><location><page_21><loc_39><loc_9><loc_92><loc_14></location>Γ eq /similarequal ( θ 4 j 3( x -1) 4 + 1 x 4 ω 4 θ 4 f ) -1 4 , (A17)</formula>
<text><location><page_21><loc_8><loc_7><loc_17><loc_8></location>valid for all x .</text>
<figure>
<location><page_22><loc_30><loc_60><loc_71><loc_92></location>
<caption>FIG. 15.- Lorentz factor at which material in a thin jet ( θ j = 0 . 2) feels a vanishing radiation force F rad . Upper panel: Moderately flared magnetic field [ δθ = 1 in equation (51)], with black lines corresponding to different footprints at the breakout radius: θ f ∗ = 0 . 05 , 0 . 1 , 0 . 15 (solid, dotted and dashed). Lower panel: Different degrees of magnetic flaring, δθ = 10 , 1 , 0 . 3 (weak, medium, strong flaring) for a field line anchored at θ f ∗ = 0 . 1. Long-dashed red line: Γ eq for a spherical emission surface and monopolar poloidal field.</caption>
</figure>
<section_header_level_1><location><page_22><loc_33><loc_50><loc_68><loc_51></location>ACCOUNTINGFOR ROTATION OF THE PHOTON FIELD</section_header_level_1>
<text><location><page_22><loc_8><loc_47><loc_92><loc_50></location>The photon source rotates rapidly in some cases, e.g. a rapidly rotating star such as a millisecond magnetar, or the merged remnant of a white dwarf binary. We can approximate the effect of a rotating emission surface by setting</text>
<formula><location><page_22><loc_45><loc_43><loc_92><loc_46></location>β φ → β φ -β φ , R x θ f (B1)</formula>
<text><location><page_22><loc_8><loc_40><loc_92><loc_42></location>in equations (43). Here β φ , R is a constant representing the aberration of the outflowing photons at r = rs ( x = 1). In this situation, plasma near the emission surface can more easily co-rotate with the radiation field while still being accelerated outward.</text>
<text><location><page_22><loc_8><loc_34><loc_92><loc_40></location>The value of β φ , R depends on the type of source. One has β φ , R ∼ Ω rs / c ≡ ω when the photons flow from the surface of a star of radius rs through a transparent wind. On the other hand, if the outflow is optically thick in a narrow radial zone close to the engine, then one expects β φ , R ∼ ( Ω rs / c ) -1 ∼ ω -1 based on the conservation of angular momentum from the light cylinder out to the transparency surface ( x = 1).</text>
<section_header_level_1><location><page_22><loc_38><loc_32><loc_62><loc_33></location>WIND EQUATIONS FOR JET MODEL II</section_header_level_1>
<text><location><page_22><loc_8><loc_27><loc_92><loc_31></location>Here we derive the equations (46)-(50) for the longitudinal development of Lorentz factor and particle angular momentum along magnetic flux surfaces. Beginning with the poloidal and toroidal components of the Euler equation, (41) and (42), we expand the derivatives on the right hand side as</text>
<formula><location><page_22><loc_33><loc_22><loc_92><loc_27></location>∂ l ( r θ B φ ) = B φ ∂ l ( r θ f ) + r θ B φ Br ∂ l Br + r θ f Br ∂ l ( B φ Br ) . (C1)</formula>
<text><location><page_22><loc_8><loc_21><loc_66><loc_23></location>This can be evaluated using ∂ l ( r θ f ) /similarequal θ f + B θ / Br = θ f + ∆ θ B , equation (39) for ∂ l Br , and</text>
<text><location><page_22><loc_8><loc_15><loc_12><loc_16></location>where</text>
<formula><location><page_22><loc_30><loc_16><loc_92><loc_21></location>vr ∂ l ( B φ Br ) = ∂ l v φ ( 1 + v φ vr B φ Br ) -B φ Br ∂ l Γ vr Γ 3 -Ω f ( θ f + ∆ θ B ) , (C2)</formula>
<formula><location><page_22><loc_38><loc_11><loc_92><loc_16></location>∂ l v φ v φ = ∂ l L m L m -1 r ( 1 + ∆ θ B θ f ) -∂ l Γ Γ . (C3)</formula>
<text><location><page_22><loc_10><loc_10><loc_92><loc_11></location>The wind equations (41), (42) are now transformed into ordinary differential equations by ignoring the cross-field force balance:</text>
<formula><location><page_22><loc_18><loc_5><loc_92><loc_10></location>[ 1 -σ ( x θ f ω ) 2 Γ ( β φ Λ + 1 β r Γ 2 B φ Br ) B φ Br ] d Γ dl -1 x θ f [ β φ -σ ( x θ f ω ) 2 Γ B φ Br Λ ] d L m dl = σ Ψ ( x θ f ω ) 2 B φ Br + χ ∗ Rj ; (C4)</formula>
<text><location><page_23><loc_8><loc_87><loc_12><loc_88></location>where</text>
<formula><location><page_23><loc_90><loc_93><loc_92><loc_94></location>23</formula>
<formula><location><page_23><loc_23><loc_88><loc_92><loc_93></location>σ ( x θ f ω ) 2 Γ ( β φ Λ + 1 β r Γ 2 B φ Br ) d Γ dl + 1 x θ f [ β r -σ ( x θ f ω ) 2 Γ Λ ] d L m dl = -σ Ψ ( x θ f ω ) 2 + χ ∗ Pj , (C5)</formula>
<formula><location><page_23><loc_30><loc_83><loc_92><loc_88></location>Λ ≡ 1 + β φ β r B φ Br ; Ψ ≡ ( 1 + ∆ θ B θ f ) (1 + Λ ) β φ x + B φ Br β r A dA dl . (C6)</formula>
<text><location><page_23><loc_8><loc_81><loc_92><loc_83></location>Two simple tests of these equations are made possible by neglecting the radiation force. The energy and angular momentum integrals (38) are now related by</text>
<formula><location><page_23><loc_45><loc_78><loc_92><loc_81></location>d Γ dl -ω d L m dl = 0 . (C7)</formula>
<text><location><page_23><loc_8><loc_73><loc_92><loc_77></location>This equation is recovered by summing (C4) and B φ / Br times (C5), and making use of Ferraro's law (4). Second, outside the fast point the inertia of the magnetofluid is dominated by the matter: the coefficient of d Γ / dl in equation (C4) is /similarequal 1 -σ/ Γ 3 and approaches unity. Since in addition β φ → 0, the term involving L m can be neglected and one finds</text>
<formula><location><page_23><loc_41><loc_69><loc_92><loc_72></location>d Γ dl /similarequal σ ∗ A 2 dA dl ( Γ 3 /greatermuch σ ) . (C8)</formula>
<text><location><page_23><loc_8><loc_67><loc_59><loc_69></location>The same result can be obtained from the integral equations (8), (38) and (39),</text>
<text><location><page_23><loc_8><loc_63><loc_60><loc_64></location>Equation (46) is then obtained by solving (C4) and (C5) for d Γ / dl and d L m / dl .</text>
<formula><location><page_23><loc_43><loc_63><loc_92><loc_67></location>Γ = Γ ∗ + σ ∗ ( 1 -A -1 ) . (C9)</formula>
<section_header_level_1><location><page_23><loc_43><loc_61><loc_58><loc_61></location>CROSS-FIELD FORCES</section_header_level_1>
<text><location><page_23><loc_8><loc_56><loc_92><loc_60></location>Though we ignore the cross-field force balance, it is useful to estimate the transverse radiation force and compare it with the Lorentz force that is implied by a given field-line profile. Our procedure becomes inconsistent if the transverse radiation force dominates, because the radiation field will then comb out the field lines in the radial direction.</text>
<text><location><page_23><loc_10><loc_55><loc_47><loc_56></location>The polar component of equation (20) gives the estimate,</text>
<formula><location><page_23><loc_35><loc_50><loc_92><loc_54></location>F rad θ /similarequal ¯ mc 2 rs χ ∗ ( x ∗ -1) 2 2 x ∗ ( x -1) 2 Γ 2 ( θ f x -1 -1 2 ∆ θ B ) . (D1)</formula>
<text><location><page_23><loc_8><loc_46><loc_92><loc_50></location>The first term on the right-hand side represents the force imparted by photons streaming from a finite polar cap toward particles on off-axis field lines. The second represents the drag imparted as the poloidal particle flow bends across the radiation field. The cross-field Lorentz force is given by</text>
<formula><location><page_23><loc_36><loc_42><loc_92><loc_46></location>¯ m 4 πρ [( ∇ × B ) × B ] θ /similarequal ¯ mB 2 φ 4 πρ r θ f = ¯ mc 2 σ r θ f . (D2)</formula>
<text><location><page_23><loc_8><loc_40><loc_85><loc_41></location>Requiring this to be greater than (D1) gives an upper bound on the radiation compactness at jet breakout ( x > x ∗ /greatermuch 1),</text>
<formula><location><page_23><loc_41><loc_35><loc_92><loc_40></location>χ ∗ σ < 2 x Γ 2 x ∗ θ f ( θ f x -∆ θ B 2 ) -1 . (D3)</formula>
<text><location><page_23><loc_8><loc_32><loc_92><loc_35></location>Our calculations can admit values of χ ∗ as large as ∼ 10 4 σ without any inconsistency, given the typical jet parameters θ j ∼ 0 . 2, x ∗ ∼ 3, Γ > Γ ∗ ∼ 10.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "We consider the interaction between radiation, matter and a magnetic field in a compact, relativistic jet. The entrained matter accelerates outward as the jet breaks out of a star or other confining medium. In some circumstances, such as gamma-ray bursts (GRBs), the magnetization of the jet is greatly reduced by an advected radiation field while the jet is optically thick to scattering. Where magnetic flux surfaces diverge rapidly, a strong outward Lorentz force develops and radiation and matter begin to decouple. The increase in magnetization is coupled to a rapid growth in Lorentz factor. We take two approaches to this problem. The first examines the flow outside the fast magnetosonic critical surface, and calculates the flow speed and the angular distribution of the radiation field over a range of scattering depths. The second considers the flow structure on both sides of the critical surface in the optically thin regime, using a relaxation method. In both approaches, we find how the terminal Lorentz factor, and radial profile of the outflow, depend on the radiation intensity and optical depth at breakout. The effect of bulk Compton scattering on the radiation spectrum is calculated by a Monte Carlo method, while neglecting the effects of internal dissipation. The peak of the scattered spectrum sits near the seed peak if radiation pressure dominates the acceleration, but is pushed to a higher frequency if the Lorentz force dominates, and especially if the seed photon cone is broadened by interaction with a slower component of the outflow. Subject headings: MHD-plasmas - radiative transfer - scattering - gamma rays: stars",
"pages": [
1
]
},
{
"title": "MATTHEW RUSSO",
"content": "Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7, Canada.",
"pages": [
1
]
},
{
"title": "CHRISTOPHER THOMPSON",
"content": "Canadian Institute for Theoretical Astrophysics, 60 St. George St., Toronto, ON M5S 3H8, Canada. Submitted to The Astrophysical Journal",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Gamma-ray bursts involve collimated, relativistic outflows, as deduced from their rapid variability, extreme apparent energies (which can exceed the binding energy of a neutron star: Kulkarni et al. 1999; Amati et al. 2002), and the expected presence of non-relativistic material surrounding the engine. The jet is heated as it works through this denser material, which may represent a stellar envelope (Woosley 1993; Paczynski 1998), or neutron-rich debris from a binary neutron star merger (e.g. Dessart et al. 2009). As a result, a nearly blackbody radiation field may carry a significant fraction of the energy flux near the point of breakout. We focus here on strongly magnetized jets that are driven outward by a combination of the Lorentz force, and the force of radiation scattering off ionized matter. The acceleration of such a 'hot electromagnetic outflow' (Thompson 1994; Meszaros & Rees 1997; Drenkhahn & Spruit 2002; Thompson 2006; Giannios & Spruit 2007; Zhang & Yan 2011), in which radiation pressure dominates matter pressure, has been treated quantitatively in Russo & Thompson (2012) (Paper I) in the approximation that the poloidal magnetic field lines threading the outflow are radial and monopolar. The radiation field is self-collimating outside the scattering photosphere, but may continue to interact with slower material that it entrained by the jet. In Paper I, the outflow was followed both inside and outside the fast magnetosonic critical point. The radiation force is especially important outside the fast point: even where the kinetic energy flux of the entrained charged particles is small compared with the magnetic Poynting flux, they provide an efficient couple between magnetic field and radiation. The relative influence of the two stresses on the asymptotic Lorentz factor depends on the radiation compactness. Generally, the importance of radiation pressure is enhanced by bulk relativistic motion at the photosphere. In this paper we generalize the calculation of Paper I to include non-spherical effects. A magnetized outflow experiences a strong Lorentz force where poloidal flux surfaces in the jet diverge from each other faster than in a monopolar geometry (Camenzind 1987; Li et al. 1992b; Begelman & Li 1994; Vlahakis & Königl 2003a,b; Beskin & Nokhrina 2006; Tchekhovskoy et al. 2009). In particular, a magnetized jet accelerates rapidly when it breaks out of the confining material (Tchekhovskoy et al. 2010). The simulations in that paper demonstrated the effect for a cold magnetohydrodynamic (MHD) outflow, but did not include the effects of radiation pressure and drag. The magnetization of a hot electromagnetic outflow remains modest inside its scattering photosphere, where the radiation is tied to the matter, and the radiation enthalpy contributes to the inertia. Our first task in this paper is, therefore, to examine how the radiation field begins to decouple from the matter when the jet material breaks out. We define a bulk frame in which the radiation force vanishes, by taking angular moments of the radiation field, and then track the proportions of the energy flux carried by matter, radiation, and magnetic field, at both large and small optical depths. Given the flow profile so obtained, the radiation spectrum is calculated by a Monte Carlo method. Here we focus on the effects of bulk Compton scattering, which provide a direct probe of the outflow dynamics. We neglect the effects of internal dissipation by various process such as MHD wave damping, magnetic reconnection, or shocks. The second principal goal of this paper is to obtain the longitudinal motion along a magnetic flux surface, taking into account both the radiation force and the singularity in the flow equations which appears at the fast point. Our focus here is on the zone near and outside the transparency surface; previous efforts to calculate the effect of pressure gradient forces on relativistic outflows (e.g. Vlahakis & Königl 2003b) have focused on the optically thin regime. We argued in Paper I that the effect of a magnetic pressure gradient driven by internal reconnection (Drenkhahn & Spruit 2002) has been overestimated, because it neglects the addition to the outflow inertia from particle heating and a strong non-radial magnetic field. Coupled wind equations for the matter Lorentz factor and angular momentum are derived in an arbitrary poloidal field geometry, restricted to the case of small angles near the rotational axis, but allowing for arbitrary relative flaring of the flux surfaces. The fast point generally sits close to the breakout surface of the jet. Our main simplification of the problem is to impose a particular shape for the poloidal flux surfaces, and not to solve self-consistently for the cross-field force balance. Two constraints are applied to the imposed magnetic field profile: that the rate of flaring is causal, and that the transverse component of the radiation force is at most a perturbation to the transverse Lorentz force. The plan of this paper is as follows. Section 2 reviews the acceleration of a relativistic MHD outflow driven by the differential flaring of magnetic flux surfaces, and considers the radiation transfer equation in the limit of small angles. Equations are derived for the acceleration of a steady MHD outflow outside its fast point, in combination with the radial evolution of the magnetization, radiation energy flux, scattering depth, and the frame in which the radiation force vanishes. These equations are solved in particular cases relevant to GRB jets. Section 3 presents a simple model of a spreading thin jet outside its photosphere, and derives the corresponding steady flow equations for arbitrary radiation force and magnetization. The effect of radiation pressure on the fast point is considered analytically, and numerical solutions for the flow both inside and outside the fast point are presented. Section 4 describes Monte Carlo calculations of the emerging radiation spectrum in both the causal jet model of Section 2, and the optically thin model of Section 3. Section 5 summarizes our results. The Appendix presents a derivation of the radiation force in a thin, transparent jet.",
"pages": [
1,
2
]
},
{
"title": "2. FLARING, HOT MAGNETIZED JET: TRANSITION TO LOW OPTICAL DEPTH (MODEL I).",
"content": "We consider a stationary, axisymmetric outflow of perfectly conducting material that is tied to a very strong magnetic field. The outflow is also a strong source of radiation, which scatters off the advected light particles (electrons as well as positrons). Matter pressure gradients are neglected in comparison with inertial and Lorentz forces as well as the radiation force. We start by considering the exchange of energy between different components of the outflow. Deviations from radial motion are assumed to be small compared with the angular width of the photon beam: that is, the interaction between matter and radiation is calculated assuming radial matter motion, but allowance is made for strong radial Lorentz forces driven by a small amount of magnetic field line flaring. The beam angular width is set, more or less, by the Lorentz factor of the outflow at its transparency surface. Here allowance is made for a finite optical depth of the magnetofluid. By taking angular moments of the radiation field, we track the difference between the Lorentz factor of the matter, and of the frame in which the radiation force vanishes, as the matter is accelerated by a strong Lorentz force. This approach is suited to a single-component magnetofluid, but also allows for the presence of a second, slower component that scatters the radiation field into a broader cone, and plausibly is present in GRBs (Paper I). Given the complications introduced by a finite optical depth, we now consider only supermagnetosonic outflows. In a second approach (Section 3), we account for non-radial matter motion and follow the flow across the fast critical surface, but restrict the calculation to low optical depth. The geometry of the model is shown in Figure 6. After being launched by the central engine (with angular frequency Ω ) the flow enters the jet zone along the rotation axis. We ignore the details of the acceleration while the jet is still very optically thick, and laterally confined. Our calculation begins a short distance inside breakout (at radius r ∗ ), by which point the flow is assumed to be supermagnetosonic. Outside breakout, transverse pressure support effectively vanishes and field lines begin to diverge differentially. The outward Lorentz force increases dramatically over a narrow range of radius, until a loss of causal contact across the jet forces the flow lines to straighten out, and the acceleration is cut off. Although the scattering photosphere could, in principal, sit anywhere in the outflow, breakout is associated with a large drop in optical depth. In our calculations, the photosphere therefore usually sits just outside breakout. Low optical depth at breakout does produce an interesting imprint of bulk Compton scattering on the emergent spectrum (Section 4).",
"pages": [
2,
3
]
},
{
"title": "2.1. Exchange of Energy between Radiation and Magnetofluid",
"content": "We consider the flow along a poloidal magnetic field line θ f ( r ), starting at a large enough radius that the streamline sits well outside the light cylinder of the central engine. Deviations from radial motion are neglected, except in so far that they influence the radial Lorentz force. Then the outflow has a fixed total luminosity per sterad, including contributions from matter, magnetic field, and radiation, Here is the kinetic energy flux of material of proper density ρ , poloidal (radial) speed vp , and Lorentz factor Γ . The poloidal Poynting flux is expressed in terms of the electric and magnetic vectors E , B by Substituting E = -v × B / c into the induction equation gives ∂ B /∂ t = ∇ × ( v × B ), where v is the fluid velocity. The steady solution to this equation involves the pattern angular velocity Ω f of the magnetic field, which is constant along a poloidal flux surface. It relates the toroidal components of B and v via Substituting this into (3) gives Far outside the light cylinder, the outflow rotates slowly and the magnetic field is predominantly toroidal: v φ /lessmuch vp /similarequal c and | B φ | /greatermuch | Bp | . Hence It is useful to normalize all components of the energy flux to the poloidal mass flux, which is conserved along a poloidal flux surface in a steady MHD wind, d ˙ M / d Φ p = Γ ρ vp / Bp = const. Assuming further that Γ /greatermuch 1, the magnetization becomes ∣ The radius r ∗ and the label ∗ denote a position in the jet where the confining medium changes rapidly, e.g. the jet moves beyond the photosphere of a Wolf-Rayet star. (We will distinguish this from an inner boundary ri for the jet integration, which typically is set just interior to the breakout radius.) Taking r ∗ /greatermuch c / Ω f , σ ∗ σ ( r sin θ ( r sin θ f f ) ) 2 2 ∗ Bp ∗ Bp (Note that our definition of σ differs by a factor Γ from the one used by Tchekhovskoy et al. 2009 in a similar derivation.) Defining the normalized photon luminosity by = . (8) the equation of energy conservation (1) can be written Note that R is related to the photon compactness and the scattering depth measured outward from radius r by where σ T is the Thomson cross section and ¯ m is the material inertia per scattering charge. The coefficient here depends on the acceleration of the outflow, as can be seen from the expression for the optical depth of a (radially moving) photon [see equation (26) for notation]. The coefficient is ∼ 2 when the Lorentz factor is constant and reaches ∼ 6 for a linear growth, Γ ∝ r .",
"pages": [
3,
4
]
},
{
"title": "2.2. Importance of Radiative Driving in Outflows with a Relativistically Moving Photosphere",
"content": "Jets of a high magnetization can encounter a scattering photosphere not too far outside breakout from a confining medium such as a Wolf-Rayet envelope or or neutron-rich debris cloud. Let us take a fiducial luminosity 4 π dL γ / d Ω = 10 51 L 51 erg s -1 and a deconfinement radius r ∗ = 10 10 r ∗ , 10 cm. The corresponding compactness (11) is χ ∗ = 1 × 10 8 L 51 r -1 ∗ , 10 ( mp / ¯ m ). Since the Lorentz factor increases rapidly after breakout due to MHD stresses, we fix r and then consider the condition for a photosphere to emerge at a radius r τ /greaterorsimilar r ∗ . This corresponds to Γ 2 ( r τ ) R ( r τ ) ∼ 10 7 ( mp / ¯ m ). For example, if the jet is hot and strongly magnetized, R∼ σ ∼ 10 5 , and pairs have largely annihilated within the bulk of the jet material, then the photosphere emerges at Γ ( r τ ) ∼ 10. The radiation field is capable of driving a light baryonic outflow to a terminal Lorentz factor (see Section 2 of Paper I), Moderately relativistic motion at the photosphere enhances Γ ∞ and, as we now motivate, a larger radiation compactness. When the Lorentz force is taken into account self-consistently, Γ ∞ can be greater or smaller than (13), as we detail in this paper. An upper limit on the photon compactness is derived by demanding that the fluid be optically thin at breakout, τ es( r ∗ ) ≤ 1. Then the photosphere sits at r τ < r ∗ , and the compactness (11) at breakout is Hence Γ ∞ ∝ Γ ( r τ ) 3 / 4 in a jet of a fixed R . The radiation flux at breakout is below the Poynting flux if In Figure 2 we relate the compactness, magnetization and optical depth at breakout for different ratios of Poynting to radiation flux. The aforementioned hot jet moving at Γ ( r τ ) ∼ 10 at its photosphere, with a magnetization σ ∼ R ∼ 10 5 , can be pushed by radiation pressure up to a terminal Lorentz factor Γ ∞ ∼ (1 × 10 9 ) 0 . 25 ∼ 200. More relativistic material accelerated by the Lorentz force will, alternatively, feel a retarding force from the radiation field.",
"pages": [
4,
5
]
},
{
"title": "2.3. Cold MHD Flow without Radiation Pressure",
"content": "To begin, we review the case where photons are absent, and assume a thin jet in which the magnetic field lines have poloidal angle θ f /lessmuch 1. Only a small differential bending of the field lines is needed to push a cold magnetofluid to large Γ : their polar angle must deviate from conical geometry by δθ f /θ f ∼ Γ /σ . A basic constraint on the rate of bending is obtained if the transverse component of the Lorentz force in the matter rest frame is limited to The prime ' denotes the rest frame, in which r / Γ is a characteristic causal distance, and β ≡ v / c . Then so that typically δθ f ∼ 1 / Γ . This is seen in the dynamic cold MHD calculations of Tchekhovskoy et al. (2009), where strong Lorentz forces are generated in a narrow fan near the jet edge. Conservation of magnetic flux implies that Bpr 2 θ f d θ f = const. Hence, writing θ f = θ f ( r ∗ ) + δθ f ≡ θ f ∗ + δθ f , equation (8) becomes The change in the ratio of Poynting and mass fluxes can then be written The envelope function K ( θ f ) ∼ 1 away from the jet axis, and vanishes on the axis given the assumption of axisymmetry.",
"pages": [
5
]
},
{
"title": "2.4. Radiation Force",
"content": "Given the relativistic motion of the matter, the radiation field can be assumed to interact with it via Thomson scattering. In a frame where the matter moves with velocity β c , and a photon has wave vector k = k ˆ k , a scattering charge feels a force Here I ( µ ) = ∫ d ν I ν is the spectral intensity integrated over frequency, and µ is the direction cosine µ = cos( θ ) = ˆ k · ˆ r . It is useful to define angular moments of I , so that for a narrow beam, ∆ µ /similarequal 1 2 θ 2 /lessmuch 1, the radiation energy flux is approximately equal to F 0 = R Γ ρ c 3 . We may define a frame moving at Lorentz factor Γ eq (speed β eq) in which the radiation field is nearly isotropic and the radiation force vanishes. Defining the bulk frame radiation energy density by u ' , one has Substituting this into (21) yields the relations Expanding the radiation force (20) in ∆ µ gives The main approximation here is that each field line experiences a small differential bending, so that the bending angle is small compared with (2 ∆ µ ) 1 / 2 . This is consistent with rapid acceleration by the Lorentz force near the jet edge (Tchekhovskoy et al. 2010), e.g. δθ f ∼ θ j -θ f /lessmuch θ f . In the context of GRBs, we can also assume that the flow has propagated far outside the light cylinder, so that β φ /lessmuch 1 and the toroidal radiation force can be neglected.",
"pages": [
5,
6
]
},
{
"title": "2.5. Transfer of a Narrow Photon Beam Near a Relativistic Photosphere",
"content": "We work with the transfer equation in the inertial frame into which the outflow is expanding; a prime denotes the matter rest frame. The radiation transfer equation is written (e.g. Mihalas 1978) where is the grey scattering opacity, and is the source function in the isotropic scattering approximation. The Doppler relation between unscattered and scattered photon frequencies is ˜ ν (1 -β ˜ µ ) = ν (1 -βµ ), and I ' ν = [ Γ (1 -βµ )] 3 I ν ; d Ω ' = 2 π d µ ' = 2 π d µ [ Γ (1 -βµ )] 2 (28) are the usual transformations. Integrating over frequency gives Setting ∆ µ → 0, the path length is ds = dr /µ /similarequal dr , and one has d ∆ µ/ dr /similarequal -2 ∆ µ/ r . Making use of gives and where we have set β → 1 in the coefficient. These two equations, in combination with (23), allow us to evolve Γ eq near the scattering photosphere. The radial evolution of Γ and R is obtained by differentiating (10), substituting (19) and (31), and expressing the radiation energy flux in terms of R ,",
"pages": [
6
]
},
{
"title": "2.6. Numerical Results",
"content": "Profiles are obtained for Γ ( x ), Γ eq( x ), R ( x ) and θ f ( x ) by integrating in the radial dimension. We have made the substitutions d / d θ f → δθ -1 gradient and K = θ f ∗ /θ j in (33). This choice forces the field-line bending to zero near the center of the jet. The gradient angle δθ gradient is of the order of θ j , but may be smaller near the edge of the jet as it emerges from a confining medium. For example, the strong acceleration seen near the jet edge in the simulations of Tchekhovskoy et al. (2010) is consistent with δθ gradient ∼ γ -1 ∼ 0 . 1 θ j ; it would presumably be reduced if the jet did not have a sharp edge. In our fiducial model we consider a field line anchored at θ f ∗ = 0 . 1, and take the jet opening half-angle to be θ j = 0 . 2. To illustrate the effect of jet breakout on the flow parameters, we begin the integration just inside the breakout radius, ri = 0 . 8 r ∗ . In our first set of integrations, the scattering optical depth is chosen to be large at the breakout radius. At this point, the radiation is still tied to the matter, Γ eq( r ∗ ) = Γ ( r ∗ ), but the rapid MHD acceleration experienced by the flaring jet quickly forces a transition to low τ es. The optical depth for a photon propagating radially from r = r ∗ is given by equation (12), and is thus unknown a priori . To impose a particular value of τ es( r ∗ ), we first choose an approximate value of α es ∗ , evolve the equations of motion and then iterate. The Lorentz force term in d Γ / dr is only valid outside the fast magnetosonic critical point, and so we take Γ ( ri ) /greaterorsimilar Γ c /similarequal σ 1 / 3 ∗ . Radial integrations are done using a 5th-order Runge-Kutta algorithm with adaptive step size (see Sections 7.3, 7.5 of Kiusalaas 2010). Results are plotted in Figure 3 for an outflow with magnetization σ i = σ ∗ = 1000, and both low and high radiation fluxes ( R i = 1 , 1000) at the inner boundary. The action of the Lorentz force is concentrated at a small radius where the flaring is most severe, causing an increase in Γ that is initially much faster than linear. When the radiation energy flux is weak compared with the magnetic Poynting flux, the outflow experiences strong but logarithmic acceleration after breakout with Γ ∝ ln 1 / 2 x , a direct consequence of causally limited flaring, δθ f ∼ 1 / Γ [equation (33)]. While the optical depth is large, the photon field is advected with the plasma, remaining nearly isotropic in the comoving frame. Once the optical depth falls below unity the photon field decouples and is free to self-collimate, so that Γ eq ∝ x . High radiation fluxes ( R∼ σ ) force the flow back to the shallower profile Γ /similarequal Γ eq, even while the magnetic flaring grows stronger (1 / Γ is larger). The acceleration zone is therefore widened in the radial direction compared with the radiation-free jet. Quite generally, we find that the terminal Lorentz factor is insensitive to the initial radiation energy flux. The growth in radiation energy flux outside the photosphere is therefore largely compensated by a further reduction in outflow magnetization. We also consider a low scattering depth at the breakout radius. In this case the matter is only weakly coupled to the radiation field, and the Lorentz factor is forced well above Γ eq a small distance outside the breakout radius (Figure 4). As in the case of higher optical depths, high radiation fluxes limit the growth of Γ and force it toward Γ eq. But the mismatch between Γ and Γ eq remains unless R /greaterorsimilar σ . Energy is transferred from the magnetic field to the photons, resulting in a significantly modified spectrum (Section 4). Faster jet flaring, corresponding to a jet edge with δθ gradient = 0 . 5 θ j , produces faster acceleration and terminal Lorentz factors closer to σ ∗ , but otherwise qualitatively similar behavior (Figure 5). A novel effect becomes clear when the compactness is large: the magnetization can show a significant reduction, dropping significantly below R and even Γ , and therefore resulting in a weakly magnetized outflow. This is caused by the strong radiation drag at small radius, which restricts the growth of Γ which allows for stronger jet flaring.",
"pages": [
6,
8
]
},
{
"title": "3. FLARING, HOT MAGNETIZED JET: TRANSPARENT FLOW",
"content": "ACROSS THE FAST CRITICAL SURFACE (MODEL II) The dynamics of the outflow can be calculated more precisely in the optically thin regime, where the radiation field is prescribed at an emitting surface (radius rs ) and passively collimates outside that surface. This allows us to study the critical point structure of the flow, at the price of neglecting the effects of multiple scattering. In the spherical case, the emission surface could, if one wanted, be identified with the physical surface of a star. But the model of a passively collimating photon field can also be applied to outflows that are already relativistic at the photosphere, including those with a jet geometry. In this section, we solve the wind equations for a steady, flaring jet which is optically thin but sub-magnetosonic at breakout. In contrast to the model presented in Section 2, here we prescribe the flaring profile in advance. The flow geometry is shown in Figure 6. The photon source radius sits in the confined portion of the jet, inside the breakout radius r ∗ . After breakout, the optically thin flow is accelerated though the magnetosonic surface, whose location and shape are calculated self consistently (analytic approximations to the position of the critical surface can be found in Section 3.5). We follow the flow along a field line θ f ( r ), situated well outside the light cylinder, from just outside the source radius. Our solution to the flow below the breakout point formally is in the optically thin regime. Because the jet has already typically attained relativistic motion before breaking out, we can view the photon emission as arising from a virtual surface located below the physical photosphere, at a radius rs , eff ∼ r τ / Γ ( r τ ). At a high radiation intensity, the matter is locked into the bulk frame defined by the photon field, Γ /similarequal Γ eq ∼ ( r -rs ) / ( θ jrs ), around breakout. This means that the flow profile closely mimics an optically thick, radiation-dominated flow inside breakout, and we expect that our flow solutions should adequately represent the dynamics of a jet which encounters a photosphere at a radius r ∗ ∼ r τ > rs . Our procedure is first to choose the poloidal field geometry and radiation profile, and then evolve the energy and angular momentum along the poloidal flux surfaces. A simple description of the photon field is possible when the jet geometry is locally spherical - that is, when the streamlines are conical inside breakout. This constrains the non-radial Lorentz force to vanish at r < r ∗ , which in the small-angle limit can be written as A jet with such a line current profile will de-collimate at r > r ∗ , as the external pressure is removed. This decollimation leads to rapid outward acceleration of the cold matter entrained in the jet, even in the absence of radiative forcing. Other jet profiles are easily constructed and may be more natural: in the cold MHD jet calculation of Tchekhovskoy et al. (2010), the confining surface has a parabolic structure inside breakout, transitioning to a conical geometry outside. Nonetheless, the radial Lorentz factor profiles that we obtain are (in the absence of radiation) very similar to those of Tchekhovskoy et al. (2010), and only depend on the magnitude of the differential flaring between magnetic flux surfaces. We focus on the local dynamics within magnetic flux surfaces, taking into account the effect of radiation pressure. This longitudinal dynamics is sensitive to the relative flaring rates of neighboring flux surfaces, but not to the global profile of Poynting flux transverse to the jet axis. Although the transverse force balance is not explicitly taken into account, we do check that i) the degree of magnetic flaring is consistent with causal stresses; and ii) that the transverse component of the radiation force is weak compared with the transverse Lorentz force (so that the radiation flow is not strong enough to comb out the field lines into a conical geometry: see Appendix D).",
"pages": [
9,
10
]
},
{
"title": "3.1. Jet Properties",
"content": "To construct an optically thin radiation field, we consider the simplest case of uniform intensity I = ∫ I ν d ν at the emission radius rs , as we did in Paper I, but now restrict the sampling of the radiation field to polar angles θ < θ j . The emission patch covers a small angular disk of area π ( θ jrs ) 2 (Figure 6), and the luminosity per sterad is dL γ ∗ / d Ω ∼ πθ 2 j I . This allows an analytic calculation of the radiation force acting on a particle of arbitrary Lorentz factor and direction, which is presented in Appendix A. This result generalizes the simpler angular moment formalism used in Section 2 and presented in equation (24). We showed in Paper I that if we normalize the photon intensity and the angular width of the photon beam by fixing i) the radiation force and ii) the relativistic frame Γ eq in which this force vanishes, then other quantities, such as the mean power radiated by an electron in its bulk frame, are nearly identical to those obtained from a radiation field that is isotropic at a relativistically moving photosphere. The radiation streams freely outward at r > rs , and its cone contracts with increasing radius. The size and orientation of this cone now vary with distance from the jet axis (in contrast with the case of a spherical emission surface; Paper I). There is generally a misalignment of the direction of peak radiation intensity with respect to both the radial direction, and the local flow direction. The alignment is strongest at a small but finite distance from the rotation axis, and produces a peak in the radiation force there. 1 We normalize distances to rs , but measure the photon compactness (11) at the breakout radius, In a GRB outflow, the photosphere generally lies outside the light cylinder of the rotating engine, so we take ω = Ω f rs / c > 1 in our calculations. In this context, the magnetization can be most simply defined as 2 Neglecting the radiation field, the energy and angular momentum per unit rest mass are given by and in a steady MHD outflow are conserved along field lines. They can be written in a dimensionless form,",
"pages": [
10
]
},
{
"title": "3.2. Poloidal Field Configuration",
"content": "To incorporate a strong radial Lorentz force into the outflow, we choose the poloidal flux surfaces by fixing the function θ f ( x , θ f ∗ ), where θ f ∗ is the polar angle at the breakout radius. The Lorentz force is large and positive if neighboring flux surfaces diverge from each other more rapidly than in a monopolar geometry. The effect of this differential expansion appears in the wind equations via the function We focus on the dynamics along a single flux surface, and so do not have to consider the angular dependence of Br ∗ = Br ( r ∗ ). The critical point structure of the longitudinal flow is insensitive to angular gradients in the flow magnetization. The flaring profile used in our calculations is described in Section 3.4, followed by the numerical results.",
"pages": [
10
]
},
{
"title": "3.3. Longitudinal Wind Equations",
"content": "We now consider the longitudinal evolution of the outflow variables along a magnetic flux surface. A radiation force (20) is added to the Euler equation, which becomes Taking the dot product of equation (40) with the unit poloidal field vector ˆ B p, defining the longitudinal derivative ∂ l = ˆ Bp · ∇ , and taking the small-angle limit, we have The φ -component of equation (40) is Here L m is the specific matter angular momentum [equation (38)], and we have made use of the fact that the poloidal flow velocity v p is aligned with B p . The Coulomb force only contributes to the transverse force balance and does not appear in equations (41) or (42). Both of these features are easily derived by noting that the toroidal electric field vanishes in a steady, axisymmetric MHD wind ( E · B = 0), which implies that v p × B p = 0 and E p · B p = 0. In Appendix A we calculate the radiation force (20) in a thin jet, and express the poloidal and toroidal components in terms of dimensionless functions Rj , Pj , Rotation of the photon field at the emission surface tends to reduce the azimuthal drag. It can be incorporated by modifying the β φ -dependence of equations (43), as is discussed in Appendix B, but is generally negligible when the outflow lies far outside the light cylinder ( ω /greatermuch 1). A good approximation to the poloidal force can be obtained on field lines ( x ω ) -1 /lessmuch θ f /lessmuch θ j , in agreement with equation (24). The result for a spherical emission surface (Paper I) differs only in the absence of the factor θ 4 j . The vanishing of the radiation force occurs at a significantly higher Lorentz factor when the photon beam is collimated, up to a numerical factor of order unity as shown in Figure 15. The deviation of the field lines from a purely radial direction is measured by ∆ θ B = B θ / Br , which we take to be small, so that Bp = (1 + ∆ θ 2 B ) 1 / 2 Br /similarequal Br , vp /similarequal vr . As is detailed in Appendix C, the derivatives along field lines on the right hand side of equations (41) and (42) can be written in the small-angle approximation. Ignoring the cross-field force balance then allows us to express (41), (42) as two ordinary differential equations, which can be re-written in terms of d Γ / dl and d L m / dl . The various terms on the right-hand side of these equations can be separated into purely magnetocentrifugal pieces (which do not depend on the radiation force), the direct radiation force, and a cross term: where where and is the effective inertia.",
"pages": [
10,
11
]
},
{
"title": "3.4. Poloidal Field Profile",
"content": "We now prescribe the poloidal field profile outside the breakout surface, which, in a steady jet, also determines the poloidal streamlines. The profile inside r ∗ is assumed to be straight and conical, θ f ∗ = θ f , s . A strong Lorentz force is obtained outside r ∗ if the net change θ f , ∞ -θ f ∗ in polar angle is itself a growing function of θ f ∗ . A simple choice, that is asymptotically conical at a large radius, is This connects smoothly with the inner cone if α > 1. The net change in polar angle is determined by 3 δθ , The local change in the field line direction, relative to the total bend, is The flux spreading factor works out to A = 2 -θ f ∗ /θ f for any field-line profile of the form (51). In the absence of radiation, the Lorentz factor can be obtained by imposing energy conservation. It depends on the flaring profile of the jet via The acceleration tends to be more concentrated in radius for smaller values of the parameter α ; in what follows α = 2. In Figure 7 we show sample field lines given by (51) with strong flaring ( δθ = 0 . 3) for several values of θ f ∗ .",
"pages": [
12
]
},
{
"title": "3.5. Position of Fast Magnetosonic Surface",
"content": "When the flow speed surpasses the fast magnetosonic speed, radial magnetic disturbances are swept downstream and cannot interact with the part of the jet interior to the fast critical surface. The inertia of the electromagnetic field also becomes insignificant in the radial force balance, so that radiation pressure is relatively more important. We first consider how the position xc = rc / rs of the critical surface is modified by field-line flaring, and then consider the effects of radiation. The critical surface sits at infinite radius only if the poloidal magnetic field is constrained to be radial and radiation is absent (Goldreich & Julian 1970). The critical surface is obtained by setting µ eff = 0 in equations (46). Retaining χ ∗ = 0, and assuming σ /greatermuch 1, this corresponds to Γ /similarequal σ 1 / 3 [a vanishing coefficient of d Γ / dl in equation (C4)], and Ψ = 0. When δθ f = O ( θ j ), the magnetofluid rapidly accelerates outside radius r ∗ , and so we can expand A /similarequal 1 near this radius: Here we have approximated β φ /similarequal 1 / x θ f ω /lessmuch 1. Then, for α = 2, In the absence of magnetic-field flaring, the radiation stress forces the fast surface in from infinity (Paper I). Taking instead δθ = ∞ but allowing for finite χ ∗ , the fast surface corresponds to Γ /similarequal σ 1 / 3 and Γ ' σ /similarequal Γ ' χ . Then This differs from the spherical case (Paper I) mainly by the factor 1 /θ 2 f ∗ . At a very high compactness, the flow is tied to the collimating radiation field, and thus the critical surface is pulled in to where Γ eq( x , θ f ) /similarequal Γ c /similarequal σ 1 / 3 . The fast surface is shown as a function of angle in Figure 8, for a breakout radius x ∗ = 3. At low radiation compactness, this surface typically lies just outside breakout, xc /greaterorsimilar x ∗ , in agreement with equation (56). As the compactness is increased, the critical surface can either move inward or outward, depending on the location where Γ eq = σ 1 / 3 . The critical surface is typically pulled inward near the rotation axis if the magnetic field is weakly flared, and also at larger polar angles if x ∗ /greatermuch θ j σ 1 / 3 . Then its position follows equation (57) until reaching the high-compactness limit at If alternatively the breakout radius is small, then the critical surface is pushed out by radiation drag, reaching its high-compactness limit at The deviation of xc toward large radius that is seen close to the rotation axis is due to a combination of effects: a reduction in the outward Lorentz force due to the weaker field-line flaring; and a mis-match between the radiation and matter flows driven by strong rotation. The first effect dominates at low χ ∗ . The change in critical radius at high χ ∗ can be estimated using equation (A17) for Γ eq near the axis:",
"pages": [
12,
13,
14
]
},
{
"title": "3.6. Numerical Results",
"content": "We now examine the solutions to the wind equations (46)-(50) that we have derived for a geometrically and optically thin jet. The singularity at the fast magnetosonic critical point, and the stiffness of the equations associated with large values of σ and χ , means that simple integration techniques such as Runge-Kutta are inadequate. To determine the position of the critical point and the flow solution inside it, we use the relaxation method described in Paper I (see also London & Flannery 1982). The inner boundary radius ri of the integration is chosen somewhat differently than in Paper I: we set it to twice the photon emission radius ( xi = 2) because we only evaluate the radiation force where photons propagate at small angles with respect to the jet axis (requiring that xi -1 /greatermuch θ j ). The solutions for Γ and L m obtained by an integration inside the critical point are required to be smooth near xi ; avoiding sharp gradients restricts the boundary values at xi to a narrow range. We also make a first guess for the critical point radius xc . The regularity of the solution at xc then allows us to determine the flow variables at the critical point from the equations An approximate solution is chosen which connects the inner boundary values to the critical point. 4 This solution, along with the position of the critical point, is then relaxed to within a desired tolerance using a Newton-Raphson method, all the while satisfying the regularity condition (62). As a last step, the flow outside the critical point is obtained by shooting outward using a fifth-order Runge-Kutta algorithm. Solutions are obtained for a range of photon compactness and a high magnetization ( σ ∗ = 1000). The part of the jet studied sits well outside the light cylinder, ω = 100 in equation (35). Choosing the flaring profile (51), we follow the flow along a field line with initial footprint θ f ∗ = 0 . 1, in a jet of half-opening angle θ j = 0 . 2 and a breakout radius x ∗ = 3 = 1 . 5 xi . The magnitude of the jet flaring is adjusted by choosing the parameter δθ , with values 10 , 1 , 0 . 3 corresponding to a net angular shift θ f , ∞ /θ f ∗ -1 = 0 . 1 θ f ∗ , θ f ∗ , 3 . 3 θ f ∗ between breakout and infinity. The maximal flaring chosen ( δθ = 0 . 3) still satisfies equation (17), and so the divergence of neighboring magnetic field lines is consistent with causal stresses. The results are show in Figure 9. At low radiation compactness, they resemble those obtained by Tchekhovskoy et al. (2010) for a cold MHD jet. A slow, nearly linear, increase in Γ within the star is followed by rapid (but logarithmic) growth beyond the breakout point, where the field lines begin to diverge. As χ ∗ increases above ∼ σ , photon drag begins to dominate the weak Lorentz force inside the breakout radius, and Γ tends to Γ eq /similarequal x /θ j [equation (45)]. After breaking out, the fluid is quickly accelerated through the fast point. A strong radiation field forces the position of the critical point to a radius where Γ eq /similarequal σ 1 / 3 ∗ (in this case, the displacement is outward). We do not search for solutions with the fast point inside the star, corresponding to x ∗ /greaterorsimilar 3. The influence of the radiation field can be clearly seen in the dependence of asymptotic Lorentz factor Γ ∞ on χ ∗ (Figure 10). When flaring is strong ( δθ /lessorsimilar 1), the matter is pushed rapidly to Γ > Γ eq and it feels a net drag outside the magnetosonic point. The asymptotic Lorentz factor is reduced from (54). At very high χ ∗ , the radiation drag is able to suppress the acceleration and, therefore, the asymptotic Lorentz factor. The minimal compactness needed to significantly affect the post-breakout flow can be estimated by equating the leading terms in (47) at x = 3 x ∗ / 2, the point where the relative flaring of poloidal field lines is maximal. This gives In this case, the sign of the effect of radiation pressure outside the critical point still depends on the degree of magnetic field line flaring. If flaring is weaker ( δθ /greaterorsimilar 1) then the details of the flow profile near breakout differ from the unmagnetized flow, but Γ ∞ is still well approximated by an unmagnetized, radiatively driven flow: Our solutions, in the part of parameter space that we have explored, satisfy two basic constraints. First, the outflow is optically thin at (or near) breakout if the compactness sits below the bound (15). Second, the component of the radiation force transverse to the poloidal flux surfaces must remain small compared with the transverse Lorentz force that is implied by the chosen flaring profile. The corresponding upper bound (D3) on the compactness is derived in Appendix D.",
"pages": [
14,
15,
16
]
},
{
"title": "4. SPECTRUM OF SCATTERED PHOTONS",
"content": "We now consider the self-consistent spectrum of photons that scatter off a hot electromagnetic outflow near its photosphere. Our focus is solely on the signature of the differential flow of matter and photons - that is, we neglect any internal processes that would heat particles or induce small-scale deviations from a uniform flow. We first consider the jet model of Section 2, in which the optical depth is finite but the flow is considered only outside its fast magnetosonic surface. Then we turn to the optically thin jet model of Sections 3 and 3.6, in which the entire flow is solved inside and outside the critical surface, but the region interior to the photosphere is ignored. As in Paper I, we neglect any internal dissipation in the outflow, which can contribute to the high-energy tail of the spectrum (Thompson 1994; Giannios 2006; Beloborodov 2010).",
"pages": [
16
]
},
{
"title": "4.1. Spectrum in Jet Model I (Super-magnetosonic): Monte Carlo Method",
"content": "Here we follow the photon field self-consistently across the jet photosphere, which is assumed to sit outside the fast magnetosonic point (Figure 1). The exchange of energy between photons and magnetic field was calculated in Section 2 in parallel with the flaring rate of the poloidal field lines outside a fixed breakout radius. The radiation force on the matter, and the evolution of the equilibrium Lorentz factor Γ eq of the radiation field, defined in equations (23) and (24), are both calculated by taking angular moments (21) of the intensity. To calculate the emergent spectrum, we i) take the flow velocity profile as a given background, and then ii) inject photons from the inner radius ri = 0 . 8 r ∗ with an isotropic distribution in a frame moving with Lorentz factor Γ eq , i . Photon parameters in the rest frame of the 'star' at r > ri are obtained by a simple Lorentz boost. Defining a radial direction cosine by µ = ˆ k · ˆ r , one has µ = ( µ ' + β ) / (1 + βµ ' ), ω = Γ (1 + βµ ' ) ω ' , where the prime labels the matter rest frame. Deviations from radial flow are assumed small compared with the width of the photon beam. Electron scatterings are handled in the Thomson approximation (the outflow moves relativistically in the case of a GRB), by drawing a random number 1 -e -∆ τ es . The position of the next scatter point is calculated by integrating along the photon ray. Note that the outflow solution of Section 2 has been iterated so that the coefficient α es ∗ corresponds to a prescribed value of the radial optical depth τ es( r ∗ , ∞ , 1) at the breakout radius. Other initial flow parameters are defined at ri . The direction cosine evolves from a scattering radius r to r 2 > r according to The frequency distribution of the outgoing photons is first obtained with a monochromatic photon source, I ν = I 0 ν 0 δ ( ν -ν 0). This output spectrum is then convolved a source spectrum that is either a pure blackbody, or a function 5 that mimics the lowfrequency slope of a GRB, F ν = const × e -h ν / kT 0 . For both types of seed spectrum, the temperature T 0 is normalized by requiring F ν to peak at the fixed reference frequency ν 0. The photon escapes if ∆ τ es exceeds the total optical depth along the ray. Scatterings are taken to be elastic in the bulk frame, where the matter is assumed cold, so that the outgoing and ingoing frequencies satisfy the usual Doppler relation, After transforming µ to the local bulk frame, we pick scattering angles θ ' s , φ ' s with respect to the flow direction. The direction cosine of the outgoing photon is determined via µ ' em = µ ' cos θ ' s + (1 -µ ' 2 ) 1 / 2 sin θ ' s cos φ ' s , followed by a boost to the stellar frame. The peak of the seed photon distribution is stretched to higher frequencies when the outflow Lorentz factor Γ /greaterorsimilar Γ eq [equation (45)]. A scattered photon has a frequency in the range ν min <ν < ν max, where and ν min = [(1 -β ) / (1 + β )] ν 0 ∼ ν 0 / 4 Γ 2 .",
"pages": [
16,
17
]
},
{
"title": "4.2. Spectrum in Jet Model I: Results",
"content": "Figure 11 shows spectra for the case where matter and radiation field are initially locked together at Γ i = Γ eq , i = 10. The curves correspond to a variety of optical depths, as well as low and high initial photon fluxes, R i = 1 , 10 3 . The peak of the spectrum is somewhat broadened compared with a pure blackbody, and the segment shortward in frequency of the peak has a flattened spectrum, although not as flat as is seen in GRBs. A similar effect was seen in Paper I in the case of hot electromagnetic outflows accelerating along a radial, monopolar monopolar magnetic field. The spectrum below the peak is flattened even more if the radiation field emerging at the jet photosphere is broader than the matter Lorentz cone: the dashed curve in the R i = 1 panels is the result for Γ eq , i = Γ i / 2 = 5 and a low optical depth ( τ es ∗ = 0 . 1) at the breakout radius . As expected from the above argument, the peak of the spectrum is stretched upward in frequency above the peak of the seed spectrum.",
"pages": [
17,
18
]
},
{
"title": "4.3. Spectrum in Jet Model II (Trans-magnetosonic)",
"content": "The output spectrum is calculated by a similar method to that described in Section 4.1. The background flow is prescribed, in this case by the solutions obtained in Section 3.6, and the flow is approximated as radial. Since we are not, now, following the outflow across its photosphere, and the entire simulation volume is assumed optically thin, we take a similar input photon distribution as was used to calculate the flow acceleration: the intensity is constant, I = I 0 for θ < θ j = 0 . 2 radian. The jet breakout radius is taken to be x ∗ = 3, as in Figure 9, and the radial optical depth ∆ τ res( xi = 2 , ∞ , µ = 1) = 1. Results are shown in Figures 12-13 for three different degrees of magnetic field flaring: strong [corresponding to δθ = 0 . 3 in equation (51)], intermediate ( δθ = 1), and weak ( δθ = 10). The high-energy extension of the spectrum becomes broader as the radiation compactness is reduced: stronger radiation drag limits the increase in Γ above Γ eq. In the case of a monochromatic input spectrum, one notices the appearance of a few distinct orders of Compton scattering. The bumps in the spectrum are smoothed out when convolved with a blackbody source.",
"pages": [
18
]
},
{
"title": "5. SUMMARY",
"content": "We have examined the effect of intense radiation pressure on a cold, magnetized outflow with a jet geometry. The poloidal magnetic field lines are allowed to deviate from spherical symmetry, e.g. due to breakout from a confining medium. The outflow experiences a strong outward Lorentz force as a result, so that the magnetofluid and radiation field have a tendency to flow differentially outside the transparency surface. We have considered the combined dynamics of the magnetofluid and radiation, and as well as the modification to the radiation spectrum by multiple scattering. We first considered the transition zone straddling the scattering photosphere. While the jet is still optically thick, its magnetization is suppressed by the inertia of the advected radiation. Outside the breakout point, the jet experiences a strong outward Lorentz force, which forces a rapid reduction in optical depth. This approach assumes that the fast critical surface lies deep in the jet, but calculates the radial flaring of the field lines self-consistently with a simple causal prescription, and calculates the interaction between the radiation and matter for arbitrary scattering depth. If the jet is still optically thick at breakout, then the emergent spectrum is modestly broadened and hardened below the peak. On the other hand, breakout outside the transparency surface results in a photon beam that is significantly broader than the Lorentz cone of the accelerating jet, and therefore results in a more extended high-energy component to the spectrum. A stronger radiation field suppresses the accelerating effect of jet flaring and brings the spectrum closer to the original thermal input. Broadening of the photon beam could also be due to scattering by a shell of slower material entrained at the jet head (Thompson 2006). Our second approach to the problem focuses on the zone outside the jet photosphere, but allows for large enough magnetization that the flow passes through the fast critical surface just outside the breakout radius. We then solve for the flow profile along magnetic flux surfaces, both inside and outside the critical point. In doing this, we choose a realistic angular distribution for the radiation field but prescribe a flaring profile for the poloidal field lines. The cross-field force balance is not solved selfconsistently, but we check that in all cases the transverse component of the radiation force is small compared with the transverse Lorentz force that is implied by the chosen field profiles. As regards the longitudinal motion along magnetic flux surfaces, we define the critical compactness χ of the radiation field above which the matter and radiation are locked, and the Lorentz force is subdominant. For small jet flaring, the radiation force leads to an increase in terminal Lorentz factor at high values of χ , but can somewhat suppress the acceleration if the flaring is strong. The extent of the high-energy component of the spectrum is shown to depend in an interesting way on the degree of flaring and the position of the photosphere relative to the breakout radius. Issues not addressed in this paper include the effects of multiple scattering at the magnetosonic critical surface, an ambient radiation field generated far outside the engine (e.g. Li et al. 1992a; Beskin et al. 2004), or the feedback of an intense radiation flow on the poloidal structure of the magnetic field. An effect specific to gamma-ray bursts involves the sidescattering of gammarays outside the forward shock, combined with the radiative acceleration of the pair-enriched material up to a Lorentz factor comparable to that of the relativistic ejecta (Thompson & Madau 2000; Beloborodov 2002). This delays the deceleration of the ejecta, and makes the medium ahead of the shock optically thick to scattering (Thompson 2006). Photons side-scattered through large angles would continue to interact with jet material at a smaller radius, creating pairs downstream of the forward shock, delaying the decoupling of the photons from the jet fluid, and generating a high-energy tail to the photon spectrum by bulk Comptonization. This means that the outermost shell of jet material (of a thickness ∼ θ 2 j r ∗ ) may avoid strong outward acceleration during jet breakout. However, jet material flowing at much greater distances back of the jet head sees weaker Compton drag and rates of pair creation during breakout. The slow forward shell becomes geometrically thin as it is pushed outward and, eventually, subject to a corrugation instability (Thompson 2006). We thank the NSERC of Canada for support.",
"pages": [
18,
19,
20
]
},
{
"title": "GEOMETRYOF SCATTERING IN A NARROW JET",
"content": "We now calculate the radiation force on plasma moving on a general trajectory within a thin jet of opening angle θ j /lessmuch 1, following the setup of Section 3.1. Our goal is to obtain an analytic expression for this force, which is possible by assuming a uniform intensity I = ∫ I ν d ν at the 'emission' surface (radius rs ), and taking this surface to be locally spherical. When considering the interaction with matter, this intensity distribution gives similar results to a radiation field that is locally isotropic in the relativistic frame of the emitting medium. (See the discussion in Section 3.1 and Section 3.3 of Paper I.) The result generalizes the simpler angular moment formalism used in Section 2 and presented in equation (24). Photons are emitted from coordinates { θ γ , φ γ } within a patch of angular radius θ γ ≤ θ j , and scatter in the jet the position { x = r / rs > 1, θ f , φ f = 0}. The presence of an absorbing surface at the edge of the jet would change the radiation force at angles θ f > θ j . Given the uncertain nature of the medium outside the jet, we restrict the calculation of the force to angles < θ j . The photon trajectory is tilted with respect to the radial line passing through the scattering point, by an angle (Figure 14) Here is the corresponding angle measured on the 'emission' surface, and we have assumed that x -1 /greatermuch θ j in making the expansion in x . The intensity at the point of scattering can then be expressed as with The unit wave vector in the local ( ˆ r , ˆ θ, ˆ φ ) coordinate system is with the poloidal component where ∆ θ B = B θ / Br is the angle that a bending field line makes with the local radial vector. To evaluate the lab-frame radiation force (20) we relate the solid angle of incoming photons to the emission coordinates via The poloidal and toroidal radiation force is then evaluated as follows. We begin by writing and express the components of the wave vector as Integrating first over φ γ and then θ γ at the 'emission' surface gives where Gp and Hp are accurate to first order in Γ -2 and ( θ/ x ) 2 . The equilibrium Lorentz factor of the photon field, the frame in which F rad vanishes, is found by solving Γ ' χ = 0 in (47). The results are shown in Figure 15 for the poloidal field line profile described in Sec. 3.2. At a radius x -1 /greatermuch θ j one finds Γ eq /similarequal x /θ j , with a coefficient of order unity that depends on the footprint angle and flaring profile. A thin jet defines a relativistic frame at relatively small distances from the 'emission' surface, as compared with a spherically symmetric outflow (for which Γ eq /similarequal 3 1 / 4 x ). Photons arriving at a scattering point from large angles provide relatively strong drag. The jet fluid maintains rapid rotation around the light cylinder, θ f ∼ 1 / x ω , where the fluid flow is less aligned with the radiation field and Γ eq is reduced. Estimating β φ /similarequal 1 / x ωθ f (just outside the light cylinder), one finds valid for all x .",
"pages": [
20,
21
]
},
{
"title": "ACCOUNTINGFOR ROTATION OF THE PHOTON FIELD",
"content": "The photon source rotates rapidly in some cases, e.g. a rapidly rotating star such as a millisecond magnetar, or the merged remnant of a white dwarf binary. We can approximate the effect of a rotating emission surface by setting in equations (43). Here β φ , R is a constant representing the aberration of the outflowing photons at r = rs ( x = 1). In this situation, plasma near the emission surface can more easily co-rotate with the radiation field while still being accelerated outward. The value of β φ , R depends on the type of source. One has β φ , R ∼ Ω rs / c ≡ ω when the photons flow from the surface of a star of radius rs through a transparent wind. On the other hand, if the outflow is optically thick in a narrow radial zone close to the engine, then one expects β φ , R ∼ ( Ω rs / c ) -1 ∼ ω -1 based on the conservation of angular momentum from the light cylinder out to the transparency surface ( x = 1).",
"pages": [
22
]
},
{
"title": "WIND EQUATIONS FOR JET MODEL II",
"content": "Here we derive the equations (46)-(50) for the longitudinal development of Lorentz factor and particle angular momentum along magnetic flux surfaces. Beginning with the poloidal and toroidal components of the Euler equation, (41) and (42), we expand the derivatives on the right hand side as This can be evaluated using ∂ l ( r θ f ) /similarequal θ f + B θ / Br = θ f + ∆ θ B , equation (39) for ∂ l Br , and where The wind equations (41), (42) are now transformed into ordinary differential equations by ignoring the cross-field force balance: where Two simple tests of these equations are made possible by neglecting the radiation force. The energy and angular momentum integrals (38) are now related by This equation is recovered by summing (C4) and B φ / Br times (C5), and making use of Ferraro's law (4). Second, outside the fast point the inertia of the magnetofluid is dominated by the matter: the coefficient of d Γ / dl in equation (C4) is /similarequal 1 -σ/ Γ 3 and approaches unity. Since in addition β φ → 0, the term involving L m can be neglected and one finds The same result can be obtained from the integral equations (8), (38) and (39), Equation (46) is then obtained by solving (C4) and (C5) for d Γ / dl and d L m / dl .",
"pages": [
22,
23
]
},
{
"title": "CROSS-FIELD FORCES",
"content": "Though we ignore the cross-field force balance, it is useful to estimate the transverse radiation force and compare it with the Lorentz force that is implied by a given field-line profile. Our procedure becomes inconsistent if the transverse radiation force dominates, because the radiation field will then comb out the field lines in the radial direction. The polar component of equation (20) gives the estimate, The first term on the right-hand side represents the force imparted by photons streaming from a finite polar cap toward particles on off-axis field lines. The second represents the drag imparted as the poloidal particle flow bends across the radiation field. The cross-field Lorentz force is given by Requiring this to be greater than (D1) gives an upper bound on the radiation compactness at jet breakout ( x > x ∗ /greatermuch 1), Our calculations can admit values of χ ∗ as large as ∼ 10 4 σ without any inconsistency, given the typical jet parameters θ j ∼ 0 . 2, x ∗ ∼ 3, Γ > Γ ∗ ∼ 10.",
"pages": [
23
]
},
{
"title": "REFERENCES",
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"pages": [
23
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}
]
2013ApJ...773..177N
https://arxiv.org/pdf/1307.0907.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_82><loc_86><loc_86></location>Time series analysis of gamma-ray blazars and implications for the central black-hole mass</section_header_level_1>
<text><location><page_1><loc_36><loc_77><loc_64><loc_79></location>Kenji Nakagawa and Masaki Mori</text>
<text><location><page_1><loc_12><loc_74><loc_88><loc_76></location>Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan</text>
<text><location><page_1><loc_20><loc_70><loc_27><loc_71></location>Received</text>
<text><location><page_1><loc_48><loc_70><loc_49><loc_71></location>;</text>
<text><location><page_1><loc_52><loc_70><loc_59><loc_71></location>accepted</text>
<text><location><page_1><loc_37><loc_64><loc_63><loc_65></location>To be submitted for publication</text>
<section_header_level_1><location><page_2><loc_44><loc_85><loc_56><loc_86></location>ABSTRACT</section_header_level_1>
<text><location><page_2><loc_17><loc_59><loc_83><loc_80></location>Radiation from the blazar class of active galactic nuclei (AGN) exhibits fast time variability which is usually ascribed to instabilities in the emission region near the central supermassive black hole. The variability time scale is generally faster in higher energy region, and data recently provided by the Fermi Gammaray Space Telescope in the GeV energy band enable a detailed study of the temporal behavior of AGN. Due to its wide field-of-view in the scanning mode, most sky regions are observed for several hours per day and daily light curves of many AGN have been accumulated for more than 4 r.</text>
<text><location><page_2><loc_17><loc_38><loc_83><loc_57></location>In this paper we investigate the time variability of 15 well-detected AGNs by studying the normalized power spectrum density of their light curves in the GeV energy band. One source, 3C 454.3, shows a specific time scale of 6 . 8 × 10 5 s, and this value suggests, assuming the internal shock model, a mass for the central black hole of (10 8 -10 10 ) M /circledot which is consistent with other estimates. It also indicates the typical time interval of ejected blobs is (7-70) times the light crossing time of the Schwarzschild radius.</text>
<text><location><page_2><loc_17><loc_31><loc_82><loc_35></location>Subject headings: BL Lacertae objects: general - galaxies: active - gamma rays: galaxies</text>
<section_header_level_1><location><page_3><loc_42><loc_85><loc_58><loc_86></location>1. Introduction</section_header_level_1>
<text><location><page_3><loc_12><loc_42><loc_88><loc_82></location>About 1% of galaxies have an active galactic nucleus (AGN), which emits 10 9 -10 14 times the solar power over a wide range of the energy spectrum, from radio to gamma-ray energies. AGNs constitute one of the most violently variable and interesting classes of object in the universe. The activity of AGN is believed to originate from the central supermassive black hole, with masses of 10 6 -10 9 solar mass ( M /circledot ), and part of their energy is emitted in electromagnetic radiation from the surrounding region including the accretion disk formed around the black hole and relativistic jets ejected along rotation axes (e.g., Urry & Padovani 1995). A subclass of radio-loud AGN are called blazars, in which the line of sight lies close to the jet axis, and the emission from relativistic jets is only visible in this class of AGN due to the relativistic beaming effect, especially in the high-energy region. The electromagnetic spectra of blazars are dominated by non-thermal radiation produced in the jets. The popular scenario to explain these emission spectra assumes that the particles in the jets are accelerated to high energies by diffusive shocks in the jets and induce emission via interaction with surrounding matter/radiation (e.g., Fossati et al. 1998) 1 .</text>
<text><location><page_3><loc_12><loc_24><loc_88><loc_40></location>Observations of blazars at various wavelengths have revealed fast time variability which is most plausibly related to instabilities in the emission environment near the black hole (e.g., Ulrich, Maraschi & Urry 1997). Past observations suggest the variability is larger at higher energies (the most extreme example is Mrk 501 Nowak et al. 2012), which may indicate the higher energy emission comes from the region closer to the central black holes. The variability time scale reflects the size of the emission region, and thus the study of</text>
<text><location><page_4><loc_12><loc_82><loc_88><loc_86></location>temporal behavior of gamma-ray flux is an excellent probe of the region close to the central engine, i.e., the supermassive black hole.</text>
<text><location><page_4><loc_12><loc_60><loc_88><loc_79></location>Blazars are known to show flaring activity which occurs randomly and continues for several days to months. In order to study their temporal variability precisely, blazars should be monitored continuously, or at least frequently. It is not an easy task for narrow field-of-view telescopes like optical, X-ray, and Cherenkov (TeV gamma-ray) instruments to monitor many blazars for long periods. Besides, their observations are limited as ground-based telescopes can only operate on dark, clear nights and X-ray satellites are used in pointing-mode observations.</text>
<text><location><page_4><loc_12><loc_39><loc_88><loc_58></location>Nevertheless, in the X-ray band, Hayashida et al. (1998) evaluated the central black hole masses in several AGNs based on their rather well-sampled X-ray light curves obtained with the Ginga satellite and suggested the masses 1 ∼ 2 orders of magnitude smaller than previous estimates. Kataoka et al. (2001) studied time variability of three TeV-detected AGNs based on ASCA and/or RXTE observations and showed that (10 7 ∼ 10 10 ) M /circledot black holes and internal shocks that start to develop at 100 times the Schwarzschild radii could explain the observed properties.</text>
<text><location><page_4><loc_12><loc_14><loc_88><loc_36></location>In the GeV gamma-ray band, the Fermi Gamma-ray Space Telescope has been monitoring the whole sky with the Large Area Telescope (LAT) since 2008. The LAT is a wide field-of-view gamma-ray imager that observes one-fifth of the sky at any instant and that scans the whole sky in a day (Atwood et al. 2009). The second Fermi -LAT catalog, which contains 1092 (28 identified and 1064 associated) AGN among the 1873 detected sources in the 100 MeV to 100 GeV range (Nolan et al. 2012). Gamma-ray light curves of several tens of blazars are provided on a daily basis and this is a good database to study the time variability of blazars.</text>
<text><location><page_4><loc_16><loc_11><loc_88><loc_12></location>Abdo et al. (2010b) reported a detailed analysis of the variability of 106 objects in the</text>
<text><location><page_5><loc_12><loc_73><loc_88><loc_86></location>Fermi -LAT Bright AGN Sample. They showed that the temporal behavior of gamma-ray fluxes of variable sources can be described by power-law power spectral density (PSD) in general, with a few blazars that showed strong activity exhibiting complex and structured temporal profiles. They examined whether it was possible to characterize blazar type with the PSD slope, but the results were not conclusive.</text>
<text><location><page_5><loc_12><loc_54><loc_88><loc_70></location>In this paper, we report the time series analysis of gamma-ray light curves of 15 blazars based on Fermi -LAT data and discuss the results in relation to the properties of the central engine. Our analysis is the first systematic study of long-term variability of blazar emission in the gamma-ray energy band, although the analysis method itself has been applied and reported previously ((e.g., in the X-ray band, Lawrence et al. 1987; McHardy & Czerny 1987; Miyamoto et al. 1994; Hayashida et al. 1998; Kataoka et al. 2001).</text>
<section_header_level_1><location><page_5><loc_39><loc_47><loc_61><loc_49></location>2. Data and Analysis</section_header_level_1>
<text><location><page_5><loc_12><loc_22><loc_88><loc_44></location>We use the 'monitored source light curves' provided by the Fermi Science Support Center (FSSC) 2 for bright and transient gamma-ray sources. They are regularly updated throughout the mission. In this paper, we analyze the daily light curves of 15 AGN (Table 1) in the energy range 100 MeV - 300 GeV. The data period is between 2008 August 9 and 2012 April 26. These sources are selected because a large fraction of data points are detections, not upper limits, so that we can extract useful information on time variability. Note that the usage of daily light curves spanning 44 months naturally limits our time series analysis to the 10 -8 -10 -5 Hz range. Faster variability observed in the case of 3C</text>
<text><location><page_5><loc_12><loc_12><loc_88><loc_19></location>2 http://fermi.gsfc.nasa.gov/ssc/data/access/lat/msl_lc/ Note that, as stated here, these light curves are preliminary and fluxes do not have absolute calibration, and a preliminary instrument response function is used.</text>
<text><location><page_6><loc_12><loc_85><loc_79><loc_86></location>454.3 (Abdo et al. 2011), for example, is out of the scope of the present analysis.</text>
<text><location><page_6><loc_12><loc_57><loc_88><loc_82></location>As we noted in Section 1, the variability time scale of AGN flares reflects the size of the emission region, and thus the study of temporal behavior of gamma-ray flux can be a good probe to explore the physical environment close to the central engine. However, characterizing the time scale is not a simple task since we know that the intensity of gamma-ray emission from AGN flares varies very irregularly. The fastest doubling time has been widely used (see Barr & Mushotzky 1986, for example) as a variability measure, but it depends on data quality and coverage. Here we adopt a spectral analysis, the normalized power spectrum density (NPSD), to evaluate the characteristic timescale of light curves which fluctuate chaotically, after Miyamoto et al. (1994).</text>
<section_header_level_1><location><page_6><loc_30><loc_50><loc_70><loc_52></location>2.1. Normalized Power Spectral Density</section_header_level_1>
<text><location><page_6><loc_12><loc_43><loc_88><loc_47></location>The PSD shows the degree of variation at every frequency (or cycle) by calculating the Fourier transform of time variable data (Lawrence et al. 1987; McHardy & Czerny 1987).</text>
<text><location><page_6><loc_12><loc_33><loc_86><loc_40></location>The NPSD, which is obtained by dividing the PSD by the average source intensity squared, has proven to be useful to compare variability at each frequency even if the brightness changes (Miyamoto et al. 1994; Kataoka et al. 2001). It is defined as</text>
<formula><location><page_6><loc_35><loc_28><loc_88><loc_32></location>P ( f ) = [ a 2 ( f ) + b 2 ( f ) -σ 2 stat /n ] T F 2 av (1)</formula>
<formula><location><page_6><loc_35><loc_22><loc_88><loc_28></location>a ( f ) = 1 n n -1 ∑ j =0 F j cos(2 πft j ) (2)</formula>
<text><location><page_6><loc_12><loc_10><loc_88><loc_17></location>where F j is the source count rate at time t j (0 < t j < n -1), T is the total time length, F av is the mean value of source count rates, and σ stat is the error due to counting statistics. In our analysis, we calculated the power P ( f ) for some discrete frequencies given by f = k/T</text>
<formula><location><page_6><loc_35><loc_17><loc_88><loc_23></location>b ( f ) = 1 n n -1 ∑ j =0 F j sin(2 πft j ) (3)</formula>
<text><location><page_7><loc_12><loc_67><loc_88><loc_86></location>( k is an integer and 1 < k < n/ 2) and averaged. The Fermi -LAT light curves are given with flux errors ( e j ) and their standard deviation ( √ ∑ j e 2 j /N ) is substituted for σ stat as a rough estimate of error of counting statistics (see Section 2.2 for more discussion). The error bars of the NPSD are standard deviations of powers in each frequency bin (see Hayashida et al. 1998; Kataoka et al. 2001, for more discussion of NPSD analyses). In our calculation of the NPSD, we did not use upper limits in the light curves. In addition, we did not interpolate any blank (i.e., missing) data contained in the light curves.</text>
<section_header_level_1><location><page_7><loc_41><loc_60><loc_59><loc_61></location>2.2. Poisson Noise</section_header_level_1>
<text><location><page_7><loc_12><loc_41><loc_88><loc_57></location>If the time series is a continuous counting rate binned into intervals, as it is here, the effect of Poisson noise is to add an approximately constant amount of power to the NPSD at all frequencies. At high frequencies, where the counting rate is low, the NPSD will be dominated by the flat (white) Poisson noise spectrum. In the definition of NPSD (Equation 1) this noise is subtracted in the term σ 2 stat /n (see Vaughan, Fabian and Nandra 2003, for further discussion).</text>
<text><location><page_7><loc_12><loc_13><loc_88><loc_38></location>In the present case, F j ( e j ) is calculated as the counts (count error) divided by the exposure, and the daily exposure is almost uniform for the Fermi -LAT observations. The Poisson noise is therefore approximately subtracted in the calculation of the NPSD (Equation 1). This treatment formally assumes zero background flux, but this is a reasonable approximation in our case, since the Fermi -LAT light curves are released after subtracting background counts when they are processed at the FSSC. If the subtraction of the Poisson noise estimated by the quoted flux errors is not sufficiently accurate, there will be a residual constant which becomes dominant at high frequencies in the NPSD, which can be seen in some cases in our results (next section).</text>
<section_header_level_1><location><page_8><loc_45><loc_85><loc_55><loc_86></location>3. Results</section_header_level_1>
<text><location><page_8><loc_12><loc_74><loc_86><loc_81></location>We calculated the NPSD for the Fermi -LAT daily light curves of 15 AGNs using 9 frequency bins divided logarithmically from 10 -7 Hz to 10 -5 . 2 Hz. Plots are shown in Figure 1.</text>
<text><location><page_8><loc_12><loc_61><loc_88><loc_72></location>One may note that data points at high frequencies are missing for most of the sources in Figure 1. One reason is that many observations in the Fermi -LAT light curves yield only upper limits. Another reason is that large flares which last for ten of days or more are rare: we cannot have points above ∼ 10 -6 Hz without such flares.</text>
<text><location><page_8><loc_16><loc_58><loc_71><loc_59></location>We applied least-square fits to these points assuming a power-law</text>
<formula><location><page_8><loc_46><loc_54><loc_88><loc_55></location>f ( ν ) ∝ ν γ (4)</formula>
<text><location><page_8><loc_12><loc_50><loc_34><loc_51></location>and/or a broken power-law</text>
<formula><location><page_8><loc_40><loc_45><loc_88><loc_50></location>f ( ν ) ∝ { ν γ 1 ( ν < ν b ) ν γ 2 ( ν ≥ ν b ) , (5)</formula>
<text><location><page_8><loc_12><loc_31><loc_88><loc_44></location>where ν is the frequency and ν b is the 'turnover' frequency. Fit parameters are summarized in Table 1. The fit lines are overplotted in Figure 1, where broken power-law lines are plotted only when the reduced χ 2 values are smaller than single power-law values.. We see NPSDs for four sources, PKS 0537 -441, 3C 279, 3C 454.3 and PKS 2326 -502, are better fitted by broken power-laws than by single power-laws.</text>
<text><location><page_8><loc_12><loc_7><loc_88><loc_29></location>The NPSD plots for PKS 0537 -502, 3C 279 and PKS 2326 -502 show upward turnovers above 10 -6 . 18 Hz, 10 -5 . 88 Hz and 10 -6 . 10 Hz, respectively, but the slopes above these frequencies ( γ 2 ) have large uncertainties and are consistent with zero: thus they may have reached a constant Poisson-like noise level which is not removed by our rough estimate of counting statistical error (see section 2.1). We checked the difference of NPSD values before and after removing the Poisson noise, assuming the value of Poisson noise is the normalized square-root of sum of squares of several flux's error: √ ∑ e 2 i /N . With this</text>
<text><location><page_9><loc_12><loc_76><loc_88><loc_86></location>procedure, the NPSD values at high frequencies showed smaller values than those before removal, but the slope above the turnover of the NPSD plot remained flat (consistent with zero slope). Thus, even if we could not remove the effect of Poisson noise completely, it seems this flattening behavior does not have a physical origin.</text>
<text><location><page_9><loc_12><loc_57><loc_88><loc_74></location>On the other hand, the NPSD plot for 3C 454.3 show a turnover at 10 -5 . 83 Hz and the slope above it, -3 . 08 ± 0 . 83, is well determined. The reduced χ 2 value decreases from 1.29 for single power-law fit, which is not at acceptable level, to 0.23 for broken power-law fit, which is acceptable. Thus, only the plot for 3C 454.3, which exhibited an extraordinary large flare in 2010 November (Abdo et al. 2011), seems to show a physically meaningful turnover, at 10 -5 . 83 Hz, which we discuss further in the next section.</text>
<text><location><page_10><loc_16><loc_86><loc_18><loc_86></location>t</text>
<text><location><page_10><loc_16><loc_85><loc_18><loc_86></location>o</text>
<paragraph><location><page_10><loc_16><loc_78><loc_69><loc_85></location>lim it s a r e n χ 2 / d . o . f 0 . 0 7 2 0 . 1 2 5 0 . 2 2 8 0 . 4 8 7</paragraph>
<text><location><page_10><loc_16><loc_77><loc_18><loc_77></location>r</text>
<text><location><page_10><loc_16><loc_76><loc_18><loc_77></location>e</text>
<text><location><page_10><loc_43><loc_77><loc_45><loc_78></location>3</text>
<text><location><page_10><loc_43><loc_77><loc_45><loc_77></location>8</text>
<text><location><page_10><loc_43><loc_76><loc_45><loc_77></location>1</text>
<text><location><page_10><loc_56><loc_77><loc_57><loc_78></location>9</text>
<text><location><page_10><loc_56><loc_77><loc_57><loc_77></location>7</text>
<text><location><page_10><loc_56><loc_76><loc_57><loc_77></location>8</text>
<text><location><page_10><loc_65><loc_77><loc_67><loc_78></location>4</text>
<text><location><page_10><loc_65><loc_77><loc_67><loc_77></location>3</text>
<text><location><page_10><loc_65><loc_76><loc_67><loc_77></location>8</text>
<text><location><page_10><loc_68><loc_77><loc_69><loc_78></location>3</text>
<text><location><page_10><loc_68><loc_77><loc_69><loc_77></location>0</text>
<text><location><page_10><loc_68><loc_76><loc_69><loc_77></location>1</text>
<table>
<location><page_10><loc_12><loc_30><loc_85><loc_76></location>
</table>
<text><location><page_10><loc_16><loc_29><loc_18><loc_30></location>A</text>
<text><location><page_10><loc_16><loc_27><loc_18><loc_28></location>d</text>
<text><location><page_10><loc_16><loc_27><loc_18><loc_27></location>e</text>
<text><location><page_10><loc_16><loc_26><loc_18><loc_27></location>z</text>
<text><location><page_10><loc_16><loc_25><loc_18><loc_26></location>ly</text>
<text><location><page_10><loc_16><loc_24><loc_18><loc_25></location>a</text>
<text><location><page_10><loc_16><loc_23><loc_18><loc_24></location>n</text>
<text><location><page_10><loc_16><loc_22><loc_18><loc_23></location>a</text>
<text><location><page_10><loc_16><loc_21><loc_18><loc_22></location>A</text>
<text><location><page_10><loc_16><loc_20><loc_18><loc_21></location>f</text>
<text><location><page_10><loc_16><loc_20><loc_18><loc_20></location>o</text>
<text><location><page_10><loc_16><loc_19><loc_18><loc_19></location>t</text>
<text><location><page_10><loc_16><loc_18><loc_18><loc_19></location>is</text>
<text><location><page_10><loc_16><loc_17><loc_18><loc_18></location>L</text>
<text><location><page_10><loc_16><loc_15><loc_18><loc_15></location>.</text>
<text><location><page_10><loc_16><loc_14><loc_18><loc_15></location>1</text>
<text><location><page_10><loc_16><loc_13><loc_18><loc_14></location>le</text>
<text><location><page_10><loc_16><loc_12><loc_18><loc_13></location>b</text>
<text><location><page_10><loc_16><loc_11><loc_18><loc_12></location>a</text>
<text><location><page_10><loc_16><loc_10><loc_18><loc_11></location>T</text>
<text><location><page_10><loc_26><loc_29><loc_28><loc_30></location>0</text>
<text><location><page_10><loc_26><loc_29><loc_28><loc_29></location>0</text>
<text><location><page_10><loc_26><loc_28><loc_28><loc_29></location>2</text>
<text><location><page_10><loc_26><loc_28><loc_28><loc_28></location>(</text>
<text><location><page_10><loc_26><loc_27><loc_28><loc_27></location>δ</text>
<text><location><page_10><loc_26><loc_25><loc_28><loc_25></location>)</text>
<text><location><page_10><loc_26><loc_24><loc_28><loc_25></location>0</text>
<text><location><page_10><loc_26><loc_24><loc_28><loc_24></location>0</text>
<text><location><page_10><loc_26><loc_23><loc_28><loc_24></location>0</text>
<text><location><page_10><loc_26><loc_22><loc_28><loc_23></location>2</text>
<text><location><page_10><loc_26><loc_22><loc_28><loc_23></location>(</text>
<text><location><page_10><loc_26><loc_21><loc_28><loc_22></location>α</text>
<text><location><page_10><loc_26><loc_17><loc_28><loc_17></location>e</text>
<text><location><page_10><loc_26><loc_16><loc_28><loc_17></location>c</text>
<text><location><page_10><loc_26><loc_16><loc_28><loc_16></location>r</text>
<text><location><page_10><loc_26><loc_15><loc_28><loc_16></location>u</text>
<text><location><page_10><loc_26><loc_15><loc_28><loc_15></location>o</text>
<text><location><page_10><loc_26><loc_14><loc_28><loc_15></location>S</text>
<text><location><page_10><loc_29><loc_77><loc_30><loc_78></location>b</text>
<text><location><page_10><loc_29><loc_77><loc_30><loc_77></location>ν</text>
<text><location><page_10><loc_29><loc_76><loc_30><loc_77></location>0</text>
<text><location><page_10><loc_29><loc_30><loc_30><loc_30></location>)</text>
<text><location><page_10><loc_29><loc_29><loc_30><loc_30></location>g</text>
<text><location><page_10><loc_29><loc_29><loc_30><loc_29></location>e</text>
<text><location><page_10><loc_29><loc_28><loc_30><loc_29></location>d</text>
<text><location><page_10><loc_29><loc_28><loc_30><loc_28></location>(</text>
<text><location><page_10><loc_29><loc_24><loc_30><loc_24></location>)</text>
<text><location><page_10><loc_29><loc_23><loc_30><loc_24></location>g</text>
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<text><location><page_10><loc_29><loc_22><loc_30><loc_22></location>(</text>
<text><location><page_10><loc_29><loc_17><loc_30><loc_17></location>e</text>
<text><location><page_10><loc_29><loc_16><loc_30><loc_17></location>m</text>
<text><location><page_10><loc_29><loc_15><loc_30><loc_16></location>a</text>
<text><location><page_10><loc_29><loc_14><loc_30><loc_15></location>N</text>
<text><location><page_10><loc_38><loc_29><loc_40><loc_30></location>9</text>
<text><location><page_10><loc_38><loc_29><loc_40><loc_29></location>.</text>
<text><location><page_10><loc_38><loc_28><loc_40><loc_29></location>7</text>
<text><location><page_10><loc_38><loc_28><loc_40><loc_28></location>3</text>
<text><location><page_10><loc_38><loc_27><loc_39><loc_28></location>-</text>
<text><location><page_10><loc_38><loc_24><loc_40><loc_25></location>8</text>
<text><location><page_10><loc_38><loc_24><loc_40><loc_24></location>6</text>
<text><location><page_10><loc_38><loc_23><loc_40><loc_24></location>1</text>
<text><location><page_10><loc_38><loc_23><loc_40><loc_23></location>.</text>
<text><location><page_10><loc_38><loc_22><loc_40><loc_23></location>7</text>
<text><location><page_10><loc_38><loc_22><loc_40><loc_22></location>6</text>
<text><location><page_10><loc_38><loc_19><loc_40><loc_20></location>0</text>
<text><location><page_10><loc_38><loc_18><loc_40><loc_19></location>8</text>
<text><location><page_10><loc_38><loc_18><loc_40><loc_18></location>3</text>
<text><location><page_10><loc_38><loc_17><loc_39><loc_18></location>-</text>
<text><location><page_10><loc_38><loc_17><loc_40><loc_17></location>6</text>
<text><location><page_10><loc_38><loc_16><loc_40><loc_17></location>2</text>
<text><location><page_10><loc_38><loc_16><loc_40><loc_16></location>4</text>
<text><location><page_10><loc_38><loc_15><loc_40><loc_16></location>0</text>
<text><location><page_10><loc_38><loc_14><loc_40><loc_15></location>S</text>
<text><location><page_10><loc_38><loc_13><loc_40><loc_14></location>K</text>
<text><location><page_10><loc_38><loc_12><loc_40><loc_13></location>P</text>
<text><location><page_10><loc_41><loc_29><loc_42><loc_30></location>4</text>
<text><location><page_10><loc_41><loc_29><loc_42><loc_29></location>.</text>
<text><location><page_10><loc_41><loc_28><loc_42><loc_29></location>3</text>
<text><location><page_10><loc_41><loc_28><loc_42><loc_28></location>2</text>
<text><location><page_10><loc_41><loc_27><loc_42><loc_28></location>-</text>
<text><location><page_10><loc_41><loc_24><loc_42><loc_25></location>3</text>
<text><location><page_10><loc_41><loc_24><loc_42><loc_24></location>6</text>
<text><location><page_10><loc_41><loc_23><loc_42><loc_24></location>2</text>
<text><location><page_10><loc_41><loc_23><loc_42><loc_23></location>.</text>
<text><location><page_10><loc_41><loc_22><loc_42><loc_23></location>4</text>
<text><location><page_10><loc_41><loc_22><loc_42><loc_22></location>7</text>
<text><location><page_10><loc_41><loc_19><loc_42><loc_20></location>4</text>
<text><location><page_10><loc_41><loc_18><loc_42><loc_19></location>3</text>
<text><location><page_10><loc_41><loc_18><loc_42><loc_18></location>2</text>
<text><location><page_10><loc_41><loc_17><loc_42><loc_18></location>-</text>
<text><location><page_10><loc_41><loc_17><loc_42><loc_17></location>4</text>
<text><location><page_10><loc_41><loc_16><loc_42><loc_17></location>5</text>
<text><location><page_10><loc_41><loc_16><loc_42><loc_16></location>4</text>
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<text><location><page_10><loc_51><loc_15><loc_52><loc_16></location>1</text>
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<text><location><page_10><loc_63><loc_29><loc_64><loc_30></location>7</text>
<text><location><page_10><loc_63><loc_29><loc_64><loc_29></location>2</text>
<text><location><page_10><loc_63><loc_29><loc_64><loc_29></location>.</text>
<text><location><page_10><loc_63><loc_28><loc_64><loc_29></location>2</text>
<text><location><page_10><loc_63><loc_28><loc_64><loc_28></location>4</text>
<text><location><page_10><loc_63><loc_24><loc_64><loc_25></location>0</text>
<text><location><page_10><loc_63><loc_24><loc_64><loc_24></location>8</text>
<text><location><page_10><loc_63><loc_23><loc_64><loc_24></location>6</text>
<text><location><page_10><loc_63><loc_23><loc_64><loc_23></location>.</text>
<text><location><page_10><loc_63><loc_23><loc_64><loc_23></location>0</text>
<text><location><page_10><loc_63><loc_22><loc_64><loc_23></location>3</text>
<text><location><page_10><loc_63><loc_21><loc_64><loc_22></location>3</text>
<text><location><page_10><loc_63><loc_17><loc_64><loc_18></location>c</text>
<text><location><page_10><loc_63><loc_17><loc_64><loc_17></location>a</text>
<text><location><page_10><loc_63><loc_16><loc_64><loc_17></location>L</text>
<text><location><page_10><loc_63><loc_15><loc_64><loc_16></location>L</text>
<text><location><page_10><loc_63><loc_14><loc_64><loc_15></location>B</text>
<figure>
<location><page_11><loc_18><loc_67><loc_45><loc_81></location>
</figure>
<figure>
<location><page_11><loc_57><loc_67><loc_84><loc_81></location>
</figure>
<text><location><page_11><loc_31><loc_65><loc_36><loc_65></location>PKS 0426-380</text>
<figure>
<location><page_11><loc_18><loc_52><loc_45><loc_65></location>
</figure>
<text><location><page_11><loc_31><loc_50><loc_36><loc_50></location>PKS 0537-441</text>
<figure>
<location><page_11><loc_18><loc_37><loc_45><loc_50></location>
</figure>
<text><location><page_11><loc_32><loc_35><loc_35><loc_35></location>Mrk 421</text>
<figure>
<location><page_11><loc_18><loc_22><loc_45><loc_35></location>
</figure>
<text><location><page_11><loc_70><loc_65><loc_75><loc_65></location>PKS 0454-234</text>
<figure>
<location><page_11><loc_57><loc_52><loc_84><loc_65></location>
</figure>
<text><location><page_11><loc_70><loc_50><loc_74><loc_50></location>S4 1030+61</text>
<figure>
<location><page_11><loc_57><loc_37><loc_84><loc_50></location>
</figure>
<text><location><page_11><loc_69><loc_35><loc_74><loc_35></location>PKS B1222+216</text>
<figure>
<location><page_11><loc_57><loc_22><loc_84><loc_34></location>
<caption>Fig. 1.- Plots of NPSD for 15 AGNs. Lines show the fitting results. Broken lines are drawn when the fitting with a broken power-law gives a better fit (i.e., smaller reducedχ 2 ).</caption>
</figure>
<figure>
<location><page_12><loc_18><loc_72><loc_45><loc_86></location>
</figure>
<figure>
<location><page_12><loc_57><loc_72><loc_84><loc_86></location>
</figure>
<text><location><page_12><loc_31><loc_70><loc_36><loc_70></location>PKS 1510-089</text>
<figure>
<location><page_12><loc_18><loc_57><loc_45><loc_70></location>
</figure>
<figure>
<location><page_12><loc_18><loc_42><loc_45><loc_55></location>
</figure>
<figure>
<location><page_12><loc_57><loc_42><loc_84><loc_55></location>
</figure>
<text><location><page_12><loc_31><loc_40><loc_36><loc_40></location>PKS 2326-502</text>
<figure>
<location><page_12><loc_18><loc_27><loc_45><loc_40></location>
<caption>Fig. 1.Continued.</caption>
</figure>
<text><location><page_12><loc_69><loc_70><loc_74><loc_70></location>PKS 2155-304</text>
<figure>
<location><page_12><loc_57><loc_57><loc_84><loc_70></location>
</figure>
<text><location><page_12><loc_70><loc_55><loc_74><loc_55></location>3C 454.3</text>
<text><location><page_12><loc_69><loc_42><loc_70><loc_42></location>10</text>
<section_header_level_1><location><page_13><loc_43><loc_85><loc_57><loc_86></location>4. Discussion</section_header_level_1>
<text><location><page_13><loc_12><loc_57><loc_88><loc_81></location>The internal shock model is a popular scenario of blazar emission as it can explain spectral energy distributions and time-lag features (Bottcher & Dermer 2010, and references therein). Wehrle et al. (2012) studied multiwavelength variations of the 3C 454.3 outburst from 2010 November to 2011 January with observations by Herschel , Swift , Fermi -LAT, optical telescopes and submillimeter arrays. They proposed a model in which turbulent plasma crosses a conical standing shock in the parsec-scale region of the jet, based on time-resolved spectral energy distributions for this outburst. Thus, here we assume the internal shock model as the emission mechanism for gamma-ray flares and we interpret the characteristic time scale that we found in terms of this model.</text>
<text><location><page_13><loc_12><loc_32><loc_88><loc_54></location>Kataoka et al. (2001) studied the X-ray variability of three TeV blazars, Mrk 421, Mrk501 and PKS 2155 -304, using ASCA and RXTE data. In order to interpret the observed characteristic time scale which they found in their NPSD plots, they assumed a simple model based on the internal shock model. They considered two relativistic blobs with bulk Lorentz factors Γ and a 0 Γ ( a 0 > 1) ejected at the times t = 0 and t = τ 0 ( > 0), respectively, and when the second, faster blob catches up and collide with the first, slower blob, the resulting shock generates a high-energy flare. In this model, the mass of the central black hole, M CBH , is derived from the variation time-scale, t var , as</text>
<formula><location><page_13><loc_36><loc_27><loc_88><loc_31></location>M CBH /similarequal 9 × 10 8 M /circledot t var day 10 k a 2 0 -1 2 a 2 0 (6)</formula>
<text><location><page_13><loc_12><loc_21><loc_87><loc_26></location>where M /circledot is the solar mass and k = cτ 0 /R g ≥ 3 with the Schwarzschild radius R g . They derived (10 7 -10 10 ) M /circledot as the masses of the central black holes of these blazars.</text>
<text><location><page_13><loc_12><loc_14><loc_88><loc_19></location>Though this model was devised to explain the X-ray time variability of blazars, here we assume the same mechanism works for the gamma-ray time variability 3 , and we applied the</text>
<text><location><page_14><loc_12><loc_67><loc_88><loc_86></location>above equation to estimate the central black-hole mass of 3C 454.3. We take the variation time-scale as the inverse of the turnover frequency which we observed in the NPSD plot of 3C454.3, t var = 1 / (10 -5 . 834 Hz) = 6 . 82 × 10 5 s = 7 . 89 days. Figure 2 shows the result for several values of model parameters: a 0 = 1-100 and k = 5 , 20 , 100 following Kataoka et al. (2001). We can infer the central black hole mass is in the range (10 8 -10 10 ) M /circledot from this plot in most of the parameter space ( a 0 /greaterorsimilar 2, which means the Lorentz factors of colliding blobs differ significantly).</text>
<text><location><page_14><loc_12><loc_57><loc_88><loc_65></location>Alternatively, we can infer the range of the unknown parameter k , or the light crossing time in units of the Schwarzschild radius, by assuming the central black hole mass estimated by other methods.</text>
<text><location><page_14><loc_12><loc_45><loc_88><loc_55></location>3C454.3 is one of the most well-known and well-studied gamma-ray sources. Recently it and estimated the central black hole mass by refining the discussion of Gu et al. (2001), who</text>
<text><location><page_14><loc_12><loc_27><loc_88><loc_52></location>showed two large flares, in 2009 November-December (Ackermann et al. 2011; Striani et al. 2010) and 2010 December (Abdo et al. 2011). Bonnoli et al. (2011) analyzed the 2009 flare used the broad line width and the distance of the broad line region (BLR) from the center. Assuming the broad emission lines being produced in clouds which are gravitationally bound and orbiting with Keplerian velocities (Dibai 1981), the central black hole mass can be given by M CBH R BLR V 2 G -1 , where R BLR is the radius of the BLR and V is the velocity of the clouds in the BLR. Gu et al. (2001) and Bonnoli et al. (2011) estimated the central black hole mass of 3C 454.3 is 4 × 10 9 M /circledot and 5 × 10 8 M /circledot , respectively.</text>
<text><location><page_14><loc_12><loc_20><loc_88><loc_25></location>Figure 3 shows the variation of k = cτ 0 /R g as a function of the ratio of blob Lorentz factor, a 0 , for two estimated values of the central black hole mass. We see k is in the range</text>
<text><location><page_15><loc_12><loc_79><loc_87><loc_86></location>of 7 to 70 for a 0 /greaterorsimilar 2. This parameter range is more restrictive than in the case of general consideration for blazar X-ray flares by Kataoka et al. (2001), where k in the range of 5 ∼ 100 for t var = 1 ∼ 10 day and M CBH = (10 7 ∼ 10 10 ) M /circledot .</text>
<figure>
<location><page_15><loc_24><loc_49><loc_76><loc_75></location>
<caption>Fig. 2.- The central black hole mass as a function of the ratio of blob Lorentz factor, a 0 , assuming the internal shock model for time variation scale t var and some values of k (the light-crossing time in unit of R g (Schwarzschild radius) /c ).</caption>
</figure>
<text><location><page_15><loc_12><loc_10><loc_88><loc_32></location>The GeV gamma-ray flux during the strong outburst of 3C454.3 in 2010 November exhibited a very fast variability with the rise time of 4 . 5 ± 1 hr and the fall time of 14 ± 2 hr (Abdo et al. 2011). We tried to apply the Equation 6 assuming the variation time scale as this rise time, and the results are shown in Figures 2 and 3. The central black hole mass inferred from this time scale ( < 2 × 10 8 M /circledot , see Figure 2) is much smaller than that inferred from the characteristic time scale in NPSD, and the light crossing time ( k < 2, see Figure 3) is less than the time to cross the last stable orbit of the black hole. Thus it seems unreasonable to assign the short time scale of 4.5 hr to the internal shock model under</text>
<figure>
<location><page_16><loc_24><loc_41><loc_76><loc_68></location>
<caption>Fig. 3.- The light-crossing time k in units of R g /c , (where R g is the Schwarzschild radius) as a function of the ratio of blob Lorentz factor, a 0 , assuming the internal shock model for the variation time-scale, t var , and central black hole mass.</caption>
</figure>
<text><location><page_17><loc_12><loc_76><loc_87><loc_86></location>consideration in this paper: it should be interpreted as, e.g., shocks forming with strong anisotropic geometries, albeit a low duty cycle (e.g., Salvati, Spada and Pacini (1998)), or existence of small active regions, inside a larger jet, moving faster than the rest of the plasma, occasionally pointing toward us (Ghisellini & Tavecchio 2008).</text>
<section_header_level_1><location><page_17><loc_43><loc_69><loc_57><loc_70></location>5. Conclusion</section_header_level_1>
<text><location><page_17><loc_12><loc_55><loc_88><loc_66></location>Using the gamma-ray daily light curves observed by Fermi -LAT over 3.6 yr, we studied the temporal behavior of 15 AGNs by calculating the NPSDs for each sources. One source, 3C454.3, showed a clear turnover in the NPSD curve which corresponds to a characteristic time scale of 6 . 82 × 10 5 s.</text>
<text><location><page_17><loc_12><loc_43><loc_88><loc_53></location>This time scale can be interpreted as a result of an collision of blobs in the internal shock of the blazar jet, as discussed by Kataoka et al. (2001) for the NPSD of X-ray data on blazars. The time variation scale we found indicates the central black hole mass of 3C 454.3 is in the range of (10 8 -10 10 ) M /circledot .</text>
<text><location><page_17><loc_12><loc_30><loc_88><loc_40></location>Alternatively, if we assume the central black hole mass of 3C 454.3 is (0 . 5-4) × 10 9 M /circledot after Gu et al. (2001) and Bonnoli et al. (2011), we can infer the time interval emitted the internal shock wave is 7-70 times the light crossing time of the Schwarzschild radius of the central black hole.</text>
<text><location><page_17><loc_12><loc_18><loc_87><loc_26></location>We thank the anonymous referee for useful comments and suggestions. This work is supported in part by the Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, No. 22540315.</text>
<section_header_level_1><location><page_18><loc_43><loc_85><loc_58><loc_86></location>REFERENCES</section_header_level_1>
<text><location><page_18><loc_12><loc_80><loc_47><loc_82></location>Abdo, A.A. et al., 2010a, Nature, 463, 919</text>
<text><location><page_18><loc_12><loc_76><loc_45><loc_78></location>Abdo, A.A. et al., 2010b, ApJ, 722, 520</text>
<text><location><page_18><loc_12><loc_72><loc_44><loc_74></location>Abdo, A.A. et al., 2011, ApJ, 733, L26</text>
<text><location><page_18><loc_12><loc_14><loc_87><loc_69></location>Ackermann, M. et al., 2010, ApJ, 721, 1383 Aharonian. F., et al., 2007, ApJ, 664, L71 Aleksi´c, B., et al., 2011, ApJ, ApJ, 730, L8 Atwood, W.B., Abdo, A.A. et al., 2009, ApJ, 697, 1071 Bonnoli, G. et al., 2011, MNRAS, 410, 368 Barr, P. and Mushstzky, R.F., Nature, 1986, 320, 421 B¨ottcher, M. and Dermer, C.D., 2010, ApJ, 445 Chatterjee, R. et al., 2012, ApJ, 749, 191 Czerny, B. et al., 2001, MNRAS, 325, 865 Dibai, E.A., 1981, Soviet Ast., 24, 389 Fossati, G., Maraschi, L., Celotti, A., Comastri, A., Ghisellini, G. 1998, MNRAS, 299, 433 Ghisellini, G. & Tavecchio, F., 2001, MNRAS, 386, L28 Gu, M. et al., 2001, MNRAS, 327, 1111 Hayashida, K., Miyamoto, S. et al., 1998, ApJ, 500, 642</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Radiation from the blazar class of active galactic nuclei (AGN) exhibits fast time variability which is usually ascribed to instabilities in the emission region near the central supermassive black hole. The variability time scale is generally faster in higher energy region, and data recently provided by the Fermi Gammaray Space Telescope in the GeV energy band enable a detailed study of the temporal behavior of AGN. Due to its wide field-of-view in the scanning mode, most sky regions are observed for several hours per day and daily light curves of many AGN have been accumulated for more than 4 r. In this paper we investigate the time variability of 15 well-detected AGNs by studying the normalized power spectrum density of their light curves in the GeV energy band. One source, 3C 454.3, shows a specific time scale of 6 . 8 × 10 5 s, and this value suggests, assuming the internal shock model, a mass for the central black hole of (10 8 -10 10 ) M /circledot which is consistent with other estimates. It also indicates the typical time interval of ejected blobs is (7-70) times the light crossing time of the Schwarzschild radius. Subject headings: BL Lacertae objects: general - galaxies: active - gamma rays: galaxies",
"pages": [
2
]
},
{
"title": "Time series analysis of gamma-ray blazars and implications for the central black-hole mass",
"content": "Kenji Nakagawa and Masaki Mori Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan Received ; accepted To be submitted for publication",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "About 1% of galaxies have an active galactic nucleus (AGN), which emits 10 9 -10 14 times the solar power over a wide range of the energy spectrum, from radio to gamma-ray energies. AGNs constitute one of the most violently variable and interesting classes of object in the universe. The activity of AGN is believed to originate from the central supermassive black hole, with masses of 10 6 -10 9 solar mass ( M /circledot ), and part of their energy is emitted in electromagnetic radiation from the surrounding region including the accretion disk formed around the black hole and relativistic jets ejected along rotation axes (e.g., Urry & Padovani 1995). A subclass of radio-loud AGN are called blazars, in which the line of sight lies close to the jet axis, and the emission from relativistic jets is only visible in this class of AGN due to the relativistic beaming effect, especially in the high-energy region. The electromagnetic spectra of blazars are dominated by non-thermal radiation produced in the jets. The popular scenario to explain these emission spectra assumes that the particles in the jets are accelerated to high energies by diffusive shocks in the jets and induce emission via interaction with surrounding matter/radiation (e.g., Fossati et al. 1998) 1 . Observations of blazars at various wavelengths have revealed fast time variability which is most plausibly related to instabilities in the emission environment near the black hole (e.g., Ulrich, Maraschi & Urry 1997). Past observations suggest the variability is larger at higher energies (the most extreme example is Mrk 501 Nowak et al. 2012), which may indicate the higher energy emission comes from the region closer to the central black holes. The variability time scale reflects the size of the emission region, and thus the study of temporal behavior of gamma-ray flux is an excellent probe of the region close to the central engine, i.e., the supermassive black hole. Blazars are known to show flaring activity which occurs randomly and continues for several days to months. In order to study their temporal variability precisely, blazars should be monitored continuously, or at least frequently. It is not an easy task for narrow field-of-view telescopes like optical, X-ray, and Cherenkov (TeV gamma-ray) instruments to monitor many blazars for long periods. Besides, their observations are limited as ground-based telescopes can only operate on dark, clear nights and X-ray satellites are used in pointing-mode observations. Nevertheless, in the X-ray band, Hayashida et al. (1998) evaluated the central black hole masses in several AGNs based on their rather well-sampled X-ray light curves obtained with the Ginga satellite and suggested the masses 1 ∼ 2 orders of magnitude smaller than previous estimates. Kataoka et al. (2001) studied time variability of three TeV-detected AGNs based on ASCA and/or RXTE observations and showed that (10 7 ∼ 10 10 ) M /circledot black holes and internal shocks that start to develop at 100 times the Schwarzschild radii could explain the observed properties. In the GeV gamma-ray band, the Fermi Gamma-ray Space Telescope has been monitoring the whole sky with the Large Area Telescope (LAT) since 2008. The LAT is a wide field-of-view gamma-ray imager that observes one-fifth of the sky at any instant and that scans the whole sky in a day (Atwood et al. 2009). The second Fermi -LAT catalog, which contains 1092 (28 identified and 1064 associated) AGN among the 1873 detected sources in the 100 MeV to 100 GeV range (Nolan et al. 2012). Gamma-ray light curves of several tens of blazars are provided on a daily basis and this is a good database to study the time variability of blazars. Abdo et al. (2010b) reported a detailed analysis of the variability of 106 objects in the Fermi -LAT Bright AGN Sample. They showed that the temporal behavior of gamma-ray fluxes of variable sources can be described by power-law power spectral density (PSD) in general, with a few blazars that showed strong activity exhibiting complex and structured temporal profiles. They examined whether it was possible to characterize blazar type with the PSD slope, but the results were not conclusive. In this paper, we report the time series analysis of gamma-ray light curves of 15 blazars based on Fermi -LAT data and discuss the results in relation to the properties of the central engine. Our analysis is the first systematic study of long-term variability of blazar emission in the gamma-ray energy band, although the analysis method itself has been applied and reported previously ((e.g., in the X-ray band, Lawrence et al. 1987; McHardy & Czerny 1987; Miyamoto et al. 1994; Hayashida et al. 1998; Kataoka et al. 2001).",
"pages": [
3,
4,
5
]
},
{
"title": "2. Data and Analysis",
"content": "We use the 'monitored source light curves' provided by the Fermi Science Support Center (FSSC) 2 for bright and transient gamma-ray sources. They are regularly updated throughout the mission. In this paper, we analyze the daily light curves of 15 AGN (Table 1) in the energy range 100 MeV - 300 GeV. The data period is between 2008 August 9 and 2012 April 26. These sources are selected because a large fraction of data points are detections, not upper limits, so that we can extract useful information on time variability. Note that the usage of daily light curves spanning 44 months naturally limits our time series analysis to the 10 -8 -10 -5 Hz range. Faster variability observed in the case of 3C 2 http://fermi.gsfc.nasa.gov/ssc/data/access/lat/msl_lc/ Note that, as stated here, these light curves are preliminary and fluxes do not have absolute calibration, and a preliminary instrument response function is used. 454.3 (Abdo et al. 2011), for example, is out of the scope of the present analysis. As we noted in Section 1, the variability time scale of AGN flares reflects the size of the emission region, and thus the study of temporal behavior of gamma-ray flux can be a good probe to explore the physical environment close to the central engine. However, characterizing the time scale is not a simple task since we know that the intensity of gamma-ray emission from AGN flares varies very irregularly. The fastest doubling time has been widely used (see Barr & Mushotzky 1986, for example) as a variability measure, but it depends on data quality and coverage. Here we adopt a spectral analysis, the normalized power spectrum density (NPSD), to evaluate the characteristic timescale of light curves which fluctuate chaotically, after Miyamoto et al. (1994).",
"pages": [
5,
6
]
},
{
"title": "2.1. Normalized Power Spectral Density",
"content": "The PSD shows the degree of variation at every frequency (or cycle) by calculating the Fourier transform of time variable data (Lawrence et al. 1987; McHardy & Czerny 1987). The NPSD, which is obtained by dividing the PSD by the average source intensity squared, has proven to be useful to compare variability at each frequency even if the brightness changes (Miyamoto et al. 1994; Kataoka et al. 2001). It is defined as where F j is the source count rate at time t j (0 < t j < n -1), T is the total time length, F av is the mean value of source count rates, and σ stat is the error due to counting statistics. In our analysis, we calculated the power P ( f ) for some discrete frequencies given by f = k/T ( k is an integer and 1 < k < n/ 2) and averaged. The Fermi -LAT light curves are given with flux errors ( e j ) and their standard deviation ( √ ∑ j e 2 j /N ) is substituted for σ stat as a rough estimate of error of counting statistics (see Section 2.2 for more discussion). The error bars of the NPSD are standard deviations of powers in each frequency bin (see Hayashida et al. 1998; Kataoka et al. 2001, for more discussion of NPSD analyses). In our calculation of the NPSD, we did not use upper limits in the light curves. In addition, we did not interpolate any blank (i.e., missing) data contained in the light curves.",
"pages": [
6,
7
]
},
{
"title": "2.2. Poisson Noise",
"content": "If the time series is a continuous counting rate binned into intervals, as it is here, the effect of Poisson noise is to add an approximately constant amount of power to the NPSD at all frequencies. At high frequencies, where the counting rate is low, the NPSD will be dominated by the flat (white) Poisson noise spectrum. In the definition of NPSD (Equation 1) this noise is subtracted in the term σ 2 stat /n (see Vaughan, Fabian and Nandra 2003, for further discussion). In the present case, F j ( e j ) is calculated as the counts (count error) divided by the exposure, and the daily exposure is almost uniform for the Fermi -LAT observations. The Poisson noise is therefore approximately subtracted in the calculation of the NPSD (Equation 1). This treatment formally assumes zero background flux, but this is a reasonable approximation in our case, since the Fermi -LAT light curves are released after subtracting background counts when they are processed at the FSSC. If the subtraction of the Poisson noise estimated by the quoted flux errors is not sufficiently accurate, there will be a residual constant which becomes dominant at high frequencies in the NPSD, which can be seen in some cases in our results (next section).",
"pages": [
7
]
},
{
"title": "3. Results",
"content": "We calculated the NPSD for the Fermi -LAT daily light curves of 15 AGNs using 9 frequency bins divided logarithmically from 10 -7 Hz to 10 -5 . 2 Hz. Plots are shown in Figure 1. One may note that data points at high frequencies are missing for most of the sources in Figure 1. One reason is that many observations in the Fermi -LAT light curves yield only upper limits. Another reason is that large flares which last for ten of days or more are rare: we cannot have points above ∼ 10 -6 Hz without such flares. We applied least-square fits to these points assuming a power-law and/or a broken power-law where ν is the frequency and ν b is the 'turnover' frequency. Fit parameters are summarized in Table 1. The fit lines are overplotted in Figure 1, where broken power-law lines are plotted only when the reduced χ 2 values are smaller than single power-law values.. We see NPSDs for four sources, PKS 0537 -441, 3C 279, 3C 454.3 and PKS 2326 -502, are better fitted by broken power-laws than by single power-laws. The NPSD plots for PKS 0537 -502, 3C 279 and PKS 2326 -502 show upward turnovers above 10 -6 . 18 Hz, 10 -5 . 88 Hz and 10 -6 . 10 Hz, respectively, but the slopes above these frequencies ( γ 2 ) have large uncertainties and are consistent with zero: thus they may have reached a constant Poisson-like noise level which is not removed by our rough estimate of counting statistical error (see section 2.1). We checked the difference of NPSD values before and after removing the Poisson noise, assuming the value of Poisson noise is the normalized square-root of sum of squares of several flux's error: √ ∑ e 2 i /N . With this procedure, the NPSD values at high frequencies showed smaller values than those before removal, but the slope above the turnover of the NPSD plot remained flat (consistent with zero slope). Thus, even if we could not remove the effect of Poisson noise completely, it seems this flattening behavior does not have a physical origin. On the other hand, the NPSD plot for 3C 454.3 show a turnover at 10 -5 . 83 Hz and the slope above it, -3 . 08 ± 0 . 83, is well determined. The reduced χ 2 value decreases from 1.29 for single power-law fit, which is not at acceptable level, to 0.23 for broken power-law fit, which is acceptable. Thus, only the plot for 3C 454.3, which exhibited an extraordinary large flare in 2010 November (Abdo et al. 2011), seems to show a physically meaningful turnover, at 10 -5 . 83 Hz, which we discuss further in the next section. t o r e 3 8 1 9 7 8 4 3 8 3 0 1 A d e z ly a n a A f o t is L . 1 le b a T 0 0 2 ( δ ) 0 0 0 2 ( α e c r u o S b ν 0 ) g e d ( ) g e d ( e m a N 9 . 7 3 - 8 6 1 . 7 6 0 8 3 - 6 2 4 0 S K P 4 . 3 2 - 3 6 2 . 4 7 4 3 2 - 4 5 4 0 S K P 0 . 4 4 - 0 1 7 . 4 8 1 4 4 - 7 3 5 0 S K P 0 5 . 2 8 7 2 . 7 8 1 3 7 2 C 3 8 7 . 5 - 7 4 0 . 4 9 1 9 7 2 C 3 0 1 . 9 - 1 1 2 . 8 2 2 9 8 0 - 0 1 5 1 S K P 2 . 0 3 - 7 1 7 . 9 2 3 4 0 3 - 5 5 1 2 S K P 9 . 9 4 - 7 3 3 . 2 5 3 2 0 5 - 6 2 3 2 S K P 4 1 . 6 1 1 9 4 . 3 4 3 3 . 4 5 4 C 3 3 0 . 3 4 5 6 6 . 6 3 A 6 6 C 3 0 8 . 8 2 8 6 4 . 9 3 7 0 . 8 2 + C 4 5 8 . 0 6 4 6 4 . 8 5 1 1 6 + 0 3 0 1 4 S - 10 - 0 2 . 8 3 4 1 1 . 6 6 1 1 2 4 k r M 8 3 . 1 2 7 2 2 . 6 8 1 6 1 2 + 2 2 2 1 S K P 7 2 . 2 4 0 8 6 . 0 3 3 c a L L B PKS 0426-380 PKS 0537-441 Mrk 421 PKS 0454-234 S4 1030+61 PKS B1222+216 PKS 1510-089 PKS 2326-502 PKS 2155-304 3C 454.3 10",
"pages": [
8,
9,
10,
11,
12
]
},
{
"title": "4. Discussion",
"content": "The internal shock model is a popular scenario of blazar emission as it can explain spectral energy distributions and time-lag features (Bottcher & Dermer 2010, and references therein). Wehrle et al. (2012) studied multiwavelength variations of the 3C 454.3 outburst from 2010 November to 2011 January with observations by Herschel , Swift , Fermi -LAT, optical telescopes and submillimeter arrays. They proposed a model in which turbulent plasma crosses a conical standing shock in the parsec-scale region of the jet, based on time-resolved spectral energy distributions for this outburst. Thus, here we assume the internal shock model as the emission mechanism for gamma-ray flares and we interpret the characteristic time scale that we found in terms of this model. Kataoka et al. (2001) studied the X-ray variability of three TeV blazars, Mrk 421, Mrk501 and PKS 2155 -304, using ASCA and RXTE data. In order to interpret the observed characteristic time scale which they found in their NPSD plots, they assumed a simple model based on the internal shock model. They considered two relativistic blobs with bulk Lorentz factors Γ and a 0 Γ ( a 0 > 1) ejected at the times t = 0 and t = τ 0 ( > 0), respectively, and when the second, faster blob catches up and collide with the first, slower blob, the resulting shock generates a high-energy flare. In this model, the mass of the central black hole, M CBH , is derived from the variation time-scale, t var , as where M /circledot is the solar mass and k = cτ 0 /R g ≥ 3 with the Schwarzschild radius R g . They derived (10 7 -10 10 ) M /circledot as the masses of the central black holes of these blazars. Though this model was devised to explain the X-ray time variability of blazars, here we assume the same mechanism works for the gamma-ray time variability 3 , and we applied the above equation to estimate the central black-hole mass of 3C 454.3. We take the variation time-scale as the inverse of the turnover frequency which we observed in the NPSD plot of 3C454.3, t var = 1 / (10 -5 . 834 Hz) = 6 . 82 × 10 5 s = 7 . 89 days. Figure 2 shows the result for several values of model parameters: a 0 = 1-100 and k = 5 , 20 , 100 following Kataoka et al. (2001). We can infer the central black hole mass is in the range (10 8 -10 10 ) M /circledot from this plot in most of the parameter space ( a 0 /greaterorsimilar 2, which means the Lorentz factors of colliding blobs differ significantly). Alternatively, we can infer the range of the unknown parameter k , or the light crossing time in units of the Schwarzschild radius, by assuming the central black hole mass estimated by other methods. 3C454.3 is one of the most well-known and well-studied gamma-ray sources. Recently it and estimated the central black hole mass by refining the discussion of Gu et al. (2001), who showed two large flares, in 2009 November-December (Ackermann et al. 2011; Striani et al. 2010) and 2010 December (Abdo et al. 2011). Bonnoli et al. (2011) analyzed the 2009 flare used the broad line width and the distance of the broad line region (BLR) from the center. Assuming the broad emission lines being produced in clouds which are gravitationally bound and orbiting with Keplerian velocities (Dibai 1981), the central black hole mass can be given by M CBH R BLR V 2 G -1 , where R BLR is the radius of the BLR and V is the velocity of the clouds in the BLR. Gu et al. (2001) and Bonnoli et al. (2011) estimated the central black hole mass of 3C 454.3 is 4 × 10 9 M /circledot and 5 × 10 8 M /circledot , respectively. Figure 3 shows the variation of k = cτ 0 /R g as a function of the ratio of blob Lorentz factor, a 0 , for two estimated values of the central black hole mass. We see k is in the range of 7 to 70 for a 0 /greaterorsimilar 2. This parameter range is more restrictive than in the case of general consideration for blazar X-ray flares by Kataoka et al. (2001), where k in the range of 5 ∼ 100 for t var = 1 ∼ 10 day and M CBH = (10 7 ∼ 10 10 ) M /circledot . The GeV gamma-ray flux during the strong outburst of 3C454.3 in 2010 November exhibited a very fast variability with the rise time of 4 . 5 ± 1 hr and the fall time of 14 ± 2 hr (Abdo et al. 2011). We tried to apply the Equation 6 assuming the variation time scale as this rise time, and the results are shown in Figures 2 and 3. The central black hole mass inferred from this time scale ( < 2 × 10 8 M /circledot , see Figure 2) is much smaller than that inferred from the characteristic time scale in NPSD, and the light crossing time ( k < 2, see Figure 3) is less than the time to cross the last stable orbit of the black hole. Thus it seems unreasonable to assign the short time scale of 4.5 hr to the internal shock model under consideration in this paper: it should be interpreted as, e.g., shocks forming with strong anisotropic geometries, albeit a low duty cycle (e.g., Salvati, Spada and Pacini (1998)), or existence of small active regions, inside a larger jet, moving faster than the rest of the plasma, occasionally pointing toward us (Ghisellini & Tavecchio 2008).",
"pages": [
13,
14,
15,
17
]
},
{
"title": "5. Conclusion",
"content": "Using the gamma-ray daily light curves observed by Fermi -LAT over 3.6 yr, we studied the temporal behavior of 15 AGNs by calculating the NPSDs for each sources. One source, 3C454.3, showed a clear turnover in the NPSD curve which corresponds to a characteristic time scale of 6 . 82 × 10 5 s. This time scale can be interpreted as a result of an collision of blobs in the internal shock of the blazar jet, as discussed by Kataoka et al. (2001) for the NPSD of X-ray data on blazars. The time variation scale we found indicates the central black hole mass of 3C 454.3 is in the range of (10 8 -10 10 ) M /circledot . Alternatively, if we assume the central black hole mass of 3C 454.3 is (0 . 5-4) × 10 9 M /circledot after Gu et al. (2001) and Bonnoli et al. (2011), we can infer the time interval emitted the internal shock wave is 7-70 times the light crossing time of the Schwarzschild radius of the central black hole. We thank the anonymous referee for useful comments and suggestions. This work is supported in part by the Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, No. 22540315.",
"pages": [
17
]
},
{
"title": "REFERENCES",
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"pages": [
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}
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2013ApJ...773L...5M
https://arxiv.org/pdf/1303.4309.pdf
<document>
<section_header_level_1><location><page_1><loc_9><loc_81><loc_86><loc_85></location>The hard X-ray spectrum of NGC 1365: scattered light, not black hole spin</section_header_level_1>
<section_header_level_1><location><page_1><loc_44><loc_76><loc_51><loc_77></location>L. Miller</section_header_level_1>
<text><location><page_1><loc_11><loc_73><loc_84><loc_76></location>Dept. of Physics, Oxford University, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, U.K. and</text>
<section_header_level_1><location><page_1><loc_42><loc_69><loc_53><loc_70></location>T. J. Turner</section_header_level_1>
<text><location><page_1><loc_15><loc_67><loc_80><loc_68></location>Dept. of Physics, University of Maryland Baltimore County, Baltimore, MD 21250, U.S.A.</text>
<section_header_level_1><location><page_1><loc_41><loc_60><loc_54><loc_61></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_13><loc_34><loc_82><loc_59></location>Active Galactic Nuclei (AGN) show excess X-ray emission above 10 keV compared with extrapolation of spectra from lower energies. Risaliti et al. have recently attempted to model the hard X-ray excess in the type 1.8 AGN NGC 1365, concluding that the hard excess most likely arises from Compton-scattered reflection of X-rays from an inner accretion disk close to the black hole. Their analysis disfavored a model in which the hard excess arises from a high column density of circumnuclear gas partially covering a primary X-ray source, despite such components being required in the NGC 1365 data below 10 keV. Using a Monte Carlo radiative transfer approach, we demonstrate that this conclusion is invalidated by (i) use of slab absorption models, which have unrealistic transmission spectra for partial covering gas, (ii) neglect of the effect of Compton scattering on transmitted spectra and (iii) inadequate modeling of the spectrum of scattered X-rays. The scattered spectrum is geometry dependent and, for high global covering factors, may dominate above 10 keV. We further show that, in models of circumnuclear gas, the suppression of the observed hard X-ray flux by reprocessing may be no larger than required by the 'light bending' model invoked for inner disk reflection, and the expected emission line strengths lie within the observed range. We conclude that the time-invariant 'red wing' in AGN X-ray spectra is probably caused by continuum transmitted through and scattered from circumnuclear gas, not by highly redshifted line emission, and that measurement of black hole spin is not possible.</text>
<text><location><page_1><loc_13><loc_30><loc_82><loc_33></location>Subject headings: radiative transfer - galaxies: active - X-rays: galaxies - X-rays: individual (NGC 1365)</text>
<section_header_level_1><location><page_1><loc_9><loc_28><loc_23><loc_29></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_9><loc_10><loc_48><loc_26></location>Observations of AGN reveal evidence for absorbing gas surrounding an accreting black hole system at both X-ray (see Turner & Miller 2009, for a review) and UV wavelengths (e.g. Crenshaw et al. 2003). High column density outflowing gas may be seen in up to 40% of type 1 AGN (e.g. Cappi et al. 2009; Tombesi et al. 2012). A recent Suzaku study (Tatum et al. 2013) of a hard X-ray selected sample of type 1 AGN has shown luminosities above 10keV to be much higher than expected from extrapolation of models from the 0.5-10keV band.</text>
<text><location><page_1><loc_51><loc_18><loc_86><loc_29></location>This 'hard excess' is ubiquitous in local type 1 AGN and, owing to the sharp absorption edges associated with the hardest source spectra, cannot be explained other than by the presence of a Compton-thick layer of low-ionization absorbing gas, covering a large fraction of the continuum source (Tatum et al. 2013).</text>
<text><location><page_1><loc_51><loc_11><loc_86><loc_18></location>Partial-covering absorption by gas below the Compton-thick limit has long been known in type 1 AGN (Piro et al. 2005; Miller et al. 2008) and changes in the absorber may explain Xray spectral variability on long timescales. The</text>
<text><location><page_2><loc_9><loc_83><loc_45><loc_86></location>Tatum et al. (2013) analysis extends the paradigm into the Compton-thick regime.</text>
<text><location><page_2><loc_9><loc_71><loc_45><loc_83></location>It has also long been claimed that X-ray spectra show features caused by Compton scattering and absorption (known as 'reflection') from an inner accretion disk, blurred by relativistic effects. Spectral curvature over the 2-8 keV band may be fit with a model that convolves reflection spectra (Ross & Fabian 2005) with general relativistic effects (c.f. Laor 1991).</text>
<text><location><page_2><loc_9><loc_57><loc_45><loc_70></location>However, it is difficult to distinguish absorption and reflection signatures by fitting individual Xray spectra, because Compton scattering and absorption shape both models, leading to similarities in overall shape. Consideration of AGN variability can help, and perhaps the biggest problem for the blurred reflection-dominated picture is the lack of any clear correlation between continuum and reflection flux in variable AGN (section 4).</text>
<text><location><page_2><loc_9><loc_45><loc_45><loc_57></location>A particularly interesting case is the type 1.8 AGN NGC 1365, which has been observed extensively at 0.5-10keV (Risaliti et al. 2000, 2005a,b, 2007, 2009b,c) and higher energies (Risaliti et al. 2009a, 2013). These observations have shown spectral variability on timescales as short as a few hours, attributed to changes in the X-ray absorber.</text>
<text><location><page_2><loc_9><loc_26><loc_46><loc_44></location>Risaliti et al. (2013) present simultaneous XMMNewton and NuSTAR data for NGC 1365, covering 0.5-79 keV. The authors claim that the data show relativistic disk features: broad Fe K α line emission and Compton scattering excess above 10keV. Risaliti et al. claim that the reflected component arises within 2.5 gravitational radii of a rapidly spinning black hole and that absorptiondominated models that do not include relativistic disk reflection can be ruled out. As this is a very strong assertion, we investigate here the assumptions upon which it is based.</text>
<text><location><page_2><loc_9><loc_11><loc_45><loc_26></location>There are two key processes that shape AGN X-ray spectra: Compton scattering and photoelectric absorption. At the high energies observed by NuSTAR , and for Compton-thick gas, it is crucial to include both effects. Risaliti et al. (2013) created models representing slabs of ionized absorbing gas. However, those models fitted to NGC 1365 required column density N H ∼ 5 × 10 24 cm -2 . Such gas would be Compton-thick, but current ionized absorption models do not in-</text>
<text><location><page_2><loc_51><loc_80><loc_86><loc_86></location>de Compton scattering. The circumnuclear gas also results in production of a scattered X-ray component which is highly dependent on the geometry of the scattering region.</text>
<text><location><page_2><loc_51><loc_68><loc_86><loc_80></location>In this paper we present Monte Carlo simulations that demonstrate the importance of the inclusion of Compton scattering for the column density regime applicable to NGC 1365. We also demonstrate the strong geometry-dependence of the predictions for both transmitted and scattered X-rays and discuss the implications for modeling and interpretation of AGN X-ray spectra.</text>
<section_header_level_1><location><page_2><loc_51><loc_63><loc_86><loc_66></location>2. Absorption and scattering by a spherical cloud</section_header_level_1>
<section_header_level_1><location><page_2><loc_51><loc_61><loc_79><loc_62></location>2.1. The importance of geometry</section_header_level_1>
<text><location><page_2><loc_51><loc_30><loc_86><loc_60></location>In this section, we consider a single cloud of constant density, absorbing photons from a distant source, to demonstrate the key effects that must be taken into account. The gas is assumed to be cold, with solar abundances (Anders & Grevesse 1989) and cross-sections of Verner et al. (1996). We first consider the effect of cloud geometry alone, omitting the effects of Compton scattering, for a cloud with column density 5 × 10 24 cm -2 , as found by Risaliti et al. (2013). The cloud is illuminated by a power-law of photon index Γ = 2 and has a normalization, that would be seen by the observer in the absence of absorption, of unity at 1 keV. Fig. 1 plots the transmitted spectrum Ef ( E ), for photon energy E and energy spectral flux density f ( E ). The lowest dashed curve shows the standard calculation obtained for a plane slab of uniform density, where the transmitted flux f ( E ) ∝ exp( -N H σ ( E )) for photoelectric absorption crosssection per hydrogen atom σ ( E ).</text>
<text><location><page_2><loc_51><loc_14><loc_86><loc_29></location>However, a plane slab is an unlikely choice for a clumpy distribution of gas that partially covers the source. The distribution of column density is likely to be complex, and it is instructive to compare with a uniform spherical cloud. Now, there is a distribution of column density associated with the cloud, p ( N H ) = 2 N H /N 2 H , max for N H ≤ N H , max , where N H , max is the maximum column density through the cloud. Integrating over this distribution, and in the absence of Compton</text>
<text><location><page_3><loc_9><loc_85><loc_36><loc_86></location>scattering, we expect transmitted flux</text>
<formula><location><page_3><loc_10><loc_79><loc_45><loc_84></location>f ( E ) ∝ 2 ( 1 -[1 + N H , max σ ( E )] e -N H , max σ ( E ) ) ( N H , max σ ( E )) 2 . (1)</formula>
<text><location><page_3><loc_9><loc_65><loc_45><loc_79></location>The upper dashed line in Fig. 1 shows the results for a cloud with mean density the same as the slab and for which N H , max is 3/2 times the mean column density. At high optical depths the transmitted flux f ( E ) → 2 ( N H , max σ ( E )) -2 , and since σ ( E ) has an approximately power-law form, a hard, powerlaw spectrum develops. In this regime, the dominant contribution to the transmitted flux comes from the periphery of the cloud.</text>
<text><location><page_3><loc_9><loc_55><loc_45><loc_65></location>The spherical cloud has a significantly different transmitted spectrum from the slab. Such a cloud model has the same number of model parameters as the slab, and is likely to be a better representation of a partial-covering cloud. This calculation alone demonstrates how careful one must be when fitting absorption models to AGN X-ray spectra.</text>
<section_header_level_1><location><page_3><loc_9><loc_52><loc_41><loc_53></location>2.2. The effect of Compton scattering</section_header_level_1>
<text><location><page_3><loc_9><loc_31><loc_45><loc_51></location>At high column densities, incident radiation is Compton scattered out of the line of sight. To model the transmitted and scattered spectra, we carried out a Monte Carlo radiative transfer simulation, following Miller et al. (2009). Multiple scatterings were allowed, and when photons were absorbed by a K shell of Fe, an Fe K line photon could be produced. Angle-dependent KleinNishina Compton scattering was calculated. The Monte Carlo spectra have been smoothed with a gaussian of FWHM ∆ E/E = 0 . 0283, appropriate for the resolution of typical CCD spectral data around Fe K.</text>
<text><location><page_3><loc_9><loc_16><loc_45><loc_31></location>The transmitted spectrum is shown by the lower, solid, red line in Fig. 1. At high energies the transmitted flux is significantly attenuated by Compton scattering. However, the spectrum is significantly different from either the slab or sphere when Compton scattering is neglected. At low energies, the transmitted flux is again dominated by light leaking through the periphery of the cloud, so that the spectrum tends towards the same form as the spherical, non-scattering cloud.</text>
<text><location><page_3><loc_9><loc_10><loc_45><loc_16></location>However, the light that is lost due to Compton scattering reappears in the scattered spectrum, shown in Fig. 1 by the upper solid curve. The spectrum has been integrated over all solid angles, so</text>
<text><location><page_3><loc_51><loc_64><loc_86><loc_86></location>that the normalization is such that this is the scattered spectrum that would be measured by an observer if the primary source were fully surrounded by such clouds, but neglecting the effect of radiation being reabsorbed or scattered by other clouds (which will be discussed in section 3). If instead only some fraction of lines of sight are intercepted by clouds, the normalization should be multiplied by the global covering factor. For any global covering factor C G /greaterorsimilar 0 . 1, the scattered spectrum dominates over the transmitted spectrum, and both spectra have considerably different shapes from the non-scattering slab and sphere. It is worth noting the low equivalent width of the Fe K α emission line (Miller et al. 2009; Yaqoob et al. 2010).</text>
<text><location><page_3><loc_51><loc_27><loc_90><loc_63></location>Finally, Fig. 1 shows a comparison with reflection from a plane, neutral, optically-thick slab as calculated by the pexrav model (Magdziarz & Zdziarski 1995) within xspec (Arnaud 1996), without calculation of the emission line strength. The normalization and shape of the pexrav spectrum varies with inclination: the curve shows the case for cos θ = 0 . 5, which matches most closely the cloud scattered spectrum around 10 keV. The pexrav spectrum is qualitatively similar to the cloud spectrum, although there are differences in shape, especially above 20 keV when the cloud spectrum has a less pronounced 'Compton hump'. Given also the significant differences in the transmitted spectra, we cannot expect to model even simple Compton-thick clouds with combinations of absorption by plane slabs and planar reflection. We shall see in the next section that, in models with a high covering factor of clumpy circumnuclear gas, the scattered spectrum shows much larger departures from the pexrav model. The importance of geometry for the observed spectrum has previously been demonstrated by Murphy & Yaqoob (2009) for a smooth toroidal reprocessor.</text>
<section_header_level_1><location><page_3><loc_51><loc_23><loc_86><loc_25></location>3. Scattering and absorption by a complex distribution of circumnuclear gas</section_header_level_1>
<text><location><page_3><loc_51><loc_11><loc_86><loc_21></location>In this section we consider the case of a high global covering factor of clumpy gas, when scattering of photons between clouds cannot be ignored (Nandra & George 1994, see also Merloni et al. 2006). As in Tatum et al. (2013), a simple, clumpy distribution was created by placing 1000 spherical clouds of equal radius between inner and</text>
<figure>
<location><page_4><loc_10><loc_46><loc_43><loc_78></location>
<caption>Fig. 1.Transmitted and scattered spectra from a single cloud: lower, dashed : transmitted spectrum through a uniform plane slab, neglecting Compton scattering; upper, dashed : transmitted spectrum through a uniform spherical cloud of same mean density as the plane slab, neglecting Compton scattering; lower, solid : transmitted spectrum through a uniform spherical cloud, including Compton scattering; upper, solid : scattered spectrum from the uniform spherical cloud; dotted : reflection from a plane slab calculated by pexrav .</caption>
</figure>
<text><location><page_4><loc_51><loc_53><loc_86><loc_86></location>outer radii r min and r max from a central X-ray source. Gas was placed inside each cloud with a uniform density (the density was not increased within overlapping clouds). For illustration, we chose N H = 1 . 5 × 10 24 cm -2 per unit cloud radius, chosen to approximately maximize the hard excess. In order to simulate the effect that in type 2 AGN we might be looking through a denser distribution of clouds than in type 1 AGN, the number density of clouds increased towards the equatorial plane as sin φ , where φ is the polar angle of observation. In Fig. 2 we show two models: model A has r min = 10, r max = 20 in units of the cloud radius; model B has r min = 10, r max = 30. The fraction of sightlines that were empty of gas was 0 . 35 at φ /similarequal 0, decreasing to < 0 . 15 for φ > 60 · in modelA, and 0 . 55 at φ /similarequal 0 decreasing to < 0 . 25 for φ > 60 · in model B. We emphasize that these are simplified models of circumnuclear material, designed to illustrate the radiative transfer effects, and are not to be taken as a proposal for the actual gas distribution.</text>
<text><location><page_4><loc_51><loc_24><loc_86><loc_53></location>Spectra were created using 6 × 10 10 input quanta with energy 0 . 1 -400keV. The input spectrum was a powerlaw of photon index Γ = 2 . 2, as inferred for NGC 1365 (e.g. Risaliti et al. 2009a). It was assumed that photons that propagated through the equatorial plane were absorbed by an accretion disk and, to avoid possible confusion with disk reflection, the disk did not re-emit photons. As in section 2 the gas was assumed cold and angle-dependent Klein-Nishina Compton scattering was calculated. Spectra can be accumulated only by averaging over finite solid angle, and here we adopted a solid angle corresponding to that subtended from the central source by a cloud at r max . A point source was placed at the center of the cloud distribution, but the averaging of photons over solid angle has the effect of mimicking the partial covering of an extended source of comparable size to a cloud.</text>
<text><location><page_4><loc_51><loc_10><loc_86><loc_24></location>Fig. 2 shows example spectra obtained for models A and B, viewed at polar angle φ = 60 · , for three azimuthal angles. The spectra have been smoothed as in section 2, but Monte Carlo noise is visible at low flux values. The spectra cover a range similar to that observed in the AGN population, from 'reflection dominated', through intermediate states where primary continuum is visible, to high states where the primary continuum</text>
<figure>
<location><page_5><loc_14><loc_31><loc_81><loc_78></location>
<caption>Fig. 2.- Spectra from the models of circumnuclear gas in section 3 for models A (upper panels) and B (lower panels). Each panel presents spectra from a different azimuthal angle, selected to show, from left-to-right, a low, intermediate and high flux state. The panels show the incident continuum (dashed powerlaw line), the spectrum of photons that have passed through holes in the gas distribution (green powerlaw line, not present in the left panels), the absorbed spectrum transmitted through the gas (blue curve), the spectrum of scattered light, including Fe K line emission (red curve), and the total spectrum (black solid curve). The left panels also show a pexrav model (dotted curve).</caption>
</figure>
<text><location><page_5><loc_45><loc_5><loc_46><loc_7></location>1</text>
<text><location><page_6><loc_9><loc_70><loc_45><loc_86></location>dominates. All states have significant hard excesses above 20 keV. Unobscured sightlines have total light at high energy that exceeds the input continuum amplitude. The panels show the contributions from various components: photons that pass through the holes in the distribution, photons that pass through clouds but are not scattered, and scattered photons, including Fe K α and Fe K β line emission. The incident continuum is also shown as a dashed line. The chief results are as follows.</text>
<unordered_list>
<list_item><location><page_6><loc_9><loc_63><loc_45><loc_69></location>(i) The transmitted, unscattered spectrum (blue curves) is variable and does not look like the spectrum expected from transmission through a slab model (section 2).</list_item>
<list_item><location><page_6><loc_9><loc_54><loc_45><loc_63></location>(ii) The scattered radiation is different from that calculated in either the isolated cloud or pexrav models (the left panels of Fig. 2 shows a pexrav model for photon index Γ = 2 . 2 and cos θ = 0 . 5). The hardness of the scattered spectrum increases with global covering factor.</list_item>
<list_item><location><page_6><loc_9><loc_46><loc_45><loc_54></location>(iii) Within each model, the scattered radiation is invariant with azimuthal viewing angle, because it does not depend on whether the primary source happens to be covered, or not, along any one sightline.</list_item>
<list_item><location><page_6><loc_9><loc_37><loc_45><loc_46></location>(iv) In all but the highest flux states, the scattered light is the dominant spectral component above 20keV, where the total amplitude is only a factor 3-4 below the incident continuum, even in this regime where the 2 -10keV continuum may be suppressed by much larger factors.</list_item>
<list_item><location><page_6><loc_9><loc_26><loc_45><loc_37></location>(v) The line flux of Fe K α is low, as expected (Miller et al. 2009; Yaqoob et al. 2010). Equivalent widths vary from 1500eV in the reflectiondominated state down to 10eV in the highest state. The equivalent width of Fe K α found in the three Suzaku observations of NGC 1365 is 330520eV (Tatum et al., in preparation).</list_item>
</unordered_list>
<section_header_level_1><location><page_6><loc_9><loc_24><loc_21><loc_25></location>4. Discussion</section_header_level_1>
<section_header_level_1><location><page_6><loc_9><loc_21><loc_40><loc_22></location>4.1. The 'red wing' in AGN spectra</section_header_level_1>
<text><location><page_6><loc_9><loc_11><loc_45><loc_20></location>The results of section 3 show that, on long timescales where spectral variability may be dominated by variations in observer covering fraction, there should be a spectrum of largely invariant scattered light that creates an apparent 'red wing' at energies below the Fe K edge. Such an invariant</text>
<text><location><page_6><loc_51><loc_59><loc_86><loc_86></location>red wing is well known (e.g. Fabian & Vaughan 2003), and using principal components analysis, Miller et al. (2007, 2008, 2010) showed that there is an approximately invariant 'offset' component in AGN spectra. The effect leads to a problem with the explanation of the red wing as reflection by the inner accretion disk. If the disk is close to the primary X-ray source, its flux variations should be closely tracked by the reflected light, but apparently they are not. Fabian & Vaughan (2003), Miniutti et al. (2003) and subsequent papers proposed a 'light bending' model in which a compact, primary source near the black hole moves towards or away from the disk, such that bending of light causes an apparent variation in flux from the primary source, but not from the reflected light. This model has to be finely tuned to obtain invariant reflected flux (Miniutti & Fabian 2004).</text>
<text><location><page_6><loc_51><loc_47><loc_86><loc_59></location>Such an a posteriori model is not required if the red wing arises from a combination of transmitted and scattered continua, as suggested by Turner et al. (2007), and not from highly redshifted line emission. Merloni et al. (2006) have also suggested this explanation in the context of scattered light arising in a model of an inhomogeneous accretion flow.</text>
<section_header_level_1><location><page_6><loc_51><loc_44><loc_86><loc_45></location>4.2. Modeling the spectrum of NGC 1365</section_header_level_1>
<text><location><page_6><loc_51><loc_10><loc_86><loc_43></location>In modeling the spectrum of NGC 1365, Risaliti et al. (2013) recognize that partial covering absorption is required, regardless of whether there is also a component of blurred reflection. In an initial comparison (Fig. 3 of Risaliti et al. 2013), a model of blurred reflection plus one absorber component was compared against a model of two absorber components. The models were only fit to the XMM-Newton data below 10 keV, and it was then seen how well each model extrapolated to higher energy. However, the blurred reflection included Compton scattering, but the two-absorber model did not. Hence it is no surprise that the first model extrapolated better above 10keV. In a subsequent test, Risaliti et al. (2013) fit also to the hard X-ray NuSTAR data and claimed that the blurred model is statistically better. But the transmitted and scattered light components were modeled with non-scattering, slab absorbers plus a pexrav component, so such a test is invalid. Point (ii) above demonstrates that existing models such as pexrav cannot ac-</text>
<text><location><page_7><loc_9><loc_83><loc_45><loc_86></location>curately account for reprocessing by a complex circumnuclear gas distribution.</text>
<text><location><page_7><loc_9><loc_69><loc_45><loc_83></location>Estimates of the continuum suppression arising from Compton scattering require proper inclusion of light scattered back into the line of sight by circumnuclear gas. Risaliti et al. (2013) considered the expected effect for Compton optical depth τ /similarequal 3 -4, using the plcabs model (Yaqoob 1997), and inferred that the intrinsic continuum would be a factor 8 larger than the observed continuum. The problems with this approach are:</text>
<unordered_list>
<list_item><location><page_7><loc_9><loc_63><loc_45><loc_69></location>(i) the assumed Compton depth was obtained from fitting slab absorption models, which is likely to be incorrect and thus lead to a significant error in the Compton loss estimate;</list_item>
<list_item><location><page_7><loc_9><loc_59><loc_45><loc_63></location>(ii) the approximations used in plcabs are not valid above 10 keV for high column density (Yaqoob 1997);</list_item>
<list_item><location><page_7><loc_9><loc_51><loc_45><loc_59></location>(iii) the plcabs model assumes full covering by a spherical shell, and we do not expect this to yield the same scattered light spectrum as clumpy, partial covering gas - our Monte Carlo simulations supersede the use of plcabs in this context.</list_item>
</unordered_list>
<text><location><page_7><loc_9><loc_44><loc_45><loc_51></location>In our models, the Compton loss correction is only a factor 3-4 at high energy, comparable to that in the 'light bending' model of inner disk reflection, where up to 75% of light is lost (Miniutti & Fabian 2004).</text>
<text><location><page_7><loc_9><loc_31><loc_45><loc_43></location>The scattering models presented here also show that the expected equivalent width of Fe K α covers a wide range that includes the observed range for NGC 1365. Finally, Tatum et al. (2013) argue that all type 1 AGN are affected by high-column, partial covering gas distributions, so the ratio of X-ray to infrared or optical line emission for NGC 1365 would not be expected to appear anomalous.</text>
<section_header_level_1><location><page_7><loc_9><loc_27><loc_45><loc_30></location>4.3. On the difficulty of measuring black hole spin</section_header_level_1>
<text><location><page_7><loc_9><loc_10><loc_45><loc_26></location>It has been claimed that black hole spin can be measured from the shape of the 'red wing', whose profile varies as a function of spin parameter a , which requires red wing measurement down to energies /lessorsimilar 3 keV, free from the effects of other modifications to the continuum. Even in the absence of circumnuclear reprocessing, a is difficult to measure free from degeneracies with other parameters (Dovˇciak et al. 2004). Given that in AGN such as NGC 1365, Mrk 766 (Miller et al. 2007) and MCG-6-30-15 (Miller et al. 2008) the entire red</text>
<text><location><page_7><loc_51><loc_74><loc_86><loc_86></location>wing may be modeled as scattered and absorbed continuum, and given that complex absorption must be present (e.g. NGC 1365, Risaliti et al. 2013), it is not possible to unambiguously identify and measure any alleged blurred red wing component with sufficient accuracy to determine spin in any of the AGN that have been subject to detailed study to date.</text>
<section_header_level_1><location><page_7><loc_51><loc_71><loc_64><loc_72></location>5. Conclusions</section_header_level_1>
<text><location><page_7><loc_51><loc_43><loc_86><loc_70></location>AGN spectra may contain significant levels of transmitted and scattered continua from partiallycovering circumnuclear gas, producing the timeinvariant 'red wing' below the Fe K edge and modifying the spectrum above 10 keV. Such gas is already known in NGC 1365. Geometry-dependent Compton scattering must be taken into account, using 3D radiative transfer calculations, when making spectral models and when accounting for the source total luminosity. The expected red wing, low Fe K α equivalent width and high energy excess may be easily confused with 'reflection' from an accretion disk, and spectral analyses to date have not established that there is any requirement for inner-disk reflection. Improved models of clumpy, ionized circumnuclear gas are required to achieve a full understanding of AGN X-ray spectra.</text>
<text><location><page_7><loc_53><loc_40><loc_86><loc_41></location>TJT acknowledges NASA grant NNX11AJ57G.</text>
<section_header_level_1><location><page_7><loc_51><loc_37><loc_63><loc_38></location>REFERENCES</section_header_level_1>
<text><location><page_7><loc_51><loc_33><loc_86><loc_36></location>Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53, 197</text>
<text><location><page_7><loc_51><loc_27><loc_86><loc_32></location>Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17-+</text>
<text><location><page_7><loc_51><loc_23><loc_86><loc_26></location>Cappi, M., Tombesi, F., Bianchi, S., et al. 2009, A&A, 504, 401</text>
<text><location><page_7><loc_51><loc_20><loc_86><loc_22></location>Crenshaw, D. M., Kraemer, S. B., & George, I. M. 2003, ARA&A, 41, 117</text>
<text><location><page_7><loc_51><loc_16><loc_86><loc_19></location>Dovˇciak, M., Karas, V., & Yaqoob, T. 2004, ApJS, 153, 205</text>
<text><location><page_7><loc_51><loc_13><loc_86><loc_15></location>Fabian, A. C., & Vaughan, S. 2003, MNRAS, 340, L28</text>
<text><location><page_7><loc_51><loc_11><loc_70><loc_12></location>Laor, A. 1991, ApJ, 376, 90</text>
<table>
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</table>
<text><location><page_8><loc_51><loc_83><loc_86><loc_86></location>Turner, T. J., Miller, L., Reeves, J. N., & Kraemer, S. B. 2007, A&A, 475, 121</text>
<text><location><page_8><loc_51><loc_80><loc_86><loc_83></location>Verner, D. A., Ferland, G. J., Korista, K. T., & Yakovlev, D. G. 1996, ApJ, 465, 487</text>
<text><location><page_8><loc_51><loc_78><loc_73><loc_79></location>Yaqoob, T. 1997, ApJ, 479, 184</text>
<text><location><page_8><loc_51><loc_74><loc_86><loc_77></location>Yaqoob, T., Murphy, K. D., Miller, L., & Turner, T. J. 2010, MNRAS, 401, 411</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Active Galactic Nuclei (AGN) show excess X-ray emission above 10 keV compared with extrapolation of spectra from lower energies. Risaliti et al. have recently attempted to model the hard X-ray excess in the type 1.8 AGN NGC 1365, concluding that the hard excess most likely arises from Compton-scattered reflection of X-rays from an inner accretion disk close to the black hole. Their analysis disfavored a model in which the hard excess arises from a high column density of circumnuclear gas partially covering a primary X-ray source, despite such components being required in the NGC 1365 data below 10 keV. Using a Monte Carlo radiative transfer approach, we demonstrate that this conclusion is invalidated by (i) use of slab absorption models, which have unrealistic transmission spectra for partial covering gas, (ii) neglect of the effect of Compton scattering on transmitted spectra and (iii) inadequate modeling of the spectrum of scattered X-rays. The scattered spectrum is geometry dependent and, for high global covering factors, may dominate above 10 keV. We further show that, in models of circumnuclear gas, the suppression of the observed hard X-ray flux by reprocessing may be no larger than required by the 'light bending' model invoked for inner disk reflection, and the expected emission line strengths lie within the observed range. We conclude that the time-invariant 'red wing' in AGN X-ray spectra is probably caused by continuum transmitted through and scattered from circumnuclear gas, not by highly redshifted line emission, and that measurement of black hole spin is not possible. Subject headings: radiative transfer - galaxies: active - X-rays: galaxies - X-rays: individual (NGC 1365)",
"pages": [
1
]
},
{
"title": "L. Miller",
"content": "Dept. of Physics, Oxford University, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, U.K. and",
"pages": [
1
]
},
{
"title": "T. J. Turner",
"content": "Dept. of Physics, University of Maryland Baltimore County, Baltimore, MD 21250, U.S.A.",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Observations of AGN reveal evidence for absorbing gas surrounding an accreting black hole system at both X-ray (see Turner & Miller 2009, for a review) and UV wavelengths (e.g. Crenshaw et al. 2003). High column density outflowing gas may be seen in up to 40% of type 1 AGN (e.g. Cappi et al. 2009; Tombesi et al. 2012). A recent Suzaku study (Tatum et al. 2013) of a hard X-ray selected sample of type 1 AGN has shown luminosities above 10keV to be much higher than expected from extrapolation of models from the 0.5-10keV band. This 'hard excess' is ubiquitous in local type 1 AGN and, owing to the sharp absorption edges associated with the hardest source spectra, cannot be explained other than by the presence of a Compton-thick layer of low-ionization absorbing gas, covering a large fraction of the continuum source (Tatum et al. 2013). Partial-covering absorption by gas below the Compton-thick limit has long been known in type 1 AGN (Piro et al. 2005; Miller et al. 2008) and changes in the absorber may explain Xray spectral variability on long timescales. The Tatum et al. (2013) analysis extends the paradigm into the Compton-thick regime. It has also long been claimed that X-ray spectra show features caused by Compton scattering and absorption (known as 'reflection') from an inner accretion disk, blurred by relativistic effects. Spectral curvature over the 2-8 keV band may be fit with a model that convolves reflection spectra (Ross & Fabian 2005) with general relativistic effects (c.f. Laor 1991). However, it is difficult to distinguish absorption and reflection signatures by fitting individual Xray spectra, because Compton scattering and absorption shape both models, leading to similarities in overall shape. Consideration of AGN variability can help, and perhaps the biggest problem for the blurred reflection-dominated picture is the lack of any clear correlation between continuum and reflection flux in variable AGN (section 4). A particularly interesting case is the type 1.8 AGN NGC 1365, which has been observed extensively at 0.5-10keV (Risaliti et al. 2000, 2005a,b, 2007, 2009b,c) and higher energies (Risaliti et al. 2009a, 2013). These observations have shown spectral variability on timescales as short as a few hours, attributed to changes in the X-ray absorber. Risaliti et al. (2013) present simultaneous XMMNewton and NuSTAR data for NGC 1365, covering 0.5-79 keV. The authors claim that the data show relativistic disk features: broad Fe K α line emission and Compton scattering excess above 10keV. Risaliti et al. claim that the reflected component arises within 2.5 gravitational radii of a rapidly spinning black hole and that absorptiondominated models that do not include relativistic disk reflection can be ruled out. As this is a very strong assertion, we investigate here the assumptions upon which it is based. There are two key processes that shape AGN X-ray spectra: Compton scattering and photoelectric absorption. At the high energies observed by NuSTAR , and for Compton-thick gas, it is crucial to include both effects. Risaliti et al. (2013) created models representing slabs of ionized absorbing gas. However, those models fitted to NGC 1365 required column density N H ∼ 5 × 10 24 cm -2 . Such gas would be Compton-thick, but current ionized absorption models do not in- de Compton scattering. The circumnuclear gas also results in production of a scattered X-ray component which is highly dependent on the geometry of the scattering region. In this paper we present Monte Carlo simulations that demonstrate the importance of the inclusion of Compton scattering for the column density regime applicable to NGC 1365. We also demonstrate the strong geometry-dependence of the predictions for both transmitted and scattered X-rays and discuss the implications for modeling and interpretation of AGN X-ray spectra.",
"pages": [
1,
2
]
},
{
"title": "2.1. The importance of geometry",
"content": "In this section, we consider a single cloud of constant density, absorbing photons from a distant source, to demonstrate the key effects that must be taken into account. The gas is assumed to be cold, with solar abundances (Anders & Grevesse 1989) and cross-sections of Verner et al. (1996). We first consider the effect of cloud geometry alone, omitting the effects of Compton scattering, for a cloud with column density 5 × 10 24 cm -2 , as found by Risaliti et al. (2013). The cloud is illuminated by a power-law of photon index Γ = 2 and has a normalization, that would be seen by the observer in the absence of absorption, of unity at 1 keV. Fig. 1 plots the transmitted spectrum Ef ( E ), for photon energy E and energy spectral flux density f ( E ). The lowest dashed curve shows the standard calculation obtained for a plane slab of uniform density, where the transmitted flux f ( E ) ∝ exp( -N H σ ( E )) for photoelectric absorption crosssection per hydrogen atom σ ( E ). However, a plane slab is an unlikely choice for a clumpy distribution of gas that partially covers the source. The distribution of column density is likely to be complex, and it is instructive to compare with a uniform spherical cloud. Now, there is a distribution of column density associated with the cloud, p ( N H ) = 2 N H /N 2 H , max for N H ≤ N H , max , where N H , max is the maximum column density through the cloud. Integrating over this distribution, and in the absence of Compton scattering, we expect transmitted flux The upper dashed line in Fig. 1 shows the results for a cloud with mean density the same as the slab and for which N H , max is 3/2 times the mean column density. At high optical depths the transmitted flux f ( E ) → 2 ( N H , max σ ( E )) -2 , and since σ ( E ) has an approximately power-law form, a hard, powerlaw spectrum develops. In this regime, the dominant contribution to the transmitted flux comes from the periphery of the cloud. The spherical cloud has a significantly different transmitted spectrum from the slab. Such a cloud model has the same number of model parameters as the slab, and is likely to be a better representation of a partial-covering cloud. This calculation alone demonstrates how careful one must be when fitting absorption models to AGN X-ray spectra.",
"pages": [
2,
3
]
},
{
"title": "2.2. The effect of Compton scattering",
"content": "At high column densities, incident radiation is Compton scattered out of the line of sight. To model the transmitted and scattered spectra, we carried out a Monte Carlo radiative transfer simulation, following Miller et al. (2009). Multiple scatterings were allowed, and when photons were absorbed by a K shell of Fe, an Fe K line photon could be produced. Angle-dependent KleinNishina Compton scattering was calculated. The Monte Carlo spectra have been smoothed with a gaussian of FWHM ∆ E/E = 0 . 0283, appropriate for the resolution of typical CCD spectral data around Fe K. The transmitted spectrum is shown by the lower, solid, red line in Fig. 1. At high energies the transmitted flux is significantly attenuated by Compton scattering. However, the spectrum is significantly different from either the slab or sphere when Compton scattering is neglected. At low energies, the transmitted flux is again dominated by light leaking through the periphery of the cloud, so that the spectrum tends towards the same form as the spherical, non-scattering cloud. However, the light that is lost due to Compton scattering reappears in the scattered spectrum, shown in Fig. 1 by the upper solid curve. The spectrum has been integrated over all solid angles, so that the normalization is such that this is the scattered spectrum that would be measured by an observer if the primary source were fully surrounded by such clouds, but neglecting the effect of radiation being reabsorbed or scattered by other clouds (which will be discussed in section 3). If instead only some fraction of lines of sight are intercepted by clouds, the normalization should be multiplied by the global covering factor. For any global covering factor C G /greaterorsimilar 0 . 1, the scattered spectrum dominates over the transmitted spectrum, and both spectra have considerably different shapes from the non-scattering slab and sphere. It is worth noting the low equivalent width of the Fe K α emission line (Miller et al. 2009; Yaqoob et al. 2010). Finally, Fig. 1 shows a comparison with reflection from a plane, neutral, optically-thick slab as calculated by the pexrav model (Magdziarz & Zdziarski 1995) within xspec (Arnaud 1996), without calculation of the emission line strength. The normalization and shape of the pexrav spectrum varies with inclination: the curve shows the case for cos θ = 0 . 5, which matches most closely the cloud scattered spectrum around 10 keV. The pexrav spectrum is qualitatively similar to the cloud spectrum, although there are differences in shape, especially above 20 keV when the cloud spectrum has a less pronounced 'Compton hump'. Given also the significant differences in the transmitted spectra, we cannot expect to model even simple Compton-thick clouds with combinations of absorption by plane slabs and planar reflection. We shall see in the next section that, in models with a high covering factor of clumpy circumnuclear gas, the scattered spectrum shows much larger departures from the pexrav model. The importance of geometry for the observed spectrum has previously been demonstrated by Murphy & Yaqoob (2009) for a smooth toroidal reprocessor.",
"pages": [
3
]
},
{
"title": "3. Scattering and absorption by a complex distribution of circumnuclear gas",
"content": "In this section we consider the case of a high global covering factor of clumpy gas, when scattering of photons between clouds cannot be ignored (Nandra & George 1994, see also Merloni et al. 2006). As in Tatum et al. (2013), a simple, clumpy distribution was created by placing 1000 spherical clouds of equal radius between inner and outer radii r min and r max from a central X-ray source. Gas was placed inside each cloud with a uniform density (the density was not increased within overlapping clouds). For illustration, we chose N H = 1 . 5 × 10 24 cm -2 per unit cloud radius, chosen to approximately maximize the hard excess. In order to simulate the effect that in type 2 AGN we might be looking through a denser distribution of clouds than in type 1 AGN, the number density of clouds increased towards the equatorial plane as sin φ , where φ is the polar angle of observation. In Fig. 2 we show two models: model A has r min = 10, r max = 20 in units of the cloud radius; model B has r min = 10, r max = 30. The fraction of sightlines that were empty of gas was 0 . 35 at φ /similarequal 0, decreasing to < 0 . 15 for φ > 60 · in modelA, and 0 . 55 at φ /similarequal 0 decreasing to < 0 . 25 for φ > 60 · in model B. We emphasize that these are simplified models of circumnuclear material, designed to illustrate the radiative transfer effects, and are not to be taken as a proposal for the actual gas distribution. Spectra were created using 6 × 10 10 input quanta with energy 0 . 1 -400keV. The input spectrum was a powerlaw of photon index Γ = 2 . 2, as inferred for NGC 1365 (e.g. Risaliti et al. 2009a). It was assumed that photons that propagated through the equatorial plane were absorbed by an accretion disk and, to avoid possible confusion with disk reflection, the disk did not re-emit photons. As in section 2 the gas was assumed cold and angle-dependent Klein-Nishina Compton scattering was calculated. Spectra can be accumulated only by averaging over finite solid angle, and here we adopted a solid angle corresponding to that subtended from the central source by a cloud at r max . A point source was placed at the center of the cloud distribution, but the averaging of photons over solid angle has the effect of mimicking the partial covering of an extended source of comparable size to a cloud. Fig. 2 shows example spectra obtained for models A and B, viewed at polar angle φ = 60 · , for three azimuthal angles. The spectra have been smoothed as in section 2, but Monte Carlo noise is visible at low flux values. The spectra cover a range similar to that observed in the AGN population, from 'reflection dominated', through intermediate states where primary continuum is visible, to high states where the primary continuum 1 dominates. All states have significant hard excesses above 20 keV. Unobscured sightlines have total light at high energy that exceeds the input continuum amplitude. The panels show the contributions from various components: photons that pass through the holes in the distribution, photons that pass through clouds but are not scattered, and scattered photons, including Fe K α and Fe K β line emission. The incident continuum is also shown as a dashed line. The chief results are as follows.",
"pages": [
3,
4,
5,
6
]
},
{
"title": "4.1. The 'red wing' in AGN spectra",
"content": "The results of section 3 show that, on long timescales where spectral variability may be dominated by variations in observer covering fraction, there should be a spectrum of largely invariant scattered light that creates an apparent 'red wing' at energies below the Fe K edge. Such an invariant red wing is well known (e.g. Fabian & Vaughan 2003), and using principal components analysis, Miller et al. (2007, 2008, 2010) showed that there is an approximately invariant 'offset' component in AGN spectra. The effect leads to a problem with the explanation of the red wing as reflection by the inner accretion disk. If the disk is close to the primary X-ray source, its flux variations should be closely tracked by the reflected light, but apparently they are not. Fabian & Vaughan (2003), Miniutti et al. (2003) and subsequent papers proposed a 'light bending' model in which a compact, primary source near the black hole moves towards or away from the disk, such that bending of light causes an apparent variation in flux from the primary source, but not from the reflected light. This model has to be finely tuned to obtain invariant reflected flux (Miniutti & Fabian 2004). Such an a posteriori model is not required if the red wing arises from a combination of transmitted and scattered continua, as suggested by Turner et al. (2007), and not from highly redshifted line emission. Merloni et al. (2006) have also suggested this explanation in the context of scattered light arising in a model of an inhomogeneous accretion flow.",
"pages": [
6
]
},
{
"title": "4.2. Modeling the spectrum of NGC 1365",
"content": "In modeling the spectrum of NGC 1365, Risaliti et al. (2013) recognize that partial covering absorption is required, regardless of whether there is also a component of blurred reflection. In an initial comparison (Fig. 3 of Risaliti et al. 2013), a model of blurred reflection plus one absorber component was compared against a model of two absorber components. The models were only fit to the XMM-Newton data below 10 keV, and it was then seen how well each model extrapolated to higher energy. However, the blurred reflection included Compton scattering, but the two-absorber model did not. Hence it is no surprise that the first model extrapolated better above 10keV. In a subsequent test, Risaliti et al. (2013) fit also to the hard X-ray NuSTAR data and claimed that the blurred model is statistically better. But the transmitted and scattered light components were modeled with non-scattering, slab absorbers plus a pexrav component, so such a test is invalid. Point (ii) above demonstrates that existing models such as pexrav cannot ac- curately account for reprocessing by a complex circumnuclear gas distribution. Estimates of the continuum suppression arising from Compton scattering require proper inclusion of light scattered back into the line of sight by circumnuclear gas. Risaliti et al. (2013) considered the expected effect for Compton optical depth τ /similarequal 3 -4, using the plcabs model (Yaqoob 1997), and inferred that the intrinsic continuum would be a factor 8 larger than the observed continuum. The problems with this approach are: In our models, the Compton loss correction is only a factor 3-4 at high energy, comparable to that in the 'light bending' model of inner disk reflection, where up to 75% of light is lost (Miniutti & Fabian 2004). The scattering models presented here also show that the expected equivalent width of Fe K α covers a wide range that includes the observed range for NGC 1365. Finally, Tatum et al. (2013) argue that all type 1 AGN are affected by high-column, partial covering gas distributions, so the ratio of X-ray to infrared or optical line emission for NGC 1365 would not be expected to appear anomalous.",
"pages": [
6,
7
]
},
{
"title": "4.3. On the difficulty of measuring black hole spin",
"content": "It has been claimed that black hole spin can be measured from the shape of the 'red wing', whose profile varies as a function of spin parameter a , which requires red wing measurement down to energies /lessorsimilar 3 keV, free from the effects of other modifications to the continuum. Even in the absence of circumnuclear reprocessing, a is difficult to measure free from degeneracies with other parameters (Dovˇciak et al. 2004). Given that in AGN such as NGC 1365, Mrk 766 (Miller et al. 2007) and MCG-6-30-15 (Miller et al. 2008) the entire red wing may be modeled as scattered and absorbed continuum, and given that complex absorption must be present (e.g. NGC 1365, Risaliti et al. 2013), it is not possible to unambiguously identify and measure any alleged blurred red wing component with sufficient accuracy to determine spin in any of the AGN that have been subject to detailed study to date.",
"pages": [
7
]
},
{
"title": "5. Conclusions",
"content": "AGN spectra may contain significant levels of transmitted and scattered continua from partiallycovering circumnuclear gas, producing the timeinvariant 'red wing' below the Fe K edge and modifying the spectrum above 10 keV. Such gas is already known in NGC 1365. Geometry-dependent Compton scattering must be taken into account, using 3D radiative transfer calculations, when making spectral models and when accounting for the source total luminosity. The expected red wing, low Fe K α equivalent width and high energy excess may be easily confused with 'reflection' from an accretion disk, and spectral analyses to date have not established that there is any requirement for inner-disk reflection. Improved models of clumpy, ionized circumnuclear gas are required to achieve a full understanding of AGN X-ray spectra. TJT acknowledges NASA grant NNX11AJ57G.",
"pages": [
7
]
},
{
"title": "REFERENCES",
"content": "Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53, 197 Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17-+ Cappi, M., Tombesi, F., Bianchi, S., et al. 2009, A&A, 504, 401 Crenshaw, D. M., Kraemer, S. B., & George, I. M. 2003, ARA&A, 41, 117 Dovˇciak, M., Karas, V., & Yaqoob, T. 2004, ApJS, 153, 205 Fabian, A. C., & Vaughan, S. 2003, MNRAS, 340, L28 Laor, A. 1991, ApJ, 376, 90 Turner, T. J., Miller, L., Reeves, J. N., & Kraemer, S. B. 2007, A&A, 475, 121 Verner, D. A., Ferland, G. J., Korista, K. T., & Yakovlev, D. G. 1996, ApJ, 465, 487 Yaqoob, T. 1997, ApJ, 479, 184 Yaqoob, T., Murphy, K. D., Miller, L., & Turner, T. J. 2010, MNRAS, 401, 411",
"pages": [
7,
8
]
}
]
2013ApJ...773L...9W
https://arxiv.org/pdf/1306.2317.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_85><loc_88><loc_87></location>X-RAY OUTFLOWS AND SUPER-EDDINGTON ACCRETION IN THE ULTRALUMINOUS X-RAY SOURCE HOLMBERG IX X-1</section_header_level_1>
<text><location><page_1><loc_14><loc_82><loc_86><loc_84></location>D. J. WALTON 1 , J. M. MILLER 2 , F. A. HARRISON 1 , A. C. FABIAN 3 , T. P. ROBERTS 4 , M. J. MIDDLETON 5 , R. C. REIS 2 1</text>
<text><location><page_1><loc_27><loc_81><loc_75><loc_82></location>Space Radiation Laboratory, California Institute of Technology, Pasadena, CA 91125, USA</text>
<text><location><page_1><loc_24><loc_80><loc_76><loc_81></location>2 Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109, USA</text>
<text><location><page_1><loc_25><loc_79><loc_75><loc_80></location>3 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK</text>
<text><location><page_1><loc_29><loc_78><loc_71><loc_79></location>4 Department of Physics, Durham University, South Road, Durham DH1 3LE, UK</text>
<text><location><page_1><loc_17><loc_77><loc_83><loc_78></location>Astronomical Institute Anton Pannekoek, University of Amsterdam, Postbus 94249, NL-1090 GE Amsterdam, the Netherlands</text>
<text><location><page_1><loc_41><loc_75><loc_59><loc_76></location>Draft version September 26, 2018</text>
<section_header_level_1><location><page_1><loc_46><loc_73><loc_54><loc_74></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_51><loc_86><loc_72></location>Studies of X-ray continuum emission and flux variability have not conclusively revealed the nature of ultraluminous X-ray sources (ULXs) at the high-luminosity end of the distribution (those with L X ≥ 10 40 erg s -1 ). These are of particular interest because the luminosity requires either super-Eddington accretion onto a black hole of ∼ 10 M /circledot , or more standard accretion onto an intermediate-mass black hole. Super-Eddington accretion models predict strong outflowing winds, making atomic absorption lines a key diagnostic of the nature of extreme ULXs. To search for such features, we have undertaken a long, 500 ks observing campaign on HolmbergIX X-1 with Suzaku . This is the most sensitive dataset in the iron K bandpass for a bright, isolated ULX to date, yet we find no statistically significant atomic features in either emission or absorption; any undetected narrow features must have equivalent widths less than 15-20 eV at 99% confidence. These limits are far below the /greaterorsimilar 150eV lines expected if observed trends between mass inflow and outflow rates extend into the super-Eddington regime, and in fact rule out the line strengths observed from disk winds in a variety of sub-Eddington black holes. We therefore cannot be viewing the central regions of HolmbergIX X-1 through any substantial column of material, ruling out models of spherical super-Eddington accretion. If Holmberg IX X-1 is a super-Eddington source, any associated outflow must have an anisotropic geometry. Finally, the lack of iron emission suggests that the stellar companion cannot be launching a strong wind, and that Holmberg IX X-1 must primarily accrete via roche-lobe overflow.</text>
<section_header_level_1><location><page_1><loc_22><loc_48><loc_34><loc_49></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_23><loc_49><loc_47></location>Ultraluminous X-ray sources(ULXs) are off-nuclear point sources found in nearby galaxies that require extraordinary accretion-power. The nature of the most luminous sources within this class - those with L X ≥ 10 40 erg s -1 ( e.g. Farrell et al. 2009; Walton et al. 2011b; Sutton et al. 2012; Jonker et al. 2012) - is particularly interesting. These sources may be standard stellar-remnant black holes ( M BH ∼ 10 M /circledot ) accreting at super-Eddington rates (Poutanen et al. 2007, Finke & Bottcher 2007), or intermediate-mass black holes (IMBHs: 10 2 /lessorsimilar M BH /lessorsimilar 10 5 M /circledot ) accreting at sub-Eddington rates (Miller et al. 2004; Strohmayer & Mushotzky 2009). Indeed, the high-luminosity end of the ULX distribution may include both extremes, or even a continuum in between (Zampieri & Roberts 2009). ULXs with L X ≥ 10 40 erg s -1 represent a regime in which our knowledge of black hole accretion can be extended and tested. For recent reviews focusing on ULXs see Roberts (2007) and Feng & Soria (2011).</text>
<text><location><page_1><loc_8><loc_7><loc_48><loc_23></location>A robust prediction for accretion at high rates (near Eddington or above) is that strong outflows or winds should be launched from the accretion disk (Shakura & Sunyaev 1973; Poutanen et al. 2007; Ohsuga & Mineshige 2011; Dotan & Shaviv 2011; Vinokurov et al. 2013). Indeed, Galactic stellar mass black holes (StMBHs) at moderately high accretion rates (states dominated by thermal disk emission) frequently display evidence for such disk winds (Miller et al. 2006; Neilsen & Lee 2009; King et al. 2012), with outflow velocities v out /lessorsimilar 10 , 000 km s -1 . When these outflows cover our line of sight to the central source, absorption features are imprinted onto the intrinsic X-ray continuum, the</text>
<text><location><page_1><loc_52><loc_36><loc_92><loc_49></location>most prominent of which are typically the K α transitions of highly ionised iron (Fe XXV and/or XXVI). As expected, the strength of the outflows observed appears to increase with the inferred accretion rate in both StMBHs (Ponti et al. 2012) and in active galactic nuclei (AGN; King et al. 2013). For subEddington StMBHs, outflows are seen predominantly in high inclination sources, so the outflow geometry is inferred to be roughly equatorial. Numerical simulations of winds from thin (sub-Eddington) disks further support such an outflow geometry (Proga & Kallman 2004).</text>
<text><location><page_1><loc_52><loc_17><loc_92><loc_35></location>The majority of ULXs have luminosities of a few × 10 39 erg s -1 , and likely represent a high luminosity extension of the disk-dominated thermal states observed in Galactic StMBHs (Kajava & Poutanen 2009; Middleton et al. 2013). Outflow geometries in these cases are likely to still be largely equatorial. However, a common prediction of superEddington accretion and the subsequent outflows is that, as the accretion rate increases, the solid angle subtended by the outflow should also increase (Abramowicz 2005; King 2009; Dotan & Shaviv 2011). At the high Eddington rates required to explain the L X ≥ 10 40 erg s -1 ULXs (assuming M BH ∼ 10M /circledot ), one might expect that atomic iron features associated with a strong, large solid angle outflow would be a common feature of the X-ray spectra.</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_17></location>Walton et al. (2012) describes initial searches for iron features in ULX spectra, using archival XMM-Newton data for two bright ( L X ∼ 10 40 erg s -1 ) sources, HolmbergIX X-1 and NGC1313 X-1. No statistically significant features were found in either source, and the limits obtained required any lines to be relatively weak in comparison to simple scaling of the sub-Eddington features observed from other accreting</text>
<text><location><page_1><loc_16><loc_77><loc_17><loc_78></location>5</text>
<figure>
<location><page_2><loc_9><loc_66><loc_47><loc_92></location>
<caption>FIG. 1.2.5-10.0 keV data/model ratios of the full Holmberg IX X-1 Suzaku dataset to a simple powerlaw ( Γ = 1 . 72 ± 0 . 01 ; top panel ) and a powerlaw with a high energy cut-off ( Γ = 1 . 27 ± 0 . 07 , E cut = 10 +2 -1 keV; bottom panel ). The latter provides a far superior fit to the data, indicating a curved continuum is favoured.</caption>
</figure>
<text><location><page_2><loc_8><loc_51><loc_48><loc_59></location>black holes up to the super-Eddington regime. In order to enhance the sensitivity to atomic iron features, we undertook deep observations of the luminous source HolmbergIX X-1 with Suzaku . In this Letter we present the results from our search for X-ray spectral features in the iron-K energy range with this new dataset.</text>
<section_header_level_1><location><page_2><loc_22><loc_49><loc_35><loc_50></location>2. DATA REDUCTION</section_header_level_1>
<text><location><page_2><loc_8><loc_18><loc_48><loc_48></location>HolmbergIX X-1 was observed for a total exposure of ∼ 500ks during 2012 by the Suzaku observatory (Mitsuda et al. 2007). To extract science products, we reprocessed the unfiltered event files for each of the XIS CCDs (XIS0, 1, 3; Koyama et al. 2007) and editing modes (3x3, 5x5) operational using the latest HEASOFT software package (version 6.13), as recommended in the Suzaku Data Reduction Guide 1 . Cleaned event files were generated by re-running the Suzaku pipeline with the latest calibration, as well as the associated screening criteria files. For each of the observation segments, source products were extracted with XSELECT from circular regions ∼ 200' in radius, and the background was extracted from adjacent regions free of any contaminating sources, with care taken to avoid the calibration sources in the corners. Instrumental responses were generated for each individual spectrum using the XISRESP script with a medium resolution. The spectra and response files for the front-illuminated (FI) detectors (XIS0, 3) were combined using the FTOOL ADDASCASPEC. Finally, we grouped the spectra to have a minimum signal-to-noise (S/N) of 5 per energy bin with the SPECGROUP task (part of the XMM-Newton SAS), to allow the use of χ 2 minimization during spectral fitting.</text>
<section_header_level_1><location><page_2><loc_24><loc_14><loc_33><loc_15></location>2.1. HXD PIN</section_header_level_1>
<text><location><page_2><loc_8><loc_10><loc_48><loc_13></location>Due to the level of systematic uncertainty in the PIN background model ( /greaterorsimilar 25% of the 'source' flux given the weak detection of the HolmbergIX field; see e.g. discussion in</text>
<table>
<location><page_2><loc_55><loc_74><loc_88><loc_87></location>
<caption>TABLE 1 Continuum parameters obtained for Holmberg IX X-1.</caption>
</table>
<text><location><page_2><loc_52><loc_59><loc_92><loc_71></location>Walton et al. 2013), and the variable nature of the contaminating M 81 nucleus (Markoff et al. 2008; Miller et al. 2010), it is not possible to constrain the high energy ( E > 10 keV) properties of HolmbergIX X-1 with the collimating PIN detector. The imaging capabilities of the recently launched NuSTAR observatory (Harrison et al. 2013) are required. Therefore, we do not consider the PIN data here, and stress that any interpretation based on these data should be regarded with extreme skepticism.</text>
<section_header_level_1><location><page_2><loc_64><loc_57><loc_79><loc_58></location>3. SPECTRAL ANALYSIS</section_header_level_1>
<text><location><page_2><loc_52><loc_26><loc_92><loc_56></location>Throughout this work, spectral modeling is performed with XSPEC v12.8.0 (Arnaud 1996), and absorption by intervening neutral material is treated with TBNEW (Wilms et al. 2000) using the appropriate solar abundances. We include two absorption components, one fixed at the Galactic column ( N H;Gal = 5 . 54 × 10 20 atom cm -2 ; Kalberla et al. 2005), and another with variable column at the redshift of Holmberg IX ( z = 0 . 000153 ). During modelling, we only consider data from the FI detectors in the 1-10 keV energy range, owing to a calibration mismatch between XIS0 and XIS3 below ∼ 1keV. For the same reasons, we only consider data from the backilluminated (BI) XIS1 detector over the 2.5-9.0 keV energy range. We also exclude the 1.6-2.5keV energy range from the FI data owing to remaining calibration uncertainties associated with the instrumental silicon K and gold M edges, and the 7.3-7.6 keV energy range from the BI data owing to a residual background feature. The data from the FI and BI detectors are modelled simultaneously, with all parameters tied between the spectra, and we attempt to account for any further cross-calibration uncertainties above 2.5 keV by allowing a variable multiplicative cross-normalisation constant to vary between them. This value is always found to be within ∼ 10% of unity.</text>
<section_header_level_1><location><page_2><loc_63><loc_23><loc_81><loc_24></location>3.1. Continuum Modelling</section_header_level_1>
<text><location><page_2><loc_52><loc_7><loc_92><loc_23></location>We begin with a brief assessment of the form of the continuum, focusing first on the 2.5-10.0keV energy range. Specifically, we wish to determine whether a simple powerlawlike continuum is sufficient, or whether there is evidence for curvature similar to other high quality ULX datasets (Stobbart et al. 2006; Gladstone et al. 2009; Walton et al. 2011a). Similar to previous works, we compare the results obtained with a simple powerlaw continuum, with and without a high energy exponential cut-off. We indeed find that allowing a cut-off offers a significant improvement ( ∆ χ 2 = 135 , one additional free parameter; see Fig. 1), i.e. the 2.5-10.0keV spectrum does show curvature.</text>
<figure>
<location><page_3><loc_9><loc_59><loc_46><loc_92></location>
<caption>FIG. 2.Top panel: the ∆ χ 2 improvement provided by a narrow Gaussian line, as a function of (rest frame) line energy, for the full Suzaku Holmberg IX X-1 dataset. Positive (negative) values of ∆ χ 2 indicate the improvement is obtained with an emission (absorption) line. We find no compelling evidence for any narrow iron K features. Bottom panel: 90% ( blue ) and 99% ( red ) confidence contours for the equivalent width of a narrow line, indicating the line strengths any narrow features intrinsically present could have and still remain undetected. The rest frame transitions of neutral, helium-like and hydrogen-like iron (6.4, 6.67 and 6.97 keV) are shown with vertical dashed lines, and we also plot dashed horizontal lines representing EW = ± 30 eV. Finally, we also show the 99% EW limits obtained from archival XMMNewton data in Walton et al. (2012) for direct comparison (red dotted lines).</caption>
</figure>
<text><location><page_3><loc_8><loc_19><loc_48><loc_44></location>Considering the 1-10keV bandpass, we utilize a common parameterisation of the continuum for ULXs, modeling the data with cool, optically thick Comptonisation (Stobbart et al. 2006; Gladstone et al. 2009; Middleton et al. 2011; Walton et al. 2011a). We note that this parameterisation is largely empirical, and should not be ascribed too much physical significance. The nature of the continuum emission will be addressed in more detail in future work (Walton et al. in prep ) utilising the necessary NuSTAR data. Here, we use the COMPTT code (Titarchuk 1994), which provides an excellent fit ( χ 2 ν = 1730/1694). As we do not consider the data below 1 keV, we are not sensitive to the presence of any additional low-temperature ( ∼ 0.2keV) thermal component similar to those seen previously in bright, unabsorbed ULXs (Miller et al. 2004), so we fix the seed photon temperature to 0.1 keV. The continuum parameters obtained are summarised in Table 1, and are broadly similar to those obtained with previous observations (Gladstone et al. 2009; Vierdayanti et al. 2010; Walton et al. 2012).</text>
<section_header_level_1><location><page_3><loc_19><loc_17><loc_38><loc_18></location>3.2. Narrow Iron K Features</section_header_level_1>
<text><location><page_3><loc_8><loc_7><loc_48><loc_16></location>Walton et al. (2012) describes constraints on atomic iron K features for ULXs, focusing on the archival XMM-Newton data available for HolmbergIX X-1, revisited here with Suzaku , and NGC1313 X-1. In order to search for atomic features in this new dedicated dataset, we follow the same approach adopted in that work, varying a narrow ( σ = 10 eV) Gaussian across the 5-9 keV energy range, to include the rest</text>
<text><location><page_3><loc_52><loc_77><loc_92><loc_92></location>frame energies of the iron K transitions and also generously allow for the possibility of blue-shifted features, in steps of 0.04 keV. For each energy step, we record the ∆ χ 2 improvement resulting from the inclusion of the Gaussian line, as well as the best fit equivalent width ( EW ) and its 90 and 99% confidence limits 2 . The latter quantities are obtained with the EQWIDTH command in XSPEC, generating 10,000 parameter sets based on the best fit model and the covariance matrix, which includes information on the model parameter uncertainties, and extracting the confidence limits from the distribution of equivalent widths obtained.</text>
<text><location><page_3><loc_52><loc_53><loc_92><loc_77></location>The results obtained are shown in Fig. 2; the top panel shows the ∆ χ 2 improvement, multiplied by the sign of the best fit normalisation to differentiate between emission and absorption, and the limits on EW obtained are shown in the bottom panel. For clarity, we highlight the energies of the K α transitions of neutral, helium-like and hydrogen-like iron, as well as EW = ± 30 eV, representative of the strongest absorption features observed in GRS 1915+105 (Neilsen & Lee 2009). In addition, we also show the limits we obtained previously with XMM-Newton . As in our previous analysis, we find no statistically significant line detections, so we again focus on the limits that can be placed instead. Any narrow aromic features in the Suzaku data in the immediate Fe K band (6-7keV) must have equivalent widths less than ∼ 15-20eV (99% confidence); previously we were only able to constrain such features to EW /lessorsimilar 30 eV. On average, the allowed EW range at a given energy is a factor of ∼ 1.5 smaller with our new dataset than obtained previously (Walton et al. 2012).</text>
<section_header_level_1><location><page_3><loc_67><loc_51><loc_77><loc_52></location>4. DISCUSSION</section_header_level_1>
<text><location><page_3><loc_52><loc_35><loc_92><loc_51></location>Using our long 500 ks Suzaku observation of HolmbergIX X-1, we have undertaken the deepest study in the Fe K region of a bright, isolated ULX to date, to search for iron absorption/emission features similar to those frequently observed in other accreting black holes. Iron is ideally suited to identifying the presence of atomic processes, as it is both difficult to fully ionize and cosmically abundant. Despite the high sensitivity of the observations, we do not detect any discrete atomic iron features. The limits on any persistent narrow features (either in emission or absorption) as yet undetected are now EW /lessorsimilar 15 -20 eV (99% confidence) over the immediate Fe K energy range.</text>
<text><location><page_3><loc_52><loc_14><loc_92><loc_35></location>As shown in Fig. 3, these limits are now extremely restrictive when considered in the context of the lines observed from other sources. Remarkably, in terms of absorption, the constraints are such that any iron features present in HolmbergIX X-1 must be weaker than the absorption lines observed in numerous sub-Eddington Galactic StMBHs (Miller et al. 2006; Neilsen & Lee 2009; King et al. 2012) and AGN (Tombesi et al. 2010; Gofford et al. 2013). Meanwhile, any neutral iron emission from HolmbergIX X-1 must be weaker than that observed in the vast majority of Galactic high-mass X-ray binaries (HMXBs), which ubiquitously display such emission features (Torrej'on et al. 2010), and there cannot be any substantial emission from helium- or hydrogenlike iron either. At the energies of these transitions, the 99% limits on emission lines are EW < 15 , 11 and 4 eV respectively.</text>
<text><location><page_3><loc_52><loc_7><loc_92><loc_13></location>2 We again note that we are computing confidence limits on line strength, which are not formally the same as the upper limits on the strength of lines that should be detected at a given confidence level (Kashyap et al. 2010), but are simpler to calculate, and provide more conservative estimates for the maximum strength of any lines intrinsically present.</text>
<text><location><page_4><loc_8><loc_53><loc_48><loc_92></location>It is clear from the lack of absorption features that we cannot be viewing the central hard X-ray emitting regions of HolmbergIX X-1 through any substantial column of partially ionized material. We can therefore exclude the presence of any massive, spherical outflow in HolmbergIX X-1, as discussed in King & Pounds (2003), and wind-dominated spectral models (Vierdayanti et al. 2010) are also ruled out. If HolmbergIX X-1 truly is a StMBH accreting substantially in excess of the Eddington limit, we must be viewing it through a line of sight that is not covered by the massive outflow launched in such an accretion regime. The most natural conclusion is that, in this scenario, we would have to be viewing the source close to face-on (see also Roberts et al. 2011), with the wind still retaining some kind of roughly equatorial geometry, broadly similar to that inferred for sub-Eddington disk winds (Ponti et al. 2012), although presumably with a much larger scale-height for both the disk and the outflow (Poutanen et al. 2007). Furthermore, our results require that any equatorial outflow must be launched further out than the central hard X-ray emitting region, despite this presumably being the most irradiated region of the accretion flow. If this is the case, observation of atomic iron emission from such a massive outflow might be expected instead. The expected line profile might well be more complex than a simple narrow Gaussian, however we stress that there are no clear residual features that would readily be interpreted as re-emission from a strong wind, which may prove problematic for any extreme super-Eddington scenario. This will be addressed in more detail in future work.</text>
<text><location><page_4><loc_8><loc_37><loc_48><loc_53></location>The lack of narrow iron emission lines has strong implications for the broader nature of the accretion onto Holmberg IX X-1, regardless of the black hole mass. In many respects, ULXs are widely expected to be analogues to black hole HMXBs. However, Galactic HMXBs ubiquitously display neutral iron emission lines (Torrej'on et al. 2010), owing to illumination of the stellar winds in which they are embedded, and from which they may primarily accrete. Since there is no iron emission observed, either neutral or highly ionized, we infer that either the stellar wind is weak (or even absent), or the accretion geometry is such that this material is not illuminated by the hard X-rays emitted from the central regions.</text>
<text><location><page_4><loc_8><loc_12><loc_48><loc_37></location>Returning to the possible scenario in which ULXs are powered by a large scale height, optically thick super-Eddington accretion flow; the inner regions of such accretion flows are expected to have a roughly conical geometry, with the hard X-rays being produced in the hotter, central regions. If this funnel covers a large enough solid angle, it may be able to shield the majority of the stellar wind from the hard X-rays, which would be scattered and collimated preferentially out of the equatorial plane. Given the expected large-scale extent of the stellar wind, the optically thick regions of the accretion flow would have to cover an extremely large solid angle in order to prevent substantial iron line emission. However, the observed luminosity of the He II λ 4686 emission line, presumed to be associated with the cool outer disk, appears to require that the X-ray luminosity cannot be highly anisotropic via photon counting arguments (Moon et al. 2011), and optical/UV photometry is also indicative of X-ray reprocessing in the outer disk (Gris'e et al. 2011), so it is not clear that this offers a self-consistent scenario.</text>
<text><location><page_4><loc_8><loc_7><loc_48><loc_12></location>Alternatively, if the scale-height of the accretion flow is not sufficient to provide substantial shielding, the lack of iron emission would therefore tell us that there is no strong stellar wind. Indeed, for a spherically symmetric repro-</text>
<figure>
<location><page_4><loc_52><loc_66><loc_90><loc_92></location>
<caption>FIG. 3.The line limits obtained for Holmberg IX X-1 placed in the broader context of the absorption features detected in both AGN (Tombesi et al. 2010; Gofford et al. 2013) and selected Galactic StMBHs (Neilsen & Lee 2009; King et al. 2012), and the emission lines detected in Galactic HMXBs (Torrej'on et al. 2010). Some notable sources have been highlighted. For further comparison, we also show the GRS 1915+105 absorption (assumed solar metallicity) scaled up by factors of 5 and 10, accounting for the metallicity of Holmberg IX ( ∼ 0.5 Z /circledot ; Makarova et al. 2002). These may be conservative scalings for the expected EW , as the mass outflow rate should increase faster than linearly with Eddington ratio.</caption>
</figure>
<text><location><page_4><loc_52><loc_17><loc_92><loc_53></location>cessing geometry, which works well for Galactic HMXBs (Torrej'on et al. 2010), and the metallicity of Holmberg IX ( ∼ 0.5 Z /circledot ; Makarova et al. 2002), the specific emission line limits obtained for neutral and hydrogen-like iron correspond to reprocessing columns of N H /lessorsimilar 10 and 3 × 10 22 atom cm -2 respectively (see Walton et al. 2012). For comparison, the HMXBs analysed by Torrej'on et al. (2010), which have companion masses M ∗ /greaterorsimilar 10M /circledot , typically display columns of N H /greaterorsimilar 10 23 atom cm -2 . In turn, these observational constraints mean that any stellar wind present most likely cannot provide the mass accretion rate of ˙ M /greaterorsimilar 1 . 5 × 10 -6 M /circledot yr -1 required to power the observed X-ray luminosity from HolmbergIX X-1. Instead, HolmbergIX X-1 most likely accretes via Roche-lobe overflow, as suggested by Gris'e et al. (2011), the accretion mechanism more typically associated with low mass X-ray binaries (LMXBs). However, Galactic LMXBs are generally transient sources, spending the majority of the time in quiescence, occasionally undergoing accretion events resulting in bright ∼ month-to-year long X-ray outbursts. In contrast, HolmbergIX X-1 appears to be a much more persistent source, requiring a sufficiently close binary system such that Roche-lobe overflow/mass transfer remains roughly continuous. Gris'e et al. (2011) found a lower limit to the mass of the stellar companion of M ∗ /greaterorsimilar 10M /circledot . We suggest that the absent/weak stellar wind implies that the companion cannot be substantially more massive than this lower limit, given that more massive stars generally launch stronger winds.</text>
<text><location><page_4><loc_52><loc_7><loc_92><loc_17></location>Finally, in addition to improving the narrow line limits, we also confirm the presence of curvature in the ∼ 310keV energy range, as previously indicated by XMMNewton (Gladstone et al. 2009). We defer a detailed consideration of the continuum to future work, which will focus on broadband spectral analysis utilising the required NuSTAR data, although we do comment here that the 3-10 keV spectrum does not appear consistent with the powerlaw-like emis-</text>
<text><location><page_5><loc_8><loc_91><loc_43><loc_92></location>on expected from a standard sub-Eddington corona.</text>
<section_header_level_1><location><page_5><loc_23><loc_88><loc_34><loc_89></location>5. CONCLUSIONS</section_header_level_1>
<text><location><page_5><loc_8><loc_72><loc_48><loc_88></location>Our long Suzaku program on HolmbergIX X-1 has provided the most sensitive dataset in the Fe K region obtained for any luminous, isolated ULX to date. Despite the high sensitivity of these data, we find no statistically significant narrow atomic features in either emission or absorption across the 5-9 keV energy range. Furthermore, the data are of sufficient quality to limit any undetected features to have equivalent widths EW /lessorsimilar 15 -20 eV across the immediate Fe K bandpass at 99% confidence, i.e. weaker than the features associated with sub-Eddington outflows in a number of other black holes. Therefore, we cannot be viewing the central hard X-ray emitting regions of HolmbergIX X-1 through any</text>
<text><location><page_5><loc_52><loc_80><loc_92><loc_92></location>substantial column of material. Models of spherical superEddington accretion can be rejected, as can wind-dominated spectral models. If HolmbergIX X-1 is accreting at highly super-Eddington rates, our viewing angle must be close to face on, such that the associated outflow is directed away from our line-of-sight. Finally, the lack of iron emission implies that the stellar companion is unlikely to be launching a strong wind, and therefore the black hole must primarily accrete via roche-lobe overflow.</text>
<section_header_level_1><location><page_5><loc_65><loc_78><loc_79><loc_79></location>ACKNOWLEDGEMENTS</section_header_level_1>
<text><location><page_5><loc_52><loc_72><loc_92><loc_77></location>The authors thank the reviewer for helpful comments. This research has made use of data obtained from the Suzaku observatory, a collaborative mission between the space agencies of Japan (JAXA) and the USA (NASA).</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Studies of X-ray continuum emission and flux variability have not conclusively revealed the nature of ultraluminous X-ray sources (ULXs) at the high-luminosity end of the distribution (those with L X ≥ 10 40 erg s -1 ). These are of particular interest because the luminosity requires either super-Eddington accretion onto a black hole of ∼ 10 M /circledot , or more standard accretion onto an intermediate-mass black hole. Super-Eddington accretion models predict strong outflowing winds, making atomic absorption lines a key diagnostic of the nature of extreme ULXs. To search for such features, we have undertaken a long, 500 ks observing campaign on HolmbergIX X-1 with Suzaku . This is the most sensitive dataset in the iron K bandpass for a bright, isolated ULX to date, yet we find no statistically significant atomic features in either emission or absorption; any undetected narrow features must have equivalent widths less than 15-20 eV at 99% confidence. These limits are far below the /greaterorsimilar 150eV lines expected if observed trends between mass inflow and outflow rates extend into the super-Eddington regime, and in fact rule out the line strengths observed from disk winds in a variety of sub-Eddington black holes. We therefore cannot be viewing the central regions of HolmbergIX X-1 through any substantial column of material, ruling out models of spherical super-Eddington accretion. If Holmberg IX X-1 is a super-Eddington source, any associated outflow must have an anisotropic geometry. Finally, the lack of iron emission suggests that the stellar companion cannot be launching a strong wind, and that Holmberg IX X-1 must primarily accrete via roche-lobe overflow.",
"pages": [
1
]
},
{
"title": "X-RAY OUTFLOWS AND SUPER-EDDINGTON ACCRETION IN THE ULTRALUMINOUS X-RAY SOURCE HOLMBERG IX X-1",
"content": "D. J. WALTON 1 , J. M. MILLER 2 , F. A. HARRISON 1 , A. C. FABIAN 3 , T. P. ROBERTS 4 , M. J. MIDDLETON 5 , R. C. REIS 2 1 Space Radiation Laboratory, California Institute of Technology, Pasadena, CA 91125, USA 2 Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109, USA 3 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK 4 Department of Physics, Durham University, South Road, Durham DH1 3LE, UK Astronomical Institute Anton Pannekoek, University of Amsterdam, Postbus 94249, NL-1090 GE Amsterdam, the Netherlands Draft version September 26, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Ultraluminous X-ray sources(ULXs) are off-nuclear point sources found in nearby galaxies that require extraordinary accretion-power. The nature of the most luminous sources within this class - those with L X ≥ 10 40 erg s -1 ( e.g. Farrell et al. 2009; Walton et al. 2011b; Sutton et al. 2012; Jonker et al. 2012) - is particularly interesting. These sources may be standard stellar-remnant black holes ( M BH ∼ 10 M /circledot ) accreting at super-Eddington rates (Poutanen et al. 2007, Finke & Bottcher 2007), or intermediate-mass black holes (IMBHs: 10 2 /lessorsimilar M BH /lessorsimilar 10 5 M /circledot ) accreting at sub-Eddington rates (Miller et al. 2004; Strohmayer & Mushotzky 2009). Indeed, the high-luminosity end of the ULX distribution may include both extremes, or even a continuum in between (Zampieri & Roberts 2009). ULXs with L X ≥ 10 40 erg s -1 represent a regime in which our knowledge of black hole accretion can be extended and tested. For recent reviews focusing on ULXs see Roberts (2007) and Feng & Soria (2011). A robust prediction for accretion at high rates (near Eddington or above) is that strong outflows or winds should be launched from the accretion disk (Shakura & Sunyaev 1973; Poutanen et al. 2007; Ohsuga & Mineshige 2011; Dotan & Shaviv 2011; Vinokurov et al. 2013). Indeed, Galactic stellar mass black holes (StMBHs) at moderately high accretion rates (states dominated by thermal disk emission) frequently display evidence for such disk winds (Miller et al. 2006; Neilsen & Lee 2009; King et al. 2012), with outflow velocities v out /lessorsimilar 10 , 000 km s -1 . When these outflows cover our line of sight to the central source, absorption features are imprinted onto the intrinsic X-ray continuum, the most prominent of which are typically the K α transitions of highly ionised iron (Fe XXV and/or XXVI). As expected, the strength of the outflows observed appears to increase with the inferred accretion rate in both StMBHs (Ponti et al. 2012) and in active galactic nuclei (AGN; King et al. 2013). For subEddington StMBHs, outflows are seen predominantly in high inclination sources, so the outflow geometry is inferred to be roughly equatorial. Numerical simulations of winds from thin (sub-Eddington) disks further support such an outflow geometry (Proga & Kallman 2004). The majority of ULXs have luminosities of a few × 10 39 erg s -1 , and likely represent a high luminosity extension of the disk-dominated thermal states observed in Galactic StMBHs (Kajava & Poutanen 2009; Middleton et al. 2013). Outflow geometries in these cases are likely to still be largely equatorial. However, a common prediction of superEddington accretion and the subsequent outflows is that, as the accretion rate increases, the solid angle subtended by the outflow should also increase (Abramowicz 2005; King 2009; Dotan & Shaviv 2011). At the high Eddington rates required to explain the L X ≥ 10 40 erg s -1 ULXs (assuming M BH ∼ 10M /circledot ), one might expect that atomic iron features associated with a strong, large solid angle outflow would be a common feature of the X-ray spectra. Walton et al. (2012) describes initial searches for iron features in ULX spectra, using archival XMM-Newton data for two bright ( L X ∼ 10 40 erg s -1 ) sources, HolmbergIX X-1 and NGC1313 X-1. No statistically significant features were found in either source, and the limits obtained required any lines to be relatively weak in comparison to simple scaling of the sub-Eddington features observed from other accreting 5 black holes up to the super-Eddington regime. In order to enhance the sensitivity to atomic iron features, we undertook deep observations of the luminous source HolmbergIX X-1 with Suzaku . In this Letter we present the results from our search for X-ray spectral features in the iron-K energy range with this new dataset.",
"pages": [
1,
2
]
},
{
"title": "2. DATA REDUCTION",
"content": "HolmbergIX X-1 was observed for a total exposure of ∼ 500ks during 2012 by the Suzaku observatory (Mitsuda et al. 2007). To extract science products, we reprocessed the unfiltered event files for each of the XIS CCDs (XIS0, 1, 3; Koyama et al. 2007) and editing modes (3x3, 5x5) operational using the latest HEASOFT software package (version 6.13), as recommended in the Suzaku Data Reduction Guide 1 . Cleaned event files were generated by re-running the Suzaku pipeline with the latest calibration, as well as the associated screening criteria files. For each of the observation segments, source products were extracted with XSELECT from circular regions ∼ 200' in radius, and the background was extracted from adjacent regions free of any contaminating sources, with care taken to avoid the calibration sources in the corners. Instrumental responses were generated for each individual spectrum using the XISRESP script with a medium resolution. The spectra and response files for the front-illuminated (FI) detectors (XIS0, 3) were combined using the FTOOL ADDASCASPEC. Finally, we grouped the spectra to have a minimum signal-to-noise (S/N) of 5 per energy bin with the SPECGROUP task (part of the XMM-Newton SAS), to allow the use of χ 2 minimization during spectral fitting.",
"pages": [
2
]
},
{
"title": "2.1. HXD PIN",
"content": "Due to the level of systematic uncertainty in the PIN background model ( /greaterorsimilar 25% of the 'source' flux given the weak detection of the HolmbergIX field; see e.g. discussion in Walton et al. 2013), and the variable nature of the contaminating M 81 nucleus (Markoff et al. 2008; Miller et al. 2010), it is not possible to constrain the high energy ( E > 10 keV) properties of HolmbergIX X-1 with the collimating PIN detector. The imaging capabilities of the recently launched NuSTAR observatory (Harrison et al. 2013) are required. Therefore, we do not consider the PIN data here, and stress that any interpretation based on these data should be regarded with extreme skepticism.",
"pages": [
2
]
},
{
"title": "3. SPECTRAL ANALYSIS",
"content": "Throughout this work, spectral modeling is performed with XSPEC v12.8.0 (Arnaud 1996), and absorption by intervening neutral material is treated with TBNEW (Wilms et al. 2000) using the appropriate solar abundances. We include two absorption components, one fixed at the Galactic column ( N H;Gal = 5 . 54 × 10 20 atom cm -2 ; Kalberla et al. 2005), and another with variable column at the redshift of Holmberg IX ( z = 0 . 000153 ). During modelling, we only consider data from the FI detectors in the 1-10 keV energy range, owing to a calibration mismatch between XIS0 and XIS3 below ∼ 1keV. For the same reasons, we only consider data from the backilluminated (BI) XIS1 detector over the 2.5-9.0 keV energy range. We also exclude the 1.6-2.5keV energy range from the FI data owing to remaining calibration uncertainties associated with the instrumental silicon K and gold M edges, and the 7.3-7.6 keV energy range from the BI data owing to a residual background feature. The data from the FI and BI detectors are modelled simultaneously, with all parameters tied between the spectra, and we attempt to account for any further cross-calibration uncertainties above 2.5 keV by allowing a variable multiplicative cross-normalisation constant to vary between them. This value is always found to be within ∼ 10% of unity.",
"pages": [
2
]
},
{
"title": "3.1. Continuum Modelling",
"content": "We begin with a brief assessment of the form of the continuum, focusing first on the 2.5-10.0keV energy range. Specifically, we wish to determine whether a simple powerlawlike continuum is sufficient, or whether there is evidence for curvature similar to other high quality ULX datasets (Stobbart et al. 2006; Gladstone et al. 2009; Walton et al. 2011a). Similar to previous works, we compare the results obtained with a simple powerlaw continuum, with and without a high energy exponential cut-off. We indeed find that allowing a cut-off offers a significant improvement ( ∆ χ 2 = 135 , one additional free parameter; see Fig. 1), i.e. the 2.5-10.0keV spectrum does show curvature. Considering the 1-10keV bandpass, we utilize a common parameterisation of the continuum for ULXs, modeling the data with cool, optically thick Comptonisation (Stobbart et al. 2006; Gladstone et al. 2009; Middleton et al. 2011; Walton et al. 2011a). We note that this parameterisation is largely empirical, and should not be ascribed too much physical significance. The nature of the continuum emission will be addressed in more detail in future work (Walton et al. in prep ) utilising the necessary NuSTAR data. Here, we use the COMPTT code (Titarchuk 1994), which provides an excellent fit ( χ 2 ν = 1730/1694). As we do not consider the data below 1 keV, we are not sensitive to the presence of any additional low-temperature ( ∼ 0.2keV) thermal component similar to those seen previously in bright, unabsorbed ULXs (Miller et al. 2004), so we fix the seed photon temperature to 0.1 keV. The continuum parameters obtained are summarised in Table 1, and are broadly similar to those obtained with previous observations (Gladstone et al. 2009; Vierdayanti et al. 2010; Walton et al. 2012).",
"pages": [
2,
3
]
},
{
"title": "3.2. Narrow Iron K Features",
"content": "Walton et al. (2012) describes constraints on atomic iron K features for ULXs, focusing on the archival XMM-Newton data available for HolmbergIX X-1, revisited here with Suzaku , and NGC1313 X-1. In order to search for atomic features in this new dedicated dataset, we follow the same approach adopted in that work, varying a narrow ( σ = 10 eV) Gaussian across the 5-9 keV energy range, to include the rest frame energies of the iron K transitions and also generously allow for the possibility of blue-shifted features, in steps of 0.04 keV. For each energy step, we record the ∆ χ 2 improvement resulting from the inclusion of the Gaussian line, as well as the best fit equivalent width ( EW ) and its 90 and 99% confidence limits 2 . The latter quantities are obtained with the EQWIDTH command in XSPEC, generating 10,000 parameter sets based on the best fit model and the covariance matrix, which includes information on the model parameter uncertainties, and extracting the confidence limits from the distribution of equivalent widths obtained. The results obtained are shown in Fig. 2; the top panel shows the ∆ χ 2 improvement, multiplied by the sign of the best fit normalisation to differentiate between emission and absorption, and the limits on EW obtained are shown in the bottom panel. For clarity, we highlight the energies of the K α transitions of neutral, helium-like and hydrogen-like iron, as well as EW = ± 30 eV, representative of the strongest absorption features observed in GRS 1915+105 (Neilsen & Lee 2009). In addition, we also show the limits we obtained previously with XMM-Newton . As in our previous analysis, we find no statistically significant line detections, so we again focus on the limits that can be placed instead. Any narrow aromic features in the Suzaku data in the immediate Fe K band (6-7keV) must have equivalent widths less than ∼ 15-20eV (99% confidence); previously we were only able to constrain such features to EW /lessorsimilar 30 eV. On average, the allowed EW range at a given energy is a factor of ∼ 1.5 smaller with our new dataset than obtained previously (Walton et al. 2012).",
"pages": [
3
]
},
{
"title": "4. DISCUSSION",
"content": "Using our long 500 ks Suzaku observation of HolmbergIX X-1, we have undertaken the deepest study in the Fe K region of a bright, isolated ULX to date, to search for iron absorption/emission features similar to those frequently observed in other accreting black holes. Iron is ideally suited to identifying the presence of atomic processes, as it is both difficult to fully ionize and cosmically abundant. Despite the high sensitivity of the observations, we do not detect any discrete atomic iron features. The limits on any persistent narrow features (either in emission or absorption) as yet undetected are now EW /lessorsimilar 15 -20 eV (99% confidence) over the immediate Fe K energy range. As shown in Fig. 3, these limits are now extremely restrictive when considered in the context of the lines observed from other sources. Remarkably, in terms of absorption, the constraints are such that any iron features present in HolmbergIX X-1 must be weaker than the absorption lines observed in numerous sub-Eddington Galactic StMBHs (Miller et al. 2006; Neilsen & Lee 2009; King et al. 2012) and AGN (Tombesi et al. 2010; Gofford et al. 2013). Meanwhile, any neutral iron emission from HolmbergIX X-1 must be weaker than that observed in the vast majority of Galactic high-mass X-ray binaries (HMXBs), which ubiquitously display such emission features (Torrej'on et al. 2010), and there cannot be any substantial emission from helium- or hydrogenlike iron either. At the energies of these transitions, the 99% limits on emission lines are EW < 15 , 11 and 4 eV respectively. 2 We again note that we are computing confidence limits on line strength, which are not formally the same as the upper limits on the strength of lines that should be detected at a given confidence level (Kashyap et al. 2010), but are simpler to calculate, and provide more conservative estimates for the maximum strength of any lines intrinsically present. It is clear from the lack of absorption features that we cannot be viewing the central hard X-ray emitting regions of HolmbergIX X-1 through any substantial column of partially ionized material. We can therefore exclude the presence of any massive, spherical outflow in HolmbergIX X-1, as discussed in King & Pounds (2003), and wind-dominated spectral models (Vierdayanti et al. 2010) are also ruled out. If HolmbergIX X-1 truly is a StMBH accreting substantially in excess of the Eddington limit, we must be viewing it through a line of sight that is not covered by the massive outflow launched in such an accretion regime. The most natural conclusion is that, in this scenario, we would have to be viewing the source close to face-on (see also Roberts et al. 2011), with the wind still retaining some kind of roughly equatorial geometry, broadly similar to that inferred for sub-Eddington disk winds (Ponti et al. 2012), although presumably with a much larger scale-height for both the disk and the outflow (Poutanen et al. 2007). Furthermore, our results require that any equatorial outflow must be launched further out than the central hard X-ray emitting region, despite this presumably being the most irradiated region of the accretion flow. If this is the case, observation of atomic iron emission from such a massive outflow might be expected instead. The expected line profile might well be more complex than a simple narrow Gaussian, however we stress that there are no clear residual features that would readily be interpreted as re-emission from a strong wind, which may prove problematic for any extreme super-Eddington scenario. This will be addressed in more detail in future work. The lack of narrow iron emission lines has strong implications for the broader nature of the accretion onto Holmberg IX X-1, regardless of the black hole mass. In many respects, ULXs are widely expected to be analogues to black hole HMXBs. However, Galactic HMXBs ubiquitously display neutral iron emission lines (Torrej'on et al. 2010), owing to illumination of the stellar winds in which they are embedded, and from which they may primarily accrete. Since there is no iron emission observed, either neutral or highly ionized, we infer that either the stellar wind is weak (or even absent), or the accretion geometry is such that this material is not illuminated by the hard X-rays emitted from the central regions. Returning to the possible scenario in which ULXs are powered by a large scale height, optically thick super-Eddington accretion flow; the inner regions of such accretion flows are expected to have a roughly conical geometry, with the hard X-rays being produced in the hotter, central regions. If this funnel covers a large enough solid angle, it may be able to shield the majority of the stellar wind from the hard X-rays, which would be scattered and collimated preferentially out of the equatorial plane. Given the expected large-scale extent of the stellar wind, the optically thick regions of the accretion flow would have to cover an extremely large solid angle in order to prevent substantial iron line emission. However, the observed luminosity of the He II λ 4686 emission line, presumed to be associated with the cool outer disk, appears to require that the X-ray luminosity cannot be highly anisotropic via photon counting arguments (Moon et al. 2011), and optical/UV photometry is also indicative of X-ray reprocessing in the outer disk (Gris'e et al. 2011), so it is not clear that this offers a self-consistent scenario. Alternatively, if the scale-height of the accretion flow is not sufficient to provide substantial shielding, the lack of iron emission would therefore tell us that there is no strong stellar wind. Indeed, for a spherically symmetric repro- cessing geometry, which works well for Galactic HMXBs (Torrej'on et al. 2010), and the metallicity of Holmberg IX ( ∼ 0.5 Z /circledot ; Makarova et al. 2002), the specific emission line limits obtained for neutral and hydrogen-like iron correspond to reprocessing columns of N H /lessorsimilar 10 and 3 × 10 22 atom cm -2 respectively (see Walton et al. 2012). For comparison, the HMXBs analysed by Torrej'on et al. (2010), which have companion masses M ∗ /greaterorsimilar 10M /circledot , typically display columns of N H /greaterorsimilar 10 23 atom cm -2 . In turn, these observational constraints mean that any stellar wind present most likely cannot provide the mass accretion rate of ˙ M /greaterorsimilar 1 . 5 × 10 -6 M /circledot yr -1 required to power the observed X-ray luminosity from HolmbergIX X-1. Instead, HolmbergIX X-1 most likely accretes via Roche-lobe overflow, as suggested by Gris'e et al. (2011), the accretion mechanism more typically associated with low mass X-ray binaries (LMXBs). However, Galactic LMXBs are generally transient sources, spending the majority of the time in quiescence, occasionally undergoing accretion events resulting in bright ∼ month-to-year long X-ray outbursts. In contrast, HolmbergIX X-1 appears to be a much more persistent source, requiring a sufficiently close binary system such that Roche-lobe overflow/mass transfer remains roughly continuous. Gris'e et al. (2011) found a lower limit to the mass of the stellar companion of M ∗ /greaterorsimilar 10M /circledot . We suggest that the absent/weak stellar wind implies that the companion cannot be substantially more massive than this lower limit, given that more massive stars generally launch stronger winds. Finally, in addition to improving the narrow line limits, we also confirm the presence of curvature in the ∼ 310keV energy range, as previously indicated by XMMNewton (Gladstone et al. 2009). We defer a detailed consideration of the continuum to future work, which will focus on broadband spectral analysis utilising the required NuSTAR data, although we do comment here that the 3-10 keV spectrum does not appear consistent with the powerlaw-like emis- on expected from a standard sub-Eddington corona.",
"pages": [
3,
4,
5
]
},
{
"title": "5. CONCLUSIONS",
"content": "Our long Suzaku program on HolmbergIX X-1 has provided the most sensitive dataset in the Fe K region obtained for any luminous, isolated ULX to date. Despite the high sensitivity of these data, we find no statistically significant narrow atomic features in either emission or absorption across the 5-9 keV energy range. Furthermore, the data are of sufficient quality to limit any undetected features to have equivalent widths EW /lessorsimilar 15 -20 eV across the immediate Fe K bandpass at 99% confidence, i.e. weaker than the features associated with sub-Eddington outflows in a number of other black holes. Therefore, we cannot be viewing the central hard X-ray emitting regions of HolmbergIX X-1 through any substantial column of material. Models of spherical superEddington accretion can be rejected, as can wind-dominated spectral models. If HolmbergIX X-1 is accreting at highly super-Eddington rates, our viewing angle must be close to face on, such that the associated outflow is directed away from our line-of-sight. Finally, the lack of iron emission implies that the stellar companion is unlikely to be launching a strong wind, and therefore the black hole must primarily accrete via roche-lobe overflow.",
"pages": [
5
]
},
{
"title": "ACKNOWLEDGEMENTS",
"content": "The authors thank the reviewer for helpful comments. This research has made use of data obtained from the Suzaku observatory, a collaborative mission between the space agencies of Japan (JAXA) and the USA (NASA).",
"pages": [
5
]
},
{
"title": "REFERENCES",
"content": "Gofford J., Reeves J. N., Tombesi F., et al., 2013, MNRAS, 430, 60 Moon D.-S., Harrison F. A., Cenko S. B., Shariff J. A., 2011, ApJ, 731, L32 Neilsen J., Lee J. C., 2009, Nat, 458, 481",
"pages": [
5
]
}
]
2013ApJ...774L...8S
https://arxiv.org/pdf/1307.0850.pdf
<document>
<section_header_level_1><location><page_1><loc_30><loc_84><loc_65><loc_85></location>A Porous, Layered Heliopause</section_header_level_1>
<text><location><page_1><loc_32><loc_78><loc_64><loc_80></location>M. Swisdak 1 , J. F. Drake 2 , M. Opher 3</text>
<section_header_level_1><location><page_1><loc_41><loc_71><loc_54><loc_73></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_13><loc_53><loc_82><loc_71></location>The picture of the heliopause (HP) - the boundary between the domains of the sun and the local interstellar medium (LISM) - as a pristine interface with a large rotation in the magnetic field fails to describe recent Voyager 1 (V1) spacecraft data. Magnetohydrodynamic (MHD) simulations of the global heliosphere reveal that the rotation angle of the magnetic field across the HP at V1 is small. Particle-in-cell simulations, based on cuts through the MHD model at the location of V1, suggest that the sectored region of the heliosheath (HS) produces large-scale magnetic islands that reconnect with the interstellar magnetic field and mix LISM and HS plasma. Cuts across the simulation data reveal multiple, anti-correlated jumps in the number densities of LISM and HS particles at the magnetic separatrices of the islands, similar to those observed by V1. A model is presented, based on both the observations and simulation data, of the HP as a porous, multi-layered structure threaded by magnetic fields. This model further suggests that, contrary to the conclusions of recent papers, V1 has already crossed the HP.</text>
<text><location><page_1><loc_13><loc_49><loc_82><loc_52></location>Subject headings: ISM: magnetic fields - magnetic reconnection - magnetohydrodynamics (MHD) solar neighborhood - Sun: heliosphere</text>
<section_header_level_1><location><page_1><loc_9><loc_47><loc_28><loc_48></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_9><loc_24><loc_45><loc_45></location>The Voyager 1 and 2 spacecraft have been mapping the structure of the outer heliosphere as they leave the solar system. In 2005, V1 crossed the termination shock (Stone et al. 2005; Burlaga et al. 2005; Decker et al. 2005), where the supersonic solar wind becomes subsonic, and has since been traversing the HS. The HP, whose location and structure are unknown, separates the magnetic field and plasma associated with the sun from that of the LISM (Parker 1963; Baranov et al. 1979). The magnetic field in the HS has remained dominantly in the azimuthal (east-west) direction given by the Parker spiral but could rotate and acquire measurable north-south and</text>
<text><location><page_1><loc_51><loc_25><loc_86><loc_48></location>radial components upon crossing the HP. In ideal (non-dissipative) models of the heliosphere, the local magnetic field is transverse to the boundary and the HP is a tangential discontinuity (Parker 1963; Baranov et al. 1979). However, whether the HP is a smooth interface, or breaks up due to instabilities, has been the subject of substantial discussion in the literature (Fahr et al. 1986; Baranov et al. 1992; Liewer et al. 1996; Zank et al. 1996; Swisdak et al. 2010). The structure of the HP, and in particular whether the boundary is porous to some classes of particles, is of great importance because of its impact on the transport of energetic particles into and out of the heliosphere.</text>
<text><location><page_1><loc_51><loc_10><loc_86><loc_25></location>Beginning on day 210 of 2012, the V1 spacecraft measured a series of dropouts in the intensities of energetic particles produced in the heliosphere: the Anomalous Cosmic Rays (ACRs) and the lower-energy Termination Shock Particles (TSPs) (Webber & McDonald 2013; Stone et al. 2013; Krimigis et al. 2013). Simultaneous with the dropouts were abrupt increases in the Galactic Cosmic Ray (GCR) electrons and protons and an increase in the magnetic field intensity</text>
<text><location><page_2><loc_9><loc_59><loc_45><loc_86></location>(Burlaga et al. 2013). Finally, on around day 238, the heliospheric-produced particles dropped to noise levels and the GCRs underwent a final increase. Both have since exhibited no significant variations, which suggests that V1 crossed the HP, with the repeated dropouts and increases perhaps due to radial fluctuations caused by changes in the solar wind dynamic pressure. However, during this time the direction of the magnetic field remained dominantly azimuthal (Burlaga et al. 2013), consistent with the spacecraft remaining in the HS. While MHD models of the heliosphere suggested that the rotation of the magnetic field across the HP at the location of V1 would be small (Opher et al. 2009b,a), the lack of any significant change in the magnetic field direction across the final transition on day 238 suggested that V1 remained within the magnetic domain of the HS.</text>
<text><location><page_2><loc_9><loc_20><loc_45><loc_59></location>We present here a model of the magnetic structure of the HP at V1's location that produces particle and magnetic signatures consistent with the observations. By pairing a global MHD simulation with a local PIC simulation, we show that magnetic reconnection can produce a complex, nested set of magnetic islands at the HP. Tongues of LISM plasma penetrate into the HS along reconnected field lines. These tongues correspond to local depletions of the HS plasma and enhancements in the magnetic pressure. A key result of the simulations is that sharp anti-correlated jumps in the HS and LISM number density can occur across the separatrices emanating from reconnection sites while the magnetic field undergoes essentially no rotation. Such behavior undercuts the primary argument suggesting that V1 has not crossed the HP - that no field rotation was seen on day 238 where the final drop in ACRs was measured (Burlaga et al. 2013). We therefore suggest that V1 actually crossed the HP on day 209, the time of the last reversal in the azimuthal magnetic field B T , and that the steady values of the normal B N ∼ 0 . 12 nT and B T ∼ -0 . 40 nT fields since that time are the draped interstellar field just outside of the HP.</text>
<section_header_level_1><location><page_2><loc_9><loc_17><loc_27><loc_18></location>2. MHD Simulation</section_header_level_1>
<text><location><page_2><loc_9><loc_11><loc_45><loc_15></location>To establish local conditions at the HP, we first explore the heliosphere's large-scale structure with a global MHD simulation that includes both neu-</text>
<text><location><page_2><loc_51><loc_53><loc_86><loc_86></location>tral and ionized components (and both thermal and pick-up ions in the solar wind) (Zieger et al. 2013). The LISM field, B ISM , has a magnitude of 0 . 44 nT and a direction defined by α Bv = 15 . 9 · and β Bv = 51 . 5 · , where α Bv and β Bv are the angle between B ISM and the velocity of the interstellar wind v ISM and the angle between the B ISM -v ISM plane and the solar equator (for further discussion of these choices see Opher et al. 2009b). The Z -axis is along the solar rotation axis and the X -axis is chosen so that v ISM lies in the X -Z plane. The MHD simulation did not include the sector zone (where the Parker spiral field periodically reverses polarity due to the tilt between the solar magnetic and rotation axes) since this leads to field reversals that cannot be numerically resolved upstream of the HP and therefore produces incorrect values of B = | B | (Opher et al. 2011; Borovikov et al. 2011). The solar field polarity corresponds to solar cycle 24, with the azimuthal angle λ (between the radial and T directions in heliospheric coordinates) 90 · in the north and 270 · in the south.</text>
<text><location><page_2><loc_51><loc_27><loc_86><loc_53></location>In Fig. 1, B from the simulation reveals the solar wind compression at the termination shock, the downstream HS, and the HP. Profiles (solid curves in Fig. 2) along the V1 trajectory of the pick-up ( n pui ) and thermal ( n th ) ion densities and the azimuthal ( B T ) and normal ( B N ) magnetic fields near the HP are inputs for the PIC simulations. n pui decreases from ≈ 7 × 10 -4 / cm 3 in the HS to zero in the LISM while n th rises from 0 . 003 / cm 3 to ≈ 0 . 08 / cm 3 . B N (Fig. 2C) is small at V1's latitude in the LISM. B T flips direction across the HP, but remains the dominant component on both sides of the boundary (Fig. 2D). The polar angle δ (the angle between B N and the equatorial field) in the simulations approaches 14 · just outside of the HP, which is consistent with the steady values seen in the V1 data.</text>
<text><location><page_2><loc_51><loc_10><loc_86><loc_27></location>The MHD simulation does not match Voyager observations in several respects - the sign of the HS azimuthal magnetic field orientation, the strength of the flows in the HS and the characteristic scale length of the HP - none of which is essential for calculating initial conditions for the PIC simulations. First, because V1 continued to measure sector boundaries in the HS during 2012, and therefore probably remained in the sector zone, the sign of B T in the HS in the MHD model is irrelevant since a 'correct' model should include the</text>
<text><location><page_3><loc_9><loc_61><loc_45><loc_86></location>reversals associated with the sector region. Second, in contrast to the simulation, indirect measurements by the V1 LECP instrument indicate little to no normal flow in the HS (Decker et al. 2012). No published global model has explained the observed flows, although simulations that include the sectored field (e.g., Opher et al. 2012) are closer to the observations than those presented here (see also Pogorelov et al. 2012, for an alternative explanation). Finally, since the MHD model does not include the physics necessary to describe the structure of the HP, the scale length of this transition is not physical, but is instead a numerical artifact. On the other hand, what is essential for input into the PIC simulations is the strength of the HS field and the strength and orientation of the field in the LISM.</text>
<section_header_level_1><location><page_3><loc_9><loc_58><loc_26><loc_59></location>3. PIC Simulations</section_header_level_1>
<text><location><page_3><loc_9><loc_16><loc_45><loc_56></location>The initial profiles of the magnetic field, density, and temperature for the 2-D PIC simulations (dotted lines in Fig. 2; right-hand scale) were constructed with input from the MHD profiles although, in keeping with the Voyager 1 observations, there are no initial flows. The PIC code is written in normalized units based on a field strength B 0 and density n 0 (lengths normalized to the ion inertial length d i = c/ω pi , with ω pi the ion plasma frequency, times to the ion cyclotron time Ω -1 i 0 and velocities to the Alfv'en speed c A 0 ). In the HS, thermal ( n th = 0 . 25 n 0 , T th = 0 . 25 m i c 2 A 0 ) and pick-up ions ( n pui = 0 . 01 n 0 , T pui = 15 . 0 m i c 2 A 0 ) were included as independent species while the LISM only included a thermal component ( n th = 2 . 0 n 0 , T th = 0 . 2 m i c 2 A 0 ). The simulations were performed in a domain with dimensions ( L T , L R ) = (409 . 6 d i , 204 . 8 d i ). The ionto-electron mass ratio was 25 and the velocity of light was 15 c A 0 . Not shown in Fig. 2 are the three current sheets, of initial half-width 0 . 5 d i , that produce the sectored HS field. This scale reflects satellite measurements at the Earth's magnetopause that such boundaries collapse to kinetic scales (Sonnerup et al. 1981). Pressure balance across each reversal is achieved by adjusting the out-of-plane component B N (Smith 2001).</text>
<text><location><page_3><loc_9><loc_11><loc_45><loc_15></location>For HS-appropriate values, n = 10 -2 cm -3 and B = 0 . 3 nT, d i ≈ 2 × 10 -5 AU, Ω -1 ci ≈ 30 s, and c A ≈ 100 km/s. Resolving kinetic scales forces the</text>
<text><location><page_3><loc_51><loc_79><loc_86><loc_86></location>simulation domain to be much smaller than the actual system. Despite this limitation, the important physical processes can still be understood by appropriately scaling the results (Schoeffler et al. 2012).</text>
<text><location><page_3><loc_51><loc_47><loc_86><loc_78></location>The simulations are evolved with no initially imposed perturbations. Because of the lower density, which leads to a locally higher c A and effectively thinner current sheets (when normalized to the local d i ), magnetic reconnection first starts in the sectored HS. Small magnetic islands grow on individual current layers in the HS and merge to become larger islands until they are comparable in size to the sector spacing (Fig. 3A). A chain of small islands grows at the HP. These merge, forming larger islands, and are compressed by HS islands pushing against the HP (Fig. 3A). By late time, the HS magnetic field has reconnected with that of the LISM, forming a complex, nested chain of islands (Fig. 3A) at the HP with sizes comparable to the original sector spacing. Along a cut from the HS to the LISM (dark line in Fig. 3A) the HP is at ∆ R/d i ∼ 25 where B T reverses sign (Fig. 3D). The rotation to the LISM field direction is complete by ∆ R/d i ∼ 35 after which δ and λ are nearly constant.</text>
<text><location><page_3><loc_51><loc_19><loc_86><loc_46></location>We can independently track every particle in the PIC model and therefore can explore the mixing of the LISM and HS plasmas. The overall result is a highly structured distribution in the densities of the LISM ( n LISM ) and HS ( n HS ), with each experiencing sharp jumps across the separatrices bounding the outflows ejected from reconnection sites (Fig. 3A-C). Particles initially in the LISM continue to dominate the density on the unreconnected LISM field lines, have mixed with HS particles in the nested islands formed from HSLISM reconnection, and are largely excluded from islands formed from reconnection of the HS sectored field (Fig. 3B). Particles initially in the HS dominate islands resulting from reconnection of the sectored field, are mixed with LISM particles in the HP islands, and are nearly excluded from un-reconnected regions of the LISM (Fig. 3C).</text>
<text><location><page_3><loc_51><loc_10><loc_86><loc_19></location>Radial cuts through the simulation reveal that the increases and decreases in n LISM and n HS are typically anti-correlated (Fig. 3G). Moving from a pure HS magnetic island into an island or outflow jet where LISM and HS plasma has mixed reduces n HS and increases n LISM . Along the cut the first</text>
<text><location><page_4><loc_9><loc_49><loc_45><loc_86></location>drop in n HS occurs downstream of a magnetic separatrix, where HS particles have an open path to the LISM along open field lines (∆ R/d i ∼ 8 in Fig. 3G). Similar behavior has been documented in satellite measurements at the Earth's magnetopause (Sonnerup et al. 1981) and echoes V1's observations of the anti-correlated variations in the fluxes of ACRs/TSPs and galactic electrons/GCRs (Stone et al. 2013; Krimigis et al. 2013; Webber & McDonald 2013). Most important, the cuts further reveal that, when crossing the last magnetic separatrix on the LISM side of the HP before finally entering the pristine LISM plasma, the sharp decrease in n HS and increase in n LISM (in the interval ∆ R/d i = 38 -50 in Fig. 3G) occur over an interval where there is no directional change in the magnetic field (Fig. 3D-E). The absence of a directional change in B at locations with strong variations in the particle densities is consistent with one of the most significant of the V1 observations (Burlaga et al. 2013). The fact that, in our simulation, this occurs on the LISM side of the HP therefore suggests that it may be incorrect to conclude that V1 has not crossed the HP.</text>
<text><location><page_4><loc_9><loc_20><loc_45><loc_48></location>The simulation cuts also reveal that local decreases in the HS density typically correspond to increases in the local magnetic field (Figs. 3FG). The total pressure across the HP is balanced. While the dominant pressure in the HS is from the plasma, the dominant pressure in the LISM is magnetic. Thus, when reconnection opens a path for HS plasma to escape into the LISM and mix with the lower-pressure LISM plasma, there is nothing to balance the total pressure and so the region compresses to increase the magnetic field amplitude. This behavior is primarily seen at separatrix crossings remote from where reconnection locally reduces the magnetic field strength (the interval ∆ R/d i = 38 -50 in Figs. 3F-G). In the V1 data, the magnetic field strength is also observed to increase where the local flux of HS plasma decreases (Stone et al. 2013; Krimigis et al. 2013; Webber & McDonald 2013; Burlaga et al. 2013).</text>
<text><location><page_4><loc_9><loc_10><loc_45><loc_19></location>Thus, based on our simulations, we suggest that the V1 observations of simultaneous drops (increases) in HS (LISM) particle fluxes occur at a series of separatrix crossings outside of the HP that are associated with a nested set of magnetic islands that form at the HP (Fig. 4). At such cross-</text>
<text><location><page_4><loc_51><loc_62><loc_86><loc_86></location>ings the magnetic field direction does not change significantly, while, as seen in the simulation data, particle fluxes can change sharply. Three active reconnection sites at the HP, and associated separatrices with two nested islands, are sufficient to explain the sequence of Voyager events. On day 166 the spacecraft crossed a current layer, on day 190 the flux of HS electrons began dropping, on day 209 another current layer was crossed and on days 210, 222 and 238 three successive drops (increases) in the HS (LISM) particle fluxes occurred. The day 190 drop in the HS electrons suggests that after this time the magnetic field was no longer laminar so that these electrons, with their small Larmor radii and large velocities, could leak into the LISM.</text>
<text><location><page_4><loc_51><loc_11><loc_86><loc_62></location>Islands and x-lines flowing away from an active x-line (e.g., the rightmost x-line in Fig. 4) correspond to reconnection sites that developed earlier in time. The separatrix field lines connect to x-lines, which act as bottlenecks to particle transport across the HP. There are two reasons for this. First, at the x-line the magnetic field turns into the N direction since the R and T magnetic field components are zero. Thus, the x-line halts the field-aligned streaming of particles across the HP. Second, to the extent that B N is weak compared with B T energetic particles can scatter near xlines, which further limits transport across the HP. In contrast, downstream of separatrices (to the left in Fig. 4) particles can freely stream across the HP. Thus, the day 210 drop in ACRs (rise in GCRs) occurred at the separatrix corresponding to the leftmost x-line of Fig. 4 which blocked the transport of ACRs (GCRs) across the HP. The ACR (GCR) intensity rose (dropped) as the spacecraft crossed field lines that formed an open corridor across the HP to the left of the middle x-line in Fig. 4. In this region the flow of GCRs into the HS acts as a sink for the intensity of these particles. The second ACR drop on day 222 and subsequent recovery is similar. The final drop of the HS particle fluxes on day 238 occurred at the separatrix of the right-most x-line in Fig. 4. LECP measurements of ACR anisotropies (Krimigis et al. 2013) show that particles propagating parallel to the magnetic field dropped more rapidly than those with perpendicular pitch angles on day 238. Such behavior is consistent with our schematic - in a weakly stochastic field parallel moving particles will more</text>
<text><location><page_5><loc_9><loc_85><loc_29><loc_86></location>quickly escape in the LISM.</text>
<text><location><page_5><loc_9><loc_63><loc_45><loc_84></location>An inconsistency between our PIC simulations and the observations concerns the spatial region where sharp jumps in the ACRs and GCRs take place. In the simulations the anti-correlated jumps occur on both sides of the HP but if our cartoon is correct, they occur only on the LISM side in the V1 data. The contradiction is possibly because the simulations are in a 2-D system. A magnetic field in a real 3-D system will likely be at least mildly stochastic so that wandering field lines will smooth the variability of ACR and GCR intensities far from the HP boundary. More challenging 3-D simulations will be required to explore this issue.</text>
<text><location><page_5><loc_9><loc_33><loc_45><loc_63></location>A second issue is the angle δ of the magnetic field outside of the HP, which for the present MHD simulation is 14 · . B ISM for this simulation was chosen to match heliospheric asymmetries (Opher et al. 2009b,a). Other MHD simulations based on fitting the IBEX ribbon yield δ ∼ 30 · (Pogorelov 2013). Such values are considerably smaller than those implied by cartoons in recent publications (Burlaga et al. 2013). In any case our conclusion that significant variations in the density of the ACRs and GCRs can occur in regions with essentially no variation in the field line orientation is not sensitive to the value of δ in the LISM. Any rotation in the magnetic field outside of the HP propagates at the local Alfv'en speed, which is well below the velocities of the particles of interest. Thus, outside of the HP separatrices should retain their original LISM orientation in locations where there are significant variations in particle intensity.</text>
<text><location><page_5><loc_9><loc_19><loc_46><loc_32></location>Combining a typical aspect ratio of reconnectionproduced islands (0.1), the typical time between dropouts (10 days), and the speed of Voyager 1 with respect to the HS plasma ( ≈ 20 km/s), yields the approximate size of the islands in Fig. 4 as 1 AU. This roughly equals the sector spacing downstream of the TS and is consistent with previous simulation-derived estimates of magnetic islands in the HS (Schoeffler et al. 2012).</text>
<text><location><page_5><loc_9><loc_10><loc_45><loc_19></location>If the schematic with nested magnetic islands (Fig. 4) is correct, the dropouts in the HS particle fluxes occurred on the LISM side of the HP on field lines that had a LISM source. Thus, according to this picture V1 crossed the HP on day 208 and has been crossing LISM fields since that time.</text>
<text><location><page_5><loc_51><loc_83><loc_86><loc_86></location>Our results thus suggest that B T in the LISM is negative (i.e., has a polarity of 270 · ).</text>
<text><location><page_5><loc_51><loc_60><loc_86><loc_81></location>The authors acknowledge the support of NSF grant AGS-1202330 to the University of Maryland, and NSF grant ATM-0747654 and NASA grant NNX07AH20G to Boston University. The PIC simulations were performed at the National Energy Research Scientific Computing Center and the MHD simulations at the Ames NASA Supercomputer Center. We acknowledge fruitful discussions with L. F. Burlaga, R. B. Decker, M. E. Hill and E. C. Stone on the Voyager observations. This research benefited greatly from discussions held at the meetings of the Heliopause International Team at the International Space Science Institute in Bern, Switzerland.</text>
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<text><location><page_6><loc_9><loc_78><loc_45><loc_82></location>Opher, M., Alouani Bibi, F., Toth, G., Richardson, J. D., Izmodenov, V. V., & Gombosi, T. I. 2009a, Nature, 462, 1036</text>
<text><location><page_6><loc_9><loc_73><loc_45><loc_77></location>Opher, M., Drake, J. F., Swisdak, M., Schoeffler, K. M., Richardson, J. D., Decker, R. B., & Toth, G. 2011, Ap. J., 734</text>
<text><location><page_6><loc_9><loc_69><loc_45><loc_72></location>Opher, M., Drake, J. F., Velli, M., Decker, R. B., & Toth, G. 2012, Ap. J., 751</text>
<text><location><page_6><loc_9><loc_65><loc_45><loc_68></location>Opher, M., Richardson, J. D., Toth, G., & Gombosi, T. I. 2009b, Space Sci. Rev., 143, 43</text>
<text><location><page_6><loc_9><loc_61><loc_45><loc_64></location>Parker, E. N. 1963, Interplanetary Dynamical Processes (New York: Interscience)</text>
<text><location><page_6><loc_9><loc_56><loc_45><loc_60></location>Pogorelov, N. V. 2013, private communication at the ISSI Workshop on the Nature of the Heliopause in Bern, Switzerland</text>
<text><location><page_6><loc_9><loc_50><loc_45><loc_55></location>Pogorelov, N. V., Borovikov, S. N., Zank, G. P., Burlaga, L. F., Decker, R. A., & Stone, E. C. 2012, Ap. J. Lett., 750, L4</text>
<text><location><page_6><loc_9><loc_47><loc_45><loc_49></location>Schoeffler, K. M., Drake, J. F., & Swisdak, M. 2012, Ap. J. Lett., 750, L30</text>
<text><location><page_6><loc_9><loc_44><loc_43><loc_46></location>Smith, E. J. 2001, J. Geophys. Res., 106, 15819</text>
<text><location><page_6><loc_9><loc_39><loc_45><loc_44></location>Sonnerup, B. U. O., Paschmann, G., Papamastorakis, I., Sckopke, N., Haerendel, G., et al. 1981, J. Geophys. Res., 86, 10049</text>
<text><location><page_6><loc_9><loc_34><loc_45><loc_38></location>Stone, E. C., Cummings, A. C., McDonald, F. B., Heikkila, B. C., Lal, N., & Webber, W. R. 2005, Science, 309, 2017</text>
<text><location><page_6><loc_9><loc_31><loc_44><loc_33></location>-. 2013, Science, published online 27 June 2013</text>
<text><location><page_6><loc_9><loc_27><loc_45><loc_30></location>Swisdak, M., Opher, M., Drake, J. F., & Alouani Bibi, F. 2010, Ap. J., 710, 1769</text>
<text><location><page_6><loc_9><loc_24><loc_45><loc_26></location>Webber, W. R., & McDonald, F. B. 2013, Geophys. Res. Lett., accepted</text>
<text><location><page_6><loc_9><loc_20><loc_45><loc_23></location>Zank, G. P., Pauls, H. L., Williams, L. L., & Hall, D. T. 1996, J. Geophys. Res., 101, 21,639</text>
<text><location><page_6><loc_9><loc_14><loc_45><loc_19></location>Zieger, B., Opher, M., Schwadron, N. A., McComas, D. J., & Toth, G. 2013, Geophys. Res. Lett., published online 21 June 2013</text>
<figure>
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<caption>Fig. 1.- A meridional cut from the global MHD simulation showing the magnetic field amplitude B (background), the flow streamlines (solid curves with arrows) and the V1 trajectory (red). The HP is where the flows from the LISM and the HS meet. The blue line in the HS is the heliospheric current sheet.</caption>
</figure>
<text><location><page_6><loc_88><loc_39><loc_88><loc_39></location>/s48</text>
<text><location><page_6><loc_88><loc_38><loc_88><loc_38></location>/s80/s85/s73</text>
<text><location><page_6><loc_88><loc_35><loc_88><loc_35></location>/s48</text>
<text><location><page_6><loc_88><loc_34><loc_88><loc_34></location>/s116/s104/s32</text>
<text><location><page_6><loc_88><loc_31><loc_88><loc_32></location>/s48</text>
<text><location><page_6><loc_88><loc_30><loc_88><loc_31></location>/s78/s32</text>
<text><location><page_6><loc_88><loc_28><loc_88><loc_28></location>/s48</text>
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<figure>
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<caption>Fig. 2.- Cuts of various parameters along the V1 trajectory near the HP from the MHD model (solid with left scale) and as initial conditions for the PIC model (dotted with right scale). Shown are in (A) the pick-up ion density, in (B) the thermal ion density, in (C) B T and in (D) B N . Note that the scales on the right and left differ.</caption>
</figure>
<text><location><page_6><loc_69><loc_23><loc_72><loc_24></location>/s114/s97/s100/s105/s117/s115/s32/s40/s65/s85/s41</text>
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<caption>Fig. 3.- The structure of the HP and adjacent LISM and HS at late time. In the R / T plane in (A) the magnetic field lines and in (B) and (C) the number density n LISM ( n HS ) of particles that were originally in the LISM (HS), respectively. Panels (D)-(G) are cuts along the vertical line in panels (A)-(C). In (D) the azimuthal angle λ is the angle of B in the R -T plane with respect to the R direction. In (E) the polar angle δ is the angle between B and the R -T plane. In (F), the magnitude of B and, in (G), the number density n LISM (solid) and the number density n HS (dashed red).</caption>
</figure>
<figure>
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<caption>Fig. 4.- A schematic, based on the results of our simulations, of the inferred magnetic structure of the HP during the time when V1 documented strong variations in the HS and LISM particles. The times corresponding to several of the Voyager events are marked by the days of 2012 on which they occurred.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "The picture of the heliopause (HP) - the boundary between the domains of the sun and the local interstellar medium (LISM) - as a pristine interface with a large rotation in the magnetic field fails to describe recent Voyager 1 (V1) spacecraft data. Magnetohydrodynamic (MHD) simulations of the global heliosphere reveal that the rotation angle of the magnetic field across the HP at V1 is small. Particle-in-cell simulations, based on cuts through the MHD model at the location of V1, suggest that the sectored region of the heliosheath (HS) produces large-scale magnetic islands that reconnect with the interstellar magnetic field and mix LISM and HS plasma. Cuts across the simulation data reveal multiple, anti-correlated jumps in the number densities of LISM and HS particles at the magnetic separatrices of the islands, similar to those observed by V1. A model is presented, based on both the observations and simulation data, of the HP as a porous, multi-layered structure threaded by magnetic fields. This model further suggests that, contrary to the conclusions of recent papers, V1 has already crossed the HP. Subject headings: ISM: magnetic fields - magnetic reconnection - magnetohydrodynamics (MHD) solar neighborhood - Sun: heliosphere",
"pages": [
1
]
},
{
"title": "A Porous, Layered Heliopause",
"content": "M. Swisdak 1 , J. F. Drake 2 , M. Opher 3",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "The Voyager 1 and 2 spacecraft have been mapping the structure of the outer heliosphere as they leave the solar system. In 2005, V1 crossed the termination shock (Stone et al. 2005; Burlaga et al. 2005; Decker et al. 2005), where the supersonic solar wind becomes subsonic, and has since been traversing the HS. The HP, whose location and structure are unknown, separates the magnetic field and plasma associated with the sun from that of the LISM (Parker 1963; Baranov et al. 1979). The magnetic field in the HS has remained dominantly in the azimuthal (east-west) direction given by the Parker spiral but could rotate and acquire measurable north-south and radial components upon crossing the HP. In ideal (non-dissipative) models of the heliosphere, the local magnetic field is transverse to the boundary and the HP is a tangential discontinuity (Parker 1963; Baranov et al. 1979). However, whether the HP is a smooth interface, or breaks up due to instabilities, has been the subject of substantial discussion in the literature (Fahr et al. 1986; Baranov et al. 1992; Liewer et al. 1996; Zank et al. 1996; Swisdak et al. 2010). The structure of the HP, and in particular whether the boundary is porous to some classes of particles, is of great importance because of its impact on the transport of energetic particles into and out of the heliosphere. Beginning on day 210 of 2012, the V1 spacecraft measured a series of dropouts in the intensities of energetic particles produced in the heliosphere: the Anomalous Cosmic Rays (ACRs) and the lower-energy Termination Shock Particles (TSPs) (Webber & McDonald 2013; Stone et al. 2013; Krimigis et al. 2013). Simultaneous with the dropouts were abrupt increases in the Galactic Cosmic Ray (GCR) electrons and protons and an increase in the magnetic field intensity (Burlaga et al. 2013). Finally, on around day 238, the heliospheric-produced particles dropped to noise levels and the GCRs underwent a final increase. Both have since exhibited no significant variations, which suggests that V1 crossed the HP, with the repeated dropouts and increases perhaps due to radial fluctuations caused by changes in the solar wind dynamic pressure. However, during this time the direction of the magnetic field remained dominantly azimuthal (Burlaga et al. 2013), consistent with the spacecraft remaining in the HS. While MHD models of the heliosphere suggested that the rotation of the magnetic field across the HP at the location of V1 would be small (Opher et al. 2009b,a), the lack of any significant change in the magnetic field direction across the final transition on day 238 suggested that V1 remained within the magnetic domain of the HS. We present here a model of the magnetic structure of the HP at V1's location that produces particle and magnetic signatures consistent with the observations. By pairing a global MHD simulation with a local PIC simulation, we show that magnetic reconnection can produce a complex, nested set of magnetic islands at the HP. Tongues of LISM plasma penetrate into the HS along reconnected field lines. These tongues correspond to local depletions of the HS plasma and enhancements in the magnetic pressure. A key result of the simulations is that sharp anti-correlated jumps in the HS and LISM number density can occur across the separatrices emanating from reconnection sites while the magnetic field undergoes essentially no rotation. Such behavior undercuts the primary argument suggesting that V1 has not crossed the HP - that no field rotation was seen on day 238 where the final drop in ACRs was measured (Burlaga et al. 2013). We therefore suggest that V1 actually crossed the HP on day 209, the time of the last reversal in the azimuthal magnetic field B T , and that the steady values of the normal B N ∼ 0 . 12 nT and B T ∼ -0 . 40 nT fields since that time are the draped interstellar field just outside of the HP.",
"pages": [
1,
2
]
},
{
"title": "2. MHD Simulation",
"content": "To establish local conditions at the HP, we first explore the heliosphere's large-scale structure with a global MHD simulation that includes both neu- tral and ionized components (and both thermal and pick-up ions in the solar wind) (Zieger et al. 2013). The LISM field, B ISM , has a magnitude of 0 . 44 nT and a direction defined by α Bv = 15 . 9 · and β Bv = 51 . 5 · , where α Bv and β Bv are the angle between B ISM and the velocity of the interstellar wind v ISM and the angle between the B ISM -v ISM plane and the solar equator (for further discussion of these choices see Opher et al. 2009b). The Z -axis is along the solar rotation axis and the X -axis is chosen so that v ISM lies in the X -Z plane. The MHD simulation did not include the sector zone (where the Parker spiral field periodically reverses polarity due to the tilt between the solar magnetic and rotation axes) since this leads to field reversals that cannot be numerically resolved upstream of the HP and therefore produces incorrect values of B = | B | (Opher et al. 2011; Borovikov et al. 2011). The solar field polarity corresponds to solar cycle 24, with the azimuthal angle λ (between the radial and T directions in heliospheric coordinates) 90 · in the north and 270 · in the south. In Fig. 1, B from the simulation reveals the solar wind compression at the termination shock, the downstream HS, and the HP. Profiles (solid curves in Fig. 2) along the V1 trajectory of the pick-up ( n pui ) and thermal ( n th ) ion densities and the azimuthal ( B T ) and normal ( B N ) magnetic fields near the HP are inputs for the PIC simulations. n pui decreases from ≈ 7 × 10 -4 / cm 3 in the HS to zero in the LISM while n th rises from 0 . 003 / cm 3 to ≈ 0 . 08 / cm 3 . B N (Fig. 2C) is small at V1's latitude in the LISM. B T flips direction across the HP, but remains the dominant component on both sides of the boundary (Fig. 2D). The polar angle δ (the angle between B N and the equatorial field) in the simulations approaches 14 · just outside of the HP, which is consistent with the steady values seen in the V1 data. The MHD simulation does not match Voyager observations in several respects - the sign of the HS azimuthal magnetic field orientation, the strength of the flows in the HS and the characteristic scale length of the HP - none of which is essential for calculating initial conditions for the PIC simulations. First, because V1 continued to measure sector boundaries in the HS during 2012, and therefore probably remained in the sector zone, the sign of B T in the HS in the MHD model is irrelevant since a 'correct' model should include the reversals associated with the sector region. Second, in contrast to the simulation, indirect measurements by the V1 LECP instrument indicate little to no normal flow in the HS (Decker et al. 2012). No published global model has explained the observed flows, although simulations that include the sectored field (e.g., Opher et al. 2012) are closer to the observations than those presented here (see also Pogorelov et al. 2012, for an alternative explanation). Finally, since the MHD model does not include the physics necessary to describe the structure of the HP, the scale length of this transition is not physical, but is instead a numerical artifact. On the other hand, what is essential for input into the PIC simulations is the strength of the HS field and the strength and orientation of the field in the LISM.",
"pages": [
2,
3
]
},
{
"title": "3. PIC Simulations",
"content": "The initial profiles of the magnetic field, density, and temperature for the 2-D PIC simulations (dotted lines in Fig. 2; right-hand scale) were constructed with input from the MHD profiles although, in keeping with the Voyager 1 observations, there are no initial flows. The PIC code is written in normalized units based on a field strength B 0 and density n 0 (lengths normalized to the ion inertial length d i = c/ω pi , with ω pi the ion plasma frequency, times to the ion cyclotron time Ω -1 i 0 and velocities to the Alfv'en speed c A 0 ). In the HS, thermal ( n th = 0 . 25 n 0 , T th = 0 . 25 m i c 2 A 0 ) and pick-up ions ( n pui = 0 . 01 n 0 , T pui = 15 . 0 m i c 2 A 0 ) were included as independent species while the LISM only included a thermal component ( n th = 2 . 0 n 0 , T th = 0 . 2 m i c 2 A 0 ). The simulations were performed in a domain with dimensions ( L T , L R ) = (409 . 6 d i , 204 . 8 d i ). The ionto-electron mass ratio was 25 and the velocity of light was 15 c A 0 . Not shown in Fig. 2 are the three current sheets, of initial half-width 0 . 5 d i , that produce the sectored HS field. This scale reflects satellite measurements at the Earth's magnetopause that such boundaries collapse to kinetic scales (Sonnerup et al. 1981). Pressure balance across each reversal is achieved by adjusting the out-of-plane component B N (Smith 2001). For HS-appropriate values, n = 10 -2 cm -3 and B = 0 . 3 nT, d i ≈ 2 × 10 -5 AU, Ω -1 ci ≈ 30 s, and c A ≈ 100 km/s. Resolving kinetic scales forces the simulation domain to be much smaller than the actual system. Despite this limitation, the important physical processes can still be understood by appropriately scaling the results (Schoeffler et al. 2012). The simulations are evolved with no initially imposed perturbations. Because of the lower density, which leads to a locally higher c A and effectively thinner current sheets (when normalized to the local d i ), magnetic reconnection first starts in the sectored HS. Small magnetic islands grow on individual current layers in the HS and merge to become larger islands until they are comparable in size to the sector spacing (Fig. 3A). A chain of small islands grows at the HP. These merge, forming larger islands, and are compressed by HS islands pushing against the HP (Fig. 3A). By late time, the HS magnetic field has reconnected with that of the LISM, forming a complex, nested chain of islands (Fig. 3A) at the HP with sizes comparable to the original sector spacing. Along a cut from the HS to the LISM (dark line in Fig. 3A) the HP is at ∆ R/d i ∼ 25 where B T reverses sign (Fig. 3D). The rotation to the LISM field direction is complete by ∆ R/d i ∼ 35 after which δ and λ are nearly constant. We can independently track every particle in the PIC model and therefore can explore the mixing of the LISM and HS plasmas. The overall result is a highly structured distribution in the densities of the LISM ( n LISM ) and HS ( n HS ), with each experiencing sharp jumps across the separatrices bounding the outflows ejected from reconnection sites (Fig. 3A-C). Particles initially in the LISM continue to dominate the density on the unreconnected LISM field lines, have mixed with HS particles in the nested islands formed from HSLISM reconnection, and are largely excluded from islands formed from reconnection of the HS sectored field (Fig. 3B). Particles initially in the HS dominate islands resulting from reconnection of the sectored field, are mixed with LISM particles in the HP islands, and are nearly excluded from un-reconnected regions of the LISM (Fig. 3C). Radial cuts through the simulation reveal that the increases and decreases in n LISM and n HS are typically anti-correlated (Fig. 3G). Moving from a pure HS magnetic island into an island or outflow jet where LISM and HS plasma has mixed reduces n HS and increases n LISM . Along the cut the first drop in n HS occurs downstream of a magnetic separatrix, where HS particles have an open path to the LISM along open field lines (∆ R/d i ∼ 8 in Fig. 3G). Similar behavior has been documented in satellite measurements at the Earth's magnetopause (Sonnerup et al. 1981) and echoes V1's observations of the anti-correlated variations in the fluxes of ACRs/TSPs and galactic electrons/GCRs (Stone et al. 2013; Krimigis et al. 2013; Webber & McDonald 2013). Most important, the cuts further reveal that, when crossing the last magnetic separatrix on the LISM side of the HP before finally entering the pristine LISM plasma, the sharp decrease in n HS and increase in n LISM (in the interval ∆ R/d i = 38 -50 in Fig. 3G) occur over an interval where there is no directional change in the magnetic field (Fig. 3D-E). The absence of a directional change in B at locations with strong variations in the particle densities is consistent with one of the most significant of the V1 observations (Burlaga et al. 2013). The fact that, in our simulation, this occurs on the LISM side of the HP therefore suggests that it may be incorrect to conclude that V1 has not crossed the HP. The simulation cuts also reveal that local decreases in the HS density typically correspond to increases in the local magnetic field (Figs. 3FG). The total pressure across the HP is balanced. While the dominant pressure in the HS is from the plasma, the dominant pressure in the LISM is magnetic. Thus, when reconnection opens a path for HS plasma to escape into the LISM and mix with the lower-pressure LISM plasma, there is nothing to balance the total pressure and so the region compresses to increase the magnetic field amplitude. This behavior is primarily seen at separatrix crossings remote from where reconnection locally reduces the magnetic field strength (the interval ∆ R/d i = 38 -50 in Figs. 3F-G). In the V1 data, the magnetic field strength is also observed to increase where the local flux of HS plasma decreases (Stone et al. 2013; Krimigis et al. 2013; Webber & McDonald 2013; Burlaga et al. 2013). Thus, based on our simulations, we suggest that the V1 observations of simultaneous drops (increases) in HS (LISM) particle fluxes occur at a series of separatrix crossings outside of the HP that are associated with a nested set of magnetic islands that form at the HP (Fig. 4). At such cross- ings the magnetic field direction does not change significantly, while, as seen in the simulation data, particle fluxes can change sharply. Three active reconnection sites at the HP, and associated separatrices with two nested islands, are sufficient to explain the sequence of Voyager events. On day 166 the spacecraft crossed a current layer, on day 190 the flux of HS electrons began dropping, on day 209 another current layer was crossed and on days 210, 222 and 238 three successive drops (increases) in the HS (LISM) particle fluxes occurred. The day 190 drop in the HS electrons suggests that after this time the magnetic field was no longer laminar so that these electrons, with their small Larmor radii and large velocities, could leak into the LISM. Islands and x-lines flowing away from an active x-line (e.g., the rightmost x-line in Fig. 4) correspond to reconnection sites that developed earlier in time. The separatrix field lines connect to x-lines, which act as bottlenecks to particle transport across the HP. There are two reasons for this. First, at the x-line the magnetic field turns into the N direction since the R and T magnetic field components are zero. Thus, the x-line halts the field-aligned streaming of particles across the HP. Second, to the extent that B N is weak compared with B T energetic particles can scatter near xlines, which further limits transport across the HP. In contrast, downstream of separatrices (to the left in Fig. 4) particles can freely stream across the HP. Thus, the day 210 drop in ACRs (rise in GCRs) occurred at the separatrix corresponding to the leftmost x-line of Fig. 4 which blocked the transport of ACRs (GCRs) across the HP. The ACR (GCR) intensity rose (dropped) as the spacecraft crossed field lines that formed an open corridor across the HP to the left of the middle x-line in Fig. 4. In this region the flow of GCRs into the HS acts as a sink for the intensity of these particles. The second ACR drop on day 222 and subsequent recovery is similar. The final drop of the HS particle fluxes on day 238 occurred at the separatrix of the right-most x-line in Fig. 4. LECP measurements of ACR anisotropies (Krimigis et al. 2013) show that particles propagating parallel to the magnetic field dropped more rapidly than those with perpendicular pitch angles on day 238. Such behavior is consistent with our schematic - in a weakly stochastic field parallel moving particles will more quickly escape in the LISM. An inconsistency between our PIC simulations and the observations concerns the spatial region where sharp jumps in the ACRs and GCRs take place. In the simulations the anti-correlated jumps occur on both sides of the HP but if our cartoon is correct, they occur only on the LISM side in the V1 data. The contradiction is possibly because the simulations are in a 2-D system. A magnetic field in a real 3-D system will likely be at least mildly stochastic so that wandering field lines will smooth the variability of ACR and GCR intensities far from the HP boundary. More challenging 3-D simulations will be required to explore this issue. A second issue is the angle δ of the magnetic field outside of the HP, which for the present MHD simulation is 14 · . B ISM for this simulation was chosen to match heliospheric asymmetries (Opher et al. 2009b,a). Other MHD simulations based on fitting the IBEX ribbon yield δ ∼ 30 · (Pogorelov 2013). Such values are considerably smaller than those implied by cartoons in recent publications (Burlaga et al. 2013). In any case our conclusion that significant variations in the density of the ACRs and GCRs can occur in regions with essentially no variation in the field line orientation is not sensitive to the value of δ in the LISM. Any rotation in the magnetic field outside of the HP propagates at the local Alfv'en speed, which is well below the velocities of the particles of interest. Thus, outside of the HP separatrices should retain their original LISM orientation in locations where there are significant variations in particle intensity. Combining a typical aspect ratio of reconnectionproduced islands (0.1), the typical time between dropouts (10 days), and the speed of Voyager 1 with respect to the HS plasma ( ≈ 20 km/s), yields the approximate size of the islands in Fig. 4 as 1 AU. This roughly equals the sector spacing downstream of the TS and is consistent with previous simulation-derived estimates of magnetic islands in the HS (Schoeffler et al. 2012). If the schematic with nested magnetic islands (Fig. 4) is correct, the dropouts in the HS particle fluxes occurred on the LISM side of the HP on field lines that had a LISM source. Thus, according to this picture V1 crossed the HP on day 208 and has been crossing LISM fields since that time. Our results thus suggest that B T in the LISM is negative (i.e., has a polarity of 270 · ). The authors acknowledge the support of NSF grant AGS-1202330 to the University of Maryland, and NSF grant ATM-0747654 and NASA grant NNX07AH20G to Boston University. The PIC simulations were performed at the National Energy Research Scientific Computing Center and the MHD simulations at the Ames NASA Supercomputer Center. We acknowledge fruitful discussions with L. F. Burlaga, R. B. Decker, M. E. Hill and E. C. Stone on the Voyager observations. This research benefited greatly from discussions held at the meetings of the Heliopause International Team at the International Space Science Institute in Bern, Switzerland.",
"pages": [
3,
4,
5
]
},
{
"title": "REFERENCES",
"content": "Baranov, V. B., Fahr, H. J., & Ruderman, M. S. 1992, Astron. Astrophys., 261, 341 Baranov, V. B., Lebedev, M. G., & Ruderman, M. S. 1979, Astrophys. Space Sci., 66, 441 Borovikov, S. N., Pogorelov, N. V., Burlaga, L. F., & Richardson, J. D. 2011, Astrophys. J. Lett., 728, L21 Burlaga, L. F., Ness, N. F., Acu˜na, M. H., Lepping, R. P., Connerney, J. E. P., Stone, E. C., & McDonald, F. B. 2005, Science, 309, 2027 Burlaga, L. F., Ness, N. F., & Stone, E. C. 2013, Science, published online 27 June 2013 Decker, R. B., Krimigis, S. M., Roelof, E. C., & Hill, M. E. 2012, Nature, 489, 124 Decker, R. B., Krimigis, S. M., Roelof, E. C., Hill, M. E., Armstrong, T. P., Gloeckler, G., Hamilton, D. C., & Lanzerotti, L. J. 2005, Science, 309, 2020 Fahr, H. J., Neutsch, W., Grzedzielski, S., Macek, W., & Ratkiewicz-Landowska, R. 1986, Space Sci. Rev., 43, 329 Krimigis, S. M., Decker, R. B., Roelof, E. C., Hill, M. E., Armstrong, T. P., Gloeckler, G., Hamilton, D. C., & Lanzerotti, L. J. 2013, Science, published online 27 June 2013 Liewer, P. C., Karmesin, S. R., & Brackbill, J. U. 1996, J. Geophys. Res., 101, 17,119 Opher, M., Alouani Bibi, F., Toth, G., Richardson, J. D., Izmodenov, V. V., & Gombosi, T. I. 2009a, Nature, 462, 1036 Opher, M., Drake, J. F., Swisdak, M., Schoeffler, K. M., Richardson, J. D., Decker, R. B., & Toth, G. 2011, Ap. J., 734 Opher, M., Drake, J. F., Velli, M., Decker, R. B., & Toth, G. 2012, Ap. J., 751 Opher, M., Richardson, J. D., Toth, G., & Gombosi, T. I. 2009b, Space Sci. Rev., 143, 43 Parker, E. N. 1963, Interplanetary Dynamical Processes (New York: Interscience) Pogorelov, N. V. 2013, private communication at the ISSI Workshop on the Nature of the Heliopause in Bern, Switzerland Pogorelov, N. V., Borovikov, S. N., Zank, G. P., Burlaga, L. F., Decker, R. A., & Stone, E. C. 2012, Ap. J. Lett., 750, L4 Schoeffler, K. M., Drake, J. F., & Swisdak, M. 2012, Ap. J. Lett., 750, L30 Smith, E. J. 2001, J. Geophys. Res., 106, 15819 Sonnerup, B. U. O., Paschmann, G., Papamastorakis, I., Sckopke, N., Haerendel, G., et al. 1981, J. Geophys. Res., 86, 10049 Stone, E. C., Cummings, A. C., McDonald, F. B., Heikkila, B. C., Lal, N., & Webber, W. R. 2005, Science, 309, 2017 -. 2013, Science, published online 27 June 2013 Swisdak, M., Opher, M., Drake, J. F., & Alouani Bibi, F. 2010, Ap. J., 710, 1769 Webber, W. R., & McDonald, F. B. 2013, Geophys. Res. Lett., accepted Zank, G. P., Pauls, H. L., Williams, L. L., & Hall, D. T. 1996, J. Geophys. Res., 101, 21,639 Zieger, B., Opher, M., Schwadron, N. A., McComas, D. J., & Toth, G. 2013, Geophys. Res. Lett., published online 21 June 2013 /s48 /s80/s85/s73 /s48 /s116/s104/s32 /s48 /s78/s32 /s48 /s84 /s114/s97/s100/s105/s117/s115/s32/s40/s65/s85/s41",
"pages": [
5,
6
]
}
]
2013ApJ...774L..14S
https://arxiv.org/pdf/1309.3181.pdf
<document>
<section_header_level_1><location><page_1><loc_18><loc_82><loc_82><loc_86></location>PDR Model Mapping of Obscured H 2 Emission and the Line-of-Sight Structure of M17-SW</section_header_level_1>
<text><location><page_1><loc_38><loc_78><loc_62><loc_80></location>Y. Sheffer and M. G. Wolfire</text>
<text><location><page_1><loc_15><loc_75><loc_85><loc_77></location>Department of Astronomy, University of Maryland, College Park, MD 20742, USA</text>
<section_header_level_1><location><page_1><loc_44><loc_71><loc_56><loc_72></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_38><loc_83><loc_67></location>We observed H 2 line emission with Spitzer -IRS toward M17-SW and modeled the data with our PDR code. Derived gas density values of up to few times 10 7 cm -3 indicate that H 2 emission originates in high-density clumps. We discover that the PDR code can be utilized to map the amount of intervening extinction obscuring the H 2 emission layers, and thus we obtain the radial profile of A V relative to the central ionizing cluster NGC 6618. The extinction has a positive radial gradient, varying between 15-47 mag over the projected distance of 0.92.5 pc from the primary ionizer, CEN 1. These high extinction values are in good agreement with previous studies of A V toward stellar targets in M17-SW. The ratio of data to PDR model values is used to infer the global line-of-sight structure of the PDR surface, which is revealed to resemble a concave surface relative to NGC 6618. Such a configuration confirms that this PDR can be described as a bowl-shaped boundary of the central H II region in M17. The derived structure and physical conditions are important for interpreting the finestructure and rotational line emission from the PDR.</text>
<text><location><page_1><loc_17><loc_30><loc_83><loc_35></location>Subject headings: infrared: ISM - ISM: clouds - ISM: individual objects (M17) - ISM: molecules - photon-dominated region (PDR) - open clusters and associations: individual (NGC 6618)</text>
<section_header_level_1><location><page_1><loc_42><loc_24><loc_58><loc_25></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_10><loc_88><loc_21></location>The star forming region M17 is notable for its asymmetry in terms of its appearance in different wavelength regimes. Optically, it is visible as a nebula with a prominent northern bar marking the location of an ionization front, which suffers only a low level of optical extinction (Felli et al. 1984, and references therein). On the other hand, radio maps have long revealed the presence of the southern bar, part of the M17-SW region, which has no obvious optical counterpart, and is thus understood to suffer a much higher level of extinction</text>
<text><location><page_2><loc_12><loc_78><loc_88><loc_86></location>along our line of sight (LOS). Also noteworthy is the high-extinction patch situated in front of a number of O-type stellar members belonging to the ionizing cluster NGC 6618, which from our direction can be found between the two ionization bars (e.g., Dickel 1968; Beetz et al. 1976; Povich et al. 2007).</text>
<text><location><page_2><loc_12><loc_65><loc_88><loc_77></location>Given that the southern bar includes an ionization front and a PDR that are both obscured in optical wavelength, it is best studied in the IR and radio regimes. Previous IR and radio studies of M17-SW have described it as almost edge-on PDR (Stutzki et al. 1988), or as a bowl carved into the molecular cloud (Meixner et al. 1992; Brogan & Troland 2001; Pellegrini et al. 2006), and have concluded that it is comprised of a clumpy medium (Stutzki & Gusten 1990; Meixner et al. 1992).</text>
<text><location><page_2><loc_12><loc_50><loc_88><loc_64></location>For this study we obtained Spitzer spectroscopy of rotational emission lines of H 2 toward M17-SW in order to model the data with our PDR code. Specifically, we performed model mapping of the gas density over the field of view, and inferred the LOS configuration of the PDR layer (see Sheffer et al. 2011). Owing to the presence of extinction obscuring the interface between the H II region and the molecular cloud, we also included A V in model mapping as means of dereddening the H 2 line intensities. We shall present our results as a function of the radial distance from CEN 1, the primary O4 member of NGC 6618.</text>
<section_header_level_1><location><page_2><loc_33><loc_44><loc_67><loc_46></location>2. Spitzer -IRS Data and Analysis</section_header_level_1>
<text><location><page_2><loc_12><loc_27><loc_88><loc_42></location>Our Spitzer observations of M17-SW belong to programs P03697 (SH and LH data) and P30295 (SL data). Data acquisitions for P03697 were executed on three dates between 2004 Oct 02 and 2005 Apr 23, and those for P30295 on the two dates 2007 Sep 30 and Oct 12. The target area was covered by multiple AORs: 11 for SH, and 4 each for LH and SL data, see Table 1. Following re-gridding onto the LH pixel frame, the area available for full analysis based on five emission lines includes 480 LH pixels. Each LH pixel is 4 . '' 46 wide, corresponding to 8900 AU, or 0.043 pc at a distance of 2.0 kpc ( ± 7% precision, see Xu et al. 2011).</text>
<text><location><page_2><loc_12><loc_16><loc_88><loc_25></location>We employed version 1.7 of CUBISM (Smith et al. 2007) for the reduction of observations and the construction of data cubes therefrom, assuring a match with the Spitzer Science Center pipeline version S18.7.0. Left panel of Figure 1 shows the proper celestial location and orientation of the area of intersection of all modules over an 8 µ m image from Spitzer /IRAC.</text>
<text><location><page_2><loc_12><loc_11><loc_88><loc_14></location>Four pure-rotational emission lines of H 2 were detected and mapped toward the target: S(1) and S(2) at 17.03 and 12.28 µ m, respectively, from the SH module, and S(3) and S(5)</text>
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<caption>Fig. 1.- Left panel shows the area of overlap for all IRS modules (red irregular outline) overlaying the IRAC channel 4 image of M17-SW. The positions of 19 O stars are indicated by squares, along with their CEN numbers (Chini et al. 1980). The IR-bright point source inside our field is known as the KW object (Kleinmann & Wright 1973). Right panels present observed intensity values for four H 2 emission lines, using a common intensity scale (right ordinate values, in units of 10 -4 erg s -1 cm -2 sr -1 ). Error bars on intensity values show the ± 2 σ uncertainties. Each intensity plot is converted into column density values, as given by the left ordinate scales in cm -2 .</caption>
</figure>
<text><location><page_4><loc_12><loc_62><loc_88><loc_86></location>at 9.66 and 6.91 µ m, respectively, from orders 1 and 2, respectively, of the SL module. Owing to lack of reliable signal from S(0) at 28.22 µ m, albeit located within the wavelength interval of coverage of the LH module, our PDR modeling did not include the S(0) line. Emission line maps were constructed by using in-house IDL procedures to fit line profiles and to derive integrated line intensities that included continuum removal following its fitting by a low-order polynomial. The presence in these spectra of emission lines of ionized atomic species appreciably stronger than the emission lines from H 2 necessitated an additional step of deblending S(5) and [Ar II ] at 6.98 µ m. Such a challenge did not arise in the analysis of similar data toward NGC 2023-South, where lines of ionized species were either weak or undetectable (Sheffer et al. 2011). We note that the spectral co-presence of H II region and PDR emission lines shows that both regions are sampled along the LOS toward M17-SW, thus indicating that their configuration cannot be strictly edge-on.</text>
<text><location><page_4><loc_12><loc_51><loc_88><loc_61></location>No attempt was made to correct for zodiacal background emission owing to the bright nature of this target and the insensitivity of continuum-subtracted emission lines to such uniform contribution. Based on the discussion in Sheffer et al. (2011), data from the LH and SH modules were corrected by a factor of 0.84 in order to obtain calibration match with the SL module flux values.</text>
<text><location><page_4><loc_12><loc_36><loc_88><loc_50></location>In order to compare emission data with PDR models, line intensities were converted to column density via N J = 4 πI J /A J ∆ E J cm -2 , where N J , I J , A J , and ∆ E J stand for the column density, emission intensity, Einstein A-coefficient, and transition energy for each rotational upper level J . This conversion is linear owing to insignificant self-absorption of these quadrupole transitions. The four right panels of Figure 1 show the radial variation of H 2 emission lines with distance from CEN 1, following data averaging along the orthogonal direction. Both intensity and column density scales are provided.</text>
<section_header_level_1><location><page_4><loc_33><loc_30><loc_67><loc_32></location>3. PDR Modeling of H 2 Emission</section_header_level_1>
<text><location><page_4><loc_12><loc_17><loc_88><loc_28></location>The two primary PDR parameters are n H , the total hydrogen number density, and G 0 , the ratio of the incident 6-13.6 eV far-ultraviolet (FUV) flux over the Habing flux of 1 . 6 × 10 -3 erg s -1 cm -2 (Habing 1968). We employed the Kaufman et al. (2006) PDR code to generate a ( n H , G 0 ) grid of 950 normal models, where 'normal' means that the incident radiation field is normal to the PDR surface ( φ = 0 · ). Model output consists of N J (H 2 ) values following an integration along the normal as well, with grid step being 0.1 dex.</text>
<text><location><page_4><loc_12><loc_12><loc_88><loc_15></location>Model mapping was performed with the parameter G 0 constrained to predicted values. This was motivated by the availability of lists of O-type stars residing in and around NGC</text>
<text><location><page_5><loc_12><loc_78><loc_88><loc_86></location>6618 (e.g., Broos et al. 2007; Povich et al. 2009), as well as by the knowledge of precise (albeit projected) linear distances between each star and each mapped data pixel. Thus G 0 was obtained by summing the FUV flux of 19 O-type stars listed in Hoffmeister et al. (2008) and using</text>
<formula><location><page_5><loc_41><loc_74><loc_88><loc_78></location>G pr 0 = 850 D 2 ∑ i L FUV i θ 2 i , (1)</formula>
<text><location><page_5><loc_12><loc_66><loc_88><loc_73></location>where the superscript 'pr' may stand for 'predicted' or 'projected,' D is the distance to M17SW in kpc, L FUV i is the FUV luminosity of stellar radiator i in solar units (Parravano et al. 2003), and θ i is the angular separation between star i and any map pixel in seconds of arc. The left panel of Figure 2 shows that the values of G pr 0 range over ∼ (1-8) × 10 4 .</text>
<text><location><page_5><loc_12><loc_39><loc_88><loc_64></location>We perform a search for the smallest root mean square deviation (RMSD) of the differences in dex between modeled and observed N J values, thus yielding values for the ratio f eff = data/model. This ratio may be decomposed into two ≥ 1 and two ≤ 1 factors, f eff = f P f θ × f φ f B , where f P is the number of PDRs along the LOS and here assumed to be 1, f θ = 1 / cos( θ ) accounts for limb brightening owing to inclination angle θ , f φ = cos( φ ) accounts for the angle of incidence of the radiation field on the PDR, and f B is the beam area filling factor, also assumed to be 1. This assumption is consistent with the ≥ 0 . 1 pc sizes of both observationally-derived C 18 O clumps toward M17-SW (Stutzki & Gusten 1990) and PDR-modelled clumps with n H = 10 7 cm -3 (Meixner and Tielens 1993), as well as with the ≤ 0 . 04 pc (at D = 2 . 0 kpc) beam widths of the SH and SL modules of Spitzer -IRS. Owing to the dependence of the two angular factors, f θ and f φ , on the local orientation of the cloud surface (Sheffer et al. 2011), we shall employ them to infer clues about the LOS variations of the PDR over the field of view, see § 5.</text>
<section_header_level_1><location><page_5><loc_27><loc_33><loc_73><loc_34></location>4. PDR Modeling with A V as a Free Parameter</section_header_level_1>
<text><location><page_5><loc_12><loc_11><loc_88><loc_30></location>It is customary to de-redden the observed I J values by the known or assumed value of extinction, A V , prior to comparing A V -corrected N J values with model output. Here we employ the Mathis (1990) reddening law. Our initial PDR mapping runs employed a global (or spatially-invariant) correction by A V = 8 mag, approximating the average value toward the central members of NGC 6618 (Hanson et al. 1997; Povich et al. 2007). However, some of the OB stars in the M17 region appear to show appreciably higher extinction values, with A V ≥ 15 mag (Tokunaga & Thompson 1979; Chini et al. 1980; Hanson et al. 1997). Follow-up modeling with A V = 15 mag returned fits with RMSD values smaller by factors of 1.3-1.5, whereas further reductions by factors of 1.3-1.8 were achieved by fits employing a global A V > 20 mag. Inevitably, we included A V as a free parameter that was allowed to</text>
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<caption>Fig. 2.- Left panel shows log G pr 0 values from Eq. 1, based on D = 2 . 0 kpc. Stellar FUV luminosities for 19 O-type members of NGC 6618 are summed, including luminosity values corrected by × 4 for CEN 1, and by × 2 for CEN 3, CEN 18, and CEN 37, owing to stellar multiplicity (Hoffmeister et al. 2008). Right panels show modeled physical parameters as a function of distance from CEN 1. Top panels show the RMSD of the fits, with a mean of 0.03 dex (7%), and n H , with a mean of 2 . 5 × 10 7 cm -3 . Lower panels provide modeled values of A V toward M17-SW, and of f eff , the ratio of data to modeled H 2 line intensities.</caption>
</figure>
<text><location><page_7><loc_12><loc_78><loc_88><loc_86></location>vary over the entire field of view. Superficially, both f eff and A V corrections affect the ratios of data to model intensities. However, whereas the former applies the same factor to all emission lines, the latter has different values for different emission lines. Thus A V affects the ratios between emission lines from different J levels, unlike f eff .</text>
<text><location><page_7><loc_12><loc_51><loc_88><loc_77></location>The right panels of Figure 2 present our PDR model mapping results, with a mean RMSD of 0.029, or ∼ 7%. Values of n H are found to be mostly between (2.0-2.5) × 10 7 cm -3 , or ∼ 100 times higher than the density modeled for the Southern Ridge (SR) in NGC 2023 (Sheffer et al. 2011). Such values are consistent with H 2 emission production in high-density clumps immersed in an interclump gas of density lower by 2 or 3 orders of magnitude (Meixner and Tielens 1993). The (unshown) fixed parameter G 0 follows the values of G pr 0 from Eq. 1 by design. The next panel presents model output for A V , which to our knowledge is the first attempt to derive extinction values from PDR modeling. The mean of visual extinction preferred by the models is 30 mag, about 2-4 times as high as the initially presumed values of 8 and 15 mag. Values of A V , which range over 15-47 mag, are clearly increasing away from NGC 6618 with a gradient of 21 ± 2 mag pc -1 . Such a positive gradient is not unexpected: the structure of M17-SW includes a sequence of H II region, a PDR, and a dense molecular cloud along the same radial direction.</text>
<text><location><page_7><loc_12><loc_10><loc_88><loc_50></location>Our high values of modeled A V are in very good agreement with other indicators of extinction over the M17-SW field, i.e, away from the central region of NGC 6618. For example, determinations based on reddening toward individual M17-SW stellar sources have presented the following values: A V ∼ 40 mag for the optically thickest regions, as well as A V > 25 mag for the molecular cloud core based on the K s -band luminosity function (Jiang et al. 2002); a range of 14 /lessorsimilar A V /lessorsimilar 30 mag for 55 stars within 0.7 pc of the KW object, as well as A V of 24 and 30 mag toward the two components of the KW object itself (Chini et al. 2004); and A V > 30 mag for a large number of sources along the reddening vector (Hoffmeister et al. 2008). Furthermore, even higher extinction estimates have been derived from far-IR and mm-wave observations that dissect the entire molecular cloud surrounding our field of view toward M17-SW. For example, Gatley et al. (1979) found A V ∼ 100 mag through the core of the molecular cloud; Thronson & Lada (1983) estimated A V ≤ 200 mag at the peak of 13 CO emission; Keene et al. (1985) found A V ≈ 100 mag based on 13 CO data; and finally, Wilson et al. (2003) decomposed cloud B into individual clumps with inferred N (H 2 ) = (1 . 9-10 . 4) × 10 22 cm -2 for clumps B25, B27, B29, B32, and B34, which are the ones that are either partially or fully overlapped by our Spitzer field of view. Focusing on B27 and B29, the two 13 CO clumps wholly enclosed inside our field, and employing the relationship A V = 2 × N (H 2 ) / 1 . 8 × 10 21 mag, values of A V = 21 and 29 mag can be inferred through these two clumps in cloud B. We consider such a consistent picture as a confirmation that PDR modeling may be employed for reliable mapping of A V values</text>
<text><location><page_8><loc_12><loc_84><loc_43><loc_86></location>toward H 2 emission obscured by dust.</text>
<text><location><page_8><loc_12><loc_45><loc_88><loc_83></location>Although we find here very good agreement between PDR-modeled A V values and values that have been derived by other means, it is important to cross-check our method toward another well-studied PDR, owing to the novelty involved. NGC 2023 is such a PDR, toward which a previously successful PDR modeling has been achieved with a fixed value of A V (Sheffer et al. 2011, and references therein). We performed the parameterizedA V test successfully, resulting in model fits similar to those previously obtained, as well as in A V output consistent with results from other studies. Whereas our previous modeling employed a fixed value of A K = 0 . 5 mag, or equivalently, A V = 4 . 6 mag, the new test returns a field-wide median of A V = 8 mag. Our PDR modeling is again indicating a positive radial gradient of extinction across the field, starting with much lower values of A V in the region between the SR and the exciting star, HD 37903, and reaching A V ∼ 20 mag on the other side of the SR, or deeper into the dense molecular cloud. In this case, as is the case with M17SW, the larger PDR-modeled A V values are consistent with previous studies. DePoy et al. (1990) concluded that over small scales, the extinction toward stars in NGC 2023 varies over 0-10 mag. Furthermore, the total extinction through the molecular cloud is expected to be ≥ 25 mag (DePoy et al. 1990). Over the SR, the range of A V values is 10 ± 5 mag, where the inferred semi-amplitude of the range is comparable to the level of uncertainty in the visual extinction determinations toward heavily obscured targets (e.g., Nielbock et al. 2008). For M17-SW we find a dispersion of ± 4 mag along the fitted gradient.</text>
<section_header_level_1><location><page_8><loc_31><loc_39><loc_69><loc_41></location>5. Visualization of the LOS Dimension</section_header_level_1>
<text><location><page_8><loc_12><loc_20><loc_88><loc_37></location>A visually stunning depiction of the radially increasing A V field is provided in the left panel of Figure 3, which is based on Figure 1 from Jiang et al. (2002). Our basic assumption is that the observed H 2 emission originates on a cloud surface facing away from our direction and basking in the FUV starshine of NGC 6618. We thus view the obscured back side of the PDR surface through the bulk of cloud B, as measured by our modeled A V extinction values along the LOS, see right panel of Figure 3. Any C II or highJ CO line emission (e.g., P'erez-Beaupuits et al. 2012) would also be observed from the far side of the intervening molecular cloud and its interpretation should account for the face-on geometry and intervening cold gas layer.</text>
<text><location><page_8><loc_12><loc_11><loc_88><loc_18></location>The last panel of Figure 2 showed that f eff < 1, which means that φ > θ under the assumption of f B = 1, and therefore a shallow grazing angle for the FUV influx from NGC 6618. We further assume that the cos( φ )/cos( θ ) curve is defined by three continuous segments of the PDR surface and not by local variations over pixel-sized scales. Each construction of</text>
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<caption>Fig. 3.- Left panel shows the region of IRS data coverage over a JHK image from Figure 1 of Jiang et al. (2002). It can be seen that our Spitzer observations (red border) overlap a dusty ridge of foreground gas, which is obscuring a background PDR and is producing an extinction with a positive A V radial gradient. Right panel presents a schematic interpretation of the 3-D configuration of M17-SW in terms of a PDR surface on the back side of Cloud B. Varying distance from NGC 6618 controls the level of incident FUV radiation, G 0 , whereas varying thickness of obscuring material controls the level of visual extinction, A V , in our direction ( ⊕ ). Gradual variations in θ and φ may explain the behavior of modeled f eff in terms of changing PDR surface orientation relative to both NGC 6618 and our LOS.</caption>
</figure>
<text><location><page_10><loc_12><loc_80><loc_88><loc_86></location>a PDR surface begins at any arbitrarily chosen location along the LOS, and proceeds by forcing neighboring segments to be smoothly connected in order to avoid the introduction of FUV shadowing between segments.</text>
<text><location><page_10><loc_12><loc_59><loc_88><loc_79></location>Figure 4 presents four examples of PDR surfaces that share the same curve of f eff values. The first three surfaces, shown in the left panel, belong to our basic assumption that the PDR is viewed from its back side. Each derived concave surface is consistent with the general 3-D configuration of a bowl-shaped interface originally suggested by Meixner et al. (1992), see also Figure 2 of Pellegrini et al. (2006). The right panel show an alternate configuration in which the PDR is viewed from its front side and is physically separated from the layer of foreground extinction. Although the cos( φ )/cos( θ ) curve fixes the relative curvature of the surface, and thus provides a '3-D view' of the PDR layer along the LOS, both the absolute location along the LOS and the state of reflection about the abscissa are, unfortunately, degenerate.</text>
<text><location><page_10><loc_12><loc_40><loc_88><loc_58></location>Future studies could incorporate additional clues for a more robust characterization of the location and the reflection of the PDR surface. For example, our initial tests involving a freely variable G 0 show that its values start to drop significantly below G pr 0 values half way along the mapped radial distance from NGC 6618. Such a behavior may indicate that the line of sight is probing a more extreme case of geometry than derived here. Among the PDR surfaces depicted in Figure 4, only 'A', and therefore ' -A', affect G 0 values in a similar fashion, owing to their increasing deviation from the plane of projection. On the other hand, the role of pixel-to-pixel variations, such as those seen in modeling output, remains to be evaluated in terms of orientation and mutual shadowing among individual clumps.</text>
<section_header_level_1><location><page_10><loc_43><loc_34><loc_57><loc_36></location>6. Summary</section_header_level_1>
<unordered_list>
<list_item><location><page_10><loc_12><loc_29><loc_88><loc_32></location>1. Spitzer -IRS spectra were obtained and employed in our quest to measure the intensity of H 2 emission lines toward the PDR M17-SW.</list_item>
<list_item><location><page_10><loc_12><loc_22><loc_88><loc_27></location>2. Following conversion of H 2 intensity into column density, we employed our PDR code in order to map physical quantities as a function of distance from the source of FUV radiation.</list_item>
<list_item><location><page_10><loc_12><loc_17><loc_88><loc_20></location>3. We introduced A V as a free parameter into the PDR code, and subsequently successfully derived radial mapping of the extinction suffered by H 2 lines.</list_item>
<list_item><location><page_10><loc_12><loc_12><loc_89><loc_15></location>4. Our analysis of the data-to-model column density ratio in terms of f eff = cos( φ ) / cos( θ ) provided a '3-D view' of the line-of-sight structure of the PDR surface, showing it to be</list_item>
</unordered_list>
<figure>
<location><page_11><loc_14><loc_41><loc_87><loc_80></location>
<caption>Fig. 4.- Top left panel presents three possible LOS configurations of the PDR surface, all possessing the same f eff = cos( φ ) / cos( θ ) curves. Bottom left panel shows such overlapping f eff curves in comparison with modeled values (squares) taken from Figure 2. The (colorized) PDR layer (of thickness ≤ 10 -4 pc) is assumed to constitute the back side of an obscuring cloud as viewed along our LOS ( ⊕ ). Clouds are projected onto an (X, Y) plane that includes the observer, the FUV source ( /star at the location of CEN 1), and the radial axis of the mapped PDR area. The degeneracy in LOS cloud positions can be extended to include their reflection across the abscissa, as shown in the right panel. Thus PDR surface ' -A' is characterized by the same f eff curve as PDR surface 'A'. In this configuration, however, the intervening extinction toward the PDR arises in an isolated cloud at an unspecifiable position along the LOS. The illustrated cloud thickness along the LOS has been converted from modeled A V values by employing the arbitrary n H = 4 × 10 4 cm -3 .</caption>
</figure>
<text><location><page_12><loc_12><loc_82><loc_88><loc_86></location>globally curved, thus confirming the suggested description of a bowl-shaped PDR in M17SW.</text>
<section_header_level_1><location><page_12><loc_43><loc_76><loc_58><loc_78></location>REFERENCES</section_header_level_1>
<text><location><page_12><loc_12><loc_16><loc_88><loc_74></location>Beetz, M., Elsasser, H., Poulakos, C., & Weinberger, R. 1976, A&A, 50, 41 Brogan, C. L., & Troland, T. H. 2001, ApJ, 560, 821 Broos, P. S., Feigelson, E. D., Townsley, L. K., Getman, K. V., Wang, J., Garmire, G. P., Jiang, Z., & Tsuboi, Y. 2007, ApJS, 169, 353 Chini, R., Elsasser, H., & Neckel, Th. 1980, A&A, 91, 186 Chini, R., Hoffmeister, V. H., Kampgen, K., Kimeswenger, S., Nielbock, M., & Siebenmorgen, R. 2004, A&A, 427, 849 DePoy, D. L., Lada, E. A., Gatley, I., & Probst, R. 1990, ApJ, 356, L55 Dickel, H. R. 1968, ApJ, 152, 651 Felli, M., Churchwell, E., & Massi, M. 1984, A&A, 136, 53 Gatley, I., Becklin, E. E., Sellgren, K., & Werner, M. W. 1979, ApJ, 233, 575 Habing, H. J. 1968, Bull. Astron. Inst. Netherlands, 19, 421 Hanson, M. M., Howarth, I. D., & Conti, P. S. 1997, ApJ, 489, 698 Hoffmeister, V. H., Chini, R., Scheyda, C. M., Schulze, D., Watermann, R, Nurnberger, D., & Vogt, N. 2003, ApJ, 686, 310 Jiang, Z., Yao, Y., Yang, J. et al. 2002, ApJ, 577, 245 Kaufman, M. J., Wolfire, M. G., & Hollenbach, D. J. 2006, ApJ, 644, 283 Keene, J., Blake, G. A., Phillips, T. G., Huggins, P. J., & Beichman, C. A. 1985, ApJ, 299, 967 Kleinmann, D. E., & Wright, E. L. 1973, ApJ, 185, L133</text>
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<text><location><page_13><loc_12><loc_79><loc_55><loc_81></location>Meixner, M., & Tielens, A. G. G. M. ApJ, 405, 216</text>
<text><location><page_13><loc_12><loc_74><loc_88><loc_77></location>Nielbock, M., Chini, R., Hoffmeister, V. H., Nurnberger, D. E. A., Scheyda, C. M., & Steinacker, J. 2008, MNRAS, 388, 1031</text>
<text><location><page_13><loc_12><loc_71><loc_71><loc_72></location>Parravano, A., Hollenbach, D. J., & McKee, C. F. 2003, ApJ, 584, 797</text>
<text><location><page_13><loc_12><loc_67><loc_75><loc_69></location>Pellegrini, E. W., Baldwin, J. A., Brogan, C. L. et al. 2006, ApJ, 658, 1119</text>
<text><location><page_13><loc_12><loc_62><loc_88><loc_66></location>P'erez-Beaupuits, J. P., Wiesemeyer, H., Ossenkopf, V., Stutzki, J., Gusten, R., Simon, R., Hubers, H. W., & Ricken, O. 2012, A&A, 542, L13</text>
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<text><location><page_13><loc_12><loc_50><loc_88><loc_54></location>Sheffer, Y., Wolfire, M. G., Hollenbach, D. J., Kaufman, M. J., & Cordier, M. 2011, ApJ, 741, 45</text>
<text><location><page_13><loc_12><loc_47><loc_70><loc_49></location>Smith, J. D. T., Armus, L., Dale, D. A., et al. 2007, PASP, 119, 1133</text>
<text><location><page_13><loc_12><loc_42><loc_88><loc_45></location>Stutzki, J., Stacey, G. J., Genzel, R., Harris, A. I., Jaffe, D. T., & Lugten, J. B. 1988, ApJ, 332, 379</text>
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<text><location><page_13><loc_12><loc_24><loc_88><loc_27></location>Xu, Y., Moscadelli, L., Reid, M. J., Menten, K. M., Zhang, B., Zheng, X. W., & Brunthaler, A. 2011, ApJ, 733, 25</text>
<table>
<location><page_14><loc_23><loc_24><loc_77><loc_71></location>
<caption>Table 1. Log of Spitzer Observations of M17-SW</caption>
</table>
</document>
[
{
"title": "ABSTRACT",
"content": "We observed H 2 line emission with Spitzer -IRS toward M17-SW and modeled the data with our PDR code. Derived gas density values of up to few times 10 7 cm -3 indicate that H 2 emission originates in high-density clumps. We discover that the PDR code can be utilized to map the amount of intervening extinction obscuring the H 2 emission layers, and thus we obtain the radial profile of A V relative to the central ionizing cluster NGC 6618. The extinction has a positive radial gradient, varying between 15-47 mag over the projected distance of 0.92.5 pc from the primary ionizer, CEN 1. These high extinction values are in good agreement with previous studies of A V toward stellar targets in M17-SW. The ratio of data to PDR model values is used to infer the global line-of-sight structure of the PDR surface, which is revealed to resemble a concave surface relative to NGC 6618. Such a configuration confirms that this PDR can be described as a bowl-shaped boundary of the central H II region in M17. The derived structure and physical conditions are important for interpreting the finestructure and rotational line emission from the PDR. Subject headings: infrared: ISM - ISM: clouds - ISM: individual objects (M17) - ISM: molecules - photon-dominated region (PDR) - open clusters and associations: individual (NGC 6618)",
"pages": [
1
]
},
{
"title": "PDR Model Mapping of Obscured H 2 Emission and the Line-of-Sight Structure of M17-SW",
"content": "Y. Sheffer and M. G. Wolfire Department of Astronomy, University of Maryland, College Park, MD 20742, USA",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The star forming region M17 is notable for its asymmetry in terms of its appearance in different wavelength regimes. Optically, it is visible as a nebula with a prominent northern bar marking the location of an ionization front, which suffers only a low level of optical extinction (Felli et al. 1984, and references therein). On the other hand, radio maps have long revealed the presence of the southern bar, part of the M17-SW region, which has no obvious optical counterpart, and is thus understood to suffer a much higher level of extinction along our line of sight (LOS). Also noteworthy is the high-extinction patch situated in front of a number of O-type stellar members belonging to the ionizing cluster NGC 6618, which from our direction can be found between the two ionization bars (e.g., Dickel 1968; Beetz et al. 1976; Povich et al. 2007). Given that the southern bar includes an ionization front and a PDR that are both obscured in optical wavelength, it is best studied in the IR and radio regimes. Previous IR and radio studies of M17-SW have described it as almost edge-on PDR (Stutzki et al. 1988), or as a bowl carved into the molecular cloud (Meixner et al. 1992; Brogan & Troland 2001; Pellegrini et al. 2006), and have concluded that it is comprised of a clumpy medium (Stutzki & Gusten 1990; Meixner et al. 1992). For this study we obtained Spitzer spectroscopy of rotational emission lines of H 2 toward M17-SW in order to model the data with our PDR code. Specifically, we performed model mapping of the gas density over the field of view, and inferred the LOS configuration of the PDR layer (see Sheffer et al. 2011). Owing to the presence of extinction obscuring the interface between the H II region and the molecular cloud, we also included A V in model mapping as means of dereddening the H 2 line intensities. We shall present our results as a function of the radial distance from CEN 1, the primary O4 member of NGC 6618.",
"pages": [
1,
2
]
},
{
"title": "2. Spitzer -IRS Data and Analysis",
"content": "Our Spitzer observations of M17-SW belong to programs P03697 (SH and LH data) and P30295 (SL data). Data acquisitions for P03697 were executed on three dates between 2004 Oct 02 and 2005 Apr 23, and those for P30295 on the two dates 2007 Sep 30 and Oct 12. The target area was covered by multiple AORs: 11 for SH, and 4 each for LH and SL data, see Table 1. Following re-gridding onto the LH pixel frame, the area available for full analysis based on five emission lines includes 480 LH pixels. Each LH pixel is 4 . '' 46 wide, corresponding to 8900 AU, or 0.043 pc at a distance of 2.0 kpc ( ± 7% precision, see Xu et al. 2011). We employed version 1.7 of CUBISM (Smith et al. 2007) for the reduction of observations and the construction of data cubes therefrom, assuring a match with the Spitzer Science Center pipeline version S18.7.0. Left panel of Figure 1 shows the proper celestial location and orientation of the area of intersection of all modules over an 8 µ m image from Spitzer /IRAC. Four pure-rotational emission lines of H 2 were detected and mapped toward the target: S(1) and S(2) at 17.03 and 12.28 µ m, respectively, from the SH module, and S(3) and S(5) at 9.66 and 6.91 µ m, respectively, from orders 1 and 2, respectively, of the SL module. Owing to lack of reliable signal from S(0) at 28.22 µ m, albeit located within the wavelength interval of coverage of the LH module, our PDR modeling did not include the S(0) line. Emission line maps were constructed by using in-house IDL procedures to fit line profiles and to derive integrated line intensities that included continuum removal following its fitting by a low-order polynomial. The presence in these spectra of emission lines of ionized atomic species appreciably stronger than the emission lines from H 2 necessitated an additional step of deblending S(5) and [Ar II ] at 6.98 µ m. Such a challenge did not arise in the analysis of similar data toward NGC 2023-South, where lines of ionized species were either weak or undetectable (Sheffer et al. 2011). We note that the spectral co-presence of H II region and PDR emission lines shows that both regions are sampled along the LOS toward M17-SW, thus indicating that their configuration cannot be strictly edge-on. No attempt was made to correct for zodiacal background emission owing to the bright nature of this target and the insensitivity of continuum-subtracted emission lines to such uniform contribution. Based on the discussion in Sheffer et al. (2011), data from the LH and SH modules were corrected by a factor of 0.84 in order to obtain calibration match with the SL module flux values. In order to compare emission data with PDR models, line intensities were converted to column density via N J = 4 πI J /A J ∆ E J cm -2 , where N J , I J , A J , and ∆ E J stand for the column density, emission intensity, Einstein A-coefficient, and transition energy for each rotational upper level J . This conversion is linear owing to insignificant self-absorption of these quadrupole transitions. The four right panels of Figure 1 show the radial variation of H 2 emission lines with distance from CEN 1, following data averaging along the orthogonal direction. Both intensity and column density scales are provided.",
"pages": [
2,
4
]
},
{
"title": "3. PDR Modeling of H 2 Emission",
"content": "The two primary PDR parameters are n H , the total hydrogen number density, and G 0 , the ratio of the incident 6-13.6 eV far-ultraviolet (FUV) flux over the Habing flux of 1 . 6 × 10 -3 erg s -1 cm -2 (Habing 1968). We employed the Kaufman et al. (2006) PDR code to generate a ( n H , G 0 ) grid of 950 normal models, where 'normal' means that the incident radiation field is normal to the PDR surface ( φ = 0 · ). Model output consists of N J (H 2 ) values following an integration along the normal as well, with grid step being 0.1 dex. Model mapping was performed with the parameter G 0 constrained to predicted values. This was motivated by the availability of lists of O-type stars residing in and around NGC 6618 (e.g., Broos et al. 2007; Povich et al. 2009), as well as by the knowledge of precise (albeit projected) linear distances between each star and each mapped data pixel. Thus G 0 was obtained by summing the FUV flux of 19 O-type stars listed in Hoffmeister et al. (2008) and using where the superscript 'pr' may stand for 'predicted' or 'projected,' D is the distance to M17SW in kpc, L FUV i is the FUV luminosity of stellar radiator i in solar units (Parravano et al. 2003), and θ i is the angular separation between star i and any map pixel in seconds of arc. The left panel of Figure 2 shows that the values of G pr 0 range over ∼ (1-8) × 10 4 . We perform a search for the smallest root mean square deviation (RMSD) of the differences in dex between modeled and observed N J values, thus yielding values for the ratio f eff = data/model. This ratio may be decomposed into two ≥ 1 and two ≤ 1 factors, f eff = f P f θ × f φ f B , where f P is the number of PDRs along the LOS and here assumed to be 1, f θ = 1 / cos( θ ) accounts for limb brightening owing to inclination angle θ , f φ = cos( φ ) accounts for the angle of incidence of the radiation field on the PDR, and f B is the beam area filling factor, also assumed to be 1. This assumption is consistent with the ≥ 0 . 1 pc sizes of both observationally-derived C 18 O clumps toward M17-SW (Stutzki & Gusten 1990) and PDR-modelled clumps with n H = 10 7 cm -3 (Meixner and Tielens 1993), as well as with the ≤ 0 . 04 pc (at D = 2 . 0 kpc) beam widths of the SH and SL modules of Spitzer -IRS. Owing to the dependence of the two angular factors, f θ and f φ , on the local orientation of the cloud surface (Sheffer et al. 2011), we shall employ them to infer clues about the LOS variations of the PDR over the field of view, see § 5.",
"pages": [
4,
5
]
},
{
"title": "4. PDR Modeling with A V as a Free Parameter",
"content": "It is customary to de-redden the observed I J values by the known or assumed value of extinction, A V , prior to comparing A V -corrected N J values with model output. Here we employ the Mathis (1990) reddening law. Our initial PDR mapping runs employed a global (or spatially-invariant) correction by A V = 8 mag, approximating the average value toward the central members of NGC 6618 (Hanson et al. 1997; Povich et al. 2007). However, some of the OB stars in the M17 region appear to show appreciably higher extinction values, with A V ≥ 15 mag (Tokunaga & Thompson 1979; Chini et al. 1980; Hanson et al. 1997). Follow-up modeling with A V = 15 mag returned fits with RMSD values smaller by factors of 1.3-1.5, whereas further reductions by factors of 1.3-1.8 were achieved by fits employing a global A V > 20 mag. Inevitably, we included A V as a free parameter that was allowed to vary over the entire field of view. Superficially, both f eff and A V corrections affect the ratios of data to model intensities. However, whereas the former applies the same factor to all emission lines, the latter has different values for different emission lines. Thus A V affects the ratios between emission lines from different J levels, unlike f eff . The right panels of Figure 2 present our PDR model mapping results, with a mean RMSD of 0.029, or ∼ 7%. Values of n H are found to be mostly between (2.0-2.5) × 10 7 cm -3 , or ∼ 100 times higher than the density modeled for the Southern Ridge (SR) in NGC 2023 (Sheffer et al. 2011). Such values are consistent with H 2 emission production in high-density clumps immersed in an interclump gas of density lower by 2 or 3 orders of magnitude (Meixner and Tielens 1993). The (unshown) fixed parameter G 0 follows the values of G pr 0 from Eq. 1 by design. The next panel presents model output for A V , which to our knowledge is the first attempt to derive extinction values from PDR modeling. The mean of visual extinction preferred by the models is 30 mag, about 2-4 times as high as the initially presumed values of 8 and 15 mag. Values of A V , which range over 15-47 mag, are clearly increasing away from NGC 6618 with a gradient of 21 ± 2 mag pc -1 . Such a positive gradient is not unexpected: the structure of M17-SW includes a sequence of H II region, a PDR, and a dense molecular cloud along the same radial direction. Our high values of modeled A V are in very good agreement with other indicators of extinction over the M17-SW field, i.e, away from the central region of NGC 6618. For example, determinations based on reddening toward individual M17-SW stellar sources have presented the following values: A V ∼ 40 mag for the optically thickest regions, as well as A V > 25 mag for the molecular cloud core based on the K s -band luminosity function (Jiang et al. 2002); a range of 14 /lessorsimilar A V /lessorsimilar 30 mag for 55 stars within 0.7 pc of the KW object, as well as A V of 24 and 30 mag toward the two components of the KW object itself (Chini et al. 2004); and A V > 30 mag for a large number of sources along the reddening vector (Hoffmeister et al. 2008). Furthermore, even higher extinction estimates have been derived from far-IR and mm-wave observations that dissect the entire molecular cloud surrounding our field of view toward M17-SW. For example, Gatley et al. (1979) found A V ∼ 100 mag through the core of the molecular cloud; Thronson & Lada (1983) estimated A V ≤ 200 mag at the peak of 13 CO emission; Keene et al. (1985) found A V ≈ 100 mag based on 13 CO data; and finally, Wilson et al. (2003) decomposed cloud B into individual clumps with inferred N (H 2 ) = (1 . 9-10 . 4) × 10 22 cm -2 for clumps B25, B27, B29, B32, and B34, which are the ones that are either partially or fully overlapped by our Spitzer field of view. Focusing on B27 and B29, the two 13 CO clumps wholly enclosed inside our field, and employing the relationship A V = 2 × N (H 2 ) / 1 . 8 × 10 21 mag, values of A V = 21 and 29 mag can be inferred through these two clumps in cloud B. We consider such a consistent picture as a confirmation that PDR modeling may be employed for reliable mapping of A V values toward H 2 emission obscured by dust. Although we find here very good agreement between PDR-modeled A V values and values that have been derived by other means, it is important to cross-check our method toward another well-studied PDR, owing to the novelty involved. NGC 2023 is such a PDR, toward which a previously successful PDR modeling has been achieved with a fixed value of A V (Sheffer et al. 2011, and references therein). We performed the parameterizedA V test successfully, resulting in model fits similar to those previously obtained, as well as in A V output consistent with results from other studies. Whereas our previous modeling employed a fixed value of A K = 0 . 5 mag, or equivalently, A V = 4 . 6 mag, the new test returns a field-wide median of A V = 8 mag. Our PDR modeling is again indicating a positive radial gradient of extinction across the field, starting with much lower values of A V in the region between the SR and the exciting star, HD 37903, and reaching A V ∼ 20 mag on the other side of the SR, or deeper into the dense molecular cloud. In this case, as is the case with M17SW, the larger PDR-modeled A V values are consistent with previous studies. DePoy et al. (1990) concluded that over small scales, the extinction toward stars in NGC 2023 varies over 0-10 mag. Furthermore, the total extinction through the molecular cloud is expected to be ≥ 25 mag (DePoy et al. 1990). Over the SR, the range of A V values is 10 ± 5 mag, where the inferred semi-amplitude of the range is comparable to the level of uncertainty in the visual extinction determinations toward heavily obscured targets (e.g., Nielbock et al. 2008). For M17-SW we find a dispersion of ± 4 mag along the fitted gradient.",
"pages": [
5,
7,
8
]
},
{
"title": "5. Visualization of the LOS Dimension",
"content": "A visually stunning depiction of the radially increasing A V field is provided in the left panel of Figure 3, which is based on Figure 1 from Jiang et al. (2002). Our basic assumption is that the observed H 2 emission originates on a cloud surface facing away from our direction and basking in the FUV starshine of NGC 6618. We thus view the obscured back side of the PDR surface through the bulk of cloud B, as measured by our modeled A V extinction values along the LOS, see right panel of Figure 3. Any C II or highJ CO line emission (e.g., P'erez-Beaupuits et al. 2012) would also be observed from the far side of the intervening molecular cloud and its interpretation should account for the face-on geometry and intervening cold gas layer. The last panel of Figure 2 showed that f eff < 1, which means that φ > θ under the assumption of f B = 1, and therefore a shallow grazing angle for the FUV influx from NGC 6618. We further assume that the cos( φ )/cos( θ ) curve is defined by three continuous segments of the PDR surface and not by local variations over pixel-sized scales. Each construction of a PDR surface begins at any arbitrarily chosen location along the LOS, and proceeds by forcing neighboring segments to be smoothly connected in order to avoid the introduction of FUV shadowing between segments. Figure 4 presents four examples of PDR surfaces that share the same curve of f eff values. The first three surfaces, shown in the left panel, belong to our basic assumption that the PDR is viewed from its back side. Each derived concave surface is consistent with the general 3-D configuration of a bowl-shaped interface originally suggested by Meixner et al. (1992), see also Figure 2 of Pellegrini et al. (2006). The right panel show an alternate configuration in which the PDR is viewed from its front side and is physically separated from the layer of foreground extinction. Although the cos( φ )/cos( θ ) curve fixes the relative curvature of the surface, and thus provides a '3-D view' of the PDR layer along the LOS, both the absolute location along the LOS and the state of reflection about the abscissa are, unfortunately, degenerate. Future studies could incorporate additional clues for a more robust characterization of the location and the reflection of the PDR surface. For example, our initial tests involving a freely variable G 0 show that its values start to drop significantly below G pr 0 values half way along the mapped radial distance from NGC 6618. Such a behavior may indicate that the line of sight is probing a more extreme case of geometry than derived here. Among the PDR surfaces depicted in Figure 4, only 'A', and therefore ' -A', affect G 0 values in a similar fashion, owing to their increasing deviation from the plane of projection. On the other hand, the role of pixel-to-pixel variations, such as those seen in modeling output, remains to be evaluated in terms of orientation and mutual shadowing among individual clumps.",
"pages": [
8,
10
]
},
{
"title": "6. Summary",
"content": "globally curved, thus confirming the suggested description of a bowl-shaped PDR in M17SW.",
"pages": [
12
]
},
{
"title": "REFERENCES",
"content": "Beetz, M., Elsasser, H., Poulakos, C., & Weinberger, R. 1976, A&A, 50, 41 Brogan, C. L., & Troland, T. H. 2001, ApJ, 560, 821 Broos, P. S., Feigelson, E. D., Townsley, L. K., Getman, K. V., Wang, J., Garmire, G. P., Jiang, Z., & Tsuboi, Y. 2007, ApJS, 169, 353 Chini, R., Elsasser, H., & Neckel, Th. 1980, A&A, 91, 186 Chini, R., Hoffmeister, V. H., Kampgen, K., Kimeswenger, S., Nielbock, M., & Siebenmorgen, R. 2004, A&A, 427, 849 DePoy, D. L., Lada, E. A., Gatley, I., & Probst, R. 1990, ApJ, 356, L55 Dickel, H. R. 1968, ApJ, 152, 651 Felli, M., Churchwell, E., & Massi, M. 1984, A&A, 136, 53 Gatley, I., Becklin, E. E., Sellgren, K., & Werner, M. W. 1979, ApJ, 233, 575 Habing, H. J. 1968, Bull. Astron. Inst. Netherlands, 19, 421 Hanson, M. M., Howarth, I. D., & Conti, P. S. 1997, ApJ, 489, 698 Hoffmeister, V. H., Chini, R., Scheyda, C. M., Schulze, D., Watermann, R, Nurnberger, D., & Vogt, N. 2003, ApJ, 686, 310 Jiang, Z., Yao, Y., Yang, J. et al. 2002, ApJ, 577, 245 Kaufman, M. J., Wolfire, M. G., & Hollenbach, D. J. 2006, ApJ, 644, 283 Keene, J., Blake, G. A., Phillips, T. G., Huggins, P. J., & Beichman, C. A. 1985, ApJ, 299, 967 Kleinmann, D. E., & Wright, E. L. 1973, ApJ, 185, L133 Mathis, J. S. 1990 ARA&A, 28, 37 Meixner, M., Haas, M. R., Tielens, A. G. G. M., Erickson, E. F., & Werner, M. 1992, ApJ, 390, 499 Meixner, M., & Tielens, A. G. G. M. ApJ, 405, 216 Nielbock, M., Chini, R., Hoffmeister, V. H., Nurnberger, D. E. A., Scheyda, C. M., & Steinacker, J. 2008, MNRAS, 388, 1031 Parravano, A., Hollenbach, D. J., & McKee, C. F. 2003, ApJ, 584, 797 Pellegrini, E. W., Baldwin, J. A., Brogan, C. L. et al. 2006, ApJ, 658, 1119 P'erez-Beaupuits, J. P., Wiesemeyer, H., Ossenkopf, V., Stutzki, J., Gusten, R., Simon, R., Hubers, H. W., & Ricken, O. 2012, A&A, 542, L13 Povich, M. S., Sone, J. M., Churchwell, E., et al. 2007, ApJ, 660, 346 Povich, M. S., Churchwell, E., Bieging, J. H. et al. 2009, ApJ, 696, 1278 Sheffer, Y., Wolfire, M. G., Hollenbach, D. J., Kaufman, M. J., & Cordier, M. 2011, ApJ, 741, 45 Smith, J. D. T., Armus, L., Dale, D. A., et al. 2007, PASP, 119, 1133 Stutzki, J., Stacey, G. J., Genzel, R., Harris, A. I., Jaffe, D. T., & Lugten, J. B. 1988, ApJ, 332, 379 Stutzki, J., & Gusten, R. 1990, ApJ, 356, 513 Thronson, H. A., & Lada, C. J. 1983, ApJ, 269, 175 Tokunaga, A. T., & Thompson, R. I. 1979, ApJ, 229, 583 Wilson, T. L., Hanson, M. M., & Muders, D. 2003, ApJ, 590, 895 Xu, Y., Moscadelli, L., Reid, M. J., Menten, K. M., Zhang, B., Zheng, X. W., & Brunthaler, A. 2011, ApJ, 733, 25",
"pages": [
12,
13
]
}
]
2013ApJ...775L..22M
https://arxiv.org/pdf/1308.2062.pdf
<document>
<section_header_level_1><location><page_1><loc_20><loc_86><loc_80><loc_87></location>QUIESCENT NUCLEAR BURNING IN LOW-METALLICITY WHITE DWARFS</section_header_level_1>
<text><location><page_1><loc_25><loc_79><loc_76><loc_85></location>Marcelo M. Miller Bertolami 1,2 , Leandro G. Althaus Facultad de Ciencias Astron'omicas y Geof'ısicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900 La Plata, Argentina. Instituto de Astrof'ısica de La Plata, UNLP-CONICET, Paseo del Bosque s/n, 1900 La Plata, Argentina.</text>
<text><location><page_1><loc_49><loc_78><loc_51><loc_79></location>and</text>
<section_header_level_1><location><page_1><loc_41><loc_76><loc_59><loc_77></location>Enrique Garc'ıa-Berro</section_header_level_1>
<text><location><page_1><loc_14><loc_74><loc_87><loc_76></location>Departament de F'ısica Aplicada, Universitat Polit'ecnica de Catalunya, c/Esteve Terrades 5, 08860 Castelldefels, Spain. Institute for Space Studies of Catalonia, c/Gran Capita 2-4, Edif. Nexus 104, 08034 Barcelona, Spain.</text>
<text><location><page_1><loc_41><loc_73><loc_59><loc_73></location>Draft version October 3, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_70><loc_55><loc_71></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_48><loc_86><loc_70></location>We discuss the impact of residual nuclear burning in the cooling sequences of hydrogen-rich DA white dwarfs with very low metallicity progenitors ( Z = 0 . 0001). These cooling sequences are appropriate for the study of very old stellar populations. The results presented here are the product of self-consistent, fully evolutionary calculations. Specifically, we follow the evolution of white dwarf progenitors from the zero-age main sequence through all the evolutionary phases, namely the core hydrogen-burning phase, the helium-burning phase, and the thermally pulsing asymptotic giant branch phase to the white dwarf stage. This is done for the most relevant range of main sequence masses, covering the most usual interval of white dwarf masses - from 0 . 53 M /circledot to 0 . 83 M /circledot . Due to the low metallicity of the progenitor stars, white dwarfs are born with thicker hydrogen envelopes, leading to more intense hydrogen burning shells as compared with their solar metallicity counterparts. We study the phase in which nuclear reactions are still important and find that nuclear energy sources play a key role during long periods of time, considerably increasing the cooling times from those predicted by standard white dwarf models. In particular, we find that for this metallicity and for white dwarf masses smaller than about 0 . 6 M /circledot , nuclear reactions are the main contributor to the stellar luminosity for luminosities as low as log( L/L /circledot ) /similarequal -3 . 2. This, in turn, should have a noticeable impact in the white dwarf luminosity function of low-metallicity stellar populations.</text>
<text><location><page_1><loc_14><loc_47><loc_67><loc_48></location>Subject headings: stars: evolution - stars: interiors - stars: white dwarfs</text>
<section_header_level_1><location><page_1><loc_21><loc_43><loc_36><loc_44></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_15><loc_48><loc_43></location>White dwarf stars are the most common end-point of stellar evolution and as such are routinely used in constraining several properties of stellar populations including our Galaxy as a whole, as well as globular and open clusters - see, for instance, Hansen et al. (2007), Winget et al. (2009), Garc'ıa-Berro et al. (2010), and Bono et al. (2013), and references therein. In addition to these applications, white dwarfs have also been employed to test physics under conditions that cannot be attained in terrestial laboratories. In particular, they have been used to place constraints on the properties of elementary particles such as axions - see Isern et al. (2008), and C'orsico et al. (2012a,b) for recent efforts - and neutrinos (Winget et al. 2004), or on alternative theories of gravitation (Garcia-Berro et al. 1995; Garc'ıa-Berro et al. 2011; C'orsico et al. 2013). The use of white dwarfs for all of these applications and as precise stellar chronometers requires a detailed knowledge of the main physical processes that control their evolution - see Fontaine & Brassard (2008), Winget & Kepler (2008) and Althaus et al. (2010b) for extensive reviews.</text>
<text><location><page_1><loc_10><loc_13><loc_48><loc_15></location>These and other potential applications of white dwarfs</text>
<text><location><page_1><loc_52><loc_7><loc_92><loc_44></location>has led to renewed efforts in computing full evolutionary models for these stars, taking into account all the relevant sources and sinks of energy (Renedo et al. 2010; Salaris et al. 2010; Althaus et al. 2010c). However, in most calculations, stable nuclear burning is not considered. This assumption is well justified because stable hydrogen shell burning is expected to be a minor source of energy for stellar luminosities below ∼ 100 L /circledot . Thus, in a typical white dwarf, H burning is not a relevant energy source as soon as the hot part of the white dwarf cooling track is reached. Nevertheless, in regular white dwarfs H burning never ceases completely, and depending on the mass of the white dwarf and on the precise mass of H left during the previous evolutionary phases (which depends critically on metallicity) it may become a nonnegligible energy source for white dwarfs with hydrogen atmospheres. Actually, a correct assessment of the role played by residual H burning during the cooling phase requires a detailed calculation of the white dwarf progenitor history. As a matter of fact, the full evolutionary calculations of Renedo et al. (2010) already showed that in white dwarfs resulting from progenitors with Z = 0 . 001 residual H burning via the proton-proton chains may contribute by about 30% to the luminosity by the time cooling has proceeded down to luminosities ranging from L ∼ 10 -2 L /circledot to 10 -3 L /circledot . Nevertheless, the impact of nuclear burning on the cooling times has been found to be almost negligible in almost all the cases studied so</text>
<table>
<location><page_2><loc_12><loc_76><loc_43><loc_89></location>
<caption>TABLE 1 Characteristics of our initial white dwarf models.</caption>
</table>
<text><location><page_2><loc_8><loc_66><loc_48><loc_74></location>far. However, it is worth noting that with the exception of a few sequences computed by Miller Bertolami et al. (2011), the only white dwarf cooling sequences derived from the consistent evolution of their low-metallicity progenitor stars computed up to now have been performed for metallicities Z ≥ 0 . 001 (Renedo et al. 2010).</text>
<text><location><page_2><loc_8><loc_47><loc_48><loc_66></location>In this letter, we show that stable H burning becomes the dominant energy source of white dwarfs resulting from very low-metallicity progenitors, namely with Z ≈ 0 . 0001, delaying their cooling for significant time intervals. To arrive at this result, we have computed the full evolution of white dwarf stars taking into account the evolutionary history throughout all the evolutionary stages of their progenitor stars with Z = 0 . 0001. This is the metal content of some old stellar populations like the galactic halo or globular clusters. Thus, we are forced to conclude that standard white dwarf sequences that do not take into account the energy release of the H-burning shell are not appropriate for the study of such very lowmetallicity populations.</text>
<section_header_level_1><location><page_2><loc_9><loc_45><loc_48><loc_46></location>2. EVOLUTIONARY CODE AND INPUT PHYSICS</section_header_level_1>
<text><location><page_2><loc_8><loc_7><loc_48><loc_44></location>The calculations reported here have been done using the LPCODE stellar evolutionary code (Althaus et al. 2012). This code has been used to study different problems related to the formation and evolution of white dwarfs (Garc'ıa-Berro et al. 2010; Althaus et al. 2010a; Renedo et al. 2010; Miller Bertolami et al. 2011). A description of the input physics and numerical procedures employed in LPCODE can be found in these works. In particular, convective overshooting has been considered during the core H and He burning, but not during the thermally-pulsing Asympotic Giant Branch (TP-AGB). Mass loss during the RGB and AGB phases has been considered following the prescriptions of Schroder & Cuntz (2005) and Groenewegen et al. (2009). The nuclear network accounts for 16 isotopes together with 34 thermonuclear reaction rates for the pp-chains, CNO bi-cycle, helium burning, and carbon ignition that are identical to those described in Althaus et al. (2005), with the exception of the 12 C + p → 13 N + γ → 13 C + e + + ν e and 13 C(p, γ ) 14 N reaction rates, which are taken from Angulo et al. (1999). Radiative opacities are those of OPAL (Iglesias & Rogers 1996). Conductive opacities are from Cassisi et al. (2007). The screening factors adopted in this work are those of Graboske et al. (1973). The equation of state during the main sequence evolution is that of the OPAL project for H- and He-rich compositions for the appropriate metallicity. Finally, updated low-temperature molecular opacities with varying</text>
<figure>
<location><page_2><loc_53><loc_73><loc_88><loc_92></location>
<caption>Fig. 1.Total hydrogen content of the white dwarf models at the beginning of the cooling branch of the very low-metallicity models presented here ( Z = 0 . 0001) as a function of the mass, compared with the hydrogen content of the models of higher metallicity computed by Renedo et al. (2010) ( Z = 0 . 001 and Z = 0 . 01). Note the change in the slope due to the occurrence of the third dredge-up for the two more massive model sequences, which tends to reduce the size of the resulting H envelope.</caption>
</figure>
<text><location><page_2><loc_52><loc_53><loc_92><loc_61></location>carbon-oxygen ratios are used. To this end, we have adopted the low temperature opacities of Ferguson et al. (2005) and Weiss & Ferguson (2009). In LPCODE molecular opacities are computed adopting the opacity tables with the correct abundances of the unenhanced metals (e.g., Fe) and the appropriate carbon-oxygen ratio.</text>
<text><location><page_2><loc_52><loc_31><loc_92><loc_53></location>For the white dwarf regime, we take into account the effects of element diffusion due to gravitational settling, chemical and thermal diffusion, see Althaus et al. (2003) for details. For effective temperatures lower than 10,000 K, outer boundary conditions are derived from non-grey model atmospheres Rohrmann et al. (2012). Both latent heat release and the release of gravitational energy resulting from carbon-oxygen phase separation (Isern et al. 2000, 1997) have been included following the phase diagram of Horowitz et al. (2010), see Althaus et al. (2012) for details of the numerical implementation. Finally, we emphasize that recently, LPCODE has been tested against other white dwarf evolutionary codes and uncertainties in the cooling ages arising from different numerical implementations of stellar evolution equations were found to be below 2% (Salaris et al. 2013).</text>
<text><location><page_2><loc_52><loc_7><loc_92><loc_31></location>It is worth commenting that for, a correct assessment of the H content and of the residual nuclear burning on cool white dwarfs, the full calculation of the evolutionary stages leading to the formation of the white dwarf is absolutely necessary. This cannot be done using artificial initial white dwarf structures, since in this case the mass of the hydrogen envelope, which determines the importance of nuclear burning, is artificially imposed and then lacks predictive power. For this reason we have followed the complete evolution of the progenitor stars computing all the evolutionary stages throughout the entire lifetime of the progenitor of the white dwarf, starting from the ZAMS and continuing through the rather computationally complex TP-AGB phase. In particular, we computed full nine white dwarf evolutionary sequences adopting for the progenitor stars Z = 0 . 0001 and an initial H mass fraction of X H = 0 . 7547. We note that in our calculations we did not find any third dredge-up episode during</text>
<figure>
<location><page_3><loc_9><loc_73><loc_44><loc_92></location>
<caption>Fig. 2.Fraction of the total luminosity due to nuclear burning for different white dwarf sequences with Z = 0 . 0001. Note that for white dwarf masses below ∼ 0 . 6 M /circledot nuclear burning becomes the main energy source of the white dwarf.</caption>
</figure>
<text><location><page_3><loc_8><loc_44><loc_48><loc_66></location>the TP-AGB phase, except for the two more massive sequences, those with initial ZAMS masses 2.0 and 2 . 5 M /circledot . This is due to the low initial stellar masses and metallicity, of the sequences computed in this work. In Table 1, we list the main results of our calculations. In particular, we list the initial mass of the progenitor stars at the ZAMS, the final mass of the resulting white dwarf both in solar units - the progenitor lifetime (in Gyr), and the mass of H at the beginning of the cooling branch - that is, at the point of maximum effective temperature - in solar masses. As expected, the residual H content decreases with increasing white dwarf masses, a trend which helps to understand the dependence of residual nuclear burning on the stellar mass discussed in the next Section. In all cases, the white dwarf evolution has been computed down to log( L/L /circledot ) = -5 . 0.</text>
<section_header_level_1><location><page_3><loc_8><loc_41><loc_48><loc_43></location>3. THE IMPACT OF NUCLEAR BURNING ON THE COOLING TIMES</section_header_level_1>
<text><location><page_3><loc_8><loc_7><loc_48><loc_40></location>As shown by Iben & MacDonald (1986) low-metallicity progenitors depart from the AGB with more massive envelopes, leading to white dwarfs with thicker H envelopes. This well-known behavior can be seen in Fig. 1, where the total hydrogen content of the initial white dwarf models computed in the present work ( Z = 0 . 0001) is compared with that of models with higher metallicity computed by Renedo et al. (2010), that have somewhat larger metallicities ( Z = 0 . 001 and Z = 0 . 01). As a result of the larger H envelopes, residual H burning is expected to become more relevant in white dwarfs with low-metallicity progenitors. In particular our results show that, at the metallicity of the galactic halo and some old globular cluster ( Z ∼ 0 . 0001), stable H burning becomes one of the main energy sources of low-mass white dwarfs for substantial periods of time. This is better illustrated in Fig. 2, where we show the fraction of the surface luminosity that is generated by nuclear burning at different stages of the white dwarf cooling phase. It is apparent that the luminosity of white dwarfs descending from metal poor progenitors is completely dominated by nuclear burning, even at rather low luminosities. Specifically, note that for white dwarfs with M /lessorsimilar 0 . 6 M /circledot nuclear energy release constitutes the main energy source at intermediate luminosities ( -3 . 2 /lessorsimilar log( L/L /circledot ) /lessorsimilar -1).</text>
<figure>
<location><page_3><loc_52><loc_57><loc_89><loc_92></location>
<caption>Fig. 3.Impact of the nuclear burning on the cooling time of representative Z = 0 . 0001 white dwarf sequences. Note that between log( L/L /circledot ) = -2 and log( L/L /circledot ) = -4, disregarding the energy released by nuclear burning underestimates the cooling times by more than a factor of 2.</caption>
</figure>
<text><location><page_3><loc_52><loc_23><loc_92><loc_50></location>This leads to a very significant delay in the cooling times, as compared with stars with solar metallicity in which nuclear burning does not play a leading role, and most of the energy release comes from the thermal energy stored in the interior. This is shown in Fig. 3, which displays the different cooling curves (left panels) of selected low-metallicity white dwarf sequences when nuclear energy sources are considered or disregarded, and the corresponding delays introduced by nuclear burning (right panels). It is quite apparent that neglecting the energy released by nuclear burning leads to an underestimation of the cooling times by more than a factor of 2 at intermediate luminosities. This is true for white dwarfs resulting from low-metallicity progenitors with M WD /lessorsimilar 0 . 6 M /circledot (progenitor masses M ZAMS /lessorsimilar 1 M /circledot ). Hence, our calculations demonstrate that, contrary to the accepted paradigm, stable nuclear burning in lowmass, low-metallicity white dwarfs can be the main energy source, delaying substantially their cooling times at low luminosities.</text>
<section_header_level_1><location><page_3><loc_58><loc_21><loc_86><loc_22></location>4. SUMMARY AND CONCLUSIONS</section_header_level_1>
<text><location><page_3><loc_52><loc_7><loc_92><loc_20></location>We have computed a set of cooling sequences for hydrogen-rich white dwarfs with very low metallicity progenitors, which are appropriate for precision white dwarf cosmochronology of old stellar systems. Our evolutionary sequences have been self-consistently evolved through all the stellar phases. That is, we have computed the evolution of the progenitors of white dwarfs from the ZAMS, through the core hydrogen- and helium-burning phases to the thermally pulsing AGB phase. Finally, we have used these self-consistent models to compute</text>
<text><location><page_4><loc_8><loc_55><loc_48><loc_92></location>white dwarf cooling tracks. To the best of our knowledge, this is the first set of fully evolutionary calculations of low-metallicity progenitors resulting in white dwarfs cooling tracks covering the relevant range of initial main sequence and, correspondingly, white dwarf masses. We emphasize that our complete evolutionary calculations of the history of the progenitors of white dwarfs allowed us to have self-consistent white dwarf initial models. Specifically, in our calculations the masses of the hydrogen-rich envelopes and of the helium shells beneath them were obtained from evolutionary calculations, instead of using typical values and artificial initial white dwarf models. We have shown that this has implications for the cooling of low-mass white dwarfs resulting from low-metallicity progenitors, as the masses of these layers not only control the cooling speed of these white dwarfs, but also determine if they are able to sustain residual nuclear burning. Specifically, our calculations show that the masses of the envelopes of the resulting white dwarfs are more massive than those of their solar metallicity counterparts. These white dwarfs having more massive envelopes, the role of nuclear energy release becomes more prominent and the white dwarf cooling times for the same luminosity turn out to be considerably larger than those of white dwarfs descending from progenitors with larger metallicity. In particular, we found that for Z = 0 . 0001, and for white dwarf masses smaller than about 0 . 6 M /circledot , the nuclear energy release is the main energy source contribut-</text>
<text><location><page_4><loc_52><loc_89><loc_92><loc_92></location>ing to the stellar luminosity until luminosities as low as log( L/L /circledot ) /similarequal -3 . 2 are reached.</text>
<text><location><page_4><loc_52><loc_64><loc_92><loc_89></location>Since very low metallicity stars are expected to be members of the galactic halo or very old globular cdlusters our findings could have consequences not only for the determination of the ages of low-mass white dwarfs, but also may have a noticeable effect on the shape of their white dwarf luminosity functions. However, we expect that the impact of residual nuclear burning on the age determinations of such low-metallicity populations should be modest, of the order of ∼ 5%. Nevertheless, this finding questions the correctness of using standard white dwarf cooling sequences in which no nuclear burning is considered, or which oversimplify the previous evolutionary history of the progenitor star, to date individual lowmass white dwarfs - those with masses /lessorsimilar 0 . 6 M /circledot -belonging to low metallicity populations. However, the detailed study of how quiescent nuclear burning affects the shape of the white dwarf luminosity function of old populations is out of the scope of the present paper and will be explored in forthcoming works.</text>
<text><location><page_4><loc_52><loc_53><loc_92><loc_62></location>Part of this work was supported by AGENCIA through the Programa de Modernizaci'on Tecnol'ogica BID 1728/OC-AR, by PIP 112-200801-00940 grant from CONICET, by MCINN grant AYA2011-23102, by the ESF EUROCORES Program EuroGENESIS (MICINN grant EUI2009-04170), by the European Union FEDER funds, and by the AGAUR.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "We discuss the impact of residual nuclear burning in the cooling sequences of hydrogen-rich DA white dwarfs with very low metallicity progenitors ( Z = 0 . 0001). These cooling sequences are appropriate for the study of very old stellar populations. The results presented here are the product of self-consistent, fully evolutionary calculations. Specifically, we follow the evolution of white dwarf progenitors from the zero-age main sequence through all the evolutionary phases, namely the core hydrogen-burning phase, the helium-burning phase, and the thermally pulsing asymptotic giant branch phase to the white dwarf stage. This is done for the most relevant range of main sequence masses, covering the most usual interval of white dwarf masses - from 0 . 53 M /circledot to 0 . 83 M /circledot . Due to the low metallicity of the progenitor stars, white dwarfs are born with thicker hydrogen envelopes, leading to more intense hydrogen burning shells as compared with their solar metallicity counterparts. We study the phase in which nuclear reactions are still important and find that nuclear energy sources play a key role during long periods of time, considerably increasing the cooling times from those predicted by standard white dwarf models. In particular, we find that for this metallicity and for white dwarf masses smaller than about 0 . 6 M /circledot , nuclear reactions are the main contributor to the stellar luminosity for luminosities as low as log( L/L /circledot ) /similarequal -3 . 2. This, in turn, should have a noticeable impact in the white dwarf luminosity function of low-metallicity stellar populations. Subject headings: stars: evolution - stars: interiors - stars: white dwarfs",
"pages": [
1
]
},
{
"title": "QUIESCENT NUCLEAR BURNING IN LOW-METALLICITY WHITE DWARFS",
"content": "Marcelo M. Miller Bertolami 1,2 , Leandro G. Althaus Facultad de Ciencias Astron'omicas y Geof'ısicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900 La Plata, Argentina. Instituto de Astrof'ısica de La Plata, UNLP-CONICET, Paseo del Bosque s/n, 1900 La Plata, Argentina. and",
"pages": [
1
]
},
{
"title": "Enrique Garc'ıa-Berro",
"content": "Departament de F'ısica Aplicada, Universitat Polit'ecnica de Catalunya, c/Esteve Terrades 5, 08860 Castelldefels, Spain. Institute for Space Studies of Catalonia, c/Gran Capita 2-4, Edif. Nexus 104, 08034 Barcelona, Spain. Draft version October 3, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "White dwarf stars are the most common end-point of stellar evolution and as such are routinely used in constraining several properties of stellar populations including our Galaxy as a whole, as well as globular and open clusters - see, for instance, Hansen et al. (2007), Winget et al. (2009), Garc'ıa-Berro et al. (2010), and Bono et al. (2013), and references therein. In addition to these applications, white dwarfs have also been employed to test physics under conditions that cannot be attained in terrestial laboratories. In particular, they have been used to place constraints on the properties of elementary particles such as axions - see Isern et al. (2008), and C'orsico et al. (2012a,b) for recent efforts - and neutrinos (Winget et al. 2004), or on alternative theories of gravitation (Garcia-Berro et al. 1995; Garc'ıa-Berro et al. 2011; C'orsico et al. 2013). The use of white dwarfs for all of these applications and as precise stellar chronometers requires a detailed knowledge of the main physical processes that control their evolution - see Fontaine & Brassard (2008), Winget & Kepler (2008) and Althaus et al. (2010b) for extensive reviews. These and other potential applications of white dwarfs has led to renewed efforts in computing full evolutionary models for these stars, taking into account all the relevant sources and sinks of energy (Renedo et al. 2010; Salaris et al. 2010; Althaus et al. 2010c). However, in most calculations, stable nuclear burning is not considered. This assumption is well justified because stable hydrogen shell burning is expected to be a minor source of energy for stellar luminosities below ∼ 100 L /circledot . Thus, in a typical white dwarf, H burning is not a relevant energy source as soon as the hot part of the white dwarf cooling track is reached. Nevertheless, in regular white dwarfs H burning never ceases completely, and depending on the mass of the white dwarf and on the precise mass of H left during the previous evolutionary phases (which depends critically on metallicity) it may become a nonnegligible energy source for white dwarfs with hydrogen atmospheres. Actually, a correct assessment of the role played by residual H burning during the cooling phase requires a detailed calculation of the white dwarf progenitor history. As a matter of fact, the full evolutionary calculations of Renedo et al. (2010) already showed that in white dwarfs resulting from progenitors with Z = 0 . 001 residual H burning via the proton-proton chains may contribute by about 30% to the luminosity by the time cooling has proceeded down to luminosities ranging from L ∼ 10 -2 L /circledot to 10 -3 L /circledot . Nevertheless, the impact of nuclear burning on the cooling times has been found to be almost negligible in almost all the cases studied so far. However, it is worth noting that with the exception of a few sequences computed by Miller Bertolami et al. (2011), the only white dwarf cooling sequences derived from the consistent evolution of their low-metallicity progenitor stars computed up to now have been performed for metallicities Z ≥ 0 . 001 (Renedo et al. 2010). In this letter, we show that stable H burning becomes the dominant energy source of white dwarfs resulting from very low-metallicity progenitors, namely with Z ≈ 0 . 0001, delaying their cooling for significant time intervals. To arrive at this result, we have computed the full evolution of white dwarf stars taking into account the evolutionary history throughout all the evolutionary stages of their progenitor stars with Z = 0 . 0001. This is the metal content of some old stellar populations like the galactic halo or globular clusters. Thus, we are forced to conclude that standard white dwarf sequences that do not take into account the energy release of the H-burning shell are not appropriate for the study of such very lowmetallicity populations.",
"pages": [
1,
2
]
},
{
"title": "2. EVOLUTIONARY CODE AND INPUT PHYSICS",
"content": "The calculations reported here have been done using the LPCODE stellar evolutionary code (Althaus et al. 2012). This code has been used to study different problems related to the formation and evolution of white dwarfs (Garc'ıa-Berro et al. 2010; Althaus et al. 2010a; Renedo et al. 2010; Miller Bertolami et al. 2011). A description of the input physics and numerical procedures employed in LPCODE can be found in these works. In particular, convective overshooting has been considered during the core H and He burning, but not during the thermally-pulsing Asympotic Giant Branch (TP-AGB). Mass loss during the RGB and AGB phases has been considered following the prescriptions of Schroder & Cuntz (2005) and Groenewegen et al. (2009). The nuclear network accounts for 16 isotopes together with 34 thermonuclear reaction rates for the pp-chains, CNO bi-cycle, helium burning, and carbon ignition that are identical to those described in Althaus et al. (2005), with the exception of the 12 C + p → 13 N + γ → 13 C + e + + ν e and 13 C(p, γ ) 14 N reaction rates, which are taken from Angulo et al. (1999). Radiative opacities are those of OPAL (Iglesias & Rogers 1996). Conductive opacities are from Cassisi et al. (2007). The screening factors adopted in this work are those of Graboske et al. (1973). The equation of state during the main sequence evolution is that of the OPAL project for H- and He-rich compositions for the appropriate metallicity. Finally, updated low-temperature molecular opacities with varying carbon-oxygen ratios are used. To this end, we have adopted the low temperature opacities of Ferguson et al. (2005) and Weiss & Ferguson (2009). In LPCODE molecular opacities are computed adopting the opacity tables with the correct abundances of the unenhanced metals (e.g., Fe) and the appropriate carbon-oxygen ratio. For the white dwarf regime, we take into account the effects of element diffusion due to gravitational settling, chemical and thermal diffusion, see Althaus et al. (2003) for details. For effective temperatures lower than 10,000 K, outer boundary conditions are derived from non-grey model atmospheres Rohrmann et al. (2012). Both latent heat release and the release of gravitational energy resulting from carbon-oxygen phase separation (Isern et al. 2000, 1997) have been included following the phase diagram of Horowitz et al. (2010), see Althaus et al. (2012) for details of the numerical implementation. Finally, we emphasize that recently, LPCODE has been tested against other white dwarf evolutionary codes and uncertainties in the cooling ages arising from different numerical implementations of stellar evolution equations were found to be below 2% (Salaris et al. 2013). It is worth commenting that for, a correct assessment of the H content and of the residual nuclear burning on cool white dwarfs, the full calculation of the evolutionary stages leading to the formation of the white dwarf is absolutely necessary. This cannot be done using artificial initial white dwarf structures, since in this case the mass of the hydrogen envelope, which determines the importance of nuclear burning, is artificially imposed and then lacks predictive power. For this reason we have followed the complete evolution of the progenitor stars computing all the evolutionary stages throughout the entire lifetime of the progenitor of the white dwarf, starting from the ZAMS and continuing through the rather computationally complex TP-AGB phase. In particular, we computed full nine white dwarf evolutionary sequences adopting for the progenitor stars Z = 0 . 0001 and an initial H mass fraction of X H = 0 . 7547. We note that in our calculations we did not find any third dredge-up episode during the TP-AGB phase, except for the two more massive sequences, those with initial ZAMS masses 2.0 and 2 . 5 M /circledot . This is due to the low initial stellar masses and metallicity, of the sequences computed in this work. In Table 1, we list the main results of our calculations. In particular, we list the initial mass of the progenitor stars at the ZAMS, the final mass of the resulting white dwarf both in solar units - the progenitor lifetime (in Gyr), and the mass of H at the beginning of the cooling branch - that is, at the point of maximum effective temperature - in solar masses. As expected, the residual H content decreases with increasing white dwarf masses, a trend which helps to understand the dependence of residual nuclear burning on the stellar mass discussed in the next Section. In all cases, the white dwarf evolution has been computed down to log( L/L /circledot ) = -5 . 0.",
"pages": [
2,
3
]
},
{
"title": "3. THE IMPACT OF NUCLEAR BURNING ON THE COOLING TIMES",
"content": "As shown by Iben & MacDonald (1986) low-metallicity progenitors depart from the AGB with more massive envelopes, leading to white dwarfs with thicker H envelopes. This well-known behavior can be seen in Fig. 1, where the total hydrogen content of the initial white dwarf models computed in the present work ( Z = 0 . 0001) is compared with that of models with higher metallicity computed by Renedo et al. (2010), that have somewhat larger metallicities ( Z = 0 . 001 and Z = 0 . 01). As a result of the larger H envelopes, residual H burning is expected to become more relevant in white dwarfs with low-metallicity progenitors. In particular our results show that, at the metallicity of the galactic halo and some old globular cluster ( Z ∼ 0 . 0001), stable H burning becomes one of the main energy sources of low-mass white dwarfs for substantial periods of time. This is better illustrated in Fig. 2, where we show the fraction of the surface luminosity that is generated by nuclear burning at different stages of the white dwarf cooling phase. It is apparent that the luminosity of white dwarfs descending from metal poor progenitors is completely dominated by nuclear burning, even at rather low luminosities. Specifically, note that for white dwarfs with M /lessorsimilar 0 . 6 M /circledot nuclear energy release constitutes the main energy source at intermediate luminosities ( -3 . 2 /lessorsimilar log( L/L /circledot ) /lessorsimilar -1). This leads to a very significant delay in the cooling times, as compared with stars with solar metallicity in which nuclear burning does not play a leading role, and most of the energy release comes from the thermal energy stored in the interior. This is shown in Fig. 3, which displays the different cooling curves (left panels) of selected low-metallicity white dwarf sequences when nuclear energy sources are considered or disregarded, and the corresponding delays introduced by nuclear burning (right panels). It is quite apparent that neglecting the energy released by nuclear burning leads to an underestimation of the cooling times by more than a factor of 2 at intermediate luminosities. This is true for white dwarfs resulting from low-metallicity progenitors with M WD /lessorsimilar 0 . 6 M /circledot (progenitor masses M ZAMS /lessorsimilar 1 M /circledot ). Hence, our calculations demonstrate that, contrary to the accepted paradigm, stable nuclear burning in lowmass, low-metallicity white dwarfs can be the main energy source, delaying substantially their cooling times at low luminosities.",
"pages": [
3
]
},
{
"title": "4. SUMMARY AND CONCLUSIONS",
"content": "We have computed a set of cooling sequences for hydrogen-rich white dwarfs with very low metallicity progenitors, which are appropriate for precision white dwarf cosmochronology of old stellar systems. Our evolutionary sequences have been self-consistently evolved through all the stellar phases. That is, we have computed the evolution of the progenitors of white dwarfs from the ZAMS, through the core hydrogen- and helium-burning phases to the thermally pulsing AGB phase. Finally, we have used these self-consistent models to compute white dwarf cooling tracks. To the best of our knowledge, this is the first set of fully evolutionary calculations of low-metallicity progenitors resulting in white dwarfs cooling tracks covering the relevant range of initial main sequence and, correspondingly, white dwarf masses. We emphasize that our complete evolutionary calculations of the history of the progenitors of white dwarfs allowed us to have self-consistent white dwarf initial models. Specifically, in our calculations the masses of the hydrogen-rich envelopes and of the helium shells beneath them were obtained from evolutionary calculations, instead of using typical values and artificial initial white dwarf models. We have shown that this has implications for the cooling of low-mass white dwarfs resulting from low-metallicity progenitors, as the masses of these layers not only control the cooling speed of these white dwarfs, but also determine if they are able to sustain residual nuclear burning. Specifically, our calculations show that the masses of the envelopes of the resulting white dwarfs are more massive than those of their solar metallicity counterparts. These white dwarfs having more massive envelopes, the role of nuclear energy release becomes more prominent and the white dwarf cooling times for the same luminosity turn out to be considerably larger than those of white dwarfs descending from progenitors with larger metallicity. In particular, we found that for Z = 0 . 0001, and for white dwarf masses smaller than about 0 . 6 M /circledot , the nuclear energy release is the main energy source contribut- ing to the stellar luminosity until luminosities as low as log( L/L /circledot ) /similarequal -3 . 2 are reached. Since very low metallicity stars are expected to be members of the galactic halo or very old globular cdlusters our findings could have consequences not only for the determination of the ages of low-mass white dwarfs, but also may have a noticeable effect on the shape of their white dwarf luminosity functions. However, we expect that the impact of residual nuclear burning on the age determinations of such low-metallicity populations should be modest, of the order of ∼ 5%. Nevertheless, this finding questions the correctness of using standard white dwarf cooling sequences in which no nuclear burning is considered, or which oversimplify the previous evolutionary history of the progenitor star, to date individual lowmass white dwarfs - those with masses /lessorsimilar 0 . 6 M /circledot -belonging to low metallicity populations. However, the detailed study of how quiescent nuclear burning affects the shape of the white dwarf luminosity function of old populations is out of the scope of the present paper and will be explored in forthcoming works. Part of this work was supported by AGENCIA through the Programa de Modernizaci'on Tecnol'ogica BID 1728/OC-AR, by PIP 112-200801-00940 grant from CONICET, by MCINN grant AYA2011-23102, by the ESF EUROCORES Program EuroGENESIS (MICINN grant EUI2009-04170), by the European Union FEDER funds, and by the AGAUR.",
"pages": [
3,
4
]
},
{
"title": "REFERENCES",
"content": "M. S. 1973, ApJ, 181, 457 Iben, Jr., I., & MacDonald, J. 1986, ApJ, 301, 164 Iglesias, C. A., & Rogers, F. J. 1996, ApJ, 464, 943",
"pages": [
4
]
}
]
2013ApJ...776...17M
https://arxiv.org/pdf/1309.5257.pdf
<document>
<section_header_level_1><location><page_1><loc_16><loc_82><loc_84><loc_86></location>Application of Jitter Radiation: Gamma-ray Burst Prompt Polarization</section_header_level_1>
<text><location><page_1><loc_34><loc_78><loc_66><loc_80></location>Jirong Mao 1 , 2 , 3 and Jiancheng Wang 2 , 3</text>
<text><location><page_1><loc_40><loc_75><loc_59><loc_76></location>[email protected]</text>
<section_header_level_1><location><page_1><loc_44><loc_70><loc_56><loc_71></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_33><loc_83><loc_67></location>Ahigh-degree of polarization of gamma-ray burst (GRB) prompt emission has been confirmed in recent years. In this paper, we apply jitter radiation to study the polarization feature of GRB prompt emission. In our framework, relativistic electrons are accelerated by turbulent acceleration. Random and small-scale magnetic fields are generated by turbulence. We further determine that the polarization property of GRB prompt emission is governed by the configuration of the random and small-scale magnetic fields. A two-dimensional compressed slab, which contains stochastic magnetic fields, is applied in our model. If the jitter condition is satisfied, the electron deflection angle in the magnetic field is very small and the electron trajectory can be treated as a straight line. A high-degree of polarization can be achieved when the angle between the line of sight and the slab plane is small. Moreover, micro-emitters with mini-jet structure are considered to be within a bulk GRB jet. The jet 'off-axis' effect is intensely sensitive to the observed polarization degree. We discuss the depolarization effect on GRB prompt emission and afterglow. We also speculate that the rapid variability of GRB prompt polarization may be correlated with the stochastic variability of the turbulent dynamo or the magnetic reconnection of plasmas.</text>
<text><location><page_1><loc_17><loc_27><loc_83><loc_31></location>Subject headings: gamma ray burst: general - radiation mechanisms: nonthermal - shock waves - turbulence</text>
<section_header_level_1><location><page_2><loc_42><loc_85><loc_58><loc_86></location>1. Introduction</section_header_level_1>
<text><location><page_2><loc_12><loc_73><loc_88><loc_82></location>One of the important properties of celestial radiation is polarization. Polarization is produced by relativistic electrons emitting in magnetic fields and can be detected by either high-energy satellites or ground-based telescopes. Through this kind of polarization research, we can investigate both the radiation mechanisms and the magnetic field characteristics of celestial objects.</text>
<text><location><page_2><loc_12><loc_48><loc_88><loc_71></location>Gamma-ray bursts (GRBs) are the most energetic explosions in the universe. Some polarization detections of GRBs in the prompt γ -ray band were performed. A linear polarization with a degree of Π = 80% ± 20% in GRB 021206 was detected by RHESSI (Coburn & Boggs 2003). GRB 041219A, observed by the International Gamma-Ray Astrophysics Laboratory, also has a high degree of polarization. Values of Π = 98% ± 33% and Π = 63% ± 30% were reported by Kalemci et al. (2007) and McGlynn et al. (2007), respectively. Recently, γ -ray prompt polarizations of three GRBs were detected by the GRB polarimeter onboard IKAROS : GRB 100826A has an average polarization degree of 27% ± 11% (Yonetoku et al. 2011); GRB 110301A and GRB 110721A have high polarization degrees of 70% ± 22% and 84 +16 -28 %, respectively (Yonetoku et al. 2012). Meanwhile, theoretical models are strongly required to constrain the physical origin of these highly polarized GRB prompt photons and to explore possible magnetic field configurations.</text>
<text><location><page_2><loc_12><loc_21><loc_88><loc_46></location>Synchrotron radiation is one kind of emission from relativistic electrons in an ordered and large-scale magnetic field. In general, the linear polarization degree is given as Π = (3 ν S + 3) / (3 ν S +5), where ν S is the synchrotron spectral index (Rybicki & Lightman 1979). Some comprehensive models of GRB polarization have been proposed. Granot (2003) studied the polarization of prompt emission in GRB 021026 considering a jet structure. A polarization degree larger than 50% can be produced in the case of an ordered magnetic field. A jet structure was also studied by Ghisellini & Lazzati (1999) and Waxman (2003). About a few percent of the polarization in GRB optical afterglows can be produced when a tangled magnetic field is introduced. Toma et al. (2009) presented a statistical study in X-ray band (60 -500 keV) from Monte Carlo simulations. If the polarization detection ratio is larger than 30% and 0 . 2 < Π < 0 . 7, synchrotron radiation in an ordered magnetic field is the favored mechanism. If the polarization detection ratio is less than 15%, a random magnetic field may be possible.</text>
<text><location><page_2><loc_12><loc_10><loc_88><loc_19></location>If the magnetic field is small-scale and randomly oriented, the isotropic emission of relativistic electrons in such a magnetic field cannot show any significant net polarization pattern. In this case, Medvedev & Loeb (1999) propose a polarization origin from interstellar scintillation. If the emission was in some magnetic patches, the measured polarization was estimated as Π = Π 0 / √ N , where Π 0 is the intrinsic polarization degree and N is the</text>
<text><location><page_3><loc_12><loc_76><loc_88><loc_86></location>patch number (Gruzinov & Waxman 1999). These studies indicate that low-degree polarization is related to tangled magnetic fields. However, we note that Lazzati & Begelman (2009) obtained a highly polarized GRB from a fragmented fireball. The pulse with high polarization, originating from a single fragment, is 10 times fainter than the brightest pulse of a GRB.</text>
<text><location><page_3><loc_12><loc_41><loc_88><loc_75></location>Despite some popular literature results on synchrotron polarization, we propose in this paper an alternative possibility to explain the high degree of polarization of GRB prompt emission. In general, jitter radiation originates from relativistic electrons accelerating in stochastic magnetic fields. As these stochastic magnetic fields are randomly distributed, the electrons feel almost the same Lorentz force on average from different directions. Therefore, in the electron radiative plane, jitter radiation is highly symmetric and the polarization degree is nearly zero. However, if the symmetric feature of radiation breaks down due to certain reasons, a strong polarization will appear in the jitter radiation. In this paper, we apply a special magnetic field slab for the jitter radiation. Although the magnetic fields in this two-dimensional slab are randomly distributed, this slab provides an asymmetric configuration such that the jitter radiation is anisotropic in the radiative plane. Thus, the jitter radiation can be highly polarized. There are two special physical points to our model: (1) a two-dimensional compressed slab as a particular magnetic field configuration, and (2) a bulk relativistic jet with a Lorentz factor Γ j and many micro-emitters with relativistic turbulent Lorentz factors Γ t within the bulk jet. Therefore, we expect the possibility of highly polarized GRB prompt emission due to the strongly anisotropic properties of the jitter radiation within a jet-in-jet structure.</text>
<text><location><page_3><loc_12><loc_10><loc_88><loc_40></location>In our scenario, with propagation and collision of internal shocks from the GRB central engine, turbulence is produced behind the shock front. Random and small-scale magnetic fields can be generated by turbulence. Those electrons can be accelerated not only by diffusive shock acceleration but also by turbulent acceleration. The radiation mechanism of relativistic electrons radiating γ -ray photons in random and small-scale magnetic fields is the so-called jitter radiation. As turbulence is important for particle acceleration, the electron energy distribution combines a power-law shape and a Maxwellian shape. Due to the domination of random and small-scale magnetic fields, jitter photons come from those micro-emitters with a jet structure. These mini-jets with turbulent Lorentz factors Γ t are within the bulk jet with a Lorentz factor Γ j . The total observed emission is all of the contributions from these mini-jets. The framework of this scenario was previously built: a small-scale turbulent dynamo was realized by hydrodynamical simulations (Schekochihin et al. 2004), jitter radiation was presented (Medvedev 2000, 2006; Kelner et al. 2013) and examined numerically (Sironi & Spitkovsky 2009; Frederiksen et al. 2010), the radiative synthetic spectra from relativistic shocks were also simulated by Martins et al.</text>
<text><location><page_4><loc_12><loc_64><loc_88><loc_86></location>(2009) and Nishikawa et al. (2011), the radiation process in a sub-Larmor scale magnetic field was re-examined by Medvedev et al. (2011), the electron energy distribution was given by Stawarz & Petrosian (2008) and Giannios & Spitkovsky (2009), turbulence-induced random and small-scale magnetic fields and related jitter radiation for GRB prompt emission were explored by Mao & Wang (2011), this radiation spectrum is fully consistent with the high-frequency spectrum derived from numerical calculations (Teraki & Takahara 2011), and GRB mini-jets were discussed by Mao & Wang (2012). Very recently, some detailed calculations of the microturbulent dynamics behind relativistic shock fronts (Lemoine 2013) and comprehensive analyses of pulses seen in Swift -Burst Alert Telescope GRB lightcurves (Bhatt & Bhattacharyya 2012) also shed light on the physics of jitter radiation, tangled magnetic fields, and relativistic turbulence.</text>
<text><location><page_4><loc_12><loc_27><loc_88><loc_63></location>We further apply our previous model (Mao & Wang 2011, 2012) to investigate GRB prompt polarization in this paper. Magnetic field topology is essential for jitter radiation properties (Reynolds et al. 2010; Retnolds & Medvedev 2012). The configuration effect of random magnetic fields was presented by Laing (1980). In that work, a tangled magnetic field in a three-dimensional cube was compressed into a two-dimensional slab. In the slab, the magnetic field is still random. The line of sight from an observer has a certain angle to the plane of magnetic slab. Thus, the symmetric feature of random magnetic fields is broken. The compressibility properties of magnetic fields were studied in detail by Hughes et al. (1985). The polarization from oblique and conical shocks was given by Cawthorne & Cobb (1990) and Nalewajko (2009). Some numerical simulations of tangled magnetic fields were also performed (Matthews & Scheuer 1990a,b). Laing (2002) developed a calculation of chaotic magnetic field compression. The polarization degrees and angles were put straightforward in some cases. In our work, we propose that turbulence appears behind the shock front. Random and small-scale magnetic fields are generated by turbulence. Mini-emitters radiate jitter photons in a bulk jet structure. Thus, the configuration of tangled magnetic fields in a compressed slab exactly matches the physical conditions presented in our proposal. We can apply the magnetic field configuration of Laing (1980, 2002) to our jitter radiation process and obtain the polarization features of GRB prompt emission.</text>
<text><location><page_4><loc_12><loc_18><loc_88><loc_26></location>We review jitter radiation and turbulent properties in Section 2.1. The polarization feature in the case of a stochastic magnetic field configuration is given in Section 2.2. The observed polarization quantities in a jet-in-jet scenario are presented in Section 2.3. We briefly summarize our results in Section 3 and we present a discussion in Section 4.</text>
<section_header_level_1><location><page_5><loc_37><loc_85><loc_63><loc_86></location>2. Polarization Processes</section_header_level_1>
<text><location><page_5><loc_12><loc_67><loc_88><loc_82></location>GRB explosion produces relativistic shocks propagating in a bulk jet. Turbulence is thought to appear behind shocks. Random and small-scale magnetic fields can be generated by turbulence. This kind of magnetic field is within one slab, which is likely to be compressed by relativistic shocks. Relativistic electrons emit jitter photons in random and small-scale magnetic fields. The linear polarization feature is determined by this specific magnetic field topology. We sum up all the contributions of those mini-emitters in the slab and the observed polarization degree can be finally obtained in jet-in-jet scenario. The main physical points are illustrated in Figure 2.</text>
<section_header_level_1><location><page_5><loc_32><loc_61><loc_68><loc_62></location>2.1. Jitter Radiation and Turbulence</section_header_level_1>
<text><location><page_5><loc_12><loc_49><loc_88><loc_58></location>We propose that jitter radiation can dominate GRB prompt emission and that random and small-scale magnetic fields are generated by turbulence (Mao & Wang 2011). In this subsection, we briefly describe the major physical processes. The radiation intensity (energy per unit frequency per unit time) of a single relativistic electron in small-scale magnetic field was given by Landau & Lifshitz (1971) as</text>
<formula><location><page_5><loc_30><loc_44><loc_88><loc_48></location>I ω = e 2 ω 2 πc 3 ∫ ∞ ω/ 2 γ 2 ∗ | w ω ' | 2 ω ' 2 (1 -ω ω ' γ 2 ∗ + ω 2 2 ω ' 2 γ 4 ∗ ) dω ' , (1)</formula>
<text><location><page_5><loc_12><loc_29><loc_88><loc_43></location>where γ -2 ∗ = ( γ -2 + ω 2 pe /ω 2 ), ω ' = ( ω/ 2)( γ -2 + θ 2 + ω 2 pe /ω 2 ), ω pe is the background plasma frequency, θ ∼ 1 /γ is the angle between the electron velocity and the radiation direction, γ is the electron Lorentz factor, ω is the radiative frequency, and w ω ' is the Fourier transform of electron acceleration term. In order to calculate the averaged acceleration term, a Fourier transform of the Lorentz force should be performed. The random and small-scale magnetic fields are introduced in the Lorentz force. Following the treatment of (Fleishman 2006) and Mao & Wang (2011), we further obtain the jitter radiation feature as</text>
<formula><location><page_5><loc_12><loc_22><loc_89><loc_28></location>I ω = e 4 m 2 c 3 γ 2 ∫ ∞ 1 / 2 γ 2 ∗ d ( ω ' ω )( ω ω ' ) 2 (1 -ω ω ' γ 2 ∗ + ω 2 2 ω ' 2 γ 4 ∗ ) ∫ dq 0 d q δ ( w ' -q 0 + qv ) K ( q ) δ [ q 0 -q 0 ( q )] , (2)</formula>
<text><location><page_5><loc_12><loc_8><loc_88><loc_22></location>where the term of K ( q ) is related to the random magnetic field. The dispersion relation q 0 = q 0 ( q ) is in the fluid field, q and q 0 are the wave-number and frequency of the disturbed fluid field, respectively, v is the electron velocity introduced in perturbation theory, and the radiation field can be linked with the fluid field by the relation ω ' = q 0 -qv . We adopt the dispersion relation of relativistic collisionless shocks presented by Milosavljevi'c et al. (2006) and find that q 0 = cq [1 + √ 1 + 4 ω 2 pe /γc 2 q 2 / 2] 1 / 2 . The relativistic electron frequency</text>
<text><location><page_6><loc_12><loc_75><loc_88><loc_86></location>is ω pe = (4 πe 2 n/ Γ sh m e ) 1 / 2 = 9 . 8 × 10 9 Γ -1 / 2 sh s -1 , where we take the value of n = 3 × 10 10 cm -3 as the number density in relativistic shocks, and Γ sh is the shock Lorentz factor. Thus, we have γc 2 q 2 /greatermuch ω pe for the case of GRB prompt emission. Finally, we obtain the relation ω = γ 2 vq (1 -cosθ k ), where θ k is the angle between the electron velocity and the fluid field direction. If v ∼ c , we have a radiation frequency range of cq/ 2 < ω < γ 2 cq .</text>
<text><location><page_6><loc_12><loc_71><loc_88><loc_75></location>The stochastic magnetic field < B ( q ) > in Equation (2) generated by turbulent cascade can be given by</text>
<formula><location><page_6><loc_35><loc_68><loc_88><loc_72></location>K ( q ) ∼ < B 2 ( q ) > ∼ ∫ ∞ q F ( q ' ) d q ' , (3)</formula>
<text><location><page_6><loc_12><loc_11><loc_88><loc_67></location>where F ( q ) ∝ q -ζ p and ζ p is the index of the turbulent energy spectrum. q is within the range q ν < q < q η . q ν is linked to the viscous dissipation and q η is related to the magnetic resistive transfer. The Prandtl number Pr = 10 -5 T 4 /n constrains the value of q by q η /q ν = Pr 1 / 2 (Schekochihin & Cowley 2007), where aT/m e c 2 = Θ, Θ ∼ Γ sh and a is the Boltzmann constant. We adopt a length scale of viscous eddies (Kumar & Narayan 2009; Narayan & Kumar 2009; Lazar et al. 2009) for GRB prompt emission and obtain q ν = 2 πl -1 eddy = 2 π ( R/ Γ sh Γ t ) -1 = 6 . 3 × 10 -10 ( R/ 10 13 cm) -1 (Γ sh / 100)(Γ t / 10) cm -1 , where Γ t is the Lorentz factor of turbulent eddies. The magnetic resistive scale is q η = 3 . 9 × 10 4 ( n/ 3 × 10 10 cm -3 ) -1 / 2 (T / 5 . 6 × 10 11 K) 2 cm -1 . In the compressed two-dimensional case, magnetic fields can be < B > = [ ∫ q η q ν q -ζ p d q ] 1 / 2 = √ 2 πq (2 -ζ p ) / 2 ν / √ ζ p -2 under the condition q η /greatermuch q ν . Through the cascade process of a turbulent fluid, turbulent energy dissipation has a hierarchical fluctuation structure. A set of inertial-range scaling laws of fully developed turbulence can be derived. From the research of She & Leveque (1994) and She & Waymire (1995), the energy spectrum index ζ p of turbulent fields is related to the cascade process number p by the universal relation of ζ p = p/ 9+2[1 -(2 / 3) p/ 3 ]. The Kolmogorov turbulence is presented as ζ p = p/ 3. This turbulent feature was found recently to be valid in the relativistic regime (Zrake & MacFadyen 2012). At the fireball radius of R ∼ 10 13 cm, taking the turbulent spectrum index of ζ p = 3 . 25 from She & Leveque (1994), we obtain a the magnetic field value of 1 . 3 × 10 6 G. In the fireball scenario, a magnetic field of 10 14 G at 10 6 cm can easily reach 10 6 G at 10 14 cm, providing powerful prompt emission (Piran 2005). This estimation is dependent on the exact shock location and on the equipartition parameters. In our model, we take a magnetic field number of 10 6 G as a reference value. As we have shown in our model, the random magnetic field is generated by turbulence and the magnetic field number is dependent on the turbulent energy spectral index ζ p . Therefore, we solve Equation (2) and obtain the radiation property I ω ∝ ω -( ζ p -2) . This radiation spectrum can be reproduced by the numerical calculations of Teraki & Takahara (2011) in high-frequency regime. The gross radiative emission should be the contribution from all of the relativistic electrons with a certain electron energy distribution. However, we note that</text>
<text><location><page_7><loc_12><loc_80><loc_88><loc_86></location>the jitter spectral index ζ p -2 of single electrons is fully determined by the fluid turbulence. Thus, the spectral index of the gross radiative emission is not related to the electron energy distribution. Finally, from Equation (2), we obtain</text>
<formula><location><page_7><loc_46><loc_76><loc_88><loc_79></location>I ω ∝ B 2 . (4)</formula>
<text><location><page_7><loc_12><loc_74><loc_79><loc_76></location>We note that the term of the magnetic field is not related to the spectral index.</text>
<section_header_level_1><location><page_7><loc_41><loc_68><loc_59><loc_69></location>2.2. Polarization</section_header_level_1>
<text><location><page_7><loc_12><loc_22><loc_88><loc_66></location>Magnetic field configurations is a dominant issue for the research of GRB radiation and polarization. In this paper, we apply the topology of random magnetic fields introduced by Laing (1980, 2002). A three-dimensional cube containing random and small-scale magnetic fields can be compressed into a two-dimensional slab by relativistic shocks. In the slab plane, the distribution of magnetic fields is still stochastic. The magnetic field vector at one point, denoted in rectangular coordinates, is B = B 0 (cos φ sin θ B , sin φ, cos φ cos θ B ), where θ B is the angle between the slab plane and the line of sight (see Figure 1) and φ is the azimuthal angle at any point randomly distributed in the slab plane. The position angle of the E -vector χ can be given as cos 2 χ = -(sin 2 θ B -tan 2 φ ) / (sin 2 θ B +tan 2 φ ). Thus, the magnetic field acting on the radiation is B = B 0 (cos 2 φ sin 2 θ B +sin 2 φ ) 1 / 2 . Because an electron obtains same acceleration on average from different directions in a random and small-scale magnetic field, the electron trajectory of jitter radiation can be approximated as a straight line (Medvedev 2000; Medvedev et al. 2011). Thus, jitter radiation is limited to the small radiation cone along the line of sight to the observer. Since the acceleration term of jitter radiation is proportional to B 2 , we can do a decomposition of jitter radiation in the electron radiation plane and obtain the polarization degree (see the detailed examination in the Appendix). If the slab is orientated so that the E -vector of the polarization radiation has a position angle of zero degrees, then the Stokes parameter U = 0. Following the magnetic field topology given by Laing (1980, 2002), we obtain Stokes parameters of single electron jitter radiation given by: I = C ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) dφ , Q = I cos2 χ = -C ∫ 2 π 0 (cos 2 φ sin 2 θ B -sin 2 φ )d φ , U = 0, and V = 0, where C = C ( γ, B 0 ). With a certain electron energy distribution N ( γ ), we obtain the following Stokes parameters of the gross jitter radiation:</text>
<formula><location><page_7><loc_27><loc_17><loc_88><loc_21></location>I = ∫ γ 2 γ 1 C ( γ, B 0 ) N ( γ ) dγ ∫ 2 π 0 (cos 2 φ sin 2 θ B +sin 2 φ ) dφ, (5)</formula>
<formula><location><page_7><loc_25><loc_12><loc_88><loc_16></location>Q = -∫ γ 2 γ 1 C ( γ, B 0 ) N ( γ ) dγ ∫ 2 π 0 (cos 2 φ sin 2 θ B -sin 2 φ ) dφ, (6)</formula>
<formula><location><page_7><loc_47><loc_10><loc_88><loc_11></location>U = 0 , (7)</formula>
<text><location><page_8><loc_12><loc_85><loc_15><loc_86></location>and</text>
<formula><location><page_8><loc_47><loc_82><loc_88><loc_84></location>V = 0 . (8)</formula>
<text><location><page_8><loc_12><loc_80><loc_65><loc_81></location>Thus, the final polarization degree of the gross jitter emission is</text>
<formula><location><page_8><loc_32><loc_72><loc_88><loc_78></location>Π = Q I = -∫ 2 π 0 (cos 2 φ sin 2 θ B -sin 2 φ ) dφ ∫ 2 π 0 (cos 2 φ sin 2 θ B +sin 2 φ ) dφ . (9)</formula>
<text><location><page_8><loc_12><loc_63><loc_88><loc_72></location>In our case, we emphasize that the magnetic field configuration is the only parameter that impacts the jitter polarization. Moreover, this polarization result is only valid in the jitter radiation case where the electron deflection angle is small (see Equation (11) in Section 4). Thus, in this two-dimensional case, we only select electrons moving roughly perpendicular to the slab plane.</text>
<text><location><page_8><loc_12><loc_48><loc_88><loc_61></location>We present synchrotron polarization of a single electron applying the same magnetic field topology in the Appendix. We also repeat the Stokes parameters of the gross synchrotron radiation given by Laing (1980): I = C ( γ, B 0 ) ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) ( ν S +1) / 2 dφ , Q = -C ( γ, B 0 )( 3 ν S +3 3 ν S +5 ) ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) ( ν S -1) / 2 (cos 2 φ sin 2 θ B -sin 2 φ ) dφ , U = 0, and V = 0, where ν S is the synchrotron spectral index. We compare synchrotron polarization and jitter polarization in Figure 2. In this paper, we neglect the effect of light propagation in a thick and highly magnetized plasma screen (Macquart & Melrose 2000).</text>
<section_header_level_1><location><page_8><loc_38><loc_41><loc_62><loc_43></location>2.3. Jet-in-jet Scenario</section_header_level_1>
<text><location><page_8><loc_12><loc_10><loc_88><loc_39></location>The mini-jets emit photons in a bulk GRB jet. We simply take into account the geometric effect of the bulk jet. The solid angle element of the jet is 2 π sin θdθ . Since observers always see the forward jet and the backward jet is not observed, the detection probability is half of the result of above the estimation. As the full opening angle is θ , we suggest an upper limit of the integral to be θ/ 2. The probability should be normalized by the entire solid angle of 4 π . Thus, the observational probability of these mini-jets in a bulk GRB jet can be calculated as P = π ∫ θ/ 2 0 sin θ ' dθ ' / 4 π = 1 / 32Γ 2 and Γ ∼ θ . The gross Lorentz factor Γ was given by Giannios et al. (2010) as Γ = 2Γ j Γ t /α 2 , where Γ j ∼ Γ sh is the Lorentz factor of the bulk jet, Γ t is the Lorentz factor of relativistic turbulence in these mini-jets, and textbf α is the 'offaxis' parameter defined as θ j = α/ Γ j . From the investigation of the mini-jets emitting angle distribution (Giannios et al. 2010), the range of α is given as 0 < α < 2. We can furthermore estimate the number of mini-jets affected by the turbulent fluid as n ( γ ) = 4 πR 2 Γ j ct cool /l 3 s , where R is the fireball radius and t cool = 6 πm e c/σ T γB 2 is the cooling timescale of relativistic electrons. The length scale of those mini-jets is l s = γ Γ t ct cool . As the number of mini-jets n ( γ ) is a function of the electron Lorentz factor γ , the electron energy distribution N e ( γ ) is</text>
<text><location><page_9><loc_12><loc_72><loc_88><loc_86></location>required to obtain a total number of mini-jets given by n = ∫ ∞ 1 n ( γ ) N e ( γ ) dγ/ ∫ ∞ 1 N e ( γ ) dγ . Due to diffusive shock acceleration, electrons can be accelerated and a power-law energy distribution is given. In our paper, turbulence is considered not only to generate magnetic fields but also to accelerate electrons and the electron energy distribution has a Maxwellian component (Stawarz & Petrosian 2008). If turbulent acceleration is considered in addition to shock acceleration, the electron energy distribution has a dual-natured shape with a Maxwellian component and a power-law component (Giannios & Spitkovsky 2009):</text>
<formula><location><page_9><loc_28><loc_67><loc_88><loc_71></location>N e ( γ ) = { Cγ 2 exp( γ/ Θ) / 2Θ 3 , γ ≤ γ th , Cγ 2 th exp( γ th / Θ)( γ/γ th ) p e / 2Θ 3 , γ > γ th , (10)</formula>
<text><location><page_9><loc_12><loc_57><loc_88><loc_66></location>where C is a constant. In the case that only a fraction of electrons have a non-thermal distribution, we take the characteristic temperature to be Θ = kT/m e c 2 ∼ 100. In our calculation, we adopt γ th = 10 3 ; p e = 2 . 2 is the power-law index. Combined with the observational probability P and the total number n of mini-jets affected by turbulence, the final observed polarization degree is Π obs = nP Π.</text>
<section_header_level_1><location><page_9><loc_45><loc_50><loc_55><loc_52></location>3. Results</section_header_level_1>
<text><location><page_9><loc_12><loc_25><loc_88><loc_48></location>The intrinsic polarization results of GRB prompt emission without jet effects are shown in Figure 2. The jitter polarization degree is strongly dependent on θ B , which is the angle between the line of sight and the slab plane. If the line of sight is perpendicular to the slab plane, we successfully obtain jitter photons, but jitter radiation in the electron radiative plane is symmetric and the polarization degree is zero. Except in this extreme case, the degree of polarization can be measured with different values of θ B . With the same magnetic field configuration, we can compare jitter polarization and synchrotron polarization. Both jitter polarization and synchrotron polarization are related to θ B . On the other hand, as we discussed in Section 2.2, jitter polarization is not related to the radiation spectrum and it can reach a maximum value of 100 percent. Synchrotron polarization (see details in the Appendix) is related to the radiation spectral index and its maximum value is ( ν S +3) / ( ν S + 5). The cases of ν s = 2 . 0 , 1 . 0, and 0.6 are shown in Figure 2 as examples.</text>
<text><location><page_9><loc_12><loc_10><loc_88><loc_23></location>We further provide examples of the observed jitter polarization degree in our jet-in-jet scenario shown in Figures 3 and 4. Different jet 'off-axis' parameters, 1.55, 1.3 and 1.0, are used to calculate the observed polarization degree shown in Figure 3. Here, we take Γ sh = 100, Γ t = 10, and R = 10 13 cm. We show that the polarization degree is significantly sensitive to the jet 'off-axis' parameter. A stronger jet 'off-axis' effect yields a stronger observed polarization degree. In Figure 4, we present examples of jitter polarization results affected by the shock Lorentz factor Γ sh . We fix the 'off-axis' parameter as 1.3, Γ t = 10,</text>
<text><location><page_10><loc_12><loc_76><loc_88><loc_86></location>and R = 10 13 cm. Shock Lorentz factor values of 85, 100, and 120 are adopted. We see that a low polarization degree can be induced by a large shock Lorentz factor. This fact suggest that a large shock Lorentz factor provides powerful radiation along the jet axis while a powerful polarization can be measured in the strong off-axis case, which has a relatively small Lorentz factor and weak radiation.</text>
<text><location><page_10><loc_12><loc_33><loc_88><loc_75></location>It is also useful to review the GRB polarization feature under the mechanism of synchrotron radiation in the jet structure. Gruzinov (1999) and Sari (1999) proposed the possibility of high-degree GRB polarization. Granot (2003) comprehensively discussed different GRB jet polarization cases. Here, for simplicity, we apply the model of Gruzinov (1999) to illustrate the configuration differences between the tangled magnetic field and the ordered magnetic field. The polarization degree derived from the magnetic field parallel/perpendicular to the jet direction was given as Π = Π 0 sin 2 α B ( B 2 ‖ -0 . 5 B 2 ⊥ ) / [ B 2 ‖ sin 2 α B + 0 . 5 B 2 ⊥ (1 + cos 2 α B )], where B ‖ is the magnetic field parallel to the shock propagation direction, B ⊥ is the magnetic field perpendicular to the shock propagation, and α B = π/ 2 -θ B is the angle between the line of sight from observer and the direction of the shock propagation (Gruzinov 1999). In our model, we have fully obtained the polarization feature of GRB prompt emission in the case of B ‖ /lessmuch B ⊥ (Laing 1980, 2002) and this condition is necessary for jitter radiation. If B ‖ /greatermuch B ⊥ , the polarization degree is Π ∼ Π 0 , which is the result obtained from an ordered magnetic field aligned with the jet direction. This result reproduces exactly the polarization degree of synchrotron radiation as Π 0 = (3 ν S +3) / (3 ν S +5); the electron energy distribution has a power-law distribution with a power-law index p e and ν S = ( p e -1) / 2. Considering a certain jet structure and line of sight effects, a high degree of GRB prompt polarization can be obtained (Granot 2003; Lazzati & Begelman 2009). In our paper, the two-dimensional magnetic slab and the jet-in-jet structure provide the possibility of asymmetric radiation in the electron radiative plane. Thus, the GRB prompt emission can be highly polarized as well.</text>
<section_header_level_1><location><page_10><loc_35><loc_27><loc_65><loc_29></location>4. Discussion and Conclusions</section_header_level_1>
<text><location><page_10><loc_12><loc_11><loc_88><loc_25></location>Relativistic electrons accelerated by diffusive shock acceleration with a power-law energy distribution can emit high-energy photons in an ordered magnetic field. Therefore, it is possible to explain the high-degree polarization detected in GRB prompt emission by synchrotron radiation. Alternatively, we present in this paper that turbulence can accelerate electrons and generate random and small-scale magnetic fields. The relativistic electrons emit X-ray/ γ -ray jitter photons in the jet-in-jet structure. Some important physical components, such as turbulence behind the shock front, random and small-scale magnetic fields,</text>
<text><location><page_11><loc_12><loc_72><loc_88><loc_86></location>the electron energy distribution, and mini-jets, are self-consistently organized in the process of jitter radiation. We obtain a high-degree polarization of GRB prompt emission through jitter radiation considering a two-dimensional compressed magnetic field configuration. The intrinsic polarization degree is a function of the angle between the line of sight and the slab plane, and large polarization values can be achieved in the case of small angles. Moreover, the final observed polarization degree in the jet-in-jet scenario is affected by the 'off-axis' parameter and the shock Lorentz factor.</text>
<text><location><page_11><loc_12><loc_61><loc_88><loc_71></location>In this paper, the electron trajectory of jitter radiation in random and small-scale magnetic fields is assumed to be a straight line. In other words, the condition of θ d /lessmuch 1 /γ should be satisfied by jitter radiation (Medvedev et al. 2011). Here, θ d = eBλ B /γm e c 2 is the deflection angle of electrons in a magnetic field, and λ B ∼ c/ω pe is the length scale of the magnetic field. We obtain</text>
<formula><location><page_11><loc_28><loc_56><loc_88><loc_61></location>θ d = ( B 1 . 2 × 10 6 G )( n 1 . 5 × 10 19 cm -3 ) -1 / 2 ( Γ sh 100 ) 1 / 2 γ -1 . (11)</formula>
<text><location><page_11><loc_12><loc_33><loc_88><loc_56></location>This condition is strongly dependent on the magnetic field and the electron number density. We constrain the condition of jitter radiation in an example below. The electron number density is given by n = N/ ∆Ω R 2 ∆ R . N = 1 . 0 × 10 52 ∼ 6 × 10 54 is the total number of electrons in the radiative region (Kumar & Narayan 2009). We take the fireball radius to be R = 10 13 cm and fireball shell to be ∆ R = 10 10 cm. If the jet opening angle is about 5 degree, we obtain a solid angle ∆Ω = 3 . 3 × 10 -4 and the estimated value of number density is n = 3 . 0 × 10 20 cm -3 ∼ 1 . 8 × 10 22 cm -3 . Thus, θ d /lessmuch 1 /γ and the electron trajectory can be treated as a straight line. In order to satisfy this jitter condition in the two-dimensional case, we select electrons moving roughly perpendicular to the slab plane so that the electron deflection angle is small. The general case of electrons moving in a random walk in a stochastic magnetic field with a large deflection angle was discussed by Fleishman (2006) and numerical simulations may be required to solve this complicated issue.</text>
<text><location><page_11><loc_12><loc_10><loc_88><loc_31></location>It is expected that the so-called depolarization due to the Faraday rotation of the polarization screen (Burn 1966) can be a powerful tool to further constrain the source structure and magnetic field topology. In general, stochastic Faraday rotation creates a polarization degree of Π ∝ exp( -λ 4 ), where λ is wavelength (Melrose & Macquart 1998). Tribble (1991) discussed a power-law structure function for a Faraday rotation measurement. The polarization degree was given as Π ∝ λ -4 /m , where m is related to the turbulent cascade. Even if we consider a polarization fluctuation proportional to λ , the final polarization degree still dramatically decreases as Π ∝ λ -2 . 2 if we adopt a typical value of m = ζ p -2 given in our model. Therefore, GRB prompt polarization measured in the soft band is about 20% of that measured in the hard band. This prediction can be examined by future observations if GRB prompt polarization measurements can be performed simultaneously in different</text>
<text><location><page_12><loc_12><loc_44><loc_88><loc_86></location>energy bands. This simple analysis of the depolarization effect also indicates that GRB prompt polarization in optical bands is nearly impossible detect even if GRB is highly polarized in high-energy bands. On the other hand, the polarization of GRB optical afterglows was detected. The radiation case of external shocks of GRBs sweeping into the surrounding interstellar medium is beyond the scope of this paper. Here, we make some simple speculations. As optical afterglow is onset at early times after the GRB is triggered, and the jet is strongly anisotropic with a narrow beaming angle. Thus, the optical polarization degree can reach values of 10% (Uehara et al. 2012) and even higher polarization degrees were expected (Steele et al. 2009). In late times after a GRB is triggered, the beaming angle of the jet is wide and the jet anisotropy is not prominent. Thus, the polarization of the optical afterglow is weak 1 (Covino et al. 1999; Hjorth et al. 1999; Wijers et al. 1999). Moreover, high-energy photons from GRB prompt emission can pass through a dense medium without being strongly absorbed. Thus, the depolarization effect is weak and a high polarization degree can be detected, while UV/optical photons of GRB afterglows can be strongly absorbed by the surrounding dense material. Therefore, even though the initial polarization degree of GRB optical afterglows is very high, the external depolarization effect is strong as the diffraction in a Faraday prism is taken into account (Sazonov 1969; Macquart & Melrose 2000). Thus, due to the strong depolarization effect, the detected polarization degree of GRB optical afterglows is low. Further quantitative computations can be executed since the magnetic field configuration adopted in this paper is still valid for the depolarization cases mentioned above (Rossi et al. 2004).</text>
<text><location><page_12><loc_12><loc_17><loc_88><loc_43></location>Rapid time variations of the polarization angle and polarization degree have been measured either in GRB prompt emission cases (Gotz et al. (2009) for GRB 041219A and Yonetoku et al. (2011) for GRB 100826A) or in GRB afterglow cases (Rol et al. (2000) for GRB 990712, Greiner et al. (2003) for GRB 030329, and Wiersema et al. (2012) for GRB 091018). The observed timescale of polarization variation in GRB prompt emission is about 50-100 s (Yonetoku et al. 2011), which corresponds to an intrinsic timescale of 0.5-1 s. Here, we list three possibilities to explain this rapid variation. First, GRB helical jets with helical magnetic fields and helical rotation generated by black holes (Mizuno et al. 2012) should be considered. With a helical jet, the slab may rotate and the magnetic field configuration may change quickly. Then, rapid polarization variation occurs. Second, Lazzati & Begelman (2009) proposed that faint pulses of GRB prompt emission are a main contributor to the polarization. If this is true, we can obtain the rapid time variation of the polarization since the pulses shown in GRB prompt lightcurves show rapid variation; Third, the turbulent feature</text>
<text><location><page_13><loc_12><loc_68><loc_88><loc_86></location>in the slab should be revisited. We estimate the variability of GRB prompt polarization due to the variability of stochastic eddies as δt ∼ l eddy /c s . Given l eddy ∼ R/ Γ j Γ t and c s ∼ c/ √ 3, δt is about 1.7 s, which can be comparable to the observational timescale. Moreover, small-scale fluid turbulence and magnetic reconnection was suggested by Matthews & Scheuer (1990b). Recently, Zhang & Yan (2011) and McKinney & Uzdensky (2012) illustrated the possibility of magnetic reconnection for GRB energy dissipation. We suggest that small-scale magnetic reconnection in the compressed slab is likely to affect the rapid polarization variation. More observations (TSUBAME, NuSTAR, Astro-H) and quantitative explanations in detail are expected in the future.</text>
<text><location><page_13><loc_12><loc_44><loc_88><loc_65></location>We thank the referee for his/her helpful suggestions and comments. We are grateful to Teraki, Y., Toma, K., Nagataki, S., Ito, H., Ono, M., and Lee, S.-H. for their useful discussions. The numerical computation in this work was carried out at the Yukawa Institute Computer Facility. This work is supported by Grants-in-Aid for Foreign JSPS Fellow (Number 24.02022). We acknowledge support from the Ministry of Education, Culture, Sports, Science and Technology (No. 23105709), the Japan Society for the Promotion of Science (No. 19104006 and No. 23340069), and the Global COE Program, The Next Generation of Physics, Spun from University and Emergence, from MEXT of Japan. J. Wang is supported by the National Basic Research Program of China (973 Program 2009CB824800), the National Natural Science Foundation of China 11133006, 11163006, 11173054, and the Policy Research Program of the Chinese Academy of Sciences (KJCX2-YW-T24).</text>
<section_header_level_1><location><page_13><loc_18><loc_37><loc_82><loc_39></location>A. Polarization of Single Electrons in A Random Magnetic Field</section_header_level_1>
<text><location><page_13><loc_12><loc_30><loc_88><loc_35></location>In this Appendix, we first introduce the polarization feature of single relativistic electrons in a magnetic field assuming jitter condition. We repeat the radiation property by Landau & Lifshitz (1971) as</text>
<formula><location><page_13><loc_41><loc_26><loc_88><loc_30></location>E ω = 1 2 π ∫ Ee iωt dt, (A1)</formula>
<text><location><page_13><loc_12><loc_21><loc_88><loc_26></location>where the retarded time is t ' = t -R ( t ' ) /c ∼ = t -R 0 /c + n · r ( t ' ) /c ∼ = t -R 0 /c + n · v t ' /c ; n is the radiation direction. If we take dt = dt ' (1 -n · v /c ), we obtain</text>
<formula><location><page_13><loc_22><loc_16><loc_88><loc_21></location>E ω = e c 2 e ikR 0 R 0 (1 -n · v /c ) 2 ∫ n ×{ ( n -v /c ) × w ( t ' ) } e iωt ' (1 -n · v /c ) dt ' . (A2)</formula>
<text><location><page_13><loc_12><loc_13><loc_58><loc_16></location>If we adopt the notation ω ' = ω (1 -n · v /c ), we obtain</text>
<formula><location><page_13><loc_32><loc_9><loc_88><loc_13></location>E ω = e c 2 e ikR 0 R 0 ( ω ω ' ) 2 n ×{ ( n -v /c ) × w ω ' } . (A3)</formula>
<text><location><page_14><loc_12><loc_72><loc_88><loc_86></location>The acceleration term is w ω ' = e v × B /γm e c . The electron trajectory is necessary to obtain the acceleration term and the calculation in Equation (A3). If the electron trajectory can be treated as a straight line in a magnetic field (see Equation (11) of jitter radiation condition), we have a compressed magnetic slab plane with an angle of θ B to the radiative X -Y plane, and the electron velocity is perpendicular to the slab plane since the electron deflection angle of the jitter radiation is smaller than 1 /γ . The jitter radiation direction follows the direction of the electron. Thus, we obtain the X -axis component as</text>
<formula><location><page_14><loc_40><loc_67><loc_88><loc_71></location>E x = e 2 B y 2 γ 3 m e c 2 ( ω ω ' ) 2 e ikR 0 R 0 (A4)</formula>
<text><location><page_14><loc_12><loc_65><loc_36><loc_66></location>and the Y -axis component as</text>
<formula><location><page_14><loc_39><loc_60><loc_88><loc_63></location>E y = -e 2 B x 2 γ 3 m e c 2 ( ω ω ' ) 2 e ikR 0 R 0 . (A5)</formula>
<text><location><page_14><loc_12><loc_56><loc_82><loc_58></location>The radiation intensity is I = c | E | 2 R 2 0 / 2 π . The Stokes parameters can be defined as</text>
<formula><location><page_14><loc_27><loc_52><loc_88><loc_56></location>I = < E x E ∗ x > + < E y E ∗ y > = e 4 8 πγ 6 m 2 e c 3 ( ω ω ' ) 4 ( B 2 x + B 2 y ) (A6)</formula>
<text><location><page_14><loc_12><loc_49><loc_15><loc_50></location>and</text>
<formula><location><page_14><loc_26><loc_45><loc_88><loc_49></location>Q = < E x E ∗ x > -< E y E ∗ y > = e 4 8 πγ 6 m 2 e c 3 ( ω ω ' ) 4 ( B 2 y -B 2 x ) . (A7)</formula>
<text><location><page_14><loc_12><loc_39><loc_88><loc_45></location>From Section 2.2, we know B x = B 0 cos φ sin θ B and B y = B 0 sin φ . Finally, we obtain the jitter polarization Π = Q/I , which is only related to the configuration of the magnetic field; Equation (9) is verified.</text>
<text><location><page_14><loc_12><loc_30><loc_88><loc_38></location>In this Appendix, we also review the synchrotron polarization of a single electron. We keep the same random magnetic field topology used in the jitter polarization case to calculate the synchrotron polarization and we can repeat the calculation of Laing (1980). The radiation intensity of the synchrotron mechanism is</text>
<formula><location><page_14><loc_36><loc_25><loc_88><loc_30></location>I = 2 π √ 3 e 2 ν L c [ ν ν c ∫ ∞ ν/ν c K 5 / 3 ( t ) dt ] , (A8)</formula>
<text><location><page_14><loc_12><loc_20><loc_88><loc_24></location>where ν c = (3 / 2) γ 2 ν L , ν L = eB/ (2 πm e c ) is the Larmor frequency ,and K is a modified Bessel function. The synchrotron polarization of a single electron is</text>
<formula><location><page_14><loc_42><loc_13><loc_88><loc_19></location>Π = K 2 / 3 ( ν/ν c ) ∫ ∞ ν/ν c K 5 / 3 ( t ) dt , (A9)</formula>
<text><location><page_14><loc_12><loc_10><loc_95><loc_13></location>related to the magnetic field, electron Lorentz factor γ and radiation frequency ν (Rybicki & Lightman 1979).</text>
<text><location><page_15><loc_12><loc_64><loc_88><loc_86></location>In order to compare synchrotron polarization with jitter polarization, we apply the same magnetic field topology described in Section 2.2 to synchrotron polarization; our results are shown in Figure 5. In the calculation, we fix the magnetic field value at 1 . 3 × 10 6 G. For a given θ B , the degree of synchrotron polarization increases, if the radiation is toward a higher frequency ν and/or the electron Lorentz factor γ tends toward smaller values. This property is typical of synchrotron polarization of single electrons. In Figure 5, we plot the jitter polarization as well, which is independent of the radiation frequency ν and the electron Lorentz factor γ . Even though synchrotron polarization degrees can be coincidentally the same as the jitter polarization degree by adjusting the parameters of ν and γ , we emphasize that jitter polarization and synchrotron polarization are physically different because jitter radiation and synchrotron radiation are two different radiation mechanisms.</text>
<text><location><page_15><loc_12><loc_57><loc_88><loc_63></location>If the synchrotron power-law spectrum with a power-law index ν S is given and an electron energy distribution is assumed to be a power-law with an index of 2 ν S + 1, we obtain the Stokes parameters of the gross electrons:</text>
<formula><location><page_15><loc_32><loc_52><loc_88><loc_56></location>I = C ∫ 2 π 0 (cos 2 φ sin 2 θ B +sin 2 φ ) ( ν s +1) / 2 dφ, (A10)</formula>
<formula><location><page_15><loc_15><loc_47><loc_88><loc_51></location>Q = -C (3 ν S +3) (3 ν S +5) ∫ 2 π 0 (cos 2 φ sin 2 θ B +sin 2 φ ) ( ν s -1) / 2 (cos 2 φ sin 2 θ B -sin 2 φ ) dφ, (A11)</formula>
<formula><location><page_15><loc_47><loc_45><loc_88><loc_46></location>U = 0 , (A12)</formula>
<text><location><page_15><loc_12><loc_42><loc_15><loc_44></location>and</text>
<formula><location><page_15><loc_47><loc_40><loc_88><loc_42></location>V = 0 , (A13)</formula>
<text><location><page_15><loc_12><loc_37><loc_88><loc_39></location>where C is constant. Thus, the final polarization degree of the gross synchrotron emission is</text>
<formula><location><page_15><loc_14><loc_30><loc_88><loc_36></location>Π = Q I = -(3 ν +3) (3 ν s +5) ∫ 2 π 0 (cos 2 φ sin 2 θ B +sin 2 φ ) ( ν s -1) / 2 (cos 2 φ sin 2 θ B -sin 2 φ ) dφ ∫ 2 π 0 (cos 2 φ sin 2 θ B +sin 2 φ ) ( ν s +1) / 2 dφ . (A14)</formula>
<text><location><page_15><loc_12><loc_29><loc_78><loc_30></location>These are the results given by Laing (1980) and we also plot them in Figure 2.</text>
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<figure>
<location><page_20><loc_17><loc_49><loc_78><loc_70></location>
<caption>Fig. 1.- GRB prompt emission and polarization within a compressed slab. Shock propagation is in the bulk jet structure and turbulence occurs behind the shock front. Random and small-scale magnetic field are generated by turbulence in a three-dimensional cube. This cube can be compressed to be a two-dimensional slab. GRB prompt emission is the total emission from those mini-jets. The GRB prompt polarization feature is dependent on the magnetic field configuration. B x = B 0 cos φ sin θ B and B y = B 0 sin φ are two components in the slab plane, where φ is the azimuthal angle at any point randomly distributed in the slab plane (Laing 1980). The angle between the line of sight from the observer and the slab plane is labeled as θ B .</caption>
</figure>
<figure>
<location><page_21><loc_12><loc_33><loc_86><loc_73></location>
<caption>Fig. 2.- Intrinsic polarization degree as a function of θ B . The solid line (red) denotes the polarization result of jitter radiation. The long-dashed line (blue), the short-dashed line (pink), and the dotted line (cyan) denote the polarization results calculated from synchrotron radiation with a spectral index of 2.0, 1.0, and 0.6, respectively.</caption>
</figure>
<figure>
<location><page_22><loc_12><loc_33><loc_86><loc_72></location>
<caption>Fig. 3.- Observational jet 'off-axis' effect on GRB prompt polarization. The solid line (red), the long-dashed line (blue), and the short-dashed line (pink) denote the jitter polarization results given by 'off-axis' parameter values of 1.55, 1.3, and 1.0, respectively. The shock Lorentz factor Γ sh is fixed at 100.</caption>
</figure>
<figure>
<location><page_23><loc_12><loc_33><loc_86><loc_72></location>
<caption>Fig. 4.- Shock Lorentz factor effect on GRB prompt polarization. The solid line (red), the long-dashed line (blue), and the short-dashed line denote the jitter polarization results given by shock Lorentz factors Γ sh of 85, 100, and 120, respectively. The 'off-axis' parameter is taken to be 1.3.</caption>
</figure>
<figure>
<location><page_24><loc_12><loc_23><loc_69><loc_86></location>
<caption>Fig. 5.- Synchrotron polarization vs jitter polarization for a single electron. Top panel: synchrotron polarization degree results are calculated as a function of θ B with radiation frequencies of ν = 1 keV, ν = 50 keV, ν = 250 keV, ν = 500 keV, and ν = 1 MeV denoted by the long-dashed line (blue), the short-dashed line (pink), the dotted line (cyan), the long-dash-dotted line (yellow), and the short-dash-dotted line (black), respectively. The electron Lorentz factor is fixed at γ = 10 3 . Bottom panel: synchrotron polarization degree results calculated as a function of θ B with electron Lorentz factors γ = 500, γ = 10 3 , and γ = 10 4 denoted by the long-dashed line (blue), the short-dashed line (pink), and the dotted line (cyan), respectively. The radiation frequency is fixed at ν = 500 keV. The jitter polarization denoted by the solid line (red) is shown in both panels as well.</caption>
</figure>
<text><location><page_24><loc_39><loc_23><loc_40><loc_24></location>B</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Ahigh-degree of polarization of gamma-ray burst (GRB) prompt emission has been confirmed in recent years. In this paper, we apply jitter radiation to study the polarization feature of GRB prompt emission. In our framework, relativistic electrons are accelerated by turbulent acceleration. Random and small-scale magnetic fields are generated by turbulence. We further determine that the polarization property of GRB prompt emission is governed by the configuration of the random and small-scale magnetic fields. A two-dimensional compressed slab, which contains stochastic magnetic fields, is applied in our model. If the jitter condition is satisfied, the electron deflection angle in the magnetic field is very small and the electron trajectory can be treated as a straight line. A high-degree of polarization can be achieved when the angle between the line of sight and the slab plane is small. Moreover, micro-emitters with mini-jet structure are considered to be within a bulk GRB jet. The jet 'off-axis' effect is intensely sensitive to the observed polarization degree. We discuss the depolarization effect on GRB prompt emission and afterglow. We also speculate that the rapid variability of GRB prompt polarization may be correlated with the stochastic variability of the turbulent dynamo or the magnetic reconnection of plasmas. Subject headings: gamma ray burst: general - radiation mechanisms: nonthermal - shock waves - turbulence",
"pages": [
1
]
},
{
"title": "Application of Jitter Radiation: Gamma-ray Burst Prompt Polarization",
"content": "Jirong Mao 1 , 2 , 3 and Jiancheng Wang 2 , 3 [email protected]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "One of the important properties of celestial radiation is polarization. Polarization is produced by relativistic electrons emitting in magnetic fields and can be detected by either high-energy satellites or ground-based telescopes. Through this kind of polarization research, we can investigate both the radiation mechanisms and the magnetic field characteristics of celestial objects. Gamma-ray bursts (GRBs) are the most energetic explosions in the universe. Some polarization detections of GRBs in the prompt γ -ray band were performed. A linear polarization with a degree of Π = 80% ± 20% in GRB 021206 was detected by RHESSI (Coburn & Boggs 2003). GRB 041219A, observed by the International Gamma-Ray Astrophysics Laboratory, also has a high degree of polarization. Values of Π = 98% ± 33% and Π = 63% ± 30% were reported by Kalemci et al. (2007) and McGlynn et al. (2007), respectively. Recently, γ -ray prompt polarizations of three GRBs were detected by the GRB polarimeter onboard IKAROS : GRB 100826A has an average polarization degree of 27% ± 11% (Yonetoku et al. 2011); GRB 110301A and GRB 110721A have high polarization degrees of 70% ± 22% and 84 +16 -28 %, respectively (Yonetoku et al. 2012). Meanwhile, theoretical models are strongly required to constrain the physical origin of these highly polarized GRB prompt photons and to explore possible magnetic field configurations. Synchrotron radiation is one kind of emission from relativistic electrons in an ordered and large-scale magnetic field. In general, the linear polarization degree is given as Π = (3 ν S + 3) / (3 ν S +5), where ν S is the synchrotron spectral index (Rybicki & Lightman 1979). Some comprehensive models of GRB polarization have been proposed. Granot (2003) studied the polarization of prompt emission in GRB 021026 considering a jet structure. A polarization degree larger than 50% can be produced in the case of an ordered magnetic field. A jet structure was also studied by Ghisellini & Lazzati (1999) and Waxman (2003). About a few percent of the polarization in GRB optical afterglows can be produced when a tangled magnetic field is introduced. Toma et al. (2009) presented a statistical study in X-ray band (60 -500 keV) from Monte Carlo simulations. If the polarization detection ratio is larger than 30% and 0 . 2 < Π < 0 . 7, synchrotron radiation in an ordered magnetic field is the favored mechanism. If the polarization detection ratio is less than 15%, a random magnetic field may be possible. If the magnetic field is small-scale and randomly oriented, the isotropic emission of relativistic electrons in such a magnetic field cannot show any significant net polarization pattern. In this case, Medvedev & Loeb (1999) propose a polarization origin from interstellar scintillation. If the emission was in some magnetic patches, the measured polarization was estimated as Π = Π 0 / √ N , where Π 0 is the intrinsic polarization degree and N is the patch number (Gruzinov & Waxman 1999). These studies indicate that low-degree polarization is related to tangled magnetic fields. However, we note that Lazzati & Begelman (2009) obtained a highly polarized GRB from a fragmented fireball. The pulse with high polarization, originating from a single fragment, is 10 times fainter than the brightest pulse of a GRB. Despite some popular literature results on synchrotron polarization, we propose in this paper an alternative possibility to explain the high degree of polarization of GRB prompt emission. In general, jitter radiation originates from relativistic electrons accelerating in stochastic magnetic fields. As these stochastic magnetic fields are randomly distributed, the electrons feel almost the same Lorentz force on average from different directions. Therefore, in the electron radiative plane, jitter radiation is highly symmetric and the polarization degree is nearly zero. However, if the symmetric feature of radiation breaks down due to certain reasons, a strong polarization will appear in the jitter radiation. In this paper, we apply a special magnetic field slab for the jitter radiation. Although the magnetic fields in this two-dimensional slab are randomly distributed, this slab provides an asymmetric configuration such that the jitter radiation is anisotropic in the radiative plane. Thus, the jitter radiation can be highly polarized. There are two special physical points to our model: (1) a two-dimensional compressed slab as a particular magnetic field configuration, and (2) a bulk relativistic jet with a Lorentz factor Γ j and many micro-emitters with relativistic turbulent Lorentz factors Γ t within the bulk jet. Therefore, we expect the possibility of highly polarized GRB prompt emission due to the strongly anisotropic properties of the jitter radiation within a jet-in-jet structure. In our scenario, with propagation and collision of internal shocks from the GRB central engine, turbulence is produced behind the shock front. Random and small-scale magnetic fields can be generated by turbulence. Those electrons can be accelerated not only by diffusive shock acceleration but also by turbulent acceleration. The radiation mechanism of relativistic electrons radiating γ -ray photons in random and small-scale magnetic fields is the so-called jitter radiation. As turbulence is important for particle acceleration, the electron energy distribution combines a power-law shape and a Maxwellian shape. Due to the domination of random and small-scale magnetic fields, jitter photons come from those micro-emitters with a jet structure. These mini-jets with turbulent Lorentz factors Γ t are within the bulk jet with a Lorentz factor Γ j . The total observed emission is all of the contributions from these mini-jets. The framework of this scenario was previously built: a small-scale turbulent dynamo was realized by hydrodynamical simulations (Schekochihin et al. 2004), jitter radiation was presented (Medvedev 2000, 2006; Kelner et al. 2013) and examined numerically (Sironi & Spitkovsky 2009; Frederiksen et al. 2010), the radiative synthetic spectra from relativistic shocks were also simulated by Martins et al. (2009) and Nishikawa et al. (2011), the radiation process in a sub-Larmor scale magnetic field was re-examined by Medvedev et al. (2011), the electron energy distribution was given by Stawarz & Petrosian (2008) and Giannios & Spitkovsky (2009), turbulence-induced random and small-scale magnetic fields and related jitter radiation for GRB prompt emission were explored by Mao & Wang (2011), this radiation spectrum is fully consistent with the high-frequency spectrum derived from numerical calculations (Teraki & Takahara 2011), and GRB mini-jets were discussed by Mao & Wang (2012). Very recently, some detailed calculations of the microturbulent dynamics behind relativistic shock fronts (Lemoine 2013) and comprehensive analyses of pulses seen in Swift -Burst Alert Telescope GRB lightcurves (Bhatt & Bhattacharyya 2012) also shed light on the physics of jitter radiation, tangled magnetic fields, and relativistic turbulence. We further apply our previous model (Mao & Wang 2011, 2012) to investigate GRB prompt polarization in this paper. Magnetic field topology is essential for jitter radiation properties (Reynolds et al. 2010; Retnolds & Medvedev 2012). The configuration effect of random magnetic fields was presented by Laing (1980). In that work, a tangled magnetic field in a three-dimensional cube was compressed into a two-dimensional slab. In the slab, the magnetic field is still random. The line of sight from an observer has a certain angle to the plane of magnetic slab. Thus, the symmetric feature of random magnetic fields is broken. The compressibility properties of magnetic fields were studied in detail by Hughes et al. (1985). The polarization from oblique and conical shocks was given by Cawthorne & Cobb (1990) and Nalewajko (2009). Some numerical simulations of tangled magnetic fields were also performed (Matthews & Scheuer 1990a,b). Laing (2002) developed a calculation of chaotic magnetic field compression. The polarization degrees and angles were put straightforward in some cases. In our work, we propose that turbulence appears behind the shock front. Random and small-scale magnetic fields are generated by turbulence. Mini-emitters radiate jitter photons in a bulk jet structure. Thus, the configuration of tangled magnetic fields in a compressed slab exactly matches the physical conditions presented in our proposal. We can apply the magnetic field configuration of Laing (1980, 2002) to our jitter radiation process and obtain the polarization features of GRB prompt emission. We review jitter radiation and turbulent properties in Section 2.1. The polarization feature in the case of a stochastic magnetic field configuration is given in Section 2.2. The observed polarization quantities in a jet-in-jet scenario are presented in Section 2.3. We briefly summarize our results in Section 3 and we present a discussion in Section 4.",
"pages": [
2,
3,
4
]
},
{
"title": "2. Polarization Processes",
"content": "GRB explosion produces relativistic shocks propagating in a bulk jet. Turbulence is thought to appear behind shocks. Random and small-scale magnetic fields can be generated by turbulence. This kind of magnetic field is within one slab, which is likely to be compressed by relativistic shocks. Relativistic electrons emit jitter photons in random and small-scale magnetic fields. The linear polarization feature is determined by this specific magnetic field topology. We sum up all the contributions of those mini-emitters in the slab and the observed polarization degree can be finally obtained in jet-in-jet scenario. The main physical points are illustrated in Figure 2.",
"pages": [
5
]
},
{
"title": "2.1. Jitter Radiation and Turbulence",
"content": "We propose that jitter radiation can dominate GRB prompt emission and that random and small-scale magnetic fields are generated by turbulence (Mao & Wang 2011). In this subsection, we briefly describe the major physical processes. The radiation intensity (energy per unit frequency per unit time) of a single relativistic electron in small-scale magnetic field was given by Landau & Lifshitz (1971) as where γ -2 ∗ = ( γ -2 + ω 2 pe /ω 2 ), ω ' = ( ω/ 2)( γ -2 + θ 2 + ω 2 pe /ω 2 ), ω pe is the background plasma frequency, θ ∼ 1 /γ is the angle between the electron velocity and the radiation direction, γ is the electron Lorentz factor, ω is the radiative frequency, and w ω ' is the Fourier transform of electron acceleration term. In order to calculate the averaged acceleration term, a Fourier transform of the Lorentz force should be performed. The random and small-scale magnetic fields are introduced in the Lorentz force. Following the treatment of (Fleishman 2006) and Mao & Wang (2011), we further obtain the jitter radiation feature as where the term of K ( q ) is related to the random magnetic field. The dispersion relation q 0 = q 0 ( q ) is in the fluid field, q and q 0 are the wave-number and frequency of the disturbed fluid field, respectively, v is the electron velocity introduced in perturbation theory, and the radiation field can be linked with the fluid field by the relation ω ' = q 0 -qv . We adopt the dispersion relation of relativistic collisionless shocks presented by Milosavljevi'c et al. (2006) and find that q 0 = cq [1 + √ 1 + 4 ω 2 pe /γc 2 q 2 / 2] 1 / 2 . The relativistic electron frequency is ω pe = (4 πe 2 n/ Γ sh m e ) 1 / 2 = 9 . 8 × 10 9 Γ -1 / 2 sh s -1 , where we take the value of n = 3 × 10 10 cm -3 as the number density in relativistic shocks, and Γ sh is the shock Lorentz factor. Thus, we have γc 2 q 2 /greatermuch ω pe for the case of GRB prompt emission. Finally, we obtain the relation ω = γ 2 vq (1 -cosθ k ), where θ k is the angle between the electron velocity and the fluid field direction. If v ∼ c , we have a radiation frequency range of cq/ 2 < ω < γ 2 cq . The stochastic magnetic field < B ( q ) > in Equation (2) generated by turbulent cascade can be given by where F ( q ) ∝ q -ζ p and ζ p is the index of the turbulent energy spectrum. q is within the range q ν < q < q η . q ν is linked to the viscous dissipation and q η is related to the magnetic resistive transfer. The Prandtl number Pr = 10 -5 T 4 /n constrains the value of q by q η /q ν = Pr 1 / 2 (Schekochihin & Cowley 2007), where aT/m e c 2 = Θ, Θ ∼ Γ sh and a is the Boltzmann constant. We adopt a length scale of viscous eddies (Kumar & Narayan 2009; Narayan & Kumar 2009; Lazar et al. 2009) for GRB prompt emission and obtain q ν = 2 πl -1 eddy = 2 π ( R/ Γ sh Γ t ) -1 = 6 . 3 × 10 -10 ( R/ 10 13 cm) -1 (Γ sh / 100)(Γ t / 10) cm -1 , where Γ t is the Lorentz factor of turbulent eddies. The magnetic resistive scale is q η = 3 . 9 × 10 4 ( n/ 3 × 10 10 cm -3 ) -1 / 2 (T / 5 . 6 × 10 11 K) 2 cm -1 . In the compressed two-dimensional case, magnetic fields can be < B > = [ ∫ q η q ν q -ζ p d q ] 1 / 2 = √ 2 πq (2 -ζ p ) / 2 ν / √ ζ p -2 under the condition q η /greatermuch q ν . Through the cascade process of a turbulent fluid, turbulent energy dissipation has a hierarchical fluctuation structure. A set of inertial-range scaling laws of fully developed turbulence can be derived. From the research of She & Leveque (1994) and She & Waymire (1995), the energy spectrum index ζ p of turbulent fields is related to the cascade process number p by the universal relation of ζ p = p/ 9+2[1 -(2 / 3) p/ 3 ]. The Kolmogorov turbulence is presented as ζ p = p/ 3. This turbulent feature was found recently to be valid in the relativistic regime (Zrake & MacFadyen 2012). At the fireball radius of R ∼ 10 13 cm, taking the turbulent spectrum index of ζ p = 3 . 25 from She & Leveque (1994), we obtain a the magnetic field value of 1 . 3 × 10 6 G. In the fireball scenario, a magnetic field of 10 14 G at 10 6 cm can easily reach 10 6 G at 10 14 cm, providing powerful prompt emission (Piran 2005). This estimation is dependent on the exact shock location and on the equipartition parameters. In our model, we take a magnetic field number of 10 6 G as a reference value. As we have shown in our model, the random magnetic field is generated by turbulence and the magnetic field number is dependent on the turbulent energy spectral index ζ p . Therefore, we solve Equation (2) and obtain the radiation property I ω ∝ ω -( ζ p -2) . This radiation spectrum can be reproduced by the numerical calculations of Teraki & Takahara (2011) in high-frequency regime. The gross radiative emission should be the contribution from all of the relativistic electrons with a certain electron energy distribution. However, we note that the jitter spectral index ζ p -2 of single electrons is fully determined by the fluid turbulence. Thus, the spectral index of the gross radiative emission is not related to the electron energy distribution. Finally, from Equation (2), we obtain We note that the term of the magnetic field is not related to the spectral index.",
"pages": [
5,
6,
7
]
},
{
"title": "2.2. Polarization",
"content": "Magnetic field configurations is a dominant issue for the research of GRB radiation and polarization. In this paper, we apply the topology of random magnetic fields introduced by Laing (1980, 2002). A three-dimensional cube containing random and small-scale magnetic fields can be compressed into a two-dimensional slab by relativistic shocks. In the slab plane, the distribution of magnetic fields is still stochastic. The magnetic field vector at one point, denoted in rectangular coordinates, is B = B 0 (cos φ sin θ B , sin φ, cos φ cos θ B ), where θ B is the angle between the slab plane and the line of sight (see Figure 1) and φ is the azimuthal angle at any point randomly distributed in the slab plane. The position angle of the E -vector χ can be given as cos 2 χ = -(sin 2 θ B -tan 2 φ ) / (sin 2 θ B +tan 2 φ ). Thus, the magnetic field acting on the radiation is B = B 0 (cos 2 φ sin 2 θ B +sin 2 φ ) 1 / 2 . Because an electron obtains same acceleration on average from different directions in a random and small-scale magnetic field, the electron trajectory of jitter radiation can be approximated as a straight line (Medvedev 2000; Medvedev et al. 2011). Thus, jitter radiation is limited to the small radiation cone along the line of sight to the observer. Since the acceleration term of jitter radiation is proportional to B 2 , we can do a decomposition of jitter radiation in the electron radiation plane and obtain the polarization degree (see the detailed examination in the Appendix). If the slab is orientated so that the E -vector of the polarization radiation has a position angle of zero degrees, then the Stokes parameter U = 0. Following the magnetic field topology given by Laing (1980, 2002), we obtain Stokes parameters of single electron jitter radiation given by: I = C ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) dφ , Q = I cos2 χ = -C ∫ 2 π 0 (cos 2 φ sin 2 θ B -sin 2 φ )d φ , U = 0, and V = 0, where C = C ( γ, B 0 ). With a certain electron energy distribution N ( γ ), we obtain the following Stokes parameters of the gross jitter radiation: and Thus, the final polarization degree of the gross jitter emission is In our case, we emphasize that the magnetic field configuration is the only parameter that impacts the jitter polarization. Moreover, this polarization result is only valid in the jitter radiation case where the electron deflection angle is small (see Equation (11) in Section 4). Thus, in this two-dimensional case, we only select electrons moving roughly perpendicular to the slab plane. We present synchrotron polarization of a single electron applying the same magnetic field topology in the Appendix. We also repeat the Stokes parameters of the gross synchrotron radiation given by Laing (1980): I = C ( γ, B 0 ) ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) ( ν S +1) / 2 dφ , Q = -C ( γ, B 0 )( 3 ν S +3 3 ν S +5 ) ∫ 2 π 0 (cos 2 φ sin 2 θ B + sin 2 φ ) ( ν S -1) / 2 (cos 2 φ sin 2 θ B -sin 2 φ ) dφ , U = 0, and V = 0, where ν S is the synchrotron spectral index. We compare synchrotron polarization and jitter polarization in Figure 2. In this paper, we neglect the effect of light propagation in a thick and highly magnetized plasma screen (Macquart & Melrose 2000).",
"pages": [
7,
8
]
},
{
"title": "2.3. Jet-in-jet Scenario",
"content": "The mini-jets emit photons in a bulk GRB jet. We simply take into account the geometric effect of the bulk jet. The solid angle element of the jet is 2 π sin θdθ . Since observers always see the forward jet and the backward jet is not observed, the detection probability is half of the result of above the estimation. As the full opening angle is θ , we suggest an upper limit of the integral to be θ/ 2. The probability should be normalized by the entire solid angle of 4 π . Thus, the observational probability of these mini-jets in a bulk GRB jet can be calculated as P = π ∫ θ/ 2 0 sin θ ' dθ ' / 4 π = 1 / 32Γ 2 and Γ ∼ θ . The gross Lorentz factor Γ was given by Giannios et al. (2010) as Γ = 2Γ j Γ t /α 2 , where Γ j ∼ Γ sh is the Lorentz factor of the bulk jet, Γ t is the Lorentz factor of relativistic turbulence in these mini-jets, and textbf α is the 'offaxis' parameter defined as θ j = α/ Γ j . From the investigation of the mini-jets emitting angle distribution (Giannios et al. 2010), the range of α is given as 0 < α < 2. We can furthermore estimate the number of mini-jets affected by the turbulent fluid as n ( γ ) = 4 πR 2 Γ j ct cool /l 3 s , where R is the fireball radius and t cool = 6 πm e c/σ T γB 2 is the cooling timescale of relativistic electrons. The length scale of those mini-jets is l s = γ Γ t ct cool . As the number of mini-jets n ( γ ) is a function of the electron Lorentz factor γ , the electron energy distribution N e ( γ ) is required to obtain a total number of mini-jets given by n = ∫ ∞ 1 n ( γ ) N e ( γ ) dγ/ ∫ ∞ 1 N e ( γ ) dγ . Due to diffusive shock acceleration, electrons can be accelerated and a power-law energy distribution is given. In our paper, turbulence is considered not only to generate magnetic fields but also to accelerate electrons and the electron energy distribution has a Maxwellian component (Stawarz & Petrosian 2008). If turbulent acceleration is considered in addition to shock acceleration, the electron energy distribution has a dual-natured shape with a Maxwellian component and a power-law component (Giannios & Spitkovsky 2009): where C is a constant. In the case that only a fraction of electrons have a non-thermal distribution, we take the characteristic temperature to be Θ = kT/m e c 2 ∼ 100. In our calculation, we adopt γ th = 10 3 ; p e = 2 . 2 is the power-law index. Combined with the observational probability P and the total number n of mini-jets affected by turbulence, the final observed polarization degree is Π obs = nP Π.",
"pages": [
8,
9
]
},
{
"title": "3. Results",
"content": "The intrinsic polarization results of GRB prompt emission without jet effects are shown in Figure 2. The jitter polarization degree is strongly dependent on θ B , which is the angle between the line of sight and the slab plane. If the line of sight is perpendicular to the slab plane, we successfully obtain jitter photons, but jitter radiation in the electron radiative plane is symmetric and the polarization degree is zero. Except in this extreme case, the degree of polarization can be measured with different values of θ B . With the same magnetic field configuration, we can compare jitter polarization and synchrotron polarization. Both jitter polarization and synchrotron polarization are related to θ B . On the other hand, as we discussed in Section 2.2, jitter polarization is not related to the radiation spectrum and it can reach a maximum value of 100 percent. Synchrotron polarization (see details in the Appendix) is related to the radiation spectral index and its maximum value is ( ν S +3) / ( ν S + 5). The cases of ν s = 2 . 0 , 1 . 0, and 0.6 are shown in Figure 2 as examples. We further provide examples of the observed jitter polarization degree in our jet-in-jet scenario shown in Figures 3 and 4. Different jet 'off-axis' parameters, 1.55, 1.3 and 1.0, are used to calculate the observed polarization degree shown in Figure 3. Here, we take Γ sh = 100, Γ t = 10, and R = 10 13 cm. We show that the polarization degree is significantly sensitive to the jet 'off-axis' parameter. A stronger jet 'off-axis' effect yields a stronger observed polarization degree. In Figure 4, we present examples of jitter polarization results affected by the shock Lorentz factor Γ sh . We fix the 'off-axis' parameter as 1.3, Γ t = 10, and R = 10 13 cm. Shock Lorentz factor values of 85, 100, and 120 are adopted. We see that a low polarization degree can be induced by a large shock Lorentz factor. This fact suggest that a large shock Lorentz factor provides powerful radiation along the jet axis while a powerful polarization can be measured in the strong off-axis case, which has a relatively small Lorentz factor and weak radiation. It is also useful to review the GRB polarization feature under the mechanism of synchrotron radiation in the jet structure. Gruzinov (1999) and Sari (1999) proposed the possibility of high-degree GRB polarization. Granot (2003) comprehensively discussed different GRB jet polarization cases. Here, for simplicity, we apply the model of Gruzinov (1999) to illustrate the configuration differences between the tangled magnetic field and the ordered magnetic field. The polarization degree derived from the magnetic field parallel/perpendicular to the jet direction was given as Π = Π 0 sin 2 α B ( B 2 ‖ -0 . 5 B 2 ⊥ ) / [ B 2 ‖ sin 2 α B + 0 . 5 B 2 ⊥ (1 + cos 2 α B )], where B ‖ is the magnetic field parallel to the shock propagation direction, B ⊥ is the magnetic field perpendicular to the shock propagation, and α B = π/ 2 -θ B is the angle between the line of sight from observer and the direction of the shock propagation (Gruzinov 1999). In our model, we have fully obtained the polarization feature of GRB prompt emission in the case of B ‖ /lessmuch B ⊥ (Laing 1980, 2002) and this condition is necessary for jitter radiation. If B ‖ /greatermuch B ⊥ , the polarization degree is Π ∼ Π 0 , which is the result obtained from an ordered magnetic field aligned with the jet direction. This result reproduces exactly the polarization degree of synchrotron radiation as Π 0 = (3 ν S +3) / (3 ν S +5); the electron energy distribution has a power-law distribution with a power-law index p e and ν S = ( p e -1) / 2. Considering a certain jet structure and line of sight effects, a high degree of GRB prompt polarization can be obtained (Granot 2003; Lazzati & Begelman 2009). In our paper, the two-dimensional magnetic slab and the jet-in-jet structure provide the possibility of asymmetric radiation in the electron radiative plane. Thus, the GRB prompt emission can be highly polarized as well.",
"pages": [
9,
10
]
},
{
"title": "4. Discussion and Conclusions",
"content": "Relativistic electrons accelerated by diffusive shock acceleration with a power-law energy distribution can emit high-energy photons in an ordered magnetic field. Therefore, it is possible to explain the high-degree polarization detected in GRB prompt emission by synchrotron radiation. Alternatively, we present in this paper that turbulence can accelerate electrons and generate random and small-scale magnetic fields. The relativistic electrons emit X-ray/ γ -ray jitter photons in the jet-in-jet structure. Some important physical components, such as turbulence behind the shock front, random and small-scale magnetic fields, the electron energy distribution, and mini-jets, are self-consistently organized in the process of jitter radiation. We obtain a high-degree polarization of GRB prompt emission through jitter radiation considering a two-dimensional compressed magnetic field configuration. The intrinsic polarization degree is a function of the angle between the line of sight and the slab plane, and large polarization values can be achieved in the case of small angles. Moreover, the final observed polarization degree in the jet-in-jet scenario is affected by the 'off-axis' parameter and the shock Lorentz factor. In this paper, the electron trajectory of jitter radiation in random and small-scale magnetic fields is assumed to be a straight line. In other words, the condition of θ d /lessmuch 1 /γ should be satisfied by jitter radiation (Medvedev et al. 2011). Here, θ d = eBλ B /γm e c 2 is the deflection angle of electrons in a magnetic field, and λ B ∼ c/ω pe is the length scale of the magnetic field. We obtain This condition is strongly dependent on the magnetic field and the electron number density. We constrain the condition of jitter radiation in an example below. The electron number density is given by n = N/ ∆Ω R 2 ∆ R . N = 1 . 0 × 10 52 ∼ 6 × 10 54 is the total number of electrons in the radiative region (Kumar & Narayan 2009). We take the fireball radius to be R = 10 13 cm and fireball shell to be ∆ R = 10 10 cm. If the jet opening angle is about 5 degree, we obtain a solid angle ∆Ω = 3 . 3 × 10 -4 and the estimated value of number density is n = 3 . 0 × 10 20 cm -3 ∼ 1 . 8 × 10 22 cm -3 . Thus, θ d /lessmuch 1 /γ and the electron trajectory can be treated as a straight line. In order to satisfy this jitter condition in the two-dimensional case, we select electrons moving roughly perpendicular to the slab plane so that the electron deflection angle is small. The general case of electrons moving in a random walk in a stochastic magnetic field with a large deflection angle was discussed by Fleishman (2006) and numerical simulations may be required to solve this complicated issue. It is expected that the so-called depolarization due to the Faraday rotation of the polarization screen (Burn 1966) can be a powerful tool to further constrain the source structure and magnetic field topology. In general, stochastic Faraday rotation creates a polarization degree of Π ∝ exp( -λ 4 ), where λ is wavelength (Melrose & Macquart 1998). Tribble (1991) discussed a power-law structure function for a Faraday rotation measurement. The polarization degree was given as Π ∝ λ -4 /m , where m is related to the turbulent cascade. Even if we consider a polarization fluctuation proportional to λ , the final polarization degree still dramatically decreases as Π ∝ λ -2 . 2 if we adopt a typical value of m = ζ p -2 given in our model. Therefore, GRB prompt polarization measured in the soft band is about 20% of that measured in the hard band. This prediction can be examined by future observations if GRB prompt polarization measurements can be performed simultaneously in different energy bands. This simple analysis of the depolarization effect also indicates that GRB prompt polarization in optical bands is nearly impossible detect even if GRB is highly polarized in high-energy bands. On the other hand, the polarization of GRB optical afterglows was detected. The radiation case of external shocks of GRBs sweeping into the surrounding interstellar medium is beyond the scope of this paper. Here, we make some simple speculations. As optical afterglow is onset at early times after the GRB is triggered, and the jet is strongly anisotropic with a narrow beaming angle. Thus, the optical polarization degree can reach values of 10% (Uehara et al. 2012) and even higher polarization degrees were expected (Steele et al. 2009). In late times after a GRB is triggered, the beaming angle of the jet is wide and the jet anisotropy is not prominent. Thus, the polarization of the optical afterglow is weak 1 (Covino et al. 1999; Hjorth et al. 1999; Wijers et al. 1999). Moreover, high-energy photons from GRB prompt emission can pass through a dense medium without being strongly absorbed. Thus, the depolarization effect is weak and a high polarization degree can be detected, while UV/optical photons of GRB afterglows can be strongly absorbed by the surrounding dense material. Therefore, even though the initial polarization degree of GRB optical afterglows is very high, the external depolarization effect is strong as the diffraction in a Faraday prism is taken into account (Sazonov 1969; Macquart & Melrose 2000). Thus, due to the strong depolarization effect, the detected polarization degree of GRB optical afterglows is low. Further quantitative computations can be executed since the magnetic field configuration adopted in this paper is still valid for the depolarization cases mentioned above (Rossi et al. 2004). Rapid time variations of the polarization angle and polarization degree have been measured either in GRB prompt emission cases (Gotz et al. (2009) for GRB 041219A and Yonetoku et al. (2011) for GRB 100826A) or in GRB afterglow cases (Rol et al. (2000) for GRB 990712, Greiner et al. (2003) for GRB 030329, and Wiersema et al. (2012) for GRB 091018). The observed timescale of polarization variation in GRB prompt emission is about 50-100 s (Yonetoku et al. 2011), which corresponds to an intrinsic timescale of 0.5-1 s. Here, we list three possibilities to explain this rapid variation. First, GRB helical jets with helical magnetic fields and helical rotation generated by black holes (Mizuno et al. 2012) should be considered. With a helical jet, the slab may rotate and the magnetic field configuration may change quickly. Then, rapid polarization variation occurs. Second, Lazzati & Begelman (2009) proposed that faint pulses of GRB prompt emission are a main contributor to the polarization. If this is true, we can obtain the rapid time variation of the polarization since the pulses shown in GRB prompt lightcurves show rapid variation; Third, the turbulent feature in the slab should be revisited. We estimate the variability of GRB prompt polarization due to the variability of stochastic eddies as δt ∼ l eddy /c s . Given l eddy ∼ R/ Γ j Γ t and c s ∼ c/ √ 3, δt is about 1.7 s, which can be comparable to the observational timescale. Moreover, small-scale fluid turbulence and magnetic reconnection was suggested by Matthews & Scheuer (1990b). Recently, Zhang & Yan (2011) and McKinney & Uzdensky (2012) illustrated the possibility of magnetic reconnection for GRB energy dissipation. We suggest that small-scale magnetic reconnection in the compressed slab is likely to affect the rapid polarization variation. More observations (TSUBAME, NuSTAR, Astro-H) and quantitative explanations in detail are expected in the future. We thank the referee for his/her helpful suggestions and comments. We are grateful to Teraki, Y., Toma, K., Nagataki, S., Ito, H., Ono, M., and Lee, S.-H. for their useful discussions. The numerical computation in this work was carried out at the Yukawa Institute Computer Facility. This work is supported by Grants-in-Aid for Foreign JSPS Fellow (Number 24.02022). We acknowledge support from the Ministry of Education, Culture, Sports, Science and Technology (No. 23105709), the Japan Society for the Promotion of Science (No. 19104006 and No. 23340069), and the Global COE Program, The Next Generation of Physics, Spun from University and Emergence, from MEXT of Japan. J. Wang is supported by the National Basic Research Program of China (973 Program 2009CB824800), the National Natural Science Foundation of China 11133006, 11163006, 11173054, and the Policy Research Program of the Chinese Academy of Sciences (KJCX2-YW-T24).",
"pages": [
10,
11,
12,
13
]
},
{
"title": "A. Polarization of Single Electrons in A Random Magnetic Field",
"content": "In this Appendix, we first introduce the polarization feature of single relativistic electrons in a magnetic field assuming jitter condition. We repeat the radiation property by Landau & Lifshitz (1971) as where the retarded time is t ' = t -R ( t ' ) /c ∼ = t -R 0 /c + n · r ( t ' ) /c ∼ = t -R 0 /c + n · v t ' /c ; n is the radiation direction. If we take dt = dt ' (1 -n · v /c ), we obtain If we adopt the notation ω ' = ω (1 -n · v /c ), we obtain The acceleration term is w ω ' = e v × B /γm e c . The electron trajectory is necessary to obtain the acceleration term and the calculation in Equation (A3). If the electron trajectory can be treated as a straight line in a magnetic field (see Equation (11) of jitter radiation condition), we have a compressed magnetic slab plane with an angle of θ B to the radiative X -Y plane, and the electron velocity is perpendicular to the slab plane since the electron deflection angle of the jitter radiation is smaller than 1 /γ . The jitter radiation direction follows the direction of the electron. Thus, we obtain the X -axis component as and the Y -axis component as The radiation intensity is I = c | E | 2 R 2 0 / 2 π . The Stokes parameters can be defined as and From Section 2.2, we know B x = B 0 cos φ sin θ B and B y = B 0 sin φ . Finally, we obtain the jitter polarization Π = Q/I , which is only related to the configuration of the magnetic field; Equation (9) is verified. In this Appendix, we also review the synchrotron polarization of a single electron. We keep the same random magnetic field topology used in the jitter polarization case to calculate the synchrotron polarization and we can repeat the calculation of Laing (1980). The radiation intensity of the synchrotron mechanism is where ν c = (3 / 2) γ 2 ν L , ν L = eB/ (2 πm e c ) is the Larmor frequency ,and K is a modified Bessel function. The synchrotron polarization of a single electron is related to the magnetic field, electron Lorentz factor γ and radiation frequency ν (Rybicki & Lightman 1979). In order to compare synchrotron polarization with jitter polarization, we apply the same magnetic field topology described in Section 2.2 to synchrotron polarization; our results are shown in Figure 5. In the calculation, we fix the magnetic field value at 1 . 3 × 10 6 G. For a given θ B , the degree of synchrotron polarization increases, if the radiation is toward a higher frequency ν and/or the electron Lorentz factor γ tends toward smaller values. This property is typical of synchrotron polarization of single electrons. In Figure 5, we plot the jitter polarization as well, which is independent of the radiation frequency ν and the electron Lorentz factor γ . Even though synchrotron polarization degrees can be coincidentally the same as the jitter polarization degree by adjusting the parameters of ν and γ , we emphasize that jitter polarization and synchrotron polarization are physically different because jitter radiation and synchrotron radiation are two different radiation mechanisms. If the synchrotron power-law spectrum with a power-law index ν S is given and an electron energy distribution is assumed to be a power-law with an index of 2 ν S + 1, we obtain the Stokes parameters of the gross electrons: and where C is constant. Thus, the final polarization degree of the gross synchrotron emission is These are the results given by Laing (1980) and we also plot them in Figure 2.",
"pages": [
13,
14,
15
]
},
{
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}
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2013ApJ...776...25K
https://arxiv.org/pdf/1307.2709.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_74><loc_80><loc_82></location>PHOTODETACHMENT AS DESTRUCTION MECHANISM FOR CN -and C 3 N -ANIONS IN CIRCUMSTELLAR ENVELOPES</section_header_level_1>
<text><location><page_1><loc_23><loc_70><loc_84><loc_72></location>S. S. Kumar 1 , D. Hauser 1 , R. Jindra 1 , T. Best 1 , ˇ S. Rouˇcka 2 , W.</text>
<section_header_level_1><location><page_1><loc_23><loc_68><loc_65><loc_70></location>D. Geppert 3 , T. J. Millar 4 , and R. Wester 1</section_header_level_1>
<text><location><page_1><loc_23><loc_64><loc_82><loc_67></location>1 Institut fur Ionenphysik und Angewandte Physik, Universitat Innsbruck, A -6020 Innsbruck, Austria</text>
<text><location><page_1><loc_23><loc_61><loc_83><loc_64></location>2 Charles University in Prague, Faculty of Mathematics and Physics, Department of Surface and Plasma Science, 18000 Prague, Czech Republic</text>
<text><location><page_1><loc_23><loc_58><loc_81><loc_61></location>3 Department of Physics, AlbaNova, Stockholm University, SE -10691 Stockholm, Sweden</text>
<text><location><page_1><loc_23><loc_54><loc_78><loc_57></location>4 Astrophysics Research Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, UK</text>
<text><location><page_1><loc_23><loc_52><loc_29><loc_53></location>E-mail:</text>
<text><location><page_1><loc_29><loc_53><loc_50><loc_53></location>[email protected]</text>
<text><location><page_1><loc_23><loc_27><loc_84><loc_50></location>Abstract. Absolute photodetachment cross sections of two anions of astrophysical importance CN -and C 3 N -were measured to be (1.18 ± (0.03) stat (0.17) sys ) × 10 -17 cm 2 and (1.43 ± (0.14) stat (0.37) sys ) × 10 -17 cm 2 respectively at the ultraviolet wavelength of 266 nm (4.66 eV). These relatively large values of the cross sections imply that photodetachment can play a major role in the destruction mechanisms of these anions particularly in photon-dominated regions. We have therefore carried out model calculations using the newly measured cross sections to investigate the abundance of these molecular anions in the cirumstellar envelope of the carbon-rich star IRC+10216. The model predicts the relative importance of the various mechanisms of formation and destruction of these species in different regions of the envelope. UV photodetachment was found to be the major destruction mechanism for both CN -and C 3 N -anions in those regions of the envelope, where they occur in peak abundance. It was also found that photodetachment plays a crucial role in the degradation of these anions throughout the circumstellar envelope.</text>
<section_header_level_1><location><page_2><loc_12><loc_87><loc_27><loc_88></location>1. Introduction</section_header_level_1>
<section_header_level_1><location><page_2><loc_12><loc_84><loc_72><loc_85></location>1.1. Molecular anions in space: Observation and astrophysical relevance</section_header_level_1>
<text><location><page_2><loc_12><loc_32><loc_84><loc_82></location>The discovery of molecules in the interstellar medium about seven decades ago was particularly intriguing since the chemistry governing the formation of molecules in such hostile regions of space was not familiar. Gradually the number of molecules and their cations found in extraterrestrial space increased and it became clear that we in fact live in a 'molecular Universe' (Larsson et al. 2012). However, after the first molecule was identified in the interstellar medium, it took six decades before a molecular anion could be discovered in such environment. This delay was primarily due to the low abundance of anions in space compared to their neutral counterparts and due to the lack of laboratory measurements of high resolution rotational spectra of the anions that could allow their search in space. The first molecular anion ever observed outside our solar system is C 6 H -(McCarthy et al. 2006), which was detected in the envelope of the carbon-rich star IRC+10216. The identification of this molecular anion was followed by the discovery of several other carbon chain anions, C n H -( n = 4, 8) and C n N -( n = 1, 3, 5) in various regions of space such as dark clouds, circumstellar envelopes, and also in Titan's atmosphere (Cernicharo et al. 2007, Cernicharo et al. 2008, Sakai et al. 2007, Sakai et al. 2008, Sakai et al. 2010, Ag'undez et al. 2008, Ag'undez et al. 2010, Remijan et al. 2007, Brunken et al. 2007, Kasai et al. 2007, Kawaguchi et al. 2007, Thaddeus et al. 2008, Gupta et al. 2009). Of these anions, C 5 N -was only tentatively identified. The role of anions in the synthesis of molecules in the interstellar medium has been investigated by Dalgarno & McCray (1973) many years ago, whereas the formation of molecular hydrogen in stars from H -had been pointed out by McDowell (1961) much earlier. The recent discovery of anions in extraterrestrial environments has initiated a fresh interest towards the understanding of anion chemistry in exotic environments. The importance of gas-phase molecular ions in space has been described in detail in a recent review by Larsson et al. (2012).</text>
<section_header_level_1><location><page_2><loc_12><loc_28><loc_42><loc_30></location>1.2. Significance of the present work</section_header_level_1>
<text><location><page_2><loc_12><loc_5><loc_84><loc_27></location>Extraterrestrial molecular anions are believed to be produced predominantly via electron capture processes such as dissociative or radiative attachment (Larsson et al. 2012). The destruction processes are largely due to photodetachment, associative detachment and mutual neutralization reactions. In photon-dominated regions, the abundance of molecular anions can be mainly determined by their UV photodetachment. Even in the dark clouds where UV photons cannot penetrate UV photodetachment may still contribute to photodestruction of anions because the secondary electrons produced by cosmic rays can excite the molecules to high Rydberg states, which emit UV radiation upon decay. The study of photodetachment processes is also of particular importance in fundamental physics since the extra electron in an anion is bound to the system by means of strong correlated motion of the electrons in the system and the electron-</text>
<text><location><page_3><loc_12><loc_65><loc_84><loc_89></location>electron correlation plays the most crucial role in such processes. In addition, no theoretical or experimental values of photodetachment cross sections for CN -or C 3 N -have been reported in the literature despite the fact that there have been a number of studies on these molecular anions (Andersen et al. 2001, Bradforth et al. 1993, Gottlieb et al. 2007, Yen et al. 2010). Since these anions have high electron affinities (CN -: 3.862 ± 0.004 eV (Bradforth et al. 1993), C 3 N -: 4.305 ± 0.001 eV (Yen et al. 2010)) their photodetachment requires photons in the ultraviolet range. In the present work, we measured the photodetachment cross sections of CN -and C 3 N -anions at an energy (4.66 eV) near the photodetachment thresholds. Furthermore, we used the measured values as an input to model calculations to investigate the impact of the new cross sections on the predicted abundance of anions in the circumstellar envelope of IRC+10216.</text>
<section_header_level_1><location><page_3><loc_12><loc_61><loc_62><loc_62></location>2. Experimental Method and Theoretical Modelling</section_header_level_1>
<section_header_level_1><location><page_3><loc_12><loc_57><loc_32><loc_59></location>2.1. Experimental Setup</section_header_level_1>
<text><location><page_3><loc_12><loc_14><loc_84><loc_56></location>The basic elements of the experimental setup are an ion source, an octupole ion trap, an MCP detector and a laser system. The ion source consists of a piezoelectric pulsed gas valve with a pair of electrodes (referred to as 'plasma electrodes') attached at the exit of the valve. A suitable gas mixture is sent through the gas valve at a certain repetition rate. The ions are generated in a pulsed DC discharge of the gas jet between the plasma electrodes when a high potential difference is applied between them. These ions are then extracted towards the ion trap by a Wiley-McLaren time-of-flight spectrometer oriented perpendicular to the gas jet from the piezo valve. Deflection plates and lenses are used for guiding and focusing the ions into the ion trap. The unique octupole ion trap is made of 100 µ m gold plated molybdenum wires unlike in conventional designs where rods of specific diameter are used as RF electrodes. A short description of this ion trap has been provided by Deiglmayr et al. (2012), where it was used in conjunction with a magneto-optical trap to study reactive collisions of trapped OH -anions with trapped rubidium atoms. A second piezoelectric pulsed gas valve allows for helium buffer gas cooling of the trapped ions. There are two additional electrodes (termed as 'shield plates') above and below the trap that enable us to shape the ion density distribution inside the ion trap. The use of thin wires to construct the trap allows one to probe the trapped ions, for instance with a laser, from the sides. The laser beam can be focused at various positions inside the trap by means of a two-dimensional translation stage with a lens attached to it. This configuration is used to map the ion density distribution inside the trap.</text>
<text><location><page_3><loc_12><loc_6><loc_84><loc_13></location>In the present experiments, CN -and C 3 N -anions were generated by passing argon gas (at a pressure of about 2-3 bar) over acetonitrile vapor and sending the resulting mixture into the source piezo valve which was operated at 14 Hz. The discharge between the plasma electrodes ionized the gas mixture resulting in the production of several</text>
<text><location><page_4><loc_12><loc_65><loc_84><loc_89></location>anions including CN -and C 3 N -. The plasma was stabilized by the electrons emitted from a hot filament placed opposite to the pulsed gas valve. The ions were injected into the Wiley-McLaren region, where they were extracted towards the trap with an average kinetic energy of about 240 eV. The desired ionic species can be stored in the ion trap by appropriate timing of the switchable voltages applied on the entrance and exit electrodes of the ion trap in accordance with the time of flight of the various molecular ions. The trap was operated at a radiofrequency of 9 MHz with an amplitude of 180 V on top of a DC voltage of about 240 V. The DC voltage of the trap served to reduce the kinetic energy of the ions coming from the source region to about a few eV. The entrance and exit endcap electrodes of the ion trap were between 10 V and 30 V, the exact value of which did not significantly affect the ion distribution except that the signal strength was slightly modified.</text>
<text><location><page_4><loc_12><loc_43><loc_84><loc_64></location>The photodetachment measurements were performed with a pulsed laser beam (266 nm, 10 Hz) obtained by frequency quadrupling of the output from a 1064 nm IR laser system with output pulse energy of about 30 mJ and with pulse width of 7 ns. The pulse energy of the laser beam was reduced to a few tens of microjoule and was then sent through a beam splitter. The transmitted beam was used to measure the fluctuations in the laser energy throughout the experiment and these data were used to correct the measured photodetachment cross section. The reflected beam was focused into the trap using the lens attached on the translation stage. The pulse energy of the beam fired into the trap was as low as 25 µ J so as to ensure that there was only single photon absorption and that the wires constituting the trap were not damaged when the laser beam struck them.</text>
<section_header_level_1><location><page_4><loc_12><loc_39><loc_35><loc_40></location>2.2. Measurement procedure</section_header_level_1>
<text><location><page_4><loc_12><loc_13><loc_84><loc_37></location>The measurement procedure was very similar to the one described previously (Trippel et al. 2006, Hlavenka et al. 2009, Best et al. 2011) except that in the present experiments the laser beam was sent into the ion trap perpendicular to its symmetry axis. Briefly, the ions can be stored in the trap for a few hundred seconds (1 /e lifetime, determined from the exponential decay of the ions stored in the trap). In the first part of the experiment, the background decay rate was determined by measuring the amount of ions left in the trap after different storage times. In the second part, the rates of decay were measured with the UV laser pointing at different positions inside the trap. The photodetachment decay rates when plotted as a function of the positions form a tomography image which reflects the ion density distribution inside the trap. The integral of the rate map is proportional to the photodetachment cross section as detailed elsewhere (Trippel et al. 2006, Best et al. 2011).</text>
<text><location><page_4><loc_12><loc_9><loc_84><loc_13></location>The photodetachment cross section, σ pd , is given by the expression (Trippel et al. 2006, Best et al. 2011):</text>
<formula><location><page_4><loc_23><loc_5><loc_84><loc_9></location>σ pd = 1 Φ L ∫ [ k pd ( x, y ) -k bg ] dx dy, (1)</formula>
<text><location><page_5><loc_12><loc_85><loc_84><loc_89></location>where k pd ( x, y ) is the position dependent decay rate due to photodetachment, k bg is the background decay rate (decay rate measured without laser) and Φ L is the photon flux.</text>
<section_header_level_1><location><page_5><loc_12><loc_81><loc_45><loc_82></location>2.3. Model Calculations for IRC+10216</section_header_level_1>
<text><location><page_5><loc_12><loc_68><loc_84><loc_79></location>The photodetachment cross sections measured for CN -and C 3 N -anions in the present experiments, together with those obtained previously (Best et al. 2011) for the carbon chain anions C 2 H -, C 4 H -and C 6 H -, were used as input for model calculations of the circumstellar envelope of IRC+10216. The photodetachment cross sections of CN -and C 3 N -were fitted to the expression used in previous model calculations (Millar et al. 2007):</text>
<formula><location><page_5><loc_23><loc_63><loc_84><loc_67></location>σ = σ ∞ √ 1 -E A //epsilon1, (2)</formula>
<text><location><page_5><loc_12><loc_28><loc_84><loc_64></location>in which σ is the cross section, σ ∞ the cross section at infinite photon energy, E A the photodetachment threshold energy and /epsilon1 the photon energy. Since our cross section measurements have been carried out only at a wavelength of 266 nm (at which a sufficiently intense UV beam was available from our laser systems) only two points exist for the fit of the photon energy/cross section curve for each of the nitrile anions, the cross section at threshold energy (where σ = 0) and the one measured at 266 nm. Of course, there exists the possibility of strong resonances, especially at photon energies only slightly above the threshold, which cannot be ruled out in the absence of complementary experimental data on photodetachment cross sections of these anions. For a more accurate treatment of the model, one would require experimental cross sections at higher photon energies necessitating radiation from sources such as synchrotrons or free electron lasers (FELs). Regarding the threshold energy ( E A ) of CN -, the value obtained by Bradforth et al. (1993) who employed a pulsed fixed-frequency negative ion photoelectron spectrometer (3.862 ± 0.004 eV) was used for the fit. In the case of C 3 N -the result from Yen et al. (2010) measured using slow electron velocity-map imaging (4.305 ± 0.001 eV) and field-free time-of-flight was applied. For the photodetachment cross sections of the hydrocarbon anions the fitted values from Best et al. (2011) were used.</text>
<text><location><page_5><loc_12><loc_4><loc_84><loc_28></location>The chemical models are based on the assumption of a uniform mass-loss rate for the circumstellar envelope of IRC+10216 described by Millar et al. (2000) together with a second model, described by Cordiner & Millar (2009), in which density-enhanced shells are included. With density-enhanced shells of gas and dust, a more realistic modelling of the circumstellar envelope is achieved by introducing a set of density enhancements with the physical parameters of the envelope based on the dust-shell observation by Mauron & Huggins (2000). For modelling, the conditions expected for the well-studied circumstellar envelope of IRC+10216 were applied. Consequently, a spherically symmetric outflow velocity from the central star of 1.45 × 10 6 cm s -1 and a mass loss of 1.5 × 10 -5 solar masses per year were assumed for the envelope (Men'shchikov et al. 2001). The adopted temperature profile is based on a fit to the gas kinetic temperature profile of Crosas & Menten (1997), with a minimum temperature</text>
<table>
<location><page_6><loc_29><loc_48><loc_68><loc_89></location>
<caption>Table 1. Abundances of parent species used in the model.</caption>
</table>
<text><location><page_6><loc_12><loc_13><loc_84><loc_43></location>of 10 K fixed in the outer region of the envelope and is the same as used by Cordiner & Millar (2009). The initial chemical abundances of parent molecules relative to that of H 2 used in the model are listed in Table 1. These species are formed in the inner envelope close to the star at high density and temperature and blown outwards in a spherically symmetric outflow (Millar et al. 2000). The calculations begin at an inner radius of 10 15 cm where photons from the external, interstellar radiation field begin to destroy parent species creating reactive radicals and ions and initiating the synthesis of anions and other species. The number density n ( r ) declines with the radius as 1 /r 2 . In the second set of calculations, in addition to the 1 /r 2 dependence of the number density, a series of step-like density enhancements of the form βn ( r ) is introduced. The parameter β is set to 5 for all shells in the model. According to dust shell parameters deduced from scattered light observations by Mauron & Huggins (2000), we assume that each shell has a thickness of 2 arcsec and the spacing between the shells is 12 arcsec. This distance corresponds to roughly 530 years between the peaks of enhanced mass loss (See Cordiner & Millar (2009) for details.).</text>
<section_header_level_1><location><page_7><loc_12><loc_87><loc_36><loc_88></location>3. Results and Discussion</section_header_level_1>
<section_header_level_1><location><page_7><loc_12><loc_84><loc_33><loc_85></location>3.1. Experimental results</section_header_level_1>
<figure>
<location><page_7><loc_13><loc_33><loc_47><loc_49></location>
<caption>Figure 1 presents the tomography images for the CN -anions at two different configurations of the shield plate voltages. One can clearly see a difference in the ion distributions inside the trap. In fact, the ion trap exhibits two local minima in the vertical direction due to the presence of the holes in the shield plates placed above and below the trap. By adjusting the voltages on these plates, one can redistribute the ions in the trap into these local minima. On the left-hand side of Figure 1, the ions are more or less equally distributed in the two minima, whereas on the right-hand side, the lower minimum is mostly populated. The cross sections measured from these strongly different distributions agree to within 4%. A similar procedure was employed for C 3 N -. For C 3 N -, the error is larger, about 10%, because its signal strength was almost an order of magnitude less than that of CN -, and hence the fluctuations in the ion signal limited the accuracy with which the rates could be determined. The values of the measured cross sections for both CN -and C 3 N -from different measurements are summarized in Table 2. The determination of the systematic uncertainties (as percentage error) in the measurements involves several factors which are listed in Table 3.</caption>
</figure>
<figure>
<location><page_7><loc_50><loc_33><loc_83><loc_49></location>
<caption>Figure 1. Tomography images for the CN -ions for two different ion density distributions in the trap. The numbers on the color bars are in the units of s -1 . The cross sections determined from these distributions agree to within 4%. Similar results were obtained for C 3 N -also (not shown).</caption>
</figure>
<table>
<location><page_7><loc_22><loc_14><loc_74><loc_21></location>
<caption>Table 2. Cross sections ( × 10 -17 cm 2 ) from a few sets of measurements on CN -and C 3 N -at 266 nm together with the average values and the values from the fit to Equation (2). For accuracy, see Table 3.</caption>
</table>
<table>
<location><page_8><loc_12><loc_74><loc_92><loc_89></location>
<caption>Photodetachment as destruction mechanism for CN -and C 3 N -anions ... 8Table 3. Possible contribution of errors (%) in calculating the cross sections of CN -and C 3 N -. The various contributions are assumed to be independent. Integration limits and background subtraction are in fact not completely independent. However, the dependence is not systematic. Further, this correction does not make any significant difference in the estimation of errors.</caption>
</table>
<text><location><page_8><loc_12><loc_48><loc_84><loc_62></location>The photodetachment cross sections of CN -and C 3 N -are a factor of at least two larger than the cross sections measured for other carbon chain anions C n H -(Best et al. 2011). Hence the abundance of these cyano anions in photon-dominated regions is likely to be significantly influenced by their photodetachment. Furthermore, the cross sections are determined at an energy which is not far away from the photodetachment threshold for both CN -and C 3 N -. Therefore, the large cross section values may indicate the presence of strong resonances.</text>
<section_header_level_1><location><page_8><loc_12><loc_44><loc_42><loc_45></location>3.2. Results from model calculations</section_header_level_1>
<text><location><page_8><loc_12><loc_11><loc_84><loc_42></location>The photodetachment rate constants that function as input data for the model calculations were obtained using a standard interstellar radiation field (Draine 1978). The obtained values were 2.55 × 10 -9 , 1.99 × 10 -9 , 1.16 × 10 -9 , 6.72 × 10 -9 and 1.03 × 10 -8 s -1 for C 2 H -, C 4 H -, C 6 H -, CN -and C 3 N -, respectively. In this calculation we have used the entire reaction set and the rate coefficients of the UMIST database for astrochemistry 2012 (McElroy et al. 2013), which includes the additional anion production mechanisms mentioned by Cordiner et al. (2008), to calculate molecular abundances as a function of the radial distance from the centre of the star (See Cordiner & Millar (2009) for details.). In a second set of calculations, shells of matter with densities that are enhanced relative to the surrounding circumstellar medium were included in the model. Figures 2a (no shells) and 2b (with shells) show the fractional abundances of the important anions, as well as the electron fraction, as a function of radius in the circumstellar envelope. When integrated over radius, these abundances yield the total column densities which were compared with those using the cross section function, σ = 1 × 10 -17 √ 1 -E A //epsilon1 cm 2 , employed in previous studies (Millar et al. 2007). The column densities using these two approaches are listed in Table 4.</text>
<text><location><page_8><loc_12><loc_5><loc_84><loc_10></location>It can be seen that the input of the experimental cross sections somewhat reduces the column densities and thus slightly deteriorates the agreement between the modelled and observed cross sections. Also, the C 3 N -/C 3 N ratio predicted by the model</text>
<text><location><page_9><loc_34><loc_89><loc_34><loc_89></location>/s32</text>
<figure>
<location><page_9><loc_12><loc_66><loc_85><loc_89></location>
<caption>Figure 2. Fractional abundances of the important anions, as well as the electron fraction, as a function of radius in the circumstellar envelope of IRC+10216 without (a) and with (b) shells.</caption>
</figure>
<table>
<location><page_9><loc_12><loc_53><loc_90><loc_58></location>
<caption>Table 4. Calculated and observed column densities (in cm -2 ) of anions in IRC+10216.</caption>
</table>
<text><location><page_9><loc_12><loc_40><loc_84><loc_47></location>(1 . 4 × 10 -3 ) now lies below the observed value (5 × 10 -3 ), whereas previous models tended to overestimate it (Herbst 2009, and references therein). The inclusion of highdensity shells does increase the anion column densities by around 10-20%. However, they remain smaller, but within the same order of magnitude, than those observed.</text>
<text><location><page_9><loc_12><loc_32><loc_84><loc_39></location>The predicted densities not only depend strongly on the rates of photodetachment but also on the efficiency of the formation reactions, such as radiative attachment, radical-ion and dissociative attachment reactions. Regarding the generation of the two cyano anions the model predicts that reactions of N radicals with C -n ions, e.g.,</text>
<formula><location><page_9><loc_23><loc_29><loc_84><loc_30></location>C -6 +N → C 3 N -+C 3 (3)</formula>
<formula><location><page_9><loc_23><loc_26><loc_84><loc_28></location>C -6 +N → CN -+C 5 (4)</formula>
<text><location><page_9><loc_12><loc_14><loc_84><loc_25></location>dominate as formation pathways in the outer and middle parts of the envelope (r ≥ 10 16 cm) for both CN -and C 3 N -. These processes might be partly responsible for the extraordinarily high anion to neutral abundance ratio for C 3 N -(Cordiner & Millar 2009, Ag'undez et al. 2010, Thaddeus et al. 2008, Cernicharo et al. 2007). In the innermost regions (r ≤ 10 16 cm), formation of CN -proceeds via reaction of H -with HCN:</text>
<formula><location><page_9><loc_23><loc_11><loc_84><loc_12></location>H -+HCN → CN -+H 2 . (5)</formula>
<text><location><page_9><loc_12><loc_6><loc_84><loc_10></location>The importance of the latter process is due to the formation of H -through cosmic ray induced ion pair formation in the inner shells of the envelope (Cordiner &</text>
<text><location><page_9><loc_85><loc_78><loc_85><loc_78></location>/s32</text>
<text><location><page_10><loc_12><loc_85><loc_84><loc_89></location>Millar 2009, Prasad & Huntress Jr 1980). At these small radii, radiative attachment of C 3 N and dissociative attachment of HNC 3 are predominant formation routes of C 3 N -:</text>
<formula><location><page_10><loc_23><loc_80><loc_84><loc_81></location>C 3 N+e -→ C 3 N -+h ν (6)</formula>
<formula><location><page_10><loc_23><loc_77><loc_84><loc_79></location>HNC 3 +e -→ C 3 N -+H . (7)</formula>
<text><location><page_10><loc_12><loc_70><loc_84><loc_76></location>Whereas the reactions of N atoms with C n chain anions have been characterized in a selected ion flow tube experiment (Eichelberger et al. 2007), there are, as yet, no laboratory studies on the formation of the cyanide anion from H -and HCN.</text>
<text><location><page_10><loc_12><loc_22><loc_84><loc_70></location>There are also uncertainties in the destruction processes. At a distance from the central star of around 6 × 10 16 cm, where the abundance of the CN -and the C 3 N -anions peaks, photodetachment clearly is the most important degradation mechanism of the two anions and accounts for 45 % of the breakdown of C 3 N -and 35 % for CN -. In the case of CN -, other decay processes are mutual neutralization with C + (30 %) and Si + (7 %) as well as associative detachment with H (15 %). Minor loss processes of C 3 N -are mutual neutralization with C + (25 %) and Si + (6 %) and associative detachment with H (11 %). In the outer regions of the cloud (r > 10 17 cm) mutual neutralization with C + actually becomes predominant for both C 3 N -(accounting for 72 % of the loss at a distance of 2 . 5 × 10 17 cm from the star) and CN -(79 % at the same radius). This behavior is most likely due to the increase of C + abundance towards the edge of the cloud (the peak density of this species there is around 5.4 × 10 -2 cm -3 with an abundance ratio C + /H 2 of 2 . 1 × 10 -4 at a radius of 2 . 2 × 10 17 cm), which is caused by photoionization of C through the interstellar radiation field. In the inner regions of the circumstellar envelope (r < 10 16 cm) mutual neutralization with Mg + is predicted to be the main degradation process. This can be explained by the fact that the Mg + number density is fairly constant throughout the envelope (ranging between 2 × 10 -4 cm -3 and 2 × 10 -3 cm -3 ), whereas the C + abundance is as low as 1 . 5 × 10 -6 cm -3 at a radius of 2 × 10 16 cm. Consequently, the abundance ratio of C + to H 2 increases from 1 . 0 × 10 -12 at a radius of 2 . 2 × 10 15 cm to 7 . 8 × 10 -4 at a radius of 7 . 1 × 10 17 cm, whereas the one of Mg + to H 2 spans only 5 orders of magnitude, rising from 2 . 1 × 10 -10 at a radius of 2 . 2 × 10 15 cm to 1 . 0 × 10 -5 at a radius of 7 . 1 × 10 17 cm. But even at the outermost and the innermost distances photodetachment significantly contributes to the destruction of CN -and C 3 N -.</text>
<text><location><page_10><loc_12><loc_4><loc_84><loc_22></location>The peak abundances of the two cyano anions investigated in this study lie at the radii 6 . 3 × 10 16 cm and 5 . 6 × 10 16 cm for CN -and C 3 N -, respectively, and the maxima of the fractional abundances at 7 . 9 × 10 16 cm for CN -and 7 . 1 × 10 16 cm for C 3 N -. This implies that the CN -peak radius predicted by the model is somewhat larger than the one concluded from observations (2 × 10 16 cm), but slightly lower than the one predicted by model calculations of Ag'undez et al. (2010) (8 × 10 16 cm). From the present data it can be concluded that photodetachment is a very crucial process in the degradation of anions throughout the envelope. However, one has to consider the uncertainties regarding the rate constants of the formation and destruction mechanisms</text>
<text><location><page_11><loc_12><loc_79><loc_84><loc_89></location>of the two anions. The relative importance of photodetachment depends on the rate constants of the competing processes, namely the mutual neutralization processes of the cyano anions with C + and other metallic ions. Harada & Herbst (2008) estimated the rate constant of the reaction of C 3 N -with C + based on earlier flowing afterglow Langmuir probe measurements (Smith et al. 1978) of other ions to follow the expression:</text>
<formula><location><page_11><loc_23><loc_76><loc_84><loc_78></location>k = 7 . 5 × 10 -8 (T / 300) -0 . 5 cm 3 s -1 . (8)</formula>
<text><location><page_11><loc_12><loc_69><loc_84><loc_75></location>To the best of our knowledge, no experimental data on the reaction rate constants of these processes have so far been obtained. The new DESIREE double storage ring at Stockholm University will amend this shortcoming (Schmidt et al. 2008).</text>
<text><location><page_11><loc_12><loc_57><loc_84><loc_69></location>In agreement with other model calculations, the abundances of the anions peak at larger radii than the corresponding neutrals (Guelin et al. 2011). The inclusion of shells with enhanced density similar to the model of Cordiner & Millar (2009) increases the column densities of the anions by about 20% and improves the agreement with observed column densities, predominantly through reducing the rates of photodetachment through the increased dust extinction that they provide.</text>
<section_header_level_1><location><page_11><loc_12><loc_53><loc_26><loc_54></location>4. Conclusions</section_header_level_1>
<text><location><page_11><loc_12><loc_17><loc_84><loc_51></location>The absolute photodetachment cross sections of two molecular anions of astrophysical importance, CN -and C 3 N -, were measured at the ultraviolet wavelength of 266 nm. The measured cross sections are relatively high and might indicate the possibility of strong resonances near the photodetachment threshold. High cross sections imply that the abundance of these molecular anions can be crucially dependent on their destruction by photodetachment especially in photon-dominated regions. The presented model calculations, carried out to investigate molecular anions in the circumstellar envelope of IRC+10216, predict the relative importance of the various mechanisms of production and destruction of cyano anions in different regions of the envelope. It was found that in regions where these molecular anions have their peak abundance, photodetachment serves as the most important destruction mechanism. The calculations also predict that photodetachment significantly contributes to the destruction of these anions throughout the circumstellar envelope. Thus photodetachment plays a fundamental role in the degradation of anions in circumstellar envelopes. However, its exact significance can only be determined if more data on other competing pathways are available. Future experimental investigations on these processes are therefore vital for our understanding of the anion chemistry of circumstellar envelopes.</text>
<text><location><page_11><loc_12><loc_5><loc_84><loc_17></location>This work has been supported by the European Research Council under ERC grant agreement No. 279898 and by the ESF COST Action CM0805 'The Chemical Cosmos: Understanding Chemistry in Astronomical Environments'. We thank Eric Endres for his support during the experiments. Research in molecular astrophysics at QUB is supported by a grant from the STFC. ˇ S. R. ackowledges support by Czech Grant Agency under contract No. P209/12/0233.</text>
<section_header_level_1><location><page_12><loc_12><loc_87><loc_25><loc_88></location>5. References</section_header_level_1>
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<text><location><page_12><loc_12><loc_25><loc_69><loc_26></location>Kasai Y, Kagi E & Kawaguchi K 2007 The Astrophysical Journal 661 , L61-L64.</text>
<text><location><page_12><loc_12><loc_20><loc_84><loc_25></location>Kawaguchi K, Fujimori R, Aimi S, Takano S, Okabayashi E Y, Gupta H, Brunken S, Gottlieb C A, McCarthy M C & Thaddeus P 2007 Publications of the Astronomical Society of Japan 59 , L47L50.</text>
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<text><location><page_12><loc_12><loc_17><loc_64><loc_18></location>Mauron N & Huggins P J 2000 Astronomy & Astrophysics 359 , 707-715.</text>
<text><location><page_12><loc_12><loc_14><loc_84><loc_17></location>McCarthy M C, Gottlieb C A, Gupta H & Thaddeus P 2006 The Astrophysical Journal 652 (2), L141. McDowell M R C 1961 The Observatory 81 , 240-243.</text>
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</document>
[
{
"title": "PHOTODETACHMENT AS DESTRUCTION MECHANISM FOR CN -and C 3 N -ANIONS IN CIRCUMSTELLAR ENVELOPES",
"content": "S. S. Kumar 1 , D. Hauser 1 , R. Jindra 1 , T. Best 1 , ˇ S. Rouˇcka 2 , W.",
"pages": [
1
]
},
{
"title": "D. Geppert 3 , T. J. Millar 4 , and R. Wester 1",
"content": "1 Institut fur Ionenphysik und Angewandte Physik, Universitat Innsbruck, A -6020 Innsbruck, Austria 2 Charles University in Prague, Faculty of Mathematics and Physics, Department of Surface and Plasma Science, 18000 Prague, Czech Republic 3 Department of Physics, AlbaNova, Stockholm University, SE -10691 Stockholm, Sweden 4 Astrophysics Research Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, UK E-mail: [email protected] Abstract. Absolute photodetachment cross sections of two anions of astrophysical importance CN -and C 3 N -were measured to be (1.18 ± (0.03) stat (0.17) sys ) × 10 -17 cm 2 and (1.43 ± (0.14) stat (0.37) sys ) × 10 -17 cm 2 respectively at the ultraviolet wavelength of 266 nm (4.66 eV). These relatively large values of the cross sections imply that photodetachment can play a major role in the destruction mechanisms of these anions particularly in photon-dominated regions. We have therefore carried out model calculations using the newly measured cross sections to investigate the abundance of these molecular anions in the cirumstellar envelope of the carbon-rich star IRC+10216. The model predicts the relative importance of the various mechanisms of formation and destruction of these species in different regions of the envelope. UV photodetachment was found to be the major destruction mechanism for both CN -and C 3 N -anions in those regions of the envelope, where they occur in peak abundance. It was also found that photodetachment plays a crucial role in the degradation of these anions throughout the circumstellar envelope.",
"pages": [
1
]
},
{
"title": "1.1. Molecular anions in space: Observation and astrophysical relevance",
"content": "The discovery of molecules in the interstellar medium about seven decades ago was particularly intriguing since the chemistry governing the formation of molecules in such hostile regions of space was not familiar. Gradually the number of molecules and their cations found in extraterrestrial space increased and it became clear that we in fact live in a 'molecular Universe' (Larsson et al. 2012). However, after the first molecule was identified in the interstellar medium, it took six decades before a molecular anion could be discovered in such environment. This delay was primarily due to the low abundance of anions in space compared to their neutral counterparts and due to the lack of laboratory measurements of high resolution rotational spectra of the anions that could allow their search in space. The first molecular anion ever observed outside our solar system is C 6 H -(McCarthy et al. 2006), which was detected in the envelope of the carbon-rich star IRC+10216. The identification of this molecular anion was followed by the discovery of several other carbon chain anions, C n H -( n = 4, 8) and C n N -( n = 1, 3, 5) in various regions of space such as dark clouds, circumstellar envelopes, and also in Titan's atmosphere (Cernicharo et al. 2007, Cernicharo et al. 2008, Sakai et al. 2007, Sakai et al. 2008, Sakai et al. 2010, Ag'undez et al. 2008, Ag'undez et al. 2010, Remijan et al. 2007, Brunken et al. 2007, Kasai et al. 2007, Kawaguchi et al. 2007, Thaddeus et al. 2008, Gupta et al. 2009). Of these anions, C 5 N -was only tentatively identified. The role of anions in the synthesis of molecules in the interstellar medium has been investigated by Dalgarno & McCray (1973) many years ago, whereas the formation of molecular hydrogen in stars from H -had been pointed out by McDowell (1961) much earlier. The recent discovery of anions in extraterrestrial environments has initiated a fresh interest towards the understanding of anion chemistry in exotic environments. The importance of gas-phase molecular ions in space has been described in detail in a recent review by Larsson et al. (2012).",
"pages": [
2
]
},
{
"title": "1.2. Significance of the present work",
"content": "Extraterrestrial molecular anions are believed to be produced predominantly via electron capture processes such as dissociative or radiative attachment (Larsson et al. 2012). The destruction processes are largely due to photodetachment, associative detachment and mutual neutralization reactions. In photon-dominated regions, the abundance of molecular anions can be mainly determined by their UV photodetachment. Even in the dark clouds where UV photons cannot penetrate UV photodetachment may still contribute to photodestruction of anions because the secondary electrons produced by cosmic rays can excite the molecules to high Rydberg states, which emit UV radiation upon decay. The study of photodetachment processes is also of particular importance in fundamental physics since the extra electron in an anion is bound to the system by means of strong correlated motion of the electrons in the system and the electron- electron correlation plays the most crucial role in such processes. In addition, no theoretical or experimental values of photodetachment cross sections for CN -or C 3 N -have been reported in the literature despite the fact that there have been a number of studies on these molecular anions (Andersen et al. 2001, Bradforth et al. 1993, Gottlieb et al. 2007, Yen et al. 2010). Since these anions have high electron affinities (CN -: 3.862 ± 0.004 eV (Bradforth et al. 1993), C 3 N -: 4.305 ± 0.001 eV (Yen et al. 2010)) their photodetachment requires photons in the ultraviolet range. In the present work, we measured the photodetachment cross sections of CN -and C 3 N -anions at an energy (4.66 eV) near the photodetachment thresholds. Furthermore, we used the measured values as an input to model calculations to investigate the impact of the new cross sections on the predicted abundance of anions in the circumstellar envelope of IRC+10216.",
"pages": [
2,
3
]
},
{
"title": "2.1. Experimental Setup",
"content": "The basic elements of the experimental setup are an ion source, an octupole ion trap, an MCP detector and a laser system. The ion source consists of a piezoelectric pulsed gas valve with a pair of electrodes (referred to as 'plasma electrodes') attached at the exit of the valve. A suitable gas mixture is sent through the gas valve at a certain repetition rate. The ions are generated in a pulsed DC discharge of the gas jet between the plasma electrodes when a high potential difference is applied between them. These ions are then extracted towards the ion trap by a Wiley-McLaren time-of-flight spectrometer oriented perpendicular to the gas jet from the piezo valve. Deflection plates and lenses are used for guiding and focusing the ions into the ion trap. The unique octupole ion trap is made of 100 µ m gold plated molybdenum wires unlike in conventional designs where rods of specific diameter are used as RF electrodes. A short description of this ion trap has been provided by Deiglmayr et al. (2012), where it was used in conjunction with a magneto-optical trap to study reactive collisions of trapped OH -anions with trapped rubidium atoms. A second piezoelectric pulsed gas valve allows for helium buffer gas cooling of the trapped ions. There are two additional electrodes (termed as 'shield plates') above and below the trap that enable us to shape the ion density distribution inside the ion trap. The use of thin wires to construct the trap allows one to probe the trapped ions, for instance with a laser, from the sides. The laser beam can be focused at various positions inside the trap by means of a two-dimensional translation stage with a lens attached to it. This configuration is used to map the ion density distribution inside the trap. In the present experiments, CN -and C 3 N -anions were generated by passing argon gas (at a pressure of about 2-3 bar) over acetonitrile vapor and sending the resulting mixture into the source piezo valve which was operated at 14 Hz. The discharge between the plasma electrodes ionized the gas mixture resulting in the production of several anions including CN -and C 3 N -. The plasma was stabilized by the electrons emitted from a hot filament placed opposite to the pulsed gas valve. The ions were injected into the Wiley-McLaren region, where they were extracted towards the trap with an average kinetic energy of about 240 eV. The desired ionic species can be stored in the ion trap by appropriate timing of the switchable voltages applied on the entrance and exit electrodes of the ion trap in accordance with the time of flight of the various molecular ions. The trap was operated at a radiofrequency of 9 MHz with an amplitude of 180 V on top of a DC voltage of about 240 V. The DC voltage of the trap served to reduce the kinetic energy of the ions coming from the source region to about a few eV. The entrance and exit endcap electrodes of the ion trap were between 10 V and 30 V, the exact value of which did not significantly affect the ion distribution except that the signal strength was slightly modified. The photodetachment measurements were performed with a pulsed laser beam (266 nm, 10 Hz) obtained by frequency quadrupling of the output from a 1064 nm IR laser system with output pulse energy of about 30 mJ and with pulse width of 7 ns. The pulse energy of the laser beam was reduced to a few tens of microjoule and was then sent through a beam splitter. The transmitted beam was used to measure the fluctuations in the laser energy throughout the experiment and these data were used to correct the measured photodetachment cross section. The reflected beam was focused into the trap using the lens attached on the translation stage. The pulse energy of the beam fired into the trap was as low as 25 µ J so as to ensure that there was only single photon absorption and that the wires constituting the trap were not damaged when the laser beam struck them.",
"pages": [
3,
4
]
},
{
"title": "2.2. Measurement procedure",
"content": "The measurement procedure was very similar to the one described previously (Trippel et al. 2006, Hlavenka et al. 2009, Best et al. 2011) except that in the present experiments the laser beam was sent into the ion trap perpendicular to its symmetry axis. Briefly, the ions can be stored in the trap for a few hundred seconds (1 /e lifetime, determined from the exponential decay of the ions stored in the trap). In the first part of the experiment, the background decay rate was determined by measuring the amount of ions left in the trap after different storage times. In the second part, the rates of decay were measured with the UV laser pointing at different positions inside the trap. The photodetachment decay rates when plotted as a function of the positions form a tomography image which reflects the ion density distribution inside the trap. The integral of the rate map is proportional to the photodetachment cross section as detailed elsewhere (Trippel et al. 2006, Best et al. 2011). The photodetachment cross section, σ pd , is given by the expression (Trippel et al. 2006, Best et al. 2011): where k pd ( x, y ) is the position dependent decay rate due to photodetachment, k bg is the background decay rate (decay rate measured without laser) and Φ L is the photon flux.",
"pages": [
4,
5
]
},
{
"title": "2.3. Model Calculations for IRC+10216",
"content": "The photodetachment cross sections measured for CN -and C 3 N -anions in the present experiments, together with those obtained previously (Best et al. 2011) for the carbon chain anions C 2 H -, C 4 H -and C 6 H -, were used as input for model calculations of the circumstellar envelope of IRC+10216. The photodetachment cross sections of CN -and C 3 N -were fitted to the expression used in previous model calculations (Millar et al. 2007): in which σ is the cross section, σ ∞ the cross section at infinite photon energy, E A the photodetachment threshold energy and /epsilon1 the photon energy. Since our cross section measurements have been carried out only at a wavelength of 266 nm (at which a sufficiently intense UV beam was available from our laser systems) only two points exist for the fit of the photon energy/cross section curve for each of the nitrile anions, the cross section at threshold energy (where σ = 0) and the one measured at 266 nm. Of course, there exists the possibility of strong resonances, especially at photon energies only slightly above the threshold, which cannot be ruled out in the absence of complementary experimental data on photodetachment cross sections of these anions. For a more accurate treatment of the model, one would require experimental cross sections at higher photon energies necessitating radiation from sources such as synchrotrons or free electron lasers (FELs). Regarding the threshold energy ( E A ) of CN -, the value obtained by Bradforth et al. (1993) who employed a pulsed fixed-frequency negative ion photoelectron spectrometer (3.862 ± 0.004 eV) was used for the fit. In the case of C 3 N -the result from Yen et al. (2010) measured using slow electron velocity-map imaging (4.305 ± 0.001 eV) and field-free time-of-flight was applied. For the photodetachment cross sections of the hydrocarbon anions the fitted values from Best et al. (2011) were used. The chemical models are based on the assumption of a uniform mass-loss rate for the circumstellar envelope of IRC+10216 described by Millar et al. (2000) together with a second model, described by Cordiner & Millar (2009), in which density-enhanced shells are included. With density-enhanced shells of gas and dust, a more realistic modelling of the circumstellar envelope is achieved by introducing a set of density enhancements with the physical parameters of the envelope based on the dust-shell observation by Mauron & Huggins (2000). For modelling, the conditions expected for the well-studied circumstellar envelope of IRC+10216 were applied. Consequently, a spherically symmetric outflow velocity from the central star of 1.45 × 10 6 cm s -1 and a mass loss of 1.5 × 10 -5 solar masses per year were assumed for the envelope (Men'shchikov et al. 2001). The adopted temperature profile is based on a fit to the gas kinetic temperature profile of Crosas & Menten (1997), with a minimum temperature of 10 K fixed in the outer region of the envelope and is the same as used by Cordiner & Millar (2009). The initial chemical abundances of parent molecules relative to that of H 2 used in the model are listed in Table 1. These species are formed in the inner envelope close to the star at high density and temperature and blown outwards in a spherically symmetric outflow (Millar et al. 2000). The calculations begin at an inner radius of 10 15 cm where photons from the external, interstellar radiation field begin to destroy parent species creating reactive radicals and ions and initiating the synthesis of anions and other species. The number density n ( r ) declines with the radius as 1 /r 2 . In the second set of calculations, in addition to the 1 /r 2 dependence of the number density, a series of step-like density enhancements of the form βn ( r ) is introduced. The parameter β is set to 5 for all shells in the model. According to dust shell parameters deduced from scattered light observations by Mauron & Huggins (2000), we assume that each shell has a thickness of 2 arcsec and the spacing between the shells is 12 arcsec. This distance corresponds to roughly 530 years between the peaks of enhanced mass loss (See Cordiner & Millar (2009) for details.).",
"pages": [
5,
6
]
},
{
"title": "3.1. Experimental results",
"content": "The photodetachment cross sections of CN -and C 3 N -are a factor of at least two larger than the cross sections measured for other carbon chain anions C n H -(Best et al. 2011). Hence the abundance of these cyano anions in photon-dominated regions is likely to be significantly influenced by their photodetachment. Furthermore, the cross sections are determined at an energy which is not far away from the photodetachment threshold for both CN -and C 3 N -. Therefore, the large cross section values may indicate the presence of strong resonances.",
"pages": [
8
]
},
{
"title": "3.2. Results from model calculations",
"content": "The photodetachment rate constants that function as input data for the model calculations were obtained using a standard interstellar radiation field (Draine 1978). The obtained values were 2.55 × 10 -9 , 1.99 × 10 -9 , 1.16 × 10 -9 , 6.72 × 10 -9 and 1.03 × 10 -8 s -1 for C 2 H -, C 4 H -, C 6 H -, CN -and C 3 N -, respectively. In this calculation we have used the entire reaction set and the rate coefficients of the UMIST database for astrochemistry 2012 (McElroy et al. 2013), which includes the additional anion production mechanisms mentioned by Cordiner et al. (2008), to calculate molecular abundances as a function of the radial distance from the centre of the star (See Cordiner & Millar (2009) for details.). In a second set of calculations, shells of matter with densities that are enhanced relative to the surrounding circumstellar medium were included in the model. Figures 2a (no shells) and 2b (with shells) show the fractional abundances of the important anions, as well as the electron fraction, as a function of radius in the circumstellar envelope. When integrated over radius, these abundances yield the total column densities which were compared with those using the cross section function, σ = 1 × 10 -17 √ 1 -E A //epsilon1 cm 2 , employed in previous studies (Millar et al. 2007). The column densities using these two approaches are listed in Table 4. It can be seen that the input of the experimental cross sections somewhat reduces the column densities and thus slightly deteriorates the agreement between the modelled and observed cross sections. Also, the C 3 N -/C 3 N ratio predicted by the model /s32 (1 . 4 × 10 -3 ) now lies below the observed value (5 × 10 -3 ), whereas previous models tended to overestimate it (Herbst 2009, and references therein). The inclusion of highdensity shells does increase the anion column densities by around 10-20%. However, they remain smaller, but within the same order of magnitude, than those observed. The predicted densities not only depend strongly on the rates of photodetachment but also on the efficiency of the formation reactions, such as radiative attachment, radical-ion and dissociative attachment reactions. Regarding the generation of the two cyano anions the model predicts that reactions of N radicals with C -n ions, e.g., dominate as formation pathways in the outer and middle parts of the envelope (r ≥ 10 16 cm) for both CN -and C 3 N -. These processes might be partly responsible for the extraordinarily high anion to neutral abundance ratio for C 3 N -(Cordiner & Millar 2009, Ag'undez et al. 2010, Thaddeus et al. 2008, Cernicharo et al. 2007). In the innermost regions (r ≤ 10 16 cm), formation of CN -proceeds via reaction of H -with HCN: The importance of the latter process is due to the formation of H -through cosmic ray induced ion pair formation in the inner shells of the envelope (Cordiner & /s32 Millar 2009, Prasad & Huntress Jr 1980). At these small radii, radiative attachment of C 3 N and dissociative attachment of HNC 3 are predominant formation routes of C 3 N -: Whereas the reactions of N atoms with C n chain anions have been characterized in a selected ion flow tube experiment (Eichelberger et al. 2007), there are, as yet, no laboratory studies on the formation of the cyanide anion from H -and HCN. There are also uncertainties in the destruction processes. At a distance from the central star of around 6 × 10 16 cm, where the abundance of the CN -and the C 3 N -anions peaks, photodetachment clearly is the most important degradation mechanism of the two anions and accounts for 45 % of the breakdown of C 3 N -and 35 % for CN -. In the case of CN -, other decay processes are mutual neutralization with C + (30 %) and Si + (7 %) as well as associative detachment with H (15 %). Minor loss processes of C 3 N -are mutual neutralization with C + (25 %) and Si + (6 %) and associative detachment with H (11 %). In the outer regions of the cloud (r > 10 17 cm) mutual neutralization with C + actually becomes predominant for both C 3 N -(accounting for 72 % of the loss at a distance of 2 . 5 × 10 17 cm from the star) and CN -(79 % at the same radius). This behavior is most likely due to the increase of C + abundance towards the edge of the cloud (the peak density of this species there is around 5.4 × 10 -2 cm -3 with an abundance ratio C + /H 2 of 2 . 1 × 10 -4 at a radius of 2 . 2 × 10 17 cm), which is caused by photoionization of C through the interstellar radiation field. In the inner regions of the circumstellar envelope (r < 10 16 cm) mutual neutralization with Mg + is predicted to be the main degradation process. This can be explained by the fact that the Mg + number density is fairly constant throughout the envelope (ranging between 2 × 10 -4 cm -3 and 2 × 10 -3 cm -3 ), whereas the C + abundance is as low as 1 . 5 × 10 -6 cm -3 at a radius of 2 × 10 16 cm. Consequently, the abundance ratio of C + to H 2 increases from 1 . 0 × 10 -12 at a radius of 2 . 2 × 10 15 cm to 7 . 8 × 10 -4 at a radius of 7 . 1 × 10 17 cm, whereas the one of Mg + to H 2 spans only 5 orders of magnitude, rising from 2 . 1 × 10 -10 at a radius of 2 . 2 × 10 15 cm to 1 . 0 × 10 -5 at a radius of 7 . 1 × 10 17 cm. But even at the outermost and the innermost distances photodetachment significantly contributes to the destruction of CN -and C 3 N -. The peak abundances of the two cyano anions investigated in this study lie at the radii 6 . 3 × 10 16 cm and 5 . 6 × 10 16 cm for CN -and C 3 N -, respectively, and the maxima of the fractional abundances at 7 . 9 × 10 16 cm for CN -and 7 . 1 × 10 16 cm for C 3 N -. This implies that the CN -peak radius predicted by the model is somewhat larger than the one concluded from observations (2 × 10 16 cm), but slightly lower than the one predicted by model calculations of Ag'undez et al. (2010) (8 × 10 16 cm). From the present data it can be concluded that photodetachment is a very crucial process in the degradation of anions throughout the envelope. However, one has to consider the uncertainties regarding the rate constants of the formation and destruction mechanisms of the two anions. The relative importance of photodetachment depends on the rate constants of the competing processes, namely the mutual neutralization processes of the cyano anions with C + and other metallic ions. Harada & Herbst (2008) estimated the rate constant of the reaction of C 3 N -with C + based on earlier flowing afterglow Langmuir probe measurements (Smith et al. 1978) of other ions to follow the expression: To the best of our knowledge, no experimental data on the reaction rate constants of these processes have so far been obtained. The new DESIREE double storage ring at Stockholm University will amend this shortcoming (Schmidt et al. 2008). In agreement with other model calculations, the abundances of the anions peak at larger radii than the corresponding neutrals (Guelin et al. 2011). The inclusion of shells with enhanced density similar to the model of Cordiner & Millar (2009) increases the column densities of the anions by about 20% and improves the agreement with observed column densities, predominantly through reducing the rates of photodetachment through the increased dust extinction that they provide.",
"pages": [
8,
9,
10,
11
]
},
{
"title": "4. Conclusions",
"content": "The absolute photodetachment cross sections of two molecular anions of astrophysical importance, CN -and C 3 N -, were measured at the ultraviolet wavelength of 266 nm. The measured cross sections are relatively high and might indicate the possibility of strong resonances near the photodetachment threshold. High cross sections imply that the abundance of these molecular anions can be crucially dependent on their destruction by photodetachment especially in photon-dominated regions. The presented model calculations, carried out to investigate molecular anions in the circumstellar envelope of IRC+10216, predict the relative importance of the various mechanisms of production and destruction of cyano anions in different regions of the envelope. It was found that in regions where these molecular anions have their peak abundance, photodetachment serves as the most important destruction mechanism. The calculations also predict that photodetachment significantly contributes to the destruction of these anions throughout the circumstellar envelope. Thus photodetachment plays a fundamental role in the degradation of anions in circumstellar envelopes. However, its exact significance can only be determined if more data on other competing pathways are available. Future experimental investigations on these processes are therefore vital for our understanding of the anion chemistry of circumstellar envelopes. This work has been supported by the European Research Council under ERC grant agreement No. 279898 and by the ESF COST Action CM0805 'The Chemical Cosmos: Understanding Chemistry in Astronomical Environments'. We thank Eric Endres for his support during the experiments. Research in molecular astrophysics at QUB is supported by a grant from the STFC. ˇ S. R. ackowledges support by Czech Grant Agency under contract No. P209/12/0233.",
"pages": [
11
]
},
{
"title": "5. References",
"content": "Ag'undez M, Cernicharo J, Gu'elin M, Gerin M, McCarthy M C & Thaddeus P 2008 Astronomy & Astrophysics 478 (1), L19-L22. Ag'undez M, Cernicharo J, Gu'elin M, Kahane C, Roueff E, K/suppresslos J, Aoiz F J, Lique F, Marcelino N, Goicoechea J R, Gonz'alez Garc'ıa M, Gottlieb C A, McCarthy M C & Thaddeus P 2010 Astronomy & Astrophysics 517 , L2. Andersen L H, Bak J, Boye S, Clausen M, Hovgaard M, Jensen M J, Lapierre A & Seiersen K 2001 The Journal of Chemical Physics 115 , 3566. Best T, Otto R, Trippel S, Hlavenka P, von Zastrow A, Eisenbach S, J'ezouin S, Wester R, Vigren E, Hamberg M & Geppert W D 2011 The Astrophysical Journal 742 (2), 63. Bradforth S E, Kim E H, Arnold D W & Neumark D M 1993 The Journal of Chemical Physics 98 (2), 800. Brunken S, Gupta H, Gottlieb C A, McCarthy M C & Thaddeus P 2007 The Astrophysical Journal 664 (1), L43-L46. Cernicharo J, Gu'elin M, Ag'undez M, Kawaguchi K, McCarthy M & Thaddeus P 2007 Astronomy & Astrophysics 467 (2), L37-L40. Cernicharo J, Gu'elin M, Ag'undez M, McCarthy M C & Thaddeus P 2008 The Astrophysical Journal 688 , L83-L86. Cordiner M A & Millar T J 2009 The Astrophysical Journal 697 (1), 68. Cordiner M A, Millar T J, Walsh C, Herbst E, Lis D C, Bell T A & Roueff E 2008 Proceedings of the International Astronomical Union 251 , 157. Crosas M & Menten K M 1997 The Astrophysical Journal 483 (2), 913. Dalgarno A & McCray R A 1973 The Astrophysical Journal 181 , 95-100. Deiglmayr J, Goritz A, Best T, Weidemuller M & Wester R 2012 Physical Review A 86 (4), 043438. Draine B T 1978 The Astrophysical Journal Supplement Series 36 , 595. Eichelberger B, Snow T P, Barckholtz C & Bierbaum V M 2007 The Astrophysical Journal 667 (2), 1283. Gottlieb C A, Brunken S, McCarthy M C & Thaddeus P 2007 The Journal of Chemical Physics 126 (19), 191101. Guelin M, Agundez M, Cernicharo J, Gottlieb C, McCarthy M & Thaddeus P 2011 in 'IAU Symposium' Vol. 280 p. 21. Gupta H, Gottlieb C A, McCarthy M C & Thaddeus P 2009 The Astrophysical Journal 691 (2), 14941500. Harada N & Herbst E 2008 The Astrophysical Journal 685 (1), 272. Herbst E 2009 in 'Submillimeter Astrophysics and Technology: a Symposium Honoring Thomas G. Phillips' Vol. 417 p. 153. Hlavenka P, Otto R, Trippel S, Mikosch J, Weidemuller M & Wester R 2009 The Journal of Chemical Physics 130 (6), 061105. Kasai Y, Kagi E & Kawaguchi K 2007 The Astrophysical Journal 661 , L61-L64. Kawaguchi K, Fujimori R, Aimi S, Takano S, Okabayashi E Y, Gupta H, Brunken S, Gottlieb C A, McCarthy M C & Thaddeus P 2007 Publications of the Astronomical Society of Japan 59 , L47L50. Larsson M, Geppert W D & Nyman G 2012 Reports on Progress in Physics 75 (6), 066901. Mauron N & Huggins P J 2000 Astronomy & Astrophysics 359 , 707-715. McCarthy M C, Gottlieb C A, Gupta H & Thaddeus P 2006 The Astrophysical Journal 652 (2), L141. McDowell M R C 1961 The Observatory 81 , 240-243. McElroy D, Walsh C, Markwick A J, Cordiner M A, Smith K & Millar T J 2013 Astronomy & Astrophysics 550 , A36. Men'shchikov A B, Balega Y, Blocker T, Osterbart R & Weigelt G 2001 Astronomy & Astrophysics 368 (2), 497-526. Millar T J, Herbst E & Bettens R P A 2000 Monthly Notices of the Royal Astronomical Society 316 (1), 195-203. Millar T J, Walsh C, Cordiner M A, N'ı Chuim'ın R & Herbst E 2007 The Astrophysical Journal Letters 662 (2), L87-L90. Prasad S S & Huntress Jr W T 1980 The Astrophysical Journal Supplement Series 43 , 1-35. Remijan A J, Hollis J M, Lovas F J, Cordiner M A, Millar T J, Markwick-Kemper A J & Jewell P R 2007 The Astrophysical Journal 664 (1), L47-L50. Sakai N, Sakai T, Osamura Y & Yamamoto S 2007 The Astrophysical Journal 667 (1), L65-L68. Sakai N, Sakai T & Yamamoto S 2008 The Astrophysical Journal 673 (1), L71-L74. Sakai N, Shiino T, Hirota T, Sakai T & Yamamoto S 2010 The Astrophysical Journal Letters 718 (2), L49-L52. Schmidt H T, Johansson H A B, Thomas R D, Geppert W D, Haag N, Reinhed P, Ros'en S, Larsson M, Danared H, Rensfelt K G et al. 2008 International Journal of Astrobiology 7 (3-4), 205-208. Smith D, Church M J & Miller T M 1978 The Journal of Chemical Physics 68 , 1224. Thaddeus P, Gottlieb C A, Gupta H, Brunken S, McCarthy M C, Ag'undez M, Gu'elin M & Cernicharo J 2008 The Astrophysical Journal 677 (2), 1132. Yen T A, Garand E, Shreve A T & Neumark D M 2010 The Journal of Physical Chemistry A 114 (9), 3215-3220.",
"pages": [
12,
13
]
}
]
2013ApJ...776...53B
https://arxiv.org/pdf/1307.8038.pdf
<document>
<section_header_level_1><location><page_1><loc_17><loc_86><loc_83><loc_87></location>MAGNETICALLY CONTROLLED CIRCULATION ON HOT EXTRASOLAR PLANETS</section_header_level_1>
<text><location><page_1><loc_27><loc_84><loc_73><loc_85></location>Konstantin Batygin 1 , Sabine Stanley 2 & David J. Stevenson 3</text>
<text><location><page_1><loc_11><loc_81><loc_89><loc_84></location>1 Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 2 Department of Physics, University of Toronto, 60 St. George St., Toronto, ON and 3</text>
<text><location><page_1><loc_12><loc_81><loc_89><loc_82></location>Division of Geological and Planetary Sciences, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125</text>
<text><location><page_1><loc_40><loc_79><loc_60><loc_80></location>Draft version September 19, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_77><loc_55><loc_78></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_63><loc_86><loc_76></location>Through the process of thermal ionization, intense stellar irradiation renders Hot Jupiter atmospheres electrically conductive. Simultaneously, lateral variability in the irradiation drives the global circulation with peak wind speeds of order ∼ km/s. In turn, the interactions between the atmospheric flows and the background magnetic field give rise to Lorentz forces that can act to perturb the flow away from its purely hydrodynamical counterpart. Using analytical theory and numerical simulations, here we show that significant deviations away from axisymmetric circulation are unstable in presence of a non-negligible axisymmetric magnetic field. Specifically, our results suggest that dayside-to-nightside flows, often obtained within the context of three-dimensional circulation models, only exist on objects with anomalously low magnetic fields, while the majority of highly irradiated exoplanetary atmospheres are entirely dominated by zonal jets.</text>
<section_header_level_1><location><page_1><loc_22><loc_60><loc_35><loc_61></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_44><loc_48><loc_59></location>The last decade's discovery and rapid accumulation of the transiting extrasolar planetary aggregate has uncovered a multitude of previously unexplored regimes of various physical phenomena. Perhaps the first unexpected discovery was the existence of Hot Jupiters (i.e. gaseous giant planets that reside within ∼ 0 . 1AU of their host star), which arose from the earliest exoplanetary detections (Mayor & Queloz 1995; Marcy & Butler 1996). Accordingly, among the most intriguing novel theoretical subjects, is the study of atmospheric dynamics on highly irradiated planets.</text>
<text><location><page_1><loc_8><loc_35><loc_48><loc_44></location>Today, it is well known that the orbital region occupied by Hot Jupiters can also be occupied by lower mass (including terrestrial) planets (Batalha et al. 2012). However, because of their higher likelihood of transit and comparative predisposition for characterization, Hot Jupiters remain at the forefront of the study of extrasolar atmospheric circulation (Showman et al. 2011).</text>
<section_header_level_1><location><page_1><loc_12><loc_33><loc_44><loc_34></location>1.1. Hydrodynamic Global Circulation Models</section_header_level_1>
<text><location><page_1><loc_8><loc_21><loc_48><loc_32></location>Dynamic meteorology is a phenomenologically rich subject because of the lack of separation of physical scales. In other words, differences in microphysical nature of a given system can have profound effects on its macroscopic state. As a result, it comes as no surprise that circulation patterns on Hot Jupiters generally do not resemble those on Solar System gas giants (Showman et al. 2008; Menou & Rauscher 2009).</text>
<text><location><page_1><loc_8><loc_9><loc_48><loc_21></location>From a hydrodynamical point of view, the circulational modes of typical Hot Jupiter atmospheres differ in two principal ways, compared to Solar System gas giants. The first and most obvious difference is the energetics. Unlike the outer Solar System, Hot Jupiters reside in an environment where the incoming stellar irradiation completely dominates over the intrinsic planetary heat-flux. As a result, circulation patterns on Hot Jupiters are driven primarily by the congenital</text>
<text><location><page_1><loc_10><loc_7><loc_25><loc_8></location>[email protected]</text>
<text><location><page_1><loc_52><loc_53><loc_92><loc_61></location>dayside-to-nightside temperature differences (Showman & Polvani 2011). Furthermore, concurrent with the cooling of the planetary interior, the top-down heating of the atmosphere ensures the onset of stable stratification in the observable ( P > 100 bars) atmospheric region (Guillot & Showman 2002; Burrows et al. 2007).</text>
<text><location><page_1><loc_52><loc_41><loc_92><loc_53></location>The second difference lies in the extent to which the atmospheres are rotationally dominated. While Solar System gas giants rotate rapidly (i.e. T Jup glyph[similarequal] T Sat glyph[similarequal] 10 hours), Hot Jupiters are thought to rotate pseudosynchronously with their orbital periods (i.e. T HJ ∼ 3 -5 days) as a result of tidal de-spinning (see Hut (1981)). This implies that although still dynamically significant, rotation alone does not exhibit commanding control over the atmospheric flow.</text>
<text><location><page_1><loc_52><loc_9><loc_92><loc_41></location>Since the discovery of the first transiting extrasolar gas giant HD209458b (Charbonneau et al. 2000; Henry et al. 2000), numerous authors have explored the atmospheric dynamics of Hot Jupiters with a variety of numerical techniques. Because of the inherent differences in the frameworks of the simulations, today, there exists a hierarchical collection of results that correspond to variable degrees of sophistication. On the simpler end of the spectrum are 2D shallow-water simulations (Cho et al. 2008, 2003; Langton & Laughlin 2008, 2007) while the more intricate global circulation models (GCM's) include solvers of the 3D 'primitive' equations (Cooper & Showman 2005; Showman et al. 2008; Menou & Rauscher 2009; Heng et al. 2011) as well as the 3D fully compressible Navier-Stokes equations (Dobbs-Dixon & Lin 2008; Dobbs-Dixon & Agol 2012). Simultaneously, various groups have gone to different lengths in their treatment of radiative transfer, with exploited models ranging from simple prescriptions such as Newtonian cooling (Showman et al. 2008) to double-gray (Rauscher & Menou 2012) and non-gray (Showman et al. 2009) schemes. An important step towards delineating the correspondence among results obtained with different solvers has been recently performed by Heng et al. (2011).</text>
<text><location><page_1><loc_53><loc_8><loc_92><loc_9></location>Although there are quantitative differences in the re-</text>
<text><location><page_2><loc_8><loc_73><loc_48><loc_92></location>sults generated by different GCM's, there is general agreement on the qualitative features of the circulation. Specifically, there are three aspects of interest. First, super-rotating zonal jets exist in all simulations. Their number (and naturally, the widths) ranges between 1 and 4, depending on the model (see Showman et al. (2009)), but the relative sparsity of the jets compared to Jupiter and Saturn is understood to be a result of diminished rotation rate (Showman & Guillot 2002). Moreover, in a recent study, Showman & Polvani (2011) showed that the formation of jets is ordained by the interaction of the atmospheric flow with standing Rossby waves that in turn result from the strong difference in the radiative forcing between the planetary dayside and the nightside.</text>
<text><location><page_2><loc_8><loc_57><loc_48><loc_73></location>Second, the characteristic wind speeds produced by different models are consistent within a factor of a few, and are generally in the ∼ km/s range. This is likely a direct result of the overall similarity in the force-balance setup within the models. Specifically, Showman et al. (2011) argue that near the equator, the horizontal pressuregradient acceleration caused by the asymmetric irradiation is balanced by the advective acceleration. Meanwhile, Coriolis force takes the place of advective acceleration as the primary balancing term in the mid-latitudes. Both force-balances yield ∼ km/s as the characteristic wind speeds, in agreement with the numerical models.</text>
<text><location><page_2><loc_8><loc_33><loc_48><loc_57></location>Finally, in GCMs that resolve the vertical structure of the atmosphere (e.g. Showman et al. (2008); Menou & Rauscher (2009); Heng et al. (2011)) eastward jets consistently dominate the lower atmosphere while the upper atmosphere is characterized by more or less symmetric dayside-to-nightside circulation. In other words, winds originate at the sub-solar point and flow to the anti-solar point over the terminator in the upper atmosphere. The transition between the circulation patterns takes place at P ∼ 0 . 1 -0 . 01 bars and is a consequence of the substantial reduction of the radiative time constant with diminishing pressure (Iro et al. 2005). In particular, because the radiative adjustment timescale is much shorter than the advective timescale in the upper atmosphere, the flow is unable to perturb the temperature structure away from radiative equilibrium significantly. Figure (1) depicts a schematic representation of the characteristic features of atmospheric circulation on Hot Jupiters.</text>
<section_header_level_1><location><page_2><loc_10><loc_30><loc_47><loc_31></location>1.2. Magnetically Dragged Global Circulation Models</section_header_level_1>
<text><location><page_2><loc_8><loc_7><loc_48><loc_29></location>There exists another important, distinctive feature of Hot Jupiter atmospheres, namely their non-negligible electrical conductivity (see Figure 2). Electrical conductivity in Hot Jupiter atmospheres does not originate from the ionization of H or He, but rather from the stripping of the valence electrons belonging to alkali metals such as K and Na (Batygin & Stevenson 2010; Perna et al. 2010). While these elements are thought to be present in trace abundances (e.g. [K]/[H] ∼ 10 -6 . 5 , [Na]/[H] ∼ 10 -5 . 5 ) (Lodders 1999), temperatures of ∼ 2000K at upper atmospheric pressures, lead to total and partial ionization of K and Na respectively. In fact, at mbar levels, the conductivity can reach values as high as σ ∼ 1 S/m (Batygin et al. 2011; Rauscher & Menou 2012; Heng 2012). Furthermore, it is generally expected that much like solar system gas giants, Hot Jupiters posses interior dynamos, that produce surface fields comparable to, or in slight ex-</text>
<figure>
<location><page_2><loc_52><loc_68><loc_91><loc_92></location>
<caption>Fig. 1.A schematic diagram of the problem considered in this work. A spin-pole aligned dipole magnetic field is thought to arise from a dynamo operating in the deep interior of the planet. As a result of thermal ionization of Alkali metals present in the radiative atmosphere, the interactions between high-velocity flows and the background field lead to non-trivial corrections to the hydrodynamic solution of the global atmospheric circulation. It is likely that the topologically more complex dayside-to-nightside flows in the upper atmosphere ( P ∼ mbar) are more affected by magnetohydrodynamic effects than the zonal flows that reside in the deep atmosphere.</caption>
</figure>
<text><location><page_2><loc_52><loc_45><loc_92><loc_54></location>upiter's field 1 (e.g. B ∼ 3 -30 Gauss) (Stevenson 2003; Christensen et al. 2009). Consequently, there is a distinct possibility that atmospheric circulation on Hot Jupiters may be in part magnetically controlled. That is to say, highly irradiated atmospheres may be sufficiently conductive for the Lorentz force to play an appreciable, if not dominant role in the force-balance.</text>
<text><location><page_2><loc_52><loc_13><loc_92><loc_45></location>Realizing the potential importance of the coupling between the mean flow and the planetary magnetic field, Perna et al. (2010) modeled the Lorentz force as a Rayleigh drag (a velocity-dependent force that opposes the flow) and incorporated it into the GCM previously utilized by Menou & Rauscher (2010). This effort was later amended by Rauscher & Menou (2013), who also modeled the Lorentz force as a Rayleigh drag but selfconsistently accounted for spatial variability in the electrical conductivity (by extension the drag timescale) in the weather layer. The results obtained with dragged GCMs exhibit significant differences in the obtained flow velocities relative to the standard GCMs. Namely, Perna et al. (2010) found a factor of ∼ 3 decrease in the peak wind speeds as the background dipole magnetic field was increased from B dip = 3 G to B dip = 30 G, while Rauscher & Menou (2012) found a similar decline in the jet speeds as the field was increased from B dip = 0 G to B dip = 10 G. The magnetic limitation of the peak wind speeds is of considerable importance as it may prevent the global circulation from approaching a super-sonic state (note that the characteristic sound speed is order c s ∼ √ k B T/µ ∼ 3 km/s, where k B is Boltzmann's con-</text>
<unordered_list>
<list_item><location><page_2><loc_52><loc_7><loc_92><loc_13></location>1 Although, it is possible that bodies with diminished internal heat fluxes (see e.g. Burrows et al. (2007)) may have comparatively lower fields. Unfortunately at present, strengths and morphologies of exoplanetary magnetic fields remain observationally elusive (Hallinan et al. 2013).</list_item>
</unordered_list>
<figure>
<location><page_3><loc_9><loc_73><loc_48><loc_92></location>
<caption>Fig. 2.Electrical conductivity at various pressure levels in a typical Hot Jupiter atmosphere. The conductivity arises as a result of thermal ionization of Alkali metals and the curves are computed as done in (Batygin & Stevenson 2010). While the ionization of K dominates at lower temperatures, it saturates at T ∼ 1500K, giving way to Na as the primary additional source of free electrons. Note that the conductivity is only weakly dependent on density.</caption>
</figure>
<text><location><page_3><loc_8><loc_60><loc_48><loc_63></location>stant, T is the temperature, and µ is the mean molecular weight), thereby inhibiting the formation of shocks.</text>
<section_header_level_1><location><page_3><loc_12><loc_57><loc_44><loc_59></location>1.3. The Necessity for Magnetohydrodynamic Circulation Models</section_header_level_1>
<text><location><page_3><loc_8><loc_21><loc_48><loc_56></location>Although dragged 3D GCMs clearly highlight the quantitative importance of the magnetic effects in Hot Jupiter atmospheres, they fail to accentuate significant qualitative differences in the obtained flows. Specifically, much like conventional GCMs, magnetically dragged GCMs still show deep-seated zonal jets, overlaid by complex flow patterns that intersect the poles of the planets. This lack of qualitative differences may arise from two distinct possibilities. The first is that beyond diminishing the peak wind speeds, the background magnetic field has little effect on the global circulation. In actuality, this may very well be true for pressure levels where the circulation is dominated by zonal jets, because of the geometrical simplicity of the flow-field interactions. Indeed, the coupling between the zonal flow and the polealigned background dipole field is azimuthally symmetric: differentially rotating jets convert the poloidal field into toroidal field (Liu et al. 2008; Batygin & Stevenson 2010). As will be discussed in detail below, beyond the reduction of velocities, this conversion poses few dynamical ramifications for the jets. Furthermore, owing to higher pressure and somewhat diminished temperatures compared with the upper atmosphere (and the associated decrease in conductivity), the zonal jets may reside in the kinematic regime, where the effects of the Lorentz force are modest (Batygin et al. 2011; Menou 2012).</text>
<text><location><page_3><loc_8><loc_7><loc_48><loc_21></location>The second possibility is that although in reality the interactions with the background field impel the circulation to strongly deviate from its purely hydrodynamical counterpart, the procedure of modeling the Lorentz force as a Rayleigh drag does not capture the essential features of the dynamics. This is likely true in the upper atmosphere, where azimuthal symmetry is broken and the flow takes on a more topologically complex form. After all, in such a setting there is no requirement for the Lorentz force to simply oppose the flow everywhere, as is done by Rayleigh drag. Thus, there is a distinct possibil-</text>
<text><location><page_3><loc_52><loc_87><loc_92><loc_92></location>ity that previous modeling efforts have consistently misrepresented the circulation patterns of the upper atmospheres of Hot Jupiters. Accordingly, the investigation of this possibility is the primary purpose of this work.</text>
<text><location><page_3><loc_52><loc_57><loc_92><loc_86></location>A statistically sound comparison between theoretical models and observations requires the incremental decrease in the goodness of fit to outweigh the cost of introducing new degrees of freedom into the model (see Rodgers (2000) for an in-depth review). Within the context of extrasolar planets, the limitations in observational capabilities and the quality of the data render the construction of highly sophisticated models unjustified (Line et al. 2012). Although a rigorous comparison with observational data is not the focus of this paper, our modeling efforts will lie in the same rudimentary spirit. In other words, here we shall focus on understanding the qualitative, rather than quantitative nature of the circulation. Numerous simplifying assumptions will be made and the representation of the flow (including flow velocities, dayside-to-nightside temperature differences, etc) should only be viewed as approximate. However unlike all previous works on the subject, the model we shall utilize will remain self-consistently magneto-hydrodynamic (MHD). In taking this approach, we hope to successfully capture the essential features of magnetic effects in highly irradiated planetary atmospheres.</text>
<text><location><page_3><loc_52><loc_36><loc_92><loc_57></location>The paper is organized as follows. In section 2, we describe the equations inherent to our numerical GCM and reproduce the main features of Hot Jupiter atmospheric flows in the purely hydrodynamic regime. In section 3, we discuss the qualitative features of the atmospheric flows, treating the Lorentz force as a hydrodynamic drag. Specifically, we develop an analytical theory for magetically-dragged circulation patterns in the upper atmosphere and test the resulting scaling law against numerical simulations with enhanced viscosity and explore the effects of varying the radiative timescale. In section 4, we introduce a pole-aligned background magnetic field and demonstrate the transition of the upper atmosphere's dayside-to-nightside circulation into a globally zonal state with the onset of the background field. We conclude and discuss our results in section 5.</text>
<section_header_level_1><location><page_3><loc_55><loc_34><loc_88><loc_35></location>2. NUMERICAL GLOBAL CIRCULATION MODEL</section_header_level_1>
<text><location><page_3><loc_52><loc_20><loc_92><loc_34></location>The Hot Jupiter GCM we have adopted here is a variant of the numerical geodynamo model constructed by Kuang & Bloxham (1999). Since its conception, the model's versatility has been exploited extensively to explain the geodynamo (Kuang & Bloxham 1999; Dumberry & Bloxham 2002), the ancient Martian dyanamo (Stanley et al. 2008), Mercury's thin-shell dyanamo (Stanley et al. 2005; Zuber et al. 2007), Saturn's dynamo (Stanley 2010), as well as dynamos of Uranus & Neptune (Stanley & Bloxham 2004, 2006).</text>
<text><location><page_3><loc_52><loc_10><loc_92><loc_20></location>The details of the implementation of the model and the utilized numerical methods are throughly described by Kuang & Bloxham (1999). Here, rather than exhaustively restating the particularities of the framework, we limit ourselves to presenting the set of equations under consideration and the underlying assumptions, while referring the interested reader to Kuang & Bloxham (1999) for further information.</text>
<section_header_level_1><location><page_3><loc_61><loc_8><loc_83><loc_9></location>2.1. The Governing Equations</section_header_level_1>
<text><location><page_4><loc_8><loc_88><loc_48><loc_92></location>Momentum. -The circulation model solves the NavierStokes equation for an electrically conductive, Boussinesq fluid</text>
<formula><location><page_4><loc_10><loc_84><loc_48><loc_87></location>D v Dt = -2 Ω × v -∇P ¯ ρ + δρ ¯ ρ g + J × B ¯ ρ + ν ∇ 2 v (1)</formula>
<text><location><page_4><loc_8><loc_71><loc_48><loc_83></location>in a rotating spherical shell of finite thickness. Here, D/Dt = ∂/∂t + v · ∇ is the material derivative, v is the velocity vector, Ω = (2 π/ T ) ˆz is the rotation vector, P is the modified pressure, ρ is the density, J is the current density and ν is the kinematic viscosity. The bar denotes an average, whereas δ denotes the perturbation away from the background state. The density and temperature are related to the pressure through the ideal gas equation of state 2 :</text>
<formula><location><page_4><loc_24><loc_68><loc_48><loc_71></location>P = ρ µ k B T, (2)</formula>
<text><location><page_4><loc_8><loc_62><loc_48><loc_67></location>where P is the total pressure. The dynamic domain where the equation is solved is confined above a rigidly rotating spherical shell. We denote the inner and outer radii of the atmosphere as r 1 < r 2 respectively.</text>
<text><location><page_4><loc_8><loc_57><loc_48><loc_61></location>Continuity. -The model is formally 3D and the vertical component of the motion enters into the continuity equation:</text>
<formula><location><page_4><loc_25><loc_55><loc_48><loc_57></location>∇· v = 0 . (3)</formula>
<text><location><page_4><loc_8><loc_48><loc_48><loc_55></location>However, the nearly-constant density, incompressible fluid approximation prevents us from self-consistently modeling a radially extensive atmosphere. Indeed, the atmospheric density does not change, except by thermal expansion/contraction 3 :</text>
<formula><location><page_4><loc_24><loc_44><loc_48><loc_47></location>δρ ¯ ρ = -δT ¯ T . (4)</formula>
<text><location><page_4><loc_8><loc_37><loc_48><loc_43></location>Consequently, we limit the thickness of the atmosphere to a single scale-height in our simulations: r 2 -r 1 = H = k B ¯ T/µg , where g is the acceleration due to gravity. Additionally, we set r 1 = R , the radius of the planet.</text>
<text><location><page_4><loc_8><loc_27><loc_48><loc_38></location>Generally, because of the above-stated reasons, our model should be viewed as more closely related to the 2D shallow-water GCMs (Cho et al. 2003; Langton & Laughlin 2008) rather than the family of 3D models (Showman et al. 2009; Perna et al. 2010; Rauscher & Menou 2012). However, proper treatment of the of the induction equation (see below) in absence of pre-described symmetry requires the model to remain 3 dimensional.</text>
<text><location><page_4><loc_8><loc_24><loc_48><loc_27></location>Energy. -The energy equation, that governs the temperature, inherent to the model reads:</text>
<formula><location><page_4><loc_23><loc_20><loc_48><loc_23></location>DT Dt = κ ∇ 2 T, (5)</formula>
<text><location><page_4><loc_8><loc_13><loc_48><loc_19></location>where κ is the coefficient of thermal diffusivity (kept constant throughout the computational domain). Strictly speaking, this equation governs diffusive heat flux and (in direct interpretation) is unsuitable for modeling a medium where energy transport is accomplished mainly</text>
<text><location><page_4><loc_52><loc_77><loc_92><loc_92></location>by radiation. This is because the above equation rests on the approximations of short photon mean free path and the neglect of the temperature-dependence of the opacity (in the context of the Boussinesq treatment employed here, the latter makes sense but the former breaks down at pressure levels corresponding to optical depth of order unity, allowing for only a crude approximation to reality). However, shall it be possible to relate κ to radiative properties of the gas, the above energy equation can still be used to effectively mimic the appropriate heat transport.</text>
<text><location><page_4><loc_52><loc_75><loc_92><loc_77></location>In a radiatively-dominated atmosphere, the correct energy equation reads (Peixoto & Oort 1992)</text>
<formula><location><page_4><loc_66><loc_71><loc_92><loc_74></location>DT Dt = 1 ¯ ρc p ∇· F , (6)</formula>
<text><location><page_4><loc_52><loc_66><loc_92><loc_70></location>where c p is the specific heat capacity at constant pressure and F is the radiative heat flux. The expression for the radiative heat flux reads (Clayton 1968):</text>
<formula><location><page_4><loc_66><loc_62><loc_92><loc_65></location>F = 4 σ sb ¯ T 3 3¯ ρψ ∇ T, (7)</formula>
<text><location><page_4><loc_52><loc_51><loc_92><loc_61></location>where σ sb is the Stefan-Boltzmann constant and ψ is the opacity. At this point, the relationship between κ and the atmospheric temperature, density, opacity, and heat capacity is obvious. However, before proceeding further, let us recall that to an order of magnitude, the Newtonian cooling timescale τ N is given by the ratio of the atmosphere's excess heat content to its excess radiative flux:</text>
<formula><location><page_4><loc_67><loc_48><loc_92><loc_51></location>τ N glyph[similarequal] ¯ ρc p H 4 σ sb ¯ T 3 . (8)</formula>
<text><location><page_4><loc_52><loc_46><loc_74><loc_47></location>Consequently, we may express:</text>
<formula><location><page_4><loc_65><loc_42><loc_92><loc_45></location>κ = 4 σ sb ¯ T 3 3¯ ρ 2 c P ψ glyph[similarequal] H 2 τ N , (9)</formula>
<text><location><page_4><loc_52><loc_31><loc_92><loc_41></location>where we have implicitly assumed an infrared optical depth of order unity at the pressure-level of interest. The relationship between κ and τ N is convenient, as it can be related to previous works. In particular, Showman et al. (2008) have calculated τ N using a state of the art radiative transfer model and tabulated the results on a pressure-temperature grid. Here, we utilize their computations as a guide in estimating the thermal diffusivity.</text>
<text><location><page_4><loc_52><loc_19><loc_92><loc_31></location>Note that we could have arrived at the relationship (9) more intuitively by dimensional analysis. Specifically, noting that the radial extent of the atmosphere is much smaller than the lateral extent, the relevant length scale is the vertical scale-height, H . Meanwhile, because the heat transport is primarily radiative, τ N is clearly the relevant timescale. Bearing in mind the units of diffusivities (i.e. m 2 /s), equation (9) naturally emerges as an estimate.</text>
<text><location><page_4><loc_52><loc_15><loc_92><loc_18></location>Magnetic Field. -The evolution of the magnetic field is governed by the induction equation (Moffatt 1978)</text>
<formula><location><page_4><loc_62><loc_11><loc_92><loc_14></location>∂ B ∂t = η ∇ 2 B + ∇× ( v × B ) , (10)</formula>
<text><location><page_4><loc_52><loc_7><loc_92><loc_11></location>where η = 1 /µ 0 σ is the magnetic diffusivity (kept constant throughout the computational domain) and µ 0 is the permeability of free space. Meanwhile, the absence of</text>
<text><location><page_5><loc_8><loc_89><loc_48><loc_92></location>magnetic monopoles implies a divergence-free magnetic field:</text>
<formula><location><page_5><loc_25><loc_87><loc_48><loc_89></location>∇· B = 0 . (11)</formula>
<text><location><page_5><loc_8><loc_84><loc_48><loc_87></location>Once the structure of B is known, the current density (within the MHD approximation) is given by</text>
<formula><location><page_5><loc_23><loc_81><loc_48><loc_84></location>J = 1 µ 0 ∇× B . (12)</formula>
<text><location><page_5><loc_8><loc_75><loc_48><loc_80></location>At this point, the full set of governing differential equations is presented. Paired with a matching set of boundary and initial conditions, the system can be integrated forward in time self-consistently.</text>
<text><location><page_5><loc_8><loc_64><loc_48><loc_75></location>The equations are solved using a mixed spectral-finite difference algorithm and following Kuang & Bloxham (1999), the spherical harmonic decomposition is taken up to degree glyph[lscript] max = 33 in the latitude m max = 21 in the azimuthal angle. The computational domain is broken up into 64 radial shells. The model is integrated forward in time until equilibration in the thermal, kinetic and magnetic energies is attained.</text>
<section_header_level_1><location><page_5><loc_15><loc_62><loc_42><loc_63></location>2.2. Boundary and Initial Conditions</section_header_level_1>
<text><location><page_5><loc_8><loc_46><loc_48><loc_61></location>The physical parameters employed in the numerical experiments we report are loosely based on the planet HD209458b (Charbonneau et al. 2000). Aside from being the first extrasolar planet found to transit its host star, it has become a canonical example used in the studies of Hot Jupiter atmospheres (Burrows et al. 2007; Snellen et al. 2010). To this day, (along with HD189733b (Knutson et al. 2009)) it remains the best characterized extrasolar planet. The object has a mass M = 0 . 69 M Jup , a radius R = 1 . 35 R Jup and a rotational (assumed synchronous with orbit) period of T HD209458b = 3 . 5 days.</text>
<text><location><page_5><loc_8><loc_36><loc_48><loc_46></location>Momentum. -Because we are integrating a quasi-2D atmospheric shell, intended to be representative of a single pressure level, we apply impenetrable, stress-free boundary conditions to the velocity field. Thus, flows are free to develop without friction along the boundaries, although at initialization the planet is cast into solid-body rotation meaning v = 0 at t = 0.</text>
<text><location><page_5><loc_8><loc_14><loc_48><loc_36></location>Energy. -The temperature is initialized at ¯ T = 2000K with δT/ ¯ T = δρ/ ¯ ρ = 0. The atmosphere is kept stablystratified by the imposition of a stable background temperature gradient (set to the adiabatic lapse rate h = g/c p ) similar to the implementation in other Boussinesq dynamo models with stable layers (e.g. Stanley & Mohammadi (2008); Stanley (2010); Christensen & Wicht (2008)). Additionally, an azimuthally variable heat-flux is applied at the outer boundary, r 2 , to account for the variable stellar irradiation (in practice it doesn't matter whether the variable heat flux is applied at the outer or the inner boundaries, since it is the horizontal temperature gradient that controls the flow). The functional form of the heat-flux is chosen to be that of the F ∝ Y 1 1 spherical harmonic, while the amplitude is taken to be a free parameter (see the discussion in the next section).</text>
<text><location><page_5><loc_8><loc_6><loc_48><loc_13></location>Magnetic Field. -Nominally, an electrical conductivity of σ = 1S/m, characteristic of P glyph[similarequal] 1mbar, T glyph[similarequal] 2000K is prescribed to the computational domain. Simultaneously, negligible electrical conductivity is assigned outside the computational domain. That is, σ glyph[similarequal] 0 at r < r 1</text>
<text><location><page_5><loc_52><loc_83><loc_92><loc_92></location>and r > r 2 , meaning all of the current generated by the atmospheric flow is confined to the weather layer. This is in agreement with the approach of Perna et al. (2010); Rauscher & Menou (2013), but in some contrast with the analytical work of Batygin & Stevenson (2010); Batygin et al. (2011), where the current is allowed to penetrate the convective interior of the planet.</text>
<text><location><page_5><loc_52><loc_62><loc_92><loc_82></location>Because this work is primarily aimed at studying the upper atmosphere, the pressure-level of interest may reside above the atmospheric temperature inversion, characteristic of some Hot Jupiter atmospheres (Burrows et al. 2007; Spiegel et al. 2009). The presence of such an inversion may provide an electrically insulating layer 4 , justifying σ glyph[similarequal] 0 at r < r 1 . The capability of electrical currents to penetrate the upper atmosphere and close in the magnetosphere is determined by the upper atmosphere's temperature structure and the abundance of Alkali metals at P glyph[lessorsimilar] 1 mbar altitudes. Although a clear possibility, the physics of atmosphere-magnetosphere coupling is no-doubt complex and is beyond the scope of the present study. Consequently, we neglect it for the sake of simplicity.</text>
<text><location><page_5><loc_52><loc_56><loc_92><loc_62></location>In all of our simulations, we initialize J = 0 in the weather layer. However, the weather layer is still permeated by the background magnetic field, B dip , presumed to be generated by dynamo action in the convective interior of the planet. This zero current field reads:</text>
<formula><location><page_5><loc_62><loc_52><loc_92><loc_55></location>B dip = ∇× ( k m sin( θ ) r 2 ˆ φ ) , (13)</formula>
<text><location><page_5><loc_52><loc_37><loc_92><loc_51></location>where k m is a constant that sets the surface field strength i.e. | B dip | = k m / R 3 at the equator. Within the context of the model, the background field is implemented by modifying the governing equations to account for a timeindependent axially-dipolar external field. This occurs specifically in two terms. In the momentum equation (1), the Lorenz force ( J × B ) / ¯ ρ is replaced by J × ( B + B dip ) / ¯ ρ . In the magnetic induction equation (10), the induction term ∇× ( v × B ) is replaced by ∇× ( v × ( B + B dip )). This method is similar to that used by Sarson et al. (1997) and Cebron et al. (2012) to implement external fields.</text>
<section_header_level_1><location><page_5><loc_62><loc_34><loc_82><loc_35></location>2.3. Dimensionless Numbers</section_header_level_1>
<text><location><page_5><loc_52><loc_22><loc_92><loc_34></location>Upon non-dimensionalization of the governing equations (Kuang & Bloxham 1999), we obtain 6 dimensionless numbers that completely describe the system. They are the Ekman number E , the magnetic Rossby number R o , the magnetic Prandtl number q , the magnetic Rayleigh number R th and the aspect ratio χ as well as an additional value, Γ, that parameterizes the incoming stellar flux. In terms of physical parameters, these quantities read:</text>
<formula><location><page_5><loc_57><loc_14><loc_92><loc_21></location>E ≡ ν 2Ω R 2 , R o ≡ η 2Ω R 2 , Γ ≡ F κ ¯ ρc p h , q ≡ κ η , R th ≡ gh R 2 2 ¯ T Ω η , χ ≡ H R . (14)</formula>
<text><location><page_5><loc_53><loc_13><loc_92><loc_14></location>The aspect ratio of the atmosphere we consider is</text>
<text><location><page_5><loc_52><loc_7><loc_92><loc_11></location>4 This idea is not new. The models of Batygin & Stevenson (2010) as well as Batygin et al. (2011) used the presence of such a layer to confine the current generated by zonal flows to the lower atmosphere and the interior of the planet.</text>
<text><location><page_6><loc_1><loc_74><loc_48><loc_92></location>χ = 7 × 10 -3 . For numerical stability, the model requires the Ekman number to exceed a critical value (which we adopt in the simulations) of order E crit ∼ 10 -5 . If we consider the molecular viscosity of Hydrogen ν = ¯ na √ 3 k B ¯ T/m H 2 / 2, where ¯ n is the number density and a is the molecular cross-section, we obtain a hopelessly small E ∼ 10 -20 glyph[lessmuch] E crit at mbar pressure. We note that the actual Ekman number is orders of magnitude higher, since on the global planetary scale, small-scale turbulence is a far more relevant source of viscosity than transfer of momentum at the molecular level (Peixoto & Oort 1992). Still, the true value of E is probably much smaller than E crit . x = 619K = 104 m/s</text>
<text><location><page_6><loc_1><loc_58><loc_7><loc_62></location>003</text>
<text><location><page_6><loc_2><loc_55><loc_48><loc_74></location>For a given electrical conductivity (equivalently diffusivity), R o and R th simply encompass the physical units of the model. Specifically, for σ = 1S/m, R o = 1 . 79 × 10 -6 and R th = 1 . 38 × 10 9 . Meanwhile, all of the information regarding the considered pressure level is provided by q . Taking σ = 1S/m as before, we obtain q glyph[similarequal] 6 , 60 and 600, corresponding to τ N = 10 5 , 10 4 , and 10 3 sec, appropriate for P = 1 , 0 . 1 and 0 . 001 bars respectively. Finally, as already mentioned above, we take Γ to be an adjustable parameter, tuned to obtain the desired temperature gradients. It is important to note that our model differs somewhat from typical dynamo models in a sense that Γ, rather than R th , parameterizes the extent to which the system is driven. 680K m/s</text>
<text><location><page_6><loc_0><loc_33><loc_48><loc_55></location>Let us conclude the description of the numerical model with a brief discussion of its shortcomings as a guide for future work. First and foremost, the limitation of the atmosphere to a single scale-height may be prejudicial, as previous work has shown that including an extended vertical extent of the atmosphere is important to capture circulation features (Heng et al. 2011). Second, while we have kept thermal and magnetic diffusivities uniform throughout the computational domain, it should be understood that in reality these values vary with temperature and pressure. Third, an implicit assumption of an infrared optical depth of order unity is rather crude at ∼ mbar pressure levels and should be lifted in more rigorous treatments of radiative transfer. Finally, as already mentioned above, the artificially enhanced viscosity inherent to our model almost certainly smoothes out smaller-scale flow to an unphysical extent. x = 258K = 442 m/s</text>
<section_header_level_1><location><page_6><loc_16><loc_30><loc_40><loc_31></location>2.4. Hydrodynamical Simulations</section_header_level_1>
<text><location><page_6><loc_8><loc_20><loc_48><loc_29></location>Prior to performing unabridged MHD simulations, it is useful to first compare our model to previously published results. Accordingly, we begin by setting the strength of the background field to B dip = 0. Because the computational domain is initialized with a null current density, no magnetic fields are generated yielding purely hydrodynamic simulations.</text>
<text><location><page_6><loc_8><loc_9><loc_48><loc_20></location>Horizontal slices of the atmosphere (through the center of the computational domain) in the cylindrical projection are shown in Figure (3). The figures are centered on the substellar point and the background color shows the temperature distribution. The arrows denote the circulation vector field. Peak wind speeds as well as the maximal temperature deviations from ¯ T = 2000K are labeled.</text>
<text><location><page_6><loc_8><loc_7><loc_48><loc_9></location>The typically observed transition from zonal flows to dayside-nightside flows is observed as the pressure is de-</text>
<figure>
<location><page_6><loc_52><loc_73><loc_91><loc_92></location>
</figure>
<figure>
<location><page_6><loc_52><loc_51><loc_91><loc_71></location>
</figure>
<figure>
<location><page_6><loc_52><loc_28><loc_91><loc_50></location>
<caption>Fig. 3.Hydrodynamical simulations of the global circulation obtained using the numerical global circulation model of Kuang & Bloxham (1999). The arrows depict the currents of the flow and the color map is representative of the temperature structure. The background and initial atmospheric magnetic fields are set to zero, while the variable heat flux used to mimic insolation is tuned such that the maximal deviation of temperature from the background state is δT max = 620K. The three panels of the Figure correspond to different pressure levels: P = 1 mbar (A), P = 0 . 1 bar (B) and P = 1 bar (C). Note that here, we have plotted the latitude, rather than colatitude used throughout the paper on the y-axis.</caption>
</figure>
<text><location><page_6><loc_52><loc_7><loc_92><loc_15></location>creased sequentially from P = 1 bars (Panel C of Figure 3) to P = 0 . 001 bars (Panel A of Figure 3). However, important differences exist in our results, contrasted against say, the results of Showman et al. (2008). The first important distinction is that in the zonally-dominated parameter regime, rather than developing a single broad</text>
<text><location><page_7><loc_8><loc_89><loc_48><loc_92></location>jet, our model shows the development of three counterrotating jets.</text>
<text><location><page_7><loc_8><loc_65><loc_48><loc_89></location>This is a simple consequence of angular momentum conservation in the computational domain, and is not uncharacteristic of 2D models (Showman et al. 2011). Because of free-slip boundary conditions employed in our model, the atmosphere is not allowed to exchange angular momentum with the interior. As such, because the atmosphere is initialized in solid-body rotation, the development of any prograde jets must be accompanied by the development of retrograde jets. Because the retrograde jets reside at a high latitude θ ret , whereas the prograde jets are essentially equatorial, angular momentum conservation requires them to be faster by a factor of | v ret / v pro | ∼ 1 / cos θ ret , as observed in the simulations. The angular momentum conserving 3D simulations of Heng et al. (2011) exhibit similar behavior, although in their model the counter-rotating jets develop below the prograde ones, and are considerably slower because of the associated density enhancement.</text>
<text><location><page_7><loc_8><loc_52><loc_48><loc_65></location>The second distinction of interest is the direction of the equatorial jet. While 3D GCMs consistently produce eastward equatorial jets, the equatorial jets in our hydrodynamical simulations are westward. This is not too surprising, as shallow-water and equivalent barotropic models are known to produce both eastward and westward equatorial jets, depending on the details of the simulation setup (Showman et al. 2011; Heng et al. 2011). Consequently, this difference can probably be attributed to the limited vertical extent of our model.</text>
<text><location><page_7><loc_8><loc_20><loc_48><loc_52></location>The third important difference is the fact that flow velocities are not consistent along the pressure levels. In particular for the same values of δT , zonal flows have ∼ few km/s peak wind speeds, while the dayside-tonightside flows are more than an order of magnitdue slower. This is largely a consequence of difference in the geometry of the circulation and the fact that viscosity enters as a significant member in the force balance for dayside-to-nightside flows. This can be seen by approximating ν ∇ 2 ∼ ν/ L 2 (Holton 1992), where L is a characteristic length scale associated with the curvature of the circulation. For zonal jets, L z ∼ R while for dayside-to-nightside circulation, the return flow is in part radial implying L dn ∼ H . As will be shown in the following section, faster velocities can be attained by either increasing the aspect ratio of the atmosphere or by artificially enhancing the radiative heat flux, as a result of a linear proportionality between peak wind speeds and δT . An additional point of importance is that in typical 3D simulations, dayside-to-nightside circulation is nearly uniform over the terminator with the return flow residing at greater depth, while our results depict a partial return flow over the poles. This is again a consequence of the quasi-2D geometry of our model.</text>
<text><location><page_7><loc_8><loc_8><loc_48><loc_20></location>Although these quantitative distinctions are certainly worthy of attention, the typical features of the flow are approximately captured by our simplified model. Consequently, while being mindful of the model's limitation we do not view the quantitative dissimilarities as critical, as they are not central to the argument of the paper. After all, recall that we are primarily concerned with the possibility of a qualitative alteration of the dayside-tonightside flow by magnetic effects.</text>
<section_header_level_1><location><page_7><loc_57><loc_90><loc_87><loc_92></location>3. DRAGGED CIRCULATION IN THE UPPER ATMOSPHERE</section_header_level_1>
<text><location><page_7><loc_52><loc_68><loc_92><loc_89></location>In the previous section, we performed baseline hydrodynamical simulations of atmospheric circulation at different pressure levels. In the following sections, we will focus primarily on the mbar pressure level, where the flow takes on a dayside-to-nightside character. As discussed above, in our simulations viscosity plays an important role in determining the flow velocities. Conceptually, the situation may be synonymous to simulations of invicid GCMs that parameterize the effect of magnetic coupling as Rayleigh drag (Perna et al. 2010; Rauscher & Menou 2012). In interest of understanding the dependence of the flow velocities on the magnitude of the dayside-tonightside temperature gradient as well as the imposed frictional forces, in this section we shall develop a simple analytical model for dragged upper-atmospheric circulation and confirm it numerically.</text>
<section_header_level_1><location><page_7><loc_64><loc_65><loc_80><loc_66></location>3.1. Analytical Theory</section_header_level_1>
<text><location><page_7><loc_52><loc_59><loc_92><loc_64></location>Let us begin with estimation of characteristic timescales. In order to accomplish this, we first simplify the Lorentz and viscous forces to resemble the functional form of Rayleigh drag. Utilizing Ohm's law, we have 5 :</text>
<formula><location><page_7><loc_54><loc_51><loc_92><loc_58></location>J × B ¯ ρ ∼ σ ( v × B dip ) × B dip ¯ ρ ∼ -( σk 2 m R 6 ¯ ρ ) v = -v τ L ν ∇ 2 v ∼-( 3 ν R 2 ) v = -v τ ν (15)</formula>
<text><location><page_7><loc_52><loc_50><loc_91><loc_51></location>This allows us to rewrite equation (1) in a simpler form:</text>
<formula><location><page_7><loc_59><loc_46><loc_92><loc_49></location>D v Dt = -2 Ω × v -∇P ¯ ρ + δρ ¯ ρ g -v τ f , (16)</formula>
<text><location><page_7><loc_52><loc_36><loc_92><loc_45></location>where τ f = (1 /τ L + 1 /τ ν ) -1 . Taking | B dip | = 1 G, the characteristic timescales are: τ L ∼ 10 3 sec and τ ν ∼ 10 5 sec. Other relevant timescales in the problem is the rotational (Coriolis) timescale τ Ω ∼ 2 π/ Ω ∼ 10 5 sec, radiative timescale τ N ∼ 10 3 sec and the advective timescale τ adv ∼ R /v ∼ 10 5 sec.</text>
<text><location><page_7><loc_52><loc_15><loc_92><loc_36></location>There exists a clear separation of timescales in the system. As a result, upon including the parameterized Lorentz force into the equations of motion, the inertial and Coriolis terms can be dropped (the viscous term can be dropped as well, although this simplification is unnecessary). The removal of the inertial terms implies a steady-state solution. The removal of the Coriolis term creates a symmetry characterized by an axis that intersects the sub-solar and anti-solar points. Taking advantage of this symmetry, we orient the polar axis of the coordinate system such that it intersects the sub-solar point. Upon doing so, we can specify a null azimuthal velocity and drop all azimuthal derivatives in the equations of motion. In a local cartesian reference frame, this leaves us with horizontal (ˆ y ) and vertical (ˆ z ) momentum equations, where the latter simplifies to the equation of</text>
<text><location><page_7><loc_52><loc_7><loc_92><loc_14></location>5 Although this approximation is often made, it is not necessarily sensible for systems where the magnetic Reynold's number, Re m ≡ v L /η glyph[greatermuch] 1. Adopting v ∼ km/s and L ∼ H , we obtain Re m ∼ 10 3 , placing the magnetic drag approximation on shaky footing. Further, the electric field in Ohm's law can only be neglected when the radial current is negligible.</text>
<text><location><page_8><loc_8><loc_91><loc_23><loc_92></location>hydrostatic balance:</text>
<formula><location><page_8><loc_24><loc_83><loc_48><loc_90></location>1 ¯ ρ ∂ P ∂y = -v y τ f 1 ¯ ρ ∂ P ∂z = g δT ¯ T (17)</formula>
<text><location><page_8><loc_8><loc_77><loc_48><loc_83></location>Following Schneider & Lindzen (1977) and Held & Hou (1980), we shall adopt a Newtonian energy equation with implicit stable stratification (recall that we have set the potential temperature gradient to h = g/c p ):</text>
<formula><location><page_8><loc_19><loc_73><loc_48><loc_76></location>ξv z ( g c p ) = -δT -δT rad τ N . (18)</formula>
<text><location><page_8><loc_8><loc_67><loc_48><loc_73></location>Here, ξ glyph[greaterorequalslant] 1 is a constant that parameterizes lateral heat advection and δT rad is a purely radiative perturbation to the background state, ¯ T . In other words, as the damping of the circulation is strengthened and v → 0, δT → δT rad .</text>
<text><location><page_8><loc_8><loc_61><loc_48><loc_67></location>Retaining the incompressibility condition (3), we introduce a stream-function Ψ, defined through v = ∇× Ψ (Landau & Lifshitz 1959). Taking a partial derivative of the y -momentum equation with respect to z and of the z -momentum equation with respect to y , we obtain</text>
<formula><location><page_8><loc_21><loc_57><loc_48><loc_60></location>-1 τ f ∂ 2 Ψ ∂z 2 = g ¯ T ∂ ( δT ) ∂y . (19)</formula>
<text><location><page_8><loc_8><loc_53><loc_48><loc_56></location>Taking a derivative of equation (19) with respect to y and switching the order of partial differentiation yields:</text>
<formula><location><page_8><loc_17><loc_50><loc_48><loc_53></location>-1 τ f ∂ ∂z ( ∂ 2 Ψ ∂y∂z ) = g ¯ T ∂ 2 ( δT ) ∂y 2 . (20)</formula>
<text><location><page_8><loc_8><loc_46><loc_48><loc_49></location>Meanwhile, differentiating the Newtonian cooling equation (18) with respect to z gives:</text>
<formula><location><page_8><loc_16><loc_42><loc_48><loc_46></location>( ∂ 2 Ψ ∂y∂z ) = c p gξ ∂ ∂z ( δT -δT rad τ N ) , (21)</formula>
<text><location><page_8><loc_8><loc_40><loc_34><loc_42></location>allowing us to eliminate ∂ 2 Ψ /∂y∂z :</text>
<formula><location><page_8><loc_14><loc_36><loc_48><loc_39></location>∂ 2 ( δT rad ) ∂z 2 -∂ 2 ( δT ) ∂z 2 = ξ τ f τ N g 2 c p ¯ T ∂ 2 ( δT ) ∂y 2 . (22)</formula>
<text><location><page_8><loc_24><loc_34><loc_48><loc_35></location>simply the square of the Brunt-</text>
<text><location><page_8><loc_8><loc_33><loc_43><loc_36></location>Note that g 2 /c p ¯ T is Vaisala frequency for an isothermal atmosphere.</text>
<text><location><page_8><loc_10><loc_31><loc_38><loc_33></location>Equation (22) admits the trial solutions</text>
<formula><location><page_8><loc_16><loc_24><loc_48><loc_31></location>δ T rad = ( δT 0 rad ) cos ( y R ) sin ( πz H ) δ T = ( δT 0 ) cos ( y R ) sin ( πz H ) , (23)</formula>
<text><location><page_8><loc_8><loc_16><loc_48><loc_25></location>where ( δT 0 rad ) and ( δT 0 ) are constants that represent the maximal deviations in the respective quantities from the background state. Note that ( δT 0 rad ) is a parameter inherent to the model rather than a variable. Upon substitution of the above solutions (23) into equation (22), we obtain a relationship between ( δT 0 ) and ( δT 0 rad ):</text>
<formula><location><page_8><loc_12><loc_11><loc_48><loc_16></location>( δT 0 ) = ( δT 0 rad ) [ 1 + ξζ τ f τ N g 2 π 2 c p ¯ T ( H R ) 2 ] -1 . (24)</formula>
<text><location><page_8><loc_8><loc_7><loc_48><loc_11></location>In the above equation, ζ is an empirical factor that has been introduced to account for the approximations inherent to equations (15).</text>
<text><location><page_8><loc_52><loc_88><loc_92><loc_92></location>With an analytical solution for the temperature perturbation in hand, we substitute equations (23) into equation (19) and integrate twice to obtain:</text>
<formula><location><page_8><loc_56><loc_83><loc_92><loc_87></location>Ψ = [ gζτ f H 2 ( δT 0 ) π 2 ¯ T R ] sin ( y R ) sin ( πz H ) ˆ x . (25)</formula>
<text><location><page_8><loc_52><loc_75><loc_92><loc_83></location>This solution implies the same functional form for laterally-averaged heat transport in the vertical and horizontal advection terms in the energy equation (6), lending some support for the approximation inherent to equation (18). Once the stream function is obtained, the maximal horizontal and vertical velocities are given by:</text>
<formula><location><page_8><loc_61><loc_71><loc_92><loc_75></location>v max y = Ψ 0 π H v max z = Ψ 0 1 R , (26)</formula>
<text><location><page_8><loc_52><loc_66><loc_92><loc_71></location>where Ψ 0 is the term in square brackets in (25). Note that the above theory automatically implies a quasi-2D flow since v max z /v max y ∼ ( H / R ) glyph[lessmuch] 1 .</text>
<section_header_level_1><location><page_8><loc_62><loc_65><loc_82><loc_66></location>3.2. Numerical Experiments</section_header_level_1>
<text><location><page_8><loc_52><loc_51><loc_92><loc_64></location>With a simple analytical theory at hand, we performed a series of numerical simulations, varying the radiative and drag timescales in the ranges 10 2 < τ N < 10 3 sec and 10 3 < τ f < 10 5 sec. Although we observed a considerable variability in the wind speeds and dayside-to-nightside temperature differences in our simulations, the nature of the flow was largely the same as that seen in panel A of Figure (3) across the runs. The peak wind speeds obtained in the simulations as functions of τ N and τ f are presented as black dots in Figure (4).</text>
<text><location><page_8><loc_52><loc_35><loc_92><loc_51></location>In addition to the simulation results, Figure (4) shows v max y given by equation (26) for the same parameters. As can be seen from the figures, the scaling law inherent to equation (25) matches the numerical experiments quite well. Extrapolating towards larger values of τ f , it can be inferred that our simulations would have produced peak wind speeds of order ∼ km/s if not for the numerical requirements of enhanced viscosity. However, it can also be expected that the character of the flow would also change qualitatively with diminishing viscosity, as the force balance shifts away from that implied by equations (15) 6 .</text>
<text><location><page_8><loc_52><loc_19><loc_92><loc_35></location>It should be kept in mind that the adjustable parameters ξ and ζ were fit to the data. Moreover, the value of ( δT 0 rad ) = 3360K 7 was chosen by running a simulation where viscous forces completely dominated the force balance ensuring v = 0. In other words, the quantitative agreement seen in Figure (4) is a consequence of the fact that the adjustable parameters of the analytical solution have been fit to the numerical data, but the fact that the functional form of the analytical model conforms with numerical experiments suggest that the stream-function (25) captures the main features of dragged upper-atmospheric circulation on Hot Jupiters.</text>
<section_header_level_1><location><page_8><loc_55><loc_17><loc_89><loc_18></location>4. MAGNETICALLY CONTROLLED CIRCULATION</section_header_level_1>
<text><location><page_8><loc_52><loc_14><loc_92><loc_16></location>In the last section, we examined the extent to which dayside-nightside flow can be damped by imposing a</text>
<figure>
<location><page_9><loc_9><loc_71><loc_91><loc_92></location>
<caption>Fig. 4.Dependence of peak wind speeds on the radiative and drag timescales obtained within the context of dragged hydrodynamical solutions. The black points represent the results of numerical experiments, where enhanced viscosity is used to mimic the effects of the magnetic field, while the curves represent the analytical solution derived from equations (23) and (25). The values ξ = 8630 and ζ = 0 . 16 have been adopted for the analytical solution. Note that the fact that ξ glyph[greatermuch] 1 is simply a consequence of the fact that lateral advection of heat completely dominates over vertical advection of heat as the transport mechanism of importance. That is to say that in the numerical solutions, v z ( ∂T/∂z ) glyph[lessmuch] v y ( ∂T/∂y ) Nominal values of τ f and τ N are adopted in panels A and B respectively.</caption>
</figure>
<text><location><page_9><loc_8><loc_51><loc_48><loc_62></location>drag. However, both the analytical theory and numerical experiments showed that the qualitative character of the circulation remained largely unchanged. As already mentioned in the introduction, the rough consistency of the flow patterns across a range of characteristic drag timescales is in broad agreement with the results of 'primitive' 3D GCMs (Perna et al. 2010; Rauscher & Menou 2012). In this section, we challenge this assertion with MHD calculations.</text>
<section_header_level_1><location><page_9><loc_19><loc_48><loc_38><loc_50></location>4.1. Theoretical Arguments</section_header_level_1>
<text><location><page_9><loc_8><loc_27><loc_48><loc_48></location>With the exception of a rather limited number of problems, self-consistent magneto-hydrodynamic solutions can only be attained with the aid of numerical simulations. However, for the system at hand, the qualitative effect of magnetic induction can be understood from simple theoretical considerations. As we already argued, the two characteristic states of Hot Jupiter atmospheric circulation are a zonally-dominated state and a meridionally-dominated state (Showman et al. 2011). Whether or not a given configuration will be significantly affected by the introduction of the magnetic field can be established by analyzing its stability. More specifically, we can work within a purely kinematic (rather than dynamic) framework to understand if the Lorentz force acts to perturb the flow away from its hydrodynamic counterpart or simply damps the circulation.</text>
<text><location><page_9><loc_8><loc_13><loc_48><loc_26></location>Zonal Flows. -Although not directly applicable, recent studies of Ohmic dissipation that arises from zonal flows performed by Liu et al. (2008) (within the context of solar system gas giants) and by Batygin & Stevenson (2010) as well as Menou (2012) (within the context of Hot Jupiters) have already produced some results on a related problem. Here we work in the same spirit as these studies and prescribe the following functional form to the zonal flow to approximately represent three jets, such as those shown in panel C of Figure (3):</text>
<formula><location><page_9><loc_22><loc_10><loc_48><loc_12></location>˜ v = ˜ v 0 sin(3 θ ) ˆ φ, (27)</formula>
<text><location><page_9><loc_8><loc_7><loc_48><loc_9></location>where ˜ v 0 is a negative constant, whose magnitude corresponds to the peak wind speed. This prescription triv-</text>
<text><location><page_9><loc_52><loc_59><loc_92><loc_62></location>ally satisfies the continuity equation (3), although we note that a more realistic zonal flow should also exhibit differential rotation.</text>
<text><location><page_9><loc_52><loc_47><loc_92><loc_58></location>The interaction between this flow and the background magnetic field (13) will induce a field B ind in the atmosphere. Because B dip is entirely poloidal, and ˜ v is strictly toroidal, B ind will also be strictly toroidal (Moffatt 1978). As can be readily deduced from equation (10), this means that B ind cannot interact with ˜ v to further induce new field unless ˜ v deviates from a purely zonal flow. As a result, in steady state, the induction equation reads:</text>
<formula><location><page_9><loc_52><loc_42><loc_92><loc_46></location>-η ∇ 2 B ind = ∇× (˜ v × B dip ) = -6 k m ˜ v 0 r 4 cos( θ ) sin( θ ) ˆ φ. (28)</formula>
<text><location><page_9><loc_52><loc_30><loc_92><loc_42></location>It is noteworthy that had we chosen to represent a single broad jet (such as that seen in most 3D simulations (Showman et al. 2008; Menou & Rauscher 2010; Rauscher & Menou 2013)) by setting ˜ v ∝ sin( θ ) (in this case ˜ v 0 is positive), equation (28) would have looked the same, with the exception of the coefficient on the RHS, which would have been 2 instead of 6. As a result, it should be kept in mind that the following kinematic solution applies to the case of a single jet as well.</text>
<text><location><page_9><loc_52><loc_27><loc_92><loc_30></location>φ (deg) The angular part of equation (28) is satisfied by the expression</text>
<formula><location><page_9><loc_62><loc_24><loc_92><loc_27></location>B ind = A ( r ) cos( θ ) sin( θ ) ˆ φ, (29)</formula>
<text><location><page_9><loc_52><loc_16><loc_92><loc_24></location>where A ( r ) is a yet undefined function. This form ensures that the meridional component of the induced current vanishes at the poles. Meanwhile, the radial impenetrability of the boundaries requires A ( R ) = A ( R + H ) = 0 as dictated by equation (12). With these boundary conditions, equation (28) can be solved to yield</text>
<formula><location><page_9><loc_52><loc_9><loc_92><loc_16></location>A ( r ) = 3 k m ˜ v 0 ( Rr )( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +4 R 4 -R 3 r -R 2 r 2 -R r 3 -r 4 ) / (2 ηr 3 × ( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +5 R 4 )) . (30)</formula>
<text><location><page_9><loc_52><loc_7><loc_92><loc_9></location>The induced field and the associated electrical current are shown in panel A of Figure (5).</text>
<text><location><page_10><loc_8><loc_82><loc_11><loc_83></location>r</text>
<figure>
<location><page_10><loc_9><loc_71><loc_48><loc_92></location>
</figure>
<text><location><page_10><loc_8><loc_60><loc_11><loc_61></location>r</text>
<figure>
<location><page_10><loc_9><loc_49><loc_47><loc_70></location>
<caption>Fig. 5.Toroidal magnetic fields induced in the atmospheric shell. Panel A represents the kinematic analytical solution obtained through equations (29) and (30), while panel B depicts a result obtained from a dynamic numerical simulation, also shown in panel C of Figure (6). Green colors correspond to eastward (positive) fields, and the converse is true for blue colors. The contour lines depict the associated electrical currents. The maximal induced field strengths are max(B ind ) = 0 . 64 G and max(B ind ) = 0 . 52 G corresponding to the analytical solution (panel A) and the numerical solution (panel B) respectively. Because the Lorentz force associated with this induced field acts in the same sense as the flow itself, it can only act to accelerate/decelerate the jets but not alter their directions.</caption>
</figure>
<text><location><page_10><loc_8><loc_31><loc_48><loc_34></location>The Lorentz force that arises from the interactions between B ind and B dip takes the form</text>
<formula><location><page_10><loc_10><loc_15><loc_48><loc_30></location>F L = ( ∇× B ind ) × B dip ρµ 0 = ( σk 2 m r 6 ρ ) ˜ v 0 ˆ φ × (3 sin( θ )( -11 R ( H + R )( H +2 R )( H 2 +2 HR +2 R 2 ) + 9 r ( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +5 R 4 ) -r 5 ) + sin(3 θ )( -7 R ( H + R )( H +2 R ) × ( H 2 +2 HR +2 R 2 ) + 5 r ( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +5 R 4 ) + 3 r 5 )) / (8 r × ( H 4 +5 H 3 R +10 H 2 R 2 +10 HR 3 +5 R 4 )) . (31)</formula>
<text><location><page_10><loc_8><loc_7><loc_48><loc_15></location>Because the Lorentz force acts in the same sense as the flow itself (that is, F L × ˜ v = 0), it can only act to accelerate/decelerate the jets but not alter their directions. Indeed, the functional form of F L is that of a Rayleigh drag (equation 15), however the characteristic timescale is non-uniform in latitude and radius i.e.</text>
<text><location><page_10><loc_52><loc_87><loc_92><loc_92></location>τ L = f ( r, θ ). The non-uniformity we derive here should not be confused with the variability in F L that can arise from the spatial dependence of the electrical conductivity (see Rauscher & Menou (2013)).</text>
<text><location><page_10><loc_52><loc_73><loc_92><loc_86></location>It is noteworthy that the radial dependence of F L can give rise to differential rotation. However, this is not particularly important, since in some similarity with the above discussion, differential rotation will only induce toroidal fields through the ω -effect (Moffatt 1978) and will therefore only change the solution obtained here on a detailed level (i.e. the added dependence of ˜ B on r will subtly modify the function A ( r )). In other words, a differentially rotating zonal flow still results in a purely toroidal induced field.</text>
<text><location><page_10><loc_52><loc_63><loc_92><loc_73></location>For a sensible comparison with previous works (e.g. (Perna et al. 2010; Menou 2012; Rauscher & Menou 2012)) and the simple theory presented in the previous section, it is instructive to evaluate the maximal magnitude of F L , which corresponds to the upper and lower boundaries of the domain in question 8 i.e. r = R , r = R + H . To leading order in χ , the expression reads:</text>
<formula><location><page_10><loc_55><loc_59><loc_92><loc_63></location>max( F L ) glyph[similarequal] -6 ( σ k 2 m R 6 ρ ) ˜ v 0 χ cos( θ ) 2 sin( θ ) ˆ φ. (32)</formula>
<text><location><page_10><loc_52><loc_38><loc_92><loc_59></location>From this expression it is clear that F L acts primarily in the mid-latiudes rather than the equator. As a result, the damping of the jets is latitudinally differential, meaning that even if the flow is initially composed of multiple bands (as we consider here), it will approach a single equatorial jet as the conductivity and/or the magnetic field is increased. Furthermore, recall that the functional form of equation (32) is also valid in the case of a single jet. Qualitatively, this seems to imply that the Lorentz force acts to collimate the jet towards the equator. Such an effect is sensible given that the radial component of the field is stronger as one approaches the pole for a simple dipole. However, it should also be kept in mind that a true planetary magnetic field might be more complicated, leading to further lack of triviality in the circulation.</text>
<text><location><page_10><loc_52><loc_22><loc_92><loc_36></location>Dayside-to-Nightside Flows. -Let us now consider the more topologically complex interaction between meridional flows and a spin-pole aligned dipole magnetic field. As in section (3.1) we shall work in a coordinate frame where the polar axis intersects the sub-solar point and is directed at the host star. Unlike the case of zonal circulation, this configuration has no exploitable symmetry. Consequently, a simple solution to the steady-state induction equation (28) is difficult, if not impossible, to obtain. We shall therefore make substantial simplifications.</text>
<text><location><page_10><loc_52><loc_18><loc_92><loc_22></location>In our prescription for the velocity field, we neglect radial flow altogether (thereby violating continuity) and adopt an expression similar to equation (27):</text>
<formula><location><page_10><loc_67><loc_15><loc_92><loc_17></location>˜ v = ˜ v 0 sin( θ ) ˆ θ. (33)</formula>
<text><location><page_10><loc_52><loc_12><loc_92><loc_14></location>Because of our choice of coordinate system, equation (13) cannot be used directly. However, keeping in mind</text>
<text><location><page_10><loc_52><loc_7><loc_92><loc_10></location>8 Although the Lorentz force is equal and opposite at r = R and r = R + H , its radial distribution is such that its vertically integrated value acts to oppose the flow on average.</text>
<text><location><page_11><loc_8><loc_87><loc_48><loc_92></location>that the background dipole field originates in a much deeper region of the planet than the atmosphere, we can write down the magnetic field in a current-free representation (Jackson 1998):</text>
<formula><location><page_11><loc_12><loc_83><loc_48><loc_86></location>B dip = -∇ Υ = -∇ ( k m sin( θ ) cos( φ ) r 2 ) . (34)</formula>
<text><location><page_11><loc_8><loc_74><loc_48><loc_82></location>As in Batygin & Stevenson (2010), we assume that the induction term is dominated by the interaction with the background field, rather than the induced field: (˜ v × B ) glyph[similarequal] (˜ v × B dip ). Upon making this simplification and uncurling equation (10), the steady state induction equation reduces to Ohm's law:</text>
<formula><location><page_11><loc_20><loc_71><loc_48><loc_73></location>J = σ (˜ v ×∇ Υ -∇ Φ) , (35)</formula>
<text><location><page_11><loc_8><loc_69><loc_30><loc_71></location>where ∇ Φ is the electric field.</text>
<text><location><page_11><loc_8><loc_66><loc_48><loc_70></location>Because the current is necessarily divergence-free, the scalar potential Φ can be obtained from the following equation:</text>
<formula><location><page_11><loc_12><loc_62><loc_48><loc_65></location>∇ 2 Φ = ∇· (˜ v ×∇ Υ) = k m ˜ v 0 r 3 sin( θ ) sin( φ ) . (36)</formula>
<text><location><page_11><loc_8><loc_59><loc_48><loc_61></location>It can be easily checked that the angular part of this relationship is satisfied by:</text>
<formula><location><page_11><loc_20><loc_56><loc_48><loc_58></location>Φ = A ( r ) sin( θ ) sin( φ ) . (37)</formula>
<text><location><page_11><loc_8><loc_50><loc_48><loc_56></location>As before, confining the current to the atmosphere implies the boundary conditions: k m ˜ v 0 = R 3 A ( R ) = ( R + H ) 3 A ( R + H ). In turn, the radial part of the solution reads:</text>
<formula><location><page_11><loc_11><loc_42><loc_48><loc_50></location>A ( r ) = k m ˜ v 0 (( -H ( H 2 +3 HR +3 R 2 )(log( r ) + 2) +log( R )( H 3 +3 H 2 R +3 HR 2 + R 3 +2 r 3 ) -( R 3 +2 r 3 ) log( H + R ))) / (3 H r 2 × ( H 2 +3 HR +3 R 2 )) . (38)</formula>
<text><location><page_11><loc_8><loc_39><loc_48><loc_42></location>The induced current density can now be obtained through Ohm's law.</text>
<text><location><page_11><loc_8><loc_30><loc_48><loc_39></location>The Lorentz force can be approximated as originating from the interactions between the induced current and the background magnetic field. The resulting expression is quite cumbersome. However, all of the important features of F L can be seen by evaluating it at the center of the dynamic domain. To leading order in χ , the expression takes the form:</text>
<formula><location><page_11><loc_13><loc_18><loc_48><loc_29></location>F L | ( r = R + H / 2) glyph[similarequal] ( σk 2 m R 6 ρ ) ˜ v 0 × [ ˆ r cos( θ )(1 -2 sin 2 ( θ ) cos(2 φ ) + cos(2 θ )) / 2 + ˆ θ (sin(3 θ ) -sin( θ )) cos 2 ( φ ) -2 ˆ φ sin( θ ) cos( θ ) sin( φ ) cos( φ ) ] . (39)</formula>
<text><location><page_11><loc_8><loc_13><loc_48><loc_18></location>Asimilar evaluation of F L at r = R and r = R + H shows that the ˆ r and ˆ φ components of the force do not change significantly with radius, although the ˆ θ component does.</text>
<text><location><page_11><loc_8><loc_7><loc_48><loc_13></location>Indeed, the Lorentz force that arises from the interactions between the dayside-to-nightside circulation and the background magnetic field does not only oppose the flow. Instead, it acts to introduce both radial and zonal components to the circulation. Importantly, the typical</text>
<text><location><page_11><loc_52><loc_80><loc_92><loc_92></location>magnitude of the zonal component of F L is commensurate with the meridional component (although of course their spatial dependence is different). As argued in section (3.1), the characteristic timescale associated with the Lorentz force is comparable to the radiative timescale at mbar pressures and is generally shorter than that, corresponding to other relevant forces. This means that the force-balance implied by equations (17) is in essence not relevant to circulation on hot planetary atmospheres.</text>
<text><location><page_11><loc_52><loc_68><loc_92><loc_80></location>In summary, we conclude that dayside-to-nightside flow is unstable to perturbations arising from the Lorentz force. Consequently, we expect that the upper atmospheric circulation will change qualitatively once a substantial magnetic field is introduced into the system. We now turn our attention to numerical MHD simulations with the aim of testing this presumption and quantifying the dynamical state of magnetized upper atmospheres of Hot Jupters.</text>
<section_header_level_1><location><page_11><loc_58><loc_66><loc_86><loc_67></location>4.2. Magnetohydrodynamic Simulations</section_header_level_1>
<text><location><page_11><loc_52><loc_45><loc_92><loc_65></location>The hydrodynamic simulation parameters are chosen as described in section (2), corresponding to the P = 1mbar pressure level (i.e. τ L = 10 3 sec.). We start out with the equilibrated hydrodynamic flow shown in panel A of Figure (3) and introduce a weak pole-aligned dipole magnetic field into the system. Upon equilibration, we take the approach of sequentially increasing the magnitude of B dip . At each step, we allow the flow to reach a steady state before increasing the field strength further. We have checked that the flows obtained by successive enhancement of B dip are identical to those obtained by initializing the atmosphere in solid-body rotation with a given value of B dip . Consequently, in agreement with Liu & Showman (2012), we conclude that the obtained flows are insensitive to initial conditions.</text>
<text><location><page_11><loc_52><loc_27><loc_92><loc_45></location>The panels of Figure (6) show the upper atmospheric circulation for a series of magnetic field strengths. From this series of results, a clear pattern emerges: as the magnitude of B dip is increased, the flow takes on an exclusively zonal character. Specifically, it is clear that the circulation patterns characteristic of | B dip | = 0 . 33 G (panel B) are already markedly different from the | B dip | = 0 . 025 G case (panel A), which clearly resembles the unmagnetized circulation. The flow is in essence entirely azimuthal once the field is increased to | B dip | = 0 . 5 G (panel C). This is in contrast to the non-uniformly dragged simulations of Rauscher & Menou (2013), who find the flow to become less zonally-dominated with enhanced field strength.</text>
<text><location><page_11><loc_52><loc_15><loc_92><loc_27></location>It is noteworthy that the flow speeds up once it takes on a zonal nature. This is almost certainly due to the fact that viscosity acting on vertical motion more strongly affects the divergent flow, and is therefore not a physically significant result. Increasing the field strength further diminished the flow velocities but did not alter the qualitative nature of the solution, although somewhat higher values of the Ekman number were required to ensure numerical stability.</text>
<text><location><page_11><loc_52><loc_7><loc_92><loc_15></location>At the expense of a great inflation in the required computational time, we have extended the simulations presented in Figure (6) to higher resolution. Namely, we prolonged the spherical harmonic decomposition up to degree glyph[lscript] max = 34 and m max = 29 while eliminating hyperviscosity from our runs entirely. Aside from a mild</text>
<figure>
<location><page_12><loc_9><loc_73><loc_47><loc_92></location>
</figure>
<figure>
<location><page_12><loc_9><loc_51><loc_47><loc_71></location>
</figure>
<figure>
<location><page_12><loc_9><loc_28><loc_47><loc_49></location>
<caption>Fig. 6.Magnetohydrodynamical simulations of the global circulation performed using the numerical model of Kuang & Bloxham (1999). The arrows depict the currents of the flow and the color map is representative of the temperature structure. All panels correspond to the same pressure level, namely P = 1 mbar. However, the background magnetic field is gradually increased from panel A to panel C. Clearly, the qualitative character of the flow changes substantially once the field is increased above B glyph[similarequal] 0 . 3 G (Panel B). The fact that the flow transitions to a globally zonal state at a value of background field strength that is considerably smaller than the inferred field surface strengths of Hot Jupiters suggests that dayside-to-nightside flows exist only on planets occupying the cooler end of close-in orbital distribution. For reference, the amplitudes of the axisymmetric component of the induced field corresponding to panels A, B, and C are max(B ind ) = 0 . 075 , 0 . 35, and 0 . 52 G respectively. Note that here, we have plotted the latitude, rather than colatitude used throughout the paper on the y-axis.</caption>
</figure>
<text><location><page_12><loc_52><loc_81><loc_92><loc_92></location>(i.e. few percent) increase in the velocities, the results observed in these simulations were largely unchanged from the nominal simulations. This implies that the presented solutions do not depend sensitively on small-scale flows. In other words, the transition of the atmosphere to a state dominated by zonal jets is a result of interactions between global circulation and the large-scale magnetic field.</text>
<text><location><page_12><loc_52><loc_60><loc_92><loc_81></location>Provided the zonal nature of the flow observed in the magnetized simulation, we can expect that the induced field will be almost entirely toroidal and will approximately be described by equations (29) and (30). As shown in Figure (5), this indeed appears to be the case. The numerically obtained azimuthal component of the field (panel B) is qualitatively similar to its analytically computed counterpart (panel A), although the field lines are concentrated towards the vicinity of the equator in the numerical solution (this is simply a consequence of the fact that the circulation is not exactly given by the expression (27)). The magnitude of the induced field is also in good agreement with the analytical theory. For ˜ v 0 = 440 m/s, and k m / R 3 = 0 . 5 G, equation (29) yields max(B ind ) = 0 . 64 G, where as the numerically computed value is max(B ind ) = 0 . 52 G.</text>
<text><location><page_12><loc_52><loc_37><loc_92><loc_60></location>Unlike the case considered in the previous section (where the Lorentz force is treated as a drag), within the framework of MHD simulations, the relationship between the peak wind speed and the temperature perturbation is not necessarily simple. Consequently, in order to preliminarily explore the sensitivity of our results on irradiation, we performed an additional suite of simulations where the applied heat flux was enhanced by a factor of three, compared to the simulations shown in Figure (6). In these overdriven simulations, we found the peak wind speeds to be a factor of ∼ 2 -2 . 5 higher. However, the characteristic flow patterns closely resembled those, shown in Figure (6) and specifically, the circulation with | B dip | = 0 . 5 G remained dominated by azimuthal jets. Consequently, we conclude that the transition of the circulation to a zonal regime with increasing magnetic field strength is robust within the context of our model.</text>
<text><location><page_12><loc_52><loc_16><loc_92><loc_37></location>It is interesting to note that the zonal nature of the circulation is ensured at a comparatively low magnetic field strength. If we adopt a scaling based on an Elsasser number of order unity (Stevenson 2003), typical hot Jupiter magnetic fields should exceed that of Jupiter by a factor of a few e.g. | B dip | ∼ 10 G. Moreover, the arguably more physically sensible scaling based on the intrinsic energy flux (Christensen et al. 2009) suggests that typical hot Jupiter fields may be still higher by another factor of ∼ 5. Cumulatively, this places the critical magnetic field needed for the onset of zonal flows a factor of ∼ 10 -100 below the typical field strengths. As a result, it would be surprising if a more sophisticated treatment of the hydrodynamics and radiative transfer proved the critical field strength to be higher than the typical one. Nevertheless, such simulations should no doubt be performed.</text>
<section_header_level_1><location><page_12><loc_67><loc_14><loc_77><loc_15></location>5. DISCUSSION</section_header_level_1>
<text><location><page_12><loc_52><loc_7><loc_92><loc_13></location>In this paper, we have characterized the nature of atmospheric circulation on Hot Jupiters, in a regime where magnetic effects play an appreciable role. We began by performing baseline Boussinesq hydrodynamical simulations and augmenting them to crudely account for the</text>
<text><location><page_13><loc_8><loc_73><loc_48><loc_92></location>Lorentz force by expressing it in the form of a Rayleigh drag. Using a simple analytical theory, we showed that within the framework of such a treatment, the interactions between the circulation and the background magnetic field lead to a well-formulated reduction in wind velocities. However, in agreement with published literature (Perna et al. 2010; Rauscher & Menou 2012) and dragged simulations of our own, we noted that regardless of the background field strength, the functional form of the upper-atmospheric stream function remains characteristic of a flow pattern where wind originates at the substellar point and blows towards the anti-stellar points quasi-symmetrically over the terminator (see also Showman et al. (2008)).</text>
<text><location><page_13><loc_8><loc_53><loc_48><loc_73></location>Although simplifying, the assumption that the Lorentz force (even approximately) opposes the flow everywhere, as done by a Rayleigh drag, appears inappropriate for dayside-to-nightside circulation. Consequently, relying on theoretical considerations based on a kinematic treatment of magnetic induction (Moffatt 1978), we showed that if the Lorentz force is not reduced to a form of a drag, dayside-to-nighside flows become unstable in presence of a spin pole aligned magnetic field. On the contrary, the interactions between zonal jets and the background magnetic field do not give rise to meridional or radial flows, thanks to an inherent symmetry. Instead, the jets are stably damped by the background field (Liu et al. 2008; Menou 2012). However, the damping rate generally need not be latitudinally uniform.</text>
<text><location><page_13><loc_8><loc_20><loc_48><loc_53></location>As demonstrated by magnetohydrodynamical simulations, this has profound implications for upperatmospheric circulation. Specifically, the MHD calculations indicate that once the background magnetic field is stronger than a critical value, the upper atmospheric circulation transitions from a state dominated by daysideto-nightside flows to an azimuthally symmetric pattern dominated by zonal jets. Qualitatively, this transition can be understood as a point where redistribution of heat from the dayside to the nightside by flow patterns that intersect the magnetic poles ceases to be energetically favorable against purely zonal circulation. For the standard case considered here (that is, τ N = 10 3 sec), the critical field strength is approximately B crit glyph[similarequal] 0 . 5 G, considerably less than the typically inferred field strengths of Hot Jupiters (Christensen et al. 2009). However, it should be understood that the critical field strength must unavoidably depend on various system parameters including the radiative timescale and the electrical conductivity. The variability due to the latter may be particularly important since thermal ionization is extremely sensitive to the atmospheric temperature (see Figure 2). The form of this dependence and the extent to which atmospheres within the current observational aggregate are magnetically dominated merits further investigation.</text>
<text><location><page_13><loc_8><loc_7><loc_48><loc_20></location>The fact that dayside-to-nightside flows tend to simplify to a zonal state in magnetized atmospheres has a number of important implications. As already discussed to some extent in section (3), axisymmetric flows give rise to exclusively toroidal fields (Moffatt 1978). This means that additional atmospheric dynamo generation, that would act to augment a deep seated field, cannot be supported by large-scale circulation. Moreover, because the induced field lacks a strong poloidal component, its observational characterization is at present hopeless.</text>
<text><location><page_13><loc_52><loc_88><loc_92><loc_92></location>Consequently, observational inference of magnetohydrodynamic processes in exoplanetary atmospheres is likely to be limited to indirect methods.</text>
<text><location><page_13><loc_52><loc_75><loc_92><loc_88></location>This discussion overlooks the possibility of field generation by small-scale turbulence (i.e. the α -effect) in the atmosphere. Indeed such a process may be at play if the turbulent magnetic Reynolds number Re t m ≡ ν/η glyph[greaterorsimilar] 1 -10. For highly turbulent atmospheres, this criterion may indeed be satisfied. Our simulations aimed at determining the viability as well as characterization of field generation by small-scale turbulence in Hot Jupiter atmospheres are currently ongoing and will be reported in a follow-up study.</text>
<text><location><page_13><loc_52><loc_51><loc_92><loc_75></location>In this work, we briefly hinted at the fact that the damping of zonal jets by dipole magnetic fields is not only non-uniform latitudinally but also radially. The radial dependence of the Lorentz force found here is specific to the boundary conditions imposed on the induced current. However, if we do not choose to confine the current to a single scale-height but allow it to penetrate the convective interior of the planet (as for example envisioned within the context of the Batygin & Stevenson (2010) Ohmic dissipation model), the induced toroidal field is free to occupy a much deeper portion of the planet. In such a case, the resulting Lorentz force may act to produce deep-seated azimuthal flows and give rise to largescale differential rotation within the planet (Goldreich private communication). However, the extent to which such differential rotation can persist is subject to a number of constraints, including the magnitude of interior Ohmic dissipation (Liu et al. 2008).</text>
<text><location><page_13><loc_52><loc_25><loc_92><loc_51></location>In addition to the various simplifications inherent to our model that are already described throughout the paper, it is further noteworthy that we have restricted the morphology of the background magnetic field to a pole-aligned dipole for simplicity. Within the solar system, a dipolar, axisymmetric magnetic field created by an internal dynamo is possessed only by Saturn (Acuna & Ness 1980; Dougherty et al. 2005). On the contrary, Jupiter and the Earth have dipole-dominated fields that are significantly tilted with respect to their spin-axes, while Neptune and Uranus possess rather unusual nondipolar, non-axisymmetric fields (Stevenson 2003). As a result it is quite likely that even on a qualitative level, the discussion presented in this work is not comprehensive. That is, unlike axisymmetric jets found in this work, one could envision the generation of substantial stationary eddies, yielding longitudinally and latitudinally asymmetric jets in exoplanetary atmospheres, by complex background magnetic fields.</text>
<text><location><page_13><loc_52><loc_7><loc_92><loc_25></location>Furthermore, orbital variations may also be of importance. Specifically, while the assumption of a circular orbit is secure for the majority of hot Jupiters, null eccentricities are certainly not universal to the observational sample (an extreme example is HD80606b (Naef et al. 2001) which has e = 0 . 93). The time-variability of stellar irradiation associated with significant eccentricity produces rather complex circulation patterns even in hydrodynamic regime (Langton & Laughlin 2008; Kataria et al. 2013). However, recalling that electrical conductivity in hot planetary atmospheres arises primarily as a result of thermal ionization, the circulation patterns are likely to be even more complex than those typically envisioned, since magnetic effects in the atmosphere will</text>
<text><location><page_14><loc_8><loc_91><loc_25><loc_92></location>also be time-dependent.</text>
<text><location><page_14><loc_8><loc_73><loc_48><loc_90></location>We would like to finish with a few words about observational implications of our results. At present, the resolution and signal to noise of the spectroscopic data aimed at characterizing the temperature structure and chemical composition of exoplanetary atmospheres (Charbonneau et al. 2005; Knutson et al. 2008; Swain et al. 2010) is such that even fits obtained with one-dimensional atmospheric models are susceptible to numerous degeneracies (Madhusudhan & Seager 2009). Consequently, it is unlikely that the qualitative change in the flow structure observed in this work will strongly affect the already-limited interpretation of the information contained within this data, in the near future (Line et al. 2012).</text>
<text><location><page_14><loc_8><loc_53><loc_48><loc_73></location>On the other hand, theoretical interpretation of observed dayside-to-nightside temperature differences and the associated shifts in the location of the subsolar hot spot (Knutson 2007) rely heavily on a sensible understanding of atmospheric dynamics, which as we have seen requires a more or less self-consistent account of magnetic effects. To this end, the results obtained in this study are of great importance. Indeed, one can expect that the advective transport of heat changes character and weakens with increased electrical conductivity (by extension, the atmospheric temperature) and magnetic field due to the mechanism described above (see also Liu et al. (2008); Perna et al. (2010); Batygin et al. (2011); Menou (2012); Rauscher & Menou (2012)). Thus, a thorough comparison between a substantial sample of model</text>
<text><location><page_14><loc_52><loc_79><loc_92><loc_92></location>results and data may eventually shed light on the typical atmospheric conductivity structure and field strengths of Hot Jupiters. Such activity would no-doubt further benefit from direct measurements of high-altitude atmospheric wind velocities obtained via ground-based spectroscopy (Snellen et al. 2010). That said, in order for an endeavor of this sort to be meaningful, substantial improvements in theoretical modeling aimed at meliorating the shortcomings outlined above are required, along with a wealth of additional observational data.</text>
<text><location><page_14><loc_52><loc_67><loc_92><loc_78></location>In conclusion, the above discussion clearly indicates that the degree of complexity of the physical regime in which hot exoplanetary atmospheres reside is indeed very extensive. There is no doubt that much additional work remains. In this work, we have taken an ample step towards a self-consistent characterization of magnetically controlled circulation on Hot Jupiters. As such, this study should serve as a stepping stone for future developments.</text>
<text><location><page_14><loc_52><loc_51><loc_92><loc_64></location>Acknowledgments . We thank Adam Showman, Tami Rogers, Kristen Menou, Peter Goldreich and Greg Laughlin for useful conversations, as well as the anonymous referee for a thorough and insightful report. K.B. acknowledges the generous support from the ITC Prize Postdoctoral Fellowship at the Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics. S.S. acknowledges funding by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Alfred P. Sloan Foundation.</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Through the process of thermal ionization, intense stellar irradiation renders Hot Jupiter atmospheres electrically conductive. Simultaneously, lateral variability in the irradiation drives the global circulation with peak wind speeds of order ∼ km/s. In turn, the interactions between the atmospheric flows and the background magnetic field give rise to Lorentz forces that can act to perturb the flow away from its purely hydrodynamical counterpart. Using analytical theory and numerical simulations, here we show that significant deviations away from axisymmetric circulation are unstable in presence of a non-negligible axisymmetric magnetic field. Specifically, our results suggest that dayside-to-nightside flows, often obtained within the context of three-dimensional circulation models, only exist on objects with anomalously low magnetic fields, while the majority of highly irradiated exoplanetary atmospheres are entirely dominated by zonal jets.",
"pages": [
1
]
},
{
"title": "MAGNETICALLY CONTROLLED CIRCULATION ON HOT EXTRASOLAR PLANETS",
"content": "Konstantin Batygin 1 , Sabine Stanley 2 & David J. Stevenson 3 1 Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 2 Department of Physics, University of Toronto, 60 St. George St., Toronto, ON and 3 Division of Geological and Planetary Sciences, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125 Draft version September 19, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "The last decade's discovery and rapid accumulation of the transiting extrasolar planetary aggregate has uncovered a multitude of previously unexplored regimes of various physical phenomena. Perhaps the first unexpected discovery was the existence of Hot Jupiters (i.e. gaseous giant planets that reside within ∼ 0 . 1AU of their host star), which arose from the earliest exoplanetary detections (Mayor & Queloz 1995; Marcy & Butler 1996). Accordingly, among the most intriguing novel theoretical subjects, is the study of atmospheric dynamics on highly irradiated planets. Today, it is well known that the orbital region occupied by Hot Jupiters can also be occupied by lower mass (including terrestrial) planets (Batalha et al. 2012). However, because of their higher likelihood of transit and comparative predisposition for characterization, Hot Jupiters remain at the forefront of the study of extrasolar atmospheric circulation (Showman et al. 2011).",
"pages": [
1
]
},
{
"title": "1.1. Hydrodynamic Global Circulation Models",
"content": "Dynamic meteorology is a phenomenologically rich subject because of the lack of separation of physical scales. In other words, differences in microphysical nature of a given system can have profound effects on its macroscopic state. As a result, it comes as no surprise that circulation patterns on Hot Jupiters generally do not resemble those on Solar System gas giants (Showman et al. 2008; Menou & Rauscher 2009). From a hydrodynamical point of view, the circulational modes of typical Hot Jupiter atmospheres differ in two principal ways, compared to Solar System gas giants. The first and most obvious difference is the energetics. Unlike the outer Solar System, Hot Jupiters reside in an environment where the incoming stellar irradiation completely dominates over the intrinsic planetary heat-flux. As a result, circulation patterns on Hot Jupiters are driven primarily by the congenital [email protected] dayside-to-nightside temperature differences (Showman & Polvani 2011). Furthermore, concurrent with the cooling of the planetary interior, the top-down heating of the atmosphere ensures the onset of stable stratification in the observable ( P > 100 bars) atmospheric region (Guillot & Showman 2002; Burrows et al. 2007). The second difference lies in the extent to which the atmospheres are rotationally dominated. While Solar System gas giants rotate rapidly (i.e. T Jup glyph[similarequal] T Sat glyph[similarequal] 10 hours), Hot Jupiters are thought to rotate pseudosynchronously with their orbital periods (i.e. T HJ ∼ 3 -5 days) as a result of tidal de-spinning (see Hut (1981)). This implies that although still dynamically significant, rotation alone does not exhibit commanding control over the atmospheric flow. Since the discovery of the first transiting extrasolar gas giant HD209458b (Charbonneau et al. 2000; Henry et al. 2000), numerous authors have explored the atmospheric dynamics of Hot Jupiters with a variety of numerical techniques. Because of the inherent differences in the frameworks of the simulations, today, there exists a hierarchical collection of results that correspond to variable degrees of sophistication. On the simpler end of the spectrum are 2D shallow-water simulations (Cho et al. 2008, 2003; Langton & Laughlin 2008, 2007) while the more intricate global circulation models (GCM's) include solvers of the 3D 'primitive' equations (Cooper & Showman 2005; Showman et al. 2008; Menou & Rauscher 2009; Heng et al. 2011) as well as the 3D fully compressible Navier-Stokes equations (Dobbs-Dixon & Lin 2008; Dobbs-Dixon & Agol 2012). Simultaneously, various groups have gone to different lengths in their treatment of radiative transfer, with exploited models ranging from simple prescriptions such as Newtonian cooling (Showman et al. 2008) to double-gray (Rauscher & Menou 2012) and non-gray (Showman et al. 2009) schemes. An important step towards delineating the correspondence among results obtained with different solvers has been recently performed by Heng et al. (2011). Although there are quantitative differences in the re- sults generated by different GCM's, there is general agreement on the qualitative features of the circulation. Specifically, there are three aspects of interest. First, super-rotating zonal jets exist in all simulations. Their number (and naturally, the widths) ranges between 1 and 4, depending on the model (see Showman et al. (2009)), but the relative sparsity of the jets compared to Jupiter and Saturn is understood to be a result of diminished rotation rate (Showman & Guillot 2002). Moreover, in a recent study, Showman & Polvani (2011) showed that the formation of jets is ordained by the interaction of the atmospheric flow with standing Rossby waves that in turn result from the strong difference in the radiative forcing between the planetary dayside and the nightside. Second, the characteristic wind speeds produced by different models are consistent within a factor of a few, and are generally in the ∼ km/s range. This is likely a direct result of the overall similarity in the force-balance setup within the models. Specifically, Showman et al. (2011) argue that near the equator, the horizontal pressuregradient acceleration caused by the asymmetric irradiation is balanced by the advective acceleration. Meanwhile, Coriolis force takes the place of advective acceleration as the primary balancing term in the mid-latitudes. Both force-balances yield ∼ km/s as the characteristic wind speeds, in agreement with the numerical models. Finally, in GCMs that resolve the vertical structure of the atmosphere (e.g. Showman et al. (2008); Menou & Rauscher (2009); Heng et al. (2011)) eastward jets consistently dominate the lower atmosphere while the upper atmosphere is characterized by more or less symmetric dayside-to-nightside circulation. In other words, winds originate at the sub-solar point and flow to the anti-solar point over the terminator in the upper atmosphere. The transition between the circulation patterns takes place at P ∼ 0 . 1 -0 . 01 bars and is a consequence of the substantial reduction of the radiative time constant with diminishing pressure (Iro et al. 2005). In particular, because the radiative adjustment timescale is much shorter than the advective timescale in the upper atmosphere, the flow is unable to perturb the temperature structure away from radiative equilibrium significantly. Figure (1) depicts a schematic representation of the characteristic features of atmospheric circulation on Hot Jupiters.",
"pages": [
1,
2
]
},
{
"title": "1.2. Magnetically Dragged Global Circulation Models",
"content": "There exists another important, distinctive feature of Hot Jupiter atmospheres, namely their non-negligible electrical conductivity (see Figure 2). Electrical conductivity in Hot Jupiter atmospheres does not originate from the ionization of H or He, but rather from the stripping of the valence electrons belonging to alkali metals such as K and Na (Batygin & Stevenson 2010; Perna et al. 2010). While these elements are thought to be present in trace abundances (e.g. [K]/[H] ∼ 10 -6 . 5 , [Na]/[H] ∼ 10 -5 . 5 ) (Lodders 1999), temperatures of ∼ 2000K at upper atmospheric pressures, lead to total and partial ionization of K and Na respectively. In fact, at mbar levels, the conductivity can reach values as high as σ ∼ 1 S/m (Batygin et al. 2011; Rauscher & Menou 2012; Heng 2012). Furthermore, it is generally expected that much like solar system gas giants, Hot Jupiters posses interior dynamos, that produce surface fields comparable to, or in slight ex- upiter's field 1 (e.g. B ∼ 3 -30 Gauss) (Stevenson 2003; Christensen et al. 2009). Consequently, there is a distinct possibility that atmospheric circulation on Hot Jupiters may be in part magnetically controlled. That is to say, highly irradiated atmospheres may be sufficiently conductive for the Lorentz force to play an appreciable, if not dominant role in the force-balance. Realizing the potential importance of the coupling between the mean flow and the planetary magnetic field, Perna et al. (2010) modeled the Lorentz force as a Rayleigh drag (a velocity-dependent force that opposes the flow) and incorporated it into the GCM previously utilized by Menou & Rauscher (2010). This effort was later amended by Rauscher & Menou (2013), who also modeled the Lorentz force as a Rayleigh drag but selfconsistently accounted for spatial variability in the electrical conductivity (by extension the drag timescale) in the weather layer. The results obtained with dragged GCMs exhibit significant differences in the obtained flow velocities relative to the standard GCMs. Namely, Perna et al. (2010) found a factor of ∼ 3 decrease in the peak wind speeds as the background dipole magnetic field was increased from B dip = 3 G to B dip = 30 G, while Rauscher & Menou (2012) found a similar decline in the jet speeds as the field was increased from B dip = 0 G to B dip = 10 G. The magnetic limitation of the peak wind speeds is of considerable importance as it may prevent the global circulation from approaching a super-sonic state (note that the characteristic sound speed is order c s ∼ √ k B T/µ ∼ 3 km/s, where k B is Boltzmann's con- stant, T is the temperature, and µ is the mean molecular weight), thereby inhibiting the formation of shocks.",
"pages": [
2,
3
]
},
{
"title": "1.3. The Necessity for Magnetohydrodynamic Circulation Models",
"content": "Although dragged 3D GCMs clearly highlight the quantitative importance of the magnetic effects in Hot Jupiter atmospheres, they fail to accentuate significant qualitative differences in the obtained flows. Specifically, much like conventional GCMs, magnetically dragged GCMs still show deep-seated zonal jets, overlaid by complex flow patterns that intersect the poles of the planets. This lack of qualitative differences may arise from two distinct possibilities. The first is that beyond diminishing the peak wind speeds, the background magnetic field has little effect on the global circulation. In actuality, this may very well be true for pressure levels where the circulation is dominated by zonal jets, because of the geometrical simplicity of the flow-field interactions. Indeed, the coupling between the zonal flow and the polealigned background dipole field is azimuthally symmetric: differentially rotating jets convert the poloidal field into toroidal field (Liu et al. 2008; Batygin & Stevenson 2010). As will be discussed in detail below, beyond the reduction of velocities, this conversion poses few dynamical ramifications for the jets. Furthermore, owing to higher pressure and somewhat diminished temperatures compared with the upper atmosphere (and the associated decrease in conductivity), the zonal jets may reside in the kinematic regime, where the effects of the Lorentz force are modest (Batygin et al. 2011; Menou 2012). The second possibility is that although in reality the interactions with the background field impel the circulation to strongly deviate from its purely hydrodynamical counterpart, the procedure of modeling the Lorentz force as a Rayleigh drag does not capture the essential features of the dynamics. This is likely true in the upper atmosphere, where azimuthal symmetry is broken and the flow takes on a more topologically complex form. After all, in such a setting there is no requirement for the Lorentz force to simply oppose the flow everywhere, as is done by Rayleigh drag. Thus, there is a distinct possibil- ity that previous modeling efforts have consistently misrepresented the circulation patterns of the upper atmospheres of Hot Jupiters. Accordingly, the investigation of this possibility is the primary purpose of this work. A statistically sound comparison between theoretical models and observations requires the incremental decrease in the goodness of fit to outweigh the cost of introducing new degrees of freedom into the model (see Rodgers (2000) for an in-depth review). Within the context of extrasolar planets, the limitations in observational capabilities and the quality of the data render the construction of highly sophisticated models unjustified (Line et al. 2012). Although a rigorous comparison with observational data is not the focus of this paper, our modeling efforts will lie in the same rudimentary spirit. In other words, here we shall focus on understanding the qualitative, rather than quantitative nature of the circulation. Numerous simplifying assumptions will be made and the representation of the flow (including flow velocities, dayside-to-nightside temperature differences, etc) should only be viewed as approximate. However unlike all previous works on the subject, the model we shall utilize will remain self-consistently magneto-hydrodynamic (MHD). In taking this approach, we hope to successfully capture the essential features of magnetic effects in highly irradiated planetary atmospheres. The paper is organized as follows. In section 2, we describe the equations inherent to our numerical GCM and reproduce the main features of Hot Jupiter atmospheric flows in the purely hydrodynamic regime. In section 3, we discuss the qualitative features of the atmospheric flows, treating the Lorentz force as a hydrodynamic drag. Specifically, we develop an analytical theory for magetically-dragged circulation patterns in the upper atmosphere and test the resulting scaling law against numerical simulations with enhanced viscosity and explore the effects of varying the radiative timescale. In section 4, we introduce a pole-aligned background magnetic field and demonstrate the transition of the upper atmosphere's dayside-to-nightside circulation into a globally zonal state with the onset of the background field. We conclude and discuss our results in section 5.",
"pages": [
3
]
},
{
"title": "2. NUMERICAL GLOBAL CIRCULATION MODEL",
"content": "The Hot Jupiter GCM we have adopted here is a variant of the numerical geodynamo model constructed by Kuang & Bloxham (1999). Since its conception, the model's versatility has been exploited extensively to explain the geodynamo (Kuang & Bloxham 1999; Dumberry & Bloxham 2002), the ancient Martian dyanamo (Stanley et al. 2008), Mercury's thin-shell dyanamo (Stanley et al. 2005; Zuber et al. 2007), Saturn's dynamo (Stanley 2010), as well as dynamos of Uranus & Neptune (Stanley & Bloxham 2004, 2006). The details of the implementation of the model and the utilized numerical methods are throughly described by Kuang & Bloxham (1999). Here, rather than exhaustively restating the particularities of the framework, we limit ourselves to presenting the set of equations under consideration and the underlying assumptions, while referring the interested reader to Kuang & Bloxham (1999) for further information.",
"pages": [
3
]
},
{
"title": "2.1. The Governing Equations",
"content": "Momentum. -The circulation model solves the NavierStokes equation for an electrically conductive, Boussinesq fluid in a rotating spherical shell of finite thickness. Here, D/Dt = ∂/∂t + v · ∇ is the material derivative, v is the velocity vector, Ω = (2 π/ T ) ˆz is the rotation vector, P is the modified pressure, ρ is the density, J is the current density and ν is the kinematic viscosity. The bar denotes an average, whereas δ denotes the perturbation away from the background state. The density and temperature are related to the pressure through the ideal gas equation of state 2 : where P is the total pressure. The dynamic domain where the equation is solved is confined above a rigidly rotating spherical shell. We denote the inner and outer radii of the atmosphere as r 1 < r 2 respectively. Continuity. -The model is formally 3D and the vertical component of the motion enters into the continuity equation: However, the nearly-constant density, incompressible fluid approximation prevents us from self-consistently modeling a radially extensive atmosphere. Indeed, the atmospheric density does not change, except by thermal expansion/contraction 3 : Consequently, we limit the thickness of the atmosphere to a single scale-height in our simulations: r 2 -r 1 = H = k B ¯ T/µg , where g is the acceleration due to gravity. Additionally, we set r 1 = R , the radius of the planet. Generally, because of the above-stated reasons, our model should be viewed as more closely related to the 2D shallow-water GCMs (Cho et al. 2003; Langton & Laughlin 2008) rather than the family of 3D models (Showman et al. 2009; Perna et al. 2010; Rauscher & Menou 2012). However, proper treatment of the of the induction equation (see below) in absence of pre-described symmetry requires the model to remain 3 dimensional. Energy. -The energy equation, that governs the temperature, inherent to the model reads: where κ is the coefficient of thermal diffusivity (kept constant throughout the computational domain). Strictly speaking, this equation governs diffusive heat flux and (in direct interpretation) is unsuitable for modeling a medium where energy transport is accomplished mainly by radiation. This is because the above equation rests on the approximations of short photon mean free path and the neglect of the temperature-dependence of the opacity (in the context of the Boussinesq treatment employed here, the latter makes sense but the former breaks down at pressure levels corresponding to optical depth of order unity, allowing for only a crude approximation to reality). However, shall it be possible to relate κ to radiative properties of the gas, the above energy equation can still be used to effectively mimic the appropriate heat transport. In a radiatively-dominated atmosphere, the correct energy equation reads (Peixoto & Oort 1992) where c p is the specific heat capacity at constant pressure and F is the radiative heat flux. The expression for the radiative heat flux reads (Clayton 1968): where σ sb is the Stefan-Boltzmann constant and ψ is the opacity. At this point, the relationship between κ and the atmospheric temperature, density, opacity, and heat capacity is obvious. However, before proceeding further, let us recall that to an order of magnitude, the Newtonian cooling timescale τ N is given by the ratio of the atmosphere's excess heat content to its excess radiative flux: Consequently, we may express: where we have implicitly assumed an infrared optical depth of order unity at the pressure-level of interest. The relationship between κ and τ N is convenient, as it can be related to previous works. In particular, Showman et al. (2008) have calculated τ N using a state of the art radiative transfer model and tabulated the results on a pressure-temperature grid. Here, we utilize their computations as a guide in estimating the thermal diffusivity. Note that we could have arrived at the relationship (9) more intuitively by dimensional analysis. Specifically, noting that the radial extent of the atmosphere is much smaller than the lateral extent, the relevant length scale is the vertical scale-height, H . Meanwhile, because the heat transport is primarily radiative, τ N is clearly the relevant timescale. Bearing in mind the units of diffusivities (i.e. m 2 /s), equation (9) naturally emerges as an estimate. Magnetic Field. -The evolution of the magnetic field is governed by the induction equation (Moffatt 1978) where η = 1 /µ 0 σ is the magnetic diffusivity (kept constant throughout the computational domain) and µ 0 is the permeability of free space. Meanwhile, the absence of magnetic monopoles implies a divergence-free magnetic field: Once the structure of B is known, the current density (within the MHD approximation) is given by At this point, the full set of governing differential equations is presented. Paired with a matching set of boundary and initial conditions, the system can be integrated forward in time self-consistently. The equations are solved using a mixed spectral-finite difference algorithm and following Kuang & Bloxham (1999), the spherical harmonic decomposition is taken up to degree glyph[lscript] max = 33 in the latitude m max = 21 in the azimuthal angle. The computational domain is broken up into 64 radial shells. The model is integrated forward in time until equilibration in the thermal, kinetic and magnetic energies is attained.",
"pages": [
4,
5
]
},
{
"title": "2.2. Boundary and Initial Conditions",
"content": "The physical parameters employed in the numerical experiments we report are loosely based on the planet HD209458b (Charbonneau et al. 2000). Aside from being the first extrasolar planet found to transit its host star, it has become a canonical example used in the studies of Hot Jupiter atmospheres (Burrows et al. 2007; Snellen et al. 2010). To this day, (along with HD189733b (Knutson et al. 2009)) it remains the best characterized extrasolar planet. The object has a mass M = 0 . 69 M Jup , a radius R = 1 . 35 R Jup and a rotational (assumed synchronous with orbit) period of T HD209458b = 3 . 5 days. Momentum. -Because we are integrating a quasi-2D atmospheric shell, intended to be representative of a single pressure level, we apply impenetrable, stress-free boundary conditions to the velocity field. Thus, flows are free to develop without friction along the boundaries, although at initialization the planet is cast into solid-body rotation meaning v = 0 at t = 0. Energy. -The temperature is initialized at ¯ T = 2000K with δT/ ¯ T = δρ/ ¯ ρ = 0. The atmosphere is kept stablystratified by the imposition of a stable background temperature gradient (set to the adiabatic lapse rate h = g/c p ) similar to the implementation in other Boussinesq dynamo models with stable layers (e.g. Stanley & Mohammadi (2008); Stanley (2010); Christensen & Wicht (2008)). Additionally, an azimuthally variable heat-flux is applied at the outer boundary, r 2 , to account for the variable stellar irradiation (in practice it doesn't matter whether the variable heat flux is applied at the outer or the inner boundaries, since it is the horizontal temperature gradient that controls the flow). The functional form of the heat-flux is chosen to be that of the F ∝ Y 1 1 spherical harmonic, while the amplitude is taken to be a free parameter (see the discussion in the next section). Magnetic Field. -Nominally, an electrical conductivity of σ = 1S/m, characteristic of P glyph[similarequal] 1mbar, T glyph[similarequal] 2000K is prescribed to the computational domain. Simultaneously, negligible electrical conductivity is assigned outside the computational domain. That is, σ glyph[similarequal] 0 at r < r 1 and r > r 2 , meaning all of the current generated by the atmospheric flow is confined to the weather layer. This is in agreement with the approach of Perna et al. (2010); Rauscher & Menou (2013), but in some contrast with the analytical work of Batygin & Stevenson (2010); Batygin et al. (2011), where the current is allowed to penetrate the convective interior of the planet. Because this work is primarily aimed at studying the upper atmosphere, the pressure-level of interest may reside above the atmospheric temperature inversion, characteristic of some Hot Jupiter atmospheres (Burrows et al. 2007; Spiegel et al. 2009). The presence of such an inversion may provide an electrically insulating layer 4 , justifying σ glyph[similarequal] 0 at r < r 1 . The capability of electrical currents to penetrate the upper atmosphere and close in the magnetosphere is determined by the upper atmosphere's temperature structure and the abundance of Alkali metals at P glyph[lessorsimilar] 1 mbar altitudes. Although a clear possibility, the physics of atmosphere-magnetosphere coupling is no-doubt complex and is beyond the scope of the present study. Consequently, we neglect it for the sake of simplicity. In all of our simulations, we initialize J = 0 in the weather layer. However, the weather layer is still permeated by the background magnetic field, B dip , presumed to be generated by dynamo action in the convective interior of the planet. This zero current field reads: where k m is a constant that sets the surface field strength i.e. | B dip | = k m / R 3 at the equator. Within the context of the model, the background field is implemented by modifying the governing equations to account for a timeindependent axially-dipolar external field. This occurs specifically in two terms. In the momentum equation (1), the Lorenz force ( J × B ) / ¯ ρ is replaced by J × ( B + B dip ) / ¯ ρ . In the magnetic induction equation (10), the induction term ∇× ( v × B ) is replaced by ∇× ( v × ( B + B dip )). This method is similar to that used by Sarson et al. (1997) and Cebron et al. (2012) to implement external fields.",
"pages": [
5
]
},
{
"title": "2.3. Dimensionless Numbers",
"content": "Upon non-dimensionalization of the governing equations (Kuang & Bloxham 1999), we obtain 6 dimensionless numbers that completely describe the system. They are the Ekman number E , the magnetic Rossby number R o , the magnetic Prandtl number q , the magnetic Rayleigh number R th and the aspect ratio χ as well as an additional value, Γ, that parameterizes the incoming stellar flux. In terms of physical parameters, these quantities read: The aspect ratio of the atmosphere we consider is 4 This idea is not new. The models of Batygin & Stevenson (2010) as well as Batygin et al. (2011) used the presence of such a layer to confine the current generated by zonal flows to the lower atmosphere and the interior of the planet. χ = 7 × 10 -3 . For numerical stability, the model requires the Ekman number to exceed a critical value (which we adopt in the simulations) of order E crit ∼ 10 -5 . If we consider the molecular viscosity of Hydrogen ν = ¯ na √ 3 k B ¯ T/m H 2 / 2, where ¯ n is the number density and a is the molecular cross-section, we obtain a hopelessly small E ∼ 10 -20 glyph[lessmuch] E crit at mbar pressure. We note that the actual Ekman number is orders of magnitude higher, since on the global planetary scale, small-scale turbulence is a far more relevant source of viscosity than transfer of momentum at the molecular level (Peixoto & Oort 1992). Still, the true value of E is probably much smaller than E crit . x = 619K = 104 m/s 003 For a given electrical conductivity (equivalently diffusivity), R o and R th simply encompass the physical units of the model. Specifically, for σ = 1S/m, R o = 1 . 79 × 10 -6 and R th = 1 . 38 × 10 9 . Meanwhile, all of the information regarding the considered pressure level is provided by q . Taking σ = 1S/m as before, we obtain q glyph[similarequal] 6 , 60 and 600, corresponding to τ N = 10 5 , 10 4 , and 10 3 sec, appropriate for P = 1 , 0 . 1 and 0 . 001 bars respectively. Finally, as already mentioned above, we take Γ to be an adjustable parameter, tuned to obtain the desired temperature gradients. It is important to note that our model differs somewhat from typical dynamo models in a sense that Γ, rather than R th , parameterizes the extent to which the system is driven. 680K m/s Let us conclude the description of the numerical model with a brief discussion of its shortcomings as a guide for future work. First and foremost, the limitation of the atmosphere to a single scale-height may be prejudicial, as previous work has shown that including an extended vertical extent of the atmosphere is important to capture circulation features (Heng et al. 2011). Second, while we have kept thermal and magnetic diffusivities uniform throughout the computational domain, it should be understood that in reality these values vary with temperature and pressure. Third, an implicit assumption of an infrared optical depth of order unity is rather crude at ∼ mbar pressure levels and should be lifted in more rigorous treatments of radiative transfer. Finally, as already mentioned above, the artificially enhanced viscosity inherent to our model almost certainly smoothes out smaller-scale flow to an unphysical extent. x = 258K = 442 m/s",
"pages": [
5,
6
]
},
{
"title": "2.4. Hydrodynamical Simulations",
"content": "Prior to performing unabridged MHD simulations, it is useful to first compare our model to previously published results. Accordingly, we begin by setting the strength of the background field to B dip = 0. Because the computational domain is initialized with a null current density, no magnetic fields are generated yielding purely hydrodynamic simulations. Horizontal slices of the atmosphere (through the center of the computational domain) in the cylindrical projection are shown in Figure (3). The figures are centered on the substellar point and the background color shows the temperature distribution. The arrows denote the circulation vector field. Peak wind speeds as well as the maximal temperature deviations from ¯ T = 2000K are labeled. The typically observed transition from zonal flows to dayside-nightside flows is observed as the pressure is de- creased sequentially from P = 1 bars (Panel C of Figure 3) to P = 0 . 001 bars (Panel A of Figure 3). However, important differences exist in our results, contrasted against say, the results of Showman et al. (2008). The first important distinction is that in the zonally-dominated parameter regime, rather than developing a single broad jet, our model shows the development of three counterrotating jets. This is a simple consequence of angular momentum conservation in the computational domain, and is not uncharacteristic of 2D models (Showman et al. 2011). Because of free-slip boundary conditions employed in our model, the atmosphere is not allowed to exchange angular momentum with the interior. As such, because the atmosphere is initialized in solid-body rotation, the development of any prograde jets must be accompanied by the development of retrograde jets. Because the retrograde jets reside at a high latitude θ ret , whereas the prograde jets are essentially equatorial, angular momentum conservation requires them to be faster by a factor of | v ret / v pro | ∼ 1 / cos θ ret , as observed in the simulations. The angular momentum conserving 3D simulations of Heng et al. (2011) exhibit similar behavior, although in their model the counter-rotating jets develop below the prograde ones, and are considerably slower because of the associated density enhancement. The second distinction of interest is the direction of the equatorial jet. While 3D GCMs consistently produce eastward equatorial jets, the equatorial jets in our hydrodynamical simulations are westward. This is not too surprising, as shallow-water and equivalent barotropic models are known to produce both eastward and westward equatorial jets, depending on the details of the simulation setup (Showman et al. 2011; Heng et al. 2011). Consequently, this difference can probably be attributed to the limited vertical extent of our model. The third important difference is the fact that flow velocities are not consistent along the pressure levels. In particular for the same values of δT , zonal flows have ∼ few km/s peak wind speeds, while the dayside-tonightside flows are more than an order of magnitdue slower. This is largely a consequence of difference in the geometry of the circulation and the fact that viscosity enters as a significant member in the force balance for dayside-to-nightside flows. This can be seen by approximating ν ∇ 2 ∼ ν/ L 2 (Holton 1992), where L is a characteristic length scale associated with the curvature of the circulation. For zonal jets, L z ∼ R while for dayside-to-nightside circulation, the return flow is in part radial implying L dn ∼ H . As will be shown in the following section, faster velocities can be attained by either increasing the aspect ratio of the atmosphere or by artificially enhancing the radiative heat flux, as a result of a linear proportionality between peak wind speeds and δT . An additional point of importance is that in typical 3D simulations, dayside-to-nightside circulation is nearly uniform over the terminator with the return flow residing at greater depth, while our results depict a partial return flow over the poles. This is again a consequence of the quasi-2D geometry of our model. Although these quantitative distinctions are certainly worthy of attention, the typical features of the flow are approximately captured by our simplified model. Consequently, while being mindful of the model's limitation we do not view the quantitative dissimilarities as critical, as they are not central to the argument of the paper. After all, recall that we are primarily concerned with the possibility of a qualitative alteration of the dayside-tonightside flow by magnetic effects.",
"pages": [
6,
7
]
},
{
"title": "3. DRAGGED CIRCULATION IN THE UPPER ATMOSPHERE",
"content": "In the previous section, we performed baseline hydrodynamical simulations of atmospheric circulation at different pressure levels. In the following sections, we will focus primarily on the mbar pressure level, where the flow takes on a dayside-to-nightside character. As discussed above, in our simulations viscosity plays an important role in determining the flow velocities. Conceptually, the situation may be synonymous to simulations of invicid GCMs that parameterize the effect of magnetic coupling as Rayleigh drag (Perna et al. 2010; Rauscher & Menou 2012). In interest of understanding the dependence of the flow velocities on the magnitude of the dayside-tonightside temperature gradient as well as the imposed frictional forces, in this section we shall develop a simple analytical model for dragged upper-atmospheric circulation and confirm it numerically.",
"pages": [
7
]
},
{
"title": "3.1. Analytical Theory",
"content": "Let us begin with estimation of characteristic timescales. In order to accomplish this, we first simplify the Lorentz and viscous forces to resemble the functional form of Rayleigh drag. Utilizing Ohm's law, we have 5 : This allows us to rewrite equation (1) in a simpler form: where τ f = (1 /τ L + 1 /τ ν ) -1 . Taking | B dip | = 1 G, the characteristic timescales are: τ L ∼ 10 3 sec and τ ν ∼ 10 5 sec. Other relevant timescales in the problem is the rotational (Coriolis) timescale τ Ω ∼ 2 π/ Ω ∼ 10 5 sec, radiative timescale τ N ∼ 10 3 sec and the advective timescale τ adv ∼ R /v ∼ 10 5 sec. There exists a clear separation of timescales in the system. As a result, upon including the parameterized Lorentz force into the equations of motion, the inertial and Coriolis terms can be dropped (the viscous term can be dropped as well, although this simplification is unnecessary). The removal of the inertial terms implies a steady-state solution. The removal of the Coriolis term creates a symmetry characterized by an axis that intersects the sub-solar and anti-solar points. Taking advantage of this symmetry, we orient the polar axis of the coordinate system such that it intersects the sub-solar point. Upon doing so, we can specify a null azimuthal velocity and drop all azimuthal derivatives in the equations of motion. In a local cartesian reference frame, this leaves us with horizontal (ˆ y ) and vertical (ˆ z ) momentum equations, where the latter simplifies to the equation of 5 Although this approximation is often made, it is not necessarily sensible for systems where the magnetic Reynold's number, Re m ≡ v L /η glyph[greatermuch] 1. Adopting v ∼ km/s and L ∼ H , we obtain Re m ∼ 10 3 , placing the magnetic drag approximation on shaky footing. Further, the electric field in Ohm's law can only be neglected when the radial current is negligible. hydrostatic balance: Following Schneider & Lindzen (1977) and Held & Hou (1980), we shall adopt a Newtonian energy equation with implicit stable stratification (recall that we have set the potential temperature gradient to h = g/c p ): Here, ξ glyph[greaterorequalslant] 1 is a constant that parameterizes lateral heat advection and δT rad is a purely radiative perturbation to the background state, ¯ T . In other words, as the damping of the circulation is strengthened and v → 0, δT → δT rad . Retaining the incompressibility condition (3), we introduce a stream-function Ψ, defined through v = ∇× Ψ (Landau & Lifshitz 1959). Taking a partial derivative of the y -momentum equation with respect to z and of the z -momentum equation with respect to y , we obtain Taking a derivative of equation (19) with respect to y and switching the order of partial differentiation yields: Meanwhile, differentiating the Newtonian cooling equation (18) with respect to z gives: allowing us to eliminate ∂ 2 Ψ /∂y∂z : simply the square of the Brunt- Note that g 2 /c p ¯ T is Vaisala frequency for an isothermal atmosphere. Equation (22) admits the trial solutions where ( δT 0 rad ) and ( δT 0 ) are constants that represent the maximal deviations in the respective quantities from the background state. Note that ( δT 0 rad ) is a parameter inherent to the model rather than a variable. Upon substitution of the above solutions (23) into equation (22), we obtain a relationship between ( δT 0 ) and ( δT 0 rad ): In the above equation, ζ is an empirical factor that has been introduced to account for the approximations inherent to equations (15). With an analytical solution for the temperature perturbation in hand, we substitute equations (23) into equation (19) and integrate twice to obtain: This solution implies the same functional form for laterally-averaged heat transport in the vertical and horizontal advection terms in the energy equation (6), lending some support for the approximation inherent to equation (18). Once the stream function is obtained, the maximal horizontal and vertical velocities are given by: where Ψ 0 is the term in square brackets in (25). Note that the above theory automatically implies a quasi-2D flow since v max z /v max y ∼ ( H / R ) glyph[lessmuch] 1 .",
"pages": [
7,
8
]
},
{
"title": "3.2. Numerical Experiments",
"content": "With a simple analytical theory at hand, we performed a series of numerical simulations, varying the radiative and drag timescales in the ranges 10 2 < τ N < 10 3 sec and 10 3 < τ f < 10 5 sec. Although we observed a considerable variability in the wind speeds and dayside-to-nightside temperature differences in our simulations, the nature of the flow was largely the same as that seen in panel A of Figure (3) across the runs. The peak wind speeds obtained in the simulations as functions of τ N and τ f are presented as black dots in Figure (4). In addition to the simulation results, Figure (4) shows v max y given by equation (26) for the same parameters. As can be seen from the figures, the scaling law inherent to equation (25) matches the numerical experiments quite well. Extrapolating towards larger values of τ f , it can be inferred that our simulations would have produced peak wind speeds of order ∼ km/s if not for the numerical requirements of enhanced viscosity. However, it can also be expected that the character of the flow would also change qualitatively with diminishing viscosity, as the force balance shifts away from that implied by equations (15) 6 . It should be kept in mind that the adjustable parameters ξ and ζ were fit to the data. Moreover, the value of ( δT 0 rad ) = 3360K 7 was chosen by running a simulation where viscous forces completely dominated the force balance ensuring v = 0. In other words, the quantitative agreement seen in Figure (4) is a consequence of the fact that the adjustable parameters of the analytical solution have been fit to the numerical data, but the fact that the functional form of the analytical model conforms with numerical experiments suggest that the stream-function (25) captures the main features of dragged upper-atmospheric circulation on Hot Jupiters.",
"pages": [
8
]
},
{
"title": "4. MAGNETICALLY CONTROLLED CIRCULATION",
"content": "In the last section, we examined the extent to which dayside-nightside flow can be damped by imposing a drag. However, both the analytical theory and numerical experiments showed that the qualitative character of the circulation remained largely unchanged. As already mentioned in the introduction, the rough consistency of the flow patterns across a range of characteristic drag timescales is in broad agreement with the results of 'primitive' 3D GCMs (Perna et al. 2010; Rauscher & Menou 2012). In this section, we challenge this assertion with MHD calculations.",
"pages": [
8,
9
]
},
{
"title": "4.1. Theoretical Arguments",
"content": "With the exception of a rather limited number of problems, self-consistent magneto-hydrodynamic solutions can only be attained with the aid of numerical simulations. However, for the system at hand, the qualitative effect of magnetic induction can be understood from simple theoretical considerations. As we already argued, the two characteristic states of Hot Jupiter atmospheric circulation are a zonally-dominated state and a meridionally-dominated state (Showman et al. 2011). Whether or not a given configuration will be significantly affected by the introduction of the magnetic field can be established by analyzing its stability. More specifically, we can work within a purely kinematic (rather than dynamic) framework to understand if the Lorentz force acts to perturb the flow away from its hydrodynamic counterpart or simply damps the circulation. Zonal Flows. -Although not directly applicable, recent studies of Ohmic dissipation that arises from zonal flows performed by Liu et al. (2008) (within the context of solar system gas giants) and by Batygin & Stevenson (2010) as well as Menou (2012) (within the context of Hot Jupiters) have already produced some results on a related problem. Here we work in the same spirit as these studies and prescribe the following functional form to the zonal flow to approximately represent three jets, such as those shown in panel C of Figure (3): where ˜ v 0 is a negative constant, whose magnitude corresponds to the peak wind speed. This prescription triv- ally satisfies the continuity equation (3), although we note that a more realistic zonal flow should also exhibit differential rotation. The interaction between this flow and the background magnetic field (13) will induce a field B ind in the atmosphere. Because B dip is entirely poloidal, and ˜ v is strictly toroidal, B ind will also be strictly toroidal (Moffatt 1978). As can be readily deduced from equation (10), this means that B ind cannot interact with ˜ v to further induce new field unless ˜ v deviates from a purely zonal flow. As a result, in steady state, the induction equation reads: It is noteworthy that had we chosen to represent a single broad jet (such as that seen in most 3D simulations (Showman et al. 2008; Menou & Rauscher 2010; Rauscher & Menou 2013)) by setting ˜ v ∝ sin( θ ) (in this case ˜ v 0 is positive), equation (28) would have looked the same, with the exception of the coefficient on the RHS, which would have been 2 instead of 6. As a result, it should be kept in mind that the following kinematic solution applies to the case of a single jet as well. φ (deg) The angular part of equation (28) is satisfied by the expression where A ( r ) is a yet undefined function. This form ensures that the meridional component of the induced current vanishes at the poles. Meanwhile, the radial impenetrability of the boundaries requires A ( R ) = A ( R + H ) = 0 as dictated by equation (12). With these boundary conditions, equation (28) can be solved to yield The induced field and the associated electrical current are shown in panel A of Figure (5). r r The Lorentz force that arises from the interactions between B ind and B dip takes the form Because the Lorentz force acts in the same sense as the flow itself (that is, F L × ˜ v = 0), it can only act to accelerate/decelerate the jets but not alter their directions. Indeed, the functional form of F L is that of a Rayleigh drag (equation 15), however the characteristic timescale is non-uniform in latitude and radius i.e. τ L = f ( r, θ ). The non-uniformity we derive here should not be confused with the variability in F L that can arise from the spatial dependence of the electrical conductivity (see Rauscher & Menou (2013)). It is noteworthy that the radial dependence of F L can give rise to differential rotation. However, this is not particularly important, since in some similarity with the above discussion, differential rotation will only induce toroidal fields through the ω -effect (Moffatt 1978) and will therefore only change the solution obtained here on a detailed level (i.e. the added dependence of ˜ B on r will subtly modify the function A ( r )). In other words, a differentially rotating zonal flow still results in a purely toroidal induced field. For a sensible comparison with previous works (e.g. (Perna et al. 2010; Menou 2012; Rauscher & Menou 2012)) and the simple theory presented in the previous section, it is instructive to evaluate the maximal magnitude of F L , which corresponds to the upper and lower boundaries of the domain in question 8 i.e. r = R , r = R + H . To leading order in χ , the expression reads: From this expression it is clear that F L acts primarily in the mid-latiudes rather than the equator. As a result, the damping of the jets is latitudinally differential, meaning that even if the flow is initially composed of multiple bands (as we consider here), it will approach a single equatorial jet as the conductivity and/or the magnetic field is increased. Furthermore, recall that the functional form of equation (32) is also valid in the case of a single jet. Qualitatively, this seems to imply that the Lorentz force acts to collimate the jet towards the equator. Such an effect is sensible given that the radial component of the field is stronger as one approaches the pole for a simple dipole. However, it should also be kept in mind that a true planetary magnetic field might be more complicated, leading to further lack of triviality in the circulation. Dayside-to-Nightside Flows. -Let us now consider the more topologically complex interaction between meridional flows and a spin-pole aligned dipole magnetic field. As in section (3.1) we shall work in a coordinate frame where the polar axis intersects the sub-solar point and is directed at the host star. Unlike the case of zonal circulation, this configuration has no exploitable symmetry. Consequently, a simple solution to the steady-state induction equation (28) is difficult, if not impossible, to obtain. We shall therefore make substantial simplifications. In our prescription for the velocity field, we neglect radial flow altogether (thereby violating continuity) and adopt an expression similar to equation (27): Because of our choice of coordinate system, equation (13) cannot be used directly. However, keeping in mind 8 Although the Lorentz force is equal and opposite at r = R and r = R + H , its radial distribution is such that its vertically integrated value acts to oppose the flow on average. that the background dipole field originates in a much deeper region of the planet than the atmosphere, we can write down the magnetic field in a current-free representation (Jackson 1998): As in Batygin & Stevenson (2010), we assume that the induction term is dominated by the interaction with the background field, rather than the induced field: (˜ v × B ) glyph[similarequal] (˜ v × B dip ). Upon making this simplification and uncurling equation (10), the steady state induction equation reduces to Ohm's law: where ∇ Φ is the electric field. Because the current is necessarily divergence-free, the scalar potential Φ can be obtained from the following equation: It can be easily checked that the angular part of this relationship is satisfied by: As before, confining the current to the atmosphere implies the boundary conditions: k m ˜ v 0 = R 3 A ( R ) = ( R + H ) 3 A ( R + H ). In turn, the radial part of the solution reads: The induced current density can now be obtained through Ohm's law. The Lorentz force can be approximated as originating from the interactions between the induced current and the background magnetic field. The resulting expression is quite cumbersome. However, all of the important features of F L can be seen by evaluating it at the center of the dynamic domain. To leading order in χ , the expression takes the form: Asimilar evaluation of F L at r = R and r = R + H shows that the ˆ r and ˆ φ components of the force do not change significantly with radius, although the ˆ θ component does. Indeed, the Lorentz force that arises from the interactions between the dayside-to-nightside circulation and the background magnetic field does not only oppose the flow. Instead, it acts to introduce both radial and zonal components to the circulation. Importantly, the typical magnitude of the zonal component of F L is commensurate with the meridional component (although of course their spatial dependence is different). As argued in section (3.1), the characteristic timescale associated with the Lorentz force is comparable to the radiative timescale at mbar pressures and is generally shorter than that, corresponding to other relevant forces. This means that the force-balance implied by equations (17) is in essence not relevant to circulation on hot planetary atmospheres. In summary, we conclude that dayside-to-nightside flow is unstable to perturbations arising from the Lorentz force. Consequently, we expect that the upper atmospheric circulation will change qualitatively once a substantial magnetic field is introduced into the system. We now turn our attention to numerical MHD simulations with the aim of testing this presumption and quantifying the dynamical state of magnetized upper atmospheres of Hot Jupters.",
"pages": [
9,
10,
11
]
},
{
"title": "4.2. Magnetohydrodynamic Simulations",
"content": "The hydrodynamic simulation parameters are chosen as described in section (2), corresponding to the P = 1mbar pressure level (i.e. τ L = 10 3 sec.). We start out with the equilibrated hydrodynamic flow shown in panel A of Figure (3) and introduce a weak pole-aligned dipole magnetic field into the system. Upon equilibration, we take the approach of sequentially increasing the magnitude of B dip . At each step, we allow the flow to reach a steady state before increasing the field strength further. We have checked that the flows obtained by successive enhancement of B dip are identical to those obtained by initializing the atmosphere in solid-body rotation with a given value of B dip . Consequently, in agreement with Liu & Showman (2012), we conclude that the obtained flows are insensitive to initial conditions. The panels of Figure (6) show the upper atmospheric circulation for a series of magnetic field strengths. From this series of results, a clear pattern emerges: as the magnitude of B dip is increased, the flow takes on an exclusively zonal character. Specifically, it is clear that the circulation patterns characteristic of | B dip | = 0 . 33 G (panel B) are already markedly different from the | B dip | = 0 . 025 G case (panel A), which clearly resembles the unmagnetized circulation. The flow is in essence entirely azimuthal once the field is increased to | B dip | = 0 . 5 G (panel C). This is in contrast to the non-uniformly dragged simulations of Rauscher & Menou (2013), who find the flow to become less zonally-dominated with enhanced field strength. It is noteworthy that the flow speeds up once it takes on a zonal nature. This is almost certainly due to the fact that viscosity acting on vertical motion more strongly affects the divergent flow, and is therefore not a physically significant result. Increasing the field strength further diminished the flow velocities but did not alter the qualitative nature of the solution, although somewhat higher values of the Ekman number were required to ensure numerical stability. At the expense of a great inflation in the required computational time, we have extended the simulations presented in Figure (6) to higher resolution. Namely, we prolonged the spherical harmonic decomposition up to degree glyph[lscript] max = 34 and m max = 29 while eliminating hyperviscosity from our runs entirely. Aside from a mild (i.e. few percent) increase in the velocities, the results observed in these simulations were largely unchanged from the nominal simulations. This implies that the presented solutions do not depend sensitively on small-scale flows. In other words, the transition of the atmosphere to a state dominated by zonal jets is a result of interactions between global circulation and the large-scale magnetic field. Provided the zonal nature of the flow observed in the magnetized simulation, we can expect that the induced field will be almost entirely toroidal and will approximately be described by equations (29) and (30). As shown in Figure (5), this indeed appears to be the case. The numerically obtained azimuthal component of the field (panel B) is qualitatively similar to its analytically computed counterpart (panel A), although the field lines are concentrated towards the vicinity of the equator in the numerical solution (this is simply a consequence of the fact that the circulation is not exactly given by the expression (27)). The magnitude of the induced field is also in good agreement with the analytical theory. For ˜ v 0 = 440 m/s, and k m / R 3 = 0 . 5 G, equation (29) yields max(B ind ) = 0 . 64 G, where as the numerically computed value is max(B ind ) = 0 . 52 G. Unlike the case considered in the previous section (where the Lorentz force is treated as a drag), within the framework of MHD simulations, the relationship between the peak wind speed and the temperature perturbation is not necessarily simple. Consequently, in order to preliminarily explore the sensitivity of our results on irradiation, we performed an additional suite of simulations where the applied heat flux was enhanced by a factor of three, compared to the simulations shown in Figure (6). In these overdriven simulations, we found the peak wind speeds to be a factor of ∼ 2 -2 . 5 higher. However, the characteristic flow patterns closely resembled those, shown in Figure (6) and specifically, the circulation with | B dip | = 0 . 5 G remained dominated by azimuthal jets. Consequently, we conclude that the transition of the circulation to a zonal regime with increasing magnetic field strength is robust within the context of our model. It is interesting to note that the zonal nature of the circulation is ensured at a comparatively low magnetic field strength. If we adopt a scaling based on an Elsasser number of order unity (Stevenson 2003), typical hot Jupiter magnetic fields should exceed that of Jupiter by a factor of a few e.g. | B dip | ∼ 10 G. Moreover, the arguably more physically sensible scaling based on the intrinsic energy flux (Christensen et al. 2009) suggests that typical hot Jupiter fields may be still higher by another factor of ∼ 5. Cumulatively, this places the critical magnetic field needed for the onset of zonal flows a factor of ∼ 10 -100 below the typical field strengths. As a result, it would be surprising if a more sophisticated treatment of the hydrodynamics and radiative transfer proved the critical field strength to be higher than the typical one. Nevertheless, such simulations should no doubt be performed.",
"pages": [
11,
12
]
},
{
"title": "5. DISCUSSION",
"content": "In this paper, we have characterized the nature of atmospheric circulation on Hot Jupiters, in a regime where magnetic effects play an appreciable role. We began by performing baseline Boussinesq hydrodynamical simulations and augmenting them to crudely account for the Lorentz force by expressing it in the form of a Rayleigh drag. Using a simple analytical theory, we showed that within the framework of such a treatment, the interactions between the circulation and the background magnetic field lead to a well-formulated reduction in wind velocities. However, in agreement with published literature (Perna et al. 2010; Rauscher & Menou 2012) and dragged simulations of our own, we noted that regardless of the background field strength, the functional form of the upper-atmospheric stream function remains characteristic of a flow pattern where wind originates at the substellar point and blows towards the anti-stellar points quasi-symmetrically over the terminator (see also Showman et al. (2008)). Although simplifying, the assumption that the Lorentz force (even approximately) opposes the flow everywhere, as done by a Rayleigh drag, appears inappropriate for dayside-to-nightside circulation. Consequently, relying on theoretical considerations based on a kinematic treatment of magnetic induction (Moffatt 1978), we showed that if the Lorentz force is not reduced to a form of a drag, dayside-to-nighside flows become unstable in presence of a spin pole aligned magnetic field. On the contrary, the interactions between zonal jets and the background magnetic field do not give rise to meridional or radial flows, thanks to an inherent symmetry. Instead, the jets are stably damped by the background field (Liu et al. 2008; Menou 2012). However, the damping rate generally need not be latitudinally uniform. As demonstrated by magnetohydrodynamical simulations, this has profound implications for upperatmospheric circulation. Specifically, the MHD calculations indicate that once the background magnetic field is stronger than a critical value, the upper atmospheric circulation transitions from a state dominated by daysideto-nightside flows to an azimuthally symmetric pattern dominated by zonal jets. Qualitatively, this transition can be understood as a point where redistribution of heat from the dayside to the nightside by flow patterns that intersect the magnetic poles ceases to be energetically favorable against purely zonal circulation. For the standard case considered here (that is, τ N = 10 3 sec), the critical field strength is approximately B crit glyph[similarequal] 0 . 5 G, considerably less than the typically inferred field strengths of Hot Jupiters (Christensen et al. 2009). However, it should be understood that the critical field strength must unavoidably depend on various system parameters including the radiative timescale and the electrical conductivity. The variability due to the latter may be particularly important since thermal ionization is extremely sensitive to the atmospheric temperature (see Figure 2). The form of this dependence and the extent to which atmospheres within the current observational aggregate are magnetically dominated merits further investigation. The fact that dayside-to-nightside flows tend to simplify to a zonal state in magnetized atmospheres has a number of important implications. As already discussed to some extent in section (3), axisymmetric flows give rise to exclusively toroidal fields (Moffatt 1978). This means that additional atmospheric dynamo generation, that would act to augment a deep seated field, cannot be supported by large-scale circulation. Moreover, because the induced field lacks a strong poloidal component, its observational characterization is at present hopeless. Consequently, observational inference of magnetohydrodynamic processes in exoplanetary atmospheres is likely to be limited to indirect methods. This discussion overlooks the possibility of field generation by small-scale turbulence (i.e. the α -effect) in the atmosphere. Indeed such a process may be at play if the turbulent magnetic Reynolds number Re t m ≡ ν/η glyph[greaterorsimilar] 1 -10. For highly turbulent atmospheres, this criterion may indeed be satisfied. Our simulations aimed at determining the viability as well as characterization of field generation by small-scale turbulence in Hot Jupiter atmospheres are currently ongoing and will be reported in a follow-up study. In this work, we briefly hinted at the fact that the damping of zonal jets by dipole magnetic fields is not only non-uniform latitudinally but also radially. The radial dependence of the Lorentz force found here is specific to the boundary conditions imposed on the induced current. However, if we do not choose to confine the current to a single scale-height but allow it to penetrate the convective interior of the planet (as for example envisioned within the context of the Batygin & Stevenson (2010) Ohmic dissipation model), the induced toroidal field is free to occupy a much deeper portion of the planet. In such a case, the resulting Lorentz force may act to produce deep-seated azimuthal flows and give rise to largescale differential rotation within the planet (Goldreich private communication). However, the extent to which such differential rotation can persist is subject to a number of constraints, including the magnitude of interior Ohmic dissipation (Liu et al. 2008). In addition to the various simplifications inherent to our model that are already described throughout the paper, it is further noteworthy that we have restricted the morphology of the background magnetic field to a pole-aligned dipole for simplicity. Within the solar system, a dipolar, axisymmetric magnetic field created by an internal dynamo is possessed only by Saturn (Acuna & Ness 1980; Dougherty et al. 2005). On the contrary, Jupiter and the Earth have dipole-dominated fields that are significantly tilted with respect to their spin-axes, while Neptune and Uranus possess rather unusual nondipolar, non-axisymmetric fields (Stevenson 2003). As a result it is quite likely that even on a qualitative level, the discussion presented in this work is not comprehensive. That is, unlike axisymmetric jets found in this work, one could envision the generation of substantial stationary eddies, yielding longitudinally and latitudinally asymmetric jets in exoplanetary atmospheres, by complex background magnetic fields. Furthermore, orbital variations may also be of importance. Specifically, while the assumption of a circular orbit is secure for the majority of hot Jupiters, null eccentricities are certainly not universal to the observational sample (an extreme example is HD80606b (Naef et al. 2001) which has e = 0 . 93). The time-variability of stellar irradiation associated with significant eccentricity produces rather complex circulation patterns even in hydrodynamic regime (Langton & Laughlin 2008; Kataria et al. 2013). However, recalling that electrical conductivity in hot planetary atmospheres arises primarily as a result of thermal ionization, the circulation patterns are likely to be even more complex than those typically envisioned, since magnetic effects in the atmosphere will also be time-dependent. We would like to finish with a few words about observational implications of our results. At present, the resolution and signal to noise of the spectroscopic data aimed at characterizing the temperature structure and chemical composition of exoplanetary atmospheres (Charbonneau et al. 2005; Knutson et al. 2008; Swain et al. 2010) is such that even fits obtained with one-dimensional atmospheric models are susceptible to numerous degeneracies (Madhusudhan & Seager 2009). Consequently, it is unlikely that the qualitative change in the flow structure observed in this work will strongly affect the already-limited interpretation of the information contained within this data, in the near future (Line et al. 2012). On the other hand, theoretical interpretation of observed dayside-to-nightside temperature differences and the associated shifts in the location of the subsolar hot spot (Knutson 2007) rely heavily on a sensible understanding of atmospheric dynamics, which as we have seen requires a more or less self-consistent account of magnetic effects. To this end, the results obtained in this study are of great importance. Indeed, one can expect that the advective transport of heat changes character and weakens with increased electrical conductivity (by extension, the atmospheric temperature) and magnetic field due to the mechanism described above (see also Liu et al. (2008); Perna et al. (2010); Batygin et al. (2011); Menou (2012); Rauscher & Menou (2012)). Thus, a thorough comparison between a substantial sample of model results and data may eventually shed light on the typical atmospheric conductivity structure and field strengths of Hot Jupiters. Such activity would no-doubt further benefit from direct measurements of high-altitude atmospheric wind velocities obtained via ground-based spectroscopy (Snellen et al. 2010). That said, in order for an endeavor of this sort to be meaningful, substantial improvements in theoretical modeling aimed at meliorating the shortcomings outlined above are required, along with a wealth of additional observational data. In conclusion, the above discussion clearly indicates that the degree of complexity of the physical regime in which hot exoplanetary atmospheres reside is indeed very extensive. There is no doubt that much additional work remains. In this work, we have taken an ample step towards a self-consistent characterization of magnetically controlled circulation on Hot Jupiters. As such, this study should serve as a stepping stone for future developments. Acknowledgments . We thank Adam Showman, Tami Rogers, Kristen Menou, Peter Goldreich and Greg Laughlin for useful conversations, as well as the anonymous referee for a thorough and insightful report. K.B. acknowledges the generous support from the ITC Prize Postdoctoral Fellowship at the Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics. S.S. acknowledges funding by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Alfred P. Sloan Foundation.",
"pages": [
12,
13,
14
]
},
{
"title": "REFERENCES",
"content": "Heng, K. 2012, ApJ, 748, L17",
"pages": [
14
]
}
]
2013ApJ...776..135M
https://arxiv.org/pdf/1308.3160.pdf
<document>
<text><location><page_1><loc_38><loc_85><loc_88><loc_86></location>Submitted: ApJ, March 03, 2013; Revised: August 09, 2013</text>
<section_header_level_1><location><page_1><loc_22><loc_73><loc_78><loc_81></location>A Preliminary Calibration of the RR Lyrae Period-Luminosity Relation at Mid-Infrared Wavelengths: WISE Data</section_header_level_1>
<section_header_level_1><location><page_1><loc_40><loc_62><loc_60><loc_64></location>Barry F. Madore</section_header_level_1>
<text><location><page_1><loc_26><loc_57><loc_74><loc_61></location>Observatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101</text>
<section_header_level_1><location><page_1><loc_40><loc_53><loc_60><loc_55></location>Douglas Hoffman</section_header_level_1>
<text><location><page_1><loc_32><loc_48><loc_68><loc_52></location>Infrared Processing and Analysis Center 770 South Wilson, Pasadena, CA 91125</text>
<section_header_level_1><location><page_1><loc_18><loc_44><loc_82><loc_46></location>Wendy L. Freedman, Juna A. Kollmeier, Andy Monson</section_header_level_1>
<section_header_level_1><location><page_1><loc_12><loc_41><loc_88><loc_42></location>S. Eric Persson, Jeff A. Rich Jr., Victoria Scowcroft, Mark Seibert</section_header_level_1>
<text><location><page_1><loc_26><loc_35><loc_74><loc_39></location>Observatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101</text>
<text><location><page_1><loc_18><loc_24><loc_82><loc_33></location>[email protected], [email protected][email protected], [email protected][email protected], [email protected][email protected], [email protected], [email protected]</text>
<section_header_level_1><location><page_2><loc_44><loc_77><loc_56><loc_78></location>ABSTRACT</section_header_level_1>
<text><location><page_2><loc_17><loc_66><loc_83><loc_74></location>Using time-resolved, mid-infrared data from WISE and geometric parallaxes from HST for four Galactic RR Lyrae variables, we derive the following Population II Period-Luminosity (PL) relations for the WISE[W1], [W2] and [W3] bands at 3.4, 4.6 & 12 µ m, respectively:</text>
<formula><location><page_2><loc_26><loc_56><loc_74><loc_64></location>M [ W 1] = -2 . 44 ( ± 0 . 95) × log ( P ) -1 . 26 ( ± 0 . 25) σ = 0 . 10 M [ W 2] = -2 . 55 ( ± 0 . 89) × log ( P ) -1 . 29 ( ± 0 . 23) σ = 0 . 10 10</formula>
<formula><location><page_2><loc_26><loc_55><loc_72><loc_58></location>M [ W 3] = -2 . 58 ( ± 0 . 97) × log ( P ) -1 . 32 ( ± 0 . 25) σ = 0 .</formula>
<text><location><page_2><loc_17><loc_44><loc_83><loc_55></location>The slopes and the scatter around the fits are consistent with a smooth extrapolation of those same quantities from previously-published K-band observations at 2.2 µ m, where the asymptotic (long-wavelength) behavior is consistent with a Period-Radius relation having a slope of 0.5. No obvious correlation with metallicity (spanning 0.4 dex in [Fe/H]) is found in the residuals of the four calibrating RR Lyrae stars about the mean PL regression line.</text>
<text><location><page_2><loc_17><loc_38><loc_83><loc_41></location>Subject headings: Stars: Variables: RR Lyrae stars- Stars: Variables: W Virginis stars</text>
<section_header_level_1><location><page_2><loc_42><loc_31><loc_58><loc_33></location>1. Introduction</section_header_level_1>
<text><location><page_2><loc_12><loc_10><loc_88><loc_29></location>The advantages of moving the Population I calibration of the Classical Cepheid PeriodLuminosity relation (the Leavitt Law) from the optical to the infrared were outlined some three decades ago by McGonegal et al. (1983), and they have been borne out repeatedly over the years, as reviewed and elaborated upon by Freedman & Madore (2010). But only now is it possible to extend these same advantages to the parallel path offered by the Population II variable stars (the short-period RR Lyrae variables and their longer-period siblings the W Virginis stars). Two impressive accomplishments have made this possible: (1) the completion of the WISE mission (Wright et al. 2010) and the release of its sky survey of point sources measured in the mid-infrared in four bands ranging from 3.4 to 22 µ m, and then (2) the innovative application of the HST Fine-Guidance Sensor ( FGS ) cameras to the</text>
<text><location><page_3><loc_12><loc_82><loc_88><loc_86></location>determination of trigonometric parallaxes to four field RR Lyrae variables by Benedict et al. (2011).</text>
<text><location><page_3><loc_12><loc_45><loc_88><loc_81></location>The many, now well-known, advantages of calibrating and using period-luminosity relations in the mid-IR include the following: (1) the effects of line-of-sight extinction are reduced with respect to optical observations by at least an order of magnitude for even the shortest wavelength ([W1] at 3.4 µ m) observations, (2) concerns about the systematic impact of the possible non-universality of the reddening law are similarly reduced by going away from the optical and into the mid-IR, (3) the total amplitude of the light variation of the target star during its pulsation cycle is greatly reduced because of the largely diminished contribution of temperature variation to the change in surface brightness, in comparison to the much smaller (but essentially irreducible) wavelength-independent radius/areal variations, (4) the corresponding collapse in the width (i.e., intrinsic scatter) of the period-luminosity relations, again because of the reduced sensitivity of infrared luminosities to temperature variations (across the instability strip), combined with the intrinsic narrowness of the residual periodradius relations. And finally, (5) at mid-infrared wavelengths, for the temperatures and surface gravities encountered in Population I & II Cepheids and RR Lyrae stars, there are so few metallic line or molecular transitions in those parts of the spectrum that atmospheric metallicity effects are expected to have minimal impact on the calibration. 1 This is especially true for the RR Lyrae stars which are significantly hotter than their longer-period (cooler) Cepheid counterparts.</text>
<text><location><page_3><loc_12><loc_32><loc_88><loc_44></location>As described in Freedman et al. (2012), the Carnegie Hubble Program (CHP) is designed to minimize and/or eliminate the remaining known systematics in the measurement of the Hubble constant using mid-infrared data from NASA's Spitzer Space Telescope . Here we broaden the base in two distinct ways: (a) the incorporation of WISE mid-infrared data and (b) the preliminary calibration of the Population II RR Lyrae variables as mid-infrared distance indicators. This new initiative is known as the Carnegie RR Lyrae Program (CRRP).</text>
<section_header_level_1><location><page_4><loc_30><loc_85><loc_70><loc_86></location>2. The Calibrators: WISE Observations</section_header_level_1>
<text><location><page_4><loc_12><loc_61><loc_88><loc_82></location>WISE conducted an all-sky survey at four mid-infrared wavelengths, 3.4, 4.6, 12 and 22 µ m (W1, W2, W3 and W4, hereafter). As such all of the RR Lyrae variables having trigonometric parallaxes (Benedict et al. 2011) were also observed by the satellite. By design, the slowly precessing orbit of WISE, allowed the satellite to scan across every object on the sky at least 12 times (with progressively more coverage at higher ecliptic latitudes). These successive observations were obtained within a relatively narrow window of time (over about 18 hours for those fields nearest the ecliptic equator) with each observation being separated by about 90 minutes (the orbital period of the satellite). Fortuitously RR Lyrae stars have periods that are generally less than 16 hours, meaning that even the sparsest of these multiple mid-infrared observations covered at least one full pulsational cycle of these particular variable stars.</text>
<text><location><page_4><loc_12><loc_26><loc_88><loc_59></location>The light curves based on the time-resolved WISE observations of our calibrating stars are shown in Figures 1 & 2 for the four RR Lyrae variables, SU Dra , RR Lyr , XZ Cyg , & UV Oct . These stars were observed by WISE 51, 23, 24 and 23 times, respectively. Data were retrieved from the WISE All-Sky Single Exposure (L1b) Source Table, which is available at the Infrared Science Archive (http://irsa.ipac.caltech.edu/Missions/wise.html). The source positions were queried with a 2.5 arcsec cone search radius, ignoring observations flagged as contaminated by artifacts. The observations are very uniformly distributed around the cycle and the resulting light curves are exceedingly well defined. All three of the shortest-wavelength light curves show convergence in their properties, exemplified by their mutual phases, shapes and amplitudes 2 . As expected these light curves closely track the anticipated light variations due to surface-area variations of the star, where at these wavelengths the sensitivity of the surface brightness to a temperature variation is much diminished as compared to its sensitivity at optical wavelengths. This then fully accounts for the mutual phasing (tracking the radius variations, and not the off-set temperature variations), the shape (the cycloid-like radius variation, in contrast to the highly asymmetric color/temperature variation) and the low amplitude (around 0.3 mag, peak-to-peak, in line with the small, radius-induced cyclical change in surface area of these stars).</text>
<text><location><page_4><loc_12><loc_21><loc_88><loc_24></location>The non-parametric fitting methodology, GLOESS was used to derive intensity-averaged magnitudes and amplitudes, as given in Table 1 (see Persson et al. 2004 for a description</text>
<text><location><page_5><loc_12><loc_85><loc_54><loc_86></location>and an early application of this fitting technique).</text>
<section_header_level_1><location><page_5><loc_29><loc_78><loc_71><loc_80></location>3. RR Lyrae Period-Luminosity Relations</section_header_level_1>
<text><location><page_5><loc_12><loc_45><loc_88><loc_76></location>Table 1 contains the parameters needed to compute absolute mean magnitudes. The parallaxes, E(B-V) reddenings, and Lutz-Kelker-Hanson (LKH; Lutz and Kelker 1973; Hanson 1979) corrections as taken from Benedict et al 2011, are listed for convenience. We have converted the A V extinctions listed by Benedict et al. (2011) to those in the W1 and W2 bands using the Yuan et al. (2011) compilation of A WISE /E(B-V) results with A V /E(B-V) = 3.1. Indebetouw et al. (2005) give values of A Spitzer / A K 3 , which we converted to A WISE / A V via the Cardelli et al.(1989) law. The values of A WISE /A V given by Yuan et al. (2011) and our pseudo-values from Indebetouw et al. (2005) agree well. Neither the Yuan et al. (2011) nor Indebetouw et al. (2005) results extend to the W3 band, and here we have referred to Fitzpatrick (1999) for an approximate value. The extinctions for the four stars are so small as to make no difference to the absolute magnitude values and we take A W 3 /A V to be 0.01. The adopted mid-IR extinctions A WISE /A V we adopt are 0.065, 0.052, and 0.01 for W1, W2, and W3, respectively. The adopted mid-IR extinctions A WISE /E(B-V) are also given in Table 1. The above parameters and our observed mean magnitudes lead to the W1, W2, and W3 absolute magnitudes in Table 1 4 . and the Period-Luminosity relations for RR Lyrae variables follow:</text>
<formula><location><page_5><loc_26><loc_34><loc_74><loc_41></location>M [ W 1] = -2 . 44 ( ± 0 . 95) × log ( P ) -1 . 26 ( ± 0 . 25) σ = 0 . 10 M [ W 2] = -2 . 55 ( ± 0 . 89) × log ( P ) -1 . 29 ( ± 0 . 23) σ = 0 . 10 10</formula>
<formula><location><page_5><loc_26><loc_33><loc_72><loc_35></location>M [ W 3] = -2 . 58 ( ± 0 . 97) × log ( P ) -1 . 32 ( ± 0 . 25) σ = 0 .</formula>
<text><location><page_5><loc_12><loc_22><loc_88><loc_32></location>The absolute magnitude values and the respective fits to the first two WISE bands and as well as K-band data (from Benedict et al. 2011 and Dall'Ora et al. 2004, respectively) are shown in Figure 3. Despite the very small (less than a factor of two) range in period covered by RR Lyrae stars, the PL relations are well defined, largely because of their intrinsically small scatter. The intrinsic scatter is especially well illustrated by the K-band PL relation,</text>
<text><location><page_6><loc_12><loc_70><loc_88><loc_86></location>where we also show the RR Lyrae data of Dall'Ora et al. for 21 fundamental-mode RR Lyrae stars in the well-populated LMC globular cluster, Reticulum (shifted by 18.47 mag). A comparison of these two datasets is very illuminating. The slope of the adopted PL relation at K and the total width of it, as defined by the two samples, are for all intents and purposes, identical. The very good agreement in these two independently-determined slopes and the small dispersion in each of the datasets suggest that the means of the Milky Way variables are already well constrained even though the Galactic calibrating sample itself is currently very small.</text>
<text><location><page_6><loc_12><loc_11><loc_88><loc_69></location>On the other hand, we note that the small (observed) scatter of the Milky Way RR Lyrae variables around each of the adopted PL relations is apparently at variance with the individually quoted error bars for each of the calibrating variables. That is, the formal scatter of ± 0 . 10 mag in the WISE PL relations is to be compared with the quoted parallax errors on the individual distance moduli of ± 0 . 22, ± 0 . 16, ± 0 . 25 and ± 0 . 07 mag for XZ Cyg, UV Oct, SU Dra and RR Lyr, respectively. The average scatter for the variables ( ± 0 . 18 mag) is then about two time larger that their observed scatter around the PL fit. This suggests that the published errors may be somewhat overestimated. There are independent data that support this assertion. The 10 Galactic Cepheids for which Benedict et al. (2010) obtained parallaxes, using the same instrument, telescope and reduction methodology have individually quoted internal errors in their true distance moduli ranging from ± 0 . 11 to ± 0 . 30 mag. Their average uncertainty is ± 0 . 19 mag, and yet, once again, as with the RR Lyrae variables the PL fit to these data yields a formal dispersion of only ± 0 . 10 mag. In both cases the observed dispersions, for the Galactic samples, are in total agreement with independently determined dispersions for the much more robustly determined dispersions for the LMC samples. We suggest therefore that the random errors reported for the HST parallaxes for both the Cepheids and for the RR Lyrae variables may have been over-estimated. This is not simply of academic interest. If the observed scatter is used to calculate the systematic uncertainty in the calibration of the RR Lyrae PL relation that uncertainty would be 0 . 10 / √ 4 = ± 0 . 05 mag, a 2-3% error in the Population II distance scale. However, if the quoted errors on the individual distance moduli are used, then the uncertainty rises to 0 . 18 / √ 4 = ± 0 . 09 mag, a 5% error. Similar conclusions would also apply to the base uncertainty in the Cepheid distance scale using the Benedict sample; is the uncertainty in the Galactic Cepheid zero point 1.6% in distance, or is it 3.0%? It is therefore important to note that in their first paper discussing the use of FGS on HST , Benedict et al. (2002) state that the 'standard deviations of the HST and Hipparcos data points may have been overstated by a factor of ∼ 1.5.' and since the Hipparcos errors had been subjected to many confirming tests '... that it is likely that the HST errors are overstated.' Parallaxes from Gaia are anxiously awaited; they will improve the number of calibrators by orders of magnitude and convincingly set the zero point.</text>
<text><location><page_7><loc_12><loc_70><loc_88><loc_86></location>In Figure 3 we show, using thick vertical lines, the full magnitude of the LKH corrections as published by Benedict et al (2011) and applied to the true distance moduli used here. It is noteworthy that, if these corrections had not been applied, the dispersion in the data points around the fit would have exceeded the independently determined dispersion from the Reticulum data, and the slope of the Milky Way solution would have been more shallow than the LMC slope. We take the final agreement of both the slopes and the dispersions to suggest that the individually determined and independently-applied LKH corrections are appropriate.</text>
<text><location><page_7><loc_12><loc_55><loc_88><loc_69></location>Finally, it needs to be noted that Klein et al. (2011) have published slopes that are much shallower than the ones derived here (e.g., -1.7 compared to our -2.6). This is because in their Bayesian analysis they chose to leave the overtone pulsators in the global solution, without correcting them to their equivalent fundamental periods. We have recomputed the slopes from their data after applying the appropriate period shift to the overtones, and those PL slopes are plotted in Figure 4. Their slopes and ours now agree well within the errors, but they are still systematically somewhat shallower than our solutions.</text>
<section_header_level_1><location><page_7><loc_29><loc_49><loc_71><loc_51></location>4. The Run of PL Slope with Wavelength</section_header_level_1>
<text><location><page_7><loc_12><loc_18><loc_88><loc_47></location>For Cepheids it is well known that the slope of the PL relation is a monotonically increasing function of wavelength. In Figure 4 we show that the same overall trend is now made explicit for the first time for the RR Lyrae variables as well, and for the same physical reasons. As one moves from shorter to longer wavelengths one is moving from PL relations where the slope is dominated by the trend of decreasing temperature (i.e., decreasing surface brightness) with period, to relations that are dominated by the opposing run of increasing mean radius with period. The plotted slopes of the optical and nearinfrared PL relations are representative of a variety of published studies (e.g, Catelan, Pritzl & Smith 2004, Benedict et al. 2011, Dall'Ora et al. 2004) while the mid-IR slopes are from this study. As the relative contribution from the temperature-sensitive surface brightness drops off with wavelength, the observed slope is expected to asymptotically approach the wavelength-independent (geometric) slope of the Period-Area relation. That behavior is indeed seen in Figure 4. Moreover the level at which the plateau is occurring would suggest that the period-radius relation of Burki & Meylan (1986) (giving a slope of -2.60, based on Baade-Wesselink studies) is marginally preferred over the period-radius (slope = -3.25) and</text>
<text><location><page_8><loc_12><loc_85><loc_80><loc_86></location>period-radius-metallicity (slope = -2.90) solutions given by Marconi et al. (2005) 5</text>
<text><location><page_8><loc_12><loc_67><loc_88><loc_83></location>From a practical point of view it is not immediately clear what advantage the increased slope of the long-wavelength PL relations would have to offer applications to the distance scale, until it is realized that increased slope in the PL relation is causally and physically connected to decreased width (i.e., decreased intrinsic scatter and therefore increased precision) in the PL relation as proven in the general case by Madore & Freedman (2012). This effect can be seen for the RR Lyrae variables in Figure 2 of Catelan, Pritzl & Smith (2004), and it is apparent here in Figure 3 where the scatter has already reached a minimum in the K-band where simultaneously the plateau in slope (seen in Figure 4) is very nearly complete.</text>
<section_header_level_1><location><page_8><loc_20><loc_61><loc_80><loc_63></location>5. A First Test of the Metallicity Dependence in the Mid-IR</section_header_level_1>
<text><location><page_8><loc_12><loc_50><loc_88><loc_59></location>In Figure 5 we plot the measured magnitude residuals from the [W1] 3.4 µ m PL relation versus the published metallicities of the four RR Lyrae stars in our sample, as given in Table 1 of Benedict et al. (2011). The RR Lyrae stars only sample a 0.4 dex range in [Fe/H] so the test is not a strong one, but there is clearly no significant dependence of the already small magnitude residuals on metallicity.</text>
<section_header_level_1><location><page_8><loc_42><loc_43><loc_58><loc_45></location>6. Conclusions</section_header_level_1>
<text><location><page_8><loc_12><loc_24><loc_88><loc_41></location>As can be dramatically seen in the study of Catelan, Pritzl & Smith (2008, especially their Figure 2) operating anywhere in the near to mid-infrared, from H = 1.6 µ m (accessible to HST ) to 3.6 µ m (accessible to Spitzer now, and with JWST in the near future) will each accrue the benefits of low scatter and ever decreasing sensitivity (with wavelength) to line-of-sight extinction. Collecting power, availability and spatial resolution will determine which of these instruments will be used at any given time. But suffice it to say that the Population II RR Lyrae variables are proving themselves to be a powerful means of establishing an independent, highly precise and accurate distance scale that is completely decoupled in its systematics from the Population I Cepheid path to the extragalactic distance scale and</text>
<text><location><page_9><loc_12><loc_85><loc_29><loc_86></location>the Hubble constant.</text>
<text><location><page_9><loc_12><loc_64><loc_88><loc_82></location>This work is based in part on observations made with the Wide-field Infrared Survey Explorer (WISE), which was is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. This research also made use of the NASA/IPAC Extragalactic Database (NED) and the NASA/ IPAC Infrared Science Archive (IRSA), both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We thank Fritz Benedict for numerous frank and useful communications. The referee was especially helpful in bringing this paper to a more correct and fruitful completion.</text>
<section_header_level_1><location><page_10><loc_44><loc_85><loc_55><loc_86></location>References</section_header_level_1>
<table>
<location><page_10><loc_12><loc_18><loc_85><loc_82></location>
</table>
<text><location><page_11><loc_41><loc_81><loc_60><loc_82></location>XZCyg, P = 0.466584 days</text>
<figure>
<location><page_11><loc_24><loc_21><loc_73><loc_82></location>
<caption>Fig. 1.- WISE Mid-Infrared light curves for XZ Cyg (upper panel) and UV Oct (lower panel) phase-folded over two and a half cycles using the periods given in the titles. GLOESS fits are shown as solid black lines.</caption>
</figure>
<text><location><page_12><loc_42><loc_81><loc_60><loc_82></location>RRLyr, P = 0.566826 days</text>
<figure>
<location><page_12><loc_25><loc_21><loc_73><loc_82></location>
<caption>Fig. 2.- WISE Mid-Infrared light curves for RR Lyr (upper panel) and SU Dra (lower panel) phase-folded over two and a half cycles using the periods given in the titles. GLOESS fits are shown as solid black lines.</caption>
</figure>
<figure>
<location><page_13><loc_12><loc_24><loc_75><loc_82></location>
<caption>Fig. 3.RR Lyrae PL relations in the K-band (top) and the two WISE bands [W1] (middle and [W2] bottom. The K-band relation also contains data from Dall'Ora et al. (2004) for the LMC globular cluster, Reticulum, shifted by 18.47 mag. (This distance modulus shift is remarkably close to the independentlydetermined true modulus of 18.48 mag recently reported by Monson et al. 2012 for the LMC Cepheid mid-infrared distance modulus.) The Reticulum data are shown only for the RRab (fundamental) pulsators, and are presented here to illustrate that they are consistent in slope and scatter in comparison with the Galactic calibration. A detailed discussion of Reticulum will be given in a forthcoming paper (Monson et al. 2013). The solid lines flanking each of the fitted PL relations are each separated by two sigma from their respective ridge lines. Despite the small numbers of stars represented here the full width of the PL relation in each of the bands is well defined. The solid vertical lines to the right of each of the [W1] data points</caption>
</figure>
<figure>
<location><page_14><loc_18><loc_37><loc_92><loc_78></location>
<caption>Fig. 4.The expected monotonic increase of the slope of the RR Lyrae Period-Luminosity relation as a function of increasing wavelength. The asymptotic behavior of the slope, approaching a value of about -2.6 indicates that the PL relation is converging on the Period-Radius relation, as theory would predict, given that the sensitivity of the surface brightness to temperature rapidly drops as one progressively moves into the infrared. The open diamonds are the slopes published by Klein et al. (2011); the filled (red) diamonds indicate the 'fundamentalized' slopes (where we have corrected the periods of the overtone pulsators to their corresponding fundamental periods by adding 0.127 to the log of their observed periods, as in Dall'Ora et al. 2004), based on the data published by Klein et al. (2011) and re-fit for this paper. The optical and near-infrared PL relation slopes are from Catelan, Pritzl & Smith (2004), Benedict et al. (2011) and Sollima, Cacciari & Valenti al. (2006), while the mid-IR slopes are from this study. The equivalent slopes derived from Period-Radius relations are from Burki & Meylan (1986; BM86) and Marconi et al. (2005; M05).</caption>
</figure>
<figure>
<location><page_15><loc_19><loc_41><loc_81><loc_62></location>
<caption>Fig. 5.- Mid-Infrared [W1] (3.4 µ m) deviations from the mean Period-Luminosity relation as a function of metallicity. The currently available sample is small, and the metallicity range is limited. No obvious correlation is seen.</caption>
</figure>
<table>
<location><page_16><loc_20><loc_23><loc_80><loc_76></location>
<caption>Table 1. Mid-Infrared (WISE) Magnitudes for Galactic RR Lyrae Variables</caption>
</table>
<table>
<location><page_17><loc_20><loc_21><loc_80><loc_74></location>
<caption>Table 2. WISE Observations of RR Lyrae</caption>
</table>
<table>
<location><page_18><loc_20><loc_22><loc_80><loc_73></location>
<caption>Table 3. WISE Observations of SU Draconis</caption>
</table>
<table>
<location><page_19><loc_20><loc_22><loc_80><loc_73></location>
<caption>Table 4. WISE Observations of UV Oct</caption>
</table>
<table>
<location><page_20><loc_20><loc_20><loc_80><loc_77></location>
<caption>Table 5. WISE Observations of XZ Cyg</caption>
</table>
<table>
<location><page_21><loc_20><loc_20><loc_80><loc_75></location>
<caption>Table 5-Continued</caption>
</table>
</document>
[
{
"title": "ABSTRACT",
"content": "Using time-resolved, mid-infrared data from WISE and geometric parallaxes from HST for four Galactic RR Lyrae variables, we derive the following Population II Period-Luminosity (PL) relations for the WISE[W1], [W2] and [W3] bands at 3.4, 4.6 & 12 µ m, respectively: The slopes and the scatter around the fits are consistent with a smooth extrapolation of those same quantities from previously-published K-band observations at 2.2 µ m, where the asymptotic (long-wavelength) behavior is consistent with a Period-Radius relation having a slope of 0.5. No obvious correlation with metallicity (spanning 0.4 dex in [Fe/H]) is found in the residuals of the four calibrating RR Lyrae stars about the mean PL regression line. Subject headings: Stars: Variables: RR Lyrae stars- Stars: Variables: W Virginis stars",
"pages": [
2
]
},
{
"title": "Barry F. Madore",
"content": "Observatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101",
"pages": [
1
]
},
{
"title": "Douglas Hoffman",
"content": "Infrared Processing and Analysis Center 770 South Wilson, Pasadena, CA 91125",
"pages": [
1
]
},
{
"title": "S. Eric Persson, Jeff A. Rich Jr., Victoria Scowcroft, Mark Seibert",
"content": "Observatories of the Carnegie Institution of Washington 813 Santa Barbara St., Pasadena, CA 91101 [email protected], [email protected][email protected], [email protected][email protected], [email protected][email protected], [email protected], [email protected]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The advantages of moving the Population I calibration of the Classical Cepheid PeriodLuminosity relation (the Leavitt Law) from the optical to the infrared were outlined some three decades ago by McGonegal et al. (1983), and they have been borne out repeatedly over the years, as reviewed and elaborated upon by Freedman & Madore (2010). But only now is it possible to extend these same advantages to the parallel path offered by the Population II variable stars (the short-period RR Lyrae variables and their longer-period siblings the W Virginis stars). Two impressive accomplishments have made this possible: (1) the completion of the WISE mission (Wright et al. 2010) and the release of its sky survey of point sources measured in the mid-infrared in four bands ranging from 3.4 to 22 µ m, and then (2) the innovative application of the HST Fine-Guidance Sensor ( FGS ) cameras to the determination of trigonometric parallaxes to four field RR Lyrae variables by Benedict et al. (2011). The many, now well-known, advantages of calibrating and using period-luminosity relations in the mid-IR include the following: (1) the effects of line-of-sight extinction are reduced with respect to optical observations by at least an order of magnitude for even the shortest wavelength ([W1] at 3.4 µ m) observations, (2) concerns about the systematic impact of the possible non-universality of the reddening law are similarly reduced by going away from the optical and into the mid-IR, (3) the total amplitude of the light variation of the target star during its pulsation cycle is greatly reduced because of the largely diminished contribution of temperature variation to the change in surface brightness, in comparison to the much smaller (but essentially irreducible) wavelength-independent radius/areal variations, (4) the corresponding collapse in the width (i.e., intrinsic scatter) of the period-luminosity relations, again because of the reduced sensitivity of infrared luminosities to temperature variations (across the instability strip), combined with the intrinsic narrowness of the residual periodradius relations. And finally, (5) at mid-infrared wavelengths, for the temperatures and surface gravities encountered in Population I & II Cepheids and RR Lyrae stars, there are so few metallic line or molecular transitions in those parts of the spectrum that atmospheric metallicity effects are expected to have minimal impact on the calibration. 1 This is especially true for the RR Lyrae stars which are significantly hotter than their longer-period (cooler) Cepheid counterparts. As described in Freedman et al. (2012), the Carnegie Hubble Program (CHP) is designed to minimize and/or eliminate the remaining known systematics in the measurement of the Hubble constant using mid-infrared data from NASA's Spitzer Space Telescope . Here we broaden the base in two distinct ways: (a) the incorporation of WISE mid-infrared data and (b) the preliminary calibration of the Population II RR Lyrae variables as mid-infrared distance indicators. This new initiative is known as the Carnegie RR Lyrae Program (CRRP).",
"pages": [
2,
3
]
},
{
"title": "2. The Calibrators: WISE Observations",
"content": "WISE conducted an all-sky survey at four mid-infrared wavelengths, 3.4, 4.6, 12 and 22 µ m (W1, W2, W3 and W4, hereafter). As such all of the RR Lyrae variables having trigonometric parallaxes (Benedict et al. 2011) were also observed by the satellite. By design, the slowly precessing orbit of WISE, allowed the satellite to scan across every object on the sky at least 12 times (with progressively more coverage at higher ecliptic latitudes). These successive observations were obtained within a relatively narrow window of time (over about 18 hours for those fields nearest the ecliptic equator) with each observation being separated by about 90 minutes (the orbital period of the satellite). Fortuitously RR Lyrae stars have periods that are generally less than 16 hours, meaning that even the sparsest of these multiple mid-infrared observations covered at least one full pulsational cycle of these particular variable stars. The light curves based on the time-resolved WISE observations of our calibrating stars are shown in Figures 1 & 2 for the four RR Lyrae variables, SU Dra , RR Lyr , XZ Cyg , & UV Oct . These stars were observed by WISE 51, 23, 24 and 23 times, respectively. Data were retrieved from the WISE All-Sky Single Exposure (L1b) Source Table, which is available at the Infrared Science Archive (http://irsa.ipac.caltech.edu/Missions/wise.html). The source positions were queried with a 2.5 arcsec cone search radius, ignoring observations flagged as contaminated by artifacts. The observations are very uniformly distributed around the cycle and the resulting light curves are exceedingly well defined. All three of the shortest-wavelength light curves show convergence in their properties, exemplified by their mutual phases, shapes and amplitudes 2 . As expected these light curves closely track the anticipated light variations due to surface-area variations of the star, where at these wavelengths the sensitivity of the surface brightness to a temperature variation is much diminished as compared to its sensitivity at optical wavelengths. This then fully accounts for the mutual phasing (tracking the radius variations, and not the off-set temperature variations), the shape (the cycloid-like radius variation, in contrast to the highly asymmetric color/temperature variation) and the low amplitude (around 0.3 mag, peak-to-peak, in line with the small, radius-induced cyclical change in surface area of these stars). The non-parametric fitting methodology, GLOESS was used to derive intensity-averaged magnitudes and amplitudes, as given in Table 1 (see Persson et al. 2004 for a description and an early application of this fitting technique).",
"pages": [
4,
5
]
},
{
"title": "3. RR Lyrae Period-Luminosity Relations",
"content": "Table 1 contains the parameters needed to compute absolute mean magnitudes. The parallaxes, E(B-V) reddenings, and Lutz-Kelker-Hanson (LKH; Lutz and Kelker 1973; Hanson 1979) corrections as taken from Benedict et al 2011, are listed for convenience. We have converted the A V extinctions listed by Benedict et al. (2011) to those in the W1 and W2 bands using the Yuan et al. (2011) compilation of A WISE /E(B-V) results with A V /E(B-V) = 3.1. Indebetouw et al. (2005) give values of A Spitzer / A K 3 , which we converted to A WISE / A V via the Cardelli et al.(1989) law. The values of A WISE /A V given by Yuan et al. (2011) and our pseudo-values from Indebetouw et al. (2005) agree well. Neither the Yuan et al. (2011) nor Indebetouw et al. (2005) results extend to the W3 band, and here we have referred to Fitzpatrick (1999) for an approximate value. The extinctions for the four stars are so small as to make no difference to the absolute magnitude values and we take A W 3 /A V to be 0.01. The adopted mid-IR extinctions A WISE /A V we adopt are 0.065, 0.052, and 0.01 for W1, W2, and W3, respectively. The adopted mid-IR extinctions A WISE /E(B-V) are also given in Table 1. The above parameters and our observed mean magnitudes lead to the W1, W2, and W3 absolute magnitudes in Table 1 4 . and the Period-Luminosity relations for RR Lyrae variables follow: The absolute magnitude values and the respective fits to the first two WISE bands and as well as K-band data (from Benedict et al. 2011 and Dall'Ora et al. 2004, respectively) are shown in Figure 3. Despite the very small (less than a factor of two) range in period covered by RR Lyrae stars, the PL relations are well defined, largely because of their intrinsically small scatter. The intrinsic scatter is especially well illustrated by the K-band PL relation, where we also show the RR Lyrae data of Dall'Ora et al. for 21 fundamental-mode RR Lyrae stars in the well-populated LMC globular cluster, Reticulum (shifted by 18.47 mag). A comparison of these two datasets is very illuminating. The slope of the adopted PL relation at K and the total width of it, as defined by the two samples, are for all intents and purposes, identical. The very good agreement in these two independently-determined slopes and the small dispersion in each of the datasets suggest that the means of the Milky Way variables are already well constrained even though the Galactic calibrating sample itself is currently very small. On the other hand, we note that the small (observed) scatter of the Milky Way RR Lyrae variables around each of the adopted PL relations is apparently at variance with the individually quoted error bars for each of the calibrating variables. That is, the formal scatter of ± 0 . 10 mag in the WISE PL relations is to be compared with the quoted parallax errors on the individual distance moduli of ± 0 . 22, ± 0 . 16, ± 0 . 25 and ± 0 . 07 mag for XZ Cyg, UV Oct, SU Dra and RR Lyr, respectively. The average scatter for the variables ( ± 0 . 18 mag) is then about two time larger that their observed scatter around the PL fit. This suggests that the published errors may be somewhat overestimated. There are independent data that support this assertion. The 10 Galactic Cepheids for which Benedict et al. (2010) obtained parallaxes, using the same instrument, telescope and reduction methodology have individually quoted internal errors in their true distance moduli ranging from ± 0 . 11 to ± 0 . 30 mag. Their average uncertainty is ± 0 . 19 mag, and yet, once again, as with the RR Lyrae variables the PL fit to these data yields a formal dispersion of only ± 0 . 10 mag. In both cases the observed dispersions, for the Galactic samples, are in total agreement with independently determined dispersions for the much more robustly determined dispersions for the LMC samples. We suggest therefore that the random errors reported for the HST parallaxes for both the Cepheids and for the RR Lyrae variables may have been over-estimated. This is not simply of academic interest. If the observed scatter is used to calculate the systematic uncertainty in the calibration of the RR Lyrae PL relation that uncertainty would be 0 . 10 / √ 4 = ± 0 . 05 mag, a 2-3% error in the Population II distance scale. However, if the quoted errors on the individual distance moduli are used, then the uncertainty rises to 0 . 18 / √ 4 = ± 0 . 09 mag, a 5% error. Similar conclusions would also apply to the base uncertainty in the Cepheid distance scale using the Benedict sample; is the uncertainty in the Galactic Cepheid zero point 1.6% in distance, or is it 3.0%? It is therefore important to note that in their first paper discussing the use of FGS on HST , Benedict et al. (2002) state that the 'standard deviations of the HST and Hipparcos data points may have been overstated by a factor of ∼ 1.5.' and since the Hipparcos errors had been subjected to many confirming tests '... that it is likely that the HST errors are overstated.' Parallaxes from Gaia are anxiously awaited; they will improve the number of calibrators by orders of magnitude and convincingly set the zero point. In Figure 3 we show, using thick vertical lines, the full magnitude of the LKH corrections as published by Benedict et al (2011) and applied to the true distance moduli used here. It is noteworthy that, if these corrections had not been applied, the dispersion in the data points around the fit would have exceeded the independently determined dispersion from the Reticulum data, and the slope of the Milky Way solution would have been more shallow than the LMC slope. We take the final agreement of both the slopes and the dispersions to suggest that the individually determined and independently-applied LKH corrections are appropriate. Finally, it needs to be noted that Klein et al. (2011) have published slopes that are much shallower than the ones derived here (e.g., -1.7 compared to our -2.6). This is because in their Bayesian analysis they chose to leave the overtone pulsators in the global solution, without correcting them to their equivalent fundamental periods. We have recomputed the slopes from their data after applying the appropriate period shift to the overtones, and those PL slopes are plotted in Figure 4. Their slopes and ours now agree well within the errors, but they are still systematically somewhat shallower than our solutions.",
"pages": [
5,
6,
7
]
},
{
"title": "4. The Run of PL Slope with Wavelength",
"content": "For Cepheids it is well known that the slope of the PL relation is a monotonically increasing function of wavelength. In Figure 4 we show that the same overall trend is now made explicit for the first time for the RR Lyrae variables as well, and for the same physical reasons. As one moves from shorter to longer wavelengths one is moving from PL relations where the slope is dominated by the trend of decreasing temperature (i.e., decreasing surface brightness) with period, to relations that are dominated by the opposing run of increasing mean radius with period. The plotted slopes of the optical and nearinfrared PL relations are representative of a variety of published studies (e.g, Catelan, Pritzl & Smith 2004, Benedict et al. 2011, Dall'Ora et al. 2004) while the mid-IR slopes are from this study. As the relative contribution from the temperature-sensitive surface brightness drops off with wavelength, the observed slope is expected to asymptotically approach the wavelength-independent (geometric) slope of the Period-Area relation. That behavior is indeed seen in Figure 4. Moreover the level at which the plateau is occurring would suggest that the period-radius relation of Burki & Meylan (1986) (giving a slope of -2.60, based on Baade-Wesselink studies) is marginally preferred over the period-radius (slope = -3.25) and period-radius-metallicity (slope = -2.90) solutions given by Marconi et al. (2005) 5 From a practical point of view it is not immediately clear what advantage the increased slope of the long-wavelength PL relations would have to offer applications to the distance scale, until it is realized that increased slope in the PL relation is causally and physically connected to decreased width (i.e., decreased intrinsic scatter and therefore increased precision) in the PL relation as proven in the general case by Madore & Freedman (2012). This effect can be seen for the RR Lyrae variables in Figure 2 of Catelan, Pritzl & Smith (2004), and it is apparent here in Figure 3 where the scatter has already reached a minimum in the K-band where simultaneously the plateau in slope (seen in Figure 4) is very nearly complete.",
"pages": [
7,
8
]
},
{
"title": "5. A First Test of the Metallicity Dependence in the Mid-IR",
"content": "In Figure 5 we plot the measured magnitude residuals from the [W1] 3.4 µ m PL relation versus the published metallicities of the four RR Lyrae stars in our sample, as given in Table 1 of Benedict et al. (2011). The RR Lyrae stars only sample a 0.4 dex range in [Fe/H] so the test is not a strong one, but there is clearly no significant dependence of the already small magnitude residuals on metallicity.",
"pages": [
8
]
},
{
"title": "6. Conclusions",
"content": "As can be dramatically seen in the study of Catelan, Pritzl & Smith (2008, especially their Figure 2) operating anywhere in the near to mid-infrared, from H = 1.6 µ m (accessible to HST ) to 3.6 µ m (accessible to Spitzer now, and with JWST in the near future) will each accrue the benefits of low scatter and ever decreasing sensitivity (with wavelength) to line-of-sight extinction. Collecting power, availability and spatial resolution will determine which of these instruments will be used at any given time. But suffice it to say that the Population II RR Lyrae variables are proving themselves to be a powerful means of establishing an independent, highly precise and accurate distance scale that is completely decoupled in its systematics from the Population I Cepheid path to the extragalactic distance scale and the Hubble constant. This work is based in part on observations made with the Wide-field Infrared Survey Explorer (WISE), which was is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. This research also made use of the NASA/IPAC Extragalactic Database (NED) and the NASA/ IPAC Infrared Science Archive (IRSA), both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We thank Fritz Benedict for numerous frank and useful communications. The referee was especially helpful in bringing this paper to a more correct and fruitful completion.",
"pages": [
8,
9
]
},
{
"title": "References",
"content": "XZCyg, P = 0.466584 days RRLyr, P = 0.566826 days",
"pages": [
11,
12
]
}
]
2013ApJ...777...32X
https://arxiv.org/pdf/1308.3376.pdf
<document>
<section_header_level_1><location><page_1><loc_9><loc_85><loc_91><loc_87></location>USING COORDINATED OBSERVATIONS IN POLARISED WHITE LIGHT AND FARADAY ROTATION TO PROBE THE SPATIAL POSITION AND MAGNETIC FIELD OF AN INTERPLANETARY SHEATH</section_header_level_1>
<text><location><page_1><loc_8><loc_82><loc_92><loc_84></location>Ming Xiong 1, 2 , Jackie A. Davies 3 , Xueshang Feng 1 , Mathew J. Owens 4 , Richard A. Harrison 3 , Chris J. Davis 4 , and Ying D. Liu 1</text>
<text><location><page_1><loc_40><loc_80><loc_60><loc_81></location>Draft version September 8, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_77><loc_55><loc_79></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_53><loc_86><loc_77></location>Coronal mass ejections (CMEs) can be continuously tracked through a large portion of the inner heliosphere by direct imaging in visible and radio wavebands. White-light (WL) signatures of solar wind transients, such as CMEs, result from Thomson scattering of sunlight by free electrons, and therefore depend on both the viewing geometry and the electron density. The Faraday rotation (FR) of radio waves from extragalactic pulsars and quasars, which arises due to the presence of such solar wind features, depends on the line-of-sight magnetic field component B ‖ , and the electron density. To understand coordinated WL and FR observations of CMEs, we perform forward magnetohydrodynamic modelling of an Earth-directed shock and synthesise the signatures that would be remotely sensed at a number of widely distributed vantage points in the inner heliosphere. Removal of the background solar wind contribution reveals the shock-associated enhancements in WL and FR. While the efficiency of Thomson scattering depends on scattering angle, WL radiance I decreases with heliocentric distance r roughly according to the expression I ∝ r -3 . The sheath region downstream of the Earth-directed shock is well viewed from the L4 and L5 Lagrangian points, demonstrating the benefits of these points in terms of space weather forecasting. The spatial position of the main scattering site r sheath and the mass of plasma at that position M sheath can be inferred from the polarisation of the shock-associated enhancement in WL radiance. From the FR measurements, the local B ‖ sheath at r sheath can then be estimated. Simultaneous observations in polarised WL and FR can not only be used to detect CMEs, but also to diagnose their plasma and magnetic field properties.</text>
<text><location><page_1><loc_14><loc_50><loc_86><loc_53></location>Subject headings: methods: numerical - shock waves - solar-terrestrial relations - solar wind Sun: coronal mass ejections (CMEs) - Sun: heliosphere</text>
<section_header_level_1><location><page_1><loc_22><loc_47><loc_35><loc_48></location>1. INTRODUCTION</section_header_level_1>
<section_header_level_1><location><page_1><loc_19><loc_45><loc_38><loc_46></location>1.1. The Inner Heliosphere</section_header_level_1>
<text><location><page_1><loc_8><loc_24><loc_48><loc_44></location>The inner heliosphere is permeated with the magnetised solar wind from the Sun. At solar minimum, the solar wind is inherently bimodal (McComas et al. 2000), with slow flow tending to emanate from near the ecliptic and fast flow tending to emanate at higher latitudes. Several large-scale structures, which pervade interplanetary space, are associated with the 'ambient' solar wind: (1) a spiralling interplanetary magnetic field (the Parker spiral) that forms as a result of solar rotation (Parker 1958), (2) corotating interacting regions (CIRs) that are formed at the interface between a preceding slow solar wind stream and a following fast solar wind stream (Gosling & Pizzo 1999), and (3) the heliospheric current sheet typically embedded in the heliospheric plasma sheet (Winterhalter et al. 1994; Crooker et al. 2004).</text>
<text><location><page_1><loc_8><loc_18><loc_48><loc_24></location>The background solar wind flow is frequently disturbed by coronal mass ejections (CMEs), large-scale expulsions of plasma and magnetic field from the solar atmosphere. CMEs typically expand during their propagation, because the total solar wind pressure de-</text>
<text><location><page_1><loc_10><loc_16><loc_26><loc_17></location>[email protected]</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_12><loc_48><loc_16></location>1 State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing, China</list_item>
<list_item><location><page_1><loc_10><loc_10><loc_48><loc_13></location>2 Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing Aerospace Control Center, Beijing, China</list_item>
<list_item><location><page_1><loc_10><loc_8><loc_48><loc_10></location>3 Rutherford-Appleton Laboratory (RAL) Space, Harwell Oxford, UK</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_7><loc_32><loc_8></location>4 Reading University, Reading, UK</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_48></location>creases with heliocentric distance (D'emoulin & Dasso 2009; Gulisano et al. 2010). The expansion speed of a CME depends on its spatial size, translation speed, and heliocentric distance, as well as the pre-existing solar wind conditions (Nakwacki et al. 2011; Gulisano et al. 2012). A number of popular models describe the motion of a CME as governed by two forces: a propelling Lorentz force (Chen 1989, 1996; Chen et al. 2006) and an aerodynamic drag force (Cargill et al. 1996; Vrˇsnak & Gopalswamy 2002; Cargill 2004). According to these models, the drag force gradually becomes dominant in interplanetary space, and the CME speed finally adjusts to the ambient solar wind speed. The equalisation of the CME and solar wind speed occurs at very different heliospheric distances, from below 30 solar radii to beyond 1 AU, depending on the characteristics of the CME and the solar wind (Temmer et al. 2011). A CME can undergo significant, nonlinear, and irreversible evolution during its propagation, as it interacts with the ambient solar wind and other CMEs (e.g., Burlaga et al. 2002; D'emoulin 2010). Coronagraph observations show that CME morphology is distorted rapidly and significantly in a structured solar wind (e.g., Savani et al. 2010, 2012; Feng et al. 2012a). Such a distortion occurs over a relatively short heliocentric distance. Interaction between multiple CMEs has been revealed by in-situ observations (e.g., Burlaga et al. 1987; Wang et al. 2003a; Steed et al. 2011; Mostl et al. 2012), radio burst observations (e.g., Gopalswamy et al. 2001; Oliveros et al. 2012), white-light (WL) imaging (e.g., Harrison et al.</text>
<text><location><page_2><loc_8><loc_85><loc_48><loc_92></location>2012; Liu et al. 2012; Lugaz et al. 2012; Temmer et al. 2012; Shen et al. 2012a; Bemporad et al. 2012), and numerical magnetohydrodynamic (MHD) simulation (e.g., Lugaz et al. 2005; Xiong et al. 2007, 2009; Shen et al. 2012b).</text>
<text><location><page_2><loc_8><loc_49><loc_48><loc_85></location>CMEs cause phenomena at Earth, such as geomagnetic storms and solar energetic particles, that can result in major space weather effects (Gopalswamy 2006; Webb & Howard 2012). Traditionally, a CME has been defined in terms of a three-part structure, involving a bright sheath, a dark cavity, and a bright filament. It is now accepted that the cavity component is an escaping magnetic flux rope that drives the CME (e.g., Rouillard et al. 2009b; DeForest et al. 2011). A highspeed flux rope can drive a fast shock ahead of itself that is much wider in angular extent than the flux rope itself. The region between the shock front and the flux rope is defined as a sheath. Within the sheath, (1) magnetic field lines are draped and compressed, and (2) a plasma flow is deviated, compressed, and turbulent (e.g., Gosling & McComas 1987; Owens et al. 2005; Liu et al. 2008). Precursor southward magnetic fields ahead of CMEs are generally compressed, making them particularly geoeffective (Tsurutani et al. 1992; Gonzalez et al. 1999). The magnetic fields in the sheath and in the flux rope can be equally important in driving major geomagnetic storms (Tsurutani et al. 1988, 1992; Szajko et al. 2013). In so-called two-dip storms, it is often the case that the first dip in the Dst index is produced by the upstream sheath and the second is produced by the driving flux rope (Echer et al. 2004; Zhang et al. 2008; Mostl et al. 2012).</text>
<section_header_level_1><location><page_2><loc_13><loc_47><loc_44><loc_49></location>1.2. Heliospheric White Light Observations</section_header_level_1>
<text><location><page_2><loc_8><loc_23><loc_48><loc_47></location>Heliospheric imagers (HIs) detect WL that has been Thomson-scattered from free electrons. For resolved objects, such as CMEs, the power detected by an individual pixel depends linearly on the solid angle subtended by that pixel ( δω ) and the area subtended by the corresponding aperture ( δA ), and is proportional to the radiance (measured in W m -2 SR -1 ). The light from unresolved objects, such as stars, which are much narrower in angular extent, tends to fall within individual pixels. For a resolved heliospheric electron density feature, such as a CME, a single pixel provides a measure of its radiance (surface brightness), while summing contributions from all pixels over the entire extent of the feature provides a measure of its intensity (total brightness). The intensity is an integral of the radiance over the apparent feature size. Therefore, the feature's intensity determines its detectability of an object, be it resolved or unresolved (Howard & DeForest 2012).</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_23></location>The background zodiacal and stellar signals detected by heliospheric imagers are much more intense than the signal due to Thomson-scattering from plasma features such as CMEs (Leinert & Pitz 1989). Fortunately, using an image-differencing technique, the much more stable background radiance can be removed, such that the more transient Thomson-scattering signal can be extracted. From such processed Thomsonscattering images, the sunlight-irradiated CMEs can be easily identified and tracked. According to theory, the heliospheric Thomson-scattering radiance is governed by the Thomson-scattering geometry fac-</text>
<text><location><page_2><loc_52><loc_84><loc_92><loc_92></location>tors and electron number density (Vourlidas & Howard 2006; Howard & Tappin 2009; Howard & DeForest 2012; Xiong et al. 2013). The CME detectability in WL is actually more limited by perspective and field-of-view (FOV) effects than by location relative to the Thomsonscattering sphere (Howard & DeForest 2012).</text>
<text><location><page_2><loc_52><loc_32><loc_92><loc_84></location>Heliospheric imaging from two vantage points, both off the Sun-Earth line, was made possible by the Heliospheric Imagers (HIs) onboard the Solar-TErrestrial RElations Observatory ( STEREO ) (Eyles et al. 2009). With the STEREO /SECCHI package, a CME can be imaged from its nascent stage in the inner corona all the way out to 1 AU and beyond (e.g., Harrison et al. 2008; Davies et al. 2009; Davis et al. 2009; Liu et al. 2010b; DeForest et al. 2011; Liu et al. 2013). In particular, images from STEREO /HI-2 have revealed detailed spatial structures within interplanetary CMEs, including leading-edge pileup, interior cavities, filamentary structure, and rear cusps (DeForest et al. 2011). Comparison with in-situ observations has revealed that the leadingedge pileup of solar wind material, which is evident as a bright arc in WL imaging, corresponds to the sheath region. However, the interpretation of the leading edge of the radiance pattern, especially at larger elongations, is fraught with ambiguity (e.g., Howard & Tappin 2009; Xiong et al. 2013). Elongation ε is defined as the angle between the Sun-observer line and a line-of-sight (LOS). Because a CME occupies a significant three-dimensional (3D) volume, different parts of the CME will contribute to the radiance pattern imaged by observers situated at different heliocentric longitudes (Xiong et al. 2013). Even for an observer at a fixed longitude, a different part of the CME will contribute to the imaged radiance at any given time (Xiong et al. 2013). Various techniques have been developed that enable the spatial locations and propagation directions of CMEs to be inferred, based on the fitting of their moving radiance patterns (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Thernisien et al. 2009; Liu et al. 2010b; Lugaz et al. 2010; Mostl et al. 2011; Davies et al. 2012). However, the determination of interplanetary CME kinematics, propagation direction in particular, are somewhat ambiguous (Howard & Tappin 2009; Davis et al. 2010; Davies et al. 2012; Howard & DeForest 2012; Xiong et al. 2013; Lugaz & Kintner 2013).</text>
<section_header_level_1><location><page_2><loc_59><loc_30><loc_85><loc_31></location>1.3. Faraday Rotation Measurement</section_header_level_1>
<text><location><page_2><loc_52><loc_7><loc_92><loc_30></location>Faraday rotation (FR) is the rotation of the plane of polarisation of an incident electromagnetic wave as it passes through a magnetised ionic medium. The FR observations of linearly polarised radio sources can be used to estimate magnetic field in the corona and interplanetary space (e.g., Levy et al. 1969; Bird et al. 1980; Sakurai & Spangler 1994; Liu et al. 2007; Jensen 2007; Jensen & Russell 2008; You et al. 2012; Jensen et al. 2013). The FR measurement of a radio signal corresponds to the path integral of the product of electron density n and the projection of the magnetic field along the LOS, B ‖ . The first FR experiment was conducted in 1968 by Levy et al. (1969), when solar plasma occulted the radio down-link from the Pioneer 6 spacecraft. As well as man-made radio sources, FR experiments can also exploit natural radio sources such as pulsars and quasars. The first FR experiments of this type were conducted by</text>
<text><location><page_3><loc_8><loc_84><loc_48><loc_92></location>Bird et al. (1980) during the solar occultation of a pulsar. In terms of their locations on a sky map, many pulsars and quasars lie in the vicinity of the Sun. Therefore, simultaneous FR measurements along multiple beams can be used to map the inner heliosphere with a reasonable spatial resolution.</text>
<text><location><page_3><loc_8><loc_57><loc_48><loc_84></location>Additional observations, for example in WL, would generally be necessary to confirm whether an FR transient was indeed caused by a CME. For instance, the first FR event, reported by Levy et al. (1969), could not be attributed unambiguously to the presence of any particular solar wind structure. The FR signatures, observed by Levy et al. (1969), exhibited a W-shaped profile over a time period of 2 -3 hours, with rotation angles of up to 40 · relative to the quiescent baseline. Woo (1997) interpreted the FR signature as the result of a coronal streamer stalk of angular size 1 · -2 · , whereas Patzold & Bird (1998) argued that it was caused by the passage of a series of CMEs. However, by comparing observations from the Solwind coronagraph and measurements of Helios down-link radio signals, Bird et al. (1985) were able to identify the signatures of five CMEs simultaneously in WL and FR. Moreover, the electron density derived from WL imaging can be used to enable magnetic field magnitude to be inferred from FR measurements.</text>
<text><location><page_3><loc_8><loc_13><loc_48><loc_57></location>The heliospheric magnetic field can be remotely probed in FR, using low-frequency radio interferometers such as the Murchison Widefield Array (MWA) (Lonsdale, C. J., et. al. 2009), the LOw Frequency ARray (LOFAR) (de Vos et al. 2009), and the Very Large Array (VLA) (Thompson et al. 1980). Disturbance of the background solar wind by CMEs will cause the observed FR signatures to become variable (e.g., Levy et al. 1969; Bird et al. 1985; Jensen & Russell 2008). A change in either the electron density ( δn ) or the LOS magnetic field component ( δB ‖ ), or indeed both, will contribute to the rotation in the plane of polarisation of the radio signal by δ Ω RM . Interplanetary magnetic clouds (MCs) in particular, which have a magnetic flux rope configuration (Burlaga et al. 1981; Klein & Burlaga 1982; Lepping et al. 1990), can be identified from WL images (Rouillard et al. 2009b; DeForest et al. 2011) and are expected to be easily identifiable in FR measurements. Moreover, δn and | δ B | are often enhanced simultaneously within the sheath ahead of a fast MC. The FR due to a MC-driven sheath can be comparable to that due to the MC itself (Jensen et al. 2010). It is expected that the orientation and helicity of a MC will be able to be determined unambiguously from multi-beam FR measurements (Liu et al. 2007; Jensen 2007; Jensen et al. 2010). In contrast, the in-situ detection of magnetic flux ropes can be significantly hindered by the location of the observing spacecraft (e.g., Hu & Sonnerup 2002; Mostl et al. 2012; D'emoulin et al. 2013). FR imaging can be used to provide the magnetic orientation of a fast MC, and indeed its preceding sheath, prior to its arrival at Earth, which is crucial for predicting potential space weather effects at Earth.</text>
<section_header_level_1><location><page_3><loc_12><loc_11><loc_45><loc_13></location>1.4. Forward Magnetohydrodynamic Modelling</section_header_level_1>
<text><location><page_3><loc_8><loc_7><loc_48><loc_11></location>Forward modelling of WL and FR signatures is proving extremely useful for inferring the in-situ properties of interplanetary CMEs from remote-sensing data. Sophis-</text>
<text><location><page_3><loc_52><loc_57><loc_92><loc_92></location>ticated numerical MHD models of the inner heliosphere (e.g., Groth et al. 2000; Lugaz et al. 2005; Hayashi 2005; Xiong et al. 2006a; Li et al. 2006; Wu et al. 2006; Li & Li 2008; Odstrˇcil & Pizzo 2009; Shen et al. 2012b) can serve as a digital laboratory, to enable the synthesis of a variety of observable remote-sensing signatures. In this paper, we perform a numerical MHD simulation of an interplanetary shock in the ecliptic, from which we synthesise the signatures of that feature that would be remotely sensed at visible and radio wavelengths. Details of the MHD model, and the formulae required to synthesise the remote-sensing observations, are given in Section 2. The resultant synthesised remote-sensing signatures of the sheath, which would be observed from vantage points at 0.5 and 1 AU, are described and compared in Section 3. In Section 4, we discuss the radiance patterns that are observed in the synthesised WL and FR sky maps. In Section 5, we explore the role that the vantage point of the observer plays in the 'observability' of such WL and FR features. CME detection in the presence of background noise, and the heliospheric imaging of more complex interplanetary phenomena, are discussed in Section 6. The potentially important role that forward modelling can play in our understanding of coordinated WL and FR observations is summarised in Section 7.</text>
<section_header_level_1><location><page_3><loc_68><loc_55><loc_76><loc_56></location>2. METHOD</section_header_level_1>
<text><location><page_3><loc_52><loc_31><loc_92><loc_55></location>Forward MHD modelling can self-consistently establish the links between interplanetary dynamics and the resultant observable signatures. A complete flow chart of forward modelling is illustrated in Figure 8 from Xiong et al. (2011). The travelling fast shock studied by Xiong et al. (2013) is revisited here. Our methodology consists of three general steps: (1) forward modelling of the shock using the numerical Inner-Heliosphere MHD (IH-MHD) model (Xiong et al. 2006a, 2013), (2) calculation of its Thomson-scattered WL signature, in Section 2.1, and (3) calculation of its FR signature, in Section 2.2. Characterisation of the IH-MHD model, the background solar wind conditions, and the initial shock injection is summarised respectively in Tables 1, 2, and 3 of Xiong et al. (2013). The simulated electron density n and magnetic field B are used to generate synthetic WL and FR images, which enable us to explore the WL and FR signatures of an interplanetary sheath.</text>
<text><location><page_3><loc_52><loc_7><loc_92><loc_31></location>A plasma parcel emitted from the Sun would be observed, at the same elongation and the same Thomsonscattering angle, firstly by an observer situated at a radial distance of 0.5 AU from the Sun centre, and subsequently by an observer at 1 AU (Figure 1a). Such a configuration was discussed qualitatively by Jackson et al. (2010) and is analysed quantitatively in Section 3 of this paper. Observations from STEREO /HI suggest that a travelling sheath can be approximated as an expanding bubble (e.g., Howard & Tappin 2009; Lugaz et al. 2010; Davies et al. 2012; Mostl & Davies 2013). In-situ observations indicate that CMEs undergo self-similar expansion, as the speed profiles within CMEs themselves tend to be a linear function of time (e.g., Farrugia et al. 1993; Gulisano et al. 2012). In the schematic Figures 1b-d, the sheath region following an Earth-directed interplanetary shock is represented as a self-similarly expanding bubble. The sheath can look quite different when viewed</text>
<text><location><page_4><loc_8><loc_88><loc_48><loc_92></location>from different heliocentric distances (Figures 1b and 1c) and/or different heliospheric longitudes (Figures 1b and 1d).</text>
<section_header_level_1><location><page_4><loc_14><loc_86><loc_42><loc_87></location>2.1. Thomson-Scattering WL Formulae</section_header_level_1>
<text><location><page_4><loc_8><loc_51><loc_48><loc_85></location>A small parcel of free electrons, that is illuminated by a known intensity of incident sunlight (measured in W m -2 ), will scatter a certain amount of power per unit solid angle (measured in W rad -1 ). The effect of the Thomson-scattering geometry can be characterised by the so-called scattering angle χ , as depicted in Figure 1 of Xiong et al. (2013). Scattering can be backward ( χ < 90 · ), perpendicular ( χ = 90 · ), and forward ( χ > 90 · ). All photons that are scattered into an optical cone defined by the point spread function of an individual pixel will be attributed to that pixel (Figure 1b, Xiong et al. 2013). The classic principles of WL Thomson-scattering, as applied to coronagraph observations (Billings 1966), have been adapted to heliospheric imaging (Vourlidas & Howard 2006; Howard & Tappin 2009; Jackson et al. 2010; Howard & DeForest 2012; Xiong et al. 2013). The transverse electric field oscillation δ E of the Thomson-scattered radiance, which is inherently a continuum, can be considered in terms of its two orthogonal components, a tangential component δ E T and a radial component δ E R . The amplitudes of these two orthogonal oscillations ( I T = | δ E T | 2 and I R = | δ E R | 2 ) can be measured separately, using a polariser. The total radiance I and degree of polarisation p are defined as follows:</text>
<formula><location><page_4><loc_24><loc_49><loc_48><loc_51></location>I = I T + I R (1)</formula>
<formula><location><page_4><loc_24><loc_46><loc_48><loc_49></location>p = I T -I R I (2)</formula>
<text><location><page_4><loc_8><loc_38><loc_48><loc_45></location>Although the incident sunlight is unpolarised ( p = 0), the scattered WL radiance remains unpolarised only when the scattering angle | χ -90 · | = 90 · . The scattered light is elliptically polarised (0 < p < 1) for 0 · < | χ -90 · | < 90 · and linearly polarised ( p = 1) for χ = 90 · . Each pixel of a detector records the LOS integral of local WL radiance.</text>
<formula><location><page_4><loc_10><loc_32><loc_48><loc_37></location>( I I T I R ) = ∫ ∞ 0 ( i i T i R ) dz = ∫ ∞ 0 nz 2 ( G G T G R ) dz (3)</formula>
<text><location><page_4><loc_8><loc_23><loc_48><loc_32></location>Here z refers to a distance between the detector and the scattering site, as shown in Figure 1b of Xiong et al. (2013). The mathematical expressions for G , G R , and G T are given by Equations 1 and 2 of Xiong et al. (2013). The observed WL radiance is determined jointly by the heliospheric distribution of electrons n and Thomsonscattering geometry factors ( z 2 G , z 2 G R , z 2 G T ).</text>
<text><location><page_4><loc_8><loc_7><loc_48><loc_23></location>As noted above, the efficiency of Thomson scattering depends significantly on the Thomson scattering angle χ . The perpendicular scattering, χ = 90 · , received by an observer comes from the Thomson Sphere. The 'Thomson sphere', sometimes called the 'Thomson surface', is the sphere in which the Sun and observer lie at opposite ends of a diameter (e.g., Vourlidas & Howard 2006; Howard & DeForest 2012). The ecliptic cross sections of the Thomson scattering spheres for three observers are shown as dotted circles in Figures 1b-d. The LOS from an observer crosses its Thomson sphere at a so-called p point (Figure 2, Tappin et al. 2004), where both the</text>
<text><location><page_4><loc_52><loc_73><loc_92><loc_92></location>intensity of incident sunlight and local electron density are greatest, but the efficiency of Thomson scattering is least. Competition between these three effects results in the spread of local radiance ( i , i T , i R in Equation 3) to large distances from the Thomson surface, an effect that is greater at larger elongations ε from the Sun. Howard & DeForest (2012) described this broad spreading effect, using the term 'Thomson plateau'. Namely, along a single LOS, the radiance per unit electron density is virtually constant over a broad range of scattering angles χ centred at the p point. The Thomson plateau, in terms of its relevance to heliospheric image, was discussed in detail by Howard & Tappin (2009), Howard & DeForest (2012), and Xiong et al. (2013).</text>
<text><location><page_4><loc_52><loc_39><loc_92><loc_73></location>A major milestone in stereoscopic WL imaging of interplanetary CMEs was achieved by the STEREO /HI instruments (e.g., Eyles et al. 2009; Davies et al. 2009; Davis et al. 2009; Harrison et al. 2009). This heliospheric imaging capability was built on the heritage of the Solar Mass Ejection Imager ( SMEI ) instrument on the Coriolis spacecraft (Eyles et al. 2003). The STEREO mission is comprised of two spacecraft, with one leading ( STEREO A) and the other trailing ( STEREO B) the Earth in its orbit. Both spacecraft separate from the Earth by 22 . 5 · per year. The HI instrument on each STEREO spacecraft consists of two cameras, HI-1 and HI-2, whose optical axes lie in the ecliptic. Elongation coverage in the ecliptic is 4 · - 24 · for HI-1 and 18 . 7 · - 88 . 7 · for HI-2. The field of view (FOV) is 20 · × 20 · for HI-1 and 70 · × 70 · for HI-2. The cadence of HI1 is usually 40 minutes and that of HI-2 is 2 hours (Eyles et al. 2009). The current generation of heliospheric imagers do not have WL polarisers. Polarisation measurements have, up until now, only been made by coronagraphs (e.g., Poland & Munro 1976; Crifo et al. 1983; Moran & Davila 2004; Pizzo & Biesecker 2004; de Koning et al. 2009; Moran et al. 2010). For instance, Moran & Davila (2004) used polarisation measurements of WL radiance by the SOHO /LASCO coronagraph to reconstruct CME orientations near the Sun.</text>
<text><location><page_4><loc_52><loc_21><loc_92><loc_39></location>Sky maps, often presented in the Hammer-Aitoff projection, can be used to highlight and track WL transients (e.g., Tappin et al. 2004; Zhang et al. 2013). Timeelongation maps (J-maps) are usually constructed by stacking differenced radiance between observed sky maps along a fixed position angle (sometimes background subtracted images are used instead of difference images). Using such J-maps, transients such as CMEs are manifest as inclined streaks (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Xiong et al. 2011; Harrison et al. 2012; Davies et al. 2012; Xiong et al. 2013). As a propagating transient is viewed along larger elongations, its WL signatures become fainter.</text>
<section_header_level_1><location><page_4><loc_61><loc_18><loc_83><loc_19></location>2.2. Faraday Rotation Formula</section_header_level_1>
<text><location><page_4><loc_52><loc_10><loc_92><loc_18></location>Due to a FR effect, the plane of polarisation of linearly polarised radio emission is continuously rotated as the radio wave passes through the heliosphere. For radio waves, the ubiquitous magnetised solar wind flow serves as a magneto-optical birefringence medium. The formulae for FR are expressed below:</text>
<formula><location><page_4><loc_60><loc_7><loc_92><loc_8></location>Ω = Ω RM · λ 2 (4)</formula>
<formula><location><page_5><loc_17><loc_88><loc_48><loc_92></location>Ω RM = ∫ ω RM dz (5)</formula>
<formula><location><page_5><loc_17><loc_80><loc_48><loc_82></location>δ ω RM ∝ δ ( nB ‖ ) (7)</formula>
<formula><location><page_5><loc_17><loc_82><loc_48><loc_89></location>ω RM = e 3 8 π 2 /epsilon1 0 m 2 e c 3 nB ‖ = [ 2 . 63 × 10 -13 rad T ] nB ‖ (6)</formula>
<formula><location><page_5><loc_17><loc_76><loc_48><loc_80></location>δ Ω RM ∝ ∫ δ ω RM dz (8)</formula>
<text><location><page_5><loc_8><loc_59><loc_48><loc_76></location>Where q , /epsilon1 , m e , and c represent the constants that are the electron charge, the permittivity of free space, the mass of an electron, and the speed of light, respectively. A FR measurement of Ω RM = 1 rad m -2 corresponds to Ω = 0 . 97 · at 2.3 GHz (wavelength λ = 0 . 13 m), Ω = 57 . 3 · at 300 MHz ( λ = 1 m), and Ω = 1432 · at 60 MHz ( λ = 5 m). The calibration of ground-based FR observations is difficult, as the radio wave passes through the magnetised plasma of the ionosphere, magnetosphere (including the plasmasphere), and solar wind. Oberoi & Lonsdale (2012) surveyed and compared the FR signatures associated with each of these different regions.</text>
<text><location><page_5><loc_8><loc_26><loc_48><loc_59></location>A large portion of the inner heliosphere can be monitored, using FR imaging. Prime heliospheric targets measured in FR include interplanetary CMEs and CIRs (Oberoi & Lonsdale 2012). Because the low-frequency radio interferometers such as the MWA , LOFAR , and VLA feature a wide FOV, high sensitivity, and multibeam forming capabilities, it is expected to be capable of mapping the magnetic field in the inner heliosphere with a remarkable sensitivity. The high sensitivity of FR measurements enables fluctuations in the heliospheric/interstellar magnetic field and plasma density, resulting from MHD turbulence, to be revealed (e.g., Jokipii & Lerche 1969; Goldshmidt & Rephaeli 1993; Hollweg et al. 2010). For instance, gradients in FR measurement have been observed across active Galactic Nuclei (AGN) jets, using the Very Long Baseline Array , which demonstrate that ordered helical magnetic fields are associated with these jets (e.g., Zavala & Taylor 2002; G'omez et al. 2008; Reichstein & Gabuzda 2012). The sheath region associated with a fast CME can be similarly probed. FR measurements of the sheath would provide a value for Ω RM in Equations 4-8. Any measured value of the FR, Ω RM , would correspond to a statistical average, as the plasma and magnetic fields within such sheath regions are in a highly turbulent state.</text>
<section_header_level_1><location><page_5><loc_10><loc_23><loc_47><loc_25></location>3. WHITE-LIGHT AND FARADAY ROTATION SIGNALS RECEIVED AT 0.5 AND 1 AU</section_header_level_1>
<text><location><page_5><loc_8><loc_11><loc_48><loc_22></location>The remote imaging in WL and FR of an Earthdirected sheath from two vantage points, one at 0.5 AU and the other at 1 AU, is considered in Section 3.1. Section 3.2 demonstrates how spatial position and electron number density can be inferred from polarisation observations of WL radiance. Section 3.3 presents a means by which magnetic field can be diagnosed from FR measurements.</text>
<text><location><page_5><loc_12><loc_8><loc_46><loc_10></location>3.1. Comparing Remotely-Sensed WL and FR Observations from Different Vantage Points</text>
<text><location><page_5><loc_52><loc_39><loc_92><loc_92></location>Figure 2 shows the modelling results of an Earthdirected sheath propagating from the Sun to 1 AU. The travelling sheath is supposed to be imaged simultaneously by two observers at 0.5 and 1 AU. The WL and FR signatures of the sheath are synthesised, using the methods in Section 2. Representative LOSs, which cut through the sheath (LOS1-6), are denoted using arrows in Figure 2. The variations of various physical parameters along LOS1-3 are shown in Figure 3. LOS1, LOS2, LOS3, and LOS5 are approximately tangential to the left flank of the shock; LOS4 and LOS6 are tangential to the nose of the shock. LOS1 and LOS4 are directed towards the observer situated at 0.5 AU; all other LOSs are directed towards the observer at 1 AU. The viewing configuration for LOS1 (Figure 2a) is equivalent to that for LOS3 (Figure 2c), as the elongation of the shock front is the same for LOS1 and LOS3. Thus, the Thomson scattering geometry is identical for these two LOSs, leading to similar LOS profiles in Figure 3. Of course, the observed radiance along LOS1 is much stronger than that along LOS3 (Table 1). Similarly, the observations along LOS4 and LOS6 (Figures 2d and 2f) have identical Thomson scattering geometries. At any given time, the sheath is viewed at greater elongations from a vantage point closer to the Sun. For instance, at an elapsed time of 5.5 hours, the foremost elongation ε of the sheath is 20 · for an observer at 1 AU (LOS1) compared with 7 · for an observer at 0.5 AU (LOS2). While the sheath is undetectable in WL along LOS2 (Figure 3g), it can be observed in FR (Figure 3l). The portion of an LOS that contributes most to the WL radiance broadens and flattens with increasing elongation, and shifts gradually towards the observer. At elongations beyond 90 · , only back-scattered photons are received; electrons in the vicinity of the observer mainly contribute to remote-sensing signatures for elongations beyond 90 · . Such observations for elongations of ε ≥ 90 · are less useful for the purposes of space weather prediction. In Figures 2d and 2f, the shock front has already reached the observer, and can be detected in-situ.</text>
<section_header_level_1><location><page_5><loc_52><loc_35><loc_92><loc_38></location>3.2. Inferences of Sheath Position from Polarised White Light</section_header_level_1>
<text><location><page_5><loc_52><loc_7><loc_92><loc_35></location>The WL radiance of CMEs is determined by both the electron number density distribution and the Thomsonscattering geometry (Equation 3). The total radiance at a scattering site ( i ), and its constituent radial ( i R ) and tangential ( i T ) components, are associated with Thomson-scattering factors z 2 G , z 2 G R , and z 2 G T , respectively. Near the Thomson-scattering surface, z 2 G T is much larger than z 2 G R . If a dense parcel of plasma, viewed at large elongations, approaches the Thomson surface, its WL signatures will comprise (1) an increase in I , (2) an increase in I T , (3) a decrease in I R , and (4) an increase in the degree of polarisation p . The variation of p is largest, while that of I is negligible. A plasma parcel's distance from the Thomson sphere has a less significant effect on I at larger elongations. However, the determination of the plasma parcel's location will be more uncertain, if only unpolarised WL observations are available, as with current operational heliospheric imaging systems. Polarisation observations can provide an important clue to the primary scattering site. LOS1 in Figure 2 is used to demonstrate these inferences.</text>
<text><location><page_6><loc_8><loc_69><loc_48><loc_92></location>The Thomson-scattering geometry is independent of the distribution of heliospheric electrons. The degree of polarisation ( p ) and the Thomson-scattering factors ( z 2 G , z 2 G R , z 2 G T ), as presented in Figure 3b and 3d, only depend on the modified scattering angle χ ∗ = 90 · -χ . The profiles of p , z 2 G , z 2 G R , and z 2 G T are symmetrical around χ ∗ = 0 · . The dependence of χ ∗ , z 2 G , and LOS distance z on p can be seen in Figure 4. p = 1 corresponds to perpendicular scattering (i.e. χ ∗ = 0 · ). p = 1 corresponds to two solutions for χ ∗ : one resulting from forward scattering ( χ ∗ < 0 · ), and the other associated with backward scattering ( χ ∗ > 0 · ). In response to the passage of the shock, the initial radiance components at t = 0, I T0 and I R0 , are enhanced to values denoted by I T and I R , respectively. The increase in the radiance components define a so-called modified degree of polarisation that we denote using p ∗ . p ∗ is given by</text>
<text><location><page_6><loc_46><loc_80><loc_46><loc_81></location>/negationslash</text>
<formula><location><page_6><loc_19><loc_65><loc_48><loc_68></location>p ∗ = I T -I T0 -I R + I R0 I -I 0 (9)</formula>
<text><location><page_6><loc_8><loc_24><loc_48><loc_64></location>p is 0.62 along LOS1 at t = 0 hours. This effectively defines the degree of polarisation associated with the background solar wind. During the sheath passage, at t = 5 . 5 hours, p is 0.58 along this LOS. The modified degree of polarisation p ∗ , derived using Equation 9, is therefore 0.29 at t = 5 . 5 hours. The radiance enhancement is due to the presence of the sheath in the LOS. The sheath, which trails the shock front, occupies a relatively small volume of interplanetary space. The sheath occupies the portion of LOS1 bounded by -55 · < χ ∗ < -35 · (Figures 3a and 3c). Within this region, p smoothly varies from 0.15 to 0.5 (Figure 3d). The average value of p ∗ within the sheath is 0.29. In an inverse approach, p ∗ can be used to estimate the scattering angle χ ∗ within the sheath. This is demonstrated in Figure 4a. p ∗ = 0 . 29 corresponds to χ ∗ = ± 46 · and z 2 G = 6 . 5 × 10 -29 , where z 2 G is the average value of z 2 G in the sheath. The solution of χ ∗ = 46 · can be immediately excluded, as an Earth-directed CME can generally be identified (indeed much earlier) as being front-sided based on Extreme Ultraviolet (EUV) images of the full solar disk (e.g., Thompson et al. 1998; Plunkett et al. 1998). The other solution, χ ∗ = -46 · , is physical and yields a value of 60 R S for the distance, z , of the main scattering site (corresponding to the sheath) from the detector. How best to judge which solutions for χ ∗ are physical is explained in detail in Section 4. Once the Thomsonscattering factor z 2 G of the sheath has been inferred, its column-integrated electron number density can be estimated based on the following equation:</text>
<formula><location><page_6><loc_16><loc_19><loc_48><loc_23></location>δN sheath = ∫ δndz /similarequal ∫ δnz 2 Gdz z 2 G (10)</formula>
<text><location><page_6><loc_8><loc_15><loc_48><loc_19></location>It is clear that WL polarisation measurement can prove extremely valuable in the study of interplanetary CMEs and shocks.</text>
<section_header_level_1><location><page_6><loc_10><loc_13><loc_47><loc_14></location>3.3. Magnetic Field Inferred from Faraday Rotation</section_header_level_1>
<text><location><page_6><loc_8><loc_7><loc_48><loc_12></location>As discussed in Section 3.2, the column-integrated electron number density along any LOS can be inferred from its WL observations. Thus, if a radio beam lies within the FOV of a WL imager such that they remotely probe</text>
<text><location><page_6><loc_52><loc_80><loc_92><loc_92></location>the same plasma volume, the WL density measurements can be used to retrieve magnetic field strength from the received FR signal. We demonstrate this, for LOS1, in Figure 5. After subtracting the background solar wind contribution, the enhancements in FR measurement and WL radiance, due to the presence of the sheath of the simulated Earth-directed shock, are given by δ Ω RM and δI , respectively. The ratio of δ Ω RM and δI can be expressed as</text>
<formula><location><page_6><loc_57><loc_70><loc_92><loc_79></location>δ Ω RM δ I = ∫ δ ω RM dz ∫ δ i dz = ∫ δ ( nB ‖ ) dz ∫ z 2 Gδn dz ≈ ∫ δ ( nB ‖ ) dz z 2 G ∫ δn dz ≈ 1 z 2 G δ ( nB ‖ ) δ n (11)</formula>
<text><location><page_6><loc_52><loc_66><loc_92><loc_71></location>As discussed in Section 3.2, z 2 G corresponds to the average value of z 2 G in the sheath. The derivable parameter δ ( nB ‖ ) δ n , which we call B ∗ ‖ , can be expressed in the form</text>
<formula><location><page_6><loc_52><loc_61><loc_92><loc_65></location>B ∗ ‖ ≡ δ ( nB ‖ ) δ n = δB ‖ + B ‖ 0 + n 0 δB ‖ δn = B ‖ + n 0 δB ‖ δn > B ‖ (12)</formula>
<text><location><page_6><loc_52><loc_57><loc_92><loc_61></location>where B ‖ 0 and n 0 denote the initial background values of B ‖ and n , respectively. The inferred value of B ∗ ‖ serves as an upper limit for B ‖ .</text>
<section_header_level_1><location><page_6><loc_53><loc_54><loc_91><loc_56></location>4. RADIANCE PATTERNS IN J-MAPS OF WHITE LIGHT AND FARADAY ROTATION</section_header_level_1>
<text><location><page_6><loc_52><loc_24><loc_92><loc_53></location>Shock propagation through the inner heliosphere can be identified through the inclined trace with which it is associated in a time-elongation map (J-map). J-maps of WL radiance ( I/I ∗ , I ) and degree of polarisation ( p , p ∗ ), and FR measurement | δ Ω RM | , as viewed from observers at 0.5 and 1 AU, are presented in Figure 6 and compared in Figure 7. The normalisation factor I ∗ in Figure 6 corresponds to an electron number density distribution that varies according to n ∝ r -2 . A radiance threshold of I/I ∗ ≥ 3 . 68 × 10 -15 is used to demarcate the sheath region in time-elongation ( t -ε ) parameter space. The modified polarisation p ∗ is only calculated, using Equation 9, inside the sheath (Figures 6g-h). The absolute values of I and | δ Ω RM | within the sheath region are much larger for the observer at 0.5 AU, whereas the sheath values of I/I ∗ , p , and p ∗ are comparable when viewed from either vantage point. Over the elongation range 15 · ≤ ε ≤ 180 · , the radiance ratio Max. ( I 0 . 5AU ) Max. ( I 1AU ) is limited to values between 8 and 11 (Figure 7c). This demonstrates that interplanetary CMEs and shocks are viewed better from a location closer to the Sun.</text>
<text><location><page_6><loc_52><loc_7><loc_92><loc_24></location>The position, mass, and magnetic field of the sheath can be inferred from those directly-measurable parameters presented in Figure 6, using the analytical methods presented in Sections 2.1 and 3.3. As shown in Figure 4, and explained in Section 3.2, the Thomson-scattering factors are symmetrical around χ ∗ = 0 · . As a result, a single value of degree of polarisation p ∗ corresponds to two symmetrical solutions for the scattering angle χ ∗ . The results shown in Figure 8 are derived from those in Figure 6 (for an observer at 0.5 AU) under the assumption of forward scattering, while those in Figure 9 assume backward scattering. For the forward-scattering situation, presented in Figure 8b, the inferred longitude</text>
<text><location><page_7><loc_8><loc_41><loc_48><loc_92></location>of the sheath ϕ sheath is 22 · at an elapsed time of 5 hours and 9 · at 11 hours. For the backward-scattering case, shown in Figure 9b, the sheath is at ϕ sheath = 140 · and 60 · at these times. So, an observer at 0.5 AU infers a longitude change ∆ ϕ sheath of 13 · (Figure 8b) and 80 · (Figure 9b) for the forward and backward-scattering cases, respectively. The dramatic change in sheath longitude for the backward-scattering case might indicate that the shock is significantly deflected during its interplanetary propagation. However, such an abnormal degree of lateral deflection of ∆ ϕ sheath = 80 · would be highly unphysical, and may imply a 'ghost trajectory' (Figure 6, DeForest et al. 2013). The east-west symmetry of the radiance pattern suggests that the shock is actually front-sided and Earth-directed, rendering the assumption of backward-scattering invalid (Figure 9). If we assume that the radiance pattern shown in Figure 6 is attributable to forward scattering, the inferred position of the sheath is shown as the solid white curve in Figure 2. This agrees very well with the actual position of the sheath. At any given time, only a certain portion of the sheath will be visible from a fixed observing location (Xiong et al. 2013). For example, at an elapsed time of 5.5 hours, it is the flank of the sheath (Figure 2a) that corresponds to the leading edge of the radiance pattern in 6a, while 6 hours later it is the nose (Figure 2d). So, in fact, the longitudinal change of ∆ ϕ sheath = 13 · inferred from Figure 8b is actually an artefact of the viewing geometry and does not represent an actual deflection of the shock front. Along with the inferred position of the sheath, the column-integrated electron number density, δN sheath , and the parallel magnetic field component, B ‖ , are also presented in Figure 8. The derived value of | B ‖ | provides an upper limit for the actual magnetic field, as explained in Section 3.3. By making coordinated observations in WL and FR, CMEs can not only be continuously tracked, but quantitatively diagnosed as they propagate through interplanetary space.</text>
<section_header_level_1><location><page_7><loc_10><loc_38><loc_46><loc_40></location>5. INTERPLANETARY IMAGING FROM DIFFERENT OBSERVATION SITES</section_header_level_1>
<text><location><page_7><loc_8><loc_22><loc_48><loc_37></location>An interplanetary CME looks different when viewed from different vantage points, but can be readily imaged from a wide range of longitudes. The observed WL radiance pattern depends not only on the longitude ϕ o of the observer, as discussed by Xiong et al. (2013), but also on its heliocentric distance r o . In Section 3.1, we compare observations made from radial distances of 0.5 and 1 AU. In Section 5.1, we consider two particular observation sites that are often considered favourable in terms of WL imaging, the L4 and L5 Lagrangian points. In Section 5.2, we quantify more fully the dependence of WL imaging on r o .</text>
<section_header_level_1><location><page_7><loc_8><loc_18><loc_48><loc_21></location>5.1. Observing an Earth-Directed shock from the L4 and L5 Lagrangian Points</section_header_level_1>
<text><location><page_7><loc_8><loc_7><loc_48><loc_17></location>The L4 and L5 Lagrangian points of the Sun-Earth system are often considered advantageous for observing Earth-directed CMEs. There are five Lagrangian points, all in the ecliptic, i.e., L1-L5. A spacecraft at L1, L2, or L3 is metastable in terms of its orbital configuration, and hence must frequently use propulsion to remain in the same orbit. In contrast, a spacecraft at L4 or L5 is resistant to gravitational perturbations, and</text>
<text><location><page_7><loc_52><loc_79><loc_92><loc_92></location>is believed to be more stable. The L4 and L5 points lie 60 · ahead of and behind the Earth in its orbit, respectively. STEREO A reached the L4 point in September 2009 and STEREO B reached L5 in October 2009. The twin STEREO spacecraft were pathfinders for future L4/L5 missions (Akioka et al. 2005; Biesecker et al. 2008; Gopalswamy et al. 2011). A spacecraft at either L4 or L5 can perform routine side-on imaging of Earthdirected CMEs, and hence is of great merit for space weather monitoring.</text>
<text><location><page_7><loc_52><loc_25><loc_92><loc_78></location>Figure 10a illustrates the imaging, be it in WL or FR, of an Earth-directed sheath from the L5 point. LOS7 intersects the nose of the shock at an elapsed time of 14.5 hours, when the shock nose lies on the Thomsonscattering sphere. The variation, along LOS7, of a number of salient physical parameters is shown in Figures 10 e-j. The interplanetary magnetic field lines are compressed and rotated within the sheath. This rotation results in the closer alignment of the field lines with LOS7, such that the magnetic field component along the LOS, | B ‖ | , is greatly enhanced (Figure 10i). The enhancements of both | B ‖ | and electron number density n within the sheath are responsible for the resultant increases in WL radiance I and FR measurement | Ω RM | . The degree of WL polarisation p , as viewed along LOS7 that is at an elongation of 34 · , is 0.67 for the background solar wind and increases to 0.75 during the shock passage at 14.5 hours. This corresponds to a value of the modified WL polarisation p ∗ of 0.98, based on Equation 9. As was done for LOS1 in Section 3, we evaluate the WL radiance along LOS7 (Figure 10a), from which we infer the shock position (Figure 10d). Again, a single value of p ∗ corresponds to two symmetrical solutions for scattering angle χ ∗ , i.e., p ∗ = 0 . 29 and χ ∗ = ± 46 · for LOS1, and p ∗ = 0 . 98 and χ ∗ = ± 5 · for LOS7. For LOS1, only one solution for χ ∗ = -46 · was deemed physical; for LOS7, both solutions for χ ∗ are potentially physical. The scattering sites corresponding to χ ∗ = ± 5 · are very close to one another, and both agree well with the actual position of the sheath (Figure 10a). The section of LOS7 bounded by -5 · ≤ χ ∗ ≤ 5 · lies within the sheath. Both forward scattering ( -5 · ≤ χ ∗ < 0 · ) and backward scattering (0 · < χ ∗ ≤ 5 · ) will contribute to the radiance I observed along this LOS. The propagating sheath can be tracked continuously and easily in WL from the L5 vantage point, such that it leaves an obvious signature in the J-map of synthesised radiance (Figures 10b and 10c). This confirms previous assertions that the L4 and L5 points are very favourable in terms of space weather monitoring.</text>
<section_header_level_1><location><page_7><loc_56><loc_22><loc_88><loc_24></location>5.2. Dependence of White-Light Radiance on Heliocentric Distance</section_header_level_1>
<text><location><page_7><loc_52><loc_7><loc_92><loc_21></location>The background intensity at a fixed elongation in a WL sky map is greater for an observer closer to the Sun. For a heliospheric imager at any distance from the Sun, Jackson et al. (2010) proposed the following Thomsonscattering principles: (1) The WL radiance I at a given solar elongation falls off with the heliocentric distance r according to r -3 ; (2) Such a dependence of I ∝ r -3 is valid for almost any viewing elongation, and for any radial distance from 0.1 AU out to 1 AU and beyond. The WL radiance I depends on the heliospheric distribution of electron number density n . In interplanetary space,</text>
<text><location><page_8><loc_8><loc_65><loc_48><loc_92></location>the background solar wind speed is nearly constant, and the background electron number density n 0 varies approximately with r -2 . However, the equilibrium defined by n 0 ∝ r -2 is disturbed by the presence of interplanetary transients, such as CMEs and CIRs. A travelling shock can sweep up, and hence compress significantly, the background solar wind plasma. Figures 2 and 10a show a density enhancement of n -n 0 n 0 ≈ 2 . 2 within the sheath. The associated compression ratio n n 0 ≈ 3 . 2 indicates that the shock is very strong. However, when viewed along elongations less than 60 · , the strongest signatures of shock passage (characterised by Max.( I )) vary very closely with r -3 (Figures 11b and 11c). The relationship of Max.( I ) ∝ r -3 is slightly violated at large elongations ε > 60 · . Figure 7c reveals that the ratio between Max.( I 0 . 5AU ) and Max.( I 1AU ) is close to 8 for ε ≤ 60 · , increasing thereafter to 10.8 at ε = 180 · . The premise that the WL radiance decreases with the third power of Sun-observer distance generally holds true for both the background solar wind and propagating CMEs.</text>
<section_header_level_1><location><page_8><loc_23><loc_62><loc_34><loc_63></location>6. DISCUSSION</section_header_level_1>
<text><location><page_8><loc_8><loc_43><loc_48><loc_61></location>The detectability in WL of a particular electron density feature is determined by its signal above the noise background. In STEREO /HI-1 images, the dominant WL signal is zodiacal light due to scattering of sunlight from the F-corona, which is centred around the ecliptic. In the STEREO /HI-2 FOV, the noise floor is primarily determined by photon noise and the background star-field (DeForest et al. 2011). Away from the ecliptic, the background WL noise has a sharp radial gradient in coronal images, and is nearly constant in heliospheric images. The signal-to-noise ratio for heliospheric electron density features is discussed by Howard et al. (2013). We will address the detection of CMEs in the presence of background noise in future forward-modelling work.</text>
<text><location><page_8><loc_8><loc_7><loc_48><loc_43></location>If both a transient CME and background (Heliospheric Current Sheet (HCS) - Heliospheric Plasma Sheet (HPS)) plasma structures are present along the same LOS, both will contribute to the total LOS-integrated radiance. In this case, the interpretation of the data would clearly be more problematic. Moreover, if the LOS were to penetrate a HCS, the magnetic field vector would, at that point, rotate through 180 · . Due to the mutual cancellation of B ‖ across the HCS, there may be no net FR signature according to Equations 4-6. Hence, even such a significant interplanetary structure may be associated with only a weak FR measurement. Conversely, the relatively dense plasma within a HPS can significantly contribute to WL radiance. Thus the potential effects of the presence of HCS-HPS structures need to be borne in mind in the remote imaging of CMEs. In the current work, however, we find that such effects are negligible. In our numerical simulation, there are two HCS-HPS structures, which are initially rooted at longitudes of ϕ = ± 90 · at the inner boundary of our numerical simulation. The simulated shock emerges at a longitude of ϕ = 0 · . The large longitudinal difference between the HCS-HPS and the shock means that the remote-sensing signatures are principally contributed by the sheath. Thus, in our forward-modelling work, the signal enhancements of synthesised imaging in WL and FR are unambiguously the result of the propagating sheath.</text>
<text><location><page_8><loc_52><loc_37><loc_92><loc_92></location>In general, the more complex the interplanetary dynamics, the more complex the resultant remote-sensing observations will be. For instance, a CME can interact with other CMEs and/or background solar wind structures such as CIRs, HCSs, and HPSs; mutual interaction between CMEs is, however, generally more perturbing than interactions between CMEs and such background structures. Interactions can result in the background solar wind structures becoming warped or distorted (e.g., Odstrˇcil et al. 1996; Hu & Jia 2001), and CMEs being accelerated/decelerated (e.g., Lugaz et al. 2005; Xiong et al. 2007; Shen et al. 2012b), deflected (e.g., Xiong et al. 2006b, 2009; Lugaz et al. 2012), distorted (e.g., Xiong et al. 2006b, 2009), or entrained (e.g., Rouillard et al. 2009a). In particular, during such interactions, the behavior of a sheath can become much more complex: the shock aphelion can be deflected, spatial asymmetries can develop along the shock front, and the shock front can potentially merge completely with other shock fronts. At an interaction site, both the plasma density and magnetic field would be compressed; this would lead to enhanced signatures in both WL and FR observations. For example, the interaction between two CMEs was manifest as a very bright arc in WL images (e.g., Harrison et al. 2012; Liu et al. 2012; Temmer et al. 2012). Different types of interaction would likely result in different WL radiance signatures; in fact, through a single interaction, the corresponding radiance pattern would evolve. The interpretation of such complex WL radiance patterns would be prone to large uncertainties, but can be rigorously constrained if interplanetary imaging was performed from multiple vantage points and complemented by numerical modelling. For stereoscopic WLimaging, ray-paths from one observer intersect those from the other observer. Thus the 3D distribution of electrons in the inner heliosphere can be reconstructed using a time-dependent tomography algorithm (Jackson et al. 2006; Bisi et al. 2008; Webb et al. 2013). With the aid of numerical modelling, coordinated imaging in WL and FR would enable the properties and evolution of complex interplanetary dynamics to be diagnosed.</text>
<section_header_level_1><location><page_8><loc_62><loc_35><loc_82><loc_36></location>7. CONCLUDING REMARKS</section_header_level_1>
<text><location><page_8><loc_52><loc_7><loc_92><loc_35></location>In this paper, we have investigated the WL and FR signatures of an interplanetary shock based on an approach of forward MHD modelling. The WL Thomsonscattering geometry is increasingly more significant at larger elongations. The degree of WL polarisation can be used to estimate the 3D location of the main scattering region, while FR measurement can be used to infer, to some extent, the magnetic configurations of CMEs. This work presented here demonstrates, as a proof-of-concept, that the availability of coordinated observations in polarised WL and FR measurement would enable the local LOS magnetic component to be estimated. Although the current generation of heliospheric WL imagers, such as the STEREO /HI instruments, do not have polarisers, there are advances underway in terms of FR imaging using Low-frequency radio arrays. Coordinated imaging in WL and FR would enable the inner heliosphere to be mapped in fine detail; the location, mass, and magnetic field of CMEs can be diagnosed on the basis of such combined observations. Forward modelling is crucial in establishing the causal link between interplanetary dynam-</text>
<text><location><page_9><loc_8><loc_89><loc_48><loc_92></location>ics and observable signatures, and can provide valuable guidance for future coordinated WL and FR imaging.</text>
<text><location><page_9><loc_8><loc_73><loc_48><loc_89></location>Although not the methodology of the current work, numerical MHD models of the inner heliosphere can also be directly driven by photospheric observations (e.g., Hayashi 2005; Wu et al. 2006; Feng et al. 2012b). A comparison of synthesised and observed WL and FR sky maps, the former based on the use of such datadriven models, would prove highly beneficial in validating the forward modelling and interpreting the observations. Such an integration of observation data analysis and numerical forward modelling will be explored as the continuation of the preliminary modelling work presented in this paper.</text>
<text><location><page_9><loc_8><loc_66><loc_48><loc_71></location>This work is jointly supported by the National Basic Research Program (973 program) under grant 2012CB825601, the Chinese Academy of Sciences (KZZD-EW-01-4), the National Natural Science Foun-</text>
<text><location><page_9><loc_52><loc_67><loc_92><loc_92></location>dation of China (41231068, 41031066, 41204129), the Strategic Priority Research Program on Space Science from the Chinese Academy of Sciences (XDA04060801), the Specialized Research Fund for State Key Laboratories of China, the Chinese Public Science and Technology Research Funds Projects of Ocean (201005017), open research foundation of Science and Technology on Aerospace Flight Dynamics Laboratory of China (AFDL2012002), research fund for recipient of excellent award of the Chinese Academy of Sciences President's scholarship (startup fund). Ming Xiong is also partially supported by an institutional project of 'Key Fostering Direction in Pulsar Science and Application' from the Center of Space Science and Applied Research, China. Ming Xiong sincerely thanks Drs. Bo Li, Ding Chen, Craig DeForest, James Tappin, and Tim Howard for their beneficial discussions and thoughtful suggestions. We sincerely thank the anonymous referee for his/her constructive suggestions.</text>
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</unordered_list>
<figure>
<location><page_11><loc_20><loc_75><loc_68><loc_92></location>
</figure>
<figure>
<location><page_11><loc_8><loc_53><loc_80><loc_72></location>
<caption>Fig. 1.Examples of the Thomson-scattering geometry for observers at different radial distances r o and longitudes ϕ o . In panel (a), a radially-propagating solar wind parcel is viewed sequentially, but at the same scattering angle, by observers situated at radial distances of 0.5 AU (point A ) and 1 AU (point B ). Panels (b-d) illustrate the observation of an interplanetary sheath, denoted as a shaded region, by observers with different combinations of r o and ϕ o . Longitude is defined to be positive (negative) for an observer situated to the west (east) of Earth.</caption>
</figure>
<figure>
<location><page_11><loc_8><loc_16><loc_91><loc_46></location>
<caption>Fig. 2.Relative enhancement of electron number density, in the ecliptic, ( n -n 0 ) /n 0 within an Earth-directed interplanetary sheath. Red and black solid lines indicate sunward and anti-sunward interplanetary magnetic field lines, respectively. The sheath is imaged by two observers on the Sun-Earth line ( ϕ = 0 · ), at heliocentric distances of r o = 0 . 5 (left column) and 1 AU (central and right columns). For each observer, the ecliptic cross-section of its corresponding WL Thomson-scattering sphere is depicted as a dotted circle. Six lines-of-sight, LOS1-LOS6, are superimposed as straight arrows. All LOSs look westward. At any given time t , the two observers, both located on the Sun-Earth line, detect the sheath at different elongations ε (compare panel a with panel b, and panel d with panel e). Conversely, when viewing along the same ε , the two observers detect the sheath at different t (compare panel a with panel c, and panel d with panel f). Solid white curves overlaid on each panel indicate the position of the sheath inferred from polarised WL imaging.</caption>
</figure>
<figure>
<location><page_12><loc_8><loc_20><loc_88><loc_92></location>
<caption>Fig. 3.WL radiance i , WL Thomson-scattering geometry factors ( z 2 G , z 2 G R , z 2 G T ), electron number density n , degree of WL polarisation p , parallel magnetic field | B ‖ | , and FR measurement | ω RM | , plotted as a function of modified scattering angle χ ∗ = 90 -χ along LOS1 (column A), LOS2 (column B), and LOS3 (column C). Each parameter is normalised to its maximum value along each LOS, as given in Table 1. Note that i = nZ 2 G and ω RM ∝ nB ‖ . For the parameters i , n , | B ‖ | , and | ω RM | , initial and disturbed profiles are depicted as dashed and solid lines, respectively. The black and red sections of the | B ‖ | and | ω RM | profiles (two bottom rows) correspond to negative and positive values of B ‖ , respectively.</caption>
</figure>
<figure>
<location><page_13><loc_9><loc_29><loc_46><loc_92></location>
<caption>Fig. 4.Dependence of the scattering angle χ ∗ , the Thomson-scattering geometry factor z 2 G , and the LOS depth z on the degree of polarisation p for LOS1 in Figure 2a. In response to shock passage, the initial radiance components, I T0 and I R0 , are enhanced to values of I T and I R , respectively. The enhancement in these radiance components determines the modified degree of polarisation p ∗ , according to the expression p ∗ = I T -I T0 -I R + I R0 I -I 0 . The vertical dashed line, demarking p ∗ , crosses the χ ∗ and z profiles twice.</caption>
</figure>
<figure>
<location><page_14><loc_9><loc_17><loc_46><loc_92></location>
<caption>Fig. 5.The deviation of various parameters, from their initial values, plotted as a function of z along LOS1. Note that δ ( nB ‖ ) δ n = δB ‖ + B ‖ 0 + n 0 δB ‖ δn = B ‖ + n 0 δB ‖ δn . The parallel magnetic field component B ∗ ‖ (plotted as a horizontal dashed line in panel d) is calculated using the expression δ Ω RM δ I = ∫ δ ω RM dz ∫ δ i dz = ∫ δ ( nB ‖ ) dz ∫ z 2 Gδn dz ≈ 1 z 2 G δ ( nB ‖ ) δ n = 1 z 2 G B ∗ ‖ .</caption>
</figure>
<figure>
<location><page_15><loc_8><loc_22><loc_75><loc_92></location>
<caption>Fig. 6.Time-elongation maps of WL radiance (panels a and b: I/I ∗ , panels c and d: I ), degree of WL polarisation (panels e and f: p , panels g and h: p ∗ ), and FR measurement (panels i and j: | δ Ω RM | ), as viewed by observers at longitude ϕ o = 0 · and at radii r o = 0.5 AU (left column) and 1 AU (right column). I ∗ is the normalisation factor for I , and corresponds to the radial variation of electron number density n ∝ r -2 . The dotted lines in panels a-f correspond to I/I ∗ = 3 . 68 × 10 -15 . p and p ∗ are determined from the radiance and the enhancement in the radiance, respectively, as given by p = I T -I R I and p ∗ = I T -I T0 -I R + I R0 I -I 0 . Panels g and h only show p ∗ within the sheath region.</caption>
</figure>
<figure>
<location><page_16><loc_8><loc_20><loc_46><loc_92></location>
<caption>Fig. 7.A comparison of the WL radiance I (panels a, b, and c), the degree of WL polarisation p (panel d), and the FR measurement δ Ω RM (panel e) over the elongation range from 15 · to 180 · , as viewed by observers at 0.5 AU (solid line) and 1 AU (dashed line). The attribution 'Max' refers to the strongest signal during the sheath passage.</caption>
</figure>
<figure>
<location><page_17><loc_8><loc_43><loc_91><loc_92></location>
<caption>Fig. 8.Panels a-e present the location of the scattering site ( z sheath , ϕ sheath , r sheath ), the column-integrated electron number density δN sheath , and the parallel magnetic field B ‖ , plotted as a function of time and elongation, derived by assuming forward-scattering ( χ ∗ < 0 · ).</caption>
</figure>
<figure>
<location><page_17><loc_8><loc_12><loc_91><loc_35></location>
<caption>Fig. 9.Panels a-b present the location of the scattering site ( z sheath , ϕ sheath ), plotted as a function of time and elongation, derived by assuming backward-scattering ( χ ∗ > 0 · ).</caption>
</figure>
<figure>
<location><page_18><loc_8><loc_23><loc_91><loc_89></location>
<caption>Fig. 10.Simulated results corresponding to the observation of an Earth-directed shock from the L5 vantage point, i.e., along LOS7 ( r o = 1 AU, ϕ o = -60 · ): (panel a) relative enhancement of electron number density ( n -n 0 ) /n 0 in the ecliptic; (panels b and c) synthesised WL time-elongation maps of I/I ∗ and I ; (panel d) modified scattering angle χ ∗ as a function of the degree of polarisation p ; (panels e-j) a number of synthesised WL and FR parameters, plotted as a function of χ ∗ along LOS7.</caption>
</figure>
<figure>
<location><page_19><loc_8><loc_35><loc_50><loc_92></location>
<caption>Fig. 11.Simulated WL radiance, as a function of r o , viewed along an elongation of 30 · by an observer on the Sun-Earth line ( ϕ o = 0 · , 50 R S ≤ r ≤ 215 R S ). Again, 'Max' refers to the strongest signal associated with the sheath passage. The dashed red lines in the two upper panels show, for comparison, an r -3 variation. Both I ∗ and Max.( I ) are well described by such a variation.</caption>
</figure>
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<text><location><page_20><loc_44><loc_59><loc_46><loc_60></location>a</text>
<text><location><page_20><loc_44><loc_58><loc_46><loc_59></location>6</text>
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<text><location><page_20><loc_43><loc_87><loc_44><loc_87></location>-</text>
<text><location><page_20><loc_43><loc_86><loc_44><loc_87></location>e</text>
<text><location><page_20><loc_43><loc_86><loc_44><loc_86></location>0</text>
<text><location><page_20><loc_43><loc_85><loc_44><loc_86></location>1</text>
<text><location><page_20><loc_43><loc_84><loc_44><loc_85></location>d</text>
<text><location><page_20><loc_43><loc_83><loc_44><loc_84></location>n</text>
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<text><location><page_20><loc_43><loc_82><loc_44><loc_82></location>3</text>
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<text><location><page_20><loc_43><loc_80><loc_44><loc_81></location>e</text>
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<text><location><page_20><loc_43><loc_79><loc_44><loc_79></location>g</text>
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<text><location><page_20><loc_43><loc_76><loc_44><loc_77></location>i</text>
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<text><location><page_20><loc_43><loc_74><loc_44><loc_74></location>t</text>
<text><location><page_20><loc_43><loc_73><loc_44><loc_74></location>a</text>
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<text><location><page_20><loc_43><loc_72><loc_44><loc_73></location>i</text>
<text><location><page_20><loc_43><loc_72><loc_44><loc_72></location>l</text>
<text><location><page_20><loc_43><loc_71><loc_44><loc_72></location>a</text>
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<text><location><page_20><loc_43><loc_70><loc_44><loc_71></location>r</text>
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<text><location><page_20><loc_43><loc_67><loc_44><loc_68></location>o</text>
<text><location><page_20><loc_43><loc_67><loc_44><loc_67></location>f</text>
<text><location><page_20><loc_43><loc_65><loc_44><loc_66></location>d</text>
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<text><location><page_20><loc_43><loc_64><loc_44><loc_65></location>s</text>
<text><location><page_20><loc_43><loc_64><loc_44><loc_64></location>u</text>
<text><location><page_20><loc_43><loc_63><loc_44><loc_63></location>,</text>
<text><location><page_20><loc_43><loc_63><loc_44><loc_63></location>7</text>
<text><location><page_20><loc_43><loc_62><loc_44><loc_63></location>S</text>
<text><location><page_20><loc_43><loc_61><loc_44><loc_62></location>O</text>
<text><location><page_20><loc_43><loc_60><loc_44><loc_61></location>L</text>
<text><location><page_20><loc_43><loc_59><loc_44><loc_60></location>d</text>
<text><location><page_20><loc_43><loc_59><loc_44><loc_59></location>n</text>
<text><location><page_20><loc_43><loc_58><loc_44><loc_59></location>a</text>
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<text><location><page_20><loc_43><loc_40><loc_44><loc_40></location>n</text>
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<text><location><page_20><loc_43><loc_33><loc_44><loc_34></location>G</text>
<text><location><page_20><loc_43><loc_32><loc_44><loc_33></location>2</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Coronal mass ejections (CMEs) can be continuously tracked through a large portion of the inner heliosphere by direct imaging in visible and radio wavebands. White-light (WL) signatures of solar wind transients, such as CMEs, result from Thomson scattering of sunlight by free electrons, and therefore depend on both the viewing geometry and the electron density. The Faraday rotation (FR) of radio waves from extragalactic pulsars and quasars, which arises due to the presence of such solar wind features, depends on the line-of-sight magnetic field component B ‖ , and the electron density. To understand coordinated WL and FR observations of CMEs, we perform forward magnetohydrodynamic modelling of an Earth-directed shock and synthesise the signatures that would be remotely sensed at a number of widely distributed vantage points in the inner heliosphere. Removal of the background solar wind contribution reveals the shock-associated enhancements in WL and FR. While the efficiency of Thomson scattering depends on scattering angle, WL radiance I decreases with heliocentric distance r roughly according to the expression I ∝ r -3 . The sheath region downstream of the Earth-directed shock is well viewed from the L4 and L5 Lagrangian points, demonstrating the benefits of these points in terms of space weather forecasting. The spatial position of the main scattering site r sheath and the mass of plasma at that position M sheath can be inferred from the polarisation of the shock-associated enhancement in WL radiance. From the FR measurements, the local B ‖ sheath at r sheath can then be estimated. Simultaneous observations in polarised WL and FR can not only be used to detect CMEs, but also to diagnose their plasma and magnetic field properties. Subject headings: methods: numerical - shock waves - solar-terrestrial relations - solar wind Sun: coronal mass ejections (CMEs) - Sun: heliosphere",
"pages": [
1
]
},
{
"title": "USING COORDINATED OBSERVATIONS IN POLARISED WHITE LIGHT AND FARADAY ROTATION TO PROBE THE SPATIAL POSITION AND MAGNETIC FIELD OF AN INTERPLANETARY SHEATH",
"content": "Ming Xiong 1, 2 , Jackie A. Davies 3 , Xueshang Feng 1 , Mathew J. Owens 4 , Richard A. Harrison 3 , Chris J. Davis 4 , and Ying D. Liu 1 Draft version September 8, 2018",
"pages": [
1
]
},
{
"title": "1.1. The Inner Heliosphere",
"content": "The inner heliosphere is permeated with the magnetised solar wind from the Sun. At solar minimum, the solar wind is inherently bimodal (McComas et al. 2000), with slow flow tending to emanate from near the ecliptic and fast flow tending to emanate at higher latitudes. Several large-scale structures, which pervade interplanetary space, are associated with the 'ambient' solar wind: (1) a spiralling interplanetary magnetic field (the Parker spiral) that forms as a result of solar rotation (Parker 1958), (2) corotating interacting regions (CIRs) that are formed at the interface between a preceding slow solar wind stream and a following fast solar wind stream (Gosling & Pizzo 1999), and (3) the heliospheric current sheet typically embedded in the heliospheric plasma sheet (Winterhalter et al. 1994; Crooker et al. 2004). The background solar wind flow is frequently disturbed by coronal mass ejections (CMEs), large-scale expulsions of plasma and magnetic field from the solar atmosphere. CMEs typically expand during their propagation, because the total solar wind pressure de- [email protected] 4 Reading University, Reading, UK creases with heliocentric distance (D'emoulin & Dasso 2009; Gulisano et al. 2010). The expansion speed of a CME depends on its spatial size, translation speed, and heliocentric distance, as well as the pre-existing solar wind conditions (Nakwacki et al. 2011; Gulisano et al. 2012). A number of popular models describe the motion of a CME as governed by two forces: a propelling Lorentz force (Chen 1989, 1996; Chen et al. 2006) and an aerodynamic drag force (Cargill et al. 1996; Vrˇsnak & Gopalswamy 2002; Cargill 2004). According to these models, the drag force gradually becomes dominant in interplanetary space, and the CME speed finally adjusts to the ambient solar wind speed. The equalisation of the CME and solar wind speed occurs at very different heliospheric distances, from below 30 solar radii to beyond 1 AU, depending on the characteristics of the CME and the solar wind (Temmer et al. 2011). A CME can undergo significant, nonlinear, and irreversible evolution during its propagation, as it interacts with the ambient solar wind and other CMEs (e.g., Burlaga et al. 2002; D'emoulin 2010). Coronagraph observations show that CME morphology is distorted rapidly and significantly in a structured solar wind (e.g., Savani et al. 2010, 2012; Feng et al. 2012a). Such a distortion occurs over a relatively short heliocentric distance. Interaction between multiple CMEs has been revealed by in-situ observations (e.g., Burlaga et al. 1987; Wang et al. 2003a; Steed et al. 2011; Mostl et al. 2012), radio burst observations (e.g., Gopalswamy et al. 2001; Oliveros et al. 2012), white-light (WL) imaging (e.g., Harrison et al. 2012; Liu et al. 2012; Lugaz et al. 2012; Temmer et al. 2012; Shen et al. 2012a; Bemporad et al. 2012), and numerical magnetohydrodynamic (MHD) simulation (e.g., Lugaz et al. 2005; Xiong et al. 2007, 2009; Shen et al. 2012b). CMEs cause phenomena at Earth, such as geomagnetic storms and solar energetic particles, that can result in major space weather effects (Gopalswamy 2006; Webb & Howard 2012). Traditionally, a CME has been defined in terms of a three-part structure, involving a bright sheath, a dark cavity, and a bright filament. It is now accepted that the cavity component is an escaping magnetic flux rope that drives the CME (e.g., Rouillard et al. 2009b; DeForest et al. 2011). A highspeed flux rope can drive a fast shock ahead of itself that is much wider in angular extent than the flux rope itself. The region between the shock front and the flux rope is defined as a sheath. Within the sheath, (1) magnetic field lines are draped and compressed, and (2) a plasma flow is deviated, compressed, and turbulent (e.g., Gosling & McComas 1987; Owens et al. 2005; Liu et al. 2008). Precursor southward magnetic fields ahead of CMEs are generally compressed, making them particularly geoeffective (Tsurutani et al. 1992; Gonzalez et al. 1999). The magnetic fields in the sheath and in the flux rope can be equally important in driving major geomagnetic storms (Tsurutani et al. 1988, 1992; Szajko et al. 2013). In so-called two-dip storms, it is often the case that the first dip in the Dst index is produced by the upstream sheath and the second is produced by the driving flux rope (Echer et al. 2004; Zhang et al. 2008; Mostl et al. 2012).",
"pages": [
1,
2
]
},
{
"title": "1.2. Heliospheric White Light Observations",
"content": "Heliospheric imagers (HIs) detect WL that has been Thomson-scattered from free electrons. For resolved objects, such as CMEs, the power detected by an individual pixel depends linearly on the solid angle subtended by that pixel ( δω ) and the area subtended by the corresponding aperture ( δA ), and is proportional to the radiance (measured in W m -2 SR -1 ). The light from unresolved objects, such as stars, which are much narrower in angular extent, tends to fall within individual pixels. For a resolved heliospheric electron density feature, such as a CME, a single pixel provides a measure of its radiance (surface brightness), while summing contributions from all pixels over the entire extent of the feature provides a measure of its intensity (total brightness). The intensity is an integral of the radiance over the apparent feature size. Therefore, the feature's intensity determines its detectability of an object, be it resolved or unresolved (Howard & DeForest 2012). The background zodiacal and stellar signals detected by heliospheric imagers are much more intense than the signal due to Thomson-scattering from plasma features such as CMEs (Leinert & Pitz 1989). Fortunately, using an image-differencing technique, the much more stable background radiance can be removed, such that the more transient Thomson-scattering signal can be extracted. From such processed Thomsonscattering images, the sunlight-irradiated CMEs can be easily identified and tracked. According to theory, the heliospheric Thomson-scattering radiance is governed by the Thomson-scattering geometry fac- tors and electron number density (Vourlidas & Howard 2006; Howard & Tappin 2009; Howard & DeForest 2012; Xiong et al. 2013). The CME detectability in WL is actually more limited by perspective and field-of-view (FOV) effects than by location relative to the Thomsonscattering sphere (Howard & DeForest 2012). Heliospheric imaging from two vantage points, both off the Sun-Earth line, was made possible by the Heliospheric Imagers (HIs) onboard the Solar-TErrestrial RElations Observatory ( STEREO ) (Eyles et al. 2009). With the STEREO /SECCHI package, a CME can be imaged from its nascent stage in the inner corona all the way out to 1 AU and beyond (e.g., Harrison et al. 2008; Davies et al. 2009; Davis et al. 2009; Liu et al. 2010b; DeForest et al. 2011; Liu et al. 2013). In particular, images from STEREO /HI-2 have revealed detailed spatial structures within interplanetary CMEs, including leading-edge pileup, interior cavities, filamentary structure, and rear cusps (DeForest et al. 2011). Comparison with in-situ observations has revealed that the leadingedge pileup of solar wind material, which is evident as a bright arc in WL imaging, corresponds to the sheath region. However, the interpretation of the leading edge of the radiance pattern, especially at larger elongations, is fraught with ambiguity (e.g., Howard & Tappin 2009; Xiong et al. 2013). Elongation ε is defined as the angle between the Sun-observer line and a line-of-sight (LOS). Because a CME occupies a significant three-dimensional (3D) volume, different parts of the CME will contribute to the radiance pattern imaged by observers situated at different heliocentric longitudes (Xiong et al. 2013). Even for an observer at a fixed longitude, a different part of the CME will contribute to the imaged radiance at any given time (Xiong et al. 2013). Various techniques have been developed that enable the spatial locations and propagation directions of CMEs to be inferred, based on the fitting of their moving radiance patterns (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Thernisien et al. 2009; Liu et al. 2010b; Lugaz et al. 2010; Mostl et al. 2011; Davies et al. 2012). However, the determination of interplanetary CME kinematics, propagation direction in particular, are somewhat ambiguous (Howard & Tappin 2009; Davis et al. 2010; Davies et al. 2012; Howard & DeForest 2012; Xiong et al. 2013; Lugaz & Kintner 2013).",
"pages": [
2
]
},
{
"title": "1.3. Faraday Rotation Measurement",
"content": "Faraday rotation (FR) is the rotation of the plane of polarisation of an incident electromagnetic wave as it passes through a magnetised ionic medium. The FR observations of linearly polarised radio sources can be used to estimate magnetic field in the corona and interplanetary space (e.g., Levy et al. 1969; Bird et al. 1980; Sakurai & Spangler 1994; Liu et al. 2007; Jensen 2007; Jensen & Russell 2008; You et al. 2012; Jensen et al. 2013). The FR measurement of a radio signal corresponds to the path integral of the product of electron density n and the projection of the magnetic field along the LOS, B ‖ . The first FR experiment was conducted in 1968 by Levy et al. (1969), when solar plasma occulted the radio down-link from the Pioneer 6 spacecraft. As well as man-made radio sources, FR experiments can also exploit natural radio sources such as pulsars and quasars. The first FR experiments of this type were conducted by Bird et al. (1980) during the solar occultation of a pulsar. In terms of their locations on a sky map, many pulsars and quasars lie in the vicinity of the Sun. Therefore, simultaneous FR measurements along multiple beams can be used to map the inner heliosphere with a reasonable spatial resolution. Additional observations, for example in WL, would generally be necessary to confirm whether an FR transient was indeed caused by a CME. For instance, the first FR event, reported by Levy et al. (1969), could not be attributed unambiguously to the presence of any particular solar wind structure. The FR signatures, observed by Levy et al. (1969), exhibited a W-shaped profile over a time period of 2 -3 hours, with rotation angles of up to 40 · relative to the quiescent baseline. Woo (1997) interpreted the FR signature as the result of a coronal streamer stalk of angular size 1 · -2 · , whereas Patzold & Bird (1998) argued that it was caused by the passage of a series of CMEs. However, by comparing observations from the Solwind coronagraph and measurements of Helios down-link radio signals, Bird et al. (1985) were able to identify the signatures of five CMEs simultaneously in WL and FR. Moreover, the electron density derived from WL imaging can be used to enable magnetic field magnitude to be inferred from FR measurements. The heliospheric magnetic field can be remotely probed in FR, using low-frequency radio interferometers such as the Murchison Widefield Array (MWA) (Lonsdale, C. J., et. al. 2009), the LOw Frequency ARray (LOFAR) (de Vos et al. 2009), and the Very Large Array (VLA) (Thompson et al. 1980). Disturbance of the background solar wind by CMEs will cause the observed FR signatures to become variable (e.g., Levy et al. 1969; Bird et al. 1985; Jensen & Russell 2008). A change in either the electron density ( δn ) or the LOS magnetic field component ( δB ‖ ), or indeed both, will contribute to the rotation in the plane of polarisation of the radio signal by δ Ω RM . Interplanetary magnetic clouds (MCs) in particular, which have a magnetic flux rope configuration (Burlaga et al. 1981; Klein & Burlaga 1982; Lepping et al. 1990), can be identified from WL images (Rouillard et al. 2009b; DeForest et al. 2011) and are expected to be easily identifiable in FR measurements. Moreover, δn and | δ B | are often enhanced simultaneously within the sheath ahead of a fast MC. The FR due to a MC-driven sheath can be comparable to that due to the MC itself (Jensen et al. 2010). It is expected that the orientation and helicity of a MC will be able to be determined unambiguously from multi-beam FR measurements (Liu et al. 2007; Jensen 2007; Jensen et al. 2010). In contrast, the in-situ detection of magnetic flux ropes can be significantly hindered by the location of the observing spacecraft (e.g., Hu & Sonnerup 2002; Mostl et al. 2012; D'emoulin et al. 2013). FR imaging can be used to provide the magnetic orientation of a fast MC, and indeed its preceding sheath, prior to its arrival at Earth, which is crucial for predicting potential space weather effects at Earth.",
"pages": [
2,
3
]
},
{
"title": "1.4. Forward Magnetohydrodynamic Modelling",
"content": "Forward modelling of WL and FR signatures is proving extremely useful for inferring the in-situ properties of interplanetary CMEs from remote-sensing data. Sophis- ticated numerical MHD models of the inner heliosphere (e.g., Groth et al. 2000; Lugaz et al. 2005; Hayashi 2005; Xiong et al. 2006a; Li et al. 2006; Wu et al. 2006; Li & Li 2008; Odstrˇcil & Pizzo 2009; Shen et al. 2012b) can serve as a digital laboratory, to enable the synthesis of a variety of observable remote-sensing signatures. In this paper, we perform a numerical MHD simulation of an interplanetary shock in the ecliptic, from which we synthesise the signatures of that feature that would be remotely sensed at visible and radio wavelengths. Details of the MHD model, and the formulae required to synthesise the remote-sensing observations, are given in Section 2. The resultant synthesised remote-sensing signatures of the sheath, which would be observed from vantage points at 0.5 and 1 AU, are described and compared in Section 3. In Section 4, we discuss the radiance patterns that are observed in the synthesised WL and FR sky maps. In Section 5, we explore the role that the vantage point of the observer plays in the 'observability' of such WL and FR features. CME detection in the presence of background noise, and the heliospheric imaging of more complex interplanetary phenomena, are discussed in Section 6. The potentially important role that forward modelling can play in our understanding of coordinated WL and FR observations is summarised in Section 7.",
"pages": [
3
]
},
{
"title": "2. METHOD",
"content": "Forward MHD modelling can self-consistently establish the links between interplanetary dynamics and the resultant observable signatures. A complete flow chart of forward modelling is illustrated in Figure 8 from Xiong et al. (2011). The travelling fast shock studied by Xiong et al. (2013) is revisited here. Our methodology consists of three general steps: (1) forward modelling of the shock using the numerical Inner-Heliosphere MHD (IH-MHD) model (Xiong et al. 2006a, 2013), (2) calculation of its Thomson-scattered WL signature, in Section 2.1, and (3) calculation of its FR signature, in Section 2.2. Characterisation of the IH-MHD model, the background solar wind conditions, and the initial shock injection is summarised respectively in Tables 1, 2, and 3 of Xiong et al. (2013). The simulated electron density n and magnetic field B are used to generate synthetic WL and FR images, which enable us to explore the WL and FR signatures of an interplanetary sheath. A plasma parcel emitted from the Sun would be observed, at the same elongation and the same Thomsonscattering angle, firstly by an observer situated at a radial distance of 0.5 AU from the Sun centre, and subsequently by an observer at 1 AU (Figure 1a). Such a configuration was discussed qualitatively by Jackson et al. (2010) and is analysed quantitatively in Section 3 of this paper. Observations from STEREO /HI suggest that a travelling sheath can be approximated as an expanding bubble (e.g., Howard & Tappin 2009; Lugaz et al. 2010; Davies et al. 2012; Mostl & Davies 2013). In-situ observations indicate that CMEs undergo self-similar expansion, as the speed profiles within CMEs themselves tend to be a linear function of time (e.g., Farrugia et al. 1993; Gulisano et al. 2012). In the schematic Figures 1b-d, the sheath region following an Earth-directed interplanetary shock is represented as a self-similarly expanding bubble. The sheath can look quite different when viewed from different heliocentric distances (Figures 1b and 1c) and/or different heliospheric longitudes (Figures 1b and 1d).",
"pages": [
3,
4
]
},
{
"title": "2.1. Thomson-Scattering WL Formulae",
"content": "A small parcel of free electrons, that is illuminated by a known intensity of incident sunlight (measured in W m -2 ), will scatter a certain amount of power per unit solid angle (measured in W rad -1 ). The effect of the Thomson-scattering geometry can be characterised by the so-called scattering angle χ , as depicted in Figure 1 of Xiong et al. (2013). Scattering can be backward ( χ < 90 · ), perpendicular ( χ = 90 · ), and forward ( χ > 90 · ). All photons that are scattered into an optical cone defined by the point spread function of an individual pixel will be attributed to that pixel (Figure 1b, Xiong et al. 2013). The classic principles of WL Thomson-scattering, as applied to coronagraph observations (Billings 1966), have been adapted to heliospheric imaging (Vourlidas & Howard 2006; Howard & Tappin 2009; Jackson et al. 2010; Howard & DeForest 2012; Xiong et al. 2013). The transverse electric field oscillation δ E of the Thomson-scattered radiance, which is inherently a continuum, can be considered in terms of its two orthogonal components, a tangential component δ E T and a radial component δ E R . The amplitudes of these two orthogonal oscillations ( I T = | δ E T | 2 and I R = | δ E R | 2 ) can be measured separately, using a polariser. The total radiance I and degree of polarisation p are defined as follows: Although the incident sunlight is unpolarised ( p = 0), the scattered WL radiance remains unpolarised only when the scattering angle | χ -90 · | = 90 · . The scattered light is elliptically polarised (0 < p < 1) for 0 · < | χ -90 · | < 90 · and linearly polarised ( p = 1) for χ = 90 · . Each pixel of a detector records the LOS integral of local WL radiance. Here z refers to a distance between the detector and the scattering site, as shown in Figure 1b of Xiong et al. (2013). The mathematical expressions for G , G R , and G T are given by Equations 1 and 2 of Xiong et al. (2013). The observed WL radiance is determined jointly by the heliospheric distribution of electrons n and Thomsonscattering geometry factors ( z 2 G , z 2 G R , z 2 G T ). As noted above, the efficiency of Thomson scattering depends significantly on the Thomson scattering angle χ . The perpendicular scattering, χ = 90 · , received by an observer comes from the Thomson Sphere. The 'Thomson sphere', sometimes called the 'Thomson surface', is the sphere in which the Sun and observer lie at opposite ends of a diameter (e.g., Vourlidas & Howard 2006; Howard & DeForest 2012). The ecliptic cross sections of the Thomson scattering spheres for three observers are shown as dotted circles in Figures 1b-d. The LOS from an observer crosses its Thomson sphere at a so-called p point (Figure 2, Tappin et al. 2004), where both the intensity of incident sunlight and local electron density are greatest, but the efficiency of Thomson scattering is least. Competition between these three effects results in the spread of local radiance ( i , i T , i R in Equation 3) to large distances from the Thomson surface, an effect that is greater at larger elongations ε from the Sun. Howard & DeForest (2012) described this broad spreading effect, using the term 'Thomson plateau'. Namely, along a single LOS, the radiance per unit electron density is virtually constant over a broad range of scattering angles χ centred at the p point. The Thomson plateau, in terms of its relevance to heliospheric image, was discussed in detail by Howard & Tappin (2009), Howard & DeForest (2012), and Xiong et al. (2013). A major milestone in stereoscopic WL imaging of interplanetary CMEs was achieved by the STEREO /HI instruments (e.g., Eyles et al. 2009; Davies et al. 2009; Davis et al. 2009; Harrison et al. 2009). This heliospheric imaging capability was built on the heritage of the Solar Mass Ejection Imager ( SMEI ) instrument on the Coriolis spacecraft (Eyles et al. 2003). The STEREO mission is comprised of two spacecraft, with one leading ( STEREO A) and the other trailing ( STEREO B) the Earth in its orbit. Both spacecraft separate from the Earth by 22 . 5 · per year. The HI instrument on each STEREO spacecraft consists of two cameras, HI-1 and HI-2, whose optical axes lie in the ecliptic. Elongation coverage in the ecliptic is 4 · - 24 · for HI-1 and 18 . 7 · - 88 . 7 · for HI-2. The field of view (FOV) is 20 · × 20 · for HI-1 and 70 · × 70 · for HI-2. The cadence of HI1 is usually 40 minutes and that of HI-2 is 2 hours (Eyles et al. 2009). The current generation of heliospheric imagers do not have WL polarisers. Polarisation measurements have, up until now, only been made by coronagraphs (e.g., Poland & Munro 1976; Crifo et al. 1983; Moran & Davila 2004; Pizzo & Biesecker 2004; de Koning et al. 2009; Moran et al. 2010). For instance, Moran & Davila (2004) used polarisation measurements of WL radiance by the SOHO /LASCO coronagraph to reconstruct CME orientations near the Sun. Sky maps, often presented in the Hammer-Aitoff projection, can be used to highlight and track WL transients (e.g., Tappin et al. 2004; Zhang et al. 2013). Timeelongation maps (J-maps) are usually constructed by stacking differenced radiance between observed sky maps along a fixed position angle (sometimes background subtracted images are used instead of difference images). Using such J-maps, transients such as CMEs are manifest as inclined streaks (e.g., Sheeley et al. 2008; Rouillard et al. 2008; Xiong et al. 2011; Harrison et al. 2012; Davies et al. 2012; Xiong et al. 2013). As a propagating transient is viewed along larger elongations, its WL signatures become fainter.",
"pages": [
4
]
},
{
"title": "2.2. Faraday Rotation Formula",
"content": "Due to a FR effect, the plane of polarisation of linearly polarised radio emission is continuously rotated as the radio wave passes through the heliosphere. For radio waves, the ubiquitous magnetised solar wind flow serves as a magneto-optical birefringence medium. The formulae for FR are expressed below: Where q , /epsilon1 , m e , and c represent the constants that are the electron charge, the permittivity of free space, the mass of an electron, and the speed of light, respectively. A FR measurement of Ω RM = 1 rad m -2 corresponds to Ω = 0 . 97 · at 2.3 GHz (wavelength λ = 0 . 13 m), Ω = 57 . 3 · at 300 MHz ( λ = 1 m), and Ω = 1432 · at 60 MHz ( λ = 5 m). The calibration of ground-based FR observations is difficult, as the radio wave passes through the magnetised plasma of the ionosphere, magnetosphere (including the plasmasphere), and solar wind. Oberoi & Lonsdale (2012) surveyed and compared the FR signatures associated with each of these different regions. A large portion of the inner heliosphere can be monitored, using FR imaging. Prime heliospheric targets measured in FR include interplanetary CMEs and CIRs (Oberoi & Lonsdale 2012). Because the low-frequency radio interferometers such as the MWA , LOFAR , and VLA feature a wide FOV, high sensitivity, and multibeam forming capabilities, it is expected to be capable of mapping the magnetic field in the inner heliosphere with a remarkable sensitivity. The high sensitivity of FR measurements enables fluctuations in the heliospheric/interstellar magnetic field and plasma density, resulting from MHD turbulence, to be revealed (e.g., Jokipii & Lerche 1969; Goldshmidt & Rephaeli 1993; Hollweg et al. 2010). For instance, gradients in FR measurement have been observed across active Galactic Nuclei (AGN) jets, using the Very Long Baseline Array , which demonstrate that ordered helical magnetic fields are associated with these jets (e.g., Zavala & Taylor 2002; G'omez et al. 2008; Reichstein & Gabuzda 2012). The sheath region associated with a fast CME can be similarly probed. FR measurements of the sheath would provide a value for Ω RM in Equations 4-8. Any measured value of the FR, Ω RM , would correspond to a statistical average, as the plasma and magnetic fields within such sheath regions are in a highly turbulent state.",
"pages": [
4,
5
]
},
{
"title": "3. WHITE-LIGHT AND FARADAY ROTATION SIGNALS RECEIVED AT 0.5 AND 1 AU",
"content": "The remote imaging in WL and FR of an Earthdirected sheath from two vantage points, one at 0.5 AU and the other at 1 AU, is considered in Section 3.1. Section 3.2 demonstrates how spatial position and electron number density can be inferred from polarisation observations of WL radiance. Section 3.3 presents a means by which magnetic field can be diagnosed from FR measurements. 3.1. Comparing Remotely-Sensed WL and FR Observations from Different Vantage Points Figure 2 shows the modelling results of an Earthdirected sheath propagating from the Sun to 1 AU. The travelling sheath is supposed to be imaged simultaneously by two observers at 0.5 and 1 AU. The WL and FR signatures of the sheath are synthesised, using the methods in Section 2. Representative LOSs, which cut through the sheath (LOS1-6), are denoted using arrows in Figure 2. The variations of various physical parameters along LOS1-3 are shown in Figure 3. LOS1, LOS2, LOS3, and LOS5 are approximately tangential to the left flank of the shock; LOS4 and LOS6 are tangential to the nose of the shock. LOS1 and LOS4 are directed towards the observer situated at 0.5 AU; all other LOSs are directed towards the observer at 1 AU. The viewing configuration for LOS1 (Figure 2a) is equivalent to that for LOS3 (Figure 2c), as the elongation of the shock front is the same for LOS1 and LOS3. Thus, the Thomson scattering geometry is identical for these two LOSs, leading to similar LOS profiles in Figure 3. Of course, the observed radiance along LOS1 is much stronger than that along LOS3 (Table 1). Similarly, the observations along LOS4 and LOS6 (Figures 2d and 2f) have identical Thomson scattering geometries. At any given time, the sheath is viewed at greater elongations from a vantage point closer to the Sun. For instance, at an elapsed time of 5.5 hours, the foremost elongation ε of the sheath is 20 · for an observer at 1 AU (LOS1) compared with 7 · for an observer at 0.5 AU (LOS2). While the sheath is undetectable in WL along LOS2 (Figure 3g), it can be observed in FR (Figure 3l). The portion of an LOS that contributes most to the WL radiance broadens and flattens with increasing elongation, and shifts gradually towards the observer. At elongations beyond 90 · , only back-scattered photons are received; electrons in the vicinity of the observer mainly contribute to remote-sensing signatures for elongations beyond 90 · . Such observations for elongations of ε ≥ 90 · are less useful for the purposes of space weather prediction. In Figures 2d and 2f, the shock front has already reached the observer, and can be detected in-situ.",
"pages": [
5
]
},
{
"title": "3.2. Inferences of Sheath Position from Polarised White Light",
"content": "The WL radiance of CMEs is determined by both the electron number density distribution and the Thomsonscattering geometry (Equation 3). The total radiance at a scattering site ( i ), and its constituent radial ( i R ) and tangential ( i T ) components, are associated with Thomson-scattering factors z 2 G , z 2 G R , and z 2 G T , respectively. Near the Thomson-scattering surface, z 2 G T is much larger than z 2 G R . If a dense parcel of plasma, viewed at large elongations, approaches the Thomson surface, its WL signatures will comprise (1) an increase in I , (2) an increase in I T , (3) a decrease in I R , and (4) an increase in the degree of polarisation p . The variation of p is largest, while that of I is negligible. A plasma parcel's distance from the Thomson sphere has a less significant effect on I at larger elongations. However, the determination of the plasma parcel's location will be more uncertain, if only unpolarised WL observations are available, as with current operational heliospheric imaging systems. Polarisation observations can provide an important clue to the primary scattering site. LOS1 in Figure 2 is used to demonstrate these inferences. The Thomson-scattering geometry is independent of the distribution of heliospheric electrons. The degree of polarisation ( p ) and the Thomson-scattering factors ( z 2 G , z 2 G R , z 2 G T ), as presented in Figure 3b and 3d, only depend on the modified scattering angle χ ∗ = 90 · -χ . The profiles of p , z 2 G , z 2 G R , and z 2 G T are symmetrical around χ ∗ = 0 · . The dependence of χ ∗ , z 2 G , and LOS distance z on p can be seen in Figure 4. p = 1 corresponds to perpendicular scattering (i.e. χ ∗ = 0 · ). p = 1 corresponds to two solutions for χ ∗ : one resulting from forward scattering ( χ ∗ < 0 · ), and the other associated with backward scattering ( χ ∗ > 0 · ). In response to the passage of the shock, the initial radiance components at t = 0, I T0 and I R0 , are enhanced to values denoted by I T and I R , respectively. The increase in the radiance components define a so-called modified degree of polarisation that we denote using p ∗ . p ∗ is given by /negationslash p is 0.62 along LOS1 at t = 0 hours. This effectively defines the degree of polarisation associated with the background solar wind. During the sheath passage, at t = 5 . 5 hours, p is 0.58 along this LOS. The modified degree of polarisation p ∗ , derived using Equation 9, is therefore 0.29 at t = 5 . 5 hours. The radiance enhancement is due to the presence of the sheath in the LOS. The sheath, which trails the shock front, occupies a relatively small volume of interplanetary space. The sheath occupies the portion of LOS1 bounded by -55 · < χ ∗ < -35 · (Figures 3a and 3c). Within this region, p smoothly varies from 0.15 to 0.5 (Figure 3d). The average value of p ∗ within the sheath is 0.29. In an inverse approach, p ∗ can be used to estimate the scattering angle χ ∗ within the sheath. This is demonstrated in Figure 4a. p ∗ = 0 . 29 corresponds to χ ∗ = ± 46 · and z 2 G = 6 . 5 × 10 -29 , where z 2 G is the average value of z 2 G in the sheath. The solution of χ ∗ = 46 · can be immediately excluded, as an Earth-directed CME can generally be identified (indeed much earlier) as being front-sided based on Extreme Ultraviolet (EUV) images of the full solar disk (e.g., Thompson et al. 1998; Plunkett et al. 1998). The other solution, χ ∗ = -46 · , is physical and yields a value of 60 R S for the distance, z , of the main scattering site (corresponding to the sheath) from the detector. How best to judge which solutions for χ ∗ are physical is explained in detail in Section 4. Once the Thomsonscattering factor z 2 G of the sheath has been inferred, its column-integrated electron number density can be estimated based on the following equation: It is clear that WL polarisation measurement can prove extremely valuable in the study of interplanetary CMEs and shocks.",
"pages": [
5,
6
]
},
{
"title": "3.3. Magnetic Field Inferred from Faraday Rotation",
"content": "As discussed in Section 3.2, the column-integrated electron number density along any LOS can be inferred from its WL observations. Thus, if a radio beam lies within the FOV of a WL imager such that they remotely probe the same plasma volume, the WL density measurements can be used to retrieve magnetic field strength from the received FR signal. We demonstrate this, for LOS1, in Figure 5. After subtracting the background solar wind contribution, the enhancements in FR measurement and WL radiance, due to the presence of the sheath of the simulated Earth-directed shock, are given by δ Ω RM and δI , respectively. The ratio of δ Ω RM and δI can be expressed as As discussed in Section 3.2, z 2 G corresponds to the average value of z 2 G in the sheath. The derivable parameter δ ( nB ‖ ) δ n , which we call B ∗ ‖ , can be expressed in the form where B ‖ 0 and n 0 denote the initial background values of B ‖ and n , respectively. The inferred value of B ∗ ‖ serves as an upper limit for B ‖ .",
"pages": [
6
]
},
{
"title": "4. RADIANCE PATTERNS IN J-MAPS OF WHITE LIGHT AND FARADAY ROTATION",
"content": "Shock propagation through the inner heliosphere can be identified through the inclined trace with which it is associated in a time-elongation map (J-map). J-maps of WL radiance ( I/I ∗ , I ) and degree of polarisation ( p , p ∗ ), and FR measurement | δ Ω RM | , as viewed from observers at 0.5 and 1 AU, are presented in Figure 6 and compared in Figure 7. The normalisation factor I ∗ in Figure 6 corresponds to an electron number density distribution that varies according to n ∝ r -2 . A radiance threshold of I/I ∗ ≥ 3 . 68 × 10 -15 is used to demarcate the sheath region in time-elongation ( t -ε ) parameter space. The modified polarisation p ∗ is only calculated, using Equation 9, inside the sheath (Figures 6g-h). The absolute values of I and | δ Ω RM | within the sheath region are much larger for the observer at 0.5 AU, whereas the sheath values of I/I ∗ , p , and p ∗ are comparable when viewed from either vantage point. Over the elongation range 15 · ≤ ε ≤ 180 · , the radiance ratio Max. ( I 0 . 5AU ) Max. ( I 1AU ) is limited to values between 8 and 11 (Figure 7c). This demonstrates that interplanetary CMEs and shocks are viewed better from a location closer to the Sun. The position, mass, and magnetic field of the sheath can be inferred from those directly-measurable parameters presented in Figure 6, using the analytical methods presented in Sections 2.1 and 3.3. As shown in Figure 4, and explained in Section 3.2, the Thomson-scattering factors are symmetrical around χ ∗ = 0 · . As a result, a single value of degree of polarisation p ∗ corresponds to two symmetrical solutions for the scattering angle χ ∗ . The results shown in Figure 8 are derived from those in Figure 6 (for an observer at 0.5 AU) under the assumption of forward scattering, while those in Figure 9 assume backward scattering. For the forward-scattering situation, presented in Figure 8b, the inferred longitude of the sheath ϕ sheath is 22 · at an elapsed time of 5 hours and 9 · at 11 hours. For the backward-scattering case, shown in Figure 9b, the sheath is at ϕ sheath = 140 · and 60 · at these times. So, an observer at 0.5 AU infers a longitude change ∆ ϕ sheath of 13 · (Figure 8b) and 80 · (Figure 9b) for the forward and backward-scattering cases, respectively. The dramatic change in sheath longitude for the backward-scattering case might indicate that the shock is significantly deflected during its interplanetary propagation. However, such an abnormal degree of lateral deflection of ∆ ϕ sheath = 80 · would be highly unphysical, and may imply a 'ghost trajectory' (Figure 6, DeForest et al. 2013). The east-west symmetry of the radiance pattern suggests that the shock is actually front-sided and Earth-directed, rendering the assumption of backward-scattering invalid (Figure 9). If we assume that the radiance pattern shown in Figure 6 is attributable to forward scattering, the inferred position of the sheath is shown as the solid white curve in Figure 2. This agrees very well with the actual position of the sheath. At any given time, only a certain portion of the sheath will be visible from a fixed observing location (Xiong et al. 2013). For example, at an elapsed time of 5.5 hours, it is the flank of the sheath (Figure 2a) that corresponds to the leading edge of the radiance pattern in 6a, while 6 hours later it is the nose (Figure 2d). So, in fact, the longitudinal change of ∆ ϕ sheath = 13 · inferred from Figure 8b is actually an artefact of the viewing geometry and does not represent an actual deflection of the shock front. Along with the inferred position of the sheath, the column-integrated electron number density, δN sheath , and the parallel magnetic field component, B ‖ , are also presented in Figure 8. The derived value of | B ‖ | provides an upper limit for the actual magnetic field, as explained in Section 3.3. By making coordinated observations in WL and FR, CMEs can not only be continuously tracked, but quantitatively diagnosed as they propagate through interplanetary space.",
"pages": [
6,
7
]
},
{
"title": "5. INTERPLANETARY IMAGING FROM DIFFERENT OBSERVATION SITES",
"content": "An interplanetary CME looks different when viewed from different vantage points, but can be readily imaged from a wide range of longitudes. The observed WL radiance pattern depends not only on the longitude ϕ o of the observer, as discussed by Xiong et al. (2013), but also on its heliocentric distance r o . In Section 3.1, we compare observations made from radial distances of 0.5 and 1 AU. In Section 5.1, we consider two particular observation sites that are often considered favourable in terms of WL imaging, the L4 and L5 Lagrangian points. In Section 5.2, we quantify more fully the dependence of WL imaging on r o .",
"pages": [
7
]
},
{
"title": "5.1. Observing an Earth-Directed shock from the L4 and L5 Lagrangian Points",
"content": "The L4 and L5 Lagrangian points of the Sun-Earth system are often considered advantageous for observing Earth-directed CMEs. There are five Lagrangian points, all in the ecliptic, i.e., L1-L5. A spacecraft at L1, L2, or L3 is metastable in terms of its orbital configuration, and hence must frequently use propulsion to remain in the same orbit. In contrast, a spacecraft at L4 or L5 is resistant to gravitational perturbations, and is believed to be more stable. The L4 and L5 points lie 60 · ahead of and behind the Earth in its orbit, respectively. STEREO A reached the L4 point in September 2009 and STEREO B reached L5 in October 2009. The twin STEREO spacecraft were pathfinders for future L4/L5 missions (Akioka et al. 2005; Biesecker et al. 2008; Gopalswamy et al. 2011). A spacecraft at either L4 or L5 can perform routine side-on imaging of Earthdirected CMEs, and hence is of great merit for space weather monitoring. Figure 10a illustrates the imaging, be it in WL or FR, of an Earth-directed sheath from the L5 point. LOS7 intersects the nose of the shock at an elapsed time of 14.5 hours, when the shock nose lies on the Thomsonscattering sphere. The variation, along LOS7, of a number of salient physical parameters is shown in Figures 10 e-j. The interplanetary magnetic field lines are compressed and rotated within the sheath. This rotation results in the closer alignment of the field lines with LOS7, such that the magnetic field component along the LOS, | B ‖ | , is greatly enhanced (Figure 10i). The enhancements of both | B ‖ | and electron number density n within the sheath are responsible for the resultant increases in WL radiance I and FR measurement | Ω RM | . The degree of WL polarisation p , as viewed along LOS7 that is at an elongation of 34 · , is 0.67 for the background solar wind and increases to 0.75 during the shock passage at 14.5 hours. This corresponds to a value of the modified WL polarisation p ∗ of 0.98, based on Equation 9. As was done for LOS1 in Section 3, we evaluate the WL radiance along LOS7 (Figure 10a), from which we infer the shock position (Figure 10d). Again, a single value of p ∗ corresponds to two symmetrical solutions for scattering angle χ ∗ , i.e., p ∗ = 0 . 29 and χ ∗ = ± 46 · for LOS1, and p ∗ = 0 . 98 and χ ∗ = ± 5 · for LOS7. For LOS1, only one solution for χ ∗ = -46 · was deemed physical; for LOS7, both solutions for χ ∗ are potentially physical. The scattering sites corresponding to χ ∗ = ± 5 · are very close to one another, and both agree well with the actual position of the sheath (Figure 10a). The section of LOS7 bounded by -5 · ≤ χ ∗ ≤ 5 · lies within the sheath. Both forward scattering ( -5 · ≤ χ ∗ < 0 · ) and backward scattering (0 · < χ ∗ ≤ 5 · ) will contribute to the radiance I observed along this LOS. The propagating sheath can be tracked continuously and easily in WL from the L5 vantage point, such that it leaves an obvious signature in the J-map of synthesised radiance (Figures 10b and 10c). This confirms previous assertions that the L4 and L5 points are very favourable in terms of space weather monitoring.",
"pages": [
7
]
},
{
"title": "5.2. Dependence of White-Light Radiance on Heliocentric Distance",
"content": "The background intensity at a fixed elongation in a WL sky map is greater for an observer closer to the Sun. For a heliospheric imager at any distance from the Sun, Jackson et al. (2010) proposed the following Thomsonscattering principles: (1) The WL radiance I at a given solar elongation falls off with the heliocentric distance r according to r -3 ; (2) Such a dependence of I ∝ r -3 is valid for almost any viewing elongation, and for any radial distance from 0.1 AU out to 1 AU and beyond. The WL radiance I depends on the heliospheric distribution of electron number density n . In interplanetary space, the background solar wind speed is nearly constant, and the background electron number density n 0 varies approximately with r -2 . However, the equilibrium defined by n 0 ∝ r -2 is disturbed by the presence of interplanetary transients, such as CMEs and CIRs. A travelling shock can sweep up, and hence compress significantly, the background solar wind plasma. Figures 2 and 10a show a density enhancement of n -n 0 n 0 ≈ 2 . 2 within the sheath. The associated compression ratio n n 0 ≈ 3 . 2 indicates that the shock is very strong. However, when viewed along elongations less than 60 · , the strongest signatures of shock passage (characterised by Max.( I )) vary very closely with r -3 (Figures 11b and 11c). The relationship of Max.( I ) ∝ r -3 is slightly violated at large elongations ε > 60 · . Figure 7c reveals that the ratio between Max.( I 0 . 5AU ) and Max.( I 1AU ) is close to 8 for ε ≤ 60 · , increasing thereafter to 10.8 at ε = 180 · . The premise that the WL radiance decreases with the third power of Sun-observer distance generally holds true for both the background solar wind and propagating CMEs.",
"pages": [
7,
8
]
},
{
"title": "6. DISCUSSION",
"content": "The detectability in WL of a particular electron density feature is determined by its signal above the noise background. In STEREO /HI-1 images, the dominant WL signal is zodiacal light due to scattering of sunlight from the F-corona, which is centred around the ecliptic. In the STEREO /HI-2 FOV, the noise floor is primarily determined by photon noise and the background star-field (DeForest et al. 2011). Away from the ecliptic, the background WL noise has a sharp radial gradient in coronal images, and is nearly constant in heliospheric images. The signal-to-noise ratio for heliospheric electron density features is discussed by Howard et al. (2013). We will address the detection of CMEs in the presence of background noise in future forward-modelling work. If both a transient CME and background (Heliospheric Current Sheet (HCS) - Heliospheric Plasma Sheet (HPS)) plasma structures are present along the same LOS, both will contribute to the total LOS-integrated radiance. In this case, the interpretation of the data would clearly be more problematic. Moreover, if the LOS were to penetrate a HCS, the magnetic field vector would, at that point, rotate through 180 · . Due to the mutual cancellation of B ‖ across the HCS, there may be no net FR signature according to Equations 4-6. Hence, even such a significant interplanetary structure may be associated with only a weak FR measurement. Conversely, the relatively dense plasma within a HPS can significantly contribute to WL radiance. Thus the potential effects of the presence of HCS-HPS structures need to be borne in mind in the remote imaging of CMEs. In the current work, however, we find that such effects are negligible. In our numerical simulation, there are two HCS-HPS structures, which are initially rooted at longitudes of ϕ = ± 90 · at the inner boundary of our numerical simulation. The simulated shock emerges at a longitude of ϕ = 0 · . The large longitudinal difference between the HCS-HPS and the shock means that the remote-sensing signatures are principally contributed by the sheath. Thus, in our forward-modelling work, the signal enhancements of synthesised imaging in WL and FR are unambiguously the result of the propagating sheath. In general, the more complex the interplanetary dynamics, the more complex the resultant remote-sensing observations will be. For instance, a CME can interact with other CMEs and/or background solar wind structures such as CIRs, HCSs, and HPSs; mutual interaction between CMEs is, however, generally more perturbing than interactions between CMEs and such background structures. Interactions can result in the background solar wind structures becoming warped or distorted (e.g., Odstrˇcil et al. 1996; Hu & Jia 2001), and CMEs being accelerated/decelerated (e.g., Lugaz et al. 2005; Xiong et al. 2007; Shen et al. 2012b), deflected (e.g., Xiong et al. 2006b, 2009; Lugaz et al. 2012), distorted (e.g., Xiong et al. 2006b, 2009), or entrained (e.g., Rouillard et al. 2009a). In particular, during such interactions, the behavior of a sheath can become much more complex: the shock aphelion can be deflected, spatial asymmetries can develop along the shock front, and the shock front can potentially merge completely with other shock fronts. At an interaction site, both the plasma density and magnetic field would be compressed; this would lead to enhanced signatures in both WL and FR observations. For example, the interaction between two CMEs was manifest as a very bright arc in WL images (e.g., Harrison et al. 2012; Liu et al. 2012; Temmer et al. 2012). Different types of interaction would likely result in different WL radiance signatures; in fact, through a single interaction, the corresponding radiance pattern would evolve. The interpretation of such complex WL radiance patterns would be prone to large uncertainties, but can be rigorously constrained if interplanetary imaging was performed from multiple vantage points and complemented by numerical modelling. For stereoscopic WLimaging, ray-paths from one observer intersect those from the other observer. Thus the 3D distribution of electrons in the inner heliosphere can be reconstructed using a time-dependent tomography algorithm (Jackson et al. 2006; Bisi et al. 2008; Webb et al. 2013). With the aid of numerical modelling, coordinated imaging in WL and FR would enable the properties and evolution of complex interplanetary dynamics to be diagnosed.",
"pages": [
8
]
},
{
"title": "7. CONCLUDING REMARKS",
"content": "In this paper, we have investigated the WL and FR signatures of an interplanetary shock based on an approach of forward MHD modelling. The WL Thomsonscattering geometry is increasingly more significant at larger elongations. The degree of WL polarisation can be used to estimate the 3D location of the main scattering region, while FR measurement can be used to infer, to some extent, the magnetic configurations of CMEs. This work presented here demonstrates, as a proof-of-concept, that the availability of coordinated observations in polarised WL and FR measurement would enable the local LOS magnetic component to be estimated. Although the current generation of heliospheric WL imagers, such as the STEREO /HI instruments, do not have polarisers, there are advances underway in terms of FR imaging using Low-frequency radio arrays. Coordinated imaging in WL and FR would enable the inner heliosphere to be mapped in fine detail; the location, mass, and magnetic field of CMEs can be diagnosed on the basis of such combined observations. Forward modelling is crucial in establishing the causal link between interplanetary dynam- ics and observable signatures, and can provide valuable guidance for future coordinated WL and FR imaging. Although not the methodology of the current work, numerical MHD models of the inner heliosphere can also be directly driven by photospheric observations (e.g., Hayashi 2005; Wu et al. 2006; Feng et al. 2012b). A comparison of synthesised and observed WL and FR sky maps, the former based on the use of such datadriven models, would prove highly beneficial in validating the forward modelling and interpreting the observations. Such an integration of observation data analysis and numerical forward modelling will be explored as the continuation of the preliminary modelling work presented in this paper. This work is jointly supported by the National Basic Research Program (973 program) under grant 2012CB825601, the Chinese Academy of Sciences (KZZD-EW-01-4), the National Natural Science Foun- dation of China (41231068, 41031066, 41204129), the Strategic Priority Research Program on Space Science from the Chinese Academy of Sciences (XDA04060801), the Specialized Research Fund for State Key Laboratories of China, the Chinese Public Science and Technology Research Funds Projects of Ocean (201005017), open research foundation of Science and Technology on Aerospace Flight Dynamics Laboratory of China (AFDL2012002), research fund for recipient of excellent award of the Chinese Academy of Sciences President's scholarship (startup fund). Ming Xiong is also partially supported by an institutional project of 'Key Fostering Direction in Pulsar Science and Application' from the Center of Space Science and Applied Research, China. Ming Xiong sincerely thanks Drs. Bo Li, Ding Chen, Craig DeForest, James Tappin, and Tim Howard for their beneficial discussions and thoughtful suggestions. We sincerely thank the anonymous referee for his/her constructive suggestions.",
"pages": [
8,
9
]
},
{
"title": "REFERENCES",
"content": "Feng, L., Inhester, B., Wei, Y., et al. 2012a, ApJ, 751, 18 Roca-Sogorb, M. 2008, ApJ, 681, L69 Space Sci. Rev., 88, 529 20 Xiong et al. ) t n e m e r u s a e m R F c i t e n g a m l e l l a r a P n o r t c e l E 3 - m d a r 2 1 - 0 1 × ( ) T n ( ) 3 - m c ( ) . 0 1 e r u g i F n o d i a l r e v o s i 7 S O L d n a 2 e r u g i F n o d i a l r e v o e r a 6 - , L O S 3 L O S s 1 t t e r i n g o r s G T h c a E . j - e 0 1 d n a 3 s e r u g i F n i n o i t a s i l a m r o n r o f d e s u , 7 S O L d n a , 2 ; t c | ‖ B | n y t i s n e d 2 z n a , | ‖ B | , n , T G 2 z , R G 2 z , G 2 z , i s r e t e m a r a p e h t f o s e u l a v m u m i x a M l e n a d n a , o ϕ e d u t i g n o l a , o r s u i d a r a , t e m i t a d e t a n g i s e d s i S O L a c L W n o i t a g n o l E e d u t i g n o L i i d a R e m i T S O L ( ) · ( ) ε o ϕ o r t · ( ) U A ( ) r u o h ( d l e fi r e b m u n | M R ω | 4 . 4 1 7 0 2 2 9 3 0 2 0 5 . 0 5 . 5 1 S O L 2 . 8 1 3 2 2 3 9 8 1 7 0 1 5 . 5 2 S O L 1 5 . 1 9 . 8 6 7 8 0 2 0 1 4 1 3 S O L 2 4 . 0 5 . 8 2 3 . 0 6 4 3 0 6 - 1 5 . 4 1 7 S O L",
"pages": [
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2013ApJ...777...82K
https://arxiv.org/pdf/1308.5468.pdf
<document>
<section_header_level_1><location><page_1><loc_13><loc_80><loc_87><loc_86></location>K s BAND LUMINOSITY EVOLUTION OF THE ASYMPTOTIC GIANT BRANCH POPULATION BASED ON STAR CLUSTERS IN THE LARGE MAGELLANIC CLOUD</section_header_level_1>
<text><location><page_1><loc_28><loc_76><loc_72><loc_78></location>Youkyung Ko, Myung Gyoon Lee, and Sungsoon Lim</text>
<text><location><page_1><loc_13><loc_71><loc_87><loc_75></location>Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea</text>
<text><location><page_1><loc_17><loc_68><loc_83><loc_69></location>[email protected], [email protected], [email protected]</text>
<section_header_level_1><location><page_1><loc_44><loc_64><loc_56><loc_65></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_27><loc_83><loc_61></location>We present a study of K s band luminosity evolution of the asymptotic giant branch (AGB) population in simple stellar systems using star clusters in the Large Magellanic Cloud (LMC). We determine physical parameters of LMC star clusters including center coordinates, radii, and foreground reddenings. Ages of 83 star clusters are derived from isochrone fitting with the Padova models, and those of 19 star clusters are taken from the literature. The AGB stars in 102 star clusters with log(age) = 7.3 - 9.5 are selected using near-infrared color magnitude diagrams based on 2MASS photometry. Then we obtain the K s band luminosity fraction of AGB stars in these star clusters as a function of ages. The K s band luminosity fraction of AGB stars increases, on average, as age increases from log(age) ∼ 8.0, reaching a maximum at log(age) ∼ 8.5, and it decreases thereafter. There is a large scatter in the AGB luminosity fraction for given ages, which is mainly due to stochastic effects. We discuss this result in comparison with five simple stellar population models. The maximum K s band AGB luminosity fraction for bright clusters is reproduced by the models that expect the value of 0.7 - 0.8 at log(age) = 8.5 - 8.7. We discuss the implication of our results with regard to the study of size and mass evolution of galaxies.</text>
<text><location><page_1><loc_17><loc_22><loc_83><loc_25></location>Subject headings: galaxies: star clusters: general - infrared: stars - stars: AGB and post-AGB - Magellanic Clouds - galaxies: evolution</text>
<section_header_level_1><location><page_1><loc_42><loc_15><loc_58><loc_17></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_10><loc_88><loc_13></location>The asymptotic giant branch (AGB), a representative intermediate-age population, is the most luminous evolutionary stage for low- and intermediate-mass (1 - 8 M /circledot ) stars.</text>
<text><location><page_2><loc_12><loc_74><loc_88><loc_86></location>AGB stars emit a huge amount of near- to mid-infrared light because of their low effective temperature (T eff ∼ 1000 - 4000 K) and circumstellar dust. Hence it is expected that they contribute significantly to the infrared light of galaxies. However, their infrared luminosity contribution in galaxies, even in a simple stellar population (SSP), is still a debating issue with regard to constructing evolutionary population synthesis (EPS) models (Maraston 2011, Bruzual et al. 2013, Noel et al. 2013, and references therein).</text>
<text><location><page_2><loc_12><loc_57><loc_88><loc_73></location>The EPS models are an useful tool to determine physical parameters of stellar complexes such as star clusters and galaxies by spectral energy distribution (SED) fitting. These models reproduce SEDs of stellar systems by synthesizing the SEDs of stellar populations in various evolutionary stages, assuming age, metallicity, foreground and internal reddening values, star formation history, and so on. Therefore, the spectral energy contribution of individual stellar populations influences the estimation of physical parameters of stellar systems, and especially that of the AGB population plays a key for understanding of the SEDs for stellar systems expected by EPS models.</text>
<text><location><page_2><loc_12><loc_12><loc_96><loc_56></location>There are various EPS models that include the AGB evolutionary process (e.g., Charlot & Bruzual 1991, Bruzual & Charlot 1993, Fioc & Rocca-Volmerange 1997, Maraston 1998, Leitherer et al. 1999, Vazdekis 1999, Schulz et al. 2002, Bruzual & Charlot 2003, Jimenez et al. 2004, Maraston 2005, Conroy et al. 2009, Kotulla et al. 2009, Conroy & Gunn 2010, Vazdekis et al. 2010, Maraston & Stromback 2011). Bruzual & Charlot (2003, hereafter BC03), for example, presented an EPS model based on Padova evolutionary tracks including just two evolutionary stages for thermally pulsing AGB (TP-AGB) (Girardi et al. 2000), while their recent model includes 15 evolutionary stages of the TP-AGB oxygen-rich and carbon-rich phases (Bruzual A. 2010). The Padova evolutionary tracks adopted in the BC03 model include a given core overshooting efficiency. On the other hand, Maraston (1998, 2005) used evolutionary tracks assuming zero efficiency of the core overshooting from Cassisi et al.(1997, 2000) to determine luminosity contribution of main-sequence populations. It makes the lifetime of main-sequence stars in the Maraston (2005) model shorter compared with Padova isochrones. In addition, she used the fuel consumption theorem (Renzini & Buzzoni 1986) for post-main-sequence stars, not adopting the isochrone synthesis method. In the model of Maraston (1998), the TP-AGB evolutionary process is modified in the fuel consumption theorem, applying the advanced envelope burning process of AGB stars. Renzini & Buzzoni (1986) estimated the contribution of TP-AGB population in the young SSPs with ages < 10 8 yr, and compared it with the star clusters in the the Magellanic Clouds (MCs). They found that it is too high to be consistent with the observational results based on these star clusters. Considering this difference, Maraston (2005) suggested a revised model, assuming shorter lifetime and lower fuel consumption of TP-AGB stars than Renzini & Buzzoni (1986).</text>
<text><location><page_3><loc_12><loc_56><loc_88><loc_86></location>BC03 and Maraston (2005) adopted different stellar population synthetic methods, and the SEDs reproduced by these models show recognizable differences. A number of studies argue whether or not these EPS models reproduce well observational quantities of stellar systems related with the AGB population as follows. Some studies found that spectra and SEDs of post-starburst galaxies or distant galaxies (z ∼ 1 - 2) have no near-infrared boosted features, which is similar to the expectation of the BC03 model (Muzzin et al. 2009, Kriek et al. 2010, Zibetti et al. 2013). In addition, Conroy & Gunn (2010) suggested that the BC03 model and their own EPS model, a flexible stellar population synthesis model, reproduce the color of star clusters and post-starburst galaxies better than the Maraston (2005) model. In contrast, others confirmed that the Maraston (2005) model performs well in reproducing near-infrared colors, ( Y -K ) and ( H -K ), and SEDs of low to high redshift galaxies (Maraston et al. 2006, Eminian et al. 2008, MacArthur et al. 2010). Moreover, van der Wel et al. (2006) and Henriques et al. (2011) showed that the rest-frame K band mass-to-light ratio evolution and K s band luminosity evolution of galaxies are explained better by the Maraston (2005) model than by the BC03 model.</text>
<text><location><page_3><loc_12><loc_17><loc_88><loc_55></location>In addition to these galaxy studies, there are several studies investigating star clusters, especially star clusters in the MCs, considering the relevance between the model performance and ages of stellar systems. Because of their proximity, they are very useful to examine not only the individual stellar population directly but also the integrated properties of star clusters. Therefore, they are an ideal object to calibrate SSP models. Pessev et al. (2008) investigated optical to near-infrared colors, ( B -J ), ( V -J ), and ( J -K ), of 54 star clusters in the MCs, and concluded that the BC03 and the Maraston (2005) present the best performance for intermediate-age (0.2 - 2 Gyr) and old ( > 2 Gyr) star clusters, respectively. Lyubenova et al. (2010, 2012) analyzed integrated near-infrared high-resolution spectra of six globular clusters in the Large Magellanic Cloud (LMC) with ages ∼ 1 - 13 Gyr. They showed that the Maraston (2005) model expects J and H band spectra of all their sample star clusters adequately, while it does not for K band spectra of the star clusters with ages < 2 Gyr. Recently Noel et al. (2013) presented the calibration data for stellar population models using 43 star clusters in the MCs. They compared the observed colors of the star clusters, ( V -K ) 0 , ( J -K ) 0 , and ( V -I ) 0 , as a function of ages with the theoretical expectation of various models including BC03 and Maraston (2005). In conclusion, for the ages older than 1 Gyr, the models of Maraston (2005) and BC03 are along the upper end lower end of the observed color, respectively. In the case of the younger ages, BC03 model reproduces well the observed color of star clusters, while Maraston (2005) model expects them too red.</text>
<text><location><page_3><loc_12><loc_10><loc_90><loc_16></location>While above studies investigated the integrated properties of star clusters, Mucciarelli et al. (2006) analyzed the resolved AGB population in the LMC star clusters in detail. They investigated 19 LMC star clusters in terms of K s band luminosity contribution of AGB stars</text>
<text><location><page_4><loc_12><loc_76><loc_88><loc_86></location>as a function of cluster ages. The star clusters used in Mucciarelli et al. (2006) have ages of 100 Myr - 3 Gyr (log(age) ∼ 8.0 - 9.5). They concluded that their empirical results are consistent with the expectation of Maraston (2005) for this age range. Later, Mucciarelli et al. (2009) suggested a similar conclusion from the additional study of four old star clusters in the Small Magellanic Cloud (SMC).</text>
<text><location><page_4><loc_12><loc_59><loc_88><loc_75></location>In this study, we investigate the evolution of AGB luminosity contribution with a large number of LMC star clusters with log(age) ∼ 7.3 - 9.5, overcoming the shortcomings in the previous studies. Because Mucciarelli et al. (2006, 2009) included few star clusters with log(age) ∼ 8.3 - 8.7 (see Figure 5 in Mucciarelli et al. 2009), we enlarged the number of star cluster samples with this age range. In this age range, the AGB luminosity contribution is expected to change rapidly according to the Maraston (2005) model. In addition, most of previous star cluster studies adopted star cluster ages from various literature. We determine ages of LMC star clusters by isochrone fitting homogeneously, using the resolved stars.</text>
<text><location><page_4><loc_12><loc_42><loc_88><loc_58></location>This paper is organized as follows. In § 2, we introduce the photometric data and images used in this study. § 3 describes the method to estimate physical parameters of sample star clusters such as center coordinates, radii, ages, and foreground reddenings including the cluster sample section. In § 4, we select AGB stars in each star cluster and derive the K s band luminosity contribution of AGB stars to total luminosity of star clusters as a function of ages. In § 5, we compare our results with previous studies, and also compare the primary results with the theoretical expectation from EPS models, including the discussion of stochastic effects. Final section summarizes the main results and presents the conclusion of this study.</text>
<section_header_level_1><location><page_4><loc_46><loc_36><loc_54><loc_38></location>2. Data</section_header_level_1>
<text><location><page_4><loc_12><loc_21><loc_88><loc_34></location>Bica et al. (2008) presented an extended source catalog of the MCs including star clusters, emission nebulae, associations, and HI shells. They compiled data from various literature including the findings based on photographic survey plates. It contains center coordinates (R.A. and Declination), major and minor axes, and position angles of 3,700 star clusters of the MCs including the LMC, SMC, and the Magellanic Bridge regions. We redetermined the centers and radii of LMC star clusters based on the center coordinates presented in Bica et al. (2008).</text>
<text><location><page_4><loc_12><loc_12><loc_88><loc_19></location>We used optical ( UBVI ) and near-infrared ( JHK s ) point source catalogs of the LMC. Zaritsky et al. (2004) presented U, B, V , and I band photometry of 24,107,004 point sources in the central 64 deg 2 of the LMC from the Magellanic Clouds Photometric Survey (MCPS; Zaritsky et al. 1997). The MCPS obtained drift-scan images using 1-m Las Campanas Swope</text>
<text><location><page_5><loc_12><loc_78><loc_88><loc_86></location>Telescope and Great Circle Camera (Zaritsky et al. 1996). Their photometry is incomplete below 21.5, 23.5, 23, and 22 mag in U, B, V , and I bands in sparse regions, respectively. This catalog is used to determine center coordinates, radii, ages, and foreground reddenings of the star clusters.</text>
<text><location><page_5><loc_12><loc_59><loc_88><loc_77></location>In order to distinguish AGB stars from other populations, we used a near-infrared point source catalog from the two micron all sky survey (2MASS; Skrutskie et al. 2006). In the central 100 deg 2 region of the LMC (10 · × 10 · ), there are 1,430,676 point sources detected in the 2MASS. The limiting magnitudes of photometry are 15.8, 15.1, and 14.3 mag in J, H , and K s bands, respectively, which correspond to 10 σ point source detection level. The AGB stars in the LMC are brighter than K s ∼ 12 . 3 mag, much brighter than the limiting magnitudes. We also used 2MASS Atlas Images to estimate the integrated luminosity of the star clusters, retrieving the K s band images of our sample clusters using 2MASS interactive image service 1 .</text>
<section_header_level_1><location><page_5><loc_17><loc_53><loc_83><loc_55></location>3. Physical Parameters of LMC Star Clusters and Sample Selection</section_header_level_1>
<section_header_level_1><location><page_5><loc_25><loc_50><loc_75><loc_51></location>3.1. Center Coordinates and Sizes of Star Clusters</section_header_level_1>
<text><location><page_5><loc_12><loc_22><loc_88><loc_47></location>We determined centers for 1,645 star clusters and radii for 1,708 star clusters, respectively, using the MCPS catalog (Zaritsky et al. 2004) as a part of our study of LMC star clusters. We constructed 2-dimensional number density maps of bright stars with V < 20.5 mag around the center coordinates of the star clusters presented by Bica et al. (2008). The number density maps are smoothed with a boxcar filter whose width is 20 '' . Center coordinates, coordinate errors, and position angles of each star cluster were estimated by 2-dimensional Gaussian fitting of this smoothed number density map. The field of view for the fitting region is 3 times larger than the radius of each cluster given in Bica et al. (2008). Figure 1 shows an example of centering process for one cluster NGC 1861. We attempted 2-dimensional Gaussian fitting to 3,064 LMC star clusters in Bica et al. (2008), but stellar number density maps could obtain acceptable fits for only 1,645 star clusters. The fitting results are not reliable in the case of poor, faint, or binary clusters, in which case that the center coordinates presented by Bica et al. (2008) are adopted.</text>
<text><location><page_5><loc_12><loc_15><loc_88><loc_20></location>The radius of each cluster was determined from radial number density profiles (see Figure 2). The radial number density profile is obtained by counting point sources with V < 20.5 mag. We estimated a median value of the background number density (n bg ) of</text>
<text><location><page_6><loc_12><loc_72><loc_88><loc_86></location>stars located between 200 '' and 300 '' from the center of each cluster. The standard deviation from n bg ( σ bg ) is calculated, and the area of which number density greater than n bg +3 σ bg is considered as a cluster area. Finally, we determined radii of 1,708 LMC star clusters, and radii of the other clusters that do not show a prominent concentration are adopted from Bica et al. (2008). Most of these clusters are poor, faint, or binary ones. Bica et al. (2008) presented major and minor axes of star clusters, from which we define the radius of each star cluster as the mean value of semi-major and semi-minor axes.</text>
<text><location><page_6><loc_12><loc_57><loc_88><loc_71></location>In addition to Bica et al. (2008), Werchan & Zaritsky (2011) also presented a catalog of star clusters they found in the MCPS images. They investigated stellar overdensities in LMC fields using stars brighter than 20.5 mag in V band. By both King and Elson-FallFreeman model fitting of the surface brightness profiles of each cluster, they determined center coordinates, central surface brightness, tidal radii, and 90% enclosed luminosity radii of 1,066 LMC star clusters. We compare the center coordinates and radii determined in this study with those given by Bica et al. (2008) and Werchan & Zaritsky (2011) in Figure 3.</text>
<text><location><page_6><loc_12><loc_30><loc_93><loc_56></location>Figure 3(a) - (f) show the differences of center coordinates of star clusters among three studies. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 626, 1,645, and 677, respectively. The center coordinates of star clusters from all three different studies are mostly consistent within 10 '' . Figure 3(g) - (i) show the differences of radii of star clusters. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 615, 1,708, and 681, respectively. Werchan & Zaritsky (2011) presented four kinds of radii for each cluster, core radii and 90% enclosed luminosity radii obtained by fitting using two different models, respectively, and we adopted the 90% enclosed luminosity radius from King model fitting results as a radius to compare with the results from other studies. The values for the cluster radii derived in this study are in better agreement with Bica et al. (2008) than with Werchan & Zaritsky (2011).</text>
<section_header_level_1><location><page_6><loc_25><loc_24><loc_75><loc_26></location>3.2. Cluster Sample Selection and Age Estimation</section_header_level_1>
<text><location><page_6><loc_12><loc_13><loc_88><loc_22></location>For this study, we selected 102 star clusters that have red and bright stars in nearinfrared ( K s -( J -K s )) CMDs based on 2MASS catalog (Skrutskie et al. 2006). These stars are considered as AGB star candidates. The AGB selection method is described in § 4.1. For 96 and 83 of these star clusters, we estimated foreground reddenings and ages, respectively, with reasonable optical photometry as follows.</text>
<text><location><page_7><loc_12><loc_72><loc_88><loc_86></location>We chose member stars of each star cluster using the center coordinates and the radii estimated before (see § 3.1). The value of foreground reddening, E ( B -V ), was estimated by shifting the zero age main-sequence (ZAMS) in the (( U -B ) -( B -V )) color-color diagram (CCD). We used the bright main-sequence stars ( V /lessorsimilar 18) located in the outer region up to 200 - 300 '' of each star cluster to obtain the CCDs, and compared the sequence of stars in the CCDs with the ZAMS in the Padova models (Marigo et al. 2008) as in Figure 4(b). The errors of E ( B -V ) values are about 0.02 mag typically.</text>
<text><location><page_7><loc_12><loc_37><loc_88><loc_71></location>Figure 5(a) and (b) show ( V -( B -V )) CMDs of both a cluster and a field region for NGC 1861, as an example. The cluster CMD is expected to contain field stars as well as cluster stars. In order to minimize the field contamination, we performed statistical subtraction of field CMDs for cluster CMDs. We counted the number of stars in cluster CMDs with that of stars in field CMDs for the same area as the cluster area for each color and magnitude bin (∆( B -V ) ∼ 0 . 5 and ∆ V ∼ 1), and subtracted statistically field stars from cluster stars for each bin. Figure 5(c) displays a field-subtracted CMD of NGC 1861. It shows a clear stellar sequence with a smaller number of stars than the original CMD. We determined ages of 83 star clusters by isochrone fitting in the field-subtracted ( V -( B -V )) CMDs, assuming the distance modulus (m -M) 0 = 18.50 mag and Z = 0 . 008 . Cluster ages were derived using isochrones of Marigo et al. (2008). We used only the stars with small errors of colors with err ( B -V ) < 0 . 1 mag for isochrone fitting. The ages of the other 19 star clusters could not be derived, because they were not covered by the MCPS observation fields or are older than 1 Gyr. In this case, we adopted the ages of these clusters from the literature (Elson & Fall 1985, Girardi et al. 1995, Pietrzynski & Udalski 2000, Goudfrooij et al. 2011, Popescu et al. 2012). Table 1 lists physical parameters of 102 star clusters that will be used for AGB star selection.</text>
<text><location><page_7><loc_12><loc_10><loc_88><loc_36></location>We compared the ages derived in this study with those given in other references, Elson & Fall (1985), Pietrzynski & Udalski (2000), Hunter et al. (2003), Glatt et al. (2010), and Popescu et al. (2012), as shown in Figure 6. The isochrone fitting method used for the resolved stars in star clusters is considered to be more reliable than other age-dating methods based on the integrated color or spectra of the star clusters. Pietrzynski & Udalski (2000), Glatt et al. (2010), and this study used the isochrone fitting method, while Elson & Fall (1985), Hunter et al. (2003), and Popescu et al. (2012) analyzed the integrated color of the star clusters. Elson & Fall (1985) and Hunter et al. (2003) analyzed ( U -B ) and ( B -V ) colors of the star clusters, and Popescu et al. (2012) performed a Monte Carlo simulation with their own star cluster simulation software (MASSive CLuster Evolution and ANalysis, MASSCLEAN; Popescu & Hanson 2010) to reproduce the cluster colors, ( U -B ) 0 and ( B -V ) 0 . The ages based on the isochrone fitting method show good agreement with each other. They also show correlations with the ages based on integrated colors, but with signif-</text>
<text><location><page_8><loc_12><loc_80><loc_88><loc_86></location>icant scatters and non-unity slopes. It is noted that the ages derived from integrated colors by Popescu et al. (2012) show a better correlation with the isochrone-fitting ages, compared with other results in Elson & Fall (1985) and Hunter et al. (2003).</text>
<text><location><page_8><loc_12><loc_59><loc_89><loc_79></location>Figure 7 shows the CMDs of five star clusters that have the largest difference of ages between this study and others: SL482 (Glatt et al. 2010), NGC 1782 (Elson & Fall 1985), SL294 (Popescu et al. 2012), SL503 (Hunter et al. 2003), and H88-182 (Pietrzynski & Udalski 2000). We plotted the Padova isochrones for Z = 0 . 008 and the ages corresponding to the values derived in this study and other references. In the case of SL482, NGC 1782, and H88182, it is difficult to determine their ages reliably because the number of the brightest stars around the main-sequence turnoff is small. However, in the case of other two star clusters, SL294 and SL503, their CMDs are not matched by the isochrones for the ages derived by Popescu et al. (2012) and Hunter et al. (2003) respectively, while they are by the isochrones for the ages derived in this study.</text>
<section_header_level_1><location><page_8><loc_45><loc_53><loc_55><loc_55></location>4. Results</section_header_level_1>
<section_header_level_1><location><page_8><loc_36><loc_50><loc_64><loc_51></location>4.1. Selection of AGB Stars</section_header_level_1>
<text><location><page_8><loc_12><loc_28><loc_88><loc_47></location>While it is difficult to distinguish AGB stars from RGB stars in optical CMDs, it is relatively easier in near-infrared CMDs. Therefore, we plotted the near-infrared ( K s, 0 -( J -K s ) 0 ) CMDs of resolved stars in 102 star clusters using the 2MASS point source catalog (Skrutskie et al. 2006), and selected AGB stars using two criteria: (1) stars brighter than the tip of the RGB (TRGB); K s, 0 < 12 . 3, and (2) stars redder than the RGB; ( J -K s ) 0 > -0 . 075 × K s, 0 +1 . 85. We adopted the TRGB magnitude, K s = 12.3 ± 0.1 estimated from 2MASS point sources in the LMC region (Nikolaev & Weinberg 2000). The second criterion was suggested from the analysis of the 2MASS photometry for LMC stars by Cioni et al. (2006). There is no constraint for the brightest and reddest stars. We use the extinction law in Cardelli et al. (1989) to derive extinction values for each band, adopting R V = 3 . 1.</text>
<text><location><page_8><loc_12><loc_11><loc_88><loc_26></location>Figure 8(b) and (d) show the combined ( K s, 0 -( J -K s ) 0 ) CMDs of all stars in 41 young star clusters with log(age) < 8 . 5 and 61 old star clusters with log(age) ≥ 8 . 5, respectively. We selected the AGB stars brighter and redder than AGB boundary lines as described above (dashed lines). We also plotted other AGB boundaries used in the references in Figure 8(b) and (d): dot-dashed lines used by Mucciarelli et al. (2006) and gray shaded regions used by Nikolaev & Weinberg (2000). The AGB boundary used in this study is working in the similar way to that in Nikolaev & Weinberg (2000). However, the AGB boundary used by Mucciarelli et al. (2006) includes a significant number of bluer stars, compared with that in</text>
<text><location><page_9><loc_12><loc_85><loc_55><loc_86></location>this study. This difference will be discussed in § 5.1.</text>
<section_header_level_1><location><page_9><loc_12><loc_76><loc_88><loc_80></location>4.2. Measurement of K s Band Luminosity Fraction of the AGB Population in Star Clusters</section_header_level_1>
<text><location><page_9><loc_12><loc_55><loc_88><loc_74></location>We estimated the K s band luminosity of star clusters by aperture photometry using 2MASS K s band images. Photometry was performed with IRAF 2 APPHOT package. For background estimation we used annular apertures with the inner radius to be the sum of the star cluster radius and its error and the aperture width of 10 '' . The background level was estimated using the mode value of the annulus region. For cluster photometry we used circular apertures with radius that is the same as the cluster radius. Figure 9 displays a K s band image of an example star cluster, NGC 1861, showing the position of apertures for the cluster and background area. We calculated the K s band luminosity of AGB stars in each cluster by summing their luminosity converted from 2MASS magnitudes, and obtained the K s band luminosity fraction of AGB stars in the star clusters.</text>
<text><location><page_9><loc_12><loc_40><loc_88><loc_53></location>Table 2 summarizes the properties of AGB populations as well as other basic parameters of 102 LMC star clusters. It lists the number of AGB stars, and the K s band luminosity and luminosity fraction of AGB stars in each cluster, as well as K s band integrated magnitude and luminosity of the star clusters. The magnitudes are based on 2MASS magnitude system. We adopted the K s band absolute magnitude M K s /circledot = 3 . 27 mag for the Sun, using M V /circledot = 3 . 83 mag (Allen 1976) and ( V -K s ) = 1 . 56 mag (Casagrande et al. 2012), to convert the magnitude into the luminosity.</text>
<text><location><page_9><loc_12><loc_19><loc_88><loc_38></location>The error of the AGB luminosity fraction is contributed by various errors in addition to the photometric ones estimated for the integrated magnitude of star clusters and presented for the 2MASS magnitude of AGB stars. First, there exist the errors of center coordinates and radii of star clusters, influencing the estimation of their integrated luminosity. We performed aperture photometry for all sample clusters, setting different center positions and radii according to their errors. We selected the upper and lower errors of the integrated luminosity of star clusters, also considering photometric errors. Secondly, there are the errors for the luminosity of AGB stars, which consist of (a) 2MASS photometric error for individual AGB stars and (b) the uncertainty from the Poisson error for the number of AGB stars in each star cluster associated with AGB star counts. Of these two, the latter is much larger</text>
<text><location><page_10><loc_12><loc_74><loc_88><loc_86></location>than the former. The AGB luminosity error from Poisson error is calculated by multiplying the square root of the number of AGB stars by the mean luminosity for an AGB star in each cluster. We tabulated upper and lower errors of the K s band luminosity fraction obtained by error propagation, considering overall error budget mentioned above (see Table 2). Note that the smaller the numbers of AGB stars in star clusters are, the larger the errors of the luminosity fraction are.</text>
<text><location><page_10><loc_12><loc_57><loc_88><loc_73></location>Additionally, we checked the field contamination in AGB star count. We investigated the outer region of each star cluster with the radius five times larger than the cluster radius. The number of the AGB stars in this field region is normalized to the cluster area. We calculated the amount of field contamination by multiplying the mean luminosity of AGB stars in star clusters by the number of the normalized field AGB stars, and subtracted it from the luminosity of AGB stars in star clusters. However, the effect of the field contamination to estimating the luminosity fraction of AGB stars is much smaller than that of the Poisson error of the AGB star count. These field-subtracted values are also listed in Table 2.</text>
<text><location><page_10><loc_12><loc_32><loc_88><loc_56></location>Figure 10(a) shows the K s band luminosity fraction of AGB stars in our sample clusters as a function of ages. Figure 10(b) displays the mean values of the K s band luminosity fraction of AGB stars in the star clusters. These values are also listed in Table 3 including the field-subtracted values. The mean values represent the ratios of the total K s band luminosity of AGB stars in the star clusters to the total K s band luminosity of the star clusters for each age bin. The error of mean values is calculated from the individual errors of the star clusters by error propagation. We also derived a sequence to represent approximately the sequence of bright clusters, as plotted in the figure. The bright clusters have the luminosity of L K s > 8 . 5 × 10 4 L /circledot . Following features are noted in Figure 10. First, the mean values and the bright cluster sequence increase, as log(age) increases from 8.0 to 8.5, reaching 0.6 and 0.8 at log(age) ∼ 8 . 5, respectively. They decrease thereafter. Second, there is a large scatter in the mean values for given ages. We discuss these features in § 5.2.2 in detail.</text>
<section_header_level_1><location><page_10><loc_43><loc_26><loc_57><loc_28></location>5. Discussion</section_header_level_1>
<section_header_level_1><location><page_10><loc_31><loc_23><loc_69><loc_24></location>5.1. Comparison with Previous Studies</section_header_level_1>
<text><location><page_10><loc_12><loc_11><loc_93><loc_20></location>In Figure 10(b), we also plotted the results for 19 LMC star clusters given by Mucciarelli et al. (2006) for comparison. There are 12 star clusters common between this study and Mucciarelli et al. (2006). We determined foreground reddenings of six star clusters (NGC 1806, NGC 1866, NGC 1987, NGC 2108, NGC 2134, and NGC 2136) by using the method mentioned above (see § 3.2). For the other three star clusters(NGC 1831, NGC 2173, and NGC 2249), the field</text>
<text><location><page_11><loc_12><loc_66><loc_88><loc_86></location>stars were not covered by the MCPS. In this case, we adopted foreground reddening values from the optical reddening map of the MCs given by Haschke et al. (2011). Haschke et al. (2011) presented the optical reddening map of the MCs obtained by comparing the theoretical color of the red clump with its observed one based on the OGLE III data. The reddening values of the others (NGC 2162, NGC 2190, and NGC 2231) could not be determined neither in this study nor in Haschke et al. (2011). We assumed the typical extinction value, E ( B -V ) = 0 . 1, for these three clusters. For ages, we determined ages of three of these clusters (NGC 1866, NGC 2134, and NGC 2136). The ages of the others are adopted from Elson & Fall (1985) and Girardi et al. (1995), because we could not use the MCPS catalog for these clusters.</text>
<text><location><page_11><loc_12><loc_41><loc_88><loc_65></location>We also noticed that the AGB selection criteria of Mucciarelli et al. (2006) are different from those of this study (see Figure 8). Mucciarelli et al. (2006) included as AGB candidates the blue stars that are excluded in this study, but the color and magnitude of these stars indicate that they are bright RGB and supergiant populations according to the analysis of Nikolaev & Weinberg (2000). The color distribution of the stars brighter than K s = 12.3 for young star clusters with log(age) < 8.5 shows a blue excess at ( J -K s ) 0 < 1 . 0 (see Figure 8(a)), while little blue excess is seen for the case of old star clusters with log(age) > 8.5 (see Figure 8(c)). However, those blue stars used in the analysis of Mucciarelli et al. (2006) do not significantly influence the luminosity fraction of AGB stars in the star clusters, because they are somewhat faint (see Figure 11). In addition, there are three red stars not included in the AGB boundary of Mucciarelli et al. (2006) but contained in that of this study, which can be dusty AGB stars. We found that these stars affect little our results.</text>
<text><location><page_11><loc_12><loc_34><loc_92><loc_40></location>The number of AGB stars shows a large discrepancy between our results and Mucciarelli et al. (2006) for the young star clusters as shown in Figure 11(a), but the difference in the luminosity fraction of AGB stars in the star clusters is much smaller as shown in Figure 11(b).</text>
<text><location><page_11><loc_12><loc_19><loc_88><loc_33></location>In Figure 10(b), the results for 19 star clusters from Mucciarelli et al. (2006) are included, and those derived in this study are also plotted for four star clusters that show a large discrepancy ( > 0.2) in the AGB luminosity fraction (see Figure 11(b)). Other eight clusters show the consistent results with Mucciarelli et al. (2006). Most of these clusters studied by Mucciarelli et al. (2006) are brighter than L K s = 10 5 L /circledot , except for two star clusters, NGC 2249 and NGC 2231. Indeed they are following the bright cluster sequence derived in this study, with some scatter.</text>
<section_header_level_1><location><page_12><loc_33><loc_85><loc_67><loc_86></location>5.2. Comparison with SSP Models</section_header_level_1>
<section_header_level_1><location><page_12><loc_28><loc_81><loc_72><loc_82></location>5.2.1. Mock Cluster Experiments with SSP models</section_header_level_1>
<text><location><page_12><loc_12><loc_57><loc_88><loc_79></location>We compare our results with the expectation of five theoretical models: (1) an EPS model of Maraston (2005) (called Maraston model), (2) a model based on the isochrone set of Girardi et al. (2002) (called Padova02 model), (3) a model based on the improved isochrone set of Marigo et al. (2008) corrected by Girardi et al. (2010) (called Padova10 model), (4) a model based on the isochrone set of Pietrinferni et al. (2004, 2006) assuming a given overshooting efficiency (called BaSTI os model), and (5) the same as (4), but for null overshooting efficiency (called BaSTI std model). The Maraston model calculates the luminosity contribution of AGB stars directly using the fuel consumption approach. Girardi et al. (2002) and Marigo et al. (2008) corrected by Girardi et al. (2010) presented theoretical stellar evolutionary tracks and isochrones used in various EPS models. The detailed information of these models is described as follows.</text>
<text><location><page_12><loc_12><loc_46><loc_88><loc_56></location>The Maraston model calculated the amount of the fuel consumption of each population in the post-main-sequence phases (Renzini & Buzzoni 1986) directly, and converted it to observables assuming the effective temperature and surface gravity for evolutionary stages. We obtained the Maraston model prediction for the luminosity contribution of AGB stars in SSPs as a function of ages (Mucciarelli et al. 2006).</text>
<text><location><page_12><loc_12><loc_35><loc_89><loc_45></location>The theoretical isochrones of Girardi et al. (2002) are based on isochrones of Girardi et al. (2000) for low- and intermediate-mass stars (M ≤ 7 M /circledot ) and Bertelli et al. (1994) for highmass stars (M > 7 M /circledot ). Note that stellar evolutionary tracks of Girardi et al. (2000) are adopted in the BC03 model. In this model, they included the simplified TP-AGB phase and no circumstellar dust that form in AGB stars.</text>
<text><location><page_12><loc_12><loc_14><loc_88><loc_34></location>Marigo et al. (2008) presented optical to far-infrared isochrones with improved TP-AGB models. Girardi et al. (2010) searched for the TP-AGB population of 12 galaxies in the ACS Nearby Galaxy Survey Treasury, and found that the model of Marigo et al. (2008) creates more TP-AGB populations than observed ones. They corrected the mass-loss rate of TPAGB stars in this model by reducing their lifetime (Bowen & Willson 1991, Willson 2000). This model reproduces the number of TP-AGB stars well, but still has uncertainties in their 1.6 µ m band flux contribution (Melbourne et al. 2012). Additionally, we adopted the isochrone set that includes the circumstellar dust from AGB stars (Groenewegen 2006) and assumed that the dust composition is 100% silicate and 100% amorphous carbonate dust for O-rich and C-rich AGB stars, respectively.</text>
<text><location><page_12><loc_16><loc_11><loc_88><loc_13></location>These two kinds of Padova isochrones consider the core convective overshooting. In</text>
<text><location><page_13><loc_12><loc_70><loc_88><loc_86></location>order to investigate this effect, we used the BaSTI isochrone dataset (Pietrinferni et al. 2004, 2006) without overshooting efficiency. We selected a scaled solar isochrone set that contains the extended AGB population. We calculated the predicted K s band luminosity fraction of AGB stars in SSPs by analyzing the mock star clusters produced from the isochrones of Girardi et al. (2002), Marigo et al. (2008), and Pietrinferni et al. (2004). We used the isochrone sets with metallicity Z = 0.008, corresponding to [Z/H] ∼ -0.35 for mock cluster experiments. This value is close to the mean value for the LMC, for our cluster samples. The method is described as follows.</text>
<text><location><page_13><loc_12><loc_41><loc_88><loc_69></location>We created model stars in mock star clusters assuming the Salpeter initial mass function, and assigned J and K s magnitudes to each star using four different isochrone sets. In addition, we considered magnitude errors for each star in order to make the model prediction more realistic. In the 2MASS catalog, mean magnitude errors and error variances of stars in each magnitude bin vary as a function of magnitudes. We assumed that photometric errors of model stars are distributed normally with the mean value and the variance according to magnitude bins. In ( K s, 0 -( J -K s ) 0 ) CMDs of model stars in mock star clusters with empirical magnitude errors, AGB stars are selected with the same criteria as done for observational data (see § 4.1). The K s band luminosities of mock star clusters and AGB stars are calculated by summing the K s band luminosity of member stars and AGB stars, respectively. Note that for the BaSTI models, they do not provide the magnitudes of 2MASS filter system, so that we adopted those of the Bessell filter system. Finally, we obtained the K s band luminosity fraction of AGB stars in mock star clusters with three different mass (10 4 , 10 5 , and 10 6 M /circledot ), assuming 15 different ages (8.0 ≤ log(age) ≤ 9.5) for each mass scale.</text>
<section_header_level_1><location><page_13><loc_24><loc_35><loc_76><loc_37></location>5.2.2. Stochastic Effect in Estimating Light from AGB Stars</section_header_level_1>
<text><location><page_13><loc_12><loc_18><loc_88><loc_33></location>Stochastic effects are inevitable in AGB star counts because of the short lifetime of AGB stars. In Figure 10(a), there is a large scatter in the K s band luminosity fraction of AGB stars in the star clusters derived in this study. The AGB stars evolve fast, and become blue and faint when they enter the post-AGB phase. Therefore, we cannot detect all stars that have entered the AGB phase. As a result it makes the luminosity fraction of AGB stars in star clusters lower than expected. Especially, this effect becomes significant for faint star clusters, because of a smaller number of stars. Bright star clusters (L K s tot /greaterorsimilar 8 . 5 × 10 4 L /circledot ) show relatively smaller scatters and seem to be located along a sequence.</text>
<text><location><page_13><loc_12><loc_11><loc_88><loc_16></location>This trend also appears in the mock star clusters (see Figure 12). We made mock star clusters with 15 different ages and three different masses using four different isochrone sets as above. For each age and mass bin, we made 10 mock star clusters in order to analyze</text>
<text><location><page_14><loc_12><loc_72><loc_88><loc_86></location>them statistically. Figure 12 shows the K s band luminosity fraction of AGB stars in the mock star clusters as a function of ages. In this figure, the most massive mock star clusters with M = 10 6 M /circledot show the smallest scatter among mock clusters with other mass scale, and make a well-defined sequence (shaded region). However, mock star clusters with M = 10 5 M /circledot (circles) are distributed with large scatter from the massive mock cluster sequence. Therefore we presented two representatives for the observational data: mean values and the bright cluster sequence.</text>
<section_header_level_1><location><page_14><loc_32><loc_66><loc_68><loc_68></location>5.2.3. Comparison with Model Expectation</section_header_level_1>
<text><location><page_14><loc_12><loc_22><loc_88><loc_64></location>Figure 13 shows a comparison of our results and those expected from five models. In the case of Padova and BaSTI models, we adopted the mean locus line of the massive mock star clusters presented in Figure 12. Note that the Padova02 and BaSTI os models show almost same results of AGB luminosity evolution in SSPs. It reflects that the Padova models include the same ingredients as the BaSTI os model in terms of the core overshooting. Except for these two models, there are several differences in model expectations. First, peak values of the luminosity contribution of AGB stars expected in models are different. The Maraston and Padova10 models suggest 0.7 - 0.8 for the value of the highest AGB fraction, while other three models (Padova02, BaSTI std, and BaSTI os) do just up to ∼ 0.6. Second, all models expect peak values at the similar age range with log(age) ∼ 8.6 - 8.8, except for the BaSTI std model. The peak position of the BaSTI model expectation lies at slightly younger age compared with the expectation of other models. It is because the null overshooting efficiency leads to the shorter lifetime of main-sequence stars. Third, both young and old parts are different between the Maraston model and other models. Padova02, Padova10, and BaSTI os models show that the AGB luminosity fraction in SSPs is lowest at log(age) ∼ 8.0 and increases continuously up to the highest value as SSPs are getting older, while the Maraston model suggests that it comes up to already ∼ 0.4 at log(age) = 8.0 - 8.3 and increases drastically afterwards. The BaSTI std model, however, expects higher AGB luminosity contribution than any other models at log(age) ∼ 8.0 as mentioned above. In the case of SSPs older than 1 Gyr, the AGB luminosity contribution decreases in all models, but the Maraston model shows the steepest decrease.</text>
<text><location><page_14><loc_12><loc_11><loc_88><loc_21></location>The bright cluster sequence represents well-populated systems that are less influenced by the stochastic fluctuation than faint star clusters, so that it is more appropriate to compare with the expectation of SSP models. In Figure 13, we notice two points with regard to the comparison between the bright cluster sequence and the model expectation: (1) the maximum value of the bright cluster sequence and (2) the age range corresponding to the</text>
<text><location><page_15><loc_12><loc_74><loc_88><loc_86></location>maximum AGB luminosity contribution. First, the peak value of the AGB luminosity contribution for bright clusters is up to 0.7 - 0.8. Only two models, Maraston and Padova10 models, reproduce this maximum value. Second, the peak position for the bright cluster sequence appears at log(age) = 8.5 - 8.7, which is slightly younger than for model predictions (log(age) = 8.6 - 8.8). However, this discrepancy is not significant because the errors of ages are around 0.1.</text>
<section_header_level_1><location><page_15><loc_17><loc_68><loc_83><loc_70></location>5.3. Implication for the study of size and mass evolution of galaxies</section_header_level_1>
<text><location><page_15><loc_12><loc_39><loc_88><loc_66></location>The calibration of the EPS models influences galaxy studies because the determination of physical parameters of galaxies depends on the amount of the AGB near-infrared luminosity contribution in EPS models. The difference between the AGB luminosity fractions expected by Padova02 and Maraston models is largest at log(age) ∼ 8.7 - 8.9 (age ∼ 0.5 - 0.8 Gyr), as shown Figure 13. This indicates that the differences of galaxy mass estimates based on the EPS models can be significant at this age range. This can be important for galaxies with young stellar ages, such as high-redshift ( z ≥ 2 - 3) or post-starburst galaxies. In these kinds of galaxies, the young stellar component with ages ∼ 1 Gyr is dominant. For example, Raichoor et al. (2011) presented SED fitting results of 79 early-type galaxies at z ∼ 1.3, finding the differences in stellar ages and masses of galaxies estimated with the BC03 and Maraston models, respectively. They showed that the masses of galaxies derived with the Maraston model tend to be lower than those estimated with the BC03 model, and this discrepancy is prominent (by a factor of two) at galaxy ages ∼ 1.0 - 1.3 Gyr with uncertainty of ∼ 1.0 - 1.5 Gyr (see Figure 5 in Raichoor et al. 2011).</text>
<text><location><page_15><loc_12><loc_22><loc_88><loc_37></location>Muzzin et al. (2009) reported how the galaxy evolution process depends on EPS models. They investigated the size and mass growth of high-redshift galaxies ( z ∼ 2.3). From the galaxy mass differences based on the EPS models, they found that the galaxy size growth from z ∼ 2.3 to z = 0 is faster in the case of the BC03 model than the case of the Maraston model, assuming that the mass growth rate is same in these two cases. Thus, the sizemass relation of galaxies can be influenced by the AGB luminosity contribution in each EPS model. Our results of the bright cluster sequence are closer to the Maraston model so that they support the size-mass relation of galaxies derived with this model.</text>
<section_header_level_1><location><page_16><loc_36><loc_85><loc_64><loc_86></location>6. Summary and Conclusion</section_header_level_1>
<text><location><page_16><loc_12><loc_55><loc_88><loc_82></location>We investigated the K s band luminosity evolution of the AGB population in SSPs using 102 LMC star clusters. First, we determined ages and foreground reddening of star clusters from the UBV photometry in the MCPS (Zaritsky et al. 2004) using Padova isochrones (Marigo et al. 2008). Then AGB stars in each cluster were selected using 2MASS ( K s -( J -K s )) CMDs. We derived the K s band luminosity fraction of AGB stars in 102 star clusters as a function of ages. The K s band luminosity fraction of AGB stars in star clusters increases as age increases from log(age) ∼ 8.0. It reaches a maximum up to ∼ 0.6 for mean values and ∼ 0.8 for bright cluster sequences at log(age) ∼ 8.5, and decreases afterwards. The AGB luminosity fraction for given ages shows a large scatter caused by stochastic effects. We compared our results with five SSP models: Padova02, Padova10, Maraston, BaSTI std, and BaSTI os models. It is found that the only two models (Padova10 and Maraston models) match approximately the observational K s band AGB luminosity contribution of bright star clusters derived in this study, while other models predict the AGB luminosity contribution much lower.</text>
<text><location><page_16><loc_12><loc_48><loc_88><loc_51></location>This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 2012R1A4A1028713).</text>
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<table>
<location><page_20><loc_16><loc_45><loc_84><loc_60></location>
<caption>Table 1. Physical parameters of 102 star clusters in the LMC</caption>
</table>
<text><location><page_20><loc_16><loc_37><loc_84><loc_40></location>Note. - Table 1 is published in its entirety in the electronic edition. The five sample star clusters are shown here regarding its form and content.</text>
<text><location><page_21><loc_15><loc_64><loc_17><loc_64></location>r</text>
<text><location><page_21><loc_21><loc_89><loc_23><loc_89></location>)</text>
<text><location><page_21><loc_21><loc_88><loc_23><loc_89></location>t</text>
<text><location><page_21><loc_21><loc_87><loc_23><loc_88></location>e</text>
<text><location><page_21><loc_21><loc_87><loc_23><loc_87></location>n</text>
<text><location><page_21><loc_21><loc_86><loc_23><loc_87></location>(</text>
<text><location><page_21><loc_22><loc_85><loc_22><loc_86></location>s</text>
<text><location><page_21><loc_21><loc_85><loc_22><loc_85></location>K</text>
<text><location><page_21><loc_22><loc_85><loc_23><loc_86></location>t</text>
<text><location><page_21><loc_22><loc_85><loc_23><loc_85></location>o</text>
<text><location><page_21><loc_22><loc_82><loc_23><loc_82></location>G</text>
<text><location><page_21><loc_22><loc_81><loc_23><loc_82></location>A</text>
<paragraph><location><page_21><loc_21><loc_82><loc_42><loc_85></location>B / L t .4 1 8 2 0 ± .6 6 0 .5 6 7 .3 3 6 m a n</paragraph>
<text><location><page_21><loc_22><loc_82><loc_22><loc_82></location>s</text>
<text><location><page_21><loc_21><loc_81><loc_22><loc_82></location>K</text>
<text><location><page_21><loc_21><loc_80><loc_23><loc_81></location>L</text>
<text><location><page_21><loc_21><loc_63><loc_22><loc_63></location>4</text>
<text><location><page_21><loc_21><loc_62><loc_23><loc_63></location>0</text>
<text><location><page_21><loc_21><loc_62><loc_23><loc_62></location>1</text>
<text><location><page_21><loc_21><loc_61><loc_23><loc_62></location>(</text>
<text><location><page_21><loc_22><loc_60><loc_23><loc_61></location>B</text>
<text><location><page_21><loc_41><loc_90><loc_42><loc_90></location>.</text>
<text><location><page_21><loc_41><loc_89><loc_42><loc_90></location>t</text>
<text><location><page_21><loc_41><loc_89><loc_42><loc_89></location>n</text>
<text><location><page_21><loc_41><loc_88><loc_42><loc_89></location>e</text>
<text><location><page_21><loc_41><loc_88><loc_42><loc_88></location>t</text>
<text><location><page_21><loc_41><loc_87><loc_42><loc_88></location>n</text>
<text><location><page_21><loc_41><loc_86><loc_42><loc_87></location>o</text>
<text><location><page_21><loc_41><loc_86><loc_42><loc_86></location>c</text>
<text><location><page_21><loc_41><loc_85><loc_42><loc_85></location>d</text>
<text><location><page_21><loc_41><loc_82><loc_42><loc_82></location>r</text>
<text><location><page_21><loc_41><loc_81><loc_42><loc_82></location>o</text>
<text><location><page_21><loc_41><loc_80><loc_42><loc_81></location>f</text>
<table>
<location><page_21><loc_10><loc_64><loc_90><loc_81></location>
</table>
<text><location><page_21><loc_15><loc_63><loc_17><loc_64></location>e</text>
<text><location><page_21><loc_15><loc_62><loc_17><loc_63></location>t</text>
<text><location><page_21><loc_15><loc_62><loc_17><loc_63></location>s</text>
<text><location><page_21><loc_15><loc_61><loc_17><loc_62></location>lu</text>
<text><location><page_21><loc_15><loc_60><loc_17><loc_61></location>c</text>
<text><location><page_21><loc_25><loc_63><loc_27><loc_64></location>±</text>
<text><location><page_21><loc_25><loc_62><loc_27><loc_63></location>4</text>
<text><location><page_21><loc_25><loc_61><loc_27><loc_62></location>.4</text>
<text><location><page_21><loc_25><loc_60><loc_27><loc_61></location>1</text>
<text><location><page_21><loc_27><loc_63><loc_29><loc_64></location>±</text>
<text><location><page_21><loc_27><loc_62><loc_29><loc_63></location>0</text>
<text><location><page_21><loc_27><loc_61><loc_29><loc_62></location>.4</text>
<text><location><page_21><loc_27><loc_60><loc_29><loc_61></location>3</text>
<text><location><page_21><loc_29><loc_63><loc_31><loc_64></location>±</text>
<text><location><page_21><loc_29><loc_62><loc_31><loc_63></location>9</text>
<text><location><page_21><loc_29><loc_61><loc_31><loc_62></location>.9</text>
<text><location><page_21><loc_29><loc_60><loc_31><loc_61></location>2</text>
<text><location><page_21><loc_32><loc_63><loc_33><loc_64></location>±</text>
<text><location><page_21><loc_31><loc_62><loc_33><loc_63></location>0</text>
<text><location><page_21><loc_31><loc_61><loc_33><loc_62></location>.3</text>
<text><location><page_21><loc_31><loc_60><loc_33><loc_61></location>3</text>
<text><location><page_21><loc_34><loc_63><loc_35><loc_64></location>±</text>
<text><location><page_21><loc_34><loc_62><loc_35><loc_63></location>7</text>
<text><location><page_21><loc_34><loc_61><loc_35><loc_62></location>.7</text>
<text><location><page_21><loc_34><loc_60><loc_35><loc_61></location>7</text>
<text><location><page_21><loc_41><loc_63><loc_42><loc_64></location>r</text>
<text><location><page_21><loc_41><loc_63><loc_42><loc_63></location>e</text>
<text><location><page_21><loc_41><loc_62><loc_42><loc_63></location>t</text>
<text><location><page_21><loc_41><loc_62><loc_42><loc_62></location>s</text>
<text><location><page_21><loc_41><loc_61><loc_42><loc_62></location>lu</text>
<text><location><page_21><loc_41><loc_60><loc_42><loc_61></location>c</text>
<text><location><page_21><loc_41><loc_60><loc_42><loc_60></location>r</text>
<text><location><page_21><loc_15><loc_55><loc_42><loc_60></location>0 2 s t a r ) L K s A G m p le s t a</text>
<text><location><page_21><loc_25><loc_54><loc_27><loc_55></location>9</text>
<text><location><page_21><loc_25><loc_53><loc_27><loc_54></location>.5</text>
<text><location><page_21><loc_25><loc_53><loc_27><loc_53></location>1</text>
<text><location><page_21><loc_25><loc_51><loc_27><loc_52></location>±</text>
<text><location><page_21><loc_25><loc_50><loc_27><loc_51></location>9</text>
<text><location><page_21><loc_25><loc_49><loc_27><loc_50></location>.5</text>
<text><location><page_21><loc_25><loc_49><loc_27><loc_49></location>1</text>
<text><location><page_21><loc_25><loc_45><loc_27><loc_45></location>0</text>
<text><location><page_21><loc_25><loc_44><loc_27><loc_45></location>.1</text>
<text><location><page_21><loc_25><loc_43><loc_27><loc_44></location>0</text>
<text><location><page_21><loc_25><loc_39><loc_27><loc_39></location>1</text>
<text><location><page_21><loc_25><loc_34><loc_26><loc_34></location>5</text>
<text><location><page_21><loc_25><loc_33><loc_26><loc_34></location>5</text>
<text><location><page_21><loc_25><loc_33><loc_26><loc_33></location>.</text>
<text><location><page_21><loc_25><loc_32><loc_26><loc_33></location>0</text>
<text><location><page_21><loc_25><loc_32><loc_26><loc_32></location>+</text>
<text><location><page_21><loc_26><loc_34><loc_27><loc_34></location>6</text>
<text><location><page_21><loc_26><loc_33><loc_27><loc_34></location>3</text>
<text><location><page_21><loc_26><loc_33><loc_27><loc_33></location>.</text>
<text><location><page_21><loc_26><loc_32><loc_27><loc_33></location>0</text>
<text><location><page_21><loc_26><loc_32><loc_27><loc_32></location>-</text>
<text><location><page_21><loc_25><loc_31><loc_27><loc_31></location>4</text>
<text><location><page_21><loc_25><loc_30><loc_27><loc_31></location>.4</text>
<text><location><page_21><loc_25><loc_29><loc_27><loc_30></location>3</text>
<text><location><page_21><loc_25><loc_26><loc_27><loc_26></location>7</text>
<text><location><page_21><loc_25><loc_25><loc_27><loc_26></location>2</text>
<text><location><page_21><loc_25><loc_24><loc_27><loc_25></location>.0</text>
<text><location><page_21><loc_25><loc_23><loc_27><loc_24></location>0</text>
<text><location><page_21><loc_25><loc_22><loc_27><loc_23></location>±</text>
<text><location><page_21><loc_25><loc_21><loc_27><loc_22></location>9</text>
<text><location><page_21><loc_25><loc_20><loc_27><loc_21></location>2</text>
<text><location><page_21><loc_25><loc_19><loc_27><loc_20></location>.4</text>
<text><location><page_21><loc_25><loc_19><loc_27><loc_19></location>0</text>
<text><location><page_21><loc_25><loc_18><loc_27><loc_19></location>1</text>
<text><location><page_21><loc_25><loc_12><loc_27><loc_13></location>8</text>
<text><location><page_21><loc_25><loc_11><loc_27><loc_12></location>L</text>
<text><location><page_21><loc_25><loc_11><loc_27><loc_11></location>S</text>
<text><location><page_21><loc_27><loc_54><loc_29><loc_55></location>7</text>
<text><location><page_21><loc_27><loc_53><loc_29><loc_54></location>.6</text>
<text><location><page_21><loc_27><loc_53><loc_29><loc_53></location>2</text>
<text><location><page_21><loc_27><loc_51><loc_29><loc_52></location>±</text>
<text><location><page_21><loc_27><loc_50><loc_29><loc_51></location>8</text>
<text><location><page_21><loc_27><loc_49><loc_29><loc_50></location>.7</text>
<text><location><page_21><loc_27><loc_49><loc_29><loc_49></location>3</text>
<text><location><page_21><loc_27><loc_45><loc_29><loc_45></location>0</text>
<text><location><page_21><loc_27><loc_44><loc_29><loc_45></location>.2</text>
<text><location><page_21><loc_27><loc_43><loc_29><loc_44></location>0</text>
<text><location><page_21><loc_27><loc_39><loc_29><loc_39></location>2</text>
<text><location><page_21><loc_27><loc_34><loc_28><loc_35></location>2</text>
<text><location><page_21><loc_27><loc_34><loc_28><loc_34></location>5</text>
<text><location><page_21><loc_27><loc_33><loc_28><loc_34></location>.</text>
<text><location><page_21><loc_27><loc_33><loc_28><loc_33></location>0</text>
<text><location><page_21><loc_27><loc_32><loc_28><loc_33></location>+</text>
<text><location><page_21><loc_28><loc_34><loc_29><loc_35></location>7</text>
<text><location><page_21><loc_28><loc_34><loc_29><loc_34></location>7</text>
<text><location><page_21><loc_28><loc_33><loc_29><loc_34></location>.</text>
<text><location><page_21><loc_28><loc_33><loc_29><loc_33></location>0</text>
<text><location><page_21><loc_28><loc_32><loc_29><loc_33></location>-</text>
<text><location><page_21><loc_27><loc_31><loc_29><loc_32></location>9</text>
<text><location><page_21><loc_27><loc_30><loc_29><loc_31></location>.4</text>
<text><location><page_21><loc_27><loc_29><loc_29><loc_30></location>5</text>
<text><location><page_21><loc_27><loc_29><loc_29><loc_29></location>1</text>
<text><location><page_21><loc_27><loc_25><loc_29><loc_26></location>9</text>
<text><location><page_21><loc_27><loc_25><loc_29><loc_25></location>0</text>
<text><location><page_21><loc_27><loc_24><loc_29><loc_25></location>.0</text>
<text><location><page_21><loc_27><loc_23><loc_29><loc_24></location>0</text>
<text><location><page_21><loc_27><loc_22><loc_29><loc_23></location>±</text>
<text><location><page_21><loc_27><loc_21><loc_29><loc_21></location>5</text>
<text><location><page_21><loc_27><loc_20><loc_29><loc_21></location>9</text>
<text><location><page_21><loc_27><loc_19><loc_29><loc_20></location>.7</text>
<text><location><page_21><loc_27><loc_18><loc_29><loc_19></location>8</text>
<text><location><page_21><loc_27><loc_16><loc_29><loc_17></location>3</text>
<text><location><page_21><loc_27><loc_15><loc_29><loc_16></location>9</text>
<text><location><page_21><loc_27><loc_15><loc_29><loc_15></location>6</text>
<text><location><page_21><loc_27><loc_14><loc_29><loc_15></location>1</text>
<text><location><page_21><loc_27><loc_13><loc_29><loc_14></location>C</text>
<text><location><page_21><loc_27><loc_12><loc_29><loc_13></location>G</text>
<text><location><page_21><loc_27><loc_11><loc_29><loc_12></location>N</text>
<text><location><page_21><loc_29><loc_54><loc_31><loc_55></location>9</text>
<text><location><page_21><loc_29><loc_53><loc_31><loc_54></location>.4</text>
<text><location><page_21><loc_29><loc_53><loc_31><loc_53></location>3</text>
<text><location><page_21><loc_29><loc_51><loc_31><loc_52></location>±</text>
<text><location><page_21><loc_29><loc_50><loc_31><loc_51></location>9</text>
<text><location><page_21><loc_29><loc_49><loc_31><loc_50></location>.4</text>
<text><location><page_21><loc_29><loc_49><loc_31><loc_49></location>3</text>
<text><location><page_21><loc_29><loc_45><loc_31><loc_45></location>4</text>
<text><location><page_21><loc_29><loc_44><loc_31><loc_45></location>.1</text>
<text><location><page_21><loc_29><loc_43><loc_31><loc_44></location>0</text>
<text><location><page_21><loc_29><loc_39><loc_31><loc_39></location>1</text>
<text><location><page_21><loc_29><loc_34><loc_30><loc_34></location>5</text>
<text><location><page_21><loc_29><loc_33><loc_30><loc_34></location>1</text>
<text><location><page_21><loc_29><loc_33><loc_30><loc_33></location>.</text>
<text><location><page_21><loc_29><loc_32><loc_30><loc_33></location>0</text>
<text><location><page_21><loc_29><loc_32><loc_30><loc_32></location>+</text>
<text><location><page_21><loc_30><loc_34><loc_31><loc_34></location>8</text>
<text><location><page_21><loc_30><loc_33><loc_31><loc_34></location>0</text>
<text><location><page_21><loc_30><loc_33><loc_31><loc_33></location>.</text>
<text><location><page_21><loc_30><loc_32><loc_31><loc_33></location>0</text>
<text><location><page_21><loc_30><loc_32><loc_31><loc_32></location>-</text>
<text><location><page_21><loc_29><loc_31><loc_31><loc_31></location>3</text>
<text><location><page_21><loc_29><loc_30><loc_31><loc_31></location>.5</text>
<text><location><page_21><loc_29><loc_29><loc_31><loc_30></location>4</text>
<text><location><page_21><loc_29><loc_26><loc_31><loc_26></location>5</text>
<text><location><page_21><loc_29><loc_25><loc_31><loc_26></location>1</text>
<text><location><page_21><loc_29><loc_24><loc_31><loc_25></location>.0</text>
<text><location><page_21><loc_29><loc_23><loc_31><loc_24></location>0</text>
<text><location><page_21><loc_29><loc_22><loc_31><loc_23></location>±</text>
<text><location><page_21><loc_29><loc_21><loc_31><loc_22></location>9</text>
<text><location><page_21><loc_29><loc_20><loc_31><loc_21></location>2</text>
<text><location><page_21><loc_29><loc_19><loc_31><loc_20></location>.1</text>
<text><location><page_21><loc_29><loc_19><loc_31><loc_19></location>0</text>
<text><location><page_21><loc_29><loc_18><loc_31><loc_19></location>1</text>
<text><location><page_21><loc_29><loc_13><loc_31><loc_14></location>7</text>
<text><location><page_21><loc_29><loc_12><loc_31><loc_13></location>3</text>
<text><location><page_21><loc_29><loc_12><loc_31><loc_12></location>S</text>
<text><location><page_21><loc_29><loc_11><loc_31><loc_12></location>H</text>
<text><location><page_21><loc_31><loc_54><loc_33><loc_55></location>9</text>
<text><location><page_21><loc_31><loc_53><loc_33><loc_54></location>.8</text>
<text><location><page_21><loc_31><loc_53><loc_33><loc_53></location>2</text>
<text><location><page_21><loc_32><loc_51><loc_33><loc_52></location>±</text>
<text><location><page_21><loc_31><loc_50><loc_33><loc_51></location>9</text>
<text><location><page_21><loc_31><loc_49><loc_33><loc_50></location>.0</text>
<text><location><page_21><loc_31><loc_49><loc_33><loc_49></location>4</text>
<text><location><page_21><loc_31><loc_45><loc_33><loc_45></location>9</text>
<text><location><page_21><loc_31><loc_44><loc_33><loc_45></location>.3</text>
<text><location><page_21><loc_31><loc_43><loc_33><loc_44></location>0</text>
<text><location><page_21><loc_31><loc_39><loc_33><loc_39></location>2</text>
<text><location><page_21><loc_31><loc_34><loc_32><loc_34></location>9</text>
<text><location><page_21><loc_31><loc_33><loc_32><loc_34></location>9</text>
<text><location><page_21><loc_31><loc_33><loc_32><loc_33></location>.</text>
<text><location><page_21><loc_31><loc_32><loc_32><loc_33></location>1</text>
<text><location><page_21><loc_31><loc_32><loc_32><loc_32></location>+</text>
<text><location><page_21><loc_32><loc_34><loc_33><loc_34></location>3</text>
<text><location><page_21><loc_32><loc_33><loc_33><loc_34></location>7</text>
<text><location><page_21><loc_33><loc_33><loc_33><loc_33></location>.</text>
<text><location><page_21><loc_32><loc_32><loc_33><loc_33></location>1</text>
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<text><location><page_21><loc_31><loc_31><loc_33><loc_31></location>2</text>
<text><location><page_21><loc_31><loc_30><loc_33><loc_31></location>.8</text>
<text><location><page_21><loc_31><loc_29><loc_33><loc_30></location>5</text>
<text><location><page_21><loc_31><loc_25><loc_33><loc_26></location>9</text>
<text><location><page_21><loc_31><loc_25><loc_33><loc_25></location>1</text>
<text><location><page_21><loc_31><loc_24><loc_33><loc_25></location>.0</text>
<text><location><page_21><loc_31><loc_23><loc_33><loc_24></location>0</text>
<text><location><page_21><loc_32><loc_22><loc_33><loc_23></location>±</text>
<text><location><page_21><loc_31><loc_21><loc_33><loc_21></location>8</text>
<text><location><page_21><loc_31><loc_20><loc_33><loc_21></location>5</text>
<text><location><page_21><loc_31><loc_19><loc_33><loc_20></location>.8</text>
<text><location><page_21><loc_31><loc_18><loc_33><loc_19></location>9</text>
<text><location><page_21><loc_31><loc_13><loc_33><loc_14></location>0</text>
<text><location><page_21><loc_31><loc_12><loc_33><loc_13></location>7</text>
<text><location><page_21><loc_31><loc_11><loc_33><loc_12></location>L</text>
<text><location><page_21><loc_31><loc_11><loc_33><loc_11></location>S</text>
<text><location><page_21><loc_34><loc_54><loc_35><loc_55></location>.8</text>
<text><location><page_21><loc_34><loc_53><loc_35><loc_54></location>7</text>
<text><location><page_21><loc_34><loc_52><loc_35><loc_53></location>±</text>
<text><location><page_21><loc_34><loc_50><loc_35><loc_51></location>.6</text>
<text><location><page_21><loc_34><loc_50><loc_35><loc_50></location>5</text>
<text><location><page_21><loc_34><loc_49><loc_35><loc_50></location>1</text>
<text><location><page_21><loc_34><loc_45><loc_35><loc_45></location>1</text>
<text><location><page_21><loc_34><loc_44><loc_35><loc_45></location>.0</text>
<text><location><page_21><loc_34><loc_43><loc_35><loc_44></location>2</text>
<text><location><page_21><loc_34><loc_39><loc_35><loc_39></location>4</text>
<text><location><page_21><loc_33><loc_34><loc_34><loc_35></location>5</text>
<text><location><page_21><loc_33><loc_34><loc_34><loc_34></location>0</text>
<text><location><page_21><loc_34><loc_33><loc_34><loc_34></location>.</text>
<text><location><page_21><loc_33><loc_33><loc_34><loc_33></location>2</text>
<text><location><page_21><loc_33><loc_32><loc_34><loc_33></location>+</text>
<text><location><page_21><loc_34><loc_34><loc_35><loc_35></location>7</text>
<text><location><page_21><loc_34><loc_34><loc_35><loc_34></location>3</text>
<text><location><page_21><loc_35><loc_33><loc_35><loc_34></location>.</text>
<text><location><page_21><loc_34><loc_33><loc_35><loc_33></location>3</text>
<text><location><page_21><loc_35><loc_32><loc_35><loc_33></location>-</text>
<text><location><page_21><loc_34><loc_31><loc_35><loc_32></location>4</text>
<text><location><page_21><loc_34><loc_30><loc_35><loc_31></location>.1</text>
<text><location><page_21><loc_34><loc_29><loc_35><loc_30></location>3</text>
<text><location><page_21><loc_34><loc_29><loc_35><loc_29></location>2</text>
<text><location><page_21><loc_34><loc_25><loc_35><loc_26></location>1</text>
<text><location><page_21><loc_34><loc_25><loc_35><loc_25></location>1</text>
<text><location><page_21><loc_34><loc_24><loc_35><loc_25></location>.0</text>
<text><location><page_21><loc_34><loc_23><loc_35><loc_24></location>0</text>
<text><location><page_21><loc_34><loc_22><loc_35><loc_23></location>±</text>
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<text><location><page_21><loc_44><loc_20><loc_45><loc_21></location>A</text>
<text><location><page_21><loc_43><loc_21><loc_43><loc_21></location>s</text>
<text><location><page_21><loc_43><loc_20><loc_43><loc_21></location>K</text>
<text><location><page_21><loc_43><loc_19><loc_44><loc_20></location>L</text>
<text><location><page_21><loc_43><loc_18><loc_44><loc_19></location>d</text>
<text><location><page_21><loc_43><loc_17><loc_44><loc_18></location>n</text>
<text><location><page_21><loc_43><loc_17><loc_44><loc_17></location>a</text>
<text><location><page_21><loc_43><loc_16><loc_44><loc_16></location>)</text>
<text><location><page_21><loc_43><loc_15><loc_44><loc_16></location>t</text>
<text><location><page_21><loc_43><loc_15><loc_44><loc_15></location>e</text>
<text><location><page_21><loc_43><loc_14><loc_44><loc_15></location>n</text>
<text><location><page_21><loc_43><loc_14><loc_44><loc_14></location>(</text>
<text><location><page_21><loc_44><loc_12><loc_45><loc_13></location>B</text>
<text><location><page_21><loc_44><loc_12><loc_45><loc_12></location>G</text>
<text><location><page_21><loc_44><loc_11><loc_45><loc_12></location>A</text>
<text><location><page_21><loc_43><loc_12><loc_43><loc_12></location>s</text>
<text><location><page_21><loc_43><loc_11><loc_43><loc_12></location>K</text>
<text><location><page_21><loc_43><loc_10><loc_44><loc_11></location>L</text>
<text><location><page_21><loc_47><loc_89><loc_53><loc_91></location>- 21 -</text>
<text><location><page_22><loc_15><loc_58><loc_17><loc_59></location>G</text>
<text><location><page_22><loc_24><loc_82><loc_26><loc_82></location>s</text>
<text><location><page_22><loc_24><loc_81><loc_26><loc_82></location>o</text>
<text><location><page_22><loc_24><loc_80><loc_26><loc_81></location>I</text>
<paragraph><location><page_22><loc_26><loc_82><loc_27><loc_83></location>g )</paragraph>
<text><location><page_22><loc_26><loc_82><loc_27><loc_82></location>n</text>
<text><location><page_22><loc_26><loc_81><loc_27><loc_82></location>i</text>
<text><location><page_22><loc_26><loc_81><loc_27><loc_81></location>t</text>
<text><location><page_22><loc_26><loc_81><loc_27><loc_81></location>o</text>
<text><location><page_22><loc_29><loc_81><loc_30><loc_81></location>6</text>
<text><location><page_22><loc_31><loc_81><loc_32><loc_81></location>0</text>
<text><location><page_22><loc_33><loc_81><loc_34><loc_81></location>5</text>
<text><location><page_22><loc_34><loc_81><loc_36><loc_81></location>8</text>
<text><location><page_22><loc_36><loc_81><loc_37><loc_81></location>3</text>
<text><location><page_22><loc_38><loc_81><loc_39><loc_81></location>0</text>
<text><location><page_22><loc_39><loc_81><loc_41><loc_81></location>2</text>
<table>
<location><page_22><loc_12><loc_59><loc_85><loc_80></location>
</table>
<text><location><page_22><loc_15><loc_57><loc_17><loc_58></location>A</text>
<text><location><page_22><loc_15><loc_56><loc_17><loc_57></location>f</text>
<text><location><page_22><loc_15><loc_55><loc_17><loc_56></location>o</text>
<text><location><page_22><loc_24><loc_58><loc_26><loc_59></location>P</text>
<text><location><page_22><loc_24><loc_56><loc_26><loc_56></location>a</text>
<text><location><page_22><loc_24><loc_55><loc_26><loc_56></location>v</text>
<text><location><page_22><loc_29><loc_55><loc_30><loc_56></location>1</text>
<text><location><page_22><loc_31><loc_55><loc_32><loc_56></location>3</text>
<text><location><page_22><loc_33><loc_55><loc_34><loc_56></location>1</text>
<text><location><page_22><loc_34><loc_55><loc_36><loc_56></location>5</text>
<text><location><page_22><loc_36><loc_55><loc_37><loc_56></location>1</text>
<text><location><page_22><loc_38><loc_55><loc_39><loc_56></location>8</text>
<text><location><page_22><loc_39><loc_55><loc_41><loc_56></location>9</text>
<text><location><page_22><loc_15><loc_53><loc_46><loc_55></location>io n P a d o 0 2 0 . 2 0 . 4 0 . 5 0 . 5 0 . 5 0 . 3 0 . 2 a l u e s</text>
<text><location><page_22><loc_15><loc_52><loc_17><loc_53></location>t</text>
<text><location><page_22><loc_15><loc_52><loc_17><loc_52></location>c</text>
<text><location><page_22><loc_15><loc_51><loc_17><loc_52></location>a</text>
<text><location><page_22><loc_15><loc_50><loc_17><loc_51></location>r</text>
<text><location><page_22><loc_15><loc_50><loc_17><loc_50></location>f</text>
<text><location><page_22><loc_15><loc_49><loc_17><loc_49></location>y</text>
<text><location><page_22><loc_15><loc_48><loc_17><loc_49></location>it</text>
<text><location><page_22><loc_15><loc_47><loc_17><loc_48></location>s</text>
<text><location><page_22><loc_15><loc_46><loc_17><loc_47></location>o</text>
<text><location><page_22><loc_15><loc_45><loc_17><loc_46></location>in</text>
<text><location><page_22><loc_15><loc_44><loc_17><loc_45></location>m</text>
<text><location><page_22><loc_15><loc_43><loc_17><loc_44></location>lu</text>
<text><location><page_22><loc_15><loc_41><loc_17><loc_42></location>d</text>
<text><location><page_22><loc_15><loc_41><loc_17><loc_41></location>n</text>
<text><location><page_22><loc_15><loc_40><loc_17><loc_40></location>a</text>
<text><location><page_22><loc_15><loc_39><loc_17><loc_40></location>b</text>
<text><location><page_22><loc_16><loc_38><loc_17><loc_38></location>s</text>
<text><location><page_22><loc_16><loc_37><loc_17><loc_38></location>K</text>
<text><location><page_22><loc_15><loc_36><loc_17><loc_36></location>f</text>
<text><location><page_22><loc_15><loc_35><loc_17><loc_36></location>o</text>
<text><location><page_22><loc_15><loc_34><loc_17><loc_34></location>n</text>
<text><location><page_22><loc_15><loc_33><loc_17><loc_34></location>o</text>
<text><location><page_22><loc_15><loc_32><loc_17><loc_33></location>is</text>
<text><location><page_22><loc_15><loc_31><loc_17><loc_32></location>r</text>
<text><location><page_22><loc_15><loc_31><loc_17><loc_31></location>a</text>
<text><location><page_22><loc_15><loc_30><loc_17><loc_31></location>p</text>
<text><location><page_22><loc_15><loc_29><loc_17><loc_30></location>m</text>
<text><location><page_22><loc_15><loc_28><loc_17><loc_29></location>o</text>
<text><location><page_22><loc_15><loc_27><loc_17><loc_28></location>C</text>
<text><location><page_22><loc_15><loc_25><loc_17><loc_25></location>.</text>
<text><location><page_22><loc_15><loc_24><loc_17><loc_25></location>3</text>
<text><location><page_22><loc_15><loc_23><loc_17><loc_24></location>le</text>
<text><location><page_22><loc_15><loc_22><loc_17><loc_23></location>b</text>
<text><location><page_22><loc_15><loc_21><loc_17><loc_22></location>a</text>
<text><location><page_22><loc_15><loc_20><loc_17><loc_21></location>T</text>
<text><location><page_22><loc_45><loc_55><loc_46><loc_56></location>.</text>
<text><location><page_22><loc_45><loc_52><loc_46><loc_53></location>v</text>
<text><location><page_22><loc_45><loc_51><loc_46><loc_52></location>d</text>
<text><location><page_22><loc_45><loc_51><loc_46><loc_51></location>e</text>
<text><location><page_22><loc_45><loc_51><loc_46><loc_51></location>t</text>
<text><location><page_22><loc_45><loc_50><loc_46><loc_51></location>c</text>
<text><location><page_22><loc_45><loc_50><loc_46><loc_50></location>a</text>
<text><location><page_22><loc_45><loc_49><loc_46><loc_50></location>r</text>
<text><location><page_22><loc_45><loc_49><loc_46><loc_49></location>t</text>
<text><location><page_22><loc_45><loc_48><loc_46><loc_49></location>b</text>
<text><location><page_22><loc_45><loc_48><loc_46><loc_48></location>u</text>
<text><location><page_22><loc_45><loc_47><loc_46><loc_48></location>s</text>
<text><location><page_22><loc_45><loc_47><loc_46><loc_47></location>-</text>
<text><location><page_22><loc_45><loc_46><loc_46><loc_47></location>d</text>
<text><location><page_22><loc_45><loc_46><loc_46><loc_46></location>l</text>
<text><location><page_22><loc_45><loc_45><loc_46><loc_46></location>e</text>
<text><location><page_22><loc_45><loc_45><loc_46><loc_45></location>fi</text>
<text><location><page_22><loc_45><loc_44><loc_46><loc_44></location>e</text>
<text><location><page_22><loc_45><loc_43><loc_46><loc_44></location>h</text>
<text><location><page_22><loc_45><loc_43><loc_46><loc_43></location>t</text>
<text><location><page_22><loc_45><loc_42><loc_46><loc_43></location>e</text>
<text><location><page_22><loc_45><loc_42><loc_46><loc_42></location>t</text>
<text><location><page_22><loc_45><loc_41><loc_46><loc_42></location>a</text>
<text><location><page_22><loc_45><loc_41><loc_46><loc_41></location>c</text>
<text><location><page_22><loc_45><loc_40><loc_46><loc_41></location>i</text>
<text><location><page_22><loc_45><loc_40><loc_46><loc_40></location>d</text>
<text><location><page_22><loc_45><loc_39><loc_46><loc_40></location>n</text>
<text><location><page_22><loc_45><loc_39><loc_46><loc_39></location>i</text>
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<text><location><page_22><loc_45><loc_37><loc_46><loc_38></location>e</text>
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<text><location><page_22><loc_45><loc_35><loc_46><loc_35></location>c</text>
<text><location><page_22><loc_45><loc_34><loc_46><loc_35></location>n</text>
<text><location><page_22><loc_45><loc_34><loc_46><loc_34></location>e</text>
<text><location><page_22><loc_45><loc_33><loc_46><loc_34></location>u</text>
<text><location><page_22><loc_45><loc_33><loc_46><loc_33></location>q</text>
<text><location><page_22><loc_45><loc_32><loc_46><loc_33></location>e</text>
<text><location><page_22><loc_45><loc_32><loc_46><loc_32></location>s</text>
<text><location><page_22><loc_45><loc_31><loc_46><loc_31></location>r</text>
<text><location><page_22><loc_45><loc_31><loc_46><loc_31></location>e</text>
<text><location><page_22><loc_45><loc_30><loc_46><loc_31></location>t</text>
<text><location><page_22><loc_45><loc_30><loc_46><loc_30></location>s</text>
<text><location><page_22><loc_45><loc_29><loc_46><loc_30></location>u</text>
<text><location><page_22><loc_45><loc_29><loc_46><loc_29></location>l</text>
<text><location><page_22><loc_45><loc_28><loc_46><loc_29></location>c</text>
<text><location><page_22><loc_45><loc_28><loc_46><loc_28></location>t</text>
<text><location><page_22><loc_45><loc_27><loc_46><loc_28></location>h</text>
<text><location><page_22><loc_45><loc_26><loc_46><loc_27></location>g</text>
<text><location><page_22><loc_45><loc_26><loc_46><loc_26></location>i</text>
<text><location><page_22><loc_45><loc_26><loc_46><loc_26></location>r</text>
<text><location><page_22><loc_45><loc_25><loc_46><loc_26></location>b</text>
<text><location><page_22><loc_45><loc_24><loc_46><loc_25></location>d</text>
<text><location><page_22><loc_45><loc_24><loc_46><loc_24></location>n</text>
<text><location><page_22><loc_45><loc_23><loc_46><loc_24></location>a</text>
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<text><location><page_22><loc_45><loc_21><loc_46><loc_22></location>e</text>
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<text><location><page_22><loc_45><loc_19><loc_46><loc_19></location>a</text>
<text><location><page_22><loc_45><loc_18><loc_46><loc_19></location>e</text>
<text><location><page_22><loc_45><loc_17><loc_46><loc_18></location>M</text>
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<text><location><page_22><loc_21><loc_33><loc_22><loc_34></location>i</text>
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<text><location><page_22><loc_21><loc_32><loc_22><loc_33></location>a</text>
<text><location><page_22><loc_21><loc_32><loc_22><loc_32></location>v</text>
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<text><location><page_22><loc_21><loc_30><loc_22><loc_31></location>s</text>
<text><location><page_22><loc_21><loc_30><loc_22><loc_30></location>b</text>
<text><location><page_22><loc_21><loc_29><loc_22><loc_30></location>O</text>
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<text><location><page_22><loc_24><loc_47><loc_26><loc_47></location>u</text>
<text><location><page_22><loc_24><loc_47><loc_26><loc_47></location>l</text>
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<text><location><page_22><loc_24><loc_43><loc_26><loc_43></location>B</text>
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<text><location><page_22><loc_26><loc_15><loc_27><loc_16></location>g</text>
<text><location><page_22><loc_26><loc_15><loc_27><loc_15></location>a</text>
<text><location><page_22><loc_26><loc_14><loc_27><loc_15></location>(</text>
<text><location><page_22><loc_26><loc_14><loc_27><loc_14></location>g</text>
<text><location><page_22><loc_26><loc_13><loc_27><loc_14></location>o</text>
<text><location><page_22><loc_26><loc_13><loc_27><loc_13></location>l</text>
<text><location><page_22><loc_29><loc_47><loc_30><loc_47></location>0</text>
<text><location><page_22><loc_29><loc_46><loc_30><loc_47></location>2</text>
<text><location><page_22><loc_29><loc_46><loc_30><loc_46></location>.</text>
<text><location><page_22><loc_29><loc_45><loc_30><loc_46></location>0</text>
<text><location><page_22><loc_29><loc_38><loc_30><loc_39></location>0</text>
<text><location><page_22><loc_29><loc_38><loc_30><loc_38></location>3</text>
<text><location><page_22><loc_29><loc_37><loc_30><loc_38></location>.</text>
<text><location><page_22><loc_29><loc_37><loc_30><loc_37></location>0</text>
<text><location><page_22><loc_29><loc_32><loc_30><loc_33></location>7</text>
<text><location><page_22><loc_29><loc_32><loc_30><loc_32></location>0</text>
<text><location><page_22><loc_29><loc_31><loc_30><loc_32></location>.</text>
<text><location><page_22><loc_29><loc_31><loc_30><loc_31></location>0</text>
<text><location><page_22><loc_29><loc_30><loc_30><loc_30></location>±</text>
<text><location><page_22><loc_29><loc_29><loc_30><loc_29></location>4</text>
<text><location><page_22><loc_29><loc_28><loc_30><loc_29></location>2</text>
<text><location><page_22><loc_29><loc_28><loc_30><loc_28></location>.</text>
<text><location><page_22><loc_29><loc_27><loc_30><loc_28></location>0</text>
<text><location><page_22><loc_29><loc_25><loc_30><loc_25></location>6</text>
<text><location><page_22><loc_29><loc_24><loc_30><loc_25></location>0</text>
<text><location><page_22><loc_29><loc_24><loc_29><loc_24></location>.</text>
<text><location><page_22><loc_29><loc_23><loc_30><loc_24></location>0</text>
<text><location><page_22><loc_29><loc_23><loc_30><loc_23></location>+</text>
<text><location><page_22><loc_30><loc_25><loc_31><loc_25></location>7</text>
<text><location><page_22><loc_30><loc_24><loc_31><loc_25></location>0</text>
<text><location><page_22><loc_30><loc_24><loc_30><loc_24></location>.</text>
<text><location><page_22><loc_30><loc_23><loc_31><loc_24></location>0</text>
<text><location><page_22><loc_30><loc_23><loc_30><loc_23></location>-</text>
<text><location><page_22><loc_29><loc_22><loc_30><loc_23></location>5</text>
<text><location><page_22><loc_29><loc_22><loc_30><loc_22></location>2</text>
<text><location><page_22><loc_29><loc_21><loc_30><loc_22></location>.</text>
<text><location><page_22><loc_29><loc_21><loc_30><loc_21></location>0</text>
<text><location><page_22><loc_29><loc_16><loc_30><loc_17></location>0</text>
<text><location><page_22><loc_29><loc_16><loc_30><loc_16></location>0</text>
<text><location><page_22><loc_29><loc_15><loc_30><loc_16></location>.</text>
<text><location><page_22><loc_29><loc_15><loc_30><loc_15></location>8</text>
<text><location><page_22><loc_31><loc_47><loc_32><loc_47></location>0</text>
<text><location><page_22><loc_31><loc_46><loc_32><loc_47></location>5</text>
<text><location><page_22><loc_31><loc_46><loc_32><loc_46></location>.</text>
<text><location><page_22><loc_31><loc_45><loc_32><loc_46></location>0</text>
<text><location><page_22><loc_31><loc_38><loc_32><loc_39></location>2</text>
<text><location><page_22><loc_31><loc_38><loc_32><loc_38></location>6</text>
<text><location><page_22><loc_31><loc_37><loc_32><loc_38></location>.</text>
<text><location><page_22><loc_31><loc_37><loc_32><loc_37></location>0</text>
<text><location><page_22><loc_31><loc_32><loc_32><loc_33></location>0</text>
<text><location><page_22><loc_31><loc_32><loc_32><loc_32></location>1</text>
<text><location><page_22><loc_31><loc_31><loc_32><loc_32></location>.</text>
<text><location><page_22><loc_31><loc_31><loc_32><loc_31></location>0</text>
<text><location><page_22><loc_31><loc_30><loc_32><loc_30></location>±</text>
<text><location><page_22><loc_31><loc_29><loc_32><loc_29></location>8</text>
<text><location><page_22><loc_31><loc_28><loc_32><loc_29></location>3</text>
<text><location><page_22><loc_31><loc_28><loc_32><loc_28></location>.</text>
<text><location><page_22><loc_31><loc_27><loc_32><loc_28></location>0</text>
<text><location><page_22><loc_31><loc_25><loc_32><loc_26></location>1</text>
<text><location><page_22><loc_31><loc_25><loc_32><loc_25></location>1</text>
<text><location><page_22><loc_31><loc_24><loc_32><loc_25></location>.</text>
<text><location><page_22><loc_31><loc_24><loc_32><loc_24></location>0</text>
<text><location><page_22><loc_31><loc_23><loc_32><loc_23></location>±</text>
<text><location><page_22><loc_31><loc_22><loc_32><loc_22></location>3</text>
<text><location><page_22><loc_31><loc_21><loc_32><loc_22></location>5</text>
<text><location><page_22><loc_31><loc_21><loc_32><loc_21></location>.</text>
<text><location><page_22><loc_31><loc_20><loc_32><loc_21></location>0</text>
<text><location><page_22><loc_31><loc_16><loc_32><loc_17></location>5</text>
<text><location><page_22><loc_31><loc_16><loc_32><loc_16></location>2</text>
<text><location><page_22><loc_31><loc_15><loc_32><loc_16></location>.</text>
<text><location><page_22><loc_31><loc_15><loc_32><loc_15></location>8</text>
<text><location><page_22><loc_33><loc_47><loc_34><loc_47></location>7</text>
<text><location><page_22><loc_33><loc_46><loc_34><loc_47></location>6</text>
<text><location><page_22><loc_33><loc_46><loc_34><loc_46></location>.</text>
<text><location><page_22><loc_33><loc_45><loc_34><loc_46></location>0</text>
<text><location><page_22><loc_33><loc_38><loc_34><loc_39></location>1</text>
<text><location><page_22><loc_33><loc_38><loc_34><loc_38></location>8</text>
<text><location><page_22><loc_33><loc_37><loc_34><loc_38></location>.</text>
<text><location><page_22><loc_33><loc_37><loc_34><loc_37></location>0</text>
<text><location><page_22><loc_33><loc_32><loc_34><loc_33></location>1</text>
<text><location><page_22><loc_33><loc_32><loc_34><loc_32></location>1</text>
<text><location><page_22><loc_33><loc_31><loc_34><loc_32></location>.</text>
<text><location><page_22><loc_33><loc_31><loc_34><loc_31></location>0</text>
<text><location><page_22><loc_33><loc_30><loc_34><loc_30></location>±</text>
<text><location><page_22><loc_33><loc_29><loc_34><loc_29></location>7</text>
<text><location><page_22><loc_33><loc_28><loc_34><loc_29></location>4</text>
<text><location><page_22><loc_33><loc_28><loc_34><loc_28></location>.</text>
<text><location><page_22><loc_33><loc_27><loc_34><loc_28></location>0</text>
<text><location><page_22><loc_33><loc_25><loc_34><loc_26></location>1</text>
<text><location><page_22><loc_33><loc_25><loc_34><loc_25></location>1</text>
<text><location><page_22><loc_33><loc_24><loc_34><loc_25></location>.</text>
<text><location><page_22><loc_33><loc_24><loc_34><loc_24></location>0</text>
<text><location><page_22><loc_33><loc_23><loc_34><loc_23></location>±</text>
<text><location><page_22><loc_33><loc_22><loc_34><loc_22></location>4</text>
<text><location><page_22><loc_33><loc_21><loc_34><loc_22></location>5</text>
<text><location><page_22><loc_33><loc_21><loc_34><loc_21></location>.</text>
<text><location><page_22><loc_33><loc_20><loc_34><loc_21></location>0</text>
<text><location><page_22><loc_33><loc_16><loc_34><loc_17></location>0</text>
<text><location><page_22><loc_33><loc_16><loc_34><loc_16></location>5</text>
<text><location><page_22><loc_33><loc_15><loc_34><loc_16></location>.</text>
<text><location><page_22><loc_33><loc_15><loc_34><loc_15></location>8</text>
<text><location><page_22><loc_34><loc_47><loc_36><loc_47></location>0</text>
<text><location><page_22><loc_34><loc_46><loc_36><loc_47></location>7</text>
<text><location><page_22><loc_34><loc_46><loc_36><loc_46></location>.</text>
<text><location><page_22><loc_34><loc_45><loc_36><loc_46></location>0</text>
<text><location><page_22><loc_34><loc_38><loc_36><loc_39></location>8</text>
<text><location><page_22><loc_34><loc_38><loc_36><loc_38></location>7</text>
<text><location><page_22><loc_34><loc_37><loc_36><loc_38></location>.</text>
<text><location><page_22><loc_34><loc_37><loc_36><loc_37></location>0</text>
<text><location><page_22><loc_34><loc_32><loc_36><loc_33></location>3</text>
<text><location><page_22><loc_34><loc_32><loc_36><loc_32></location>1</text>
<text><location><page_22><loc_34><loc_31><loc_36><loc_32></location>.</text>
<text><location><page_22><loc_34><loc_31><loc_36><loc_31></location>0</text>
<text><location><page_22><loc_34><loc_30><loc_35><loc_30></location>±</text>
<text><location><page_22><loc_34><loc_29><loc_36><loc_29></location>2</text>
<text><location><page_22><loc_34><loc_28><loc_36><loc_29></location>5</text>
<text><location><page_22><loc_34><loc_28><loc_36><loc_28></location>.</text>
<text><location><page_22><loc_34><loc_27><loc_36><loc_28></location>0</text>
<text><location><page_22><loc_34><loc_25><loc_35><loc_25></location>4</text>
<text><location><page_22><loc_34><loc_24><loc_35><loc_25></location>1</text>
<text><location><page_22><loc_34><loc_24><loc_35><loc_24></location>.</text>
<text><location><page_22><loc_34><loc_23><loc_35><loc_24></location>0</text>
<text><location><page_22><loc_34><loc_23><loc_35><loc_23></location>+</text>
<text><location><page_22><loc_35><loc_25><loc_36><loc_25></location>3</text>
<text><location><page_22><loc_35><loc_24><loc_36><loc_25></location>1</text>
<text><location><page_22><loc_35><loc_24><loc_36><loc_24></location>.</text>
<text><location><page_22><loc_35><loc_23><loc_36><loc_24></location>0</text>
<text><location><page_22><loc_35><loc_23><loc_36><loc_23></location>-</text>
<text><location><page_22><loc_34><loc_22><loc_36><loc_23></location>7</text>
<text><location><page_22><loc_34><loc_22><loc_36><loc_22></location>5</text>
<text><location><page_22><loc_34><loc_21><loc_36><loc_22></location>.</text>
<text><location><page_22><loc_34><loc_21><loc_36><loc_21></location>0</text>
<text><location><page_22><loc_34><loc_16><loc_36><loc_17></location>5</text>
<text><location><page_22><loc_34><loc_16><loc_36><loc_16></location>7</text>
<text><location><page_22><loc_34><loc_15><loc_36><loc_16></location>.</text>
<text><location><page_22><loc_34><loc_15><loc_36><loc_15></location>8</text>
<text><location><page_22><loc_36><loc_47><loc_37><loc_47></location>5</text>
<text><location><page_22><loc_36><loc_46><loc_37><loc_47></location>5</text>
<text><location><page_22><loc_36><loc_46><loc_37><loc_46></location>.</text>
<text><location><page_22><loc_36><loc_45><loc_37><loc_46></location>0</text>
<text><location><page_22><loc_36><loc_38><loc_37><loc_39></location>0</text>
<text><location><page_22><loc_36><loc_38><loc_37><loc_38></location>6</text>
<text><location><page_22><loc_36><loc_37><loc_37><loc_38></location>.</text>
<text><location><page_22><loc_36><loc_37><loc_37><loc_37></location>0</text>
<text><location><page_22><loc_36><loc_32><loc_37><loc_33></location>9</text>
<text><location><page_22><loc_36><loc_32><loc_37><loc_32></location>0</text>
<text><location><page_22><loc_36><loc_31><loc_37><loc_32></location>.</text>
<text><location><page_22><loc_36><loc_31><loc_37><loc_31></location>0</text>
<text><location><page_22><loc_36><loc_30><loc_37><loc_30></location>±</text>
<text><location><page_22><loc_36><loc_29><loc_37><loc_29></location>8</text>
<text><location><page_22><loc_36><loc_28><loc_37><loc_29></location>3</text>
<text><location><page_22><loc_36><loc_28><loc_37><loc_28></location>.</text>
<text><location><page_22><loc_36><loc_27><loc_37><loc_28></location>0</text>
<text><location><page_22><loc_36><loc_25><loc_37><loc_26></location>1</text>
<text><location><page_22><loc_36><loc_25><loc_37><loc_25></location>1</text>
<text><location><page_22><loc_36><loc_24><loc_37><loc_25></location>.</text>
<text><location><page_22><loc_36><loc_24><loc_37><loc_24></location>0</text>
<text><location><page_22><loc_36><loc_23><loc_37><loc_23></location>±</text>
<text><location><page_22><loc_36><loc_22><loc_37><loc_22></location>2</text>
<text><location><page_22><loc_36><loc_21><loc_37><loc_22></location>5</text>
<text><location><page_22><loc_36><loc_21><loc_37><loc_21></location>.</text>
<text><location><page_22><loc_36><loc_20><loc_37><loc_21></location>0</text>
<text><location><page_22><loc_36><loc_16><loc_37><loc_17></location>0</text>
<text><location><page_22><loc_36><loc_16><loc_37><loc_16></location>0</text>
<text><location><page_22><loc_36><loc_15><loc_37><loc_16></location>.</text>
<text><location><page_22><loc_36><loc_15><loc_37><loc_15></location>9</text>
<text><location><page_22><loc_38><loc_47><loc_39><loc_47></location>0</text>
<text><location><page_22><loc_38><loc_46><loc_39><loc_47></location>3</text>
<text><location><page_22><loc_38><loc_46><loc_39><loc_46></location>.</text>
<text><location><page_22><loc_38><loc_45><loc_39><loc_46></location>0</text>
<text><location><page_22><loc_38><loc_38><loc_39><loc_39></location>3</text>
<text><location><page_22><loc_38><loc_38><loc_39><loc_38></location>3</text>
<text><location><page_22><loc_38><loc_37><loc_39><loc_38></location>.</text>
<text><location><page_22><loc_38><loc_37><loc_39><loc_37></location>0</text>
<text><location><page_22><loc_38><loc_32><loc_39><loc_33></location>8</text>
<text><location><page_22><loc_38><loc_32><loc_39><loc_32></location>0</text>
<text><location><page_22><loc_38><loc_31><loc_39><loc_32></location>.</text>
<text><location><page_22><loc_38><loc_31><loc_39><loc_31></location>0</text>
<text><location><page_22><loc_38><loc_30><loc_39><loc_30></location>±</text>
<text><location><page_22><loc_38><loc_29><loc_39><loc_29></location>7</text>
<text><location><page_22><loc_38><loc_28><loc_39><loc_29></location>2</text>
<text><location><page_22><loc_38><loc_28><loc_39><loc_28></location>.</text>
<text><location><page_22><loc_38><loc_27><loc_39><loc_28></location>0</text>
<text><location><page_22><loc_38><loc_25><loc_39><loc_26></location>9</text>
<text><location><page_22><loc_38><loc_25><loc_39><loc_25></location>0</text>
<text><location><page_22><loc_38><loc_24><loc_39><loc_25></location>.</text>
<text><location><page_22><loc_38><loc_24><loc_39><loc_24></location>0</text>
<text><location><page_22><loc_38><loc_23><loc_39><loc_23></location>±</text>
<text><location><page_22><loc_38><loc_22><loc_39><loc_22></location>1</text>
<text><location><page_22><loc_38><loc_21><loc_39><loc_22></location>3</text>
<text><location><page_22><loc_38><loc_21><loc_39><loc_21></location>.</text>
<text><location><page_22><loc_38><loc_20><loc_39><loc_21></location>0</text>
<text><location><page_22><loc_38><loc_16><loc_39><loc_17></location>5</text>
<text><location><page_22><loc_38><loc_16><loc_39><loc_16></location>2</text>
<text><location><page_22><loc_38><loc_15><loc_39><loc_16></location>.</text>
<text><location><page_22><loc_38><loc_15><loc_39><loc_15></location>9</text>
<text><location><page_22><loc_39><loc_47><loc_41><loc_47></location>5</text>
<text><location><page_22><loc_39><loc_46><loc_41><loc_47></location>1</text>
<text><location><page_22><loc_39><loc_46><loc_41><loc_46></location>.</text>
<text><location><page_22><loc_39><loc_45><loc_41><loc_46></location>0</text>
<text><location><page_22><loc_39><loc_38><loc_41><loc_39></location>0</text>
<text><location><page_22><loc_39><loc_38><loc_41><loc_38></location>2</text>
<text><location><page_22><loc_39><loc_37><loc_41><loc_38></location>.</text>
<text><location><page_22><loc_39><loc_37><loc_41><loc_37></location>0</text>
<text><location><page_22><loc_39><loc_32><loc_41><loc_33></location>5</text>
<text><location><page_22><loc_39><loc_32><loc_41><loc_32></location>1</text>
<text><location><page_22><loc_39><loc_31><loc_41><loc_32></location>.</text>
<text><location><page_22><loc_39><loc_31><loc_41><loc_31></location>0</text>
<text><location><page_22><loc_39><loc_30><loc_41><loc_30></location>±</text>
<text><location><page_22><loc_39><loc_29><loc_41><loc_29></location>1</text>
<text><location><page_22><loc_39><loc_28><loc_41><loc_29></location>2</text>
<text><location><page_22><loc_39><loc_28><loc_41><loc_28></location>.</text>
<text><location><page_22><loc_39><loc_27><loc_41><loc_28></location>0</text>
<text><location><page_22><loc_39><loc_25><loc_41><loc_26></location>9</text>
<text><location><page_22><loc_39><loc_25><loc_41><loc_25></location>1</text>
<text><location><page_22><loc_39><loc_24><loc_41><loc_25></location>.</text>
<text><location><page_22><loc_39><loc_24><loc_41><loc_24></location>0</text>
<text><location><page_22><loc_39><loc_23><loc_41><loc_23></location>±</text>
<text><location><page_22><loc_39><loc_22><loc_41><loc_22></location>2</text>
<text><location><page_22><loc_39><loc_21><loc_41><loc_22></location>3</text>
<text><location><page_22><loc_39><loc_21><loc_41><loc_21></location>.</text>
<text><location><page_22><loc_39><loc_20><loc_41><loc_21></location>0</text>
<text><location><page_22><loc_39><loc_16><loc_41><loc_17></location>0</text>
<text><location><page_22><loc_39><loc_16><loc_41><loc_16></location>5</text>
<text><location><page_22><loc_39><loc_15><loc_41><loc_16></location>.</text>
<text><location><page_22><loc_39><loc_15><loc_41><loc_15></location>9</text>
<text><location><page_22><loc_47><loc_89><loc_53><loc_91></location>- 22 -</text>
<figure>
<location><page_23><loc_13><loc_28><loc_88><loc_84></location>
<caption>Fig. 1.- An example for determination of the center of a star cluster, NGC 1861. (a) 2-dimensional number density map smoothed with a boxcar filter for the bright stars with V < 20 . 5 mag around NGC 1861 derived from the MCPS catalog of Zaritsky et al. (2004), (b) Fitted number density map with 2-dimensional Gaussian fitting. The plus and cross mark, respectively, represent the cluster center presented by Bica et al. (2008) and that derived in this study. (c) Residual number density map derived from subtraction of (b) from (a). (d) A gray scale map of a digitized sky survey R band image. The plus and cross mark represent the same as in (b).</caption>
</figure>
<figure>
<location><page_24><loc_17><loc_29><loc_86><loc_82></location>
<caption>Fig. 2.- Radial number density profile for the bright stars with V < 20 . 5 mag around NGC 1861 in the MCPS catalog of Zaritsky et al. (2004). Error bars indicate the Poisson errors estimated in each bin. The solid line and dot-dashed line represent the cluster radius presented by Bica et al. (2008) and that determined in this study, respectively. The background level (dotted line) is the median value of the number density of the stars located in the annulus, 200 '' < R < 300 '' . We adopted 3 σ upper level (dashed line) to determine the radius of each cluster (see texts). The stamp image is a gray scale map of a digitized sky survey R band image of NGC 1861, showing the cluster size determined in this study by a large circle.</caption>
</figure>
<figure>
<location><page_25><loc_14><loc_30><loc_86><loc_85></location>
<caption>Fig. 3.- Comparison of center coordinates and radii of star clusters between this study and other references, Werchan & Zaritsky (2011) (a,d, and g panels) and Bica et al. (2008) (b, e, and h panels). The bottom three panels show the differences between Bica et al. (2008) and Werchan & Zaritsky (2011). In the case of Werchan & Zaritsky (2011), the 90% enclosed luminosity radii are adopted to compare with other studies. These histograms are normalized by peak values. The numbers of star clusters found in both studies are presented in each panel. The solid and dashed lines represent zero points and peak positions of differences, respectively.</caption>
</figure>
<figure>
<location><page_26><loc_13><loc_27><loc_86><loc_81></location>
<caption>Fig. 4.- (a) ( V -( B -V )) CMD of stars at 44 '' - 200 '' from the center of NGC 1861. The box represents a region where most of stars are field main-sequence stars (open circles). (b) (( U -B ) -( B -V )) CCD of field main-sequence stars selected in (a). The solid line is a ZAMS (Marigo et al. 2008) shifted according to E ( B -V ) = 0 . 10 mag. The arrow indicates a direction of reddening vector.</caption>
</figure>
<figure>
<location><page_27><loc_12><loc_31><loc_88><loc_82></location>
<caption>Fig. 5.- (a) ( V -( B -V )) CMD of stars in NGC 1861 region. (b) ( V -( B -V )) CMD of stars in the field region around NGC 1861 with the same area as the cluster region. (c) ( V -( B -V )) CMD of stars in NGC 1861 after statistical subtraction of field stars. The filled and open circles represent the stars with the photometric errors of err ( B -V ) ≤ 0.1 mag and > 0.1 mag, respectively. The solid line is a Padova isochrone for log(age [yr]) = 8.55 and Z = 0 . 008 (Marigo et al. 2008). It is shifted according to E ( B -V ) = 0 . 10 mag and ( m -M ) 0 = 18 . 50 mag, and the two dashed lines represent isochrones for log(age[yr]) = 8.5 and 8.6, which tell errors of ages. The arrow indicates a direction of reddening vector. The values of physical parameters of NGC 1861 (metallicity, distance modulus, reddening, and age) are shown in the right lower corner.</caption>
</figure>
<figure>
<location><page_28><loc_15><loc_27><loc_85><loc_81></location>
<caption>Fig. 6.- Comparison of the ages determined by various references (Elson & Fall 1985; EF85, Pietrzynski & Udalski 2000; PU00, Hunter et al. 2003; Hun+03, Glatt et al. 2010; Gla+10, Popescu et al. 2012; Pop+12). The dotted lines are one-to-one relations. The dashed lines represent linear fitting results, and their slopes, zero points, and the root mean square errors are shown in the left upper corner of each panel.</caption>
</figure>
<figure>
<location><page_29><loc_13><loc_28><loc_87><loc_86></location>
<caption>Fig. 7.- ( V -( B -V )) CMDs and isochrone fitting results of the star clusters that show the largest difference of ages from other references: (a) SL482 (Glatt et al. 2010), (b) NGC 1782 (Elson & Fall 1985), (c) SL294 (Popescu et al. 2012), (d) SL503 (Hunter et al. 2003), and (e) H88-182 (Pietrzynski & Udalski 2000). The filled and open circles represent the same as in Figure 5(c). The solid lines and dashed lines represent Padova isochrones ( Z = 0 . 008) for the ages determined in this study and other studies, respectively. These are shifted according to the determined foreground reddening and ( m -M ) 0 = 18 . 50 mag. The arrow indicates a direction of reddening vector.</caption>
</figure>
<figure>
<location><page_30><loc_13><loc_28><loc_87><loc_85></location>
<caption>Fig. 8.- AGB selection criteria. (a) The color distribution of the bright stars brighter with K s < 12 . 3 in 41 young star clusters with log(age) < 8.5. (b) A combined and dereddened ( K s, 0 -( J -K s ) 0 ) CMD for star clusters with log(age) < 8.5. The dashed lines and the dot-dashed lines indicate criteria to distinguish AGB stars from other populations in this study and Mucciarelli et al. (2006), respectively. The shaded area represents the area where Nikolaev & Weinberg (2000) suggested that AGB stars are concentrated. (c) and (d) the same as (a) and (b) for 61 star clusters with log(age) ≥ 8.5.</caption>
</figure>
<figure>
<location><page_31><loc_14><loc_25><loc_85><loc_78></location>
<caption>Fig. 9.- A gray scale map of a 2MASS K s band image of NGC 1861. The solid line circle indicates an aperture with radius 44 '' for cluster photometry. The two dashed line circles represent the annuli with radii 48 '' and 58 '' , used for background estimation.</caption>
</figure>
<figure>
<location><page_32><loc_21><loc_34><loc_80><loc_86></location>
<caption>Fig. 10.- (a) The K s band luminosity fraction of AGB stars in 102 LMC star clusters as a function of ages. The circles and other symbols represent the star clusters of which ages were determined in this study and other studies, respectively (triangles: Elson & Fall 1985 and Girardi et al. 1995, stars: Goudfrooij et al. 2011, upside-down triangles: Pietrzynski & Udalski 2000, and squares: Popescu et al. 2012). The symbol size reflects the integrated luminosity of each cluster. (b) Mean values in each age bin (squares) and bright cluster sequence (shaded region) of the K s band luminosity fraction of AGB stars in star clusters. The lower boundary of the shaded region show the result after fieldsubtraction, and for mean values, the field-subtracted results are within error bars. The error bars for mean values indicate the errors estimated by error propagation. The open circles represent the result from Mucciarelli et al. (2006) including NGC 2249 and NGC2231 with L K s < 10 5 L /circledot (cross marks). The filled circles indicate the result derived in this study for the star clusters that show a large discrepancy in the AGB luminosity contribution.</caption>
</figure>
<figure>
<location><page_33><loc_16><loc_27><loc_88><loc_81></location>
<caption>Fig. 11.- (a) The difference of the number of AGB stars in 12 star clusters between Mucciarelli et al. (2006) and this study (filled circles). The open diamonds represent the field-subtracted results. The error bars indicate Poisson errors for the number of AGB stars. (b) Same as (a) but for the K s band luminosity fraction of AGB stars in star clusters. The error bars indicate the errors estimated by error propagation.</caption>
</figure>
<figure>
<location><page_34><loc_13><loc_27><loc_87><loc_85></location>
<caption>Fig. 12.- The K s band luminosity fraction of AGB stars in mock star clusters using four different isochrone sets: (a) Padova02, (b) Padova10, (c) BaSTI std, and (d) BaSTI os models. The shaded region indicates the sequence of the massive mock clusters with M = 10 6 M /circledot . The circles represent the mock star clusters with M = 10 5 M /circledot . Note that the scatter in the AGB luminosity fraction in SSPs is smaller in the Padova10 model than other models. The Padova10 model creates more AGB stars than other models, so that the stochastic fluctuation can be less.</caption>
</figure>
<figure>
<location><page_35><loc_18><loc_35><loc_84><loc_73></location>
<caption>Fig. 13.- Comparison of five SSP model predictions with our results. Squares and shaded region are the same as in Figure 10(b). The solid line represents the Maraston model expectation for both the E-AGB and TP-AGB computed at [Z/H] = - 0.33, and the dashed line and the dot-dashed line indicate respectively Padova02 and Padova10 model expectations from massive mock star clusters with M = 10 6 M /circledot . The BaSTI std (triple-dot dashed line) and BaSTI os (long dashed line) model predictions for massive clusters are also plotted.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "We present a study of K s band luminosity evolution of the asymptotic giant branch (AGB) population in simple stellar systems using star clusters in the Large Magellanic Cloud (LMC). We determine physical parameters of LMC star clusters including center coordinates, radii, and foreground reddenings. Ages of 83 star clusters are derived from isochrone fitting with the Padova models, and those of 19 star clusters are taken from the literature. The AGB stars in 102 star clusters with log(age) = 7.3 - 9.5 are selected using near-infrared color magnitude diagrams based on 2MASS photometry. Then we obtain the K s band luminosity fraction of AGB stars in these star clusters as a function of ages. The K s band luminosity fraction of AGB stars increases, on average, as age increases from log(age) ∼ 8.0, reaching a maximum at log(age) ∼ 8.5, and it decreases thereafter. There is a large scatter in the AGB luminosity fraction for given ages, which is mainly due to stochastic effects. We discuss this result in comparison with five simple stellar population models. The maximum K s band AGB luminosity fraction for bright clusters is reproduced by the models that expect the value of 0.7 - 0.8 at log(age) = 8.5 - 8.7. We discuss the implication of our results with regard to the study of size and mass evolution of galaxies. Subject headings: galaxies: star clusters: general - infrared: stars - stars: AGB and post-AGB - Magellanic Clouds - galaxies: evolution",
"pages": [
1
]
},
{
"title": "K s BAND LUMINOSITY EVOLUTION OF THE ASYMPTOTIC GIANT BRANCH POPULATION BASED ON STAR CLUSTERS IN THE LARGE MAGELLANIC CLOUD",
"content": "Youkyung Ko, Myung Gyoon Lee, and Sungsoon Lim Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea [email protected], [email protected], [email protected]",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "The asymptotic giant branch (AGB), a representative intermediate-age population, is the most luminous evolutionary stage for low- and intermediate-mass (1 - 8 M /circledot ) stars. AGB stars emit a huge amount of near- to mid-infrared light because of their low effective temperature (T eff ∼ 1000 - 4000 K) and circumstellar dust. Hence it is expected that they contribute significantly to the infrared light of galaxies. However, their infrared luminosity contribution in galaxies, even in a simple stellar population (SSP), is still a debating issue with regard to constructing evolutionary population synthesis (EPS) models (Maraston 2011, Bruzual et al. 2013, Noel et al. 2013, and references therein). The EPS models are an useful tool to determine physical parameters of stellar complexes such as star clusters and galaxies by spectral energy distribution (SED) fitting. These models reproduce SEDs of stellar systems by synthesizing the SEDs of stellar populations in various evolutionary stages, assuming age, metallicity, foreground and internal reddening values, star formation history, and so on. Therefore, the spectral energy contribution of individual stellar populations influences the estimation of physical parameters of stellar systems, and especially that of the AGB population plays a key for understanding of the SEDs for stellar systems expected by EPS models. There are various EPS models that include the AGB evolutionary process (e.g., Charlot & Bruzual 1991, Bruzual & Charlot 1993, Fioc & Rocca-Volmerange 1997, Maraston 1998, Leitherer et al. 1999, Vazdekis 1999, Schulz et al. 2002, Bruzual & Charlot 2003, Jimenez et al. 2004, Maraston 2005, Conroy et al. 2009, Kotulla et al. 2009, Conroy & Gunn 2010, Vazdekis et al. 2010, Maraston & Stromback 2011). Bruzual & Charlot (2003, hereafter BC03), for example, presented an EPS model based on Padova evolutionary tracks including just two evolutionary stages for thermally pulsing AGB (TP-AGB) (Girardi et al. 2000), while their recent model includes 15 evolutionary stages of the TP-AGB oxygen-rich and carbon-rich phases (Bruzual A. 2010). The Padova evolutionary tracks adopted in the BC03 model include a given core overshooting efficiency. On the other hand, Maraston (1998, 2005) used evolutionary tracks assuming zero efficiency of the core overshooting from Cassisi et al.(1997, 2000) to determine luminosity contribution of main-sequence populations. It makes the lifetime of main-sequence stars in the Maraston (2005) model shorter compared with Padova isochrones. In addition, she used the fuel consumption theorem (Renzini & Buzzoni 1986) for post-main-sequence stars, not adopting the isochrone synthesis method. In the model of Maraston (1998), the TP-AGB evolutionary process is modified in the fuel consumption theorem, applying the advanced envelope burning process of AGB stars. Renzini & Buzzoni (1986) estimated the contribution of TP-AGB population in the young SSPs with ages < 10 8 yr, and compared it with the star clusters in the the Magellanic Clouds (MCs). They found that it is too high to be consistent with the observational results based on these star clusters. Considering this difference, Maraston (2005) suggested a revised model, assuming shorter lifetime and lower fuel consumption of TP-AGB stars than Renzini & Buzzoni (1986). BC03 and Maraston (2005) adopted different stellar population synthetic methods, and the SEDs reproduced by these models show recognizable differences. A number of studies argue whether or not these EPS models reproduce well observational quantities of stellar systems related with the AGB population as follows. Some studies found that spectra and SEDs of post-starburst galaxies or distant galaxies (z ∼ 1 - 2) have no near-infrared boosted features, which is similar to the expectation of the BC03 model (Muzzin et al. 2009, Kriek et al. 2010, Zibetti et al. 2013). In addition, Conroy & Gunn (2010) suggested that the BC03 model and their own EPS model, a flexible stellar population synthesis model, reproduce the color of star clusters and post-starburst galaxies better than the Maraston (2005) model. In contrast, others confirmed that the Maraston (2005) model performs well in reproducing near-infrared colors, ( Y -K ) and ( H -K ), and SEDs of low to high redshift galaxies (Maraston et al. 2006, Eminian et al. 2008, MacArthur et al. 2010). Moreover, van der Wel et al. (2006) and Henriques et al. (2011) showed that the rest-frame K band mass-to-light ratio evolution and K s band luminosity evolution of galaxies are explained better by the Maraston (2005) model than by the BC03 model. In addition to these galaxy studies, there are several studies investigating star clusters, especially star clusters in the MCs, considering the relevance between the model performance and ages of stellar systems. Because of their proximity, they are very useful to examine not only the individual stellar population directly but also the integrated properties of star clusters. Therefore, they are an ideal object to calibrate SSP models. Pessev et al. (2008) investigated optical to near-infrared colors, ( B -J ), ( V -J ), and ( J -K ), of 54 star clusters in the MCs, and concluded that the BC03 and the Maraston (2005) present the best performance for intermediate-age (0.2 - 2 Gyr) and old ( > 2 Gyr) star clusters, respectively. Lyubenova et al. (2010, 2012) analyzed integrated near-infrared high-resolution spectra of six globular clusters in the Large Magellanic Cloud (LMC) with ages ∼ 1 - 13 Gyr. They showed that the Maraston (2005) model expects J and H band spectra of all their sample star clusters adequately, while it does not for K band spectra of the star clusters with ages < 2 Gyr. Recently Noel et al. (2013) presented the calibration data for stellar population models using 43 star clusters in the MCs. They compared the observed colors of the star clusters, ( V -K ) 0 , ( J -K ) 0 , and ( V -I ) 0 , as a function of ages with the theoretical expectation of various models including BC03 and Maraston (2005). In conclusion, for the ages older than 1 Gyr, the models of Maraston (2005) and BC03 are along the upper end lower end of the observed color, respectively. In the case of the younger ages, BC03 model reproduces well the observed color of star clusters, while Maraston (2005) model expects them too red. While above studies investigated the integrated properties of star clusters, Mucciarelli et al. (2006) analyzed the resolved AGB population in the LMC star clusters in detail. They investigated 19 LMC star clusters in terms of K s band luminosity contribution of AGB stars as a function of cluster ages. The star clusters used in Mucciarelli et al. (2006) have ages of 100 Myr - 3 Gyr (log(age) ∼ 8.0 - 9.5). They concluded that their empirical results are consistent with the expectation of Maraston (2005) for this age range. Later, Mucciarelli et al. (2009) suggested a similar conclusion from the additional study of four old star clusters in the Small Magellanic Cloud (SMC). In this study, we investigate the evolution of AGB luminosity contribution with a large number of LMC star clusters with log(age) ∼ 7.3 - 9.5, overcoming the shortcomings in the previous studies. Because Mucciarelli et al. (2006, 2009) included few star clusters with log(age) ∼ 8.3 - 8.7 (see Figure 5 in Mucciarelli et al. 2009), we enlarged the number of star cluster samples with this age range. In this age range, the AGB luminosity contribution is expected to change rapidly according to the Maraston (2005) model. In addition, most of previous star cluster studies adopted star cluster ages from various literature. We determine ages of LMC star clusters by isochrone fitting homogeneously, using the resolved stars. This paper is organized as follows. In § 2, we introduce the photometric data and images used in this study. § 3 describes the method to estimate physical parameters of sample star clusters such as center coordinates, radii, ages, and foreground reddenings including the cluster sample section. In § 4, we select AGB stars in each star cluster and derive the K s band luminosity contribution of AGB stars to total luminosity of star clusters as a function of ages. In § 5, we compare our results with previous studies, and also compare the primary results with the theoretical expectation from EPS models, including the discussion of stochastic effects. Final section summarizes the main results and presents the conclusion of this study.",
"pages": [
1,
2,
3,
4
]
},
{
"title": "2. Data",
"content": "Bica et al. (2008) presented an extended source catalog of the MCs including star clusters, emission nebulae, associations, and HI shells. They compiled data from various literature including the findings based on photographic survey plates. It contains center coordinates (R.A. and Declination), major and minor axes, and position angles of 3,700 star clusters of the MCs including the LMC, SMC, and the Magellanic Bridge regions. We redetermined the centers and radii of LMC star clusters based on the center coordinates presented in Bica et al. (2008). We used optical ( UBVI ) and near-infrared ( JHK s ) point source catalogs of the LMC. Zaritsky et al. (2004) presented U, B, V , and I band photometry of 24,107,004 point sources in the central 64 deg 2 of the LMC from the Magellanic Clouds Photometric Survey (MCPS; Zaritsky et al. 1997). The MCPS obtained drift-scan images using 1-m Las Campanas Swope Telescope and Great Circle Camera (Zaritsky et al. 1996). Their photometry is incomplete below 21.5, 23.5, 23, and 22 mag in U, B, V , and I bands in sparse regions, respectively. This catalog is used to determine center coordinates, radii, ages, and foreground reddenings of the star clusters. In order to distinguish AGB stars from other populations, we used a near-infrared point source catalog from the two micron all sky survey (2MASS; Skrutskie et al. 2006). In the central 100 deg 2 region of the LMC (10 · × 10 · ), there are 1,430,676 point sources detected in the 2MASS. The limiting magnitudes of photometry are 15.8, 15.1, and 14.3 mag in J, H , and K s bands, respectively, which correspond to 10 σ point source detection level. The AGB stars in the LMC are brighter than K s ∼ 12 . 3 mag, much brighter than the limiting magnitudes. We also used 2MASS Atlas Images to estimate the integrated luminosity of the star clusters, retrieving the K s band images of our sample clusters using 2MASS interactive image service 1 .",
"pages": [
4,
5
]
},
{
"title": "3.1. Center Coordinates and Sizes of Star Clusters",
"content": "We determined centers for 1,645 star clusters and radii for 1,708 star clusters, respectively, using the MCPS catalog (Zaritsky et al. 2004) as a part of our study of LMC star clusters. We constructed 2-dimensional number density maps of bright stars with V < 20.5 mag around the center coordinates of the star clusters presented by Bica et al. (2008). The number density maps are smoothed with a boxcar filter whose width is 20 '' . Center coordinates, coordinate errors, and position angles of each star cluster were estimated by 2-dimensional Gaussian fitting of this smoothed number density map. The field of view for the fitting region is 3 times larger than the radius of each cluster given in Bica et al. (2008). Figure 1 shows an example of centering process for one cluster NGC 1861. We attempted 2-dimensional Gaussian fitting to 3,064 LMC star clusters in Bica et al. (2008), but stellar number density maps could obtain acceptable fits for only 1,645 star clusters. The fitting results are not reliable in the case of poor, faint, or binary clusters, in which case that the center coordinates presented by Bica et al. (2008) are adopted. The radius of each cluster was determined from radial number density profiles (see Figure 2). The radial number density profile is obtained by counting point sources with V < 20.5 mag. We estimated a median value of the background number density (n bg ) of stars located between 200 '' and 300 '' from the center of each cluster. The standard deviation from n bg ( σ bg ) is calculated, and the area of which number density greater than n bg +3 σ bg is considered as a cluster area. Finally, we determined radii of 1,708 LMC star clusters, and radii of the other clusters that do not show a prominent concentration are adopted from Bica et al. (2008). Most of these clusters are poor, faint, or binary ones. Bica et al. (2008) presented major and minor axes of star clusters, from which we define the radius of each star cluster as the mean value of semi-major and semi-minor axes. In addition to Bica et al. (2008), Werchan & Zaritsky (2011) also presented a catalog of star clusters they found in the MCPS images. They investigated stellar overdensities in LMC fields using stars brighter than 20.5 mag in V band. By both King and Elson-FallFreeman model fitting of the surface brightness profiles of each cluster, they determined center coordinates, central surface brightness, tidal radii, and 90% enclosed luminosity radii of 1,066 LMC star clusters. We compare the center coordinates and radii determined in this study with those given by Bica et al. (2008) and Werchan & Zaritsky (2011) in Figure 3. Figure 3(a) - (f) show the differences of center coordinates of star clusters among three studies. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 626, 1,645, and 677, respectively. The center coordinates of star clusters from all three different studies are mostly consistent within 10 '' . Figure 3(g) - (i) show the differences of radii of star clusters. The numbers of star clusters common in both this study and Werchan & Zaritsky (2011), both this study and Bica et al. (2008), and both Bica et al. (2008) and Werchan & Zaritsky (2011) are 615, 1,708, and 681, respectively. Werchan & Zaritsky (2011) presented four kinds of radii for each cluster, core radii and 90% enclosed luminosity radii obtained by fitting using two different models, respectively, and we adopted the 90% enclosed luminosity radius from King model fitting results as a radius to compare with the results from other studies. The values for the cluster radii derived in this study are in better agreement with Bica et al. (2008) than with Werchan & Zaritsky (2011).",
"pages": [
5,
6
]
},
{
"title": "3.2. Cluster Sample Selection and Age Estimation",
"content": "For this study, we selected 102 star clusters that have red and bright stars in nearinfrared ( K s -( J -K s )) CMDs based on 2MASS catalog (Skrutskie et al. 2006). These stars are considered as AGB star candidates. The AGB selection method is described in § 4.1. For 96 and 83 of these star clusters, we estimated foreground reddenings and ages, respectively, with reasonable optical photometry as follows. We chose member stars of each star cluster using the center coordinates and the radii estimated before (see § 3.1). The value of foreground reddening, E ( B -V ), was estimated by shifting the zero age main-sequence (ZAMS) in the (( U -B ) -( B -V )) color-color diagram (CCD). We used the bright main-sequence stars ( V /lessorsimilar 18) located in the outer region up to 200 - 300 '' of each star cluster to obtain the CCDs, and compared the sequence of stars in the CCDs with the ZAMS in the Padova models (Marigo et al. 2008) as in Figure 4(b). The errors of E ( B -V ) values are about 0.02 mag typically. Figure 5(a) and (b) show ( V -( B -V )) CMDs of both a cluster and a field region for NGC 1861, as an example. The cluster CMD is expected to contain field stars as well as cluster stars. In order to minimize the field contamination, we performed statistical subtraction of field CMDs for cluster CMDs. We counted the number of stars in cluster CMDs with that of stars in field CMDs for the same area as the cluster area for each color and magnitude bin (∆( B -V ) ∼ 0 . 5 and ∆ V ∼ 1), and subtracted statistically field stars from cluster stars for each bin. Figure 5(c) displays a field-subtracted CMD of NGC 1861. It shows a clear stellar sequence with a smaller number of stars than the original CMD. We determined ages of 83 star clusters by isochrone fitting in the field-subtracted ( V -( B -V )) CMDs, assuming the distance modulus (m -M) 0 = 18.50 mag and Z = 0 . 008 . Cluster ages were derived using isochrones of Marigo et al. (2008). We used only the stars with small errors of colors with err ( B -V ) < 0 . 1 mag for isochrone fitting. The ages of the other 19 star clusters could not be derived, because they were not covered by the MCPS observation fields or are older than 1 Gyr. In this case, we adopted the ages of these clusters from the literature (Elson & Fall 1985, Girardi et al. 1995, Pietrzynski & Udalski 2000, Goudfrooij et al. 2011, Popescu et al. 2012). Table 1 lists physical parameters of 102 star clusters that will be used for AGB star selection. We compared the ages derived in this study with those given in other references, Elson & Fall (1985), Pietrzynski & Udalski (2000), Hunter et al. (2003), Glatt et al. (2010), and Popescu et al. (2012), as shown in Figure 6. The isochrone fitting method used for the resolved stars in star clusters is considered to be more reliable than other age-dating methods based on the integrated color or spectra of the star clusters. Pietrzynski & Udalski (2000), Glatt et al. (2010), and this study used the isochrone fitting method, while Elson & Fall (1985), Hunter et al. (2003), and Popescu et al. (2012) analyzed the integrated color of the star clusters. Elson & Fall (1985) and Hunter et al. (2003) analyzed ( U -B ) and ( B -V ) colors of the star clusters, and Popescu et al. (2012) performed a Monte Carlo simulation with their own star cluster simulation software (MASSive CLuster Evolution and ANalysis, MASSCLEAN; Popescu & Hanson 2010) to reproduce the cluster colors, ( U -B ) 0 and ( B -V ) 0 . The ages based on the isochrone fitting method show good agreement with each other. They also show correlations with the ages based on integrated colors, but with signif- icant scatters and non-unity slopes. It is noted that the ages derived from integrated colors by Popescu et al. (2012) show a better correlation with the isochrone-fitting ages, compared with other results in Elson & Fall (1985) and Hunter et al. (2003). Figure 7 shows the CMDs of five star clusters that have the largest difference of ages between this study and others: SL482 (Glatt et al. 2010), NGC 1782 (Elson & Fall 1985), SL294 (Popescu et al. 2012), SL503 (Hunter et al. 2003), and H88-182 (Pietrzynski & Udalski 2000). We plotted the Padova isochrones for Z = 0 . 008 and the ages corresponding to the values derived in this study and other references. In the case of SL482, NGC 1782, and H88182, it is difficult to determine their ages reliably because the number of the brightest stars around the main-sequence turnoff is small. However, in the case of other two star clusters, SL294 and SL503, their CMDs are not matched by the isochrones for the ages derived by Popescu et al. (2012) and Hunter et al. (2003) respectively, while they are by the isochrones for the ages derived in this study.",
"pages": [
6,
7,
8
]
},
{
"title": "4.1. Selection of AGB Stars",
"content": "While it is difficult to distinguish AGB stars from RGB stars in optical CMDs, it is relatively easier in near-infrared CMDs. Therefore, we plotted the near-infrared ( K s, 0 -( J -K s ) 0 ) CMDs of resolved stars in 102 star clusters using the 2MASS point source catalog (Skrutskie et al. 2006), and selected AGB stars using two criteria: (1) stars brighter than the tip of the RGB (TRGB); K s, 0 < 12 . 3, and (2) stars redder than the RGB; ( J -K s ) 0 > -0 . 075 × K s, 0 +1 . 85. We adopted the TRGB magnitude, K s = 12.3 ± 0.1 estimated from 2MASS point sources in the LMC region (Nikolaev & Weinberg 2000). The second criterion was suggested from the analysis of the 2MASS photometry for LMC stars by Cioni et al. (2006). There is no constraint for the brightest and reddest stars. We use the extinction law in Cardelli et al. (1989) to derive extinction values for each band, adopting R V = 3 . 1. Figure 8(b) and (d) show the combined ( K s, 0 -( J -K s ) 0 ) CMDs of all stars in 41 young star clusters with log(age) < 8 . 5 and 61 old star clusters with log(age) ≥ 8 . 5, respectively. We selected the AGB stars brighter and redder than AGB boundary lines as described above (dashed lines). We also plotted other AGB boundaries used in the references in Figure 8(b) and (d): dot-dashed lines used by Mucciarelli et al. (2006) and gray shaded regions used by Nikolaev & Weinberg (2000). The AGB boundary used in this study is working in the similar way to that in Nikolaev & Weinberg (2000). However, the AGB boundary used by Mucciarelli et al. (2006) includes a significant number of bluer stars, compared with that in this study. This difference will be discussed in § 5.1.",
"pages": [
8,
9
]
},
{
"title": "4.2. Measurement of K s Band Luminosity Fraction of the AGB Population in Star Clusters",
"content": "We estimated the K s band luminosity of star clusters by aperture photometry using 2MASS K s band images. Photometry was performed with IRAF 2 APPHOT package. For background estimation we used annular apertures with the inner radius to be the sum of the star cluster radius and its error and the aperture width of 10 '' . The background level was estimated using the mode value of the annulus region. For cluster photometry we used circular apertures with radius that is the same as the cluster radius. Figure 9 displays a K s band image of an example star cluster, NGC 1861, showing the position of apertures for the cluster and background area. We calculated the K s band luminosity of AGB stars in each cluster by summing their luminosity converted from 2MASS magnitudes, and obtained the K s band luminosity fraction of AGB stars in the star clusters. Table 2 summarizes the properties of AGB populations as well as other basic parameters of 102 LMC star clusters. It lists the number of AGB stars, and the K s band luminosity and luminosity fraction of AGB stars in each cluster, as well as K s band integrated magnitude and luminosity of the star clusters. The magnitudes are based on 2MASS magnitude system. We adopted the K s band absolute magnitude M K s /circledot = 3 . 27 mag for the Sun, using M V /circledot = 3 . 83 mag (Allen 1976) and ( V -K s ) = 1 . 56 mag (Casagrande et al. 2012), to convert the magnitude into the luminosity. The error of the AGB luminosity fraction is contributed by various errors in addition to the photometric ones estimated for the integrated magnitude of star clusters and presented for the 2MASS magnitude of AGB stars. First, there exist the errors of center coordinates and radii of star clusters, influencing the estimation of their integrated luminosity. We performed aperture photometry for all sample clusters, setting different center positions and radii according to their errors. We selected the upper and lower errors of the integrated luminosity of star clusters, also considering photometric errors. Secondly, there are the errors for the luminosity of AGB stars, which consist of (a) 2MASS photometric error for individual AGB stars and (b) the uncertainty from the Poisson error for the number of AGB stars in each star cluster associated with AGB star counts. Of these two, the latter is much larger than the former. The AGB luminosity error from Poisson error is calculated by multiplying the square root of the number of AGB stars by the mean luminosity for an AGB star in each cluster. We tabulated upper and lower errors of the K s band luminosity fraction obtained by error propagation, considering overall error budget mentioned above (see Table 2). Note that the smaller the numbers of AGB stars in star clusters are, the larger the errors of the luminosity fraction are. Additionally, we checked the field contamination in AGB star count. We investigated the outer region of each star cluster with the radius five times larger than the cluster radius. The number of the AGB stars in this field region is normalized to the cluster area. We calculated the amount of field contamination by multiplying the mean luminosity of AGB stars in star clusters by the number of the normalized field AGB stars, and subtracted it from the luminosity of AGB stars in star clusters. However, the effect of the field contamination to estimating the luminosity fraction of AGB stars is much smaller than that of the Poisson error of the AGB star count. These field-subtracted values are also listed in Table 2. Figure 10(a) shows the K s band luminosity fraction of AGB stars in our sample clusters as a function of ages. Figure 10(b) displays the mean values of the K s band luminosity fraction of AGB stars in the star clusters. These values are also listed in Table 3 including the field-subtracted values. The mean values represent the ratios of the total K s band luminosity of AGB stars in the star clusters to the total K s band luminosity of the star clusters for each age bin. The error of mean values is calculated from the individual errors of the star clusters by error propagation. We also derived a sequence to represent approximately the sequence of bright clusters, as plotted in the figure. The bright clusters have the luminosity of L K s > 8 . 5 × 10 4 L /circledot . Following features are noted in Figure 10. First, the mean values and the bright cluster sequence increase, as log(age) increases from 8.0 to 8.5, reaching 0.6 and 0.8 at log(age) ∼ 8 . 5, respectively. They decrease thereafter. Second, there is a large scatter in the mean values for given ages. We discuss these features in § 5.2.2 in detail.",
"pages": [
9,
10
]
},
{
"title": "5.1. Comparison with Previous Studies",
"content": "In Figure 10(b), we also plotted the results for 19 LMC star clusters given by Mucciarelli et al. (2006) for comparison. There are 12 star clusters common between this study and Mucciarelli et al. (2006). We determined foreground reddenings of six star clusters (NGC 1806, NGC 1866, NGC 1987, NGC 2108, NGC 2134, and NGC 2136) by using the method mentioned above (see § 3.2). For the other three star clusters(NGC 1831, NGC 2173, and NGC 2249), the field stars were not covered by the MCPS. In this case, we adopted foreground reddening values from the optical reddening map of the MCs given by Haschke et al. (2011). Haschke et al. (2011) presented the optical reddening map of the MCs obtained by comparing the theoretical color of the red clump with its observed one based on the OGLE III data. The reddening values of the others (NGC 2162, NGC 2190, and NGC 2231) could not be determined neither in this study nor in Haschke et al. (2011). We assumed the typical extinction value, E ( B -V ) = 0 . 1, for these three clusters. For ages, we determined ages of three of these clusters (NGC 1866, NGC 2134, and NGC 2136). The ages of the others are adopted from Elson & Fall (1985) and Girardi et al. (1995), because we could not use the MCPS catalog for these clusters. We also noticed that the AGB selection criteria of Mucciarelli et al. (2006) are different from those of this study (see Figure 8). Mucciarelli et al. (2006) included as AGB candidates the blue stars that are excluded in this study, but the color and magnitude of these stars indicate that they are bright RGB and supergiant populations according to the analysis of Nikolaev & Weinberg (2000). The color distribution of the stars brighter than K s = 12.3 for young star clusters with log(age) < 8.5 shows a blue excess at ( J -K s ) 0 < 1 . 0 (see Figure 8(a)), while little blue excess is seen for the case of old star clusters with log(age) > 8.5 (see Figure 8(c)). However, those blue stars used in the analysis of Mucciarelli et al. (2006) do not significantly influence the luminosity fraction of AGB stars in the star clusters, because they are somewhat faint (see Figure 11). In addition, there are three red stars not included in the AGB boundary of Mucciarelli et al. (2006) but contained in that of this study, which can be dusty AGB stars. We found that these stars affect little our results. The number of AGB stars shows a large discrepancy between our results and Mucciarelli et al. (2006) for the young star clusters as shown in Figure 11(a), but the difference in the luminosity fraction of AGB stars in the star clusters is much smaller as shown in Figure 11(b). In Figure 10(b), the results for 19 star clusters from Mucciarelli et al. (2006) are included, and those derived in this study are also plotted for four star clusters that show a large discrepancy ( > 0.2) in the AGB luminosity fraction (see Figure 11(b)). Other eight clusters show the consistent results with Mucciarelli et al. (2006). Most of these clusters studied by Mucciarelli et al. (2006) are brighter than L K s = 10 5 L /circledot , except for two star clusters, NGC 2249 and NGC 2231. Indeed they are following the bright cluster sequence derived in this study, with some scatter.",
"pages": [
10,
11
]
},
{
"title": "5.2.1. Mock Cluster Experiments with SSP models",
"content": "We compare our results with the expectation of five theoretical models: (1) an EPS model of Maraston (2005) (called Maraston model), (2) a model based on the isochrone set of Girardi et al. (2002) (called Padova02 model), (3) a model based on the improved isochrone set of Marigo et al. (2008) corrected by Girardi et al. (2010) (called Padova10 model), (4) a model based on the isochrone set of Pietrinferni et al. (2004, 2006) assuming a given overshooting efficiency (called BaSTI os model), and (5) the same as (4), but for null overshooting efficiency (called BaSTI std model). The Maraston model calculates the luminosity contribution of AGB stars directly using the fuel consumption approach. Girardi et al. (2002) and Marigo et al. (2008) corrected by Girardi et al. (2010) presented theoretical stellar evolutionary tracks and isochrones used in various EPS models. The detailed information of these models is described as follows. The Maraston model calculated the amount of the fuel consumption of each population in the post-main-sequence phases (Renzini & Buzzoni 1986) directly, and converted it to observables assuming the effective temperature and surface gravity for evolutionary stages. We obtained the Maraston model prediction for the luminosity contribution of AGB stars in SSPs as a function of ages (Mucciarelli et al. 2006). The theoretical isochrones of Girardi et al. (2002) are based on isochrones of Girardi et al. (2000) for low- and intermediate-mass stars (M ≤ 7 M /circledot ) and Bertelli et al. (1994) for highmass stars (M > 7 M /circledot ). Note that stellar evolutionary tracks of Girardi et al. (2000) are adopted in the BC03 model. In this model, they included the simplified TP-AGB phase and no circumstellar dust that form in AGB stars. Marigo et al. (2008) presented optical to far-infrared isochrones with improved TP-AGB models. Girardi et al. (2010) searched for the TP-AGB population of 12 galaxies in the ACS Nearby Galaxy Survey Treasury, and found that the model of Marigo et al. (2008) creates more TP-AGB populations than observed ones. They corrected the mass-loss rate of TPAGB stars in this model by reducing their lifetime (Bowen & Willson 1991, Willson 2000). This model reproduces the number of TP-AGB stars well, but still has uncertainties in their 1.6 µ m band flux contribution (Melbourne et al. 2012). Additionally, we adopted the isochrone set that includes the circumstellar dust from AGB stars (Groenewegen 2006) and assumed that the dust composition is 100% silicate and 100% amorphous carbonate dust for O-rich and C-rich AGB stars, respectively. These two kinds of Padova isochrones consider the core convective overshooting. In order to investigate this effect, we used the BaSTI isochrone dataset (Pietrinferni et al. 2004, 2006) without overshooting efficiency. We selected a scaled solar isochrone set that contains the extended AGB population. We calculated the predicted K s band luminosity fraction of AGB stars in SSPs by analyzing the mock star clusters produced from the isochrones of Girardi et al. (2002), Marigo et al. (2008), and Pietrinferni et al. (2004). We used the isochrone sets with metallicity Z = 0.008, corresponding to [Z/H] ∼ -0.35 for mock cluster experiments. This value is close to the mean value for the LMC, for our cluster samples. The method is described as follows. We created model stars in mock star clusters assuming the Salpeter initial mass function, and assigned J and K s magnitudes to each star using four different isochrone sets. In addition, we considered magnitude errors for each star in order to make the model prediction more realistic. In the 2MASS catalog, mean magnitude errors and error variances of stars in each magnitude bin vary as a function of magnitudes. We assumed that photometric errors of model stars are distributed normally with the mean value and the variance according to magnitude bins. In ( K s, 0 -( J -K s ) 0 ) CMDs of model stars in mock star clusters with empirical magnitude errors, AGB stars are selected with the same criteria as done for observational data (see § 4.1). The K s band luminosities of mock star clusters and AGB stars are calculated by summing the K s band luminosity of member stars and AGB stars, respectively. Note that for the BaSTI models, they do not provide the magnitudes of 2MASS filter system, so that we adopted those of the Bessell filter system. Finally, we obtained the K s band luminosity fraction of AGB stars in mock star clusters with three different mass (10 4 , 10 5 , and 10 6 M /circledot ), assuming 15 different ages (8.0 ≤ log(age) ≤ 9.5) for each mass scale.",
"pages": [
12,
13
]
},
{
"title": "5.2.2. Stochastic Effect in Estimating Light from AGB Stars",
"content": "Stochastic effects are inevitable in AGB star counts because of the short lifetime of AGB stars. In Figure 10(a), there is a large scatter in the K s band luminosity fraction of AGB stars in the star clusters derived in this study. The AGB stars evolve fast, and become blue and faint when they enter the post-AGB phase. Therefore, we cannot detect all stars that have entered the AGB phase. As a result it makes the luminosity fraction of AGB stars in star clusters lower than expected. Especially, this effect becomes significant for faint star clusters, because of a smaller number of stars. Bright star clusters (L K s tot /greaterorsimilar 8 . 5 × 10 4 L /circledot ) show relatively smaller scatters and seem to be located along a sequence. This trend also appears in the mock star clusters (see Figure 12). We made mock star clusters with 15 different ages and three different masses using four different isochrone sets as above. For each age and mass bin, we made 10 mock star clusters in order to analyze them statistically. Figure 12 shows the K s band luminosity fraction of AGB stars in the mock star clusters as a function of ages. In this figure, the most massive mock star clusters with M = 10 6 M /circledot show the smallest scatter among mock clusters with other mass scale, and make a well-defined sequence (shaded region). However, mock star clusters with M = 10 5 M /circledot (circles) are distributed with large scatter from the massive mock cluster sequence. Therefore we presented two representatives for the observational data: mean values and the bright cluster sequence.",
"pages": [
13,
14
]
},
{
"title": "5.2.3. Comparison with Model Expectation",
"content": "Figure 13 shows a comparison of our results and those expected from five models. In the case of Padova and BaSTI models, we adopted the mean locus line of the massive mock star clusters presented in Figure 12. Note that the Padova02 and BaSTI os models show almost same results of AGB luminosity evolution in SSPs. It reflects that the Padova models include the same ingredients as the BaSTI os model in terms of the core overshooting. Except for these two models, there are several differences in model expectations. First, peak values of the luminosity contribution of AGB stars expected in models are different. The Maraston and Padova10 models suggest 0.7 - 0.8 for the value of the highest AGB fraction, while other three models (Padova02, BaSTI std, and BaSTI os) do just up to ∼ 0.6. Second, all models expect peak values at the similar age range with log(age) ∼ 8.6 - 8.8, except for the BaSTI std model. The peak position of the BaSTI model expectation lies at slightly younger age compared with the expectation of other models. It is because the null overshooting efficiency leads to the shorter lifetime of main-sequence stars. Third, both young and old parts are different between the Maraston model and other models. Padova02, Padova10, and BaSTI os models show that the AGB luminosity fraction in SSPs is lowest at log(age) ∼ 8.0 and increases continuously up to the highest value as SSPs are getting older, while the Maraston model suggests that it comes up to already ∼ 0.4 at log(age) = 8.0 - 8.3 and increases drastically afterwards. The BaSTI std model, however, expects higher AGB luminosity contribution than any other models at log(age) ∼ 8.0 as mentioned above. In the case of SSPs older than 1 Gyr, the AGB luminosity contribution decreases in all models, but the Maraston model shows the steepest decrease. The bright cluster sequence represents well-populated systems that are less influenced by the stochastic fluctuation than faint star clusters, so that it is more appropriate to compare with the expectation of SSP models. In Figure 13, we notice two points with regard to the comparison between the bright cluster sequence and the model expectation: (1) the maximum value of the bright cluster sequence and (2) the age range corresponding to the maximum AGB luminosity contribution. First, the peak value of the AGB luminosity contribution for bright clusters is up to 0.7 - 0.8. Only two models, Maraston and Padova10 models, reproduce this maximum value. Second, the peak position for the bright cluster sequence appears at log(age) = 8.5 - 8.7, which is slightly younger than for model predictions (log(age) = 8.6 - 8.8). However, this discrepancy is not significant because the errors of ages are around 0.1.",
"pages": [
14,
15
]
},
{
"title": "5.3. Implication for the study of size and mass evolution of galaxies",
"content": "The calibration of the EPS models influences galaxy studies because the determination of physical parameters of galaxies depends on the amount of the AGB near-infrared luminosity contribution in EPS models. The difference between the AGB luminosity fractions expected by Padova02 and Maraston models is largest at log(age) ∼ 8.7 - 8.9 (age ∼ 0.5 - 0.8 Gyr), as shown Figure 13. This indicates that the differences of galaxy mass estimates based on the EPS models can be significant at this age range. This can be important for galaxies with young stellar ages, such as high-redshift ( z ≥ 2 - 3) or post-starburst galaxies. In these kinds of galaxies, the young stellar component with ages ∼ 1 Gyr is dominant. For example, Raichoor et al. (2011) presented SED fitting results of 79 early-type galaxies at z ∼ 1.3, finding the differences in stellar ages and masses of galaxies estimated with the BC03 and Maraston models, respectively. They showed that the masses of galaxies derived with the Maraston model tend to be lower than those estimated with the BC03 model, and this discrepancy is prominent (by a factor of two) at galaxy ages ∼ 1.0 - 1.3 Gyr with uncertainty of ∼ 1.0 - 1.5 Gyr (see Figure 5 in Raichoor et al. 2011). Muzzin et al. (2009) reported how the galaxy evolution process depends on EPS models. They investigated the size and mass growth of high-redshift galaxies ( z ∼ 2.3). From the galaxy mass differences based on the EPS models, they found that the galaxy size growth from z ∼ 2.3 to z = 0 is faster in the case of the BC03 model than the case of the Maraston model, assuming that the mass growth rate is same in these two cases. Thus, the sizemass relation of galaxies can be influenced by the AGB luminosity contribution in each EPS model. Our results of the bright cluster sequence are closer to the Maraston model so that they support the size-mass relation of galaxies derived with this model.",
"pages": [
15
]
},
{
"title": "6. Summary and Conclusion",
"content": "We investigated the K s band luminosity evolution of the AGB population in SSPs using 102 LMC star clusters. First, we determined ages and foreground reddening of star clusters from the UBV photometry in the MCPS (Zaritsky et al. 2004) using Padova isochrones (Marigo et al. 2008). Then AGB stars in each cluster were selected using 2MASS ( K s -( J -K s )) CMDs. We derived the K s band luminosity fraction of AGB stars in 102 star clusters as a function of ages. The K s band luminosity fraction of AGB stars in star clusters increases as age increases from log(age) ∼ 8.0. It reaches a maximum up to ∼ 0.6 for mean values and ∼ 0.8 for bright cluster sequences at log(age) ∼ 8.5, and decreases afterwards. The AGB luminosity fraction for given ages shows a large scatter caused by stochastic effects. We compared our results with five SSP models: Padova02, Padova10, Maraston, BaSTI std, and BaSTI os models. It is found that the only two models (Padova10 and Maraston models) match approximately the observational K s band AGB luminosity contribution of bright star clusters derived in this study, while other models predict the AGB luminosity contribution much lower. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 2012R1A4A1028713).",
"pages": [
16
]
},
{
"title": "REFERENCES",
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"pages": [
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}
]
2013ApJ...777..109Z
https://arxiv.org/pdf/1309.4956.pdf
<document>
<section_header_level_1><location><page_1><loc_13><loc_85><loc_87><loc_87></location>SYNCHROTRON LIGHTCURVES OF BLAZARS IN A TIME-DEPENDENT SYNCHROTRON-SELF COMPTON COOLING SCENARIO</section_header_level_1>
<text><location><page_1><loc_33><loc_83><loc_67><loc_84></location>Michael Zacharias & Reinhard Schlickeiser</text>
<text><location><page_1><loc_11><loc_80><loc_89><loc_83></location>Institut fur Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universitat Bochum, 44780 Bochum, Germany (Received; Revised; Accepted) Draft version September 7, 2021</text>
<section_header_level_1><location><page_1><loc_45><loc_77><loc_55><loc_78></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_58><loc_86><loc_77></location>Blazars emit non-thermal radiation in all frequency bands from radio to γ -rays. Additionally, they often exhibit rapid flaring events at all frequencies with doubling time scale of the TeV and X-ray flux on the order of minutes, and such rapid flaring events are hard to explain theoretically. We explore the effect of the synchrotron-self Compton cooling, which is inherently time-dependent, leading to a rapid cooling of the electrons. Having discussed intensively the resulting effects of this cooling scenario on the spectral energy distribution of blazars in previous papers, the effects of the time-dependent approach on the synchrotron lightcurve are investigated here. Taking into account the retardation due to the finite size of the source and the source geometry, we show that the time-dependent synchrotronself Compton (SSC) cooling still has profound effects on the lightcurve compared to the usual linear (synchrotron and external Compton) cooling terms. This is most obvious if the SSC cooling takes longer than the light crossing time scale. Then in most frequency bands the variability time scale is up to an order of magnitude shorter than under linear cooling conditions. This is yet another strong indication that the time-dependent approach should be taken into account for modeling blazar flares from compact emission regions.</text>
<text><location><page_1><loc_14><loc_55><loc_86><loc_58></location>Subject headings: radiation mechanisms: non-thermal - BL Lacertae objects: general - gamma-rays: theory</text>
<section_header_level_1><location><page_1><loc_22><loc_52><loc_35><loc_53></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_36><loc_48><loc_51></location>Blazars, a subclass of active galactic nuclei in the accepted unification scheme of Urry & Padovani (1995), are characterized by a broad non-thermal spectrum exhibiting two characteristic humps and stretching from radio to γ -ray frequencies. In leptonic models the lowenergy component is attributed to synchrotron radiation of highly relativistic electrons, while the high-energy component is inverse Compton emission of the same electron population (for recent reviews see Bottcher 2007, 2012). Several target photon fields are relevant for the inverse Compton process.</text>
<text><location><page_1><loc_8><loc_31><loc_48><loc_36></location>Jones et al. (1974) proposed the synchrotron radiation emitted by the relativistic electrons as the target photon field, which is then up-scattered by the same electrons, the so-called synchrotron-self Compton (SSC) process.</text>
<text><location><page_1><loc_8><loc_17><loc_48><loc_31></location>The vicinity of an active galactic nucleus harbors also additional strong external (to the jet) photon fields, which can potentially contribute in the form of so-called external Compton radiation to the high-energy component of blazars. Such external fields could come from the accretion disk (Dermer & Schlickeiser 1993), the broad line region (Sikora et al. 1994) or the dusty torus (Blazejowski et al. 2000, Arbeiter et al. 2002). These external fields are usually preferred over the SSC, if the highenergy component dominates the synchrotron component in the spectral energy distribution (SED) of blazars.</text>
<text><location><page_1><loc_8><loc_10><loc_48><loc_16></location>It is well established that blazars are far from being steady sources. They exhibit strong flares in all frequency bands, which can in some cases outshine even the brightest galactic sources. The brightest γ -ray flare ever detected is from 3C 454.3, reported by Vercellone et al.</text>
<text><location><page_1><loc_52><loc_43><loc_92><loc_53></location>(2011), reaching a γ -ray flux of F γ = (6 . 8 ± 1 . 0) × 10 -5 photons cm -2 s -1 , which is six times higher than the Vela pulsar. Additionally, blazars also exhibit very rapid flares with doubling time scales on the order of minutes as in the case of PKS 2155-304 (Aharonian et al. 2007) or PKS 1222+216 (Tavecchio et al. 2011) in the TeV regime, or Mrk 421 in the X-rays (Cui 2004).</text>
<text><location><page_1><loc_52><loc_25><loc_92><loc_43></location>Such rapid flares are theoretically challenging, since typical cooling time scales of the radiating electrons are considerably longer. Several models have thus been invoked to explain these rapid flares, such as the jet-in-a-jet model (Giannios et al. 2009), the similar minijets-in-a-jet model (Biteau & Giebels 2012, Giannios 2013), magnetocentrifugal acceleration of beams of particles (Ghisellini et al. 2009a), a star traversing the jet (Barkov et al. 2012), and others. Quite common in all these models is the assumption of an emission blob being smaller than the jet cross-section and moving much faster than the surrounding relativistic jet material. This gives rise to a very short light-crossing time scale, which is usually equaled to the variability time scale.</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_25></location>In many theoretical investigations, as the ones cited above, and in most modeling attempts (e.g. Ghisellini et al. 2009b) the electron distribution is assumed to be stationary. This eases the computational effort, of course, and might be suitable for steady sources or those varying over a long time scale. However, it is certainly not justified for rapid flares as in PKS 2155-304 or PKS 1222+216. The time-dependence of the relativistic electron distribution function has important effects on the resulting SED, as is demonstrated in a recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (hereafter SBM); Zacharias & Schlickeiser 2010, 2012a (hereafter ZSa), 2012b (hereafter ZSb)).</text>
<figure>
<location><page_2><loc_8><loc_73><loc_49><loc_92></location>
<caption>Figure 1. Sketch of the situation: The light of the slice at position l (with volume d V ( l ) = A ( l ) d l ) is received by the observer at time t = t em + l/c .</caption>
</figure>
<text><location><page_2><loc_8><loc_42><loc_48><loc_68></location>Relativistic electrons in a relativistically moving emission blob along the jet of the active galactic nucleus lose energy by emitting synchrotron radiation. These synchrotron photons are a prime target for the same electrons to inverse Compton scatter them to higher energies. This is the SSC process, as mentioned above, which is an additional energy loss process for the electrons. This in turn implies that the subsequently emitted synchrotron photons are less energetic, and so will be the SSC photons. Thus, this results in a decreased efficiency of the SSC process and in a decreased efficiency of the SSC energy loss process with respect to time. Consequently, even if the SSC process dominates initially the electron losses, eventually the time-independent loss processes such as synchrotron and external Compton losses dominate the loss rate. Schlickeiser (2009), as well as Zacharias & Schlickeiser (2010) were able to show that the time-dependent treatment of the SSC losses leads to a much faster electron cooling compared to the steadystate approach.</text>
<text><location><page_2><loc_8><loc_38><loc_48><loc_41></location>Therefore, it is interesting to discuss the effects of this rapid cooling on blazar lightcurves, where the variability can be displayed in an obvious way.</text>
<text><location><page_2><loc_8><loc_19><loc_48><loc_37></location>It is the purpose of this paper to highlight the different effects of the linear and the time-dependent (nonlinear) SSC cooling on the synchrotron lightcurves. To keep the problem simple and analytically tractable, we utilize only the retardation effect due to the finite size of the emission region, and the geometry of the source. This will be discussed in section 2, where we will derive the necessary formula to calculate the lightcurve from the synchrotron intensity. The latter was already calculated by SBM, and we will summarize their results in section 3 for the sake of completeness. We will then use the derived formula from section 2 to calculate the resulting lightcurves in sections 4 and 5. We will discuss the results in section 6 and conclude in section 7.</text>
<text><location><page_2><loc_8><loc_16><loc_48><loc_19></location>The more involved calculations of the inverse Compton lightcurves will be discussed in a future publication.</text>
<section_header_level_1><location><page_2><loc_16><loc_14><loc_41><loc_15></location>2. GEOMETRY OF THE SITUATION</section_header_level_1>
<text><location><page_2><loc_8><loc_11><loc_48><loc_13></location>We assume a spherical, uniform radiation zone in the jet as depicted in figure 1.</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_11></location>For negligible retardation the received monochromatic intensity at intrinsic time t em is I ( t em , /epsilon1 ), where /epsilon1 is the intrinsic energy of the photon. Since, however, the source</text>
<text><location><page_2><loc_52><loc_85><loc_92><loc_92></location>has a finite size, photons emitted at the back of the source will arrive at the observer at a later time ∆ t = 2 R/c than the photons emitted at the front, with R being the radius of the spherical source and c = 3 · 10 10 cm / s the speed of light.</text>
<text><location><page_2><loc_52><loc_72><loc_92><loc_85></location>We include this retardation effect, but assume that the source is (i) spatially homogeneous, and (ii) optically thin. For optically thin sources all photons can leave the emission region without further spatial diffusion (Eichmann et al. 2010). Then the received intensity is just a function of the distance l of the production site from the front. Using a similar approach as Chiaberge & Ghisellini (1999), we cut the source into slices of length d l , as shown in figure 1. The received intensity of each slice is</text>
<formula><location><page_2><loc_54><loc_68><loc_92><loc_71></location>d I ( t -l/c, l, /epsilon1 ) = I ( t -l/c, /epsilon1 ) d V ( l ) V H [ t -l/c ] . (1)</formula>
<text><location><page_2><loc_52><loc_61><loc_92><loc_67></location>Here, t is the time of the observer, which equals t em for l = 0 (the front of the source). The Heaviside function H [ x ] displays the fact that light from a specific slice can only be detected after it has crossed the distance l to the front of the source.</text>
<text><location><page_2><loc_52><loc_50><loc_92><loc_61></location>The fraction d V ( l ) /V is a geometrical weight function, which is defined in such a way that the integral over d V ( l ) /V equals unity. Since in a spherical source each slice has a different volume than the other slices, its contribution depends on its position in the source. The volume of the slice is given by d V ( l ) = A ( l ) d l , where A ( l ) = π (2 Rl -l 2 ) is the cross section of the slice at position l . The geometrical weight function then becomes</text>
<formula><location><page_2><loc_54><loc_44><loc_92><loc_49></location>d V ( l ) V = π (2 Rl -l 2 ) 4 3 πR 3 d l = 3 R [ l 2 R -( l 2 R ) 2 ] d l . (2)</formula>
<text><location><page_2><loc_52><loc_40><loc_92><loc_44></location>The complete received monochromatic lightcurve L ( t, /epsilon1 ) then equals the sum over the contribution from all slices:</text>
<formula><location><page_2><loc_54><loc_25><loc_92><loc_39></location>L ( t, /epsilon1 ) = ∫ d I ( t -l/c, l, /epsilon1 ) = 2 R ∫ 0 I ( t -l/c, /epsilon1 ) H [ t -l/c ] 3 R [ l 2 R -( l 2 R ) 2 ] d l = 6 1 ∫ 0 I ( t -λ 0 λ, /epsilon1 )( λ -λ 2 ) H [ t -λ 0 λ ] d λ , (3)</formula>
<text><location><page_2><loc_52><loc_22><loc_92><loc_24></location>after an obvious substitution. Here we introduced the light-crossing time scale λ 0 = 2 R/c .</text>
<text><location><page_2><loc_52><loc_11><loc_92><loc_22></location>We note that equation (1) is general as long as the assumptions (i) and (ii) are satisfied. Thus, it is not limited to spherical geometries, and for example cylindrical sources could also be chosen. In fact, a cylindrical geometry would lead to a simpler form of the geometrical weight function. However, the assumption of isotropy for the electron distribution and the radiation fields (see below) would not be valid any more. 1</text>
<unordered_list>
<list_item><location><page_2><loc_52><loc_7><loc_92><loc_9></location>1 For example, Chiaberge & Ghisellini (1999) chose a cubed geometry.</list_item>
</unordered_list>
<section_header_level_1><location><page_3><loc_18><loc_91><loc_39><loc_92></location>3. SYNCHROTRON INTENSITY</section_header_level_1>
<text><location><page_3><loc_8><loc_86><loc_48><loc_90></location>In this section we summarize results previously obtained (SBM, ZSa, ZSb) in order to introduce the relevant functions and parameters.</text>
<text><location><page_3><loc_8><loc_82><loc_48><loc_86></location>The isotropic, optically thin synchrotron intensity from relativistic electrons with the volume-averaged differential density n ( γ, t ) is given by</text>
<formula><location><page_3><loc_14><loc_77><loc_48><loc_81></location>I syn ( /epsilon1, t ) = R 4 π ∞ ∫ 0 n ( γ, t ) P syn ( /epsilon1, γ ) d γ , (4)</formula>
<text><location><page_3><loc_8><loc_74><loc_11><loc_76></location>with</text>
<text><location><page_3><loc_52><loc_85><loc_92><loc_92></location>relative strength of external to synchrotron cooling, and has profound consequences for the SED, as we showed in Zacharias & Schlickeiser (2012b). We note that it is less important for the discussion of synchrotron lightcurves and only introduced for the sake of completeness.</text>
<text><location><page_3><loc_52><loc_72><loc_92><loc_85></location>More importantly, as one can see from equation (9), is the fact that the SSC cooling term by its dependence on n ( γ, t ) is time-dependent, which means that its strength decreases over time. Consequently, even if the SSC cooling dominates the total cooling term initially, after some time the SSC cooling will become weaker than the linear cooling, and thus the synchrotron or external Compton cooling will dominate for later times. Obviously, if the linear cooling terms are stronger than the SSC cooling at the beginning, they will be stronger for all times.</text>
<text><location><page_3><loc_52><loc_69><loc_92><loc_72></location>This can be further quantified by the injection parameter</text>
<formula><location><page_3><loc_64><loc_66><loc_92><loc_69></location>α = √ A 0 q 0 D 0 (1 + l ec ) γ 0 . (11)</formula>
<text><location><page_3><loc_52><loc_63><loc_74><loc_65></location>It is defined in such a way that</text>
<formula><location><page_3><loc_64><loc_59><loc_92><loc_63></location>α 2 = | ˙ γ ( t em = 0) | ssc | ˙ γ | syn + | ˙ γ | ec . (12)</formula>
<text><location><page_3><loc_52><loc_53><loc_92><loc_59></location>As a consequence (ZSa and ZSb) the Compton dominance in the SED depends on α 2 , at least in the Thomson limit. This demonstrates the importance of this parameter, which can also be expressed as</text>
<formula><location><page_3><loc_63><loc_49><loc_92><loc_52></location>α = 46 γ 4 N 1 / 2 50 R 15 (1 + l ec ) 1 / 2 , (13)</formula>
<text><location><page_3><loc_52><loc_39><loc_92><loc_48></location>where we scale the total number of electrons N = 10 50 N 50 , and the initial electron Lorentz factor γ 0 = 10 4 γ 4 . Obviously, α increases for increasing γ 0 and N , and decreases for increasing R and l ec . If α /greatermuch 1 the cooling will initially be dominated by the SSC cooling, while for α /lessmuch 1 the cooling is dominated by the linear terms for all times.</text>
<text><location><page_3><loc_52><loc_31><loc_92><loc_39></location>We note that both inverse Compton cooling terms operate in the Thomson limit. In the Klein-Nishina limit the efficiencies of both cooling terms are much reduced, and become unimportant compared to the synchrotron cooling. This resembles the case α /lessmuch 1 and l ec /lessmuch 1 and is, therefore, covered by our approach.</text>
<text><location><page_3><loc_52><loc_27><loc_92><loc_31></location>The differential equation (7) with the loss term (9) and the source term (8) has been solved by SBM. For α /lessmuch 1 (i.e. negligible SSC-losses) they obtained</text>
<formula><location><page_3><loc_54><loc_22><loc_92><loc_26></location>n ( γ, t em ) = q 0 δ ( γ -γ 0 1 + D 0 (1 + l ec ) γ 0 t em ) , (14)</formula>
<text><location><page_3><loc_52><loc_18><loc_92><loc_22></location>which is, indeed, a linear cooling solution. For α /greatermuch 1 (i.e. initially dominating SSC-losses) SBM found</text>
<formula><location><page_3><loc_56><loc_12><loc_92><loc_17></location>n ( γ, t em < t c ) = q 0 H [ t c -t em ] × δ ( γ -γ 0 (1 + 3 α 2 D 0 (1 + l ec ) γ 0 t em ) 1 / 3 ) , (15)</formula>
<text><location><page_3><loc_52><loc_9><loc_92><loc_12></location>yielding a nonlinear dependence of γ on time. For later times the electron density approaches</text>
<formula><location><page_3><loc_63><loc_7><loc_85><loc_8></location>n ( γ, t em > t c ) = q 0 H [ t em -t c ]</formula>
<formula><location><page_3><loc_18><loc_71><loc_48><loc_75></location>P syn ( /epsilon1, γ ) = P 0 /epsilon1 γ 2 CS ( 2 /epsilon1 3 /epsilon1 0 γ 2 ) (5)</formula>
<text><location><page_3><loc_8><loc_64><loc_48><loc_71></location>being the synchrotron power of a single electron in a large-scale random magnetic field of constant strength B = b Gauss (Crusius & Schlickeiser 1988). Here P 0 = 2 · 10 24 erg -1 s -1 , and /epsilon1 0 = 1 . 9 · 10 -20 b erg. The function CS ( x ) is well approximated by</text>
<formula><location><page_3><loc_20><loc_61><loc_48><loc_63></location>CS ( x ) ≈ a 0 x -2 / 3 e -x , (6)</formula>
<text><location><page_3><loc_8><loc_59><loc_22><loc_61></location>with a 0 = 1 . 151275.</text>
<text><location><page_3><loc_8><loc_57><loc_48><loc_59></location>The differential relativistic electron density can be calculated from the kinetic equation (Kardashev 1962)</text>
<formula><location><page_3><loc_12><loc_53><loc_48><loc_56></location>∂n ( γ, t em ) ∂t -∂ ∂γ [ | ˙ γ | n ( γ, t em )] = S ( γ, t em ) , (7)</formula>
<text><location><page_3><loc_8><loc_49><loc_48><loc_52></location>where | ˙ γ | is the electron energy loss term, and S ( γ, t em ) is the source term.</text>
<text><location><page_3><loc_8><loc_47><loc_48><loc_49></location>For demonstration purposes and ease of calculation we use a relatively simple source term</text>
<formula><location><page_3><loc_16><loc_44><loc_48><loc_46></location>S ( γ, t em ) = q 0 δ ( γ -γ 0 ) δ ( t em ) , (8)</formula>
<text><location><page_3><loc_8><loc_39><loc_48><loc_43></location>that is a single injection of monochromatic electrons with the injection Lorentz factor γ 0 and the electron density q 0 .</text>
<text><location><page_3><loc_8><loc_30><loc_48><loc_39></location>In the scenario depicted here we consider electron losses via the synchrotron, external Compton and synchrotron-self Compton channels. Since the latter depends on the produced synchrotron radiation, and thus directly on the electron distribution, the kinetic equation becomes non-linear (Schlickeiser 2009). The total electron loss term is given by</text>
<formula><location><page_3><loc_13><loc_23><loc_48><loc_29></location>| ˙ γ | = | ˙ γ | syn + | ˙ γ | ec + | ˙ γ ( t em ) | ssc = D 0 (1 + l ec ) γ 2 + A 0 γ 2 ∞ ∫ 0 γ 2 n ( γ, t em ) d γ . (9)</formula>
<text><location><page_3><loc_8><loc_18><loc_48><loc_22></location>The parameters are D 0 = 1 . 3 · 10 -9 b 2 s -1 , and A 0 = 1 . 2 · 10 -18 R 15 b 2 cm 3 s -1 , where we scaled the radius of the source as R = 10 15 R 15 cm.</text>
<text><location><page_3><loc_10><loc_17><loc_17><loc_18></location>We define</text>
<formula><location><page_3><loc_20><loc_13><loc_48><loc_16></location>l ec = | ˙ γ | ec | ˙ γ | syn = 4Γ 2 b 3 u ' ec u B . (10)</formula>
<text><location><page_3><loc_8><loc_7><loc_48><loc_12></location>where Γ b is the Lorentz factor of the plasma blob, u ' ec is the isotropic energy density of the external radiation field in the frame of the host galaxy, and u B is the energy density of the magnetic field. This parameter describes the</text>
<formula><location><page_4><loc_14><loc_88><loc_48><loc_92></location>× δ ( γ -γ 0 1+2 α 3 3 α 2 + D 0 (1 + l ec ) γ 0 t em ) , (16)</formula>
<text><location><page_4><loc_8><loc_85><loc_48><loc_87></location>which is a modified linear cooling solution. The transition time is defined as</text>
<formula><location><page_4><loc_20><loc_81><loc_48><loc_84></location>t c = α 3 -1 3 α 2 D 0 (1 + l ec ) γ 0 . (17)</formula>
<text><location><page_4><loc_8><loc_76><loc_48><loc_80></location>The intensity (4) for both cases of α has also been calculated by SBM. For α /lessmuch 1 they obtained with equation (14)</text>
<formula><location><page_4><loc_13><loc_69><loc_48><loc_75></location>I syn ( t em , /epsilon1 ) = I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t em t syn ) 2 / 3 × e -/epsilon1 E 0 ( 1+ tem tsyn ) 2 . (18)</formula>
<text><location><page_4><loc_8><loc_67><loc_37><loc_68></location>For α /greatermuch 1 with equations (15) and (16)</text>
<formula><location><page_4><loc_10><loc_60><loc_48><loc_66></location>I syn ( t em < t c , /epsilon1 ) = I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + 3 α 2 t syn t em ) 2 / 9 × e -/epsilon1 E 0 ( 1+ 3 α 2 tsyn t em ) 2 / 3 , (19)</formula>
<text><location><page_4><loc_8><loc_57><loc_11><loc_59></location>and</text>
<formula><location><page_4><loc_11><loc_51><loc_48><loc_57></location>I syn ( t em > t c , /epsilon1 ) = I 0 ( /epsilon1 E 0 ) 1 / 3 ( α g + t em t syn ) 2 / 3 × e -/epsilon1 E 0 ( α g + tem tsyn ) 2 . (20)</formula>
<text><location><page_4><loc_8><loc_45><loc_48><loc_50></location>Here we used the definitions I 0 = 3 a 0 RP 0 q 0 /epsilon1 0 / (8 π ), t syn = 1 / ( D 0 (1 + l ec ) γ 0 ), E 0 = 3 /epsilon1 0 γ 2 0 / 2, and α g = (1 + 2 α 3 ) / (3 α 2 ).</text>
<text><location><page_4><loc_8><loc_40><loc_48><loc_45></location>These intensities are equal to a monochromatic lightcurve, where the retardation and, thus, the source's finite size have not been taken into account. Below, we will refer to them as the 'unretarded' lightcurves.</text>
<text><location><page_4><loc_8><loc_36><loc_48><loc_40></location>Now, we have collected all necessary ingredients to calculate the retarded synchrotron lightcurves, which we present in the following sections.</text>
<section_header_level_1><location><page_4><loc_10><loc_33><loc_47><loc_35></location>4. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING LINEAR COOLING</section_header_level_1>
<text><location><page_4><loc_8><loc_29><loc_48><loc_32></location>Using equation (18) in equation (3) we obtain the retarded lightcurve for the case α /lessmuch 1:</text>
<formula><location><page_4><loc_12><loc_21><loc_48><loc_28></location>L ( t, /epsilon1 ) = 6 I 0 ( /epsilon1 E 0 ) 1 / 3 1 ∫ 0 ( 1 + t -λ 0 λ t syn ) 2 / 3 × e -/epsilon1 E 0 ( 1+ t -λ 0 λ tsyn ) 2 λ -λ 2 H [ t -λ 0 λ ] d λ . (21)</formula>
<text><location><page_4><loc_8><loc_12><loc_48><loc_20></location>The integral (21) can be solved in terms of several incomplete Gamma-functions. However, this would not give many insights. Instead, we will use meaningful approximations for the integral in three time domains. These domains can later be glued together to give a continuous analytic result.</text>
<formula><location><page_4><loc_25><loc_19><loc_31><loc_23></location>( )</formula>
<text><location><page_4><loc_8><loc_7><loc_48><loc_12></location>First of all, we define two characteristic time scales of the unretarded lightcurve. They can later be connected to the light-crossing time scale, yielding some information about the resulting retarded lightcurve. The first</text>
<text><location><page_4><loc_52><loc_89><loc_92><loc_92></location>one is the local maximum of the unretarded lightcurve, which is:</text>
<formula><location><page_4><loc_62><loc_85><loc_92><loc_89></location>t 1 ( /epsilon1 ) = t syn ( √ E 0 3 /epsilon1 -1 ) . (22)</formula>
<text><location><page_4><loc_52><loc_78><loc_92><loc_84></location>This expression is negative for /epsilon1 > E 0 / 3, indicating that for such energies there is no local maximum. If t 1 ( /epsilon1 ) > λ 0 the variability will mostly take place for times later than the light-crossing time scale. Solving the resulting inequality for /epsilon1 , results in</text>
<formula><location><page_4><loc_61><loc_71><loc_92><loc_77></location>/epsilon1 < /epsilon1 1 = E 0 3 ( 1 + λ 0 t syn ) 2 < E 0 3 . (23)</formula>
<text><location><page_4><loc_52><loc_65><loc_92><loc_72></location>This equation implies that for energies /epsilon1 < /epsilon1 1 the variability due to the flare will be longer than the lightcrossing time scale. Hence, we expect the global maximum of the lightcurve to occur later than λ 0 , and thus be unaffected by the retardation.</text>
<text><location><page_4><loc_52><loc_57><loc_92><loc_65></location>The second characteristic time scale is related to the argument of the exponential in the unretarded lightcurve A = /epsilon1 E 0 (1 + t em /t syn ) 2 . As soon as t em ≥ t syn the unretarded lightcurve exponentially decays, which should also be visible in the retarded lightcurve. Since, however, A ≈ /epsilon1 E 0 for t em /lessmuch t syn , we set</text>
<formula><location><page_4><loc_64><loc_49><loc_92><loc_56></location>A = /epsilon1 E 0 ( 1 + t em t syn ) 2 = /epsilon1 E 0 + A ∗ ( /epsilon1, t em ) , (24)</formula>
<text><location><page_4><loc_52><loc_47><loc_55><loc_49></location>with</text>
<formula><location><page_4><loc_58><loc_43><loc_92><loc_47></location>A ∗ ( /epsilon1, t em ) = /epsilon1 E 0 [ ( 1 + t em t syn ) 2 -1 ] . (25)</formula>
<text><location><page_4><loc_52><loc_37><loc_92><loc_43></location>Once A ∗ ( /epsilon1, t em ) is larger than unity the unretarded lightcurve will exponentially decay. Thus, we obtain the second characteristic time scale t 2 ( /epsilon1 ) by A ( /epsilon1, t 2 ( /epsilon1 )) = 1, yielding</text>
<formula><location><page_4><loc_61><loc_33><loc_92><loc_37></location>t 2 ( /epsilon1 ) = t syn ( √ 1 + E 0 /epsilon1 -1 ) . (26)</formula>
<text><location><page_4><loc_52><loc_26><loc_92><loc_32></location>Unlike t 1 ( /epsilon1 ), the second characteristic time scale exhibits no restrictions by /epsilon1 . Obviously, t 1 ( /epsilon1 ) < t 2 ( /epsilon1 ). For t 2 ( /epsilon1 ) > λ 0 the exponential will become important only after the light-crossing time scale. Solving the inequality for /epsilon1 we obtain</text>
<text><location><page_4><loc_52><loc_10><loc_92><loc_21></location>We can now begin with the actual calculation of the retarded lightcurve. The simplest case is obviously for t > λ 0 , since in this case the retarded lightcurve should be the same as the unretarded lightcurve. This is due to the fact that the retardation is not important for time scales much longer than λ 0 . Inspecting the difference t -λ 0 λ , we see that λ 0 λ can be at most equal to λ 0 . Thus, for t /greatermuch λ 0 we can approximate t -λ 0 λ ≈ t . Hence,</text>
<formula><location><page_4><loc_62><loc_20><loc_92><loc_26></location>/epsilon1 < /epsilon1 2 = E 0 ( 1 + λ 0 t syn ) 2 -1 . (27)</formula>
<formula><location><page_4><loc_57><loc_5><loc_88><loc_9></location>L ( t > λ 0 , /epsilon1 ) ≈ 6 I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t t syn ) 2 / 3</formula>
<formula><location><page_5><loc_12><loc_83><loc_48><loc_92></location>× e -/epsilon1 E 0 ( 1+ t tsyn ) 2 1 ∫ 0 ( λ -λ 2 ) d λ = I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 , (28)</formula>
<text><location><page_5><loc_8><loc_82><loc_43><loc_83></location>which, indeed, equals the unretarded lightcurve.</text>
<text><location><page_5><loc_8><loc_74><loc_48><loc_82></location>The other rather simple case is for t < λ 0 with the further requirement that t < t 1 , 2 ( /epsilon1 ) (the subscript refers to both t 1 and t 2 ). The latter implies that the unretarded lightcurves were neither variable nor have they decayed already. Then in eq. (21) the terms ( t -λ 0 λ ) /t syn can be neglected compared to unity, yielding</text>
<formula><location><page_5><loc_11><loc_63><loc_48><loc_73></location>L ( t < λ 0 , /epsilon1 ) ≈ 6 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 t/λ 0 ∫ 0 ( λ -λ 2 ) d λ = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 [ 1 -2 3 t λ 0 ] . (29)</formula>
<text><location><page_5><loc_8><loc_59><loc_48><loc_63></location>For times below the light-crossing time scale and below the variability time scale of the unretarded lightcurve the retarded lightcurve increases rapidly L ∝ t 2 .</text>
<text><location><page_5><loc_8><loc_55><loc_48><loc_59></location>For intermediate times the calculation is quite involved, and the details can be found in appendix A. We obtain</text>
<formula><location><page_5><loc_9><loc_45><loc_47><loc_55></location>L ( t 1 , 2 < t < λ 0 , /epsilon1 ) = 6 I 0 ( /epsilon1 E 0 ) 1 / 3 × t/λ 0 ∫ 0 ( 1 + t -λ 0 λ t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t -λ 0 λ tsyn ) 2 ( λ -λ 2 ) d λ 2 / 3</formula>
<formula><location><page_5><loc_14><loc_42><loc_48><loc_46></location>≈ 3 I 0 ( /epsilon1 E 0 ) -e -/epsilon1 E 0 t 2 syn λ 2 0 ( t t syn )[ 1 -t λ 0 ] . (30)</formula>
<text><location><page_5><loc_8><loc_30><loc_48><loc_42></location>We note that the exact form of the intermediate regime is not so important, since it will be glued to the approximation (29) at t ≈ t 2 . The most important result is the linear increase of the the lightcurve (30), which leads to a break at t 2 in the retarded lightcurve. However, if t 1 , 2 ( /epsilon1 ) > λ 0 the intermediate part does not play a role, and the lightcurve breaks immediately at t = λ 0 from the initial t 2 -dependence to the time dependence given by equation (28).</text>
<text><location><page_5><loc_8><loc_24><loc_48><loc_30></location>Depending on the synchrotron photon energy /epsilon1 , we can now construct the lightcurves from the three approximations (28) - (30). We obtain two cases, divided in additional sub-cases.</text>
<text><location><page_5><loc_10><loc_23><loc_34><loc_24></location>Beginning with /epsilon1 < E 0 / 3, we get:</text>
<formula><location><page_5><loc_14><loc_12><loc_48><loc_22></location>L ( t, /epsilon1 < /epsilon1 1 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 , (31)</formula>
<formula><location><page_5><loc_12><loc_4><loc_44><loc_11></location>L ( t, /epsilon1 1 < /epsilon1 < /epsilon1 2 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 ( 1 + t t 2 ) 5 / 3</formula>
<formula><location><page_5><loc_64><loc_88><loc_92><loc_92></location>× ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 , (32)</formula>
<formula><location><page_5><loc_52><loc_76><loc_92><loc_86></location>L ( t, /epsilon1 2 < /epsilon1 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 ( 1 + t 2 t 2 ) 5 / 3 × ( 1 + t t syn ) 2 / 3 [ 1 -t λ 0 ] . (33)</formula>
<text><location><page_5><loc_52><loc_74><loc_77><loc_76></location>For /epsilon1 > E 0 / 3 the solutions become:</text>
<formula><location><page_5><loc_55><loc_63><loc_92><loc_73></location>L ( t, E 0 / 3 < /epsilon1 < /epsilon1 2 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 , (34)</formula>
<formula><location><page_5><loc_53><loc_57><loc_92><loc_62></location>L ( t, /epsilon1 2 < /epsilon1 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 1 + t 2 t 2 [ 1 -t λ 0 ] . (35)</formula>
<text><location><page_5><loc_52><loc_51><loc_92><loc_56></location>The lightcurves (33) and (35) cut off at t = λ 0 . Obviously, light from the back reaches the observer only at later times, causing the radiation to be visible on longer time scales than implied by the unretarded lightcurve.</text>
<text><location><page_5><loc_52><loc_45><loc_92><loc_51></location>The analytical results (31) - (35) are plotted along with a numerical integration of equation (21) in Figure 2 for two cases of γ 0 . For comparison, we also show the unretarded lightcurve.</text>
<text><location><page_5><loc_52><loc_40><loc_92><loc_45></location>The first obvious result is that the retarded synchrotron lightcurve increases rapidly as long as t < λ 0 . Afterwards the retarded lightcurve behaves as the unretarded one, which is reasonable, as we discussed above.</text>
<text><location><page_5><loc_52><loc_28><loc_92><loc_40></location>The other points mentioned earlier are also quite obvious. Even though the unretarded lightcurve for very high energies cuts off long before the light-crossing time scale, the retarded lightcurves are extended until λ 0 . The break in the lightcurve in the intermediate time regime is also evident. However, as discussed above, the low energetic cases, where the variability time scales are much longer than the light-crossing time scale, do not exhibit this break.</text>
<text><location><page_5><loc_52><loc_12><loc_92><loc_28></location>As one can see, the analytical result matches the numerical integration rather well, which is reassuring and validates a posteriori our approximations. However, there is one caveat: The distinction of cases by t 2 and /epsilon1 2 is rather sharp (esp. equations (33) and (35)). This is obvious in the left plot of Figure 2 in the analytical curve for /epsilon1 = 10 E 0 , which cuts off at t = λ 0 . On the other hand, the numerical curve in this case decays exponentially. The distinction of the cases divided by /epsilon1 2 is, therefore, not as strict as implied by the analytical result. It is a more gradual transition, which is, however, difficult to implement in one equation.</text>
<text><location><page_5><loc_52><loc_7><loc_92><loc_12></location>The problem is probably due to the rather artificial definition of t 2 , which is also indicated by the fact that the break for the high-energy lightcurves is better placed at 2 t 2 instead of t 2 .</text>
<figure>
<location><page_6><loc_9><loc_69><loc_46><loc_92></location>
</figure>
<figure>
<location><page_6><loc_51><loc_69><loc_88><loc_92></location>
<caption>Figure 2. Unretarded (full), as well as numerical (dashed) and analytical (dotted) retarded lightcurve for α /greatermuch 1 and two cases of γ 0 over a logarithmic time-axis. The values of /epsilon1 in the legend are given in units of E 0 . The curves are normalized with I 0 and we set b = 1.</caption>
</figure>
<section_header_level_1><location><page_6><loc_10><loc_62><loc_47><loc_65></location>5. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING INITIAL SSC COOLING</section_header_level_1>
<text><location><page_6><loc_8><loc_59><loc_48><loc_62></location>For the case α /greatermuch 1 we use equations (19) and (20) in equation (3) to obtain the retarded lightcurve</text>
<formula><location><page_6><loc_10><loc_54><loc_46><loc_58></location>L 1 ( t, /epsilon1 ) = 6 I 0 /epsilon1 E 0 1 / 3 1 1 + 3 α 2 t syn ( t -λ 0 λ ) 2 / 9</formula>
<formula><location><page_6><loc_20><loc_48><loc_48><loc_57></location>( ) ∫ 0 ( ) × e -/epsilon1 E 0 ( 1+ 3 α 2 tsyn ( t -λ 0 λ ) ) 2 / 3 ( λ -λ 2 ) × H [ t -λ 0 λ ] H [ t c -( t -λ 0 λ )] d λ , (36)</formula>
<formula><location><page_6><loc_12><loc_41><loc_44><loc_46></location>L 2 ( t, /epsilon1 ) = 6 I 0 ( /epsilon1 E 0 ) 1 / 3 1 ∫ 0 ( α g + t -λ 0 λ t syn ) 2 / 3</formula>
<formula><location><page_6><loc_18><loc_36><loc_48><loc_41></location>× e -/epsilon1 E 0 ( α g + t -λ 0 λ tsyn ) 2 ( λ -λ 2 ) × H [ t -λ 0 λ ] H [( t -λ 0 λ ) -t c ] d λ . (37)</formula>
<text><location><page_6><loc_8><loc_24><loc_48><loc_36></location>For t c < t < t c + λ 0 both L 1 and L 2 contribute to the emitted lightcurve, which differs from the strict division of the unretarded lightcurves (19) and (20). This is, again, an effect of the retardation: Even if light received from the front of the source is from electrons already cooling in the linear regime ( t em > t c ), the light received from the back of the source is still from electrons cooling in the nonlinear regime ( t em < t c ). If t c < λ 0 this period can be quite extended.</text>
<text><location><page_6><loc_8><loc_13><loc_48><loc_24></location>Although there are several sub-cases to consider in the analytical calculation, we can use the same approximation for the integrals (36) and (37), as we used to obtain equations (28) - (30). It is therefore unnecessary to repeat them in detail. Instead, we will summarize the results in the most compact form possible, where the sub-cases are combined in such a way that the resulting lightcurve is continuous.</text>
<text><location><page_6><loc_8><loc_11><loc_48><loc_13></location>The characteristic time scales t 3 ( /epsilon1 ) and t 4 ( /epsilon1 ) are obtained by the same arguments as t 1 ( /epsilon1 ) and t 2 ( /epsilon1 ), giving</text>
<formula><location><page_6><loc_16><loc_5><loc_48><loc_10></location>t 3 ( /epsilon1 ) = t syn 3 α 2 [ ( E 0 3 /epsilon1 ) 3 / 2 -1 ] , (38)</formula>
<formula><location><page_6><loc_60><loc_61><loc_92><loc_65></location>t 4 ( /epsilon1 ) = t syn 3 α 2 [ ( 1 + E 0 /epsilon1 ) 3 / 2 -1 ] . (39)</formula>
<text><location><page_6><loc_52><loc_59><loc_69><loc_60></location>For t 3 , 4 ( /epsilon1 ) > λ 0 we find</text>
<formula><location><page_6><loc_62><loc_52><loc_92><loc_58></location>/epsilon1 < /epsilon1 3 = E 0 3 ( 1 + 3 α 2 λ 0 t syn ) 2 / 3 , (40)</formula>
<text><location><page_6><loc_52><loc_46><loc_74><loc_48></location>while for t 3 , 4 ( /epsilon1 ) > t c we obtain</text>
<formula><location><page_6><loc_61><loc_47><loc_92><loc_53></location>/epsilon1 < /epsilon1 4 = E 0 ( 1 + 3 α 2 λ 0 t syn ) 2 / 3 -1 , (41)</formula>
<formula><location><page_6><loc_67><loc_43><loc_92><loc_45></location>/epsilon1 < /epsilon1 c 3 = E 0 3 α 2 , (42)</formula>
<formula><location><page_6><loc_65><loc_39><loc_92><loc_42></location>/epsilon1 < /epsilon1 c 4 = E 0 α 2 -1 , (43)</formula>
<text><location><page_6><loc_52><loc_37><loc_61><loc_39></location>respectively.</text>
<text><location><page_6><loc_52><loc_35><loc_92><loc_37></location>With these definitions, we sum up the results of the analytical calculation.</text>
<text><location><page_6><loc_53><loc_33><loc_76><loc_35></location>We begin with the case t c < λ 0 :</text>
<formula><location><page_6><loc_86><loc_32><loc_86><loc_32></location>2</formula>
<formula><location><page_6><loc_55><loc_22><loc_92><loc_32></location>L ( t, /epsilon1 < /epsilon1 3 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( α g + t tsyn ) 2 , (44)</formula>
<formula><location><page_6><loc_52><loc_11><loc_92><loc_21></location>L ( t, /epsilon1 3 < /epsilon1 < /epsilon1 c 3 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( α g + t tsyn ) 2 , (45)</formula>
<formula><location><page_6><loc_56><loc_5><loc_87><loc_9></location>L ( t, /epsilon1 c 3 < /epsilon1 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2</formula>
<formula><location><page_7><loc_19><loc_88><loc_48><loc_92></location>× ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( α g + t tsyn ) 2 , (46)</formula>
<formula><location><page_7><loc_9><loc_82><loc_48><loc_87></location>L ( t, E 0 / 3 < /epsilon1 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 1 + t 2 t 4 [ 1 -t λ 0 ] . (47)</formula>
<text><location><page_7><loc_8><loc_80><loc_48><loc_82></location>For t c > λ 0 the analytical calculation yields for /epsilon1 < E 0 / 3</text>
<formula><location><page_7><loc_11><loc_69><loc_48><loc_80></location>L ( t < t c , /epsilon1 < E 0 / 3) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 9 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 / 3 (48)</formula>
<formula><location><page_7><loc_15><loc_60><loc_48><loc_68></location>L ( t > t c , /epsilon1 < E 0 / 3) = I 0 ( /epsilon1 E 0 ) 1 / 3 × ( α g + t t syn ) 2 / 3 e -/epsilon1 E 0 ( α g + t tsyn ) 2 , (49)</formula>
<text><location><page_7><loc_8><loc_58><loc_48><loc_60></location>which is the only case where L must be divided. For /epsilon1 > E 0 / 3 we obtain</text>
<formula><location><page_7><loc_11><loc_47><loc_48><loc_57></location>L ( t, E 0 / 3 < /epsilon1 < /epsilon1 4 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 ( t λ 0 ) 2 1 + 3 ( t λ 0 ) 2 × ( 1 + t t syn ) 2 / 9 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 / 3 , (50)</formula>
<formula><location><page_7><loc_8><loc_41><loc_51><loc_46></location>L ( t, E 0 / 3 < /epsilon1 4 < /epsilon1 ) = 3 I 0 ( /epsilon1 E 0 ) 1 / 3 e -/epsilon1 E 0 ( t λ 0 ) 2 1 + t 2 t 4 [ 1 -t λ 0 ] . (51)</formula>
<text><location><page_7><loc_8><loc_36><loc_48><loc_40></location>In Figure 3 we compare the analytical results with the numerical results, and achieve quite good agreement. The unretarded lightcurve is shown again for comparison.</text>
<text><location><page_7><loc_8><loc_31><loc_48><loc_36></location>Since the basic properties of the plot are the same as in Figure 2, we do not need to repeat them here. The problem with t 4 and /epsilon1 4 , mentioned in the discussion for Figure 2, is evident here, again.</text>
<section_header_level_1><location><page_7><loc_23><loc_29><loc_34><loc_30></location>6. DISCUSSION</section_header_level_1>
<text><location><page_7><loc_8><loc_15><loc_48><loc_28></location>In Figures 2 and 3 we show lightcurves in a logarithmic plot, which has the advantage of having several cases in one plot. This makes it much easier to compare variability aspects which occur on very different time scales. Our discussion will focus on these logarithmic plots. On the other hand, lightcurves are commonly displayed in a linear plot, which highlights the behavior of lightcurves around their respective maxima. We present such linear plots in Figure 4. The results are completely compatible.</text>
<text><location><page_7><loc_8><loc_11><loc_48><loc_15></location>Comparing Figures 2 and 3 one can see that there are some points, where the results are similar, and some other points, which are remarkably different.</text>
<text><location><page_7><loc_8><loc_7><loc_48><loc_11></location>First of all, we note that the 'variability time scale' of any given lightcurve is determined by its global maximum. Thus, the minimal variability time scale, which is</text>
<text><location><page_7><loc_52><loc_78><loc_92><loc_92></location>possible at all, is given by the light-crossing time scale, since the source is evenly contributing to the radiative output. If the source only partially radiates, the variability time scale can be much lower (Eichmann et al. 2010). The rising phase until λ 0 is dominated by the source geometry, giving a t 2 -dependence up to the break times t 2 ( /epsilon1 ) for α /lessmuch 1 and t 4 ( /epsilon1 ) for α /greatermuch 1, respectively. If t 2 , 4 ( /epsilon1 ) < λ 0 , the lightcurve exhibits a break to a t 1 -dependence. Otherwise the spectrum breaks directly to the unretarded lightcurve at λ 0 . 2</text>
<text><location><page_7><loc_52><loc_69><loc_92><loc_78></location>Secondly, for larger initial electron energies γ 0 the variability time scale is much reduced compared to lower initial electron energies. Hence, in the low-energetic frequency bands the variability time scale shifts closer to λ 0 for larger γ 0 . Thus, one can get information about the initial electron energy by observing the peak times of different frequency bands.</text>
<text><location><page_7><loc_52><loc_48><loc_92><loc_69></location>The plots for the high-energetic cases ( γ 0 = 10 5 ) look quite similar in both cases of α , since t c is smaller than λ 0 , and the lightcurves are the same for t > t c . However, they can be distinguished by the high-energetic frequency bands. Both are less luminous for α /greatermuch 1 compared to α /lessmuch 1, because the synchrotron SED exhibits a broken power-law for α /greatermuch 1, leading to a decreased flux for high energies compared to the α /lessmuch 1 case (cf. SBM). Additionally, the break in the lightcurve from the quadratic time-dependence to the linear timedependence takes place a factor 3 α 2 earlier in the α /greatermuch 1 case than for α /lessmuch 1, since the unretarded lightcurve cuts off much earlier for α /greatermuch 1 than for α /lessmuch 1. Thus, the sum over all unretarded lightcurves of each slice (that is the retarded lightcurve) for α /greatermuch 1 must be less luminous and increase less strongly than for α /lessmuch 1.</text>
<text><location><page_7><loc_52><loc_16><loc_92><loc_48></location>The low-energetic cases ( γ 0 = 10 3 ) differ strongly for α larger and smaller than unity, since t c is larger than λ 0 . The features, which are plainly visible in the unretarded lightcurve, are thus also visible in the retarded lightcurve. The lightcurve for /epsilon1 = 10 E 0 cuts off in both cases at around λ 0 . However, for α /greatermuch 1 the break is clearly visible in the lightcurve, which is due to the faster cooling of the electrons in this case of α . Similarly, the lightcurve for /epsilon1 = E 0 cuts off for α /greatermuch 1 at λ 0 because of the faster cooling, and for α /lessmuch 1 the lightcurve shows a rather broad exponential decay. 3 The lightcurves for /epsilon1 = 10 -2 E 0 can be distinguished quite well, since the lightcurve for α /lessmuch 1 shows a rapid increase to the narrow maximum, while the light curve for α /greatermuch 1 exhibits a broad and flat maximum, which covers almost two orders of magnitude in time. As stated above, because of the broken power-law in the SED for α /greatermuch 1 the maximum of the SED is attained at /epsilon1 = E 0 /α 2 , which is in our example the lightcurve for /epsilon1 = 10 -2 E 0 . This explains the broad maximum, and also why the higher energies are again less luminous compared to the α /lessmuch 1 case. In the lightcurves for /epsilon1 = 10 -4 E 0 there is only a very slight difference, since the rising part after λ 0 sets in earlier for α /greatermuch 1 than for α /lessmuch 1. However, the increase is quite</text>
<text><location><page_7><loc_52><loc_12><loc_92><loc_15></location>2 The powers of t depend sensitively on the chosen geometry. E.g. for a cylindrical source the power is reduced by unity giving a t 1 - and a flat t 0 -dependence.</text>
<figure>
<location><page_8><loc_9><loc_69><loc_46><loc_92></location>
</figure>
<figure>
<location><page_8><loc_51><loc_69><loc_88><loc_92></location>
<caption>Figure 3. Unretarded (full), as well as numerical (dashed) and analytical (dotted) retarded lightcurve for α /lessmuch 1 and two cases of γ 0 over a logarithmic time-axis. The values of /epsilon1 in the legend are given in units of E 0 . The curves are normalized with I 0 and we set b = 1.</caption>
</figure>
<text><location><page_8><loc_8><loc_62><loc_48><loc_65></location>small until t c and detailed observations are needed to distinguish the models.</text>
<text><location><page_8><loc_8><loc_50><loc_48><loc_62></location>Obviously, for smaller emission regions the lightcrossing time scale λ 0 is reduced and the effects of the time-dependent cooling will be even more pronounced with very short variability time scales. Additionally, a smaller emission region leads to a larger α according to equation (13). Thus, the time-dependent SSC cooling is quite important for models which assume a small emission region to explain the rapid variability in blazars, like those cited in the introduction.</text>
<text><location><page_8><loc_8><loc_44><loc_48><loc_50></location>We numerically checked if our results are also valid for different injection scenarios, such as a power-law, and obtained qualitatively similar results as one can see in Figure 5 of appendix B. Thus, we are confident that the discussion presented here is robust.</text>
<section_header_level_1><location><page_8><loc_18><loc_41><loc_38><loc_42></location>6.1. Caveats of the approach</section_header_level_1>
<text><location><page_8><loc_8><loc_37><loc_48><loc_40></location>Of course, our approach is simplified, leaving aside several, possibly important aspects.</text>
<text><location><page_8><loc_8><loc_19><loc_48><loc_37></location>As stated in section 2, we assume that the source is spatially homogeneous. Additionally, we neglect the 'internal' retardation of the inverse Compton processes. The time, a photon travels before it is inverse Compton scattered, should on average be much less than λ 0 . Thus, the effect on the light curve is small, apart from a short delay of the SSC light curve (which we do not calculate in this paper). However, cooling might be affected, since the SSC cooling should be similarly delayed as the SSC light curve. On the other hand, as shown in Schlickeiser (2009) and Zacharias & Schlickeiser (2010), the SSC cooling is orders of magnitude quicker than the synchrotron and external Compton cooling, which should more than compensate the small retardation delay.</text>
<text><location><page_8><loc_8><loc_13><loc_48><loc_19></location>We do not expect a delay effect for the external Compton scattering, since they are present all the time and are more or less homogeneously distributed (ZSb, Sokolov & Marscher 2005).</text>
<text><location><page_8><loc_8><loc_7><loc_48><loc_13></location>We also do not discuss the acceleration of the electrons. This might have a significant impact on the light curve, since the variability is governed by the longest time scale (in our case just λ 0 and t syn , with an influence by t c for α /greatermuch 1). If the acceleration takes particularly long the</text>
<text><location><page_8><loc_52><loc_57><loc_92><loc_65></location>effects due to retardation or cooling would be washed out. If the acceleration takes only a small amount of time, it will certainly influence the rising phase of the light curve, but its effect on the main part of the variability will not be significant. This argument might not hold for very small emission regions.</text>
<text><location><page_8><loc_52><loc_45><loc_92><loc_57></location>On the other hand, the acceleration time scale is only important, if the acceleration and radiation zone are spatially and temporally coincident. This is still under debate, and only recently these conditions are incorporated in numerical studies (e.g. Weidinger et al. 2010; Weidinger & Spanier 2010). Thus, we follow the assumption or simplification that acceleration and radiation are (especially) temporally separated. Then, the acceleration time scale does not influence the resulting light curve.</text>
<text><location><page_8><loc_52><loc_25><loc_92><loc_45></location>Chiaberge & Ghisellini (1999), and also e.g. Kataoka et al. (2000) or Li & Kusunose (2000), used similar assumptions in their numerical analysis. In fact, most theoretical investigations use numerical schemes with the advantage of employing more and more realistic scenarios, such as time-dependency (Bottcher & Chiang, 2002), inclusion of shock acceleration (Sokolov et al., 2004), hydrodynamic simulations (Mimica et al., 2004; Cabrera et al., 2013), and multizone models that incorporate the full retardation of all processes (Graff et al., 2008, Joshi & Bottcher 2011). In our analytical discussion we are for obvious reason not able to include all these details. That is why we focus on the details of the time-dependency, showing analytically that time-dependent effects, especially from SSC, are very important for rapid flares.</text>
<section_header_level_1><location><page_8><loc_66><loc_23><loc_78><loc_24></location>7. CONCLUSIONS</section_header_level_1>
<text><location><page_8><loc_52><loc_7><loc_92><loc_23></location>In this paper we introduced our approach to calculate theoretical synchrotron lightcurves for flaring blazars, where the radiating relativistic electrons are cooled by the combined synchrotron, external Compton and timedependent SSC mechanisms. This complements the recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (SBM); Zacharias & Schlickeiser 2010, 2012a (ZSa), 2012b (ZSb)) on the effects of the combined cooling on the SED. Lightcurves show the intensity of a specific frequency band over time. Thus, they are a perfect tool to analyze the flaring behavior of blazars in different energies, such as correlations between different frequency</text>
<figure>
<location><page_9><loc_9><loc_45><loc_89><loc_92></location>
<caption>Figure 4. Analytical (dotted) and numerical (dashed) retarded lightcurves over a liner time-axis. The parameters are given at the top and values of /epsilon1 in the legend are given in units of E 0 . The curves are normalized by the respective maximum. The vertical line marks the light-crossing time scale λ 0 , and the horizontal range is 15 λ 0 .</caption>
</figure>
<text><location><page_9><loc_8><loc_38><loc_13><loc_40></location>bands.</text>
<text><location><page_9><loc_8><loc_25><loc_48><loc_38></location>We were able to show that the synchrotron lightcurves exhibit a different form, if the time-dependent nature of the SSC cooling is taken into account, compared to the usual time-independent approaches. For that we first derived a formula to calculate the lightcurve from the intensity distribution, where we introduced the retardation due to the finite size of the radiation source. Using the intensities derived by SBM for the time-independent and the time-dependent cooling scenarios, we calculated the resulting lightcurves.</text>
<text><location><page_9><loc_8><loc_19><loc_48><loc_25></location>Our calculations highlight the differences between the usual linear and the time-dependent cooling scenarios, giving us confidence that the important effects in the lightcurves are really due to the different cooling terms, and are not hidden by other effects.</text>
<text><location><page_9><loc_10><loc_17><loc_44><loc_18></location>The main results can be summarized as follows.</text>
<text><location><page_9><loc_8><loc_8><loc_48><loc_17></location>(1) Until the light crossing time scale λ 0 is reached, the initial synchrotron lightcurves depend strongly on the geometry of the source. In our example of a spherical source the lightcurve increases ∝ t 2 , which, depending on the synchrotron photon energy /epsilon1 , is followed by a linear t -dependence. We note, however, that this rising phase might be hard to observe depending on the sampling rate</text>
<text><location><page_9><loc_52><loc_38><loc_71><loc_40></location>in specific frequency bands.</text>
<text><location><page_9><loc_52><loc_24><loc_92><loc_38></location>(2) If the transition time t c from time-dependent SSC to linear cooling is larger than the light crossing time scale (i.e., t c > λ 0 ), the effects of the rapid SSC cooling are clearly visible for t > λ 0 . The lightcurves exhibit their respective maximum up to an order of magnitude earlier, if the electrons cool initially by the timedependent SSC process. In this cooling regime variability can be 10 times faster than in the linear cooling regime. The different spectral powers below and above the transition time t c probably need very precise measurements to be distinguishable in the data of blazars.</text>
<text><location><page_9><loc_52><loc_20><loc_92><loc_24></location>(3) The lightcurves are rather similar, if t c < λ 0 , since the effects of the time-dependent SSC cooling are smeared out by the retardation.</text>
<text><location><page_9><loc_52><loc_8><loc_92><loc_20></location>The results (2) and (3) obviously depend sensitively on the source parameters. In very compact emission regions with a short light crossing time scale and a large injection parameter α , the effects of the time-dependent SSC cooling are most significant. This in combination with the strong effects on the SED (e.g. ZSb) should help to clearly discriminate between different models, and to restrict the parameter space. In this context theoretical prediction of the SSC and EC lightcurve are also manda-</text>
<text><location><page_10><loc_8><loc_88><loc_48><loc_92></location>ory, and we intend to publish the results in a future work, where also a much deeper discussion of correlations is possible.</text>
<text><location><page_10><loc_8><loc_83><loc_48><loc_88></location>To conclude, we argue for a wide utilization of the timedependent SSC cooling scenario, at least for the modeling of rapid flares in blazars, where compact emission regions are necessary.</text>
<text><location><page_10><loc_8><loc_76><loc_48><loc_80></location>We thank the anonymous referee for constructive comments, which helped significantly to improve the manuscript.</text>
<text><location><page_10><loc_8><loc_70><loc_48><loc_76></location>We acknowledge support from the German Ministry for Education and Research (BMBF) through Verbundforschung Astroteilchenphysik grant 05A11PC1 and the Deutsche Forschungsgemeinschaft through grant Schl 201/23-1.</text>
<section_header_level_1><location><page_10><loc_24><loc_67><loc_33><loc_68></location>REFERENCES</section_header_level_1>
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<section_header_level_1><location><page_10><loc_46><loc_45><loc_54><loc_46></location>APPENDIX</section_header_level_1>
<section_header_level_1><location><page_10><loc_34><loc_43><loc_67><loc_44></location>CALCULATION OF THE INTERMEDIATE PART</section_header_level_1>
<text><location><page_10><loc_8><loc_40><loc_92><loc_42></location>The intermediate time regime t 1 , 2 < t < λ 0 requires another approach. The approximations of the other regimes cannot be used here.</text>
<formula><location><page_10><loc_9><loc_18><loc_92><loc_37></location>L ( t 1 , 2 < t < λ 0 , /epsilon1 ) = 6 I 0 ( /epsilon1 E 0 ) 1 / 3 t/λ 0 ∫ 0 ( 1 + t -λ 0 λ t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t -λ 0 λ tsyn ) 2 ( λ -λ 2 ) d λ ≈ 6 I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 t/λ 0 ∫ 0 ( 1 -2 3 λ 0 λ t syn + t ) e 2 /epsilon1 E 0 ( 1+ t tsyn ) λ 0 λ tsyn ( λ -λ 2 ) d λ =6 I 0 ( /epsilon1 E 0 ) 1 / 3 ( 1 + t t syn ) 2 / 3 e -/epsilon1 E 0 ( 1+ t tsyn ) 2 × t/λ 0 ∫ 0 ( λ -( 1 + 2 λ 0 3( t syn + t ) ) λ 2 + 2 λ 0 3( t syn + t ) λ 3 ) e 2 /epsilon1λ 0 E 0 tsyn ( 1+ t tsyn ) λ d λ (A1)</formula>
<text><location><page_10><loc_8><loc_15><loc_51><loc_17></location>Integrating by parts and approximating to first order yields</text>
<formula><location><page_10><loc_27><loc_10><loc_92><loc_14></location>L ( t 1 , 2 < t < λ 0 , /epsilon1 ) ≈ 3 I 0 ( /epsilon1 E 0 ) -2 / 3 e -/epsilon1 E 0 t 2 syn λ 2 0 ( t t syn )[ 1 -t λ 0 ] , (A2)</formula>
<text><location><page_10><loc_8><loc_7><loc_92><loc_9></location>where we also approximated for t < t syn . This is the result (30), which fits very well the numerical solution for intermediate times.</text>
<figure>
<location><page_11><loc_9><loc_44><loc_88><loc_92></location>
<caption>Figure 5. Unretarded (full) and numerical (dashed) retarded lightcurves for a power-law injection with spectral index s = 2. The parameters are given at the top. The legend is for frequencies ν . The vertical dotted line marks the light-crossing time scale λ 0 .</caption>
</figure>
<paragraph><location><page_11><loc_43><loc_40><loc_58><loc_41></location>POWER-LAW PLOTS</paragraph>
<text><location><page_11><loc_8><loc_36><loc_92><loc_39></location>In order to check if our analytical results can be regarded as qualitatively general, we performed a numerical integration of equation (3) with a power-law injection of the form</text>
<formula><location><page_11><loc_32><loc_34><loc_92><loc_36></location>S ( γ, t em ) = q 0 γ -s H [ γ -γ 1 ] H [ γ 2 -γ ] δ ( t em ) . (B1)</formula>
<text><location><page_11><loc_8><loc_31><loc_92><loc_33></location>The differential equation (7) with this type of injection has been solved by Zacharias & Schlickeiser (2010), and we use their result in equation (4) in order to calculate the intensity distribution.</text>
<text><location><page_11><loc_8><loc_27><loc_92><loc_31></location>For the illustrative case s = 2 the results are plotted in Fig. 5 for two cases of α and two cases of the upper limit γ 2 , respectively. Without going into details, one can see that the results discussed in section 6 are qualitatively recovered, which gives us confidence that our approach is robust.</text>
</document>
[
{
"title": "ABSTRACT",
"content": "Blazars emit non-thermal radiation in all frequency bands from radio to γ -rays. Additionally, they often exhibit rapid flaring events at all frequencies with doubling time scale of the TeV and X-ray flux on the order of minutes, and such rapid flaring events are hard to explain theoretically. We explore the effect of the synchrotron-self Compton cooling, which is inherently time-dependent, leading to a rapid cooling of the electrons. Having discussed intensively the resulting effects of this cooling scenario on the spectral energy distribution of blazars in previous papers, the effects of the time-dependent approach on the synchrotron lightcurve are investigated here. Taking into account the retardation due to the finite size of the source and the source geometry, we show that the time-dependent synchrotronself Compton (SSC) cooling still has profound effects on the lightcurve compared to the usual linear (synchrotron and external Compton) cooling terms. This is most obvious if the SSC cooling takes longer than the light crossing time scale. Then in most frequency bands the variability time scale is up to an order of magnitude shorter than under linear cooling conditions. This is yet another strong indication that the time-dependent approach should be taken into account for modeling blazar flares from compact emission regions. Subject headings: radiation mechanisms: non-thermal - BL Lacertae objects: general - gamma-rays: theory",
"pages": [
1
]
},
{
"title": "SYNCHROTRON LIGHTCURVES OF BLAZARS IN A TIME-DEPENDENT SYNCHROTRON-SELF COMPTON COOLING SCENARIO",
"content": "Michael Zacharias & Reinhard Schlickeiser Institut fur Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universitat Bochum, 44780 Bochum, Germany (Received; Revised; Accepted) Draft version September 7, 2021",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Blazars, a subclass of active galactic nuclei in the accepted unification scheme of Urry & Padovani (1995), are characterized by a broad non-thermal spectrum exhibiting two characteristic humps and stretching from radio to γ -ray frequencies. In leptonic models the lowenergy component is attributed to synchrotron radiation of highly relativistic electrons, while the high-energy component is inverse Compton emission of the same electron population (for recent reviews see Bottcher 2007, 2012). Several target photon fields are relevant for the inverse Compton process. Jones et al. (1974) proposed the synchrotron radiation emitted by the relativistic electrons as the target photon field, which is then up-scattered by the same electrons, the so-called synchrotron-self Compton (SSC) process. The vicinity of an active galactic nucleus harbors also additional strong external (to the jet) photon fields, which can potentially contribute in the form of so-called external Compton radiation to the high-energy component of blazars. Such external fields could come from the accretion disk (Dermer & Schlickeiser 1993), the broad line region (Sikora et al. 1994) or the dusty torus (Blazejowski et al. 2000, Arbeiter et al. 2002). These external fields are usually preferred over the SSC, if the highenergy component dominates the synchrotron component in the spectral energy distribution (SED) of blazars. It is well established that blazars are far from being steady sources. They exhibit strong flares in all frequency bands, which can in some cases outshine even the brightest galactic sources. The brightest γ -ray flare ever detected is from 3C 454.3, reported by Vercellone et al. (2011), reaching a γ -ray flux of F γ = (6 . 8 ± 1 . 0) × 10 -5 photons cm -2 s -1 , which is six times higher than the Vela pulsar. Additionally, blazars also exhibit very rapid flares with doubling time scales on the order of minutes as in the case of PKS 2155-304 (Aharonian et al. 2007) or PKS 1222+216 (Tavecchio et al. 2011) in the TeV regime, or Mrk 421 in the X-rays (Cui 2004). Such rapid flares are theoretically challenging, since typical cooling time scales of the radiating electrons are considerably longer. Several models have thus been invoked to explain these rapid flares, such as the jet-in-a-jet model (Giannios et al. 2009), the similar minijets-in-a-jet model (Biteau & Giebels 2012, Giannios 2013), magnetocentrifugal acceleration of beams of particles (Ghisellini et al. 2009a), a star traversing the jet (Barkov et al. 2012), and others. Quite common in all these models is the assumption of an emission blob being smaller than the jet cross-section and moving much faster than the surrounding relativistic jet material. This gives rise to a very short light-crossing time scale, which is usually equaled to the variability time scale. In many theoretical investigations, as the ones cited above, and in most modeling attempts (e.g. Ghisellini et al. 2009b) the electron distribution is assumed to be stationary. This eases the computational effort, of course, and might be suitable for steady sources or those varying over a long time scale. However, it is certainly not justified for rapid flares as in PKS 2155-304 or PKS 1222+216. The time-dependence of the relativistic electron distribution function has important effects on the resulting SED, as is demonstrated in a recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (hereafter SBM); Zacharias & Schlickeiser 2010, 2012a (hereafter ZSa), 2012b (hereafter ZSb)). Relativistic electrons in a relativistically moving emission blob along the jet of the active galactic nucleus lose energy by emitting synchrotron radiation. These synchrotron photons are a prime target for the same electrons to inverse Compton scatter them to higher energies. This is the SSC process, as mentioned above, which is an additional energy loss process for the electrons. This in turn implies that the subsequently emitted synchrotron photons are less energetic, and so will be the SSC photons. Thus, this results in a decreased efficiency of the SSC process and in a decreased efficiency of the SSC energy loss process with respect to time. Consequently, even if the SSC process dominates initially the electron losses, eventually the time-independent loss processes such as synchrotron and external Compton losses dominate the loss rate. Schlickeiser (2009), as well as Zacharias & Schlickeiser (2010) were able to show that the time-dependent treatment of the SSC losses leads to a much faster electron cooling compared to the steadystate approach. Therefore, it is interesting to discuss the effects of this rapid cooling on blazar lightcurves, where the variability can be displayed in an obvious way. It is the purpose of this paper to highlight the different effects of the linear and the time-dependent (nonlinear) SSC cooling on the synchrotron lightcurves. To keep the problem simple and analytically tractable, we utilize only the retardation effect due to the finite size of the emission region, and the geometry of the source. This will be discussed in section 2, where we will derive the necessary formula to calculate the lightcurve from the synchrotron intensity. The latter was already calculated by SBM, and we will summarize their results in section 3 for the sake of completeness. We will then use the derived formula from section 2 to calculate the resulting lightcurves in sections 4 and 5. We will discuss the results in section 6 and conclude in section 7. The more involved calculations of the inverse Compton lightcurves will be discussed in a future publication.",
"pages": [
1,
2
]
},
{
"title": "2. GEOMETRY OF THE SITUATION",
"content": "We assume a spherical, uniform radiation zone in the jet as depicted in figure 1. For negligible retardation the received monochromatic intensity at intrinsic time t em is I ( t em , /epsilon1 ), where /epsilon1 is the intrinsic energy of the photon. Since, however, the source has a finite size, photons emitted at the back of the source will arrive at the observer at a later time ∆ t = 2 R/c than the photons emitted at the front, with R being the radius of the spherical source and c = 3 · 10 10 cm / s the speed of light. We include this retardation effect, but assume that the source is (i) spatially homogeneous, and (ii) optically thin. For optically thin sources all photons can leave the emission region without further spatial diffusion (Eichmann et al. 2010). Then the received intensity is just a function of the distance l of the production site from the front. Using a similar approach as Chiaberge & Ghisellini (1999), we cut the source into slices of length d l , as shown in figure 1. The received intensity of each slice is Here, t is the time of the observer, which equals t em for l = 0 (the front of the source). The Heaviside function H [ x ] displays the fact that light from a specific slice can only be detected after it has crossed the distance l to the front of the source. The fraction d V ( l ) /V is a geometrical weight function, which is defined in such a way that the integral over d V ( l ) /V equals unity. Since in a spherical source each slice has a different volume than the other slices, its contribution depends on its position in the source. The volume of the slice is given by d V ( l ) = A ( l ) d l , where A ( l ) = π (2 Rl -l 2 ) is the cross section of the slice at position l . The geometrical weight function then becomes The complete received monochromatic lightcurve L ( t, /epsilon1 ) then equals the sum over the contribution from all slices: after an obvious substitution. Here we introduced the light-crossing time scale λ 0 = 2 R/c . We note that equation (1) is general as long as the assumptions (i) and (ii) are satisfied. Thus, it is not limited to spherical geometries, and for example cylindrical sources could also be chosen. In fact, a cylindrical geometry would lead to a simpler form of the geometrical weight function. However, the assumption of isotropy for the electron distribution and the radiation fields (see below) would not be valid any more. 1",
"pages": [
2
]
},
{
"title": "3. SYNCHROTRON INTENSITY",
"content": "In this section we summarize results previously obtained (SBM, ZSa, ZSb) in order to introduce the relevant functions and parameters. The isotropic, optically thin synchrotron intensity from relativistic electrons with the volume-averaged differential density n ( γ, t ) is given by with relative strength of external to synchrotron cooling, and has profound consequences for the SED, as we showed in Zacharias & Schlickeiser (2012b). We note that it is less important for the discussion of synchrotron lightcurves and only introduced for the sake of completeness. More importantly, as one can see from equation (9), is the fact that the SSC cooling term by its dependence on n ( γ, t ) is time-dependent, which means that its strength decreases over time. Consequently, even if the SSC cooling dominates the total cooling term initially, after some time the SSC cooling will become weaker than the linear cooling, and thus the synchrotron or external Compton cooling will dominate for later times. Obviously, if the linear cooling terms are stronger than the SSC cooling at the beginning, they will be stronger for all times. This can be further quantified by the injection parameter It is defined in such a way that As a consequence (ZSa and ZSb) the Compton dominance in the SED depends on α 2 , at least in the Thomson limit. This demonstrates the importance of this parameter, which can also be expressed as where we scale the total number of electrons N = 10 50 N 50 , and the initial electron Lorentz factor γ 0 = 10 4 γ 4 . Obviously, α increases for increasing γ 0 and N , and decreases for increasing R and l ec . If α /greatermuch 1 the cooling will initially be dominated by the SSC cooling, while for α /lessmuch 1 the cooling is dominated by the linear terms for all times. We note that both inverse Compton cooling terms operate in the Thomson limit. In the Klein-Nishina limit the efficiencies of both cooling terms are much reduced, and become unimportant compared to the synchrotron cooling. This resembles the case α /lessmuch 1 and l ec /lessmuch 1 and is, therefore, covered by our approach. The differential equation (7) with the loss term (9) and the source term (8) has been solved by SBM. For α /lessmuch 1 (i.e. negligible SSC-losses) they obtained which is, indeed, a linear cooling solution. For α /greatermuch 1 (i.e. initially dominating SSC-losses) SBM found yielding a nonlinear dependence of γ on time. For later times the electron density approaches being the synchrotron power of a single electron in a large-scale random magnetic field of constant strength B = b Gauss (Crusius & Schlickeiser 1988). Here P 0 = 2 · 10 24 erg -1 s -1 , and /epsilon1 0 = 1 . 9 · 10 -20 b erg. The function CS ( x ) is well approximated by with a 0 = 1 . 151275. The differential relativistic electron density can be calculated from the kinetic equation (Kardashev 1962) where | ˙ γ | is the electron energy loss term, and S ( γ, t em ) is the source term. For demonstration purposes and ease of calculation we use a relatively simple source term that is a single injection of monochromatic electrons with the injection Lorentz factor γ 0 and the electron density q 0 . In the scenario depicted here we consider electron losses via the synchrotron, external Compton and synchrotron-self Compton channels. Since the latter depends on the produced synchrotron radiation, and thus directly on the electron distribution, the kinetic equation becomes non-linear (Schlickeiser 2009). The total electron loss term is given by The parameters are D 0 = 1 . 3 · 10 -9 b 2 s -1 , and A 0 = 1 . 2 · 10 -18 R 15 b 2 cm 3 s -1 , where we scaled the radius of the source as R = 10 15 R 15 cm. We define where Γ b is the Lorentz factor of the plasma blob, u ' ec is the isotropic energy density of the external radiation field in the frame of the host galaxy, and u B is the energy density of the magnetic field. This parameter describes the which is a modified linear cooling solution. The transition time is defined as The intensity (4) for both cases of α has also been calculated by SBM. For α /lessmuch 1 they obtained with equation (14) For α /greatermuch 1 with equations (15) and (16) and Here we used the definitions I 0 = 3 a 0 RP 0 q 0 /epsilon1 0 / (8 π ), t syn = 1 / ( D 0 (1 + l ec ) γ 0 ), E 0 = 3 /epsilon1 0 γ 2 0 / 2, and α g = (1 + 2 α 3 ) / (3 α 2 ). These intensities are equal to a monochromatic lightcurve, where the retardation and, thus, the source's finite size have not been taken into account. Below, we will refer to them as the 'unretarded' lightcurves. Now, we have collected all necessary ingredients to calculate the retarded synchrotron lightcurves, which we present in the following sections.",
"pages": [
3,
4
]
},
{
"title": "4. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING LINEAR COOLING",
"content": "Using equation (18) in equation (3) we obtain the retarded lightcurve for the case α /lessmuch 1: The integral (21) can be solved in terms of several incomplete Gamma-functions. However, this would not give many insights. Instead, we will use meaningful approximations for the integral in three time domains. These domains can later be glued together to give a continuous analytic result. First of all, we define two characteristic time scales of the unretarded lightcurve. They can later be connected to the light-crossing time scale, yielding some information about the resulting retarded lightcurve. The first one is the local maximum of the unretarded lightcurve, which is: This expression is negative for /epsilon1 > E 0 / 3, indicating that for such energies there is no local maximum. If t 1 ( /epsilon1 ) > λ 0 the variability will mostly take place for times later than the light-crossing time scale. Solving the resulting inequality for /epsilon1 , results in This equation implies that for energies /epsilon1 < /epsilon1 1 the variability due to the flare will be longer than the lightcrossing time scale. Hence, we expect the global maximum of the lightcurve to occur later than λ 0 , and thus be unaffected by the retardation. The second characteristic time scale is related to the argument of the exponential in the unretarded lightcurve A = /epsilon1 E 0 (1 + t em /t syn ) 2 . As soon as t em ≥ t syn the unretarded lightcurve exponentially decays, which should also be visible in the retarded lightcurve. Since, however, A ≈ /epsilon1 E 0 for t em /lessmuch t syn , we set with Once A ∗ ( /epsilon1, t em ) is larger than unity the unretarded lightcurve will exponentially decay. Thus, we obtain the second characteristic time scale t 2 ( /epsilon1 ) by A ( /epsilon1, t 2 ( /epsilon1 )) = 1, yielding Unlike t 1 ( /epsilon1 ), the second characteristic time scale exhibits no restrictions by /epsilon1 . Obviously, t 1 ( /epsilon1 ) < t 2 ( /epsilon1 ). For t 2 ( /epsilon1 ) > λ 0 the exponential will become important only after the light-crossing time scale. Solving the inequality for /epsilon1 we obtain We can now begin with the actual calculation of the retarded lightcurve. The simplest case is obviously for t > λ 0 , since in this case the retarded lightcurve should be the same as the unretarded lightcurve. This is due to the fact that the retardation is not important for time scales much longer than λ 0 . Inspecting the difference t -λ 0 λ , we see that λ 0 λ can be at most equal to λ 0 . Thus, for t /greatermuch λ 0 we can approximate t -λ 0 λ ≈ t . Hence, which, indeed, equals the unretarded lightcurve. The other rather simple case is for t < λ 0 with the further requirement that t < t 1 , 2 ( /epsilon1 ) (the subscript refers to both t 1 and t 2 ). The latter implies that the unretarded lightcurves were neither variable nor have they decayed already. Then in eq. (21) the terms ( t -λ 0 λ ) /t syn can be neglected compared to unity, yielding For times below the light-crossing time scale and below the variability time scale of the unretarded lightcurve the retarded lightcurve increases rapidly L ∝ t 2 . For intermediate times the calculation is quite involved, and the details can be found in appendix A. We obtain We note that the exact form of the intermediate regime is not so important, since it will be glued to the approximation (29) at t ≈ t 2 . The most important result is the linear increase of the the lightcurve (30), which leads to a break at t 2 in the retarded lightcurve. However, if t 1 , 2 ( /epsilon1 ) > λ 0 the intermediate part does not play a role, and the lightcurve breaks immediately at t = λ 0 from the initial t 2 -dependence to the time dependence given by equation (28). Depending on the synchrotron photon energy /epsilon1 , we can now construct the lightcurves from the three approximations (28) - (30). We obtain two cases, divided in additional sub-cases. Beginning with /epsilon1 < E 0 / 3, we get: For /epsilon1 > E 0 / 3 the solutions become: The lightcurves (33) and (35) cut off at t = λ 0 . Obviously, light from the back reaches the observer only at later times, causing the radiation to be visible on longer time scales than implied by the unretarded lightcurve. The analytical results (31) - (35) are plotted along with a numerical integration of equation (21) in Figure 2 for two cases of γ 0 . For comparison, we also show the unretarded lightcurve. The first obvious result is that the retarded synchrotron lightcurve increases rapidly as long as t < λ 0 . Afterwards the retarded lightcurve behaves as the unretarded one, which is reasonable, as we discussed above. The other points mentioned earlier are also quite obvious. Even though the unretarded lightcurve for very high energies cuts off long before the light-crossing time scale, the retarded lightcurves are extended until λ 0 . The break in the lightcurve in the intermediate time regime is also evident. However, as discussed above, the low energetic cases, where the variability time scales are much longer than the light-crossing time scale, do not exhibit this break. As one can see, the analytical result matches the numerical integration rather well, which is reassuring and validates a posteriori our approximations. However, there is one caveat: The distinction of cases by t 2 and /epsilon1 2 is rather sharp (esp. equations (33) and (35)). This is obvious in the left plot of Figure 2 in the analytical curve for /epsilon1 = 10 E 0 , which cuts off at t = λ 0 . On the other hand, the numerical curve in this case decays exponentially. The distinction of the cases divided by /epsilon1 2 is, therefore, not as strict as implied by the analytical result. It is a more gradual transition, which is, however, difficult to implement in one equation. The problem is probably due to the rather artificial definition of t 2 , which is also indicated by the fact that the break for the high-energy lightcurves is better placed at 2 t 2 instead of t 2 .",
"pages": [
4,
5
]
},
{
"title": "5. MONOCHROMATIC SYNCHROTRON LIGHTCURVE FOR DOMINATING INITIAL SSC COOLING",
"content": "For the case α /greatermuch 1 we use equations (19) and (20) in equation (3) to obtain the retarded lightcurve For t c < t < t c + λ 0 both L 1 and L 2 contribute to the emitted lightcurve, which differs from the strict division of the unretarded lightcurves (19) and (20). This is, again, an effect of the retardation: Even if light received from the front of the source is from electrons already cooling in the linear regime ( t em > t c ), the light received from the back of the source is still from electrons cooling in the nonlinear regime ( t em < t c ). If t c < λ 0 this period can be quite extended. Although there are several sub-cases to consider in the analytical calculation, we can use the same approximation for the integrals (36) and (37), as we used to obtain equations (28) - (30). It is therefore unnecessary to repeat them in detail. Instead, we will summarize the results in the most compact form possible, where the sub-cases are combined in such a way that the resulting lightcurve is continuous. The characteristic time scales t 3 ( /epsilon1 ) and t 4 ( /epsilon1 ) are obtained by the same arguments as t 1 ( /epsilon1 ) and t 2 ( /epsilon1 ), giving For t 3 , 4 ( /epsilon1 ) > λ 0 we find while for t 3 , 4 ( /epsilon1 ) > t c we obtain respectively. With these definitions, we sum up the results of the analytical calculation. We begin with the case t c < λ 0 : For t c > λ 0 the analytical calculation yields for /epsilon1 < E 0 / 3 which is the only case where L must be divided. For /epsilon1 > E 0 / 3 we obtain In Figure 3 we compare the analytical results with the numerical results, and achieve quite good agreement. The unretarded lightcurve is shown again for comparison. Since the basic properties of the plot are the same as in Figure 2, we do not need to repeat them here. The problem with t 4 and /epsilon1 4 , mentioned in the discussion for Figure 2, is evident here, again.",
"pages": [
6,
7
]
},
{
"title": "6. DISCUSSION",
"content": "In Figures 2 and 3 we show lightcurves in a logarithmic plot, which has the advantage of having several cases in one plot. This makes it much easier to compare variability aspects which occur on very different time scales. Our discussion will focus on these logarithmic plots. On the other hand, lightcurves are commonly displayed in a linear plot, which highlights the behavior of lightcurves around their respective maxima. We present such linear plots in Figure 4. The results are completely compatible. Comparing Figures 2 and 3 one can see that there are some points, where the results are similar, and some other points, which are remarkably different. First of all, we note that the 'variability time scale' of any given lightcurve is determined by its global maximum. Thus, the minimal variability time scale, which is possible at all, is given by the light-crossing time scale, since the source is evenly contributing to the radiative output. If the source only partially radiates, the variability time scale can be much lower (Eichmann et al. 2010). The rising phase until λ 0 is dominated by the source geometry, giving a t 2 -dependence up to the break times t 2 ( /epsilon1 ) for α /lessmuch 1 and t 4 ( /epsilon1 ) for α /greatermuch 1, respectively. If t 2 , 4 ( /epsilon1 ) < λ 0 , the lightcurve exhibits a break to a t 1 -dependence. Otherwise the spectrum breaks directly to the unretarded lightcurve at λ 0 . 2 Secondly, for larger initial electron energies γ 0 the variability time scale is much reduced compared to lower initial electron energies. Hence, in the low-energetic frequency bands the variability time scale shifts closer to λ 0 for larger γ 0 . Thus, one can get information about the initial electron energy by observing the peak times of different frequency bands. The plots for the high-energetic cases ( γ 0 = 10 5 ) look quite similar in both cases of α , since t c is smaller than λ 0 , and the lightcurves are the same for t > t c . However, they can be distinguished by the high-energetic frequency bands. Both are less luminous for α /greatermuch 1 compared to α /lessmuch 1, because the synchrotron SED exhibits a broken power-law for α /greatermuch 1, leading to a decreased flux for high energies compared to the α /lessmuch 1 case (cf. SBM). Additionally, the break in the lightcurve from the quadratic time-dependence to the linear timedependence takes place a factor 3 α 2 earlier in the α /greatermuch 1 case than for α /lessmuch 1, since the unretarded lightcurve cuts off much earlier for α /greatermuch 1 than for α /lessmuch 1. Thus, the sum over all unretarded lightcurves of each slice (that is the retarded lightcurve) for α /greatermuch 1 must be less luminous and increase less strongly than for α /lessmuch 1. The low-energetic cases ( γ 0 = 10 3 ) differ strongly for α larger and smaller than unity, since t c is larger than λ 0 . The features, which are plainly visible in the unretarded lightcurve, are thus also visible in the retarded lightcurve. The lightcurve for /epsilon1 = 10 E 0 cuts off in both cases at around λ 0 . However, for α /greatermuch 1 the break is clearly visible in the lightcurve, which is due to the faster cooling of the electrons in this case of α . Similarly, the lightcurve for /epsilon1 = E 0 cuts off for α /greatermuch 1 at λ 0 because of the faster cooling, and for α /lessmuch 1 the lightcurve shows a rather broad exponential decay. 3 The lightcurves for /epsilon1 = 10 -2 E 0 can be distinguished quite well, since the lightcurve for α /lessmuch 1 shows a rapid increase to the narrow maximum, while the light curve for α /greatermuch 1 exhibits a broad and flat maximum, which covers almost two orders of magnitude in time. As stated above, because of the broken power-law in the SED for α /greatermuch 1 the maximum of the SED is attained at /epsilon1 = E 0 /α 2 , which is in our example the lightcurve for /epsilon1 = 10 -2 E 0 . This explains the broad maximum, and also why the higher energies are again less luminous compared to the α /lessmuch 1 case. In the lightcurves for /epsilon1 = 10 -4 E 0 there is only a very slight difference, since the rising part after λ 0 sets in earlier for α /greatermuch 1 than for α /lessmuch 1. However, the increase is quite 2 The powers of t depend sensitively on the chosen geometry. E.g. for a cylindrical source the power is reduced by unity giving a t 1 - and a flat t 0 -dependence. small until t c and detailed observations are needed to distinguish the models. Obviously, for smaller emission regions the lightcrossing time scale λ 0 is reduced and the effects of the time-dependent cooling will be even more pronounced with very short variability time scales. Additionally, a smaller emission region leads to a larger α according to equation (13). Thus, the time-dependent SSC cooling is quite important for models which assume a small emission region to explain the rapid variability in blazars, like those cited in the introduction. We numerically checked if our results are also valid for different injection scenarios, such as a power-law, and obtained qualitatively similar results as one can see in Figure 5 of appendix B. Thus, we are confident that the discussion presented here is robust.",
"pages": [
7,
8
]
},
{
"title": "6.1. Caveats of the approach",
"content": "Of course, our approach is simplified, leaving aside several, possibly important aspects. As stated in section 2, we assume that the source is spatially homogeneous. Additionally, we neglect the 'internal' retardation of the inverse Compton processes. The time, a photon travels before it is inverse Compton scattered, should on average be much less than λ 0 . Thus, the effect on the light curve is small, apart from a short delay of the SSC light curve (which we do not calculate in this paper). However, cooling might be affected, since the SSC cooling should be similarly delayed as the SSC light curve. On the other hand, as shown in Schlickeiser (2009) and Zacharias & Schlickeiser (2010), the SSC cooling is orders of magnitude quicker than the synchrotron and external Compton cooling, which should more than compensate the small retardation delay. We do not expect a delay effect for the external Compton scattering, since they are present all the time and are more or less homogeneously distributed (ZSb, Sokolov & Marscher 2005). We also do not discuss the acceleration of the electrons. This might have a significant impact on the light curve, since the variability is governed by the longest time scale (in our case just λ 0 and t syn , with an influence by t c for α /greatermuch 1). If the acceleration takes particularly long the effects due to retardation or cooling would be washed out. If the acceleration takes only a small amount of time, it will certainly influence the rising phase of the light curve, but its effect on the main part of the variability will not be significant. This argument might not hold for very small emission regions. On the other hand, the acceleration time scale is only important, if the acceleration and radiation zone are spatially and temporally coincident. This is still under debate, and only recently these conditions are incorporated in numerical studies (e.g. Weidinger et al. 2010; Weidinger & Spanier 2010). Thus, we follow the assumption or simplification that acceleration and radiation are (especially) temporally separated. Then, the acceleration time scale does not influence the resulting light curve. Chiaberge & Ghisellini (1999), and also e.g. Kataoka et al. (2000) or Li & Kusunose (2000), used similar assumptions in their numerical analysis. In fact, most theoretical investigations use numerical schemes with the advantage of employing more and more realistic scenarios, such as time-dependency (Bottcher & Chiang, 2002), inclusion of shock acceleration (Sokolov et al., 2004), hydrodynamic simulations (Mimica et al., 2004; Cabrera et al., 2013), and multizone models that incorporate the full retardation of all processes (Graff et al., 2008, Joshi & Bottcher 2011). In our analytical discussion we are for obvious reason not able to include all these details. That is why we focus on the details of the time-dependency, showing analytically that time-dependent effects, especially from SSC, are very important for rapid flares.",
"pages": [
8
]
},
{
"title": "7. CONCLUSIONS",
"content": "In this paper we introduced our approach to calculate theoretical synchrotron lightcurves for flaring blazars, where the radiating relativistic electrons are cooled by the combined synchrotron, external Compton and timedependent SSC mechanisms. This complements the recent series of papers (Schlickeiser 2009; Schlickeiser et al. 2010 (SBM); Zacharias & Schlickeiser 2010, 2012a (ZSa), 2012b (ZSb)) on the effects of the combined cooling on the SED. Lightcurves show the intensity of a specific frequency band over time. Thus, they are a perfect tool to analyze the flaring behavior of blazars in different energies, such as correlations between different frequency bands. We were able to show that the synchrotron lightcurves exhibit a different form, if the time-dependent nature of the SSC cooling is taken into account, compared to the usual time-independent approaches. For that we first derived a formula to calculate the lightcurve from the intensity distribution, where we introduced the retardation due to the finite size of the radiation source. Using the intensities derived by SBM for the time-independent and the time-dependent cooling scenarios, we calculated the resulting lightcurves. Our calculations highlight the differences between the usual linear and the time-dependent cooling scenarios, giving us confidence that the important effects in the lightcurves are really due to the different cooling terms, and are not hidden by other effects. The main results can be summarized as follows. (1) Until the light crossing time scale λ 0 is reached, the initial synchrotron lightcurves depend strongly on the geometry of the source. In our example of a spherical source the lightcurve increases ∝ t 2 , which, depending on the synchrotron photon energy /epsilon1 , is followed by a linear t -dependence. We note, however, that this rising phase might be hard to observe depending on the sampling rate in specific frequency bands. (2) If the transition time t c from time-dependent SSC to linear cooling is larger than the light crossing time scale (i.e., t c > λ 0 ), the effects of the rapid SSC cooling are clearly visible for t > λ 0 . The lightcurves exhibit their respective maximum up to an order of magnitude earlier, if the electrons cool initially by the timedependent SSC process. In this cooling regime variability can be 10 times faster than in the linear cooling regime. The different spectral powers below and above the transition time t c probably need very precise measurements to be distinguishable in the data of blazars. (3) The lightcurves are rather similar, if t c < λ 0 , since the effects of the time-dependent SSC cooling are smeared out by the retardation. The results (2) and (3) obviously depend sensitively on the source parameters. In very compact emission regions with a short light crossing time scale and a large injection parameter α , the effects of the time-dependent SSC cooling are most significant. This in combination with the strong effects on the SED (e.g. ZSb) should help to clearly discriminate between different models, and to restrict the parameter space. In this context theoretical prediction of the SSC and EC lightcurve are also manda- ory, and we intend to publish the results in a future work, where also a much deeper discussion of correlations is possible. To conclude, we argue for a wide utilization of the timedependent SSC cooling scenario, at least for the modeling of rapid flares in blazars, where compact emission regions are necessary. We thank the anonymous referee for constructive comments, which helped significantly to improve the manuscript. We acknowledge support from the German Ministry for Education and Research (BMBF) through Verbundforschung Astroteilchenphysik grant 05A11PC1 and the Deutsche Forschungsgemeinschaft through grant Schl 201/23-1.",
"pages": [
8,
9,
10
]
},
{
"title": "REFERENCES",
"content": "Aharonian F.A., et al., 2007, ApJ 664, L71 Arbeiter C., Pohl M., Schlickeiser R., 2002, A&A 386, 415 Barkov M.V., Aharonian F.A., Bogovalov S.V., Kelner S.R., Khangulyan D, 2012, ApJ 749, 119 Biteau J., Giebels B., 2012, A&A 548, A123 Blazejowski M., et al., 2000, ApJ 545, 107 B¨ottcher M., 2007, Astroph. & Space Sci. 309, 95 B¨ottcher M., 2012, preprint: arXiv:1205.0539 B¨ottcher M., Chiang J., 2002, ApJ 581, 127 Cabrera J.I., Coronade Y., Benitez E., Mendoza S., Hiriart D., Sorcia M., 2013, MNRASL, 434, L6 Chiaberge M., Ghisellini G., 1999, MNRAS 306, 551 Crusius A., Schlickeiser R., 1988, A&A 196, 327 Cui W., 2004, ApJ 605, 662 Dermer C. D., Schlickeiser R., 1993, ApJ 416, 458 Eichmann B., Schlickeiser R., Rhode W., 2010, A&A 511, A26 Giannios D., 2013, MNRAS 431, 355 Ghisellini G., Tavecchio F., Bodo G., Celotti A., 2009a, MNRAS 393, L16 Ghisellini G., Tavecchio F., Ghirlanda G., 2009b, MNRAS 399, 2041 Kataoka J., et al., 2000, ApJ 528, 243 Kardashev, N. S., 1962, Sov. Astron. J. 6, 317 Schlickeiser R., 2009, MNRAS 398, 1483 Sokolov A., Marscher A.P., 2005, ApJ 629, 52 Tavecchio F., Becerra-Gonzalez J. Ghisellini G., Stamerra A., Bonnoli G., Foschini L., Maraschi L., 2011, A&A 534, A86 Urry C. M., Padovani P., 1995, PASP 107, 803 Vercellone S., et al., 2011, ApJL 736, L38 Weidinger M., Ruger M., Spanier F., 2010, ASTRA 6, 1 Weidinger M., Spanier F., 2010, A&A 515, A18 Zacharias M., Schlickeiser R., 2010, A&A 524, A31 Zacharias M., Schlickeiser R., 2012a, MNRAS 420, 84 (ZSa) Zacharias M., Schlickeiser R., 2012b, ApJ 761, 110 (ZSb)",
"pages": [
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},
{
"title": "CALCULATION OF THE INTERMEDIATE PART",
"content": "The intermediate time regime t 1 , 2 < t < λ 0 requires another approach. The approximations of the other regimes cannot be used here. Integrating by parts and approximating to first order yields where we also approximated for t < t syn . This is the result (30), which fits very well the numerical solution for intermediate times. In order to check if our analytical results can be regarded as qualitatively general, we performed a numerical integration of equation (3) with a power-law injection of the form The differential equation (7) with this type of injection has been solved by Zacharias & Schlickeiser (2010), and we use their result in equation (4) in order to calculate the intensity distribution. For the illustrative case s = 2 the results are plotted in Fig. 5 for two cases of α and two cases of the upper limit γ 2 , respectively. Without going into details, one can see that the results discussed in section 6 are qualitatively recovered, which gives us confidence that our approach is robust.",
"pages": [
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11
]
}
]
2013ApJ...778...45C
https://arxiv.org/pdf/1309.4119.pdf
<document>
<section_header_level_1><location><page_1><loc_9><loc_85><loc_91><loc_87></location>SUPERORBITAL PERIODIC MODULATION IN WIND-ACCRETION HIGH-MASS X-RAY BINARIES FROM Swift BAT OBSERVATIONS</section_header_level_1>
<text><location><page_1><loc_48><loc_83><loc_66><loc_84></location>1,2 3,4</text>
<text><location><page_1><loc_33><loc_81><loc_64><loc_84></location>Robin H. D. Corbet and Hans A. Krimm Draft version October 17, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_78><loc_55><loc_80></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_61><loc_86><loc_78></location>We report the discovery using data from the Swift Burst Alert Telescope (BAT) of superorbital modulation in the wind-accretion supergiant high-mass X-ray binaries 4U 1909+07 (= X 1908+075), IGR J16418-4532, and IGR J16479-4514. Together with already known superorbital periodicities in 2S0114+650 and IGR J16493-4348, the systems exhibit a monotonic relationship between superorbital and orbital periods. These systems include both supergiant fast X-ray transients (SFXTs) and classical supergiant systems, and have a range of inclination angles. This suggests an underlying physical mechanism which is connected to the orbital period. In addition to these sources with clear detections of superorbital periods, IGR J16393-4643 (= AX J16390.4-4642) is identified as a system that may have superorbital modulation due to the coincidence of low-amplitude peaks in power spectra derived from BAT, RXTE PCA, and INTEGRAL light curves. 1E 1145.1-6141 may also be worthy of further attention due to the amount of low-frequency modulation of its light curve. However, we find that the presence of superorbital modulation is not a universal feature of wind-accretion supergiant X-ray binaries.</text>
<text><location><page_1><loc_14><loc_57><loc_86><loc_61></location>Subject headings: stars: individual (2S 0114+650, 1E 1145.1-6141, IGR J16393-4643, IGR J164184532, IGR J16479-4514, IGR J16493-4348, 4U 1909+07) - stars: neutron - Xrays: stars</text>
<section_header_level_1><location><page_1><loc_22><loc_53><loc_35><loc_54></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_31><loc_48><loc_52></location>Superorbital modulation is seen in a variety of X-ray binaries. A review of superorbital modulation in several types of systems is presented by Kotze & Charles (2012). In some cases such as Her X-1, SMC X-1 and LMC X-4, where accretion occurs by Roche-lobe overflow via an accretion disk onto a neutron star, the mechanism driving superorbital modulation can be understood as either precession of the accretion disk (e.g. Petterson 1975) or of the neutron star (e.g. Postnov et al. 2013). Irradiation of the accretion disk by the central X-ray source provides a possible mechanism for driving disk precession (e.g. Ogilvie & Dubus 2001, and references therein). Be star systems also exhibit long timescale, possibly periodic, variability at optical wavelengths. This long timescale variability has been claimed to be correlated with orbital period (Rajoelimanana et al. 2011).</text>
<text><location><page_1><loc_8><loc_19><loc_48><loc_31></location>A more puzzling variety of superorbital variability was found in a supergiant high-mass X-ray binary (sgHMXB). The sgHMXBs can be broadly classified into 'classical' systems, which may suffer from high levels of absorption, and supergiant fast X-ray transients (SFXTs; e.g. Blay et al. 2012; Sidoli 2013). In the sgHMXB 2S0114+650 there are three periodicities: a ∼ 9700 s neutron star rotation period, an 11.6 day orbital period, and a 30.7 day superorbital modulation (Corbet et al.</text>
<text><location><page_1><loc_10><loc_16><loc_48><loc_18></location>1 University of Maryland, Baltimore County, MD, USA; [email protected]</text>
<text><location><page_1><loc_10><loc_12><loc_48><loc_16></location>2 CRESST/Mail Code 662, X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA</text>
<text><location><page_1><loc_10><loc_10><loc_48><loc_13></location>3 Universities Space Research Association, 10211 Wincopin Circle, Suite 500, Columbia, MD 21044, USA</text>
<text><location><page_1><loc_10><loc_7><loc_48><loc_10></location>4 CRESST/Mail Code 661, Astroparticle Physics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA</text>
<text><location><page_1><loc_52><loc_40><loc_92><loc_54></location>1999; Wen et al. 2006; Farrell et al. 2008). A question has been whether 2S 0114+650 is exceptional, perhaps because of its unusually long pulse period, or whether other wind-accretion HMXBs also show similar superorbital periodicities. If similar behavior is found in other systems, then this may provide a way to determine, or at least constrain, the underlying mechanism. A suggestion that the phenomenon might be more general than just the case of 2S 0114+650 came when a superorbital period was found in the sgHMXB IGR J16493-4348 (Corbet et al. 2010b).</text>
<text><location><page_1><loc_52><loc_13><loc_92><loc_40></location>The Swift BAT provides an excellent way to monitor sgHMXBs. These systems are often highly absorbed, which presents difficulties for an instrument such as the Rossi X-ray Timing Explorer ( RXTE ) All Sky Monitor (ASM) which is sensitive in the 2 - 12 keV band (Levine et al. 1996). The Swift BAT's sensitivity to higher energy X-rays ( > 15 keV) provides a way to peer through this absorption. We present here a review of our searches of BAT light curves of sources thought to be HMXBs, in order to find additional sources that may also display superorbital modulation. In a few cases we also employ data collected from Galactic plane scans (Markwardt 2006) made with the RXTE Proportional Counter Array (PCA). The large effective area of the PCA enables observations to be made in the lower energy range of 2 - 10 keV. Although the PCA data cover only a limited fraction of the sky they have greater sensitivity than the RXTE ASM. MAXI light curves (Sugizaki et al. 2011) are not available for the majority of systems considered here.</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_13></location>We present here the results of a search for superorbital modulation in additional wind-accretion supergiant HMXBs. We find three new systems with clear superorbital modulation, initial reports of which were made in</text>
<text><location><page_2><loc_8><loc_83><loc_48><loc_92></location>Corbet & Krimm (2013a,b). We also find hints of modulation in two other systems. Although the number of systems is small, three new systems plus two previously known, we note a monotonic relationship between orbital and superorbital periods. We consider possible mechanisms that might cause superorbital modulation in some, but not all, sgHMXBs.</text>
<section_header_level_1><location><page_2><loc_20><loc_81><loc_37><loc_82></location>2. DATA AND ANALYSIS</section_header_level_1>
<text><location><page_2><loc_8><loc_45><loc_48><loc_80></location>The Burst Alert Telescope (BAT) on board the Swift satellite (Gehrels et al. 2004) is described in detail by Barthelmy et al. (2005). It uses a 2.7 m 2 coded-aperture mask and a 0.52 m 2 CdZnTe detector array. The BAT has a wide field of view, 1.4 sr half-coded, 2.85 sr 0% coded. The pointing direction of Swift is driven by the narrow-field XRT and UVOT instruments on board the satellite. The BAT typically observes 50%-80% of the sky each day. We used data from the Swift /BAT transient monitor (Krimm et al. 2006, 2013) covering the energy range 15 - 50 keV, and selected data with time resolution of Swift pointing durations. The transient monitor data are available shortly after observations have been performed. The light curves considered here cover the time range of MJD 53,416 to 56,452 (2005-02-15 to 2013-06-09). The light curves of some sources, not including the ones discussed in detail here, were more recently added to the analysis and hence have shorter durations. BAT light curves are also available from the catalogs such as described by Tueller et al. (2010). However, the most recent BAT catalog is from 70 months of data (Baumgartner et al. 2012) and the transient monitor light curves are hence of longer duration. The transient monitor light curves generally cover more than 3000 days, approximately 50% longer than the 70-month catalog light curves.</text>
<text><location><page_2><loc_8><loc_33><loc_48><loc_45></location>We used only data for which the data quality flag ('DATA FLAG') was set to 0, indicating good quality. In addition, we found that even data flagged as 'good' were sometimes suspect. In particular we identified a small number of data points with very low fluxes and implausibly small uncertainties. We therefore removed these points from the light curves. A total of 1244 light curves were available, this includes 106 blank fields that are used for test purposes.</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_33></location>To search for periodic modulation in the light curves, we calculated discrete Fourier transforms (DFTs) of all available light curves. We calculated the DFTs for a frequency range which corresponds to periods of between 0.07 days to the length of the light curves - i.e. generally ∼ 3000 days. The contribution of each data point to the power spectrum was weighted by its uncertainty using the 'semi-weighting' technique (Corbet et al. 2007a,b). This takes into account both the error bars on each data point and the excess variability of the light curve. Scargle (1989) notes that the weighting of data points in a power spectrum can be compared to combining individual data points. In this way, the use of semi-weighting is analogous to combining data points using the semi-weighted mean (Cochran 1937, 1954). We oversampled the DFTs by a factor of five compared to their nominal resolution. Calculations of the significance of peaks seen are expressed in terms of false alarm probability (FAP; Scargle 1982) which takes into account the DFT oversampling. Uncertainties in periods are generally derived using the</text>
<text><location><page_2><loc_52><loc_83><loc_92><loc_92></location>expression of Horne & Baliunas (1986). In the figures showing power spectra we mark in 'white noise' 99.9% and 99.99% significance levels. However, many sources exhibit noise continua which are not 'white'. In our calculations of FAP, we therefore determined local noise levels by fitting the continuum power levels in a narrow frequency range around each peak of interest.</text>
<section_header_level_1><location><page_2><loc_53><loc_80><loc_91><loc_82></location>3. SOURCES WITH PREVIOUSLY REPORTED PERIODIC SUPERORBITAL MODULATION</section_header_level_1>
<section_header_level_1><location><page_2><loc_66><loc_78><loc_78><loc_79></location>3.1. 2S0114+650</section_header_level_1>
<text><location><page_2><loc_52><loc_44><loc_92><loc_77></location>2S0114+650 is an unusual HMXB system that has an exceptionally long pulse period of ∼ 9700 s (e.g. Corbet et al. 1999). There has been controversy over the spectral classification of the mass donor, but Reig et al. (1996) derive a spectral type of B1 Ia. From optical radial velocity measurements, Grundstrom et al. (2007) determine an orbital period of 11.5983 ± 0.0006 days and a moderate eccentricity of 0.18 ± 0.05. The orbital period is also seen in the RXTE ASM light curve (Corbet et al. 1999; Wen et al. 2006). A 30.7 ± 0.1 day superorbital period was found by Farrell et al. (2006) from RXTE ASM observations, and the period was later refined to 30.75 ± 0.03 days by Wen et al. (2006). Farrell et al. (2008) performed extensive RXTE PCA observations covering approximately 2 cycles of the superorbital period. Although Farrell et al. (2008) found variations in the X-ray absorption on the orbital period, they found no such changes over the superorbital period. However, a significant increase in the photon index of the power-law model used to fit the X-ray spectrum was reported at the minimum flux phase of the superorbital period. Farrell et al. (2008) concluded that the superorbital modulation was due to mass-accretion rate variations, although the mechanism causing this could not be determined.</text>
<text><location><page_2><loc_52><loc_23><loc_92><loc_44></location>The power spectrum of the BAT light curve of 2S0114+650 is shown in Figure 1, both the orbital and superorbital periods are strongly detected, with the superorbital period being stronger than the orbital modulation. We determine orbital and superorbital periods of 11.591 ± 0.003 and 30.76 ± 0.03 days respectively. The BAT light curve of 2S0114+650 folded on the orbital and superorbital periods is shown in Figure 2. For consistency with the work of Farrell et al. (2008) the light curve folded on the superorbital period uses a definition of phase zero as the time of minimum flux. However, for the other sources considered in this paper we use the time of maximum flux as phase zero. Both the orbital and superorbital modulations are quasi-sinusoidal and no evidence for an eclipse is seen in the light curve folded on the orbital period.</text>
<section_header_level_1><location><page_2><loc_64><loc_21><loc_80><loc_22></location>3.2. IGR J16493-4348</section_header_level_1>
<text><location><page_2><loc_52><loc_7><loc_92><loc_20></location>IGR J16493-4348 was discovered by Grebenev et al. (2005) and subsequent X-ray observations suggested that the source is an X-ray binary (Hill et al. 2008). Nespoli et al. (2010) classified the infrared counterpart as a B0.5 I supergiant. A 6.8 day orbital period was independently found by Corbet et al. (2010b) and Cusumano et al. (2010) using BAT 54 month survey data with the two groups finding periods of 6.7906 ± 0.0020 and 6.782 ± 0.005 days respectively. The BAT modulation was interpreted by Cusumano et al. (2010) as show-</text>
<figure>
<location><page_3><loc_14><loc_71><loc_44><loc_90></location>
<caption>Figure 1. Power spectrum of the BAT light curve of 2S 0114+650. Note that the superorbital peak at 30.7 days is stronger than the orbital modulation at 11.6 days. The horizontal dashed lines indicate 'white noise' 99.9% and 99.99% significance levels.</caption>
</figure>
<figure>
<location><page_3><loc_16><loc_37><loc_41><loc_62></location>
<caption>Figure 2. Swift BAT light curve of 2S 0114+650 folded on its orbital period (top) and folded on its superorbital period (bottom). The period values are given in Table 1. Phase zero for the orbital period is the time of periastron passage from Grundstrom et al. (2007) and is MJD 51,824.8. Phase zero for the superorbital period is the time of minimum flux from Farrell et al. (2008) and is MJD 53,488. We note that this definition of phase zero differs from the other sources considered in this paper where phase zero for the superorbital modulation is defined as the time of maximum flux.</caption>
</figure>
<text><location><page_3><loc_8><loc_8><loc_48><loc_24></location>g the presence of an eclipse. Corbet et al. (2010b) confirmed the orbital period using PCA Galactic plane scan data which gave an orbital period of 6.7851 ± 0.0016 days. In addition, Corbet et al. (2010b) noted the presence of a 20.07 ± 0.02 day superorbital period in the BAT data which was confirmed by modulation at 20.09 ± 0.02 days in the PCA observations. Pointed RXTE PCA observations revealed a ∼ 1093 s pulse period (Corbet et al. 2010c), and pulse timing with the PCA yielded a mass function of 14.0 ± 2.3 M /circledot (Pearlman et al. 2013) which confirms the interpretation of IGR J16493-4348 as a supergiant HMXB.</text>
<text><location><page_3><loc_10><loc_7><loc_48><loc_8></location>The power spectrum of the BAT light curve of IGR</text>
<figure>
<location><page_3><loc_58><loc_71><loc_87><loc_90></location>
<caption>Figure 3. Power spectrum of the BAT light curve of IGR J164934348.</caption>
</figure>
<figure>
<location><page_3><loc_59><loc_39><loc_85><loc_64></location>
<caption>Figure 4. Swift BAT light curve of IGR J16493-4348 folded on its orbital period (top) and folded on its superorbital period (bottom). Phase zero for the orbital light curve corresponds to the center of the eclipse and is MJD 54,175.92 (Cusumano et al. 2010). Phase zero for the superorbital light curve corresponds to the time of maximum flux and is MJD 54,265.1 (Corbet et al. 2010b).</caption>
</figure>
<text><location><page_3><loc_52><loc_14><loc_92><loc_30></location>J16493-4348 is shown in Figure 3. This clearly shows the presence of the already known orbital and superorbital periods. However, the statistical significances of the periods are somewhat less than previously found from the BAT 54-month catalog data and the FAPs were ∼ 10 -6 and 0.04 respectively. We refine the period measurements to be 6.782 ± 0.001 and 20.07 ± 0.01 days for the orbital and superorbital periods respectively. The BAT light curve of IGR J16493-4348 folded on the orbital and superorbital periods is shown in Figure 4. The orbital modulation shows the presence of an eclipse, while the superorbital modulation is quasi-sinusoidal.</text>
<section_header_level_1><location><page_3><loc_53><loc_11><loc_90><loc_13></location>4. SOURCES WITH NEW DETECTIONS OF PERIODIC SUPERORBITAL MODULATION</section_header_level_1>
<text><location><page_3><loc_64><loc_9><loc_80><loc_10></location>4.1. IGR J16418-4532</text>
<text><location><page_3><loc_53><loc_7><loc_92><loc_8></location>Chaty et al. (2008) determined that the optical coun-</text>
<figure>
<location><page_4><loc_14><loc_71><loc_43><loc_90></location>
<caption>Figure 5. Power spectrum of the BAT light curve of IGR J164184532.</caption>
</figure>
<text><location><page_4><loc_8><loc_45><loc_48><loc_66></location>terpart of IGR J16418-4532 is probably an OB supergiant. Rahoui et al. (2008) fitted the spectral energy distribution of the likely 2MASS counterpart and found that this was consistent with an O/B massive star classification with a best fit spectral type of O8.5, although the luminosity type could not be determined. IGR J16418-4532 exhibits large flux variability, classifying it as an SFXT (Romano et al. 2011, 2012; Sidoli et al. 2012). Pulsations from the source were discovered by Walter et al. (2006) and refined to a period of 1212 ± 6 s by Sidoli et al. (2012). A 3.74 day orbital period has been found for IGR J16418-4532 from RXTE ASM and Swift BAT observations (e.g. Corbet et al. 2006; Levine et al. 2011). INTEGRAL and XMMNewton observations of IGR J16418-4532 are discussed by Drave et al. (2013a).</text>
<text><location><page_4><loc_8><loc_34><loc_48><loc_45></location>The power spectrum of the BAT light curve of IGR J16418-4532 (Figure 5) shows modulation at the 3.74 day orbital period and the second and third harmonics of this. In addition the power spectrum shows a peak near 14.7 days with an FAP of < 10 -6 . The light curve folded on this period (Figure 6) shows an approximately sinusoidal modulation. From a sine wave fit to the light curve we obtain:</text>
<section_header_level_1><location><page_4><loc_11><loc_32><loc_46><loc_33></location>T max = MJD 55 , 994 . 6 ± 0 . 4 + n × 14 . 730 ± 0 . 006</section_header_level_1>
<text><location><page_4><loc_8><loc_30><loc_38><loc_31></location>where T max is the time of maximum flux.</text>
<text><location><page_4><loc_8><loc_17><loc_48><loc_30></location>The full amplitude of the modulation, defined as (maximum - minimum)/ mean flux, from the sine fit is approximately 70%. From the fundamental of the orbital peak in the power spectrum we determine an orbital period of 3.73834 ± 0.00022 days, while the second harmonic yields 3.73886 ± 0.00014 days. This is consistent with the period of 3.73886 +0.00028, -0.00140 days given by Levine et al. (2011). The BAT light curve of IGR J16418-4532 folded on the orbital period is also shown in Figure 6 and this shows the presence of an eclipse.</text>
<section_header_level_1><location><page_4><loc_20><loc_14><loc_36><loc_15></location>4.2. IGR J16479-4514</section_header_level_1>
<text><location><page_4><loc_8><loc_7><loc_48><loc_13></location>IGR J16479-4514 is an SFXT with a rather short orbital period of near 3.3 days with periods of 3.3194 ± 0.0010 and 3.3193 ± 0.0005 days determined by Jain et al. (2009) and Romano et al. (2009), respectively, using Swift BAT data in both cases. The folded light</text>
<figure>
<location><page_4><loc_59><loc_67><loc_85><loc_91></location>
<caption>Figure 6. Swift BAT light curve of IGR J16418-4532 folded on its orbital period (top), and folded on its superorbital period (bottom). The period values are given in Table 1. Phase zero for the orbital period corresponds to the time of minimum flux and is MJD 52,735.84 (Levine et al. 2011). For the superorbital period phase zero corresponds to the time of maximum flux and is MJD 55,994.6 (Section 4.1).</caption>
</figure>
<text><location><page_4><loc_52><loc_51><loc_92><loc_56></location>curve shows the presence of X-ray eclipses. The mass donor has a spectral type of O8.5I (Chaty et al. 2008; Rahoui et al. 2008) or O9.5 Iab (Nespoli et al. 2008). No X-ray pulsations have yet been reported.</text>
<text><location><page_4><loc_52><loc_25><loc_92><loc_51></location>The power spectrum of the BAT light curve (Figure 7) shows modulation at the 3.32 day orbital period and harmonics of this. From the fundamental we determine an orbital period of 3.3199 ± 0.0005 days. In addition to this, peaks are seen near 11.9 days and its second harmonic. The FAP of the harmonic is 0.0006 while that of the fundamental is 0.05. The second harmonic is stronger than the fundamental and from this we derive a superorbital period of 11.880 ± 0.002 days. The period determined from the fundamental is consistent with this at 11.871 ± 0.005 days. The BAT light curve of IGR J16479-4514 folded on the orbital and superorbital periods is shown in Figure 8. An eclipse is clearly seen in the light curve folded on the orbital period. The light curve folded on the superorbital period shows a relatively sharp rise from minimum to maximum followed by a plateau. The time of minimum flux is approximately MJD 55,993 ± 1.0 with maximum flux occurring approximately 0.25 in phase after this. The full amplitude of the modulation is approximately 130%.</text>
<section_header_level_1><location><page_4><loc_60><loc_22><loc_83><loc_23></location>4.3. 4U 1909+07 (X 1908+075)</section_header_level_1>
<text><location><page_4><loc_52><loc_7><loc_92><loc_21></location>Wen et al. (2000) found a 4.400 ± 0.001 day orbital period for the X-ray binary 4U 1909+07 using RXTE ASM observations. X-ray pulsations with a period of 605 s were found with the RXTE PCA by Levine et al. (2004) and from a pulse arrival time analysis they found the orbit to be circular with an orbital period of 4.4007 ± 0.0009 days and derived a mass function of 6.1 M /circledot . Although Levine et al. (2004) proposed that the primary might be a Wolf-Rayet star, Morel & Grosdidier (2005) identified a likely near-IR candidate which they proposed to be a late O-type supergiant. Levine et al. (2004)</text>
<figure>
<location><page_5><loc_15><loc_71><loc_43><loc_90></location>
<caption>Figure 7. Power spectrum of the BAT light curve of IGR J164794514.</caption>
</figure>
<figure>
<location><page_5><loc_16><loc_39><loc_41><loc_64></location>
<caption>Figure 8. Swift BAT light curve of IGR J16479-4514 folded on its orbital period (top) and folded on its superorbital period (bottom). The period values are given in Table 1. Phase zero for the orbital period is the center of the eclipse and is MJD 54,547.05 (Bozzo et al. 2009). Phase zero for the superorbital period corresponds to maximum flux and is MJD 55,996 (Section 4.2).</caption>
</figure>
<text><location><page_5><loc_8><loc_24><loc_48><loc_29></location>found large orbital phase dependence of the X-ray absorption. The orbital period was further refined with additional ASM observations to 4.4005 ± 0.0004 days by Wen et al. (2006).</text>
<text><location><page_5><loc_8><loc_13><loc_48><loc_24></location>The power spectrum of the BAT light curve of 4U 1909+07 (Figure 9) shows strong modulation at the orbital period and we derive a period of 4.4003 ± 0.0004 days. In addition, significant modulation at a superorbital period near 15.2 days (FAP ∼ 10 -5 ) and the second harmonic of this are seen. Combining the detections at the fundamental and second harmonic, we determine a period of 15.180 ± 0.003 days.</text>
<text><location><page_5><loc_8><loc_7><loc_48><loc_13></location>As expected from the presence of harmonics in the power spectrum, the light curve folded on the superorbital period (Figure 10) shows a multi-peaked profile. The minimum is somewhat more clearly defined than the maximum. From an inspection of the folded light curve,</text>
<figure>
<location><page_5><loc_58><loc_71><loc_87><loc_90></location>
<caption>Figure 9. Power spectrum of the BAT light curve of 4U 1909+07.</caption>
</figure>
<figure>
<location><page_5><loc_59><loc_40><loc_85><loc_65></location>
<caption>Figure 10. Swift BAT light curve of 4U 1909+07 folded on its orbital period (top) and folded on its superorbital period (bottom). The period values are given in Table 1. Phase zero for the orbital period is the time of superior conjunction from Levine et al. (2004) and is MJD 52,631.383. Phase zero for the superorbital period is the time of maximum flux and is MJD 56,004 (Section 4.3).</caption>
</figure>
<text><location><page_5><loc_52><loc_18><loc_92><loc_28></location>the minimum occurs at approximately MJD 55,999 ± 1.5. The time of maximum flux occurs about 0.35 in phase after the minimum. The amplitude of the modulation, defined as (maximum - minimum)/ mean flux is approximately 50%. The BAT light curve folded on the orbital period is shown in Figure 10. This shows a quasisinusoidal modulation with no evidence for the presence of an eclipse.</text>
<section_header_level_1><location><page_5><loc_55><loc_15><loc_89><loc_16></location>5. PROPERTIES OF SELECTED OTHER SGHMXBS</section_header_level_1>
<text><location><page_5><loc_52><loc_7><loc_92><loc_15></location>For comparison with the sgHMXB systems discussed above where superorbital modulation is seen, we present here examples of systems where there is no strong superorbital modulation, and two examples of systems which appear to be weak candidates for also possessing superorbital modulation.</text>
<figure>
<location><page_6><loc_14><loc_71><loc_43><loc_90></location>
<caption>Figure 11. Power spectra of the BAT light curves of IGR J180272016 (top), IGR J18483-0311 (middle), and IGR J19140+0951 (bottom) The horizontal dashed lines indicate 'white noise' 99.9% and 99.99% significance levels..</caption>
</figure>
<section_header_level_1><location><page_6><loc_12><loc_61><loc_47><loc_63></location>5.1. Examples of Systems with Strong Orbital Modulation but Lacking Superorbital Modulation</section_header_level_1>
<text><location><page_6><loc_8><loc_49><loc_48><loc_60></location>The Swift BAT set of light curves includes a number of other sgHMXBs. However, the majority of these do not show evidence for superorbital modulation. As examples we discuss here three systems. We choose 'IGR' systems which are typically rather hard sources and so suitable for study with the BAT. The examples selected here all have very significant orbital modulations of their light curves which have previously been reported.</text>
<section_header_level_1><location><page_6><loc_12><loc_47><loc_44><loc_48></location>5.1.1. IGR J18027-2016 (= SAX J1802.7-2017)</section_header_level_1>
<text><location><page_6><loc_8><loc_30><loc_48><loc_46></location>IGR J18027-2016 (= SAX J1802.7-2017) has a pulse period of 139.6s (Augello et al. 2003) and pulse arrival time analysis suggested a ∼ 4.6 day orbital period. From a timing analysis Hill et al. (2005) refined this to 4.5696 ± 0.0009 days. The spectral type of the mass donor has been proposed to be B1 Ib (Torrej'on et al. 2010) and B0-B1 I (Mason et al. 2011), thus making it an sgHMXB. The power spectrum of the BAT light curve of IGR J18027-2016 (Figure 11, bottom panel) is very flat with the exception of the orbital period and its second and third harmonics, together with a small peak corresponding to a period of one year.</text>
<section_header_level_1><location><page_6><loc_20><loc_28><loc_36><loc_29></location>5.1.2. IGR J18483-0311</section_header_level_1>
<text><location><page_6><loc_8><loc_10><loc_48><loc_27></location>IGR J18483-0311 is an SFXT with an early B supergiant optical counterpart (Rahoui & Chaty 2008). Orbital modulation is seen at a period near 18.55 days in RXTE ASM (Levine et al. 2011), BAT (Jain et al. 2009) and INTEGRAL observations (Sguera et al. 2007). This source also has a 21 s pulse period (Sguera et al. 2007). The power spectrum of the BAT light curve of IGR J18483-0311 (Figure 11, middle panel) shows strong modulation at the orbital period and the second harmonic of this. The power spectrum exhibits somewhat larger 'noise' at intermediate frequencies. A small nonstatistically significant ∼ 95 day bump is the third highest peak.</text>
<text><location><page_6><loc_52><loc_73><loc_92><loc_92></location>IGR J19140+0951 (= IGR J19140+098) was discovered with INTEGRAL (Hannikainen et al. 2004) and a 13.558 ± 0.004 day period was found from RXTE ASM and Swift BAT observations (Corbet et al. 2004). From infrared observations the optical counterpart was determined to be a B0.5 supergiant (Hannikainen et al. 2007), later refined to B0.5 Ia by Torrej'on et al. (2010). No pulsations have yet been reported from this source despite INTEGRAL and RXTE PCA observations (Prat et al. 2008). The power spectrum of the BAT light curve of IGR J19140+0951 (Figure 11, top panel) shows an extremely flat power spectrum with the exception of strong peaks at the orbital period and the second harmonic of this.</text>
<section_header_level_1><location><page_6><loc_56><loc_70><loc_88><loc_72></location>5.2. Sources of Potential Superorbital Interest</section_header_level_1>
<text><location><page_6><loc_52><loc_59><loc_92><loc_70></location>Although the presence of superorbital periods in sgHMXBs does not appear to be ubiquitous, we can examine the power spectra of other wind-accretion HMXBs for the possible presence of superorbital periods under the assumption that the apparent correlation between orbital period and superorbital periods discussed in Section 6.3 is indeed correct. This then yields a restricted frequency range to be searched for superorbital modulation.</text>
<section_header_level_1><location><page_6><loc_64><loc_57><loc_79><loc_58></location>5.2.1. 1E 1145.1-6141</section_header_level_1>
<text><location><page_6><loc_52><loc_36><loc_92><loc_56></location>The spectral type of the primary of 1E 1145.1-6141 was found to be B2 Iae by Hutchings et al. (1981) and Densham & Charles (1982). The pulse period is ∼ 297 s and pulse timing enabled Ray & Chakrabarty (2002) to determine a 14.365 ± 0.002 day orbital period with a modest eccentricity of 0.20 ± 0.03. Ray & Chakrabarty (2002) report that no eclipse was seen. No detection of orbital modulation of the X-ray flux from RXTE ASM observations is reported in the papers of Wen et al. (2006) and Levine et al. (2011). However, Corbet et al. (2007b) reported detection of the orbital period of 1E 1145.1-6141 in Swift BAT data with the presence of flares at both periastron and apastron. The presence of flares at apastron is also reported from INTEGRAL observations by Ferrigno et al. (2008).</text>
<text><location><page_6><loc_52><loc_17><loc_92><loc_36></location>For 1E 1145.1-6141, the strongest peak in the power spectrum of the BAT light curve (Figure 12) is at the second harmonic of the 14.4 day orbital period and the second highest peak is at the orbital period itself. The blind-search FAPs of the fundamental and second harmonic peaks would be 0.1 and ∼ 10 -5 respectively. The much lower significance of the fundamental is due to the increase in continuum power at lower frequencies. From the second harmonic we derive an orbital period of 14.365 ± 0.003 days, which is the same as that derived by Ray & Chakrabarty (2002) from pulse timing. The peak at the fundamental yields a period of 14.373 ± 0.007 days, which is also consistent, although with a somewhat larger uncertainty.</text>
<text><location><page_6><loc_52><loc_7><loc_92><loc_17></location>The BAT light curve folded on the orbital period (Figure 13) shows a double-peaked profile with maxima at periastron and apastron based on the ephemeris of Ray & Chakrabarty (2002). The third and the fourth highest peaks in the power spectrum are at periods of 67.8 ± 0.2 (equivalent to 135.6 ± 0.4, if regarded as a second harmonic) and 131.4 ± 0.8 days. The very low FAP of 0.2 of the ∼ 68 day peak means that this is not a</text>
<figure>
<location><page_7><loc_14><loc_71><loc_43><loc_90></location>
<caption>Figure 12. Power spectrum of the BAT light curve of 1E 1145.16141.</caption>
</figure>
<figure>
<location><page_7><loc_16><loc_39><loc_41><loc_64></location>
<caption>Figure 13. Swift BAT light curve of 1E 1145.1-6141 folded on its orbital period (top) and folded on a 67.8 day period (bottom). For the orbital period phase zero corresponds to the time of periastron passage (MJD 51,008.1) determined by Ray & Chakrabarty (2002). For the 68 day modulation, phase zero corresponds to the time of maximum flux from a sine wave fit to the BAT light curve and is MJD 55,142.4 (Section 5.2.1).</caption>
</figure>
<text><location><page_7><loc_8><loc_18><loc_48><loc_28></location>strong candidate for a superorbital period. However, the large amount of variability in the light curve compared to the orbital modulation makes this a potentially interesting system to continue to monitor. From a sine wave fit to the BAT light curve, we derive an epoch of maximum flux for the 68 day modulation of MJD 55,142.4 ± 0.6. The BAT light curve folded on the 68 day period is shown in Figure 13.</text>
<section_header_level_1><location><page_7><loc_12><loc_15><loc_44><loc_17></location>5.2.2. IGR J16393-4643 (= AX J16390.4-4642)</section_header_level_1>
<text><location><page_7><loc_8><loc_7><loc_48><loc_15></location>The 910 s X-ray pulsar IGR J16393-4643 was reported by Thompson et al. (2006) to have a 3.7 day orbital period from a pulse timing analysis, although other solutions with orbital periods of 50.2 and 8.1 days could not be excluded. Thompson et al. (2006) proposed, on the basis of their orbital parameters, that IGR J16393-</text>
<figure>
<location><page_7><loc_58><loc_71><loc_87><loc_90></location>
<caption>Figure 14. Power spectrum of the BAT light curve of IGR J16393-4643.</caption>
</figure>
<text><location><page_7><loc_52><loc_53><loc_92><loc_65></location>4643 is a supergiant wind-accretion powered HMXB. Nespoli et al. (2010) instead suggested that this is a symbiotic X-ray binary with a 50 day period. However, Swift BAT and PCA Galactic plane scan observations clearly showed the system to have a 4.2 day orbital period (Corbet et al. 2010a) which is consistent with an interpretation of the system as an sgHMXB. The periods obtained from the BAT and PCA were 4.2368 ± 0.0007 and 4.2371 ± 0.0007 days respectively.</text>
<text><location><page_7><loc_52><loc_45><loc_92><loc_53></location>Bodaghee et al. (2012) obtained a precise position for IGR J16393-4643 using a Chandra observation, which excluded a previously proposed counterpart that had led to the symbiotic classification by Nespoli et al. (2010), and instead suggested that the correct counterpart to IGR J16393-4643 might be a distant reddened star.</text>
<text><location><page_7><loc_52><loc_37><loc_92><loc_45></location>The 4.2 day orbital period of IGR J16393-4643 is similar to the 4.4 day orbital period of 4U 1909+07 which has a superorbital period of 15.2 days. If there is indeed a relationship between superorbital and orbital periods, as discussed in Section 6.3, a superorbital period of ∼ 15 days would thus be predicted.</text>
<text><location><page_7><loc_52><loc_8><loc_92><loc_37></location>The strongest peak in the power spectrum of the updated Swift BAT light curve (Figure 14) is at the orbital period with a value of 4.2380 ± 0.0005 days. The second highest peak in the power spectrum (Figures 14 and 15) is at a period near 15 days at 14.99 ± 0.01 days, and there is another peak at half this period. The possible second harmonic is at a period of 7.485 ± 0.002 days, equivalent to a fundamental period of 14.971 ± 0.005 days if regarded as a harmonic. However, the 'blind search' FAPs of both peaks, even restricting ourselves to a search of periods longer than the orbital period, are very high at ∼ 17% and ∼ 7% for the 15 and 15/2 day peaks respectively. From a sine wave fit to the BAT light curve, with the period held fixed at 14.99 days, we obtain an epoch of maximum flux of MJD 55,092.6 ± 0.4. The BAT light curve of IGR J16393-4643 folded on the orbital period and the possible 14.99 day period are shown in Figure 16. The folded profile on the 14.99 day period suggests any modulation may not be perfectly sinusoidal, with the maximum slightly preceding the value predicted by the sine wave fit. The light curve folded on the orbital period suggests the presence of an eclipse.</text>
<text><location><page_7><loc_53><loc_7><loc_92><loc_8></location>We therefore also investigated the PCA Galactic plane</text>
<figure>
<location><page_8><loc_13><loc_71><loc_43><loc_91></location>
<caption>Figure 15. Power spectra of Swift BAT (top), RXTE PCA Galactic Plane scan (middle) and INTEGRAL (bottom) light curves of IGR J16393-4643 for periods longer than the orbital period. The vertical dashed red lines and the arrow mark the possible superorbital period.</caption>
</figure>
<figure>
<location><page_8><loc_16><loc_36><loc_41><loc_61></location>
<caption>Figure 16. Swift BAT light curve of IGR J16393-4643 folded on its orbital period (top) and folded on its possible superorbital period (bottom). Period values are given in Table 1. Phase zero for the orbital period is time of maximum flux from Corbet et al. (2010a) (MJD 54,352.50) and for the possible superorbital period it is MJD 55,092.6, the epoch of maximum flux from a sine wave fit to the BAT light curve (Section 5.2.2)</caption>
</figure>
<text><location><page_8><loc_8><loc_13><loc_48><loc_25></location>scans of this source obtained between MJD 53163 and 55863 (2004-06-07 and 2011-10-29). This is 566 days longer than the light curve used in Corbet et al. (2010a). The PCA data yield an orbital period of 4.2376 ± 0.0005 days, consistent with our updated BAT result. In the power spectrum of the PCA scan observations (Figure 15), the largest peak for periods longer than the orbital period is at 14.99 ± 0.01 days, consistent with the possible BAT period.</text>
<text><location><page_8><loc_8><loc_7><loc_48><loc_13></location>We next examined the INTEGRAL light curve of IGR J16393-4643 that we obtained from the Heavens service of the ISDC. This covers a time range of MJD 52,650 to 55,856 (2003-01-11 to 2011-10-22) although with only very sparse sampling. This limited sampling yields large</text>
<figure>
<location><page_8><loc_59><loc_66><loc_85><loc_91></location>
<caption>Figure 17. Swift BAT (top), INTEGRAL IBIS (middle) and RXTE PCA scan (bottom) light curves of IGR J16393-4643 folded on its possible superorbital period. Phase zero is MJD 55,092.6, the epoch of maximum flux from a sine wave fit to the BAT light curve (Section 5.2.2)</caption>
</figure>
<text><location><page_8><loc_52><loc_45><loc_92><loc_58></location>amounts of artifacts in the power spectrum of the light curve. For example, the 4.2 day orbital period is not the strongest peak. However, examining the peak nearest the orbital period yields a value of 4.2382 ± 0.0006, consistent with the periods derived from the BAT and PCA observations. The INTEGRAL power spectrum for periods longer than the orbital period (Figure 15) also shows a small peak near 15 days. This has a value of 14.98 ± 0.01 days, which is consistent with the periods obtained from the BAT and PCA observations.</text>
<text><location><page_8><loc_52><loc_27><loc_92><loc_45></location>The BAT, PCA, and INTEGRAL data folded on the possible superorbital period derived from the BAT data are shown in Figure 17. The three light curves appear to have roughly coincident maxima. While the coincidence of the periods obtained from three separate instruments is intriguing, additional data are required to confirm whether there truly is a superorbital period in this system. Such data may come from continued monitoring with the BAT, or from future missions such as the proposed Wide Field Monitor (WFM; Bozzo & LOFT Consortium 2013) on board the Large Observatory for X-ray Timing (LOFT; Feroci et al. 2012).</text>
<section_header_level_1><location><page_8><loc_67><loc_25><loc_77><loc_26></location>6. DISCUSSION</section_header_level_1>
<section_header_level_1><location><page_8><loc_61><loc_23><loc_83><loc_25></location>6.1. Excluding Period Artifacts</section_header_level_1>
<text><location><page_8><loc_52><loc_7><loc_92><loc_23></location>Since the presence of superorbital periods in sgHMXBs is somewhat surprising, we consider whether they could be some type of artifact. We note that they are not present in other types of systems, and there is no obvious way to create superorbital modulation in only a subset of supergiant wind accretors. Superorbital modulation in 2S 0114+650 and IGR J16493-4348 was previously seen in other detectors ( RXTE ASM and RXTE PCA Galactic plane scan data respectively). In several cases there are pulse arrival time orbits that show that the orbital period really is the orbital period. In addition, Drave et al. (2013b) report that INTEGRAL /IBIS data</text>
<text><location><page_9><loc_8><loc_89><loc_48><loc_92></location>confirm the superorbital periods found for 4U 1909+07, IGR J16418-4532, and IGR J16479-4514.</text>
<text><location><page_9><loc_8><loc_64><loc_48><loc_89></location>The superorbital periods are rather prominent relative to the orbital periods in the BAT energy range. This appears to differ from results of lower-energy observations such as RXTE ASM observations of 4U 1909+07, where the orbital period is strongly detected, but the superorbital period is not seen. Similarly, for 2S 0114+650, although the superorbital period was initially detected from RXTE ASM data (Farrell et al. 2006), the superorbital modulation has lower amplitude than the orbital modulation in the ASM energy band. In contrast, the superorbital modulation of 2S 0114+650 is stronger than the orbital modulation in the BAT observations. One reason for this is likely to be the lower fractional modulation of the X-ray flux on the orbital period in the BAT energy range for non-eclipsing systems. For these types of systems a large component of the orbital modulation seen with lower-energy instruments is due to the changing absorption as the neutron star orbits its companion, which the BAT is relatively insensitive to.</text>
<section_header_level_1><location><page_9><loc_23><loc_61><loc_34><loc_62></location>6.2. Coherence</section_header_level_1>
<text><location><page_9><loc_8><loc_30><loc_48><loc_61></location>Superorbital modulation from Roche-lobe overflow systems is not necessarily coherent. For example, there is considerable variation in the superorbital periods of SMC X-1 (Coe et al. 2013; Wojdowski et al. 1998) and Her X-1 (Leahy & Igna 2010), although not in LMC X4 (Hung et al. 2010). The sampling of the BAT light curves is very variable. This potentially makes it more difficult to calculate the true resolution of the power spectra. Therefore, in order to investigate the coherency of the superorbital modulation, we compared the widths of the superorbital peaks to those of the orbital peaks. This uses the assumption that the orbital modulation should be essentially periodic. We fitted Gaussian functions to the superorbital and orbital peaks in the power spectra in the five systems for which superorbital modulation is definitely observed and determined the following ratios of superorbital to orbital peak widths: 2S 0114+650, 1.05; IGR J16493-4348, 1.16; IGR J16418-4532, 0.92; IGR J16479-4514, 0.98; 4U 1909+07, 0.92. We therefore conclude that the superorbital modulations have very high coherence. For the two low-significance candidates we obtain ratios of superorbital to orbital peak widths of: IGR J16393-4643, 0.66; 1E 1145.1-6141, 0.89.</text>
<section_header_level_1><location><page_9><loc_10><loc_26><loc_46><loc_29></location>6.3. Relationship Between Superorbital and Orbital Periods</section_header_level_1>
<text><location><page_9><loc_8><loc_7><loc_48><loc_25></location>System parameters are summarized in Table 1, and in Figure 18 we plot superorbital period against orbital period. For the five systems with definite superorbital modulation, the linear correlation coefficient between P super and P orb is 0.996 and the associated probability of obtaining this level of correlation from a random data set is 0.03%. Because this possible correlation comes from such a small number of systems, a determination whether this possible dependence of superorbital period on orbital period is correct requires the candidate superorbital period in IGR J16393-4643 to be investigated with additional data, and further superorbital periods must be found in other systems. For the five systems the best linear fit for superorbital periods vs. orbital period has parameters</text>
<figure>
<location><page_9><loc_56><loc_71><loc_87><loc_90></location>
<caption>Figure 18. Superorbital period plotted against orbital period for the wind-accretion HMXBs discussed in the text. Statistical uncertainties on period measurements are smaller than symbol sizes. The filled symbols show definite superorbital period detections. The gray open symbol marks the modulation seen in IGR J163934643 which is not yet considered to be a definite detection of a superorbital period.</caption>
</figure>
<text><location><page_9><loc_52><loc_59><loc_54><loc_60></location>of:</text>
<formula><location><page_9><loc_57><loc_57><loc_87><loc_59></location>P super = 2 . 2 ± 0 . 1 × P orb +5 . 6 ± 0 . 8 days</formula>
<text><location><page_9><loc_52><loc_26><loc_92><loc_56></location>For comparison, in Figure 19 we plot superorbital period against orbital period for a wide variety of systems. These include these Roche-lobe overflow powered systems: LMC X-4 (neutron star HMXB, P orb = 1.4 days, P super = 30.3 days), Her X-1 (neutron star intermediatemass system, P orb =1.7 days, P super = 35 days), SMC X-1 (neutron star HMXB, P orb = 3.89 days, P super = 56 days), and SS 433 (black hole candidate microquasar, P orb = 13.1 days, P super = 162.5 days). These parameters are taken from Kotze & Charles (2012). Be star systems are also shown with their parameters taken from Rajoelimanana et al. (2011). For the Be star systems the superorbital modulation periods may be quasi-periodic rather than strictly periodic. It the mechanisms driving superorbital modulation differ between different types of object, then the different types of system could be located in different regions of this diagram. We note that the sgHMXB superorbital periods are rather short relative to their orbital periods, compared to other types of systems. This is suggestive that, as expected, a different driving mechanism may be at work in the sgHMXBs superorbital modulation compared to the other types of system.</text>
<section_header_level_1><location><page_9><loc_55><loc_22><loc_88><loc_25></location>6.4. Possible Mechanisms Driving Superorbital Modulation</section_header_level_1>
<text><location><page_9><loc_52><loc_7><loc_92><loc_21></location>We note that Farrell et al. (2008)'s extensive RXTE PCA observations of 2S 0114+650 showed that there were changes in absorption over the orbital period of this system, but not on the superorbital period. Farrell et al. (2008) therefore concluded that the superorbital modulation was related to variability in the mass accretion rate caused by an unknown mechanism. This is consistent with the stronger detection of superorbital periods with the BAT compared to orbital periods for noneclipsing systems than is the case with the RXTE ASM (Section 6.1). The ASM is more sensitive to changes in</text>
<figure>
<location><page_10><loc_12><loc_71><loc_44><loc_91></location>
<caption>Figure 19. Superorbital period plotted against orbital period for the a variety of HMXBs including both neutron star and black hole systems. 'R' indicates Roche-lobe overflow systems, 'W' are the five wind-accretion systems discussed in this paper, and 'B' shows Be star system parameters taken from Rajoelimanana et al. (2011). The sources included as Roche-lobe overflow systems are the high-mass neutron star systems LMC X-4 and SMC X-1, the intermediate-mass neutron star system Her X-1, and the black hole candidate SS 433.</caption>
</figure>
<text><location><page_10><loc_8><loc_53><loc_48><loc_57></location>absorption over the orbital period. However, the BAT has overall better sensitivity for changes in the flux of highly-absorbed systems.</text>
<text><location><page_10><loc_8><loc_12><loc_48><loc_53></location>If mass-transfer rate variations are the cause of periodic superorbital modulation, then this suggests that the wind from the primary star could itself be modulated in some way by a mechanism related to the length of the orbital period. However, any satisfactory model must be able to account for the lack of superorbital variability in many systems. Thus, the modulation must be related to some parameter independent of inclination angle and whether the system is an SFXT or classical supergiant system. For example, an offset between the orbital plane and the rotation axis of the primary star, or a small orbital eccentricity, might satisfy such a requirement. The light curves folded on the superorbital periods exhibit a variety of morphologies, and so any model for the modulation must be able to account for this. We note the work of Koenigsberger et al. (2003) and Moreno et al. (2005) indicates that oscillations can be induced in nonsynchronously rotating stars in binary systems on periods longer than the orbital period. As discussed by Koenigsberger et al. (2006), such oscillations result in changes in the mass-loss rate of the primary star which would cause correlated changes in the X-ray luminosity. This model may also be consistent with the lack of superorbital modulation in all systems if only a fraction of primary stars are rotating non-synchronously. However, as noted by Farrell et al. (2008), the Koenigsberger et al. (2006) model applies to circular orbits and 2S 0114+650 has a modest eccentricity of 0.2. In addition, the high coherency of the superorbital modulations seems difficult to account for with oscillations of the primary star unless there is some way to keep strict phase stability.</text>
<text><location><page_10><loc_8><loc_7><loc_48><loc_12></location>In principle, the presence of a third object in the systems might drive superorbital modulation. The modulation from a third body would also naturally account for the coherency of the superorbital modulation. How-</text>
<text><location><page_10><loc_52><loc_84><loc_92><loc_92></location>ever, the apparent correlation between superorbital and orbital periods would, if confirmed, place stringent constraints on how such multi-star systems might be formed. In addition, typically such triple body models for X-ray sources involve hierarchical systems with a distant third object (e.g. Mazeh & Shaham 1979).</text>
<section_header_level_1><location><page_10><loc_66><loc_61><loc_78><loc_62></location>7. CONCLUSION</section_header_level_1>
<text><location><page_10><loc_52><loc_36><loc_92><loc_60></location>Observations with the Swift BAT have shown the presence of superorbital periods in three additional sgHMXBs for a total of five definite such systems. The superorbital modulations have a variety of morphologies, ranging from approximately sinusoidal to multi-peaked profiles. However, superorbital modulation is not a ubiquitous property of sgHMXBs. With this limited set of data, a possible dependence of superorbital period on orbital period is suggested. The mechanism(s) driving such superorbital modulation remain unclear. However, possible models based on oscillations in the primary star driven by non-synchronous rotation, and three-body systems deserve further investigation. Continued monitoring of sgHMXBs in hard X-rays both with additional Swift BAT data and also potential new missions with high-energy X-ray sensitivity such as the LOFT WFM may reveal additional sources with superorbital periodicities.</text>
<text><location><page_10><loc_52><loc_7><loc_92><loc_15></location>We thank an anonymous referee for useful comments. This paper used Swift /BAT transient monitor results provided by the Swift /BAT team. The Swift/BAT transient monitor and H. A. K. are supported by NASA under Swift Guest Observer grants NNX09AU85G, NNX12AD32G, NNX12AE57G and NNX13AC75G.</text>
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</unordered_list>
<table>
<location><page_12><loc_11><loc_75><loc_88><loc_88></location>
<caption>Table 1 Wind-Accretion sgHMXBs with Periodic Superorbital Modulation</caption>
</table>
<text><location><page_12><loc_11><loc_71><loc_88><loc_75></location>Note . - The superorbital period for the system below the line is a candidate and not a definite detection. The references for system parameters are given in the individual sections on each source. The orbital and superorbital periods and their errors are derived from the BAT light curves. For some systems additional determinations of periods may be available from other work, as given in the individual source sections.</text>
</document>
[
{
"title": "ABSTRACT",
"content": "We report the discovery using data from the Swift Burst Alert Telescope (BAT) of superorbital modulation in the wind-accretion supergiant high-mass X-ray binaries 4U 1909+07 (= X 1908+075), IGR J16418-4532, and IGR J16479-4514. Together with already known superorbital periodicities in 2S0114+650 and IGR J16493-4348, the systems exhibit a monotonic relationship between superorbital and orbital periods. These systems include both supergiant fast X-ray transients (SFXTs) and classical supergiant systems, and have a range of inclination angles. This suggests an underlying physical mechanism which is connected to the orbital period. In addition to these sources with clear detections of superorbital periods, IGR J16393-4643 (= AX J16390.4-4642) is identified as a system that may have superorbital modulation due to the coincidence of low-amplitude peaks in power spectra derived from BAT, RXTE PCA, and INTEGRAL light curves. 1E 1145.1-6141 may also be worthy of further attention due to the amount of low-frequency modulation of its light curve. However, we find that the presence of superorbital modulation is not a universal feature of wind-accretion supergiant X-ray binaries. Subject headings: stars: individual (2S 0114+650, 1E 1145.1-6141, IGR J16393-4643, IGR J164184532, IGR J16479-4514, IGR J16493-4348, 4U 1909+07) - stars: neutron - Xrays: stars",
"pages": [
1
]
},
{
"title": "SUPERORBITAL PERIODIC MODULATION IN WIND-ACCRETION HIGH-MASS X-RAY BINARIES FROM Swift BAT OBSERVATIONS",
"content": "1,2 3,4 Robin H. D. Corbet and Hans A. Krimm Draft version October 17, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Superorbital modulation is seen in a variety of X-ray binaries. A review of superorbital modulation in several types of systems is presented by Kotze & Charles (2012). In some cases such as Her X-1, SMC X-1 and LMC X-4, where accretion occurs by Roche-lobe overflow via an accretion disk onto a neutron star, the mechanism driving superorbital modulation can be understood as either precession of the accretion disk (e.g. Petterson 1975) or of the neutron star (e.g. Postnov et al. 2013). Irradiation of the accretion disk by the central X-ray source provides a possible mechanism for driving disk precession (e.g. Ogilvie & Dubus 2001, and references therein). Be star systems also exhibit long timescale, possibly periodic, variability at optical wavelengths. This long timescale variability has been claimed to be correlated with orbital period (Rajoelimanana et al. 2011). A more puzzling variety of superorbital variability was found in a supergiant high-mass X-ray binary (sgHMXB). The sgHMXBs can be broadly classified into 'classical' systems, which may suffer from high levels of absorption, and supergiant fast X-ray transients (SFXTs; e.g. Blay et al. 2012; Sidoli 2013). In the sgHMXB 2S0114+650 there are three periodicities: a ∼ 9700 s neutron star rotation period, an 11.6 day orbital period, and a 30.7 day superorbital modulation (Corbet et al. 1 University of Maryland, Baltimore County, MD, USA; [email protected] 2 CRESST/Mail Code 662, X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 3 Universities Space Research Association, 10211 Wincopin Circle, Suite 500, Columbia, MD 21044, USA 4 CRESST/Mail Code 661, Astroparticle Physics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 1999; Wen et al. 2006; Farrell et al. 2008). A question has been whether 2S 0114+650 is exceptional, perhaps because of its unusually long pulse period, or whether other wind-accretion HMXBs also show similar superorbital periodicities. If similar behavior is found in other systems, then this may provide a way to determine, or at least constrain, the underlying mechanism. A suggestion that the phenomenon might be more general than just the case of 2S 0114+650 came when a superorbital period was found in the sgHMXB IGR J16493-4348 (Corbet et al. 2010b). The Swift BAT provides an excellent way to monitor sgHMXBs. These systems are often highly absorbed, which presents difficulties for an instrument such as the Rossi X-ray Timing Explorer ( RXTE ) All Sky Monitor (ASM) which is sensitive in the 2 - 12 keV band (Levine et al. 1996). The Swift BAT's sensitivity to higher energy X-rays ( > 15 keV) provides a way to peer through this absorption. We present here a review of our searches of BAT light curves of sources thought to be HMXBs, in order to find additional sources that may also display superorbital modulation. In a few cases we also employ data collected from Galactic plane scans (Markwardt 2006) made with the RXTE Proportional Counter Array (PCA). The large effective area of the PCA enables observations to be made in the lower energy range of 2 - 10 keV. Although the PCA data cover only a limited fraction of the sky they have greater sensitivity than the RXTE ASM. MAXI light curves (Sugizaki et al. 2011) are not available for the majority of systems considered here. We present here the results of a search for superorbital modulation in additional wind-accretion supergiant HMXBs. We find three new systems with clear superorbital modulation, initial reports of which were made in Corbet & Krimm (2013a,b). We also find hints of modulation in two other systems. Although the number of systems is small, three new systems plus two previously known, we note a monotonic relationship between orbital and superorbital periods. We consider possible mechanisms that might cause superorbital modulation in some, but not all, sgHMXBs.",
"pages": [
1,
2
]
},
{
"title": "2. DATA AND ANALYSIS",
"content": "The Burst Alert Telescope (BAT) on board the Swift satellite (Gehrels et al. 2004) is described in detail by Barthelmy et al. (2005). It uses a 2.7 m 2 coded-aperture mask and a 0.52 m 2 CdZnTe detector array. The BAT has a wide field of view, 1.4 sr half-coded, 2.85 sr 0% coded. The pointing direction of Swift is driven by the narrow-field XRT and UVOT instruments on board the satellite. The BAT typically observes 50%-80% of the sky each day. We used data from the Swift /BAT transient monitor (Krimm et al. 2006, 2013) covering the energy range 15 - 50 keV, and selected data with time resolution of Swift pointing durations. The transient monitor data are available shortly after observations have been performed. The light curves considered here cover the time range of MJD 53,416 to 56,452 (2005-02-15 to 2013-06-09). The light curves of some sources, not including the ones discussed in detail here, were more recently added to the analysis and hence have shorter durations. BAT light curves are also available from the catalogs such as described by Tueller et al. (2010). However, the most recent BAT catalog is from 70 months of data (Baumgartner et al. 2012) and the transient monitor light curves are hence of longer duration. The transient monitor light curves generally cover more than 3000 days, approximately 50% longer than the 70-month catalog light curves. We used only data for which the data quality flag ('DATA FLAG') was set to 0, indicating good quality. In addition, we found that even data flagged as 'good' were sometimes suspect. In particular we identified a small number of data points with very low fluxes and implausibly small uncertainties. We therefore removed these points from the light curves. A total of 1244 light curves were available, this includes 106 blank fields that are used for test purposes. To search for periodic modulation in the light curves, we calculated discrete Fourier transforms (DFTs) of all available light curves. We calculated the DFTs for a frequency range which corresponds to periods of between 0.07 days to the length of the light curves - i.e. generally ∼ 3000 days. The contribution of each data point to the power spectrum was weighted by its uncertainty using the 'semi-weighting' technique (Corbet et al. 2007a,b). This takes into account both the error bars on each data point and the excess variability of the light curve. Scargle (1989) notes that the weighting of data points in a power spectrum can be compared to combining individual data points. In this way, the use of semi-weighting is analogous to combining data points using the semi-weighted mean (Cochran 1937, 1954). We oversampled the DFTs by a factor of five compared to their nominal resolution. Calculations of the significance of peaks seen are expressed in terms of false alarm probability (FAP; Scargle 1982) which takes into account the DFT oversampling. Uncertainties in periods are generally derived using the expression of Horne & Baliunas (1986). In the figures showing power spectra we mark in 'white noise' 99.9% and 99.99% significance levels. However, many sources exhibit noise continua which are not 'white'. In our calculations of FAP, we therefore determined local noise levels by fitting the continuum power levels in a narrow frequency range around each peak of interest.",
"pages": [
2
]
},
{
"title": "3.1. 2S0114+650",
"content": "2S0114+650 is an unusual HMXB system that has an exceptionally long pulse period of ∼ 9700 s (e.g. Corbet et al. 1999). There has been controversy over the spectral classification of the mass donor, but Reig et al. (1996) derive a spectral type of B1 Ia. From optical radial velocity measurements, Grundstrom et al. (2007) determine an orbital period of 11.5983 ± 0.0006 days and a moderate eccentricity of 0.18 ± 0.05. The orbital period is also seen in the RXTE ASM light curve (Corbet et al. 1999; Wen et al. 2006). A 30.7 ± 0.1 day superorbital period was found by Farrell et al. (2006) from RXTE ASM observations, and the period was later refined to 30.75 ± 0.03 days by Wen et al. (2006). Farrell et al. (2008) performed extensive RXTE PCA observations covering approximately 2 cycles of the superorbital period. Although Farrell et al. (2008) found variations in the X-ray absorption on the orbital period, they found no such changes over the superorbital period. However, a significant increase in the photon index of the power-law model used to fit the X-ray spectrum was reported at the minimum flux phase of the superorbital period. Farrell et al. (2008) concluded that the superorbital modulation was due to mass-accretion rate variations, although the mechanism causing this could not be determined. The power spectrum of the BAT light curve of 2S0114+650 is shown in Figure 1, both the orbital and superorbital periods are strongly detected, with the superorbital period being stronger than the orbital modulation. We determine orbital and superorbital periods of 11.591 ± 0.003 and 30.76 ± 0.03 days respectively. The BAT light curve of 2S0114+650 folded on the orbital and superorbital periods is shown in Figure 2. For consistency with the work of Farrell et al. (2008) the light curve folded on the superorbital period uses a definition of phase zero as the time of minimum flux. However, for the other sources considered in this paper we use the time of maximum flux as phase zero. Both the orbital and superorbital modulations are quasi-sinusoidal and no evidence for an eclipse is seen in the light curve folded on the orbital period.",
"pages": [
2
]
},
{
"title": "3.2. IGR J16493-4348",
"content": "IGR J16493-4348 was discovered by Grebenev et al. (2005) and subsequent X-ray observations suggested that the source is an X-ray binary (Hill et al. 2008). Nespoli et al. (2010) classified the infrared counterpart as a B0.5 I supergiant. A 6.8 day orbital period was independently found by Corbet et al. (2010b) and Cusumano et al. (2010) using BAT 54 month survey data with the two groups finding periods of 6.7906 ± 0.0020 and 6.782 ± 0.005 days respectively. The BAT modulation was interpreted by Cusumano et al. (2010) as show- g the presence of an eclipse. Corbet et al. (2010b) confirmed the orbital period using PCA Galactic plane scan data which gave an orbital period of 6.7851 ± 0.0016 days. In addition, Corbet et al. (2010b) noted the presence of a 20.07 ± 0.02 day superorbital period in the BAT data which was confirmed by modulation at 20.09 ± 0.02 days in the PCA observations. Pointed RXTE PCA observations revealed a ∼ 1093 s pulse period (Corbet et al. 2010c), and pulse timing with the PCA yielded a mass function of 14.0 ± 2.3 M /circledot (Pearlman et al. 2013) which confirms the interpretation of IGR J16493-4348 as a supergiant HMXB. The power spectrum of the BAT light curve of IGR J16493-4348 is shown in Figure 3. This clearly shows the presence of the already known orbital and superorbital periods. However, the statistical significances of the periods are somewhat less than previously found from the BAT 54-month catalog data and the FAPs were ∼ 10 -6 and 0.04 respectively. We refine the period measurements to be 6.782 ± 0.001 and 20.07 ± 0.01 days for the orbital and superorbital periods respectively. The BAT light curve of IGR J16493-4348 folded on the orbital and superorbital periods is shown in Figure 4. The orbital modulation shows the presence of an eclipse, while the superorbital modulation is quasi-sinusoidal.",
"pages": [
2,
3
]
},
{
"title": "4. SOURCES WITH NEW DETECTIONS OF PERIODIC SUPERORBITAL MODULATION",
"content": "4.1. IGR J16418-4532 Chaty et al. (2008) determined that the optical coun- terpart of IGR J16418-4532 is probably an OB supergiant. Rahoui et al. (2008) fitted the spectral energy distribution of the likely 2MASS counterpart and found that this was consistent with an O/B massive star classification with a best fit spectral type of O8.5, although the luminosity type could not be determined. IGR J16418-4532 exhibits large flux variability, classifying it as an SFXT (Romano et al. 2011, 2012; Sidoli et al. 2012). Pulsations from the source were discovered by Walter et al. (2006) and refined to a period of 1212 ± 6 s by Sidoli et al. (2012). A 3.74 day orbital period has been found for IGR J16418-4532 from RXTE ASM and Swift BAT observations (e.g. Corbet et al. 2006; Levine et al. 2011). INTEGRAL and XMMNewton observations of IGR J16418-4532 are discussed by Drave et al. (2013a). The power spectrum of the BAT light curve of IGR J16418-4532 (Figure 5) shows modulation at the 3.74 day orbital period and the second and third harmonics of this. In addition the power spectrum shows a peak near 14.7 days with an FAP of < 10 -6 . The light curve folded on this period (Figure 6) shows an approximately sinusoidal modulation. From a sine wave fit to the light curve we obtain:",
"pages": [
3,
4
]
},
{
"title": "T max = MJD 55 , 994 . 6 ± 0 . 4 + n × 14 . 730 ± 0 . 006",
"content": "where T max is the time of maximum flux. The full amplitude of the modulation, defined as (maximum - minimum)/ mean flux, from the sine fit is approximately 70%. From the fundamental of the orbital peak in the power spectrum we determine an orbital period of 3.73834 ± 0.00022 days, while the second harmonic yields 3.73886 ± 0.00014 days. This is consistent with the period of 3.73886 +0.00028, -0.00140 days given by Levine et al. (2011). The BAT light curve of IGR J16418-4532 folded on the orbital period is also shown in Figure 6 and this shows the presence of an eclipse.",
"pages": [
4
]
},
{
"title": "4.2. IGR J16479-4514",
"content": "IGR J16479-4514 is an SFXT with a rather short orbital period of near 3.3 days with periods of 3.3194 ± 0.0010 and 3.3193 ± 0.0005 days determined by Jain et al. (2009) and Romano et al. (2009), respectively, using Swift BAT data in both cases. The folded light curve shows the presence of X-ray eclipses. The mass donor has a spectral type of O8.5I (Chaty et al. 2008; Rahoui et al. 2008) or O9.5 Iab (Nespoli et al. 2008). No X-ray pulsations have yet been reported. The power spectrum of the BAT light curve (Figure 7) shows modulation at the 3.32 day orbital period and harmonics of this. From the fundamental we determine an orbital period of 3.3199 ± 0.0005 days. In addition to this, peaks are seen near 11.9 days and its second harmonic. The FAP of the harmonic is 0.0006 while that of the fundamental is 0.05. The second harmonic is stronger than the fundamental and from this we derive a superorbital period of 11.880 ± 0.002 days. The period determined from the fundamental is consistent with this at 11.871 ± 0.005 days. The BAT light curve of IGR J16479-4514 folded on the orbital and superorbital periods is shown in Figure 8. An eclipse is clearly seen in the light curve folded on the orbital period. The light curve folded on the superorbital period shows a relatively sharp rise from minimum to maximum followed by a plateau. The time of minimum flux is approximately MJD 55,993 ± 1.0 with maximum flux occurring approximately 0.25 in phase after this. The full amplitude of the modulation is approximately 130%.",
"pages": [
4
]
},
{
"title": "4.3. 4U 1909+07 (X 1908+075)",
"content": "Wen et al. (2000) found a 4.400 ± 0.001 day orbital period for the X-ray binary 4U 1909+07 using RXTE ASM observations. X-ray pulsations with a period of 605 s were found with the RXTE PCA by Levine et al. (2004) and from a pulse arrival time analysis they found the orbit to be circular with an orbital period of 4.4007 ± 0.0009 days and derived a mass function of 6.1 M /circledot . Although Levine et al. (2004) proposed that the primary might be a Wolf-Rayet star, Morel & Grosdidier (2005) identified a likely near-IR candidate which they proposed to be a late O-type supergiant. Levine et al. (2004) found large orbital phase dependence of the X-ray absorption. The orbital period was further refined with additional ASM observations to 4.4005 ± 0.0004 days by Wen et al. (2006). The power spectrum of the BAT light curve of 4U 1909+07 (Figure 9) shows strong modulation at the orbital period and we derive a period of 4.4003 ± 0.0004 days. In addition, significant modulation at a superorbital period near 15.2 days (FAP ∼ 10 -5 ) and the second harmonic of this are seen. Combining the detections at the fundamental and second harmonic, we determine a period of 15.180 ± 0.003 days. As expected from the presence of harmonics in the power spectrum, the light curve folded on the superorbital period (Figure 10) shows a multi-peaked profile. The minimum is somewhat more clearly defined than the maximum. From an inspection of the folded light curve, the minimum occurs at approximately MJD 55,999 ± 1.5. The time of maximum flux occurs about 0.35 in phase after the minimum. The amplitude of the modulation, defined as (maximum - minimum)/ mean flux is approximately 50%. The BAT light curve folded on the orbital period is shown in Figure 10. This shows a quasisinusoidal modulation with no evidence for the presence of an eclipse.",
"pages": [
4,
5
]
},
{
"title": "5. PROPERTIES OF SELECTED OTHER SGHMXBS",
"content": "For comparison with the sgHMXB systems discussed above where superorbital modulation is seen, we present here examples of systems where there is no strong superorbital modulation, and two examples of systems which appear to be weak candidates for also possessing superorbital modulation.",
"pages": [
5
]
},
{
"title": "5.1. Examples of Systems with Strong Orbital Modulation but Lacking Superorbital Modulation",
"content": "The Swift BAT set of light curves includes a number of other sgHMXBs. However, the majority of these do not show evidence for superorbital modulation. As examples we discuss here three systems. We choose 'IGR' systems which are typically rather hard sources and so suitable for study with the BAT. The examples selected here all have very significant orbital modulations of their light curves which have previously been reported.",
"pages": [
6
]
},
{
"title": "5.1.1. IGR J18027-2016 (= SAX J1802.7-2017)",
"content": "IGR J18027-2016 (= SAX J1802.7-2017) has a pulse period of 139.6s (Augello et al. 2003) and pulse arrival time analysis suggested a ∼ 4.6 day orbital period. From a timing analysis Hill et al. (2005) refined this to 4.5696 ± 0.0009 days. The spectral type of the mass donor has been proposed to be B1 Ib (Torrej'on et al. 2010) and B0-B1 I (Mason et al. 2011), thus making it an sgHMXB. The power spectrum of the BAT light curve of IGR J18027-2016 (Figure 11, bottom panel) is very flat with the exception of the orbital period and its second and third harmonics, together with a small peak corresponding to a period of one year.",
"pages": [
6
]
},
{
"title": "5.1.2. IGR J18483-0311",
"content": "IGR J18483-0311 is an SFXT with an early B supergiant optical counterpart (Rahoui & Chaty 2008). Orbital modulation is seen at a period near 18.55 days in RXTE ASM (Levine et al. 2011), BAT (Jain et al. 2009) and INTEGRAL observations (Sguera et al. 2007). This source also has a 21 s pulse period (Sguera et al. 2007). The power spectrum of the BAT light curve of IGR J18483-0311 (Figure 11, middle panel) shows strong modulation at the orbital period and the second harmonic of this. The power spectrum exhibits somewhat larger 'noise' at intermediate frequencies. A small nonstatistically significant ∼ 95 day bump is the third highest peak. IGR J19140+0951 (= IGR J19140+098) was discovered with INTEGRAL (Hannikainen et al. 2004) and a 13.558 ± 0.004 day period was found from RXTE ASM and Swift BAT observations (Corbet et al. 2004). From infrared observations the optical counterpart was determined to be a B0.5 supergiant (Hannikainen et al. 2007), later refined to B0.5 Ia by Torrej'on et al. (2010). No pulsations have yet been reported from this source despite INTEGRAL and RXTE PCA observations (Prat et al. 2008). The power spectrum of the BAT light curve of IGR J19140+0951 (Figure 11, top panel) shows an extremely flat power spectrum with the exception of strong peaks at the orbital period and the second harmonic of this.",
"pages": [
6
]
},
{
"title": "5.2. Sources of Potential Superorbital Interest",
"content": "Although the presence of superorbital periods in sgHMXBs does not appear to be ubiquitous, we can examine the power spectra of other wind-accretion HMXBs for the possible presence of superorbital periods under the assumption that the apparent correlation between orbital period and superorbital periods discussed in Section 6.3 is indeed correct. This then yields a restricted frequency range to be searched for superorbital modulation.",
"pages": [
6
]
},
{
"title": "5.2.1. 1E 1145.1-6141",
"content": "The spectral type of the primary of 1E 1145.1-6141 was found to be B2 Iae by Hutchings et al. (1981) and Densham & Charles (1982). The pulse period is ∼ 297 s and pulse timing enabled Ray & Chakrabarty (2002) to determine a 14.365 ± 0.002 day orbital period with a modest eccentricity of 0.20 ± 0.03. Ray & Chakrabarty (2002) report that no eclipse was seen. No detection of orbital modulation of the X-ray flux from RXTE ASM observations is reported in the papers of Wen et al. (2006) and Levine et al. (2011). However, Corbet et al. (2007b) reported detection of the orbital period of 1E 1145.1-6141 in Swift BAT data with the presence of flares at both periastron and apastron. The presence of flares at apastron is also reported from INTEGRAL observations by Ferrigno et al. (2008). For 1E 1145.1-6141, the strongest peak in the power spectrum of the BAT light curve (Figure 12) is at the second harmonic of the 14.4 day orbital period and the second highest peak is at the orbital period itself. The blind-search FAPs of the fundamental and second harmonic peaks would be 0.1 and ∼ 10 -5 respectively. The much lower significance of the fundamental is due to the increase in continuum power at lower frequencies. From the second harmonic we derive an orbital period of 14.365 ± 0.003 days, which is the same as that derived by Ray & Chakrabarty (2002) from pulse timing. The peak at the fundamental yields a period of 14.373 ± 0.007 days, which is also consistent, although with a somewhat larger uncertainty. The BAT light curve folded on the orbital period (Figure 13) shows a double-peaked profile with maxima at periastron and apastron based on the ephemeris of Ray & Chakrabarty (2002). The third and the fourth highest peaks in the power spectrum are at periods of 67.8 ± 0.2 (equivalent to 135.6 ± 0.4, if regarded as a second harmonic) and 131.4 ± 0.8 days. The very low FAP of 0.2 of the ∼ 68 day peak means that this is not a strong candidate for a superorbital period. However, the large amount of variability in the light curve compared to the orbital modulation makes this a potentially interesting system to continue to monitor. From a sine wave fit to the BAT light curve, we derive an epoch of maximum flux for the 68 day modulation of MJD 55,142.4 ± 0.6. The BAT light curve folded on the 68 day period is shown in Figure 13.",
"pages": [
6,
7
]
},
{
"title": "5.2.2. IGR J16393-4643 (= AX J16390.4-4642)",
"content": "The 910 s X-ray pulsar IGR J16393-4643 was reported by Thompson et al. (2006) to have a 3.7 day orbital period from a pulse timing analysis, although other solutions with orbital periods of 50.2 and 8.1 days could not be excluded. Thompson et al. (2006) proposed, on the basis of their orbital parameters, that IGR J16393- 4643 is a supergiant wind-accretion powered HMXB. Nespoli et al. (2010) instead suggested that this is a symbiotic X-ray binary with a 50 day period. However, Swift BAT and PCA Galactic plane scan observations clearly showed the system to have a 4.2 day orbital period (Corbet et al. 2010a) which is consistent with an interpretation of the system as an sgHMXB. The periods obtained from the BAT and PCA were 4.2368 ± 0.0007 and 4.2371 ± 0.0007 days respectively. Bodaghee et al. (2012) obtained a precise position for IGR J16393-4643 using a Chandra observation, which excluded a previously proposed counterpart that had led to the symbiotic classification by Nespoli et al. (2010), and instead suggested that the correct counterpart to IGR J16393-4643 might be a distant reddened star. The 4.2 day orbital period of IGR J16393-4643 is similar to the 4.4 day orbital period of 4U 1909+07 which has a superorbital period of 15.2 days. If there is indeed a relationship between superorbital and orbital periods, as discussed in Section 6.3, a superorbital period of ∼ 15 days would thus be predicted. The strongest peak in the power spectrum of the updated Swift BAT light curve (Figure 14) is at the orbital period with a value of 4.2380 ± 0.0005 days. The second highest peak in the power spectrum (Figures 14 and 15) is at a period near 15 days at 14.99 ± 0.01 days, and there is another peak at half this period. The possible second harmonic is at a period of 7.485 ± 0.002 days, equivalent to a fundamental period of 14.971 ± 0.005 days if regarded as a harmonic. However, the 'blind search' FAPs of both peaks, even restricting ourselves to a search of periods longer than the orbital period, are very high at ∼ 17% and ∼ 7% for the 15 and 15/2 day peaks respectively. From a sine wave fit to the BAT light curve, with the period held fixed at 14.99 days, we obtain an epoch of maximum flux of MJD 55,092.6 ± 0.4. The BAT light curve of IGR J16393-4643 folded on the orbital period and the possible 14.99 day period are shown in Figure 16. The folded profile on the 14.99 day period suggests any modulation may not be perfectly sinusoidal, with the maximum slightly preceding the value predicted by the sine wave fit. The light curve folded on the orbital period suggests the presence of an eclipse. We therefore also investigated the PCA Galactic plane scans of this source obtained between MJD 53163 and 55863 (2004-06-07 and 2011-10-29). This is 566 days longer than the light curve used in Corbet et al. (2010a). The PCA data yield an orbital period of 4.2376 ± 0.0005 days, consistent with our updated BAT result. In the power spectrum of the PCA scan observations (Figure 15), the largest peak for periods longer than the orbital period is at 14.99 ± 0.01 days, consistent with the possible BAT period. We next examined the INTEGRAL light curve of IGR J16393-4643 that we obtained from the Heavens service of the ISDC. This covers a time range of MJD 52,650 to 55,856 (2003-01-11 to 2011-10-22) although with only very sparse sampling. This limited sampling yields large amounts of artifacts in the power spectrum of the light curve. For example, the 4.2 day orbital period is not the strongest peak. However, examining the peak nearest the orbital period yields a value of 4.2382 ± 0.0006, consistent with the periods derived from the BAT and PCA observations. The INTEGRAL power spectrum for periods longer than the orbital period (Figure 15) also shows a small peak near 15 days. This has a value of 14.98 ± 0.01 days, which is consistent with the periods obtained from the BAT and PCA observations. The BAT, PCA, and INTEGRAL data folded on the possible superorbital period derived from the BAT data are shown in Figure 17. The three light curves appear to have roughly coincident maxima. While the coincidence of the periods obtained from three separate instruments is intriguing, additional data are required to confirm whether there truly is a superorbital period in this system. Such data may come from continued monitoring with the BAT, or from future missions such as the proposed Wide Field Monitor (WFM; Bozzo & LOFT Consortium 2013) on board the Large Observatory for X-ray Timing (LOFT; Feroci et al. 2012).",
"pages": [
7,
8
]
},
{
"title": "6.1. Excluding Period Artifacts",
"content": "Since the presence of superorbital periods in sgHMXBs is somewhat surprising, we consider whether they could be some type of artifact. We note that they are not present in other types of systems, and there is no obvious way to create superorbital modulation in only a subset of supergiant wind accretors. Superorbital modulation in 2S 0114+650 and IGR J16493-4348 was previously seen in other detectors ( RXTE ASM and RXTE PCA Galactic plane scan data respectively). In several cases there are pulse arrival time orbits that show that the orbital period really is the orbital period. In addition, Drave et al. (2013b) report that INTEGRAL /IBIS data confirm the superorbital periods found for 4U 1909+07, IGR J16418-4532, and IGR J16479-4514. The superorbital periods are rather prominent relative to the orbital periods in the BAT energy range. This appears to differ from results of lower-energy observations such as RXTE ASM observations of 4U 1909+07, where the orbital period is strongly detected, but the superorbital period is not seen. Similarly, for 2S 0114+650, although the superorbital period was initially detected from RXTE ASM data (Farrell et al. 2006), the superorbital modulation has lower amplitude than the orbital modulation in the ASM energy band. In contrast, the superorbital modulation of 2S 0114+650 is stronger than the orbital modulation in the BAT observations. One reason for this is likely to be the lower fractional modulation of the X-ray flux on the orbital period in the BAT energy range for non-eclipsing systems. For these types of systems a large component of the orbital modulation seen with lower-energy instruments is due to the changing absorption as the neutron star orbits its companion, which the BAT is relatively insensitive to.",
"pages": [
8,
9
]
},
{
"title": "6.2. Coherence",
"content": "Superorbital modulation from Roche-lobe overflow systems is not necessarily coherent. For example, there is considerable variation in the superorbital periods of SMC X-1 (Coe et al. 2013; Wojdowski et al. 1998) and Her X-1 (Leahy & Igna 2010), although not in LMC X4 (Hung et al. 2010). The sampling of the BAT light curves is very variable. This potentially makes it more difficult to calculate the true resolution of the power spectra. Therefore, in order to investigate the coherency of the superorbital modulation, we compared the widths of the superorbital peaks to those of the orbital peaks. This uses the assumption that the orbital modulation should be essentially periodic. We fitted Gaussian functions to the superorbital and orbital peaks in the power spectra in the five systems for which superorbital modulation is definitely observed and determined the following ratios of superorbital to orbital peak widths: 2S 0114+650, 1.05; IGR J16493-4348, 1.16; IGR J16418-4532, 0.92; IGR J16479-4514, 0.98; 4U 1909+07, 0.92. We therefore conclude that the superorbital modulations have very high coherence. For the two low-significance candidates we obtain ratios of superorbital to orbital peak widths of: IGR J16393-4643, 0.66; 1E 1145.1-6141, 0.89.",
"pages": [
9
]
},
{
"title": "6.3. Relationship Between Superorbital and Orbital Periods",
"content": "System parameters are summarized in Table 1, and in Figure 18 we plot superorbital period against orbital period. For the five systems with definite superorbital modulation, the linear correlation coefficient between P super and P orb is 0.996 and the associated probability of obtaining this level of correlation from a random data set is 0.03%. Because this possible correlation comes from such a small number of systems, a determination whether this possible dependence of superorbital period on orbital period is correct requires the candidate superorbital period in IGR J16393-4643 to be investigated with additional data, and further superorbital periods must be found in other systems. For the five systems the best linear fit for superorbital periods vs. orbital period has parameters of: For comparison, in Figure 19 we plot superorbital period against orbital period for a wide variety of systems. These include these Roche-lobe overflow powered systems: LMC X-4 (neutron star HMXB, P orb = 1.4 days, P super = 30.3 days), Her X-1 (neutron star intermediatemass system, P orb =1.7 days, P super = 35 days), SMC X-1 (neutron star HMXB, P orb = 3.89 days, P super = 56 days), and SS 433 (black hole candidate microquasar, P orb = 13.1 days, P super = 162.5 days). These parameters are taken from Kotze & Charles (2012). Be star systems are also shown with their parameters taken from Rajoelimanana et al. (2011). For the Be star systems the superorbital modulation periods may be quasi-periodic rather than strictly periodic. It the mechanisms driving superorbital modulation differ between different types of object, then the different types of system could be located in different regions of this diagram. We note that the sgHMXB superorbital periods are rather short relative to their orbital periods, compared to other types of systems. This is suggestive that, as expected, a different driving mechanism may be at work in the sgHMXBs superorbital modulation compared to the other types of system.",
"pages": [
9
]
},
{
"title": "6.4. Possible Mechanisms Driving Superorbital Modulation",
"content": "We note that Farrell et al. (2008)'s extensive RXTE PCA observations of 2S 0114+650 showed that there were changes in absorption over the orbital period of this system, but not on the superorbital period. Farrell et al. (2008) therefore concluded that the superorbital modulation was related to variability in the mass accretion rate caused by an unknown mechanism. This is consistent with the stronger detection of superorbital periods with the BAT compared to orbital periods for noneclipsing systems than is the case with the RXTE ASM (Section 6.1). The ASM is more sensitive to changes in absorption over the orbital period. However, the BAT has overall better sensitivity for changes in the flux of highly-absorbed systems. If mass-transfer rate variations are the cause of periodic superorbital modulation, then this suggests that the wind from the primary star could itself be modulated in some way by a mechanism related to the length of the orbital period. However, any satisfactory model must be able to account for the lack of superorbital variability in many systems. Thus, the modulation must be related to some parameter independent of inclination angle and whether the system is an SFXT or classical supergiant system. For example, an offset between the orbital plane and the rotation axis of the primary star, or a small orbital eccentricity, might satisfy such a requirement. The light curves folded on the superorbital periods exhibit a variety of morphologies, and so any model for the modulation must be able to account for this. We note the work of Koenigsberger et al. (2003) and Moreno et al. (2005) indicates that oscillations can be induced in nonsynchronously rotating stars in binary systems on periods longer than the orbital period. As discussed by Koenigsberger et al. (2006), such oscillations result in changes in the mass-loss rate of the primary star which would cause correlated changes in the X-ray luminosity. This model may also be consistent with the lack of superorbital modulation in all systems if only a fraction of primary stars are rotating non-synchronously. However, as noted by Farrell et al. (2008), the Koenigsberger et al. (2006) model applies to circular orbits and 2S 0114+650 has a modest eccentricity of 0.2. In addition, the high coherency of the superorbital modulations seems difficult to account for with oscillations of the primary star unless there is some way to keep strict phase stability. In principle, the presence of a third object in the systems might drive superorbital modulation. The modulation from a third body would also naturally account for the coherency of the superorbital modulation. How- ever, the apparent correlation between superorbital and orbital periods would, if confirmed, place stringent constraints on how such multi-star systems might be formed. In addition, typically such triple body models for X-ray sources involve hierarchical systems with a distant third object (e.g. Mazeh & Shaham 1979).",
"pages": [
9,
10
]
},
{
"title": "7. CONCLUSION",
"content": "Observations with the Swift BAT have shown the presence of superorbital periods in three additional sgHMXBs for a total of five definite such systems. The superorbital modulations have a variety of morphologies, ranging from approximately sinusoidal to multi-peaked profiles. However, superorbital modulation is not a ubiquitous property of sgHMXBs. With this limited set of data, a possible dependence of superorbital period on orbital period is suggested. The mechanism(s) driving such superorbital modulation remain unclear. However, possible models based on oscillations in the primary star driven by non-synchronous rotation, and three-body systems deserve further investigation. Continued monitoring of sgHMXBs in hard X-rays both with additional Swift BAT data and also potential new missions with high-energy X-ray sensitivity such as the LOFT WFM may reveal additional sources with superorbital periodicities. We thank an anonymous referee for useful comments. This paper used Swift /BAT transient monitor results provided by the Swift /BAT team. The Swift/BAT transient monitor and H. A. K. are supported by NASA under Swift Guest Observer grants NNX09AU85G, NNX12AD32G, NNX12AE57G and NNX13AC75G. MNRAS, 413, 1600 Note . - The superorbital period for the system below the line is a candidate and not a definite detection. The references for system parameters are given in the individual sections on each source. The orbital and superorbital periods and their errors are derived from the BAT light curves. For some systems additional determinations of periods may be available from other work, as given in the individual source sections.",
"pages": [
10,
11,
12
]
}
]
2013ApJ...778...51K
https://arxiv.org/pdf/1310.0456.pdf
<document>
<section_header_level_1><location><page_1><loc_10><loc_85><loc_90><loc_87></location>INVESTIGATING THE PRESENCE OF 500 µ M SUBMILLIMETER EXCESS EMISSION IN LOCAL STAR FORMING GALAXIES</section_header_level_1>
<text><location><page_1><loc_10><loc_80><loc_90><loc_84></location>Allison Kirkpatrick 1 , Daniela Calzetti 1 , Maud Galametz 2 , Rob Kennicutt, Jr. 2 , Daniel Dale 3 , Gonzalo Aniano 4 , Karin Sandstrom 5 , Lee Armus 6 , Alison Crocker 7 , Joannah Hinz 8 , Leslie Hunt 9 , Jin Koda 10 , Fabian Walter 5</text>
<text><location><page_1><loc_40><loc_79><loc_60><loc_80></location>Draft version September 24, 2018</text>
<section_header_level_1><location><page_1><loc_45><loc_76><loc_55><loc_78></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_55><loc_86><loc_76></location>Submillimeter excess emission has been reported at 500 µ m in a handful of local galaxies, and previous studies suggest that it could be correlated with metal abundance. We investigate the presence of an excess submillimeter emission at 500 µ m for a sample of 20 galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH) that span a range of morphologies and metallicities (12 + log(O/H) = 7 . 8 -8 . 7). We probe the far-infrared (IR) emission using images from the Spitzer Space Telescope and Herschel Space Observatory in the wavelength range 24 -500 µ m. We model the far-IR peak of the dust emission with a two-temperature modified blackbody and measure excess of the 500 µ m photometry relative to that predicted by our model. We compare the submillimeter excess, where present, with global galaxy metallicity and, where available, resolved metallicity measurements. We do not find any correlation between the 500 µ m excess and metallicity. A few individual sources do show excess (10-20%) at 500 µ m; conversely, for other sources, the model overpredicts the measured 500 µ m flux density by as much as 20%, creating a 500 µ m 'deficit'. None of our sources has an excess larger than the calculated 1 σ uncertainty, leading us to conclude that there is no substantial excess at submillimeter wavelengths at or shorter than 500 µ m in our sample. Our results differ from previous studies detecting 500 µ m excess in KINGFISH galaxies largely due to new, improved photometry used in this study.</text>
<section_header_level_1><location><page_1><loc_22><loc_51><loc_35><loc_52></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_37><loc_48><loc_50></location>Dust in the interstellar medium (ISM) is formed by grain growth in both the diffuse ISM and the ejecta of dying stars, such as red giant winds, planetary nebula, and supernovae (Draine 2009). Once formed, dust absorbs UV and optical light and reemits this radiation in the infrared. UV radiation is dominated by photons from young O and B stars, so the dust mass and infrared (IR) radiation can provide important constraints on the current star formation rates and the star formation history of a galaxy.</text>
<text><location><page_1><loc_8><loc_31><loc_48><loc_37></location>Space-based telescopes such as the Spitzer Space Telescope, the InfraRed Astronomical Satellite, and the Infrared Space Observatory have provided insights on the dust emission from mid-IR wavelengths out to ∼ 200 µ m. However, the majority, by mass, of the dust is cold</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_26><loc_48><loc_29></location>1 Department of Astronomy, University of Massachusetts, Amherst, MA 01002, USA, [email protected]</list_item>
<list_item><location><page_1><loc_10><loc_24><loc_48><loc_26></location>2 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK</list_item>
<list_item><location><page_1><loc_10><loc_22><loc_48><loc_24></location>3 Department of Physics & Astronomy, University of Wyoming, Laramie, WY 82071, USA</list_item>
<list_item><location><page_1><loc_10><loc_20><loc_48><loc_22></location>4 Institut d'Astrophysique Spatiale, Universit'e of Paris-Sud, 91405 Orsay, France</list_item>
<list_item><location><page_1><loc_10><loc_18><loc_48><loc_20></location>5 Max-Planck Institut f ' 'ur Astronomie, K ' 'onigstuhl 17, D69117, Heidelberg, Germany</list_item>
<list_item><location><page_1><loc_10><loc_16><loc_48><loc_18></location>6 Spitzer Science Center, California Institute of Technology, MC 314-6, Pasadena, CA 91125, USA</list_item>
<list_item><location><page_1><loc_10><loc_14><loc_48><loc_16></location>7 Ritter Astrophysical Observatory, University of Toledo, Toledo, OH 43606, USA</list_item>
<list_item><location><page_1><loc_10><loc_11><loc_48><loc_14></location>8 MMT Observatory, University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA</list_item>
<list_item><location><page_1><loc_10><loc_9><loc_48><loc_12></location>9 INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy</list_item>
<list_item><location><page_1><loc_10><loc_7><loc_48><loc_9></location>10 Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA</list_item>
</unordered_list>
<text><location><page_1><loc_52><loc_39><loc_92><loc_52></location>( T /lessorsimilar 25 K, Dunne & Eales 2001) and emits at far-IR and submillimeter wavelengths, where the emission spectrum is dominated by large grains in thermal equilibrium. Ground-based observations of these wavelengths are limited to a few atmospheric windows, and until recently, space-based observatories lacked coverage of the far-IR beyond ∼ 200 µ m. Now, with the advent of the Herschel Space Observatory, the peak and long wavelength tail of the dust spectral energy distribution (SED) is being observed at unprecedented angular resolution.</text>
<text><location><page_1><loc_52><loc_10><loc_92><loc_39></location>With submillimeter observations, the dust mass and the dust to gas ratios can be more accurately estimated. Dust formation models show that the dust to gas ratios should be tied to the chemical enrichment of galaxies, as measured by the metallicity (Dwek 1998; Edmunds 2001). Galametz et al. (2011) combine submillimeter data at 450 and 850 µ m with shorter wavelength IR observations ( /lessorsimilar 160 µ m) for a large sample of local star forming galaxies. They model the spectral energy distributions of each galaxy with and without the submillimeter data and find that for high metallicity galaxies, not including the submillimeter data can cause the dust mass to be overestimated by factors of 2-10, whereas for low metallicity galaxies (12+log(O/H) /lessorsimilar 8 . 0), the SEDs without the submillimeter data can underpredict the true dust mass by as much as a factor of three. Gordon et al. (2010) use Herschel photometry to model the dust emission from the Large Magellanic Cloud (LMC) and find that dust mass derived using just 100 µ m and 160 µ m photometry underestimate the dust mass derived when using 350 µ m and 500 µ m photometry as well by as much as 36%.</text>
<text><location><page_1><loc_52><loc_7><loc_92><loc_10></location>In measuring dust masses by modeling the far-IR and submillimeter SED, a variety of studies have sug-</text>
<text><location><page_2><loc_8><loc_73><loc_48><loc_92></location>gested the existence of excess emission at submillimeter wavelengths above what is predicted by fits to shorter wavelength data. Furthermore, this excess could preferentially affect lower metallicity and dwarf galaxies. Dale et al. (2012, hereafter D12) report significant excess emission at 500 µ m, above that predicted by fitting the observed SEDs with the Draine & Li (2007) models, for a sample of eight dwarf and irregular galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH, Kennicutt et al. 2011). Excess emission has also been reported in the Small Magellanic Cloud (SMC) and LMC, both of which have lower than solar metallicities (12+log(O/H) = 8 . 0 , 8 . 4, respectively Bot et al. 2010; Gordon et al. 2010).</text>
<text><location><page_2><loc_8><loc_61><loc_48><loc_73></location>On the other hand, excess emission is also seen at solar metallicities or larger. Paradis et al. (2012) model emission in the Galaxy and find excess emission (16 -20%) at 500 µ m in peripheral H ii regions. Recently, Galametz et al. (2013, in prep.) have detected excess at 870 µ m on a resolved and global scale for a sample of 11 KINGFISH galaxies. Galametz et al. (2011) finds a submillmeter excess at 870 µ m for 8 galaxies spanning a metallicity range of 12 + log(O/H) = 7 . 8 -9 . 0.</text>
<text><location><page_2><loc_8><loc_48><loc_48><loc_61></location>The presence of excess emission does not appear to be universal, however, as Draine et al. (2007) found only a marginal difference in deriving the dust masses for a set of SINGS galaxies with and without including submillimeter data from SCUBA 12 + log(O/H) ≈ 7 . 5 -8 . 7 . More recently, Aniano et al. (2012) apply the Draine & Li (2007) models to the IR SEDs (3 . 6 -500 µ m) of the local star forming galaxies NGC 0628 and NGC 6946 and do not detect any significant excess ( > 10%) at 500 µ m.</text>
<text><location><page_2><loc_8><loc_35><loc_48><loc_48></location>The excess emission seen at submillimeter wavelengths can be attributed to a cold dust component which is shielded from starlight (T < 10K; e.g., Galametz et al. 2009; O'Halloran et al. 2010). However, in the Milky Way, excess emission is seen at high latitudes, making it unlikely to be due to shielded cold dust (Reach et al. 1995). Studies of other galaxies have argued that a cold dust origin for the excess emission leads to unphysically high dust to gas ratios (Lisenfeld et al. 2002; Zhu et al. 2009; Galametz et al. 2010).</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_35></location>A competing explanation is that the spectral emissivity index, β , of the dust grains changes to lower values at longer wavelengths, leading to a flattening of the submillimeter spectrum, thus mimicking a cold dust component (Dupac et al. 2003; Augierre et al. 2003; Planck Collaboration 2011). Such a change in emissivity has been suggested in the Milky Way (Paradis et al. 2009). (Galametz et al. 2012) showed that modeling the far-IR /submillimeter emission with a modified blackbody with β = 1 . 5 can increase the dust masses up to 50% compared to when β = 2, possibly explaining the discrepancies between dust masses calculated with far-IR data alone and those calculated with farIR and submillimeter data. The emission from very small grains exhibits a frequency dependence with a spectral emissivity index of β = 1, and if a galaxy has a relative abundance of very small grains greater than the Milky Way, this can cause a flattening of the emissivity index at longer wavelengths (Lisenfeld et al. 2002; Zhu et al. 2009). Alternatively, the properties of amorphous solids could explain the change in emissivity</text>
<text><location><page_2><loc_52><loc_80><loc_92><loc_92></location>(Meny et al. 2007). Modeling the emission of amorphous solids accounts for the submillimeter excess in the LMC and SMC (Bot et al. 2010), although recent work suggests that much of the excess emission in the LMC is accounted for by fluctuations in the cosmic microwave background (Planck Collaboration 2011). Finally, an increase in the amount of magnetic material has also been proposed as a plausible explanation for the SMC submillimeter excess (Draine & Hensley 2012).</text>
<text><location><page_2><loc_52><loc_68><loc_92><loc_80></location>Achange in dust properties can also be linked to metallicity. Draine et al. (2007) showed that 12 + log(O/H) = 8 . 1 is a threshold metallicity for galaxies in the range 12 + log(O/H) ≈ 7 . 5 -8 . 7, above which the percentage of dust mass contained in PAH molecules drastically increases. If submillimeter excess emission is due to a change in the emissivity properties of the dust population, then there might be a correlation with abundances in this metallicity range.</text>
<text><location><page_2><loc_52><loc_48><loc_92><loc_68></location>In the present study, we seek to investigate the submillimeter excess at 500 µ m for a sample of KINGFISH galaxies. We define such excess as being emission above that predicted by a two-temperature modified blackbody model where the emissivity is not constrained, following the method outlined in Galametz et al. (2012). We have selected a sample that spans a range of metallicities, including many dwarf galaxies, in order to probe whether such excess correlates with metallicity, as has been found in some earlier studies (Galametz et al. 2009, 2011). The paper is laid out as follows: in Section 2, we describe our sample selection and modeling of the dust emission; in Section 3, we report on the excess emission and how our findings relate to the results of D12; and in Section 4, we present our conclusions.</text>
<section_header_level_1><location><page_2><loc_65><loc_45><loc_79><loc_46></location>2. DATA ANALYSIS</section_header_level_1>
<section_header_level_1><location><page_2><loc_62><loc_43><loc_82><loc_45></location>2.1. The KINGFISH Sample</section_header_level_1>
<text><location><page_2><loc_52><loc_27><loc_92><loc_43></location>The KINGFISH sample (Kennicutt et al. 2011) was selected to include a wide range of luminosities, morphologies, and metallicities in local galaxies. The sample overlaps with 57 of the galaxies observed as part of the Spitzer Infrared Nearby Galaxies Survey (SINGS, Kennicutt et al. 2003b), as well as incorporating NGC 2146, NGC 3077, M 101 (NGC 5457), and IC 342 for a total of 61 galaxies. The luminosity range spans four orders of magnitude, but all galaxies have L < 10 11 L /circledot . While some of the galaxies display a nucleus with LINER or Seyfert properties, no galaxy's global SED is dominated by an AGN.</text>
<text><location><page_2><loc_52><loc_7><loc_92><loc_27></location>We select a sample (7) of disk galaxies possessing a large angular size ( ∼ 30arcmin 2 ) and a known metallicity gradient with which we perform a resolved study of the excess emission and search for any correspondence with metallicity. We refer to this sample as the 'extended' galaxies. Since excess emission seems to be found in dwarf/irregular galaxies, we include the dwarf/irregular galaxies (9) in KINGFISH for which we have a signal-tonoise ratio (SNR) > 3 σ in all of the SPIRE bandpasses. The dwarf/irregulars are more compact objects than our normal disk galaxies, and in general, do not have a known metallicity gradients, so we measure the excess emission globally for these objects. The resolved nature of the normal disk galaxies might bias our comparison with the dwarf/irregular galaxies, so we complement our sample</text>
<text><location><page_3><loc_8><loc_81><loc_48><loc_92></location>(4) with normal disk galaxies that have small angular size which allows for global measurements of excess emission. These more compact, normal galaxies were selected to span a range of metallicity and have high SNRs at the SPIRE bandwidths. Our complete sample consists of 20 galaxies and is listed in Table 1. We also list in Table 1 dwarf/irregular galaxies that were rejected due to low SNRs.</text>
<section_header_level_1><location><page_3><loc_21><loc_79><loc_35><loc_80></location>2.2. Data Reduction</section_header_level_1>
<text><location><page_3><loc_8><loc_63><loc_48><loc_78></location>Data observations and reduction are discussed in detail in Engelbracht et al. (2010), Sandstrom et al. (2010) and Kennicutt et al. (2011). In the present study, we use images from the PACS and SPIRE instruments on the Herschel Space Observatory spanning a wavelength range of 70 -500 µ m and MIPS 24 µ m images from the Spitzer Space Telescope (Kennicutt et al. 2003b). We use PACS 70 and 160 µ m images instead of MIPS due to the better resolution provided by PACS. All galaxy maps are at least 1.5 times the diameter of the optical disk, allowing us to probe the cold dust emission beyond the optical disk.</text>
<text><location><page_3><loc_8><loc_35><loc_48><loc_63></location>The raw PACS and SPIRE images were processed from level 0 to 1 with Herschel Interactive Processing Environment (HIPE) v. 8. The PACS and SPIRE maps were then created using the IDL package Scanamorphos v. 17 (Roussel 2012). Scanamorphos is preferred to HIPE for its ability to better preserve low level flux density, reduce striping in area of high background, and correct brightness drifts caused by low level noise. The maps are converted from units of Jy beam -1 to MJy sr -1 by accounting for beam sizes of 469.1, 827.2, and 1779.6 arcsec 2 for the 250, 350, and 500 µ m maps, respectively. The design and performance of the SPIRE instrument is discussed in detail in Griffin et al. (2010). In the SPIRE images used in this study, the full width at half maximum (FWHM) of the beam profile has been modeled with a wavelength dependence, so that FWHM ∝ λ γ , where γ = 0 . 85. As part of the calibration process, a 'color-correction' has been applied to each beam so that the measured specific intensity I ν will be equal to the actual specific intensity I 0 when ν = ν 0 . The correction factors applied to these images assume a power-law spectrum with α = -1 . 9.</text>
<text><location><page_3><loc_8><loc_19><loc_48><loc_35></location>We compare our results to those of D12, so it is crucial to explicitly state that we are using different versions of the PACS and SPIRE images. In D12, the raw PACS and SPIRE images were processed from level 0 to 1 with HIPE v.5. The SPIRE data were then mosaicked using the mapper in HIPE. The images were converted to MJy sr -1 using beam sizes of 423, 751, and 1587 arcsec 2 at 250, 350, and 500 µ m, respectively, and the FWHM was not modeled with a wavelength dependence; furthermore, the color-correction was not included in the beam size, but was applied a posteriori.The PACS data were mapped using Scanamorphos v. 12.5.</text>
<text><location><page_3><loc_8><loc_7><loc_48><loc_19></location>The main difference between the version of KINGFISH images that we use and the previous version used by D12 is that the SPIRE 250 and 350 µ m images contain slightly less flux density ( ∼ 2%) while the 500 µ m image is less luminous by ∼ 10%. The point response function area is also slightly larger ( ∼ 3%) than for the v. 2 images. The more recent HIPE v. 11 pipeline has revised the SPIRE beam sizes in the direction of yielding lower fluxes for extended sources by ∼ 6%, 6%, and 8% at 250,</text>
<text><location><page_3><loc_52><loc_89><loc_92><loc_92></location>350, and 500 µ m, respectively. This is in the direction of reinforcing the results that are presented in this paper.</text>
<section_header_level_1><location><page_3><loc_52><loc_86><loc_92><loc_88></location>2.3. Background subtraction and Convolution of Images</section_header_level_1>
<text><location><page_3><loc_52><loc_71><loc_92><loc_86></location>The background subtraction is described in detail in Aniano et al. (2012), and we will briefly summarize here. 'Non-background' regions are determined in all cameras (IRAC, MIPS, PACS, and SPIRE) by those pixels which have a SNR > 2. Masks of the non-background regions are made, and then the masked images from all cameras are combined in order to unambiguously determine which regions are truly background regions. The signals in the background regions are then averaged, smoothed, and subtracted according to an algorithm outlined in Aniano et al. (2012).</text>
<text><location><page_3><loc_52><loc_58><loc_92><loc_71></location>Since we compare our results with those of D12, it is worthwhile to note that a different procedure for background subtraction is followed in that study. The authors use a set of sky apertures to measure the local sky around each galaxy while avoiding any contamination from galaxy emission. The mean sky level per pixel is computed from these sky apertures, scaled to the number of pixels in the galaxy photometry aperture, and the result is subtracted from the overall galaxy photometry aperture counts.</text>
<text><location><page_3><loc_52><loc_43><loc_92><loc_58></location>In order to consistently measure photometry for each galaxy, we used images that had been convolved to the resolution of the SPIRE 500 µ m bandpass. The convolution was done with publicly available kernels from Aniano et al. (2011) which transform the point source functions (PSFs) of individual images to the PSF of the SPIRE instrument at 500 µ m (FWHM of 38'). The convolution kernels and methodology are described in detail in Aniano et al. (2011, 2012). After the convolution to a common PSF, the images for each galaxy are resampled to a standard grid, where each pixel is ∼ 14'.</text>
<section_header_level_1><location><page_3><loc_60><loc_41><loc_84><loc_42></location>2.4. Photometry and SED fitting</section_header_level_1>
<text><location><page_3><loc_52><loc_23><loc_92><loc_40></location>For the extended galaxies, we measure photometry in apertures with diameters of 42', chosen to be slightly larger than the beam size of the SPIRE 500 µ m bandpass, from the center of the galaxy to the outskirts. We reject regions of galaxies without at least 3 σ flux density measurements at every bandpass from 24 -500 µ m. For the galaxies which are compact at the 500 µ m resolution, including the dwarf/irregulars, we measure the photometry globally in apertures with diameters ranging from 42' to 1' 52', which is the angular area covered by the galaxies with a signal to noise ratio > 3 σ . The diameter and the physical scales of each photometric aperture are listed in Table 1.</text>
<text><location><page_3><loc_52><loc_13><loc_92><loc_23></location>The dwarf/irregular galaxies DDO 053, DDO 154, and DDO 165 have a 3 σ flux density measurement in only one of the far-IR bandpasses; Ho I, Ho II, and M 81 DwB have measurements in three of the six bandpasses. We do not model the far-IR emission for these galaxies, but we do plot the photometry and 3 σ upper limits in Figure 1.</text>
<text><location><page_3><loc_52><loc_7><loc_92><loc_13></location>The physically-based DL07 models have been used to derive dust properties at global and local scales (e.g., Draine et al. 2007; Aniano et al. 2012). The DL07 models use the assumption of a diffuse ISM component to describe the shape of the interstellar radiation field, and</text>
<table>
<location><page_4><loc_12><loc_55><loc_88><loc_88></location>
<caption>TABLE 1 Basic properties of our sample</caption>
</table>
<text><location><page_4><loc_12><loc_51><loc_88><loc_54></location>We do not calculate an excess for Ho I, Ho II, DDO 053, DDO 154, DDO 165, and M81 DwB since we are not able to measure flux densities at the 3 σ level covering the full wavelength range 24 -500 µ m. The metallicity range for which we can derive excess measurements is then 12 + log(O/H) = 7 . 8 -8 . 7.</text>
<unordered_list>
<list_item><location><page_4><loc_12><loc_50><loc_54><loc_51></location>a Morphology as listed in the NASA Extragalactic Database (NED).</list_item>
<list_item><location><page_4><loc_12><loc_48><loc_88><loc_50></location>b We indicate how we have classified the galaxies in this study. E = extended, C = compact, and D = dwarf/irregular/Magellanic.</list_item>
<list_item><location><page_4><loc_12><loc_47><loc_57><loc_48></location>c Distances are taken from Kennicutt et al. (2011) and references therein.</list_item>
<list_item><location><page_4><loc_12><loc_41><loc_88><loc_47></location>d Characteristic metallicity for most galaxies is taken from Moustakas et al. (2010) where the metallicity is calculated using the method of Pilyugin & Thuan (2005). For the extended galaxies, we list the metallicity gradients in the brackets, where ρ is the radius in arcminutes. The metal abundance of NGC 1377 is calculated using the luminosity-metallicity relationship (Kennicutt et al. 2011), the abundance for NGC 3077 is empirically calculated in Storchi-Bergmann et al. (1994), and the metallcity for M 101 is derived from observations in Kennicutt et al. (2003a) and Bresolin et al. (2004).</list_item>
<list_item><location><page_4><loc_12><loc_40><loc_87><loc_41></location>e The ratio of the major axis to minor axis, which we use to correct for inclination effects when calculating the metallicity.</list_item>
<list_item><location><page_4><loc_12><loc_39><loc_45><loc_40></location>f The physical region size of the photometry aperture.</list_item>
<list_item><location><page_4><loc_12><loc_38><loc_69><loc_39></location>g The diameter (in arcminutes and arcseconds) of the circular apertures used for photometry.</list_item>
<list_item><location><page_4><loc_12><loc_37><loc_54><loc_38></location>h The number of circular apertures used to calculate the photometry.</list_item>
</unordered_list>
<text><location><page_4><loc_8><loc_21><loc_48><loc_36></location>use distribution function to represent the distribution of starlight intensities, which are then scaled to the SED being modeled. In addition, the submm slope of the DL07 models tends to resemble that of a modified blackbody with an emissivity of β = 2, which could prevent us from testing for flattening of the submm slope or variations in the emissivity index. We choose to model the farIR SEDs with a simple modified blackbody equation to test various assumptions on the emissivity index and will compare our results to the D12 study to investigate how the choice of model affects the observed excess emission.</text>
<text><location><page_4><loc_8><loc_17><loc_48><loc_21></location>We model the far-IR SEDs of each region within each galaxy using a two temperature modified blackbody of the form</text>
<formula><location><page_4><loc_11><loc_15><loc_48><loc_17></location>F ν = a w × B ν ( T w ) × ν β w + a c × B ν ( T c ) × ν β c (1)</formula>
<text><location><page_4><loc_8><loc_7><loc_48><loc_15></location>where B ν is the Planck function. The temperatures of the warm and cold dust components are T w and T c , the scalings for each component are a w and a c , and β w and β c are the emissivity indexes. Only the scalings, T c , and β c are allowed to be free parameters, due to the limited number of data points being fit. The warm dust com-</text>
<text><location><page_4><loc_52><loc_17><loc_92><loc_36></location>nt is necessary to account for some of the emission at 70 µ m and 100 µ m so as not to bias the cold dust temperature or emissivity. When only one temperature is used, the peak of the modified blackbody is biased towards shorter wavelengths, leading to warmer temperatures, which is then compensated at longer wavelengths by a β c shallower than otherwise measured. We include the 24 µ m data point in the fit to better constrain the warm dust modified blackbody, but the fitted warm dust parameters should not be interpreted in a physical manner, since this portion of the SED also likely contains contribution from stochastically heated dust. We list the fraction of 100 µ m flux density due to the warm dust component in Table 2.</text>
<text><location><page_4><loc_52><loc_7><loc_92><loc_17></location>The effective dust emissivity we derive comprises the intrinsic spectral emissivity properties of dust and the variation of the dust temperature within a resolution element that could lead to a shallower β c than that obtained in isothermal cases (e.g., Shetty et al. 2009). We nevertheless allow both the cold temperature and cold emissivity, β c , to vary simultaneously, though the two parameters are degenerate. We refer to Galametz et al.</text>
<figure>
<location><page_5><loc_19><loc_39><loc_83><loc_90></location>
<caption>Fig. 1.Our photometry for the dwarfs/irregular galaxies in the KINGFISH sample is plotted as the black circles. The photometry listed in D12 is over plotted as the red squares. The two sets of photometry were extracted from slightly different calibrations of the PACS and SPIRE images, and our photometry was taken after the images had been convolved to the 500 µ m resolution. When we fit the D12 photometry with our model, we are able to reproduce the excesses reported in that work.</caption>
</figure>
<text><location><page_5><loc_8><loc_28><loc_48><loc_32></location>(2012) and Kirkpatrick et al. (2013b, in prep.), and references therein, for a further discussion of degeneracies on the individual temperatures and emissivities.</text>
<text><location><page_5><loc_8><loc_14><loc_48><loc_28></location>We fit the photometry from 24 -350 µ m. The 500 µ m data are not included to allow comparison with our model predictions at the same wavelength. We use a Monte Carlo technique to determine the parameters and errors. We randomly sample each data point within its errors 1000 times and determine the parameters of the two temperature modified blackbody via χ 2 minimization. The final parameters and associated errors are the medians and standard deviations of our Monte Carlo simulation. An example of the SED fitting is shown in Figure 2.</text>
<text><location><page_5><loc_8><loc_8><loc_48><loc_14></location>When fitting, we allow the cold dust temperature, T c , to vary between 0 and 50 K and β c to vary between 0 and 5. We experimented with allowing T w to vary, but the derived temperature was approximately constant in the range 55 -60K, and simultaneously varying T w did not</text>
<text><location><page_5><loc_52><loc_10><loc_92><loc_32></location>change the derived cold dust temperature or emissivity values. Since the warm dust component peaks in an area of the SED that is sparsely sampled, we opt to hold both T w and β w fixed. We hold the emissivity of the warm dust component fixed to a value of two and T w fixed to 60K. Fixing β w = 2 is a good approximation of the opacity of graphite/silicate dust models (Li & Draine 2001). Galametz et al. (2012) find that changing β w to 1.5 decreases the cold dust temperatures by less than 1.6%, and Tabatabaei et al. (2011) test the two temperature modified blackbody approach on M33, holding β w fixed to 1.0, 1.5, and 2.0, and conclude that β w = 2 most accurately reproduces the observed flux densities. We test a fixed β c in Section 3.3. As β w is always fixed to a value of two in all of our subsequent analysis, in the remainder of this paper, we refer to β c simply as β .</text>
<figure>
<location><page_6><loc_12><loc_75><loc_44><loc_92></location>
<caption>Fig. 2.The SED of NGC 337 is fitted with a two-temperature modified blackbody. The warm temperature component is shown in green, the cold temperature component in orange, and the composite in blue. The excess emission is calculated relative to the composite fit at 500 µ m. The 24 µ m photometric data is from Spitzer MIPS, while the other far-IR/submillimeter photometric data are from Herschel PACS and SPIRE.</caption>
</figure>
<section_header_level_1><location><page_6><loc_19><loc_64><loc_37><loc_66></location>3.1. PACS-SPIRE colors</section_header_level_1>
<text><location><page_6><loc_8><loc_37><loc_48><loc_64></location>The color S 100 /S 160 , where S 100 is the flux density in the 100 µ m bandpass, is commonly used as a proxy for temperature, since it usually spans the peak of the blackbody emission, while S 350 /S 500 depends sensitively on the slope of the Rayleigh-Jeans tail, and so is a good proxy for β (with the same caveats given earlier about the mixing of dust with different temperatures along the line of sight). We plot these two colors in the left panel of Figure 3 for each of the regions in our extended galaxies. We calculate the positions of theoretical modified blackbodies and overplot as a grid. When calculating the theoretical tracks, we use a two temperature modified blackbody (Equation 1); we set T w = 60 K, β w = 2, and we scale the warm dust component to peak at a flux density 10% of the cold dust component peak flux density, which is the average scaling we see in our fitted SEDs at the SPIRE wavelengths. We set β = 1 , 1 . 5 , and 2, and we set T c to discrete temperature values between 15 and 27 K. Lines of constant β and T c are marked on the figure.</text>
<text><location><page_6><loc_8><loc_16><loc_48><loc_37></location>The colors of our galaxies tend to cluster around the β = 2 , T c = 20K lines. At higher temperatures, galaxy colors start to sparsely occupy the same part of color space as the β = 1 model. No galaxies exhibit colors indicating a low temperature ( T c < 21 K) and a shallow emissivity, which could hint at physical link between the two parameters (see Yang & Phillips 2007; Ysard et al. 2012; Kirkpatrick et al. 2013b, in prep., for a discussion of the physical nature of the T c -β relationship). Although our galaxy colors tend to lie near the β = 2 model line, we observe a large scatter. This illustrates a significant difference of physical conditions from one object to another but also within our objects. Letting both parameters vary in our multiple blackbody approach can be a way to probe these variations, in spite of the degeneracies.</text>
<text><location><page_6><loc_8><loc_7><loc_48><loc_16></location>In the right panel of Figure 3, we plot the same colors, but this time we use the predicted 500 µ m flux density, which has been calculated by fitting Equation 1 to the 24 -350 µ m flux densities. Substituting the predicted 500 µ m flux density has two interesting effects. First, it increases the amount of scatter visible in the colors. For example, in both NGC 5055 and NGC 4321, which dis-</text>
<text><location><page_6><loc_52><loc_68><loc_92><loc_92></location>y the largest increase in scatter, the mean S 350 /S 500 observed ratio and predicted ratio is approximately the same ( ∼ 2 . 7). For NGC 5055, the standard deviation increases from 0.16 to 0.24, and for NGC 4321 it increases from 0.11 to 0.23. This increase is indicative of the uncertainties inherent in fitting modified blackbody models without enough data to adequately constrain the slope of the Rayleigh-Jeans tail. The second effect we see is that now the galaxy colors, particularly for M 101, occupy a region of the color space to the right of the β = 2 model line. The predicted S 350 /S 500 ratio is larger than the observed S 350 /S 500 ratio. Again, this illustrates the importance of using data above 350 µ m to constrain the submillimeter SED. Without including the 500 µ m data point in the modeling of the far-IR/submillimeter SED, the predicted slope will be steeper than the true value; in other words, the model underpredicts the measured 500 µ m flux density.</text>
<formula><location><page_6><loc_60><loc_65><loc_84><loc_67></location>3.2. 500 µ m excess when β varies</formula>
<text><location><page_6><loc_53><loc_63><loc_86><loc_65></location>We calculate the excess emission at 500 µ m as</text>
<formula><location><page_6><loc_59><loc_59><loc_92><loc_63></location>excess = S ν (500 µ m) -F ν (500 µ m) S ν (500 µ m) (2)</formula>
<text><location><page_6><loc_52><loc_40><loc_92><loc_59></location>where F ν (500 µ m) is the predicted flux density of the two-temperature modified blackbody and S ν is the measured flux density. We plot the excess emission as a function of metallicity in Figure 4. We correct the radius of each photometric region for the inclination of the galaxy, and then convert the radius to metallicity using the gradients listed in Moustakas et al. (2010) which were calculated according to the Pilyugin & Thuan (2005) relationship (see Table 1). For M 101, which is not included in Moustakas et al. (2010), we use a metallicity gradient calculated directly from electron temperature measurements in H ii regions (Kennicutt et al. 2003a; Bresolin et al. 2004), which creates a slight offset between M 101 and the rest of our sample in metallicity.</text>
<text><location><page_6><loc_52><loc_15><loc_92><loc_40></location>Figure 4 shows that there is no systematic dependence of the excess emission on metallicity for the sample as a whole, nor is there any trend within the individual galaxies that have a metallicity gradient. None of the galaxies display an excess larger than 25%, and for many galaxies, the modeling actually overpredicts the 500 µ m emission by this amount, creating a 500 µ m deficit. Furthermore, the spread in excess is largely accounted for by the uncertainty attached to each data point (the typical uncertainty for each region in the extended galaxies is shown in the bottom right of Figure 4). For some of the dwarf/irregulars, the uncertainties are rather large (particularly NGC 1377, NGC 2915, NGC 3773, NGC 5408, and IC 2574). The uncertainties are correlated with the SNR ratios of the SPIRE data since noisier photometry exacerbates the degeneracy between temperature and β (Juvela & Ysard 2012). The dwarf/irregulars with the lowest SNRs have the largest uncertainty on the derived β .</text>
<text><location><page_6><loc_52><loc_7><loc_92><loc_15></location>We find that no extended galaxy has an excess emission greater than 10%, in agreement with the results of Gordon et al. (2010) for a resolved study of the LMC using a modified blackbody model, and with Aniano et al. (2013, in prep.), in which the authors create dust maps for the full sample of KINGFISH galaxies using the DL07</text>
<figure>
<location><page_7><loc_18><loc_63><loc_84><loc_90></location>
<caption>Fig. 3.LeftWe plot the far-IR colors of each region in our extended galaxies. We calculate the theoretical colors of a two-temperature modified blackbody for different temperatures and different values any regions with low temperatures and low emissivity values, hinting at a physical link between the two parameters. The typical errors are shown in the lower righthand corner. RightWe replace the observed 500 µ m flux densities by those predicted from our two-temperature modified blackbody fitting. Using the predicted the 500 µ m flux density increases the scatter in color space for some galaxies, and increases the S 350 /S 500 ratios, illustrating the importance of including submillimeter data when modeling the far-IR dust emission.</caption>
</figure>
<text><location><page_7><loc_8><loc_40><loc_48><loc_54></location>models. We show the distribution of excess emission in the right panel of Figure 4 for all regions in the extended galaxies, as well as the galaxies that were fit globally. We find that the resolved elements of the extended galaxies do not preferentially show an excess or a deficit. The mean excess of our sample is ∼ 0 . 02. This confirms that the majority of regions display a low excess or deficit ( < 10%). Given the large uncertainties (the dispersion is ∼ 0 . 1), this excess is thus marginal. In practice, we do not find excess 500 µ m emission greater than the scatter in the data.</text>
<section_header_level_1><location><page_7><loc_15><loc_38><loc_41><loc_39></location>3.3. 500 µ m excess dependence on β</section_header_level_1>
<text><location><page_7><loc_8><loc_12><loc_48><loc_37></location>The derived emissivity contains information about the slope of the Rayleigh-Jeans tail, and it is possible that β is correlated with the measured excess emission (Galametz et al. 2012) We test this hypothesis for our sample in Figure 5. For simplicity, we average together all of the derived excesses and β values for each galaxy as we do not see any trends for individual galaxies. There is no apparent correlation between the excess emission and the value of β when β is allowed to be a free parameter. However, since β and T c exhibit a degeneracy which is possibly enhanced by the particular fitting method used (e.g., Juvela et al. 2013), a common technique for blackbody fitting is to hold β fixed (e.g., Yang & Phillips 2007; Xilouris et al. 2012). It is possible that holding β fixed will cause us to measure an excess emission, since the slope of the Rayleigh-Jeans tail changes from region to region within each galaxy (see Figure 3). We test this hypothesis by refitting all of our photometry holding β fixed to the values of 1, 1.5, and 2.</text>
<text><location><page_7><loc_8><loc_7><loc_48><loc_12></location>The 500 µ m excesses for each value of β are plotted in Figure 6. An emissivity of one generally produces very bad fits to the SEDs with high χ 2 values for several galaxies, reflected in the error bars. The slope of</text>
<text><location><page_7><loc_52><loc_28><loc_92><loc_54></location>the Rayleigh-Jeans tail is too shallow and overestimates the 500 µ m emission, as can be seen in the top panel of Figure 6. Setting β = 2 provides the best fits to the SEDs when fixing the emissivity as can be seen by the small uncertainties in the bottom panel of Figure 6. The excess emission is now ∼ 30% for galaxies which had only a 10% excess when β was allowed to vary (Figure 4). The result is consistent with R'emy-Ruyer et al. (2013), who also calculate the excess 500 µ m emission keeping β fixed at a value of 2. Holding β fixed does increase the amount of excess emission measured. It also increases the so-called emission 'deficit', meaning we now overpredict the 500 µ m emission by ∼ 20 -30%; the excess emission for each galaxy is listed in Table 2. We stress that the amount of excess emission is affected by the particular fitting method used. In our study, where we achieve good reduced χ 2 fits when holding β fixed to a value of two, and when letting β be a free parameter, we find excess values differing by as much as 20% depending on the fitting method.</text>
<text><location><page_7><loc_52><loc_9><loc_92><loc_28></location>There is a linear correlation between the excess emission and the metallicity. This is most strongly exhibited by M 101, which has a Pearsons correlation coefficient of ρ = -0 . 86 for all three values of β . NGC 4321 also has a strong trend between excess emission and metallicity. With the exception of NGC 5055, the other extended galaxies have fewer points, so it is difficult to see a trend. The dwarf galaxies also display a high correlation with ρ in the range 0 . 54 -0 . 61 depending on the value of β . On the other hand, NGC 4321 shows no correlation between metallicity and excess for any value of β . When all of the galaxies are considered together, there is a strong anti-correlation ( ρ = -0 . 70) for β = 1 and only a low anti-correlation ( ρ = -0 . 30) for β = 2.</text>
<text><location><page_7><loc_53><loc_8><loc_92><loc_9></location>IC 2574, NGC 2915, and NGC 5408 have a marked ex-</text>
<figure>
<location><page_8><loc_16><loc_63><loc_86><loc_91></location>
<caption>Fig. 4.Excess emission as a function of metallicity. We plot the excess for each individual region within an extended galaxy (colored crosses). The typical uncertainty is shown in the lower right corner. The dwarf/irregulars and compact galaxies are plotted as the black symbols. The galaxies with large uncertainties have low SPIRE SNRs. There is no trend in excess emission with decreasing metallicity for the extended galaxies or dwarf/irregular galaxies. On the right, we plot the distribution of the 500 µ m excess for all regions in the extended galaxies, as well as the galaxies that were fit globally; we have scaled the distribution to have a peak value of 1. The mean excess is ∼ 2%. We indicate the mean with the dotted line. The spike in excess above 2% is largely due to NGC 5457 (M 101).</caption>
</figure>
<figure>
<location><page_8><loc_10><loc_35><loc_48><loc_55></location>
<caption>Fig. 5.The excess emission as a function of the derived emissivity. No obvious trend is evident, so allowing β to vary does not produce any dependence between the derived β and measured excess. The large uncertainties on the emissivities are caused by an increased degeneracy between temperature and β with low SNRs.</caption>
</figure>
<text><location><page_8><loc_8><loc_12><loc_48><loc_27></location>cess when β = 2. However, for IC 2574 and NGC 2915, there is no substantial excess when β = 1 , 1 . 5 or when β is allowed to vary. From this, we conclude that there is a flattening of the SED in these two galaxies that a steeper value of β is unable to account for. Because β is an effective emissivity, and contains information about the intrinsic properties of the dust grains as well as the heating of the dust within a resolution element, we cannot conclusively determine whether this flattening is due to changing properties of the dust grains in low metallicity galaxies.</text>
<text><location><page_8><loc_8><loc_7><loc_48><loc_12></location>For most galaxies, including the individual regions in the extended galaxies, the use of β = 2 as opposed to β = 1 produces much lower reduced χ 2 values during the Monte Carlo fitting. We plot the distribution of reduced</text>
<text><location><page_8><loc_52><loc_38><loc_92><loc_56></location>χ 2 values over 1000 Monte Carlo fits for NGC 1377 in the top panel of Figure 7. The mean reduced χ 2 is 2.3 when β = 2 but is 10.6 when β = 1. We also show the distribution of reduced χ 2 values for NGC 2915, for which the choice of β makes little difference in the goodness of the fits. When β = 2, the mean reduced χ 2 = 1 . 1, and when β = 1, the mean reduced χ 2 = 1 . 3. This effect is also seen for NGC 3773, NGC 5408, and IC 2574, all of which exhibit no decrease in the uncertainty on the excess depending on the value of β . These are the four galaxies with the lowest SNRs at 250 µ m and 350 µ m, illustrating the difficulty of using modified blackbody fitting with low signal-to-noise photometry.</text>
<section_header_level_1><location><page_8><loc_55><loc_35><loc_89><loc_36></location>3.4. Exploring the Submillimeter Dust Emission</section_header_level_1>
<text><location><page_8><loc_52><loc_7><loc_92><loc_35></location>When β is a free parameter, we do not see any systematic excess trend with metallicity, nor do we measure strong excess emission. However, when β = 2, we see a weak dependence on metallicity, and we do detect some excess for individual galaxies (Table 2). One explanation for excess submillimeter emission is temperature mixing within a resolution element (e.g., Shetty et al. 2009). The emissivity we measure is comprised both of the intrinsic emissivity of the dust and the range of temperatures of the dust components in the resolution element. This range of temperatures can produce a shallower effective β than would be measured in the ideal case of only one temperature component. We can test this explanation by comparing the excess emission with both the distance of our galaxies and the physical region size subtended by the photometry aperture (see Table 1). Both a larger region size and a larger distance will correspond to more dust emission within the resolution element, and hence more temperature mixing. We find no trend between physical size and excess emission, demonstrating that the particular photometry aperture used does not</text>
<figure>
<location><page_9><loc_11><loc_50><loc_48><loc_91></location>
<caption>Fig. 6.We explore the effect of holding the emissivity constant on the measured excess emission. We set β = 1 (top panel), β = 1 . 5 (middle panel), and β = 2 (bottom panel). The typical uncertainty for the regions in the extended galaxies is shown in the upper right corner of each panel. When β = 2, we have the smallest uncertainties and best χ 2 fits, whereas β = 1 results in very poor χ 2 values.</caption>
</figure>
<text><location><page_9><loc_8><loc_39><loc_27><loc_40></location>affect the resulting excess.</text>
<text><location><page_9><loc_8><loc_9><loc_48><loc_39></location>In Figure 8, we plot the excess emission calculated when the emissivity was allowed to vary (see Figure 4) and when β = 2 (see Figure 6) as a function of distance. There is a weak trend between the excess emission and the distance when β = 2. When the emissivity is held fixed, galaxies that are within 10 Mpc have on average a higher excess emission, whereas the 500 µ m emission has in general been overpredicted for the galaxies further than 10 Mpc. This does not appear to be an effect of galaxy type, since the nearby galaxies showing excess are both extended and dwarfs. The trend seen when β = 2 is the opposite of what is expected. Galaxies that are further should have more temperature mixing within the resolution element producing a shallower farIR slope, which would cause an excess when compared to the emission predicted with β = 2. With the exceptions of NGC 0925 and NGC 4559, this trend is driven by the dwarf galaxies. Since we see no correlation between excess emission and physical region size, or excess emission and distance when β is a free parameter, we conclude that the excess emission is not due to temperature variations within the resolution element.</text>
<text><location><page_9><loc_8><loc_7><loc_48><loc_9></location>NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574 have the highest excesses when β = 2. Mul-</text>
<figure>
<location><page_9><loc_55><loc_72><loc_91><loc_90></location>
</figure>
<figure>
<location><page_9><loc_55><loc_51><loc_91><loc_69></location>
<caption>Fig. 7.The distribution of reduced χ 2 values from each Monte Carlo repitiion when holding the emissivity fixed to a value of one (red) and two (black). For NGC 1377 (top), the choice of β makes a large difference in the goodness of the fits, but for NGC 2915 (bottom), it does not, though it does change the amount of excess emission calculated.</caption>
</figure>
<text><location><page_9><loc_52><loc_7><loc_92><loc_43></location>iple studies advocate using a third temperature component (T ∼ 10K) instead of a lower emissivity to account for the submillimeter excess (Galametz et al. 2011; Galliano et al. 2003, 2005; Marleau et al. 2006). We attempted to fit these four galaxies with a three temperature modified blackbody. We have only six photometric data points in each galaxy to fit three modified blackbodies to, so we hold several parameters constant to avoid degeneracies. We set T w = 60K and β w = 2, as described in Section2.4. We hold the emissivities of the cold components fixed to a commonly applied value of 1.8, though we note that using β = 2 caused our derived temperatures to change by only ± 1 K. We hold the scaling of the warm dust component fixed to what we derived when fitting only two modified blackbodies. Finally, we restrict the temperature range of one of the cold components to be T ∈ [20 , 50] K and the other to be T ∈ [0 , 20] K. We find that if we do not restrict the temperature ranges, then both cold components will have the same derived temperature. We are able to achieve good fits (reduced χ 2 < 1) for NGC 5408 and NGC 5398 but not for NGC 2915 or IC 2574. For NGC 5408, our three dust temperatures are 60 K, 29 ± 3K, and 13 ± 7K; for NGC 5398, they are 60 K, 22 ± 1K, and 13 ± 5K. Also, it is important to note that not only are the uncertainties rather large on the coldest dust temperature, but the distribution of the derived temperatures for the</text>
<figure>
<location><page_10><loc_14><loc_58><loc_44><loc_91></location>
<caption>Fig. 8.The excess emission as a function of distance for the cases of a free emissivity (top see Fig. 4) and β = 2 (bottom, see Fig. 6). When the emissivity is held fixed, there is a trend with distance with the closer galaxies having more excess, and the farthest galaxies having on average a negative excess.</caption>
</figure>
<text><location><page_10><loc_8><loc_42><loc_48><loc_51></location>Monte Carlo simulations is not gaussian. There is only marginal excess ( < 10%) when using three temperatures for these two galaxies, but given the large uncertainties, non-gaussian distribution, and the necessity of imposing many restrictions on the fitting routine, we do not consider this method an improvement over using only two temperatures but allowing β to vary.</text>
<section_header_level_1><location><page_10><loc_14><loc_39><loc_43><loc_40></location>3.5. Comparison with Dale et al. (2012)</section_header_level_1>
<text><location><page_10><loc_8><loc_13><loc_48><loc_39></location>D12 calculate the excess emission at 500 µ m for all galaxies in the KINGFISH sample. They use a different approach and fit the physically motivated DL07 models and find that a dozen galaxies, including eight dwarf/irregular/Magellanic have an excess > 0 . 6 at 500 µ m. We do not fit three of the dwarf/irregulars (Ho I, Ho II, and M81dwB) because we do not have 3 σ detections at all far-IR wavelengths. For the remaining dwarf/irregulars with substantial reported excess (NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574) we find at most excesses of 30% when β is fixed at two. Another key difference in the two fitting approaches is that we are only concerned with fitting photometry spanning the range 24 -500 µ m, while D12 fit all IR photometry from 3.6 µ m and long ward. Specifically, D12 had to balance emission from the stellar continuum, PAH features, and thermal dust emission, meaning that they were unable to tailor their fits to the far-IR/submillimeter portion of the SED.</text>
<text><location><page_10><loc_8><loc_7><loc_48><loc_13></location>The discrepancy between the results of the present study and those of D12 can also be attributed to a difference in the photometry (Section 2.2). The KINGFISH 500 µ m images used in D12 were recently recalibrated downward by of order 10%. In addition, the</text>
<text><location><page_10><loc_52><loc_71><loc_92><loc_92></location>PACS images were processed with different versions of the Scanamorphos package (Roussel 2012). In this work, all images were convolved to the 500 µ m resolution before measuring the photometry, whereas in D12, photometry was calculated using the original images. As noted in Section 2.3, our background subtraction methods are different. It is also important to bear in mind that our photometry aperture sizes are not identical to D12. We use circular apertures whose diameters are listed in Table 1 while D12 uses elliptical apertures of varying sizes. Figure 1 shows our photometry and the photometry for D12 overplotted. The main discrepancies are between the PACS data and the 500 µ m. D12 calculate the excess slightly differently than this work; namely, they divide the excess by the model flux density, whereas we use the measured flux density (Eq. 2).</text>
<text><location><page_10><loc_52><loc_55><loc_92><loc_71></location>We fit the D12 photometry for NGC 2915, NGC 4236, NGC5398, NGC 5408, and IC 2574 with our two temperature modified blackbody model. We hold the emissivity fixed to a value of two, and we calculate the fractional excess according to the prescription in D12. For four of the galaxies, we find fractional excesses between 55% and 75% (IC 2574 has an excess of 44%), leading us to conclude that discrepancy between our work and D12 is primarily due to the difference in the flux density calibration and convolution of the images, and the photometric apertures, and not a result of using different modeling techniques.</text>
<section_header_level_1><location><page_10><loc_66><loc_53><loc_78><loc_54></location>4. CONCLUSIONS</section_header_level_1>
<text><location><page_10><loc_52><loc_37><loc_92><loc_52></location>We measure the emission at 500 µ m for a sample of star forming KINGFISH galaxies spanning a range of metallicities. We model the far-IR SED with a two temperature modified blackbody, and calculate the excess emission as the measured 500 µ memission relative to the predicted emission. For extended galaxies, we measure the excess in circular apertures with a diameter of 42' from the center to the edge of the galaxy. We supplement the sample of extended galaxies with a sample of compact and of dwarf/irregular galaxies, for which we model the far-IR emission on a global scale.</text>
<text><location><page_10><loc_52><loc_11><loc_92><loc_37></location>While we do see excesses of ∼ 10% for a handful of galaxies when we allow β to vary, we do not see any overall trend as a function of metallicity for the range 12 + log(O/H) = 7 . 8 -8 . 7. Furthermore, this excess is completely accounted for by the uncertainties in the fitting procedure. In addition, several of our galaxies exhibit a 500 µ m deficit of ∼ 10%. We conclude that if any strong excess is present at 500 µ m in lower metallicity galaxies, it must occur in galaxies with 12 + log(O/H) < 7 . 8. Our findings are qualitatively consistent with the work of Galametz et al. (2011). They find a submillimeter excess at 870 µ m in galaxies with 8 < 12 + log(O/H) < 9; however, when this excess is present, it is not universally seen at 500 µ m. The authors successfully account for the excess with a very cold (T ∼ 10K) dust component. Galametz et al. (2013, in prep.) reports a submillimeter excess in some of the galaxies in this sample, but it is detected at 870 µ m. It is possible that such an excess is present universally in our sample, but that longer wavelength observations are required to detect it.</text>
<text><location><page_10><loc_52><loc_7><loc_92><loc_11></location>As for the flattening of the Rayleigh Jeans tail in the submillimeter regime, we find that β = 2 most accurately reproduces the slope of SED around 500 µ m.</text>
<table>
<location><page_11><loc_8><loc_63><loc_99><loc_88></location>
<caption>TABLE 2 Derived Properties from SED fitting</caption>
</table>
<text><location><page_11><loc_8><loc_61><loc_98><loc_63></location>For the 7 extended galaxies, all of the values listed in this table are averages and standard deviations of all of the photometric regions we modeled. a The percentage of the 100 µ m flux density due to the warm temperature modified blackbody (see Eq. 1).</text>
<text><location><page_11><loc_8><loc_41><loc_48><loc_60></location>In fact, using β = 1, as has been suggested to be appropriate at longer submillimeter wavelengths, consistently overestimates the emission at 500 µ m. Therefore, any change in the emissivity does not occur until λ > 500 µ m. An emissivity index of two results in the lowest uncertainties in the SED fits and shows only a weak trend metallicity, which varies from galaxy to galaxy. Fitting with a standard value of β = 2, which results in reduced χ 2 < 1, produces an excess of ∼ 30% in six galaxies, but over predicts emission by ∼ 20% in five galaxies. We conclude that though a small 500 µ m excess may be present in individual galaxies, this is compensated by equal amounts of 500 µ m'deficiency' in comparable numbers of galaxies, and only preferentially</text>
<text><location><page_11><loc_52><loc_57><loc_92><loc_60></location>affects the lower metallicity galaxies when modeling with a fixed β .</text>
<text><location><page_11><loc_52><loc_41><loc_92><loc_56></location>Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. IRAF, the Image Reduction and Analysis Facility, has been developed by the National Optical Astronomy Observatories and the Space Telescope Science Institute. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.</text>
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[
{
"title": "ABSTRACT",
"content": "Submillimeter excess emission has been reported at 500 µ m in a handful of local galaxies, and previous studies suggest that it could be correlated with metal abundance. We investigate the presence of an excess submillimeter emission at 500 µ m for a sample of 20 galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH) that span a range of morphologies and metallicities (12 + log(O/H) = 7 . 8 -8 . 7). We probe the far-infrared (IR) emission using images from the Spitzer Space Telescope and Herschel Space Observatory in the wavelength range 24 -500 µ m. We model the far-IR peak of the dust emission with a two-temperature modified blackbody and measure excess of the 500 µ m photometry relative to that predicted by our model. We compare the submillimeter excess, where present, with global galaxy metallicity and, where available, resolved metallicity measurements. We do not find any correlation between the 500 µ m excess and metallicity. A few individual sources do show excess (10-20%) at 500 µ m; conversely, for other sources, the model overpredicts the measured 500 µ m flux density by as much as 20%, creating a 500 µ m 'deficit'. None of our sources has an excess larger than the calculated 1 σ uncertainty, leading us to conclude that there is no substantial excess at submillimeter wavelengths at or shorter than 500 µ m in our sample. Our results differ from previous studies detecting 500 µ m excess in KINGFISH galaxies largely due to new, improved photometry used in this study.",
"pages": [
1
]
},
{
"title": "INVESTIGATING THE PRESENCE OF 500 µ M SUBMILLIMETER EXCESS EMISSION IN LOCAL STAR FORMING GALAXIES",
"content": "Allison Kirkpatrick 1 , Daniela Calzetti 1 , Maud Galametz 2 , Rob Kennicutt, Jr. 2 , Daniel Dale 3 , Gonzalo Aniano 4 , Karin Sandstrom 5 , Lee Armus 6 , Alison Crocker 7 , Joannah Hinz 8 , Leslie Hunt 9 , Jin Koda 10 , Fabian Walter 5 Draft version September 24, 2018",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Dust in the interstellar medium (ISM) is formed by grain growth in both the diffuse ISM and the ejecta of dying stars, such as red giant winds, planetary nebula, and supernovae (Draine 2009). Once formed, dust absorbs UV and optical light and reemits this radiation in the infrared. UV radiation is dominated by photons from young O and B stars, so the dust mass and infrared (IR) radiation can provide important constraints on the current star formation rates and the star formation history of a galaxy. Space-based telescopes such as the Spitzer Space Telescope, the InfraRed Astronomical Satellite, and the Infrared Space Observatory have provided insights on the dust emission from mid-IR wavelengths out to ∼ 200 µ m. However, the majority, by mass, of the dust is cold ( T /lessorsimilar 25 K, Dunne & Eales 2001) and emits at far-IR and submillimeter wavelengths, where the emission spectrum is dominated by large grains in thermal equilibrium. Ground-based observations of these wavelengths are limited to a few atmospheric windows, and until recently, space-based observatories lacked coverage of the far-IR beyond ∼ 200 µ m. Now, with the advent of the Herschel Space Observatory, the peak and long wavelength tail of the dust spectral energy distribution (SED) is being observed at unprecedented angular resolution. With submillimeter observations, the dust mass and the dust to gas ratios can be more accurately estimated. Dust formation models show that the dust to gas ratios should be tied to the chemical enrichment of galaxies, as measured by the metallicity (Dwek 1998; Edmunds 2001). Galametz et al. (2011) combine submillimeter data at 450 and 850 µ m with shorter wavelength IR observations ( /lessorsimilar 160 µ m) for a large sample of local star forming galaxies. They model the spectral energy distributions of each galaxy with and without the submillimeter data and find that for high metallicity galaxies, not including the submillimeter data can cause the dust mass to be overestimated by factors of 2-10, whereas for low metallicity galaxies (12+log(O/H) /lessorsimilar 8 . 0), the SEDs without the submillimeter data can underpredict the true dust mass by as much as a factor of three. Gordon et al. (2010) use Herschel photometry to model the dust emission from the Large Magellanic Cloud (LMC) and find that dust mass derived using just 100 µ m and 160 µ m photometry underestimate the dust mass derived when using 350 µ m and 500 µ m photometry as well by as much as 36%. In measuring dust masses by modeling the far-IR and submillimeter SED, a variety of studies have sug- gested the existence of excess emission at submillimeter wavelengths above what is predicted by fits to shorter wavelength data. Furthermore, this excess could preferentially affect lower metallicity and dwarf galaxies. Dale et al. (2012, hereafter D12) report significant excess emission at 500 µ m, above that predicted by fitting the observed SEDs with the Draine & Li (2007) models, for a sample of eight dwarf and irregular galaxies from the Key Insights on Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH, Kennicutt et al. 2011). Excess emission has also been reported in the Small Magellanic Cloud (SMC) and LMC, both of which have lower than solar metallicities (12+log(O/H) = 8 . 0 , 8 . 4, respectively Bot et al. 2010; Gordon et al. 2010). On the other hand, excess emission is also seen at solar metallicities or larger. Paradis et al. (2012) model emission in the Galaxy and find excess emission (16 -20%) at 500 µ m in peripheral H ii regions. Recently, Galametz et al. (2013, in prep.) have detected excess at 870 µ m on a resolved and global scale for a sample of 11 KINGFISH galaxies. Galametz et al. (2011) finds a submillmeter excess at 870 µ m for 8 galaxies spanning a metallicity range of 12 + log(O/H) = 7 . 8 -9 . 0. The presence of excess emission does not appear to be universal, however, as Draine et al. (2007) found only a marginal difference in deriving the dust masses for a set of SINGS galaxies with and without including submillimeter data from SCUBA 12 + log(O/H) ≈ 7 . 5 -8 . 7 . More recently, Aniano et al. (2012) apply the Draine & Li (2007) models to the IR SEDs (3 . 6 -500 µ m) of the local star forming galaxies NGC 0628 and NGC 6946 and do not detect any significant excess ( > 10%) at 500 µ m. The excess emission seen at submillimeter wavelengths can be attributed to a cold dust component which is shielded from starlight (T < 10K; e.g., Galametz et al. 2009; O'Halloran et al. 2010). However, in the Milky Way, excess emission is seen at high latitudes, making it unlikely to be due to shielded cold dust (Reach et al. 1995). Studies of other galaxies have argued that a cold dust origin for the excess emission leads to unphysically high dust to gas ratios (Lisenfeld et al. 2002; Zhu et al. 2009; Galametz et al. 2010). A competing explanation is that the spectral emissivity index, β , of the dust grains changes to lower values at longer wavelengths, leading to a flattening of the submillimeter spectrum, thus mimicking a cold dust component (Dupac et al. 2003; Augierre et al. 2003; Planck Collaboration 2011). Such a change in emissivity has been suggested in the Milky Way (Paradis et al. 2009). (Galametz et al. 2012) showed that modeling the far-IR /submillimeter emission with a modified blackbody with β = 1 . 5 can increase the dust masses up to 50% compared to when β = 2, possibly explaining the discrepancies between dust masses calculated with far-IR data alone and those calculated with farIR and submillimeter data. The emission from very small grains exhibits a frequency dependence with a spectral emissivity index of β = 1, and if a galaxy has a relative abundance of very small grains greater than the Milky Way, this can cause a flattening of the emissivity index at longer wavelengths (Lisenfeld et al. 2002; Zhu et al. 2009). Alternatively, the properties of amorphous solids could explain the change in emissivity (Meny et al. 2007). Modeling the emission of amorphous solids accounts for the submillimeter excess in the LMC and SMC (Bot et al. 2010), although recent work suggests that much of the excess emission in the LMC is accounted for by fluctuations in the cosmic microwave background (Planck Collaboration 2011). Finally, an increase in the amount of magnetic material has also been proposed as a plausible explanation for the SMC submillimeter excess (Draine & Hensley 2012). Achange in dust properties can also be linked to metallicity. Draine et al. (2007) showed that 12 + log(O/H) = 8 . 1 is a threshold metallicity for galaxies in the range 12 + log(O/H) ≈ 7 . 5 -8 . 7, above which the percentage of dust mass contained in PAH molecules drastically increases. If submillimeter excess emission is due to a change in the emissivity properties of the dust population, then there might be a correlation with abundances in this metallicity range. In the present study, we seek to investigate the submillimeter excess at 500 µ m for a sample of KINGFISH galaxies. We define such excess as being emission above that predicted by a two-temperature modified blackbody model where the emissivity is not constrained, following the method outlined in Galametz et al. (2012). We have selected a sample that spans a range of metallicities, including many dwarf galaxies, in order to probe whether such excess correlates with metallicity, as has been found in some earlier studies (Galametz et al. 2009, 2011). The paper is laid out as follows: in Section 2, we describe our sample selection and modeling of the dust emission; in Section 3, we report on the excess emission and how our findings relate to the results of D12; and in Section 4, we present our conclusions.",
"pages": [
1,
2
]
},
{
"title": "2.1. The KINGFISH Sample",
"content": "The KINGFISH sample (Kennicutt et al. 2011) was selected to include a wide range of luminosities, morphologies, and metallicities in local galaxies. The sample overlaps with 57 of the galaxies observed as part of the Spitzer Infrared Nearby Galaxies Survey (SINGS, Kennicutt et al. 2003b), as well as incorporating NGC 2146, NGC 3077, M 101 (NGC 5457), and IC 342 for a total of 61 galaxies. The luminosity range spans four orders of magnitude, but all galaxies have L < 10 11 L /circledot . While some of the galaxies display a nucleus with LINER or Seyfert properties, no galaxy's global SED is dominated by an AGN. We select a sample (7) of disk galaxies possessing a large angular size ( ∼ 30arcmin 2 ) and a known metallicity gradient with which we perform a resolved study of the excess emission and search for any correspondence with metallicity. We refer to this sample as the 'extended' galaxies. Since excess emission seems to be found in dwarf/irregular galaxies, we include the dwarf/irregular galaxies (9) in KINGFISH for which we have a signal-tonoise ratio (SNR) > 3 σ in all of the SPIRE bandpasses. The dwarf/irregulars are more compact objects than our normal disk galaxies, and in general, do not have a known metallicity gradients, so we measure the excess emission globally for these objects. The resolved nature of the normal disk galaxies might bias our comparison with the dwarf/irregular galaxies, so we complement our sample (4) with normal disk galaxies that have small angular size which allows for global measurements of excess emission. These more compact, normal galaxies were selected to span a range of metallicity and have high SNRs at the SPIRE bandwidths. Our complete sample consists of 20 galaxies and is listed in Table 1. We also list in Table 1 dwarf/irregular galaxies that were rejected due to low SNRs.",
"pages": [
2,
3
]
},
{
"title": "2.2. Data Reduction",
"content": "Data observations and reduction are discussed in detail in Engelbracht et al. (2010), Sandstrom et al. (2010) and Kennicutt et al. (2011). In the present study, we use images from the PACS and SPIRE instruments on the Herschel Space Observatory spanning a wavelength range of 70 -500 µ m and MIPS 24 µ m images from the Spitzer Space Telescope (Kennicutt et al. 2003b). We use PACS 70 and 160 µ m images instead of MIPS due to the better resolution provided by PACS. All galaxy maps are at least 1.5 times the diameter of the optical disk, allowing us to probe the cold dust emission beyond the optical disk. The raw PACS and SPIRE images were processed from level 0 to 1 with Herschel Interactive Processing Environment (HIPE) v. 8. The PACS and SPIRE maps were then created using the IDL package Scanamorphos v. 17 (Roussel 2012). Scanamorphos is preferred to HIPE for its ability to better preserve low level flux density, reduce striping in area of high background, and correct brightness drifts caused by low level noise. The maps are converted from units of Jy beam -1 to MJy sr -1 by accounting for beam sizes of 469.1, 827.2, and 1779.6 arcsec 2 for the 250, 350, and 500 µ m maps, respectively. The design and performance of the SPIRE instrument is discussed in detail in Griffin et al. (2010). In the SPIRE images used in this study, the full width at half maximum (FWHM) of the beam profile has been modeled with a wavelength dependence, so that FWHM ∝ λ γ , where γ = 0 . 85. As part of the calibration process, a 'color-correction' has been applied to each beam so that the measured specific intensity I ν will be equal to the actual specific intensity I 0 when ν = ν 0 . The correction factors applied to these images assume a power-law spectrum with α = -1 . 9. We compare our results to those of D12, so it is crucial to explicitly state that we are using different versions of the PACS and SPIRE images. In D12, the raw PACS and SPIRE images were processed from level 0 to 1 with HIPE v.5. The SPIRE data were then mosaicked using the mapper in HIPE. The images were converted to MJy sr -1 using beam sizes of 423, 751, and 1587 arcsec 2 at 250, 350, and 500 µ m, respectively, and the FWHM was not modeled with a wavelength dependence; furthermore, the color-correction was not included in the beam size, but was applied a posteriori.The PACS data were mapped using Scanamorphos v. 12.5. The main difference between the version of KINGFISH images that we use and the previous version used by D12 is that the SPIRE 250 and 350 µ m images contain slightly less flux density ( ∼ 2%) while the 500 µ m image is less luminous by ∼ 10%. The point response function area is also slightly larger ( ∼ 3%) than for the v. 2 images. The more recent HIPE v. 11 pipeline has revised the SPIRE beam sizes in the direction of yielding lower fluxes for extended sources by ∼ 6%, 6%, and 8% at 250, 350, and 500 µ m, respectively. This is in the direction of reinforcing the results that are presented in this paper.",
"pages": [
3
]
},
{
"title": "2.3. Background subtraction and Convolution of Images",
"content": "The background subtraction is described in detail in Aniano et al. (2012), and we will briefly summarize here. 'Non-background' regions are determined in all cameras (IRAC, MIPS, PACS, and SPIRE) by those pixels which have a SNR > 2. Masks of the non-background regions are made, and then the masked images from all cameras are combined in order to unambiguously determine which regions are truly background regions. The signals in the background regions are then averaged, smoothed, and subtracted according to an algorithm outlined in Aniano et al. (2012). Since we compare our results with those of D12, it is worthwhile to note that a different procedure for background subtraction is followed in that study. The authors use a set of sky apertures to measure the local sky around each galaxy while avoiding any contamination from galaxy emission. The mean sky level per pixel is computed from these sky apertures, scaled to the number of pixels in the galaxy photometry aperture, and the result is subtracted from the overall galaxy photometry aperture counts. In order to consistently measure photometry for each galaxy, we used images that had been convolved to the resolution of the SPIRE 500 µ m bandpass. The convolution was done with publicly available kernels from Aniano et al. (2011) which transform the point source functions (PSFs) of individual images to the PSF of the SPIRE instrument at 500 µ m (FWHM of 38'). The convolution kernels and methodology are described in detail in Aniano et al. (2011, 2012). After the convolution to a common PSF, the images for each galaxy are resampled to a standard grid, where each pixel is ∼ 14'.",
"pages": [
3
]
},
{
"title": "2.4. Photometry and SED fitting",
"content": "For the extended galaxies, we measure photometry in apertures with diameters of 42', chosen to be slightly larger than the beam size of the SPIRE 500 µ m bandpass, from the center of the galaxy to the outskirts. We reject regions of galaxies without at least 3 σ flux density measurements at every bandpass from 24 -500 µ m. For the galaxies which are compact at the 500 µ m resolution, including the dwarf/irregulars, we measure the photometry globally in apertures with diameters ranging from 42' to 1' 52', which is the angular area covered by the galaxies with a signal to noise ratio > 3 σ . The diameter and the physical scales of each photometric aperture are listed in Table 1. The dwarf/irregular galaxies DDO 053, DDO 154, and DDO 165 have a 3 σ flux density measurement in only one of the far-IR bandpasses; Ho I, Ho II, and M 81 DwB have measurements in three of the six bandpasses. We do not model the far-IR emission for these galaxies, but we do plot the photometry and 3 σ upper limits in Figure 1. The physically-based DL07 models have been used to derive dust properties at global and local scales (e.g., Draine et al. 2007; Aniano et al. 2012). The DL07 models use the assumption of a diffuse ISM component to describe the shape of the interstellar radiation field, and We do not calculate an excess for Ho I, Ho II, DDO 053, DDO 154, DDO 165, and M81 DwB since we are not able to measure flux densities at the 3 σ level covering the full wavelength range 24 -500 µ m. The metallicity range for which we can derive excess measurements is then 12 + log(O/H) = 7 . 8 -8 . 7. use distribution function to represent the distribution of starlight intensities, which are then scaled to the SED being modeled. In addition, the submm slope of the DL07 models tends to resemble that of a modified blackbody with an emissivity of β = 2, which could prevent us from testing for flattening of the submm slope or variations in the emissivity index. We choose to model the farIR SEDs with a simple modified blackbody equation to test various assumptions on the emissivity index and will compare our results to the D12 study to investigate how the choice of model affects the observed excess emission. We model the far-IR SEDs of each region within each galaxy using a two temperature modified blackbody of the form where B ν is the Planck function. The temperatures of the warm and cold dust components are T w and T c , the scalings for each component are a w and a c , and β w and β c are the emissivity indexes. Only the scalings, T c , and β c are allowed to be free parameters, due to the limited number of data points being fit. The warm dust com- nt is necessary to account for some of the emission at 70 µ m and 100 µ m so as not to bias the cold dust temperature or emissivity. When only one temperature is used, the peak of the modified blackbody is biased towards shorter wavelengths, leading to warmer temperatures, which is then compensated at longer wavelengths by a β c shallower than otherwise measured. We include the 24 µ m data point in the fit to better constrain the warm dust modified blackbody, but the fitted warm dust parameters should not be interpreted in a physical manner, since this portion of the SED also likely contains contribution from stochastically heated dust. We list the fraction of 100 µ m flux density due to the warm dust component in Table 2. The effective dust emissivity we derive comprises the intrinsic spectral emissivity properties of dust and the variation of the dust temperature within a resolution element that could lead to a shallower β c than that obtained in isothermal cases (e.g., Shetty et al. 2009). We nevertheless allow both the cold temperature and cold emissivity, β c , to vary simultaneously, though the two parameters are degenerate. We refer to Galametz et al. (2012) and Kirkpatrick et al. (2013b, in prep.), and references therein, for a further discussion of degeneracies on the individual temperatures and emissivities. We fit the photometry from 24 -350 µ m. The 500 µ m data are not included to allow comparison with our model predictions at the same wavelength. We use a Monte Carlo technique to determine the parameters and errors. We randomly sample each data point within its errors 1000 times and determine the parameters of the two temperature modified blackbody via χ 2 minimization. The final parameters and associated errors are the medians and standard deviations of our Monte Carlo simulation. An example of the SED fitting is shown in Figure 2. When fitting, we allow the cold dust temperature, T c , to vary between 0 and 50 K and β c to vary between 0 and 5. We experimented with allowing T w to vary, but the derived temperature was approximately constant in the range 55 -60K, and simultaneously varying T w did not change the derived cold dust temperature or emissivity values. Since the warm dust component peaks in an area of the SED that is sparsely sampled, we opt to hold both T w and β w fixed. We hold the emissivity of the warm dust component fixed to a value of two and T w fixed to 60K. Fixing β w = 2 is a good approximation of the opacity of graphite/silicate dust models (Li & Draine 2001). Galametz et al. (2012) find that changing β w to 1.5 decreases the cold dust temperatures by less than 1.6%, and Tabatabaei et al. (2011) test the two temperature modified blackbody approach on M33, holding β w fixed to 1.0, 1.5, and 2.0, and conclude that β w = 2 most accurately reproduces the observed flux densities. We test a fixed β c in Section 3.3. As β w is always fixed to a value of two in all of our subsequent analysis, in the remainder of this paper, we refer to β c simply as β .",
"pages": [
3,
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]
},
{
"title": "3.1. PACS-SPIRE colors",
"content": "The color S 100 /S 160 , where S 100 is the flux density in the 100 µ m bandpass, is commonly used as a proxy for temperature, since it usually spans the peak of the blackbody emission, while S 350 /S 500 depends sensitively on the slope of the Rayleigh-Jeans tail, and so is a good proxy for β (with the same caveats given earlier about the mixing of dust with different temperatures along the line of sight). We plot these two colors in the left panel of Figure 3 for each of the regions in our extended galaxies. We calculate the positions of theoretical modified blackbodies and overplot as a grid. When calculating the theoretical tracks, we use a two temperature modified blackbody (Equation 1); we set T w = 60 K, β w = 2, and we scale the warm dust component to peak at a flux density 10% of the cold dust component peak flux density, which is the average scaling we see in our fitted SEDs at the SPIRE wavelengths. We set β = 1 , 1 . 5 , and 2, and we set T c to discrete temperature values between 15 and 27 K. Lines of constant β and T c are marked on the figure. The colors of our galaxies tend to cluster around the β = 2 , T c = 20K lines. At higher temperatures, galaxy colors start to sparsely occupy the same part of color space as the β = 1 model. No galaxies exhibit colors indicating a low temperature ( T c < 21 K) and a shallow emissivity, which could hint at physical link between the two parameters (see Yang & Phillips 2007; Ysard et al. 2012; Kirkpatrick et al. 2013b, in prep., for a discussion of the physical nature of the T c -β relationship). Although our galaxy colors tend to lie near the β = 2 model line, we observe a large scatter. This illustrates a significant difference of physical conditions from one object to another but also within our objects. Letting both parameters vary in our multiple blackbody approach can be a way to probe these variations, in spite of the degeneracies. In the right panel of Figure 3, we plot the same colors, but this time we use the predicted 500 µ m flux density, which has been calculated by fitting Equation 1 to the 24 -350 µ m flux densities. Substituting the predicted 500 µ m flux density has two interesting effects. First, it increases the amount of scatter visible in the colors. For example, in both NGC 5055 and NGC 4321, which dis- y the largest increase in scatter, the mean S 350 /S 500 observed ratio and predicted ratio is approximately the same ( ∼ 2 . 7). For NGC 5055, the standard deviation increases from 0.16 to 0.24, and for NGC 4321 it increases from 0.11 to 0.23. This increase is indicative of the uncertainties inherent in fitting modified blackbody models without enough data to adequately constrain the slope of the Rayleigh-Jeans tail. The second effect we see is that now the galaxy colors, particularly for M 101, occupy a region of the color space to the right of the β = 2 model line. The predicted S 350 /S 500 ratio is larger than the observed S 350 /S 500 ratio. Again, this illustrates the importance of using data above 350 µ m to constrain the submillimeter SED. Without including the 500 µ m data point in the modeling of the far-IR/submillimeter SED, the predicted slope will be steeper than the true value; in other words, the model underpredicts the measured 500 µ m flux density. We calculate the excess emission at 500 µ m as where F ν (500 µ m) is the predicted flux density of the two-temperature modified blackbody and S ν is the measured flux density. We plot the excess emission as a function of metallicity in Figure 4. We correct the radius of each photometric region for the inclination of the galaxy, and then convert the radius to metallicity using the gradients listed in Moustakas et al. (2010) which were calculated according to the Pilyugin & Thuan (2005) relationship (see Table 1). For M 101, which is not included in Moustakas et al. (2010), we use a metallicity gradient calculated directly from electron temperature measurements in H ii regions (Kennicutt et al. 2003a; Bresolin et al. 2004), which creates a slight offset between M 101 and the rest of our sample in metallicity. Figure 4 shows that there is no systematic dependence of the excess emission on metallicity for the sample as a whole, nor is there any trend within the individual galaxies that have a metallicity gradient. None of the galaxies display an excess larger than 25%, and for many galaxies, the modeling actually overpredicts the 500 µ m emission by this amount, creating a 500 µ m deficit. Furthermore, the spread in excess is largely accounted for by the uncertainty attached to each data point (the typical uncertainty for each region in the extended galaxies is shown in the bottom right of Figure 4). For some of the dwarf/irregulars, the uncertainties are rather large (particularly NGC 1377, NGC 2915, NGC 3773, NGC 5408, and IC 2574). The uncertainties are correlated with the SNR ratios of the SPIRE data since noisier photometry exacerbates the degeneracy between temperature and β (Juvela & Ysard 2012). The dwarf/irregulars with the lowest SNRs have the largest uncertainty on the derived β . We find that no extended galaxy has an excess emission greater than 10%, in agreement with the results of Gordon et al. (2010) for a resolved study of the LMC using a modified blackbody model, and with Aniano et al. (2013, in prep.), in which the authors create dust maps for the full sample of KINGFISH galaxies using the DL07 models. We show the distribution of excess emission in the right panel of Figure 4 for all regions in the extended galaxies, as well as the galaxies that were fit globally. We find that the resolved elements of the extended galaxies do not preferentially show an excess or a deficit. The mean excess of our sample is ∼ 0 . 02. This confirms that the majority of regions display a low excess or deficit ( < 10%). Given the large uncertainties (the dispersion is ∼ 0 . 1), this excess is thus marginal. In practice, we do not find excess 500 µ m emission greater than the scatter in the data.",
"pages": [
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},
{
"title": "3.3. 500 µ m excess dependence on β",
"content": "The derived emissivity contains information about the slope of the Rayleigh-Jeans tail, and it is possible that β is correlated with the measured excess emission (Galametz et al. 2012) We test this hypothesis for our sample in Figure 5. For simplicity, we average together all of the derived excesses and β values for each galaxy as we do not see any trends for individual galaxies. There is no apparent correlation between the excess emission and the value of β when β is allowed to be a free parameter. However, since β and T c exhibit a degeneracy which is possibly enhanced by the particular fitting method used (e.g., Juvela et al. 2013), a common technique for blackbody fitting is to hold β fixed (e.g., Yang & Phillips 2007; Xilouris et al. 2012). It is possible that holding β fixed will cause us to measure an excess emission, since the slope of the Rayleigh-Jeans tail changes from region to region within each galaxy (see Figure 3). We test this hypothesis by refitting all of our photometry holding β fixed to the values of 1, 1.5, and 2. The 500 µ m excesses for each value of β are plotted in Figure 6. An emissivity of one generally produces very bad fits to the SEDs with high χ 2 values for several galaxies, reflected in the error bars. The slope of the Rayleigh-Jeans tail is too shallow and overestimates the 500 µ m emission, as can be seen in the top panel of Figure 6. Setting β = 2 provides the best fits to the SEDs when fixing the emissivity as can be seen by the small uncertainties in the bottom panel of Figure 6. The excess emission is now ∼ 30% for galaxies which had only a 10% excess when β was allowed to vary (Figure 4). The result is consistent with R'emy-Ruyer et al. (2013), who also calculate the excess 500 µ m emission keeping β fixed at a value of 2. Holding β fixed does increase the amount of excess emission measured. It also increases the so-called emission 'deficit', meaning we now overpredict the 500 µ m emission by ∼ 20 -30%; the excess emission for each galaxy is listed in Table 2. We stress that the amount of excess emission is affected by the particular fitting method used. In our study, where we achieve good reduced χ 2 fits when holding β fixed to a value of two, and when letting β be a free parameter, we find excess values differing by as much as 20% depending on the fitting method. There is a linear correlation between the excess emission and the metallicity. This is most strongly exhibited by M 101, which has a Pearsons correlation coefficient of ρ = -0 . 86 for all three values of β . NGC 4321 also has a strong trend between excess emission and metallicity. With the exception of NGC 5055, the other extended galaxies have fewer points, so it is difficult to see a trend. The dwarf galaxies also display a high correlation with ρ in the range 0 . 54 -0 . 61 depending on the value of β . On the other hand, NGC 4321 shows no correlation between metallicity and excess for any value of β . When all of the galaxies are considered together, there is a strong anti-correlation ( ρ = -0 . 70) for β = 1 and only a low anti-correlation ( ρ = -0 . 30) for β = 2. IC 2574, NGC 2915, and NGC 5408 have a marked ex- cess when β = 2. However, for IC 2574 and NGC 2915, there is no substantial excess when β = 1 , 1 . 5 or when β is allowed to vary. From this, we conclude that there is a flattening of the SED in these two galaxies that a steeper value of β is unable to account for. Because β is an effective emissivity, and contains information about the intrinsic properties of the dust grains as well as the heating of the dust within a resolution element, we cannot conclusively determine whether this flattening is due to changing properties of the dust grains in low metallicity galaxies. For most galaxies, including the individual regions in the extended galaxies, the use of β = 2 as opposed to β = 1 produces much lower reduced χ 2 values during the Monte Carlo fitting. We plot the distribution of reduced χ 2 values over 1000 Monte Carlo fits for NGC 1377 in the top panel of Figure 7. The mean reduced χ 2 is 2.3 when β = 2 but is 10.6 when β = 1. We also show the distribution of reduced χ 2 values for NGC 2915, for which the choice of β makes little difference in the goodness of the fits. When β = 2, the mean reduced χ 2 = 1 . 1, and when β = 1, the mean reduced χ 2 = 1 . 3. This effect is also seen for NGC 3773, NGC 5408, and IC 2574, all of which exhibit no decrease in the uncertainty on the excess depending on the value of β . These are the four galaxies with the lowest SNRs at 250 µ m and 350 µ m, illustrating the difficulty of using modified blackbody fitting with low signal-to-noise photometry.",
"pages": [
7,
8
]
},
{
"title": "3.4. Exploring the Submillimeter Dust Emission",
"content": "When β is a free parameter, we do not see any systematic excess trend with metallicity, nor do we measure strong excess emission. However, when β = 2, we see a weak dependence on metallicity, and we do detect some excess for individual galaxies (Table 2). One explanation for excess submillimeter emission is temperature mixing within a resolution element (e.g., Shetty et al. 2009). The emissivity we measure is comprised both of the intrinsic emissivity of the dust and the range of temperatures of the dust components in the resolution element. This range of temperatures can produce a shallower effective β than would be measured in the ideal case of only one temperature component. We can test this explanation by comparing the excess emission with both the distance of our galaxies and the physical region size subtended by the photometry aperture (see Table 1). Both a larger region size and a larger distance will correspond to more dust emission within the resolution element, and hence more temperature mixing. We find no trend between physical size and excess emission, demonstrating that the particular photometry aperture used does not affect the resulting excess. In Figure 8, we plot the excess emission calculated when the emissivity was allowed to vary (see Figure 4) and when β = 2 (see Figure 6) as a function of distance. There is a weak trend between the excess emission and the distance when β = 2. When the emissivity is held fixed, galaxies that are within 10 Mpc have on average a higher excess emission, whereas the 500 µ m emission has in general been overpredicted for the galaxies further than 10 Mpc. This does not appear to be an effect of galaxy type, since the nearby galaxies showing excess are both extended and dwarfs. The trend seen when β = 2 is the opposite of what is expected. Galaxies that are further should have more temperature mixing within the resolution element producing a shallower farIR slope, which would cause an excess when compared to the emission predicted with β = 2. With the exceptions of NGC 0925 and NGC 4559, this trend is driven by the dwarf galaxies. Since we see no correlation between excess emission and physical region size, or excess emission and distance when β is a free parameter, we conclude that the excess emission is not due to temperature variations within the resolution element. NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574 have the highest excesses when β = 2. Mul- iple studies advocate using a third temperature component (T ∼ 10K) instead of a lower emissivity to account for the submillimeter excess (Galametz et al. 2011; Galliano et al. 2003, 2005; Marleau et al. 2006). We attempted to fit these four galaxies with a three temperature modified blackbody. We have only six photometric data points in each galaxy to fit three modified blackbodies to, so we hold several parameters constant to avoid degeneracies. We set T w = 60K and β w = 2, as described in Section2.4. We hold the emissivities of the cold components fixed to a commonly applied value of 1.8, though we note that using β = 2 caused our derived temperatures to change by only ± 1 K. We hold the scaling of the warm dust component fixed to what we derived when fitting only two modified blackbodies. Finally, we restrict the temperature range of one of the cold components to be T ∈ [20 , 50] K and the other to be T ∈ [0 , 20] K. We find that if we do not restrict the temperature ranges, then both cold components will have the same derived temperature. We are able to achieve good fits (reduced χ 2 < 1) for NGC 5408 and NGC 5398 but not for NGC 2915 or IC 2574. For NGC 5408, our three dust temperatures are 60 K, 29 ± 3K, and 13 ± 7K; for NGC 5398, they are 60 K, 22 ± 1K, and 13 ± 5K. Also, it is important to note that not only are the uncertainties rather large on the coldest dust temperature, but the distribution of the derived temperatures for the Monte Carlo simulations is not gaussian. There is only marginal excess ( < 10%) when using three temperatures for these two galaxies, but given the large uncertainties, non-gaussian distribution, and the necessity of imposing many restrictions on the fitting routine, we do not consider this method an improvement over using only two temperatures but allowing β to vary.",
"pages": [
8,
9,
10
]
},
{
"title": "3.5. Comparison with Dale et al. (2012)",
"content": "D12 calculate the excess emission at 500 µ m for all galaxies in the KINGFISH sample. They use a different approach and fit the physically motivated DL07 models and find that a dozen galaxies, including eight dwarf/irregular/Magellanic have an excess > 0 . 6 at 500 µ m. We do not fit three of the dwarf/irregulars (Ho I, Ho II, and M81dwB) because we do not have 3 σ detections at all far-IR wavelengths. For the remaining dwarf/irregulars with substantial reported excess (NGC 2915, NGC 4236, NGC 5398, NGC 5408, and IC 2574) we find at most excesses of 30% when β is fixed at two. Another key difference in the two fitting approaches is that we are only concerned with fitting photometry spanning the range 24 -500 µ m, while D12 fit all IR photometry from 3.6 µ m and long ward. Specifically, D12 had to balance emission from the stellar continuum, PAH features, and thermal dust emission, meaning that they were unable to tailor their fits to the far-IR/submillimeter portion of the SED. The discrepancy between the results of the present study and those of D12 can also be attributed to a difference in the photometry (Section 2.2). The KINGFISH 500 µ m images used in D12 were recently recalibrated downward by of order 10%. In addition, the PACS images were processed with different versions of the Scanamorphos package (Roussel 2012). In this work, all images were convolved to the 500 µ m resolution before measuring the photometry, whereas in D12, photometry was calculated using the original images. As noted in Section 2.3, our background subtraction methods are different. It is also important to bear in mind that our photometry aperture sizes are not identical to D12. We use circular apertures whose diameters are listed in Table 1 while D12 uses elliptical apertures of varying sizes. Figure 1 shows our photometry and the photometry for D12 overplotted. The main discrepancies are between the PACS data and the 500 µ m. D12 calculate the excess slightly differently than this work; namely, they divide the excess by the model flux density, whereas we use the measured flux density (Eq. 2). We fit the D12 photometry for NGC 2915, NGC 4236, NGC5398, NGC 5408, and IC 2574 with our two temperature modified blackbody model. We hold the emissivity fixed to a value of two, and we calculate the fractional excess according to the prescription in D12. For four of the galaxies, we find fractional excesses between 55% and 75% (IC 2574 has an excess of 44%), leading us to conclude that discrepancy between our work and D12 is primarily due to the difference in the flux density calibration and convolution of the images, and the photometric apertures, and not a result of using different modeling techniques.",
"pages": [
10
]
},
{
"title": "4. CONCLUSIONS",
"content": "We measure the emission at 500 µ m for a sample of star forming KINGFISH galaxies spanning a range of metallicities. We model the far-IR SED with a two temperature modified blackbody, and calculate the excess emission as the measured 500 µ memission relative to the predicted emission. For extended galaxies, we measure the excess in circular apertures with a diameter of 42' from the center to the edge of the galaxy. We supplement the sample of extended galaxies with a sample of compact and of dwarf/irregular galaxies, for which we model the far-IR emission on a global scale. While we do see excesses of ∼ 10% for a handful of galaxies when we allow β to vary, we do not see any overall trend as a function of metallicity for the range 12 + log(O/H) = 7 . 8 -8 . 7. Furthermore, this excess is completely accounted for by the uncertainties in the fitting procedure. In addition, several of our galaxies exhibit a 500 µ m deficit of ∼ 10%. We conclude that if any strong excess is present at 500 µ m in lower metallicity galaxies, it must occur in galaxies with 12 + log(O/H) < 7 . 8. Our findings are qualitatively consistent with the work of Galametz et al. (2011). They find a submillimeter excess at 870 µ m in galaxies with 8 < 12 + log(O/H) < 9; however, when this excess is present, it is not universally seen at 500 µ m. The authors successfully account for the excess with a very cold (T ∼ 10K) dust component. Galametz et al. (2013, in prep.) reports a submillimeter excess in some of the galaxies in this sample, but it is detected at 870 µ m. It is possible that such an excess is present universally in our sample, but that longer wavelength observations are required to detect it. As for the flattening of the Rayleigh Jeans tail in the submillimeter regime, we find that β = 2 most accurately reproduces the slope of SED around 500 µ m. For the 7 extended galaxies, all of the values listed in this table are averages and standard deviations of all of the photometric regions we modeled. a The percentage of the 100 µ m flux density due to the warm temperature modified blackbody (see Eq. 1). In fact, using β = 1, as has been suggested to be appropriate at longer submillimeter wavelengths, consistently overestimates the emission at 500 µ m. Therefore, any change in the emissivity does not occur until λ > 500 µ m. An emissivity index of two results in the lowest uncertainties in the SED fits and shows only a weak trend metallicity, which varies from galaxy to galaxy. Fitting with a standard value of β = 2, which results in reduced χ 2 < 1, produces an excess of ∼ 30% in six galaxies, but over predicts emission by ∼ 20% in five galaxies. We conclude that though a small 500 µ m excess may be present in individual galaxies, this is compensated by equal amounts of 500 µ m'deficiency' in comparable numbers of galaxies, and only preferentially affects the lower metallicity galaxies when modeling with a fixed β . Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. IRAF, the Image Reduction and Analysis Facility, has been developed by the National Optical Astronomy Observatories and the Space Telescope Science Institute. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.",
"pages": [
10,
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]
},
{
"title": "REFERENCES",
"content": "Meny, C., Gromov, V., Boudet, N., et al. 2007, A&A, 468, 171 Moustakas, J., Kennicutt, R. C., Tremonti, C. A., et al. 2010, ApJS, 190, 233 O'Halloran, B., Galametz, M., Madden, S. C., et al. 2010, A&A, 518, L58 Paradis, D., Bernard, J.-Ph., and Meny, C. 2009, A&A, 506, 745 Paradis, D., Paladini, R., Noriega-Crespo, A., et al. 2012, A&A, 537, A113 Pilyugin, L. S., & Thuan, T. X. 2005, ApJ, 631, 231 Planck Collaboration. 2011, A&A, 536, 17 Reach, W. T., Dwek, E., Fixsen, D. J., et al. 1995, ApJ, 451, 188 R'emy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2013, A&A, accepted. [arXiv:1309.1371] Sandstrom, K., Krause, O., Linz, H., et al. 2010, A&A, 518, L59 Storchi-Bergmann, T., Calzetti, D., and Kinney, A. L. 1994, ApJ, 429, 572",
"pages": [
12
]
}
]
2013ApJ...778..116N
https://arxiv.org/pdf/1309.4967.pdf
<document>
<section_header_level_1><location><page_1><loc_11><loc_86><loc_89><loc_87></location>RE-APPEARANCE OF MCNEIL'S NEBULA (V1647 ORIONIS) AND ITS OUTBURST ENVIRONMENT</section_header_level_1>
<section_header_level_1><location><page_1><loc_41><loc_84><loc_59><loc_85></location>J. P. Ninan, D. K. Ojha</section_header_level_1>
<text><location><page_1><loc_10><loc_82><loc_91><loc_84></location>Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India</text>
<section_header_level_1><location><page_1><loc_46><loc_78><loc_54><loc_79></location>B. C. Bhatt</section_header_level_1>
<text><location><page_1><loc_28><loc_77><loc_73><loc_78></location>Indian Institute of Astrophysics, Koramangala, Bangalore 560 034, India</text>
<section_header_level_1><location><page_1><loc_46><loc_74><loc_54><loc_74></location>S. K. Ghosh</section_header_level_1>
<text><location><page_1><loc_20><loc_72><loc_82><loc_73></location>National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune 411 007, India</text>
<section_header_level_1><location><page_1><loc_46><loc_69><loc_54><loc_69></location>V. Mohan</section_header_level_1>
<text><location><page_1><loc_27><loc_67><loc_74><loc_68></location>Inter-University Centre for Astronomy and Astrophysics, Pune 411 007, India</text>
<section_header_level_1><location><page_1><loc_45><loc_64><loc_55><loc_65></location>K. K. Mallick</section_header_level_1>
<text><location><page_1><loc_10><loc_62><loc_91><loc_64></location>Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India</text>
<section_header_level_1><location><page_1><loc_46><loc_58><loc_54><loc_59></location>M. Tamura</section_header_level_1>
<text><location><page_1><loc_27><loc_57><loc_74><loc_58></location>National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan</text>
<text><location><page_1><loc_49><loc_55><loc_51><loc_56></location>and</text>
<section_header_level_1><location><page_1><loc_45><loc_54><loc_55><loc_54></location>Th. Henning</section_header_level_1>
<text><location><page_1><loc_26><loc_51><loc_75><loc_53></location>Max-Planck-Institute for Astronomy, Konigstuhl 17, 69117 Heidelberg, Germany Draft version September 5, 2021</text>
<section_header_level_1><location><page_1><loc_45><loc_48><loc_55><loc_49></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_24><loc_86><loc_48></location>We present a detailed study of McNeil's nebula (V1647 Ori) in its ongoing outburst phase starting from September 2008 to March 2013. Our 124 nights of photometric observations were carried out in optical V , R , I and near-infrared (NIR) J , H , K bands, and 59 nights of medium resolution spectroscopic observations were done in 5200 - 9000 ˚ A wavelength range. All observations were carried out with 2-m Himalayan Chandra Telescope (HCT) and 2-m IUCAA Girawali Telescope. Our observations show that over last four and a half years, V1647 Ori and the region C near Herbig-Haro object, HH 22A, have been undergoing a slow dimming at a rate of ∼ 0 . 04 mag yr -1 and ∼ 0 . 05 mag yr -1 respectively in R -band, which is 6 times slower than the rate during similar stage of V1647 Ori in 2003 outburst. We detected change in flux distribution over the reflection nebula implying changes in circumstellar matter distribution between 2003 and 2008 outbursts. Apart from steady wind of velocity ∼ 350 km s -1 we detected two episodic magnetic reconnection driven winds. Forbidden [O I] 6300 ˚ A and [Fe II] 7155 ˚ A lines were also detected implying shock regions probably from jets. We tried to explain the outburst timescales of V1647 Ori using the standard models of FUors kind of outburst and found that pure thermal instability models like Bell & Lin (1994) cannot explain the variations in timescales. In the framework of various instability models we conclude that one possible reason for sudden ending of 2003 outburst in 2005 November was due to a low density region or gap in the inner region ( ∼ 1 AU) of the disc.</text>
<text><location><page_1><loc_14><loc_21><loc_86><loc_24></location>Subject headings: stars: formation, stars: pre-main-sequence, stars: outflows, stars: variables: general, stars: individual: (V1647 Ori), ISM: individual: (McNeil's nebula)</text>
<section_header_level_1><location><page_1><loc_22><loc_18><loc_35><loc_19></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_8><loc_48><loc_17></location>When low-mass stars like our Sun are born, they slowly accrete gas from the collapsing cloud through an accretion disc. Collimated outflows are also typically seen in most of these objects. The discontinuous knots seen in outflows from these objects, and the mismatch of accretion rate between envelope to disc and disc to star (known as 'Luminosity Problem') in young stellar ob-</text>
<text><location><page_1><loc_52><loc_5><loc_92><loc_19></location>jects (YSOs), all hint to an episodic nature of accretion instead of an ideal steady inflow (Kenyon et al. 1990; Evans et al. 2009; Ioannidis & Froebrich 2012). The other important feature seen in these objects is the outburst. Rare outbursts that we see among these YSOs are found to be correlated with an order of magnitude increase in mass infall rate and they could be the episodic accretion events required to explain the outflow discontinuities and 'Luminosity Problem'. These outbursts are empirically classified as FUors (decades long outbursts</text>
<text><location><page_2><loc_8><loc_61><loc_48><loc_92></location>with 4-5 magnitude change in optical) and EXors (few months-years long outbursts with 2-3 magnitude change in optical) (Herbig 1977; Hartmann 1998; Hartmann & Kenyon 1996). Due to the short timescales of outbursts in comparison to millions of years timescale of star formation, these events are extremely rare and only less than a dozen confirmed FUor outbursts have been detected so far. From their frequency of outburst it is estimated that every low-mass YSO should go through these outbursts at least 50 times in its protostellar phase (Scholz et al. 2013). Regarding the discontinuous knots seen in outflows, it should be noted that the timescales between discontinuities were estimated to be of the order of 10 3 years by Ioannidis & Froebrich (2012) and the timescales between FUor outbursts in a single star were estimated to be of the order of 10 4 years by Scholz et al. (2013). So the discontinuities could be due to some other shorter timescale variations in accretion rate rather than classical FUors. But as Scholz et al. (2013) pointed out, we do not have a good estimate of FUors' timescales in the early Class I stage. Hence we cannot rule out the possibility that discontinuities in outflows are created during FUors events.</text>
<text><location><page_2><loc_8><loc_6><loc_48><loc_61></location>One such object which was extensively studied recently in literature is V1647 Ori (V1647 Orionis), 400 pc away in the L1630 dark cloud of Orion. It underwent a sudden outburst of ∼ 5 mag in optical in 2003 (McNeil 2004; Brice˜no et al. 2004) and illuminated a reflection nebula, now named as McNeil's nebula after its discoverer Jay McNeil. Reipurth & Aspin (2004) reported 3 mag increase in near-infrared (NIR) and Andrews et al. (2004) reported 25 times increase in 12 µm flux and no flux change in submillimeter of V1647 Ori during the outburst. Kastner et al. (2004) reported a 50 times increase in X-ray flux of V1647 Ori during the outburst, and noted that the derived temperature of the plasma is too high for accretion alone to explain and hinted that magnetic reconnection events might be heating up the plasma. Based on the upper limit on radio continuum emission from McNeil's nebula at 1272 MHz from Giant Metrewave Radio Telescope (GMRT), India, Vig et al. (2006) constrained the extent of HII region corresponding to a temperature glyph[greaterorsimilar] 2500 K to be glyph[lessorsimilar] 26 AU. Spectroscopic studies showed strong H α and Ca II IR triplet lines in emission (Brice˜no et al. 2004; Ojha et al. 2006). In NIR region, strong CO bandheads (2.29 µm ) and Br γ line (2.16 µm ; implying strong accretion) were detected in emission (Reipurth & Aspin 2004; Vacca et al. 2004). The strong P-Cygni profile in H α emission indicated wind-velocity ranging from 600 - 300 km s -1 (Ojha et al. 2006; Vacca et al. 2004). ' Abrah'am et al. (2006) carried out AU scale observations using Very Large Telescope Interferometer/ Mid-Infrared interferometric Instrument (VLTI/MIDI). By fitting both spectral energy distribution (SED) and visibility values they deduced a moderately flaring disc with temperature profile T ∼ r -0 . 53 (T(1AU)=680K) and mass ∼ 0 . 05 M glyph[circledot] , with inner radius of 7 R glyph[circledot] (0.03 AU) and outer radius of 100 AU. This temperature profile is shallower than the T ∼ r -0 . 75 canonical model (Pringle 1981). They also reported that the mid-infrared emitting region at 10 µm has a size of ∼ 7 AU. Rettig et al. (2005) used the CO lines in infrared (IR) to measure the temperature of the</text>
<text><location><page_2><loc_52><loc_89><loc_92><loc_92></location>inner accretion disc region which was estimated to be T ≈ 2500 K.</text>
<text><location><page_2><loc_52><loc_73><loc_92><loc_89></location>Ojha et al. (2006) and K'osp'al et al. (2005) reported a sudden dimming and termination of the 2003 outburst in November 2005. Thus, 2003 outburst lasted for a total of ∼ 2 years and V1647 Ori returned to its pre-outburst phase in early 2006. Acosta-Pulido et al. (2007) estimated the inclination angle of disc to be 61 · and also estimated the accretion rate to be 5 × 10 -6 M glyph[circledot] yr -1 during outburst and 5 × 10 -7 M glyph[circledot] yr -1 in 2006 quiescent state. Aspin et al. (2006) reported that ∼ 37 years prior to 2003 outburst, i.e. in 1966, V1647 Ori had undergone a similar magnitude of outburst, lasting for a duration somewhere between 5 to 20 months.</text>
<text><location><page_2><loc_52><loc_49><loc_92><loc_73></location>Contrary to expected decades long quiescense, V1647 Ori underwent a second outburst in 2008 just after spending two years in quiescent state (Aspin et al. 2009). It brightened up to the same magnitude and had almost identical spectral features in optical and NIR as the first outburst. One striking difference was that the strong CO bandhead emission at 2.29 µm was absent in second outburst (Aspin 2011). The X-ray flux with plasma temperature of 2-6 keV during both outbursts was postulated to be due to magnetic reconnection events in the disc-star magnetic field interaction (Teets et al. 2011, and references therein). Hamaguchi et al. (2012) normalised and combined both outbursts' data in X-ray and detected one day periodicity in light curve, which they modeled with two accretion hot spots on the top and bottom hemispheres of the star rotating with one day period and inclination of 68 · . Figure 1 shows the overall cross-section picture of the surroundings of V1647 Ori we know so far.</text>
<text><location><page_2><loc_52><loc_30><loc_92><loc_48></location>V1647 Ori provides a unique opportunity to understand the physical processes undergone in FUors or EXors kind of outbursts. The short time scale behaviors of this object make it possible for us to make a detailed study of the object. In literature there exists mainly three kinds of model for explaining the outburst phenomena (see Section 4). The differences between these models are all in the inner region of disc ( < 1 AU), and optical and NIR are the right wavelength regime to probe this region of the disc. Detailed understanding of V1647 Ori will thus provide us a laboratory to check our understanding of various instabilities like thermal, gravitational and magnetorotational in proto-planetary disc around young low-mass stars.</text>
<text><location><page_2><loc_52><loc_8><loc_92><loc_29></location>We have carried out continuous observations for more than four and a half years (2008 - 2013) of V1647 Ori in optical and NIR wavelengths for detailed study of its dynamics during outburst and post-outburst stages of the second outburst. This data combined with previous outbursts' provide us more insight on the nature of outburst and also constrain the existing physical models. In this paper, we present the results of our long-term optical and NIR photometric and spectroscopic observations of the outburst source and associated McNeil's nebula. In Section 2 we describe the observational details and the data reduction procedures. In Section 3 we present our new findings and results from observations. In Section 4 we analyse the ability of each existing physical models to explain V1647 Ori's outburst history. Finally, in Section 5 we summarise our main results.</text>
<section_header_level_1><location><page_3><loc_20><loc_91><loc_37><loc_92></location>2.1. Optical Photometry</section_header_level_1>
<text><location><page_3><loc_8><loc_63><loc_52><loc_90></location>Our long-term optical observations span from 2008 September 14 to 2013 March 11 and were carried out with 2-m Himalayan Chandra Telescope (HCT) at Indian Astronomical Observatory, Hanle (Ladakh), India and with 2-m Inter-University Centre for Astronomy and Astrophysics (IUCAA) Girawali Telescope at IUCAA Girawali Observatory (IGO), Girawali (Pune), India. At HCT, for photometry central 2K × 2K section of Himalaya Faint Object Spectrograph & Camera (HFOSC) CCD, which has a pixel scale of 0.296 arcsec was used, giving us a field of view (FoV) of ∼ 10 × 10 arcmin 2 . At IGO, 2K × 2K IUCAA Faint Object Spectrograph & Camera (IFOSC) CCD was used which also has a similar pixel scale of 0.3 arcsec, giving us a FoV of ∼ 10 × 10 arcmin 2 . Further details of the instruments and telescopes are available at http://www.iiap.res.in/iao/hfosc.html and http://www.iucaa.ernet.in/ itp/igoweb/igo tele and inst.htm. Out of our total observation of 110 nights, 84 nights were observed from HCT and 26 nights from IGO.</text>
<text><location><page_3><loc_8><loc_38><loc_48><loc_63></location>The V1647 Ori's field ( α, δ ) 2000 = (05 h 46 m 13 s . 135 , -00 · 06 ' 04 '' . 82) was observed in standard V RI Bessel filters. Nearby Landolt's standard star fields (Landolt 1992) were also observed for magnitude calibration and for solving color transformation equation coefficients of each night. For nights which do not have standard star observations, we identified six stars in the object's frame whose magnitudes remain constant throughout. Four of them were used as secondary standards (see Figure 2) and other two were used to check consistency and error. Apart from object frames, bias and sky flats were also taken in each night for the basic data reduction. For fringe removal in IGO I -band images, blank sky frames were also taken. The log of photometric observations is given in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material.</text>
<text><location><page_3><loc_8><loc_14><loc_48><loc_38></location>Blank sky images in I -band were used to create fringe templates by MKFRINGECOR task in IRAF 1 , which were later used to subtract the fringes that appeared in I -band images taken from IGO. Data reduction was done with the semi-automatic pipeline written in PyRAF 2 and IRAF CL scripts. Standard photometric data reduction steps like bias-subtraction and median flat-fielding were done for all the nights. Point-spread function (PSF) photometry (using PSF & ALLSTAR tasks in DAOPHOT package of IRAF) on V1647 Ori was not able to fully remove the nebular contamination. We found a strong correlation between fluctuation in magnitude of V1647 Ori and fluctuation in atmospheric seeing condition. This is because the contamination of flux from nebula into V1647 Ori's aperture was a function of atmospheric seeing. So we generated a set of images by convolving each frame with 2-D Gaussian kernel of different standard deviation (using IMFILTER.GAUSS task in IRAF) for sim-</text>
<unordered_list>
<list_item><location><page_3><loc_8><loc_8><loc_48><loc_13></location>1 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.</list_item>
</unordered_list>
<text><location><page_3><loc_52><loc_77><loc_92><loc_92></location>ulating different atmospheric seeing conditions. We then recalculated the magnitudes by DAOPHOT, PSF and ALLSTAR algorithms of IRAF for various atmospheric seeing conditions. The differential magnitudes obtained from each frame's set was interpolated to obtain magnitude at an atmospheric seeing of 1.18 arcsec, which was taken to be the seeing to be interpolated to, for all nights and it was chosen to minimise interpolation error. This method reduced our error bars in magnitude by a factor of 2. Apart from the Gaussian convolution step, the PSF photometry steps were all same as Ojha et al. (2006).</text>
<text><location><page_3><loc_52><loc_66><loc_92><loc_77></location>Magnitudes of the whole nebula and other objects in the nebula like region C (near HH 22A) and region B defined by Brice˜no et al. (2004) in their figure 2 (also see Figure 2) were measured by simple aperture photometry with an aperture radius of 80 arcsec for nebula and 12 arcsec for the regions C and B. For obtaining the flux, the aperture of the objects like regions C and B were centered at the objects itself.</text>
<section_header_level_1><location><page_3><loc_63><loc_64><loc_81><loc_65></location>2.2. Optical Spectroscopy</section_header_level_1>
<text><location><page_3><loc_52><loc_24><loc_92><loc_63></location>Our long-term spectroscopic observations also span the same duration as that of photometric observations (2008 September to 2013 March) using both 2-m HCT and 2-m IGO. The full 2K × 4K section of HFOSC CCD spectrograph was used in HCT observations and 2K × 2K IFOSC CCD spectrograph was used for IGO observations. Spectroscopic observations were carried out on 35 nights from HCT and 24 nights from IGO, thus totalling to 59 nights of V1647 Ori's spectroscopic observations. The log of spectroscopic observations is listed in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. In order to detect the prominent Hα λ 6563 ˚ A and Ca II IR triplet lines ( λ 8498, λ 8542, λ 8662 ˚ A ), we observed in the effective wavelength range of 5200 -9000 ˚ A using grism 8 (center wavelength 7200 ˚ A ) and grism 7 (center wavelength 5300 ˚ A ). The spectral resolution obtained for grism 8 and 7 with 150 micron slit at IGO and 167 micron slit at HCT was ∼ 7 ˚ A . Nebulosity contamination in spectrum of V1647 Ori was minimised by keeping the slit in east-west orientation. Standard IRAF tasks like APALL and APSUM were used for spectral reduction. Wavelength calibration was carried out using the FeNe, FeAr and HeCu lamps. For final measurement of equivalent width the extracted 1-D spectra were normalised with respect to continuum. For spectroscopic data reduction of HCT and IGO data, semi-automated pipeline written in PyRAF was used.</text>
<section_header_level_1><location><page_3><loc_61><loc_22><loc_83><loc_23></location>2.3. Near-Infrared Photometry</section_header_level_1>
<text><location><page_3><loc_52><loc_5><loc_92><loc_21></location>Along with optical monitoring we also carried out photometric monitoring in JHK bands using the HCT NIR camera (NIRCAM) and TIFR NIR Imaging CameraII (TIRCAM2). NIRCAM has a 512 × 512 Mercury Cadmium Telluride (HgCdTe) array, with a pixel size of 18 µm , which gives a FoV of 3 . 6 × 3 . 6 arcmin 2 with HCT. Filters used for observation were J ( λ center = 1.28 µm , ∆ λ = 0.28 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.33 µm ) and K ( λ center = 2.22 µm , ∆ λ = 0.38 µm ). Further details of the instrument are available at http://www.iiap.res.in/iao/nir.html. TIRCAM2 has a 512 × 512 Indium Antimonide (InSb) array with a pixel</text>
<text><location><page_4><loc_8><loc_53><loc_48><loc_92></location>size of 27 µm . We observed McNeil's nebula during the engineering run of TIRCAM2 at 2-m IGO and 1.2-m Physical Research Laboratory (PRL) Mount Abu telescope. Filters used for observation were J ( λ center = 1.20 µm , ∆ λ = 0.36 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.30 µm ) and K ( λ center = 2.19 µm , ∆ λ = 0.40 µm ). Further details of the instrument are available in Naik et al. (2012). We have a total of 14 nights of NIR photometric observations, with the first set of data taken during the quiescent phase in 2007, i.e. before the 2008 outburst. Observations of V1647 Ori were carried out by taking several sets of exposures; each set contains exposure with the telescope pointing at five different dithered positions. The master sky frame for sky-subtraction was generated by median combining all the dithered object frames. Data reduction and final photometry were done using standard IRAF aperture photometric tasks. To be consistent with magnitude estimates by Ojha et al. (2006), for flux calibration we used an aperture ∼ 7 arcsec, and for background sky estimation we used an annulus with an inner radius of ∼ 50 '' and width ∼ 5 '' . For instrumental to apparent magnitude calibration, we observed standard stars around AS13, AS9 and HD225023 fields (Hunt et al 1998) on the same night with similar airmass as V1647 Ori observations. On 2011 December 6, standard stars were not observed, hence we used the magnitude measured on other nights of the nearby star (2MASS J05461162-0006279) for photometric calibration.</text>
<section_header_level_1><location><page_4><loc_18><loc_51><loc_39><loc_52></location>3. RESULTS AND DISCUSSION</section_header_level_1>
<section_header_level_1><location><page_4><loc_19><loc_49><loc_37><loc_50></location>3.1. Photometric Results</section_header_level_1>
<text><location><page_4><loc_8><loc_5><loc_48><loc_48></location>Figure 2 shows the three-color composite image ( V : blue, R : green, I : red) of the McNeil's nebula field (FoV ∼ 10 × 10 arcmin 2 ) obtained from IGO on 2010 February 13. Secondary standard stars used for flux calibration are marked as A, B, C and D. The outburst source V1647 Ori, illuminating the nebula, is marked at the center. The region C, possibly unrelated to Herbig-Haro object, HH 22A, which is illuminated by V1647 Ori is also marked. V1647 Ori had already reached its peak outburst phase before our first optical observation in September 2008. Its light curve steadily continued in peak outburst flux ('high plateau') phase even until our last observation taken in March 2013. However, our longterm continuous monitoring from 2008 September 14 to 2013 March 11 shows a slow but steady linear declining trend in the brightness of the source and nebula (Ninan et al. 2012). The linear slopes and the error in estimates of slopes were obtained by simple linear regression by ordinary least square fitting. V , R and I magnitudes of V1647 Ori and of region C, which is illuminated by the V1647 Ori from its face-on angle of the disc, are listed in Table 2. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. Light curves of V1647 Ori in I and R -bands clearly show a steady dimming (see Figure 3). During the last four and a half years of its second outburst, the brightness in I and R bands have decreased by ∼ 0 . 2 mag. The rate of decline in magnitude of V1647 Ori is 0.036 ± 0 . 007 mag yr -1 in I -band and 0.038 ± 0 . 007 mag yr -1 in R -band. We do not see any statistically significant decline in V -band magnitude of V1647 Ori. This could be due to higher fraction of contamination of</text>
<text><location><page_4><loc_52><loc_59><loc_92><loc_92></location>nebula over V1647 Ori's aperture and slightly higher error in magnitudes due to faintness of source in V -band. These flux changes are along our direct line of sight at an angle of ∼ 30 · to the plane of disc (Acosta-Pulido et al. 2007). However, the flux measured along the cavity in perpendicular direction to the disc, which is reflected from region C, shows a dimming trend of 0.059 ± 0 . 005 mag yr -1 in I -band, 0.051 ± 0 . 005 mag yr -1 in R -band and 0.060 ± 0 . 005 mag yr -1 in V -band (see Figure 4). Hence, the region C, seems to be dimming faster than V1647 Ori. This could be either due to material inflow into cavity between region C and V1647 Ori as the outburst is progressing or due to a change in extinction along the cavity induced by slow dimming of V1647 Ori's brightness. During the first outburst in 2003, the linear dimming rate during the plateau stage was 0.24 mag yr -1 in R -band (Fedele et al. 2007), which was ∼ 6 . 3 times faster in magnitude scale than the present dimming rate in second outburst. Just like in other T-Tauri stars, we also see a lot of short time scale random variations in the source magnitude (peak-to-peak ∆ V glyph[similarequal] 0 . 35 mag, ∆ R glyph[similarequal] 0 . 30 mag and ∆ I glyph[similarequal] 0 . 20 mag), which could be due to density fluctuations in the infalling gas on to the star.</text>
<text><location><page_4><loc_52><loc_42><loc_92><loc_59></location>Our lightcurve of V1647 Ori does not show any 56 day periodicity which was reported by Acosta-Pulido et al. (2007) during the first 2003 outburst. Based on the correlated reddening of flux during the minima of light curve, they proposed that periodicity was due to occultation of a dense clump in accretion disc at a distance of 0.25 AU from the star. The peak-to-peak amplitude in I -band was ∼ 0.3 mag in 2003. We have not detected this variability in 2008 outburst which implies the dense clump might have got dissipated between 2003 and 2008 outburst events. Our Lomb-Scargle periodogram analysis of magnitudes did not show any other statistically significant periodicity.</text>
<text><location><page_4><loc_52><loc_31><loc_92><loc_42></location>The optical magnitudes during the second outburst are almost similar to that of the first outburst in 2003. In fact the first known outburst of V1647 Ori in 1966 ( ∼ 38 years prior to 2003), reported by Aspin et al. (2006), also had similar magnitude to the present one, however, all these three outbursts have different timescales. Implications of this fact on outburst model will be discussed in Section 4.</text>
<text><location><page_4><loc_52><loc_5><loc_92><loc_31></location>Our NIR J , H and K magnitudes are listed in Table 3. Similar to optical light curve, there is a faint dimming trend in NIR also. Venkata Raman et al. (2013), with more NIR data points, estimated the fading rate in J -band to be 0.08 ± 0 . 02 mag yr -1 . The J -H/H -K color-color (CC) diagram (Figure 5) shows the movement of V1647 Ori from 2007 data point taken in quiescent phase to outburst state. It is similar to what was seen in 2003 outburst. From the quiescent phase position in CC diagram, V1647 Ori has moved towards the classical T-Tauri (CTT) locus along the redenning vector and presently occupies the same position as in 2003 outburst. The position of V1647 Ori in CC diagram is consistent with similar CC diagram published by Venkata Raman et al. (2013). This implies that the decrease in line of sight extinction during the outburst is same as that seen during the 2003 outburst. Since our line of sight is through the envelope, it must be likely due to a reversible mechanism like dust sublimation in the inner region of en-</text>
<text><location><page_5><loc_8><loc_77><loc_48><loc_92></location>elope during each outburst (Acosta-Pulido et al. 2007; Mosoni et al. 2013; Aspin et al. 2009). Since the star is deeply embedded, we have reflections and dust emission effects also affecting the position of V1647 Ori in the CC diagram. So the extinction estimated from CC diagram is not very reliable. Otherwise, we can see that the second outburst has cleared out circumstellar matter of δA V ∼ 6 ± 2 mag. This is also consistent with the estimate of extinction change during first outburst by Mosoni et al. (2013), δA V ∼ 4 . 5 mag (see also Aspin et al. (2008)).</text>
<section_header_level_1><location><page_5><loc_19><loc_75><loc_38><loc_76></location>3.2. Morphological Results</section_header_level_1>
<text><location><page_5><loc_8><loc_26><loc_48><loc_74></location>Between 2003 and 2008 outbursts, the McNeil's nebula does not have any significant morphological changes, however the intensity distribution of the nebula has changed between the outbursts. Figure 6 shows the difference in R -band flux along the nebula between 2011 and 2004. Images of similar atmospheric conditions were taken and scaled to match the brightness of V1647 Ori before subtracting 2004 image from that of 2011. Brighter shade implies that region is brighter in 2011 than 2004. We can see that the region C is brighter in second outburst than it was in 2004. This could be due to dust clearing up between the last two outbursts along the cavity seen in NIR in region C direction (Ojha et al. 2005). Our photometric results show region C is dimming faster than V1647 Ori and one of the explanations for that could be material inflow into cavity during the outburst. However, region C is relatively brighter in 2008 outburst than in 2004 for the same brightness of V1647 Ori. This implies that the matter inflow to cavity was not occurring during the quiescent phase between 2006 and 2008. This is also based on the implicit assumption that the extinction along the line of sight direction to V1647 Ori is same between 2003 and 2008 outbursts. The other significant change is in illumination of the south-western knot (region B) of the nebula; its illumination seems to have shifted slightly towards west. These illumination changes in nebula imply a structural change in the circumstellar matter above the disc and cavity. A similar pattern and conclusion were also reported between 1966, 2003 and 2008 outbursts by Aspin et al. (2006, 2009). Similar analysis of image pairs taken between 2008 and 2012 did not show any significant morphological changes. Our image pairs had a seeing of 1.6 '' . Hence, to check whether any change in illumination of nebula is undergoing during the present outburst, we need images with seeing less than 1.6 '' .</text>
<section_header_level_1><location><page_5><loc_19><loc_23><loc_37><loc_24></location>3.3. Spectroscopic Results</section_header_level_1>
<text><location><page_5><loc_8><loc_11><loc_48><loc_23></location>V1647 Ori optical spectra show strong H α (6563 ˚ A ) emission and Ca II IR triplet at 8498, 8542 and 8662 ˚ A in emission. Other weak lines seen are Na D (5890+5896 ˚ A ) and OI (7773 ˚ A ) in absorption, and [O I] (6300 ˚ A ), O I (8446 ˚ A ), [Fe II] (7155 ˚ A ) and Fe I (8388, 8514 ˚ A ) in emission (see Figure 7). The equivalent widths of H α , Ca II IR triplet lines and OI (7773 ˚ A ) are listed in Table 4.</text>
<section_header_level_1><location><page_5><loc_23><loc_8><loc_33><loc_10></location>3.3.1. H α line</section_header_level_1>
<text><location><page_5><loc_8><loc_5><loc_48><loc_8></location>Strong Hα line in V1647 Ori shows a clear P-Cygni profile as well as substantial variations. Figure 8 shows</text>
<text><location><page_5><loc_52><loc_56><loc_92><loc_92></location>the variations of Hα profiles during our four and a half years of observations. P-Cygni profiles were more prominent in early part of the outburst in 2008. To see the absorption component clearly, a Gaussian is fitted to the right wing of the profile in red color and the difference of the fit to actual spectra is plotted in green color. Figure 9 shows the outflow velocity and associated error bar of expanding wind from the blue-shifted absorption minima in Hα profile. These blue-shifted absorption components were present in 2003 outburst also and disappeared during the fading stage of the outburst (Ojha et al. 2006; Fedele et al. 2007). Figure 10 shows the variation in equivalent width ( W λ in ˚ A ) of Hα emission. The calculation of W λ was very sensitive to the weak continuum flux around λ 6563 ˚ A , and the error estimate for each data point is ∼ ± 3 ˚ A . The W λ of 2008 outburst is in similar range of that during first outburst in 2003. Since Hα emission comes from the innermost accretion powered hot zone, we can expect its strength to be proportional to the accretion rate. The optical photometric magnitude in second outburst is similar to that of first outburst, which implies the continuum flux is almost of the same value. Hence from the fact that W λ is of similar value as of first outburst, we can deduce that the accretion rate is also of the same order in both the outbursts during its 'high plateau'stage.</text>
<section_header_level_1><location><page_5><loc_62><loc_54><loc_82><loc_55></location>3.3.2. Ca II IR triplet lines</section_header_level_1>
<text><location><page_5><loc_52><loc_5><loc_92><loc_53></location>The plots of equivalent widths of Ca II IR triplet lines (8498, 8542 and 8662 ˚ A ) are shown in Figure 11. We have much lesser error bars ( ± 0 . 5 ˚ A ) for the W λ due to the higher continuum flux in these wavelengths. The Ca II IR triplet emission lines are seen to be in the ratio 1 . 07 ± 0 . 09 : 1 . 15 ± 0 . 1 : 1. This nearly equal ratio is due to optically thick gas with the collision decay rates larger than the effective radiative decay rates of upper states of Ca II lines. Such environment is typically seen in many T-Tauri stars. Optical thickness along with the non-detection of forbidden [Ca II] lines above noise, implies number density of electrons to be ≈ 10 11 cm -3 (Hamann & Persson 1992). For comparison with Figure 8 of Hamann & Persson (1992), Figure 12 shows the scatter plot between the ratios of equivalent widths, W λ 8498 / W λ 8542 and W λ 8662 / W λ 8542 , of our data as well as previously published data from literature. The error bar in our new data (black squares) is ± 0 . 1. From the position of 2007 data point (red diamond) taken during quiescent phase (Aspin et al. 2008) in this scatter plot, Aspin et al. (2008, 2009) had concluded that the optical density of the region emitting Ca II IR triplet lines changed significantly between outburst and quiescent phases. But since there is only one data point from quiescent phase and it is lying within the scatter of points from ongoing outburst, it might be difficult to conclude that the change in ratios observed was actually due to V1647 Ori moving from quiescent phase to outburst phase. We could see strong correlation between the equivalent widths ( W λ ) of Ca II IR triplet lines (see Figure 13). The Pearson correlation coefficient (PCC) between both W λ 8662 and W λ 8498 , and W λ 8542 and W λ 8498 is 0.88 with a 2-tailed p value glyph[lessmuch] 0 . 0001. This implies that the fluctuations in W λ are not random statistical error. It could be due to fluctuations of continuum flux around λ 8500 ˚ A . Peak-to-</text>
<text><location><page_6><loc_8><loc_78><loc_48><loc_92></location>W λ is ∼ 5 ˚ A , which means if the flux from these lines is assumed to be constant then the continuum flux has fluctuated by a factor of ∼ 1 . 6, which in terms of the log scale of magnitude is ∼ 0 . 5. This indeed matches with peak-to-peak fluctuation in I -band magnitude during the entire period. We do not see any strong correlation between W λ of Hα line and Ca II IR triplets. However, it should be noted that the error bars in W λ of Hα are much higher than that of Ca II IR lines due to low continuum flux around λ 6563 ˚ A .</text>
<text><location><page_6><loc_8><loc_59><loc_48><loc_78></location>In 2008 October 29 spectrum, we could clearly detect P-Cygni profile in Ca II IR triplet lines (Figure 14). The strengths of absorption trough of the three lines were in the same pattern as that of T-Tauri star WL 22 (Hamann & Persson 1992), i.e. the pattern with strongest absorption in λ 8542 ˚ A , then λ 8662 ˚ A and very weak in λ 8498 ˚ A . The ratio of W λ of the blue-shifted absorption between λ 8542 ˚ A and λ 8662 ˚ A is 0.76 : 0.45 =1.69 : 1. This ratio is consistent within error bars to the 1.8 : 1 ratio of intensity from atomic transition strength of these lines. Hence, unlike the region producing emission lines, this absorption regions are optically thin. So by using optically thin assumption, we can estimate the column density of Ca II by the formula (Spitzer 1978):</text>
<formula><location><page_6><loc_8><loc_56><loc_36><loc_59></location>N CaII = 1 . 1 × 10 20 × ˚ A λ 2 1 f W λ ˚ cm -2 ,</formula>
<text><location><page_6><loc_8><loc_22><loc_48><loc_57></location>lu A where the oscillator strength f lu for the lines 8542 and 8662 ˚ A are 0.39355 and 0.21478 respectively, taken from Merle et al. (2011). Substituting the W λ , wavelength and oscillator strength for both the lines, we get the column density ( N CaII ) as 2 . 9 × 10 12 cm -2 and 3 × 10 12 cm -2 respectively. This is the column density of Ca II atoms in this small duration of outflow wind. Assuming reasonable estimates of temperature T= 2600K (disc temperature estimated by Rettig et al. (2005)) and pressure P=1 Pascal (typical pressure in solar winds), we get the fraction of ionisation using Saha's formula to be ≈ 0 . 004. Hence, dividing by this fraction we obtain the column density of Ca atoms in gas blob to be ≈ 7 . 5 × 10 14 cm -2 . Assuming solar metalicity, we obtained column density of hydrogen (H) in outflowing gas blob as ≈ 3 . 4 × 10 20 cm -2 . From the doppler shift of the absorption minima, we also obtained the wind velocity to be 313 ± 10 km s -1 (in λ 8542 ˚ A line) and 303 ± 10 km s -1 (in λ 8662 ˚ A line). We also detected a faint P-Cygni profile in λ 8542 ˚ A line on 2008 December 30, with a blue-shifted velocity of 329 ± 10 km s -1 . Apart from these two episodic events, none of our other spectra show any detectable P-Cygni profile. The episodic nature of these two winds implies they are magnetic reconnection driven winds rather than pressure driven steady winds.</text>
<text><location><page_6><loc_8><loc_6><loc_48><loc_22></location>Even though our medium resolution spectra cannot be used to study line widths, since the Ca II IR triplets are near by, we could do relative comparison of the widths of the Ca II IR triplet lines, where width is taken to be the full width half maximum (FWHM) of Gaussian fit of the continuum normalised profile. Since this quantity is the FWHM of Gaussian profile that we get after the convolution of instrument response on the actual line, it is not the FWHM of the line. However, since the lines are very close and the instrumental convolution is common, the wider line will give a wider FWHM after convolution. Figure 15 shows a scatter plot of the ratio</text>
<text><location><page_6><loc_52><loc_71><loc_92><loc_92></location>of the widths of λ 8498 ˚ A and λ 8542 ˚ A versus equivalent width of the line λ 8542 ˚ A . Most of the points lie below 1.0 in the ratio axis. Using the 'test statistic' for mean with 34 data points, we could reject null hypothesis H o : The mean of the ratio is 1, with 6 sigma confidence. This shows that the λ 8498 ˚ A line is slightly narrower than λ 8542 ˚ A line. Similar trend is seen in most of the T-Tauri stars (Hamann & Persson 1992). Apart from showing this skewness, since our spectra are of only medium resolution, we cannot quantify the narrowness of the line. This narrowness of optically thinner line λ 8498 ˚ A could be explained by either substantial opacity broadening in λ 8542 ˚ A (since 1:9 is the ratio of atomic line strength) or by lower dispersion velocity in the inner part of the region of Ca II IR emission (Hamann & Persson 1992).</text>
<text><location><page_6><loc_52><loc_42><loc_92><loc_70></location>Our period search in the equivalent width ( W λ ) of Ca II IR triplet lines found six faint periodicities in all three lines in the range of 1 - 100 days with ∼ 2 sigma confidence level in amplitude. The possible periodicities and confidence were estimated by Lomb-Scargle periodogram along with Monte Carlo simulation. The possible periods are 3.39, 8.09, 27.94, 30.8, 40.77 and 45.81 day. Since the amplitudes are only of 2 sigma confidence level, they can be confirmed only with more observations. Figure Set 16 shows the folded data of the entire four and a half year observations and the statistical significance of the amplitudes. The amplitude of the least square fitted cosine function is ∼ 1. If this periodicity is due to change in the continuum flux, the corresponding amplitude of magnitude change we expect in logarithmatic I -band magnitude is ∼ 0 . 1. This is not much above our error in magnitude estimate, so the fact that we do not see similar periodicity in I -band magnitude does not rule out the cause of change in W λ as change in continuum flux. We also do not see any corresponding significant periodicity in W λ of H α .</text>
<text><location><page_6><loc_52><loc_16><loc_92><loc_42></location>Aspin et al. (2008) took the spectrum of V1647 Ori during the quiescent phase in February 2007. The W λ of both Ca II IR triplet lines and H α were ∼ 3 . 3 times the present value. Aspin & Reipurth (2009) had used ratio of W λ of H α between 2003 outburst and quiescent phase to estimate change in accretion rate. Similarly, since the continuum flux changed by a factor of ∼ 40 between the quiescent and 2008 outburst phase, we can estimate that the change in the line flux of both set of lines is by a factor of ∼ 10. This agrees with the change in accretion rate. Thus the origin of Ca II IR triplet lines are directly connected to the accretion rate just like H α . This is in agreement with finding of tight correlation between Ca II IR line flux and accretion rate in T-Tauri stars by Muzerolle et al. (1998), which suggests the origin of these lines to be in the magnetospheric infall zone. The similar value of W λ of Ca II IR lines with that of 2003 also strengthens the claim that the accretion rate on to the star from inner disc was same during both the outbursts.</text>
<section_header_level_1><location><page_6><loc_65><loc_13><loc_79><loc_14></location>3.3.3. Oxygen lines</section_header_level_1>
<text><location><page_6><loc_52><loc_5><loc_92><loc_12></location>The most prominent oxygen line is OI 7773 ˚ A in absorption, however, weak OI 8446 ˚ A line is also detected in emission. We should be careful in interpreting the W λ of OI λ 7773 ˚ A absorption line because the profile shape of the line seems to be a combination of red-shifted emis-</text>
<text><location><page_7><loc_8><loc_59><loc_48><loc_92></location>component and more stronger blue-shifted absorption component (see Figure 7). A weak anti-correlation is seen between H α and OI λ 7773 ˚ A (see Figure 17). Correlation had PCC = 0.54, with a 2 tailed p value of 0.001. This anti-correlation in W λ of OI 7773 ˚ A and H α could be due to positive correlation between emission component of OI λ 7773 ˚ A filling in the absorption dip and H α . Since OI λ 7773 ˚ A cannot be formed in photosphere of cool stars, the absorption component is due to warm gas in the envelope or hot photosphere above disc, while the emission component might be due to the hot gas region from which H α is also being emitted. Ojha et al. (2006) reported a decreasing trend in the W λ of OI λ 7773 ˚ A from the beginning till end of the 2003 outburst which was interpreted to be possible decrease in turbulence in outer envelope during the outburst period. We do not see such a trend in 2008 outburst, but the values of W λ in 2008 outburst remain same as that during the second half of the 2003 outburst. A slight decrease of W λ in the later part of 2003 outburst observed on 2005 September 8, as reported by Ojha et al. (2006), in contrast to the increase of W λ of other lines, could be due to increase in the W λ of OI λ 7773 ˚ A emission component.</text>
<section_header_level_1><location><page_7><loc_21><loc_57><loc_36><loc_58></location>3.3.4. Forbidden lines</section_header_level_1>
<text><location><page_7><loc_8><loc_34><loc_48><loc_56></location>We detected [O I] (6300 ˚ A ) and [Fe II] (7155 ˚ A ) forbidden line emissions in V1647 Ori's spectra. The presence of [O I] λ 6300 ˚ A and [Fe II] λ 7155 ˚ A implies shock regions probably originating from jets. This combined with non-detection of [S II] (6731 ˚ A ) line above our noise level implies the shock region has temperature T ≈ 9000 -11000 K and electron number density ≈ 10 5 -10 6 cm -3 (Hamann 1994). We see significant variations in the strengths of the forbidden lines [O I] and [Fe II], however, the lines are too faint in our individual spectra to quantify statistically. During the fading stage of 2003 outburst in 2006 January, when the bright continuum flux decreased, Fedele et al. (2007) were also able to detect various strong forbidden line emissions, namely [O I] λλ 6300 ˚ A, 6363 ˚ A , [S II] λλ 6717 ˚ A, 6731 ˚ A and [Fe II] λ 7172 ˚ A .</text>
<section_header_level_1><location><page_7><loc_12><loc_31><loc_44><loc_32></location>4. IMPLICATION ON MODELS OF OUTBURST</section_header_level_1>
<text><location><page_7><loc_8><loc_5><loc_48><loc_31></location>The models which are known for FUor / EXor outbursts can be broadly classified into three. First kind of model is purely a thermal instability model, initially proposed for dwarf nova systems and was later adapted for FUors kind of outbursts (Bell & Lin 1994). The second kind of model involves a binary companion or planet, which perturbs the disc causing repeated sudden high accretion events (Bonnell & Bastien 1992; Lodato & Clarke 2004 ). The third kind involves mainly gravitational instability triggering magnetorotational instability (MRI) (Zhu et al. 2009, and references therein). Bell & Lin (1994) model (hereafter BL94) is a pure thermal instability model. In BL94, the thermal instability is triggered when the surface density at a region in disc rises above a critical density. The viscous timescales determine duration of outbursts and quiescent phase. The inner region at a radius r during outburst will deplete below the critical surface density in viscous time scale τ visc = r 2 /ν . Based on α prescription of viscosity, ν = αc s H , where</text>
<text><location><page_7><loc_52><loc_87><loc_92><loc_92></location>c s is the isothermal sound speed, H ≈ c s / Ω is the disc thickness, Ω is orbital angular velocity at radius r and α ( < 1) is a dimensionless parameter (see Figure 18). Substituting, we get a relation :</text>
<section_header_level_1><location><page_7><loc_52><loc_84><loc_68><loc_86></location>τ visc = r 2 Ω αc 2 s = 1 α Ω ( r H ) 2 .</section_header_level_1>
<text><location><page_7><loc_52><loc_56><loc_92><loc_84></location>Let v R ≈ r/τ visc ≈ ν/r be the effective inward radial velocity component of gas in inner accretion disc. Then the mass infall rate at radius R is ˙ M = -2 πR Σ v R , where Σ is the surface density of disc at that radius. Substituting v R , ν and H in above equation of ˙ M , we get ˙ M ≈ 2 π Σ αc 2 s / Ω. The time scale of transition between outburst and quiescent phases is much smaller than the viscous timescale. Hence, Σ will remain constant, Ω will also remain constant at a given R , which leaves only the parameter αc 2 s to explain the change by a factor of ∼ 10 in inner disc accretion rate to V1647 Ori between the outburst and quiescent phases. Since the square of isothermal sound speed c 2 s = R g T/µ (where R g is the gas constant, T is temperature and µ is mean molecular weight), the temperature change by a factor 10 between the phases at the trigger of thermal instability (Zhu et al. (2009), Appendix B, their Figure 14) alone will cause a net change in accretion rate by factor of 10. Hence, at least in the inner region of disc, α can change only by a multiplicative factor of order 1 to remain consistent with the observed change in accretion rate.</text>
<text><location><page_7><loc_52><loc_32><loc_92><loc_55></location>In BL94, assuming the mass infall rate to the inner disc region ˙ M in = constant , the α determines the timescales and the ratio α outburst /α quiescent is proportional to the ratio of time in quiescent phase to time in outburst phase (BL94; Table 2). Figure 19 shows the schematic of the lightcurve of V1647 Ori in optical band we know so far. The photometric magnitudes and overall SED during the quiescent phase in 2007 match with pre 2003 outburst data (Aspin et al. 2008). Even though accretion rate had fallen by a factor of 10 during quiescent phase, it was still in the order of 10 -6 M glyph[circledot] yr -1 . Based on this, Aspin et al. (2009) had suggested that the 2003 outburst might not have actually terminated in 2006. Since we do not have a good estimate of pre-outburst accretion rate, we shall consider this sudden drop in accretion rate by a factor of 10 as a drop from outburst state to quiescent phase in outburst models.</text>
<text><location><page_7><loc_52><loc_22><loc_92><loc_32></location>Let α o 1 , α o 2 and α o 3 represent the three outburst phase α values and α q 1 and α q 2 represent the two quiescent phase α values. If we assume ˙ M in = constant in BL94, from the ratio of periods, we get the following relations: α o 1 = k (22 -89) α q 1 ; α o 2 = k 21 α q 1 ; α o 3 < k 9 α q 1 ; α o 3 < k 0 . 6 α q 2 ; where k is just the proportionality constant corresponding to the constant ˙ M in .</text>
<text><location><page_7><loc_52><loc_19><loc_92><loc_22></location>We also get α o 2 = (0 . 23 -0 . 95) α o 1 ; α o 3 < 0 . 4 α o 2 ; α q 2 = 15 α q 1 .</text>
<text><location><page_7><loc_52><loc_6><loc_92><loc_19></location>This is a very huge variation in α parameter. However, our accretion estimates, during the 2003 as well as 2008 outbursts show the accretion rate of matter on to the star from inner disc was quite stable at ∼ 10 times the rate in quiescent phase. Thus the α parameter cannot be fluctuating as much as we estimated; especially α o 3 < k 0 . 6 α q 2 is impossible from the fact that viscosity has to be more in outburst phase than quiescent phase. Then the assumption ˙ M in = constant in BL94 might be wrong. An increase in ˙ M in can decrease the draining rate of inner</text>
<text><location><page_8><loc_8><loc_87><loc_48><loc_92></location>disc and can account for a longer duration of outburst period. It can also explain the slower rate of dimming in the magnitude of the V1647 Ori during its plateau stage in present outburst compared to 2003 outburst.</text>
<text><location><page_8><loc_8><loc_69><loc_48><loc_86></location>By letting ˙ M in to be a variable and substituting R limit to be the radius upto which instability extends, to constrain parameters, we compared the viscous timescale τ visc = R 2 limit /ν ≈ R 2 limit Ω /αc 2 s between 2003 and 2008 outbursts. The instability triggering temperature at the boundary has to be same for both outbursts, so the sound speed c s will be the same. Parameter α can also be taken to be same during both the outbursts based on our previous conclusion. Now the only free variable parameter which determines the timescale is R limit . Substituting Keplarian Ω ∝ R -3 2 , we finally obtain the relation for viscous timescale in terms of R to be τ ∝ R 1 2 .</text>
<formula><location><page_8><loc_8><loc_64><loc_47><loc_67></location>R limit = 20 R glyph[circledot] ( ˙ M in 3 × 10 -6 M glyph[circledot] yr -1 ) 1 3 ( M ∗ M glyph[circledot] ) 1 3 ( T eff 2000 ) -4 3 ∝ ˙ M 1 3 in</formula>
<text><location><page_8><loc_8><loc_67><loc_48><loc_70></location>limit visc limit BL94 gives the radius upto which instability extends to be :</text>
<text><location><page_8><loc_44><loc_63><loc_45><loc_64></location>˙ 1</text>
<text><location><page_8><loc_8><loc_53><loc_48><loc_64></location>Substituting this proportionality, we get τ visc ∝ M 6 in . Thus the ratios of mass infall rate from outer to inner disc during each outburst is related to the duration of outburst by the relation ˙ M in 2008 ˙ M in 2003 > ( 52 21 ) 6 ≈ 230. Thus the infall of gas from outer to inner disc during 2008 outburst is at least 230 times (2 orders) more than that during 2003 outburst.</text>
<text><location><page_8><loc_8><loc_44><loc_48><loc_53></location>Model presented by Zhu et al. (2010) includes an MRI instability contribution to viscosity parameter if the temperature of the disc goes above MRI triggering temperature ( T M ) and also includes an effective viscosity contribution from gravitational instability beyond the radius given by Toomre's instability parameter Q. The relation between R limit and ˙ M in this model is R limit ∝ ˙ M 2 9</text>
<formula><location><page_8><loc_8><loc_41><loc_47><loc_44></location>Thus, τ visc ∝ ˙ M 1 9 in , and hence ˙ M in 2008 ˙ M in > ( 52 21 ) 9 ≈ 3500.</formula>
<text><location><page_8><loc_8><loc_28><loc_48><loc_42></location>2003 Therefore, the infall of gas from outer to inner disc during 2008 outburst is at least 3500 times (3 orders) more than that during 2003 outburst. This estimate is one order more than BL94. It should be kept in mind that the viscosity timescale gives only order of magnitude estimate of the duration of outburst. For a comparison of actual simulated duration of outburst and viscous timescale see Table 1 in Zhu et al. (2010). If the present outburst continues for a larger period, ˙ M in 2008 ˙ M in 2003 ratio will further</text>
<text><location><page_8><loc_8><loc_20><loc_48><loc_28></location>increase. Since we have an upper limit in ˙ M in for FUors, the increased ratio could only be explained as a dip in mass inflow in 2003. For example, a gap in disc could have resulted in sudden ending of 2003 outburst. This gap or low density region has to be near the typical R limit predicted by each model, i.e. ∼ 1 AU .</text>
<text><location><page_8><loc_8><loc_6><loc_48><loc_19></location>To estimate the change in photometric magnitudes between 2003 and 2008 outburst phase due to predicted change in radius R limit , we modelled a disc with temperature profile given by outburst accretion rate inside R limit and quiescent accretion rate outside R limit . The magnitude variations in optical I and NIR J bands were found to be less than 1 mag for variation of R limit by a factor of 6. Mosoni et al. (2013) reported an increase in visibility of resolved interferometric study of V1647 Ori using VLTI/MIDI observations in 8-13 µ m range during</text>
<text><location><page_8><loc_52><loc_81><loc_92><loc_92></location>the early stage of fading in 2003 outburst (between 2005 March and 2005 September). Apart from the possible scenarios discussed by Mosoni et al. (2013), it could also be explained by the relative increase in contribution in total flux from the extended outburst disc when the central star's accretion slowed down. A similar VLTI/MIDI visibility study of the ongoing 2008 outburst will give more input to constrain R limit and outburst models.</text>
<text><location><page_8><loc_52><loc_65><loc_92><loc_81></location>Thus, we conclude that a pure thermal instability alone cannot explain the varying timescales of outbursts occurring in V1647 Ori. As proposed for other short rise timescale FUors, V1647 Ori can also be explained only by an outside-in triggering of the instability from outer radius (Bell & Lin 1994). The change in inflow of material from outer to inner disc could be due to many possibilities like MRI, gravitational instability (GI) or planet perturbation. The smooth surface density assumptions of disc also might not be a good model in light of detection of clump in the disc at 0.27 AU and disappearance of it in second outburst.</text>
<text><location><page_8><loc_52><loc_38><loc_92><loc_65></location>Our observations detected a variety of episodic events like sudden short duration winds with hydrogen column density ≈ 3 . 4 × 10 20 cm -2 , fluctuations in H α flux, short timescale variation in continuum flux etc. The short timescale variation in continuum flux could be explained by the convections in the inner disc as suggested by Zhu et al. (2009) for their model of FU Orionis disc. The variations in Hα flux could have origin in some magnetic phenomena in the accretion funnel. The episodic wind events, [Fe II] λ 7155 and [OI] λ 6300 could be originating from jets or disc/stellar winds region. If we compare between 2008 and 2003 outbursts, the accretion rate on to the star from inner disc, extinction in NIR colorcolor diagram, outburst magnitude and spectral signatures in optical are the same. The main difference between 2008 compared to 2003 is the larger duration of outburst phase, 6 times slower dimming rate in optical during its 'plateau' stage and the change in circumstellar gas distribution revealed by morphological change in nebula's illumination.</text>
<section_header_level_1><location><page_8><loc_66><loc_36><loc_78><loc_37></location>5. CONCLUSIONS</section_header_level_1>
<text><location><page_8><loc_52><loc_31><loc_92><loc_35></location>We have carried out four and a half years of continuous monitoring of V1647 Ori in its second outburst phase starting from 2008. Following are our main conclusions:</text>
<unordered_list>
<list_item><location><page_8><loc_54><loc_21><loc_92><loc_30></location>1. V1647 Ori is still in outburst 'plateau' stage, at similar magnitude to 2003 outburst in optical and NIR bands. It is undergoing a slow dimming at a rate of 0.04 mag yr -1 , which is 6 times slower than the rate during 2003 outburst. The magnitude shows significant short timescale ( ∼ 1 day) variations.</list_item>
<list_item><location><page_8><loc_54><loc_14><loc_92><loc_19></location>2. Morphological studies on illumination of nebula show a consistent change in the circumstellar gas distribution between 2008, 2003 and 1966 outbursts.</list_item>
<list_item><location><page_8><loc_54><loc_5><loc_92><loc_13></location>3. P-Cygni profiles in H α emission lines show outflowing wind velocities of ∼ 350 km s -1 . Apart from the continuous wind we also detected twice short duration episodic winds driven by magnetic reconnection events, with H column density ≈ 3 . 4 × 10 20 cm -2 from P-Cygni profiles in Ca II IR triplet lines</list_item>
</unordered_list>
<text><location><page_9><loc_12><loc_87><loc_48><loc_92></location>in 2008 October and December. From Ca II IR triplet and H α line strengths, the accretion rate was found to be same as that during the 2003 outburst and is ∼ 10 times more than quiescent phase.</text>
<unordered_list>
<list_item><location><page_9><loc_10><loc_83><loc_48><loc_85></location>4. We could not detect the 56 day periodicity seen in 2003 outburst.</list_item>
<list_item><location><page_9><loc_10><loc_76><loc_48><loc_82></location>5. Detection of the forbidden [OI] λ 6300 and [Fe II] λ 7155 lines implies shock regions of T ≈ 9000 -11000 K and n e ≈ 10 5 -10 6 cm -3 , probably originating from jets.</list_item>
<list_item><location><page_9><loc_10><loc_66><loc_48><loc_75></location>6. Timescales of outburst history of V1647 Ori cannot be explained by a simple thermal instability model by Bell & Lin (1994) alone. To explain the large change in accretion rate from outer to inner disc between last two outbursts we require more comprehensive models which includes contribution from MRI, GI and planetary perturbations. From</list_item>
</unordered_list>
<text><location><page_9><loc_56><loc_87><loc_92><loc_92></location>the framework of instability models we conclude that the sudden ending of 2003 outburst could be due to a gap or low density region in inner ( ∼ 1 AU) disc.</text>
<text><location><page_9><loc_52><loc_66><loc_92><loc_81></location>We thank the anonymous referee for giving us invaluable comments and suggestions that improved the content of the paper. The authors thank the staff of HCT, operated by Indian Institute of Astrophysics, Bangalore and IGO at Girawali, operated by Inter-University Centre for Astronomy and Astrophysics, Pune for their assistance and support during observations. It is a pleasure to thank J. S. Joshi and all the members of the Infrared Astronomy Group of TIFR for their support during the TIRCAM2 campaign. All the plots were generated using the 2D graphics environment Matplotlib (Hunter 2007).</text>
<section_header_level_1><location><page_9><loc_45><loc_64><loc_55><loc_65></location>REFERENCES</section_header_level_1>
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<figure>
<location><page_10><loc_13><loc_18><loc_87><loc_50></location>
</figure>
<figure>
<location><page_11><loc_10><loc_17><loc_65><loc_53></location>
<caption>Fig. 2.Color-composite image of McNeil's nebula (V1647 Ori) region taken from IGO ( V : blue, R : green, I : red) on 2010 February 13. FoV is ∼ 10 × 10 arcmin 2 . North is up and east is to the left-hand side. Stars marked as A, B, C and D are the secondary standard stars used for magnitude calibration. The location of V1647 Ori is marked at the center by two perpendicular lines. Region C, overlapping Herbig-Haro object HH 22A, is marked together. A knot in south-western section (region B) of nebula is also marked. At 400 pc distance, the scale 1 ' corresponds to 24000 AU.</caption>
</figure>
<figure>
<location><page_12><loc_9><loc_9><loc_54><loc_61></location>
<caption>Fig. 3.Magnitude variation of V1647 Ori in the I, R and V -band from September 2008 to March 2013. Typical photometric error bar is given at the left bottom corner. The filled circles are from HCT and filled squares are from IGO measurements. The rate of dimming in I, R and V -bands are 0 . 036 ± 0 . 007 mag yr -1 , 0 . 038 ± 0 . 007 mag yr -1 and 0 . 021 ± 0 . 009 mag yr -1 respectively.</caption>
</figure>
<figure>
<location><page_13><loc_9><loc_9><loc_54><loc_61></location>
<caption>Fig. 4.Magnitude variation of region C, illuminated by V1647 Ori, in the I, R and V -band from September 2008 to March 2013. Typical photometric error bar is given at the left bottom corner. The filled circles are from HCT and filled squares are from IGO measurements. The rate of dimming in I, R and V -bands are 0 . 059 ± 0 . 005 mag yr -1 , 0 . 051 ± 0 . 005 mag yr -1 and 0 . 060 ± 0 . 005 mag yr -1 respectively.</caption>
</figure>
<figure>
<location><page_14><loc_28><loc_34><loc_72><loc_67></location>
</figure>
<figure>
<location><page_15><loc_10><loc_10><loc_65><loc_59></location>
<caption>Fig. 6.HCT R -band image of 2011 minus 2004, after normalising with respect to the brightness of V1647 Ori. The images were chosen from the nights with same atmospheric seeing and aligned using other field stars in the FoV. The bright portions show the regions which were relatively brighter in 2011 and dark portions show the regions which were relatively brighter in 2004. For example, region C shown in upper box is brighter in 2011. Also note the change in illumination of south-western knot region B marked by lower box in the nebula. North is up and east is to the left-hand side.</caption>
</figure>
<figure>
<location><page_16><loc_9><loc_9><loc_89><loc_32></location>
<caption>Fig. 7.The spectral lines present in the spectrum of V1647 Ori are labelled above. To improve the S/N ratio, the normalised spectrum was obtained by weighted averaging of 33 HCT spectra taken over the outburst period 2008 September to 2013 March, each with an average exposure time of 40 minutes. The spectra are not corrected for atmospheric absorption lines. The absorption lines which are not labelled are atmospheric lines. H α and OI λ 7773 line profiles are shown more clearly in insets.</caption>
</figure>
<figure>
<location><page_17><loc_9><loc_9><loc_52><loc_45></location>
<caption>Fig. 8.The variations of Hα profiles during our four and a half year observations. P-Cygni profiles were more prominent in the early part of the outburst in 2008. A Gaussian is fitted to the right wing of the profile in red color and the difference of that Gaussian fit to actual spectra is plotted in green color to see the absorption component clearly. Figure 8 with 70 other plots of remaining nights are available in the online version of the Journal.</caption>
</figure>
<figure>
<location><page_18><loc_9><loc_9><loc_92><loc_37></location>
<caption>Fig. 9.The velocity of expanding wind from the blue-shifted absorption minima in Hα P-Cygni profile. The filled circles are from HCT, and grey filled squares are from IGO measurements. The error bar on the bottom right corner shows the typical ± 39 km/sec error estimated for data points.</caption>
</figure>
<figure>
<location><page_19><loc_9><loc_9><loc_92><loc_37></location>
<caption>Fig. 10.The variation in equivalent width of Hα emission. The filled circles are from HCT, and filled grey squares are from IGO measurements. Each data point has an error bar of ∼ ± 3 ˚ A . This error bar is shown at the right bottom corner.</caption>
</figure>
<text><location><page_19><loc_8><loc_4><loc_9><loc_5></location>.</text>
<figure>
<location><page_20><loc_9><loc_9><loc_92><loc_49></location>
<caption>Fig. 11.The variation in equivalent widths of Ca II IR triplet lines (8498, 8542 and 8662 ˚ A ) during the outburst period 2008 September to 2013 March. All data points are from HCT measurement and each point has an error bar of ∼ ± 0 . 5 ˚ A . This error bar is shown at the right bottom corner.</caption>
</figure>
<text><location><page_20><loc_8><loc_3><loc_64><loc_4></location>Due to limited spectral range in IGO grism, Ca II triplet lines were not observed from IGO.</text>
<figure>
<location><page_21><loc_9><loc_9><loc_53><loc_43></location>
<caption>Fig. 12.Ratio of Ca II IR triplet lines' equivalent widths, W λ 8498 / W λ 8542 versus W λ 8662 / W λ 8542 , of our data as well as previously published data from literature. 2003 outburst points are shown as circles (Walter et al. 2004; Ojha et al. 2006), 2008 outburst points are shown as squares (Kun 2008; Aspin et al. 2009; Aspin 2011, and this work) and 2007 quiescent phase point is shown as diamond (Aspin et al. 2008). The typical error bar on our new data (black squares) is ∼ ± 0 . 1.</caption>
</figure>
<figure>
<location><page_22><loc_9><loc_9><loc_61><loc_68></location>
<caption>Fig. 13.Strong correlation between the equivalent widths of Ca II IR triplet lines. Typical error bar is given at the right bottom corner. The Pearson correlation coefficient (PCC) between both W λ 8662 and W λ 8498 , and W λ 8542 and W λ 8498 is 0.88 with a 2-tailed p value glyph[lessmuch] 0 . 0001.</caption>
</figure>
<figure>
<location><page_23><loc_9><loc_9><loc_52><loc_61></location>
<caption>Fig. 14.The spectrum of V1647 Ori taken on 2008 October 29 showing clear P-Cygni profile in Ca II IR triplet lines. Similar, but fainter profile was once more detected in 2008 December 30. None of the other nights' spectra showed this profile. For comparison, available nearby nights' spectra are also plotted.</caption>
</figure>
<figure>
<location><page_24><loc_8><loc_9><loc_52><loc_32></location>
<caption>Fig. 15.Scatter plot of the ratio of the widths of 8498 and 8542 ˚ A versus equivalent width of the line 8542 ˚ A . Most of the points lie below 1.0 in Y-axis. Box and whisker plot of the distribution is also ploted on the right side. This shows that the 8498 ˚ A line is slightly narrower than 8542 ˚ A line.</caption>
</figure>
<figure>
<location><page_25><loc_9><loc_9><loc_39><loc_49></location>
<caption>Fig. 16.Folded phase plot of the W λ of Ca II IR triplet lines λ 8498, λ 8542 and λ 8662 (in ˚ A ), and I -band magnitude. The folding is done over the entire four and a half years of data. The red, black, green, pink and blue circles correspond to data of 2008, 2009, 2010, 2011, and 2012 winter observations respectively. The amplitudes (in ˚ A ) of the three lines in each folded plot are as follows. For a period of 3.39 days:- 1.26 ± 0.69, 1.22 ± 0.75, 1.03 ± 0.67; For a period of 8.09 days:- 1.13 ± 0.70, 1.33 ± 0.71, 1.17 ± 0.65; For a period of 27.94 days:- 1.13 ± 0.72, 1.11 ± 0.79, 1.14 ± 0.67; For a period of 30.8 days:- 1.26 ± 0.61, 1.25 ± 0.63, 0.98 ± 0.58; For a period of 40.77 days:1.26 ± 0.65, 1.42 ± 0.58, 1.18 ± 0.59; For a period of 45.81 days:- 0.95 ± 0.76, 1.29 ± 0.74, 1.10 ± 0.68. Figures 16.2 - 16.6 are available in the online version of the Journal.</caption>
</figure>
<figure>
<location><page_26><loc_9><loc_9><loc_54><loc_33></location>
<caption>Fig. 17.Correlation between equivalent width of H α and OI λ 7773 ˚ A . Typical error bar is given at the right bottom corner. PCC is 0.54 with a 2-tailed p value of 0.001. The weak anti-correlation could be due to a positive correlation between the H α and red-shifted emission component which is filling the absorption component in OI λ 7773 ˚ A profile. Bootstrap analysis gave 95% confidence range of PCC to be [0.29, 0.72].</caption>
</figure>
<figure>
<location><page_27><loc_10><loc_10><loc_47><loc_26></location>
<caption>Fig. 18.Cross-section of an α disc is shown above. R is the radial distance from the star and H is the thickness of the disc, which flares up as the radius R increases. R limit is the radius upto which the outburst extends. We are looking into the system at ∼ 60 · along the dashed line drawn in the figure. In α disc model, the viscosity is due to large turbulent eddies. The speed of eddies is upperbounded by the velocity of sound ( c s ) because any supersonic flow will get dissipated by shock. The size of eddies is also upper bounded by the thickness ( H ) of disc. Thus taking α to be a free parameter < 1 we get the viscosity in the disc as ν = αc s H . The orbital velocity is taken to be Keplarian in our problem.</caption>
</figure>
<figure>
<location><page_28><loc_12><loc_11><loc_91><loc_29></location>
<caption>Fig. 19.Optical light curve history of V1647 Ori. The duration of each outburst and quiescent period is marked in units of months. The X-axis of the image is not drawn to scale.</caption>
</figure>
<paragraph><location><page_29><loc_47><loc_90><loc_53><loc_90></location>TABLE 1</paragraph>
<table>
<location><page_29><loc_25><loc_76><loc_75><loc_88></location>
<caption>Observation log of the photometric and spectroscopic observations</caption>
</table>
<text><location><page_29><loc_25><loc_73><loc_74><loc_76></location>Note . - Table 1 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.</text>
<unordered_list>
<list_item><location><page_29><loc_26><loc_72><loc_62><loc_73></location>† Measured average FWHM. This is a measure of the seeing.</list_item>
<list_item><location><page_29><loc_25><loc_70><loc_58><loc_71></location>†† Observed from IGO, all other nights are from HCT.</list_item>
</unordered_list>
<table>
<location><page_29><loc_30><loc_50><loc_69><loc_64></location>
<caption>TABLE 2 Optical V RI photometry of V1647 Ori and region C</caption>
</table>
<text><location><page_29><loc_30><loc_47><loc_69><loc_50></location>Note . - Table 2 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.</text>
<text><location><page_29><loc_30><loc_45><loc_63><loc_46></location>†† Observed from IGO, all other nights are from HCT.</text>
<table>
<location><page_29><loc_34><loc_20><loc_65><loc_39></location>
<caption>TABLE 3 NIR JHK photometry of V1647 Ori</caption>
</table>
<text><location><page_29><loc_35><loc_17><loc_65><loc_20></location>Note . - Estimated error in magnitude is ≤ ± 0.1 ( K ) and ≤ ± 0.05 ( H and J ).</text>
<table>
<location><page_30><loc_27><loc_79><loc_73><loc_87></location>
<caption>TABLE 4 Equivalent widths (in ˚ A ) of optical lines in V1647 Ori</caption>
</table>
<text><location><page_30><loc_27><loc_75><loc_72><loc_78></location>Note . -Table 4 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.</text>
</document>
[
{
"title": "ABSTRACT",
"content": "We present a detailed study of McNeil's nebula (V1647 Ori) in its ongoing outburst phase starting from September 2008 to March 2013. Our 124 nights of photometric observations were carried out in optical V , R , I and near-infrared (NIR) J , H , K bands, and 59 nights of medium resolution spectroscopic observations were done in 5200 - 9000 ˚ A wavelength range. All observations were carried out with 2-m Himalayan Chandra Telescope (HCT) and 2-m IUCAA Girawali Telescope. Our observations show that over last four and a half years, V1647 Ori and the region C near Herbig-Haro object, HH 22A, have been undergoing a slow dimming at a rate of ∼ 0 . 04 mag yr -1 and ∼ 0 . 05 mag yr -1 respectively in R -band, which is 6 times slower than the rate during similar stage of V1647 Ori in 2003 outburst. We detected change in flux distribution over the reflection nebula implying changes in circumstellar matter distribution between 2003 and 2008 outbursts. Apart from steady wind of velocity ∼ 350 km s -1 we detected two episodic magnetic reconnection driven winds. Forbidden [O I] 6300 ˚ A and [Fe II] 7155 ˚ A lines were also detected implying shock regions probably from jets. We tried to explain the outburst timescales of V1647 Ori using the standard models of FUors kind of outburst and found that pure thermal instability models like Bell & Lin (1994) cannot explain the variations in timescales. In the framework of various instability models we conclude that one possible reason for sudden ending of 2003 outburst in 2005 November was due to a low density region or gap in the inner region ( ∼ 1 AU) of the disc. Subject headings: stars: formation, stars: pre-main-sequence, stars: outflows, stars: variables: general, stars: individual: (V1647 Ori), ISM: individual: (McNeil's nebula)",
"pages": [
1
]
},
{
"title": "J. P. Ninan, D. K. Ojha",
"content": "Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India",
"pages": [
1
]
},
{
"title": "B. C. Bhatt",
"content": "Indian Institute of Astrophysics, Koramangala, Bangalore 560 034, India",
"pages": [
1
]
},
{
"title": "S. K. Ghosh",
"content": "National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune 411 007, India",
"pages": [
1
]
},
{
"title": "V. Mohan",
"content": "Inter-University Centre for Astronomy and Astrophysics, Pune 411 007, India",
"pages": [
1
]
},
{
"title": "K. K. Mallick",
"content": "Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India",
"pages": [
1
]
},
{
"title": "M. Tamura",
"content": "National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan and",
"pages": [
1
]
},
{
"title": "Th. Henning",
"content": "Max-Planck-Institute for Astronomy, Konigstuhl 17, 69117 Heidelberg, Germany Draft version September 5, 2021",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "When low-mass stars like our Sun are born, they slowly accrete gas from the collapsing cloud through an accretion disc. Collimated outflows are also typically seen in most of these objects. The discontinuous knots seen in outflows from these objects, and the mismatch of accretion rate between envelope to disc and disc to star (known as 'Luminosity Problem') in young stellar ob- jects (YSOs), all hint to an episodic nature of accretion instead of an ideal steady inflow (Kenyon et al. 1990; Evans et al. 2009; Ioannidis & Froebrich 2012). The other important feature seen in these objects is the outburst. Rare outbursts that we see among these YSOs are found to be correlated with an order of magnitude increase in mass infall rate and they could be the episodic accretion events required to explain the outflow discontinuities and 'Luminosity Problem'. These outbursts are empirically classified as FUors (decades long outbursts with 4-5 magnitude change in optical) and EXors (few months-years long outbursts with 2-3 magnitude change in optical) (Herbig 1977; Hartmann 1998; Hartmann & Kenyon 1996). Due to the short timescales of outbursts in comparison to millions of years timescale of star formation, these events are extremely rare and only less than a dozen confirmed FUor outbursts have been detected so far. From their frequency of outburst it is estimated that every low-mass YSO should go through these outbursts at least 50 times in its protostellar phase (Scholz et al. 2013). Regarding the discontinuous knots seen in outflows, it should be noted that the timescales between discontinuities were estimated to be of the order of 10 3 years by Ioannidis & Froebrich (2012) and the timescales between FUor outbursts in a single star were estimated to be of the order of 10 4 years by Scholz et al. (2013). So the discontinuities could be due to some other shorter timescale variations in accretion rate rather than classical FUors. But as Scholz et al. (2013) pointed out, we do not have a good estimate of FUors' timescales in the early Class I stage. Hence we cannot rule out the possibility that discontinuities in outflows are created during FUors events. One such object which was extensively studied recently in literature is V1647 Ori (V1647 Orionis), 400 pc away in the L1630 dark cloud of Orion. It underwent a sudden outburst of ∼ 5 mag in optical in 2003 (McNeil 2004; Brice˜no et al. 2004) and illuminated a reflection nebula, now named as McNeil's nebula after its discoverer Jay McNeil. Reipurth & Aspin (2004) reported 3 mag increase in near-infrared (NIR) and Andrews et al. (2004) reported 25 times increase in 12 µm flux and no flux change in submillimeter of V1647 Ori during the outburst. Kastner et al. (2004) reported a 50 times increase in X-ray flux of V1647 Ori during the outburst, and noted that the derived temperature of the plasma is too high for accretion alone to explain and hinted that magnetic reconnection events might be heating up the plasma. Based on the upper limit on radio continuum emission from McNeil's nebula at 1272 MHz from Giant Metrewave Radio Telescope (GMRT), India, Vig et al. (2006) constrained the extent of HII region corresponding to a temperature glyph[greaterorsimilar] 2500 K to be glyph[lessorsimilar] 26 AU. Spectroscopic studies showed strong H α and Ca II IR triplet lines in emission (Brice˜no et al. 2004; Ojha et al. 2006). In NIR region, strong CO bandheads (2.29 µm ) and Br γ line (2.16 µm ; implying strong accretion) were detected in emission (Reipurth & Aspin 2004; Vacca et al. 2004). The strong P-Cygni profile in H α emission indicated wind-velocity ranging from 600 - 300 km s -1 (Ojha et al. 2006; Vacca et al. 2004). ' Abrah'am et al. (2006) carried out AU scale observations using Very Large Telescope Interferometer/ Mid-Infrared interferometric Instrument (VLTI/MIDI). By fitting both spectral energy distribution (SED) and visibility values they deduced a moderately flaring disc with temperature profile T ∼ r -0 . 53 (T(1AU)=680K) and mass ∼ 0 . 05 M glyph[circledot] , with inner radius of 7 R glyph[circledot] (0.03 AU) and outer radius of 100 AU. This temperature profile is shallower than the T ∼ r -0 . 75 canonical model (Pringle 1981). They also reported that the mid-infrared emitting region at 10 µm has a size of ∼ 7 AU. Rettig et al. (2005) used the CO lines in infrared (IR) to measure the temperature of the inner accretion disc region which was estimated to be T ≈ 2500 K. Ojha et al. (2006) and K'osp'al et al. (2005) reported a sudden dimming and termination of the 2003 outburst in November 2005. Thus, 2003 outburst lasted for a total of ∼ 2 years and V1647 Ori returned to its pre-outburst phase in early 2006. Acosta-Pulido et al. (2007) estimated the inclination angle of disc to be 61 · and also estimated the accretion rate to be 5 × 10 -6 M glyph[circledot] yr -1 during outburst and 5 × 10 -7 M glyph[circledot] yr -1 in 2006 quiescent state. Aspin et al. (2006) reported that ∼ 37 years prior to 2003 outburst, i.e. in 1966, V1647 Ori had undergone a similar magnitude of outburst, lasting for a duration somewhere between 5 to 20 months. Contrary to expected decades long quiescense, V1647 Ori underwent a second outburst in 2008 just after spending two years in quiescent state (Aspin et al. 2009). It brightened up to the same magnitude and had almost identical spectral features in optical and NIR as the first outburst. One striking difference was that the strong CO bandhead emission at 2.29 µm was absent in second outburst (Aspin 2011). The X-ray flux with plasma temperature of 2-6 keV during both outbursts was postulated to be due to magnetic reconnection events in the disc-star magnetic field interaction (Teets et al. 2011, and references therein). Hamaguchi et al. (2012) normalised and combined both outbursts' data in X-ray and detected one day periodicity in light curve, which they modeled with two accretion hot spots on the top and bottom hemispheres of the star rotating with one day period and inclination of 68 · . Figure 1 shows the overall cross-section picture of the surroundings of V1647 Ori we know so far. V1647 Ori provides a unique opportunity to understand the physical processes undergone in FUors or EXors kind of outbursts. The short time scale behaviors of this object make it possible for us to make a detailed study of the object. In literature there exists mainly three kinds of model for explaining the outburst phenomena (see Section 4). The differences between these models are all in the inner region of disc ( < 1 AU), and optical and NIR are the right wavelength regime to probe this region of the disc. Detailed understanding of V1647 Ori will thus provide us a laboratory to check our understanding of various instabilities like thermal, gravitational and magnetorotational in proto-planetary disc around young low-mass stars. We have carried out continuous observations for more than four and a half years (2008 - 2013) of V1647 Ori in optical and NIR wavelengths for detailed study of its dynamics during outburst and post-outburst stages of the second outburst. This data combined with previous outbursts' provide us more insight on the nature of outburst and also constrain the existing physical models. In this paper, we present the results of our long-term optical and NIR photometric and spectroscopic observations of the outburst source and associated McNeil's nebula. In Section 2 we describe the observational details and the data reduction procedures. In Section 3 we present our new findings and results from observations. In Section 4 we analyse the ability of each existing physical models to explain V1647 Ori's outburst history. Finally, in Section 5 we summarise our main results.",
"pages": [
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},
{
"title": "2.1. Optical Photometry",
"content": "Our long-term optical observations span from 2008 September 14 to 2013 March 11 and were carried out with 2-m Himalayan Chandra Telescope (HCT) at Indian Astronomical Observatory, Hanle (Ladakh), India and with 2-m Inter-University Centre for Astronomy and Astrophysics (IUCAA) Girawali Telescope at IUCAA Girawali Observatory (IGO), Girawali (Pune), India. At HCT, for photometry central 2K × 2K section of Himalaya Faint Object Spectrograph & Camera (HFOSC) CCD, which has a pixel scale of 0.296 arcsec was used, giving us a field of view (FoV) of ∼ 10 × 10 arcmin 2 . At IGO, 2K × 2K IUCAA Faint Object Spectrograph & Camera (IFOSC) CCD was used which also has a similar pixel scale of 0.3 arcsec, giving us a FoV of ∼ 10 × 10 arcmin 2 . Further details of the instruments and telescopes are available at http://www.iiap.res.in/iao/hfosc.html and http://www.iucaa.ernet.in/ itp/igoweb/igo tele and inst.htm. Out of our total observation of 110 nights, 84 nights were observed from HCT and 26 nights from IGO. The V1647 Ori's field ( α, δ ) 2000 = (05 h 46 m 13 s . 135 , -00 · 06 ' 04 '' . 82) was observed in standard V RI Bessel filters. Nearby Landolt's standard star fields (Landolt 1992) were also observed for magnitude calibration and for solving color transformation equation coefficients of each night. For nights which do not have standard star observations, we identified six stars in the object's frame whose magnitudes remain constant throughout. Four of them were used as secondary standards (see Figure 2) and other two were used to check consistency and error. Apart from object frames, bias and sky flats were also taken in each night for the basic data reduction. For fringe removal in IGO I -band images, blank sky frames were also taken. The log of photometric observations is given in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. Blank sky images in I -band were used to create fringe templates by MKFRINGECOR task in IRAF 1 , which were later used to subtract the fringes that appeared in I -band images taken from IGO. Data reduction was done with the semi-automatic pipeline written in PyRAF 2 and IRAF CL scripts. Standard photometric data reduction steps like bias-subtraction and median flat-fielding were done for all the nights. Point-spread function (PSF) photometry (using PSF & ALLSTAR tasks in DAOPHOT package of IRAF) on V1647 Ori was not able to fully remove the nebular contamination. We found a strong correlation between fluctuation in magnitude of V1647 Ori and fluctuation in atmospheric seeing condition. This is because the contamination of flux from nebula into V1647 Ori's aperture was a function of atmospheric seeing. So we generated a set of images by convolving each frame with 2-D Gaussian kernel of different standard deviation (using IMFILTER.GAUSS task in IRAF) for sim- ulating different atmospheric seeing conditions. We then recalculated the magnitudes by DAOPHOT, PSF and ALLSTAR algorithms of IRAF for various atmospheric seeing conditions. The differential magnitudes obtained from each frame's set was interpolated to obtain magnitude at an atmospheric seeing of 1.18 arcsec, which was taken to be the seeing to be interpolated to, for all nights and it was chosen to minimise interpolation error. This method reduced our error bars in magnitude by a factor of 2. Apart from the Gaussian convolution step, the PSF photometry steps were all same as Ojha et al. (2006). Magnitudes of the whole nebula and other objects in the nebula like region C (near HH 22A) and region B defined by Brice˜no et al. (2004) in their figure 2 (also see Figure 2) were measured by simple aperture photometry with an aperture radius of 80 arcsec for nebula and 12 arcsec for the regions C and B. For obtaining the flux, the aperture of the objects like regions C and B were centered at the objects itself.",
"pages": [
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},
{
"title": "2.2. Optical Spectroscopy",
"content": "Our long-term spectroscopic observations also span the same duration as that of photometric observations (2008 September to 2013 March) using both 2-m HCT and 2-m IGO. The full 2K × 4K section of HFOSC CCD spectrograph was used in HCT observations and 2K × 2K IFOSC CCD spectrograph was used for IGO observations. Spectroscopic observations were carried out on 35 nights from HCT and 24 nights from IGO, thus totalling to 59 nights of V1647 Ori's spectroscopic observations. The log of spectroscopic observations is listed in Table 1. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. In order to detect the prominent Hα λ 6563 ˚ A and Ca II IR triplet lines ( λ 8498, λ 8542, λ 8662 ˚ A ), we observed in the effective wavelength range of 5200 -9000 ˚ A using grism 8 (center wavelength 7200 ˚ A ) and grism 7 (center wavelength 5300 ˚ A ). The spectral resolution obtained for grism 8 and 7 with 150 micron slit at IGO and 167 micron slit at HCT was ∼ 7 ˚ A . Nebulosity contamination in spectrum of V1647 Ori was minimised by keeping the slit in east-west orientation. Standard IRAF tasks like APALL and APSUM were used for spectral reduction. Wavelength calibration was carried out using the FeNe, FeAr and HeCu lamps. For final measurement of equivalent width the extracted 1-D spectra were normalised with respect to continuum. For spectroscopic data reduction of HCT and IGO data, semi-automated pipeline written in PyRAF was used.",
"pages": [
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},
{
"title": "2.3. Near-Infrared Photometry",
"content": "Along with optical monitoring we also carried out photometric monitoring in JHK bands using the HCT NIR camera (NIRCAM) and TIFR NIR Imaging CameraII (TIRCAM2). NIRCAM has a 512 × 512 Mercury Cadmium Telluride (HgCdTe) array, with a pixel size of 18 µm , which gives a FoV of 3 . 6 × 3 . 6 arcmin 2 with HCT. Filters used for observation were J ( λ center = 1.28 µm , ∆ λ = 0.28 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.33 µm ) and K ( λ center = 2.22 µm , ∆ λ = 0.38 µm ). Further details of the instrument are available at http://www.iiap.res.in/iao/nir.html. TIRCAM2 has a 512 × 512 Indium Antimonide (InSb) array with a pixel size of 27 µm . We observed McNeil's nebula during the engineering run of TIRCAM2 at 2-m IGO and 1.2-m Physical Research Laboratory (PRL) Mount Abu telescope. Filters used for observation were J ( λ center = 1.20 µm , ∆ λ = 0.36 µm ), H ( λ center = 1.66 µm , ∆ λ = 0.30 µm ) and K ( λ center = 2.19 µm , ∆ λ = 0.40 µm ). Further details of the instrument are available in Naik et al. (2012). We have a total of 14 nights of NIR photometric observations, with the first set of data taken during the quiescent phase in 2007, i.e. before the 2008 outburst. Observations of V1647 Ori were carried out by taking several sets of exposures; each set contains exposure with the telescope pointing at five different dithered positions. The master sky frame for sky-subtraction was generated by median combining all the dithered object frames. Data reduction and final photometry were done using standard IRAF aperture photometric tasks. To be consistent with magnitude estimates by Ojha et al. (2006), for flux calibration we used an aperture ∼ 7 arcsec, and for background sky estimation we used an annulus with an inner radius of ∼ 50 '' and width ∼ 5 '' . For instrumental to apparent magnitude calibration, we observed standard stars around AS13, AS9 and HD225023 fields (Hunt et al 1998) on the same night with similar airmass as V1647 Ori observations. On 2011 December 6, standard stars were not observed, hence we used the magnitude measured on other nights of the nearby star (2MASS J05461162-0006279) for photometric calibration.",
"pages": [
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},
{
"title": "3.1. Photometric Results",
"content": "Figure 2 shows the three-color composite image ( V : blue, R : green, I : red) of the McNeil's nebula field (FoV ∼ 10 × 10 arcmin 2 ) obtained from IGO on 2010 February 13. Secondary standard stars used for flux calibration are marked as A, B, C and D. The outburst source V1647 Ori, illuminating the nebula, is marked at the center. The region C, possibly unrelated to Herbig-Haro object, HH 22A, which is illuminated by V1647 Ori is also marked. V1647 Ori had already reached its peak outburst phase before our first optical observation in September 2008. Its light curve steadily continued in peak outburst flux ('high plateau') phase even until our last observation taken in March 2013. However, our longterm continuous monitoring from 2008 September 14 to 2013 March 11 shows a slow but steady linear declining trend in the brightness of the source and nebula (Ninan et al. 2012). The linear slopes and the error in estimates of slopes were obtained by simple linear regression by ordinary least square fitting. V , R and I magnitudes of V1647 Ori and of region C, which is illuminated by the V1647 Ori from its face-on angle of the disc, are listed in Table 2. Only a portion of the table is provided here. The complete table is available in electronic form as part of the online material. Light curves of V1647 Ori in I and R -bands clearly show a steady dimming (see Figure 3). During the last four and a half years of its second outburst, the brightness in I and R bands have decreased by ∼ 0 . 2 mag. The rate of decline in magnitude of V1647 Ori is 0.036 ± 0 . 007 mag yr -1 in I -band and 0.038 ± 0 . 007 mag yr -1 in R -band. We do not see any statistically significant decline in V -band magnitude of V1647 Ori. This could be due to higher fraction of contamination of nebula over V1647 Ori's aperture and slightly higher error in magnitudes due to faintness of source in V -band. These flux changes are along our direct line of sight at an angle of ∼ 30 · to the plane of disc (Acosta-Pulido et al. 2007). However, the flux measured along the cavity in perpendicular direction to the disc, which is reflected from region C, shows a dimming trend of 0.059 ± 0 . 005 mag yr -1 in I -band, 0.051 ± 0 . 005 mag yr -1 in R -band and 0.060 ± 0 . 005 mag yr -1 in V -band (see Figure 4). Hence, the region C, seems to be dimming faster than V1647 Ori. This could be either due to material inflow into cavity between region C and V1647 Ori as the outburst is progressing or due to a change in extinction along the cavity induced by slow dimming of V1647 Ori's brightness. During the first outburst in 2003, the linear dimming rate during the plateau stage was 0.24 mag yr -1 in R -band (Fedele et al. 2007), which was ∼ 6 . 3 times faster in magnitude scale than the present dimming rate in second outburst. Just like in other T-Tauri stars, we also see a lot of short time scale random variations in the source magnitude (peak-to-peak ∆ V glyph[similarequal] 0 . 35 mag, ∆ R glyph[similarequal] 0 . 30 mag and ∆ I glyph[similarequal] 0 . 20 mag), which could be due to density fluctuations in the infalling gas on to the star. Our lightcurve of V1647 Ori does not show any 56 day periodicity which was reported by Acosta-Pulido et al. (2007) during the first 2003 outburst. Based on the correlated reddening of flux during the minima of light curve, they proposed that periodicity was due to occultation of a dense clump in accretion disc at a distance of 0.25 AU from the star. The peak-to-peak amplitude in I -band was ∼ 0.3 mag in 2003. We have not detected this variability in 2008 outburst which implies the dense clump might have got dissipated between 2003 and 2008 outburst events. Our Lomb-Scargle periodogram analysis of magnitudes did not show any other statistically significant periodicity. The optical magnitudes during the second outburst are almost similar to that of the first outburst in 2003. In fact the first known outburst of V1647 Ori in 1966 ( ∼ 38 years prior to 2003), reported by Aspin et al. (2006), also had similar magnitude to the present one, however, all these three outbursts have different timescales. Implications of this fact on outburst model will be discussed in Section 4. Our NIR J , H and K magnitudes are listed in Table 3. Similar to optical light curve, there is a faint dimming trend in NIR also. Venkata Raman et al. (2013), with more NIR data points, estimated the fading rate in J -band to be 0.08 ± 0 . 02 mag yr -1 . The J -H/H -K color-color (CC) diagram (Figure 5) shows the movement of V1647 Ori from 2007 data point taken in quiescent phase to outburst state. It is similar to what was seen in 2003 outburst. From the quiescent phase position in CC diagram, V1647 Ori has moved towards the classical T-Tauri (CTT) locus along the redenning vector and presently occupies the same position as in 2003 outburst. The position of V1647 Ori in CC diagram is consistent with similar CC diagram published by Venkata Raman et al. (2013). This implies that the decrease in line of sight extinction during the outburst is same as that seen during the 2003 outburst. Since our line of sight is through the envelope, it must be likely due to a reversible mechanism like dust sublimation in the inner region of en- elope during each outburst (Acosta-Pulido et al. 2007; Mosoni et al. 2013; Aspin et al. 2009). Since the star is deeply embedded, we have reflections and dust emission effects also affecting the position of V1647 Ori in the CC diagram. So the extinction estimated from CC diagram is not very reliable. Otherwise, we can see that the second outburst has cleared out circumstellar matter of δA V ∼ 6 ± 2 mag. This is also consistent with the estimate of extinction change during first outburst by Mosoni et al. (2013), δA V ∼ 4 . 5 mag (see also Aspin et al. (2008)).",
"pages": [
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},
{
"title": "3.2. Morphological Results",
"content": "Between 2003 and 2008 outbursts, the McNeil's nebula does not have any significant morphological changes, however the intensity distribution of the nebula has changed between the outbursts. Figure 6 shows the difference in R -band flux along the nebula between 2011 and 2004. Images of similar atmospheric conditions were taken and scaled to match the brightness of V1647 Ori before subtracting 2004 image from that of 2011. Brighter shade implies that region is brighter in 2011 than 2004. We can see that the region C is brighter in second outburst than it was in 2004. This could be due to dust clearing up between the last two outbursts along the cavity seen in NIR in region C direction (Ojha et al. 2005). Our photometric results show region C is dimming faster than V1647 Ori and one of the explanations for that could be material inflow into cavity during the outburst. However, region C is relatively brighter in 2008 outburst than in 2004 for the same brightness of V1647 Ori. This implies that the matter inflow to cavity was not occurring during the quiescent phase between 2006 and 2008. This is also based on the implicit assumption that the extinction along the line of sight direction to V1647 Ori is same between 2003 and 2008 outbursts. The other significant change is in illumination of the south-western knot (region B) of the nebula; its illumination seems to have shifted slightly towards west. These illumination changes in nebula imply a structural change in the circumstellar matter above the disc and cavity. A similar pattern and conclusion were also reported between 1966, 2003 and 2008 outbursts by Aspin et al. (2006, 2009). Similar analysis of image pairs taken between 2008 and 2012 did not show any significant morphological changes. Our image pairs had a seeing of 1.6 '' . Hence, to check whether any change in illumination of nebula is undergoing during the present outburst, we need images with seeing less than 1.6 '' .",
"pages": [
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},
{
"title": "3.3. Spectroscopic Results",
"content": "V1647 Ori optical spectra show strong H α (6563 ˚ A ) emission and Ca II IR triplet at 8498, 8542 and 8662 ˚ A in emission. Other weak lines seen are Na D (5890+5896 ˚ A ) and OI (7773 ˚ A ) in absorption, and [O I] (6300 ˚ A ), O I (8446 ˚ A ), [Fe II] (7155 ˚ A ) and Fe I (8388, 8514 ˚ A ) in emission (see Figure 7). The equivalent widths of H α , Ca II IR triplet lines and OI (7773 ˚ A ) are listed in Table 4.",
"pages": [
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},
{
"title": "3.3.1. H α line",
"content": "Strong Hα line in V1647 Ori shows a clear P-Cygni profile as well as substantial variations. Figure 8 shows the variations of Hα profiles during our four and a half years of observations. P-Cygni profiles were more prominent in early part of the outburst in 2008. To see the absorption component clearly, a Gaussian is fitted to the right wing of the profile in red color and the difference of the fit to actual spectra is plotted in green color. Figure 9 shows the outflow velocity and associated error bar of expanding wind from the blue-shifted absorption minima in Hα profile. These blue-shifted absorption components were present in 2003 outburst also and disappeared during the fading stage of the outburst (Ojha et al. 2006; Fedele et al. 2007). Figure 10 shows the variation in equivalent width ( W λ in ˚ A ) of Hα emission. The calculation of W λ was very sensitive to the weak continuum flux around λ 6563 ˚ A , and the error estimate for each data point is ∼ ± 3 ˚ A . The W λ of 2008 outburst is in similar range of that during first outburst in 2003. Since Hα emission comes from the innermost accretion powered hot zone, we can expect its strength to be proportional to the accretion rate. The optical photometric magnitude in second outburst is similar to that of first outburst, which implies the continuum flux is almost of the same value. Hence from the fact that W λ is of similar value as of first outburst, we can deduce that the accretion rate is also of the same order in both the outbursts during its 'high plateau'stage.",
"pages": [
5
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},
{
"title": "3.3.2. Ca II IR triplet lines",
"content": "The plots of equivalent widths of Ca II IR triplet lines (8498, 8542 and 8662 ˚ A ) are shown in Figure 11. We have much lesser error bars ( ± 0 . 5 ˚ A ) for the W λ due to the higher continuum flux in these wavelengths. The Ca II IR triplet emission lines are seen to be in the ratio 1 . 07 ± 0 . 09 : 1 . 15 ± 0 . 1 : 1. This nearly equal ratio is due to optically thick gas with the collision decay rates larger than the effective radiative decay rates of upper states of Ca II lines. Such environment is typically seen in many T-Tauri stars. Optical thickness along with the non-detection of forbidden [Ca II] lines above noise, implies number density of electrons to be ≈ 10 11 cm -3 (Hamann & Persson 1992). For comparison with Figure 8 of Hamann & Persson (1992), Figure 12 shows the scatter plot between the ratios of equivalent widths, W λ 8498 / W λ 8542 and W λ 8662 / W λ 8542 , of our data as well as previously published data from literature. The error bar in our new data (black squares) is ± 0 . 1. From the position of 2007 data point (red diamond) taken during quiescent phase (Aspin et al. 2008) in this scatter plot, Aspin et al. (2008, 2009) had concluded that the optical density of the region emitting Ca II IR triplet lines changed significantly between outburst and quiescent phases. But since there is only one data point from quiescent phase and it is lying within the scatter of points from ongoing outburst, it might be difficult to conclude that the change in ratios observed was actually due to V1647 Ori moving from quiescent phase to outburst phase. We could see strong correlation between the equivalent widths ( W λ ) of Ca II IR triplet lines (see Figure 13). The Pearson correlation coefficient (PCC) between both W λ 8662 and W λ 8498 , and W λ 8542 and W λ 8498 is 0.88 with a 2-tailed p value glyph[lessmuch] 0 . 0001. This implies that the fluctuations in W λ are not random statistical error. It could be due to fluctuations of continuum flux around λ 8500 ˚ A . Peak-to- W λ is ∼ 5 ˚ A , which means if the flux from these lines is assumed to be constant then the continuum flux has fluctuated by a factor of ∼ 1 . 6, which in terms of the log scale of magnitude is ∼ 0 . 5. This indeed matches with peak-to-peak fluctuation in I -band magnitude during the entire period. We do not see any strong correlation between W λ of Hα line and Ca II IR triplets. However, it should be noted that the error bars in W λ of Hα are much higher than that of Ca II IR lines due to low continuum flux around λ 6563 ˚ A . In 2008 October 29 spectrum, we could clearly detect P-Cygni profile in Ca II IR triplet lines (Figure 14). The strengths of absorption trough of the three lines were in the same pattern as that of T-Tauri star WL 22 (Hamann & Persson 1992), i.e. the pattern with strongest absorption in λ 8542 ˚ A , then λ 8662 ˚ A and very weak in λ 8498 ˚ A . The ratio of W λ of the blue-shifted absorption between λ 8542 ˚ A and λ 8662 ˚ A is 0.76 : 0.45 =1.69 : 1. This ratio is consistent within error bars to the 1.8 : 1 ratio of intensity from atomic transition strength of these lines. Hence, unlike the region producing emission lines, this absorption regions are optically thin. So by using optically thin assumption, we can estimate the column density of Ca II by the formula (Spitzer 1978): lu A where the oscillator strength f lu for the lines 8542 and 8662 ˚ A are 0.39355 and 0.21478 respectively, taken from Merle et al. (2011). Substituting the W λ , wavelength and oscillator strength for both the lines, we get the column density ( N CaII ) as 2 . 9 × 10 12 cm -2 and 3 × 10 12 cm -2 respectively. This is the column density of Ca II atoms in this small duration of outflow wind. Assuming reasonable estimates of temperature T= 2600K (disc temperature estimated by Rettig et al. (2005)) and pressure P=1 Pascal (typical pressure in solar winds), we get the fraction of ionisation using Saha's formula to be ≈ 0 . 004. Hence, dividing by this fraction we obtain the column density of Ca atoms in gas blob to be ≈ 7 . 5 × 10 14 cm -2 . Assuming solar metalicity, we obtained column density of hydrogen (H) in outflowing gas blob as ≈ 3 . 4 × 10 20 cm -2 . From the doppler shift of the absorption minima, we also obtained the wind velocity to be 313 ± 10 km s -1 (in λ 8542 ˚ A line) and 303 ± 10 km s -1 (in λ 8662 ˚ A line). We also detected a faint P-Cygni profile in λ 8542 ˚ A line on 2008 December 30, with a blue-shifted velocity of 329 ± 10 km s -1 . Apart from these two episodic events, none of our other spectra show any detectable P-Cygni profile. The episodic nature of these two winds implies they are magnetic reconnection driven winds rather than pressure driven steady winds. Even though our medium resolution spectra cannot be used to study line widths, since the Ca II IR triplets are near by, we could do relative comparison of the widths of the Ca II IR triplet lines, where width is taken to be the full width half maximum (FWHM) of Gaussian fit of the continuum normalised profile. Since this quantity is the FWHM of Gaussian profile that we get after the convolution of instrument response on the actual line, it is not the FWHM of the line. However, since the lines are very close and the instrumental convolution is common, the wider line will give a wider FWHM after convolution. Figure 15 shows a scatter plot of the ratio of the widths of λ 8498 ˚ A and λ 8542 ˚ A versus equivalent width of the line λ 8542 ˚ A . Most of the points lie below 1.0 in the ratio axis. Using the 'test statistic' for mean with 34 data points, we could reject null hypothesis H o : The mean of the ratio is 1, with 6 sigma confidence. This shows that the λ 8498 ˚ A line is slightly narrower than λ 8542 ˚ A line. Similar trend is seen in most of the T-Tauri stars (Hamann & Persson 1992). Apart from showing this skewness, since our spectra are of only medium resolution, we cannot quantify the narrowness of the line. This narrowness of optically thinner line λ 8498 ˚ A could be explained by either substantial opacity broadening in λ 8542 ˚ A (since 1:9 is the ratio of atomic line strength) or by lower dispersion velocity in the inner part of the region of Ca II IR emission (Hamann & Persson 1992). Our period search in the equivalent width ( W λ ) of Ca II IR triplet lines found six faint periodicities in all three lines in the range of 1 - 100 days with ∼ 2 sigma confidence level in amplitude. The possible periodicities and confidence were estimated by Lomb-Scargle periodogram along with Monte Carlo simulation. The possible periods are 3.39, 8.09, 27.94, 30.8, 40.77 and 45.81 day. Since the amplitudes are only of 2 sigma confidence level, they can be confirmed only with more observations. Figure Set 16 shows the folded data of the entire four and a half year observations and the statistical significance of the amplitudes. The amplitude of the least square fitted cosine function is ∼ 1. If this periodicity is due to change in the continuum flux, the corresponding amplitude of magnitude change we expect in logarithmatic I -band magnitude is ∼ 0 . 1. This is not much above our error in magnitude estimate, so the fact that we do not see similar periodicity in I -band magnitude does not rule out the cause of change in W λ as change in continuum flux. We also do not see any corresponding significant periodicity in W λ of H α . Aspin et al. (2008) took the spectrum of V1647 Ori during the quiescent phase in February 2007. The W λ of both Ca II IR triplet lines and H α were ∼ 3 . 3 times the present value. Aspin & Reipurth (2009) had used ratio of W λ of H α between 2003 outburst and quiescent phase to estimate change in accretion rate. Similarly, since the continuum flux changed by a factor of ∼ 40 between the quiescent and 2008 outburst phase, we can estimate that the change in the line flux of both set of lines is by a factor of ∼ 10. This agrees with the change in accretion rate. Thus the origin of Ca II IR triplet lines are directly connected to the accretion rate just like H α . This is in agreement with finding of tight correlation between Ca II IR line flux and accretion rate in T-Tauri stars by Muzerolle et al. (1998), which suggests the origin of these lines to be in the magnetospheric infall zone. The similar value of W λ of Ca II IR lines with that of 2003 also strengthens the claim that the accretion rate on to the star from inner disc was same during both the outbursts.",
"pages": [
5,
6
]
},
{
"title": "3.3.3. Oxygen lines",
"content": "The most prominent oxygen line is OI 7773 ˚ A in absorption, however, weak OI 8446 ˚ A line is also detected in emission. We should be careful in interpreting the W λ of OI λ 7773 ˚ A absorption line because the profile shape of the line seems to be a combination of red-shifted emis- component and more stronger blue-shifted absorption component (see Figure 7). A weak anti-correlation is seen between H α and OI λ 7773 ˚ A (see Figure 17). Correlation had PCC = 0.54, with a 2 tailed p value of 0.001. This anti-correlation in W λ of OI 7773 ˚ A and H α could be due to positive correlation between emission component of OI λ 7773 ˚ A filling in the absorption dip and H α . Since OI λ 7773 ˚ A cannot be formed in photosphere of cool stars, the absorption component is due to warm gas in the envelope or hot photosphere above disc, while the emission component might be due to the hot gas region from which H α is also being emitted. Ojha et al. (2006) reported a decreasing trend in the W λ of OI λ 7773 ˚ A from the beginning till end of the 2003 outburst which was interpreted to be possible decrease in turbulence in outer envelope during the outburst period. We do not see such a trend in 2008 outburst, but the values of W λ in 2008 outburst remain same as that during the second half of the 2003 outburst. A slight decrease of W λ in the later part of 2003 outburst observed on 2005 September 8, as reported by Ojha et al. (2006), in contrast to the increase of W λ of other lines, could be due to increase in the W λ of OI λ 7773 ˚ A emission component.",
"pages": [
6,
7
]
},
{
"title": "3.3.4. Forbidden lines",
"content": "We detected [O I] (6300 ˚ A ) and [Fe II] (7155 ˚ A ) forbidden line emissions in V1647 Ori's spectra. The presence of [O I] λ 6300 ˚ A and [Fe II] λ 7155 ˚ A implies shock regions probably originating from jets. This combined with non-detection of [S II] (6731 ˚ A ) line above our noise level implies the shock region has temperature T ≈ 9000 -11000 K and electron number density ≈ 10 5 -10 6 cm -3 (Hamann 1994). We see significant variations in the strengths of the forbidden lines [O I] and [Fe II], however, the lines are too faint in our individual spectra to quantify statistically. During the fading stage of 2003 outburst in 2006 January, when the bright continuum flux decreased, Fedele et al. (2007) were also able to detect various strong forbidden line emissions, namely [O I] λλ 6300 ˚ A, 6363 ˚ A , [S II] λλ 6717 ˚ A, 6731 ˚ A and [Fe II] λ 7172 ˚ A .",
"pages": [
7
]
},
{
"title": "4. IMPLICATION ON MODELS OF OUTBURST",
"content": "The models which are known for FUor / EXor outbursts can be broadly classified into three. First kind of model is purely a thermal instability model, initially proposed for dwarf nova systems and was later adapted for FUors kind of outbursts (Bell & Lin 1994). The second kind of model involves a binary companion or planet, which perturbs the disc causing repeated sudden high accretion events (Bonnell & Bastien 1992; Lodato & Clarke 2004 ). The third kind involves mainly gravitational instability triggering magnetorotational instability (MRI) (Zhu et al. 2009, and references therein). Bell & Lin (1994) model (hereafter BL94) is a pure thermal instability model. In BL94, the thermal instability is triggered when the surface density at a region in disc rises above a critical density. The viscous timescales determine duration of outbursts and quiescent phase. The inner region at a radius r during outburst will deplete below the critical surface density in viscous time scale τ visc = r 2 /ν . Based on α prescription of viscosity, ν = αc s H , where c s is the isothermal sound speed, H ≈ c s / Ω is the disc thickness, Ω is orbital angular velocity at radius r and α ( < 1) is a dimensionless parameter (see Figure 18). Substituting, we get a relation :",
"pages": [
7
]
},
{
"title": "τ visc = r 2 Ω αc 2 s = 1 α Ω ( r H ) 2 .",
"content": "Let v R ≈ r/τ visc ≈ ν/r be the effective inward radial velocity component of gas in inner accretion disc. Then the mass infall rate at radius R is ˙ M = -2 πR Σ v R , where Σ is the surface density of disc at that radius. Substituting v R , ν and H in above equation of ˙ M , we get ˙ M ≈ 2 π Σ αc 2 s / Ω. The time scale of transition between outburst and quiescent phases is much smaller than the viscous timescale. Hence, Σ will remain constant, Ω will also remain constant at a given R , which leaves only the parameter αc 2 s to explain the change by a factor of ∼ 10 in inner disc accretion rate to V1647 Ori between the outburst and quiescent phases. Since the square of isothermal sound speed c 2 s = R g T/µ (where R g is the gas constant, T is temperature and µ is mean molecular weight), the temperature change by a factor 10 between the phases at the trigger of thermal instability (Zhu et al. (2009), Appendix B, their Figure 14) alone will cause a net change in accretion rate by factor of 10. Hence, at least in the inner region of disc, α can change only by a multiplicative factor of order 1 to remain consistent with the observed change in accretion rate. In BL94, assuming the mass infall rate to the inner disc region ˙ M in = constant , the α determines the timescales and the ratio α outburst /α quiescent is proportional to the ratio of time in quiescent phase to time in outburst phase (BL94; Table 2). Figure 19 shows the schematic of the lightcurve of V1647 Ori in optical band we know so far. The photometric magnitudes and overall SED during the quiescent phase in 2007 match with pre 2003 outburst data (Aspin et al. 2008). Even though accretion rate had fallen by a factor of 10 during quiescent phase, it was still in the order of 10 -6 M glyph[circledot] yr -1 . Based on this, Aspin et al. (2009) had suggested that the 2003 outburst might not have actually terminated in 2006. Since we do not have a good estimate of pre-outburst accretion rate, we shall consider this sudden drop in accretion rate by a factor of 10 as a drop from outburst state to quiescent phase in outburst models. Let α o 1 , α o 2 and α o 3 represent the three outburst phase α values and α q 1 and α q 2 represent the two quiescent phase α values. If we assume ˙ M in = constant in BL94, from the ratio of periods, we get the following relations: α o 1 = k (22 -89) α q 1 ; α o 2 = k 21 α q 1 ; α o 3 < k 9 α q 1 ; α o 3 < k 0 . 6 α q 2 ; where k is just the proportionality constant corresponding to the constant ˙ M in . We also get α o 2 = (0 . 23 -0 . 95) α o 1 ; α o 3 < 0 . 4 α o 2 ; α q 2 = 15 α q 1 . This is a very huge variation in α parameter. However, our accretion estimates, during the 2003 as well as 2008 outbursts show the accretion rate of matter on to the star from inner disc was quite stable at ∼ 10 times the rate in quiescent phase. Thus the α parameter cannot be fluctuating as much as we estimated; especially α o 3 < k 0 . 6 α q 2 is impossible from the fact that viscosity has to be more in outburst phase than quiescent phase. Then the assumption ˙ M in = constant in BL94 might be wrong. An increase in ˙ M in can decrease the draining rate of inner disc and can account for a longer duration of outburst period. It can also explain the slower rate of dimming in the magnitude of the V1647 Ori during its plateau stage in present outburst compared to 2003 outburst. By letting ˙ M in to be a variable and substituting R limit to be the radius upto which instability extends, to constrain parameters, we compared the viscous timescale τ visc = R 2 limit /ν ≈ R 2 limit Ω /αc 2 s between 2003 and 2008 outbursts. The instability triggering temperature at the boundary has to be same for both outbursts, so the sound speed c s will be the same. Parameter α can also be taken to be same during both the outbursts based on our previous conclusion. Now the only free variable parameter which determines the timescale is R limit . Substituting Keplarian Ω ∝ R -3 2 , we finally obtain the relation for viscous timescale in terms of R to be τ ∝ R 1 2 . limit visc limit BL94 gives the radius upto which instability extends to be : ˙ 1 Substituting this proportionality, we get τ visc ∝ M 6 in . Thus the ratios of mass infall rate from outer to inner disc during each outburst is related to the duration of outburst by the relation ˙ M in 2008 ˙ M in 2003 > ( 52 21 ) 6 ≈ 230. Thus the infall of gas from outer to inner disc during 2008 outburst is at least 230 times (2 orders) more than that during 2003 outburst. Model presented by Zhu et al. (2010) includes an MRI instability contribution to viscosity parameter if the temperature of the disc goes above MRI triggering temperature ( T M ) and also includes an effective viscosity contribution from gravitational instability beyond the radius given by Toomre's instability parameter Q. The relation between R limit and ˙ M in this model is R limit ∝ ˙ M 2 9 2003 Therefore, the infall of gas from outer to inner disc during 2008 outburst is at least 3500 times (3 orders) more than that during 2003 outburst. This estimate is one order more than BL94. It should be kept in mind that the viscosity timescale gives only order of magnitude estimate of the duration of outburst. For a comparison of actual simulated duration of outburst and viscous timescale see Table 1 in Zhu et al. (2010). If the present outburst continues for a larger period, ˙ M in 2008 ˙ M in 2003 ratio will further increase. Since we have an upper limit in ˙ M in for FUors, the increased ratio could only be explained as a dip in mass inflow in 2003. For example, a gap in disc could have resulted in sudden ending of 2003 outburst. This gap or low density region has to be near the typical R limit predicted by each model, i.e. ∼ 1 AU . To estimate the change in photometric magnitudes between 2003 and 2008 outburst phase due to predicted change in radius R limit , we modelled a disc with temperature profile given by outburst accretion rate inside R limit and quiescent accretion rate outside R limit . The magnitude variations in optical I and NIR J bands were found to be less than 1 mag for variation of R limit by a factor of 6. Mosoni et al. (2013) reported an increase in visibility of resolved interferometric study of V1647 Ori using VLTI/MIDI observations in 8-13 µ m range during the early stage of fading in 2003 outburst (between 2005 March and 2005 September). Apart from the possible scenarios discussed by Mosoni et al. (2013), it could also be explained by the relative increase in contribution in total flux from the extended outburst disc when the central star's accretion slowed down. A similar VLTI/MIDI visibility study of the ongoing 2008 outburst will give more input to constrain R limit and outburst models. Thus, we conclude that a pure thermal instability alone cannot explain the varying timescales of outbursts occurring in V1647 Ori. As proposed for other short rise timescale FUors, V1647 Ori can also be explained only by an outside-in triggering of the instability from outer radius (Bell & Lin 1994). The change in inflow of material from outer to inner disc could be due to many possibilities like MRI, gravitational instability (GI) or planet perturbation. The smooth surface density assumptions of disc also might not be a good model in light of detection of clump in the disc at 0.27 AU and disappearance of it in second outburst. Our observations detected a variety of episodic events like sudden short duration winds with hydrogen column density ≈ 3 . 4 × 10 20 cm -2 , fluctuations in H α flux, short timescale variation in continuum flux etc. The short timescale variation in continuum flux could be explained by the convections in the inner disc as suggested by Zhu et al. (2009) for their model of FU Orionis disc. The variations in Hα flux could have origin in some magnetic phenomena in the accretion funnel. The episodic wind events, [Fe II] λ 7155 and [OI] λ 6300 could be originating from jets or disc/stellar winds region. If we compare between 2008 and 2003 outbursts, the accretion rate on to the star from inner disc, extinction in NIR colorcolor diagram, outburst magnitude and spectral signatures in optical are the same. The main difference between 2008 compared to 2003 is the larger duration of outburst phase, 6 times slower dimming rate in optical during its 'plateau' stage and the change in circumstellar gas distribution revealed by morphological change in nebula's illumination.",
"pages": [
7,
8
]
},
{
"title": "5. CONCLUSIONS",
"content": "We have carried out four and a half years of continuous monitoring of V1647 Ori in its second outburst phase starting from 2008. Following are our main conclusions: in 2008 October and December. From Ca II IR triplet and H α line strengths, the accretion rate was found to be same as that during the 2003 outburst and is ∼ 10 times more than quiescent phase. the framework of instability models we conclude that the sudden ending of 2003 outburst could be due to a gap or low density region in inner ( ∼ 1 AU) disc. We thank the anonymous referee for giving us invaluable comments and suggestions that improved the content of the paper. The authors thank the staff of HCT, operated by Indian Institute of Astrophysics, Bangalore and IGO at Girawali, operated by Inter-University Centre for Astronomy and Astrophysics, Pune for their assistance and support during observations. It is a pleasure to thank J. S. Joshi and all the members of the Infrared Astronomy Group of TIFR for their support during the TIRCAM2 campaign. All the plots were generated using the 2D graphics environment Matplotlib (Hunter 2007).",
"pages": [
8,
9
]
},
{
"title": "REFERENCES",
"content": "' Abrah'am, P., Mosoni, L., Henning, T., et al. 2006, A&A, 449, 13 Acosta-Pulido, J. A., Kun, M., ' Abrah'am, P., et al. 2007, AJ, 133, 2020 Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90 Lodato, G. & Clarke, C.J. 2004, MNRAS, 353, 841 McNeil, J.W. 2004, IAU Circ. 8284 . Due to limited spectral range in IGO grism, Ca II triplet lines were not observed from IGO. Note . - Table 1 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content. Note . - Table 2 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content. †† Observed from IGO, all other nights are from HCT. Note . - Estimated error in magnitude is ≤ ± 0.1 ( K ) and ≤ ± 0.05 ( H and J ). Note . -Table 4 is published in its entirety in the electronic edition of the Astrophysical Journal. A portion is shown here for guidance regarding its form and content.",
"pages": [
9,
19,
20,
29,
30
]
}
]
2013ApJ...779..145N
https://arxiv.org/pdf/1310.4824.pdf
<document>
<section_header_level_1><location><page_1><loc_18><loc_86><loc_82><loc_87></location>A TIDALLY-STRIPPED STELLAR COMPONENT OF THE MAGELLANIC BRIDGE</section_header_level_1>
<text><location><page_1><loc_20><loc_83><loc_80><loc_85></location>David L. Nidever 1,2 , Antonela Monachesi 1 , Eric F. Bell 1 , Steven R. Majewski 2 , Ricardo R. Mu˜noz 3 , Rachael L. Beaton 2</text>
<text><location><page_1><loc_40><loc_81><loc_60><loc_82></location>Draft version September 14, 2021</text>
<section_header_level_1><location><page_1><loc_45><loc_79><loc_55><loc_80></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_57><loc_86><loc_79></location>Deep photometry of the Small Magellanic Cloud (SMC) stellar periphery ( R =4 · , 4.2 kpc) is used to study its line-of-sight depth with red clump (RC) stars. The RC luminosity function is affected little by young ( glyph[lessorsimilar] 1 Gyr) blue-loop stars in these regions because their main-sequence counterparts are not observed in the color magnitude diagrams. The SMC's eastern side is found to have a large line-of-sight depth ( ∼ 23 kpc) while the western side has a much shallower depth ( ∼ 10 kpc), consistent with previous photographic plate photometry results. We use a model SMC RC luminosity function to deconvolve the observed RC magnitudes and construct the density function in distance for our fields. Three of the eastern fields show a distance bimodality with one component at the 'systemic' ∼ 67 kpc SMC distance and a second component at ∼ 55 kpc. Our data are not reproduced well by the various extant Magellanic Cloud and Stream simulations. However, the models predict that the known H I Magellanic Bridge (stretching from the SMC eastward towards the LMC) has a decreasing distance with angle from the SMC and should be seen in both the gaseous and stellar components. From comparison with these models we conclude that the most likely explanation for our newly identified ∼ 55 kpc stellar structure in the eastern SMC is a stellar counterpart of the H I Magellanic Bridge that was tidally stripped from the SMC ∼ 200 Myr ago during a close encounter with the LMC. This discovery has important implications for microlensing surveys of the SMC.</text>
<text><location><page_1><loc_14><loc_54><loc_86><loc_57></location>Subject headings: Galaxies: interactions - Local Group - Magellanic Clouds - Galaxies: dwarf Galaxies: individual (SMC) - Galaxies: photometry</text>
<section_header_level_1><location><page_1><loc_22><loc_51><loc_35><loc_52></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_26><loc_48><loc_50></location>The Large and Small Magellanic Clouds (LMC and SMC respectively) are the two largest satellite galaxies of the Milky Way (MW) and, due to their proximity, offer the best possibility for detailed study of dwarf galaxies, especially interacting dwarf irregulars. One of the most striking features of the Magellanic system is the vast extent of its H I component - including the 200 · -long Magellanic Stream (MS) and Leading Arm (Nidever et al. 2010) as well as the Magellanic Bridge (Muller et al. 2003). These gaseous structures are the result of past interactions of the Magellanic Clouds (MCs) with each other and the MW galaxy (Murai & Fujimoto 1980; Gardiner & Noguchi 1996; Connors et al. 2006; R˚uˇziˇcka et al. 2010; Diaz & Bekki 2012; Besla et al. 2010, 2012, 2013). The Magellanic Bridge is widely believed to have been tidally stripped from the SMC by a recent close encounter with the LMC ∼ 200 Myr ago (e.g., Muller & Bekki 2007).</text>
<text><location><page_1><loc_8><loc_16><loc_48><loc_26></location>While the evidence of MC interactions is quite evident in H I it is less obvious in the stellar structures of the Clouds. The SMC, which is approximately ten times less massive than the LMC, is more likely to be affected by any past interactions (and is the source of much of the MS H I material in many models), and, therefore, may be the most obvious place to search for stellar signs of tidal disturbances.</text>
<unordered_list>
<list_item><location><page_1><loc_10><loc_12><loc_48><loc_14></location>1 Dept. of Astronomy, University of Michigan, Ann Arbor, MI, 48104, USA ([email protected])</list_item>
<list_item><location><page_1><loc_10><loc_9><loc_48><loc_11></location>2 Dept. of Astronomy, University of Virginia, Charlottesville, VA, 22904-4325, USA</list_item>
<list_item><location><page_1><loc_10><loc_7><loc_48><loc_9></location>3 Departamento de Astronom'ıa, Universidad de Chile, Casilla 36-D, Santiago, Chile ([email protected])</list_item>
</unordered_list>
<text><location><page_1><loc_52><loc_8><loc_92><loc_52></location>Two decades ago, a series of papers analyzing photographic plate photometry (Hatzidimitriou et al. 1989) reaching to just below the SMC horizontal branch (HB) performed the first detailed study of the SMC stellar periphery. Using red clump (RC) stars as standard candles in two fields, Hatzidimitriou & Hawkins (1989) found the line-of-sight depth to be much larger in the northeast than in the southwest. Follow-up spectroscopy showed a correlation between distance and radial velocity (RV) in the northeast RC stars (Hatzidimitriou et al. 1993) similar to that seen by Mathewson et al. (1986) in Cepheid variables closer to the center. Gardiner & Hatzidimitriou (1992) used the photographic plate photometry of all their SMC fields to trace HB stars to R ∼ 5 · in all directions, uncovering a fairly symmetric structure but with a quick decline in density towards the west. In contrast, the young main-sequence stars have a much more irregular shape extending towards the LMC into the Magellanic Bridge region (see black contours in Fig. 1). Gardiner & Hawkins (1991) found that the change of line-of-sight depth with radius in the western SMC, increasing with radius, was more consistent with a spheroidal than disklike structure. The notion of the stellar SMC having a spheroidal structure is argued by Zaritsky et al. (2000) and supported by a recent spectroscopic study of ∼ 2000 red giant branch (RGB) stars in the central 4 kpc × 2 kpc of the SMC that found no sign of rotation (Harris & Zaritsky 2006). In contrast, rotation is observed in the H I component of the SMC (Stanimirovi'c et al. 2004). Many of the structural and kinematical features of the SMC are reproduced by the LMC-SMC-MW interaction simulations of Bekki & Chiba (2009) by using a spheroidal stellar distribution and extended gaseous disk.</text>
<text><location><page_2><loc_8><loc_64><loc_48><loc_92></location>More recent work on the SMC periphery has shown it to extend much further than previously thought. Noel & Gallart (2007) detected intermediate-age and old stars in deep photometric data at ∼ 6 · south of the SMC center, while De Propris et al. (2010) found spectroscopicallyconfirmed RGB stars out to R ∼ 6 · in the eastern SMC. Nidever et al. (2011) used photometrically-selected RGB stars to trace the structure of the SMC periphery to R ∼ 11 · (in multiple directions) and showed that the SMC has a fairly azimuthally-symmetric structure. Nidever et al. also found that the center of the outer SMC population ( R> 4 · ) is offset by ∼ 0.6 · (to the east) from the center of the inner population ( R glyph[lessorsimilar] 3 · ) and postulated that this is due to a perspective effect because, on average, the stars to the eastern side are closer than the stars on the western side. In addition, Bagheri et al. (2013) used 2MASS and WISE catalogs to find evidence for some candidate older stars in the region between the Magellanic Clouds, while Noel et al. (2013) used deep photometry to find intermediate-age stars in a field at ∼ 7 · from the SMC in the Magellanic Bridge.</text>
<text><location><page_2><loc_8><loc_41><loc_48><loc_64></location>Variable stars and stars clusters have been widely used to study the 3D structure of the inner SMC. Several studies in the 1980s found a large line-of-sight depth in the central SMC using young Cepheids (Mathewson et al. 1986, 1988), with Caldwell & Coulson (1986) finding hints of two arms in the southwest. Haschke et al. (2012) used multi-epoch OGLE-III (Udalski et al. 2008) photometry to study the 3D distribution of cepheids ( ∼ 30300 Myr old) and RR Lyrae ( glyph[greaterorsimilar] 10 Gyr old) stars in the inner SMC ( R< 2 · ). While both populations are found to have an extended scale height, the older stars have a fairly homogeneous distribution whereas the young stars are in an inclined orientation that is closer in the northeast than in the southwest. Finally, Crowl et al. (2001) used populous SMC clusters to study the line-of-sight depth in the inner SMC ( R glyph[lessorsimilar] 3 kpc) and found a ± 1 σ depth between ∼ 6 and ∼ 12 kpc.</text>
<text><location><page_2><loc_8><loc_25><loc_48><loc_41></location>Even with all of these studies, the detailed 3D structure of the SMC stellar periphery is still not well understood in large part due to the lack of high-quality, wide-area CCD photometry in this region of the southern sky. This is unfortunate because this knowledge would enable us not only to produce a better 3D map of the SMC but also provide us with observational data of collisionless particles that would much better constrain the recent ( ∼ 200 Myr) close encounter of the MCs with each other. It is thought that during that encounter the SMC might have passed right through the LMC disk (Besla et al. 2012) and produced the H I Magellanic Bridge.</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_25></location>In this paper we use deep Washington M and T 2 photometry from the MAgellanic Periphery Survey (MAPS) to study the line-of-sight depth of core helium-burning RC stars in the SMC periphery. We find a much larger line-of-sight depth ( ∼ 23 kpc) in four eastern fields than in our four western fields ( ∼ 10 kpc), and a distance bimodality in three eastern fields with a newly identified component at ∼ 55 kpc ( ∼ 12 kpc closer than the component at the 'systemic', ∼ 67 kpc SMC distance) that is most likely an intermediate-age/old stellar counterpart of the recently tidally-stripped H I Magellanic Bridge. In Section 2 we briefly describe the observations and main features of the color magnitude diagrams (CMDs). We argue in Section 3 that the extended RC seen in many of</text>
<figure>
<location><page_2><loc_53><loc_67><loc_91><loc_92></location>
<caption>Fig. 1.Map of the SMC showing our CTIO-4m+MOSAIC fields as filled squares (red-shallow, purple-deep). A circle at R SMC =4 · highlights the eight fields used in our analysis. The colored image of the SMC shows the RGB starcounts using the combined Magellanic Clouds Photometric Survey (Zaritsky et al. 2002) and OGLE-III (Udalski et al. 2008) photometry (for R glyph[lessorsimilar] 2 · ) and RC starcounts from the photographic plate photometry of Hatzidimitriou et al. (1989) at larger radii. The LMC is shown in RGB starcounts selected from 2MASS (Skrutskie et al. 2006). The black contours indicate the HI in the Magellanic Clouds and Bridge from Bruns et al. (2005) at levels of log( N HI )=20.7, 21.1, 21.5 and 21.9.</caption>
</figure>
<text><location><page_2><loc_52><loc_44><loc_92><loc_52></location>our CMDs are due to large line-of-sight depths and not population effects. Density distributions as a function of distance are derived in Section 4 and compared to simulations in Section 5. Finally, a discussion of the results and their implications are presented in Section 6 and a brief summary in Section 7.</text>
<section_header_level_1><location><page_2><loc_69><loc_42><loc_75><loc_43></location>2. DATA</section_header_level_1>
<text><location><page_2><loc_52><loc_29><loc_92><loc_41></location>We use CTIO-4m+MOSAIC Washington M and T 2 (equivalent to I C ) photometry from the MAgellanic Periphery Survey (MAPS) for our analysis. The observations and data reduction are described in Nidever et al. (2011). Figure 1 shows the MAPS fields (filled squares) in the area of the SMC. While we have 'deep' photometry (to M ∼ 24) in fields extending to R ≈ 12 · the red clump (RC) is most prominent in our R =4 · fields, which are the focus of the present study.</text>
<text><location><page_2><loc_52><loc_11><loc_92><loc_29></location>Figure 2 shows the full M 0 vs. ( M -T 2 ) 0 Hess diagrams (dereddened with the Schlegel et al. 1998 extinction maps) of four, evenly spaced in azimuth, deep fields 4 at R =4 · . The SMC RGB, RC, and main-sequence stars are clearly visible. Hess diagrams of the RC region for all eight R =4 · fields are shown in Figure 3. The RC morphology clearly varies substantially from field to field. The eastern fields (PA=26-161 · ) show a much larger RC extent in magnitude than the western fields (PA=206-341 · ). It was previously noted by Hatzidimitriou & Hawkins (1989) that the horizontal branch stars in the northeast of the SMC periphery have a larger lineof-sight depth (and extend to brighter magnitudes) than in the southwest.</text>
<text><location><page_2><loc_52><loc_7><loc_92><loc_9></location>4 The field names are constructured from the field's radius and position angle (east of north), i.e. 40S026 is R=4.0 · and PA=26 · .</text>
<figure>
<location><page_3><loc_12><loc_54><loc_87><loc_91></location>
<caption>Fig. 2.Hess diagrams for the four deepest fields at R =4 · showing the RGB, RC and main-sequence populations. The extended RC can be seen in the two eastern fields (40S026 and 40S116) while the two western fields display a much more compact RC. The 40S116 field is in the HI Magellanic Bridge where there is ongoing star formation and young stars extending to bright magnitudes at ( M -T 2 ) 0 ∼-0.2 can be seen.</caption>
</figure>
<section_header_level_1><location><page_3><loc_11><loc_45><loc_46><loc_47></location>3. THE NATURE OF THE EXTENDED RED CLUMP LUMINOSITY FUNCTION</section_header_level_1>
<text><location><page_3><loc_8><loc_13><loc_48><loc_44></location>An elongated distribution of the red clump (to the bright end) can be caused by reasons other than a large line-of-sight depth. The evolution of intermediate-mass He-core burning stars moves them along loops in the HR diagram at nearly constant luminosity ('blue loop' stars). Their age at a given magnitude depends on metallicity but blue loop stars are generally quite young (a few hundred Myr to 1 Gyr; Sweigart 1987; Xu & Li 2004, and references therein) and theoretical models predict that their CMD location depends strongly on metallicity (e.g., Girardi et al. 2000). Many stars pile up on the red end of the blue loops (BL) and define a nearly vertical feature that stretches to brighter magnitudes than the RC (often spanning ∼ 2-3 mag) and trending to the blue (as seen in Fig. 3 of Gallart 1998). This feature of stellar evolution can be easily confused with an extended red clump and was the primary point of contention regarding the nature of the 'vertical red clump' of the LMC identified by Zaritsky & Lin (1997); these authors interpreted the feature as an intervening stellar population but this was subsequently called into question by Beaulieu & Sackett (1998). Given this precedent, we have taken steps to rule out BL stars as the cause for the extended feature observed in the CMDs of the eastern SMC fields.</text>
<text><location><page_3><loc_8><loc_7><loc_48><loc_12></location>We have computed a synthetic CMD that reproduces the overall features of the stellar populations of the SMC in the CMD (see Fig. 2) to compare its RC and BL distributions with the elongated feature observed at the RC</text>
<text><location><page_3><loc_52><loc_19><loc_92><loc_47></location>level. We have assumed a constant star formation rate (SFR) from 0.7 to 12 Gyr and metallicities of [Fe/H]= -1 dex ([Fe/H]= -1 . 5 dex) for stars younger (older) than 6 Gyr 5 . The model CMD was computed using the IAC-STAR code (Aparicio & Gallart 2004) adopting the BaSTI stellar library (Pietrinferni et al. 2004), a Reimers mass loss efficiency parameter value of η =0.2, and a Kroupa (2002) initial mass function (IMF) from 0.1 to 100 M glyph[circledot] . The magnitudes of the model CMD are expressed in the Johnson-Cousins photometric system; in particular we have chosen the bolometric correction library from Girardi et al. (2002). The magnitudes were transformed into the Washington M and T 2 photometric system using the transformation equations from Majewski et al. (2000). We assumed a distance modulus of 18.9 for the SMC and did not correct the model CMD due to observational effects (incompleteness and photometric errors). Given that we expect a near 100% completeness and a ∼ 2% photometric accuracy ( ∼ 0.3% internal precision) at the RC level, this correction should have little impact on the model CMD for our purposes.</text>
<text><location><page_3><loc_52><loc_13><loc_92><loc_19></location>Figures 4 and 5 show the observed (a) and model (b) CMDs for the 40S026 (eastern SMC) and 40S206 (western SMC) fields, respectively. The model in Figure 4b has ages ranging from 1.4 Gyr to 12 Gyr whereas the model in Figure 5b has ages ranging from 2.0 Gyr to 12</text>
<figure>
<location><page_4><loc_12><loc_57><loc_85><loc_91></location>
<caption>Fig. 3.Hess diagrams of the RC region for the eight fields at R=4 · (arranged from left to right with increasing position angle). The Hess diagrams are scaled to the same density of SMC stars to highlight the differences in RC morphology. The four eastern fields (40S026-40S161) show an extended RC that is not seen in the western fields (40S206-40S341).</caption>
</figure>
<text><location><page_4><loc_8><loc_7><loc_48><loc_51></location>Gyr. These age ranges were chosen so that the position and characteristics of the main features (main sequence, subgiant branch, tip of the RGB) are well reproduced by the models. In Figure 4, however, there is a clear difference in the RC morphology between the model and the data. We find that the RC is much less elongated in magnitude in the model than in the CMD of the observed eastern field. This discrepancy cannot be accounted for by stellar evolutionary features such as BL stars; the model predicts that there should be almost no BL stars, given that its youngest population has an age of 1.4 Gyr. A CMD model with stars as young as 0.7 Gyr predicts more BL stars, but also shows evidence of a brighter and more populous young main-sequence, which is not seen in the data. Moreover, even if the young main-sequence from the model CMD were to agree with the data, the density of the model BL stars would still be significantly lower than that of the RC stars. Figure 6a is an attempt to reproduce the morphology of the RC region of the CMD (seen in panel b) using a spread in age and star formation rate only (which requires most of the young and old stars to be removed). The resulting simulated Hess diagram is not a good representation of the observed data, particularly on the main sequence. On the other hand, the simulated Hess diagram with a distance spread (convolved with the distance function for this field found in § 4) in Figure 6c is a good representation. Thus, a BL population cannot explain the elongated RC that we observe in the eastern field. On the other hand, Figure 5 shows that the western field and model RC morphologies agree fairly well. Figures 4c and 5c show the RC luminosity function both for the data and the model. The RC stars were isolated as explained in the next section.</text>
<text><location><page_4><loc_52><loc_48><loc_92><loc_51></location>Note the much wider RC distribution in the eastern field when compared with the model.</text>
<section_header_level_1><location><page_4><loc_67><loc_46><loc_77><loc_47></location>4. DISTANCES</section_header_level_1>
<text><location><page_4><loc_52><loc_8><loc_92><loc_45></location>To study the distance distributions, we isolate the RC stars in the CMD. Because the RC and RGB are very close in the CMD and sometimes overlap we decided to model the RGB distributions to produce a 'clean' RC sample. A Hess density map of stars was created for each field in ( M -I ) 0 and M 0 in bins of 0.02 and 0.05 mag respectively. These were then smoothed with a Gaussian kernel having FWHM=2 bins. Each row, at a given magnitude, was modeled with a double-Gaussian for the RC and RGB over the magnitude range 18.5 <M 0 < 20.5. After the first iteration over the magnitude range, robust linear fits with magnitude were performed to the RGB Gaussian heights, centers and widths. On the second iteration, the RGB Gaussian components were constrained to lie close to the linear fit values (especially the centers). The final RGB model was then subtracted from the density map. The final image was summed over RC colors, 0.94 < ( M -I ) 0 < 1.12, and a similarly sized region blueward of the RC (for MW foreground) was summed and subtracted. The final RC luminosity functions are shown in Figure 7a (with Poisson errors). In some fields there is a residual RGB signal left at faint magnitudes ( M 0 glyph[greaterorsimilar] 20 or RC d glyph[greaterorsimilar] 80 kpc) in the subtracted density image (which can be seen in some of the luminosity functions). However, no obvious signs of an extension of the RC are seen at these magnitudes in the CMD and so the RC luminosity functions for M 0 glyph[greaterorsimilar] 20 are ignored for the rest of the distance analysis.</text>
<text><location><page_4><loc_53><loc_7><loc_92><loc_8></location>Next, we use the model SMC CMD to construct an ab-</text>
<text><location><page_5><loc_36><loc_81><loc_37><loc_82></location>2</text>
<figure>
<location><page_5><loc_37><loc_70><loc_61><loc_92></location>
</figure>
<figure>
<location><page_5><loc_64><loc_70><loc_87><loc_91></location>
</figure>
<figure>
<location><page_5><loc_12><loc_70><loc_36><loc_92></location>
<caption>Fig. 4.(a) Hess diagram of the 40S026 field in the eastern portion of the SMC. (b) Simulated CMD for the 40S026 field with ages of 1.4 to 12 Gyr. The red lines are [Fe/H]= -1.488 age=8.0 Gyr BaSTI isochrones (Pietrinferni et al. 2004) at 60 kpc. (c) Red clump luminosity function for the data (red) and simulation (black). The observed luminosity function is much broader than the model suggesting a large line-of-sight depth.</caption>
</figure>
<figure>
<location><page_5><loc_12><loc_40><loc_36><loc_62></location>
</figure>
<figure>
<location><page_5><loc_37><loc_40><loc_60><loc_62></location>
</figure>
<figure>
<location><page_5><loc_64><loc_40><loc_87><loc_61></location>
<caption>Fig. 5.Same as Figure 4 but for the 40S206 field with model ages of 2.0 to 12 Gyr. While not as wide as the RC luminosity function of 40S026, the observed luminosity function of 40S206 is wider than the model and indicates some depth is needed to explain the observations.</caption>
</figure>
<text><location><page_5><loc_8><loc_8><loc_48><loc_34></location>solute RC luminosity function (isolating RC stars with 1.025 <M -I< 1.12 and 18.7 <M< 19.8) and reconstruct the density function in distance (or rather distance modulus) for each field's observed RC luminosity function. A technique somewhat similar to the 'annealing' method (which iteratively finds the state of maximum entropy) was used to derive the density function. A discrete density function in distance modulus (in 0.05 mag steps) is convolved by the absolute luminosity function (Fig. 8) to produce a model RC luminosity function that can be compared to the observed data and used to calculate χ 2 (using Poisson errors). The reconstructed density function in distance is then found by an iterative approach. The density function is initialized with the observed RC luminosity function shifted by -0 . 41 mag (the mean SMC model RC magnitude is M RC =+0.41 mag). Each distance bin is then successively stepped through and its density varied until the best-fitting χ 2 value is found between the RC luminosity data and model. After stepping through all the distance bins the density</text>
<text><location><page_5><loc_52><loc_8><loc_92><loc_34></location>function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner.</text>
<figure>
<location><page_6><loc_15><loc_57><loc_85><loc_92></location>
<caption>Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data.</caption>
</figure>
<text><location><page_6><loc_8><loc_30><loc_48><loc_47></location>The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields.</text>
<section_header_level_1><location><page_6><loc_18><loc_27><loc_39><loc_28></location>5. COMPARISON TO MODELS</section_header_level_1>
<text><location><page_6><loc_8><loc_7><loc_48><loc_27></location>To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors</text>
<text><location><page_6><loc_52><loc_15><loc_92><loc_47></location>suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream).</text>
<text><location><page_6><loc_52><loc_11><loc_92><loc_15></location>Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to</text>
<figure>
<location><page_7><loc_15><loc_17><loc_50><loc_92></location>
<caption>Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process.</caption>
</figure>
<text><location><page_7><loc_54><loc_90><loc_56><loc_92></location>40</text>
<text><location><page_7><loc_54><loc_88><loc_56><loc_89></location>30</text>
<text><location><page_7><loc_54><loc_86><loc_56><loc_87></location>20</text>
<text><location><page_7><loc_54><loc_84><loc_56><loc_85></location>10</text>
<text><location><page_7><loc_55><loc_82><loc_56><loc_83></location>0</text>
<text><location><page_7><loc_54><loc_82><loc_56><loc_83></location>40</text>
<text><location><page_7><loc_54><loc_79><loc_56><loc_81></location>30</text>
<text><location><page_7><loc_54><loc_77><loc_56><loc_78></location>20</text>
<text><location><page_7><loc_54><loc_75><loc_56><loc_76></location>10</text>
<text><location><page_7><loc_55><loc_73><loc_56><loc_74></location>0</text>
<text><location><page_7><loc_54><loc_73><loc_56><loc_74></location>40</text>
<text><location><page_7><loc_54><loc_70><loc_56><loc_72></location>30</text>
<text><location><page_7><loc_54><loc_68><loc_56><loc_69></location>20</text>
<text><location><page_7><loc_54><loc_66><loc_56><loc_67></location>10</text>
<text><location><page_7><loc_55><loc_64><loc_56><loc_65></location>0</text>
<text><location><page_7><loc_54><loc_64><loc_56><loc_65></location>40</text>
<text><location><page_7><loc_54><loc_61><loc_56><loc_63></location>30</text>
<text><location><page_7><loc_54><loc_59><loc_56><loc_60></location>20</text>
<text><location><page_7><loc_54><loc_57><loc_56><loc_58></location>10</text>
<text><location><page_7><loc_55><loc_55><loc_56><loc_56></location>0</text>
<text><location><page_7><loc_54><loc_55><loc_56><loc_56></location>40</text>
<text><location><page_7><loc_54><loc_53><loc_56><loc_54></location>30</text>
<text><location><page_7><loc_54><loc_50><loc_56><loc_51></location>20</text>
<text><location><page_7><loc_54><loc_48><loc_56><loc_49></location>10</text>
<text><location><page_7><loc_55><loc_46><loc_56><loc_47></location>0</text>
<text><location><page_7><loc_54><loc_46><loc_56><loc_47></location>40</text>
<text><location><page_7><loc_54><loc_44><loc_56><loc_45></location>30</text>
<text><location><page_7><loc_54><loc_41><loc_56><loc_43></location>20</text>
<text><location><page_7><loc_54><loc_39><loc_56><loc_40></location>10</text>
<text><location><page_7><loc_55><loc_37><loc_56><loc_39></location>0</text>
<text><location><page_7><loc_54><loc_37><loc_56><loc_38></location>40</text>
<text><location><page_7><loc_54><loc_35><loc_56><loc_36></location>30</text>
<text><location><page_7><loc_54><loc_32><loc_56><loc_34></location>20</text>
<text><location><page_7><loc_54><loc_30><loc_56><loc_31></location>10</text>
<text><location><page_7><loc_55><loc_28><loc_56><loc_30></location>0</text>
<text><location><page_7><loc_54><loc_28><loc_56><loc_29></location>40</text>
<text><location><page_7><loc_54><loc_26><loc_56><loc_27></location>30</text>
<text><location><page_7><loc_54><loc_24><loc_56><loc_25></location>20</text>
<text><location><page_7><loc_54><loc_21><loc_56><loc_22></location>10</text>
<text><location><page_7><loc_55><loc_20><loc_56><loc_21></location>0</text>
<text><location><page_7><loc_55><loc_18><loc_58><loc_19></location>18.0</text>
<text><location><page_7><loc_63><loc_18><loc_66><loc_19></location>18.5</text>
<text><location><page_7><loc_71><loc_18><loc_74><loc_19></location>19.0</text>
<text><location><page_7><loc_79><loc_18><loc_82><loc_19></location>19.5</text>
<text><location><page_7><loc_65><loc_17><loc_77><loc_18></location>Distance Modulus</text>
<text><location><page_7><loc_57><loc_90><loc_73><loc_91></location>Reconstructed Distance</text>
<text><location><page_7><loc_57><loc_89><loc_63><loc_90></location>Modulus</text>
<text><location><page_7><loc_52><loc_86><loc_53><loc_87></location>N</text>
<text><location><page_7><loc_52><loc_78><loc_53><loc_78></location>N</text>
<text><location><page_7><loc_52><loc_69><loc_53><loc_69></location>N</text>
<text><location><page_7><loc_52><loc_60><loc_53><loc_60></location>N</text>
<text><location><page_7><loc_52><loc_51><loc_53><loc_52></location>N</text>
<text><location><page_7><loc_52><loc_42><loc_53><loc_43></location>N</text>
<text><location><page_7><loc_52><loc_33><loc_53><loc_34></location>N</text>
<text><location><page_7><loc_52><loc_24><loc_53><loc_25></location>N</text>
<text><location><page_7><loc_79><loc_89><loc_85><loc_90></location>10.9 kpc</text>
<text><location><page_7><loc_79><loc_80><loc_84><loc_81></location>8.1 kpc</text>
<text><location><page_7><loc_79><loc_71><loc_85><loc_72></location>11.6 kpc</text>
<text><location><page_7><loc_79><loc_62><loc_85><loc_63></location>13.7 kpc</text>
<text><location><page_7><loc_79><loc_53><loc_85><loc_54></location>24.3 kpc</text>
<text><location><page_7><loc_79><loc_44><loc_85><loc_46></location>24.1 kpc</text>
<text><location><page_7><loc_79><loc_35><loc_85><loc_37></location>22.0 kpc</text>
<text><location><page_7><loc_79><loc_27><loc_85><loc_28></location>26.0 kpc</text>
<figure>
<location><page_8><loc_13><loc_66><loc_44><loc_91></location>
<caption>Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41.</caption>
</figure>
<text><location><page_8><loc_8><loc_46><loc_48><loc_60></location>the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section).</text>
<section_header_level_1><location><page_8><loc_23><loc_43><loc_34><loc_44></location>6. DISCUSSION</section_header_level_1>
<text><location><page_8><loc_8><loc_22><loc_48><loc_43></location>We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'.</text>
<text><location><page_8><loc_8><loc_7><loc_48><loc_21></location>In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80</text>
<text><location><page_8><loc_52><loc_59><loc_92><loc_92></location>kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge.</text>
<text><location><page_8><loc_52><loc_15><loc_92><loc_58></location>Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC.</text>
<text><location><page_8><loc_52><loc_7><loc_92><loc_15></location>The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of</text>
<figure>
<location><page_9><loc_11><loc_19><loc_91><loc_87></location>
<caption>Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc.</caption>
</figure>
<figure>
<location><page_10><loc_9><loc_35><loc_48><loc_92></location>
<caption>Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc.</caption>
</figure>
<text><location><page_10><loc_8><loc_23><loc_48><loc_27></location>the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected.</text>
<text><location><page_10><loc_8><loc_7><loc_48><loc_23></location>A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago.</text>
<figure>
<location><page_10><loc_52><loc_51><loc_92><loc_92></location>
<caption>Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component.</caption>
</figure>
<text><location><page_10><loc_52><loc_7><loc_92><loc_39></location>While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the</text>
<text><location><page_11><loc_8><loc_87><loc_48><loc_92></location>central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012).</text>
<text><location><page_11><loc_8><loc_69><loc_48><loc_86></location>In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC.</text>
<text><location><page_11><loc_8><loc_60><loc_48><loc_69></location>We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure.</text>
<text><location><page_11><loc_8><loc_49><loc_48><loc_60></location>Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV).</text>
<section_header_level_1><location><page_11><loc_24><loc_46><loc_33><loc_47></location>7. SUMMARY</section_header_level_1>
<text><location><page_11><loc_8><loc_33><loc_48><loc_46></location>We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are:</text>
<unordered_list>
<list_item><location><page_11><loc_10><loc_28><loc_48><loc_31></location>1. The four eastern fields show very large line-of-sight depths ( ∼ 23 kpc) over ∼ 135 · of position angle.</list_item>
<list_item><location><page_11><loc_10><loc_24><loc_48><loc_26></location>2. Three eastern fields show a strong distance bimodality with one component at ∼ 67 kpc (near the</list_item>
</unordered_list>
<text><location><page_11><loc_56><loc_85><loc_92><loc_92></location>mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances.</text>
<unordered_list>
<list_item><location><page_11><loc_54><loc_74><loc_92><loc_84></location>3. The newly-found stellar component in the east at ∼ 55 kpc is qualitatively consistent with the Diaz & Bekki (2012) model distribution of particles in the tidally-stripped Magellanic Bridge, previously only detected in H I . We conclude that this new component is likely an intermediate-age/old ( ∼ 112 Gyr) stellar component of the Magellanic Bridge and call it the SMC 'eastern stellar structure'.</list_item>
</unordered_list>
<text><location><page_11><loc_52><loc_63><loc_92><loc_73></location>A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge.</text>
<text><location><page_11><loc_52><loc_52><loc_92><loc_63></location>We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered.</text>
<text><location><page_11><loc_52><loc_25><loc_92><loc_50></location>We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013.</text>
<text><location><page_11><loc_53><loc_24><loc_76><loc_25></location>Facilities: CTIO (MOSAIC II).</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "Deep photometry of the Small Magellanic Cloud (SMC) stellar periphery ( R =4 · , 4.2 kpc) is used to study its line-of-sight depth with red clump (RC) stars. The RC luminosity function is affected little by young ( glyph[lessorsimilar] 1 Gyr) blue-loop stars in these regions because their main-sequence counterparts are not observed in the color magnitude diagrams. The SMC's eastern side is found to have a large line-of-sight depth ( ∼ 23 kpc) while the western side has a much shallower depth ( ∼ 10 kpc), consistent with previous photographic plate photometry results. We use a model SMC RC luminosity function to deconvolve the observed RC magnitudes and construct the density function in distance for our fields. Three of the eastern fields show a distance bimodality with one component at the 'systemic' ∼ 67 kpc SMC distance and a second component at ∼ 55 kpc. Our data are not reproduced well by the various extant Magellanic Cloud and Stream simulations. However, the models predict that the known H I Magellanic Bridge (stretching from the SMC eastward towards the LMC) has a decreasing distance with angle from the SMC and should be seen in both the gaseous and stellar components. From comparison with these models we conclude that the most likely explanation for our newly identified ∼ 55 kpc stellar structure in the eastern SMC is a stellar counterpart of the H I Magellanic Bridge that was tidally stripped from the SMC ∼ 200 Myr ago during a close encounter with the LMC. This discovery has important implications for microlensing surveys of the SMC. Subject headings: Galaxies: interactions - Local Group - Magellanic Clouds - Galaxies: dwarf Galaxies: individual (SMC) - Galaxies: photometry",
"pages": [
1
]
},
{
"title": "A TIDALLY-STRIPPED STELLAR COMPONENT OF THE MAGELLANIC BRIDGE",
"content": "David L. Nidever 1,2 , Antonela Monachesi 1 , Eric F. Bell 1 , Steven R. Majewski 2 , Ricardo R. Mu˜noz 3 , Rachael L. Beaton 2 Draft version September 14, 2021",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "The Large and Small Magellanic Clouds (LMC and SMC respectively) are the two largest satellite galaxies of the Milky Way (MW) and, due to their proximity, offer the best possibility for detailed study of dwarf galaxies, especially interacting dwarf irregulars. One of the most striking features of the Magellanic system is the vast extent of its H I component - including the 200 · -long Magellanic Stream (MS) and Leading Arm (Nidever et al. 2010) as well as the Magellanic Bridge (Muller et al. 2003). These gaseous structures are the result of past interactions of the Magellanic Clouds (MCs) with each other and the MW galaxy (Murai & Fujimoto 1980; Gardiner & Noguchi 1996; Connors et al. 2006; R˚uˇziˇcka et al. 2010; Diaz & Bekki 2012; Besla et al. 2010, 2012, 2013). The Magellanic Bridge is widely believed to have been tidally stripped from the SMC by a recent close encounter with the LMC ∼ 200 Myr ago (e.g., Muller & Bekki 2007). While the evidence of MC interactions is quite evident in H I it is less obvious in the stellar structures of the Clouds. The SMC, which is approximately ten times less massive than the LMC, is more likely to be affected by any past interactions (and is the source of much of the MS H I material in many models), and, therefore, may be the most obvious place to search for stellar signs of tidal disturbances. Two decades ago, a series of papers analyzing photographic plate photometry (Hatzidimitriou et al. 1989) reaching to just below the SMC horizontal branch (HB) performed the first detailed study of the SMC stellar periphery. Using red clump (RC) stars as standard candles in two fields, Hatzidimitriou & Hawkins (1989) found the line-of-sight depth to be much larger in the northeast than in the southwest. Follow-up spectroscopy showed a correlation between distance and radial velocity (RV) in the northeast RC stars (Hatzidimitriou et al. 1993) similar to that seen by Mathewson et al. (1986) in Cepheid variables closer to the center. Gardiner & Hatzidimitriou (1992) used the photographic plate photometry of all their SMC fields to trace HB stars to R ∼ 5 · in all directions, uncovering a fairly symmetric structure but with a quick decline in density towards the west. In contrast, the young main-sequence stars have a much more irregular shape extending towards the LMC into the Magellanic Bridge region (see black contours in Fig. 1). Gardiner & Hawkins (1991) found that the change of line-of-sight depth with radius in the western SMC, increasing with radius, was more consistent with a spheroidal than disklike structure. The notion of the stellar SMC having a spheroidal structure is argued by Zaritsky et al. (2000) and supported by a recent spectroscopic study of ∼ 2000 red giant branch (RGB) stars in the central 4 kpc × 2 kpc of the SMC that found no sign of rotation (Harris & Zaritsky 2006). In contrast, rotation is observed in the H I component of the SMC (Stanimirovi'c et al. 2004). Many of the structural and kinematical features of the SMC are reproduced by the LMC-SMC-MW interaction simulations of Bekki & Chiba (2009) by using a spheroidal stellar distribution and extended gaseous disk. More recent work on the SMC periphery has shown it to extend much further than previously thought. Noel & Gallart (2007) detected intermediate-age and old stars in deep photometric data at ∼ 6 · south of the SMC center, while De Propris et al. (2010) found spectroscopicallyconfirmed RGB stars out to R ∼ 6 · in the eastern SMC. Nidever et al. (2011) used photometrically-selected RGB stars to trace the structure of the SMC periphery to R ∼ 11 · (in multiple directions) and showed that the SMC has a fairly azimuthally-symmetric structure. Nidever et al. also found that the center of the outer SMC population ( R> 4 · ) is offset by ∼ 0.6 · (to the east) from the center of the inner population ( R glyph[lessorsimilar] 3 · ) and postulated that this is due to a perspective effect because, on average, the stars to the eastern side are closer than the stars on the western side. In addition, Bagheri et al. (2013) used 2MASS and WISE catalogs to find evidence for some candidate older stars in the region between the Magellanic Clouds, while Noel et al. (2013) used deep photometry to find intermediate-age stars in a field at ∼ 7 · from the SMC in the Magellanic Bridge. Variable stars and stars clusters have been widely used to study the 3D structure of the inner SMC. Several studies in the 1980s found a large line-of-sight depth in the central SMC using young Cepheids (Mathewson et al. 1986, 1988), with Caldwell & Coulson (1986) finding hints of two arms in the southwest. Haschke et al. (2012) used multi-epoch OGLE-III (Udalski et al. 2008) photometry to study the 3D distribution of cepheids ( ∼ 30300 Myr old) and RR Lyrae ( glyph[greaterorsimilar] 10 Gyr old) stars in the inner SMC ( R< 2 · ). While both populations are found to have an extended scale height, the older stars have a fairly homogeneous distribution whereas the young stars are in an inclined orientation that is closer in the northeast than in the southwest. Finally, Crowl et al. (2001) used populous SMC clusters to study the line-of-sight depth in the inner SMC ( R glyph[lessorsimilar] 3 kpc) and found a ± 1 σ depth between ∼ 6 and ∼ 12 kpc. Even with all of these studies, the detailed 3D structure of the SMC stellar periphery is still not well understood in large part due to the lack of high-quality, wide-area CCD photometry in this region of the southern sky. This is unfortunate because this knowledge would enable us not only to produce a better 3D map of the SMC but also provide us with observational data of collisionless particles that would much better constrain the recent ( ∼ 200 Myr) close encounter of the MCs with each other. It is thought that during that encounter the SMC might have passed right through the LMC disk (Besla et al. 2012) and produced the H I Magellanic Bridge. In this paper we use deep Washington M and T 2 photometry from the MAgellanic Periphery Survey (MAPS) to study the line-of-sight depth of core helium-burning RC stars in the SMC periphery. We find a much larger line-of-sight depth ( ∼ 23 kpc) in four eastern fields than in our four western fields ( ∼ 10 kpc), and a distance bimodality in three eastern fields with a newly identified component at ∼ 55 kpc ( ∼ 12 kpc closer than the component at the 'systemic', ∼ 67 kpc SMC distance) that is most likely an intermediate-age/old stellar counterpart of the recently tidally-stripped H I Magellanic Bridge. In Section 2 we briefly describe the observations and main features of the color magnitude diagrams (CMDs). We argue in Section 3 that the extended RC seen in many of our CMDs are due to large line-of-sight depths and not population effects. Density distributions as a function of distance are derived in Section 4 and compared to simulations in Section 5. Finally, a discussion of the results and their implications are presented in Section 6 and a brief summary in Section 7.",
"pages": [
1,
2
]
},
{
"title": "2. DATA",
"content": "We use CTIO-4m+MOSAIC Washington M and T 2 (equivalent to I C ) photometry from the MAgellanic Periphery Survey (MAPS) for our analysis. The observations and data reduction are described in Nidever et al. (2011). Figure 1 shows the MAPS fields (filled squares) in the area of the SMC. While we have 'deep' photometry (to M ∼ 24) in fields extending to R ≈ 12 · the red clump (RC) is most prominent in our R =4 · fields, which are the focus of the present study. Figure 2 shows the full M 0 vs. ( M -T 2 ) 0 Hess diagrams (dereddened with the Schlegel et al. 1998 extinction maps) of four, evenly spaced in azimuth, deep fields 4 at R =4 · . The SMC RGB, RC, and main-sequence stars are clearly visible. Hess diagrams of the RC region for all eight R =4 · fields are shown in Figure 3. The RC morphology clearly varies substantially from field to field. The eastern fields (PA=26-161 · ) show a much larger RC extent in magnitude than the western fields (PA=206-341 · ). It was previously noted by Hatzidimitriou & Hawkins (1989) that the horizontal branch stars in the northeast of the SMC periphery have a larger lineof-sight depth (and extend to brighter magnitudes) than in the southwest. 4 The field names are constructured from the field's radius and position angle (east of north), i.e. 40S026 is R=4.0 · and PA=26 · .",
"pages": [
2
]
},
{
"title": "3. THE NATURE OF THE EXTENDED RED CLUMP LUMINOSITY FUNCTION",
"content": "An elongated distribution of the red clump (to the bright end) can be caused by reasons other than a large line-of-sight depth. The evolution of intermediate-mass He-core burning stars moves them along loops in the HR diagram at nearly constant luminosity ('blue loop' stars). Their age at a given magnitude depends on metallicity but blue loop stars are generally quite young (a few hundred Myr to 1 Gyr; Sweigart 1987; Xu & Li 2004, and references therein) and theoretical models predict that their CMD location depends strongly on metallicity (e.g., Girardi et al. 2000). Many stars pile up on the red end of the blue loops (BL) and define a nearly vertical feature that stretches to brighter magnitudes than the RC (often spanning ∼ 2-3 mag) and trending to the blue (as seen in Fig. 3 of Gallart 1998). This feature of stellar evolution can be easily confused with an extended red clump and was the primary point of contention regarding the nature of the 'vertical red clump' of the LMC identified by Zaritsky & Lin (1997); these authors interpreted the feature as an intervening stellar population but this was subsequently called into question by Beaulieu & Sackett (1998). Given this precedent, we have taken steps to rule out BL stars as the cause for the extended feature observed in the CMDs of the eastern SMC fields. We have computed a synthetic CMD that reproduces the overall features of the stellar populations of the SMC in the CMD (see Fig. 2) to compare its RC and BL distributions with the elongated feature observed at the RC level. We have assumed a constant star formation rate (SFR) from 0.7 to 12 Gyr and metallicities of [Fe/H]= -1 dex ([Fe/H]= -1 . 5 dex) for stars younger (older) than 6 Gyr 5 . The model CMD was computed using the IAC-STAR code (Aparicio & Gallart 2004) adopting the BaSTI stellar library (Pietrinferni et al. 2004), a Reimers mass loss efficiency parameter value of η =0.2, and a Kroupa (2002) initial mass function (IMF) from 0.1 to 100 M glyph[circledot] . The magnitudes of the model CMD are expressed in the Johnson-Cousins photometric system; in particular we have chosen the bolometric correction library from Girardi et al. (2002). The magnitudes were transformed into the Washington M and T 2 photometric system using the transformation equations from Majewski et al. (2000). We assumed a distance modulus of 18.9 for the SMC and did not correct the model CMD due to observational effects (incompleteness and photometric errors). Given that we expect a near 100% completeness and a ∼ 2% photometric accuracy ( ∼ 0.3% internal precision) at the RC level, this correction should have little impact on the model CMD for our purposes. Figures 4 and 5 show the observed (a) and model (b) CMDs for the 40S026 (eastern SMC) and 40S206 (western SMC) fields, respectively. The model in Figure 4b has ages ranging from 1.4 Gyr to 12 Gyr whereas the model in Figure 5b has ages ranging from 2.0 Gyr to 12 Gyr. These age ranges were chosen so that the position and characteristics of the main features (main sequence, subgiant branch, tip of the RGB) are well reproduced by the models. In Figure 4, however, there is a clear difference in the RC morphology between the model and the data. We find that the RC is much less elongated in magnitude in the model than in the CMD of the observed eastern field. This discrepancy cannot be accounted for by stellar evolutionary features such as BL stars; the model predicts that there should be almost no BL stars, given that its youngest population has an age of 1.4 Gyr. A CMD model with stars as young as 0.7 Gyr predicts more BL stars, but also shows evidence of a brighter and more populous young main-sequence, which is not seen in the data. Moreover, even if the young main-sequence from the model CMD were to agree with the data, the density of the model BL stars would still be significantly lower than that of the RC stars. Figure 6a is an attempt to reproduce the morphology of the RC region of the CMD (seen in panel b) using a spread in age and star formation rate only (which requires most of the young and old stars to be removed). The resulting simulated Hess diagram is not a good representation of the observed data, particularly on the main sequence. On the other hand, the simulated Hess diagram with a distance spread (convolved with the distance function for this field found in § 4) in Figure 6c is a good representation. Thus, a BL population cannot explain the elongated RC that we observe in the eastern field. On the other hand, Figure 5 shows that the western field and model RC morphologies agree fairly well. Figures 4c and 5c show the RC luminosity function both for the data and the model. The RC stars were isolated as explained in the next section. Note the much wider RC distribution in the eastern field when compared with the model.",
"pages": [
3,
4
]
},
{
"title": "4. DISTANCES",
"content": "To study the distance distributions, we isolate the RC stars in the CMD. Because the RC and RGB are very close in the CMD and sometimes overlap we decided to model the RGB distributions to produce a 'clean' RC sample. A Hess density map of stars was created for each field in ( M -I ) 0 and M 0 in bins of 0.02 and 0.05 mag respectively. These were then smoothed with a Gaussian kernel having FWHM=2 bins. Each row, at a given magnitude, was modeled with a double-Gaussian for the RC and RGB over the magnitude range 18.5 Next, we use the model SMC CMD to construct an ab- 2 Fig. 4.(a) Hess diagram of the 40S026 field in the eastern portion of the SMC. (b) Simulated CMD for the 40S026 field with ages of 1.4 to 12 Gyr. The red lines are [Fe/H]= -1.488 age=8.0 Gyr BaSTI isochrones (Pietrinferni et al. 2004) at 60 kpc. (c) Red clump luminosity function for the data (red) and simulation (black). The observed luminosity function is much broader than the model suggesting a large line-of-sight depth. Fig. 4.(a) Hess diagram of the 40S026 field in the eastern portion of the SMC. (b) Simulated CMD for the 40S026 field with ages of 1.4 to 12 Gyr. The red lines are [Fe/H]= -1.488 age=8.0 Gyr BaSTI isochrones (Pietrinferni et al. 2004) at 60 kpc. (c) Red clump luminosity function for the data (red) and simulation (black). The observed luminosity function is much broader than the model suggesting a large line-of-sight depth. Fig. 5.Same as Figure 4 but for the 40S206 field with model ages of 2.0 to 12 Gyr. While not as wide as the RC luminosity function of 40S026, the observed luminosity function of 40S206 is wider than the model and indicates some depth is needed to explain the observations. Fig. 5.Same as Figure 4 but for the 40S206 field with model ages of 2.0 to 12 Gyr. While not as wide as the RC luminosity function of 40S026, the observed luminosity function of 40S206 is wider than the model and indicates some depth is needed to explain the observations. solute RC luminosity function (isolating RC stars with 1.025 function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields. 5. COMPARISON TO MODELS To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section). 6. DISCUSSION We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV). 7. SUMMARY We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: 1. The four eastern fields show very large line-of-sight depths ( ∼ 23 kpc) over ∼ 135 · of position angle. 2. Three eastern fields show a strong distance bimodality with one component at ∼ 67 kpc (near the mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. 3. The newly-found stellar component in the east at ∼ 55 kpc is qualitatively consistent with the Diaz & Bekki (2012) model distribution of particles in the tidally-stripped Magellanic Bridge, previously only detected in H I . We conclude that this new component is likely an intermediate-age/old ( ∼ 112 Gyr) stellar component of the Magellanic Bridge and call it the SMC 'eastern stellar structure'. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II). REFERENCES Abbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. D. 1998, AJ, 116, 209 Bekki, K., & Chiba, M. 2009, PASA, 26, 48 Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. 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F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stanimirovi'c, S., Staveley-Smith, L., & Jones, P. A. 2004, ApJ, 604, 176 Sweigart, A. V. 1987, ApJS, 65, 95 Udalski, A., et al. 2008, Acta Astronomica, 58, 329 Xu, H. Y., & Li, Y. 2004, A&A, 418, 225 Zaritsky, D., & Lin, D. N. C. 1997, AJ, 114, 2545 Zaritsky, D., Harris, J., Grebel, E. K., & Thompson, I. B. 2000, ApJ, 534, L53 Zaritsky, D., Harris, J., Thompson, I. B., Grebel, E. K., & Massey, P. 2002, AJ, 123, 855 Next, we use the model SMC CMD to construct an ab- 2 solute RC luminosity function (isolating RC stars with 1.025 function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. Fig. 6.(a) A simulated Hess diagram for 40S026 using the synthetic stellar populations and age/SFR spread only to reproduce the morphology of the RC region (with added photometric noise using the formal observational uncertainties). To achieve this, nearly all of the young and old populations are removed to leave many stars with 0.7-1.2 Gyr. This is clearly not a good representation of the entire observed CMD. (b) Observed Hess diagram of 40S026 with red MW dwarfs removed, using the ( M -T 2 , M -DDO51) 0 diagram (Majewski et al. 2000), to reveal the structure of the upper RGB. (c) A simulated Hess diagram for 40S026 using synthetic stellar populations ( ≥ 1.4 Gyr) convolved with a distance spread (as derived in § 4 for this field) and added photometric noise (as in panel a ). This is a good representation of the observed data. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields. 5. COMPARISON TO MODELS To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. Fig. 7.(left) Red clump luminosity functions for the eight R=4 · fields (with Poisson errors). Some residual RGB stars are visible at faint magnitudes in 40S026 and 40S071. The best-fitting model from the iterative procedure (see text for details) is overplotted in red. Overall the models fit well except for 40S341 which might require a narrower intrinsic RC function to fit the data. (right) Reconstructed density function with distance modulus. The errorbars show internal uncertainties found with a Monte Carlo simulation. Spans of the distribution used to calculate the depth (in upper right-hand corner) are shown as dotted lines. Three of the eastern fields (40S071-40S161) show bimodal distance distributions that have been enhanced through the reconstruction process. 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. Fig. 8.The red clump absolute magnitude luminosity function using the SMC simulated CMD. Ages from 1.4 to 12 to Gyr are included. The mean magnitude from a Gaussian fit is M RC =+0 . 41. the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section). 6. DISCUSSION We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 9.Density function with distance modulus for our red clump data and various models: (a) data, (b) Connors et al. (2006) model (scaled by 1/2.5), (c) Diaz & Bekki (2012) model disk component (scaled by 1/4), (d) Diaz & Bekki (2012) model spheroid1 component, (e) Besla et al. (2012) model1 (scaled by 1/3.5), and (e) Besla et al. (2012) model2 (scaled by 1/5). The field names are given in the upper left hand corner of column a . Vertical dotted lines indicate 50, 60 and 70 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. Fig. 10.Distance-∆ α diagrams for the Diaz & Bekki (2012) disk (a) and spheroid1 (b) models (for particles with | ∆ δ | < 10 · ). Both models show the bridge extending to the east and closer distances, while only the disk model shows the counter-bridge prominently extending to distances of ∼ 80 kpc. the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. Fig. 11.Hess diagrams showing the dependence of the density of the two distance components (at ∼ 55 kpc and ∼ 67 kpc) with SMC radius for two position angles. (a) 40S116, (b) 51S116, (c) 40S026, and (d) 51S026. At PA=116 · the density of both components drops with radius but the distant component more quickly than the closer component. At PA=26 · the density of both components again drops with radius but this time the closer component drops more rapidly (almost vanishing) than the distant component. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV). 7. SUMMARY We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: 1. The four eastern fields show very large line-of-sight depths ( ∼ 23 kpc) over ∼ 135 · of position angle. 2. Three eastern fields show a strong distance bimodality with one component at ∼ 67 kpc (near the mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. 3. The newly-found stellar component in the east at ∼ 55 kpc is qualitatively consistent with the Diaz & Bekki (2012) model distribution of particles in the tidally-stripped Magellanic Bridge, previously only detected in H I . We conclude that this new component is likely an intermediate-age/old ( ∼ 112 Gyr) stellar component of the Magellanic Bridge and call it the SMC 'eastern stellar structure'. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II). REFERENCES Abbott, T., Abdalla, F., Achitouv, I., et al. 2012, The Astronomer's Telegram, 4668, 1 Aparicio, A., & Gallart, C. 2004, AJ, 128, 1465 Bagheri, G., Cioni, M.-R. L., & Napiwotzki, R. 2013, A&A, 551, A78 Beaulieu, J.-P., & Sackett, P. D. 1998, AJ, 116, 209 Bekki, K., & Chiba, M. 2009, PASA, 26, 48 Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. 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T., Weiss, A., & Salaris, M. 1998, MNRAS, 301, 149 Girardi, L., Bressan, A., Bertelli, G., & Chiosi, C. 2000, A&AS, 141, 371 Girardi, L., Bertelli, G., Bressan, A., Chiosi, C., Groenewegen, M. A. T., Marigo, P., Salasnich, B., & Weiss, A. 2002, A&A, 391, 195 Harris, J., & Zaritsky, D. 2006, AJ, 131, 2514 Haschke, R., Grebel, E. K., & Duffau, S. 2012, AJ, 144, 107 Hatzidimitriou, D., Hawkins, M. R. S., & Gyldenkerne, K. 1989, MNRAS, 241, 645 Hatzidimitriou, D., & Hawkins, M. R. S. 1989, MNRAS, 241, 667 Hatzidimitriou, D., Cannon, R. D., & Hawkins, M. R. S. 1993, MNRAS, 261, 873 Keller, S. C., Skymapper Team, & Aegis Team 2012, Galactic Archaeology: Near-Field Cosmology and the Formation of the Milky Way, 458, 409 Kozlowski, S., Udalski, A., Wyrzykowski, L., et al. 2013, Acta Astron., 63, 1 Kroupa, P. 2002, Science, 295, 82 Kunkel, W. E., Demers, S., & Irwin, M. J. 2000, AJ, 119, 2789 Majewski, S. R., Ostheimer, J. C., Kunkel, W. E., & Patterson, R. J. 2000, AJ, 120, 2550 Mathewson, D. S., Ford, V. L., & Visvanathan, N. 1986, ApJ, 301, 664 Mathewson, D. S., Ford, V. L., & Visvanathan, N. 1988, ApJ, 333, 617 Muller, E., Staveley-Smith, L., Zealey, W., & Stanimirovi'c, S. 2003, MNRAS, 339, 105 Muller, E., & Bekki, K. 2007, MNRAS, 381, L11 Murai, T., & Fujimoto, M. 1980, PASJ, 32, 581 Nidever, D. L., Majewski, S. R., Butler Burton, W., & Nigra, L. 2010, ApJ, 723, 1618 Nidever, D. L., Majewski, S. R., Mu˜noz, R. R., Beaton, R. L., Patterson, R. J., & Kunkel, W. E. 2011, ApJ, 733, L10 Noel, N. E. D., & Gallart, C. 2007, ApJ, 665, L23 Noel, N. E. D., Conn, B. C., Carrera, R., et al. 2013, ApJ, 768, 109 Olsen, K. A. G., Zaritsky, D., Blum, R. D., Boyer, M. L., & Gordon, K. D. 2011, ApJ, 737, 29 Pagel, B. E. J., & Tautvaisiene, G. 1998, MNRAS, 299, 535 Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ, 612, 168 R˚uˇziˇcka, A., Theis, C., & Palouˇs, J. 2010, ApJ, 725, 369 Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525 Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stanimirovi'c, S., Staveley-Smith, L., & Jones, P. A. 2004, ApJ, 604, 176 Sweigart, A. V. 1987, ApJS, 65, 95 Udalski, A., et al. 2008, Acta Astronomica, 58, 329 Xu, H. Y., & Li, Y. 2004, A&A, 418, 225 Zaritsky, D., & Lin, D. N. C. 1997, AJ, 114, 2545 Zaritsky, D., Harris, J., Grebel, E. K., & Thompson, I. B. 2000, ApJ, 534, L53 Zaritsky, D., Harris, J., Thompson, I. B., Grebel, E. K., & Massey, P. 2002, AJ, 123, 855 function is smoothed with a FWHM=1.0 bin Gaussian kernel to smooth small-scale fluctuations. This process is then iterated many times until convergence (normally after ∼ 10 iterations) is achieved. To ascertain internal uncertainties in the derived density functions with distance, we performed a simple Monte Carlo simulation for each field. Poisson noise was added to the RC luminosity function and the iterative procedure performed. This was repeated 50 times and the standard deviation for each distance modulus bin (over the 50 mocks) was calculated and used as the internal uncertainty. The final density functions in distance modulus (and the uncertainties) can be seen in the right panels of Figure 7 and the best-fitting models (red) in the left panels. To estimate the depth of a field we used the span of the curve at a density level that 'bisects' the distribution (i.e., half the area under the curve falls below this line and half above). The spans are shown as dotted lines in right panels of Figure 7 and the corresponding depths are indicated in the upper right-hand corner. The models are not perfect matches to the data and any small-scale structure in the density functions in distance should not be taken to represent real structures. However, we can use the density functions to discern broad features. The eastern fields (40S026-40S161) show large line-of-sight depths ( ∼ 23 kpc) over a position angle range of 135 · , while the western fields have much shallower depths of ∼ 10 kpc. Furthermore, three of the eastern fields (40S071, 40S116 and 40S161) show evidence for a distance bimodality (with one component at ∼ 55 kpc and the second at ∼ 63 kpc) and the fourth eastern field (40S026) has a broadened distribution, and is potentially consistent with the trend seen in the other three fields.",
"pages": [
4,
5,
6
]
},
{
"title": "5. COMPARISON TO MODELS",
"content": "To help understand the nature of the large depth and bimodality in the eastern fields we compare our density functions to various simulations of the Magellanic Clouds and Stream: Connors et al. (2006), Diaz & Bekki (2012, hereafter DB12), and Besla et al. (2012, hereafter B12). For each simulation, particles were selected at our field locations relative to the center of the SMC in the simulation (which was sometimes shifted slightly from the observed center). There were often not enough model particles within the 0.36 deg 2 area of our field sizes to make useable distance histograms. Therefore, a matching radius of 0.5 · was used for the Connors and DB12 models, and 0.7 · for the DB12 models. Figure 9 shows (a) our density functions, (b) the model of Connors et al. (2006), (c) the DB12 disk model, which these authors suggest primarily represents the H I component of the SMC, (d) the DB12 spheroid1 model, which they suggest represents a spheroidal-shaped stellar component of the SMC, and (e) the B12 model1 and (f) model2 (both with stars older than 1 Gyr). It is quite immediately clear that none of the models adequately reproduce the shape and line-of-sight depth of the observed fields, although this is not entirely surprising given that these models were optimized to reproduce the gaseous Magellanic Stream. The DB12 disk model does show a bimodality in some of the eastern fields caused by the main SMC body at ∼ 60 kpc and the 'counter-bridge' (see section 3.5 of DB12) at ∼ 80 kpc. In contrast, however, the two components in the data appear at ∼ 67 kpc (likely the main SMC body) and at ∼ 55 kpc (a newly-found stellar component) with very few stars beyond ∼ 70 kpc (except in 40S026). Therefore, it is unlikely that the observed bimodality is related to the DB12 counter-bridge (which our data effectively rule out as a stellar feature at these positions, though it could still exist at smaller radii). We note that the counter-bridge is not very prominent in the spheroid1 model (the model most likely to represent the stars) and it therefore might effectively be an H I -only feature (similar to the Magellanic Stream). Figure 10 shows the distance-∆ α 6 distribution of particles near the SMC in the DB12 disk (a) and DB12 spheroid1 (b) models. Both models show extensions to 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 18.0 18.5 19.0 19.5 Distance Modulus Reconstructed Distance Modulus N N N N N N N N 10.9 kpc 8.1 kpc 11.6 kpc 13.7 kpc 24.3 kpc 24.1 kpc 22.0 kpc 26.0 kpc the east forming the well-known structure of the Magellanic Bridge, prominently seen in H I and young stars ( glyph[lessorsimilar] 200 Myr) forming in the gas. The model predictions of a significant number of particles towards the east and at closer distances, with very few to the west at those same distances, is quite similar, qualititatively, to what is seen in our stellar data. Therefore, we find that the newly-found stellar component to the eastern side of the SMC may be an intermediate-age/old ( ∼ 1-12 Gyr) stellar component of the tidally-stripped Magellanic Bridge (further discussed in next section).",
"pages": [
6,
7,
8
]
},
{
"title": "6. DISCUSSION",
"content": "We detect a large line-of-sight depth ( ∼ 23 kpc) in our four eastern fields covering at least 135 · in position angle. The western fields have a much shallower depth of ∼ 10 kpc with a quite sudden increase in depth between PA=341 · and 26 · . Three of the eastern fields (PA=71 · , 116 · , and 161 · ) show a distance bimodality with the farther component having d ∼ 67 kpc, similar to the distance of the main body of the SMC and the western fields, and the closer component at d ∼ 55 kpc, between the SMC and LMC distance. The fourth eastern field (PA=26 · ) has a large line-of-sight depth and is potentially consistent with the trend seen in the other three eatern fields. This is the first clear evidence of a distance bimodality in the eastern SMC and a newly identified structure (the component at ∼ 55 kpc) which we call the SMC 'eastern stellar structure'. In Section 5 we compared our data to Magellanic Clouds interaction models (Connors et al. 2006; Diaz & Bekki 2012; Besla et al. 2012, see Fig. 9). Overall the models do not match the data very well. The Connors, DB12 spheroid1 and B12 models do not show the large depth in the eastern fields that is seen in the data. In contrast, the DB12 disk model shows a large depth in some western and northwestern fields and a distance bimodality in northern and northeastern fields. The two components are from the main SMC body and the 'counterbridge', which is a tidal stream at large distances ( ∼ 80 kpc) and behind the SMC. While the model does have 'a' bimodality, the distances do not match the data. In contrast, all of the observed fields show a component at d ∼ 66 kpc and the eastern fields have an extra component in front of the SMC at d ∼ 55 kpc, with almost no stars beyond 70 kpc. Therefore, there is no sign of the counter-bridge in our stellar sample. However, the DB12 disk model does show a small number of particles between ∼ 50-60 kpc in the northeastern and eastern fields that are not seen in the other fields. In fact, when all particles with d< 55 kpc are selected they cover a wide region in the eastern SMC spanning PA ≈ 321-144 · (range of 183 · ). The DB12 spheroid1 model shows a similar pattern of particles at this distance but at lower density and spanning a smaller position angle range of 121 · (PA ≈ 65186 · ). It is possible that this is the feature that we are detecting, although at a higher density than predicted by the models. At larger radii this model feature extends to even smaller distances and towards the LMC (see Fig. 10). For the DB12 disk model, which is supposed to represent the gaseous component of the SMC, this arm should represent the well-known H I Magellanic Bridge. If our new component at R =4 · and d ∼ 55 kpc is related to this feature then we very well might be seeing, for the first time, a stellar component of the Magellanic Bridge. Even though the proximity of the new eastern structure to the center of the SMC and its large extent argues for an SMC origin, we must consider other possibilities. Could this be a stream of the LMC, a satellite of the SMC, or something else entirely (e.g., MW halo substructure)? The new structure is likely not related to the LMC because the RC color is too blue. The LMC is more metal-rich ([Fe/H] ∼-0.4) than the SMC ([Fe/H] ∼-1.0; Pagel & Tautvaisiene 1998) and this difference would be evident in the mean RC color, which is metallicity-dependent (Girardi et al. 1998). For a 3.2 Gyr population (log(age)=9.5), the Padova isochrones (Girardi et al. 2002) give a mean RC color of M -T 2 ≈ 1.05 for [Fe/H]= -1 . 0 and M -T 2 ≈ 1.22 for [Fe/H]= -0 . 40 with a difference of ∼ 0.17 mag. On the other hand, the observed mean RC colors in our MAPS LMC and SMC dereddened CMDs show a difference of ∼ 0.04-0.05 mag, a smaller difference than from the theoretical isochrones, likely because we are sampling the more metal-poor peripheries of both objects. However, even a difference of ∼ 0.05 mag between the two components would be visible in the CMDs studied here. While there are some small changes in mean RC color with magnitude they are not more than ∼ 0.01-0.02 mag (Fig. 3). Furthermore, for an LMC-origin, the density of the new structure should increase towards the LMC. However, we have two eastern fields at R =5.1 · from the SMC (closer to the LMC than the four eastern fields analyzed here) that have extended RCs but at lower densities than in the R =4.0 · fields (Fig. 11). This indicates that the new structure decreases in density from the SMC center, but not from the LMC center. The new structure is, therefore, unlikely to be related to the LMC. The large extent in position angle of this structure (corresponding to ∼ 9 kpc), and its fairly uniform density across that distance, makes it unlikely to be a completely new satellite galaxy. A stream of a satellite galaxy of the SMC could span such a large region of the sky, but the density of the stream would have to rival that of the SMC itself in those regions (and exceed it in some places), which would imply a truly massive satellite and a core that should have been previously detected. A new MW halo substructure is also unlikely because it would need to have nearly the identical metallicity, position in the sky, and distance (closer by ∼ 10 kpc) as the SMC (producing a nearly identical distribution in the CMD) and, additionally, have a density fall-off with SMC radius. Therefore, we conclude that the most likely explanation is that the new component at d ∼ 55 kpc is a stream of the SMC itself. The new component's location (to the east) and distance roughly match that expected for a tidally stripped stream of stars from the Diaz & Bekki (2012) simulations that were 'loosened' in the last close encounter of the MCs ∼ 200 Myr ago. While it is more difficult to use RC stars to study the depth of the inner SMC (where there are many young stars) because of age effects, nevertheless such an extended RC as seen in the eastern SMC might be detectable. The RC luminosity function in the inner SMC ( R glyph[lessorsimilar] 2 · ), using MCPS (Zaritsky et al. 2002) and OGLEIII (Udalski et al. 2008) data, looks much more like those in our western fields than our eastern fields, and there is little variation in the shape of the RC with position angle and radius. However, there are three reasons why we are not likely to detect much structure in the density function with distance near the center of the SMC: (1) Near the center the density is very centrally-peaked (in distance) making it difficult to detect a lower-density structure at a non-systemic distance; at larger radii the density distribution is much less centrally-peaked and it becomes easier to detect deviations. (2) It is more difficult to strip stars from the center (because they are more tightly bound) than from the periphery. (3) For stripped stars, deviations in distance from the systemic value should grow with radius (see Fig. 10). Therefore, it is not too surprising that the RC shape in the central region of the SMC looks quite regular and any deviations become visible only at larger radius. We note that the central SMC RR Lyrae also show little spatial pattern or variations and have a depth of only ∼ 8 kpc, similar to what we observe in our western fields (Haschke et al. 2012). In the near future several wide-field photometric surveys will be able to provide the data needed to study the 3D structure of the SMC periphery in great detail. OGLE-IV (Kozlowski et al. 2013) will provide highquality time-series photometry with which RR Lyrae and Cepheids can be identified and accurate distances measured, as was done by Haschke et al. (2012) with OGLEIII. OGLE-IV, SkyMapper (Keller et al. 2012) and DES (Abbott et al. 2012), as well as other DECam programs, will provide photometry to well-below the SMC horizontal branch over a large area of the MCs and with which RC stars can be exploited to study the 3D structure of the SMC. We plan to study the radial velocities and metallicities of stars in the SMC periphery, especially in the east, to help understand any kinematical or chemical differences that may exist between the two components (as previously seen by Hatzidimitriou et al. 1993) and that might shed more light on the origin of the newly found stellar structure. Finally, we note that the existence of a stellar structure in front of the main SMC stellar population could have important implications for microlensing surveys, in that this will increase the self-lensing of SMC stars (Besla et al. 2013; Calchi Novati et al. 2013). We recommend that this newly identified structure be taken into account in the analysis of microlensing surveys probing the eastern periphery of the SMC (e.g., OGLE-IV).",
"pages": [
8,
10,
11
]
},
{
"title": "7. SUMMARY",
"content": "We use high-quality CTIO-4m+MOSAIC photometry in eight fields at R =4 · in the SMC to study the outer galaxy's line-of-sight distribution. Many of the fields show very extended red clump luminosity distributions, as previously seen by Hatzidimitriou & Hawkins (1989) and Gardiner & Hawkins (1991). We show that the extended red clump luminosity distributions cannot be accounted for by age effects because the main-sequence counterparts of very young populations ( glyph[lessorsimilar] 1 Gyr) are not observed. Our main results and conclusions are: mean SMC distance) and a second component at ∼ 55 kpc. The fourth eastern field (40S026) has a broadened distance distribution, and is potentially consistent with the trend seen in the other three eastern fields but at slightly larger distances. A tidally-stripped stellar component of the Magellanic Bridge is consistent with the discovery of accreted SMC stars in the LMC by Olsen et al. (2011) and the claim by Besla et al. (2013) of a tidal origin for the microlensing events reported towards the LMC. In the future, we plan to follow-up our discovery using spectroscopy in SMC fields to compare the stellar velocities to those predicted by the models for the Magellanic Bridge. We find that even though there are some similarities between our data presented here and models from the literature, the differences are much more apparent and it is clear that more work is needed on the simulations to match the SMC stellar distribution. It might be that the stellar components of the SMC (disk or halo) are initially more extended than the simulations have so far considered. We dedicate this paper to Robert T. Rood who did pioneering work on horizontal branch stars and found the extended SMC RC very fascinating. We thank J.D. Diaz, Gurtina Besla and Mario Mateo for useful discussions, and Diaz, Besla and Connors for sharing their models with us so we could compare them to our data. We also thank Sebastian Hidalgo for running IAC-star population synthesis models for us. We thank the OGLE and MCPS projects for making their SMC photometric databases available to the public, and Despina Hatzidimitriou for providing us with her photographic plate photometric of the SMC periphery. D.L.N. was supported by a Dean B. McLaughlin fellowship at the University of Michigan. E.F.B. acknowledges support from NSF grant AST 1008342. We acknowledge funding from NSF grants AST-0307851 and AST-0807945, and NASA/JPL contract 1228235. R.R.M. acknowledges support from CONICYT through project BASAL PFB-06 and from the FONDECYT project N · 1120013. Facilities: CTIO (MOSAIC II).",
"pages": [
11
]
},
{
"title": "REFERENCES",
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"pages": [
11,
12
]
}
]
2013ApJ...779L...5O
https://arxiv.org/pdf/1311.1706.pdf
<document>
<section_header_level_1><location><page_1><loc_9><loc_83><loc_85><loc_85></location>The Terzan 5 puzzle: discovery of a third, metal-poor component</section_header_level_1>
<section_header_level_1><location><page_1><loc_10><loc_76><loc_82><loc_80></location>L. Origlia 2 , D. Massari 3 , R. M. Rich 4 , A. Mucciarelli 3 , F. R. Ferraro 3 , E. Dalessandro 3 Lanzoni 3</section_header_level_1>
<unordered_list>
<list_item><location><page_1><loc_82><loc_78><loc_85><loc_80></location>, B.</list_item>
<list_item><location><page_1><loc_17><loc_73><loc_78><loc_76></location>2 INAF-Osservatorio Astronomico di Bologna, Via Ranzani 1, I-40127 Bologna, Italy, [email protected]</list_item>
<list_item><location><page_1><loc_11><loc_70><loc_85><loc_73></location>3 Dipartimento di Fisica e Astronomia, Universit'a degli Studi di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy</list_item>
<list_item><location><page_1><loc_11><loc_67><loc_84><loc_70></location>4 Physics and Astronomy Bldg, 430 Portola Plaza Box 951547 Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, CA 90095-1547</list_item>
</unordered_list>
<section_header_level_1><location><page_1><loc_41><loc_60><loc_54><loc_61></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_13><loc_49><loc_82><loc_59></location>We report on the discovery of 3 metal-poor giant stars in Terzan 5, a complex stellar system in the the Galactic bulge, known to have two populations at [Fe/H]=-0.25 and +0.3. For these 3 stars we present new echelle spectra obtained with NIRSPEC at Keck II, which confirm their radial velocity membership and provide average [Fe/H]=-0.79 dex iron abundance and [alpha/Fe]=+0.36 dex enhancement. This new population extends the metallicity range of Terzan 5 0.5 dex more metal poor, and it has properties consistent with having formed from a gas polluted by core collapse supernovae.</text>
<text><location><page_1><loc_13><loc_46><loc_82><loc_48></location>Subject headings: Galaxy: bulge - Galaxy: abundances - stars: abundances - stars: late-type techniques: spectroscopic - infrared: stars</text>
<section_header_level_1><location><page_1><loc_9><loc_43><loc_23><loc_44></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_9><loc_28><loc_45><loc_41></location>Terzan 5 is a complex stellar system in the Galactic Bulge. It suffers from huge extinction, its average color excess being E( B -V ) = 2 . 38 (Barbuy et al. 1998; Valenti et al. 2007), and it is also affected by significant differential reddening (∆E( B -V ) /similarequal 0 . 7 mag, Massari et al. 2013). For years it has been classified as a globular cluster, although soon after its discovery its true nature was already disputed (see, e.g., King 1972).</text>
<text><location><page_1><loc_9><loc_20><loc_45><loc_28></location>Recent high resolution imaging in the near infrared (IR) obtained with the Multi-conjugate Adaptive Optics Demonstrator (MAD) at ESOVLT, revealed the presence of two distinct red clumps that cannot be explained by differen-</text>
<text><location><page_1><loc_51><loc_11><loc_86><loc_44></location>tial reddening or distance effects (Ferraro et al. 2009). Prompt near infrared spectroscopy with NIRSPEC at Keck II demonstrated that the two stellar populations are characterized by very different iron abundances ([Fe/H]= -0 . 2 and +0.3). Subsequent spectroscopic studies of 33 red giant stars (Origlia et al. 2011) fully confirmed the large metallicity difference between the two populations. The sub-Solar component has [Fe/H]= -0 . 25 ± 0 . 07 r.m.s. and it is α -enhanced, similar to the old bulge population that likely formed at early epochs and from a gas enriched by a huge amount of type II supernovae (SNe). The super-Solar component, which is possibly a few Gyr younger, has [Fe/H]= +0 . 27 ± 0 . 04 and approximately Solar [ α /Fe] abundance ratio, indicating that it should have originated from a gas polluted by both SNe II and Ia on a longer timescale. Both components show a small internal metallicity spread and the most metal-rich population is also more centrally concentrated (Ferraro et al. 2009; Lanzoni et al. 2010). These observational</text>
<text><location><page_1><loc_86><loc_84><loc_87><loc_85></location>1</text>
<text><location><page_2><loc_9><loc_77><loc_45><loc_86></location>facts could be accounted for by a proto-Terzan 5 more massive in the past than today (its current mass being 2 ∼ 10 6 M /circledot , Lanzoni et al. 2010), which possibly experienced at least two relatively short episodes of star formation with a time delay of a few Gyr.</text>
<text><location><page_2><loc_9><loc_39><loc_45><loc_77></location>There is an interesting chemical similarity between Terzan 5 and the bulge stellar population, which shows a metallicity distribution with two major peaks at sub-Solar and superSolar [Fe/H] and a third, minor component with significantly lower ([Fe/H] ≈ -1 . 0) metallicity (see e.g. Zoccali et al. 2008; Hill et al. 2011; Johnson et al. 2011; Rich, Origlia & Valenti 2012; Uttenthaler et al. 2012; Ness et al. 2013a,b, and references therein). These bulge stellar populations show [ α /Fe] enhancement up to about Solar [Fe/H], and then a progressive decline towards Solar values at super-Solar [Fe/H]. Such a trend is at variance either with the one observed in the thick disk, where the knee occurs at significantly lower values of [Fe/H], and with the rather flat distribution of the thin disc with about Solar [ α /Fe]. Chemical abundances of bulge dwarf stars from microlensing experiments (see e.g. Cohen et al. 2010; Bensby et al. 2013, and references therein) also suggest the presence of two populations, a sub-Solar and old one with [ α /Fe] enhancement, and a possibly younger, more metal-rich one with decreasing [ α /Fe] enhancement with increasing [Fe/H].</text>
<text><location><page_2><loc_9><loc_34><loc_45><loc_39></location>This Letter presents the discovery of 3 red giant stars belonging to Terzan 5, with metallicity far below the sub-Solar component observed so far.</text>
<section_header_level_1><location><page_2><loc_9><loc_30><loc_45><loc_33></location>2. Observations and chemical abundance analysis</section_header_level_1>
<text><location><page_2><loc_9><loc_11><loc_45><loc_29></location>In the context of an ongoing spectroscopic survey with VLT-FLAMES and Keck-DEIMOS of the Terzan 5 stellar populations, aimed at constructing a massive database of radial velocities and metallicities (Massari et al.; Ferraro et al.; 2014 in preparation), we found some indications of the presence of a minor ( ∼ 3%) component significantly more metal-poor than the sub-Solar population of Terzan 5. We acquired high resolution spectra of 3 radial velocity candidate metal-poor giants members of Terzan 5. Observations using NIRSPEC (McLean 1998) at Keck II were under-</text>
<text><location><page_2><loc_51><loc_80><loc_86><loc_86></location>ken on 17 June 2013. We used the NIRSPEC-5 setting to enable observations in the H -band and a 0 . 43 '' slit width that provides an overall spectral resolution R=25,000.</text>
<text><location><page_2><loc_51><loc_59><loc_86><loc_80></location>Data reduction has been performed by using the REDSPEC IDL-based package developed at the UCLA IR Laboratory. Each spectrum has been sky subtracted by using nod pairs, corrected for flat-field and calibrated in wavelength using arc lamps. An O-star spectrum observed during the same night has been used to remove to check and remove telluric features. The signal to noise ratio iper rersolution element of the final spectra is always > 30. Figure 1 shows portions of the observed spectra and the comparison with a Terzan 5 giant with similar stellar parameters and higher iron content from the sub-Solar population studied by Origlia et al. (2011).</text>
<text><location><page_2><loc_51><loc_50><loc_86><loc_58></location>We compare the observed spectra with synthetic ones and we obtain accurate chemical abundances of C and O using molecular lines and of Fe, Ca, Si, Mg, Ti and Al using neutral atomic lines, as also described in Origlia et al. (2011) and references therein.</text>
<text><location><page_2><loc_51><loc_31><loc_86><loc_49></location>We made use of both spectral synthesis analysis and equivalent width measurements of isolated lines. Synthetic spectra covering a wide range of stellar parameters and elemental abundances have been computed by using the same code as in Origlia et al. (2011) and described in detail in Origlia, Rich & Castro (2002) and Origlia & Rich (2004). The code uses the LTE approximation, the molecular blanketed model atmospheres of Johnson, Bernat & Krupp (1980) at temperatures ≤ 4000 K, and the Grevesse & Sauval (1998) abundances for the Solar reference.</text>
<text><location><page_2><loc_51><loc_10><loc_87><loc_31></location>Stellar temperatures have been first estimated from colors, by using the reddening estimates by Massari et al. (2013) and the color-temperature scale by Montegriffo et al. (1998), calibrated on globular cluster giants. Gravity has been estimated from theoretical isochrones (Pietrinferni et al. 2004, 2006), according to the position of the stars on the red giant branch (RGB). An average microturbulence velocity of 2 km/s has been adopted (see e.g. Origlia et al. 1997, for a detailed discussion). The simultaneous spectral fitting of the CO and OH molecular lines that are especially sensitive to temperature, gravity and microturbulence variations (see also Origlia, Rich & Castro 2002),</text>
<text><location><page_3><loc_9><loc_83><loc_45><loc_86></location>allow us to fine-tune our best-fit adopted stellar parameters.</text>
<section_header_level_1><location><page_3><loc_9><loc_80><loc_19><loc_81></location>3. Results</section_header_level_1>
<text><location><page_3><loc_9><loc_73><loc_45><loc_79></location>Our provisional estimate for the systemic velocity of Terzan 5, as inferred from our VLTFLAMES and Keck-DEIMOS survey, is -82 km/s with a velocity dispersion of ≈ 15 km/s.</text>
<text><location><page_3><loc_9><loc_53><loc_45><loc_73></location>From the NIRSPEC spectra we first measured the radial velocity of the 3 stars under study and confirm values within ≈ 1 σ from the systemic velocity of Terzan 5 (see Table 1). These stars are located in the central region of Terzan 5, at distances between 13 and 71 arcsec from the center (see Table 1). Our VLT-FLAMES and KeckDEIMOS survey shows that in this central region the contamination by field stars with similar radial velocities and metallicity is negligible (well below 1%). Preliminary analysis of proper motions also indicates that these stars are likely members of Terzan 5.</text>
<text><location><page_3><loc_9><loc_29><loc_45><loc_53></location>We then measured the chemical abundances of iron, alpha-elements, carbon and aluminum. Our best-fit estimates of the stellar temperature and gravity, radial velocity and chemical abundances with 1 σ random errors are listed in Table 1. In the evaluation of the overall error budget we also estimate that systematics due to ∆T eff ± 200 K, ∆log g ± 0.5 dex, ∆ ξ ± 0.5 km/s variations in the adopted stellar parameters can affect the inferred abundances by ≈ ± 0 . 15 dex. However, the derived abundance ratios are less dependent on the systematic error, since most of the spectral features used to measure abundance ratios have similar trends with varying the stellar parameters, and at least some degeneracy between abundance and the latter is canceled out.</text>
<text><location><page_3><loc_9><loc_18><loc_45><loc_28></location>We find the average iron abundance [Fe/H]=0.79 ± 0.04 r.m.s. to be significantly lower (by a factor of ∼ 3) than the value of the sub-Solar population ([Fe/H]= -0 . 25), pointing towards the presence of a distinct population in Terzan 5, rather than to the low metallicity tail of the subSolar component.</text>
<text><location><page_3><loc_9><loc_10><loc_45><loc_17></location>As shown in Figure 2, our newly discovered metal-poor population has an average α -enhancement ([ α /Fe]= +0 . 36 ± 0 . 04 r.m.s.) similar to that of the sub-Solar one, indicating that both populations likely formed early and on short</text>
<text><location><page_3><loc_51><loc_85><loc_84><loc_86></location>timescales from a gas polluted by type II SNe.</text>
<text><location><page_3><loc_51><loc_74><loc_86><loc_84></location>As the stars belonging to the sub-Solar component, also these other giants with low iron content show an enhanced [Al/Fe] abundance ratio (average [Al/Fe]= +0 . 41 ± 0 . 18 r.m.s.) and no evidence of Al-Mg and Al-O anti-correlations, and/or large [O/Fe] and [Al/Fe] scatters, although no firm conclusion can be drawn with 3 stars only.</text>
<text><location><page_3><loc_51><loc_66><loc_86><loc_73></location>We also measured some [C/Fe] depletion (at least in stars #243 and #262), as commonly found in giant stars and explained with mixing processes in the stellar interiors during the evolution along the RGB.</text>
<section_header_level_1><location><page_3><loc_51><loc_63><loc_76><loc_64></location>4. Discussion and Conclusions</section_header_level_1>
<text><location><page_3><loc_51><loc_55><loc_86><loc_62></location>New spectroscopic observations of 3 stars, members of Terzan 5, have provided a further evidence of the complex nature of this stellar system and of its likely connection with the bulge formation and evolution history.</text>
<text><location><page_3><loc_51><loc_44><loc_86><loc_54></location>We find that Terzan 5 hosts a third, metalpoorer population with average [Fe/H]= -0 . 79 ± 0 . 04 r.m.s. and [ α /Fe] enhancement. From our VLT-FLAMES/Keck-DEIMOS survey, we estimate that this component represents a minor fraction (a few percent) of the stellar populations in Terzan 5.</text>
<text><location><page_3><loc_51><loc_34><loc_86><loc_43></location>Notably, a similar fraction ( ≈ 5%) of metalpoor stars ([Fe/H] ≈ -1) has been also detected in the bulge (see e.g. Ness et al. 2013a,b, and references therein). This metal-poor population shows a kinematics typical of a slowly rotating spheroidal or a metal weak thick disk component.</text>
<text><location><page_3><loc_51><loc_13><loc_86><loc_34></location>Our discovery significantly enlarges the metallicity range covered by Terzan 5, which amounts to ∆[Fe/H] ≈ 1 dex. Such a value is completely unexpected and unobserved in genuine globular clusters. Indeed, within the Galaxy only another globular-like system, namely ω Centauri, harbors stellar populations with a large ( > 1 dex) spread in iron (Norris & Da Costa 1995; Sollima et al. 2005; Johnson & Pilachowski 2010; Pancino et al. 2011). This evidence strongly sets Terzan 5 and ω Centauri apart from the class of genuine globular clusters, and suggests a more complex formation and evolutionary history for these two multi-iron systems.</text>
<text><location><page_3><loc_51><loc_10><loc_86><loc_12></location>It is also interesting to note that detailed spectroscopic screening recently performed in</text>
<text><location><page_4><loc_9><loc_76><loc_45><loc_86></location>ω Centauri revealed an additional sub-component significantly more metal-poor (by ∆[Fe/H] ∼ 0 . 3 -0 . 4 dex) than the dominant population (Pancino et al. 2011). The authors suggest that this is best accounted for in a self-enrichment scenario, where these stars could be the remnants of the fist stellar generation in ω Centauri.</text>
<text><location><page_4><loc_9><loc_56><loc_45><loc_75></location>The three populations of Terzan 5 may also be explained with some self-enrichment. The narrow peaks in their metallicity distribution can be the result of a quite bursty star formation activity in the proto-Terzan 5, which should have been much more massive in the past to retain the SN ejecta and progressively enrich in metals its gas. However, Terzan 5 might also be the result of an early merging of fragments with sub-Solar metallicity at the epoch of the bulge/bar formation, and with younger and more metal-rich sub-structures following subsequent interactions with the central disk.</text>
<text><location><page_4><loc_9><loc_39><loc_45><loc_55></location>However, apart from the similarity in terms of large iron range and possible self-enrichment, ω Centauri and Terzan 5 likely had quite different origins and evolution. It is now commonly accepted that ω Centauri can be the remnant of a dwarf galaxy accreted from outside the Milky Way (e.g. Bekki & Freeman 2003). At variance, the much higher metallicity of Terzan 5 and its chemical similarity to the bulge populations suggests some symbiotic evolution between these two stellar systems.</text>
<text><location><page_4><loc_9><loc_16><loc_46><loc_37></location>This research was supported by the Istituto Nazionale di Astrofisica (INAF, under contract PRIN-INAF 2010). The research is also part of the project COSMIC-LAB (http://www.cosmic-lab.eu) funded by the European Research Council (under contract ERC-2010-AdG-267675). The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The authors wish to thank the anonymous Referee for his/her useful comments.</text>
<section_header_level_1><location><page_4><loc_51><loc_85><loc_63><loc_86></location>REFERENCES</section_header_level_1>
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<figure>
<location><page_6><loc_15><loc_31><loc_77><loc_75></location>
<caption>Fig. 1.- Portion of the NIRSPEC H -band spectra of two red giants of Terzan 5 with similar temperature (T eff ≈ 3800 K), but different chemical abundance patterns (solid line for the metal-poor star #243, dotted line for a sub-Solar star at [Fe/H] ≈ -0.22 from Origlia et al. 2011). The metal poor giant #243 has significantly shallower features. A few atomic lines and molecular bands of interest are marked.</caption>
</figure>
<figure>
<location><page_7><loc_24><loc_28><loc_76><loc_75></location>
<caption>Fig. 2.- Individual [ α /Fe] and [Al/Fe] abundance ratios as a function of [Fe/H] for the 3 observed metalpoor giants (solid dots), and the 20 sub-Solar (open squares) and 13 super-Solar (open triangles) giants from Origlia et al. (2011), for comparison. Typical errorbars are plotted in the top-right corner of each panel.</caption>
</figure>
<table>
<location><page_8><loc_9><loc_44><loc_95><loc_53></location>
<caption>Table 1 Stellar parameters and abundances for the 3 observed giants in Terzan 5.</caption>
</table>
</document>
[
{
"title": "ABSTRACT",
"content": "We report on the discovery of 3 metal-poor giant stars in Terzan 5, a complex stellar system in the the Galactic bulge, known to have two populations at [Fe/H]=-0.25 and +0.3. For these 3 stars we present new echelle spectra obtained with NIRSPEC at Keck II, which confirm their radial velocity membership and provide average [Fe/H]=-0.79 dex iron abundance and [alpha/Fe]=+0.36 dex enhancement. This new population extends the metallicity range of Terzan 5 0.5 dex more metal poor, and it has properties consistent with having formed from a gas polluted by core collapse supernovae. Subject headings: Galaxy: bulge - Galaxy: abundances - stars: abundances - stars: late-type techniques: spectroscopic - infrared: stars",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Terzan 5 is a complex stellar system in the Galactic Bulge. It suffers from huge extinction, its average color excess being E( B -V ) = 2 . 38 (Barbuy et al. 1998; Valenti et al. 2007), and it is also affected by significant differential reddening (∆E( B -V ) /similarequal 0 . 7 mag, Massari et al. 2013). For years it has been classified as a globular cluster, although soon after its discovery its true nature was already disputed (see, e.g., King 1972). Recent high resolution imaging in the near infrared (IR) obtained with the Multi-conjugate Adaptive Optics Demonstrator (MAD) at ESOVLT, revealed the presence of two distinct red clumps that cannot be explained by differen- tial reddening or distance effects (Ferraro et al. 2009). Prompt near infrared spectroscopy with NIRSPEC at Keck II demonstrated that the two stellar populations are characterized by very different iron abundances ([Fe/H]= -0 . 2 and +0.3). Subsequent spectroscopic studies of 33 red giant stars (Origlia et al. 2011) fully confirmed the large metallicity difference between the two populations. The sub-Solar component has [Fe/H]= -0 . 25 ± 0 . 07 r.m.s. and it is α -enhanced, similar to the old bulge population that likely formed at early epochs and from a gas enriched by a huge amount of type II supernovae (SNe). The super-Solar component, which is possibly a few Gyr younger, has [Fe/H]= +0 . 27 ± 0 . 04 and approximately Solar [ α /Fe] abundance ratio, indicating that it should have originated from a gas polluted by both SNe II and Ia on a longer timescale. Both components show a small internal metallicity spread and the most metal-rich population is also more centrally concentrated (Ferraro et al. 2009; Lanzoni et al. 2010). These observational 1 facts could be accounted for by a proto-Terzan 5 more massive in the past than today (its current mass being 2 ∼ 10 6 M /circledot , Lanzoni et al. 2010), which possibly experienced at least two relatively short episodes of star formation with a time delay of a few Gyr. There is an interesting chemical similarity between Terzan 5 and the bulge stellar population, which shows a metallicity distribution with two major peaks at sub-Solar and superSolar [Fe/H] and a third, minor component with significantly lower ([Fe/H] ≈ -1 . 0) metallicity (see e.g. Zoccali et al. 2008; Hill et al. 2011; Johnson et al. 2011; Rich, Origlia & Valenti 2012; Uttenthaler et al. 2012; Ness et al. 2013a,b, and references therein). These bulge stellar populations show [ α /Fe] enhancement up to about Solar [Fe/H], and then a progressive decline towards Solar values at super-Solar [Fe/H]. Such a trend is at variance either with the one observed in the thick disk, where the knee occurs at significantly lower values of [Fe/H], and with the rather flat distribution of the thin disc with about Solar [ α /Fe]. Chemical abundances of bulge dwarf stars from microlensing experiments (see e.g. Cohen et al. 2010; Bensby et al. 2013, and references therein) also suggest the presence of two populations, a sub-Solar and old one with [ α /Fe] enhancement, and a possibly younger, more metal-rich one with decreasing [ α /Fe] enhancement with increasing [Fe/H]. This Letter presents the discovery of 3 red giant stars belonging to Terzan 5, with metallicity far below the sub-Solar component observed so far.",
"pages": [
1,
2
]
},
{
"title": "2. Observations and chemical abundance analysis",
"content": "In the context of an ongoing spectroscopic survey with VLT-FLAMES and Keck-DEIMOS of the Terzan 5 stellar populations, aimed at constructing a massive database of radial velocities and metallicities (Massari et al.; Ferraro et al.; 2014 in preparation), we found some indications of the presence of a minor ( ∼ 3%) component significantly more metal-poor than the sub-Solar population of Terzan 5. We acquired high resolution spectra of 3 radial velocity candidate metal-poor giants members of Terzan 5. Observations using NIRSPEC (McLean 1998) at Keck II were under- ken on 17 June 2013. We used the NIRSPEC-5 setting to enable observations in the H -band and a 0 . 43 '' slit width that provides an overall spectral resolution R=25,000. Data reduction has been performed by using the REDSPEC IDL-based package developed at the UCLA IR Laboratory. Each spectrum has been sky subtracted by using nod pairs, corrected for flat-field and calibrated in wavelength using arc lamps. An O-star spectrum observed during the same night has been used to remove to check and remove telluric features. The signal to noise ratio iper rersolution element of the final spectra is always > 30. Figure 1 shows portions of the observed spectra and the comparison with a Terzan 5 giant with similar stellar parameters and higher iron content from the sub-Solar population studied by Origlia et al. (2011). We compare the observed spectra with synthetic ones and we obtain accurate chemical abundances of C and O using molecular lines and of Fe, Ca, Si, Mg, Ti and Al using neutral atomic lines, as also described in Origlia et al. (2011) and references therein. We made use of both spectral synthesis analysis and equivalent width measurements of isolated lines. Synthetic spectra covering a wide range of stellar parameters and elemental abundances have been computed by using the same code as in Origlia et al. (2011) and described in detail in Origlia, Rich & Castro (2002) and Origlia & Rich (2004). The code uses the LTE approximation, the molecular blanketed model atmospheres of Johnson, Bernat & Krupp (1980) at temperatures ≤ 4000 K, and the Grevesse & Sauval (1998) abundances for the Solar reference. Stellar temperatures have been first estimated from colors, by using the reddening estimates by Massari et al. (2013) and the color-temperature scale by Montegriffo et al. (1998), calibrated on globular cluster giants. Gravity has been estimated from theoretical isochrones (Pietrinferni et al. 2004, 2006), according to the position of the stars on the red giant branch (RGB). An average microturbulence velocity of 2 km/s has been adopted (see e.g. Origlia et al. 1997, for a detailed discussion). The simultaneous spectral fitting of the CO and OH molecular lines that are especially sensitive to temperature, gravity and microturbulence variations (see also Origlia, Rich & Castro 2002), allow us to fine-tune our best-fit adopted stellar parameters.",
"pages": [
2,
3
]
},
{
"title": "3. Results",
"content": "Our provisional estimate for the systemic velocity of Terzan 5, as inferred from our VLTFLAMES and Keck-DEIMOS survey, is -82 km/s with a velocity dispersion of ≈ 15 km/s. From the NIRSPEC spectra we first measured the radial velocity of the 3 stars under study and confirm values within ≈ 1 σ from the systemic velocity of Terzan 5 (see Table 1). These stars are located in the central region of Terzan 5, at distances between 13 and 71 arcsec from the center (see Table 1). Our VLT-FLAMES and KeckDEIMOS survey shows that in this central region the contamination by field stars with similar radial velocities and metallicity is negligible (well below 1%). Preliminary analysis of proper motions also indicates that these stars are likely members of Terzan 5. We then measured the chemical abundances of iron, alpha-elements, carbon and aluminum. Our best-fit estimates of the stellar temperature and gravity, radial velocity and chemical abundances with 1 σ random errors are listed in Table 1. In the evaluation of the overall error budget we also estimate that systematics due to ∆T eff ± 200 K, ∆log g ± 0.5 dex, ∆ ξ ± 0.5 km/s variations in the adopted stellar parameters can affect the inferred abundances by ≈ ± 0 . 15 dex. However, the derived abundance ratios are less dependent on the systematic error, since most of the spectral features used to measure abundance ratios have similar trends with varying the stellar parameters, and at least some degeneracy between abundance and the latter is canceled out. We find the average iron abundance [Fe/H]=0.79 ± 0.04 r.m.s. to be significantly lower (by a factor of ∼ 3) than the value of the sub-Solar population ([Fe/H]= -0 . 25), pointing towards the presence of a distinct population in Terzan 5, rather than to the low metallicity tail of the subSolar component. As shown in Figure 2, our newly discovered metal-poor population has an average α -enhancement ([ α /Fe]= +0 . 36 ± 0 . 04 r.m.s.) similar to that of the sub-Solar one, indicating that both populations likely formed early and on short timescales from a gas polluted by type II SNe. As the stars belonging to the sub-Solar component, also these other giants with low iron content show an enhanced [Al/Fe] abundance ratio (average [Al/Fe]= +0 . 41 ± 0 . 18 r.m.s.) and no evidence of Al-Mg and Al-O anti-correlations, and/or large [O/Fe] and [Al/Fe] scatters, although no firm conclusion can be drawn with 3 stars only. We also measured some [C/Fe] depletion (at least in stars #243 and #262), as commonly found in giant stars and explained with mixing processes in the stellar interiors during the evolution along the RGB.",
"pages": [
3
]
},
{
"title": "4. Discussion and Conclusions",
"content": "New spectroscopic observations of 3 stars, members of Terzan 5, have provided a further evidence of the complex nature of this stellar system and of its likely connection with the bulge formation and evolution history. We find that Terzan 5 hosts a third, metalpoorer population with average [Fe/H]= -0 . 79 ± 0 . 04 r.m.s. and [ α /Fe] enhancement. From our VLT-FLAMES/Keck-DEIMOS survey, we estimate that this component represents a minor fraction (a few percent) of the stellar populations in Terzan 5. Notably, a similar fraction ( ≈ 5%) of metalpoor stars ([Fe/H] ≈ -1) has been also detected in the bulge (see e.g. Ness et al. 2013a,b, and references therein). This metal-poor population shows a kinematics typical of a slowly rotating spheroidal or a metal weak thick disk component. Our discovery significantly enlarges the metallicity range covered by Terzan 5, which amounts to ∆[Fe/H] ≈ 1 dex. Such a value is completely unexpected and unobserved in genuine globular clusters. Indeed, within the Galaxy only another globular-like system, namely ω Centauri, harbors stellar populations with a large ( > 1 dex) spread in iron (Norris & Da Costa 1995; Sollima et al. 2005; Johnson & Pilachowski 2010; Pancino et al. 2011). This evidence strongly sets Terzan 5 and ω Centauri apart from the class of genuine globular clusters, and suggests a more complex formation and evolutionary history for these two multi-iron systems. It is also interesting to note that detailed spectroscopic screening recently performed in ω Centauri revealed an additional sub-component significantly more metal-poor (by ∆[Fe/H] ∼ 0 . 3 -0 . 4 dex) than the dominant population (Pancino et al. 2011). The authors suggest that this is best accounted for in a self-enrichment scenario, where these stars could be the remnants of the fist stellar generation in ω Centauri. The three populations of Terzan 5 may also be explained with some self-enrichment. The narrow peaks in their metallicity distribution can be the result of a quite bursty star formation activity in the proto-Terzan 5, which should have been much more massive in the past to retain the SN ejecta and progressively enrich in metals its gas. However, Terzan 5 might also be the result of an early merging of fragments with sub-Solar metallicity at the epoch of the bulge/bar formation, and with younger and more metal-rich sub-structures following subsequent interactions with the central disk. However, apart from the similarity in terms of large iron range and possible self-enrichment, ω Centauri and Terzan 5 likely had quite different origins and evolution. It is now commonly accepted that ω Centauri can be the remnant of a dwarf galaxy accreted from outside the Milky Way (e.g. Bekki & Freeman 2003). At variance, the much higher metallicity of Terzan 5 and its chemical similarity to the bulge populations suggests some symbiotic evolution between these two stellar systems. This research was supported by the Istituto Nazionale di Astrofisica (INAF, under contract PRIN-INAF 2010). The research is also part of the project COSMIC-LAB (http://www.cosmic-lab.eu) funded by the European Research Council (under contract ERC-2010-AdG-267675). The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The authors wish to thank the anonymous Referee for his/her useful comments.",
"pages": [
3,
4
]
},
{
"title": "REFERENCES",
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"pages": [
4,
5
]
}
]
2013ApJS..205...19F
https://arxiv.org/pdf/1302.2087.pdf
<document>
<section_header_level_1><location><page_1><loc_16><loc_85><loc_84><loc_86></location>MHD modeling of solar system processes on geodesic grids</section_header_level_1>
<text><location><page_1><loc_27><loc_80><loc_73><loc_82></location>V. Florinski 1 , 2 , X. Guo 2 , D. S. Balsara 3 , and C. Meyer 3</text>
<text><location><page_1><loc_20><loc_75><loc_27><loc_76></location>Received</text>
<text><location><page_1><loc_48><loc_75><loc_49><loc_76></location>;</text>
<text><location><page_1><loc_52><loc_75><loc_59><loc_76></location>accepted</text>
<section_header_level_1><location><page_2><loc_44><loc_85><loc_56><loc_86></location>ABSTRACT</section_header_level_1>
<text><location><page_2><loc_17><loc_41><loc_83><loc_80></location>This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.</text>
<text><location><page_2><loc_17><loc_33><loc_83><loc_38></location>Subject headings: magnetohydrodynamics (MHD) - methods: numerical - planets and satellites: magnetic fields - solar wind</text>
<section_header_level_1><location><page_3><loc_42><loc_85><loc_58><loc_86></location>1. Introduction</section_header_level_1>
<text><location><page_3><loc_12><loc_42><loc_88><loc_81></location>Many astrophysical plasma processes occur is regions of space surrounding a central compact object such as a star or a planet. Examples include stellar winds, planetary magnetospheres, supernova blast waves, and mass accretion onto compact objects. In all these environments the central body (a star or a planet) is typically much smaller than the characteristic scales of the plasma flows. In solving this class of problem on a computer, radial grids are commonly used because resolution can be readily increased near the origin. The simplest and the most commonly used is the standard spherical polar ( r , θ , ϕ ) grid (e.g., Washimi & Tanaka 1996; Pogorelov & Matsuda 1998; Ratkiewicz et al. 1998). This grid has a singularity on the z axis, where the control volume ∆ V = r 2 ∆ r sin θ ∆ θ ∆ ϕ , ∆ r , ∆ θ and ∆ ϕ being the grid cell dimensions in the radial, latitudinal, and azimuthal directions, respectively, vanishes as sin θ → 0. For explicit methods, this requires a small global time step to satisfy the Courant stability condition for a system of hyperbolic conservation laws for the entire grid (implicit or semi-implicit methods (e.g., T'oth et al. 1998) don't suffer from this limitation).</text>
<text><location><page_3><loc_12><loc_18><loc_88><loc_40></location>Spherical grids are also used in simulating the transport of energetic charged particle, such as galactic cosmic rays, in turbulent astrophysical flows (Florinski & Pogorelov 2009). Transport models based on stochastic trajectory (Monte-Carlo) methods also suffer from the singularity on the polar axis. For example, in modeling cosmic-ray transport in the heliosphere it is common to align the z axis with the solar rotation axis. Because energetic particle transport (diffusion and drift) is very rapid at high latitudes due to a weaker magnetic field, a model must take vanishingly small time steps when a particle ventures close to the polar axis, which results in an inferior overall model efficiency.</text>
<text><location><page_3><loc_12><loc_11><loc_87><loc_15></location>Time step requirements can be relaxed substantially by employing a grid that has a (nearly) uniform solid angle coverage. Examples include triangle, hexagon, or diamond</text>
<text><location><page_4><loc_12><loc_58><loc_88><loc_86></location>based geodesic grids (Du et al. 2003; Yeh 2007; Upadhyaya et al. 2010), obtained by a recursive division of a base platonic solid, and cubed sphere grids (Ronchi et al. 1996; Putman & Lin 2007). This paper introduces a framework for finite volume methods of solution of hyperbolic conservation laws in three dimensions, such as gas-dynamic or MHD systems, using spherical geodesic grids composed of hexagonal prism elements. Results are illustrated on a three-dimensional simulation of solar rotation and formation of corotating interaction regions (CIRs), an interaction between the solar wind and the surrounding local interstellar medium or LISM, and a simulation of Earth's magnetosphere. The new framework can be employed to model a broad range of large-scale 3D astrophysical plasma flows around a compact object where high computational efficiency is a priority.</text>
<section_header_level_1><location><page_4><loc_41><loc_51><loc_59><loc_53></location>2. Grid structure</section_header_level_1>
<text><location><page_4><loc_12><loc_23><loc_88><loc_48></location>Our three-dimensional grid consist of a 2D geodesic unstructured grid on a sphere combined with a concentric nonuniform radial stepping with smaller cells near the origin. The 2D surface grid is a Voronoi tesselation of a sphere produced from a dual triangular (Delaunay) tesselation. The latter is generated by a recursive subdivision of an icosahedron. We use the geodesic grid generator software developed by the ICON project ( http://icon.enes.org ) for use in atmospheric circulation modeling. An optimization algorithm (Heikes & Randall 1995), included in their code, produces a mesh with a difference in spherical surface areas between the largest and the smallest cells of less than 10%.</text>
<text><location><page_4><loc_12><loc_16><loc_88><loc_21></location>The number of vertices (V), edges (E) and faces (F) on a grid produced by l th division is given by</text>
<formula><location><page_4><loc_29><loc_12><loc_88><loc_15></location>N V = 20 · 2 2 l , N E = 30 · 2 2 l , N F = 10 · 2 2 l +2 . (1)</formula>
<text><location><page_4><loc_12><loc_10><loc_86><loc_11></location>In this notation a level 0 grid is dual to the original icosahedron projected onto a unit</text>
<figure>
<location><page_5><loc_15><loc_25><loc_85><loc_79></location>
<caption>Fig. 1.- From left to right: level 3, 4, and 5 geodesic Voronoi grids produced by a recursive division of the base icosahedron.</caption>
</figure>
<text><location><page_6><loc_12><loc_79><loc_87><loc_86></location>sphere. The base shape of a control volume in a finite volume method is a spherical hexagonal prism with the exception of 12 pentagonal prisms located at the vertices of the original icosahedron. Level 3, 4, and 5 hexagonal geodesic grids are shown in Figure 1.</text>
<text><location><page_6><loc_12><loc_43><loc_88><loc_76></location>A more detailed view of the Voronoi grid structure is given in Figure 2. A hexagonal face F m (shaded) is shown surrounded by six adjacent faces F m 1 .. F m 6 . The face centers of the dual triangle-based Delaunay grid (blue lines) are located at the Voronoi vertices (V); likewise, the former's vertices are at the Voronoi grid's face centers (F). The edges of the Voronoi and Delaunay grids on a sphere are mutually orthogonal and intersect at their midpoints. To achieve acceptable resolution in typical astrophysical flow modeling problems level 5 or higher geodesic grids should be used. Most of our simulations use level 6 mesh containing 40,962 Voronoi polygons. We emphasize that these 40,962 hexagons are distributed evenly over the surface of each spherical layer of cells. This gives us a resolution of about 3 × 10 -4 steradians in solid angle which corresponds to an angular resolution of one degree. By condensing the mesh in the radial direction, one can achieve a further degree of refinement as required by the problem.</text>
<text><location><page_6><loc_12><loc_24><loc_88><loc_40></location>We introduce a set of unit vectors normal to the edges of the Voronoi grid ˆ n mn , where the index m refers to the m th face and n = [1 , 6] is the number of the edge counted in a counter-clockwise direction. The unit vectors are tangential to the surface of the sphere. The corresponding edge lengths, measured along great circles, are designated L mn . The outward radial unit vector at the cell center is ˆ r m . We also designate the area of the face on the unit sphere as A m . In this notation the control volume is equal to</text>
<formula><location><page_6><loc_42><loc_20><loc_88><loc_22></location>∆ V im = A m r 2 i ∆ r i , (2)</formula>
<text><location><page_6><loc_12><loc_10><loc_88><loc_17></location>where i is the index on the radial axis. The areas A m are calculated by dividing each hexagonal face into six (five for pentagons) spherical triangles and adding up their areas using standard expressions from spherical trigonometry. Having defined our cell dimensions</text>
<figure>
<location><page_7><loc_21><loc_36><loc_79><loc_70></location>
<caption>Fig. 2.- A close up view of the geodesic grid illustrating the relationships between a face F m and its neighboring faces F m 1 .. F m 6 . Unit vectors normal to the edges of the Voronoi face ˆ n m 1 .. ˆ n m 6 are shown. A fragment of the Delaunay grid is drawn with blue lines.</caption>
</figure>
<text><location><page_8><loc_12><loc_82><loc_85><loc_86></location>is this way we can proceed to integrate a system of conservation laws inside a control volume.</text>
<text><location><page_8><loc_12><loc_60><loc_88><loc_79></location>It is worth pointing out that a similar geodesic-mesh-based model was developed by Nakamizo et al. (2009) Their mesh was generated from a dodecahedron by first dividing each face into five triangles followed by a recursive subdivision of each triangle into four smaller triangles. The resulting unstructured grid topology is similar (but not identical) to our dual Delaunay grid. Interestingly, in the model of Nakamizo et al. (2009) computations are also performed on a hexagonal grid, generated by connecting the centroids of the Delaunay triangles.</text>
<section_header_level_1><location><page_8><loc_37><loc_53><loc_63><loc_54></location>3. MHD conservation laws</section_header_level_1>
<text><location><page_8><loc_12><loc_46><loc_88><loc_50></location>For the heliospheric and magnetospheric problems ( § 6) we solve a modified set of MHD equations, written in terms of conservative variables U and fluxes F as</text>
<formula><location><page_8><loc_43><loc_40><loc_88><loc_44></location>∂ U ∂t + ∇· F = Q , (3)</formula>
<text><location><page_8><loc_12><loc_37><loc_17><loc_38></location>where</text>
<text><location><page_8><loc_12><loc_17><loc_87><loc_25></location>in CGS units. Here ρ is density, u is velocity, B is magnetic field, I is a unit dyadic, p = p g + B 2 / (8 π ) is the total pressure, p g being the gas kinetic pressure, and the energy density e is given by</text>
<formula><location><page_8><loc_27><loc_24><loc_88><loc_37></location>U = ρ ρ u e B , F = ρ u ρ uu + p I -BB / (4 π ) ( e + p ) u -B ( u · B ) / (4 π ) uB -Bu (4)</formula>
<formula><location><page_8><loc_40><loc_12><loc_88><loc_17></location>e = ρu 2 2 + p g γ -1 + B 2 8 π . (5)</formula>
<text><location><page_8><loc_16><loc_10><loc_88><loc_11></location>We employ two alternative models to control the divergence of magnetic field. The first</text>
<text><location><page_9><loc_12><loc_79><loc_87><loc_86></location>is the numerical scheme proposed by Powell et al. (1999), where numerical magnetic field divergence is advected out of the simulation domain with the flow velocity. This scheme modifies the system of conservation laws with a hyperbolic source term</text>
<formula><location><page_9><loc_37><loc_64><loc_88><loc_77></location>Q = -∇· B 0 B / (4 π ) u · B / (4 π ) u . (6)</formula>
<text><location><page_9><loc_12><loc_57><loc_87><loc_64></location>The second scheme employs a generalized Lagrange multiplier (GLM) ψ for a mixed hyperbolic-parabolic correction (Dedner et al. 2002). The system (4) is extended with an additional transport equation for ψ</text>
<formula><location><page_9><loc_40><loc_52><loc_88><loc_56></location>∂ψ ∂t + ∇· ( c 2 h B ) = -c 2 h c 2 p ψ, (7)</formula>
<text><location><page_9><loc_12><loc_31><loc_88><loc_50></location>where c h is a constant, isotropic advection speed, taken to be somewhat faster than the fastest wave speed in the problem, and c p is related to the rate of decay of ψ . Dedner et al. (2002) proposed two methods to fix the value of c p : (a) by fixing the time rate of decay of the GLM variable r d = exp( -∆ tc 2 h /c 2 p ), where ∆ t is the time step, and (b) by fixing the characteristic length over which the decay occurs, given by l d = c 2 p /c h . Both methods are available in our code. In the GLM scheme the conservation law for magnetic field (Faraday's law) is modified to read</text>
<formula><location><page_9><loc_37><loc_26><loc_88><loc_30></location>∂ B ∂t + ∇· ( uB -Bu + ψ I ) = 0 . (8)</formula>
<text><location><page_9><loc_12><loc_19><loc_88><loc_24></location>The system (3) is integrated over a control volume ∆ V im shown in Figure 3 to obtain the finite volume method</text>
<formula><location><page_9><loc_25><loc_8><loc_88><loc_18></location>∆ V im ∆ U im ∆ t = -A m ( r 2 i +1 / 2 F i +1 / 2 ,m -r 2 i -1 / 2 F i -1 / 2 ,m ) · ˆ r m -r i ∆ r i 6 ∑ n =1 L mn F i ( mn ) · ˆ n mn +∆ V im Q im . (9)</formula>
<figure>
<location><page_10><loc_28><loc_29><loc_72><loc_72></location>
<caption>Fig. 3.- A prismatic control volume showing the unit vectors normal to the interfaces.</caption>
</figure>
<text><location><page_11><loc_12><loc_76><loc_88><loc_86></location>Here F i ( mn ) is the flux at the center of the edge shared by the m th cell and its n th neighbor (where n = [1 , 6]). Note that the source term Q does not involve the right hand side of Eq. (7). The parabolic correction is applied by multiplying the value of ψ obtained from the finite volume scheme (9) by the decay factor,</text>
<formula><location><page_11><loc_35><loc_65><loc_88><loc_74></location>ψ → ψ × r d , method (a) , e -∆ tc h /l d , method (b) . (10)</formula>
<text><location><page_11><loc_12><loc_62><loc_87><loc_67></location>In our simulations we typically use 0 . 9 < r d < 1 and l d equal to several times the smallest linear grid size.</text>
<text><location><page_11><loc_12><loc_53><loc_88><loc_60></location>The divergence of the magnetic field is obtained from Gauss's theorem in the same way as ∇· F is calculated in Eq. (9). More generally, the divergence and curl operators acting on an arbitrary vector v may be written as</text>
<formula><location><page_11><loc_22><loc_45><loc_88><loc_51></location>∇· v = ˆ r m · ( r 2 i +1 / 2 v i +1 / 2 ,m -r 2 i -1 / 2 v i -1 / 2 ,m ) r 2 i ∆ r i + 6 ∑ n =1 L mn ˆ n mn · v i ( mn ) r i A m , (11)</formula>
<formula><location><page_11><loc_20><loc_39><loc_88><loc_45></location>∇× v = ˆ r m × ( r 2 i +1 / 2 v i +1 / 2 ,m -r 2 i -1 / 2 v i -1 / 2 ,m ) r 2 i ∆ r i + 6 ∑ n =1 L mn ˆ n mn × v i ( mn ) r i A m . (12)</formula>
<text><location><page_11><loc_12><loc_22><loc_88><loc_39></location>An evaluation of a curl is necessary when modeling energetic charged particle transport, where the particle's drift velocity is proportional to ∇× ( B /B 2 ). The values of primitive variables at face centers v i ± 1 / 2 and v i ( mn ) may be approximated as arithmetic averages of the values in the two cells separated by the face. A more accurate approach, adopted here, is to use interface resolved states obtained from a solution to the corresponding Riemann problem (see § 5).</text>
<text><location><page_11><loc_12><loc_11><loc_88><loc_21></location>The finite volume system of conservation laws is integrated with a second order unsplit TVD-like method (see below). Right and left interface values are calculated in the usual way using some appropriate linear reconstruction to achieve second-order spatial accuracy. Fluxes are calculated from a solution to a one-dimensional (projected) Riemann problem</text>
<text><location><page_12><loc_12><loc_82><loc_88><loc_86></location>at each cell interface. Finally, time is advanced using either a first order (Euler) or, more commonly, a second order (Runge-Kutta) scheme, depending on the nature of the problem.</text>
<section_header_level_1><location><page_12><loc_41><loc_75><loc_59><loc_76></location>4. Reconstruction</section_header_level_1>
<text><location><page_12><loc_12><loc_64><loc_85><loc_71></location>To achieve second order spatial accuracy we employ limited piecewise linear reconstruction on primitive variables V = ( ρ, u , p g , B , ψ ) T . In the radial direction the simplest and the most robust limiter available is the MinMod, with slopes S im given by</text>
<formula><location><page_12><loc_39><loc_60><loc_88><loc_62></location>S MM im = minmod( S -im , S + im ) , (13)</formula>
<text><location><page_12><loc_12><loc_56><loc_76><loc_57></location>where the left and the right slopes on an asymmetric stencil are, respectively</text>
<formula><location><page_12><loc_30><loc_51><loc_88><loc_54></location>S -im = 2 V im -V i -1 ,m ∆ r i -1 +∆ r i , S + im = 2 V i +1 ,m -V im ∆ r i +∆ r i +1 . (14)</formula>
<text><location><page_12><loc_12><loc_45><loc_87><loc_49></location>Also available is the more compressive monotonized central (MC) limiter (van Leer 1977) with</text>
<formula><location><page_12><loc_21><loc_40><loc_88><loc_45></location>S MC im = minmod [ 2 S -im , 2 S + im , (∆ r i +∆ r i +1 ) S -im +(∆ r i -1 +∆ r i ) S + im ∆ r i -1 +2∆ r i +∆ r i +1 ] . (15)</formula>
<text><location><page_12><loc_12><loc_38><loc_76><loc_40></location>The third option is the weighted essentially non-oscillatory (WENO) limiter</text>
<formula><location><page_12><loc_38><loc_34><loc_88><loc_36></location>S WENO im = ¯ w -im S -im + ¯ w + im S + im , (16)</formula>
<text><location><page_12><loc_12><loc_30><loc_47><loc_32></location>where the WENO weights ¯ w are given by</text>
<formula><location><page_12><loc_19><loc_25><loc_88><loc_29></location>¯ w -im = ( S -im 2 + /epsilon1 ) -p ( S -im 2 + /epsilon1 ) -p +( S + im 2 + /epsilon1 ) -p , ¯ w + im = ( S + im 2 + /epsilon1 ) -p ( S -im 2 + /epsilon1 ) -p +( S + im 2 + /epsilon1 ) -p , (17)</formula>
<text><location><page_12><loc_12><loc_16><loc_88><loc_24></location>where p is an integer constant here taken to be 2, and /epsilon1 is a small number, which we took to be 10 -12 in our simulations. The ( S + im ) 2 p and ( S -im ) 2 p terms are traditionally referred to as smoothness measures in WENO methodology.</text>
<text><location><page_12><loc_12><loc_10><loc_88><loc_14></location>For two-dimensional reconstruction on the surface of a sphere the code can use either a minimum angle plane (MAPR) method (Christov & Popov 2008) or a 2D version of the</text>
<text><location><page_13><loc_12><loc_64><loc_88><loc_86></location>weighted essentially non-oscillatory (WENO) scheme (Friedrich 1998). Common to both schemes, a local two-dimensional coordinate system ( ξ , η ) is introduced on the sphere, with its origin at the face center F m . The coordinates of the six adjacent cell centers ( ξ mn , η mn ) are then calculated in this frame. These coordinates are measured along two arbitrary great circles intersecting at right angles at the position of the central face F m . The procedure is illustrated in Figure 4. The angle A and the great circle distance between the face centers c are effectively polar coordinates on the surface of a sphere. The local coordinates of F mn are calculated as</text>
<formula><location><page_13><loc_37><loc_61><loc_88><loc_63></location>ξ mn = c cos A, η mn = c sin A. (18)</formula>
<text><location><page_13><loc_12><loc_54><loc_86><loc_58></location>Next, the six two-dimensional slopes S ξ , S η are calculated from the triangles with vertices located at the cell centers F m , F mn , F m,n +1 (shown in blue in Figure 2) as</text>
<formula><location><page_13><loc_28><loc_47><loc_88><loc_52></location>S ξ imn = η mn ( V im,n +1 -V im ) -η m,n +1 ( V imn -V im ) η mn ξ m,n +1 -ξ mn η m,n +1 , (19)</formula>
<formula><location><page_13><loc_28><loc_42><loc_88><loc_47></location>S η imn = -ξ mn ( V im,n +1 -V im ) -ξ m,n +1 ( V imn -V im ) η mn ξ m,n +1 -ξ mn η m,n +1 . (20)</formula>
<text><location><page_13><loc_12><loc_41><loc_60><loc_42></location>In the MAPR method we evaluated the average slopes as</text>
<formula><location><page_13><loc_40><loc_34><loc_88><loc_39></location>¯ S imn = √ S ξ imn 2 + S η imn 2 . (21)</formula>
<text><location><page_13><loc_12><loc_23><loc_88><loc_34></location>The reconstructed slopes S MAPR ξ,η im are those given by Eqs. (19) and (20) for which the average slope (20) is the smallest. Thus the method is a two-dimensional equivalent of the MinMod limiter. In the WENO method the reconstructed slopes are weighted arithmetic averages of all six slopes, namely</text>
<formula><location><page_13><loc_39><loc_16><loc_88><loc_22></location>S WENO ξ,η im = 6 ∑ n =1 ¯ w imn S ξ,η imn . (22)</formula>
<text><location><page_13><loc_12><loc_15><loc_53><loc_16></location>The weights ¯ w imn of each slope are calculated as</text>
<formula><location><page_13><loc_42><loc_6><loc_88><loc_13></location>¯ w imn = w imn ∑ n w imn , (23)</formula>
<figure>
<location><page_14><loc_29><loc_38><loc_71><loc_66></location>
<caption>Fig. 4.- Calculation of adjacent cell center (F mn ) coordinates in a local coordinate frame associated with a face F m . Every line shown is a segment of a great circle.</caption>
</figure>
<text><location><page_15><loc_12><loc_85><loc_17><loc_86></location>where</text>
<formula><location><page_15><loc_37><loc_79><loc_88><loc_84></location>w imn = ( S ξ imn 2 + S η imn 2 + /epsilon1 ) -p , (24)</formula>
<text><location><page_15><loc_12><loc_72><loc_87><loc_80></location>where we again use p = 2 and /epsilon1 = 10 -12 . Because edge centers lie midway between the corresponding two face centers F m and F mn on the Voronoi grid, the reconstructed values at edge midpoints V i ( mn ) can be computed as</text>
<formula><location><page_15><loc_34><loc_67><loc_88><loc_70></location>V i ( mn ) = V im + 1 2 S ξ im ξ mn + 1 2 S η im η mn . (25)</formula>
<text><location><page_15><loc_12><loc_63><loc_86><loc_65></location>These values are used to calculate the intercell fluxes according to Eqs. (4), (7), and (8).</text>
<text><location><page_15><loc_12><loc_42><loc_88><loc_61></location>The code also implements a slope flattening algorithm that reduces the value of the slopes calculated by the reconstruction module in the vicinity of strong compressions (shocks). This prevents the occurrence of oscillations downstream of the shock. To construct a flattener, we calculate the minimum value of the fast magnetosonic wave speed a min f,im in each computational cell and its neighbors in the same spherical layer and in the layers above and below (a total of 21 cells). The shock detector function in each cell d im is then calculated as (Balsara et al. 2009)</text>
<formula><location><page_15><loc_24><loc_33><loc_88><loc_40></location>d im = min [ 1 , ∣ ∣ ∣ ∣ ( ∇· u ) im ∆ l im a min f,im δ +1 ∣ ∣ ∣ ∣ ] H [ -( ∇· u ) im ∆ l im a min f,im δ -1 ] , (26)</formula>
<text><location><page_15><loc_12><loc_21><loc_88><loc_37></location>∣ ∣ where ∆ l im is a characteristic dimension of the cell ∆ V im , δ is a constant of order 1 and H is the Heaviside step function. Subsequently, the slope in the cell im is calculated as a weighted sum of a slope obtained with the standard limiter, such as WENO, and that from a more diffusive limiter, such as MinMod or MAPR. For example, in the radial direction we could use</text>
<formula><location><page_15><loc_36><loc_17><loc_88><loc_20></location>S im = (1 -d im ) S WENO im + d im S MM im . (27)</formula>
<section_header_level_1><location><page_16><loc_40><loc_85><loc_60><loc_86></location>5. Riemann solvers</section_header_level_1>
<text><location><page_16><loc_12><loc_54><loc_88><loc_81></location>The fluxes F are calculated from an (approximate) solution to the one-dimensional Riemann problem at each interface between the prismatic cells. A suitable solver must be able to handle supersonic and transonic flows without losing positivity. Our tests revealed that modern HLL-type solvers (Batten et al. 1997; Gurski 2004) were generally superior to other solver types for the solar wind-LISM interaction problem, where they were least likely to produce a negative pressure upstream of a very strong (Mach number > 10) shock. Genuinely multi-dimensional Riemann solvers are now appearing in the literature (Balsara 2010, 2012), and they offer substantial advantages on logically rectangular meshes. However, the analogous work for unstructured meshes is the topic of vigorous research and was not incorporated in the present work.</text>
<text><location><page_16><loc_12><loc_41><loc_88><loc_51></location>An HLLC solver consists of four states: the left and the right unperturbed states plus two intermediate states separated by a tangential discontinuity. Designating the left and the right bounding wave speeds of the Riemann fan by S l and S r , respectively, the intercell flux may be written as</text>
<formula><location><page_16><loc_32><loc_26><loc_88><loc_40></location>F = F l , S l > 0 , F l + S l ( U ∗ l -U l ) , S l ≤ 0 ≤ S ∗ , F r + S r ( U ∗ r -U r ) , S ∗ ≤ 0 ≤ S r , F r , S r < 0 , (28)</formula>
<text><location><page_16><loc_12><loc_14><loc_88><loc_30></location> where F l = F ( U l ), F r = F ( U r ), and S ∗ is the speed of the intermediate wave (a tangential discontinuity). Because in a HLLC solver the normal velocity component and the total pressure only change across the outermost waves, the speed of the tangential discontinuity is readily calculated by applying the Rankine-Hugoniot conditions across these waves. This yields the speed</text>
<formula><location><page_16><loc_17><loc_8><loc_88><loc_13></location>S ∗ = ρ r u n,r ( S r -u n,r ) -p r + B 2 n,r / (4 π ) -ρ l u n,l ( S l -u n,l ) + p l -B 2 n,l / (4 π ) ρ r ( S r -u n,r ) -ρ l ( S l -u n,l ) , (29)</formula>
<text><location><page_17><loc_12><loc_70><loc_88><loc_86></location>where u n ( l,r ) and B n ( l,r ) are the normal-projected velocities and magnetic fields in the left and right states, respectively. Suppose two prismatic cells ( i, m 1 ) and ( i, m 2 ) share an interface with an index n 1 = [1 , 6] in the neighbor list of the first cell and n 2 = [1 , 6] in the neighbor list of the second cell (the definitions of 'first' and ''second' are arbitrary here; they could be defined, for example, by using the condition that m 1 < m 2 ). Then a normal velocity projection is defined as</text>
<formula><location><page_17><loc_30><loc_64><loc_88><loc_67></location>u n,l = u i ( m 1 n 1 ) · ˆ n m 1 n 1 , u n,r = u i ( m 2 n 2 ) · ˆ n m 1 n 1 , (30)</formula>
<text><location><page_17><loc_12><loc_55><loc_88><loc_63></location>where u i ( m 1 n 1 ) and u i ( m 2 n 2 ) are the reconstructed velocities given by (25), and ˆ n n 1 n 1 is the unit vector normal to the interface n 1 of the cell ( i, m 1 ), pointing outward. The values for B n ( l,r ) are computed in the same way.</text>
<text><location><page_17><loc_12><loc_40><loc_88><loc_53></location>Several HLLC MHD solvers may be found in the literature, distinguished by their choice of the tangential velocity and magnetic field components in the intermediate states U ∗ l,r (unlike in gas dynamics, these states are not unique in MHD). Currently we employ a solver proposed by Li (2005). Its main feature is that no jump in magnetic field is permitted across the tangential discontinuity.</text>
<text><location><page_17><loc_12><loc_27><loc_88><loc_37></location>A second option available in our model is the HLLD Riemann solver (Miyoshi & Kusano 2005). This type of solver incorporates two additional states U ∗∗ l,r separated from the corresponding 'single star' states by rotational (Alfv'enic) discontinuities, propagating to the left and to the right of the middle wave with speeds S ∗ l and S ∗ r respectively, given by</text>
<formula><location><page_17><loc_31><loc_21><loc_88><loc_25></location>S ∗ l = S ∗ -| B ∗ n | (4 πρ ∗ l ) 1 / 2 , S ∗ r = S ∗ + | B ∗ n | (4 πρ ∗ r ) 1 / 2 , (31)</formula>
<text><location><page_17><loc_12><loc_18><loc_47><loc_20></location>where B ∗ n is given by Eq. (34) below, and</text>
<formula><location><page_17><loc_35><loc_12><loc_88><loc_16></location>ρ ∗ l = ρ l S l -u n,l S l -S ∗ , ρ ∗ r = ρ r S r -u n,r S r -S ∗ . (32)</formula>
<text><location><page_18><loc_12><loc_85><loc_39><loc_86></location>The intercell flux is computed as</text>
<formula><location><page_18><loc_25><loc_63><loc_88><loc_83></location>F = F l , S l > 0 , F l + S l ( U ∗ l -U l ) , S l ≤ 0 ≤ S ∗ l , F l + S l ( U ∗ l -U l ) + S ∗ l ( U ∗∗ l -U ∗ l ) , S ∗ l ≤ 0 ≤ S ∗ , F r + S r ( U ∗ r -U r ) + S ∗ r ( U ∗∗ r -U ∗ r ) , S ∗ ≤ 0 ≤ S ∗ r , F r + S r ( U ∗ r -U r ) , S ∗ r ≤ 0 ≤ S r , F r , S r < 0 , (33)</formula>
<text><location><page_18><loc_12><loc_57><loc_87><loc_67></location> The HLLD solver is somewhat less robust than the HLLC counterpart because it has a singularity when one of the extremal waves is a switch-on shock. When this condition is encountered, the program falls back to the HLLC algorithm which is singularity-free.</text>
<text><location><page_18><loc_12><loc_33><loc_88><loc_55></location>Because of nonlinearity of the solvers, under rare circumstances one of the intermediate waves could fall outside of the bounding (fast) waves. To prevent this from happening, we take the speed of the bounding waves to be the maximum of the left, right, and intermediate HLL states. Because the HLL state depends on the wave speeds themselves, we perform an iteration procedure until the external waves could be moved out no further. In the event that either HLLC or HLLD solver fails to produce a positive pressure in any of the intermediate states, we fall back to the very robust but dissipative HLLE Riemann solver (Einfeldt et al. 1991) with a single intermediate state U ∗ .</text>
<text><location><page_18><loc_12><loc_14><loc_88><loc_30></location>The methods described above are used without modification with the source term divergence cleaning algorithm (Eq. 6). However, the GLM method introduces two additional waves moving with the speeds ± c h that carry changes in B n and ψ only. Because c h is the fastest wave speed, these waves bound the 'base' Riemann fan, comprised of 2, 3, or 5 waves in the HLLE, HLLC, and HLLD solvers, respectively. The intermediate states are readily obtained from the Rankine-Hugoniot conditions at the bounding waves as</text>
<formula><location><page_18><loc_38><loc_9><loc_61><loc_13></location>B ∗ n = B n,l + B n,r 2 -ψ r -ψ l 2 c h ,</formula>
<figure>
<location><page_19><loc_28><loc_30><loc_77><loc_71></location>
<caption>Fig. 5.- Magnetic field magnitude at time t = 0 . 07 from the blast wave problem.</caption>
</figure>
<formula><location><page_20><loc_35><loc_83><loc_88><loc_86></location>ψ ∗ = ψ l + ψ r 2 -c h ( B n,r -B n,l ) 2 . (34)</formula>
<text><location><page_20><loc_12><loc_74><loc_88><loc_81></location>These intermediate states serve as both the right and the left states for the actual Riemann solver. The advantage of this approach is that any possible jump in the normal component of B is taken up by these additional external waves.</text>
<text><location><page_20><loc_12><loc_47><loc_88><loc_71></location>Very few genuinely three-dimensional test problems are available for spherical grids. For code verification we used a 3D blast wave problem similar to those presented by Gardiner & Stone (2008) and Balsara et al. (2009). The simulation region is constrained between r min = 0 . 01 and r max = 0 . 5. The radial cell width ∆ r increased outward monotonically from 0.00052 to 0.047. The inner boundary was treated as a perfectly conducting sphere with reflecting boundary conditions imposed. The initial conditions are ρ = 1, u = 0, and p = 10 ( r < 0 . 1), p = 0 . 1 ( r > 0 . 1). The initial magnetic field is given by the standard potential solution for a perfectly conducting sphere in a uniform external field, namely</text>
<formula><location><page_20><loc_38><loc_40><loc_88><loc_45></location>B r = B 0 ( 1 -r 3 min r 3 ) cos θ, (35)</formula>
<formula><location><page_20><loc_37><loc_36><loc_88><loc_41></location>B θ = -B 0 ( 1 + r 3 min 2 r 3 ) sin θ. (36)</formula>
<text><location><page_20><loc_12><loc_31><loc_88><loc_35></location>This solution was rotated such that the external field pointed in the direction (1 / √ 3 , 1 / √ 3 , 1 / √ 3). We used B 0 = 10 and γ = 1 . 4. The system was evolved until t = 0 . 07.</text>
<text><location><page_20><loc_12><loc_10><loc_88><loc_29></location>For this problem we chose a level 6 grid with 256 cells in the radial direction. The GLM version of the numerical scheme was used with the HLLC Riemann solver and WENO reconstruction. Figure 5 shows the magnitude of magnetic field at the end of the simulation on a linear scale. The flow structure of the solution is qualitatively similar to Gardiner & Stone (2008) and Balsara et al. (2009), consisting of an outermost fast shock wave and two dense shells of material elongated along the magnetic field. This problem did not trigger the slope flattening or positivity correction routines meaning it is not a very</text>
<text><location><page_21><loc_12><loc_82><loc_88><loc_86></location>good stress test of the code. Several more difficult problems simulating actual astrophysical plasma flows are discussed next.</text>
<section_header_level_1><location><page_21><loc_30><loc_75><loc_70><loc_76></location>6. Numerical solutions of test problems</section_header_level_1>
<text><location><page_21><loc_12><loc_44><loc_88><loc_71></location>To illustrate the capabilities of the new model we present results from three different simulations of solar system plasma environments. The first is a dynamic MHD simulation of compressive structures in the solar wind known as corotating interaction regions (CIRs). This is a simple test problem with a strong degree of spherical symmetry. The second is a simulation of the structure of the global heliosphere, including regions on each side of the interface between the solar wind and LISM known as the heliopause. This problem involves mode complex transonic flows and a population of neutral atoms in addition to the plasma. Finally, our third test problem is a stationary structure of the Earth's magnetosphere. Unlike the two previous cases, this one is an example of a highly magnetized plasma environment.</text>
<section_header_level_1><location><page_21><loc_16><loc_37><loc_84><loc_38></location>6.1. Test problem 1: Corotating interaction regions in the solar wind</section_header_level_1>
<text><location><page_21><loc_12><loc_12><loc_88><loc_33></location>Corotating interaction regions (CIRs) are compressive structures produced through an interaction between high and low speed streams in the solar wind. CIRs are fully formed by the time they reach Earth's orbit (Siscoe 1972; Gosling et al. 1972). When the streams emanating from the Sun are approximately steady in the co-rotating frame, these compression regions form spirals in the solar equatorial plane that co-rotate with the Sun. The leading edge of a CIR is a forward compressional wave propagating into the slower solar wind ahead, whereas the tailing edge is a reverse wave propagating back into the trailing high speed stream. At large heliospheric distances the waves steepen into forward</text>
<text><location><page_22><loc_12><loc_82><loc_88><loc_86></location>and reverse shocks. The entire plasma structure is convected with the solar wind and plays an important role in the dynamics of the heliosphere.</text>
<text><location><page_22><loc_12><loc_56><loc_88><loc_79></location>CIRs have been extensively studied using global MHD simulation (Pizzo 1994; Riley et al. 2001; Usmanov & Goldstein 2006). To generate CIRs in a global MHD simulation we adopt the tilted-dipole flow geometry of Pizzo (1982) at the inner boundary, which is illustrated in Figure 6. In this figure 0 xyz is the fixed (heliographic) frame, where z is the solar rotation axis, and 0 x ' y ' z ' is a frame aligned with the Sun's magnetic axis z ' . The parameter γ is the dipole tilt angle, and β is the latitude of the fast-slow transition boundaries (blue circles) in the coordinate system 0 x ' y ' z ' . In the simulation discussed below we used β = ± 30 · .</text>
<text><location><page_22><loc_12><loc_50><loc_85><loc_55></location>Following Pogorelov et al. (2007), one readily derives a quadratic equation for the latitude of the transition line θ as a function of the azimuthal angle ϕ ,</text>
<formula><location><page_22><loc_40><loc_47><loc_88><loc_48></location>a sin 2 θ + b sin θ + c = 0 , (37)</formula>
<text><location><page_22><loc_12><loc_43><loc_17><loc_44></location>where</text>
<formula><location><page_22><loc_28><loc_31><loc_88><loc_40></location>a = cos 2 γ +sin 2 γ tan 2 ϕ (cot γ cos γ +sin γ ) 2 b = 2sin β cos γ (1 + tan 2 ϕ ) (38) c = sin 2 β (1 + tan 2 ϕ cos 2 γ ) -cos 2 β sin 2 γ tan 2 ϕ.</formula>
<text><location><page_22><loc_12><loc_25><loc_86><loc_30></location>Note that when β = 0, θ ( ϕ ) reduces to the expression for the latitude of the magnetic equator given by Eq. (A6) of Pogorelov et al. (2007).</text>
<text><location><page_22><loc_12><loc_10><loc_88><loc_23></location>We simulated a region of the solar wind between r min = 0 . 5 AU and r max = 30 AU using 512 concentric grid layers of variable thickness (increasing outward). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s in the fast solar wind and n = 7 cm -3 , u = 400 km/s in the slow solar wind. The radial component of the magnetic field at 1 AU was B r = 28 µ G. These conditions were extended</text>
<figure>
<location><page_23><loc_23><loc_32><loc_77><loc_71></location>
<caption>Fig. 6.- A diagram of the assumed titled-dipole plasma flow geometry for the CIR simulation.</caption>
</figure>
<text><location><page_24><loc_12><loc_67><loc_88><loc_86></location>to the inner boundary using the conventional Parker solution for the solar wind and its magnetic field (Parker 1958). The dipole tilt angle was taken to be γ = 20 · . The boundary (shear layer) between the fast and the slow solar wind flows was located at a latitude of 30 · in the coordinate system aligned with the dipole axis. This simulation was performed on a level 6 geodesic grid. We chose the HLLC solver to evolve the time-dependent MHD equations, combined with the GLM divergence cleaning method; WENO reconstructions was used in all directions.</text>
<text><location><page_24><loc_12><loc_46><loc_88><loc_65></location>Figure 7 (left) shows the logarithm of the magnetic field magnitude in the xz and xy planes using a cutout plot. Plasma velocity vectors are shown as arrows of variable length. The CIRs can be visually identified as higher density and magnetic field intensity regions (red). The maximum latitudinal extent of CIRs is given by the sum of the angle between the rotation and the dipole axes and the extent of the slow solar wind in the frame aligned with the dipole axis, i.e., γ + β = 50 · . In the equatorial plane, the spiral CIR structure is seen to be bounded by shock-like discontinuities.</text>
<text><location><page_24><loc_12><loc_13><loc_88><loc_43></location>Several characteristic CIR features can be recognized in the plasma radial profiles shown in Figure 7 (right). We chose the profile along the direction 25 · northern latitude relative to the solar equatorial ( xy ) plane. The forward-reverse shock pairs are commonly observed at mid-latitudes, below the heliographic latitude of 26 · (Gosling & Pizzo 1999). They are shown with vertical dashed lines in the Figure. Shock pairs associated with CIRs are believed to be responsible for the observed 26-day recurrent decreases in galactic cosmic-ray intensity (Kota & Jokipii 1991; McKibben et al. 1999). Other features, such as the south-north flows are also identified through the north-south flow deflection angle /epsilon1 = sin -1 ( -u θ / | u | ) shown in the bottom panel. The transitions from northward (positive) to southward (negative) velocity are separated by roughly one Carrington rotation period (26 days) in our simulation. We conclude that the model is capable of reproducing the</text>
<text><location><page_25><loc_50><loc_65><loc_51><loc_67></location>(km/s)</text>
<text><location><page_25><loc_50><loc_64><loc_51><loc_65></location>v</text>
<figure>
<location><page_25><loc_50><loc_43><loc_88><loc_72></location>
</figure>
<figure>
<location><page_25><loc_12><loc_43><loc_50><loc_71></location>
<caption>Fig. 7.- Left: Magnetic field magnitude (log scale) in the meridional plane ( xz ) and the solar equatorial plane ( xy ) for the CIR simulation. Arrows are the plasma velocity vectors. Right: radial profiles along the direction ( θ , ϕ ) = (25 · , 135 · ) of (from top to bottom): plasma density (log scale), radial velocity, log thermal pressure, log magnetic field intensity, log temperature, and the north-south flow deflection angle /epsilon1 . Arrows mark the forward (pointing right) and reverse (pointing left) propagation of wave fronts.</caption>
</figure>
<text><location><page_26><loc_12><loc_85><loc_86><loc_86></location>essential CIR features and is consistent with the earlier simulations of this phenomenon.</text>
<section_header_level_1><location><page_26><loc_28><loc_77><loc_72><loc_79></location>6.2. Test problem 2: The global heliosphere</section_header_level_1>
<text><location><page_26><loc_12><loc_41><loc_88><loc_74></location>The energy density in a supersonic stellar wind, such as the solar wind, decreases in inverse proportion to the square of the distance from the star. Eventually the outflow is unable to maintain pressure balance with the galactic environment near the star, comprised mostly of partially ionized hydrogen gas. The stellar wind undergoes a transition to a subsonic flow at a structure called a termination shock. A tangential discontinuity called an astropause (heliopause for the solar wind) separates the shocked stellar flow from the interstellar gas. A bow shock may develop in front of the astropause if the relative motion between the star and LISM is supersonic. In the case of heliosphere, the region between the termination shock and the boundary is called the heliosheath. The theory of stellar wind interfaces (as applied primarily to the heliosphere) has been developed in Parker (1961), Axford (1972), and Baranov et al. (1976). Recent three-dimensional MHD simulations of the interface could be found in Pogorelov et al. (2007) and Opher et al. (2007).</text>
<text><location><page_26><loc_12><loc_16><loc_88><loc_38></location>To simulate the structure of the heliospheric interface we used a relatively coarse level 5 geodesic grid with 240 radial points. As in the CIR problem, the concentric layer spacing was nonuniform with the smallest cells at the inner radial boundary located at 10 AU; the outer boundary was placed at 900 AU. A heliographic coordinate system is used here, where the z axis is aligned with the solar rotation axis (Beck & Giles 2005), and the x axis is in the plane formed by the z axis and the interstellar helium flow direction (Lallement et al. 2005). The y axis completes the right-handed orthogonal system. The geometry of the problem is illustrated in Figure 8.</text>
<text><location><page_26><loc_16><loc_13><loc_86><loc_14></location>The heliospheric configuration computed here is representative of a solar minimum</text>
<figure>
<location><page_27><loc_23><loc_33><loc_77><loc_77></location>
<caption>Fig. 8.- The heliographic coordinate system used in the simulation of the global heliosphere. The directions of the flow of interstellar hydrogen ( V H ) and helium ( V He ) span the so-called hydrogen deflection plane (HDP) with a normal n . Here the interstellar magnetic field B lies in the HDP, with an angle of 45 · relative to V He .</caption>
</figure>
<text><location><page_28><loc_12><loc_61><loc_88><loc_86></location>(Florinski 2011). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s at heliographic latitudes above 30 · (fast solar wind) and n = 7 cm -3 , u = 400 km/s at low latitudes (slow solar wind). The magnetic field is a Parker spiral with a radial component B r = 28 µ G at 1 AU. The azimuthal magnetic field component is a function of the solar wind speed. The heliospheric current sheet is not included in this simulation, so that the solar magnetic field is always directed outward from the Sun. The observed current sheet is between 10 4 km (1 AU, Winterhalter et al. 1994) and a few times 10 5 km (heliosheath, Burlaga & Ness 2011) in width, which is much too narrow to be resolved with a global model.</text>
<text><location><page_28><loc_12><loc_22><loc_88><loc_59></location>The interstellar flow has a total density of 0.2 cm -3 , and is ionization rate of 0.25. Its velocity vector is V He = ( -26 . 3 , 0 , -0 . 23) km/s in the chosen heliographic coordinate system. The interstellar magnetic field lies in the so-called hydrogen deflection plane (the plane spanned by the velocity vectors of neutral interstellar hydrogen and helium) and is inclined by 45 · with respect to the LISM flow vector. Its components are ( -1 . 3 , 1 . 38 , -2 . 32) µ G in our coordinate system. The temperature of both ionized and neutral components in the LISM is taken to be 6530 K. The neutral and the plasma fluids are coupled via the charge exchange process (Axford 1972). We simulate both fluids using the same code by explicitly fixing B = 0 for the neutral hydrogen. The charge exchange terms used are those of Pauls et al. (1995). For simplicity we only include interstellar hydrogen in this simulation and ignore atoms produced by charge exchange in the heliosheath or the solar wind. To separate the interstellar region from the heliosphere we use a passively advected indicator variable q which satisfies the equation</text>
<formula><location><page_28><loc_41><loc_17><loc_88><loc_20></location>∂ ( ρq ) ∂t + ∇· ( ρq u ) = 0 . (39)</formula>
<text><location><page_28><loc_12><loc_10><loc_86><loc_15></location>The indicator variable is set to 1 in the solar wind and -1 in the interstellar flow. The condition q = 0 then gives the location of the heliopause.</text>
<figure>
<location><page_29><loc_50><loc_43><loc_88><loc_72></location>
<caption>Fig. 9.- Left: Constant plasma pressure surfaces (log scale) cut by the meridional ( xz ) plane for the heliosphere simulation. Selected magnetic field lines in the LISM are shown. Right: Radial profiles in the upwind (nose) direction of (from top to bottom): log plasma number density, radial speed, log thermal pressure, magnetic field magnitude, and log temperature. The positions of the termination shock and the heliopause are marked with vertical dashed lines.</caption>
</figure>
<figure>
<location><page_29><loc_12><loc_43><loc_50><loc_71></location>
</figure>
<text><location><page_29><loc_65><loc_43><loc_76><loc_44></location>Heliocentric Distance (AU)</text>
<text><location><page_30><loc_12><loc_64><loc_88><loc_86></location>We chose the HLLC solver for this work because of its more robust handling of a strong flow shear between the fast and the slow solar wind. We used the GLM ∇· B control method and WENO reconstruction in all directions. Simulations were run until a steady state was achieved which took about 300 years of simulated time. Figure 9, left, shows a cutout view of the heliospheric interface. Surfaces of constant plasma pressure are plotted together with magnetic field lines in the LISM, illustrating their draping around the heliopause (the transition between the red and the green colors). The innermost pressure surface approximately traces the outline of the termination shock.</text>
<text><location><page_30><loc_12><loc_31><loc_88><loc_62></location>We show radial profiles of several physical quantities in the upwind, or 'nose' direction in the right panel of Figure 9. Before the termination shock, located at 67 AU in this simulation, the solar wind velocity is gradually decreasing because of a loss of momentum to charge exchange with interstellar hydrogen. In the heliosheath, the plasma density is nearly a constant while the magnetic pressure increases toward the heliopause where the flow becomes essentially stagnant. The effective heliosheath temperature ( ∼ 3 × 10 6 K) is that of the solar-wind and pickup-ion mixture, which is significantly higher than that of the core solar wind ( ∼ 2 × 10 5 K, Richardson et al. 2008). From the top panel one can see that the density on the interstellar side of the heliopause is some 25 times higher than in the heliosheath. There is a very weak bow shock in this model barely visible in the pressure and temperature profiles.</text>
<text><location><page_30><loc_12><loc_15><loc_88><loc_29></location>The results presented here were obtained using a single population of neutral hydrogen (the interstellar atoms). The computer code is actually capable of integrating conservation laws for multiple neutral hydrogen populations. It would be straightforward to include the heliosheath energetic neutral atoms and the neutral solar wind atoms in a simulation, at an added computational time expense (e.g., Williams et al. 1997).</text>
<section_header_level_1><location><page_31><loc_27><loc_85><loc_73><loc_86></location>6.3. Test problem 3: Magnetosphere of Earth</section_header_level_1>
<text><location><page_31><loc_12><loc_57><loc_88><loc_81></location>The Earth's magnetosphere is a product of an interaction between the supersonic solar wind and the geomagnetic field. Two major discontinuities, the bow shock and the magnetopause, are located between the undisturbed solar wind region and the geomagnetic field. The magnetosheath, filled with shocked solar wind plasma, lies between the bow shock and the magnetopause, which is the external boundary of the magnetosphere. The magnetopause thus separates the hot, tenuous magnetospheric plasma from the cold and dense solar wind plasma in the magnetosheath. Global MHD simulations, coupled with ionospheric models, have been widely used to study large-scale processes in the magnetosphere (e.g., Fedder & Lyon 1995; Tanaka 1995; Raeder 1999; Hu et al. 2007).</text>
<text><location><page_31><loc_12><loc_24><loc_88><loc_54></location>The geomagnetic field can be treated as a dipole field in the inner magnetosphere, its strength varying as r -3 , where r is the distance from the center of the Earth. The thermal pressure varies more modestly leading to a very low plasma β (the ratio of the plasma thermal pressure to the magnetic field pressure) in the inner magnetosphere. Such low values of β ( ∼ 10 -5 -10 -4 ) tend to produce numerical errors with conservative numerical schemes (Raeder 1999). To overcome this difficulty, the dipole field is treated apart from the total magnetic field according to the decomposition method introduced by Tanaka (1995). The momentum and energy fluxes in the Riemann solvers are revised accordingly. The WENO reconstruction method is used in all directions and the GLM algorithm is used to control ∇· B . An interested reader will find more details on the GLM-MHD equations with a dipole field decomposition in the Appendix.</text>
<text><location><page_31><loc_12><loc_11><loc_88><loc_21></location>The Geocentric Solar Magnetospheric (GSM) coordinate system is used in this simulation. It is centered at Earth, and the x , y , and z axes point to the Sun, the dawn-dusk direction, and along the north dipole axis, respectively. We choose the inner boundary to be a sphere with a radius r = 3 R E (Earth radii), and apply the Dirichlet boundary</text>
<text><location><page_32><loc_12><loc_67><loc_88><loc_86></location>conditions. In particular, the number density is 370 cm -3 , which is 1/27 of a typical value in the ionosphere. The thermal pressure is 4 . 65 × 10 -10 dyn/cm 2 , which is 9 times smaller than its ionospheric value. The magnetic field is taken to be a dipole field at the inner boundary. For the sake of simplicity, the magnetosphere-ionosphere electrostatic coupling (e.g., Janhunen 1998) is not included, therefore the feedback of the ionosphere on the magnetosphere is ignored. We simply set the velocity to zero, which means there is no convection at the inner boundary. The free outer boundary is located at r = 100 R E .</text>
<text><location><page_32><loc_12><loc_46><loc_88><loc_65></location>We simulate a common configuration with a southward interplanetary magnetic field (IMF) of 50 µ G. The solar wind velocity is 600 km/s along the Sun-Earth line (the negative x direction), its number density is 5 cm -3 and temperature 9 . 1 × 10 4 K. The magnetic field is initially calculated as a superposition of a dipole field, centered at the origin, and a mirror dipole, located at (30 R E , 0 , 0), The field on the sunward side is subsequently replaced with the solar wind field with B z = -50 µ G to make the initial configuration divergence free. In the simulation we used a level 6 geodesic grid and 256 grid points along the radial direction.</text>
<text><location><page_32><loc_12><loc_13><loc_88><loc_43></location>A steady state configuration is obtained some 30 minutes (simulated time) into the simulation. The left panel of Figure 10 shows the color contours of the thermal pressure in the meridional ( xz ) plane and in the equatorial ( xy ) plane. The geomagnetic field and the IMF lines of force are also plotted. In the equatorial plane the geomagnetic field points northward, being opposite to the polarity of the southward IMF. We can see that the magnetosphere is open to the interplanetary medium and the geomagnetic field lines connect with the IMF (Dungey 1961). In that case the solar wind plasma momentum and energy can be transported into the magnetosphere through the site of magnetic reconnection. We did not observe surface waves or vortices induced by the Kelvin-Helmholtz instability (e.g., Guo et al. 2010) along the low-latitude magnetopause (the surface of the magnetopause is smooth in the equatorial plane).</text>
<figure>
<location><page_33><loc_10><loc_44><loc_88><loc_72></location>
<caption>Fig. 10.- Left: plasma pressure (color) and magnetic field lines for the magnetosphere simulation. Plane cuts for z = 0 and y = 0 are shown. The magnitude of the magnetic field is shown by the color of the field lines in the figure. Right: radial profiles along the Sun-Earth line of (from top to bottom): log plasma number density, velocity, log thermal pressure, log magnetic field intensity, and log temperature. The bow shock and the magnetopause are marked by vertical dashed lines.</caption>
</figure>
<text><location><page_34><loc_12><loc_67><loc_88><loc_86></location>The profiles of the physical quantities along the Sun-Earth line are shown in the right panel of Figure 10. The magnetopause is located at the neutral point for southward IMF case. The x velocity component approaches zero at the subsolar point, where the Sun-Earth line intersects the magnetopause. The shocked plasma becomes dense and hot in the magnetosheath, compared with the undisturbed solar wind. For southward IMF, the neutral point is found from the magnetic field strength profile (fourth panel from the top), where magnetic reconnection could occur in the presence of dissipation.</text>
<text><location><page_34><loc_12><loc_54><loc_88><loc_65></location>Our result has all the relevant features of a typical MHD magnetospheric simulation. In this illustrative solution, we only calculate a steady state representative magnetosphere. Of course, the model can be also used with more realistic time-dependent IMF conditions derived from observations.</text>
<section_header_level_1><location><page_34><loc_43><loc_47><loc_57><loc_49></location>7. Summary</section_header_level_1>
<text><location><page_34><loc_16><loc_43><loc_86><loc_44></location>In this report we have presented a novel approach to numerical modeling of space</text>
<text><location><page_34><loc_12><loc_19><loc_88><loc_41></location>plasma flows using geodesic spherical meshes with a nearly uniform solid angle coverage. This approach avoids the singularity on the symmetry axis inherent in polar spherical grids, leading to improved efficiency by allowing larger time steps. Our integration technique for gas-dynamic or MHD conservation laws is based on dimensionally unsplit time advance and uses two-dimensional reconstruction on the surface of a sphere. The new code has a number of useful features, such as a choice of multiple nonlinear Riemann solvers, weighted reconstruction limiters, and slope flattening to reduce possible oscillations near strong shocks.</text>
<text><location><page_34><loc_12><loc_13><loc_84><loc_17></location>We have tested the new model on several common problems in space physics: a formation of corotating interaction regions in the solar wind, global modeling of the</text>
<text><location><page_35><loc_12><loc_52><loc_88><loc_86></location>heliospheric interface, and finally, the magnetosphere of a planet. Our results are consistent with those found in the literature and every feature of the resulting structures is well reproduced. At this time the model lacks an adaptive mesh refinement feature, which would permit a superior numerical resolution of shocks and discontinuities. Whereas a hexagonal (Voronoi) grid cannot be easily refined, its dual Delaunay grid can. The process starts with the original icosahedron that divides a sphere into 20 identical spherical triangles. Each triangle then may be recursively subdivided into four smaller triangles by connecting the midpoints of the original cell edges with great circle arcs. The Delaunay mesh is therefore naturally amenable to refinement based on an oct-tree formulation. Because each locally refined zone is further split in the radial direction, this is tantamount to each 3D patch giving rise to 8 identically-sized refined patches if it is to undergo one more level of refinement.</text>
<text><location><page_35><loc_12><loc_34><loc_88><loc_50></location>The model could be potentially adapted to solve problems where the compact object is not at the center of the region of interest. For example, following Tanaka (2000), one could introduce a non-concentric grid, where different spherical layer boundaries are offset from the origin. The offset distance increases for each subsequent layer, so that the mesh becomes denser in one direction and more rarefied in the opposite direction. Such an arrangement could be more efficient for modeling, e.g., a magnetosphere with a long tail.</text>
<text><location><page_35><loc_12><loc_15><loc_88><loc_32></location>The new code by itself could be a valuable tool to investigate plasma flows around a source whose dimensions are small compared with the scale of the flow. Nevertheless, its chief intended purpose is to provide plasma background for subsequent simulations of the transport of energetic charged particles in the solar system and other astrophysical environments. Additional modules, recently added to the code, calculate the diffusion coefficients and drift velocity vectors based on magnetic field and other plasma properties.</text>
<text><location><page_35><loc_12><loc_13><loc_88><loc_14></location>The use of geodesic grids will permit a more efficient calculation of phase space trajectories</text>
<text><location><page_36><loc_12><loc_76><loc_88><loc_86></location>in the stochastic integration method popular in cosmic-ray transport work (Ball et al. 2005; Florinski & Pogorelov 2009). The difference with polar grid-based models is expected to be quite pronounced in the polar regions of the heliosphere, where the diffusion and drift coefficients are typically very large.</text>
<text><location><page_36><loc_12><loc_64><loc_86><loc_71></location>V.F. and X.G. were supported, in part, by NASA grants NNX10AE46G and NNX12AH44G, NSF grant AGS-0955700, and by a cooperative agreement with NASA Marshall Space Flight Center NNM11AA01A.</text>
<section_header_level_1><location><page_36><loc_35><loc_57><loc_65><loc_58></location>A. Dipole field decomposition</section_header_level_1>
<text><location><page_36><loc_12><loc_47><loc_88><loc_54></location>In the magnetosphere, the external field B 1 = B -B d , where B is the total magnetic field, and B d is the internal dipole field. Since B d is both curl-free (no current) and divergence free, we can write</text>
<formula><location><page_36><loc_39><loc_40><loc_88><loc_45></location>∇· ( B d B d -1 2 B 2 d I ) = 0 , (A1)</formula>
<formula><location><page_36><loc_40><loc_37><loc_88><loc_39></location>( ∇× B d ) · ( u × B ) = 0 . (A2)</formula>
<text><location><page_36><loc_12><loc_34><loc_67><loc_35></location>Using (A1) the momemtum flux from Eq. (4) can be expressed as</text>
<formula><location><page_36><loc_33><loc_28><loc_88><loc_32></location>ρ uu + p I -1 4 π ( BB + 1 2 B 2 d I -B d B d ) . (A3)</formula>
<text><location><page_36><loc_12><loc_25><loc_34><loc_27></location>Next, from (A2) we obtain</text>
<formula><location><page_36><loc_32><loc_20><loc_88><loc_22></location>B d · ∇ × ( u × B ) -∇· ( u × B ) × B d = 0 , (A4)</formula>
<text><location><page_36><loc_12><loc_16><loc_64><loc_18></location>which, upon substitution into the magnetic induction equation</text>
<formula><location><page_36><loc_40><loc_11><loc_88><loc_14></location>∂ B ∂t -∇× ( u × B ) = 0 (A5)</formula>
<text><location><page_37><loc_12><loc_85><loc_16><loc_86></location>yields</text>
<formula><location><page_37><loc_32><loc_81><loc_88><loc_84></location>B d · ∂ B 1 ∂t -∇· [ B ( u · B d ) -u ( B · B d )] = 0 . (A6)</formula>
<text><location><page_37><loc_12><loc_78><loc_24><loc_80></location>We now define</text>
<formula><location><page_37><loc_33><loc_73><loc_88><loc_78></location>p ∗ 1 = p g + B 2 1 8 π , e 1 = ρu 2 2 + p g γ -1 + B 2 1 8 π . (A7)</formula>
<text><location><page_37><loc_12><loc_72><loc_64><loc_73></location>Using these definitions the energy equation may be written as</text>
<formula><location><page_37><loc_23><loc_62><loc_88><loc_70></location>∂e 1 ∂t + B d 4 π · ∂ B 1 ∂t + ∇· { ( e 1 + p ∗ 1 ) u + 1 4 π [ u ( B 1 · B d ) + u ( B · B d ) -B ( u · B 1 ) -B ( u · B d )] } = 0 . (A8)</formula>
<text><location><page_37><loc_12><loc_60><loc_48><loc_62></location>Combining equations (A6) and (A8) yields</text>
<formula><location><page_37><loc_18><loc_55><loc_88><loc_59></location>∂e 1 ∂t + ∇· { ( e 1 + p ∗ 1 ) u -1 4 π [ B 1 ( u · B 1 ) -u ( B d · B 1 ) + B d ( u · B 1 )] } = 0 . (A9)</formula>
<text><location><page_37><loc_12><loc_49><loc_81><loc_53></location>Using (A3) and (A9) the system of GLM-MHD equations with dipole field decomposition may be written as</text>
<formula><location><page_37><loc_42><loc_44><loc_88><loc_48></location>∂ρ ∂t + ∇· ( ρ u ) = 0 , (A10)</formula>
<formula><location><page_37><loc_25><loc_39><loc_88><loc_43></location>∂ ( ρ u ) ∂t + ∇· [ ρ uu + p ∗ I -1 4 π ( BB + 1 2 B 2 d I -B d B d )] = 0 , (A11)</formula>
<formula><location><page_37><loc_36><loc_36><loc_88><loc_39></location>∂ B 1 ∂t + ∇· ( uB -Bu + ψ I ) = 0 , (A12)</formula>
<formula><location><page_37><loc_23><loc_31><loc_88><loc_35></location>∂e 1 ∂t + ∇· { ( e 1 + p ∗ 1 ) u -1 4 π [( u · B 1 ) B 1 -( B d × u ) × B 1 ] } = 0 , (A13)</formula>
<formula><location><page_37><loc_40><loc_27><loc_88><loc_31></location>∂ψ ∂t + c 2 h ∇· B 1 = -c 2 h c 2 p ψ, (A14)</formula>
<text><location><page_37><loc_12><loc_25><loc_88><loc_26></location>Note that the system (A10)-A(14) uses B 1 and e 1 instead of B and e as conserved quantities</text>
<text><location><page_37><loc_12><loc_18><loc_88><loc_23></location>Consider the simplest three-state HLL solver (Harten et al. 1983). Its Riemann flux is given by</text>
<formula><location><page_37><loc_39><loc_6><loc_88><loc_18></location>F = F l , S l > 0 , F lr , S l ≤ 0 ≤ S r , F r , S r < 0 , (A15)</formula>
<text><location><page_38><loc_12><loc_81><loc_88><loc_86></location>where F l = F ( U l ) and F r = F ( U r ) are the left and right unperturbed fluxes, respectively. The intermediate flux F lr is given by</text>
<formula><location><page_38><loc_35><loc_75><loc_88><loc_80></location>F lr = S r F l -S l F r + S l S r ( U r -U l ) S r -S l . (A16)</formula>
<text><location><page_38><loc_12><loc_70><loc_83><loc_74></location>Since only the definition of a conserved flux is required to solve (A15), the system (A10)-(A14) can be readily used in place of (4).</text>
<text><location><page_38><loc_12><loc_63><loc_88><loc_67></location>The decomposition of magnetic field does not affect the GLM scheme. For example, in the x direction we have two GLM equations,</text>
<formula><location><page_38><loc_43><loc_58><loc_88><loc_61></location>∂B 1 x ∂t + ∂ψ ∂x = 0 , (A17)</formula>
<formula><location><page_38><loc_40><loc_52><loc_88><loc_56></location>∂ψ ∂t + ∂ ( c 2 h B 1 x ) ∂x = -c 2 h c 2 p ψ. (A18)</formula>
<text><location><page_38><loc_12><loc_47><loc_87><loc_51></location>One can see that the external field component B 1 x can be integrated directly because the internal field ( B d related terms) does not appear in these equations.</text>
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<text><location><page_41><loc_12><loc_10><loc_88><loc_83></location>J. Geophys. Res., 114, A07109 Opher, M., Stone, E. C., & Gombosi, T. I. 2007, Science, 316, 875 Parker, E. N. 1958, ApJ, 128, 664 Parker, E. N. 1961, ApJ, 134, 20 Pauls, H. L., Zank, G. P., & Williams, L. L. 1995, J. Geophys. Res., 100, 21,595 Pizzo, V. J. 1982, J. Geophys. Res., 87, 4374 Pizzo, V. J. 1994, J. Geophys. Res., 99, 4173 Pogorelov, N. V., & Matsuda, T. 1998, J. Geophys. Res., 103, 237 Pogorelov, N. V., Stone, E. C., Florinski, V., & Zank, G. P. 2007, ApJ, 668, 611 Powell, K. G., Roe, P. L., Linde, T. J., Gombosi, T. I., & De Zeeuw, D. L. 1999, J. Comput. Phys., 154, 284 Putman, W. M., & Lin, S.-J. 2007, J. Comput. Phys., 227, 55 Raeder, J. 1999, J. Geophys. Res., 104, 17,357 Ratkiewicz, R., Barnes, A., Molvik, G. A., Spreiter, J. R., Stahara, S. S., Vinokur, M., & Venkateswaran, S. 1998, A&A, 335, 363 Richardson, J. D., Kasper, J. C., Wang, C., Belcher, J. W., & Lazarus, A. J. 2008, Nature, 454, 63 Riley, P., Linker, J. A., & Mikic, Z. 2001, J. Geophys. Res., 106, 15,889 Ronchi, C., Iacono, R., & Paolucci, P. S. 1996, J. Comput. Phys., 124, 93</text>
<text><location><page_42><loc_12><loc_41><loc_88><loc_86></location>Siscoe, G. L. 1972, J. Geophys. Res., 77, 27 Tanaka, T. 1995, J. Geophys. Res., 100, 12057 Tanaka, T. 2000, J. Geophys. Res., 105, 21,081 T'oth, G., Keppens, R., & Botchev, M. A. 1998, A&A, 332, 1159 Upadhyaya, H. C., Sharma, O. P., Mittal, R., & Fatima, H. 2010, Asia-Pac. J. Chem. Eng., doi: 10.1029/apj.479 Usmanov, A. V., & Goldstein, M. L. 2006, J. Geophys. Res., 111, A07101 van Leer, B. 1977, J. Comput. Phys., 23, 276 Washimi, H., & Tanaka, T. 1996, Space Sci. Rev., 78, 85 Williams, L. L., Hall, D. T., Pauls, H. L., & Zank, G. P. 1997, ApJ, 476, 366 Winterhalter, D., Smith, E. J., Burton, M. E., Murphy, N., & McComas, D. J. 1994, J. Geophys. Res., 99, 6667</text>
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</document>
[
{
"title": "ABSTRACT",
"content": "This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere. Subject headings: magnetohydrodynamics (MHD) - methods: numerical - planets and satellites: magnetic fields - solar wind",
"pages": [
2
]
},
{
"title": "MHD modeling of solar system processes on geodesic grids",
"content": "V. Florinski 1 , 2 , X. Guo 2 , D. S. Balsara 3 , and C. Meyer 3 Received ; accepted",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Many astrophysical plasma processes occur is regions of space surrounding a central compact object such as a star or a planet. Examples include stellar winds, planetary magnetospheres, supernova blast waves, and mass accretion onto compact objects. In all these environments the central body (a star or a planet) is typically much smaller than the characteristic scales of the plasma flows. In solving this class of problem on a computer, radial grids are commonly used because resolution can be readily increased near the origin. The simplest and the most commonly used is the standard spherical polar ( r , θ , ϕ ) grid (e.g., Washimi & Tanaka 1996; Pogorelov & Matsuda 1998; Ratkiewicz et al. 1998). This grid has a singularity on the z axis, where the control volume ∆ V = r 2 ∆ r sin θ ∆ θ ∆ ϕ , ∆ r , ∆ θ and ∆ ϕ being the grid cell dimensions in the radial, latitudinal, and azimuthal directions, respectively, vanishes as sin θ → 0. For explicit methods, this requires a small global time step to satisfy the Courant stability condition for a system of hyperbolic conservation laws for the entire grid (implicit or semi-implicit methods (e.g., T'oth et al. 1998) don't suffer from this limitation). Spherical grids are also used in simulating the transport of energetic charged particle, such as galactic cosmic rays, in turbulent astrophysical flows (Florinski & Pogorelov 2009). Transport models based on stochastic trajectory (Monte-Carlo) methods also suffer from the singularity on the polar axis. For example, in modeling cosmic-ray transport in the heliosphere it is common to align the z axis with the solar rotation axis. Because energetic particle transport (diffusion and drift) is very rapid at high latitudes due to a weaker magnetic field, a model must take vanishingly small time steps when a particle ventures close to the polar axis, which results in an inferior overall model efficiency. Time step requirements can be relaxed substantially by employing a grid that has a (nearly) uniform solid angle coverage. Examples include triangle, hexagon, or diamond based geodesic grids (Du et al. 2003; Yeh 2007; Upadhyaya et al. 2010), obtained by a recursive division of a base platonic solid, and cubed sphere grids (Ronchi et al. 1996; Putman & Lin 2007). This paper introduces a framework for finite volume methods of solution of hyperbolic conservation laws in three dimensions, such as gas-dynamic or MHD systems, using spherical geodesic grids composed of hexagonal prism elements. Results are illustrated on a three-dimensional simulation of solar rotation and formation of corotating interaction regions (CIRs), an interaction between the solar wind and the surrounding local interstellar medium or LISM, and a simulation of Earth's magnetosphere. The new framework can be employed to model a broad range of large-scale 3D astrophysical plasma flows around a compact object where high computational efficiency is a priority.",
"pages": [
3,
4
]
},
{
"title": "2. Grid structure",
"content": "Our three-dimensional grid consist of a 2D geodesic unstructured grid on a sphere combined with a concentric nonuniform radial stepping with smaller cells near the origin. The 2D surface grid is a Voronoi tesselation of a sphere produced from a dual triangular (Delaunay) tesselation. The latter is generated by a recursive subdivision of an icosahedron. We use the geodesic grid generator software developed by the ICON project ( http://icon.enes.org ) for use in atmospheric circulation modeling. An optimization algorithm (Heikes & Randall 1995), included in their code, produces a mesh with a difference in spherical surface areas between the largest and the smallest cells of less than 10%. The number of vertices (V), edges (E) and faces (F) on a grid produced by l th division is given by In this notation a level 0 grid is dual to the original icosahedron projected onto a unit sphere. The base shape of a control volume in a finite volume method is a spherical hexagonal prism with the exception of 12 pentagonal prisms located at the vertices of the original icosahedron. Level 3, 4, and 5 hexagonal geodesic grids are shown in Figure 1. A more detailed view of the Voronoi grid structure is given in Figure 2. A hexagonal face F m (shaded) is shown surrounded by six adjacent faces F m 1 .. F m 6 . The face centers of the dual triangle-based Delaunay grid (blue lines) are located at the Voronoi vertices (V); likewise, the former's vertices are at the Voronoi grid's face centers (F). The edges of the Voronoi and Delaunay grids on a sphere are mutually orthogonal and intersect at their midpoints. To achieve acceptable resolution in typical astrophysical flow modeling problems level 5 or higher geodesic grids should be used. Most of our simulations use level 6 mesh containing 40,962 Voronoi polygons. We emphasize that these 40,962 hexagons are distributed evenly over the surface of each spherical layer of cells. This gives us a resolution of about 3 × 10 -4 steradians in solid angle which corresponds to an angular resolution of one degree. By condensing the mesh in the radial direction, one can achieve a further degree of refinement as required by the problem. We introduce a set of unit vectors normal to the edges of the Voronoi grid ˆ n mn , where the index m refers to the m th face and n = [1 , 6] is the number of the edge counted in a counter-clockwise direction. The unit vectors are tangential to the surface of the sphere. The corresponding edge lengths, measured along great circles, are designated L mn . The outward radial unit vector at the cell center is ˆ r m . We also designate the area of the face on the unit sphere as A m . In this notation the control volume is equal to where i is the index on the radial axis. The areas A m are calculated by dividing each hexagonal face into six (five for pentagons) spherical triangles and adding up their areas using standard expressions from spherical trigonometry. Having defined our cell dimensions is this way we can proceed to integrate a system of conservation laws inside a control volume. It is worth pointing out that a similar geodesic-mesh-based model was developed by Nakamizo et al. (2009) Their mesh was generated from a dodecahedron by first dividing each face into five triangles followed by a recursive subdivision of each triangle into four smaller triangles. The resulting unstructured grid topology is similar (but not identical) to our dual Delaunay grid. Interestingly, in the model of Nakamizo et al. (2009) computations are also performed on a hexagonal grid, generated by connecting the centroids of the Delaunay triangles.",
"pages": [
4,
6,
8
]
},
{
"title": "3. MHD conservation laws",
"content": "For the heliospheric and magnetospheric problems ( § 6) we solve a modified set of MHD equations, written in terms of conservative variables U and fluxes F as where in CGS units. Here ρ is density, u is velocity, B is magnetic field, I is a unit dyadic, p = p g + B 2 / (8 π ) is the total pressure, p g being the gas kinetic pressure, and the energy density e is given by We employ two alternative models to control the divergence of magnetic field. The first is the numerical scheme proposed by Powell et al. (1999), where numerical magnetic field divergence is advected out of the simulation domain with the flow velocity. This scheme modifies the system of conservation laws with a hyperbolic source term The second scheme employs a generalized Lagrange multiplier (GLM) ψ for a mixed hyperbolic-parabolic correction (Dedner et al. 2002). The system (4) is extended with an additional transport equation for ψ where c h is a constant, isotropic advection speed, taken to be somewhat faster than the fastest wave speed in the problem, and c p is related to the rate of decay of ψ . Dedner et al. (2002) proposed two methods to fix the value of c p : (a) by fixing the time rate of decay of the GLM variable r d = exp( -∆ tc 2 h /c 2 p ), where ∆ t is the time step, and (b) by fixing the characteristic length over which the decay occurs, given by l d = c 2 p /c h . Both methods are available in our code. In the GLM scheme the conservation law for magnetic field (Faraday's law) is modified to read The system (3) is integrated over a control volume ∆ V im shown in Figure 3 to obtain the finite volume method Here F i ( mn ) is the flux at the center of the edge shared by the m th cell and its n th neighbor (where n = [1 , 6]). Note that the source term Q does not involve the right hand side of Eq. (7). The parabolic correction is applied by multiplying the value of ψ obtained from the finite volume scheme (9) by the decay factor, In our simulations we typically use 0 . 9 < r d < 1 and l d equal to several times the smallest linear grid size. The divergence of the magnetic field is obtained from Gauss's theorem in the same way as ∇· F is calculated in Eq. (9). More generally, the divergence and curl operators acting on an arbitrary vector v may be written as An evaluation of a curl is necessary when modeling energetic charged particle transport, where the particle's drift velocity is proportional to ∇× ( B /B 2 ). The values of primitive variables at face centers v i ± 1 / 2 and v i ( mn ) may be approximated as arithmetic averages of the values in the two cells separated by the face. A more accurate approach, adopted here, is to use interface resolved states obtained from a solution to the corresponding Riemann problem (see § 5). The finite volume system of conservation laws is integrated with a second order unsplit TVD-like method (see below). Right and left interface values are calculated in the usual way using some appropriate linear reconstruction to achieve second-order spatial accuracy. Fluxes are calculated from a solution to a one-dimensional (projected) Riemann problem at each cell interface. Finally, time is advanced using either a first order (Euler) or, more commonly, a second order (Runge-Kutta) scheme, depending on the nature of the problem.",
"pages": [
8,
9,
11,
12
]
},
{
"title": "4. Reconstruction",
"content": "To achieve second order spatial accuracy we employ limited piecewise linear reconstruction on primitive variables V = ( ρ, u , p g , B , ψ ) T . In the radial direction the simplest and the most robust limiter available is the MinMod, with slopes S im given by where the left and the right slopes on an asymmetric stencil are, respectively Also available is the more compressive monotonized central (MC) limiter (van Leer 1977) with The third option is the weighted essentially non-oscillatory (WENO) limiter where the WENO weights ¯ w are given by where p is an integer constant here taken to be 2, and /epsilon1 is a small number, which we took to be 10 -12 in our simulations. The ( S + im ) 2 p and ( S -im ) 2 p terms are traditionally referred to as smoothness measures in WENO methodology. For two-dimensional reconstruction on the surface of a sphere the code can use either a minimum angle plane (MAPR) method (Christov & Popov 2008) or a 2D version of the weighted essentially non-oscillatory (WENO) scheme (Friedrich 1998). Common to both schemes, a local two-dimensional coordinate system ( ξ , η ) is introduced on the sphere, with its origin at the face center F m . The coordinates of the six adjacent cell centers ( ξ mn , η mn ) are then calculated in this frame. These coordinates are measured along two arbitrary great circles intersecting at right angles at the position of the central face F m . The procedure is illustrated in Figure 4. The angle A and the great circle distance between the face centers c are effectively polar coordinates on the surface of a sphere. The local coordinates of F mn are calculated as Next, the six two-dimensional slopes S ξ , S η are calculated from the triangles with vertices located at the cell centers F m , F mn , F m,n +1 (shown in blue in Figure 2) as In the MAPR method we evaluated the average slopes as The reconstructed slopes S MAPR ξ,η im are those given by Eqs. (19) and (20) for which the average slope (20) is the smallest. Thus the method is a two-dimensional equivalent of the MinMod limiter. In the WENO method the reconstructed slopes are weighted arithmetic averages of all six slopes, namely The weights ¯ w imn of each slope are calculated as where where we again use p = 2 and /epsilon1 = 10 -12 . Because edge centers lie midway between the corresponding two face centers F m and F mn on the Voronoi grid, the reconstructed values at edge midpoints V i ( mn ) can be computed as These values are used to calculate the intercell fluxes according to Eqs. (4), (7), and (8). The code also implements a slope flattening algorithm that reduces the value of the slopes calculated by the reconstruction module in the vicinity of strong compressions (shocks). This prevents the occurrence of oscillations downstream of the shock. To construct a flattener, we calculate the minimum value of the fast magnetosonic wave speed a min f,im in each computational cell and its neighbors in the same spherical layer and in the layers above and below (a total of 21 cells). The shock detector function in each cell d im is then calculated as (Balsara et al. 2009) ∣ ∣ where ∆ l im is a characteristic dimension of the cell ∆ V im , δ is a constant of order 1 and H is the Heaviside step function. Subsequently, the slope in the cell im is calculated as a weighted sum of a slope obtained with the standard limiter, such as WENO, and that from a more diffusive limiter, such as MinMod or MAPR. For example, in the radial direction we could use",
"pages": [
12,
13,
15
]
},
{
"title": "5. Riemann solvers",
"content": "The fluxes F are calculated from an (approximate) solution to the one-dimensional Riemann problem at each interface between the prismatic cells. A suitable solver must be able to handle supersonic and transonic flows without losing positivity. Our tests revealed that modern HLL-type solvers (Batten et al. 1997; Gurski 2004) were generally superior to other solver types for the solar wind-LISM interaction problem, where they were least likely to produce a negative pressure upstream of a very strong (Mach number > 10) shock. Genuinely multi-dimensional Riemann solvers are now appearing in the literature (Balsara 2010, 2012), and they offer substantial advantages on logically rectangular meshes. However, the analogous work for unstructured meshes is the topic of vigorous research and was not incorporated in the present work. An HLLC solver consists of four states: the left and the right unperturbed states plus two intermediate states separated by a tangential discontinuity. Designating the left and the right bounding wave speeds of the Riemann fan by S l and S r , respectively, the intercell flux may be written as where F l = F ( U l ), F r = F ( U r ), and S ∗ is the speed of the intermediate wave (a tangential discontinuity). Because in a HLLC solver the normal velocity component and the total pressure only change across the outermost waves, the speed of the tangential discontinuity is readily calculated by applying the Rankine-Hugoniot conditions across these waves. This yields the speed where u n ( l,r ) and B n ( l,r ) are the normal-projected velocities and magnetic fields in the left and right states, respectively. Suppose two prismatic cells ( i, m 1 ) and ( i, m 2 ) share an interface with an index n 1 = [1 , 6] in the neighbor list of the first cell and n 2 = [1 , 6] in the neighbor list of the second cell (the definitions of 'first' and ''second' are arbitrary here; they could be defined, for example, by using the condition that m 1 < m 2 ). Then a normal velocity projection is defined as where u i ( m 1 n 1 ) and u i ( m 2 n 2 ) are the reconstructed velocities given by (25), and ˆ n n 1 n 1 is the unit vector normal to the interface n 1 of the cell ( i, m 1 ), pointing outward. The values for B n ( l,r ) are computed in the same way. Several HLLC MHD solvers may be found in the literature, distinguished by their choice of the tangential velocity and magnetic field components in the intermediate states U ∗ l,r (unlike in gas dynamics, these states are not unique in MHD). Currently we employ a solver proposed by Li (2005). Its main feature is that no jump in magnetic field is permitted across the tangential discontinuity. A second option available in our model is the HLLD Riemann solver (Miyoshi & Kusano 2005). This type of solver incorporates two additional states U ∗∗ l,r separated from the corresponding 'single star' states by rotational (Alfv'enic) discontinuities, propagating to the left and to the right of the middle wave with speeds S ∗ l and S ∗ r respectively, given by where B ∗ n is given by Eq. (34) below, and The intercell flux is computed as The HLLD solver is somewhat less robust than the HLLC counterpart because it has a singularity when one of the extremal waves is a switch-on shock. When this condition is encountered, the program falls back to the HLLC algorithm which is singularity-free. Because of nonlinearity of the solvers, under rare circumstances one of the intermediate waves could fall outside of the bounding (fast) waves. To prevent this from happening, we take the speed of the bounding waves to be the maximum of the left, right, and intermediate HLL states. Because the HLL state depends on the wave speeds themselves, we perform an iteration procedure until the external waves could be moved out no further. In the event that either HLLC or HLLD solver fails to produce a positive pressure in any of the intermediate states, we fall back to the very robust but dissipative HLLE Riemann solver (Einfeldt et al. 1991) with a single intermediate state U ∗ . The methods described above are used without modification with the source term divergence cleaning algorithm (Eq. 6). However, the GLM method introduces two additional waves moving with the speeds ± c h that carry changes in B n and ψ only. Because c h is the fastest wave speed, these waves bound the 'base' Riemann fan, comprised of 2, 3, or 5 waves in the HLLE, HLLC, and HLLD solvers, respectively. The intermediate states are readily obtained from the Rankine-Hugoniot conditions at the bounding waves as These intermediate states serve as both the right and the left states for the actual Riemann solver. The advantage of this approach is that any possible jump in the normal component of B is taken up by these additional external waves. Very few genuinely three-dimensional test problems are available for spherical grids. For code verification we used a 3D blast wave problem similar to those presented by Gardiner & Stone (2008) and Balsara et al. (2009). The simulation region is constrained between r min = 0 . 01 and r max = 0 . 5. The radial cell width ∆ r increased outward monotonically from 0.00052 to 0.047. The inner boundary was treated as a perfectly conducting sphere with reflecting boundary conditions imposed. The initial conditions are ρ = 1, u = 0, and p = 10 ( r < 0 . 1), p = 0 . 1 ( r > 0 . 1). The initial magnetic field is given by the standard potential solution for a perfectly conducting sphere in a uniform external field, namely This solution was rotated such that the external field pointed in the direction (1 / √ 3 , 1 / √ 3 , 1 / √ 3). We used B 0 = 10 and γ = 1 . 4. The system was evolved until t = 0 . 07. For this problem we chose a level 6 grid with 256 cells in the radial direction. The GLM version of the numerical scheme was used with the HLLC Riemann solver and WENO reconstruction. Figure 5 shows the magnitude of magnetic field at the end of the simulation on a linear scale. The flow structure of the solution is qualitatively similar to Gardiner & Stone (2008) and Balsara et al. (2009), consisting of an outermost fast shock wave and two dense shells of material elongated along the magnetic field. This problem did not trigger the slope flattening or positivity correction routines meaning it is not a very good stress test of the code. Several more difficult problems simulating actual astrophysical plasma flows are discussed next.",
"pages": [
16,
17,
18,
20,
21
]
},
{
"title": "6. Numerical solutions of test problems",
"content": "To illustrate the capabilities of the new model we present results from three different simulations of solar system plasma environments. The first is a dynamic MHD simulation of compressive structures in the solar wind known as corotating interaction regions (CIRs). This is a simple test problem with a strong degree of spherical symmetry. The second is a simulation of the structure of the global heliosphere, including regions on each side of the interface between the solar wind and LISM known as the heliopause. This problem involves mode complex transonic flows and a population of neutral atoms in addition to the plasma. Finally, our third test problem is a stationary structure of the Earth's magnetosphere. Unlike the two previous cases, this one is an example of a highly magnetized plasma environment.",
"pages": [
21
]
},
{
"title": "6.1. Test problem 1: Corotating interaction regions in the solar wind",
"content": "Corotating interaction regions (CIRs) are compressive structures produced through an interaction between high and low speed streams in the solar wind. CIRs are fully formed by the time they reach Earth's orbit (Siscoe 1972; Gosling et al. 1972). When the streams emanating from the Sun are approximately steady in the co-rotating frame, these compression regions form spirals in the solar equatorial plane that co-rotate with the Sun. The leading edge of a CIR is a forward compressional wave propagating into the slower solar wind ahead, whereas the tailing edge is a reverse wave propagating back into the trailing high speed stream. At large heliospheric distances the waves steepen into forward and reverse shocks. The entire plasma structure is convected with the solar wind and plays an important role in the dynamics of the heliosphere. CIRs have been extensively studied using global MHD simulation (Pizzo 1994; Riley et al. 2001; Usmanov & Goldstein 2006). To generate CIRs in a global MHD simulation we adopt the tilted-dipole flow geometry of Pizzo (1982) at the inner boundary, which is illustrated in Figure 6. In this figure 0 xyz is the fixed (heliographic) frame, where z is the solar rotation axis, and 0 x ' y ' z ' is a frame aligned with the Sun's magnetic axis z ' . The parameter γ is the dipole tilt angle, and β is the latitude of the fast-slow transition boundaries (blue circles) in the coordinate system 0 x ' y ' z ' . In the simulation discussed below we used β = ± 30 · . Following Pogorelov et al. (2007), one readily derives a quadratic equation for the latitude of the transition line θ as a function of the azimuthal angle ϕ , where Note that when β = 0, θ ( ϕ ) reduces to the expression for the latitude of the magnetic equator given by Eq. (A6) of Pogorelov et al. (2007). We simulated a region of the solar wind between r min = 0 . 5 AU and r max = 30 AU using 512 concentric grid layers of variable thickness (increasing outward). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s in the fast solar wind and n = 7 cm -3 , u = 400 km/s in the slow solar wind. The radial component of the magnetic field at 1 AU was B r = 28 µ G. These conditions were extended to the inner boundary using the conventional Parker solution for the solar wind and its magnetic field (Parker 1958). The dipole tilt angle was taken to be γ = 20 · . The boundary (shear layer) between the fast and the slow solar wind flows was located at a latitude of 30 · in the coordinate system aligned with the dipole axis. This simulation was performed on a level 6 geodesic grid. We chose the HLLC solver to evolve the time-dependent MHD equations, combined with the GLM divergence cleaning method; WENO reconstructions was used in all directions. Figure 7 (left) shows the logarithm of the magnetic field magnitude in the xz and xy planes using a cutout plot. Plasma velocity vectors are shown as arrows of variable length. The CIRs can be visually identified as higher density and magnetic field intensity regions (red). The maximum latitudinal extent of CIRs is given by the sum of the angle between the rotation and the dipole axes and the extent of the slow solar wind in the frame aligned with the dipole axis, i.e., γ + β = 50 · . In the equatorial plane, the spiral CIR structure is seen to be bounded by shock-like discontinuities. Several characteristic CIR features can be recognized in the plasma radial profiles shown in Figure 7 (right). We chose the profile along the direction 25 · northern latitude relative to the solar equatorial ( xy ) plane. The forward-reverse shock pairs are commonly observed at mid-latitudes, below the heliographic latitude of 26 · (Gosling & Pizzo 1999). They are shown with vertical dashed lines in the Figure. Shock pairs associated with CIRs are believed to be responsible for the observed 26-day recurrent decreases in galactic cosmic-ray intensity (Kota & Jokipii 1991; McKibben et al. 1999). Other features, such as the south-north flows are also identified through the north-south flow deflection angle /epsilon1 = sin -1 ( -u θ / | u | ) shown in the bottom panel. The transitions from northward (positive) to southward (negative) velocity are separated by roughly one Carrington rotation period (26 days) in our simulation. We conclude that the model is capable of reproducing the (km/s) v essential CIR features and is consistent with the earlier simulations of this phenomenon.",
"pages": [
21,
22,
24,
25,
26
]
},
{
"title": "6.2. Test problem 2: The global heliosphere",
"content": "The energy density in a supersonic stellar wind, such as the solar wind, decreases in inverse proportion to the square of the distance from the star. Eventually the outflow is unable to maintain pressure balance with the galactic environment near the star, comprised mostly of partially ionized hydrogen gas. The stellar wind undergoes a transition to a subsonic flow at a structure called a termination shock. A tangential discontinuity called an astropause (heliopause for the solar wind) separates the shocked stellar flow from the interstellar gas. A bow shock may develop in front of the astropause if the relative motion between the star and LISM is supersonic. In the case of heliosphere, the region between the termination shock and the boundary is called the heliosheath. The theory of stellar wind interfaces (as applied primarily to the heliosphere) has been developed in Parker (1961), Axford (1972), and Baranov et al. (1976). Recent three-dimensional MHD simulations of the interface could be found in Pogorelov et al. (2007) and Opher et al. (2007). To simulate the structure of the heliospheric interface we used a relatively coarse level 5 geodesic grid with 240 radial points. As in the CIR problem, the concentric layer spacing was nonuniform with the smallest cells at the inner radial boundary located at 10 AU; the outer boundary was placed at 900 AU. A heliographic coordinate system is used here, where the z axis is aligned with the solar rotation axis (Beck & Giles 2005), and the x axis is in the plane formed by the z axis and the interstellar helium flow direction (Lallement et al. 2005). The y axis completes the right-handed orthogonal system. The geometry of the problem is illustrated in Figure 8. The heliospheric configuration computed here is representative of a solar minimum (Florinski 2011). At 1 AU we assume the following conditions: density n = 3 . 5 cm -3 and radial velocity u = 800 km/s at heliographic latitudes above 30 · (fast solar wind) and n = 7 cm -3 , u = 400 km/s at low latitudes (slow solar wind). The magnetic field is a Parker spiral with a radial component B r = 28 µ G at 1 AU. The azimuthal magnetic field component is a function of the solar wind speed. The heliospheric current sheet is not included in this simulation, so that the solar magnetic field is always directed outward from the Sun. The observed current sheet is between 10 4 km (1 AU, Winterhalter et al. 1994) and a few times 10 5 km (heliosheath, Burlaga & Ness 2011) in width, which is much too narrow to be resolved with a global model. The interstellar flow has a total density of 0.2 cm -3 , and is ionization rate of 0.25. Its velocity vector is V He = ( -26 . 3 , 0 , -0 . 23) km/s in the chosen heliographic coordinate system. The interstellar magnetic field lies in the so-called hydrogen deflection plane (the plane spanned by the velocity vectors of neutral interstellar hydrogen and helium) and is inclined by 45 · with respect to the LISM flow vector. Its components are ( -1 . 3 , 1 . 38 , -2 . 32) µ G in our coordinate system. The temperature of both ionized and neutral components in the LISM is taken to be 6530 K. The neutral and the plasma fluids are coupled via the charge exchange process (Axford 1972). We simulate both fluids using the same code by explicitly fixing B = 0 for the neutral hydrogen. The charge exchange terms used are those of Pauls et al. (1995). For simplicity we only include interstellar hydrogen in this simulation and ignore atoms produced by charge exchange in the heliosheath or the solar wind. To separate the interstellar region from the heliosphere we use a passively advected indicator variable q which satisfies the equation The indicator variable is set to 1 in the solar wind and -1 in the interstellar flow. The condition q = 0 then gives the location of the heliopause. Heliocentric Distance (AU) We chose the HLLC solver for this work because of its more robust handling of a strong flow shear between the fast and the slow solar wind. We used the GLM ∇· B control method and WENO reconstruction in all directions. Simulations were run until a steady state was achieved which took about 300 years of simulated time. Figure 9, left, shows a cutout view of the heliospheric interface. Surfaces of constant plasma pressure are plotted together with magnetic field lines in the LISM, illustrating their draping around the heliopause (the transition between the red and the green colors). The innermost pressure surface approximately traces the outline of the termination shock. We show radial profiles of several physical quantities in the upwind, or 'nose' direction in the right panel of Figure 9. Before the termination shock, located at 67 AU in this simulation, the solar wind velocity is gradually decreasing because of a loss of momentum to charge exchange with interstellar hydrogen. In the heliosheath, the plasma density is nearly a constant while the magnetic pressure increases toward the heliopause where the flow becomes essentially stagnant. The effective heliosheath temperature ( ∼ 3 × 10 6 K) is that of the solar-wind and pickup-ion mixture, which is significantly higher than that of the core solar wind ( ∼ 2 × 10 5 K, Richardson et al. 2008). From the top panel one can see that the density on the interstellar side of the heliopause is some 25 times higher than in the heliosheath. There is a very weak bow shock in this model barely visible in the pressure and temperature profiles. The results presented here were obtained using a single population of neutral hydrogen (the interstellar atoms). The computer code is actually capable of integrating conservation laws for multiple neutral hydrogen populations. It would be straightforward to include the heliosheath energetic neutral atoms and the neutral solar wind atoms in a simulation, at an added computational time expense (e.g., Williams et al. 1997).",
"pages": [
26,
28,
29,
30
]
},
{
"title": "6.3. Test problem 3: Magnetosphere of Earth",
"content": "The Earth's magnetosphere is a product of an interaction between the supersonic solar wind and the geomagnetic field. Two major discontinuities, the bow shock and the magnetopause, are located between the undisturbed solar wind region and the geomagnetic field. The magnetosheath, filled with shocked solar wind plasma, lies between the bow shock and the magnetopause, which is the external boundary of the magnetosphere. The magnetopause thus separates the hot, tenuous magnetospheric plasma from the cold and dense solar wind plasma in the magnetosheath. Global MHD simulations, coupled with ionospheric models, have been widely used to study large-scale processes in the magnetosphere (e.g., Fedder & Lyon 1995; Tanaka 1995; Raeder 1999; Hu et al. 2007). The geomagnetic field can be treated as a dipole field in the inner magnetosphere, its strength varying as r -3 , where r is the distance from the center of the Earth. The thermal pressure varies more modestly leading to a very low plasma β (the ratio of the plasma thermal pressure to the magnetic field pressure) in the inner magnetosphere. Such low values of β ( ∼ 10 -5 -10 -4 ) tend to produce numerical errors with conservative numerical schemes (Raeder 1999). To overcome this difficulty, the dipole field is treated apart from the total magnetic field according to the decomposition method introduced by Tanaka (1995). The momentum and energy fluxes in the Riemann solvers are revised accordingly. The WENO reconstruction method is used in all directions and the GLM algorithm is used to control ∇· B . An interested reader will find more details on the GLM-MHD equations with a dipole field decomposition in the Appendix. The Geocentric Solar Magnetospheric (GSM) coordinate system is used in this simulation. It is centered at Earth, and the x , y , and z axes point to the Sun, the dawn-dusk direction, and along the north dipole axis, respectively. We choose the inner boundary to be a sphere with a radius r = 3 R E (Earth radii), and apply the Dirichlet boundary conditions. In particular, the number density is 370 cm -3 , which is 1/27 of a typical value in the ionosphere. The thermal pressure is 4 . 65 × 10 -10 dyn/cm 2 , which is 9 times smaller than its ionospheric value. The magnetic field is taken to be a dipole field at the inner boundary. For the sake of simplicity, the magnetosphere-ionosphere electrostatic coupling (e.g., Janhunen 1998) is not included, therefore the feedback of the ionosphere on the magnetosphere is ignored. We simply set the velocity to zero, which means there is no convection at the inner boundary. The free outer boundary is located at r = 100 R E . We simulate a common configuration with a southward interplanetary magnetic field (IMF) of 50 µ G. The solar wind velocity is 600 km/s along the Sun-Earth line (the negative x direction), its number density is 5 cm -3 and temperature 9 . 1 × 10 4 K. The magnetic field is initially calculated as a superposition of a dipole field, centered at the origin, and a mirror dipole, located at (30 R E , 0 , 0), The field on the sunward side is subsequently replaced with the solar wind field with B z = -50 µ G to make the initial configuration divergence free. In the simulation we used a level 6 geodesic grid and 256 grid points along the radial direction. A steady state configuration is obtained some 30 minutes (simulated time) into the simulation. The left panel of Figure 10 shows the color contours of the thermal pressure in the meridional ( xz ) plane and in the equatorial ( xy ) plane. The geomagnetic field and the IMF lines of force are also plotted. In the equatorial plane the geomagnetic field points northward, being opposite to the polarity of the southward IMF. We can see that the magnetosphere is open to the interplanetary medium and the geomagnetic field lines connect with the IMF (Dungey 1961). In that case the solar wind plasma momentum and energy can be transported into the magnetosphere through the site of magnetic reconnection. We did not observe surface waves or vortices induced by the Kelvin-Helmholtz instability (e.g., Guo et al. 2010) along the low-latitude magnetopause (the surface of the magnetopause is smooth in the equatorial plane). The profiles of the physical quantities along the Sun-Earth line are shown in the right panel of Figure 10. The magnetopause is located at the neutral point for southward IMF case. The x velocity component approaches zero at the subsolar point, where the Sun-Earth line intersects the magnetopause. The shocked plasma becomes dense and hot in the magnetosheath, compared with the undisturbed solar wind. For southward IMF, the neutral point is found from the magnetic field strength profile (fourth panel from the top), where magnetic reconnection could occur in the presence of dissipation. Our result has all the relevant features of a typical MHD magnetospheric simulation. In this illustrative solution, we only calculate a steady state representative magnetosphere. Of course, the model can be also used with more realistic time-dependent IMF conditions derived from observations.",
"pages": [
31,
32,
34
]
},
{
"title": "7. Summary",
"content": "In this report we have presented a novel approach to numerical modeling of space plasma flows using geodesic spherical meshes with a nearly uniform solid angle coverage. This approach avoids the singularity on the symmetry axis inherent in polar spherical grids, leading to improved efficiency by allowing larger time steps. Our integration technique for gas-dynamic or MHD conservation laws is based on dimensionally unsplit time advance and uses two-dimensional reconstruction on the surface of a sphere. The new code has a number of useful features, such as a choice of multiple nonlinear Riemann solvers, weighted reconstruction limiters, and slope flattening to reduce possible oscillations near strong shocks. We have tested the new model on several common problems in space physics: a formation of corotating interaction regions in the solar wind, global modeling of the heliospheric interface, and finally, the magnetosphere of a planet. Our results are consistent with those found in the literature and every feature of the resulting structures is well reproduced. At this time the model lacks an adaptive mesh refinement feature, which would permit a superior numerical resolution of shocks and discontinuities. Whereas a hexagonal (Voronoi) grid cannot be easily refined, its dual Delaunay grid can. The process starts with the original icosahedron that divides a sphere into 20 identical spherical triangles. Each triangle then may be recursively subdivided into four smaller triangles by connecting the midpoints of the original cell edges with great circle arcs. The Delaunay mesh is therefore naturally amenable to refinement based on an oct-tree formulation. Because each locally refined zone is further split in the radial direction, this is tantamount to each 3D patch giving rise to 8 identically-sized refined patches if it is to undergo one more level of refinement. The model could be potentially adapted to solve problems where the compact object is not at the center of the region of interest. For example, following Tanaka (2000), one could introduce a non-concentric grid, where different spherical layer boundaries are offset from the origin. The offset distance increases for each subsequent layer, so that the mesh becomes denser in one direction and more rarefied in the opposite direction. Such an arrangement could be more efficient for modeling, e.g., a magnetosphere with a long tail. The new code by itself could be a valuable tool to investigate plasma flows around a source whose dimensions are small compared with the scale of the flow. Nevertheless, its chief intended purpose is to provide plasma background for subsequent simulations of the transport of energetic charged particles in the solar system and other astrophysical environments. Additional modules, recently added to the code, calculate the diffusion coefficients and drift velocity vectors based on magnetic field and other plasma properties. The use of geodesic grids will permit a more efficient calculation of phase space trajectories in the stochastic integration method popular in cosmic-ray transport work (Ball et al. 2005; Florinski & Pogorelov 2009). The difference with polar grid-based models is expected to be quite pronounced in the polar regions of the heliosphere, where the diffusion and drift coefficients are typically very large. V.F. and X.G. were supported, in part, by NASA grants NNX10AE46G and NNX12AH44G, NSF grant AGS-0955700, and by a cooperative agreement with NASA Marshall Space Flight Center NNM11AA01A.",
"pages": [
34,
35,
36
]
},
{
"title": "A. Dipole field decomposition",
"content": "In the magnetosphere, the external field B 1 = B -B d , where B is the total magnetic field, and B d is the internal dipole field. Since B d is both curl-free (no current) and divergence free, we can write Using (A1) the momemtum flux from Eq. (4) can be expressed as Next, from (A2) we obtain which, upon substitution into the magnetic induction equation yields We now define Using these definitions the energy equation may be written as Combining equations (A6) and (A8) yields Using (A3) and (A9) the system of GLM-MHD equations with dipole field decomposition may be written as Note that the system (A10)-A(14) uses B 1 and e 1 instead of B and e as conserved quantities Consider the simplest three-state HLL solver (Harten et al. 1983). Its Riemann flux is given by where F l = F ( U l ) and F r = F ( U r ) are the left and right unperturbed fluxes, respectively. The intermediate flux F lr is given by Since only the definition of a conserved flux is required to solve (A15), the system (A10)-(A14) can be readily used in place of (4). The decomposition of magnetic field does not affect the GLM scheme. For example, in the x direction we have two GLM equations, One can see that the external field component B 1 x can be integrated directly because the internal field ( B d related terms) does not appear in these equations.",
"pages": [
36,
37,
38
]
},
{
"title": "REFERENCES",
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"pages": [
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}
]
2013ApJS..206....6D
https://arxiv.org/pdf/1304.4064.pdf
<document>
<section_header_level_1><location><page_1><loc_10><loc_85><loc_90><loc_87></location>H TO ZN IONIZATION EQUILIBRIUM FOR THE NON-MAXWELLIAN ELECTRON κ -DISTRIBUTIONS: UPDATED CALCULATIONS</section_header_level_1>
<text><location><page_1><loc_44><loc_83><loc_56><loc_84></location>E. Dzifˇc'akov'a 1</text>
<text><location><page_1><loc_14><loc_81><loc_87><loc_82></location>Astronomical Institute of the Academy of Sciences of the Czech Republic, Friˇcova 298, 251 65 Ondˇrejov, Czech Republic</text>
<section_header_level_1><location><page_1><loc_47><loc_78><loc_53><loc_79></location>J. Dud'ık 1</section_header_level_1>
<text><location><page_1><loc_10><loc_76><loc_90><loc_78></location>Newton International Fellow, DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom Draft version March 7, 2022</text>
<section_header_level_1><location><page_1><loc_45><loc_73><loc_55><loc_74></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_14><loc_59><loc_86><loc_72></location>New data for calculation of the ionization and recombination rates have have been published in the past few years. Most of these are included in CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian κ -distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The κ -distributions significantly influence both the ionization and recombination rates and widen the ion abundance peaks. In comparison with Maxwellian distribution, the ion abundance peaks can also be shifted to lower or higher temperatures. The updated ionization equilibrium calculations result in large changes for several ions, notably Fe VIII-XIV. The results are supplied in electronic form compatible with the CHIANTI database.</text>
<text><location><page_1><loc_14><loc_57><loc_86><loc_59></location>Keywords: Atomic data - Atomic processes - Radiation mechanisms: non-thermal - Sun: corona Sun: UV radiation - Sun: X-rays, gamma rays</text>
<section_header_level_1><location><page_1><loc_22><loc_53><loc_35><loc_54></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_43><loc_48><loc_52></location>One of the most widely used assumptions in the interpretation of astrophysical spectra is that the emitting system is in thermal equilibrium. This means that the distribution of particle energies is at least locally Maxwellian, and can be characterized by the BoltzmannGibbs statistics which has one parameter, the temperature.</text>
<text><location><page_1><loc_8><loc_13><loc_48><loc_43></location>The generalization of the Bolzmann-Gibbs statistics proposed by Tsallis (1988, 2009), results in κ -distributions (e.g., Leubner 2002, 2004a,b; Collier 2004; Livadiotis & McComas 2009), characterized by a parameter κ and exhibiting a near-Maxwellian core and a high-energy power-law tail (Sect. 2). First proposed by Vasyliunas (1968), the κ distributions are now used to fit the observations of a wide variety of astrophysical environments, e.g. in-situ measurements of particle distributions in planetary magnetic environments (e.g., Pierrard & Lemaire 1996; Mauk et al. 2004; Schippers et al. 2008; Xiao et al. 2008; Dialynas et al. 2009) and solar wind (e.g., Collier et al. 1996; Maksimovic et al. 1997a,b; Pierrard et al. 1999; Nieves-Chinchilla & Vi˜nas 2008; Le Chat et al. 2009, 2011; Pierrard 2012), as well as photon spectra of solar flare plasmas (e.g., Kaˇsparov'a & Karlick'y 2009; Oka et al. 2013), emission line spectra of planetary nebulae and galactic sources (Nicholls et al. 2012; see also Binette et al. 2012) and even solar transition region (Dzifˇc'akov'a et al. 2011). A review on the κ -distributions and their applications in astrophysical plasma can be found, e.g., in Pierrard & Lazar (2010).</text>
<text><location><page_1><loc_10><loc_10><loc_20><loc_11></location>[email protected]</text>
<text><location><page_1><loc_10><loc_7><loc_48><loc_10></location>1 DAPEM, Faculty of Mathematics Physics and Computer Science, Comenius University, Mlynsk'a Dolina F2, 842 48 Bratislava, Slovakia</text>
<text><location><page_1><loc_52><loc_18><loc_92><loc_54></location>In the solar corona, presence of the κ -distributions, or distributions exhibiting high-energy tails, can be expected due to particle acceleration processes arising as a result of 'nanoflare' heating. The nanoflares are an unknown energy release process of impulsive nature, occuring possibly in storms heating the solar corona (e.g., Tripathi et al. 2010; Viall & Klimchuk 2011; Bradshaw et al. 2012; Winebarger 2012). While the direct evidence for enhanced suprathermal populations in the solar corona is still lacking (Feldman et al. 2007; Hannah et al. 2010), Pinfield et al. (1999) reported that the intensities of the Si III transition region lines observed by the SOHO/SUMER instrument do not correspond to a single Maxwellian distribution. Using their data, Dzifˇc'akov'a & Kulinov'a (2011) showed that the observed intensities can be explained by κ -distributions once the photoexcitation is taken into account. These authors diagnosed κ =7 in the active region observed on the solar limb. Higher values of κ were diagnosed for the quiet Sun and coronal hole, indiciating that the departures from the Maxwellian distribution can be connected to the local magnetic activity. The diagnostic method also works for inhomogeneous plasmas characterized by differential emission measure. That the κ -distributions can be present in the solar corona is also suggested by their presence in the solar wind (e.g., Pierrard et al. 1999; Vocks & Mann 2003).</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_18></location>Direct diagnostics of κ -distributions in the solar corona using extreme-ultraviolet lines observed by the Hinode/EIS spectrometer (Culhane et al. 2007) were attempted by Dzifˇc'akov'a & Kulinov'a (2010) and Mackovjak et al. (2013). These authors proposed methods for simultaneous diagnostics of the plasma temperature, electron density, and κ . However, majority of the line ratios sensitive to κ -distributions suffer from poor</text>
<text><location><page_2><loc_8><loc_77><loc_48><loc_92></location>photon statistics, errors in atomic data and/or plasma inhomogeneities. In spite of this, one of the main results of these works is that the sensitivity to κ -distributions, or to departures from the Maxwellian distribution in general, is enhanced if the line ratios involve lines originating in neighbooring ionization stages. This is due the sensitivity of the line emissivity to the abundance of the emitting ion that depends directly on the ionization equilibrium in turn highly dependent on the type of the distribution (e.g., Dzifˇc'akov'a 2002; Wannawichian et al. 2003; Dzifˇc'akov'a 2006).</text>
<text><location><page_2><loc_8><loc_65><loc_48><loc_77></location>In the past decade, new calculations of the ionization, recombination rates and ionization equilibirium for the Maxwellian electron distribution were published. These are summarized in the continually updated CHIANTI database, currently available in version 7.1 (e.g., Dere et al. 1997, 2009; Landi et al. 2012, 2013). These new calculations of the ionization and recombination rates result in significant differences with respect to the earlier calculations, e.g. of Mazzotta et al. (1998).</text>
<text><location><page_2><loc_8><loc_45><loc_48><loc_65></location>The availability of accurate atomic data are of crucial importance in correct determination of the properties of the radiating astrophysical environment, and the solar corona in particular. In this paper, we present upto-date calculations of the ionization and recombination rates (Sect. 3), and ionization equilibria (Sect. 4) for κ -distributions for elements from H to Zn. Such calculations are necessary for diagnostics of the κ -distributions in both the solar transition region and the corona, as well as subsequent calculations of the radiative losses (Dud'ık et al. 2011) or responses of various extremeultraviolet or X-ray filters (Dud'ık et al. 2009) used both to model and observe these portions of the solar atmosphere, with potential applications to other astrophysical environments.</text>
<section_header_level_1><location><page_2><loc_12><loc_43><loc_44><loc_45></location>2. THE NON-MAXWELLIAN κ -DISTRIBUTIONS</section_header_level_1>
<text><location><page_2><loc_8><loc_39><loc_48><loc_43></location>The κ -distributions of electron kinetic energies E represent a family of non-Maxwellian distributions characterized by two parameters, κ and T</text>
<formula><location><page_2><loc_10><loc_35><loc_48><loc_38></location>f κ ( E ) d E = A κ 2 π 1 / 2 ( k B T ) 3 / 2 E 1 / 2 d E (1 + E ( κ -1 . 5) kT ) κ +1 , (1)</formula>
<text><location><page_2><loc_8><loc_25><loc_48><loc_34></location>where the A κ = Γ( κ +1) / [ Γ( κ -0 . 5)( κ -1 . 5) 3 / 2 ] is the normalization constant, k B =1.38 × 10 -23 J kg -1 is the Boltzmann constant, and κ ∈ (3 / 2 , + ∞ ), T ∈ (0 , + ∞ ). We note that the definition of κ -distributions in Eq. (1 top ) corresponds to the κ -distributions of the second kind (e.g., Livadiotis & McComas 2009).</text>
<text><location><page_2><loc_8><loc_7><loc_48><loc_25></location>The shape of the distribution is controlled by the parameter κ . Maxwellian distribution is recovered for κ → + ∞ , while the departures from the Maxwellian increase with κ → 3/2. The departures from the Maxwellian distribution with decreasing κ include increase of the number of particles in the high-energy tail as well as increase in the relative number of lowenergy electrons (Fig. 1 top ). However, the mean energy 〈E〉 =3/2 k B T of the distribution does not depend on κ . This allows for calculation of all quantities depending on the mean energy of the distribution, e.g. pressure (Dzifˇc'akov'a 2006). The parameter T has in the frame of nonextensive statistics (Tsallis 1988, 2009) an analogous meaning as thermodynamic temperature in the</text>
<text><location><page_2><loc_52><loc_88><loc_92><loc_92></location>Boltzmann-Gibbs statistics. The reader is referred e.g. to the work of Livadiotis & McComas (2009, 2010) for details.</text>
<text><location><page_2><loc_52><loc_77><loc_92><loc_88></location>While the shape of the κ -distribution differs from the Maxwellian with the same T at all energies E , the core of the κ -distribution can be approximated by a Maxwellian distribution with lower T C = T ( κ -3 / 2) /κ (Oka et al. 2013). An example for κ =5 and T =1MK is shown in Fig. 1 bottom , where the approximating Maxwellian distribution has T C = 0 . 7 T and has been scaled by the factor C</text>
<formula><location><page_2><loc_56><loc_73><loc_92><loc_77></location>C = 2 . 718 Γ( κ +1) Γ( κ -1 / 2) κ -3 / 2 ( 1 + 1 κ ) -( κ +1) (2)</formula>
<text><location><page_2><loc_52><loc_64><loc_92><loc_72></location>(Oka et al. 2013), which is ≈ 0.84 for κ =5. The difference between the f κ ( T ) and f Maxw ( T C ) are then mainly in the pronounced high-energy tail. This shows that the κ distributions offer straightforward approximation of situations where a non-Maxwellian high-energy tail is present.</text>
<section_header_level_1><location><page_2><loc_56><loc_62><loc_88><loc_63></location>3. IONIZATION AND RECOMBINATION RATES</section_header_level_1>
<text><location><page_2><loc_52><loc_47><loc_92><loc_62></location>To calculate the ionization and recombination rates for κ -distributions, we use the atomic data available through the CHIANTI database for astrophysical spectroscopy of optically thin plasmas (Dere et al. 1997; Landi et al. 2013). The analytical functional form of the κ -distributions allows for relatively simple direct integration of the ionization cross-sections (Sect 3.2). However, the recombination cross-sections are not contained in CHIANTI. These then have to be reverse-engineered from the Maxwellian recombination rates using assumptions detailed in Sect. 3.3.</text>
<text><location><page_2><loc_52><loc_38><loc_92><loc_47></location>We note that the CHIANTI database allows for the treatment of non-Maxwellian distributions only if these can be represented by a series of individual Maxwellian distributions (with different T s). The technique for calculation of ionization and recombination rates presented here can in principle be extended for any type of particle distribution, not only κ -distributions.</text>
<section_header_level_1><location><page_2><loc_66><loc_35><loc_78><loc_36></location>3.1. Atomic Data</section_header_level_1>
<text><location><page_2><loc_52><loc_7><loc_92><loc_35></location>The CHIANTI atomic database since version 6 (Dere et al. 2009) contains continually updated ionization equilibrium for the Maxwellian distribution. This ionization equilibrium utilizes the cross-sections for direct ionization and autoionization, and the corresponding rate coefficients from the work of Dere (2007). Dielectronic and radiative recombination coefficients for the H to Al and Ar isoelectronic sequences are taken from the works of N. Badnell and colleagues, listed at http://amdpp.phys.strath.ac.uk/tamoc/DATA/ (Badnell et al. 2003; Colgan et al. 2003, 2004; Mitnik & Badnell 2004; Badnell 2006; Altun et al. 2005, 2006, 2007; Zatsarinny et al. 2005a,b, 2006; Bautista & Badnell 2007; Nikoli'c et al. 2010; Abdel-Naby et al. 2012). For the Si to Mn isoelectronic sequences, the recombination rates are based on the works of Shull & van Steenberg (1982), Nahar (1996, 1997), Nahar & Bautista (2001), Mazzotta et al. (1998) and Mazzitelli & Mattioli (2002). The reader is referred to Dere et al. (2009) for details. In the calculations presented in this paper, all atomic data for</text>
<text><location><page_3><loc_8><loc_84><loc_48><loc_92></location>ionization and recombination correspond to the ones used to produce the chianti.ioneq file in the CHIANTI v7.1. We note that ionization equilibria were published also by other authors (e.g. Bryans et al. 2009), but these use mostly the same atomic data as the CHIANTI database.</text>
<section_header_level_1><location><page_3><loc_21><loc_82><loc_36><loc_83></location>3.2. Ionization Rates</section_header_level_1>
<text><location><page_3><loc_8><loc_77><loc_48><loc_81></location>The ionization rates have been calculated by a numerical integration of the ionization cross section, σ i , available in CHIANTI database</text>
<formula><location><page_3><loc_13><loc_73><loc_48><loc_77></location>R i = < σ i v > = ∫ ∞ 0 σ i ( 2 E m ) 1 / 2 f κ ( E ) d E , (3)</formula>
<text><location><page_3><loc_8><loc_69><loc_48><loc_73></location>for κ =2,3,5,7,10, 25, and 33. Each numerical integral is calculated as a sum of individual integrals splitted according to the ionization and auto-ionizaton energies.</text>
<text><location><page_3><loc_8><loc_51><loc_48><loc_69></location>Typical changes in behaviour of the direct ionization and autoionization rates with κ -distributions are shown in Fig. 2 for the ions C IV , Fe XII , and Fe XVII formed at transition region, quiet coronal, and flare conditions, respectively. For lower κ , the temperature dependence of the ionization rates is much flatter, with lower maxima. Typically, for temperatures lower than those at which the ion abundance peaks (denoted by arrow in Fig. 2, see also Sect. 4), the κ -distributions result in increase of the ionization rates by up to several orders of magnitude with respect to the Maxwellian distribution. These deviations from Maxwellian ionization rates increase with decreasing κ .</text>
<section_header_level_1><location><page_3><loc_19><loc_49><loc_37><loc_50></location>3.3. Recombination Rates</section_header_level_1>
<text><location><page_3><loc_8><loc_39><loc_48><loc_49></location>Since the individual recombination cross-sections are not available in CHIANTI, the calculation of the recombination rates for κ -distributions was performed using the method of Dzifˇc'akov'a (1992), used also by Wannawichian et al. (2003). This method allows for calculation of the recombination rates using approximations to the rates for the Maxwellian distribution.</text>
<text><location><page_3><loc_8><loc_35><loc_48><loc_39></location>The cross-section σ RR for the radiative recombination is assumed to have a power-law dependence on energy (Osterbrock 1974)</text>
<formula><location><page_3><loc_20><loc_33><loc_48><loc_35></location>σ RR ( E ) = C RR / E η +0 . 5 , (4)</formula>
<text><location><page_3><loc_8><loc_28><loc_48><loc_32></location>where C RR is a constant and η +0 . 5 is a power-law index. Subsequently, the radiative recombination rate for the κ -distribution is of the form:</text>
<formula><location><page_3><loc_9><loc_23><loc_48><loc_28></location>R κ RR = 4 C RR (2 πm ) 1 / 2 Γ( κ + η -0 . 5)( κ -1 . 5) η Γ( κ -0 . 5) Γ(1 . 5 -η ) ( k B T ) η , (5)</formula>
<text><location><page_3><loc_8><loc_21><loc_48><loc_23></location>while the radiative recombition rate for the Maxwellian distribution is</text>
<formula><location><page_3><loc_17><loc_17><loc_48><loc_20></location>R Maxw RR = 4 C RR (2 πm ) 1 / 2 Γ(1 . 5 -η ) ( k B T ) η . (6)</formula>
<text><location><page_3><loc_8><loc_15><loc_25><loc_17></location>Therefore, it holds that</text>
<formula><location><page_3><loc_14><loc_12><loc_48><loc_15></location>R κ RR = R Maxw RR Γ( κ + η -0 . 5)( κ -1 . 5) η Γ( κ -0 . 5) . (7)</formula>
<text><location><page_3><loc_8><loc_7><loc_48><loc_11></location>The level of error introduced by this approximation is typically several per cent, i.e., lower than the error of the atomic data themselves.</text>
<text><location><page_3><loc_52><loc_89><loc_92><loc_92></location>For the dielectronic recombination, following approximation has been taken (Dzifˇc'akov'a 1992)</text>
<formula><location><page_3><loc_57><loc_85><loc_92><loc_88></location>R κ DR = A κ T 1 / 3 ∑ i a i (1 + t i / ( κ -1 . 5) T ) ( κ +1) , (8)</formula>
<text><location><page_3><loc_52><loc_81><loc_92><loc_84></location>where parameters a i and t i are the same as in similar expressions for the Maxwellian distribution</text>
<formula><location><page_3><loc_60><loc_77><loc_92><loc_81></location>R Maxw DR = 1 T 1 / 3 ∑ i a i exp( -t i /T ) , (9)</formula>
<text><location><page_3><loc_52><loc_70><loc_92><loc_76></location>where the coefficients a i and t i are provided within the CHIANTI database. The precision of this approximation is given by the magnitude of the second-order terms in the expansion of the coefficients a i and t i into series (Eqs. 37-44 in Dzifˇc'akov'a 1992).</text>
<text><location><page_3><loc_52><loc_54><loc_92><loc_70></location>The typical behavior of the total recombination rates ( R RR + R DR ) for κ -distributions and for Maxwellian distribution is shown in Fig. 2. It can be seen that the radiative recombination rate increases with decrease of κ . This is a result of increasing number of low energy electrons for the κ -distributions (Fig. 1), which dominate the recombination processes. The local change of slope of total recombination rate is caused by the contribution of dielectronic recombination. For some ions, e.g. Fe XVII , the contribution of dielectronic recombination is dominant in temperature interval where these ions have a non-negligible abundance.</text>
<section_header_level_1><location><page_3><loc_60><loc_51><loc_84><loc_52></location>4. THE IONIZATION EQUILIBRIUM</section_header_level_1>
<text><location><page_3><loc_52><loc_31><loc_92><loc_51></location>Calculations of the collisional ionization equilibrium assume that there are no temporal variations in plasma temperature T . In the coronal conditions, the resulting relative ion populations are given by the equilibrium between the direct collisional ionization with autoionization and the radiative and dielectronic recombination. Three-body processes can be neglected at low electron densities typical in the solar corona (Phillips et al. 2008). The radiative field is also usually assumed to be too weak, i.e., photoionization can be neglected as well. However, we note that photoionization may be important for some transition-region ions with low ionization thresholds, but the effect will vary depending on the distance from the radiation field (e.g., the solar photosphere).</text>
<text><location><page_3><loc_52><loc_9><loc_92><loc_31></location>The ionization equilibrium for κ -distributions with κ =2,3,5,7,10, 25, and 33 was calculated for ions of astrophysical interests, ranging from H ( Z =1) to Zn ( Z =30). Previous calculations of Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002), and Wannawichian et al. (2003) involved only 12 most abundant elements. The current calculations are performed for the same set of temperatures as the calculations in the CHIANTI database in the chianti.ioneq file. I.e., the temperature spans the interval of log( T /K) ∈〈 4 , 9 〉 with the step of ∆log( T /K)=0.05. The calculations are available in the same format as the chianti.ioneq file and are easily readable using the routines read ioneq.pro and plot ioneq.pro available in CHIANTI running under SolarSoftware in IDL. More information on the CHIANTI .ioneq file format is provided in Appendix A.</text>
<text><location><page_3><loc_52><loc_7><loc_92><loc_9></location>Examples of the current ionization equilibrium calculations for iron are in Fig. 3 and for carbon in</text>
<text><location><page_4><loc_8><loc_72><loc_48><loc_92></location>Fig. 4. The typical behavior is that the lower κ , the flatter the ionization peaks. In addition, ionization peaks can be shifted to lower or higher T , depending on κ , T and the individual ion. This means that a given relative ion abundance can be formed at a wider range of T for a κ -distribution, with different peak formation temperature. Such behavior was already reported by Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002) and Wannawichian et al. (2003). Typically, the shifts of Fe and C ion abundance peaks are to lower T with respect to the Maxwellian ionization equilibrium if log( T /K) /lessorapproxeql 5.5. At coronal temperatures, the Fe IX - Fe XVI ions are shifted to higher T . An interesting example is the ion Fe XVII , whose ionization peak is shifted to lower T for κ lessapprox 3, but to higher T for κ =2(Fig. 3 bottom ).</text>
<text><location><page_4><loc_8><loc_52><loc_48><loc_72></location>There are a number of differences with respect to the earlier calculations of Dzifˇc'akov'a (2002), which used the atomic data corresponding to those of Mazzotta et al. (1998). These differences are illustrated in Fig. 5. In general, the lower the value of κ , the greater the differences with respect to the previous calculations. The most conspicuous examples are the Fe IX , which is shifted to slightly higher T instead to lower T as in the previous calculations of Dzifˇc'akov'a (2002). The Fe XII and Fe XIII ions are shifted to higher T (up to 0.1-0.15 dex). We note that the changes in the ionization equilibria due to the updated atomic data will reflect e.g. on changes in the total radiative losses (Dud'ık et al. 2011) and will also modify the proposed diagnostic methods for κ -distributions (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013).</text>
<text><location><page_4><loc_8><loc_33><loc_48><loc_52></location>Ratios of relative abundances of individual ions can be used to diagnose the value of κ and simultaneously T . Such diagnostics can be applied e.g. in the solar wind (Owocki & Scudder 1983). An example of diagnostic diagrams is given in Fig. 6. We note that such diagrams cannot be directly applied on the observed line intensities unless the additional effect of κ -distributions on the excitation and deexcitation rates is considered. However, these diagrams provide quantification of the expected changes to ratios of line intensities due to ionization equilibrium. Ratios of lines involving different ionization stages provide better options for determining κ , as noted already by (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013).</text>
<section_header_level_1><location><page_4><loc_24><loc_31><loc_33><loc_32></location>5. SUMMARY</section_header_level_1>
<text><location><page_4><loc_52><loc_83><loc_92><loc_92></location>Collisional ionization equilibrium calculations for κ -distributions and optically thin plasmas were performed for all ions of elements H to Zn. To do that, the latest available atomic data for ionization and recombination were used. The calculations are available in the form of ionization equilibrium files compatible with the CHIANTI database, v7.1.</text>
<text><location><page_4><loc_52><loc_65><loc_92><loc_82></location>For κ -distributions, the ionization peaks are in general flatter and can be shifted to lower or higher T . This means that for κ -distributions, individual ions are typically formed in a wider range of temperatures, with different peak formation temperatures. Typically, ions formed at transition region temperatures are shifted to lower T , while the majority of coronal iron ions are shifted to higher T . Comparison to previous calculations is provided. Due to updated atomic data calculations, several ions in the present calculations are shifted to different temperatures with respect to previous calculations of Dzifˇc'akov'a (2002). The effect of κ on the ratios of ion abundances is documented.</text>
<text><location><page_4><loc_52><loc_55><loc_92><loc_65></location>The present calculations provide an accurate, necessary and useful tool for detection of astrophysical plasmas out of thermal equilibrium, where the distribution of particles is characterized by an enhanced power-law tail. The supplied files compatible with the CHIANTI database and software should greatly facilitate synthetization of both line and continuum spectra for optically thin astrophysical plasmas.</text>
<text><location><page_4><loc_52><loc_31><loc_92><loc_52></location>The authors are grateful to Dr. G. Del Zanna and Dr. H. E. Mason for helpful discussions. This work was supported by Grant Agency of the Czech Republic, Grant No. P209/12/1652, the project RVO:67985815, Scientific Grant Agency, VEGA, Slovakia, Grant No. 1/0240/11, and the bilateral project APVV CZ-SK0153-11 (7AMB12SK154) involving the Slovak Research and Development Agency and the Ministry of Education of the Czech Republic. JD acknowledges support from the Comenius University Grant No. UK/11/2012. CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK), the Universities of Florence (Italy) and Cambridge (UK), and George Mason University (USA). CHIANTI is great spectroscopic database and software, and the authors are very grateful for its existence and availability.</text>
<section_header_level_1><location><page_4><loc_46><loc_28><loc_54><loc_29></location>APPENDIX</section_header_level_1>
<section_header_level_1><location><page_4><loc_39><loc_27><loc_62><loc_27></location>CHIANTI .IONEQ FILE FORMAT</section_header_level_1>
<text><location><page_4><loc_8><loc_16><loc_92><loc_26></location>The .ioneq files, used by the CHIANTI database and software to store data on the ionization equilibrium, are in essence formatted ASCII files. An example of their format is given in Table 1. The file begins with two numbers, N , giving the number of temperature points T i , 1 ≤ i ≤ N , and Z max , denoting the maximum proton number Z for which the ionization equilibrium is provided. The next line gives the tabulated temperatures log( T i / K). All other following lines begin with the Z and a positive integer + k denoting the roman numeral for the corresponding ion; e.g., 26 and 9 stands for Fe IX . The line then contains relative ion abundances A + k -1 Z ( T i ) in floating-point precision for the tabulated temperatures.</text>
<text><location><page_4><loc_8><loc_14><loc_92><loc_16></location>Portion of the actual content of the kappa 05.ioneq file is given in Table 2. There, the relative abundances of the ions Fe IX -Fe XI are listed for κ =5 and for log( T/ K)=5.80 - 6.15.</text>
<table>
<location><page_5><loc_14><loc_70><loc_86><loc_88></location>
<caption>Table 1 ASCII format of the CHIANTI .ioneq file. Explanation of the symbols is given in the text.</caption>
</table>
<paragraph><location><page_6><loc_47><loc_90><loc_53><loc_91></location>Table 2</paragraph>
<table>
<location><page_6><loc_16><loc_79><loc_84><loc_88></location>
<caption>Example of the kappa 05.ioneq file produced for κ = 5. The table shows relative abundances of the ions Fe IX - Fe XI .</caption>
</table>
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<figure>
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</figure>
<figure>
<location><page_7><loc_52><loc_70><loc_90><loc_92></location>
<caption>Figure 1. Top : The κ -distributions with κ =2, 3, 5, 10, 25 and the Maxwellian distribution plotted for log( T /K)=6.0. Bottom : The κ =5 distribution and the approximation of its core with Maxwellian distribution with lower T C . Colors and linestyles correspond to different values of κ . (A color version of this figure is available in the online journal.)</caption>
</figure>
<figure>
<location><page_8><loc_14><loc_26><loc_86><loc_92></location>
<caption>Figure 2. Total ionization and recombination rates for C IV ( top row ), Fe XII ( middle row ) and Fe XVII ( bottom row ). Different linestyles correspond to different κ . Black and red arrows denote maximum of the relative ion abundance for the Maxwellian and κ =2 distributions, respectively. (A color version of this figure is available in the online journal.)</caption>
</figure>
<figure>
<location><page_9><loc_11><loc_17><loc_89><loc_92></location>
<caption>Figure 3. Changes in the ionization equilibrium with κ for iron. Top : κ =10; Second row : κ =5; Third row : κ =5; Bottom row : κ =2. Individual ionization stages are indicated. (A color version of this figure is available in the online journal.)</caption>
</figure>
<figure>
<location><page_10><loc_11><loc_70><loc_89><loc_92></location>
<caption>Figure 4. Ionization equilibrium for Carbon. Different linestyles correspond to different κ . (A color version of this figure is available in the online journal.)</caption>
</figure>
<figure>
<location><page_11><loc_11><loc_36><loc_89><loc_92></location>
<caption>Figure 5. Comparison of the current, updated calculations with the previous ones. Top : Comparison between the ionization equilibrium according to Dere et al. (2009) and Mazzotta et al. (1998). Middle and Bottom : Comparison of the current calculations with the ones of Dzifˇc'akov'a (2002) for κ =5 and2, respectively. Individual ionization stages are indicated. (A color version of this figure is available in the online journal.)</caption>
</figure>
<figure>
<location><page_12><loc_15><loc_64><loc_48><loc_91></location>
</figure>
<figure>
<location><page_12><loc_53><loc_64><loc_86><loc_91></location>
<caption>Figure 6. Diagnostics of κ from ratios of ion abundances. The values of κ for each line are indicated. Thin lines represent isotherms for the given value of log( T /K). (A color version of this figure is available in the online journal.)</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "New data for calculation of the ionization and recombination rates have have been published in the past few years. Most of these are included in CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian κ -distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The κ -distributions significantly influence both the ionization and recombination rates and widen the ion abundance peaks. In comparison with Maxwellian distribution, the ion abundance peaks can also be shifted to lower or higher temperatures. The updated ionization equilibrium calculations result in large changes for several ions, notably Fe VIII-XIV. The results are supplied in electronic form compatible with the CHIANTI database. Keywords: Atomic data - Atomic processes - Radiation mechanisms: non-thermal - Sun: corona Sun: UV radiation - Sun: X-rays, gamma rays",
"pages": [
1
]
},
{
"title": "H TO ZN IONIZATION EQUILIBRIUM FOR THE NON-MAXWELLIAN ELECTRON κ -DISTRIBUTIONS: UPDATED CALCULATIONS",
"content": "E. Dzifˇc'akov'a 1 Astronomical Institute of the Academy of Sciences of the Czech Republic, Friˇcova 298, 251 65 Ondˇrejov, Czech Republic",
"pages": [
1
]
},
{
"title": "J. Dud'ık 1",
"content": "Newton International Fellow, DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom Draft version March 7, 2022",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "One of the most widely used assumptions in the interpretation of astrophysical spectra is that the emitting system is in thermal equilibrium. This means that the distribution of particle energies is at least locally Maxwellian, and can be characterized by the BoltzmannGibbs statistics which has one parameter, the temperature. The generalization of the Bolzmann-Gibbs statistics proposed by Tsallis (1988, 2009), results in κ -distributions (e.g., Leubner 2002, 2004a,b; Collier 2004; Livadiotis & McComas 2009), characterized by a parameter κ and exhibiting a near-Maxwellian core and a high-energy power-law tail (Sect. 2). First proposed by Vasyliunas (1968), the κ distributions are now used to fit the observations of a wide variety of astrophysical environments, e.g. in-situ measurements of particle distributions in planetary magnetic environments (e.g., Pierrard & Lemaire 1996; Mauk et al. 2004; Schippers et al. 2008; Xiao et al. 2008; Dialynas et al. 2009) and solar wind (e.g., Collier et al. 1996; Maksimovic et al. 1997a,b; Pierrard et al. 1999; Nieves-Chinchilla & Vi˜nas 2008; Le Chat et al. 2009, 2011; Pierrard 2012), as well as photon spectra of solar flare plasmas (e.g., Kaˇsparov'a & Karlick'y 2009; Oka et al. 2013), emission line spectra of planetary nebulae and galactic sources (Nicholls et al. 2012; see also Binette et al. 2012) and even solar transition region (Dzifˇc'akov'a et al. 2011). A review on the κ -distributions and their applications in astrophysical plasma can be found, e.g., in Pierrard & Lazar (2010). [email protected] 1 DAPEM, Faculty of Mathematics Physics and Computer Science, Comenius University, Mlynsk'a Dolina F2, 842 48 Bratislava, Slovakia In the solar corona, presence of the κ -distributions, or distributions exhibiting high-energy tails, can be expected due to particle acceleration processes arising as a result of 'nanoflare' heating. The nanoflares are an unknown energy release process of impulsive nature, occuring possibly in storms heating the solar corona (e.g., Tripathi et al. 2010; Viall & Klimchuk 2011; Bradshaw et al. 2012; Winebarger 2012). While the direct evidence for enhanced suprathermal populations in the solar corona is still lacking (Feldman et al. 2007; Hannah et al. 2010), Pinfield et al. (1999) reported that the intensities of the Si III transition region lines observed by the SOHO/SUMER instrument do not correspond to a single Maxwellian distribution. Using their data, Dzifˇc'akov'a & Kulinov'a (2011) showed that the observed intensities can be explained by κ -distributions once the photoexcitation is taken into account. These authors diagnosed κ =7 in the active region observed on the solar limb. Higher values of κ were diagnosed for the quiet Sun and coronal hole, indiciating that the departures from the Maxwellian distribution can be connected to the local magnetic activity. The diagnostic method also works for inhomogeneous plasmas characterized by differential emission measure. That the κ -distributions can be present in the solar corona is also suggested by their presence in the solar wind (e.g., Pierrard et al. 1999; Vocks & Mann 2003). Direct diagnostics of κ -distributions in the solar corona using extreme-ultraviolet lines observed by the Hinode/EIS spectrometer (Culhane et al. 2007) were attempted by Dzifˇc'akov'a & Kulinov'a (2010) and Mackovjak et al. (2013). These authors proposed methods for simultaneous diagnostics of the plasma temperature, electron density, and κ . However, majority of the line ratios sensitive to κ -distributions suffer from poor photon statistics, errors in atomic data and/or plasma inhomogeneities. In spite of this, one of the main results of these works is that the sensitivity to κ -distributions, or to departures from the Maxwellian distribution in general, is enhanced if the line ratios involve lines originating in neighbooring ionization stages. This is due the sensitivity of the line emissivity to the abundance of the emitting ion that depends directly on the ionization equilibrium in turn highly dependent on the type of the distribution (e.g., Dzifˇc'akov'a 2002; Wannawichian et al. 2003; Dzifˇc'akov'a 2006). In the past decade, new calculations of the ionization, recombination rates and ionization equilibirium for the Maxwellian electron distribution were published. These are summarized in the continually updated CHIANTI database, currently available in version 7.1 (e.g., Dere et al. 1997, 2009; Landi et al. 2012, 2013). These new calculations of the ionization and recombination rates result in significant differences with respect to the earlier calculations, e.g. of Mazzotta et al. (1998). The availability of accurate atomic data are of crucial importance in correct determination of the properties of the radiating astrophysical environment, and the solar corona in particular. In this paper, we present upto-date calculations of the ionization and recombination rates (Sect. 3), and ionization equilibria (Sect. 4) for κ -distributions for elements from H to Zn. Such calculations are necessary for diagnostics of the κ -distributions in both the solar transition region and the corona, as well as subsequent calculations of the radiative losses (Dud'ık et al. 2011) or responses of various extremeultraviolet or X-ray filters (Dud'ık et al. 2009) used both to model and observe these portions of the solar atmosphere, with potential applications to other astrophysical environments.",
"pages": [
1,
2
]
},
{
"title": "2. THE NON-MAXWELLIAN κ -DISTRIBUTIONS",
"content": "The κ -distributions of electron kinetic energies E represent a family of non-Maxwellian distributions characterized by two parameters, κ and T where the A κ = Γ( κ +1) / [ Γ( κ -0 . 5)( κ -1 . 5) 3 / 2 ] is the normalization constant, k B =1.38 × 10 -23 J kg -1 is the Boltzmann constant, and κ ∈ (3 / 2 , + ∞ ), T ∈ (0 , + ∞ ). We note that the definition of κ -distributions in Eq. (1 top ) corresponds to the κ -distributions of the second kind (e.g., Livadiotis & McComas 2009). The shape of the distribution is controlled by the parameter κ . Maxwellian distribution is recovered for κ → + ∞ , while the departures from the Maxwellian increase with κ → 3/2. The departures from the Maxwellian distribution with decreasing κ include increase of the number of particles in the high-energy tail as well as increase in the relative number of lowenergy electrons (Fig. 1 top ). However, the mean energy 〈E〉 =3/2 k B T of the distribution does not depend on κ . This allows for calculation of all quantities depending on the mean energy of the distribution, e.g. pressure (Dzifˇc'akov'a 2006). The parameter T has in the frame of nonextensive statistics (Tsallis 1988, 2009) an analogous meaning as thermodynamic temperature in the Boltzmann-Gibbs statistics. The reader is referred e.g. to the work of Livadiotis & McComas (2009, 2010) for details. While the shape of the κ -distribution differs from the Maxwellian with the same T at all energies E , the core of the κ -distribution can be approximated by a Maxwellian distribution with lower T C = T ( κ -3 / 2) /κ (Oka et al. 2013). An example for κ =5 and T =1MK is shown in Fig. 1 bottom , where the approximating Maxwellian distribution has T C = 0 . 7 T and has been scaled by the factor C (Oka et al. 2013), which is ≈ 0.84 for κ =5. The difference between the f κ ( T ) and f Maxw ( T C ) are then mainly in the pronounced high-energy tail. This shows that the κ distributions offer straightforward approximation of situations where a non-Maxwellian high-energy tail is present.",
"pages": [
2
]
},
{
"title": "3. IONIZATION AND RECOMBINATION RATES",
"content": "To calculate the ionization and recombination rates for κ -distributions, we use the atomic data available through the CHIANTI database for astrophysical spectroscopy of optically thin plasmas (Dere et al. 1997; Landi et al. 2013). The analytical functional form of the κ -distributions allows for relatively simple direct integration of the ionization cross-sections (Sect 3.2). However, the recombination cross-sections are not contained in CHIANTI. These then have to be reverse-engineered from the Maxwellian recombination rates using assumptions detailed in Sect. 3.3. We note that the CHIANTI database allows for the treatment of non-Maxwellian distributions only if these can be represented by a series of individual Maxwellian distributions (with different T s). The technique for calculation of ionization and recombination rates presented here can in principle be extended for any type of particle distribution, not only κ -distributions.",
"pages": [
2
]
},
{
"title": "3.1. Atomic Data",
"content": "The CHIANTI atomic database since version 6 (Dere et al. 2009) contains continually updated ionization equilibrium for the Maxwellian distribution. This ionization equilibrium utilizes the cross-sections for direct ionization and autoionization, and the corresponding rate coefficients from the work of Dere (2007). Dielectronic and radiative recombination coefficients for the H to Al and Ar isoelectronic sequences are taken from the works of N. Badnell and colleagues, listed at http://amdpp.phys.strath.ac.uk/tamoc/DATA/ (Badnell et al. 2003; Colgan et al. 2003, 2004; Mitnik & Badnell 2004; Badnell 2006; Altun et al. 2005, 2006, 2007; Zatsarinny et al. 2005a,b, 2006; Bautista & Badnell 2007; Nikoli'c et al. 2010; Abdel-Naby et al. 2012). For the Si to Mn isoelectronic sequences, the recombination rates are based on the works of Shull & van Steenberg (1982), Nahar (1996, 1997), Nahar & Bautista (2001), Mazzotta et al. (1998) and Mazzitelli & Mattioli (2002). The reader is referred to Dere et al. (2009) for details. In the calculations presented in this paper, all atomic data for ionization and recombination correspond to the ones used to produce the chianti.ioneq file in the CHIANTI v7.1. We note that ionization equilibria were published also by other authors (e.g. Bryans et al. 2009), but these use mostly the same atomic data as the CHIANTI database.",
"pages": [
2,
3
]
},
{
"title": "3.2. Ionization Rates",
"content": "The ionization rates have been calculated by a numerical integration of the ionization cross section, σ i , available in CHIANTI database for κ =2,3,5,7,10, 25, and 33. Each numerical integral is calculated as a sum of individual integrals splitted according to the ionization and auto-ionizaton energies. Typical changes in behaviour of the direct ionization and autoionization rates with κ -distributions are shown in Fig. 2 for the ions C IV , Fe XII , and Fe XVII formed at transition region, quiet coronal, and flare conditions, respectively. For lower κ , the temperature dependence of the ionization rates is much flatter, with lower maxima. Typically, for temperatures lower than those at which the ion abundance peaks (denoted by arrow in Fig. 2, see also Sect. 4), the κ -distributions result in increase of the ionization rates by up to several orders of magnitude with respect to the Maxwellian distribution. These deviations from Maxwellian ionization rates increase with decreasing κ .",
"pages": [
3
]
},
{
"title": "3.3. Recombination Rates",
"content": "Since the individual recombination cross-sections are not available in CHIANTI, the calculation of the recombination rates for κ -distributions was performed using the method of Dzifˇc'akov'a (1992), used also by Wannawichian et al. (2003). This method allows for calculation of the recombination rates using approximations to the rates for the Maxwellian distribution. The cross-section σ RR for the radiative recombination is assumed to have a power-law dependence on energy (Osterbrock 1974) where C RR is a constant and η +0 . 5 is a power-law index. Subsequently, the radiative recombination rate for the κ -distribution is of the form: while the radiative recombition rate for the Maxwellian distribution is Therefore, it holds that The level of error introduced by this approximation is typically several per cent, i.e., lower than the error of the atomic data themselves. For the dielectronic recombination, following approximation has been taken (Dzifˇc'akov'a 1992) where parameters a i and t i are the same as in similar expressions for the Maxwellian distribution where the coefficients a i and t i are provided within the CHIANTI database. The precision of this approximation is given by the magnitude of the second-order terms in the expansion of the coefficients a i and t i into series (Eqs. 37-44 in Dzifˇc'akov'a 1992). The typical behavior of the total recombination rates ( R RR + R DR ) for κ -distributions and for Maxwellian distribution is shown in Fig. 2. It can be seen that the radiative recombination rate increases with decrease of κ . This is a result of increasing number of low energy electrons for the κ -distributions (Fig. 1), which dominate the recombination processes. The local change of slope of total recombination rate is caused by the contribution of dielectronic recombination. For some ions, e.g. Fe XVII , the contribution of dielectronic recombination is dominant in temperature interval where these ions have a non-negligible abundance.",
"pages": [
3
]
},
{
"title": "4. THE IONIZATION EQUILIBRIUM",
"content": "Calculations of the collisional ionization equilibrium assume that there are no temporal variations in plasma temperature T . In the coronal conditions, the resulting relative ion populations are given by the equilibrium between the direct collisional ionization with autoionization and the radiative and dielectronic recombination. Three-body processes can be neglected at low electron densities typical in the solar corona (Phillips et al. 2008). The radiative field is also usually assumed to be too weak, i.e., photoionization can be neglected as well. However, we note that photoionization may be important for some transition-region ions with low ionization thresholds, but the effect will vary depending on the distance from the radiation field (e.g., the solar photosphere). The ionization equilibrium for κ -distributions with κ =2,3,5,7,10, 25, and 33 was calculated for ions of astrophysical interests, ranging from H ( Z =1) to Zn ( Z =30). Previous calculations of Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002), and Wannawichian et al. (2003) involved only 12 most abundant elements. The current calculations are performed for the same set of temperatures as the calculations in the CHIANTI database in the chianti.ioneq file. I.e., the temperature spans the interval of log( T /K) ∈〈 4 , 9 〉 with the step of ∆log( T /K)=0.05. The calculations are available in the same format as the chianti.ioneq file and are easily readable using the routines read ioneq.pro and plot ioneq.pro available in CHIANTI running under SolarSoftware in IDL. More information on the CHIANTI .ioneq file format is provided in Appendix A. Examples of the current ionization equilibrium calculations for iron are in Fig. 3 and for carbon in Fig. 4. The typical behavior is that the lower κ , the flatter the ionization peaks. In addition, ionization peaks can be shifted to lower or higher T , depending on κ , T and the individual ion. This means that a given relative ion abundance can be formed at a wider range of T for a κ -distribution, with different peak formation temperature. Such behavior was already reported by Dzifˇc'akov'a (1992), Dzifˇc'akov'a (2002) and Wannawichian et al. (2003). Typically, the shifts of Fe and C ion abundance peaks are to lower T with respect to the Maxwellian ionization equilibrium if log( T /K) /lessorapproxeql 5.5. At coronal temperatures, the Fe IX - Fe XVI ions are shifted to higher T . An interesting example is the ion Fe XVII , whose ionization peak is shifted to lower T for κ lessapprox 3, but to higher T for κ =2(Fig. 3 bottom ). There are a number of differences with respect to the earlier calculations of Dzifˇc'akov'a (2002), which used the atomic data corresponding to those of Mazzotta et al. (1998). These differences are illustrated in Fig. 5. In general, the lower the value of κ , the greater the differences with respect to the previous calculations. The most conspicuous examples are the Fe IX , which is shifted to slightly higher T instead to lower T as in the previous calculations of Dzifˇc'akov'a (2002). The Fe XII and Fe XIII ions are shifted to higher T (up to 0.1-0.15 dex). We note that the changes in the ionization equilibria due to the updated atomic data will reflect e.g. on changes in the total radiative losses (Dud'ık et al. 2011) and will also modify the proposed diagnostic methods for κ -distributions (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013). Ratios of relative abundances of individual ions can be used to diagnose the value of κ and simultaneously T . Such diagnostics can be applied e.g. in the solar wind (Owocki & Scudder 1983). An example of diagnostic diagrams is given in Fig. 6. We note that such diagrams cannot be directly applied on the observed line intensities unless the additional effect of κ -distributions on the excitation and deexcitation rates is considered. However, these diagrams provide quantification of the expected changes to ratios of line intensities due to ionization equilibrium. Ratios of lines involving different ionization stages provide better options for determining κ , as noted already by (Dzifˇc'akov'a & Kulinov'a 2010; Mackovjak et al. 2013).",
"pages": [
3,
4
]
},
{
"title": "5. SUMMARY",
"content": "Collisional ionization equilibrium calculations for κ -distributions and optically thin plasmas were performed for all ions of elements H to Zn. To do that, the latest available atomic data for ionization and recombination were used. The calculations are available in the form of ionization equilibrium files compatible with the CHIANTI database, v7.1. For κ -distributions, the ionization peaks are in general flatter and can be shifted to lower or higher T . This means that for κ -distributions, individual ions are typically formed in a wider range of temperatures, with different peak formation temperatures. Typically, ions formed at transition region temperatures are shifted to lower T , while the majority of coronal iron ions are shifted to higher T . Comparison to previous calculations is provided. Due to updated atomic data calculations, several ions in the present calculations are shifted to different temperatures with respect to previous calculations of Dzifˇc'akov'a (2002). The effect of κ on the ratios of ion abundances is documented. The present calculations provide an accurate, necessary and useful tool for detection of astrophysical plasmas out of thermal equilibrium, where the distribution of particles is characterized by an enhanced power-law tail. The supplied files compatible with the CHIANTI database and software should greatly facilitate synthetization of both line and continuum spectra for optically thin astrophysical plasmas. The authors are grateful to Dr. G. Del Zanna and Dr. H. E. Mason for helpful discussions. This work was supported by Grant Agency of the Czech Republic, Grant No. P209/12/1652, the project RVO:67985815, Scientific Grant Agency, VEGA, Slovakia, Grant No. 1/0240/11, and the bilateral project APVV CZ-SK0153-11 (7AMB12SK154) involving the Slovak Research and Development Agency and the Ministry of Education of the Czech Republic. JD acknowledges support from the Comenius University Grant No. UK/11/2012. CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK), the Universities of Florence (Italy) and Cambridge (UK), and George Mason University (USA). CHIANTI is great spectroscopic database and software, and the authors are very grateful for its existence and availability.",
"pages": [
4
]
},
{
"title": "CHIANTI .IONEQ FILE FORMAT",
"content": "The .ioneq files, used by the CHIANTI database and software to store data on the ionization equilibrium, are in essence formatted ASCII files. An example of their format is given in Table 1. The file begins with two numbers, N , giving the number of temperature points T i , 1 ≤ i ≤ N , and Z max , denoting the maximum proton number Z for which the ionization equilibrium is provided. The next line gives the tabulated temperatures log( T i / K). All other following lines begin with the Z and a positive integer + k denoting the roman numeral for the corresponding ion; e.g., 26 and 9 stands for Fe IX . The line then contains relative ion abundances A + k -1 Z ( T i ) in floating-point precision for the tabulated temperatures. Portion of the actual content of the kappa 05.ioneq file is given in Table 2. There, the relative abundances of the ions Fe IX -Fe XI are listed for κ =5 and for log( T/ K)=5.80 - 6.15.",
"pages": [
4
]
},
{
"title": "REFERENCES",
"content": "Collier, M. R., Hamilton, D. C., Gloeckler, G., Bochsler, P., & Sheldon, R. B. 1996, Geophys. Res. Lett., 23, 1191 J. Geophys. Res., 114, A01212 -. 2006, Sol. Phys., 234, 243 Geophys. Res. Lett., 24, 1151 Tripathi, D., Mason, H. E., & Klimchuk, J. A. 2010, ApJ, 723, 713 Tsallis, C. 1988, Journal of Statistical Physics, 52, 479 Viall, N. M., & Klimchuk, J. A. 2011, ApJ, 738, 24 Xiao, F., Shen, C., Wang, Y., Zheng, H., & Wang, S. 2008, Journal of Geophysical Research (Space Physics), 113, 5203",
"pages": [
6
]
}
]
2013ApJS..207...12R
https://arxiv.org/pdf/1307.2321.pdf
<document>
<section_header_level_1><location><page_1><loc_22><loc_86><loc_78><loc_87></location>METHYL CYANIDE OBSERVATIONS TOWARD MASSIVE PROTOSTARS</section_header_level_1>
<text><location><page_1><loc_26><loc_84><loc_74><loc_85></location>V. Rosero 1 , P. Hofner 1 , † , S. Kurtz 2 , J. Bieging 3 & E. D. Araya 4</text>
<text><location><page_1><loc_26><loc_83><loc_75><loc_84></location>1 Physics Department, New Mexico Tech, 801 Leroy Pl., Socorro, NM 87801, USA</text>
<text><location><page_1><loc_10><loc_78><loc_91><loc_83></location>2 Centro de Radioastronom'ıa y Astrof'ısica, Universidad Nacional Aut'onoma de M'exico, Morelia 58090, M'exico 3 Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA and 4 Physics Department, Western Illinois University, 1 University Circle, Macomb, IL 61455, USA To appear in The Astrophysical Journal Supplement Series.</text>
<section_header_level_1><location><page_1><loc_45><loc_76><loc_55><loc_77></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_8><loc_59><loc_92><loc_75></location>We report the results of a survey in the CH 3 CN J=12 → 11 transition toward a sample of massive proto-stellar candidates. The observations were carried out with the 10 m Submillimeter telescope on Mount Graham, AZ. We detected this molecular line in 9 out of 21 observed sources. In six cases this is the first detection of this transition. We also obtained full beam sampled cross-scans for five sources which show that the lower K -components can be extended on the arcminute angular scale. The higher K -components however are always found to be compact with respect to our 36 '' beam. A Boltzmann population diagram analysis of the central spectra indicates CH 3 CN column densities of about 10 14 cm -2 , and rotational temperatures above 50 K, which confirms these sources as hot molecular cores. Independent fits to line velocity and width for the individual K -components resulted in the detection of an increasing blue shift with increasing line excitation for four sources. Comparison with mid-infrared images from the SPITZER GLIMPSE /IRAC archive for six sources show that the CH 3 CN emission is generally coincident with a bright mid-IR source. Our data clearly show that the CH 3 CN J=12 → 11 transition is a good probe of the hot molecular gas near massive protostars, and provide the basis for future interferometric studies.</text>
<text><location><page_1><loc_14><loc_58><loc_51><loc_59></location>Subject headings: ISM: molecules - stars: formation</text>
<section_header_level_1><location><page_1><loc_22><loc_54><loc_35><loc_55></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_8><loc_38><loc_48><loc_54></location>Despite the central role of massive stars in almost all areas of astronomy, the physical processes involved in the formation of stars with masses > 8 M /circledot are at present poorly understood (e.g., Zinnecker & Yorke (2007)). Theoretical and observational studies favor the idea that massive stars, similar to their lower mass counterparts, form from a collapsing cloud core. However, whether the subsequent formation of a protostar and further mass accretion occurs from an isolated massive molecular core (e.g., McKee & Tan (2003), Keto (2007)), or under the influence of a cluster environment (e.g., Bonnell et al. (2004)) remains a persistent question.</text>
<text><location><page_1><loc_8><loc_23><loc_48><loc_38></location>One of the earliest observational manifestations of massive proto-stars are so-called hot molecular cores (hereafter HMCs). Named after the prototype object in the Orion KL region, they have been surveyed throughout the Galaxy in an effort to identify candidates for massive proto-stars (e.g., Sridharan et al. (2002)). Common search criteria were high FIR luminosity, high molecular column densities and temperature, and the absence of strong radio continuum emission - the latter to ensure an earlier evolutionary phase than ultra-compact (UC) or hyper-compact (HC) HII regions.</text>
<text><location><page_1><loc_8><loc_11><loc_48><loc_23></location>A particularly useful tracer of HMCs is the methyl cyanide (CH 3 CN) molecule. Due to the centrifugal deformation of this symmetric top molecule, its rotational spectrum consists of a series of closely spaced K -components tracing rapidly increasing excitation energies. The K -ladders are connected only through collisions so that excitation temperatures can in principle be measured from the ratios of K -components, thus avoiding the usual calibration uncertainties that occur when</text>
<text><location><page_1><loc_52><loc_43><loc_92><loc_55></location>comparing rotational transitions observed in different frequency bands. An extensive discussion of the microwave spectroscopy of methyl cyanide is given in Boucher et al. (1980). Because of these spectroscopic properties, the CH 3 CNmolecule is frequently used to determine temperatures in the dense molecular cores where massive stars form, using both statistical equilibrium calculations (e.g., Loren & Mundy (1984)), or the simpler rotation diagram technique (e.g., Goldsmith & Langer (1999)).</text>
<text><location><page_1><loc_52><loc_22><loc_92><loc_43></location>Another factor that favors the use of CH 3 CN as a tracer of HMCs is its enhanced abundance in warm (T= 100 -300 K), dense ( n H 2 = 10 6 -10 8 cm -3 ) environments (e.g., Blake et al. (1987)). This is generally thought to be caused by grain surface chemistry, either by primary reactions on the grain surface with subsequent release into the gas phase when the grain mantle evaporates, or, alternatively, by secondary reactions in the gas phase (e.g., Charnley et al. (1992), Bisschop et al. (2008)). Recently, Codella et al. (2009) reported detection of CH 3 CN in the outflow lobes of the low-mass protostar L1157-B1, and attributed the enhanced CH 3 CN abundance to shock chemistry. From these studies it is well-established that CH 3 CN traces an energetic environment similar to that expected in the immediate vicinity of massive proto-stars.</text>
<text><location><page_1><loc_52><loc_8><loc_92><loc_22></location>To investigate the HMC phase of massive star formation, several single dish CH 3 CN surveys have been made (e.g., Olmi et al. (1993), Araya et al. (2005), Pankonin et al. (2001)), and a small number of sources have also been studied with mm-interferometers (e.g., Cesaroni et al. (1994), Hofner et al. (1996), Furuya et al. (2008)). Several of the interferometric studies resulted in images of CH 3 CN structures that are elongated perpendicular to the direction of molecular outflows, with velocity gradients along the elongated structures; this is usually explained as rotational motion of a circum-</text>
<table>
<location><page_2><loc_16><loc_52><loc_84><loc_88></location>
<caption>Table 1 Observed Sources</caption>
</table>
<text><location><page_2><loc_16><loc_49><loc_84><loc_51></location>Note . -Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds.</text>
<text><location><page_2><loc_16><loc_44><loc_84><loc_49></location>References. (1) Sridharan et al. (2002); (2) Codella et al. (1997); (3) Beuther & Steinacker (2007); (4) Brunthaler et al. (2009); (5) Araya et al. (2008); (6) Pestalozzi et al. (2005); (7) Sewilo et al. (2004); (8) Araya et al. (2006); (9) Purcell et al. (2006); (10) Churchwell et al. (1990); (11) Watt & Mundy (1999); (12) Shepherd et al. (2000); (13) Truch et al. (2008); (14) Molinari et al. (2002); (15) Su et al. (2004); (16) Werner et al. (1979); (17) Sandell & Sievers (2004); (18) Thronson & Harper (1979)</text>
<text><location><page_2><loc_8><loc_33><loc_48><loc_40></location>stellar disk or torus (e.g., Beltr'an et al. (2011)). The CH 3 CN molecule is thus a good choice to trace accretion disks around massive proto-stars, whose existence (if confirmed), and properties will be important input for current models of massive star formation.</text>
<text><location><page_2><loc_8><loc_21><loc_48><loc_33></location>From the above discussion it is clear that observations of CH 3 CN with high sensitivity and angular resolution are well-suited to study accretion disks around massive stars. Such observations have recently become more accessible using instruments such as the Submillimeter Array (SMA) and ALMA. To facilitate such observations in the CH 3 CN J=12 → 11 line, the present study adds to the existing database of single dish studies of methyl cyanide.</text>
<text><location><page_2><loc_8><loc_16><loc_48><loc_21></location>In Section 2 we describe the observations and data reduction, and we present the observational results in Section 3. We conclude in Section 4 with a discussion of these observational results.</text>
<section_header_level_1><location><page_2><loc_13><loc_10><loc_43><loc_11></location>2. OBSERVATIONS AND DATA REDUCTION</section_header_level_1>
<text><location><page_2><loc_8><loc_7><loc_48><loc_9></location>We observed 21 sources in 2008 from May 26 to 31 in the 1.3 mm CH 3 CN J=12 → 11 transition with the</text>
<text><location><page_2><loc_52><loc_20><loc_92><loc_40></location>10 m Heinrich Hertz Submillimeter Telescope (SMT) 2 on Mt. Graham, AZ. The telescope beam width at 1 . 3 mm is approximately 36 '' , and the pointing accuracy during our observing run was better than 7 '' . The pointing positions and LSR velocities for the observed sources are given in Table 1. Most of our target sources are prominent HMC candidates with large IRAS luminosities. They all show the typical observational indicators of massive star formation in the HMC stage, namely massive molecular cores, H 2 O and CH 3 OH maser emission, warm molecular gas, weak (or absent) radio continuum emission, and the presence of jets and molecular flows. An exception is IRDC 18223-3, which is a massive infrared dark cloud with an embedded protostar, which may be in an earlier evolutionary state (Beuther & Steinacker 2007).</text>
<text><location><page_2><loc_52><loc_12><loc_92><loc_20></location>The observations were conducted in double sideband mode using the 1.3 mm J-T ALMA sideband separating receiver 3 , which simultaneously recorded two linear orthogonal polarizations. The CH 3 CN J=12 → 11 K = 5 transition ( ν 0 = 220 . 641089 GHz, Boucher et al. 1980) was tuned to the center of the lower sideband. We used</text>
<text><location><page_3><loc_8><loc_74><loc_48><loc_92></location>all six available backends; four low spectral resolution and two high spectral resolution. The low spectral resolution backends were the acoustic-optic spectrometers (AOSs) AOS-A and AOS-B with bandwidths and spectral resolutions of 975 MHz (1325 km s -1 ) and 953 kHz (1 . 3 kms -1 ), and two filterbanks which have bandwidths and spectral resolutions of 1.024 GHz (1392 km s -1 ) and 1 MHz (1 . 4 kms -1 ), respectively. Most of the data used for the analysis in this paper were taken with the AOSC and the Chirp Transform Spectrometers (CTS-A), which have bandwidths and channel widths of 250 . 5 MHz (340 km s -1 ) and 122kHz (0 . 17 kms -1 ) and 215MHz (292 km s -1 ) and 29 kHz (0 . 04 kms -1 ), respectively.</text>
<text><location><page_3><loc_8><loc_55><loc_48><loc_74></location>The AOS-C bandwidth does not cover all K -components of the CH 3 CN J=12 → 11 transition, hence we centered this backend on the K = 5 component. This setup allowed us to observe the K = 0 -7 components simultaneously. The AOS-A and AOS-B and the filterbanks offer bandwidths between 950 and 1000 MHz so in principle the higher K -components could be detected. In practice, however, the lower line strengths of the higher components prevented us from detecting them in all but the strongest source, G34.26+0.15. Furthermore, the 13 CO J=2 → 1 transition blends with the K = 9 component of the CH 3 CN J=12 → 11 transition, thus limiting the usefulness of this K -component.</text>
<text><location><page_3><loc_8><loc_41><loc_48><loc_55></location>The 12 CO J=2 → 1 transition located in the upper sideband (USB) contaminated the lower sideband data approximately 50 MHz away from the CH 3 CN J=12 → 11 K = 0 line. With the exception of G28.87+0.07, this contamination had little effect on the quality of our data. The USB rejection was approximately 17 dB over the course of our observations. Given the relatively weak appearance of the 12 CO J=2 → 1 line (normally a very strong line) in our spectra, we do not believe that there is significant contamination from other spectral lines located in the USB.</text>
<text><location><page_3><loc_8><loc_22><loc_48><loc_41></location>Our observations were conducted using double beam switching with a switch rate of 2 Hz and a beamthrow of 2 ' with a total on/off cycle of approximately 6 minutes per scan. System temperatures ranged from 350 K to just under 200K with an average temperature of 212K. Focus corrections were obtained from observations of Jupiter. Whenever possible we also derived pointing corrections from cross scans of Jupiter. When Jupiter was not available or was located at a large angular distance from the target source, pointing corrections were made by observing asymptotic giant branch stars in the CO J = 2 → 1 transition falling in the USB. In the case of IRAS 20126+4104 we could line point using the 13 CO J=1 → 0 emission from the source.</text>
<text><location><page_3><loc_8><loc_7><loc_48><loc_22></location>At the beginning of each night of observations, we observed the strong source G34.26+0.15 for at least one scan to check for day-to-day consistency of our observations and to obtain a template source to identify contaminating spectral lines. Subsequently, all sources were observed for 12-18 minutes to determine the intensity of the K -components of the CH 3 CN J=12 → 11 transition. Promising sources were then re-observed for at least 2 hr. Additionally, we obtained full beam spaced cross scans for five sources, typically with 1 . 5 hr spent at each offset position.</text>
<text><location><page_3><loc_52><loc_69><loc_92><loc_92></location>The data were reduced in CLASS, which is part of the GILDAS 4 software package. All spectra were first inspected to check for bad channels or any obvious artifacts; bad scans were discarded. Subsequently, we subtracted baselines using low order polynomials, and initially averaged the spectra for each spectrometer and each day separately. After further inspection, all data taken on different days were averaged to form a final data set for each source. After Hanning smoothing and resampling to the same spectral resolution, we averaged the AOS-C and CTS-A spectrometer data. We will refer to the latter data set as 'high resolution' spectra. The data were calibrated using the chopper-wheel method and the antenna temperature was converted to mainbeam brightness temperature by dividing the antenna temperature by the main-beam efficiency of the telescope ( η b = 0 . 74) 5 .</text>
<text><location><page_3><loc_52><loc_60><loc_92><loc_69></location>Using the daily spectra of the strong source G34.26+0.15, we checked our data for amplitude stability, which maximum deviation from the average was found to be smaller than 16 %. Measured line widths had maximum deviations of 13 %, and the repeatability of measured frequencies, as well as the linearity of the spectrometers, was better than 1 %.</text>
<text><location><page_3><loc_52><loc_49><loc_92><loc_60></location>We have three common sources with Pankonin et al. (2001), who observed the same CH 3 CN transition with the SMT, albeit with a different receiver. These three sources are G34.26+0.15, IRAS 23139+5939 and IRAS 23385+6053, the latter two being non-detections by us as well. The results of our line fitting of G34.26+0.15 agree very well with the spectrum of the same source shown in Pankonin et al. (2001).</text>
<section_header_level_1><location><page_3><loc_68><loc_47><loc_76><loc_48></location>3. RESULTS</section_header_level_1>
<section_header_level_1><location><page_3><loc_63><loc_45><loc_81><loc_46></location>3.1. Line Contamination</section_header_level_1>
<text><location><page_3><loc_52><loc_31><loc_92><loc_44></location>As mentioned above, we obtained spectra of the strong source G34.26+0.15 to study possible line contamination of the CH 3 CN J=12 → 11 transition. In Figure 1 we show the full 1 GHz bandpass for this source. In addition to the K -components of the CH 3 CN J=12 → 11 transition many other molecular lines were detected. We used the JPL Molecular Spectroscopy Catalog (Pickett et al. 1998) in conjunction with the Cologne Database for molecular spectroscopy (CDMS, Muller et al. (2001)) to identify the detected lines.</text>
<text><location><page_3><loc_52><loc_11><loc_92><loc_31></location>In some cases there was a high level of ambiguity in the identities of the spectral lines. In these cases, molecules that were unambiguously detected elsewhere in the bandpass were preferentially chosen. Lines that we were unable to identify are labeled as 'U' for unknown lines and are numbered according to their order of appearance. Over 60 lines were identified across the full bandpass and we have detections in the CH 3 CN J=12 → 11 transition up to K = 10. The same transitions in the isotopologue CH 13 3 CN were also detected, possibly out to K = 9. In the case of this isotopologue the K = 0 , 1 and 3 components and the K = 7 and higher components are blended with other lines. Absorption features are observed around the 13 CO J= 2 → 1 line; these features are possible artifacts arising from 13 CO emission in the</text>
<figure>
<location><page_4><loc_19><loc_27><loc_78><loc_94></location>
<caption>Figure 1. The above spectrum shows the full bandwidth of the combined AOS-A and B spectrometers for the source G34.26+0.15. The spectral resolution is about 1 MHz. Line identifications are indicated by vertical lines.</caption>
</figure>
<text><location><page_4><loc_8><loc_19><loc_48><loc_22></location>off-beam, and the line identifications in this area of the spectrum are tentative at best.</text>
<text><location><page_4><loc_8><loc_7><loc_48><loc_19></location>From inspection of Figure 1, we conclude that the CH 3 CN J=12 → 11 K = 0 - 4 , 7, 8, and 10 suffer no significant contamination but the K = 5, 6 components suffer some blending with lines from other molecular species. The K = 9 component is rendered useless by overlap with the 13 CO(2 -1) line. In the analysis that follows we use the K = 5, 6 components only when we are confident that we can reasonably separate them from the other lines; the K = 9 component we do not use at</text>
<text><location><page_4><loc_52><loc_21><loc_54><loc_22></location>all.</text>
<section_header_level_1><location><page_4><loc_57><loc_18><loc_87><loc_19></location>3.2. CH 3 CN Line Detection and Analysis</section_header_level_1>
<text><location><page_4><loc_52><loc_8><loc_92><loc_17></location>We detected emission in the CH 3 CN J=12 → 11 transition towards 9 of the 21 sources of the sample (see Table 1). In Figure 2 we show our high resolution spectra at the center position. K -components were detected up to K = 7 for several sources. The upper excitation energy of the K = 7 component is about 420 K (Boucher et al. 1980), thus indicating the presence of hot molecular gas.</text>
<text><location><page_4><loc_53><loc_7><loc_92><loc_8></location>We have performed simultaneous Gaussian fits for all</text>
<figure>
<location><page_5><loc_11><loc_34><loc_87><loc_88></location>
<caption>Figure 2. Spectra at the central position for the sources with CH 3 CN J=12 → 11 detections. The dashed lines indicate K -components for the main isotopologue. In the spectrum for the source G34.26+0.15 we also indicate the detected K -components of CH 3 13 CN with solid lines. USB emission is affecting the K = 0, 1, 2 lines in G28.87+0.07.</caption>
</figure>
<text><location><page_5><loc_8><loc_14><loc_48><loc_26></location>K -components of the CH 3 CN J=12 → 11 transition. The FWHM of all lines was kept constant at the value measured for the unblended K = 3 component, and the relative position of all lines was fixed at the theoretical values. For the main isotopologue the K = 5 line was fit with 3 Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN.</text>
<text><location><page_5><loc_8><loc_7><loc_48><loc_14></location>The magnitude of the hyperfine splitting (hfs) of the CH 3 CN molecule reported in Boucher et al. (1980) for the CH 3 CN J=12 → 11 transition is ≤ 0 . 3 MHz. Due to the large FWHM ( ∼ 8 MHz), and the relatively low signal-to-noise detections of the higher K -components,</text>
<text><location><page_5><loc_52><loc_23><loc_92><loc_26></location>we omitted the hfs in the line fitting. In Table 2 we list the line parameters from the Gaussian fits.</text>
<text><location><page_5><loc_52><loc_10><loc_92><loc_23></location>In Figure 3 we show the full beam spaced cross scans that we obtained toward five sources. Inspection of the figure shows that the methyl cyanide emission peaks strongly at the central position. Occasionally the lower K -components ( K = 0 -2) were detected away from the center position (IRAS20126+4104, NGC 7538S), indicating that for these sources the warm gas giving rise to the emission is extended on arc-minute scales, but the higher K -components ( K > 3) are always found to be compact with respect to our beam.</text>
<text><location><page_5><loc_52><loc_7><loc_92><loc_10></location>We used the population diagram technique to derive the rotation temperature and column density for our</text>
<figure>
<location><page_6><loc_50><loc_66><loc_82><loc_90></location>
</figure>
<figure>
<location><page_6><loc_50><loc_39><loc_82><loc_63></location>
</figure>
<figure>
<location><page_6><loc_14><loc_66><loc_46><loc_90></location>
</figure>
<figure>
<location><page_6><loc_14><loc_39><loc_46><loc_63></location>
</figure>
<figure>
<location><page_6><loc_14><loc_12><loc_46><loc_37></location>
<caption>Figure 3. Full beam spaced cross scans towards 5 sources obtained with the SMT 10 m telescope (beam size 36 '' ). The dashed lines below the spectra indicate the position of the K -components of the CH 3 CN J=12 → 11 transition. The telescope beam at FWHM is shown at the bottom left corner.</caption>
</figure>
<table>
<location><page_7><loc_14><loc_69><loc_42><loc_87></location>
<caption>Table 3 CH 3 CN J=12 → 11 Population Diagram Results</caption>
</table>
<text><location><page_7><loc_15><loc_67><loc_42><loc_68></location>Note . - A Gaussian source with FWHM of ''</text>
<text><location><page_7><loc_8><loc_51><loc_48><loc_65></location>targets. This analysis assumes optically thin lines and level populations described by a Boltzmann distribution (e.g., Goldsmith & Langer (1999)) and furthermore that all lines trace the same volume of gas. The data are characterized by a linear fit where the negative reciprocal of the slope is T rot and the y -intercept is used to infer the column density (N CH 3 CN ) (see Araya et al. (2005) for a detailed description). When calculating the CH 3 CN column density we adopted a gaussian source size of FWHM of 10 '' .</text>
<text><location><page_7><loc_8><loc_42><loc_48><loc_50></location>Figure 4 shows Boltzmann plots for all detected sources. N JK , g JK and E JK are the column density, statistical weight and upper state energy for the (J,K) state, respectively. The linear fit was made using only the CH 3 CN main isotopologue data. The results of our population diagram analysis are presented in Table 3.</text>
<text><location><page_7><loc_8><loc_30><loc_48><loc_42></location>With the low signal-to-noise (S/N) ratio of our spectra, detection of the CH 3 13 CN isotopologue would indicate optically thick lines. However, only for G34.26+0.15 we detected the first three K -components of CH 3 13 CN above a 3 σ level. The optical depth of the main line K = 2 (which is less blended) estimated from the ratio of the line intensities is ∼ 8, assuming 12 C/ 13 C= 50. The ratio was calculated based on the abundance variation with galacto-centric distance (Wilson & Rood 1994).</text>
<text><location><page_7><loc_8><loc_19><loc_48><loc_30></location>For the other targets, no reliable detection of isotopologue lines was made, therefore a detailed analysis correcting for optical depth effects was not feasible. If the assumption of optically thin conditions is incorrect, the derived temperature values are overestimated, and the column density underestimated. However, optical depths effects will not affect our principal result that relatively hot molecular gas is present in our targets.</text>
<section_header_level_1><location><page_7><loc_23><loc_17><loc_34><loc_18></location>3.3. Kinematics</section_header_level_1>
<text><location><page_7><loc_8><loc_7><loc_48><loc_16></location>The above analysis of the physical parameters assumed uniform conditions in the emitting gas. This is clearly a simplification, as in most cases one would expect gradients in the density and temperature. Allowing for nonuniformity in these parameters is not possible with the present low angular resolution data, however we consider here whether kinematic features can be detected in the</text>
<text><location><page_7><loc_52><loc_90><loc_62><loc_92></location>CH 3 CN lines.</text>
<text><location><page_7><loc_52><loc_80><loc_92><loc_90></location>Our data in principle allow us to check for gradients in line velocity and/or line width. For most of our sources the assumption of central heating, and hence increasing temperature toward the center of the core is reasonable. Thus, any change of line kinematic parameters for the different K -components which have rapidly increasing excitation energies, would imply radial gradients toward the core center.</text>
<text><location><page_7><loc_52><loc_64><loc_92><loc_80></location>To search for radial gradients we have thus obtained independent fits for each line, where each K -component was fit with a Gaussian function independent of the other components. Therefore, the FWHM, line position, and intensity of the lines are free parameters in the fit. For the main isotopologue the K = 5 line was fit with three Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN and a vibrational line of CH 3 CH 2 OH. The results of these alternative fits are shown in Table 4.</text>
<text><location><page_7><loc_52><loc_48><loc_92><loc_64></location>Figures 5 and 6 show plots of velocity and linewidth as a function of the upper level energy. From Figure 5 there appears to be a trend in velocity for G16.59 -0.05, G34.26+0.15, IRAS 18566+0408, and IRAS 20126+4104. In all cases the putative velocity gradient is towards lower velocity with increasing upper state energy. The situation for the line-widths (Figure 6) is less clear. Weak evidence for increasing line width towards higher energies is present in IRAS 18264 -1152, and G23.01 -0.41, whereas the opposite trend is seen in IRAS 20126+4104. We comment further on these findings in the next section.</text>
<section_header_level_1><location><page_7><loc_67><loc_46><loc_77><loc_47></location>4. DISCUSSION</section_header_level_1>
<text><location><page_7><loc_52><loc_33><loc_92><loc_45></location>We have used the 10 m SMT to search for CH 3 CN emission toward 21 regions of massive star formation. All of the regions (except for G34.26+0.15) are clearly in an evolutionary phase prior to that of UC or HC HII regions. We detected nine sources in the CH 3 CN J=12 → 11 transition. For six of these sources this is the first detection in this transition. The low detection rate is likely due to the limited sensitivity of a single dish telescope with the relatively small aperture of 10 m.</text>
<text><location><page_7><loc_52><loc_20><loc_92><loc_33></location>Our cross scans for 5 sources show that the K ≤ 3 are occasionally detected outside the central beam, but the higher K -components are always compact with respect to our angular resolution. This is consistent with a warm (T ≤ 50 K), extended envelope which surrounds a much smaller and hotter (T ≥ 50 K) region near the massive star. This finding is consistent with observations of other molecular transitions of lower excitation and critical density (e.g., NH 3 (1,1)) which probe the more extended envelope.</text>
<text><location><page_7><loc_52><loc_7><loc_92><loc_20></location>Our data thus indicate the presence of gradients in temperature and density. Hence, to obtain precise physical parameters interferometric observations are necessary. The single dish beam will receive emission from regions of different physical characteristics, and performing the simple technique of rotation diagram technique corresponds to obtaining average physical properties of the emitting gas. Taking also into account a number of additional uncertainties intrinsic to single dish data analyzed with the rotation diagram method (e.g., Pankonin et al.</text>
<figure>
<location><page_8><loc_10><loc_31><loc_87><loc_90></location>
<caption>Figure 4. The above figure shows Boltzmann plots for the detected sources. No reliable fit could be obtained for G28.87+0.07. A FWHM of 10 '' gaussian source size have been adopted. The error bars are 1 σ .</caption>
</figure>
<text><location><page_8><loc_8><loc_8><loc_48><loc_27></location>(2001)) it is difficult to compare our results with the of Olmi et al. (1993) and Araya et al. (2005). Nonetheless we note that our results for the column densities ( ≈ 10 14 cm -2 ) are quite similar to what was obtained in these studies. However, our derived temperatures appear to be higher compared to the values of Olmi et al. (1993) and Araya et al. (2005). This might be related to the different evolutionary state of the target samples. Olmi et al. (1993) observed many known UCHII regions and the Araya et al. (2005) sample was selected from IRAS colors typical of UCHII regions, whereas our sample should represent a pre-UCHII region evolutionary phase. Higher S/N ratio data, which can put more stringent constraints on the optical depth in the lines will be required to verify</text>
<text><location><page_8><loc_52><loc_26><loc_64><loc_27></location>this speculation.</text>
<text><location><page_8><loc_52><loc_16><loc_92><loc_25></location>We conclude that all detected regions contain molecular gas with T > 50 K and methyl cyanide column densities of approximately 10 14 cm -2 . Assuming a strongly enhanced CH 3 CN abundance of 10 -8 the hydrogen column density in these regions on a scale of 10 '' , is then approximately 10 22 cm -2 . These numbers are consistent with the HMC nature of the detected sources.</text>
<text><location><page_8><loc_52><loc_7><loc_92><loc_16></location>If the core is heated from the center, then lower K -component emission arises predominantly from outer, and hence cooler regions and higher K -components will dominate in the inner, hotter regions. Consequently, velocity gradients in the K -ladder components can trace radial dynamics and possible kinematic scenarios may be either collapse, out-</text>
<figure>
<location><page_9><loc_11><loc_31><loc_87><loc_90></location>
<caption>Figure 5. Plots of central line velocity vs. upper energy level for all K -components which could be fitted independently. Trends of increasing blueshift with increasing energy are evident for four sources. The error bars are 1 σ .</caption>
</figure>
<text><location><page_9><loc_8><loc_20><loc_48><loc_27></location>flows, expansion or rotation (e.g, Cesaroni et al. (1997), Beltr'an et al. (2004)). We have searched our high resolution spectra for evidence of systematic variation in velocity or line-width as a function of excitation energies.</text>
<text><location><page_9><loc_8><loc_7><loc_48><loc_20></location>A small number of kinematic analyses in CH 3 CN has been done but often no conclusive results have been found due to spectral resolution or S/N limitations. For instance, Olmi et al. (1993) did not find any reliable trend in their results. On the other hand, Cesaroni et al. (1999) observed IRAS 20126+4104 using the IRAM Plateau de Bure interferometer. These authors reported an increase in the velocity and line-width toward the center of the core. They suggested that this behavior may be due to rotation of a Keplerian disk sur-</text>
<text><location><page_9><loc_52><loc_18><loc_92><loc_27></location>rounding an embedded massive protostar. Our results for this same region show a decrease in the velocity and the line-width toward the center, contrary to the results obtained by Cesaroni et al. (1999). A possible explanation for this discrepancy is the much larger beam of the SMT which will include more extended gas than the observations of Cesaroni et al. (1999).</text>
<text><location><page_9><loc_52><loc_7><loc_92><loc_17></location>We detected an increasing blue-shift, i.e., toward lower velocities with higher K -component for four sources. This trend could be explained by expansion or outflow motion as seen in an optically thick line. Another explanation for this behavior could be self absorption of an infalling molecular core which causes a blue asymmetry in an optically thick line. However with the given S/N ratio of our spectra we cannot clearly distinguish these</text>
<figure>
<location><page_10><loc_11><loc_31><loc_87><loc_90></location>
<caption>Figure 6. Plots of line width vs. upper energy level for all K -components which could be fitted independently. The error bars are 1 σ .</caption>
</figure>
<text><location><page_10><loc_8><loc_20><loc_48><loc_28></location>scenarios. A further complication that we can not address is the multiple core scenario. In this case, the cores have some dispersion of radial velocities that may be unresolved in the beam. Therefore, to correctly interpret the detected velocity trends, further observations with higher S/N and angular resolution are needed.</text>
<text><location><page_10><loc_8><loc_8><loc_48><loc_20></location>Most of the HMCs observed in this paper are associated with bright IRAS sources, indicating that a massive object has already heated the surrounding matter. In Figure 7 we show mid-infrared images of six sources for which SPITZER GLIMPSE /IRAC data are available. For five out of these six sources there is evidence for extended 4 . 5 µ m excess emission (e.g., Cyganowski et al. (2008)). The presence of an extended 4 . 5 µ m excess is generally thought to be caused by emission of high ex-</text>
<text><location><page_10><loc_52><loc_8><loc_92><loc_28></location>tation lines from the H 2 molecule, and is hence an indicator of shocked gas. Also, five out of the six sources shown in Figure 7 have strong mid-IR sources, which clearly shows that at least these HMCs have already formed massive stars which cause substantial heating of the molecular cores. One source, G25.83 -0.18, shows only a dark cloud at the suspected position of the massive protostar. This source also harbors one of the few 6 cm H 2 CO masers known (Araya et al. 2008). We note that this source shows quite strong CH 3 CNemission, and since this molecule is thought be effectively formed only with the presence of an energy source, it is likely that a massive protostar is present in this dark cloud also. It is tempting then to speculate that due to the different mid-IR properties G25.83 -0.18 is in an earlier evolution-ar</text>
<figure>
<location><page_11><loc_17><loc_72><loc_47><loc_91></location>
</figure>
<figure>
<location><page_11><loc_19><loc_50><loc_47><loc_70></location>
</figure>
<figure>
<location><page_11><loc_18><loc_29><loc_47><loc_49></location>
</figure>
<figure>
<location><page_11><loc_53><loc_29><loc_81><loc_49></location>
<caption>Figure 7. SPITZER GLIMPSE /IRAC three-color (3.6 µm -blue, 4.5 µm -green and 8.0 µm -red) images toward six of our target sources. The CH 3 CN J=12 → 11 spectra toward these sources are overlaid on the images. The center of each spectrum is placed at the corresponding pointing position, and the size of each spectrum corresponds to the beam size.</caption>
</figure>
<text><location><page_11><loc_8><loc_12><loc_48><loc_23></location>y state compared to the other sources which have very bright mid-IR emission. However, using the extinction curve of Mathis (1990) we find that hydrogen column densities of ≥ 2 × 10 23 cm -2 could render a possible midIR source undetectable. Since hydrogen column densities of this order, and larger, are common in massive star forming cores, it is conceivable that the different mid-IR appearance of G25.83 -0.18 is caused by extinction.</text>
<section_header_level_1><location><page_11><loc_24><loc_10><loc_33><loc_11></location>5. SUMMARY</section_header_level_1>
<text><location><page_11><loc_8><loc_7><loc_48><loc_9></location>We have observed a sample of 21 massive proto-stellar candidates in the CH 3 CN J=12 → 11 transition using</text>
<text><location><page_11><loc_52><loc_20><loc_92><loc_23></location>the 10 m SMT. We detected methyl cyanide in nine of the sources of the sample.</text>
<text><location><page_11><loc_52><loc_11><loc_92><loc_20></location>Rotation temperatures and column densities were estimated using the population diagram technique. Detected sources have temperatures > 50 K and column densities of ∼ 10 14 cm -2 , hence they are consistent with HMC nature. Higher spectral resolution is needed in order to understand the structure of the kinematics in molecular cores.</text>
<text><location><page_11><loc_53><loc_7><loc_92><loc_8></location>This project was partially supported by the New Mex-</text>
<figure>
<location><page_11><loc_51><loc_72><loc_81><loc_92></location>
</figure>
<figure>
<location><page_11><loc_52><loc_50><loc_81><loc_70></location>
</figure>
<text><location><page_12><loc_8><loc_84><loc_48><loc_92></location>ico Space Grant Consortium. PH acknowledges partial support from NSF grant AST-0908901. SK acknowledges partial support from UNAM DGAPA grant IN101310. We thank E. Jordan for help with the observations and initial data reduction. We thank the anonymous referee for suggestions which improved this manuscript.</text>
<section_header_level_1><location><page_12><loc_24><loc_81><loc_33><loc_82></location>REFERENCES</section_header_level_1>
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<table>
<location><page_13><loc_8><loc_71><loc_97><loc_89></location>
<caption>Table 2 CH 3 CN J=12 → 11 Line ParametersTable 4 CH 3 CN J=12 → 11 Line Parameters (Free Fits)</caption>
</table>
<table>
<location><page_13><loc_24><loc_7><loc_76><loc_65></location>
</table>
<section_header_level_1><location><page_14><loc_47><loc_93><loc_56><loc_94></location>Rosero et al.</section_header_level_1>
<table>
<location><page_14><loc_24><loc_38><loc_76><loc_91></location>
<caption>Table 4 -Continued</caption>
</table>
<unordered_list>
<list_item><location><page_14><loc_9><loc_32><loc_35><loc_33></location>d Molecule t -CH 3 CH 2 OH not included in fit.</list_item>
</unordered_list>
</document>
[
{
"title": "ABSTRACT",
"content": "We report the results of a survey in the CH 3 CN J=12 → 11 transition toward a sample of massive proto-stellar candidates. The observations were carried out with the 10 m Submillimeter telescope on Mount Graham, AZ. We detected this molecular line in 9 out of 21 observed sources. In six cases this is the first detection of this transition. We also obtained full beam sampled cross-scans for five sources which show that the lower K -components can be extended on the arcminute angular scale. The higher K -components however are always found to be compact with respect to our 36 '' beam. A Boltzmann population diagram analysis of the central spectra indicates CH 3 CN column densities of about 10 14 cm -2 , and rotational temperatures above 50 K, which confirms these sources as hot molecular cores. Independent fits to line velocity and width for the individual K -components resulted in the detection of an increasing blue shift with increasing line excitation for four sources. Comparison with mid-infrared images from the SPITZER GLIMPSE /IRAC archive for six sources show that the CH 3 CN emission is generally coincident with a bright mid-IR source. Our data clearly show that the CH 3 CN J=12 → 11 transition is a good probe of the hot molecular gas near massive protostars, and provide the basis for future interferometric studies. Subject headings: ISM: molecules - stars: formation",
"pages": [
1
]
},
{
"title": "METHYL CYANIDE OBSERVATIONS TOWARD MASSIVE PROTOSTARS",
"content": "V. Rosero 1 , P. Hofner 1 , † , S. Kurtz 2 , J. Bieging 3 & E. D. Araya 4 1 Physics Department, New Mexico Tech, 801 Leroy Pl., Socorro, NM 87801, USA 2 Centro de Radioastronom'ıa y Astrof'ısica, Universidad Nacional Aut'onoma de M'exico, Morelia 58090, M'exico 3 Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA and 4 Physics Department, Western Illinois University, 1 University Circle, Macomb, IL 61455, USA To appear in The Astrophysical Journal Supplement Series.",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Despite the central role of massive stars in almost all areas of astronomy, the physical processes involved in the formation of stars with masses > 8 M /circledot are at present poorly understood (e.g., Zinnecker & Yorke (2007)). Theoretical and observational studies favor the idea that massive stars, similar to their lower mass counterparts, form from a collapsing cloud core. However, whether the subsequent formation of a protostar and further mass accretion occurs from an isolated massive molecular core (e.g., McKee & Tan (2003), Keto (2007)), or under the influence of a cluster environment (e.g., Bonnell et al. (2004)) remains a persistent question. One of the earliest observational manifestations of massive proto-stars are so-called hot molecular cores (hereafter HMCs). Named after the prototype object in the Orion KL region, they have been surveyed throughout the Galaxy in an effort to identify candidates for massive proto-stars (e.g., Sridharan et al. (2002)). Common search criteria were high FIR luminosity, high molecular column densities and temperature, and the absence of strong radio continuum emission - the latter to ensure an earlier evolutionary phase than ultra-compact (UC) or hyper-compact (HC) HII regions. A particularly useful tracer of HMCs is the methyl cyanide (CH 3 CN) molecule. Due to the centrifugal deformation of this symmetric top molecule, its rotational spectrum consists of a series of closely spaced K -components tracing rapidly increasing excitation energies. The K -ladders are connected only through collisions so that excitation temperatures can in principle be measured from the ratios of K -components, thus avoiding the usual calibration uncertainties that occur when comparing rotational transitions observed in different frequency bands. An extensive discussion of the microwave spectroscopy of methyl cyanide is given in Boucher et al. (1980). Because of these spectroscopic properties, the CH 3 CNmolecule is frequently used to determine temperatures in the dense molecular cores where massive stars form, using both statistical equilibrium calculations (e.g., Loren & Mundy (1984)), or the simpler rotation diagram technique (e.g., Goldsmith & Langer (1999)). Another factor that favors the use of CH 3 CN as a tracer of HMCs is its enhanced abundance in warm (T= 100 -300 K), dense ( n H 2 = 10 6 -10 8 cm -3 ) environments (e.g., Blake et al. (1987)). This is generally thought to be caused by grain surface chemistry, either by primary reactions on the grain surface with subsequent release into the gas phase when the grain mantle evaporates, or, alternatively, by secondary reactions in the gas phase (e.g., Charnley et al. (1992), Bisschop et al. (2008)). Recently, Codella et al. (2009) reported detection of CH 3 CN in the outflow lobes of the low-mass protostar L1157-B1, and attributed the enhanced CH 3 CN abundance to shock chemistry. From these studies it is well-established that CH 3 CN traces an energetic environment similar to that expected in the immediate vicinity of massive proto-stars. To investigate the HMC phase of massive star formation, several single dish CH 3 CN surveys have been made (e.g., Olmi et al. (1993), Araya et al. (2005), Pankonin et al. (2001)), and a small number of sources have also been studied with mm-interferometers (e.g., Cesaroni et al. (1994), Hofner et al. (1996), Furuya et al. (2008)). Several of the interferometric studies resulted in images of CH 3 CN structures that are elongated perpendicular to the direction of molecular outflows, with velocity gradients along the elongated structures; this is usually explained as rotational motion of a circum- Note . -Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. References. (1) Sridharan et al. (2002); (2) Codella et al. (1997); (3) Beuther & Steinacker (2007); (4) Brunthaler et al. (2009); (5) Araya et al. (2008); (6) Pestalozzi et al. (2005); (7) Sewilo et al. (2004); (8) Araya et al. (2006); (9) Purcell et al. (2006); (10) Churchwell et al. (1990); (11) Watt & Mundy (1999); (12) Shepherd et al. (2000); (13) Truch et al. (2008); (14) Molinari et al. (2002); (15) Su et al. (2004); (16) Werner et al. (1979); (17) Sandell & Sievers (2004); (18) Thronson & Harper (1979) stellar disk or torus (e.g., Beltr'an et al. (2011)). The CH 3 CN molecule is thus a good choice to trace accretion disks around massive proto-stars, whose existence (if confirmed), and properties will be important input for current models of massive star formation. From the above discussion it is clear that observations of CH 3 CN with high sensitivity and angular resolution are well-suited to study accretion disks around massive stars. Such observations have recently become more accessible using instruments such as the Submillimeter Array (SMA) and ALMA. To facilitate such observations in the CH 3 CN J=12 → 11 line, the present study adds to the existing database of single dish studies of methyl cyanide. In Section 2 we describe the observations and data reduction, and we present the observational results in Section 3. We conclude in Section 4 with a discussion of these observational results.",
"pages": [
1,
2
]
},
{
"title": "2. OBSERVATIONS AND DATA REDUCTION",
"content": "We observed 21 sources in 2008 from May 26 to 31 in the 1.3 mm CH 3 CN J=12 → 11 transition with the 10 m Heinrich Hertz Submillimeter Telescope (SMT) 2 on Mt. Graham, AZ. The telescope beam width at 1 . 3 mm is approximately 36 '' , and the pointing accuracy during our observing run was better than 7 '' . The pointing positions and LSR velocities for the observed sources are given in Table 1. Most of our target sources are prominent HMC candidates with large IRAS luminosities. They all show the typical observational indicators of massive star formation in the HMC stage, namely massive molecular cores, H 2 O and CH 3 OH maser emission, warm molecular gas, weak (or absent) radio continuum emission, and the presence of jets and molecular flows. An exception is IRDC 18223-3, which is a massive infrared dark cloud with an embedded protostar, which may be in an earlier evolutionary state (Beuther & Steinacker 2007). The observations were conducted in double sideband mode using the 1.3 mm J-T ALMA sideband separating receiver 3 , which simultaneously recorded two linear orthogonal polarizations. The CH 3 CN J=12 → 11 K = 5 transition ( ν 0 = 220 . 641089 GHz, Boucher et al. 1980) was tuned to the center of the lower sideband. We used all six available backends; four low spectral resolution and two high spectral resolution. The low spectral resolution backends were the acoustic-optic spectrometers (AOSs) AOS-A and AOS-B with bandwidths and spectral resolutions of 975 MHz (1325 km s -1 ) and 953 kHz (1 . 3 kms -1 ), and two filterbanks which have bandwidths and spectral resolutions of 1.024 GHz (1392 km s -1 ) and 1 MHz (1 . 4 kms -1 ), respectively. Most of the data used for the analysis in this paper were taken with the AOSC and the Chirp Transform Spectrometers (CTS-A), which have bandwidths and channel widths of 250 . 5 MHz (340 km s -1 ) and 122kHz (0 . 17 kms -1 ) and 215MHz (292 km s -1 ) and 29 kHz (0 . 04 kms -1 ), respectively. The AOS-C bandwidth does not cover all K -components of the CH 3 CN J=12 → 11 transition, hence we centered this backend on the K = 5 component. This setup allowed us to observe the K = 0 -7 components simultaneously. The AOS-A and AOS-B and the filterbanks offer bandwidths between 950 and 1000 MHz so in principle the higher K -components could be detected. In practice, however, the lower line strengths of the higher components prevented us from detecting them in all but the strongest source, G34.26+0.15. Furthermore, the 13 CO J=2 → 1 transition blends with the K = 9 component of the CH 3 CN J=12 → 11 transition, thus limiting the usefulness of this K -component. The 12 CO J=2 → 1 transition located in the upper sideband (USB) contaminated the lower sideband data approximately 50 MHz away from the CH 3 CN J=12 → 11 K = 0 line. With the exception of G28.87+0.07, this contamination had little effect on the quality of our data. The USB rejection was approximately 17 dB over the course of our observations. Given the relatively weak appearance of the 12 CO J=2 → 1 line (normally a very strong line) in our spectra, we do not believe that there is significant contamination from other spectral lines located in the USB. Our observations were conducted using double beam switching with a switch rate of 2 Hz and a beamthrow of 2 ' with a total on/off cycle of approximately 6 minutes per scan. System temperatures ranged from 350 K to just under 200K with an average temperature of 212K. Focus corrections were obtained from observations of Jupiter. Whenever possible we also derived pointing corrections from cross scans of Jupiter. When Jupiter was not available or was located at a large angular distance from the target source, pointing corrections were made by observing asymptotic giant branch stars in the CO J = 2 → 1 transition falling in the USB. In the case of IRAS 20126+4104 we could line point using the 13 CO J=1 → 0 emission from the source. At the beginning of each night of observations, we observed the strong source G34.26+0.15 for at least one scan to check for day-to-day consistency of our observations and to obtain a template source to identify contaminating spectral lines. Subsequently, all sources were observed for 12-18 minutes to determine the intensity of the K -components of the CH 3 CN J=12 → 11 transition. Promising sources were then re-observed for at least 2 hr. Additionally, we obtained full beam spaced cross scans for five sources, typically with 1 . 5 hr spent at each offset position. The data were reduced in CLASS, which is part of the GILDAS 4 software package. All spectra were first inspected to check for bad channels or any obvious artifacts; bad scans were discarded. Subsequently, we subtracted baselines using low order polynomials, and initially averaged the spectra for each spectrometer and each day separately. After further inspection, all data taken on different days were averaged to form a final data set for each source. After Hanning smoothing and resampling to the same spectral resolution, we averaged the AOS-C and CTS-A spectrometer data. We will refer to the latter data set as 'high resolution' spectra. The data were calibrated using the chopper-wheel method and the antenna temperature was converted to mainbeam brightness temperature by dividing the antenna temperature by the main-beam efficiency of the telescope ( η b = 0 . 74) 5 . Using the daily spectra of the strong source G34.26+0.15, we checked our data for amplitude stability, which maximum deviation from the average was found to be smaller than 16 %. Measured line widths had maximum deviations of 13 %, and the repeatability of measured frequencies, as well as the linearity of the spectrometers, was better than 1 %. We have three common sources with Pankonin et al. (2001), who observed the same CH 3 CN transition with the SMT, albeit with a different receiver. These three sources are G34.26+0.15, IRAS 23139+5939 and IRAS 23385+6053, the latter two being non-detections by us as well. The results of our line fitting of G34.26+0.15 agree very well with the spectrum of the same source shown in Pankonin et al. (2001).",
"pages": [
2,
3
]
},
{
"title": "3.1. Line Contamination",
"content": "As mentioned above, we obtained spectra of the strong source G34.26+0.15 to study possible line contamination of the CH 3 CN J=12 → 11 transition. In Figure 1 we show the full 1 GHz bandpass for this source. In addition to the K -components of the CH 3 CN J=12 → 11 transition many other molecular lines were detected. We used the JPL Molecular Spectroscopy Catalog (Pickett et al. 1998) in conjunction with the Cologne Database for molecular spectroscopy (CDMS, Muller et al. (2001)) to identify the detected lines. In some cases there was a high level of ambiguity in the identities of the spectral lines. In these cases, molecules that were unambiguously detected elsewhere in the bandpass were preferentially chosen. Lines that we were unable to identify are labeled as 'U' for unknown lines and are numbered according to their order of appearance. Over 60 lines were identified across the full bandpass and we have detections in the CH 3 CN J=12 → 11 transition up to K = 10. The same transitions in the isotopologue CH 13 3 CN were also detected, possibly out to K = 9. In the case of this isotopologue the K = 0 , 1 and 3 components and the K = 7 and higher components are blended with other lines. Absorption features are observed around the 13 CO J= 2 → 1 line; these features are possible artifacts arising from 13 CO emission in the off-beam, and the line identifications in this area of the spectrum are tentative at best. From inspection of Figure 1, we conclude that the CH 3 CN J=12 → 11 K = 0 - 4 , 7, 8, and 10 suffer no significant contamination but the K = 5, 6 components suffer some blending with lines from other molecular species. The K = 9 component is rendered useless by overlap with the 13 CO(2 -1) line. In the analysis that follows we use the K = 5, 6 components only when we are confident that we can reasonably separate them from the other lines; the K = 9 component we do not use at all.",
"pages": [
3,
4
]
},
{
"title": "3.2. CH 3 CN Line Detection and Analysis",
"content": "We detected emission in the CH 3 CN J=12 → 11 transition towards 9 of the 21 sources of the sample (see Table 1). In Figure 2 we show our high resolution spectra at the center position. K -components were detected up to K = 7 for several sources. The upper excitation energy of the K = 7 component is about 420 K (Boucher et al. 1980), thus indicating the presence of hot molecular gas. We have performed simultaneous Gaussian fits for all K -components of the CH 3 CN J=12 → 11 transition. The FWHM of all lines was kept constant at the value measured for the unblended K = 3 component, and the relative position of all lines was fixed at the theoretical values. For the main isotopologue the K = 5 line was fit with 3 Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN. The magnitude of the hyperfine splitting (hfs) of the CH 3 CN molecule reported in Boucher et al. (1980) for the CH 3 CN J=12 → 11 transition is ≤ 0 . 3 MHz. Due to the large FWHM ( ∼ 8 MHz), and the relatively low signal-to-noise detections of the higher K -components, we omitted the hfs in the line fitting. In Table 2 we list the line parameters from the Gaussian fits. In Figure 3 we show the full beam spaced cross scans that we obtained toward five sources. Inspection of the figure shows that the methyl cyanide emission peaks strongly at the central position. Occasionally the lower K -components ( K = 0 -2) were detected away from the center position (IRAS20126+4104, NGC 7538S), indicating that for these sources the warm gas giving rise to the emission is extended on arc-minute scales, but the higher K -components ( K > 3) are always found to be compact with respect to our beam. We used the population diagram technique to derive the rotation temperature and column density for our Note . - A Gaussian source with FWHM of '' targets. This analysis assumes optically thin lines and level populations described by a Boltzmann distribution (e.g., Goldsmith & Langer (1999)) and furthermore that all lines trace the same volume of gas. The data are characterized by a linear fit where the negative reciprocal of the slope is T rot and the y -intercept is used to infer the column density (N CH 3 CN ) (see Araya et al. (2005) for a detailed description). When calculating the CH 3 CN column density we adopted a gaussian source size of FWHM of 10 '' . Figure 4 shows Boltzmann plots for all detected sources. N JK , g JK and E JK are the column density, statistical weight and upper state energy for the (J,K) state, respectively. The linear fit was made using only the CH 3 CN main isotopologue data. The results of our population diagram analysis are presented in Table 3. With the low signal-to-noise (S/N) ratio of our spectra, detection of the CH 3 13 CN isotopologue would indicate optically thick lines. However, only for G34.26+0.15 we detected the first three K -components of CH 3 13 CN above a 3 σ level. The optical depth of the main line K = 2 (which is less blended) estimated from the ratio of the line intensities is ∼ 8, assuming 12 C/ 13 C= 50. The ratio was calculated based on the abundance variation with galacto-centric distance (Wilson & Rood 1994). For the other targets, no reliable detection of isotopologue lines was made, therefore a detailed analysis correcting for optical depth effects was not feasible. If the assumption of optically thin conditions is incorrect, the derived temperature values are overestimated, and the column density underestimated. However, optical depths effects will not affect our principal result that relatively hot molecular gas is present in our targets.",
"pages": [
4,
5,
7
]
},
{
"title": "3.3. Kinematics",
"content": "The above analysis of the physical parameters assumed uniform conditions in the emitting gas. This is clearly a simplification, as in most cases one would expect gradients in the density and temperature. Allowing for nonuniformity in these parameters is not possible with the present low angular resolution data, however we consider here whether kinematic features can be detected in the CH 3 CN lines. Our data in principle allow us to check for gradients in line velocity and/or line width. For most of our sources the assumption of central heating, and hence increasing temperature toward the center of the core is reasonable. Thus, any change of line kinematic parameters for the different K -components which have rapidly increasing excitation energies, would imply radial gradients toward the core center. To search for radial gradients we have thus obtained independent fits for each line, where each K -component was fit with a Gaussian function independent of the other components. Therefore, the FWHM, line position, and intensity of the lines are free parameters in the fit. For the main isotopologue the K = 5 line was fit with three Gaussians when blending with CH 3 13 CN K = 0 and K = 1 was suspected. The K = 6 line was fit taking into account that its high-frequency wing is blended with the K = 3 component of CH 3 13 CN and a vibrational line of CH 3 CH 2 OH. The results of these alternative fits are shown in Table 4. Figures 5 and 6 show plots of velocity and linewidth as a function of the upper level energy. From Figure 5 there appears to be a trend in velocity for G16.59 -0.05, G34.26+0.15, IRAS 18566+0408, and IRAS 20126+4104. In all cases the putative velocity gradient is towards lower velocity with increasing upper state energy. The situation for the line-widths (Figure 6) is less clear. Weak evidence for increasing line width towards higher energies is present in IRAS 18264 -1152, and G23.01 -0.41, whereas the opposite trend is seen in IRAS 20126+4104. We comment further on these findings in the next section.",
"pages": [
7
]
},
{
"title": "4. DISCUSSION",
"content": "We have used the 10 m SMT to search for CH 3 CN emission toward 21 regions of massive star formation. All of the regions (except for G34.26+0.15) are clearly in an evolutionary phase prior to that of UC or HC HII regions. We detected nine sources in the CH 3 CN J=12 → 11 transition. For six of these sources this is the first detection in this transition. The low detection rate is likely due to the limited sensitivity of a single dish telescope with the relatively small aperture of 10 m. Our cross scans for 5 sources show that the K ≤ 3 are occasionally detected outside the central beam, but the higher K -components are always compact with respect to our angular resolution. This is consistent with a warm (T ≤ 50 K), extended envelope which surrounds a much smaller and hotter (T ≥ 50 K) region near the massive star. This finding is consistent with observations of other molecular transitions of lower excitation and critical density (e.g., NH 3 (1,1)) which probe the more extended envelope. Our data thus indicate the presence of gradients in temperature and density. Hence, to obtain precise physical parameters interferometric observations are necessary. The single dish beam will receive emission from regions of different physical characteristics, and performing the simple technique of rotation diagram technique corresponds to obtaining average physical properties of the emitting gas. Taking also into account a number of additional uncertainties intrinsic to single dish data analyzed with the rotation diagram method (e.g., Pankonin et al. (2001)) it is difficult to compare our results with the of Olmi et al. (1993) and Araya et al. (2005). Nonetheless we note that our results for the column densities ( ≈ 10 14 cm -2 ) are quite similar to what was obtained in these studies. However, our derived temperatures appear to be higher compared to the values of Olmi et al. (1993) and Araya et al. (2005). This might be related to the different evolutionary state of the target samples. Olmi et al. (1993) observed many known UCHII regions and the Araya et al. (2005) sample was selected from IRAS colors typical of UCHII regions, whereas our sample should represent a pre-UCHII region evolutionary phase. Higher S/N ratio data, which can put more stringent constraints on the optical depth in the lines will be required to verify this speculation. We conclude that all detected regions contain molecular gas with T > 50 K and methyl cyanide column densities of approximately 10 14 cm -2 . Assuming a strongly enhanced CH 3 CN abundance of 10 -8 the hydrogen column density in these regions on a scale of 10 '' , is then approximately 10 22 cm -2 . These numbers are consistent with the HMC nature of the detected sources. If the core is heated from the center, then lower K -component emission arises predominantly from outer, and hence cooler regions and higher K -components will dominate in the inner, hotter regions. Consequently, velocity gradients in the K -ladder components can trace radial dynamics and possible kinematic scenarios may be either collapse, out- flows, expansion or rotation (e.g, Cesaroni et al. (1997), Beltr'an et al. (2004)). We have searched our high resolution spectra for evidence of systematic variation in velocity or line-width as a function of excitation energies. A small number of kinematic analyses in CH 3 CN has been done but often no conclusive results have been found due to spectral resolution or S/N limitations. For instance, Olmi et al. (1993) did not find any reliable trend in their results. On the other hand, Cesaroni et al. (1999) observed IRAS 20126+4104 using the IRAM Plateau de Bure interferometer. These authors reported an increase in the velocity and line-width toward the center of the core. They suggested that this behavior may be due to rotation of a Keplerian disk sur- rounding an embedded massive protostar. Our results for this same region show a decrease in the velocity and the line-width toward the center, contrary to the results obtained by Cesaroni et al. (1999). A possible explanation for this discrepancy is the much larger beam of the SMT which will include more extended gas than the observations of Cesaroni et al. (1999). We detected an increasing blue-shift, i.e., toward lower velocities with higher K -component for four sources. This trend could be explained by expansion or outflow motion as seen in an optically thick line. Another explanation for this behavior could be self absorption of an infalling molecular core which causes a blue asymmetry in an optically thick line. However with the given S/N ratio of our spectra we cannot clearly distinguish these scenarios. A further complication that we can not address is the multiple core scenario. In this case, the cores have some dispersion of radial velocities that may be unresolved in the beam. Therefore, to correctly interpret the detected velocity trends, further observations with higher S/N and angular resolution are needed. Most of the HMCs observed in this paper are associated with bright IRAS sources, indicating that a massive object has already heated the surrounding matter. In Figure 7 we show mid-infrared images of six sources for which SPITZER GLIMPSE /IRAC data are available. For five out of these six sources there is evidence for extended 4 . 5 µ m excess emission (e.g., Cyganowski et al. (2008)). The presence of an extended 4 . 5 µ m excess is generally thought to be caused by emission of high ex- tation lines from the H 2 molecule, and is hence an indicator of shocked gas. Also, five out of the six sources shown in Figure 7 have strong mid-IR sources, which clearly shows that at least these HMCs have already formed massive stars which cause substantial heating of the molecular cores. One source, G25.83 -0.18, shows only a dark cloud at the suspected position of the massive protostar. This source also harbors one of the few 6 cm H 2 CO masers known (Araya et al. 2008). We note that this source shows quite strong CH 3 CNemission, and since this molecule is thought be effectively formed only with the presence of an energy source, it is likely that a massive protostar is present in this dark cloud also. It is tempting then to speculate that due to the different mid-IR properties G25.83 -0.18 is in an earlier evolution-ar y state compared to the other sources which have very bright mid-IR emission. However, using the extinction curve of Mathis (1990) we find that hydrogen column densities of ≥ 2 × 10 23 cm -2 could render a possible midIR source undetectable. Since hydrogen column densities of this order, and larger, are common in massive star forming cores, it is conceivable that the different mid-IR appearance of G25.83 -0.18 is caused by extinction.",
"pages": [
7,
8,
9,
10,
11
]
},
{
"title": "5. SUMMARY",
"content": "We have observed a sample of 21 massive proto-stellar candidates in the CH 3 CN J=12 → 11 transition using the 10 m SMT. We detected methyl cyanide in nine of the sources of the sample. Rotation temperatures and column densities were estimated using the population diagram technique. Detected sources have temperatures > 50 K and column densities of ∼ 10 14 cm -2 , hence they are consistent with HMC nature. Higher spectral resolution is needed in order to understand the structure of the kinematics in molecular cores. This project was partially supported by the New Mex- ico Space Grant Consortium. PH acknowledges partial support from NSF grant AST-0908901. SK acknowledges partial support from UNAM DGAPA grant IN101310. We thank E. Jordan for help with the observations and initial data reduction. We thank the anonymous referee for suggestions which improved this manuscript.",
"pages": [
11,
12
]
},
{
"title": "REFERENCES",
"content": "Araya, E., Hofner, P., Goss, W. M., et al. 2006, ApJ, 643, L33 Araya, E., Hofner, P., Kurtz, S., Bronfman, L., & DeDeo, S. 2005, ApJS, 157, 279 Bonnell, I. A., Vine, S. G., & Bate, M. R. 2004, MNRAS, 349, 735 Boucher, D., Burie, J., Bauer, A., Dubrulle, A., & Demaison, J. 1980, Journal of Physical and Chemical Reference Data, 9, 659 Brunthaler, A., Reid, M. J., Menten, K. M., et al. 2009, ApJ, 693, 424",
"pages": [
12
]
}
]
2013ApJS..209...29K
https://arxiv.org/pdf/1309.4490.pdf
<document>
<text><location><page_1><loc_64><loc_85><loc_89><loc_86></location>Accepted 12 September, 2013</text>
<section_header_level_1><location><page_1><loc_13><loc_77><loc_87><loc_82></location>A Massive Young Star-Forming Complex Study in Infrared and X-ray: Mid-Infrared Observations and Catalogs</section_header_level_1>
<text><location><page_1><loc_13><loc_72><loc_87><loc_76></location>Michael A. Kuhn 1 , Matthew S. Povich 1 , 2 , Kevin L. Luhman 1 , 3 , Konstantin V. Getman 1 , Heather S. Busk 1 , Eric D. Feigelson 1 , 3</text>
<section_header_level_1><location><page_1><loc_44><loc_67><loc_56><loc_69></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_29><loc_85><loc_64></location>Spitzer IRAC observations and stellar photometric catalogs are presented for the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX). MYStIX is a multiwavelength census of young stellar members of twenty nearby ( d < 4 kpc), Galactic, star-forming regions that contain at least one O star. All regions have data available from the Spitzer Space Telescope, consisting of GLIMPSE or other published catalogs for eleven regions and results of our own photometric analysis of archival data for the remaining nine regions. This paper seeks to construct deep and reliable catalogs of sources from the Spitzer images. Mid-infrared study of these regions faces challenges of crowding and high nebulosity. Our new catalogs typically contain fainter sources than existing Spitzer studies, which improves the match rate to Chandra X-ray sources that are likely to be young stars, but increases the possibility of spurious point-source detections, especially peaks in the nebulosity. IRAC color-color diagrams help distinguish spurious detections of nebular PAH emission from the infrared excess associated with dusty disks around young stars. The distributions of sources on the mid-infrared color-magnitude and color-color diagrams reflect differences between MYStIX regions, including astrophysical effects such as stellar ages and disk evolution.</text>
<text><location><page_1><loc_17><loc_23><loc_84><loc_26></location>Subject headings: methods: data analysis - stars: pre-main-sequence - infrared: stars - planetary systems: protoplanetary disks</text>
<section_header_level_1><location><page_2><loc_42><loc_85><loc_58><loc_86></location>1. Introduction</section_header_level_1>
<text><location><page_2><loc_12><loc_53><loc_89><loc_83></location>A significant fraction of star formation activity in the Galaxy occurs in massive starforming complexes, dominated by OB stars and containing thousands of young stars. Studies of the cluster mass function indicate that stars are more likely to be born in rich clusters than in small groups (e.g. Lada & Lada 2003; Fall et al. 2009; Chandar et al. 2011). Because of the importance of such clusters, the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX) constructs a census of stars in twenty of the nearest ( d < 4 kpc), Galactic massive star-forming regions (Feigelson et al. 2013) with the Chandra X-ray Observatory , the Spitzer Space Telescope , and ground based near-infrared (NIR) observatories. Studies in the IR and X-ray provide complementary pictures of populations of new stars in star-forming regions. The infrared (IR) images identify stars with circumstellar disks or infalling envelopes through infrared excess (IRE), but cannot distinguish disk-free cluster members from field stars. Meanwhile, X-ray images can detect both disk-bearing and disk-free stars, although the sensitivity to the former is lower (Getman et al. 2009; Stelzer et al. 2011). Thus, the combination of both X-ray and IR observations provide more complete and less biased samples of complex members than either waveband alone.</text>
<text><location><page_2><loc_12><loc_14><loc_89><loc_52></location>In this paper, we describe the observations and source catalogs used by the MYStIX project from the Infrared Array Camera (IRAC; Fazio et al. 2004) onboard the Spitzer Space Telescope (Werner et al. 2004). This instrument has four bands centered at 3.6, 4.5, 5.8, and 8.0 µ m, which are useful for identifying IRE stars (e.g. Allen et al. 2004; Hartmann et al. 2005; Robitaille et al. 2006; Gutermuth et al. 2009). We use source catalogs produced by the pipeline of the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE; Benjamin et al. 2003) for nine regions, and we measure new aperture photometry from archival IRAC data for nine regions. We adopt pre-existing IRE star catalogs for two additional regions, the Orion Nebula (Megeath et al. 2012) and the Carina Nebula (Povich et al. 2011). In addition to the data from Spitzer , the MYStIX project includes NIR data obtained by United Kingdom Infra-Red Telescope (King et al. 2013) and the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and X-ray data obtained by the Chandra X-ray Observatory (Kuhn et al. 2013a). The procedures for constructing the combined sample of X-ray selected member, IRE selected members, and spectrally selected OB members is described by Naylor et al. (2013), Povich et al. (2013), and Broos et al. (2013). We describe the available GLIMPSE data (Section 2) and our procedures for analyzing other archival images from IRAC (Section 3). We then discuss the distributions of probable members and field stars on color-magnitude and color-color diagrams (Section 4) and summarize our results (Section 5).</text>
<section_header_level_1><location><page_3><loc_40><loc_85><loc_59><loc_86></location>2. GLIMPSE Data</section_header_level_1>
<text><location><page_3><loc_12><loc_67><loc_89><loc_83></location>The GLIMPSE survey is a Legacy Science Program of NASAÕs Spitzer Space Telescope to study star formation in the disk of the Milky Way Galaxy (Benjamin et al. 2003; Churchwell et al. 2009). It contains six MYStIX regions Ð the Lagoon Nebula, the Trifid Nebula, NGC 6334, the Eagle Nebula, M 17, and NGC 6357 Ð within the 2 · -wide strip along the Galactic equator (GLIMPSE I and II data releases). Furthermore, Spitzer images and photometry for RCW 38 and NGC 3576 come from the Vela-Carina survey (Majewski et al. 2007), using a similar observing strategy with mosaicking and photometric analysis performed with GLIMPSE pipeline.</text>
<text><location><page_3><loc_12><loc_48><loc_89><loc_66></location>For the GLIMPSE observations, every position was visited at least twice with 1.2 s integrations. The data-reduction pipeline produces image mosaics (v3.0) and point-source lists (v2.0) for all four IRAC bands, which are publicly available 1 . Photometry is obtained through point response function (PRF) fitting. A 5 σ detection limit is used, corresponding to fluxes 0.2, 0.2, 0.4, and 0.4 mJy in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively (Benjamin et al. 2003). However, the detection sensitivity is lower in nebulous regions, and bright sources or regions with high backgrounds may be saturated. The GLIMPSE Catalog contains the sources with reliability ≥ 99.5%, and the GLIMPSE Archive contains all sources ≥ 5 σ above the background level.</text>
<text><location><page_3><loc_12><loc_39><loc_89><loc_47></location>The GLIMPSE pipeline was run on a deep, high-dynamic range observation of the W 3 star-forming region (AOR 5050624). This GLIMPSE Catalog (Archive) contains > 10,000 ( > 16,000 sources) shown in Table 2. These data were also reduced using the aperture photometry method ( / 3) to compare results from the two methodologies.</text>
<section_header_level_1><location><page_3><loc_38><loc_33><loc_61><loc_34></location>3. New IRAC Analysis</section_header_level_1>
<text><location><page_3><loc_12><loc_17><loc_89><loc_31></location>The MYStIX project uses a combination of IRAC data from multiple provenances, as available. In addition to the GLIMPSE data described above, new analysis is performed on archival IRAC data for remaining MYStIX targets Ð the new catalogs have photometry extracted using aperture photometry (hereafter the aperture photometry catalogs) in contrast to GLIMPSE which makes use of PRF-fitting photometry. To guarantee that the MYStIX project has uniform data quality, our analysis includes a method comparison to study the effect of any biases produced by the variation in photometric method.</text>
<text><location><page_4><loc_12><loc_63><loc_89><loc_86></location>The aperture photometry catalogs contain fainter sources than the GLIMPSE catalogs Ð which is primarily an effect of the longer observations from which the aperture photometry catalogs are derived, rather than an effect of differences in extraction method. This will improve the match rate to Chandra sources that are likely to be young stars, but a greater source density in the MIR catalogs will also increase the chance of incorrect matches (e.g. Naylor et al. 2013). Many such sources can be removed from further studies due to incongruous NIR/MIR photometry (Povich et al. 2013). In addition more extragalactic MIR sources are detected in the deeper catalogs, many of which have extragalactic X-ray counterparts. This is desirable because MIR properties (e.g. [4 . 5] > 13 mag) may help classify an X-ray source as being extragalactic (Harvey et al. 2007; Broos et al. 2013). Extragalactic IR sources without X-ray matches can be filtered out using cuts on the IR color-color diagram (Povich et al. 2013).</text>
<section_header_level_1><location><page_4><loc_41><loc_56><loc_59><loc_58></location>3.1. Observations</section_header_level_1>
<text><location><page_4><loc_12><loc_39><loc_89><loc_55></location>We obtained publicly available raw IRAC images from the Spitzer Heritage Archive 2 for nine MYStIX regions without GLIMPSE coverage. The target list and details of the Astronomical Observation Requests (AORs) are provided in Table 1. The IRAC field of view is 5 . 1 2 × 5 . 1 2, and various mapping and/or dither strategies were used for the IRAC observation programs included in this analysis. The camera spatial resolutions are FWHM = 1 . 11 6 to 1 . 11 9 from 3.6 to 8.0 µ m. Each field was observed in high dynamic range (HDR) mode where both 0.4 s and 10.4 s exposures are collected to provide unsaturated photometry for both brighter and fainter sources. Observations from different epochs are combined in our analysis.</text>
<text><location><page_4><loc_12><loc_26><loc_89><loc_37></location>We also analyzed archival data for M 17 and W 3 for comparison to the GLIMPSE data. For M 17 we analyzed images that are deeper than the Spitzer images from the GLIMPSE survey Ð useful for comparing relative sensitivities for the different catalogs. However, for W 3 we analyzed the same deep, archival Spitzer data using both the GLIMPSE and aperture photometry methods Ð useful for investigating biases of different data reduction methodologies.</text>
<section_header_level_1><location><page_5><loc_43><loc_85><loc_56><loc_86></location>3.2. Mosaics</section_header_level_1>
<text><location><page_5><loc_12><loc_65><loc_89><loc_83></location>The basic calibrated data (BCD) products were created by the Spitzer pipeline. Image reduction and mosaicking was performed via WCSmosaic IDL package (Gutermuth et al. 2008). This procedure uses algorithms developed by the IRAC instrument team to mitigate image artifacts, such as jailbar, pulldown, muxbleed, and banding (Hora et al. 2004; Pipher et al. 2004). Long and short frames were merged to create an HDR mosaic for each target, and corrections are applied including cosmic ray identification, distortion corrections in each frame, derotation and subpixel offsetting, and background matching. Sub-pixel sampling was performed using the dithered images. The pixel size of the reduced mosaics is 0 . 11 86 × 0 . 11 86, which is 1 / √ 2 the native pixel width.</text>
<text><location><page_5><loc_12><loc_36><loc_89><loc_63></location>Mosaicked images of two sample targets Ð W 40 and NGC 2264 Ð are shown in Figure 1 in 3.6 and 8.0 µ m bands. These examples demonstrate some of the variety of MYStIX regions in the MIR. For example, the stars in W 40 are centrally concentrated in the region where infrared nebulosity is highest, while the stars in NGC 2264 are divided into a number of subclusters and lie in regions with both high and low nebulosity (Feigelson et al. 2013, Kuhn et al. in preparation). Both regions have large amounts of absorption from dust Ð the dust absorption for W 40 is highest in a dust lane crossing the middle of the hour-glass structure (partially visible in the mosaics as infrared dark clouds), while the most highly absorbed stars in NGC 2264 are in subclusters that are embedded in their natal molecular cloud. The surface density of field stars also varies from region to region depending on the Galactic coordinates Ð W 40, ( l, b ) = (28 . 8 , +03 . 5), has a particularly high surface density, while the Flame Nebula, ( l, b ) = (206 . 5 , -16 . 4), has a much lower density. Several MYStIX regions, like NGC 2362, have almost no nebulosity around the star clusters because most of the molecular material has been removed.</text>
<section_header_level_1><location><page_5><loc_35><loc_30><loc_65><loc_31></location>3.3. Point-Source Photometry</section_header_level_1>
<text><location><page_5><loc_12><loc_14><loc_89><loc_28></location>The data reduction makes use of photometric procedures from Luhman et al. (2008a, 2008b, 2010), software from the Image Reduction and Analysis Facility (IRAF), codes from the IDL Astronomy Users Library (Landsman 1993), and visualization software from Broos et al. (2010). The methods are modified for the MYStIX regions, which are more distant, and have higher stellar crowding and nebulosity than the Taurus and Chamaeleon star forming regions treated by Luhman and colleagues. These modified methods have also been used by Getman et al. (2012) in their study of the IC 1396A star-forming region.</text>
<text><location><page_5><loc_16><loc_11><loc_88><loc_13></location>Source detection was performed on mosaicked images using the IRAF task STARFIND.</text>
<text><location><page_6><loc_12><loc_75><loc_89><loc_86></location>Some spurious detections appear in these initial lists, including statistically insignificant sources, IRAC image artifacts, the point-spread-function (PSF) wings of bright sources, and extended sources. The extended sources include peaks in the nebulosity, which are particularly prevalent in regions with bright, complex nebulosity, particularly in the 5.8 and 8.0 µ m bands. Several strategies are used later to filter out unreliable sources. However, sources with bad or saturated pixels and duplicate detections are removed immediately.</text>
<text><location><page_6><loc_12><loc_40><loc_89><loc_73></location>Aperture photometry was performed on mosaicked images using the IRAF task PHOT. The targets lie near the Galactic plane and are crowded by field stars, so photometry is calculated for several small aperture sizes: 2-pixel (1.7 11 ), 3-pixel (2.6 11 ), 4-pixel (3.5 11 ), and 14-pixel (12.1 11 ) radii with an adjoining background annuli 1 pixel (0.86 11 ) in width. The aperture/background sizes were chosen in accordance with the strategy of Lada et al. (2006), Luhman et al. (2008), Getman et al. (2009), and Getman et al. (2012); the latter finding no evident improvement in photometry using a ÒstandardÓ 4-pixel-wide background instead of a 1-pixel-wide background used here. The zero-point IRAC magnitudes for the 14-pixel aperture are from Reach et al. (2005): ZP = 19.670, 18.921, 16.855, and 17.394 in the 3.6, 4.5, 5.8, and 8.0 µ m bands, where M = -2 . 5 log(DN / sec) + ZP. Aperture corrections for the other apertures are 0.640 -0.016, 0.725 -0.012, 0.968 -0.030, and 0.955 -0.040 for the 2 pixel aperture; 0.384 -0.011, 0.298 -0.010, 0.474 -0.033, 0.699 -0.031, for the 3 pixel aperture; 0.175 -0.011, 0.169 -0.010, 0.144 -0.021, and 0.222 -0.025 for the 4 pixel aperture in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Aperture sizes of 2, 3, or 4 pixels were assigned to each source depending on the crowding so that the error in flux is minimized. Calculation of aperture corrections, choice of apertures, and identification of crowded sources are discussed in Appendix A.</text>
<text><location><page_6><loc_12><loc_27><loc_89><loc_38></location>A cross-correlated IRAC catalog was generated from the four bands, using a threshold of 2 11 for matching (see Appendix B). To ensure the quality of the aperture photometry catalog in Table 3, only > 5 σ detections are reported and every object must be detected in both 3.6 and 4.5 µ m bands to be included. Sources with high levels of contamination from a neighboring source ( > 100% of the source flux) are excluded. An archive of the less reliable sources detected at > 3 σ is also preserved (see Appendix C).</text>
<section_header_level_1><location><page_6><loc_38><loc_20><loc_61><loc_22></location>3.4. IRAC Source Lists</section_header_level_1>
<text><location><page_6><loc_12><loc_11><loc_89><loc_18></location>Table 3 presents the aperture photometry catalog for the nine MYStIX fields analyzed here. Columns in Table 3 include positions, IRAC band magnitudes and their uncertainties, and aperture size flags. The uncertainty incorporates the statistical uncertainty calculated by aperture photometry, added in quadrature to a ∼ 0.02 mag uncertainty in the calibration</text>
<text><location><page_7><loc_12><loc_77><loc_89><loc_86></location>of IRAC (Reach et al. 2005), and a ∼ 0.01 mag uncertainty in the aperture correction. YSO variability of ∼ 0.05 mag to ∼ 0.2 mag may contribute to photometric scatter from one observation to another (Morales-Calder«on et al. 2009). The aperture flag indicates which photometric aperture size is used and whether errors due to crowding exceed 10% of the flux in the 3.6 µ m band.</text>
<text><location><page_7><loc_12><loc_62><loc_89><loc_75></location>Table 4 summarizes the aperture photometry and GLIMPSE catalogs for each region Ð the total number of sources is given in Column 8. Variation in number of sources is strongly related to the size of the field of view (Column 3), its Galactic coordinates (Column 2), and the depth of the observation. Of the aperture photometry sources, only 25% are detected in the 5.8 µ m band and 18% are detected in the 8.0 µ m band (14% are detected in both bands). The distribution of aperture sizes is: 13% use 4 pixels, 11% use 3 pixels, and 76% use 2 pixels (43% of catalog sources have flags indicating crowding).</text>
<section_header_level_1><location><page_7><loc_38><loc_55><loc_62><loc_57></location>3.4.1. Completeness Limits</section_header_level_1>
<text><location><page_7><loc_12><loc_32><loc_89><loc_54></location>Photometric reliability and completeness are spatially variable in regions with bright, structured background. Histograms of source flux provide a rough estimate of spatial completeness due to the sharp turnover beyond the completeness limit. The histograms of IRAC magnitudes for each field are shown in Figure 2 with bin widths of 0.2 mag. The completeness limits, estimated to be the center for the bin preceding the bin with the most sources, are listed in Table 4. However, these values do not hold where there is high nebulosity. For a typical field Ð a cluster age of 2 Myr, a distance of 2 kpc, and a completeness limit of [3 . 6] c = 16 . 0 Ð disk-free members would be detectible down to ∼ 0.1 M 8 in regions with low nebulosity for the pre-main-sequence models of Siess et al. (1997). Completeness limits for IRE sources may occur at lower magnitudes due to selection effects when multiple bands and their errors are combined.</text>
<section_header_level_1><location><page_7><loc_26><loc_26><loc_74><loc_27></location>3.4.2. Photometric Quality in Comparison to GLIMPSE</section_header_level_1>
<text><location><page_7><loc_12><loc_14><loc_89><loc_24></location>It is helpful to compare the aperture photometry to the GLIMPSE photometry to examine how the various MIR challenges in MYStIX regions, such as nebulosity and crowding, affect the catalogs. For comparative purposes, aperture photometry catalogs were produced for W 3 using the same deep HDR data used by GLIMPSE, and for M 17 using a deeper observation than GLIMPSE (see Table 1).</text>
<text><location><page_7><loc_16><loc_11><loc_89><loc_13></location>The aperture photometry catalog for W 3 is sensitive to ∼ 1 magnitude deeper than</text>
<text><location><page_8><loc_12><loc_81><loc_89><loc_86></location>GLIMPSE. More than 90% of GLIMPSE W 3 sources are detected at > 5 σ by our aperture photometry method, and many of the undetected sources are the dimmer components of close double sources.</text>
<text><location><page_8><loc_12><loc_58><loc_89><loc_79></location>Figure 3 shows difference in measurements of magnitude for the two W 3 catalogs. As expected, scatter increases with magnitude: the root mean square (RMS) 3.6 µ m band residuals are 0.06 mag for bright sources ([3 . 6] < 12 mag) and 0.17 mag for dim sources ([3 . 6] > 12 mag). There is also a slight systematic shift in the 3.6 µ m band of +0 . 01 mag for bright sources and +0 . 05 mag for dim sources. Overall, the RMS residuals are 0.17 mag, 0.18 mag, 0.21 mag, and 0.22 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Furthermore, the scatter increases for smaller aperture sizes: in the 3.6 µ m band for sources with [3 . 6] < 12 mag the RMS residuals are 0.05 mag for 4 pixels, 0.06 mag for 3 pixels, 0.10 mag for 2 pixels (without high crowding or 0.14 for 2 pixels with high crowding). This is consistent with the aperture comparisons in the IC 1396A field performed by Getman et al. (2012).</text>
<text><location><page_8><loc_12><loc_33><loc_89><loc_56></location>Similar trends are seen in for M 17 (Figure 4), for which we compare aperture photometry of HDR observation of M 17 to the shallower GLIMPSE survey data. For bright sources ([3 . 6] < 12 mag) the RMS residuals are 0.14 mag, 0.13 mag, 0.22 mag, and 0.29 mag, and for dim sources ([3 . 6] > 12 mag), these are 0.22 mag, 0.23 mag, 0.33 mag, and 0.50 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. For bright sources ([3 . 6] < 12 mag) in the two M 17 catalogs, 95% of the photometry is within 0.2 mag in the 3.6 µ m band, which drops to 85% for the 8.0 µ m band. For dim sources, the consistency is ∼ 73% for the 3.6 µ m band, dropping to ∼ 68% for the 8.0 µ m band. A comparison of Figures 3 and 4 shows significantly more scatter for M 17 than for W 3; this is due to the shallowness of the M 17 GLIMPSE observation, which demonstrates, not only the benefits of the deeper HDR observations, but that the effect of net exposure duration is more important than any bias due to different photometry extraction methods in MYStIX.</text>
<text><location><page_8><loc_12><loc_20><loc_89><loc_31></location>Figure 5 shows a band-by-band comparison of signal-to-noise from the two W 3 catalogs. Sources that are in one catalog but not in the other are also indicated. As expected, the aperture photometry catalog includes somewhat more sources with low signal-to-noise (5 < S/N < 10) than in the GLIMPSE Catalog. For sources in both catalogs, the signal-to-noise values lie near y = x (for the 3.6 and 4.5 µ m bands, signal-to-noise from aperture photometry is on average 1.5 times smaller) but can vary by a factor of ∼ 2.</text>
<text><location><page_8><loc_12><loc_11><loc_89><loc_18></location>In Figure 5, the overlap between the catalogs decreases with increasing wavelength bands, with most sources in common in the 3.6 µ m band and fewest in the 8.0 µ m band. This may be an effect of marginally detectable sources in the nebulous and crowded W 3 region; detection sensitivity decreases with longer wavelength bands due to lower efficiency</text>
<text><location><page_9><loc_12><loc_81><loc_89><loc_86></location>of the detectors, less photospheric flux, and higher nebulosity. Both GLIMPSE catalogs and the aperture photometry catalogs may capture only a fraction of the sources near the sensitivity limit, but the sources that are detected are not necessarily the same sources.</text>
<text><location><page_9><loc_12><loc_74><loc_89><loc_79></location>Sources that are likely to be spurious detections of nebulosity (see / 3.5) are also indicated. Many of these are have low signal-to-noise (particularly sources not detected by GLIMPSE); however, a few have high signal-to-noise values.</text>
<section_header_level_1><location><page_9><loc_33><loc_67><loc_67><loc_69></location>3.5. Contamination by Nebulosity</section_header_level_1>
<text><location><page_9><loc_12><loc_42><loc_89><loc_66></location>The 3.6, 5.8, and 8.0 µ m bands are tuned to emission bands of polycyclic aromatic hydrocarbons (PAH; Reach et al. 2006) excited by the ultraviolet light of OB stars in the MYStIX fields. This results in extremely bright nebulosity in these bands when observing massive star-forming complexes. This nebulosity is often similar in surface brightness to young stars at the resolution of Spitzer , making it difficult to distinguish between point sources and contaminants due to confusion. Ideally, peaks in the nebulosity should be filtered out by STARFIND using the source profile, but this often fails, and this judgement is often difficult to make by eye as well. The level of nebulosity ranges from almost none in NGC 2362 to levels at which IRAC point-source photometry is impossible. In Figure 1, the 8 µ m nebular emission can be seen to be higher in W 40 than in NGC 2264. For the regions with most nebulosity, including W 40, RCW 36, and W 3, source detection sensitivity can be severely limited.</text>
<text><location><page_9><loc_12><loc_21><loc_89><loc_40></location>Nebular contamination may result in two types of spurious entries in the aperture photometry catalog: patches of nebulosity with emission in all four bands that mimic stars, and false matches between stellar sources in the 3.6 and 4.5 µ m bands and nebular patches in the 5.8 and 8.0 µ m bands. These effects are also present in GLIMPSE (Povich et al. 2013), but are more prevalent here due to both the improved identification of extended sources using GLIMPSEÕs PSF fitting and the higher sensitivity of our aperture extraction method. Selecting sources with high signal-to-noise (reported in Table 3) can produce lists of more reliable sources, since nebulous sources are likely to have background extraction with greater pixel-to-pixel variation. However, nebulous sources can occasionally have small measurement errors because these sources can be very bright.</text>
<text><location><page_9><loc_12><loc_12><loc_89><loc_19></location>Nebulosity at 5.8 or 8.0 µ m can make a source appear red, but the colors are distinct from the colors of young stellar objects. The [4.5]-[5.8] vs. [5.8]-[8.0] diagram can be used to separate these sources from stellar sources (Povich et al. 2013). In Figure 6 this diagram is shown for NGC 2264 and W 40, with sources color-coded by signal-to-noise < 10 (green)</text>
<text><location><page_10><loc_12><loc_71><loc_89><loc_86></location>and > 10 (black). This plot includes only sources with photometric data in all four bands, which is the minority of MYStIX MIR sources, and is strongly biased toward IRE sources or sources with nebulosity in the 5.8 and 8.0 µ m bands. Stars without IRE are centered near (0,0) on the diagram, while stars with IRE are shifted slightly to the upper right. However, there is another population with [4 . 5] -[8 . 0] ≥ 1 . 6 and [5 . 8] -[8 . 0] ≥ 0 . 5 that are likely due to nebulosity (Povich et al. 2013). Nearly all of these sources have S/N < 10 σ in at least one band. However, a number of low signal-to-noise sources also have colors consistent with stellar photospheres or young stellar objects.</text>
<text><location><page_10><loc_12><loc_48><loc_89><loc_69></location>Figure 7 shows the 8.0 µ m sources from the aperture photometry catalog and from the literature plotted on the 8.0 µ m image for NGC 2264 (Sung et al. 2009), NGC 2362 (Currie et al. 2009), Rosette (Balog et al. 2007), and NGC 1893 (Caramazza et al. 2008). In this comparison there are examples of detections in the aperture photometry catalog that are not in theirs and vice versa. It is difficult to determine through visual inspection of the 8 µ m images which of these are real. The X-ray sources from Kuhn et al. (2013a) are also plotted Ð most of which are young stars Ð and these show that many of the new 8 µ m sources found from aperture photometry coincide with X-ray sources. This phenomenon is particularly strong for NGC 1893, which has a long X-ray exposure but is distant, so many of the young stars are near the detection threshold in the MIR. Thus, we gain many new MIR counterparts for cluster members by using these more sensitive catalogs.</text>
<section_header_level_1><location><page_10><loc_36><loc_41><loc_63><loc_43></location>4. Classes of MIR Sources</section_header_level_1>
<text><location><page_10><loc_12><loc_18><loc_89><loc_39></location>The MYStIX MIR catalogs include young stellar members of the star-forming complex (with and without IRE), non-member point sources (field stars, extragalactic sources, shock emission), and spurious sources. MYStIX IRE Sources (MIRES; Povich et al. 2013) are identified using the MIR and NIR photometry, and a list of MYStIX Probable Complex Members (MPCM; Broos et al. 2013) is generated using X-ray selected members, IRE selected members, and spectroscopic OB stars. The distributions of these classes of sources on the MIR color-magnitude and color-color diagrams can give insight into how the MYStIX census is affected by the MIR catalog properties Ð properties such as the completeness limits, uncertainties on photometry, and spurious sources. Furthermore, these diagrams reveal global differences from region to region in terms of member populations, disk evolution, and star-formation environments.</text>
<section_header_level_1><location><page_11><loc_32><loc_85><loc_68><loc_86></location>4.1. MIR Color-Magnitude Diagram</section_header_level_1>
<text><location><page_11><loc_12><loc_63><loc_89><loc_83></location>Figure 8 shows the [3 . 6] vs. [3 . 6] -[4 . 5] diagrams for the nine regions analyzed here. The distributions of disk-free MPCMs (green circles) and MIRES sources (red circles) are plotted along with unclassified MIR sources (grey points). The A K = 2 reddening vector points to the lower right. Selection effects such as the size of the sample, the completeness limit, and larger photometric uncertainties for faint points can be seen for each region. The locus of disk-free members overlaps with the locus of field stars, and the 3.6 µ m band magnitude relates to stellar mass. In older or more distant regions, the dereddened, disk-free isochrones are shifted downwards on the plot (e.g. Roccatagliata et al. 2011, their Figure 7). The MYStIX MIR catalogs are typically deeper than the MYStIX X-ray catalogs, so X-ray selected MPCMs have a lower 3.6 µ m band magnitude completeness limit.</text>
<text><location><page_11><loc_12><loc_34><loc_89><loc_62></location>There is a population of stars that shows [3 . 6] -[4 . 5] excess on this diagram, many of which are identified as IRE sources in the MIRES catalog (red circles). However, the distribution of these sources varies from region to region. In some cases there are many sources with [3 . 6] -[4 . 5] > 1 . 5 (including NGC 2264, Rosette, and DR 21) while for other cases nearly all IRE sources have [3 . 6] -[4 . 5] < 1 . 0 (including NGC 2362, W 4, and NGC 1893). Other fields (like Flame, W 40, and RCW 36) are intermediate. NGC 2264, Rosette, and DR 21 all have young embedded clusters, while the clusters in NGC 2362, W 4, and NGC 1893 are mostly lightly absorbed. The sources with [3 . 6] -[4 . 5] > 1 . 5 are mostly clustered within the embedded clusters identified by (Kuhn et al. in preparation). The different distributions of [3 . 6] -[4 . 5] colors for different regions is primarily due to effects of IRE emission rather than reddening from dust. It would require ∼ 100 mag of absorption in the V band to cause a reddening of 1 mag in [3 . 6] -[4 . 5], and most of the cluster members in our sample do not have this much reddening (Povich et al. 2013; Broos et al. 2013). Therefore, the larger [3 . 6] -[4 . 5] excesses in some regions is likely to be an age effect of disk evolution.</text>
<section_header_level_1><location><page_11><loc_35><loc_28><loc_66><loc_30></location>4.2. MIR Color-Color Diagram</section_header_level_1>
<text><location><page_11><loc_12><loc_10><loc_89><loc_26></location>Figure 9 shows the [3.6]-[4.5] vs. [4.5]-[8.0] color-color diagram for sources in the Rosette Nebula. Here, the reddening vector is nearly vertical, and IRE from disks or envelopes appears as an excess in both colors. Sources contaminated by PAH nebulosity will have large [4.5]-[8.0] values but [3.6]-[4.5] colors near or below 0, so they can be distinguished from young stars. There are a variety of possible cuts on the color-color diagram that are designed to identify young stars, and the IRE selection polygon from Simon et al. (2007) is shown as an example that uses this color-color plot. But, the IRE sources found by Povich et al. (2013) in the MYStIX IR catalogs are a somewhat different set of sources than are</text>
<text><location><page_12><loc_12><loc_79><loc_89><loc_86></location>found using the other schemes 3 . Figure 10 shows color-color diagrams for each region with points color-coded by results of the classification done by Povich et al. (2013) and Broos et al. (2013), which includes cluster members with and without IRE in addition to various types of contaminants and spurious sources.</text>
<text><location><page_12><loc_12><loc_66><loc_89><loc_77></location>Reddened stellar photosphere fitting may quickly remove a large fraction of IR catalog sources from a list of possible IRE stars and relies on well understood field-star photospheric models. The procedures for fitting these stars using photometry in seven NIR and MIR bands are described in Povich et al. (2013). Some of the sources rejected for being insignificantly different from the reddened photospheric model (shown in black in Figure 10) would have been selected as IRE stars by the color cuts from Simon et al. (2007).</text>
<text><location><page_12><loc_12><loc_45><loc_89><loc_64></location>The color-color polygon used by Simon et al. (2007), and other color-based decision trees, have both false positives and false negatives with respect to the more elaborate analysis of the infrared spectral energy distributions by Povich et al. (2013) for the MYStIX analysis. Many of the stars lying in the polygon do not satisfy the more conservative criteria for disk-bearing young stars adopted by Povich et al. These sources may often be nebular (rather than stellar) sources in the 8.0 µ m band, as they are more common in the W 40 and DR 21 where the PAH contamination is high. The MPCM source lists also show a small population of disk-free stars (green circles in Figure 10) with MIR colors likely to arise from PAH nebulosity. These may be faulty matches between true X-ray sources and spurious MIR PAH sources.</text>
<section_header_level_1><location><page_12><loc_43><loc_38><loc_56><loc_40></location>5. Summary</section_header_level_1>
<text><location><page_12><loc_12><loc_21><loc_89><loc_36></location>This work describes the Spitzer IRAC observations and source catalogs that will be used by the MYStIX project. These data include nine regions where archival data is available, and we perform aperture photometry on the HDR observations. The MYStIX MIR catalogs will be combined with X-ray (Kuhn et al. 2013, Townsley et al. in preparation) and NIR (King et al. 2013) for a multiwavelength study of star formation in massive young starforming complexes (Feigelson et al. 2013; Naylor et al. 2013; Povich et al. 2013; Broos et al. 2013). The aperture photometry catalogs are typically deeper and have higher photometric precision than typical GLIMPSE fields or other available catalogs of the same regions.</text>
<text><location><page_13><loc_12><loc_79><loc_89><loc_86></location>In addition, the MYStIX project makes use of the GLIMPSE photometry for ten regions (including a deep catalog for W 3 presented here). Furthermore, the MYStIX study of the Orion Nebula and Carina Nebula uses stellar membership censuses from the literature, and we do not reanalyze Spitzer data for these regions.</text>
<text><location><page_13><loc_12><loc_64><loc_89><loc_77></location>There are a total of ∼ 750,000 infrared sources in the aperture photometry catalogs. Photometry is extracted using variable aperture size depending on source crowding. We use a > 5 σ detection threshold, require sources to be detected in both the shorter wavelength IRAC bands, and clean the catalog of various instrumental and data-processing effects. In the study of MYStIX X-ray sources, lower reliability ( > 3 σ ) detections will also be included (the aperture-photometry archive) because the presence of an X-ray counterpart provides corroborating evidence for a sourceÕs legitimacy.</text>
<text><location><page_13><loc_12><loc_45><loc_89><loc_62></location>We investigate a variety of possible photometric problems empirically by comparing detection rates, fluxes, and flux uncertainties for the aperture photometry catalogs to other available catalogs. A particular problem we encounter is spurious sources due to nebulosity, which affect all bands, but particularly strongly affect the 5.8 and 8.0 µ m bands. These sources are difficult to eliminate completely through signal-to-noise cuts, although they usually affect detections with 5 < S/N < 10. However, color-color diagrams can be used to separate colors associated with PAH nebulosity from IRE candidate young stars. In addition, spatial completeness limits vary across the field due to strong variation in nebulosity and crowding.</text>
<text><location><page_13><loc_12><loc_36><loc_89><loc_43></location>Finally, we present MIR color-magnitude and color-color diagrams showing the locus of MYStIX Probable Cluster Members (Broos et al. 2013) in comparison to the field stars. The nine MYStIX regions studied here show considerable differences in the distribution of IRE stars in these plots.</text>
<text><location><page_13><loc_12><loc_11><loc_89><loc_32></location>The MYStIX project is supported at Penn State by NASA grant NNX09AC74G, NSF grant AST-0908038, and the Chandra ACIS Team contract SV4-74018 (G. Garmire & L. Townsley, Principal Investigators), issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. We thank Marilyn R. Meade and Brian L. Babler for providing us with the reduced images and photometry for W 3. We thank the anonymous referee for closely reading the manuscript and providing useful comments and suggestions. This work is based on observations made with the Spitzer Space Telescope, obtained from the NASA/ IPAC Infrared Science Archive, both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. This research has also made use of SAOImage DS9 software de-</text>
<text><location><page_14><loc_12><loc_83><loc_88><loc_86></location>veloped by Smithsonian Astrophysical Observatory and NASAÕs Astrophysics Data System Bibliographic Services.</text>
<section_header_level_1><location><page_14><loc_34><loc_76><loc_66><loc_78></location>A. Photometric Aperture Sizes</section_header_level_1>
<text><location><page_14><loc_12><loc_63><loc_89><loc_75></location>Larger aperture sizes are favored for stars that are not in crowded regions because they have less Òaperture noise,Ó which is an effect of resampling the pixelated image into the aperture (Shahbaz et al. 1994). This effect can lead to several percent error in flux measurement using our two-pixel apertures, which is independent of source flux. Thus, we use simulations of artificial sources to determine the largest aperture size that will not cause inaccurate flux measurements due to crowding.</text>
<text><location><page_14><loc_12><loc_34><loc_89><loc_62></location>Using the IRAC PSF 4 , pairs of point sources were simulated with various separation angles (1 to 20 pixels), orientations, and flux differences (10 -3 to 10 3 ), and their photometry was extracted using PHOT to investigate the effect of nearby neighbors on flux measurements. This was performed using the same 2-pixel, 3-pixel, and 4-pixel apertures with 1-pixel-wide background annuluses that were used for the photometric analysis. For each separation angle and difference in difference in flux, the largest aperture (2-pixels, 3-pixels, or 4-pixels) is chosen that keeps contamination from a nearby source < 5% of the true flux; these choices are listed in Table 5 along with the associated error in flux. For sources in the Spitzer catalogs using the 2-pixel aperture, sources with flux errors larger than 10% are flagged and sources with flux errors larger than 100% of the true flux are excluded from the catalog. Getman et al. (2012, / 2.2) has shown that the use of small aperture extraction produces negligible bias in derived magnitudes, but leads to reduced photometric precision. These larger photometric uncertainties are incorporated in the aperture photometry catalogs given in the present paper.</text>
<text><location><page_14><loc_12><loc_17><loc_89><loc_33></location>Aperture corrections for the 2-pixel, 3-pixel, and 4-pixel apertures are calculated for each field with respect to magnitudes derived for the 14 pixel aperture, which is assumed to contain all the light. Corrections are found by comparing magnitudes for the 14-pixel aperture to the 4-pixel aperture, the 4-pixel aperture to the 3-pixel aperture, and the 4-pixel aperture to the 2-pixel aperture. Typically, bright sources that are not saturated and do not show signs of anomalous magnitudes in either aperture are used, and the correction is the median difference in calculated magnitudes. For IRAC channels 3 and 4, there is an artifact in the PSF of bright sources, so dimmer sources are used for the calibration.</text>
<section_header_level_1><location><page_15><loc_26><loc_85><loc_74><loc_86></location>B. Matching Sources from Different IRAC Bands</section_header_level_1>
<text><location><page_15><loc_12><loc_69><loc_89><loc_83></location>The matching algorithm is based on the Delaunay triangulation, which is a computationally efficient strategy for identifying neighboring points in a set of points (see review by de Berg et al. 2008). To match sources from two bands, the sets of source positions from the two bands are combined, the Delaunay triangulation is constructed for the union of both sets, and matches are obtained as a subset of edges in the triangulation that join points from both bands and are shorter than a threshold length. In ambiguous cases, preference is given to the smallest separation.</text>
<text><location><page_15><loc_12><loc_58><loc_89><loc_68></location>Here, we use a matching radius of 2 11 , and match sources in the 4.5, 5.8, and 8.0 µ m bands to the 3.6 µ m band sources. An astrometric correction is applied to the entire field in the 4.5, 5.8, and 8.0 µ m bands based on the median offsets relative to 3 . 6 µ m band positions, and matching is performed again with the improved positions. Right ascensions and declinations are reported for the 3.6 µ m source.</text>
<text><location><page_15><loc_12><loc_39><loc_89><loc_57></location>The PSF has a similar size for all bands, so it is uncommon for matches to be ambiguous within the IRAC aperture photometry catalogs. Ambiguous matches do commonly occur when comparing IRAC catalogs with UKIRT (King et al. 2013) or C handra (Kuhn et al. 2013, Townsley et al. in preparation) catalogs later in the MYStIX analysis. For this reason, a probabilistic approach to cross-waveband source matching is developed by Naylor et al. (2013). However, occasional intra-IRAC matching errors do arise from matches between real 3.6 and 4.5 µ m point sources to peaks in the nebulosity at 5.8 or 8.0 µ m within the 2 11 radius. These are filtered out using a conservative analysis of the near- and mid-infrared spectral energy distributions later in the MYStIX analysis (Povich et al. 2013).</text>
<section_header_level_1><location><page_15><loc_27><loc_33><loc_73><loc_34></location>C. Archive of Lower-Reliability IRAC Sources</section_header_level_1>
<text><location><page_15><loc_12><loc_11><loc_89><loc_31></location>For the matching of IR sources to X-ray sources, the MYStIX project makes use of some MIR counterparts that have less-reliable photometry, including measurements with 5 > S/N > 3 and measurements that may be contaminated by bright, neighboring sources. The extra information provided by X-ray selection allows us to take this bifurcated approach to MIR reliability criteria. When we are considering the tens-of-thousands to hundredsof-thousands of MIR sources without X-ray counterparts, rare photometric errors could produce numerous false IRE-star candidates, so the reliability criteria must be strict. In contrast, there are orders-of-magnitude fewer MIR sources with X-ray counterparts Ð which already have a good chance of being young stars by virtue of X-ray emission Ð so rare photometric errors will be less important. The same approach is taken with the GLIMPSE</text>
<text><location><page_16><loc_12><loc_81><loc_89><loc_86></location>data with respect to the highly reliable GLIMPSE Catalog and the less reliable GLIMPSE Archive. MIR photometry for MYStIX sources that used data from the GLIMPSE Archive or aperture-photometry archive is provided by Broos et al. (2013, their Table 2).</text>
<section_header_level_1><location><page_16><loc_43><loc_74><loc_58><loc_76></location>REFERENCES</section_header_level_1>
<text><location><page_16><loc_12><loc_10><loc_88><loc_73></location>Allen, L. E., Calvet, N., DÕAlessio, P., et al. 2004, ApJS, 154, 363 Balog, Z., Muzerolle, J., Rieke, G. H., et al. 2007, ApJ, 660, 1532 Benjamin, R. A., et al. 2003, PASP, 115, 953 Broos, P. B., Getman, K. V., Povich, M. S., et al. 2013, ApJS, in press Broos, P. S., Townsley, L. K., Feigelson, E. D., et al. 2010, ApJ, 714, 1582 Caramazza, M., Micela, G., Prisinzano, L., et al. 2008, A&A, 488, 211 Chandar, R., Whitmore, B. C., Calzetti, D., et al. 2011, ApJ, 727, 88 Churchwell, E., Babler, B. L., Meade, M. R., et al. 2009, PASP, 121, 213 Currie, T., Lada, C. J., Plavchan, P., et al. 2009, ApJ, 698, 1 de Berg, M., Cheong, O., van Kreveld, M. 2008, Computational Geometry: Algorithms and Applications, (3rd ed.; New York, NY: Springer) Fall, S. M., Chandar, R., & Whitmore, B. C. 2009, ApJ, 704, 453 Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10 Feigelson, E. D., Townsley, L. K., & Broos, P. S. 2013, ApJS, in press Getman, K. V., Feigelson, E. D., Luhman, K. L., et al. 2009, ApJ, 699, 1454 Getman, K. V., Feigelson, E. D., Sicilia-Aguilar, A., et al. 2012, MNRAS, 426, 2917 Gutermuth, R. A., Megeath, S. T., Myers, P. C., et al. 2009, ApJS, 184, 18 Gutermuth, R. A., Myers, P. C., Megeath, S. T., et al. 2008, ApJ, 674, 336 Hartmann, L., Megeath, S. T., Allen, L., et al. 2005, ApJ, 629, 881 Harvey, P., Mer«õn, B., Huard, T. L., et al. 2007, ApJ, 663, 1149</text>
<text><location><page_17><loc_12><loc_13><loc_88><loc_86></location>Hora, J. L., Fazio, G. G., Allen, L. E., et al. 2004, Proc. SPIE, 5487, 77 Indebetouw, R., Mathis, J. S., Babler, B. L., et al. 2005, ApJ, 619, 931 King, R. R., Naylor, T., Broos, P. S., Getman, K. V., & Feigelson, E. D. 2013, ApJS, in press Kuhn, M. A., Getman, K. V., Broos, P. B., Townsley, L. K, & Feigelson, E. D. 2013, ApJS, in press Kuhn, M. A., Getman, K. V., Feigelson, E. D., et al. 2010, ApJ, 725, 2485 Lada, C. J. & Lada, E. A. 2003, ARA&A, 41, 57 Lada, C. J., Muench, A. A., Luhman, K. L., et al. 2006, AJ, 131, 1574 Landsman, W. B. 1993, Astronomical Data Analysis Software and Systems II, 52, 246 Luhman, K. L., Allen, L. E., Allen, P. R., et al. 2008, ApJ, 675, 1375 Luhman, K. L., Allen, P. R., Espaillat, C., Hartmann, L., & Calvert, N. 2010, ApJS, 186, 111 Luhman, K. L. & Muench, A. A. 2008, ApJ, 684, 654 Majewski, S., Babler, B., Churchwell, E., et al. 2007, Spitzer Proposal, 40791 Megeath, S. T., Gutermuth, R., Muzerolle, J., et al. 2012, AJ, 144, 192 Morales-Calder«on, M., Stauffer, J. R., Rebull, L., et al. 2009, ApJ, 702, 1507 Naylor, T., Broos, P. S., & Feigelson, E. D. 2013, ApJS, submitted Pipher, J. L., McMurtry, C. W., Forrest, W. J., et al. 2004, Proc. SPIE, 5487, 234 Povich, M. S., Kuhn, M. A., Getman, K. V., et al. 2013, ApJS, in press Povich, M. S., Smith, N., Majewski, S. R., et al. 2011, ApJS, 194, 14 Reach, W. T., Megeath, S. T., Cohen, M., et al. 2005, PASP, 117, 978 Reach, W. T., Rho, J., Tappe, A., et al. 2006, AJ, 131, 1479 Robitaille, T. P., Whitney, B. A., Indebetouw, R., & Wood, K. 2007, ApJS, 169, 328</text>
<code><location><page_18><loc_12><loc_57><loc_88><loc_86></location>Robitaille, T. P., Whitney, B. A., Indebetouw, R., Wood, K., & Denzmore, P. 2006, ApJS, 167, 256 Roccatagliata, V., Bouwman, J., Henning, T., et al. 2011, ApJ, 733, 113 Shahbaz, T., Naylor, T., & Charles, P. A. 1994, MNRAS, 268, 756 Siess, L., Forestini, M., & Dougados, C. 1997, A&A, 324, 556 Simon, J. D., Bolatto, A. D., Whitney, B. A., et al. 2007, ApJ, 669, 327 Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 Stelzer, B., Preibisch, T., Alexander, F., et al. 2012, A&A, 537, A135 Sung, H., Stauffer, J. R., & Bessell, M. S. 2009, AJ, 138, 1116 Werner, M. W., Roellig, T. L., Low, F. J., et al. 2004, ApJS, 154, 1</code>
<table>
<location><page_19><loc_12><loc_15><loc_88><loc_81></location>
<caption>Table 1. IRAC Observing Log</caption>
</table>
<table>
<location><page_20><loc_12><loc_38><loc_88><loc_68></location>
<caption>Table 1ÑContinued</caption>
</table>
<text><location><page_20><loc_12><loc_28><loc_89><loc_35></location>Note. Ñ Column 1: Target name. Column 2: Astronomical Object Request number. Column 3: Spitzer program identification number. Column 4: AOR central right ascension and declination for epoch (J2000.0). Column 5: The total area of the AOR field of view. Column 6: Total integration time per pixel for long frames. Column 7: Date of the start of the observation.</text>
<table>
<location><page_21><loc_17><loc_43><loc_83><loc_57></location>
<caption>Table 2. GLIMPSE W 3 IRAC Photometry</caption>
</table>
<text><location><page_21><loc_17><loc_38><loc_84><loc_41></location>Note. Ñ Column 1: GLIMPSE source designation. Column 2: A - source is in the GLIMPSE Archive, C - source is in the GLIMPSE Catalog. Columns 3-4: Right ascension and declination for epoch (J2000.0). Columns 5-8: GLIMPSE IRAC magnitudes.</text>
<table>
<location><page_22><loc_14><loc_43><loc_86><loc_58></location>
<caption>Table 3. IRAC Aperture Photometry</caption>
</table>
<text><location><page_22><loc_14><loc_39><loc_87><loc_41></location>Note. Ñ Column 1: Target name. Column 2: Source Designation. Columns 3-4: Right ascension and declination for epoch (J2000.0). Columns 5-8: IRAC magnitudes from aperture photometry. Column 9: Aperture size in pixels used for photometric extraction. Table 3 is published in its entirety in an electronic form. A portion is shown here for guidance regarding its form and content.</text>
<table>
<location><page_23><loc_19><loc_29><loc_82><loc_77></location>
<caption>Table 4. IRAC Catalog Properties</caption>
</table>
<text><location><page_23><loc_18><loc_18><loc_82><loc_25></location>Note. Ñ Column 1: Target name. Column 2: Galactic coordinates. Column 3: Angular area of IRAC mosaic field of view. Columns 4-7: Completeness limits for catalog sources (bands [3.6], [4.5], [5.8], and [8.0], respectively). Column 8: The number of point sources in the catalog.</text>
<table>
<location><page_24><loc_13><loc_39><loc_83><loc_78></location>
<caption>Table 5. Aperture Size</caption>
</table>
<text><location><page_24><loc_13><loc_34><loc_83><loc_37></location>Note. Ñ For each pair of magnitude difference (first column) and angular separation (first row), the chosen aperture size (in pixels) and the simulated error in flux measurement for that aperture size (rounded to the nearest percentage) are given.</text>
<text><location><page_24><loc_89><loc_52><loc_91><loc_53></location>Ð</text>
<text><location><page_24><loc_89><loc_49><loc_91><loc_51></location>24</text>
<text><location><page_24><loc_89><loc_47><loc_91><loc_48></location>Ð</text>
<figure>
<location><page_25><loc_20><loc_30><loc_80><loc_76></location>
<caption>Fig. 1.Ñ IRAC mosaics. (a) 3.6 µ m band image of W 40. (b) 8.0 µ m band image of W 40. (c) 3.6 µ m band image of NGC 2264. (d) 8.0 µ m band image of NGC 2264. Both regions have structurally complex nebulosity; however, nebulosity is higher in W 40 than in NGC 2264.</caption>
</figure>
<figure>
<location><page_26><loc_14><loc_33><loc_80><loc_68></location>
<caption>Fig. 2.Ñ Histograms of 3.6 (a), 4.5 (b), 5.8 (c), and 8.0 µ m (d) band point-source magnitudes for nine MYStIX regions using a bin width of 0.2 mag. The completeness limit is assumed to be one bin brighter than the peak of the histogram.</caption>
</figure>
<figure>
<location><page_27><loc_12><loc_33><loc_94><loc_78></location>
<caption>Fig. 3.Ñ A comparison of aperture photometry to GLIMPSE photometry for W 3. Plot of magnitude residuals (aperture minus GLIMPSE) vs. magnitude using aperture and GLIMPSE catalogs produced from the HDR Spitzer observation of the W 3 region. Plots ( top to bottom ) are the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Colors indicate the aperture used: black for the 4 pixel aperture, red for the 3 pixel aperture, blue for the 2 pixel aperture with low crowding, and green for the 2 pixel aperture with high crowding.</caption>
</figure>
<figure>
<location><page_28><loc_12><loc_31><loc_94><loc_76></location>
<caption>Fig. 4.Ñ A comparison of aperture photometry to GLIMPSE photometry for M 17, similar to Figure 3. Plots ( top to bottom ) are the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Here, the M 17 GLIMPSE data comes from significantly shorter observations than the aperturephotometry data, leading to more scatter than is seen in the comparison for W 3.</caption>
</figure>
<figure>
<location><page_29><loc_15><loc_28><loc_83><loc_78></location>
<caption>Fig. 5.Ñ Signal-to-noise of the aperture photometry catalog vs. signal-to-noise in the GLIMPSE catalog for all W 3 sources present in both catalogs for each band; non-detections are set to S/N=4 on the graph. The green points are the sources flagged as possible spurious detections of nebulosity. The red line indicates equal error from both catalogs.</caption>
</figure>
<figure>
<location><page_30><loc_12><loc_39><loc_86><loc_67></location>
<caption>Fig. 6.Ñ [4.5]-[5.8] vs. [5.8]-[8.0] color-color diagrams -Left: NGC 2264, Right: W 40. Sources with S/N > 10 in all four IRAC bands are black circles and sources with S/N < 10 in at least one band are green circles. The dashed lines show the color cuts for PAH knots from Povich et al. (2013).</caption>
</figure>
<figure>
<location><page_31><loc_15><loc_17><loc_85><loc_86></location>
<caption>Fig. 8.Ñ [3.6] vs. [3.6]-[4.6] color-magnitude diagrams for MIR sources in the each region. MPCMs with no IRE are shown by green circles, MPCMs with IRE are shown by red circles, and remaining sources (field stars, unclassified members, and non-stellar sources) are shown by grey circles. The arrow indicates reddening of A K = 2 mag using the Indebetouw et al. (2005) extinction law.</caption>
</figure>
<figure>
<location><page_32><loc_27><loc_34><loc_73><loc_72></location>
<caption>Fig. 9.Ñ [3 . 6] -[4 . 5] vs. [4 . 5] -[8 . 0] color-color diagrams for MIR sources in the Rosette Nebula. The color cuts used by Simon et al. (2007) are shown with the gray lines. These cuts identify a slightly different set of IRE sources compared to Povich et al. (2013). The black arrow is the A K = 2 mag reddening vector.</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "Spitzer IRAC observations and stellar photometric catalogs are presented for the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX). MYStIX is a multiwavelength census of young stellar members of twenty nearby ( d < 4 kpc), Galactic, star-forming regions that contain at least one O star. All regions have data available from the Spitzer Space Telescope, consisting of GLIMPSE or other published catalogs for eleven regions and results of our own photometric analysis of archival data for the remaining nine regions. This paper seeks to construct deep and reliable catalogs of sources from the Spitzer images. Mid-infrared study of these regions faces challenges of crowding and high nebulosity. Our new catalogs typically contain fainter sources than existing Spitzer studies, which improves the match rate to Chandra X-ray sources that are likely to be young stars, but increases the possibility of spurious point-source detections, especially peaks in the nebulosity. IRAC color-color diagrams help distinguish spurious detections of nebular PAH emission from the infrared excess associated with dusty disks around young stars. The distributions of sources on the mid-infrared color-magnitude and color-color diagrams reflect differences between MYStIX regions, including astrophysical effects such as stellar ages and disk evolution. Subject headings: methods: data analysis - stars: pre-main-sequence - infrared: stars - planetary systems: protoplanetary disks",
"pages": [
1
]
},
{
"title": "A Massive Young Star-Forming Complex Study in Infrared and X-ray: Mid-Infrared Observations and Catalogs",
"content": "Michael A. Kuhn 1 , Matthew S. Povich 1 , 2 , Kevin L. Luhman 1 , 3 , Konstantin V. Getman 1 , Heather S. Busk 1 , Eric D. Feigelson 1 , 3",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "A significant fraction of star formation activity in the Galaxy occurs in massive starforming complexes, dominated by OB stars and containing thousands of young stars. Studies of the cluster mass function indicate that stars are more likely to be born in rich clusters than in small groups (e.g. Lada & Lada 2003; Fall et al. 2009; Chandar et al. 2011). Because of the importance of such clusters, the Massive Young Star-Forming Complex Study in the Infrared and X-ray (MYStIX) constructs a census of stars in twenty of the nearest ( d < 4 kpc), Galactic massive star-forming regions (Feigelson et al. 2013) with the Chandra X-ray Observatory , the Spitzer Space Telescope , and ground based near-infrared (NIR) observatories. Studies in the IR and X-ray provide complementary pictures of populations of new stars in star-forming regions. The infrared (IR) images identify stars with circumstellar disks or infalling envelopes through infrared excess (IRE), but cannot distinguish disk-free cluster members from field stars. Meanwhile, X-ray images can detect both disk-bearing and disk-free stars, although the sensitivity to the former is lower (Getman et al. 2009; Stelzer et al. 2011). Thus, the combination of both X-ray and IR observations provide more complete and less biased samples of complex members than either waveband alone. In this paper, we describe the observations and source catalogs used by the MYStIX project from the Infrared Array Camera (IRAC; Fazio et al. 2004) onboard the Spitzer Space Telescope (Werner et al. 2004). This instrument has four bands centered at 3.6, 4.5, 5.8, and 8.0 µ m, which are useful for identifying IRE stars (e.g. Allen et al. 2004; Hartmann et al. 2005; Robitaille et al. 2006; Gutermuth et al. 2009). We use source catalogs produced by the pipeline of the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE; Benjamin et al. 2003) for nine regions, and we measure new aperture photometry from archival IRAC data for nine regions. We adopt pre-existing IRE star catalogs for two additional regions, the Orion Nebula (Megeath et al. 2012) and the Carina Nebula (Povich et al. 2011). In addition to the data from Spitzer , the MYStIX project includes NIR data obtained by United Kingdom Infra-Red Telescope (King et al. 2013) and the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and X-ray data obtained by the Chandra X-ray Observatory (Kuhn et al. 2013a). The procedures for constructing the combined sample of X-ray selected member, IRE selected members, and spectrally selected OB members is described by Naylor et al. (2013), Povich et al. (2013), and Broos et al. (2013). We describe the available GLIMPSE data (Section 2) and our procedures for analyzing other archival images from IRAC (Section 3). We then discuss the distributions of probable members and field stars on color-magnitude and color-color diagrams (Section 4) and summarize our results (Section 5).",
"pages": [
2
]
},
{
"title": "2. GLIMPSE Data",
"content": "The GLIMPSE survey is a Legacy Science Program of NASAÕs Spitzer Space Telescope to study star formation in the disk of the Milky Way Galaxy (Benjamin et al. 2003; Churchwell et al. 2009). It contains six MYStIX regions Ð the Lagoon Nebula, the Trifid Nebula, NGC 6334, the Eagle Nebula, M 17, and NGC 6357 Ð within the 2 · -wide strip along the Galactic equator (GLIMPSE I and II data releases). Furthermore, Spitzer images and photometry for RCW 38 and NGC 3576 come from the Vela-Carina survey (Majewski et al. 2007), using a similar observing strategy with mosaicking and photometric analysis performed with GLIMPSE pipeline. For the GLIMPSE observations, every position was visited at least twice with 1.2 s integrations. The data-reduction pipeline produces image mosaics (v3.0) and point-source lists (v2.0) for all four IRAC bands, which are publicly available 1 . Photometry is obtained through point response function (PRF) fitting. A 5 σ detection limit is used, corresponding to fluxes 0.2, 0.2, 0.4, and 0.4 mJy in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively (Benjamin et al. 2003). However, the detection sensitivity is lower in nebulous regions, and bright sources or regions with high backgrounds may be saturated. The GLIMPSE Catalog contains the sources with reliability ≥ 99.5%, and the GLIMPSE Archive contains all sources ≥ 5 σ above the background level. The GLIMPSE pipeline was run on a deep, high-dynamic range observation of the W 3 star-forming region (AOR 5050624). This GLIMPSE Catalog (Archive) contains > 10,000 ( > 16,000 sources) shown in Table 2. These data were also reduced using the aperture photometry method ( / 3) to compare results from the two methodologies.",
"pages": [
3
]
},
{
"title": "3. New IRAC Analysis",
"content": "The MYStIX project uses a combination of IRAC data from multiple provenances, as available. In addition to the GLIMPSE data described above, new analysis is performed on archival IRAC data for remaining MYStIX targets Ð the new catalogs have photometry extracted using aperture photometry (hereafter the aperture photometry catalogs) in contrast to GLIMPSE which makes use of PRF-fitting photometry. To guarantee that the MYStIX project has uniform data quality, our analysis includes a method comparison to study the effect of any biases produced by the variation in photometric method. The aperture photometry catalogs contain fainter sources than the GLIMPSE catalogs Ð which is primarily an effect of the longer observations from which the aperture photometry catalogs are derived, rather than an effect of differences in extraction method. This will improve the match rate to Chandra sources that are likely to be young stars, but a greater source density in the MIR catalogs will also increase the chance of incorrect matches (e.g. Naylor et al. 2013). Many such sources can be removed from further studies due to incongruous NIR/MIR photometry (Povich et al. 2013). In addition more extragalactic MIR sources are detected in the deeper catalogs, many of which have extragalactic X-ray counterparts. This is desirable because MIR properties (e.g. [4 . 5] > 13 mag) may help classify an X-ray source as being extragalactic (Harvey et al. 2007; Broos et al. 2013). Extragalactic IR sources without X-ray matches can be filtered out using cuts on the IR color-color diagram (Povich et al. 2013).",
"pages": [
3,
4
]
},
{
"title": "3.1. Observations",
"content": "We obtained publicly available raw IRAC images from the Spitzer Heritage Archive 2 for nine MYStIX regions without GLIMPSE coverage. The target list and details of the Astronomical Observation Requests (AORs) are provided in Table 1. The IRAC field of view is 5 . 1 2 × 5 . 1 2, and various mapping and/or dither strategies were used for the IRAC observation programs included in this analysis. The camera spatial resolutions are FWHM = 1 . 11 6 to 1 . 11 9 from 3.6 to 8.0 µ m. Each field was observed in high dynamic range (HDR) mode where both 0.4 s and 10.4 s exposures are collected to provide unsaturated photometry for both brighter and fainter sources. Observations from different epochs are combined in our analysis. We also analyzed archival data for M 17 and W 3 for comparison to the GLIMPSE data. For M 17 we analyzed images that are deeper than the Spitzer images from the GLIMPSE survey Ð useful for comparing relative sensitivities for the different catalogs. However, for W 3 we analyzed the same deep, archival Spitzer data using both the GLIMPSE and aperture photometry methods Ð useful for investigating biases of different data reduction methodologies.",
"pages": [
4
]
},
{
"title": "3.2. Mosaics",
"content": "The basic calibrated data (BCD) products were created by the Spitzer pipeline. Image reduction and mosaicking was performed via WCSmosaic IDL package (Gutermuth et al. 2008). This procedure uses algorithms developed by the IRAC instrument team to mitigate image artifacts, such as jailbar, pulldown, muxbleed, and banding (Hora et al. 2004; Pipher et al. 2004). Long and short frames were merged to create an HDR mosaic for each target, and corrections are applied including cosmic ray identification, distortion corrections in each frame, derotation and subpixel offsetting, and background matching. Sub-pixel sampling was performed using the dithered images. The pixel size of the reduced mosaics is 0 . 11 86 × 0 . 11 86, which is 1 / √ 2 the native pixel width. Mosaicked images of two sample targets Ð W 40 and NGC 2264 Ð are shown in Figure 1 in 3.6 and 8.0 µ m bands. These examples demonstrate some of the variety of MYStIX regions in the MIR. For example, the stars in W 40 are centrally concentrated in the region where infrared nebulosity is highest, while the stars in NGC 2264 are divided into a number of subclusters and lie in regions with both high and low nebulosity (Feigelson et al. 2013, Kuhn et al. in preparation). Both regions have large amounts of absorption from dust Ð the dust absorption for W 40 is highest in a dust lane crossing the middle of the hour-glass structure (partially visible in the mosaics as infrared dark clouds), while the most highly absorbed stars in NGC 2264 are in subclusters that are embedded in their natal molecular cloud. The surface density of field stars also varies from region to region depending on the Galactic coordinates Ð W 40, ( l, b ) = (28 . 8 , +03 . 5), has a particularly high surface density, while the Flame Nebula, ( l, b ) = (206 . 5 , -16 . 4), has a much lower density. Several MYStIX regions, like NGC 2362, have almost no nebulosity around the star clusters because most of the molecular material has been removed.",
"pages": [
5
]
},
{
"title": "3.3. Point-Source Photometry",
"content": "The data reduction makes use of photometric procedures from Luhman et al. (2008a, 2008b, 2010), software from the Image Reduction and Analysis Facility (IRAF), codes from the IDL Astronomy Users Library (Landsman 1993), and visualization software from Broos et al. (2010). The methods are modified for the MYStIX regions, which are more distant, and have higher stellar crowding and nebulosity than the Taurus and Chamaeleon star forming regions treated by Luhman and colleagues. These modified methods have also been used by Getman et al. (2012) in their study of the IC 1396A star-forming region. Source detection was performed on mosaicked images using the IRAF task STARFIND. Some spurious detections appear in these initial lists, including statistically insignificant sources, IRAC image artifacts, the point-spread-function (PSF) wings of bright sources, and extended sources. The extended sources include peaks in the nebulosity, which are particularly prevalent in regions with bright, complex nebulosity, particularly in the 5.8 and 8.0 µ m bands. Several strategies are used later to filter out unreliable sources. However, sources with bad or saturated pixels and duplicate detections are removed immediately. Aperture photometry was performed on mosaicked images using the IRAF task PHOT. The targets lie near the Galactic plane and are crowded by field stars, so photometry is calculated for several small aperture sizes: 2-pixel (1.7 11 ), 3-pixel (2.6 11 ), 4-pixel (3.5 11 ), and 14-pixel (12.1 11 ) radii with an adjoining background annuli 1 pixel (0.86 11 ) in width. The aperture/background sizes were chosen in accordance with the strategy of Lada et al. (2006), Luhman et al. (2008), Getman et al. (2009), and Getman et al. (2012); the latter finding no evident improvement in photometry using a ÒstandardÓ 4-pixel-wide background instead of a 1-pixel-wide background used here. The zero-point IRAC magnitudes for the 14-pixel aperture are from Reach et al. (2005): ZP = 19.670, 18.921, 16.855, and 17.394 in the 3.6, 4.5, 5.8, and 8.0 µ m bands, where M = -2 . 5 log(DN / sec) + ZP. Aperture corrections for the other apertures are 0.640 -0.016, 0.725 -0.012, 0.968 -0.030, and 0.955 -0.040 for the 2 pixel aperture; 0.384 -0.011, 0.298 -0.010, 0.474 -0.033, 0.699 -0.031, for the 3 pixel aperture; 0.175 -0.011, 0.169 -0.010, 0.144 -0.021, and 0.222 -0.025 for the 4 pixel aperture in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Aperture sizes of 2, 3, or 4 pixels were assigned to each source depending on the crowding so that the error in flux is minimized. Calculation of aperture corrections, choice of apertures, and identification of crowded sources are discussed in Appendix A. A cross-correlated IRAC catalog was generated from the four bands, using a threshold of 2 11 for matching (see Appendix B). To ensure the quality of the aperture photometry catalog in Table 3, only > 5 σ detections are reported and every object must be detected in both 3.6 and 4.5 µ m bands to be included. Sources with high levels of contamination from a neighboring source ( > 100% of the source flux) are excluded. An archive of the less reliable sources detected at > 3 σ is also preserved (see Appendix C).",
"pages": [
5,
6
]
},
{
"title": "3.4. IRAC Source Lists",
"content": "Table 3 presents the aperture photometry catalog for the nine MYStIX fields analyzed here. Columns in Table 3 include positions, IRAC band magnitudes and their uncertainties, and aperture size flags. The uncertainty incorporates the statistical uncertainty calculated by aperture photometry, added in quadrature to a ∼ 0.02 mag uncertainty in the calibration of IRAC (Reach et al. 2005), and a ∼ 0.01 mag uncertainty in the aperture correction. YSO variability of ∼ 0.05 mag to ∼ 0.2 mag may contribute to photometric scatter from one observation to another (Morales-Calder«on et al. 2009). The aperture flag indicates which photometric aperture size is used and whether errors due to crowding exceed 10% of the flux in the 3.6 µ m band. Table 4 summarizes the aperture photometry and GLIMPSE catalogs for each region Ð the total number of sources is given in Column 8. Variation in number of sources is strongly related to the size of the field of view (Column 3), its Galactic coordinates (Column 2), and the depth of the observation. Of the aperture photometry sources, only 25% are detected in the 5.8 µ m band and 18% are detected in the 8.0 µ m band (14% are detected in both bands). The distribution of aperture sizes is: 13% use 4 pixels, 11% use 3 pixels, and 76% use 2 pixels (43% of catalog sources have flags indicating crowding).",
"pages": [
6,
7
]
},
{
"title": "3.4.1. Completeness Limits",
"content": "Photometric reliability and completeness are spatially variable in regions with bright, structured background. Histograms of source flux provide a rough estimate of spatial completeness due to the sharp turnover beyond the completeness limit. The histograms of IRAC magnitudes for each field are shown in Figure 2 with bin widths of 0.2 mag. The completeness limits, estimated to be the center for the bin preceding the bin with the most sources, are listed in Table 4. However, these values do not hold where there is high nebulosity. For a typical field Ð a cluster age of 2 Myr, a distance of 2 kpc, and a completeness limit of [3 . 6] c = 16 . 0 Ð disk-free members would be detectible down to ∼ 0.1 M 8 in regions with low nebulosity for the pre-main-sequence models of Siess et al. (1997). Completeness limits for IRE sources may occur at lower magnitudes due to selection effects when multiple bands and their errors are combined.",
"pages": [
7
]
},
{
"title": "3.4.2. Photometric Quality in Comparison to GLIMPSE",
"content": "It is helpful to compare the aperture photometry to the GLIMPSE photometry to examine how the various MIR challenges in MYStIX regions, such as nebulosity and crowding, affect the catalogs. For comparative purposes, aperture photometry catalogs were produced for W 3 using the same deep HDR data used by GLIMPSE, and for M 17 using a deeper observation than GLIMPSE (see Table 1). The aperture photometry catalog for W 3 is sensitive to ∼ 1 magnitude deeper than GLIMPSE. More than 90% of GLIMPSE W 3 sources are detected at > 5 σ by our aperture photometry method, and many of the undetected sources are the dimmer components of close double sources. Figure 3 shows difference in measurements of magnitude for the two W 3 catalogs. As expected, scatter increases with magnitude: the root mean square (RMS) 3.6 µ m band residuals are 0.06 mag for bright sources ([3 . 6] < 12 mag) and 0.17 mag for dim sources ([3 . 6] > 12 mag). There is also a slight systematic shift in the 3.6 µ m band of +0 . 01 mag for bright sources and +0 . 05 mag for dim sources. Overall, the RMS residuals are 0.17 mag, 0.18 mag, 0.21 mag, and 0.22 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. Furthermore, the scatter increases for smaller aperture sizes: in the 3.6 µ m band for sources with [3 . 6] < 12 mag the RMS residuals are 0.05 mag for 4 pixels, 0.06 mag for 3 pixels, 0.10 mag for 2 pixels (without high crowding or 0.14 for 2 pixels with high crowding). This is consistent with the aperture comparisons in the IC 1396A field performed by Getman et al. (2012). Similar trends are seen in for M 17 (Figure 4), for which we compare aperture photometry of HDR observation of M 17 to the shallower GLIMPSE survey data. For bright sources ([3 . 6] < 12 mag) the RMS residuals are 0.14 mag, 0.13 mag, 0.22 mag, and 0.29 mag, and for dim sources ([3 . 6] > 12 mag), these are 0.22 mag, 0.23 mag, 0.33 mag, and 0.50 mag in the 3.6, 4.5, 5.8, and 8.0 µ m bands, respectively. For bright sources ([3 . 6] < 12 mag) in the two M 17 catalogs, 95% of the photometry is within 0.2 mag in the 3.6 µ m band, which drops to 85% for the 8.0 µ m band. For dim sources, the consistency is ∼ 73% for the 3.6 µ m band, dropping to ∼ 68% for the 8.0 µ m band. A comparison of Figures 3 and 4 shows significantly more scatter for M 17 than for W 3; this is due to the shallowness of the M 17 GLIMPSE observation, which demonstrates, not only the benefits of the deeper HDR observations, but that the effect of net exposure duration is more important than any bias due to different photometry extraction methods in MYStIX. Figure 5 shows a band-by-band comparison of signal-to-noise from the two W 3 catalogs. Sources that are in one catalog but not in the other are also indicated. As expected, the aperture photometry catalog includes somewhat more sources with low signal-to-noise (5 < S/N < 10) than in the GLIMPSE Catalog. For sources in both catalogs, the signal-to-noise values lie near y = x (for the 3.6 and 4.5 µ m bands, signal-to-noise from aperture photometry is on average 1.5 times smaller) but can vary by a factor of ∼ 2. In Figure 5, the overlap between the catalogs decreases with increasing wavelength bands, with most sources in common in the 3.6 µ m band and fewest in the 8.0 µ m band. This may be an effect of marginally detectable sources in the nebulous and crowded W 3 region; detection sensitivity decreases with longer wavelength bands due to lower efficiency of the detectors, less photospheric flux, and higher nebulosity. Both GLIMPSE catalogs and the aperture photometry catalogs may capture only a fraction of the sources near the sensitivity limit, but the sources that are detected are not necessarily the same sources. Sources that are likely to be spurious detections of nebulosity (see / 3.5) are also indicated. Many of these are have low signal-to-noise (particularly sources not detected by GLIMPSE); however, a few have high signal-to-noise values.",
"pages": [
7,
8,
9
]
},
{
"title": "3.5. Contamination by Nebulosity",
"content": "The 3.6, 5.8, and 8.0 µ m bands are tuned to emission bands of polycyclic aromatic hydrocarbons (PAH; Reach et al. 2006) excited by the ultraviolet light of OB stars in the MYStIX fields. This results in extremely bright nebulosity in these bands when observing massive star-forming complexes. This nebulosity is often similar in surface brightness to young stars at the resolution of Spitzer , making it difficult to distinguish between point sources and contaminants due to confusion. Ideally, peaks in the nebulosity should be filtered out by STARFIND using the source profile, but this often fails, and this judgement is often difficult to make by eye as well. The level of nebulosity ranges from almost none in NGC 2362 to levels at which IRAC point-source photometry is impossible. In Figure 1, the 8 µ m nebular emission can be seen to be higher in W 40 than in NGC 2264. For the regions with most nebulosity, including W 40, RCW 36, and W 3, source detection sensitivity can be severely limited. Nebular contamination may result in two types of spurious entries in the aperture photometry catalog: patches of nebulosity with emission in all four bands that mimic stars, and false matches between stellar sources in the 3.6 and 4.5 µ m bands and nebular patches in the 5.8 and 8.0 µ m bands. These effects are also present in GLIMPSE (Povich et al. 2013), but are more prevalent here due to both the improved identification of extended sources using GLIMPSEÕs PSF fitting and the higher sensitivity of our aperture extraction method. Selecting sources with high signal-to-noise (reported in Table 3) can produce lists of more reliable sources, since nebulous sources are likely to have background extraction with greater pixel-to-pixel variation. However, nebulous sources can occasionally have small measurement errors because these sources can be very bright. Nebulosity at 5.8 or 8.0 µ m can make a source appear red, but the colors are distinct from the colors of young stellar objects. The [4.5]-[5.8] vs. [5.8]-[8.0] diagram can be used to separate these sources from stellar sources (Povich et al. 2013). In Figure 6 this diagram is shown for NGC 2264 and W 40, with sources color-coded by signal-to-noise < 10 (green) and > 10 (black). This plot includes only sources with photometric data in all four bands, which is the minority of MYStIX MIR sources, and is strongly biased toward IRE sources or sources with nebulosity in the 5.8 and 8.0 µ m bands. Stars without IRE are centered near (0,0) on the diagram, while stars with IRE are shifted slightly to the upper right. However, there is another population with [4 . 5] -[8 . 0] ≥ 1 . 6 and [5 . 8] -[8 . 0] ≥ 0 . 5 that are likely due to nebulosity (Povich et al. 2013). Nearly all of these sources have S/N < 10 σ in at least one band. However, a number of low signal-to-noise sources also have colors consistent with stellar photospheres or young stellar objects. Figure 7 shows the 8.0 µ m sources from the aperture photometry catalog and from the literature plotted on the 8.0 µ m image for NGC 2264 (Sung et al. 2009), NGC 2362 (Currie et al. 2009), Rosette (Balog et al. 2007), and NGC 1893 (Caramazza et al. 2008). In this comparison there are examples of detections in the aperture photometry catalog that are not in theirs and vice versa. It is difficult to determine through visual inspection of the 8 µ m images which of these are real. The X-ray sources from Kuhn et al. (2013a) are also plotted Ð most of which are young stars Ð and these show that many of the new 8 µ m sources found from aperture photometry coincide with X-ray sources. This phenomenon is particularly strong for NGC 1893, which has a long X-ray exposure but is distant, so many of the young stars are near the detection threshold in the MIR. Thus, we gain many new MIR counterparts for cluster members by using these more sensitive catalogs.",
"pages": [
9,
10
]
},
{
"title": "4. Classes of MIR Sources",
"content": "The MYStIX MIR catalogs include young stellar members of the star-forming complex (with and without IRE), non-member point sources (field stars, extragalactic sources, shock emission), and spurious sources. MYStIX IRE Sources (MIRES; Povich et al. 2013) are identified using the MIR and NIR photometry, and a list of MYStIX Probable Complex Members (MPCM; Broos et al. 2013) is generated using X-ray selected members, IRE selected members, and spectroscopic OB stars. The distributions of these classes of sources on the MIR color-magnitude and color-color diagrams can give insight into how the MYStIX census is affected by the MIR catalog properties Ð properties such as the completeness limits, uncertainties on photometry, and spurious sources. Furthermore, these diagrams reveal global differences from region to region in terms of member populations, disk evolution, and star-formation environments.",
"pages": [
10
]
},
{
"title": "4.1. MIR Color-Magnitude Diagram",
"content": "Figure 8 shows the [3 . 6] vs. [3 . 6] -[4 . 5] diagrams for the nine regions analyzed here. The distributions of disk-free MPCMs (green circles) and MIRES sources (red circles) are plotted along with unclassified MIR sources (grey points). The A K = 2 reddening vector points to the lower right. Selection effects such as the size of the sample, the completeness limit, and larger photometric uncertainties for faint points can be seen for each region. The locus of disk-free members overlaps with the locus of field stars, and the 3.6 µ m band magnitude relates to stellar mass. In older or more distant regions, the dereddened, disk-free isochrones are shifted downwards on the plot (e.g. Roccatagliata et al. 2011, their Figure 7). The MYStIX MIR catalogs are typically deeper than the MYStIX X-ray catalogs, so X-ray selected MPCMs have a lower 3.6 µ m band magnitude completeness limit. There is a population of stars that shows [3 . 6] -[4 . 5] excess on this diagram, many of which are identified as IRE sources in the MIRES catalog (red circles). However, the distribution of these sources varies from region to region. In some cases there are many sources with [3 . 6] -[4 . 5] > 1 . 5 (including NGC 2264, Rosette, and DR 21) while for other cases nearly all IRE sources have [3 . 6] -[4 . 5] < 1 . 0 (including NGC 2362, W 4, and NGC 1893). Other fields (like Flame, W 40, and RCW 36) are intermediate. NGC 2264, Rosette, and DR 21 all have young embedded clusters, while the clusters in NGC 2362, W 4, and NGC 1893 are mostly lightly absorbed. The sources with [3 . 6] -[4 . 5] > 1 . 5 are mostly clustered within the embedded clusters identified by (Kuhn et al. in preparation). The different distributions of [3 . 6] -[4 . 5] colors for different regions is primarily due to effects of IRE emission rather than reddening from dust. It would require ∼ 100 mag of absorption in the V band to cause a reddening of 1 mag in [3 . 6] -[4 . 5], and most of the cluster members in our sample do not have this much reddening (Povich et al. 2013; Broos et al. 2013). Therefore, the larger [3 . 6] -[4 . 5] excesses in some regions is likely to be an age effect of disk evolution.",
"pages": [
11
]
},
{
"title": "4.2. MIR Color-Color Diagram",
"content": "Figure 9 shows the [3.6]-[4.5] vs. [4.5]-[8.0] color-color diagram for sources in the Rosette Nebula. Here, the reddening vector is nearly vertical, and IRE from disks or envelopes appears as an excess in both colors. Sources contaminated by PAH nebulosity will have large [4.5]-[8.0] values but [3.6]-[4.5] colors near or below 0, so they can be distinguished from young stars. There are a variety of possible cuts on the color-color diagram that are designed to identify young stars, and the IRE selection polygon from Simon et al. (2007) is shown as an example that uses this color-color plot. But, the IRE sources found by Povich et al. (2013) in the MYStIX IR catalogs are a somewhat different set of sources than are found using the other schemes 3 . Figure 10 shows color-color diagrams for each region with points color-coded by results of the classification done by Povich et al. (2013) and Broos et al. (2013), which includes cluster members with and without IRE in addition to various types of contaminants and spurious sources. Reddened stellar photosphere fitting may quickly remove a large fraction of IR catalog sources from a list of possible IRE stars and relies on well understood field-star photospheric models. The procedures for fitting these stars using photometry in seven NIR and MIR bands are described in Povich et al. (2013). Some of the sources rejected for being insignificantly different from the reddened photospheric model (shown in black in Figure 10) would have been selected as IRE stars by the color cuts from Simon et al. (2007). The color-color polygon used by Simon et al. (2007), and other color-based decision trees, have both false positives and false negatives with respect to the more elaborate analysis of the infrared spectral energy distributions by Povich et al. (2013) for the MYStIX analysis. Many of the stars lying in the polygon do not satisfy the more conservative criteria for disk-bearing young stars adopted by Povich et al. These sources may often be nebular (rather than stellar) sources in the 8.0 µ m band, as they are more common in the W 40 and DR 21 where the PAH contamination is high. The MPCM source lists also show a small population of disk-free stars (green circles in Figure 10) with MIR colors likely to arise from PAH nebulosity. These may be faulty matches between true X-ray sources and spurious MIR PAH sources.",
"pages": [
11,
12
]
},
{
"title": "5. Summary",
"content": "This work describes the Spitzer IRAC observations and source catalogs that will be used by the MYStIX project. These data include nine regions where archival data is available, and we perform aperture photometry on the HDR observations. The MYStIX MIR catalogs will be combined with X-ray (Kuhn et al. 2013, Townsley et al. in preparation) and NIR (King et al. 2013) for a multiwavelength study of star formation in massive young starforming complexes (Feigelson et al. 2013; Naylor et al. 2013; Povich et al. 2013; Broos et al. 2013). The aperture photometry catalogs are typically deeper and have higher photometric precision than typical GLIMPSE fields or other available catalogs of the same regions. In addition, the MYStIX project makes use of the GLIMPSE photometry for ten regions (including a deep catalog for W 3 presented here). Furthermore, the MYStIX study of the Orion Nebula and Carina Nebula uses stellar membership censuses from the literature, and we do not reanalyze Spitzer data for these regions. There are a total of ∼ 750,000 infrared sources in the aperture photometry catalogs. Photometry is extracted using variable aperture size depending on source crowding. We use a > 5 σ detection threshold, require sources to be detected in both the shorter wavelength IRAC bands, and clean the catalog of various instrumental and data-processing effects. In the study of MYStIX X-ray sources, lower reliability ( > 3 σ ) detections will also be included (the aperture-photometry archive) because the presence of an X-ray counterpart provides corroborating evidence for a sourceÕs legitimacy. We investigate a variety of possible photometric problems empirically by comparing detection rates, fluxes, and flux uncertainties for the aperture photometry catalogs to other available catalogs. A particular problem we encounter is spurious sources due to nebulosity, which affect all bands, but particularly strongly affect the 5.8 and 8.0 µ m bands. These sources are difficult to eliminate completely through signal-to-noise cuts, although they usually affect detections with 5 < S/N < 10. However, color-color diagrams can be used to separate colors associated with PAH nebulosity from IRE candidate young stars. In addition, spatial completeness limits vary across the field due to strong variation in nebulosity and crowding. Finally, we present MIR color-magnitude and color-color diagrams showing the locus of MYStIX Probable Cluster Members (Broos et al. 2013) in comparison to the field stars. The nine MYStIX regions studied here show considerable differences in the distribution of IRE stars in these plots. The MYStIX project is supported at Penn State by NASA grant NNX09AC74G, NSF grant AST-0908038, and the Chandra ACIS Team contract SV4-74018 (G. Garmire & L. Townsley, Principal Investigators), issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. We thank Marilyn R. Meade and Brian L. Babler for providing us with the reduced images and photometry for W 3. We thank the anonymous referee for closely reading the manuscript and providing useful comments and suggestions. This work is based on observations made with the Spitzer Space Telescope, obtained from the NASA/ IPAC Infrared Science Archive, both of which are operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. This research has also made use of SAOImage DS9 software de- veloped by Smithsonian Astrophysical Observatory and NASAÕs Astrophysics Data System Bibliographic Services.",
"pages": [
12,
13,
14
]
},
{
"title": "A. Photometric Aperture Sizes",
"content": "Larger aperture sizes are favored for stars that are not in crowded regions because they have less Òaperture noise,Ó which is an effect of resampling the pixelated image into the aperture (Shahbaz et al. 1994). This effect can lead to several percent error in flux measurement using our two-pixel apertures, which is independent of source flux. Thus, we use simulations of artificial sources to determine the largest aperture size that will not cause inaccurate flux measurements due to crowding. Using the IRAC PSF 4 , pairs of point sources were simulated with various separation angles (1 to 20 pixels), orientations, and flux differences (10 -3 to 10 3 ), and their photometry was extracted using PHOT to investigate the effect of nearby neighbors on flux measurements. This was performed using the same 2-pixel, 3-pixel, and 4-pixel apertures with 1-pixel-wide background annuluses that were used for the photometric analysis. For each separation angle and difference in difference in flux, the largest aperture (2-pixels, 3-pixels, or 4-pixels) is chosen that keeps contamination from a nearby source < 5% of the true flux; these choices are listed in Table 5 along with the associated error in flux. For sources in the Spitzer catalogs using the 2-pixel aperture, sources with flux errors larger than 10% are flagged and sources with flux errors larger than 100% of the true flux are excluded from the catalog. Getman et al. (2012, / 2.2) has shown that the use of small aperture extraction produces negligible bias in derived magnitudes, but leads to reduced photometric precision. These larger photometric uncertainties are incorporated in the aperture photometry catalogs given in the present paper. Aperture corrections for the 2-pixel, 3-pixel, and 4-pixel apertures are calculated for each field with respect to magnitudes derived for the 14 pixel aperture, which is assumed to contain all the light. Corrections are found by comparing magnitudes for the 14-pixel aperture to the 4-pixel aperture, the 4-pixel aperture to the 3-pixel aperture, and the 4-pixel aperture to the 2-pixel aperture. Typically, bright sources that are not saturated and do not show signs of anomalous magnitudes in either aperture are used, and the correction is the median difference in calculated magnitudes. For IRAC channels 3 and 4, there is an artifact in the PSF of bright sources, so dimmer sources are used for the calibration.",
"pages": [
14
]
},
{
"title": "B. Matching Sources from Different IRAC Bands",
"content": "The matching algorithm is based on the Delaunay triangulation, which is a computationally efficient strategy for identifying neighboring points in a set of points (see review by de Berg et al. 2008). To match sources from two bands, the sets of source positions from the two bands are combined, the Delaunay triangulation is constructed for the union of both sets, and matches are obtained as a subset of edges in the triangulation that join points from both bands and are shorter than a threshold length. In ambiguous cases, preference is given to the smallest separation. Here, we use a matching radius of 2 11 , and match sources in the 4.5, 5.8, and 8.0 µ m bands to the 3.6 µ m band sources. An astrometric correction is applied to the entire field in the 4.5, 5.8, and 8.0 µ m bands based on the median offsets relative to 3 . 6 µ m band positions, and matching is performed again with the improved positions. Right ascensions and declinations are reported for the 3.6 µ m source. The PSF has a similar size for all bands, so it is uncommon for matches to be ambiguous within the IRAC aperture photometry catalogs. Ambiguous matches do commonly occur when comparing IRAC catalogs with UKIRT (King et al. 2013) or C handra (Kuhn et al. 2013, Townsley et al. in preparation) catalogs later in the MYStIX analysis. For this reason, a probabilistic approach to cross-waveband source matching is developed by Naylor et al. (2013). However, occasional intra-IRAC matching errors do arise from matches between real 3.6 and 4.5 µ m point sources to peaks in the nebulosity at 5.8 or 8.0 µ m within the 2 11 radius. These are filtered out using a conservative analysis of the near- and mid-infrared spectral energy distributions later in the MYStIX analysis (Povich et al. 2013).",
"pages": [
15
]
},
{
"title": "C. Archive of Lower-Reliability IRAC Sources",
"content": "For the matching of IR sources to X-ray sources, the MYStIX project makes use of some MIR counterparts that have less-reliable photometry, including measurements with 5 > S/N > 3 and measurements that may be contaminated by bright, neighboring sources. The extra information provided by X-ray selection allows us to take this bifurcated approach to MIR reliability criteria. When we are considering the tens-of-thousands to hundredsof-thousands of MIR sources without X-ray counterparts, rare photometric errors could produce numerous false IRE-star candidates, so the reliability criteria must be strict. In contrast, there are orders-of-magnitude fewer MIR sources with X-ray counterparts Ð which already have a good chance of being young stars by virtue of X-ray emission Ð so rare photometric errors will be less important. The same approach is taken with the GLIMPSE data with respect to the highly reliable GLIMPSE Catalog and the less reliable GLIMPSE Archive. MIR photometry for MYStIX sources that used data from the GLIMPSE Archive or aperture-photometry archive is provided by Broos et al. (2013, their Table 2).",
"pages": [
15,
16
]
},
{
"title": "REFERENCES",
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"pages": [
16,
17,
20,
21,
22,
23,
24
]
}
]
2013AsBio..13.1030K
https://arxiv.org/pdf/1212.4710.pdf
<document>
<section_header_level_1><location><page_1><loc_15><loc_83><loc_86><loc_91></location>XUV exposed, non-hydrostatic hydrogen-rich upper atmospheres of terrestrial planets II: Hydrogen coronae and ion escape</section_header_level_1>
<text><location><page_1><loc_16><loc_74><loc_85><loc_82></location>Kristina G. Kislyakova 1,2 , Helmut Lammer 1 , Mats Holmström 3 , Mykhaylo Panchenko 1 , Petra Odert 1,2 , Nikolai V. Erkaev 4 , Martin Leitzinger 2 , Maxim L. Khodachenko 1 , Yuri N. Kulikov 5 , Manuel Güdel 6 , Arnold Hanslmeier 2</text>
<text><location><page_1><loc_27><loc_72><loc_28><loc_73></location>1</text>
<text><location><page_1><loc_28><loc_71><loc_73><loc_73></location>Austrian Academy of Sciences, Space Research Institute,</text>
<text><location><page_1><loc_15><loc_47><loc_86><loc_71></location>Schmiedlstr. 6, A-8042 Graz, Austria ([email protected], [email protected], [email protected], [email protected], [email protected]) 2 Institute for Physics, University of Graz, Universitätsplatz 5, A-8010 Graz, Austria ([email protected], [email protected]) 3 Swedish Institute of Space Physics, P.O. Box 812, SE-98128 Kiruna, Sweden ([email protected]) 4 Institute of Computational Modelling, Siberian Division of Russian Academy of Sciences, Akademgorodok 28/44 660036 Krasnoyarsk, Russian Federation ([email protected]) 5 Polar Geophysical Institute (PGI), Russian Academy of Sciences, Khalturina Str. 15, Murmansk, 183010, Russian Federation ([email protected]) 6 Institute for Astrophysics, University of Vienna, Türkenschanzstr. 17, 1180, Austria</text>
<text><location><page_1><loc_38><loc_45><loc_62><loc_47></location>([email protected])</text>
<text><location><page_1><loc_15><loc_21><loc_47><loc_33></location>Corresponding Authors: Kristina G. Kislyakova E-mail: [email protected] Austrian Academy of Sciences Space Research Institute Schmiedlstr. 6, A-8042 Graz Austria</text>
<text><location><page_1><loc_37><loc_12><loc_63><loc_14></location>Submitted to ASTROBIOLOGY</text>
<section_header_level_1><location><page_2><loc_45><loc_89><loc_56><loc_91></location>ABSTRACT</section_header_level_1>
<text><location><page_2><loc_15><loc_31><loc_86><loc_88></location>We study the interactions between the stellar wind plasma flow of a typical M star, such as GJ 436, and hydrogen-rich upper atmospheres of an Earth-like planet and a 'superEarth' with the radius of 2 R Earth and a mass of 10 M Earth, located within the habitable zone at ~0.24 AU. We investigate the formation of extended atomic hydrogen coronae under the influences of the stellar XUV flux (soft X-rays and EUV), stellar wind density and velocity, shape of a planetary obstacle (e.g., magnetosphere, ionopause), and the loss of planetary pick-up ions on the evolution of hydrogen-dominated upper atmospheres. Stellar XUV fluxes which are 1, 10, 50 and 100 times higher compared to that of the present-day Sun are considered and the formation of high-energy neutral hydrogen clouds around the planets due to the charge-exchange reaction under various stellar conditions have been modeled. Charge-exchange between stellar wind protons with planetary hydrogen atoms, and photoionization, leads to the production of initially cold ions of planetary origin. We found that the ion production rates for the studied planets can vary over a wide range, from ~ 25 10 0 . 1 s -1 to ~ 30 10 3 . 5 s -1 , depending on the stellar wind conditions and the assumed XUV exposure of the upper atmosphere. Our findings indicate that most likely the majority of these planetary ions are picked up by the stellar wind and lost from the planet. Finally, we estimate the long-time non-thermal ion pick-up escape for the studied planets and compare them with the thermal escape. According to our estimates, non-thermal escape of picked up ionized hydrogen atoms over a planet's lifetime varies between ~0.4 Earth ocean equivalent amounts of hydrogen (EOH) to < 3 EOH and usually is several times smaller in comparison to the thermal atmospheric escape rates.</text>
<text><location><page_2><loc_15><loc_24><loc_86><loc_28></location>Keywords: stellar activity, low mass stars, early atmospheres, Earth-like exoplanets, ENAs, ion escape, habitability</text>
<section_header_level_1><location><page_2><loc_42><loc_18><loc_61><loc_20></location>1. INTRODUCTION</section_header_level_1>
<text><location><page_2><loc_15><loc_11><loc_86><loc_17></location>Recent discoveries of so-called low density 'super-Earths' by various ground- and spacebased exoplanet-transit surveys indicate large populations of volatile-rich big rocky planets. Findings from ESOs High Accuracy Radial velocity Planetary Search project</text>
<text><location><page_3><loc_15><loc_60><loc_86><loc_91></location>(HARPS), and from NASAs Kepler space observatory, revealed that planets which are slightly larger and more massive compared to the Earth may be very common in the Universe. From the available statistics and the discovery of Kepler-22b, a 'super-Earth' with the size of about 2.38 ± 0.13REarth within the habitable zone (HZ) of a Sun-type star, one can expect that planets orbiting within the HZ should be frequent in the Universe and should also orbit cooler, lower mass M dwarfs. Approximately 100 of them are found in the immediate neighborhood of the Sun (Scalo et al. 2007; Bonfils et al. 2011). These earlier estimations are now supported by a recent study by Dressing and Charbonneau (2013), which used optical and near-infrared photometry from the Kepler Input Catalog to estimate the occurrence rate of Earth-like planets orbiting dwarf stars. The estimation of Dressing and Charbonneau (2013), from the 248 early M dwarfs within 10 parsecs of the Sun, shows that there should be at least 9 Earth-size planets in their habitable zones.</text>
<text><location><page_3><loc_15><loc_32><loc_86><loc_60></location>Moreover, from the radius-mass relation and the resulting density of discovered 'super-Earths', one finds that these bodies probably have rocky cores but are surrounded by significant H/He and/or H2O envelopes. These findings are in agreement with recent theoretical studies, which suggest that small planets are not necessarily rocky Earth-like bodies (e.g., Wuchterl 1993; Kuchner 2003; Léger et al . 2004; Ikoma and Hory 2012; Elkins-Tanton 2011; Lammer, 2012; Lammer et al. 2011a). For explaining the mean density of Kepler 11d, Kepler 11e, and Kepler 11f these 'super-Earths'' require dense H/He envelopes, similar to Uranus and Neptune, while Kepler-11b and 11c may have also additional H2O to their H/He gas envelopes (Lissauer et al . 2011), and GJ 1214b (Charbonneau et al. , 2009) or 55Cnc e (Endl et al. , 2012) may contain a huge amount of H2O.</text>
<text><location><page_3><loc_15><loc_11><loc_86><loc_31></location>If Earth-like and 'super-Earth'- type exoplanets can accumulate hydrogen from the nebula gas of an equivalent amount of 100 to 1000, and even up to 10 4 times, that of an Earth ocean depends on the nebula dissipation time, the formation time of the protoplanet, its luminosity, and nebula characteristics such as grain depletion factors, etc. (e.g., Mizuno et al ., 1978; Hayashi et al ., 1979; Ikoma and Genda, 2006; Rafikov, 2006). Although Solar System planets such as Venus, Earth and Mars lost their nebula-based hydrogen envelopes during the first 100 Myr after their origin, or never accumulated such huge amounts due to step-wise accretion after the nebula gas disappeared, terrestrial</text>
<text><location><page_4><loc_15><loc_84><loc_86><loc_91></location>planets in other systems evolve under different conditions and may capture such a dense protoatmosphere which they may not lose during the extreme active period of their host stars.</text>
<text><location><page_4><loc_15><loc_76><loc_86><loc_83></location>To understand how frequent 'rocky' terrestrial planets really are, more observations are certainly needed. From the available statistics one can conclude that Earth-analogue class I habitats (Lammer et al. , 2009a; Lammer, 2013) have to be</text>
<unordered_list>
<list_item><location><page_4><loc_15><loc_74><loc_65><loc_75></location>-located at the right distance inside the HZ of their host stars,</list_item>
<list_item><location><page_4><loc_15><loc_66><loc_86><loc_73></location>-must lose their nebula-captured H/He or degassed H2O and volatile-rich protoatmospheres during the right time period, i.e. not remain as mini-Neptune type bodies,</list_item>
<list_item><location><page_4><loc_15><loc_60><loc_86><loc_65></location>-should maintain plate tectonics, liquid water and landmass above the water level over the planet's lifetime,</list_item>
</unordered_list>
<section_header_level_1><location><page_4><loc_15><loc_58><loc_18><loc_60></location>and</section_header_level_1>
<unordered_list>
<list_item><location><page_4><loc_15><loc_53><loc_86><loc_57></location>-nitrogen should be the main atmospheric species after the stellar activity decreased to moderate values.</list_item>
</unordered_list>
<text><location><page_4><loc_15><loc_34><loc_86><loc_52></location>The question if more massive 'super-Earths' can maintain plate tectonics over time spans of several Gyr is controversial (e.g., Valencia et al. , 2007; van Heck and Tackley, 2011; Korenaga, 2010). However, in this work we will not discuss the pro and contra about geophysical processes, but focus on the stellar wind erosion of captured H/He envelopes, orand? the hydrogen content of outgassed hydrogen-rich steam atmospheres, because the proto-atmosphere escape determines if a planet will evolve to an Earth-like habitat or may remain as a mini-Neptune.</text>
<text><location><page_4><loc_15><loc_11><loc_86><loc_33></location>As it is shown by Erkaev et al. (2013) (part I of this study), depending on the availability of possible IR-cooling molecules and the planets average density, hydrogenrich 'super-Earths' orbiting inside the HZ will experience hydrodynamic blow-off only for XUV fluxes several 10 times higher compared to today's Sun. Most of their lifetime the upper atmospheres of these planets will experience strong Jeans escape which is still weaker compared to blow-off, so that they may not lose efficiently their dense hydrogen envelopes. Jeans escape is the classical thermal escape mechanism based on the fact that the atmospheric particles have velocities according to the Maxwell distribution. Individual particles in the high tail of the distribution may reach escape velocity at the</text>
<text><location><page_5><loc_15><loc_71><loc_86><loc_91></location>exobase altitude, where the mean free path is comparable to the scale height, so that they can escape from the planet's atmosphere. When the thermosphere temperature rises due to heating by the stellar XUV radiation, the number of these energetic particles increases and the atmosphere finally reaches the state when the majority of the particles have velocities equal to or exceeding the escape velocity. In this case the atmosphere is not hydrostatic anymore, and starts to expand similar to the Parker-type solar corona. This mechanism is called blow-off and leads to a stronger escape in comparison to the Jeans mechanism.</text>
<text><location><page_5><loc_15><loc_45><loc_86><loc_70></location>The blow-off stage is more easily reached at less massive hydrogen-rich planets with mass equal to that of the Earth. These planets experience hydrodynamic blow-off for much longer, and change from the blow-off regime to the Jeans-type escape for XUV fluxes which are < 10 times of today's Sun. Because of XUV heating and expansion of their upper atmospheres, both of our test planets should produce extended exospheres or hydrogen coronae distributed above possible magnetic obstacles defined by intrinsic or induced magnetic fields. In such cases the hydrogen-rich upper atmosphere will not be protected by possible magnetospheres like on present-day Earth, but could be eroded by the stellar wind plasma flow and lost from the planet in the form of ions (Erkaev et al ., 2005; Lammer et al. , 2007).</text>
<text><location><page_5><loc_15><loc_11><loc_86><loc_44></location>Besides thermal escape from the hydrogen-dominated upper atmosphere of the two considered test-planets (Erkaev et al ., 2013), briefly discussed above, one can expect that non-thermal atmospheric escape processes will also contribute to the losses. Nonthermal escape processes can be separated in ion escape and photochemical, as well as kinetic, processes which accelerate atoms beyond escape energy. Ions can escape from an upper atmosphere if the exosphere is not protected by a strong magnetic field and stretches above the magnetopause. In such a case exospheric neutral atoms can interact with the host stars solar/stellar plasma (i.e., winds, CMEs) environment. The hydrogen atoms which flow upward from the lower thermosphere will be ionized by the stellar radiation, electron impact or charge exchange and then accelerated by electric fields within the solar/stellar wind plasma flow around the planetary obstacle (i.e. ionopause, magnetopause), so that they are finally picked up and lost form the planet's gravity field (e.g., Lammer et al ., 2007; Ma and Nagy, 2007; Lammer, 2013).</text>
<text><location><page_6><loc_15><loc_76><loc_86><loc_91></location>From space missions to non- or weakly magnetized planets such as Venus and/or Mars it is known that planetary ions can also be detached from an ionopause by plasma instabilities in the form of ionospheric clouds (Terada et al ., 2002; Penz et al. , 2004; Möstl et al ., 2011), or by momentum transport triggered outflow through the planetary tail. On Earth ions outflow also over Polar Regions along open magnetic field lines (Lundin et al ., 2007; Yau and André, 1997; Wei et al ., 2012).</text>
<text><location><page_6><loc_15><loc_58><loc_86><loc_75></location>From the analysis of the available ion escape data from Venus and Mars by the ASPERA instruments on board of Venus Express and Mars Express, as well as from theoretical models, one can conclude that ion pick-up is a very dominant permanently acting non-thermal ion escape process, and most likely more efficient compared to the sporadic losses triggered by plasma instabilities or outflow through the planets tail. However, there may be extreme solar events which can enhance the ion outflow sporadically by cool ion outflow or plasma instabilities.</text>
<text><location><page_6><loc_15><loc_29><loc_86><loc_57></location>Non-thermal escape processes of neutral atoms are caused by sputtering of atmospheric neutral atoms, photochemical processes such as dissociative recombination, and charge exchange. Direct escape by sputtering is only a relevant process for low mass bodies which have a mass ≤ Mars. utHowever, even in the case of Mars one can expect that sputter loss rates are an order of magnitude lower compared for instance to ion pickup (e.g., Leblanc and Johnson, 2002; Chassefière and Leblanc, 2004; Lammer et al ., 2013). Direct escape of heavy neutral atoms, such as O and C, caused by photochemical processes is expected to be higher compared to ion escape from Mars (e.g., Krestyanikova and Shematovich, 2005; Chaufray et al., 2007; 2006; Fox and Hać, 2009; Lammer et al., 2013) but negligible or lower at more massive planets such as Venus (Gröller et al., 2010; 2012) or the Earth.</text>
<text><location><page_6><loc_15><loc_13><loc_86><loc_28></location>Lighter atoms such as atomic hydrogen can also escape directly from more massive planets with escape rates lower or comparable to ion escape. Theoretical models which studied the photochemical escape rates of H atoms (Shematovich, 2010) and ion pick-up ion escape rates (Erkaev et al ., 2005) from the hot Jupiter HD 208459b indicate comparable loss rates of the order of ≤ 10 9 g s -1 , which are an order of magnitude lower compared to the modeled thermal escape (e.g., Yelle, 2004; 2006; Tian et al ., 2005a;</text>
<text><location><page_7><loc_15><loc_87><loc_86><loc_91></location>Penz et al ., 2008b; García Muñoz, 2007; Murray-Clay et al. , 2009; Linsky et al ., 2010; Koskinen et al ., 2012).</text>
<text><location><page_7><loc_15><loc_37><loc_86><loc_86></location>From the brief overview on various non-thermal atmospheric escape processes, one can conclude that stellar wind induced ion erosion from XUV-heated and extended hydrogen-rich thermospheres (Erkaev et al ., 2013), where H atoms will most likely not be protected by a possible magnetosphere, so-called ion pick-up will be one of the most efficient non-thermal atmospheric escape process. Because of many unknowns related to minor atmospheric species in exoplanet atmospheres, as well as magnetic field properties, a study of more complex but most likely less effective processes, such as cool ion or polar outflow and photochemical non-thermal escape processes which are not even well understood at Solar System planets including the Earth, would yield highly speculative results. Therefore, in this study we focus on the modeling of the stellar wind plasma interaction, related ion production rates via charge-exchange and photoionization, and escape estimates of planetary pick-up ions from XUV exposed upper atmospheres which originate from hydrogen-rich thermospheres of an Earth-like ( R pl=1 R Earth, M pl=1 M Earth) planet in comparison with a 'super-Earth' ( R pl=2 R Earth, M pl=10 M Earth). For reasons of comparative escape studies between thermal and non-thermal ion pick-up, we study the same test planets as investigated by Erkaev et al. (2013) within an orbit of a typical HZ of an M star with the size and mass of ~0.45 R Sun. For the host star of our test planets we use the well observed dwarf star GJ 436 (Ehrenreich et al. , 2011; von Braun et al. , 2012, France et al. , 2012) as a proxy.</text>
<text><location><page_7><loc_15><loc_24><loc_86><loc_36></location>So far the formation of such extended hydrogen coronae was only addressed in a brief way in Lammer et al. (2011a; 2011b), but never modeled in detail. In this study we apply a coupled Direct Simulation Monte Carlo (DSMC) upper atmosphere - stellar wind plasma interaction model (Holmström et al. , 2008; Ekenbäck et al. , 2010) to the results of Erkaev et al. (2012).</text>
<text><location><page_7><loc_15><loc_11><loc_86><loc_23></location>In Sect. 2 we describe the DSMC model, which is used for the calculation of the exosphere and related hydrogen coronae, as well as the coupled solar/stellar wind plasma upper atmosphere interaction model. We validate our model by applying it to the Earth's geocorona and comparing the simulation results with the present-day exosphere hydrogen density and energetic neutral atom (ENA) observations by NASAs Interstellar Boundary</text>
<text><location><page_8><loc_15><loc_63><loc_86><loc_91></location>Explorer (IBEX) satellite near the magnetopause boundary at ~10 R Earth. After validating our model for the geocorona of present-day Earth, in Sect. 3 we describe the radiation and plasma parameters of our chosen M-type host star proxy, Gliese 436. In Sect. 4 we present the modeling results for the extended hydrogen coronae. In Sect. 4.1 the results of the stellar wind plasma interaction and the production of ENAs are shown as well as related planetary hydrogen ion pick-up escape rates as a function of the XUV flux values from 1 to 100 times that of today's Sun. The atmospheric ion escape rates are compared with the thermal hydrogen neutral loss rates modeled by Erkaev et al. (2012) in Section 4.2. In Section 4.3 we estimate the possible mass loss of hydrogen ions during the planetary lifetime and discuss the implications of our findings for the evolution of Earthlike and more massive 'super-Earths'. Section 5 summarizes the findings of our study.</text>
<section_header_level_1><location><page_8><loc_24><loc_60><loc_77><loc_62></location>2 STELLAR WIND-UPPER ATMOSPHERE INTERACTION</section_header_level_1>
<text><location><page_8><loc_15><loc_32><loc_86><loc_60></location>As shown by previous studies of Watson et al. (1981), Kasting and Pollack (1983), Tian et al. (2005b; 2008a; 2008b), Volkov et al. (2011), and Erkaev et al. (2013), hydrogen-rich terrestrial planets experience XUV-heated and hydrodynamically expanding non-hydrostatic upper atmosphere conditions. Depending on the particular environment (e.g., XUV flux, orbital distance, availability of IR-cooling molecules, the planet's average density, etc.) the results of these studies indicate that such planets can expand their exobase level, which separates the collision dominated atmosphere from the collisionless region to distances from a few R pl up to more than 20 R pl. As a result of such an expansion of the upper atmosphere an intrinsic planetary magnetic field will most likely not protect the exosphere against the stellar wind plasma flow (Lichtenegger et al ., 2010; Lammer, 2012; Lammer et al ., 2011a).</text>
<text><location><page_8><loc_15><loc_13><loc_86><loc_31></location>Due to the interaction between the stellar wind plasma flow and the XUV-heated non-hydrostatic upper neutral atmosphere of the planet, energetic neutral atoms (ENAs) are produced. ENAs originate due to charge-exchange when an electron is transferred from a planetary neutral atom to a stellar wind proton which then becomes an ENA. This interaction process between the stellar wind plasma and the upper atmosphere plays a significant role in the ion erosion of upper planetary atmospheres (e.g., Lundin et al. , 2007; Lammer, 2013). The production of ENAs after the interaction of stellar wind</text>
<text><location><page_9><loc_15><loc_87><loc_86><loc_91></location>protons via charge exchange with various upper atmosphere species is described by the reactions in eq. (1-3).</text>
<formula><location><page_9><loc_21><loc_83><loc_82><loc_86></location>ENA pl pl SW H H H H (1)</formula>
<formula><location><page_9><loc_21><loc_80><loc_82><loc_82></location>ENA pl pl SW H O O H (2)</formula>
<formula><location><page_9><loc_21><loc_77><loc_82><loc_79></location>ENA pl pl SW H N N H (3)</formula>
<text><location><page_9><loc_15><loc_61><loc_86><loc_75></location>After its production an ENA continues to travel with the initial velocity and energy of the stellar wind proton. The atmospheric atom in turn becomes an initially cold ion which can afterwards be lost from the atmosphere due to the ion pick-up process (Lammer, 2013). In the current study we focus our attention only on the reaction shown in eq. (1) which will dominate the stellar wind interaction with planetary hydrogen coronae around hydrogen-rich terrestrial planets.</text>
<section_header_level_1><location><page_9><loc_41><loc_58><loc_59><loc_60></location>2.1 Model description</section_header_level_1>
<text><location><page_9><loc_15><loc_27><loc_86><loc_57></location>In the current study the plasma interaction between the stellar wind and the upper atmosphere of the Earth-like planet and 'super-Earth' is modeled applying a Direct Simulation Monte Carlo (DSMC) upper atmosphere-exosphere particle model which is coupled with a stellar wind particle interaction code. The 3D model is described in detail in Holmström et al. (2008) and Ekenbäck et al. (2010) and includes stellar wind protons and planetary hydrogen atoms. The latter are launched into the simulation domain from the upper atmosphere. The applied collision cross sections for hydrogen atoms, σ H-H, and for protons and hydrogen atoms, σ H+-H, are 10 -17 cm 2 and 2 × 10 -15 cm 2 (Ekenbäck et al ., 2010) respectively. Charge exchange between stellar wind protons and exospheric hydrogen atoms takes place outside a conic shaped obstacle that represents the magnetoionopause of the studied planet. Stellar wind protons that have charge-exchanged according to the reaction shown in eq. (1) become ENAs.</text>
<text><location><page_9><loc_15><loc_11><loc_86><loc_26></location>Besides of the charge-exchange reaction, the model includes gravitation of the planet and tidal effects as well as scattering by atmospheric atoms of UV photons (radiation pressure) and photoionization by stellar photons. Inclusion of the tidalgenerating potential into the equations leads to the extension of the atmosphere toward and backward from the host star, and in extreme cases to Roche lobe overflow. Nevertheless, these effects are important for 'hot Jupiters' which are located at very</text>
<text><location><page_10><loc_15><loc_67><loc_86><loc_91></location>close distance to their host stars, and do not play a significant role for the test planets we consider in the present study. All collisions are modeled using a DSMC algorithm (Holmström et al., 2008; Ekenbäck et al., 2010). The main code uses the FLASH software developed at the University of Chicago which provides adaptive grids and is fully parallelized (Fryxell et al. , 2000). The coordinate system is centered at the center of the planet with mass pl M , the 1 x -axis is pointing towards the center of mass of the system, the 3 x -axis is parallel to the direction of the angular velocity of rotation , and the 2 x -axis points in the opposite direction to the planet's velocity. St M is the mass of the planets host star.</text>
<text><location><page_10><loc_15><loc_59><loc_86><loc_66></location>Tidal potential, Coriolis and centrifugal forces, as well as the gravitation of the star and planet acting on a hydrogen neutral atom, are included in the code in the following way (Chandrasekhar, 1963)</text>
<formula><location><page_10><loc_15><loc_53><loc_82><loc_58></location> l il St pl St St i i v x M M R M R GM x x x x x x dt dv 3 1 2 2 2 3 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 1 (4)</formula>
<text><location><page_10><loc_15><loc_34><loc_86><loc_51></location>Here i v are the components of the velocity vector of a particle, G is Newton's gravitational constant, R the distance between the centers of mass, the Levi-Civita symbol, and 3 R GM St . The first term in the right-hand side of the eq. (4) represents the centrifugal force, the second is the tidal-generating potential, the third the gravitation of the planet's host star and the planet while the last term stands for the Coriolis force. The self-gravitational potential of a particle is neglected.</text>
<text><location><page_10><loc_15><loc_26><loc_86><loc_33></location>Charge exchange reactions between a neutral planetary hydrogen atom and a stellar wind proton may take place outside the obstacle representing a magneto- or ionopause</text>
<formula><location><page_10><loc_21><loc_21><loc_82><loc_25></location> 2 2 3 2 2 1 1 t s R x x R x (5)</formula>
<text><location><page_10><loc_15><loc_12><loc_86><loc_20></location>Here s R stands for the magnetosphere or planetary obstacle stand-off distance and t R the width of the obstacle. Since the obstacle shape and location depend strongly on the planetary magnetic field strength, one may model the interaction of the stellar wind with</text>
<text><location><page_11><loc_15><loc_86><loc_86><loc_91></location>magnetized as well as with non- or weakly magnetized planets by the appropriate choice of s R and t R .</text>
<section_header_level_1><location><page_11><loc_21><loc_83><loc_79><loc_85></location>2.2 Exosphere modeling of Earth's observed atomic hydrogen geocorona</section_header_level_1>
<text><location><page_11><loc_15><loc_68><loc_86><loc_83></location>ENAs have been observed around all Solar System planets where a spacecraft was equipped with a corresponding instrument (e.g., Futaana et al ., 2006; Galli et al. , 2008; Lammer et al ., 2011a; 2011b). As shown in Fig. 1, the Interstellar Boundary Explorer (IBEX) satellite recently observed an ENA formation zone around Earth's subsolar magnetopause stand-off distance, which is located at 10 R Earth from the planet's center (Fuselier et al. , 2010).</text>
<text><location><page_11><loc_15><loc_55><loc_86><loc_67></location>Before we apply our model to hydrogen-rich exoplanets, we validate it by reproducing the geocorona and recent ENA observations (Fuselier et al. 2010) around the Earth's magnetopause by the NASAs IBEX satellite of present-day Earth. Fig. 2 shows our modeling results for Earth's geocorona interacting with the present-day solar wind by taking all parameters of Earth's exosphere as given in Table 1 as an input.</text>
<text><location><page_11><loc_15><loc_31><loc_86><loc_54></location>The average neutral hydrogen atom density at the magnetopause level obtained from our model is estimated to be ~8 cm -3 at the distance of ~10 R Earth. This density value coincides very well with the exospheric number densities inferred from the IBEX observations of ENAs near the magnetopause. In the case of the IBEX observation at March 28 2009, the computed and observed proton fluxes show an exosphere hydrogen density at a geocentric distance of ~10 R Earth of ~4 - 11 cm -3 (Fuselier et al ., 2010). The estimates of the modeled ENA flux are in good agreement with the observed flux as well, predicting the flux of approximately 600 (cm² s sr keV) -1 . This value falls inside the observed ENA interval of ~530 - 2300 (cm² s sr keV) -1 (Fuselier et al ., 2010).</text>
<text><location><page_11><loc_15><loc_13><loc_86><loc_30></location>The IBEX observation and our model validation can also be seen as a confirmation that under extreme radiation and plasma environments of the young Sun or more active stars a huge ENA formation zone, as suggested by Chassefière (1996) and Lammer et al. (2011; 2012), should be produced in the stellar wind interaction region of a hydrogen-rich extended upper atmosphere of an Earth-size planet when the exosphere density near the magnetopause is more than 10 6 times larger than that observed at present-day Earth. In the following sections we describe the input parameters and our</text>
<text><location><page_12><loc_15><loc_87><loc_86><loc_91></location>applied exosphere and ENA models to the XUV exposed hydrogen-rich Earth-size test planets.</text>
<section_header_level_1><location><page_12><loc_22><loc_81><loc_79><loc_86></location>3. GLIESE 436: A HOST STAR PROXY FOR HYDROGEN-RICH TERRESTRIAL TEST PLANETS</section_header_level_1>
<text><location><page_12><loc_33><loc_79><loc_67><loc_80></location>3.1 The radiation environment of Gliese 436</text>
<text><location><page_12><loc_15><loc_13><loc_86><loc_78></location>Recently Ehrenreich et al. (2011) observed with the Hubble Space Telescope Imaging Spectrograph (HST/STIS) the Lyman-α emission (1215.67 Å) of neutral hydrogen atoms from the low mass M star, GJ 436. Because this emission is a main contributor to the ultraviolet flux it can also be used as a main tracer in studies of thermospheric heating, thermal escape, and possible absorption by extended hydrogen coronae and/or ENAs (e.g. Vidal-Madjar et al. , 2003; Holmström et al ., 2008; Ekenbäck et al ., 2010; Ben-Jaffel and Hosseini, 2010; Lecavelier des Etangs et al ., 2010; Lammer et al. , 2011b; Ehrenreich et al ., 2012, Lammer, 2013) during transit observations with ultraviolet transmission spectroscopy. We use GJ 436 as a typical M-type host star for our test-planet parameter studies. GJ 436 is a M2.5 dwarf star which is 10.2 pc away from the Sun. The dwarf star hosts a transiting 'hot Neptune' at an orbital distance of about 0.03 AU (Butler et al. , 2004; Gillon et al. , 2007). We adopt values for stellar mass and radius of 0.45 MSun and 0.45 RSun, respectively, which are consistent with several independent parameter determinations of GJ 436 (Torres, 2007; Maness et al. , 2007; von Braun et al. , 2012). The location of the habitable zone (HZ) is calculated following Selsis et al. (2007). As their relations are only valid for effective temperatures down to 3700 K, this value is used instead of the true temperature of GJ 436, which is slightly lower (3400-3600 K; Torres 2007; von Braun et al. 2012). Further, we adopt a bolometric luminosity of 0.026 LSun (Torres, 2007). This leads to a HZ extent of 0.12-0.36 AU assuming the limit of 50% clouds, as typical for the Earth. Hence, the center of the HZ is located at 0.24 AU, which we adopt as the orbit of our hypothetical exo-Earth. The orbital period of an Earth-analog planet within the HZ of GJ 436 corresponds to approximately 63.7 days, the orbital velocity to about 41 km s -1 , and the angular velocity to 1.14·10 -6 rad s -1 . The age of GJ 436 is about 6±5 Gyr and is not well constrained (Torres, 2007). However, the rotation period of 48 days (Demory et al. , 2007) yields an estimated age of 2.5-3 Gyr (Barnes,</text>
<text><location><page_13><loc_15><loc_87><loc_86><loc_91></location>2007; Engle and Guinan, 2011). This estimation is in agreement with the lack of chromospheric activity indicated by the presence of Hα in absorption spectra.</text>
<text><location><page_13><loc_15><loc_63><loc_86><loc_86></location>GJ 436 has been detected by the ROSAT All-Sky Survey, which revealed an Xray luminosity of log LX = 27.13 erg s -1 . Recent observations by the XMM-Newton spacecraft yielded a smaller value of only ~25.96 erg s -1 (Sanz-Forcada et al. , 2011). We adopt the latter result because of the longer exposure time and better S/N of the XMMNewton observations compared to ROSAT data. Using coronal models, Sanz-Forcada et al . (2011) extrapolated the stellar emission in the total XUV range (5 - 920Å) and found log L XUV=26.92 erg s -1 . Adopting this value and scaling it to the HZ center at 0.24 AU, we estimate an XUV flux of about 5.14 erg cm -2 s -1 , comparable to the present solar XUV flux at 1 AU of 4.64 erg cm -2 s -1 (Ribas et al. , 2005).</text>
<text><location><page_13><loc_15><loc_47><loc_86><loc_62></location>In the past, the stellar XUV flux, which was emitted from GJ 436 was certainly higher. The high-energy emission of young M dwarfs is saturated at log( L X/ L bol)~ -3 (e.g. Scalo et al ., 2007), hence the maximum possible log( L X) for GJ 436 is ~29 erg s -1 . Assuming that the XUV emission of young stars occurs predominantly in X-rays because of their hotter coronae, the maximum XUV flux at the Earth-equivalent orbit around GJ 436 was roughly 700 erg cm -2 s -1 , or ~150 F XUV,now.</text>
<text><location><page_13><loc_15><loc_19><loc_86><loc_46></location>Lyman-alpha emission of GJ 436 was detected by Ehrenreich et al. (2011) using HST/STIS observations. They reconstructed the intrinsic stellar emission by correcting for interstellar medium (ISM) absorption, leading to an apparent flux observed at Earth of ~2.7±0.7 × 10 -13 erg cm -2 s -1 . Scaled to the HZ center, this yields ~20.51 erg cm -2 s -1 , a factor of ~3.3 larger than the present solar value at 1 AU of 6.19 erg cm -2 s -1 (Ribas et al ., 2005). Recently, France et al. (2013) reconstructed the intrinsic Lyman-alpha flux of GJ 436 by using a different approach. They obtained a value of 3.5 × 10 -13 erg cm -2 s -1 with an uncertainty of about 15 - 30 %, which is slightly higher than the value given by Ehrenreich et al. (2011), but is consistent with the errors. The relevant stellar parameters and the measured radiation properties used in the model simulations for various assumed XUV flux values of a Gliese 436-type M dwarf are shown in Table 2.</text>
<text><location><page_13><loc_15><loc_11><loc_86><loc_18></location>The photoionization rates corresponding to the four XUV flux enhancement factors were scaled from the average present solar value at Earth (1.1 × 10 -7 s -1 ; Hodges, 1994, Bzowski, 2008) to the corresponding enhancement factors. The photoionization</text>
<text><location><page_14><loc_15><loc_79><loc_86><loc_91></location>rate is usually calculated as the product of ionization cross-section and spectral flux integrated over all wavelengths below the ionization threshold. Since full M star XUV spectra for different activity levels are currently not available, we assume that the present spectral energy distribution is equal to the solar one and scale it up by the constant factors given in Table 2.</text>
<text><location><page_14><loc_15><loc_55><loc_86><loc_78></location>The UV absorption rates correspond to the product of the photon flux at the center of the Lyman-alpha line and the total absorption cross-section (5.47 × 10 -15 cm 2 Å; e.g. Quémerais, 2006). Adopting the reconstructed intrinsic line profile of Ehrenreich et al. (2011), the present value of the photon flux at the HZ center of GJ 436 is estimated to be ~6.9 × 10 -3 s -1 .. To scale the Lyman-alpha flux and, hence, the absorption rate to higher XUV flux emission levels, we use the scaling between X-rays and Lyman-α from Ehrenreich et al. (2011). This assumes that L X/ L bol ≈ L XUV/ L bol and that the central Lyman-α flux scales approximately as the integrated line emission. The resulting absorption rates are also shown in Table 2.</text>
<section_header_level_1><location><page_14><loc_33><loc_53><loc_68><loc_54></location>3.2 Expected stellar wind plasma properties</section_header_level_1>
<text><location><page_14><loc_15><loc_24><loc_86><loc_52></location>Depending on the mass, size and resulting luminosity of the host star, the corresponding scaled HZ location in the case of GJ 436 is at 0.24 AU. This is a much closer orbital distance compared to that of the Earth (1 AU). As pointed out by Khodachenko et al. (2007), at orbital locations < 0.5 AU the flow of dense plasma related to stellar winds and coronal mass ejections (CMEs), energetic particle fluxes and XUV radiation cannot be neglected. Depending on the stand-off distance of the planetary obstacle which forms when the stellar plasma flow is deflected around the planet, previous test particle model results of Lammer et al. (2007) indicate that CO2-rich Earth-like exoplanets having no or only weak magnetic moments may lose from tens to hundreds of bars of atmospheric pressure, or even their whole atmospheres, due to the CME induced O + ion pick-up at orbital distances ≤ 0.2 AU.</text>
<text><location><page_14><loc_15><loc_11><loc_86><loc_23></location>Due to the uncertainties on the mass loss and related plasma outflow from M dwarfs, we assume in our study, as in Khodachenko et al. (2007) and Lammer et al . (2007), the plasma environment close to the stars obtained from solar observations. There exist a limited number of measurements of the mass loss rates for M stars (Wood et al., 2005, Ehrenreich et al. , 2011), which in principle may be used for estimation of specific</text>
<text><location><page_15><loc_15><loc_68><loc_86><loc_91></location>stellar wind density and velocity. For these stars the mass loss rates are comparable or less than the mass loss rate of the Sun. At the same time, for the Sun we have a much better knowledge of the distribution and evolution of active solar regions and of the mass outflow in the form of solar wind and CMEs, which we use in the present study. Note that stellar wind density and/or velocity lower than the solar (assumed) values would reduce the portion of the produced and picked up ions. Such a reduction would not change our main conclusion that the ion pick-up loss makes up only several percent of the thermal loss, and the further results can be considered as an upper limit for ion pickup near an M dwarf like Gliese 436.</text>
<text><location><page_15><loc_15><loc_32><loc_86><loc_67></location>For the accurate study of stellar-planetary interactions one needs a reliable model which can simulate the propagation and evolution of the stellar wind plasma. For modeling the propagation and evolution of the stellar wind we use the Versatile Advection Code (VAC) (Toth, 1996). This model is able to simulate spatial and temporal evolution of the solar/stellar wind, as well as CMEs, from orbital distances ≥0.14 AU. It/The model includes a self-consistent Parker-type co-rotating magnetic field, and is based on the solution of the set of the ideal (non-resistive) non-relativistic magnetohydrodynamic equations (Toth, 1996). We use a spherical uniform computation domain, which occupies a radial distance region between 0.14 < R < 1 AU. The stellar wind in the model flows through the inner boundary of the computation domain at a semi-major axis location d = 0.14 AU and propagates out through the outer radial boundary at d = 1 AU. A self-consistent expanding stellar wind plasma flow under the conditions of a frozen-in, co-rotating, Parker-type, spiral magnetic field is numerically simulated (Odstrčil et al ., 1999; Rucker et al. , 2008).</text>
<text><location><page_15><loc_15><loc_13><loc_86><loc_31></location>The typical parameters of the expected flow of the stellar wind plasma at d = 0.14 AU are imposed along the inner radial boundary (Odstrčil et al ., 1999) with an initial proton concentration n 0 = 500 cm -3 , stellar wind proton temperature, T 0 = 500 kK, and a radial stellar wind velocity v r0 = 300 km s -1 . For investigating the propagation of CMEs, in a second step the simulation of a CME cloud with an initial proton density n 0 = 1000 cm -3 , proton temperature, T 0 = 1700 kK, and a radial stellar wind velocity v r0 = 600 km s -1 is imposed at the inner boundary of the computation domain as a time-dependent</text>
<text><location><page_16><loc_15><loc_87><loc_86><loc_91></location>injection of hot and dense plasma into the ambient stellar wind (Odstrčil et al ., 1999; Odstrčil et al. , 2004).</text>
<text><location><page_16><loc_15><loc_68><loc_86><loc_86></location>Fig. 3 shows radial profiles of the maximum values of plasma parameters ( n , v r, T ) during a solar analogue CME event (dashed lines, Case II) for a typical M-star with mass M s ~ 0.45 M Sun and a rotation period 2.5 days, and those for the stellar wind itself (solid lines Case I). Therefore, in the stellar wind plasma interaction modeling with the upper atmosphere, described below, two types of stellar plasma parameters representing the lower (Case I) and upper limit (Case II) conditions at the HZ location of our test planets at 0.24 AU were used as inputs:</text>
<unordered_list>
<list_item><location><page_16><loc_24><loc_65><loc_69><loc_67></location> Case I: 250 SW n cm -3 , 330 SW v km/s, 6 10 SW T K,</list_item>
<list_item><location><page_16><loc_24><loc_62><loc_73><loc_64></location> Case II: 700 SW n cm -3 , 550 SW v km/s, 6 10 2 SW T K.</list_item>
</unordered_list>
<text><location><page_16><loc_15><loc_41><loc_86><loc_61></location>Here n sw corresponds to stellar wind concentration, v sw denotes its bulk velocity and T sw stands for the stellar wind temperature. These values cover the predicted range for the expected stellar wind plasma parameters of GJ 436 at the HZ of the system. The upper limit (Case II) can also be considered as a proxy for modeling of frequent CME events in the system when the next CME event hits the planet immediately after the previous one. We can estimate the recovery time of the planetary atmosphere after the CME event on a very simple way. Since the test planets considered in the article are not magnetized, we assume that the recovery speed coincides with the sound speed (or the speed of slow</text>
<text><location><page_16><loc_15><loc_35><loc_86><loc_40></location>magnetoacoustic wave), so that 2 / 1 / H exo B t s t CME m T k R c R where t R is the obstacle</text>
<text><location><page_16><loc_15><loc_21><loc_86><loc_34></location>width, 3 / 5 is the ratio of the specific heats, B k is the Boltzmann constant, H m is the mass of a hydrogen atom and exo T is the exobase temperature. Taking the parameters from Tables 3 and 4 and depending on the characteristic size of the obstacle and the temperature, this time varies between approximately 7 and 14 hours for the Earth-type planet and 64 and 80 hours for the 'super-Earth'.</text>
<text><location><page_16><loc_15><loc_16><loc_86><loc_20></location>The next section is dedicated to the discussion of the obtained results and presents also the ion production rates for the hydrogen-rich Earth-like planet and the 'super-Earth'.</text>
<section_header_level_1><location><page_16><loc_18><loc_10><loc_82><loc_12></location>4. HYDROGEN EXOSPHERES, ENA PRODUCTION AND ION ESCAPE</section_header_level_1>
<text><location><page_17><loc_15><loc_74><loc_86><loc_91></location>In the following section we study the modification of the extended hydrogen exosphere due to the interaction of it with the stellar XUV and plasma flux. Because our hydrogenrich test-planets orbit within a typical M-star HZ at ~0.24 AU they will be affected by tides. As it was discussed in Khodachenko et al. (2007) tides arise because of the finite extension of the planetary body in the inhomogeneous gravitational field of its host star so that the continuous action of the tides will reduce the planetary rotation rate or may result in a synchronous rotation (Grießmeier et al. , 2005).</text>
<text><location><page_17><loc_15><loc_50><loc_86><loc_73></location>The intrinsic magnetic field of a terrestrial planet is an essential factor for planetary protection from the ion pick-up atmosphere loss process. As shown in Khodachenko et al. (2007) and Lammer et al . (2007), because of the close orbital location within M-star HZs, the magnetosphere field of a terrestrial planet is more compressed due to the denser stellar wind impact compared with that of the solar wind at present-day Earth at 1 AU. In view of this fact the radial distance of the extended exobase of an XUV heated hydrogen rich upper atmosphere will most likely coincide with the planetary magnetopause or ionopause distance (e.g., Lammer et al ., 2009a; Lammer et al ., 2012, Lammer, 2013).</text>
<section_header_level_1><location><page_17><loc_33><loc_47><loc_67><loc_49></location>4.1 Input parameters and modeling results</section_header_level_1>
<text><location><page_17><loc_15><loc_13><loc_86><loc_46></location>As it was briefly discussed in Sect. 3.2, the magnetic moments of terrestrial planets, and especially that of 'super-Earths' within close orbital distances, are expected to be weak (e.g., Gaidos et al ., 2010; Tachinami et al ., 2011; Morad et al ., 2011; Stamenkovic' et al., 2011Stamenkovi'c et al., 2012). This would lead to magnetoshperes or ionospheres which are compressed towards the planet's expanded non-hydrostatic upper atmosphere by the strong dynamic ram pressure of the dense stellar wind plasma. On the other hand if the exobase level expands beyond several planetary radii one can also expect that an Earth-type magnetosphere will not protect the exosphere (Fig. 5: Lammer et al ., 2007; Fig. 6 right panel: Lammer et al ., 2011a). Taking this considerations into account, the planetary obstacle most likely is located very close above the exobase level (Lammer et al. 2009b). Because the shape of the planetary obstacle affects the ENA production and resulting loss of planetary hydrogen ions, we study also the influence of the obstacle width on the ion production rate and the upper atmosphere erosion.</text>
<text><location><page_18><loc_15><loc_64><loc_86><loc_91></location>In the first case the magnetic obstacle width t R in the eq. (5) was assumed to be 1.5 times greater than the magnetopause distance. This relation and its resulting obstacle shape is close to the observed magnetosphere of the present-day Earth and may occur if the planet has an intrinsic magnetic dynamo. In the second case we choose t s R R so that it resembles more a Venus-type planetary obstacle which may correspond to a planet with no magnetic field, or only a very weak dynamo. By decreasing of the planetary obstacle width the ion production will significantly increase, so that a terrestrial planet with a Venus-type obstacle, where t s R R , may lose larger amounts of atmospheric gas in ionized form (see Sect. 4.2). In the present study we do not specify the magnetic moment of a planet, but only chose a magnetospheric obstacle.</text>
<text><location><page_18><loc_15><loc_25><loc_86><loc_63></location>For illustrating the differences between the stellar wind plasma interaction with a hydrogen-rich terrestrial planet which is exposed to both a weak XUV flux and an extremely strong one, we irradiate the two test-planets with the XUV flux of the present Sun (1 XUV) and with a 100 times higher XUV flux (100 XUV). Moreover, we investigate for these two XUV flux cases several stellar wind and obstacle scenarios. The main input parameters at the inner boundary of our simulation domain are shown for 4 selected cases in Tables 3 and 4. As it was mentioned earlier, we apply the results obtained by Erkaev et al. (2012) to the upper atmosphere input paramters of our model. Erkaev et al. (2012) studied the thermosphere structure of a hydrogen-dominated Earth and a 'super-Earth' ( R pl=2 R Earth; M pl=10 M pl) with a hydrodynamic upper atmosphere model which solves the equations of mass, momentum and energy conservation for low and high heating efficiencies, η of 15 % and 40 %, respectively. η defines the percentage of the incoming XUV energy which is transferred into heating of the neutral gas. Table 4 shows the same input paramters for our model for a hotter atmosphere corresponding to the upper atmosphere values of Erkaev et al . (2013) with η = 40%.</text>
<text><location><page_18><loc_15><loc_9><loc_86><loc_24></location>As one can see from Tables 3 and 4, the exobase distance which is chosen as our inner model boundary and the temperature are increasing for higher XUV fluxes. This behavior can be expected by taking into account a more intensive radiation flux from the parent star. Enhanced heating flux makes the scale height of the atmosphere increase, which in its turn moves the exobase to higher location. One can also see that an increase of the heating efficiency leads to an increase of the planet's obstacle stand-off (which for</text>
<text><location><page_19><loc_15><loc_84><loc_86><loc_91></location>the studied non-magnetized planets practically coincides with the exobase) distances as well. Because of the expansion of the upper atmosphere under more extreme heating conditions (40%) the exobase densities are smaller in comparison to the 15% cases.</text>
<text><location><page_19><loc_15><loc_68><loc_86><loc_83></location>Figs. 4 and 5 show the modeled hydrogen exospheres and the related stellar plasma interaction under various conditions around the test planets. All the figures show cross-sections of a 3D cloud in the 2 1 , x x plane similar to those in Fig. 2. Fig. 4 illustrates the appearance of the extended hydrogen coronae around the Earth-type planet while Fig. 5 corresponds to the 'super-Earth'. In all the cases the wider Earth-type planetary obstacle is assumed, except for Fig. 4d where a smaller Venus-like obstacle is adopted.</text>
<text><location><page_19><loc_15><loc_39><loc_86><loc_67></location>The white area around the planets (which are shown as black dots) represents the inner atmosphere (non-hydrostatic thermosphere), which is not considered in the present study. Fig.4a and Fig.4b illustrate the influence of the XUV flux on the cloud formation. All simulation parameters for these two pictures are the same except for the XUV flux, which is chosen to be equal to and 50 times higher than the XUV flux of the present Sun. As one can see, the higher XUV flux leads to a more efficient expansion of the upper atmosphere so that charge exchange can be more intensive in the surrounding hydrogen corona. The effect of the planetary obstacle can be seen in a comparison of Fig. 4c, for an Earth-type planetary obstacle shape, with Fig.4d, for a Venus-type obstacle. In these two cases the upper atmosphere is exposed to the XUV flux which is 50 times higher compared to that of today's Sun.</text>
<text><location><page_19><loc_15><loc_23><loc_86><loc_38></location>Figs. 5a and 5b illustrate the importance of the heating efficiency. We show two model runs for the 'super-Earth' for a comparison. Only the upper atmosphere parameters corresponding to the heating efficiencies were changed. A higher heating efficiency results in additional expansion of the upper atmosphere and in increasing production of ENAs in the vicinity of the planet (blue and red dots). Figs. 5c and 5d show the effect of the stellar wind velocity and density on the hydrogen coronae formation.</text>
<text><location><page_19><loc_15><loc_18><loc_86><loc_23></location>Both figures, 5c and 5d, correspond to the most extreme XUV case, which is 100 times higher than that of today's Sun.</text>
<text><location><page_19><loc_15><loc_10><loc_86><loc_17></location>As expected, the extreme stellar conditions result in a denser and faster stellar plasma flow, higher XUV fluxes and more intense heating of the upper atmosphere, as well as a decrease of the planetary obstacle width, which all lead to more intensive interaction</text>
<text><location><page_20><loc_15><loc_79><loc_86><loc_91></location>processes. The ENA part of the hydrogen corona (blue and red dots) becomes more visible, meaning an increase of the atmospheric erosion processes. One can see that a huge amount of exospheric hydrogen atoms is ionized or underwent charge exchange reactions in both cases, but stronger stellar wind significantly increases the number of ENAs in the vicinity of the planet as suggested by Chassefière, (1996).</text>
<text><location><page_20><loc_15><loc_50><loc_86><loc_78></location>Chassefìère (1996) studied the hydrodynamic outflow and escape of hydrogen atoms from a hydrogen-dominated expanded thermosphere from early Venus. From this study it was estimated that the huge ENA cloud, which is generated via charge exchange due to the interaction between an extended exosphere and the surrounding solar wind plasma of the young Sun, may contribute to about 75 % of the energy inside the thermosphere which is used for escape of the outward flowing H atoms (see Fig. 3 in Chassefière, 1996). The stellar EUV flux is deposited mainly in the lower thermosphere (Erkaev et al ., 2013), while the ENA flux directed toward the planet should be deposited at an atmospheric layer below the exobase. It can contribute to thermospheric heating and may as a consequence modify the upper atmosphere structure which could result in an enhancement of the thermal escape rate.</text>
<text><location><page_20><loc_15><loc_26><loc_86><loc_49></location>Our results related to the efficient production of ENAs around the planetary obstacle support the hypothesis of Chassefière (1996) that ENAs may contribute to upper atmosphere heating. A study which investigates the possible heating contribution of ENAs additionally to the stellar XUV flux is beyond the scope of this particular work, but is in progress for a follow up study during the near future. We note also that ENA clouds near the terrestrial exoplanets within orbits around M dwarfs might be observable in the stellar Lyman-alpha line by the Hubble Space Telescope and in higher resolution beyond the geocorona in the near future by the World Space Observatory-UV (Shustov et al. , 2009; Lammer et al ., 2011b).</text>
<text><location><page_20><loc_15><loc_19><loc_86><loc_26></location>In the next section we estimate how many of the produced planetary ions in the hydrogen coronae are picked up by the stellar wind plasma, and hence are lost from the planet.</text>
<section_header_level_1><location><page_20><loc_24><loc_16><loc_82><loc_18></location>4.2 Stellar wind induced atmospheric erosion of planetary hydrogen ions</section_header_level_1>
<text><location><page_20><loc_15><loc_11><loc_86><loc_15></location>As discussed above, interaction processes between the stellar wind and the upper atmosphere together with the photoionization by stellar photons lead in the case of</text>
<text><location><page_21><loc_15><loc_76><loc_86><loc_91></location>hydrogen-rich atmospheres to the production of atmospheric H + ions, see eq. (1). After ionization, the ions can be picked up by the stellar wind plasma and swept away from the planet. Because we are interested in the efficiency of the atmospheric ion escape, we estimate the average ion production rates under various conditions. We assume as discussed below that in the considered cases the production of planetary ions and the escape rate are most likely of the same order.</text>
<text><location><page_21><loc_15><loc_60><loc_86><loc_75></location>Ions produced near and above the planet's obstacle can be lost because of the ion pick-up process. Since these particles are not neutral anymore, they can follow the magnetic field lines in the stellar wind plasma and can be swept away from the planet's gravity field. We consider the H + ions produced above the planetary obstacle, where the collisions between atmospheric particles can be neglected. It is assumed that the ions may be lost if the gyro radius</text>
<formula><location><page_21><loc_23><loc_55><loc_82><loc_59></location>(6) , qB v m r i i g </formula>
<text><location><page_21><loc_15><loc_10><loc_86><loc_55></location>is small enough in comparison to the planetary radius (e.g. if the magnetic field in the vicinity of a planet is strong enough to change the trajectory of the ions significantly). Here i m is the mass of the ion, i v is the velocity of the 'cold' planetary ion assumed to be ~7 km s -1 , q is the ion charge and B is the magnetic field near the planetary obstacle. In the case of a pure hydrogen upper atmosphere the ion mass and charge coincide with the mass and charge of a proton. The velocity of ~7 km s -1 is chosen as being slightly faster than the mean thermal velocity of a hydrogen atom for a temperature of about 2000 K. The magnetic field at the distance ~0.24 AU from an M dwarf can be roughly estimated if one assumes a dipole character of the stellar field with the initial global value in the range of ~2 - 3 kG or ~0.2 - 0.3 T (Phan-Bao et al. , 2009, Reiners, 2012). By assuming an average magnetic field on the star of 2 kG, the magnetic field at 0.24 AU is ≈ 3 10 4 . 1 G, which yields for an ion velocity of 7 km s -1 an ion gyro radius of ~525 m which is several orders of magnitude smaller compared to the radii of the studied planets. In such a case it is justified to assume that most of the produced H + ions will be swept away from the planets by the stellar wind. If we assume that the ions are accelerated by the stellar wind electric field to the velocity of the stellar wind (Case I: 330 km/s, Case II: 550 km/s), the ion gyro radius increases proportionally to ~25 - 40 km in two extreme</text>
<text><location><page_22><loc_15><loc_87><loc_86><loc_91></location>cases. Here we assume the filling factor f=1 (see Phan-Bao et al. , 2009), i.e. the maximal possible field strength.</text>
<text><location><page_22><loc_15><loc_57><loc_86><loc_86></location>Since the magnetic field of ~2 - 3 kG is typical for young and active M dwarfs, it could be convenient to determine the gyro radii for a weaker field of ~50 G for an older star with the age of several Gyr (Phan-Bao et al. , 2009). The magnetic field at 0.24 AU is approximately 5 10 57 . 3 G. A decrease of the magnetic field causes a proportional increase of the gyro radius (21 km for an ion velocity of 7 km s -1 , 10 3 km and 3 10 6 . 1 km for 330 km/s and 550 km/s respectively). But even the highest value of ~1600 km is several times less if compared to the planetary radius, and more than an order of magnitude lower compared to the exobase radius where most ENAs are produced. These estimates support our assumption that the majority of the exospheric ions are lost from the planet and that the ion production rate is balanced by the escape rate at least during a significant part of the stellar life time.</text>
<text><location><page_22><loc_15><loc_23><loc_86><loc_56></location>Estimates of the ion production rates and corresponding escape rates described in the previous sections are summarized in the Tables 5 and 6 for planetary obstacles which have an Earth-like magnetosphere shape. Table 5 presents the results obtained for a hydrogen-rich Earth-like planet for two stellar wind conditions and a heating efficiency η =15% and of a higher heating efficiency η = 40%, while Table 6 summarize the similar scenarios for the 'super-Earth'. Atmospheric loss rates L ion are given in units of particles per second. As one can see from Tables 5 and 6, in the most cases the ion production and loss rate increases with the increasing XUV flux. Loss rates for faster stellar wind also exceed the corresponding values for the wind with lower velocity which is not surprising. Since the ion production rates depend not only on the assumed heating efficiency and the XUV flux, but also on the exobase density, the values for the lower-density case corresponding to a heating efficiency of 40% (Erkaev et al. , 2013) are slightly lower in comparison to the 15% case shown in Table 6.</text>
<text><location><page_22><loc_15><loc_10><loc_86><loc_22></location>This is also the reason why the values for the cases where the stellar XUV flux is about 100 times higher than that of the present Sun are not dramatically higher (or even slightly smaller) that the ion production rates for the lower XUV fluxes, although the intensity of the interaction increases. Under the intensity of the interaction in this case we mean the ratio of produced ions to the mean exospheric density. This value increases</text>
<text><location><page_23><loc_15><loc_81><loc_86><loc_91></location>monotonically for higher XUV fluxes in all cases considered in the present study. The reason for that is related to the corresponding exobase density that is lower because of expansion in the case of a hydrogen-rich upper atmosphere which is exposed to high XUV fluxes such as in the 100 XUV case (Erkaev et al. , 2013).</text>
<text><location><page_23><loc_15><loc_52><loc_86><loc_81></location>To investigate the influence of the planetary obstacle shape on the H + escape rate L ion, we performed an analogous set of simulations by assuming a Venusian type planetary obstacle ( t s R R ). Tables 7 and 8 present the calculated ion production rates and estimated ion escape rates for the two test planets under the same conditions as described in Tables 5 and 6 except for the shape of the planetary obstacle. As one may see from the comparison of Tables 5 - 6 and Tables 7 - 8, reducing the width of the obstacle by 1.5 times leads to an increase in the ion production rate (i.e. the escape in general) of ≈30%. Other factors which lead to an increase of the ion production rate are related to the increase of the stellar wind density and velocity, heating efficiency η , and enhancement of the stellar XUV flux of the parent star. All these dependencies should be considered and expected.</text>
<text><location><page_23><loc_15><loc_38><loc_86><loc_51></location>For comparison, thermal loss rates change in the range from 29 10 0 . 4 (1 XUV, η=15%) to 31 10 3 . 4 (100 XUV, η=40%) for a hydrogen-rich Earth-type planet and from 29 10 6 . 1 (1 XUV, η=15%) to 31 10 3 . 5 (100 XUV, η=40%) for a hydrogen-rich 'superEarth'. In all cases these rates exceed the presented in the current study. For more information, see Erkaev et al., (2013).</text>
<text><location><page_23><loc_15><loc_17><loc_86><loc_37></location>If we compare the modeled H + ion pick-up loss rates with that of Mars (e.g., Lammer et al ., 2003) or Venus (Lammer et al. , 2006), which are in the order of ~10 25 s -1 , one can see that the pick-up loss rates for the hydrogen-dominated Earth-like planet are comparable for the 1 XUV case with a heating efficiency of 15 % and an Earth-like magnetopause shape, but would be a factor 10 3 higher in the case of 40 % heating efficiency and/or a more narrower Venus-type planetary obstacle. For the larger 'superEarth' and XUV cases with higher values than that of the present-day Sun the loss rates are up to 10 4 - 10 5 times higher.</text>
<text><location><page_23><loc_42><loc_14><loc_58><loc_15></location>4.3 Total ion escape</text>
<text><location><page_24><loc_15><loc_74><loc_86><loc_91></location>The loss rates shown in Tables 5 - 8 can be used for rough estimation of the total ion loss from the hydrogen envelopes around the studied planets. This question is important because, as shown by Erkaev et al. (2013), volatile rich 'super-Earths' which contain IRcooling molecules can result in lower heating efficiencies of about 15 % so that for most of their lifetime they will not be in the hydrodynamic blow-off regime. In such cases nonthermal atmospheric escape processes, like the studied H + ion pick-up process, will contribute to the loss of their hydrogen-rich protoatmospheres.</text>
<text><location><page_24><loc_15><loc_60><loc_86><loc_73></location>Before we investigate this mass loss one needs to know how long a typical M dwarf like Gliese 436 may keep a high level of the XUV and X-ray flux. According to Penz et al. (2008a) the temporal scaling law for the soft X-ray (0.6-12.4 nm or 0.1-2 keV) flux of a typical M dwarf with the mass of ≈ Sun M 4 . 0 can be described by the following relation</text>
<formula><location><page_24><loc_21><loc_56><loc_82><loc_58></location>77 . 0 0 17 . 0 ) 6 . 0 ( t L Gyr t L X , 34 . 1 0 13 . 0 ) 6 . 0 ( t L Gyr t L X , (6)</formula>
<text><location><page_24><loc_15><loc_48><loc_86><loc_54></location>where 28 0 10 6 . 5 L erg s -1 and t is given in Gyr. The soft X-ray flux can then be scaled for the appropriate orbital distance by using the relation 2 4 / d L F X X .</text>
<text><location><page_24><loc_15><loc_25><loc_86><loc_47></location>Fig. 6 shows, approximately, the decrease of the soft X-ray flux of a Gliese 436 analogous M dwarf during the first 1.3 Gyr of its life time. Since at present time the scaling law for the XUV radiation of M dwarfs is not yet well constrained, we use this soft X-ray scaling law instead of the XUV scaling law in our estimation for the total H + escape. Assuming this temporal scaling law for the star and taking the ion production rates from Tables 5 - 8, we can estimate the mass loss from the hydrogen-rich Earth-like planet and the 'super-Earth' in the HZ of a Gliese 436 type M star after 4.5 Gyr (see Tables 9 and 10). For comparison the thermal escape rates are shown by using the values from Table 2 in Erkaev et al. (2013).</text>
<text><location><page_24><loc_15><loc_11><loc_86><loc_24></location>The total ion loss is given in Earth ocean equivalent amounts of hydrogen (1EOH = 23 10 5 . 1 g) . It should also be mentioned that we do not consider escape during the first ~100 Myr, the time of extreme stellar activity of an M dwarf, so that our estimates cover the time span ~0.1 - 4.5 Gyr. As discussed in Erkaev et al. (2013) during this early extreme period the temperature in the lower thermosphere may be >> 250 K, due to</text>
<text><location><page_25><loc_15><loc_84><loc_86><loc_91></location>magma oceans and frequent impacts. Hot lower atmosphere will enhance the atmospheric thermal escape during this early period. A follow up study which will investigate the earliest extreme evolutionary periods is in progress.</text>
<text><location><page_25><loc_15><loc_68><loc_86><loc_83></location>In the present work we do not take into account the gradual decrease of the amount of gas in the planetary atmosphere due to escape processes, as we assume that the hydrogen reservoir contains much more gas in comparison to the amount lost . As discussed in Sect. 1, such scenarios can be considered as real because most of the recently discovered 'super-Earths' may have huge hydrogen envelopes which contain a few % of their whole mass (e.g., Lammer, 2013).</text>
<text><location><page_25><loc_15><loc_50><loc_86><loc_67></location>If we compare the estimated atmospheric escape rates obtained for the thermal and ion pick-up processes for both test-planets in the HZ, it is clear that the thermal escape rate substantially exceeds the pick-up rate under the studied conditions. This is also the case when we consider the most extreme XUV and stellar plasma conditions, including a narrow planetary obstacle. A fraction of the evaporating neutral exosphere will be ionized so that ion pick-up will contribute to the total atmospheric escape rate, but as long as the upper atmosphere is in blow-off thermal escape will be the most important.</text>
<text><location><page_25><loc_15><loc_40><loc_86><loc_49></location>In our study the escape rate of ionized hydrogen atoms can vary for an Earth-type planet from ~0.6 EOH under moderate conditions (15% heating efficiency, moderate stellar wind, Earth-type planetary obstacle) up to ~2.5 EOH for extreme environments (40% heating efficiency, denser and faster wind and a narrow Venusian obstacle type).</text>
<text><location><page_25><loc_15><loc_21><loc_86><loc_39></location>The stronger gravity of the more massive 'super-Earth' keeps the atmosphere closer to the planet's surface, which slows down the charge exchange and photoionization processes. In this case the escape changes from ~0.4 EOH to ~2.14 EOH depending on the environment but remains smaller compared to escape from an Earthtype planet (ranging from ~0.6 EOH to 2.5 EOH, see above). In all studied cases the nonthermal H + pick-up rate is several times smaller in comparison with the thermal one, but makes up a significant fraction of the whole loss processes.</text>
<text><location><page_25><loc_15><loc_11><loc_86><loc_20></location>The results of our study, together with those of Erkaev et al. (2013), indicate that terrestrial exoplanets ranging in mass and size from Earth- to 'super-Earths' may experience difficulties in losing dense hydrogen envelopes if they have H-dominated protoatmosphere remnants with >9 EOH (Earth: η = 15%) and >19 EOH (Earth: η = 40%).</text>
<text><location><page_26><loc_15><loc_74><loc_86><loc_91></location>For 'super-Earth' these amounts are >3.5 EOH (η = 15%) and >10 (η = 40%). Dense hydrogen envelopes may be removed more easily if a particular exoplanet is located closer to its parent star such as Corot-7b or Kepler-10b (e.g., Leitzinger et al ., 2011) which orbit their parent stars at ~ 0.017 AU, but not inside the HZ. We note also that due to the HZ location at greater distances from the parent stars, the stellar wind erosion of hydrogen-envelopes will be less efficient for planets inside the HZs of K, G and F-type stars.</text>
<section_header_level_1><location><page_26><loc_42><loc_71><loc_59><loc_73></location>5. CONCLUSIONS</section_header_level_1>
<text><location><page_26><loc_15><loc_13><loc_86><loc_69></location>In this study we investigated the non-thermal ion pick-up escape process from hydrogenrich, non-hydrostatic upper atmospheres of an Earth-like planet, and a hydrogen-rich 'super-Earth' which is twice as large as Earth and ten times more massive. Both planets are supposed to be located inside the HZ of a typical M dwarf star with stellar properties similar as GJ 436. We showed that in the case of an M dwarf the produced planetary H + ions have a high probability to be picked up from the extended hydrogen coronae by the stellar wind plasma flow so that the ion production rate and the ion escape rate are perhaps of the same order. We exposed the two test-planets to various XUV fluxes from 1 to 100 times that of the present Sun and found that in all studied cases the ionization of exospheric neutral hydrogen atoms by charge-exchange and photoionization contributes to the total atmospheric escape of the upper atmosphere, but do not prevail over the thermal escape. The total non-thermal atmospheric escape by ion pick-up from possible dense hydrogen envelopes during the life time of the studied planets is < 3 EOH. Our results indicate that if a rocky exoplanet did not lose the majority of its nebula captured hydrogen gas envelope, or degassed a huge amount of hydrogen-rich volatiles by thermal blow-off during the first hundred Myr after the planet's origin, it is questionable if the stellar wind can erode a remaining dense hydrogen envelope non-thermally. The thermal escape is higher during the planet's history, but is probably unable to remove such dense hydrogen envelopes as well. The situation may change dramatically for exoplanets which are located closer to their parent stars. Depending on the nebula life time, the formation process, planetary mass, stellar activity and plasma properties in the vicinity of the planet, the initial amount of hydrogen, thermal and non-thermal atmospheric escape processes</text>
<text><location><page_27><loc_15><loc_87><loc_86><loc_91></location>will determine if a planet becomes a world with an Earth-type atmosphere (and no hydrogen envelope) or remains a sub-Neptune type body.</text>
<section_header_level_1><location><page_27><loc_15><loc_81><loc_37><loc_83></location>ACKNOWLEDGEMENTS</section_header_level_1>
<text><location><page_27><loc_15><loc_29><loc_86><loc_80></location>M. Güdel, K. G. Kislyakova, M. L. Khodachenko, and H. Lammer acknowledge the support by the FWF NFN project S116 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subprojects, S116 604-N16 'Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond', S116 606-N16 'Magnetospheric Electrodynamics of Exoplanets', S116607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. K. G. Kislyakova, Yu. N. Kulikov, H. Lammer, and P. Odert thank also the Helmholtz Alliance project 'Planetary Evolution and Life'. P. Odert and M. Leitzinger acknowledges support from the FWF project P22950-N16. The authors also acknowledge support from the EU FP7 project IMPEx (No.262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science WG5. The authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar- and exoplanetary environments'. Finally, N. V. Erkaev acknowledges support by the RFBR grant No 12-05-00152-a. This research was conducted using resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North (HPC2N), Umeå University, Sweden. The software used in this work was in part developed by the DOE-supported ASC / Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. Finally, the authors thank the referees for very useful suggestions and recommendations which helped to improve the work.</text>
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<text><location><page_40><loc_15><loc_74><loc_86><loc_80></location>Volkov, A. N., Johnson, R. E., Tucker, O. J., Erwin, J. T. (2011) Thermally driven atmospheric escape: Transition from hydrodynamic to Jeans escape, ApJ , 729, art. id. L24.</text>
<text><location><page_40><loc_15><loc_55><loc_86><loc_70></location>Von Braun, K., Boyajian, T. S., Kane, S. R., Hebb, L., van Belle, G. T., Farrington, C. C., David R. Knutson, H. A., ten Brummelaar, T. A., López-Morales, 9.119864e+2M., McAlister, H. A., Schaefer, G., Ridgway, S., Collier Cameron, A., Goldfinger, P. J.; Turner, N. H., Sturmann, L., Sturmann, J. (2012) The GJ 436 system: Directly determined astrophysical parameters of an M dwarf and implications for the transiting hot Neptune, ApJ , 753, Issue 2, article id. 171.</text>
<text><location><page_40><loc_15><loc_45><loc_86><loc_52></location>Watson, A. J., Donahue, T. M., Walker, J. C. G. (1981) The dynamics of a rapidly escaping atmosphere - Applications to the evolution of earth and Venus , Icarus , 48, 150 166.</text>
<text><location><page_40><loc_15><loc_32><loc_86><loc_41></location>Wei, Y., Fraenz, M., Dubinin, E., Woch, J., Lühr, H., Wan, W., Zong, Q.-G., Zhang, T.L., Pu, Z. Y., Fu, S. Y., Barabash, S., Lundin, R., Dandouras, I. (2012) Enhanced atmospheric oxygen outflow on Earth and Mars driven by a corotating interaction region. J. Geophys. Res ., 117, A03208.</text>
<text><location><page_40><loc_15><loc_24><loc_85><loc_28></location>Wood, B. E., Müller, H.-R., Zank, G. P., Linksky, J. L., Redfield, S. (2005) New massloss measurements from Asrospheric Ly-alpha absorption. ApJ , 628, Issue 2, L143-L146.</text>
<text><location><page_40><loc_15><loc_16><loc_86><loc_20></location>Wuchterl, G. (1993) The critical mass for protoplanets revised - Massive envelopes through convection. Icarus , 106, 323-334.</text>
<text><location><page_41><loc_15><loc_87><loc_86><loc_91></location>Yau, A. W., André, M. (1997) Sources of ion outflow in the high latitude ionosphere, Space Sci. Rev. , 37, 1-25.</text>
<text><location><page_41><loc_15><loc_79><loc_86><loc_83></location>Yelle, R. V. (2004) Aeronomy of extra-solar giant planets at small orbital distances, Icarus , 170, 167- 179.</text>
<text><location><page_41><loc_15><loc_71><loc_86><loc_75></location>Yelle, R. (2006) Corrigendum to Aeronomy of extra-solar giant planets at small orbital distances (Icarus 170 (2004) 167-179). Icarus , 183, 508.</text>
<table>
<location><page_42><loc_14><loc_78><loc_85><loc_84></location>
<caption>Table 1. Model inner boundary 'ib' atmospheric and solar wind input parameters for present-day Earth's geocorona (Prölss, 2004).Table 2 . Default stellar parameters as well as values of constants used in the simulations.</caption>
</table>
<table>
<location><page_42><loc_15><loc_47><loc_86><loc_71></location>
<caption>Table 3 . Planetary input parameters taken from Erkaev et al . (2013) for different stellar wind properties and XUV fluxes which correspond to that of the present Sun and an XUV enhancement factor of about 100 times for a low heating efficiency η = 15%.</caption>
</table>
<table>
<location><page_42><loc_15><loc_16><loc_85><loc_36></location>
<caption>TABLES</caption>
</table>
<table>
<location><page_43><loc_15><loc_64><loc_85><loc_84></location>
<caption>Table 4 . Planetary input parameters taken from Erkaev et al. (2013) for different stellar wind properties and XUV fluxes which correspond to that of the present Sun and an XUV enhancement factor of about 100 times for a higher heating efficiency η = 40%.Table 5 . Ion escape rates Lion in s -1 for a hydrogen-rich Earth-like planet and for a heating efficiency of 15 %, exposed to the XUV flux values which are 1, 10, 50 and 100 times higher than that of the present Sun. The shape of the planetary obstacle is assumed to be similar to an Earth-type magnetosphere.</caption>
</table>
<table>
<location><page_43><loc_15><loc_27><loc_88><loc_54></location>
</table>
<table>
<location><page_44><loc_15><loc_57><loc_88><loc_84></location>
<caption>Table 6 . Ion escape rates Lion in s -1 for a hydrogen-rich 'super-Earth' for a heating efficiency of 15 % and 40%, exposed to the XUV flux values which are 1, 10, 50 and 100 times higher than that of the present Sun. The shape of the planetary obstacle is assumed to be similar to an Earth-type magnetosphere.Table 7 . Ion escape rates Lion in s -1 for a hydrogen-rich Earth-like planet for a heating efficiency of 15% and 40%, exposed to the XUV flux values which are 1, 10, 50 and 100 times higher compared to that of the present Sun. The shape of the planetary obstacle is assumed to be Venus-like.</caption>
</table>
<table>
<location><page_44><loc_14><loc_18><loc_86><loc_45></location>
</table>
<table>
<location><page_45><loc_15><loc_57><loc_88><loc_84></location>
<caption>Table 8 . Ion escape rates Lion in s -1 for a hydrogen-rich 'super-Earth' for a heating efficiency of 15 % and 40%, exposed to the XUV flux values which are 1, 10, 50 and 100 times higher compared to that of the present Sun. The shape of the planetary obstacle is assumed to be Venus-like.Table 9 . Thermal ( th L ) and non-thermal ( ion L , H + ion pick-up) loss over the time span of 4.5 Gyr for a H-rich Earth-like planet and a H-rich 'super-Earth', orbiting an M dwarf in the habitable zone at 0.24 AU by considering an Earth-type magnetosphere shape for the planetary obstacle form and the low and high heating efficiency of 15% and 40 %.</caption>
</table>
<table>
<location><page_45><loc_15><loc_25><loc_85><loc_44></location>
</table>
<table>
<location><page_46><loc_15><loc_69><loc_85><loc_82></location>
<caption>Table 10 . Non-thermal ( ion L , H + ion pick-up) loss over the time span of 4.5 Gyr for an H-rich Earth-like planet and an H-rich 'super-Earth', orbiting an M dwarf in the habitable zone at 0.24 AU by considering a Venusian-type planetary obstacle shape and the low and high heating efficiency of 15% and 40 %.</caption>
</table>
<section_header_level_1><location><page_47><loc_41><loc_89><loc_60><loc_91></location>FIGURE CAPTIONS</section_header_level_1>
<text><location><page_47><loc_15><loc_79><loc_86><loc_88></location>FIG. 1 : Observed hydrogen ENAs by the IBEX spacecraft around Earth. The H ENAs count rate was integrated from 0.7-6 keV on 28 March 2009 from 04:54-15:54 UT. The peak is centered on the subsolar magnetopause and a significant ENA flux extends to ±10 R Earth (Fuselier et al ., 2010).</text>
<text><location><page_47><loc_15><loc_60><loc_86><loc_75></location>FIG. 2 . Modeling results of Earth's solar wind plasma interaction with the present-day geocorona. Green dots correspond to the solar wind protons, yellow dots represent the neutral hydrogen atoms moving with velocities below 10 km s -1 (particles which belong to the atmosphere) while the red and the blue dots represent ENAs with velocities above 10 km s -1 , moving towards and away from the Sun respectively. The dashed line denotes the magnetosphere obstacle.</text>
<text><location><page_47><loc_15><loc_37><loc_86><loc_57></location>FIG. 3 . Radial profiles for density, velocity and temperature as a function of orbital location in AU and of expected plasma properties of an ordinary stellar wind (solid lines) and during an CME event (dashed lines) on an M-type star with a mass M s ~0.45 M Sun and a rotation period 2.5 days. For the simulation of stellar wind the initial proton density at 0.1 AU n 0 = 400 cm -3 , temperature T 0 = 500 kK, and radial stellar wind velocity v r0 = 300 km s -1 were taken. Simulation of a solar-analogue CME event uses the initial proton density n 0 = 800 cm -3 , proton temperature T 0 = 1500 kK, and a radial stellar wind velocity v r0 = 600 km s -1 .</text>
<text><location><page_47><loc_15><loc_13><loc_86><loc_33></location>FIG. 4 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around an Earth-like hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig.4a corresponds to the XUV flux which is equal to that of the present Sun, the moderate stellar wind (Case I) and a lower heating efficiency of 15%. Fig.4b corresponds to the similar input parameters as in Fig.4a, but the XUV flux is 50 times higher. Fig.4c corresponds to the 10 times higher XUV flux than the present one and a heating efficiency of 15%, as well as the moderate stellar wind</text>
<text><location><page_48><loc_15><loc_87><loc_86><loc_91></location>(Case I). Fig.4d: corresponds to the similar input parameters as in Fig.4c, but for the Venus-type narrower planetary obstacle.</text>
<text><location><page_48><loc_15><loc_60><loc_86><loc_83></location>FIG. 5 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around a 'super-Earth' hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig5a: the XUV flux is 50 times higher than that of the present Sun, heating efficiency of 15%, the planet is exposed to a moderate stellar wind (Case I). Fig5b: similar conditions except for heating efficiency of 40%. Fig.5c: the XUV flux is 100 times higher compared to that of the present Sun, 40% heating efficiency, moderate stellar wind (Case I). Fig.5d: similar input parameters as in Fig.5c, but exposed to a faster and denser stellar plasma flow (case II).</text>
<text><location><page_48><loc_15><loc_45><loc_86><loc_57></location>FIG. 6 . Illustration of the soft X-ray flux time-dependence for an M dwarf star with 0.4 solar masses (dashed line) and the same curve for a Sun-like star (solid line) in the corresponding HZs normalized by the present Sun flux. The M star within this mass range remains about 200 Myr longer in its activity saturation phase compared to a solar like G star.</text>
<figure>
<location><page_49><loc_21><loc_51><loc_51><loc_83></location>
<caption>IBEX-Hi (0.7 6 kev) 2009-03-28, FIG 1 15.54 UTFIG 2</caption>
</figure>
<figure>
<location><page_49><loc_15><loc_10><loc_63><loc_46></location>
</figure>
<figure>
<location><page_50><loc_14><loc_49><loc_86><loc_88></location>
<caption>FIG 3</caption>
</figure>
<figure>
<location><page_51><loc_15><loc_33><loc_83><loc_88></location>
<caption>FIG 4</caption>
</figure>
<figure>
<location><page_52><loc_16><loc_31><loc_85><loc_88></location>
<caption>FIG 5</caption>
</figure>
<figure>
<location><page_53><loc_15><loc_56><loc_68><loc_86></location>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "We study the interactions between the stellar wind plasma flow of a typical M star, such as GJ 436, and hydrogen-rich upper atmospheres of an Earth-like planet and a 'superEarth' with the radius of 2 R Earth and a mass of 10 M Earth, located within the habitable zone at ~0.24 AU. We investigate the formation of extended atomic hydrogen coronae under the influences of the stellar XUV flux (soft X-rays and EUV), stellar wind density and velocity, shape of a planetary obstacle (e.g., magnetosphere, ionopause), and the loss of planetary pick-up ions on the evolution of hydrogen-dominated upper atmospheres. Stellar XUV fluxes which are 1, 10, 50 and 100 times higher compared to that of the present-day Sun are considered and the formation of high-energy neutral hydrogen clouds around the planets due to the charge-exchange reaction under various stellar conditions have been modeled. Charge-exchange between stellar wind protons with planetary hydrogen atoms, and photoionization, leads to the production of initially cold ions of planetary origin. We found that the ion production rates for the studied planets can vary over a wide range, from ~ 25 10 0 . 1 s -1 to ~ 30 10 3 . 5 s -1 , depending on the stellar wind conditions and the assumed XUV exposure of the upper atmosphere. Our findings indicate that most likely the majority of these planetary ions are picked up by the stellar wind and lost from the planet. Finally, we estimate the long-time non-thermal ion pick-up escape for the studied planets and compare them with the thermal escape. According to our estimates, non-thermal escape of picked up ionized hydrogen atoms over a planet's lifetime varies between ~0.4 Earth ocean equivalent amounts of hydrogen (EOH) to < 3 EOH and usually is several times smaller in comparison to the thermal atmospheric escape rates. Keywords: stellar activity, low mass stars, early atmospheres, Earth-like exoplanets, ENAs, ion escape, habitability",
"pages": [
2
]
},
{
"title": "XUV exposed, non-hydrostatic hydrogen-rich upper atmospheres of terrestrial planets II: Hydrogen coronae and ion escape",
"content": "Kristina G. Kislyakova 1,2 , Helmut Lammer 1 , Mats Holmström 3 , Mykhaylo Panchenko 1 , Petra Odert 1,2 , Nikolai V. Erkaev 4 , Martin Leitzinger 2 , Maxim L. Khodachenko 1 , Yuri N. Kulikov 5 , Manuel Güdel 6 , Arnold Hanslmeier 2 1 Austrian Academy of Sciences, Space Research Institute, Schmiedlstr. 6, A-8042 Graz, Austria ([email protected], [email protected], [email protected], [email protected], [email protected]) 2 Institute for Physics, University of Graz, Universitätsplatz 5, A-8010 Graz, Austria ([email protected], [email protected]) 3 Swedish Institute of Space Physics, P.O. Box 812, SE-98128 Kiruna, Sweden ([email protected]) 4 Institute of Computational Modelling, Siberian Division of Russian Academy of Sciences, Akademgorodok 28/44 660036 Krasnoyarsk, Russian Federation ([email protected]) 5 Polar Geophysical Institute (PGI), Russian Academy of Sciences, Khalturina Str. 15, Murmansk, 183010, Russian Federation ([email protected]) 6 Institute for Astrophysics, University of Vienna, Türkenschanzstr. 17, 1180, Austria ([email protected]) Corresponding Authors: Kristina G. Kislyakova E-mail: [email protected] Austrian Academy of Sciences Space Research Institute Schmiedlstr. 6, A-8042 Graz Austria Submitted to ASTROBIOLOGY",
"pages": [
1
]
},
{
"title": "1. INTRODUCTION",
"content": "Recent discoveries of so-called low density 'super-Earths' by various ground- and spacebased exoplanet-transit surveys indicate large populations of volatile-rich big rocky planets. Findings from ESOs High Accuracy Radial velocity Planetary Search project (HARPS), and from NASAs Kepler space observatory, revealed that planets which are slightly larger and more massive compared to the Earth may be very common in the Universe. From the available statistics and the discovery of Kepler-22b, a 'super-Earth' with the size of about 2.38 ± 0.13REarth within the habitable zone (HZ) of a Sun-type star, one can expect that planets orbiting within the HZ should be frequent in the Universe and should also orbit cooler, lower mass M dwarfs. Approximately 100 of them are found in the immediate neighborhood of the Sun (Scalo et al. 2007; Bonfils et al. 2011). These earlier estimations are now supported by a recent study by Dressing and Charbonneau (2013), which used optical and near-infrared photometry from the Kepler Input Catalog to estimate the occurrence rate of Earth-like planets orbiting dwarf stars. The estimation of Dressing and Charbonneau (2013), from the 248 early M dwarfs within 10 parsecs of the Sun, shows that there should be at least 9 Earth-size planets in their habitable zones. Moreover, from the radius-mass relation and the resulting density of discovered 'super-Earths', one finds that these bodies probably have rocky cores but are surrounded by significant H/He and/or H2O envelopes. These findings are in agreement with recent theoretical studies, which suggest that small planets are not necessarily rocky Earth-like bodies (e.g., Wuchterl 1993; Kuchner 2003; Léger et al . 2004; Ikoma and Hory 2012; Elkins-Tanton 2011; Lammer, 2012; Lammer et al. 2011a). For explaining the mean density of Kepler 11d, Kepler 11e, and Kepler 11f these 'super-Earths'' require dense H/He envelopes, similar to Uranus and Neptune, while Kepler-11b and 11c may have also additional H2O to their H/He gas envelopes (Lissauer et al . 2011), and GJ 1214b (Charbonneau et al. , 2009) or 55Cnc e (Endl et al. , 2012) may contain a huge amount of H2O. If Earth-like and 'super-Earth'- type exoplanets can accumulate hydrogen from the nebula gas of an equivalent amount of 100 to 1000, and even up to 10 4 times, that of an Earth ocean depends on the nebula dissipation time, the formation time of the protoplanet, its luminosity, and nebula characteristics such as grain depletion factors, etc. (e.g., Mizuno et al ., 1978; Hayashi et al ., 1979; Ikoma and Genda, 2006; Rafikov, 2006). Although Solar System planets such as Venus, Earth and Mars lost their nebula-based hydrogen envelopes during the first 100 Myr after their origin, or never accumulated such huge amounts due to step-wise accretion after the nebula gas disappeared, terrestrial planets in other systems evolve under different conditions and may capture such a dense protoatmosphere which they may not lose during the extreme active period of their host stars. To understand how frequent 'rocky' terrestrial planets really are, more observations are certainly needed. From the available statistics one can conclude that Earth-analogue class I habitats (Lammer et al. , 2009a; Lammer, 2013) have to be",
"pages": [
2,
3,
4
]
},
{
"title": "and",
"content": "The question if more massive 'super-Earths' can maintain plate tectonics over time spans of several Gyr is controversial (e.g., Valencia et al. , 2007; van Heck and Tackley, 2011; Korenaga, 2010). However, in this work we will not discuss the pro and contra about geophysical processes, but focus on the stellar wind erosion of captured H/He envelopes, orand? the hydrogen content of outgassed hydrogen-rich steam atmospheres, because the proto-atmosphere escape determines if a planet will evolve to an Earth-like habitat or may remain as a mini-Neptune. As it is shown by Erkaev et al. (2013) (part I of this study), depending on the availability of possible IR-cooling molecules and the planets average density, hydrogenrich 'super-Earths' orbiting inside the HZ will experience hydrodynamic blow-off only for XUV fluxes several 10 times higher compared to today's Sun. Most of their lifetime the upper atmospheres of these planets will experience strong Jeans escape which is still weaker compared to blow-off, so that they may not lose efficiently their dense hydrogen envelopes. Jeans escape is the classical thermal escape mechanism based on the fact that the atmospheric particles have velocities according to the Maxwell distribution. Individual particles in the high tail of the distribution may reach escape velocity at the exobase altitude, where the mean free path is comparable to the scale height, so that they can escape from the planet's atmosphere. When the thermosphere temperature rises due to heating by the stellar XUV radiation, the number of these energetic particles increases and the atmosphere finally reaches the state when the majority of the particles have velocities equal to or exceeding the escape velocity. In this case the atmosphere is not hydrostatic anymore, and starts to expand similar to the Parker-type solar corona. This mechanism is called blow-off and leads to a stronger escape in comparison to the Jeans mechanism. The blow-off stage is more easily reached at less massive hydrogen-rich planets with mass equal to that of the Earth. These planets experience hydrodynamic blow-off for much longer, and change from the blow-off regime to the Jeans-type escape for XUV fluxes which are < 10 times of today's Sun. Because of XUV heating and expansion of their upper atmospheres, both of our test planets should produce extended exospheres or hydrogen coronae distributed above possible magnetic obstacles defined by intrinsic or induced magnetic fields. In such cases the hydrogen-rich upper atmosphere will not be protected by possible magnetospheres like on present-day Earth, but could be eroded by the stellar wind plasma flow and lost from the planet in the form of ions (Erkaev et al ., 2005; Lammer et al. , 2007). Besides thermal escape from the hydrogen-dominated upper atmosphere of the two considered test-planets (Erkaev et al ., 2013), briefly discussed above, one can expect that non-thermal atmospheric escape processes will also contribute to the losses. Nonthermal escape processes can be separated in ion escape and photochemical, as well as kinetic, processes which accelerate atoms beyond escape energy. Ions can escape from an upper atmosphere if the exosphere is not protected by a strong magnetic field and stretches above the magnetopause. In such a case exospheric neutral atoms can interact with the host stars solar/stellar plasma (i.e., winds, CMEs) environment. The hydrogen atoms which flow upward from the lower thermosphere will be ionized by the stellar radiation, electron impact or charge exchange and then accelerated by electric fields within the solar/stellar wind plasma flow around the planetary obstacle (i.e. ionopause, magnetopause), so that they are finally picked up and lost form the planet's gravity field (e.g., Lammer et al ., 2007; Ma and Nagy, 2007; Lammer, 2013). From space missions to non- or weakly magnetized planets such as Venus and/or Mars it is known that planetary ions can also be detached from an ionopause by plasma instabilities in the form of ionospheric clouds (Terada et al ., 2002; Penz et al. , 2004; Möstl et al ., 2011), or by momentum transport triggered outflow through the planetary tail. On Earth ions outflow also over Polar Regions along open magnetic field lines (Lundin et al ., 2007; Yau and André, 1997; Wei et al ., 2012). From the analysis of the available ion escape data from Venus and Mars by the ASPERA instruments on board of Venus Express and Mars Express, as well as from theoretical models, one can conclude that ion pick-up is a very dominant permanently acting non-thermal ion escape process, and most likely more efficient compared to the sporadic losses triggered by plasma instabilities or outflow through the planets tail. However, there may be extreme solar events which can enhance the ion outflow sporadically by cool ion outflow or plasma instabilities. Non-thermal escape processes of neutral atoms are caused by sputtering of atmospheric neutral atoms, photochemical processes such as dissociative recombination, and charge exchange. Direct escape by sputtering is only a relevant process for low mass bodies which have a mass ≤ Mars. utHowever, even in the case of Mars one can expect that sputter loss rates are an order of magnitude lower compared for instance to ion pickup (e.g., Leblanc and Johnson, 2002; Chassefière and Leblanc, 2004; Lammer et al ., 2013). Direct escape of heavy neutral atoms, such as O and C, caused by photochemical processes is expected to be higher compared to ion escape from Mars (e.g., Krestyanikova and Shematovich, 2005; Chaufray et al., 2007; 2006; Fox and Hać, 2009; Lammer et al., 2013) but negligible or lower at more massive planets such as Venus (Gröller et al., 2010; 2012) or the Earth. Lighter atoms such as atomic hydrogen can also escape directly from more massive planets with escape rates lower or comparable to ion escape. Theoretical models which studied the photochemical escape rates of H atoms (Shematovich, 2010) and ion pick-up ion escape rates (Erkaev et al ., 2005) from the hot Jupiter HD 208459b indicate comparable loss rates of the order of ≤ 10 9 g s -1 , which are an order of magnitude lower compared to the modeled thermal escape (e.g., Yelle, 2004; 2006; Tian et al ., 2005a; Penz et al ., 2008b; García Muñoz, 2007; Murray-Clay et al. , 2009; Linsky et al ., 2010; Koskinen et al ., 2012). From the brief overview on various non-thermal atmospheric escape processes, one can conclude that stellar wind induced ion erosion from XUV-heated and extended hydrogen-rich thermospheres (Erkaev et al ., 2013), where H atoms will most likely not be protected by a possible magnetosphere, so-called ion pick-up will be one of the most efficient non-thermal atmospheric escape process. Because of many unknowns related to minor atmospheric species in exoplanet atmospheres, as well as magnetic field properties, a study of more complex but most likely less effective processes, such as cool ion or polar outflow and photochemical non-thermal escape processes which are not even well understood at Solar System planets including the Earth, would yield highly speculative results. Therefore, in this study we focus on the modeling of the stellar wind plasma interaction, related ion production rates via charge-exchange and photoionization, and escape estimates of planetary pick-up ions from XUV exposed upper atmospheres which originate from hydrogen-rich thermospheres of an Earth-like ( R pl=1 R Earth, M pl=1 M Earth) planet in comparison with a 'super-Earth' ( R pl=2 R Earth, M pl=10 M Earth). For reasons of comparative escape studies between thermal and non-thermal ion pick-up, we study the same test planets as investigated by Erkaev et al. (2013) within an orbit of a typical HZ of an M star with the size and mass of ~0.45 R Sun. For the host star of our test planets we use the well observed dwarf star GJ 436 (Ehrenreich et al. , 2011; von Braun et al. , 2012, France et al. , 2012) as a proxy. So far the formation of such extended hydrogen coronae was only addressed in a brief way in Lammer et al. (2011a; 2011b), but never modeled in detail. In this study we apply a coupled Direct Simulation Monte Carlo (DSMC) upper atmosphere - stellar wind plasma interaction model (Holmström et al. , 2008; Ekenbäck et al. , 2010) to the results of Erkaev et al. (2012). In Sect. 2 we describe the DSMC model, which is used for the calculation of the exosphere and related hydrogen coronae, as well as the coupled solar/stellar wind plasma upper atmosphere interaction model. We validate our model by applying it to the Earth's geocorona and comparing the simulation results with the present-day exosphere hydrogen density and energetic neutral atom (ENA) observations by NASAs Interstellar Boundary Explorer (IBEX) satellite near the magnetopause boundary at ~10 R Earth. After validating our model for the geocorona of present-day Earth, in Sect. 3 we describe the radiation and plasma parameters of our chosen M-type host star proxy, Gliese 436. In Sect. 4 we present the modeling results for the extended hydrogen coronae. In Sect. 4.1 the results of the stellar wind plasma interaction and the production of ENAs are shown as well as related planetary hydrogen ion pick-up escape rates as a function of the XUV flux values from 1 to 100 times that of today's Sun. The atmospheric ion escape rates are compared with the thermal hydrogen neutral loss rates modeled by Erkaev et al. (2012) in Section 4.2. In Section 4.3 we estimate the possible mass loss of hydrogen ions during the planetary lifetime and discuss the implications of our findings for the evolution of Earthlike and more massive 'super-Earths'. Section 5 summarizes the findings of our study.",
"pages": [
4,
5,
6,
7,
8
]
},
{
"title": "2 STELLAR WIND-UPPER ATMOSPHERE INTERACTION",
"content": "As shown by previous studies of Watson et al. (1981), Kasting and Pollack (1983), Tian et al. (2005b; 2008a; 2008b), Volkov et al. (2011), and Erkaev et al. (2013), hydrogen-rich terrestrial planets experience XUV-heated and hydrodynamically expanding non-hydrostatic upper atmosphere conditions. Depending on the particular environment (e.g., XUV flux, orbital distance, availability of IR-cooling molecules, the planet's average density, etc.) the results of these studies indicate that such planets can expand their exobase level, which separates the collision dominated atmosphere from the collisionless region to distances from a few R pl up to more than 20 R pl. As a result of such an expansion of the upper atmosphere an intrinsic planetary magnetic field will most likely not protect the exosphere against the stellar wind plasma flow (Lichtenegger et al ., 2010; Lammer, 2012; Lammer et al ., 2011a). Due to the interaction between the stellar wind plasma flow and the XUV-heated non-hydrostatic upper neutral atmosphere of the planet, energetic neutral atoms (ENAs) are produced. ENAs originate due to charge-exchange when an electron is transferred from a planetary neutral atom to a stellar wind proton which then becomes an ENA. This interaction process between the stellar wind plasma and the upper atmosphere plays a significant role in the ion erosion of upper planetary atmospheres (e.g., Lundin et al. , 2007; Lammer, 2013). The production of ENAs after the interaction of stellar wind protons via charge exchange with various upper atmosphere species is described by the reactions in eq. (1-3). After its production an ENA continues to travel with the initial velocity and energy of the stellar wind proton. The atmospheric atom in turn becomes an initially cold ion which can afterwards be lost from the atmosphere due to the ion pick-up process (Lammer, 2013). In the current study we focus our attention only on the reaction shown in eq. (1) which will dominate the stellar wind interaction with planetary hydrogen coronae around hydrogen-rich terrestrial planets.",
"pages": [
8,
9
]
},
{
"title": "2.1 Model description",
"content": "In the current study the plasma interaction between the stellar wind and the upper atmosphere of the Earth-like planet and 'super-Earth' is modeled applying a Direct Simulation Monte Carlo (DSMC) upper atmosphere-exosphere particle model which is coupled with a stellar wind particle interaction code. The 3D model is described in detail in Holmström et al. (2008) and Ekenbäck et al. (2010) and includes stellar wind protons and planetary hydrogen atoms. The latter are launched into the simulation domain from the upper atmosphere. The applied collision cross sections for hydrogen atoms, σ H-H, and for protons and hydrogen atoms, σ H+-H, are 10 -17 cm 2 and 2 × 10 -15 cm 2 (Ekenbäck et al ., 2010) respectively. Charge exchange between stellar wind protons and exospheric hydrogen atoms takes place outside a conic shaped obstacle that represents the magnetoionopause of the studied planet. Stellar wind protons that have charge-exchanged according to the reaction shown in eq. (1) become ENAs. Besides of the charge-exchange reaction, the model includes gravitation of the planet and tidal effects as well as scattering by atmospheric atoms of UV photons (radiation pressure) and photoionization by stellar photons. Inclusion of the tidalgenerating potential into the equations leads to the extension of the atmosphere toward and backward from the host star, and in extreme cases to Roche lobe overflow. Nevertheless, these effects are important for 'hot Jupiters' which are located at very close distance to their host stars, and do not play a significant role for the test planets we consider in the present study. All collisions are modeled using a DSMC algorithm (Holmström et al., 2008; Ekenbäck et al., 2010). The main code uses the FLASH software developed at the University of Chicago which provides adaptive grids and is fully parallelized (Fryxell et al. , 2000). The coordinate system is centered at the center of the planet with mass pl M , the 1 x -axis is pointing towards the center of mass of the system, the 3 x -axis is parallel to the direction of the angular velocity of rotation , and the 2 x -axis points in the opposite direction to the planet's velocity. St M is the mass of the planets host star. Tidal potential, Coriolis and centrifugal forces, as well as the gravitation of the star and planet acting on a hydrogen neutral atom, are included in the code in the following way (Chandrasekhar, 1963) Here i v are the components of the velocity vector of a particle, G is Newton's gravitational constant, R the distance between the centers of mass, the Levi-Civita symbol, and 3 R GM St . The first term in the right-hand side of the eq. (4) represents the centrifugal force, the second is the tidal-generating potential, the third the gravitation of the planet's host star and the planet while the last term stands for the Coriolis force. The self-gravitational potential of a particle is neglected. Charge exchange reactions between a neutral planetary hydrogen atom and a stellar wind proton may take place outside the obstacle representing a magneto- or ionopause Here s R stands for the magnetosphere or planetary obstacle stand-off distance and t R the width of the obstacle. Since the obstacle shape and location depend strongly on the planetary magnetic field strength, one may model the interaction of the stellar wind with magnetized as well as with non- or weakly magnetized planets by the appropriate choice of s R and t R .",
"pages": [
9,
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},
{
"title": "2.2 Exosphere modeling of Earth's observed atomic hydrogen geocorona",
"content": "ENAs have been observed around all Solar System planets where a spacecraft was equipped with a corresponding instrument (e.g., Futaana et al ., 2006; Galli et al. , 2008; Lammer et al ., 2011a; 2011b). As shown in Fig. 1, the Interstellar Boundary Explorer (IBEX) satellite recently observed an ENA formation zone around Earth's subsolar magnetopause stand-off distance, which is located at 10 R Earth from the planet's center (Fuselier et al. , 2010). Before we apply our model to hydrogen-rich exoplanets, we validate it by reproducing the geocorona and recent ENA observations (Fuselier et al. 2010) around the Earth's magnetopause by the NASAs IBEX satellite of present-day Earth. Fig. 2 shows our modeling results for Earth's geocorona interacting with the present-day solar wind by taking all parameters of Earth's exosphere as given in Table 1 as an input. The average neutral hydrogen atom density at the magnetopause level obtained from our model is estimated to be ~8 cm -3 at the distance of ~10 R Earth. This density value coincides very well with the exospheric number densities inferred from the IBEX observations of ENAs near the magnetopause. In the case of the IBEX observation at March 28 2009, the computed and observed proton fluxes show an exosphere hydrogen density at a geocentric distance of ~10 R Earth of ~4 - 11 cm -3 (Fuselier et al ., 2010). The estimates of the modeled ENA flux are in good agreement with the observed flux as well, predicting the flux of approximately 600 (cm² s sr keV) -1 . This value falls inside the observed ENA interval of ~530 - 2300 (cm² s sr keV) -1 (Fuselier et al ., 2010). The IBEX observation and our model validation can also be seen as a confirmation that under extreme radiation and plasma environments of the young Sun or more active stars a huge ENA formation zone, as suggested by Chassefière (1996) and Lammer et al. (2011; 2012), should be produced in the stellar wind interaction region of a hydrogen-rich extended upper atmosphere of an Earth-size planet when the exosphere density near the magnetopause is more than 10 6 times larger than that observed at present-day Earth. In the following sections we describe the input parameters and our applied exosphere and ENA models to the XUV exposed hydrogen-rich Earth-size test planets.",
"pages": [
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},
{
"title": "3. GLIESE 436: A HOST STAR PROXY FOR HYDROGEN-RICH TERRESTRIAL TEST PLANETS",
"content": "3.1 The radiation environment of Gliese 436 Recently Ehrenreich et al. (2011) observed with the Hubble Space Telescope Imaging Spectrograph (HST/STIS) the Lyman-α emission (1215.67 Å) of neutral hydrogen atoms from the low mass M star, GJ 436. Because this emission is a main contributor to the ultraviolet flux it can also be used as a main tracer in studies of thermospheric heating, thermal escape, and possible absorption by extended hydrogen coronae and/or ENAs (e.g. Vidal-Madjar et al. , 2003; Holmström et al ., 2008; Ekenbäck et al ., 2010; Ben-Jaffel and Hosseini, 2010; Lecavelier des Etangs et al ., 2010; Lammer et al. , 2011b; Ehrenreich et al ., 2012, Lammer, 2013) during transit observations with ultraviolet transmission spectroscopy. We use GJ 436 as a typical M-type host star for our test-planet parameter studies. GJ 436 is a M2.5 dwarf star which is 10.2 pc away from the Sun. The dwarf star hosts a transiting 'hot Neptune' at an orbital distance of about 0.03 AU (Butler et al. , 2004; Gillon et al. , 2007). We adopt values for stellar mass and radius of 0.45 MSun and 0.45 RSun, respectively, which are consistent with several independent parameter determinations of GJ 436 (Torres, 2007; Maness et al. , 2007; von Braun et al. , 2012). The location of the habitable zone (HZ) is calculated following Selsis et al. (2007). As their relations are only valid for effective temperatures down to 3700 K, this value is used instead of the true temperature of GJ 436, which is slightly lower (3400-3600 K; Torres 2007; von Braun et al. 2012). Further, we adopt a bolometric luminosity of 0.026 LSun (Torres, 2007). This leads to a HZ extent of 0.12-0.36 AU assuming the limit of 50% clouds, as typical for the Earth. Hence, the center of the HZ is located at 0.24 AU, which we adopt as the orbit of our hypothetical exo-Earth. The orbital period of an Earth-analog planet within the HZ of GJ 436 corresponds to approximately 63.7 days, the orbital velocity to about 41 km s -1 , and the angular velocity to 1.14·10 -6 rad s -1 . The age of GJ 436 is about 6±5 Gyr and is not well constrained (Torres, 2007). However, the rotation period of 48 days (Demory et al. , 2007) yields an estimated age of 2.5-3 Gyr (Barnes, 2007; Engle and Guinan, 2011). This estimation is in agreement with the lack of chromospheric activity indicated by the presence of Hα in absorption spectra. GJ 436 has been detected by the ROSAT All-Sky Survey, which revealed an Xray luminosity of log LX = 27.13 erg s -1 . Recent observations by the XMM-Newton spacecraft yielded a smaller value of only ~25.96 erg s -1 (Sanz-Forcada et al. , 2011). We adopt the latter result because of the longer exposure time and better S/N of the XMMNewton observations compared to ROSAT data. Using coronal models, Sanz-Forcada et al . (2011) extrapolated the stellar emission in the total XUV range (5 - 920Å) and found log L XUV=26.92 erg s -1 . Adopting this value and scaling it to the HZ center at 0.24 AU, we estimate an XUV flux of about 5.14 erg cm -2 s -1 , comparable to the present solar XUV flux at 1 AU of 4.64 erg cm -2 s -1 (Ribas et al. , 2005). In the past, the stellar XUV flux, which was emitted from GJ 436 was certainly higher. The high-energy emission of young M dwarfs is saturated at log( L X/ L bol)~ -3 (e.g. Scalo et al ., 2007), hence the maximum possible log( L X) for GJ 436 is ~29 erg s -1 . Assuming that the XUV emission of young stars occurs predominantly in X-rays because of their hotter coronae, the maximum XUV flux at the Earth-equivalent orbit around GJ 436 was roughly 700 erg cm -2 s -1 , or ~150 F XUV,now. Lyman-alpha emission of GJ 436 was detected by Ehrenreich et al. (2011) using HST/STIS observations. They reconstructed the intrinsic stellar emission by correcting for interstellar medium (ISM) absorption, leading to an apparent flux observed at Earth of ~2.7±0.7 × 10 -13 erg cm -2 s -1 . Scaled to the HZ center, this yields ~20.51 erg cm -2 s -1 , a factor of ~3.3 larger than the present solar value at 1 AU of 6.19 erg cm -2 s -1 (Ribas et al ., 2005). Recently, France et al. (2013) reconstructed the intrinsic Lyman-alpha flux of GJ 436 by using a different approach. They obtained a value of 3.5 × 10 -13 erg cm -2 s -1 with an uncertainty of about 15 - 30 %, which is slightly higher than the value given by Ehrenreich et al. (2011), but is consistent with the errors. The relevant stellar parameters and the measured radiation properties used in the model simulations for various assumed XUV flux values of a Gliese 436-type M dwarf are shown in Table 2. The photoionization rates corresponding to the four XUV flux enhancement factors were scaled from the average present solar value at Earth (1.1 × 10 -7 s -1 ; Hodges, 1994, Bzowski, 2008) to the corresponding enhancement factors. The photoionization rate is usually calculated as the product of ionization cross-section and spectral flux integrated over all wavelengths below the ionization threshold. Since full M star XUV spectra for different activity levels are currently not available, we assume that the present spectral energy distribution is equal to the solar one and scale it up by the constant factors given in Table 2. The UV absorption rates correspond to the product of the photon flux at the center of the Lyman-alpha line and the total absorption cross-section (5.47 × 10 -15 cm 2 Å; e.g. Quémerais, 2006). Adopting the reconstructed intrinsic line profile of Ehrenreich et al. (2011), the present value of the photon flux at the HZ center of GJ 436 is estimated to be ~6.9 × 10 -3 s -1 .. To scale the Lyman-alpha flux and, hence, the absorption rate to higher XUV flux emission levels, we use the scaling between X-rays and Lyman-α from Ehrenreich et al. (2011). This assumes that L X/ L bol ≈ L XUV/ L bol and that the central Lyman-α flux scales approximately as the integrated line emission. The resulting absorption rates are also shown in Table 2.",
"pages": [
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},
{
"title": "3.2 Expected stellar wind plasma properties",
"content": "Depending on the mass, size and resulting luminosity of the host star, the corresponding scaled HZ location in the case of GJ 436 is at 0.24 AU. This is a much closer orbital distance compared to that of the Earth (1 AU). As pointed out by Khodachenko et al. (2007), at orbital locations < 0.5 AU the flow of dense plasma related to stellar winds and coronal mass ejections (CMEs), energetic particle fluxes and XUV radiation cannot be neglected. Depending on the stand-off distance of the planetary obstacle which forms when the stellar plasma flow is deflected around the planet, previous test particle model results of Lammer et al. (2007) indicate that CO2-rich Earth-like exoplanets having no or only weak magnetic moments may lose from tens to hundreds of bars of atmospheric pressure, or even their whole atmospheres, due to the CME induced O + ion pick-up at orbital distances ≤ 0.2 AU. Due to the uncertainties on the mass loss and related plasma outflow from M dwarfs, we assume in our study, as in Khodachenko et al. (2007) and Lammer et al . (2007), the plasma environment close to the stars obtained from solar observations. There exist a limited number of measurements of the mass loss rates for M stars (Wood et al., 2005, Ehrenreich et al. , 2011), which in principle may be used for estimation of specific stellar wind density and velocity. For these stars the mass loss rates are comparable or less than the mass loss rate of the Sun. At the same time, for the Sun we have a much better knowledge of the distribution and evolution of active solar regions and of the mass outflow in the form of solar wind and CMEs, which we use in the present study. Note that stellar wind density and/or velocity lower than the solar (assumed) values would reduce the portion of the produced and picked up ions. Such a reduction would not change our main conclusion that the ion pick-up loss makes up only several percent of the thermal loss, and the further results can be considered as an upper limit for ion pickup near an M dwarf like Gliese 436. For the accurate study of stellar-planetary interactions one needs a reliable model which can simulate the propagation and evolution of the stellar wind plasma. For modeling the propagation and evolution of the stellar wind we use the Versatile Advection Code (VAC) (Toth, 1996). This model is able to simulate spatial and temporal evolution of the solar/stellar wind, as well as CMEs, from orbital distances ≥0.14 AU. It/The model includes a self-consistent Parker-type co-rotating magnetic field, and is based on the solution of the set of the ideal (non-resistive) non-relativistic magnetohydrodynamic equations (Toth, 1996). We use a spherical uniform computation domain, which occupies a radial distance region between 0.14 < R < 1 AU. The stellar wind in the model flows through the inner boundary of the computation domain at a semi-major axis location d = 0.14 AU and propagates out through the outer radial boundary at d = 1 AU. A self-consistent expanding stellar wind plasma flow under the conditions of a frozen-in, co-rotating, Parker-type, spiral magnetic field is numerically simulated (Odstrčil et al ., 1999; Rucker et al. , 2008). The typical parameters of the expected flow of the stellar wind plasma at d = 0.14 AU are imposed along the inner radial boundary (Odstrčil et al ., 1999) with an initial proton concentration n 0 = 500 cm -3 , stellar wind proton temperature, T 0 = 500 kK, and a radial stellar wind velocity v r0 = 300 km s -1 . For investigating the propagation of CMEs, in a second step the simulation of a CME cloud with an initial proton density n 0 = 1000 cm -3 , proton temperature, T 0 = 1700 kK, and a radial stellar wind velocity v r0 = 600 km s -1 is imposed at the inner boundary of the computation domain as a time-dependent injection of hot and dense plasma into the ambient stellar wind (Odstrčil et al ., 1999; Odstrčil et al. , 2004). Fig. 3 shows radial profiles of the maximum values of plasma parameters ( n , v r, T ) during a solar analogue CME event (dashed lines, Case II) for a typical M-star with mass M s ~ 0.45 M Sun and a rotation period 2.5 days, and those for the stellar wind itself (solid lines Case I). Therefore, in the stellar wind plasma interaction modeling with the upper atmosphere, described below, two types of stellar plasma parameters representing the lower (Case I) and upper limit (Case II) conditions at the HZ location of our test planets at 0.24 AU were used as inputs: Here n sw corresponds to stellar wind concentration, v sw denotes its bulk velocity and T sw stands for the stellar wind temperature. These values cover the predicted range for the expected stellar wind plasma parameters of GJ 436 at the HZ of the system. The upper limit (Case II) can also be considered as a proxy for modeling of frequent CME events in the system when the next CME event hits the planet immediately after the previous one. We can estimate the recovery time of the planetary atmosphere after the CME event on a very simple way. Since the test planets considered in the article are not magnetized, we assume that the recovery speed coincides with the sound speed (or the speed of slow magnetoacoustic wave), so that 2 / 1 / H exo B t s t CME m T k R c R where t R is the obstacle width, 3 / 5 is the ratio of the specific heats, B k is the Boltzmann constant, H m is the mass of a hydrogen atom and exo T is the exobase temperature. Taking the parameters from Tables 3 and 4 and depending on the characteristic size of the obstacle and the temperature, this time varies between approximately 7 and 14 hours for the Earth-type planet and 64 and 80 hours for the 'super-Earth'. The next section is dedicated to the discussion of the obtained results and presents also the ion production rates for the hydrogen-rich Earth-like planet and the 'super-Earth'.",
"pages": [
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},
{
"title": "4. HYDROGEN EXOSPHERES, ENA PRODUCTION AND ION ESCAPE",
"content": "In the following section we study the modification of the extended hydrogen exosphere due to the interaction of it with the stellar XUV and plasma flux. Because our hydrogenrich test-planets orbit within a typical M-star HZ at ~0.24 AU they will be affected by tides. As it was discussed in Khodachenko et al. (2007) tides arise because of the finite extension of the planetary body in the inhomogeneous gravitational field of its host star so that the continuous action of the tides will reduce the planetary rotation rate or may result in a synchronous rotation (Grießmeier et al. , 2005). The intrinsic magnetic field of a terrestrial planet is an essential factor for planetary protection from the ion pick-up atmosphere loss process. As shown in Khodachenko et al. (2007) and Lammer et al . (2007), because of the close orbital location within M-star HZs, the magnetosphere field of a terrestrial planet is more compressed due to the denser stellar wind impact compared with that of the solar wind at present-day Earth at 1 AU. In view of this fact the radial distance of the extended exobase of an XUV heated hydrogen rich upper atmosphere will most likely coincide with the planetary magnetopause or ionopause distance (e.g., Lammer et al ., 2009a; Lammer et al ., 2012, Lammer, 2013).",
"pages": [
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},
{
"title": "4.1 Input parameters and modeling results",
"content": "As it was briefly discussed in Sect. 3.2, the magnetic moments of terrestrial planets, and especially that of 'super-Earths' within close orbital distances, are expected to be weak (e.g., Gaidos et al ., 2010; Tachinami et al ., 2011; Morad et al ., 2011; Stamenkovic' et al., 2011Stamenkovi'c et al., 2012). This would lead to magnetoshperes or ionospheres which are compressed towards the planet's expanded non-hydrostatic upper atmosphere by the strong dynamic ram pressure of the dense stellar wind plasma. On the other hand if the exobase level expands beyond several planetary radii one can also expect that an Earth-type magnetosphere will not protect the exosphere (Fig. 5: Lammer et al ., 2007; Fig. 6 right panel: Lammer et al ., 2011a). Taking this considerations into account, the planetary obstacle most likely is located very close above the exobase level (Lammer et al. 2009b). Because the shape of the planetary obstacle affects the ENA production and resulting loss of planetary hydrogen ions, we study also the influence of the obstacle width on the ion production rate and the upper atmosphere erosion. In the first case the magnetic obstacle width t R in the eq. (5) was assumed to be 1.5 times greater than the magnetopause distance. This relation and its resulting obstacle shape is close to the observed magnetosphere of the present-day Earth and may occur if the planet has an intrinsic magnetic dynamo. In the second case we choose t s R R so that it resembles more a Venus-type planetary obstacle which may correspond to a planet with no magnetic field, or only a very weak dynamo. By decreasing of the planetary obstacle width the ion production will significantly increase, so that a terrestrial planet with a Venus-type obstacle, where t s R R , may lose larger amounts of atmospheric gas in ionized form (see Sect. 4.2). In the present study we do not specify the magnetic moment of a planet, but only chose a magnetospheric obstacle. For illustrating the differences between the stellar wind plasma interaction with a hydrogen-rich terrestrial planet which is exposed to both a weak XUV flux and an extremely strong one, we irradiate the two test-planets with the XUV flux of the present Sun (1 XUV) and with a 100 times higher XUV flux (100 XUV). Moreover, we investigate for these two XUV flux cases several stellar wind and obstacle scenarios. The main input parameters at the inner boundary of our simulation domain are shown for 4 selected cases in Tables 3 and 4. As it was mentioned earlier, we apply the results obtained by Erkaev et al. (2012) to the upper atmosphere input paramters of our model. Erkaev et al. (2012) studied the thermosphere structure of a hydrogen-dominated Earth and a 'super-Earth' ( R pl=2 R Earth; M pl=10 M pl) with a hydrodynamic upper atmosphere model which solves the equations of mass, momentum and energy conservation for low and high heating efficiencies, η of 15 % and 40 %, respectively. η defines the percentage of the incoming XUV energy which is transferred into heating of the neutral gas. Table 4 shows the same input paramters for our model for a hotter atmosphere corresponding to the upper atmosphere values of Erkaev et al . (2013) with η = 40%. As one can see from Tables 3 and 4, the exobase distance which is chosen as our inner model boundary and the temperature are increasing for higher XUV fluxes. This behavior can be expected by taking into account a more intensive radiation flux from the parent star. Enhanced heating flux makes the scale height of the atmosphere increase, which in its turn moves the exobase to higher location. One can also see that an increase of the heating efficiency leads to an increase of the planet's obstacle stand-off (which for the studied non-magnetized planets practically coincides with the exobase) distances as well. Because of the expansion of the upper atmosphere under more extreme heating conditions (40%) the exobase densities are smaller in comparison to the 15% cases. Figs. 4 and 5 show the modeled hydrogen exospheres and the related stellar plasma interaction under various conditions around the test planets. All the figures show cross-sections of a 3D cloud in the 2 1 , x x plane similar to those in Fig. 2. Fig. 4 illustrates the appearance of the extended hydrogen coronae around the Earth-type planet while Fig. 5 corresponds to the 'super-Earth'. In all the cases the wider Earth-type planetary obstacle is assumed, except for Fig. 4d where a smaller Venus-like obstacle is adopted. The white area around the planets (which are shown as black dots) represents the inner atmosphere (non-hydrostatic thermosphere), which is not considered in the present study. Fig.4a and Fig.4b illustrate the influence of the XUV flux on the cloud formation. All simulation parameters for these two pictures are the same except for the XUV flux, which is chosen to be equal to and 50 times higher than the XUV flux of the present Sun. As one can see, the higher XUV flux leads to a more efficient expansion of the upper atmosphere so that charge exchange can be more intensive in the surrounding hydrogen corona. The effect of the planetary obstacle can be seen in a comparison of Fig. 4c, for an Earth-type planetary obstacle shape, with Fig.4d, for a Venus-type obstacle. In these two cases the upper atmosphere is exposed to the XUV flux which is 50 times higher compared to that of today's Sun. Figs. 5a and 5b illustrate the importance of the heating efficiency. We show two model runs for the 'super-Earth' for a comparison. Only the upper atmosphere parameters corresponding to the heating efficiencies were changed. A higher heating efficiency results in additional expansion of the upper atmosphere and in increasing production of ENAs in the vicinity of the planet (blue and red dots). Figs. 5c and 5d show the effect of the stellar wind velocity and density on the hydrogen coronae formation. Both figures, 5c and 5d, correspond to the most extreme XUV case, which is 100 times higher than that of today's Sun. As expected, the extreme stellar conditions result in a denser and faster stellar plasma flow, higher XUV fluxes and more intense heating of the upper atmosphere, as well as a decrease of the planetary obstacle width, which all lead to more intensive interaction processes. The ENA part of the hydrogen corona (blue and red dots) becomes more visible, meaning an increase of the atmospheric erosion processes. One can see that a huge amount of exospheric hydrogen atoms is ionized or underwent charge exchange reactions in both cases, but stronger stellar wind significantly increases the number of ENAs in the vicinity of the planet as suggested by Chassefière, (1996). Chassefìère (1996) studied the hydrodynamic outflow and escape of hydrogen atoms from a hydrogen-dominated expanded thermosphere from early Venus. From this study it was estimated that the huge ENA cloud, which is generated via charge exchange due to the interaction between an extended exosphere and the surrounding solar wind plasma of the young Sun, may contribute to about 75 % of the energy inside the thermosphere which is used for escape of the outward flowing H atoms (see Fig. 3 in Chassefière, 1996). The stellar EUV flux is deposited mainly in the lower thermosphere (Erkaev et al ., 2013), while the ENA flux directed toward the planet should be deposited at an atmospheric layer below the exobase. It can contribute to thermospheric heating and may as a consequence modify the upper atmosphere structure which could result in an enhancement of the thermal escape rate. Our results related to the efficient production of ENAs around the planetary obstacle support the hypothesis of Chassefière (1996) that ENAs may contribute to upper atmosphere heating. A study which investigates the possible heating contribution of ENAs additionally to the stellar XUV flux is beyond the scope of this particular work, but is in progress for a follow up study during the near future. We note also that ENA clouds near the terrestrial exoplanets within orbits around M dwarfs might be observable in the stellar Lyman-alpha line by the Hubble Space Telescope and in higher resolution beyond the geocorona in the near future by the World Space Observatory-UV (Shustov et al. , 2009; Lammer et al ., 2011b). In the next section we estimate how many of the produced planetary ions in the hydrogen coronae are picked up by the stellar wind plasma, and hence are lost from the planet.",
"pages": [
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},
{
"title": "4.2 Stellar wind induced atmospheric erosion of planetary hydrogen ions",
"content": "As discussed above, interaction processes between the stellar wind and the upper atmosphere together with the photoionization by stellar photons lead in the case of hydrogen-rich atmospheres to the production of atmospheric H + ions, see eq. (1). After ionization, the ions can be picked up by the stellar wind plasma and swept away from the planet. Because we are interested in the efficiency of the atmospheric ion escape, we estimate the average ion production rates under various conditions. We assume as discussed below that in the considered cases the production of planetary ions and the escape rate are most likely of the same order. Ions produced near and above the planet's obstacle can be lost because of the ion pick-up process. Since these particles are not neutral anymore, they can follow the magnetic field lines in the stellar wind plasma and can be swept away from the planet's gravity field. We consider the H + ions produced above the planetary obstacle, where the collisions between atmospheric particles can be neglected. It is assumed that the ions may be lost if the gyro radius is small enough in comparison to the planetary radius (e.g. if the magnetic field in the vicinity of a planet is strong enough to change the trajectory of the ions significantly). Here i m is the mass of the ion, i v is the velocity of the 'cold' planetary ion assumed to be ~7 km s -1 , q is the ion charge and B is the magnetic field near the planetary obstacle. In the case of a pure hydrogen upper atmosphere the ion mass and charge coincide with the mass and charge of a proton. The velocity of ~7 km s -1 is chosen as being slightly faster than the mean thermal velocity of a hydrogen atom for a temperature of about 2000 K. The magnetic field at the distance ~0.24 AU from an M dwarf can be roughly estimated if one assumes a dipole character of the stellar field with the initial global value in the range of ~2 - 3 kG or ~0.2 - 0.3 T (Phan-Bao et al. , 2009, Reiners, 2012). By assuming an average magnetic field on the star of 2 kG, the magnetic field at 0.24 AU is ≈ 3 10 4 . 1 G, which yields for an ion velocity of 7 km s -1 an ion gyro radius of ~525 m which is several orders of magnitude smaller compared to the radii of the studied planets. In such a case it is justified to assume that most of the produced H + ions will be swept away from the planets by the stellar wind. If we assume that the ions are accelerated by the stellar wind electric field to the velocity of the stellar wind (Case I: 330 km/s, Case II: 550 km/s), the ion gyro radius increases proportionally to ~25 - 40 km in two extreme cases. Here we assume the filling factor f=1 (see Phan-Bao et al. , 2009), i.e. the maximal possible field strength. Since the magnetic field of ~2 - 3 kG is typical for young and active M dwarfs, it could be convenient to determine the gyro radii for a weaker field of ~50 G for an older star with the age of several Gyr (Phan-Bao et al. , 2009). The magnetic field at 0.24 AU is approximately 5 10 57 . 3 G. A decrease of the magnetic field causes a proportional increase of the gyro radius (21 km for an ion velocity of 7 km s -1 , 10 3 km and 3 10 6 . 1 km for 330 km/s and 550 km/s respectively). But even the highest value of ~1600 km is several times less if compared to the planetary radius, and more than an order of magnitude lower compared to the exobase radius where most ENAs are produced. These estimates support our assumption that the majority of the exospheric ions are lost from the planet and that the ion production rate is balanced by the escape rate at least during a significant part of the stellar life time. Estimates of the ion production rates and corresponding escape rates described in the previous sections are summarized in the Tables 5 and 6 for planetary obstacles which have an Earth-like magnetosphere shape. Table 5 presents the results obtained for a hydrogen-rich Earth-like planet for two stellar wind conditions and a heating efficiency η =15% and of a higher heating efficiency η = 40%, while Table 6 summarize the similar scenarios for the 'super-Earth'. Atmospheric loss rates L ion are given in units of particles per second. As one can see from Tables 5 and 6, in the most cases the ion production and loss rate increases with the increasing XUV flux. Loss rates for faster stellar wind also exceed the corresponding values for the wind with lower velocity which is not surprising. Since the ion production rates depend not only on the assumed heating efficiency and the XUV flux, but also on the exobase density, the values for the lower-density case corresponding to a heating efficiency of 40% (Erkaev et al. , 2013) are slightly lower in comparison to the 15% case shown in Table 6. This is also the reason why the values for the cases where the stellar XUV flux is about 100 times higher than that of the present Sun are not dramatically higher (or even slightly smaller) that the ion production rates for the lower XUV fluxes, although the intensity of the interaction increases. Under the intensity of the interaction in this case we mean the ratio of produced ions to the mean exospheric density. This value increases monotonically for higher XUV fluxes in all cases considered in the present study. The reason for that is related to the corresponding exobase density that is lower because of expansion in the case of a hydrogen-rich upper atmosphere which is exposed to high XUV fluxes such as in the 100 XUV case (Erkaev et al. , 2013). To investigate the influence of the planetary obstacle shape on the H + escape rate L ion, we performed an analogous set of simulations by assuming a Venusian type planetary obstacle ( t s R R ). Tables 7 and 8 present the calculated ion production rates and estimated ion escape rates for the two test planets under the same conditions as described in Tables 5 and 6 except for the shape of the planetary obstacle. As one may see from the comparison of Tables 5 - 6 and Tables 7 - 8, reducing the width of the obstacle by 1.5 times leads to an increase in the ion production rate (i.e. the escape in general) of ≈30%. Other factors which lead to an increase of the ion production rate are related to the increase of the stellar wind density and velocity, heating efficiency η , and enhancement of the stellar XUV flux of the parent star. All these dependencies should be considered and expected. For comparison, thermal loss rates change in the range from 29 10 0 . 4 (1 XUV, η=15%) to 31 10 3 . 4 (100 XUV, η=40%) for a hydrogen-rich Earth-type planet and from 29 10 6 . 1 (1 XUV, η=15%) to 31 10 3 . 5 (100 XUV, η=40%) for a hydrogen-rich 'superEarth'. In all cases these rates exceed the presented in the current study. For more information, see Erkaev et al., (2013). If we compare the modeled H + ion pick-up loss rates with that of Mars (e.g., Lammer et al ., 2003) or Venus (Lammer et al. , 2006), which are in the order of ~10 25 s -1 , one can see that the pick-up loss rates for the hydrogen-dominated Earth-like planet are comparable for the 1 XUV case with a heating efficiency of 15 % and an Earth-like magnetopause shape, but would be a factor 10 3 higher in the case of 40 % heating efficiency and/or a more narrower Venus-type planetary obstacle. For the larger 'superEarth' and XUV cases with higher values than that of the present-day Sun the loss rates are up to 10 4 - 10 5 times higher. 4.3 Total ion escape The loss rates shown in Tables 5 - 8 can be used for rough estimation of the total ion loss from the hydrogen envelopes around the studied planets. This question is important because, as shown by Erkaev et al. (2013), volatile rich 'super-Earths' which contain IRcooling molecules can result in lower heating efficiencies of about 15 % so that for most of their lifetime they will not be in the hydrodynamic blow-off regime. In such cases nonthermal atmospheric escape processes, like the studied H + ion pick-up process, will contribute to the loss of their hydrogen-rich protoatmospheres. Before we investigate this mass loss one needs to know how long a typical M dwarf like Gliese 436 may keep a high level of the XUV and X-ray flux. According to Penz et al. (2008a) the temporal scaling law for the soft X-ray (0.6-12.4 nm or 0.1-2 keV) flux of a typical M dwarf with the mass of ≈ Sun M 4 . 0 can be described by the following relation where 28 0 10 6 . 5 L erg s -1 and t is given in Gyr. The soft X-ray flux can then be scaled for the appropriate orbital distance by using the relation 2 4 / d L F X X . Fig. 6 shows, approximately, the decrease of the soft X-ray flux of a Gliese 436 analogous M dwarf during the first 1.3 Gyr of its life time. Since at present time the scaling law for the XUV radiation of M dwarfs is not yet well constrained, we use this soft X-ray scaling law instead of the XUV scaling law in our estimation for the total H + escape. Assuming this temporal scaling law for the star and taking the ion production rates from Tables 5 - 8, we can estimate the mass loss from the hydrogen-rich Earth-like planet and the 'super-Earth' in the HZ of a Gliese 436 type M star after 4.5 Gyr (see Tables 9 and 10). For comparison the thermal escape rates are shown by using the values from Table 2 in Erkaev et al. (2013). The total ion loss is given in Earth ocean equivalent amounts of hydrogen (1EOH = 23 10 5 . 1 g) . It should also be mentioned that we do not consider escape during the first ~100 Myr, the time of extreme stellar activity of an M dwarf, so that our estimates cover the time span ~0.1 - 4.5 Gyr. As discussed in Erkaev et al. (2013) during this early extreme period the temperature in the lower thermosphere may be >> 250 K, due to magma oceans and frequent impacts. Hot lower atmosphere will enhance the atmospheric thermal escape during this early period. A follow up study which will investigate the earliest extreme evolutionary periods is in progress. In the present work we do not take into account the gradual decrease of the amount of gas in the planetary atmosphere due to escape processes, as we assume that the hydrogen reservoir contains much more gas in comparison to the amount lost . As discussed in Sect. 1, such scenarios can be considered as real because most of the recently discovered 'super-Earths' may have huge hydrogen envelopes which contain a few % of their whole mass (e.g., Lammer, 2013). If we compare the estimated atmospheric escape rates obtained for the thermal and ion pick-up processes for both test-planets in the HZ, it is clear that the thermal escape rate substantially exceeds the pick-up rate under the studied conditions. This is also the case when we consider the most extreme XUV and stellar plasma conditions, including a narrow planetary obstacle. A fraction of the evaporating neutral exosphere will be ionized so that ion pick-up will contribute to the total atmospheric escape rate, but as long as the upper atmosphere is in blow-off thermal escape will be the most important. In our study the escape rate of ionized hydrogen atoms can vary for an Earth-type planet from ~0.6 EOH under moderate conditions (15% heating efficiency, moderate stellar wind, Earth-type planetary obstacle) up to ~2.5 EOH for extreme environments (40% heating efficiency, denser and faster wind and a narrow Venusian obstacle type). The stronger gravity of the more massive 'super-Earth' keeps the atmosphere closer to the planet's surface, which slows down the charge exchange and photoionization processes. In this case the escape changes from ~0.4 EOH to ~2.14 EOH depending on the environment but remains smaller compared to escape from an Earthtype planet (ranging from ~0.6 EOH to 2.5 EOH, see above). In all studied cases the nonthermal H + pick-up rate is several times smaller in comparison with the thermal one, but makes up a significant fraction of the whole loss processes. The results of our study, together with those of Erkaev et al. (2013), indicate that terrestrial exoplanets ranging in mass and size from Earth- to 'super-Earths' may experience difficulties in losing dense hydrogen envelopes if they have H-dominated protoatmosphere remnants with >9 EOH (Earth: η = 15%) and >19 EOH (Earth: η = 40%). For 'super-Earth' these amounts are >3.5 EOH (η = 15%) and >10 (η = 40%). Dense hydrogen envelopes may be removed more easily if a particular exoplanet is located closer to its parent star such as Corot-7b or Kepler-10b (e.g., Leitzinger et al ., 2011) which orbit their parent stars at ~ 0.017 AU, but not inside the HZ. We note also that due to the HZ location at greater distances from the parent stars, the stellar wind erosion of hydrogen-envelopes will be less efficient for planets inside the HZs of K, G and F-type stars.",
"pages": [
20,
21,
22,
23,
24,
25,
26
]
},
{
"title": "5. CONCLUSIONS",
"content": "In this study we investigated the non-thermal ion pick-up escape process from hydrogenrich, non-hydrostatic upper atmospheres of an Earth-like planet, and a hydrogen-rich 'super-Earth' which is twice as large as Earth and ten times more massive. Both planets are supposed to be located inside the HZ of a typical M dwarf star with stellar properties similar as GJ 436. We showed that in the case of an M dwarf the produced planetary H + ions have a high probability to be picked up from the extended hydrogen coronae by the stellar wind plasma flow so that the ion production rate and the ion escape rate are perhaps of the same order. We exposed the two test-planets to various XUV fluxes from 1 to 100 times that of the present Sun and found that in all studied cases the ionization of exospheric neutral hydrogen atoms by charge-exchange and photoionization contributes to the total atmospheric escape of the upper atmosphere, but do not prevail over the thermal escape. The total non-thermal atmospheric escape by ion pick-up from possible dense hydrogen envelopes during the life time of the studied planets is < 3 EOH. Our results indicate that if a rocky exoplanet did not lose the majority of its nebula captured hydrogen gas envelope, or degassed a huge amount of hydrogen-rich volatiles by thermal blow-off during the first hundred Myr after the planet's origin, it is questionable if the stellar wind can erode a remaining dense hydrogen envelope non-thermally. The thermal escape is higher during the planet's history, but is probably unable to remove such dense hydrogen envelopes as well. The situation may change dramatically for exoplanets which are located closer to their parent stars. Depending on the nebula life time, the formation process, planetary mass, stellar activity and plasma properties in the vicinity of the planet, the initial amount of hydrogen, thermal and non-thermal atmospheric escape processes will determine if a planet becomes a world with an Earth-type atmosphere (and no hydrogen envelope) or remains a sub-Neptune type body.",
"pages": [
26,
27
]
},
{
"title": "ACKNOWLEDGEMENTS",
"content": "M. Güdel, K. G. Kislyakova, M. L. Khodachenko, and H. Lammer acknowledge the support by the FWF NFN project S116 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subprojects, S116 604-N16 'Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond', S116 606-N16 'Magnetospheric Electrodynamics of Exoplanets', S116607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. K. G. Kislyakova, Yu. N. Kulikov, H. Lammer, and P. Odert thank also the Helmholtz Alliance project 'Planetary Evolution and Life'. P. Odert and M. Leitzinger acknowledges support from the FWF project P22950-N16. The authors also acknowledge support from the EU FP7 project IMPEx (No.262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science WG5. The authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar- and exoplanetary environments'. Finally, N. V. Erkaev acknowledges support by the RFBR grant No 12-05-00152-a. This research was conducted using resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North (HPC2N), Umeå University, Sweden. The software used in this work was in part developed by the DOE-supported ASC / Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. Finally, the authors thank the referees for very useful suggestions and recommendations which helped to improve the work.",
"pages": [
27
]
},
{
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"pages": [
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},
{
"title": "FIGURE CAPTIONS",
"content": "FIG. 1 : Observed hydrogen ENAs by the IBEX spacecraft around Earth. The H ENAs count rate was integrated from 0.7-6 keV on 28 March 2009 from 04:54-15:54 UT. The peak is centered on the subsolar magnetopause and a significant ENA flux extends to ±10 R Earth (Fuselier et al ., 2010). FIG. 2 . Modeling results of Earth's solar wind plasma interaction with the present-day geocorona. Green dots correspond to the solar wind protons, yellow dots represent the neutral hydrogen atoms moving with velocities below 10 km s -1 (particles which belong to the atmosphere) while the red and the blue dots represent ENAs with velocities above 10 km s -1 , moving towards and away from the Sun respectively. The dashed line denotes the magnetosphere obstacle. FIG. 3 . Radial profiles for density, velocity and temperature as a function of orbital location in AU and of expected plasma properties of an ordinary stellar wind (solid lines) and during an CME event (dashed lines) on an M-type star with a mass M s ~0.45 M Sun and a rotation period 2.5 days. For the simulation of stellar wind the initial proton density at 0.1 AU n 0 = 400 cm -3 , temperature T 0 = 500 kK, and radial stellar wind velocity v r0 = 300 km s -1 were taken. Simulation of a solar-analogue CME event uses the initial proton density n 0 = 800 cm -3 , proton temperature T 0 = 1500 kK, and a radial stellar wind velocity v r0 = 600 km s -1 . FIG. 4 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around an Earth-like hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig.4a corresponds to the XUV flux which is equal to that of the present Sun, the moderate stellar wind (Case I) and a lower heating efficiency of 15%. Fig.4b corresponds to the similar input parameters as in Fig.4a, but the XUV flux is 50 times higher. Fig.4c corresponds to the 10 times higher XUV flux than the present one and a heating efficiency of 15%, as well as the moderate stellar wind (Case I). Fig.4d: corresponds to the similar input parameters as in Fig.4c, but for the Venus-type narrower planetary obstacle. FIG. 5 . Modeled atomic hydrogen coronae and stellar wind plasma interaction around a 'super-Earth' hydrogen-rich planet inside an M star HZ at 0.24 AU (green: protons, yellow: H atoms, blue ENAs flying away from the star, red ENAs flying towards the star; dotted line: magnetopause/planetary obstacle). Fig5a: the XUV flux is 50 times higher than that of the present Sun, heating efficiency of 15%, the planet is exposed to a moderate stellar wind (Case I). Fig5b: similar conditions except for heating efficiency of 40%. Fig.5c: the XUV flux is 100 times higher compared to that of the present Sun, 40% heating efficiency, moderate stellar wind (Case I). Fig.5d: similar input parameters as in Fig.5c, but exposed to a faster and denser stellar plasma flow (case II). FIG. 6 . Illustration of the soft X-ray flux time-dependence for an M dwarf star with 0.4 solar masses (dashed line) and the same curve for a Sun-like star (solid line) in the corresponding HZs normalized by the present Sun flux. The M star within this mass range remains about 200 Myr longer in its activity saturation phase compared to a solar like G star.",
"pages": [
47,
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2013AstBu..68...14S
https://arxiv.org/pdf/1203.2763.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_88><loc_91><loc_93></location>Magnetic fields of active galactic nuclei and quasars with polarized broad H α lines</section_header_level_1>
<text><location><page_1><loc_18><loc_76><loc_85><loc_87></location>N.A. Silant'ev 1 , Yu.N. Gnedin 1 , 2 ∗ , S.D. Buliga 1 , M.Yu. Piotrovich 1 and T.M. Natsvlishvili 1 1 Central Astronomical Observatory at Pulkovo of Russian Academy of Sciences, Pulkovskoye chaussee 65, Saint-Petersburg, 196140, Russia 2 St.-Petersburg State Polytechnical University, Polytechnicheskaya 29, Saint-Petersburg, 195251, Russia</text>
<text><location><page_1><loc_44><loc_73><loc_59><loc_75></location>February 19, 2018</text>
<section_header_level_1><location><page_1><loc_7><loc_68><loc_17><loc_70></location>Abstract</section_header_level_1>
<section_header_level_1><location><page_1><loc_52><loc_68><loc_70><loc_70></location>1 Introduction</section_header_level_1>
<text><location><page_1><loc_7><loc_15><loc_50><loc_66></location>We present estimates of magnetic field in a number of AGNs from the Spectropolarimetric atlas of Smith, Young & Robinson (2002) from the observed degrees of linear polarization and the positional angles of spectral lines (H α ) (broad line regions of AGNs) and nearby continuum. The observed degree of polarization is lower than the Milne value in a nonmagnetized atmosphere. We hypothesize that the polarized radiation escapes from optically thick magnetized accretion discs and is weakened by the Faraday rotation effect. The Faraday rotation depolarization effect is able to explain both the value of the polarization and the position angle. We estimate the required magnetic field in the broad line region by using simple asymptotic analytical formulas for Milne's problem in magnetized atmosphere, which take into account the last scattering of radiation before escaping from the accretion disc. The polarization of a broad spectral line escaping from disc is described by the same mechanism. The characteristic features of polarization of a broad line is the minimum of the degree of polarization in the center of the line and continuous rotation of the position angle from one wing to another. These effects can be explained by existence of clouds in the left (keplerian velocity is directed to an observer) and the right (keplerian velocity is directed from an observer) parts of the orbit in a rotating keplerian magnetized accretion disc. The base of explanation is existence of azimuthal magnetic field in the orbit. The existence of normal component of magnetic field (usually weak) makes the picture of polarization asymmetric. The existence of clouds in left and right parts of the orbit with different emissions also give the contribution in asymmetry effect. Assuming a power-law dependence of the magnetic field inside the disc, we obtain the estimate of the magnetic field strength at first stable orbit near the central supermassive black hole (SMBH) for a number of AGNs from the mentioned Spectropolarimetric atlas.</text>
<text><location><page_1><loc_7><loc_11><loc_50><loc_14></location>Keywords : accretion discs, magnetic fields, polarization, active galactic nuclei.</text>
<text><location><page_1><loc_52><loc_50><loc_95><loc_66></location>Smith et al. (2002) presented optical spectropolarimetric atlas of 36 nuclei of Seyfert 1 Galaxies. The data were obtained with the William Herschel and the Anglo-Australian Telescopes from 1996 to 1999. It is well-known that spectropolarimetry is an important tool in studies of active galactic nuclei (AGN). The spectropolarimetric data provide the detailed view into the inner regions of active galactic nuclei, including an accretion disc and accretion flows around a supermassive black hole (SMBH), thus allowing one to probe the structure and kinematics of the polarizing material around the accreting SMBH.</text>
<text><location><page_1><loc_52><loc_12><loc_95><loc_50></location>Smith et al. (2002) objects exhibit a variety of characteristics with the average degree of polarization ranging from 0 . 2 to 5 percent. They show many variations both in the degree p line ( λ ) and position angle χ line ( λ ) of polarization across the broad H α emission line. The characteristic feature of p line ( λ ) is the minimum in the line centre, which is usually less than the polarization degree p c ( λ ) in nearby continuum. The second feature is the monotonic increase of positional angle from one line wing to the other. Note also that there exists little difference in the mean polarization degrees and position angles of nearby continuum and H α line for nine of Seyfert galaxies (Mrk 6, Akn 120, Mrk 896, Mrk 926, NGC 4051, NGC 6814, NGC 7603, UGC 3478, ESO 012-G21). For 22 measurements out of 45, the mean positional angles χ line and χ c are practically the same. It should be emphasized that the position angles of polarized continuum and H α line coincide more frequently than their polarization degrees. The mean value of the polarization degree in continuum over all sources is 0.68%, and the same value for H α lines is 0.66%. A position angle is most sensitive to the geometry of emitting region. For that reason, it is most probable that both emitting regions are located near one another, i.e. they located in an accretion disc and their scale sizes are similar: R BLR ≈ R λ , where R λ corresponds to the scale size of an accretion disc for the continuum radiation with given wavelength λ .</text>
<text><location><page_1><loc_52><loc_7><loc_95><loc_11></location>It is generally accepted that AGNs are powered by the release of gravitational energy from gas accreted onto supermassive black holes (SMBH). The well-known anti-correlation</text>
<text><location><page_2><loc_7><loc_89><loc_50><loc_97></location>between the radius of the broad-line region (BLR) and the velocity width of broad emission lines for AGNs supports the idea that the BLR gas is virialized and that its velocity is dominated by the gravity of the SMBH (Peterson & Wandel 2000; Onken & Peterson 2002).</text>
<text><location><page_2><loc_7><loc_74><loc_50><loc_89></location>Most of the recent results lead to the conclusion that BLR presents a flattened rotating system. Many authors (Vestergaard et al. 2000; Nikolajuk et al. 2006; Sulentic et al. 2006; La Mura et al. 2009; Bon et al. 2009; Punsly & Zhang 2010) pointed out that considerable flattening and a predominantly planar orientation are likely to be the intrinsic property of the BLR structure. This conclusion allows us to consider BLR as an outer part of geometrically thin accretion disc that is optically thick with respect to the electron Thomson and the Rayleigh scattering processes.</text>
<text><location><page_2><loc_7><loc_54><loc_50><loc_74></location>Seyfert galaxies were traditionally divided into two classes according to the presence or absence of broad optical lines. Antonucci & Miller (1985) explained this phenomenon by obscuration by a dusty torus with different orientation with respect to an observer. The orientation-based unification model has become quite popular, but it has also been confronted by more specialized observations (see, for example, Zhang & Wang 2006; Wang & Zhang 2007); in particular, there is evidence for the existence of a special subclass of Seyfert 2 lacking hidden broad-line regions (Zhang & Wang 2006). Thus, the paradigm of unification scheme for all Seyfert galaxies remains a matter of debate (Miller & Goodrich 1990; Tran 2001, 2003).</text>
<text><location><page_2><loc_7><loc_26><loc_50><loc_54></location>The basic feature of Smith et al. (2002, 2004, 2005) models is that the polarization plane for most of Seyfert galaxies is parallel to the direction of the radio jet. Simultaneously, these models postulate that the radio jet direction is perpendicular to the accretion plane. The latter assumption is questionable. In reality, the radio jets frequently have significant bends near the radio core. The angle of the bend depends on the ratio of radial and toroidal magnetic fields in the accretion disc. Besides, the direction of the jet appears to change with time (see, for example, Britzen et al. 2009; Rastorgueva et al. 2011). Therefore, the coincidence of the direction of the radio jet and the polarization plane does not mean that the electrical vector of the polarized radiation E is perpendicular to the accretion disc. Of course, one can introduce the angle between the radio jet and the electric field E as an additional characteristic of AGNs. But, strictly speaking, this angle is not necessarily related to the real inclination of E with respect to the accretion disc. As a last resort, this angle may be considered in a probabilistic sense.</text>
<text><location><page_2><loc_7><loc_12><loc_50><loc_25></location>The existence of many cases when the position angle of radiation has intermediate value between parallel or perpendicular to the direction of the radio jet also demonstrates that real direction of E does not correlate with the jet direction. As a result, we conclude that the models describing the polarization behavior in AGNs should not assume that the radio jets are perpendicular to accretion discs; instead, the explicit dependence on the inclination angle i of the accretion disc needs to be taken into account.</text>
<text><location><page_2><loc_7><loc_7><loc_50><loc_11></location>It is commonly accepted (see, for example, Blaes, 2003) that the accretion discs are magnetized. The existence of radio jets is usually associated with strong magnetic fields in</text>
<text><location><page_2><loc_52><loc_79><loc_95><loc_97></location>centers of AGNs and quasars. Numerous theoretical models demonstrate the power-law dependence of the magnetic field distribution in an accretion disc. Usually accretion discs are considered as geometrically thin slabs with Thomson optically depth τ /greatermuch 1. The scattering-induced linear polarization can be as high as ∼ 12% for edge-on viewing (Chandrasekhar 1960). However, in the real situation of a magnetized accretion disc, the degree of polarization p will be reduced due to Faraday rotation of the radiation polarization plane while a free photon travels between the consequent scatterings. Recall that the angle of Faraday rotation Ψ at the Thomson optical length τ is equal to</text>
<formula><location><page_2><loc_63><loc_74><loc_95><loc_77></location>Ψ = 1 2 δτ cos Θ , δ = 0 . 8 λ 2 B, (1)</formula>
<text><location><page_2><loc_52><loc_68><loc_95><loc_74></location>where the wavelength of radiation λ is measured in microns and the magnetic field B is measured in Gauss. The angle Θ is the angle between the direction of light propagation n and the direction of B .</text>
<text><location><page_2><loc_52><loc_50><loc_95><loc_67></location>The decrease of the polarization degree due to Faraday rotation occurs as a result of summation of chaotic angles of rotations in the multiple scattering process. This process has been considered in many papers (for example, Silant'ev 1994; Agol & Blaes 1996; Gnedin & Silant'ev 1997). Clearly, the value Ψ ∼ 1 at the mean free path τ ∼ 1 can decrease considerably the standard Chandrasekhar's polarization degree. Besides, the dependence of Ψ on the wavelength and magnetic field gives rise to characteristic dependencies of the polarization degree p and the position angle χ of radiation on λ , which allows us to estimate the strength and direction of the magnetic field in the scattering region.</text>
<text><location><page_2><loc_52><loc_18><loc_95><loc_49></location>Below we develop a new model for the formation of polarization in AGNs, which does not use the assumption of the position angle of observed radiation being correlated with the direction of the radio jet. We hypothesize that the observed polarization is due to intrinsic polarization of radiation outgoing from the magnetized optically thick accretion disc (the Milne problem in magnetized atmosphere). In our model, the characteristic features of polarization mentioned above are explained by the topology of the magnetic field in the accretion disc, when the Faraday rotation of the polarization plane is taken into account. Primarily, we suppose that the whole radiating surface of the magnetized accretion disc is observed, i.e. that the inclination angle i is such that the obscuring torus (if it really exists) does not intersect the line of sight. We also consider the case when we observe only a part of total surface of accretion disc, i.e. we take into account the obscuring torus. It appears that our model and the usual pure geometrical model of Smith et al. (2002, 2004, 2005), which takes into account single scattering of BLR-photons in nearby clouds, are two competing explanations for the polarization properties of the accretion discs.</text>
<text><location><page_2><loc_52><loc_6><loc_95><loc_18></location>All actually observed polarization degrees p c are much smaller than the value in the Milne problem in nonmagnetized atmosphere at the same inclination angle. Recall that the Milne problem deals with the radiative transfer in an optically thick atmosphere, where the sources of thermal radiation are located far from the surface, at depth with τ /greatermuch 1. In optically thick accretion discs the main source</text>
<text><location><page_3><loc_7><loc_80><loc_50><loc_97></location>of thermal radiation is found at the midplane of the disc, and the outgoing radiation is described by the solution of the Milne problem. The mean value of p c in the atmosphere with pure electron scattering is equal to 3.1%, and the maximum value is 11.7%. The outgoing radiation in case of an absorbing atmosphere has a much greater polarization, because the intensity peaks near the surface. In this case, most of polarization arises analogously to the process of a single scattering of a radiation beam near the surface. For the Milne problem in spectral lines, the value p line is less than in continuum (see, for example, Ivanov et al. 1997).</text>
<text><location><page_3><loc_7><loc_59><loc_50><loc_80></location>For the accretion disc models, the main challenge is to determine the scale length of the disc - i.e. the radius where the disc temperature matches the rest frame wavelength of the monitoring band. A semi-empirical method for measuring the disc scale length has been developed (Kochanek et al. 2006; Morgan et al. 2006, 2008; Poindexter, Morgan & Kochanek 2008). These authors used microlensing variability, observed for gravitationally lensed quasars, to find the accretion disc scale length for a given observed (or rest-frame) wavelength. Clearly, such a scaling has to be consistent with the most popular accretion disc model of Shakura & Sunyaev (1973). As a result, Poindexter et al. (2008) presented the following relation for the scale length of a standard geometrically thin accretion disc:</text>
<formula><location><page_3><loc_8><loc_52><loc_50><loc_56></location>R λ = 10 9 . 987 ( λ rest µm ) 4 / 3 ( M BH M /circledot ) 2 / 3 ( L bol εL Edd ) 1 / 3 cm. (2)</formula>
<text><location><page_3><loc_7><loc_39><loc_50><loc_51></location>The wavelength dependence, R λ ∼ λ 4 / 3 rest , corresponds to the typical (for Shakura-Sunyaev disc model) effective temperature: T e = T in ( R/R in ) -3 / 4 , where R in is the inner radius of an accretion disc and T in is the temperature corresponding to that radius. Here L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ) erg s -1 is the Eddington luminosity, M BH is the black hole mass, ε is the rest-mass radiation conversion efficiency, and L bol is the bolometric luminosity.</text>
<text><location><page_3><loc_7><loc_30><loc_50><loc_39></location>Numerous papers provided measurements of BLR sizes for AGNs (see, for example, Peterson et al. 1994, 2004; Wu et al. 2004; Bentz et al. 2009; Shen & Loeb 2010; Greene et al. 2010). Kaspi et al. (2007) have compiled the observational data for Seyfert galaxies and nearby quasars with black hole masses estimated with the reverberation mapping technique.</text>
<text><location><page_3><loc_7><loc_25><loc_50><loc_30></location>Most recently Shen & Loeb (2010) have suggested an empirical analytic formula for R BLR that is very useful for various estimates and applications:</text>
<formula><location><page_3><loc_16><loc_20><loc_50><loc_24></location>R BLR = 2 . 1 · 10 17 M 1 / 2 8 ( L bol L Edd ) 1 / 2 . (3)</formula>
<text><location><page_3><loc_7><loc_16><loc_50><loc_19></location>Here M 8 = M BH / 10 8 M /circledot . We will use this formula in our further calculations.</text>
<text><location><page_3><loc_7><loc_7><loc_50><loc_16></location>Below we estimate the magnetic field strength in BLR of AGN and QSO from the data from the spectropolarimetric atlas presented by Smith et al. (2002). The λ - dependence of the observed polarization degree and position angle in H α line is very complicated. It appears to be produced by large-scale chaotic motions in the accretion disc.</text>
<section_header_level_1><location><page_3><loc_52><loc_95><loc_74><loc_97></location>2 Basic equations</section_header_level_1>
<text><location><page_3><loc_52><loc_79><loc_95><loc_94></location>To estimate the degree of polarization p and the position angle χ of radiation escaping from the magnetized atmosphere we use the standard radiative transfer equations for Stokes parameters I, Q and U (see, for example, Silant'ev 1994; Dolginov, Gnedin & Silant'ev 1995; Silant'ev 2002, 2005). This system of equations has a fairly complicated form. Numerical solutions have so far been obtained only for the case when magnetic field B is parallel to the normal N to an atmosphere (see Silant'ev 1994; Agol and Blaes 1996; Shternin et al. 2003).</text>
<text><location><page_3><loc_52><loc_67><loc_95><loc_79></location>For our purpose, however, it is sufficient to use a simple asymptotic theory, which can be presented in an analytical form for an arbitrary direction of the magnetic field in the atmosphere (Silant'ev 2002, 2005; Silant'ev et al. 2009). In this approximation, the intensity of the radiation I ( z, µ ) obeys a usual transfer equation with the Rayleigh phase function, and the system of equations for parameters Q and U can be presented in the following form:</text>
<formula><location><page_3><loc_67><loc_63><loc_80><loc_66></location>µ d dz ( -Q + iU ) =</formula>
<formula><location><page_3><loc_54><loc_57><loc_95><loc_59></location>= -α [1 + C + i (1 -q ) δ cos Θ]( -Q + iU ) + B Q ( z, µ ) , (4)</formula>
<text><location><page_3><loc_52><loc_38><loc_95><loc_57></location>where B Q ( z, µ ) describes the source function for parameter Q due to the contribution of intensity scattering in nonmagnetized atmosphere (in this case B U ≡ 0), µ = nN is the cosine of the angle between the direction of light propagation n and the normal N to the atmosphere, α is the total extinction factor due to Thomson scattering and pure absorption on dust particles, the value q = σ a / ( σ a + σ s ) (Silant'ev et al., 2009) is the degree of absorption, C describes the additional extinction of polarized radiation due to the fluctuating component B ' of the magnetic field in the atmosphere (see below). Eq.(4) is valid in the limit of large Faraday rotation parameter δ ≥ 1.</text>
<text><location><page_3><loc_52><loc_34><loc_95><loc_38></location>A solution of Eq.(4) results in the following expression for parameters Q ( n , B ) and U ( n , B ) for the radiation escaping from the magnetized atmosphere:</text>
<formula><location><page_3><loc_65><loc_30><loc_82><loc_32></location>-Q ( n , B ) + iU ( n , B ) =</formula>
<formula><location><page_3><loc_54><loc_23><loc_95><loc_28></location>= -∫ ∞ 0 dτ µ B Q ( τ, µ ) exp ( -[1 + C + i (1 -q ) δ cos Θ] τ µ ) (5)</formula>
<text><location><page_3><loc_92><loc_16><loc_92><loc_18></location>/negationslash</text>
<text><location><page_3><loc_52><loc_15><loc_95><loc_23></location>At δ ≥ 1, the first non-zero term of integrating by parts of Eq.(5) gives rise to the asymptotic expression which has an analytical form and can be used for an arbitrary direction of the magnetic field. For example, for the case B Q (0 , µ ) = 0 we have:</text>
<formula><location><page_3><loc_59><loc_6><loc_95><loc_14></location>Q ( n , B ) /similarequal B Q (0 , µ )(1 + C ) (1 + C ) 2 +(1 -q ) 2 δ 2 cos 2 Θ , U ( n , B ) /similarequal B Q (0 , µ )(1 -q ) δ cos Θ (1 + C ) 2 +(1 -q ) 2 δ 2 cos 2 Θ . (6)</formula>
<text><location><page_4><loc_7><loc_92><loc_50><loc_97></location>For the Milne problem in absorbing atmosphere, a more sophisticated theory (see Silant'ev 1994, 2002) gives rise to the following expressions:</text>
<formula><location><page_4><loc_13><loc_83><loc_50><loc_91></location>Q ( n , B ) /similarequal I (0 , µ ) p (1) ( µ )(1 -sµ ) (1 + C -sµ ) 2 +(1 -q ) 2 δ 2 cos 2 Θ , U ( n , B ) Q ( n , B ) /similarequal (1 -q ) δ cos Θ 1 + C -sµ . (7)</formula>
<text><location><page_4><loc_7><loc_67><loc_50><loc_83></location>Here p (1) ( µ ) is the polarization degree of outgoing radiation, which takes into account only the last scattering before escaping the atmosphere. The value p (1) ( µ ) gives the main contribution to p ( µ ) - exact polarization degree of outgoing radiation for a non-magnetized atmosphere. For this reason, below we use the value p ( µ ) instead of p (1) ( µ ), which for q = 0 is presented in Chandrasekhar (1960), and for the absorbing atmosphere in Silant'ev (1980). The value s is the root of the characteristic equation, tabulated by Silant'ev (1980). If the degree of the true absorption is small ( q /lessmuch 1), the parameter s = √ 3 q .</text>
<text><location><page_4><loc_7><loc_37><loc_50><loc_67></location>First, let us consider the case when the whole surface of a radiating accretion disc is observed. In this case, the Stokes polarization parameters of continuum radiation Q c ( ϕ ) and U c ( ϕ ) must be averaged over all azimuthal angles ϕ , characterizing the position of a radiating surface element on a circular orbit in the accretion disc ( -π ≤ ϕ ≤ π ). The normal N and the direction to an observer n are the same for all parts of the accretion disc surface. Therefore, the reference frame of the accretion disc is common to all parameters Q c ( ϕ ) and U c ( ϕ ) of radiation escaping from the disc. In this case, the averaging procedure consists of integrating these parameters over the azimuthal angle ϕ . Note, that cos Θ depends on ϕ and the integral over ϕ can be taken analytically only over the interval ( -π, π ). As a result, the observed values for the degree of polarization and the position angle can be derived analytically. Silant'ev et al. (2009) presented the detailed description of the behavior of these quantities for continuum radiation. The degree of linear polarization of continuum p c and the position angle χ c for an accretion disc can be expressed in the analytical form:</text>
<formula><location><page_4><loc_12><loc_31><loc_50><loc_35></location>p c ( B , µ ) = p c ( µ )(1 -sµ ) [ g 4 c +2 g 2 c ( a 2 + b 2 ) + ( a 2 -b 2 ) 2 ] 1 / 4 , (8)</formula>
<formula><location><page_4><loc_23><loc_27><loc_34><loc_30></location>tan2 χ c = U c Q c =</formula>
<formula><location><page_4><loc_13><loc_22><loc_50><loc_26></location>= 2 ag c ( p c ( µ )(1 -sµ ) /p c ( B , µ )) 2 +( g 2 c + b 2 -a 2 ) . (9)</formula>
<text><location><page_4><loc_7><loc_10><loc_50><loc_22></location>Here µ = cos i , where i is the inclination angle (angle between the light propagation direction n and the normal N to the accretion disc). The degree of polarization p c ( µ ) corresponds to a non-magnetized accretion disc. The value of p c ( µ ) for the continuum radiation presents the classical solution of Milne problem (Chandrasekhar 1960) with p (0) = 11 . 7%. The value of the position angle χ c = 0 corresponds to oscillations of the wave electric vector perpendicular to the plane ( nN ).</text>
<text><location><page_4><loc_7><loc_7><loc_50><loc_10></location>For spectral lines in isotropic medium the value p line ( µ ) depends on the specific quantum numbers of the transitions (see,</text>
<text><location><page_4><loc_52><loc_70><loc_95><loc_97></location>for example, Chandrasekhar 1960) and on the shape of the line. For a dipole type transition and the Doppler line shape, p line ( µ ) in the atmosphere with pure electron scattering has the same functional form as Chandrasekhar value p c ( µ ), with maximum value of 9.44% instead of 11.71% (see Ivanov et al. 1997). In isotropic medium we have to average an atom over all orientations. For such medium the transfer equation coincides with the usual system for Rayleigh scattering with an additional term, which describes unpolarized radiation. Such average naturally occurs due to usual thermal motions. Considering various quantum numbers for H α line, we see that this additional term is larger than the Rayleigh scattering term (see Chandrasekhar 1960), and the maximum degree of polarization becomes ∼ 3% instead of 9.44%. Therefore, the observed polarization can be explained if the atmosphere also has pure absorption of H α line (the existence of dust). In absorbing atmosphere the polarization degree p line can be larger than that in the non-absorbing atmosphere.</text>
<text><location><page_4><loc_52><loc_52><loc_95><loc_70></location>Broad H α lines presented in atlas Smith et al. (2002) have very high widths, laying in the interval 50 - 200 angstroms. In such situations the total line (sum of 5 sub levels) can be described by one absorption coefficient with the Doppler shape (see, for example, Varshalovich, Ivanchik & Babkovskaya 2006; Lekht et al. 2008). Our technique takes into account the Faraday rotation during propagation of polarized radiation after the last scattering before escaping from the atmosphere. The region of broad-line emission is too far from the center of an accretion disc and has low magnetic fields. For this reason, one does not need to take into account the known Zeeman effect.</text>
<text><location><page_4><loc_54><loc_50><loc_64><loc_51></location>The parameter</text>
<formula><location><page_4><loc_67><loc_46><loc_95><loc_48></location>g c = 1 + C -sµ, (10)</formula>
<text><location><page_4><loc_52><loc_33><loc_95><loc_46></location>where the negative term ( -sµ ) arises in the Milne problem in absorbing atmosphere (see Chandrasekhar 1960). For small degree of true absorption q = σ absorb / ( σ scattering + σ absorb ) /lessmuch 1 the factor s /similarequal √ 3 q . The regions of the line emission are different from those of continuum radiation. Usually one assumes that the parameter g c /similarequal 1 in most of areas of the accretion disc. To explain polarization of the line emission, we have to consider that this emission escapes from optically thick clouds with its own dimensionless parameters g line .</text>
<text><location><page_4><loc_52><loc_30><loc_95><loc_33></location>The dimensionless parameters a and b describe the Faraday depolarization of radiation:</text>
<formula><location><page_4><loc_60><loc_24><loc_95><loc_28></location>a = 0 . 8 λ 2 µB z , b = 0 . 8 λ 2 √ 1 -µ 2 B ⊥ , (11)</formula>
<text><location><page_4><loc_52><loc_10><loc_95><loc_26></location>where B z ≡ B ‖ is the component of the magnetic field directed perpendicular to the accretion disc surface, and B ⊥ = √ B 2 ρ + B 2 ϕ is the magnetic field in the accretion disc plane. The component B ⊥ is perpendicular to B ‖ . Due to axial symmetry, the inclination angle ϕ ∗ ( B ϕ /B ρ = tan ϕ ∗ ) is constant along a circular orbit. The value 0 . 8 λ 2 B is numerically equal to the Faraday rotation angle at the Thomson optical depth of τ = 2, if the polarized radiation propagates along the magnetic field direction. Here and in what follows, we take magnetic field in Gauss and wavelengths in microns.</text>
<text><location><page_4><loc_52><loc_7><loc_95><loc_10></location>The dimensionless parameter C describes the real situation in a turbulent magnetized plasma and characterizes a</text>
<text><location><page_5><loc_7><loc_92><loc_50><loc_97></location>new effect - additional extinction of the polarized radiation (parameters Q and U ) due to incoherence of the Faraday rotation in small-scale turbulent eddies (see Silant'ev 2005):</text>
<formula><location><page_5><loc_20><loc_88><loc_50><loc_91></location>C = 0 . 64 τλ 4 〈 ( B ' ) 2 〉 f B 3 , (12)</formula>
<text><location><page_5><loc_7><loc_80><loc_50><loc_88></location>where τ is the Thomson optical depth of a turbulent eddy ( τ /lessmuch 1), 〈 ( B ' ) 2 〉 is the mean value of fluctuations of the magnetic field, and f B ≈ 1 is a parameter describing the integrated correlation of the B ' values at two-closely spaced points in the accretion disc.</text>
<text><location><page_5><loc_7><loc_64><loc_50><loc_80></location>It should be noted that the diffusion of radiation in the inner regions of the accretion disc also produces depolarization due to multiple scatterings. Presence of magnetic field and, therefore, the Faraday rotation effect, only increases the depolarization process. As a result, the polarized radiation emitted by a plane-parallel atmosphere at a specific inclination angle is considerably lower as compared to the classical Chandrasekhar-Sobolev value (see, for example, Gnedin & Silant'ev 1997). But the main feature of Faraday depolarization is the explicit wavelength dependence for both the polarization degree and the position angle.</text>
<text><location><page_5><loc_7><loc_56><loc_50><loc_63></location>It is interesting to note that at a = b the polarization degree p c ( B , µ ) takes a maximum value (the term ( a 2 -b 2 ) 2 is zero in expression (8)). This effect takes place due to the opposite Faraday rotations from magnetic fields B ‖ and B ⊥ in some places along an orbit.</text>
<text><location><page_5><loc_7><loc_35><loc_50><loc_56></location>All formulas presented above show that polarimetric observations allow us to derive the magnetic field strength and its topology in the BLR region, where the polarized radiation escapes the accretion disc. Using various models connecting magnetic field B H at the black hole horizon with the magnetic field B ms at the first stable orbit R ms nearest to the centre of the system, and then using the power law dependence of the magnetic field from R ms up to R BLR , we can estimate the magnetic field strength and the parameters that control it, such as the spin of the black hole a ∗ , the conversion efficiency of kinetic into radiative energy ε , and the magnetization parameter k = P magn /P gas ( P magn and P gas are magnetic pressure and gas pressure, in accreting plasma, respectively).</text>
<text><location><page_5><loc_7><loc_30><loc_50><loc_35></location>Frequently one uses simple formulas for p c and χ c , corresponding to particular cases of pure normal B ‖ and of pure perpendicular B ⊥ :</text>
<formula><location><page_5><loc_14><loc_23><loc_50><loc_29></location>p c ( B ‖ , µ ) = p c ( µ )(1 -sµ ) √ g 2 c + a 2 , tan 2 χ c = a g c , (13)</formula>
<text><location><page_5><loc_7><loc_18><loc_50><loc_21></location>In the latter case χ c ≡ 0 due to the axial symmetry of the problem.</text>
<formula><location><page_5><loc_16><loc_19><loc_50><loc_25></location>p c ( B ⊥ , µ ) = p c ( µ )(1 -sµ ) √ g 2 c + b 2 , χ c ≡ 0 . (14)</formula>
<text><location><page_5><loc_7><loc_7><loc_50><loc_18></location>Now let us consider the case when the radiating gas along a particular orbit in the accretion disc is partly obscured by some dust cloud (an obscuring torus). Clearly, for pure normal magnetic field B ‖ N , the unobscured part of the orbit has the same polarization degree p c ( B ‖ ) and the position angle χ c ( B ‖ ) as in the case of completely unobscured orbit (see Eq. (13)). If the magnetic field is toroidal B ϕ , i.e. is tangent</text>
<figure>
<location><page_5><loc_52><loc_75><loc_90><loc_96></location>
<caption>Figure 1: Dependence of p c ( B ϕ ) /p c ( µ )(1 -sµ ) on ϕ 0 .</caption>
</figure>
<text><location><page_5><loc_52><loc_66><loc_95><loc_68></location>to the orbit, we can derive the following analytical expressions:</text>
<formula><location><page_5><loc_59><loc_59><loc_88><loc_65></location>p c ( B ϕ ) = p c ( µ )(1 -sµ ) √ g 2 c + b 2 ϕ f Q ( ϕ 0 ) , χ c ≡ 0 ,</formula>
<formula><location><page_5><loc_59><loc_53><loc_95><loc_59></location>f Q ( ϕ 0 ) = 1 ϕ 0 arctan √ g 2 c + b 2 ϕ g c tan ϕ 0 . (15)</formula>
<text><location><page_5><loc_52><loc_42><loc_95><loc_54></location>Here the parameter b ϕ = 0 . 8 λ 2 B ϕ √ 1 -µ 2 , the angle ϕ 0 describes the unobscured part of the orbit (we see the orbit within azimuthal angles -ϕ 0 ≤ ϕ ≤ ϕ 0 ). At ϕ 0 = π (complete orbit), Eq.(15) coincides with Eq.(14). Eq.(15) for f Q ( ϕ 0 ) is valid for ϕ 0 ≤ π/ 2. For π/ 2 ≤ ϕ 0 ≤ π one can use the relation f Q ( ϕ 0 ) = [ πf Q ( π/ 2) -( π -ϕ 0 ) f Q ( π -ϕ 0 )] /ϕ 0 . A more detailed derivation of these formulas is given below, in subsection 2.2 (for a spectral line case).</text>
<text><location><page_5><loc_52><loc_34><loc_95><loc_41></location>Dependence of p c ( B ϕ ) /p c ( µ )(1 -sµ ) on ϕ 0 is presented in Fig.1 for values g c = 1, b ϕ = 1 , 2 , 3 , 4 , 5, and s = 0. It is interesting that for ϕ 0 = π/ 2 (half of the full orbit is observed) the polarization degree coincides with the result (14) for the fully unobscured orbit ( f Q ( π/ 2) = f Q ( π ) = 1).</text>
<section_header_level_1><location><page_5><loc_52><loc_31><loc_91><loc_32></location>2.1 The case of a spectral emission line</section_header_level_1>
<text><location><page_5><loc_52><loc_12><loc_95><loc_30></location>In the catalog of Smith et al. (2002) the polarimetric data both in the continuum and in the H α emission line are presented. In our model of a rotating accretion disc (with the Keplerian velocity u k ) one part (the right side) of the disc ( ϕ = 0 ÷ π ) corresponds to motion from an observer and the second part (the left side) moves towards the observer ( ϕ = π ÷ 2 π ). According to the Doppler formula, wavelengths of radiation from the first part are greater than the central value λ 0 , and from the second part are smaller than λ 0 . The value λ 0 = (1 + z ) λ rest , where z is redshift parameter of the system and λ rest = 0 . 6563 µ m is the rest frame wavelength of the H α line.</text>
<text><location><page_5><loc_52><loc_7><loc_95><loc_11></location>Here we restrict ourselves to a specific case of a spectral line with the Doppler shape. The line is described by following normalized shape function:</text>
<formula><location><page_6><loc_15><loc_91><loc_50><loc_96></location>φ ( λ ) = 1 √ π ∆ λ T exp [ -( λ -λ 0 ∆ λ T ) 2 ] . (16)</formula>
<text><location><page_6><loc_7><loc_76><loc_50><loc_91></location>As in the previous case of continuum radiation, we assume that the X-axis is perpendicular to plane ( nN ). The Keplerian velocity u k corresponds to the radius R BLR : u k = √ GM BH /R BLR , where G is gravitation constant. The usual Doppler line width ∆ λ T = ( u turb /c ) λ 0 is mainly due to chaotic turbulent velocities. The displacement of the line centre for radiation emitted from the part of the disc with the azimuthal angle ϕ is ( u k /c ) λ 0 √ 1 -µ 2 sin ϕ . Thus, the normalized shape function of radiation emitted from ϕ -part of the orbit has the form:</text>
<formula><location><page_6><loc_10><loc_66><loc_50><loc_75></location>φ ( λ, ϕ ) = = 1 √ π ∆ λ T exp -( λ -λ 0 -u k c λ 0 √ 1 -µ 2 sin ϕ ∆ λ T ) 2 . (17)</formula>
<text><location><page_6><loc_7><loc_57><loc_50><loc_66></location>Observed radiation flux F λ from a surface element dS of the ring with the radius R BLR is proportional to dϕ . The flux from the total radiating circular orbit can be obtained by integration over all azimuthal angles ϕ . If we suppose that all sources are distributed uniformly along the orbit, this flux is described by the following expression:</text>
<formula><location><page_6><loc_16><loc_52><loc_50><loc_56></location>F ( λ ) = dSµI ( µ ) 1 2 π ∫ π -π dϕφ ( λ, ϕ ) . (18)</formula>
<text><location><page_6><loc_7><loc_50><loc_50><loc_52></location>Observed fluxes of linearly polarized radiation differ from the continuum radiation case by an additional factor φ ( λ, ϕ ):</text>
<formula><location><page_6><loc_26><loc_47><loc_32><loc_48></location>F Q ( λ ) =</formula>
<formula><location><page_6><loc_9><loc_41><loc_50><loc_46></location>= dSµI ( µ ) p line ( µ )(1 -sµ ) 1 2 π ∫ π -π dϕ φ ( λ, ϕ ) g line g 2 line + δ 2 cos 2 Θ , (19)</formula>
<formula><location><page_6><loc_26><loc_38><loc_32><loc_39></location>F U ( λ ) =</formula>
<formula><location><page_6><loc_8><loc_33><loc_50><loc_37></location>= dSµI ( µ ) p line ( µ )(1 -sµ ) 1 2 π ∫ π -π dϕ φ ( λ, ϕ ) δ cos Θ g 2 line + δ 2 cos 2 Θ . (20)</formula>
<text><location><page_6><loc_7><loc_24><loc_50><loc_33></location>Here Θ is the angle between the magnetic field B and the light propagation direction n , I ( µ ) is total intensity of the spectral line escaping from the surface dS . The azimuthal angle ϕ = 0 corresponds to a surface element dS perpendicular to the plane ( nN ). Faraday depolarization term δ cos Θ has the form:</text>
<formula><location><page_6><loc_14><loc_18><loc_43><loc_23></location>δ cos Θ = 0 . 8 λ 2 Bn = a + b cos( ϕ + ϕ ∗ ) = = a + b ρ cos ϕ -b ϕ sin ϕ,</formula>
<text><location><page_6><loc_7><loc_17><loc_33><loc_18></location>where the parameters b ρ and b ϕ are:</text>
<formula><location><page_6><loc_17><loc_9><loc_41><loc_15></location>b ρ = 0 . 8 λ 2 √ 1 -µ 2 B ρ ≡ b cos ϕ ∗ , b ϕ = 0 . 8 λ 2 √ 1 -µ 2 B ϕ ≡ b sin ϕ ∗ .</formula>
<formula><location><page_6><loc_47><loc_19><loc_50><loc_20></location>(21)</formula>
<formula><location><page_6><loc_47><loc_11><loc_50><loc_12></location>(22)</formula>
<text><location><page_6><loc_7><loc_7><loc_50><loc_10></location>Here angle ϕ ∗ is the angle between B ⊥ and the radius-vector ρ , lying in the disc plane. The sign minus before b ϕ sin ϕ</text>
<text><location><page_6><loc_52><loc_91><loc_95><loc_97></location>corresponds to the right-hand screw rotation of the accretion disc with the frozen magnetic field B ϕ directed along the rotation velocity. If the rotation of the disc is opposite, we have to change b ϕ to b ϕ .</text>
<text><location><page_6><loc_52><loc_73><loc_95><loc_91></location>If we take the factor φ ( λ, ϕ ) = 1 and g line → g c , all the formulas will describe the case of the continuum radiation. In this case the integrals over ϕ can be evaluated analytically (for the combination -F Q + iF U the ϕ -integral can be evaluated by the complex residue method, and we obtain Eqs.(8) and (9)). Note, that these formulas are approximate, they take into account only the last scattering before the escape from the atmosphere. This is a rather satisfactory approximation (see Silant'ev 2002). It describes the main contribution to the polarization. The main merit of these analytical formulas is that they describe the polarization for any direction of the magnetic field. For our purpose this approach is sufficient.</text>
<text><location><page_6><loc_52><loc_65><loc_95><loc_73></location>We note that ϕ -integration in Eqs.(18) - (20) gives rise to rather low polarization effects. For this reason they hardly can be used for describing the polarization data presented in the atlas (Smith et al. 2002). Below we present two models that are more acceptable for explaining the data.</text>
<section_header_level_1><location><page_6><loc_52><loc_58><loc_95><loc_63></location>2.2 The model of H α line polarization with parameters p and χ , averaged over the right and left parts of an orbit</section_header_level_1>
<text><location><page_6><loc_52><loc_42><loc_95><loc_57></location>It is clear from Eqs.(18), (19) and (20) that the right parts of circular orbits mostly contribute to gaussian shape lines at wavelengths λ > λ 0 , and the left parts mostly contribute to λ < λ 0 . Qualitatively, we can consider that these contributions are equivalent to sum of two gaussian shaped polarized lines. We assume that the effective polarizations and position angles of these lines correspond to mean values from the right side ( p right , χ right ) and the left side ( p left , χ left ) of the orbit. These values follow from Eqs.(19) and (20) if we take there the factor φ ( λ, ϕ ) = 1.</text>
<text><location><page_6><loc_52><loc_30><loc_95><loc_42></location>Unlike the situation described by Eqs.(19) and (20), in this model we assume that a part of the accretion disc is invisible due to obscuring torus. The right part corresponds to integration over ϕ = 0 ÷ ϕ 0 , and the left part corresponds to integration in the interval ϕ = 0 ÷ -ϕ 0 . Here the angle ϕ 0 characterizes the boundary azimuthal angle for the visible part of the BLR orbit. The mean values 〈 Q 〉 and 〈 U 〉 for visible right part are described by the integrals:</text>
<formula><location><page_6><loc_55><loc_22><loc_92><loc_26></location>= I line p line ( µ )(1 -sµ ) 1 ϕ 0 0 dϕ g line g 2 + δ 2 cos 2 Θ ,</formula>
<formula><location><page_6><loc_68><loc_18><loc_83><loc_29></location>〈 Q right ( n , B ) 〉 = ∫ ϕ 0 line 〈 U right ( n , B ) 〉 =</formula>
<formula><location><page_6><loc_54><loc_12><loc_95><loc_16></location>= I line p line ( µ )(1 -sµ ) 1 ϕ 0 ∫ ϕ 0 0 dϕ δ cos Θ g 2 line + δ 2 cos 2 Θ , (23)</formula>
<text><location><page_6><loc_52><loc_6><loc_95><loc_11></location>where δ cos Θ is given in Eqs. (21) and (22). The corresponding mean values for the left part of the BLR orbit are given by integrals in the interval (0 , -ϕ 0 ).</text>
<text><location><page_7><loc_23><loc_92><loc_23><loc_94></location>/negationslash</text>
<text><location><page_7><loc_7><loc_86><loc_50><loc_97></location>These integrals cannot be evaluated analytically in a general case. We present below the cases ( a = 0 , b ρ = 0 , b ϕ = 0) and ( a = 0 , b ρ = 0 , b ϕ = 0). The first case corresponds to the magnetic field B ‖ parallel to normal N . Clearly, in this case the polarization degree and the position angle are the same in the right and left parts of the orbit, and can be obtained from Eqs.(8) and (9) (see Eq.(13)).</text>
<text><location><page_7><loc_36><loc_93><loc_36><loc_95></location>/negationslash</text>
<text><location><page_7><loc_7><loc_74><loc_50><loc_86></location>The second case corresponds to a toroidal magnetic field B ⊥ , laying in the plane of the accretion disc and tangential to the radiating circular orbit. In this case the Faraday rotations are opposite in the right and the left parts of the orbit. This gives the same value for the polarization degree p right = p left and the opposite values for the position angles χ right = -χ left . We present below the results for the right part of the orbit:</text>
<formula><location><page_7><loc_14><loc_67><loc_43><loc_73></location>〈 Q right 〉 = I right p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ f Q ( ϕ 0 ) ,</formula>
<formula><location><page_7><loc_11><loc_61><loc_50><loc_67></location>f Q ( ϕ 0 ) = 1 ϕ 0 arctan √ g 2 line + b 2 ϕ g line tan ϕ 0 , (24)</formula>
<text><location><page_7><loc_25><loc_55><loc_26><loc_57></location>f</text>
<formula><location><page_7><loc_14><loc_56><loc_43><loc_62></location>〈 U right 〉 = I right p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ f U ( ϕ 0 ) .</formula>
<text><location><page_7><loc_26><loc_55><loc_27><loc_56></location>U</text>
<text><location><page_7><loc_27><loc_55><loc_28><loc_57></location>(</text>
<text><location><page_7><loc_28><loc_55><loc_29><loc_57></location>ϕ</text>
<text><location><page_7><loc_29><loc_55><loc_30><loc_56></location>0</text>
<text><location><page_7><loc_30><loc_55><loc_32><loc_57></location>) =</text>
<formula><location><page_7><loc_8><loc_47><loc_50><loc_54></location>-1 2 ϕ 0 ln ∣ ∣ ∣ ∣ ∣ √ g 2 line + b 2 ϕ + b ϕ √ g 2 line + b 2 ϕ -b ϕ · √ g 2 line + b 2 ϕ -b ϕ cos ϕ 0 √ g 2 line + b 2 ϕ + b ϕ cos ϕ 0 ∣ ∣ ∣ ∣ ∣ . (25)</formula>
<text><location><page_7><loc_7><loc_31><loc_50><loc_36></location>It is interesting to note that f Q ( ϕ 0 ) monotonically grows from f Q ( π/ 2) = 1 to f Q = √ g 2 line + b 2 ϕ /g line ≥ 1 as ϕ 0 → 0.</text>
<text><location><page_7><loc_7><loc_36><loc_50><loc_50></location>∣ ∣ The expression for f Q is valid only for ϕ 0 ≤ π/ 2, and the formula for f U is valid for total interval 0 ≤ ϕ 0 ≤ π . The integrands in Eqs. (23) are symmetric relative to the angle ϕ 0 = π/ 2. This gives equalities f Q ( π/ 2) = f Q ( π ) = 1 and f U ( π/ 2) = f U ( π ). Due to the aforementioned symmetry, we can calculate values f Q and f U for π/ 2 ≤ ϕ 0 ≤ π from the values for interval 0 ≤ ϕ 0 ≤ π/ 2: f Q,U ( ϕ 0 ) = [ f Q,U ( π ) π -f Q,U ( π -ϕ 0 )( π -ϕ 0 )] /ϕ 0 .</text>
<text><location><page_7><loc_7><loc_28><loc_50><loc_32></location>The mean polarization degree p right ( B ϕ ) and the position angle χ right ( B ϕ ) can be derived from the following expressions:</text>
<formula><location><page_7><loc_26><loc_19><loc_50><loc_21></location>χ right = U f . (26)</formula>
<formula><location><page_7><loc_14><loc_18><loc_43><loc_27></location>p right ( B ϕ ) = p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ √ f 2 Q + f 2 U , tan2 f Q</formula>
<text><location><page_7><loc_7><loc_7><loc_50><loc_18></location>In Fig.2 we present the values p right ( B ϕ ) /p ( µ )(1 -sµ ) and | χ right | at b ϕ = 1 , 2 , 3 , 4 , 5 and g line = 1 , s = 0. Comparison of p right ( B ϕ ) with p c ( B ϕ ) in Fig.1 shows that p right > p c . This is evident, because p c corresponds to the sum of radiation from the right and the left parts of the observed areas (in this sum U = 0), and p right corresponds to the half of this area, where parameter U = 0. It means that in the wings of</text>
<text><location><page_7><loc_25><loc_6><loc_25><loc_8></location>/negationslash</text>
<figure>
<location><page_7><loc_52><loc_77><loc_91><loc_96></location>
<caption>Figure 2: The values p right ( B ϕ ) /p ( µ )(1 -sµ ) and | χ right | (dotted lines) at b ϕ = 1 , 2 , 3 , 4 , 5 and g line = 1 , s = 0.</caption>
</figure>
<text><location><page_7><loc_52><loc_66><loc_95><loc_69></location>the emitting lines the polarization is greater than in nearby continuum.</text>
<text><location><page_7><loc_52><loc_54><loc_95><loc_66></location>Let us consider the behavior of the polarization degree p line ( B ϕ , λ ) and the position angle χ line ( B ϕ , λ ) inside the broad spectral line in more detail, using our simple model of two equal gaussian lines with the equal right and left displacements from the central wavelength λ 0 . We label the intensities of these lines as I right and I left . According to Eqs.(24) and (25), we present the total observed Stokes parameters I, Q and U in the form:</text>
<formula><location><page_7><loc_64><loc_51><loc_95><loc_52></location>I ( µ ) = I right ( λ ) + I left ( λ ) , (27)</formula>
<formula><location><page_7><loc_53><loc_42><loc_95><loc_48></location>Q ( B ϕ , λ ) = ( I right ( λ ) + I left ( λ )) p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ f Q , (28)</formula>
<formula><location><page_7><loc_53><loc_35><loc_95><loc_41></location>U ( B ϕ , λ ) = ( I right ( λ ) -I left ( λ )) p line ( µ )(1 -sµ ) √ g 2 line + b 2 ϕ f U . (29)</formula>
<text><location><page_7><loc_52><loc_27><loc_95><loc_35></location>Recall that due to the displacement of the centers of the right and left lines with the gaussian shape the intensities I right ( λ ) and I left ( λ ) are different at a particular considered wavelength inside the full line. Only at the central wavelength λ 0 these intensities are equal due to the axial symmetry of our model.</text>
<text><location><page_7><loc_52><loc_22><loc_95><loc_26></location>Using Eqs.(27), (28) and (29), we obtain the following expressions for the total observed polarization degree p ( B ϕ , λ ) and the position angle χ ( B ϕ , λ ):</text>
<formula><location><page_7><loc_62><loc_17><loc_83><loc_20></location>p ( B ϕ , λ ) = p line ( µ )(1 -sµ ) f Q g 2 line + b 2 ϕ ( µ )</formula>
<formula><location><page_7><loc_63><loc_11><loc_95><loc_15></location>√ 1 + ( I right -I left ) 2 ( I right + I left ) 2 f U f Q 2 , (30)</formula>
<formula><location><page_7><loc_62><loc_10><loc_85><loc_20></location>√ × × ( )</formula>
<formula><location><page_7><loc_61><loc_7><loc_95><loc_10></location>tan 2 χ ( B ϕ , λ ) = I right -I left I right + I left · f U f Q . (31)</formula>
<figure>
<location><page_8><loc_9><loc_62><loc_84><loc_95></location>
<caption>Figure 3: The schematic illustration of the model of two emitting clouds.</caption>
</figure>
<text><location><page_8><loc_7><loc_52><loc_50><loc_54></location>Taking in Eqs.(30) and (31) I left = 0, we revert to Eq.(26) for the right part of the orbit.</text>
<text><location><page_8><loc_7><loc_44><loc_50><loc_51></location>The total rotation of the position angle inside the line width is equal to the difference of ∆ χ ≡ χ right -χ left , where χ right corresponds to the right-hand wing of line with I right /greatermuch I left . The χ left corresponds to the left-hand wing with I left /greatermuch I right . As a result, we have:</text>
<formula><location><page_8><loc_22><loc_37><loc_50><loc_42></location>| ∆ χ | = arctan ∣ ∣ ∣ f U f Q ∣ ∣ ∣ . (32)</formula>
<text><location><page_8><loc_7><loc_14><loc_50><loc_26></location>Now let us discuss shortly the polarization degree p inside the broad line. First of all, we notice that in the centre of the line λ = λ 0 the polarization is less than in the wings (c.f. Eq.(30) with I right = I left ). The polarization grows with the departure from λ 0 . This behavior of p line ( λ ) is observed in many objects from the catalog of Smith et al.(2002). According to Eq.(30), the ratio of p wing ( B ϕ , λ ) to p center ( B ϕ , λ ) becomes</text>
<text><location><page_8><loc_7><loc_25><loc_50><loc_40></location>∣ ∣ Note that the difference ∆ χ does not depend on the choice of the observer's reference frame. A non-zero value of ∆ χ is observed in many objects presented in the catalog of Smith et al. (2002) and is due to two reasons - the presence of the magnetic field B ϕ and the Keplerian rotation of the magnetized accretion disc. Fig.2 shows that ∆ χ depends on the parameter b ϕ and the angle ϕ 0 . Thus, for b ϕ = 5 and ϕ 0 /similarequal (140 · -160 · ) the value | ∆ χ | /similarequal 60 · .</text>
<formula><location><page_8><loc_16><loc_8><loc_50><loc_13></location>p wing ( B ϕ , λ ) p centre ( B ϕ , λ ) = √ 1 + (tan | ∆ χ | ) 2 . (33)</formula>
<text><location><page_8><loc_7><loc_7><loc_34><loc_9></location>For ∆ χ = 60 · this ratio is equal to 2.</text>
<text><location><page_8><loc_52><loc_49><loc_95><loc_54></location>Clearly, it is not possible to explain all details of p and χ in the our model of the sum of two spectral lines. But, above considerations tell us that the main characteristic features can be explained.</text>
<section_header_level_1><location><page_8><loc_52><loc_41><loc_95><loc_46></location>2.3 The model of H α line as two emitting compact clouds located in the right and left part of the orbit</section_header_level_1>
<text><location><page_8><loc_52><loc_31><loc_95><loc_40></location>The spectra of H α lines in the atlas of Smith et al.(2002) for many objects have sufficiently complicated structure - the existence of separate peaks and asymmetric shapes. There are only a few objects with symmetric shapes. They have comparatively small widths as compared to other, more complicated spectra.</text>
<text><location><page_8><loc_52><loc_19><loc_95><loc_31></location>A line with a complicated shape frequently can be approximated as a sum of two or more lines with gaussian shapes. For this reason we present the model of two compact optically thick clouds located in the opposite parts of an orbit in the accretion disc (Fig.3). The advantage of this model compared with the previous one is that we can take into account all the depolarizing Faraday parameters a, b ϕ and b ρ in a simple analytical form.</text>
<text><location><page_8><loc_52><loc_7><loc_95><loc_19></location>Let us take the first cloud in the right part of the orbit, characterized by the azimuthal angle ϕ , and the second cloud in the left part, characterized by ϕ . If it is necessary, locations of the emitting clouds can be chosen at arbitrary angles along the orbit. Our choice is the simplest for consideration. As usually, we write the Stokes parameters in the coordinate system with X-axis being perpendicular to the plane ( nN ), where the formulas have the simplest form. Further we will</text>
<text><location><page_9><loc_7><loc_88><loc_50><loc_97></location>use the observed polarization degree p and the total difference of the position angles between right and left parts of the spectral line ∆ χ , which do not depend on the choice of the reference frame. We also include in our formulas the contribution of the continuum radiation ( I c , Q c , U c ) in the region of spectral line. Then, the observed Stokes parameters are:</text>
<formula><location><page_9><loc_16><loc_84><loc_50><loc_87></location>I = I c + I right + I left , ξ = I right I left , (34)</formula>
<formula><location><page_9><loc_19><loc_75><loc_50><loc_77></location>+ I left p line ( µ )(1 -sµ ) g line , (35)</formula>
<formula><location><page_9><loc_15><loc_74><loc_42><loc_82></location>Q = Q c + I right p line ( µ )(1 -sµ ) g line A + + A -</formula>
<formula><location><page_9><loc_14><loc_69><loc_44><loc_73></location>U = U c + I right p line ( µ )(1 -sµ )( a + b ϕ ) A + +</formula>
<formula><location><page_9><loc_17><loc_65><loc_50><loc_68></location>+ I left p line ( µ )(1 -sµ )( a -b ϕ ) A -, (36)</formula>
<formula><location><page_9><loc_20><loc_61><loc_37><loc_63></location>A + = g 2 line +( a + b ϕ ) 2 ,</formula>
<formula><location><page_9><loc_21><loc_58><loc_50><loc_61></location>A -= g 2 line +( a -b ϕ ) 2 (37)</formula>
<text><location><page_9><loc_9><loc_57><loc_45><loc_58></location>The explicit formulas for Q c and U c are as follows:</text>
<formula><location><page_9><loc_14><loc_53><loc_44><loc_56></location>Q c = r +( g 2 c + b 2 -a 2 ) I c p c ( µ )(1 sµ ) ,</formula>
<formula><location><page_9><loc_14><loc_48><loc_50><loc_51></location>U c = r -( g 2 c + b 2 -a 2 ) √ I c p c ( µ )(1 sµ ) . (38)</formula>
<formula><location><page_9><loc_18><loc_47><loc_41><loc_56></location>√ √ 2 r -√ 2 r -</formula>
<text><location><page_9><loc_7><loc_41><loc_50><loc_47></location>Here r 2 = ( g 2 c + b 2 -a 2 ) 2 +4 a 2 g 2 c = g 4 c +2 g 2 c ( a 2 + b 2 )+( a 2 -b 2 ) 2 . Introducing the notation η c = p c ( µ )(1 -sµ ) /p c ( B , µ ), and using expressions (8) and (9), we can present formulas for Q c and U c in a simpler form:</text>
<formula><location><page_9><loc_10><loc_36><loc_47><loc_40></location>Q c = √ 1 + √ 1 -2 ag c η 2 c 2 I c p c ( B , µ ) √ 2 → I c p c ( B , µ ) ,</formula>
<formula><location><page_9><loc_13><loc_28><loc_44><loc_34></location>U c = √ √ √ √ 1 -√ 1 -( 2 ag c η 2 c ) 2 I c p c ( B , µ ) √ 2 → 0 .</formula>
<formula><location><page_9><loc_14><loc_31><loc_50><loc_39></location>√ √ √ ( ) (39)</formula>
<text><location><page_9><loc_7><loc_26><loc_48><loc_29></location>The last expressions are valid in the limit (2 ag c ) /η 2 c → 0.</text>
<text><location><page_9><loc_7><loc_21><loc_50><loc_27></location>In most sources from the catalog of Smith et al. (2002), the intensity I c is much smaller than I right + I left . For these cases one can neglect the contribution of the continuum radiation and the formulas for p line and χ line acquire fairly simple form:</text>
<formula><location><page_9><loc_10><loc_16><loc_50><loc_19></location>tan2 χ line = U line Q line = a g line + b ϕ g line · 1 -ξA + /A -1 + ξA + /A -, (40)</formula>
<formula><location><page_9><loc_13><loc_10><loc_45><loc_13></location>p line = p line ( µ )(1 -sµ ) g line (1 + ξA + /A -) (1 + ξ ) A + ×</formula>
<formula><location><page_9><loc_21><loc_5><loc_50><loc_9></location>× √ 1 + (tan 2 χ line ) 2 . (41)</formula>
<text><location><page_9><loc_54><loc_95><loc_82><loc_97></location>In the right wing, where ξ /similarequal 0, we have</text>
<formula><location><page_9><loc_66><loc_91><loc_95><loc_94></location>tan 2 χ right = a + b ϕ g line . (42)</formula>
<text><location><page_9><loc_52><loc_84><loc_95><loc_90></location>For the left wing one finds the same expression with ( -b ϕ ) instead of b ϕ . Using formula (42), we can obtain expression for the difference of the position angles between the right and left wings of the line:</text>
<formula><location><page_9><loc_66><loc_80><loc_81><loc_82></location>∆ χ = χ right -χ left =</formula>
<formula><location><page_9><loc_60><loc_73><loc_95><loc_77></location>= 1 2 ( arctan a + b ϕ g line -arctan a -b ϕ g line ) . (43)</formula>
<text><location><page_9><loc_52><loc_70><loc_95><loc_73></location>For the polarization degree in the right wing we derive the formula:</text>
<formula><location><page_9><loc_63><loc_63><loc_95><loc_68></location>p right = p line ( µ )(1 -sµ ) √ g 2 line +( a + b ϕ ) 2 . (44)</formula>
<text><location><page_9><loc_52><loc_48><loc_95><loc_62></location>For the left wing the polarization degree is higher because the Faraday depolarization parameter | a -b ϕ | is lower than in the right wing. If a = 0, the polarization degree p right = p left and χ right = -χ left . Presence of the magnetic field B ‖ (parameter a = 0) diminishes the polarization degree both in the right and left wings of the line, and also diminishes the difference | ∆ χ | = | χ right -χ left | . Besides, the functions p line ( λ ) and χ line ( λ ) become asymmetric relative to the center of the line λ 0 (if the intensities of lines I right ( λ ) and I left ( λ ) are the same gaussian functions).</text>
<text><location><page_9><loc_52><loc_62><loc_93><loc_64></location>Analogously, for the left wing one replaces b ϕ with ( -b ϕ ).</text>
<text><location><page_9><loc_59><loc_54><loc_59><loc_56></location>/negationslash</text>
<text><location><page_9><loc_52><loc_37><loc_95><loc_47></location>It is interesting to compare the polarization degrees in the wings and in the center of line. The general formula for ratio p wing /p center is very complex and we consider only the case a = 0, where this ratio reaches a maximum value. Taking ξ = 1 for the center of the line and ξ = 0 for the line wing, we obtain the following expression from the general formula (41):</text>
<formula><location><page_9><loc_66><loc_31><loc_95><loc_35></location>p wing p center = √ g 2 line + b 2 ϕ . (45)</formula>
<text><location><page_9><loc_52><loc_18><loc_95><loc_31></location>For b ϕ = 5 and g line = 1 this ratio is equal to 5.1, i.e. is considerably greater than the value from formula (33). It is quite natural, because formula (33) describes the mean value of the effect. Clearly, the averaging procedure diminishes the effect. Physically this effect arises as a consequence of the Faraday rotation of the polarization plane. In the center of the line the rotations from the right and the left lines have opposite directions and the parameter Q center reaches a lower value than that in the line wing.</text>
<text><location><page_9><loc_52><loc_7><loc_95><loc_18></location>The most important conclusion from the theoretical consideration of the structure of broad lines in AGN is the treatment of the symmetry of the polarization degree p line ( λ ) as the result of the azimuthal magnetic field B ϕ . If the symmetry of p ( λ ) is considerably broken, one can consider that B ϕ ∼ B ‖ , or the intensities of the right and the left emitting clouds are different.</text>
<section_header_level_1><location><page_10><loc_7><loc_93><loc_50><loc_97></location>3 The magnetic field strength in a broad line region of AGN</section_header_level_1>
<text><location><page_10><loc_7><loc_80><loc_50><loc_92></location>The standard Unified Sheme for AGN includes a central source of continuum (accreting SMBH); a region close to the outer radius of the accretion disc emitting broad emission lines (broad line region - BLR); a dusty rotating 'torus' on parsec scales; and gas emitting narrow emission lines on a scale of tens to hundreds of parsecs, ionized through the open cone defined by the torus edge (Antonucci & Miller 1985; Krolik & Begelman 1988; Urry & Padovani 1995).</text>
<text><location><page_10><loc_7><loc_66><loc_50><loc_80></location>The main unknown is the mechanism for the generation of the magnetic field during the process of accretion onto SMBH. Li (2002), Wang et al. (2002, 2003), Zhang et al. (2005) have studied the magnetic coupling process (MC) as an affective mechanism for transforming the kinetic energy of accreting gas into the magnetic energy. It is assumed that the disc is stable, perfectly conducting and Keplerian. The magnetic field on the black hole horizon is poloidal and varying as a power law with the distance from the central region.</text>
<text><location><page_10><loc_7><loc_60><loc_50><loc_66></location>Since the magnetic field on the horizon B H is brought and held by its surrounding magnetized matter of the accretion disc, there must exist the relation between the magnetic field strength near the BH horizon and the accretion rate ˙ M .</text>
<text><location><page_10><loc_7><loc_54><loc_50><loc_60></location>As a result, the magnetic field strength on the event horizon R H = R G (1+ √ 1 -a 2 ∗ ) is determined by the relation between the magnetic energy and the accretion kinetic energy densities (see Li 2002; Wang et al. 2002):</text>
<formula><location><page_10><loc_15><loc_46><loc_50><loc_53></location>B H = √ 2 k ˙ Mc R H = (2 kL bol /εc ) 1 / 2 R G [ 1 + √ 1 -a 2 ∗ ] . (46)</formula>
<text><location><page_10><loc_7><loc_35><loc_50><loc_47></location>Here R G = GM BH /c 2 , the bolometric luminosity L bol = ε ˙ Mc 2 , ˙ M is the accretion rate, c is the light velocity and ε is the radiative efficiency calculated by numerical simulations of Novikov & Thorne 1973, Krolik 2007, Shapiro 2007. The coefficient k presents the inverse plasma parameter k = P magn /P gas = 1 /β , where P gas and P magn are the gas and the magnetic pressures, respectively. For the equipartition case β = 1 and k = 1.</text>
<text><location><page_10><loc_9><loc_34><loc_33><loc_35></location>Eq.(46) is easily transformed into:</text>
<formula><location><page_10><loc_9><loc_25><loc_50><loc_31></location>B H = 6 . 3 · 10 8 ( M /circledot M BH ) 1 / 2 ( kl E ε ) 1 / 2 1 1 + √ 1 -a 2 ∗ , (47)</formula>
<text><location><page_10><loc_7><loc_16><loc_50><loc_23></location>The basic problem is the relation between the magnetic fields strengths at the first stable circular orbit R ms and the event horizon R H . The value of the radius R ms depends on the radius R G and the spin a ∗ , and can be presented in a form:</text>
<text><location><page_10><loc_7><loc_22><loc_50><loc_26></location>where l E = L bol /L Edd and the Eddington luminosity L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ).</text>
<formula><location><page_10><loc_23><loc_13><loc_50><loc_14></location>R ms = q ( a ∗ ) R G , (48)</formula>
<text><location><page_10><loc_7><loc_7><loc_50><loc_11></location>where parameter q > 1. For example, for a Schwarzschild black hole q = 6 and for the Kerr BH with the spin a ∗ = 0 . 998 q = 1 . 22 (Murphy et al. 2009).</text>
<text><location><page_10><loc_52><loc_82><loc_95><loc_97></location>Reynolds, Garofalo & Begelman (2006) argued that the plunging inflow can greatly enhance the trapping of large scale magnetic field on the black hole. Blandford (1990) has shown that the interaction of the large-scale magnetic field with the event horizon of rotating black hole can enhance the trapping of large-scale poloidal magnetic field on the horizon of the black hole, compared with the inner accretion flow and compared to the magnetic field strength derived from the relation between magnetic energy and accretion kinetic energy (Eq.(47)).</text>
<text><location><page_10><loc_52><loc_68><loc_95><loc_82></location>Recently Garofalo (2009) has showed that the dynamics of the plunge region of a thin black hole accretion disc and magnetic flux trapping can enhance the strength of the magnetic field threading the horizon by a significant factor. The results of his calculations were presented in fig.7 of Garofalo paper. It means that we obtain the following relation between the magnetic field strength at the first stable orbit B ms and the magnetic field strength at the event horizon of a black hole B H :</text>
<formula><location><page_10><loc_68><loc_65><loc_95><loc_66></location>B H = η ( a ∗ ) B ms . (49)</formula>
<text><location><page_10><loc_52><loc_58><loc_95><loc_64></location>The coefficient η can be obtained from fig.7 of the paper by Garofalo (2009). From this figure it follows that for a ∗ = 0 . 5 the value is η = 5 and for a ∗ = 0 . 0 and a ∗ = 0 . 998 we have η = 7 . 5.</text>
<text><location><page_10><loc_52><loc_42><loc_95><loc_58></location>Numerical simulations have been used to study magnetic field generation in astrophysical objects. For example, the existence of large-scale dynamos in magneto-convection under the influence of shear and rotation has been studied by Kapyla, Korpi & Brandenburg (2008). These authors have shown that the saturation field strength reaches, practically, the equipartition level B ≈ 0 . 7 B eq , i.e. k ≈ 0 . 5. Taking into account the shear flows can increase the magnetic field level. It means that the magnetization parameter can be equal to k ≈ 1.</text>
<text><location><page_10><loc_52><loc_34><loc_95><loc_43></location>We suggest that the magnetic field far inside in the accretion disc, and, especially, in the Broad Line Region (BLR) takes the toroidal form. Namely, the differential rotation in the accretion disc leads to an increase of the azimuthal field by winding up the poloidal field lines into the toroidal field lines (Bonanno & Urpin 2007).</text>
<text><location><page_10><loc_52><loc_22><loc_95><loc_34></location>In astrophysical objects differential rotation is often associated with magnetic fields of various strength and geometry. If the poloidal field has a component parallel to the gradient of the angular velocity, then differential rotation can stretch toroidal field lines from the poloidal ones. In the presence of the magnetic field, differential rotation can be a reason for various MHD instabilities, especially if the field geometry is complex.</text>
<text><location><page_10><loc_52><loc_17><loc_95><loc_22></location>Mayer & Pringle (2006) assumed that a dynamo process generates a local poloidal field B z in the accretion disc, and the magnitude of the poloidal component is small: B z /lessmuch B ⊥ .</text>
<text><location><page_10><loc_52><loc_11><loc_95><loc_17></location>Usually one assumes that regular dependence of the magnetic field on the radius R in the accretion disc exists from the first stable orbit R ms , and that dependence has a power law form:</text>
<formula><location><page_10><loc_65><loc_6><loc_95><loc_10></location>B ⊥ ( R ) = B ms ( R ms R ) n . (50)</formula>
<text><location><page_11><loc_7><loc_89><loc_50><loc_97></location>We assume two values for the parameter n . The value n = 1 derives the toroidal topology of the magnetic field (see Bonanno & Urpin 2007). The value n = 5 / 4 corresponds to the accretion process with hot accretion flows (Medvedev 2000).</text>
<text><location><page_11><loc_7><loc_80><loc_50><loc_89></location>For pure toroidal topology of the magnetic field in the accretion disc we have the depolarization parameter a = 0, and in this case Eqs.(8) and (9) for non-turbulent case ( C = 0) are transformed into Eq.(14). Recall that, according to definitions (11), magnetic field B ( R BLR ) can be determined, if the parameter b is known from the observed polarization:</text>
<formula><location><page_11><loc_19><loc_74><loc_50><loc_79></location>B ( R BLR ) = b 0 . 8 λ 2 √ 1 -µ 2 . (51)</formula>
<text><location><page_11><loc_7><loc_72><loc_50><loc_75></location>This field can be related to B ms . In the case of a power-law dependence (50) with n = 1, this relation becomes</text>
<formula><location><page_11><loc_8><loc_65><loc_50><loc_70></location>B ( R BLR ) = B ms R ms R BLR = 2 . 22 · 10 -4 ( M 9 l E ) 1 / 2 q ( a ∗ ) B ms . (52)</formula>
<text><location><page_11><loc_7><loc_60><loc_50><loc_64></location>We used here Eq.(3) for determining R BLR . Note that M 9 = M BH / 10 9 M /circledot . In this situation the depolarization parameter b for H α wavelength ( λ = 0 . 6563 µ m) is:</text>
<formula><location><page_11><loc_14><loc_54><loc_50><loc_59></location>b = 7 . 7 √ 1 -µ 2 q ( a ∗ ) ( M 9 l E ) 1 / 2 ( B ms 10 5 G ) . (53)</formula>
<text><location><page_11><loc_7><loc_52><loc_50><loc_55></location>For hot accretion flows n = 5 / 4 and the depolarization parameter b becomes</text>
<formula><location><page_11><loc_11><loc_44><loc_50><loc_49></location>b = 0 . 93 √ 1 -µ 2 ( M 9 l E ) 5 / 8 q 5 / 4 ( a ∗ ) ( B ms 10 5 G ) , (54)</formula>
<text><location><page_11><loc_7><loc_41><loc_50><loc_44></location>where q ( a ∗ ) = R ms /R G and R G = GM BH /c 2 . The explicit form of q ( a ∗ ) is given, for example, in Zhang et al. (2005).</text>
<text><location><page_11><loc_7><loc_34><loc_50><loc_41></location>Below we shall also consider the case of the equipartition between the gas and the magnetic pressures, i.e. k ≈ 1. Namely, the magnetic coupling process corresponds to this case (Li 2002; Wang et al. 2003; Zhang et al. 2005; Ma, Wang & Zuo 2006).</text>
<text><location><page_11><loc_7><loc_31><loc_50><loc_34></location>Using Eqs.(47) and (49), we transform relations (53) and (54) into the following forms:</text>
<text><location><page_11><loc_7><loc_24><loc_19><loc_25></location>and for n = 5 / 4:</text>
<formula><location><page_11><loc_14><loc_24><loc_50><loc_29></location>b = 1 . 53 √ 1 -µ 2 √ k ε q ( a ∗ ) η ( a ∗ )(1 + √ 1 -a 2 ∗ ) , (55)</formula>
<formula><location><page_11><loc_22><loc_14><loc_50><loc_17></location>q ( a ∗ ) η ( a ∗ )(1 + 1 a 2 ) . (56)</formula>
<text><location><page_11><loc_7><loc_7><loc_50><loc_13></location>Eqs.(55) and (56) allow us to estimate the radiation efficiency and therefore the rotation rate a ∗ of an accreting black holes. Below we use the spectropolarimetric atlas of AGNs by Smith et al. (2002) for specific estimates.</text>
<section_header_level_1><location><page_11><loc_52><loc_95><loc_95><loc_97></location>4 Magnetic field strength of Akn 120</section_header_level_1>
<text><location><page_11><loc_52><loc_79><loc_95><loc_94></location>According to Smith et al. (2002) the mean polarization degree in the continuum of Akn 120 is equal to p c /similarequal 0 . 35%, and is equal to /similarequal 0 . 4% in the H α line emission. We use here the data obtained by Smith et al. (2002) in 1998 October. The mean observed position angle have the same value for the continuum and line emission χ /similarequal 76 · . The inclination angle i = 48 · , µ /similarequal 0 . 67. Its value has been derived by Braatz & Gugliucci (2008) from water maser observations. The central black hole mass in Akn 120 is equal to M BH /similarequal 10 7 . 74 M /circledot (see Peterson et al. 2004).</text>
<text><location><page_11><loc_52><loc_55><loc_95><loc_79></location>For the inclination angle i = 48 · the polarization in the continuum from the accretion disc without magnetic field is expected at the level p c ( µ ) = 1 . 26% (Chandrasekhar 1960). This value is higher than the observed polarization degree and it means that the Faraday depolarization effect is really acting. The H α line spectrum shows the two-peak structure and can be represented as sum of two intensities with gaussian shapes. The difference of the positional angles ∆ χ is estimated to be between 70 · and 80 · . The intensity of the continuum radiation reaches ≈ 18% of the maximum line intensity near the centre. The behaviour of polarization in the continuum is very complex. It seems this behaviour occurs due to the existence of large-scale turbulent curls along the observed orbit. For that reason, it is more convenient to use the continuum - subtracted spectrum of Akn 120, presented in fig.24 of the mentioned Atlas by Smith et al. (2002).</text>
<text><location><page_11><loc_52><loc_40><loc_95><loc_55></location>We used formulas (31)-(37) to find the estimates for the parameters a, b ϕ , p line ( µ ) and g line . Attempts to estimate these parameters under the assumption p c ( µ ) /similarequal p line ( µ ) were unsuccessful. We propose that in the line radiating clouds there is true absorption of radiation (the existence of dust particles). As it is known (see, for example, Silant'ev 1980), the existence of absorption gives rise to a considerable increase of polarization escaping from the optically thick atmosphere. This effect is the consequence of absorption creating a peak like form of escaping emission.</text>
<formula><location><page_11><loc_53><loc_34><loc_95><loc_37></location>g c /similarequal 1 , a g line /similarequal 0 , b ϕ g line /similarequal 3 . 55 , p line ( µ ) g line /similarequal 4 . 07% . (57)</formula>
<text><location><page_11><loc_52><loc_11><loc_95><loc_33></location>Introducing first three parameters in Eq.(8), we obtain g line /similarequal 0 . 975. The estimate g line = 0 . 975 = 1 + C -sµ gives the relation between C and s . It means that the clouds are absorbing and the small scales are turbulent. The existence of large scale turbulence in clouds directly follows from very high line width. For the rest of radiation from the accretion disc outside the compact clouds we assume that absorption is absent and small scale turbulence is negligible ( C ≈ 0). From Eq.(57) it follows that p line /similarequal 3 . 97% and b ϕ /similarequal 3 . 46. The estimated value p line /similarequal 3 . 97% corresponds to the case when one takes into account the pure absorption of radiation by dust particles existing into emitting clouds. From Eq.(11) one can obtain an estimate of magnetic fields B ‖ /similarequal 0 G and B ϕ /similarequal 14 G.</text>
<text><location><page_11><loc_52><loc_7><loc_95><loc_11></location>In Fig.4 we present the observed intensity, polarization degree and variation of the azimuthal angle χ , and our model results. It is seen that the model curves practi-</text>
<formula><location><page_11><loc_14><loc_12><loc_43><loc_22></location>b = 0 . 19 √ 1 -µ 2 ( M 9 l E ) 1 / 8 q 1 / 4 ( a ∗ ) √ k ε × × √ -∗</formula>
<text><location><page_12><loc_28><loc_97><loc_28><loc_97></location>/s32</text>
<figure>
<location><page_12><loc_8><loc_70><loc_45><loc_96></location>
<caption>Figure 4: The comparison of observed (solid curves) and model data (dot curves) for Akn 120</caption>
</figure>
<text><location><page_12><loc_7><loc_50><loc_50><loc_62></location>cally coincide with the observed values. The observed intensity is approximated as sum of two gaussian intensities from symmetrically located clouds. The Doppler widths of these intensities are taken equal to ∆ λ T =70 ˚ A, the value ( u k /u turb ) sin ϕ √ 1 -µ 2 = 0 . 3, the ratio of maximum intensities of gaussians is I left /I right = 20 / 18. The centers of gaussian curves coincide with the observed places in Fig.24 of Smith et al. (2002).</text>
<text><location><page_12><loc_7><loc_41><loc_50><loc_50></location>The main problem is that the exact value of index n is unknown and its value depends strongly on the model of the accretion disc. Pariev, Blackman & Boldyrev (2003) suggest the following interval of values of this index 1 ≤ n ≤ 2. The value n = 1 corresponds to toroidal magnetic field (see Bonanno & Urpin 2007).</text>
<text><location><page_12><loc_7><loc_22><loc_50><loc_41></location>To estimate the magnetic field strength at the last inner circular orbit B ms we need to know the rotation rate of the central supermassive black hole (parameter a ∗ ). For a Schwarzschild black hole with a ∗ = 0 and q = 6 and for the toroidal magnetic field ( n = 1) we obtain from Eq.(49) B ms = 14 . 5 · 10 3 G . Now we can estimate the magnetic field strength B H at the horizon of the central black hole using the results of calculations by Garofalo (2009). He has calculated the ratio of the horizon-threading magnetic field and the magnetic field in the accretion disc as a function of the black hole spin. According to this calculations, for a ∗ = 0 the ratio B H /B ms = 7 . 5 and B H = 10 . 7 · 10 4 G .</text>
<text><location><page_12><loc_7><loc_7><loc_50><loc_16></location>Our results demonstrate that for a given value of the polarization degree the magnetic field strength at the inner radius r ms (and therefore on the horizon radius) is stronger for a Kerr black hole compared to Schwarzschild one. This result means also that for black holes with the same magnetic field strengths the degree of polarization for Kerr black holes is</text>
<text><location><page_12><loc_52><loc_94><loc_95><loc_97></location>larger than for Schwarzschild black holes (see Silant'ev et al. 2011).</text>
<section_header_level_1><location><page_12><loc_52><loc_90><loc_94><loc_91></location>5 Magnetic field strength of Mrk 6</section_header_level_1>
<text><location><page_12><loc_52><loc_66><loc_95><loc_88></location>According to Ho, Darling & Greene (2008), the mass of the central black hole in Mrk 6 is log( M BH /M /circledot ) = 7 . 97 ± 0 . 5, the ratio of the bolometric luminosity to the Eddington value is log( L bol /L E dd ) = -1 . 72. The inclination angle is i = 62 · . 7 , µ = 0 . 46 (Ho et al. 2008). It means that the standard (Sobolev-Chandrasekhar) magnitude of the polarization degree is p c ( µ ) = 2 . 52%. The observed mean polarization has been found at the level of p c = 0 . 90 ± 0 . 03, p ( H α ) = 0 . 85 ± 0 . 04 (Smith et al. 2002). The most remarkable fact is the jump of the mean position angle for two observational seasons of Feb 97 and Oct 98: ∆ χ ≈ 25 · . It is interesting that the value of the mean polarization remained the same. This jump occurred over 1-2 years, which is too short a time for such a large object as the accretion disc near the supermassive black hole. Thus, this problem remains unsolved.</text>
<text><location><page_12><loc_52><loc_35><loc_95><loc_65></location>Let us return now to the analysis of the data in the H α line. First of all, we see that the polarization degrees in the right and the left sides of the spectrum are practically equal - the left side has p line /similarequal 1 . 5%, and in the right side p line /similarequal 1 . 4%. From the theoretical considerations in section 2, it is clear that such a symmetrical form of the polarization degree can occur if the magnetic field B ‖ is much less than the azimuthal magnetic field B ϕ . A small decrease of polarization in the right-hand part is due to the reason that small value of the B ‖ component, directed to an observer, coincides with direction of B ϕ . In this situation the polarization of radiation slightly decreases compared to the left-hand part of the orbit, where the aforementioned magnetic fields are directed opposite to each other. Considering polarization near the line center, we assume p line ( centre ) /similarequal 0 . 5%. We also assume that in the center of the line the intensity from the left part of the orbit is approximately equal to that from the right part. The value of the intensity of the continuum radiation in Mrk 6 is relatively small, and we neglect it in our computation. Using formulas (34)-(36), one obtain:</text>
<formula><location><page_12><loc_54><loc_28><loc_95><loc_33></location>g c /similarequal 1 , a g line /similarequal 0 . 1 , b ϕ g line /similarequal 2 . 615 , p line ( µ ) g line /similarequal 3 . 9% . (58)</formula>
<text><location><page_12><loc_52><loc_9><loc_95><loc_28></location>Substitution of these parameters in Eq.(8) gives g line /similarequal 1 . 0006, i.e. practically 1. As in the case of Akn 120, the polarization p line /similarequal 3 . 9% implies that in H α -clouds there exists the absorption of radiation. Under the assumption of dipole radiation we have q c /similarequal 0 . 01 and the parameter s /similarequal 0 . 17. Because g line = 1 . 0006 /similarequal 1 = 1+ C -0 . 17 · 0 . 46 we find that the small scale turbulent parameter C /similarequal 0 . 08. For the difference ∆ χ of the position angles between the left and the right wings of the spectral line the expression (43) gives ∆ χ = 42 · . This value is consistent with the observational results. Eqs.(11) and (58) give estimate: B ‖ /similarequal 0 . 6G and B ϕ /similarequal 8 . 5G. Note that expression (58) supposes that I c p c /lessmuch I right,left p line ( µ ).</text>
<text><location><page_12><loc_52><loc_7><loc_95><loc_10></location>Now let us estimate the magnetic field strength in the accretion disc of Mrk 6 using the results of the polarimetric obser-</text>
<text><location><page_12><loc_7><loc_16><loc_50><loc_22></location>For the spin value of a ∗ = 0 . 5, ε = 0 . 081, q = 4 . 25 (Novikov & Thorne 1973) we obtain B ms = 6 . 8 · 10 3 G and B H = 3 . 4 · 10 4 G . At last, for a ∗ = 0 . 998, q = 1 . 22, ε = 0 . 32 we have B ms = 2 . 8 · 10 4 G and B H = 14 · 10 4 G .</text>
<text><location><page_12><loc_46><loc_91><loc_47><loc_91></location>/s32</text>
<text><location><page_12><loc_46><loc_84><loc_47><loc_84></location>/s32</text>
<text><location><page_12><loc_46><loc_76><loc_47><loc_76></location>/s32</text>
<text><location><page_13><loc_7><loc_83><loc_50><loc_97></location>vations from Smith et al. (2002). Eqs. (53)-(56) allow us to derive the magnetic field strength B ms at the inner radius of the accretion disc: B ms = (1 . 72 × 10 4 /q ) G . For a Swarzschild black hole, when q = 6, the magnetic field B ms = 2 . 9 · 10 3 G . For a Kerr black hole with a ∗ = 0 . 998 the parameter q = 1 . 22 and the magnetic field strength B ms = 1 . 4 · 10 4 G . According to Garofalo (2009, fig.7) the magnetic field strength at the horizon of the supermassive black hole is B H = 1 . 4 · 10 4 G for a ∗ = 0 and B H = 10 5 G for a ∗ = 0 . 998.</text>
<section_header_level_1><location><page_13><loc_7><loc_77><loc_50><loc_80></location>6 Magnetic fields of Mrk 985 and IZw1</section_header_level_1>
<text><location><page_13><loc_7><loc_66><loc_50><loc_75></location>The intensity spectrum of Mrk 985 has a two-peak shape and the spectrum of the polarization degree p line ( λ ) is quite symmetric (the p line ( left ) /similarequal 1 . 27% and p line ( right ) /similarequal 1 . 16%). In the centre of line p line ( centre ) /similarequal 0 . 5%. The mean polarization of the continuum radiation is 1.12%. Using formulas (33)-(37), we find that</text>
<formula><location><page_13><loc_21><loc_62><loc_37><loc_65></location>g c /similarequal 1 , a g line /similarequal 0 . 114 ,</formula>
<formula><location><page_13><loc_17><loc_57><loc_50><loc_60></location>b ϕ g line /similarequal 2 . 035 , p line ( µ ) g line /similarequal 2 . 75% . (59)</formula>
<text><location><page_13><loc_7><loc_53><loc_50><loc_56></location>We see that a nearly symmetric form of p line ( λ ) implies that a /lessmuch b ϕ , i.e. B ‖ /lessmuch B ϕ .</text>
<text><location><page_13><loc_7><loc_23><loc_50><loc_34></location>From Fig.15 in the atlas of Smith et al. (2002) we see that the difference of position angles between the right wing and the centre of line is equal ∆ χ /similarequal 31 -33 · . From general theory one finds that tan2∆ χ = a/g line + b ϕ /g line . Our estimates (59) give this value for the angle difference. The estimates of magnetic fields at distances R ms and R H can be obtained analogously as in the previous sections.</text>
<text><location><page_13><loc_7><loc_33><loc_50><loc_53></location>In the atlas of Smith et al. (2002) there is no information on the inclination angle i . It is interesting to estimate this angle assuming that g line /similarequal 1. Substituting parameters g c = 1 , a = 0 . 114 and b ϕ = 2 . 035 into formula (8) gives the value p c ( µ ) = 2 . 54%. This implies an estimate i /similarequal 64 · , µ /similarequal 0 . 44. Using the value p c ( µ ) = 2 . 54% we can calculate the value g line , corresponding to this polarization. This calculation demonstrates that the parameter g line acquires the value g line /similarequal 1 . 0013. The value p line ( µ ) = 2 . 75 at µ = 0 . 44 takes place at q a /similarequal 0 . 01 ( s = 0 . 17). The value g line /similarequal 1 . 0013 = 1 + C -0 . 17 · 0 . 44 occurs at C /similarequal 0 . 08. Using Eq.(11) and the value µ /similarequal 0 . 44, we find the estimates: B ‖ /similarequal 0 . 75 G and B ϕ /similarequal 6 . 6 G.</text>
<text><location><page_13><loc_7><loc_16><loc_50><loc_23></location>Now let consider the AGN IZw1. This object has p c /similarequal 0 . 67%, p line ( left ) /similarequal 0 . 7%, p line ( centre ) /similarequal 0 . 2% and p line ( right ) /similarequal 0 . 9%. The form of the polarization spectrum is slightly more asymmetric than in Mrk 985. Using general formulas (33)-(35) we find the following estimates:</text>
<formula><location><page_13><loc_29><loc_13><loc_29><loc_14></location>a</formula>
<formula><location><page_13><loc_21><loc_11><loc_36><loc_14></location>g c /similarequal 1 , g line /similarequal 0 . 52 ,</formula>
<formula><location><page_13><loc_17><loc_7><loc_50><loc_10></location>b ϕ g line /similarequal 3 . 905 , p line ( µ ) g line /similarequal 3 . 18% . (60)</formula>
<table>
<location><page_13><loc_61><loc_85><loc_86><loc_93></location>
<caption>Table 1: The obtained estimates of the magnetic field strengths.</caption>
</table>
<text><location><page_13><loc_52><loc_75><loc_95><loc_82></location>As in the case of Mrk 985, we found, that g line /similarequal 1 and p c ( µ ) /similarequal 2 . 68%. This corresponds to µ /similarequal 0 . 44. The value p line /similarequal 3 . 9% occurs at the absorption degree q a /similarequal 0 . 01 , s /similarequal 0 . 17. As a result, the small scale turbulence parameter C /similarequal 0 . 08.</text>
<text><location><page_13><loc_52><loc_67><loc_95><loc_75></location>As in the previous cases, using Eq.(11) and the value µ = 0 . 44 we can estimate the magnetic field strength for IZw 1: B ‖ = 3 . 42G and B ⊥ = 12 . 7G. It should be noted that in these cases we estimated the inclination angle i from the analysis of the polarization data.</text>
<text><location><page_13><loc_52><loc_58><loc_95><loc_67></location>The obtained estimates of the magnetic field strengths in BLR of these AGNs are presented in Table 1. The last value in the table is close to the one estimated by Afanasiev et al.(2011) where the polarimetric observations were made only for the continuum emission and did not include the emission from the broad line region.</text>
<section_header_level_1><location><page_13><loc_52><loc_54><loc_70><loc_56></location>7 Conclusions</section_header_level_1>
<text><location><page_13><loc_52><loc_37><loc_95><loc_52></location>For many objects of Smith et al. (2002) spectropolarimetric atlas the polarization spectra of a broad H α -line p line ( λ ) have a characteristic minimum at the center of the line and different maxima at the left and right wings. Usually the wing polarizations are higher than those in the nearby continuum. For many objects the position angle changes continuously from the left wing to the right one. We develop a new theoretical explanation for these features, different from the original explanation of Smith et al. (2002, 2004, 2005), taking into account that accretion discs can be magnetized.</text>
<text><location><page_13><loc_52><loc_15><loc_95><loc_37></location>Smith et al. explain the characteristic features of the H α -line assuming that the observed polarization is due to single scattering of non-polarized radiation from the BLR on two types of scattering clouds - a polar cloud around the radio jet, and clouds in the equatorial region. It appears (see Smith et al. 2005) that their mechanism has two characteristic features: a relatively low amplitude ( | ∆ χ | ≤ 20 -40 · ) of the position angle rotation from one line wing to the other one, and the need for a very high electron temperature ( T ∼ 10 6 K) in a nearby scattering cloud. In their atlas there are cases with both low ∆ χ < 20 · and high ∆ χ ∼ 80 · position angle rotations. The need for the high electron temperature arises from the observed polarization minimum in the line core. Besides, they neglect the intrinsic linear polarization of the radiation in BLR.</text>
<text><location><page_13><loc_52><loc_7><loc_95><loc_14></location>In our mechanism both effects can be explain by a single cause - the Faraday rotation of the polarization plane. The wide line width results from turbulence, which is related to the Keplerian rotation in the orbit. Clearly both explanations take place in reality.</text>
<text><location><page_14><loc_7><loc_86><loc_50><loc_97></location>The basis of our explanation is the assumption that both the continuum radiation and the spectral line emission originate in an optically thick magnetized accretion disc around the center of an AGN. The observed characteristic shape of the line polarization appears as a result of the Faraday rotation of the polarization plane in the accretion disc having a normal magnetic field B ‖ and an azimuthal field B ϕ .</text>
<text><location><page_14><loc_7><loc_46><loc_50><loc_85></location>We propose that the regions of the line emission can be represented as a comparatively dense absorbing turbulent clouds rotating with the Keplerian velocity around the center of the AGN. These clouds are flattened, optically thick and magnetized. They emit the polarized radiation in accordance with the Milne problem law. The observed emission line is a sum of radiation from clouds rotating in the right and the left sides of the orbit. Due to Doppler displacements, emission from the one side is, as a whole, reddened ( λ ≥ λ 0 ), and emission from the other side has the opposite λ -displacement. The Faraday rotations by azimuthal magnetic field B ϕ in the left and the right sides of the orbit are opposite and, as a result, in the center of line the sum of emissions is less polarized than in the wings. The continuous rotation of the position angle χ from one wing of line to the opposite wing arises for the same reason. The projection of the normal magnetic field B ‖ along the line of sight gives an additional Faraday rotation. It is the same in both sides of the radiating orbit. This additional rotation in one side of orbit increases the total Faraday rotation, and in opposite side decreases the total rotation. For this reason B ‖ magnetic field gives rise to an asymmetric (relative to the central wavelength λ 0 ) profiles for both the polarization degree p line ( λ ) and the position angle χ line ( λ ). The presented theory allows us to estimate the components B ϕ and B ‖ in the broad line emission regions, and also in nearby regions of the continuum radiation.</text>
<text><location><page_14><loc_7><loc_28><loc_50><loc_44></location>If the polarizations in the left and the right wings are slightly different, then the value B ‖ /lessmuch B ϕ . This helps us to estimate the B ϕ -component from more simple formulas for continuum polarization. Objects in which this is the case are ESO 141-635, IZw1, Mrk 6, Mrk 290, Mrk 985 and NGC 5548. The objects with a strong asymmetry of p line ( λ ) are characterized by magnetic fields B ϕ ∼ B ‖ . Such objects are Akn 120, Akn 564,KUV 18217+6419, Mrk 304, Mrk 335, Mrk 841, MS1849.2-7832 and NGC 4593. Other objects have fairly complex polarization spectra, they appear to be distorted by large-scale turbulent motions.</text>
<text><location><page_14><loc_7><loc_7><loc_50><loc_27></location>Using the estimated values of the magnetic field in broad line regions (usually B ‖ /lessmuch B ϕ and B ϕ ∼ 10 G) , one can estimate the magnetic field B ms at the last stable orbit near the black hole, and then the field B H at the radius of the event horizon. These estimates are dependent on the different assumptions about the slope of the power-law distribution of the magnetic field inside the accretion disc. We have used the most common assumptions to obtain the values of the magnetic field ∼ 10 4 -10 5 G. These values of the magnetic field are in a good agreement with other estimates. Thus, we determined the magnetic field strengths in various places in the accretion discs of AGNs from the real observational polarization data.</text>
<section_header_level_1><location><page_14><loc_52><loc_95><loc_73><loc_97></location>Acknowledgments</section_header_level_1>
<text><location><page_14><loc_52><loc_85><loc_95><loc_94></location>This research was supported by the program of Prezidium of RAS No.21, the program of the Department of Physical Sciences of RAS No.16, by the Federal Target Program 'Scientific and scientific-pedagogical personnel of innovative Russia' 2009-2013 and the Grant from President of the Russian Federation 'The Basic Scientific Schools' NSh-1625.2012.2.</text>
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</document>
[
{
"title": "Magnetic fields of active galactic nuclei and quasars with polarized broad H α lines",
"content": "N.A. Silant'ev 1 , Yu.N. Gnedin 1 , 2 ∗ , S.D. Buliga 1 , M.Yu. Piotrovich 1 and T.M. Natsvlishvili 1 1 Central Astronomical Observatory at Pulkovo of Russian Academy of Sciences, Pulkovskoye chaussee 65, Saint-Petersburg, 196140, Russia 2 St.-Petersburg State Polytechnical University, Polytechnicheskaya 29, Saint-Petersburg, 195251, Russia February 19, 2018",
"pages": [
1
]
},
{
"title": "1 Introduction",
"content": "We present estimates of magnetic field in a number of AGNs from the Spectropolarimetric atlas of Smith, Young & Robinson (2002) from the observed degrees of linear polarization and the positional angles of spectral lines (H α ) (broad line regions of AGNs) and nearby continuum. The observed degree of polarization is lower than the Milne value in a nonmagnetized atmosphere. We hypothesize that the polarized radiation escapes from optically thick magnetized accretion discs and is weakened by the Faraday rotation effect. The Faraday rotation depolarization effect is able to explain both the value of the polarization and the position angle. We estimate the required magnetic field in the broad line region by using simple asymptotic analytical formulas for Milne's problem in magnetized atmosphere, which take into account the last scattering of radiation before escaping from the accretion disc. The polarization of a broad spectral line escaping from disc is described by the same mechanism. The characteristic features of polarization of a broad line is the minimum of the degree of polarization in the center of the line and continuous rotation of the position angle from one wing to another. These effects can be explained by existence of clouds in the left (keplerian velocity is directed to an observer) and the right (keplerian velocity is directed from an observer) parts of the orbit in a rotating keplerian magnetized accretion disc. The base of explanation is existence of azimuthal magnetic field in the orbit. The existence of normal component of magnetic field (usually weak) makes the picture of polarization asymmetric. The existence of clouds in left and right parts of the orbit with different emissions also give the contribution in asymmetry effect. Assuming a power-law dependence of the magnetic field inside the disc, we obtain the estimate of the magnetic field strength at first stable orbit near the central supermassive black hole (SMBH) for a number of AGNs from the mentioned Spectropolarimetric atlas. Keywords : accretion discs, magnetic fields, polarization, active galactic nuclei. Smith et al. (2002) presented optical spectropolarimetric atlas of 36 nuclei of Seyfert 1 Galaxies. The data were obtained with the William Herschel and the Anglo-Australian Telescopes from 1996 to 1999. It is well-known that spectropolarimetry is an important tool in studies of active galactic nuclei (AGN). The spectropolarimetric data provide the detailed view into the inner regions of active galactic nuclei, including an accretion disc and accretion flows around a supermassive black hole (SMBH), thus allowing one to probe the structure and kinematics of the polarizing material around the accreting SMBH. Smith et al. (2002) objects exhibit a variety of characteristics with the average degree of polarization ranging from 0 . 2 to 5 percent. They show many variations both in the degree p line ( λ ) and position angle χ line ( λ ) of polarization across the broad H α emission line. The characteristic feature of p line ( λ ) is the minimum in the line centre, which is usually less than the polarization degree p c ( λ ) in nearby continuum. The second feature is the monotonic increase of positional angle from one line wing to the other. Note also that there exists little difference in the mean polarization degrees and position angles of nearby continuum and H α line for nine of Seyfert galaxies (Mrk 6, Akn 120, Mrk 896, Mrk 926, NGC 4051, NGC 6814, NGC 7603, UGC 3478, ESO 012-G21). For 22 measurements out of 45, the mean positional angles χ line and χ c are practically the same. It should be emphasized that the position angles of polarized continuum and H α line coincide more frequently than their polarization degrees. The mean value of the polarization degree in continuum over all sources is 0.68%, and the same value for H α lines is 0.66%. A position angle is most sensitive to the geometry of emitting region. For that reason, it is most probable that both emitting regions are located near one another, i.e. they located in an accretion disc and their scale sizes are similar: R BLR ≈ R λ , where R λ corresponds to the scale size of an accretion disc for the continuum radiation with given wavelength λ . It is generally accepted that AGNs are powered by the release of gravitational energy from gas accreted onto supermassive black holes (SMBH). The well-known anti-correlation between the radius of the broad-line region (BLR) and the velocity width of broad emission lines for AGNs supports the idea that the BLR gas is virialized and that its velocity is dominated by the gravity of the SMBH (Peterson & Wandel 2000; Onken & Peterson 2002). Most of the recent results lead to the conclusion that BLR presents a flattened rotating system. Many authors (Vestergaard et al. 2000; Nikolajuk et al. 2006; Sulentic et al. 2006; La Mura et al. 2009; Bon et al. 2009; Punsly & Zhang 2010) pointed out that considerable flattening and a predominantly planar orientation are likely to be the intrinsic property of the BLR structure. This conclusion allows us to consider BLR as an outer part of geometrically thin accretion disc that is optically thick with respect to the electron Thomson and the Rayleigh scattering processes. Seyfert galaxies were traditionally divided into two classes according to the presence or absence of broad optical lines. Antonucci & Miller (1985) explained this phenomenon by obscuration by a dusty torus with different orientation with respect to an observer. The orientation-based unification model has become quite popular, but it has also been confronted by more specialized observations (see, for example, Zhang & Wang 2006; Wang & Zhang 2007); in particular, there is evidence for the existence of a special subclass of Seyfert 2 lacking hidden broad-line regions (Zhang & Wang 2006). Thus, the paradigm of unification scheme for all Seyfert galaxies remains a matter of debate (Miller & Goodrich 1990; Tran 2001, 2003). The basic feature of Smith et al. (2002, 2004, 2005) models is that the polarization plane for most of Seyfert galaxies is parallel to the direction of the radio jet. Simultaneously, these models postulate that the radio jet direction is perpendicular to the accretion plane. The latter assumption is questionable. In reality, the radio jets frequently have significant bends near the radio core. The angle of the bend depends on the ratio of radial and toroidal magnetic fields in the accretion disc. Besides, the direction of the jet appears to change with time (see, for example, Britzen et al. 2009; Rastorgueva et al. 2011). Therefore, the coincidence of the direction of the radio jet and the polarization plane does not mean that the electrical vector of the polarized radiation E is perpendicular to the accretion disc. Of course, one can introduce the angle between the radio jet and the electric field E as an additional characteristic of AGNs. But, strictly speaking, this angle is not necessarily related to the real inclination of E with respect to the accretion disc. As a last resort, this angle may be considered in a probabilistic sense. The existence of many cases when the position angle of radiation has intermediate value between parallel or perpendicular to the direction of the radio jet also demonstrates that real direction of E does not correlate with the jet direction. As a result, we conclude that the models describing the polarization behavior in AGNs should not assume that the radio jets are perpendicular to accretion discs; instead, the explicit dependence on the inclination angle i of the accretion disc needs to be taken into account. It is commonly accepted (see, for example, Blaes, 2003) that the accretion discs are magnetized. The existence of radio jets is usually associated with strong magnetic fields in centers of AGNs and quasars. Numerous theoretical models demonstrate the power-law dependence of the magnetic field distribution in an accretion disc. Usually accretion discs are considered as geometrically thin slabs with Thomson optically depth τ /greatermuch 1. The scattering-induced linear polarization can be as high as ∼ 12% for edge-on viewing (Chandrasekhar 1960). However, in the real situation of a magnetized accretion disc, the degree of polarization p will be reduced due to Faraday rotation of the radiation polarization plane while a free photon travels between the consequent scatterings. Recall that the angle of Faraday rotation Ψ at the Thomson optical length τ is equal to where the wavelength of radiation λ is measured in microns and the magnetic field B is measured in Gauss. The angle Θ is the angle between the direction of light propagation n and the direction of B . The decrease of the polarization degree due to Faraday rotation occurs as a result of summation of chaotic angles of rotations in the multiple scattering process. This process has been considered in many papers (for example, Silant'ev 1994; Agol & Blaes 1996; Gnedin & Silant'ev 1997). Clearly, the value Ψ ∼ 1 at the mean free path τ ∼ 1 can decrease considerably the standard Chandrasekhar's polarization degree. Besides, the dependence of Ψ on the wavelength and magnetic field gives rise to characteristic dependencies of the polarization degree p and the position angle χ of radiation on λ , which allows us to estimate the strength and direction of the magnetic field in the scattering region. Below we develop a new model for the formation of polarization in AGNs, which does not use the assumption of the position angle of observed radiation being correlated with the direction of the radio jet. We hypothesize that the observed polarization is due to intrinsic polarization of radiation outgoing from the magnetized optically thick accretion disc (the Milne problem in magnetized atmosphere). In our model, the characteristic features of polarization mentioned above are explained by the topology of the magnetic field in the accretion disc, when the Faraday rotation of the polarization plane is taken into account. Primarily, we suppose that the whole radiating surface of the magnetized accretion disc is observed, i.e. that the inclination angle i is such that the obscuring torus (if it really exists) does not intersect the line of sight. We also consider the case when we observe only a part of total surface of accretion disc, i.e. we take into account the obscuring torus. It appears that our model and the usual pure geometrical model of Smith et al. (2002, 2004, 2005), which takes into account single scattering of BLR-photons in nearby clouds, are two competing explanations for the polarization properties of the accretion discs. All actually observed polarization degrees p c are much smaller than the value in the Milne problem in nonmagnetized atmosphere at the same inclination angle. Recall that the Milne problem deals with the radiative transfer in an optically thick atmosphere, where the sources of thermal radiation are located far from the surface, at depth with τ /greatermuch 1. In optically thick accretion discs the main source of thermal radiation is found at the midplane of the disc, and the outgoing radiation is described by the solution of the Milne problem. The mean value of p c in the atmosphere with pure electron scattering is equal to 3.1%, and the maximum value is 11.7%. The outgoing radiation in case of an absorbing atmosphere has a much greater polarization, because the intensity peaks near the surface. In this case, most of polarization arises analogously to the process of a single scattering of a radiation beam near the surface. For the Milne problem in spectral lines, the value p line is less than in continuum (see, for example, Ivanov et al. 1997). For the accretion disc models, the main challenge is to determine the scale length of the disc - i.e. the radius where the disc temperature matches the rest frame wavelength of the monitoring band. A semi-empirical method for measuring the disc scale length has been developed (Kochanek et al. 2006; Morgan et al. 2006, 2008; Poindexter, Morgan & Kochanek 2008). These authors used microlensing variability, observed for gravitationally lensed quasars, to find the accretion disc scale length for a given observed (or rest-frame) wavelength. Clearly, such a scaling has to be consistent with the most popular accretion disc model of Shakura & Sunyaev (1973). As a result, Poindexter et al. (2008) presented the following relation for the scale length of a standard geometrically thin accretion disc: The wavelength dependence, R λ ∼ λ 4 / 3 rest , corresponds to the typical (for Shakura-Sunyaev disc model) effective temperature: T e = T in ( R/R in ) -3 / 4 , where R in is the inner radius of an accretion disc and T in is the temperature corresponding to that radius. Here L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ) erg s -1 is the Eddington luminosity, M BH is the black hole mass, ε is the rest-mass radiation conversion efficiency, and L bol is the bolometric luminosity. Numerous papers provided measurements of BLR sizes for AGNs (see, for example, Peterson et al. 1994, 2004; Wu et al. 2004; Bentz et al. 2009; Shen & Loeb 2010; Greene et al. 2010). Kaspi et al. (2007) have compiled the observational data for Seyfert galaxies and nearby quasars with black hole masses estimated with the reverberation mapping technique. Most recently Shen & Loeb (2010) have suggested an empirical analytic formula for R BLR that is very useful for various estimates and applications: Here M 8 = M BH / 10 8 M /circledot . We will use this formula in our further calculations. Below we estimate the magnetic field strength in BLR of AGN and QSO from the data from the spectropolarimetric atlas presented by Smith et al. (2002). The λ - dependence of the observed polarization degree and position angle in H α line is very complicated. It appears to be produced by large-scale chaotic motions in the accretion disc.",
"pages": [
1,
2,
3
]
},
{
"title": "2 Basic equations",
"content": "To estimate the degree of polarization p and the position angle χ of radiation escaping from the magnetized atmosphere we use the standard radiative transfer equations for Stokes parameters I, Q and U (see, for example, Silant'ev 1994; Dolginov, Gnedin & Silant'ev 1995; Silant'ev 2002, 2005). This system of equations has a fairly complicated form. Numerical solutions have so far been obtained only for the case when magnetic field B is parallel to the normal N to an atmosphere (see Silant'ev 1994; Agol and Blaes 1996; Shternin et al. 2003). For our purpose, however, it is sufficient to use a simple asymptotic theory, which can be presented in an analytical form for an arbitrary direction of the magnetic field in the atmosphere (Silant'ev 2002, 2005; Silant'ev et al. 2009). In this approximation, the intensity of the radiation I ( z, µ ) obeys a usual transfer equation with the Rayleigh phase function, and the system of equations for parameters Q and U can be presented in the following form: where B Q ( z, µ ) describes the source function for parameter Q due to the contribution of intensity scattering in nonmagnetized atmosphere (in this case B U ≡ 0), µ = nN is the cosine of the angle between the direction of light propagation n and the normal N to the atmosphere, α is the total extinction factor due to Thomson scattering and pure absorption on dust particles, the value q = σ a / ( σ a + σ s ) (Silant'ev et al., 2009) is the degree of absorption, C describes the additional extinction of polarized radiation due to the fluctuating component B ' of the magnetic field in the atmosphere (see below). Eq.(4) is valid in the limit of large Faraday rotation parameter δ ≥ 1. A solution of Eq.(4) results in the following expression for parameters Q ( n , B ) and U ( n , B ) for the radiation escaping from the magnetized atmosphere: /negationslash At δ ≥ 1, the first non-zero term of integrating by parts of Eq.(5) gives rise to the asymptotic expression which has an analytical form and can be used for an arbitrary direction of the magnetic field. For example, for the case B Q (0 , µ ) = 0 we have: For the Milne problem in absorbing atmosphere, a more sophisticated theory (see Silant'ev 1994, 2002) gives rise to the following expressions: Here p (1) ( µ ) is the polarization degree of outgoing radiation, which takes into account only the last scattering before escaping the atmosphere. The value p (1) ( µ ) gives the main contribution to p ( µ ) - exact polarization degree of outgoing radiation for a non-magnetized atmosphere. For this reason, below we use the value p ( µ ) instead of p (1) ( µ ), which for q = 0 is presented in Chandrasekhar (1960), and for the absorbing atmosphere in Silant'ev (1980). The value s is the root of the characteristic equation, tabulated by Silant'ev (1980). If the degree of the true absorption is small ( q /lessmuch 1), the parameter s = √ 3 q . First, let us consider the case when the whole surface of a radiating accretion disc is observed. In this case, the Stokes polarization parameters of continuum radiation Q c ( ϕ ) and U c ( ϕ ) must be averaged over all azimuthal angles ϕ , characterizing the position of a radiating surface element on a circular orbit in the accretion disc ( -π ≤ ϕ ≤ π ). The normal N and the direction to an observer n are the same for all parts of the accretion disc surface. Therefore, the reference frame of the accretion disc is common to all parameters Q c ( ϕ ) and U c ( ϕ ) of radiation escaping from the disc. In this case, the averaging procedure consists of integrating these parameters over the azimuthal angle ϕ . Note, that cos Θ depends on ϕ and the integral over ϕ can be taken analytically only over the interval ( -π, π ). As a result, the observed values for the degree of polarization and the position angle can be derived analytically. Silant'ev et al. (2009) presented the detailed description of the behavior of these quantities for continuum radiation. The degree of linear polarization of continuum p c and the position angle χ c for an accretion disc can be expressed in the analytical form: Here µ = cos i , where i is the inclination angle (angle between the light propagation direction n and the normal N to the accretion disc). The degree of polarization p c ( µ ) corresponds to a non-magnetized accretion disc. The value of p c ( µ ) for the continuum radiation presents the classical solution of Milne problem (Chandrasekhar 1960) with p (0) = 11 . 7%. The value of the position angle χ c = 0 corresponds to oscillations of the wave electric vector perpendicular to the plane ( nN ). For spectral lines in isotropic medium the value p line ( µ ) depends on the specific quantum numbers of the transitions (see, for example, Chandrasekhar 1960) and on the shape of the line. For a dipole type transition and the Doppler line shape, p line ( µ ) in the atmosphere with pure electron scattering has the same functional form as Chandrasekhar value p c ( µ ), with maximum value of 9.44% instead of 11.71% (see Ivanov et al. 1997). In isotropic medium we have to average an atom over all orientations. For such medium the transfer equation coincides with the usual system for Rayleigh scattering with an additional term, which describes unpolarized radiation. Such average naturally occurs due to usual thermal motions. Considering various quantum numbers for H α line, we see that this additional term is larger than the Rayleigh scattering term (see Chandrasekhar 1960), and the maximum degree of polarization becomes ∼ 3% instead of 9.44%. Therefore, the observed polarization can be explained if the atmosphere also has pure absorption of H α line (the existence of dust). In absorbing atmosphere the polarization degree p line can be larger than that in the non-absorbing atmosphere. Broad H α lines presented in atlas Smith et al. (2002) have very high widths, laying in the interval 50 - 200 angstroms. In such situations the total line (sum of 5 sub levels) can be described by one absorption coefficient with the Doppler shape (see, for example, Varshalovich, Ivanchik & Babkovskaya 2006; Lekht et al. 2008). Our technique takes into account the Faraday rotation during propagation of polarized radiation after the last scattering before escaping from the atmosphere. The region of broad-line emission is too far from the center of an accretion disc and has low magnetic fields. For this reason, one does not need to take into account the known Zeeman effect. The parameter where the negative term ( -sµ ) arises in the Milne problem in absorbing atmosphere (see Chandrasekhar 1960). For small degree of true absorption q = σ absorb / ( σ scattering + σ absorb ) /lessmuch 1 the factor s /similarequal √ 3 q . The regions of the line emission are different from those of continuum radiation. Usually one assumes that the parameter g c /similarequal 1 in most of areas of the accretion disc. To explain polarization of the line emission, we have to consider that this emission escapes from optically thick clouds with its own dimensionless parameters g line . The dimensionless parameters a and b describe the Faraday depolarization of radiation: where B z ≡ B ‖ is the component of the magnetic field directed perpendicular to the accretion disc surface, and B ⊥ = √ B 2 ρ + B 2 ϕ is the magnetic field in the accretion disc plane. The component B ⊥ is perpendicular to B ‖ . Due to axial symmetry, the inclination angle ϕ ∗ ( B ϕ /B ρ = tan ϕ ∗ ) is constant along a circular orbit. The value 0 . 8 λ 2 B is numerically equal to the Faraday rotation angle at the Thomson optical depth of τ = 2, if the polarized radiation propagates along the magnetic field direction. Here and in what follows, we take magnetic field in Gauss and wavelengths in microns. The dimensionless parameter C describes the real situation in a turbulent magnetized plasma and characterizes a new effect - additional extinction of the polarized radiation (parameters Q and U ) due to incoherence of the Faraday rotation in small-scale turbulent eddies (see Silant'ev 2005): where τ is the Thomson optical depth of a turbulent eddy ( τ /lessmuch 1), 〈 ( B ' ) 2 〉 is the mean value of fluctuations of the magnetic field, and f B ≈ 1 is a parameter describing the integrated correlation of the B ' values at two-closely spaced points in the accretion disc. It should be noted that the diffusion of radiation in the inner regions of the accretion disc also produces depolarization due to multiple scatterings. Presence of magnetic field and, therefore, the Faraday rotation effect, only increases the depolarization process. As a result, the polarized radiation emitted by a plane-parallel atmosphere at a specific inclination angle is considerably lower as compared to the classical Chandrasekhar-Sobolev value (see, for example, Gnedin & Silant'ev 1997). But the main feature of Faraday depolarization is the explicit wavelength dependence for both the polarization degree and the position angle. It is interesting to note that at a = b the polarization degree p c ( B , µ ) takes a maximum value (the term ( a 2 -b 2 ) 2 is zero in expression (8)). This effect takes place due to the opposite Faraday rotations from magnetic fields B ‖ and B ⊥ in some places along an orbit. All formulas presented above show that polarimetric observations allow us to derive the magnetic field strength and its topology in the BLR region, where the polarized radiation escapes the accretion disc. Using various models connecting magnetic field B H at the black hole horizon with the magnetic field B ms at the first stable orbit R ms nearest to the centre of the system, and then using the power law dependence of the magnetic field from R ms up to R BLR , we can estimate the magnetic field strength and the parameters that control it, such as the spin of the black hole a ∗ , the conversion efficiency of kinetic into radiative energy ε , and the magnetization parameter k = P magn /P gas ( P magn and P gas are magnetic pressure and gas pressure, in accreting plasma, respectively). Frequently one uses simple formulas for p c and χ c , corresponding to particular cases of pure normal B ‖ and of pure perpendicular B ⊥ : In the latter case χ c ≡ 0 due to the axial symmetry of the problem. Now let us consider the case when the radiating gas along a particular orbit in the accretion disc is partly obscured by some dust cloud (an obscuring torus). Clearly, for pure normal magnetic field B ‖ N , the unobscured part of the orbit has the same polarization degree p c ( B ‖ ) and the position angle χ c ( B ‖ ) as in the case of completely unobscured orbit (see Eq. (13)). If the magnetic field is toroidal B ϕ , i.e. is tangent to the orbit, we can derive the following analytical expressions: Here the parameter b ϕ = 0 . 8 λ 2 B ϕ √ 1 -µ 2 , the angle ϕ 0 describes the unobscured part of the orbit (we see the orbit within azimuthal angles -ϕ 0 ≤ ϕ ≤ ϕ 0 ). At ϕ 0 = π (complete orbit), Eq.(15) coincides with Eq.(14). Eq.(15) for f Q ( ϕ 0 ) is valid for ϕ 0 ≤ π/ 2. For π/ 2 ≤ ϕ 0 ≤ π one can use the relation f Q ( ϕ 0 ) = [ πf Q ( π/ 2) -( π -ϕ 0 ) f Q ( π -ϕ 0 )] /ϕ 0 . A more detailed derivation of these formulas is given below, in subsection 2.2 (for a spectral line case). Dependence of p c ( B ϕ ) /p c ( µ )(1 -sµ ) on ϕ 0 is presented in Fig.1 for values g c = 1, b ϕ = 1 , 2 , 3 , 4 , 5, and s = 0. It is interesting that for ϕ 0 = π/ 2 (half of the full orbit is observed) the polarization degree coincides with the result (14) for the fully unobscured orbit ( f Q ( π/ 2) = f Q ( π ) = 1).",
"pages": [
3,
4,
5
]
},
{
"title": "2.1 The case of a spectral emission line",
"content": "In the catalog of Smith et al. (2002) the polarimetric data both in the continuum and in the H α emission line are presented. In our model of a rotating accretion disc (with the Keplerian velocity u k ) one part (the right side) of the disc ( ϕ = 0 ÷ π ) corresponds to motion from an observer and the second part (the left side) moves towards the observer ( ϕ = π ÷ 2 π ). According to the Doppler formula, wavelengths of radiation from the first part are greater than the central value λ 0 , and from the second part are smaller than λ 0 . The value λ 0 = (1 + z ) λ rest , where z is redshift parameter of the system and λ rest = 0 . 6563 µ m is the rest frame wavelength of the H α line. Here we restrict ourselves to a specific case of a spectral line with the Doppler shape. The line is described by following normalized shape function: As in the previous case of continuum radiation, we assume that the X-axis is perpendicular to plane ( nN ). The Keplerian velocity u k corresponds to the radius R BLR : u k = √ GM BH /R BLR , where G is gravitation constant. The usual Doppler line width ∆ λ T = ( u turb /c ) λ 0 is mainly due to chaotic turbulent velocities. The displacement of the line centre for radiation emitted from the part of the disc with the azimuthal angle ϕ is ( u k /c ) λ 0 √ 1 -µ 2 sin ϕ . Thus, the normalized shape function of radiation emitted from ϕ -part of the orbit has the form: Observed radiation flux F λ from a surface element dS of the ring with the radius R BLR is proportional to dϕ . The flux from the total radiating circular orbit can be obtained by integration over all azimuthal angles ϕ . If we suppose that all sources are distributed uniformly along the orbit, this flux is described by the following expression: Observed fluxes of linearly polarized radiation differ from the continuum radiation case by an additional factor φ ( λ, ϕ ): Here Θ is the angle between the magnetic field B and the light propagation direction n , I ( µ ) is total intensity of the spectral line escaping from the surface dS . The azimuthal angle ϕ = 0 corresponds to a surface element dS perpendicular to the plane ( nN ). Faraday depolarization term δ cos Θ has the form: where the parameters b ρ and b ϕ are: Here angle ϕ ∗ is the angle between B ⊥ and the radius-vector ρ , lying in the disc plane. The sign minus before b ϕ sin ϕ corresponds to the right-hand screw rotation of the accretion disc with the frozen magnetic field B ϕ directed along the rotation velocity. If the rotation of the disc is opposite, we have to change b ϕ to b ϕ . If we take the factor φ ( λ, ϕ ) = 1 and g line → g c , all the formulas will describe the case of the continuum radiation. In this case the integrals over ϕ can be evaluated analytically (for the combination -F Q + iF U the ϕ -integral can be evaluated by the complex residue method, and we obtain Eqs.(8) and (9)). Note, that these formulas are approximate, they take into account only the last scattering before the escape from the atmosphere. This is a rather satisfactory approximation (see Silant'ev 2002). It describes the main contribution to the polarization. The main merit of these analytical formulas is that they describe the polarization for any direction of the magnetic field. For our purpose this approach is sufficient. We note that ϕ -integration in Eqs.(18) - (20) gives rise to rather low polarization effects. For this reason they hardly can be used for describing the polarization data presented in the atlas (Smith et al. 2002). Below we present two models that are more acceptable for explaining the data.",
"pages": [
5,
6
]
},
{
"title": "2.2 The model of H α line polarization with parameters p and χ , averaged over the right and left parts of an orbit",
"content": "It is clear from Eqs.(18), (19) and (20) that the right parts of circular orbits mostly contribute to gaussian shape lines at wavelengths λ > λ 0 , and the left parts mostly contribute to λ < λ 0 . Qualitatively, we can consider that these contributions are equivalent to sum of two gaussian shaped polarized lines. We assume that the effective polarizations and position angles of these lines correspond to mean values from the right side ( p right , χ right ) and the left side ( p left , χ left ) of the orbit. These values follow from Eqs.(19) and (20) if we take there the factor φ ( λ, ϕ ) = 1. Unlike the situation described by Eqs.(19) and (20), in this model we assume that a part of the accretion disc is invisible due to obscuring torus. The right part corresponds to integration over ϕ = 0 ÷ ϕ 0 , and the left part corresponds to integration in the interval ϕ = 0 ÷ -ϕ 0 . Here the angle ϕ 0 characterizes the boundary azimuthal angle for the visible part of the BLR orbit. The mean values 〈 Q 〉 and 〈 U 〉 for visible right part are described by the integrals: where δ cos Θ is given in Eqs. (21) and (22). The corresponding mean values for the left part of the BLR orbit are given by integrals in the interval (0 , -ϕ 0 ). /negationslash These integrals cannot be evaluated analytically in a general case. We present below the cases ( a = 0 , b ρ = 0 , b ϕ = 0) and ( a = 0 , b ρ = 0 , b ϕ = 0). The first case corresponds to the magnetic field B ‖ parallel to normal N . Clearly, in this case the polarization degree and the position angle are the same in the right and left parts of the orbit, and can be obtained from Eqs.(8) and (9) (see Eq.(13)). /negationslash The second case corresponds to a toroidal magnetic field B ⊥ , laying in the plane of the accretion disc and tangential to the radiating circular orbit. In this case the Faraday rotations are opposite in the right and the left parts of the orbit. This gives the same value for the polarization degree p right = p left and the opposite values for the position angles χ right = -χ left . We present below the results for the right part of the orbit: f U ( ϕ 0 ) = It is interesting to note that f Q ( ϕ 0 ) monotonically grows from f Q ( π/ 2) = 1 to f Q = √ g 2 line + b 2 ϕ /g line ≥ 1 as ϕ 0 → 0. ∣ ∣ The expression for f Q is valid only for ϕ 0 ≤ π/ 2, and the formula for f U is valid for total interval 0 ≤ ϕ 0 ≤ π . The integrands in Eqs. (23) are symmetric relative to the angle ϕ 0 = π/ 2. This gives equalities f Q ( π/ 2) = f Q ( π ) = 1 and f U ( π/ 2) = f U ( π ). Due to the aforementioned symmetry, we can calculate values f Q and f U for π/ 2 ≤ ϕ 0 ≤ π from the values for interval 0 ≤ ϕ 0 ≤ π/ 2: f Q,U ( ϕ 0 ) = [ f Q,U ( π ) π -f Q,U ( π -ϕ 0 )( π -ϕ 0 )] /ϕ 0 . The mean polarization degree p right ( B ϕ ) and the position angle χ right ( B ϕ ) can be derived from the following expressions: In Fig.2 we present the values p right ( B ϕ ) /p ( µ )(1 -sµ ) and | χ right | at b ϕ = 1 , 2 , 3 , 4 , 5 and g line = 1 , s = 0. Comparison of p right ( B ϕ ) with p c ( B ϕ ) in Fig.1 shows that p right > p c . This is evident, because p c corresponds to the sum of radiation from the right and the left parts of the observed areas (in this sum U = 0), and p right corresponds to the half of this area, where parameter U = 0. It means that in the wings of /negationslash the emitting lines the polarization is greater than in nearby continuum. Let us consider the behavior of the polarization degree p line ( B ϕ , λ ) and the position angle χ line ( B ϕ , λ ) inside the broad spectral line in more detail, using our simple model of two equal gaussian lines with the equal right and left displacements from the central wavelength λ 0 . We label the intensities of these lines as I right and I left . According to Eqs.(24) and (25), we present the total observed Stokes parameters I, Q and U in the form: Recall that due to the displacement of the centers of the right and left lines with the gaussian shape the intensities I right ( λ ) and I left ( λ ) are different at a particular considered wavelength inside the full line. Only at the central wavelength λ 0 these intensities are equal due to the axial symmetry of our model. Using Eqs.(27), (28) and (29), we obtain the following expressions for the total observed polarization degree p ( B ϕ , λ ) and the position angle χ ( B ϕ , λ ): Taking in Eqs.(30) and (31) I left = 0, we revert to Eq.(26) for the right part of the orbit. The total rotation of the position angle inside the line width is equal to the difference of ∆ χ ≡ χ right -χ left , where χ right corresponds to the right-hand wing of line with I right /greatermuch I left . The χ left corresponds to the left-hand wing with I left /greatermuch I right . As a result, we have: Now let us discuss shortly the polarization degree p inside the broad line. First of all, we notice that in the centre of the line λ = λ 0 the polarization is less than in the wings (c.f. Eq.(30) with I right = I left ). The polarization grows with the departure from λ 0 . This behavior of p line ( λ ) is observed in many objects from the catalog of Smith et al.(2002). According to Eq.(30), the ratio of p wing ( B ϕ , λ ) to p center ( B ϕ , λ ) becomes ∣ ∣ Note that the difference ∆ χ does not depend on the choice of the observer's reference frame. A non-zero value of ∆ χ is observed in many objects presented in the catalog of Smith et al. (2002) and is due to two reasons - the presence of the magnetic field B ϕ and the Keplerian rotation of the magnetized accretion disc. Fig.2 shows that ∆ χ depends on the parameter b ϕ and the angle ϕ 0 . Thus, for b ϕ = 5 and ϕ 0 /similarequal (140 · -160 · ) the value | ∆ χ | /similarequal 60 · . For ∆ χ = 60 · this ratio is equal to 2. Clearly, it is not possible to explain all details of p and χ in the our model of the sum of two spectral lines. But, above considerations tell us that the main characteristic features can be explained.",
"pages": [
6,
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},
{
"title": "2.3 The model of H α line as two emitting compact clouds located in the right and left part of the orbit",
"content": "The spectra of H α lines in the atlas of Smith et al.(2002) for many objects have sufficiently complicated structure - the existence of separate peaks and asymmetric shapes. There are only a few objects with symmetric shapes. They have comparatively small widths as compared to other, more complicated spectra. A line with a complicated shape frequently can be approximated as a sum of two or more lines with gaussian shapes. For this reason we present the model of two compact optically thick clouds located in the opposite parts of an orbit in the accretion disc (Fig.3). The advantage of this model compared with the previous one is that we can take into account all the depolarizing Faraday parameters a, b ϕ and b ρ in a simple analytical form. Let us take the first cloud in the right part of the orbit, characterized by the azimuthal angle ϕ , and the second cloud in the left part, characterized by ϕ . If it is necessary, locations of the emitting clouds can be chosen at arbitrary angles along the orbit. Our choice is the simplest for consideration. As usually, we write the Stokes parameters in the coordinate system with X-axis being perpendicular to the plane ( nN ), where the formulas have the simplest form. Further we will use the observed polarization degree p and the total difference of the position angles between right and left parts of the spectral line ∆ χ , which do not depend on the choice of the reference frame. We also include in our formulas the contribution of the continuum radiation ( I c , Q c , U c ) in the region of spectral line. Then, the observed Stokes parameters are: The explicit formulas for Q c and U c are as follows: Here r 2 = ( g 2 c + b 2 -a 2 ) 2 +4 a 2 g 2 c = g 4 c +2 g 2 c ( a 2 + b 2 )+( a 2 -b 2 ) 2 . Introducing the notation η c = p c ( µ )(1 -sµ ) /p c ( B , µ ), and using expressions (8) and (9), we can present formulas for Q c and U c in a simpler form: The last expressions are valid in the limit (2 ag c ) /η 2 c → 0. In most sources from the catalog of Smith et al. (2002), the intensity I c is much smaller than I right + I left . For these cases one can neglect the contribution of the continuum radiation and the formulas for p line and χ line acquire fairly simple form: In the right wing, where ξ /similarequal 0, we have For the left wing one finds the same expression with ( -b ϕ ) instead of b ϕ . Using formula (42), we can obtain expression for the difference of the position angles between the right and left wings of the line: For the polarization degree in the right wing we derive the formula: For the left wing the polarization degree is higher because the Faraday depolarization parameter | a -b ϕ | is lower than in the right wing. If a = 0, the polarization degree p right = p left and χ right = -χ left . Presence of the magnetic field B ‖ (parameter a = 0) diminishes the polarization degree both in the right and left wings of the line, and also diminishes the difference | ∆ χ | = | χ right -χ left | . Besides, the functions p line ( λ ) and χ line ( λ ) become asymmetric relative to the center of the line λ 0 (if the intensities of lines I right ( λ ) and I left ( λ ) are the same gaussian functions). Analogously, for the left wing one replaces b ϕ with ( -b ϕ ). /negationslash It is interesting to compare the polarization degrees in the wings and in the center of line. The general formula for ratio p wing /p center is very complex and we consider only the case a = 0, where this ratio reaches a maximum value. Taking ξ = 1 for the center of the line and ξ = 0 for the line wing, we obtain the following expression from the general formula (41): For b ϕ = 5 and g line = 1 this ratio is equal to 5.1, i.e. is considerably greater than the value from formula (33). It is quite natural, because formula (33) describes the mean value of the effect. Clearly, the averaging procedure diminishes the effect. Physically this effect arises as a consequence of the Faraday rotation of the polarization plane. In the center of the line the rotations from the right and the left lines have opposite directions and the parameter Q center reaches a lower value than that in the line wing. The most important conclusion from the theoretical consideration of the structure of broad lines in AGN is the treatment of the symmetry of the polarization degree p line ( λ ) as the result of the azimuthal magnetic field B ϕ . If the symmetry of p ( λ ) is considerably broken, one can consider that B ϕ ∼ B ‖ , or the intensities of the right and the left emitting clouds are different.",
"pages": [
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},
{
"title": "3 The magnetic field strength in a broad line region of AGN",
"content": "The standard Unified Sheme for AGN includes a central source of continuum (accreting SMBH); a region close to the outer radius of the accretion disc emitting broad emission lines (broad line region - BLR); a dusty rotating 'torus' on parsec scales; and gas emitting narrow emission lines on a scale of tens to hundreds of parsecs, ionized through the open cone defined by the torus edge (Antonucci & Miller 1985; Krolik & Begelman 1988; Urry & Padovani 1995). The main unknown is the mechanism for the generation of the magnetic field during the process of accretion onto SMBH. Li (2002), Wang et al. (2002, 2003), Zhang et al. (2005) have studied the magnetic coupling process (MC) as an affective mechanism for transforming the kinetic energy of accreting gas into the magnetic energy. It is assumed that the disc is stable, perfectly conducting and Keplerian. The magnetic field on the black hole horizon is poloidal and varying as a power law with the distance from the central region. Since the magnetic field on the horizon B H is brought and held by its surrounding magnetized matter of the accretion disc, there must exist the relation between the magnetic field strength near the BH horizon and the accretion rate ˙ M . As a result, the magnetic field strength on the event horizon R H = R G (1+ √ 1 -a 2 ∗ ) is determined by the relation between the magnetic energy and the accretion kinetic energy densities (see Li 2002; Wang et al. 2002): Here R G = GM BH /c 2 , the bolometric luminosity L bol = ε ˙ Mc 2 , ˙ M is the accretion rate, c is the light velocity and ε is the radiative efficiency calculated by numerical simulations of Novikov & Thorne 1973, Krolik 2007, Shapiro 2007. The coefficient k presents the inverse plasma parameter k = P magn /P gas = 1 /β , where P gas and P magn are the gas and the magnetic pressures, respectively. For the equipartition case β = 1 and k = 1. Eq.(46) is easily transformed into: The basic problem is the relation between the magnetic fields strengths at the first stable circular orbit R ms and the event horizon R H . The value of the radius R ms depends on the radius R G and the spin a ∗ , and can be presented in a form: where l E = L bol /L Edd and the Eddington luminosity L Edd = 1 . 3 · 10 38 ( M BH /M /circledot ). where parameter q > 1. For example, for a Schwarzschild black hole q = 6 and for the Kerr BH with the spin a ∗ = 0 . 998 q = 1 . 22 (Murphy et al. 2009). Reynolds, Garofalo & Begelman (2006) argued that the plunging inflow can greatly enhance the trapping of large scale magnetic field on the black hole. Blandford (1990) has shown that the interaction of the large-scale magnetic field with the event horizon of rotating black hole can enhance the trapping of large-scale poloidal magnetic field on the horizon of the black hole, compared with the inner accretion flow and compared to the magnetic field strength derived from the relation between magnetic energy and accretion kinetic energy (Eq.(47)). Recently Garofalo (2009) has showed that the dynamics of the plunge region of a thin black hole accretion disc and magnetic flux trapping can enhance the strength of the magnetic field threading the horizon by a significant factor. The results of his calculations were presented in fig.7 of Garofalo paper. It means that we obtain the following relation between the magnetic field strength at the first stable orbit B ms and the magnetic field strength at the event horizon of a black hole B H : The coefficient η can be obtained from fig.7 of the paper by Garofalo (2009). From this figure it follows that for a ∗ = 0 . 5 the value is η = 5 and for a ∗ = 0 . 0 and a ∗ = 0 . 998 we have η = 7 . 5. Numerical simulations have been used to study magnetic field generation in astrophysical objects. For example, the existence of large-scale dynamos in magneto-convection under the influence of shear and rotation has been studied by Kapyla, Korpi & Brandenburg (2008). These authors have shown that the saturation field strength reaches, practically, the equipartition level B ≈ 0 . 7 B eq , i.e. k ≈ 0 . 5. Taking into account the shear flows can increase the magnetic field level. It means that the magnetization parameter can be equal to k ≈ 1. We suggest that the magnetic field far inside in the accretion disc, and, especially, in the Broad Line Region (BLR) takes the toroidal form. Namely, the differential rotation in the accretion disc leads to an increase of the azimuthal field by winding up the poloidal field lines into the toroidal field lines (Bonanno & Urpin 2007). In astrophysical objects differential rotation is often associated with magnetic fields of various strength and geometry. If the poloidal field has a component parallel to the gradient of the angular velocity, then differential rotation can stretch toroidal field lines from the poloidal ones. In the presence of the magnetic field, differential rotation can be a reason for various MHD instabilities, especially if the field geometry is complex. Mayer & Pringle (2006) assumed that a dynamo process generates a local poloidal field B z in the accretion disc, and the magnitude of the poloidal component is small: B z /lessmuch B ⊥ . Usually one assumes that regular dependence of the magnetic field on the radius R in the accretion disc exists from the first stable orbit R ms , and that dependence has a power law form: We assume two values for the parameter n . The value n = 1 derives the toroidal topology of the magnetic field (see Bonanno & Urpin 2007). The value n = 5 / 4 corresponds to the accretion process with hot accretion flows (Medvedev 2000). For pure toroidal topology of the magnetic field in the accretion disc we have the depolarization parameter a = 0, and in this case Eqs.(8) and (9) for non-turbulent case ( C = 0) are transformed into Eq.(14). Recall that, according to definitions (11), magnetic field B ( R BLR ) can be determined, if the parameter b is known from the observed polarization: This field can be related to B ms . In the case of a power-law dependence (50) with n = 1, this relation becomes We used here Eq.(3) for determining R BLR . Note that M 9 = M BH / 10 9 M /circledot . In this situation the depolarization parameter b for H α wavelength ( λ = 0 . 6563 µ m) is: For hot accretion flows n = 5 / 4 and the depolarization parameter b becomes where q ( a ∗ ) = R ms /R G and R G = GM BH /c 2 . The explicit form of q ( a ∗ ) is given, for example, in Zhang et al. (2005). Below we shall also consider the case of the equipartition between the gas and the magnetic pressures, i.e. k ≈ 1. Namely, the magnetic coupling process corresponds to this case (Li 2002; Wang et al. 2003; Zhang et al. 2005; Ma, Wang & Zuo 2006). Using Eqs.(47) and (49), we transform relations (53) and (54) into the following forms: and for n = 5 / 4: Eqs.(55) and (56) allow us to estimate the radiation efficiency and therefore the rotation rate a ∗ of an accreting black holes. Below we use the spectropolarimetric atlas of AGNs by Smith et al. (2002) for specific estimates.",
"pages": [
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},
{
"title": "4 Magnetic field strength of Akn 120",
"content": "According to Smith et al. (2002) the mean polarization degree in the continuum of Akn 120 is equal to p c /similarequal 0 . 35%, and is equal to /similarequal 0 . 4% in the H α line emission. We use here the data obtained by Smith et al. (2002) in 1998 October. The mean observed position angle have the same value for the continuum and line emission χ /similarequal 76 · . The inclination angle i = 48 · , µ /similarequal 0 . 67. Its value has been derived by Braatz & Gugliucci (2008) from water maser observations. The central black hole mass in Akn 120 is equal to M BH /similarequal 10 7 . 74 M /circledot (see Peterson et al. 2004). For the inclination angle i = 48 · the polarization in the continuum from the accretion disc without magnetic field is expected at the level p c ( µ ) = 1 . 26% (Chandrasekhar 1960). This value is higher than the observed polarization degree and it means that the Faraday depolarization effect is really acting. The H α line spectrum shows the two-peak structure and can be represented as sum of two intensities with gaussian shapes. The difference of the positional angles ∆ χ is estimated to be between 70 · and 80 · . The intensity of the continuum radiation reaches ≈ 18% of the maximum line intensity near the centre. The behaviour of polarization in the continuum is very complex. It seems this behaviour occurs due to the existence of large-scale turbulent curls along the observed orbit. For that reason, it is more convenient to use the continuum - subtracted spectrum of Akn 120, presented in fig.24 of the mentioned Atlas by Smith et al. (2002). We used formulas (31)-(37) to find the estimates for the parameters a, b ϕ , p line ( µ ) and g line . Attempts to estimate these parameters under the assumption p c ( µ ) /similarequal p line ( µ ) were unsuccessful. We propose that in the line radiating clouds there is true absorption of radiation (the existence of dust particles). As it is known (see, for example, Silant'ev 1980), the existence of absorption gives rise to a considerable increase of polarization escaping from the optically thick atmosphere. This effect is the consequence of absorption creating a peak like form of escaping emission. Introducing first three parameters in Eq.(8), we obtain g line /similarequal 0 . 975. The estimate g line = 0 . 975 = 1 + C -sµ gives the relation between C and s . It means that the clouds are absorbing and the small scales are turbulent. The existence of large scale turbulence in clouds directly follows from very high line width. For the rest of radiation from the accretion disc outside the compact clouds we assume that absorption is absent and small scale turbulence is negligible ( C ≈ 0). From Eq.(57) it follows that p line /similarequal 3 . 97% and b ϕ /similarequal 3 . 46. The estimated value p line /similarequal 3 . 97% corresponds to the case when one takes into account the pure absorption of radiation by dust particles existing into emitting clouds. From Eq.(11) one can obtain an estimate of magnetic fields B ‖ /similarequal 0 G and B ϕ /similarequal 14 G. In Fig.4 we present the observed intensity, polarization degree and variation of the azimuthal angle χ , and our model results. It is seen that the model curves practi- /s32 cally coincide with the observed values. The observed intensity is approximated as sum of two gaussian intensities from symmetrically located clouds. The Doppler widths of these intensities are taken equal to ∆ λ T =70 ˚ A, the value ( u k /u turb ) sin ϕ √ 1 -µ 2 = 0 . 3, the ratio of maximum intensities of gaussians is I left /I right = 20 / 18. The centers of gaussian curves coincide with the observed places in Fig.24 of Smith et al. (2002). The main problem is that the exact value of index n is unknown and its value depends strongly on the model of the accretion disc. Pariev, Blackman & Boldyrev (2003) suggest the following interval of values of this index 1 ≤ n ≤ 2. The value n = 1 corresponds to toroidal magnetic field (see Bonanno & Urpin 2007). To estimate the magnetic field strength at the last inner circular orbit B ms we need to know the rotation rate of the central supermassive black hole (parameter a ∗ ). For a Schwarzschild black hole with a ∗ = 0 and q = 6 and for the toroidal magnetic field ( n = 1) we obtain from Eq.(49) B ms = 14 . 5 · 10 3 G . Now we can estimate the magnetic field strength B H at the horizon of the central black hole using the results of calculations by Garofalo (2009). He has calculated the ratio of the horizon-threading magnetic field and the magnetic field in the accretion disc as a function of the black hole spin. According to this calculations, for a ∗ = 0 the ratio B H /B ms = 7 . 5 and B H = 10 . 7 · 10 4 G . Our results demonstrate that for a given value of the polarization degree the magnetic field strength at the inner radius r ms (and therefore on the horizon radius) is stronger for a Kerr black hole compared to Schwarzschild one. This result means also that for black holes with the same magnetic field strengths the degree of polarization for Kerr black holes is larger than for Schwarzschild black holes (see Silant'ev et al. 2011).",
"pages": [
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},
{
"title": "5 Magnetic field strength of Mrk 6",
"content": "According to Ho, Darling & Greene (2008), the mass of the central black hole in Mrk 6 is log( M BH /M /circledot ) = 7 . 97 ± 0 . 5, the ratio of the bolometric luminosity to the Eddington value is log( L bol /L E dd ) = -1 . 72. The inclination angle is i = 62 · . 7 , µ = 0 . 46 (Ho et al. 2008). It means that the standard (Sobolev-Chandrasekhar) magnitude of the polarization degree is p c ( µ ) = 2 . 52%. The observed mean polarization has been found at the level of p c = 0 . 90 ± 0 . 03, p ( H α ) = 0 . 85 ± 0 . 04 (Smith et al. 2002). The most remarkable fact is the jump of the mean position angle for two observational seasons of Feb 97 and Oct 98: ∆ χ ≈ 25 · . It is interesting that the value of the mean polarization remained the same. This jump occurred over 1-2 years, which is too short a time for such a large object as the accretion disc near the supermassive black hole. Thus, this problem remains unsolved. Let us return now to the analysis of the data in the H α line. First of all, we see that the polarization degrees in the right and the left sides of the spectrum are practically equal - the left side has p line /similarequal 1 . 5%, and in the right side p line /similarequal 1 . 4%. From the theoretical considerations in section 2, it is clear that such a symmetrical form of the polarization degree can occur if the magnetic field B ‖ is much less than the azimuthal magnetic field B ϕ . A small decrease of polarization in the right-hand part is due to the reason that small value of the B ‖ component, directed to an observer, coincides with direction of B ϕ . In this situation the polarization of radiation slightly decreases compared to the left-hand part of the orbit, where the aforementioned magnetic fields are directed opposite to each other. Considering polarization near the line center, we assume p line ( centre ) /similarequal 0 . 5%. We also assume that in the center of the line the intensity from the left part of the orbit is approximately equal to that from the right part. The value of the intensity of the continuum radiation in Mrk 6 is relatively small, and we neglect it in our computation. Using formulas (34)-(36), one obtain: Substitution of these parameters in Eq.(8) gives g line /similarequal 1 . 0006, i.e. practically 1. As in the case of Akn 120, the polarization p line /similarequal 3 . 9% implies that in H α -clouds there exists the absorption of radiation. Under the assumption of dipole radiation we have q c /similarequal 0 . 01 and the parameter s /similarequal 0 . 17. Because g line = 1 . 0006 /similarequal 1 = 1+ C -0 . 17 · 0 . 46 we find that the small scale turbulent parameter C /similarequal 0 . 08. For the difference ∆ χ of the position angles between the left and the right wings of the spectral line the expression (43) gives ∆ χ = 42 · . This value is consistent with the observational results. Eqs.(11) and (58) give estimate: B ‖ /similarequal 0 . 6G and B ϕ /similarequal 8 . 5G. Note that expression (58) supposes that I c p c /lessmuch I right,left p line ( µ ). Now let us estimate the magnetic field strength in the accretion disc of Mrk 6 using the results of the polarimetric obser- For the spin value of a ∗ = 0 . 5, ε = 0 . 081, q = 4 . 25 (Novikov & Thorne 1973) we obtain B ms = 6 . 8 · 10 3 G and B H = 3 . 4 · 10 4 G . At last, for a ∗ = 0 . 998, q = 1 . 22, ε = 0 . 32 we have B ms = 2 . 8 · 10 4 G and B H = 14 · 10 4 G . /s32 /s32 /s32 vations from Smith et al. (2002). Eqs. (53)-(56) allow us to derive the magnetic field strength B ms at the inner radius of the accretion disc: B ms = (1 . 72 × 10 4 /q ) G . For a Swarzschild black hole, when q = 6, the magnetic field B ms = 2 . 9 · 10 3 G . For a Kerr black hole with a ∗ = 0 . 998 the parameter q = 1 . 22 and the magnetic field strength B ms = 1 . 4 · 10 4 G . According to Garofalo (2009, fig.7) the magnetic field strength at the horizon of the supermassive black hole is B H = 1 . 4 · 10 4 G for a ∗ = 0 and B H = 10 5 G for a ∗ = 0 . 998.",
"pages": [
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},
{
"title": "6 Magnetic fields of Mrk 985 and IZw1",
"content": "The intensity spectrum of Mrk 985 has a two-peak shape and the spectrum of the polarization degree p line ( λ ) is quite symmetric (the p line ( left ) /similarequal 1 . 27% and p line ( right ) /similarequal 1 . 16%). In the centre of line p line ( centre ) /similarequal 0 . 5%. The mean polarization of the continuum radiation is 1.12%. Using formulas (33)-(37), we find that We see that a nearly symmetric form of p line ( λ ) implies that a /lessmuch b ϕ , i.e. B ‖ /lessmuch B ϕ . From Fig.15 in the atlas of Smith et al. (2002) we see that the difference of position angles between the right wing and the centre of line is equal ∆ χ /similarequal 31 -33 · . From general theory one finds that tan2∆ χ = a/g line + b ϕ /g line . Our estimates (59) give this value for the angle difference. The estimates of magnetic fields at distances R ms and R H can be obtained analogously as in the previous sections. In the atlas of Smith et al. (2002) there is no information on the inclination angle i . It is interesting to estimate this angle assuming that g line /similarequal 1. Substituting parameters g c = 1 , a = 0 . 114 and b ϕ = 2 . 035 into formula (8) gives the value p c ( µ ) = 2 . 54%. This implies an estimate i /similarequal 64 · , µ /similarequal 0 . 44. Using the value p c ( µ ) = 2 . 54% we can calculate the value g line , corresponding to this polarization. This calculation demonstrates that the parameter g line acquires the value g line /similarequal 1 . 0013. The value p line ( µ ) = 2 . 75 at µ = 0 . 44 takes place at q a /similarequal 0 . 01 ( s = 0 . 17). The value g line /similarequal 1 . 0013 = 1 + C -0 . 17 · 0 . 44 occurs at C /similarequal 0 . 08. Using Eq.(11) and the value µ /similarequal 0 . 44, we find the estimates: B ‖ /similarequal 0 . 75 G and B ϕ /similarequal 6 . 6 G. Now let consider the AGN IZw1. This object has p c /similarequal 0 . 67%, p line ( left ) /similarequal 0 . 7%, p line ( centre ) /similarequal 0 . 2% and p line ( right ) /similarequal 0 . 9%. The form of the polarization spectrum is slightly more asymmetric than in Mrk 985. Using general formulas (33)-(35) we find the following estimates: As in the case of Mrk 985, we found, that g line /similarequal 1 and p c ( µ ) /similarequal 2 . 68%. This corresponds to µ /similarequal 0 . 44. The value p line /similarequal 3 . 9% occurs at the absorption degree q a /similarequal 0 . 01 , s /similarequal 0 . 17. As a result, the small scale turbulence parameter C /similarequal 0 . 08. As in the previous cases, using Eq.(11) and the value µ = 0 . 44 we can estimate the magnetic field strength for IZw 1: B ‖ = 3 . 42G and B ⊥ = 12 . 7G. It should be noted that in these cases we estimated the inclination angle i from the analysis of the polarization data. The obtained estimates of the magnetic field strengths in BLR of these AGNs are presented in Table 1. The last value in the table is close to the one estimated by Afanasiev et al.(2011) where the polarimetric observations were made only for the continuum emission and did not include the emission from the broad line region.",
"pages": [
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},
{
"title": "7 Conclusions",
"content": "For many objects of Smith et al. (2002) spectropolarimetric atlas the polarization spectra of a broad H α -line p line ( λ ) have a characteristic minimum at the center of the line and different maxima at the left and right wings. Usually the wing polarizations are higher than those in the nearby continuum. For many objects the position angle changes continuously from the left wing to the right one. We develop a new theoretical explanation for these features, different from the original explanation of Smith et al. (2002, 2004, 2005), taking into account that accretion discs can be magnetized. Smith et al. explain the characteristic features of the H α -line assuming that the observed polarization is due to single scattering of non-polarized radiation from the BLR on two types of scattering clouds - a polar cloud around the radio jet, and clouds in the equatorial region. It appears (see Smith et al. 2005) that their mechanism has two characteristic features: a relatively low amplitude ( | ∆ χ | ≤ 20 -40 · ) of the position angle rotation from one line wing to the other one, and the need for a very high electron temperature ( T ∼ 10 6 K) in a nearby scattering cloud. In their atlas there are cases with both low ∆ χ < 20 · and high ∆ χ ∼ 80 · position angle rotations. The need for the high electron temperature arises from the observed polarization minimum in the line core. Besides, they neglect the intrinsic linear polarization of the radiation in BLR. In our mechanism both effects can be explain by a single cause - the Faraday rotation of the polarization plane. The wide line width results from turbulence, which is related to the Keplerian rotation in the orbit. Clearly both explanations take place in reality. The basis of our explanation is the assumption that both the continuum radiation and the spectral line emission originate in an optically thick magnetized accretion disc around the center of an AGN. The observed characteristic shape of the line polarization appears as a result of the Faraday rotation of the polarization plane in the accretion disc having a normal magnetic field B ‖ and an azimuthal field B ϕ . We propose that the regions of the line emission can be represented as a comparatively dense absorbing turbulent clouds rotating with the Keplerian velocity around the center of the AGN. These clouds are flattened, optically thick and magnetized. They emit the polarized radiation in accordance with the Milne problem law. The observed emission line is a sum of radiation from clouds rotating in the right and the left sides of the orbit. Due to Doppler displacements, emission from the one side is, as a whole, reddened ( λ ≥ λ 0 ), and emission from the other side has the opposite λ -displacement. The Faraday rotations by azimuthal magnetic field B ϕ in the left and the right sides of the orbit are opposite and, as a result, in the center of line the sum of emissions is less polarized than in the wings. The continuous rotation of the position angle χ from one wing of line to the opposite wing arises for the same reason. The projection of the normal magnetic field B ‖ along the line of sight gives an additional Faraday rotation. It is the same in both sides of the radiating orbit. This additional rotation in one side of orbit increases the total Faraday rotation, and in opposite side decreases the total rotation. For this reason B ‖ magnetic field gives rise to an asymmetric (relative to the central wavelength λ 0 ) profiles for both the polarization degree p line ( λ ) and the position angle χ line ( λ ). The presented theory allows us to estimate the components B ϕ and B ‖ in the broad line emission regions, and also in nearby regions of the continuum radiation. If the polarizations in the left and the right wings are slightly different, then the value B ‖ /lessmuch B ϕ . This helps us to estimate the B ϕ -component from more simple formulas for continuum polarization. Objects in which this is the case are ESO 141-635, IZw1, Mrk 6, Mrk 290, Mrk 985 and NGC 5548. The objects with a strong asymmetry of p line ( λ ) are characterized by magnetic fields B ϕ ∼ B ‖ . Such objects are Akn 120, Akn 564,KUV 18217+6419, Mrk 304, Mrk 335, Mrk 841, MS1849.2-7832 and NGC 4593. Other objects have fairly complex polarization spectra, they appear to be distorted by large-scale turbulent motions. Using the estimated values of the magnetic field in broad line regions (usually B ‖ /lessmuch B ϕ and B ϕ ∼ 10 G) , one can estimate the magnetic field B ms at the last stable orbit near the black hole, and then the field B H at the radius of the event horizon. These estimates are dependent on the different assumptions about the slope of the power-law distribution of the magnetic field inside the accretion disc. We have used the most common assumptions to obtain the values of the magnetic field ∼ 10 4 -10 5 G. These values of the magnetic field are in a good agreement with other estimates. Thus, we determined the magnetic field strengths in various places in the accretion discs of AGNs from the real observational polarization data.",
"pages": [
13,
14
]
},
{
"title": "Acknowledgments",
"content": "This research was supported by the program of Prezidium of RAS No.21, the program of the Department of Physical Sciences of RAS No.16, by the Federal Target Program 'Scientific and scientific-pedagogical personnel of innovative Russia' 2009-2013 and the Grant from President of the Russian Federation 'The Basic Scientific Schools' NSh-1625.2012.2.",
"pages": [
14
]
},
{
"title": "References",
"content": "Afanasiev V.L., Borisov N.V., Gnedin Yu.N., Natsvlishvili T.M., Piotrovich M.Yu., Buliga S.D., 2011, Astron.Letters, 37, 302 Agol E., Blaes O., 1996, MNRAS, 282, 965 Antonucci R.R.J., Miller J.S., 1985, ApJ, 297, 621 Bentz M.C., Peterson B.M., Netzer H., Pogge R. W., Vestergaard M., 2009, ApJ, 697, 160 Blaes O.M., in: Accretion discs, jets and high energy phenomena in astrophysics, Les Houches Session LXXVIII, eds. V.Beskin et al., Springer, N.Y. 2003, p.147 Blandford R.D., 1990, in Courvoiseir T.J.-L., Mayor M., eds, Active galactic nuclear. Springer, Berlin, p. 161 Bon E., Popovic L.C., Gavrilova N., La Mura G., Medavilla E., 2009, MNRAS, 400, 924 Bonanno A., Urpin V., 2007, A&A, 473, 701 Braatz J.A., Gugliucci N.E., 2008, ApJ, 678, 96 Britzen S., Kam V.A., Witzel A. et al., 2009, A&A, 508, 1205 Chandrasekhar S., 1960, Radiative Transfer, Dover Publ., New York. Dolginov A.Z., Gnedin Yu.N., Silant'ev N.A., 1995, Propagation and polarization of radiation in cosmic media, Gordon&Breach, New York, p.72 Garofalo D., 2009, ApJ, 699, 400 Gnedin Y.N., Silant'ev N.A., 1997, Ap&SSR, 10, 1 Greene J.E., Peng C.Y., Ludwig R.R., 2010, ApJ, 709, 937 Ho L.S., Darling J., Greene J.E., 2008, ApJ, 177, 103 Ivanov V. V., Grachev S. I., Loskutov V. M., 1997, A&A, 321, 968 Kaspi S., Brandt W.N., Maoz D., Netzer H., Schneider D.P., Shemmer O., 2007, ApJ, 659, 997 Kochanek C.S., Dai X., Morgan C., Morgan N., Poindexter S., Chartas G., 2006, preprint (astro-ph/0609112) Krolik J.H., Begelman M.C., 1988, ApJ, 329, 702 Krolik J.H., 2007, preprint (astro-ph/0709.1489)",
"pages": [
14
]
}
]
2013AuArc..77...30F
https://arxiv.org/pdf/1305.0881.pdf
<document>
<section_header_level_1><location><page_1><loc_12><loc_86><loc_89><loc_92></location>Astronomical Orientations of Bora Ceremonial Grounds in Southeast Australia</section_header_level_1>
<text><location><page_1><loc_24><loc_83><loc_76><loc_85></location>Robert S. Fuller 1,2 , Duane W. Hamacher 1,3 and Ray P. Norris 1,2,4</text>
<text><location><page_1><loc_18><loc_79><loc_82><loc_81></location>1 Warawara - Department of Indigenous Studies, Macquarie University, NSW, 2109, Australia Email: [email protected]</text>
<text><location><page_1><loc_12><loc_76><loc_88><loc_77></location>2 Research Centre for Astronomy, Astrophysics & Astrophotonics, Macquarie University, NSW, 2109, Australia</text>
<text><location><page_1><loc_16><loc_72><loc_84><loc_75></location>3 Nura Gili Centre for Indigenous Programs, University of New South Wales, NSW, 2052, Australia Email: [email protected]</text>
<text><location><page_1><loc_22><loc_68><loc_79><loc_70></location>4 CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW, 1710, Australia Email: [email protected]</text>
<section_header_level_1><location><page_1><loc_46><loc_64><loc_54><loc_66></location>Abstract</section_header_level_1>
<text><location><page_1><loc_17><loc_40><loc_84><loc_63></location>Ethnographic evidence indicates that bora (initiation) ceremonial sites in southeast Australia, which typically comprise a pair of circles connected by a pathway, are symbolically reflected in the Milky Way as the ÔSky BoraÕ. This evidence also indicates that the position of the Sky Bora signifies the time of the year when initiation ceremonies are held. We use archaeological data to test the hypothesis that southeast Australian bora grounds have a preferred orientation to the position of the Milky Way in the night sky in August, when the plane of the galaxy from Crux to Sagittarius is roughly vertical in the evening sky to the south-southwest. We accomplish this by measuring the orientations of 68 bora grounds using a combination of data from the archaeological literature and site cards in the New South Wales Aboriginal Heritage Information Management System database. We find that bora grounds have a preferred orientation to the south and southwest, consistent with the Sky Bora hypothesis. Monte Carlo statistics show that these preferences were not the result of chance alignments, but were deliberate.</text>
<section_header_level_1><location><page_1><loc_26><loc_36><loc_75><loc_38></location>Notice to Aboriginal and Torres Strait Islander Readers</section_header_level_1>
<text><location><page_1><loc_17><loc_27><loc_84><loc_35></location>This paper discusses bora ceremonies and contains the names of people who have passed away. The exact locations of these sites are concealed in order to protect them. The coordinates provided are within 10 km of the site and are used only to demonstrate the general distribution of the known bora grounds in southeast Australia.</text>
<text><location><page_1><loc_17><loc_23><loc_76><loc_25></location>Keywords: Aboriginal Australian, Cultural Astronomy, Ceremonial Sites</text>
<section_header_level_1><location><page_1><loc_12><loc_19><loc_23><loc_21></location>Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_10><loc_89><loc_18></location>In traditional Aboriginal cultures across Australia, young males are taught the laws, customs and traditions of the community and undergo a transition ceremony from boyhood to manhood. This ceremony often includes a Ôrite of passageÕ event in which the initiated males undergo some form of body modification (Jacob 1991), typically involving tooth evulsion in southeast Australia (e.g. Berndt 1974:27Ð30). This ceremony goes by many names, but in</text>
<text><location><page_2><loc_12><loc_78><loc_89><loc_92></location>Queensland (Qld) and New South Wales (NSW) it has come to be generally known as ÔboraÕ, the name used by the Kamilaroi of north-central NSW (Ridley 1873:269). Bora grounds generally consist of two circles of differing diameter connected by a pathway. The larger circle is regarded as a public space, while the smaller circle some distance away is restricted to initiates and elders. Bora ceremonies were one of the first Aboriginal cultural activities described by early Australian colonists in the Sydney region (Collins 1798:468-480; Hunter 1793:499-500). Because information about bora ceremonies is culturally sensitive, here we limit discussion of the ceremony itself.</text>
<text><location><page_2><loc_12><loc_70><loc_89><loc_77></location>There is a variety of evidence from the anthropological literature (e.g. Berndt 1974; Love 1988; Winterbotham 1957) that bora ceremonies are related to the Milky Way and that ceremonial grounds are oriented to the position of the Milky Way in the night sky at particular times of the year.</text>
<text><location><page_2><loc_12><loc_60><loc_89><loc_69></location>In this paper, we begin by exploring connections between bora ceremonies and the Milky Way using ethnographic and ethnohistoric literature. We then use the archaeological record to determine if bora grounds are oriented to the position of the Milky Way at particular times of the year. Finally, we use Monte Carlo statistics to see if these orientations were deliberate or the result of chance.</text>
<section_header_level_1><location><page_2><loc_12><loc_57><loc_35><loc_59></location>Bora Ceremonial Grounds</section_header_level_1>
<text><location><page_2><loc_12><loc_33><loc_89><loc_55></location>The layout of bora grounds is similar across southeast Australia, with only minor differences from region to region (Bowdler 2001:3; Mathews 1894:99). Several reports (e.g. Black 1944; Collins 1798:391; Fraser 1883; Howitt 1904; Mathews 1897a) describe the grounds as consisting of two rings of different sizes, connected by a pathway. In some places, Bora sites may comprise three or more rings (Steele 1984; Bowdler 2001). The border of each ring is made of raised earth or stone, and the area within is cleared of debris and the earth is stamped until firm. The larger ring, which is considered public, has a typical diameter of 20Ð30 m. The smaller ring (generally 10Ð15 m diameter) is considered the sacred area, where body modification takes place, and is restricted to initiates and elders. The two rings are connected by a pathway that ranges from a few tens to a few hundred metres in length. In 2004, an Aboriginal man from Marulan, NSW advised that parts of many such sites were destroyed immediately after the ceremony to conceal their location (Hardie 2004). For this reason, some bora sites reported in the archaeological literature feature only a single circle, with the smaller, sacred circle having been destroyed.</text>
<text><location><page_2><loc_12><loc_10><loc_89><loc_31></location>Bora grounds are distributed throughout southeast Australia, covering most of NSW and southern Qld and may extend into South Australia (Howitt 1904:501Ð508) and northern Qld (Roth 1909). Ceremonial rings, which may be bora grounds, have been found near Sunbury, Victoria (Vic.), although there are no ethnographic records attesting to their ceremonial use (Frankel 1982). Howitt (1904:512) cited a western boundary for bora running from the mouth of the Murray River to the Gulf of Carpentaria. Mathews (1897b:114) noted the bora can be found across three-quarters of NSW and some distance into western Qld, with a boundary extending from Twofold Bay near Eden, NSW in the south, to Moulamein, NSW in the west, and Barringun, Qld in the north. We recognise that the geographical area covered by this paper includes several distinct language groups, each of whom may have separate culture and traditions, and it may be misleading to aggregate the data from such a wide area. However, (a) the existence of similarly constructed bora rings implies some commonality in culture, and (b) aggregating orientations from a large geographic area will dilute any preferred orientations</text>
<text><location><page_3><loc_12><loc_88><loc_89><loc_92></location>arising from a single Aboriginal group, rather than forming a correlation of spurious significance.</text>
<text><location><page_3><loc_12><loc_70><loc_89><loc_87></location>According to Love (1988), the bora ceremonies were predominantly held in August each year, although other authors report a variety of dates including MarchÐMay (Winterbotham 1957), AprilÐJune (Mathews 1894:99), MayÐJuly (Mathews 1894), August (Needham 1981:70), SeptemberÐNovember (Winterbotham 1957), and OctoberÐDecember (Mathews 1894). This suggests that, in some cases, a number of variables influence the date of the bora ceremony, including the availability of food and water or having a sufficient number of boys to initiate (e.g. Mathews 1910). While these factors vary across the region, here we test the hypothesis advanced by Love (1988) who presents evidence associating the bora ceremony with the night sky and the orientation of the Milky Way, and suggests that most initiation ceremonies occur around August.</text>
<section_header_level_1><location><page_3><loc_12><loc_67><loc_61><loc_69></location>Anthropological Support of an Astronomical Connection</section_header_level_1>
<text><location><page_3><loc_12><loc_44><loc_89><loc_65></location>It is well established that the night sky plays a significant role in several Aboriginal cultures (e.g. Cairns and Harney 2004; Johnson 1998; Norris and Hamacher 2009; Hamacher 2012). In Aboriginal astronomical traditions, dark spaces within the Milky Way are as significant as bright objects. Two animals symbolically link bora ceremonies to these dark spaces. One was a spiritual serpent, commonly referred to as the ÔRainbow SerpentÕ across Australia, traced out by the curving dust lanes in the Milky Way. Needham (1981:69) explained that in Aboriginal communities of the Hunter Valley, motifs of the spiritual serpent were represented in bora ceremonies, with information about the serpent being recounted during the ceremony itself. The other animal was an emu, which is also traced by dust lanes in the Milky Way (Norris and Norris 2009). Love (1988:129Ð138) argued that the emu was an important part of the bora ceremony in southeast Australia, as did Berndt (1974:27Ð30), since male emus brood and hatch the emu chicks and rear the young (Love 1987). This is symbolic of the initiation of adolescent boys by their male elders.</text>
<text><location><page_3><loc_12><loc_13><loc_89><loc_42></location>Needham (1981) provided an illustration of the night sky and associated stars in local Aboriginal astronomical traditions. The illustration, which cites the ÔAll FatherÕ as the star Altair, provides the positions of celestial objects in August, Ôthe month when Aboriginal initiation ceremonies were heldÕ (Needham 1981:70). During the early part of the night in August, the Milky Way stretches across the sky from the northeast to the southwest. Many early colonial reports referred to an Aboriginal religion based on a deity variously described as Baiame, Bunjil or Mungan-ngaua (Henderson 1832:147; Howitt 1904:490Ð491; Ridley 1873:268). These names roughly translate to ÔfatherÕ or Ôfather of all of usÕ (Howitt 1904:491). According to Fraser (1883:208) and Howitt (1884:458), Baiame gave his son, Daramulan, to the people and it is through Daramulan that Baiame sees all. Baiame is worshipped at the bora ceremony (Ridley 1873:269) and Daramulan is believed to come back to the earth by a pathway from the sky (Fraser 1883:212). Eliade (1996:41) reported that Baiame Ôdwells in the sky, beside a great stream of waterÕ (i.e. the Milky Way) and various reports (e.g. Berndt 1974; Hartland 1898; Howitt 1884) have claimed that the wife of Baiame (or in some cases Daramulan) is an emu. Reports of Baiame, Daramulan and Bunjil come from various cultures across southeast Australia, resulting in variations in these reports. However, they share some features, such as a close connection between bora ceremonies and the Milky Way.</text>
<section_header_level_1><location><page_4><loc_12><loc_90><loc_32><loc_92></location>Testing the Hypothesis</section_header_level_1>
<text><location><page_4><loc_12><loc_80><loc_89><loc_88></location>To focus the discussion, we concentrate specifically on the hypothesis advanced by Love (1987, 1988), who argued that ancestral spirits in the heavens held bora ceremonies in the Milky Way, which we refer to as the ÔSky BoraÕ. Love based his work, in part, on Winterbotham (1957), who obtained information from a Jinibara man from southeast Qld named Gaiarbau. According to Winterbotham (1957:38), bora circles,</text>
<text><location><page_4><loc_17><loc_74><loc_79><loc_78></location>É were always oriented towards points of the compass, the larger one to the north, and the smaller to the south ... They conformed in this rule to the position of two dark (black) spaces (circles)Ñthe Coal Sacks in the heavens.</text>
<text><location><page_4><loc_12><loc_56><loc_89><loc_73></location>According to Love (1988 : 130Ð131), the Jinibara account identifies the Sky Bora with the Emu in the Sky (Gaiarbau et al. 1982:77; Winterbotham 1957:46). The ÔCoal SacksÕ, or Mimburi , to which Winterbotham referred, are a dark absorption nebula bordering the western constellations Crux (Southern Cross), Centaurus and Musca, representing the head of the emu, with the star BZ Crucis representing the eye. The dust lanes that run through the stars Alpha and Beta Centauri represent the neck, while the Galactic bulge, near the intersection of Sagittarius, Scorpius and Ophiuchus, represents the body. This area is the centre of our Milky Way galaxy. The dust lanes along the Milky Way through Sagittarius trace out the legs (Figure 1). The motif of the celestial emu is found across Australia (e.g. Cairns and Harney 2004; Norris and Hamacher 2009:13; Stanbridge 1861:302; Wellard 1983:51).</text>
<figure>
<location><page_4><loc_30><loc_14><loc_69><loc_55></location>
<caption>Figure 1: The ÔEmu in the SkyÕ visible over an emu engraving at Elvina Track in Kuringai Chase National Park north of Sydney, which may represent her celestial counterpart (image reproduced courtesy of Barnaby Norris).</caption>
</figure>
<text><location><page_5><loc_12><loc_78><loc_89><loc_92></location>According to Winterbotham, other Aboriginal groups also knew of the dark nebulae, including the Badjala people of Fraser Island and the adjacent mainland, who call them Wurubilum , and the Wakka Wakka people near Murgon, Qld. This concept extends beyond southeast Australia. For example, Smith (1913) explained that during an initiation ceremony in Western Australia (WA) the initiate is left tied to the ground until the Milky Way is visible. He is then asked if Ôhe can see the two dark spotsÕ and when he is able to see them, he is released. While this account is not from the area of this study, it may be similar to the example that Gaiarbau described.</text>
<text><location><page_5><loc_12><loc_62><loc_89><loc_77></location>Gaiarbau said that bora ceremonies were not held until the celestial bora rings returned to their Ôproper points of the compassÕ (Winterbotham 1957:38). In clear winter skies in southeast Australia, the Milky Way is visible about an hour after sunset. The orientation of the plane of the Milky Way, as seen from southeast Australia an hour after sunset, changes from near vertical in the south-southeast in March to horizontal across the southern sky from east-southeast to west in June and back to vertical (but inverted) in the southwest in September. The Galactic bulge and the Coalsack (celestial emu) are not visible in the sky together an hour after sunset until May. At this time, the emu is not vertical in the sky (perpendicular to the horizon), but stretches from south to east.</text>
<text><location><page_5><loc_12><loc_52><loc_89><loc_60></location>The only time that the Sky Bora is vertically aligned to the horizon and can be seen in the sky together an hour after sunset is in August (or later in the night as the year progresses). The Galactic plane, which goes straight through the celestial emu, is vertical in August an hour or two after sunset (earlier in the evening later in the month, Figure 2). At this time, the azimuth is approximately 213¼ (south-southwest).</text>
<figure>
<location><page_5><loc_28><loc_18><loc_72><loc_51></location>
<caption>Figure 2: The sky bora in the Milky Way oriented vertically in the south-southwest sky in mid-August an hour after sunset, as seen from Brisbane. The large circle represents the larger bora circle and the body of the emu (near zenith). The smaller circle represents the Coalsack and the head of the emu. Graphics are from the Stellarium astronomical software package.</caption>
</figure>
<text><location><page_6><loc_12><loc_83><loc_89><loc_92></location>If LoveÕs hypothesis is correct, we expect the orientation of each bora site from the larger circle to the smaller circle to be oriented to roughly 213¼, corresponding to the time ceremonies are held (August). This expectation agrees with Needham (1981:70), who claimed that bora ceremonies in the Hunter Valley (NSW) were held in August when the Milky Way was vertical in the south-southwest.</text>
<text><location><page_6><loc_12><loc_64><loc_89><loc_82></location>Other researchers report that bora ceremonies in Qld and NSW are held at various times of the year, as noted in the previous section (Winterbotham 1957; Mathews 1894:99). Bora ceremonies may be held at times of the year that have little or nothing to do with the position of the Milky Way in the sky, even if the ceremonies are symbolically linked to the Milky Way. For example, Mathews (1894:128) claimed that the direction of one bora ring to the other Ôis entirely dependent on the conformation of the country within which the ceremony is being heldÕ. If bora grounds are not oriented to any particular object or direction, we expect to find a roughly uniform distribution in their orientations. However, if at least some bora grounds are oriented to the position of the Sky Bora, then we expect to find a preference for south-southwest orientations when we look at the overall distribution of bora ground orientations.</text>
<section_header_level_1><location><page_6><loc_12><loc_60><loc_24><loc_62></location>Methodology</section_header_level_1>
<text><location><page_6><loc_12><loc_49><loc_89><loc_59></location>To determine the orientations of bora ceremonial sites, we obtained data for 63 such sites from the following published literature: Mathews (1894, 1896a, 1896b, 1897a, 1907, 1917), Hopkins (1901), Towle (1942), Bartholomai and Breeden (1961), Anon. (1973), McBryde (1974), Steele (1984), Satterthwait and Heather (1987), and Bowdler (2001). We also obtained 1107 archaeological site cards from the NSW Aboriginal Heritage Information Management System (AHIMS) related to stone arrangements and ceremonial grounds.</text>
<text><location><page_6><loc_12><loc_44><loc_89><loc_47></location>We then filtered the data through a rigorous selection process, discarding data for any bora ground that failed to meet any of the following criteria:</text>
<unordered_list>
<list_item><location><page_6><loc_15><loc_41><loc_65><loc_42></location>1. The site is clearly described as a bora ceremonial ground;</list_item>
<list_item><location><page_6><loc_15><loc_39><loc_60><loc_41></location>2. The site is in NSW or southeast Qld (see Figure 3);</list_item>
<list_item><location><page_6><loc_15><loc_36><loc_89><loc_39></location>3. Measurements were made by an appropriately trained or qualified person (e.g. a surveyor or archaeologist);</list_item>
<list_item><location><page_6><loc_15><loc_34><loc_73><loc_36></location>4. The data are either first-hand, or second-hand from a trusted source;</list_item>
<list_item><location><page_6><loc_15><loc_31><loc_89><loc_34></location>5. There is unambiguous information on the direction from the large to the small circle; and,</list_item>
<list_item><location><page_6><loc_15><loc_29><loc_69><loc_31></location>6. a. Both rings and the pathway between them are identifiable, or</list_item>
<list_item><location><page_6><loc_18><loc_28><loc_64><loc_29></location>b. Both rings and at least one opening are identifiable , or</list_item>
<list_item><location><page_6><loc_18><loc_24><loc_89><loc_28></location>c. Only one ring is identifiable, but it has a clearly identifiable opening and there is unambiguous information as to whether it is the larger or the smaller ring.</list_item>
</unordered_list>
<text><location><page_6><loc_12><loc_11><loc_89><loc_23></location>The orientation of each site was measured from the centre of the largest circle to the centre of the smaller circle. If the second circle was missing, the orientation was taken from the centre of the circle to the middle of the opening. Measurements were either taken directly from the records given by the surveyor or measured from the survey with a protractor and ruler. We divided the azimuths into 16 bins (N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, NNW), each with a width of 22.5¼ with N centred at 0¡, NNE at 22.5¡, and so on (see Table 1).</text>
<section_header_level_1><location><page_7><loc_33><loc_94><loc_67><loc_96></location>Australian Archaeology, No. 77 | Preprint</section_header_level_1>
<table>
<location><page_7><loc_12><loc_59><loc_88><loc_86></location>
<caption>Table 1: Azimuths of the inter-ordinal (left), ordinal (right top) and cardinal (right bottom) orientations (in degrees) used to bin the data in Figure 4, given in degrees. Each bin in the left-hand column has a width of 22.5 ¡ (±11.25¡) centred on the Central Azimuth.</caption>
</table>
<section_header_level_1><location><page_7><loc_12><loc_56><loc_30><loc_57></location>Results and Analysis</section_header_level_1>
<text><location><page_7><loc_12><loc_51><loc_89><loc_54></location>Of the 1170 sites obtained from the literature and AHIMS site card search, only 68 fit the specified selection criteria (Table 2, Figure 3). The 68 sites can be divided into two groups:</text>
<unordered_list>
<list_item><location><page_7><loc_15><loc_46><loc_89><loc_49></location>1) Those 46 sites for which the orientation has been recorded individually for each site; and,</list_item>
<list_item><location><page_7><loc_15><loc_41><loc_89><loc_44></location>2) Those 22 sites in Satterthwait and Heather (1987: Table 9), which provide the distribution of orientations without providing individual site orientations.</list_item>
</unordered_list>
<text><location><page_7><loc_12><loc_24><loc_89><loc_39></location>The 46 data points whose orientations are recorded individually, are provided in Table 2 and are grouped into 22.5¼ bins, shown as a histogram in Figure 4a. The histogram reveals a clear preference for the S, SW and W orientations. Table 2 contains 34 orientations in ordinal (N, S, E, W, NW, NE, SE, SW) directions, but only 12 orientations in inter-ordinal (NNE, ENE, etc.) directions. The low number of inter-ordinal orientations suggests either that the sites tend to be oriented on ordinal points, or that some authors rounded to the nearest ordinal point. To avoid a statistical bias in our results, we re-binned the data into the eight ordinal directions, dividing the counts of each inter-ordinal bin equally between the two neighbouring ordinal bins, resulting in eight 45¼ bins (Table 1, Figure 4b).</text>
<text><location><page_7><loc_12><loc_16><loc_89><loc_23></location>A preferred orientation to the south is evident (28% of the 46 data points), with lesser but significant preferences to the SW (17%) and W (15%) bins. The combined S, SW and W bins account for 61% of the total data points, while the remaining are evenly spread across the remaining bins. The highest peak of 12.5 orientations occurs in the S bin.</text>
<text><location><page_7><loc_12><loc_10><loc_89><loc_15></location>We compare this result with the 22 data points from Satterthwait and Heather (1987) (hereafter referred to as ÔSHÕ) by re-binning our data to four quadrants centred on the cardinal points (N, S, E, W), as shown in Figure 4c. This reveals a strong preference for the southern</text>
<text><location><page_8><loc_12><loc_80><loc_89><loc_92></location>quadrant and a lesser but significant preference to the western quadrant, which, when combined, account for 74% of the 46 data points. The SH data (Figure 4d) is similar, with a significant preference for the southern quadrant (68% of the 22 data points), but with an even distribution among the remaining quadrants. We then combined our 46 data points with the 22 SH data points, resulting in Figure 4e. A clear preference for the southern quadrant is evident, with 35 of the 68 orientations (51%) falling in the S bin. This result is consistent with the Love hypothesis.</text>
<figure>
<location><page_8><loc_12><loc_53><loc_88><loc_79></location>
<caption>Figure 3: Locations of all bora grounds in Table 2, excluding the data from Satterthwait and Heather (1987). The coordinates given are adjusted to as to protect exact location of each site. The coordinates given are within 10 km of the site, which is why some appear over the sea.</caption>
</figure>
<text><location><page_8><loc_12><loc_32><loc_89><loc_45></location>To determine if this is a chance clumping of a random distribution of orientations, we conducted a Monte Carlo simulation, in which 68 orientations were distributed randomly in each of the bins shown in Figure 4e. We repeated this process 100 million times. In only 303 of the 100 million runs did the number in any one bin equal or exceed 35, from which we can conclude that the likelihood of the peak in Figure 4b occurring by chance is about 3x10 -6 or 0.0003%. We therefore conclude that this distribution is clearly not the result of chance, and that the constructors of the bora rings intentionally aligned most of them to the south quadrant.</text>
<table>
<location><page_8><loc_13><loc_9><loc_87><loc_19></location>
<caption>Table 2: The bora grounds after filtering the original data through the selection criteria, grouped alphabetically by reference author, followed by the SH data. The coordinates given are approximate and do not reveal the exact location of the site. Data includes the site number, name and location. Also included is the site layout type: Type 1 consists of two circles and a pathway; Type 2 consists of two circles and one opening; Type 3 consists of one circle and an opening. All orientations are given in terms of cardinal, ordinal or inter-ordinal points measured from the large ring to the small ring, with the specific azimuth given where applicable. SH do not give coordinates or azimuthsÑonly orientations in four quadrants (N, S, E and W).</caption>
</table>
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</table>
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<table>
<location><page_10><loc_13><loc_86><loc_86><loc_92></location>
</table>
<figure>
<location><page_10><loc_12><loc_43><loc_88><loc_82></location>
<caption>Figure 4: Orientations of bora sites using data from Table 1. Data in (a) is given in 22.5¼ bins, (b) is given in 45¼ bins, and (c) through (e) are given in 90¼ bins.</caption>
</figure>
<section_header_level_1><location><page_10><loc_12><loc_36><loc_35><loc_38></location>Discussion and Conclusion</section_header_level_1>
<text><location><page_10><loc_12><loc_16><loc_89><loc_34></location>We have shown that the bora grounds studied have a preferred orientation to southerly directions and that these orientations are not the result of chance, but were deliberate. The reason for this is not known, but it is consistent with the Love hypothesis that southeast Australian bora ceremonial grounds have a preferred orientation to the celestial emu in the Milky Way in the south-southwest skies. The celestial emu is in this position in the evening sky during the month of August, the time during which Winterbotham (1957) and Needham (1981) claimed that bora ceremonies were held. Hamacher et al. (2012) showed that linear stone arrangements in NSW also have a preferred orientation to the cardinal points, especially north-south orientations. Since many stone arrangements are ceremonial sites, this lends support to the claim that orientation is an important factor utilised by Aboriginal people when laying out ceremonial sites.</text>
<text><location><page_10><loc_12><loc_10><loc_89><loc_15></location>Although our analysis supports the Love hypothesis, it is not definitive evidence that bora grounds are oriented to the Sky Bora. Some researchers, including Winterbotham (1957) and Mathews (1894), state that many Bora ceremonies across NSW and Qld were held at various</text>
<text><location><page_11><loc_12><loc_82><loc_89><loc_92></location>times throughout the year, which do not correspond to any particular orientation of the Milky Way. However, there is strong ethnographic evidence that the Milky Way is associated with the bora ceremony and we consider it likely that some ceremonies were timed, and bora sites oriented, such that the vertical Milky Way was visible above the path connecting the two circles during bora ceremonies. Additional research is necessary to understand these links; we are currently engaged in further research projects to explore this.</text>
<section_header_level_1><location><page_11><loc_12><loc_78><loc_29><loc_80></location>Acknowledgements</section_header_level_1>
<text><location><page_11><loc_12><loc_64><loc_89><loc_77></location>We acknowledge the Aboriginal Elders and custodians, past and present, on whose land the bora sites are located. For archaeological data and literature sources, we thank staff from the State Library of NSW, the Australian Institute for Aboriginal and Torres Strait Islander Studies and the NSW Office of Environment and Heritage. This research made use of the TROVE and JSTOR databases, Google Maps, and the Stellarium astronomical software package. Hamacher conducted his component of this research while a PhD student at Macquarie University, but finished the analysis and writing as a staff member at the University of New South Wales.</text>
<section_header_level_1><location><page_11><loc_12><loc_60><loc_22><loc_62></location>References</section_header_level_1>
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</document>
[
{
"title": "Astronomical Orientations of Bora Ceremonial Grounds in Southeast Australia",
"content": "Robert S. Fuller 1,2 , Duane W. Hamacher 1,3 and Ray P. Norris 1,2,4 1 Warawara - Department of Indigenous Studies, Macquarie University, NSW, 2109, Australia Email: [email protected] 2 Research Centre for Astronomy, Astrophysics & Astrophotonics, Macquarie University, NSW, 2109, Australia 3 Nura Gili Centre for Indigenous Programs, University of New South Wales, NSW, 2052, Australia Email: [email protected] 4 CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW, 1710, Australia Email: [email protected]",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "Ethnographic evidence indicates that bora (initiation) ceremonial sites in southeast Australia, which typically comprise a pair of circles connected by a pathway, are symbolically reflected in the Milky Way as the ÔSky BoraÕ. This evidence also indicates that the position of the Sky Bora signifies the time of the year when initiation ceremonies are held. We use archaeological data to test the hypothesis that southeast Australian bora grounds have a preferred orientation to the position of the Milky Way in the night sky in August, when the plane of the galaxy from Crux to Sagittarius is roughly vertical in the evening sky to the south-southwest. We accomplish this by measuring the orientations of 68 bora grounds using a combination of data from the archaeological literature and site cards in the New South Wales Aboriginal Heritage Information Management System database. We find that bora grounds have a preferred orientation to the south and southwest, consistent with the Sky Bora hypothesis. Monte Carlo statistics show that these preferences were not the result of chance alignments, but were deliberate.",
"pages": [
1
]
},
{
"title": "Notice to Aboriginal and Torres Strait Islander Readers",
"content": "This paper discusses bora ceremonies and contains the names of people who have passed away. The exact locations of these sites are concealed in order to protect them. The coordinates provided are within 10 km of the site and are used only to demonstrate the general distribution of the known bora grounds in southeast Australia. Keywords: Aboriginal Australian, Cultural Astronomy, Ceremonial Sites",
"pages": [
1
]
},
{
"title": "Introduction",
"content": "In traditional Aboriginal cultures across Australia, young males are taught the laws, customs and traditions of the community and undergo a transition ceremony from boyhood to manhood. This ceremony often includes a Ôrite of passageÕ event in which the initiated males undergo some form of body modification (Jacob 1991), typically involving tooth evulsion in southeast Australia (e.g. Berndt 1974:27Ð30). This ceremony goes by many names, but in Queensland (Qld) and New South Wales (NSW) it has come to be generally known as ÔboraÕ, the name used by the Kamilaroi of north-central NSW (Ridley 1873:269). Bora grounds generally consist of two circles of differing diameter connected by a pathway. The larger circle is regarded as a public space, while the smaller circle some distance away is restricted to initiates and elders. Bora ceremonies were one of the first Aboriginal cultural activities described by early Australian colonists in the Sydney region (Collins 1798:468-480; Hunter 1793:499-500). Because information about bora ceremonies is culturally sensitive, here we limit discussion of the ceremony itself. There is a variety of evidence from the anthropological literature (e.g. Berndt 1974; Love 1988; Winterbotham 1957) that bora ceremonies are related to the Milky Way and that ceremonial grounds are oriented to the position of the Milky Way in the night sky at particular times of the year. In this paper, we begin by exploring connections between bora ceremonies and the Milky Way using ethnographic and ethnohistoric literature. We then use the archaeological record to determine if bora grounds are oriented to the position of the Milky Way at particular times of the year. Finally, we use Monte Carlo statistics to see if these orientations were deliberate or the result of chance.",
"pages": [
1,
2
]
},
{
"title": "Bora Ceremonial Grounds",
"content": "The layout of bora grounds is similar across southeast Australia, with only minor differences from region to region (Bowdler 2001:3; Mathews 1894:99). Several reports (e.g. Black 1944; Collins 1798:391; Fraser 1883; Howitt 1904; Mathews 1897a) describe the grounds as consisting of two rings of different sizes, connected by a pathway. In some places, Bora sites may comprise three or more rings (Steele 1984; Bowdler 2001). The border of each ring is made of raised earth or stone, and the area within is cleared of debris and the earth is stamped until firm. The larger ring, which is considered public, has a typical diameter of 20Ð30 m. The smaller ring (generally 10Ð15 m diameter) is considered the sacred area, where body modification takes place, and is restricted to initiates and elders. The two rings are connected by a pathway that ranges from a few tens to a few hundred metres in length. In 2004, an Aboriginal man from Marulan, NSW advised that parts of many such sites were destroyed immediately after the ceremony to conceal their location (Hardie 2004). For this reason, some bora sites reported in the archaeological literature feature only a single circle, with the smaller, sacred circle having been destroyed. Bora grounds are distributed throughout southeast Australia, covering most of NSW and southern Qld and may extend into South Australia (Howitt 1904:501Ð508) and northern Qld (Roth 1909). Ceremonial rings, which may be bora grounds, have been found near Sunbury, Victoria (Vic.), although there are no ethnographic records attesting to their ceremonial use (Frankel 1982). Howitt (1904:512) cited a western boundary for bora running from the mouth of the Murray River to the Gulf of Carpentaria. Mathews (1897b:114) noted the bora can be found across three-quarters of NSW and some distance into western Qld, with a boundary extending from Twofold Bay near Eden, NSW in the south, to Moulamein, NSW in the west, and Barringun, Qld in the north. We recognise that the geographical area covered by this paper includes several distinct language groups, each of whom may have separate culture and traditions, and it may be misleading to aggregate the data from such a wide area. However, (a) the existence of similarly constructed bora rings implies some commonality in culture, and (b) aggregating orientations from a large geographic area will dilute any preferred orientations arising from a single Aboriginal group, rather than forming a correlation of spurious significance. According to Love (1988), the bora ceremonies were predominantly held in August each year, although other authors report a variety of dates including MarchÐMay (Winterbotham 1957), AprilÐJune (Mathews 1894:99), MayÐJuly (Mathews 1894), August (Needham 1981:70), SeptemberÐNovember (Winterbotham 1957), and OctoberÐDecember (Mathews 1894). This suggests that, in some cases, a number of variables influence the date of the bora ceremony, including the availability of food and water or having a sufficient number of boys to initiate (e.g. Mathews 1910). While these factors vary across the region, here we test the hypothesis advanced by Love (1988) who presents evidence associating the bora ceremony with the night sky and the orientation of the Milky Way, and suggests that most initiation ceremonies occur around August.",
"pages": [
2,
3
]
},
{
"title": "Anthropological Support of an Astronomical Connection",
"content": "It is well established that the night sky plays a significant role in several Aboriginal cultures (e.g. Cairns and Harney 2004; Johnson 1998; Norris and Hamacher 2009; Hamacher 2012). In Aboriginal astronomical traditions, dark spaces within the Milky Way are as significant as bright objects. Two animals symbolically link bora ceremonies to these dark spaces. One was a spiritual serpent, commonly referred to as the ÔRainbow SerpentÕ across Australia, traced out by the curving dust lanes in the Milky Way. Needham (1981:69) explained that in Aboriginal communities of the Hunter Valley, motifs of the spiritual serpent were represented in bora ceremonies, with information about the serpent being recounted during the ceremony itself. The other animal was an emu, which is also traced by dust lanes in the Milky Way (Norris and Norris 2009). Love (1988:129Ð138) argued that the emu was an important part of the bora ceremony in southeast Australia, as did Berndt (1974:27Ð30), since male emus brood and hatch the emu chicks and rear the young (Love 1987). This is symbolic of the initiation of adolescent boys by their male elders. Needham (1981) provided an illustration of the night sky and associated stars in local Aboriginal astronomical traditions. The illustration, which cites the ÔAll FatherÕ as the star Altair, provides the positions of celestial objects in August, Ôthe month when Aboriginal initiation ceremonies were heldÕ (Needham 1981:70). During the early part of the night in August, the Milky Way stretches across the sky from the northeast to the southwest. Many early colonial reports referred to an Aboriginal religion based on a deity variously described as Baiame, Bunjil or Mungan-ngaua (Henderson 1832:147; Howitt 1904:490Ð491; Ridley 1873:268). These names roughly translate to ÔfatherÕ or Ôfather of all of usÕ (Howitt 1904:491). According to Fraser (1883:208) and Howitt (1884:458), Baiame gave his son, Daramulan, to the people and it is through Daramulan that Baiame sees all. Baiame is worshipped at the bora ceremony (Ridley 1873:269) and Daramulan is believed to come back to the earth by a pathway from the sky (Fraser 1883:212). Eliade (1996:41) reported that Baiame Ôdwells in the sky, beside a great stream of waterÕ (i.e. the Milky Way) and various reports (e.g. Berndt 1974; Hartland 1898; Howitt 1884) have claimed that the wife of Baiame (or in some cases Daramulan) is an emu. Reports of Baiame, Daramulan and Bunjil come from various cultures across southeast Australia, resulting in variations in these reports. However, they share some features, such as a close connection between bora ceremonies and the Milky Way.",
"pages": [
3
]
},
{
"title": "Testing the Hypothesis",
"content": "To focus the discussion, we concentrate specifically on the hypothesis advanced by Love (1987, 1988), who argued that ancestral spirits in the heavens held bora ceremonies in the Milky Way, which we refer to as the ÔSky BoraÕ. Love based his work, in part, on Winterbotham (1957), who obtained information from a Jinibara man from southeast Qld named Gaiarbau. According to Winterbotham (1957:38), bora circles, É were always oriented towards points of the compass, the larger one to the north, and the smaller to the south ... They conformed in this rule to the position of two dark (black) spaces (circles)Ñthe Coal Sacks in the heavens. According to Love (1988 : 130Ð131), the Jinibara account identifies the Sky Bora with the Emu in the Sky (Gaiarbau et al. 1982:77; Winterbotham 1957:46). The ÔCoal SacksÕ, or Mimburi , to which Winterbotham referred, are a dark absorption nebula bordering the western constellations Crux (Southern Cross), Centaurus and Musca, representing the head of the emu, with the star BZ Crucis representing the eye. The dust lanes that run through the stars Alpha and Beta Centauri represent the neck, while the Galactic bulge, near the intersection of Sagittarius, Scorpius and Ophiuchus, represents the body. This area is the centre of our Milky Way galaxy. The dust lanes along the Milky Way through Sagittarius trace out the legs (Figure 1). The motif of the celestial emu is found across Australia (e.g. Cairns and Harney 2004; Norris and Hamacher 2009:13; Stanbridge 1861:302; Wellard 1983:51). According to Winterbotham, other Aboriginal groups also knew of the dark nebulae, including the Badjala people of Fraser Island and the adjacent mainland, who call them Wurubilum , and the Wakka Wakka people near Murgon, Qld. This concept extends beyond southeast Australia. For example, Smith (1913) explained that during an initiation ceremony in Western Australia (WA) the initiate is left tied to the ground until the Milky Way is visible. He is then asked if Ôhe can see the two dark spotsÕ and when he is able to see them, he is released. While this account is not from the area of this study, it may be similar to the example that Gaiarbau described. Gaiarbau said that bora ceremonies were not held until the celestial bora rings returned to their Ôproper points of the compassÕ (Winterbotham 1957:38). In clear winter skies in southeast Australia, the Milky Way is visible about an hour after sunset. The orientation of the plane of the Milky Way, as seen from southeast Australia an hour after sunset, changes from near vertical in the south-southeast in March to horizontal across the southern sky from east-southeast to west in June and back to vertical (but inverted) in the southwest in September. The Galactic bulge and the Coalsack (celestial emu) are not visible in the sky together an hour after sunset until May. At this time, the emu is not vertical in the sky (perpendicular to the horizon), but stretches from south to east. The only time that the Sky Bora is vertically aligned to the horizon and can be seen in the sky together an hour after sunset is in August (or later in the night as the year progresses). The Galactic plane, which goes straight through the celestial emu, is vertical in August an hour or two after sunset (earlier in the evening later in the month, Figure 2). At this time, the azimuth is approximately 213¼ (south-southwest). If LoveÕs hypothesis is correct, we expect the orientation of each bora site from the larger circle to the smaller circle to be oriented to roughly 213¼, corresponding to the time ceremonies are held (August). This expectation agrees with Needham (1981:70), who claimed that bora ceremonies in the Hunter Valley (NSW) were held in August when the Milky Way was vertical in the south-southwest. Other researchers report that bora ceremonies in Qld and NSW are held at various times of the year, as noted in the previous section (Winterbotham 1957; Mathews 1894:99). Bora ceremonies may be held at times of the year that have little or nothing to do with the position of the Milky Way in the sky, even if the ceremonies are symbolically linked to the Milky Way. For example, Mathews (1894:128) claimed that the direction of one bora ring to the other Ôis entirely dependent on the conformation of the country within which the ceremony is being heldÕ. If bora grounds are not oriented to any particular object or direction, we expect to find a roughly uniform distribution in their orientations. However, if at least some bora grounds are oriented to the position of the Sky Bora, then we expect to find a preference for south-southwest orientations when we look at the overall distribution of bora ground orientations.",
"pages": [
4,
5,
6
]
},
{
"title": "Methodology",
"content": "To determine the orientations of bora ceremonial sites, we obtained data for 63 such sites from the following published literature: Mathews (1894, 1896a, 1896b, 1897a, 1907, 1917), Hopkins (1901), Towle (1942), Bartholomai and Breeden (1961), Anon. (1973), McBryde (1974), Steele (1984), Satterthwait and Heather (1987), and Bowdler (2001). We also obtained 1107 archaeological site cards from the NSW Aboriginal Heritage Information Management System (AHIMS) related to stone arrangements and ceremonial grounds. We then filtered the data through a rigorous selection process, discarding data for any bora ground that failed to meet any of the following criteria: The orientation of each site was measured from the centre of the largest circle to the centre of the smaller circle. If the second circle was missing, the orientation was taken from the centre of the circle to the middle of the opening. Measurements were either taken directly from the records given by the surveyor or measured from the survey with a protractor and ruler. We divided the azimuths into 16 bins (N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, NNW), each with a width of 22.5¼ with N centred at 0¡, NNE at 22.5¡, and so on (see Table 1).",
"pages": [
6
]
},
{
"title": "Results and Analysis",
"content": "Of the 1170 sites obtained from the literature and AHIMS site card search, only 68 fit the specified selection criteria (Table 2, Figure 3). The 68 sites can be divided into two groups: The 46 data points whose orientations are recorded individually, are provided in Table 2 and are grouped into 22.5¼ bins, shown as a histogram in Figure 4a. The histogram reveals a clear preference for the S, SW and W orientations. Table 2 contains 34 orientations in ordinal (N, S, E, W, NW, NE, SE, SW) directions, but only 12 orientations in inter-ordinal (NNE, ENE, etc.) directions. The low number of inter-ordinal orientations suggests either that the sites tend to be oriented on ordinal points, or that some authors rounded to the nearest ordinal point. To avoid a statistical bias in our results, we re-binned the data into the eight ordinal directions, dividing the counts of each inter-ordinal bin equally between the two neighbouring ordinal bins, resulting in eight 45¼ bins (Table 1, Figure 4b). A preferred orientation to the south is evident (28% of the 46 data points), with lesser but significant preferences to the SW (17%) and W (15%) bins. The combined S, SW and W bins account for 61% of the total data points, while the remaining are evenly spread across the remaining bins. The highest peak of 12.5 orientations occurs in the S bin. We compare this result with the 22 data points from Satterthwait and Heather (1987) (hereafter referred to as ÔSHÕ) by re-binning our data to four quadrants centred on the cardinal points (N, S, E, W), as shown in Figure 4c. This reveals a strong preference for the southern quadrant and a lesser but significant preference to the western quadrant, which, when combined, account for 74% of the 46 data points. The SH data (Figure 4d) is similar, with a significant preference for the southern quadrant (68% of the 22 data points), but with an even distribution among the remaining quadrants. We then combined our 46 data points with the 22 SH data points, resulting in Figure 4e. A clear preference for the southern quadrant is evident, with 35 of the 68 orientations (51%) falling in the S bin. This result is consistent with the Love hypothesis. To determine if this is a chance clumping of a random distribution of orientations, we conducted a Monte Carlo simulation, in which 68 orientations were distributed randomly in each of the bins shown in Figure 4e. We repeated this process 100 million times. In only 303 of the 100 million runs did the number in any one bin equal or exceed 35, from which we can conclude that the likelihood of the peak in Figure 4b occurring by chance is about 3x10 -6 or 0.0003%. We therefore conclude that this distribution is clearly not the result of chance, and that the constructors of the bora rings intentionally aligned most of them to the south quadrant.",
"pages": [
7,
8
]
},
{
"title": "Discussion and Conclusion",
"content": "We have shown that the bora grounds studied have a preferred orientation to southerly directions and that these orientations are not the result of chance, but were deliberate. The reason for this is not known, but it is consistent with the Love hypothesis that southeast Australian bora ceremonial grounds have a preferred orientation to the celestial emu in the Milky Way in the south-southwest skies. The celestial emu is in this position in the evening sky during the month of August, the time during which Winterbotham (1957) and Needham (1981) claimed that bora ceremonies were held. Hamacher et al. (2012) showed that linear stone arrangements in NSW also have a preferred orientation to the cardinal points, especially north-south orientations. Since many stone arrangements are ceremonial sites, this lends support to the claim that orientation is an important factor utilised by Aboriginal people when laying out ceremonial sites. Although our analysis supports the Love hypothesis, it is not definitive evidence that bora grounds are oriented to the Sky Bora. Some researchers, including Winterbotham (1957) and Mathews (1894), state that many Bora ceremonies across NSW and Qld were held at various times throughout the year, which do not correspond to any particular orientation of the Milky Way. However, there is strong ethnographic evidence that the Milky Way is associated with the bora ceremony and we consider it likely that some ceremonies were timed, and bora sites oriented, such that the vertical Milky Way was visible above the path connecting the two circles during bora ceremonies. Additional research is necessary to understand these links; we are currently engaged in further research projects to explore this.",
"pages": [
10,
11
]
},
{
"title": "Acknowledgements",
"content": "We acknowledge the Aboriginal Elders and custodians, past and present, on whose land the bora sites are located. For archaeological data and literature sources, we thank staff from the State Library of NSW, the Australian Institute for Aboriginal and Torres Strait Islander Studies and the NSW Office of Environment and Heritage. This research made use of the TROVE and JSTOR databases, Google Maps, and the Stellarium astronomical software package. Hamacher conducted his component of this research while a PhD student at Macquarie University, but finished the analysis and writing as a staff member at the University of New South Wales.",
"pages": [
11
]
},
{
"title": "References",
"content": "Anon. 1973 The layout of bora grounds. Bulletin of the Richmond River Historical Society 65:12Ð13. Bartholomai, A. and S. Breeden 1961 Stone ceremonial grounds of the Aborigines in the Darling Downs area, Queensland. Memoirs of the Queensland Museum 13(6):231Ð237. Berndt, R.M. 1974 Aboriginal Religion . Leiden: Brill Archive. Black, L. 1944 The Bora Ground: Being a Continuation of a Series on the Customs of the Aborigines of the Darling River Valley and of Central New South Wales, Part IV . Sydney: F.H. Booth. Bowdler, S. 2001 The management of Indigenous ceremonial (ÔboraÕ) sites as components of cultural landscapes. In M. Cotter, W.E. Boyd and J. Gardiner (eds), Heritage Landscapes: Understanding Place and Communities , pp.1Ð19. Lismore: Southern Cross University Press. Cairns, H.C. and B. Yidumduma Harney 2004 Dark Sparklers . Sydney: Hugh Cairns. Collins, D. 1798 An Account of the English Colony in New South Wales, Vol. I . London: T. Cadell Jr and W. Davies. Eliade, M. 1996 Patterns in Comparative Religion . Lincoln: University of Nebraska Press. Frankel, D. 1982 Earth rings at Sunbury, Victoria. Archaeology in Oceania 17:83Ð89. Fraser, J.F. 1883 The Aborigines of New South Wales. Transactions and Proceedings of the Royal Society of New South Wales 16:193Ð233. Langevad, G. 1982 Some Original Views Around Kilcoy. Book 1: The Aboriginal Perspective . Queensland Ethnographic Transcripts 1. Brisbane: Archaeology Branch, Queensland Department of Aboriginal and Islanders Advancement. Hamacher, D.W. 2012 On the Astronomical Knowledge and Traditions of Aboriginal Australians . PhD thesis by publication, Department of Indigenous Studies, Macquarie University. [ www.academia.edu/1905624/On_the_Astronomical_Knowledge_and_Traditions_of_Aboriginal_Australians ] Hamacher, D.W., R.S. Fuller and R.P. Norris 2012 Orientations of linear stone arrangements in New South Wales. Australian Archaeology 75:46Ð54.",
"pages": [
11
]
},
{
"title": "Australian Archaeology, No. 77 | Preprint",
"content": "Boksenberg (eds), The Role of Astronomy in Society and Culture , pp.39Ð47. Cambridge: Cambridge University Press. Norris, R. and P. Norris 2009 Emu Dreaming: An Introduction to Australian Aboriginal Astronomy . Sydney: Emu Dreaming Press. Ridley, W. 1873 Australian languages and traditions. The Journal of the Anthropological Institute Great Britain and Ireland 2:257Ð275. Roth, W.E. 1909 On Certain Initiation ceremonies. North Queensland Ethnography 12:166-85 Satterthwait, L. and A. Heather 1987 Determinants of earth circle site location in the Moreton region, southeast Queensland. Queensland Archaeological Research 4:1Ð33. Smith, W. 1913 Sketcher, Aboriginal folk-lore. The Queenslander , 11 October, p. 8. Stanbridge, W. 1861 Some Particulars of the General Characteristics, Astronomy, and Mythology of the Tribes in the Central Part of Victoria, Southern Australia. Transactions of the Ethnological Society of London 1:286304. Steele, J.G. 1984 Aboriginal Pathways in Southeast Queensland and the Richmond River . Brisbane: University of Queensland Press. Towle, C.C. 1942 Bora ground near Ruby Creek, NSW. Victorian Naturalist 59(5):80Ð81. Winterbotham, L. 1957 GaiarbauÕs Story of the Jinibara Tribe of Southeast Queensland. Unpublished manuscript held on file at the Australian Institute for Aboriginal and Torres Strait Islander Studies, Canberra (MS #45/7460). Wellard, G.E.P. 1983 Bushlore - or this and that from here and there . Perth: Artlook Books.",
"pages": [
13
]
}
]
2013BrJPh..43..375K
https://arxiv.org/pdf/1305.2363.pdf
<document>
<section_header_level_1><location><page_1><loc_27><loc_80><loc_73><loc_85></location>Ultra-High Energy Cosmic Rays: Results and Prospects</section_header_level_1>
<section_header_level_1><location><page_1><loc_41><loc_77><loc_59><loc_78></location>Karl-Heinz Kampert</section_header_level_1>
<text><location><page_1><loc_22><loc_74><loc_79><loc_75></location>University of Wuppertal, Department of Physics, Gaußstrasse 20, D-42119 Wuppertal 1</text>
<text><location><page_1><loc_18><loc_53><loc_82><loc_71></location>Abstract. Observations of cosmic rays have been improved at all energies, both in terms of higher statistics and reduced systematics. As a result, the all particle cosmic ray energy spectrum starts to exhibit more structures than could be seen previously. Most importantly, a second knee in the cosmic ray spectrum - dominated by heavy primaries - is reported just below 10 17 eV. The light component, on the other hand, exhibits an ankle like feature above 10 17 eV and starts to dominate the flux at the ankle. The key question at the highest energies is about the origin of the flux suppression observed at energies above 5 · 10 19 eV. Is this the long awaited GZK-effect or the exhaustion of sources? The key to answering this question is again given by the still largely unknown mass composition at the highest energies. Data from different observatories don't quite agree and common efforts have been started to settle that question. The high level of isotropy observed even at the highest energies starts to challenge a proton dominated composition if extragalactic (EG) magnetic fields are on the order of a few nG or more. We shall discuss the experimental and theoretical progress in the field and the prospects for the next decade.</text>
<text><location><page_1><loc_18><loc_51><loc_25><loc_52></location>Keywords:</text>
<text><location><page_1><loc_26><loc_51><loc_36><loc_52></location>UHECR, EAS</text>
<text><location><page_1><loc_18><loc_50><loc_22><loc_51></location>PACS:</text>
<text><location><page_1><loc_23><loc_50><loc_42><loc_51></location>13.85.Tp, 96.50.sd, 96.50.sb,</text>
<section_header_level_1><location><page_1><loc_41><loc_45><loc_59><loc_47></location>INTRODUCTION</section_header_level_1>
<text><location><page_1><loc_16><loc_16><loc_84><loc_43></location>The Texas-Symposium 2012 completes a series of conferences at which the discovery of cosmic rays (CR) a hundred years ago by Franz Viktor Hess has been commemorated. Less known is a breakthrough made 50 years ago by John Linsley: in 1962 he reported the first observation of a primary CR particle with an energy exceeding 10 20 eV [1]. This event remains one of the most energetic CRs ever recorded and Linsley was extremely lucky to observe such an event after just three years of data taking of the 2 km 2 large Volcano Ranch air shower array. The cosmic microwave background (CMB) radiation, discovered three years later, immediately led to the prediction of a flux suppression either due to photo-pion production by protons propagating through the CMB at energies above 5 · 10 19 eV or due to photodisintegration of nuclei at about the same threshold energy. This process is known as GZK-effect, predicted independently by Greisen and by Zatsepin and Kuz'min [2, 3]. This has been the only firm prediction about a structure in the CR energy spectrum [4] and it has taken nearly 50 years to observe such a feature in data [5, 6]. However, can we be sure about having observed the GZK-effect? The spectral feature may equally be caused by the exhaustion of nearby sources or by a mixture of both as will be discussed below.</text>
<text><location><page_2><loc_16><loc_75><loc_84><loc_89></location>At lower energies, Kulikov and Khristiansen [7] in 1958 reported a structure in the shower size spectrum which became known as the 'knee' in the CR spectrum. Observations made by KASCADE [8] and other air shower experiments showed that the mean mass increases above the knee, indicating that the knee marks the maximum acceleration energy of the most abundant Galactic sources. This led to speculations that heavy primaries would experience the same limitation of particle acceleration and a second, so-called 'Iron-knee', would be observed around E Fe knee ∼ 26 × E p knee . Such an observation has now been reported and it may mark the end of the Galactic CR spectrum.</text>
<text><location><page_2><loc_16><loc_58><loc_84><loc_75></location>Large- and small-scale anisotropies in the arrival directions have been reported at TeV energies and now reach to beyond a PeV. This has come as a surprise and its interpretation starts to result in a better understanding and modeling of CR propagation within our Galaxy and about the transition from Galactic to EG CRs. At the highest energies, only upper limits on large scale anisotropies have been reported so far but, due to limited statistics, the amplitudes cannot be probed down to the levels observed below the knee region. Instead, a weak correlation of the highest energy particles to the position of nearby AGN has been reported by Auger [9]. This gave support to the picture that some fraction of the highest energy CRs results from sources within about 200 Mpc distance.</text>
<text><location><page_2><loc_16><loc_43><loc_84><loc_58></location>Much progress has also been made in particle acceleration emphasizing the importance of non-linear effects in diffuse shock acceleration (DSA) with magnetic field amplification due to CR current driven instabilities. These effects may not only substantially increase the maximum energy reachable in CR accelerators but may also reduce the time scales required for the acceleration process. While Galactic CRs are believed to originate from supernova remnants (SNR), those at the highest energies are thought to originate in the lobes of Radio Galaxies (RG) if they are large and luminous enough and, again, a substantial energy is contained in the turbulent component of the magnetic field.</text>
<text><location><page_2><loc_16><loc_36><loc_84><loc_43></location>Thus, it is fair so say that enormous progress has been made in CR physics particularly in recent years, both in observations and in accompanying theory. However, despite such advancements, the key questions about the CR origin and acceleration remain open even 100 years after their discovery. This paper aims to address some key topics in the field.</text>
<section_header_level_1><location><page_2><loc_28><loc_31><loc_72><loc_33></location>THE COSMIC RAY ENERGY SPECTRUM</section_header_level_1>
<text><location><page_2><loc_16><loc_11><loc_84><loc_29></location>Recent progress in the knee-to-ankle energy range has been driven mostly by KASCADE-Grande with Tunka and IceTop ramping up and providing more data with high statistics and good resolution. Using complex 2-dimensional unfolding techniques to the electron vs muon numbers measured on shower-by-shower basis by the KASCADE air shower experiment, the mean mass was shown to become heavier above the knee energy with the energy spectra of primary mass groups supporting a scaling with rigidity according to E Z knee glyph[similarequal] Z × 3 · 10 15 eV [8], such as was suggested long time ago by Peters [10]. This observation, supported by other experiments, has renewed the question about the existence of a Fe-like knee at about 10 17 eV. Such a structure has been reported very recently and is shown in Fig. 1. The significance of the second knee at E glyph[similarequal] 80 PeV in the all-particle energy spectrum of KASCADE-Grande is just above</text>
<text><location><page_3><loc_50><loc_88><loc_51><loc_89></location>17</text>
<figure>
<location><page_3><loc_31><loc_65><loc_68><loc_89></location>
<caption>FIGURE 1. All-particle, electron-poor, and electron rich energy spectra from KASCADE-Grande. The all-particle (black triangles; 105,000 events) and heavy enriched spectrum (blue circles; 52,000 events) is taken from [11] and the all-particle (grey squares) and light primary spectrum (red triangles; 6,300 events) results from a larger data set and employs stronger cuts to the light-component to select essentially p+He primaries [13]. The bands indicate systematic uncertainties resulting mostly from hadronic interaction models. The heavy enriched data sample exhibits a knee at 10 16 . 9 eV with a statistical significance of 3 . 5 s while the ankle-like feature in the light component is found at 10 17 . 1 eV with a significance of 5 . 8 s .</caption>
</figure>
<text><location><page_3><loc_16><loc_38><loc_84><loc_48></location>2 s but increases to 3 . 5 s for the electron poor (heavy) sample [11]. Similarly, IceTop data [12] show an indication of a flattening above 22 PeV, i.e. in the energy range between the two knees. Another very interesting recent result by KASCADE-Grande is reported in [13]. Using a larger data set and applying stronger cuts to electron-rich showers than were applied in [11], to accept essentially only p+He primaries, there is an ankle-like feature at 10 17 . 1 eV with a significance of 5 . 8 s .</text>
<text><location><page_3><loc_16><loc_21><loc_84><loc_38></location>Obviously, the CR energy spectrum, once measured with high precision, exhibits much more structure and information than just the knee energy and the indices of an apparent power-law like spectrum below and above. The observation of the 'Fe-knee' and 'p-ankle' (with 'Fe' and 'p' meant as synonym for 'heavy' and 'light' primaries, respectively) is a remarkable achievement. The Fe-knee at 8 · 10 16 eV supports the picture of a rigidity scaling - also named the 'Peters cycle' [10] - in the knee energy range and the p-ankle E glyph[similarequal] 1 . 2 · 10 17 eV has in fact been expected because of the steep fall-off of the p-component at the knee [8] and the p-like composition at the ankle (see next section). Thus, the p-ankle would either mark the transition from Galactic to EG sources or the onset of a new high energy (Galactic) source population (see e.g. [14, 15]).</text>
<text><location><page_3><loc_16><loc_11><loc_84><loc_21></location>At the highest energies, from the ankle to beyond 10 20 eV, the Pierre Auger Observatory [16, 17] is the flagship in the field with an accumulated exposure of about 30 000 km 2 sr yr. The Telescope Array [18], due to a later start and its more than 4 times smaller area, has collected about 10 times less events. A detailed comparison of the energy spectra of various observatories is presented in Fig. 2. As discussed in great detail in [19], it is found that the energy spectra determined by the larger experiments are con-</text>
<figure>
<location><page_4><loc_21><loc_60><loc_79><loc_89></location>
<caption>FIGURE 2. Compilation of cosmic ray energy spectra, with the flux multiplied by E 3 , published by Auger (combined Hybrid/SD), TA SD, Yakutsk SD, HiRes I, and HiRes II after energy-rescaling as shown in the figure has been applied. The reference spectrum is the average of those from Auger and TA. From [19] where also references to the respective data sets can be found.</caption>
</figure>
<text><location><page_4><loc_16><loc_32><loc_84><loc_49></location>sistent in normalization and shape after energy scaling factors, as shown in Fig. 2, are applied. Those scaling factors are within systematic uncertainties in the energy scale quoted by the experiments. This is quite remarkable and demonstrates how well the data are understood. Nevertheless, cross-checks of photometric calibrations and atmospheric corrections have been started and as a next step, common models (e.g. fluorescence yield) should be used where possible. The data in Fig. 2 clearly exhibit the ankle at ∼ 4 · 10 18 eV and a flux suppression above ∼ 4 · 10 19 eV. The flux suppression at the highest energies is in accordance with the long-awaited GZK-effect [5, 6]. However, as discussed below, the data of the Auger observatory suggest that the maximum energy of nearby sources or the source population is seen, instead.</text>
<section_header_level_1><location><page_4><loc_18><loc_27><loc_82><loc_29></location>COSMIC RAY COMPOSITION AND INTERACTION MODELS</section_header_level_1>
<text><location><page_4><loc_16><loc_12><loc_84><loc_25></location>Obviously the energy spectra by itself, despite their high level of precision reached, do not allow one to conclude about the origin of the spectral structures and thereby about the origin of CRs in different energy regions. Additional key information is obtained from the mass composition of CRs. Unfortunately, the measurement of primary masses is the most difficult task in air shower physics as such measurements rely on comparisons of data to EAS simulations with the latter serving as reference [20]. EAS simulations, however, are subject to uncertainties mostly because hadronic interaction models need to be employed at energy ranges much beyond those accessible to man-made particle accel-</text>
<figure>
<location><page_5><loc_16><loc_68><loc_84><loc_89></location>
<caption>FIGURE 3. Left: Average logarithmic mass of cosmic rays as a function of energy derived from X max measurements with optical detectors for the EPOS 1.99 interaction model. Lines are estimates of the experimental systematics, i.e. upper and lower boundaries of the data presented [20]. Right: Propagated CR spectrum assuming a mixed composition similar to the Galactic one with a maximum energy at the sources of E max ( Z ) = Z × 4 · 10 18 eV and a spectral index b = 1 . 6 [24].</caption>
</figure>
<text><location><page_5><loc_16><loc_38><loc_84><loc_56></location>erators. Therefore, the advent of LHC data, particularly those measured in the extreme forward region of the collisions, is of great importance to CR and EAS physics and have been awaited with great interest [21]. Remarkably, interaction models employed in EAS simulations provide a somewhat better description of global observables (multiplicities, p ⊥ -distributions, forward and transverse energy flow, etc.) than typical tunes of HEP models, such as PYTHIA or PHOJET [22]. This demonstrates once more that the CR community has taken great care in extrapolating models to the highest energies. Moreover, as demonstrated e.g. in [23], CR data provide important information about particle physics at centre-of-mass energies ten or more times higher than is accessible at LHC. The pp -inelastic cross section extracted from data of the Auger Observatory supports only a modest rise of the inelastic cross section with energy [23].</text>
<text><location><page_5><loc_16><loc_14><loc_84><loc_37></location>A careful analysis of composition data from various experiments has been presented in [20] with exemplary results depicted in Fig. 3 (left). These data complement those of the energy spectrum in a remarkable way. As can be seen, the breaks in the energy spectrum coincide with the turning points of changes in the composition: the mean mass becomes increasingly heavier above the knee, reaches a maximum at the 2 nd knee, another minimum at the ankle before it starts to rise again towards the highest energies. Different interaction models provide the same answer concerning changes in the composition but differ by their absolute values of 〈 ln A 〉 . It should also be noted that the suggested increase in the mean mass at the highest energies is not without dispute. It has been looked at in great detail in [25]. At ultra-high energies, the Auger data suggest a larger 〈 ln A 〉 than all other experiments. TA and Yakutsk are consistent within systematic uncertainties with Auger data while HiRes is compatible with Auger only at energies below 10 18 . 5 eV when using QGSJet-II. When using the SIBYLL model, Auger and HiRes become compatible within a larger energy range [25].</text>
<text><location><page_5><loc_18><loc_12><loc_84><loc_13></location>The importance of measuring the composition up to the highest energy cannot be</text>
<text><location><page_6><loc_16><loc_72><loc_84><loc_89></location>overstated as it will be the key to answering the question about the origin of the GZKlike flux suppression. The same mechanism of limiting source energy that appears to cause the increasingly heavy above the knee may work also for EG-CRs above the ankle. Thereby, the break at ∼ 4 · 10 19 eV may mark the maximum energy of nearby EG CR-accelerators, rather than the GZK-effect. This is shown in Fig. 3 (right), where propagated CR spectra are shown for a maximum energy at the source of E max ( Z ) = Z × 4 · 10 18 eV and assuming a hard spectral source index of b = 1 . 6 [24]. Clearly, such a - in view of the hard spectral index - more exotic scenario provides a good description of the energy spectrum. Moreover, other than the GZK-like interpretation, it also describes the 〈 X max 〉 and the fluctuation RMS( X max ) of the Pierre Auger Observatory [26].</text>
<text><location><page_6><loc_16><loc_67><loc_84><loc_72></location>A mixture of light and intermediate/heavy primaries at the highest energies may also explain the low level of directional correlations to nearby AGN. Enhancements, presently foreseen by the Auger Collaboration will address this issue.</text>
<text><location><page_6><loc_16><loc_38><loc_84><loc_67></location>Two models about the putative transition from Galactic- to EG-CRs have received much attention: In the classical 'ankle model' the transition is assumed to occur at the ankle. In this model, Galactic CRs above the 2 nd knee are dominated by heavy primaries before protons of EG origin start to take over and to dominate at the ankle. In the dipmodel [27], on the other hand, the transition occurs already at the 2 nd knee and is characterized by a sharp change of the composition from Galactic iron to EG protons while the ankle is due to e + e -production of protons in the CMB. A third, 'mixed composition', model has been suggested more recently [28] in which EG-CRs taking over are not considered being protons but an EG mixed CR composition. Clearly, the dip-model requires a proton dominated composition essentially at all energies starting somewhat above the 2 nd knee. The answer may be difficult to determine based on 〈 X max 〉 or 〈 ln A 〉 alone. A much better quantity would again be the RMS of these quantities, such as studied at higher energies in [26]. A rather abrupt change of composition as required by the dip-model near the 2 nd knee vs a smooth change of composition as expected near the ankle in the ankle model, should become distinguishable by the RMS ( X max ) -values already in the very near future. This has been a prime motivation for the HEAT and TALE extensions of Auger and TA, respectively.</text>
<section_header_level_1><location><page_6><loc_18><loc_31><loc_82><loc_35></location>ANISOTROPIES AT DIFFERENT ENERGIES AND ANGULAR SCALES</section_header_level_1>
<text><location><page_6><loc_16><loc_11><loc_84><loc_29></location>The main obstacle in identifying Galactic CR-sources is the diffusion of CRs in the Galactic magnetic field (GMF), erasing directional information on the position of their sources. The GMF has a turbulent component that varies on scales between l min ∼ 1 AU and l max few to 200 pc. Since CRs scatter on inhomogeneities with variation scales comparable to their Larmor radius, the propagation of Galactic CRs in the GMF resembles a random walk and is well described by the diffusion approximation. Large scale anisotropies observed by the Tibet Air-Shower experiment [31] in the northern hemisphere for CRs at energies of a few to several hundred TeV and at angular scales of 60 · and above, thus came as a surprise. The data have been confirmed and complemented by Milagro [32] and more recently also by high statistics measurements of IceTop in the southern hemisphere [33, 34] (cf. Fig. 4). Moreover, the structure changes with energy</text>
<figure>
<location><page_7><loc_16><loc_67><loc_52><loc_87></location>
</figure>
<figure>
<location><page_7><loc_55><loc_67><loc_84><loc_88></location>
<caption>FIGURE 4. Left: Upper limits on the equatorial dipole component as a function of energy, from several experiments [29]. Also shown are the predictions up to 1 EeV from two different Galactic magnetic field models with different symmetries (A and S), the predictions for a purely Galactic origin of UHECRs up to a few tens of 10 19 eV (Gal), and the expectations from the Compton-Getting effect for an EG component isotropic in the CMB rest frame (C-G Xgal) with references given in [29]. Right: Reconstructed declination and right-ascension of the dipole with corresponding uncertainties, as a function of the energy, in orthographic projection [30].</caption>
</figure>
<text><location><page_7><loc_16><loc_41><loc_84><loc_51></location>and appears to persist to beyond PeV energies. This anisotropy reveals a new feature of the Galactic cosmic-ray distribution, which must be incorporated into theories of the origin and propagation of cosmic rays. As was emphasized e.g. in [35, 28], changes of the anisotropy patterns with energy can, in principle, be accounted for by specific distributions (in space and time) and individual source energy spectra of nearby recent SNRs.</text>
<text><location><page_7><loc_16><loc_11><loc_84><loc_41></location>Another long-standing problem is the high level of isotropy even at energies beyond 10 18 eV. For non-relativistic diffusive acceleration g g = 2 and the index of the observed spectrum, g g + m = 2 . 7, one derives m = 0 . 7. At very high energy this results in a too large anisotropy, d ( E ) GLYPH<181> D ( E ) GLYPH<181> E m and in a too small traversed grammage, X cr ( E ) GLYPH<181> 1 / D ( E ) , with the diffusion coefficient D ( E ) , and would contradict experimental data (cf. Fig. 4). However, d ( E ) GLYPH<181> D ( E ) refers again to an average of the anisotropy amplitude computed over many source realizations, i.e. over a continuum of sources and thus does not apply to concrete realizations of nearby SNRs and turbulent magnetic fields within the cosmic ray scattering length. Moreover, as pointed out in [35], diffusion breaks down for propagation of CRs within our Galaxy at E > ∼ 10 17 eV. Recently, the Pierre Auger Observatory reported the first large scale anisotropy searches as a function of both right ascension and declination. Again, within the systematic uncertainties, no significant deviation from isotropy is revealed and the upper limits on dipole and quadrupole amplitudes challenge an origin from stationary galactic sources densely distributed in the galactic disk and emitting predominantly light particles in all directions. In Fig. 4 (right), the corresponding directions are shown in orthographic projection with the associated uncertainties, as a function of the energy. Both angles are expected to be randomly distributed in the case of independent samples whose parent distribution is isotropic. It is</text>
<text><location><page_8><loc_16><loc_84><loc_84><loc_89></location>thus interesting to note that all reconstructed declinations are in the equatorial southern hemisphere, and to note also the intriguing smooth alignment of the phases in right ascension as a function of the energy.</text>
<text><location><page_8><loc_16><loc_58><loc_84><loc_84></location>Directional correlations of the most energetic CRs with nearby AGN observed by the Pierre Auger Observatory provided the first signature about anisotropies of the most energetic CRs and thereby about their EG origin [9, 36, 37]. Initially very strong, the fraction of Auger events above 55 EeV correlating within 3 . 1 · with a nearby ( z ≤ 0 . 018) AGN from the VCV-catalogue has stabilized at a level of ( 33 ± 5 ) % [38]. With an accidental rate for an isotropic distribution of 21 %, this corresponds to a chance probability of less than 1 %. Recently, TA reported a correlation fraction of 44 % at an isotropic fraction of 24 % yielding a chance probability of about 2 % [39]. Thus, the data are in perfect agreement with each other yielding a combined chance probability of observing such a correlation at the 10 -3 level. However, more statistics is needed to consolidate the picture and to allow subdividing data sets in bins of related CR observables. The sky region around Cen A remains populated by a larger number of high energy events compared to the rest of the sky, with the largest departure from isotropy at 24 · around the center of Cen A with 19 events observed and 7.6 expected for isotropy, corresponding to a chance probability for this to occur at a level of 4 % [38].</text>
<text><location><page_8><loc_16><loc_33><loc_84><loc_58></location>The Pierre Auger Collaboration has also performed a search for ultra-high neutrons from sources located within the Galaxy [40]. Their mean path length is 9 . 2 × E kpc before decaying, where E is the energy of the neutron in EeV. A stacking analysis was performed in the direction of bright Galactic gamma-ray sources: the ones detected by Fermi-Lat instrument in the 100 MeV - 100 GeV range and the ones detected by H.E.S.S. in the range of 100 GeV - 100 TeV. Neither analysis provided evidence for significant excess and upper limits on the flux were derived for all directions within the Auger coverage. For directions along the Galactic plane for instance, the upper limits are below 0.024 km -2 yr -1 , 0.014 km -2 yr -1 and 0.026 km -2 yr -1 for energy bins of [1-2] EeV, [2-3] EeV and E ≥ 1 EeV, respectively. For energies above 1 EeV, the 95 % C.L. upper limit on the flux is 0.065 km -2 yr -1 , which corresponds to the energy flux of 0.13 EeV km -2 yr -1 = 0.4 eV cm -2 s -1 in the EeV range. Here a differential energy spectrum E -2 was assumed [40]. Those upper limits call into question the existence of persistent sources of EeV protons in the Galaxy. They also place useful constraints on the UHE emissions from the known Galactic sources of TeV gamma-rays.</text>
<section_header_level_1><location><page_8><loc_37><loc_28><loc_63><loc_30></location>ADVANCES IN THEORY</section_header_level_1>
<text><location><page_8><loc_16><loc_11><loc_84><loc_26></location>The observed knees may be interpreted as the end of the Galactic CR spectrum with their position defining the maximum acceleration energy. Although this picture may look very natural, the way to its adoption was not straight forward (see e.g. [28] for a recent review). Diffuse shock acceleration in SNR was discovered in the late 1970s but it took two decades more to realize that CR-streaming amplifies the magnetic fields upstream of the shock to create highly turbulent fields with strengths up to d B ∼ B ∼ 10 -4 G (see e.g. [41, 42]). The importance of non-linear magnetic fields amplification at SNR shocks, now also well accounted for by 3d MHD simulations, surely became one of the most discussed theory topics recently and there is general consensus that this is vital to</text>
<text><location><page_9><loc_16><loc_86><loc_84><loc_89></location>reach the knee even on relatively short timescales on the order of tens to hundreds of years, i.e. much faster than it takes to reach the Sedov phase.</text>
<text><location><page_9><loc_16><loc_74><loc_84><loc_85></location>This drives the discussion to another important theoretical CR-problem. It is challenging to allow CRs to escape from SNR into the interstellar medium in large numbers without significant energy losses. This issue was first addressed by Ptuskin and co-workers [43] where it was shown that only particles accelerated up to the maximum energy E max can escape the acceleration region. In their original model, E max reaches its highest value only at the beginning of the Sedov phase. The E -2 CR energy spectrum in this model is then given by integrating the narrow peak of E max ( t ) over time.</text>
<text><location><page_9><loc_16><loc_63><loc_84><loc_73></location>The diffusion of Galactic CRs close to their sources has been addressed recently by Kachelrieß and coworkers (see also [35]). Propagating individual CRs in purely isotropic turbulent magnetic fields with maximal scale of spatial variations l max , they find anisotropic CR diffusion at distances r < l max from their sources. As a result, the CR densities around the sources become strongly irregular and show filamentary structures that could be probed by TeV g -rays.</text>
<text><location><page_9><loc_16><loc_40><loc_84><loc_63></location>At the highest energies, Radio Galaxies (RG) remain being the most promising candidates for UHECR acceleration. An interesting argument linking UHECR sources to their luminosity at radio frequencies has been put forward in this context by Hardcastle [44] and he concludes that RGs can accelerate protons to the highest observed energies in the lobes if a substantial amount of energy is in the turbulent component of the magnetic field, i.e. B > ∼ B equipart , and the Hillas criterion is met. In Cen A, existing observations do in fact constrain B > ∼ B equipart for the kpc-scale jet. Moreover, if UHECRs are predominantly protons, then very few sources should contribute to the observed flux. These sources should be easy to identify in the radio and their UHECR spectrum should cut off steeply at the observed highest energies. In contrast, if the mass composition is heavy at the highest energies then many radio galaxies could contribute to the UHECR flux but due to the much stronger deflection only the nearby Radio Galaxy Cen A may be identifiable [44]. Of course, such a conclusion depends very much on the strength of the EG magnetic fields and the maximum energy reached in the sources.</text>
<section_header_level_1><location><page_9><loc_32><loc_35><loc_68><loc_36></location>NEWPROJECTS AND OUTLOOK</section_header_level_1>
<text><location><page_9><loc_16><loc_11><loc_84><loc_33></location>Motivated by the large body of important experimental findings and new insights, the field continues to evolve very dynamically with new projects being planned or existing ones to be upgraded. In the study of low energy CRs, AMS is the by far most complex instrument in orbit, launched on May 16, 2011. It will measure light CR isotopes from about 500 MeV to 10 GeV and is hoped to improve our understanding of CR propagation in Galaxy. First data about the positron/electron ratio have been released recently [45] and confirm findings of PAMELA. The CALET (CALorimeteric Electron Telescope) project is a Japanese led international mission being developed as part of the utilization plan for the International Space Station (ISS) and aims at studying details of particle propagation in the Galaxy by a combination of energy spectrum measurements of electrons, protons and higher-charged nuclei. In Siberia, the German-Russian project HiScore is planned to be constructed at the Tunka site. This project will use open Cherenkov counters for CR measurements around the knee and will be complemented</text>
<text><location><page_10><loc_16><loc_81><loc_84><loc_89></location>by radio antennas to explore this new detection technology. HAWK is being constructed in Mexico. Although its prime goal is the study of the g -ray sky above 100 GeV, it will also contribute to measuring CR anisotropies at TeV-energies. LHAASO , mostly driven by the Chinese community and much larger and more complex than HAWK, serves the same scientific goals.</text>
<text><location><page_10><loc_16><loc_55><loc_84><loc_80></location>At the highest energies, Auger and TA plan upgrades in performance and size, respectively: Auger aims at improving the mass composition measurement and particle physics capabilities at the highest energies to answer the question about the origin of the flux suppression and TA aims at increasing their surface detector with a 2 km grid up to 2800 km 2 . Both collaborations have started to join efforts for a Next Generation Ground-based CR Observatory NGGO , much larger than existing experiments and aiming at good energy and mass resolution and exploring particle physics aspects at the highest energies. Four proposed and planned space missions constitute the roadmap of the space oriented community: TUS, JEM-EUSO, KLPVE, and Super-EUSO aim at contributing step-by-step to establish this challenging field of research. They will reach very large exposures aimed at seeing CR sources, which will be at the expense of energy resolution, composition measurements and particle physics capabilities. Given the resources of funding available in the next decade or two, it is unlikely that all of the above mentioned projects can be realized. Thus, priority should be given to complementarity rather than on duplication.</text>
<section_header_level_1><location><page_10><loc_37><loc_50><loc_63><loc_52></location>ACKNOWLEDGMENTS</section_header_level_1>
<text><location><page_10><loc_16><loc_40><loc_84><loc_48></location>Its a pleasure to thank the organizers of the Texas Symposium 2012 for inviting me to participate in this vibrant conference. I am also grateful for many stimulating discussions with colleagues from KASCADE-Grande, Auger and TA. Financial support by the German Ministry of Research and Education (Grants 05A11PX1 and 05A11PXA) and by the Helmholtz Alliance for Astroparticle Physics (HAP) is gratefully acknowledged.</text>
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</document>
[
{
"title": "Karl-Heinz Kampert",
"content": "University of Wuppertal, Department of Physics, Gaußstrasse 20, D-42119 Wuppertal 1 Abstract. Observations of cosmic rays have been improved at all energies, both in terms of higher statistics and reduced systematics. As a result, the all particle cosmic ray energy spectrum starts to exhibit more structures than could be seen previously. Most importantly, a second knee in the cosmic ray spectrum - dominated by heavy primaries - is reported just below 10 17 eV. The light component, on the other hand, exhibits an ankle like feature above 10 17 eV and starts to dominate the flux at the ankle. The key question at the highest energies is about the origin of the flux suppression observed at energies above 5 · 10 19 eV. Is this the long awaited GZK-effect or the exhaustion of sources? The key to answering this question is again given by the still largely unknown mass composition at the highest energies. Data from different observatories don't quite agree and common efforts have been started to settle that question. The high level of isotropy observed even at the highest energies starts to challenge a proton dominated composition if extragalactic (EG) magnetic fields are on the order of a few nG or more. We shall discuss the experimental and theoretical progress in the field and the prospects for the next decade. Keywords: UHECR, EAS PACS: 13.85.Tp, 96.50.sd, 96.50.sb,",
"pages": [
1
]
},
{
"title": "INTRODUCTION",
"content": "The Texas-Symposium 2012 completes a series of conferences at which the discovery of cosmic rays (CR) a hundred years ago by Franz Viktor Hess has been commemorated. Less known is a breakthrough made 50 years ago by John Linsley: in 1962 he reported the first observation of a primary CR particle with an energy exceeding 10 20 eV [1]. This event remains one of the most energetic CRs ever recorded and Linsley was extremely lucky to observe such an event after just three years of data taking of the 2 km 2 large Volcano Ranch air shower array. The cosmic microwave background (CMB) radiation, discovered three years later, immediately led to the prediction of a flux suppression either due to photo-pion production by protons propagating through the CMB at energies above 5 · 10 19 eV or due to photodisintegration of nuclei at about the same threshold energy. This process is known as GZK-effect, predicted independently by Greisen and by Zatsepin and Kuz'min [2, 3]. This has been the only firm prediction about a structure in the CR energy spectrum [4] and it has taken nearly 50 years to observe such a feature in data [5, 6]. However, can we be sure about having observed the GZK-effect? The spectral feature may equally be caused by the exhaustion of nearby sources or by a mixture of both as will be discussed below. At lower energies, Kulikov and Khristiansen [7] in 1958 reported a structure in the shower size spectrum which became known as the 'knee' in the CR spectrum. Observations made by KASCADE [8] and other air shower experiments showed that the mean mass increases above the knee, indicating that the knee marks the maximum acceleration energy of the most abundant Galactic sources. This led to speculations that heavy primaries would experience the same limitation of particle acceleration and a second, so-called 'Iron-knee', would be observed around E Fe knee ∼ 26 × E p knee . Such an observation has now been reported and it may mark the end of the Galactic CR spectrum. Large- and small-scale anisotropies in the arrival directions have been reported at TeV energies and now reach to beyond a PeV. This has come as a surprise and its interpretation starts to result in a better understanding and modeling of CR propagation within our Galaxy and about the transition from Galactic to EG CRs. At the highest energies, only upper limits on large scale anisotropies have been reported so far but, due to limited statistics, the amplitudes cannot be probed down to the levels observed below the knee region. Instead, a weak correlation of the highest energy particles to the position of nearby AGN has been reported by Auger [9]. This gave support to the picture that some fraction of the highest energy CRs results from sources within about 200 Mpc distance. Much progress has also been made in particle acceleration emphasizing the importance of non-linear effects in diffuse shock acceleration (DSA) with magnetic field amplification due to CR current driven instabilities. These effects may not only substantially increase the maximum energy reachable in CR accelerators but may also reduce the time scales required for the acceleration process. While Galactic CRs are believed to originate from supernova remnants (SNR), those at the highest energies are thought to originate in the lobes of Radio Galaxies (RG) if they are large and luminous enough and, again, a substantial energy is contained in the turbulent component of the magnetic field. Thus, it is fair so say that enormous progress has been made in CR physics particularly in recent years, both in observations and in accompanying theory. However, despite such advancements, the key questions about the CR origin and acceleration remain open even 100 years after their discovery. This paper aims to address some key topics in the field.",
"pages": [
1,
2
]
},
{
"title": "THE COSMIC RAY ENERGY SPECTRUM",
"content": "Recent progress in the knee-to-ankle energy range has been driven mostly by KASCADE-Grande with Tunka and IceTop ramping up and providing more data with high statistics and good resolution. Using complex 2-dimensional unfolding techniques to the electron vs muon numbers measured on shower-by-shower basis by the KASCADE air shower experiment, the mean mass was shown to become heavier above the knee energy with the energy spectra of primary mass groups supporting a scaling with rigidity according to E Z knee glyph[similarequal] Z × 3 · 10 15 eV [8], such as was suggested long time ago by Peters [10]. This observation, supported by other experiments, has renewed the question about the existence of a Fe-like knee at about 10 17 eV. Such a structure has been reported very recently and is shown in Fig. 1. The significance of the second knee at E glyph[similarequal] 80 PeV in the all-particle energy spectrum of KASCADE-Grande is just above 17 2 s but increases to 3 . 5 s for the electron poor (heavy) sample [11]. Similarly, IceTop data [12] show an indication of a flattening above 22 PeV, i.e. in the energy range between the two knees. Another very interesting recent result by KASCADE-Grande is reported in [13]. Using a larger data set and applying stronger cuts to electron-rich showers than were applied in [11], to accept essentially only p+He primaries, there is an ankle-like feature at 10 17 . 1 eV with a significance of 5 . 8 s . Obviously, the CR energy spectrum, once measured with high precision, exhibits much more structure and information than just the knee energy and the indices of an apparent power-law like spectrum below and above. The observation of the 'Fe-knee' and 'p-ankle' (with 'Fe' and 'p' meant as synonym for 'heavy' and 'light' primaries, respectively) is a remarkable achievement. The Fe-knee at 8 · 10 16 eV supports the picture of a rigidity scaling - also named the 'Peters cycle' [10] - in the knee energy range and the p-ankle E glyph[similarequal] 1 . 2 · 10 17 eV has in fact been expected because of the steep fall-off of the p-component at the knee [8] and the p-like composition at the ankle (see next section). Thus, the p-ankle would either mark the transition from Galactic to EG sources or the onset of a new high energy (Galactic) source population (see e.g. [14, 15]). At the highest energies, from the ankle to beyond 10 20 eV, the Pierre Auger Observatory [16, 17] is the flagship in the field with an accumulated exposure of about 30 000 km 2 sr yr. The Telescope Array [18], due to a later start and its more than 4 times smaller area, has collected about 10 times less events. A detailed comparison of the energy spectra of various observatories is presented in Fig. 2. As discussed in great detail in [19], it is found that the energy spectra determined by the larger experiments are con- sistent in normalization and shape after energy scaling factors, as shown in Fig. 2, are applied. Those scaling factors are within systematic uncertainties in the energy scale quoted by the experiments. This is quite remarkable and demonstrates how well the data are understood. Nevertheless, cross-checks of photometric calibrations and atmospheric corrections have been started and as a next step, common models (e.g. fluorescence yield) should be used where possible. The data in Fig. 2 clearly exhibit the ankle at ∼ 4 · 10 18 eV and a flux suppression above ∼ 4 · 10 19 eV. The flux suppression at the highest energies is in accordance with the long-awaited GZK-effect [5, 6]. However, as discussed below, the data of the Auger observatory suggest that the maximum energy of nearby sources or the source population is seen, instead.",
"pages": [
2,
3,
4
]
},
{
"title": "COSMIC RAY COMPOSITION AND INTERACTION MODELS",
"content": "Obviously the energy spectra by itself, despite their high level of precision reached, do not allow one to conclude about the origin of the spectral structures and thereby about the origin of CRs in different energy regions. Additional key information is obtained from the mass composition of CRs. Unfortunately, the measurement of primary masses is the most difficult task in air shower physics as such measurements rely on comparisons of data to EAS simulations with the latter serving as reference [20]. EAS simulations, however, are subject to uncertainties mostly because hadronic interaction models need to be employed at energy ranges much beyond those accessible to man-made particle accel- erators. Therefore, the advent of LHC data, particularly those measured in the extreme forward region of the collisions, is of great importance to CR and EAS physics and have been awaited with great interest [21]. Remarkably, interaction models employed in EAS simulations provide a somewhat better description of global observables (multiplicities, p ⊥ -distributions, forward and transverse energy flow, etc.) than typical tunes of HEP models, such as PYTHIA or PHOJET [22]. This demonstrates once more that the CR community has taken great care in extrapolating models to the highest energies. Moreover, as demonstrated e.g. in [23], CR data provide important information about particle physics at centre-of-mass energies ten or more times higher than is accessible at LHC. The pp -inelastic cross section extracted from data of the Auger Observatory supports only a modest rise of the inelastic cross section with energy [23]. A careful analysis of composition data from various experiments has been presented in [20] with exemplary results depicted in Fig. 3 (left). These data complement those of the energy spectrum in a remarkable way. As can be seen, the breaks in the energy spectrum coincide with the turning points of changes in the composition: the mean mass becomes increasingly heavier above the knee, reaches a maximum at the 2 nd knee, another minimum at the ankle before it starts to rise again towards the highest energies. Different interaction models provide the same answer concerning changes in the composition but differ by their absolute values of 〈 ln A 〉 . It should also be noted that the suggested increase in the mean mass at the highest energies is not without dispute. It has been looked at in great detail in [25]. At ultra-high energies, the Auger data suggest a larger 〈 ln A 〉 than all other experiments. TA and Yakutsk are consistent within systematic uncertainties with Auger data while HiRes is compatible with Auger only at energies below 10 18 . 5 eV when using QGSJet-II. When using the SIBYLL model, Auger and HiRes become compatible within a larger energy range [25]. The importance of measuring the composition up to the highest energy cannot be overstated as it will be the key to answering the question about the origin of the GZKlike flux suppression. The same mechanism of limiting source energy that appears to cause the increasingly heavy above the knee may work also for EG-CRs above the ankle. Thereby, the break at ∼ 4 · 10 19 eV may mark the maximum energy of nearby EG CR-accelerators, rather than the GZK-effect. This is shown in Fig. 3 (right), where propagated CR spectra are shown for a maximum energy at the source of E max ( Z ) = Z × 4 · 10 18 eV and assuming a hard spectral source index of b = 1 . 6 [24]. Clearly, such a - in view of the hard spectral index - more exotic scenario provides a good description of the energy spectrum. Moreover, other than the GZK-like interpretation, it also describes the 〈 X max 〉 and the fluctuation RMS( X max ) of the Pierre Auger Observatory [26]. A mixture of light and intermediate/heavy primaries at the highest energies may also explain the low level of directional correlations to nearby AGN. Enhancements, presently foreseen by the Auger Collaboration will address this issue. Two models about the putative transition from Galactic- to EG-CRs have received much attention: In the classical 'ankle model' the transition is assumed to occur at the ankle. In this model, Galactic CRs above the 2 nd knee are dominated by heavy primaries before protons of EG origin start to take over and to dominate at the ankle. In the dipmodel [27], on the other hand, the transition occurs already at the 2 nd knee and is characterized by a sharp change of the composition from Galactic iron to EG protons while the ankle is due to e + e -production of protons in the CMB. A third, 'mixed composition', model has been suggested more recently [28] in which EG-CRs taking over are not considered being protons but an EG mixed CR composition. Clearly, the dip-model requires a proton dominated composition essentially at all energies starting somewhat above the 2 nd knee. The answer may be difficult to determine based on 〈 X max 〉 or 〈 ln A 〉 alone. A much better quantity would again be the RMS of these quantities, such as studied at higher energies in [26]. A rather abrupt change of composition as required by the dip-model near the 2 nd knee vs a smooth change of composition as expected near the ankle in the ankle model, should become distinguishable by the RMS ( X max ) -values already in the very near future. This has been a prime motivation for the HEAT and TALE extensions of Auger and TA, respectively.",
"pages": [
4,
5,
6
]
},
{
"title": "ANISOTROPIES AT DIFFERENT ENERGIES AND ANGULAR SCALES",
"content": "The main obstacle in identifying Galactic CR-sources is the diffusion of CRs in the Galactic magnetic field (GMF), erasing directional information on the position of their sources. The GMF has a turbulent component that varies on scales between l min ∼ 1 AU and l max few to 200 pc. Since CRs scatter on inhomogeneities with variation scales comparable to their Larmor radius, the propagation of Galactic CRs in the GMF resembles a random walk and is well described by the diffusion approximation. Large scale anisotropies observed by the Tibet Air-Shower experiment [31] in the northern hemisphere for CRs at energies of a few to several hundred TeV and at angular scales of 60 · and above, thus came as a surprise. The data have been confirmed and complemented by Milagro [32] and more recently also by high statistics measurements of IceTop in the southern hemisphere [33, 34] (cf. Fig. 4). Moreover, the structure changes with energy and appears to persist to beyond PeV energies. This anisotropy reveals a new feature of the Galactic cosmic-ray distribution, which must be incorporated into theories of the origin and propagation of cosmic rays. As was emphasized e.g. in [35, 28], changes of the anisotropy patterns with energy can, in principle, be accounted for by specific distributions (in space and time) and individual source energy spectra of nearby recent SNRs. Another long-standing problem is the high level of isotropy even at energies beyond 10 18 eV. For non-relativistic diffusive acceleration g g = 2 and the index of the observed spectrum, g g + m = 2 . 7, one derives m = 0 . 7. At very high energy this results in a too large anisotropy, d ( E ) GLYPH<181> D ( E ) GLYPH<181> E m and in a too small traversed grammage, X cr ( E ) GLYPH<181> 1 / D ( E ) , with the diffusion coefficient D ( E ) , and would contradict experimental data (cf. Fig. 4). However, d ( E ) GLYPH<181> D ( E ) refers again to an average of the anisotropy amplitude computed over many source realizations, i.e. over a continuum of sources and thus does not apply to concrete realizations of nearby SNRs and turbulent magnetic fields within the cosmic ray scattering length. Moreover, as pointed out in [35], diffusion breaks down for propagation of CRs within our Galaxy at E > ∼ 10 17 eV. Recently, the Pierre Auger Observatory reported the first large scale anisotropy searches as a function of both right ascension and declination. Again, within the systematic uncertainties, no significant deviation from isotropy is revealed and the upper limits on dipole and quadrupole amplitudes challenge an origin from stationary galactic sources densely distributed in the galactic disk and emitting predominantly light particles in all directions. In Fig. 4 (right), the corresponding directions are shown in orthographic projection with the associated uncertainties, as a function of the energy. Both angles are expected to be randomly distributed in the case of independent samples whose parent distribution is isotropic. It is thus interesting to note that all reconstructed declinations are in the equatorial southern hemisphere, and to note also the intriguing smooth alignment of the phases in right ascension as a function of the energy. Directional correlations of the most energetic CRs with nearby AGN observed by the Pierre Auger Observatory provided the first signature about anisotropies of the most energetic CRs and thereby about their EG origin [9, 36, 37]. Initially very strong, the fraction of Auger events above 55 EeV correlating within 3 . 1 · with a nearby ( z ≤ 0 . 018) AGN from the VCV-catalogue has stabilized at a level of ( 33 ± 5 ) % [38]. With an accidental rate for an isotropic distribution of 21 %, this corresponds to a chance probability of less than 1 %. Recently, TA reported a correlation fraction of 44 % at an isotropic fraction of 24 % yielding a chance probability of about 2 % [39]. Thus, the data are in perfect agreement with each other yielding a combined chance probability of observing such a correlation at the 10 -3 level. However, more statistics is needed to consolidate the picture and to allow subdividing data sets in bins of related CR observables. The sky region around Cen A remains populated by a larger number of high energy events compared to the rest of the sky, with the largest departure from isotropy at 24 · around the center of Cen A with 19 events observed and 7.6 expected for isotropy, corresponding to a chance probability for this to occur at a level of 4 % [38]. The Pierre Auger Collaboration has also performed a search for ultra-high neutrons from sources located within the Galaxy [40]. Their mean path length is 9 . 2 × E kpc before decaying, where E is the energy of the neutron in EeV. A stacking analysis was performed in the direction of bright Galactic gamma-ray sources: the ones detected by Fermi-Lat instrument in the 100 MeV - 100 GeV range and the ones detected by H.E.S.S. in the range of 100 GeV - 100 TeV. Neither analysis provided evidence for significant excess and upper limits on the flux were derived for all directions within the Auger coverage. For directions along the Galactic plane for instance, the upper limits are below 0.024 km -2 yr -1 , 0.014 km -2 yr -1 and 0.026 km -2 yr -1 for energy bins of [1-2] EeV, [2-3] EeV and E ≥ 1 EeV, respectively. For energies above 1 EeV, the 95 % C.L. upper limit on the flux is 0.065 km -2 yr -1 , which corresponds to the energy flux of 0.13 EeV km -2 yr -1 = 0.4 eV cm -2 s -1 in the EeV range. Here a differential energy spectrum E -2 was assumed [40]. Those upper limits call into question the existence of persistent sources of EeV protons in the Galaxy. They also place useful constraints on the UHE emissions from the known Galactic sources of TeV gamma-rays.",
"pages": [
6,
7,
8
]
},
{
"title": "ADVANCES IN THEORY",
"content": "The observed knees may be interpreted as the end of the Galactic CR spectrum with their position defining the maximum acceleration energy. Although this picture may look very natural, the way to its adoption was not straight forward (see e.g. [28] for a recent review). Diffuse shock acceleration in SNR was discovered in the late 1970s but it took two decades more to realize that CR-streaming amplifies the magnetic fields upstream of the shock to create highly turbulent fields with strengths up to d B ∼ B ∼ 10 -4 G (see e.g. [41, 42]). The importance of non-linear magnetic fields amplification at SNR shocks, now also well accounted for by 3d MHD simulations, surely became one of the most discussed theory topics recently and there is general consensus that this is vital to reach the knee even on relatively short timescales on the order of tens to hundreds of years, i.e. much faster than it takes to reach the Sedov phase. This drives the discussion to another important theoretical CR-problem. It is challenging to allow CRs to escape from SNR into the interstellar medium in large numbers without significant energy losses. This issue was first addressed by Ptuskin and co-workers [43] where it was shown that only particles accelerated up to the maximum energy E max can escape the acceleration region. In their original model, E max reaches its highest value only at the beginning of the Sedov phase. The E -2 CR energy spectrum in this model is then given by integrating the narrow peak of E max ( t ) over time. The diffusion of Galactic CRs close to their sources has been addressed recently by Kachelrieß and coworkers (see also [35]). Propagating individual CRs in purely isotropic turbulent magnetic fields with maximal scale of spatial variations l max , they find anisotropic CR diffusion at distances r < l max from their sources. As a result, the CR densities around the sources become strongly irregular and show filamentary structures that could be probed by TeV g -rays. At the highest energies, Radio Galaxies (RG) remain being the most promising candidates for UHECR acceleration. An interesting argument linking UHECR sources to their luminosity at radio frequencies has been put forward in this context by Hardcastle [44] and he concludes that RGs can accelerate protons to the highest observed energies in the lobes if a substantial amount of energy is in the turbulent component of the magnetic field, i.e. B > ∼ B equipart , and the Hillas criterion is met. In Cen A, existing observations do in fact constrain B > ∼ B equipart for the kpc-scale jet. Moreover, if UHECRs are predominantly protons, then very few sources should contribute to the observed flux. These sources should be easy to identify in the radio and their UHECR spectrum should cut off steeply at the observed highest energies. In contrast, if the mass composition is heavy at the highest energies then many radio galaxies could contribute to the UHECR flux but due to the much stronger deflection only the nearby Radio Galaxy Cen A may be identifiable [44]. Of course, such a conclusion depends very much on the strength of the EG magnetic fields and the maximum energy reached in the sources.",
"pages": [
8,
9
]
},
{
"title": "NEWPROJECTS AND OUTLOOK",
"content": "Motivated by the large body of important experimental findings and new insights, the field continues to evolve very dynamically with new projects being planned or existing ones to be upgraded. In the study of low energy CRs, AMS is the by far most complex instrument in orbit, launched on May 16, 2011. It will measure light CR isotopes from about 500 MeV to 10 GeV and is hoped to improve our understanding of CR propagation in Galaxy. First data about the positron/electron ratio have been released recently [45] and confirm findings of PAMELA. The CALET (CALorimeteric Electron Telescope) project is a Japanese led international mission being developed as part of the utilization plan for the International Space Station (ISS) and aims at studying details of particle propagation in the Galaxy by a combination of energy spectrum measurements of electrons, protons and higher-charged nuclei. In Siberia, the German-Russian project HiScore is planned to be constructed at the Tunka site. This project will use open Cherenkov counters for CR measurements around the knee and will be complemented by radio antennas to explore this new detection technology. HAWK is being constructed in Mexico. Although its prime goal is the study of the g -ray sky above 100 GeV, it will also contribute to measuring CR anisotropies at TeV-energies. LHAASO , mostly driven by the Chinese community and much larger and more complex than HAWK, serves the same scientific goals. At the highest energies, Auger and TA plan upgrades in performance and size, respectively: Auger aims at improving the mass composition measurement and particle physics capabilities at the highest energies to answer the question about the origin of the flux suppression and TA aims at increasing their surface detector with a 2 km grid up to 2800 km 2 . Both collaborations have started to join efforts for a Next Generation Ground-based CR Observatory NGGO , much larger than existing experiments and aiming at good energy and mass resolution and exploring particle physics aspects at the highest energies. Four proposed and planned space missions constitute the roadmap of the space oriented community: TUS, JEM-EUSO, KLPVE, and Super-EUSO aim at contributing step-by-step to establish this challenging field of research. They will reach very large exposures aimed at seeing CR sources, which will be at the expense of energy resolution, composition measurements and particle physics capabilities. Given the resources of funding available in the next decade or two, it is unlikely that all of the above mentioned projects can be realized. Thus, priority should be given to complementarity rather than on duplication.",
"pages": [
9,
10
]
},
{
"title": "ACKNOWLEDGMENTS",
"content": "Its a pleasure to thank the organizers of the Texas Symposium 2012 for inviting me to participate in this vibrant conference. I am also grateful for many stimulating discussions with colleagues from KASCADE-Grande, Auger and TA. Financial support by the German Ministry of Research and Education (Grants 05A11PX1 and 05A11PXA) and by the Helmholtz Alliance for Astroparticle Physics (HAP) is gratefully acknowledged.",
"pages": [
10
]
}
]
2013CEAB...37..261D
https://arxiv.org/pdf/1305.2223.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_74><loc_80><loc_77></location>BG GEM - A POORLY-STUDIED BINARY WITH A POSSIBLE BLACK HOLE COMPONENT</section_header_level_1>
<text><location><page_1><loc_16><loc_61><loc_78><loc_71></location>N. A. Drake 1 , 2 , A. S. Miroshnichenko 3 , S. Danford 3 , and C. B. Pereira 1 Observatório Nacional/MCTI, Rio de Janeiro, Brazil 2 Sobolev Astronomical Institute, Saint-Petersburg State University, Saint-Petersburg, Russia 3 University of North Carolina at Greensboro, Department of Physics and Astronomy, Greensboro, NC, USA</text>
<text><location><page_1><loc_78><loc_70><loc_78><loc_71></location>1</text>
<text><location><page_1><loc_12><loc_43><loc_83><loc_58></location>Abstract. BG Gem is an eclipsing binary with a 91.6-day orbital period. The more massive primary component does not seem to show absorption lines in the spectrum, while the less massive secondary is thought to be a K-type star, possibly a supergiant. These results were obtained with optical low-resolution spectroscopy and photometry. The primary was suggested to be a black hole, although with a low confidence. We present a high-resolution optical spectrum of the system along with new BVR -photometry. Analysis of the spectrum shows that the K-type star rotates rapidly at v sin i = 18 kms -1 compared to most evolved stars of this temperature range. We also discuss constraints on the secondary's luminosity using spectroscopic criteria and on the entire system parameters using both the spectrum and photometry.</text>
<text><location><page_1><loc_12><loc_38><loc_83><loc_41></location>Key words: Emission-line stars - circumstellar matter - binary systems - stars: fundamental parameters</text>
<section_header_level_1><location><page_1><loc_38><loc_33><loc_56><loc_35></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_12><loc_83><loc_31></location>BG Gem is a 13-mag stellar object that shows brightness variations with a period of 91.645 days and an amplitude of ∼ 0.5 mag at visible wavelengths (Benson et al. 2000). The primary eclipse is only observed at λ ≤ 4400Å, while the light curves are shallower at longer wavelengths. From low-resolution ( ∼ 6 Å) observations of the system, Kenyon, Groot, & Benson (2002) deduced that the optical spectrum is dominated by absorption lines from a K0 i secondary component. They suggested that line emission which occurs in the Balmer and some He i lines may originate from a Btype or a black hole primary component. From the radial velocity curve, they determined a components mass ratio of 0.22 ± 0.07.</text>
<text><location><page_1><loc_15><loc_10><loc_83><loc_12></location>Elebert et al. (2007) took a high-resolution optical spectrum, retrieved</text>
<text><location><page_2><loc_17><loc_67><loc_88><loc_82></location>an archival UV spectrum obtained with HST, and found an upper limit for the X-ray flux from INTEGRAL. They detected a weak UV continuum (more indicative of a black hole than of a normal star), but a low X-ray luminosity ( ≤ 10 35 erg s -1 ) and a low rotational velocity of the disk material (500 kms -1 in the Balmer lines and ≤ 1000 kms -1 in the UV emission lines). Therefore, these findings are inconclusive. However, if BG Gem does have a black hole component, it becomes the longest-period system of this kind in the Milky Way.</text>
<text><location><page_2><loc_17><loc_61><loc_88><loc_66></location>Open questions in studies of this system include the poorly known fundamental parameters of the cool secondary companion, the unknown nature of the primary component, and the evolutionary status of the entire system.</text>
<section_header_level_1><location><page_2><loc_44><loc_57><loc_62><loc_58></location>2. Observations</section_header_level_1>
<text><location><page_2><loc_17><loc_50><loc_88><loc_55></location>In order to refine the secondary component parameters as well as those of the entire system and check the light curve, we took new spectroscopic and photometric observations of the BG Gem system.</text>
<figure>
<location><page_2><loc_32><loc_20><loc_73><loc_48></location>
<caption>Figure 1 : Balmer line profiles in our spectrum of BG Gem. The intensity is normalized to the nearby continuum and plotted against the heliocentric radial velocity.</caption>
</figure>
<text><location><page_2><loc_21><loc_10><loc_89><loc_12></location>The photometric data were obtained in the V RHα filters during 11 nights</text>
<text><location><page_3><loc_12><loc_80><loc_83><loc_82></location>in 2005-2006 at the 0.81-m telescope of the Three College Observatory near</text>
<text><location><page_3><loc_12><loc_63><loc_83><loc_80></location>Greensboro, North Carolina, USA. The main goal of these observations was to look for changes of the light curves compared to the published data. Our data show the same brightness level at covered phases, but they are insufficient to detect any possible change of the orbital period. A high-resolution échelle spectrum ( λλ 4800-10500 Å, R = 60000) was obtained at the 2.7-m Harlan J. Smith telescope of the McDonald Observatory in December 2006. The spectrum was taken at an orbital phase of 0.62 (from the primary minimum). It has a signal-to-noise ratio of ∼ 30 in continuum near λ 4800 Å that rises towards longer wavelengths reaching ∼ 100</text>
<text><location><page_3><loc_12><loc_61><loc_74><loc_63></location>near λ 1 µ m. Parts of the spectrum are shown in Figures 1 and 2.</text>
<figure>
<location><page_3><loc_20><loc_33><loc_74><loc_59></location>
<caption>Figure 2 : Comparison of our spectrum of BG Gem (upper line) and that of a K1 iii star HD 19745 obtained with the same resolution. The spectral lines of HD 19745 were broadened to a rotational velocity of 18 km s -1 to match the line widths of BG Gem. The spectrum of BG Gem resembles the spectrum of HD 19745 except for the Li i line at λ 6707 . 8 Å which is absent in the spectrum of BG Gem.</caption>
</figure>
<section_header_level_1><location><page_3><loc_32><loc_16><loc_63><loc_17></location>3. Atmospheric parameters</section_header_level_1>
<text><location><page_3><loc_12><loc_10><loc_83><loc_14></location>Significant rotational broadening of the lines in the spectrum of BG Gem, an insufficient S/N ratio, and veiling of the spectrum caused by the primary's</text>
<figure>
<location><page_4><loc_20><loc_62><loc_50><loc_81></location>
</figure>
<figure>
<location><page_4><loc_57><loc_62><loc_87><loc_81></location>
<caption>Figure 3 : Comparison of the observed BG Gem spectrum (dotted line) with synthetic spectra calculated for T eff = 4500 K and log g = 0.8, 1.6, and 2.4 (from bottom to top).</caption>
</figure>
<text><location><page_4><loc_17><loc_46><loc_88><loc_52></location>accretion disk emission make it difficult to measure equivalent widths of individual Fe i and Fe ii lines and perform the usual analysis based on excitation and ionization equilibrium.</text>
<text><location><page_4><loc_17><loc_38><loc_88><loc_46></location>To derive the atmospheric parameters of BG Gem, we compared its spectrum with those of various K-type giant and supergiant stars with well-known parameters. We broadened lines in these spectra to the rotation velocity of BG Gem.</text>
<text><location><page_4><loc_17><loc_26><loc_88><loc_38></location>Projected rotation velocity of BG Gem was determined by means of fitting the observed spectrum with synthetic spectra, calculated with different values of rotation velocity. Taking into account the FWHM of the instrumental profile of the spectrograph and adopting a macroturbulent velocity of 2 km s -1 , we determined a rotation velocity of v sin i = 18 . 0 ± 1 . 0 kms -1 for BG Gem.</text>
<text><location><page_4><loc_17><loc_16><loc_88><loc_26></location>Using these parameters, we calculated a grid of synthetic spectra in a wide range of effective temperatures and surface gravities ( T eff / log g ) in the spectral region 6080 -6180 Å containing lines of neutral elements with different excitation potentials and two lines of Fe ii (at λ 6084 . 1 Å and λ 6149 . 2 Å) which are sensitive to surface gravity.</text>
<text><location><page_4><loc_17><loc_10><loc_88><loc_16></location>Synthetic spectra were calculated using the local thermodynamic equilibrium (LTE) model atmospheres of Kurucz (1993) and the current version (August 2010) of the spectral analysis code moog (Sneden 1973). The solar</text>
<text><location><page_5><loc_12><loc_70><loc_83><loc_82></location>abundances taken from Anders & Grevesse (1989) were adopted except the carbon and nitrogen abundances, which are known to be modified in giant stars (see, e.g., Lambert & Ries 1981). The VALD atomic data base (Kupka et al. 1999) was used to create the line list. A microturbulent velocity of 2.0 km s -1 was adopted in our synthetic spectra calculations. An additional flux of 30% in continuum ( F disk /F cont ) was added to the synthetic spectra.</text>
<text><location><page_5><loc_12><loc_63><loc_83><loc_70></location>As an example, in Fig. 3 we show a comparison of the observed and synthetic spectra calculated with T eff = 4500 K and different values of log g (from 0.8 to 2.4) in two spectral regions containing Fe ii lines at λ 6084 . 1 Å and λ 6149 . 2 Å used to estimate the surface gravity.</text>
<text><location><page_5><loc_12><loc_47><loc_83><loc_63></location>Among high-rotating K giants with infrared excesses, nearly half have a high Li abundance (Drake et al. 2002). Such an abundance was found by González Hernández et al. (2004) for the secondary component in the black hole binary A0620-00 and by Sabbi et al. (2003) in the companion star to the millisecond pulsar J1740-5340 in NGC 6397 suggesting some Li production in these systems. We calculated synthetic spectra in the region of the Li i 6708 Å resonance line and found a low Li abundance in BG Gem, log ε (Li) ≤ 0 . 2 (in the notation log ε (X) = log( N X /N H ) + 12 . 0) .</text>
<section_header_level_1><location><page_5><loc_41><loc_43><loc_53><loc_44></location>4. Results</section_header_level_1>
<text><location><page_5><loc_12><loc_20><loc_83><loc_41></location>Analysis of the absorption line spectrum shows that the secondary component is a K2 ii / iii star with a projected rotational velocity of 18 ± 1 kms -1 , an effective temperature of 4500 ± 300 K, and a surface gravity log g = 1.5 ± 0.5. The derived surface gravity implies a mass of the secondary component of 1 M /circledot , if it is filling its Roche lobe. Diffuse interstellar bands are weak implying a noticeable contribution of the primary's disk to the near-IR excess. Assuming an interstellar extinction of A V = 1.5 mag and M V = -0 . 8 mag for the K2-giant, the system is located at a distance of at least 3.5 kpc (no disk contribution at its eclipse by the secondary). No features that could be a result of an explosion in the system due to formation of the black hole are seen in the WISE data between λ 3.4 and λ 11.5 µ m.</text>
<section_header_level_1><location><page_5><loc_38><loc_16><loc_56><loc_17></location>5. Conclusions</section_header_level_1>
<text><location><page_5><loc_12><loc_10><loc_83><loc_14></location>We refined the fundamental parameters of the visible star in the BG Gem binary system and showed that it is a rapidly rotating K2 ii / iii star rather</text>
<text><location><page_6><loc_17><loc_80><loc_88><loc_82></location>than a K0 i star suggested by Benson et al. (2000) and Kenyon et al. (2002).</text>
<text><location><page_6><loc_17><loc_72><loc_88><loc_80></location>It is still unclear whether a black hole is present in the system. The fact that we detect no light from a hot star implies that the primary's disk completely veils it. Spectroscopic observations at both eclipses are needed to put further constraints on the system properties.</text>
<section_header_level_1><location><page_6><loc_42><loc_68><loc_63><loc_70></location>Acknowledgements</section_header_level_1>
<text><location><page_6><loc_17><loc_49><loc_88><loc_67></location>A.M. acknowledges support from the American Astronomical Society International Travel Grant program and from the Department of Physics and Astronomy of the University of North Carolina at Greensboro. N.A.D. acknowledges support of a PCI/MCTI (Brazil) grant under the Project 311.868/2011-8. This paper is party based on observations obtained at the McDonald Observatory of the University of Texas at Austin. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, as well of the Wide-Field Infrared Survey Explorer ( WISE ) database.</text>
<section_header_level_1><location><page_6><loc_47><loc_45><loc_59><loc_47></location>References</section_header_level_1>
<text><location><page_6><loc_19><loc_42><loc_85><loc_44></location>Anders, E., and Grevesse, N.: 1989, Geochim. et Cosmochim. Acta , 53 , 197.</text>
<text><location><page_6><loc_19><loc_38><loc_88><loc_41></location>Benson, P., Dullighan, A., Bonanos, A., McLeod, K.K., and Kenyon, S.J.: 2000, Astron. J. 119 , 890.</text>
<text><location><page_6><loc_19><loc_35><loc_88><loc_38></location>Drake, N.A., de la Reza, R., da Silva, L., and Lambert, D. L.: 2002, Astron. J. 123 , 2703.</text>
<text><location><page_6><loc_19><loc_31><loc_88><loc_34></location>Elebert, P., Callanan, P.J., Russel, L., and Shaw, S.E.: 2007, Proc. IAU Symp. 238 , 361.</text>
<text><location><page_6><loc_19><loc_27><loc_88><loc_30></location>González Hernández, Rebolo, R., Israelian, G., and Casares, J.: 2004, Astrophys. J., 609 , 998.</text>
<text><location><page_6><loc_19><loc_25><loc_80><loc_27></location>Kenyon, S.J., Groot, P.J., and Benson, P.: 2002, Astron. J. 124 , 1054.</text>
<text><location><page_6><loc_19><loc_22><loc_88><loc_25></location>Kupka, F., Piskunov, N., Ryabchikova, T.A., Stempels, H. C., and Weiss, W.W.: 1999, Astron. Astrophys., Suppl. Ser. 138 , 119.</text>
<text><location><page_6><loc_19><loc_18><loc_87><loc_21></location>Kurucz, R.L.: 1993, CD-ROM No. 13, Smithsonian Astrophysical Observatory . Lambert, D.L., and Ries, L.M.: 1981, Astrophys. J. 248 , 228.</text>
<text><location><page_6><loc_19><loc_14><loc_88><loc_17></location>Sabbi, E., Gratton, R.G., Bragaglia, A., Ferraro, F.R., Possenti, A., Camilo, F., and D'Amico, N. : 2003, Astron. Astrophys. 412 , 829.</text>
<text><location><page_6><loc_19><loc_12><loc_60><loc_13></location>Sneden, C.: 1973, Ph.D. Thesis, Univ. of Texas.</text>
</document>
[
{
"title": "BG GEM - A POORLY-STUDIED BINARY WITH A POSSIBLE BLACK HOLE COMPONENT",
"content": "N. A. Drake 1 , 2 , A. S. Miroshnichenko 3 , S. Danford 3 , and C. B. Pereira 1 Observatório Nacional/MCTI, Rio de Janeiro, Brazil 2 Sobolev Astronomical Institute, Saint-Petersburg State University, Saint-Petersburg, Russia 3 University of North Carolina at Greensboro, Department of Physics and Astronomy, Greensboro, NC, USA 1 Abstract. BG Gem is an eclipsing binary with a 91.6-day orbital period. The more massive primary component does not seem to show absorption lines in the spectrum, while the less massive secondary is thought to be a K-type star, possibly a supergiant. These results were obtained with optical low-resolution spectroscopy and photometry. The primary was suggested to be a black hole, although with a low confidence. We present a high-resolution optical spectrum of the system along with new BVR -photometry. Analysis of the spectrum shows that the K-type star rotates rapidly at v sin i = 18 kms -1 compared to most evolved stars of this temperature range. We also discuss constraints on the secondary's luminosity using spectroscopic criteria and on the entire system parameters using both the spectrum and photometry. Key words: Emission-line stars - circumstellar matter - binary systems - stars: fundamental parameters",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "BG Gem is a 13-mag stellar object that shows brightness variations with a period of 91.645 days and an amplitude of ∼ 0.5 mag at visible wavelengths (Benson et al. 2000). The primary eclipse is only observed at λ ≤ 4400Å, while the light curves are shallower at longer wavelengths. From low-resolution ( ∼ 6 Å) observations of the system, Kenyon, Groot, & Benson (2002) deduced that the optical spectrum is dominated by absorption lines from a K0 i secondary component. They suggested that line emission which occurs in the Balmer and some He i lines may originate from a Btype or a black hole primary component. From the radial velocity curve, they determined a components mass ratio of 0.22 ± 0.07. Elebert et al. (2007) took a high-resolution optical spectrum, retrieved an archival UV spectrum obtained with HST, and found an upper limit for the X-ray flux from INTEGRAL. They detected a weak UV continuum (more indicative of a black hole than of a normal star), but a low X-ray luminosity ( ≤ 10 35 erg s -1 ) and a low rotational velocity of the disk material (500 kms -1 in the Balmer lines and ≤ 1000 kms -1 in the UV emission lines). Therefore, these findings are inconclusive. However, if BG Gem does have a black hole component, it becomes the longest-period system of this kind in the Milky Way. Open questions in studies of this system include the poorly known fundamental parameters of the cool secondary companion, the unknown nature of the primary component, and the evolutionary status of the entire system.",
"pages": [
1,
2
]
},
{
"title": "2. Observations",
"content": "In order to refine the secondary component parameters as well as those of the entire system and check the light curve, we took new spectroscopic and photometric observations of the BG Gem system. The photometric data were obtained in the V RHα filters during 11 nights in 2005-2006 at the 0.81-m telescope of the Three College Observatory near Greensboro, North Carolina, USA. The main goal of these observations was to look for changes of the light curves compared to the published data. Our data show the same brightness level at covered phases, but they are insufficient to detect any possible change of the orbital period. A high-resolution échelle spectrum ( λλ 4800-10500 Å, R = 60000) was obtained at the 2.7-m Harlan J. Smith telescope of the McDonald Observatory in December 2006. The spectrum was taken at an orbital phase of 0.62 (from the primary minimum). It has a signal-to-noise ratio of ∼ 30 in continuum near λ 4800 Å that rises towards longer wavelengths reaching ∼ 100 near λ 1 µ m. Parts of the spectrum are shown in Figures 1 and 2.",
"pages": [
2,
3
]
},
{
"title": "3. Atmospheric parameters",
"content": "Significant rotational broadening of the lines in the spectrum of BG Gem, an insufficient S/N ratio, and veiling of the spectrum caused by the primary's accretion disk emission make it difficult to measure equivalent widths of individual Fe i and Fe ii lines and perform the usual analysis based on excitation and ionization equilibrium. To derive the atmospheric parameters of BG Gem, we compared its spectrum with those of various K-type giant and supergiant stars with well-known parameters. We broadened lines in these spectra to the rotation velocity of BG Gem. Projected rotation velocity of BG Gem was determined by means of fitting the observed spectrum with synthetic spectra, calculated with different values of rotation velocity. Taking into account the FWHM of the instrumental profile of the spectrograph and adopting a macroturbulent velocity of 2 km s -1 , we determined a rotation velocity of v sin i = 18 . 0 ± 1 . 0 kms -1 for BG Gem. Using these parameters, we calculated a grid of synthetic spectra in a wide range of effective temperatures and surface gravities ( T eff / log g ) in the spectral region 6080 -6180 Å containing lines of neutral elements with different excitation potentials and two lines of Fe ii (at λ 6084 . 1 Å and λ 6149 . 2 Å) which are sensitive to surface gravity. Synthetic spectra were calculated using the local thermodynamic equilibrium (LTE) model atmospheres of Kurucz (1993) and the current version (August 2010) of the spectral analysis code moog (Sneden 1973). The solar abundances taken from Anders & Grevesse (1989) were adopted except the carbon and nitrogen abundances, which are known to be modified in giant stars (see, e.g., Lambert & Ries 1981). The VALD atomic data base (Kupka et al. 1999) was used to create the line list. A microturbulent velocity of 2.0 km s -1 was adopted in our synthetic spectra calculations. An additional flux of 30% in continuum ( F disk /F cont ) was added to the synthetic spectra. As an example, in Fig. 3 we show a comparison of the observed and synthetic spectra calculated with T eff = 4500 K and different values of log g (from 0.8 to 2.4) in two spectral regions containing Fe ii lines at λ 6084 . 1 Å and λ 6149 . 2 Å used to estimate the surface gravity. Among high-rotating K giants with infrared excesses, nearly half have a high Li abundance (Drake et al. 2002). Such an abundance was found by González Hernández et al. (2004) for the secondary component in the black hole binary A0620-00 and by Sabbi et al. (2003) in the companion star to the millisecond pulsar J1740-5340 in NGC 6397 suggesting some Li production in these systems. We calculated synthetic spectra in the region of the Li i 6708 Å resonance line and found a low Li abundance in BG Gem, log ε (Li) ≤ 0 . 2 (in the notation log ε (X) = log( N X /N H ) + 12 . 0) .",
"pages": [
3,
4,
5
]
},
{
"title": "4. Results",
"content": "Analysis of the absorption line spectrum shows that the secondary component is a K2 ii / iii star with a projected rotational velocity of 18 ± 1 kms -1 , an effective temperature of 4500 ± 300 K, and a surface gravity log g = 1.5 ± 0.5. The derived surface gravity implies a mass of the secondary component of 1 M /circledot , if it is filling its Roche lobe. Diffuse interstellar bands are weak implying a noticeable contribution of the primary's disk to the near-IR excess. Assuming an interstellar extinction of A V = 1.5 mag and M V = -0 . 8 mag for the K2-giant, the system is located at a distance of at least 3.5 kpc (no disk contribution at its eclipse by the secondary). No features that could be a result of an explosion in the system due to formation of the black hole are seen in the WISE data between λ 3.4 and λ 11.5 µ m.",
"pages": [
5
]
},
{
"title": "5. Conclusions",
"content": "We refined the fundamental parameters of the visible star in the BG Gem binary system and showed that it is a rapidly rotating K2 ii / iii star rather than a K0 i star suggested by Benson et al. (2000) and Kenyon et al. (2002). It is still unclear whether a black hole is present in the system. The fact that we detect no light from a hot star implies that the primary's disk completely veils it. Spectroscopic observations at both eclipses are needed to put further constraints on the system properties.",
"pages": [
5,
6
]
},
{
"title": "Acknowledgements",
"content": "A.M. acknowledges support from the American Astronomical Society International Travel Grant program and from the Department of Physics and Astronomy of the University of North Carolina at Greensboro. N.A.D. acknowledges support of a PCI/MCTI (Brazil) grant under the Project 311.868/2011-8. This paper is party based on observations obtained at the McDonald Observatory of the University of Texas at Austin. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, as well of the Wide-Field Infrared Survey Explorer ( WISE ) database.",
"pages": [
6
]
},
{
"title": "References",
"content": "Anders, E., and Grevesse, N.: 1989, Geochim. et Cosmochim. Acta , 53 , 197. Benson, P., Dullighan, A., Bonanos, A., McLeod, K.K., and Kenyon, S.J.: 2000, Astron. J. 119 , 890. Drake, N.A., de la Reza, R., da Silva, L., and Lambert, D. L.: 2002, Astron. J. 123 , 2703. Elebert, P., Callanan, P.J., Russel, L., and Shaw, S.E.: 2007, Proc. IAU Symp. 238 , 361. González Hernández, Rebolo, R., Israelian, G., and Casares, J.: 2004, Astrophys. J., 609 , 998. Kenyon, S.J., Groot, P.J., and Benson, P.: 2002, Astron. J. 124 , 1054. Kupka, F., Piskunov, N., Ryabchikova, T.A., Stempels, H. C., and Weiss, W.W.: 1999, Astron. Astrophys., Suppl. Ser. 138 , 119. Kurucz, R.L.: 1993, CD-ROM No. 13, Smithsonian Astrophysical Observatory . Lambert, D.L., and Ries, L.M.: 1981, Astrophys. J. 248 , 228. Sabbi, E., Gratton, R.G., Bragaglia, A., Ferraro, F.R., Possenti, A., Camilo, F., and D'Amico, N. : 2003, Astron. Astrophys. 412 , 829. Sneden, C.: 1973, Ph.D. Thesis, Univ. of Texas.",
"pages": [
6
]
}
]
2013CEAB...37..541M
https://arxiv.org/pdf/1402.6442.pdf
<document>
<section_header_level_1><location><page_1><loc_17><loc_74><loc_77><loc_77></location>RADIO SIGNATURES OF SOLAR ENERGETIC PARTICLES DURING THE 23 RD SOLAR CYCLE</section_header_level_1>
<text><location><page_1><loc_19><loc_68><loc_75><loc_71></location>R. MITEVA 1 , K.-L. KLEIN 1 , S. W. SAMWEL 2 , A. NINDOS 3 , A. KOULOUMVAKOS 3 , 4 and H. REID 1 , 5</text>
<unordered_list>
<list_item><location><page_1><loc_13><loc_50><loc_81><loc_65></location>1 LESIA-Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon, CNRS, UPMC, Univ. Paris-Diderot, France 2 National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo, Egypt 3 Section of Astrogeophysics, Physics Department, University of Ioannina, Ioannina GR-45110, Greece 4 Department of Astrophysics, Astronomy and Mechanics, Faculty of Physics, University of Athens, Athens, Greece SUPA School of Physics and Astronomy, University of Glasgow,</list_item>
<list_item><location><page_1><loc_18><loc_48><loc_57><loc_51></location>5 Glasgow G12 8QQ, UK</list_item>
</unordered_list>
<text><location><page_1><loc_12><loc_27><loc_83><loc_46></location>Abstract. We present the association rates between solar energetic particles (SEPs) and the radio emission signatures in the corona and IP space during the entire solar cycle 23. We selected SEPs associated with X and M-class flares from the visible solar hemisphere. All SEP events are also accompanied by coronal mass ejections. Here, we focus on the correlation between the SEP events and the appearance of radio type II, III and IV bursts on dynamic spectra. For this we used the available radio data from ground-based stations and the Wind/WAVES spacecraft. The associations are presented separately for SEP events accompanying activity in the eastern and western solar hemisphere. We find the highest association rate of SEP events to be with type III bursts, followed by types II and IV. Whereas for types III and IV no longitudinal dependence is noticed, these is a tendency for a higher SEP-association rate with type II bursts in the eastern hemisphere. A comparison with reports from previous studies is briefly discussed.</text>
<text><location><page_1><loc_12><loc_24><loc_66><loc_26></location>Key words: Solar energetic particles - radio bursts - solar cycle 23</text>
<section_header_level_1><location><page_1><loc_38><loc_20><loc_56><loc_21></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_10><loc_83><loc_18></location>Solar energetic particle (SEP) events are transient flux enhancements of electrons, protons and ions due to acceleration processes in the solar corona and interplanetary (IP) space. The high energy particles can pose a serious risk for the near Earth and ground-based technological devices, may dis-</text>
<section_header_level_1><location><page_2><loc_46><loc_85><loc_60><loc_86></location>MITEVA ET AL.</section_header_level_1>
<text><location><page_2><loc_17><loc_51><loc_88><loc_82></location>turb communications and be a health hazard (Mewaldt, 2006). This is why energetic particles are of major space weather interest. The accelerator of these particles, however, is still a subject of debate. Presently, the reconnection processes during flares (Cane et al. , 2002) and the shock-acceleration at coronal mass ejections (CMEs), Reames (1999), are recognized as efficient particle accelerators. An important issue is whether both acceleration processes act simultaneously with comparable efficiency or one of them dominates the particle energization process. In the current two-class SEP picture, the flares are thought to dominate the impulsive events and the shock waves dominate the large gradual events. Observations, however, are not able to relate unambiguously the SEP parameters measured in situ to the parent solar activity (e.g., flares vs. shocks). The large uncertainties usually present when doing different correlation analyses may arise due to the poorly known particle transport in the turbulent IP magnetic field, the magnetic connection between the acceleration site and the Earth, and that SEPs are often just measured at a single point in space.</text>
<text><location><page_2><loc_17><loc_18><loc_88><loc_51></location>Radio observations can provide additional information and constraints for identifying the particle accelerator in the corona and IP space. When nonthermal electrons propagate through the solar corona they may emit radio waves, if certain conditions apply (Nindos et al. , 2008). The different types of radio bursts in the dynamic radio spectrum (see e.g., a review by Pick and Vilmer (2008)), are usually interpreted as signatures from electrons accelerated in the vicinity of a shock wave (type IIs), as electron beams (type IIIs) or as electrons confined in closed loop structure during the early evolution of a CME (type IVs). Type III bursts usually extend to low frequencies (reaching as far as the Earth orbit, ∼ 20 kHz) which is the main indicator that accelerated electrons (and by inference also protons) can efficiently escape from the solar corona (Cane et al. , 2002). Interplanetary counterparts of type II are also observed, but to lesser extent, whereas type IVs can be seen only to few MHz, but not to lower frequencies. Here we focus on the comparison of the particle (mainly proton) intensities measured in situ with the electromagnetic emission of electrons in the corona and IP space over the entire solar cycle 23.</text>
<text><location><page_2><loc_17><loc_10><loc_89><loc_18></location>Numerous previous studies reported different association rates of SEPs and emission of radio bursts of type II (Cliver et al. , 2004; Gopalswamy et al. , 2008), III (Cane et al. , 2002) and IV (Kahler, 1982). The aim here is to identify the different types of radio emission from the dynamic spectra, to</text>
<text><location><page_3><loc_12><loc_78><loc_83><loc_82></location>complement our results with reports from the different radio observatories and to compare them with previous works on the topic.</text>
<section_header_level_1><location><page_3><loc_38><loc_74><loc_56><loc_75></location>2. Particle data</section_header_level_1>
<text><location><page_3><loc_12><loc_53><loc_83><loc_72></location>In the present work we selected all proton events with energy above 25 MeV as identified by Cane et al. (2010) that are associated with both strong flares (X and M-class) at eastern and western heliolongitudes and CMEs. Here we will differentiate the SEP events into eastern/western only and not by other SEP classifications schemes (Reames, 1999; Cliver, 2009), since any classification may leave out many 'mixed' cases in abundances, charge states, associated phenomena, etc. However, in order to facilitate comparison with previous work, we note if the SEP event was described as 'gradual' or 'impulsive' in Reames and Ng (2004) and Cliver and Ling (2009) by the superscripts 'g' and 'i', respectively.</text>
<text><location><page_3><loc_12><loc_36><loc_83><loc_53></location>In order to improve the statistics for the radio analysis (see next Section) we included SEP events that have high background level due to a previous event 1 , that are observed during SOHO data gap, those for which no value for the peak intensity was given due to instrument saturation (with superscript 's') and those with parent activity at the limb (with superscript 'l' we denote events at the solar limb and with 'c', events close to the disc center, between ± 10 degrees in heliolongitude). That lead finally to 175 particle events during solar cycle 23, of which 49 had sources in the eastern hemisphere, 124 in the western and two had uncertain source locations.</text>
<section_header_level_1><location><page_3><loc_31><loc_32><loc_63><loc_33></location>3. Radio spectrograph data</section_header_level_1>
<text><location><page_3><loc_12><loc_15><loc_83><loc_30></location>The radio emission observed on ground and in space is usually presented in a frequency vs. time plot, where the strength of the radio emission is color-coded. This is known as a dynamic radio spectrum. Several features were recognized on such spectrum plots, e.g., fast drifting emission stripes extending from high to low frequencies (type IIIs); slowly drifting lanes of emission (type IIs) and a broad band stationary or/and drifting emission of type IV. Each of these radio emission types is a result of a unstable electron population (produced by a different process) generating Langmuir</text>
<table>
<location><page_4><loc_20><loc_65><loc_86><loc_78></location>
<caption>Table I : List of radio data sources</caption>
</table>
<text><location><page_4><loc_17><loc_35><loc_88><loc_60></location>waves that convert into electromagnetic radiation via wave-wave processes. Namely, type IIs are usually assumed to be the shock signatures in the corona/IP space (Nelson and Melrose, 1985), type IIIs are electron beams propagating through the corona (Suzuki and Dulk, 1985), and the type IVs are the signatures from trapped electrons in coronal loops (Stewart, 1985; Pick, 1986). Here, we will use this standard interpretation for the radio burst emission in order to identify the probable particle accelerator. As a preparatory work for the analysis we collected all available radio spectral data (summarized in Table I) and the associated GOES soft X-ray (SXR) emission for each SEP event. The results of the associated radio bursts to each particle event are summarized in Tables II and III. There, we start with the SEP event date followed by the onset (in UT) of the SXR emission associated with each event as provided by GOES satellite (1 -8 Å channel).</text>
<text><location><page_4><loc_17><loc_20><loc_88><loc_35></location>The so-identified radio emissions of type II, III and IV are organized in several frequency (wavelength) ranges in Tables II and III. Namely, the decimeter (dm) range is subdivided into high (0.8 -3 GHz) and lower (0.3 -0.8 GHz) frequency parts. Similarly, we divided the metric (m) range into 100 -300 and 30 -100 MHz subbands. The IP space (dekameter/hectometer, DH, and kilometer wavelengths) is represented by one column. The radio bursts were ordered by their type and not by their temporal appearance on the radio spectral plot.</text>
<text><location><page_4><loc_17><loc_10><loc_88><loc_20></location>Since we primarily used quicklook radio spectral data where image quality may be low, we also collected all available radio observatory reports for each event. In case radio emission of a given type was reported but could not be identified by us (due to low resolution of the actual image or because no radio spectrum plot was found), we give the result in squared brackets</text>
<text><location><page_5><loc_12><loc_63><loc_83><loc_82></location>in Tables II and III. Any uncertain radio burst identification is indicated by a question mark following the roman number of the corresponding radio burst type. Weak emission signatures are denoted with superscript 'w', delayed emission with 'd' and low (high)-frequency emission onset with 'LFo' ('HFo'). Unclassified emission is given with 'UNCLF', fine structures with 'FS' and fundamental-harmonic emission with 'FH'. Continuum ('CONT') and decimeter ('DCIM') emission in the 0.3 -3 GHz range is considered as type IV-like emission in the analysis. The complete particle event list together with the associated radio bursts is given in Tables II and III (for western and eastern events, respectively).</text>
<section_header_level_1><location><page_5><loc_41><loc_58><loc_53><loc_60></location>4. Results</section_header_level_1>
<text><location><page_5><loc_12><loc_20><loc_83><loc_56></location>The results are given as normalized number of the SEP events vs. radio frequency for each wavelength range (dm, m and DH), see the histograms on Figure 1, for eastern (on the left) and western (right) SEP events. The numerical value of the association rates, graphically presented on the histograms, is given by the height of each color bar. The SEP events associated with specific burst types as identified on the radio spectral plots are given with black color. With dark gray is shown the association in cases where the burst type was only given in the observatory reports (no spectra found at present) or where its identification is questionable. Whenever we give a value for an association rate, we will always sum up these two sections. Finally, with light gray color we denote the number of SEP events for which no radio information could be found (neither plots nor observatory reports). The majority of the missing radio plots is in the dm-range due to poor data coverage. Note that the highest discrepancy between the results given by us and by observatory reports is for the type II burst identification in the DHrange. This is mostly due to the weak and intermittent appearance of the IP type II bursts which makes an identification on quick-look plots difficult. In addition, the subjectivity of the observer plays a prominent role here, whereas the DH-type III identification, for example, is straightforward.</text>
<text><location><page_5><loc_12><loc_10><loc_83><loc_20></location>On the histograms, the number of events in each column is normalized to the total number of events in each group (eastern and western, correspondingly) and is also given explicitly in Table IV. While representing the association rate in the dm and m-range, we chose the greater association rate among their two subbands. For the total number of SEP events, given</text>
<section_header_level_1><location><page_6><loc_46><loc_85><loc_60><loc_86></location>MITEVA ET AL.</section_header_level_1>
<figure>
<location><page_6><loc_17><loc_39><loc_85><loc_82></location>
<caption>Figure 1 : Histograms of the association rates of eastern (lest) and western (right) SEP events and the corresponding radio burst types for dm (3 -0.8 and 0.8 -0.3 GHz), m (300 -100 and 100 -30 MHz) and DH (30 -0.02 MHz) range. For the color-code see text.</caption>
</figure>
<text><location><page_6><loc_17><loc_24><loc_88><loc_29></location>with 'All' in Table IV, we sum up the eastern, western and the uncertain SEP events. Since the dm-type II burst and the DH-type IV bursts are intrinsically rare phenomena, they will be excluded from the further analysis.</text>
<text><location><page_6><loc_17><loc_10><loc_88><loc_24></location>The highest association rate of SEPs is with the m and DH-type III bursts, usually /greaterorsimilar 90 % (see Table IV for details). A much lower association rate between SEPs and type IIIs is found in the dm-range (from about 30 to 50%). No dependence on the eastern vs. western heliolongitudes is seen for type III and type IV bursts, with the association rate of the type IV bursts being in the range from 50% up to 75%. In contrast, the SEP-association rate with the 30 -100 MHz metric (94%) and the DH type II bursts (88%)</text>
<text><location><page_7><loc_12><loc_80><loc_79><loc_82></location>is slightly higher for eastern SEP events than for western ones (71 %).</text>
<section_header_level_1><location><page_7><loc_39><loc_75><loc_55><loc_77></location>5. Discussion</section_header_level_1>
<text><location><page_7><loc_12><loc_62><loc_83><loc_74></location>We present the association rates of the SEP events (protons) and their accompanying radio emission (from electrons) in the corona (dm and m wavelength) and IP space (DH-range). Since there are no signatures of protons interacting with the solar atmosphere (with the exception of gamma-ray emission), we use electron signatures as a diagnostic for particle acceleration from the corona up to 1 AU.</text>
<text><location><page_7><loc_12><loc_43><loc_83><loc_62></location>Cane et al. (2002) were the first to identify long-lasting groups of DH type III bursts as a typical radio counterpart of large SEP events. They found the groups to be of significantly longer duration than type III bursts associated with impulsive flares, see also MacDowall et al. (1987). In the analysis performed here, we did not take into account the burst duration of DH-type III, nor explicitly separate the SEP events into gradual or impulsive. Still we find that SEP events have the highest association rate with type III radio bursts. This implies that the electrons accelerated in the corona (within one solar radius) have a ready access to the IP space, irrespective of whether the SEP event is impulsive or gradual.</text>
<text><location><page_7><loc_12><loc_31><loc_83><loc_43></location>Shock signatures (type II bursts) were also considered in correlation studies with SEP events. We found a lower association rate (up to 75%) of the DH-type II bursts with SEP events, compared to the m- and DH-type III association rates. The number increases when only SEP events with strong intensities are considered, in agreement with Gopalswamy et al. (2002) and Cliver et al. (2004).</text>
<text><location><page_7><loc_12><loc_10><loc_83><loc_31></location>The association of SEP events with types III and IV is comparable in the eastern and western groups (see Figure 1). But for the type II bursts there is a slight trend for a higher association rate in the eastern hemisphere. This result could be understood it terms of different sources contributing to SEP events. Shocks could be the dominant accelerator when the parent activity is poorly connected to Earth (as in the eastern solar hemisphere). In the western hemisphere (where more than twice as many events were detected) both flare and shock acceleration could contribute. When no shock signatures accompany the eastern SEP events, their propagation through the IP space and detection at Earth could be facilitated by a large-scale magnetic structure, e.g., interplanetary coronal mass ejections (ICMEs). Richardson et al.</text>
<section_header_level_1><location><page_8><loc_46><loc_85><loc_60><loc_86></location>MITEVA ET AL.</section_header_level_1>
<text><location><page_8><loc_17><loc_76><loc_88><loc_82></location>(1991) estimated that for about 15% of the eastern events this is likely the case. Recently Miteva et al. (2013) showed similar occurrence rate of ICMEs for the western SEP events (20%).</text>
<text><location><page_8><loc_17><loc_52><loc_88><loc_75></location>The association with the type IIIs seems to be increasing with the decreasing of the radio frequency (from dm to DH-range). At first, the type III identification in the dm-range might be masked due to overlying decimeter continuum often present in the dynamic radio spectra (observational bias). Hence, the obtained association rates of dm-IIIs are to be considered as lower limits only. In addition, high frequencies and dense plasma impede the production and growth of Langmuir waves. Also, the electron beam must travel an 'instability distance' from the acceleration site before Langmuir waves are generated (Reid et al. , 2011). This can cause a lack of high frequency type III emission in even the most energetic of electron beams. Moreover, collisions of both waves and electrons can suppress Langmuir wave growth at high frequencies, e.g., Kane et al. (1982); Reid and Kontar (2012).</text>
<text><location><page_8><loc_17><loc_42><loc_88><loc_51></location>Without the intention to give a complete overview on the results from previous work, we selected few statistical studies that are (partially) covering solar cycle 23. The different association rates are given in Table IV and are mostly consistent, although in many earlier studies only large SEP events were considered.</text>
<section_header_level_1><location><page_8><loc_42><loc_33><loc_63><loc_34></location>Acknowledgements</section_header_level_1>
<text><location><page_8><loc_17><loc_11><loc_88><loc_30></location>R.M. acknowledges a post-doctoral fellowship from Paris Observatory. A.N. was partly supported by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. H.R. asknowledges the suport of the Scottish Universities Physics Alliance. We acknowledge the open data policy for the radio data used in this study and partial funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 262773 (SEPServer) and HESPE network (FP7-SPACE-2010-263086).</text>
<section_header_level_1><location><page_9><loc_41><loc_80><loc_53><loc_81></location>References</section_header_level_1>
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<text><location><page_9><loc_13><loc_72><loc_83><loc_75></location>Cane, H. V., Richardson, I. G., and von Rosenvinge, T. T.: 2010, J. Geophys. Res. 115 , A08101.</text>
<text><location><page_9><loc_13><loc_70><loc_78><loc_71></location>Cliver, E. W.: 2009, Central European Astrophysical Bulletin 33 , 253-270.</text>
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<text><location><page_9><loc_13><loc_38><loc_83><loc_41></location>MacDowall, R. J., Lara, A., Manoharan, P. K., Nitta, N. V., Rosas, A. M., and Bougeret, J. L.: 2003, Geophys. Res. Lett. 30 (12), 120000-1.</text>
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<section_header_level_1><location><page_10><loc_46><loc_85><loc_60><loc_86></location>MITEVA ET AL.</section_header_level_1>
<table>
<location><page_10><loc_17><loc_11><loc_89><loc_77></location>
<caption>Table II : Solar energetic particle events with origin at western heliolongitudes: visual identification and [observatory reports] of type II, III and IV radio bursts.</caption>
</table>
<table>
<location><page_11><loc_12><loc_10><loc_87><loc_79></location>
<caption>Table II : cont'd</caption>
</table>
<section_header_level_1><location><page_12><loc_46><loc_85><loc_60><loc_86></location>MITEVA ET AL.</section_header_level_1>
<table>
<location><page_12><loc_17><loc_16><loc_88><loc_71></location>
<caption>Table III : Solar energetic particle events with origin at eastern or uncertain (with superscript 'u') heliolongitudes: visual identification and [observatory reports] of type II, III and IV radio bursts.</caption>
</table>
<text><location><page_13><loc_17><loc_29><loc_18><loc_30></location>b</text>
<text><location><page_13><loc_17><loc_28><loc_18><loc_29></location>a</text>
<text><location><page_13><loc_23><loc_79><loc_24><loc_79></location>r</text>
<text><location><page_13><loc_23><loc_13><loc_24><loc_14></location>P</text>
<text><location><page_13><loc_23><loc_12><loc_24><loc_13></location>E</text>
<text><location><page_13><loc_23><loc_12><loc_24><loc_12></location>S</text>
<text><location><page_13><loc_25><loc_29><loc_27><loc_29></location>I</text>
<text><location><page_13><loc_25><loc_28><loc_27><loc_29></location>I</text>
<text><location><page_13><loc_25><loc_21><loc_27><loc_21></location>I</text>
<text><location><page_13><loc_25><loc_79><loc_27><loc_79></location>s</text>
<text><location><page_13><loc_67><loc_79><loc_68><loc_80></location>6</text>
<text><location><page_13><loc_72><loc_81><loc_74><loc_82></location>0</text>
<text><location><page_13><loc_72><loc_81><loc_74><loc_81></location>1</text>
<text><location><page_13><loc_73><loc_79><loc_74><loc_80></location>></text>
<text><location><page_13><loc_74><loc_81><loc_76><loc_82></location>0</text>
<text><location><page_13><loc_74><loc_81><loc_76><loc_81></location>1</text>
<text><location><page_13><loc_75><loc_79><loc_76><loc_80></location>></text>
<table>
<location><page_13><loc_11><loc_30><loc_81><loc_79></location>
</table>
<text><location><page_13><loc_30><loc_29><loc_31><loc_30></location>E</text>
<text><location><page_13><loc_30><loc_28><loc_31><loc_29></location>S</text>
<text><location><page_13><loc_30><loc_85><loc_65><loc_86></location>RADIO SIGNATURES OF SEP EVENTS</text>
<text><location><page_13><loc_44><loc_80><loc_45><loc_80></location>)</text>
<text><location><page_13><loc_43><loc_79><loc_44><loc_80></location>w</text>
<text><location><page_13><loc_44><loc_79><loc_45><loc_79></location>4</text>
<text><location><page_13><loc_44><loc_29><loc_45><loc_30></location>0</text>
<text><location><page_13><loc_44><loc_29><loc_45><loc_29></location>5</text>
<text><location><page_13><loc_58><loc_29><loc_59><loc_30></location>d</text>
<text><location><page_13><loc_58><loc_29><loc_59><loc_29></location>a</text>
<text><location><page_13><loc_58><loc_28><loc_59><loc_29></location>R</text>
<text><location><page_13><loc_72><loc_29><loc_74><loc_30></location>v</text>
<text><location><page_13><loc_72><loc_28><loc_74><loc_29></location>e</text>
<text><location><page_13><loc_72><loc_21><loc_74><loc_21></location>(</text>
<text><location><page_13><loc_72><loc_20><loc_74><loc_20></location>g</text>
<text><location><page_13><loc_72><loc_19><loc_74><loc_20></location>n</text>
<text><location><page_13><loc_72><loc_18><loc_74><loc_19></location>o</text>
<text><location><page_13><loc_72><loc_18><loc_74><loc_18></location>r</text>
<text><location><page_13><loc_72><loc_17><loc_74><loc_18></location>t</text>
<text><location><page_13><loc_72><loc_17><loc_74><loc_17></location>s</text>
<text><location><page_13><loc_72><loc_16><loc_74><loc_16></location>:</text>
<text><location><page_13><loc_72><loc_16><loc_74><loc_16></location>)</text>
<text><location><page_13><loc_72><loc_15><loc_74><loc_16></location>w</text>
<text><location><page_13><loc_72><loc_14><loc_74><loc_15></location>(</text>
<text><location><page_13><loc_72><loc_13><loc_74><loc_14></location>s</text>
<text><location><page_13><loc_74><loc_29><loc_76><loc_30></location>s</text>
<text><location><page_13><loc_74><loc_29><loc_75><loc_29></location>1</text>
<text><location><page_13><loc_75><loc_28><loc_75><loc_29></location>-</text>
<text><location><page_13><loc_74><loc_20><loc_76><loc_20></location>3</text>
<text><location><page_13><loc_74><loc_19><loc_76><loc_19></location>f</text>
<text><location><page_13><loc_74><loc_18><loc_76><loc_19></location>o</text>
<text><location><page_13><loc_74><loc_18><loc_76><loc_18></location>s</text>
<text><location><page_13><loc_74><loc_17><loc_76><loc_18></location>n</text>
<text><location><page_13><loc_74><loc_16><loc_76><loc_17></location>o</text>
<text><location><page_13><loc_74><loc_16><loc_76><loc_16></location>t</text>
<text><location><page_13><loc_74><loc_15><loc_76><loc_16></location>o</text>
<text><location><page_13><loc_74><loc_14><loc_76><loc_15></location>r</text>
<text><location><page_13><loc_74><loc_14><loc_76><loc_14></location>p</text>
<text><location><page_13><loc_74><loc_12><loc_76><loc_13></location>V</text>
<text><location><page_13><loc_74><loc_12><loc_76><loc_13></location>e</text>
<text><location><page_13><loc_74><loc_11><loc_76><loc_12></location>M</text>
<text><location><page_13><loc_17><loc_21><loc_78><loc_29></location>T D H -8 8 7 1 9 0 s r 7 5 8 0 w ) 6 3 ( 9 6 s / 1 0 0 8 y N / 5 2 y Y 2 5 y N / 9 0 y Y Y / 5 2 n Y / 3 0 y N w e a k ) S E P ∼ 1 0 4 c m -2 s 1 0 c m -2 s -1</text>
<text><location><page_13><loc_25><loc_20><loc_27><loc_21></location>I</text>
<text><location><page_13><loc_25><loc_20><loc_27><loc_20></location>-</text>
<text><location><page_13><loc_25><loc_19><loc_27><loc_20></location>m</text>
<text><location><page_13><loc_25><loc_15><loc_27><loc_15></location>y</text>
<text><location><page_13><loc_25><loc_14><loc_27><loc_15></location>r</text>
<text><location><page_13><loc_25><loc_14><loc_27><loc_14></location>o</text>
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<text><location><page_13><loc_25><loc_13><loc_27><loc_13></location>e</text>
<text><location><page_13><loc_25><loc_13><loc_27><loc_13></location>t</text>
<text><location><page_13><loc_25><loc_12><loc_27><loc_13></location>a</text>
<text><location><page_13><loc_25><loc_12><loc_27><loc_12></location>c</text>
<text><location><page_13><loc_32><loc_20><loc_34><loc_21></location>4</text>
<text><location><page_13><loc_32><loc_20><loc_34><loc_20></location>9</text>
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<text><location><page_13><loc_32><loc_12><loc_34><loc_13></location>a</text>
<text><location><page_13><loc_32><loc_12><loc_34><loc_12></location>E</text>
<text><location><page_13><loc_12><loc_6><loc_33><loc_7></location>Cent. Eur. Astrophys. Bull.</text>
<text><location><page_13><loc_34><loc_6><loc_36><loc_7></location>37</text>
<text><location><page_13><loc_36><loc_6><loc_49><loc_7></location>(2018) 1, ??-??</text>
<text><location><page_13><loc_81><loc_6><loc_83><loc_8></location>13</text>
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<text><location><page_13><loc_44><loc_19><loc_45><loc_20></location>8</text>
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<text><location><page_13><loc_44><loc_18><loc_45><loc_18></location>2</text>
<text><location><page_13><loc_44><loc_17><loc_45><loc_18></location>8</text>
<text><location><page_13><loc_67><loc_21><loc_68><loc_21></location>y</text>
<text><location><page_13><loc_67><loc_20><loc_68><loc_21></location>1</text>
<text><location><page_13><loc_67><loc_20><loc_68><loc_20></location>6</text>
<text><location><page_13><loc_67><loc_13><loc_68><loc_13></location>l</text>
<text><location><page_13><loc_67><loc_12><loc_68><loc_13></location>l</text>
<text><location><page_13><loc_67><loc_12><loc_68><loc_12></location>A</text>
<text><location><page_13><loc_77><loc_29><loc_78><loc_30></location>e</text>
<text><location><page_13><loc_77><loc_28><loc_78><loc_29></location>M</text>
<text><location><page_13><loc_77><loc_20><loc_78><loc_21></location>≥</text>
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<text><location><page_13><loc_77><loc_18><loc_78><loc_18></location>s</text>
<text><location><page_13><loc_77><loc_17><loc_78><loc_18></location>n</text>
<text><location><page_13><loc_77><loc_16><loc_78><loc_17></location>o</text>
<text><location><page_13><loc_77><loc_16><loc_78><loc_16></location>t</text>
<text><location><page_13><loc_77><loc_15><loc_78><loc_16></location>o</text>
<text><location><page_13><loc_77><loc_15><loc_78><loc_15></location>r</text>
<text><location><page_13><loc_77><loc_14><loc_78><loc_15></location>p</text>
<text><location><page_13><loc_77><loc_12><loc_78><loc_13></location>V</text>
<text><location><page_13><loc_77><loc_12><loc_78><loc_13></location>e</text>
<text><location><page_13><loc_77><loc_11><loc_78><loc_12></location>M</text>
<text><location><page_13><loc_35><loc_20><loc_36><loc_21></location>1</text>
<text><location><page_13><loc_35><loc_20><loc_36><loc_20></location>7</text>
<text><location><page_13><loc_35><loc_15><loc_36><loc_15></location>n</text>
<text><location><page_13><loc_35><loc_14><loc_36><loc_15></location>r</text>
<text><location><page_13><loc_35><loc_14><loc_36><loc_14></location>e</text>
<text><location><page_13><loc_35><loc_13><loc_36><loc_14></location>t</text>
<text><location><page_13><loc_35><loc_13><loc_36><loc_13></location>s</text>
<text><location><page_13><loc_35><loc_13><loc_36><loc_13></location>e</text>
<text><location><page_13><loc_35><loc_12><loc_36><loc_13></location>W</text>
<text><location><page_13><loc_41><loc_20><loc_42><loc_21></location>8</text>
<text><location><page_13><loc_41><loc_20><loc_42><loc_20></location>7</text>
<text><location><page_13><loc_41><loc_13><loc_42><loc_13></location>l</text>
<text><location><page_13><loc_41><loc_12><loc_42><loc_13></location>l</text>
<text><location><page_13><loc_41><loc_12><loc_42><loc_12></location>A</text>
<text><location><page_13><loc_46><loc_28><loc_47><loc_29></location>m</text>
<text><location><page_13><loc_46><loc_21><loc_47><loc_21></location>m</text>
<text><location><page_13><loc_47><loc_20><loc_47><loc_21></location>,</text>
<text><location><page_13><loc_46><loc_20><loc_47><loc_20></location>f</text>
<text><location><page_13><loc_47><loc_19><loc_48><loc_20></location>0</text>
<text><location><page_13><loc_47><loc_19><loc_48><loc_19></location>9</text>
<text><location><page_13><loc_61><loc_14><loc_62><loc_15></location>n</text>
<text><location><page_13><loc_61><loc_14><loc_62><loc_14></location>r</text>
<text><location><page_13><loc_61><loc_14><loc_62><loc_14></location>e</text>
<text><location><page_13><loc_61><loc_13><loc_62><loc_14></location>t</text>
<text><location><page_13><loc_61><loc_13><loc_62><loc_13></location>s</text>
<text><location><page_13><loc_61><loc_12><loc_62><loc_13></location>a</text>
<text><location><page_13><loc_61><loc_12><loc_62><loc_12></location>E</text>
<text><location><page_13><loc_64><loc_15><loc_65><loc_15></location>n</text>
<text><location><page_13><loc_64><loc_14><loc_65><loc_15></location>r</text>
<text><location><page_13><loc_64><loc_14><loc_65><loc_14></location>e</text>
<text><location><page_13><loc_64><loc_13><loc_65><loc_14></location>t</text>
<text><location><page_13><loc_64><loc_13><loc_65><loc_13></location>s</text>
<text><location><page_13><loc_64><loc_13><loc_65><loc_13></location>e</text>
<text><location><page_13><loc_64><loc_12><loc_65><loc_13></location>W</text>
</document>
[
{
"title": "RADIO SIGNATURES OF SOLAR ENERGETIC PARTICLES DURING THE 23 RD SOLAR CYCLE",
"content": "R. MITEVA 1 , K.-L. KLEIN 1 , S. W. SAMWEL 2 , A. NINDOS 3 , A. KOULOUMVAKOS 3 , 4 and H. REID 1 , 5 Abstract. We present the association rates between solar energetic particles (SEPs) and the radio emission signatures in the corona and IP space during the entire solar cycle 23. We selected SEPs associated with X and M-class flares from the visible solar hemisphere. All SEP events are also accompanied by coronal mass ejections. Here, we focus on the correlation between the SEP events and the appearance of radio type II, III and IV bursts on dynamic spectra. For this we used the available radio data from ground-based stations and the Wind/WAVES spacecraft. The associations are presented separately for SEP events accompanying activity in the eastern and western solar hemisphere. We find the highest association rate of SEP events to be with type III bursts, followed by types II and IV. Whereas for types III and IV no longitudinal dependence is noticed, these is a tendency for a higher SEP-association rate with type II bursts in the eastern hemisphere. A comparison with reports from previous studies is briefly discussed. Key words: Solar energetic particles - radio bursts - solar cycle 23",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Solar energetic particle (SEP) events are transient flux enhancements of electrons, protons and ions due to acceleration processes in the solar corona and interplanetary (IP) space. The high energy particles can pose a serious risk for the near Earth and ground-based technological devices, may dis-",
"pages": [
1
]
},
{
"title": "MITEVA ET AL.",
"content": "b a r P E S I I I s 6 0 1 > 0 1 > E S RADIO SIGNATURES OF SEP EVENTS ) w 4 0 5 d a R v e ( g n o r t s : ) w ( s s 1 - 3 f o s n o t o r p V e M T D H -8 8 7 1 9 0 s r 7 5 8 0 w ) 6 3 ( 9 6 s / 1 0 0 8 y N / 5 2 y Y 2 5 y N / 9 0 y Y Y / 5 2 n Y / 3 0 y N w e a k ) S E P ∼ 1 0 4 c m -2 s 1 0 c m -2 s -1 I - m y r o g e t a c 4 9 n r e t s a E Cent. Eur. Astrophys. Bull. 37 (2018) 1, ??-?? 13 / s 8 8 ( 2 8 y 1 6 l l A e M ≥ f o s n o t o r p V e M 1 7 n r e t s e W 8 7 l l A m m , f 0 9 n r e t s a E n r e t s e W",
"pages": [
13
]
},
{
"title": "2. Particle data",
"content": "In the present work we selected all proton events with energy above 25 MeV as identified by Cane et al. (2010) that are associated with both strong flares (X and M-class) at eastern and western heliolongitudes and CMEs. Here we will differentiate the SEP events into eastern/western only and not by other SEP classifications schemes (Reames, 1999; Cliver, 2009), since any classification may leave out many 'mixed' cases in abundances, charge states, associated phenomena, etc. However, in order to facilitate comparison with previous work, we note if the SEP event was described as 'gradual' or 'impulsive' in Reames and Ng (2004) and Cliver and Ling (2009) by the superscripts 'g' and 'i', respectively. In order to improve the statistics for the radio analysis (see next Section) we included SEP events that have high background level due to a previous event 1 , that are observed during SOHO data gap, those for which no value for the peak intensity was given due to instrument saturation (with superscript 's') and those with parent activity at the limb (with superscript 'l' we denote events at the solar limb and with 'c', events close to the disc center, between ± 10 degrees in heliolongitude). That lead finally to 175 particle events during solar cycle 23, of which 49 had sources in the eastern hemisphere, 124 in the western and two had uncertain source locations.",
"pages": [
3
]
},
{
"title": "3. Radio spectrograph data",
"content": "The radio emission observed on ground and in space is usually presented in a frequency vs. time plot, where the strength of the radio emission is color-coded. This is known as a dynamic radio spectrum. Several features were recognized on such spectrum plots, e.g., fast drifting emission stripes extending from high to low frequencies (type IIIs); slowly drifting lanes of emission (type IIs) and a broad band stationary or/and drifting emission of type IV. Each of these radio emission types is a result of a unstable electron population (produced by a different process) generating Langmuir waves that convert into electromagnetic radiation via wave-wave processes. Namely, type IIs are usually assumed to be the shock signatures in the corona/IP space (Nelson and Melrose, 1985), type IIIs are electron beams propagating through the corona (Suzuki and Dulk, 1985), and the type IVs are the signatures from trapped electrons in coronal loops (Stewart, 1985; Pick, 1986). Here, we will use this standard interpretation for the radio burst emission in order to identify the probable particle accelerator. As a preparatory work for the analysis we collected all available radio spectral data (summarized in Table I) and the associated GOES soft X-ray (SXR) emission for each SEP event. The results of the associated radio bursts to each particle event are summarized in Tables II and III. There, we start with the SEP event date followed by the onset (in UT) of the SXR emission associated with each event as provided by GOES satellite (1 -8 Å channel). The so-identified radio emissions of type II, III and IV are organized in several frequency (wavelength) ranges in Tables II and III. Namely, the decimeter (dm) range is subdivided into high (0.8 -3 GHz) and lower (0.3 -0.8 GHz) frequency parts. Similarly, we divided the metric (m) range into 100 -300 and 30 -100 MHz subbands. The IP space (dekameter/hectometer, DH, and kilometer wavelengths) is represented by one column. The radio bursts were ordered by their type and not by their temporal appearance on the radio spectral plot. Since we primarily used quicklook radio spectral data where image quality may be low, we also collected all available radio observatory reports for each event. In case radio emission of a given type was reported but could not be identified by us (due to low resolution of the actual image or because no radio spectrum plot was found), we give the result in squared brackets in Tables II and III. Any uncertain radio burst identification is indicated by a question mark following the roman number of the corresponding radio burst type. Weak emission signatures are denoted with superscript 'w', delayed emission with 'd' and low (high)-frequency emission onset with 'LFo' ('HFo'). Unclassified emission is given with 'UNCLF', fine structures with 'FS' and fundamental-harmonic emission with 'FH'. Continuum ('CONT') and decimeter ('DCIM') emission in the 0.3 -3 GHz range is considered as type IV-like emission in the analysis. The complete particle event list together with the associated radio bursts is given in Tables II and III (for western and eastern events, respectively).",
"pages": [
3,
4,
5
]
},
{
"title": "4. Results",
"content": "The results are given as normalized number of the SEP events vs. radio frequency for each wavelength range (dm, m and DH), see the histograms on Figure 1, for eastern (on the left) and western (right) SEP events. The numerical value of the association rates, graphically presented on the histograms, is given by the height of each color bar. The SEP events associated with specific burst types as identified on the radio spectral plots are given with black color. With dark gray is shown the association in cases where the burst type was only given in the observatory reports (no spectra found at present) or where its identification is questionable. Whenever we give a value for an association rate, we will always sum up these two sections. Finally, with light gray color we denote the number of SEP events for which no radio information could be found (neither plots nor observatory reports). The majority of the missing radio plots is in the dm-range due to poor data coverage. Note that the highest discrepancy between the results given by us and by observatory reports is for the type II burst identification in the DHrange. This is mostly due to the weak and intermittent appearance of the IP type II bursts which makes an identification on quick-look plots difficult. In addition, the subjectivity of the observer plays a prominent role here, whereas the DH-type III identification, for example, is straightforward. On the histograms, the number of events in each column is normalized to the total number of events in each group (eastern and western, correspondingly) and is also given explicitly in Table IV. While representing the association rate in the dm and m-range, we chose the greater association rate among their two subbands. For the total number of SEP events, given",
"pages": [
5
]
},
{
"title": "5. Discussion",
"content": "We present the association rates of the SEP events (protons) and their accompanying radio emission (from electrons) in the corona (dm and m wavelength) and IP space (DH-range). Since there are no signatures of protons interacting with the solar atmosphere (with the exception of gamma-ray emission), we use electron signatures as a diagnostic for particle acceleration from the corona up to 1 AU. Cane et al. (2002) were the first to identify long-lasting groups of DH type III bursts as a typical radio counterpart of large SEP events. They found the groups to be of significantly longer duration than type III bursts associated with impulsive flares, see also MacDowall et al. (1987). In the analysis performed here, we did not take into account the burst duration of DH-type III, nor explicitly separate the SEP events into gradual or impulsive. Still we find that SEP events have the highest association rate with type III radio bursts. This implies that the electrons accelerated in the corona (within one solar radius) have a ready access to the IP space, irrespective of whether the SEP event is impulsive or gradual. Shock signatures (type II bursts) were also considered in correlation studies with SEP events. We found a lower association rate (up to 75%) of the DH-type II bursts with SEP events, compared to the m- and DH-type III association rates. The number increases when only SEP events with strong intensities are considered, in agreement with Gopalswamy et al. (2002) and Cliver et al. (2004). The association of SEP events with types III and IV is comparable in the eastern and western groups (see Figure 1). But for the type II bursts there is a slight trend for a higher association rate in the eastern hemisphere. This result could be understood it terms of different sources contributing to SEP events. Shocks could be the dominant accelerator when the parent activity is poorly connected to Earth (as in the eastern solar hemisphere). In the western hemisphere (where more than twice as many events were detected) both flare and shock acceleration could contribute. When no shock signatures accompany the eastern SEP events, their propagation through the IP space and detection at Earth could be facilitated by a large-scale magnetic structure, e.g., interplanetary coronal mass ejections (ICMEs). Richardson et al.",
"pages": [
7
]
},
{
"title": "Acknowledgements",
"content": "R.M. acknowledges a post-doctoral fellowship from Paris Observatory. A.N. was partly supported by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program \"Education and Lifelong Learning\" of the National Strategic Reference Framework (NSRF) Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. H.R. asknowledges the suport of the Scottish Universities Physics Alliance. We acknowledge the open data policy for the radio data used in this study and partial funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 262773 (SEPServer) and HESPE network (FP7-SPACE-2010-263086).",
"pages": [
8
]
},
{
"title": "References",
"content": "Cane, H. V., Erickson, W. C., and Prestage, N. P.: 2002, Journal of Geophysical Research (Space Physics) 107 , 1315. Cane, H. V., Richardson, I. G., and von Rosenvinge, T. T.: 2010, J. Geophys. Res. 115 , A08101. Cliver, E. W.: 2009, Central European Astrophysical Bulletin 33 , 253-270. Cliver, E. W., Kahler, S. W., and Reames, D. V.: 2004, Astrophys. J. 605 , 902910. Cliver, E. W. and Ling, A. G.: 2007, Astrophys. J. 658 , 1349-1356. Cliver, E. W. and Ling, A. G.: 2009, Astrophys. J. 690 , 598-609. Gopalswamy, N.: 2003, Geophys. Res. Lett. 30 (12), 120000-1. Gopalswamy, N., Yashiro, S., Akiyama, S., Mäkelä, P., Xie, H., Kaiser, M. L., Howard, R. A., and Bougeret, J. L.: 2008, Annales Geophysicae 26 , 30333047. Gopalswamy, N., Yashiro, S., Michałek, G., Kaiser, M. L., Howard, R. A., Reames, D. V., Leske, R., and von Rosenvinge, T.: 2002, Astrophys. J., 572 Lett. , L103-L107. Kahler, S. W.: 1982, Astrophys. J. 261 , 710-719. Kane, S. R., Benz, A. O., and Treumann, R. A.: 1982, Astrophys. J. 263 , 423-432. Klein, K.-L., Trottet, G., Samwel, S., and Malandraki, O.: 2011, Solar Phys. 269 , 309-333. MacDowall, R. J., Kundu, M. R., and Stone, R. G.: 1987, Solar Phys. 111 , 397418. MacDowall, R. J., Lara, A., Manoharan, P. K., Nitta, N. V., Rosas, A. M., and Bougeret, J. L.: 2003, Geophys. Res. Lett. 30 (12), 120000-1. Mewaldt, R. A.: 2006, Space Sci. Rev. 124 , 303-316. Miteva, R., Klein, K.-L., Malandraki, O., and Dorrian, G.: 2013, Solar Phys. 282 , 579-613. Nelson, G. J. and Melrose, D. B.: 1985, Type II bursts , pp. 333-359. Nindos, A., Aurass, H., Klein, K.-L., and Trottet, G.: 2008, Solar Phys. 253 , 341. Pick, M.: 1986, Solar Phys. 104 , 19-32. Pick, M. and Vilmer, N.: 2008, Astron. Astrophys. Rev. 16 , 1-153. Reames, D. V.: 1999, Space Sci. Rev. 90 , 413-491. Reames, D. V. and Ng, C. K.: 2004, Astrophys. J. 610 , 510-522. Reid, H. A. S. and Kontar, E. P.: 2012, Solar Phys. p. 109. Reid, H. A. S., Vilmer, N., and Kontar, E. P.: 2011, Astron. Astrophys. 529 , A66. Richardson, I. G., Cane, H. V., and von Rosenvinge, T. T.: 1991, J. Geophys. Res. 96 , 7853-7860. Stewart, R. T.: 1985, Moving Type IV bursts , pp. 361-383. Suzuki, S. and Dulk, G. A.: 1985, Bursts of Type III and Type V , pp. 289-332.",
"pages": [
9
]
}
]
2013E&PSL.379..104T
https://arxiv.org/pdf/1308.0511.pdf
<document>
<text><location><page_1><loc_11><loc_88><loc_12><loc_90></location>1</text>
<section_header_level_1><location><page_1><loc_11><loc_85><loc_12><loc_86></location>2</section_header_level_1>
<unordered_list>
<list_item><location><page_1><loc_11><loc_81><loc_12><loc_83></location>3</list_item>
</unordered_list>
<section_header_level_1><location><page_1><loc_17><loc_88><loc_83><loc_91></location>Conservation of Total Escape from Hydrodynamic</section_header_level_1>
<section_header_level_1><location><page_1><loc_35><loc_84><loc_66><loc_87></location>Planetary Atmospheres</section_header_level_1>
<section_header_level_1><location><page_1><loc_42><loc_81><loc_58><loc_84></location>Feng Tian 1,2</section_header_level_1>
<unordered_list>
<list_item><location><page_1><loc_11><loc_77><loc_83><loc_80></location>1. National Astronomical Observatories, Chinese Academy of Sciences 4</list_item>
<list_item><location><page_1><loc_11><loc_74><loc_70><loc_76></location>2. Center for Earth System Sciences, Tsinghua University 5</list_item>
</unordered_list>
<text><location><page_1><loc_11><loc_70><loc_12><loc_72></location>6</text>
<unordered_list>
<list_item><location><page_1><loc_11><loc_66><loc_85><loc_68></location>Abstract: Atmosphere escape is one key process controlling the 7</list_item>
<list_item><location><page_1><loc_11><loc_63><loc_85><loc_65></location>evolution of planets. However, estimating the escape rate in any detail 8</list_item>
<list_item><location><page_1><loc_11><loc_59><loc_86><loc_61></location>is difficult because there are many physical processes contributing to 9</list_item>
<list_item><location><page_1><loc_10><loc_55><loc_85><loc_57></location>the total escape rate. Here we show that as a result of energy 10</list_item>
<list_item><location><page_1><loc_10><loc_51><loc_85><loc_54></location>conservation the total escape rate from hydrodynamic planetary 11</list_item>
<list_item><location><page_1><loc_10><loc_48><loc_86><loc_50></location>atmospheres where the outflow remains subsonic is nearly constant 12</list_item>
<list_item><location><page_1><loc_10><loc_44><loc_85><loc_46></location>under the same stellar XUV photon flux when increasing the escape 13</list_item>
<list_item><location><page_1><loc_10><loc_40><loc_86><loc_43></location>efficiency from the exobase level, consistent with the energy limited 14</list_item>
<list_item><location><page_1><loc_10><loc_37><loc_86><loc_39></location>escape approximation. Thus the estimate of atmospheric escape in a 15</list_item>
<list_item><location><page_1><loc_10><loc_33><loc_66><loc_35></location>planet's evolution history can be greatly simplified. 16</list_item>
</unordered_list>
<text><location><page_1><loc_10><loc_29><loc_12><loc_31></location>17</text>
<section_header_level_1><location><page_1><loc_10><loc_25><loc_33><loc_28></location>1. Introduction 18</section_header_level_1>
<unordered_list>
<list_item><location><page_1><loc_10><loc_18><loc_86><loc_24></location>Recently it is proposed that a high hydrogen content (at least a few 19 percent) in early Earth's atmosphere could be important to keep early 20</list_item>
<list_item><location><page_1><loc_10><loc_14><loc_85><loc_17></location>Earth warm, contributing to the solution of the faint young Sun problem 21</list_item>
<list_item><location><page_1><loc_10><loc_11><loc_85><loc_13></location>(Wordsworth and Pierrehumbert 2013). A hydrogen rich early Earth 22</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_2><loc_10><loc_89><loc_86><loc_91></location>atmosphere has been proposed based on hydrodynamic calculations of 23</list_item>
<list_item><location><page_2><loc_10><loc_85><loc_86><loc_87></location>hydrogen escape and such an atmosphere could have been important for 24</list_item>
<list_item><location><page_2><loc_10><loc_81><loc_85><loc_83></location>prebiotic photochemistry (Tian et al. 2005a). The numerical scheme in 25</list_item>
<list_item><location><page_2><loc_10><loc_77><loc_86><loc_80></location>Tian et al. (2005a) contains large numerical diffusion especially near the 26</list_item>
<list_item><location><page_2><loc_10><loc_74><loc_86><loc_76></location>lower boundary where the density gradient is the largest (Tian et al. 27</list_item>
</unordered_list>
<text><location><page_2><loc_10><loc_70><loc_12><loc_72></location>28</text>
<text><location><page_2><loc_15><loc_70><loc_85><loc_72></location>2005b). However, the calculated upper atmosphere structures are</text>
<unordered_list>
<list_item><location><page_2><loc_10><loc_66><loc_85><loc_68></location>consistent with transit observations of hot Jupiter HD209458b 29</list_item>
<list_item><location><page_2><loc_10><loc_63><loc_86><loc_65></location>(Vidar-Madjar et al. 2003) and the calculated escape rates are consistent 30</list_item>
<list_item><location><page_2><loc_10><loc_59><loc_85><loc_61></location>with follow-up independent works (Yelle 2006, Garcia-Munoz 2007, 31</list_item>
<list_item><location><page_2><loc_10><loc_55><loc_85><loc_57></location>Penz et al. 2008, Koskinen et al. 2012). On the other hand, it is suggested 32</list_item>
<list_item><location><page_2><loc_10><loc_51><loc_85><loc_54></location>that nonthermal escape processes could have increased total hydrogen 33</list_item>
<list_item><location><page_2><loc_10><loc_48><loc_85><loc_50></location>escape (Catling 2006) so that the hydrogen content in early Earth 34</list_item>
</unordered_list>
<text><location><page_2><loc_10><loc_44><loc_12><loc_46></location>35</text>
<text><location><page_2><loc_15><loc_44><loc_85><loc_46></location>atmosphere would have been in the order of 0.1% instead of a few</text>
<unordered_list>
<list_item><location><page_2><loc_10><loc_40><loc_86><loc_43></location>percent or greater. But no calculation has been carried out to estimate the 36</list_item>
<list_item><location><page_2><loc_10><loc_37><loc_76><loc_39></location>nonthermal hydrogen escape rate from early Earth's atmosphere. 37</list_item>
</unordered_list>
<text><location><page_2><loc_10><loc_33><loc_12><loc_35></location>38</text>
<text><location><page_2><loc_10><loc_29><loc_12><loc_31></location>39</text>
<text><location><page_2><loc_19><loc_29><loc_86><loc_31></location>Lammer et al. (2007) showed that planets in the habitable zones of M</text>
<unordered_list>
<list_item><location><page_2><loc_10><loc_26><loc_85><loc_28></location>dwarfs should experience frequent exposure to stellar corona mass 40</list_item>
<list_item><location><page_2><loc_10><loc_22><loc_86><loc_24></location>ejection events and as a result Earth-like planets in such environments 41</list_item>
<list_item><location><page_2><loc_10><loc_18><loc_86><loc_20></location>could have lost hundreds of bars of CO2 in the timescale of 1 Gyrs 42</list_item>
<list_item><location><page_2><loc_10><loc_14><loc_85><loc_17></location>through stellar wind interactions. But the energy consumed in such 43</list_item>
<list_item><location><page_2><loc_10><loc_11><loc_86><loc_13></location>massive atmospheric loss is not considered. Tian (2009) showed that 44</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_3><loc_10><loc_85><loc_86><loc_91></location>CO2-dominant atmospheres of super Earths with masses greater than 6 45 Earth masses should survive the long active phase of M dwarfs. But 46</list_item>
<list_item><location><page_3><loc_10><loc_81><loc_61><loc_83></location>nonthermal escape processes were not included. 47</list_item>
</unordered_list>
<text><location><page_3><loc_10><loc_78><loc_12><loc_79></location>48</text>
<text><location><page_3><loc_10><loc_37><loc_86><loc_76></location>Observed close-in exoplanets with masses in the range between Earth 49 and Uranus/Neptune, such as Corot-7B (Leger et al. 2009), GJ1214b 50 (Charbonneau 2009), 55 Cnc e (Winn et al. 2011), and several Kepler-11 51 planets (Lissauer et al. 2011), have inferred densities much different from 52 each other. Considering the small orbital distances between these planets 53 and their parent stars, these planetary atmospheres must be highly 54 expanded and atmospheric escape must be an important physical process 55 controlling the evolution histories and the nature of these objects. A better 56 understanding of the relationship between different atmospheric escape 57 processes and how upper atmosphere structure influences atmospheric 58 escape is urgently needed. 59</text>
<text><location><page_3><loc_10><loc_33><loc_12><loc_35></location>60</text>
<text><location><page_3><loc_10><loc_11><loc_86><loc_31></location>One classical theory on atmospheric escape is the diffusion-limited 61 escape (Hunten 1973), which provides an upper limit for the total escape 62 rate of minor species. In the case of hydrogen, its escape rate should be 63 proportional to the total mixing ratio of hydrogen-bearing species at the 64 homopause level. The diffusion-limited escape theory is the result of the 65 kinetics at the homopause level and does not consider the energy aspect 66</text>
<text><location><page_4><loc_10><loc_89><loc_12><loc_90></location>67</text>
<text><location><page_4><loc_15><loc_89><loc_38><loc_91></location>of atmospheric escape.</text>
<text><location><page_4><loc_10><loc_85><loc_12><loc_87></location>68</text>
<text><location><page_4><loc_10><loc_22><loc_86><loc_83></location>When a planetary atmosphere is exposed to intense stellar XUV 69 photon flux, which occurs on terrestrial planets during their early 70 evolution histories, close-in exoplanets, and small dwarf planets such as 71 present Pluto, the upper atmosphere is heated and temperature rises and 72 the atmosphere expands. For this scenario to occur, thermal conduction 73 through the lower boundary must be less than the net heating. When the 74 atmosphere expands to large distance, the gravity of the planet at the 75 exobase, the top of the atmosphere, becomes weak enough and major 76 atmospheric species escape more efficiently through either thermal or 77 nonthermal processes. When the escape of major atmospheric species is 78 efficient, the upper atmosphere flows outward and the adiabatic cooling 79 associated with the expansion of the rapidly escaping atmosphere 80 becomes a dominant part of the energy budget of planetary atmospheres 81 -- the hydrodynamic regime or a hydrodynamic planetary atmosphere 82 (Tian et al. 2008a, b). Because the diffusion-limited theory does not 83 consider energy required to support rapid escape, it cannot provide us a 84 good estimate on escape rate of major atmospheric species 85</text>
<text><location><page_4><loc_10><loc_18><loc_12><loc_20></location>86</text>
<text><location><page_4><loc_10><loc_15><loc_12><loc_16></location>87</text>
<text><location><page_4><loc_10><loc_11><loc_12><loc_12></location>88</text>
<text><location><page_4><loc_15><loc_11><loc_86><loc_17></location>Note that there is a difference between the above-mentioned hydrodynamic planetary atmosphere and the traditional hydrodynamic</text>
<unordered_list>
<list_item><location><page_5><loc_9><loc_44><loc_12><loc_49></location>100 101</list_item>
<list_item><location><page_5><loc_10><loc_44><loc_86><loc_91></location>escape, or blowoff, in that the hydrodynamic regime is reached when the 89 outflow is important in the energy budget of the upper atmosphere, while 90 the blowoff occurs when the heating of the upper atmosphere is so strong 91 that the kinetic energy of the upper atmosphere overcomes the gravity of 92 the planet. Thus a planetary atmosphere in the hydrodynamic regime does 93 not necessarily blow off. In such an atmosphere the gravitational potential 94 energy is more than the heat content or kinetic energy of the atmosphere 95 and the atmospheric escape is Jeans-like (evaporation) no matter whether 96 the actual escape process is thermal or nonthermal. Thus a planetary 97 atmosphere could be experiencing Jeans-like escape and in the 98 hydrodynamic regime simultaneously (Tian et al. 2008a). On the other 99 hand, blowoff can be considered an extreme case of planetary atmospheres in the hydrodynamic regime and energy consumption in the</list_item>
<list_item><location><page_5><loc_9><loc_40><loc_72><loc_43></location>outflow is the ultimate factor controlling the mass loss rate. 102</list_item>
</unordered_list>
<text><location><page_5><loc_9><loc_37><loc_12><loc_38></location>103</text>
<text><location><page_5><loc_9><loc_33><loc_12><loc_35></location>104</text>
<text><location><page_5><loc_9><loc_29><loc_12><loc_31></location>105</text>
<text><location><page_5><loc_9><loc_26><loc_12><loc_27></location>106</text>
<text><location><page_5><loc_9><loc_22><loc_12><loc_24></location>107</text>
<text><location><page_5><loc_15><loc_22><loc_86><loc_35></location>Linking the hydrogen content of early Earth's atmosphere with the nature of close-in super Earths, the key question this paper intends to address is: can the energy requirement in a hydrodynamic planetary atmosphere limit atmospheric escape?</text>
<text><location><page_5><loc_9><loc_18><loc_12><loc_20></location>108</text>
<unordered_list>
<list_item><location><page_5><loc_9><loc_10><loc_86><loc_17></location>2. Hydrodynamic Planetary Upper Atmospheres and the 109 Conservation of Total Escape Rate 110</list_item>
</unordered_list>
<text><location><page_6><loc_9><loc_51><loc_86><loc_91></location>Here a 1-D upper planetary atmosphere model, validated against the 111 upper atmosphere of the present Earth, is used to study the problem. The 112 model details can be found in Tian et al. (2008a, b). A key feature of the 113 model is that it can automatically adjust its upper boundary so that the 114 exobase, defined as where the scale height is comparable to the mean free 115 path, can be found and the adjusted Jeans escape rates of all species can 116 be calculated. When increasing the level of solar XUV radiation, both the 117 upper atmosphere temperature and the exobase altitude increase. At 5 118 times present solar mean XUV level (XUVx5), the exobase altitude can 119 reach more than 10 4 km and the upper atmosphere temperature can be 120 near 9000 K (Tian et al. 2008b). 121</text>
<text><location><page_6><loc_9><loc_48><loc_12><loc_49></location>122</text>
<text><location><page_6><loc_9><loc_11><loc_86><loc_46></location>To include other escape processes at the exobase level in addition to 123 Jeans escape, the Jeans escape effusion velocity at the exobase is 124 multiplied by 3, 10, and 20 times respectively. The calculated upper 125 atmosphere temperature profiles are shown in Fig. 1. The peak 126 temperature in the upper atmosphere cools with increasing escape 127 efficiency from 9000 K in the Jeans escape only case to 8000, 7500, and 128 7000 K in the 3x, 10x, and 20x more efficient atmosphere escape cases. 129 Correspondingly the exobase altitude decreases with increased escape 130 efficiency because of decreased scaleheight. Note that although the 131 scaleheight is inversely proportional to the temperature, the exobase 132</text>
<text><location><page_7><loc_9><loc_89><loc_12><loc_90></location>133</text>
<text><location><page_7><loc_15><loc_89><loc_29><loc_91></location>altitude is not.</text>
<text><location><page_7><loc_9><loc_85><loc_12><loc_87></location>134</text>
<text><location><page_7><loc_9><loc_33><loc_86><loc_83></location>The shrinking of the upper atmosphere with increasing escape 135 efficiency at the exobase level has an interesting consequence on the total 136 atmospheric escape rate, shown as a solid curve in Fig. 2. In comparison 137 the dashed line in Fig. 2 shows a linear increase of total escape with 138 enhanced escape efficiency if the upper atmosphere structure is not 139 influenced by atmospheric escape. When considering the energy required 140 to support a strong outflow, which is a consequence of rapid escape of 141 major atmosphere species, the total escape rate of such species remains 142 almost a constant (a conservation of total escape rate) when increasing 143 escape efficiency from the exobase level. The conservation of total escape 144 rate from a hydrodynamic planetary atmosphere is a demonstration of the 145 law of the conservation of energy -- changing the escape efficiency at the 146 exobase level does not change the total amount of energy heating the 147 upper atmosphere. 148</text>
<text><location><page_7><loc_9><loc_29><loc_12><loc_31></location>149</text>
<section_header_level_1><location><page_7><loc_9><loc_25><loc_31><loc_28></location>3. Discussion 150</section_header_level_1>
<text><location><page_7><loc_9><loc_11><loc_86><loc_24></location>The heating and cooling terms in the hydrodynamic planetary 151 atmosphere are shown in Fig. 3. The solid curves correspond to the black 152 curve in Fig. 1 (Jeans escape only). The dashed curves correspond to the 153 red curve in Fig. 1 (escape efficiency 10 times that of Jeans escape). 154</text>
<text><location><page_8><loc_9><loc_66><loc_86><loc_91></location>The blue curves represent the adiabatic cooling. The red curves represent 155 the net radiative heating, which includes absorption of stellar XUV 156 photons, the ionization, excitation, and dissociation of atmospheric 157 species, and transport of energetic electrons and the deposition of their 158 energy, heating from chemical reactions, and radiative cooling (for details 159 see Tian et al. 2008a, b). The magenta curves represent the thermal 160 conduction. 161</text>
<text><location><page_8><loc_9><loc_63><loc_12><loc_64></location>162</text>
<text><location><page_8><loc_9><loc_11><loc_86><loc_61></location>Fig. 3 shows that the adiabatic cooling associated with outflow is a 163 dominant cooling term in the upper thermosphere and its importance 164 increases with altitude, reflecting the increasing velocity of the outflow. 165 Although thermal conduction cooling is dominant near where the net 166 radiative heating peaks, because the net radiative heating is inadequate to 167 match the adiabatic cooling, thermal conduction becomes an important 168 heating term in the upper thermosphere, contributing to support the 169 outflow. When increasing the escape efficiency at the exobase level, the 170 outflow is enhanced in upper thermosphere, which causes the dashed blue 171 curve to increase more rapidly with altitude than the solid blue curve does. 172 The peak of the net radiative heating moves lower in altitude because the 173 atmosphere shrinks, which allows more stellar XUV photons to penetrate 174 to deeper altitudes. Fig. 3 and Fig. 1 show how a planetary upper 175 atmosphere in the hydrodynamic regime adjusts its structure and energy 176</text>
<unordered_list>
<list_item><location><page_9><loc_9><loc_77><loc_86><loc_91></location>distribution when different escape processes occur at the exobase level. 177 As a result of the law of the conservation of energy, the total escape rates 178 from the two atmospheres with quite different structures are almost 179 identical. 180</list_item>
</unordered_list>
<text><location><page_9><loc_9><loc_74><loc_12><loc_75></location>181</text>
<text><location><page_9><loc_9><loc_33><loc_86><loc_72></location>We further tested the 1-D upper atmosphere model with greater XUV 182 levels and in all cases the enhancements of atmospheric escape efficiency 183 lead to shrink of the upper atmosphere and the conservation of total 184 escape rate. For an upper atmosphere under weak XUV heating, the 185 escape is insignificant and the increased escape efficiency does not lead 186 to a strong outflow or cooling of the upper atmosphere. Thus the total 187 escape increases linearly with enhanced escape efficiency. Analysis 188 shows that the difference between the two cases is whether the cooling 189 caused by the gas outflow is important in the energy budget of the upper 190 atmosphere, which is the division between a hydrostatic and a 191 hydrodynamic planetary upper atmosphere. 192</text>
<text><location><page_9><loc_9><loc_29><loc_12><loc_31></location>193</text>
<text><location><page_9><loc_9><loc_11><loc_86><loc_28></location>Johnson et al. (2013) pointed out that if the deposition of energy in 194 the upmost layer of the thermosphere (where the ratio between the mean 195 free path and the scaleheight is >~0.1) is inefficient, nonthermal escape 196 processes can be ignored. This is equivalent of saying that the energy 197 deposited in the collision-dominant part of the atmosphere contributes to 198</text>
<unordered_list>
<list_item><location><page_10><loc_9><loc_89><loc_86><loc_91></location>the heating of the atmosphere and not to nonthermal escape processes. 199</list_item>
</unordered_list>
<text><location><page_10><loc_9><loc_55><loc_86><loc_87></location>Our model atmospheres include this heating process. From the 200 perspective of the exobase, the escape is Jeans-like in that the bulk 201 outflow velocity in our model remains subsonic, consistent with the 202 findings in Johnson et al. (2013). From the perspective of the energy 203 budget of the upper atmosphere, the escape is hydrodynamic because the 204 outflow cooling dominates the energy budget when the atmosphere is 205 under strong XUV radiation (Tian et al. 2008a). Thus escape can be 206 Jeans-like and hydrodynamic simultaneously, depending on from which 207 point of view the issue is observed. 208</text>
<text><location><page_10><loc_9><loc_52><loc_12><loc_53></location>209</text>
<text><location><page_10><loc_9><loc_11><loc_86><loc_50></location>Garcia-Munoz (2007) showed that the model calculated escape rates 210 from HD209458b are insensitive to the upper boundary conditions but the 211 upper atmospheric structures are. Koskinen et al. (2012) compared the 212 effects of different boundary conditions on the escape from hot Jupiters 213 and found that models with similar escape rates could produce different 214 upper atmospheric structures depending on the boundary conditions 215 applied. These results are in good agreement with ours and thus the 216 conservation of total escape rate theory proposed in this paper is also 217 supported by models with transonic hydrogen outflow from hot Jupiters. 218 In agreement with Koskinen et al. (2012), we emphasize that details of 219 the escape processes functioning at the exobase level are important for 220</text>
<text><location><page_11><loc_9><loc_85><loc_86><loc_91></location>understanding the upper atmosphere structures and thus are important to 221 compare with observations. 222</text>
<text><location><page_11><loc_9><loc_81><loc_12><loc_83></location>223</text>
<text><location><page_11><loc_9><loc_33><loc_86><loc_80></location>A recent hybrid fluid/kinetic model for the upper atmosphere of Pluto 224 (Erwin et al. 2013) shows that Pluto's exobase altitude and temperature 225 decreases as a result of increasing escape efficiency at the exobase level 226 and as a result the total escape rate from Pluto's N2-dominant atmosphere 227 remains near constant. This shows that the theory of the conservation of 228 total escape rate applies to hydrodynamic planetary atmosphere with 229 different composition. Erwin et al. (2013) pointed out that in order to 230 predict the upper atmosphere structure, a hybrid fluid/kinetic model is 231 needed because the enhancement of escape efficiency at the exobase level 232 does influence the upper atmosphere structure. We emphasize that if the 233 theory of the conservation of total escape is correct, a fluid model for the 234 planetary upper atmosphere would be adequate to understand the 235 atmospheric escape history of a planet. 236</text>
<text><location><page_11><loc_9><loc_29><loc_12><loc_31></location>237</text>
<text><location><page_11><loc_9><loc_11><loc_86><loc_28></location>The conservation of total escape rate from planetary atmospheres in 238 the hydrodynamic regime is demonstrated in 1-D models for the Earth's 239 current atmosphere composition under intense XUV heating, for the 240 current N2-dominant atmosphere of Pluto (Erwin et al. 2013), and for 241 transonic outflow from hot Jupiters (Garcia-Munoz 2007, Koskinen et al. 242</text>
<text><location><page_12><loc_9><loc_66><loc_86><loc_91></location>2012). Numerical simulations for atmospheres with different composition 243 around planets with different masses in 3-D models will be needed in 244 future studies to prove or disprove it. However we speculate that the 245 theory should apply to planetary atmospheres with different composition 246 because the law of the conservation of energy is universal and the escape 247 of hydrogen from such atmospheres under intense stellar/solar XUV 248 heating is always energy-limited. 249</text>
<text><location><page_12><loc_9><loc_63><loc_12><loc_64></location>250</text>
<text><location><page_12><loc_9><loc_14><loc_86><loc_61></location>If the theory is confirmed, one implication is that early Earth's 251 atmospheric hydrogen content should be close to those in Tian et al. 252 (2005) suggested, provided that those calculations are correct, and thus 253 hydrogen could have helped early Earth to stay warm (Wordsworth and 254 Pierrehumbert 2013). And the calculations of atmosphere escape during 255 the evolution histories of different planets could be significantly 256 simplified. The theory also implies that super Earths in close-in orbits can 257 have a better chance to keep their atmospheres and oceans, which might 258 help to explain the existence of low density rocky exoplanets such as 55 259 Cnc e and GJ1214b, and planets in the habitable zones of M dwarfs 260 should be able to keep their CO2-dominant atmospheres, supporting the 261 conclusion of Tian (2009), which could have consequences in the 262 evaluation of planetary habitability. 263</text>
<text><location><page_12><loc_9><loc_11><loc_12><loc_12></location>264</text>
<section_header_level_1><location><page_13><loc_9><loc_88><loc_30><loc_91></location>4. Conclusions 265</section_header_level_1>
<text><location><page_13><loc_9><loc_59><loc_86><loc_87></location>As a result of the law of the conservation of energy, the total escape 266 rate from planetary atmospheres in the hydrodynamic regime is nearly 267 constant under the same stellar XUV photon flux when increasing the 268 escape efficiency from the exobase level. Thus an energy-limited escape 269 approximation can be applied to such atmospheres, provided that the 270 upper atmosphere structures are calculated accurately. The estimate of 271 atmospheric escape in a planet's evolution history can be greatly 272 simplified. 273</text>
<text><location><page_13><loc_9><loc_55><loc_12><loc_57></location>274</text>
<text><location><page_13><loc_9><loc_48><loc_81><loc_54></location>Acknowledgement : The author thanks R.E. Johnson and the other 275 anonymous reviewer for their helpful comments and suggestions. 276</text>
<text><location><page_13><loc_9><loc_44><loc_12><loc_46></location>277</text>
<section_header_level_1><location><page_13><loc_9><loc_40><loc_29><loc_43></location>References: 278</section_header_level_1>
<text><location><page_13><loc_9><loc_33><loc_85><loc_39></location>Catling, D.C. www.sciencemag.org/cgi/content/full/311/5757/38a. 279 Science 311, 38 (2006) 280</text>
<text><location><page_13><loc_9><loc_25><loc_85><loc_31></location>Charbonneau, David et al. A super-Earth transiting a nearby low-mass 281 star. Nature 462, 891-894 (2009). 282</text>
<text><location><page_13><loc_9><loc_18><loc_86><loc_24></location>Erwin, J., Tucker, O.J., Johnson, R.E. Hybrid fluid/kinetic modeling of 283 Pluto's atmosphere", Icarus in press (2013) [arXiv:1211.3994 (2012)] 284</text>
<text><location><page_13><loc_9><loc_15><loc_12><loc_16></location>285</text>
<text><location><page_13><loc_15><loc_14><loc_85><loc_17></location>García-Muñoz, A. Physical and chemical aeronomy of HD 209458b.</text>
<text><location><page_13><loc_9><loc_11><loc_58><loc_13></location>Planet. Space Sci. , 55 , 1426-1455 (2007) 286</text>
<text><location><page_14><loc_15><loc_89><loc_85><loc_91></location>Hunten, D.M. The escape of light gases from planetary atmospheres. J.</text>
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<text><location><page_15><loc_9><loc_85><loc_85><loc_91></location>discoveries, Part II: Long time thermal atmospheric evaporation 309 modeling. Planet. Space Sci ., 56 , 1260-1272 (2008) 310</text>
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<list_item><location><page_15><loc_9><loc_66><loc_85><loc_76></location>Tian, F., Toon, O.B., Pavlov, A.A., de Sterck, H. Transonic 313 hydrodynamic escape of hydrogen from extrasolar planetary 314 atmospheres. Astrophys. J. 621, 1049-1060 (2005b) 315</list_item>
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<text><location><page_15><loc_9><loc_29><loc_85><loc_35></location>Tian, F. Thermal escape from super-Earth atmospheres in the habitable 324 zones of M stars. ApJ 703, 905-909 (2009) 325</text>
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<text><location><page_15><loc_9><loc_11><loc_86><loc_13></location>Yelle, R.V. Corrigendum to ''Aeronomy of extra-solar giant planets at 330</text>
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<text><location><page_16><loc_9><loc_53><loc_12><loc_55></location>332</text>
<figure>
<location><page_16><loc_15><loc_54><loc_84><loc_86></location>
<caption>Fig. 1 Upper atmosphere structures of the Earth under 5 times present 333 XUV radiation level with different escape effusion velocities at the 334 exobase level, which are where the curves end. 335</caption>
</figure>
<text><location><page_16><loc_9><loc_39><loc_12><loc_40></location>336</text>
<text><location><page_17><loc_9><loc_57><loc_12><loc_58></location>337</text>
<figure>
<location><page_17><loc_16><loc_57><loc_85><loc_90></location>
<caption>Fig. 2 Total escape rate of major atmosphere species as a function of 338 escape efficiency from the exobase level. The atmospheres used in these 339 simulations have composition the same as that of present Earth but are 340 under 5 times present Earth's XUV radiation level. If the upper 341 atmosphere structure is not influenced by escape of major atmospheric 342 species and the subsequent outflow, the total escape rate would have 343 increased linearly with enhanced escape efficiency at the exobase level as 344 shown by the dashed line. However, when considering the energy 345 consumption of outflow in the upper atmosphere, the upper atmosphere 346 cools and shrinks (shown in Fig. 1) and the total escape rate remains 347 conserved with enhanced escape efficiency at the exobase level. 348</caption>
</figure>
<text><location><page_17><loc_9><loc_13><loc_12><loc_14></location>349</text>
<text><location><page_18><loc_9><loc_56><loc_12><loc_58></location>351</text>
<figure>
<location><page_18><loc_15><loc_57><loc_88><loc_91></location>
<caption>Fig. 3 Heating and cooling terms in a hydrodynamic planetary 352 atmosphere. The solid curves correspond to the black curve in Fig. 1. The 353 dashed curves correspond to the red curve in Fig. 1. The blue curves are 354 the adiabatic cooling. The red curves are the net radiative heating. The 355 magenta curves are the thermal conduction. 356</caption>
</figure>
</document>
[
{
"title": "ABSTRACT",
"content": "1",
"pages": [
1
]
},
{
"title": "Feng Tian 1,2",
"content": "6 17",
"pages": [
1
]
},
{
"title": "1. Introduction 18",
"content": "28 2005b). However, the calculated upper atmosphere structures are 35 atmosphere would have been in the order of 0.1% instead of a few 38 39 Lammer et al. (2007) showed that planets in the habitable zones of M 48 Observed close-in exoplanets with masses in the range between Earth 49 and Uranus/Neptune, such as Corot-7B (Leger et al. 2009), GJ1214b 50 (Charbonneau 2009), 55 Cnc e (Winn et al. 2011), and several Kepler-11 51 planets (Lissauer et al. 2011), have inferred densities much different from 52 each other. Considering the small orbital distances between these planets 53 and their parent stars, these planetary atmospheres must be highly 54 expanded and atmospheric escape must be an important physical process 55 controlling the evolution histories and the nature of these objects. A better 56 understanding of the relationship between different atmospheric escape 57 processes and how upper atmosphere structure influences atmospheric 58 escape is urgently needed. 59 60 One classical theory on atmospheric escape is the diffusion-limited 61 escape (Hunten 1973), which provides an upper limit for the total escape 62 rate of minor species. In the case of hydrogen, its escape rate should be 63 proportional to the total mixing ratio of hydrogen-bearing species at the 64 homopause level. The diffusion-limited escape theory is the result of the 65 kinetics at the homopause level and does not consider the energy aspect 66 67 of atmospheric escape. 68 When a planetary atmosphere is exposed to intense stellar XUV 69 photon flux, which occurs on terrestrial planets during their early 70 evolution histories, close-in exoplanets, and small dwarf planets such as 71 present Pluto, the upper atmosphere is heated and temperature rises and 72 the atmosphere expands. For this scenario to occur, thermal conduction 73 through the lower boundary must be less than the net heating. When the 74 atmosphere expands to large distance, the gravity of the planet at the 75 exobase, the top of the atmosphere, becomes weak enough and major 76 atmospheric species escape more efficiently through either thermal or 77 nonthermal processes. When the escape of major atmospheric species is 78 efficient, the upper atmosphere flows outward and the adiabatic cooling 79 associated with the expansion of the rapidly escaping atmosphere 80 becomes a dominant part of the energy budget of planetary atmospheres 81 -- the hydrodynamic regime or a hydrodynamic planetary atmosphere 82 (Tian et al. 2008a, b). Because the diffusion-limited theory does not 83 consider energy required to support rapid escape, it cannot provide us a 84 good estimate on escape rate of major atmospheric species 85 86 87 88 Note that there is a difference between the above-mentioned hydrodynamic planetary atmosphere and the traditional hydrodynamic 103 104 105 106 107 Linking the hydrogen content of early Earth's atmosphere with the nature of close-in super Earths, the key question this paper intends to address is: can the energy requirement in a hydrodynamic planetary atmosphere limit atmospheric escape? 108 Here a 1-D upper planetary atmosphere model, validated against the 111 upper atmosphere of the present Earth, is used to study the problem. The 112 model details can be found in Tian et al. (2008a, b). A key feature of the 113 model is that it can automatically adjust its upper boundary so that the 114 exobase, defined as where the scale height is comparable to the mean free 115 path, can be found and the adjusted Jeans escape rates of all species can 116 be calculated. When increasing the level of solar XUV radiation, both the 117 upper atmosphere temperature and the exobase altitude increase. At 5 118 times present solar mean XUV level (XUVx5), the exobase altitude can 119 reach more than 10 4 km and the upper atmosphere temperature can be 120 near 9000 K (Tian et al. 2008b). 121 122 To include other escape processes at the exobase level in addition to 123 Jeans escape, the Jeans escape effusion velocity at the exobase is 124 multiplied by 3, 10, and 20 times respectively. The calculated upper 125 atmosphere temperature profiles are shown in Fig. 1. The peak 126 temperature in the upper atmosphere cools with increasing escape 127 efficiency from 9000 K in the Jeans escape only case to 8000, 7500, and 128 7000 K in the 3x, 10x, and 20x more efficient atmosphere escape cases. 129 Correspondingly the exobase altitude decreases with increased escape 130 efficiency because of decreased scaleheight. Note that although the 131 scaleheight is inversely proportional to the temperature, the exobase 132 133 altitude is not. 134 The shrinking of the upper atmosphere with increasing escape 135 efficiency at the exobase level has an interesting consequence on the total 136 atmospheric escape rate, shown as a solid curve in Fig. 2. In comparison 137 the dashed line in Fig. 2 shows a linear increase of total escape with 138 enhanced escape efficiency if the upper atmosphere structure is not 139 influenced by atmospheric escape. When considering the energy required 140 to support a strong outflow, which is a consequence of rapid escape of 141 major atmosphere species, the total escape rate of such species remains 142 almost a constant (a conservation of total escape rate) when increasing 143 escape efficiency from the exobase level. The conservation of total escape 144 rate from a hydrodynamic planetary atmosphere is a demonstration of the 145 law of the conservation of energy -- changing the escape efficiency at the 146 exobase level does not change the total amount of energy heating the 147 upper atmosphere. 148 149",
"pages": [
2,
3,
4,
5,
6,
7
]
},
{
"title": "3. Discussion 150",
"content": "The heating and cooling terms in the hydrodynamic planetary 151 atmosphere are shown in Fig. 3. The solid curves correspond to the black 152 curve in Fig. 1 (Jeans escape only). The dashed curves correspond to the 153 red curve in Fig. 1 (escape efficiency 10 times that of Jeans escape). 154 The blue curves represent the adiabatic cooling. The red curves represent 155 the net radiative heating, which includes absorption of stellar XUV 156 photons, the ionization, excitation, and dissociation of atmospheric 157 species, and transport of energetic electrons and the deposition of their 158 energy, heating from chemical reactions, and radiative cooling (for details 159 see Tian et al. 2008a, b). The magenta curves represent the thermal 160 conduction. 161 162 Fig. 3 shows that the adiabatic cooling associated with outflow is a 163 dominant cooling term in the upper thermosphere and its importance 164 increases with altitude, reflecting the increasing velocity of the outflow. 165 Although thermal conduction cooling is dominant near where the net 166 radiative heating peaks, because the net radiative heating is inadequate to 167 match the adiabatic cooling, thermal conduction becomes an important 168 heating term in the upper thermosphere, contributing to support the 169 outflow. When increasing the escape efficiency at the exobase level, the 170 outflow is enhanced in upper thermosphere, which causes the dashed blue 171 curve to increase more rapidly with altitude than the solid blue curve does. 172 The peak of the net radiative heating moves lower in altitude because the 173 atmosphere shrinks, which allows more stellar XUV photons to penetrate 174 to deeper altitudes. Fig. 3 and Fig. 1 show how a planetary upper 175 atmosphere in the hydrodynamic regime adjusts its structure and energy 176 181 We further tested the 1-D upper atmosphere model with greater XUV 182 levels and in all cases the enhancements of atmospheric escape efficiency 183 lead to shrink of the upper atmosphere and the conservation of total 184 escape rate. For an upper atmosphere under weak XUV heating, the 185 escape is insignificant and the increased escape efficiency does not lead 186 to a strong outflow or cooling of the upper atmosphere. Thus the total 187 escape increases linearly with enhanced escape efficiency. Analysis 188 shows that the difference between the two cases is whether the cooling 189 caused by the gas outflow is important in the energy budget of the upper 190 atmosphere, which is the division between a hydrostatic and a 191 hydrodynamic planetary upper atmosphere. 192 193 Johnson et al. (2013) pointed out that if the deposition of energy in 194 the upmost layer of the thermosphere (where the ratio between the mean 195 free path and the scaleheight is >~0.1) is inefficient, nonthermal escape 196 processes can be ignored. This is equivalent of saying that the energy 197 deposited in the collision-dominant part of the atmosphere contributes to 198 Our model atmospheres include this heating process. From the 200 perspective of the exobase, the escape is Jeans-like in that the bulk 201 outflow velocity in our model remains subsonic, consistent with the 202 findings in Johnson et al. (2013). From the perspective of the energy 203 budget of the upper atmosphere, the escape is hydrodynamic because the 204 outflow cooling dominates the energy budget when the atmosphere is 205 under strong XUV radiation (Tian et al. 2008a). Thus escape can be 206 Jeans-like and hydrodynamic simultaneously, depending on from which 207 point of view the issue is observed. 208 209 Garcia-Munoz (2007) showed that the model calculated escape rates 210 from HD209458b are insensitive to the upper boundary conditions but the 211 upper atmospheric structures are. Koskinen et al. (2012) compared the 212 effects of different boundary conditions on the escape from hot Jupiters 213 and found that models with similar escape rates could produce different 214 upper atmospheric structures depending on the boundary conditions 215 applied. These results are in good agreement with ours and thus the 216 conservation of total escape rate theory proposed in this paper is also 217 supported by models with transonic hydrogen outflow from hot Jupiters. 218 In agreement with Koskinen et al. (2012), we emphasize that details of 219 the escape processes functioning at the exobase level are important for 220 understanding the upper atmosphere structures and thus are important to 221 compare with observations. 222 223 A recent hybrid fluid/kinetic model for the upper atmosphere of Pluto 224 (Erwin et al. 2013) shows that Pluto's exobase altitude and temperature 225 decreases as a result of increasing escape efficiency at the exobase level 226 and as a result the total escape rate from Pluto's N2-dominant atmosphere 227 remains near constant. This shows that the theory of the conservation of 228 total escape rate applies to hydrodynamic planetary atmosphere with 229 different composition. Erwin et al. (2013) pointed out that in order to 230 predict the upper atmosphere structure, a hybrid fluid/kinetic model is 231 needed because the enhancement of escape efficiency at the exobase level 232 does influence the upper atmosphere structure. We emphasize that if the 233 theory of the conservation of total escape is correct, a fluid model for the 234 planetary upper atmosphere would be adequate to understand the 235 atmospheric escape history of a planet. 236 237 The conservation of total escape rate from planetary atmospheres in 238 the hydrodynamic regime is demonstrated in 1-D models for the Earth's 239 current atmosphere composition under intense XUV heating, for the 240 current N2-dominant atmosphere of Pluto (Erwin et al. 2013), and for 241 transonic outflow from hot Jupiters (Garcia-Munoz 2007, Koskinen et al. 242 2012). Numerical simulations for atmospheres with different composition 243 around planets with different masses in 3-D models will be needed in 244 future studies to prove or disprove it. However we speculate that the 245 theory should apply to planetary atmospheres with different composition 246 because the law of the conservation of energy is universal and the escape 247 of hydrogen from such atmospheres under intense stellar/solar XUV 248 heating is always energy-limited. 249 250 If the theory is confirmed, one implication is that early Earth's 251 atmospheric hydrogen content should be close to those in Tian et al. 252 (2005) suggested, provided that those calculations are correct, and thus 253 hydrogen could have helped early Earth to stay warm (Wordsworth and 254 Pierrehumbert 2013). And the calculations of atmosphere escape during 255 the evolution histories of different planets could be significantly 256 simplified. The theory also implies that super Earths in close-in orbits can 257 have a better chance to keep their atmospheres and oceans, which might 258 help to explain the existence of low density rocky exoplanets such as 55 259 Cnc e and GJ1214b, and planets in the habitable zones of M dwarfs 260 should be able to keep their CO2-dominant atmospheres, supporting the 261 conclusion of Tian (2009), which could have consequences in the 262 evaluation of planetary habitability. 263 264",
"pages": [
7,
8,
9,
10,
11,
12
]
},
{
"title": "4. Conclusions 265",
"content": "As a result of the law of the conservation of energy, the total escape 266 rate from planetary atmospheres in the hydrodynamic regime is nearly 267 constant under the same stellar XUV photon flux when increasing the 268 escape efficiency from the exobase level. Thus an energy-limited escape 269 approximation can be applied to such atmospheres, provided that the 270 upper atmosphere structures are calculated accurately. The estimate of 271 atmospheric escape in a planet's evolution history can be greatly 272 simplified. 273 274 Acknowledgement : The author thanks R.E. Johnson and the other 275 anonymous reviewer for their helpful comments and suggestions. 276 277",
"pages": [
13
]
},
{
"title": "References: 278",
"content": "Catling, D.C. www.sciencemag.org/cgi/content/full/311/5757/38a. 279 Science 311, 38 (2006) 280 Charbonneau, David et al. A super-Earth transiting a nearby low-mass 281 star. Nature 462, 891-894 (2009). 282 Erwin, J., Tucker, O.J., Johnson, R.E. Hybrid fluid/kinetic modeling of 283 Pluto's atmosphere\", Icarus in press (2013) [arXiv:1211.3994 (2012)] 284 285 García-Muñoz, A. Physical and chemical aeronomy of HD 209458b. Planet. Space Sci. , 55 , 1426-1455 (2007) 286 Hunten, D.M. The escape of light gases from planetary atmospheres. J. , discoveries, Part II: Long time thermal atmospheric evaporation 309 modeling. Planet. Space Sci ., 56 , 1260-1272 (2008) 310 316 317 318 Tian, F. Thermal escape from super-Earth atmospheres in the habitable 324 zones of M stars. ApJ 703, 905-909 (2009) 325 Yelle, R.V. Corrigendum to ''Aeronomy of extra-solar giant planets at 330",
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{
"title": "small orbital distances''. Icarus 183, 508 (2006) 331",
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2013GReGr..45..691L
https://arxiv.org/pdf/1301.5796.pdf
<document>
<section_header_level_1><location><page_1><loc_25><loc_80><loc_72><loc_92></location>Weak field approximation in a model of de Sitter gravity: Schwarzschild solutions and galactic rotation curves</section_header_level_1>
<text><location><page_1><loc_26><loc_74><loc_70><loc_77></location>Jia-An Lu a ∗ and Chao-Guang Huang b †</text>
<unordered_list>
<list_item><location><page_1><loc_16><loc_69><loc_81><loc_73></location>a School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China</list_item>
<list_item><location><page_1><loc_19><loc_66><loc_78><loc_69></location>b Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049, China</list_item>
</unordered_list>
<section_header_level_1><location><page_1><loc_45><loc_61><loc_53><loc_62></location>Abstract</section_header_level_1>
<text><location><page_1><loc_17><loc_46><loc_81><loc_59></location>Weak field approximate solutions in the Λ → 0 limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotation curves without invoking dark matter.</text>
<text><location><page_1><loc_17><loc_42><loc_74><loc_44></location>Keywords: de Sitter gravity, Schwarzschild solutions, torsion, dark matter</text>
<section_header_level_1><location><page_1><loc_12><loc_37><loc_34><loc_39></location>1 Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_12><loc_86><loc_36></location>In the 1970s a model of de Sitter (dS) gravity had been proposed [1-4]. In this model the Einstein-Hilbert action with a cosmological term could be deduced from a gauge-like action besides two quadratic terms of the curvature and torsion. The astronomical observation [5, 6] on the asymptotically dS behavior of our universe has increased interest in the model as it may offer a way to deal with the dark energy problem [7]. If the EinsteinHilbert term is required to be the main part of the gauge-like action, the cosmological constant should be large. The large cosmological constant may be canceled out by the vacuum energy density, leaving a small cosmological constant [4]. But it is difficult to explain why the large cosmological constant and the vacuum energy density are so close, but not exactly equal, to each other. On the other hand, if the cosmological constant is required to be small [1-3, 8], the quadratic curvature term would become the main part of the action. Note that in one of the field equations, the quadratic curvature term only contributes to the symmetric trace-free part. It is worth checking carefully whether the</text>
<text><location><page_2><loc_12><loc_77><loc_86><loc_91></location>model under this case could explain the experimental observations. Actually it has been shown [9, 10] that the model with a small cosmological constant may explain the accelerating expansion of the universe and supply a natural transit from decelerating expansion to accelerating expansion without the help of introducing matter fields in addition to dust. It has also been shown [11, 12] that all torsion-free vacuum solutions of this model are the vacuum solutions of Einstein's field equation with the same cosmological constant, and vise versa. Therefore, one may expect that the model with a small cosmological constant may pass all solar-system-scale experimental tests for general relativity (GR).</text>
<text><location><page_2><loc_12><loc_59><loc_86><loc_77></location>However, it has been pointed out [9] that the energy-momentum-stress tensor of a spinless fluid in the torsion-free case of this model should be with a constant trace. Questions would then appear such as, could the torsion-free Schwarzschild-dS (S-dS) solution be smoothly connected to internal solutions with nonzero torsion, or are there any S-dS solutions with nonzero torsion? In fact, the different dS spacetimes with nonzero torsion in this model have been obtained in [13, 14], but they are sill not the S-dS solutions. On the other hand, S-dS solutions with long-range spherically symmetric torsion have been given [15] in some special cases (not necessarily under the double duality ansatz [16]) of quadratic models of Poincar'e gauge theory of gravity, but our model does not fall into those special cases.</text>
<text><location><page_2><loc_12><loc_35><loc_86><loc_58></location>We would like to firstly check the existence of the S-dS solutions with nonzero torsion in the weak field approximation. The Newtonian limit of general quadratic models in Poincar'e gauge theory of gravity has been calculated [17, 18] in the 1980's. In those calculations, quadratic terms in the field equations have been thrown away as usual. However, in the weak field approximation of our model, the quadratic curvature terms could not be easily thrown away, for the reason that they are the main parts of one of the field equations. In fact, we may let the cosmological constant be Λ → 0, then only those quadratic curvature terms would appear in the limit of the field equation which contains the energy-momentum-stress tensor of the matter field. On the other hand, as those quadratic curvature terms are symmetric and trace-free, they would not appear in the trace part and the antisymmetric part of the field equations. The Newtonian limit of the trace equations has been recently analyzed [19], but a more complete analysis of all components of the field equations is needed.</text>
<text><location><page_2><loc_12><loc_22><loc_86><loc_35></location>As was well known, Newton's theory of gravity meets great difficulties in the explanation of the flat rotation curves [20] of spiral galaxies. The most widely adopted way to resolve this problem is the dark matter hypothesis. But up to now, all of the possible candidates of dark matter (such as neutralino, axion, etc.) are either undetected or unsatisfactory. In the meanwhile, there also exist some models [21-24] which could deduce the galactic rotation curves without involving dark matter. We would like to explore the possibility of a new explanation for the galactic rotation curves from the dS gravity model.</text>
<text><location><page_2><loc_12><loc_6><loc_86><loc_22></location>The paper is arranged as follows. We first briefly review the model of the dS gravity in section 2. In the third section, after dividing a field equation into its trace part, symmetric trace-free part and antisymmetric part, we attain the Λ → 0 limit of the model and calculate its weak field approximation in the static and spherically symmetric case. The weak field approximate solutions contain the weak Schwarzschild fields with nonzero torsion, which could be smoothly linked to regular internal solutions obeying the Newtonian gravitational law. The coupling constant is determined by the existence of such solutions. Moreover, solutions that could deduce the galactic rotation curves without invoking dark matter are also attained. Finally we end with some remarks in the</text>
<text><location><page_3><loc_12><loc_90><loc_22><loc_91></location>last section.</text>
<section_header_level_1><location><page_3><loc_12><loc_85><loc_47><loc_87></location>2 A model of dS gravity</section_header_level_1>
<text><location><page_3><loc_12><loc_81><loc_74><loc_83></location>A model of dS gravity has been constructed with a gauge-like action [1-4]</text>
<formula><location><page_3><loc_28><loc_72><loc_86><loc_80></location>S G = ∫ L G = ∫ κ [ -tr( F ab F ab )] = ∫ κ [ R abcd R abcd -4 l 2 ( R -6 l 2 ) + 2 l 2 S abc S abc ] (1)</formula>
<text><location><page_3><loc_12><loc_68><loc_86><loc_71></location>in the units of /planckover2pi1 = c = 1, where κ is a dimensionless coupling constant to be determined, and</text>
<formula><location><page_3><loc_39><loc_64><loc_86><loc_68></location>F ab = ( d A + 1 2 [ A , A ]) ab (2)</formula>
<text><location><page_3><loc_12><loc_62><loc_22><loc_64></location>or explicitly</text>
<formula><location><page_3><loc_29><loc_55><loc_86><loc_61></location>F A Bab = ( d A A B ) ab + A A Ca ∧A C Bb = ( R ab α β -l -2 e α a ∧ e βb l -1 S α ab -l -1 S βab 0 ) (3)</formula>
<text><location><page_3><loc_12><loc_52><loc_40><loc_53></location>is a dS algebra-valued 2-form and</text>
<formula><location><page_3><loc_36><loc_47><loc_86><loc_50></location>A A Ba = ( Γ α βa l -1 e α a -l -1 e βa 0 ) (4)</formula>
<text><location><page_3><loc_12><loc_34><loc_86><loc_45></location>is a dS algebra-valued 1-form. Here A, B... = 0 , 1 , 2 , 3 , 4 stand for matrix indices (internal indices) and the trace in Eq. (1) is taken for those indices. In addition, { e α a } is some local orthonormal frame field on the spacetime manifold and Γ α βa is the connection 1-form in this frame field, where a, b... stand for abstract indices [25, 26] and α, β... = 0 , 1 , 2 , 3 are concrete indices related to the frame field mentioned above. The curvature 2-form R ab α β and torsion 2-form S α ab are related to the connection 1-form Γ α βa as follows:</text>
<formula><location><page_3><loc_35><loc_31><loc_86><loc_33></location>R ab α β = ( d Γ α β ) ab +Γ α γa ∧ Γ γ βb , (5)</formula>
<formula><location><page_3><loc_37><loc_28><loc_86><loc_30></location>S α ab = ( de α ) ab +Γ α βa ∧ e β b . (6)</formula>
<text><location><page_3><loc_12><loc_25><loc_20><loc_27></location>Moreover,</text>
<formula><location><page_3><loc_33><loc_21><loc_65><loc_25></location>R abc d = R abα β e α c e β d , S c ab = S α ab e α c , R ab = R acb c , R = g ab R ab .</formula>
<text><location><page_3><loc_12><loc_5><loc_86><loc_20></location>In fact, if spacetime is an umbilical submanifold of some (1+4)-dimensional ambient manifold and with positive normal curvature, then A a and F ab could be viewed [8] as the connection 1-form and curvature 2-form (in the dS-Lorentz frame) of the ambient manifold restricted to spacetime. Here, an umbilical submanifold means a submanifold with constant normal curvature, such as the dS spacetime which could be seen as an umbilical submanifold of a 5d Minkowski spacetime with positive normal curvature. A a could also be seen [27] as the Cartan connection of a Cartan geometry modeled on the dS spacetime and based on the spacetime manifold, with F ab the corresponding curvature</text>
<text><location><page_4><loc_12><loc_82><loc_86><loc_91></location>2-form. The Cartan geometry is a generalization of homogenous spaces with fibre bundle language, and one may refer to [27] for more details. In addition, it should be noted that 3 /l 2 is identified [8] with a small cosmological constant Λ here, which is very different from the viewpoint of [4] where l is identified with the Planck length. The signature is chosen such that the metric coefficients are η αβ = diag( -1 , 1 , 1 , 1).</text>
<text><location><page_4><loc_12><loc_79><loc_86><loc_82></location>The total action is S = S M + S G , where S M is the action of the matter fields and the field equations can be given via the variational principle with respect to e α a , Γ α βa :</text>
<formula><location><page_4><loc_27><loc_70><loc_86><loc_77></location>8 l 2 ( G ab +Λ g ab ) + | R | 2 g ab -4 R acde R b cde + 2 l 2 | S | 2 g ab -8 l 2 S cda S cd b + 8 l 2 ∇ c S ab c + 4 l 2 S acd T b cd + 1 κ Σ ab = 0 , (7)</formula>
<formula><location><page_4><loc_25><loc_66><loc_86><loc_69></location>-4 l 2 T a bc -4 ∇ d R da bc +2 T a de R de bc -8 l 2 S [ bc ] a + 1 κ τ bc a = 0 , (8)</formula>
<formula><location><page_4><loc_30><loc_53><loc_68><loc_64></location>G ab = R ab -1 2 Rg ab , T c ab = S c ab +2 δ c [ a S d b ] d , | R | 2 = R abcd R abcd , | S | 2 = S abc S abc , Σ α a = δS M /δe α a , Σ b a = Σ α a e α b , τ α βa = δS M /δ Γ α βa , τ b ca = τ α βa e α b e β c ,</formula>
<text><location><page_4><loc_12><loc_64><loc_17><loc_65></location>where</text>
<text><location><page_4><loc_12><loc_51><loc_58><loc_52></location>and the variational derivatives are defined as follows: if</text>
<formula><location><page_4><loc_35><loc_46><loc_63><loc_50></location>δS M = ∫ ( X α a δe α a + Y αβ a δ Γ αβ a ) ,</formula>
<text><location><page_4><loc_12><loc_43><loc_15><loc_45></location>then</text>
<formula><location><page_4><loc_32><loc_41><loc_66><loc_43></location>δS M /δe α a = X α a , δS M /δ Γ αβ a = Y [ αβ ] a .</formula>
<section_header_level_1><location><page_4><loc_12><loc_36><loc_84><loc_38></location>3 Weak field approximation in the case with Λ → 0</section_header_level_1>
<text><location><page_4><loc_12><loc_24><loc_86><loc_35></location>As Λ is very small, it is interesting to see the case with Λ → 0 ( l → ∞ ). If Λ → 0 is directly set in the first field equation, then only the quadratic curvature terms are left, which are symmetric and trace-free. Thus, we would like to perform the following procedure. Divide the first field equation into its symmetric trace-free part, trace part, and antisymmetric part, then let l tend to infinity ( l →∞ ) in the above three parts and in the second field equation. The limiting equations are:</text>
<formula><location><page_4><loc_38><loc_21><loc_86><loc_23></location>| R | 2 g ab -4 R acde R b cde = 0 , (9)</formula>
<formula><location><page_4><loc_31><loc_16><loc_86><loc_19></location>-R -∇ c S bc b + 1 2 S bcd T bcd +( l 2 / 8 κ )Σ = 0 , (10)</formula>
<formula><location><page_4><loc_29><loc_12><loc_86><loc_16></location>R [ ab ] + ∇ c S [ ab ] c + 1 2 S [ a cd T b ] cd +( l 2 / 8 κ )Σ [ ab ] = 0 , (11)</formula>
<formula><location><page_4><loc_37><loc_10><loc_86><loc_11></location>-2 ∇ d R da bc + T a de R de bc = 0 . (12)</formula>
<text><location><page_4><loc_12><loc_5><loc_86><loc_9></location>When l → ∞ , l 2 /κ should tend to a finite value, otherwise Eqs. (10) and (11) would give Σ = 0 and Σ [ ab ] = 0, which are unreasonable. In the torsion-free case, the scalar</text>
<text><location><page_5><loc_12><loc_86><loc_86><loc_91></location>curvature would be a constant from Eq. (12), and, therefore, Σ = const from Eq. (10). This property has been pointed out by [9]. Now we are going to consider the week field approximation of the above equations. It would be assumed that</text>
<formula><location><page_5><loc_32><loc_83><loc_86><loc_84></location>g ab = η ab + γ ab , γ ab = O ( s ) , S c ab = O ( s ) , (13)</formula>
<formula><location><page_5><loc_38><loc_79><loc_86><loc_81></location>Σ ab = O ( s ) , τ ab c = O ( s ) , (14)</formula>
<text><location><page_5><loc_12><loc_71><loc_86><loc_78></location>where s is a dimensionless parameter, called the weak field parameter. We will restrict ourselves to the static and O (3)-symmetric case, with the static spherical coordinate system { t, r, θ, ϕ } . η ab could be defined by its components η µν = diag( -1 , 1 , 1 , 1) in the approximate inertial coordinate system { x µ } . { x µ } is related to { t, r, θ, ϕ } as usual:</text>
<formula><location><page_5><loc_25><loc_68><loc_72><loc_70></location>x 0 = t, x 1 = r sin θ cos ϕ, x 2 = r sin θ sin ϕ, x 3 = r cos θ.</formula>
<text><location><page_5><loc_12><loc_63><loc_86><loc_66></location>It could be proved [15, 25, 28] that γ ab and S c ab have only these dependent components in the static spherical coordinate system:</text>
<formula><location><page_5><loc_36><loc_59><loc_86><loc_61></location>γ 00 = -2 φ ( r ) , γ rr = -2 ψ ( r ) , (15)</formula>
<formula><location><page_5><loc_35><loc_52><loc_86><loc_58></location> S 0 0 r = f ( r ) , S r 0 r = h ( r ) , S θ rθ = g ( r ) , S θ 0 θ = -k ( r ) , S ϕ rϕ = g ( r ) , S ϕ 0 ϕ = -k ( r ) , (16)</formula>
<text><location><page_5><loc_12><loc_46><loc_86><loc_54></location> where φ plays the role of the Newtonian gravitational potential [1-3, 25, 29] and ψ is an unknown function. It can be shown that components of γ ab and S c ab in { x µ } are as follows:</text>
<formula><location><page_5><loc_30><loc_44><loc_86><loc_46></location>γ 00 = -2 φ, γ 0 i = 0 , γ ij = ( -2 ψ ) x i x j /r 2 , (17)</formula>
<formula><location><page_5><loc_35><loc_36><loc_86><loc_43></location> S 0 0 i = fx i /r, S 0 ij = 0 , S i 0 j = ( h + k ) x i x j /r 2 -kδ i j , S i jk = ( -g/r )( δ i j x k -δ i k x j ) . (18)</formula>
<text><location><page_5><loc_12><loc_36><loc_69><loc_37></location>For this case the contorsion tensor is related to the torsion tensor by</text>
<formula><location><page_5><loc_44><loc_32><loc_86><loc_34></location>K abc = S cba . (19)</formula>
<text><location><page_5><loc_12><loc_27><loc_86><loc_31></location>Let Γ c ab = Γ σ µν ∂ σ c ( dx µ ) a ( dx ν ) b , where Γ σ µν is the connection coefficient in { x µ } . Γ c ab and the curvature tensor have the following first order approximate expressions:</text>
<formula><location><page_5><loc_32><loc_22><loc_86><loc_26></location>Γ c ab = 1 2 ( ∂ a γ b c + ∂ b γ a c -∂ c γ ab ) -K c ab , (20)</formula>
<formula><location><page_5><loc_30><loc_19><loc_86><loc_21></location>R abc d = -( ∂ c ∂ [ a γ b ] d -∂ d ∂ [ a γ b ] c ) + 2 ∂ [ a K d | c | b ] , (21)</formula>
<formula><location><page_5><loc_37><loc_13><loc_86><loc_17></location>K c ab = 1 2 ( S c ab + S ab c + S ba c ) (22)</formula>
<text><location><page_5><loc_12><loc_17><loc_17><loc_18></location>where</text>
<text><location><page_5><loc_12><loc_9><loc_86><loc_13></location>is the contorsion tensor. In the case with Σ ab = ρ ( r )( dt ) a ( dt ) b , the equations for the first order approximate g ab and S c ab are as follows:</text>
<formula><location><page_5><loc_38><loc_6><loc_86><loc_8></location>| R | 2 η ab -4 R acde R b cde = 0 , (23)</formula>
<formula><location><page_6><loc_38><loc_90><loc_86><loc_91></location>R + ∂ c S bc b +( l 2 / 8 κ ) ρ = 0 , (24)</formula>
<formula><location><page_6><loc_41><loc_87><loc_86><loc_89></location>R [ ab ] + ∂ c S [ ab ] c = 0 , (25)</formula>
<formula><location><page_6><loc_44><loc_85><loc_86><loc_87></location>∂ d R da bc = 0 . (26)</formula>
<text><location><page_6><loc_12><loc_79><loc_86><loc_84></location>The first order approximation of Eq. (9) is an identity. Here Eq. (23) is the second order approximation of Eq. (9). It should be considered for the reason that it is still an equation for the first order approximate g ab and S c ab .</text>
<text><location><page_6><loc_12><loc_75><loc_86><loc_78></location>Now we are going to solve the above weak field equations. Applying Eq. (21) to Eq. (26), we have</text>
<formula><location><page_6><loc_37><loc_73><loc_86><loc_75></location>∂ d ( ∂ [ d ∂ [ c γ b ] a ] + ∂ [ d K cb a ] ) = 0 . (27)</formula>
<text><location><page_6><loc_12><loc_71><loc_45><loc_72></location>The 00 i ( abc ) component of Eq. (27) is</text>
<formula><location><page_6><loc_38><loc_68><loc_60><loc_69></location>∂ d ( ∂ d ∂ i γ 00 +2 ∂ d K i 00 ) = 0 ,</formula>
<text><location><page_6><loc_12><loc_65><loc_21><loc_66></location>which gives</text>
<formula><location><page_6><loc_27><loc_60><loc_71><loc_65></location>/triangle [( φ ' + f ) x i /r ] = 0 , i.e. ( φ ' + f ) '' /r +2( φ ' + f ) ' /r 2 -2( φ ' + f ) /r 3 = 0 .</formula>
<text><location><page_6><loc_12><loc_58><loc_40><loc_60></location>Solving this equation we get that</text>
<formula><location><page_6><loc_40><loc_55><loc_86><loc_57></location>φ ' + f = Cr + D/r 2 . (28)</formula>
<text><location><page_6><loc_12><loc_52><loc_79><loc_54></location>The 0 ij component of Eq. (27) is an identity. The i 0 j component of Eq. (27) is</text>
<formula><location><page_6><loc_38><loc_49><loc_59><loc_51></location>∂ d ∂ d K j 0 i -∂ d ∂ i K j 0 d = 0 ,</formula>
<text><location><page_6><loc_12><loc_46><loc_21><loc_48></location>which gives</text>
<formula><location><page_6><loc_21><loc_40><loc_77><loc_45></location>δ ij ( -/triangle k -h ' /r ) + ( x i x j /r 2 )[ /triangle k + h ' /r -2 k ' /r -2( h + k ) /r 2 ] = 0 , i.e. /triangle k + h ' /r = 0 , /triangle k + h ' /r -2 k ' /r -2( h + k ) /r 2 = 0 ,</formula>
<text><location><page_6><loc_12><loc_38><loc_24><loc_39></location>or equivalently</text>
<formula><location><page_6><loc_42><loc_36><loc_86><loc_38></location>h + k + rk ' = 0 . (29)</formula>
<text><location><page_6><loc_12><loc_34><loc_40><loc_35></location>The ijk component of Eq. (27) is</text>
<formula><location><page_6><loc_17><loc_31><loc_81><loc_32></location>∂ d ∂ d ∂ k γ ji -∂ d ∂ d ∂ j γ ki -∂ d ∂ i ∂ k γ jd + ∂ d ∂ i ∂ j γ kd +2 ∂ d ∂ d K kji -2 ∂ d ∂ i K kjd = 0 ,</formula>
<text><location><page_6><loc_12><loc_28><loc_21><loc_29></location>which gives</text>
<formula><location><page_6><loc_28><loc_23><loc_70><loc_28></location>/triangle [(2 ψ/r 2 -2 g/r )( δ ik x j -δ ij x k )] = 0 , i.e. (2 ψ/r 2 -2 g/r ) '' +(4 /r )(2 ψ/r 2 -2 g/r ) ' = 0 .</formula>
<text><location><page_6><loc_12><loc_21><loc_40><loc_22></location>Solving this equation we get that</text>
<formula><location><page_6><loc_39><loc_18><loc_86><loc_20></location>ψ/r 2 -g/r = B/r 3 + A. (30)</formula>
<text><location><page_6><loc_12><loc_13><loc_86><loc_17></location>From Eqs. (21), (17) and (18) the components of R abcd in { x µ } could be attained as follows:</text>
<formula><location><page_6><loc_19><loc_3><loc_86><loc_12></location> R 0 i 0 j = ( φ '' + f ' ) x i x j /r 2 +( φ ' + f )( δ ij r 2 -x i x j ) /r 3 , R 0 ijk = 0 , R ijk 0 = (2 /r 2 )( h + k + rk ' ) x [ i δ j ] k , R ijkl = ( ψ/r 2 -g/r ) ' (2 /r ) x [ i ( δ j ] k x l -δ j ] l x k ) -4( ψ/r 2 -g/r ) δ i [ k δ l ] j . (31)</formula>
<text><location><page_7><loc_12><loc_90><loc_74><loc_91></location>Substituting Eqs. (28), (29) and (30) into the above equation, we get that</text>
<text><location><page_7><loc_12><loc_78><loc_16><loc_79></location>Then</text>
<formula><location><page_7><loc_20><loc_79><loc_86><loc_88></location> R 0 i 0 j = ( Cr + D/r 2 ) ' x i x j /r 2 +( Cr + D/r 2 )( δ ij r 2 -x i x j ) /r 3 , R 0 ijk = 0 , R ijk 0 = 0 , R ijkl = ( B/r 3 + A ) ' (2 /r ) x [ i ( δ j ] k x l -δ j ] l x k ) -4( B/r 3 + A ) δ i [ k δ l ] j . (32)</formula>
<formula><location><page_7><loc_16><loc_67><loc_86><loc_77></location>| R | 2 η 00 -4 R 0 cde R 0 cde = 12( C 2 -4 A 2 ) + 24( D 2 -B 2 ) /r 6 , | R | 2 η 0 i -4 R 0 cde R i cde = 0 , | R | 2 η ij -4 R icde R j cde = (4 C 2 -16 A 2 -16 CD/r 3 -32 AB/r 3 +16 D 2 /r 6 -16 B 2 /r 6 ) δ ij +(48 CD/r 3 +96 AB/r 3 -24 D 2 /r 6 +24 B 2 /r 6 ) x i x j /r 2 , (33)</formula>
<formula><location><page_7><loc_24><loc_59><loc_86><loc_66></location>R 00 = 3 C, R 0 i = R i 0 = 0 , R ij = -( C + D/r 3 +4 A + B/r 3 ) δ ij +[3( B + D ) /r 3 ] x i x j /r 2 , R = -6( C +2 A ) , (34)</formula>
<text><location><page_7><loc_12><loc_54><loc_86><loc_57></location>Applying Eq. (33), the symmetric trace-free equation (23) could be solved, resulting in the following relations:</text>
<formula><location><page_7><loc_33><loc_51><loc_86><loc_52></location>C = ± 2 A, B = ± D, CD +2 AB = 0 . (35)</formula>
<text><location><page_7><loc_12><loc_46><loc_86><loc_49></location>From Eq. (34) one could see that R [ ab ] = 0 and thus the antisymmetric equation (25) gives ∂ c S [ ab ] c = 0. Components of ∂ c S ab c are as follows:</text>
<formula><location><page_7><loc_30><loc_37><loc_86><loc_44></location>∂ c S 00 c = -f ' -2 f/r, ∂ c S 0 i c = 0 , ∂ c S i 0 c = x i [ h ' /r +2( h + k ) /r 2 ] , ∂ c S ij c = [ -2( g/r ) -r ( g/r ) ' ] δ ij +( g/r ) ' x i x j /r. (36)</formula>
<text><location><page_7><loc_12><loc_33><loc_39><loc_35></location>Therefore, ∂ c S [ ab ] c = 0 results in</text>
<formula><location><page_7><loc_39><loc_30><loc_86><loc_32></location>h ' /r +2( h + k ) /r 2 = 0 . (37)</formula>
<text><location><page_7><loc_12><loc_27><loc_44><loc_28></location>Combining Eqs. (29) and (37) we have</text>
<formula><location><page_7><loc_33><loc_20><loc_86><loc_25></location>( h -2 k ) ' = 0 , h + k = -r ( h + k ) ' / 3 , h = 2 k + C 1 , h + k = C 2 /r 3 . (38)</formula>
<text><location><page_7><loc_15><loc_18><loc_81><loc_19></location>Now we turn to the trace equation (24). From Eqs. (36), (28) and (30) we have</text>
<formula><location><page_7><loc_30><loc_12><loc_86><loc_16></location>∂ c S bc b = -f ' -2 f/r +2 r ( g/r ) ' +6( g/r ) = 2 ψ ' /r +2 ψ/r 2 + /triangle φ -3(2 A + C ) . (39)</formula>
<text><location><page_7><loc_12><loc_9><loc_58><loc_10></location>Substituting Eqs. (34) and (39) into Eq. (24) results in</text>
<formula><location><page_7><loc_28><loc_5><loc_86><loc_7></location>-( /triangle φ +2 ψ ' /r +2 ψ/r 2 ) + 9(2 A + C ) = ( l 2 / 8 κ ) ρ. (40)</formula>
<text><location><page_8><loc_12><loc_81><loc_86><loc_91></location>Equation. (40) is an underdetermined equation for φ and ψ . To solve it, more conditions are needed. Suppose that the external solution is the weak Schwarzschild field, i.e., φ = ψ = -GM/r and the internal solution is regular and satisfies /triangle φ = 4 πGρ . Also, it is assumed that the internal solution could be linked to the external solution smoothly at r = R S , resulting in a complete solution. For this complete solution, there would be C = -2 A ,</text>
<text><location><page_8><loc_12><loc_75><loc_15><loc_76></location>with</text>
<text><location><page_8><loc_12><loc_64><loc_15><loc_66></location>and</text>
<formula><location><page_8><loc_34><loc_62><loc_63><loc_64></location>ψ = [ -Gm ( r ) /r ]( l 2 / 64 πGκ +1 / 2) .</formula>
<text><location><page_8><loc_12><loc_60><loc_46><loc_61></location>Note that ψ ( R S ) = -Gm ( R S ) /R S , thus,</text>
<formula><location><page_8><loc_42><loc_56><loc_86><loc_58></location>ψ = -Gm ( r ) /r, (42)</formula>
<formula><location><page_8><loc_43><loc_53><loc_86><loc_55></location>κ = l 2 / 32 πG. (43)</formula>
<text><location><page_8><loc_12><loc_47><loc_86><loc_52></location>Equation. (42) is just the same as the corresponding case in GR. The result C = -2 A is in accordance with Eq. (35). The torsion solutions will be given later in the more general case.</text>
<text><location><page_8><loc_12><loc_43><loc_86><loc_47></location>Actually, Eq. (40) can also be solved with other supplementary conditions. For example, instead of assuming /triangle φ = 4 πGρ , we may let</text>
<formula><location><page_8><loc_41><loc_40><loc_86><loc_41></location>/triangle φ = 4 πG ( ρ + ˜ ρ ) , (44)</formula>
<text><location><page_8><loc_12><loc_33><loc_86><loc_38></location>where ˜ ρ is an arbitrarily given function and does not contribute to the energy-momentumstress tensors of matter fields. Fixing κ by Eq. (43), then from Eqs. (35), (40) and (44) we have</text>
<formula><location><page_8><loc_32><loc_29><loc_86><loc_33></location>φ = G ∫ r 0 { [ m ( r ) + ˜ m ( r )] /r 2 } dr + φ (0) , (45)</formula>
<formula><location><page_8><loc_32><loc_25><loc_86><loc_29></location>ψ = -G r [ m ( r ) + ˜ m ( r ) / 2] + 3 2 (2 A + C ) r 2 (46)</formula>
<formula><location><page_8><loc_31><loc_20><loc_67><loc_24></location>˜ m ( r ) = ∫ B 3 ( r ) ˜ ρ = ∫ r 0 4 π ˜ ρr 2 dr, C = ± 2 A.</formula>
<text><location><page_8><loc_12><loc_23><loc_15><loc_25></location>with</text>
<text><location><page_8><loc_12><loc_14><loc_86><loc_19></location>As the internal solutions are regular, from Eqs. (28), (30) and (38), there should be B = D = 0, C 2 = 0. Therefore, the torsion solutions corresponding to Eqs. (45) and (46) are as follows:</text>
<formula><location><page_8><loc_36><loc_12><loc_86><loc_14></location>f = Cr -G [ m ( r ) + ˜ m ( r )] /r 2 , (47)</formula>
<formula><location><page_8><loc_31><loc_9><loc_86><loc_11></location>g = (4 A +3 C ) r/ 2 -G [ m ( r ) + ˜ m ( r ) / 2] /r 2 , (48)</formula>
<formula><location><page_8><loc_42><loc_5><loc_86><loc_8></location>h = -k = 1 3 C 1 . (49)</formula>
<formula><location><page_8><loc_37><loc_77><loc_86><loc_81></location>φ = ∫ r 0 [ Gm ( r ) /r 2 ] dr + φ (0) (41)</formula>
<formula><location><page_8><loc_36><loc_71><loc_61><loc_75></location>m ( r ) = ∫ B 3 ( r ) ρ = ∫ r 0 4 πρr 2 dr,</formula>
<formula><location><page_8><loc_33><loc_66><loc_65><loc_70></location>φ (0) = -GM/R S -∫ R S 0 [ Gm ( r ) /r 2 ] dr,</formula>
<text><location><page_9><loc_12><loc_82><loc_86><loc_91></location>The former case which is compatible with the Schwarzschild solutions corresponds to the special choice with C = -2 A and ˜ ρ = 0. In fact, another choice of ˜ ρ could deduce the galactic rotation curves without invoking dark matter. To fit the galactic rotation curves, the dark matter density profile ρ DM has been given for many spiral galaxies, for example, see Refs. [30, 31], where the following choice is made:</text>
<formula><location><page_9><loc_40><loc_77><loc_86><loc_81></location>ρ DM = σ 2 2 πG ( r 2 + a 2 ) . (50)</formula>
<text><location><page_9><loc_12><loc_50><loc_86><loc_76></location>In Refs. [30, 31], the mass distribution of the galaxies is modeled as the sum of the bulge and disk stellar components and a halo of dark matter. The rotation curves are used to determine the two halo parameters σ and a . In our model, we may just let the gravitational contribution ˜ ρ to take the same form as the dark matter density profile and suitably choose the integration constants, i.e., ˜ ρ = ρ DM and C = -2 A , without the inclusion of any real dark matter. For this case, Eqs. (45) and (46) is almost equivalent to the corresponding case in GR with dark matter. The parameters σ and a can be determined in the same way as that in Refs. [30, 31] and, therefore, with the same values. For example, for the galaxy NGC 2841, σ = 232 km/s and a = 11 . 6 kpc fit the rotation curve well, for the galaxy NGC 3031, σ = 86 km/s and a = 2 . 0 kpc fit the rotation curve well, and so on. To say 'almost equivalent' but not 'equivalent', is because the term ˜ m/ 2 in Eq. (46) is different from ˜ m , which should be the case in GR with dark matter. Fortunately, ψ would not affect the rotation curves in the leading order of approximation, since the rotation velocity v c in a galaxy at a radius r in the approximation is given by</text>
<formula><location><page_9><loc_41><loc_47><loc_86><loc_49></location>v 2 c ( r ) = r ( ∂φ/∂r ) . (51)</formula>
<text><location><page_9><loc_12><loc_42><loc_86><loc_45></location>For higher order approximations, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results.</text>
<text><location><page_9><loc_12><loc_31><loc_86><loc_42></location>One may argue that ˜ ρ can not be specified a priori and could only be determined from observation. Actually, such kinds of functions also appear in other models which attempt to explain the galactic rotation curves without involving dark matter, such as Milgrom's modification of Newtonian dynamics (MOND) [21, 22] and the modified Newton's gravity in Finsler space [24]. What we can do now is to point out the geometrical meaning of ˜ ρ . From Eqs. (47) and (48), there is the relation:</text>
<formula><location><page_9><loc_33><loc_26><loc_86><loc_30></location>4 πG ˜ ρ = -2 r 2 [ r 2 ( f -g )] ' -3(4 A + C ) , (52)</formula>
<text><location><page_9><loc_12><loc_22><loc_86><loc_25></location>which shows that the dark matter density could be directly related to the spacetime torsion.</text>
<text><location><page_9><loc_12><loc_5><loc_86><loc_22></location>When l →∞ , l 2 /κ should tend to a finite value, as was mentioned before. Obviously Eq. (43) satisfies this requirement. In [1-3, 8], the coupling constant is chosen to be -l 2 / 64 πG , which is different from Eq. (43). For this case, there exists no regular internal solution which satisfies /triangle φ = 4 πGρ and has a smooth junction to the Schwarzschild solutions. In fact, with this choice, the ratio of the coefficient of the Einstein term G ab to that of the matter term Σ ab in Eq. (7) would be 1 : ( -8 πG ), just like the case in GR. But the role of the Einstein term in our model is different from that of GR. Actually, from Eq. (34), the Einstein term only contributes a constant term to Eq. (24), while the torsion term plays an important role in that equation.</text>
<text><location><page_10><loc_12><loc_81><loc_86><loc_91></location>Generally, the torsion tensor can be decomposed [32, 33] into three irreducible parts with respect to the Lorentz group: the tensor part, trace-vector part, and the axial vector part. For static and O (3)-symmetric torsion, the axial vector part vanishes automatically, the tensor part satisfies f = 2 g , h = 2 k and the trace-vector part satisfies f = -g , h = -k . By Eqs. (47) and (48), if the torsion field only contains the tensor part, the matter density should be a constant:</text>
<formula><location><page_10><loc_40><loc_78><loc_86><loc_79></location>ρ = 3(2 A + C ) / 2 πG. (53)</formula>
<text><location><page_10><loc_12><loc_74><loc_61><loc_76></location>If the torsion field only contains the trace-vector part, then</text>
<formula><location><page_10><loc_37><loc_71><loc_86><loc_73></location>4 ρ +3˜ ρ = 3(4 A +5 C ) / 4 πG. (54)</formula>
<text><location><page_10><loc_12><loc_68><loc_61><loc_70></location>When ˜ ρ = 0, the matter density has to be a constant, too.</text>
<section_header_level_1><location><page_10><loc_12><loc_63><loc_29><loc_65></location>4 Remarks</section_header_level_1>
<text><location><page_10><loc_12><loc_29><loc_86><loc_62></location>The weak field approximation of the Λ → 0 limit of the dS gravity model has been calculated in the static and spherically symmetric case. The matter field is assumed to be a smoothly distributed dust sphere with finite radius. It comes out that if and only if κ = l 2 / 32 πG , there exist regular internal solutions which satisfy /triangle φ = 4 πGρ and have a smooth junction to the weak Schwarzschild fields. Recall that the main part of the action is the quadratic curvature term, not the Einstein-Hilbert term. The existence of the above solutions is of significance. The choice of the coupling constant here is different from that of [1-3, 8], where κ = -l 2 / 64 πG . The choice in [1-3, 8] may due to a comparison between the dS gravity model and GR. But the Einstein term in the dS gravity model plays a different role from that of GR, as it only contributes to a constant term in the weak field approximate equations. Actually, the metric components and torsion components are closely related by Eqs. (28) and (30), such that the curvature tensor has to take a special form (32). Moreover, one may let C = A = 0 and B = D = 0, then R abcd = 0, i.e., the Weizenbock spacetime [34, 35] would be attained. On the other hand, the torsion tensor plays an important role in this model. In the weak field approximate solutions, if the torsion tensor only contains the tensor part, the matter density should be a constant; if it only contains the trace-vector part, Eq. (54) should be upheld. In particular, the matter density should be a constant in the torsion-free case.</text>
<text><location><page_10><loc_12><loc_14><loc_86><loc_29></location>The trace equation (24) results in an underdetermined equation for the metric components φ and ψ in the weak field approximation. Solutions with /triangle φ = 4 πG ( ρ +˜ ρ ) could be attained, which can explain the galactic rotation curves without the help of introducing dark matter. The geometrical meaning of ˜ ρ has been given by Eq. (52). It is a geometric quantity related to the spacetime torsion and can play the role of dark matter density though it is irrelevant to the energy-momentum-stress tensors of matter fields. To see the higher order behavior of the model, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results.</text>
<text><location><page_10><loc_26><loc_11><loc_26><loc_12></location>/negationslash</text>
<text><location><page_10><loc_12><loc_5><loc_86><loc_14></location>Finally, it should be remarked that all the above results need to be reexamined in the case with Λ = 0. But we can conclude, at least, that if there exist regular internal solutions which are in accordance with the Newtonian gravitational law and could be smoothly extended to the weak S-dS fields, the coupling constant should be chosen as κ = l 2 / 32 πG .</text>
<section_header_level_1><location><page_11><loc_12><loc_90><loc_37><loc_92></location>Acknowledgments</section_header_level_1>
<text><location><page_11><loc_12><loc_77><loc_86><loc_88></location>One of us (Lu) would like to thank Prof. Zhi-Bing Li, Xi-Ping Zhu, and thank the late Prof. Han-Ying Guo for their sincere help. He also expresses his appreciation for hospitality during his stay at the Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences. This work is supported by the National Natural Science Foundation of China under Grant Nos. 10975141, 10831008, 11275207, and the oriented projects of CAS under Grant No. KJCX2-EW-W01.</text>
<section_header_level_1><location><page_11><loc_12><loc_72><loc_27><loc_74></location>References</section_header_level_1>
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<list_item><location><page_12><loc_12><loc_26><loc_86><loc_29></location>[27] Wise, D.K.: MacDowell-Mansouri gravity and Cartan geometry. Class. Quantum Grav. 27 , 155010 (2010)</list_item>
<list_item><location><page_12><loc_12><loc_21><loc_86><loc_24></location>[28] Wheeler, J.T.: Symmetric solutions to themaximally Gauss-Bonnet extentded Einstein equations.Nucl. Phys. B 273 , 732-748 (1986)</list_item>
<list_item><location><page_12><loc_12><loc_16><loc_86><loc_19></location>[29] Zhang, Y.-Z.: Newtonian limit in the Poincar'e gauge field theory of gravitation. Sci. Sin. A 4 , 399-404 (1985)</list_item>
<list_item><location><page_12><loc_12><loc_11><loc_86><loc_15></location>[30] Kent, S.M.: Dark matter in spiral galaxies. I. Galaxies with optical rotation curves. Astron. J. 91 , 1301-1327 (1986)</list_item>
<list_item><location><page_12><loc_12><loc_6><loc_86><loc_10></location>[31] Kent, S.M.: Dark matter in spiral galaxies. II. Galaxies with H riptsize I rotation curves. Astron. J. 93 , 816-832 (1987)</list_item>
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<list_item><location><page_13><loc_12><loc_88><loc_86><loc_91></location>[32] Hayashi, K., Shirafuji, T.: Gravity from Poincar'e gauge theory of the fundamental particles. I. General formulation. Prog. Theor. Phys. 64 , 866-882 (1980)</list_item>
<list_item><location><page_13><loc_12><loc_81><loc_86><loc_86></location>[33] Hehl, F.W., McCrea, J.D., Mielke, E.W., Neeman, Y.: Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance. Phys. Rep. 258 , 1-171 (1995)</list_item>
<list_item><location><page_13><loc_12><loc_78><loc_70><loc_80></location>[34] R. Weitzenbock, Invarianten Theorie. Nordhoff, Groningen, 1923</list_item>
<list_item><location><page_13><loc_12><loc_75><loc_86><loc_77></location>[35] Hayashi, K., Shirafuji, T.: New general relativity. Phys. Rev. D 19 , 3524-3553 (1979)</list_item>
</unordered_list>
</document>
[
{
"title": "Weak field approximation in a model of de Sitter gravity: Schwarzschild solutions and galactic rotation curves",
"content": "Jia-An Lu a ∗ and Chao-Guang Huang b †",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "Weak field approximate solutions in the Λ → 0 limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotation curves without invoking dark matter. Keywords: de Sitter gravity, Schwarzschild solutions, torsion, dark matter",
"pages": [
1
]
},
{
"title": "1 Introduction",
"content": "In the 1970s a model of de Sitter (dS) gravity had been proposed [1-4]. In this model the Einstein-Hilbert action with a cosmological term could be deduced from a gauge-like action besides two quadratic terms of the curvature and torsion. The astronomical observation [5, 6] on the asymptotically dS behavior of our universe has increased interest in the model as it may offer a way to deal with the dark energy problem [7]. If the EinsteinHilbert term is required to be the main part of the gauge-like action, the cosmological constant should be large. The large cosmological constant may be canceled out by the vacuum energy density, leaving a small cosmological constant [4]. But it is difficult to explain why the large cosmological constant and the vacuum energy density are so close, but not exactly equal, to each other. On the other hand, if the cosmological constant is required to be small [1-3, 8], the quadratic curvature term would become the main part of the action. Note that in one of the field equations, the quadratic curvature term only contributes to the symmetric trace-free part. It is worth checking carefully whether the model under this case could explain the experimental observations. Actually it has been shown [9, 10] that the model with a small cosmological constant may explain the accelerating expansion of the universe and supply a natural transit from decelerating expansion to accelerating expansion without the help of introducing matter fields in addition to dust. It has also been shown [11, 12] that all torsion-free vacuum solutions of this model are the vacuum solutions of Einstein's field equation with the same cosmological constant, and vise versa. Therefore, one may expect that the model with a small cosmological constant may pass all solar-system-scale experimental tests for general relativity (GR). However, it has been pointed out [9] that the energy-momentum-stress tensor of a spinless fluid in the torsion-free case of this model should be with a constant trace. Questions would then appear such as, could the torsion-free Schwarzschild-dS (S-dS) solution be smoothly connected to internal solutions with nonzero torsion, or are there any S-dS solutions with nonzero torsion? In fact, the different dS spacetimes with nonzero torsion in this model have been obtained in [13, 14], but they are sill not the S-dS solutions. On the other hand, S-dS solutions with long-range spherically symmetric torsion have been given [15] in some special cases (not necessarily under the double duality ansatz [16]) of quadratic models of Poincar'e gauge theory of gravity, but our model does not fall into those special cases. We would like to firstly check the existence of the S-dS solutions with nonzero torsion in the weak field approximation. The Newtonian limit of general quadratic models in Poincar'e gauge theory of gravity has been calculated [17, 18] in the 1980's. In those calculations, quadratic terms in the field equations have been thrown away as usual. However, in the weak field approximation of our model, the quadratic curvature terms could not be easily thrown away, for the reason that they are the main parts of one of the field equations. In fact, we may let the cosmological constant be Λ → 0, then only those quadratic curvature terms would appear in the limit of the field equation which contains the energy-momentum-stress tensor of the matter field. On the other hand, as those quadratic curvature terms are symmetric and trace-free, they would not appear in the trace part and the antisymmetric part of the field equations. The Newtonian limit of the trace equations has been recently analyzed [19], but a more complete analysis of all components of the field equations is needed. As was well known, Newton's theory of gravity meets great difficulties in the explanation of the flat rotation curves [20] of spiral galaxies. The most widely adopted way to resolve this problem is the dark matter hypothesis. But up to now, all of the possible candidates of dark matter (such as neutralino, axion, etc.) are either undetected or unsatisfactory. In the meanwhile, there also exist some models [21-24] which could deduce the galactic rotation curves without involving dark matter. We would like to explore the possibility of a new explanation for the galactic rotation curves from the dS gravity model. The paper is arranged as follows. We first briefly review the model of the dS gravity in section 2. In the third section, after dividing a field equation into its trace part, symmetric trace-free part and antisymmetric part, we attain the Λ → 0 limit of the model and calculate its weak field approximation in the static and spherically symmetric case. The weak field approximate solutions contain the weak Schwarzschild fields with nonzero torsion, which could be smoothly linked to regular internal solutions obeying the Newtonian gravitational law. The coupling constant is determined by the existence of such solutions. Moreover, solutions that could deduce the galactic rotation curves without invoking dark matter are also attained. Finally we end with some remarks in the last section.",
"pages": [
1,
2,
3
]
},
{
"title": "2 A model of dS gravity",
"content": "A model of dS gravity has been constructed with a gauge-like action [1-4] in the units of /planckover2pi1 = c = 1, where κ is a dimensionless coupling constant to be determined, and or explicitly is a dS algebra-valued 2-form and is a dS algebra-valued 1-form. Here A, B... = 0 , 1 , 2 , 3 , 4 stand for matrix indices (internal indices) and the trace in Eq. (1) is taken for those indices. In addition, { e α a } is some local orthonormal frame field on the spacetime manifold and Γ α βa is the connection 1-form in this frame field, where a, b... stand for abstract indices [25, 26] and α, β... = 0 , 1 , 2 , 3 are concrete indices related to the frame field mentioned above. The curvature 2-form R ab α β and torsion 2-form S α ab are related to the connection 1-form Γ α βa as follows: Moreover, In fact, if spacetime is an umbilical submanifold of some (1+4)-dimensional ambient manifold and with positive normal curvature, then A a and F ab could be viewed [8] as the connection 1-form and curvature 2-form (in the dS-Lorentz frame) of the ambient manifold restricted to spacetime. Here, an umbilical submanifold means a submanifold with constant normal curvature, such as the dS spacetime which could be seen as an umbilical submanifold of a 5d Minkowski spacetime with positive normal curvature. A a could also be seen [27] as the Cartan connection of a Cartan geometry modeled on the dS spacetime and based on the spacetime manifold, with F ab the corresponding curvature 2-form. The Cartan geometry is a generalization of homogenous spaces with fibre bundle language, and one may refer to [27] for more details. In addition, it should be noted that 3 /l 2 is identified [8] with a small cosmological constant Λ here, which is very different from the viewpoint of [4] where l is identified with the Planck length. The signature is chosen such that the metric coefficients are η αβ = diag( -1 , 1 , 1 , 1). The total action is S = S M + S G , where S M is the action of the matter fields and the field equations can be given via the variational principle with respect to e α a , Γ α βa : where and the variational derivatives are defined as follows: if then",
"pages": [
3,
4
]
},
{
"title": "3 Weak field approximation in the case with Λ → 0",
"content": "As Λ is very small, it is interesting to see the case with Λ → 0 ( l → ∞ ). If Λ → 0 is directly set in the first field equation, then only the quadratic curvature terms are left, which are symmetric and trace-free. Thus, we would like to perform the following procedure. Divide the first field equation into its symmetric trace-free part, trace part, and antisymmetric part, then let l tend to infinity ( l →∞ ) in the above three parts and in the second field equation. The limiting equations are: When l → ∞ , l 2 /κ should tend to a finite value, otherwise Eqs. (10) and (11) would give Σ = 0 and Σ [ ab ] = 0, which are unreasonable. In the torsion-free case, the scalar curvature would be a constant from Eq. (12), and, therefore, Σ = const from Eq. (10). This property has been pointed out by [9]. Now we are going to consider the week field approximation of the above equations. It would be assumed that where s is a dimensionless parameter, called the weak field parameter. We will restrict ourselves to the static and O (3)-symmetric case, with the static spherical coordinate system { t, r, θ, ϕ } . η ab could be defined by its components η µν = diag( -1 , 1 , 1 , 1) in the approximate inertial coordinate system { x µ } . { x µ } is related to { t, r, θ, ϕ } as usual: It could be proved [15, 25, 28] that γ ab and S c ab have only these dependent components in the static spherical coordinate system: where φ plays the role of the Newtonian gravitational potential [1-3, 25, 29] and ψ is an unknown function. It can be shown that components of γ ab and S c ab in { x µ } are as follows: For this case the contorsion tensor is related to the torsion tensor by Let Γ c ab = Γ σ µν ∂ σ c ( dx µ ) a ( dx ν ) b , where Γ σ µν is the connection coefficient in { x µ } . Γ c ab and the curvature tensor have the following first order approximate expressions: where is the contorsion tensor. In the case with Σ ab = ρ ( r )( dt ) a ( dt ) b , the equations for the first order approximate g ab and S c ab are as follows: The first order approximation of Eq. (9) is an identity. Here Eq. (23) is the second order approximation of Eq. (9). It should be considered for the reason that it is still an equation for the first order approximate g ab and S c ab . Now we are going to solve the above weak field equations. Applying Eq. (21) to Eq. (26), we have The 00 i ( abc ) component of Eq. (27) is which gives Solving this equation we get that The 0 ij component of Eq. (27) is an identity. The i 0 j component of Eq. (27) is which gives or equivalently The ijk component of Eq. (27) is which gives Solving this equation we get that From Eqs. (21), (17) and (18) the components of R abcd in { x µ } could be attained as follows: Substituting Eqs. (28), (29) and (30) into the above equation, we get that Then Applying Eq. (33), the symmetric trace-free equation (23) could be solved, resulting in the following relations: From Eq. (34) one could see that R [ ab ] = 0 and thus the antisymmetric equation (25) gives ∂ c S [ ab ] c = 0. Components of ∂ c S ab c are as follows: Therefore, ∂ c S [ ab ] c = 0 results in Combining Eqs. (29) and (37) we have Now we turn to the trace equation (24). From Eqs. (36), (28) and (30) we have Substituting Eqs. (34) and (39) into Eq. (24) results in Equation. (40) is an underdetermined equation for φ and ψ . To solve it, more conditions are needed. Suppose that the external solution is the weak Schwarzschild field, i.e., φ = ψ = -GM/r and the internal solution is regular and satisfies /triangle φ = 4 πGρ . Also, it is assumed that the internal solution could be linked to the external solution smoothly at r = R S , resulting in a complete solution. For this complete solution, there would be C = -2 A , with and Note that ψ ( R S ) = -Gm ( R S ) /R S , thus, Equation. (42) is just the same as the corresponding case in GR. The result C = -2 A is in accordance with Eq. (35). The torsion solutions will be given later in the more general case. Actually, Eq. (40) can also be solved with other supplementary conditions. For example, instead of assuming /triangle φ = 4 πGρ , we may let where ˜ ρ is an arbitrarily given function and does not contribute to the energy-momentumstress tensors of matter fields. Fixing κ by Eq. (43), then from Eqs. (35), (40) and (44) we have with As the internal solutions are regular, from Eqs. (28), (30) and (38), there should be B = D = 0, C 2 = 0. Therefore, the torsion solutions corresponding to Eqs. (45) and (46) are as follows: The former case which is compatible with the Schwarzschild solutions corresponds to the special choice with C = -2 A and ˜ ρ = 0. In fact, another choice of ˜ ρ could deduce the galactic rotation curves without invoking dark matter. To fit the galactic rotation curves, the dark matter density profile ρ DM has been given for many spiral galaxies, for example, see Refs. [30, 31], where the following choice is made: In Refs. [30, 31], the mass distribution of the galaxies is modeled as the sum of the bulge and disk stellar components and a halo of dark matter. The rotation curves are used to determine the two halo parameters σ and a . In our model, we may just let the gravitational contribution ˜ ρ to take the same form as the dark matter density profile and suitably choose the integration constants, i.e., ˜ ρ = ρ DM and C = -2 A , without the inclusion of any real dark matter. For this case, Eqs. (45) and (46) is almost equivalent to the corresponding case in GR with dark matter. The parameters σ and a can be determined in the same way as that in Refs. [30, 31] and, therefore, with the same values. For example, for the galaxy NGC 2841, σ = 232 km/s and a = 11 . 6 kpc fit the rotation curve well, for the galaxy NGC 3031, σ = 86 km/s and a = 2 . 0 kpc fit the rotation curve well, and so on. To say 'almost equivalent' but not 'equivalent', is because the term ˜ m/ 2 in Eq. (46) is different from ˜ m , which should be the case in GR with dark matter. Fortunately, ψ would not affect the rotation curves in the leading order of approximation, since the rotation velocity v c in a galaxy at a radius r in the approximation is given by For higher order approximations, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results. One may argue that ˜ ρ can not be specified a priori and could only be determined from observation. Actually, such kinds of functions also appear in other models which attempt to explain the galactic rotation curves without involving dark matter, such as Milgrom's modification of Newtonian dynamics (MOND) [21, 22] and the modified Newton's gravity in Finsler space [24]. What we can do now is to point out the geometrical meaning of ˜ ρ . From Eqs. (47) and (48), there is the relation: which shows that the dark matter density could be directly related to the spacetime torsion. When l →∞ , l 2 /κ should tend to a finite value, as was mentioned before. Obviously Eq. (43) satisfies this requirement. In [1-3, 8], the coupling constant is chosen to be -l 2 / 64 πG , which is different from Eq. (43). For this case, there exists no regular internal solution which satisfies /triangle φ = 4 πGρ and has a smooth junction to the Schwarzschild solutions. In fact, with this choice, the ratio of the coefficient of the Einstein term G ab to that of the matter term Σ ab in Eq. (7) would be 1 : ( -8 πG ), just like the case in GR. But the role of the Einstein term in our model is different from that of GR. Actually, from Eq. (34), the Einstein term only contributes a constant term to Eq. (24), while the torsion term plays an important role in that equation. Generally, the torsion tensor can be decomposed [32, 33] into three irreducible parts with respect to the Lorentz group: the tensor part, trace-vector part, and the axial vector part. For static and O (3)-symmetric torsion, the axial vector part vanishes automatically, the tensor part satisfies f = 2 g , h = 2 k and the trace-vector part satisfies f = -g , h = -k . By Eqs. (47) and (48), if the torsion field only contains the tensor part, the matter density should be a constant: If the torsion field only contains the trace-vector part, then When ˜ ρ = 0, the matter density has to be a constant, too.",
"pages": [
4,
5,
6,
7,
8,
9,
10
]
},
{
"title": "4 Remarks",
"content": "The weak field approximation of the Λ → 0 limit of the dS gravity model has been calculated in the static and spherically symmetric case. The matter field is assumed to be a smoothly distributed dust sphere with finite radius. It comes out that if and only if κ = l 2 / 32 πG , there exist regular internal solutions which satisfy /triangle φ = 4 πGρ and have a smooth junction to the weak Schwarzschild fields. Recall that the main part of the action is the quadratic curvature term, not the Einstein-Hilbert term. The existence of the above solutions is of significance. The choice of the coupling constant here is different from that of [1-3, 8], where κ = -l 2 / 64 πG . The choice in [1-3, 8] may due to a comparison between the dS gravity model and GR. But the Einstein term in the dS gravity model plays a different role from that of GR, as it only contributes to a constant term in the weak field approximate equations. Actually, the metric components and torsion components are closely related by Eqs. (28) and (30), such that the curvature tensor has to take a special form (32). Moreover, one may let C = A = 0 and B = D = 0, then R abcd = 0, i.e., the Weizenbock spacetime [34, 35] would be attained. On the other hand, the torsion tensor plays an important role in this model. In the weak field approximate solutions, if the torsion tensor only contains the tensor part, the matter density should be a constant; if it only contains the trace-vector part, Eq. (54) should be upheld. In particular, the matter density should be a constant in the torsion-free case. The trace equation (24) results in an underdetermined equation for the metric components φ and ψ in the weak field approximation. Solutions with /triangle φ = 4 πG ( ρ +˜ ρ ) could be attained, which can explain the galactic rotation curves without the help of introducing dark matter. The geometrical meaning of ˜ ρ has been given by Eq. (52). It is a geometric quantity related to the spacetime torsion and can play the role of dark matter density though it is irrelevant to the energy-momentum-stress tensors of matter fields. To see the higher order behavior of the model, more work is needed to be done and experiments with higher accuracy are needed to check the corresponding results. /negationslash Finally, it should be remarked that all the above results need to be reexamined in the case with Λ = 0. But we can conclude, at least, that if there exist regular internal solutions which are in accordance with the Newtonian gravitational law and could be smoothly extended to the weak S-dS fields, the coupling constant should be chosen as κ = l 2 / 32 πG .",
"pages": [
10
]
},
{
"title": "Acknowledgments",
"content": "One of us (Lu) would like to thank Prof. Zhi-Bing Li, Xi-Ping Zhu, and thank the late Prof. Han-Ying Guo for their sincere help. He also expresses his appreciation for hospitality during his stay at the Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences. This work is supported by the National Natural Science Foundation of China under Grant Nos. 10975141, 10831008, 11275207, and the oriented projects of CAS under Grant No. KJCX2-EW-W01.",
"pages": [
11
]
}
]
2013GReGr..45.2143M
https://arxiv.org/pdf/1307.4371.pdf
<document>
<section_header_level_1><location><page_1><loc_15><loc_80><loc_90><loc_85></location>Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results</section_header_level_1>
<text><location><page_1><loc_31><loc_76><loc_76><loc_78></location>Marc Mars ∗ , Filipe C. Mena † and Ra¨ul Vera ‡</text>
<text><location><page_1><loc_22><loc_74><loc_84><loc_75></location>∗ Instituto de F´ısica Fundamental y Matem´aticas, Universidad de Salamanca,</text>
<text><location><page_1><loc_33><loc_72><loc_72><loc_73></location>Plaza de la Merced s/n, 37008 Salamanca, Spain</text>
<text><location><page_1><loc_23><loc_67><loc_83><loc_71></location>† Centro de Matem´atica, Universidade do Minho, 4710-057 Braga, Portugal ‡ Dept. of Theoretical Physics and History of Science,</text>
<text><location><page_1><loc_15><loc_65><loc_90><loc_66></location>University of the Basque Country UPV/EHU, 644 PK, Bilbao 48080, Basque Country, Spain</text>
<section_header_level_1><location><page_1><loc_49><loc_60><loc_57><loc_62></location>Abstract</section_header_level_1>
<text><location><page_1><loc_19><loc_36><loc_86><loc_60></location>The Einstein-Straus model consists of a Schwarzschild spherical vacuole in a Friedman-Lemaˆıtre-Robertson-Walker (FLRW) dust spacetime (with or without Λ). It constitutes the most widely accepted model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model is that there is no influence from the cosmic background, since the spherical vacuole is static. Spherical generalizations to other interior matter models are commonly used in the construction of lumpy inhomogeneous cosmological models. On the other hand, the model has proven to be reluctant to admit non-spherical generalizations. In this review, we summarize the known uniqueness results for this model. These seem to indicate that the only reasonable and realistic nonspherical deformations of the Einstein-Straus model require perturbing the FLRW background. We review results about linear perturbations of the Einstein-Straus model, where the perturbations in the vacuole are assumed to be stationary and axially symmetric so as to describe regions (voids in particular) in which the matter has reached an equilibrium regime.</text>
<section_header_level_1><location><page_1><loc_14><loc_31><loc_37><loc_33></location>1 Introduction</section_header_level_1>
<text><location><page_1><loc_14><loc_23><loc_91><loc_29></location>During a meal in the 19th Jena Meeting on Relativity, in September 1996, Bill Bonnor provocatively asked Jos'e Senovilla if the table could be expanding with the Universe. Not surprisingly, Bonnor later took the question seriously and wrote a paper about how the hydrogen atom is affected by the cosmic expansion [11], which is well worth reading.</text>
<text><location><page_1><loc_14><loc_9><loc_91><loc_23></location>About five decades before, Einstein and Straus asked a similar question, on a bigger scale, which led them to investigate the influence of the expansion of space on the gravitational fields surrounding individual stars [19]. They took the Schwarzschild solution representing the vacuole surrounding a star located in the centre and the FriedmanLemaitre-Robertson-Walker (FLRW) solution as the cosmological model. At the core of their model was the matching of the two solutions across a spherical surface with constant cosmological radius. Since the expansion kept the vacuole symmetry and time independence, their conclusion was that it does not affect the gravitational fields surrounding</text>
<text><location><page_2><loc_10><loc_84><loc_86><loc_90></location>stars and, in particular, it does not affect the solar system dynamics. A previous attempt to address the issue of whether the planetary orbits expand with the Universe was made by McVittie [44] who found a smooth model describing a spherically symmetric mass embedded in a flat FLRW.</text>
<text><location><page_2><loc_10><loc_68><loc_86><loc_83></location>Since then the research about this problem was scarce, although some alternatives to the McVittie model were suggested, e.g. in [22], and difficulties of the global meaning of the model were also pointed out [48, 49, 50, 51] (see also [15]). Concerning the Einstein-Straus model itself, it was revisited in [2, 8] and stability issues were raised in [57], [32] cf. also the discussion in [30]. However, the Einstein-Straus model has never stopped being considered as the correct answer to the lack of influence of the cosmological expansion on local systems. Moreover, since the vacuole can be inserted anywhere due to the homogeneity of FLRW, the Einstein-Straus model led to the original Swiss cheese model of a lumpy inhomogeneous universe (see e.g. [20]).</text>
<text><location><page_2><loc_10><loc_54><loc_86><loc_68></location>Bonnor's question, that 1996 afternoon, raised a totally new issue for the EinsteinStraus models, namely whether spherical symmetry was a crucial ingredient of the model and, therefore, for the existence of time-invariant bounded systems embedded in a FLRW universe. Indeed, the question triggered research by Senovilla and Vera [59], that led to the result about the impossibility of the Einstein-Straus model in cylindrical symmetry. In turn, this important result was the origin of over fifteen years of research about the rigidity, in the sense of uniqueness, of the model. The aim of this paper is to review these results on rigidity both for exact models and from a perturbative perspective.</text>
<text><location><page_2><loc_10><loc_44><loc_86><loc_54></location>Crucial to this endeavour was the development of a general mathematical theory of spacetime matching [41] and of its perturbative version [4, 47, 35]. This allowed to achieve quite general results about the possibility of generalizing both the shape of the cavity and the cosmological setting of the original Einstein-Straus model. As an example, described below in some detail, uniqueness of the static Λ-vacuum spherical region embedded in a non-static FLRW cosmological model has been proved [34].</text>
<text><location><page_2><loc_10><loc_25><loc_86><loc_43></location>The scope of the Einstein-Straus model has been taken well beyond both the physical scale originally considered and the physical problems for which the model was conceived. In fact, the model has been used not only at the solar system scale, but also on galaxy [27] and galaxy clusters' scales [27, 54]. On the other hand, the vacuole of the (original) Einstein-Straus model has been replaced by other spherically symmetric geometries, generally Lemaˆıtre-Tolman-Bondi (LTB), also spherically shaped regions of Szekeres, in order to construct 'generalized' Einstein-Straus models for describing extra-galactic scale and cosmic voids (we refer to the reviews in [30, 20]). Lumpy inhomogeneous cosmological models based on the generalized Einstein-Straus Swiss cheese models are being used in the search of possible explanations to the accelerated expansion of the Universe by the study of lensing effects at cosmic scales produced by the voids (see e.g. [20]).</text>
<text><location><page_2><loc_10><loc_11><loc_86><loc_24></location>So far, all these generalized Einstein-Straus (and the corresponding Swiss cheese) models have assumed spherically shaped inhomogeneities (voids). One of themes of the research we will review here is how far can one push the Einstein-Straus model towards non-spherical generalizations. The fundamental ingredient we want to keep is that the bound system remains stationary, so as to keep the absence of influence of the cosmic dynamics on astrophysical scales. We will use the term Einstein-Straus problem to the problem of finding the most general stationary regions (vacuum or not) one can embed in a realistic cosmological model in a broad sense.</text>
<text><location><page_2><loc_13><loc_9><loc_86><loc_11></location>The Einstein-Straus model has also been taken beyond the exact solutions' settings</text>
<text><location><page_3><loc_14><loc_75><loc_91><loc_90></location>to include metric perturbations. Perturbation theory in General Relativity (GR) is a natural framework to study small departures from symmetric configurations and thus to perform stability analysis. For instance, it allows to include simultaneously density, rotational and gravitational wave perturbation modes into an, otherwise, spatially homogeneous and isotropic cosmological model. Most interestingly, it allows a priori to perturb independently the interior and exterior spacetimes as well as the matching boundary. Furthermore, although the three perturbation modes are decoupled on a FLRW background, they may couple at a matching boundary. In this context, an important question is how general can the perturbations be in each model.</text>
<text><location><page_3><loc_14><loc_66><loc_91><loc_74></location>Inherent to perturbation theory is the issue of gauge freedom. In perturbed spacetime matchings, this can be complicated by the fact that three independent perturbation gauges may be in use. For the sake of completeness, we include a short review of linearized matching, where these issues are discussed, see also [47] for further details, including the definition of the so-called doubly gauge invariant variables .</text>
<text><location><page_3><loc_14><loc_49><loc_91><loc_66></location>Perturbations in the FLRW background are customarily split in scalar, vector and tensor modes, and the later are generically viewed as cosmological gravitational waves. Given that the gravitational wave detectors are already active, and gravitational waves are expected to be detected within the next five years (see e.g. [6, 55] for recent accounts and the review [56]), it would be interesting to investigate their inclusion in the models. One now certainly has the necessary mathematical machinery to do so, and preliminary results indicate the possibility of having, for instance, a stationary axially symmetric vacuole embedded in an expanding cosmological model containing tensor modes [38]. Even more, the linearized matching links the rotational and tensor modes degrees of freedom in the perturbation variables [38].</text>
<text><location><page_3><loc_14><loc_44><loc_91><loc_48></location>This is therefore an interesting timing to revise the state-of-the-art and point out potentially interesting directions of research about the Einstein-Straus problem, in the sense pointed out above.</text>
<text><location><page_3><loc_14><loc_9><loc_91><loc_43></location>The plan of the review is the following. In Section 2, the Einstein-Straus model is briefly presented. Similar summaries with different degrees of detail can be found in many places in the literature, see e.g. [20]. We include it here for the sake of completeness and in order to fix our notation. Section 3 is devoted to describing in some detail the uniqueness results concerning both general static regions and stationary and axisymmetric regions (irrespective of any symmetry consideration and/or matter content) embeddable in a FLRW expanding cosmology. Section 3.1 is devoted to the static case. The main conclusion here is that the only static vacuum region that can be embedded to an expanding FLRW is a spherically shaped region of Schwarzschild (i.e. the Einstein-Straus model). Similar uniqueness results hold for other matter models, such as vacuum with cosmological constant. Section 3.2 deals, in turn, with the uniqueness results for stationary and axially symmetric regions in FLRW expanding universes. The main result is that the stationary region must, in fact, be static, so that the previous conclusions on static regions apply. The uniqueness result thus states that the only way of having a stationary and axially symmetric or static region in an expanding FLRW is the Einstein-Straus model. Following the uniqueness results, the robustness of the Einstein-Straus model is further analyzed by considering alternative exact cosmological models. In Section 4 the replacement of the FLRW region by more general anisotropic cosmologies, i.e. the Bianchi models, is studied for static locally cylindrically symmetric interiors, leading to severe restrictions and no-go results for reasonable evolving cosmologies. The final part of the paper is devoted to</text>
<text><location><page_4><loc_10><loc_75><loc_86><loc_90></location>the generalization of the Einstein-Straus model from a perturbative perspective. After a brief overview of perturbative matching theory in Section 5, and the use of the Hodge decomposition on the sphere instead of the usual spherical harmonic decomposition in Section 6, the linearized matching between stationary and axisymmetric perturbations of Schwarzschild and general perturbed FLRW is reviewed in Section 7. We finish with some conclusions in Section 8, pointing out some ongoing research, prospects for future work on the perturbed Einstein-Straus model and its possible implications on the relationship between astrophysical bounded systems and cosmological dynamics in the form of cosmic gravitational waves.</text>
<section_header_level_1><location><page_4><loc_10><loc_70><loc_53><loc_72></location>2 The Einstein-Straus model</section_header_level_1>
<text><location><page_4><loc_10><loc_55><loc_86><loc_69></location>This model consists of a spherically symmetric (both in shape and intrinsic geometry) Ricci-flat region embedded in a FLRW universe without cosmological constant. Recall that two spacetimes can be matched across their boundary if and only if the first fundamental forms q and second fundamental forms K agree on the matching hypersurface. A consequence of this are the well-known Israel conditions, which restrict the jump of the energy-momentum tensor across the boundary. In the present context, they imply that the cosmological fluid must be dust and the vacuole must be comoving with the cosmological fluid. Writing the FLRW metric in cosmic time coordinates</text>
<formula><location><page_4><loc_19><loc_53><loc_86><loc_54></location>g RW = -dt 2 + a 2 ( t ) g M , with g M = dR 2 +Σ 2 ( R,glyph[epsilon1] ) d Ω 2 , (1)</formula>
<text><location><page_4><loc_10><loc_49><loc_86><loc_52></location>where glyph[epsilon1] = {-1 , 0 , +1 } , Σ ' 2 = 1 -glyph[epsilon1] Σ 2 with prime denoting derivative with respect to R , in units G = c = 1 the Friedman equation reads</text>
<formula><location><page_4><loc_40><loc_45><loc_52><loc_48></location>˙ a 2 + glyph[epsilon1] = 8 πρ 0 3 a ,</formula>
<text><location><page_4><loc_10><loc_32><loc_86><loc_44></location>where the dot denotes derivative with respect to t and ρ 0 is a constant such that the cosmological energy-density ρ satisfies ρ = ρ 0 /a 3 . The boundary of the vacuole can be parametrized by { t = t, R = R 0 } (we ignore the angular variables as they behave trivially, and use t both as spacetime coordinate and intrinsic coordinate on the hypersurface, the precise meaning will be clear from the context). For the matching one needs the induced metric q RW and the second fundamental form K RW . Using the outward unit normal n RW = a ( t ) dR these objects read, with Σ c := Σ | R = R 0 , and Σ ' c := Σ ' | R = R 0 ,</text>
<formula><location><page_4><loc_24><loc_30><loc_68><loc_31></location>q RW = -dt 2 + a 2 ( t )Σ 2 c d Ω 2 , K RW = a ( t )Σ c Σ ' c d Ω 2 .</formula>
<text><location><page_4><loc_10><loc_24><loc_86><loc_29></location>From Birkhoff's theorem, the geometry of the vacuole is Kruskal. Assuming that the boundary is away from the Schwarzschild horizon (this happens sufficiently away from the big bang or big crunch) the interior metric can be written in Schwarzschild coordinates</text>
<formula><location><page_4><loc_29><loc_19><loc_86><loc_23></location>g Sch = -( 1 -2 m r ) 2 dT 2 + dr 2 1 -2 m r + r 2 d Ω 2 . (2)</formula>
<text><location><page_4><loc_10><loc_14><loc_86><loc_18></location>The boundary can be parametrized as { T = T 0 ( t ) , r = r 0 ( t ) } and, given the time inversion symmetry of Schwarzschild, we can assume ˙ T 0 > 0 without loss of generality. The induced metric on the boundary is</text>
<formula><location><page_4><loc_18><loc_9><loc_74><loc_13></location>q Sch = -N 2 ( t ) dt 2 + r 2 0 ( t ) d Ω 2 , N 2 = ( 1 -2 m r 0 ) ˙ T 2 0 -˙ r 2 0 1 -2 m r 0 .</formula>
<text><location><page_5><loc_14><loc_87><loc_91><loc_90></location>Using the unit normal n Sch = 1 N ( ˙ T 0 dr -˙ r 0 dT ) (note that the global sign of N is kept free at this stage), the second fundamental form is</text>
<formula><location><page_5><loc_14><loc_82><loc_88><loc_86></location>K Sch = 1 N ( -˙ T 0 r 0 + T 0 ˙ r 0 + 3 m ˙ r 2 0 ˙ T 0 r 0 ( r 0 -2 m ) -m r 2 0 ( 1 -2 m r 0 ) ˙ T 3 0 ) dt 2 + ˙ T 0 ( r 0 -2 m ) N d Ω 2 .</formula>
<text><location><page_5><loc_14><loc_77><loc_91><loc_80></location>Equality of the t -component of the induced metric requires N 2 = 1. Then, equality of the angular parts of the first and second fundamental forms imposes N = 1 and</text>
<formula><location><page_5><loc_34><loc_72><loc_91><loc_75></location>r 0 ( t ) = Σ c a ( t ) , ˙ T 0 = a ( t )Σ c Σ ' c a ( t )Σ c -2 m . (3)</formula>
<text><location><page_5><loc_14><loc_66><loc_91><loc_71></location>A straightforward computation shows that the equality of the t -component of the induced metric and second fundamental forms are satisfied provided the values of ρ 0 and m are linked by</text>
<formula><location><page_5><loc_47><loc_63><loc_58><loc_66></location>m = 4 π 3 ρ 0 Σ 3 c ,</formula>
<text><location><page_5><loc_14><loc_59><loc_91><loc_62></location>which has a clear interpretation in terms of (Misner-Sharp)-mass conservation. This is the Einstein-Straus model [19].</text>
<text><location><page_5><loc_14><loc_52><loc_91><loc_59></location>A natural generalization consists in adding a cosmological constant Λ both to the FLRW and to the interior part (originally considered in [25] and fully solved in [2]). The Israel matching conditions on the energy-momentum tensor now impose the FLRW matter model to be dust with Λ, so that the Friedman equation is now</text>
<formula><location><page_5><loc_42><loc_47><loc_60><loc_51></location>˙ a 2 + glyph[epsilon1] = 8 πρ 0 3 a + Λ 3 a 2 .</formula>
<text><location><page_5><loc_14><loc_43><loc_95><loc_46></location>By Birkhoff's theorem, the interior metric is the Kottler solution (also known as 'Schwarzschild(anti) de Sitter'), which away from the horizons is</text>
<formula><location><page_5><loc_27><loc_38><loc_75><loc_42></location>g K = -( 1 -2 m r -Λ r 2 3 ) 2 dT 2 + dr 2 1 -2 m r -Λ r 2 3 + r 2 d Ω 2 .</formula>
<text><location><page_5><loc_14><loc_35><loc_49><loc_36></location>In this case, the matching conditions are</text>
<formula><location><page_5><loc_22><loc_30><loc_80><loc_34></location>r 0 ( t ) = Σ c a ( t ) , ˙ T 0 = a ( t )Σ c Σ ' c a ( t )Σ c -2 m -Λ 3 Σ 3 c a ( t ) 3 , m = 4 π 3 ρ 0 Σ 3 c .</formula>
<text><location><page_5><loc_14><loc_22><loc_91><loc_29></location>We emphasize that any matching of two spacetimes immediately leads to a complementary matching, at least locally, where the 'interior' and 'exterior' regions on each spacetime reverse their roles (see [21] for details). In the matching above, this leads to the Oppenheimer-Snyder collapse model [53].</text>
<section_header_level_1><location><page_5><loc_14><loc_18><loc_73><loc_19></location>3 Rigidity of the Einstein-Straus model</section_header_level_1>
<text><location><page_5><loc_14><loc_9><loc_91><loc_16></location>The Einstein-Straus model is such that, for a given total mass inside the vacuole and a given energy density in the cosmological background, the radius of the static region is uniquely fixed. This already poses difficulties for the model since it is often the case that the size of the vacuole does not match the observed sizes of clustered matter in the</text>
<text><location><page_6><loc_10><loc_80><loc_86><loc_90></location>universe, such as stars or galaxies. This fact indicates that the Einstein-Straus model may be lacking flexibility to accommodate the various situations present in cosmology (cf. [58] and [10]). In fact, the Einstein-Straus vacuole was found to be radially unstable in a certain sense [30]. The other main restriction of the model is its exact spherical symmetry. It is clear that vacuoles in the universe are not exactly spherically symmetric so a natural question is how robust is the model to non-spherical generalizations.</text>
<text><location><page_6><loc_10><loc_65><loc_86><loc_80></location>The first thing to consider is which fundamental ingredients of the model should be kept. The main motivation of the Einstein-Straus model was its ability to combine cosmological expansion at large scales with no observable effects on the local physics. Thus, the fundamental ingredient to keep is the absence of influence of the cosmic expansion inside the region. The simplest and most natural way to achieve this is imposing that the interior geometry is stationary, because then no dynamical effects whatsoever from the surrounding evolving cosmology would affect the local physics. Among stationary interiors, the simplest case corresponds to static situations, so it is natural to start with this case (note that the Einstein-Straus model is itself static).</text>
<text><location><page_6><loc_10><loc_42><loc_86><loc_64></location>The question is then how rigid or flexible is the possibility of having stationary/static regions embedded in an otherwise expanding FLRW universe. Ideally, one would like to make no further assumptions and find the most general model with these properties. The matter model inside may also be kept arbitrary, and see what are the possibilities allowed by the coexistence of a stationary/static region inside an expanding FLRW universe. This coexistence has been sometimes called the Einstein-Straus problem in the literature (see e.g. [2]). The first indication that the Einstein-Straus model might be very rigid came from a seminal work by Senovilla and Vera [59] who considered the possibility of matching a static and cylindrically symmetric region (with no restriction on the matter model) with a FLRW dynamical cosmology. The matching hypersurface was taken to be locally a cylinder, in the sense of being tangent in an open set to the two (commuting) generators of two spatial local isometries. No global consideration was needed. The result was a no-go theorem: no such model exists.</text>
<text><location><page_6><loc_10><loc_27><loc_86><loc_42></location>With the impossibility of generalizing the Einstein-Straus model to a cylindrical setting, it became of interest to study the problem in as much generality as possible. The static case was treated in complete generality in [33], [34] and it is by now well-understood. The more complicated stationary situation has been studied [52] under the additional assumptions of axisymmetry and a group action orthogonally transitive. The motivation to study this simplified problem lies in the fact that one expects equilibrium configurations to also exhibit an axial symmetry. It is worth to mention that one step in the black hole uniqueness theorems corresponds to showing that the domain of outer communications must be axially symmetric [26].</text>
<text><location><page_6><loc_10><loc_22><loc_86><loc_26></location>We devote the following Section 3.1 to describing the main results in the static setting, and Section 3.2 to review the uniqueness results in the stationary and axially symmetric setting.</text>
<section_header_level_1><location><page_6><loc_10><loc_17><loc_59><loc_19></location>3.1 Uniqueness results in the static case</section_header_level_1>
<text><location><page_6><loc_10><loc_9><loc_86><loc_16></location>This case was first considered in [33] under the additional assumption of axial symmetry, and one extra technical assumption relating cosmic and static times on the matching hypersurfaces. Both assumptions were dropped in [34] where a satisfactory uniqueness result for static region in FLRW was obtained.</text>
<text><location><page_7><loc_14><loc_72><loc_91><loc_90></location>The setup consists on a spacetime ( V , g ) composed by two regions ( W ST , g ST ) and ( W RW , g RW ) matched in absence of surface layers across their boundaries, denoted by Ω ST and Ω RW respectively, which once identified conform to a hypersurface Ω in ( V , g ). The region ( W ST , g ST ) is strictly static, i.e. admits a Killing vector ξ which is timelike and orthogonal to hypersurfaces everywhere. ( W RW , g RW ) is a codimension-zero submanifold with smooth boundary Ω RW of the FLRW spacetime ( V RW , g RW ), by which we mean the manifold V RW = I ×M , where I ⊂ R is an open interval, M is either E 3 ( glyph[epsilon1] = 0), S 3 ( glyph[epsilon1] = 1) or H 3 ( glyph[epsilon1] = -1) and the FLRW metric g RW takes the form (1). We call any coordinate system { R,θ, φ } in which the metric takes this form a spherical coordinate system . Note that since ( M , g M ) is homogeneous, there exist spherical coordinate systems centered at any point p ∈ M , and this will be used below.</text>
<text><location><page_7><loc_14><loc_66><loc_91><loc_71></location>The function a ( t ) is positive and smooth (in fact C 3 suffices). We assume that ˙ a does not vanish on any open set (this excludes uninteresting situations where the FRLW does not evolve). Define the 'geometric' energy-density ρ RW and pressure p RW by</text>
<formula><location><page_7><loc_27><loc_63><loc_91><loc_65></location>8 πρ RW := 3(˙ a 2 + glyph[epsilon1] ) /a 2 , 8 πp RW := ( -2 a a -˙ a 2 -glyph[epsilon1] ) /a 2 , (4)</formula>
<text><location><page_7><loc_88><loc_58><loc_88><loc_60></location>glyph[negationslash]</text>
<text><location><page_7><loc_14><loc_29><loc_91><loc_61></location>so that, if the spacetime has a cosmological constant Λ, the energy-density and pressure of the cosmic fluid is ρ = ρ RW -Λ 8 π , p = p RW + Λ 8 π . We make the assumption that ρ RW + p RW = 0 so that we do have a non-trivial cosmic fluid (this allows us to define t unambiguously). Concerning the boundary Ω RW it is assumed to be connected (this is irrelevant because the matching conditions are local, the assumption is made merely for notational convenience), and nowhere tangential to a hypersurface of constant cosmic time t . This assumption is physically reasonable and automatically satisfied if the boundary is causal. In fact, dropping this assumption would only make the presentation more involved, but would not spoil any of the results (see [34] for a discussion). Finally, we assume that Ω RW is spatially compact. A sufficient condition for this is the 'energy condition' ρ RW ≥ 0, see [33], and this is in fact the assumption made in [33]. However, it can be proved that spatial compactness suffices for the validity of all the results below. Note finally, that spatial compactness is indeed an assumption: allowing for non-compact boundaries, additional configurations not covered by the uniqueness results do arise, as shown in [45] (see also references therein), where configurations with planar and hyperbolic symmetries were found and analized. It would be interesting to analyze how far can one extend uniqueness without any compactness assumption on the boundary. Nevertheless, for the purposes of the Einstein-Straus problem, compactness is a completely natural assumption, as we want the local physics unaffected by the cosmological expansion be spatially confined.</text>
<text><location><page_7><loc_14><loc_21><loc_91><loc_29></location>By a detailed analysis of the matching conditions, the following restrictions on the boundary Ω RW are obtained [34]. First of all, the intersection S RW t of Ω RW with a hypersurface of constant cosmic time t is a sphere. More precisely, for any t ∈ I , there exists a point c ( t ) ∈ M so that S RW t is a coordinate sphere of radius R ( t ) in a spherical coordinate system centered at c ( t ). The radius R ( t ) is restricted to satisfy the bound</text>
<formula><location><page_7><loc_41><loc_17><loc_91><loc_19></location>Σ ' 2 -Σ 2 ˙ a 2 | R = R ( t ) > 0 . (5)</formula>
<text><location><page_7><loc_14><loc_9><loc_91><loc_16></location>This inequality means that the surface S RW t is non-trapped (i.e. has a mean curvature vector spacelike everywhere). The necessity of this condition can be understood from the fact that no closed spacelike surface in a static spacetime can have a future (or past) causal and not-identically zero mean curvature vector [42]. The spherical symmetry of</text>
<text><location><page_8><loc_10><loc_73><loc_86><loc_90></location>the surface S RW t and the fact that the matching conditions force the mean curvature vector to be continuous across the matching hypersurface implies that S RW t must be nontrapped, which is precisely (5). Note also that if the static Killing vector ξ admits Killing horizons and hence changes causal character, then the bound (5) is no longer necessary. This behaviour occurs in the Einstein-Straus model when a ( t ) is sufficiently small so that Σ c a ( t ) = 2 m . The breakdown of the ODE (3) in the Einstein-Straus model is just a manifestation of the breakdown of the the static coordinate system in the interior region. In Kruskal coordinates, the matching would continue across Σ c a ( t ) = 2 m without problem. Something similar would occur in the general setting if we allowed the static Killing to change causal character.</text>
<text><location><page_8><loc_10><loc_60><loc_86><loc_73></location>Returning to the shape of Ω RW , the center point c ( t ) follows a geodesic in ( M , g M ) (which may degenerate to a point). The parameter t is not in general an affine parameter for the geodesic, so the center c ( t ) is a priori allowed to move at any speed (in fact the trajectory can have turning points along the curve). In order to describe the matching hypersurface, choose any point c 0 along this geodesic and let c ' 0 be its tangent vector. We can choose a spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 so that the axis of symmetry ˆ θ = 0 is along the tangent vector c ' 0 . In this coordinate system, the center c ( t ) will have coordinates</text>
<formula><location><page_8><loc_34><loc_57><loc_59><loc_59></location>c ( t ) = { ˆ R = σ ( t ) , | cos ˆ θ | = 1 }</formula>
<text><location><page_8><loc_10><loc_48><loc_86><loc_56></location>(the value of ˆ θ can be 0 or π depending on whether c ( t ) lies after or before c 0 along the geodesic). The function σ ( t ) describes the motion of c ( t ) along the curve. The relationship between the spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 and a spherical coordinate system { R,θ, φ } centered at c ( t ) with parallel axis (i.e. with coincident lines | cos θ | = 1 and | cos ˆ θ | = 1) is easily found to be</text>
<formula><location><page_8><loc_24><loc_41><loc_86><loc_47></location>Σ( ˆ R ) sin ˆ θ = Σ( R ) sin θ Σ( ˆ R ) cos ˆ θ = Σ ' ( σ ( t ))Σ( R ) cos θ +Σ( σ ( t ))Σ ' ( R ) ˆ φ = φ . (6)</formula>
<text><location><page_8><loc_10><loc_37><loc_86><loc_40></location>Thus, the matching hypersurface Ω RW in the spherical coordinates centered at c 0 can be parametrized by coordinates t, θ, φ as</text>
<formula><location><page_8><loc_15><loc_29><loc_78><loc_36></location>Σ( ˆ R ( t, θ )) = √ sin 2 θ Σ 2 | R ( t ) + ( cos θ Σ ' | σ ( t ) Σ | R ( t ) +Σ | σ ( t ) Σ ' | R ( t ) ) 2 cotan( ˆ θ ( t, θ )) = cotan( θ ) Σ ' | σ ( t ) + Σ | σ ( t ) Σ ' | R ( t ) sin θ Σ | R ( t ) ˆ φ = φ ,</formula>
<text><location><page_8><loc_10><loc_22><loc_86><loc_28></location>which is a rather complicated form for the matching hypersurface. A useful alternative is to use a coordinate system { t, R, θ, φ } in ( W RW , g RW ) such that, for each t , { R,θ, φ } is the spherical coordinate system centered at c ( t ). Applying the coordinate transformation (6) to the metric</text>
<formula><location><page_8><loc_25><loc_19><loc_71><loc_21></location>g RW = -dt 2 + a 2 ( t ) ( d ˆ R 2 +Σ 2 ( ˆ R ) ( d ˆ θ 2 +sin 2 ˆ θd ˆ φ 2 ))</formula>
<text><location><page_8><loc_10><loc_16><loc_14><loc_17></location>gives</text>
<formula><location><page_8><loc_16><loc_10><loc_86><loc_15></location>ds 2 = -dt 2 + a 2 ( t ) [ ( dR + f ( t ) cos θdt ) 2 +(Σ( R ) dθ -f ( t )Σ ' ( R ) sin θdt ) 2 + + Σ 2 ( R ) sin 2 θdφ 2 ] . (7)</formula>
<text><location><page_9><loc_14><loc_85><loc_91><loc_90></location>where f ( t ) = ˙ σ ( t ). The explicit calculation leading to (7) is somewhat long, a much more elegant method of obtaining this form of the metric is discussed in the Appendix of [34]. In these coordinates, the matching hypersurface Ω RW is simply { R = R ( t ) } .</text>
<text><location><page_9><loc_14><loc_80><loc_91><loc_85></location>The matching conditions in the FLRW part are supplemented with a differential equation relating the trajectory of the center σ ( t ) with the radius R ( t ). To write it down, define a function β ( t ) via</text>
<formula><location><page_9><loc_42><loc_76><loc_91><loc_80></location>tanh β ( t ) = glyph[epsilon1] 1 Σ˙ a Σ ' ∣ ∣ ∣ ∣ R = R ( t ) , (8)</formula>
<text><location><page_9><loc_14><loc_69><loc_91><loc_75></location>where glyph[epsilon1] 1 = ± 1 depending on whether the FLRW region to be matched is R > R ( t ) or R < R ( t ) (more specifically, the manifold with boundary W RW is { glyph[epsilon1] 1 R ≥ glyph[epsilon1] 1 R ( t ) } ). Note that β ( t ) is well-defined because of (5). The ODE relating R ( t ) and σ ( t ) is conveniently written using an auxiliary function ∆( t ) = 0 as the following pair of differential equations</text>
<text><location><page_9><loc_49><loc_69><loc_49><loc_70></location>glyph[negationslash]</text>
<formula><location><page_9><loc_20><loc_58><loc_91><loc_67></location>˙ f = ( 2 glyph[epsilon1] 1 ˙ a ˙ R tanh β + ˙ ∆ ∆ -2 cosh β sinh β ˙ β ) f, f 2 Σ ' Σ ∣ ∣ ∣ ∣ R = R ( t ) -R + glyph[epsilon1] 1 ˙ a ˙ R 2 tanh β + ˙ ∆ ∆ ( ˙ R + glyph[epsilon1] 1 a tanh β ) -2 ( glyph[epsilon1] 1 a + ˙ R tanh β ) ˙ β = 0 . (9)</formula>
<text><location><page_9><loc_14><loc_47><loc_91><loc_57></location>In summary, the static domain embedded in the FLRW regions consists of a sphere with time dependent radius R ( t ) and with center moving across the FLRW spacetime along a geodesic. Speed along the geodesic and radius R ( t ) are linked by (9). The model is not spherically symmetric because the center of the sphere is allowed to move. However, it is very close to spherically symmetric and it turns out that the center of the sphere must be at rest for several relevant matter models in the static domain, as we discuss next.</text>
<text><location><page_9><loc_14><loc_28><loc_91><loc_46></location>An important consequence of the matching procedure (cf. Lemma 1 in [34]) is that the Killing vector field ξ is everywhere transverse to the matching hypersurface Ω ST in the static region. Combining this with the fact that the static geometry is invariant along ξ it follows that the static metric in the spacetime region obtained by dragging Ω ST with the static Killing vector can be fully determined in terms of hypersurface geometry of Ω ST . Since, in turn, the geometry on Ω ST is related to the geometry of Ω RW via the matching conditions, it follows that the spacetime geometry of the static region becomes completely determined [34] in a neighbourhood of its matching hypersurface in terms of the FLRW geometry and the functions R ( t ) , σ ( t ) and ∆( t ) (see Theorem 1 in [34] for details). Specifically, there exist coordinates { T, t, θ, φ } so that the metric g ST takes the form (note that t is a spacelike coordinate in the static domain)</text>
<formula><location><page_9><loc_20><loc_18><loc_91><loc_26></location>g ST = -(cosh β + µ sinh β ) 2 ∆ 2 dT 2 +( µ cosh β +sinh β ) 2 dt 2 + + a 2 ( t )Σ 2 ( R ( t )) ( dθ -f ( t ) Σ ' Σ ∣ ∣ ∣ ∣ R = R ( t ) sin θdt ) 2 +sin 2 θdφ 2 , (10)</formula>
<text><location><page_9><loc_14><loc_9><loc_91><loc_16></location>where µ := glyph[epsilon1]a ( t )( ˙ R ( t ) + f ( t ) cos θ ). The matching hypersurface Ω ST is defined by the embedding { t, θ, φ } → { T = T ( t ) , t, θ, φ } , where T ( t ) satisfies ˙ T ( t ) = ∆( t ) and the portion of the static spacetime to be matched to the exterior region is { T ≥ T ( t ) } . The metric (10) is foliated by round spheres { T = const , t = const } but it is not spherically</text>
<text><location><page_10><loc_10><loc_85><loc_86><loc_90></location>symmetric in general (unless f ( t ) = 0 and R ( t ) = 0). To complete the picture, we review the energy-momentum tensor in the static part. Introduce two one-forms and one symmetric two-tensor h by</text>
<formula><location><page_10><loc_20><loc_76><loc_76><loc_84></location>θ 0 = (cosh β + µ sinh β ) ∆ dT, θ 1 = ( µ cosh β +sinh β ) dt, h = a 2 ( t )Σ 2 ( R ( t )) ( dθ -f ( t ) Σ ' Σ ∣ ∣ ∣ ∣ R = R ( t ) sin θdt ) 2 +sin 2 θdφ 2 ,</formula>
<text><location><page_10><loc_10><loc_74><loc_63><loc_75></location>The Einstein tensor of ( W ST , g ST ) is (cf. Proposition 1 in [34])</text>
<formula><location><page_10><loc_31><loc_69><loc_65><loc_73></location>1 8 π G ST = ρ ST θ 0 ⊗ θ 0 + p ST r θ 1 ⊗ θ 1 + p ST t h</formula>
<text><location><page_10><loc_10><loc_67><loc_33><loc_69></location>where ρ ST , p ST r and p ST t read</text>
<formula><location><page_10><loc_11><loc_51><loc_86><loc_67></location>ρ ST = ρ RW µ -p RW tanh β µ +tanh β , ρ ST + p ST r = ( ρ RW + p RW ) µ ( µ sinh β +cosh β ) (sinh β + µ cosh β ) , (11) p ST t = 3 p RW -ρ RW 6 + tanh β ( 2 f 2 sin 2 θ -Σ 2 ( R ( t )) ( ρ + p ) ( µ 2 -1) ) 16 π Σ 2 ( R ( t )) ( µ +tanh β ) (1 + µ tanh β ) + + [ -¨ β + ˙ ∆ ∆ ( ˙ a a 1 tanh β + ˙ β ) -2 ˙ β ˙ a a ( 1 + µ tanh β ) + µ ( a a + µ ˙ a 2 a 2 tanh β )] 8 π cosh 2 β ( µ +tanh β ) (1 + µ tanh β ) ,</formula>
<text><location><page_10><loc_10><loc_40><loc_86><loc_49></location>and ρ RW and p RW were defined in (4). Several consequences of (11) can be drawn [33, 34]. Concerning the uniqueness of the Einstein-Straus model, under the assumption ρ ST + p ST = 0 (which includes vacuum with or without cosmological constant or a non-singular electromagnetic field) it follows that µ = 0 and hence f ( t ) = 0 and R ( t ) = 0. The second equation in (9) gives (with an appropriate but still completely general choice of integration constant),</text>
<formula><location><page_10><loc_28><loc_35><loc_65><loc_39></location>˙ T ( t ) = ∆( t ) = 1 Σ ' c cosh 2 β ( t ) = Σ ' c Σ ' c 2 -Σ 2 c ˙ a 2 ,</formula>
<text><location><page_10><loc_10><loc_31><loc_86><loc_35></location>where (8) and the definitions of Σ c and Σ ' c in Section 2 have been used. The static metric simplifies to</text>
<formula><location><page_10><loc_21><loc_27><loc_71><loc_30></location>g ST = -( Σ ' c 2 -Σ 2 c ˙ a 2 ) dT 2 + Σ 2 c ˙ a 2 Σ ' c 2 -Σ 2 c ˙ a 2 dt 2 +Σ 2 c a 2 ( t ) d Ω 2 .</formula>
<text><location><page_10><loc_10><loc_20><loc_86><loc_26></location>From this metric, uniqueness of the Einstein-Straus model as the unique static vacuum (with or without cosmological constant) region embedded in a FRLW cosmological model follows easily. So, static vacuoles in a FLRW model must be spherically symmetric both in shape and interior geometry.</text>
<text><location><page_10><loc_10><loc_9><loc_86><loc_19></location>It is an open problem to analyze whether there are any physically realistic matter models in the interior static region for which the motion of the static domain inside FLRW has interesting properties. Note that a priori nothing prevents the geodesic c ( t ) from being spacelike, so the motion of the static domain can in principle be superluminal for the cosmic observers. This is of course reminiscent to the superluminal warp drive discovered by Alcubierre [1].</text>
<section_header_level_1><location><page_11><loc_14><loc_89><loc_91><loc_90></location>3.2 Uniqueness results in the stationary and axisymmetric case</section_header_level_1>
<text><location><page_11><loc_14><loc_83><loc_91><loc_87></location>The study of axially symmetric equilibrium regions in FLRW universe was dealt with in [52], and, in short, the main result found was that those stationary regions must, in fact, be static, and therefore the results of the previous section apply.</text>
<text><location><page_11><loc_14><loc_52><loc_91><loc_82></location>With the same definitions and assumptions concerning the FLRW region ( W RW , g RW ) and its boundary Ω RW as in the previous section, we assume now that the interior region ( W SX , g SX ) is (strictly) stationary and axisymmetric. More specifically, we demand that (i) the spacetime admits a two-dimensional group of isometries G 2 acting simply-transitively on timelike surfaces T 2 and containing a (spacelike) cyclic subgroup, so that G 2 = R × S 1 , and (ii) that the set of fixed points of the cyclic group is not empty. Consequences of the definition are that the G 2 group has to be Abelian [17, 14, 3], and that the set of fixed points must form a timelike two-surface [40], which is the axis. The axial Killing η is then intrinsically defined by normalizing it demanding ∂ α η 2 ∂ α η 2 / 4 η 2 → 1 at the axis. See also [61] and [13]. In addition, we demand that the isometry group is orthogonally transitively (OT), i.e. that the two planes orthogonal to the orbits of the isometry group are surface forming. This assumption is also known as the 'circularity condition', and in many cases of interest it follows as a consequence of the Einstein field equations. Indeed, the G 2 on T 2 group must act orthogonally transitively in a region that intersects the axis of symmetry whenever the Ricci tensor has an invariant 2-plane spanned by the tangents to the orbits of the G 2 on T 2 group [16]. By the Einstein field equations, this includes Λ-term type matter (i.e. vacuum with or without cosmological constant), perfect fluids without convective motions, and also stationary and axisymmetric electrovacuum [61].</text>
<text><location><page_11><loc_14><loc_47><loc_91><loc_51></location>An OT stationary and axisymmetric spacetime ( V SX , g SX ) is locally characterized by the existence of a coordinate system { T, Φ , x M } ( M,N,... = 2 , 3) in which the line-element for the metric g SX outside the axis reads [61]</text>
<formula><location><page_11><loc_29><loc_44><loc_91><loc_46></location>g SX = -e 2 U ( dT + Ad Φ) 2 + e -2 U W 2 d Φ 2 + g MN dx M dx N , (12)</formula>
<text><location><page_11><loc_14><loc_37><loc_91><loc_43></location>where U , A , W and g MN are functions of x M , the axial Killing vector field is given by η = ∂ Φ , and a timelike (future-pointing) Killing vector field is given by ξ = ∂ T . Although useful for the sake of clarity, the use of coordinates is not essential for the results below, which only depend on the intrinsic geometric properties of of ( W SX , g SX ).</text>
<text><location><page_11><loc_14><loc_27><loc_91><loc_36></location>As before, no specific matter content is assumed in the stationary and axisymmetric region. Regarding the matching hypersurface Ω, besides those in the previous Section 3.1, we make the only extra assumption that it preserves the axial symmetry [62] of ( W SX , g SX ) and of ( W RW , g RW ). This means that Ω SX is assumed to be invariant under the axial symmetry of ( W SX , g SX ) and that there is an axial Killing vector η RW in the Killing algebra of ( W RW , g RW ) tangent to Ω RW .</text>
<text><location><page_11><loc_14><loc_15><loc_91><loc_26></location>With these assumptions at hand, in [52], it is proven, first, that the stationary (timelike) Killing vector field ξ is nowhere tangent to Ω SX . As explained in the previous section, this serves in particular to construct a neighbourhood of Ω SX by dragging it along the orbits of ξ , in which the geometry is thus fully determined by the information in Ω SX . The main result in [52] is that if a OT stationary and axisymmetric region ( W SX , g SX ) can be matched to a FLRW region through a hypersurface Ω SX preserving the axial symmetry, then the region ( W SX , g SX ) must be, in fact, static on a neighbourhood of Ω SX .</text>
<text><location><page_11><loc_14><loc_9><loc_91><loc_14></location>All in all, in that neighbourhood of the matching hypersurface the OT stationary axisymmetric region ( W SX , g SX ) thus becomes a static axisymmetric region ( W ST , g ST ), and therefore the results of the previous Section 3.1 (cf. [34]) apply.</text>
<text><location><page_12><loc_10><loc_82><loc_86><loc_90></location>So far, no explicit condition on the matter content of the stationary region has been used. When conditions on the matter content on the (OT) stationary and axisymmetric (and hence static) region are imposed, the functions that determine the matching hypersurface and the static geometry are determined by the results reviewed in Section 3.1.</text>
<text><location><page_12><loc_10><loc_66><loc_86><loc_81></location>In particular, and for completeness, let us consider a vacuum (with or without a cosmological constant) stationary and axisymmetric region ( W SX , g SX ) matched to FLRW preserving the axial symmetry. As mentioned above, a vacuum matter content forces the axial symmetry and stationary group G 2 on T 2 to act orthogonal transitively. On the other hand, a region of FLRW ( W RW , g RW ) matched to a vacuum region must satisfy the assumptions made and, in particular, have a causal Ω RW (in fact tangent to the fluid flow). The above result implies then that the vacuum region must be static. The results of Section 3.1 thus apply, and imply, in turn, that the whole region (not just its boundary) has to be spherically symmetric, and hence Schwarzschild.</text>
<text><location><page_12><loc_10><loc_60><loc_86><loc_66></location>To sum up, this means that the only stationary and axially symmetric vacuum region that can be matched to FLRW is a spherically symmetric piece of Schwarzschild. This constitutes still another uniqueness result of the Einstein-Straus model when the vacuum region lies inside FLRW.</text>
<text><location><page_12><loc_10><loc_49><loc_86><loc_59></location>The complementary result, when the vacuum region lies outside FLRW, constitutes a uniqueness result of the Oppenheimer-Snyder model [53]. It is worth noticing that this result can also be interpreted as a no-go result for the possible interiors of Kerr. Indeed, this result states that an axially symmetric region of (an evolving) FLRW, irrespective of its relative rotation with the exterior, cannot be the source of a stationary and axisymmetric vacuum region, in particular, Kerr.</text>
<section_header_level_1><location><page_12><loc_10><loc_42><loc_86><loc_46></location>4 Robustness of Einstein-Straus: Generalized exact cosmologies</section_header_level_1>
<text><location><page_12><loc_10><loc_28><loc_86><loc_40></location>In the previous sections, the robustness of the Einstein-Straus model has been discussed by considering generalizations of the interior vacuole and keeping the FLRW model as the exterior cosmological model. The question arises as to what happens if these symmetry assumptions concerning the exterior metric are relaxed. There are two different ways to study departures from the spherical FLRW: either perturbatively or using exact solutions. In this section, we concentrate on the later possibility and, in particular, we review the results found in [46] for spatially homogeneous (but anisotropic) cosmologies.</text>
<text><location><page_12><loc_10><loc_15><loc_86><loc_28></location>A step in the direction of generalising the exterior was taken by Bonnor, who considered the embedding of a Schwarzschild region in an expanding spherically symmetric inhomogeneous Lemaˆıtre-Tolman-Bondi (LTB) exterior. He found that such a matching is possible in general, and that it allows the average density of the Schwarzschild interior to be chosen independently of the exterior LTB density [12]. So, clearly, if the spherical symmetry is kept, the exterior can be readily generalized to the case of inhomogeneous dust cosmologies. An interesting review about physical aspects of spherically symmetric Einstein-Straus and McVittie type models can be found in [15].</text>
<text><location><page_12><loc_10><loc_9><loc_86><loc_14></location>While keeping the spherical symmetry of the cavity allows for straightforward generalizations of Einstein-Straus, breaking this symmetry brings in unexpected complications, as we have seen in the previous section. The same seems to hold if we consider exact</text>
<text><location><page_13><loc_14><loc_87><loc_91><loc_90></location>generalizations of the FLRW cylindrical symmetry exterior to spatially homogeneous but anisotropic spacetimes. This problem was considered in [46] and we summarize it next:</text>
<text><location><page_13><loc_14><loc_75><loc_91><loc_87></location>Consider the problem of matching, across a hypersurface Ω which is spatially a topological sphere 1 , of an interior locally cylindrically symmetric (LCS) static spacetime ( W ST , g ST ), which represents a spatially compact region, to a spatially homogeneous anisotropic exterior ( W HOM , g HOM ) having a Lie group G 3 acting on S 3 surfaces. Once more, we make no assumptions a priori on the matter contents, so the main results are purely geometric. Only at the end of the section, assumptions on the matter content will lead to a final no-go result.</text>
<text><location><page_13><loc_14><loc_58><loc_91><loc_74></location>We wish to preserve globally the axial symmetry and thus we need to impose first the existence of a group of cyclic symmetries in the exterior region. This, combined with the assumption of a spacelike spherical topological shaped 2 Ω ST , implies the existence of an exterior axis. Thus, the cyclic symmetry in the exterior must really be an axial symmetry (see the discussion in Section 3.2). Moreover, we require that the cylindrical symmetry is preserved (in the sense of [62]) at least on a non-empty open subset of Ω. This has the consequence that ( W HOM , g HOM ) must admit a G 4 on S 3 group of isometries, so that it is locally rotationally symmetric (LRS). In [46], it is shown how all the LRS spatially homogeneous metrics can be written in the form adapted to the two commuting Killing vectors defining the cylindrical symmetry ∂ ϕ and ∂ z , where ∂ ϕ is axial with axis at r = 0:</text>
<formula><location><page_13><loc_24><loc_54><loc_91><loc_56></location>g HOM = -dt 2 + b 2 ( t ) dr 2 -2 glyph[epsilon1]r b 2 ( t ) drdz + ˆ C 2 dϕ 2 +2 ˆ Edzdϕ + ˆ D 2 dz 2 (13)</formula>
<text><location><page_13><loc_14><loc_51><loc_18><loc_52></location>with</text>
<formula><location><page_13><loc_33><loc_46><loc_91><loc_49></location>ˆ C 2 = b 2 ( t )Σ 2 ( r, k ) + na 2 ( t )( F ( r, k ) + k ) 2 , ˆ D 2 = a 2 ( t ) + glyph[epsilon1]r 2 b 2 ( t ) , ˆ E = na 2 ( t )( F ( r, k ) + k ) , (14)</formula>
<text><location><page_13><loc_14><loc_42><loc_51><loc_44></location>where the functions Σ and F are given by</text>
<formula><location><page_13><loc_23><loc_36><loc_81><loc_41></location>Σ( r, k ) = sin r, k = +1 r, k = 0 sinh r, k = -1 and F ( r, k ) = -cos r, k = +1 r 2 / 2 , k = 0 cosh r, k = -1 ,</formula>
<text><location><page_13><loc_14><loc_31><loc_91><loc_34></location>and where glyph[epsilon1] and n are given such that glyph[epsilon1] = 0 , 1; n = 0 , 1; glyph[epsilon1]n = glyph[epsilon1]k = 0 3 . The metrics are classified according to these constants in Table 1.</text>
<text><location><page_13><loc_14><loc_27><loc_91><loc_30></location>The matching conditions are then investigated and a crucial step was to observe that they lead to the following necessary relations involving only exterior metric functions:</text>
<formula><location><page_13><loc_25><loc_23><loc_91><loc_25></location>ˆ D ,t ˆ C ,r -ˆ D ,r ˆ C ,t Ω = 0 , ˆ E ,t ˆ D ,r -ˆ E ,r ˆ D ,t Ω = 0 , ˆ E ,t ˆ C ,r -ˆ E ,r ˆ C ,t Ω = 0 , (15)</formula>
<text><location><page_13><loc_14><loc_14><loc_91><loc_18></location>2 This implies the existence of north and south poles on Ω ST where the axial killing vector in the interior vanishes and, therefore, also the generator of the cyclic symmetry in the exterior region on Ω HOM by construction.</text>
<text><location><page_13><loc_14><loc_9><loc_91><loc_13></location>3 Let us note that the case glyph[epsilon1] = n = 0 with k = 1 is special, since it corresponds to the Kantowski-Sachs (KS) class of metrics, which do not admit a G 3 on S 3 subgroup [61]. It was included in the study for completeness.</text>
<table>
<location><page_14><loc_36><loc_78><loc_60><loc_90></location>
<caption>Table 1: Classification of possible G 3 on S 3 subgroup types according to the values of { glyph[epsilon1], k, n } for the metric given by (13).</caption>
</table>
<text><location><page_14><loc_10><loc_67><loc_86><loc_70></location>which, for non-static exteriors, imply n = 0 and thus exclude Bianchi types II, III, VIII and IX.</text>
<text><location><page_14><loc_10><loc_58><loc_86><loc_66></location>By inserting (15) back in the matching conditions one is able to prove a series of results that lead to the following conclusion: The only expanding spatially homogeneous spacetimes which can be matched to a locally cylindrically symmetric static interior region preserving the (cylindrical) symmetry, across a non-spacelike hypersurface which is spatially a topological sphere, are given by</text>
<formula><location><page_14><loc_24><loc_55><loc_86><loc_57></location>ds 2 = -dt 2 + β 2 dz 2 + b 2 ( t ) [ ( dr -glyph[epsilon1]r dz ) 2 +Σ 2 ( r, k ) dϕ 2 ] , (16)</formula>
<text><location><page_14><loc_10><loc_50><loc_86><loc_54></location>where β is constant. This metric for k = 1 belongs to the Kantowski-Sachs class, when k = -1 admits a G 3 on S 3 of Bianchi type III, and when k = 0 of Bianchi types I,V,VII 0 ,VII h .</text>
<text><location><page_14><loc_10><loc_39><loc_86><loc_50></location>The metrics (16) are very special, partly due to the fact that condition a ,t = 0 (see (13)-(14)) imposes a strong constraint, implying that there cannot be any time (nor space) evolution along the direction orthogonal to the orbits of the subgroup G 3 on S 2 of the LRS. There are also constraints imposed through the matching in the interior region and the interested reader can find those in [46]. Note that the no-go result found in [59] is trivially recovered, since FLRW is included in the LRS class for b ( t ) = a ( t ), and the above would imply a static FLRW metric.</text>
<text><location><page_14><loc_10><loc_27><loc_86><loc_38></location>If one specifies a particular class of matter fields, then one gets further constraints on the cosmological dynamics. For example, if the matter in the static region is not specified but the dynamical (cosmological) region is assumed to contain a perfect fluid with pressure p and energy-density ρ satisfying the dominant energy condition everywhere, then glyph[epsilon1] = 0 necessarily, which corresponds to a stiff fluid equation of state ρ = p = α 2 / (4 t 2 ( α -kt ) 2 ), with b ( t ) = √ αt -kt 2 , where α > 0. On the other hand, if the interior is vacuum then the exterior must be also vacuum.</text>
<text><location><page_14><loc_10><loc_16><loc_86><loc_26></location>The overall no-go results, in this case, can be seen in two ways: either as a consequence of the assumption that the interior metric is static and cylindrically symmetric, which seems to prohibit time dependence along one direction, or as a consequence of the particular exterior metrics we are considering, which are homogeneous then prohibiting the coefficients along this direction to be space dependent. The perturbative approach described in the next sections can help to clarify this question.</text>
<text><location><page_14><loc_10><loc_9><loc_86><loc_16></location>To conclude this section we remark that there exists an example of a Einstein-Straus model with exact non-spherical inhomogeneous cosmologies. This is provided by the Szekeres dust solution which has no Killing vectors, in general, but contains intrinsic symmetries on 2-spaces of constant curvature: The Szekeres solution is divided into class</text>
<text><location><page_15><loc_14><loc_77><loc_91><loc_90></location>I, which generalizes the LTB solution having non-concentric spheres of constant mass, and class II which includes the Kantowski-Sachs solution. Class I solutions have been proved to be interiors to the Schwarzschild solution [9] and this result has been generalized to include the cosmological constant [31, 45]. As mentioned before, one can invert the roles of the two spacetimes involved and hence construct an Einstein-Straus type model with a Schwarzschild or Kottler cavity within a class I Szekeres' cosmology. Let us remark that the Szekeres class has been used recently in Swiss cheese models as interiors to FLRW (see [7] and references therein).</text>
<text><location><page_15><loc_14><loc_71><loc_91><loc_76></location>Class II Szekeres dust metrics are less known, but contain curious inhomogeneous solutions with cylindrical symmetry [60]. In this case, it seems harder to be able to get a physically reasonable Einstein-Straus model considering what we have described above.</text>
<section_header_level_1><location><page_15><loc_14><loc_66><loc_87><loc_68></location>5 Brief overview of perturbative matching theory</section_header_level_1>
<text><location><page_15><loc_14><loc_35><loc_91><loc_64></location>A perturbed spacetime consists of a symmetric two-covariant tensor (the 'perturbation metric') defined on a fixed spacetime (the 'background'). From a structural point of view, spacetime perturbation theory is a gauge theory in the sense that many perturbation metrics describe the same physical situation (i.e. they are gauge related). The underlying geometrical reason for this gauge freedom can be understood from the following intuitive picture of perturbation theory. We imagine a one-parameter family of spacetimes ( V ε , g ε ) such that all the manifolds are diffeomorphic to each other. This allows one to pull back g ε onto a single manifold in the family (say V 0 := V ε =0 ) and work with a one-parameter family of metrics on a single manifold. If all the construction is smooth in ε , derivatives with respect to this parameter can be taken. The perturbation metric g (1) is simply the derivative at ε = 0 of this family of metrics. However, the identification of points in the different manifolds (the diffeomorphism above) is highly non-unique. Any other choice of identification would lead to a different, but geometrically equivalent, perturbation metric. This is the gauge freedom of the theory. Intuitively, it is clear that the gauge freedom will consist of a vector field on the background, because this measures the shift of the new identification with respect to the previous one, and an initial direction (in ε ) is all what is required to compute derivatives with respect to ε at ε = 0.</text>
<text><location><page_15><loc_14><loc_21><loc_91><loc_35></location>When two spacetimes with boundary are matched, an identification of the boundaries is required. As already mentioned before, if the boundaries are nowhere null, the matching conditions require the equality of the induced metric and second fundamental form (with appropriate choices of orientation). To compare the tensors it is necessary to pull them back to a single manifold and this is done via the identification of boundaries. Contrarily than before, the matching theory is strongly dependent on the identification of the boundaries. In fact, the matching conditions demand the existence of one such identification for which the first and second fundamental forms agree.</text>
<text><location><page_15><loc_14><loc_9><loc_91><loc_21></location>Assume now that we are studying perturbation theory on a background spacetime constructed from the matching of two spacetimes. The question then arises of what are the conditions that the metric perturbation tensors on each side must satisfy to have a perturbed matching spacetime. This issue is somewhat more involved than one may think a priori and it was solved in a complete manner for the first time by Battye and Carter [4] and independently by Mukohyama [47] (this has been extended to second order in [35]). Previous attempts [24, 23, 43] did not take into account all the subtleties of</text>
<text><location><page_16><loc_10><loc_34><loc_86><loc_90></location>the interplay between two completely different gauge freedoms inherent to this problem. Indeed, in the picture above of perturbation theory in terms of a collection of spacetimes ( V ε , g ε ), each one of them arises now as the matching of two spacetimes with boundary W ± ε across their respective boundaries Ω ± ε . For better visualization, assume that each one of W ± ε is a submanifold with boundary of a larger boundary-less manifold ̂ W ± ε and assume that the { ̂ W + ε } manifolds are identified among themselves (say with ̂ W + 0 := ̂ W + ε =0 ) via an ε -dependent diffeomorphism. The hypersurface Ω + ε projects down to ̂ W + 0 as a hypersurface ̂ Ω + ε . Now we have a collection of hypersurfaces in one single manifold, and one can think of taking ε -derivatives of geometric quantities intrinsic to the hypersurface. The important point is that, given a point p ∈ Ω + ε =0 , we do not know how this point maps into ̂ Ω + ε . For that, it is necessary to prescribe first how p is mapped into Ω + ε . The identification of { Ω + ε } among themselves is an additional gauge freedom. It is fully independent of the standard gauge freedom in perturbation theory (called 'spacetime gauge freedom' from now on) and is referred to as hypersurface gauge freedom [47]. The composition of both identifications gives, as ε varies, and for any p ∈ Ω + ε =0 , a path γ p ( ε ) in ̂ W + 0 starting at p . Since everything is smooth in ε , the tangent vector to this path at ε = 0 defines a vector field Z + on Ω + 0 := Ω + ε =0 (= ̂ Ω ε =0 ). This vector field is not necessarily tangent (nor normal) to Ω + 0 and it depends on both gauge freedoms. A schematic figure for the definition of Z + and how it depends on the gauges is given in Figure 5. If we let n (0) + be a unit normal vector to Ω + 0 , we can decompose Z + = Q + n (0) + + T + , where T + is tangent to Ω + 0 . From the discussion above, it should be clear that Q + is independent of the hypersurface gauge while T + strongly depends on it. In fact, it can always be made zero by an appropriate choice of gauge. However, doing this is not usually a good idea because the matching has two regions and, at each value of ε , the matching requires an identification between Ω + ε and Ω -ε . After a choice of hypersurface gauge to identify Ω + ε with Ω + 0 we have no freedom left to choose a hypersurface gauge to identity Ω -ε and Ω -0 . The matching conditions will tell us how this identification must be done. So, had we chosen T + = 0, we would still have to leave T -free and let the linearized matching theory determine its value. Further details on the double gauge freedom of linearized perturbation theory can be found in the paper of Mukohyama [47] and in [37], where the issue is discussed in depth including a critical analysis of previous attempts to formulate a consistent perturbative matching theory.</text>
<text><location><page_16><loc_10><loc_9><loc_86><loc_33></location>After this brief discussion on gauge issues for linearized matching theory, let us describe the actual perturbative matching conditions (for details see [4, 47, 35]). The matching theory involves the equality of the first and second fundamental forms of the boundaries. To compare them they are pulled-back into a single boundary via the identification. In perturbative matching theory everything occurs on the abstract hypersurface Ω 0 diffeomorphic to Ω + 0 and Ω -0 of the background spacetime. On Ω ± 0 we attach two vector fields Z ± = Q ± n (0) ± + T ± whose geometric meaning has been discussed above. They are not know a priori, firstly, because of the hypersurface gauge freedom, and secondly, because the identification of the boundaries Ω + ε and Ω -ε is not known a priori. To the unknowns Z ± we add four symmetric tensors q (1) ± and K (1) ± intrinsic to Ω 0 which arise as the ε -derivative at ε = 0 of the first fundamental form q ± ε and second fundamental form K ± ε of Ω ± ε . These tensors are intrinsic to Ω ± ε , so before taking ε -derivatives they must be pulled back onto Ω 0 via the hypersurface gauges (on each side). Thus, q (1) ± and K (1) ± are hypersurface gaugedependent by construction. On the other hand, their construction is fully independent of</text>
<figure>
<location><page_17><loc_31><loc_62><loc_85><loc_91></location>
<caption>Figure 1: The different spacetimes ̂ W ε are represented by horizontal sheets, with ̂ W 0 at the bottom. On each ̂ W ε there is a hypersurface Ω ε . The hypersurfaces Ω ε for all ε span a manifold transverse to V ε (the blue sheet in the figure). The choice of spacetime gauge is represented by big dots on each ̂ W ε linked by green curves, while the choice of hypersurface gauge is represented by the grey curves on the blue sheet. The point p is mapped first to q ε through the hypersurface gauge and back to p ε ∈ ̂ W 0 through the spacetime gauge. The points p ε define on ̂ W 0 the path γ p ( ε ). The vector Z is the tangent of γ p ( ε ) at p .</caption>
</figure>
<text><location><page_17><loc_14><loc_42><loc_40><loc_44></location>the spacetime gauge freedom.</text>
<text><location><page_17><loc_14><loc_21><loc_91><loc_42></location>In order to write down their explicit expression, let g (1) ± be the perturbed metric (i.e. the fundamental unknown in metric perturbation theory) on each side of the background spacetime. Let also Ψ ± 0 : Ω 0 → W ± 0 be the embedding of the matching hypersurface on each region of the background spacetime. Let y i ( i, j, . . . = 1 , . . . , n -1) be a local coordinate system on Ω 0 and define tangent vectors e ± i = Ψ ± 0 glyph[star] ( ∂ y i ). There are also unique (up to orientation) unit one-forms n (0) ± normal to the boundaries. We choose them so that the corresponding vector n (0) + points towards W + 0 and n (0) -points outside of W -0 or viceversa. The first and second fundamental forms of the background are simply q (0) ± := Ψ ± 0 glyph[star] ( g (0) ± ) , K (0) ± := Ψ ± 0 glyph[star] ( ∇ ± n (0) ± ), where ∇ ± is the covariant derivative in ( W ± 0 , g (0) ± ). Given that the background configuration is already composed of the matching of V + 0 and V -0 through Ω + 0 := Ω 0 , we already have q (0)+ = q (0) -and K (0)+ = K (0) -. Then q (1) ± and K (1) ± are defined as follows [47]</text>
<formula><location><page_17><loc_29><loc_9><loc_91><loc_19></location>q (1) ij ± = L T ± q (0) ij ± +2 Q ± K (0) ij ± + e ± α i e ± β j g (1) αβ ± , (17) K (1) ij ± = L T ± K (0) ij ± -σD i D j Q ± + Q ± ( -n (0) ± µ n (0) ± ν R (0) ± αµβν e ± α i e ± β j + K (0) il ± K (0) l j ± ) + σ g (1) αβ ± n (0) ± α n (0) ± β K (0) ij ± -n (0) ± µ S (1) ± µ αβ e ± α i e ± β j , (18)</formula>
<formula><location><page_17><loc_39><loc_9><loc_40><loc_10></location>2</formula>
<text><location><page_18><loc_10><loc_85><loc_86><loc_90></location>where σ := g (0) ± ( n (0) ± , n (0) ± ), D is the covariant derivative of (Ω 0 , q (0) ± ), R (0) ± αµβν is the Riemann tensor of ( W ± 0 , g (0) ± ) and S (1) ± α βγ := 1 2 ( ∇ ± β g (1) ± α γ + ∇ ± γ g (1) ± α β -∇ ± α g (1) ± βγ ). The first order matching conditions (in the absence of shells) require the equalities</text>
<formula><location><page_18><loc_31><loc_82><loc_86><loc_83></location>q (1)+ = q (1) -, K (1)+ = K (1) -. (19)</formula>
<text><location><page_18><loc_10><loc_56><loc_86><loc_80></location>We emphasize that Q ± and T ± are a priori unknown quantities and fulfilling the matching conditions requires showing that two vectors Z ± exist such that (19) are satisfied. The spacetime gauge freedom can be exploited to fix either or both vectors Z ± a priori, but this should be avoided (or at least carefully analyzed) if additional spacetime gauge choices are made, in order not to restrict a priori the possible matchings. Regarding the hypersurface gauge, this can be used to fix one of the vectors T + or T -, but not both. Note also that the linearized matching conditions are, by construction, spacetime gauge invariant because, as discussed above, the tensors q (1) ± , K (1) ± are necessarily spacetime gauge invariant. In fact, it is straightforward to check explicitly that the right-hands sides of (17) and (18) are spacetime gauge invariant (the individual terms are not, and it is precisely the spacetime gauge dependence in Z ± which makes these objects spacetime gauge invariant). Moreover, the set of conditions (19) are hypersurface gauge invariant, provided the background is properly matched, since, as shown in [47], under such a hypersurface gauge transformation given by the vector ζ in Ω 0 , q (1) transforms as q (1) + L ζ q (0) , and similarly for K (1) .</text>
<section_header_level_1><location><page_18><loc_10><loc_50><loc_76><loc_52></location>6 Spherical symmetry: Hodge decomposition</section_header_level_1>
<text><location><page_18><loc_10><loc_44><loc_86><loc_49></location>After the previous summary on linearized matching, in this section we introduce the second main ingredient for the linearized Einstein-Straus model reviewed in the following sections: the Hodge decomposition on the sphere [38].</text>
<text><location><page_18><loc_10><loc_34><loc_86><loc_43></location>In order to exploit the underlying spherical symmetry of the background configuration it is common practice to decompose the perturbations, and their related objects and equations, in terms of scalar, vector and tensor harmonics on the sphere. That was the procedure used in the seminal work on perturbations around spherical matched background configurations, due to Gerlach and Sengupta (GS) in [23] and [24], revisited and improved by Mart'ın-Garc'ıa and Gundlach in [43].</text>
<text><location><page_18><loc_10><loc_18><loc_86><loc_33></location>The aim in [38] was to use an alternative method, based on the Hodge decomposition on the sphere in terms of scalars, in order to avoid the need to deal with infinite series of objects. In particular, the whole set of matching conditions for the linearized EinsteinStraus model was presented in [38] as a finite number of equations involving scalars that depend on the three coordinates in the matching hypersurface Ω 0 , in contrast with an infinite number of equations for an infinite set of functions of one variable. It is clear that one can always go from the Hodge scalars to the spherical harmonics decomposition in a straightforward way. However, it is not always easy to rewrite the infinite number of expressions appearing in a spectral decomposition in terms of Hodge scalars.</text>
<text><location><page_18><loc_10><loc_9><loc_86><loc_18></location>Consider the round unit metric Ω AB dx A dx B = dϑ 2 +sin 2 ϑdϕ 2 , with η AB and D A denoting the corresponding volume form and covariant derivative respectively, and ( glyph[star]dG ) A = η C A D C G the Hodge dual with respect to Ω AB . Let us recall that the usual Hodge decomposition on ( S 2 , Ω AB ) states that any one-form V A can be canonically decomposed as V A = D A F +( glyph[star]dG ) A , where F and G are functions on S 2 , and any symmetric tensor T AB</text>
<text><location><page_19><loc_14><loc_87><loc_91><loc_90></location>as T AB = D A U B + D B U A + H Ω AB , for some U A on S 2 , which can be in turn decomposed in terms of scalars.</text>
<text><location><page_19><loc_14><loc_83><loc_91><loc_87></location>Based on this, it is convenient to define the following two functionals. Given three scalars X tr , X 1 and X 2 on ( S 2 , Ω AB ) we define the functional one form V A ( X 1 , X 2 ) as</text>
<formula><location><page_19><loc_39><loc_80><loc_66><loc_82></location>V A ( X 1 , X 2 ) = D A X 1 +( glyph[star]d X 2 ) A ,</formula>
<text><location><page_19><loc_14><loc_77><loc_63><loc_79></location>and the functional symmetric tensor T AB ( X tr , X 1 , X 2 ) as</text>
<formula><location><page_19><loc_26><loc_74><loc_79><loc_76></location>T AB ( X tr , X 1 , X 2 ) = D A V B ( X 1 , X 2 ) + D B V A ( X 1 , X 2 ) + X tr Ω AB .</formula>
<text><location><page_19><loc_14><loc_61><loc_91><loc_73></location>Let us recall that the decomposition defines these X 's on S 2 up to the kernels of the operators V A and T AB . We allowed for the appearance of all these kernels in [38], where their relevance (or their lack of) was already discussed. In order to avoid spurious information and present a more concise review -and also to ease the translation and comparison with the quantities used in the previous literature in terms of the harmonic decompositions,we use the reformulation already presented in [39] where the Hodge decomposition is, in fact, unique.</text>
<text><location><page_19><loc_14><loc_54><loc_91><loc_61></location>Indeed, in order to fix the Hodge decomposition uniquely we define a canonical dual decomposition by demanding that the functions X 1 , X 2 in V A ( X 1 , X 2 ) are always orthogonal (in the L 2 sense on S 2 ) to 1, and the functions X 1 , X 2 in T AB ( X tr , X 1 , X 2 ) are orthogonal to 1 and to the l = 1 spherical harmonics. Schematically, we may use</text>
<formula><location><page_19><loc_30><loc_51><loc_75><loc_53></location>W A S 2 →X 1 , X 2 to indicate W A = V A ( X 1 , X 2 )</formula>
<text><location><page_19><loc_14><loc_48><loc_18><loc_49></location>and</text>
<formula><location><page_19><loc_27><loc_46><loc_78><loc_48></location>W AB S 2 →X tr , X 1 , X 2 when W AB = T AB ( X tr , X 1 , X 2 ) .</formula>
<text><location><page_19><loc_17><loc_43><loc_80><loc_45></location>We will use the following notation: given any function f on S 2 we define</text>
<formula><location><page_19><loc_21><loc_38><loc_84><loc_42></location>f || 0 := Y 0 ∫ S 2 f Y 0 d Ω 2 , f || 1 := Y 1 ∫ S 2 f Y 1 d Ω 2 ( = ∑ m Y m 1 ∫ S 2 f Y m 1 d Ω 2 ) ,</formula>
<text><location><page_19><loc_14><loc_33><loc_91><loc_36></location>so that f -f || 0 is orthogonal to the l = 0 harmonics Y 0 and f -f || 1 is orthogonal to the l = 1 harmonics Y m 1 .</text>
<text><location><page_19><loc_14><loc_25><loc_91><loc_33></location>Note finally that the Hodge decomposition in terms of scalars involves two types of objects depending on their behaviour under reflection on the sphere. The scalars with subscripts 1 and tr remain unchanged under reflection, and are typically called longitudinal, even or polar quantities, while those with subscripts 2 change, and correspond to the transversal, odd or axial quantities.</text>
<text><location><page_19><loc_14><loc_18><loc_91><loc_25></location>Let us consider now the general spherically symmetric spacetime V = M 2 × S 2 with metric g αβ = ω IJ ⊕ r 2 Ω AB , so that ( M 2 , ω IJ ) is a 2-dim Lorentzian space and r > 0 a function on M 2 . The dual in ( M 2 , ω IJ ) will be indicated by ∗ and the covariant derivative by ∇ .</text>
<text><location><page_19><loc_14><loc_9><loc_91><loc_17></location>We can now proceed to decompose any one-form (vector) or symmetric two-tensor on V by first taking the part orthogonal to the sphere and then apply the Hodge canonical decomposition to the part tangent to the sphere. In particular, given a normalized timelike one-form u α orthogonal to the spheres, its corresponding one-form u I on ( M 2 , ω IJ ) (defined by u α = ( u I , 0)) can be used to construct a convenient orthonormal basis { u I , m I }</text>
<text><location><page_20><loc_10><loc_85><loc_86><loc_90></location>so that ω IJ = -u I u J + m I m J (this is u I u I = -1 and m I := ∗ u I ), and consider then the one-form on V defined by m α := ( m I , 0). Given any vector V I we will simply denote by V u and V m the contractions u I V I and m I V I respectively.</text>
<text><location><page_20><loc_10><loc_76><loc_86><loc_85></location>We apply now this decomposition to encode the objects that will describe the (first order) perturbation of a background consisting of two spherically symmetric regions ( W + , g (0)+ ) and ( W -, g (0) -) matched across corresponding spherically symmetric boundaries Ω + 0 and Ω -0 . At each side ± (we avoid the use of ± just now for clarity) the metric perturbation tensor g (1) αβ gets thus decomposed as</text>
<formula><location><page_20><loc_40><loc_68><loc_86><loc_75></location>g (1) IJ = Z IJ , g (1) IA S 2 →Z I 1 , Z I 2 , g (1) AB S 2 →Z S 2 tr , Z S 2 1 , Z S 2 2 , (20)</formula>
<text><location><page_20><loc_10><loc_63><loc_86><loc_66></location>where Z I 1 and Z I 2 are two one-forms defined on M 2 , and analogously for any symmetric tensor. The deformation vector Z α , defined on M at points on Ω, is decomposed as</text>
<formula><location><page_20><loc_32><loc_60><loc_64><loc_62></location>Z α → { Z I → Q,T } ⊕ { Z A S 2 →T 1 , T 2 } ,</formula>
<text><location><page_20><loc_10><loc_44><loc_86><loc_58></location>whereby the part Z I gets decomposed, in turn, onto the normal and tangential parts to Ω 0 , Q and T respectively. Given the (first order) perturbation tensor and the deformation vector at either ± side of the matching hypersurface, one can calculate the symmetric tensors q (1) ij and K (1) ij , i.e. the 'perturbed first and second fundamental forms', using (17)-(18). Recalling now that q (1) ij and K (1) ij are defined on (Ω 0 , q (0) ij ) and that Ω 0 at either side are tangent to the spheres { θ, φ } , let us denote by λ the parameter that follows the direction on Ω 0 orthogonal to the spheres in order to decompose q (1) ij and K (1) ij into q (1) λλ , K (1) λλ , plus</text>
<formula><location><page_20><loc_32><loc_41><loc_86><loc_43></location>q (1) λA S 2 → F q , G q , q (1) AB S 2 → H q , P q , R q , (21)</formula>
<text><location><page_20><loc_10><loc_39><loc_13><loc_40></location>and</text>
<formula><location><page_20><loc_31><loc_37><loc_86><loc_39></location>K (1) λA S 2 → F k , G k , K (1) AB S 2 → H k , P k , R k . (22)</formula>
<text><location><page_20><loc_10><loc_33><loc_86><loc_36></location>Note that all these functions are scalars on the sphere that depend only on λ . The first order matching conditions (19) are therefore equivalent to</text>
<formula><location><page_20><loc_16><loc_27><loc_86><loc_32></location>q (1) λλ + = q (1) λλ -, F q + = F q -, G q + = G q -, H q + = H q -, P q + = P q -, R q + = R q -, K (1) λλ + = K (1) λλ -, F k + = F k -, G k + = G k -, H k + = H k -, P k + = P k -, R k + = R k -. (23)</formula>
<text><location><page_20><loc_10><loc_23><loc_86><loc_26></location>Except for the simplification of the kernels by the canonical decomposition, these are the linearized matching conditions presented in [38].</text>
<section_header_level_1><location><page_20><loc_10><loc_19><loc_67><loc_20></location>6.1 Gerlach and Sengupta (GS) 2+2 formalism</section_header_level_1>
<text><location><page_20><loc_10><loc_9><loc_86><loc_17></location>Let us emphasize again that the conditions (19), and thus (23), concern quantities defined on Ω 0 and are therefore independent on the coordinates used in W + and W -for their computation. These quantities are thus, on the one hand, spacetime gauge independent by construction. Moreover, as discussed in Section 5, the equations are also hypersurface gauge independent. All this makes it unnecessary the use of gauge invariant quantities</text>
<text><location><page_21><loc_14><loc_82><loc_91><loc_90></location>in order to establish the perturbed matching conditions. Having said that, however, the use of gauge independent quantities turns out to be convenient in the end, mostly when one eventually wants to impose the Einstein field equations. As shown in the works [23], [24], [43], the use of spacetime gauge invariants is very convenient in order to combine the Einstein field equations with the perturbed matching conditions.</text>
<text><location><page_21><loc_14><loc_78><loc_91><loc_81></location>One can proceed by constructing gauge invariants in terms of Hodge scalars using analogous expressions to those in the harmonic decomposition constructed in [24, 23, 43].</text>
<text><location><page_21><loc_14><loc_75><loc_91><loc_78></location>Let us now concentrate on the odd (axial) sector. The odd gauge invariant quantities are encoded in the vector [36] (cf. [24])</text>
<formula><location><page_21><loc_38><loc_71><loc_67><loc_73></location>K I := Z I 2 -∇ I Z S 2 2 +2 Z S 2 2 r -1 ∇ I r.</formula>
<text><location><page_21><loc_14><loc_62><loc_91><loc_70></location>Note that K I , as defined above, contains l = 1 harmonics, from Z I 2 , but only the l ≥ 2 sector is gauge invariant. In other words, the part of K I orthogonal to Y 1 (i.e. K I -K I || 1 in the notation above) is the gauge invariant part. Once the orthonormal basis { u I , m I } has been identified at both sides, the odd sector of the linearized matching, which corresponds to the set of equations</text>
<formula><location><page_21><loc_29><loc_58><loc_91><loc_60></location>G q + = G q -, R q + = R q -, G k + = G k -, R k + = R k -, (24)</formula>
<text><location><page_21><loc_14><loc_54><loc_91><loc_57></location>in (23), is equivalent in the l ≥ 2 sector (the part orthogonal to l = 0 and l = 1) to [36] (cf. [24])</text>
<formula><location><page_21><loc_29><loc_51><loc_91><loc_53></location>K + u Ω 0 = K -u , K + m Ω 0 = K -m , ∗ d ( r -2 K + ) Ω 0 = ∗ d ( r -2 K -) (25)</formula>
<text><location><page_21><loc_14><loc_49><loc_41><loc_50></location>plus an equation for T + 2 -T -2 .</text>
<section_header_level_1><location><page_21><loc_14><loc_41><loc_91><loc_46></location>7 Linearized Einstein-Straus model: matching conditions</section_header_level_1>
<text><location><page_21><loc_14><loc_30><loc_91><loc_40></location>We are ready to consider the linearized matching of the perturbed Schwarzschild and FLRW spacetimes, as it was analyzed in [38]. Take the Einstein-Straus model as described in Section 2: the FLRW geometry in cosmic time coordinates (1), the Schwarzschild in standard coordinates (2), and the background matching hypersurface Ω 0 described by Ω RW 0 : { t = t, R = R 0 } and Ω ST 0 : { T = T 0 ( t ) , r = r 0 ( t ) } respectively, where T 0 ( t ) and r 0 ( t ) satisfy (3) and the angular part is again ignored.</text>
<text><location><page_21><loc_14><loc_23><loc_91><loc_29></location>The orthonormal basis we take on the Lorentzian space orthogonal to the spheres is formed by u = dt , m = adR . Note that this choice corresponds to the tangent and normal forms to Ω 0 at Ω 0 , respectively. More precisely, m is chosen to be n (0) at points on Ω 0 . On the Schwarzschild side we have u | Ω 0 = ˙ T 0 ∂ T + ˙ r 0 ∂ r and m | Ω 0 := n (0) = -˙ r 0 dT + ˙ T 0 dr .</text>
<text><location><page_21><loc_14><loc_18><loc_91><loc_22></location>Take the first order perturbations of FLRW, in no specific gauge, formally decomposed into the usual scalar, vector and tensor (SVT) modes, i.e. 4 (Latin indices a, b, c are used for tensors on ( M , g M ))</text>
<formula><location><page_21><loc_42><loc_12><loc_67><loc_16></location>g (1) tt + = -2Ψ g (1) ta + = aW a g (1) ab + = a 2 ( -2Φ γ ab + χ ab )</formula>
<text><location><page_22><loc_10><loc_89><loc_14><loc_90></location>with</text>
<formula><location><page_22><loc_20><loc_86><loc_75><loc_89></location>W a = ∂ a W + ˜ W a , χ ab = ( ∇ a ∇ b -1 3 γ ab ∇ 2 ) χ +2 ∇ ( a Y b ) +Π ab</formula>
<text><location><page_22><loc_10><loc_84><loc_31><loc_85></location>satisfying the constraints</text>
<formula><location><page_22><loc_27><loc_80><loc_69><loc_82></location>∇ a Y a = Π a a = 0 , ∇ a Π ab = 0 , ∇ a ˜ W a = 0 .</formula>
<text><location><page_22><loc_10><loc_74><loc_86><loc_79></location>The canonical Hodge decomposition is then used to encode the part tangent to the spheres into S 2 scalars in the following schematic way [38]: vector</text>
<formula><location><page_22><loc_21><loc_72><loc_75><loc_74></location>˜ W a → ˜ W R ⊕{ ˜ W A S 2 →W 1 , W 2 } , Y a → Y R ⊕{ Y A S 2 →Y 1 , Y 2 } ,</formula>
<formula><location><page_22><loc_32><loc_68><loc_64><loc_70></location>Π RA S 2 →Q 1 , Q 2 , Π AB S 2 →H , U 1 , U 2 .</formula>
<text><location><page_22><loc_10><loc_52><loc_86><loc_67></location>All in all, encoding g (1)+ using the SVT modes together with the Hodge decomposition leaves us with 15 SVT-Hodge quantities, corresponding to the scalar modes { Ψ , Φ , W, χ } , vector modes { ˜ W R , W 1 , W 2 , Y R , Y 1 , Y 2 } and tensor modes {Q 1 , Q 2 , H , U 1 , U 2 } , all scalars on S 2 , not all independent due to the previous constraints, and, on the other hand, not unique . Consider, in particular, the only 4 scalars we have in the odd sector; vector modes {W 2 , Y 2 } and tensor modes {Q 2 , U 2 } . As discussed in the previous section, only two gauge invariant quantities exist in the odd sector. These correspond to the two components of the gauge invariant odd vector (and for l ≥ 2), K + I , which given the above construction in terms of the SVT-Hodge quantities, read [39, 36]</text>
<formula><location><page_22><loc_20><loc_48><loc_76><loc_50></location>K + u = a ( W 2 -a ( ˙ U 2 + ˙ Y 2 ) ) , K + m = a ( Q 2 -U 2 ' +2 U 2 Σ ' Σ -1 ) .</formula>
<text><location><page_22><loc_10><loc_39><loc_86><loc_46></location>Consider now the stationary and axially symmetric vacuum perturbations in the Weyl gauge. They can be described in terms of two functions U (1) ( r, θ ) and A (1) ( r, θ ), which correspond, basically, to the perturbation of the gravitational Newtonian potential and the rotational perturbation, respectively. The perturbation tensor reads [38]</text>
<formula><location><page_22><loc_15><loc_30><loc_86><loc_38></location>g (1) Sch = -2 ( 1 -2 m r ) ( U (1) dt 2 + A (1) dtdφ ) -2 r 2 sin 2 θU (1) dφ 2 +2 ( k (1) -U (1) ) [ ( 1 -2 m r ) -1 dr 2 + r 2 dθ 2 ] . (26)</formula>
<text><location><page_22><loc_10><loc_20><loc_86><loc_28></location>Note that, when using the full set of the Einstein field equations for vacuum, the function k (1) is determined up to quadratures once U (1) ( r, θ ) and A (1) ( r, θ ) are found. We stress, however, that the vacuum equations, although indicated, were not imposed in the perturbed Schwarzschild region (nor in the perturbed FLRW region) in [38], and therefore the results found there are purely geometric.</text>
<text><location><page_22><loc_10><loc_13><loc_86><loc_20></location>Instead of working with A (1) ( r, θ ), it is convenient to use an auxiliary function, G , defined by A (1) := sin θ∂ θ G . In terms of the Hodge decomposition of the perturbation tensor (20), applied to (26), we have G = -( 1 -2 M r ) -1 Z -T 2 . Another auxiliary function P can be introduced for k (1) .</text>
<text><location><page_22><loc_10><loc_9><loc_86><loc_12></location>The whole set of matching conditions (23) for the linearized Einstein-Straus model, both in the odd and even sectors, were found in [38] in terms of these functions U (1) ( r, θ ) , G</text>
<text><location><page_22><loc_10><loc_70><loc_15><loc_71></location>tensor</text>
<text><location><page_23><loc_14><loc_85><loc_91><loc_90></location>and P in the Schwarzschild side together with the above 15 SVT-Hodge scalars describing the FLRW perturbation. The whole set is too long to be included here, but in order to review the main results in [38] only the odd sector of the linearized matching is needed.</text>
<text><location><page_23><loc_14><loc_82><loc_91><loc_85></location>The odd sector of the linearized matching (24) projected to the part orthogonal to the l = 0 and l = 1 harmonics can be rewritten as the following three relations [38]</text>
<formula><location><page_23><loc_30><loc_77><loc_91><loc_79></location>W 2 -a [ ˙ U 2 + ˙ Y 2 ] Ω 0 = -G Σ ' c a -1 , (27)</formula>
<formula><location><page_23><loc_30><loc_75><loc_91><loc_77></location>Q 2 -U 2 ' +2Σ -1 c Σ ' c U 2 Ω 0 = -G a -1 ˙ a Σ c , (28)</formula>
<formula><location><page_23><loc_30><loc_71><loc_91><loc_75></location>W 2 ' -a d dt [( U 2 ' + Y 2 ' ) | Ω 0 ] Ω 0 = G Σ 3 c aglyph[epsilon1] -3 M Σ 2 c a 2 + ∂ G ∂r (Σ 2 c glyph[epsilon1] -1) , (29)</formula>
<text><location><page_23><loc_14><loc_52><loc_91><loc_69></location>plus an equation for the difference T RW 2 -T Sch 2 . The three equations above can be shown [36] to correspond indeed to (25), taking into account that K Sch = -( 1 -2 M r ) G dT . These equations were presented in [38] in full, including the parts lying on the l = 0 and l = 1 harmonics. There, a series of kernels inherent to the usual Hodge decomposition where the responsible for the usual freedom found in the l = 0 and l = 1 sectors when using harmonic decompositions. By using the canonical Hodge decomposition introduced in Section 6, we can have a better control of that freedom, and understand its nature, getting rid of the spurious terms. Indeed, by doing that it can be shown [36] that the projection of the linearized matching on the l = 1 harmonics -on the l = 0 it is trivial, since all scalars in the odd sector are orthogonal to l = 0- gives</text>
<formula><location><page_23><loc_30><loc_44><loc_91><loc_50></location>˙ aa 2 Σ 2 c [ W ' 2 -a d dt Y ' 2 | Ω 0 -2Σ -1 c Σ ' c ( W 2 -a d dt Y 2 )] || 1 Ω 0 = a (2 M -a Σ c ) ˙ G || 1 +2˙ a ( a Σ c -3 M ) G || 1 (30)</formula>
<text><location><page_23><loc_14><loc_40><loc_39><loc_42></location>while ( T RW 2 -T Sch 2 ) || 1 is free.</text>
<text><location><page_23><loc_14><loc_32><loc_91><loc_40></location>The first consequence of the above equations is that if the FLRW remains unperturbed then the stationary region must be static in the range of variation of r 0 ( t ): equations (27)-(29) imply that the part of G orthogonal to l = 1 vanishes, and (30) implies that G || 1 = Ca 3 / (2 M -a Σ c ) , where C is a constant. Therefore G = Ca 3 / (2 M -a Σ c ) cos θ , and thus 5</text>
<formula><location><page_23><loc_38><loc_29><loc_67><loc_31></location>A (1) | Ω 0 = C sin 2 θa 3 / (2 M -a Σ c ) .</formula>
<text><location><page_23><loc_14><loc_24><loc_91><loc_28></location>As shown in [38], this implies that the perturbed spacetime is static in the range of variation of r 0 ( t ).</text>
<text><location><page_23><loc_14><loc_14><loc_91><loc_24></location>This result generalizes that in [52] because now the matching hypersurface does not necessarily keep the axial symmetry. Therefore, the only way of having a stationary and axisymmetric vacuum arbitrarily shaped (at the linear level) region in FLRW is to have the Einstein-Straus model. Let us remark again that by the interior/exterior duality, this result also implies that a piece of FLRW, irrespective of its shape and its relative rotation with the exterior, cannot describe the interior of Kerr.</text>
<section_header_level_1><location><page_24><loc_10><loc_89><loc_41><loc_90></location>7.1 Constraint on FLRW</section_header_level_1>
<text><location><page_24><loc_10><loc_84><loc_86><loc_87></location>Another interesting consequence of the matching conditions is that the combination of (27) and (28) produces one equation that involves only quantities in FLRW [38]</text>
<formula><location><page_24><loc_25><loc_80><loc_67><loc_83></location>˙ a Σ c a Σ ' c ( W 2 -a [ ˙ U 2 + ˙ Y 2 ] ) Ω 0 = Q 2 -U 2 ' +2Σ -1 c Σ ' c U 2 ,</formula>
<text><location><page_24><loc_10><loc_69><loc_86><loc_78></location>and thus constitutes a constraint in FLRW. Recalling that this equation is meant to be orthogonal to l = 1 (and vanishes identically if projected on l = 0), this constraint implies that if the perturbed FLRW contains vector modes with l ≥ 2 harmonics on Ω 0 , then it must contain also tensor modes there. Since, as we have just seen above, the existence of a rotation in the stationary region implies the existence of, at least, vector perturbations in FLRW, then both vector and tensor modes must exist on Ω 0 .</text>
<text><location><page_24><loc_10><loc_53><loc_86><loc_68></location>It must be stressed that, as demonstrated in [5] (and references therein), there exist configurations of FLRW linear perturbations containing only vector perturbations which vanish identically inside a spherical surface. Such configurations are compatible with the results reviewed here, since that interior region is FLRW and the above constraints do not apply. A completely different matter is the embedding of a Schwarzschild spherical cavity (or a vacuum perturbation thereof) into any such model: the Schwarzschild cavity cannot reach the perturbed FLRW region, as otherwise the constraints above would require that tensor perturbations are also present (at least near the boundary of the Schwarzschild cavity).</text>
<text><location><page_24><loc_10><loc_48><loc_86><loc_53></location>There also exists a Einstein-Straus perturbative model by Chamorro [18] consisting on small rotation Kerr vacuole within a perturbed FLRW. Again, the constraint above does not apply to this model because there are no l ≥ 2 modes there.</text>
<text><location><page_24><loc_10><loc_38><loc_86><loc_48></location>The fact that tensor modes must exist near Ω 0 once some rotation with l ≥ 2, whatever small, exists in the stationary region, may indicate the existence of some kind of gravitational waves on FLRW near Ω 0 . In order to analyze further this issue one needs to take the Einstein field equations into consideration. That is the purpose of our work in preparation [36], some result of which will appear in the proceedings of the ERE2012 meeting.</text>
<section_header_level_1><location><page_24><loc_10><loc_33><loc_49><loc_35></location>8 Conclusions and outlook</section_header_level_1>
<text><location><page_24><loc_10><loc_18><loc_86><loc_31></location>This paper is concerned with the difficulties that the Einstein-Straus model encounters. A fundamental one refers to its high level of rigidity and the impossible generalization to non-spherical symmetry if the bound system is required to be time independent so as to retain the property that cosmic expansion does not affect the local systems. Moreover, if one views the model within the LTB class with a step function density profile, the model is unstable to perturbations [57], [32], cf. also the discussion in [30]. The rigidity result so far requires either stationarity and axial symmetry or staticity. An interesting open problem would be to relax the conditions and assume only stationarity.</text>
<text><location><page_24><loc_10><loc_9><loc_86><loc_17></location>Despite these difficulties, the Einstein-Straus model has played and plays a very important role in cosmology in different areas or research, most notably on the influence (or lack thereof) of the cosmic expansion on local systems, or in the problem of averaging in cosmology at least on an observational level (see e.g. [20]). The model is still widely used as textbook explanation of the lack of influence of the cosmic expansion on astrophysical</text>
<text><location><page_25><loc_14><loc_77><loc_91><loc_90></location>systems and, in fact, there are not many known alternatives (a notable exception is the McVittie model [44], [28], [29] which is also spherically symmetric and mimics the geometry of Schwarzschild at small scales while approaching a FLRW model at long distances, and which has been studied thoroughly, see [15] and references therein). Concerning the use of the Einstein-Straus model on observational cosmology, mainly by studying lensing effects, its generalizations have systematically consisted in keeping spherical symmetry and allowing for some dynamics in the interior. The prominent example here consists of LTB regions inside a FLRW universe (see references in [20]).</text>
<text><location><page_25><loc_14><loc_57><loc_91><loc_76></location>An important ingredient for the rigidity of the Einstein-Straus model is the large symmetry of the FLRW background. It is therefore an interesting problem to analyze how the model gets modified in the presence of cosmic perturbations. In a conservative approach, one still wants to keep the main properties (stationarity of a region inside a cosmological model) as far as possible and analyze the possible departures from the model in more realistic situations. Moreover, by studying perturbed Einstein-Straus models one seeks going beyond the problem of the influence of cosmic expansion on local systems, and tackle the problem of the influence of general cosmic dynamics. Surprisingly, it turns out that the existence of static (stationary) regions does impose conditions on the cosmic perturbations, at least near the boundary. Whether this is a real effect or simply an indication that the interior region should not be kept stationary remains to be seen.</text>
<text><location><page_25><loc_14><loc_45><loc_91><loc_56></location>Another implication of the perturbed Einstein-Straus model is that extra care is required in the standard decomposition of metric perturbations in terms of scalar, vector and tensor modes. As discussed above, any rotation in the vacuole implies necessarily the presence of both vector and tensor modes in the cosmic perturbations. It is interesting to analyze whether these tensor modes could represent cosmic gravitational waves. Some preliminary results along these lines have already been presented in [39]. A detailed and more complete approach will appear elsewhere.</text>
<text><location><page_25><loc_14><loc_39><loc_91><loc_44></location>Another interesting future line of research is to allow for non-stationary perturbations in the vacuole and study the transmission of gravitational waves from the cosmic region to the bound system.</text>
<section_header_level_1><location><page_25><loc_14><loc_30><loc_46><loc_32></location>9 Acknowledgements</section_header_level_1>
<text><location><page_25><loc_14><loc_24><loc_91><loc_27></location>MM acknowledges financial support under the projects FIS2012-30926 (MICINN) and P09-FQM-4496 (J. Andaluc'ıa-FEDER).</text>
<text><location><page_25><loc_14><loc_15><loc_91><loc_23></location>FM thanks the warm hospitality from Instituto de F'ısica, UERJ, Rio de Janeiro, Brasil, projects PTDC/MAT/108921/2008 and CERN/FP/123609/2011 from Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT), as well as CMAT, Univ. Minho, for support through FEDER funds Programa Operacional Factores de Competitividade (COMPETE) and Portuguese Funds from FCT within the project PEst-C/MAT/UI0013/2011.</text>
<text><location><page_25><loc_14><loc_9><loc_91><loc_14></location>RV thanks the kind hospitality from the Universidad de Salamanca, where parts of this work have been produced, and financial support from project IT592-13 of the Basque Government, and FIS2010-15492 from the MICINN.</text>
<section_header_level_1><location><page_26><loc_10><loc_89><loc_25><loc_90></location>References</section_header_level_1>
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</document>
[
{
"title": "Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results",
"content": "Marc Mars ∗ , Filipe C. Mena † and Ra¨ul Vera ‡ ∗ Instituto de F´ısica Fundamental y Matem´aticas, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca, Spain † Centro de Matem´atica, Universidade do Minho, 4710-057 Braga, Portugal ‡ Dept. of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 644 PK, Bilbao 48080, Basque Country, Spain",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "The Einstein-Straus model consists of a Schwarzschild spherical vacuole in a Friedman-Lemaˆıtre-Robertson-Walker (FLRW) dust spacetime (with or without Λ). It constitutes the most widely accepted model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model is that there is no influence from the cosmic background, since the spherical vacuole is static. Spherical generalizations to other interior matter models are commonly used in the construction of lumpy inhomogeneous cosmological models. On the other hand, the model has proven to be reluctant to admit non-spherical generalizations. In this review, we summarize the known uniqueness results for this model. These seem to indicate that the only reasonable and realistic nonspherical deformations of the Einstein-Straus model require perturbing the FLRW background. We review results about linear perturbations of the Einstein-Straus model, where the perturbations in the vacuole are assumed to be stationary and axially symmetric so as to describe regions (voids in particular) in which the matter has reached an equilibrium regime.",
"pages": [
1
]
},
{
"title": "1 Introduction",
"content": "During a meal in the 19th Jena Meeting on Relativity, in September 1996, Bill Bonnor provocatively asked Jos'e Senovilla if the table could be expanding with the Universe. Not surprisingly, Bonnor later took the question seriously and wrote a paper about how the hydrogen atom is affected by the cosmic expansion [11], which is well worth reading. About five decades before, Einstein and Straus asked a similar question, on a bigger scale, which led them to investigate the influence of the expansion of space on the gravitational fields surrounding individual stars [19]. They took the Schwarzschild solution representing the vacuole surrounding a star located in the centre and the FriedmanLemaitre-Robertson-Walker (FLRW) solution as the cosmological model. At the core of their model was the matching of the two solutions across a spherical surface with constant cosmological radius. Since the expansion kept the vacuole symmetry and time independence, their conclusion was that it does not affect the gravitational fields surrounding stars and, in particular, it does not affect the solar system dynamics. A previous attempt to address the issue of whether the planetary orbits expand with the Universe was made by McVittie [44] who found a smooth model describing a spherically symmetric mass embedded in a flat FLRW. Since then the research about this problem was scarce, although some alternatives to the McVittie model were suggested, e.g. in [22], and difficulties of the global meaning of the model were also pointed out [48, 49, 50, 51] (see also [15]). Concerning the Einstein-Straus model itself, it was revisited in [2, 8] and stability issues were raised in [57], [32] cf. also the discussion in [30]. However, the Einstein-Straus model has never stopped being considered as the correct answer to the lack of influence of the cosmological expansion on local systems. Moreover, since the vacuole can be inserted anywhere due to the homogeneity of FLRW, the Einstein-Straus model led to the original Swiss cheese model of a lumpy inhomogeneous universe (see e.g. [20]). Bonnor's question, that 1996 afternoon, raised a totally new issue for the EinsteinStraus models, namely whether spherical symmetry was a crucial ingredient of the model and, therefore, for the existence of time-invariant bounded systems embedded in a FLRW universe. Indeed, the question triggered research by Senovilla and Vera [59], that led to the result about the impossibility of the Einstein-Straus model in cylindrical symmetry. In turn, this important result was the origin of over fifteen years of research about the rigidity, in the sense of uniqueness, of the model. The aim of this paper is to review these results on rigidity both for exact models and from a perturbative perspective. Crucial to this endeavour was the development of a general mathematical theory of spacetime matching [41] and of its perturbative version [4, 47, 35]. This allowed to achieve quite general results about the possibility of generalizing both the shape of the cavity and the cosmological setting of the original Einstein-Straus model. As an example, described below in some detail, uniqueness of the static Λ-vacuum spherical region embedded in a non-static FLRW cosmological model has been proved [34]. The scope of the Einstein-Straus model has been taken well beyond both the physical scale originally considered and the physical problems for which the model was conceived. In fact, the model has been used not only at the solar system scale, but also on galaxy [27] and galaxy clusters' scales [27, 54]. On the other hand, the vacuole of the (original) Einstein-Straus model has been replaced by other spherically symmetric geometries, generally Lemaˆıtre-Tolman-Bondi (LTB), also spherically shaped regions of Szekeres, in order to construct 'generalized' Einstein-Straus models for describing extra-galactic scale and cosmic voids (we refer to the reviews in [30, 20]). Lumpy inhomogeneous cosmological models based on the generalized Einstein-Straus Swiss cheese models are being used in the search of possible explanations to the accelerated expansion of the Universe by the study of lensing effects at cosmic scales produced by the voids (see e.g. [20]). So far, all these generalized Einstein-Straus (and the corresponding Swiss cheese) models have assumed spherically shaped inhomogeneities (voids). One of themes of the research we will review here is how far can one push the Einstein-Straus model towards non-spherical generalizations. The fundamental ingredient we want to keep is that the bound system remains stationary, so as to keep the absence of influence of the cosmic dynamics on astrophysical scales. We will use the term Einstein-Straus problem to the problem of finding the most general stationary regions (vacuum or not) one can embed in a realistic cosmological model in a broad sense. The Einstein-Straus model has also been taken beyond the exact solutions' settings to include metric perturbations. Perturbation theory in General Relativity (GR) is a natural framework to study small departures from symmetric configurations and thus to perform stability analysis. For instance, it allows to include simultaneously density, rotational and gravitational wave perturbation modes into an, otherwise, spatially homogeneous and isotropic cosmological model. Most interestingly, it allows a priori to perturb independently the interior and exterior spacetimes as well as the matching boundary. Furthermore, although the three perturbation modes are decoupled on a FLRW background, they may couple at a matching boundary. In this context, an important question is how general can the perturbations be in each model. Inherent to perturbation theory is the issue of gauge freedom. In perturbed spacetime matchings, this can be complicated by the fact that three independent perturbation gauges may be in use. For the sake of completeness, we include a short review of linearized matching, where these issues are discussed, see also [47] for further details, including the definition of the so-called doubly gauge invariant variables . Perturbations in the FLRW background are customarily split in scalar, vector and tensor modes, and the later are generically viewed as cosmological gravitational waves. Given that the gravitational wave detectors are already active, and gravitational waves are expected to be detected within the next five years (see e.g. [6, 55] for recent accounts and the review [56]), it would be interesting to investigate their inclusion in the models. One now certainly has the necessary mathematical machinery to do so, and preliminary results indicate the possibility of having, for instance, a stationary axially symmetric vacuole embedded in an expanding cosmological model containing tensor modes [38]. Even more, the linearized matching links the rotational and tensor modes degrees of freedom in the perturbation variables [38]. This is therefore an interesting timing to revise the state-of-the-art and point out potentially interesting directions of research about the Einstein-Straus problem, in the sense pointed out above. The plan of the review is the following. In Section 2, the Einstein-Straus model is briefly presented. Similar summaries with different degrees of detail can be found in many places in the literature, see e.g. [20]. We include it here for the sake of completeness and in order to fix our notation. Section 3 is devoted to describing in some detail the uniqueness results concerning both general static regions and stationary and axisymmetric regions (irrespective of any symmetry consideration and/or matter content) embeddable in a FLRW expanding cosmology. Section 3.1 is devoted to the static case. The main conclusion here is that the only static vacuum region that can be embedded to an expanding FLRW is a spherically shaped region of Schwarzschild (i.e. the Einstein-Straus model). Similar uniqueness results hold for other matter models, such as vacuum with cosmological constant. Section 3.2 deals, in turn, with the uniqueness results for stationary and axially symmetric regions in FLRW expanding universes. The main result is that the stationary region must, in fact, be static, so that the previous conclusions on static regions apply. The uniqueness result thus states that the only way of having a stationary and axially symmetric or static region in an expanding FLRW is the Einstein-Straus model. Following the uniqueness results, the robustness of the Einstein-Straus model is further analyzed by considering alternative exact cosmological models. In Section 4 the replacement of the FLRW region by more general anisotropic cosmologies, i.e. the Bianchi models, is studied for static locally cylindrically symmetric interiors, leading to severe restrictions and no-go results for reasonable evolving cosmologies. The final part of the paper is devoted to the generalization of the Einstein-Straus model from a perturbative perspective. After a brief overview of perturbative matching theory in Section 5, and the use of the Hodge decomposition on the sphere instead of the usual spherical harmonic decomposition in Section 6, the linearized matching between stationary and axisymmetric perturbations of Schwarzschild and general perturbed FLRW is reviewed in Section 7. We finish with some conclusions in Section 8, pointing out some ongoing research, prospects for future work on the perturbed Einstein-Straus model and its possible implications on the relationship between astrophysical bounded systems and cosmological dynamics in the form of cosmic gravitational waves.",
"pages": [
1,
2,
3,
4
]
},
{
"title": "2 The Einstein-Straus model",
"content": "This model consists of a spherically symmetric (both in shape and intrinsic geometry) Ricci-flat region embedded in a FLRW universe without cosmological constant. Recall that two spacetimes can be matched across their boundary if and only if the first fundamental forms q and second fundamental forms K agree on the matching hypersurface. A consequence of this are the well-known Israel conditions, which restrict the jump of the energy-momentum tensor across the boundary. In the present context, they imply that the cosmological fluid must be dust and the vacuole must be comoving with the cosmological fluid. Writing the FLRW metric in cosmic time coordinates where glyph[epsilon1] = {-1 , 0 , +1 } , Σ ' 2 = 1 -glyph[epsilon1] Σ 2 with prime denoting derivative with respect to R , in units G = c = 1 the Friedman equation reads where the dot denotes derivative with respect to t and ρ 0 is a constant such that the cosmological energy-density ρ satisfies ρ = ρ 0 /a 3 . The boundary of the vacuole can be parametrized by { t = t, R = R 0 } (we ignore the angular variables as they behave trivially, and use t both as spacetime coordinate and intrinsic coordinate on the hypersurface, the precise meaning will be clear from the context). For the matching one needs the induced metric q RW and the second fundamental form K RW . Using the outward unit normal n RW = a ( t ) dR these objects read, with Σ c := Σ | R = R 0 , and Σ ' c := Σ ' | R = R 0 , From Birkhoff's theorem, the geometry of the vacuole is Kruskal. Assuming that the boundary is away from the Schwarzschild horizon (this happens sufficiently away from the big bang or big crunch) the interior metric can be written in Schwarzschild coordinates The boundary can be parametrized as { T = T 0 ( t ) , r = r 0 ( t ) } and, given the time inversion symmetry of Schwarzschild, we can assume ˙ T 0 > 0 without loss of generality. The induced metric on the boundary is Using the unit normal n Sch = 1 N ( ˙ T 0 dr -˙ r 0 dT ) (note that the global sign of N is kept free at this stage), the second fundamental form is Equality of the t -component of the induced metric requires N 2 = 1. Then, equality of the angular parts of the first and second fundamental forms imposes N = 1 and A straightforward computation shows that the equality of the t -component of the induced metric and second fundamental forms are satisfied provided the values of ρ 0 and m are linked by which has a clear interpretation in terms of (Misner-Sharp)-mass conservation. This is the Einstein-Straus model [19]. A natural generalization consists in adding a cosmological constant Λ both to the FLRW and to the interior part (originally considered in [25] and fully solved in [2]). The Israel matching conditions on the energy-momentum tensor now impose the FLRW matter model to be dust with Λ, so that the Friedman equation is now By Birkhoff's theorem, the interior metric is the Kottler solution (also known as 'Schwarzschild(anti) de Sitter'), which away from the horizons is In this case, the matching conditions are We emphasize that any matching of two spacetimes immediately leads to a complementary matching, at least locally, where the 'interior' and 'exterior' regions on each spacetime reverse their roles (see [21] for details). In the matching above, this leads to the Oppenheimer-Snyder collapse model [53].",
"pages": [
4,
5
]
},
{
"title": "3 Rigidity of the Einstein-Straus model",
"content": "The Einstein-Straus model is such that, for a given total mass inside the vacuole and a given energy density in the cosmological background, the radius of the static region is uniquely fixed. This already poses difficulties for the model since it is often the case that the size of the vacuole does not match the observed sizes of clustered matter in the universe, such as stars or galaxies. This fact indicates that the Einstein-Straus model may be lacking flexibility to accommodate the various situations present in cosmology (cf. [58] and [10]). In fact, the Einstein-Straus vacuole was found to be radially unstable in a certain sense [30]. The other main restriction of the model is its exact spherical symmetry. It is clear that vacuoles in the universe are not exactly spherically symmetric so a natural question is how robust is the model to non-spherical generalizations. The first thing to consider is which fundamental ingredients of the model should be kept. The main motivation of the Einstein-Straus model was its ability to combine cosmological expansion at large scales with no observable effects on the local physics. Thus, the fundamental ingredient to keep is the absence of influence of the cosmic expansion inside the region. The simplest and most natural way to achieve this is imposing that the interior geometry is stationary, because then no dynamical effects whatsoever from the surrounding evolving cosmology would affect the local physics. Among stationary interiors, the simplest case corresponds to static situations, so it is natural to start with this case (note that the Einstein-Straus model is itself static). The question is then how rigid or flexible is the possibility of having stationary/static regions embedded in an otherwise expanding FLRW universe. Ideally, one would like to make no further assumptions and find the most general model with these properties. The matter model inside may also be kept arbitrary, and see what are the possibilities allowed by the coexistence of a stationary/static region inside an expanding FLRW universe. This coexistence has been sometimes called the Einstein-Straus problem in the literature (see e.g. [2]). The first indication that the Einstein-Straus model might be very rigid came from a seminal work by Senovilla and Vera [59] who considered the possibility of matching a static and cylindrically symmetric region (with no restriction on the matter model) with a FLRW dynamical cosmology. The matching hypersurface was taken to be locally a cylinder, in the sense of being tangent in an open set to the two (commuting) generators of two spatial local isometries. No global consideration was needed. The result was a no-go theorem: no such model exists. With the impossibility of generalizing the Einstein-Straus model to a cylindrical setting, it became of interest to study the problem in as much generality as possible. The static case was treated in complete generality in [33], [34] and it is by now well-understood. The more complicated stationary situation has been studied [52] under the additional assumptions of axisymmetry and a group action orthogonally transitive. The motivation to study this simplified problem lies in the fact that one expects equilibrium configurations to also exhibit an axial symmetry. It is worth to mention that one step in the black hole uniqueness theorems corresponds to showing that the domain of outer communications must be axially symmetric [26]. We devote the following Section 3.1 to describing the main results in the static setting, and Section 3.2 to review the uniqueness results in the stationary and axially symmetric setting.",
"pages": [
5,
6
]
},
{
"title": "3.1 Uniqueness results in the static case",
"content": "This case was first considered in [33] under the additional assumption of axial symmetry, and one extra technical assumption relating cosmic and static times on the matching hypersurfaces. Both assumptions were dropped in [34] where a satisfactory uniqueness result for static region in FLRW was obtained. The setup consists on a spacetime ( V , g ) composed by two regions ( W ST , g ST ) and ( W RW , g RW ) matched in absence of surface layers across their boundaries, denoted by Ω ST and Ω RW respectively, which once identified conform to a hypersurface Ω in ( V , g ). The region ( W ST , g ST ) is strictly static, i.e. admits a Killing vector ξ which is timelike and orthogonal to hypersurfaces everywhere. ( W RW , g RW ) is a codimension-zero submanifold with smooth boundary Ω RW of the FLRW spacetime ( V RW , g RW ), by which we mean the manifold V RW = I ×M , where I ⊂ R is an open interval, M is either E 3 ( glyph[epsilon1] = 0), S 3 ( glyph[epsilon1] = 1) or H 3 ( glyph[epsilon1] = -1) and the FLRW metric g RW takes the form (1). We call any coordinate system { R,θ, φ } in which the metric takes this form a spherical coordinate system . Note that since ( M , g M ) is homogeneous, there exist spherical coordinate systems centered at any point p ∈ M , and this will be used below. The function a ( t ) is positive and smooth (in fact C 3 suffices). We assume that ˙ a does not vanish on any open set (this excludes uninteresting situations where the FRLW does not evolve). Define the 'geometric' energy-density ρ RW and pressure p RW by glyph[negationslash] so that, if the spacetime has a cosmological constant Λ, the energy-density and pressure of the cosmic fluid is ρ = ρ RW -Λ 8 π , p = p RW + Λ 8 π . We make the assumption that ρ RW + p RW = 0 so that we do have a non-trivial cosmic fluid (this allows us to define t unambiguously). Concerning the boundary Ω RW it is assumed to be connected (this is irrelevant because the matching conditions are local, the assumption is made merely for notational convenience), and nowhere tangential to a hypersurface of constant cosmic time t . This assumption is physically reasonable and automatically satisfied if the boundary is causal. In fact, dropping this assumption would only make the presentation more involved, but would not spoil any of the results (see [34] for a discussion). Finally, we assume that Ω RW is spatially compact. A sufficient condition for this is the 'energy condition' ρ RW ≥ 0, see [33], and this is in fact the assumption made in [33]. However, it can be proved that spatial compactness suffices for the validity of all the results below. Note finally, that spatial compactness is indeed an assumption: allowing for non-compact boundaries, additional configurations not covered by the uniqueness results do arise, as shown in [45] (see also references therein), where configurations with planar and hyperbolic symmetries were found and analized. It would be interesting to analyze how far can one extend uniqueness without any compactness assumption on the boundary. Nevertheless, for the purposes of the Einstein-Straus problem, compactness is a completely natural assumption, as we want the local physics unaffected by the cosmological expansion be spatially confined. By a detailed analysis of the matching conditions, the following restrictions on the boundary Ω RW are obtained [34]. First of all, the intersection S RW t of Ω RW with a hypersurface of constant cosmic time t is a sphere. More precisely, for any t ∈ I , there exists a point c ( t ) ∈ M so that S RW t is a coordinate sphere of radius R ( t ) in a spherical coordinate system centered at c ( t ). The radius R ( t ) is restricted to satisfy the bound This inequality means that the surface S RW t is non-trapped (i.e. has a mean curvature vector spacelike everywhere). The necessity of this condition can be understood from the fact that no closed spacelike surface in a static spacetime can have a future (or past) causal and not-identically zero mean curvature vector [42]. The spherical symmetry of the surface S RW t and the fact that the matching conditions force the mean curvature vector to be continuous across the matching hypersurface implies that S RW t must be nontrapped, which is precisely (5). Note also that if the static Killing vector ξ admits Killing horizons and hence changes causal character, then the bound (5) is no longer necessary. This behaviour occurs in the Einstein-Straus model when a ( t ) is sufficiently small so that Σ c a ( t ) = 2 m . The breakdown of the ODE (3) in the Einstein-Straus model is just a manifestation of the breakdown of the the static coordinate system in the interior region. In Kruskal coordinates, the matching would continue across Σ c a ( t ) = 2 m without problem. Something similar would occur in the general setting if we allowed the static Killing to change causal character. Returning to the shape of Ω RW , the center point c ( t ) follows a geodesic in ( M , g M ) (which may degenerate to a point). The parameter t is not in general an affine parameter for the geodesic, so the center c ( t ) is a priori allowed to move at any speed (in fact the trajectory can have turning points along the curve). In order to describe the matching hypersurface, choose any point c 0 along this geodesic and let c ' 0 be its tangent vector. We can choose a spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 so that the axis of symmetry ˆ θ = 0 is along the tangent vector c ' 0 . In this coordinate system, the center c ( t ) will have coordinates (the value of ˆ θ can be 0 or π depending on whether c ( t ) lies after or before c 0 along the geodesic). The function σ ( t ) describes the motion of c ( t ) along the curve. The relationship between the spherical coordinate system { ˆ R, ˆ θ, ˆ φ } centered at c 0 and a spherical coordinate system { R,θ, φ } centered at c ( t ) with parallel axis (i.e. with coincident lines | cos θ | = 1 and | cos ˆ θ | = 1) is easily found to be Thus, the matching hypersurface Ω RW in the spherical coordinates centered at c 0 can be parametrized by coordinates t, θ, φ as which is a rather complicated form for the matching hypersurface. A useful alternative is to use a coordinate system { t, R, θ, φ } in ( W RW , g RW ) such that, for each t , { R,θ, φ } is the spherical coordinate system centered at c ( t ). Applying the coordinate transformation (6) to the metric gives where f ( t ) = ˙ σ ( t ). The explicit calculation leading to (7) is somewhat long, a much more elegant method of obtaining this form of the metric is discussed in the Appendix of [34]. In these coordinates, the matching hypersurface Ω RW is simply { R = R ( t ) } . The matching conditions in the FLRW part are supplemented with a differential equation relating the trajectory of the center σ ( t ) with the radius R ( t ). To write it down, define a function β ( t ) via where glyph[epsilon1] 1 = ± 1 depending on whether the FLRW region to be matched is R > R ( t ) or R < R ( t ) (more specifically, the manifold with boundary W RW is { glyph[epsilon1] 1 R ≥ glyph[epsilon1] 1 R ( t ) } ). Note that β ( t ) is well-defined because of (5). The ODE relating R ( t ) and σ ( t ) is conveniently written using an auxiliary function ∆( t ) = 0 as the following pair of differential equations glyph[negationslash] In summary, the static domain embedded in the FLRW regions consists of a sphere with time dependent radius R ( t ) and with center moving across the FLRW spacetime along a geodesic. Speed along the geodesic and radius R ( t ) are linked by (9). The model is not spherically symmetric because the center of the sphere is allowed to move. However, it is very close to spherically symmetric and it turns out that the center of the sphere must be at rest for several relevant matter models in the static domain, as we discuss next. An important consequence of the matching procedure (cf. Lemma 1 in [34]) is that the Killing vector field ξ is everywhere transverse to the matching hypersurface Ω ST in the static region. Combining this with the fact that the static geometry is invariant along ξ it follows that the static metric in the spacetime region obtained by dragging Ω ST with the static Killing vector can be fully determined in terms of hypersurface geometry of Ω ST . Since, in turn, the geometry on Ω ST is related to the geometry of Ω RW via the matching conditions, it follows that the spacetime geometry of the static region becomes completely determined [34] in a neighbourhood of its matching hypersurface in terms of the FLRW geometry and the functions R ( t ) , σ ( t ) and ∆( t ) (see Theorem 1 in [34] for details). Specifically, there exist coordinates { T, t, θ, φ } so that the metric g ST takes the form (note that t is a spacelike coordinate in the static domain) where µ := glyph[epsilon1]a ( t )( ˙ R ( t ) + f ( t ) cos θ ). The matching hypersurface Ω ST is defined by the embedding { t, θ, φ } → { T = T ( t ) , t, θ, φ } , where T ( t ) satisfies ˙ T ( t ) = ∆( t ) and the portion of the static spacetime to be matched to the exterior region is { T ≥ T ( t ) } . The metric (10) is foliated by round spheres { T = const , t = const } but it is not spherically symmetric in general (unless f ( t ) = 0 and R ( t ) = 0). To complete the picture, we review the energy-momentum tensor in the static part. Introduce two one-forms and one symmetric two-tensor h by The Einstein tensor of ( W ST , g ST ) is (cf. Proposition 1 in [34]) where ρ ST , p ST r and p ST t read and ρ RW and p RW were defined in (4). Several consequences of (11) can be drawn [33, 34]. Concerning the uniqueness of the Einstein-Straus model, under the assumption ρ ST + p ST = 0 (which includes vacuum with or without cosmological constant or a non-singular electromagnetic field) it follows that µ = 0 and hence f ( t ) = 0 and R ( t ) = 0. The second equation in (9) gives (with an appropriate but still completely general choice of integration constant), where (8) and the definitions of Σ c and Σ ' c in Section 2 have been used. The static metric simplifies to From this metric, uniqueness of the Einstein-Straus model as the unique static vacuum (with or without cosmological constant) region embedded in a FRLW cosmological model follows easily. So, static vacuoles in a FLRW model must be spherically symmetric both in shape and interior geometry. It is an open problem to analyze whether there are any physically realistic matter models in the interior static region for which the motion of the static domain inside FLRW has interesting properties. Note that a priori nothing prevents the geodesic c ( t ) from being spacelike, so the motion of the static domain can in principle be superluminal for the cosmic observers. This is of course reminiscent to the superluminal warp drive discovered by Alcubierre [1].",
"pages": [
6,
7,
8,
9,
10
]
},
{
"title": "3.2 Uniqueness results in the stationary and axisymmetric case",
"content": "The study of axially symmetric equilibrium regions in FLRW universe was dealt with in [52], and, in short, the main result found was that those stationary regions must, in fact, be static, and therefore the results of the previous section apply. With the same definitions and assumptions concerning the FLRW region ( W RW , g RW ) and its boundary Ω RW as in the previous section, we assume now that the interior region ( W SX , g SX ) is (strictly) stationary and axisymmetric. More specifically, we demand that (i) the spacetime admits a two-dimensional group of isometries G 2 acting simply-transitively on timelike surfaces T 2 and containing a (spacelike) cyclic subgroup, so that G 2 = R × S 1 , and (ii) that the set of fixed points of the cyclic group is not empty. Consequences of the definition are that the G 2 group has to be Abelian [17, 14, 3], and that the set of fixed points must form a timelike two-surface [40], which is the axis. The axial Killing η is then intrinsically defined by normalizing it demanding ∂ α η 2 ∂ α η 2 / 4 η 2 → 1 at the axis. See also [61] and [13]. In addition, we demand that the isometry group is orthogonally transitively (OT), i.e. that the two planes orthogonal to the orbits of the isometry group are surface forming. This assumption is also known as the 'circularity condition', and in many cases of interest it follows as a consequence of the Einstein field equations. Indeed, the G 2 on T 2 group must act orthogonally transitively in a region that intersects the axis of symmetry whenever the Ricci tensor has an invariant 2-plane spanned by the tangents to the orbits of the G 2 on T 2 group [16]. By the Einstein field equations, this includes Λ-term type matter (i.e. vacuum with or without cosmological constant), perfect fluids without convective motions, and also stationary and axisymmetric electrovacuum [61]. An OT stationary and axisymmetric spacetime ( V SX , g SX ) is locally characterized by the existence of a coordinate system { T, Φ , x M } ( M,N,... = 2 , 3) in which the line-element for the metric g SX outside the axis reads [61] where U , A , W and g MN are functions of x M , the axial Killing vector field is given by η = ∂ Φ , and a timelike (future-pointing) Killing vector field is given by ξ = ∂ T . Although useful for the sake of clarity, the use of coordinates is not essential for the results below, which only depend on the intrinsic geometric properties of of ( W SX , g SX ). As before, no specific matter content is assumed in the stationary and axisymmetric region. Regarding the matching hypersurface Ω, besides those in the previous Section 3.1, we make the only extra assumption that it preserves the axial symmetry [62] of ( W SX , g SX ) and of ( W RW , g RW ). This means that Ω SX is assumed to be invariant under the axial symmetry of ( W SX , g SX ) and that there is an axial Killing vector η RW in the Killing algebra of ( W RW , g RW ) tangent to Ω RW . With these assumptions at hand, in [52], it is proven, first, that the stationary (timelike) Killing vector field ξ is nowhere tangent to Ω SX . As explained in the previous section, this serves in particular to construct a neighbourhood of Ω SX by dragging it along the orbits of ξ , in which the geometry is thus fully determined by the information in Ω SX . The main result in [52] is that if a OT stationary and axisymmetric region ( W SX , g SX ) can be matched to a FLRW region through a hypersurface Ω SX preserving the axial symmetry, then the region ( W SX , g SX ) must be, in fact, static on a neighbourhood of Ω SX . All in all, in that neighbourhood of the matching hypersurface the OT stationary axisymmetric region ( W SX , g SX ) thus becomes a static axisymmetric region ( W ST , g ST ), and therefore the results of the previous Section 3.1 (cf. [34]) apply. So far, no explicit condition on the matter content of the stationary region has been used. When conditions on the matter content on the (OT) stationary and axisymmetric (and hence static) region are imposed, the functions that determine the matching hypersurface and the static geometry are determined by the results reviewed in Section 3.1. In particular, and for completeness, let us consider a vacuum (with or without a cosmological constant) stationary and axisymmetric region ( W SX , g SX ) matched to FLRW preserving the axial symmetry. As mentioned above, a vacuum matter content forces the axial symmetry and stationary group G 2 on T 2 to act orthogonal transitively. On the other hand, a region of FLRW ( W RW , g RW ) matched to a vacuum region must satisfy the assumptions made and, in particular, have a causal Ω RW (in fact tangent to the fluid flow). The above result implies then that the vacuum region must be static. The results of Section 3.1 thus apply, and imply, in turn, that the whole region (not just its boundary) has to be spherically symmetric, and hence Schwarzschild. To sum up, this means that the only stationary and axially symmetric vacuum region that can be matched to FLRW is a spherically symmetric piece of Schwarzschild. This constitutes still another uniqueness result of the Einstein-Straus model when the vacuum region lies inside FLRW. The complementary result, when the vacuum region lies outside FLRW, constitutes a uniqueness result of the Oppenheimer-Snyder model [53]. It is worth noticing that this result can also be interpreted as a no-go result for the possible interiors of Kerr. Indeed, this result states that an axially symmetric region of (an evolving) FLRW, irrespective of its relative rotation with the exterior, cannot be the source of a stationary and axisymmetric vacuum region, in particular, Kerr.",
"pages": [
11,
12
]
},
{
"title": "4 Robustness of Einstein-Straus: Generalized exact cosmologies",
"content": "In the previous sections, the robustness of the Einstein-Straus model has been discussed by considering generalizations of the interior vacuole and keeping the FLRW model as the exterior cosmological model. The question arises as to what happens if these symmetry assumptions concerning the exterior metric are relaxed. There are two different ways to study departures from the spherical FLRW: either perturbatively or using exact solutions. In this section, we concentrate on the later possibility and, in particular, we review the results found in [46] for spatially homogeneous (but anisotropic) cosmologies. A step in the direction of generalising the exterior was taken by Bonnor, who considered the embedding of a Schwarzschild region in an expanding spherically symmetric inhomogeneous Lemaˆıtre-Tolman-Bondi (LTB) exterior. He found that such a matching is possible in general, and that it allows the average density of the Schwarzschild interior to be chosen independently of the exterior LTB density [12]. So, clearly, if the spherical symmetry is kept, the exterior can be readily generalized to the case of inhomogeneous dust cosmologies. An interesting review about physical aspects of spherically symmetric Einstein-Straus and McVittie type models can be found in [15]. While keeping the spherical symmetry of the cavity allows for straightforward generalizations of Einstein-Straus, breaking this symmetry brings in unexpected complications, as we have seen in the previous section. The same seems to hold if we consider exact generalizations of the FLRW cylindrical symmetry exterior to spatially homogeneous but anisotropic spacetimes. This problem was considered in [46] and we summarize it next: Consider the problem of matching, across a hypersurface Ω which is spatially a topological sphere 1 , of an interior locally cylindrically symmetric (LCS) static spacetime ( W ST , g ST ), which represents a spatially compact region, to a spatially homogeneous anisotropic exterior ( W HOM , g HOM ) having a Lie group G 3 acting on S 3 surfaces. Once more, we make no assumptions a priori on the matter contents, so the main results are purely geometric. Only at the end of the section, assumptions on the matter content will lead to a final no-go result. We wish to preserve globally the axial symmetry and thus we need to impose first the existence of a group of cyclic symmetries in the exterior region. This, combined with the assumption of a spacelike spherical topological shaped 2 Ω ST , implies the existence of an exterior axis. Thus, the cyclic symmetry in the exterior must really be an axial symmetry (see the discussion in Section 3.2). Moreover, we require that the cylindrical symmetry is preserved (in the sense of [62]) at least on a non-empty open subset of Ω. This has the consequence that ( W HOM , g HOM ) must admit a G 4 on S 3 group of isometries, so that it is locally rotationally symmetric (LRS). In [46], it is shown how all the LRS spatially homogeneous metrics can be written in the form adapted to the two commuting Killing vectors defining the cylindrical symmetry ∂ ϕ and ∂ z , where ∂ ϕ is axial with axis at r = 0: with where the functions Σ and F are given by and where glyph[epsilon1] and n are given such that glyph[epsilon1] = 0 , 1; n = 0 , 1; glyph[epsilon1]n = glyph[epsilon1]k = 0 3 . The metrics are classified according to these constants in Table 1. The matching conditions are then investigated and a crucial step was to observe that they lead to the following necessary relations involving only exterior metric functions: 2 This implies the existence of north and south poles on Ω ST where the axial killing vector in the interior vanishes and, therefore, also the generator of the cyclic symmetry in the exterior region on Ω HOM by construction. 3 Let us note that the case glyph[epsilon1] = n = 0 with k = 1 is special, since it corresponds to the Kantowski-Sachs (KS) class of metrics, which do not admit a G 3 on S 3 subgroup [61]. It was included in the study for completeness. which, for non-static exteriors, imply n = 0 and thus exclude Bianchi types II, III, VIII and IX. By inserting (15) back in the matching conditions one is able to prove a series of results that lead to the following conclusion: The only expanding spatially homogeneous spacetimes which can be matched to a locally cylindrically symmetric static interior region preserving the (cylindrical) symmetry, across a non-spacelike hypersurface which is spatially a topological sphere, are given by where β is constant. This metric for k = 1 belongs to the Kantowski-Sachs class, when k = -1 admits a G 3 on S 3 of Bianchi type III, and when k = 0 of Bianchi types I,V,VII 0 ,VII h . The metrics (16) are very special, partly due to the fact that condition a ,t = 0 (see (13)-(14)) imposes a strong constraint, implying that there cannot be any time (nor space) evolution along the direction orthogonal to the orbits of the subgroup G 3 on S 2 of the LRS. There are also constraints imposed through the matching in the interior region and the interested reader can find those in [46]. Note that the no-go result found in [59] is trivially recovered, since FLRW is included in the LRS class for b ( t ) = a ( t ), and the above would imply a static FLRW metric. If one specifies a particular class of matter fields, then one gets further constraints on the cosmological dynamics. For example, if the matter in the static region is not specified but the dynamical (cosmological) region is assumed to contain a perfect fluid with pressure p and energy-density ρ satisfying the dominant energy condition everywhere, then glyph[epsilon1] = 0 necessarily, which corresponds to a stiff fluid equation of state ρ = p = α 2 / (4 t 2 ( α -kt ) 2 ), with b ( t ) = √ αt -kt 2 , where α > 0. On the other hand, if the interior is vacuum then the exterior must be also vacuum. The overall no-go results, in this case, can be seen in two ways: either as a consequence of the assumption that the interior metric is static and cylindrically symmetric, which seems to prohibit time dependence along one direction, or as a consequence of the particular exterior metrics we are considering, which are homogeneous then prohibiting the coefficients along this direction to be space dependent. The perturbative approach described in the next sections can help to clarify this question. To conclude this section we remark that there exists an example of a Einstein-Straus model with exact non-spherical inhomogeneous cosmologies. This is provided by the Szekeres dust solution which has no Killing vectors, in general, but contains intrinsic symmetries on 2-spaces of constant curvature: The Szekeres solution is divided into class I, which generalizes the LTB solution having non-concentric spheres of constant mass, and class II which includes the Kantowski-Sachs solution. Class I solutions have been proved to be interiors to the Schwarzschild solution [9] and this result has been generalized to include the cosmological constant [31, 45]. As mentioned before, one can invert the roles of the two spacetimes involved and hence construct an Einstein-Straus type model with a Schwarzschild or Kottler cavity within a class I Szekeres' cosmology. Let us remark that the Szekeres class has been used recently in Swiss cheese models as interiors to FLRW (see [7] and references therein). Class II Szekeres dust metrics are less known, but contain curious inhomogeneous solutions with cylindrical symmetry [60]. In this case, it seems harder to be able to get a physically reasonable Einstein-Straus model considering what we have described above.",
"pages": [
12,
13,
14,
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]
},
{
"title": "5 Brief overview of perturbative matching theory",
"content": "A perturbed spacetime consists of a symmetric two-covariant tensor (the 'perturbation metric') defined on a fixed spacetime (the 'background'). From a structural point of view, spacetime perturbation theory is a gauge theory in the sense that many perturbation metrics describe the same physical situation (i.e. they are gauge related). The underlying geometrical reason for this gauge freedom can be understood from the following intuitive picture of perturbation theory. We imagine a one-parameter family of spacetimes ( V ε , g ε ) such that all the manifolds are diffeomorphic to each other. This allows one to pull back g ε onto a single manifold in the family (say V 0 := V ε =0 ) and work with a one-parameter family of metrics on a single manifold. If all the construction is smooth in ε , derivatives with respect to this parameter can be taken. The perturbation metric g (1) is simply the derivative at ε = 0 of this family of metrics. However, the identification of points in the different manifolds (the diffeomorphism above) is highly non-unique. Any other choice of identification would lead to a different, but geometrically equivalent, perturbation metric. This is the gauge freedom of the theory. Intuitively, it is clear that the gauge freedom will consist of a vector field on the background, because this measures the shift of the new identification with respect to the previous one, and an initial direction (in ε ) is all what is required to compute derivatives with respect to ε at ε = 0. When two spacetimes with boundary are matched, an identification of the boundaries is required. As already mentioned before, if the boundaries are nowhere null, the matching conditions require the equality of the induced metric and second fundamental form (with appropriate choices of orientation). To compare the tensors it is necessary to pull them back to a single manifold and this is done via the identification of boundaries. Contrarily than before, the matching theory is strongly dependent on the identification of the boundaries. In fact, the matching conditions demand the existence of one such identification for which the first and second fundamental forms agree. Assume now that we are studying perturbation theory on a background spacetime constructed from the matching of two spacetimes. The question then arises of what are the conditions that the metric perturbation tensors on each side must satisfy to have a perturbed matching spacetime. This issue is somewhat more involved than one may think a priori and it was solved in a complete manner for the first time by Battye and Carter [4] and independently by Mukohyama [47] (this has been extended to second order in [35]). Previous attempts [24, 23, 43] did not take into account all the subtleties of the interplay between two completely different gauge freedoms inherent to this problem. Indeed, in the picture above of perturbation theory in terms of a collection of spacetimes ( V ε , g ε ), each one of them arises now as the matching of two spacetimes with boundary W ± ε across their respective boundaries Ω ± ε . For better visualization, assume that each one of W ± ε is a submanifold with boundary of a larger boundary-less manifold ̂ W ± ε and assume that the { ̂ W + ε } manifolds are identified among themselves (say with ̂ W + 0 := ̂ W + ε =0 ) via an ε -dependent diffeomorphism. The hypersurface Ω + ε projects down to ̂ W + 0 as a hypersurface ̂ Ω + ε . Now we have a collection of hypersurfaces in one single manifold, and one can think of taking ε -derivatives of geometric quantities intrinsic to the hypersurface. The important point is that, given a point p ∈ Ω + ε =0 , we do not know how this point maps into ̂ Ω + ε . For that, it is necessary to prescribe first how p is mapped into Ω + ε . The identification of { Ω + ε } among themselves is an additional gauge freedom. It is fully independent of the standard gauge freedom in perturbation theory (called 'spacetime gauge freedom' from now on) and is referred to as hypersurface gauge freedom [47]. The composition of both identifications gives, as ε varies, and for any p ∈ Ω + ε =0 , a path γ p ( ε ) in ̂ W + 0 starting at p . Since everything is smooth in ε , the tangent vector to this path at ε = 0 defines a vector field Z + on Ω + 0 := Ω + ε =0 (= ̂ Ω ε =0 ). This vector field is not necessarily tangent (nor normal) to Ω + 0 and it depends on both gauge freedoms. A schematic figure for the definition of Z + and how it depends on the gauges is given in Figure 5. If we let n (0) + be a unit normal vector to Ω + 0 , we can decompose Z + = Q + n (0) + + T + , where T + is tangent to Ω + 0 . From the discussion above, it should be clear that Q + is independent of the hypersurface gauge while T + strongly depends on it. In fact, it can always be made zero by an appropriate choice of gauge. However, doing this is not usually a good idea because the matching has two regions and, at each value of ε , the matching requires an identification between Ω + ε and Ω -ε . After a choice of hypersurface gauge to identify Ω + ε with Ω + 0 we have no freedom left to choose a hypersurface gauge to identity Ω -ε and Ω -0 . The matching conditions will tell us how this identification must be done. So, had we chosen T + = 0, we would still have to leave T -free and let the linearized matching theory determine its value. Further details on the double gauge freedom of linearized perturbation theory can be found in the paper of Mukohyama [47] and in [37], where the issue is discussed in depth including a critical analysis of previous attempts to formulate a consistent perturbative matching theory. After this brief discussion on gauge issues for linearized matching theory, let us describe the actual perturbative matching conditions (for details see [4, 47, 35]). The matching theory involves the equality of the first and second fundamental forms of the boundaries. To compare them they are pulled-back into a single boundary via the identification. In perturbative matching theory everything occurs on the abstract hypersurface Ω 0 diffeomorphic to Ω + 0 and Ω -0 of the background spacetime. On Ω ± 0 we attach two vector fields Z ± = Q ± n (0) ± + T ± whose geometric meaning has been discussed above. They are not know a priori, firstly, because of the hypersurface gauge freedom, and secondly, because the identification of the boundaries Ω + ε and Ω -ε is not known a priori. To the unknowns Z ± we add four symmetric tensors q (1) ± and K (1) ± intrinsic to Ω 0 which arise as the ε -derivative at ε = 0 of the first fundamental form q ± ε and second fundamental form K ± ε of Ω ± ε . These tensors are intrinsic to Ω ± ε , so before taking ε -derivatives they must be pulled back onto Ω 0 via the hypersurface gauges (on each side). Thus, q (1) ± and K (1) ± are hypersurface gaugedependent by construction. On the other hand, their construction is fully independent of the spacetime gauge freedom. In order to write down their explicit expression, let g (1) ± be the perturbed metric (i.e. the fundamental unknown in metric perturbation theory) on each side of the background spacetime. Let also Ψ ± 0 : Ω 0 → W ± 0 be the embedding of the matching hypersurface on each region of the background spacetime. Let y i ( i, j, . . . = 1 , . . . , n -1) be a local coordinate system on Ω 0 and define tangent vectors e ± i = Ψ ± 0 glyph[star] ( ∂ y i ). There are also unique (up to orientation) unit one-forms n (0) ± normal to the boundaries. We choose them so that the corresponding vector n (0) + points towards W + 0 and n (0) -points outside of W -0 or viceversa. The first and second fundamental forms of the background are simply q (0) ± := Ψ ± 0 glyph[star] ( g (0) ± ) , K (0) ± := Ψ ± 0 glyph[star] ( ∇ ± n (0) ± ), where ∇ ± is the covariant derivative in ( W ± 0 , g (0) ± ). Given that the background configuration is already composed of the matching of V + 0 and V -0 through Ω + 0 := Ω 0 , we already have q (0)+ = q (0) -and K (0)+ = K (0) -. Then q (1) ± and K (1) ± are defined as follows [47] where σ := g (0) ± ( n (0) ± , n (0) ± ), D is the covariant derivative of (Ω 0 , q (0) ± ), R (0) ± αµβν is the Riemann tensor of ( W ± 0 , g (0) ± ) and S (1) ± α βγ := 1 2 ( ∇ ± β g (1) ± α γ + ∇ ± γ g (1) ± α β -∇ ± α g (1) ± βγ ). The first order matching conditions (in the absence of shells) require the equalities We emphasize that Q ± and T ± are a priori unknown quantities and fulfilling the matching conditions requires showing that two vectors Z ± exist such that (19) are satisfied. The spacetime gauge freedom can be exploited to fix either or both vectors Z ± a priori, but this should be avoided (or at least carefully analyzed) if additional spacetime gauge choices are made, in order not to restrict a priori the possible matchings. Regarding the hypersurface gauge, this can be used to fix one of the vectors T + or T -, but not both. Note also that the linearized matching conditions are, by construction, spacetime gauge invariant because, as discussed above, the tensors q (1) ± , K (1) ± are necessarily spacetime gauge invariant. In fact, it is straightforward to check explicitly that the right-hands sides of (17) and (18) are spacetime gauge invariant (the individual terms are not, and it is precisely the spacetime gauge dependence in Z ± which makes these objects spacetime gauge invariant). Moreover, the set of conditions (19) are hypersurface gauge invariant, provided the background is properly matched, since, as shown in [47], under such a hypersurface gauge transformation given by the vector ζ in Ω 0 , q (1) transforms as q (1) + L ζ q (0) , and similarly for K (1) .",
"pages": [
15,
16,
17,
18
]
},
{
"title": "6 Spherical symmetry: Hodge decomposition",
"content": "After the previous summary on linearized matching, in this section we introduce the second main ingredient for the linearized Einstein-Straus model reviewed in the following sections: the Hodge decomposition on the sphere [38]. In order to exploit the underlying spherical symmetry of the background configuration it is common practice to decompose the perturbations, and their related objects and equations, in terms of scalar, vector and tensor harmonics on the sphere. That was the procedure used in the seminal work on perturbations around spherical matched background configurations, due to Gerlach and Sengupta (GS) in [23] and [24], revisited and improved by Mart'ın-Garc'ıa and Gundlach in [43]. The aim in [38] was to use an alternative method, based on the Hodge decomposition on the sphere in terms of scalars, in order to avoid the need to deal with infinite series of objects. In particular, the whole set of matching conditions for the linearized EinsteinStraus model was presented in [38] as a finite number of equations involving scalars that depend on the three coordinates in the matching hypersurface Ω 0 , in contrast with an infinite number of equations for an infinite set of functions of one variable. It is clear that one can always go from the Hodge scalars to the spherical harmonics decomposition in a straightforward way. However, it is not always easy to rewrite the infinite number of expressions appearing in a spectral decomposition in terms of Hodge scalars. Consider the round unit metric Ω AB dx A dx B = dϑ 2 +sin 2 ϑdϕ 2 , with η AB and D A denoting the corresponding volume form and covariant derivative respectively, and ( glyph[star]dG ) A = η C A D C G the Hodge dual with respect to Ω AB . Let us recall that the usual Hodge decomposition on ( S 2 , Ω AB ) states that any one-form V A can be canonically decomposed as V A = D A F +( glyph[star]dG ) A , where F and G are functions on S 2 , and any symmetric tensor T AB as T AB = D A U B + D B U A + H Ω AB , for some U A on S 2 , which can be in turn decomposed in terms of scalars. Based on this, it is convenient to define the following two functionals. Given three scalars X tr , X 1 and X 2 on ( S 2 , Ω AB ) we define the functional one form V A ( X 1 , X 2 ) as and the functional symmetric tensor T AB ( X tr , X 1 , X 2 ) as Let us recall that the decomposition defines these X 's on S 2 up to the kernels of the operators V A and T AB . We allowed for the appearance of all these kernels in [38], where their relevance (or their lack of) was already discussed. In order to avoid spurious information and present a more concise review -and also to ease the translation and comparison with the quantities used in the previous literature in terms of the harmonic decompositions,we use the reformulation already presented in [39] where the Hodge decomposition is, in fact, unique. Indeed, in order to fix the Hodge decomposition uniquely we define a canonical dual decomposition by demanding that the functions X 1 , X 2 in V A ( X 1 , X 2 ) are always orthogonal (in the L 2 sense on S 2 ) to 1, and the functions X 1 , X 2 in T AB ( X tr , X 1 , X 2 ) are orthogonal to 1 and to the l = 1 spherical harmonics. Schematically, we may use and We will use the following notation: given any function f on S 2 we define so that f -f || 0 is orthogonal to the l = 0 harmonics Y 0 and f -f || 1 is orthogonal to the l = 1 harmonics Y m 1 . Note finally that the Hodge decomposition in terms of scalars involves two types of objects depending on their behaviour under reflection on the sphere. The scalars with subscripts 1 and tr remain unchanged under reflection, and are typically called longitudinal, even or polar quantities, while those with subscripts 2 change, and correspond to the transversal, odd or axial quantities. Let us consider now the general spherically symmetric spacetime V = M 2 × S 2 with metric g αβ = ω IJ ⊕ r 2 Ω AB , so that ( M 2 , ω IJ ) is a 2-dim Lorentzian space and r > 0 a function on M 2 . The dual in ( M 2 , ω IJ ) will be indicated by ∗ and the covariant derivative by ∇ . We can now proceed to decompose any one-form (vector) or symmetric two-tensor on V by first taking the part orthogonal to the sphere and then apply the Hodge canonical decomposition to the part tangent to the sphere. In particular, given a normalized timelike one-form u α orthogonal to the spheres, its corresponding one-form u I on ( M 2 , ω IJ ) (defined by u α = ( u I , 0)) can be used to construct a convenient orthonormal basis { u I , m I } so that ω IJ = -u I u J + m I m J (this is u I u I = -1 and m I := ∗ u I ), and consider then the one-form on V defined by m α := ( m I , 0). Given any vector V I we will simply denote by V u and V m the contractions u I V I and m I V I respectively. We apply now this decomposition to encode the objects that will describe the (first order) perturbation of a background consisting of two spherically symmetric regions ( W + , g (0)+ ) and ( W -, g (0) -) matched across corresponding spherically symmetric boundaries Ω + 0 and Ω -0 . At each side ± (we avoid the use of ± just now for clarity) the metric perturbation tensor g (1) αβ gets thus decomposed as where Z I 1 and Z I 2 are two one-forms defined on M 2 , and analogously for any symmetric tensor. The deformation vector Z α , defined on M at points on Ω, is decomposed as whereby the part Z I gets decomposed, in turn, onto the normal and tangential parts to Ω 0 , Q and T respectively. Given the (first order) perturbation tensor and the deformation vector at either ± side of the matching hypersurface, one can calculate the symmetric tensors q (1) ij and K (1) ij , i.e. the 'perturbed first and second fundamental forms', using (17)-(18). Recalling now that q (1) ij and K (1) ij are defined on (Ω 0 , q (0) ij ) and that Ω 0 at either side are tangent to the spheres { θ, φ } , let us denote by λ the parameter that follows the direction on Ω 0 orthogonal to the spheres in order to decompose q (1) ij and K (1) ij into q (1) λλ , K (1) λλ , plus and Note that all these functions are scalars on the sphere that depend only on λ . The first order matching conditions (19) are therefore equivalent to Except for the simplification of the kernels by the canonical decomposition, these are the linearized matching conditions presented in [38].",
"pages": [
18,
19,
20
]
},
{
"title": "6.1 Gerlach and Sengupta (GS) 2+2 formalism",
"content": "Let us emphasize again that the conditions (19), and thus (23), concern quantities defined on Ω 0 and are therefore independent on the coordinates used in W + and W -for their computation. These quantities are thus, on the one hand, spacetime gauge independent by construction. Moreover, as discussed in Section 5, the equations are also hypersurface gauge independent. All this makes it unnecessary the use of gauge invariant quantities in order to establish the perturbed matching conditions. Having said that, however, the use of gauge independent quantities turns out to be convenient in the end, mostly when one eventually wants to impose the Einstein field equations. As shown in the works [23], [24], [43], the use of spacetime gauge invariants is very convenient in order to combine the Einstein field equations with the perturbed matching conditions. One can proceed by constructing gauge invariants in terms of Hodge scalars using analogous expressions to those in the harmonic decomposition constructed in [24, 23, 43]. Let us now concentrate on the odd (axial) sector. The odd gauge invariant quantities are encoded in the vector [36] (cf. [24]) Note that K I , as defined above, contains l = 1 harmonics, from Z I 2 , but only the l ≥ 2 sector is gauge invariant. In other words, the part of K I orthogonal to Y 1 (i.e. K I -K I || 1 in the notation above) is the gauge invariant part. Once the orthonormal basis { u I , m I } has been identified at both sides, the odd sector of the linearized matching, which corresponds to the set of equations in (23), is equivalent in the l ≥ 2 sector (the part orthogonal to l = 0 and l = 1) to [36] (cf. [24]) plus an equation for T + 2 -T -2 .",
"pages": [
20,
21
]
},
{
"title": "7 Linearized Einstein-Straus model: matching conditions",
"content": "We are ready to consider the linearized matching of the perturbed Schwarzschild and FLRW spacetimes, as it was analyzed in [38]. Take the Einstein-Straus model as described in Section 2: the FLRW geometry in cosmic time coordinates (1), the Schwarzschild in standard coordinates (2), and the background matching hypersurface Ω 0 described by Ω RW 0 : { t = t, R = R 0 } and Ω ST 0 : { T = T 0 ( t ) , r = r 0 ( t ) } respectively, where T 0 ( t ) and r 0 ( t ) satisfy (3) and the angular part is again ignored. The orthonormal basis we take on the Lorentzian space orthogonal to the spheres is formed by u = dt , m = adR . Note that this choice corresponds to the tangent and normal forms to Ω 0 at Ω 0 , respectively. More precisely, m is chosen to be n (0) at points on Ω 0 . On the Schwarzschild side we have u | Ω 0 = ˙ T 0 ∂ T + ˙ r 0 ∂ r and m | Ω 0 := n (0) = -˙ r 0 dT + ˙ T 0 dr . Take the first order perturbations of FLRW, in no specific gauge, formally decomposed into the usual scalar, vector and tensor (SVT) modes, i.e. 4 (Latin indices a, b, c are used for tensors on ( M , g M )) with satisfying the constraints The canonical Hodge decomposition is then used to encode the part tangent to the spheres into S 2 scalars in the following schematic way [38]: vector All in all, encoding g (1)+ using the SVT modes together with the Hodge decomposition leaves us with 15 SVT-Hodge quantities, corresponding to the scalar modes { Ψ , Φ , W, χ } , vector modes { ˜ W R , W 1 , W 2 , Y R , Y 1 , Y 2 } and tensor modes {Q 1 , Q 2 , H , U 1 , U 2 } , all scalars on S 2 , not all independent due to the previous constraints, and, on the other hand, not unique . Consider, in particular, the only 4 scalars we have in the odd sector; vector modes {W 2 , Y 2 } and tensor modes {Q 2 , U 2 } . As discussed in the previous section, only two gauge invariant quantities exist in the odd sector. These correspond to the two components of the gauge invariant odd vector (and for l ≥ 2), K + I , which given the above construction in terms of the SVT-Hodge quantities, read [39, 36] Consider now the stationary and axially symmetric vacuum perturbations in the Weyl gauge. They can be described in terms of two functions U (1) ( r, θ ) and A (1) ( r, θ ), which correspond, basically, to the perturbation of the gravitational Newtonian potential and the rotational perturbation, respectively. The perturbation tensor reads [38] Note that, when using the full set of the Einstein field equations for vacuum, the function k (1) is determined up to quadratures once U (1) ( r, θ ) and A (1) ( r, θ ) are found. We stress, however, that the vacuum equations, although indicated, were not imposed in the perturbed Schwarzschild region (nor in the perturbed FLRW region) in [38], and therefore the results found there are purely geometric. Instead of working with A (1) ( r, θ ), it is convenient to use an auxiliary function, G , defined by A (1) := sin θ∂ θ G . In terms of the Hodge decomposition of the perturbation tensor (20), applied to (26), we have G = -( 1 -2 M r ) -1 Z -T 2 . Another auxiliary function P can be introduced for k (1) . The whole set of matching conditions (23) for the linearized Einstein-Straus model, both in the odd and even sectors, were found in [38] in terms of these functions U (1) ( r, θ ) , G tensor and P in the Schwarzschild side together with the above 15 SVT-Hodge scalars describing the FLRW perturbation. The whole set is too long to be included here, but in order to review the main results in [38] only the odd sector of the linearized matching is needed. The odd sector of the linearized matching (24) projected to the part orthogonal to the l = 0 and l = 1 harmonics can be rewritten as the following three relations [38] plus an equation for the difference T RW 2 -T Sch 2 . The three equations above can be shown [36] to correspond indeed to (25), taking into account that K Sch = -( 1 -2 M r ) G dT . These equations were presented in [38] in full, including the parts lying on the l = 0 and l = 1 harmonics. There, a series of kernels inherent to the usual Hodge decomposition where the responsible for the usual freedom found in the l = 0 and l = 1 sectors when using harmonic decompositions. By using the canonical Hodge decomposition introduced in Section 6, we can have a better control of that freedom, and understand its nature, getting rid of the spurious terms. Indeed, by doing that it can be shown [36] that the projection of the linearized matching on the l = 1 harmonics -on the l = 0 it is trivial, since all scalars in the odd sector are orthogonal to l = 0- gives while ( T RW 2 -T Sch 2 ) || 1 is free. The first consequence of the above equations is that if the FLRW remains unperturbed then the stationary region must be static in the range of variation of r 0 ( t ): equations (27)-(29) imply that the part of G orthogonal to l = 1 vanishes, and (30) implies that G || 1 = Ca 3 / (2 M -a Σ c ) , where C is a constant. Therefore G = Ca 3 / (2 M -a Σ c ) cos θ , and thus 5 As shown in [38], this implies that the perturbed spacetime is static in the range of variation of r 0 ( t ). This result generalizes that in [52] because now the matching hypersurface does not necessarily keep the axial symmetry. Therefore, the only way of having a stationary and axisymmetric vacuum arbitrarily shaped (at the linear level) region in FLRW is to have the Einstein-Straus model. Let us remark again that by the interior/exterior duality, this result also implies that a piece of FLRW, irrespective of its shape and its relative rotation with the exterior, cannot describe the interior of Kerr.",
"pages": [
21,
22,
23
]
},
{
"title": "7.1 Constraint on FLRW",
"content": "Another interesting consequence of the matching conditions is that the combination of (27) and (28) produces one equation that involves only quantities in FLRW [38] and thus constitutes a constraint in FLRW. Recalling that this equation is meant to be orthogonal to l = 1 (and vanishes identically if projected on l = 0), this constraint implies that if the perturbed FLRW contains vector modes with l ≥ 2 harmonics on Ω 0 , then it must contain also tensor modes there. Since, as we have just seen above, the existence of a rotation in the stationary region implies the existence of, at least, vector perturbations in FLRW, then both vector and tensor modes must exist on Ω 0 . It must be stressed that, as demonstrated in [5] (and references therein), there exist configurations of FLRW linear perturbations containing only vector perturbations which vanish identically inside a spherical surface. Such configurations are compatible with the results reviewed here, since that interior region is FLRW and the above constraints do not apply. A completely different matter is the embedding of a Schwarzschild spherical cavity (or a vacuum perturbation thereof) into any such model: the Schwarzschild cavity cannot reach the perturbed FLRW region, as otherwise the constraints above would require that tensor perturbations are also present (at least near the boundary of the Schwarzschild cavity). There also exists a Einstein-Straus perturbative model by Chamorro [18] consisting on small rotation Kerr vacuole within a perturbed FLRW. Again, the constraint above does not apply to this model because there are no l ≥ 2 modes there. The fact that tensor modes must exist near Ω 0 once some rotation with l ≥ 2, whatever small, exists in the stationary region, may indicate the existence of some kind of gravitational waves on FLRW near Ω 0 . In order to analyze further this issue one needs to take the Einstein field equations into consideration. That is the purpose of our work in preparation [36], some result of which will appear in the proceedings of the ERE2012 meeting.",
"pages": [
24
]
},
{
"title": "8 Conclusions and outlook",
"content": "This paper is concerned with the difficulties that the Einstein-Straus model encounters. A fundamental one refers to its high level of rigidity and the impossible generalization to non-spherical symmetry if the bound system is required to be time independent so as to retain the property that cosmic expansion does not affect the local systems. Moreover, if one views the model within the LTB class with a step function density profile, the model is unstable to perturbations [57], [32], cf. also the discussion in [30]. The rigidity result so far requires either stationarity and axial symmetry or staticity. An interesting open problem would be to relax the conditions and assume only stationarity. Despite these difficulties, the Einstein-Straus model has played and plays a very important role in cosmology in different areas or research, most notably on the influence (or lack thereof) of the cosmic expansion on local systems, or in the problem of averaging in cosmology at least on an observational level (see e.g. [20]). The model is still widely used as textbook explanation of the lack of influence of the cosmic expansion on astrophysical systems and, in fact, there are not many known alternatives (a notable exception is the McVittie model [44], [28], [29] which is also spherically symmetric and mimics the geometry of Schwarzschild at small scales while approaching a FLRW model at long distances, and which has been studied thoroughly, see [15] and references therein). Concerning the use of the Einstein-Straus model on observational cosmology, mainly by studying lensing effects, its generalizations have systematically consisted in keeping spherical symmetry and allowing for some dynamics in the interior. The prominent example here consists of LTB regions inside a FLRW universe (see references in [20]). An important ingredient for the rigidity of the Einstein-Straus model is the large symmetry of the FLRW background. It is therefore an interesting problem to analyze how the model gets modified in the presence of cosmic perturbations. In a conservative approach, one still wants to keep the main properties (stationarity of a region inside a cosmological model) as far as possible and analyze the possible departures from the model in more realistic situations. Moreover, by studying perturbed Einstein-Straus models one seeks going beyond the problem of the influence of cosmic expansion on local systems, and tackle the problem of the influence of general cosmic dynamics. Surprisingly, it turns out that the existence of static (stationary) regions does impose conditions on the cosmic perturbations, at least near the boundary. Whether this is a real effect or simply an indication that the interior region should not be kept stationary remains to be seen. Another implication of the perturbed Einstein-Straus model is that extra care is required in the standard decomposition of metric perturbations in terms of scalar, vector and tensor modes. As discussed above, any rotation in the vacuole implies necessarily the presence of both vector and tensor modes in the cosmic perturbations. It is interesting to analyze whether these tensor modes could represent cosmic gravitational waves. Some preliminary results along these lines have already been presented in [39]. A detailed and more complete approach will appear elsewhere. Another interesting future line of research is to allow for non-stationary perturbations in the vacuole and study the transmission of gravitational waves from the cosmic region to the bound system.",
"pages": [
24,
25
]
},
{
"title": "9 Acknowledgements",
"content": "MM acknowledges financial support under the projects FIS2012-30926 (MICINN) and P09-FQM-4496 (J. Andaluc'ıa-FEDER). FM thanks the warm hospitality from Instituto de F'ısica, UERJ, Rio de Janeiro, Brasil, projects PTDC/MAT/108921/2008 and CERN/FP/123609/2011 from Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT), as well as CMAT, Univ. Minho, for support through FEDER funds Programa Operacional Factores de Competitividade (COMPETE) and Portuguese Funds from FCT within the project PEst-C/MAT/UI0013/2011. RV thanks the kind hospitality from the Universidad de Salamanca, where parts of this work have been produced, and financial support from project IT592-13 of the Basque Government, and FIS2010-15492 from the MICINN.",
"pages": [
25
]
}
]
2013Ge&Ae..53..813K
https://arxiv.org/pdf/1307.7960.pdf
<document>
<section_header_level_1><location><page_1><loc_22><loc_86><loc_79><loc_91></location>LONG-TERM VARIATIONS OF GEOMAGNETIC ACTIVITY AND THEIR SOLAR SOURCES</section_header_level_1>
<section_header_level_1><location><page_1><loc_22><loc_83><loc_79><loc_85></location>Kirov B. 1 , Obridko V.N. 2 , Georgieva K. 1 , Nepomnyashtaya E.V. 2 ,</section_header_level_1>
<text><location><page_1><loc_44><loc_80><loc_56><loc_82></location>Shelting B.D. 2</text>
<text><location><page_1><loc_22><loc_75><loc_78><loc_78></location>1 - Space Research ant Technologies Institute - BAS, Sofia, Bulgaria 2 - IZMIRAN, Russia</text>
<text><location><page_1><loc_39><loc_72><loc_62><loc_74></location>email: [email protected]</text>
<section_header_level_1><location><page_1><loc_46><loc_69><loc_54><loc_71></location>Abstract</section_header_level_1>
<text><location><page_1><loc_12><loc_51><loc_89><loc_68></location>Geomagnetic activity in each phase of the solar cycle consists of 3 parts: (1) a 'floor' below which the geomagnetic activity cannot fall even in the absence of sunspots, related to moderate graduate commencement storms; (2) sunspot-related activity due to sudden commencement storms caused by coronal mass ejections; (3) graduate commencement storms due to high speed solar wind from solar coronal holes. We find that the changes in the 'floor' depend on the global magnetic moment of the Sun, and on the other side, from the height of the 'floor' we can judge about the amplitude of the sunspot cycle.</text>
<section_header_level_1><location><page_1><loc_43><loc_48><loc_57><loc_50></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_12><loc_25><loc_89><loc_47></location>As early as in 1852 it was noted that geomagnetic disturbances are related to solar activity [Sabine, 1852], and in 1982 it was found that geomagnetic activity is caused by two types of solar agents, the first one related to sunspots and caused by coronal mass ejections (CMEs), and the other one -not related to sunspots and caused by high speed solar wind from solar coronal holes [Feynman, 1982]. CME-caused geomagnetic disturbances have a maximum in sunspot maximum, and coronal holes-related disturbances - on the descending phase of sunspots. In the present study we aim to determine how these two components of geomagnetic activity vary from cycle to cycle, and the variations of which solar agents cause these changes.</text>
<section_header_level_1><location><page_1><loc_33><loc_22><loc_68><loc_24></location>2. Components of geomagnetic activity</section_header_level_1>
<text><location><page_1><loc_12><loc_9><loc_90><loc_21></location>Feynman [1982] noted that if a geomagnetic activity index (e.g. aa -index) is plotted as a function of the sunspot number R (Fig.1), all aa -index values lie above a line given by the equation aaR=a0 + b.R . Feynman [1982] suggested that aaR is the geomagnetic activity caused by sunspot-related solar activity, and the aa values above this line represent the geomagnetic activity caused by high speed solar wind: ааP = aa - aaR .</text>
<figure>
<location><page_2><loc_12><loc_72><loc_46><loc_90></location>
</figure>
<figure>
<location><page_2><loc_48><loc_72><loc_82><loc_90></location>
<caption>Fig.1. Dependence of аа-index on R in the period 1878-1912 (left) and 1954-1985 (right)</caption>
</figure>
<text><location><page_2><loc_12><loc_57><loc_89><loc_66></location>Feynman [1982] determined that aa R = 5.38 + 0.12. R . We calculated the values of a0 and b in consecutive periods of around 30 years, each including 3 sunspot cycles (cycles 9-11, 10-12 and so on). The calculated values of the coefficients demonstrate a clear quasi-secular cycle (Fig. 2).</text>
<figure>
<location><page_2><loc_26><loc_37><loc_73><loc_55></location>
<caption>Fig. 2 . Cyclic variations of the coefficients a0 and b</caption>
</figure>
<text><location><page_2><loc_12><loc_9><loc_89><loc_33></location>Actually, geomagnetic activity can be divided into 3 rather than 2 components. The first one is the 'floor', equal to the а0 coefficient which represents the geomagnetic activity in the absence of sunspots. It is practically determined by the activity in the cycle minimum and varies smoothly from cycle to cycle. The second component is the geomagnetic activity caused by sunspot-related solar activity which is described by the straight line aaT = b.R so that aaR = а0 + aaT . The slope b of this line also changes cyclically. The third component ааP (the value above aaR ) is caused by high speed solar wind. It can be seen that when the coefficient а0 is big (high 'floor' of the geomagnetic activity), the geomagnetic activity is almost independent on the sunspot number (small coefficient b ), and when the 'floor' is low, the geomagnetic activity quickly grows with growing sunspot number.</text>
<text><location><page_3><loc_12><loc_78><loc_89><loc_92></location>Fig.3 demonstrates that both the 'floor' of the geomagnetic activity а0 and the slope b don't depend on the phase of the sunspot cycle (upward or downward branch), but are different in different intervals. Besides, the scatter of values above aaR in any interval is much bigger during the downward branch which has to be expected because of the strong influence of high speed solar wind streams on the geomagnetic activity in this phase of the sunspot cycle [Georgieva, K., Kirov, B, 2005].</text>
<figure>
<location><page_3><loc_24><loc_53><loc_75><loc_76></location>
<caption>Fig. 3. Dependence of aa on R in the upward (upper panel) and in the downward branch (lower panel) of the sunspot cycle in the period 1844 - 1957 (left) and in the period 1955 1985 (right)</caption>
</figure>
<text><location><page_3><loc_12><loc_42><loc_88><loc_46></location>The question now is which solar agents cause the nonzero values of the geomagnetic activity 'floor', and which factors lead to the changes in the coefficients а0 and b .</text>
<section_header_level_1><location><page_3><loc_37><loc_39><loc_64><loc_40></location>3. Types of geomagnetic storms</section_header_level_1>
<text><location><page_3><loc_12><loc_8><loc_89><loc_37></location>The geomagnetic storms differ in intensity as well as in characteristics. The intensity of the storm is determined by the parameters D, H и Z - the magnetic declination, change of the horizontal and vertical components of the Earth's magnetic field, respectively, measured in nT (Table 1), and the storm can be with a sudden or gradual commencement. In order to determine the origin of different storms, [Шельтинг, Обридко , 2011] compared the occurrence frequency of all, strong, moderate and weak storms with sudden and with gradual commencement to the number of sunspots. They found that the occurrence frequency of the sudden commencement storms correlates with the sunspot number, with correlation coefficient 0.872 +/- 0.06. In contrast, the correlation coefficient of the occurrence frequency of the gradual commencement storms and the sunspot number is practically zero (0.014 +/0.13), and their maximum is shifted by 1-3 years after the sunspot maximum. Further analysis shows that there is high correlation among storms of different intensity inside each of the</text>
<text><location><page_4><loc_12><loc_78><loc_89><loc_92></location>groups, and absolutely no correlation between the two groups of storms. From there the authors make the conclusion that these two types of storms have different origin. Sudden commencement storms are caused by coronal mass ejections (CMEs). As the solar coronal mass ejections are associated with active areas, that is with local magnetic fields, a high correlation is observed between the occurrence frequency of sudden commencement storms and the number of sunspots.</text>
<text><location><page_4><loc_12><loc_67><loc_89><loc_76></location>Gradual commencement storms are caused by high speed solar wind. It originates from solar coronal holes whose maximum is on the downward branch of the sunspot cycle. This leads to two maxima in geomagnetic activity in the course of the sunspot cycle, the second one being due mainly to the occurrence of many gradual commencement storms [Tsurutani, et al. 2006].</text>
<section_header_level_1><location><page_4><loc_37><loc_64><loc_63><loc_66></location>4. Geomagnetic activity 'floor'</section_header_level_1>
<text><location><page_4><loc_12><loc_51><loc_89><loc_63></location>The geomagnetic activity 'floor' is the geomagnetic activity in the absence of any sunspots. Practically it is determined by the geomagnetic activity in the sunspot minimum. As seen in Fig.4, during the whole investigated period, the geomagnetic activity with aa -index between 10 and 30 is caused by gradual commencement storms, but this is especially well pronounced in sunspot minimum periods.</text>
<figure>
<location><page_4><loc_30><loc_32><loc_70><loc_49></location>
<caption>Fig.4 . Annual number of weak sudden commencement storms (solid line) and gradual commencement storms (dotted line).</caption>
</figure>
<text><location><page_4><loc_12><loc_10><loc_89><loc_27></location>We can conclude that the geomagnetic activity 'floor' is determined by non sunspot-related solar activity. Fig.5 demonstrates that the variations in the geomagnetic activity floor follow, with the exception of cycle 13, the variations in the number of 30hour intervals with aa -index between 10 and 30 in the minimum of the respective cycle. Moreover, from cycle 14 to 21 (around 1985), an increase is observed in both the number of 3-hour intervals with 10< аа <30, and of the geomagnetic activity floor, after which they both begin decreasing. The correlation between the two quantities is 0.85 with p<0.01.</text>
<figure>
<location><page_5><loc_31><loc_71><loc_69><loc_91></location>
<caption>Fig.5. Number of 3-hour intervals with aa between 10 and 30 (solid line) and the geomagnetic activity floor а0 (dotted line), in consecutive sunspot cycle minima.</caption>
</figure>
<text><location><page_5><loc_12><loc_48><loc_89><loc_62></location>It is seen that the geomagnetic activity floor in each cycle is determined by the geomagnetic activity in the range 10<аа<30 in the cycle minimum, and as far as this geomagnetic activity, especially in the cycle minimum, is related as shown above to gradual commencement storms, the floor is determined by the high speed solar wind streams causing gradual commencement storms. Therefore, the reason for the changing geomagnetic activity floor is the changing high speed solar wind reaching the Earth during sunspot minimum.</text>
<text><location><page_5><loc_12><loc_32><loc_89><loc_47></location>It is interesting to note that at the same time as the increase in the floor changed to decrease (cycle 21), the increase in the solar global magnetic moment changed to a sharp decrease[Обридко, Шельтинг, 2009 ] - (Fig.6). It seems that the change in the solar global magnetic moment is reflected in the geomagnetic activity caused by the high speed solar wind during the sunspot minimum through its effects on the thickness of the heliospheric current sheet [Simon and Legrand, 1987].</text>
<figure>
<location><page_5><loc_27><loc_12><loc_73><loc_29></location>
<caption>Fig.6. Evolution of the solar magnetic moment from 1918 to 2006.</caption>
</figure>
<section_header_level_1><location><page_6><loc_40><loc_90><loc_61><loc_92></location>5. Coefficient b (slope)</section_header_level_1>
<text><location><page_6><loc_12><loc_65><loc_89><loc_89></location>The sunspot-related geoeffective solar agents are the CMEs. It is known that the geoeffectiveness of CMEs vary little in the course of the sunspot cycle; considerably changes the geoeffectiveness of magnetic clouds (a subclass of CMEs with high and smoothly rotating magnetic field), but their number is negligible compared to the total number of CMEs except around sunspot minimum when their geoeffectiveness is low. Therefore, the varying contribution of CMEs to geomagnetic activity from year to year depends on their varying number. [Georgieva and Kirov, 2005]. Fig.7 presents the ratio of CMEs to the number of sunspots for the period 1996-2012. For the number of CMEs, the SOHO/LASCO CME catalog is used (http://cdaw.gsfc.nasa.gov/CME_list/) as it provides a fairly homogenous data set.</text>
<figure>
<location><page_6><loc_25><loc_37><loc_75><loc_63></location>
<caption>Fig. 7 . Ratio of the number of CMEs to the sunspot number (monthly averages).</caption>
</figure>
<text><location><page_6><loc_12><loc_10><loc_88><loc_32></location>It can be seen that the ratio is almost constant during the greater part of the sunspot cycle, with the exception of the periods of sunspot minima, especially in the minimum between cycles 23 and 24 which is known to be very peculiar. In 2007, 2008, and 2009 we had total annuals of 20, 70, and 60 CMEs, respectively, with the average annual number of sunspots between 3 and 7. A small change in the correlation between the sunspot number and the number of CMEs is observed in the previous sunspot minimum also, but it is only due to CMEs in a few single months. We can conclude that the increasing geomagnetic activity with increasing sunspot number (the coefficient b ) is due to the increasing number of CMEs with increasing number of sunspots.</text>
<section_header_level_1><location><page_7><loc_36><loc_90><loc_65><loc_92></location>6. Forecasting the following cycle</section_header_level_1>
<text><location><page_7><loc_12><loc_81><loc_89><loc_89></location>Fig.8 demonstrates that the sunspot number in the cycle maximum is related to the geomagnetic activity floor in the same cycle. The correlation between the two variables is 0,792 with p=0.001.</text>
<figure>
<location><page_7><loc_26><loc_54><loc_74><loc_79></location>
<caption>Fig.8. Geomagnetic activity floor (solid line) and sunspot number in the cycle maximum (dotted line)</caption>
</figure>
<text><location><page_7><loc_12><loc_35><loc_89><loc_47></location>From this it follows that the characteristics of the whole cycle are set already at its beginning, and measuring the geomagnetic activity we can forecast to a great extend its maximum. On the other hand, given that the evolution of the Sun's magnetic moment is indicative of the changes in а0 , we can evaluate in advance the direction of change of the geomagnetic activity 'floor'.</text>
<section_header_level_1><location><page_7><loc_38><loc_32><loc_63><loc_34></location>6. Summary and conclusions</section_header_level_1>
<text><location><page_7><loc_12><loc_9><loc_89><loc_31></location>The geomagnetic activity consists of three components: (1) a0 - the geomagnetic activity 'floor', theoretically equal to the activity at zero number of sunspots. Practically this activity is determined by the gradual commencement geomagnetic disturbances with 10< аа <30 in the beginning of the sunspot cycle; (2) aaT - the geomagnetic activity caused by CMEs whose number linearly increases with increasing number of sunspots aaT = b.R , so that aaR = a0 + b.R ; (3) ааP - the values of aa above aaR , caused by high speed solar wind streams from solar coronal holes. We have found that the variations of a0 have a quasi-secular cycle, with the direction of variation following the variation of the global magnetic moment of the Sun. On the other hand, we have found that a0 determined by the geomagnetic activity in the beginning</text>
<text><location><page_8><loc_12><loc_80><loc_89><loc_92></location>of a cycle is directly related to the sunspot maximum in the same cycle. Therefore, if we know the direction of change (increasing or decreasing) of the global magnetic moment, we can forecast the increase or decrease of a0 in the next cycle, and from there - the increase or decrease of the sunspot maximum. Moreover, during the sunspot minimum we can quite accurately forecast the following sunspot minimum.</text>
<table>
<location><page_8><loc_12><loc_63><loc_89><loc_76></location>
<caption>Table 1</caption>
</table>
<section_header_level_1><location><page_8><loc_45><loc_58><loc_55><loc_60></location>References</section_header_level_1>
<text><location><page_8><loc_12><loc_50><loc_89><loc_57></location>Обридко В.Н., Шельтинг Б.Д. Некоторые аномалии эволюции глобальных и крупномасштабных магнитных полей на Солнце как предвестники нескольких предстоящих невысоких циклов// Письма в астрономический журнал. Т. 35. №3, С. 3844. 2009.</text>
<text><location><page_8><loc_12><loc_44><loc_89><loc_49></location>Шельтинг Б.Д., Обридко В.Н. Магнитные бури с внезапным и постепенным началом как индексы солнечной активности// Всероссийская ежегодная конференция по физике Солнца. Пулково Русия. 2011.</text>
<text><location><page_8><loc_12><loc_40><loc_89><loc_44></location>Feynman J. Geomagnetic and solar wind cycles, 1900-1975// J. Geophys. Res. 87, 6153-6162 (1982)</text>
<text><location><page_8><loc_12><loc_35><loc_89><loc_40></location>Georgieva K., Kirov B. Helicity of magnetic clouds and solar cycle variations of their geoeffectiveness// Proceedings IAU Symposium 226 Coronal and Stellar Mass Ejections, Oxford University Press. P.470-472, 2005.</text>
<text><location><page_8><loc_12><loc_29><loc_89><loc_34></location>Sabine E. On Periodical Laws Discoverable in the Mean Effects of the Larger Magnetic Disturbances// Phil. Trans. R. Soc. Lond. January 1, 1852 142 103-124; doi:10.1098/rstl.1852.0009.</text>
<text><location><page_8><loc_12><loc_22><loc_89><loc_28></location>Simon P.A., Legrand J.P. : Some solar cycle phenomena related to the geomagnetic activity from 1868 to 1980. III - Quiet-days, fluctuating activity or the solar equatorial belt as the main origin of the solar wind flowing in the ecliptic plane// Astron. Astrophys. V. 182, P. 329-336, 1987.</text>
<text><location><page_8><loc_12><loc_16><loc_89><loc_21></location>Tsurutani B.T., Gonzalez W. D., Gonzalez A.L.C. et al. , Corotating solar wind streams and recurrent geomagnetic activity: A review // J. Geophys. Res., V. 111, No A07S01, P. 1110711132, 2006.</text>
</document>
[
{
"title": "Kirov B. 1 , Obridko V.N. 2 , Georgieva K. 1 , Nepomnyashtaya E.V. 2 ,",
"content": "Shelting B.D. 2 1 - Space Research ant Technologies Institute - BAS, Sofia, Bulgaria 2 - IZMIRAN, Russia email: [email protected]",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "Geomagnetic activity in each phase of the solar cycle consists of 3 parts: (1) a 'floor' below which the geomagnetic activity cannot fall even in the absence of sunspots, related to moderate graduate commencement storms; (2) sunspot-related activity due to sudden commencement storms caused by coronal mass ejections; (3) graduate commencement storms due to high speed solar wind from solar coronal holes. We find that the changes in the 'floor' depend on the global magnetic moment of the Sun, and on the other side, from the height of the 'floor' we can judge about the amplitude of the sunspot cycle.",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "As early as in 1852 it was noted that geomagnetic disturbances are related to solar activity [Sabine, 1852], and in 1982 it was found that geomagnetic activity is caused by two types of solar agents, the first one related to sunspots and caused by coronal mass ejections (CMEs), and the other one -not related to sunspots and caused by high speed solar wind from solar coronal holes [Feynman, 1982]. CME-caused geomagnetic disturbances have a maximum in sunspot maximum, and coronal holes-related disturbances - on the descending phase of sunspots. In the present study we aim to determine how these two components of geomagnetic activity vary from cycle to cycle, and the variations of which solar agents cause these changes.",
"pages": [
1
]
},
{
"title": "2. Components of geomagnetic activity",
"content": "Feynman [1982] noted that if a geomagnetic activity index (e.g. aa -index) is plotted as a function of the sunspot number R (Fig.1), all aa -index values lie above a line given by the equation aaR=a0 + b.R . Feynman [1982] suggested that aaR is the geomagnetic activity caused by sunspot-related solar activity, and the aa values above this line represent the geomagnetic activity caused by high speed solar wind: ааP = aa - aaR . Feynman [1982] determined that aa R = 5.38 + 0.12. R . We calculated the values of a0 and b in consecutive periods of around 30 years, each including 3 sunspot cycles (cycles 9-11, 10-12 and so on). The calculated values of the coefficients demonstrate a clear quasi-secular cycle (Fig. 2). Actually, geomagnetic activity can be divided into 3 rather than 2 components. The first one is the 'floor', equal to the а0 coefficient which represents the geomagnetic activity in the absence of sunspots. It is practically determined by the activity in the cycle minimum and varies smoothly from cycle to cycle. The second component is the geomagnetic activity caused by sunspot-related solar activity which is described by the straight line aaT = b.R so that aaR = а0 + aaT . The slope b of this line also changes cyclically. The third component ааP (the value above aaR ) is caused by high speed solar wind. It can be seen that when the coefficient а0 is big (high 'floor' of the geomagnetic activity), the geomagnetic activity is almost independent on the sunspot number (small coefficient b ), and when the 'floor' is low, the geomagnetic activity quickly grows with growing sunspot number. Fig.3 demonstrates that both the 'floor' of the geomagnetic activity а0 and the slope b don't depend on the phase of the sunspot cycle (upward or downward branch), but are different in different intervals. Besides, the scatter of values above aaR in any interval is much bigger during the downward branch which has to be expected because of the strong influence of high speed solar wind streams on the geomagnetic activity in this phase of the sunspot cycle [Georgieva, K., Kirov, B, 2005]. The question now is which solar agents cause the nonzero values of the geomagnetic activity 'floor', and which factors lead to the changes in the coefficients а0 and b .",
"pages": [
1,
2,
3
]
},
{
"title": "3. Types of geomagnetic storms",
"content": "The geomagnetic storms differ in intensity as well as in characteristics. The intensity of the storm is determined by the parameters D, H и Z - the magnetic declination, change of the horizontal and vertical components of the Earth's magnetic field, respectively, measured in nT (Table 1), and the storm can be with a sudden or gradual commencement. In order to determine the origin of different storms, [Шельтинг, Обридко , 2011] compared the occurrence frequency of all, strong, moderate and weak storms with sudden and with gradual commencement to the number of sunspots. They found that the occurrence frequency of the sudden commencement storms correlates with the sunspot number, with correlation coefficient 0.872 +/- 0.06. In contrast, the correlation coefficient of the occurrence frequency of the gradual commencement storms and the sunspot number is practically zero (0.014 +/0.13), and their maximum is shifted by 1-3 years after the sunspot maximum. Further analysis shows that there is high correlation among storms of different intensity inside each of the groups, and absolutely no correlation between the two groups of storms. From there the authors make the conclusion that these two types of storms have different origin. Sudden commencement storms are caused by coronal mass ejections (CMEs). As the solar coronal mass ejections are associated with active areas, that is with local magnetic fields, a high correlation is observed between the occurrence frequency of sudden commencement storms and the number of sunspots. Gradual commencement storms are caused by high speed solar wind. It originates from solar coronal holes whose maximum is on the downward branch of the sunspot cycle. This leads to two maxima in geomagnetic activity in the course of the sunspot cycle, the second one being due mainly to the occurrence of many gradual commencement storms [Tsurutani, et al. 2006].",
"pages": [
3,
4
]
},
{
"title": "4. Geomagnetic activity 'floor'",
"content": "The geomagnetic activity 'floor' is the geomagnetic activity in the absence of any sunspots. Practically it is determined by the geomagnetic activity in the sunspot minimum. As seen in Fig.4, during the whole investigated period, the geomagnetic activity with aa -index between 10 and 30 is caused by gradual commencement storms, but this is especially well pronounced in sunspot minimum periods. We can conclude that the geomagnetic activity 'floor' is determined by non sunspot-related solar activity. Fig.5 demonstrates that the variations in the geomagnetic activity floor follow, with the exception of cycle 13, the variations in the number of 30hour intervals with aa -index between 10 and 30 in the minimum of the respective cycle. Moreover, from cycle 14 to 21 (around 1985), an increase is observed in both the number of 3-hour intervals with 10< аа <30, and of the geomagnetic activity floor, after which they both begin decreasing. The correlation between the two quantities is 0.85 with p<0.01. It is seen that the geomagnetic activity floor in each cycle is determined by the geomagnetic activity in the range 10<аа<30 in the cycle minimum, and as far as this geomagnetic activity, especially in the cycle minimum, is related as shown above to gradual commencement storms, the floor is determined by the high speed solar wind streams causing gradual commencement storms. Therefore, the reason for the changing geomagnetic activity floor is the changing high speed solar wind reaching the Earth during sunspot minimum. It is interesting to note that at the same time as the increase in the floor changed to decrease (cycle 21), the increase in the solar global magnetic moment changed to a sharp decrease[Обридко, Шельтинг, 2009 ] - (Fig.6). It seems that the change in the solar global magnetic moment is reflected in the geomagnetic activity caused by the high speed solar wind during the sunspot minimum through its effects on the thickness of the heliospheric current sheet [Simon and Legrand, 1987].",
"pages": [
4,
5
]
},
{
"title": "5. Coefficient b (slope)",
"content": "The sunspot-related geoeffective solar agents are the CMEs. It is known that the geoeffectiveness of CMEs vary little in the course of the sunspot cycle; considerably changes the geoeffectiveness of magnetic clouds (a subclass of CMEs with high and smoothly rotating magnetic field), but their number is negligible compared to the total number of CMEs except around sunspot minimum when their geoeffectiveness is low. Therefore, the varying contribution of CMEs to geomagnetic activity from year to year depends on their varying number. [Georgieva and Kirov, 2005]. Fig.7 presents the ratio of CMEs to the number of sunspots for the period 1996-2012. For the number of CMEs, the SOHO/LASCO CME catalog is used (http://cdaw.gsfc.nasa.gov/CME_list/) as it provides a fairly homogenous data set. It can be seen that the ratio is almost constant during the greater part of the sunspot cycle, with the exception of the periods of sunspot minima, especially in the minimum between cycles 23 and 24 which is known to be very peculiar. In 2007, 2008, and 2009 we had total annuals of 20, 70, and 60 CMEs, respectively, with the average annual number of sunspots between 3 and 7. A small change in the correlation between the sunspot number and the number of CMEs is observed in the previous sunspot minimum also, but it is only due to CMEs in a few single months. We can conclude that the increasing geomagnetic activity with increasing sunspot number (the coefficient b ) is due to the increasing number of CMEs with increasing number of sunspots.",
"pages": [
6
]
},
{
"title": "6. Forecasting the following cycle",
"content": "Fig.8 demonstrates that the sunspot number in the cycle maximum is related to the geomagnetic activity floor in the same cycle. The correlation between the two variables is 0,792 with p=0.001. From this it follows that the characteristics of the whole cycle are set already at its beginning, and measuring the geomagnetic activity we can forecast to a great extend its maximum. On the other hand, given that the evolution of the Sun's magnetic moment is indicative of the changes in а0 , we can evaluate in advance the direction of change of the geomagnetic activity 'floor'.",
"pages": [
7
]
},
{
"title": "6. Summary and conclusions",
"content": "The geomagnetic activity consists of three components: (1) a0 - the geomagnetic activity 'floor', theoretically equal to the activity at zero number of sunspots. Practically this activity is determined by the gradual commencement geomagnetic disturbances with 10< аа <30 in the beginning of the sunspot cycle; (2) aaT - the geomagnetic activity caused by CMEs whose number linearly increases with increasing number of sunspots aaT = b.R , so that aaR = a0 + b.R ; (3) ааP - the values of aa above aaR , caused by high speed solar wind streams from solar coronal holes. We have found that the variations of a0 have a quasi-secular cycle, with the direction of variation following the variation of the global magnetic moment of the Sun. On the other hand, we have found that a0 determined by the geomagnetic activity in the beginning of a cycle is directly related to the sunspot maximum in the same cycle. Therefore, if we know the direction of change (increasing or decreasing) of the global magnetic moment, we can forecast the increase or decrease of a0 in the next cycle, and from there - the increase or decrease of the sunspot maximum. Moreover, during the sunspot minimum we can quite accurately forecast the following sunspot minimum.",
"pages": [
7,
8
]
},
{
"title": "References",
"content": "Обридко В.Н., Шельтинг Б.Д. Некоторые аномалии эволюции глобальных и крупномасштабных магнитных полей на Солнце как предвестники нескольких предстоящих невысоких циклов// Письма в астрономический журнал. Т. 35. №3, С. 3844. 2009. Шельтинг Б.Д., Обридко В.Н. Магнитные бури с внезапным и постепенным началом как индексы солнечной активности// Всероссийская ежегодная конференция по физике Солнца. Пулково Русия. 2011. Feynman J. Geomagnetic and solar wind cycles, 1900-1975// J. Geophys. Res. 87, 6153-6162 (1982) Georgieva K., Kirov B. Helicity of magnetic clouds and solar cycle variations of their geoeffectiveness// Proceedings IAU Symposium 226 Coronal and Stellar Mass Ejections, Oxford University Press. P.470-472, 2005. Sabine E. On Periodical Laws Discoverable in the Mean Effects of the Larger Magnetic Disturbances// Phil. Trans. R. Soc. Lond. January 1, 1852 142 103-124; doi:10.1098/rstl.1852.0009. Simon P.A., Legrand J.P. : Some solar cycle phenomena related to the geomagnetic activity from 1868 to 1980. III - Quiet-days, fluctuating activity or the solar equatorial belt as the main origin of the solar wind flowing in the ecliptic plane// Astron. Astrophys. V. 182, P. 329-336, 1987. Tsurutani B.T., Gonzalez W. D., Gonzalez A.L.C. et al. , Corotating solar wind streams and recurrent geomagnetic activity: A review // J. Geophys. Res., V. 111, No A07S01, P. 1110711132, 2006.",
"pages": [
8
]
}
]
2013IAUS..288..239M
https://arxiv.org/pdf/1209.3837.pdf
<document>
<section_header_level_1><location><page_1><loc_17><loc_88><loc_63><loc_90></location>Next Generation Deep 2 µ Survey</section_header_level_1>
<section_header_level_1><location><page_1><loc_34><loc_86><loc_47><loc_87></location>Jeremy Mould</section_header_level_1>
<text><location><page_1><loc_13><loc_83><loc_69><loc_85></location>Centre for Astrophysics and Supercomputing, Swinburne University, Hawthorn 3122, Australia</text>
<text><location><page_1><loc_19><loc_80><loc_62><loc_82></location>2 ARC Centre of Excellence for All-sky Astrophysics (CAASTRO) email: [email protected]</text>
<section_header_level_1><location><page_1><loc_9><loc_77><loc_16><loc_78></location>Abstract.</section_header_level_1>
<text><location><page_1><loc_9><loc_73><loc_72><loc_76></location>There is a major opportunity for the KDUST 2.5m telescope to carry out the next generation IR survey. A resolution of 0.2 arcsec is obtainable from Dome A over a wide field. This opens a unique discovery space during the 2015-2025 decade.</text>
<text><location><page_1><loc_9><loc_70><loc_72><loc_72></location>A next generation 2 µ survey will feed JWST with serendipitous targets for spectroscopy, including spectra and images of the first galaxies.</text>
<text><location><page_1><loc_9><loc_68><loc_34><loc_69></location>Keywords. infrared, survey, galaxies</text>
<section_header_level_1><location><page_1><loc_9><loc_62><loc_59><loc_63></location>1. Introduction: the state of the art of infrared surveys</section_header_level_1>
<text><location><page_1><loc_9><loc_53><loc_72><loc_62></location>UKIDSS † has surveyed 7500 square degrees of the Northern sky, extending over both high and low Galactic latitudes, in the JHK bandpasses to K=18.3. This is three magnitudes deeper than 2MASS. UKIDSS has provided a near-infrared SDSS and a panoramic atlas of the Galactic plane. UKIDSS is actually five surveys, including two deep extragalactic elements, one covering 35 sq deg to K = 21, and the other reaching K = 23 over 0.77 sq deg.</text>
<text><location><page_1><loc_9><loc_44><loc_72><loc_52></location>VIKING-VISTA ‡ is a kilo-degree infrared galaxy survey. The VIKING survey will image 1500 sq deg in Z, Y, J, H, and Ks to a limiting magnitude 1.4 mag beyond the UKIDSS Large Area Survey. It will furnish very accurate photometric redshifts, especially at z > 1, an important step in weak lensing analysis and observation of baryon acoustic oscillations. Other science drivers include the hunt for high redshift quasars, galaxy clusters, and the study of galaxy stellar masses.</text>
<text><location><page_1><loc_9><loc_41><loc_72><loc_43></location>Mould (2011) offers a summary of the prospects for improving on these surveys using the KDUST 2.5m telescope.</text>
<section_header_level_1><location><page_1><loc_9><loc_36><loc_38><loc_37></location>2. KDUST camera architecture</section_header_level_1>
<text><location><page_1><loc_9><loc_30><loc_72><loc_36></location>The simplest option for a focal plane array is a Teledyne HgCdTe 2048 2 . A better option is 4096 2 or 2 x 2 (8.5 arcmin field). ANU has delivered two such cameras to the Gemini Observatory (McGregor et al. 2004, McGregor et al. 1999). The KDUST focal plane scale is appropriate without change. JHK and Kdark filters would be required.</text>
<text><location><page_1><loc_9><loc_22><loc_72><loc_30></location>Plan B is for a Sofradir SATURN SW HgCdTe SWIR. However, these detectors have 150 electrons read noise and would require long exposures to overcome readout noise. Nevertheless they are feasible Plan B detectors for broadband survey work. Mosaicing many detectors is also acceptable for survey work, and, after mosaicing the focal plane, plan A and plan B detectors are fairly similar in cost.</text>
<text><location><page_1><loc_29><loc_19><loc_53><loc_21></location>† www.ukidss.org ‡ www.astro-wise/projects/VIKING</text>
<text><location><page_1><loc_12><loc_85><loc_13><loc_85></location>1</text>
<section_header_level_1><location><page_2><loc_9><loc_93><loc_34><loc_94></location>3. The Antarctic advantage</section_header_level_1>
<text><location><page_2><loc_9><loc_86><loc_72><loc_92></location>Above the ground layer turbulence one obtains almost diffraction limited images over a wide field with low 2 µ background. This combination is only available from the Antarctic plateau, high altitude balloons and space. The competition, then, is space. We confine ourselves to WFIRST, since the ESA Euclid mission observes at H band, but not at K.</text>
<section_header_level_1><location><page_2><loc_9><loc_83><loc_29><loc_84></location>Advantages of WFIRST</section_header_level_1>
<unordered_list>
<list_item><location><page_2><loc_11><loc_81><loc_45><loc_83></location>· Top ranked in ASTRO 2010 (Blandford 2009)</list_item>
<list_item><location><page_2><loc_11><loc_80><loc_38><loc_81></location>· Broader band possible, e.g. 1.6-3.6 µ .</list_item>
<list_item><location><page_2><loc_11><loc_78><loc_19><loc_80></location>· No clouds</list_item>
</unordered_list>
<section_header_level_1><location><page_2><loc_9><loc_77><loc_31><loc_78></location>Disadvantages of WFIRST</section_header_level_1>
<unordered_list>
<list_item><location><page_2><loc_11><loc_75><loc_28><loc_77></location>· 3 year mission lifetime</list_item>
<list_item><location><page_2><loc_11><loc_74><loc_27><loc_75></location>· Earliest launch 2025</list_item>
<list_item><location><page_2><loc_11><loc_72><loc_35><loc_74></location>· Order of magnitude higher cost</list_item>
</unordered_list>
<text><location><page_2><loc_11><loc_71><loc_72><loc_72></location>Provided the US NRO supplies a 2.5m mirror, the following Astro2010-era disadvan-</text>
<text><location><page_2><loc_9><loc_69><loc_29><loc_71></location>tages are no longer in effect.</text>
<unordered_list>
<list_item><location><page_2><loc_11><loc_68><loc_32><loc_69></location>· Smaller aperture, 1.5 metre</list_item>
<list_item><location><page_2><loc_11><loc_66><loc_24><loc_68></location>· Lower resolution</list_item>
<list_item><location><page_2><loc_11><loc_65><loc_39><loc_66></location>· 200 nJy limit vs 70 nJy with KDUST</list_item>
</unordered_list>
<section_header_level_1><location><page_2><loc_9><loc_60><loc_23><loc_61></location>4. Science case</section_header_level_1>
<text><location><page_2><loc_11><loc_58><loc_75><loc_60></location>An excellent science case for a 2.5m Antarctic telescope is presented by Burton et al. (2007).</text>
<text><location><page_2><loc_9><loc_57><loc_53><loc_58></location>A further science case is that of WFIRST (Green et al. 2012)</text>
<unordered_list>
<list_item><location><page_2><loc_11><loc_55><loc_37><loc_57></location>· Kuiper Belt census and properties</list_item>
<list_item><location><page_2><loc_11><loc_54><loc_54><loc_55></location>· Cluster and Star-Forming-Region IMFs to planetary mass</list_item>
<list_item><location><page_2><loc_11><loc_52><loc_37><loc_53></location>· The H 2 kink in star cluster CMDs</list_item>
<list_item><location><page_2><loc_11><loc_51><loc_54><loc_52></location>· The most distant Star-Forming-Regions in the Milky Way</list_item>
<list_item><location><page_2><loc_11><loc_49><loc_53><loc_50></location>· Quasars as a Reference Frame for Proper Motion Studies</list_item>
<list_item><location><page_2><loc_11><loc_48><loc_51><loc_49></location>· Proper Motions and parallaxes of disk and bulge Stars</list_item>
<list_item><location><page_2><loc_11><loc_46><loc_44><loc_47></location>· Cool white dwarfs as Galactic chronometers</list_item>
<list_item><location><page_2><loc_11><loc_45><loc_25><loc_46></location>· Planetary transits</list_item>
<list_item><location><page_2><loc_11><loc_43><loc_59><loc_44></location>· Evolution of massive Galaxies: formation of red sequence galaxies</list_item>
<list_item><location><page_2><loc_11><loc_42><loc_55><loc_43></location>· Finding and weighing distant, high mass clusters of galaxies</list_item>
<list_item><location><page_2><loc_11><loc_40><loc_25><loc_41></location>· Obscured quasars</list_item>
<list_item><location><page_2><loc_11><loc_39><loc_29><loc_40></location>· Strongly lensed quasars</list_item>
<list_item><location><page_2><loc_11><loc_37><loc_40><loc_38></location>· High-redshift quasars and Reionization</list_item>
<list_item><location><page_2><loc_11><loc_36><loc_43><loc_37></location>· Faint end of the quasar luminosity function</list_item>
<list_item><location><page_2><loc_11><loc_34><loc_51><loc_35></location>· Probing Epoch of Reionization with Lyman α emitters</list_item>
<list_item><location><page_2><loc_11><loc_33><loc_48><loc_34></location>· Shapes of galaxy haloes from gravitational flexion</list_item>
</unordered_list>
<text><location><page_2><loc_9><loc_28><loc_72><loc_31></location>To focus on one of these areas, it is interesting to note the discovery space in the investigation of the epoch of reionization:</text>
<unordered_list>
<list_item><location><page_2><loc_11><loc_26><loc_42><loc_28></location>· 1 µ band dropouts at z = 1.1/0.09 -1 = 11</list_item>
<list_item><location><page_2><loc_11><loc_25><loc_41><loc_26></location>· J band dropouts at z = 1.4/0.09 -1 = 14</list_item>
<list_item><location><page_2><loc_11><loc_23><loc_46><loc_25></location>· Galaxies with 10 8 year old stellar pops at z = 6</list_item>
<list_item><location><page_2><loc_11><loc_22><loc_47><loc_23></location>· Pair production SNe (massive stars) at M K = -23</list_item>
<list_item><location><page_2><loc_11><loc_20><loc_53><loc_21></location>· Activity from the progenitors of supermassive black holes</list_item>
<list_item><location><page_2><loc_11><loc_19><loc_35><loc_20></location>· Dark stars, see Ilie et al. (2012)</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_3><loc_11><loc_93><loc_70><loc_94></location>· Young globular clusters with 10 6 year free fall times and M/L approaching 10 -4</list_item>
<list_item><location><page_3><loc_9><loc_90><loc_72><loc_92></location>· Rare bright objects requiring wide field survey, then JWST, TMT, EELT or GMT spectra.</list_item>
</unordered_list>
<section_header_level_1><location><page_3><loc_9><loc_85><loc_25><loc_87></location>5. The next steps</section_header_level_1>
<text><location><page_3><loc_9><loc_77><loc_72><loc_85></location>The first question is whether this project is compatible with KDUST 2.5 (Cui 2010, Zhao et al. 2011). Assuming it is, we need to finalize the IR camera configuration, find IR camera partners, such as U. Tasmania, Swinburne University, UNSW, AAO/Macquarie University, Texas A&M, ANU and University of Melbourne. We then need to flowdown the science to camera requirements.</text>
<text><location><page_3><loc_9><loc_64><loc_72><loc_77></location>To maximize advantage over VISTA, the speed of a survey to a given magnitude (inverse of the number of years to complete 1 sr) is a factor of ∼ 9. The goal is to increase this and get a full order of magnitude (or better). Perhaps we should move from K to Kdark, when we have accurate measurements of the relevant backgrounds. We could consider adding a reimager to KDUST and undersample a bit. Alternatively a slightly faster secondary on KDUST could be entertained. For Sofradir chips the minimum exposure time is larger to overcome readout noise. For a background of 0.1 mJy/sq arcsec, the photon rate is half a photon per sec. This requires > 2000 sec exposures for photon noise to double the Sofradir readout noise. (70% QE assumed.)</text>
<text><location><page_3><loc_11><loc_62><loc_54><loc_64></location>A construction and operations schedule tentatively would be:</text>
<unordered_list>
<list_item><location><page_3><loc_11><loc_61><loc_65><loc_62></location>· January 2015 ARC LIEF funding, followed by Preliminary Design Review</list_item>
<list_item><location><page_3><loc_11><loc_59><loc_12><loc_60></location>·</list_item>
<list_item><location><page_3><loc_12><loc_59><loc_69><loc_60></location>2016 Texas A & M purchases Teledyne arrays; ANU purchases dewar and filters</list_item>
<list_item><location><page_3><loc_11><loc_58><loc_50><loc_59></location>· 2016 Integrate and test focal plane at ANU or AAO</list_item>
<list_item><location><page_3><loc_11><loc_56><loc_52><loc_57></location>· January 2017 Integrate telescope/ camera in Fremantle</list_item>
<list_item><location><page_3><loc_11><loc_55><loc_72><loc_56></location>· 2018-2021 operations (within the international antarctic science region) at Kunlun</list_item>
</unordered_list>
<section_header_level_1><location><page_3><loc_9><loc_53><loc_14><loc_54></location>Station</section_header_level_1>
<unordered_list>
<list_item><location><page_3><loc_11><loc_52><loc_40><loc_53></location>· 2022 return of focal plane to the USA.</list_item>
</unordered_list>
<text><location><page_3><loc_9><loc_39><loc_72><loc_50></location>This schedule is set by the time to manufacture and test the KDUST telescope in China. If it slipped a year or two, so could the instrument schedule, although we do have the precedent of GSAOI, where the camera was ready years before the adaptive optics. The Centre for All-Sky Astrophysics in Australia and the proposed Joint Australia-China research centre would provide a very appropriate context for this collaboration. At Dome A astronomy can have another world class astrophysics enterprise in Antarctica yielding major results.</text>
<section_header_level_1><location><page_3><loc_9><loc_37><loc_25><loc_38></location>Acknowledgements</section_header_level_1>
<text><location><page_3><loc_9><loc_29><loc_72><loc_36></location>I would like to thank our Chinese colleagues for hosting a workshop at the Institute of High Energy Physics of the Chinese Academy of Sciences in Beijing in November 2011, where a number of these ideas were developed. Survey astronomy is supported by the Australian Research Council through CAASTRO † . The Centre for All-sky Astrophysics is an Australian Research Council Centre of Excellence, funded by grant CE11001020.</text>
<section_header_level_1><location><page_3><loc_9><loc_24><loc_19><loc_26></location>References</section_header_level_1>
<text><location><page_3><loc_9><loc_22><loc_35><loc_24></location>Blandford, R. 2009, AAS, 213, 21301</text>
<text><location><page_3><loc_9><loc_21><loc_37><loc_22></location>Burton, M. et al. 2007, PASA 22, 199.</text>
<text><location><page_3><loc_35><loc_19><loc_47><loc_20></location>† www.caastro.org</text>
<text><location><page_4><loc_9><loc_82><loc_72><loc_94></location>Cui, Xiangqun 2010, Highlights of Astronomy, 15, 639 Green, J. et al. 2012, astro-ph 1208.4012 Ilie, C., Freese, K., Valluri, M., Iliev, I., & Shapiro, P. 2012, MNRAS, 422, 2164 McGregor, P., Hart, J., Stevanovic, D., Bloxham, G., Jones, D., Van Harmelen, J., Griesbach, J., Dawson, M., Young, P., & Jarnyk, M. 2004, SPIE, 5492, 1033 McGregor, P. J., Conroy, P., Bloxham, G., & van Harmelen, J. 1999 PASA, 16, 273 Mould, J. 2011, PASA, 28, 266 Thompson, R. et al. 2007, ApJ, 657, 669</text>
<text><location><page_4><loc_9><loc_81><loc_72><loc_82></location>Zhao, Gong-Bo, Zhan, Hu, Wang, Lifan, Fan, Zuhui, Zhang, Xinmin 2011, PASP, 123, 725</text>
<section_header_level_1><location><page_4><loc_9><loc_76><loc_18><loc_78></location>Discussion</section_header_level_1>
<text><location><page_4><loc_9><loc_74><loc_64><loc_76></location>Charling Tao: There are problems with the persistence of Sofradir arrays.</text>
<text><location><page_4><loc_9><loc_70><loc_72><loc_73></location>Jeremy Mould: There are strategies for dealing with the persistence. But, thank you, this will need to be investigated for the Plan B detectors.</text>
<text><location><page_4><loc_9><loc_67><loc_44><loc_69></location>Hans Zinnecker: What about L and M band?</text>
<text><location><page_4><loc_9><loc_63><loc_72><loc_66></location>Jeremy Mould: This is feasible. However, even in the Antarctic the thermal background comes roaring up and one becomes uncompetitive with space for broadband.</text>
<figure>
<location><page_4><loc_17><loc_24><loc_64><loc_60></location>
<caption>Figure 1. The proposed survey will reach to within a magnitude of the NICMOS deep field (Thompson et al. 2007) with similar resolution, but cover many steradians. The field shown here is a few arc minutes. Image courtesy NASA, Hubble Space Telescope, University of Arizona .</caption>
</figure>
</document>
[
{
"title": "Jeremy Mould",
"content": "Centre for Astrophysics and Supercomputing, Swinburne University, Hawthorn 3122, Australia 2 ARC Centre of Excellence for All-sky Astrophysics (CAASTRO) email: [email protected]",
"pages": [
1
]
},
{
"title": "Abstract.",
"content": "There is a major opportunity for the KDUST 2.5m telescope to carry out the next generation IR survey. A resolution of 0.2 arcsec is obtainable from Dome A over a wide field. This opens a unique discovery space during the 2015-2025 decade. A next generation 2 µ survey will feed JWST with serendipitous targets for spectroscopy, including spectra and images of the first galaxies. Keywords. infrared, survey, galaxies",
"pages": [
1
]
},
{
"title": "1. Introduction: the state of the art of infrared surveys",
"content": "UKIDSS † has surveyed 7500 square degrees of the Northern sky, extending over both high and low Galactic latitudes, in the JHK bandpasses to K=18.3. This is three magnitudes deeper than 2MASS. UKIDSS has provided a near-infrared SDSS and a panoramic atlas of the Galactic plane. UKIDSS is actually five surveys, including two deep extragalactic elements, one covering 35 sq deg to K = 21, and the other reaching K = 23 over 0.77 sq deg. VIKING-VISTA ‡ is a kilo-degree infrared galaxy survey. The VIKING survey will image 1500 sq deg in Z, Y, J, H, and Ks to a limiting magnitude 1.4 mag beyond the UKIDSS Large Area Survey. It will furnish very accurate photometric redshifts, especially at z > 1, an important step in weak lensing analysis and observation of baryon acoustic oscillations. Other science drivers include the hunt for high redshift quasars, galaxy clusters, and the study of galaxy stellar masses. Mould (2011) offers a summary of the prospects for improving on these surveys using the KDUST 2.5m telescope.",
"pages": [
1
]
},
{
"title": "2. KDUST camera architecture",
"content": "The simplest option for a focal plane array is a Teledyne HgCdTe 2048 2 . A better option is 4096 2 or 2 x 2 (8.5 arcmin field). ANU has delivered two such cameras to the Gemini Observatory (McGregor et al. 2004, McGregor et al. 1999). The KDUST focal plane scale is appropriate without change. JHK and Kdark filters would be required. Plan B is for a Sofradir SATURN SW HgCdTe SWIR. However, these detectors have 150 electrons read noise and would require long exposures to overcome readout noise. Nevertheless they are feasible Plan B detectors for broadband survey work. Mosaicing many detectors is also acceptable for survey work, and, after mosaicing the focal plane, plan A and plan B detectors are fairly similar in cost. † www.ukidss.org ‡ www.astro-wise/projects/VIKING 1",
"pages": [
1
]
},
{
"title": "3. The Antarctic advantage",
"content": "Above the ground layer turbulence one obtains almost diffraction limited images over a wide field with low 2 µ background. This combination is only available from the Antarctic plateau, high altitude balloons and space. The competition, then, is space. We confine ourselves to WFIRST, since the ESA Euclid mission observes at H band, but not at K.",
"pages": [
2
]
},
{
"title": "Disadvantages of WFIRST",
"content": "Provided the US NRO supplies a 2.5m mirror, the following Astro2010-era disadvan- tages are no longer in effect.",
"pages": [
2
]
},
{
"title": "4. Science case",
"content": "An excellent science case for a 2.5m Antarctic telescope is presented by Burton et al. (2007). A further science case is that of WFIRST (Green et al. 2012) To focus on one of these areas, it is interesting to note the discovery space in the investigation of the epoch of reionization:",
"pages": [
2
]
},
{
"title": "5. The next steps",
"content": "The first question is whether this project is compatible with KDUST 2.5 (Cui 2010, Zhao et al. 2011). Assuming it is, we need to finalize the IR camera configuration, find IR camera partners, such as U. Tasmania, Swinburne University, UNSW, AAO/Macquarie University, Texas A&M, ANU and University of Melbourne. We then need to flowdown the science to camera requirements. To maximize advantage over VISTA, the speed of a survey to a given magnitude (inverse of the number of years to complete 1 sr) is a factor of ∼ 9. The goal is to increase this and get a full order of magnitude (or better). Perhaps we should move from K to Kdark, when we have accurate measurements of the relevant backgrounds. We could consider adding a reimager to KDUST and undersample a bit. Alternatively a slightly faster secondary on KDUST could be entertained. For Sofradir chips the minimum exposure time is larger to overcome readout noise. For a background of 0.1 mJy/sq arcsec, the photon rate is half a photon per sec. This requires > 2000 sec exposures for photon noise to double the Sofradir readout noise. (70% QE assumed.) A construction and operations schedule tentatively would be:",
"pages": [
3
]
},
{
"title": "Station",
"content": "This schedule is set by the time to manufacture and test the KDUST telescope in China. If it slipped a year or two, so could the instrument schedule, although we do have the precedent of GSAOI, where the camera was ready years before the adaptive optics. The Centre for All-Sky Astrophysics in Australia and the proposed Joint Australia-China research centre would provide a very appropriate context for this collaboration. At Dome A astronomy can have another world class astrophysics enterprise in Antarctica yielding major results.",
"pages": [
3
]
},
{
"title": "Acknowledgements",
"content": "I would like to thank our Chinese colleagues for hosting a workshop at the Institute of High Energy Physics of the Chinese Academy of Sciences in Beijing in November 2011, where a number of these ideas were developed. Survey astronomy is supported by the Australian Research Council through CAASTRO † . The Centre for All-sky Astrophysics is an Australian Research Council Centre of Excellence, funded by grant CE11001020.",
"pages": [
3
]
},
{
"title": "References",
"content": "Blandford, R. 2009, AAS, 213, 21301 Burton, M. et al. 2007, PASA 22, 199. † www.caastro.org Cui, Xiangqun 2010, Highlights of Astronomy, 15, 639 Green, J. et al. 2012, astro-ph 1208.4012 Ilie, C., Freese, K., Valluri, M., Iliev, I., & Shapiro, P. 2012, MNRAS, 422, 2164 McGregor, P., Hart, J., Stevanovic, D., Bloxham, G., Jones, D., Van Harmelen, J., Griesbach, J., Dawson, M., Young, P., & Jarnyk, M. 2004, SPIE, 5492, 1033 McGregor, P. J., Conroy, P., Bloxham, G., & van Harmelen, J. 1999 PASA, 16, 273 Mould, J. 2011, PASA, 28, 266 Thompson, R. et al. 2007, ApJ, 657, 669 Zhao, Gong-Bo, Zhan, Hu, Wang, Lifan, Fan, Zuhui, Zhang, Xinmin 2011, PASP, 123, 725",
"pages": [
3,
4
]
},
{
"title": "Discussion",
"content": "Charling Tao: There are problems with the persistence of Sofradir arrays. Jeremy Mould: There are strategies for dealing with the persistence. But, thank you, this will need to be investigated for the Plan B detectors. Hans Zinnecker: What about L and M band? Jeremy Mould: This is feasible. However, even in the Antarctic the thermal background comes roaring up and one becomes uncompetitive with space for broadband.",
"pages": [
4
]
}
]
2013IAUS..291..141D
https://arxiv.org/pdf/1210.6981.pdf
<document>
<section_header_level_1><location><page_1><loc_10><loc_84><loc_70><loc_90></location>A peculiar thermonuclear X-ray burst from the transiently accreting neutron star SAX J1810.8-2609</section_header_level_1>
<section_header_level_1><location><page_1><loc_26><loc_81><loc_55><loc_83></location>N. Degenaar 1 † and R. Wijnands 2</section_header_level_1>
<text><location><page_1><loc_11><loc_78><loc_70><loc_81></location>1 University of Michigan, Dept. of Astronomy, 500 Church St, Ann Arbor, MI 48109, USA email: [email protected]</text>
<text><location><page_1><loc_17><loc_74><loc_64><loc_78></location>2 Astronomical Institute 'Anton Pannekoek', University of Amsterdam Postbus 94249, 1090 GE Amsterdam, The Netherlands email: [email protected]</text>
<text><location><page_1><loc_9><loc_59><loc_72><loc_72></location>Abstract. We report on a thermonuclear (type-I) X-ray burst that was detected from the neutron star low-mass X-ray binary SAX J1810.8-2609 in 2007 with Swift . This event was longer ( /similarequal 20 min) and more energetic (a radiated energy of E b /similarequal 6 . 5 × 10 39 erg) than other X-ray bursts observed from this source. A possible explanation for the peculiar properties is that the X-ray burst occurred during the early stage of the outburst when the neutron star was relatively cold, which allows for the accumulation of a thicker layer of fuel. We also report on a new accretion outburst of SAX J1810.8-2609 that was observed with MAXI and Swift in 2012. The outburst had a duration of /similarequal 17 days and reached a 2-10 keV peak luminosity of L X /similarequal 3 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . This is a factor > 10 more luminous than the two previous outbursts observed from the source, and classifies it as a bright rather than a faint X-ray transient.</text>
<text><location><page_1><loc_9><loc_55><loc_72><loc_58></location>Keywords. stars: neutron, X-rays: binaries, X-rays: bursts, X-rays: individual (SAX J1810.82609)</text>
<section_header_level_1><location><page_1><loc_9><loc_50><loc_23><loc_51></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_9><loc_42><loc_72><loc_49></location>SAX J1810.8-2609 is a transient neutron star LMXB that was discovered by BeppoSAX on 1998 March 10 when it exhibited an accretion outburst (Ubertini et al. 1998). BeppoSAX and ROSAT observations detected the source at a luminosity of L X /similarequal (0 . 2 -1) × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 (2-10 keV), and suggest that the outburst had a duration of /greaterorsimilar 13 days (Greiner et al. 1999; Natalucci et al. 2000).</text>
<text><location><page_1><loc_9><loc_30><loc_72><loc_42></location>Soon after its discovery, a type-I X-ray burst was detected from SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000). These thermonuclear explosions occur on the surface of accreting neutron stars due to unstable burning of helium/hydrogen. The majority of observed X-ray bursts have a duration of /similarequal 10-100 s and generate a radiated energy output of E b /similarequal 10 39 erg (e.g., Galloway et al. 2008; Chelovekov & Grebenev 2011). Occasionally intermediately-long X-ray bursts are observed, which are more energetic ( E b /similarequal 10 40 -41 erg) and longer (tens of minutes) than normal X-ray bursts (e.g., in 't Zand et al. 2008; Falanga et al. 2008; Linares et al. 2009; Degenaar et al. 2010, 2011).</text>
<text><location><page_1><loc_9><loc_21><loc_74><loc_30></location>Renewed activity was detected from SAX J1810.8-2609 with Swift , INTEGRAL and RXTE in 2007 August (Parsons et al. 2007; Degenaar et al. 2007; Haymoz et al. 2007; Fiocchi et al. 2009). During this outburst INTEGRAL detected 17 X-ray bursts, which had an observed duration of /similarequal 10-30 s (3-25 keV; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The brightest event reached a bolometric peak flux of F peak /similarequal 1 × 10 -7 erg cm -2 s -1 , implying a distance of D /lessorequalslant 5.7 kpc (Fiocchi et al. 2009).</text>
<figure>
<location><page_2><loc_40><loc_70><loc_72><loc_94></location>
<caption>Figure 1. Swift /XRT light curve showing the decay of the X-ray burst detected from SAX J1810.8-2609 on 2007 August 5 (BAT trigger 287042). The black and grey data points indicate WT and PC mode data, respectively. The dashed curve shows a fit to a power-law decay with an index of α = -1 . 43, and the solid line a fit to an exponential function with a decay time of τ = 129 s. The dotted horizontal line indicates the persistent emission level.</caption>
</figure>
<section_header_level_1><location><page_2><loc_9><loc_66><loc_68><loc_67></location>2. A long thermonuclear X-ray burst detected with Swift in 2007</section_header_level_1>
<text><location><page_2><loc_9><loc_58><loc_72><loc_65></location>On 2007 August 5 at 11:27:26 UT, the Swift /BAT was triggered by SAX J1810.8-2609 (trigger 287042; Parsons et al. 2007). We investigated the trigger data and follow-up XRT observations, and conclude that the BAT triggered on a type-I X-ray burst. For the details on the reduction and analysis procedures we refer to Degenaar et al. (2012a). We carried out exactly the same analysis for SAX J1810.8-2609.</text>
<text><location><page_2><loc_9><loc_49><loc_72><loc_58></location>The BAT light curve shows a single /similarequal 10-s long peak. The average spectrum can be described by a black body model with a temperature of kT bb /similarequal 3 . 0 keV and an emitting radius of R bb /similarequal 7 km (Table 1), which is typical for the peak emission of X-ray bursts. We estimate a bolometric peak flux of F peak /similarequal 7 × 10 -8 erg cm -2 s -1 (0.01-100 keV), which is similar to that observed for other X-ray bursts of SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011).</text>
<text><location><page_2><loc_9><loc_40><loc_72><loc_49></location>Automated follow-up XRT observations commenced /similarequal 65 s after the BAT trigger. The XRT light curve shows a continuous decay in count rate until it settles at a constant level /similarequal 1200 s after the BAT trigger (Figure 1). The light curve can be described by an exponential with a decay time of τ /similarequal 129 s, but a power law with a decay index of α /similarequal -1 . 43 provides a better fit (Figure 1). The XRT data can be described by a black body model that cools along the decay (Table 1), a typical signature of X-ray bursts.</text>
<text><location><page_2><loc_9><loc_28><loc_72><loc_40></location>The total estimated fluence of the X-ray burst inferred from the BAT and XRT data is f b /similarequal 1 . 6 × 10 -6 erg cm -2 . For an assumed distance of D = 5 . 7 kpc, this translates into a total radiated energy of E b /similarequal 6 . 5 × 10 39 erg. We use /similarequal 2 ks of XRT PC mode data obtained between /similarequal 4000-6000 s after the BAT trigger to characterize the persistent accretion emission at the time of the X-ray burst (Figure 1). This data can be described by a simple absorbed power law model with N H = (6 . 2 ± 0 . 1) × 10 21 cm -2 and Γ = 2 . 4 ± 0 . 3. We estimate a bolometric accretion luminosity of L acc /similarequal 5 × 10 35 ( D/ 5 . 7 kpc) 2 erg s -1 . The characteristics of the X-ray burst and persistent emission are summarized in Table 1.</text>
<text><location><page_2><loc_9><loc_19><loc_72><loc_28></location>SAX J1810.8-2609 was covered by the RXTE /PCA Galactic bulge scan project between 1999 February 5 and 2011 October 30 (Swank & Markwardt 2001), which reveals one outburst from the source (in 2007). The source was detected above the background level ( L X /greaterorsimilar 3 × 10 35 erg s -1 ) between 2007 August 4 and October 28 at an average 2-10 keV luminosity of L X /similarequal 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 . Non-detections on August 1 and November 1, suggest an outburst duration of /similarequal 85-92 days.</text>
<table>
<location><page_3><loc_9><loc_81><loc_72><loc_92></location>
<caption>Table 1. Time-resolved spectral analysis of the X-ray burst.</caption>
</table>
<text><location><page_3><loc_9><loc_77><loc_72><loc_80></location>Note. Quoted errors refer to 90% confidence levels. ∆ t indicates the time since the BAT trigger and F bol the estimated bolometric flux over the interval. The simultaneous fit resulted in N H = (2 . 2 ± 0 . 3) × 10 21 cm -2 ( χ 2 ν = 0 . 93 for 281 d.o.f.) and we assumed D = 5 . 7 kpc.</text>
<section_header_level_1><location><page_3><loc_9><loc_73><loc_67><loc_74></location>3. A new accretion outburst in 2012 seen with MAXI and Swift</section_header_level_1>
<text><location><page_3><loc_9><loc_66><loc_72><loc_72></location>MAXI monitoring observations show that SAX J1810.8-2609 was again active between 2012 May 7-24. We estimate an average 2-20 keV luminosity of L X /similarequal 6 . 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 , peaking at L X /similarequal 2 . 0 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . The MAXI data suggests that the source intensity was L X /greaterorsimilar 10 36 erg s -1 for /similarequal 17 days.</text>
<text><location><page_3><loc_9><loc_59><loc_72><loc_66></location>A pointed Swift /XRT observation was performed on 2012 May 12 (Obs ID 32459001). The WT spectrum is best described by a combined power law and black body model with N H = (0 . 51 ± 0 . 02) × 10 21 cm -2 , Γ = 1 . 67 ± 0 . 05, kT bb = 0 . 74 ± 0 . 03 keV, and R bb = 13 . 4 ± 1 . 4 km ( χ 2 ν = 1 . 09 for 721 d.o.f.). The resulting unabsorbed 2-10 keV model flux of F X /similarequal 6 . 9 × 10 -9 erg cm -2 s -1 implies a luminosity of L X /similarequal 2 . 7 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 .</text>
<text><location><page_3><loc_9><loc_51><loc_72><loc_59></location>Simultaneously obtained UVOT observations using the uw 1 filter ( λ 0 = 2600 ˚ A) reveal an object at R.A. = 18 h 10 m 44.487 s , decl. = -26 · 09 ' 01.30 '' , with an uncertainty of 0 . 61 '' . This coincides exactly with the Chandra position of SAX J1810.8-2609 (Jonker et al. 2004) and suggests that this is the UV counterpart of the LMXB. We determine (Vega) magnitudes of uw 1 = 18 . 80 ± 0 . 12 and 18 . 57 ± 0 . 22 mag for the two separate exposures.</text>
<section_header_level_1><location><page_3><loc_9><loc_46><loc_21><loc_48></location>4. Discussion</section_header_level_1>
<text><location><page_3><loc_9><loc_35><loc_72><loc_46></location>The X-ray burst from SAX J1810.8-2609 observed with Swift is both longer and more energetic than others observed from the source (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The duration is similar to that of intermediately long X-ray bursts, but the radiated energy output is an order of magnitude lower. This suggests that the X-ray burst observed from SAX J1810.8-2609 was a normal X-ray burst, albeit with an unusual long duration. There are different explanations for such peculiar X-ray bursts (see Degenaar et al. 2012a, and references therein).</text>
<text><location><page_3><loc_9><loc_25><loc_72><loc_35></location>The long X-ray burst occurred within a few days after the onset of the 2007 accretion outburst. This implies that the neutron star crust had likely not yet been significantly heated due to accretion, and hence the heat flux from the crust towards the surface was small. Combined with a low accretion rate ( /similarequal 0.1% of Eddington), this suggests that the temperature in the accreted envelop was likely low. This allows for the accumulation of a relatively thick layer of fuel before the ignition conditions are met, and may have caused its unusual properties compared to other X-ray bursts observed from the source.</text>
<text><location><page_3><loc_9><loc_19><loc_72><loc_24></location>The X-ray flux observed with MAXI and Swift during the 2012 outburst of SAX J1810.8-2609 is a factor of > 10 higher than seen during its 1998 and 2007 outbursts. Although the previous activity of the source classified it as a faint LMXB (Natalucci et al. 2000; Jonker et al. 2004; Fiocchi et al. 2009), this demonstrates that it is actually a bright</text>
<table>
<location><page_4><loc_10><loc_76><loc_71><loc_92></location>
<caption>Table 2. Characteristics of the X-ray burst and the post-burst persistent emission.</caption>
</table>
<text><location><page_4><loc_9><loc_72><loc_71><loc_76></location>Note. The quoted peak flux is unabsorbed and for the 0.01-100 keV energy range. The quoted accretion luminosity and mass-accretion rates were inferred from fitting /similarequal 2 ks of post-burst persistent emission. We assumed a distance of D = 5 . 7 kpc.</text>
<text><location><page_4><loc_9><loc_68><loc_72><loc_70></location>transient (cf. Wijnands et al. 2006). It is not uncommon for bright X-ray transients to exhibit faint outbursts (e.g., Degenaar & Wijnands 2009; Degenaar et al. 2012b).</text>
<section_header_level_1><location><page_4><loc_9><loc_65><loc_25><loc_66></location>Acknowledgements</section_header_level_1>
<text><location><page_4><loc_9><loc_56><loc_72><loc_64></location>ND is supported by NASA through Hubble Postdoctoral Fellowship grant number HSTHF-51287.01-A from the Space Telescope Science Institute. RW is supported by a European Research Council starting grant. This work made use of Swift data supplied by the UK Swift Science Data Centre at the University of Leicester, MAXI data provided by RIKEN, JAXA and the MAXI team, and publicly available RXTE /PCA bulge scan light curves maintained by C. Markwardt.</text>
<section_header_level_1><location><page_4><loc_9><loc_52><loc_18><loc_53></location>References</section_header_level_1>
<text><location><page_4><loc_9><loc_50><loc_55><loc_51></location>Chelovekov, I. V. & Grebenev, S. A. 2011, Astronomy Letters , 37, 597</text>
<text><location><page_4><loc_9><loc_49><loc_72><loc_50></location>Cocchi, M., Bazzano, A., Natalucci, L., et al. 1999, Astrophysical Letters and Communications ,</text>
<text><location><page_4><loc_12><loc_47><loc_17><loc_48></location>38, 133</text>
<text><location><page_4><loc_9><loc_46><loc_60><loc_47></location>Degenaar, N., Jonker, P. G., Torres, M. A. P., et al. 2010, MNRAS , 404, 1591</text>
<text><location><page_4><loc_9><loc_44><loc_67><loc_46></location>Degenaar, N., Klein-Wolt, M., & Wijnands, R. 2007, The Astronomer's Telegram , 1175</text>
<text><location><page_4><loc_9><loc_43><loc_61><loc_44></location>Degenaar, N., Linares, M., Altamirano, D., & Wijnands, R. 2012a, ApJ , 759, 8</text>
<text><location><page_4><loc_9><loc_42><loc_43><loc_43></location>Degenaar, N. & Wijnands, R. 2009, A&A , 495, 547</text>
<text><location><page_4><loc_9><loc_40><loc_58><loc_41></location>Degenaar, N., Wijnands, R., Cackett, E. M., et al. 2012b, A&A , 545, A49</text>
<text><location><page_4><loc_9><loc_39><loc_53><loc_40></location>Degenaar, N., Wijnands, R., & Kaur, R. 2011, MNRAS , 414, L104</text>
<text><location><page_4><loc_9><loc_38><loc_54><loc_39></location>Falanga, M., Chenevez, J., Cumming, A., et al. 2008, A&A , 484, 43</text>
<text><location><page_4><loc_9><loc_36><loc_53><loc_37></location>Fiocchi, M., Natalucci, L., Chenevez, J., et al. 2009, ApJ , 693, 333</text>
<text><location><page_4><loc_9><loc_35><loc_59><loc_36></location>Galloway, D. K., Muno, M. P., Hartman, J. M., et al. 2008, ApJS , 179, 360</text>
<text><location><page_4><loc_9><loc_33><loc_59><loc_35></location>Greiner, J., Castro-Tirado, A. J., Boller, T., et al. 1999, MNRAS , 308, L17</text>
<text><location><page_4><loc_9><loc_32><loc_70><loc_33></location>Haymoz, P., Eckert, D., Shaw, S., & Kuulkers, E. 2007, The Astronomer's Telegram , 1185, 1</text>
<text><location><page_4><loc_9><loc_31><loc_59><loc_32></location>in 't Zand, J. J. M., Bassa, C. G., Jonker, P. G., et al. 2008, A&A , 485, 183</text>
<text><location><page_4><loc_9><loc_29><loc_62><loc_30></location>Jonker, P. G., Galloway, D. K., McClintock, J. E., et al. 2004, MNRAS , 354, 666</text>
<text><location><page_4><loc_9><loc_28><loc_56><loc_29></location>Linares, M., Watts, A. L., Wijnands, R., et al. 2009, MNRAS , 392, L11</text>
<text><location><page_4><loc_9><loc_26><loc_52><loc_28></location>Natalucci, L., Bazzano, A., Cocchi, M., et al. 2000, ApJ , 536, 891</text>
<text><location><page_4><loc_9><loc_25><loc_70><loc_26></location>Parsons, A. M., Barthelmy, S. D., Gehrels, N., et al. 2007, GRB Coordinates Network , 6706</text>
<text><location><page_4><loc_9><loc_22><loc_72><loc_25></location>Swank, J. & Markwardt, C. 2001, in ASP Conf. Series , Vol. 251, New Century of X-ray Astron- omy, ed. H. Inoue & H. Kunieda, 94</text>
<text><location><page_4><loc_9><loc_21><loc_65><loc_22></location>Ubertini, P., in 't Zand, J., Tesseri, A., Ricci, D., & Piro, L. 1998, IAU Circ. , 6838, 1</text>
<text><location><page_4><loc_9><loc_20><loc_59><loc_21></location>Wijnands, R., in 't Zand, J. J. M., Rupen, M., et al. 2006, A&A , 449, 1117</text>
</document>
[
{
"title": "N. Degenaar 1 † and R. Wijnands 2",
"content": "1 University of Michigan, Dept. of Astronomy, 500 Church St, Ann Arbor, MI 48109, USA email: [email protected] 2 Astronomical Institute 'Anton Pannekoek', University of Amsterdam Postbus 94249, 1090 GE Amsterdam, The Netherlands email: [email protected] Abstract. We report on a thermonuclear (type-I) X-ray burst that was detected from the neutron star low-mass X-ray binary SAX J1810.8-2609 in 2007 with Swift . This event was longer ( /similarequal 20 min) and more energetic (a radiated energy of E b /similarequal 6 . 5 × 10 39 erg) than other X-ray bursts observed from this source. A possible explanation for the peculiar properties is that the X-ray burst occurred during the early stage of the outburst when the neutron star was relatively cold, which allows for the accumulation of a thicker layer of fuel. We also report on a new accretion outburst of SAX J1810.8-2609 that was observed with MAXI and Swift in 2012. The outburst had a duration of /similarequal 17 days and reached a 2-10 keV peak luminosity of L X /similarequal 3 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . This is a factor > 10 more luminous than the two previous outbursts observed from the source, and classifies it as a bright rather than a faint X-ray transient. Keywords. stars: neutron, X-rays: binaries, X-rays: bursts, X-rays: individual (SAX J1810.82609)",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "SAX J1810.8-2609 is a transient neutron star LMXB that was discovered by BeppoSAX on 1998 March 10 when it exhibited an accretion outburst (Ubertini et al. 1998). BeppoSAX and ROSAT observations detected the source at a luminosity of L X /similarequal (0 . 2 -1) × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 (2-10 keV), and suggest that the outburst had a duration of /greaterorsimilar 13 days (Greiner et al. 1999; Natalucci et al. 2000). Soon after its discovery, a type-I X-ray burst was detected from SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000). These thermonuclear explosions occur on the surface of accreting neutron stars due to unstable burning of helium/hydrogen. The majority of observed X-ray bursts have a duration of /similarequal 10-100 s and generate a radiated energy output of E b /similarequal 10 39 erg (e.g., Galloway et al. 2008; Chelovekov & Grebenev 2011). Occasionally intermediately-long X-ray bursts are observed, which are more energetic ( E b /similarequal 10 40 -41 erg) and longer (tens of minutes) than normal X-ray bursts (e.g., in 't Zand et al. 2008; Falanga et al. 2008; Linares et al. 2009; Degenaar et al. 2010, 2011). Renewed activity was detected from SAX J1810.8-2609 with Swift , INTEGRAL and RXTE in 2007 August (Parsons et al. 2007; Degenaar et al. 2007; Haymoz et al. 2007; Fiocchi et al. 2009). During this outburst INTEGRAL detected 17 X-ray bursts, which had an observed duration of /similarequal 10-30 s (3-25 keV; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The brightest event reached a bolometric peak flux of F peak /similarequal 1 × 10 -7 erg cm -2 s -1 , implying a distance of D /lessorequalslant 5.7 kpc (Fiocchi et al. 2009).",
"pages": [
1
]
},
{
"title": "2. A long thermonuclear X-ray burst detected with Swift in 2007",
"content": "On 2007 August 5 at 11:27:26 UT, the Swift /BAT was triggered by SAX J1810.8-2609 (trigger 287042; Parsons et al. 2007). We investigated the trigger data and follow-up XRT observations, and conclude that the BAT triggered on a type-I X-ray burst. For the details on the reduction and analysis procedures we refer to Degenaar et al. (2012a). We carried out exactly the same analysis for SAX J1810.8-2609. The BAT light curve shows a single /similarequal 10-s long peak. The average spectrum can be described by a black body model with a temperature of kT bb /similarequal 3 . 0 keV and an emitting radius of R bb /similarequal 7 km (Table 1), which is typical for the peak emission of X-ray bursts. We estimate a bolometric peak flux of F peak /similarequal 7 × 10 -8 erg cm -2 s -1 (0.01-100 keV), which is similar to that observed for other X-ray bursts of SAX J1810.8-2609 (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). Automated follow-up XRT observations commenced /similarequal 65 s after the BAT trigger. The XRT light curve shows a continuous decay in count rate until it settles at a constant level /similarequal 1200 s after the BAT trigger (Figure 1). The light curve can be described by an exponential with a decay time of τ /similarequal 129 s, but a power law with a decay index of α /similarequal -1 . 43 provides a better fit (Figure 1). The XRT data can be described by a black body model that cools along the decay (Table 1), a typical signature of X-ray bursts. The total estimated fluence of the X-ray burst inferred from the BAT and XRT data is f b /similarequal 1 . 6 × 10 -6 erg cm -2 . For an assumed distance of D = 5 . 7 kpc, this translates into a total radiated energy of E b /similarequal 6 . 5 × 10 39 erg. We use /similarequal 2 ks of XRT PC mode data obtained between /similarequal 4000-6000 s after the BAT trigger to characterize the persistent accretion emission at the time of the X-ray burst (Figure 1). This data can be described by a simple absorbed power law model with N H = (6 . 2 ± 0 . 1) × 10 21 cm -2 and Γ = 2 . 4 ± 0 . 3. We estimate a bolometric accretion luminosity of L acc /similarequal 5 × 10 35 ( D/ 5 . 7 kpc) 2 erg s -1 . The characteristics of the X-ray burst and persistent emission are summarized in Table 1. SAX J1810.8-2609 was covered by the RXTE /PCA Galactic bulge scan project between 1999 February 5 and 2011 October 30 (Swank & Markwardt 2001), which reveals one outburst from the source (in 2007). The source was detected above the background level ( L X /greaterorsimilar 3 × 10 35 erg s -1 ) between 2007 August 4 and October 28 at an average 2-10 keV luminosity of L X /similarequal 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 . Non-detections on August 1 and November 1, suggest an outburst duration of /similarequal 85-92 days. Note. Quoted errors refer to 90% confidence levels. ∆ t indicates the time since the BAT trigger and F bol the estimated bolometric flux over the interval. The simultaneous fit resulted in N H = (2 . 2 ± 0 . 3) × 10 21 cm -2 ( χ 2 ν = 0 . 93 for 281 d.o.f.) and we assumed D = 5 . 7 kpc.",
"pages": [
2,
3
]
},
{
"title": "3. A new accretion outburst in 2012 seen with MAXI and Swift",
"content": "MAXI monitoring observations show that SAX J1810.8-2609 was again active between 2012 May 7-24. We estimate an average 2-20 keV luminosity of L X /similarequal 6 . 3 × 10 36 ( D/ 5 . 7 kpc) 2 erg s -1 , peaking at L X /similarequal 2 . 0 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . The MAXI data suggests that the source intensity was L X /greaterorsimilar 10 36 erg s -1 for /similarequal 17 days. A pointed Swift /XRT observation was performed on 2012 May 12 (Obs ID 32459001). The WT spectrum is best described by a combined power law and black body model with N H = (0 . 51 ± 0 . 02) × 10 21 cm -2 , Γ = 1 . 67 ± 0 . 05, kT bb = 0 . 74 ± 0 . 03 keV, and R bb = 13 . 4 ± 1 . 4 km ( χ 2 ν = 1 . 09 for 721 d.o.f.). The resulting unabsorbed 2-10 keV model flux of F X /similarequal 6 . 9 × 10 -9 erg cm -2 s -1 implies a luminosity of L X /similarequal 2 . 7 × 10 37 ( D/ 5 . 7 kpc) 2 erg s -1 . Simultaneously obtained UVOT observations using the uw 1 filter ( λ 0 = 2600 ˚ A) reveal an object at R.A. = 18 h 10 m 44.487 s , decl. = -26 · 09 ' 01.30 '' , with an uncertainty of 0 . 61 '' . This coincides exactly with the Chandra position of SAX J1810.8-2609 (Jonker et al. 2004) and suggests that this is the UV counterpart of the LMXB. We determine (Vega) magnitudes of uw 1 = 18 . 80 ± 0 . 12 and 18 . 57 ± 0 . 22 mag for the two separate exposures.",
"pages": [
3
]
},
{
"title": "4. Discussion",
"content": "The X-ray burst from SAX J1810.8-2609 observed with Swift is both longer and more energetic than others observed from the source (Cocchi et al. 1999; Natalucci et al. 2000; Fiocchi et al. 2009; Chelovekov & Grebenev 2011). The duration is similar to that of intermediately long X-ray bursts, but the radiated energy output is an order of magnitude lower. This suggests that the X-ray burst observed from SAX J1810.8-2609 was a normal X-ray burst, albeit with an unusual long duration. There are different explanations for such peculiar X-ray bursts (see Degenaar et al. 2012a, and references therein). The long X-ray burst occurred within a few days after the onset of the 2007 accretion outburst. This implies that the neutron star crust had likely not yet been significantly heated due to accretion, and hence the heat flux from the crust towards the surface was small. Combined with a low accretion rate ( /similarequal 0.1% of Eddington), this suggests that the temperature in the accreted envelop was likely low. This allows for the accumulation of a relatively thick layer of fuel before the ignition conditions are met, and may have caused its unusual properties compared to other X-ray bursts observed from the source. The X-ray flux observed with MAXI and Swift during the 2012 outburst of SAX J1810.8-2609 is a factor of > 10 higher than seen during its 1998 and 2007 outbursts. Although the previous activity of the source classified it as a faint LMXB (Natalucci et al. 2000; Jonker et al. 2004; Fiocchi et al. 2009), this demonstrates that it is actually a bright Note. The quoted peak flux is unabsorbed and for the 0.01-100 keV energy range. The quoted accretion luminosity and mass-accretion rates were inferred from fitting /similarequal 2 ks of post-burst persistent emission. We assumed a distance of D = 5 . 7 kpc. transient (cf. Wijnands et al. 2006). It is not uncommon for bright X-ray transients to exhibit faint outbursts (e.g., Degenaar & Wijnands 2009; Degenaar et al. 2012b).",
"pages": [
3,
4
]
},
{
"title": "Acknowledgements",
"content": "ND is supported by NASA through Hubble Postdoctoral Fellowship grant number HSTHF-51287.01-A from the Space Telescope Science Institute. RW is supported by a European Research Council starting grant. This work made use of Swift data supplied by the UK Swift Science Data Centre at the University of Leicester, MAXI data provided by RIKEN, JAXA and the MAXI team, and publicly available RXTE /PCA bulge scan light curves maintained by C. Markwardt.",
"pages": [
4
]
},
{
"title": "References",
"content": "Chelovekov, I. V. & Grebenev, S. A. 2011, Astronomy Letters , 37, 597 Cocchi, M., Bazzano, A., Natalucci, L., et al. 1999, Astrophysical Letters and Communications , 38, 133 Degenaar, N., Jonker, P. G., Torres, M. A. P., et al. 2010, MNRAS , 404, 1591 Degenaar, N., Klein-Wolt, M., & Wijnands, R. 2007, The Astronomer's Telegram , 1175 Degenaar, N., Linares, M., Altamirano, D., & Wijnands, R. 2012a, ApJ , 759, 8 Degenaar, N. & Wijnands, R. 2009, A&A , 495, 547 Degenaar, N., Wijnands, R., Cackett, E. M., et al. 2012b, A&A , 545, A49 Degenaar, N., Wijnands, R., & Kaur, R. 2011, MNRAS , 414, L104 Falanga, M., Chenevez, J., Cumming, A., et al. 2008, A&A , 484, 43 Fiocchi, M., Natalucci, L., Chenevez, J., et al. 2009, ApJ , 693, 333 Galloway, D. K., Muno, M. P., Hartman, J. M., et al. 2008, ApJS , 179, 360 Greiner, J., Castro-Tirado, A. J., Boller, T., et al. 1999, MNRAS , 308, L17 Haymoz, P., Eckert, D., Shaw, S., & Kuulkers, E. 2007, The Astronomer's Telegram , 1185, 1 in 't Zand, J. J. M., Bassa, C. G., Jonker, P. G., et al. 2008, A&A , 485, 183 Jonker, P. G., Galloway, D. K., McClintock, J. E., et al. 2004, MNRAS , 354, 666 Linares, M., Watts, A. L., Wijnands, R., et al. 2009, MNRAS , 392, L11 Natalucci, L., Bazzano, A., Cocchi, M., et al. 2000, ApJ , 536, 891 Parsons, A. M., Barthelmy, S. D., Gehrels, N., et al. 2007, GRB Coordinates Network , 6706 Swank, J. & Markwardt, C. 2001, in ASP Conf. Series , Vol. 251, New Century of X-ray Astron- omy, ed. H. Inoue & H. Kunieda, 94 Ubertini, P., in 't Zand, J., Tesseri, A., Ricci, D., & Piro, L. 1998, IAU Circ. , 6838, 1 Wijnands, R., in 't Zand, J. J. M., Rupen, M., et al. 2006, A&A , 449, 1117",
"pages": [
4
]
}
]
2013IAUS..294..289A
https://arxiv.org/pdf/1305.5282.pdf
<document>
<section_header_level_1><location><page_1><loc_20><loc_84><loc_80><loc_86></location>Fractal multi-scale nature of solar/stellar magnetic field</section_header_level_1>
<text><location><page_1><loc_41><loc_81><loc_59><loc_83></location>Valentina I. Abramenko</text>
<text><location><page_1><loc_12><loc_76><loc_88><loc_80></location>Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314, USA</text>
<section_header_level_1><location><page_1><loc_44><loc_72><loc_56><loc_74></location>ABSTRACT</section_header_level_1>
<text><location><page_1><loc_17><loc_48><loc_83><loc_70></location>An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy release events, conditions for turbulent dynamo action, nature of turbulent magnetic diffusivity, and even the dual nature of solar dynamo. In this talk, I will briefly outline how the ideas of multi-fractality are used to explore the above mentioned aspects of solar magnetism.</text>
<section_header_level_1><location><page_1><loc_35><loc_41><loc_65><loc_43></location>1. Introduction: Why Fractals?</section_header_level_1>
<text><location><page_1><loc_12><loc_28><loc_88><loc_39></location>A mathematical fractal is a self-similar object on all possible spatial and time scales. It means that when we proceed from large to smaller scales, we will see exactly the same picture. From mathematical standpoint this means that a unique scaling law holds for all scales. A fractal (or, more rigorously, a mono-fractal) is a deterministic, predictable system. Mathematical monofractals differ drastically from what we observe in nature: fractal-like structures in nature are multi-fractals - a superposition of infinite number of mono-fractals.</text>
<text><location><page_1><loc_12><loc_15><loc_88><loc_26></location>The transition from mono-fractals to multi-fractals turns an amusing mathematical toy into a powerful tool to study real processes in nature. The matter is that multi-fractals posses the same properties in both the spatial and temporal domains. This means that if we see a very complex, jagged shape in space (multi-fractal in space), then we will observe a violent, burst-like behavior in time (multi-fractal in time). For such systems, any small perturbation can cause an avalanche of any possible size.</text>
<text><location><page_1><loc_12><loc_10><loc_88><loc_13></location>Therefore, revealing the fact that a system under study is a fractal does not allow us to make inferences about its nature and essential properties of its behavior. We need something</text>
<text><location><page_2><loc_12><loc_82><loc_88><loc_86></location>more, namely, to know of how many mono-fractals our system is made of. Numerous examples of fractals and multi-fractals can be found (e.g., Feder 1989; Schroeder 2000, Internet).</text>
<text><location><page_2><loc_12><loc_70><loc_88><loc_81></location>Mathematical details of the fractal calculus are well described as well (e.g., Baumann 2005; McAteer et al. 2007). Historically, when analyzing spatial objects, their capability to be organized into very jagged structures with extended voids and sharp peaks is addressed as a property of multi-fractality. At the sate time, while analyzing time series, we address the same property as intermittency. Thus, multi-fractality and intermittency are two terms for the same physical property of a system. I will use both of them in this talk.</text>
<text><location><page_2><loc_12><loc_56><loc_88><loc_68></location>Several approaches were elaborated during a couple of last decades to probe the properties of multi-fractality in different fields of science. In a brief review below, I will focus on multi-fractality techniques applied in astrophysics. Thus, multi-fractal systems are capable of self-organization (i.e., formation of larger entities from smaller ones via inverse cascade), and of self-organized criticality (SOC) when burst-like energy release events of any scale are possible at any moment (e.g., Charbonneau et al. 2001; Longcope & Noonan 2000; Aschwanden 2011).</text>
<text><location><page_2><loc_12><loc_49><loc_88><loc_55></location>A theory of catastrophes is also based on the multi-fractal nature of astrophysical phenomena (Priest & Forbes 2002; Isenberg & Forbes 2007). Percolating clusters (Balke et al. 1993; Seiden & Wentzel 1996; Pustil'nik 1999; Schatten 2007) are also fractals and multi-fractals.</text>
<text><location><page_2><loc_12><loc_40><loc_88><loc_48></location>Direct calculations of fractal dimensions and spectra of multi-fractality is one of the most popular tool to explore astrophysical multi-fractals (e.g., Lawrence et al. 1993; Meunier 1999; Lepreti et al. 1999; McAteer et al. 2007; Dimitropoulou et al. 2009; Abramenko & Yurchyshyn 2010a; Aschwanden 2011).</text>
<text><location><page_2><loc_12><loc_31><loc_91><loc_39></location>Another possibility to study multi-fractality is to analyze high statistical moments by means of distribution functions (Bogdan et al. 1988; Parnell et al. 2009), or structure functions (Consolini et al. 1999; Abramenko et al. 2002; Abramenko 2005; Uritsky et al. 2007; Abramenko & Yurchyshyn 2010b; Abramenko et al. 2012).</text>
<text><location><page_2><loc_16><loc_29><loc_84><loc_30></location>Essential physical properties of multi-fractals can be formulated as follows.</text>
<unordered_list>
<list_item><location><page_2><loc_16><loc_26><loc_88><loc_27></location>(i) Scaling laws change with scale, i.e., no unique power law index can be valid for all scales;</list_item>
<list_item><location><page_2><loc_12><loc_21><loc_88><loc_24></location>(ii) Large fluctuations (in both time and space domains) are not rare and contribute significantly to high statistical moments, which grow as the data set expands;</list_item>
<list_item><location><page_2><loc_12><loc_14><loc_88><loc_19></location>(iii) Direct and inverse cascades along scales are possible (fragmentation and aggregation), which results in capability to form larger features from smaller ones, i.e., self-organization and SOC state.</list_item>
</unordered_list>
<text><location><page_2><loc_16><loc_11><loc_88><loc_12></location>These properties can help us to diagnose the presence and degree of multi-fractality of various</text>
<text><location><page_3><loc_12><loc_78><loc_88><loc_86></location>astrophysical phenomena. Meanwhile, keeping in mind that in astrophysical magnetism we deal with a specific type of a multi-fractal medium, namely, intermittent turbulence in an electroconductive flow , we can take advantage of it and incorporate other very important properties and tools. So our list of properties can be extended:</text>
<unordered_list>
<list_item><location><page_3><loc_12><loc_71><loc_88><loc_77></location>(iv) Intermittent turbulent magnetized plasma is capable of amplifying a seed magnetic field, i.e., local fast dynamo is at work (Zeldovich et al. 1987; Biskamp 1993; Vogler & Schussler 2007; Pietarila Graham et al. 2010), see also a recent review by Brandenburg et al. (2012);</list_item>
<list_item><location><page_3><loc_12><loc_64><loc_88><loc_70></location>(v) Turbulent plasma at high Reynolds number displays properties of multi-fractality and intermittency in spatial/temporal structures of temperatures, velocities, density, etc. (see, e.g., Zeldovich et al. 1987; Frisch 1995);</list_item>
<list_item><location><page_3><loc_16><loc_62><loc_86><loc_63></location>(vi) The regime of diffusivity on multi-fractals is expected to be an anomalous diffusion.</list_item>
</unordered_list>
<text><location><page_3><loc_12><loc_53><loc_88><loc_60></location>Based on these properties of multi-fractal systems, I will discuss below how exploration of these properties can help us in understanding of solar and stellar magnetism. It is impossible in the framework of this invited talk to discuss all aforementioned approaches and tools in great details, so I will concentrate on the analysis of structure functions, which are used in my research.</text>
<section_header_level_1><location><page_3><loc_24><loc_46><loc_76><loc_48></location>2. Structure functions approach to study multi-fractality</section_header_level_1>
<text><location><page_3><loc_12><loc_30><loc_88><loc_44></location>Since Kolmogorov's study (Kolmogorov 1941), various models have been proposed to describe the statistical behavior of fully developed turbulence. In these studies, the flow is modeled using statistically averaged quantities, and structure functions play a significant role. They are defined as statistical moments of the q -powers of the increment of a field. The definition can be applied to different fields (e.g., velocity, temperature, magnetic field, etc). Here, in the most of the cases, I will refer to the line-of-sight component of the magnetic field, B l , for which the structure function can be written as</text>
<formula><location><page_3><loc_37><loc_28><loc_88><loc_30></location>S q ( r ) = 〈| B l ( x + r ) -B l ( x ) | q 〉 , (1)</formula>
<text><location><page_3><loc_12><loc_14><loc_88><loc_27></location>where x is the current pixel on a magnetogram, r is the separation vector between any two points used to measure the increment (see the lower right panel in Figure 1, and q is the order of a statistical moment, which takes on real values. The angular brackets denote averaging over the magnetogram, and the vector r is allowed to adopt all possible orientations, θ , on the magnetogram. The next step is to calculate the scaling of the structure functions, which is defined as the slope, ζ ( q ) , measured inside some range of scales where the S q ( r ) -function is linear and the field is intermittent. The function ζ ( q ) is shown in the upper right panel in Figure 1.</text>
<text><location><page_3><loc_16><loc_11><loc_88><loc_12></location>A weak point in the above technique is the determination of the range, ∆ r , where the slopes</text>
<figure>
<location><page_4><loc_15><loc_32><loc_84><loc_83></location>
<caption>Fig. 1.- Structure functions S q ( r ) ( upper left ) calculated from a magnetogram of active region NOAA 0501 ( lower right ) according to Eq. (1). Lower left - flatness function F ( r ) derived from the structure functions using Eq. (2). Vertical dotted lines in both left panels mark the interval of intermittency, ∆ r , where flatness grows as power law when r decreases. The index κ is the power index of the flatness function determined within ∆ r . The slopes of S q ( r ), defined for each q within ∆ r , constitute ζ ( q ) function ( upper right ), which is concave (straight) for a multi-fractal/intermittent (mono-fractal/non-intermittent) field. An example of a separation vector r and the corresponding directional angle θ are shown on the magnetogram.</caption>
</figure>
<text><location><page_5><loc_12><loc_76><loc_88><loc_86></location>of the structure functions are to be calculated. To visualize the range of intermittency, ∆ r , we suggest to use the flatness function (Abramenko 2005), which is determined as the ratio of the fourth statistical moment to the square of the second statistical moment. To better identify the effect of intermittency, we reinforced the definition of the flatness function and calculated the hyper-flatness function, namely, the ratio of the sixth moment to the cube of the second moment:</text>
<formula><location><page_5><loc_38><loc_73><loc_88><loc_75></location>F ( r ) = S 6 ( r ) / ( S 2 ( r )) 3 ∼ k -κ . (2)</formula>
<text><location><page_5><loc_12><loc_61><loc_88><loc_71></location>For simplicity, we will refer to F ( r ) as the flatness function, or multi-fractality/intermittency spectrum. For a non-intermittent structure, the flatness function is not dependent on the scale, r . On the contrary, for an intermittent/multi-fractal structure, the flatness grows as power-law, when the scale decreases. The slope of flatness function, κ , and the width of ∆ r characterize the degree of multi-fractality and intermittency.</text>
<text><location><page_5><loc_12><loc_44><loc_88><loc_60></location>Application of this technique to two hundred of solar active regions observed with SOHO/MDI in the high resolution mode (Abramenko & Yurchyshyn 2010a) demonstrated that active regions of high flare productivity display steeper and broader multifractality spectra, F ( r ) . The inference agrees with the formulated above statement that multi-fractality in spatial domain is accompanied by intermittency (burst-like behavior) in time. Moreover, for any multi-fractal system, individual bursts cannot be precisely predicted in advance. So, the exact prediction of the location and the onset moment of a flare (of any size), strictly speaking, is a hopeless task. Based on different indirect indications, one may only hope to provide a probabilistic estimate for ongoing flaring.</text>
<text><location><page_5><loc_12><loc_37><loc_88><loc_43></location>Multi-fractality of time series of X-ray emission from an individual solar flare was discussed in McAteer et al. (2007), where an inference on the fractal nature of the flaring current sheet was made.</text>
<text><location><page_5><loc_12><loc_32><loc_88><loc_36></location>I will focus below on a solar surface outside active regions, which occupy usually more than 80% of the entire solar surface. Many important aspects of solar magnetism are rooted there.</text>
<section_header_level_1><location><page_5><loc_33><loc_26><loc_67><loc_28></location>3. Multi-fractality in the solar surface</section_header_level_1>
<text><location><page_5><loc_12><loc_10><loc_88><loc_24></location>Examples of line-of-sight (LOS) magnetograms recorded in coronal holes (CHs) using different solar instruments are shown in Figure 2. The left panel shows data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO, Scherrer et al. 2012), the middle panel shows LOS magnetic field provided by Hinode Solar Optical Telescope SpectroPolarimeter (SOT/SP, Tsuneta et al. 2008), and the right panel presents a magnetogram from the New Solar Telescope (NST) (Goode et al. 2010) operating at the Big Bear Solar Observatory (BBSO). Note that the NST data were obtained at a near-infrared spectral line (1.56 µm ) and</text>
<text><location><page_6><loc_12><loc_78><loc_88><loc_86></location>represent the magnetic field in the deep photosphere at depths of about 50 km below the τ 500 = 1 level. Figure 2 clearly demonstrates that with improved telescope resolution more mixed polarity magnetic elements become visible inside a CH. In spite of the fact that the three magnetograms refer to different CHs, this tendency is well defined.</text>
<figure>
<location><page_6><loc_15><loc_44><loc_85><loc_77></location>
<caption>Fig. 2.- Examples of LOS magnetograms recorded inside CHs with three solar instruments (from left to right): SDO/HMI magnetogram (Aug 12, 2011, spatial sampling of 0. '' 5); SOT/SP magnetogram (Mar 10, 2007, spatial sampling of 0. '' 16); BBSO/NST magnetogram (Jun 2, 2012, spatial sampling of 0. '' 098). Red boxes and arrows outline areas of the same size.</caption>
</figure>
<text><location><page_6><loc_12><loc_10><loc_88><loc_29></location>Flatness functions calculated from the three above mentioned magnetograms are shown in Figure 3. The HMI data show only a hint of multi-fractality on scales above 1500 km and a very shallow slope of F ( r ) ( κ = -0 . 07 ). The HMI resolution of 1 '' obviously is not sufficient to clearly reveal multi-fractality in quiet Sun. Meanwhile, the SOT/SP data show a much broader scale range of multi-fractality down to approximately 630 km and a steeper slope ( κ = -0 . 107 ). The HMI result refers to the height of 280-360 km (the effective line formation level of the FeI 617.3 nm spectral line, Gurtovenko & R.I.Kostyk (1989)), whereas the SOT/NBF data refer to a level of 400-700 km in the photosphere (the line formation height of the NaI 589.6 nm spectral line is discussed in Sheminova (1998)). The flatness function obtained from NST data clearly reveal (at the deeper layer) strong intermittency and multi-fractality on scales down to ∼ 400 km.</text>
<figure>
<location><page_7><loc_20><loc_44><loc_79><loc_86></location>
<caption>Fig. 3.- Flatness functions calculated from the magnetograms shown in Fig.2. Dashed lines show best linear fits to the data points inside intervals starting above the small-scale cutoff, r /star . For better compatison, the curves are shifted along the vertical axis.</caption>
</figure>
<text><location><page_7><loc_12><loc_28><loc_88><loc_34></location>Thus, the multi-fractal nature of small-scale magnetic fields becomes better pronounced with depth and improvement of spatial resolution, which leads us to conclude that intermittency and multi-fractality is an intrinsic property of the near-surface magnetic fields in the quiet Sun.</text>
<text><location><page_7><loc_12><loc_21><loc_88><loc_27></location>Magnetic elements against granulation inside a CH are shown in Figure 4, where the background is an NST solar granulation image overplotted with NST LOS and transverse magnetic features and Hinode SOT Narrow Band Filter (NBF) LOS magnetic field.</text>
<text><location><page_7><loc_12><loc_10><loc_88><loc_20></location>In the upper right corner of the image, a fragment of bright points (BPs) filigree corresponding to the super-granular boundary is visible. The rest of the image shows the intra-network area, where nine isolated magnetic elements were detected by the SOT/NBF. All of them are co-spatial with BPs and with the LOS signal from the NST. In six cases there are neither opposite polarity nor transverse magnetic field features in the closest vicinity. This may indicate that these mag-</text>
<figure>
<location><page_8><loc_18><loc_50><loc_81><loc_87></location>
<caption>Fig. 4.- Background - NST/TiO image of 26.6 '' 0 × 20.1 '' in size recorded in a CH at 18:20:32 UT on Aug 12, 2011. Blue (red) contours show the line-of-sight positive (negative) component measured with NST and correspond to 90, 210, 300 G. Green contours represent the signal from the transverse magnetic field component from NST, ( Q 2 + U 2 ) 1 / 2 , corresponding to 100 and 200 G. Yellow and turquoise contours outline the Hinode SOT/NBF magnetic elements of negative (-50, -100, -300 G) and positive (50 G) polarities for the same day and time.</caption>
</figure>
<text><location><page_8><loc_12><loc_26><loc_88><loc_31></location>netic elements are footpoints of open magnetic flux tubes representing the skeleton of the CH. The presence of BPs indicates that they might be produced via the convective collapse (Parker 1978; Spruit 1979).</text>
<text><location><page_8><loc_12><loc_11><loc_88><loc_24></location>At the same time, a significant part of the intra-network population is composed of magnetic features, which are not related to BPs and scattered over granules and inter-granular lanes. These magnetic elements were not detected by SOT/NBF and they are not necessarily very weak. On the contrary, they are quite compatible (by size and intensity) with those detected by the both instruments, they are simply not visible in NBF magnetograms. A simplest explanation could be the difference in heights. As I mentioned above, the NST measures the magnetic signal formed very deep in the photosphere, precisely, at the depth of 50 km below the τ 500 = 1 level, while the</text>
<text><location><page_9><loc_12><loc_70><loc_88><loc_86></location>magnetic signal measured with SOT/NBF is formed at the hight of approximately 400-700 km. If magnetic elements associated with granules are predominantly small (200-500 km in length) closed loops anchored at a depth of about -50 km, they might not be visible at the altitude of 400-700 km. This speculation is supported by the inspection of mutual location of Stokes V features (blue and red contours) and the transverse magnetic field features (green contours) in Figure 4. Indeed, the V-signal is co-spatial with the ( Q 2 + U 2 ) signal for the granules-associated magnetic elements, which supports the idea of closed loops (or bunches of loops) rather than presence of singular footpoints of extended, high loops or open field lines.</text>
<text><location><page_9><loc_12><loc_63><loc_88><loc_69></location>As for the magnetic elements associated with BPs and visible with the both instruments, they seem to be the best candidates for the roots of the open field lines, as we mentioned above. This can explain why they are visible on different heights.</text>
<text><location><page_9><loc_12><loc_54><loc_88><loc_62></location>Thus, the data allows us to speculate that the BPs-associated magnetic elements are related to the advection and convective collapse, whereas the numerous granule-associated intra-network elements are situated deeper in the photosphere and might be produced (at least, part of them) by local turbulent dynamo (see the talk by Dr. Tsuneta in this Symposium).</text>
<text><location><page_9><loc_12><loc_41><loc_88><loc_53></location>Multi-fractality of granulation . To drive local turbulent dynamo, the environment should be a highly turbulent medium, i.e., to be a multi-fractal. Is the solar granulation pattern a multi-fractal? To explore the question, Abramenko et al. (2012) used a NST data set of solar granulation images obtained for the quiet Sun area on the solar disk center recorded under excellent seeing conditions. Flatness functions for 36 independent snapshots and their average are shown in Figure 5 a .</text>
<text><location><page_9><loc_12><loc_30><loc_88><loc_40></location>The flatness functions indicate that solar granulation is non-intermittent (a mono-fractal) on scales exceeding approximately 600 km, and it becomes highly intermittent and multi-fractal on scales below 600 km. Thus, a random, Gaussian-like distribution of granule size holds down to 600 km only. On smaller scales, the multi-fractal spatial organization of solar granulation takes over.</text>
<text><location><page_9><loc_12><loc_15><loc_88><loc_29></location>A distribution function of granular size (Figure 5 b ) further confirms this inference. On scales of approximately 600 and 1300 km, the averaged probability distribution function (PDF) rapidly changes its slope. This varying power law PDF is suggestive that the observed ensemble of granules may consist of two populations with distinct properties: regular granules and minigranules. Decomposition of the observed PDF showed that the best fit is achieved with a combination of a log-normal function, f 1 , representing mini-granules, and a Gaussian function, f 2 , representing regular granules. Their sum perfectly fits to the observational data.</text>
<text><location><page_9><loc_12><loc_10><loc_88><loc_14></location>Until now it was thought that solar convection produces convection cells, visible on the solar surface as granules, of characteristic ('dominant') spatial scale of about 1000 km and</text>
<figure>
<location><page_10><loc_18><loc_60><loc_86><loc_86></location>
<caption>Fig. 5.a - Flatness functions calculated from 36 granulation images (gray) and their average (turquoise). The dashed segments show the best linear fits to the data points. The blue arrow divides the multi-fractality range where the flatness function varies as a power law from the Gaussian range where the flatness function is scale independent. b - decomposition of the observed averaged probability distribution function (red line) into two components: a log-normal approximation, ( f 1 , green line) and a Gaussian approximation ( f 2 , blue). Their sum is plotted with the turquoise line.</caption>
</figure>
<text><location><page_10><loc_12><loc_22><loc_88><loc_41></location>a Gaussian (normal) distribution of granule sizes. In this case, the mechanism that produces granules is 'programmed' to churn up convection cells of a typical size, without much freedom in size variation. Mini-granules do not display any characteristic ('dominant') scale, their size distribution is continuous and can be described by a decreasing log-normal (Gaussian distribution does not work any longer here). A majority (about 80%) of mini-granules are smaller than 600 km and about 50% are smaller than 300 km in diameter. This non-Gaussian distribution of sizes implies that a much more sophisticated mechanism, with much more degrees of freedom may be at work, where any very small fluctuation in density, pressure, velocity and magnetic fields may have significant impact and affect the resulting dynamics. Physical differences between the log-normal and Gaussian distributions are discussed by, e.g., Abramenko & Longcope (2005).</text>
<text><location><page_10><loc_12><loc_15><loc_88><loc_20></location>An important inference from the above discussion reads that a necessary condition for the seed magnetic field to be amplified is met. So, local turbulent dynamo in the near-surface layer is quite a possibility.</text>
<text><location><page_10><loc_12><loc_10><loc_88><loc_13></location>Regime of turbulent magnetic diffusion in the photosphere . As we saw in Introduction, the anomalous diffusivity is another hallmark of multi-fractality. The dispersal process embedded</text>
<text><location><page_11><loc_12><loc_78><loc_88><loc_86></location>in a multi-fractal cannot follow the random walk with normal diffusion. For example, in the case of solar photosphere, the multi-fractal plasma cannot ensure an arbitrary displacement in an arbitrary direction for all magnetic elements. A discussion of differences between the normal and anomalous diffusion can be found, e.g., in Lawrence & Schrijver (1993); Vlahos et al. (2008).</text>
<text><location><page_11><loc_12><loc_67><loc_88><loc_77></location>The coefficient of magnetic diffusivity is an essential input parameter for meridional flux transport models and global dynamo models. Therefore, magnetic flux dispersal on the solar surface was studies extensively (e.g., Lawrence & Schrijver 1993; Schrijver et al. 1996; Berger et al. 1998a,b; Cadavid et al. 1999; Hagenaar et al. 1999; Lawrence et al. 2001; Utz et al. 2009, 2010; Crockett et al. 2010; Abramenko et al. 2011).</text>
<text><location><page_11><loc_12><loc_52><loc_88><loc_66></location>In the most of these studies, observational data were interpreted in the framework of normal diffusion, and variety of estimates for the magnetic diffusivity coefficient, η , were reported: from 50 km 2 s -1 (Berger et al. 1998b) to 350 km 2 s -1 (Utz et al. 2010). Numerical simulations of the isotropic turbulence with magnetic field (Brandenburg et al. 2008) showed that the turbulent magnetic diffusivity increases with increasing scale. Combination of MHD modeling with observations allowed Chae et al. (2008) to conclude that the turbulent diffusivity changes with scale and is smallest (about 1 km 2 s -1 ) on smallest available scale of approximately 200 km.</text>
<text><location><page_11><loc_12><loc_35><loc_88><loc_51></location>Photospheric BPs, as tracers of kilo-gauss magnetic flux tubes, were utilized to probe photospheric flux dispersal (e.g., Berger et al. 1998a,b; Utz et al. 2010; Crockett et al. 2010). Recently, the high resolution power of the NST allowed Abramenko et al. (2011) to explore the regime of diffusion in the photosphere down to scales of 10 sec in time and 25 km in space. Magnetic BPs detected from NST/TiO images were tracked, and their squared displacements (from the initial position of a given BP) were calculated as a function of a time lag, τ . Later, the routine was repeated for HMI magnetic flux concentrations in a quiet Sun area on the disk center. Figure 6 a summarizes results.</text>
<text><location><page_11><loc_12><loc_24><loc_88><loc_34></location>Recall that for normal diffusion (Brownian motions), the squared displacements of tracers are directly proportional to time, i.e., the power law index, γ , of the displacement spectrum is a unity (an example of the normal diffusion regime is illustrated in Figure 6 with thick black dashed lines). When γ > 1 ( γ < 1 ), a regime of super-diffusion (sub-diffusion) dominates. The squared displacements (∆ l ) 2 ( τ ) can be approximated, at a given range of scales, as</text>
<formula><location><page_11><loc_43><loc_21><loc_88><loc_23></location>(∆ l ) 2 ( τ ) = cτ γ , (3)</formula>
<text><location><page_11><loc_12><loc_13><loc_88><loc_19></location>where c = 10 y sect and γ and y sect are derived from the best linear lit to the data points plotted in a double-logarithmic plot. Then the diffusion coefficient can be written as (Abramenko et al. 2011):</text>
<formula><location><page_11><loc_44><loc_10><loc_88><loc_14></location>η ( τ ) = cγ 4 τ γ -1 , (4)</formula>
<figure>
<location><page_12><loc_14><loc_60><loc_52><loc_86></location>
<caption>Fig. 6.a - Squared displacements of magnetic BPs detected from a 2-hour data set from the NST/BBSO ( blue ) and squared displacements of magnetic elements detected from 9-hour data set from SDO/HMI magnetograms recorded in a quiet Sun area on the solar disk center ( red ). Dash-dot lines are the best linear fit to the data points inside ranges of linearity; the slopes of the fits, γ , are indicated. b - The turbulent magnetic diffusivity, η , as a function of linear scale derived by Eq. (5) from linear fits for the NST (blue) and HMI (red) data shown in panel a . The thick dashed lines in both panels show an example of scaling for the normal diffusion regime with γ = 1.</caption>
</figure>
<text><location><page_12><loc_62><loc_62><loc_64><loc_63></location>10</text>
<text><location><page_12><loc_64><loc_62><loc_64><loc_63></location>1</text>
<text><location><page_12><loc_68><loc_67><loc_69><loc_69></location>η</text>
<text><location><page_12><loc_69><loc_67><loc_74><loc_69></location>~ (<</text>
<text><location><page_12><loc_69><loc_62><loc_70><loc_63></location>2</text>
<text><location><page_12><loc_67><loc_62><loc_69><loc_63></location>10</text>
<text><location><page_12><loc_74><loc_67><loc_75><loc_69></location>∆</text>
<text><location><page_12><loc_75><loc_67><loc_75><loc_69></location>l</text>
<text><location><page_12><loc_75><loc_68><loc_76><loc_69></location>2</text>
<text><location><page_12><loc_75><loc_62><loc_75><loc_63></location>3</text>
<text><location><page_12><loc_75><loc_60><loc_76><loc_62></location>∆</text>
<text><location><page_12><loc_73><loc_62><loc_75><loc_63></location>10</text>
<text><location><page_12><loc_63><loc_60><loc_75><loc_61></location>Spatial Scale,</text>
<text><location><page_12><loc_78><loc_68><loc_80><loc_69></location>-1)/</text>
<text><location><page_12><loc_80><loc_68><loc_80><loc_69></location>γ</text>
<text><location><page_12><loc_79><loc_62><loc_81><loc_63></location>10</text>
<text><location><page_12><loc_76><loc_60><loc_79><loc_61></location>l, km</text>
<formula><location><page_12><loc_38><loc_37><loc_88><loc_41></location>η (∆ l ) = cγ 4 ((∆ l ) 2 /c ) ( γ -1) /γ . (5)</formula>
<text><location><page_12><loc_12><loc_20><loc_88><loc_36></location>As if follows from Figure 6, for both data sets we observe the super-diffusion regime. The coefficient of magnetic turbulent diffusivity, η (∆ l ) , derived by Eq. (5) for both data sets is shown in Figure 6 b . Two essential things should be mentioned here: first, the diffusion coefficient grows as the scale increases (the same is true for a time scale, too, see Eq. (4). Second, the slope of the power law varies with scale (which is a characteristic feature of intrinsic multi-fractality). On the minimal spatial (25 km) and temporal (10 sec) scales considered in Abramenko et al. (2011), the diffusion coefficient in QS area was found to be 19 km 2 s -1 . The HMI data provided a value of approximately 220 km 2 s -1 on the largest available scale of 4 Mm.</text>
<text><location><page_12><loc_12><loc_11><loc_88><loc_19></location>The observed tendency of the turbulent magnetic diffusivity to decrease with decreasing scales leads us to expect that the turbulent diffusivity might be close to the magnitudes of diffusivity adopted in the numerical simulations of small-scale dynamo (0.01 - 10 km 2 s -1 , e.g., Boldyrev & Cattaneo (2004); Vogler & Schussler (2007); Pietarila Graham et al. (2010)). This</text>
<text><location><page_12><loc_53><loc_85><loc_57><loc_86></location>1000</text>
<text><location><page_12><loc_54><loc_78><loc_57><loc_79></location>100</text>
<text><location><page_12><loc_55><loc_70><loc_57><loc_72></location>10</text>
<text><location><page_12><loc_56><loc_63><loc_57><loc_65></location>1</text>
<text><location><page_12><loc_58><loc_62><loc_58><loc_63></location>0</text>
<text><location><page_12><loc_56><loc_62><loc_58><loc_63></location>10</text>
<text><location><page_12><loc_77><loc_68><loc_78><loc_69></location>(</text>
<text><location><page_12><loc_76><loc_67><loc_77><loc_69></location>>)</text>
<text><location><page_12><loc_78><loc_68><loc_78><loc_69></location>γ</text>
<text><location><page_12><loc_81><loc_62><loc_81><loc_63></location>4</text>
<text><location><page_12><loc_82><loc_84><loc_83><loc_85></location>b</text>
<text><location><page_12><loc_86><loc_62><loc_87><loc_63></location>5</text>
<text><location><page_12><loc_84><loc_62><loc_86><loc_63></location>10</text>
<text><location><page_13><loc_12><loc_85><loc_45><loc_86></location>makes the simulations even more realistic.</text>
<text><location><page_13><loc_12><loc_80><loc_88><loc_83></location>In summary, a super-diffusion regime on very small scales is very favorable for pictures assuming turbulent dynamo action since it assumes decreasing diffusivity with decreasing scales.</text>
<section_header_level_1><location><page_13><loc_39><loc_73><loc_61><loc_75></location>4. Concluding remarks</section_header_level_1>
<text><location><page_13><loc_12><loc_57><loc_88><loc_71></location>Continuously varying magnetic fields are the main reason for the solar/stellar activity. The 11-year solar cycle is one of the most astonishing and widely known examples of the self-organized generation of the magnetic field. Although we know that there is no two absolutely similar solar cycles, yet, persistency and regularity of the solar periodicity through thousands of years remains impressive. A drastically different picture arises when one looks on the photosphere: chaos of mixed-polarity magnetic elements of all sizes until the resolution limits of modern instruments, continuously renewing during 1-2 days - the magnetic carpet.</text>
<text><location><page_13><loc_12><loc_38><loc_88><loc_56></location>Dualism of the solar magnetism is usually explained by a simultaneous action of two dynamos: a global dynamo operating in the convective zone and responsible for the 11-year solar cycle, and local, or turbulent dynamo, which might operate inside the near-surface layer and to be responsible for generation of small-scale magnetic fields forming the magnetic carpet. The explanation seems to oversimplify the reality because resent studies of distribution of the magnetic flux accumulated in magnetic flux tubes showed the non-interrupted power law for many decades (Parnell et al. 2009) thus supposing a common (for all scales) mechanism for the magnetic field generation. One of promising ways to handle the problem is to consider the solar dynamo process as a non-linear dynamical system (NDS), with intrinsic properties of multi-fractality and intermittency.</text>
<text><location><page_13><loc_12><loc_27><loc_88><loc_37></location>Like any NDS, the solar dynamo is then capable to self-organization on all scales (including large scales) and display a chaotic nature on small scales. Self-organization, in turn, provides for a magnetic complex a way to reach a SOC state, when burst-like energy release events of any size are possible at any time instant. The concept is very important for our understanding of flaring and heating processes in solar/stellar atmospheres.</text>
<text><location><page_13><loc_12><loc_18><loc_88><loc_26></location>Further, multi-fractal nature on the magnetic field provides a necessary condition for the local turbulent dynamo operation in the near-surface layer of the convective zone. Observational evidences for local dynamo operation are still under strong debates, e.g., compare the talks by Drs. Tsuneta and Stenflo presented at this symposium.</text>
<text><location><page_13><loc_12><loc_11><loc_88><loc_17></location>One pragmatic advise for researchers could be inferred form the observed multi-fractal nature of magnetized solar plasma. Namely, observed power laws should not be extrapolated over neighboring scales, a frequent mistake for power laws studies in various fields.</text>
<text><location><page_14><loc_12><loc_82><loc_88><loc_86></location>In summary, the paradigm of multi-fractal and highly intermittent structure of solar magnetized plasma offers new approaches to understand the solar and stellar magnetism.</text>
<section_header_level_1><location><page_14><loc_43><loc_76><loc_57><loc_78></location>REFERENCES</section_header_level_1>
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</document>
[
{
"title": "ABSTRACT",
"content": "An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy release events, conditions for turbulent dynamo action, nature of turbulent magnetic diffusivity, and even the dual nature of solar dynamo. In this talk, I will briefly outline how the ideas of multi-fractality are used to explore the above mentioned aspects of solar magnetism.",
"pages": [
1
]
},
{
"title": "Fractal multi-scale nature of solar/stellar magnetic field",
"content": "Valentina I. Abramenko Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314, USA",
"pages": [
1
]
},
{
"title": "1. Introduction: Why Fractals?",
"content": "A mathematical fractal is a self-similar object on all possible spatial and time scales. It means that when we proceed from large to smaller scales, we will see exactly the same picture. From mathematical standpoint this means that a unique scaling law holds for all scales. A fractal (or, more rigorously, a mono-fractal) is a deterministic, predictable system. Mathematical monofractals differ drastically from what we observe in nature: fractal-like structures in nature are multi-fractals - a superposition of infinite number of mono-fractals. The transition from mono-fractals to multi-fractals turns an amusing mathematical toy into a powerful tool to study real processes in nature. The matter is that multi-fractals posses the same properties in both the spatial and temporal domains. This means that if we see a very complex, jagged shape in space (multi-fractal in space), then we will observe a violent, burst-like behavior in time (multi-fractal in time). For such systems, any small perturbation can cause an avalanche of any possible size. Therefore, revealing the fact that a system under study is a fractal does not allow us to make inferences about its nature and essential properties of its behavior. We need something more, namely, to know of how many mono-fractals our system is made of. Numerous examples of fractals and multi-fractals can be found (e.g., Feder 1989; Schroeder 2000, Internet). Mathematical details of the fractal calculus are well described as well (e.g., Baumann 2005; McAteer et al. 2007). Historically, when analyzing spatial objects, their capability to be organized into very jagged structures with extended voids and sharp peaks is addressed as a property of multi-fractality. At the sate time, while analyzing time series, we address the same property as intermittency. Thus, multi-fractality and intermittency are two terms for the same physical property of a system. I will use both of them in this talk. Several approaches were elaborated during a couple of last decades to probe the properties of multi-fractality in different fields of science. In a brief review below, I will focus on multi-fractality techniques applied in astrophysics. Thus, multi-fractal systems are capable of self-organization (i.e., formation of larger entities from smaller ones via inverse cascade), and of self-organized criticality (SOC) when burst-like energy release events of any scale are possible at any moment (e.g., Charbonneau et al. 2001; Longcope & Noonan 2000; Aschwanden 2011). A theory of catastrophes is also based on the multi-fractal nature of astrophysical phenomena (Priest & Forbes 2002; Isenberg & Forbes 2007). Percolating clusters (Balke et al. 1993; Seiden & Wentzel 1996; Pustil'nik 1999; Schatten 2007) are also fractals and multi-fractals. Direct calculations of fractal dimensions and spectra of multi-fractality is one of the most popular tool to explore astrophysical multi-fractals (e.g., Lawrence et al. 1993; Meunier 1999; Lepreti et al. 1999; McAteer et al. 2007; Dimitropoulou et al. 2009; Abramenko & Yurchyshyn 2010a; Aschwanden 2011). Another possibility to study multi-fractality is to analyze high statistical moments by means of distribution functions (Bogdan et al. 1988; Parnell et al. 2009), or structure functions (Consolini et al. 1999; Abramenko et al. 2002; Abramenko 2005; Uritsky et al. 2007; Abramenko & Yurchyshyn 2010b; Abramenko et al. 2012). Essential physical properties of multi-fractals can be formulated as follows. These properties can help us to diagnose the presence and degree of multi-fractality of various astrophysical phenomena. Meanwhile, keeping in mind that in astrophysical magnetism we deal with a specific type of a multi-fractal medium, namely, intermittent turbulence in an electroconductive flow , we can take advantage of it and incorporate other very important properties and tools. So our list of properties can be extended: Based on these properties of multi-fractal systems, I will discuss below how exploration of these properties can help us in understanding of solar and stellar magnetism. It is impossible in the framework of this invited talk to discuss all aforementioned approaches and tools in great details, so I will concentrate on the analysis of structure functions, which are used in my research.",
"pages": [
1,
2,
3
]
},
{
"title": "2. Structure functions approach to study multi-fractality",
"content": "Since Kolmogorov's study (Kolmogorov 1941), various models have been proposed to describe the statistical behavior of fully developed turbulence. In these studies, the flow is modeled using statistically averaged quantities, and structure functions play a significant role. They are defined as statistical moments of the q -powers of the increment of a field. The definition can be applied to different fields (e.g., velocity, temperature, magnetic field, etc). Here, in the most of the cases, I will refer to the line-of-sight component of the magnetic field, B l , for which the structure function can be written as where x is the current pixel on a magnetogram, r is the separation vector between any two points used to measure the increment (see the lower right panel in Figure 1, and q is the order of a statistical moment, which takes on real values. The angular brackets denote averaging over the magnetogram, and the vector r is allowed to adopt all possible orientations, θ , on the magnetogram. The next step is to calculate the scaling of the structure functions, which is defined as the slope, ζ ( q ) , measured inside some range of scales where the S q ( r ) -function is linear and the field is intermittent. The function ζ ( q ) is shown in the upper right panel in Figure 1. A weak point in the above technique is the determination of the range, ∆ r , where the slopes of the structure functions are to be calculated. To visualize the range of intermittency, ∆ r , we suggest to use the flatness function (Abramenko 2005), which is determined as the ratio of the fourth statistical moment to the square of the second statistical moment. To better identify the effect of intermittency, we reinforced the definition of the flatness function and calculated the hyper-flatness function, namely, the ratio of the sixth moment to the cube of the second moment: For simplicity, we will refer to F ( r ) as the flatness function, or multi-fractality/intermittency spectrum. For a non-intermittent structure, the flatness function is not dependent on the scale, r . On the contrary, for an intermittent/multi-fractal structure, the flatness grows as power-law, when the scale decreases. The slope of flatness function, κ , and the width of ∆ r characterize the degree of multi-fractality and intermittency. Application of this technique to two hundred of solar active regions observed with SOHO/MDI in the high resolution mode (Abramenko & Yurchyshyn 2010a) demonstrated that active regions of high flare productivity display steeper and broader multifractality spectra, F ( r ) . The inference agrees with the formulated above statement that multi-fractality in spatial domain is accompanied by intermittency (burst-like behavior) in time. Moreover, for any multi-fractal system, individual bursts cannot be precisely predicted in advance. So, the exact prediction of the location and the onset moment of a flare (of any size), strictly speaking, is a hopeless task. Based on different indirect indications, one may only hope to provide a probabilistic estimate for ongoing flaring. Multi-fractality of time series of X-ray emission from an individual solar flare was discussed in McAteer et al. (2007), where an inference on the fractal nature of the flaring current sheet was made. I will focus below on a solar surface outside active regions, which occupy usually more than 80% of the entire solar surface. Many important aspects of solar magnetism are rooted there.",
"pages": [
3,
5
]
},
{
"title": "3. Multi-fractality in the solar surface",
"content": "Examples of line-of-sight (LOS) magnetograms recorded in coronal holes (CHs) using different solar instruments are shown in Figure 2. The left panel shows data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO, Scherrer et al. 2012), the middle panel shows LOS magnetic field provided by Hinode Solar Optical Telescope SpectroPolarimeter (SOT/SP, Tsuneta et al. 2008), and the right panel presents a magnetogram from the New Solar Telescope (NST) (Goode et al. 2010) operating at the Big Bear Solar Observatory (BBSO). Note that the NST data were obtained at a near-infrared spectral line (1.56 µm ) and represent the magnetic field in the deep photosphere at depths of about 50 km below the τ 500 = 1 level. Figure 2 clearly demonstrates that with improved telescope resolution more mixed polarity magnetic elements become visible inside a CH. In spite of the fact that the three magnetograms refer to different CHs, this tendency is well defined. Flatness functions calculated from the three above mentioned magnetograms are shown in Figure 3. The HMI data show only a hint of multi-fractality on scales above 1500 km and a very shallow slope of F ( r ) ( κ = -0 . 07 ). The HMI resolution of 1 '' obviously is not sufficient to clearly reveal multi-fractality in quiet Sun. Meanwhile, the SOT/SP data show a much broader scale range of multi-fractality down to approximately 630 km and a steeper slope ( κ = -0 . 107 ). The HMI result refers to the height of 280-360 km (the effective line formation level of the FeI 617.3 nm spectral line, Gurtovenko & R.I.Kostyk (1989)), whereas the SOT/NBF data refer to a level of 400-700 km in the photosphere (the line formation height of the NaI 589.6 nm spectral line is discussed in Sheminova (1998)). The flatness function obtained from NST data clearly reveal (at the deeper layer) strong intermittency and multi-fractality on scales down to ∼ 400 km. Thus, the multi-fractal nature of small-scale magnetic fields becomes better pronounced with depth and improvement of spatial resolution, which leads us to conclude that intermittency and multi-fractality is an intrinsic property of the near-surface magnetic fields in the quiet Sun. Magnetic elements against granulation inside a CH are shown in Figure 4, where the background is an NST solar granulation image overplotted with NST LOS and transverse magnetic features and Hinode SOT Narrow Band Filter (NBF) LOS magnetic field. In the upper right corner of the image, a fragment of bright points (BPs) filigree corresponding to the super-granular boundary is visible. The rest of the image shows the intra-network area, where nine isolated magnetic elements were detected by the SOT/NBF. All of them are co-spatial with BPs and with the LOS signal from the NST. In six cases there are neither opposite polarity nor transverse magnetic field features in the closest vicinity. This may indicate that these mag- netic elements are footpoints of open magnetic flux tubes representing the skeleton of the CH. The presence of BPs indicates that they might be produced via the convective collapse (Parker 1978; Spruit 1979). At the same time, a significant part of the intra-network population is composed of magnetic features, which are not related to BPs and scattered over granules and inter-granular lanes. These magnetic elements were not detected by SOT/NBF and they are not necessarily very weak. On the contrary, they are quite compatible (by size and intensity) with those detected by the both instruments, they are simply not visible in NBF magnetograms. A simplest explanation could be the difference in heights. As I mentioned above, the NST measures the magnetic signal formed very deep in the photosphere, precisely, at the depth of 50 km below the τ 500 = 1 level, while the magnetic signal measured with SOT/NBF is formed at the hight of approximately 400-700 km. If magnetic elements associated with granules are predominantly small (200-500 km in length) closed loops anchored at a depth of about -50 km, they might not be visible at the altitude of 400-700 km. This speculation is supported by the inspection of mutual location of Stokes V features (blue and red contours) and the transverse magnetic field features (green contours) in Figure 4. Indeed, the V-signal is co-spatial with the ( Q 2 + U 2 ) signal for the granules-associated magnetic elements, which supports the idea of closed loops (or bunches of loops) rather than presence of singular footpoints of extended, high loops or open field lines. As for the magnetic elements associated with BPs and visible with the both instruments, they seem to be the best candidates for the roots of the open field lines, as we mentioned above. This can explain why they are visible on different heights. Thus, the data allows us to speculate that the BPs-associated magnetic elements are related to the advection and convective collapse, whereas the numerous granule-associated intra-network elements are situated deeper in the photosphere and might be produced (at least, part of them) by local turbulent dynamo (see the talk by Dr. Tsuneta in this Symposium). Multi-fractality of granulation . To drive local turbulent dynamo, the environment should be a highly turbulent medium, i.e., to be a multi-fractal. Is the solar granulation pattern a multi-fractal? To explore the question, Abramenko et al. (2012) used a NST data set of solar granulation images obtained for the quiet Sun area on the solar disk center recorded under excellent seeing conditions. Flatness functions for 36 independent snapshots and their average are shown in Figure 5 a . The flatness functions indicate that solar granulation is non-intermittent (a mono-fractal) on scales exceeding approximately 600 km, and it becomes highly intermittent and multi-fractal on scales below 600 km. Thus, a random, Gaussian-like distribution of granule size holds down to 600 km only. On smaller scales, the multi-fractal spatial organization of solar granulation takes over. A distribution function of granular size (Figure 5 b ) further confirms this inference. On scales of approximately 600 and 1300 km, the averaged probability distribution function (PDF) rapidly changes its slope. This varying power law PDF is suggestive that the observed ensemble of granules may consist of two populations with distinct properties: regular granules and minigranules. Decomposition of the observed PDF showed that the best fit is achieved with a combination of a log-normal function, f 1 , representing mini-granules, and a Gaussian function, f 2 , representing regular granules. Their sum perfectly fits to the observational data. Until now it was thought that solar convection produces convection cells, visible on the solar surface as granules, of characteristic ('dominant') spatial scale of about 1000 km and a Gaussian (normal) distribution of granule sizes. In this case, the mechanism that produces granules is 'programmed' to churn up convection cells of a typical size, without much freedom in size variation. Mini-granules do not display any characteristic ('dominant') scale, their size distribution is continuous and can be described by a decreasing log-normal (Gaussian distribution does not work any longer here). A majority (about 80%) of mini-granules are smaller than 600 km and about 50% are smaller than 300 km in diameter. This non-Gaussian distribution of sizes implies that a much more sophisticated mechanism, with much more degrees of freedom may be at work, where any very small fluctuation in density, pressure, velocity and magnetic fields may have significant impact and affect the resulting dynamics. Physical differences between the log-normal and Gaussian distributions are discussed by, e.g., Abramenko & Longcope (2005). An important inference from the above discussion reads that a necessary condition for the seed magnetic field to be amplified is met. So, local turbulent dynamo in the near-surface layer is quite a possibility. Regime of turbulent magnetic diffusion in the photosphere . As we saw in Introduction, the anomalous diffusivity is another hallmark of multi-fractality. The dispersal process embedded in a multi-fractal cannot follow the random walk with normal diffusion. For example, in the case of solar photosphere, the multi-fractal plasma cannot ensure an arbitrary displacement in an arbitrary direction for all magnetic elements. A discussion of differences between the normal and anomalous diffusion can be found, e.g., in Lawrence & Schrijver (1993); Vlahos et al. (2008). The coefficient of magnetic diffusivity is an essential input parameter for meridional flux transport models and global dynamo models. Therefore, magnetic flux dispersal on the solar surface was studies extensively (e.g., Lawrence & Schrijver 1993; Schrijver et al. 1996; Berger et al. 1998a,b; Cadavid et al. 1999; Hagenaar et al. 1999; Lawrence et al. 2001; Utz et al. 2009, 2010; Crockett et al. 2010; Abramenko et al. 2011). In the most of these studies, observational data were interpreted in the framework of normal diffusion, and variety of estimates for the magnetic diffusivity coefficient, η , were reported: from 50 km 2 s -1 (Berger et al. 1998b) to 350 km 2 s -1 (Utz et al. 2010). Numerical simulations of the isotropic turbulence with magnetic field (Brandenburg et al. 2008) showed that the turbulent magnetic diffusivity increases with increasing scale. Combination of MHD modeling with observations allowed Chae et al. (2008) to conclude that the turbulent diffusivity changes with scale and is smallest (about 1 km 2 s -1 ) on smallest available scale of approximately 200 km. Photospheric BPs, as tracers of kilo-gauss magnetic flux tubes, were utilized to probe photospheric flux dispersal (e.g., Berger et al. 1998a,b; Utz et al. 2010; Crockett et al. 2010). Recently, the high resolution power of the NST allowed Abramenko et al. (2011) to explore the regime of diffusion in the photosphere down to scales of 10 sec in time and 25 km in space. Magnetic BPs detected from NST/TiO images were tracked, and their squared displacements (from the initial position of a given BP) were calculated as a function of a time lag, τ . Later, the routine was repeated for HMI magnetic flux concentrations in a quiet Sun area on the disk center. Figure 6 a summarizes results. Recall that for normal diffusion (Brownian motions), the squared displacements of tracers are directly proportional to time, i.e., the power law index, γ , of the displacement spectrum is a unity (an example of the normal diffusion regime is illustrated in Figure 6 with thick black dashed lines). When γ > 1 ( γ < 1 ), a regime of super-diffusion (sub-diffusion) dominates. The squared displacements (∆ l ) 2 ( τ ) can be approximated, at a given range of scales, as where c = 10 y sect and γ and y sect are derived from the best linear lit to the data points plotted in a double-logarithmic plot. Then the diffusion coefficient can be written as (Abramenko et al. 2011): 10 1 η ~ (< 2 10 ∆ l 2 3 ∆ 10 Spatial Scale, -1)/ γ 10 l, km As if follows from Figure 6, for both data sets we observe the super-diffusion regime. The coefficient of magnetic turbulent diffusivity, η (∆ l ) , derived by Eq. (5) for both data sets is shown in Figure 6 b . Two essential things should be mentioned here: first, the diffusion coefficient grows as the scale increases (the same is true for a time scale, too, see Eq. (4). Second, the slope of the power law varies with scale (which is a characteristic feature of intrinsic multi-fractality). On the minimal spatial (25 km) and temporal (10 sec) scales considered in Abramenko et al. (2011), the diffusion coefficient in QS area was found to be 19 km 2 s -1 . The HMI data provided a value of approximately 220 km 2 s -1 on the largest available scale of 4 Mm. The observed tendency of the turbulent magnetic diffusivity to decrease with decreasing scales leads us to expect that the turbulent diffusivity might be close to the magnitudes of diffusivity adopted in the numerical simulations of small-scale dynamo (0.01 - 10 km 2 s -1 , e.g., Boldyrev & Cattaneo (2004); Vogler & Schussler (2007); Pietarila Graham et al. (2010)). This 1000 100 10 1 0 10 ( >) γ 4 b 5 10 makes the simulations even more realistic. In summary, a super-diffusion regime on very small scales is very favorable for pictures assuming turbulent dynamo action since it assumes decreasing diffusivity with decreasing scales.",
"pages": [
5,
6,
7,
8,
9,
10,
11,
12,
13
]
},
{
"title": "4. Concluding remarks",
"content": "Continuously varying magnetic fields are the main reason for the solar/stellar activity. The 11-year solar cycle is one of the most astonishing and widely known examples of the self-organized generation of the magnetic field. Although we know that there is no two absolutely similar solar cycles, yet, persistency and regularity of the solar periodicity through thousands of years remains impressive. A drastically different picture arises when one looks on the photosphere: chaos of mixed-polarity magnetic elements of all sizes until the resolution limits of modern instruments, continuously renewing during 1-2 days - the magnetic carpet. Dualism of the solar magnetism is usually explained by a simultaneous action of two dynamos: a global dynamo operating in the convective zone and responsible for the 11-year solar cycle, and local, or turbulent dynamo, which might operate inside the near-surface layer and to be responsible for generation of small-scale magnetic fields forming the magnetic carpet. The explanation seems to oversimplify the reality because resent studies of distribution of the magnetic flux accumulated in magnetic flux tubes showed the non-interrupted power law for many decades (Parnell et al. 2009) thus supposing a common (for all scales) mechanism for the magnetic field generation. One of promising ways to handle the problem is to consider the solar dynamo process as a non-linear dynamical system (NDS), with intrinsic properties of multi-fractality and intermittency. Like any NDS, the solar dynamo is then capable to self-organization on all scales (including large scales) and display a chaotic nature on small scales. Self-organization, in turn, provides for a magnetic complex a way to reach a SOC state, when burst-like energy release events of any size are possible at any time instant. The concept is very important for our understanding of flaring and heating processes in solar/stellar atmospheres. Further, multi-fractal nature on the magnetic field provides a necessary condition for the local turbulent dynamo operation in the near-surface layer of the convective zone. Observational evidences for local dynamo operation are still under strong debates, e.g., compare the talks by Drs. Tsuneta and Stenflo presented at this symposium. One pragmatic advise for researchers could be inferred form the observed multi-fractal nature of magnetized solar plasma. Namely, observed power laws should not be extrapolated over neighboring scales, a frequent mistake for power laws studies in various fields. In summary, the paradigm of multi-fractal and highly intermittent structure of solar magnetized plasma offers new approaches to understand the solar and stellar magnetism.",
"pages": [
13,
14
]
},
{
"title": "REFERENCES",
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2013IAUS..295..225C
https://arxiv.org/pdf/1211.1023.pdf
<document>
<section_header_level_1><location><page_1><loc_16><loc_84><loc_65><loc_90></location>Further evidence for large central mass-to-light ratios in massive early-type galaxies</section_header_level_1>
<section_header_level_1><location><page_1><loc_14><loc_79><loc_67><loc_82></location>E. M. Corsini 1 , 2 , G. A. Wegner 3 , J. Thomas 4 , R. P. Saglia 4 , R. Bender 4 , 5 and S. B. Pu 6</section_header_level_1>
<text><location><page_1><loc_16><loc_76><loc_65><loc_79></location>1 Dipartimento di Fisica e Astronomia, Universit'a di Padova, Padova, Italy email: [email protected]</text>
<text><location><page_1><loc_21><loc_75><loc_21><loc_76></location>2</text>
<text><location><page_1><loc_14><loc_68><loc_67><loc_76></location>INAF-Osservatorio Astronomico di Padova, Padova, Italy 3 Department of Physics and Astronomy, Dartmouth College, Hanover, NH, USA 4 Max-Planck-Institut fur extraterrestrische Physik, Garching, Germany 5 Universitats-Sternwarte Munchen, Munchen, Germany 6 The Beijing No. 12 High School, Beijing, China</text>
<text><location><page_1><loc_9><loc_46><loc_72><loc_66></location>Abstract. We studied the stellar populations, distribution of dark matter, and dynamical structure of a sample of 25 early-type galaxies in the Coma and Abell 262 clusters. We derived dynamical mass-to-light ratios and dark matter densities from orbit-based dynamical models, complemented by the ages, metallicities, and α -elements abundances of the galaxies from single stellar population models. Most of the galaxies have a significant detection of dark matter and their halos are about 10 times denser than in spirals of the same stellar mass. Calibrating dark matter densities to cosmological simulations we find assembly redshifts z DM ≈ 1 -3. The dynamical mass that follows the light is larger than expected for a Kroupa stellar initial mass function, especially in galaxies with high velocity dispersion σ eff inside the effective radius r eff . We now have 5 of 25 galaxies where mass follows light to 1 -3 r eff , the dynamical mass-to-light ratio of all the mass that follows the light is large ( ≈ 8 -10 in the Kron-Cousins R band), the dark matter fraction is negligible to 1 -3 r eff . This could indicate a 'massive' initial mass function in massive early-type galaxies. Alternatively, some of the dark matter in massive galaxies could follow the light very closely suggesting a significant degeneracy between luminous and dark matter.</text>
<text><location><page_1><loc_9><loc_42><loc_72><loc_45></location>Keywords. galaxies: abundances, galaxies: elliptical and lenticular, cD, galaxies: formation, galaxies: kinematics and dynamics, galaxies: stellar content.</text>
<section_header_level_1><location><page_1><loc_9><loc_37><loc_23><loc_38></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_9><loc_32><loc_72><loc_37></location>In the past years we studied the stellar populations, mass distribution, and orbital structure of a sample of early-type galaxies in the Coma cluster with the aim of constraining the epoch and mechanism of their assembly.</text>
<text><location><page_1><loc_9><loc_19><loc_72><loc_32></location>The surface-brightness distribution was obtained from ground-based and HST data. The stellar rotation, velocity dispersion, and the H 3 and H 4 coefficients of the line-of-sight velocity distribution were measured along the major axis, minor axis, and an intermediate axis. In addition, the line index profiles of Mg, Fe and H β were derived (Mehlert et al. 2000; Wegner et al. 2002; Corsini et al. 2008). Axisymmetric orbit-based dynamical models were used to derive the mass-to-light ratio Υ ∗ of all the mass that follows the light and the dark matter (DM) halo parameters in 17 galaxies (Thomas et al. 2005, 2007a,b, 2009a,b). The comparison with masses derived through strong gravitational lensing for early-type galaxies with similar velocity dispersion and the analysis of the ionized-gas</text>
<text><location><page_2><loc_9><loc_87><loc_72><loc_94></location>kinematics gave valuable consistency checks for the total mass distribution predicted by dynamical modeling (Thomas et al. 2011). The line-strength indices were analyzed by single stellar-population models to derive the age, metallicity, α -elements abundance, and mass-to-light ratio Υ Kroupa (or Υ Salpeter depending on the adopted initial mass function, IMF) of the galaxies (Mehlert et al. 2003).</text>
<text><location><page_2><loc_9><loc_79><loc_72><loc_86></location>More recently, we have performed the same dynamical analysis for 8 early-type galaxies of the nearby cluster Abell 262 (Wegner et al. 2012). The latter is far less densely populated than Coma cluster and it is comparable to the Virgo cluster. Moreover, while the Coma galaxies were selected to be mostly flattened, the Abell 262 galaxies we measured appear predominantly round on the sky.</text>
<section_header_level_1><location><page_2><loc_9><loc_75><loc_18><loc_76></location>2. Results</section_header_level_1>
<section_header_level_1><location><page_2><loc_21><loc_73><loc_60><loc_74></location>2.1. Evidence for halo mass not associated to the light</section_header_level_1>
<text><location><page_2><loc_9><loc_59><loc_72><loc_73></location>In the Coma galaxy sample the statistical significance for DM halos is over 95% for 8 (out of 17) galaxies (Thomas et al. 2007b), whereas the Abell 262 sample reveals 4 (out of 8) galaxies of this kind (Wegner et al. 2012). In Coma, we found only one galaxy (GMP 1990) with f halo ≈ 0, i.e., with a negligible halo-mass fraction of the total mass inside r eff . This is also the case of 4 galaxies in Abell 262 (NGC 703, NGC 708, NGC 712, and UGC 1308). The evidence for a DM component in addition mass that follows light is not directly connected to the spatial extent of the kinematic data, degree of rotation, or flattening of the system. There is no relationship with the age, metallicity, and α -elements abundance of the stellar populations.</text>
<text><location><page_2><loc_9><loc_49><loc_72><loc_59></location>We can not discriminate between cuspy and logarithmic halos based on the quality of the kinematic fits, except for NGC 703 where the logarithmic halo fits better. Still the majority of cluster early-type galaxies have 2 -10 times denser halos than local spirals (e.g., Persic et al. 1996), implying a 1 . 3 -2 . 2 times higher (1 + z DM ) assuming 〈 ρ DM 〉 ∼ (1 + z DM ) 3 , where z DM is the formation redshift of the DM halos. Thus, if spirals typically formed at z DM ≈ 1, then cluster early-type galaxies assembled at z DM ≈ 1 . 6 -3 . 4.</text>
<text><location><page_2><loc_9><loc_35><loc_72><loc_48></location>Averaging over all galaxies, we find that a fraction of 〈 f halo 〉 = 0 . 2 of the total mass inside r eff is in a DM halo distinct from the light. Similar fractions come from other dynamical studies employing spherical models (e.g., Gerhard et al. 2001). The Coma and Abell 262 galaxies show an anti-correlation between Υ ∗ / Υ Kroupa , i.e. the ratio between the dynamical and stellar population mass-to-light ratios, and f halo (Fig. 1, left panel). Galaxies where the dynamical mass following the light exceeds the Kroupa value by far (Υ ∗ / Υ Kroupa > 3) seem to lack matter following the halo distribution inside r eff ( 〈 f halo 〉 ≈ 0). Not so in galaxies near the Kroupa limit (Υ ∗ / Υ Kroupa < 1 . 4), where the dark-halo mass fraction is at its maximum ( 〈 f halo 〉 = 0 . 3).</text>
<section_header_level_1><location><page_2><loc_29><loc_33><loc_51><loc_34></location>2.2. Mass that follows the light</section_header_level_1>
<text><location><page_2><loc_9><loc_19><loc_72><loc_32></location>As far as the mass-to-light ratios are concerned, the galaxies of Coma and Abell 262 follow a similar trend. While the dynamically determined Υ ∗ increases strongly with σ eff , i.e., the velocity dispersion averaged within r eff (Fig. 1, right top panel), the stellar population models indicate almost constant Υ Kroupa (Fig. 1, right middle panel). This implies that the ratio Υ ∗ / Υ Kroupa increases with σ eff (Fig. 1, right bottom panel). Around σ eff ≈ 200 km s -1 the distribution of Υ ∗ / Υ Kroupa has a sharp cutoff with almost no galaxy below Υ ∗ / Υ Kroupa = 1. For σ eff /greaterorsimilar 250 km s -1 the lower bound of Υ ∗ / Υ Kroupa increases to Υ ∗ / Υ Kroupa /greaterorsimilar 2 at σ eff ≈ 300 km s -1 . Similar trends are also observed in the SAURON sample with dynamical models lacking a separate DM halo (Cappellari</text>
<figure>
<location><page_3><loc_18><loc_65><loc_63><loc_93></location>
<caption>Figure 1. Left: Ratio of dynamical Υ ∗ to stellar-population Υ Kroupa as a function of f halo , i.e., the halo-mass fraction of the total mass inside r eff , for galaxies in Coma (open circles, Thomas et al. 2011) and Abell 262 (filled circles, Wegner et al. 2012). r eff . Υ ∗ / Υ Kroupa = 1 . 6 corresponds to a Salpeter IMF. Right: Dynamical Υ ∗ (upper panel), stellar-population Υ Kroupa (middle panel), and their ratio (bottom panel) as a function of the effective velocity dispersion, σ eff . In the bottom panel, Coma and Abell 262 galaxies are compared to SLACS (open squares, Treu et al. 2010) and SAURON galaxies (open triangles, Cappellari et al. 2006).</caption>
</figure>
<text><location><page_3><loc_9><loc_48><loc_72><loc_53></location>et al. 2006), in SLACS galaxies with combined dynamical and lensing analysis (Treu et al. 2010) and, recently, in the ATLAS3d survey with dynamical models including a DM halo (Cappellari et al. 2012).</text>
<section_header_level_1><location><page_3><loc_9><loc_43><loc_21><loc_45></location>3. Discussion</section_header_level_1>
<text><location><page_3><loc_9><loc_34><loc_72><loc_43></location>Fig. 1 provides strong evidence for large central Υ ∗ in massive early-type galaxies. However, in all gravity-based methods there is a fundamental degeneracy concerning the interpretation of mass-to-light ratios. Such methods can not uniquely discriminate between luminous and dark matter once they follow similar radial distributions. The distinction is always based on the assumption that the mass density profile of the DM differs from that of the luminous matter.</text>
<text><location><page_3><loc_9><loc_19><loc_72><loc_34></location>One extreme point of view is the assumption that the stellar masses in early-type galaxies are maximal and correspond to Υ ∗ . The immediate consequence is that the stellar IMF in early-type galaxies is not universal, varying from Kroupa-like at low velocity dispersions to Salpeter (or steeper) in the most massive galaxies (see Auger et al. 2010, Thomas et al. 2011, and Cappellari et al. 2012, for a detailed discussion). Recent attempts to measure the stellar IMF directly from near-infrared observations point in the same direction (see Conroy & van Dokkum 2012, and references therein). However, we also find the galaxies with the largest Υ ∗ / Υ Kroupa have the lowest halo-mass fractions inside r eff and vice versa. A possible explanation for this finding is a DM distribution that follows the light very closely in massive galaxies and contaminates the measured Υ ∗ , while it is</text>
<text><location><page_4><loc_9><loc_91><loc_72><loc_94></location>more distinct from the light in lower-mass systems. This has been suggested elsewhere as a signature of violent relaxation.</text>
<text><location><page_4><loc_9><loc_79><loc_72><loc_91></location>One option to further constrain the mass-decomposition of gravity-based models is to incorporate predictions from cosmological simulations that confine the maximum amount of DM that can be plausibly attached to a galaxy of a given stellar mass. Since adiabatic contraction increases the amount of DM in the galaxy center, it could be in principle a viable mechanism to lower the required stellar masses towards a Kroupa IMF (Napolitano et al. 2010, but see also Cappellari et al. 2012). An immediate consequence is that some of the mass that follows the light is actually DM, increasing the DM fraction to about 50% of the total mass inside r eff .</text>
<text><location><page_4><loc_9><loc_58><loc_72><loc_79></location>Since the (decontracted) average halo density scales with the mean density of the universe at the assembly epoch, we derived the dark-halo assembly redshift z DM for Coma (Thomas et al. 2011) and Abell 262 galaxies (Wegner et al. 2012). We compared the values of z DM to the star-formation redshifts z ∗ calculated from the stellar-population ages. For the majority of galaxies z DM ≈ z ∗ and their assembly seems to have stopped before z DM ≈ 1. The stars of some galaxies appear to be younger than the halo, which indicates a secondary star-formation episode after the main halo assembly. The photometric and kinematic properties of the remaining galaxies suggest they are the remnants of gas-poor binary mergers and their progenitors formed close to the z DM = z ∗ relation. Without trying to overinterpret the result given the assumptions, it seems that Kroupa IMF allows us to explain the formation redshifts of our galaxies. In addition, galaxies in Coma and Abell 262 where the dynamical mass that follows the light is in excess of a Kroupa stellar population do not differ in terms of their stellar population ages, metallicities and α -elements abundances from galaxies where this is not the case.</text>
<text><location><page_4><loc_9><loc_50><loc_72><loc_58></location>Taken at face value, our dynamical mass models are therefore as consistent with a universal IMF, as they are with a variable IMF. If the IMF indeed varies from galaxy to galaxy according to the average star-formation rate (Conroy & van Dokkum 2012) then the assumption of a constant stellar mass-to-light ratio inside a galaxy should be relaxed in future dynamical and lensing models.</text>
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<text><location><page_4><loc_9><loc_24><loc_54><loc_25></location>Thomas, J., Saglia, R. P., Bender, R. et al. 2011, MNRAS , 415, 545</text>
<text><location><page_4><loc_9><loc_23><loc_57><loc_24></location>Treu, T., Auger, M. W., Koopmans, L. V. E. et al. 2010, ApJ , 709, 1195</text>
<text><location><page_4><loc_9><loc_21><loc_56><loc_22></location>Wegner, G. A., Corsini, E. M., Saglia, R. P. et al. 2002, A&A , 395, 753</text>
<text><location><page_4><loc_9><loc_20><loc_53><loc_21></location>Wegner, G. A., Corsini, E. M., Thomas, J. et al. 2012, AJ , 144, 78</text>
</document>
[
{
"title": "E. M. Corsini 1 , 2 , G. A. Wegner 3 , J. Thomas 4 , R. P. Saglia 4 , R. Bender 4 , 5 and S. B. Pu 6",
"content": "1 Dipartimento di Fisica e Astronomia, Universit'a di Padova, Padova, Italy email: [email protected] 2 INAF-Osservatorio Astronomico di Padova, Padova, Italy 3 Department of Physics and Astronomy, Dartmouth College, Hanover, NH, USA 4 Max-Planck-Institut fur extraterrestrische Physik, Garching, Germany 5 Universitats-Sternwarte Munchen, Munchen, Germany 6 The Beijing No. 12 High School, Beijing, China Abstract. We studied the stellar populations, distribution of dark matter, and dynamical structure of a sample of 25 early-type galaxies in the Coma and Abell 262 clusters. We derived dynamical mass-to-light ratios and dark matter densities from orbit-based dynamical models, complemented by the ages, metallicities, and α -elements abundances of the galaxies from single stellar population models. Most of the galaxies have a significant detection of dark matter and their halos are about 10 times denser than in spirals of the same stellar mass. Calibrating dark matter densities to cosmological simulations we find assembly redshifts z DM ≈ 1 -3. The dynamical mass that follows the light is larger than expected for a Kroupa stellar initial mass function, especially in galaxies with high velocity dispersion σ eff inside the effective radius r eff . We now have 5 of 25 galaxies where mass follows light to 1 -3 r eff , the dynamical mass-to-light ratio of all the mass that follows the light is large ( ≈ 8 -10 in the Kron-Cousins R band), the dark matter fraction is negligible to 1 -3 r eff . This could indicate a 'massive' initial mass function in massive early-type galaxies. Alternatively, some of the dark matter in massive galaxies could follow the light very closely suggesting a significant degeneracy between luminous and dark matter. Keywords. galaxies: abundances, galaxies: elliptical and lenticular, cD, galaxies: formation, galaxies: kinematics and dynamics, galaxies: stellar content.",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "In the past years we studied the stellar populations, mass distribution, and orbital structure of a sample of early-type galaxies in the Coma cluster with the aim of constraining the epoch and mechanism of their assembly. The surface-brightness distribution was obtained from ground-based and HST data. The stellar rotation, velocity dispersion, and the H 3 and H 4 coefficients of the line-of-sight velocity distribution were measured along the major axis, minor axis, and an intermediate axis. In addition, the line index profiles of Mg, Fe and H β were derived (Mehlert et al. 2000; Wegner et al. 2002; Corsini et al. 2008). Axisymmetric orbit-based dynamical models were used to derive the mass-to-light ratio Υ ∗ of all the mass that follows the light and the dark matter (DM) halo parameters in 17 galaxies (Thomas et al. 2005, 2007a,b, 2009a,b). The comparison with masses derived through strong gravitational lensing for early-type galaxies with similar velocity dispersion and the analysis of the ionized-gas kinematics gave valuable consistency checks for the total mass distribution predicted by dynamical modeling (Thomas et al. 2011). The line-strength indices were analyzed by single stellar-population models to derive the age, metallicity, α -elements abundance, and mass-to-light ratio Υ Kroupa (or Υ Salpeter depending on the adopted initial mass function, IMF) of the galaxies (Mehlert et al. 2003). More recently, we have performed the same dynamical analysis for 8 early-type galaxies of the nearby cluster Abell 262 (Wegner et al. 2012). The latter is far less densely populated than Coma cluster and it is comparable to the Virgo cluster. Moreover, while the Coma galaxies were selected to be mostly flattened, the Abell 262 galaxies we measured appear predominantly round on the sky.",
"pages": [
1,
2
]
},
{
"title": "2.1. Evidence for halo mass not associated to the light",
"content": "In the Coma galaxy sample the statistical significance for DM halos is over 95% for 8 (out of 17) galaxies (Thomas et al. 2007b), whereas the Abell 262 sample reveals 4 (out of 8) galaxies of this kind (Wegner et al. 2012). In Coma, we found only one galaxy (GMP 1990) with f halo ≈ 0, i.e., with a negligible halo-mass fraction of the total mass inside r eff . This is also the case of 4 galaxies in Abell 262 (NGC 703, NGC 708, NGC 712, and UGC 1308). The evidence for a DM component in addition mass that follows light is not directly connected to the spatial extent of the kinematic data, degree of rotation, or flattening of the system. There is no relationship with the age, metallicity, and α -elements abundance of the stellar populations. We can not discriminate between cuspy and logarithmic halos based on the quality of the kinematic fits, except for NGC 703 where the logarithmic halo fits better. Still the majority of cluster early-type galaxies have 2 -10 times denser halos than local spirals (e.g., Persic et al. 1996), implying a 1 . 3 -2 . 2 times higher (1 + z DM ) assuming 〈 ρ DM 〉 ∼ (1 + z DM ) 3 , where z DM is the formation redshift of the DM halos. Thus, if spirals typically formed at z DM ≈ 1, then cluster early-type galaxies assembled at z DM ≈ 1 . 6 -3 . 4. Averaging over all galaxies, we find that a fraction of 〈 f halo 〉 = 0 . 2 of the total mass inside r eff is in a DM halo distinct from the light. Similar fractions come from other dynamical studies employing spherical models (e.g., Gerhard et al. 2001). The Coma and Abell 262 galaxies show an anti-correlation between Υ ∗ / Υ Kroupa , i.e. the ratio between the dynamical and stellar population mass-to-light ratios, and f halo (Fig. 1, left panel). Galaxies where the dynamical mass following the light exceeds the Kroupa value by far (Υ ∗ / Υ Kroupa > 3) seem to lack matter following the halo distribution inside r eff ( 〈 f halo 〉 ≈ 0). Not so in galaxies near the Kroupa limit (Υ ∗ / Υ Kroupa < 1 . 4), where the dark-halo mass fraction is at its maximum ( 〈 f halo 〉 = 0 . 3).",
"pages": [
2
]
},
{
"title": "2.2. Mass that follows the light",
"content": "As far as the mass-to-light ratios are concerned, the galaxies of Coma and Abell 262 follow a similar trend. While the dynamically determined Υ ∗ increases strongly with σ eff , i.e., the velocity dispersion averaged within r eff (Fig. 1, right top panel), the stellar population models indicate almost constant Υ Kroupa (Fig. 1, right middle panel). This implies that the ratio Υ ∗ / Υ Kroupa increases with σ eff (Fig. 1, right bottom panel). Around σ eff ≈ 200 km s -1 the distribution of Υ ∗ / Υ Kroupa has a sharp cutoff with almost no galaxy below Υ ∗ / Υ Kroupa = 1. For σ eff /greaterorsimilar 250 km s -1 the lower bound of Υ ∗ / Υ Kroupa increases to Υ ∗ / Υ Kroupa /greaterorsimilar 2 at σ eff ≈ 300 km s -1 . Similar trends are also observed in the SAURON sample with dynamical models lacking a separate DM halo (Cappellari et al. 2006), in SLACS galaxies with combined dynamical and lensing analysis (Treu et al. 2010) and, recently, in the ATLAS3d survey with dynamical models including a DM halo (Cappellari et al. 2012).",
"pages": [
2,
3
]
},
{
"title": "3. Discussion",
"content": "Fig. 1 provides strong evidence for large central Υ ∗ in massive early-type galaxies. However, in all gravity-based methods there is a fundamental degeneracy concerning the interpretation of mass-to-light ratios. Such methods can not uniquely discriminate between luminous and dark matter once they follow similar radial distributions. The distinction is always based on the assumption that the mass density profile of the DM differs from that of the luminous matter. One extreme point of view is the assumption that the stellar masses in early-type galaxies are maximal and correspond to Υ ∗ . The immediate consequence is that the stellar IMF in early-type galaxies is not universal, varying from Kroupa-like at low velocity dispersions to Salpeter (or steeper) in the most massive galaxies (see Auger et al. 2010, Thomas et al. 2011, and Cappellari et al. 2012, for a detailed discussion). Recent attempts to measure the stellar IMF directly from near-infrared observations point in the same direction (see Conroy & van Dokkum 2012, and references therein). However, we also find the galaxies with the largest Υ ∗ / Υ Kroupa have the lowest halo-mass fractions inside r eff and vice versa. A possible explanation for this finding is a DM distribution that follows the light very closely in massive galaxies and contaminates the measured Υ ∗ , while it is more distinct from the light in lower-mass systems. This has been suggested elsewhere as a signature of violent relaxation. One option to further constrain the mass-decomposition of gravity-based models is to incorporate predictions from cosmological simulations that confine the maximum amount of DM that can be plausibly attached to a galaxy of a given stellar mass. Since adiabatic contraction increases the amount of DM in the galaxy center, it could be in principle a viable mechanism to lower the required stellar masses towards a Kroupa IMF (Napolitano et al. 2010, but see also Cappellari et al. 2012). An immediate consequence is that some of the mass that follows the light is actually DM, increasing the DM fraction to about 50% of the total mass inside r eff . Since the (decontracted) average halo density scales with the mean density of the universe at the assembly epoch, we derived the dark-halo assembly redshift z DM for Coma (Thomas et al. 2011) and Abell 262 galaxies (Wegner et al. 2012). We compared the values of z DM to the star-formation redshifts z ∗ calculated from the stellar-population ages. For the majority of galaxies z DM ≈ z ∗ and their assembly seems to have stopped before z DM ≈ 1. The stars of some galaxies appear to be younger than the halo, which indicates a secondary star-formation episode after the main halo assembly. The photometric and kinematic properties of the remaining galaxies suggest they are the remnants of gas-poor binary mergers and their progenitors formed close to the z DM = z ∗ relation. Without trying to overinterpret the result given the assumptions, it seems that Kroupa IMF allows us to explain the formation redshifts of our galaxies. In addition, galaxies in Coma and Abell 262 where the dynamical mass that follows the light is in excess of a Kroupa stellar population do not differ in terms of their stellar population ages, metallicities and α -elements abundances from galaxies where this is not the case. Taken at face value, our dynamical mass models are therefore as consistent with a universal IMF, as they are with a variable IMF. If the IMF indeed varies from galaxy to galaxy according to the average star-formation rate (Conroy & van Dokkum 2012) then the assumption of a constant stellar mass-to-light ratio inside a galaxy should be relaxed in future dynamical and lensing models.",
"pages": [
3,
4
]
},
{
"title": "References",
"content": "Auger, M. W., Treu, T., Bolton, A. S. et al. 2009, ApJ , 705, 1099 Cappellari, M., Bacon, R., Bureau, M. et al. 2006, MNRAS , 366, 1126 Cappellari, M., McDermid, R. M., Alatalo, K. et al. 2012, Nature , 484, 485 Conroy, C., & van Dokkum, P. 2012, ApJ , submitted, arXiv:1205.6473 Corsini, E. M., Wegner, G. A., Saglia, R. P. et al. 2008, ApJS , 175, 462 Gerhard , O., Kronawitter, A., Saglia, R. P., & Bender, R. 2001, AJ , 121, 1936 Mehlert, D., Saglia, R. P., Bender, R., & Wegner, G. A. 2000, A&AS , 141, 449 Mehlert, D., Thomas, D., Saglia, R. P., Bender, R., & Wegner, G. A. 2000, A&A , 407, 423 Napolitano, N. R., Romanowsky, A. J., & Tortora, C. 2010, MNRAS , 405, 2351 Persic, M., Salucci, P., & Stel, F. 1996, MNRAS , 283, 1102 Thomas, J., Jesseit, R., Naab, T. et al. 2007a, MNRAS , 381, 1672 Thomas, J., Jesseit, R., Saglia, R. P. et al. 2009a, MNRAS , 393, 641 Thomas, J., Saglia, R. P., Bender, R. et al. 2005, MNRAS , 360, 1355 Thomas, J., Saglia, R. P., Bender, R. et al. 2007b, MNRAS , 382, 657 Thomas, J., Saglia, R. P., Bender, R. et al. 2009b, ApJ , 691, 770 Thomas, J., Saglia, R. P., Bender, R. et al. 2011, MNRAS , 415, 545 Treu, T., Auger, M. W., Koopmans, L. V. E. et al. 2010, ApJ , 709, 1195 Wegner, G. A., Corsini, E. M., Saglia, R. P. et al. 2002, A&A , 395, 753 Wegner, G. A., Corsini, E. M., Thomas, J. et al. 2012, AJ , 144, 78",
"pages": [
4
]
}
]
2013ICRC...33.2330F
https://arxiv.org/pdf/1309.3391.pdf
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<section_header_level_1><location><page_1><loc_10><loc_85><loc_73><loc_86></location>CosMO - A Cosmic Muon Observer Experiment for Students</section_header_level_1>
<text><location><page_1><loc_10><loc_81><loc_88><loc_84></location>R. FRANKE, M. HOLLER, B. KAMINSKY, T. KARG, H. PROKOPH, A. SCH ONWALD, C. SCHWERDT, A. ST OSSL, M. WALTER</text>
<text><location><page_1><loc_9><loc_80><loc_39><loc_81></location>DESY, Platanenallee 6, 15738 Zeuthen, Germany</text>
<text><location><page_1><loc_10><loc_78><loc_27><loc_79></location>[email protected]</text>
<text><location><page_1><loc_15><loc_59><loc_91><loc_76></location>Abstract: What are cosmic particles and where do they come from? These are questions which are not only fascinating for scientists in astrophysics. With the CosMO experiment (Cosmic Muon Observer) students can autonomously study these particles. They can perform their own hands-on experiments to become familiar with modern scientific working methods and to obtain a direct insight into astroparticle physics. In this contribution we present the experimental setup and possible measurements. The detector consists of three scintillator boxes. Events are triggered and readout by a data acquisition board developed for the QuarkNet Project. With a Python program running on a netbook under Linux, the trigger and data taking conditions can be defined. The program displays the particle rates in real-time and stores the data for offline analysis. Possible student experiments are the measurement of cosmic particle rates dependent on the zenith angle, the distribution of geometrical size of particle showers, and the lifetime of muons. Twenty CosMO detectors have been built at DESY. They are used within the German outreach network Netzwerk Teilchenwelt at 15 astroparticle-research institutes and universities for project work with students.</text>
<text><location><page_1><loc_16><loc_56><loc_66><loc_57></location>Keywords: atmospheric muons, scintillation detector, education, outreach.</text>
<section_header_level_1><location><page_1><loc_10><loc_52><loc_23><loc_53></location>1 Introduction</section_header_level_1>
<text><location><page_1><loc_10><loc_38><loc_49><loc_51></location>Cosmic particles of various types reach the Earth. They rain down constantly, some of them with energies much higher than the LHC reaches. Cosmic rays contribute to natural background radiation and produce the beautiful light of the auroras. Perhaps they also influence the formation of clouds and even the evolution of live. Although hundreds of these particles pass through us every second, most people do not know about this. Within Netzwerk Teilchenwelt [1, 2] we have developed the CosMO experiment to provide insights into this fascinating field.</text>
<text><location><page_1><loc_9><loc_20><loc_49><loc_38></location>CosMO is a scintillation counter experiment based on detector components that are used in particle and astroparticle physics. It can be operated by students on their own and brings the current topic of astroparticle physics to pupils who are interested in physics, astronomy, or computing. The project allows autonomous investigation and gets students involved in research. They are given the opportunity to experience hands-on science with the help of modern measurement techniques, as well as analysis methods in particle physics and in close collaboration with scientists. CosMO can be used in outreach projects at research institutes or within school teaching. Teachers receive training so that they are enabled to incorporate the CosMO experiment into their classes.</text>
<text><location><page_1><loc_9><loc_16><loc_48><loc_20></location>DESY and other partner institutes within Netzwerk Teilchenwelt lend the CosMO experiments for student projects and provide advise and support.</text>
<section_header_level_1><location><page_1><loc_10><loc_12><loc_25><loc_13></location>2 Detector Setup</section_header_level_1>
<text><location><page_1><loc_9><loc_5><loc_49><loc_11></location>The design goal of the CosMO detector was to develop an astroparticle-physics experiment that can be operated by students and that is easily transportable to be used at schools. The detector consists of three plastic scintillators. The scintillator tiles are connected to a data acquisition (DAQ)</text>
<text><location><page_1><loc_52><loc_48><loc_90><loc_53></location>card with software-adjustable thresholds and coincidence conditions. A netbook computer is used to control the DAQ readout and to visualize the data. Figure 1 shows the full setup during operation.</text>
<text><location><page_1><loc_51><loc_29><loc_91><loc_46></location>Scintillator. We use plastic scintillator 1 tiles with a size of 20 × 20 × 1 . 2 cm 3 . The tiles are read out with 9 optical fibres each, which are connected to a multi-pixel photon counter 2 (MPPC), a type of silicon photomultiplier. The operating voltage of about 70 V for the MPPC is generated from a 5 V input voltage using an adjustable DC-DC converter 3 . The MPPC has the advantage that only low voltages are required for operation which are considered safe for students. The scintillator material and MPPC are housed in a lightproof aluminium box with connectors for the voltage supply and coaxial cable for the analogue MPPC output signal. The layout of the scintillator boxes is shown in Figure 2.</text>
<text><location><page_1><loc_51><loc_18><loc_91><loc_27></location>DAQ card. The DAQ card used is the version 2.5 data acquisition board [3] developed by a team of Fermilab, University of Nebraska, and University of Washington for the Cosmic Ray e-Lab [4] of the QuarkNet [5] project. Up to four analogue input signals are processed by discriminators with a software-adjustable thresholds. Each crossing of the discriminator threshold is</text>
<unordered_list>
<list_item><location><page_1><loc_54><loc_14><loc_91><loc_17></location>· recorded by a time-to-digital converter with a resolution of 1 . 25 ns (rising and falling edge),</list_item>
<list_item><location><page_1><loc_54><loc_10><loc_91><loc_13></location>· processed in a complex programmable logic device (CPLD) which forms a multiplicity trigger decision,</list_item>
</unordered_list>
<figure>
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<caption>Figure 1 : Overview of the CosMO setup in operation with three scintillator boxes (right), the DAQ card (center), and the readout netbook with the graphical user interface (left).</caption>
</figure>
<figure>
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<caption>Figure 2 : Overview of an open scintillator box: 1. plastic scintillator wrapped in paper, 2. optical fibers, 3. MPPC mounting, 4. voltage converter, 5. resistor for voltage adjustment, 6. connector for power supply, 7. analogue output for MPPC signal.</caption>
</figure>
<section_header_level_1><location><page_2><loc_12><loc_26><loc_38><loc_27></location>· counted in scalers for each channel.</section_header_level_1>
<text><location><page_2><loc_10><loc_17><loc_49><loc_25></location>The required multiplicity and the trigger time window can both be set in software. If the trigger condition is fulfilled an event is generated that contains a global timestamp and all threshold crossing times. In addition, a GPS module can be connected to the DAQ card that allows recording the global timestamp in UTC with a precision of 50 ns [6].</text>
<text><location><page_2><loc_10><loc_12><loc_49><loc_17></location>The DAQ card is powered with 5 V DC and offers the possibility to distribute its input voltage to the scintillator boxes so that the whole setup can be operated with a single main power supply.</text>
<text><location><page_2><loc_10><loc_5><loc_49><loc_10></location>Readout. The DAQ card provides a virtual serial port via a standard USB interface that makes it possible to access the data from a variety of different operating systems and programming languages. We developed software (cf. Sec. 3)</text>
<text><location><page_2><loc_52><loc_57><loc_90><loc_59></location>specifically tailored to the CosMO project and running on a lightweight netbook computer.</text>
<text><location><page_2><loc_52><loc_47><loc_90><loc_54></location>The complete CosMO setup has a weight of about 5 kg and can be transported in a single briefcase, making it well usable in lectures, labs and outreach projects as well as in school projects. The detector can also be operated with a small 5 V battery pack, independent of the power grid.</text>
<section_header_level_1><location><page_2><loc_52><loc_44><loc_84><loc_45></location>3 Data Processing and Visualisation</section_header_level_1>
<text><location><page_2><loc_52><loc_35><loc_91><loc_43></location>Once connected with the netbook, DAQ communications are managed via a simple text protocol. The discriminator threshold crossing information is transmitted together with GPS and timing information via the USB interface. Commands can be issued to the DAQ card via the same interface.</text>
<text><location><page_2><loc_51><loc_20><loc_91><loc_35></location>To manage DAQ communications and visualize the data, we developed the software muonic [7]. As the main purpose of CosMO is the use for student experiments, the focus during the development of the software was to provide an easy-to-use interface. Muonic was developed entirely in Python, using PyQt4 for the graphical user interface (GUI). The software is written in a modular way, and can be extended easily. It is open-source and does not depend on closed source libraries. Muonic runs platform-independent and does not need an internet connection, which allows its operation in remote locations.</text>
<text><location><page_2><loc_51><loc_5><loc_91><loc_20></location>With muonic the user can set the DAQ configuration, like thresholds or trigger conditions by manipulating typical GUI elements. The software queries the DAQ for scaler information in a given time interval and displays this data as a simple rate per channel over time plot. Also the mean rate is calculated. The width of PMT pulses is displayed in a histogram for debugging and maintenance. The data stream from the DAQ can be stored in its raw format or as tab-separated values that can be imported into a spreadsheet. A screen shot of the GUI during a typical rate measurement is shown in Fig. 3.</text>
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<caption>Figure 3 : Screen shot of the muonic graphical user interface during a typical rate measurement.</caption>
</figure>
<section_header_level_1><location><page_3><loc_10><loc_54><loc_31><loc_55></location>4 Projects for Students</section_header_level_1>
<section_header_level_1><location><page_3><loc_10><loc_52><loc_23><loc_53></location>4.1 Calibration</section_header_level_1>
<text><location><page_3><loc_9><loc_35><loc_49><loc_52></location>With muonic students can perform calibration measurements of the scintillation detectors themselves and thus gain deeper understanding of the physical principles involved. Evaluating the trigger rate vs. averaging time students can explore the influence of statistical fluctuations and determine the measurement time necessary to get a robust rate estimate. Analysing the single channel trigger rate vs. threshold will reveal the desired plateau of stable rates due to cosmic muons, bound by electronic noise towards too low thresholds and the absence of muon signals at too high thresholds. A typical calibration measurement is shown in Fig. 4. For each threshold setting approx. 5 minutes of data were collected.</text>
<section_header_level_1><location><page_3><loc_10><loc_32><loc_34><loc_33></location>4.2 Zenith Angle Dependence</section_header_level_1>
<text><location><page_3><loc_9><loc_5><loc_49><loc_32></location>A simple project for students to become familiar with the CosMO experiment is the measurement of the rate of coincidences as a function of the zenith angle, i.e. the suppression of the atmospheric muon flux with increasing atmospheric depth. At least two scintillation detectors are used in coincidence to suppress electronic noise and are placed in parallel to each other at a mutual distance d , which defines the solid angle from which particles are accepted. It has been shown that distances between 20 and 30 cm give a good compromise between restriction to direction of arrival and too low rates. The coincidence rate is measured using the muonic software and the measurement is repeated at different zenith angles. The students can be tasked to construct a setup that allows the rotation to well defined zenith angles while keeping the scintillator plates parallel to each other and at constant distance. The resulting rate as a function of zenith angle q can be described by a cos 2 q dependence [8]. Figure 5 shows a typical result plot for a scintillator tile distance of d = 20 cm and a measurement time of 1 h at each zenith angle.</text>
<section_header_level_1><location><page_3><loc_52><loc_54><loc_67><loc_55></location>4.3 Muon Lifetime</section_header_level_1>
<text><location><page_3><loc_51><loc_42><loc_90><loc_54></location>The CosMO detector allows a measurement of the mean lifetime of muons. Three scintillator boxes are stacked on top of each other. Decaying muons leave a characteristic signature in one of the channels, which are two pulses in a time interval, typically in the microsecond range. The first of these pulses is induced by the stopping muon, the second one by the electron created in the muon decay. To suppress coincident muon events, the downmost channel can be used as a veto.</text>
<text><location><page_3><loc_51><loc_14><loc_91><loc_42></location>To enhance the stopping power of the detector, students can test the influence of different absorber materials between the scintillation detectors. A histogram of the recorded time intervals can be fitted with an exponential function by the use of muonic , and the measured mean lifetime is displayed by the software. To gather enough statistics to be confident in the fit, a measurement time of about one week is required. However, the results of the measurement must be inspected carefully, since for some scintillators the results are affected by electronic noise. To suppress this noise contribution, very short time intervals can be excluded from the fit. The values of these time intervals can be set via a GUI element within muonic . The measurement of muon decay gives students insights into coincidence and veto techniques typically used in particle physics. This experiment illustrates also the measurement of statistically fluctuating quantities as well as the law of exponential decay. The measurement of muon lifetime also provides a good introduction into discussions about special relativity, because muons are only able to reach Earth's surface due to relativistic effects.</text>
<section_header_level_1><location><page_3><loc_52><loc_12><loc_71><loc_13></location>4.4 Further Possibilities</section_header_level_1>
<text><location><page_3><loc_51><loc_5><loc_90><loc_11></location>The CosMO detector further allows the study of absorption of air shower particles in different materials and to measure the velocity of muons. With three detectors in coincidence and arranged in a plane, extended particle showers can be measured. The versatility of the setup enables students to</text>
<figure>
<location><page_4><loc_10><loc_71><loc_45><loc_89></location>
<caption>Figure 4 : Single channel trigger rate as a function of threshold. The operating threshold for each scintillator is chosen on the plateau between 250 and 350 mV.</caption>
</figure>
<text><location><page_4><loc_9><loc_58><loc_49><loc_62></location>learn about the acceptance of different detector geometries. With the stored data students can learn about statistical methods for analysing large data sets.</text>
<section_header_level_1><location><page_4><loc_10><loc_54><loc_32><loc_56></location>5 Netzwerk Teilchenwelt</section_header_level_1>
<text><location><page_4><loc_9><loc_34><loc_49><loc_54></location>Netzwerk Teilchenwelt [2] is a network of 24 German research institutes of astroparticle and particle physics with the goal to enable students to authentically experience modern physics research. More than 100 young scientists are active in the network and provide students and teachers with insights into their research in astroparticle and particle physics. Students and teachers experience the world of quarks, electrons and cosmic rays firsthand at workshops in schools, student laboratories, or museums all over Germany. As a scientist for one day, they analyse real LHC data in a masterclass. Within cosmic particle projects they perform own measurements. Netzwerk Teilchenwelt encourages discussion with scientists and diving into the world of smallest particles and the big questions about the origin and structure of the universe.</text>
<section_header_level_1><location><page_4><loc_10><loc_30><loc_34><loc_32></location>6 Conclusions and Outlook</section_header_level_1>
<text><location><page_4><loc_9><loc_5><loc_49><loc_30></location>The CosMO experiment enables students and teachers to explore the physics of cosmic rays in outreach projects or at workshops in school. They develop their own research project, analyse their own data, and discuss their results with professional scientists. This introduces students to the world of the smallest particles and to questions about the origin and structure of our universe. The hands-on experiments are currently extended by projects where the scintillation counters are installed at the German Antarctic research station Neumayer III [9] and on the German research icebreaker Polarstern [10] of the Alfred-Wegner Institute for Polar and Marine Research. These detectors take data continuously, thus enabling analyses over long time ranges with sufficient statistics. The major goal of the Polarstern project is to measure the dependence of the rate of cosmic rays on the geographical latitude, i.e. the geomagnetic cutoff. Furthermore, the influence of atmospheric pressure and temperature on the rate of atmospheric muons can be studied. On the Polarstern and at the Neumayer station</text>
<figure>
<location><page_4><loc_79><loc_92><loc_91><loc_96></location>
</figure>
<figure>
<location><page_4><loc_52><loc_71><loc_87><loc_89></location>
<caption>Figure 5 : Measured muon rate as a function of zenith angle. To guide the eye, the curve indicates the expected [8] cos 2 q dependence (including an offset for random noise).</caption>
</figure>
<text><location><page_4><loc_52><loc_57><loc_90><loc_62></location>additional neutron monitors are installed. All data will be made available on the internet to interested students and teachers and can be analysed together with the data from the CosMO detectors.</text>
<text><location><page_4><loc_52><loc_52><loc_91><loc_57></location>All these activities are implemented in and supported by Netzwerk Teilchenwelt . Everybody, no matter whether scientist, teacher, or student, is encouraged to become active and join us at Netzwerk Teilchenwelt .</text>
<text><location><page_4><loc_52><loc_43><loc_91><loc_50></location>Acknowledgment: We would like to thank the DESY mechanical and electronics workshops for the machining and production of the detector components. The authors acknowledge the support from Netzwerk Teilchenwelt which is managed by the Technical University Dresden under the auspices of the German Physical Society (DPG). We also gratefully acknowledge the financial support of the German Ministry for Education and Research (BMBF).</text>
<section_header_level_1><location><page_4><loc_52><loc_39><loc_61><loc_40></location>References</section_header_level_1>
<unordered_list>
<list_item><location><page_4><loc_52><loc_36><loc_88><loc_38></location>[1] M. Hawner, S. Schmeling, C. Schwerdt et al., PhyDid B (2012) DD 15.44.</list_item>
<list_item><location><page_4><loc_52><loc_32><loc_90><loc_36></location>[2] http://www.teilchenwelt.de/ [3] S. Hansen, T. Jordan, T. Kiper et al., IEEE Nuclear Science Symposium Conference Record 1 (2003) 130-133 doi:10.1109/NSSMIC.2003.1352014.</list_item>
<list_item><location><page_4><loc_52><loc_30><loc_89><loc_32></location>[4] http://www.i2u2.org/elab/cosmic/home/ ; http: //quarknet.fnal.gov/toolkits/ati/fnaldet.html</list_item>
<list_item><location><page_4><loc_52><loc_26><loc_89><loc_30></location>[5] http://quarknet.fnal.gov/ [6] H.-G. Berns, T. H. Burnett, R. Gran et al., IEEE Nuclear Science Symposium Conference Record 2 (2003) 789-792 doi:10.1109/NSSMIC.2003.1351816.</list_item>
<list_item><location><page_4><loc_52><loc_25><loc_80><loc_26></location>[7] https://code.google.com/p/muonic/</list_item>
<list_item><location><page_4><loc_52><loc_23><loc_90><loc_25></location>[8] J. Beringer, J.-F. Arguin, R.M. Barnett et al., Phys. Rev. D 86 (2012) 010001 doi:10.1103/PhysRevD.86.010001.</list_item>
<list_item><location><page_4><loc_52><loc_20><loc_90><loc_22></location>[9] http://www.awi.de/en/infrastructure/stations/ neumayer_station/</list_item>
<list_item><location><page_4><loc_52><loc_18><loc_88><loc_20></location>[10] http://www.awi.de/en/infrastructure/ships/ polarstern/</list_item>
</document>
[
{
"title": "CosMO - A Cosmic Muon Observer Experiment for Students",
"content": "R. FRANKE, M. HOLLER, B. KAMINSKY, T. KARG, H. PROKOPH, A. SCH ONWALD, C. SCHWERDT, A. ST OSSL, M. WALTER DESY, Platanenallee 6, 15738 Zeuthen, Germany [email protected] Abstract: What are cosmic particles and where do they come from? These are questions which are not only fascinating for scientists in astrophysics. With the CosMO experiment (Cosmic Muon Observer) students can autonomously study these particles. They can perform their own hands-on experiments to become familiar with modern scientific working methods and to obtain a direct insight into astroparticle physics. In this contribution we present the experimental setup and possible measurements. The detector consists of three scintillator boxes. Events are triggered and readout by a data acquisition board developed for the QuarkNet Project. With a Python program running on a netbook under Linux, the trigger and data taking conditions can be defined. The program displays the particle rates in real-time and stores the data for offline analysis. Possible student experiments are the measurement of cosmic particle rates dependent on the zenith angle, the distribution of geometrical size of particle showers, and the lifetime of muons. Twenty CosMO detectors have been built at DESY. They are used within the German outreach network Netzwerk Teilchenwelt at 15 astroparticle-research institutes and universities for project work with students. Keywords: atmospheric muons, scintillation detector, education, outreach.",
"pages": [
1
]
},
{
"title": "1 Introduction",
"content": "Cosmic particles of various types reach the Earth. They rain down constantly, some of them with energies much higher than the LHC reaches. Cosmic rays contribute to natural background radiation and produce the beautiful light of the auroras. Perhaps they also influence the formation of clouds and even the evolution of live. Although hundreds of these particles pass through us every second, most people do not know about this. Within Netzwerk Teilchenwelt [1, 2] we have developed the CosMO experiment to provide insights into this fascinating field. CosMO is a scintillation counter experiment based on detector components that are used in particle and astroparticle physics. It can be operated by students on their own and brings the current topic of astroparticle physics to pupils who are interested in physics, astronomy, or computing. The project allows autonomous investigation and gets students involved in research. They are given the opportunity to experience hands-on science with the help of modern measurement techniques, as well as analysis methods in particle physics and in close collaboration with scientists. CosMO can be used in outreach projects at research institutes or within school teaching. Teachers receive training so that they are enabled to incorporate the CosMO experiment into their classes. DESY and other partner institutes within Netzwerk Teilchenwelt lend the CosMO experiments for student projects and provide advise and support.",
"pages": [
1
]
},
{
"title": "2 Detector Setup",
"content": "The design goal of the CosMO detector was to develop an astroparticle-physics experiment that can be operated by students and that is easily transportable to be used at schools. The detector consists of three plastic scintillators. The scintillator tiles are connected to a data acquisition (DAQ) card with software-adjustable thresholds and coincidence conditions. A netbook computer is used to control the DAQ readout and to visualize the data. Figure 1 shows the full setup during operation. Scintillator. We use plastic scintillator 1 tiles with a size of 20 × 20 × 1 . 2 cm 3 . The tiles are read out with 9 optical fibres each, which are connected to a multi-pixel photon counter 2 (MPPC), a type of silicon photomultiplier. The operating voltage of about 70 V for the MPPC is generated from a 5 V input voltage using an adjustable DC-DC converter 3 . The MPPC has the advantage that only low voltages are required for operation which are considered safe for students. The scintillator material and MPPC are housed in a lightproof aluminium box with connectors for the voltage supply and coaxial cable for the analogue MPPC output signal. The layout of the scintillator boxes is shown in Figure 2. DAQ card. The DAQ card used is the version 2.5 data acquisition board [3] developed by a team of Fermilab, University of Nebraska, and University of Washington for the Cosmic Ray e-Lab [4] of the QuarkNet [5] project. Up to four analogue input signals are processed by discriminators with a software-adjustable thresholds. Each crossing of the discriminator threshold is",
"pages": [
1
]
},
{
"title": "· counted in scalers for each channel.",
"content": "The required multiplicity and the trigger time window can both be set in software. If the trigger condition is fulfilled an event is generated that contains a global timestamp and all threshold crossing times. In addition, a GPS module can be connected to the DAQ card that allows recording the global timestamp in UTC with a precision of 50 ns [6]. The DAQ card is powered with 5 V DC and offers the possibility to distribute its input voltage to the scintillator boxes so that the whole setup can be operated with a single main power supply. Readout. The DAQ card provides a virtual serial port via a standard USB interface that makes it possible to access the data from a variety of different operating systems and programming languages. We developed software (cf. Sec. 3) specifically tailored to the CosMO project and running on a lightweight netbook computer. The complete CosMO setup has a weight of about 5 kg and can be transported in a single briefcase, making it well usable in lectures, labs and outreach projects as well as in school projects. The detector can also be operated with a small 5 V battery pack, independent of the power grid.",
"pages": [
2
]
},
{
"title": "3 Data Processing and Visualisation",
"content": "Once connected with the netbook, DAQ communications are managed via a simple text protocol. The discriminator threshold crossing information is transmitted together with GPS and timing information via the USB interface. Commands can be issued to the DAQ card via the same interface. To manage DAQ communications and visualize the data, we developed the software muonic [7]. As the main purpose of CosMO is the use for student experiments, the focus during the development of the software was to provide an easy-to-use interface. Muonic was developed entirely in Python, using PyQt4 for the graphical user interface (GUI). The software is written in a modular way, and can be extended easily. It is open-source and does not depend on closed source libraries. Muonic runs platform-independent and does not need an internet connection, which allows its operation in remote locations. With muonic the user can set the DAQ configuration, like thresholds or trigger conditions by manipulating typical GUI elements. The software queries the DAQ for scaler information in a given time interval and displays this data as a simple rate per channel over time plot. Also the mean rate is calculated. The width of PMT pulses is displayed in a histogram for debugging and maintenance. The data stream from the DAQ can be stored in its raw format or as tab-separated values that can be imported into a spreadsheet. A screen shot of the GUI during a typical rate measurement is shown in Fig. 3.",
"pages": [
2
]
},
{
"title": "4.1 Calibration",
"content": "With muonic students can perform calibration measurements of the scintillation detectors themselves and thus gain deeper understanding of the physical principles involved. Evaluating the trigger rate vs. averaging time students can explore the influence of statistical fluctuations and determine the measurement time necessary to get a robust rate estimate. Analysing the single channel trigger rate vs. threshold will reveal the desired plateau of stable rates due to cosmic muons, bound by electronic noise towards too low thresholds and the absence of muon signals at too high thresholds. A typical calibration measurement is shown in Fig. 4. For each threshold setting approx. 5 minutes of data were collected.",
"pages": [
3
]
},
{
"title": "4.2 Zenith Angle Dependence",
"content": "A simple project for students to become familiar with the CosMO experiment is the measurement of the rate of coincidences as a function of the zenith angle, i.e. the suppression of the atmospheric muon flux with increasing atmospheric depth. At least two scintillation detectors are used in coincidence to suppress electronic noise and are placed in parallel to each other at a mutual distance d , which defines the solid angle from which particles are accepted. It has been shown that distances between 20 and 30 cm give a good compromise between restriction to direction of arrival and too low rates. The coincidence rate is measured using the muonic software and the measurement is repeated at different zenith angles. The students can be tasked to construct a setup that allows the rotation to well defined zenith angles while keeping the scintillator plates parallel to each other and at constant distance. The resulting rate as a function of zenith angle q can be described by a cos 2 q dependence [8]. Figure 5 shows a typical result plot for a scintillator tile distance of d = 20 cm and a measurement time of 1 h at each zenith angle.",
"pages": [
3
]
},
{
"title": "4.3 Muon Lifetime",
"content": "The CosMO detector allows a measurement of the mean lifetime of muons. Three scintillator boxes are stacked on top of each other. Decaying muons leave a characteristic signature in one of the channels, which are two pulses in a time interval, typically in the microsecond range. The first of these pulses is induced by the stopping muon, the second one by the electron created in the muon decay. To suppress coincident muon events, the downmost channel can be used as a veto. To enhance the stopping power of the detector, students can test the influence of different absorber materials between the scintillation detectors. A histogram of the recorded time intervals can be fitted with an exponential function by the use of muonic , and the measured mean lifetime is displayed by the software. To gather enough statistics to be confident in the fit, a measurement time of about one week is required. However, the results of the measurement must be inspected carefully, since for some scintillators the results are affected by electronic noise. To suppress this noise contribution, very short time intervals can be excluded from the fit. The values of these time intervals can be set via a GUI element within muonic . The measurement of muon decay gives students insights into coincidence and veto techniques typically used in particle physics. This experiment illustrates also the measurement of statistically fluctuating quantities as well as the law of exponential decay. The measurement of muon lifetime also provides a good introduction into discussions about special relativity, because muons are only able to reach Earth's surface due to relativistic effects.",
"pages": [
3
]
},
{
"title": "4.4 Further Possibilities",
"content": "The CosMO detector further allows the study of absorption of air shower particles in different materials and to measure the velocity of muons. With three detectors in coincidence and arranged in a plane, extended particle showers can be measured. The versatility of the setup enables students to learn about the acceptance of different detector geometries. With the stored data students can learn about statistical methods for analysing large data sets.",
"pages": [
3,
4
]
},
{
"title": "5 Netzwerk Teilchenwelt",
"content": "Netzwerk Teilchenwelt [2] is a network of 24 German research institutes of astroparticle and particle physics with the goal to enable students to authentically experience modern physics research. More than 100 young scientists are active in the network and provide students and teachers with insights into their research in astroparticle and particle physics. Students and teachers experience the world of quarks, electrons and cosmic rays firsthand at workshops in schools, student laboratories, or museums all over Germany. As a scientist for one day, they analyse real LHC data in a masterclass. Within cosmic particle projects they perform own measurements. Netzwerk Teilchenwelt encourages discussion with scientists and diving into the world of smallest particles and the big questions about the origin and structure of the universe.",
"pages": [
4
]
},
{
"title": "6 Conclusions and Outlook",
"content": "The CosMO experiment enables students and teachers to explore the physics of cosmic rays in outreach projects or at workshops in school. They develop their own research project, analyse their own data, and discuss their results with professional scientists. This introduces students to the world of the smallest particles and to questions about the origin and structure of our universe. The hands-on experiments are currently extended by projects where the scintillation counters are installed at the German Antarctic research station Neumayer III [9] and on the German research icebreaker Polarstern [10] of the Alfred-Wegner Institute for Polar and Marine Research. These detectors take data continuously, thus enabling analyses over long time ranges with sufficient statistics. The major goal of the Polarstern project is to measure the dependence of the rate of cosmic rays on the geographical latitude, i.e. the geomagnetic cutoff. Furthermore, the influence of atmospheric pressure and temperature on the rate of atmospheric muons can be studied. On the Polarstern and at the Neumayer station additional neutron monitors are installed. All data will be made available on the internet to interested students and teachers and can be analysed together with the data from the CosMO detectors. All these activities are implemented in and supported by Netzwerk Teilchenwelt . Everybody, no matter whether scientist, teacher, or student, is encouraged to become active and join us at Netzwerk Teilchenwelt . Acknowledgment: We would like to thank the DESY mechanical and electronics workshops for the machining and production of the detector components. The authors acknowledge the support from Netzwerk Teilchenwelt which is managed by the Technical University Dresden under the auspices of the German Physical Society (DPG). We also gratefully acknowledge the financial support of the German Ministry for Education and Research (BMBF).",
"pages": [
4
]
}
]
2013Icar..222..766T
https://arxiv.org/pdf/1206.1185.pdf
<document>
<section_header_level_1><location><page_1><loc_14><loc_87><loc_86><loc_89></location>Activity of comet 103P / Hartley 2 at the time of the EPOXI mission fly-by 1</section_header_level_1>
<text><location><page_1><loc_9><loc_83><loc_91><loc_85></location>Gian Paolo Tozzi a , Elena Mazzotta Epifani b , Olivier R. Hainaut c , Patrizio Patriarchi a , Luisa Lara d , John Robert Brucato a , Hermann Boehnhardt e , Marco Del B'o f , Javier Licandro g , Karen Meech h , Paolo Tanga f</text>
<text><location><page_1><loc_27><loc_81><loc_28><loc_81></location>a</text>
<text><location><page_1><loc_21><loc_72><loc_79><loc_81></location>INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50 125 Firenze, Italy b INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80 131 Napoli, Italy c European Southern Observatory - Karl-Schwarzschild-Straße 2, D-85 748 Garching bei Mnchen, Germany d Instituto de Astrofis'ıca de Andaluc'ıa (IAA-CSIC) C / Glorieta de la Astronom'ıa,s / n 18008 Granada, Spain e Max-Planck Institut fur Sonnensystemforschung, D-37 191Katlenburg-Lindau, Germany f UNS-CNRS-Observatoire de la Cˆote d'Azur, Laboratoire Cassiop'ee, BP 4229, 06 304 Nice cedex 04, France g Instituto de Astrof'ısica de Canarias, V'ıa L'actea s / n, 38 200 La Laguna, Tenerife, Spain h Institute for Astronomy - University of Hawai'i, 2680 Woodlawn Drive, Honolulu, HI 96 822, USA</text>
<section_header_level_1><location><page_1><loc_6><loc_66><loc_13><loc_67></location>Abstract</section_header_level_1>
<text><location><page_1><loc_6><loc_55><loc_94><loc_65></location>Comet 103P / Hartley 2 was observed on Nov. 1-6, 2010, coinciding with the fly-by of the space probe EPOXI. The goal was to connect the large scale phenomena observed from the ground, with those at small scale observed from the spacecraft. The comet showed strong activity correlated with the rotation of its nucleus, also observed by the spacecraft. We report here the characterization of the solid component produced by this activity, via observations of the emission in two spectral regions where only grain scattering of the solar radiation is present. We show that the grains produced by this activity had a lifetime of the order of 5 hours, compatible with the spacecraft observations of the large icy chunks. Moreover, the grains produced by one of the active regions have a very red color. This suggests an organic component mixed with the ice in the grains.</text>
<text><location><page_1><loc_6><loc_53><loc_40><loc_54></location>Keywords: Comets, Comets, dust, Comets, coma</text>
<section_header_level_1><location><page_1><loc_6><loc_49><loc_18><loc_50></location>1. Introduction</section_header_level_1>
<text><location><page_1><loc_6><loc_38><loc_53><loc_47></location>Comet 103P / Hartley 2 (hereafter 103P) was discovered in March 1986 by M. Hartley (1986) with the UK Schmidt Telescope at Siding Spring (Australia). Its dynamical history (Carusi et al., 1985, and following electronic updates) shows that its orbit has been quite unstable over the last 150 years, with a perihelion distance oscillating between 1 and 2.5 AU. 103P is one of the few comets that have become an Earth crosser in the recent past.</text>
<text><location><page_1><loc_6><loc_21><loc_54><loc_37></location>103P has been frequently observed over the 20 years following its discovery, both by ground-based and space telescopes. The portrait that emerged from this harvest of ground-based data ( e.g. Licandro et al., 2000; Lowry & Fitzsimmons, 2001; Lowry et al., 2003; Snodgrass et al., 2006, 2008; Mazzotta Epifani et al., 2008) is that of a highly active comet, even at large heliocentric distance (5 AU, Snodgrass et al., 2008). In October 2007, 103P was selected as the target for the NASA Deep Impact extended mission EPOXI (A'Hearn et al., 2005); consequently, an intense world-wide observation campaign has been devoted to characterize its nucleus and coma properties in order to prepare for the spacecraft fly-by, occurring in November 2010.</text>
<text><location><page_1><loc_52><loc_36><loc_94><loc_50></location>than the nucleus to the total water production rate ( > 90% at perihelion). The presence of large grains was already inferred during the 1998 perihelion passage: analysis and modeling of ISOCAM (Cesarski et al., 1996) infrared images of the dust coma and tail (Epifani et al., 2001) implied an evolution of the dust production rate from 10 kg s -1 at 3.25 AU to 100 kg s -1 at 1.04 AU, with grains up to centimeters in size. This dust environment of 103P seems consistent with a trail structure (Lisse et al., 2009), presumably associated with millimeter-sized debris.</text>
<text><location><page_1><loc_6><loc_14><loc_52><loc_20></location>The main results of this campaign are summarized in Meech et al. (2011): the comet has a small, sub-km, nucleus, with a rotation period of 16.4 hrs when inactive, slowly increasing with activity. This possibly indicates that the rotation rate is slowed by out-gassing from the (irregular) surface.</text>
<text><location><page_1><loc_6><loc_9><loc_49><loc_13></location>The campaign data also showed that the active fraction of the nucleus' surface is, as typical, about 2%, but that it is surrounded by a large halo of (icy?) grains that contribute more</text>
<text><location><page_1><loc_52><loc_10><loc_94><loc_36></location>On UT 4.583 November 2010, the NASA mission spacecraft EPOXI flew by 103P. The closest approach was 694 km, when the comet was at 1.064 AU from the Sun. The main results of the in-situ measurements are described in A'Hearn et al. (2011): the nucleus showed a bi-lobed morphology, with a maximum length of 2.33 km and a mean radius of 0 . 58 ± 0 . 02 km. The rotation period at the time of the closest approach was measured to be 18 . 34 ± 0 . 04 h. Images obtained during the fly-by confirmed the presence of individual, 'large' chunks near the nucleus, moving at 1-2 m s -1 . Large grains had already been detected via radar observations just before the close encounter (Harmon et al., 2011): decimeter-sized grains (or possibly even larger), moving at 20-30 m s -1 , and ejected into free trajectories rather than circum-nuclear orbits were modeled to fit the grain-coma echo from 103P. A'Hearn et al. (2011) argued that the largest chunks they detected from EPOXI were icy, with radii up to 10-20 cm, dragged out by super-volatiles (specifically, CO2) and then sublimating to provide a large fraction of</text>
<table>
<location><page_2><loc_14><loc_80><loc_40><loc_86></location>
<caption>Table 2: Narrow band continuum cometary filters: central wavelength and FWHM</caption>
</table>
<text><location><page_2><loc_6><loc_75><loc_35><loc_76></location>the total H2O gaseous output of the comet.</text>
<text><location><page_2><loc_6><loc_68><loc_49><loc_75></location>Here we report observations done during 5 (half) nights around the time of the space probe fly-by. The observations were obtained with narrow band filters centered in regions with continuum emission, i.e. due to the scattering of solar radiation by the grains present in the coma.</text>
<section_header_level_1><location><page_2><loc_6><loc_64><loc_32><loc_65></location>2. Observations and data reduction</section_header_level_1>
<text><location><page_2><loc_6><loc_58><loc_49><loc_63></location>All the observations were performed with EFOSC 2 at the ESO 3.56 m New Technology Telescope (NTT), in La Silla (Chile). The observation epoch, geometry and conditions are listed in Table 1.</text>
<text><location><page_2><loc_6><loc_46><loc_49><loc_57></location>Most of the observations consisted in images of the comet obtained through Narrow Band (NB) cometary filters (similar to those described in Farnham et al., 2000). The NB filters included blue and red continuum ( Bc and Rc ), CN (0-0) Violet band, C 3 1 Π u -1 Σ + g and the C 2 Swan ( ∆ ν = 0) bands. In this paper we focus on the solid component of the coma, i.e. the data obtained with the two continuum filters. Table 2 lists their central wavelengths and full widths at half maximum.</text>
<text><location><page_2><loc_6><loc_38><loc_49><loc_46></location>To minimize the contamination by background stars and to evaluate the sky background, each comet observation sequence consisted of 5 or 8 exposures on target, moving the telescope by few tens of arcseconds in between, and one additional exposure obtained /similarequal 8 ' o ff the comet, to record the sky uncontaminated by the comet.</text>
<text><location><page_2><loc_6><loc_29><loc_49><loc_37></location>Bias and twilight sky flat-field exposures were also obtained in order to correct for the instrumental signature. Spectrophotometric standard stars and solar analog stars were observed spectroscopically and also in imaging mode, with the same filters at about the same airmass as the comet, to calibrate in flux the comet images.</text>
<text><location><page_2><loc_6><loc_22><loc_49><loc_29></location>At the beginning of the run, some images of the comet were acquired through the standard broad band filters V , R and i . They were not used in this analysis, because their pass-bands contain non negligible gas emission lines. This was verified a posteriori with the spectra.</text>
<text><location><page_2><loc_6><loc_14><loc_49><loc_22></location>All the images and spectra were at first corrected for bias and flat-field, using the appropriate ancillary frames in the customary manner. To calibrate the images in Af (see below) we computed the 'theoretical' filter color indexes ( Bc -V and Rc -V) of the observed spectrophotometric standard and solar analog stars. By using the tabulated spectra, we compared stellar</text>
<text><location><page_2><loc_52><loc_82><loc_94><loc_90></location>fluxes measured through the NB and V filters to that of a star of A0V spectral type that, by definition, has a color index equal to 0. The knowledge of the V magnitude of the observed stars allowed us to recover the NB magnitudes and hence, from the observations, the photometric zero point (ZP) of each NB filter for each night.</text>
<text><location><page_2><loc_52><loc_66><loc_94><loc_81></location>For the extinction correction, we adopted the standard extinction of La Silla 3 . Since the standard stars were observed at about the same airmass as at least one of the comet sequences, the errors introduced by possible di ff erences in the extinctions are negligible. When more than one sequence with the same filter was observed, the resulting calibrated images were in agreement within 10%. The same agreement was found also for calibrated images from consecutive photometric nights, in regions of the coma where the signature produced by periodic change of activity (see below) was not yet present. All the frames with the same filter were then inter-calibrated (see below).</text>
<text><location><page_2><loc_52><loc_61><loc_94><loc_66></location>The level of the sky contribution was then evaluated for each comet sequence, measuring the median level of the sky frame acquired through the same filter 8 ' away from the comet. This value was subtracted from each frame.</text>
<text><location><page_2><loc_52><loc_56><loc_95><loc_60></location>Thesky-subtracted frames then were re-centered on the comet photometric center, and a composite comet image was obtained through a median average of the 5 or 8 frames of the sequence.</text>
<text><location><page_2><loc_52><loc_43><loc_94><loc_56></location>The use of a median combination significantly reduces the contamination produced by background stars. The background was then refined and subtracted with a trial and error procedure using the Σ Af function (see below), by making this function independent of the projected nucleo-centric distance ( ρ ) for distances greater than 150 pixels (corresponding to /similarequal 15000 km at the comet distance) from the photometric center. The resulting continuum images were then calibrated in Af (A'Hearn et al., 1984).</text>
<section_header_level_1><location><page_2><loc_52><loc_40><loc_60><loc_41></location>3. Analysis</section_header_level_1>
<section_header_level_1><location><page_2><loc_52><loc_38><loc_77><loc_39></location>3.1. 1D analysis: background activity</section_header_level_1>
<text><location><page_2><loc_52><loc_23><loc_96><loc_37></location>As shown by the spacecraft observations (A'Hearn et al., 2011) and as already noticed at the telescope during the observations, the comet showed a strong variability with nucleus rotation. By studying the CN features in the coma, Samarasinha et al. (2011) found that rotation period varied from 17.1 h in September to 18.8 h in November 2010. Thus for this study we assume a rotation period of 18.8 h. We arbitrarily use as a starting point for the rotation phase the time of the first observation (not used here because it was recorded with a broad band filter). This point was Nov. 1, UT = 7:39.</text>
<text><location><page_2><loc_52><loc_19><loc_94><loc_23></location>To check how the emission of the continuum varied with the rotation period, we first characterized the constant background coma, which was estimated from the epoch of minimal activity.</text>
<text><location><page_2><loc_52><loc_13><loc_94><loc_18></location>A'Hearn et al. (1984) introduced the function Af ρ as a proxy for production of the solid component. A is the geometric albedo of the grains and f the filling factor, defined as the percentage of the area that is covered by the grains, and ρ the projected</text>
<table>
<location><page_3><loc_20><loc_34><loc_80><loc_71></location>
<caption>Table 1: Log of Observations through narrow band continuum cometary filters in the visible.</caption>
</table>
<text><location><page_3><loc_6><loc_27><loc_94><loc_32></location>UT str refers to the beginning of the observations; rh and ∆ are the helio- and geocentric distances; Phase is the Sun-Target-Observer angle; PA is the position angle of the extended Sun-Target vector. The sky conditions are listed: Pht is for photometric, Clr is for clear. Filt. is the identifier of the filter; Texp the is the sequence exposure time on target, in second; the airmass ( airm ) is listed for the beginning of each observations</text>
<figure>
<location><page_4><loc_6><loc_50><loc_48><loc_90></location>
<caption>Figure 1: Σ Af ( ρ ) functions for all the observations obtained with Bc (a) and Rc (b) filters. The functions have been vertically shifted by 10 cm for clarity. The plots are ordered (from bottom to top) in observational sequence, as in Table 1</caption>
</figure>
<text><location><page_4><loc_6><loc_34><loc_49><loc_43></location>nucleo-centric distance of the aperture. Typically, the filling factor, f , is proportional to 1 /ρ , while A is, at first approximation, independent of ρ . Since from the observations we get the product Af ( ρ ), it is not possible to disentangle these two parameters without additional observations in the thermal IR or without making assumptions.</text>
<text><location><page_4><loc_6><loc_19><loc_49><loc_34></location>Here we used another function derived by the above one, i.e. Σ Af ( ρ ), that is proportional to the average column density of the solid component at the projected nucleo-centric distance ρ . It is equal to 2 πρ Af ( ρ ). As shown by Tozzi et al. (2007), Σ Af should be constant with respect to the projected nuclear distance, ρ , for a comet with a dust outflow of constant velocity and production rate, and if sublimation or fragmentation of the grains are excluded. The solar radiation pressure introduces a small linear dependence with ρ , but normally its e ff ects are only noticeable at large distances from the nucleus, larger than the field of view (FoV) of EFOSC.</text>
<text><location><page_4><loc_6><loc_10><loc_49><loc_18></location>The final calibrated images were analyzed by computing their Σ Af ( ρ ) function. In Fig. 1 some examples of the Σ Af function are shown. The solid component production rate was clearly not constant, as it can be noticed by comparing the regions with ρ < 500-1000 km. However, excluding the region with ρ smaller than about 3000-5000 km, the profiles are very</text>
<figure>
<location><page_4><loc_53><loc_70><loc_93><loc_90></location>
<caption>Figure 2: Σ Af profiles corresponding to the comet at minimum activity. The solid line is for filter Bc , and the dashed line for Rc .</caption>
</figure>
<text><location><page_4><loc_52><loc_61><loc_94><loc_64></location>similar, and the signatures of the change of activity seems to overlap that of a typical, constant profile.</text>
<text><location><page_4><loc_52><loc_42><loc_94><loc_61></location>Plotting all the Σ Af profiles together, as shown in Fig. 1, we can see that they have the same behavior for ρ greater that 30005000 km and the values of Σ Af in that region are within ± 10%. These di ff erences are comparable to the uncertainty of the absolute calibration. We therefore assumed that the average value of Σ Af over ρ in the 6000-8000 km range was constant over the observations, and made small corrections to the Zero Points to adjust the profiles so they have the same average value over that range. This assumption is equivalent to considering that any change in grains production did not reach ρ = 6000 km from one day to the next. The validity of this hypothesis will be verified later. Note that using this method, the data acquired during the non-photometric night (Nov. 4) have been also calibrated to the same system as the others.</text>
<text><location><page_4><loc_52><loc_19><loc_94><loc_41></location>All the Σ Af profiles are very similar except in the region very close to the nucleus ( ρ < 2000 km) where the signature of the activity seems confined. In order to characterize the periodic emissions, a Σ Af profile corresponding to the minimum of cometary activity -what we call the 'quiet comet'- was determined for each filter as follows: for the regions with ρ > 6000 km as a median of all the profiles, and for that with ρ < 6000 km as the minimum envelope of all the profiles (excluding the region with ρ < 200 km). The median was used to reduce signatures of possible background stars, still present in the single Σ Af profiles; the minimum envelope allowed us to discard the peaks produced by the activity. However, the always present activity in the regions with ρ < 100-200 km (see below) was visually removed by spline interpolation. The Σ Af profiles, corresponding to the constant level of activity, are shown in Fig. 2 for both filters.</text>
<text><location><page_4><loc_52><loc_12><loc_94><loc_19></location>From the measurements of Σ Af , the values of Af ρ for ρ in the 6000-8000km range corresponded to 80 ± 3 cm and 91 ± 3 cm in Bc and Rc , respectively. The errors were obtained from the standard deviation of the values of the Σ Af function, with the re-normalization described above.</text>
<text><location><page_4><loc_54><loc_10><loc_94><loc_11></location>From the above values of Af ρ , it is possible to derive the</text>
<figure>
<location><page_5><loc_8><loc_70><loc_47><loc_90></location>
<caption>Figure 3: Example of Σ Af profiles produced by the periodic activity: the profile corresponding to the minimum activity was subtracted from an individual profile, leaving only the profile for additional activity. The solid line is for the observations through the Bc filter, the dashed line for observations through the Rc filter.</caption>
</figure>
<text><location><page_5><loc_6><loc_55><loc_49><loc_61></location>slope of the reflectivity spectrum for the solid component coma of the 'quiet comet'. Assuming a linear variation with lambda, the Af ρ at λ = 5550 Å would be 85 ± 3 cm and the corresponding spectral slope would be 5.2 ± 1.5 % / 1000 Å.</text>
<text><location><page_5><loc_6><loc_37><loc_49><loc_55></location>As seen in Fig. 2, the Σ Af profiles of the minimum activity are not completely constant with ρ , but they systematically increase in the inner region of the coma up to ρ equal to 20002500 km. Note that this behavior cannot be due to a residual background, because this would produce a linear variation with ρ . A profile like that means that the total grain cross-section increases with ρ in a systematic way. The only possible explanation is the fragmentation of large grains, with dimensions much larger than the observation wavelength, as they move away from the nucleus. In that way, the total grain cross-sections would increase with ρ . It is important to notice that the behavior of the quiet coma can be found in all the profiles, even though, it is partially hidden by the periodic activity</text>
<section_header_level_1><location><page_5><loc_6><loc_34><loc_21><loc_35></location>3.2. Periodic activity</section_header_level_1>
<text><location><page_5><loc_6><loc_24><loc_49><loc_33></location>By subtracting the minimum profile for Bc or Rc from the individual Σ Af profiles, we found the signature of the clouds of grains periodically ejected by the nucleus. Typical Σ Af profiles of the those clouds are shown in Figure 3. All profiles are similar, with a very strong increase towards the nucleus. There is no evidence of any motion of the clouds, as it has been seen for other outbursts (see for instance Tozzi and Licandro, 2002).</text>
<text><location><page_5><loc_6><loc_14><loc_49><loc_23></location>It would be interesting to determine the colors of the clouds of grains produced by the periodic activity, and to compare them to that of the coma at minimum activity. This measurement is complicated by the rapid evolution of the cloud and by the fact that the observations in Bc and Rc are taken at di ff erent times. To measure the color of the material produced by the activity, we have first to characterize its evolution with time.</text>
<text><location><page_5><loc_6><loc_10><loc_49><loc_14></location>We determined then the time when the comet was closer to the minimum activity, by checking the individual Σ Af profiles and then selecting the minimum ones. They were those</text>
<text><location><page_5><loc_52><loc_80><loc_94><loc_90></location>recorded on November 6 at UT 5:10 and 5:58 for the Bc and Rc filters, respectively. Their Σ Af profiles are very similar to the minimum profiles derived above: only a narrow and faint peak is present in the region with ρ < 100-200 km, indicating that the periodic activity was starting again. By chance those two observations are very close to the rotation phase equal to 0 as defined in the previous section.</text>
<text><location><page_5><loc_52><loc_76><loc_94><loc_80></location>To map the emission produced by the periodic activity, we subtract these images corresponding to the minimum of activity from the individual images.</text>
<text><location><page_5><loc_52><loc_69><loc_94><loc_76></location>As pointed out above, those two images were not acquired at the exact minimum of activity: the inner part already shows the signs of the periodic activity emission. Nevertheless, these signs are limited to the very inner coma ( ρ /lessorsimilar 200 km) and it is easy to take them into account in the following analysis.</text>
<text><location><page_5><loc_52><loc_49><loc_94><loc_69></location>The activity maps are shown as a function of the rotation phase in Figures 4 and 5 for the Bc and Rc filters, respectively. For clarity, the figures cover a limited FoV, equivalent to a projected area of 2000 × 2000 km 2 centered on the comet. The FoV actually covered by the observations is more than 10 times larger. The grains released by the periodic activity are clearly visible in both filters. They are particularly evident in two preferred directions. The first one points to the East at position angle PA ∼ 90 · and is active from a rotation phase of about 90 · to 200 · . The second one points to PA ∼ 140 · and is active from the rotation phase greater than 200 · . They don't seem produced by the same active region on the rotating nucleus, because in such a case we should see the produced grains spiraling around the nucleus.</text>
<text><location><page_5><loc_52><loc_32><loc_94><loc_49></location>We have then analyzed the two directions independently, to check whether the active regions have di ff erent origins, as found by the spacecraft (A'Hearn et al., 2011). The maps have been transformed to polar coordinates, and the profiles of the emission with respect to the nucleo-centric distance ρ have been obtained by integrating between PA = 40 · and 117 · for the first cloud, and between PA = 118 · to 165 · for the second one. The profiles have been transformed in equivalent Σ Af units (accounting for the limited angular range, as the standard definition of Σ Af implies an integration over 2 π ). Typical equivalent Σ Af profiles of the cloud during a phase of high activity are shown in Fig. 6.</text>
<text><location><page_5><loc_52><loc_22><loc_94><loc_32></location>The Σ Af profiles for the active regions are very similar to those presented earlier for the 1D analysis -only the peak intensity and signal-to-noise ratio (SNR) are di ff erent. Excluding the region with ρ /lessorsimilar 200 km, which is dominated by the seeing of the image and contaminated by the near-nucleus activity in the reference image of the 'quiet' comet, the profiles are very well represented by a constant plus an exponential function,</text>
<formula><location><page_5><loc_61><loc_19><loc_84><loc_21></location>Σ Af ( ρ ) = Σ Af 0 + Σ Af 1 exp ( -ρ L 1 ) ,</formula>
<text><location><page_5><loc_52><loc_12><loc_94><loc_18></location>where L 1 is the scale length of the cloud released by the activity (in km), and Σ Af 1 the peak intensity (in cm). The fit residuals are very small, with errors less than 10% even for profiles with medium / high activity, i.e. with high SNR.</text>
<text><location><page_5><loc_52><loc_9><loc_94><loc_12></location>The variation of L 1 with time gives the projected expansion velocity of the grains located at ρ = L 1. Of course grains</text>
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<caption>1105</caption>
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<location><page_6><loc_71><loc_62><loc_88><loc_73></location>
<caption>1105</caption>
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<paragraph><location><page_6><loc_32><loc_60><loc_48><loc_61></location>1106 5+50 Ph=103 PA_S-286</paragraph>
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<location><page_6><loc_12><loc_48><loc_29><loc_59></location>
<caption>11021106</caption>
</figure>
<paragraph><location><page_6><loc_32><loc_46><loc_35><loc_47></location>1103</paragraph>
<paragraph><location><page_6><loc_52><loc_46><loc_55><loc_47></location>1104</paragraph>
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<location><page_6><loc_12><loc_34><loc_29><loc_45></location>
<caption>1104 8:48 Ph-320 PA_S-284</caption>
</figure>
<figure>
<location><page_6><loc_71><loc_34><loc_88><loc_45></location>
<caption>Figure 4: Maps of the material released by the periodic activity of the comet as observed with the Bc filter. The images are di ff erences of the comet images minus that of Nov. 5, 5:10 UT, the one with the minimum periodic activity. Each sub-image covers a projected area FoV of 2000 × 2000 km 2 , with the comet at the center. North is up, East to the left. The sub-images have been ordered with the rotation phase (marked Ph). PA S is the position angle of the projected Sun direction. The look-up table is logarithmic.</caption>
</figure>
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<location><page_6><loc_32><loc_34><loc_48><loc_45></location>
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<figure>
<location><page_6><loc_51><loc_34><loc_68><loc_45></location>
<caption>Bc NB filter</caption>
</figure>
<paragraph><location><page_6><loc_36><loc_32><loc_40><loc_33></location>Ima</paragraph>
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<caption>1106</caption>
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<paragraph><location><page_6><loc_32><loc_74><loc_35><loc_75></location>1101</paragraph>
<paragraph><location><page_6><loc_52><loc_74><loc_55><loc_75></location>1105</paragraph>
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<caption>1105</caption>
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<caption>1101 8+18 Ph-12 PA_S-280</caption>
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<location><page_7><loc_51><loc_62><loc_68><loc_73></location>
<caption>1106 5;27 Ph-96 PA_S-286</caption>
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<paragraph><location><page_7><loc_32><loc_60><loc_35><loc_61></location>1102</paragraph>
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<location><page_7><loc_12><loc_48><loc_28><loc_59></location>
<caption>1106</caption>
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<location><page_7><loc_71><loc_48><loc_88><loc_59></location>
<caption>1103</caption>
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<location><page_7><loc_12><loc_34><loc_29><loc_45></location>
<caption>1104 8+04 Ph-307 PA_5-284</caption>
</figure>
<figure>
<location><page_7><loc_32><loc_48><loc_48><loc_59></location>
<caption>Figure 5: Maps of the material released by the periodic activity of the comet as observed with the Rc filter. The images are di ff erences of the comet images minus that of Nov. 5, 5:58 UT, the one with minimum periodic activity. Each sub-image covers a projected area FoV of 2000 × 2000 km 2 , with the comet at the center. North is up, East to the left. The sub-images have been ordered with the rotation phase (marked Ph). PA S is the position angle of the projected Sun direction. The look-up table is logarithmic.</caption>
</figure>
<figure>
<location><page_7><loc_51><loc_48><loc_68><loc_59></location>
<caption>Rc NB filter Ima 1105 5.58 Phase=6</caption>
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<location><page_7><loc_32><loc_34><loc_48><loc_45></location>
</figure>
<paragraph><location><page_7><loc_32><loc_74><loc_35><loc_75></location>1105</paragraph>
<paragraph><location><page_7><loc_52><loc_74><loc_67><loc_75></location>1105 8+19 Ph-51 PA_5-284</paragraph>
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<location><page_7><loc_32><loc_62><loc_48><loc_73></location>
<caption>1106</caption>
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<figure>
<location><page_7><loc_71><loc_62><loc_87><loc_73></location>
<caption>1106</caption>
</figure>
<figure>
<location><page_8><loc_8><loc_70><loc_47><loc_90></location>
<caption>Figure 6: Example of equivalent Σ Af profiles produced by the cloud of particles released by the activity at PA ∼ 90 · : Solid and dashed lines are for observations in Bc and Rc , respectively.</caption>
</figure>
<text><location><page_8><loc_6><loc_48><loc_49><loc_63></location>located at ρ > L 1 have larger projected velocities and those at smaller distances have smaller velocities. Since the direction of the emission of the cloud of particles in space is not known, the projected velocities are a lower limit of the real expansion velocities. To get the projected velocity we used the observations from November 6, that are most numerous and that were obtained when the level of activity was relatively high. The resulting dL 1 / dt is ≈ 15-20 m s -1 for both clouds, which is comparable to the velocity of the grains measured by radar (Harmon et al., 2011). Note that they measured radial velocities, while we measured projected velocities.</text>
<text><location><page_8><loc_6><loc_36><loc_49><loc_47></location>Those low projected velocities imply that the cloud of grains produced by periodic activity cannot move to distances greater than about 1700 km in 24 hours. This implies the grains must still be well within the FoV for observations recorded during the following night. The assumption we had made before, that the grains had not reached a projected distance larger than 6000 km from one night to the next, is therefore valid, justifying our inter-normalization of the outer part of the profiles.</text>
<text><location><page_8><loc_6><loc_26><loc_49><loc_36></location>The equivalent Σ Af ( ρ ) functions are always peaked at ρ close to 0, as can be seen in Fig. 3. A motion of the cloud away from the nucleus was never detected (apart the small increase of L 1 mentioned above) contrary to other comets, e.g. C / 1999 S4 before its breakup (Tozzi and Licandro, 2002) or 9P / Tempel 1 after the impact (Tozzi et al., 2007), for which a similar analysis revealed a clear motion of the ejecta with a Maxwellian profile.</text>
<text><location><page_8><loc_6><loc_22><loc_49><loc_26></location>The product Σ Af 1 × L 1 gives the cross-sections, S A , of the released clouds, i.e. the total surface ( S ) covered by the grains multiplied by their geometric albedo ( A ).</text>
<text><location><page_8><loc_6><loc_18><loc_49><loc_22></location>The values of S A together with those of the scale-length are reported in Table 3 for both filters. S A as function of the rotation phase is shown in Fig. 7.</text>
<section_header_level_1><location><page_8><loc_6><loc_15><loc_17><loc_16></location>3.2.1. PA ∼ 90 ·</section_header_level_1>
<text><location><page_8><loc_6><loc_10><loc_49><loc_14></location>For the activity cloud released at PA ∼ 90 · the variations of S A for Bc and Rc filters with the phase have similar behaviors, with the values for Bc lower than those of Rc . By interpolating</text>
<text><location><page_8><loc_52><loc_54><loc_53><loc_55></location>a.</text>
<text><location><page_8><loc_52><loc_34><loc_53><loc_35></location>b.</text>
<figure>
<location><page_8><loc_52><loc_34><loc_92><loc_74></location>
<caption>Figure 7: Cross-section S A in km 2 of the cloud emitted toward East (a.) and South-East directions (b.), as a function of the nucleus rotation phase. Squares are derived from observations through the Bc filter, and crossed through the Rc filter. For the cloud released into the East direction, the Bc cross-sections have been multiplied by 1.36 (see text). All the other values are plotted without multiplications. Note that the error bars are 3 times the value given in Table 3</caption>
</figure>
<table>
<location><page_9><loc_19><loc_29><loc_81><loc_69></location>
<caption>Table 3: Fitting parameters for the profiles of the clouds produced by the periodic activity. L is the scalelength and SA is the cross section, as explained in the text.</caption>
</table>
<text><location><page_10><loc_6><loc_78><loc_49><loc_90></location>the points obtained with di ff erent phases, we see that, multiplying the Bc intensities by 1.36, the two profiles overlap. As long as the grains are bigger than the wavelength, this is simply the variation of the albedo from Bc to Rc , i.e. the color of the grains. Note that in such a way those measurements of color are independent from any temporal change due to the variability of the emission. The error in the color of the grains has been evaluated as the standard deviation of the data with respect to an interpolating curve. It results of the order of 0.026 km 2 .</text>
<text><location><page_10><loc_6><loc_69><loc_49><loc_77></location>The albedo of the grains in Rc is then 36% higher than in Bc . Assuming a linear dependence with wavelength, the albedo at λ = 5550 Å is 20% higher than that at Bc and the spectral slope is (14.7 ± 1.1) % / 1000 Å. This value is more than 3 times larger than that of the background dust emission of the 'quiet comet' obtained in the previous section.</text>
<text><location><page_10><loc_6><loc_53><loc_49><loc_69></location>In Fig. 7 (a), the S A derived from the observations with the Bc filters have been multiplied by 1.36 to take into account the di ff erent albedos, in order to check how the crosssections change with the rotation phase. The points from consecutive nights interleave nicely, suggesting the repeatability of the emission period after period. However, we cannot firmly prove this asserting. In fact, for example, the data at phase around 200 · come from observations of Nov. 3 at UT 8-9, while the data for phase of 300 · come from observations taken the day after, more or less at the same UT (see tables 3). That means that the nucleus had rotated by one full turn plus 100 · .</text>
<text><location><page_10><loc_6><loc_42><loc_49><loc_53></location>Assuming a typical grain albedo of A = 0 . 04, the maximum area covered by them is of the order of 5 km 2 . The variations of S A illustrated in Fig. 7 are very large: it varies from almost 0.04 km 2 , at phase close to 0, to more than 0.2 km 2 at phase ∼ 150-200 · , with an increase of at least a factor of 5. The increases of S A between phase 0 · to 200 · can be simply explained with an increase of the production in the grains as the active area moves into sunlight.</text>
<text><location><page_10><loc_6><loc_29><loc_49><loc_42></location>Instead the factor of four decrease passing from phase 200 · to phase 300 · (see Fig. 7, a), corresponding to about 5 h if the periodicity can be trusted (or 24 h actual elapsed time), is more di ffi cult to explain: the cloud must still be well within the FoV of the observations because of the low projected velocity. This strongly supports the hypothesis that grains sublimated away, with a lifetime surely shorter than 24 h and probably of the order of 5 h. If they are transformed into gas, they will contribute no longer to the observations in the continuum bands.</text>
<text><location><page_10><loc_6><loc_21><loc_49><loc_29></location>The color of the grains ejected at this PA is similar to that of the surface of short period comets, Centaurs and scattered disk TNOs (see online MBOSS color database Hainaut & Delsanti, 2002). This color cannot be explained by pure ice; they could be ice particles with a large amount of organic material or just organic grains that sublimate under the solar radiation.</text>
<section_header_level_1><location><page_10><loc_6><loc_18><loc_18><loc_19></location>3.2.2. PA ∼ 140 ·</section_header_level_1>
<text><location><page_10><loc_6><loc_9><loc_49><loc_18></location>The clouds of particles released at PA ∼ 140 · are much fainter and the data therefore are more noisy than the other ones. However the data taken through the Bc filter overlap with those through the Rc filter, within the errors. The estimated error is here about 0.05 km 2 . The corresponding spectral slope is then 0 ± 2.4 % / 1000 Å.</text>
<text><location><page_10><loc_52><loc_83><loc_94><loc_90></location>This cloud appears during a short range of rotation period, at a phase ∼ 200 · . The S A changes by a factor 6-7 during the whole rotation. As for the other cloud, it decreases by a factor 4 passing from rotation phase of 300 · to (360 + )20 · , suggesting sublimating grains for this cloud as well.</text>
<text><location><page_10><loc_52><loc_66><loc_94><loc_83></location>However, these grains seem to have a gray color, in contrast to those released at PA ∼ 90 · . The appearance of the two clouds at di ff erent rotation phases indicates that they are produced by di ff erent active regions of the nucleus, and the great di ff erence in their color, suggest that these regions produce different kind of grains. Those at PA ∼ 140 · are more similar to the icy chunks discovered by the spacecraft, because ice should have gray color. Also those grains cannot be pure ices, since their lifetimes should be much longer that the /similarequal 5 hours indicated here (see for example Beer et al. (2006)). So also these grains should have some impurities of gray color, as for example silicates.</text>
<section_header_level_1><location><page_10><loc_52><loc_63><loc_62><loc_64></location>4. Conclusions</section_header_level_1>
<text><location><page_10><loc_52><loc_56><loc_94><loc_61></location>From the analysis of images recorded in the blue and red continuum regions of the visible spectra, we have separated the solid state emission produced by the periodic activity from the normal dust cometary coma of the 'quiet' comet.</text>
<text><location><page_10><loc_52><loc_35><loc_94><loc_56></location>We have found that the coma of the 'quiet' comet shows a peculiar behavior: its Σ Af function is not constant, but shows an increase with nucleo-centric distances ρ , for ρ < 2000-2500 km, that is not typical of a comet with constant outflow velocity and without fragmentation or sublimation. The Σ Af profiles of the 'quiet coma' obtained over the 5 nights of observations have a very similar behavior. Of course this is true for the observations where the emission due to the periodic activity does not hide completely the inner coma. This kind of profile is an indication that the scattering of the grains increases as they move away from the nucleus. Since this behavior is the same during a long period of time (5 nights), the only explanation is that the grains present in the coma of the 'quiet' comet fragment with the time, increasing their scattering area with the nucleo-centric distance.</text>
<text><location><page_10><loc_52><loc_30><loc_94><loc_34></location>The color of the solid state coma of the 'quiet' comet is red, with a spectral slope of 4.6 ± 1.5 % / 1000 Å, assuming a linear variation with wavelength.</text>
<text><location><page_10><loc_52><loc_13><loc_94><loc_30></location>By analyzing the grains produced by the periodic activity we have shown that the released clouds have two privileged projected directions: one at PA ∼ 90 · and the other at ∼ 140 · . The profiles of the equivalent Σ Af function with ρ of the clouds released in the two direction can be fitted with a constant plus an exponential function. The cross-sections S A of the two clouds vary strongly with the rotation phase of the nucleus. They move very slowly, with projected velocities of the order of 20 m / s, for both PAs. One of the two clouds (the one with PA ∼ 90 · ) has a very red color, of the order of 15 ± 3 % / 1000 Å, while the other seems to have a gray color. Assuming a periodic emission with the rotation, both sublimate with lifetimes of the order of 5 h.</text>
<text><location><page_10><loc_52><loc_10><loc_94><loc_13></location>During the flyby, the spacecraft has observed for the first time some large chunks around the nucleus, that are supposed</text>
<text><location><page_11><loc_6><loc_72><loc_49><loc_90></location>to be icy ice particles. The gray cloud can be then constituted by those chunks. However, to explain their relatively short lifetimes, those particles also need to have some impurities, gray in color, as for example silicates. The clouds released in the other direction are very red and sublimate as well with a lifetime of the order of few hours. So these grains should have lot of organics embedded in them, or they are pure organic grains that sublimate. It is important to notice that, within ρ equal to 4000 km, i.e. where most of the activity takes place, the cross section of the clouds produced by the activity is at most 6% of that of the quiet comet. This is of the same order of magnitude of the 4% contribution of the icy chunks measured by the spacecraft (A'Hearn et al., 2011).</text>
<text><location><page_11><loc_6><loc_65><loc_49><loc_72></location>Once the full geometrical analysis of the jets observed by the spacecraft becomes available, it will be interesting to connect them with the two clouds described here, and to investigate whether their di ff erent characteristics can be traced to di ff erent natures of the sublimating area.</text>
<unordered_list>
<list_item><location><page_11><loc_52><loc_87><loc_94><loc_90></location>Mazzotta Epifani E., Palumbo P., Capria M.T., Cremonese G., Fulle M., Colangeli L., 2008. The distant activity of Short Period Comets. II. MNRAS 390, 265-280</list_item>
<list_item><location><page_11><loc_52><loc_81><loc_94><loc_86></location>Meech K.J., A'Hearn M.F., Adams J.A. et al., 2011. EPOXI: comet 103P / Hartley 2 observations from a worldwide campaign. ApJ 734, L1-l9 Samarasinha N.H., Mueller B.E.A., A'Hearn M.F., Farnham T.L., Gersch, A. 2011. Rotation of Comet Hartley2 from Structures in the Coma. ApJ letters, 734, L3-L6</list_item>
<list_item><location><page_11><loc_52><loc_78><loc_94><loc_81></location>Snodgrass C., Lowry S.C., Fitzsimmons A., 2006. Photometry of cometary nuclei: Rotation rates, colors and a comparison with Kuiper Belt Objects. MNRAS 373, 1590-1602</list_item>
<list_item><location><page_11><loc_52><loc_74><loc_94><loc_77></location>Snodgrass C., Lowry S.C., Fitzsimmons A., 2008. Optical observations of 23 distant Jupiter Family Comets, including 36P / Whipple at multiple phase angles. MNRAS 385, 737-756</list_item>
<list_item><location><page_11><loc_52><loc_72><loc_94><loc_74></location>Tozzi, G. P., and Licandro, J., 2002, Icarus. Visible and Infrared Images of C / 1999 S4 (LINEAR) during the Disruption of Its Nucleus. 157, 187-192</list_item>
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<text><location><page_11><loc_52><loc_71><loc_94><loc_72></location>Tozzi, G. P., Boehnhardt, H., Kolokolova, L., et al., 2007, A&A. Dust observa-</text>
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<list_item><location><page_11><loc_53><loc_70><loc_93><loc_71></location>tions of Comet 9P / Tempel 1 at the time of the Deep Impact. 476, 979-988</list_item>
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<section_header_level_1><location><page_11><loc_6><loc_61><loc_22><loc_62></location>5. Acknowledgments</section_header_level_1>
<text><location><page_11><loc_6><loc_55><loc_52><loc_60></location>Based on Observations performed at the European Southern Observatory, La Silla, Progr. 086.C-0375. This work has been partially funded by MIUR - Ministero dell'Istruzione, dell'Universit'a e della Ricerca (Italy), under the PRIN 2008 funding.</text>
<section_header_level_1><location><page_11><loc_6><loc_51><loc_16><loc_52></location>6. References</section_header_level_1>
<section_header_level_1><location><page_11><loc_6><loc_49><loc_14><loc_50></location>References</section_header_level_1>
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<list_item><location><page_11><loc_6><loc_45><loc_49><loc_47></location>A'Hearn, M.F., Schleicher, D.G., Feldman, P.D, Millis R.L., & Thompson, D.T. 1984. Comet Bowell 1980b.0 AJ, 89, 579-591</list_item>
<list_item><location><page_11><loc_6><loc_43><loc_49><loc_45></location>A'Hearn M.F., Belton M.J.S., Delamere W.A. et al., 2005. Deep Impact: Excavating Comet Tempel 1. Science 310, 258-264</list_item>
<list_item><location><page_11><loc_6><loc_41><loc_48><loc_43></location>A'Hearn M.F., Belton M.J.S., Delamere W.A. et al., 2011. EPOXI at comet Hartley 2. Science 332, 1396-1400</list_item>
<list_item><location><page_11><loc_6><loc_36><loc_49><loc_41></location>Beer, E. H., Podolack, M. Prialnik, D., 2006. The contribution of icy grains to the activity of comets I. Grain lifetime and distribution, Icarus, 180, 473-486 Carusi A., Kresak L., Perozzi E., Valsecchi G.B., 1985. Long-term Evolution of Short-period Comets. Text book, Adam Hilger, Bristol</list_item>
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<text><location><page_11><loc_6><loc_32><loc_49><loc_36></location>Cesarsky C.J. and 65 colleagues, 1996. ISOCAM in flight. A&A 315, L32-L37 Epifani E., Colangeli L., Fulle M., Brucato J.R., Bussoletti E., De Sanctis M.C., Mennella V., Palomba E., Palumbo P., Rotundi A., 2001. ISOCAM imaging of comets 103P / Hartley 2 and 2P / Encke. Icarus 149, 339-350</text>
<text><location><page_11><loc_6><loc_29><loc_49><loc_32></location>Farnham, T. L. and Schleicher, D. G. and A'Hearn, M. F., 2000.The HB Narrowband Comet Filters: Standard Stars and Calibrations. Icarus, 147, 180204</text>
<text><location><page_11><loc_6><loc_26><loc_48><loc_28></location>Hainaut, O.R. and Delsanti, A.C., 2002. Colors of Minor Bodies in the Outer Solar System - a Statistical Analysis. A&A 389, 641-664</text>
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<text><location><page_11><loc_6><loc_20><loc_49><loc_23></location>Licandro J., Tancredi G., Lindgren M., Rickman H., Hutton R. G., 2000. CCD Photometry of Cometary Nuclei, I: Observations from 1990-1995. Icarus 147, 161-179</text>
<text><location><page_11><loc_6><loc_15><loc_49><loc_19></location>Lisse C.M., Fernadez Y.R., Reach W.T., Bauer J.M., A'Hearn M.F., Farnham T.L., Groussin O., Belton M.J., Meech K.J., Snodgrass C.D., 2009. Spizer Space Telescope Observations of the Nucleus of Comet 103P / Hartley 2. PASP 121, 968-975</text>
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</document>
[
{
"title": "Activity of comet 103P / Hartley 2 at the time of the EPOXI mission fly-by 1",
"content": "Gian Paolo Tozzi a , Elena Mazzotta Epifani b , Olivier R. Hainaut c , Patrizio Patriarchi a , Luisa Lara d , John Robert Brucato a , Hermann Boehnhardt e , Marco Del B'o f , Javier Licandro g , Karen Meech h , Paolo Tanga f a INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50 125 Firenze, Italy b INAF - Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80 131 Napoli, Italy c European Southern Observatory - Karl-Schwarzschild-Straße 2, D-85 748 Garching bei Mnchen, Germany d Instituto de Astrofis'ıca de Andaluc'ıa (IAA-CSIC) C / Glorieta de la Astronom'ıa,s / n 18008 Granada, Spain e Max-Planck Institut fur Sonnensystemforschung, D-37 191Katlenburg-Lindau, Germany f UNS-CNRS-Observatoire de la Cˆote d'Azur, Laboratoire Cassiop'ee, BP 4229, 06 304 Nice cedex 04, France g Instituto de Astrof'ısica de Canarias, V'ıa L'actea s / n, 38 200 La Laguna, Tenerife, Spain h Institute for Astronomy - University of Hawai'i, 2680 Woodlawn Drive, Honolulu, HI 96 822, USA",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "Comet 103P / Hartley 2 was observed on Nov. 1-6, 2010, coinciding with the fly-by of the space probe EPOXI. The goal was to connect the large scale phenomena observed from the ground, with those at small scale observed from the spacecraft. The comet showed strong activity correlated with the rotation of its nucleus, also observed by the spacecraft. We report here the characterization of the solid component produced by this activity, via observations of the emission in two spectral regions where only grain scattering of the solar radiation is present. We show that the grains produced by this activity had a lifetime of the order of 5 hours, compatible with the spacecraft observations of the large icy chunks. Moreover, the grains produced by one of the active regions have a very red color. This suggests an organic component mixed with the ice in the grains. Keywords: Comets, Comets, dust, Comets, coma",
"pages": [
1
]
},
{
"title": "1. Introduction",
"content": "Comet 103P / Hartley 2 (hereafter 103P) was discovered in March 1986 by M. Hartley (1986) with the UK Schmidt Telescope at Siding Spring (Australia). Its dynamical history (Carusi et al., 1985, and following electronic updates) shows that its orbit has been quite unstable over the last 150 years, with a perihelion distance oscillating between 1 and 2.5 AU. 103P is one of the few comets that have become an Earth crosser in the recent past. 103P has been frequently observed over the 20 years following its discovery, both by ground-based and space telescopes. The portrait that emerged from this harvest of ground-based data ( e.g. Licandro et al., 2000; Lowry & Fitzsimmons, 2001; Lowry et al., 2003; Snodgrass et al., 2006, 2008; Mazzotta Epifani et al., 2008) is that of a highly active comet, even at large heliocentric distance (5 AU, Snodgrass et al., 2008). In October 2007, 103P was selected as the target for the NASA Deep Impact extended mission EPOXI (A'Hearn et al., 2005); consequently, an intense world-wide observation campaign has been devoted to characterize its nucleus and coma properties in order to prepare for the spacecraft fly-by, occurring in November 2010. than the nucleus to the total water production rate ( > 90% at perihelion). The presence of large grains was already inferred during the 1998 perihelion passage: analysis and modeling of ISOCAM (Cesarski et al., 1996) infrared images of the dust coma and tail (Epifani et al., 2001) implied an evolution of the dust production rate from 10 kg s -1 at 3.25 AU to 100 kg s -1 at 1.04 AU, with grains up to centimeters in size. This dust environment of 103P seems consistent with a trail structure (Lisse et al., 2009), presumably associated with millimeter-sized debris. The main results of this campaign are summarized in Meech et al. (2011): the comet has a small, sub-km, nucleus, with a rotation period of 16.4 hrs when inactive, slowly increasing with activity. This possibly indicates that the rotation rate is slowed by out-gassing from the (irregular) surface. The campaign data also showed that the active fraction of the nucleus' surface is, as typical, about 2%, but that it is surrounded by a large halo of (icy?) grains that contribute more On UT 4.583 November 2010, the NASA mission spacecraft EPOXI flew by 103P. The closest approach was 694 km, when the comet was at 1.064 AU from the Sun. The main results of the in-situ measurements are described in A'Hearn et al. (2011): the nucleus showed a bi-lobed morphology, with a maximum length of 2.33 km and a mean radius of 0 . 58 ± 0 . 02 km. The rotation period at the time of the closest approach was measured to be 18 . 34 ± 0 . 04 h. Images obtained during the fly-by confirmed the presence of individual, 'large' chunks near the nucleus, moving at 1-2 m s -1 . Large grains had already been detected via radar observations just before the close encounter (Harmon et al., 2011): decimeter-sized grains (or possibly even larger), moving at 20-30 m s -1 , and ejected into free trajectories rather than circum-nuclear orbits were modeled to fit the grain-coma echo from 103P. A'Hearn et al. (2011) argued that the largest chunks they detected from EPOXI were icy, with radii up to 10-20 cm, dragged out by super-volatiles (specifically, CO2) and then sublimating to provide a large fraction of the total H2O gaseous output of the comet. Here we report observations done during 5 (half) nights around the time of the space probe fly-by. The observations were obtained with narrow band filters centered in regions with continuum emission, i.e. due to the scattering of solar radiation by the grains present in the coma.",
"pages": [
1,
2
]
},
{
"title": "2. Observations and data reduction",
"content": "All the observations were performed with EFOSC 2 at the ESO 3.56 m New Technology Telescope (NTT), in La Silla (Chile). The observation epoch, geometry and conditions are listed in Table 1. Most of the observations consisted in images of the comet obtained through Narrow Band (NB) cometary filters (similar to those described in Farnham et al., 2000). The NB filters included blue and red continuum ( Bc and Rc ), CN (0-0) Violet band, C 3 1 Π u -1 Σ + g and the C 2 Swan ( ∆ ν = 0) bands. In this paper we focus on the solid component of the coma, i.e. the data obtained with the two continuum filters. Table 2 lists their central wavelengths and full widths at half maximum. To minimize the contamination by background stars and to evaluate the sky background, each comet observation sequence consisted of 5 or 8 exposures on target, moving the telescope by few tens of arcseconds in between, and one additional exposure obtained /similarequal 8 ' o ff the comet, to record the sky uncontaminated by the comet. Bias and twilight sky flat-field exposures were also obtained in order to correct for the instrumental signature. Spectrophotometric standard stars and solar analog stars were observed spectroscopically and also in imaging mode, with the same filters at about the same airmass as the comet, to calibrate in flux the comet images. At the beginning of the run, some images of the comet were acquired through the standard broad band filters V , R and i . They were not used in this analysis, because their pass-bands contain non negligible gas emission lines. This was verified a posteriori with the spectra. All the images and spectra were at first corrected for bias and flat-field, using the appropriate ancillary frames in the customary manner. To calibrate the images in Af (see below) we computed the 'theoretical' filter color indexes ( Bc -V and Rc -V) of the observed spectrophotometric standard and solar analog stars. By using the tabulated spectra, we compared stellar fluxes measured through the NB and V filters to that of a star of A0V spectral type that, by definition, has a color index equal to 0. The knowledge of the V magnitude of the observed stars allowed us to recover the NB magnitudes and hence, from the observations, the photometric zero point (ZP) of each NB filter for each night. For the extinction correction, we adopted the standard extinction of La Silla 3 . Since the standard stars were observed at about the same airmass as at least one of the comet sequences, the errors introduced by possible di ff erences in the extinctions are negligible. When more than one sequence with the same filter was observed, the resulting calibrated images were in agreement within 10%. The same agreement was found also for calibrated images from consecutive photometric nights, in regions of the coma where the signature produced by periodic change of activity (see below) was not yet present. All the frames with the same filter were then inter-calibrated (see below). The level of the sky contribution was then evaluated for each comet sequence, measuring the median level of the sky frame acquired through the same filter 8 ' away from the comet. This value was subtracted from each frame. Thesky-subtracted frames then were re-centered on the comet photometric center, and a composite comet image was obtained through a median average of the 5 or 8 frames of the sequence. The use of a median combination significantly reduces the contamination produced by background stars. The background was then refined and subtracted with a trial and error procedure using the Σ Af function (see below), by making this function independent of the projected nucleo-centric distance ( ρ ) for distances greater than 150 pixels (corresponding to /similarequal 15000 km at the comet distance) from the photometric center. The resulting continuum images were then calibrated in Af (A'Hearn et al., 1984).",
"pages": [
2
]
},
{
"title": "3.1. 1D analysis: background activity",
"content": "As shown by the spacecraft observations (A'Hearn et al., 2011) and as already noticed at the telescope during the observations, the comet showed a strong variability with nucleus rotation. By studying the CN features in the coma, Samarasinha et al. (2011) found that rotation period varied from 17.1 h in September to 18.8 h in November 2010. Thus for this study we assume a rotation period of 18.8 h. We arbitrarily use as a starting point for the rotation phase the time of the first observation (not used here because it was recorded with a broad band filter). This point was Nov. 1, UT = 7:39. To check how the emission of the continuum varied with the rotation period, we first characterized the constant background coma, which was estimated from the epoch of minimal activity. A'Hearn et al. (1984) introduced the function Af ρ as a proxy for production of the solid component. A is the geometric albedo of the grains and f the filling factor, defined as the percentage of the area that is covered by the grains, and ρ the projected UT str refers to the beginning of the observations; rh and ∆ are the helio- and geocentric distances; Phase is the Sun-Target-Observer angle; PA is the position angle of the extended Sun-Target vector. The sky conditions are listed: Pht is for photometric, Clr is for clear. Filt. is the identifier of the filter; Texp the is the sequence exposure time on target, in second; the airmass ( airm ) is listed for the beginning of each observations nucleo-centric distance of the aperture. Typically, the filling factor, f , is proportional to 1 /ρ , while A is, at first approximation, independent of ρ . Since from the observations we get the product Af ( ρ ), it is not possible to disentangle these two parameters without additional observations in the thermal IR or without making assumptions. Here we used another function derived by the above one, i.e. Σ Af ( ρ ), that is proportional to the average column density of the solid component at the projected nucleo-centric distance ρ . It is equal to 2 πρ Af ( ρ ). As shown by Tozzi et al. (2007), Σ Af should be constant with respect to the projected nuclear distance, ρ , for a comet with a dust outflow of constant velocity and production rate, and if sublimation or fragmentation of the grains are excluded. The solar radiation pressure introduces a small linear dependence with ρ , but normally its e ff ects are only noticeable at large distances from the nucleus, larger than the field of view (FoV) of EFOSC. The final calibrated images were analyzed by computing their Σ Af ( ρ ) function. In Fig. 1 some examples of the Σ Af function are shown. The solid component production rate was clearly not constant, as it can be noticed by comparing the regions with ρ < 500-1000 km. However, excluding the region with ρ smaller than about 3000-5000 km, the profiles are very similar, and the signatures of the change of activity seems to overlap that of a typical, constant profile. Plotting all the Σ Af profiles together, as shown in Fig. 1, we can see that they have the same behavior for ρ greater that 30005000 km and the values of Σ Af in that region are within ± 10%. These di ff erences are comparable to the uncertainty of the absolute calibration. We therefore assumed that the average value of Σ Af over ρ in the 6000-8000 km range was constant over the observations, and made small corrections to the Zero Points to adjust the profiles so they have the same average value over that range. This assumption is equivalent to considering that any change in grains production did not reach ρ = 6000 km from one day to the next. The validity of this hypothesis will be verified later. Note that using this method, the data acquired during the non-photometric night (Nov. 4) have been also calibrated to the same system as the others. All the Σ Af profiles are very similar except in the region very close to the nucleus ( ρ < 2000 km) where the signature of the activity seems confined. In order to characterize the periodic emissions, a Σ Af profile corresponding to the minimum of cometary activity -what we call the 'quiet comet'- was determined for each filter as follows: for the regions with ρ > 6000 km as a median of all the profiles, and for that with ρ < 6000 km as the minimum envelope of all the profiles (excluding the region with ρ < 200 km). The median was used to reduce signatures of possible background stars, still present in the single Σ Af profiles; the minimum envelope allowed us to discard the peaks produced by the activity. However, the always present activity in the regions with ρ < 100-200 km (see below) was visually removed by spline interpolation. The Σ Af profiles, corresponding to the constant level of activity, are shown in Fig. 2 for both filters. From the measurements of Σ Af , the values of Af ρ for ρ in the 6000-8000km range corresponded to 80 ± 3 cm and 91 ± 3 cm in Bc and Rc , respectively. The errors were obtained from the standard deviation of the values of the Σ Af function, with the re-normalization described above. From the above values of Af ρ , it is possible to derive the slope of the reflectivity spectrum for the solid component coma of the 'quiet comet'. Assuming a linear variation with lambda, the Af ρ at λ = 5550 Å would be 85 ± 3 cm and the corresponding spectral slope would be 5.2 ± 1.5 % / 1000 Å. As seen in Fig. 2, the Σ Af profiles of the minimum activity are not completely constant with ρ , but they systematically increase in the inner region of the coma up to ρ equal to 20002500 km. Note that this behavior cannot be due to a residual background, because this would produce a linear variation with ρ . A profile like that means that the total grain cross-section increases with ρ in a systematic way. The only possible explanation is the fragmentation of large grains, with dimensions much larger than the observation wavelength, as they move away from the nucleus. In that way, the total grain cross-sections would increase with ρ . It is important to notice that the behavior of the quiet coma can be found in all the profiles, even though, it is partially hidden by the periodic activity",
"pages": [
2,
3,
4,
5
]
},
{
"title": "3.2. Periodic activity",
"content": "By subtracting the minimum profile for Bc or Rc from the individual Σ Af profiles, we found the signature of the clouds of grains periodically ejected by the nucleus. Typical Σ Af profiles of the those clouds are shown in Figure 3. All profiles are similar, with a very strong increase towards the nucleus. There is no evidence of any motion of the clouds, as it has been seen for other outbursts (see for instance Tozzi and Licandro, 2002). It would be interesting to determine the colors of the clouds of grains produced by the periodic activity, and to compare them to that of the coma at minimum activity. This measurement is complicated by the rapid evolution of the cloud and by the fact that the observations in Bc and Rc are taken at di ff erent times. To measure the color of the material produced by the activity, we have first to characterize its evolution with time. We determined then the time when the comet was closer to the minimum activity, by checking the individual Σ Af profiles and then selecting the minimum ones. They were those recorded on November 6 at UT 5:10 and 5:58 for the Bc and Rc filters, respectively. Their Σ Af profiles are very similar to the minimum profiles derived above: only a narrow and faint peak is present in the region with ρ < 100-200 km, indicating that the periodic activity was starting again. By chance those two observations are very close to the rotation phase equal to 0 as defined in the previous section. To map the emission produced by the periodic activity, we subtract these images corresponding to the minimum of activity from the individual images. As pointed out above, those two images were not acquired at the exact minimum of activity: the inner part already shows the signs of the periodic activity emission. Nevertheless, these signs are limited to the very inner coma ( ρ /lessorsimilar 200 km) and it is easy to take them into account in the following analysis. The activity maps are shown as a function of the rotation phase in Figures 4 and 5 for the Bc and Rc filters, respectively. For clarity, the figures cover a limited FoV, equivalent to a projected area of 2000 × 2000 km 2 centered on the comet. The FoV actually covered by the observations is more than 10 times larger. The grains released by the periodic activity are clearly visible in both filters. They are particularly evident in two preferred directions. The first one points to the East at position angle PA ∼ 90 · and is active from a rotation phase of about 90 · to 200 · . The second one points to PA ∼ 140 · and is active from the rotation phase greater than 200 · . They don't seem produced by the same active region on the rotating nucleus, because in such a case we should see the produced grains spiraling around the nucleus. We have then analyzed the two directions independently, to check whether the active regions have di ff erent origins, as found by the spacecraft (A'Hearn et al., 2011). The maps have been transformed to polar coordinates, and the profiles of the emission with respect to the nucleo-centric distance ρ have been obtained by integrating between PA = 40 · and 117 · for the first cloud, and between PA = 118 · to 165 · for the second one. The profiles have been transformed in equivalent Σ Af units (accounting for the limited angular range, as the standard definition of Σ Af implies an integration over 2 π ). Typical equivalent Σ Af profiles of the cloud during a phase of high activity are shown in Fig. 6. The Σ Af profiles for the active regions are very similar to those presented earlier for the 1D analysis -only the peak intensity and signal-to-noise ratio (SNR) are di ff erent. Excluding the region with ρ /lessorsimilar 200 km, which is dominated by the seeing of the image and contaminated by the near-nucleus activity in the reference image of the 'quiet' comet, the profiles are very well represented by a constant plus an exponential function, where L 1 is the scale length of the cloud released by the activity (in km), and Σ Af 1 the peak intensity (in cm). The fit residuals are very small, with errors less than 10% even for profiles with medium / high activity, i.e. with high SNR. The variation of L 1 with time gives the projected expansion velocity of the grains located at ρ = L 1. Of course grains located at ρ > L 1 have larger projected velocities and those at smaller distances have smaller velocities. Since the direction of the emission of the cloud of particles in space is not known, the projected velocities are a lower limit of the real expansion velocities. To get the projected velocity we used the observations from November 6, that are most numerous and that were obtained when the level of activity was relatively high. The resulting dL 1 / dt is ≈ 15-20 m s -1 for both clouds, which is comparable to the velocity of the grains measured by radar (Harmon et al., 2011). Note that they measured radial velocities, while we measured projected velocities. Those low projected velocities imply that the cloud of grains produced by periodic activity cannot move to distances greater than about 1700 km in 24 hours. This implies the grains must still be well within the FoV for observations recorded during the following night. The assumption we had made before, that the grains had not reached a projected distance larger than 6000 km from one night to the next, is therefore valid, justifying our inter-normalization of the outer part of the profiles. The equivalent Σ Af ( ρ ) functions are always peaked at ρ close to 0, as can be seen in Fig. 3. A motion of the cloud away from the nucleus was never detected (apart the small increase of L 1 mentioned above) contrary to other comets, e.g. C / 1999 S4 before its breakup (Tozzi and Licandro, 2002) or 9P / Tempel 1 after the impact (Tozzi et al., 2007), for which a similar analysis revealed a clear motion of the ejecta with a Maxwellian profile. The product Σ Af 1 × L 1 gives the cross-sections, S A , of the released clouds, i.e. the total surface ( S ) covered by the grains multiplied by their geometric albedo ( A ). The values of S A together with those of the scale-length are reported in Table 3 for both filters. S A as function of the rotation phase is shown in Fig. 7.",
"pages": [
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8
]
},
{
"title": "3.2.1. PA ∼ 90 ·",
"content": "For the activity cloud released at PA ∼ 90 · the variations of S A for Bc and Rc filters with the phase have similar behaviors, with the values for Bc lower than those of Rc . By interpolating a. b. the points obtained with di ff erent phases, we see that, multiplying the Bc intensities by 1.36, the two profiles overlap. As long as the grains are bigger than the wavelength, this is simply the variation of the albedo from Bc to Rc , i.e. the color of the grains. Note that in such a way those measurements of color are independent from any temporal change due to the variability of the emission. The error in the color of the grains has been evaluated as the standard deviation of the data with respect to an interpolating curve. It results of the order of 0.026 km 2 . The albedo of the grains in Rc is then 36% higher than in Bc . Assuming a linear dependence with wavelength, the albedo at λ = 5550 Å is 20% higher than that at Bc and the spectral slope is (14.7 ± 1.1) % / 1000 Å. This value is more than 3 times larger than that of the background dust emission of the 'quiet comet' obtained in the previous section. In Fig. 7 (a), the S A derived from the observations with the Bc filters have been multiplied by 1.36 to take into account the di ff erent albedos, in order to check how the crosssections change with the rotation phase. The points from consecutive nights interleave nicely, suggesting the repeatability of the emission period after period. However, we cannot firmly prove this asserting. In fact, for example, the data at phase around 200 · come from observations of Nov. 3 at UT 8-9, while the data for phase of 300 · come from observations taken the day after, more or less at the same UT (see tables 3). That means that the nucleus had rotated by one full turn plus 100 · . Assuming a typical grain albedo of A = 0 . 04, the maximum area covered by them is of the order of 5 km 2 . The variations of S A illustrated in Fig. 7 are very large: it varies from almost 0.04 km 2 , at phase close to 0, to more than 0.2 km 2 at phase ∼ 150-200 · , with an increase of at least a factor of 5. The increases of S A between phase 0 · to 200 · can be simply explained with an increase of the production in the grains as the active area moves into sunlight. Instead the factor of four decrease passing from phase 200 · to phase 300 · (see Fig. 7, a), corresponding to about 5 h if the periodicity can be trusted (or 24 h actual elapsed time), is more di ffi cult to explain: the cloud must still be well within the FoV of the observations because of the low projected velocity. This strongly supports the hypothesis that grains sublimated away, with a lifetime surely shorter than 24 h and probably of the order of 5 h. If they are transformed into gas, they will contribute no longer to the observations in the continuum bands. The color of the grains ejected at this PA is similar to that of the surface of short period comets, Centaurs and scattered disk TNOs (see online MBOSS color database Hainaut & Delsanti, 2002). This color cannot be explained by pure ice; they could be ice particles with a large amount of organic material or just organic grains that sublimate under the solar radiation.",
"pages": [
8,
10
]
},
{
"title": "3.2.2. PA ∼ 140 ·",
"content": "The clouds of particles released at PA ∼ 140 · are much fainter and the data therefore are more noisy than the other ones. However the data taken through the Bc filter overlap with those through the Rc filter, within the errors. The estimated error is here about 0.05 km 2 . The corresponding spectral slope is then 0 ± 2.4 % / 1000 Å. This cloud appears during a short range of rotation period, at a phase ∼ 200 · . The S A changes by a factor 6-7 during the whole rotation. As for the other cloud, it decreases by a factor 4 passing from rotation phase of 300 · to (360 + )20 · , suggesting sublimating grains for this cloud as well. However, these grains seem to have a gray color, in contrast to those released at PA ∼ 90 · . The appearance of the two clouds at di ff erent rotation phases indicates that they are produced by di ff erent active regions of the nucleus, and the great di ff erence in their color, suggest that these regions produce different kind of grains. Those at PA ∼ 140 · are more similar to the icy chunks discovered by the spacecraft, because ice should have gray color. Also those grains cannot be pure ices, since their lifetimes should be much longer that the /similarequal 5 hours indicated here (see for example Beer et al. (2006)). So also these grains should have some impurities of gray color, as for example silicates.",
"pages": [
10
]
},
{
"title": "4. Conclusions",
"content": "From the analysis of images recorded in the blue and red continuum regions of the visible spectra, we have separated the solid state emission produced by the periodic activity from the normal dust cometary coma of the 'quiet' comet. We have found that the coma of the 'quiet' comet shows a peculiar behavior: its Σ Af function is not constant, but shows an increase with nucleo-centric distances ρ , for ρ < 2000-2500 km, that is not typical of a comet with constant outflow velocity and without fragmentation or sublimation. The Σ Af profiles of the 'quiet coma' obtained over the 5 nights of observations have a very similar behavior. Of course this is true for the observations where the emission due to the periodic activity does not hide completely the inner coma. This kind of profile is an indication that the scattering of the grains increases as they move away from the nucleus. Since this behavior is the same during a long period of time (5 nights), the only explanation is that the grains present in the coma of the 'quiet' comet fragment with the time, increasing their scattering area with the nucleo-centric distance. The color of the solid state coma of the 'quiet' comet is red, with a spectral slope of 4.6 ± 1.5 % / 1000 Å, assuming a linear variation with wavelength. By analyzing the grains produced by the periodic activity we have shown that the released clouds have two privileged projected directions: one at PA ∼ 90 · and the other at ∼ 140 · . The profiles of the equivalent Σ Af function with ρ of the clouds released in the two direction can be fitted with a constant plus an exponential function. The cross-sections S A of the two clouds vary strongly with the rotation phase of the nucleus. They move very slowly, with projected velocities of the order of 20 m / s, for both PAs. One of the two clouds (the one with PA ∼ 90 · ) has a very red color, of the order of 15 ± 3 % / 1000 Å, while the other seems to have a gray color. Assuming a periodic emission with the rotation, both sublimate with lifetimes of the order of 5 h. During the flyby, the spacecraft has observed for the first time some large chunks around the nucleus, that are supposed to be icy ice particles. The gray cloud can be then constituted by those chunks. However, to explain their relatively short lifetimes, those particles also need to have some impurities, gray in color, as for example silicates. The clouds released in the other direction are very red and sublimate as well with a lifetime of the order of few hours. So these grains should have lot of organics embedded in them, or they are pure organic grains that sublimate. It is important to notice that, within ρ equal to 4000 km, i.e. where most of the activity takes place, the cross section of the clouds produced by the activity is at most 6% of that of the quiet comet. This is of the same order of magnitude of the 4% contribution of the icy chunks measured by the spacecraft (A'Hearn et al., 2011). Once the full geometrical analysis of the jets observed by the spacecraft becomes available, it will be interesting to connect them with the two clouds described here, and to investigate whether their di ff erent characteristics can be traced to di ff erent natures of the sublimating area. Tozzi, G. P., Boehnhardt, H., Kolokolova, L., et al., 2007, A&A. Dust observa-",
"pages": [
10,
11
]
},
{
"title": "5. Acknowledgments",
"content": "Based on Observations performed at the European Southern Observatory, La Silla, Progr. 086.C-0375. This work has been partially funded by MIUR - Ministero dell'Istruzione, dell'Universit'a e della Ricerca (Italy), under the PRIN 2008 funding.",
"pages": [
11
]
},
{
"title": "References",
"content": "Cesarsky C.J. and 65 colleagues, 1996. ISOCAM in flight. A&A 315, L32-L37 Epifani E., Colangeli L., Fulle M., Brucato J.R., Bussoletti E., De Sanctis M.C., Mennella V., Palomba E., Palumbo P., Rotundi A., 2001. ISOCAM imaging of comets 103P / Hartley 2 and 2P / Encke. Icarus 149, 339-350 Farnham, T. L. and Schleicher, D. G. and A'Hearn, M. F., 2000.The HB Narrowband Comet Filters: Standard Stars and Calibrations. Icarus, 147, 180204 Hainaut, O.R. and Delsanti, A.C., 2002. Colors of Minor Bodies in the Outer Solar System - a Statistical Analysis. A&A 389, 641-664 Hartley M., 1986. Comet Hartley (1986c). IAU Circ. 4197 Licandro J., Tancredi G., Lindgren M., Rickman H., Hutton R. G., 2000. CCD Photometry of Cometary Nuclei, I: Observations from 1990-1995. Icarus 147, 161-179 Lisse C.M., Fernadez Y.R., Reach W.T., Bauer J.M., A'Hearn M.F., Farnham T.L., Groussin O., Belton M.J., Meech K.J., Snodgrass C.D., 2009. Spizer Space Telescope Observations of the Nucleus of Comet 103P / Hartley 2. PASP 121, 968-975 Lowry S.C. & Fitzsimmons A., 2001.CCD photometry of distant comets. II. A&A 365, 204-213",
"pages": [
11
]
}
]
2013Icar..224..253N
https://arxiv.org/pdf/1303.3023.pdf
<document>
<section_header_level_1><location><page_1><loc_20><loc_79><loc_80><loc_84></location>Upper limits for PH 3 and H 2 S in Titan's atmosphere from Cassini CIRS</section_header_level_1>
<text><location><page_1><loc_20><loc_74><loc_79><loc_77></location>Conor A. Nixon a , Nicholas A. Teanby b , Patrick G. J. Irwin c , Sarah M. Horst d</text>
<unordered_list>
<list_item><location><page_1><loc_18><loc_62><loc_82><loc_72></location>a Planetary Systems Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA b School of Earth Sciences, University of Bristol, Wills Memorial Building, Queen's Road, BS8 1RJ, Bristol, UK c Atmospheric, Oceanic and Planetary Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK Cooperative Institute for Research in Environmental Sciences, University of Colorado,</list_item>
<list_item><location><page_1><loc_19><loc_60><loc_59><loc_63></location>d Boulder, CO 80309, USA</list_item>
</unordered_list>
<section_header_level_1><location><page_1><loc_18><loc_53><loc_27><loc_54></location>Abstract</section_header_level_1>
<text><location><page_1><loc_18><loc_36><loc_82><loc_51></location>We have searched for the presence of simple P and S-bearing molecules in Titan's atmosphere, by looking for the characteristic signatures of phosphine and hydrogen sulfide in infrared spectra obtained by Cassini CIRS. As a result we have placed the first upper limits on the stratospheric abundances, which are 1 ppb (PH 3 ) and 330 ppb (H 2 S), at the 2σ significance level. Keywords: Titan, Titan, atmosphere, Abundances, atmospheres,</text>
<text><location><page_1><loc_18><loc_33><loc_56><loc_34></location>Atmospheres, Composition, Saturn, satellites</text>
<section_header_level_1><location><page_1><loc_16><loc_28><loc_33><loc_29></location>1. Introduction 1</section_header_level_1>
<unordered_list>
<list_item><location><page_1><loc_16><loc_24><loc_82><loc_26></location>To date, no molecules bearing the light elements phosphorus (P) and 2</list_item>
<list_item><location><page_1><loc_16><loc_22><loc_82><loc_23></location>sulfur (S) have been detected in the atmosphere of Titan by either remote 3</list_item>
<list_item><location><page_1><loc_16><loc_19><loc_82><loc_20></location>sensing or in-situ methods. However, from cosmological considerations both 4</list_item>
<list_item><location><page_1><loc_16><loc_16><loc_82><loc_17></location>P and S must have been present in the icy planetesimals that formed Titan, 5</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_2><loc_16><loc_82><loc_82><loc_84></location>and also delivered in trace quantities by later impacts. P in the form of PH 3 6</list_item>
<list_item><location><page_2><loc_16><loc_80><loc_82><loc_81></location>is found in Jupiter's atmosphere at approximately solar abundance, while on 7</list_item>
<list_item><location><page_2><loc_16><loc_77><loc_82><loc_78></location>Saturn its abundance is around 3 × solar (Owen and Encrenaz, 2003). This 8</list_item>
<list_item><location><page_2><loc_16><loc_74><loc_82><loc_75></location>enrichment is in line with core-accretion models, which predict that Saturn 9</list_item>
<list_item><location><page_2><loc_15><loc_71><loc_82><loc_73></location>had a larger ice-to-gas fraction in its formation compared to Jupiter. Sulfur 10</list_item>
<list_item><location><page_2><loc_15><loc_69><loc_82><loc_70></location>is enriched on Jupiter by 2.5 × solar (Niemann et al., 1998) (and not yet 11</list_item>
<list_item><location><page_2><loc_15><loc_66><loc_82><loc_67></location>detected on Saturn), perhaps due to easy formation of H 2 S clathrate hydrates 12</list_item>
<list_item><location><page_2><loc_15><loc_63><loc_82><loc_65></location>Owen and Encrenaz (2003). Both P and S should therefore be present in 13</list_item>
<list_item><location><page_2><loc_15><loc_60><loc_82><loc_62></location>Titan's bulk composition at fractions greater than those on Saturn, since the 14</list_item>
<list_item><location><page_2><loc_15><loc_58><loc_56><loc_59></location>ice to gas ratio must have been much higher. 15</list_item>
<list_item><location><page_2><loc_15><loc_52><loc_82><loc_56></location>Fortes et al. (2007) considered a possible role for sulfur compounds in Ti16 tan cryovolcanism, suggesting that ammonium sulfate could form a magma 17</list_item>
<list_item><location><page_2><loc_15><loc_49><loc_82><loc_51></location>in Titan's mantle. Plumes of this magma could dissolve methane present in 18</list_item>
<list_item><location><page_2><loc_15><loc_47><loc_82><loc_48></location>crustal clathrates, allowing explosive release to the surface. One prediction 19</list_item>
<list_item><location><page_2><loc_15><loc_44><loc_82><loc_45></location>of this model is that ammonium or other sulfates should be detectable spec20</list_item>
<list_item><location><page_2><loc_15><loc_41><loc_82><loc_43></location>troscopically on Titan's surface, as is the case on Europa and Ganymede. 21</list_item>
<list_item><location><page_2><loc_15><loc_39><loc_82><loc_40></location>Such a model would presumably also release trace amounts of sulfur into 22</list_item>
<list_item><location><page_2><loc_15><loc_36><loc_82><loc_37></location>Titan's atmosphere, especially in the wake of eruptions. Pasek et al. (2011) 23</list_item>
<list_item><location><page_2><loc_15><loc_33><loc_82><loc_34></location>focused on the role of phosphorus in Titan, arguing that it could be delivered 24</list_item>
<list_item><location><page_2><loc_15><loc_30><loc_82><loc_32></location>both endogenously and exogenously to the surface. Phosphine is efficiently 25</list_item>
<list_item><location><page_2><loc_15><loc_28><loc_82><loc_29></location>trapped in clathrate hydrates, and Pasek et al. (2011) show that all clathrates 26</list_item>
<list_item><location><page_2><loc_15><loc_25><loc_82><loc_26></location>that trap H 2 S also trap at least as much PH 3 . Moreover, they show that PH 3 27</list_item>
<list_item><location><page_2><loc_15><loc_22><loc_82><loc_23></location>is more soluble in organic liquids than in water, and therefore any phosphine 28</list_item>
<list_item><location><page_2><loc_15><loc_19><loc_82><loc_21></location>released from melted clathrates could be dissolved in Titan's hydrocarbon 29</list_item>
<list_item><location><page_2><loc_15><loc_17><loc_76><loc_18></location>lakes, and would participate in the hydrocarbon meteorological cycle. 30</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_3><loc_15><loc_39><loc_82><loc_84></location>We have therefore searched the infrared spectrum of Titan for the sig31 natures of the two most likely carriers of P and S: phosphine (PH 3 ) and 32 hydrogen sulfide (H 2 S). Our data is from the Composite Infrared Spectrome33 ter (CIRS, Flasar et al., 2004), carried onboard the Cassini spacecraft, which 34 has been making close flybys of Titan since attaining Saturn orbit in mid35 2004. Both gases have signatures in the 8-11 µ m (1250-900 cm -1 ) range, 36 which is largely free of the hydrocarbon emissions that dominate much of 37 Titan's infrared spectrum. We first model and subtract out the emissions of 38 known species including methane (CH 4 ), acetylene (C 2 H 2 ), ethylene (C 2 H 4 ) 39 and deuterated methane (CH 3 D). We then add H 2 S and PH 3 incrementally 40 to our spectral calculation using standard line lists from HITRAN (Rothman 41 et al., 2009), and compare the predictions to the remaining Titan spectrum. 42 By comparing the model predictions to the instrument noise level at the 43 1, 2, and 3σ levels, we have derived the first numerical upper limits on the 44 prevalence of H 2 S and PH 3 in Titan's stratosphere. We follow a report of our 45 results with a discussion of the implications for existing models, and finish 46 with some conclusions about the prospects for future searches. 47</list_item>
</unordered_list>
<section_header_level_1><location><page_3><loc_15><loc_34><loc_28><loc_35></location>2. Method 48</section_header_level_1>
<section_header_level_1><location><page_3><loc_15><loc_30><loc_42><loc_31></location>2.1. Instrument and Dataset 49</section_header_level_1>
<unordered_list>
<list_item><location><page_3><loc_15><loc_16><loc_82><loc_28></location>The Cassini CIRS instrument is a dual design, comprising mid-infrared 50 (1400-600 cm -1 ) and far-infrared (600-10 cm -1 ) spectrometers, both with a 51 FWHM (full-width to half-maximum) spectral resolution variable from 0.552 15.5 cm -1 after Hamming apodization. The mid-IR Michelson spectrometer 53 employs two 1 × 10 detector arrays: focal plane 3 (FP3, 600-1100 cm -1 ) 54</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_4><loc_15><loc_74><loc_82><loc_84></location>and focal plane 4 (FP4, 1100-1400 cm -1 ). Both arrays have square pixels 55 with fields of view 0.3 mrad across. FP4 has the highest sensitivity (lowest 56 background noise) and least instrumental interferences, and was consequently 57 used in this study. 58</list_item>
<list_item><location><page_4><loc_15><loc_44><loc_82><loc_73></location>The observations were described in an earlier paper (Nixon et al., 2010). 59 The spectra were acquired during the 55 th Titan flyby (T55) of Cassini on 60 May 22 nd 2009, in a four-hour period when the spacecraft was at a range 61 of 116,000-177,000 km. The observation (known as 'MIRLMPAIR'-type) 62 was targeted at Titan's limb, with the two arrays above and parallel to the 63 horizon. FP4 was above FP3, with the pixels centered at an altitude of 247 64 km (0.27 mbar) and spanning approximately 44 km (just under one scale 65 height) in the vertical direction at the mid-point of the observation. Using 66 CIRS PAIR mode, all ten detectors simultaneously recorded data, paired into 67 five receiver channels. A total of 941 pair-mode spectra at 0.5 cm -1 resolution 68 were selected and then averaged to create a single, high signal-to-noise (S/N) 69</list_item>
<list_item><location><page_4><loc_15><loc_41><loc_31><loc_43></location>ratio spectrum. 70</list_item>
</unordered_list>
<section_header_level_1><location><page_4><loc_15><loc_37><loc_37><loc_38></location>2.2. Spectral Modeling 71</section_header_level_1>
<unordered_list>
<list_item><location><page_4><loc_21><loc_34><loc_82><loc_35></location>The CIRS FP4 limb spectrum was then modeled to remove the signatures</list_item>
</unordered_list>
<text><location><page_4><loc_15><loc_23><loc_82><loc_35></location>72 of known gas species. These included CH 4 ( ν 4 band at 1305 cm -1 ) and 73 CH 3 D ( ν 6 band at 1156 cm -1 ), plus some weaker contributions from the 74 hydrocarbons C 2 H 4 and C 2 H 2 . The modeling closely follows that described 75 in a recent paper (Nixon et al., 2012), and is briefly summarized here. 76</text>
<unordered_list>
<list_item><location><page_4><loc_15><loc_15><loc_82><loc_22></location>An initial vertical atmospheric model was created with 100 layers equally 77 spaced in log pressure from 1.45 bar to 0.05 µ bar, based on the temper78 ature profile and major gas abundances (N 2 , CH 4 , H 2 ) determined by the 79</list_item>
</unordered_list>
<unordered_list>
<list_item><location><page_5><loc_15><loc_82><loc_82><loc_84></location>Huygens probe (Fulchignoni et al., 2005; Niemann et al., 2010). Other gas 80</list_item>
<list_item><location><page_5><loc_15><loc_79><loc_82><loc_81></location>species (C 2 H 4 , C 2 H 2 ) were included with constant vertical abundances in the 81</list_item>
<list_item><location><page_5><loc_15><loc_77><loc_82><loc_78></location>stratosphere, at initial values taken from previous CIRS measurements at 82</list_item>
<list_item><location><page_5><loc_15><loc_74><loc_82><loc_75></location>low latitudes (Coustenis et al., 2010). Similarly a uniformly mixed (constant 83</list_item>
<list_item><location><page_5><loc_15><loc_71><loc_82><loc_73></location>particles/g atmosphere) stratospheric haze was included with optical prop84</list_item>
<list_item><location><page_5><loc_15><loc_69><loc_82><loc_70></location>erties from Khare et al. (1984). The forward radiative transfer model was 85</list_item>
<list_item><location><page_5><loc_15><loc_66><loc_82><loc_67></location>computed using the NEMESIS code (Irwin et al., 2008) applied to the model 86</list_item>
<list_item><location><page_5><loc_15><loc_63><loc_82><loc_65></location>atmosphere and using the HITRAN gas line atlas (Rothman et al., 2009), 87</list_item>
<list_item><location><page_5><loc_18><loc_60><loc_82><loc_62></location>and then convolved with the FP4 detector spatial response shapes (Nixon</list_item>
<list_item><location><page_5><loc_15><loc_58><loc_55><loc_61></location>88 et al., 2009b) to generate a model spectrum. 89</list_item>
<list_item><location><page_5><loc_15><loc_55><loc_16><loc_56></location>90</list_item>
<list_item><location><page_5><loc_21><loc_55><loc_82><loc_56></location>At this point the model was iterated to arrive at an optimum fit to the</list_item>
<list_item><location><page_5><loc_15><loc_52><loc_82><loc_54></location>measured spectrum, by adjusting the model temperature profile (at each 91</list_item>
<list_item><location><page_5><loc_15><loc_49><loc_82><loc_51></location>layer) and uniform vertical gas abundances of C H and C H , to minimize 92</list_item>
<list_item><location><page_5><loc_15><loc_25><loc_49><loc_28></location>100 wavelength calibration uncertainties. 101</list_item>
<list_item><location><page_5><loc_15><loc_28><loc_82><loc_50></location>2 2 2 4 a cost function similar to a χ 2 figure of merit. This approach has been 93 successfully used to fit the T55 limb spectrum of Titan in previous work 94 (Nixon et al., 2009a, 2010). Fig .1 (a) shows the best fit to the data. Note 95 that a weak band of propane ( ν 7 at 1158 cm -1 ) was not included in the 96 model, as a line list for this band has yet to be produced, and shows clearly 97 in the data-model residual (Fig .1 (b)). The strong CH 4 ν 4 band is fitted 98 reasonably well, but also shows some residual mismatch, which may be due 99 to imperfect knowledge of the underlying haze (continuum) opacity and/or</list_item>
</unordered_list>
<section_header_level_1><location><page_5><loc_15><loc_21><loc_58><loc_22></location>2.3. Determination of Abundance Upper Limits 102</section_header_level_1>
<text><location><page_5><loc_15><loc_15><loc_82><loc_19></location>To search for PH 3 and H 2 S, we avoided spectral regions that showed non103 random 'noise' residual: especially the C 3 H 8 ν 7 region (1140-1200 cm -1 ) and 104</text>
<text><location><page_6><loc_15><loc_63><loc_82><loc_84></location>the CH 4 region (˜ ν > 1250 cm -1 ). This permitted us to search for the ν 4 105 band of PH 3 around 1120 cm -1 , and for a portion of the weak H 2 S ν 2 band 106 at 1200-1250 cm -1 (see Fig .1 (c) and (d)). The summed line strengths in 107 these regions were 1 . 40 × 10 -18 cm molecule -1 for 1121 lines of PH 3 from 108 1080-1140 cm -1 , and 2 . 2 × 10 -20 cm molecule -1 for 130 lines of H 2 S at 1200109 1250 cm -1 , using line data from HITRAN (Rothman et al., 2009). Note that 110 the PH 3 band intensity was almost 100 × that of H 2 S in the spectral ranges 111 considered, so we expect 100 × greater sensitivity to PH 3 compared to H 2 S. 112</text>
<text><location><page_6><loc_15><loc_28><loc_82><loc_62></location>These two gas species were added to the best-fit atmospheric model at 113 fixed trial abundances of 1 ppb with other gases and temperature held con114 stant at the previously retrieved values, and NEMESIS was allowed to re115 trieve a 'best fit' abundance for the new species. In both cases, these retrievals 116 resulted in no statistically significant improvement to the model χ 2 , hereafter 117 designated χ 2 0 : the minimum χ 2 . We then proceeded to calculate upper lim118 its to the abundances, following the approach of Teanby et al. (2009) and 119 Nixon et al. (2010). Starting with very low trial gas abundances in the model, 120 these were increased incrementally, and at each value the forward spectral 121 model was calculated, without optimized fitting or inversion, and the data122 model χ 2 computed. As the trial gas abundances increase, so too does the 123 ∆ χ 2 = χ 2 -χ 2 0 . See Fig. .2. Following Press et al. (1992) the 1, 2 and 3σ 124 upper limits to the gas abundances occur at ∆ χ 2 = 1 , 4 , 9. 125</text>
<section_header_level_1><location><page_6><loc_15><loc_23><loc_43><loc_24></location>3. Results and Discussion 126</section_header_level_1>
<text><location><page_6><loc_15><loc_16><loc_82><loc_20></location>Table 1 shows our results. The derived 1, 2, 3σ maximum abundances for 127 PH 3 are 0.3, 1.1, 2.2 ppb respectively, while the corresponding values for H 2 S 128</text>
<text><location><page_7><loc_15><loc_71><loc_82><loc_84></location>are 91, 330, 700 ppb. The H 2 S upper limits are some two orders of magnitude 129 higher than those of PH 3 as expected, due to the much weaker band inten130 sity in the spectral region considered, along with a higher 1σ NESR (Noise 131 Equivalent Spectral Radiance) level in the corresponding spectral interval 132 (0.6 versus 0.3 nW cm -2 sr -1 /cm -1 ). 133</text>
<text><location><page_7><loc_15><loc_39><loc_82><loc_70></location>Sulfur compounds have been suggested to play a role in Titan cryovol134 canism (Fortes et al., 2007), and therefore be present in trace amounts in 135 Titan's atmosphere. Phosphorus is also easily dissolved in organic solvents, 136 and as such could be a component of Titan's present-day methane-ethane 137 lakes, and participate in the hydrocarbon cycle (Pasek et al., 2011). A sim138 ple calculation tracing the saturation vapor pressure (data from public NIST 139 and CRC databases) up through Titan's troposphere using the Huygens tem140 perature profile, indicates that abundances of PH 3 and H 2 S that could reach 141 the stratosphere are 6 and 0.035 ppb respectively. Therefore, our 2σ upper 142 limit of 1 ppb for PH 3 provides some constraint on tropospheric PH 3 , while 143 our H 2 S limit of 330 ppb is four orders of magnitude greater than allowed in 144 this scenario and is not constraining. 145</text>
<text><location><page_7><loc_15><loc_19><loc_82><loc_37></location>At the present time, the lack of detection of P or S-bearing species any146 where in Titan's atmosphere has caused these elements to be omitted from 147 present photochemical models, so we have no predictions for comparison. In 148 future, it could be interesting for such models to allow for some injection 149 of P and S molecules into the atmosphere through a putative eruption, and 150 to investigate subsequent chemistry, for example, conversion of sulfates to 151 sulfides. 152</text>
<section_header_level_1><location><page_8><loc_15><loc_82><loc_51><loc_84></location>4. Conclusions and Further Work 153</section_header_level_1>
<text><location><page_8><loc_15><loc_54><loc_82><loc_80></location>In this paper we have searched for simple compounds of phosphorus and 154 sulfur in Titan's infrared spectrum recorded by Cassini CIRS, placing the 155 first upper limits on the abundance of PH 3 and H 2 S. In the stratosphere 156 at 247 km we find that no more than 1 ppb of PH 3 and 330 ppb of H 2 S 157 can be present, at the 2σ level of significance. Some potential exists for 158 improving on these upper limits using CIRS, e.g. by future measurements 159 at a lower limb altitude where the atmospheric density is greater. The peak 160 sensitivity for weak trace gases is often near 10 mbar ( ∼ 100 km), at least at 161 low latitudes, so a repeat measurement in the lower stratosphere may yield 162 more stringent limits. 163</text>
<text><location><page_8><loc_15><loc_29><loc_82><loc_52></location>Searching in the far-IR spectrum may prove helpful in the case of H 2 S, 164 which has rotational lines at 50-150 cm -1 that are some 100 × stronger than 165 the ν 2 considered here. However in this region the NESR of CIRS FP1 is 166 more than 10 × higher than that of the FP4 detectors used in this work, and 167 suffers from systematic noise artifacts. Nevertheless, the sub-mm range has 168 already proved productive for molecular line searches by instruments such 169 as Herschel and ground-based sub-mm telescopes, resulting in the detections 170 of CH 3 CN (Marten et al., 2002) and HNC (Moreno et al., 2011), and will 171 doubtless reveal further new species in due course. 172</text>
<section_header_level_1><location><page_8><loc_15><loc_24><loc_28><loc_26></location>References 173</section_header_level_1>
<text><location><page_8><loc_15><loc_15><loc_82><loc_22></location>Coustenis, A., Jennings, D.E., Nixon, C.A., Achterberg, R.K., Lavvas, P., 174 Vinatier, S., Teanby, N.A., Bjoraker, G.L., Carlson, R.C., Piani, L., Bam175 pasidis, G., Flasar, F.M., Romani, P.N., 2010. Titan trace gaseous compo176</text>
<text><location><page_9><loc_15><loc_80><loc_82><loc_84></location>sition from CIRS at the end of the Cassini-Huygens prime mission. Icarus 177 207, 461-476. 178</text>
<text><location><page_9><loc_15><loc_48><loc_82><loc_77></location>Flasar, F.M., Kunde, V.G., Abbas, M.M., Achterberg, R.K., Ade, P., 179 Barucci, A., B'ezard, B., Bjoraker, G.L., Brasunas, J.C., Calcutt, S., 180 Carlson, R., C'esarsky, C.J., Conrath, B.J., Coradini, A., Courtin, R., 181 Coustenis, A., Edberg, S., Edgington, S., Ferrari, C., Fouchet, T., Gau182 tier, D., Gierasch, P.J., Grossman, K., Irwin, P., Jennings, D.E., Lel183 louch, E., Mamoutkine, A.A., Marten, A., Meyer, J.P., Nixon, C.A., Or184 ton, G.S., Owen, T.C., Pearl, J.C., Prang'e, R., Raulin, F., Read, P.L., 185 Romani, P.N., Samuelson, R.E., Segura, M.E., Showalter, M.R., Simon186 Miller, A.A., Smith, M.D., Spencer, J.R., Spilker, L.J., Taylor, F.W., 2004. 187 Exploring The Saturn System In The Thermal Infrared: The Composite 188 Infrared Spectrometer. Space Sci. Rev. 115, 169-297. 189</text>
<text><location><page_9><loc_15><loc_44><loc_16><loc_45></location>190</text>
<text><location><page_9><loc_15><loc_42><loc_16><loc_42></location>191</text>
<text><location><page_9><loc_15><loc_39><loc_16><loc_40></location>192</text>
<text><location><page_9><loc_18><loc_39><loc_82><loc_46></location>Fortes, A.D., Grindrod, P.M., Trickett, S.K., Voˇcadlo, L., 2007. Ammonium sulfate on Titan: Possible origin and role in cryovolcanism. Icarus 188, 139-153.</text>
<text><location><page_9><loc_15><loc_16><loc_82><loc_36></location>Fulchignoni, M., Ferri, F., Angrilli, F., Ball, A.J., Bar-Nun, A., Barucci, 193 M.A., Bettanini, C., Bianchini, G., Borucki, W., Colombatti, G., Cora194 dini, M., Coustenis, A., Debei, S., Falkner, P., Fanti, G., Flamini, E., Ga195 borit, V., Grard, R., Hamelin, M., Harri, A.M., Hathi, B., Jernej, I., Leese, 196 M.R., Lehto, A., Lion Stoppato, P.F., L'opez-Moreno, J.J., Makinen, T., 197 McDonnell, J.A.M., McKay, C.P., Molina-Cuberos, G., Neubauer, F.M., 198 Pirronello, V., Rodrigo, R., Saggin, B., Schwingenschuh, K., Seiff, A., 199 Sim˜oes, F., Svedhem, H., Tokano, T., Towner, M.C., Trautner, R., With200</text>
<text><location><page_10><loc_15><loc_80><loc_82><loc_84></location>ers, P., Zarnecki, J.C., 2005. In situ measurements of the physical charac201 teristics of Titan's environment. Nature 438, 785-791. 202</text>
<text><location><page_10><loc_15><loc_67><loc_82><loc_77></location>Irwin, P.G.J., Teanby, N.A., de Kok, R., Fletcher, L.N., Howett, C.J.A., 203 Tsang, C.C.C., Wilson, C.F., Calcutt, S.B., Nixon, C.A., Parrish, P.D., 204 2008. The NEMESIS planetary atmosphere radiative transfer and retrieval 205 tool. J. Quant. Spectr. Rad. Trans. 109, 1136-1150. 206</text>
<text><location><page_10><loc_15><loc_55><loc_82><loc_65></location>Khare, B.N., Sagan, C., Arakawa, E.T., Suits, F., Callcott, T.A., Williams, 207 M.W., 1984. Optical constants of organic tholins produced in a simulated 208 Titanian atmosphere - From soft X-ray to microwave frequencies. Icarus 209 60, 127-137. 210</text>
<text><location><page_10><loc_15><loc_43><loc_82><loc_53></location>Marten, A., Hidayat, T., Biraud, Y., Moreno, R., 2002. New Millimeter 211 Heterodyne Observations of Titan: Vertical Distributions of Nitriles HCN, 212 HC 3 N, CH 3 CN, and the Isotopic Ratio 15 N/ 14 N in Its Atmosphere. Icarus 213 158, 532-544. 214</text>
<text><location><page_10><loc_15><loc_31><loc_82><loc_40></location>Moreno, R., Lellouch, E., Lara, L.M., Courtin, R., Bockel'ee-Morvan, D., 215 Hartogh, P., Rengel, M., Biver, N., Banaszkiewicz, M., Gonz'alez, A., 2011. 216 First detection of hydrogen isocyanide (HNC) in Titan's atmosphere. As217 tron. and Astrophys. 536, L12. 218</text>
<text><location><page_10><loc_15><loc_16><loc_82><loc_28></location>Niemann, H.B., Atreya, S.K., Carignan, G.R., Donahue, T.M., Haberman, 219 J.A., Harpold, D.N., Hartle, R.E., Hunten, D.M., Kasprzak, W.T., Ma220 haffy, P.R., Owen, T.C., Way, S.H., 1998. The composition of the Jovian 221 atmosphere as determined by the Galileo probe mass spectrometer. J. 222 Geophys. Res. 103, 22831-22846. 223</text>
<text><location><page_11><loc_15><loc_69><loc_82><loc_84></location>Niemann, H.B., Atreya, S.K., Demick, J.E., Gautier, D., Haberman, J.A., 224 Harpold, D.N., Kasprzak, W.T., Lunine, J.I., Owen, T.C., Raulin, F., 225 2010. Composition of Titan's lower atmosphere and simple surface volatiles 226 as measured by the Cassini-Huygens probe gas chromatograph mass spec227 trometer experiment. Journal of Geophysical Research (Planets) 115, 228 12006. 229</text>
<text><location><page_11><loc_15><loc_51><loc_82><loc_66></location>Nixon, C.A., Achterberg, R.K., Teanby, N.A., Irwin, P.G.J., Flaud, J.M., 230 Kleiner, I., Dehayem-Kamadjeu, A., Brown, L.R., Sams, R.L., B'ezard, 231 B., Coustenis, A., Ansty, T.M., Mamoutkine, A., Vinatier, S., Bjoraker, 232 G.L., Jennings, D.E., Romani, P.N., Flasar, F.M., 2010. Upper limits for 233 undetected trace species in the stratosphere of Titan. Faraday Discussions 234 147, 65. 1103.0297 . 235</text>
<text><location><page_11><loc_15><loc_39><loc_82><loc_48></location>Nixon, C.A., Jennings, D.E., Flaud, J.M., B'ezard, B., Teanby, N.A., Irwin, 236 P.G.J., Ansty, T.M., Coustenis, A., Vinatier, S., Flasar, F.M., 2009a. Ti237 tan's prolific propane: The Cassini CIRS perspective. Planetary and Space 238 Science 57, 1573-1585. 0909.1794 . 239</text>
<text><location><page_11><loc_15><loc_24><loc_82><loc_36></location>Nixon, C.A., Teanby, N.A., Calcutt, S.B., Aslam, S., Jennings, D.E., Kunde, 240 V.G., Flasar, F.M., Irwin, P.G., Taylor, F.W., Glenar, D.A., Smith, M.D., 241 2009b. Infrared limb sounding of Titan with the Cassini Composite In242 fraRed Spectrometer: effects of the mid-IR detector spatial responses. Ap243 plied Optics 48, 1912. 244</text>
<text><location><page_11><loc_15><loc_17><loc_82><loc_21></location>Nixon, C.A., Temelso, B., Vinatier, S., Teanby, N.A., B'ezard, B., Achterberg, 245 R.K., Mandt, K.E., Sherrill, C.D., Irwin, P.G.J., Jennings, D.E., Romani, 246</text>
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<list_item><location><page_12><loc_15><loc_80><loc_82><loc_84></location>P.N., Coustenis, A., Flasar, F.M., 2012. Isotopic ratios in Titan's methane: 247 measurements and modeling. Astrophys. J. 749, 159. 248</list_item>
<list_item><location><page_12><loc_15><loc_73><loc_82><loc_77></location>Owen, T., Encrenaz, T., 2003. Element Abundances and Isotope Ratios in 249 the Giant Planets and Titan. Space Sci. Rev. 106, 121-138. 250</list_item>
<list_item><location><page_12><loc_15><loc_66><loc_82><loc_70></location>Pasek, M.A., Mousis, O., Lunine, J.I., 2011. Phosphorus chemistry on Titan. 251 Icarus 212, 751-761. 252</list_item>
<list_item><location><page_12><loc_15><loc_59><loc_82><loc_63></location>Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Nu253 merical recipes in FORTRAN. The art of scientific computing. 254</list_item>
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<text><location><page_12><loc_15><loc_28><loc_82><loc_57></location>Rothman, L.S., Gordon, I.E., Barbe, A., Benner, D.C., Bernath, P.F., 255 Birk, M., Boudon, V., Brown, L.R., Campargue, A., Champion, J.P., 256 Chance, K., Coudert, L.H., Dana, V., Devi, V.M., Fally, S., Flaud, J.M., 257 Gamache, R.R., Goldman, A., Jacquemart, D., Kleiner, I., Lacome, N., 258 Lafferty, W.J., Mandin, J.Y., Massie, S.T., Mikhailenko, S.N., Miller, 259 C.E., Moazzen-Ahmadi, N., Naumenko, O.V., Nikitin, A.V., Orphal, J., 260 Perevalov, V.I., Perrin, A., Predoi-Cross, A., Rinsland, C.P., Rotger, M., 261 ˇ Simeˇckov'a, M., Smith, M.A.H., Sung, K., Tashkun, S.A., Tennyson, J., 262 Toth, R.A., Vandaele, A.C., Vander Auwera, J., 2009. The HITRAN 2008 263 molecular spectroscopic database. J. Quant. Spectr. Rad. Trans. 110, 533264 572. 265</text>
<text><location><page_12><loc_15><loc_19><loc_82><loc_25></location>Teanby, N.A., Irwin, P.G.J., de Kok, R., Jolly, A., B'ezard, B., Nixon, C.A., 266 Calcutt, S.B., 2009. Titan's stratospheric C 2 N 2 , C 3 H 4 , and C 4 H 2 abun267 dances from Cassini/CIRS far-infrared spectra. Icarus 202, 620-631. 268</text>
<table>
<location><page_13><loc_18><loc_46><loc_85><loc_58></location>
<caption>Table 1: Calculated abundance upper limits for PH 3 and H 2 S</caption>
</table>
<figure>
<location><page_14><loc_19><loc_25><loc_75><loc_83></location>
<caption>Figure .1: (a): CIRS limb average spectrum of Titan from T55 flyby (black) and model fit (green). (b): data-model spectral residual. Note the ν 7 band of C 3 H 8 at 1158 cm -1 that is not included in our model (see text for details). (c) and (d) show the density and strengths of lines of PH 3 and H 2 S respectively in the interval considered.</caption>
</figure>
<figure>
<location><page_15><loc_19><loc_38><loc_88><loc_78></location>
<caption>Figure .2: Calculation of upper limits for the abundances of H 2 S and PH 3 in Titan's stratosphere. (a) & (c): residual of fit to the CIRS Titan spectrum in each region, after the modeling and removal known gas species (black line). Over-plotted is a calculation with exaggerated trial gas abundances of the undetected species to show their spectral signature (colored line). (b) & (d): the curve of growth of ∆ χ 2 over a wide range of trial abundances. The 1, 2 and 3σ upper limits are indicated by the vertical dashed lines at ∆ χ 2 = 1, 4, 9 respectively.</caption>
</figure>
</document>
[
{
"title": "Upper limits for PH 3 and H 2 S in Titan's atmosphere from Cassini CIRS",
"content": "Conor A. Nixon a , Nicholas A. Teanby b , Patrick G. J. Irwin c , Sarah M. Horst d",
"pages": [
1
]
},
{
"title": "Abstract",
"content": "We have searched for the presence of simple P and S-bearing molecules in Titan's atmosphere, by looking for the characteristic signatures of phosphine and hydrogen sulfide in infrared spectra obtained by Cassini CIRS. As a result we have placed the first upper limits on the stratospheric abundances, which are 1 ppb (PH 3 ) and 330 ppb (H 2 S), at the 2σ significance level. Keywords: Titan, Titan, atmosphere, Abundances, atmospheres, Atmospheres, Composition, Saturn, satellites",
"pages": [
1
]
},
{
"title": "2.2. Spectral Modeling 71",
"content": "72 of known gas species. These included CH 4 ( ν 4 band at 1305 cm -1 ) and 73 CH 3 D ( ν 6 band at 1156 cm -1 ), plus some weaker contributions from the 74 hydrocarbons C 2 H 4 and C 2 H 2 . The modeling closely follows that described 75 in a recent paper (Nixon et al., 2012), and is briefly summarized here. 76",
"pages": [
4
]
},
{
"title": "2.3. Determination of Abundance Upper Limits 102",
"content": "To search for PH 3 and H 2 S, we avoided spectral regions that showed non103 random 'noise' residual: especially the C 3 H 8 ν 7 region (1140-1200 cm -1 ) and 104 the CH 4 region (˜ ν > 1250 cm -1 ). This permitted us to search for the ν 4 105 band of PH 3 around 1120 cm -1 , and for a portion of the weak H 2 S ν 2 band 106 at 1200-1250 cm -1 (see Fig .1 (c) and (d)). The summed line strengths in 107 these regions were 1 . 40 × 10 -18 cm molecule -1 for 1121 lines of PH 3 from 108 1080-1140 cm -1 , and 2 . 2 × 10 -20 cm molecule -1 for 130 lines of H 2 S at 1200109 1250 cm -1 , using line data from HITRAN (Rothman et al., 2009). Note that 110 the PH 3 band intensity was almost 100 × that of H 2 S in the spectral ranges 111 considered, so we expect 100 × greater sensitivity to PH 3 compared to H 2 S. 112 These two gas species were added to the best-fit atmospheric model at 113 fixed trial abundances of 1 ppb with other gases and temperature held con114 stant at the previously retrieved values, and NEMESIS was allowed to re115 trieve a 'best fit' abundance for the new species. In both cases, these retrievals 116 resulted in no statistically significant improvement to the model χ 2 , hereafter 117 designated χ 2 0 : the minimum χ 2 . We then proceeded to calculate upper lim118 its to the abundances, following the approach of Teanby et al. (2009) and 119 Nixon et al. (2010). Starting with very low trial gas abundances in the model, 120 these were increased incrementally, and at each value the forward spectral 121 model was calculated, without optimized fitting or inversion, and the data122 model χ 2 computed. As the trial gas abundances increase, so too does the 123 ∆ χ 2 = χ 2 -χ 2 0 . See Fig. .2. Following Press et al. (1992) the 1, 2 and 3σ 124 upper limits to the gas abundances occur at ∆ χ 2 = 1 , 4 , 9. 125",
"pages": [
5,
6
]
},
{
"title": "3. Results and Discussion 126",
"content": "Table 1 shows our results. The derived 1, 2, 3σ maximum abundances for 127 PH 3 are 0.3, 1.1, 2.2 ppb respectively, while the corresponding values for H 2 S 128 are 91, 330, 700 ppb. The H 2 S upper limits are some two orders of magnitude 129 higher than those of PH 3 as expected, due to the much weaker band inten130 sity in the spectral region considered, along with a higher 1σ NESR (Noise 131 Equivalent Spectral Radiance) level in the corresponding spectral interval 132 (0.6 versus 0.3 nW cm -2 sr -1 /cm -1 ). 133 Sulfur compounds have been suggested to play a role in Titan cryovol134 canism (Fortes et al., 2007), and therefore be present in trace amounts in 135 Titan's atmosphere. Phosphorus is also easily dissolved in organic solvents, 136 and as such could be a component of Titan's present-day methane-ethane 137 lakes, and participate in the hydrocarbon cycle (Pasek et al., 2011). A sim138 ple calculation tracing the saturation vapor pressure (data from public NIST 139 and CRC databases) up through Titan's troposphere using the Huygens tem140 perature profile, indicates that abundances of PH 3 and H 2 S that could reach 141 the stratosphere are 6 and 0.035 ppb respectively. Therefore, our 2σ upper 142 limit of 1 ppb for PH 3 provides some constraint on tropospheric PH 3 , while 143 our H 2 S limit of 330 ppb is four orders of magnitude greater than allowed in 144 this scenario and is not constraining. 145 At the present time, the lack of detection of P or S-bearing species any146 where in Titan's atmosphere has caused these elements to be omitted from 147 present photochemical models, so we have no predictions for comparison. In 148 future, it could be interesting for such models to allow for some injection 149 of P and S molecules into the atmosphere through a putative eruption, and 150 to investigate subsequent chemistry, for example, conversion of sulfates to 151 sulfides. 152",
"pages": [
6,
7
]
},
{
"title": "4. Conclusions and Further Work 153",
"content": "In this paper we have searched for simple compounds of phosphorus and 154 sulfur in Titan's infrared spectrum recorded by Cassini CIRS, placing the 155 first upper limits on the abundance of PH 3 and H 2 S. In the stratosphere 156 at 247 km we find that no more than 1 ppb of PH 3 and 330 ppb of H 2 S 157 can be present, at the 2σ level of significance. Some potential exists for 158 improving on these upper limits using CIRS, e.g. by future measurements 159 at a lower limb altitude where the atmospheric density is greater. The peak 160 sensitivity for weak trace gases is often near 10 mbar ( ∼ 100 km), at least at 161 low latitudes, so a repeat measurement in the lower stratosphere may yield 162 more stringent limits. 163 Searching in the far-IR spectrum may prove helpful in the case of H 2 S, 164 which has rotational lines at 50-150 cm -1 that are some 100 × stronger than 165 the ν 2 considered here. However in this region the NESR of CIRS FP1 is 166 more than 10 × higher than that of the FP4 detectors used in this work, and 167 suffers from systematic noise artifacts. Nevertheless, the sub-mm range has 168 already proved productive for molecular line searches by instruments such 169 as Herschel and ground-based sub-mm telescopes, resulting in the detections 170 of CH 3 CN (Marten et al., 2002) and HNC (Moreno et al., 2011), and will 171 doubtless reveal further new species in due course. 172",
"pages": [
8
]
},
{
"title": "References 173",
"content": "Coustenis, A., Jennings, D.E., Nixon, C.A., Achterberg, R.K., Lavvas, P., 174 Vinatier, S., Teanby, N.A., Bjoraker, G.L., Carlson, R.C., Piani, L., Bam175 pasidis, G., Flasar, F.M., Romani, P.N., 2010. Titan trace gaseous compo176 sition from CIRS at the end of the Cassini-Huygens prime mission. Icarus 177 207, 461-476. 178 Flasar, F.M., Kunde, V.G., Abbas, M.M., Achterberg, R.K., Ade, P., 179 Barucci, A., B'ezard, B., Bjoraker, G.L., Brasunas, J.C., Calcutt, S., 180 Carlson, R., C'esarsky, C.J., Conrath, B.J., Coradini, A., Courtin, R., 181 Coustenis, A., Edberg, S., Edgington, S., Ferrari, C., Fouchet, T., Gau182 tier, D., Gierasch, P.J., Grossman, K., Irwin, P., Jennings, D.E., Lel183 louch, E., Mamoutkine, A.A., Marten, A., Meyer, J.P., Nixon, C.A., Or184 ton, G.S., Owen, T.C., Pearl, J.C., Prang'e, R., Raulin, F., Read, P.L., 185 Romani, P.N., Samuelson, R.E., Segura, M.E., Showalter, M.R., Simon186 Miller, A.A., Smith, M.D., Spencer, J.R., Spilker, L.J., Taylor, F.W., 2004. 187 Exploring The Saturn System In The Thermal Infrared: The Composite 188 Infrared Spectrometer. Space Sci. Rev. 115, 169-297. 189 190 191 192 Fortes, A.D., Grindrod, P.M., Trickett, S.K., Voˇcadlo, L., 2007. Ammonium sulfate on Titan: Possible origin and role in cryovolcanism. Icarus 188, 139-153. Fulchignoni, M., Ferri, F., Angrilli, F., Ball, A.J., Bar-Nun, A., Barucci, 193 M.A., Bettanini, C., Bianchini, G., Borucki, W., Colombatti, G., Cora194 dini, M., Coustenis, A., Debei, S., Falkner, P., Fanti, G., Flamini, E., Ga195 borit, V., Grard, R., Hamelin, M., Harri, A.M., Hathi, B., Jernej, I., Leese, 196 M.R., Lehto, A., Lion Stoppato, P.F., L'opez-Moreno, J.J., Makinen, T., 197 McDonnell, J.A.M., McKay, C.P., Molina-Cuberos, G., Neubauer, F.M., 198 Pirronello, V., Rodrigo, R., Saggin, B., Schwingenschuh, K., Seiff, A., 199 Sim˜oes, F., Svedhem, H., Tokano, T., Towner, M.C., Trautner, R., With200 ers, P., Zarnecki, J.C., 2005. In situ measurements of the physical charac201 teristics of Titan's environment. Nature 438, 785-791. 202 Irwin, P.G.J., Teanby, N.A., de Kok, R., Fletcher, L.N., Howett, C.J.A., 203 Tsang, C.C.C., Wilson, C.F., Calcutt, S.B., Nixon, C.A., Parrish, P.D., 204 2008. The NEMESIS planetary atmosphere radiative transfer and retrieval 205 tool. J. Quant. 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